You are given an array nums consisting of positive integers.

You can perform the following operation on the array any number of times:

• Choose any two adjacent elements and replace them with their sum.
  • For example, if nums = [1,2,3,1], you can apply one operation to make it [1,5,1].

Return the minimum number of operations needed to turn the array into a palindrome.

 

Example 1:

Input: nums = [4,3,2,1,2,3,1]
Output: 2
Explanation: We can turn the array into a palindrome in 2 operations as follows:
- Apply the operation on the fourth and fifth element of the array, nums becomes equal to [4,3,2,3,3,1].
- Apply the operation on the fifth and sixth element of the array, nums becomes equal to [4,3,2,3,4].
The array [4,3,2,3,4] is a palindrome.
It can be shown that 2 is the minimum number of operations needed.

Example 2:

Input: nums = [1,2,3,4]
Output: 3
Explanation: We do the operation 3 times in any position, we obtain the array [10] at the end which is a palindrome.

 

Constraints:

• 1 <= nums.length <= 105
• 1 <= nums[i] <= 106