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.PrintWriter;
import java.util.Scanner;
import java.util.TreeMap;

public class MinimumArray {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int t = 1;
        for (int i = 0; i < t; i++) {
            solve(sc, pw);
        }
        pw.close();
    }

    static void solve(Scanner in, PrintWriter out){
        int n = in.nextInt();
        int[] arr = new int[n];
        int[] brr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = in.nextInt();
        }
        TreeMap<Integer, Integer> mp = new TreeMap<>();
        for (int i = 0; i < n; i++) {
            brr[i] = in.nextInt();
            mp.put(brr[i], mp.getOrDefault(brr[i], 0) + 1);
        }
        int[] ans = new int[n];
        for (int i = 0; i < n; i++) {
            int t = arr[i];
            int tar = n - t;
            Integer ri = mp.ceilingKey(tar);
            if (ri != null){
                mp.put(ri, mp.getOrDefault(ri, 0) - 1);
                if (mp.get(ri) == 0){
                    mp.remove(ri);
                }
                ans[i] = (t + ri) % n;
            }else{
                Integer head = mp.firstKey();
                mp.put(head, mp.getOrDefault(head, 0) - 1);
                if (mp.get(head) == 0){
                    mp.remove(head);
                }
                ans[i] = (t + head) % n;
            }
        }
        for (int i = 0; i < n; i++) {
            out.print(ans[i]+" ");
        }
        out.println();
    }
}