Count Even Sum Pairs

Given an integer \(N\) and an array \(A\) of \(N\) integers, your task is to count the number of valid pairs \((i, j)\) (with \(0 \le i < j < N\)) such that the sum \(A[i] + A[j]\) is even.

A pair is valid if both numbers are even or both numbers are odd. Recall that the number of ways to choose 2 items from \(k\) items is given by the formula: $$ \binom{k}{2} = \frac{k \times (k-1)}{2} $$.

inputFormat

The input is given via standard input (stdin) in the following format:

• The first line contains an integer \(N\) (\(0 \le N \le 10^5\)).
• The second line contains \(N\) space-separated integers representing the array \(A\).

outputFormat

Output a single integer representing the number of pairs \((i, j)\) such that \(A[i] + A[j]\) is even. The answer should be printed to standard output (stdout).

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