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: Runtime Error)

import java.util.*;
public class Main {
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[][] A = new int[N][2];
		for(int i = 0; i < N; i++) {
			A[i][0] = i+1;
			A[i][1] = sc.nextInt();
		}
		Arrays.sort(A, (x,y) -> x[1]-y[1]);
		for(int i = 1; i < N; i++) {
			if(A[i][1] > A[i-1][1])
				A[i][1] = A[i-1][1] + 1;
			else
				A[i][1] = A[i-1][1];
		}
		int q = A[0][1];
		for(int i = 0; i < N; i++)
			A[i][1] -= q;
		int newN = A[N-1][1];
		int[] a = new int[newN+1];
		Arrays.sort(A, (x,y) -> x[0]-y[0]);
		TreeSet<Integer> ts = new TreeSet<>();
		ts.add(A[0][1]);
		a[A[0][1]]++;
		for(int i = 1; i < N; i++) {
			if(A[i][1] < ts.first()) {
				ts.add(A[i][1]);
				a[A[i][1]]++;
			}
			else {
				ts.add(A[i][1]);
				int x = ts.lower(A[i][1]);
				ts.remove(x);
				a[A[i][1]]++;
				a[x]--;
				if(a[x] > 0)
					ts.add(x);
			}
		}
		int ans = 0;
		for(int i = 0; i <= newN; i++)
			ans += a[i];
		System.out.println(ans);

	}

}