output_description: Print the sum modulo 998244353.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      A_0\ A_1\ \cdots\ A_{N-1}
attempt: N = 1000000
  X = [-1] * (N + 1)
  L = [{} for _ in range(N + 1)]
  k = 2
  while k <= N:
      X[k] = 1
      L[k][k] = 1
      for i in range(k * 2, N + 1, k):
          X[i] = 0
          L[i][k] = 1
      d = 2
      while k**d <= N:
          for i in range(k**d, N + 1, k**d):
              L[i][k] += 1
          d += 1
      while k <= N and X[k] >= 0:
          k += 1
  P = [i for i in range(N + 1) if X[i] == 1]
  
problem_description: Statement
  
  We have an integer sequence of length N: A_0,A_1,\cdots,A_{N-1}.
  
  Find the following sum (\mathrm{lcm}(a, b) denotes the least common multiple
  of a and b):
  
    * \sum_{i=0}^{N-2} \sum_{j=i+1}^{N-1} \mathrm{lcm}(A_i,A_j)
  
  Since the answer may be enormous, compute it modulo 998244353.
samples: [{"input": "3\n    2 4 6", "output": "22\n    \n\n\\mathrm{lcm}(2,4)+\\mathrm{lcm}(2,6)+\\mathrm{lcm}(4,6)=4+6+12=22.\n\n* * *"}, {"input": "8\n    1 2 3 4 6 8 12 12", "output": "313\n    \n\n* * *"}, {"input": "10\n    356822 296174 484500 710640 518322 888250 259161 609120 592348 713644", "output": "353891724"}]