Hyunju and Yunju's Fun Word Game

Hyunju and Yunju spend Sundays playing a word game. While playing, they noticed that some pairs of words do not like each other.

For two words A and B, suppose A comes before B in lexicographic order. If B' comes before A' in lexicographic order, then the two words do not like each other. Here X' means the word X written in reverse. For instance, if X = "kamen", then X' = "nemak".

For instance, "lova" and "novac" like each other, while "aron" and "sunce" do not like each other.

Given a list of words, write a program that counts how many unordered pairs of words do not like each other.

The first line contains the number of words N (2 <= N <= 100,000).

Each of the next N lines contains one word. Every word consists only of lowercase English letters and has length at most 10. No word appears more than once.

Print one integer: the number of pairs of input words that do not like each other.