Square Counting

Problem Description

Given $N$ positive integers, with the $i$-th denoted by $a_i$, count how many pairs $(i, j)$ satisfy that $a_i^2 + a_j$ is a perfect square.

Input Format

The first line contains a positive integer $n$.

The second line contains $n$ numbers, representing $a_1, a_2, a_3, \dots, a_n$.

Output Format

One integer on a single line: the answer.

Sample Input

5
1 2 3 4 5

Sample Output

2

Constraints

For all test data, $1 \le n \le 10^6$ and $1 \le a_i \le 10^6$.