Problem:
Score : 300 points

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.

Solution in Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

module ABC137

  ! <module>s to import
  use, intrinsic :: iso_fortran_env

  ! require all variables to be explicitly declared
  implicit none

  ! accessibility of <subroutine>s and <function>s in this <module>
  public  :: task_C
  private :: sort_string
  private :: isEqual

  ! constants for this <module>
  integer(INT8), parameter, private :: len_string = 10_INT32

  ! <type>s for this <module>
  type data_task
    character(len=len_string, kind=1), public :: string
    integer(INT64),                    public :: times
  end type data_task

  ! contained <subroutine>s and <function>s are below
  contains

  subroutine sort_string (str_target)

    ! arguments for this <subroutine>
    character(len=len_string, kind=1), intent(inout) :: str_target

    ! variables for this <subroutine>
    character(len=1, kind=1) :: buffer

    ! support variables for this <subroutine>
    integer(INT8) :: itr1, itr2

    do itr1 = 1_INT8,        len_string - 1_INT8, 1_INT8
    do itr2 = itr1 + 1_INT8, len_string,           1_INT8
      if ( str_target(itr1:itr1) .gt. str_target(itr2:itr2) ) then
        buffer                = str_target(itr1:itr1)
        str_target(itr1:itr1) = str_target(itr2:itr2)
        str_target(itr2:itr2) = buffer
      end if
    end do
    end do

    ! STEP.END
    return

  end subroutine sort_string

  pure function isEqual (str1, str2) result(stat)

    ! arguments for this <function>
    character(len=*, kind=1), intent(in) :: str1
    character(len=*, kind=1), intent(in) :: str2

    ! return value of this <function>
    logical :: stat
    
    stat = lge(str1, str2) .and. lle(str1, str2)
    return

  end function isEqual

  subroutine task_C

    ! variables for this <subroutine>
    integer(INT32) :: num_string
    integer(INT64) :: num_anagram

    ! arrays for this <module>
    type(data_task), allocatable :: given_data(:)

    ! support variables for this <subroutine>
    integer(INT32) :: itr, itr_origin, itr_target

    ! STEP.01
    ! read out the given data

    ! STEP.01.01
    ! read out the number of given strings
    read(unit=INPUT_UNIT, fmt=*) num_string

    ! STEP.01.02
    ! allocate the array to store the given strings
    allocate( given_data(1:num_string) )

    ! STEP.01.03
    ! read out the given strings
    do itr = 1_INT32, num_string, 1_INT32
      read(unit=INPUT_UNIT, fmt='(A)') given_data(itr)%string
    end do

    ! STEP.02
    ! calcualte the answer of this task

    ! STEP.02.01
    ! initialize the variables
    num_anagram         = 0_INT64
    given_data(:)%times = 0_INT64

    ! STEP.02.02
    ! count up the number of anagram
    do itr_origin = 1_INT32, num_string, 1_INT32
      
      ! sort the each given string
      call sort_string( given_data(itr_origin)%string )

      do itr_target = 1_INT32, itr_origin - 1_INT32, 1_INT32
        if ( isEqual( given_data(itr_origin)%string, given_data(itr_target)%string ) ) then
          given_data(itr_target)%times = 1_INT64     + given_data(itr_target)%times
          num_anagram                  = num_anagram + given_data(itr_target)%times
          exit
        end if
      end do

      print '(10(1X,I0))', num_anagram, given_data(:)%times

    end do

    ! STEP.03
    ! output the answer of this task
    write(unit=OUTPUT_UNIT, fmt='(I0)', advance='yes') num_anagram

    ! STEP.04
    ! deallocate the array to store the given strings
    deallocate( given_data )

    ! STEP.END
    return

  end subroutine task_C

end module ABC137


program main

  ! <module>s to import
  use, non_intrinsic :: ABC137

  ! require all variables to be explicitly declared
  implicit none

  call task_C

end program main