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)

fn lower_bound<T: std::cmp::Ord>(arr: &Vec<T>, b: T) -> usize {
    let (mut lt, mut ge) = (0, arr.len());
    // lt=-1にすると型強制しなきゃなのでここで確かめる
    if arr[lt] >= b {
        return 0;
    }
    while lt + 1 < ge {
        let m = (lt + ge) / 2;
        if arr[m] < b {
            lt = m;
        } else if arr[m] > b {
            ge = m;
        } else {
            return m;
        }
    }
    ge
}

fn main() {
    let n = read();
    let mut v: Vec<usize> = vec![];
    for _ in 0..n {
        v.push(read());
    }
    let mut dp = vec![std::usize::MAX; n];
    let mut ans = 0;
    for i in 0..n {
        let b = lower_bound(&dp, v[i]);
        dp[b] = v[i];
        ans = max(ans, b + 1);
    }
    println!("{}", ans);
}

// =========
#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{HashMap, HashSet};
#[allow(unused_imports)]
use std::process::exit;

#[allow(dead_code)]
const MOD: usize = 1000000007;

fn read<T: std::str::FromStr>() -> T {
    use std::io::Read;
    let stdin = std::io::stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed 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")
}

// =========