#include <bits/stdc++.h>
const long long nint = 1e9 + 7;
const long long i1 = 1e6 + 5;
const long long num = 1e5 + 5;
using namespace std;
bool itsrt(string s, long long n) {
  for (long long i = 0; i < n - 1; i++) {
    if (s[i] > s[i + 1]) {
      return false;
    }
  }
  return true;
}
void kkkuuu() {
  long long n;
  cin >> n;
  long long arr[n];
  for (long long i = 0; i < n; i++) cin >> arr[i];
  long long ans = 0;
  for (long long i = 0; i < n - 1; i++) {
    long long a = arr[i] * arr[i + 1];
    ans = max(a, ans);
  }
  cout << ans << "\n";
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long tct = 1;
  cin >> tct;
  while (tct--) {
    kkkuuu();
  }
}

### Prompt

Please formulate a cpp solution to the following problem:

You are given n integers a_1, a_2, …, a_n. Find the maximum value of max(a_l, a_{l + 1}, …, a_r) ⋅ min(a_l, a_{l + 1}, …, a_r) over all pairs (l, r) of integers for which 1 ≤ l < r ≤ n.

Input

The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.

The first line of each test case contains a single integer n (2 ≤ n ≤ 10^5).

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6).

It is guaranteed that the sum of n over all test cases doesn't exceed 3 ⋅ 10^5.

Output

For each test case, print a single integer — the maximum possible value of the product from the statement.

Example

Input


4
3
2 4 3
4
3 2 3 1
2
69 69
6
719313 273225 402638 473783 804745 323328


Output


12
6
4761
381274500335

Note

Let f(l, r) = max(a_l, a_{l + 1}, …, a_r) ⋅ min(a_l, a_{l + 1}, …, a_r).

In the first test case, 

  * f(1, 2) = max(a_1, a_2) ⋅ min(a_1, a_2) = max(2, 4) ⋅ min(2, 4) = 4 ⋅ 2 = 8. 
  * f(1, 3) = max(a_1, a_2, a_3) ⋅ min(a_1, a_2, a_3) = max(2, 4, 3) ⋅ min(2, 4, 3) = 4 ⋅ 2 = 8. 
  * f(2, 3) = max(a_2, a_3) ⋅ min(a_2, a_3) = max(4, 3) ⋅ min(4, 3) = 4 ⋅ 3 = 12. 



So the maximum is f(2, 3) = 12.

In the second test case, the maximum is f(1, 2) = f(1, 3) = f(2, 3) = 6.

### Response

```cpp
#include <bits/stdc++.h>
const long long nint = 1e9 + 7;
const long long i1 = 1e6 + 5;
const long long num = 1e5 + 5;
using namespace std;
bool itsrt(string s, long long n) {
  for (long long i = 0; i < n - 1; i++) {
    if (s[i] > s[i + 1]) {
      return false;
    }
  }
  return true;
}
void kkkuuu() {
  long long n;
  cin >> n;
  long long arr[n];
  for (long long i = 0; i < n; i++) cin >> arr[i];
  long long ans = 0;
  for (long long i = 0; i < n - 1; i++) {
    long long a = arr[i] * arr[i + 1];
    ans = max(a, ans);
  }
  cout << ans << "\n";
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long tct = 1;
  cin >> tct;
  while (tct--) {
    kkkuuu();
  }
}

```