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++11 (judge verdict: Accepted)

#include <iostream>
#include <algorithm>
using namespace std;

int main(){
    int n;
    cin>>n;
    int dp[n+1];
    fill(dp,dp+n+1,1e9);
    for(int i=0;i<n;i++){
        int a;
        cin>>a;
        *lower_bound(dp,dp+n+1,a)=a;
    }
    cout<<lower_bound(dp,dp+n+1,1e9)-dp<<endl;
}