Given an integer array nums, choose an index i to split nums into two non empty parts: the left part nums[0..i] and the right part nums[i+1..n-1], where n is the length of nums.

A split at index i is considered valid if the sum of the left part is greater than or equal to the sum of the right part. Return the total number of valid split indices i.

Constraints:

• $2 \leq$ nums.length $\leq 10^5$

• $-10^5 \leq$ nums[i] $\leq 10^5$

Input: nums = [5, -2, -1, -2]-List[int]
Output: 3-int
Explanation: The total sum is 0. Checking each split index i (left is 0..i, right is i+1..n-1): at i = 0, left 5 >= right -5 (valid); at i = 1, left 3 >= right -3 (valid); at i = 2, left 2 >= right -2 (valid), giving 3 valid splits.

Input: nums = [-3, -4, -2, -1]-List[int]
Output: 1-int
Explanation: The total sum is -10. At i = 0, left -3 >= right -7 (valid); at i = 1, left -7 < right -3 (invalid); at i = 2, left -9 < right -1 (invalid), giving 1 valid split.

Input: nums = [0, 0, 0, 0, 0]-List[int]
Output: 4-int
Explanation: The total sum is 0. For every split index i = 0..3, the left and right sums are both 0, so left >= right is always true, giving 4 valid splits.

Input: nums = [100000, -100000, 100000, -100000, 100000]-List[int]
Output: 2-int
Explanation: The total sum is 100000. At i = 0 (left 100000, right 0) the split is valid, at i = 1 (left 0, right 100000) it is invalid, at i = 2 (left 100000, right 0) it is valid, and at i = 3 (left 0, right 100000) it is invalid, giving 2 valid splits.

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