Given an integer array nums of length n, return true if there is a triplet (i, j, k) which satisfies the following conditions:

• 0 < i, i + 1 < j, j + 1 < k < n - 1
• The sum of subarrays (0, i - 1), (i + 1, j - 1), (j + 1, k - 1) and (k + 1, n - 1) is equal.

A subarray (l, r) represents a slice of the original array starting from the element indexed l to the element indexed r.

 

Example 1:

Input: nums = [1,2,1,2,1,2,1]
Output: true
Explanation:
i = 1, j = 3, k = 5. 
sum(0, i - 1) = sum(0, 0) = 1
sum(i + 1, j - 1) = sum(2, 2) = 1
sum(j + 1, k - 1) = sum(4, 4) = 1
sum(k + 1, n - 1) = sum(6, 6) = 1

Example 2:

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

 

Constraints:

• n == nums.length
• 1 <= n <= 2000
• -106 <= nums[i] <= 106