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 <bits/stdc++.h>
#define REP(i,n) for(int i=0;i<(n);i++)
#define ALL(a)  (a).begin(),(a).end()
#define SORT(c) sort((c).begin(),(c).end())
#define REV(c) reverse((c).begin(),(c).end())

using namespace std;
typedef pair<int,int> P;

// 最大公約数
int64_t gcd(int64_t a, int64_t b) {
  return b != 0 ? gcd(b, a % b) : a;
}

// 最小公倍数
int64_t lcm(int64_t a, int64_t b) {
  return a * b / gcd(a, b);
}

int ctoi(char c){
  return c - '0';
}

int main(){
  int64_t n;
  cin >> n;
  vector<int64_t> vec(n);
  REP(i,n){
    cin >> vec.at(i);
  }
  vector<int64_t> vec2;
  REP(i,n){
    if (vec2.size() == 0){
      vec2.push_back(vec.at(i));
    }else{
      auto tmp = lower_bound(ALL(vec2), vec.at(i)) - vec2.begin();
      if (tmp == 0){
        vec2.insert(vec2.begin(), vec.at(i));
      }else{
        vec2.at(tmp-1) = vec.at(i);
      }
      
    }
  }
  cout << vec2.size() << endl;
  return 0;
}