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

public class Main {
    public static void main(String[] args){
        InputStream  inputstream;
        OutputStream outputstream;
        inputstream = System.in;
        outputstream = System.out;
        InputReader in = new InputReader(inputstream);
        PrintWriter out = new PrintWriter(outputstream);
        Task solver = new Task();
        solver.solve(in,out);
        out.close();
    }

    static class Task{
        public void solve(InputReader in,PrintWriter out){
            int n;
            n = in.nextInt();
            int[] a = new int[n + 1];
            int[] b = new int[n + 1];
            TreeMap <Integer,Integer> tmap = new TreeMap <Integer,Integer> ();
            for(int i = 0;i < n;++i){
                a[i] = in.nextInt();
            }
            for(int i = 0;i < n;++i){
                b[i] = in.nextInt();
                if(!tmap.containsKey(b[i])){
                    tmap.put(b[i],1);
                } else {
                    tmap.replace(b[i],tmap.get(b[i]) + 1);
                }
            }
            for(int i = 0;i < n;++i){
                if(tmap.ceilingKey(n - a[i]) != null){
                    Map.Entry <Integer,Integer> t = tmap.ceilingEntry(n - a[i]);
                    out.print((a[i] + t.getKey()) % n + " ");
                    if(t.getValue() == 1){
                        tmap.remove(t.getKey());
                    } else {
                        tmap.replace(t.getKey(),t.getValue() - 1);
                    }
                } else {
                    out.print((a[i] + tmap.firstKey()) % n + " ");
                    if(tmap.get(tmap.firstKey()) == 1){
                        tmap.remove(tmap.firstKey());
                    } else {
                        tmap.replace(tmap.firstKey(),tmap.get(tmap.firstKey()) - 1);
                    }
                }
            }
        }
    }

    static class InputReader{
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream){
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public String next(){
            while(tokenizer == null || !tokenizer.hasMoreTokens()){
                try{
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e){
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt(){
            return Integer.parseInt(next());
        }

        public long nextLong(){
            return Long.parseLong(next());
        }

        public  double nextDouble(){
            return Double.parseDouble(next());
        }

        public String nextLine(){
            String ret_str = "";
            try {
                ret_str = reader.readLine();
            } catch (IOException e){
                e.printStackTrace();
            }
            return ret_str;
        }
    }
}
