use vstd::prelude::*;

fn main() {}

verus! {

pub struct Solution;

pub open spec fn subset_sum(nums: Seq<i32>, sel: Seq<bool>, hi: int) -> int
    decreases hi
{
    if hi <= 0 { 0 }
    else {
        (if sel[hi - 1] { nums[hi - 1] as int } else { 0 })
        + subset_sum(nums, sel, hi - 1)
    }
}

impl Solution {
    pub fn max_sum_div_three(nums: Vec<i32>) -> (result: i32)
        requires
            1 <= nums.len() <= 40000,
            forall |i: int| 0 <= i < nums.len() ==> 1 <= #[trigger] nums[i] <= 10000,
        ensures
            result >= 0,
            result as int % 3 == 0,
            exists |sel: Seq<bool>| sel.len() == nums.len() as int
                && subset_sum(nums@, sel, nums.len() as int) == result as int,
            forall |sel: Seq<bool>| sel.len() == nums.len() as int
                && subset_sum(nums@, sel, nums.len() as int) % 3 == 0
                ==> subset_sum(nums@, sel, nums.len() as int) <= result as int,
    {
        let n = nums.len();
        let mut dp0: i32 = 0;
        let mut dp1: i32 = 0;
        let mut dp2: i32 = 0;
        let mut i: usize = 0;
        while i < n {
            let a = nums[i];
            let old0 = dp0;
            let old1 = dp1;
            let old2 = dp2;
            let r = a % 3;
            if r == 0 {
                dp0 = old0 + a;
                dp1 = if old1 > 0 { old1 + a } else { old1 };
                dp2 = if old2 > 0 { old2 + a } else { old2 };
            } else if r == 1 {
                let new_dp0 = if old2 > 0 && old2 + a > old0 { old2 + a } else { old0 };
                let new_dp1 = if old0 + a > old1 { old0 + a } else { old1 };
                let new_dp2 = if old1 > 0 && old1 + a > old2 { old1 + a } else { old2 };
                dp0 = new_dp0;
                dp1 = new_dp1;
                dp2 = new_dp2;
            } else {
                let new_dp0 = if old1 > 0 && old1 + a > old0 { old1 + a } else { old0 };
                let new_dp1 = if old2 > 0 && old2 + a > old1 { old2 + a } else { old1 };
                let new_dp2 = if old0 + a > old2 { old0 + a } else { old2 };
                dp0 = new_dp0;
                dp1 = new_dp1;
                dp2 = new_dp2;
            }
            i += 1;
        }
        dp0
    }
}

}