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>
#include<stdlib.h>
#include<string.h>
#define df 0


int main(){
  int n;
  scanf("%d",&n);
  int a[n],i,max=-1,c,j=0;
  for(i=0;i<n;i++){
    scanf("%d",&c);
    if(max<c){
      max=c;
      continue;
    }
    a[j++]=c;
  }
  n=j;
  int dp[n+1],len=0;
  dp[0]=1000000010;dp[1]=-1;
  for(i=0;i<n;i++){
    int j=len;
    for(j=len+1;j>0;j--){
      if(a[i]>dp[j-1] || dp[j]>=a[i]){
	if(df) printf("[%d]%d %d %d :not ordered\n",j,dp[j],a[i],dp[j-1]);
	continue;
      }
      dp[j]=a[i];
      if(j!=len+1)continue;
      len++;
      dp[1+len]=-1;
    }
  }
  printf("%d\n",len+1);
  if(df){
    for(i=0;i<=len;i++){
      printf(" %d ",dp[i]);
    }
  }
  return 0;
}


/// confirm df==0 ///