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: Time Limit Exceeded)

#![allow(unused_imports)]

use std::cell::RefCell;
use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::fmt::{Debug, Formatter, Write as FmtWrite};
use std::io::{stderr, stdin, BufRead, Write};
use std::mem::{replace, swap};
use std::ops::*;
use std::rc::Rc;

// -----------------------------------------------
// Framework <https://github.com/vain0x/procon>
// -----------------------------------------------

//
// Macro debug!
//

#[cfg(debug_assertions)]
include!{"./procon/debug.rs"}

#[cfg(not(debug_assertions))]
macro_rules! debug {
    ($($arg:expr),*) => {};
}

//
// Macro input!
//

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

//
// IteratorExt
//

trait IteratorExt: Iterator + Sized {
    fn vec(self) -> Vec<Self::Item> {
        self.collect()
    }
}

impl<T: Iterator> IteratorExt for T {}


//
// Main
//

fn main() {
    input! {
        n: usize,
        xs: [isize; n],
    }

    let ans = solve(&xs);
    println!("{}", ans);
}

fn solve(xs: &[isize]) -> usize {
    debug!(xs);
    let mut a = 1;
    let mut b = 2;
    loop {
        if try_solve(xs, b) {
            break;
        } else {
            b = min(2 * b, xs.len());
        }
    }
    loop {
        debug!("loop");
        debug!(a);
        debug!(b);
        if b - a <= 1 {
            if try_solve(xs, a) {
                return a;
            } else {
                return b;
            }
        }

        let c = a + (b - a) / 2;
        if try_solve(xs, c) {
            b = c;
        } else {
            a = c;
        }
    }
}

fn try_solve(xs: &[isize], a: usize) -> bool {
    debug!("try_solve");
    debug!(a);
    let mut cs = vec![];
    cs.resize(a, -1);

    'outer: for x in xs {
        let x = *x;
        if let Some(m) = cs.clone().iter().filter(|&&y| y < x).max() {
            let m = *m;
            for i in 0..a {
                if cs[i] == m {
                    cs[i] = x;
                    continue 'outer;
                }
            }
        } else {
            debug!(("false", a, cs));
            return false;
        }
    }

    debug!(("true", a, cs));
    true
}