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: Wrong Answer)

#include <stdio.h>
int main(){
	int n,i,a[100002],ans=1,last;
	scanf("%d",&n);
	for(i=0;i<n;i++)scanf("%d",&a[i]);
	last=-1;
	for(i=n-2;i>=0;i--){ //逆から
		if(a[i]>=a[i+1]&&a[i]<last)last=a[i+1]; //かなり前のに継続
		else if(a[i]>=a[i+1]){last=a[i+1];ans++;} //新色
    }
	printf("%d", ans);
}