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: Time Limit Exceeded)

#include "bits/stdc++.h"
#include <unordered_set>
#define rep(i,n) for(int i = 0; i < n; i++)
typedef long long ll;
typedef unsigned long long ull;
using namespace std;
#define vll vector<vector<long long>>
#define vl vector<long long>
#define vi vector<int>
#define vii vector<vector<int>>
#define pb push_back
#define pf push_front
#define ld long double
#define Sort(a) sort(a.begin(),a.end())
#define cSort(a,cmp) sort(a.begin(),a.end(),cmp)
#define reSort(a) sort(a.rbegin(), a.rend())
static const ll llMAX = numeric_limits<long long>::max();
static const int intMAX = numeric_limits<int>::max();
static const ll  llMIN = numeric_limits<long long>::min();
static const int intMIN = numeric_limits<int>::min();
static const ll d_5 = 100000;
static const ll d9_7 = 1000000007;
static const ll d_9 = 1000000000;
static const double PI=3.14159265358979323846;
template<class T>
T gcd(T a,T b){
  if(a==0){
    return b;

  }else if(b==0){
    return a;
  }
  int flag1=0,flag2=0;
  if(a>0){
    flag1=1;
    a=a*(-1);
  }
  if(b>0){
    flag2=1;
    b=b*(-1);
  }
  while(1) {
    if(a < b) swap(a, b);
    if(!b) break;
    a %= b;
  }

  return a;
}
ll digitpower(ll a,ll b){//aのb乗を計算
  if(b==1){
    return a;
  }else if(b==0){
    return 1;
  }
  int mode=0;
  if(mode==0){
    if(b%2==1){
      ll tmp = digitpower(a,(b-1)/2);
      tmp%=d9_7;
      tmp*=tmp;
      tmp%=d9_7;
      tmp*=a;
      return (tmp)%d9_7;
    }else{
      ll tmp = digitpower(a,(b)/2);
      tmp%=d9_7;
      tmp*=tmp;
      tmp%=d9_7;
      return (tmp)%d9_7;
    }
  }else{
    if(b%2==1){
      ll tmp = digitpower(a,(b-1)/2);
      tmp*=tmp;
      tmp*=a;
      return (tmp);
    }else{
      ll tmp = digitpower(a,(b)/2);
      tmp*=tmp;
      return (tmp);
    }
  }
  return 0;
  
}
template<class T>
void Printvector(std::vector<T> &a){
  int size = a.size();
  rep(i,size){
    cout<<a[i]<<" ";
  }
  cout<<endl;
}
template<class T>
void Printvector(std::vector<std::vector<T> > &a){
  int size = a.size();
  rep(i,size){
    int size2=a[i].size();
    rep(j,size2){
      cout<<a[i][j]<<" ";
    }
    cout<<endl;
  }
  cout<<endl;
}
unordered_set<ll> primes(ll n){
  unordered_set<ll> ret;
  for(ll i=2;i*i<=n;i++){
    if(n%i==0){
      ret.insert(i);
      ret.insert(n/i);
    }
  }
  return ret;
}
long long modinv(long long a, long long m) {//modの逆元
    long long b = m, u = 1, v = 0;
    while (b) {
        long long t = a / b;
        a -= t * b; swap(a, b);
        u -= t * v; swap(u, v);
    }
    u %= m; 
    if (u < 0) u += m;
    return u;
}
template<class T>
vector<T> getaccum(vector<T> a){
  int size=a.size();
  vector<T> ans(size);
  ans[0]=a[0];
  for(int i=0;i<size-1;i++){
    ans[i+1]=ans[i]+a[i+1];
    //ans[i+1]%=d9_7;
  }
  return ans;
}
struct c{
  ll t;
  ll d;
};
// 比較関数を定義
bool cmp( const c& left, const c& right ) {
    return left.d>right.d;
}
    ll n,a,b,c,d;
    ll ans;
void solve(ll now,ll cost){
    if(now<0){
    return;
  }
  if(now==0){
    ans = min(ans,cost);
    return;
  }
  if(ans<=cost)return;
  if(now%5==0){

  solve(now/5,cost+c);
  }
  if(ans<=cost)return;
  if(now%3==0){

  solve(now/3,cost+b);
  }
  if(ans<=cost)return;
  if(now%2==0){

  solve(now/2,cost+a);
  }
  if(ans<=cost)return;
  solve(now-1,cost+d);
  if(ans<=cost)return;
  solve(now+1,cost+d);
  if(ans<=cost)return;
  return;
}
int main(void){
  int t;
  cin>>t;
  rep(i,t){
    cin>>n>>a>>b>>c>>d;
    ans = llMAX/10;
    solve(n,0);
    cout<<ans<<endl;
  }
  return 0;
}

//clang++ -g -fsanitize=address -fno-omit-frame-pointer 1.cpp -o test.exe

//<<std::setprecision(30)

//重複削除
 /* std::sort(vec.begin(), vec.end());
 
  vec.erase(std::unique(vec.begin(), vec.end()), vec.end());*/

  //ペアの全探索
  /*do{
		int s=0;
		for(int i=0;i<n/2;i++)s+=v[i]^v[i+n/2];
		r=max(s,r);
		reverse(v.begin()+n/2,v.end());
	}while(next_permutation(v.begin(),v.end()));*/