Problem:
Longest Increasing Subsequence

For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.

An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.

Input

n
a0
a1
:
an-1

In the first line, an integer n is given. In the next n lines, elements of A are given.

Output

The length of the longest increasing subsequence of A.

Constraints

1 ≤ n ≤ 100000

0 ≤ ai ≤ 109

Sample Input 1

5
5
1
3
2
4

Sample Output 1

3

Sample Input 2

3
1
1
1

Sample Output 2

1

Solution in C++ (judge verdict: Accepted)

#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;

#define repeat(i,n) for (int i = 0; i < (n); ++i)

#define MAX_N 100000
#define MIN_A 0
ll n;
ll a[MAX_N];
ll len = 0;
ll seq[MAX_N] = {};

int main() {
    cin >> n;
    repeat (i,n) { cin >> a[i]; ++ a[i]; }
    repeat (i,n) {
        ll *p = lower_bound(seq,seq+len,a[i]);
        if (p == seq+len) ++ len;
        *p = a[i];
    }
    cout << len << endl;
    return 0;
}