using System;

using System.Text;

public class Program

{

    public static void Main()

    {

        string[,] matrix = 

        {

            {"a1", "b1", "c1", "d1"},

            {"a2", "b2", "c2", "d2"},

            {"a3", "b2", "c3", "d3"},

            {"a4", "b4", "c4", "d4"}

        };

        Console.WriteLine(cofactors(matrix));

    }

    public static string cofactors(string[,] matrix)

    {

        if (matrix.GetLength(0) != matrix.GetLength(1))

        {

            throw new ArgumentException("must be squared", "matrix");

        }

        var order = matrix.GetLength(0);

        if (order == 1)

        {

            return matrix[0, 0];

        }

        else if (order == 2)

        {

            return string.Format("({0} * {1}) - ({2} * {3})", matrix[0,0], matrix[1, 1], matrix[1, 0], matrix[0, 1]);

        }

        var builder = new StringBuilder();

        for (var i = 0; i < order; i++)

        {

            var sign = (i % 2 == 0) ? "+" : "-";

            var multiplier = matrix[0,i];

            var submatrix = new string[order - 1, order -1];

            for (var j = 0; j < order - 1; j++)

            {

                for (var k = 0; k < order - 1; k++)

                {

                    var x = j + 1;

                    var y = (k >= i) ? k + 1 : k;

                    submatrix[j, k] = matrix[x, y];

                }

            }

            builder.Append(sign);

            builder.Append(multiplier);

            builder.Append("*(" + cofactors(submatrix) + ")");

        }

        return builder.ToString();

    }

}