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)

// abc134c: Exception Handling
#include <stdio.h>

#define upto(i,s,e,d) for(int i=(s);i<=(e);i+=(d))
#define downto(i,s,e,d) for(int i=(s);i>=(e);i-=(d))
#define in(n) scanf("%d",n)
#define out(d) printf("%d\n",d)

int search(int k, int *a, int l, int r){
  if(l>=r) return l;
  if(k>a[l]) return l;
  int m=(l+r)/2;
  int i = search(k,a,l,m);
  if(i>=0 && k>a[i]) return i;
  return search(k,a,m+1,r);
}

int main(){
  int n;in(&n);
  int g[n],gn=1;in(g);
  upto(i,1,n-1,1){
    int a;in(&a);
    int j = search(a,g,0,gn);
    if(j>=gn) j=gn++;
    g[j]=a;
  }
  out(gn);
  return 0;
}