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: Wrong Answer)

def test x, n, a, b, c, d, total
#puts
#puts "#{x}, #{n}, #{a}, #{b}, #{c}, #{d}, #{total}"

  return nil if total > $total

  if x == n
    $total = total
    return total
  end

  actions = if x > n
              [:d2]
            else
              [:a, :b, :c, :d1, :d2]
            end

  results = actions.map{ |action|
    case action
    when :a
      test (x*2), n, a, b, c, d, (total + a)
    when :b
      test (x*3), n, a, b, c, d, (total + b)
    when :c
      test (x*5), n, a, b, c, d, (total + c)
    when :d1
      test (x+1), n, a, b, c, d, (total + d)
    when :d2
      test (x-1), n, a, b, c, d, (total + d)
    end
  }

  return results.compact.min
end

t = gets.chomp.to_i
input = []
t.times do |i|
  input.push gets.chomp.split(" ").map(&:to_i)
end

t.times do |i|
  $total = Float::INFINITY
  n, a, b, c, d = input[i]
  x = 1
  total = d
  begin
    puts (test x, n, a, b, c, d, total)
  rescue SystemStackError
    puts 1
  end
end