#include <bits/stdc++.h>
using namespace std;
int Gcd(int a, int b) {
  if (b == 0) return a;
  return Gcd(b, a % b);
}
int Lcm(int a, int b) { return a / Gcd(a, b) * b; }
inline int read() {
  int f = 1, x = 0;
  char ch = getchar();
  while (ch > '9' || ch < '0') {
    if (ch == '-') f = -f;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
const int maxn = 1e6 + 10;
int main() {
  int T = read();
  while (T--) {
    int b = read(), p = read(), f = read();
    int h = read(), c = read(), ans = 0;
    for (int i = 0; i <= 100; i++) {
      for (int j = 0; j <= 100; j++) {
        int num1 = (i + j) * 2, num2 = i, num3 = j;
        if (num1 > b || num2 > p || num3 > f)
          continue;
        else
          ans = max(ans, i * h + j * c);
      }
    }
    cout << ans << endl;
  }
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

There are two types of burgers in your restaurant — hamburgers and chicken burgers! To assemble a hamburger you need two buns and a beef patty. To assemble a chicken burger you need two buns and a chicken cutlet. 

You have b buns, p beef patties and f chicken cutlets in your restaurant. You can sell one hamburger for h dollars and one chicken burger for c dollars. Calculate the maximum profit you can achieve.

You have to answer t independent queries.

Input

The first line contains one integer t (1 ≤ t ≤ 100) – the number of queries.

The first line of each query contains three integers b, p and f (1 ≤ b, ~p, ~f ≤ 100) — the number of buns, beef patties and chicken cutlets in your restaurant.

The second line of each query contains two integers h and c (1 ≤ h, ~c ≤ 100) — the hamburger and chicken burger prices in your restaurant.

Output

For each query print one integer — the maximum profit you can achieve.

Example

Input


3
15 2 3
5 10
7 5 2
10 12
1 100 100
100 100


Output


40
34
0

Note

In first query you have to sell two hamburgers and three chicken burgers. Your income is 2 ⋅ 5 + 3 ⋅ 10 = 40.

In second query you have to ell one hamburgers and two chicken burgers. Your income is 1 ⋅ 10 + 2 ⋅ 12 = 34.

In third query you can not create any type of burgers because because you have only one bun. So your income is zero.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int Gcd(int a, int b) {
  if (b == 0) return a;
  return Gcd(b, a % b);
}
int Lcm(int a, int b) { return a / Gcd(a, b) * b; }
inline int read() {
  int f = 1, x = 0;
  char ch = getchar();
  while (ch > '9' || ch < '0') {
    if (ch == '-') f = -f;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
const int maxn = 1e6 + 10;
int main() {
  int T = read();
  while (T--) {
    int b = read(), p = read(), f = read();
    int h = read(), c = read(), ans = 0;
    for (int i = 0; i <= 100; i++) {
      for (int j = 0; j <= 100; j++) {
        int num1 = (i + j) * 2, num2 = i, num3 = j;
        if (num1 > b || num2 > p || num3 > f)
          continue;
        else
          ans = max(ans, i * h + j * c);
      }
    }
    cout << ans << endl;
  }
  return 0;
}

```