Problem:
Score : 300 points

Problem Statement

There are N people. The name of the i-th person is S_i.

We would like to choose three people so that the following conditions are met:

The name of every chosen person begins with M, A, R, C or H.

There are no multiple people whose names begin with the same letter.

How many such ways are there to choose three people, disregarding order?

Note that the answer may not fit into a 32-bit integer type.

Constraints

1 \leq N \leq 10^5

S_i consists of uppercase English letters.

1 \leq |S_i| \leq 10

S_i \neq S_j (i \neq j)

Input

Input is given from Standard Input in the following format:

N
S_1
:
S_N

Output

If there are x ways to choose three people so that the given conditions are met, print x.

Sample Input 1

5
MASHIKE
RUMOI
OBIRA
HABORO
HOROKANAI

Sample Output 1

2

We can choose three people with the following names:

MASHIKE, RUMOI, HABORO

MASHIKE, RUMOI, HOROKANAI

Thus, we have two ways.

Sample Input 2

4
ZZ
ZZZ
Z
ZZZZZZZZZZ

Sample Output 2

0

Note that there may be no ways to choose three people so that the given conditions are met.

Sample Input 3

5
CHOKUDAI
RNG
MAKOTO
AOKI
RINGO

Sample Output 3

7

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

;; -*- coding:utf-8 -*-

(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter O3 '(optimize (speed 3) (safety 0) (debug 0)))
  (defparameter O2 '(optimize (speed 3) (safety 1))))

(defmacro print-line (obj &optional (stream '*standard-output*))
  `(prog1 (princ ,obj ,stream) (terpri ,stream)))


;; Hauptteil
(declaim (inline ensure-function))

(declaim (ftype (function (t) (values function &optional))
                ensure-function))
(defun ensure-function (function-designator)
  (if (functionp function-designator)
      function-designator
      (fdefinition function-designator)))

(defun map-combinations (function sequence &key (start 0) end length (copy t))
  (let* ((end (or end (length sequence)))
         (size (- end start))
         (length (or length size))
         (combination (subseq sequence 0 length))
         (function (ensure-function function)))
    (if (= length size)
        (funcall function combination)
        (flet ((call ()
                 (funcall function (if copy
                                       (copy-seq combination)
                                       combination))))
          (etypecase sequence
            (list
             (labels ((combine-list (c-tail o-tail)
                        (if (not c-tail)
                            (call)
                            (do ((tail o-tail (cdr tail)))
                                ((not tail))
                              (setf (car c-tail) (car tail))
                              (combine-list (cdr c-tail) (cdr tail))))))
               (combine-list combination (nthcdr start sequence))))
            (vector
             (labels ((combine (count start)
                        (if (zerop count)
                            (call)
                            (loop for i from start below end
                                  do (let ((j (- count 1)))
                                       (setf (aref combination j) (aref sequence i))
                                       (combine j (+ i 1)))))))
               (combine length start)))
            (sequence
             (labels ((combine (count start)
                        (if (zerop count)
                            (call)
                            (loop for i from start below end
                                  do (let ((j (- count 1)))
                                       (setf (elt combination j) (elt sequence i))
                                       (combine j (+ i 1)))))))
               (combine length start)))))))
  sequence)

(defconstant +factorial-bisection-range-limit+ 8)

(defun %multiply-range (i j)
  (labels ((bisect (j k)
             (declare (type (integer 1 #.most-positive-fixnum) j k))
             (if (< (- k j) +factorial-bisection-range-limit+)
                 (multiply-range j k)
                 (let ((middle (+ j (truncate (- k j) 2))))
                   (* (bisect j middle)
                      (bisect (+ middle 1) k)))))
           (bisect-big (j k)
             (declare (type (integer 1) j k))
             (if (= j k)
                 j
                 (let ((middle (+ j (truncate (- k j) 2))))
                   (* (if (<= middle most-positive-fixnum)
                          (bisect j middle)
                          (bisect-big j middle))
                      (bisect-big (+ middle 1) k)))))
           (multiply-range (j k)
             (declare (type (integer 1 #.most-positive-fixnum) j k))
             (do ((f k (* f m))
                  (m (1- k) (1- m)))
                 ((< m j) f)
               (declare (type (integer 0 (#.most-positive-fixnum)) m)
                        (type unsigned-byte f)))))
    (if (and (typep i 'fixnum) (typep j 'fixnum))
        (bisect i j)
	(bisect-big i j))))


(declaim (inline factorial))
(defun %factorial (n)
  (if (< n 2)
      1
      (%multiply-range 1 n)))

(defun binomial-coefficient (n k)
  (check-type n (integer 0))
  (check-type k (integer 0))
  (assert (>= n k))
  (if (or (zerop k) (= n k))
      1
      (let ((n-k (- n k)))
        (when (< k n-k)
          (rotatef k n-k))
        (if (= 1 n-k)
            n
            (/ (%multiply-range (+ k 1) n)
	       (%factorial n-k))))))

(deftype unum nil `(integer 0 ,(expt 10 9)))
(defun main ()
  (let* ((n (read))
	 (arr (make-array 5 :element-type 'fixnum :initial-element 0)))
    (dotimes (x n)
      (case (aref (read-line) 0)
	(#\M (incf (aref arr 0)))
	(#\A (incf (aref arr 1)))
	(#\R (incf (aref arr 2)))
	(#\C (incf (aref arr 3)))
	(#\H (incf (aref arr 4)))))
    (let ((sum 0))
      (map-combinations
       #'(lambda (triplet)
	   (incf sum
		 (* (aref triplet 0)
		    (aref triplet 1)
		    (aref triplet 2))))
       arr :length 3)
      (print-line sum))))

#-swank(main)


;; Für Test
(defun get-clipbrd ()
  (with-output-to-string (out)
    (run-program "C:/msys64/usr/bin/cat.exe" '("/dev/clipboard") :output out)))

(defun test ()
  (with-input-from-string (*standard-input* (delete #\return (get-clipbrd)))
    (main)))


;; Für Benchmark
(defparameter *file-path* *load-pathname*)
(defparameter *dir-path* (pathname (directory-namestring *file-path*)))
(defparameter *dat-path* (merge-pathnames "test.dat" *dir-path*))

#+swank
(defun gendat ()
  (with-open-file (out *dat-path*
		       :direction :output :if-exists :supersede)
    ))

(defun bench ()
  (let ((*standard-output* (make-broadcast-stream)))
    (with-open-file (*standard-input* *dat-path*)
      (time (main)))))