Problem:
Score : 500 points

Problem Statement

You are given a sequence with N integers: A = \{ A_1, A_2, \cdots, A_N \}.
For each of these N integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied:

If A_i and A_j (i < j) are painted with the same color, A_i < A_j.

Find the minimum number of colors required to satisfy the condition.

Constraints

1 \leq N \leq 10^5

0 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the minimum number of colors required to satisfy the condition.

Sample Input 1

5
2
1
4
5
3

Sample Output 1

2

We can satisfy the condition with two colors by, for example, painting 2 and 3 red and painting 1, 4, and 5 blue.

Sample Input 2

4
0
0
0
0

Sample Output 2

4

We have to paint all the integers with distinct colors.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <algorithm>
#include <iostream>
#include <vector>
#include <queue>

using namespace std;

typedef long long ll;

template<class T>
inline bool chmax(T &a, T b) {
    if(a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
inline bool chmin(T &a, T b) {
    if(a > b) {
        a = b;
        return true;
    }
    return false;
}

int main(void) {
    int N;
    cin >> N;

    vector<int> A(N);
    for (int i = 0; i < N; i++) {
        int v;
        cin >> v;
        A[i] = v;
    }

    deque<int> q;
    for (int i = 0; i < N; i++) {
        auto it = lower_bound(q.begin(), q.end(), A[i]);
        if (it == q.begin()) {
            q.push_front(A[i]);
        } else {
            q[it - q.begin() - 1] = A[i];
        }
    }

    cout << q.size() << endl;

    return 0;
}