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 BillCalculator {

    public static void decreaseKeyCount(TreeMap<Integer, Integer>map, int key){
        map.put(key, map.get(key) - 1);

        if(map.get(key) == 0)
            map.remove(key);
    }

    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        StringTokenizer st;
        int a[] = new int[n + 1];
        int b[] = new int[n + 1];

        st = new StringTokenizer(br.readLine());

        for(int i = 1;i <= n;i++){
            a[i] = Integer.parseInt(st.nextToken());
        }

        st = new StringTokenizer(br.readLine());
        TreeMap<Integer, Integer>map = new TreeMap<>();

        for(int i = 1;i <= n;i++){
            b[i] = Integer.parseInt(st.nextToken());
            if(map.containsKey(b[i]))
                map.put(b[i], map.get(b[i]) + 1);
            else map.put(b[i], 1);
        }

        StringBuilder sb = new StringBuilder();

        for(int i = 1;i <= n;i++){

            int diffLast = n - a[i];

            Integer key = map.ceilingKey(diffLast);

            if(key != null){
                sb.append((a[i] + key - n) + " ");
                decreaseKeyCount(map, key);
            }
            else {
                Integer smallestKey = map.firstKey();
                sb.append((smallestKey + a[i]) + " ");
                decreaseKeyCount(map, smallestKey);
            }
        }
        System.out.println(sb.toString());
    }
}