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 Python (3.4.3) (judge verdict: Accepted)

import numpy as np

mod = 998244353


def sum_mod(v):
    ans = 0
    for i in range(1, len(v)):
        ans = (ans + v[i]) % mod
    return ans


n = int(input())
a = []
for _ in range(n):
    a.append(int(input()))
A = sum(a)

dp = np.zeros((n + 1, A + 1), dtype=int)
dp2 = np.zeros((n + 1, A + 1), dtype=int)
dp[0][0] = 1
dp2[0][0] = 1
for t in range(1, n + 1):
    dp[t, :] = dp[t - 1, :] * 2 % mod
    dp2[t, :] = dp2[t - 1, :] % mod
    dp[t, a[t - 1]:] += dp[t - 1, :-a[t - 1]] % mod
    dp2[t, a[t - 1]:] += dp2[t - 1, :-a[t - 1]] % mod
#print(dp)

ans = 3 ** n % mod
ans -= np.sum(dp[n][(A + 1) // 2:]) * 3 % mod
if A % 2 == 0:
    ans += dp2[n][A // 2] * 3 % mod
print(ans % mod)