using System;
using System.Linq;

struct ShortRateTreeNode
{
    public double DF;
    public double PU;
    public double PM;
    public double PD;
    public int IU;
    public int IM;
    public int ID;

    public ShortRateTreeNode(double df, double pu, double pm, double pd, int iu, int im, int id)
    {
        this.DF = df;
        this.PU = pu;
        this.PM = pm;
        this.PD = pd;
        this.IU = iu;
        this.IM = im;
        this.ID = id;
    }
}

class Program
{
    static double[] InduceForward(double[] values, ShortRateTreeNode[] nodes)
    {
        Func<int, double> next = k => values[values.Length / 2 + k];
        return nodes
            .Select(node => (node.PU * next(node.IU) + node.PM * next(node.IM) + node.PD * next(node.ID)) * node.DF)
            .ToArray();
    }

    static void Main()
    {
        var ITERATION = 10000;
        Func<double, double[]> maturityValues = x => Enumerable.Repeat(x, 201).ToArray();
        var reversedTree = Enumerable.Range(0, 100)
            .Reverse()
            .Select(i => Enumerable.Range(-i, i * 2 + 1)
                .Select(j => new ShortRateTreeNode(1.0, 1.0 / 6.0, 2.0 / 3.0, 1.0 / 6.0, j + 1, j, j - 1))
                .ToArray())
            .ToArray();
        var result = Enumerable.Range(0, ITERATION)
            .Select(i => reversedTree.Aggregate(maturityValues(i), InduceForward)[0])
            .Max();
        Console.WriteLine(result);
    }
}