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 max(int a,int b){return a > b ? a: b;}
int main(){
    int n, i = 0;
    scanf("%d",&n);
    int a[n];
    for(; i < n; i++)
        scanf("%d",&a[i]);
    int ans = 0,count = 0;
    for(i = 0; i < n - 1; i++){
        if(a[i] >= a[i + 1])
            count ++;
        else 
            count = 0;
        ans = max(ans, count);
    }
    printf("%d\n",ans + 1);
    return 0;
}