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.*;

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