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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
using namespace std;
typedef long long ll;
int N,A[310];
ll dp[310][90010] = {},dp2[310][90010];
ll inf = 998244353;

int main(){
    cin >> N;
    int sum = 0;
    for(int i=1;i<=N;i++){
        cin >> A[i];
        sum += A[i];
    }
    dp[0][0] = 1;
    for(int i=1;i<=N;i++){
        for(int j=0;j<=sum;j++){
            if(j-A[i]>=0) (dp[i][j] += dp[i-1][j-A[i]])%=inf;
            (dp[i][j] += 2*dp[i-1][j])%=inf;
        }
    }
    dp2[0][0] = 1;
    for(int i=1;i<=N;i++){
        for(int j=0;j<=sum;j++){
            if(j-A[i]>=0) (dp2[i][j] += dp2[i-1][j-A[i]])%=inf;
            (dp2[i][j] += dp2[i-1][j])%=inf;
        }
    }
    ll ans = 1;
    ll sub = 0;
    for(int i=1;i<=N;i++) (ans *= 3)%=inf;
    for(int j=(sum+1)/2;j<=sum;j++){
        (sub += dp[N][j])%=inf;
    }
    if(sum%2==0) (sub += -dp2[N][sum/2]+inf)%=inf;
    cout << (ans-3*sub+3*inf)%inf << endl;
}