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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import sys
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))
mod = 998244353
inf = float('inf')
ans = []

N = I()
a =[0] * N
for i in range(N):
    a[i] = int(input())

sumA = sum(a)

dp = [[0]*(sumA+1) for _ in range(N)]
start = (sumA+1)//2

dp[0][0] = 2
dp[0][a[0]] = 1

for i in range(N-1):
    for j in range(sumA-a[-1]+1):
        if j<=sumA-a[i+1]:
            dp[i+1][j+a[i+1]] += dp[i][j]
        dp[i+1][j] += dp[i][j]*2

#print(dp)
out = sum(dp[N-1][start:])
ans = (3**N - out*3)%mod
#print(ans)

if sumA%2==0:
    dp2 = [[0] * (sumA + 1) for _ in range(N)]
    dp2[0][0] = 1
    dp2[0][a[0]] = 1

    for i in range(N - 1):
        for j in range(sumA//2 - a[-1] + 1):
            if j <= sumA - a[i + 1]:
                dp2[i + 1][j + a[i + 1]] += dp2[i][j]
            dp2[i + 1][j] += dp2[i][j]
    ans += dp2[N-1][sumA//2]*3
print(ans%mod)