Minimum Insertions to Avoid Zero Sum Subarray

Given an array of integers, your goal is to modify the array by inserting additional elements (at any positions) so that no contiguous segment (subarray) of the resulting array sums to zero. Determine the minimum number of insertions required to achieve this. Input An integer array arr. Output An integer, representing the minimum number of insertions. Examples Example 1: Input: arr = [1, -1, 1, -1] Output: 2 Example 2: Input: arr = [0, 0, 0] Output: 3 Constraints The array length can be up to $10^5$. Each number in the array can have an absolute value of up to $10^4$. Example Input 1 -1 1 -1