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: a = int(input())
  b = list(map(int, input().split()))
  if len(b) != 1:
      b.sort()
      mx = max(b)
      l = [2]
      for i in range(2, mx):
          for n, j in enumerate(l):
              if i % j == 0:
                  break
              if n == len(l) - 1:
                  l.append(i)
      d = 0
      lis = []
      for i in b:
          t = i
          li = []
          while t != 1:
              for j in l:
                  if t % j == 0:
                      t = t / j
                      li.append(j)
                      break
          lis.append(li)
      for j in range(len(lis) - 1):
          for m in range(j + 1, len(lis)):
              c = 1
              for n, i in enumerate(l):
                  if lis[j].count(i) <= lis[m].count(i) and lis[m].count != 0:
                      c = (c * (i ** int(lis[m].count(i)))) % 998244353
                  elif lis[j].count(i) > lis[m].count(i):
                      c = (c * (i ** int(lis[j].count(i)))) % 998244353
              d += c
      print(d % 998244353)
  else:
      print(b[0])
  
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"}]