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.PrintWriter;
import java.util.*;

public class MinimumArray
{

	public static void main(String[] args)
	{
		Scanner scan = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		int n = scan.nextInt();
		int[] arr = new int[n];
		for(int i = 0; i < n; i++){
			arr[i] = scan.nextInt();
		}
		TreeMap<Integer, Integer> map = new TreeMap<Integer, Integer>();
		for(int i = 0; i < n; i++){
			int x = scan.nextInt();
			int f = map.getOrDefault(x,0);
			map.put(x, f+1);
		}
		int[] ans = new int[n];
		int[] need = new int[n];
		for(int i = 1; i < n; i++)
			need[i] = n-i;
		for(int i = 0; i < n; i++){
			Integer p = map.ceilingKey(need[arr[i]]);
			if(p == null) p = map.ceilingKey(0);
			int pp = (int)p;
			int num = map.get(pp);
			if(num == 1) map.remove(pp);
			else map.put(pp, num-1);
			ans[i] = (arr[i]+pp)%n;
		}
		for(int i = 0; i < n; i++) out.print(ans[i]+" ");
		out.flush();
	}
}
