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>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#define MAX_N 100000

typedef struct {
  int ID;
  int A;
} st_nums;

int a_sort(const void *a, const void *b) {
  int X = ((st_nums*)a)->A - ((st_nums*)b)->A;
  if(X == 0) {
    return (((st_nums*)a)->ID - ((st_nums*)b)->ID);
  } else {
    return X;
  }
}
	     
int main(void) {
  int N;
  scanf("%d", &N);

  st_nums NUMS[MAX_N];
  for(int i = 0; i < N; i++) {
    NUMS[i].ID = i;
    scanf("%d", &NUMS[i].A);
  }
  qsort(NUMS, N, sizeof(st_nums), a_sort);
  for(int i = 0; i < N; i++) {
    printf("A=%d ID=%d\n", NUMS[i].A, NUMS[i].ID);
  }
    
  int COL_NUM = 0;
  st_nums COMPS[MAX_N];
  for(int i = 0; i < N; i++) {
    bool add = true;
    for(int j = 0; j < COL_NUM; j++) {
      if(COMPS[j].ID < NUMS[i].ID && COMPS[j].A < NUMS[i].A) {
	COMPS[j].A  = NUMS[i].A;
	COMPS[j].ID = NUMS[i].ID;
	add = false;
	break;
      }
    }
    if(add) {
      COMPS[COL_NUM].ID = NUMS[i].ID;
      COMPS[COL_NUM].A  = NUMS[i].A;
      COL_NUM++;
    }
  }

  printf("%d\n", COL_NUM);
  return 0;
}