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::prelude::*;

fn input<T: std::str::FromStr>() -> T {
    let stdin = std::io::stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}

fn main() {
    let n: usize = input();
    let a: Vec<i32> = (0..n).map(|_| input()).collect();

    let mut v = vec![];
    for i in 0..n {
        let p = v.upper_bound_by(|v| a[i].cmp(v));
        if p == v.len() {
            v.push(a[i]);
        } else {
            v[p] = a[i];
        }
    }

    println!("{}", v.len());
}

trait BinarySearch<T: Ord> {
    fn lower_bound_by<F: FnMut(&T) -> std::cmp::Ordering>(&self, f: F) -> usize;
    fn upper_bound_by<F: FnMut(&T) -> std::cmp::Ordering>(&self, f: F) -> usize;

    fn lower_bound(&self, x: &T) -> usize {
        self.lower_bound_by(|e| e.cmp(x))
    }

    fn lower_bound_by_key<U: Ord, F: FnMut(&T) -> U>(&self, x: &U, mut f: F) -> usize {
        self.lower_bound_by(|e| f(e).cmp(x))
    }

    fn upper_bound(&self, x: &T) -> usize {
        self.upper_bound_by(|e| e.cmp(x))
    }

    fn upper_bound_by_key<U: Ord, F: FnMut(&T) -> U>(&self, x: &U, mut f: F) -> usize {
        self.upper_bound_by(|e| f(e).cmp(x))
    }
}

impl<T: Ord> BinarySearch<T> for [T] {
    fn lower_bound_by<F: FnMut(&T) -> std::cmp::Ordering>(&self, mut f: F) -> usize {
        let mut l = -1 as i64;
        let mut r = self.len() as i64;
        while r - l > 1 {
            let m = ((l + r) / 2) as usize;
            if f(&self[m]) == std::cmp::Ordering::Less {
                l = m as i64;
            } else {
                r = m as i64;
            }
        }
        r as usize
    }

    fn upper_bound_by<F: FnMut(&T) -> std::cmp::Ordering>(&self, mut f: F) -> usize {
        let mut l = -1 as i64;
        let mut r = self.len() as i64;
        while r - l > 1 {
            let m = ((l + r) / 2) as usize;
            if f(&self[m]) == std::cmp::Ordering::Greater {
                r = m as i64;
            } else {
                l = m as i64;
            }
        }
        r as usize
    }
}