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 <bits/stdc++.h>
#define l_ength size
const int inf = (1<<30);
using ll = long long;
const ll mod = 998244353;
using namespace std;

const int bound = 100000;
ll sp[310][bound];
ll dp[310][bound];

int main(){
	int n;  cin >> n;
	vector<ll> a(n);
	for( auto &k : a ) cin >> k;
	dp[0][0] = 1;
	ll sum = 0;
	ll product = 1;
	for( int i = 0; i < n; ++i ){
		sum += a[i]; sum %= mod;
		product *= 3; product %= mod;
		for( int x = 0; x < bound-500; ++x ){
			dp[i+1][x] += 2*dp[i][x] % mod; dp[i+1][x] %= mod;
			dp[i+1][x+a[i]] += dp[i][x] % mod; dp[i+1][x+a[i]] %= mod;
		}
	}
	ll ngsum = 0;
	for( int x = (sum+1)/2; x < bound; ++x ){
		ngsum += dp[n][x];
		ngsum %= mod;
	}
	if( sum % 2 == 0 ){
		sp[0][0] = 1;
		for( int i = 0; i < n; ++i ){
			for( int x = 0; x < bound-500; ++x ){
				sp[i+1][x] += sp[i][x]; sp[i+1][x] %= mod;
				sp[i+1][x+a[i]] += sp[i][x] % mod; sp[i+1][x+a[i]] %= mod;
			}
		}
	}
	cout << ( product - 3*( ngsum-sp[n][sum/2] ) + 500*mod ) % mod << endl;
}