Problem:
Score : 300 points

Problem Statement

There are N cities on a 2D plane. The coordinate of the i-th city is (x_i, y_i). Here (x_1, x_2, \dots, x_N) and (y_1, y_2, \dots, y_N) are both permuations of (1, 2, \dots, N).

For each k = 1,2,\dots,N, find the answer to the following question:

Rng is in City k.
Rng can perform the following move arbitrarily many times:

move to another city that has a smaller x-coordinate and a smaller y-coordinate, or a larger x-coordinate and a larger y-coordinate, than the city he is currently in.

How many cities (including City k) are reachable from City k?

Constraints

1 \leq N \leq 200,000

(x_1, x_2, \dots, x_N) is a permutation of (1, 2, \dots, N).

(y_1, y_2, \dots, y_N) is a permutation of (1, 2, \dots, N).

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print N lines. In i-th line print the answer to the question when k = i.

Sample Input 1

4
1 4
2 3
3 1
4 2

Sample Output 1

1
1
2
2

Rng can reach City 4 from City 3, or conversely City 3 from City 4.

Sample Input 2

7
6 4
4 3
3 5
7 1
2 7
5 2
1 6

Sample Output 2

3
3
1
1
2
3
2

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#pragma GCC optimize("O3")
#include<bits/stdc++.h> 
using namespace std;
using ll=long long;
using P=pair<ll,ll>;
template<class T> using V=vector<T>; 
#define fi first
#define se second
#define all(v) (v).begin(),(v).end()
const ll inf=(1e18);
//const ll mod=998244353;
const ll mod=1000000007;
const vector<int> dy={-1,0,1,0},dx={0,-1,0,1};
ll GCD(ll a,ll b) {return b ? GCD(b,a%b):a;}
ll LCM(ll c,ll d){return c/GCD(c,d)*d;}
struct __INIT{__INIT(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(20);}} __init;
template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }
template<class T>void debag(const vector<T> &a){cerr<<"debag :";for(auto v:a)cerr<<v<<" ";cerr<<"\n";}
template<class T>void print(const vector<T> &a){for(auto v:a)cout<<v<<" ";cout<<"\n";}
class UF{
public:
	vector<int> par,num;
	int find(int v){
		return (par[v]==v)? v: (par[v]=find(par[v]));
	}
	explicit UF(int N):par(N),num(N,1){
		iota(all(par),0);
	}
	void unite(int u,int v){
		u=find(u),v=find(v);
		if(u==v)return;
		if(num[u]<num[v])swap(u,v);
		num[u]+=num[v];
		par[v]=u;
	}
	bool same(int u,int v){
		return find(u)==find(v);
	}
	bool ispar(int v){
		return v=find(v);
	}
	int size(int v){
		return num[find(v)];
	}
};
template<typename T>
struct BIT{
    //1-index
    //0-indexで取ると無限ループする
    private:
    V<T> arr;
    int n;

    public:
    BIT(int siz){
        n=siz;
        arr.assign(n+1,0);
    }
    //一点更新 aにvを加える
    void add(T a,T v){
        //x+=(x&-x) 初項a,それ以降a<=2^Nが列挙
        for(T x=a;x<=n;x+=(x&-x)){
            arr[x]+=v;
        }
    }
    T sum(T a){
        // 1からaまでの区間和
        T ret=0;
        for(T x=a;x>0;x-=(x&-x))ret+=arr[x];
        return ret;
    }
    T get(T x){//x番目に大きい数　// 区間和がw以上となる最小のindを返す
        if(x<=0) return 0;
        T N=1;
        while(N*2<=n)N*=2;
        T v=0;
        for(T i=N;i>0;i/=2){
            if(v+i<=n&&arr[v+i]<x){
                x-=arr[v+i];
                v+=i;
            }
        }
        return v+1;
    }
    T query(int l,int r){
        return sum(r)-sum(l);
    }
};
int main(){
  ll n;
  cin>>n;
  V<P> d(n);
  map<int,int> mp;
  for(int i=0;i<n;i++){
      cin>>d[i].fi>>d[i].se;
      mp[d[i].se]=i;
  }
  sort(all(d));
  UF uf(n);
  set<int> s,t;
  BIT<int> l(n+5),r(n+5);
  for(int i=1;i<=n;i++){
      r.add(i,1);
      s.insert(i);
  }
  V<int> ans(n,1);
  for(int i=0;i<n;i++){
     auto ite=s.upper_bound(d[i].se);
     auto itt=t.lower_bound(d[i].se);
      if(ite!=s.end()){
          uf.unite(mp[d[i].se],mp[*ite]);
      } 
      if(itt!=t.begin()){
          itt--;
          uf.unite(mp[d[i].se],mp[*itt]);
      }
      s.erase(d[i].se);
      t.insert(d[i].se);
  }
  for(int i=0;i<n;i++){
      cout<<uf.size(i)<<"\n";
  }
}