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 namespace std;
#define rep(i, n)  for(long long i=0;i<(long long)(n);i++)
#define REP(i,k,n) for(long long i=k;i<(long long)(n);i++)
#define all(a) a.begin(),a.end()
#define eb emplace_back
#define pb push_back
#define lb(v,k) (lower_bound(all(v),k)-v.begin())
#define ub(v,k) (upper_bound(all(v),k)-v.begin())
typedef long long ll;
typedef pair<ll,ll> P;
#define se second
#define fi first
struct PP{ll fi;ll se;ll th;};
typedef multiset<ll> S;
typedef priority_queue<ll> PQ;
typedef priority_queue<P,vector<P>,greater<P>> SPQ;
using vi=vector<ll>;
using vvi=vector<vector<ll>>;
const ll inf=1001001001001001;
const int INF=1001001001;
const int mod=1000000007;
bool chmin(auto &a,auto b){if(a>b){a=b;return true;}return false;}
bool chmax(auto &a,auto b){if(a<b){a=b;return true;}return false;}
void outvi(vi v){rep(i,v.size()){if(i)cout<<' ';cout<<v[i];}cout<<endl;}
void outvvi(vvi v){rep(i,v.size()){rep(j,v[i].size()){if(j)cout<<' ';cout<<v[i][j];}cout<<endl;}}
int main(){
    ll n;cin>>n;
    vi v(n);
    rep(i,n)cin>>v[i];
    rep(i,n)v[i]*=-1;
    vi dp(n,inf);
    rep(i,n)dp[ub(dp,v[i])]=v[i];
    cout<<lb(dp,inf)<<endl;
}