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)

# -*- coding: utf-8 -*-
from sys import stdin
import numpy as np
# import sys
# sys.setrecursionlimit(10**4)
# import time

s_in = lambda: stdin.readline()[:-1]  # s = s_in()
d_in = lambda: int(stdin.readline())  # N = d_in()
ds_in = lambda: list(map(int, stdin.readline().split()))  # List = ds_in()


MOD = 998244353

N = d_in()
total = 3 ** N - (2**N - 2) * 3 - 3

a_list = []
for _ in range(N):
    a_list.append(d_in())
sum_a = sum(a_list)

# 1要素目: i番目の整数までを考慮
# 2要素目: [both>0, 緑>0&青==0, 緑==0&青>0, both==0]
# 3要素目: 最大の色(赤とする)の和
dp = np.zeros((N+1, 3, 1 + (sum_a+1)//2), dtype=int)
dp[0, 2, 0] = 1

for i in range(1, N+1):
    # 赤に入れる
    a = a_list[i-1]
    dp[i, :, a:] += dp[i-1, :, :-a]
    dp[i, :, -1] += dp[i-1, :, -a:].sum(axis=1)

    # 緑or青に入れる
    dp[i, 0, :] += (dp[i-1, 0, :] + dp[i-1, 1, :]) * 2
    dp[i, 1, :] += dp[i-1, 1, :]
    dp[i, 1, :] += dp[i-1, 2, :]

    if i % 10 == 0:
        dp[i, :, :] %= MOD

print((total - dp[-1, 0, -1] * 3) % MOD)