Finally Fox Ciel arrived in front of her castle!

She have to type a password to enter her castle. An input device attached to her castle is a bit unusual.

The input device is a 1 × n rectangle divided into n square panels. They are numbered 1 to n from left to right. Each panel has a state either ON or OFF. Initially all panels are in the OFF state. She can enter her castle if and only if x₁-th, x₂-th, ..., x_k-th panels are in the ON state and other panels are in the OFF state.

She is given an array a₁, ..., a_l. In each move, she can perform the following operation: choose an index i (1 ≤ i ≤ l), choose consecutive a_i panels, and flip the states of those panels (i.e. ON → OFF, OFF → ON).

Unfortunately she forgets how to type the password with only above operations. Determine the minimal number of operations required to enter her castle.

The first line contains three integers n, k and l (1 ≤ n ≤ 10000, 1 ≤ k ≤ 10, 1 ≤ l ≤ 100), separated by single spaces.

The second line contains k integers x₁, ..., x_k (1 ≤ x₁ < x₂ < ... < x_k ≤ n), separated by single spaces.

The third line contains l integers a₁, ..., a_l (1 ≤ a_i ≤ n), separated by single spaces. It is possible that some elements of the array a_i are equal value.

Print the minimal number of moves required to type the password. If it's impossible, print -1.