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 <cstdio>
#include <cstdint>
#include <vector>
#include <algorithm>
#include <utility>
#include <string>
#include <tuple>
#include <set>
#include <map>
#include <queue>

int main() {
  size_t N;
  scanf("%zu", &N);

  std::vector<int> a(N);
  for (auto& ai: a) scanf("%d", &ai);

  int const inf = 2e9;

  std::multiset<int> b;
  for (size_t i = 0; i < N; ++i) {
    auto it = b.lower_bound(a[i]);
    if (it == b.begin()) {
      b.insert(a[i]);
      continue;
    }
    b.erase(--it);
    b.insert(a[i]);
  }
  printf("%zu\n", b.size());
}