You are given two arrays a and b, both of length n. All elements of both arrays are from 0 to n-1.

You can reorder elements of the array b (if you want, you may leave the order of elements as it is). After that, let array c be the array of length n, the i-th element of this array is c_i = (a_i + b_i) \% n, where x \% y is x modulo y.

Your task is to reorder elements of the array b to obtain the lexicographically minimum possible array c.

Array x of length n is lexicographically less than array y of length n, if there exists such i (1 ≤ i ≤ n), that x_i < y_i, and for any j (1 ≤ j < i) x_j = y_j.

Input

The first line of the input contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in a, b and c.

The second line of the input contains n integers a_1, a_2, ..., a_n (0 ≤ a_i < n), where a_i is the i-th element of a.

The third line of the input contains n integers b_1, b_2, ..., b_n (0 ≤ b_i < n), where b_i is the i-th element of b.

Output

Print the lexicographically minimum possible array c. Recall that your task is to reorder elements of the array b and obtain the lexicographically minimum possible array c, where the i-th element of c is c_i = (a_i + b_i) \% n.

Examples

Input


4
0 1 2 1
3 2 1 1


Output


1 0 0 2 


Input


7
2 5 1 5 3 4 3
2 4 3 5 6 5 1


Output


0 0 0 1 0 2 4 

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


public class Solution
{ 
  public static void minArray(int[] a, int[] b){
        TreeSet<Integer> ts = new TreeSet();
        int n = a.length;
        
         OutputStream outputStream = System.out;
	   PrintWriter out = new PrintWriter(outputStream);
	       
	       for(int i=0; i<n; i++)
	        if(b[i] != 0)
	          ts.add(i);
	          
        for(int i=0; i<n; i++){
           
             int key = n - a[i];
             if(key > ts.last())
               key = ts.first();
             else
              key = ts.ceiling(key);
             
             out.print((a[i]+key)%n+" ");
             b[key]--;
             if(b[key] == 0)
              ts.remove(key);
        }
        
        out.close();
    }
    
	public static void main (String[] args) throws java.lang.Exception
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());
		
		int[] a = new int[n];
		int[] b = new int[n];
		  st = new StringTokenizer(br.readLine()); 
		for(int i=0; i<n; i++)
		 a[i] = Integer.parseInt(st.nextToken());
		  st = new StringTokenizer(br.readLine());
		  for(int i=0; i<n; i++)
		 b[Integer.parseInt(st.nextToken())]++;
		 
		 minArray(a,b);
  }
}