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 with AC Library v1.1) (judge verdict: Time Limit Exceeded)

#line 2 "header.hpp"

//%snippet.set('header')%
//%snippet.fold()%
#ifndef HEADER_H
#define HEADER_H

// template version 2.0
using namespace std;
#include <bits/stdc++.h>

// varibable settings
const long long INF = 1e18;
template <class T> constexpr T inf = numeric_limits<T>::max() / 2.1;

#define _overload3(_1, _2, _3, name, ...) name
#define _rep(i, n) repi(i, 0, n)
#define repi(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i)
#define rep(...) _overload3(__VA_ARGS__, repi, _rep, )(__VA_ARGS__)
#define _rrep(i, n) rrepi(i, 0, n)
#define rrepi(i, a, b) for (ll i = (ll)((b)-1); i >= (ll)(a); --i)
#define r_rep(...) _overload3(__VA_ARGS__, rrepi, _rrep, )(__VA_ARGS__)
#define each(i, a) for (auto &&i : a)
#define all(x) (x).begin(), (x).end()
#define sz(x) ((int)(x).size())
#define pb(a) push_back(a)
#define mp(a, b) make_pair(a, b)
#define mt(...) make_tuple(__VA_ARGS__)
#define ub upper_bound
#define lb lower_bound
#define lpos(A, x) (lower_bound(all(A), x) - A.begin())
#define upos(A, x) (upper_bound(all(A), x) - A.begin())
template <class T, class U> inline void chmax(T &a, const U &b) { if ((a) < (b)) (a) = (b); }
template <class T, class U> inline void chmin(T &a, const U &b) { if ((a) > (b)) (a) = (b); }
template <typename X, typename T> auto make_table(X x, T a) { return vector<T>(x, a); }
template <typename X, typename Y, typename Z, typename... Zs> auto make_table(X x, Y y, Z z, Zs... zs) { auto cont = make_table(y, z, zs...); return vector<decltype(cont)>(x, cont); }

#define cdiv(a, b) (((a) + (b)-1) / (b))
#define is_in(x, a, b) ((a) <= (x) && (x) < (b))
#define uni(x) sort(all(x)); x.erase(unique(all(x)), x.end())
#define slice(l, r) substr(l, r - l)

typedef long long ll;
typedef long double ld;
using vl = vector<ll>;
using vvl = vector<vl>;
using pll = pair<ll, ll>;

template <typename T>
using PQ = priority_queue<T, vector<T>, greater<T>>;
void check_input() { assert(cin.eof() == 0); int tmp; cin >> tmp; assert(cin.eof() == 1); }

#if defined(PCM) || defined(LOCAL)
#else
#define dump(...) ;
#define dump_1d(...) ;
#define dump_2d(...) ;
#define cerrendl ;
#endif

#endif /* HEADER_H */
//%snippet.end()%
#line 2 "solve.cpp"
template<class T=ll> using vec = vector<T>;
struct Fast { Fast() { std::cin.tie(0); ios::sync_with_stdio(false); } } fast;

#include <atcoder/dsu>
using namespace atcoder;

template<class T>/*{{{*/
void pairsort(vector<T>& x, vector<T>& y, vector<T>& z){
    ll n = sz(x);
    vector<tuple<T, T, T>> t(n);
    rep(i, n){
        t[i] = make_tuple(x[i], y[i], z[i]);
    }
    sort(all(t));
    rep(i, n){
        x[i] = get<0>(t[i]);
        y[i] = get<1>(t[i]);
        z[i] = get<2>(t[i]);
    }
}/*}}}*/

// snippet:UnionFind {{{
struct UnionFind {
    vector<int> par;   // par[x]: parent of x. if root, -size.
    int gcount;         // count of groups

    UnionFind() {}
    UnionFind(int _n) : par(_n, -1), gcount(_n) {}
    bool merge(int x, int y) { 
        x = root(x);
        y = root(y);
        if (x != y) {
            if (par[y] < par[x]) swap(x, y);
            par[x] += par[y];
            par[y] = x;
            gcount--;
        }
        return x != y;
    } 
    int root(int x) {
        if (is_root(x)){
            return x;
        }
        else{
            return par[x] = root(par[x]);  // 経路圧縮
            // return root(par[x]);         // 経路圧縮なし
        }
    }
    bool is_root(int x) { return par[x] < 0; }
    bool same(int x, int y) { return root(x) == root(y); }
    int size(int x) { return -par[root(x)]; }

#if defined(PCM) || defined(LOCAL)  // {{{
    friend ostream& operator<<(ostream& os, UnionFind& uf) {
        map<int, vector<int>> group;
        rep(i, sz(uf.par)) { group[uf.root(i)].pb(i); }
        os << endl;
        each(g, group) { os << g << endl; }
        return os;
    }
#endif  // }}}
};
// snippet:UnionFind }}}

int solve() {
    ll n;cin>>n;
    vl x(n), y(n), z(n);
    rep(i, n){
        cin>>x[i]>>y[i];
        z[i] = i;
    }
    pairsort(x, y, z);
    dump(x);
    dump(y);
    dump(z);
    UnionFind uf(n);

    set<pll> st;
    st.insert(mp(1e7, -1));
    rep(i, n){
        cerrendl;
        auto rter = upper_bound(all(st), mp(y[i], i));
        if (rter == st.begin()){
            st.insert(mp(y[i], i));
        }
        else{
            ll remi = st.begin()->second;
            uf.merge(remi, i);
            dump(i, remi, i);
            for(auto lter=next(begin(st)); lter!=rter;){
                // 処理
                uf.merge(remi, lter->second);
                dump(i, remi, lter->second);
                // 終了処理
                lter = st.erase(lter);
            }
        }
        dump(st);
    }

    vl ans(n);
    rep(i, n){
        dump(i, uf.size(i), z[i]);
        ans[z[i]] = uf.size(i);
    }
    rep(i, n){
        cout << ans[i] << endl;
    }

    return 0; 
}


int main(){/*{{{*/
    solve();
    check_input();
    return 0;
}/*}}}*/