Sum of Altitude Changes

Background

Congcong and his friends are planning a hiking trip. They have a map recording the altitudes along the trail, and now they want to calculate the total change in altitude for a specific segment of the path.

Problem Description

We are given an array of heights, representing the altitude along a walking trail. Given start and end indexes into the array, return the sum of the absolute changes for a walk beginning at the start index and ending at the end index. For example, with the heights $\{5, 3, 6, 7, 2\}$ and start=2, end=4 yields a sum of $1 + 5 = 6$. The start and end indexes will both be valid indexes into the array with start <= end.

Input Format

Input is given from Standard Input in the following format.

[h_0 h_1 ... h_{N-1}] start end

Where h_i are the altitudes, start is the starting index, and end is the ending index.

Output Format

Output is printed to Standard Output in the following format.

sum_of_changes

Where sum_of_changes is the sum of absolute changes in adjacent altitudes for the specified path.

Sample

[5 3 6 7 2] 2 4

6

[5 3 6 7 2] 0 1

2

[5 3 6 7 2] 0 4

11

Sample Explanation

For the first sample, the altitude array is $\{5, 3, 6, 7, 2\}$, the starting index is start=2, and the ending index is end=4. The path segment to calculate is from heights[2] to heights[4], which is $\{6, 7, 2\}$. The sum of absolute changes in adjacent altitudes is: $|heights[3] - heights[2]| + |heights[4] - heights[3]|$ $= |7 - 6| + |2 - 7|$ $= 1 + 5$ $= 6$

Constraints

Time limit: 1 second, Memory limit: 1024 KiB for each test case.