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, *A = map(int, open(0).read().split())
  MOD = 998244353
  
  S = sum(A)
  dp0 = [0] * (S + 1)
  dp0[0] = 1
  for a in A:
      for i in range(S, a - 1, -1):
          dp0[i] = (dp0[i] + dp0[i - a] * 2) % MOD
  dp1 = [0] * (S + 1)
  dp1[0] = 1
  for a in A:
      for i in range(S, a - 1, -1):
          dp1[i] = (dp1[i] + dp1[i - a]) % MOD
  
  ans = pow(3, N, MOD)
  for L in range(0, S + 1):
      if L <= S - L:
          ans = (ans - dp0[L] * 3) % MOD
  if S % 2 == 0:
      ans = (ans + dp1[S // 2] * 3) % 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"}]