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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include<iostream>
#include<cmath>
#include<algorithm>
#include<string>
#include<vector>
#include<stack>
#include<queue>
#include<set>
#include<map>
#include<iomanip>
#include<bitset>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;
typedef pair<ll,P> P1;
typedef pair<P,P> P2;
#define pu push
#define pb push_back
#define mp make_pair
#define eps 1e-7
#define INF 1000000000
#define fi first
#define sc second
#define rep(i,x) for(ll i=0;i<x;i++)
#define repn(i,x) for(ll i=1;i<=x;i++)
#define SORT(x) sort(x.begin(),x.end())
#define ERASE(x) x.erase(unique(x.begin(),x.end()),x.end())
#define POSL(x,v) (lower_bound(x.begin(),x.end(),v)-x.begin())
#define POSU(x,v) (upper_bound(x.begin(),x.end(),v)-x.begin())

const int MAX = 510000;
const int MOD = 1000000007;

map<ll,ll> m;
ll A, B, C, D;
ll solve(ll N){
  if(N == 0) return 0;
  if(N == 1) return D;
  if(m.count(N)) return m[N];

  m[N] = 1e18;
  if(N / 1e9 * D < 3e9) m[N] = min(m[N] , N * D);

  m[N] = min(m[N] , A + D * (N % 2) + solve(N / 2) );
  m[N] = min(m[N] , A + D * (2 - N % 2) + solve((N + 2) / 2) );

  m[N] = min(m[N] , B + D * (N % 3) + solve(N / 3) );
  m[N] = min(m[N] , B + D * (3 - N % 3) + solve((N + 3) / 3) );

  m[N] = min(m[N] , C + D * (N % 5) + solve(N / 5) );
  m[N] = min(m[N] , C + D * (5 - N % 5) + solve((N + 5) / 5) );

  return m[N];

}

int main(){
  ll T; cin >> T;
  vector<ll> ans;
  rep(i,T){
    ll N; cin >> N; cin >> A >> B >> C >> D;
    m.clear();
    ll tmp = solve(N);
    ans.pb(tmp);
  }
  rep(i,T) cout << ans[i] << endl;
}