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)

import sys

a = 0
b = 0
c = 0
d = 0
pw = dict()

def minCost(n):
	if n == 1:
		return d
	if n == 2:
		return min(d + a, 2 * d)
	if n == 3:
		return min(d + b, 3 * d)
	if n == 5:
		return min(d + c, 5 * d)

	if n in pw:
		return pw[n]
	else:
		ns = dict()
		ns[n - (n % 2)] = 1
		ns[n + (2 - (n % 2))] = 1
		ns[n - (n % 3)] = 1
		ns[n + (3 - (n % 3))] = 1
		ns[n - (n % 5)] = 1
		ns[n + (5 - (n % 5))] = 1
		_min = n * d
		for key in ns:
			if key > 0:
				if key % 2 == 0:
					_min = min(_min, a + int(minCost(key / 2)) + d * abs(n - key))
				if key % 3 == 0:
					_min = min(_min, b + int(minCost(key / 3)) + d * abs(n - key))
				if key % 5 == 0:
					_min = min(_min, c + int(minCost(key / 5)) + d * abs(n - key))
		pw[n] = _min
		return pw[n]

t = int(sys.stdin.readline())
for i in range(0, t):
	line = sys.stdin.readline().split()
	n = int(line[0])
	a = int(line[1])
	b = int(line[2])
	c = int(line[3])
	d = int(line[4])
	pw = dict()
	print(int(minCost(n)))