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.Scanner;
import java.util.TreeMap;

public class Main { 
	
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt(); 

		long t1 = System.currentTimeMillis();
		int[] a = new int[n];
		for(int i=0;i<n;++i) {
			a[i] = in.nextInt();
		}
		TreeMap<Integer, Integer> t = new TreeMap<>();
		for(int i=0;i<n;++i) {
			int b = in.nextInt();
			t.putIfAbsent(b, 0);
			t.put(b, t.get(b)+1);
		}
		StringBuffer sb = new StringBuffer();
		for(int i=0;i<n;++i) {
			int c = n-a[i];
			Integer found = t.ceilingKey(c);
			found = found == null ? t.ceilingKey(0) : found;
			t.put(found, t.get(found)-1);
			if(t.get(found)==0) {
				t.remove(found);
			}
			sb.append((a[i] + found) % n);
			if(i<n-1) {
				sb.append(' ');
			}
		}
		System.out.println(sb.toString());
	}

}