Problem:
Score : 500 points

Problem Statement

You are given a sequence with N integers: A = \{ A_1, A_2, \cdots, A_N \}.
For each of these N integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied:

If A_i and A_j (i < j) are painted with the same color, A_i < A_j.

Find the minimum number of colors required to satisfy the condition.

Constraints

1 \leq N \leq 10^5

0 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the minimum number of colors required to satisfy the condition.

Sample Input 1

5
2
1
4
5
3

Sample Output 1

2

We can satisfy the condition with two colors by, for example, painting 2 and 3 red and painting 1, 4, and 5 blue.

Sample Input 2

4
0
0
0
0

Sample Output 2

4

We have to paint all the integers with distinct colors.

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::io::{stdin, BufRead};

fn bisect(x: &[i32], a: i32) -> usize {
    let mut lo = 0;
    let mut hi = x.len();
    while lo < hi {
        let mid = (lo + hi) / 2;
        if a < x[mid] {
            hi = mid;
        } else {
            lo = mid + 1;
        }
    }
    lo
}

fn main() {
    let stdin = stdin();
    let cin = stdin.lock();
    let mut lines = cin.lines();
    let n = {
        let line = lines.next().unwrap().unwrap();
        line.parse::<usize>().unwrap()
    };
    let mut xx = Vec::new();
    xx.push({
        let line = lines.next().unwrap().unwrap();
        -line.parse::<i32>().unwrap()
    });
    for _ in 0..n - 1 {
        let a = {
            let line = lines.next().unwrap().unwrap();
            -line.parse::<i32>().unwrap()
        };
        if a >= *xx.last().unwrap() {
            xx.push(a);
        } else {
            let mut i = bisect(&xx, a);
            if i == xx.len() {
                i -= 1;
            }
            xx[i] = a;
        }
    }
    println!("{}", xx.len());
}