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: Runtime Error)

/**
 *   author:  cryforthemoon46
 *   created: 23.05.2020 21:01:17
**/
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;

#define REP(i, n) for(ll i = 0; i < (ll)(n); i++)
#define FOR(i, a, b) for(ll i = a; i < (ll)(b); i++)
#define FOREACH(x, a) for(auto&& x : (a))

const double EPS = (double)(1e-7);
const ll INF = (ll)1e18;
const int MOD = (int)1e9 + 7;
const ll dx[4] = { 0,  1,  0, -1};
const ll dy[4] = {-1,  0,  1,  0};
const ll MAX_N = (ll)1e18;

ll T, N, A, B, C, D;

ll solve() {
    ll dp[N + 2];
    dp[0] = 0;
    FOR(i, 1, N + 2) {
        dp[i] = INF;
        if (i % 2 == 0) {
            dp[i] = min(dp[i], dp[i / 2] + A);
        }
        if (i % 3 == 0) {
            dp[i] = min(dp[i], dp[i / 3] + B);
        }
        if (i % 5 == 0) {
            dp[i] = min(dp[i], dp[i / 5] + C);
        }
        dp[i] = min(dp[i], dp[i - 1] + D);
        dp[i - 1] = min(dp[i - 1], dp[i] + D);
    }
    return dp[N];
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cin >> T;
    REP(i, T) {
        cin >> N >> A >> B >> C >> D;
        cout << solve() << endl;
    }
}