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)

s = [input() for i in range(1)]
s0 = int(s[0])
t = [input() for j in range(s0)]
li = {}
for k in range(s0):
    li[k] = list(map(int, t[k].split()))
    x = 1
    for a in range(li[k][0]):
        x = x * 5
        if x > li[k][0]:
            x = x / 5
            break
    for b in range(li[k][0]):
        x = x * 3
        if x > li[k][0]:
            x = x / 3
            break
    for c in range(li[k][0]):
        x = x * 2
        if x > li[k][0]:
            x1 = x - li[k][0]
            x2 = li[k][0] - (x / 2)
            if x1 > x2:
                y = 5 ** a * 3 ** b * 2 ** c +x2
                n = li[k][1]*a + li[k][2]*b + li[k][3]*c + li[k][4]*(x2)
                break
            if x2 > x1:
                y = 5 ** a * 3 ** b * 2 ** (c+1) - x1
                n = li[k][1]*a + li[k][2]*b + li[k][3]*(c+1) + li[k][4]*(x1)
                break
    print("n:",n)