After learning a lot about space exploration, a little girl named Ana wants to change the subject.
Ana is a girl who loves palindromes (string that can be read the same backwards as forward). She has learned how to check for a given string whether it's a palindrome or not, but soon she grew tired of this problem, so she came up with a more interesting one and she needs your help to solve it:
You are given an array of strings which consist of only small letters of the alphabet. Your task is to find how many palindrome pairs are there in the array. A palindrome pair is a pair of strings such that the following condition holds: at least one permutation of the concatenation of the two strings is a palindrome. In other words, if you have two strings, let's say "aab" and "abcac", and you concatenate them into "aababcac", we have to check if there exists a permutation of this new string such that it is a palindrome (in this case there exists the permutation "aabccbaa").
Two pairs are considered different if the strings are located on different indices. The pair of strings with indices $$$(i,j)$$$ is considered the same as the pair $$$(j,i)$$$.
The first line contains a positive integer $$$N$$$ ($$$1 \le N \le 100\,000$$$), representing the length of the input array.
Eacg of the next $$$N$$$ lines contains a string (consisting of lowercase English letters from 'a' to 'z') — an element of the input array.
The total number of characters in the input array will be less than $$$1\,000\,000$$$.
Output one number, representing how many palindrome pairs there are in the array.
The first example:
The second example: