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)

test = int(input())
test_cases = []
for a in range(test):
    number_and_coin = input()
    number_and_coin = number_and_coin.split(' ')
    test_case = [int(i) for i in number_and_coin]
    test_cases.append(test_case)
payment=[]
for i in range(0, len(test_cases)):
    x = 0
    pay = 0
    while x < test_cases[i][0]:
        if x == 0:
            x = x+1
            pay += test_cases[i][-1]
        elif (x*5) < test_cases[i][0]:
            x = x*5
            pay += test_cases[i][3]
        elif (x*3) < test_cases[i][0]:
            x = x*3
            pay += test_cases[i][2]
        elif (x*2) < test_cases[i][0]:
            x = x*2
            pay += test_cases[i][1]
        else:
            pay = pay + (test_cases[i][-1]*(test_cases[i][0]-x))
            x = x+(test_cases[i][0]-x)
    while x > test_cases[i][0]:
        x = x-1
        pay += test_cases[i][-1]
    payment.append(pay)
for i in payment:
    print(i)