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.*;
import java.io.*;
public class d {
	public static void main(String[] args) throws IOException {
		FastScanner sc = new FastScanner(System.in);
		int n = sc.nextInt();
		
		int[] a1 = new int[n];
		int[] a2 = new int[n];
		TreeMap<Integer, Integer> have = new TreeMap<>();
		for (int i = 0 ; i < n ; i++) {
			a1[i] = sc.nextInt();
		}
		
		for (int i = 0 ; i < n ; i++) {
			a2[i] = sc.nextInt();
			if (have.containsKey(a2[i])) {
				have.put(a2[i], have.get(a2[i])+1);
			} else {
				have.put(a2[i], 1);
			}
		}
		
		for (int i = 0 ; i < n ; i++) {
			//System.out.println("\ni " + i);
			if (have.containsKey(n-a1[i])) {
				System.out.print("0" + " ");
				//System.out.println("using " + (n-a1[i]));
				have.put(n-a1[i],have.get(n-a1[i])-1);
				if (have.get(n-a1[i]) == 0) {
					have.remove(n-a1[i]);
				}
				continue;
			}
			if (have.higherKey(n-a1[i]) == null) {
				int down = have.higherKey(-1);
				System.out.print((down+a1[i])%n + " ");
				have.put(down,have.get(down)-1);
				if (have.get(down) == 0) {
					have.remove(down);
				}
				continue;
			}
			int up = have.higherKey(n-a1[i]);
			int down = have.higherKey(-1);
			if ((up+a1[i])%n < (a1[i]+down)%n) {
				System.out.print((up+a1[i])%n + " ");
				have.put(up,have.get(up)-1);
				//System.out.println("using " + up);
				if (have.get(up) == 0) {
					have.remove(up);
				}
			} else {
				System.out.print((down+a1[i])%n + " ");
				have.put(down,have.get(down)-1);
				//System.out.println("using " + down);
				if (have.get(down) == 0) {
					have.remove(down);
				}
			}
		}
		
	}
	
	static class FastScanner {
	    BufferedReader br;
	    StringTokenizer st;
		
	    public FastScanner(InputStream i) {
	        br = new BufferedReader(new InputStreamReader(i));
	        st = new StringTokenizer("");
	    }
				
	    public String next() throws IOException {
	        if(st.hasMoreTokens())
	            return st.nextToken();
	        else
	            st = new StringTokenizer(br.readLine());
	        return next();
	    }

	    public int nextInt() throws IOException {
	        return Integer.parseInt(next());
	    }
	    public long nextLong() throws IOException {
	        return Long.parseLong(next());
	    }
	    public double nextDouble() throws IOException {
	        return Double.parseDouble(next());
	    }
	}

}


