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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#define rep(i,n)for(int i=0;i<(int)(n);i++)
int main(){
	int n,color,a[100002],b[100002];
	scanf("%d",&n);
	rep(i,n) scanf("%d",&a[i]);//入力終
	rep(i,n+1) b[i]=-1;
	rep(i,n){
		color=0;
		while(a[i]<=b[color]){color++;}
		b[color]=a[i];
	}
	rep(i,n+1){
		if(b[i]==-1){printf("%d",i); return 0;}
	}
}