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

public class E1157 {
    public static void main(String[] args) throws IOException{
        StringBuffer ans = new StringBuffer();
        StringTokenizer st;
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        st = new StringTokenizer(f.readLine());
        int n = Integer.parseInt(st.nextToken());
        st = new StringTokenizer(f.readLine());
        int[] arr = new int[n];
        for(int i = 0; i < n; i++){
            arr[i] = Integer.parseInt(st.nextToken());
        }
        st = new StringTokenizer(f.readLine());
        TreeSet<Integer> treeSet = new TreeSet<>();
        HashMap<Integer, Integer> hash = new HashMap<>();
        for(int x = 0; x < n; x++){
            int ft = Integer.parseInt(st.nextToken());
            if(!hash.containsKey(ft)) hash.put(ft, 0);
            hash.put(ft, hash.get(ft)+1);
            treeSet.add(ft);
        }
        f.close();
        for(int i = 0; i < n; i++){
            Integer r = treeSet.ceiling(0);
            Integer x = treeSet.ceiling(n-arr[i]);
            if(x != null){
                if(hash.get(x) == 1)
                    treeSet.remove(x);
                hash.put(x,hash.get(x)-1);
                arr[i]+=x;
                arr[i]%=n;
            }else{
                if(hash.get(r) == 1)
                    treeSet.remove(r);
                hash.put(r,hash.get(r)-1);
                arr[i]+=r;
                arr[i]%=n;
            }
        }
        for(int i : arr)
            ans.append(i).append(" ");



        System.out.println(ans);
    }

}