#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<complex>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
using namespace std;
typedef long long ll;
typedef unsigned long long ul;
typedef unsigned int ui;
typedef long double ld;
typedef pair<int, int> P;
typedef pair<ll, ll> LP;
typedef pair<ld, ld> LDP;
typedef complex<ld> Point;
const ll mod = 1000000007;
const ld INF = 1e+30;
const ld eps = 1e-8;
const ld pi = acos(-1.0);
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
int w, h;
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };
int sx, sy;
queue<P> q;
char mp[500][500];
bool used[500][500];
ld d[500][500];
vector<ld> a, b;
ld sa, sb;
bool comp(LDP x, LDP y) {
	return x.first - x.second < y.first - y.second;
}
void solve() {
	cin >> w >> h;
	rep(i, h) {
		rep(j, w) {
			d[i][j] = (ld)h*w*1000000;
		}
	}
	rep(i, h) {
		rep(j, w) {
			cin >> mp[i][j];
			if (mp[i][j] == 's') {
				sx = i, sy = j; mp[i][j] = '.';
			}
			else if (mp[i][j] == 'g') {
				q.push({ i,j }); used[i][j] = true;
			}
		}
	}
	int tmp = 0;
	while (!q.empty()) {
		int len = q.size();
		rep(aa, len) {
			P p = q.front(); q.pop();
			int x = p.first, y = p.second;
			d[x][y] = tmp;
			rep(j, 4) {
				int nx = x + dx[j], ny = y + dy[j];
				if (mp[nx][ny] == '.' && !used[nx][ny]) {
					used[nx][ny] = true; q.push({ nx,ny });
				}
			}
		}
		tmp++;
	}
	rep(i, h) {
		rep(j, w) {
			if (mp[i][j] == '.')a.push_back(d[i][j]);
			if (sx == i && sy == j)sa = d[i][j];
		}
	}
	rep(i, h)rep(j, w) {
		used[i][j] = false; d[i][j] = (ld)h*w*1000000;
		if (mp[i][j] == '*') {
			used[i][j] = true; q.push({ i,j });
		}
	}
	tmp = 0;
	while (!q.empty()) {
		int len = q.size();
		rep(aa, len) {
			P p = q.front(); q.pop();
			int x = p.first, y = p.second;
			d[x][y] = tmp;
			rep(j, 4) {
				int nx = x + dx[j], ny = y + dy[j];
				if (mp[nx][ny] == '.' && !used[nx][ny]) {
					used[nx][ny] = true; q.push({ nx,ny });
				}
			}
		}
		tmp++;
	}
	rep(i, h)rep(j, w) {
		if (mp[i][j] == '.') {
			//cout << i << " " << j << " " << d[i][j] << endl;
			b.push_back(d[i][j]);
		}
		if (sx == i && sy == j) {
			sb = d[i][j];
		}
	}
	cout << fixed << setprecision(10);
	int sz = a.size();
	ld ans = INF;
	vector<LDP> v;
	rep(i, sz) {
		v.push_back({ a[i],b[i] });
	}
	sort(v.begin(), v.end(), comp);
	ld sum = 0;
	rep(i, sz) {
		sum += b[i];
	}
	rep(i, sz) {
		//cout << v[i].first << " " << v[i].second << endl;
		//cout << v[i].first - v[i].second << endl;
		sum -= v[i].second; sum += v[i].first;
		ld csum = sum * sz / (ld)(1 + i);
		ld le = v[i].first - v[i].second;
		ld ri = INF;
		if (i + 1 < sz - 1) {
			ri = v[i + 1].first - v[i + 1].second;
		}
		//cout << sum << endl;
		if (le < csum / (ld)sz&&csum/(ld)sz<ri) {
			ans = min(ans, csum);
		}
	}
	cout << min(sa, sb + ans / (ld)sz) << endl;
}
int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	solve();
	//stop
	return 0;
}


Measured memory_bytes: 26536