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 
//package codeforces.div2;

import java.util.Map;
import java.util.Scanner;
import java.util.TreeMap;

public class MinimumArray {

    static public void print(int arr[], int brr[]) {


        TreeMap<Integer, Integer> map = new TreeMap<>();

        for(int i = 0; i < brr.length; i++) {
            map.put(brr[i], map.getOrDefault(brr[i], 0) + 1);
        }

        int crr[] = new int[arr.length];
        for(int i = 0; i < arr.length; i++) {

            Integer min = map.ceilingKey( arr.length - arr[i]);
            if(min != null) {
                crr[i] = (min + (arr[i]))%arr.length;
                if (map.get(min) == 1) {
                    map.remove(min);
                } else {
                    Integer val = map.get(min);
                    map.put(min, val - 1);
                }
            } else {
                min = map.ceilingKey(0);
                crr[i] = (min + (arr[i]))%arr.length;
                if (map.get(min) == 1) {
                    map.remove(min);
                } else {
                    Integer val = map.get(min);
                    map.put(min, val - 1);
                }
            }
        }

        for(int i = 0; i < arr.length; i++) {
            System.out.print(crr[i] + " ");
        }
    }

    public static void main(String []args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int i = 0;
        int arr[] = new int[n];
        int brr[] = new int[n];
        while ( i < n) {
            arr[i++] = sc.nextInt();
        }
        i = 0;
        while ( i < n) {
            brr[i++] = sc.nextInt();
        }
        print(arr, brr);
    }
}
