Problem:
Longest Increasing Subsequence

For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.

An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.

Input

n
a0
a1
:
an-1

In the first line, an integer n is given. In the next n lines, elements of A are given.

Output

The length of the longest increasing subsequence of A.

Constraints

1 ≤ n ≤ 100000

0 ≤ ai ≤ 109

Sample Input 1

5
5
1
3
2
4

Sample Output 1

3

Sample Input 2

3
1
1
1

Sample Output 2

1

Solution in Rust (judge verdict: Accepted)

use std::io::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("filed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let n:usize = read();
    let arr:Vec<usize> = (0..n).map(|_| read()).collect();
    let mut dp = vec![std::usize::MAX; n+1];
    for i in 0..n {
        let index = lower_bound(&dp, arr[i]);
        dp[index] = arr[i];
    }
    println!("{}", lower_bound(&dp, std::usize::MAX));
}

fn lower_bound(v:&Vec<usize>, x:usize) -> usize {
    let mut l = 0;
    let mut h = v.len() - 1;
    while l < h {
        let mid  = (l + h) / 2;
        if x <= v[mid] {
            h = mid;
        } else {
            l = mid + 1;
        }
    }   l
}