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>
         
int main(){
         int N;
          scanf("%d",&N);
         int a[200001][2];
    int i;
    for(i=0;i<N;i++){
        scanf("%d",&a[i][0]);
        a[i][1]=0;
    }

i=1;
int j;
while(i<N){
    for(j=i;j<N;j++){
        if(a[i-1][1]==a[j][1] && a[i-1][0]>=a[j][0]){
            a[j][1]++; 
    }

    }
    i++;
}

int tmp;
tmp=0;
for(i=0;i<N;i++){
    if(a[i][1]>tmp)tmp=a[i][1];
}
    printf("%d\n",tmp+1);



return 0;
}