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: Time Limit Exceeded)

#include <stdio.h>

int main() {
  int n;
  scanf("%d", &n);
  int a[n], c[n], ans = 0, j = 0;
  for (int i=0; i<n; i++) scanf("%d", a+i);
  for (int i=n-1; i>=0; i--) {
    for (j=0; j<ans; j++) {
      if (a[i]<c[j]) {
        c[j] = a[i];
        break;
      }
    }
    if (j==ans) c[ans++] = a[i];
  }
  printf("%d\n", ans);
  return 0;
}