The Intelligent Defragmenter

A storage system contains N files, each occupying a block [S_i, E_i]. You need to group these files into 'clusters'. The clustering algorithm follows two rules: 1. If two files overlap or touch (e.g., [1, 3] and [3, 5]), they MUST be merged into a single continuous block first. 2. Once all overlapping files are merged, two resulting blocks can be part of the same cluster if the gap between them is no more than G units, AND the total span of the cluster (from the start of the first block to the end of the last block) does not exceed L units. Files are assigned to clusters greedily from left to right. Calculate the total number of clusters formed. Input Format: The first line contains N, G, and L. The next N lines each contain S_i and E_i (files are not necessarily sorted). Output Format: A single integer representing the number of clusters. Example: Input: 3 2 10 1 3 4 6 8 12 Output: 2 (Explanation: Files [1, 3] and [4, 6] have a gap of 1 (<= G) and a total span of 5 (<= L), so they cluster. File [8, 12] has a gap of 2 (<= G) from the previous block, but adding it would make the span 11 (> L). Thus, [8, 12] starts a new cluster.)