You are given an array nums.

A split of an array nums is beautiful if:

  1. The array nums is split into three subarrays: nums1, nums2, and nums3, such that nums can be formed by concatenating nums1, nums2, and nums3 in that order.
  2. The subarray nums1 is a prefix of nums2 OR nums2 is a prefix of nums3.

Return the number of ways you can make this split.

 

Example 1:

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

Output: 2

Explanation:

The beautiful splits are:

  1. A split with nums1 = [1], nums2 = [1,2], nums3 = [1].
  2. A split with nums1 = [1], nums2 = [1], nums3 = [2,1].

Example 2:

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

Output: 0

Explanation:

There are 0 beautiful splits.

 

Constraints: