output_description: Print the answer.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
attempt: def resolve():
      def factorization(n):
          arr = []
          temp = n
          for i in range(2, int(-(-(n**0.5) // 1)) + 1):
              if temp % i == 0:
                  cnt = 0
                  while temp % i == 0:
                      cnt += 1
                      temp //= i
                  arr.append([i, cnt])
          if temp != 1:
              arr.append([temp, 1])
          if arr == []:
              arr.append([n, 1])
          return arr
  
      n = int(input())
      a = list(map(int, input().split()))
      mod = 10**9 + 7
      import copy
  
      gcddict = {}
      adiv = []
      for i in range(n):
          primes = factorization(a[i])
          adiv.append(primes)
          for j in range(len(primes)):
              if primes[j][0] in gcddict:
                  gcddict[primes[j][0]] = max(gcddict[primes[j][0]], primes[j][1])
              else:
                  gcddict[primes[j][0]] = primes[j][1]
      ans = 0
      for i in range(n):
          val = 1
          test = copy.deepcopy(gcddict)
          primes = adiv[i]
          for j in range(len(primes)):
              test[primes[j][0]] -= primes[j][1]
          for k in test.keys():
              val *= pow(k, test[k], mod)
          ans += val
      print(ans % mod)
  
  
  resolve()
  
problem_description: Statement
  
  Given is a positive integer N.  
  Find the number of pairs (A, B) of positive integers not greater than N that
  satisfy the following condition:
  
    * When A and B are written in base ten without leading zeros, the last digit of A is equal to the first digit of B, and the first digit of A is equal to the last digit of B.
samples: [{"input": "25", "output": "17\n    \n\nThe following 17 pairs satisfy the condition: (1,1), (1,11), (2,2), (2,22),\n(3,3), (4,4), (5,5), (6,6), (7,7), (8,8), (9,9), (11,1), (11,11), (12,21),\n(21,12), (22,2), and (22,22).\n\n* * *"}, {"input": "1", "output": "1\n    \n\n* * *"}, {"input": "100", "output": "108\n    \n\n* * *"}, {"input": "2020", "output": "40812\n    \n\n* * *"}, {"input": "200000", "output": "400000008"}]