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: Time Limit Exceeded)

import sys
import resource
n = int(input())
e = [[int(i) for i in input().split()] for i in range(n)]
sys.setrecursionlimit(10 ** 9)


class Solve:

    def __init__(self,n,e):
        self.min = False
        self.T = n
        self.E = e
        self.i = 0

    def solve(self,num,cnt):
        if (num == self.E[self.i][0]):
            if min == False:
                self.min = cnt
            elif self.min > cnt:
                self.min = cnt
            return cnt
        if (num > self.E[self.i][0]):
            return cnt + (num - self.E[self.i][0]) * self.E[self.i][4]
        if (self.min != False) and (self.min < cnt):
            return self.cnt
        else:
            a = self.solve(num*2,cnt+self.E[self.i][1])
            b = self.solve(num*3,cnt+self.E[self.i][2])
            c = self.solve(num*5,cnt+self.E[self.i][3])
            d = cnt + (self.E[self.i][0] - num ) * self.E[self.i][4]
            e = self.solve(num+1,cnt+self.E[self.i][4])
            res = min(a,b,c,d,e)
            return res

    def init_func(self):
        for i in range(self.T):
            ans = self.solve(1,self.E[self.i][4])
            print(ans)
            self.i += 1
            self.min = False

sv = Solve(n,e)

sv.init_func()