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.*;
import java.io.*;
import java.math.BigInteger;

public class Main
{
	static final long mod=(int)1e9+7;
	public static void main(String[] args) throws Exception
	{
		FastReader in=new FastReader();
		PrintWriter pw=new PrintWriter(System.out);
		int n=in.nextInt();
		int[] arr1=new int[n];
		int[] arr2=new int[n];
		TreeMap<Integer,Integer> tm=new TreeMap();
		for(int i=0;i<n;i++)
			arr1[i]=in.nextInt();
		for(int i=0;i<n;i++)
		{
			arr2[i]=in.nextInt();
			tm.put(arr2[i],tm.getOrDefault(arr2[i],0)+1);
		}
		for(int i=0;i<n;i++)
		{
			int a=n-arr1[i];
			int b=0,b1=Integer.MAX_VALUE;
			if(tm.ceilingKey(a)!=null)
			{
				b=tm.ceilingKey(a);
				b1=(arr1[i]+b)%n;
			}
			int c=tm.firstKey();
			int c1=(arr1[i]+c)%n;
			if(c1<=b1)
			{
				a=c;
				arr2[i]=c1;
			}
			else
			{
				a=b;
				arr2[i]=b1;
			}
			if(tm.get(a)>1)
				tm.put(a,tm.get(a)-1);
			else
				tm.remove(a);
		}
		for(int i:arr2)
			pw.print(i+" ");
		pw.flush();
	}
}

class FastReader
{
	BufferedReader br;
	StringTokenizer st;

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

	public String next() throws IOException
	{
	    if(st==null || !st.hasMoreElements())
	    {
	        st=new StringTokenizer(br.readLine());
	    }
	    return st.nextToken();
	}

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

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