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: Wrong Answer)

use input::*;
use std::cmp::*;
use std::io::*;
use std::num::*;
use std::str::*;

mod input {
    use super::*;
    pub fn read<T: FromStr>() -> T {
        stdin()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>()
            .parse::<T>()
            .ok()
            .unwrap()
    }
    pub fn string() -> String {
        read()
    }
    pub fn int() -> i64 {
        read()
    }
    pub fn char() -> char {
        read::<String>().pop().unwrap()
    }
    pub fn vecchar() -> Vec<char> {
        string().chars().collect()
    }
    pub fn vecint(n: i64) -> Vec<i64> {
        let mut vec = Vec::new();
        for i in 0..n {
            vec.push(int())
        }
        vec
    }
}
fn main() {
    let n = int() as usize;
    let a = vecint(n as i64);

    let mut ans = 1;
    let mut cur = a[0];
    let mut min = a[0];
    for i in 1..n {
        if a[i] > cur {
            cur = a[i]
        } else if a[i] == cur {
            ans += 1
        } else if a[i] < cur {
            if min < a[i] {
                min = a[i];
            } else {
                ans += 1;
            }
            cur = a[i]
        }
    }
    println!("{}", ans)
}