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: Wrong Answer)

import sys
import numpy as np
input = sys.stdin.readline

n = int(input())
a = [int(input()) for i in range(n)]
w = sum(a)
mod =998244353

#dp = [[0]*(w+1) for i in range(n)]
dp = np.zeros((n, w+1))
cnt = a[0]
dp[0][a[0]] = 1
dp[0][0] = 2
for i in range(1,n):
    cnt += a[i]
    for j in range(cnt+1):
        dp[i][j] = dp[i-1][j]*2
        if j >= a[i]:
            dp[i][j] += dp[i-1][j-a[i]]
        


#sより大きいのはブー
s = w//2+1
if w %2 == 0:
    #d = [[0]*(s+1) for i in range(n)]
    d = np.zeros((n, s+1))
    d[0][0] = 1
    d[0][a[0]] = 1
    cnt = a[0]

    for i in range(1,n):
        cnt += a[i]
        for j in range(min(cnt+1,s+1)):
            d[i][j] = d[i-1][j]
            if j >= a[i]:
                d[i][j] += d[i-1][j-a[i]]
            d[i][j] = d[i][j]%mod
    mns = d[-1][w//2]
if w%2 == 0:
    s -= 1
cnt = 0
for i in range(s,w+1):
    cnt += dp[-1][i]
    cnt = cnt%mod

res = (pow(3,n,mod)-cnt*3)%mod

if w % 2 == 0:
    res = (res+mns*3)%mod
print(int(res))