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 PyPy3 (7.3.0) (judge verdict: Accepted)

import sys
from collections import deque
from functools import lru_cache
import bisect
import copy
import heapq
import itertools
import math
input = sys.stdin.readline
sys.setrecursionlimit(1000000)
mod = 10 ** 9 + 7

def read_values(): return map(int, input().split())
def read_index(): return map(lambda x: int(x) - 1, input().split())
def read_list(): return list(read_values())
def read_lists(N): return [read_list() for n in range(N)]


def f(N, E, memo):
    if N == 0:
        return 0
    
    if N == 1:
        return E[-1]

    if N in memo:
        return memo[N]

    res = N * E[-1]
    for k in (2, 3, 5):
        l = (N // k) * k
        r = ((N - 1) // k + 1) * k

        res = min(res, (N - l) * E[-1] + E[k] + f(l // k, E, memo))
        res = min(res, (r - N) * E[-1] + E[k] + f(r // k, E, memo))
    memo[N] = res
    return res
   

def main():
    T = int(input())
    for _ in range(T):
        N, A, B, C, D = read_values()
        E = (0, 0, A, B, 0, C, D)
        memo = dict()
        print(f(N, E, memo))


if __name__ == "__main__":
    main()