Maximize Balanced Subarray Length with One Modification

You are given an array of integers of length \(N\). You are allowed to perform at most one modification on the array: choose any element and replace it with any integer of your choice.

Your goal is to maximize the length of a contiguous subarray in which the number of positive elements equals the number of negative elements. Note that zero is considered neutral and does not contribute to either count.

Definition: A subarray is a contiguous portion of the array.

Balanced subarray condition: Let \(pos\) be the count of positive numbers and \(neg\) be the count of negative numbers in the subarray, then we require \(pos = neg\).

Constraints:

• \(1 \leq N \leq 10^5\)
• \(-10^9 \leq A[i] \leq 10^9\)

If no balanced subarray exists, the answer is 0. You may opt not to perform any modification if the array already contains an optimal subarray.

Example 1:

Input:
5
1 -1 1 1 -1
Output:
4

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Example 2:

Input:
4
1 1 -1 -1
Output:
4

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Example 3:

Input:
3
1 2 3
Output:
2

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inputFormat

The input is read from stdin and has the following format:

1. The first line contains a single integer \(N\), denoting the number of elements in the array.
2. The second line contains \(N\) space-separated integers representing the array \(A\).

outputFormat

Output to stdout a single integer: the maximum length of a contiguous subarray which can be made balanced (equal number of positive and negative numbers) by performing at most one modification.

## sample

5
1 -1 1 1 -1

4

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