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: Runtime Error)

import sys
sys.setrecursionlimit(20000000)
input = sys.stdin.readline
mod = 998244353
n = int(input())
a = [int(input()) for i in range(n)]
d = max(a)
dp = [[[0]*(d*n+1) for i in range(d*n+1)] for j in range(n+1)]
dp[0][0][0] = 1
for i in range(n):
    for j in range(d*n+1-d):
        for k in range(d*n+1-d):
            dp[i+1][j+a[i]][k] += dp[i][j][k]
            dp[i+1][j][k+a[i]] += dp[i][j][k]
            dp[i+1][j][k] += dp[i][j][k]
            dp[i+1][j+a[i]][k] %= mod
            dp[i+1][j][k+a[i]] %= mod
            dp[i+1][j][k] %= mod
go = sum(a)
ans = 0
for j in range(1,d*n+1):
    for k in range(1,d*n+1):
        if dp[n][j][k]:
            side1 = j
            side2 = k
            side3 = go-j-k
            if side3 == 0:
                continue
            if(side1+side2>side3)and(side2+side3>side1)and(side3+side1>side2):
                ans += dp[n][j][k]
                ans %= mod
print(ans)