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 Main {
    public static void main(String args[])
    {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=1;
        while(T-->0)
        {
            int n=input.nextInt();
            int a[]=new int[n];
            for(int i=0;i<n;i++)
            {
                a[i]=input.nextInt();
            }
            TreeMap<Integer,Integer> map=new TreeMap<>();
            for(int i=0;i<n;i++)
            {
                int b=input.nextInt();
                if(map.containsKey(b))
                {
                    map.put(b, map.get(b)+1);
                }
                else
                {
                    map.put(b,1);
                }
            }
            ArrayList<Integer> list=new ArrayList<>();
            for(int i=0;i<n;i++)
            {
                int x=n-a[i];
                if(map.ceilingEntry(x)!=null)
                {
                    int v=map.ceilingKey(x);
                    list.add(v);
                    if(map.get(v)==1)
                    {
                        map.remove(v);
                    }
                    else
                    {
                        map.put(v,map.get(v)-1);
                    }
                }
                else
                {
                    int v=map.ceilingKey(0);
                    list.add(v);
                    if(map.get(v)==1)
                    {
                        map.remove(v);
                    }
                    else
                    {
                        map.put(v,map.get(v)-1);
                    }
                }
            }
            for(int i=0;i<n;i++)
            {
                out.print(((a[i]+list.get(i))%n)+" ");
            }
        }
        out.close();
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}