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>
#define max(a,b) (a)>(b)?a:b
#define N 100000
int n,l[N],i,j,dp[N];
int main()
{

	scanf("%d",&n);
	for(i=0;i<n;i++)
		scanf("%d",&l[i]),dp[i]=1;
	for(i=0;i<n;i++)
		for(j=i;j<n;j++)
			if(l[i]<l[j])
				dp[j]=max(dp[j],dp[i]+1);
	for(i=j=0;i<n;i++)
		j=max(j,dp[i]);
	printf("%d\n",j);
	return 0;
}