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: Accepted)

T = gets.to_i

class A
  def initialize(n, a, b, c, d)
    @n, @a, @b, @c, @d = n, a, b, c, d
    @m = {0 => 0, 1 => @d}
  end

  def go(n)
    @m[n] ||= begin
                f5, f3, f2 = n/5, n/3, n/2
                c5, c3, c2 = (n + 4)/5, (n + 2)/3, (n + 1)/2
                @m[n] = [@d*n,
                         @d*(n - f5*5) + @c + go(f5),
                         @d*(n - f3*3) + @b + go(f3),
                         @d*(n - f2*2) + @a + go(f2),
                         @d*(c5*5 - n) + @c + go(c5),
                         @d*(c3*3 - n) + @b + go(c3),
                         @d*(c2*2 - n) + @a + go(c2)].min
              end
  end

  def solve
    puts go(@n)
  end
end

T.times{A.new(*gets.split.map(&:to_i)).solve}