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;

int DP[100001];
int DS[100001];
int T;
int LIS(){
    int maxan=0;
    for(int k=0;k<T;k++){
        DP[k]=1;
        for(int i=0;i<k;i++){
            if(DS[i]<DS[k])DP[k]=max(DP[k],DP[i]+1);
        }
        maxan = max(maxan,DP[k]);
    }
    return maxan;





}

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cin>>T;

    for(int i=0;i<T;i++)cin>>DS[i];
    cout<<LIS()<<endl;





    return 0;
}