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>

int asc(const void *a, const void *b) {
  return *(int *)b - *(int *)a;
}

int main(){
   int n,h[100000],m,i,j,lo,mi,hi;
    
   scanf("%d",&n);
   scanf("%d",&h[0]);
   m=1;
   for (i=1;i<n;i++) {
      scanf("%d",&j);
      if (j<=h[m-1]) {
         h[m]=j;
         m++;
         continue;
      }
      lo=0;hi=m-1;
      while (hi>=lo) {
         mi=(lo+hi)/2;
         if (j<=h[mi]) lo=mi+1;
         else          hi=mi-1;
      }
      if (mi>0 && j>h[mi-1]) mi--;
      h[mi]=j;
      if (mi>0 && h[mi]>=h[mi-1])
         qsort(h,mi,sizeof(int),asc);
   }
   printf("%d\n",m);
   return 0;
}