Trapping Rain Water
Given an elevation map, compute how much water it can trap after raining.
Input format
The first line contains N. The second line contains N non-negative heights.
Output format
Print the total units of water trapped.
Constraints
- Values fit in a 64-bit signed integer
- Trailing whitespace and a trailing newline are ignored by the judge
Read from stdin, write to stdout. Sample cases below show the exact format.
Sample cases
Example 1
Input
12
0 1 0 2 1 0 1 3 2 1 2 1Expected output
6Example 2
Input
6
4 2 0 3 2 5Expected output
9