Let N be a positive integer. Integers 1, 2, 3, ..., 2N are divided into three sets A, B and C. Write a program table, which calculates the number of ways to fill the table with two rows and N columns so that:</p>

• Each cell of the table contains a single integer;
• The integers of the set A should be written on the first row of the table;
• The integers of the set B should be written on the second row of the table;
• The integers of the set C can be written on any table row;
• The numbers in each row of the table should form an increasing sequence;
• The numbers in each column of the table should form an increasing sequence.

For example, if N = 4 , A = {2, 3} , B = {4, 7, 8} and C = {1, 5, 6} , then there are exactly two tables of required type. 

입력 형식

On the first row of the standard input is given the integer N (1 < N ≤ 35). On the second row are given M – the number of integers of the set A , and integers of the set A (0 ≤ M ≤ N). On the third row are given K – the number of integers of the set B, and integers of the set B (0 ≤ K ≤ N). 

출력 형식

The program should print on the standard output a single line holding the result. 

예제 입력

4
2 3 2
3 4 8 7

예제 출력

2