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 
/* package codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int arr[]=new int[n];
		for(int i=0;i<n;i++)
		arr[i]=sc.nextInt();
		TreeMap<Integer,Integer> tm=new TreeMap<Integer,Integer>();
		for(int i=0;i<n;i++)
		{
		    int num=sc.nextInt();
		    if(!tm.containsKey(num))
		    {
		        tm.put(num,1);
		    }
		    else
		    {
		        tm.put(num,tm.get(num)+1);
		    }
		}
		for(int i=0;i<n;i++)
		{
		    int n1=arr[i];
		    int j=(n-n1)%n;
		    Integer k=tm.ceilingKey(j);
		    if(k==null)
		    {
		        k=tm.firstKey();
		    }
		    System.out.print((n1+k)%n+" ");
		    if(tm.get(k)>1)
		    {
		        tm.put(k,tm.get(k)-1);
		    }
		    else
		    tm.remove(k);
		}
	}
}
