Alice has three different types of sweets. There are $N$ sweets of each type, and each sweet has a tastiness value. The tastiness values for sweets are given in three arrays $A$, $B$, and $C$. The tastiness value of two sweets of a particular type can differ.

Alice wants to choose three sweets, exactly one of each type. Let the chosen sweets’ tastiness values be $a$, $b$, and $c$. You need to choose the sweets such that the value of the equation $abs(a - b) + abs(b - c) + abs(c - a)$ is minimized. Here, $abs(x)$ is the absolute value function.

Input Format

• The first line contains a single integer $N$ denoting the number of sweets of each type.
• The second line contains $N$ space-separated integers denoting the array $A$.
• The third line contains $N$ space-separated integers denoting the array $B$.
• The fourth line contains $N$ space-separated integers denoting the array $C$.

Output Format

Print the minimum value of the equation mentioned in the problem statement if we can choose exactly one sweet of each type.

Constraints

$1 \leq N \leq 10^5 \\ 1 \leq A[i], B[i], C[i] \leq 10^8$