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 IOException{
        //BufferedReader f = new BufferedReader(new FileReader("uva.in"));
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int n = Integer.parseInt(f.readLine());
        int[] a = new int[n];
        StringTokenizer st = new StringTokenizer(f.readLine());
        for(int i = 0; i < n; i++) {
            a[i] = Integer.parseInt(st.nextToken());
        }
        TreeMap<Integer, Integer> b = new TreeMap<>();
        st = new StringTokenizer(f.readLine());
        for(int i = 0; i < n; i++) {
            int temp = Integer.parseInt(st.nextToken());
            b.put(temp, b.getOrDefault(temp, 0)+1);
        }
        int[] c = new int[n];
        for(int i = 0; i < n; i++) {
            Integer temp = b.higherKey(n-a[i]-1);
            if(temp == null) {
                temp = b.firstKey();
            }
            c[i] = (a[i]+temp)%n;
            b.put(temp, b.get(temp)-1);
            if(b.get(temp) == 0) {
                b.remove(temp);
            }
        }
        out.print(c[0]);
        for(int i = 1; i < n; i++) {
            out.print(" " + c[i]);
        }
        out.println();
        f.close();
        out.close();
    }
}
