105. 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.

Input: Integer array height of length n.

Output: Integer — total water trapped.

Examples

Example 1

Input: [0,1,0,2,1,0,1,3,2,1,2,1]
Output: 6
Explanation: 6 units of water trapped.

Example 2

Input: [4,2,0,3,2,5]
Output: 9
Explanation: 9 units trapped.

Example 3

Input: [1,0,1]
Output: 1
Explanation: 1 unit between height 1 bars.