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 Solution
{
    public static void main(String []args)
    {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int a[] = new int[n];
        for(int i = 0 ; i < n ; i++)
        {
            a[i] = sc.nextInt();
        }
        TreeMap<Integer , Integer> map = new TreeMap<>();
        for(int i = 0 ; i < n ; i++)
        {
           int x = sc.nextInt();
           if(map.containsKey(x))
           map.put(x , map.get(x) + 1);
           
           else
           map.put(x , 1);
        }
        
        StringBuffer str = new StringBuffer("");
        for(int i = 0 ; i < n ; i++)
        {
            Integer it = map.ceilingKey(n - a[i]);
            if(it == null)
            it = map.firstKey();
            
            str.append(((a[i] + it)%n) + " ");
            
            map.replace(it , map.get(it) - 1);
            if(map.get(it) == 0)
            map.remove(it);
        }
        System.out.println(str);
    }
}