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 E {

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        Solver solver = new Solver();
        solver.solve(in, out);
        out.close();
    }

    private static class Solver {

        private void solve(InputReader in, PrintWriter out) {
            int n = in.nextInt();

            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = in.nextInt();

            TreeMap<Integer, Integer> b = new TreeMap<>();
            for (int i = 0; i < n; i++) {
                int x = in.nextInt();
                b.putIfAbsent(x, 0);
                b.put(x, b.get(x) + 1);
            }

            for (int i = 0; i < n; i++) {
                Integer k = b.ceilingKey((n - a[i]) % n);
                if (k == null)
                    k = b.firstKey();

                out.print((a[i] + k) % n + " ");

                if (b.get(k) == 1) {
                    b.remove(k);
                } else {
                    b.put(k, b.get(k) - 1);
                }
            }
            out.println();
        }
    }

    private static class InputReader {
        private BufferedReader br;
        private StringTokenizer st;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
        }

        private int nextInt() {
            return Integer.parseInt(next());
        }

        private long nextLong() {
            return Long.parseLong(next());
        }

        private double nextDouble() {
            return Double.parseDouble(next());
        }

        private String nextLine() {
            String s = "";
            try {
                s = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return s;
        }

        private String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
    }
}