| **This problem statement differs from that of Leapfrog Ch. 1 in only one spot, highlighted in bold below.** |
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| A colony of frogs peacefully resides in a pond. The colony is led by a single |
| Alpha Frog, and also includes 0 or more Beta Frogs. In order to be a good |
| leader, the Alpha Frog diligently studies the high art of fractions every day. |
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| There are **N** lilypads in a row on the pond's surface, numbered 1 to **N** |
| from left to right, each of which is large enough to fit at most one frog at a |
| time. Today, the Alpha Frog finds itself on the leftmost lilypad, and must |
| leap its way to the rightmost lilypad before it can begin its fractions |
| practice. |
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| The initial state of each lilypad _i_ is described by a character **Li**, |
| which is one of the following: |
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| * "`A`": Occupied by the Alpha Frog (it's guaranteed that **Li** = "`A`" if and only if _i_ = 1) |
| * "`B`": Occupied by a Beta Frog |
| * "`.`": Unoccupied |
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| At each point in time, one of the following things may occur: |
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| 1) The Alpha Frog may leap over one or more lilypads immediately to either its |
| left or right which are occupied by Beta Frogs, and land on the next |
| unoccupied lilypad past them, if such a lilypad exists. The Alpha Frog must |
| leap over at least one Beta Frog; it may not just leap to an adjacent lilypad. |
| **Note that, unlike in Leapfrog Ch. 1, the Alpha Frog may leap to either its |
| left or right.** |
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| 2) Any Beta Frog may leap to the next lilypad to either its left or right, if |
| such a lilypad exists and is unoccupied. |
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| Assuming the frogs all cooperate, determine whether or not it's possible for |
| the Alpha Frog to ever reach the rightmost lilypad and begin its daily |
| fractions practice. |
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| ### Input |
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| Input begins with an integer **T**, the number of days on which the Alpha Frog |
| studies fractions. For each day, there is a single line containing the |
| length-**N** string **L**. |
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| ### Output |
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| For the _i_th day, print a line containing "Case #_i_: " followed by a single |
| character: "`Y`" if the Alpha Frog can reach the rightmost lilypad, or "`N`" |
| otherwise. |
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| ### Constraints |
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| 1 ≤ **T** ≤ 500 |
| 2 ≤ **N** ≤ 5,000 |
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| ### Explanation of Sample |
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| In the first case, the Alpha Frog can't leap anywhere. |
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| In the second case, the Alpha Frog can leap over the Beta Frog to reach the |
| rightmost lilypad. |
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| In the third case, neither the Alpha Frog nor either of the Beta Frogs can |
| leap anywhere. |
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| In the fourth case, if the first Beta Frog leaps one lilypad to the left, and |
| then the second Beta Frog also leaps one lilypad to the left, then the Alpha |
| Frog can leap over both of them to reach the rightmost lilypad. |
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