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 INF 2147483647
#define INFF 9223372036854775807
#define ll long long
#define pb push_back
#define REP(i,n) for(int i=0;i<n;i++)
#define REPP(i,m,n) for(int i=m;i<n;i++)
#define ALL(N) (N.begin(),N.end())

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int N, cnt=0;
  cin >> N;
  vector<int> A(N);
  REP(i,N) cin >> A[i];
  REP(i,N-1) {
    if(A[i]>=A[i+1]) cnt++;
  }
  if(cnt+1==A.size()) cout << cnt+1 << endl;
  else cout << cnt << endl;
}