Trapping Rain Water

Given n non-negative integers representing an elevation map where the width of each bar is 1, compute how much water it can trap after raining. Example 1: Input: height = [0,1,0,2,1,0,1,3,2,1,2,1] Output: 6 Explanation: The above elevation map (black section) is represented by array [0,1,0,2,1,0,1,3,2,1,2,1]. In this case, 6 units of rain water (blue section) are being trapped. Example 2: Input: height = [4,2,0,3,2,5] Output: 9

Constraints:

n == height.length 1 <= n <= 2 * 104 0 <= height[i] <= 105

Test case 1

Input

height = [0,1,0,2,1,0,1,3,2,1,2,1]

Output

6

Test case 2

Input

height = [4,2,0,3,2,5]

Output

9