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 C (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>
#include <limits.h>
#include <stdlib.h>
#include <math.h>

int main(void)
{
	long int i, j;
	long int n, d;
	long int count;
	long int flg;
	long int min;
	long int a[100000];
	long int b[100000];
	
	scanf("%ld", &n);
	
	scanf("%ld", &a[0]);
	
	b[0] = a[0];
	count = 1;
	min = a[0];
	
	for(i = 1; i < n; i++) {
		scanf("%ld", &a[i]);
		flg = 0;
		if(a[i] <= min) {
			min = a[i];
			b[count] = a[i];
			count++;
			continue;
		}
		for(j = 0; j < count; j++) {
			if(b[j] < a[i]) {
				flg = 1;
				b[j] = a[i];
				break;
			}
		}
		if(flg == 0) {
			b[count] = a[i];
			count++;
		}
	}
	
	printf("%ld\n", count);
	
	return 0;
}