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.InputStreamReader;
import java.util.TreeMap;

public class CodeforcesEMinimumArray {
	
	public static void main(String[] args) throws Exception
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		String[] split = br.readLine().split(" ");
		int[] a = new int[n];
		for(int i = 0; i < n; i ++)
		{
			a[i] = Integer.parseInt(split[i]);
		}
		split = br.readLine().split(" ");
		int[] b = new int[n];
		TreeMap<Integer,Integer> map = new TreeMap<Integer,Integer>();
		for(int i = 0; i < n; i ++)
		{
			b[i] = Integer.parseInt(split[i]);
			AddOrAdd(map,b[i]);
		}
		
		String[] ans = new String[n];
		for(int i = 0; i < n; i ++)
		{
			int look = n-a[i];
			Integer x = map.ceilingKey(look);
			//System.out.println(x);
			if(x == null) x = map.firstKey();
			//System.out.println(x);
			Remove(map,x);
			ans[i] = ""+(a[i]+x)%n;
		}
		
		System.out.println(String.join(" ", ans));
	}
	
	public static void AddOrAdd(TreeMap<Integer,Integer> map, int x)
	{
		int cur = 0;
		if(map.containsKey(x))
		{
			cur = map.get(x);
			map.replace(x, cur+1);
		}
		else
		{
			map.put(x,1);
		}
	}
	
	public static void Remove(TreeMap<Integer,Integer> map, int x)
	{
		if(!map.containsKey(x)) return;
		int cur = map.get(x);
		if(cur-1 == 0) map.remove(x);
		else map.replace(x, cur-1);
	}

}
