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

public class CF1157E {
	public CF1157E() {
		FS scan = new FS();
		PrintWriter out = new PrintWriter(System.out);
		int n = scan.nextInt();
		int[] a = new int[n];
		int[] b = new int[n];
		for(int i = 0 ; i < n ; i++) a[i] = scan.nextInt();
		for(int i = 0 ; i < n ; i++) b[i] = scan.nextInt();
		int[] c = new int[n];
		TreeMap<Integer, Integer> map = new TreeMap<>();
		for(int i = 0 ; i < n ; i++)
			map.put(b[i], map.getOrDefault(b[i], 0) + 1);
		for(int i = 0 ; i < n ; i++) {
			int goal = n - a[i], key = 0;
			if(map.ceilingKey(goal) != null) key = map.ceilingKey(goal);
			else key = map.ceilingKey(0);
			c[i] = (a[i] + key) % n;
			if(map.get(key) - 1 == 0) map.remove(key);
			else map.put(key, map.get(key) - 1);
		}
		for(int i = 0 ; i < n ; i++)
			out.print(c[i] + " ");
		out.close();
	}
	class FS {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");
		public String next() {
			while(!st.hasMoreTokens()) {
				try { st = new StringTokenizer(br.readLine()); }
				catch(Exception e) { e.printStackTrace(); }
			}
			return st.nextToken();
		}
		public int nextInt() { return Integer.parseInt(next()); }
	}
	public static void main(String[] args) { new CF1157E(); }
}