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>
#define REP(i, n) for (int i = 0; i < n; i++)
#define REPR(i, n) for (int i = n; i >= 0; i--)
#define FOR(i, m, n) for (int i = m; i < n; i++)
#define FORR(i, m, n) for (int i = m; i >= n; i--)
#define ALL(x) (x).begin(), (x).end()
const long long INF = 1e18;
using namespace std;
typedef long long ll;
int main() {
  ll N;
  cin >> N;
  ll A[N];
  REP(i, N) { cin >> A[i]; }
  ll max = 0;
  ll r = 0;
  ll next = 0;
  ll ans = 0;
  while (true) {
    FOR(i, r, N) {
      if (A[i] == max) {
        next = i + 1;
        break;
      } else if (A[i] > max) {
        max = A[i];
        next = i + 1;
      }
    }
    if (next == N) {
      ans++;
      break;
    }
    ans++;
    r = next;
    max = 0;
  }
  cout << ans;
  return 0;
}