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.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class Main1157E
{
    static TreeMap<Integer,Integer> treeMap = new TreeMap<>();
    public static void main(String[] args) throws IOException
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        int N =Integer.parseInt(br.readLine());
        int[] arr1 = new int[N];
        int[] ans = new int[N];
        ArrayList<Integer> ar = new ArrayList<>();
        StringTokenizer st = new StringTokenizer(br.readLine());
        for(int i=0;i<N;++i)
        {
            arr1[i] = Integer.parseInt(st.nextToken());
        }
        st = new StringTokenizer(br.readLine());
        for(int i=0;i<N;++i)
        {
            int input = Integer.parseInt(st.nextToken());
            if(treeMap.containsKey(input))
            {
                treeMap.put(input,treeMap.get(input)+1);
            }
            else
            {
                treeMap.put(input,1);
            }
        }
        for(int i=0;i<N;++i)
        {
            int idx = treeMap.ceilingKey((N-arr1[i])%N)==null?treeMap.firstKey():treeMap.ceilingKey((N-arr1[i])%N);
            ans[i] = (arr1[i]+idx)%N;
            int tmp;
            if((tmp =treeMap.get(idx))==1)
            {
                treeMap.remove(idx);
            }
            else
            {
                treeMap.put(idx,tmp-1);
            }
        }
        StringBuilder sb = new StringBuilder();
        for(int i : ans)
        {
            sb.append(i+" ");
        }
        bw.write(sb.toString().trim());
        bw.close();
    }

}
