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.*;
import java.util.stream.*;

public class ProblemE {
    private static boolean debug = false;

    private static int N;
    private static int[] A, B;

    private static void solveProblem(InputStream instr) {
        Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(instr)));
        int testCount = 1;
        if (debug) {
            testCount = sc.nextInt();
        }
        for (int t = 1; t <= testCount; t++) {
            N = sc.nextInt();
            A = readInts(sc, N);
            B = readInts(sc, N);
            Object result = solveTestCase();
            System.out.println(result);
        }
    }

    private static Object solveTestCase() {

        TreeMap<Integer, Integer> tree = new TreeMap<>();
        for (int i = 0; i < N; i++) {
            tree.putIfAbsent(B[i], 0);
            tree.put(B[i], tree.get(B[i]) + 1);
        }

        List<String> values = new ArrayList<>();
        for (int i = 0; i < N; i++) {
            Integer k = tree.ceilingKey((N - A[i]));
            if (k == null)
                k = tree.firstKey();

            values.add(String.valueOf((A[i] + k) % N));

            if (tree.get(k) == 1) {
                tree.remove(k);
            } else {
                tree.put(k, tree.get(k) - 1);
            }
        }
        return joinValues(values, " ");
    }

    private static int[] readInts(Scanner sc, int N) {
        int[] arr = new int[N];
        for (int i = 0; i < N; i++) {
            arr[i] = sc.nextInt();
        }
        return arr;
    }

    private static <T> String joinValues(List<T> list, String delim) {
        return list.stream().map(T::toString).collect(Collectors.joining(delim));
    }

    public static void printDebug(Object str) {
        if (debug) {
            System.out.println("DEBUG: " + str);
        }
    }

    public static void main(String[] args) throws Exception {
        if (debug) {
            solveProblem(new FileInputStream(new File("input.in")));
        } else {
            solveProblem(System.in);
        }
    }

}
