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.lang.*;

public class MinArray{
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int[] array = new int[n];
		for(int i=0;i<array.length;i++){
			array[i] = scan.nextInt();
		}

		TreeMap<Integer,Integer> treemap = new TreeMap<>();
		for(int i=0;i<n;i++){
			int t = scan.nextInt();
			treemap.put(t, treemap.getOrDefault(t, 0)+1);
		}

		List<Integer> list = new ArrayList<>();

		for(int i=0;i<n;i++){
			int key = n-array[i];
			Integer ceilingKey = treemap.ceilingKey(key);
			if(ceilingKey!=null){
				list.add((array[i]+ceilingKey)%n);
				treemap.put(ceilingKey, treemap.get(ceilingKey)-1);
				if(treemap.get(ceilingKey)==0){
					treemap.remove(ceilingKey);
				}
			}else{
				Integer lowestKey = treemap.firstKey();
				list.add((array[i]+lowestKey)%n);
				treemap.put(lowestKey, treemap.get(lowestKey)-1);
				if(treemap.get(lowestKey)==0){
					treemap.remove(lowestKey);
				}
			}
		}

		for(int ele: list){
			System.out.print(ele+" ");
		}


	}
}