AT_abc457_g [ABC457G] Catch All Apples

$ N $ apples fall on a number line. Apple $ i $ falls at coordinate $ X_i $ at time $ T_i $ . You want to place some robots on the number line to collect all $ N $ apples. The robots can be placed at any coordinates. Each robot starts operating from time $ 0 $ and can move freely along the number line at a speed of at most $ 1 $ . Multiple robots may occupy the same coordinate at the same time. Each robot can collect apple $ i $ if and only if it is at coordinate $ X_i $ at time $ T_i $ . Find the minimum number of robots needed to collect all apples.

The input is given from Standard Input in the following format: > $ N $ $ T_1 $ $ X_1 $ $ T_2 $ $ X_2 $ $ \vdots $ $ T_N $ $ X_N $

Output the answer.

### Sample Explanation 1 All apples can be collected with two robots by moving them as follows: - Place robot $ 1 $ at coordinate $ 0 $ and robot $ 2 $ at coordinate $ 2 $ . - Time $ 0 $ : Robot $ 2 $ collects apple $ 1 $ . - Time $ 1 $ : Robot $ 1 $ collects apple $ 2 $ . Move both robots in the positive direction at speed $ 1 $ until time $ 2 $ . - Time $ 2 $ : Robot $ 1 $ collects apple $ 3 $ and robot $ 2 $ collects apple $ 4 $ . It is impossible to collect all apples with fewer than two robots, so output $ 2 $ . ### Constraints - $ 1 \le N \le 3 \times 10^5 $ - $ 0 \le T_i \le 3 \times 10^5 $ - $ 0 \le X_i \le 3 \times 10^5 $ - $ (T_i, X_i) \neq (T_j, X_j) $ $ (i \neq j) $ - All input values are integers.