Russian Doll Envelopes (Maximum Nesting)

Russian Doll Envelopes (LC 354) You are given n envelopes, each represented as (w, h) for width and height. Envelope A(w1,h1) can fit into B(w2,h2) iff: w1 < w2 h1 < h2 Return the maximum number of envelopes you can nest (the length of the longest nesting chain). Input (stdin) The first line contains an integer n. The next n lines each contain two integers w h. Output (stdout) Print a single integer: the maximum nesting count. Constraints 1 <= n <= 2 * 10^5 1 <= w, h <= 10^9 Note You must handle envelopes with the same width correctly so they are not incorrectly counted in the same increasing chain. Examples Example Input 4 5 4 6 4 6 7 2 3 Output 3