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{
	public static int MAX = 200001;
	public static void main(String[] args){
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int[] a= new int[MAX];
		int[] b= new int[MAX];
		int[] counts = new int[201];
		for(int i = 0;i<n;++i){
			a[i] = in.nextInt();
		}
		for(int i = 0;i<n;++i){
			int temp = in.nextInt();
			b[temp]++;
			counts[temp/1000]++;
		}
		StringBuilder str = new StringBuilder();
		for(int i = 0;i<n;++i){
			int min = n - a[i];
			int block = min/1000;
			int nes = -1;
			for(int j = min; j < block*1000 + 1000 && j < n;++j){
				if(b[j] != 0){
					b[j]--;
					counts[block]--;
					nes = j;
					break;
				}
			}
			block++;
			if(block == 201) block  = 0;
			if(nes == -1){
				while(counts[block] == 0){
					block++;
					if(block == 201) block = 0;
				}
				counts[block]--;
				for(int j = block*1000; j < (block+1)*1000;++j){
					if(b[j] != 0){
						b[j]--;
						nes = j;
						break;
					}
				}
			}
			str.append(((a[i]+nes)%n) + " ");
		}
		System.out.println(str);
	}
}
