Problem C
Metro building

There are $n$ ($n\le {10}^5$) cities in OI Kingdom. The emperor of the Kingdom wants to build some undirected metro-lines to make the Kingdom connected. Each city has an official name $A_i$, and an unofficial name $B_i$. The beauty of a metro-line between city $i$ and $j$ is $w=|LCP(A_i,B_j)|+|LCP(B_i,A_j)|$, where $LCP$ denotes the longest common prefix of two strings, and $|S|$ denotes the length of a string $S$. The overall beauty of a plan is the sum of beauty of all the metro-line in the plan. The king wants to know the highest possible overall beauty of the Kingdom, if it’s connected using the least possible number of metro-lines.

It is guaranteed that $\sum |A_i|+|B_i|\le {10}^5$. It is also guaranteed that $A_i$ and $B_i$ only contains lowercase English letters.

Input

In the first there is an integer $n\le {10}^5$.

Then follow $n$ lines, the $i^{th}$ of which contains the string $A_i$.

Then follow $n$ more lines, the $i^{th}$ of which contains the string $B_i$.

Output

Output a single line containing an integer, the maximum overall beauty of the kingdom.

3
aaa
bbc
bb
bbb
ac
bbc

6