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;
#define ll long long
#define pb push_back
#define F first
#define S second
const int mod = 1e9 + 7, A = 5e5 + 2;

int main() {
    ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0);
    int n;
    cin >> n;
    int a[n], acc[n], mx = 0;
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }
    map <int, bool> mop;
    int ans = 0;
    for (int i = n - 1; i >= 0; i--) {
        if (i == n - 1) acc[i] = i;
        if (mx > a[i])
            acc[i] = acc[i + 1];
        else
            acc[i] = i;
        if (!mop[acc[i]]) mop[acc[i]] = 1, ans++;
    }
    cout << ans;
    return 0;
}