Pasture Parcels

# Pasture Parcels ## Problem Farmer John has a long fence along his pasture, and different sections of it have been grazed by his cows. Each grazed section is represented as a closed interval `[l, r]` on the fence. Your task is to determine the total length of fence that has been grazed. When multiple grazed sections overlap or touch, they merge into a single contiguous section. ## Input The first line contains an integer `N` (1 ≤ N ≤ 10^5), the number of grazed intervals. The next `N` lines each contain two integers `l` and `r` (−2^31 ≤ l ≤ r ≤ 2^31 − 1), representing a closed interval `[l, r]` of grazed fence. ## Output Output a single integer: the total length of fence that has been grazed, calculated as the sum of the lengths of all merged intervals. For an interval `[l, r]`, the length is `r - l`. ## Constraints - 1 ≤ N ≤ 10^5 - −2^31 ≤ l ≤ r ≤ 2^31 − 1 - Coordinates fit in 32-bit signed integers ## Sample Input ``` 4 1 4 3 7 10 12 11 15 ``` ## Sample Output ``` 11 ``` ## Explanation The intervals `[1, 4]` and `[3, 7]` overlap and merge into `[1, 7]` with length 7 − 1 = 6. The intervals `[10, 12]` and `[11, 15]` overlap and merge into `[10, 15]` with length 15 − 10 = 5. The total grazed length is 6 + 5 = 11.