101372: [AtCoder]ABC137 C - Green Bin

Problem Statement

We will call a string obtained by arranging the characters contained in a string $a$ in some order, an anagram of $a$.

For example, greenbin is an anagram of beginner. As seen here, when the same character occurs multiple times, that character must be used that number of times.

Given are $N$ strings $s_1, s_2, \ldots, s_N$. Each of these strings has a length of $10$ and consists of lowercase English characters. Additionally, all of these strings are distinct. Find the number of pairs of integers $i, j$ $(1 \leq i < j \leq N)$ such that $s_i$ is an anagram of $s_j$.

Constraints

• $2 \leq N \leq 10^5$
• $s_i$ is a string of length $10$.
• Each character in $s_i$ is a lowercase English letter.
• $s_1, s_2, \ldots, s_N$ are all distinct.

Input

Input is given from Standard Input in the following format:

$N$
$s_1$
$s_2$
$:$
$s_N$

Output

Print the number of pairs of integers $i, j$ $(1 \leq i < j \leq N)$ such that $s_i$ is an anagram of $s_j$.

Sample Input 1

3
acornistnt
peanutbomb
constraint

Sample Output 1

1

$s_1 =$ acornistnt is an anagram of $s_3 =$ constraint. There are no other pairs $i, j$ such that $s_i$ is an anagram of $s_j$, so the answer is $1$.

Sample Input 2

2
oneplustwo
ninemodsix

Sample Output 2

0

If there is no pair $i, j$ such that $s_i$ is an anagram of $s_j$, print $0$.

Sample Input 3

5
abaaaaaaaa
oneplustwo
aaaaaaaaba
twoplusone
aaaabaaaaa

Sample Output 3

4

Note that the answer may not fit into a $32$-bit integer type, though we cannot put such a case here.