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>
int N,C[100000],i,j,dp[100000],r=0;
int main()
{
	scanf("%d",&N);
	for(i=0;i<N;i++)
		scanf("%d",&C[i]);
	for(i=0;i<N;r=r<dp[i]?dp[i]:r,i++)
		for(dp[i]=1,j=0;j<i;j++)
		{
			if(C[j]<C[i])
				dp[i]=dp[i]<dp[j]+1?dp[j]+1:dp[i];
		}
	printf("%d\n",r);
	return 0;
}