Powers of Two

Description:

Input:

The first line contains the single positive integer n (1 ≤ n ≤ 10⁵) — the number of integers.

The second line contains n positive integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁹).

Output:

Print the number of pairs of indexes i, j (i < j) that a_i + a_j is a power of 2.

Sample Input:

4
7 3 2 1

Sample Output:

2

Sample Input:

3
1 1 1

Sample Output:

3

Note:

In the first example the following pairs of indexes include in answer: (1, 4) and (2, 4).

In the second example all pairs of indexes (i, j) (where i < j) include in answer.