Trapping Water

Have the function TrappingWater(arr) take the array of non-negative integers stored in arr, and determine the largest amount of water that can be trapped. The numbers in the array represent the height of a building (where the width of each building is 1) and if you imagine it raining, water will be trapped between the two tallest buildings. For example: if arr is [3, 0, 0, 2, 0, 4] then this array of building heights looks like the following picture if we draw it out:



Now if you imagine it rains and water gets trapped in this picture, then it'll look like the following (the x's represent water):



This is the most water that can be trapped in this picture, and if you calculate the area you get 10, so your program should return 10.

Examples

Input: [1, 2, 1, 2]
Output: 1

Input: [0, 2, 4, 0, 2, 1, 2, 6]
Output: 11