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.*;

/******************************\
 * The solution is at the top *
 *                            *
 *   Created by : azhar556    *
\******************************/

public class Solution {
    static void solve() {
        int n = ni();
        int[] arrA = new int[n];
        for (int i = 0; i < n; i++) {
            arrA[i] = ni();
        }
        int[] numB = new int[200001];
        NavigableSet<Integer> setB = new TreeSet<>();
        for (int i = 0; i < n; i++) {
            int masuk = ni();
            setB.add(masuk);
            numB[masuk]++;
        }
        for (int i = 0; i < n; i++) {
            int target = n - arrA[i];
            if (setB.ceiling(target) != null) {
                target = setB.ceiling(target);
            }
            else {
                target = setB.first();
            }
            out.print((arrA[i] + target) % n + " ");
            numB[target]--;
            if (numB[target] == 0) {
                setB.remove(target);
            }
        }
    }    

    public static void main(String[] args) {
        long time = System.currentTimeMillis();
        int t;// = ni();
        t = 1;
        while (t-- > 0) solve(); 
        err.println("Time elapsed : " + (System.currentTimeMillis() - time) / 1000F + " s.");
        err.close(); out.close();
    }

    static PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    static PrintWriter err = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.err)));
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer token;
        
    static String ns() {
        while (token == null || !token.hasMoreTokens()) {
            try {
                token = new StringTokenizer(br.readLine());
            }
            catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return token.nextToken();
    }
    static char nc() {
        return Character.valueOf(ns().charAt(0));
    }
    static int ni() {
        return Integer.parseInt(ns());
    }
    static double nd() {
        return Double.parseDouble(ns());
    }
    static long nl() {
        return Long.parseLong(ns());
    }
}
