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 pb push_back
#define eb emplace_back
#define rep(i, a, b) for (long i = (a); i <= (b); ++i)
#define per(i, a, b) for (long i = (a); i >= (b); --i)
#define mmst(v) memset(v, 0, sizeof(v))

const long kMax2 = 109;
const long kMax3 = 1009;
const long kMax4 = 10009;
const long kMax5 = 100009;
const long kMax6 = 1000009;
const long kInfI = 0x3F3F3F3F;
const float kInfF = 1e15;

using namespace std;
using ll = long long;

void solve() {
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(0);

  int n;
  int dplen = 0;
  int dp[kMax5];
  vector<int> a;
  cin >> n;
  rep(i, 0, n - 1) {
    int a_i;
    cin >> a_i;
    a.pb(kInfI - a_i);
  }

  mmst(dp);

  rep(i, 0, n - 1) {
    int idx = upper_bound(dp, dp + dplen, a[i]) - dp;
    dp[idx] = a[i];
    if (idx + 1 > dplen) {
        dplen = idx + 1;
    }
  }

  cout << dplen << endl;

  return 0;
}