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.*;
import java.math.*;
 
public class E
{
    public static void process()throws IOException
    {
        int n=ni(),a[]=new int[n+1],b[]=new int[n+1];

        for(int i=1;i<=n;i++) a[i]=ni();
        for(int i=1;i<=n;i++) b[i]=ni();

        StringBuilder res = new StringBuilder();        

        MultiTreeSet<Integer> set=new MultiTreeSet<>();

        for(int i=1;i<=n;i++)
            set.add(b[i]);

        for(int i=1;i<=n;i++){
            int req=n-a[i];
            Integer x=set.ceiling(req);
            if(x==null){
                Integer y1=set.ceiling(a[i]),y2=set.first();
                if(y1==null)
                    x=y2;
                else if(y2==null)
                    x=y1;
                else{
                    if((a[i]+y1)%n<(a[i]+y2)%n)
                        x=y1;
                    else
                        x=y2;
                }
            }

            set.remove(x);

            int y=x.intValue();
            y=(y+a[i])%n;
            res.append(y+" ");
        }
        pn(res);
    }
        
    static class MultiTreeSet<E> {
        TreeMap<E, Integer> freqTreeMap = new TreeMap<E, Integer>();
        int size;
        
        public MultiTreeSet() {}
        
        public MultiTreeSet(Collection<? extends E> c) {
            for(E element : c)
                add(element);
        }
        
        public int size() {
            return size;
        }
        
        public void add(E element) {
            Integer freq = freqTreeMap.get(element);
            if(freq==null)
                freqTreeMap.put(element, 1);
            else
                freqTreeMap.put(element,freq+1);
            ++size;
        }
        
        public void remove(E element) {
            Integer freq = freqTreeMap.get(element);
            if(freq!=null) {
                if(freq==1)
                    freqTreeMap.remove(element);
                else
                    freqTreeMap.put(element, freq-1);
                --size;
            }
        }
        
        public int get(E element) {
            Integer freq = freqTreeMap.get(element);
            if(freq==null)
                return 0;
            return freq;
        }
        
        public boolean contains(E element) {
            return get(element)>0;
        }
        
        public boolean isEmpty() {
            return size==0;
        }
        
        public E first() {
            return freqTreeMap.firstKey();
        }

        public E last() {
            return freqTreeMap.lastKey();
        }
        
        public E ceiling(E element) {
            return freqTreeMap.ceilingKey(element);
        }
        
        public E floor(E element) {
            return freqTreeMap.floorKey(element);
        }
        
        public E higher(E element) {
            return freqTreeMap.higherKey(element);
        }
        
        public E lower(E element) {
            return freqTreeMap.lowerKey(element);
        }
    }

    static FastReader sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        out = new PrintWriter(System.out);
        sc=new FastReader();
 
        long s = System.currentTimeMillis();
        int t=1;
        //t=ni();
        while(t-->0)
            process();
 
        out.flush();
        System.err.println(System.currentTimeMillis()-s+"ms");
    }
    
    
    static void pn(Object o){out.println(o);}
    static void p(Object o){out.print(o);}
    static int ni()throws IOException{return Integer.parseInt(sc.next());}
    static long nl()throws IOException{return Long.parseLong(sc.next());}
    static double nd()throws IOException{return Double.parseDouble(sc.next());}
    static String nln()throws IOException{return sc.nextLine();}
    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}
    
    static long mod=(long)1e9+7l;
 
    static<T> void r_sort(T arr[],int n){
        Random r = new Random(); 
        for (int i = n-1; i > 0; i--){ 
            int j = r.nextInt(i+1); 
                  
            T temp = arr[i]; 
            arr[i] = arr[j]; 
            arr[j] = temp; 
        } 
        Arrays.sort(arr); 
    }
    
/////////////////////////////////////////////////////////////////////////////////////////////////////////
    static class FastReader{ 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader(){ 
            br = new BufferedReader(new InputStreamReader(System.in)); 
        } 
  
        String next(){ 
            while (st == null || !st.hasMoreElements()){ 
                try{ st = new StringTokenizer(br.readLine()); } catch (IOException  e){ e.printStackTrace(); } 
            } 
            return st.nextToken(); 
        } 
  
        String nextLine(){ 
            String str = ""; 
            try{ str = br.readLine(); } catch (IOException e) { e.printStackTrace(); } 
            return str; 
        } 
    } 
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
}