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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		int[]A = new int[N];
		long sum = 0;
		for(var i=0;i<N;i++){
			A[i] = int.Parse(Console.ReadLine());
			sum += A[i];
		}
		Array.Sort(A);
		long[,]D = new long[N,sum+1];
		long mod = 998244353;
		D[0,A[0]] = 1;
		D[0,0] = 2;
		for(var i=1;i<N;i++){
			for(var j=0;j<=sum;j++){
				if(j+A[i]<=sum){
					D[i,j+A[i]] = (D[i,j+A[i]]+D[i-1,j]) % mod;
				}
				D[i,j] = (D[i,j]+D[i-1,j]*2) % mod;
			}
		}
		long ans = 1;
		for(var i=0;i<N;i++){
			ans = ans * 3 % mod;
		}
		for(var i=(sum+1)/2;i<=sum;i++){
			ans = ans + mod * 3 - D[N-1,i] * 3;
			ans %= mod;
		}
		ans %= mod;
		long[,]D2 = new long[N,sum+1];
		D2[0,A[0]] = 1;
		D2[0,0] = 1;
		for(var i=1;i<N;i++){
			for(var j=0;j<=sum;j++){
				if((j+A[i])*2<=sum){
					D2[i,j+A[i]] = (D2[i,j+A[i]]+D2[i-1,j]) % mod;
				}
				D2[i,j] = (D2[i,j]+D2[i-1,j]) % mod;
			}
		}
		if(sum%2==0){
			ans += D2[N-1,sum/2] * 3;
		}
		ans %= mod;
		Console.WriteLine(ans);
	}
}