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 
//package minimumarray;

import java.util.*;
import java.io.*;

public class minimumarray {
	
	static TreeMap<Integer, Integer> dict;
	
	public static void main(String[] args) throws IOException {
		BufferedReader fin = new BufferedReader(new InputStreamReader(System.in));
		dict = new TreeMap<Integer, Integer>();
		int n = Integer.parseInt(fin.readLine());
		int[] a = new int[n];
		int[] b = new int[n];
		StringTokenizer st = new StringTokenizer(fin.readLine());
		for(int i = 0; i < n; i++) {
			a[i] = Integer.parseInt(st.nextToken());
		}
		st = new StringTokenizer(fin.readLine());
		for(int i = 0; i < n; i++) {
			b[i] = Integer.parseInt(st.nextToken());
			dict.put(b[i], dict.getOrDefault(b[i], 0) + 1);
		}
		StringBuilder fout = new StringBuilder();
		for(int i = 0; i < n; i++) {
			int next = a[i];
			int t = n - next;
			int minimum = (dict.firstKey() + next) % n;
			int targetNum = n + 1;
			if(dict.ceilingKey(t) != null) {
				targetNum = (dict.ceilingKey(t) + next) % n;
			}
			if(minimum <= targetNum) {
				if(dict.get(dict.firstKey()) == 1) {
					dict.remove(dict.firstKey());
				}
				else {
					dict.put(dict.firstKey(), dict.get(dict.firstKey()) - 1);
				}
			}
			else {
				if(dict.get(dict.ceilingKey(t)) == 1) {
					dict.remove(dict.ceilingKey(t));
				}
				else {
					dict.put(dict.ceilingKey(t), dict.get(dict.ceilingKey(t)) - 1);
				}
			}
			fout.append(Math.min(minimum, targetNum)).append(" ");
		}
		System.out.println(fout);
	}
}
