Since time immemorial, the citizens of Dmojistan and Pegland have been at war. Now, they have finally signed a truce. They have decided to participate in a tandem bicycle ride to celebrate the truce. There are N citizens from each country. They must be assigned to pairs so that each pair contains one person from Dmojistan and one person from Pegland.</p>

Each citizen has a cycling speed. In a pair, the fastest person will always operate the tandem bicycle while the slower person simply enjoys the ride. In other words, if the members of a pair have speeds a and b, then the bike speed of the pair is max(a, b). The total speed is the sum of the N individual bike speeds.

For this problem, in each test case, you will be asked to answer one of two questions:

• Question 1: what is the minimum total speed, out of all possible assignments into pairs?
• Question 2: what is the maximum total speed, out of all possible assignments into pairs?

The first line will contain the type of question you are to solve, which is either 1 or 2.

The second line contains N (1 ≤ N ≤ 100).

The third line contains N space-separated integers: the speeds of the citizens of Dmojistan.

The fourth line contains N space-separated integers: the speeds of the citizens of Pegland.

Each person’s speed will be an integer between 1 and 1 000 000.

출력 형식

Output the maximum or minimum total speed that answers the question asked.

예제 입력 1

1
3
5 1 4
6 2 4

예제 출력 1

12

예제 입력 2

2
3
5 1 4
6 2 4

예제 출력 2

15

예제 입력 3

2
5
202 177 189 589 102
17 78 1 496 540

예제 출력 3

2016