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 Main
{
    public static void main(String args[])throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw=new PrintWriter(System.out);
        int n=Integer.parseInt(br.readLine());
        String str[]=br.readLine().split(" ");
        int a[]=new int[n];
        for(int i=0;i<n;i++)
        a[i]=Integer.parseInt(str[i]);
        str=br.readLine().split(" ");
        int b[]=new int[n];
        for(int i=0;i<n;i++)
        b[i]=Integer.parseInt(str[i]);
        TreeMap<Integer,Integer> tmap=new TreeMap<>();
        TreeSet<Integer> ts=new TreeSet<>();
        for(int i=0;i<n;i++)
        {
            ts.add(b[i]);
            tmap.put(b[i],tmap.getOrDefault(b[i],0)+1);
        }
        int res[]=new int[n];
        for(int i=0;i<n;i++)
        {
            int req=(n-a[i])%n;
            if(ts.ceiling(req)!=null)
            {
                int num=ts.ceiling(req);
                res[i]=(num+a[i])%n;
                if(tmap.get(num)==1)
                {
                    tmap.remove(num);
                    ts.remove(num);
                }
                else
                tmap.put(num,tmap.get(num)-1);
            }
            else
            {
                int num=ts.ceiling(0);
                res[i]=(num+a[i])%n;
                if(tmap.get(num)==1)
                {
                    tmap.remove(num);
                    ts.remove(num);
                }
                else
                tmap.put(num,tmap.get(num)-1);
            }
        }
        for(int i=0;i<n;i++)
        pw.print(res[i]+" ");
        pw.println();
        pw.flush();
        pw.close();
    }
}