In the array \(a\), we call a pair of indices \(i, j\) beautiful if the following condition holds:

• \(a_i \cdot a_j = j - i\).

Count the number of beautiful pairs in the array \(a\).

Input Specification

Each test contains multiple test cases. The first line contains the number of test cases \(t\) (\(1 \le t \le 10^4\)). The description of the test cases follows.

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

The second line of each test case contains \(n\) integers \(a_i\) (\(1 \le a_i \le 10^9\)).

Additional constraints on the input:

• The sum of \(n\) across all test cases does not exceed \(2 \cdot 10^5\).

Output Specification

For each test case, output a single integer — the answer to the problem.

Examples

Example Input 1

4
5
1 1 2 100 4
6
2 2 1 1 2 2
10
1 1 2 3 4 1 1 7 3 9
2
1000000000 1000000000

Output

3
7
10
0

Note

In the first example, there are \(3\) beautiful pairs: \((1, 2)\), \((1, 3)\), and \((1, 5)\).

In the second example, there are \(7\) beautiful pairs: \((1, 3)\), \((1, 5)\), \((2, 4)\), \((2, 6)\), \((3, 4)\), \((3, 5)\), and \((4, 6)\).

Source

Codeforces