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 {
        br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        int n = nextInt();
        int a[] = new int[n];
        for (int i = 0; i < n; i++) a[i] = nextInt();
        TreeMap<Integer, Integer> b = new TreeMap<>();
        for (int i = 0; i < n; i++) {
            int value = nextInt();
            if (b.containsKey(value)) b.put(value, b.get(value) + 1);
            else b.put(value, 1);
        }
        int c[] = new int[n];
        for (int i = 0; i < n; i++) {
            if (b.ceilingKey(n - a[i]) != null) {
                int u = b.ceilingKey(n - a[i]);
                c[i] = (a[i] + u) % n;
                b.put(u, b.get(u) - 1);
                if (b.get(u) == 0) b.remove(u);
            } else {
                int u = b.ceilingKey(0);
                c[i] = (a[i] + u) % n;
                b.put(u, b.get(u) - 1);
                if (b.get(u) == 0) b.remove(u);
            }
        }
        for (int i = 0; i < n; i++) {
            System.out.print(c[i] + " ");
        }
    }


    static BufferedReader br;

    static StringTokenizer in = new StringTokenizer("");

    static String next() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
}