In Berland each high school student is characterized by academic performance — integer value between 1 and 5.

In high school 0xFF there are two groups of pupils: the group A and the group B. Each group consists of exactly n students. An academic performance of each student is known — integer value between 1 and 5.

The school director wants to redistribute students between groups so that each of the two groups has the same number of students whose academic performance is equal to 1, the same number of students whose academic performance is 2 and so on. In other words, the purpose of the school director is to change the composition of groups, so that for each value of academic performance the numbers of students in both groups are equal.

To achieve this, there is a plan to produce a series of exchanges of students between groups. During the single exchange the director selects one student from the class A and one student of class B. After that, they both change their groups.

Print the least number of exchanges, in order to achieve the desired equal numbers of students for each academic performance.

Input

The first line of the input contains integer number n (1 ≤ n ≤ 100) — number of students in both groups.

The second line contains sequence of integer numbers a1, a2, ..., an (1 ≤ ai ≤ 5), where ai is academic performance of the i-th student of the group A.

The third line contains sequence of integer numbers b1, b2, ..., bn (1 ≤ bi ≤ 5), where bi is academic performance of the i-th student of the group B.

Output

Print the required minimum number of exchanges or -1, if the desired distribution of students can not be obtained.

Examples

Input

4
5 4 4 4
5 5 4 5


Output

1


Input

6
1 1 1 1 1 1
5 5 5 5 5 5


Output

3


Input

1
5
3


Output

-1


Input

9
3 2 5 5 2 3 3 3 2
4 1 4 1 1 2 4 4 1


Output

4
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Comparator;
import java.util.StringTokenizer;
		public class Solution123{
			static int count[] = new int[200002];
			static int fcount[] = new int[200002];
			public static void main(String[] args) throws IOException{
				FastReader sc = new FastReader();
				int n = sc.nextInt();
				//String s = sc.next();
				int[] arr = new int[6];
				int[] arr2 = new int[6];
				for(int i = 0;i < n;i++){
					int a=  sc.nextInt();
					arr[a]++;
				}
				for(int i = 0;i < n;i++){
					int a= sc.nextInt();
					arr2[a]++;
				}
				int count = 0;
				for(int i = 1;i <= 5;i++){
					if(arr[i] == arr2[i]){
						continue;
					}else{
						if((arr2[i] - arr[i]) % 2 == 0){
							count += Math.abs(arr2[i] - arr[i])/2;
						}else{
							System.out.println("-1");
							System.exit(0);
						}
					}
				}
				if(count % 2 == 0){
					System.out.println(count/2);
				}else{
					System.out.println("-1");
				}
			}
			int gcd(int a, int b)
			{
			    if (b==0)
			        return a;
			    return gcd(b, a%b);
			}
			 
			 // Returns LCM of array elements
			static long findlcm(int arr[], int n)
			{
			    // Initialize result
			    long ans = arr[0];
			 
			    // ans contains LCM of arr[0],..arr[i]
			    // after i'th iteration,
			    for (int i=1; i<n; i++)
			        ans = ( ((arr[i]*ans)) /
			                (gcd(arr[i], ans)) );
			 
			    return ans;
			}
			public static boolean isPalindrome(String s){
				StringBuilder st = new StringBuilder(s);
				if(st.reverse().toString().equals(s)){
					return true;
				}
				return false;
			}
			public static int digits(int a){
				int count = 0;
				while(a != 0){
					count++;
					a = a/10;
				}
				return count;
			}
			public static long min(long n,long k){
				long ans = 0;
				long calc = n/k;
				long calc2 = n % k;
				long recalc = k - calc2;
				ans += calc * (calc - 1)/2 * recalc;
				ans += (calc + 1) * calc/2 * calc2;
				return ans;
			}
			public static long max(long n,long k){
				long ans = 0;
				long calc = n - k + 1;
				ans += calc * (calc - 1)/2;
				return ans;
			}
			public static boolean isOk(int[] arr,int size){
				if(size % 2 == 0){
					for(int i = 0;i < arr.length;i++){
						if(arr[i] % 2 != 0){
							return false;
						}
					}
					return true;
				}else{
					int count = 0;
					for(int i = 0;i < arr.length;i++){
						if(arr[i] % 2 != 0){
							count++;
						}
					}
					if(count > 1){
						return false;
					}
					return true;
				}
			}
			public static int complement(int index){
				if(index == 0){
					return 1;
				}
				return 0;
			}
			private static long gcd(long a, long b)
			{
			    while (b > 0)
			    {
			        long temp = b;
			        b = a % b; // % is remainder
			        a = temp;
			    }
			    return a;
			}
			void convertDegree(){
				
			}
			private static long gcd(long[] input)
			{
			    long result = input[0];
			    for(int i = 1; i < input.length; i++) result = gcd(result, input[i]);
			    return result;
			}
			private static long lcm(long a, long b)
			{
			    return a * (b / gcd(a, b));
			}
		
			private static long lcm(long[] input)
			{
			    long result = input[0];
			    for(int i = 1; i < input.length; i++) result = lcm(result, input[i]);
			    return result;
			}
			public static boolean[] sieveAlgo(int n){
				boolean isPrime[] = new boolean[n + 1];
				for (int i = 2; i <= n; i++) {
		            isPrime[i] = true;
		        }
		
		        // mark non-primes <= n using Sieve of Eratosthenes
		        for (int factor = 2; factor*factor <= n; factor++) {
		
		            // if factor is prime, then mark multiples of factor as nonprime
		            // suffices to consider mutiples factor, factor+1, ...,  n/factor
		            if (isPrime[factor]) {
		                for (int j = factor; factor*j <= n; j++) {
		                    isPrime[factor*j] = false;
		                }
		            }
		        }
		        return isPrime;
			}
			public static int binarySearch(int[] arr,int low,int high,int key){
				while(low <= high){
					int mid = (low + high)/2;
					if(arr[mid] == key){
						return mid;
					}else if(arr[mid] < key){
						low = mid + 1;
					}else{
						high = mid - 1;
					}
				}
				return -1;
			}
			public static int ternarySearch(int[] arr,int l,int r,int key){
				if(r >= l){
					int mid1 = l + (r-1)/3;
					int mid2 = r - (r-1)/3;
					if(arr[mid1] == key){
						return mid1;
					}else if(arr[mid2] == key){
						return mid2;
					}
					if(key < arr[mid1]){
						return ternarySearch(arr,l,mid1-1,key);
					}else if(key > arr[mid2]){
						return ternarySearch(arr,mid2 + 1,r,key);
					}else{
						return ternarySearch(arr,mid1 + 1,mid2 - 1,key);
					}
				}
				return -1;
			}
			public static double fun(double x){
				return 2 * x * x - 12 * x + 7;
			}
			
			public static double tsModified(double start,double end){
				double l = start;
				double r = end;
				for(int i = 0;i < 200;i++){
					double mid1 = (l * 2 + r)/3;
					double mid2 = (l + 2 * r)/3;
					if(fun(mid1) < fun(mid2)){
						r = mid2;
					}else{
						l = mid1;
					}
				}
				double x = l;
				return fun(x);
			}
			public static String fmt(double d)
			{
			    if(d == (long) d)
			        return String.format("%d",(long)d);
			    else
			        return String.format("%s",d);
			}
			public static int[][] comparator(int[][] arr){
				Arrays.sort(arr, new Comparator<int[]>() {
		            @Override
		            public int compare(int[] a,int[] b) {
		                Integer a1 = a[1];
		                Integer b1 = b[1];
		            	return a1.compareTo(b1);
		            }
		        });
				return arr;
			}
			public static StringBuilder[][] comparator2(StringBuilder[][] arr){
				Arrays.sort(arr, new Comparator<StringBuilder[]>() {
		            @Override
		            public int compare(StringBuilder[] a,StringBuilder[] b) {
		                StringBuilder a1 = a[0];
		                StringBuilder b1 = b[0];
		            	return a1.toString().compareTo(b1.toString());
		            }
		        });
				return arr;
			}
			public static int[][] comparator2(int[][] arr){
				Arrays.sort(arr, new Comparator<int[]>() {
		            @Override
		            public int compare(int[] a,int[] b) {
		                Integer a1 = a[0];
		                Integer b1 = b[0];
		            	return b1.compareTo(a1);
		            }
		        });
				return 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();
		        }
		 
		        int nextInt()
		        {
		            return Integer.parseInt(next());
		        }
		 
		        long nextLong()
		        {
		            return Long.parseLong(next());
		        }
		 
		        double nextDouble()
		        {
		            return Double.parseDouble(next());
		        }
		 
		        String nextLine()
		        {
		            String str = "";
		            try
		            {
		                str = br.readLine();
		            }
		            catch (IOException e)
		            {
		                e.printStackTrace();
		            }
		            return str;
		        }
		    }
			public static String min(int m,int n){
				int[] arr = new int[m];
				arr[0] = 1;
				int sum = 1;
				int j = m - 1;
				for(int i = 1;i <= 18* m + 10;i++){
					if(sum != n){
						if(arr[j] == 9){
							j--;
						}else{
							arr[j]++;
							sum++;
						}
					}
					else{
						break;
					}
				}
				StringBuilder min = new StringBuilder("");
				for(int i = 0;i < arr.length;i++){
					min.append(arr[i]);
				}
				return min.toString();
			}
			
			public static String max(int m,int n){
				int[] arr = new int[m];
				arr[0] = 1;
				int sum = 1;
				int j = 0;
				for(int i = 1;i <= 9 * m + 10;i++){
					if(sum != n){
						if(arr[j] == 9){
							j++;
						}else{
							arr[j]++;
							sum++;
						}
					}
					else{
						break;
					}
				}
				StringBuilder min = new StringBuilder("");
				for(int i = 0;i < arr.length;i++){
					min.append(arr[i]);
				}
				return min.toString();
			}
		    public static int KMPSearch(String txt,String pat){
				int m = pat.length();
				int n = txt.length();
				int lps[] = new int[m];
				int j = 0;
				int count = 0;
				PrefixTable(pat,m,lps);
				int i = 0;
				while (i < n)
			        {
			            if (pat.charAt(j) == txt.charAt(i))
			            {
			                j++;
			                i++;
			            }
			            if (j == m)
			            {
			            	count++;
			                j = lps[j-1];
			            }
			            else if (i < n && pat.charAt(j) != txt.charAt(i))
			            {
			                if (j != 0)
			                    j = lps[j-1];
			                else
			                    i = i+1;
			            }
			        }
				return count;
			}
			public static void PrefixTable(String pat,int m,int[] lps){
				int len = 0;
				int i = 1;
				lps[0] = 0;
				while(i < m){
					if(pat.charAt(i) == pat.charAt(len)){
						lps[i] = len + 1;
						i++;
						len++;
					}else if(len > 0){
						len = lps[len - 1];
					}else{
						lps[i] = 0;
						i++;
					}
				}
			}
		    public int digit(int x){
		    	int temp = x;
		    	int count = 0;
		    	while(temp != 0){
		    		count++;
		    		temp = temp/10;
		    	}
		    	return count;
		    }
		    public int sum(int x){
		    	int temp = x;
		    	int count = 0;
		    	while(temp != 0){
		    		count += temp % 10;
		    		temp = temp/10;
		    	}
		    	return count;
		    }
		    public int product(int x){
		    	int temp = x;
		    	int count = 1;
		    	while(temp != 0){
		    		count*=temp % 10;
		    		temp = temp/10;
		    	}
		    	return count;
		    }
		    public boolean isValid2(int x){
		    	int temp = x;
		    	while(temp != 0){
		    		if(temp % 10 == 0){
		    			return false;
		    		}
		    		temp = temp/10;
		    	}
		    	return true;
		    }
		    public boolean isValid(int x){
		    	if(!isValid2(x)){
		    		return false;
		    	}else{
		    		if(product(x) <= sum(x)){
		    			return true;
		    		}
		    		return false; 
		    	}
		    }
		}