Trio

Let $A$ be any set of $n$ natural numbers whose decimal representations have exactly four digits, none of which is $0$.

A trio is a set of three numbers $\{a, b, c\}$ chosen from $A$ that satisfies all of the following conditions at once.

• The ones digits of $a$, $b$, $c$ are either all equal or all distinct.
• The tens digits of $a$, $b$, $c$ are either all equal or all distinct.
• The hundreds digits of $a$, $b$, $c$ are either all equal or all distinct.
• The thousands digits of $a$, $b$, $c$ are either all equal or all distinct.

For example, $\{1425, 1113, 1354\}$ is a trio if all three numbers are in $A$. Their ones digits are all distinct, their tens digits are all distinct, their hundreds digits are all distinct, and their thousands digits are all equal. The set $\{1425, 1113, 5436\}$ is not a trio, even if $A$ contains all three numbers.

The first line contains a single integer $n$ ($1 \le n \le 2,000$), the number of members in $A$. Each of the following $n$ lines contains one positive integer with exactly four digits, none of which is $0$. The $n$ numbers are all distinct and are the members of $A$.

Print the number of different trios for $A$ on one line.