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<bits/stdc++.h>
using namespace std;
const int N=100000;
int dp[100000],a[100000];
signed main(void){
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
		scanf("%d",a+i);
	for(int i=1;i<=n;i++){
		dp[i]=1;
		for(int j=1;j<i;j++)
			if(a[j]<a[i])
				dp[i]=max(dp[i],dp[j]+1);
	}
	int ans=0;
	for(int i=1;i<=n;i++)
		ans=max(ans,dp[i]);
	printf("%d\n",ans);
	return 0;
}