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 9.2.1) (judge verdict: Accepted)

#include <stdio.h>

int main()
{
	int i, N, A[100001];
	scanf("%d", &N);
	for (i = 1; i <= N; i++) scanf("%d", &(A[i]));
	
	int k, l, r, max[100001] = {A[1]};
	for (i = 2, k = 1; i <= N; i++) {
		if (max[k-1] >= A[i]) max[k++] = A[i];
		else {
			for (l = 0, r = k - 1; l < r; ) {
				if (max[(l+r)/2] < A[i]) r = (l + r) / 2;
				else l = (l + r) / 2 + 1;
			}
			max[l] = A[i];
		}
	}
	
	printf("%d\n", k);
	fflush(stdout);
	return 0;
}