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.Scanner;
import java.util.TreeMap;

public class Main {	
	
	private static int[] a = new int[200010];
	private static int[] b = new int[200010];
	
	public static void main(String[] args) {							
		
		Scanner scan = new Scanner(System.in);			
		int i , n = scan.nextInt();
		for (i = 0;i < n;i ++) {
			a[i] = scan.nextInt();			
		}
		for (i = 0;i < n;i ++) {
			b[i] = scan.nextInt();			
		}
		TreeMap<Integer , Integer> map = new TreeMap<>();
		for (i = 0;i < n;i ++) {
			map.put(b[i] , map.getOrDefault(b[i] , 0) + 1);			
		}
		for (i = 0;i < n;i ++) {
			int target = n - a[i];
			Integer result = map.ceilingKey(target);
			if (result != null) {
				a[i] = (a[i] + result) % n;
				map.put(result , map.get(result) - 1);
				if (map.get(result) == 0) {
					map.remove(result);					
				}
			} else {
				int firstKey = map.firstKey();
				a[i] = (a[i] + firstKey) % n;
				map.put(firstKey , map.get(firstKey) - 1);
				if (map.get(firstKey) == 0) {
					map.remove(firstKey);
				}
			}
		}
		StringBuilder builder = new StringBuilder();		
		for (i = 0;i < n;i ++) {
			if (i > 0) {
				builder.append(" ");
			}
			builder.append(a[i]);
		}	
		System.out.println(builder.toString());
		
	}
    
    	
}