Problem:
Score : 600 points

Problem Statement

You are given N integers. The i-th integer is a_i.
Find the number, modulo 998244353, of ways to paint each of the integers red, green or blue so that the following condition is satisfied:

Let R, G and B be the sums of the integers painted red, green and blue, respectively. There exists a triangle with positive area whose sides have lengths R, G and B.

Constraints

3 \leq N \leq 300

1 \leq a_i \leq 300(1\leq i\leq N)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
a_1
:
a_N

Output

Print the number, modulo 998244353, of ways to paint each of the integers red, green or blue so that the condition is satisfied.

Sample Input 1

4
1
1
1
2

Sample Output 1

18

We can only paint the integers so that the lengths of the sides of the triangle will be 1, 2 and 2, and there are 18 such ways.

Sample Input 2

6
1
3
2
3
5
2

Sample Output 2

150

Sample Input 3

20
3
1
4
1
5
9
2
6
5
3
5
8
9
7
9
3
2
3
8
4

Sample Output 3

563038556

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}


fn main() {
    const MOD: i64 = 998244353;
    input! {
        n: usize,
        aaa: [usize; n],
    }
    let s = aaa.iter().fold(0, |sum, a| sum + a);
    let mut dp = vec![vec![0i64; n + 1]; (s + 1) as usize];
    dp[0][0] = 1;
    let mut tmp_sum = 0;
    for a in aaa {
        for i in (0..tmp_sum + 1).rev() {
            let j = i + a;
            for k in 0..n {
                if dp[i][k] > 0 {
                    dp[j][k + 1] += dp[i][k];
                    dp[j][k + 1] %= MOD;
                }
            }
        }
        tmp_sum += a;
    }
    let mut sub = 0;
    let h = (s + 1) / 2;
    for dpi in &dp[h..] {
        for k in 1..(n + 1) {
            if dpi[k] > 0 {
                sub += dpi[k] * 3 * (1 << (n - k));
                sub %= MOD;
            }
        }
    }
    if s % 2 == 0 {
        for k in 1..(n + 1) {
            sub -= dp[h][k] * 3;
        }
        sub %= MOD;
    }
    let mut ans = 1;
    for _ in 0..n {
        ans = ans * 3 % MOD;
    }
    ans = (ans - sub) % MOD;
    if ans < 0 {
        ans += MOD;
    }
    println!("{}", ans);
}