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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
	public static void main(String[] args) throws Exception {
		FastReader in = new FastReader();
		int n = in.nextInt();
		int[] a = in.nextIntArray(n);
		int[] b = in.nextIntArray(n);
		TreeMap <Integer, Integer> map = new TreeMap <> ();
		for(int i = 0; i < n; i ++) {
			if(!map.containsKey(b[i]))
				map.put(b[i], 0);
			map.put(b[i], map.get(b[i]) + 1);
		}
		int[] ans = new int[n];
		for(int i = 0; i < n; i ++) {
			Integer min = map.higherKey(n - a[i] - 1);
			if(min == null) 
				min = map.firstKey();
			ans[i] = min;
			if(map.get(min) > 1)
				map.put(min, map.get(min) - 1);
			else
				map.remove(min);
		}
		StringBuilder sb = new StringBuilder();
		for(int i = 0; i < n; i ++)
			sb.append((a[i] + ans[i]) % n + " ");
		System.out.print(sb);
	}
}

class FastReader {
    BufferedReader br;
    StringTokenizer st;

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

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

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

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

    public String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
    
    public int[] nextIntArray(int n) {
    	int[] a = new int[n];
    	for(int i = 0; i < n; i ++)
    		a[i] = nextInt();
    	return a;
    }
    
    public long[] nextLongArray(int n) {
    	long[] a = new long[n];
    	for(int i = 0; i < n; i ++)
    		a[i] = nextLong();
    	return a;
    }
    
    public double[] nextDoubleArray(int n) {
    	double[] a = new double[n];
    	for(int i = 0; i < n; i ++)
    		a[i] = nextDouble();
    	return a;
    }
}