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.util.*;
import java.io.*;

import static java.lang.Math.*;

public class Educfs46C {

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        StringBuilder sb = new StringBuilder();
        int n = sc.nextInt();
        Point[] points = new Point[2*n];
        for (int i = 0; i < n; i++) {
            long start = sc.nextLong();
            long end = sc.nextLong()+1;
            points[i*2] = new Point(1, start);
            points[i*2+1] = new Point(-1, end);
        }
        long[] ans = new long[n+1];
        Arrays.sort(points);
        long prev = -1;
        int currSeg = 0;
        for (int i = 0; i < 2*n; i++) {
            // add to total any time when curr loc != prev loc
            if (points[i].loc != prev) {
                ans[currSeg] += points[i].loc - prev;
                prev = points[i].loc;
            }
            currSeg += points[i].type;
        }
        for (int i = 1; i <= n; i++) {
            sb.append(ans[i] + " ");
        }

        System.out.print(sb);
    }
    static class Point implements Comparable<Point>{
        int type;
        long loc;
        public Point(int _type, long _loc) {
            type = _type;
            loc = _loc;
        }
        public int compareTo(Point o) {
            return Long.compare(loc, o.loc);
        }
    }


    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }

        public FastScanner() {
            this(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

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

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