You are given an integer array `nums`. You can choose exactly one index (0-indexed) and remove the element. Notice that the index of the elements may change after the removal.

For example, if `nums = [6,1,7,4,1]`:

- Choosing to remove index `1` results in `nums = [6,7,4,1]`.
- Choosing to remove index `2` results in `nums = [6,1,4,1]`.
- Choosing to remove index `4` results in `nums = [6,1,7,4]`.

An array is fair if the sum of the odd-indexed values equals the sum of the even-indexed values.

Return the number of indices that you could choose such that after the removal, `nums` is fair.

Example 1:

    Input: nums = [2,1,6,4]
    Output: 1
    Explanation:
    Remove index 0: [1,6,4] -> Even sum: 1 + 4 = 5. Odd sum: 6. Not fair.
    Remove index 1: [2,6,4] -> Even sum: 2 + 4 = 6. Odd sum: 6. Fair.
    Remove index 2: [2,1,4] -> Even sum: 2 + 4 = 6. Odd sum: 1. Not fair.
    Remove index 3: [2,1,6] -> Even sum: 2 + 6 = 8. Odd sum: 1. Not fair.
    There is 1 index that you can remove to make nums fair.

Example 2:

    Input: nums = [1,1,1]
    Output: 3
    Explanation: You can remove any index and the remaining array is fair.

Example 3:

    Input: nums = [1,2,3]
    Output: 0
    Explanation: You cannot make a fair array after removing any index.

Constraints:

- `1 <= nums.length <= 105`
- `1 <= nums[i] <= 104`