Description

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.

Examples

Input:height = [0,1,0,2,1,0,1,3,2,1,2,1]
Output:6
Explanation:

The elevation map traps 6 units of rain water.

Input:height = [4,2,0,3,2,5]
Output:9
Explanation:

9 units of water are trapped.

Input:height = [1,2,3,4,5]
Output:0
Explanation:

Edge case returning zero.

Constraints

  • n == height.length
  • 1 ≤ n ≤ 2 × 10⁴
  • 0 ≤ height[i] ≤ 10⁵

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