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

int lis(const vector<int>& A) {
    int n = A.size();
    vector<int> L(n, 0);
    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.begin(), L.begin() + length, A[i]) = A[i];
    }
    return length;
}

int main(void) {
    int n;
    cin >> n;
    vector<int> a(n, 0);
    for (int i = 0; i < n; i++) {
        int ai;
        cin >> ai;
        a[i] = ai;
    }
    cout << lis(a) << endl;
    return 0;
}