K. Kitchen
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Xiangtan University students absolutely adore the pig's trotter rice from Lianjian, which is a dish composed of pig's trotters and rice. They currently offer $$$n$$$ varieties of pig's trotter rice, with the deliciousness level of the i-th variety being $$$a_i$$$.

For these $$$n$$$ varieties of pig's trotter rice, there is a concept known as the discord degree $$$D$$$. The discord degree is calculated by sorting all the deliciousness levels from smallest to largest, and then taking the maximum difference between consecutive items, as follows

$$$$$$D = \max\big\{a_2-a_1,~a_3-a_2,~\ldots~,~a_n-a_{n-1}\big\}$$$$$$

You, as a prospective seller of pig's trotter rice at Lianjian, do not wish for the discord degree $$$D$$$ of all the pig's trotter rice you sell to be too high. Therefore, you are considering introducing new combinations of pig's trotters and rice. You currently have $$$X$$$ types of pig's trotters, with the deliciousness level of the i-th type being $$$x_i$$$, and $$$Y$$$ types of rice, with the deliciousness level of the j-th type being $$$y_j$$$.

You can create a new variety of pig's trotter rice by choosing any one type of pig's trotter and any one type of rice. For example, if you select the i-th type of pig's trotter and the j-th type of rice, the deliciousness level of the new combination would be $$$x_i \times y_j$$$.

Now, you want to calculate the minimum possible discord degree $$$D$$$ after adding any number of new combinations of pig's trotters and rice.

Input

The problem consists of a single test case, with the first line containing three integers, $$$n~(2 \le n \le 10^3)$$$,$$$~X,~Y,~(1 \le ~X,~Y \le 10^{3})$$$; the second line contains $$$n$$$ integers $$$a_i,~(1 \le a_i \le 10^{6})$$$; the third line contains $$$X$$$ integers $$$x_i,~(1 \le x_i \le 10^{6})$$$; and the fourth line contains $$$Y$$$ integers $$$y_i,~(1 \le y_i \le 10^{6})$$$.

It is guaranteed that the sum of $$$n,~X,~Y$$$ does not exceed $$$10^3$$$.

Example
Input
3 3 3
11 45 14
191 98 10
192 608 17
Output
31