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

class Util
{
    public static function input($isSplitSpace = false)
    {
        $input = trim(fgets(STDIN));
        if (!$isSplitSpace) {
            return $input;
        }

        return explode(' ', $input);
    }
}

// START
if ($argv[1]) {
    $search = new Search(11, 1, 2, 4, 8);$search->run();
    $search = new Search(11,1,2,2,8);$search->run();
    $search = new Search(32,10,8,5,4);$search->run();
    $search = new Search(29384293847243,454353412,332423423,934923490,1);$search->run();
} else {
    $N = Util::input();
    $testCase = [];
    for ($i = 0; $i, $i < $N; ++$i) {
        $testCase[] = Util::input(true);
    }

    foreach ($testCase as $case) {
        $search = new Search($case[0], $case[1], $case[2], $case[3], $case[4]);$search->run();
    }
}

class Search
{
    private $_targetNum;
    private $_a;
    private $_b;
    private $_c;
    private $_d;
    private $_e;

    private $_memo;

    public function __construct($n, $a, $b, $c, $d)
    {
        $this->_targetNum = $n;
        $this->_a = $a;
        $this->_b = $b;
        $this->_c = $c;
        $this->_d = $d;
        $this->_e = $d;

        $this->_memo = [];
    }

    public function run()
    {
        echo $this->walk($this->_targetNum) . PHP_EOL;
    }

    protected function walk($n)
    {
        $n = (int)$n;

        if ($n == 0) {
            return 0;
        }
        if ($n == 1) {
            return $this->_d;
        }

        if (isset($this->_memo[$n])) {
            return $this->_memo[$n];
        }

        $result = min([
            $this->_d * (ceil($n / 5) * 5 - $n) + $this->_c + self::walk(ceil($n / 5)), // $nにxを足して5の倍数にして、5で割ったときのコスト
            $this->_d * ($n - floor($n / 5) * 5) + $this->_c + self::walk(floor($n / 5)), // $nにxを引いて5の倍数にして、5で割ったときのコスト
            $this->_d * (ceil($n / 3) * 3 - $n) + $this->_b + self::walk(ceil($n / 3)), // $nにxを足して3の倍数にして、3で割ったときのコスト
            $this->_d * ($n - floor($n / 3) * 3) + $this->_b + self::walk(floor($n / 3)), // $nにxを引いて3の倍数にして、3で割ったときのコスト
            $this->_d * (ceil($n / 2) * 2 - $n) + $this->_a + self::walk(ceil($n / 2)), // $nにxを足して2の倍数にして、2で割ったときのコスト
            $this->_d * ($n - floor($n / 2) * 2) + $this->_a + self::walk(floor($n / 2)), // $nにxを引いて2の倍数にして、2で割ったときのコスト
            $this->_d * $n
        ]);

        $this->_memo[$n] = $result;

        return $result;
    }
}