output_description: For each testcase, print the answer on Standard Output followed by a newline.
  
  * * *
input_description: The input is given from Standard Input. The first line of the input is
  
      
      
      T
      
  
  Then, T lines follow describing the T testcases. Each of the T lines has the
  format
  
      
      
      N A B C D
attempt: import functools
  
  
  def solve(N, A, B, C, D):
      @functools.lru_cache(None)
      def dp(N):
          if N <= 0:
              return float("inf")
          if N == 1:
              return 0
          ans = (N - 1) * D
          # BY TWO
          mod_2 = N % 2
          if not mod_2:
              ans = min(ans, dp(N // 2) + A)
          else:
              ans = min(ans, dp((N + (2 - mod_2)) // 2) + (A + D * (2 - mod_2)))
              ans = min(dp((N - mod_2) // 2) + (A + D * mod_2), ans)
          mod_3 = N % 3
          if not mod_3:
              ans = min(ans, dp(N // 3) + B)
          else:
              ans = min(ans, dp((N + (3 - mod_3)) // 3) + (B + D * (3 - mod_3)))
              ans = min(dp((N - mod_3) // 3) + (B + D * mod_3), ans)
          mod_5 = N % 5
          if not mod_5:
              ans = min(ans, dp(N // 5) + C)
          else:
              ans = min(ans, dp((N + (5 - mod_5)) // 5) + (C + D * (5 - mod_5)))
              ans = min(dp((N - mod_5) // 5) + (C + D * mod_5), ans)
          return ans
  
      return dp(N) + D
  
  
  t = int(input())
  for _ in range(t):
      N, A, B, C, D = list(map(int, input().split()))
      print(solve(N, A, B, C, D))
  
problem_description: Statement
  
  You start with the number 0 and you want to reach the number N.
  
  You can change the number, paying a certain amount of coins, with the
  following operations:
  
    * Multiply the number by 2, paying A coins.
    * Multiply the number by 3, paying B coins.
    * Multiply the number by 5, paying C coins.
    * Increase or decrease the number by 1, paying D coins.
  
  You can perform these operations in arbitrary order and an arbitrary number of
  times.
  
  What is the minimum number of coins you need to reach N?
  
  **You have to solve T testcases.**
samples: [{"input": "5\n    11 1 2 4 8\n    11 1 2 2 8\n    32 10 8 5 4\n    29384293847243 454353412 332423423 934923490 1\n    900000000000000000 332423423 454353412 934923490 987654321", "output": "20\n    19\n    26\n    3821859835\n    23441258666\n    \n\nFor the first testcase, a sequence of moves that achieves the minimum cost of\n20 is:\n\n  * Initially x = 0.\n  * Pay 8 to increase by 1 (x = 1).\n  * Pay 1 to multiply by 2 (x = 2).\n  * Pay 1 to multiply by 2 (x = 4).\n  * Pay 2 to multiply by 3 (x = 12).\n  * Pay 8 to decrease by 1 (x = 11).\n\nFor the second testcase, a sequence of moves that achieves the minimum cost of\n19 is:\n\n  * Initially x = 0.\n  * Pay 8 to increase by 1 (x = 1).\n  * Pay 1 to multiply by 2 (x = 2).\n  * Pay 2 to multiply by 5 (x = 10).\n  * Pay 8 to increase by 1 (x = 11)."}]