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.

Constraints

* 1 ≤ n ≤ 100000
* 0 ≤ ai ≤ 109

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.

Examples

Input

5
5
1
3
2
4


Output

3


Input

3
1
1
1


Output

1
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MOD = 1e9 + 7;
const int inf = 1e9;
const ll INF = 1e18;
const double pi = 3.14159265358979323846;

int main(){
	int n;cin>>n;
	int a[n];for(int i=0;i<n;i++) cin>>a[i];

	int dp[n];fill(dp,dp+n,inf);
	for(int i=0;i<n;i++){
		*lower_bound(dp,dp+n,a[i])=a[i];
		//for(int i=0;i<n;i++) cout<<dp[i]<<", ";
		//cout<<endl;
	}

	cout<<lower_bound(dp,dp+n,inf)-dp<<endl;
}
