Longest Zero Sum Subarray

Problem Description

You are given T test cases. Each test case begins with an integer N which denotes the number of elements in an array, followed by N integers. For each test case, your task is to find the length of the longest contiguous subarray whose sum is zero. If no such subarray exists, output -1.

The problem can be described mathematically as: find the maximum value of l such that there exists an index i with \[ \sum_{j=i}^{i+l-1} a_j = 0 \] where \(a_j\) represents the jth element of the array. If no subarray sums to zero, return -1.

Note: The entire subarray is considered, and the elements are consecutive.

inputFormat

Input Format

The first line of the input contains an integer T representing the number of test cases. Each test case is described as follows:

• The first line contains an integer N — the number of elements in the array.
• The second line contains N space-separated integers representing the elements of the array.

All input is read from stdin.

outputFormat

Output Format

For each test case, output a single line containing one integer — the length of the longest contiguous subarray with a sum of zero. If no such subarray exists, output -1.

All output should be written to stdout.

## sample

3
5
1 -1 3 2 -2
4
1 2 3 4
6
1 -1 2 -2 3 -3

2
-1
6

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