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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Map;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main {
    public static void main(String[] args) throws IOException {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in), 1024 * 1024 * 2);

        int n = Integer.valueOf(br.readLine());
        int a[] =readArrayLine(br.readLine(), n);
        int b[] = readArrayLine(br.readLine(), n);

        int c[] = solve(a, b);

        StringBuilder sb = new StringBuilder();
        for (int i = 0 ; i < n ; i ++) {
            sb.append(c[i]).append(' ');
        }
        System.out.println(sb.toString());
    }

    private static int[] solve(int[] a, int[] b) {
        int n = a.length;

        TreeMap<Integer, Integer> map  = new TreeMap<>();
        for (int x : b) {
            Integer count = map.getOrDefault(x, 0);
            map.put(x, count + 1);
        }

        int c[] = new int[n];
        for (int i = 0 ; i < n ; i ++) {
            int x = a[i];
            int desired = n - x;
            Map.Entry<Integer, Integer> entry = map.ceilingEntry(desired);
            if (entry == null) {
                entry = map.ceilingEntry(0);
            }
            int key = entry.getKey();
            int count = entry.getValue();
            if (count > 1) {
                map.put(key, count - 1);
            } else {
                map.remove(key);
            }
            c[i] = (x + key) % n;
        }

        return c;
    }

    public static int[] readArrayLine(String line, int n) {
        return readArrayLine(line, n, null, 0);
    }

    private static int[] readArrayLine(String line, int n, int array[], int pos) {
        int[] ret = array == null ? new int[n] : array;
        int start = 0;
        int end = line.indexOf(' ', start);
        for (int i = pos; i < pos + n; i++) {
            if (end > 0)
                ret[i] = Integer.parseInt(line.substring(start, end));
            else
                ret[i] = Integer.parseInt(line.substring(start));
            start = end + 1;
            end = line.indexOf(' ', start);
        }
        return ret;
    }
}
