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>
using namespace std;
#define int long long
#define double long double
#define fo(a,b) for(int a=0;a<b;a++)
#define Sort(a) sort(a.begin(),a.end())
#define rev(a) reverse(a.begin(),a.end())
#define fi first
#define se second
#define co(a) cout<<a<<endl
#define sz size()
#define bgn begin()
#define en end()
#define pb push_back
#define pp() pop_back()
#define V vector
#define P pair
#define V2(a,b,c) V<V<int>> a(b,V<int>(c))
#define V2a(a,b,c,d) V<V<int>> a(b,V<int>(c,d))
#define incin(a) int a; cin>>a
#define yuko(a) setprecision(a)
#define uni(a) a.erase(unique(a.begin(),a.end()),a.end())
#define pri priority_queue
#define Pri priority_queue<int,vector<int>,greater<int>>
#define ff fi.fi
#define fs fi.se
#define sf se.fi
#define ss se.se
#define all(a)  (a).begin(),(a).end()
#define Pi P<int,int>
#define elif else if
int low(V<int> a,int b){
  decltype(a)::iterator c=lower_bound(a.begin(),a.end(),b);
  int d=c-a.bgn;
  return d;
}
int upp(V<int> a,int b){
  decltype(a)::iterator c=upper_bound(a.begin(),a.end(),b);
  int d=c-a.bgn;
  return d;
}
template<class T>
 void cou(vector<vector<T>> a){
  int b=a.size();
  int c=a[0].size();
  fo(i,b){
    fo(j,c){
      cout<<a[i][j];
      if(j==c-1)
        cout<<endl;
      else
        cout<<' ';
    }
  }
}
int wari(int a,int b) {
  if(a%b==0)
    return a/b;
  else
    return a/b+1;
}
int keta(int a){
  double b=a;
  b=log10(b);
  int c=b;
  return c+1;
}
int souwa(int a){
  return a*(a+1)/2;
}
int gcm(int a,int b){
  if(a%b==0)
    return b;
  return gcm(b,a%b);
}
bool prime(int a){
  if(a<2)
    return false;
  else if(a==2)
    return true;
  else if(a%2==0)
    return false;
  double b=sqrt(a);
  for(int i=3;i<=b;i+=2){
    if(a%i==0){
      return false;
    }
  }
  return true;
}
struct Union{
  vector<int> par;
  Union(int a){
  par=vector<int>(a,-1);
  }
  int find(int a){
    if(par[a]<0)
      return a;
    else
      return par[a]=find(par[a]);
  }
  bool same(int a,int b){
    return find(a)==find(b);
  }
  int Size(int a){
    return -par[find(a)];
  }
  void unite(int a,int b){
    a=find(a);
    b=find(b);
    if(a==b)
      return;
    if(Size(b)>Size(a))
      swap<int>(a,b);
    par[a]+=par[b];
    par[b]=a;
  }
};
int ketas(int a){
  string b=to_string(a);
  int c=0;
  fo(i,keta(a)){
    c+=b[i]-'0';
  }
  return c;
}
int lcm(int a,int b){
    return a/gcm(a,b)*b;
}
bool fe(int a,int b){
  a%=10;
  b%=10;
  if(a==0)
    a=10;
  if(b==0)
    b=10;
  if(a>b)
    return true;
  else
    return false;
}
int INF=1000000007;
struct edge{int s,t,d; };
V<int> mojisyu(string a){
  V<int> b(26,0);
  fo(i,a.sz){
    b[a[i]-'a']++;
  }
  return b;
}
int wa2(int a){
  if(a%2==1)
    return a/2;
  return a/2-1;
}
/*signed main(){
  int a,b,c;
  cin>>a>>b>>c;
  V<V<edge>> d(a);
  fo(i,b){
    edge e;
    cin>>e.s>>e.t>>e.d;
    d[e.s].pb(e);
  }
  V<int> e(a,INF);
  e[c]=0;
  priority_queue<P<int,int>,V<P<int,int>>,greater<P<int,int>>> f;
  f.push({0,c});
  int h=INF;
  while(!f.empty()){
    P<int,int> g;
    g=f.top();
    f.pop();
    int v = g.second, i = g.first;
    for(edge l : d[v]){
      if(e[l.t] > i + l.d){
        e[l.t] = i + l.d;
        f.push({i+l.d , l.t});
      }
    }
  }
  fo(i,a){
    if(e[i]==INF)
      cout<<"INF"<<endl;
    else
      cout<<e[i]<<endl;
  }
}
?*/
int nCr(int n,int r){
  int a=1;
  r=min(r,n-r);
  for(int i=n;i>n-r;i--){
    a*=i;
    a/=n-i+1;
  }
  return a;
}
/*void sea(int x,int y){
  if(x<0||a<=x||y<0||b<=y||c[x][y]=='#')
    return;
  if(d[x][y])
    return;
  d[x][y]++;
  sea(x+1,y);
  sea(x-1,y);
  sea(x,y+1);
  sea(x,y-1);
}*/
int kaijou(int a){
  int b=1;
  fo(i,a)
    b*=i+1;
  return b;
}
int nPr(int a,int b){
  int c=1;
  for(int i=a;i>=b;i--)
    c*=i;
  return c;
}
int MOD=INF;
int fac[1000010], finv[1000010], inv[1000010]; 
// テーブルを作る前処理
//先にCOMinit()で前処理をする
//ABC145D
void COMinit() {
  fac[0]=fac[1]=1;
  finv[0]=finv[1]=1;
  inv[1]=1;
  for(int i=2;i<1000010;i++){
    fac[i]=fac[i-1]*i%MOD;
    inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;
    finv[i]=finv[i-1]*inv[i]%MOD;
  }
}
// 二項係数計算
int COM(int n,int k){
  if(n<k)
    return 0;
  if(n<0||k<0)
    return 0;
  return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;
}
signed main(){
  int a;
  cin>>a;
  V<int> b(a);
  fo(i,a)
  cin>>b[i];
  rev(b);
  V<int> dp(a,INF);
  fo(i,a){
    //dp[upp(dp,b[i])]=b[i];
  }
  cout<<low(dp,INF)<<endl;
}