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)

def enq(a,x)
  b=a[i=-1] and b=a and until b.frozen?
    x < (a=b)[-1] or return a << x
    x > a[0] or return a.unshift x
    b = a[i = a.bsearch_index{|y| x < (y.frozen? ? y: y[0])}-1]
  end
  a[i+9] or return a.insert i+1, x
  i>0 ? a[i]=[b,x] : enq(a[i+=1].to_a,x)  rescue a[i]=[x,a[i]]
end
def deq(a) r=a.shift; a[0].frozen? or a.unshift *a.shift; r end
Q,E,N = [],{},{}
F =->(e,n) { N[n] ? next : enq(Q,e); (E[e]||={})[n] = 0 }
gets.to_i.times {
  n,a,b,c,d = gets.split.map &:to_i
  Q.replace [0]
  E.replace({0=>{n=>0}})
  N.clear
  p (catch(:e) { while 1
    E[e=deq(Q)].keys.each {|n|
      N[n] ? next : N[n]=e
      throw :e,e  if n == 0
      [[a,2],[b,3],[c,5]].each {|p,m|
        q,r = n.divmod m
        if r == 0
          p > (x=q*d*(m-1)) and p = x
          F[e+p,q]
        else
          F[e+d*r,n-r]
          F[e+d*(m-r),n-r+m]
        end
      }
    }
    E.delete e
    deq Q  while Q[0] == e
  end })
}