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: Time Limit Exceeded)

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)*}
    };
}

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)*}
    };
}

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>>()
    };

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

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

const md : i64 = 998244353;

fn main() {
    input!{
        n: usize,
        a: [usize; n],
    }

    let mut pow3 = vec![1; n+1];
    let mut pow2 = vec![1; n+1];
    for i in 0..n {
        pow3[i+1] = (pow3[i] * 3) % md;
        pow2[i+1] = (pow2[i] * 2) % md;
    }
    let al : i64 = pow3[n] - 3 * pow2[n] + 3;
    
    let mut sm : usize = 0;
    for i in 0..n {sm += a[i];}
    let mut dp = vec![vec![0i64; sm+1] ; n+1];
    dp[0][0] = 1;
    for i in 0..n {
        let ai = a[i];
        for k in (1..(n+1)).rev() {
            for s in (0..(sm+1)).rev() {
                if s >= ai {
                    //println!("<-[{}][{}]={}",k-1, s-ai, dp[(k-1) as usize][(s-ai) as usize]);
                    dp[k][s] += dp[(k-1) as usize][(s-ai) as usize];
                    dp[k][s] = dp[k][s] % md;
                    //println!("k={}, s={}, i={} => dp[k][s]={}",k,s,i,dp[k][s]);
                }
            }
        }
    }
    //println!("{}", dp[2][4]);

    let mut ng : i64 = 0;
    for s in ((sm+1) / 2)..(sm + 1) {
        for k in 1..(n-2+1) {
            let cm = dp[k][s]; 
            let r =  (cm * 3 * (pow2[(n - k) as usize] - 2))%md;
            //println!("k={}, s={}, n-k={}, cm={} => {}", k, s, n-k, cm, r);
            ng = (ng + r) % md;
        }
    }

    //println!("{}, {}", al, ng);
    println!("{}", ((al%md - ng%md)+10*md) %md);
}