CSES Increasing Subsequence solution

 You are given an array containing 

$n$ integers. Your task is to determine the longest increasing subsequence in the array, i.e., the longest subsequence where every element is larger than the previous one.

A subsequence is a sequence that can be derived from the array by deleting some elements without changing the order of the remaining elements.

Input

The first line contains an integer $n$: the size of the array.

After this there are $n$ integers $x_1,x_2,\ldots,x_n$: the contents of the array.

Output

Print the length of the longest increasing subsequence.

Constraints

• $1 \le n \le 2 \cdot 10^5$
• $1 \le x_i \le 10^9$

Example

Input:

8
7 3 5 3 6 2 9 8

Output:

4

#include <bits/stdc++.h>
using namespace std;
void solve(){
    int n;
    cin>>n;
    vector<int> arr(n);
    for(int i=0;i<n;i++){
        cin>>arr[i];
    }
    vector<int> lis;
    for(int i=0;i<n;i++){
        if(lis.empty()||lis.back()<arr[i]){
            lis.push_back(arr[i]);
        }
        else{
            auto it=lower_bound(lis.begin(),lis.end(),arr[i]);
            *it=arr[i];
        }
    }
    cout<<lis.size()<<endl;
}
int main() {
	solve();
 
}