Given $$$n$$$ strings $$$S_1, S_2, \ldots S_n$$$, you need to calculate the number of different P-P-Palindromes given by these $$$n$$$ strings.

A palindrome is a string that can be read the same from left to right and from right to left. For example, "a", "level", and "otto" are palindromes, while "aab" and "icpc" are not.

A P-P-Palindrome is an ordered pair of nonempty palindromes $$$(P, Q)$$$ such that both $$$P$$$ and $$$Q$$$ are the substrings of some in $$$S_1, S_2, \ldots S_n$$$ and $$$P + Q$$$ is also a palindrome. Here $$$P + Q$$$ means concatenating $$$P$$$ and $$$Q$$$ in order, or more specifically, let $$$P = p_1 p_2 \ldots p_{|P|}$$$ and $$$Q = q_1 q_2 \ldots q_{|Q|}$$$, then $$$P + Q = p_1 p_2 \ldots p_{|P|} q_1 q_2\ldots q_{|Q|}$$$, where $$$|S|$$$ is the length of string $$$S$$$.

Note that two P-P-Palindromes are considered different if and only if $$$P$$$ differs or $$$Q$$$ differs.