Problem:
Longest Increasing Subsequence

For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.

An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.

Input

n
a0
a1
:
an-1

In the first line, an integer n is given. In the next n lines, elements of A are given.

Output

The length of the longest increasing subsequence of A.

Constraints

1 ≤ n ≤ 100000

0 ≤ ai ≤ 109

Sample Input 1

5
5
1
3
2
4

Sample Output 1

3

Sample Input 2

3
1
1
1

Sample Output 2

1

Solution in C (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
int dp(int i,int n,int a[],int d[]);
int main()
{
    int n,i,t,ans=0;
    scanf("%d",&n);
    int a[n],d[n];
    for(i=0;i<n;i++)
        scanf("%d",&a[i]);
    memset(d,0,sizeof(d));
    d[n-1]=1;
    for(i=0;i<n;i++)
    {
        t=dp(i,n,a,d);
        ans=ans>t?ans:t;
    }
    printf("%d\n",ans);
    return 0;
}
int dp(int i,int n,int a[],int d[])
{
    int j;
    if(i==n)
        return 0;
    if(d[i]>0)
        return d[i];
    d[i]=1;
    for(j=i+1;j<n;j++)
        if(a[i]<a[j])
            d[i]=d[i]>dp(j,n,a,d)+1?d[i]:dp(j,n,a,d)+1;
    return d[i];
}