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: Time Limit Exceeded)

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

int main() {
	long long int N;
	cin >> N;
	vector<long long int>dp( N + 1, LLONG_MAX / 6 );
	dp[0] = -100;
	for( size_t i = 0; i < N; i++ ) {
		long long int a;
		cin >> a;
		auto dp_ = dp;
		for( size_t j = 0; j < N; j++ ) {
			if( dp[j] < a ) {
				dp[j + 1] = min( dp[j + 1], a );
			} else {
				break;
			}
		}
	}
	long long int ans = 0;
	for( size_t i = 0; i < N + 1; i++ ) {
		if( dp[i] != LLONG_MAX / 6 ) {
			ans = i;
		}
	}
	cout << ans << endl;
}