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 Ruby (2.7.1) (judge verdict: Runtime Error)

enum = {
  1=>'a',
  2=>'b',
  3=>'c',
  4=>'d'
}    
t = gets.to_i
ary = t.times.map { gets.split.map(&:to_i) }
a_d = ary.map { |i| i[1,4].map.with_index(1) { |el, i| [enum[i], el] }.sort { |a, b| a[1] <=> b[1] }.reverse.to_h }
n = ary.map { |i| i.first }

def cal(n)
  flg = false
  ans = []
  cmp = 0
  d = 1
  while d <= 10**9
    c = 0
    while c <= 10**9
      b = 0
      while b <= 10**9
        a = 0
        while a <= 10**9
          cmp = a_d['d'] * d + a_d['c'] * c + a_d['b'] * b + a_d['a'] * a
          if cmp >= n
            ans << cmp
            cal(n)
            break
          end
          a += 1
        end
        break if flg
        b += 1
      end
      break if flg
      c += 1
    end
    d += 1
  end
end

n.each do |e|
 puts cal(e)
end