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++14 (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(i,n) for (int i=0; i<(n); ++i)
using namespace std;
typedef long long ll;

template<class T>
int LIS(const vector<T> &a) {
    vector<T> L;
    for (T x : a) {
        auto it = lower_bound(L.begin(), L.end(), x);
        if (it == L.end()) L.push_back(x);
        else *it = x;
    }
    return (int)L.size();
}

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