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: Accepted)

# -*- coding: utf-8 -*-
"""
Created on Sun Apr 21 18:51:07 2019

@author: Yamazaki Kenichi
"""

N = int(input())
A = [int(input()) for i in range(N)]
mod = 998244353
def mof(x):
    return x % mod
total = sum(A)
dp1 = [[0 for i in range(300*N+1)] for i in range(N+1)]
dp2 = [[0 for i in range(300*N+1)] for i in range(N+1)]
dp1[0][0], dp2[0][0] = 1,1
for i in range(N):
    for j in range(N*300+1):
        dp1[i+1][j] = mof(dp1[i][j]*2 + (dp1[i][j-A[i]] if j >= A[i] else 0))
        dp2[i+1][j] = mof(dp2[i][j] + (dp2[i][j-A[i]] if j >= A[i] else 0))
        
ex = mof(sum(dp1[N][(total+1)//2:]))
a = dp2[N][total//2] if total % 2 == 0 else 0

ans = mof(3**N - 3*ex + 3*a)
print(ans)