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 N;
int f[100001];

void input(int,int);

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

    int A[N];

    int i;
    for(i=0;i<N;i++){
        scanf("%d",&A[i]);
        f[i]=-1;    
        input(0,A[i]);
    }
    

    i=0;
    int count=0;
    while(f[i]>0){
        count++;
    }

    printf("%d",count);

    return 0;
   
}

void input(int i,int a){

    if(f[i]<a){
        f[i]=a;
        return ;
    }else{
        i++;
        input(i,a);
        return ;
    }
}