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.*;
public class CoveredPointsCount {
    
    
    
    /************************ SOLUTION STARTS HERE ************************/
    
    
    private static void solve() {
        
        int n = nextInt();
        
        HashMap<Long, Integer> start = new HashMap<>();
        HashMap<Long, Integer> end   = new HashMap<>();
        
        for(int i = 0; i < n; i++) {
            start.merge(nextLong(), 1, Integer::sum);
            end.merge(nextLong(), 1, Integer::sum);
        }
        
        long cnt[] = new long[n + 1];
        
        ArrayList<long[]> points = new ArrayList<>(start.size() + end.size());
        
        start.forEach((k , v) -> {
            long point[] = new long[3]; // index, start - 0, end - 1, freq
            point[0] = k;
            point[1] = 0;
            point[2] = v;
            points.add(point);
        });
        
        end.forEach((k , v) -> {
            long point[] = new long[3]; 
            point[0] = k;
            point[1] = 1;
            point[2] = v;
            points.add(point);
        });
        
        Collections.sort(points, (p1, p2) -> p1[0] != p2[0] ? Long.compare(p1[0], p2[0]) : Long.compare(p1[1], p2[1]));
        
//        points.stream().forEach(x -> System.out.println(Arrays.toString(x)));
        
        int curr = (int) points.get(0)[2];
        long prev = points.get(0)[0];
        int prevPt = 0;
        for(int i = 1, len = points.size(); i < len; i++) {
            long pt[] = points.get(i);
            
            if(pt[1] == 0) { // start
                cnt[curr] += pt[0] - prev - prevPt;
                curr += (int) pt[2];
                prevPt = 0;
            }
             else {
                 cnt[curr] += pt[0] - prev + (1 - prevPt);                 
                 curr -= (int) pt[2];
                 prevPt = 1;
             }
            
            prev = pt[0];
//            System.out.println(Arrays.toString(cnt));
        }
        
        for(int i = 1; i <= n; i++)
            print(cnt[i] + " ");
    }
    
    
    
    /************************ SOLUTION ENDS HERE ************************/
    
    
    
    
    
    /************************ TEMPLATE STARTS HERE **********************/
    
    public static void main(String[] args) throws IOException {
        reader = new BufferedReader(new InputStreamReader(System.in));
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)), false);
        st     = null;
        solve();
        reader.close();
        writer.close();
    }
    
    static BufferedReader reader;
    static PrintWriter    writer;
    static StringTokenizer st;
    
    static String next()
    {while(st == null || !st.hasMoreTokens()){try{String line = reader.readLine();if(line == null){return null;}            
    st = new StringTokenizer(line);}catch (Exception e){throw new RuntimeException();}}return st.nextToken();}
    static String nextLine()  {String s=null;try{s=reader.readLine();}catch(IOException e){e.printStackTrace();}return s;}             
    static int    nextInt()   {return Integer.parseInt(next());}
    static long   nextLong()  {return Long.parseLong(next());}     
    static double nextDouble(){return Double.parseDouble(next());}
    static char   nextChar()  {return next().charAt(0);}
    static int[]  nextIntArray(int n)         {int[] a= new int[n];   int i=0;while(i<n){a[i++]=nextInt();}  return a;}
    static long[] nextLongArray(int n)        {long[]a= new long[n];  int i=0;while(i<n){a[i++]=nextLong();} return a;}    
    static int[]  nextIntArrayOneBased(int n) {int[] a= new int[n+1]; int i=1;while(i<=n){a[i++]=nextInt();} return a;}            
    static long[] nextLongArrayOneBased(int n){long[]a= new long[n+1];int i=1;while(i<=n){a[i++]=nextLong();}return a;}            
    static void   print(Object o)  { writer.print(o);  }
    static void   println(Object o){ writer.println(o);}
    
    /************************ TEMPLATE ENDS HERE ************************/
    
}