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;

int main() {

    int n, len = 0;

    cin >> n;

    int num[n], dp[n];

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

    dp[0] = num[0];
    for(int i = 1; i < n; ++i) {
        if(dp[len] < num[i]) {
            dp[++len] = num[i];
        } else {
            *lower_bound(dp, dp + len, num[i]) = num[i];
        }
    }

    cout << len + 1 << endl;

}