using System;
using System.Linq;
using System.Collections.Generic;
using Debug = System.Diagnostics.Trace;
using SB = System.Text.StringBuilder;
using Number = System.Int64;
using C = System.Int32;
using V = System.Int32;
namespace Program
{
    public class Solver
    {
        public void Solve()
        {
            var m = ri;
            var n = ri;
            var s = Enumerate(n, x => rs.ToCharArray());
            var q = new Queue<int>();
            var qq = new Queue<int>();
            var dist = Enumerate(n * m, x => 1L << 61);
            var eist = Enumerate(n * m, x => 1L << 61);
            var g = -1;
            var cnt = 0;
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                {
                    if (s[i][j] == 's') { g = i * m + j; s[i][j] = '.'; }
                    if (s[i][j] == 'g') { dist[i * m + j] = 0; q.Enqueue(i * m + j); }
                    if (s[i][j] == '*') { eist[i * m + j] = 0; qq.Enqueue(i * m + j); }
                    if (s[i][j] == '.') cnt++;
                }
            bfs(s, q, m, dist);
            bfs(s, qq, m, eist);
            decimal l = 0.0M; decimal r = 1e15M;
            for (int _ = 0; _ < 100; _++)
            {
                var mid = (l + r) / 2;
                var sum = 0.0M;
                for (int i = 0; i < n; i++)
                    for (int j = 0; j < m; j++)
                        if (s[i][j] == '.') sum += Math.Min(dist[i * m + j], eist[i * m + j] + mid);
                sum /= cnt;
                if (sum > mid) l = mid;
                else r = mid;
            }
            //Debug.WriteLine($"{l} {r}");
            Console.WriteLine("{0:0.000000000000}", Math.Min(dist[g], eist[g] + l));

        }
        void bfs(char[][] s, Queue<int> q, int m, long[] dist)
        {
            while (q.Any())
            {
                var p = q.Dequeue();
                var i = p / m;
                var j = p % m;
                for (int k = 0; k < 4; k++)
                {
                    var ni = i + dx[k];
                    var nj = j + dy[k];
                    if (s[ni][nj] != '.') continue;
                    if (dist[ni * m + nj] > dist[p] + 1)
                    {
                        dist[ni * m + nj] = dist[p] + 1;
                        q.Enqueue(ni * m + nj);
                    }
                }
            }
        }
        const long INF = 1L << 60;
        int[] dx = { -1, 0, 1, 0 };
        int[] dy = { 0, 1, 0, -1 };
        //*
        int ri { get { return sc.Integer(); } }
        long rl { get { return sc.Long(); } }
        double rd { get { return sc.Double(); } }
        string rs { get { return sc.Scan(); } }
        //*/

        public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());
        static T[] Enumerate<T>(int n, Func<int, T> f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; }
        static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
    }
}

#region main
static class Ex
{
    static public string AsString(this IEnumerable<char> ie) { return new string(ie.ToArray()); }
    static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ")
    {
        return string.Join(st, ie.Select(x => x.ToString()).ToArray());
        //return string.Join(st, ie);
    }
    static public void Main()
    {
        Console.SetOut(new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        var solver = new Program.Solver();
        solver.Solve();
        Console.Out.Flush();
    }
}
#endregion
#region Ex
namespace Program.IO
{
    using System.IO;
    using System.Text;
    using System.Globalization;
    public class Printer: StreamWriter
    {
        public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
        public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
    }
    public class StreamScanner
    {
        public StreamScanner(Stream stream) { str = stream; }
        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }
        private byte read()
        {
            if (isEof) return 0;
            if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } }
            return buf[ptr++];
        }
        public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; }

        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        public string ScanLine()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n' && b != 0; b = (char)read())
                if (b != '\r') sb.Append(b);
            return sb.ToString();
        }
        public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
        public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
        public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
}
#endregion


Measured memory_bytes: 18280