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"

using ll = long long;

using namespace std;
#define int ll

// 0 -> a-1
#define rep(i, a) for (int i = 0; (i) < (int)(a); (i)++)
// a -> b-1
#define reps(i, a, b) for (int i = (int)(a); (i) < (int)(b); (i)++)
// a-1 -> 0
#define rrep(i, a) for (int i = (int)a - 1; (i) >= 0; (i)--)
// a-1 -> b
#define rreps(i, a, b) for (int i = (int)(a)-1; (i) >= (int)(b); (i)--)
#define MP(a, b) make_pair((a), (b))
#define PB(a) push_back((a))
#define all(v) (v).begin(), (v).end()
// next_permutation(all(v))
#define PERM(v) next_permutation(all(v))
/*sort(all(v));
(v).erase(unique(all(v)), v.end())*/
#define UNIQUE(v)                                                              \
	sort(all(v));                                                              \
	(v).erase(unique(all(v)), v.end())
#define CIN(type, x)                                                           \
	type x;                                                                    \
	cin >> x
#define YES(f)                                                                 \
	if ((f)) {                                                                 \
		cout << "YES" << endl;                                                 \
	} else {                                                                   \
		cout << "NO" << endl;                                                  \
	}
#define Yes(f)                                                                 \
	if ((f)) {                                                                 \
		cout << "Yes" << endl;                                                 \
	} else {                                                                   \
		cout << "No" << endl;                                                  \
	}
#define MINV(v) min_element(all(v))
#define MAXV(v) max_element(all(v))
#define MIN3(a, b, c) min(min(a, b), c)
#define MIN4(a, b, c, d) min(MIN3(a, b, c), d)
#define MIN5(a, b, c, d, e) min(MIN4(a, b, c, d), e)
#define MIN6(a, b, c, d, e, f) min(MIN5(a, b, c, d, e), f)
#define MAX3(a, b, c) max(max(a, b), c)
#define MAX4(a, b, c, d) max(MAX3(a, b, c), d)
#define MAX5(a, b, c, d, e) max(MAX4(a, b, c, d), e)
#define MAX6(a, b, c, d, e, f) max(MAX5(a, b, c, d, e), f)
// b is [a, c)
#define RANGE(a, b, c) ((a) <= (b) && (b) < (c))
// c is [a, e) && d is [b, f)
#define RANGE2D(a, b, c, d, e, f) (RANGE((a), (c), (e)) && RANGE((b), (d), (f)))
#define chmin(a, b) a = min(a, (b))
#define chmin3(a, b, c) a = MIN3(a, (b), (c))
#define chmin4(a, b, c, d) a = MIN4(a, (b), (c), (d))
#define chmin5(a, b, c, d, e) a = MIN5(a, (b), (c), (d), (e))
#define chmin6(a, b, c, d, e, f) a = MIN6(a, (b), (c), (d), (e), (f))
#define chmax(a, b) a = max(a, (b))
#define chmax3(a, b, c) a = MAX3(a, (b), (c))
#define chmax4(a, b, c, d) a = MAX4(a, (b), (c), (d))
#define chmax5(a, b, c, d, e) a = MAX5(a, (b), (c), (d), (e))
#define chmax6(a, b, c, d, e, f) a = MAX6(a, (b), (c), (d), (e), (f))
#define fcout cout << fixed << setprecision(12)
#define RS resize
#define CINV(v, N)                                                             \
	do {                                                                       \
		v.RS(N);                                                               \
		rep (i, N)                                                             \
			cin >> v[i];                                                       \
	} while (0);

#define RCINV(v, N)                                                            \
	do {                                                                       \
		v.RS(N);                                                               \
		rrep (i, N)                                                            \
			cin >> v[i];                                                       \
	} while (0);
#define MOD 1000000007

template <class T> inline T GET()
{
	T x;
	cin >> x;
	return x;
}

void init();
void solve();

signed main()
{
	init();
	solve();
}

const int INF = 1e9;

void init()
{
	int N;
	cin >> N;
	deque<int> dp;
	rep(i, N) {
		int t;
		cin >> t;
		if (dp.size() == 0) {
			dp.push_back(t);
			continue;
		}
		auto itr = lower_bound(all(dp), t);
		if (itr == dp.begin()) {
			dp.push_front(t);
		} else {
			itr--;
			*itr = t;
		}
	}
	cout << dp.size() << endl;
}

void solve()
{
}