Problem Description

Given an integer array A of non-negative integers representing an elevation map where the width of each bar is 1, compute how much water it is able to trap after raining.

Problem Constraints

1 <= |A| <= 100000

Input Format

The only argument given is integer array A.

Output Format

Return the total water it is able to trap after raining.

Example Input

Input 1:

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

A = [1, 2]

Example Output

Output 1:

6

Output 2:

0

Example Explanation

Explanation 1:

In this case, 6 units of rain water (blue section) are being trapped.

Explanation 2:

No water is trapped.