You are given an integer array nums.

Start by selecting a starting position curr such that nums[curr] == 0, and choose a movement direction of either left or right.

After that, you repeat the following process:

A selection of the initial position curr and movement direction is considered valid if every element in nums becomes 0 by the end of the process.

Return the number of possible valid selections.

 

Example 1:

Input: nums = [1,0,2,0,3]

Output: 2

Explanation:

The only possible valid selections are the following:

Example 2:

Input: nums = [2,3,4,0,4,1,0]

Output: 0

Explanation:

There are no possible valid selections.

 

Constraints: