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 CFP {

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int length = scan.nextInt();
        int[] a = new int[length];
        int[] number = new int[length];
        for (int i=0; i<length; i++) {
            a[i] = scan.nextInt();
        } 
        for (int i=0; i<length; i++) {
            number[scan.nextInt()]++;
        }
        {
            int last = length;
            for (int i=length-1; i>=0; i--) {
                if (number[i] != 0) {
                    last = i;
                } else {
                    number[i] = -last;
                }
            }
        }
        
        for (int i=0; i<length; i++) {
            int j = (length - a[i]) % length;
            int edge = j;
            //int steps = 0;
            do {
                //System.out.println(i+":"+j);
                if (number[j] > 0) {
                    number[j]--;
                    System.out.print( ((a[i] + j) % length) + " ");/*
                    int limit;*/
                    if (edge != j) {/*
                        if (steps > 100) {
                            if (j > edge) {
                                limit = j;
                            }  else {
                                limit = j+length;
                            }
                            for (int k=edge; k<limit; k+=100) {
                                number[k%length] = -j;
                            }
                        } else {*/
                            if (j == 0) {
                                number[edge] = -length;
                            } else {
                                number[edge] = -j;
                            }/*
                        }*/
                    }
                    break;
                } else if (number[j] < 0) {
                    //System.out.println(j+">"+-number[j]);
                    j = -number[j] % length;
                } else {
                    j = ++j % length;
                }
                //steps++;
            } while (j!=edge);
        }
        System.out.println();
    }
}
