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 std::io::Read;
use std::collections::BTreeMap;

fn main() {
  let mut buf = String::new();

  std::io::stdin().read_to_string(&mut buf).unwrap();

  let mut iter = buf.split_whitespace();

  let n: usize = iter.next().unwrap().parse().unwrap();

  let mut colors: BTreeMap<usize, usize> = BTreeMap::new();

  let mut first = true;

  let arr = (0..n)
      .map(|_| iter.next().unwrap().parse().unwrap())
      .collect::<Vec<usize>>();

  arr
      .iter()
      .fold(0, |before, n| {
        let now = *n;
        if first {
          first = false;
          return now;
        }

        if before < now {
          return now;
        }
        
        let cs = &mut colors;

        let mut color_min: Option<usize> = None;
        for c in cs.keys().rev() {
          if before < *c {
            color_min = Some(*c);
            break;
          }
        }
        if let Some(c_min) = color_min {
          *cs.get_mut(&c_min).unwrap() -= 1;
        }

        *cs.entry(before).or_insert(0) += 1;

        now
      });

  {
    let cs = &mut colors;
    
    let mut color_min: Option<usize> = None;
    for c in cs.keys().rev() {
      if *arr.last().unwrap() < *c {
        color_min = Some(*c);
        break;
      }
    }
    if let Some(c_min) = color_min {
      *cs.get_mut(&c_min).unwrap() -= 1;
    }

    *cs.entry(*arr.last().unwrap()).or_insert(0) += 1;
  }
  
  println!("{}", colors.values().sum::<usize>())
}