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: Accepted)

#include<bits/stdc++.h>
using namespace std;
#define MAX 100000

int n,A[MAX+1],L[MAX];
int lis(){
  L[0]=A[0];
  int length=1;
  for(int i=1;i<n;i++){
    if(L[length-1]<A[i]){L[length++]=A[i];}
    else{*lower_bound(L,L+length,A[i])=A[i];}
  }
  return length;
}

int main(){
  cin >> n;
  for(int i=0;i<n;i++)cin >> A[i];
  cout << lis() << endl;
}