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.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.TreeMap;

import static java.lang.Integer.parseInt;

public class CFD {
    public static void main(String args[]) throws Throwable{
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        for(String ln;(ln=in.readLine())!=null;) {
            int N=parseInt(ln);
            int[] A=new int[N], C=new int[N];
            TreeMap<Integer, Integer> map=new TreeMap<>();
            StringTokenizer st = new StringTokenizer(in.readLine());
            for(int i=0;i<N;i++)A[i]=parseInt(st.nextToken());
            st = new StringTokenizer(in.readLine());
            for(int i=0;i<N;i++){
                int a=parseInt(st.nextToken());
                if(map.containsKey(a))map.put(a, map.get(a)+1);
                else map.put(a,1);
            }
            for(int i=0;i<A.length;i++) {
                Integer a=map.ceilingKey(N-A[i]);
                if(a==null)
                    a=map.firstKey();
                C[i]=(a+A[i])%N;
                if(map.get(a)==1)map.remove(a);
                else map.put(a, map.get(a)-1);
            }
            for(int i=0;i<N;i++)
                System.out.print((i>0?" ":"")+C[i]);
            System.out.println();
        }
    }
}
