Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Pupils Redistribution

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIn 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 *a* _{1}, *a* _{2}, ..., *a* _{ n} (1 ≤ *a* _{ i} ≤ 5), where *a* _{ i} is academic performance of the *i*-th student of the group *A*.

The third line contains sequence of integer numbers *b* _{1}, *b* _{2}, ..., *b* _{ n} (1 ≤ *b* _{ i} ≤ 5), where *b* _{ i} 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

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/09/2020 03:05:51 (g2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|