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 JavaScript (node.js v5.12) (judge verdict: Accepted)

function Main(input) {
	input = input.split("\n")
	var namesN = input[0]
	var names = input.slice(1)
	var nameInitialCounts = {}
	for(var name of names) {
		nameInitialCounts[name.charAt(0)]
			= ++nameInitialCounts[name.charAt(0)] || 1;
	}
	var cases = k_combinations(["M", "A", "R", "C", "H"], 3)
	var result = 0
	for(var c of cases) {
		result += (nameInitialCounts[c[0]] || 0) * (nameInitialCounts[c[1]] || 0) * (nameInitialCounts[c[2]] || 0)
	}
	console.log(result)
}


function k_combinations(set, k) {
	var i, j, combs, head, tailcombs;
	
	// There is no way to take e.g. sets of 5 elements from
	// a set of 4.
	if (k > set.length || k <= 0) {
		return [];
	}
	
	// K-sized set has only one K-sized subset.
	if (k == set.length) {
		return [set];
	}
	
	// There is N 1-sized subsets in a N-sized set.
	if (k == 1) {
		combs = [];
		for (i = 0; i < set.length; i++) {
			combs.push([set[i]]);
		}
		return combs;
	}
	
	// Assert {1 < k < set.length}
	
	// Algorithm description:
	// To get k-combinations of a set, we want to join each element
	// with all (k-1)-combinations of the other elements. The set of
	// these k-sized sets would be the desired result. However, as we
	// represent sets with lists, we need to take duplicates into
	// account. To avoid producing duplicates and also unnecessary
	// computing, we use the following approach: each element i
	// divides the list into three: the preceding elements, the
	// current element i, and the subsequent elements. For the first
	// element, the list of preceding elements is empty. For element i,
	// we compute the (k-1)-computations of the subsequent elements,
	// join each with the element i, and store the joined to the set of
	// computed k-combinations. We do not need to take the preceding
	// elements into account, because they have already been the i:th
	// element so they are already computed and stored. When the length
	// of the subsequent list drops below (k-1), we cannot find any
	// (k-1)-combs, hence the upper limit for the iteration:
	combs = [];
	for (i = 0; i < set.length - k + 1; i++) {
		// head is a list that includes only our current element.
		head = set.slice(i, i + 1);
		// We take smaller combinations from the subsequent elements
		tailcombs = k_combinations(set.slice(i + 1), k - 1);
		// For each (k-1)-combination we join it with the current
		// and store it to the set of k-combinations.
		for (j = 0; j < tailcombs.length; j++) {
			combs.push(head.concat(tailcombs[j]));
		}
	}
	return combs;
}

//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));