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 qf{
    public static void main(String args[]){
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int a[]=new int[n];
        int b[]=new int[n];
        for(int i=0;i<n;i++){
            a[i]=sc.nextInt();
        }
        TreeMap<Integer,Integer> tm=new TreeMap<Integer,Integer>();
        for(int i=0;i<n;i++){
            b[i]=sc.nextInt();
            if(tm.containsKey(b[i])){
                tm.put(b[i], tm.get(b[i])+1);
            }
            else{
                tm.put(b[i],1);
            }
        }
        int ans[]=new int[n];
        for(int i=0;i<n;i++){
            int temp=n-a[i];
            if(tm.containsKey(temp)){
                int x=tm.get(temp);
                if(x==1){
                    tm.remove(temp);
                }
                else{
                    tm.put(temp,x-1);
                }
                ans[i]=temp;
            }
            else{
                int x;
                if(tm.ceilingKey(temp)==null){
                    temp=tm.ceilingKey(0);
                }
                else temp=tm.ceilingKey(temp);
                x=tm.get(temp);
                if(x==1){
                    tm.remove(temp);
                }
                else{
                    tm.put(temp,x-1);
                }
                ans[i]=temp;
            }
        }
        for(int i=0;i<n;i++){
            System.out.print(((ans[i]+a[i])%n)+" ");
        }
    }
}