#include <bits/stdc++.h>

using namespace std;

const int N = 307;

int _n, l;
bool acc[N];

int cnt;
int p[N];
int T[N][2];
string in[N];

int n;
long double dp[N][N];

char s[100];
void add(int a){
	int cur = 0;
	scanf("%s", s + 1);

	for(int i = 1; i <= l; ++i){
		bool t = s[i] == 'T';
		if(T[cur][t] == -1){
			T[cur][t] = ++cnt;
			in[cnt] = in[cur];
			in[cnt].push_back(t + '0');
		}
		
		cur = T[cur][t];
	}
	
	acc[cur] = true;
}

int Find(string a){
	int cur = 0, licz = 0;
	for(char c: a){
		cur = T[cur][c - '0']; ++licz;
		if(cur < 0 || (int)in[cur].size() < licz)
			return -1;
	}
	
	return cur;
}

int check(int a, int b){
	string t = in[a];
	t.push_back(b + '0');
	
	while(t.size()){
		int id = Find(t);
		if(id != -1)
			return id;
		
		reverse(t.begin(), t.end());
		t.pop_back();
		reverse(t.begin(), t.end());
	}
	
	return 0;
}

long double res[N];
void solveGauss(){
	for(int i = 0; i <= n; ++i){
		for(int j = i + 1; j <= n; ++j){
			if(dp[j][i] == 0.0)
				continue;
			
			double t = dp[j][i] / dp[i][i];
			for(int k = 0; k <= n + 1; ++k)
				dp[j][k] -= t * dp[i][k];
		}
	}
	
	res[n] = dp[n][n + 1] / dp[n][n];
	for(int i = n - 1; i >= 0; --i){
		res[i] = dp[i][n + 1];
		for(int j = n; j > i; --j)
			res[i] -= res[j] * dp[i][j];
		res[i] /= dp[i][i];
	}
}

int main(){
	scanf("%d %d", &_n, &l);
	for(int i = 0; i <= _n * l; ++i)
		T[i][0] = T[i][1] = -1;

	for(int i = 1; i <= _n; ++i)
		add(i);
	
	for(int i = 0; i <= cnt; ++i){
		if(acc[i])
			continue;

		if(T[i][0] == -1)
			T[i][0] = check(i, 0);
		if(T[i][1] == -1)
			T[i][1] = check(i, 1);
//		printf("%d :: %d %d\n", i, T[i][0], T[i][1]);
	}
	
	n = cnt;
	for(int i = 0; i <= cnt; ++i)
		if(acc[i])
			dp[i][i] = 1;
		else{
			dp[i][i] = 1;
			dp[i][T[i][0]] -= 0.5;
			dp[i][T[i][1]] -= 0.5;
			dp[i][cnt + 1] = 1;
		}
	
//	for(int i = 0; i <= cnt; ++i){
//		for(int j = 0; j <= cnt + 1; ++j)
//			printf("%Lf ", dp[i][j]);
//		puts("");
//	}

	solveGauss();
	printf("%.9Lf\n", res[0]);
	return 0;
}