Zero Sum Disjoint Pairs

Given an array of integers, find the maximum number of disjoint pairs \( (i,j) \) with \( i < j \) such that \( a_i + a_j = 0 \). In other words, each element in the array can be used in at most one pair. For example, for the array [-1, 1, 2, -2], the answer is 2. 

Note: A pair is defined as two indices \( i \) and \( j \) with \( i < j \), and once an element is used in a pair, it cannot be reused.

The relationship can be mathematically stated as: find the maximum \( k \) such that there exists \( k \) pairs \( (i, j) \) with \( i < j \) and \( a_i + a_j = 0 \).

inputFormat

Input is read from standard input (stdin).

outputFormat

Output should be written to standard output (stdout). Each test case output should be on a new line.

## sample

2
4
-1 1 2 -2
5
3 -3 0 1 -1

2
2

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