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.HashSet;
import java.util.Hashtable;
import java.util.Scanner;
import java.util.TreeSet;

public class D555 {
	public static void main(String args[]) {
		Scanner s=new Scanner(System.in);
		int n=s.nextInt();
		int a[]=new int[n];
		for(int i=0;i<n;i++) {
			a[i]=s.nextInt();
		}
		TreeSet<Integer> set=new TreeSet<>();
		Hashtable<Integer, Integer> tab=new Hashtable<>();
		for(int i=0;i<n;i++) {
			int k=s.nextInt();
			if(set.contains(k))
				tab.put(k, tab.get(k)+1);
			else {
				set.add(k);
				tab.put(k, 1);
			}	
		}
		int c[]=new int[n];
		for(int i=0;i<n;i++) {
			int k=n-a[i];
			int temp;
			if(set.ceiling(k)!=null) 
				temp=set.ceiling(k);
			else 
				temp=set.first();
			c[i]=(a[i]+temp)%n;
			tab.put(temp, tab.get(temp)-1);
			if(tab.get(temp)==0)
				set.remove(temp);
		}
		for(int i=0;i<n;i++) {
			System.out.print(c[i]+" ");
		}
	}
}
