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) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        int n = Integer.parseInt(in.readLine());
        int[] a = new int[n];
        StringTokenizer st = new StringTokenizer(in.readLine());
        for (int i = 0; i < n; i++) a[i] = Integer.parseInt(st.nextToken());
        TreeMap<Integer, Integer> map = new TreeMap<>();
        st = new StringTokenizer(in.readLine());
        for (int i = 0; i < n; i++) {
            int x = Integer.parseInt(st.nextToken());
            if (map.containsKey(x)) {
                map.put(x, map.get(x)+1);
            } else {
                map.put(x, 1);
            }
            //System.out.println("KEY: " + x + " VAL: " + map.get(x));
        }
        for (int i = 0; i < n; i++) {
            int query = (n-a[i])%n;
            int ans = -1;
            if (map.ceilingEntry(query) != null) {
                ans = map.ceilingEntry(query).getKey();
            } else {
                ans = map.ceilingEntry(0).getKey();
            }
            //System.out.println("Q: " + query + " A: " + ans);
            map.put(ans, map.get(ans)-1);
            //System.out.println((map.get(ans) == null) + " bc ans=" + ans);
            //System.out.println(map.get(1));
            if (map.get(ans) == 0) {
                map.remove(ans);
            }
            if (i > 0) out.print(' ');
            out.print((a[i]+ans)%n);
        }
        out.print('\n');
        out.close();
    }

}
/*

 */
