You are given n segments on a coordinate line; each endpoint of every segment has integer coordinates. Some segments can degenerate to points. Segments can intersect with each other, be nested in each other or even coincide.

Your task is the following: for every k ∈ [1..n], calculate the number of points with integer coordinates such that the number of segments that cover these points equals k. A segment with endpoints l_i and r_i covers point x if and only if l_i ≤ x ≤ r_i.

Input

The first line of the input contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of segments.

The next n lines contain segments. The i-th line contains a pair of integers l_i, r_i (0 ≤ l_i ≤ r_i ≤ 10^{18}) — the endpoints of the i-th segment.

Output

Print n space separated integers cnt_1, cnt_2, ..., cnt_n, where cnt_i is equal to the number of points such that the number of segments that cover these points equals to i.

Examples

Input

3
0 3
1 3
3 8


Output

6 2 1 


Input

3
1 3
2 4
5 7


Output

5 2 0 

Note

The picture describing the first example:

<image>

Points with coordinates [0, 4, 5, 6, 7, 8] are covered by one segment, points [1, 2] are covered by two segments and point [3] is covered by three segments.

The picture describing the second example:

<image>

Points [1, 4, 5, 6, 7] are covered by one segment, points [2, 3] are covered by two segments and there are no points covered by three segments.
import java.io.*;
import java.util.*;

public class C {
    String fileName = "<name>";

    public static class Event implements Comparable<Event> {
        public static final int OPEN_TYPE = 0;
        public static final int CLOSE_TYPE = 1;

        public long x;
        public int type;

        public Event(long x, int type) {
            this.x = x;
            this.type = type;
        }

        @Override
        public int compareTo(Event event) {
            if (Long.compare(x, event.x) != 0)
                return Long.compare(x, event.x);
            else
                return Integer.compare(type, event.type);
        }
    }

    public void solve() throws IOException {
        int n = nextInt();
        Event[] events = new Event[2 * n];
        Map<Long, Integer> cnt = new HashMap<>((int) 1e6, 1f);
        for (int i = 0; i < n; i++) {
            long l = nextLong();
            long r = nextLong();
            events[2 * i] = new Event(l, Event.OPEN_TYPE);
            events[2 * i + 1] = new Event(r, Event.CLOSE_TYPE);
        }
        Arrays.sort(events);
        long prevX = 0;
        int balance = 0;
        long[] ans = new long[n + 1];
        for (int i = 0; i < 2 * n; i++) {
            Event event = events[i];
            cnt.putIfAbsent(event.x, 0);
            ans[balance] += Math.max(event.x - prevX - 1, 0);
            int finalBalance = balance;
            cnt.computeIfPresent(event.x, (k, v) -> Math.max(v, finalBalance));
            if (event.type == Event.OPEN_TYPE) {
                balance++;
            } else {
                balance--;
            }
            int finalBalance2 = balance;
            cnt.computeIfPresent(event.x, (k, v) -> Math.max(v, finalBalance2));
            prevX = event.x;
        }
        cnt.forEach((k, v) -> {
            ans[v]++;
        });
        for (int i = 1; i <= n; i++) {
            out.print(ans[i]);
            out.print(" ");
        }
    }

    public void run() {
        try {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);

            solve();

            out.close();
        } catch (IOException e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    BufferedReader br;
    StringTokenizer in;
    PrintWriter out;

    public String nextToken() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    public static void main(String[] args) throws IOException {
        Locale.setDefault(Locale.US);
        new C().run();
    }
}