#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <tuple>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;

class PalindromePermutations { public:
	double palindromeProbability(string word)
	{
		map<char, int> cnt;
		for(char c: word) cnt[c]++;

		vector<int> ns;
		for(auto cn: cnt) ns.emplace_back(cn.second);

		return solve(ns);
	}

	double solve(vector<int> c)
	{
		if(count_if(c.begin(), c.end(), [&](int x){return x%2==1;}) >= 2)
			return 0.0;
		return rec(c);
	}

	double rec(vector<int> c)
	{
		if(c.size() <= 1)
			return 1.0;

		int n = accumulate(c.begin(), c.end(), 0);
		int n2 = n/2;
		int k = c.back();
		int k2 = k/2;
		c.pop_back();
		return C(n2,k2) / C(n,k) * rec(c);
	}

	double C(int n, int k)
	{
		double v = 1.0;
		for(int i=1; i<=k; ++i)
			v = v * (n+1-i) / i;
		return v;
	}
};

// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
 { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
 { os << "{ ";
   for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
   os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const double& Expected, const double& Received) {
 bool ok = (abs(Expected - Received) < 1e-9);
 if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
 cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END	 verify_case(_, PalindromePermutations().palindromeProbability(word));}
int main(){

CASE(0)
	string word = "haha"; 
	double _ = 0.3333333333333333; 
END
CASE(1)
	string word = "xxxxy"; 
	double _ = 0.2; 
END
CASE(2)
	string word = "xxxx"; 
	double _ = 1.0; 
END
CASE(3)
	string word = "abcde"; 
	double _ = 0.0; 
END
CASE(4)
	string word = "hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhff"; 
	double _ = 0.025641025641025637; 
END
/*
CASE(5)
	string word = ; 
	double _ = ; 
END
CASE(6)
	string word = ; 
	double _ = ; 
END
*/
}
// END CUT HERE
