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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;
import java.util.function.*;

public class Main {
    static In in = new In();
    static Out out = new Out();
    static final long inf = 0x1fffffffffffffffL;
    static final int iinf = 0x3fffffff;
    static final double eps = 1e-9;
    static long mod = 1000000007;

    void solve(boolean naive) {
        int n = in.nextInt();
        List<IntPair> posX = new ArrayList<>();
        List<IntPair> posY = new ArrayList<>();
        List<IntPair> input = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            IntPair pair = new IntPair(in.nextInt() - 1, in.nextInt() - 1);
            posX.add(pair);
            posY.add(pair);
            input.add(pair);
        }
        posX.sort(Comparator.comparingInt(pair -> pair.first));
        posY.sort(Comparator.comparingInt(pair -> pair.second));
        SegmentTree<Integer> tree = new SegmentTree<>(Monoid.MAX_INTEGER);
        LazySegmentTree<Integer, Integer> id = new LazySegmentTree<>(Monoid.SUM_INTEGER, Monoid.SET_INTEGER, (a, b, len) -> b);
        List<Integer> list = new ArrayList<>();
        for (IntPair pair : posY) {
            list.add(pair.first);
        }
        tree.build(list);
        id.build(n, -1);
        int index = 0;
        int[] size = new int[n + 1];
        for (int i = 0; i < n; i++) {
            int left = posX.get(i).first;
            int right = tree.get(posX.get(i).second, n);
            Integer newId = id.get(left);
            if (newId == -1) {
                newId = index++;
            }
            id.update(left, right + 1, newId);
            size[newId]++;
        }
        for (int i = 0; i < n; i++) {
            out.println(size[id.get(input.get(i).first)]);
        }
    }

    public static void main(String[] args) {
        new Main().solve(args.length == 1 && args[0].equals("naive"));
        out.flush();
    }
}

class LazySegmentTree<T, U> {
    private boolean isBuilt;
    private List<T> node;
    private List<U> lazy;
    private int n;
    private int m;
    private int height;
    private final Monoid<T> monoidNode;
    private final Monoid<U> monoidLazy;
    private final Merge<T, U> mergeFunction;

    LazySegmentTree(Monoid<T> monoidNode, Monoid<U> monoidLazy, Merge<T, U> mergeFunction) {
        this.monoidNode = monoidNode;
        this.monoidLazy = monoidLazy;
        this.mergeFunction = mergeFunction;
    }

    void build(int m) {
        build(m, i -> monoidNode.identity());
    }

    void build(int m, T init) {
        build(m, i -> init);
    }

    void build(List<T> data) {
        build(data.size(), data::get);
    }

    void build(int m, IntFunction<T> initFunc) {
        this.m = m;
        this.n = Integer.highestOneBit(m) * 2;
        this.height = Integer.bitCount(n - 1);
        this.node = new ArrayList<>(n * 2);
        this.lazy = new ArrayList<>(n * 2);
        for (int i = 0; i < n; i++) {
            node.add(null);
        }
        for (int i = 0; i < n; i++) {
            node.add(i < m ? initFunc.apply(i) : monoidNode.identity());
        }
        for (int i = n - 1; i > 0; i--) {
            node.set(i, monoidNode.merge(node.get(i * 2), node.get(i * 2 + 1)));
        }
        for (int i = 0; i < n * 2; i++) {
            lazy.add(monoidLazy.identity());
        }
        this.isBuilt = true;
    }

    void update(int i, U x) {
        update(i, i + 1, x);
    }

    void update(int l, int r, U x) {
        checkBuilt();
        for (int i = height; i > 0; i--) {
            propagate((l + n) >> i);
            propagate((r + n - 1) >> i);
        }
        for (int ll = l + n, rr = r + n; ll < rr; ll /= 2, rr /= 2) {
            if (ll % 2 == 1) {
                lazy.set(ll, monoidLazy.merge(lazy.get(ll), x));
                propagate(ll);
                ll++;
            }
            if (rr % 2 == 1) {
                rr--;
                lazy.set(rr, monoidLazy.merge(lazy.get(rr), x));
                propagate(rr);
            }
        }
        for (int ll = (l + n) / 2, rr = (r + n - 1) / 2; ll > 0; ll /= 2, rr /= 2) {
            if (monoidLazy.equalsIdentity(lazy.get(ll))) {
                node.set(ll, monoidNode.merge(merge(ll * 2), merge(ll * 2 + 1)));
            }
            if (monoidLazy.equalsIdentity(lazy.get(rr))) {
                node.set(rr, monoidNode.merge(merge(rr * 2), merge(rr * 2 + 1)));
            }
        }
    }

    T get(int i) {
        return get(i, i + 1);
    }

    T get(int l, int r) {
        checkBuilt();
        for (int i = height; i > 0; i--) {
            propagate((l + n) >> i);
            propagate((r + n - 1) >> i);
        }
        T vl = monoidNode.identity();
        T vr = monoidNode.identity();
        for (int ll = l + n, rr = r + n; ll < rr; ll /= 2, rr /= 2) {
            if (ll % 2 == 1) {
                vl = monoidNode.merge(vl, merge(ll));
                ll++;
            }
            if (rr % 2 == 1) {
                rr--;
                vr = monoidNode.merge(merge(rr), vr);
            }
        }
        return monoidNode.merge(vl, vr);
    }

    List<T> getAll() {
        List<T> all = new ArrayList<>();
        for (int i = 0; i < m; i++) {
            all.add(get(i));
        }
        return all;
    }

    int binarySearch(Predicate<T> predicate) {
        return binarySearch(0, m, predicate);
    }

    int binarySearch(int l, int r, Predicate<T> predicate) {
        checkBuilt();
        if (l < 0 || m < r || l >= r) {
            return -1;
        }
        for (int i = height; i > 0; i--) {
            propagate((l + n) >> i);
            propagate((r + n - 1) >> i);
        }
        T res = monoidNode.identity();
        int offset = l;
        for (int i = l + n; i < n * 2 && offset < r; ) {
            T t = monoidNode.merge(res, merge(i));
            if (rangeRight(i) <= r && !predicate.test(t)) {
                res = t;
                offset = rangeRight(i++);
                if (i % 2 == 0) {
                    i /= 2;
                }
            } else {
                i *= 2;
            }
        }
        return offset;
    }

    private void propagate(int k) {
        if (monoidLazy.equalsIdentity(lazy.get(k))) {
            return;
        }
        node.set(k, merge(k));
        if (k < n) {
            lazy.set(k * 2, monoidLazy.merge(lazy.get(k * 2), lazy.get(k)));
            lazy.set(k * 2 + 1, monoidLazy.merge(lazy.get(k * 2 + 1), lazy.get(k)));
        }
        lazy.set(k, monoidLazy.identity());
    }

    private T merge(int i) {
        if (monoidLazy.equalsIdentity(lazy.get(i))) {
            return node.get(i);
        } else {
            return mergeFunction.merge(node.get(i), lazy.get(i), range(i));
        }
    }

    private int rangeRight(int k) {
        return ((k ^ Integer.highestOneBit(k)) + 1) * range(k);
    }

    private int range(int k) {
        return 1 << (height - Integer.bitCount(Integer.highestOneBit(k) - 1));
    }

    private void checkBuilt() {
        if (!isBuilt) {
            throw new IllegalStateException("segment tree is not built");
        }
    }

    @Override
    public String toString() {
        return getAll().toString();
    }

    interface Merge<T, U> {
        T merge(T t, U u, int length);
    }
}

class IntPair implements Comparable<IntPair> {
    int first;
    int second;

    IntPair(int first, int second) {
        this.first = first;
        this.second = second;
    }

    @Override
    public boolean equals(Object o) {
        if (!(o instanceof IntPair)) {
            return false;
        }
        IntPair that = (IntPair)o;
        return first == that.first && second == that.second;
    }

    @Override
    public int hashCode() {
        return first * 31 + second;
    }

    @Override
    public int compareTo(IntPair o) {
        return first == o.first ? Integer.compare(second, o.second) : Integer.compare(first, o.first);
    }

    @Override
    public String toString() {
        return String.format("[%d, %d]", first, second);
    }
}

class SegmentTree<T> {
    private boolean isBuilt;
    private final Monoid<T> monoid;
    private List<T> node;
    private int n;
    private int m;
    private int[] left;
    private int[] right;

    SegmentTree(Monoid<T> monoid) {
        this.monoid = monoid;
    }

    void build(int m) {
        build(m, i -> monoid.identity());
    }

    void build(int m, T init) {
        build(m, i -> init);
    }

    void build(List<T> data) {
        build(data.size(), data::get);
    }

    void build(int m, IntFunction<T> initFunc) {
        this.m = m;
        this.n = Integer.highestOneBit(m * 2 - 1);
        this.node = new ArrayList<>(n * 2);
        this.left = new int[n * 2];
        this.right = new int[n * 2];
        for (int i = 0; i < n; i++) {
            node.add(null);
        }
        for (int i = 0; i < n; i++) {
            node.add(i < m ? initFunc.apply(i) : monoid.identity());
            left[i + n] = i;
            right[i + n] = i + 1;
        }
        for (int i = n - 1; i > 0; i--) {
            node.set(i, monoid.merge(node.get(i * 2), node.get(i * 2 + 1)));
            left[i] = left[i * 2];
            right[i] = right[i * 2 + 1];
        }
        this.isBuilt = true;
    }

    void set(int i, T value) {
        checkBuilt();
        i += n;
        node.set(i, value);
        while (i > 1) {
            i >>= 1;
            node.set(i, monoid.merge(node.get(i * 2), node.get(i * 2 + 1)));
        }
    }

    T get(int i) {
        checkBuilt();
        return node.get(i + n);
    }

    T get(int l, int r) {
        checkBuilt();
        l += n;
        r += n;
        T xl = monoid.identity();
        T xr = monoid.identity();
        while (l < r) {
            if (l % 2 == 1) {
                xl = monoid.merge(xl, node.get(l++));
            }
            if (r % 2 == 1) {
                xr = monoid.merge(node.get(--r), xr);
            }
            l >>= 1;
            r >>= 1;
        }
        return monoid.merge(xl, xr);
    }

    // check(get(0,index-1)) && !check(get(0,index)
    int binarySearchLeft(Predicate<T> predicate) {
        return binarySearchLeft(0, n, predicate);
    }

    int binarySearchLeft(int l, int r, Predicate<T> predicate) {
        checkBuilt();
        T current = monoid.identity();
        for (int i = l + n; i < n * 2 && l < r; ) {
            T t = monoid.merge(current, node.get(i));
            if (right[i] <= r && predicate.test(t)) {
                current = t;
                l = right[i];
                i++;
                if (i % 2 == 0) {
                    i >>= 1;
                }
            } else {
                i <<= 1;
            }
        }
        return l < r ? l + 1 : -1;
    }

    // !check(get(index-1,n)) && check(get(index,n)
    int binarySearchRight(Predicate<T> predicate) {
        return binarySearchRight(0, n, predicate);
    }

    int binarySearchRight(int l, int r, Predicate<T> predicate) {
        checkBuilt();
        T current = monoid.identity();
        for (int i = r + n - 1; i < n * 2 && l < r; ) {
            T t = monoid.merge(node.get(i), current);
            if (left[i] >= l && predicate.test(t)) {
                current = t;
                r = left[i];
                i--;
                if (i % 2 == 1) {
                    i >>= 1;
                }
            } else {
                i = i * 2 + 1;
            }
        }
        return l < r ? r : -1;
    }

    List<T> getAll() {
        return new ArrayList<>(node.subList(n, n + m));
    }

    private void checkBuilt() {
        if (!isBuilt) {
            throw new IllegalStateException("segment tree is not built");
        }
    }

    @Override
    public String toString() {
        return getAll().toString();
    }
}

class Monoid<T> {
    static final Monoid<Integer> SET_INTEGER = new Monoid<>((Integer)null, (a, b) -> b);
    static final Monoid<Integer> SUM_INTEGER = new Monoid<>(0, Integer::sum);
    static final Monoid<Integer> PRODUCT_INTEGER = new Monoid<>(1, (a, b) -> a * b);
    static final Monoid<Integer> XOR_INTEGER = new Monoid<>(0, (a, b) -> a ^ b);
    static final Monoid<Integer> GCD = new Monoid<>(0, (a, b) -> {
        if (b == 0) {
            return a;
        }
        while (a % b != 0) {
            int t = a % b;
            a = b;
            b = t;
        }
        return b;
    });
    static final Monoid<Integer> MIN_INTEGER = new Monoid<>(Main.iinf, Math::min);
    static final Monoid<Integer> MAX_INTEGER = new Monoid<>(-Main.iinf, Math::max);
    static final Monoid<Long> SET_LONG = new Monoid<>((Long)null, (a, b) -> b);
    static final Monoid<Long> SUM_LONG = new Monoid<>(0L, Long::sum);
    static final Monoid<Long> PRODUCT_LONG = new Monoid<>(1L, (a, b) -> a * b);
    static final Monoid<Long> XOR_LONG = new Monoid<>(0L, (a, b) -> a ^ b);
    static final Monoid<Long> MIN_LONG = new Monoid<>(Main.inf, Math::min);
    static final Monoid<Long> MAX_LONG = new Monoid<>(-Main.inf, Math::max);
    static final Monoid<Long> SUM_MOD = new Monoid<>(0L, (a, b) -> (a + b) % Main.mod);
    private T identity;
    private Supplier<T> identitySupplier;
    private BinaryOperator<T> operation;

    Monoid(BinaryOperator<T> operation) {
        this.operation = operation;
    }

    Monoid(T identity, BinaryOperator<T> operation) {
        this(operation);
        this.identity = identity;
    }

    Monoid(Supplier<T> identitySupplier, BinaryOperator<T> operation) {
        this(operation);
        this.identitySupplier = identitySupplier;
    }

    T merge(T x, T y) {
        T identity = identity();
        if (Objects.equals(x, identity)) {
            if (Objects.equals(y, identity)) {
                return identity;
            }
            return y;
        } else if (Objects.equals(y, identity)) {
            return x;
        } else {
            return operation.apply(x, y);
        }
    }

    public T identity() {
        return identitySupplier == null ? identity : identitySupplier.get();
    }

    public boolean equalsIdentity(T obj) {
        return Objects.equals(obj, identity());
    }
}

class In {
    private BufferedReader reader = new BufferedReader(new InputStreamReader(System.in), 0x10000);
    private StringTokenizer tokenizer;

    String next() {
        try {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }
        } catch (IOException ignored) {
        }
        return tokenizer.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    char[] nextCharArray() {
        return next().toCharArray();
    }

    char[][] nextCharGrid(int n, int m) {
        char[][] a = new char[n][m];
        for (int i = 0; i < n; i++) {
            a[i] = next().toCharArray();
        }
        return a;
    }

    int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    int[] nextIntArray(int n, IntUnaryOperator op) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsInt(nextInt());
        }
        return a;
    }

    long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextLong();
        }
        return a;
    }

    long[] nextLongArray(int n, LongUnaryOperator op) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsLong(nextLong());
        }
        return a;
    }

    List<List<Integer>> nextEdges(int n, int m) {
        List<List<Integer>> res = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            res.add(new ArrayList<>());
        }
        for (int i = 0; i < m; i++) {
            int u = nextInt() - 1;
            int v = nextInt() - 1;
            res.get(u).add(v);
            res.get(v).add(u);
        }
        return res;
    }
}

class Out {
    private PrintWriter out = new PrintWriter(System.out);
    boolean autoFlush = false;

    void println(Object... a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (Object obj : a) {
            joiner.add(String.valueOf(obj));
        }
        out.println(joiner);
        if (autoFlush) {
            out.flush();
        }
    }

    void println(char[] s) {
        out.println(String.valueOf(s));
        if (autoFlush) {
            out.flush();
        }
    }

    void println(int[] a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (int i : a) {
            joiner.add(Integer.toString(i));
        }
        out.println(joiner);
        if (autoFlush) {
            out.flush();
        }
    }

    void println(long[] a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (long i : a) {
            joiner.add(Long.toString(i));
        }
        out.println(joiner);
        if (autoFlush) {
            out.flush();
        }
    }

    void flush() {
        out.flush();
    }
}