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) {
    int N;    	//1<=N<=10^5
    int[] A;	//0<=Ai<=10^9
    try(Scanner sc = new Scanner(System.in)) {
      N = sc.nextInt();
      A = new int[N];
      for(int i = 0; i < N; i++) {
        A[i] = sc.nextInt();
      }
    }
    int answer = solve(A);
    System.out.println(answer);
  }

  private static int solve(int[] a) {
    int n = a.length;
    if ( n == 0 ) {
      return 0;
    }
    if ( n == 1 ) {
      return 1;
    }
    int[] a0 = new int[n-1];
    System.arraycopy(a, 1, a0, 0, n-1);
    int v0 = solve(a0);
    boolean bDependent = false;
    for(int elem : a0) {
      if ( a[0] < elem ) {
        bDependent = true;
        break;
      }
    }
    return bDependent ? v0 : (v0+1);
  }
}