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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

# coding: utf-8
from collections import defaultdict


def solve(*args: str) -> str:
    t = int(args[0])
    NABCD = [tuple(map(int, nabcd.split())) for nabcd in args[1:]]

    ret = []
    for n, a, b, c, d in NABCD:
        ABC = ((2, a), (3, b), (5, c))
        dp = defaultdict(lambda: n*d)
        stack = [(n, 0)]
        while stack:
            rem, cost = stack.pop()
            if dp[rem] <= cost:
                continue

            dp[rem] = cost
            dp[0] = min(dp[0], cost+rem*d)

            if 0 < rem:
                for x, y in ABC:
                    l, h = rem//x, -(-rem//x)
                    stack.append((l, d*abs(l*x-rem)+cost+y*(0 < l)))
                    stack.append((h, d*abs(h*x-rem)+cost+y))

        ret.append(str(dp[0]))

    return '\n'.join(ret)


if __name__ == "__main__":
    print(solve(*(open(0).read().splitlines())))