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: Wrong Answer)

from functools import *
from math import *

t = int(input())

@lru_cache(maxsize=None)
def sol(n, a, b, c, d):
    if n == 1: return d
    ans = n * d
    cn = ceil(n / 2)
    fn = floor(n / 2)
    if cn: ans = min(ans, sol(cn, a, b, c, d) + abs(cn * 2 - n) * d + a)
    if fn: ans = min(ans, sol(fn, a, b, c, d) + abs(fn * 2 - n) * d + a)
    cn = ceil(n / 3)
    fn = floor(n / 3)
    if cn: ans = min(ans, sol(cn, a, b, c, d) + abs(cn * 3 - n) * d + b)
    if fn: ans = min(ans, sol(fn, a, b, c, d) + abs(fn * 3 - n) * d + b)
    cn = ceil(n / 5)
    fn = floor(n / 5)
    if cn: ans = min(ans, sol(cn, a, b, c, d) + abs(cn * 5 - n) * d + c)
    if fn: ans = min(ans, sol(fn, a, b, c, d) + abs(fn * 5 - n) * d + c)
    # print(str(n) + ", " + str(ans))
    return ans

for _ in range(t):
    n, a, b, c, d = list(map(int, input().split()))
    sol.cache_clear()
    print(min(d * n, sol(n, a, b, c, d)))