There are n children numbered from 1 to n in a kindergarten. Kindergarten teacher gave a_i (1 ≤ a_i ≤ n) candies to the i-th child. Children were seated in a row in order from 1 to n from left to right and started eating candies. 

While the i-th child was eating candies, he calculated two numbers l_i and r_i — the number of children seating to the left of him that got more candies than he and the number of children seating to the right of him that got more candies than he, respectively.

Formally, l_i is the number of indices j (1 ≤ j < i), such that a_i < a_j and r_i is the number of indices j (i < j ≤ n), such that a_i < a_j.

Each child told to the kindergarten teacher the numbers l_i and r_i that he calculated. Unfortunately, she forgot how many candies she has given to each child. So, she asks you for help: given the arrays l and r determine whether she could have given the candies to the children such that all children correctly calculated their values l_i and r_i, or some of them have definitely made a mistake. If it was possible, find any way how she could have done it.

Input

On the first line there is a single integer n (1 ≤ n ≤ 1000) — the number of children in the kindergarten.

On the next line there are n integers l_1, l_2, …, l_n (0 ≤ l_i ≤ n), separated by spaces.

On the next line, there are n integer numbers r_1, r_2, …, r_n (0 ≤ r_i ≤ n), separated by spaces.

Output

If there is no way to distribute the candies to the children so that all of them calculated their numbers correctly, print «NO» (without quotes).

Otherwise, print «YES» (without quotes) on the first line. On the next line, print n integers a_1, a_2, …, a_n, separated by spaces — the numbers of candies the children 1, 2, …, n received, respectively. Note that some of these numbers can be equal, but all numbers should satisfy the condition 1 ≤ a_i ≤ n. The number of children seating to the left of the i-th child that got more candies than he should be equal to l_i and the number of children seating to the right of the i-th child that got more candies than he should be equal to r_i. If there is more than one solution, find any of them.

Examples

Input

5
0 0 1 1 2
2 0 1 0 0


Output

YES
1 3 1 2 1


Input

4
0 0 2 0
1 1 1 1


Output

NO


Input

3
0 0 0
0 0 0


Output

YES
1 1 1

Note

In the first example, if the teacher distributed 1, 3, 1, 2, 1 candies to 1-st, 2-nd, 3-rd, 4-th, 5-th child, respectively, then all the values calculated by the children are correct. For example, the 5-th child was given 1 candy, to the left of him 2 children were given 1 candy, 1 child was given 2 candies and 1 child — 3 candies, so there are 2 children to the left of him that were given more candies than him.

In the second example it is impossible to distribute the candies, because the 4-th child made a mistake in calculating the value of r_4, because there are no children to the right of him, so r_4 should be equal to 0.

In the last example all children may have got the same number of candies, that's why all the numbers are 0. Note that each child should receive at least one candy.
//    A Computer is Like a mischievous genie.
//    It will give you exactly what you ask for,
//    but not always what you want
//    A code by Rahul Verma


import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Set;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import javax.swing.plaf.basic.BasicScrollPaneUI.HSBChangeListener;


public class Main {


    static class Clock {

        protected long start, stop;

        public void start() {
            start = System.currentTimeMillis();
        }

        public void stop() {
            stop = System.currentTimeMillis();
        }

        public String getTime() {
            return ((stop - start) + " ms");
        }
    }


    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

    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();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String[] nextSArray() {
            String sr[] = null;
            try {
                sr = br.readLine().trim().split(" ");
            } catch (IOException e) {
                e.printStackTrace();
            }
            return sr;
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }

            return str;
        }
    }


    static long powmodulo(long a, long p) {
        if (p == 0) {
            return 1 % mod;
        }
        if (p == 1) {
            return a % mod;
        }
        long ans = 1;
        while (p > 0) {
            if ((p & 1) > 0) {
                ans = (ans * a) % mod;
            }
            a = (a * a) % mod;
            p = p >> 1;
        }
        return ans % mod;
    }


    static long mod = 1000000007;

    static long gcd(long a, long b) {
        if (a == 0) {
            return b;
        }
        return gcd(b % a, a);
    }

    static long fast_powerNumbers(long a, long n) {
        if (n == 1) {
            return a;
        }
        long ans = fast_powerNumbers(a, n / 2);
        if (n % 2 == 0) {
            return (ans * ans);
        } else {
            return ((ans * ans) * (a));
        }
    }


    static void dfs_helper(int[][] arr, int i, int j, int team, int n, int m) {
        arr[i][j] = team;
        if (i - 1 >= 0 && arr[i - 1][j] == 1) {
            dfs(arr, i - 1, j, team, n, m);
        }
        if (j - 1 >= 0 && arr[i][j - 1] == 1) {
            dfs(arr, i, j - 1, team, n, m);
        }
        if (i + 1 < n && arr[i + 1][j] == 1) {
            dfs(arr, i + 1, j, team, n, m);
        }
        if (j + 1 < m && arr[i][j + 1] == 1) {
            dfs(arr, i, j + 1, team, n, m);
        }

    }

    static void dfs(int[][] arr, int i, int j, int team, int n, int m) {
        dfs_helper(arr, i, j, team, n, m);

    }

    static int parent[];
    static int rank[];

    static int find(int i) {
        if (parent[i] == -1) {
            parent[i] = i;
            return i;
        }

        if (parent[i] == i) {
            return i;
        } else {
            parent[i] = find(parent[i]);
        }
        return parent[i];

    }

    static void unite(int s1, int s2) {

        if (rank[s1] > rank[s2]) {
            parent[s2] = s1;
            rank[s1] += rank[s2];
        } else {
            parent[s1] = s2;
            rank[s2] += rank[s1];
        }
    }


    static int arr[];

    static void seive(int n) {
        arr = new int[n + 1];
        arr[0] = arr[1] = 1;
        for (int i = 4; i <= n; i = i + 2) {
            arr[i] = 1;
        }
        for (int i = 3; i * i <= n; i = i + 2) {
            if (arr[i] == 0) {
                for (int j = i * i; j <= n; j = j + i) {
                    arr[j] = 1;
                }

            }
        }
    }



   static long dp[][];
    static long max=0;

    public static void main(String[] args) throws Exception {
        FastReader sc = new FastReader();

        Clock clock = new Clock();
        clock.start();
       int n=sc.nextInt();
       int arr[][]=new int[2][n];
       int max=0;
        for (int i = 0; i <n ; i++) {
            arr[0][i]=sc.nextInt();
        }
        for (int i = 0; i <n ; i++) {
            arr[1][i]=sc.nextInt();
            max=Math.max(arr[1][i]+arr[0][i],max);
        }
        max=max+1;
        int ans[]=new int[n];
        boolean isPresent=true;
        if(arr[0][0]!=0||arr[1][n-1]!=0)
        {
            System.out.println("NO");
            return;
        }
        for (int i = 0; i <n ; i++) {
            ans[i]= max - (arr[0][i]+arr[1][i]);
            //out.println(arr[0][1]+arr[1][i]);
            if(ans[i]<=0)
            {
                isPresent=false;
                break;
            }
        }
        if(!isPresent)
        {
            System.out.println("NO");
            return;
        }
        for (int i = 0; i <n ; i++) {
            int a =ans[i];

            int l=0,r=0;
            for (int j = i-1; j >=0 ; --j) {
                if(ans[j]>a)
                    ++l;
            }
            for (int j = i+1; j <n ; j++) {
                if(ans[j]>a)
                    ++r;
            }
            if(l==arr[0][i]&&r==arr[1][i])
            {
                continue;
            }
            else
            {
                isPresent=false;
                break;
            }

        }

        if(isPresent)
        {
            out.println("YES");
            for (int i = 0; i <n ; i++) {
                out.print(ans[i]+" ");
            }
            out.close();
        }
        else
            out.print("NO");
        out.close();







    }}



class Pair {

    int a;
    int b;

    Pair(int a, int b) {
        this.a = a;
        this.b = b;
    }
}
class DSU
{
    int parent[];
    int rank[];
    DSU(int n)
    {
        this.parent=new int[n];
        this.rank=new int[n];
        Arrays.fill(parent,-1);
        Arrays.fill(rank,1);
    }

    int find(int s1)
    {
        if(parent[s1]==-1)
            return s1;
        return parent[s1]=find(parent[s1]);
    }

    void unite(int s1,int s2)
    {
        int p1=this.find(s1);
        int p2=this.find(s2);
        if(p1==p2)
            return;
        if(rank[p1]>rank[p2])
        {
            parent[p2]=p1;
            rank[p1]+=rank[p2];
        }
        else
        {
            parent[p1]=p2;
            rank[p2]+=rank[p1];
        }
    }


}


class Graph {

    HashMap<Integer, ArrayList<Integer>> hm;

    Graph() {
        hm = new HashMap<>();
    }

    Graph(int n) {

        hm = new HashMap<>();
        for (int i = 0; i < n; i++) {
            hm.put(i, new ArrayList<Integer>());
        }
    }

    // function for adding an edge.................................................
    public void addEdge(int a, int b, boolean isDir) {
        if (isDir) {
            if (hm.containsKey(a)) {
                hm.get(a).add(b);
            } else {
                hm.put(a, new ArrayList<>(Arrays.asList(b)));
            }
        } else {
            if (hm.containsKey(a)) {
                hm.get(a).add(b);
            } else if (!hm.containsKey(a)) {
                hm.put(a, new ArrayList<>(Arrays.asList(b)));
            }

            if (hm.containsKey(b)) {
                hm.get(b).add(a);
            } else if (!hm.containsKey(b)) {
                hm.put(b, new ArrayList<>(Arrays.asList(a)));
            }
        }
    }


}

// out.println(al.toString().replaceAll("[\\[|\\]|,]",""));