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.*;
import java.util.*;

public class Codeforces
{
    public static void main(String args[])throws Exception
    {
        BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb=new StringBuilder();
        int n=Integer.parseInt(bu.readLine());
        int a[]=new int[n],b,i;
        TreeMap<Integer,Integer> tm=new TreeMap<>();
        String s[]=bu.readLine().split(" ");
        for(i=0;i<n;i++) a[i]=Integer.parseInt(s[i]);
        s=bu.readLine().split(" ");
        for(i=0;i<n;i++)
        {
            b=Integer.parseInt(s[i]);
            tm.put(b,tm.getOrDefault(b,0)+1);
            tm.put(n+b,tm.getOrDefault(n+b,0)+1);
        }
        for(i=0;i<n;i++)
        {
            int r=n-a[i]-1;
            r=tm.higherKey(r);
            a[i]+=r;
            if(tm.get(r)==1)
            {
                tm.remove(r);
                if(tm.get(n+r)!=null) tm.remove(n+r);
                if(tm.get(r-n)!=null) tm.remove(r-n);
            }
            else
            {
                tm.put(r,tm.get(r)-1);
                if(tm.get(r+n)!=null) tm.put(r+n,tm.get(r+n)-1);
                if(tm.get(r-n)!=null) tm.put(r-n,tm.get(r-n)-1);
            }
        }
        for(i=0;i<n;i++) sb.append((a[i]%n)+" ");
        System.out.println(sb);
    }
}
