#include <bits/stdc++.h>
using namespace std;
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
int mulmd(long long a, long long b) {
  long long ret = (a * b) % 1000000007;
  return (int)ret;
}
inline int power(long long x, long long y, int p) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = mulmd(res, x);
    y = y >> 1;
    x = mulmd(x, x);
  }
  return (int)res;
}
int submd(long long a, long long b) {
  long long ret = a - b;
  if (ret < 0) {
    ret += 1000000007;
  }
  return (int)ret;
}
int addmd(long long a, long long b) {
  long long ret = (a + b) % 1000000007;
  return (int)ret;
}
int phi(int n) {
  int result = n;
  for (int i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      while (n % i == 0) {
        n = n / i;
      }
      result -= result / i;
    }
  }
  if (n > 1) result -= result / n;
  return result;
}
const int N = 1e5 + 5;
int arr[N];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  while (t--) {
    int b, p, f;
    cin >> b >> p >> f;
    int h, c;
    cin >> h >> c;
    int ans = 0;
    for (int i = 0; i <= p; i++) {
      int temp = 0;
      int x = b;
      if (i * 2 <= x) {
        x -= i * 2;
        temp += i * h;
      }
      int cnt = min(x / 2, f);
      temp += cnt * c;
      ans = max(ans, temp);
    }
    cout << ans << "\n";
  }
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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;
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
int mulmd(long long a, long long b) {
  long long ret = (a * b) % 1000000007;
  return (int)ret;
}
inline int power(long long x, long long y, int p) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = mulmd(res, x);
    y = y >> 1;
    x = mulmd(x, x);
  }
  return (int)res;
}
int submd(long long a, long long b) {
  long long ret = a - b;
  if (ret < 0) {
    ret += 1000000007;
  }
  return (int)ret;
}
int addmd(long long a, long long b) {
  long long ret = (a + b) % 1000000007;
  return (int)ret;
}
int phi(int n) {
  int result = n;
  for (int i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      while (n % i == 0) {
        n = n / i;
      }
      result -= result / i;
    }
  }
  if (n > 1) result -= result / n;
  return result;
}
const int N = 1e5 + 5;
int arr[N];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  while (t--) {
    int b, p, f;
    cin >> b >> p >> f;
    int h, c;
    cin >> h >> c;
    int ans = 0;
    for (int i = 0; i <= p; i++) {
      int temp = 0;
      int x = b;
      if (i * 2 <= x) {
        x -= i * 2;
        temp += i * h;
      }
      int cnt = min(x / 2, f);
      temp += cnt * c;
      ans = max(ans, temp);
    }
    cout << ans << "\n";
  }
}

```