import java.io.IOException; import java.io.InputStream; import java.io.OutputStream; import java.io.PrintStream; import java.io.PrintWriter; import java.math.BigInteger; import java.util.ArrayList; import java.util.Arrays; import java.util.Collections; import java.util.HashMap; import java.util.HashSet; import java.util.Iterator; import java.util.List; import java.util.Map.Entry; import java.util.Map; import java.util.NoSuchElementException; import java.util.Random; import java.util.Set; import java.util.TreeMap; import java.util.function.BiFunction; import java.util.function.DoubleUnaryOperator; import java.util.function.IntBinaryOperator; import java.util.function.LongBinaryOperator; import java.util.function.LongToDoubleFunction; import java.util.function.Predicate; import java.util.random.RandomGenerator; public class Main { static MyPrintWriter pw = MyPrintWriter.getInstance(); static FastScanner sc = FastScanner.getInstance(); public static void main(String[] args) throws IOException { Thread.setDefaultUncaughtExceptionHandler((t, e) -> System.exit(1)); new Main().run(); pw.flush(); } void run() { int N = sc.nextInt(); int M = sc.nextInt(); long[] A = new long[N]; for (int i = 0; i < N; i++) { char[] S = sc.next().toCharArray(); for (int j = 0; j < S.length; j++) { if (S[j] == 'o') { A[i] |= 1L << j; } } } var f = new long[1 << N]; Arrays.fill(f, (1L << M) - 1); for (int i = 0; i < N; i++) { f[1 << i] = A[i]; } f = BooleanLattice.subsetZeta(f, (x, y) -> x & y); var dp = new double[1 << N]; for (int i = dp.length - 1; i >= 0; i--) { if (Long.bitCount(f[i]) <= 1) { continue; } int size = N - Long.bitCount(i); dp[i] = 1; for (int next = 0; next < N; ++next) { if (((i >> next) % 2) == 1) { continue; } dp[i] += (1.0 / size) * dp[i | (1 << next)]; } } double ans = dp[0]; pw.println(ans); } } class BooleanLattice { /** * b(S) = op_{T ⊆ S} a(T) を計算する。 * * @param a * 入力配列 * @param op * 二項演算 * @return subset zeta transform */ public static long[] subsetZeta(long[] a, LongBinaryOperator op) { long[] b = Arrays.copyOf(a, a.length); int N = MathUtils.floorLog2(a.length); for (int i = 0; i < N; ++i) { for (int s = 0; s < (1 << N); ++s) { if (Ints.bitAt(s, i) == 0) { continue; } b[s] = op.applyAsLong(b[s], b[s ^ (1 << i)]); } } return b; } } class FastScanner { private static FastScanner instance = null; private final InputStream in = System.in; private final byte[] buffer = new byte[1 << 16]; private int ptr = 0; private int buflen = 0; private FastScanner() { } public static FastScanner getInstance() { if (instance == null) { instance = new FastScanner(); } return instance; } private boolean hasNextByte() { if (ptr < buflen) { return true; } ptr = 0; try { buflen = in.read(buffer); } catch (IOException e) { e.printStackTrace(); } return buflen > 0; } private int readByte() { if (hasNextByte()) { return buffer[ptr++]; } else { return -1; } } private boolean isPrintableChar(int c) { return (33 <= c) && (c <= 126); } public boolean hasNext() { while (hasNextByte() && (!isPrintableChar(buffer[ptr]))) { ptr++; } return hasNextByte(); } public String next() { if (!hasNext()) { throw new NoSuchElementException(); } StringBuilder sb = new StringBuilder(); int b = readByte(); while (isPrintableChar(b)) { sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } public long nextLong() { if (!hasNext()) { throw new NoSuchElementException(); } long n = 0; boolean minus = false; int b = readByte(); if (b == '-') { minus = true; b = readByte(); } while ((b >= '0') && (b <= '9')) { // n = n * 10 + (b - '0'); n = ((n << 1) + (n << 3)) + (b - '0'); b = readByte(); } return minus ? -n : n; } public int nextInt() { return ((int) (nextLong())); } } class Ints { public static int bitAt(int binary, int pos) { if (pos >= 32) { return 0; } return (binary >>> pos) % 2; } } class MathUtils { /** * x=0のときは-1 * * @param x * @return */ public static int floorLog2(long x) { if (x == 0) { return -1; } return 63 - Long.numberOfLeadingZeros(x); } } class MyPrintWriter extends PrintWriter { private static MyPrintWriter instance = null; private MyPrintWriter() { super(System.out); } public static MyPrintWriter getInstance() { if (instance == null) { instance = new MyPrintWriter(); } return instance; } } // --- Original Code --- // // // import java.io.IOException; // import java.util.Arrays; // // import library.tools.FastScanner; // import library.tools.MergeFiles; // import library.tools.MyPrintWriter; // import library.util.ArrayUtils; // import library.util.Longs; // import library.util.fold.WaveletMatrix; // import library.util.poset.BooleanLattice; // // public class Main { // static MyPrintWriter pw = MyPrintWriter.getInstance(); // static FastScanner sc = FastScanner.getInstance(); // // public static void main(String[] args) throws IOException { // new Main().run(); // pw.flush(); // MergeFiles.export(); // } // // // void run() { // int N=sc.nextInt(); // int M=sc.nextInt(); // long[]A=new long[N]; // for (int i = 0; i < N; i++) { // char[]S=sc.next().toCharArray(); // for (int j = 0; j < S.length; j++) { // if(S[j]=='o')A[i]|=1L< x & y); // var dp=new double[1<= 0; i--) { // if (Long.bitCount(f[i])<=1)continue; // int size=N-Long.bitCount(i); // dp[i]=1; // for (int next=0;next> next) % 2 == 1) continue; // dp[i]+=1./size*dp[i|(1<