Score : 400 points

Problem 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.

Constraints

  • 1 \le T \le 10
  • 1 \le N \le 10^{18}
  • 1 \le A, B, C, D \le 10^9
  • All numbers N, A, B, C, D are integers.

Input

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

Output

For each testcase, print the answer on Standard Output followed by a newline.

Sample Input 1

5
11 1 2 4 8
11 1 2 2 8
32 10 8 5 4
29384293847243 454353412 332423423 934923490 1
900000000000000000 332423423 454353412 934923490 987654321

Sample Output 1

20
19
26
3821859835
23441258666

For the first testcase, a sequence of moves that achieves the minimum cost of 20 is:

  • Initially x = 0.
  • Pay 8 to increase by 1 (x = 1).
  • Pay 1 to multiply by 2 (x = 2).
  • Pay 1 to multiply by 2 (x = 4).
  • Pay 2 to multiply by 3 (x = 12).
  • Pay 8 to decrease by 1 (x = 11).

For the second testcase, a sequence of moves that achieves the minimum cost of 19 is:

  • Initially x = 0.
  • Pay 8 to increase by 1 (x = 1).
  • Pay 1 to multiply by 2 (x = 2).
  • Pay 2 to multiply by 5 (x = 10).
  • Pay 8 to increase by 1 (x = 11).