using System;

using System.Linq;

public class Program

{

    public static double Score(double[] ratings, double[] prior = null, double[] util = null, double z = 1.65){

        // http://www.evanmiller.org/ranking-items-with-star-ratings.html

        // https://stackoverflow.com/questions/1411199/what-is-a-better-way-to-sort-by-a-5-star-rating#answer-40958702

        prior = prior ?? new[]{ 0d, 0d, 0d, 0d, 0d };

        util  = util  ?? new[]{ 1d, 2d, 3d, 4d, 5d };

        var ns = ratings.Zip(prior, (r, p) => r + p).ToArray();

        var N = ns.Sum();

        var K = ns.Length;

        var s = util;

        var s2 = s.Select(x => x*x).ToArray();

        Func<double[], double> f = (fs) => {

            return fs.Zip(ns, (fsk, nk) => fsk*(nk+1)).Sum() / (N+K);

        };

        var fsns = f(s);

        return fsns - z * Math.Sqrt((f(s2) - (fsns*fsns)) / (N+K+1));

    }

    public static double Width(double[] ratings, double[] prior = null, double[] util = null, double z = 1.65){

        prior = prior ?? new[]{ 1d, 1d, 1d, 1d, 1d };

        util  = util  ?? new[]{ 1d, 2d, 3d, 4d, 5d };

        var ns = ratings.Zip(prior, (r, p) => r + p).ToArray();

        var N = ns.Sum();

        var K = ns.Length;

        var s = util;

        var s2 = s.Select(x => x*x).ToArray();

        Func<double[], double> f = (fs) => {

            return fs.Zip(ns, (fsk, nk) => fsk*(nk+1)).Sum() / (N+K);

        };

        var fsns = f(s);

        return 2 * z * Math.Sqrt((f(s2) - (fsns*fsns)) / (N+K+1));

    }

    public static void Main()

    {

        var ratingCounts = new[]{ 0d, 0d, 0d, 0d, 40d };

        var score = Score(ratingCounts);

        var width = Width(ratingCounts);

        Console.WriteLine(score);

        Console.WriteLine(width);

    }

}