Problem:
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).

Solution in PHP (7.4.4) (judge verdict: Wrong Answer)

<?php
  $coin = 0;
  fscanf(STDIN, "%d", $t);

  function x(&$n, $x, $c){
    $coin = 0;
    while(true) {
        if(($n/$x) > 1) {
          $coin = $coin + $c;
          $n = floor($n/$x);
        }
        if(($n/$x) < 1) {
          break;
        }
        if(($n/$x) == 1) {
          $coin++;
          break;
        }
    }
    return $coin;
  }
  for($i=0;$i<$t;$i++) {
    $coin = 0;
    fscanf(STDIN, "%d %d %d %d %d ", $n, $a, $b, $c, $d);

    $coin = $coin + x($n, 5, $c);
    $coin = $coin + x($n, 3, $b);
    $coin = $coin + x($n, 2, $a);
    $coin = $coin + $n * $d;
    echo $coin.PHP_EOL;
  }