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.Arrays;
import java.util.TreeMap;

public class E2157 {
	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		final int N = sc.nextInt();
		Integer[] a = new Integer[N];
		TreeMap<Integer, Integer> b = new TreeMap<>();
		for (int i = 0; i < N; i++) 
			a[i] = sc.nextInt();

		for (int i = 0; i < N; i++) {
			Integer temp = sc.nextInt();
			Integer qty = b.get(temp);
			if (qty == null) 
				b.put(temp, 1);
			else 
				b.put(temp, qty + 1);
		}

		for (int i = 0; i < N; i++) {
			Integer ai = a[i];
			Integer aim = ai == 0 || i == N - 1 ? 0 : N - ai;
			// System.out.println(aim);
			if (b.get(aim) == null) {
				// System.out.println("Hello" + aim);
				aim = b.higherKey(aim);
				// System.out.println(aim);
			}
			if (aim == null) {
				aim = 0;
			}
			if (b.get(aim) == null) {
				aim = b.higherKey(aim);
			}
			System.out.print((aim + ai) % N + " ");
			Integer qty = b.get(aim);
			if (qty == 1)
				b.remove(aim);
			else
				b.put(aim, qty - 1);
		}

		System.out.println();

	}
}