Leetcode 312 - burst balloon - with a bug - the value is 218 instead of 167, need to look into the bug in the code

Leetcode312_burstBalloon_WithBug.cs

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Leetcode312_burstBalloons
{
    /// <summary>
    /// the code is written by learning from the video
    /// https://www.youtube.com/watch?v=Ci39lcoLbyw
    /// 
    /// </summary>
    class Program
    {
        static void Main(string[] args)
        {
            RunTestcase(); 
        }

        static public void RunTestcase()
        {
            var numbers = new int[] { 3, 1, 5, 8 };
            Debug.Assert(RunBurstBalloons(numbers) == 167);
        }

        public static int RunBurstBalloons(int[] numbers)
        {
            var length = numbers.Length; 
            var size = length + 2; 
            var preprocessed = new int[size];
            preprocessed[0] = 1;
            preprocessed[length + 1] = 1;

            for (int i = 0; i < length; i++)
            {
                preprocessed[i + 1] = numbers[i];
            }

            var dp = new int[size, size];

            for (int i = 0; i + 1 < size; i++)
            {
                dp[i, i + 1] = preprocessed[i] * preprocessed[i + 1]; 
            }

            for (int i = 0; i + 2 < size; i++)
            {
                dp[i, i + 2] = preprocessed[i] * preprocessed[i + 1] * preprocessed[i + 2];
            }

            for (int range = 3; range < size; range++)
            {
                for (int start = 0; start + range < size; start++)
                {
                    // start, end -> calculate dp[start, end] 
                    var end = start + range;
                    dp[start, end] = calculateMaxByLastBurst(dp, start, end, preprocessed); 
                }
            }

            return dp[0, size - 1]; 
        }

        private static int calculateMaxByLastBurst(int[,] dp, int start, int end, int[] numbers)
        {
            var max = int.MinValue;
            var startValue = numbers[start];
            var endValue   = numbers[end];

            for (int lastBurst = start + 1; lastBurst < end; lastBurst++)
            {
                var current = startValue * endValue * numbers[lastBurst];
                current += dp[start, lastBurst] + dp[lastBurst, end];

                if (current > max)
                    max = current; 
            }

            return max; 
        }
    }
}