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 Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
	    Scanner sc=new Scanner(System.in);
	    PrintWriter out=new PrintWriter(System.out);
	   // BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	    int t=1;
	   // t=sc.nextInt();
	  //  int t=Integer.parseInt(br.readLine());
	    while(--t>=0){
	        int n=sc.nextInt();
	         int a[]=new int[n];
	        for(int i=0;i<n;i++)a[i]=sc.nextInt();
	        TreeSet<Integer> tree=new TreeSet<>();
	        int freq[]=new int[n];
	        for(int i=0;i<n;i++){
	            int q=sc.nextInt();
	            tree.add(q);
	            freq[q]++;
	        }
	        for(int i=0;i<n;i++){
	            int l=(a[i]+tree.first())%n;
	            if(tree.contains(n-a[i])){
	               out.print(0+" ");
	               freq[n-a[i]]--;
	               if(freq[n-a[i]]<=0)
	               tree.remove(n-a[i]);
	            }
	            else{
	                if(tree.higher(n-a[i])==null){
	                    out.print(l+" ");
	                    int z=tree.first();
	                    freq[z]--;
	                    if(freq[z]<=0)
	                    tree.remove(z);
	                }
	                else{
	                    int r=(a[i]+tree.higher(n-a[i]))%n;
	                    if(l<r){
	                        out.print(l+" ");
	                    int z=tree.first();
	                    freq[z]--;
	                    if(freq[z]<=0)
	                    tree.remove(z);
	                    }
	                    else{
	                           out.print(r+" ");
	                    int z=tree.higher(n-a[i]);
	                    freq[z]--;
	                    if(freq[z]<=0)
	                    tree.remove(z);
	                        
	                        
	                    }
	                }
	                
	            }
	            
	            
	        }
	            out.println();
	        out.close();
	    }
	    
	}
}
