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.io.*;
public class Solution {
	
	
        
  
  public static void main(String[] args){
    Scanner sc=new Scanner(System.in);
    int n = sc.nextInt();
    int a[]=new int[n];
   
    for(int i=0;i<n;i++) {
    	a[i]=sc.nextInt();	
    }
    int f[]=new int[n];
    TreeSet<Integer> b=new TreeSet<>();
    for(int i=0;i<n;i++) {
    	int x=sc.nextInt();
    	f[x]++;
    	b.add(x);
    }
 
    for(int i=0;i<n;i++) {
    	int x=n-a[i];
    	Integer y=b.ceiling(x);
    	if(y==null)
		y=b.first();
    	a[i]=(a[i]+y)%n;
    	f[y]--;
	if(f[y]==0)
		b.remove(y);
    }
  
    
    for(int x:a)
    	System.out.print(x+" ");
    System.out.println();
    
    
  }
}