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;

public class E {

	@SuppressWarnings("resource")
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		Integer size = sc.nextInt();
		Integer A[] = new Integer[size];
		Integer B[] = new Integer[size];
		Integer C[] = new Integer[size];
		
		for ( int i = 0; i < size; i++ ) {
			A[i] = sc.nextInt();
			B[i] = 0;
		}
		for ( int i = 0; i < size; i++ ) {
			int b = sc.nextInt();
			B[b] += 1;
		}
		int map[] = new int[size];
		for ( int i = 0; i < size - 1; i++ ) {
			map[i] = i + 1;
		}
		map[size - 1] = 0;
		for ( int i = 0; i < size; i++) {
			int target = ( size - A[i] ) % size;
			while ( B[target] == 0 ) {
				if ( B[map[target]] == 0 )
					map[target] = map[map[target]];
				target = map[target];
			}
			C[i] = ( A[i] + target ) % size;
			B[target] -= 1;
		}
		for ( int i = 0; i < size; i++ ) { 
			System.out.print(C[i] + " ");
		}
		System.out.println();
	}

}
