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I. Palindrome Pairs
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$(j,i)$$$.

Input

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

Output one number, representing how many palindrome pairs there are in the array.

Examples
Input
3
aa
bb
cd
Output
1
Input
6
aab
abcac
dffe
ed
aa
aade
Output
6
Note

The first example:

  1. aa $$$+$$$ bb $$$\to$$$ abba.

The second example:

  1. aab $$$+$$$ abcac $$$=$$$ aababcac $$$\to$$$ aabccbaa
  2. aab $$$+$$$ aa $$$=$$$ aabaa
  3. abcac $$$+$$$ aa $$$=$$$ abcacaa $$$\to$$$ aacbcaa
  4. dffe $$$+$$$ ed $$$=$$$ dffeed $$$\to$$$ fdeedf
  5. dffe $$$+$$$ aade $$$=$$$ dffeaade $$$\to$$$ adfaafde
  6. ed $$$+$$$ aade $$$=$$$ edaade $$$\to$$$ aeddea