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.lang.*;
import java.math.*;
import java.io.*;
import static java.lang.Math.*;
public class Solution{ 
    static InputReader sc;
    static PrintWriter wc;
     
    public static void main(String[] args) {
        sc=new InputReader(System.in);
        wc=new PrintWriter(System.out);
        int n=sc.nextInt();
        int a[] = new int[n],t;
        int i;
        TreeMap<Integer, Integer> map = new TreeMap<>();
        for(i=0;i<n;i++){
            a[i]=sc.nextInt();
        }
        for(i=0;i<n;i++){
            t=sc.nextInt();
            if(map.containsKey(t)) map.put(t,map.get(t)+1);
            else map.put(t,1);
        }
        int a1, a2;
        Integer b1, b2;
        for(i=0;i<n;i++){
            b1 = map.higherKey(-1);
            b2 = map.higherKey(n-a[i]-1);
            if(b2==null){
                wc.print((a[i]+b1)%n+" ");
                map.put(b1,map.get(b1)-1);
                if(map.get(b1)==0) map.remove(b1);
            }
            else{
                a1 = (b1+a[i])%n;
                a2 = (b2+a[i])%n;
                if(a1<a2){
                    wc.print(a1+" ");
                    map.put(b1,map.get(b1)-1);
                    if(map.get(b1)==0) map.remove(b1);
                }
                else{
                    wc.print(a2+" ");
                    map.put(b2,map.get(b2)-1);
                    if(map.get(b2)==0) map.remove(b2);
                }
            }
        }
        wc.close();
    }
    static class InputReader {
        
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        
        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }
        
        public int read()
        {
            if (numChars==-1) 
                throw new InputMismatchException();
            
            if (curChar >= numChars)
            {
                curChar = 0;
                try 
                {
                    numChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                
                if(numChars <= 0)               
                    return -1;
            }
            return buf[curChar++];
        }
     
        public String nextLine()
        {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt()
        {
            int c = read();
            
            while(isSpaceChar(c)) 
                c = read();
            
            int sgn = 1;
            
            if (c == '-') 
            {
                sgn = -1;
                c = read();
            }
            
            int res = 0;
            do 
            {
                if(c<'0'||c>'9') 
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c)); 
            
            return res * sgn;
        }
        
        public long nextLong() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = read();
            }
            long res = 0;
            
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
                return res * sgn;
        }
        
        public double nextDouble() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') 
            {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') 
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) 
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
        
        public String readString() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = read();
            } 
            while (!isSpaceChar(c));
            
            return res.toString();
        }
     
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
     
        public String next() 
        {
            return readString();
        }
        
        public interface SpaceCharFilter 
        {
            public boolean isSpaceChar(int ch);
        }
    }   
}
