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.Map;
import java.util.Scanner;
import java.util.TreeMap;

/**
 * @author neo82
 */
public class MinimumArray {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);

		int n = scanner.nextInt();

		int [] A = new int[n];

		for (int i = 0; i < n; i++) {
			A[i] = scanner.nextInt();
		}

		TreeMap<Integer, Integer> map = new TreeMap<>();

		for (int i = 0; i < n; i++) {
			map.merge(scanner.nextInt(), 1, Integer::sum);
		}

		StringBuilder sb = new StringBuilder();

		for (int i = 0; i < n; i++) {

			Integer min = map.firstKey();
			Integer max = map.ceilingKey(n - A[i]);

			if (max == null) {
				sb.append((A[i] + min) % n).append(" ");
				decreaseAndRemove(map, min);
			} else if (min == null) {
				sb.append((A[i] + max) % n).append(" ");
				decreaseAndRemove(map, max);
			} else if ((A[i] + min) % n <= (A[i] + max) % n) {
				sb.append((A[i] + min) % n).append(" ");
				decreaseAndRemove(map, min);
			} else {
				sb.append((A[i] + max) % n).append(" ");
				decreaseAndRemove(map, max);
			}
		}

		System.out.println(sb.toString());
	}

	static void decreaseAndRemove(Map<Integer, Integer> map, int key) {
		map.merge(key, -1, Integer::sum);

		if (map.get(key) <= 0) {
			map.remove(key);
		}
	}
}
