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: Wrong Answer)

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

bool chmax(long long &a, long long b){
    if(a <= b){
        a = b;
        return true;
    }else{
        return false;
    }
}

int main(){
    int N;
    cin >> N;
    vector<long long> A(N);
    for(int i = 0; i < N; i++)cin >> A[i];
    reverse(A.begin(), A.end());
    long long now = A[0];
    int cnt = 1;
    for(int i = 1; i < N; i++){
        if(chmax(now, A[i])){
            cnt++;
        }
    }
    cout << cnt << endl;
    return 0;
}