import std.conv, std.functional, std.range, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons;
import core.bitop;

class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }

bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }

int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }


enum PROB = 1.0L / 3.0L;

void main() {
  try {
    for (; ; ) {
      const N = readInt;
      const S = readToken;
      
      auto dp = new real[N];
      auto ps = new real[N];
      auto qs = new real[N];
      auto fs = new real[N];
      auto gs = new real[N];
      dp[] = 0.0L;
      ps[] = 0.0L;
      qs[] = 0.0L;
      fs[] = 0.0L;
      gs[] = 0.0L;
      ps[N - 1] = 1.0L;
      foreach_reverse (i; 0 .. N - 1) if (S[i] == '.') {
        foreach (di; 1 .. 2 + 1) {
          if (i + di < N && S[i + di] == '.') {
            ps[i] += PROB * ps[i + di];
            qs[i] += PROB * qs[i + di];
            fs[i] += PROB * (ps[i + di] + fs[i + di]);
            gs[i] += PROB * (qs[i + di] + gs[i + di]);
          } else {
            qs[i] += PROB * 1.0L;
            gs[i] += PROB * 1.0L;
          }
        }
        debug {
          writeln(i, ": ", ps[i], " ", fs[i], " ", gs[i], " -> ", dp[i]);
        }
        dp[i] = (fs[i] + gs[i] + PROB * 1.0L) / ps[i];
        ps[i] += PROB * 1.0L;
        fs[i] += PROB * (1.0L + dp[i]);
      }
      debug {
        writeln("dp = ", dp);
        writeln("ps = ", ps);
        writeln("qs = ", qs);
        writeln("fs = ", fs);
        writeln("gs = ", gs);
      }
      writefln("%.12f", dp[0]);
    }
  } catch (EOFException e) {
  }
}