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>
#include <string.h>
#include <stdbool.h>
#include <stdint.h>
#include <stdlib.h>
int max(const void *a, const void *b){return *(int*)b - *(int*)a;}

int n;
int c[100001];
int ci;

int main(void)
{
    uint32_t a1;

    scanf("%d",&n);
    c[0]=1000000001;
    ci = 0;
    for(int i=0;i<n;i++) 
    {
        int a;
        scanf("%d",&a);

        if(a<=c[ci])
        {
            ci++;
            c[ci] = a;
        }else
        {
            for(int j=ci;j>0;j--)
            {
                if(a < c[j-1] )
                {
                    c[j] = a;
                    break;
                }
            }
        }
    }
    printf("%d\n",ci);

    return 0;
}