Score : 300 points

Problem Statement

We have N clocks. The hand of the i-th clock (1≤i≤N) rotates through 360° in exactly T_i seconds.

Initially, the hand of every clock stands still, pointing directly upward.

Now, Dolphin starts all the clocks simultaneously.

In how many seconds will the hand of every clock point directly upward again?

Constraints

1≤N≤100

1≤T_i≤10^{18}

All input values are integers.

The correct answer is at most 10^{18} seconds.

Input

Input is given from Standard Input in the following format:

N
T_1
:
T_N

Output

Print the number of seconds after which the hand of every clock point directly upward again.

Sample Input 1

2
2
3

Sample Output 1

6

We have two clocks. The time when the hand of each clock points upward is as follows:

Clock 1: 2, 4, 6, ... seconds after the beginning

Clock 2: 3, 6, 9, ... seconds after the beginning

Therefore, it takes 6 seconds until the hands of both clocks point directly upward.

Sample Input 2

5
2
5
10
1000000000000000000
1000000000000000000

Sample Output 2

1000000000000000000


Global OOD problem IDs are disjoint from train, validation, and in-distribution test problem IDs.

Score : 100 points

Problem Statement

In K-city, there are n streets running east-west, and m streets running north-south. Each street running east-west and each street running north-south cross each other. We will call the smallest area that is surrounded by four streets a block. How many blocks there are in K-city?

Constraints

2 ≤ n, m ≤ 100

Input

Input is given from Standard Input in the following format:

n m

Output

Print the number of blocks in K-city.

Sample Input 1

3 4

Sample Output 1

6

There are six blocks, as shown below:

Sample Input 2

2 2

Sample Output 2

1

There are one block, as shown below:

Submitted source-code file size, in bytes.

Execution CPU time reported by official Project CodeNet metadata, in milliseconds.

Peak memory usage reported by official Project CodeNet metadata, in kilobytes.


Score : 200 points

Problem Statement

The word internationalization is sometimes abbreviated to i18n.
This comes from the fact that there are 18 letters between the first i and the last n.

You are given a string s of length at least 3 consisting of lowercase English letters.
Abbreviate s in the same way.

Constraints

3 ≤ |s| ≤ 100 (|s| denotes the length of s.)

s consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

s

Output

Print the abbreviation of s.

Sample Input 1

internationalization

Sample Output 1

i18n

Sample Input 2

smiles

Sample Output 2

s4s

Sample Input 3

xyz

Sample Output 3

x1z


Score : 400 points

Problem Statement

We have a grid with H rows and W columns of squares.
Snuke is painting these squares in colors 1, 2, ..., N.
Here, the following conditions should be satisfied:

For each i (1 ≤ i ≤ N), there are exactly a_i squares painted in Color i. Here, a_1 + a_2 + ... + a_N = H W.

For each i (1 ≤ i ≤ N), the squares painted in Color i are 4-connected. That is, every square painted in Color i can be reached from every square painted in Color i by repeatedly traveling to a horizontally or vertically adjacent square painted in Color i.

Find a way to paint the squares so that the conditions are satisfied.
It can be shown that a solution always exists.

Constraints

1 ≤ H, W ≤ 100

1 ≤ N ≤ H W

a_i ≥ 1

a_1 + a_2 + ... + a_N = H W

Input

Input is given from Standard Input in the following format:

H W
N
a_1 a_2 ... a_N

Output

Print one way to paint the squares that satisfies the conditions.
Output in the following format:

c_{1 1} ... c_{1 W}
:
c_{H 1} ... c_{H W}

Here, c_{i j} is the color of the square at the i-th row from the top and j-th column from the left.

Sample Input 1

2 2
3
2 1 1

Sample Output 1

1 1
2 3

Below is an example of an invalid solution:

1 2
3 1

This is because the squares painted in Color 1 are not 4-connected.

Sample Input 2

3 5
5
1 2 3 4 5

Sample Output 2

1 4 4 4 3
2 5 4 5 3
2 5 5 5 3

Sample Input 3

1 1
1
1

Sample Output 3

1


Score : 100 points

Problem Statement

This contest, AtCoder Beginner Contest, is abbreviated as ABC.

When we refer to a specific round of ABC, a three-digit number is appended after ABC. For example, ABC680 is the 680th round of ABC.

What is the abbreviation for the N-th round of ABC? Write a program to output the answer.

Constraints

100 ≤ N ≤ 999

Input

Input is given from Standard Input in the following format:

N

Output

Print the abbreviation for the N-th round of ABC.

Sample Input 1

100

Sample Output 1

ABC100

The 100th round of ABC is ABC100.

Sample Input 2

425

Sample Output 2

ABC425

Sample Input 3

999

Sample Output 3

ABC999


Score : 200 points

Problem Statement

Takahashi loves numbers divisible by 2.

You are given a positive integer N. Among the integers between 1 and N (inclusive), find the one that can be divisible by 2 for the most number of times. The solution is always unique.

Here, the number of times an integer can be divisible by 2, is how many times the integer can be divided by 2 without remainder.

For example,

6 can be divided by 2 once: 6 -> 3.

8 can be divided by 2 three times: 8 -> 4 -> 2 -> 1.

3 can be divided by 2 zero times.

Constraints

1 ≤ N ≤ 100

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.

Sample Input 1

7

Sample Output 1

4

4 can be divided by 2 twice, which is the most number of times among 1, 2, ..., 7.

Sample Input 2

32

Sample Output 2

32

Sample Input 3

1

Sample Output 3

1

Sample Input 4

100

Sample Output 4

64


Score : 300 points

Problem Statement

In Takahashi Kingdom, there is an archipelago of N islands, called Takahashi Islands.
For convenience, we will call them Island 1, Island 2, ..., Island N.

There are M kinds of regular boat services between these islands.
Each service connects two islands. The i-th service connects Island a_i and Island b_i.

Cat Snuke is on Island 1 now, and wants to go to Island N.
However, it turned out that there is no boat service from Island 1 to Island N, so he wants to know whether it is possible to go to Island N by using two boat services.

Help him.

Constraints

3 ≤ N ≤ 200 000

1 ≤ M ≤ 200 000

1 ≤ a_i < b_i ≤ N

(a_i, b_i) \neq (1, N)

If i \neq j, (a_i, b_i) \neq (a_j, b_j).

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

If it is possible to go to Island N by using two boat services, print POSSIBLE; otherwise, print IMPOSSIBLE.

Sample Input 1

3 2
1 2
2 3

Sample Output 1

POSSIBLE

Sample Input 2

4 3
1 2
2 3
3 4

Sample Output 2

IMPOSSIBLE

You have to use three boat services to get to Island 4.

Sample Input 3

100000 1
1 99999

Sample Output 3

IMPOSSIBLE

Sample Input 4

5 5
1 3
4 5
2 3
2 4
1 4

Sample Output 4

POSSIBLE

You can get to Island 5 by using two boat services: Island 1 -> Island 4 -> Island 5.


Score : 600 points

Problem Statement

We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.

Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.

It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.

You are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.

Constraints

0 ≤ K ≤ 50 \times 10^{16}

Input

Input is given from Standard Input in the following format:

K

Output

Print a solution in the following format:

N
a_1 a_2 ... a_N

Here, 2 ≤ N ≤ 50 and 0 ≤ a_i ≤ 10^{16} + 1000 must hold.

Sample Input 1

0

Sample Output 1

4
3 3 3 3

Sample Input 2

1

Sample Output 2

3
1 0 3

Sample Input 3

2

Sample Output 3

2
2 2

The operation will be performed twice: [2, 2] -> [0, 3] -> [1, 1].

Sample Input 4

3

Sample Output 4

7
27 0 0 0 0 0 0

Sample Input 5

1234567894848

Sample Output 5

10
1000 193 256 777 0 1 1192 1234567891011 48 425


Score : 600 points

Problem Statement

We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller. (The operation is the same as the one in Problem D.)

Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.

It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.

You are given the sequence a_i. Find the number of times we will perform the above operation.

Constraints

2 ≤ N ≤ 50

0 ≤ a_i ≤ 10^{16} + 1000

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the number of times the operation will be performed.

Sample Input 1

4
3 3 3 3

Sample Output 1

0

Sample Input 2

3
1 0 3

Sample Output 2

1

Sample Input 3

2
2 2

Sample Output 3

2

Sample Input 4

7
27 0 0 0 0 0 0

Sample Output 4

3

Sample Input 5

10
1000 193 256 777 0 1 1192 1234567891011 48 425

Sample Output 5

1234567894848


Score : 300 points

Problem Statement

There is a box containing N balls. The i-th ball has the integer A_i written on it.
Snuke can perform the following operation any number of times:

Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.

Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.

Constraints

1 \leq N \leq 10^5

1 \leq A_i \leq 10^9

1 \leq K \leq 10^9

All input values are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 ... A_N

Output

If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print POSSIBLE; if it is not possible, print IMPOSSIBLE.

Sample Input 1

3 7
9 3 4

Sample Output 1

POSSIBLE

First, take out the two balls 9 and 4, and return them back along with a new ball, abs(9-4)=5.
Next, take out 3 and 5, and return them back along with abs(3-5)=2.
Finally, take out 9 and 2, and return them back along with abs(9-2)=7.
Now we have 7 in the box, and the answer is therefore POSSIBLE.

Sample Input 2

3 5
6 9 3

Sample Output 2

IMPOSSIBLE

No matter what we do, it is not possible to have 5 in the box. The answer is therefore IMPOSSIBLE.

Sample Input 3

4 11
11 3 7 15

Sample Output 3

POSSIBLE

The box already contains 11 before we do anything. The answer is therefore POSSIBLE.

Sample Input 4

5 12
10 2 8 6 4

Sample Output 4

IMPOSSIBLE


Score : 100 points

Problem Statement

Snuke is giving cookies to his three goats.

He has two cookie tins. One contains A cookies, and the other contains B cookies. He can thus give A cookies, B cookies or A+B cookies to his goats (he cannot open the tins).

Your task is to determine whether Snuke can give cookies to his three goats so that each of them can have the same number of cookies.

Constraints

1 \leq A,B \leq 100

Both A and B are integers.

Input

Input is given from Standard Input in the following format:

A B

Output

If it is possible to give cookies so that each of the three goats can have the same number of cookies, print Possible; otherwise, print Impossible.

Sample Input 1

4 5

Sample Output 1

Possible

If Snuke gives nine cookies, each of the three goats can have three cookies.

Sample Input 2

1 1

Sample Output 2

Impossible

Since there are only two cookies, the three goats cannot have the same number of cookies no matter what Snuke gives to them.


Score : 300 points

Problem Statement

Snuke and Raccoon have a heap of N cards. The i-th card from the top has the integer a_i written on it.

They will share these cards.
First, Snuke will take some number of cards from the top of the heap, then Raccoon will take all the remaining cards.
Here, both Snuke and Raccoon have to take at least one card.

Let the sum of the integers on Snuke's cards and Raccoon's cards be x and y, respectively.
They would like to minimize |x-y|.
Find the minimum possible value of |x-y|.

Constraints

2 \leq N \leq 2 \times 10^5

-10^{9} \leq a_i \leq 10^{9}

a_i is an integer.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_{N}

Output

Print the answer.

Sample Input 1

6
1 2 3 4 5 6

Sample Output 1

1

If Snuke takes four cards from the top, and Raccoon takes the remaining two cards, x=10, y=11, and thus |x-y|=1. This is the minimum possible value.

Sample Input 2

2
10 -10

Sample Output 2

20

Snuke can only take one card from the top, and Raccoon can only take the remaining one card. In this case, x=10, y=-10, and thus |x-y|=20.


use List::Util qw(sum);

my $N = <STDIN>;
my @cards = split(/ /, <STDIN>);

if ($N == 2) {
    print abs($cards[0] - $cards[1]);
    exit(0);
} else {
    my $sum = sum(@cards);
    my $sunuke = 0;
    for $card (@cards) {
        $sunuke += $card;
        next;
        if ($sunuke > $sum/2) {
            if (abs(($sum - $sunuke) - ($sum - $sunuke - $card)) == 0) {
                print 0;
            } elsif (abs(($sum - $sunuke) - ($sum - $sunuke - $card)) < 0) {
                my $araisan = $sum - $sunuke;
                print abs($sunuke - $araisan);
            } else {
                $sunuke = $sunuke - $card;
                my $araisan = $sum - $sunuke;
                print abs($sunuke - $araisan);
            }
            exit(0);
        }
    }
}


$n = <>; chomp $n;

@adj = ();
push @adj, [] for (0..$n);

for (0..$n-2) {
    $input = <>; chomp $input;
    @p = split / /, $input;

    push $adj[$p[0]], $p[1];
    push $adj[$p[1]], $p[0];
}

# 訪問判別フラグ
push @F, 0 for (0..$n);

# Stack
@S = ();

# 距離
push @dist, 0 for (0..$n);

# 先頭から深さ優先探索
push @S, 1;

while (scalar @S != 0) {
    my $v = pop @S;

    if ($F[$v] == 0) {
        $F[$v] = 1;

        for my $u (@{$adj[$v]}) {
            if ($F[$u] == 0)  {
                push @S, $u;
                $dist[$u] = $dist[$v] + 1;
            }
        }
    }
}

# 訪問判別フラグ
@F = ();
push @F, 0 for (0..$n);

# Stack
@S = ();

# 距離
push @dist2, 0 for (0..$n);

# 最後から深さ優先探索
push @S, $n;

while (scalar @S != 0) {
    my $v = pop @S;

    if ($F[$v] == 0) {
        $F[$v] = 1;

        for my $u (@{$adj[$v]}) {
            if ($F[$u] == 0)  {
                push @S, $u;
                $dist2[$u] = $dist2[$v] + 1;
            }
        }
    }
}

$fennec = 0;
$sunuke = 0;

for (1..$n) {
    if ($dist[$_] <= $dist2[$_]) {
        $fennec += 1;
    }
    else {
        $sunuke += 1;
    }
}

$fennec > $sunuke ? print 'Fennec';

Score : 400 points

Problem Statement

Fennec and Snuke are playing a board game.

On the board, there are N cells numbered 1 through N, and N-1 roads, each connecting two cells. Cell a_i is adjacent to Cell b_i through the i-th road. Every cell can be reached from every other cell by repeatedly traveling to an adjacent cell. In terms of graph theory, the graph formed by the cells and the roads is a tree.

Initially, Cell 1 is painted black, and Cell N is painted white. The other cells are not yet colored.
Fennec (who goes first) and Snuke (who goes second) alternately paint an uncolored cell.
More specifically, each player performs the following action in her/his turn:

Fennec: selects an uncolored cell that is adjacent to a black cell, and paints it black.

Snuke: selects an uncolored cell that is adjacent to a white cell, and paints it white.

A player loses when she/he cannot paint a cell. Determine the winner of the game when Fennec and Snuke play optimally.

Constraints

2 \leq N \leq 10^5

1 \leq a_i, b_i \leq N

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

N
a_1 b_1
:
a_{N-1} b_{N-1}

Output

If Fennec wins, print Fennec; if Snuke wins, print Snuke.

Sample Input 1

7
3 6
1 2
3 1
7 4
5 7
1 4

Sample Output 1

Fennec

For example, if Fennec first paints Cell 2 black, she will win regardless of Snuke's moves.

Sample Input 2

4
1 4
4 2
2 3

Sample Output 2

Snuke


$n = <>; chomp $n;

@adj = ();
push @adj, [] for (0..$n);

for (0..$n-2) {
    $input = <>; chomp $input;
    @p = split / /, $input;

    push $adj[$p[0]], $p[1];
    push $adj[$p[1]], $p[0];
}

# 訪問判別フラグ
push @F, 0 for (0..$n);

# Stack
@S = ();

# 距離
push @dist, 0 for (0..$n);

# 先頭から深さ優先探索
push @S, 1;

while (scalar @S != 0) {
    my $v = pop @S;

    if ($F[$v] == 0) {
        $F[$v] = 1;

        for my $u (@{$adj[$v]}) {
            if ($F[$u] == 0)  {
                push @S, $u;
                $dist[$u] = $dist[$v] + 1;
            }
        }
    }
}

# 訪問判別フラグ
@F = ();
push @F, 0 for (0..$n);

# Stack
@S = ();

# 距離
push @dist2, 0 for (0..$n);

# 先頭から深さ優先探索
push @S, $n;

while (scalar @S != 0) {
    my $v = pop @S;

    if ($F[$v] == 0) {
        $F[$v] = 1;

        for my $u (@{$adj[$v]}) {
            if ($F[$u] == 0)  {
                push @S, $u;
                $dist2[$u] = $dist2[$v] + 1;
            }
        }
    }
}

$fennec = 0;
$sunuke = 0;

for (1..$n) {
    if ($dist[$_] <= $dist2[$_]) {
        $fennec += 1;
    }
    else {
        $sunuke += 1;
    }
}

$fennec > $sunuke ? print 'Fennec' : print 'Sunuke';


Score : 200 points

Problem Statement

There are N bags of biscuits. The i-th bag contains A_i biscuits.

Takaki will select some of these bags and eat all of the biscuits inside.
Here, it is also possible to select all or none of the bags.

He would like to select bags so that the total number of biscuits inside is congruent to P modulo 2.
How many such ways to select bags there are?

Constraints

1 \leq N \leq 50

P = 0 or 1

1 \leq A_i \leq 100

Input

Input is given from Standard Input in the following format:

N P
A_1 A_2 ... A_N

Output

Print the number of ways to select bags so that the total number of biscuits inside is congruent to P modulo 2.

Sample Input 1

2 0
1 3

Sample Output 1

2

There are two ways to select bags so that the total number of biscuits inside is congruent to 0 modulo 2:

Select neither bag. The total number of biscuits is 0.

Select both bags. The total number of biscuits is 4.

Sample Input 2

1 1
50

Sample Output 2

0

Sample Input 3

3 0
1 1 1

Sample Output 3

4

Two bags are distinguished even if they contain the same number of biscuits.

Sample Input 4

45 1
17 55 85 55 74 20 90 67 40 70 39 89 91 50 16 24 14 43 24 66 25 9 89 71 41 16 53 13 61 15 85 72 62 67 42 26 36 66 4 87 59 91 4 25 26

Sample Output 4

17592186044416


Score : 1000 points

Problem Statement

There are N balls in a row.
Initially, the i-th ball from the left has the integer A_i written on it.

When Snuke cast a spell, the following happens:

Let the current number of balls be k. All the balls with k written on them disappear at the same time.

Snuke's objective is to vanish all the balls by casting the spell some number of times.
This may not be possible as it is. If that is the case, he would like to modify the integers on the minimum number of balls to make his objective achievable.

By the way, the integers on these balls sometimes change by themselves.
There will be M such changes. In the j-th change, the integer on the X_j-th ball from the left will change into Y_j.

After each change, find the minimum number of modifications of integers on the balls Snuke needs to make if he wishes to achieve his objective before the next change occurs. We will assume that he is quick enough in modifying integers. Here, note that he does not actually perform those necessary modifications and leaves them as they are.

Constraints

1 \leq N \leq 200000

1 \leq M \leq 200000

1 \leq A_i \leq N

1 \leq X_j \leq N

1 \leq Y_j \leq N

Subscore

In the test set worth 500 points, N \leq 200 and M \leq 200.

Input

Input is given from Standard Input in the following format:

N M
A_1 A_2 ... A_N
X_1 Y_1
X_2 Y_2
:
X_M Y_M

Output

Print M lines.
The j-th line should contain the minimum necessary number of modifications of integers on the balls to make Snuke's objective achievable.

Sample Input 1

5 3
1 1 3 4 5
1 2
2 5
5 4

Sample Output 1

0
1
1

After the first change, the integers on the balls become 2, 1, 3, 4, 5, from left to right. Here, all the balls can be vanished by casting the spell five times. Thus, no modification is necessary.

After the second change, the integers on the balls become 2, 5, 3, 4, 5, from left to right. In this case, at least one modification must be made. One optimal solution is to modify the integer on the fifth ball from the left to 2, and cast the spell four times.

After the third change, the integers on the balls become 2, 5, 3, 4, 4, from left to right. Also in this case, at least one modification must be made. One optimal solution is to modify the integer on the third ball from the left to 2, and cast the spell three times.

Sample Input 2

4 4
4 4 4 4
4 1
3 1
1 1
2 1

Sample Output 2

0
1
2
3

Sample Input 3

10 10
8 7 2 9 10 6 6 5 5 4
8 1
6 3
6 2
7 10
9 7
9 9
2 4
8 1
1 8
7 7

Sample Output 3

1
0
1
2
2
3
3
3
3
2


Score : 1100 points

Problem Statement

There is a tree with N vertices numbered 1, 2, ..., N.
The edges of the tree are denoted by (x_i, y_i).

On this tree, Alice and Bob play a game against each other.
Starting from Alice, they alternately perform the following operation:

Select an existing edge and remove it from the tree, disconnecting it into two separate connected components. Then, remove the component that does not contain Vertex 1.

A player loses the game when he/she is unable to perform the operation.
Determine the winner of the game assuming that both players play optimally.

Constraints

2 \leq N \leq 100000

1 \leq x_i, y_i \leq N

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_{N-1} y_{N-1}

Output

Print Alice if Alice wins; print Bob if Bob wins.

Sample Input 1

5
1 2
2 3
2 4
4 5

Sample Output 1

Alice

If Alice first removes the edge connecting Vertices 1 and 2, the tree becomes a single vertex tree containing only Vertex 1.
Since there is no edge anymore, Bob cannot perform the operation and Alice wins.

Sample Input 2

5
1 2
2 3
1 4
4 5

Sample Output 2

Bob

Sample Input 3

6
1 2
2 4
5 1
6 3
3 2

Sample Output 3

Alice

Sample Input 4

7
1 2
3 7
4 6
2 3
2 4
1 5

Sample Output 4

Bob


Score : 100 points

Problem Statement

Snuke is buying a bicycle.
The bicycle of his choice does not come with a bell, so he has to buy one separately.

He has very high awareness of safety, and decides to buy two bells, one for each hand.

The store sells three kinds of bells for the price of a, b and c yen (the currency of Japan), respectively.
Find the minimum total price of two different bells.

Constraints

1 \leq a,b,c \leq 10000

a, b and c are integers.

Input

Input is given from Standard Input in the following format:

a b c

Output

Print the minimum total price of two different bells.

Sample Input 1

700 600 780

Sample Output 1

1300

Buying a 700-yen bell and a 600-yen bell costs 1300 yen.

Buying a 700-yen bell and a 780-yen bell costs 1480 yen.

Buying a 600-yen bell and a 780-yen bell costs 1380 yen.

The minimum among these is 1300 yen.

Sample Input 2

10000 10000 10000

Sample Output 2

20000

Buying any two bells costs 20000 yen.


my @b=sort map{$_-0} split / /,<STDIN>;
print "$b[0] $b[1]";


use strict;
use warnings;
use utf8;
use feature qw/say/;

my $S = <STDIN>;
my $length = length($S);
for (1..$length) {
  chop($S);
  if (length($S)%2 == 0){
    if (substr($S, 0, length($S)/2) eq substr($S, length($S)/2, length($S))){
      print length($S);
      return;
    }
  }
}

Score : 200 points

Problem Statement

We will call a string that can be obtained by concatenating two equal strings an even string.
For example, xyzxyz and aaaaaa are even, while ababab and xyzxy are not.

You are given an even string S consisting of lowercase English letters.
Find the length of the longest even string that can be obtained by deleting one or more characters from the end of S.
It is guaranteed that such a non-empty string exists for a given input.

Constraints

2 \leq |S| \leq 200

S is an even string consisting of lowercase English letters.

There exists a non-empty even string that can be obtained by deleting one or more characters from the end of S.

Input

Input is given from Standard Input in the following format:

S

Output

Print the length of the longest even string that can be obtained.

Sample Input 1

abaababaab

Sample Output 1

6

abaababaab itself is even, but we need to delete at least one character.

abaababaa is not even.

abaababa is not even.

abaabab is not even.

abaaba is even. Thus, we should print its length, 6.

Sample Input 2

xxxx

Sample Output 2

2

xxx is not even.

xx is even.

Sample Input 3

abcabcabcabc

Sample Output 3

6

The longest even string that can be obtained is abcabc, whose length is 6.

Sample Input 4

akasakaakasakasakaakas

Sample Output 4

14

The longest even string that can be obtained is akasakaakasaka, whose length is 14.


use strict;
use warnings;
use utf8;
use feature qw/say/;

my $n = <STDIN>;
my $str = <STDIN>;
my @aa = split(/ /, $str);
my @b;
for my $a (@aa){
  push(@b, $a);
  @b = reverse(@b);
}
print(join(' ', @b));

Score : 300 points

Problem Statement

You are given an integer sequence of length n, a_1, ..., a_n.
Let us consider performing the following n operations on an empty sequence b.

The i-th operation is as follows:

Append a_i to the end of b.

Reverse the order of the elements in b.

Find the sequence b obtained after these n operations.

Constraints

1 \leq n \leq 2\times 10^5

0 \leq a_i \leq 10^9

n and a_i are integers.

Input

Input is given from Standard Input in the following format:

n
a_1 a_2 ... a_n

Output

Print n integers in a line with spaces in between.
The i-th integer should be b_i.

Sample Input 1

4
1 2 3 4

Sample Output 1

4 2 1 3

After step 1 of the first operation, b becomes: 1.

After step 2 of the first operation, b becomes: 1.

After step 1 of the second operation, b becomes: 1, 2.

After step 2 of the second operation, b becomes: 2, 1.

After step 1 of the third operation, b becomes: 2, 1, 3.

After step 2 of the third operation, b becomes: 3, 1, 2.

After step 1 of the fourth operation, b becomes: 3, 1, 2, 4.

After step 2 of the fourth operation, b becomes: 4, 2, 1, 3.

Thus, the answer is 4 2 1 3.

Sample Input 2

3
1 2 3

Sample Output 2

3 1 2

As shown above in Sample Output 1, b becomes 3, 1, 2 after step 2 of the third operation. Thus, the answer is 3 1 2.

Sample Input 3

1
1000000000

Sample Output 3

1000000000

Sample Input 4

6
0 6 7 6 7 0

Sample Output 4

0 6 6 0 7 7


$n = <>;chomp $n;
$an = <>;chomp $an;
@a = split / /, $an;

for (0..$n-1) {
    push @b, $a[$_];
    @b = reverse @b;
}

print join " ", @b;


Score : 100 points

Problem Statement

Takahashi has a strong stomach. He never gets a stomachache from eating something whose "best-by" date is at most X days earlier.
He gets a stomachache if the "best-by" date of the food is X+1 or more days earlier, though.

Other than that, he finds the food delicious if he eats it not later than the "best-by" date. Otherwise, he does not find it delicious.

Takahashi bought some food A days before the "best-by" date, and ate it B days after he bought it.

Write a program that outputs delicious if he found it delicious, safe if he did not found it delicious but did not get a stomachache either, and dangerous if he got a stomachache.

Constraints

1 ≤ X,A,B ≤ 10^9

Input

Input is given from Standard Input in the following format:

X A B

Output

Print delicious if Takahashi found the food delicious; print safe if he neither found it delicious nor got a stomachache; print dangerous if he got a stomachache.

Sample Input 1

4 3 6

Sample Output 1

safe

He ate the food three days after the "best-by" date. It was not delicious or harmful for him.

Sample Input 2

6 5 1

Sample Output 2

delicious

He ate the food by the "best-by" date. It was delicious for him.

Sample Input 3

3 7 12

Sample Output 3

dangerous

He ate the food five days after the "best-by" date. It was harmful for him.


Score : 200 points

Problem Statement

Takahashi wants to gain muscle, and decides to work out at AtCoder Gym.

The exercise machine at the gym has N buttons, and exactly one of the buttons is lighten up.
These buttons are numbered 1 through N.
When Button i is lighten up and you press it, the light is turned off, and then Button a_i will be lighten up. It is possible that i=a_i.
When Button i is not lighten up, nothing will happen by pressing it.

Initially, Button 1 is lighten up. Takahashi wants to quit pressing buttons when Button 2 is lighten up.

Determine whether this is possible. If the answer is positive, find the minimum number of times he needs to press buttons.

Constraints

2 ≤ N ≤ 10^5

1 ≤ a_i ≤ N

Input

Input is given from Standard Input in the following format:

N
a_1
a_2
:
a_N

Output

Print -1 if it is impossible to lighten up Button 2.
Otherwise, print the minimum number of times we need to press buttons in order to lighten up Button 2.

Sample Input 1

3
3
1
2

Sample Output 1

2

Press Button 1, then Button 3.

Sample Input 2

4
3
4
1
2

Sample Output 2

-1

Pressing Button 1 lightens up Button 3, and vice versa, so Button 2 will never be lighten up.

Sample Input 3

5
3
3
4
2
4

Sample Output 3

3


use List::Util qw/first reduce max/;
my $n = <stdin>;
chomp($n);
my @a;
push @a, $_ for (<stdin>);
my $c = 0;
my $i = 1;
while ($i != 2 && $c < $n){
   $i = $a[$i-1];
   $c++;
}
print ( $c < $n ? $c : -1);


Score : 300 points

Problem Statement

Snuke has N dogs and M monkeys. He wants them to line up in a row.

As a Japanese saying goes, these dogs and monkeys are on bad terms. ("ken'en no naka", literally "the relationship of dogs and monkeys", means a relationship of mutual hatred.) Snuke is trying to reconsile them, by arranging the animals so that there are neither two adjacent dogs nor two adjacent monkeys.

How many such arrangements there are? Find the count modulo 10^9+7 (since animals cannot understand numbers larger than that).
Here, dogs and monkeys are both distinguishable. Also, two arrangements that result from reversing each other are distinguished.

Constraints

1 ≤ N,M ≤ 10^5

Input

Input is given from Standard Input in the following format:

N M

Output

Print the number of possible arrangements, modulo 10^9+7.

Sample Input 1

2 2

Sample Output 1

8

We will denote the dogs by A and B, and the monkeys by C and D. There are eight possible arrangements: ACBD, ADBC, BCAD, BDAC, CADB, CBDA, DACB and DBCA.

Sample Input 2

3 2

Sample Output 2

12

Sample Input 3

1 8

Sample Output 3

0

Sample Input 4

100000 100000

Sample Output 4

530123477


Score : 100 points

Problem Statement

AtCoDeer has three cards, one red, one green and one blue.

An integer between 1 and 9 (inclusive) is written on each card: r on the red card, g on the green card and b on the blue card.

We will arrange the cards in the order red, green and blue from left to right, and read them as a three-digit integer.

Is this integer a multiple of 4?

Constraints

1 ≤ r, g, b ≤ 9

Input

Input is given from Standard Input in the following format:

r g b

Output

If the three-digit integer is a multiple of 4, print YES (case-sensitive); otherwise, print NO.

Sample Input 1

4 3 2

Sample Output 1

YES

432 is a multiple of 4, and thus YES should be printed.

Sample Input 2

2 3 4

Sample Output 2

NO

234 is not a multiple of 4, and thus NO should be printed.


Score : 200 points

Problem Statement

It is only six months until Christmas, and AtCoDeer the reindeer is now planning his travel to deliver gifts.

There are N houses along TopCoDeer street. The i-th house is located at coordinate a_i. He has decided to deliver gifts to all these houses.

Find the minimum distance to be traveled when AtCoDeer can start and end his travel at any positions.

Constraints

1 ≤ N ≤ 100

0 ≤ a_i ≤ 1000

a_i is an integer.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the minimum distance to be traveled.

Sample Input 1

4
2 3 7 9

Sample Output 1

7

The travel distance of 7 can be achieved by starting at coordinate 9 and traveling straight to coordinate 2.

It is not possible to do with a travel distance of less than 7, and thus 7 is the minimum distance to be traveled.

Sample Input 2

8
3 1 4 1 5 9 2 6

Sample Output 2

8

There may be more than one house at a position.


Score : 300 points

Problem Statement

In AtCoder, a person who has participated in a contest receives a color, which corresponds to the person's rating as follows:

Rating 1-399 : gray

Rating 400-799 : brown

Rating 800-1199 : green

Rating 1200-1599 : cyan

Rating 1600-1999 : blue

Rating 2000-2399 : yellow

Rating 2400-2799 : orange

Rating 2800-3199 : red

Other than the above, a person whose rating is 3200 or higher can freely pick his/her color, which can be one of the eight colors above or not.

Currently, there are N users who have participated in a contest in AtCoder, and the i-th user has a rating of a_i.

Find the minimum and maximum possible numbers of different colors of the users.

Constraints

1 ≤ N ≤ 100

1 ≤ a_i ≤ 4800

a_i is an integer.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the minimum possible number of different colors of the users, and the maximum possible number of different colors, with a space in between.

Sample Input 1

4
2100 2500 2700 2700

Sample Output 1

2 2

The user with rating 2100 is "yellow", and the others are "orange". There are two different colors.

Sample Input 2

5
1100 1900 2800 3200 3200

Sample Output 2

3 5

The user with rating 1100 is "green", the user with rating 1900 is blue and the user with rating 2800 is "red".

If the fourth user picks "red", and the fifth user picks "blue", there are three different colors. This is one possible scenario for the minimum number of colors.

If the fourth user picks "purple", and the fifth user picks "black", there are five different colors. This is one possible scenario for the maximum number of colors.

Sample Input 3

20
800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990

Sample Output 3

1 1

All the users are "green", and thus there is one color.


# 個数の標準入力
my $input1 = <STDIN>;
chomp $input1;

# 色番号の標準入力
my $input2 = <STDIN>;
chomp $input2;
my @strcolor = split(/ /, $input2);

my $color1 = 0;
my $color2 = 0;
my $color3 = 0;
my $color4 = 0;
my $color5 = 0;
my $color6 = 0;
my $color7 = 0;
my $color8 = 0;
my $allcolor = 0;

my $cnt = 0;

my $mincnt = 0;
my $maxcnt = 0;

while ($cnt < $input1) {

    if ($strcolor[$cnt] >= 1 && $strcolor[$cnt] <= 399) {
        $color1 = 1;
    }

    if ($strcolor[$cnt] >= 400 && $strcolor[$cnt] <= 799) {
        $color2 = 1;
    }

    if ($strcolor[$cnt] >= 800 && $strcolor[$cnt] <= 1199) {
        $color3 = 1;
    }

    if ($strcolor[$cnt] >= 1200 && $strcolor[$cnt] <= 1599) {
        $color4 = 1;
    }

    if ($strcolor[$cnt] >= 1600 && $strcolor[$cnt] <= 1999) {
        $color5 = 1;
    }

    if ($strcolor[$cnt] >= 2000 && $strcolor[$cnt] <= 2399) {
        $color6 = 1;
    }

    if ($strcolor[$cnt] >= 2400 && $strcolor[$cnt] <= 2799) {
        $color7 = 1;
    }

    if ($strcolor[$cnt] >= 2800 && $strcolor[$cnt] <= 3199) {
        $color8 = 1;
    }

    if ($strcolor[$cnt] >= 3200 && $strcolor[$cnt] <= 4800) {
        $allcolor = $allcolor + 1;
    }

    $cnt = $cnt + 1;
}

$mincnt = $color1 + $color2 + $color3 + $color4 + $color5 + $color6 + $color7 + $color8;

if ($mincnt == 0) {
    $mincnt = 1;
}

$maxcnt = $mincnt + $allcolor;

print $mincnt." ".$maxcnt;
print "\n";


Score : 200 points

Problem Statement

You are given a string S consisting of lowercase English letters. Determine whether all the characters in S are different.

Constraints

2 ≤ |S| ≤ 26, where |S| denotes the length of S.

S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

S

Output

If all the characters in S are different, print yes (case-sensitive); otherwise, print no.

Sample Input 1

uncopyrightable

Sample Output 1

yes

Sample Input 2

different

Sample Output 2

no

Sample Input 3

no

Sample Output 3

yes


Score : 400 points

Problem Statement

You are going out for a walk, when you suddenly encounter N monsters. Each monster has a parameter called health, and the health of the i-th monster is h_i at the moment of encounter. A monster will vanish immediately when its health drops to 0 or below.

Fortunately, you are a skilled magician, capable of causing explosions that damage monsters. In one explosion, you can damage monsters as follows:

Select an alive monster, and cause an explosion centered at that monster. The health of the monster at the center of the explosion will decrease by A, and the health of each of the other monsters will decrease by B. Here, A and B are predetermined parameters, and A > B holds.

At least how many explosions do you need to cause in order to vanish all the monsters?

Constraints

All input values are integers.

1 ≤ N ≤ 10^5

1 ≤ B < A ≤ 10^9

1 ≤ h_i ≤ 10^9

Input

Input is given from Standard Input in the following format:

N A B
h_1
h_2
:
h_N

Output

Print the minimum number of explosions that needs to be caused in order to vanish all the monsters.

Sample Input 1

4 5 3
8
7
4
2

Sample Output 1

2

You can vanish all the monsters in two explosion, as follows:

First, cause an explosion centered at the monster with 8 health. The healths of the four monsters become 3, 4, 1 and -1, respectively, and the last monster vanishes.

Second, cause an explosion centered at the monster with 4 health remaining. The healths of the three remaining monsters become 0, -1 and -2, respectively, and all the monsters are now vanished.

Sample Input 2

2 10 4
20
20

Sample Output 2

4

You need to cause two explosions centered at each monster, for a total of four.

Sample Input 3

5 2 1
900000000
900000000
1000000000
1000000000
1000000000

Sample Output 3

800000000


Score : 300 points

Problem Statement

You are taking a computer-based examination. The examination consists of N questions, and the score allocated to the i-th question is s_i. Your answer to each question will be judged as either "correct" or "incorrect", and your grade will be the sum of the points allocated to questions that are answered correctly. When you finish answering the questions, your answers will be immediately judged and your grade will be displayed... if everything goes well.

However, the examination system is actually flawed, and if your grade is a multiple of 10, the system displays 0 as your grade. Otherwise, your grade is displayed correctly. In this situation, what is the maximum value that can be displayed as your grade?

Constraints

All input values are integers.

1 ≤ N ≤ 100

1 ≤ s_i ≤ 100

Input

Input is given from Standard Input in the following format:

N
s_1
s_2
:
s_N

Output

Print the maximum value that can be displayed as your grade.

Sample Input 1

3
5
10
15

Sample Output 1

25

Your grade will be 25 if the 10-point and 15-point questions are answered correctly and the 5-point question is not, and this grade will be displayed correctly. Your grade will become 30 if the 5-point question is also answered correctly, but this grade will be incorrectly displayed as 0.

Sample Input 2

3
10
10
15

Sample Output 2

35

Your grade will be 35 if all the questions are answered correctly, and this grade will be displayed correctly.

Sample Input 3

3
10
20
30

Sample Output 3

0

Regardless of whether each question is answered correctly or not, your grade will be a multiple of 10 and displayed as 0.


Score : 400 points

Problem Statement

There is a bar of chocolate with a height of H blocks and a width of W blocks.
Snuke is dividing this bar into exactly three pieces.
He can only cut the bar along borders of blocks, and the shape of each piece must be a rectangle.

Snuke is trying to divide the bar as evenly as possible.
More specifically, he is trying to minimize S_{max} - S_{min}, where S_{max} is the area (the number of blocks contained) of the largest piece, and S_{min} is the area of the smallest piece.
Find the minimum possible value of S_{max} - S_{min}.

Constraints

2 ≤ H, W ≤ 10^5

Input

Input is given from Standard Input in the following format:

H W

Output

Print the minimum possible value of S_{max} - S_{min}.

Sample Input 1

3 5

Sample Output 1

0

In the division below, S_{max} - S_{min} = 5 - 5 = 0.

Sample Input 2

4 5

Sample Output 2

2

In the division below, S_{max} - S_{min} = 8 - 6 = 2.

Sample Input 3

5 5

Sample Output 3

4

In the division below, S_{max} - S_{min} = 10 - 6 = 4.

Sample Input 4

100000 2

Sample Output 4

1

Sample Input 5

100000 100000

Sample Output 5

50000


Score : 100 points

Problem Statement

You are given three integers A, B and C.
Determine whether C is not less than A and not greater than B.

Constraints

-100≤A,B,C≤100

A, B and C are all integers.

Input

Input is given from Standard Input in the following format:

A B C

Output

If the condition is satisfied, print Yes; otherwise, print No.

Sample Input 1

1 3 2

Sample Output 1

Yes

C=2 is not less than A=1 and not greater than B=3, and thus the output should be Yes.

Sample Input 2

6 5 4

Sample Output 2

No

C=4 is less than A=6, and thus the output should be No.

Sample Input 3

2 2 2

Sample Output 3

Yes


Score : 200 points

Problem Statement

There are N cities and M roads.
The i-th road (1≤i≤M) connects two cities a_i and b_i (1≤a_i,b_i≤N) bidirectionally.
There may be more than one road that connects the same pair of two cities.
For each city, how many roads are connected to the city?

Constraints

2≤N,M≤50

1≤a_i,b_i≤N

a_i ≠ b_i

All input values are integers.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
:
a_M b_M

Output

Print the answer in N lines.
In the i-th line (1≤i≤N), print the number of roads connected to city i.

Sample Input 1

4 3
1 2
2 3
1 4

Sample Output 1

2
2
1
1

City 1 is connected to the 1-st and 3-rd roads.

City 2 is connected to the 1-st and 2-nd roads.

City 3 is connected to the 2-nd road.

City 4 is connected to the 3-rd road.

Sample Input 2

2 5
1 2
2 1
1 2
2 1
1 2

Sample Output 2

5
5

Sample Input 3

8 8
1 2
3 4
1 5
2 8
3 7
5 2
4 1
6 8

Sample Output 3

3
3
2
2
2
1
1
2


use v5.18;
use warnings;
use utf8;
use Data::Dumper;
use List::Util qw( sum );
use Test::More;

sub line { chomp(my $str = <>); $str; }
sub split_line { (split / /, line) }

main();

sub main {
  my ($town_num, $road_num) = split_line;
  my @roads = map { [split_line] } 0 .. $road_num - 1;
  my $ret = solve($town_num, \@roads);
  say $_ for @$ret;
}

sub solve {
  my ($town_num, $roads) = @_;
  my $sets = {};
  for my $road_index (0 .. $#{ $roads }) {
    my $road_id = $road_index + 1;
    for my $town_id (@{ $roads->[$road_index] }) {
      $sets->{$town_id}{$road_id} = 1;
    }
  }
  [ map { scalar keys %{ $sets->{$_} } } 1 .. $town_num ];
}


my $N = 0;
my $M = 0;

my $input_string = <STDIN>;

($N, $M) = split(/ /, $input_string);

my @input_count = ();

for(my $i = 0; $i < $M; $i++){
	push(@input_count, 0);
}

my @input_city = ();
my $j = 0;

until($input_count[-1] == 1){
	my $row_ab = <STDIN>;

	chomp($row_ab);

	my $a = 0;
	my $b = 0;

	($a, $b) = split(/ /, $row_ab);

	push(@input_city, ($a, $b));

	$input_count[$j] = 1;
	$j++;
}

my @road_city = ();
for(my $i = 0; $i < $N; $i++){
	push(@road_city, 0);
}

foreach(@input_city){
	$road_city[$_]++;
}

shift(@road_city);

foreach(@road_city){
	print "$_\n";
}


Score : 400 points

Problem Statement

There is a directed graph with N vertices and M edges.
The i-th edge (1≤i≤M) points from vertex a_i to vertex b_i, and has a weight c_i.
We will play the following single-player game using this graph and a piece.

Initially, the piece is placed at vertex 1, and the score of the player is set to 0.
The player can move the piece as follows:

When the piece is placed at vertex a_i, move the piece along the i-th edge to vertex b_i. After this move, the score of the player is increased by c_i.

The player can end the game only when the piece is placed at vertex N.
The given graph guarantees that it is possible to traverse from vertex 1 to vertex N.

When the player acts optimally to maximize the score at the end of the game, what will the score be?
If it is possible to increase the score indefinitely, print inf.

Constraints

2≤N≤1000

1≤M≤min(N(N-1),2000)

1≤a_i,b_i≤N (1≤i≤M)

a_i≠b_i (1≤i≤M)

a_i≠a_j or b_i≠b_j (1≤i<j≤M)

-10^9≤c_i≤10^9 (1≤i≤M)

c_i is an integer.

In the given graph, there exists a path from vertex 1 to vertex N.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1 c_1
a_2 b_2 c_2
:
a_M b_M c_M

Output

Print the maximum possible score at the end of the game, if it is finite. If it is possible to increase the score indefinitely, print inf.

Sample Input 1

3 3
1 2 4
2 3 3
1 3 5

Sample Output 1

7

There are two ways to move the piece to vertex N=3:

vertex 1 → vertex 2 → vertex 3 : score 4+3=7

vertex 1 → vertex 3 : score 5

Thus, the maximum possible score at the end of the game is 7.

Sample Input 2

2 2
1 2 1
2 1 1

Sample Output 2

inf

It is possible to increase the score indefinitely by alternating between vertex 1 and 2.

Sample Input 3

6 5
1 2 -1000000000
2 3 -1000000000
3 4 -1000000000
4 5 -1000000000
5 6 -1000000000

Sample Output 3

-5000000000


Score : 300 points

Problem Statement

Takahashi, Aoki and Snuke love cookies. They have A, B and C cookies, respectively. Now, they will exchange those cookies by repeating the action below:

Each person simultaneously divides his cookies in half and gives one half to each of the other two persons.

This action will be repeated until there is a person with odd number of cookies in hand.

How many times will they repeat this action?
Note that the answer may not be finite.

Constraints

1 ≤ A,B,C ≤ 10^9

Input

Input is given from Standard Input in the following format:

A B C

Output

Print the number of times the action will be performed by the three people, if this number is finite.
If it is infinite, print -1 instead.

Sample Input 1

4 12 20

Sample Output 1

3

Initially, Takahashi, Aoki and Snuke have 4, 12 and 20 cookies. Then,

After the first action, they have 16, 12 and 8.

After the second action, they have 10, 12 and 14.

After the third action, they have 13, 12 and 11.

Now, Takahashi and Snuke have odd number of cookies, and therefore the answer is 3.

Sample Input 2

14 14 14

Sample Output 2

-1

Sample Input 3

454 414 444

Sample Output 3

1


Score : 500 points

Problem Statement

Takahashi is not good at problems about trees in programming contests, and Aoki is helping him practice.

First, Takahashi created a tree with N vertices numbered 1 through N, and wrote 0 at each edge.

Then, Aoki gave him M queries. The i-th of them is as follows:

Increment the number written at each edge along the path connecting vertices a_i and b_i, by one.

After Takahashi executed all of the queries, he told Aoki that, for every edge, the written number became an even number.
However, Aoki forgot to confirm that the graph Takahashi created was actually a tree, and it is possible that Takahashi made a mistake in creating a tree or executing queries.

Determine whether there exists a tree that has the property mentioned by Takahashi.

Constraints

2 ≤ N ≤ 10^5

1 ≤ M ≤ 10^5

1 ≤ a_i,b_i ≤ N

a_i ≠ b_i

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
:
a_M b_M

Output

Print YES if there exists a tree that has the property mentioned by Takahashi; print NO otherwise.

Sample Input 1

4 4
1 2
2 4
1 3
3 4

Sample Output 1

YES

For example, Takahashi's graph has the property mentioned by him if it has the following edges: 1-2, 1-3 and 1-4.
In this case, the number written at every edge will become 2.

Sample Input 2

5 5
1 2
3 5
5 1
3 4
2 3

Sample Output 2

NO


Score : 100 points

Problem Statement

You are given three strings A, B and C. Check whether they form a word chain.

More formally, determine whether both of the following are true:

The last character in A and the initial character in B are the same.

The last character in B and the initial character in C are the same.

If both are true, print YES. Otherwise, print NO.

Constraints

A, B and C are all composed of lowercase English letters (a - z).

1 ≤ |A|, |B|, |C| ≤ 10, where |A|, |B| and |C| are the lengths of A, B and C, respectively.

Input

Input is given from Standard Input in the following format:

A B C

Output

Print YES or NO.

Sample Input 1

rng gorilla apple

Sample Output 1

YES

They form a word chain.

Sample Input 2

yakiniku unagi sushi

Sample Output 2

NO

A and B form a word chain, but B and C do not.

Sample Input 3

a a a

Sample Output 3

YES

Sample Input 4

aaaaaaaaab aaaaaaaaaa aaaaaaaaab

Sample Output 4

NO


#!/usr/bin/perl

sub main() {
  my($A,$B,$C)=split(/ /,<>);
  chomp($C);
  my $ans = prob($A,$B,$C);
  print $ans;
}

sub prob() {
  my($A,$B,$C) = @_;
  for my $i(1..100){
    my $tmp = $B * $i + $C;
    if($tmp%$A == 0){
      return "YES";
    }
  }
  return "NO";
}

&main();

Score : 200 points

Problem Statement

We ask you to select some number of positive integers, and calculate the sum of them.

It is allowed to select as many integers as you like, and as large integers as you wish.
You have to follow these, however: each selected integer needs to be a multiple of A, and you need to select at least one integer.

Your objective is to make the sum congruent to C modulo B.
Determine whether this is possible.

If the objective is achievable, print YES. Otherwise, print NO.

Constraints

1 ≤ A ≤ 100

1 ≤ B ≤ 100

0 ≤ C < B

Input

Input is given from Standard Input in the following format:

A B C

Output

Print YES or NO.

Sample Input 1

7 5 1

Sample Output 1

YES

For example, if you select 7 and 14, the sum 21 is congruent to 1 modulo 5.

Sample Input 2

2 2 1

Sample Output 2

NO

The sum of even numbers, no matter how many, is never odd.

Sample Input 3

1 100 97

Sample Output 3

YES

You can select 97, since you may select multiples of 1, that is, all integers.

Sample Input 4

40 98 58

Sample Output 4

YES

Sample Input 5

77 42 36

Sample Output 5

NO


use Math::BigInt bgcd;@n=glob<>;print+$n[2]% bgcd($n[0],$n[1])?NO:YES


Score : 300 points

Problem Statement

In a public bath, there is a shower which emits water for T seconds when the switch is pushed.

If the switch is pushed when the shower is already emitting water, from that moment it will be emitting water for T seconds.
Note that it does not mean that the shower emits water for T additional seconds.

N people will push the switch while passing by the shower.
The i-th person will push the switch t_i seconds after the first person pushes it.

How long will the shower emit water in total?

Constraints

1 ≤ N ≤ 200,000

1 ≤ T ≤ 10^9

0 = t_1 < t_2 < t_3 < , ..., < t_{N-1} < t_N ≤ 10^9

T and each t_i are integers.

Input

Input is given from Standard Input in the following format:

N T
t_1 t_2 ... t_N

Output

Assume that the shower will emit water for a total of X seconds. Print X.

Sample Input 1

2 4
0 3

Sample Output 1

7

Three seconds after the first person pushes the water, the switch is pushed again and the shower emits water for four more seconds, for a total of seven seconds.

Sample Input 2

2 4
0 5

Sample Output 2

8

One second after the shower stops emission of water triggered by the first person, the switch is pushed again.

Sample Input 3

4 1000000000
0 1000 1000000 1000000000

Sample Output 3

2000000000

Sample Input 4

1 1
0

Sample Output 4

1

Sample Input 5

9 10
0 3 5 7 100 110 200 300 311

Sample Output 5

67


Score : 100 points

Problem Statement

You are given three words s_1, s_2 and s_3, each composed of lowercase English letters, with spaces in between.
Print the acronym formed from the uppercased initial letters of the words.

Constraints

s_1, s_2 and s_3 are composed of lowercase English letters.

1 ≤ |s_i| ≤ 10 (1≤i≤3)

Input

Input is given from Standard Input in the following format:

s_1 s_2 s_3

Output

Print the answer.

Sample Input 1

atcoder beginner contest

Sample Output 1

ABC

The initial letters of atcoder, beginner and contest are a, b and c. Uppercase and concatenate them to obtain ABC.

Sample Input 2

resident register number

Sample Output 2

RRN

Sample Input 3

k nearest neighbor

Sample Output 3

KNN

Sample Input 4

async layered coding

Sample Output 4

ALC


Score : 300 points

Problem Statement

You are given an array A of length N.
Your task is to divide it into several contiguous subarrays.
Here, all subarrays obtained must be sorted in either non-decreasing or non-increasing order.
At least how many subarrays do you need to divide A into?

Constraints

1 \leq N \leq 10^5

1 \leq A_i \leq 10^9

Each A_i is an integer.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the minimum possible number of subarrays after division of A.

Sample Input 1

6
1 2 3 2 2 1

Sample Output 1

2

One optimal solution is to divide the array into [1,2,3] and [2,2,1].

Sample Input 2

9
1 2 1 2 1 2 1 2 1

Sample Output 2

5

Sample Input 3

7
1 2 3 2 1 999999999 1000000000

Sample Output 3

3


($n, $m) = split / /, <>;

$input = <>; chomp $input;
my @base = split / /, $input;

for (1..$m-1) {
    $input = <>; chomp $input;
    @vers = split / /, $input;

    for my $index (0,1) {
        my @match_index = grep { $base[$_] == $vers[$index] } (0,1);

        if (defined $match_index[0]) {
            print "3\n";
            print $vers[1-$index] . " " . $vers[$index] . " " . $base[1-$match_index[0]];
            exit;
        }
    }
}

Score : 500 points

Problem Statement

You are given a connected undirected simple graph, which has N vertices and M edges.
The vertices are numbered 1 through N, and the edges are numbered 1 through M.
Edge i connects vertices A_i and B_i.
Your task is to find a path that satisfies the following conditions:

The path traverses two or more vertices.

The path does not traverse the same vertex more than once.

A vertex directly connected to at least one of the endpoints of the path, is always contained in the path.

It can be proved that such a path always exists.
Also, if there are more than one solution, any of them will be accepted.

Constraints

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq A_i < B_i \leq N

The given graph is connected and simple (that is, for every pair of vertices, there is at most one edge that directly connects them).

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
:
A_M B_M

Output

Find one path that satisfies the conditions, and print it in the following format.
In the first line, print the count of the vertices contained in the path.
In the second line, print a space-separated list of the indices of the vertices, in order of appearance in the path.

Sample Input 1

5 6
1 3
1 4
2 3
1 5
3 5
2 4

Sample Output 1

4
2 3 1 4

There are two vertices directly connected to vertex 2: vertices 3 and 4.
There are also two vertices directly connected to vertex 4: vertices 1 and 2.
Hence, the path 2 → 3 → 1 → 4 satisfies the conditions.

Sample Input 2

7 8
1 2
2 3
3 4
4 5
5 6
6 7
3 5
2 6

Sample Output 2

7
1 2 3 4 5 6 7


Max Score: 250 Points

Problem Statement

Mr.X, who the handle name is T, looked at the list which written N handle names, S_1, S_2, ..., S_N.

But he couldn't see some parts of the list. Invisible part is denoted ?.

Please calculate all possible index of the handle name of Mr.X when you sort N+1 handle names (S_1, S_2, ..., S_N and T) in lexicographical order.

Note: If there are pair of people with same handle name, either one may come first.

Input

The input is given from standard input in the following format.

N
S_1
S_2
:
S_N
T

Output

Calculate the possible index and print in sorted order. The output should be separated with a space. Don't print a space after last number.

Put a line break in the end.

Constraints

1 ≤ N ≤ 10000

1 ≤ |S_i|, |T| ≤ 20 (|A| is the length of A.)

S_i consists from lower-case alphabet and ?.

T consists from lower-case alphabet.

Scoring

Subtask 1 [ 130 points ]

There are no ?'s.

Subtask 2 [ 120 points ]

There are no additional constraints.

Sample Input 1

2
tourist
petr
e

Sample Output 1

1

There are no invisible part, so there are only one possibility.
The sorted handle names are e, petr, tourist, so e comes first.

Sample Input 2

2
?o?r?s?
?et?
e


Score : 200 points

Problem Statement

Snuke signed up for a new website which holds programming competitions.
He worried that he might forget his password, and he took notes of it.
Since directly recording his password would cause him trouble if stolen,
he took two notes: one contains the characters at the odd-numbered positions, and the other contains the characters at the even-numbered positions.

You are given two strings O and E. O contains the characters at the odd-numbered positions retaining their relative order, and E contains the characters at the even-numbered positions retaining their relative order.
Restore the original password.

Constraints

O and E consists of lowercase English letters (a - z).

1 \leq |O|,|E| \leq 50

|O| - |E| is either 0 or 1.

Input

Input is given from Standard Input in the following format:

O
E

Output

Print the original password.

Sample Input 1

xyz
abc

Sample Output 1

xaybzc

The original password is xaybzc. Extracting the characters at the odd-numbered positions results in xyz, and extracting the characters at the even-numbered positions results in abc.

Sample Input 2

atcoderbeginnercontest
atcoderregularcontest

Sample Output 2

aattccooddeerrbreeggiunlnaerrccoonntteesstt


use strict;
use utf8;
use warnings;

chomp(my @lines = <STDIN>);
my ($odd, $even) = @lines;
my @ans_list = ();
my @o_list = split(//, $odd);
my @e_list = split(//, $even);
foreach (1..$#e_list+1){
    push @ans_list, $o_list[$_-1];
    push @ans_list, $e_list[$_-1];
}
if ($#o_list != $#e_list){push @ans_list, $o_list[-1]}
my $ans = join("", @ans_list);
print "$ans\n";


use strict;
use warnings;
use v5.18;

package Vector {

    sub new {
        my $class = shift;
        my ( $size, $value ) = @_;

        my $data;
        if ( defined $size ) {
            $value = 0 unless defined $value;
            $data = [ map { $value } 1 .. $size ];
        }
        else {
            $data = [];
        }

        my $self = bless { _data => $data }, $class;
        return $self;
    }

    sub push_back {
        my ( $self, $x ) = @_;
        my $data = $self->{_data};
        push @$data => $x;
    }

    sub size {
        my $self = shift;
        my $data = $self->{_data};
        scalar(@$data);
    }

    sub at {
        my ( $self, $i, $x ) = @_;

        my $data = $self->{_data};
        my $len  = $self->size;
        die "invalid index: $i (size = $len)\n"
          unless 0 <= $i && $i < $self->size;

        if ( defined $x ) {
            $data->[$i] = $x;
        }
        else {
            $data->[$i];
        }
    }

    sub front {
        my $self = shift;
        $self->at(0);
    }

    sub back {
        my $self = shift;
        $self->at( $self->size - 1 );
    }
};

chomp( my $n = <> );

my $cnt = Vector->new;

for my $i ( 0 .. $n - 1 ) {
    chomp( my $s = <> );
    my @s = split( //, $s );
    $cnt->push_back( Vector->new( 26, 0 ) );
    for my $j ( 0 .. $#s ) {
        my $k = ord( $s[$j] ) - ord('a');
        my $t = $cnt->at($i)->at($k);
        $cnt->at($i)->at( $k, $t + 1 );
    }
}

for my $i ( 0 .. 25 ) {
    my $min = 100;
    for my $j ( 0 .. $n - 1 ) {
        my $t = $cnt->at($j)->at($i);
        $min = $t if ( $t < $min );
    }

    # print "min = $min\n";
    my $c = chr( $i + ord('a') );
    print $c for 1 .. $min;
}
print "\n";

Score : 300 points

Problem Statement

Snuke loves "paper cutting": he cuts out characters from a newspaper headline and rearranges them to form another string.

He will receive a headline which contains one of the strings S_1,...,S_n tomorrow.
He is excited and already thinking of what string he will create.
Since he does not know the string on the headline yet, he is interested in strings that can be created regardless of which string the headline contains.

Find the longest string that can be created regardless of which string among S_1,...,S_n the headline contains.
If there are multiple such strings, find the lexicographically smallest one among them.

Constraints

1 \leq n \leq 50

1 \leq |S_i| \leq 50 for every i = 1, ..., n.

S_i consists of lowercase English letters (a - z) for every i = 1, ..., n.

Input

Input is given from Standard Input in the following format:

n
S_1
...
S_n

Output

Print the lexicographically smallest string among the longest strings that satisfy the condition.
If the answer is an empty string, print an empty line.

Sample Input 1

3
cbaa
daacc
acacac

Sample Output 1

aac

The strings that can be created from each of cbaa, daacc and acacac, are aa, aac, aca, caa and so forth.
Among them, aac, aca and caa are the longest, and the lexicographically smallest of these three is aac.

Sample Input 2

3
a
aa
b

Sample Output 2

The answer is an empty string.


$n = <>;
$first = 1;

for (1..$n) {
    $_ = <>;
    my %hash;
    chomp;
    @a = split('');
    for (@a) {
        $hash{$_}++;
    }
    if ($first) {
        %glbl = %hash;
    } else {
        for (keys %glbl) {
            if ($glbl{$_} > $hash{$_}) {
                $glbl{$_} = $hash{$_};
            }
        }
    }
    $first = 0;
}
for (sort(keys %glbl)) {
    print $_ x $glbl{$_};
}
print "\n";


Score : 600 points

Problem Statement

Let us consider the following operations on a string consisting of A and B:

Select a character in a string. If it is A, replace it with BB. If it is B, replace with AA.

Select a substring that is equal to either AAA or BBB, and delete it from the string.

For example, if the first operation is performed on ABA and the first character is selected, the string becomes BBBA.
If the second operation is performed on BBBAAAA and the fourth through sixth characters are selected, the string becomes BBBA.

These operations can be performed any number of times, in any order.

You are given two string S and T, and q queries a_i, b_i, c_i, d_i.
For each query, determine whether S_{a_i} S_{{a_i}+1} ... S_{b_i}, a substring of S, can be made into T_{c_i} T_{{c_i}+1} ... T_{d_i}, a substring of T.

Constraints

1 \leq |S|, |T| \leq 10^5

S and T consist of letters A and B.

1 \leq q \leq 10^5

1 \leq a_i \leq b_i \leq |S|

1 \leq c_i \leq d_i \leq |T|

Input

Input is given from Standard Input in the following format:

S
T
q
a_1 b_1 c_1 d_1
...
a_q b_q c_q d_q

Output

Print q lines. The i-th line should contain the response to the i-th query. If S_{a_i} S_{{a_i}+1} ... S_{b_i} can be made into T_{c_i} T_{{c_i}+1} ... T_{d_i}, print YES. Otherwise, print NO.

Sample Input 1

BBBAAAABA
BBBBA
4
7 9 2 5
7 9 1 4
1 7 2 5
1 7 2 4

Sample Output 1

YES
NO
YES
NO

The first query asks whether the string ABA can be made into BBBA.
As explained in the problem statement, it can be done by the first operation.

The second query asks whether ABA can be made into BBBB, and the fourth query asks whether BBBAAAA can be made into BBB.
Neither is possible.

The third query asks whether the string BBBAAAA can be made into BBBA.
As explained in the problem statement, it can be done by the second operation.

Sample Input 2

AAAAABBBBAAABBBBAAAA
BBBBAAABBBBBBAAAAABB
10
2 15 2 13
2 13 6 16
1 13 2 20
4 20 3 20
1 18 9 19
2 14 1 11
3 20 3 15
6 16 1 17
4 18 8 20
7 20 3 14

Sample Output 2

YES
YES
YES
YES
YES
YES
NO
NO
NO
NO


my @data =<STDIN>;
foreach(@data) { chomp; }
my @num = split(/ /, $data[0]);
my $pn = $num[0];
my $en = $num[1];

my @result;
for(1..$pn) { push(@result, 0); }

my @edge;
for(1..$en) {
	my @ele = split(/ /, $data[$_]);
	push(@edge, "$ele[0],$ele[1]");
	push(@edge, "$ele[1],$ele[0]");
}

my $cn = $data[$en+1];

for(1..$cn) {
	my @ele = split(/ /, $data[$en+1+$_]);
	my $sp = $ele[0];
	my $d = $ele[1];
	my $c = $ele[2];

	color($sp, $d, $c);
}

for(@result) {
	print $_, "\n";
}

sub color {
	my ($s, $d, $c) = @_;

	$result[$s-1]= $c;

	print $s, "-", $d, "-", $c, "\n";
	if($d <= 0) {
		return;
	}
	print "cont\n";

	for(@edge) {
		if($_ =~ /$s,(\d+)/) {
			color($1, $d-1, $c);
		}
	}
}

Score : 700 points

Problem Statement

Squid loves painting vertices in graphs.

There is a simple undirected graph consisting of N vertices numbered 1 through N, and M edges.
Initially, all the vertices are painted in color 0. The i-th edge bidirectionally connects two vertices a_i and b_i. The length of every edge is 1.

Squid performed Q operations on this graph. In the i-th operation, he repaints all the vertices within a distance of d_i from vertex v_i, in color c_i.

Find the color of each vertex after the Q operations.

Constraints

1 ≤ N,M,Q ≤ 10^5

1 ≤ a_i,b_i,v_i ≤ N

a_i ≠ b_i

0 ≤ d_i ≤ 10

1 ≤ c_i ≤10^5

d_i and c_i are all integers.

There are no self-loops or multiple edges in the given graph.

Partial Score

200 points will be awarded for passing the testset satisfying 1 ≤ N,M,Q ≤ 2{,}000.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
:
a_{M} b_{M}
Q
v_1 d_1 c_1
:
v_{Q} d_{Q} c_{Q}

Output

Print the answer in N lines.
In the i-th line, print the color of vertex i after the Q operations.

Sample Input 1

7 7
1 2
1 3
1 4
4 5
5 6
5 7
2 3
2
6 1 1
1 2 2

Sample Output 1

2
2
2
2
2
1
0

Initially, each vertex is painted in color 0.
In the first operation, vertices 5 and 6 are repainted in color 1.
In the second operation, vertices 1, 2, 3, 4 and 5 are repainted in color 2.

Sample Input 2

14 10
1 4
5 7
7 11
4 10
14 7
14 3
6 14
8 11
5 13
8 3
8
8 6 2
9 7 85
6 9 3
6 7 5
10 3 1
12 9 4
9 6 6
8 2 3

Sample Output 2

1
0
3
1
5
5
3
3
6
1
3
4
5
3

The given graph may not be connected.


Score : 1000 points

Problem Statement

We will call a string x good if it satisfies the following condition:

Condition: x can be represented as a concatenation of two copies of another string y of length at least 1.

For example, aa and bubobubo are good; an empty string, a, abcabcabc and abba are not good.

Eagle and Owl created a puzzle on good strings.
Find one string s that satisfies the following conditions. It can be proved that such a string always exists under the constraints in this problem.

1 ≤ |s| ≤ 200

Each character of s is one of the 100 characters represented by the integers 1 through 100.

Among the 2^{|s|} subsequences of s, exactly N are good strings.

Constraints

1 ≤ N ≤ 10^{12}

Input

Input is given from Standard Input in the following format:

N

Output

In the first line, print |s|, the length of s.
In the second line, print the elements in s in order, with spaces in between. Any string that satisfies the above conditions will be accepted.

Sample Input 1

7

Sample Output 1

4
1 1 1 1

There are two good strings that appear as subsequences of s: (1,1) and (1,1,1,1). There are six occurrences of (1,1) and one occurrence of (1,1,1,1), for a total of seven.

Sample Input 2

299

Sample Output 2

23
32 11 11 73 45 8 11 83 83 8 45 32 32 10 100 73 32 83 45 73 32 11 10


Score : 100 points

Problem Statement

Dolphin loves programming contests. Today, he will take part in a contest in AtCoder.

In this country, 24-hour clock is used. For example, 9:00 p.m. is referred to as "21 o'clock".

The current time is A o'clock, and a contest will begin in exactly B hours.
When will the contest begin? Answer in 24-hour time.

Constraints

0 \leq A,B \leq 23

A and B are integers.

Input

The input is given from Standard Input in the following format:

A B

Output

Print the hour of the starting time of the contest in 24-hour time.

Sample Input 1

9 12

Sample Output 1

21

In this input, the current time is 9 o'clock, and 12 hours later it will be 21 o'clock in 24-hour time.

Sample Input 2

19 0

Sample Output 2

19

The contest has just started.

Sample Input 3

23 2

Sample Output 3

1

The contest will begin at 1 o'clock the next day.


Score : 200 points

Problem Statement

There are N students and M checkpoints on the xy-plane.

The coordinates of the i-th student (1 \leq i \leq N) is (a_i,b_i), and the coordinates of the checkpoint numbered j (1 \leq j \leq M) is (c_j,d_j).

When the teacher gives a signal, each student has to go to the nearest checkpoint measured in Manhattan distance.

The Manhattan distance between two points (x_1,y_1) and (x_2,y_2) is |x_1-x_2|+|y_1-y_2|.

Here, |x| denotes the absolute value of x.

If there are multiple nearest checkpoints for a student, he/she will select the checkpoint with the smallest index.

Which checkpoint will each student go to?

Constraints

1 \leq N,M \leq 50

-10^8 \leq a_i,b_i,c_j,d_j \leq 10^8

All input values are integers.

Input

The input is given from Standard Input in the following format:

N M
a_1 b_1
:
a_N b_N
c_1 d_1
:
c_M d_M

Output

Print N lines.

The i-th line (1 \leq i \leq N) should contain the index of the checkpoint for the i-th student to go.

Sample Input 1

2 2
2 0
0 0
-1 0
1 0

Sample Output 1

2
1

The Manhattan distance between the first student and each checkpoint is:

For checkpoint 1: |2-(-1)|+|0-0|=3

For checkpoint 2: |2-1|+|0-0|=1

The nearest checkpoint is checkpoint 2. Thus, the first line in the output should contain 2.

The Manhattan distance between the second student and each checkpoint is:

For checkpoint 1: |0-(-1)|+|0-0|=1

For checkpoint 2: |0-1|+|0-0|=1

When there are multiple nearest checkpoints, the student will go to the checkpoint with the smallest index. Thus, the second line in the output should contain 1.

Sample Input 2

3 4
10 10
-10 -10
3 3
1 2
2 3
3 5
3 5

Sample Output 2

3
1
2

There can be multiple checkpoints at the same coordinates.

Sample Input 3

5 5
-100000000 -100000000
-100000000 100000000
100000000 -100000000
100000000 100000000
0 0
0 0
100000000 100000000
100000000 -100000000
-100000000 100000000
-100000000 -100000000

Sample Output 3

5
4
3
2
1


Score : 400 points

Problem Statement

You are given N items.

The value of the i-th item (1 \leq i \leq N) is v_i.

Your have to select at least A and at most B of these items.

Under this condition, find the maximum possible arithmetic mean of the values of selected items.

Additionally, find the number of ways to select items so that the mean of the values of selected items is maximized.

Constraints

1 \leq N \leq 50

1 \leq A,B \leq N

1 \leq v_i \leq 10^{15}

Each v_i is an integer.

Input

The input is given from Standard Input in the following format:

N A B
v_1
v_2
...
v_N

Output

Print two lines.

The first line should contain the maximum possible arithmetic mean of the values of selected items. The output should be considered correct if the absolute or relative error is at most 10^{-6}.

The second line should contain the number of ways to select items so that the mean of the values of selected items is maximized.

Sample Input 1

5 2 2
1 2 3 4 5

Sample Output 1

4.500000
1

The mean of the values of selected items will be maximized when selecting the fourth and fifth items. Hence, the first line of the output should contain 4.5.

There is no other way to select items so that the mean of the values will be 4.5, and thus the second line of the output should contain 1.

Sample Input 2

4 2 3
10 20 10 10

Sample Output 2

15.000000
3

There can be multiple ways to select items so that the mean of the values will be maximized.

Sample Input 3

5 1 5
1000000000000000 999999999999999 999999999999998 999999999999997 999999999999996

Sample Output 3

1000000000000000.000000
1


Score : 100 points

Problem Statement

Two deer, AtCoDeer and TopCoDeer, are playing a game called Honest or Dishonest.
In this game, an honest player always tells the truth, and an dishonest player always tell lies.
You are given two characters a and b as the input. Each of them is either H or D, and carries the following information:

If a=H, AtCoDeer is honest; if a=D, AtCoDeer is dishonest.
If b=H, AtCoDeer is saying that TopCoDeer is honest; if b=D, AtCoDeer is saying that TopCoDeer is dishonest.

Given this information, determine whether TopCoDeer is honest.

Constraints

a=H or a=D.

b=H or b=D.

Input

The input is given from Standard Input in the following format:

a b

Output

If TopCoDeer is honest, print H. If he is dishonest, print D.

Sample Input 1

H H

Sample Output 1

H

In this input, AtCoDeer is honest. Hence, as he says, TopCoDeer is honest.

Sample Input 2

D H

Sample Output 2

D

In this input, AtCoDeer is dishonest. Hence, contrary to what he says, TopCoDeer is dishonest.

Sample Input 3

D D

Sample Output 3

H


#!/usr/bin/perl

sub main() {
  my($A,$B)=split(/ /,<>);
  print(prob($A,$B));
  print "\n";
}

sub prob() {
  my($A,$B) = @_;
  my $ab = $A.$B;
  return 'H' if $ab eq 'HH';
  return 'H' if $ab eq 'HD';
  return 'D' if $ab eq 'DH';
  return 'D' if $ab eq 'DD';
}

&main();


Score : 200 points

Problem Statement

There is a kangaroo at coordinate 0 on an infinite number line that runs from left to right, at time 0.
During the period between time i-1 and time i, the kangaroo can either stay at his position, or perform a jump of length exactly i to the left or to the right.
That is, if his coordinate at time i-1 is x, he can be at coordinate x-i, x or x+i at time i.
The kangaroo's nest is at coordinate X, and he wants to travel to coordinate X as fast as possible.
Find the earliest possible time to reach coordinate X.

Constraints

X is an integer.

1≤X≤10^9

Input

The input is given from Standard Input in the following format:

X

Output

Print the earliest possible time for the kangaroo to reach coordinate X.

Sample Input 1

6

Sample Output 1

3

The kangaroo can reach his nest at time 3 by jumping to the right three times, which is the earliest possible time.

Sample Input 2

2

Sample Output 2

2

He can reach his nest at time 2 by staying at his position during the first second, and jumping to the right at the next second.

Sample Input 3

11

Sample Output 3

5


Score : 600 points

Problem Statement

AtCoDeer the deer has N cards with positive integers written on them. The number on the i-th card (1≤i≤N) is a_i.
Because he loves big numbers, he calls a subset of the cards good when the sum of the numbers written on the cards in the subset, is K or greater.

Then, for each card i, he judges whether it is unnecessary or not, as follows:

If, for any good subset of the cards containing card i, the set that can be obtained by eliminating card i from the subset is also good, card i is unnecessary.

Otherwise, card i is NOT unnecessary.

Find the number of the unnecessary cards. Here, he judges each card independently, and he does not throw away cards that turn out to be unnecessary.

Constraints

All input values are integers.

1≤N≤5000

1≤K≤5000

1≤a_i≤10^9 (1≤i≤N)

Partial Score

300 points will be awarded for passing the test set satisfying N,K≤400.

Input

The input is given from Standard Input in the following format:

N K
a_1 a_2 ... a_N

Output

Print the number of the unnecessary cards.

Sample Input 1

3 6
1 4 3

Sample Output 1

1

There are two good sets: {2,3} and {1,2,3}.

Card 1 is only contained in {1,2,3}, and this set without card 1, {2,3}, is also good. Thus, card 1 is unnecessary.

For card 2, a good set {2,3} without card 2, {3}, is not good. Thus, card 2 is NOT unnecessary.

Neither is card 3 for a similar reason, hence the answer is 1.

Sample Input 2

5 400
3 1 4 1 5

Sample Output 2

5

In this case, there is no good set. Therefore, all the cards are unnecessary.

Sample Input 3

6 20
10 4 3 10 25 2

Sample Output 3

3


Score : 800 points

Problem Statement

Takahashi has received an undirected graph with N vertices, numbered 1, 2, ..., N.
The edges in this graph are represented by (u_i, v_i).
There are no self-loops and multiple edges in this graph.

Based on this graph, Takahashi is now constructing a new graph with N^2 vertices, where each vertex is labeled with a pair of integers (a, b) (1 \leq a \leq N, 1 \leq b \leq N).
The edges in this new graph are generated by the following rule:

Span an edge between vertices (a, b) and (a', b') if and only if both of the following two edges exist in the original graph: an edge between vertices a and a', and an edge between vertices b and b'.

How many connected components are there in this new graph?

Constraints

2 \leq N \leq 100,000

0 \leq M \leq 200,000

1 \leq u_i < v_i \leq N

There exists no pair of distinct integers i and j such that u_i = u_j and v_i = v_j.

Input

The input is given from Standard Input in the following format:

N M
u_1 v_1
u_2 v_2
:
u_M v_M

Output

Print the number of the connected components in the graph constructed by Takahashi.

Sample Input 1

3 1
1 2

Sample Output 1

7

The graph constructed by Takahashi is as follows.

Sample Input 2

7 5
1 2
3 4
3 5
4 5
2 6

Sample Output 2

18


Score : 100 points

Problem Statement

Snuke has a favorite restaurant.

The price of any meal served at the restaurant is 800 yen (the currency of Japan), and each time a customer orders 15 meals, the restaurant pays 200 yen back to the customer.

So far, Snuke has ordered N meals at the restaurant.
Let the amount of money Snuke has paid to the restaurant be x yen, and let the amount of money the restaurant has paid back to Snuke be y yen.
Find x-y.

Constraints

1 ≤ N ≤ 100

Input

The input is given from Standard Input in the following format:

N

Output

Print the answer.

Sample Input 1

20

Sample Output 1

15800

So far, Snuke has paid 16000 yen, and the restaurant has paid back 200 yen. Thus, the answer is 15800.

Sample Input 2

60

Sample Output 2

47200

Snuke has paid 48000 yen for 60 meals, and the restaurant has paid back 800 yen.


Score : 200 points

Problem Statement

Snuke loves working out. He is now exercising N times.

Before he starts exercising, his power is 1. After he exercises for the i-th time, his power gets multiplied by i.

Find Snuke's power after he exercises N times. Since the answer can be extremely large, print the answer modulo 10^{9}+7.

Constraints

1 ≤ N ≤ 10^{5}

Input

The input is given from Standard Input in the following format:

N

Output

Print the answer modulo 10^{9}+7.

Sample Input 1

3

Sample Output 1

6

After Snuke exercises for the first time, his power gets multiplied by 1 and becomes 1.

After Snuke exercises for the second time, his power gets multiplied by 2 and becomes 2.

After Snuke exercises for the third time, his power gets multiplied by 3 and becomes 6.

Sample Input 2

10

Sample Output 2

3628800

Sample Input 3

100000

Sample Output 3

457992974

Print the answer modulo 10^{9}+7.


Score : 500 points

Problem Statement

Snuke, who loves animals, built a zoo.

There are N animals in this zoo. They are conveniently numbered 1 through N, and arranged in a circle.
The animal numbered i (2≤i≤N-1) is adjacent to the animals numbered i-1 and i+1. Also, the animal numbered 1 is adjacent to the animals numbered 2 and N, and the animal numbered N is adjacent to the animals numbered N-1 and 1.

There are two kinds of animals in this zoo: honest sheep that only speak the truth, and lying wolves that only tell lies.

Snuke cannot tell the difference between these two species, and asked each animal the following question: "Are your neighbors of the same species?" The animal numbered i answered s_i. Here, if s_i is o, the animal said that the two neighboring animals are of the same species, and if s_i is x, the animal said that the two neighboring animals are of different species.

More formally, a sheep answered o if the two neighboring animals are both sheep or both wolves, and answered x otherwise.
Similarly, a wolf answered x if the two neighboring animals are both sheep or both wolves, and answered o otherwise.

Snuke is wondering whether there is a valid assignment of species to the animals that is consistent with these responses. If there is such an assignment, show one such assignment. Otherwise, print -1.

Constraints

3 ≤ N ≤ 10^{5}

s is a string of length N consisting of o and x.

Input

The input is given from Standard Input in the following format:

N
s

Output

If there does not exist an valid assignment that is consistent with s, print -1.
Otherwise, print an string t in the following format. The output is considered correct if the assignment described by t is consistent with s.

t is a string of length N consisting of S and W.

If t_i is S, it indicates that the animal numbered i is a sheep. If t_i is W, it indicates that the animal numbered i is a wolf.

Sample Input 1

6
ooxoox

Sample Output 1

SSSWWS

For example, if the animals numbered 1, 2, 3, 4, 5 and 6 are respectively a sheep, sheep, sheep, wolf, wolf, and sheep, it is consistent with their responses. Besides, there is another valid assignment of species: a wolf, sheep, wolf, sheep, wolf and wolf.

Let us remind you: if the neiboring animals are of the same species, a sheep answers o and a wolf answers x. If the neiboring animals are of different species, a sheep answers x and a wolf answers o.

Sample Input 2

3
oox

Sample Output 2

-1

Print -1 if there is no valid assignment of species.

Sample Input 3

10
oxooxoxoox

Sample Output 3

SSWWSSSWWS


#!/usr/bin/perl

while (<>) {
    ($a, $b) = split /\s/, $_;
}

$win = 'Draw';
if ($a > $b) {
    $win = 'Alice';
    if ($b == 1) {
        $win = 'Bob';
    }
} elsif ($b > $a) {
    $win = 'Bob';
    if ($a == 1) {
        $win = 'Alice';
    }
}
print "$win\n";

Score : 100 points

Problem Statement

Alice and Bob are playing One Card Poker.

One Card Poker is a two-player game using playing cards.

Each card in this game shows an integer between 1 and 13, inclusive.

The strength of a card is determined by the number written on it, as follows:

Weak 2 < 3 < 4 < 5 < 6 < 7 < 8 < 9 < 10 < 11 < 12 < 13 < 1 Strong

One Card Poker is played as follows:

Each player picks one card from the deck. The chosen card becomes the player's hand.

The players reveal their hands to each other. The player with the stronger card wins the game.

If their cards are equally strong, the game is drawn.

You are watching Alice and Bob playing the game, and can see their hands.

The number written on Alice's card is A, and the number written on Bob's card is B.

Write a program to determine the outcome of the game.

Constraints

1≦A≦13

1≦B≦13

A and B are integers.

Input

The input is given from Standard Input in the following format:

A B

Output

Print Alice if Alice will win. Print Bob if Bob will win. Print Draw if the game will be drawn.

Sample Input 1

8 6

Sample Output 1

Alice

8 is written on Alice's card, and 6 is written on Bob's card.
Alice has the stronger card, and thus the output should be Alice.

Sample Input 2

1 1

Sample Output 2

Draw

Since their cards have the same number, the game will be drawn.

Sample Input 3

13 1

Sample Output 3

Bob


Score : 200 points

Problem Statement

You are given an image A composed of N rows and N columns of pixels, and a template image B composed of M rows and M columns of pixels.

A pixel is the smallest element of an image, and in this problem it is a square of size 1×1.

Also, the given images are binary images, and the color of each pixel is either white or black.

In the input, every pixel is represented by a character: . corresponds to a white pixel, and # corresponds to a black pixel.

The image A is given as N strings A_1,...,A_N.

The j-th character in the string A_i corresponds to the pixel at the i-th row and j-th column of the image A (1≦i,j≦N).

Similarly, the template image B is given as M strings B_1,...,B_M.

The j-th character in the string B_i corresponds to the pixel at the i-th row and j-th column of the template image B (1≦i,j≦M).

Determine whether the template image B is contained in the image A when only parallel shifts can be applied to the images.

Constraints

1≦M≦N≦50

A_i is a string of length N consisting of # and ..

B_i is a string of length M consisting of # and ..

Input

The input is given from Standard Input in the following format:

N M
A_1
A_2
:
A_N
B_1
B_2
:
B_M

Output

Print Yes if the template image B is contained in the image A. Print No otherwise.

Sample Input 1

3 2
#.#
.#.
#.#
#.
.#

Sample Output 1

Yes

The template image B is identical to the upper-left 2 × 2 subimage and the lower-right 2 × 2 subimage of A. Thus, the output should be Yes.

Sample Input 2

4 1
....
....
....
....
#

Sample Output 2

No

The template image B, composed of a black pixel, is not contained in the image A composed of white pixels.


Score : 300 points

Problem Statement

You are given an undirected unweighted graph with N vertices and M edges that contains neither self-loops nor double edges.

Here, a self-loop is an edge where a_i = b_i (1≤i≤M), and double edges are two edges where (a_i,b_i)=(a_j,b_j) or (a_i,b_i)=(b_j,a_j) (1≤i<j≤M).

How many different paths start from vertex 1 and visit all the vertices exactly once?

Here, the endpoints of a path are considered visited.

For example, let us assume that the following undirected graph shown in Figure 1 is given.

Figure 1: an example of an undirected graph

The following path shown in Figure 2 satisfies the condition.

Figure 2: an example of a path that satisfies the condition

However, the following path shown in Figure 3 does not satisfy the condition, because it does not visit all the vertices.

Figure 3: an example of a path that does not satisfy the condition

Neither the following path shown in Figure 4, because it does not start from vertex 1.

Figure 4: another example of a path that does not satisfy the condition

Constraints

2≦N≦8

0≦M≦N(N-1)/2

1≦a_i<b_i≦N

The given graph contains neither self-loops nor double edges.

Input

The input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print the number of the different paths that start from vertex 1 and visit all the vertices exactly once.

Sample Input 1

3 3
1 2
1 3
2 3

Sample Output 1

2

The given graph is shown in the following figure:

The following two paths satisfy the condition:

Sample Input 2

7 7
1 3
2 7
3 4
4 5
4 6
5 6
6 7

Sample Output 2

1

This test case is the same as the one described in the problem statement.


Score : 400 points

Problem Statement

Dolphin is planning to generate a small amount of a certain chemical substance C.

In order to generate the substance C, he must prepare a solution which is a mixture of two substances A and B in the ratio of M_a:M_b.

He does not have any stock of chemicals, however, so he will purchase some chemicals at a local pharmacy.

The pharmacy sells N kinds of chemicals. For each kind of chemical, there is exactly one package of that chemical in stock.

The package of chemical i contains a_i grams of the substance A and b_i grams of the substance B, and is sold for c_i yen (the currency of Japan).

Dolphin will purchase some of these packages. For some reason, he must use all contents of the purchased packages to generate the substance C.

Find the minimum amount of money required to generate the substance C.

If it is not possible to generate the substance C by purchasing any combination of packages at the pharmacy, report that fact.

Constraints

1≦N≦40

1≦a_i,b_i≦10

1≦c_i≦100

1≦M_a,M_b≦10

gcd(M_a,M_b)=1

a_i, b_i, c_i, M_a and M_b are integers.

Input

The input is given from Standard Input in the following format:

N M_a M_b
a_1 b_1 c_1
a_2 b_2 c_2
:
a_N b_N c_N

Output

Print the minimum amount of money required to generate the substance C. If it is not possible to generate the substance C, print -1 instead.

Sample Input 1

3 1 1
1 2 1
2 1 2
3 3 10

Sample Output 1

3

The amount of money spent will be minimized by purchasing the packages of chemicals 1 and 2.

In this case, the mixture of the purchased chemicals will contain 3 grams of the substance A and 3 grams of the substance B, which are in the desired ratio: 3:3=1:1.

The total price of these packages is 3 yen.

Sample Input 2

1 1 10
10 10 10

Sample Output 2

-1

The ratio 1:10 of the two substances A and B cannot be satisfied by purchasing any combination of the packages. Thus, the output should be -1.


Score : 500 points

Problem Statement

There are N boxes arranged in a circle. The i-th box contains A_i stones.

Determine whether it is possible to remove all the stones from the boxes by repeatedly performing the following operation:

Select one box. Let the box be the i-th box. Then, for each j from 1 through N, remove exactly j stones from the (i+j)-th box. Here, the (N+k)-th box is identified with the k-th box.

Note that the operation cannot be performed if there is a box that does not contain enough number of stones to be removed.

Constraints

1 ≦ N ≦ 10^5

1 ≦ A_i ≦ 10^9

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 … A_N

Output

If it is possible to remove all the stones from the boxes, print YES. Otherwise, print NO.

Sample Input 1

5
4 5 1 2 3

Sample Output 1

YES

All the stones can be removed in one operation by selecting the second box.

Sample Input 2

5
6 9 12 10 8

Sample Output 2

YES

Sample Input 3

4
1 2 3 1

Sample Output 3

NO


Score : 100 points

Problem Statement

Smeke has decided to participate in AtCoder Beginner Contest (ABC) if his current rating is less than 1200, and participate in AtCoder Regular Contest (ARC) otherwise.

You are given Smeke's current rating, x. Print ABC if Smeke will participate in ABC, and print ARC otherwise.

Constraints

1 ≦ x ≦ 3{,}000

x is an integer.

Input

The input is given from Standard Input in the following format:

x

Output

Print the answer.

Sample Input 1

1000

Sample Output 1

ABC

Smeke's current rating is less than 1200, thus the output should be ABC.

Sample Input 2

2000

Sample Output 2

ARC

Smeke's current rating is not less than 1200, thus the output should be ARC.


use v6;
my $x = get().chomp;
if (x < 1200) {
	say "ABC";
} else {
	say "ARC";
}
exit;


use strict;
use warnings;

sub main {
    chomp(my $x = <STDIN>);
    print solve($x);
}
main() unless caller;

sub solve {
    my ($x) = @_;
    if($x < 5){
        return 1;
    }
    elsif($x < 11){
        return 2;
    }
    else{
        my $amari = $x % 11;
        my $ans = int($x / 11);
        if($amari > 5){
            $ans = $ans * 2;
        }
        else {
            $ans = $ans * 2 + 1;
        }
        warn("amari:".$amari);
        warn($ans);
        return $ans;
    }
}

Score : 300 points

Problem Statement

Snuke has decided to play with a six-sided die. Each of its six sides shows an integer 1 through 6, and two numbers on opposite sides always add up to 7.

Snuke will first put the die on the table with an arbitrary side facing upward, then repeatedly perform the following operation:

Operation: Rotate the die 90° toward one of the following directions: left, right, front (the die will come closer) and back (the die will go farther). Then, obtain y points where y is the number written in the side facing upward.

For example, let us consider the situation where the side showing 1 faces upward, the near side shows 5 and the right side shows 4, as illustrated in the figure.
If the die is rotated toward the right as shown in the figure, the side showing 3 will face upward.
Besides, the side showing 4 will face upward if the die is rotated toward the left, the side showing 2 will face upward if the die is rotated toward the front, and the side showing 5 will face upward if the die is rotated toward the back.

Find the minimum number of operation Snuke needs to perform in order to score at least x points in total.

Constraints

1 ≦ x ≦ 10^{15}

x is an integer.

Input

The input is given from Standard Input in the following format:

x

Output

Print the answer.

Sample Input 1

7

Sample Output 1

2

Sample Input 2

149696127901

Sample Output 2

27217477801


use strict;
use utf8;
use warnings;

my $x = <STDIN>;
chomp($x);
my $ans= int($x / 11);
my $d = $x - $ans*11;
$ans *= 2;
if ($d <= 6) {
    $ans += 1;
}elsif ($d <11){
    $ans += 2;
}
print "$ans\n";


Score : 400 points

Problem Statement

Snuke has decided to play a game using cards.
He has a deck consisting of N cards. On the i-th card from the top, an integer A_i is written.

He will perform the operation described below zero or more times, so that the values written on the remaining cards will be pairwise distinct. Find the maximum possible number of remaining cards. Here, N is odd, which guarantees that at least one card can be kept.

Operation: Take out three arbitrary cards from the deck. Among those three cards, eat two: one with the largest value, and another with the smallest value. Then, return the remaining one card to the deck.

Constraints

3 ≦ N ≦ 10^{5}

N is odd.

1 ≦ A_i ≦ 10^{5}

A_i is an integer.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 A_3 ... A_{N}

Output

Print the answer.

Sample Input 1

5
1 2 1 3 7

Sample Output 1

3

One optimal solution is to perform the operation once, taking out two cards with 1 and one card with 2. One card with 1 and another with 2 will be eaten, and the remaining card with 1 will be returned to deck. Then, the values written on the remaining cards in the deck will be pairwise distinct: 1, 3 and 7.

Sample Input 2

15
1 3 5 2 1 3 2 8 8 6 2 6 11 1 1

Sample Output 2

7


Score : 200 points

Problem Statement

You have an integer variable x.
Initially, x=0.

Some person gave you a string S of length N, and using the string you performed the following operation N times.
In the i-th operation, you incremented the value of x by 1 if S_i=I, and decremented the value of x by 1 if S_i=D.

Find the maximum value taken by x during the operations (including before the first operation, and after the last operation).

Constraints

1≤N≤100

|S|=N

No characters except I and D occur in S.

Input

The input is given from Standard Input in the following format:

N
S

Output

Print the maximum value taken by x during the operations.

Sample Input 1

5
IIDID

Sample Output 1

2

After each operation, the value of x becomes 1, 2, 1, 2 and 1, respectively. Thus, the output should be 2, the maximum value.

Sample Input 2

7
DDIDDII

Sample Output 2

0

The initial value x=0 is the maximum value taken by x, thus the output should be 0.


use strict;
use warnings;

sub main {
    chomp(my $Y = <STDIN>);
    chomp(my $Z = <STDIN>);
    my ($N,$M,$B) = split(/ /,$Y);
    my @X = split(/ /,$Z);
    print solve($N,$M,$B,\@X);
}
main() unless caller;

sub solve {
    my ($N,$M,$B,$X) = @_;
    my $x = int($B/$M)+1;
    my $ans=0;
    for my $i(0..$N-2) {
        my $kyori = $X->[$i+1] - $X->[$i];
        $ans += $kyori >= $x ? $B : $kyori*$M;
    }
    return $ans;
}

Score : 500 points

Problem Statement

There are N towns on a line running east-west.
The towns are numbered 1 through N, in order from west to east.
Each point on the line has a one-dimensional coordinate, and a point that is farther east has a greater coordinate value.
The coordinate of town i is X_i.

You are now at town 1, and you want to visit all the other towns.
You have two ways to travel:

Walk on the line.
Your fatigue level increases by A each time you travel a distance of 1, regardless of direction.

Teleport to any location of your choice.
Your fatigue level increases by B, regardless of the distance covered.

Find the minimum possible total increase of your fatigue level when you visit all the towns in these two ways.

Constraints

All input values are integers.

2≤N≤10^5

1≤X_i≤10^9

For all i(1≤i≤N-1), X_i<X_{i+1}.

1≤A≤10^9

1≤B≤10^9

Input

The input is given from Standard Input in the following format:

N A B
X_1 X_2 ... X_N

Output

Print the minimum possible total increase of your fatigue level when you visit all the towns.

Sample Input 1

4 2 5
1 2 5 7

Sample Output 1

11

From town 1, walk a distance of 1 to town 2, then teleport to town 3, then walk a distance of 2 to town 4.
The total increase of your fatigue level in this case is 2×1+5+2×2=11, which is the minimum possible value.

Sample Input 2

7 1 100
40 43 45 105 108 115 124

Sample Output 2

84

From town 1, walk all the way to town 7.
The total increase of your fatigue level in this case is 84, which is the minimum possible value.

Sample Input 3

7 1 2
24 35 40 68 72 99 103

Sample Output 3

12

Visit all the towns in any order by teleporting six times.
The total increase of your fatigue level in this case is 12, which is the minimum possible value.


Score : 300 points

Problem Statement

You are given an integer N.
Find the number of the positive divisors of N!, modulo 10^9+7.

Constraints

1≤N≤10^3

Input

The input is given from Standard Input in the following format:

N

Output

Print the number of the positive divisors of N!, modulo 10^9+7.

Sample Input 1

3

Sample Output 1

4

There are four divisors of 3! =6: 1, 2, 3 and 6. Thus, the output should be 4.

Sample Input 2

6

Sample Output 2

30

Sample Input 3

1000

Sample Output 3

972926972


use strict;
use warnings;

sub main {
    my $s = <STDIN>;
    print solve($s);
}

main() unless caller;

sub solve {
    my ($s) = @_;
    return join(" ", split(/,/,$s));
}

Score : 100 points

Problem Statement

As a New Year's gift, Dolphin received a string s of length 19.

The string s has the following format: [five lowercase English letters],[seven lowercase English letters],[five lowercase English letters].

Dolphin wants to convert the comma-separated string s into a space-separated string.

Write a program to perform the conversion for him.

Constraints

The length of s is 19.

The sixth and fourteenth characters in s are ,.

The other characters in s are lowercase English letters.

Input

The input is given from Standard Input in the following format:

s

Output

Print the string after the conversion.

Sample Input 1

happy,newyear,enjoy

Sample Output 1

happy newyear enjoy

Replace all the commas in happy,newyear,enjoy with spaces to obtain happy newyear enjoy.

Sample Input 2

haiku,atcoder,tasks

Sample Output 2

haiku atcoder tasks

Sample Input 3

abcde,fghihgf,edcba

Sample Output 3

abcde fghihgf edcba