Problem:
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Matrix-chain Multiplication

The goal of the matrix-chain multiplication problem is to find the most efficient way to multiply given $n$ matrices $M_1, M_2, M_3,...,M_n$.

Write a program which reads dimensions of $M_i$, and finds the minimum number of scalar multiplications to compute the maxrix-chain multiplication $M_1M_2...M_n$.

Input

In the first line, an integer $n$ is given. In the following $n$ lines, the dimension of matrix $M_i$ ($i = 1...n$) is given by two integers $r$ and $c$ which respectively represents the number of rows and columns of $M_i$.

Output

Print the minimum number of scalar multiplication in a line.

Constraints

$1 \leq n \leq 100$

$1 \leq r, c \leq 100$

Sample Input 1

6
30 35
35 15
15 5
5 10
10 20
20 25

Sample Output 1

15125

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Numerics;
using static System.Math;
using static System.Array;
using static AtCoder.Tool;
using static AtCoder.CalcL;
namespace AtCoder
{
    class AC
    {
        const int MOD = 1000000007;
        //const int MOD = 998244353;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dI = { 0, 1, 0, -1, 1, -1, -1, 1 };
        static readonly int[] dJ = { 1, 0, -1, 0, 1, 1, -1, -1 };
        //static List<List<int>> G = new List<List<int>>();
        //static List<List<Edge>> G = new List<List<Edge>>();
        //static List<Edge> E = new List<Edge>();

        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            var cin = new IO_ShortCut();

            int N = cin.Int;
            var r = new long[N];
            var c = new long[N];
            for (var i = 0; i < N; i++) cin.Input(out r[i], out c[i]);
            var dp = new long[N, N];
            for (var i = 0; i < N; i++) for (var j = 0; j < N; j++) dp[i, j] = i == j ? 0 : SINF;
            for (var L = 2; L <= N; L++)
            {
                for(var i = 0; i + L - 1 < N; i++)
                {
                    for(var j = i; j < i + L - 1; j++)
                    {
                        dp[i, i + L - 1] = Min(dp[i, i + L - 1], dp[i, j] + dp[j + 1, i + L - 1] + r[i] * r[j + 1] * c[i + L - 1]);
                    }
                }
            }
            cin.OutL(dp[0, N - 1]);

            //Console.Out.Flush();
        }
        struct Edge
        {
            public int from;

            public int to;
            public long dist;
            public Edge(int t, long c)
            {
                from = -1;
                to = t;
                dist = c;
            }
            public Edge(int f, int t, long c)
            {
                from = f;
                to = t;
                dist = c;
            }
        }
    }
    
    class IO_ShortCut
    {
        public IO_ShortCut() { }
        public string[] ReadSplit => Console.ReadLine().Split();
        public int[] ReadSplitInt => ConvertAll(Console.ReadLine().Split(), int.Parse);
        public long[] ReadSplitLong => ConvertAll(Console.ReadLine().Split(), long.Parse);
        public double[] ReadSplit_Double => ConvertAll(Console.ReadLine().Split(), double.Parse);
        public string Str => Console.ReadLine();
        public int Int => int.Parse(Console.ReadLine());
        public long Long => long.Parse(Console.ReadLine());
        public double Double => double.Parse(Console.ReadLine());
        public T Conv<T>(string input) => (T)Convert.ChangeType(input, typeof(T));
        public void Input<T>(out T a) => a = Conv<T>(Console.ReadLine());
        public void Input<T, U>(out T a, out U b)
        { var q = ReadSplit;a = Conv<T>(q[0]);b = Conv<U>(q[1]); }
        public void Input<T, U, V>(out T a, out U b, out V c)
        { var q = ReadSplit;a = Conv<T>(q[0]);b = Conv<U>(q[1]);c = Conv<V>(q[2]); }
        public void Input<T, U, V, W>(out T a, out U b, out V c, out W d)
        { var q = ReadSplit; a = Conv<T>(q[0]); b = Conv<U>(q[1]); c = Conv<V>(q[2]);d = Conv<W>(q[3]); }

        public void OutL(object s) => Console.WriteLine(s);
        public void Out_Sep<T>(IEnumerable<T> s) => Console.WriteLine(string.Join(" ", s));
        public void Out_Sep<T>(IEnumerable<T> s, string sep) => Console.WriteLine(string.Join($"{sep}", s));
        public void Out_Sep(params object[] s) => Console.WriteLine(string.Join(" ", s));
        public void Out_One(object s) => Console.Write($"{s} ");
        public void Out_One(object s, string sep) => Console.Write($"{s}{sep}");
    }
    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for (var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }
        static public void Swap<T>(ref T a, ref T b)
        {
            T keep = a;
            a = b;
            b = keep;
        }

        static public void Display<T>(T[,] array2d, int n, int m)
        {
            for (var i = 0; i < n; i++)
            {
                for (var j = 0; j < m; j++)
                {
                    Console.Write($"{array2d[i, j]} ");
                }
                Console.WriteLine();
            }
        }

        static public long LPow(int a, int b)
        {
            return (long)Pow(a, b);
        }
    }
    static public class CalcI
    {
        public static int Gcd(int a, int b)
        {
            if (a * b == 0) { return Max(a, b); }
            return a % b == 0 ? b : Gcd(b, a % b);
        }
        public static int Lcm(int a, int b)
        {
            int g = Gcd(a, b);
            return a / g * b;
        }
        public static int Ceil(int n, int div)
        {
            return (n + div - 1) / div;
        }
    }
    static public class CalcL
    {
        public static long Gcd(long a, long b)
        {
            if (a * b == 0) { return Max(a, b); }
            return a % b == 0 ? b : Gcd(b, a % b);
        }
        public static long Lcm(long a, long b)
        {
            long g = Gcd(a, b);
            return a / g * b;
        }
        public static long Ceil(long n, long div)
        {
            return (n + div - 1) / div;
        }
    }
    class Modulo
    {
        private int M;
        private readonly long[] m_facs;
        public long Mul(long a, long b)
        {
            return ((a * b) % M);
        }
        public Modulo(long n, int m)
        {
            M = m;
            m_facs = new long[n + 1];
            m_facs[0] = 1;
            for (long i = 1; i <= n; ++i)
            {
                m_facs[i] = Mul(m_facs[i - 1], i);
            }
        }
        public long Fac(long n)
        {
            return m_facs[n];
        }
        public long Pow(long a, long m)
        {
            switch (m)
            {
                case 0:
                    return 1L;
                case 1:
                    return a;
                default:
                    long p1 = Pow(a, m / 2);
                    long p2 = Mul(p1, p1);
                    return ((m % 2) == 0) ? p2 : Mul(p2, a);
            }
        }
        public long Div(long a, long b)
        {
            return Mul(a, Pow(b, M - 2));
        }
        public long Ncr(long n, long r)
        {
            if (n < r) { return 0; }
            if (n == r) { return 1; }
            long res = Fac(n);
            res = Div(res, Fac(r));
            res = Div(res, Fac(n - r));
            return res;
        }
    }
}