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(void){
  int N;
  scanf("%d", &N);

  int A[N];
  for (int i = 0; i < N; i++) {
    scanf("%d", &A[i]);
  }

  for (int i = 0; i < N-1; i++) {
    if(A[i] < A[i+1]) break;
    if(i == N-2){
      printf("%d\n", N);
      return 0;
    }
  }

  int flag[N];
  for (int i = 0; i < N; i++) {
    flag[i] = 0;
  }

  int ans = 0;
  for (int i = 0; i < N; i++) {
    if(flag[i] ==  1) continue;
    ans++;
    int cnt = 0;
    int max = A[i];
    for (int j = i; j < N; j++) {
      if(max < A[j]){
        max = A[j];
        cnt++;
        flag[j] = 1;
      }
    }
  }


  printf("%d\n", ans-1);

  return 0;
}