We define the following:
- A subarray of an -element array is an array composed from a contiguous block of the original array's elements. For example, if , then the subarrays are , , , , , and . Something like would not be a subarray as it's not a contiguous subsection of the original array.
- The sum of an array is the total sum of its elements.
- An array's sum is negative if the total sum of its elements is negative.
- An array's sum is positive if the total sum of its elements is positive.
Given an array of integers, find and print its number of negative subarrays on a new line.
Input Format
The first line contains a single integer, , denoting the length of array .
The second line contains space-separated integers describing each respective element, , in array .
Output Format
Print the number of subarrays of having negative sums.
Explanation
There are nine negative subarrays of :
Thus, we print on a new line.