output_description: Print the number, modulo 998244353, of ways to paint each of the integers red,
  green or blue so that the condition is satisfied.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      a_1
      :
      a_N
attempt: n = int(input())
  A = tuple(int(input()) for _ in range(n))
  S = sum(A)
  mod = 998244353
  ans = pow(3, n, mod) - (pow(2, n, mod) - 2) * 3 - 3
  cnt = 0
  dp = [[[0] * (S + 1) for j in range(n + 2)] for i in range(n + 1)]
  dp[0][0][0] = 1
  for i, a in enumerate(A):
      for j in range(i + 2):
          for k in range(S + 1):
              if k >= a and j:
                  dp[i + 1][j][k] = dp[i][j][k] + dp[i][j - 1][k - a]
              else:
                  dp[i + 1][j][k] = dp[i][j][k]
  for j in range(n - 1):
      for k in range((S + 1) // 2, S + 1):
          cnt += dp[n][j][k] * (pow(2, n - j, mod) - 2)
          cnt %= mod
  ans -= cnt * 3
  ans %= mod
  print(ans)
  
problem_description: 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.
samples: [{"input": "4\n    1\n    1\n    1\n    2", "output": "18\n    \n\nWe can only paint the integers so that the lengths of the sides of the\ntriangle will be 1, 2 and 2, and there are 18 such ways.\n\n* * *"}, {"input": "6\n    1\n    3\n    2\n    3\n    5\n    2", "output": "150\n    \n\n* * *"}, {"input": "20\n    3\n    1\n    4\n    1\n    5\n    9\n    2\n    6\n    5\n    3\n    5\n    8\n    9\n    7\n    9\n    3\n    2\n    3\n    8\n    4", "output": "563038556"}]