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 int
#define ff first
#define ss second
#define pb push_back

ll bexp(ll a, ll b)
{
	ll res = 1;
	while(b)
	{
		if(b & 1)
			res = res * a;
		a *= a;
		b >>= 1;
		if(res > 1000 || res <= 0)
			return 10000;
	}
	return res;
}

#define N 100100
#define M 400010

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(NULL);

	int n;
	cin >> n;

	pair<ll, ll> a[n];
	ll b[n] = {}, ans = 0;
	for (int i = 0; i < n; ++i)
	{
		cin >> a[i].ff;
		a[i].ss = i;
	}

	sort(a, a + n);

	for (int i = 0; i < n; ++i)
	{
		int k = a[i].ss;
		ans++;
		if(k == 0)
		{
			while(i + 1 < n && a[i + 1].ff == a[i].ff)
				ans++, i++;
			break;
		}
	}
	cout << ans;
	return 0; 
}