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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import static java.lang.Math.*;
import java.math.BigInteger;

public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		
		// 入力
		int n = sc.nextInt();
		int[] a = new int[n];
		for(int i = 0; i < n; i++){
		    a[i] = sc.nextInt();
		}

		// 計算
		int result = 0;
		TreeMap<Integer, Integer[]> tm = new TreeMap<Integer, Integer[]>();
		for(int i = 0; i < n; i++){
		    if(i == 0){
		        Integer[] list = {1, 0};
		        tm.put(a[i], new Integer[]{1, 0});
		    }else{
		        if(a[i-1] < a[i]) continue;
		        if(tm.containsKey(a[i-1])){
		            tm.get(a[i-1])[1]++;
		        }else{
		            tm.put(a[i-1], new Integer[]{0, 1});
		        }
		        if(tm.containsKey(a[i])){
		            tm.get(a[i])[0]++;
		        }else{
		            tm.put(a[i], new Integer[]{1, 0});
		        }
		    }
		    if(i == n-1){
		        if(tm.containsKey(a[i])){
		            tm.get(a[i])[1]++;
		        }else{
		            tm.put(a[i], new Integer[]{0, 1});
		        }
		    }
		}
		int cnt = 0;
		for(Integer i : tm.keySet()){
		    cnt += tm.get(i)[0];
		    result = max(result, cnt);
		    cnt -= tm.get(i)[1];
		}
		// 出力
		System.out.println(result);
		
	}
}