#402 (Div. 2)A. Pupils Redistribution

A. Pupils Redistribution

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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 nstudents. 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                               

這道題本來很簡單，是我想複雜了，題意是有兩組同學，每組的人數相等，每個人都有一個成績表現（1~5），現在要交換兩組的同學，使這兩個小組中每個階段的成績表現相等。解決方案，分別統計兩個每個成績表現的人數，如果某個成績表現的人數爲奇數，則不能完成交換，只有當兩個組中某個成績表現的人數之和爲偶數，並且不相等，纔可以進行交換。

import java.util.Arrays;
import java.util.Scanner;

public class Main {
	static int[] A = new int[9];
	static int[] B = new int[9];
	public static void main(String[] args){
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		for(int i=0;i<n;i++){
			A[scan.nextInt()] ++ ;
		}
		
		for(int i=0;i<n;i++){
			B[scan.nextInt()] ++ ;
		}
		
		for(int i=1;i<=5;i++){
			if((A[i]+B[i])%2!=0){
				System.out.println("-1");
				return;
			}
		}
		
		int ans = 0;
		for(int i=1;i<=5;i++){
			if(A[i]>(A[i]+B[i])/2){
				ans+=Math.abs(A[i]-(A[i]+B[i])/2);
			}
		}
		System.out.println(ans);
	}
}