Trapping Rain Water

Bars of width 1 have the given heights. After rain, water collects above each bar up to the lower of the tallest bars on its left and right. Compute the total trapped water. An O(n) two-pointer solution is expected.

Implement trapped_water(heights).

Input

heights: Bar heights from left to right.

Output

Return the total units of water.

Constraints

0 ≤ length ≤ 200,000; 0 ≤ height ≤ 100,000

Examples

Input:
heights = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]

Expected output:
expected = 6

Input:
std::vector<long long> heights = {0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1};

Expected output:
long long expected = 6;

Input:
long[] heights = new long[] {0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1};

Expected output:
long expected = 6;

Input:
heights = [3, 2, 1]

Expected output:
expected = 0

Input:
std::vector<long long> heights = {3, 2, 1};

Expected output:
long long expected = 0;

Input:
long[] heights = new long[] {3, 2, 1};

Expected output:
long expected = 0;

References

This challenge is adapted for CodeUtility. Follow the statement and constraints above.

• From Problems to Performance: Two Decades of Programming Contests in the CCSC Southeast