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 (1.42.0) (judge verdict: Wrong Answer)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};

#[fastout]
fn main() {
    input! {//
        n:usize,
        a:[usize;n],
    }
    // 増加列の個数てきな
    let mut st = BTreeSet::new();
    for i in 0..n {
        st.insert(i as usize);
    }
    let mut ans = 0;
    while st.len() > 0 {
        ans += 1;
        let nw = *st.iter().next().unwrap();
        st.remove(&nw);
        let mut nxs = st.clone();
        let mut val = a[nw];
        for &x in nxs.iter() {
            if val < a[x] {
                st.remove(&x);
            }
        }
    }
    println!("{}", ans);
}