Problem:
Score : 800 points

Problem Statement

For a positive integer n, we denote the integer obtained by reversing the decimal notation of n (without leading zeroes) by rev(n). For example, rev(123) = 321 and rev(4000) = 4.

You are given a positive integer D. How many positive integers N satisfy rev(N) = N + D?

Constraints

D is an integer.

1 ≤ D < 10^9

Input

Input is given from Standard Input in the following format:

D

Output

Print the number of the positive integers N such that rev(N) = N + D.

Sample Input 1

63

Sample Output 1

2

There are two positive integers N such that rev(N) = N + 63: N = 18 and 29.

Sample Input 2

75

Sample Output 2

0

There are no positive integers N such that rev(N) = N + 75.

Sample Input 3

864197532

Sample Output 3

1920

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Linq.Expressions;
using System.IO;
using System.Text;
using System.Diagnostics;

using Binary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.BinaryExpression>;
using Unary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.UnaryExpression>;

class Program
{
    static StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
    static Scan sc = new Scan();
//    static Scan sc = new ScanCHK();
    const int M = 1000000007;
    const double eps = 1e-9;
    static readonly int[] dd = { 0, 1, 0, -1, 0 };
    static void Main()
    {
        long d = sc.Int;
        if (d % 9 > 0)
        {
            DBG(0);
            return;
        }
        d /= 9;
        long ans = 0;
        ans += Math.Max(9 - d, 0);
        if (d % 11 == 0)
        {
            ans += Math.Max(9 - d / 11, 0) * 10;
        }
        for (int i = 0; i < 9; i++)
        {
            for (int j = -9; j < 10; j++)
            {
                if (i * 111 + j * 10 == d)
                {
                    ans += (9 - i) * (10 - Math.Abs(j));
                }
            }
        }
        for (int i = 0; i < 9; i++)
        {
            for (int j = -9; j < 10; j++)
            {
                if (i * 1111 + j * 110 == d)
                {
                    ans += (9 - i) * (10 - Math.Abs(j)) * 10;
                }
            }
        }
        for (int i = 0; i < 9; i++)
        {
            for (int j = -9; j < 10; j++)
            {
                for (int k = -9; k < 10; k++)
                {
                    if (i * 11111 + j * 1110 + k * 100 == d)
                    {
                        ans += (9 - i) * (10 - Math.Abs(j)) * (10 - Math.Abs(k));
                    }
                }
            }
        }
        for (int i = 0; i < 9; i++)
        {
            for (int j = -9; j < 10; j++)
            {
                for (int k = -9; k < 10; k++)
                {
                    if (i * 111111 + j * 11110 + k * 1100 == d)
                    {
                        ans += (9 - i) * (10 - Math.Abs(j)) * (10 - Math.Abs(k)) * 10;
                    }
                }
            }
        }
        for (int i = 0; i < 9; i++)
        {
            for (int j = -9; j < 10; j++)
            {
                for (int k = -9; k < 10; k++)
                {
                    for (int l = -9; l < 10; l++)
                    {
                        if (i * 1111111 + j * 111110 + k * 11100 + l * 1000 == d)
                        {
                            ans += (9 - i) * (10 - Math.Abs(j)) * (10 - Math.Abs(k)) * (10 - Math.Abs(l));
                        }
                    }
                }
            }
        }
        for (int i = 0; i < 9; i++)
        {
            for (int j = -9; j < 10; j++)
            {
                for (int k = -9; k < 10; k++)
                {
                    for (int l = -9; l < 10; l++)
                    {
                        if (i * 11111111 + j * 1111110 + k * 111100 + l * 11000 == d)
                        {
                            ans += (9 - i) * (10 - Math.Abs(j)) * (10 - Math.Abs(k)) * (10 - Math.Abs(l)) * 10;
                        }
                    }
                }
            }
        }
        for (long i = 0; i < 9; i++)
        {
            for (long j = -9; j < 10; j++)
            {
                for (long k = -9; k < 10; k++)
                {
                    for (long l = -9; l < 10; l++)
                    {
                        for (long p = -9; p < 10; p++)
                        {
                            if (i * 111111111 + j * 11111110 + k * 1111100 + l * 111000 + p * 10000 == d)
                            {
                                ans += (9 - i) * (10 - Math.Abs(j)) * (10 - Math.Abs(k)) * (10 - Math.Abs(l)) * (10 - Math.Abs(p));
                            }
                        }
                    }
                }
            }
        }
        for (long i = 0; i < 9; i++)
        {
            for (long j = -9; j < 10; j++)
            {
                for (long k = -9; k < 10; k++)
                {
                    for (long l = -9; l < 10; l++)
                    {
                        for (long p = -9; p < 10; p++)
                        {
                            if (i * 1111111111 + j * 111111110 + k * 11111100 + l * 1111000 + p * 110000 == d)
                            {
                                ans += (9 - i) * (10 - Math.Abs(j)) * (10 - Math.Abs(k)) * (10 - Math.Abs(l)) * (10 - Math.Abs(j)) * 10;
                            }
                        }
                    }
                }
            }
        }
        for (long i = 0; i < 9; i++)
        {
            for (long j = -9; j < 10; j++)
            {
                for (long k = -9; k < 10; k++)
                {
                    for (long l = -9; l < 10; l++)
                    {
                        for (long p = -9; p < 10; p++)
                        {
                            for (long q = -9; q < 10; q++)
                            {
                                if (i * 11111111111 + j * 1111111110 + k * 111111100 + l * 11111000 + p * 1110000 + q * 100000 == d)
                                {
                                    ans += (9 - i) * (10 - Math.Abs(j)) * (10 - Math.Abs(k)) * (10 - Math.Abs(l)) * (10 - Math.Abs(p)) * (10 - Math.Abs(q));
                                }
                            }
                        }
                    }
                }
            }
        }
        for (long i = 0; i < 9; i++)
        {
            for (long j = -9; j < 10; j++)
            {
                if (i * 111111111111 + (j - 1) * 11111111110 > d) break;
                for (long k = -9; k < 10; k++)
                {
                    for (long l = -9; l < 10; l++)
                    {
                        for (long p = -9; p < 10; p++)
                        {
                            for (long q = -9; q < 10; q++)
                            {
                                if (i * 111111111111 + j * 11111111110 + k * 1111111100 + l * 111111000 + p * 11110000 + q * 1100000 == d)
                                {
                                    ans += (9 - i) * (10 - Math.Abs(j)) * (10 - Math.Abs(k)) * (10 - Math.Abs(l)) * (10 - Math.Abs(p)) * (10 - Math.Abs(q)) * 10;
                                }
                            }
                        }
                    }
                }
            }
        }
        for (long i = 0; i < 2; i++)
        {
            for (long j = -9; j < 10; j++)
            {
                if (i * 1111111111111 + (j - 1) * 111111111110 > d) break;
                for (long k = -9; k < 10; k++)
                {
                    for (long l = -9; l < 10; l++)
                    {
                        for (long p = -9; p < 10; p++)
                        {
                            for (long q = -9; q < 10; q++)
                            {
                                for (long r = -9; r < 10; r++)
                                {
                                    if (i * 1111111111111 + j * 111111111110 + k * 11111111100 + l * 1111111000 + p * 111110000 + q * 11100000 + r * 1000000 == d)
                                    {
                                        ans += (9 - i) * (10 - Math.Abs(j)) * (10 - Math.Abs(k)) * (10 - Math.Abs(l)) * (10 - Math.Abs(p)) * (10 - Math.Abs(q)) * (10 - Math.Abs(r));
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
        for (long i = 0; i < 3; i++)
        {
            for (long j = -9; j < 10; j++)
            {
                if (i * 11111111111111 + (j - 1) * 1111111111110 > d) break;
                for (long k = -9; k < 10; k++)
                {
                    for (long l = -9; l < 10; l++)
                    {
                        for (long p = -9; p < 10; p++)
                        {
                            for (long q = -9; q < 10; q++)
                            {
                                for (long r = -9; r < 10; r++)
                                {
                                    if (i * 11111111111111 + j * 1111111111110 + k * 111111111100 + l * 11111111000 + p * 1111110000 + q * 111100000 + r * 11000000 == d)
                                    {
                                        ans += (9 - i) * (10 - Math.Abs(j)) * (10 - Math.Abs(k)) * (10 - Math.Abs(l)) * (10 - Math.Abs(p)) * (10 - Math.Abs(q)) * (10 - Math.Abs(r)) * 10;
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
        for (long i = 0; i < 1; i++)
        {
            for (long j = 0; j < 3; j++)
            {
                for (long k = -9; k < 10; k++)
                {
                    if (i * 111111111111111 + j * 11111111111110 + (k - 1) * 1111111111100 > d) break;
                    for (long l = -9; l < 10; l++)
                    {
                        for (long p = -9; p < 10; p++)
                        {
                            for (long q = -9; q < 10; q++)
                            {
                                for (long r = -9; r < 10; r++)
                                {
                                    for (long s = -9; s < 10; s++)
                                    {
                                        if (i * 111111111111111 + j * 11111111111110 + k * 1111111111100 + l * 111111111000 + p * 11111110000 + q * 1111100000 + r * 111000000 + s * 10000000 == d)
                                        {
                                            ans += (9 - i) * (10 - Math.Abs(j)) * (10 - Math.Abs(k)) * (10 - Math.Abs(l)) * (10 - Math.Abs(p)) * (10 - Math.Abs(q)) * (10 - Math.Abs(r)) * (10 - Math.Abs(s));
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
        for (long i = 0; i < 1; i++)
        {
            for (long j = 0; j < 3; j++)
            {
                for (long k = -9; k < 10; k++)
                {
                    if (i * 1111111111111111 + j * 111111111111110 + (k - 1) * 11111111111100 > d) break;
                    for (long l = -9; l < 10; l++)
                    {
                        for (long p = -9; p < 10; p++)
                        {
                            for (long q = -9; q < 10; q++)
                            {
                                for (long r = -9; r < 10; r++)
                                {
                                    for (long s = -9; s < 10; s++)
                                    {
                                        if (i * 1111111111111111 + j * 111111111111110 + k * 11111111111100 + l * 1111111111000 + p * 111111110000 + q * 11111100000 + r * 1111000000 + s * 110000000 == d)
                                        {
                                            ans += (9 - i) * (10 - Math.Abs(j)) * (10 - Math.Abs(k)) * (10 - Math.Abs(l)) * (10 - Math.Abs(p)) * (10 - Math.Abs(q)) * (10 - Math.Abs(r)) * (10 - Math.Abs(s)) * 10;
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
        for (long i = 0; i < 1; i++)
        {
            for (long j = 0; j < 1; j++)
            {
                for (long k = 0; k < 3; k++)
                {
                    for (long l = -9; l < 10; l++)
                    {
                        if (i * 11111111111111111 + j * 1111111111111110 + k * 111111111111100 + (l - 1) * 11111111111000 > d) break;
                        for (long p = -9; p < 10; p++)
                        {
                            for (long q = -9; q < 10; q++)
                            {
                                for (long r = -9; r < 10; r++)
                                {
                                    for (long s = -9; s < 10; s++)
                                    {
                                        for (long t = -9; t < 10; t++)
                                        {
                                            if (i * 11111111111111111 + j * 1111111111111110 + k * 111111111111100 + l * 11111111111000 + p * 1111111110000 + q * 111111100000 + r * 11111000000 + s * 1110000000 + t * 100000000 == d)
                                            {
                                                ans += (9 - i) * (10 - Math.Abs(j)) * (10 - Math.Abs(k)) * (10 - Math.Abs(l)) * (10 - Math.Abs(p)) * (10 - Math.Abs(q)) * (10 - Math.Abs(r)) * (10 - Math.Abs(s)) * (10 - Math.Abs(t));
                                            }
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
        for (long i = 0; i < 1; i++)
        {
            for (long j = 0; j < 1; j++)
            {
                for (long k = 0; k < 2; k++)
                {
                    for (long l = -9; l < 10; l++)
                    {
                        if (i * 111111111111111111 + j * 11111111111111110 + k * 1111111111111100 + (l - 1) * 111111111111000 > d) break;
                        for (long p = -9; p < 10; p++)
                        {
                            for (long q = -9; q < 10; q++)
                            {
                                for (long r = -9; r < 10; r++)
                                {
                                    for (long s = -9; s < 10; s++)
                                    {
                                        for (long t = -9; t < 10; t++)
                                        {
                                            if (i * 111111111111111111 + j * 11111111111111110 + k * 1111111111111100 + l * 111111111111000 + p * 11111111110000 + q * 1111111100000 + r * 111111000000 + s * 11110000000 + t * 1100000000 == d)
                                            {
                                                ans += (9 - i) * (10 - Math.Abs(j)) * (10 - Math.Abs(k)) * (10 - Math.Abs(l)) * (10 - Math.Abs(p)) * (10 - Math.Abs(q)) * (10 - Math.Abs(r)) * (10 - Math.Abs(s)) * (10 - Math.Abs(t)) * 10;
                                            }
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
        Prt(ans);

        sw.Flush();
    }

    static void swap<T>(ref T a, ref T b) { var t = a; a = b; b = t; }
    static T Max<T>(params T[] a) { return a.Max(); }
    static T Min<T>(params T[] a) { return a.Min(); }
    static void DBG(string a) { Console.WriteLine(a); }
    static void DBG<T>(IEnumerable<T> a) { Console.WriteLine(string.Join(" ", a)); }
    static void DBG(params object[] a) { Console.WriteLine(string.Join(" ", a)); }
    static void Prt(string a) { sw.WriteLine(a); }
    static void Prt<T>(IEnumerable<T> a) { sw.WriteLine(string.Join(" ", a)); }
    static void Prt(params object[] a) { sw.WriteLine(string.Join(" ", a)); }
}
static class ex
{
    public static void swap<T>(this IList<T> a, int i, int j) { var t = a[i]; a[i] = a[j]; a[j] = t; }
    public static T[] copy<T>(this IList<T> a)
    {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
}
static class Operator<T>
{
    static readonly ParameterExpression x = Expression.Parameter(typeof(T), "x");
    static readonly ParameterExpression y = Expression.Parameter(typeof(T), "y");
    public static readonly Func<T, T, T> Add = Lambda(Expression.Add);
    public static readonly Func<T, T, T> Subtract = Lambda(Expression.Subtract);
    public static readonly Func<T, T, T> Multiply = Lambda(Expression.Multiply);
    public static readonly Func<T, T, T> Divide = Lambda(Expression.Divide);
    public static readonly Func<T, T> Plus = Lambda(Expression.UnaryPlus);
    public static readonly Func<T, T> Negate = Lambda(Expression.Negate);
    public static Func<T, T, T> Lambda(Binary op) { return Expression.Lambda<Func<T, T, T>>(op(x, y), x, y).Compile(); }
    public static Func<T, T> Lambda(Unary op) { return Expression.Lambda<Func<T, T>>(op(x), x).Compile(); }
}

class ScanCHK : Scan
{
    public new string Str { get { var s = Console.ReadLine(); if (s != s.Trim()) throw new Exception(); return s; } }
}
class Scan
{
    public int Int { get { return int.Parse(Str); } }
    public long Long { get { return long.Parse(Str); } }
    public double Double { get { return double.Parse(Str); } }
    public string Str { get { return Console.ReadLine().Trim(); } }
    public int[] IntArr { get { return StrArr.Select(int.Parse).ToArray(); } }
    public long[] LongArr { get { return StrArr.Select(long.Parse).ToArray(); } }
    public double[] DoubleArr { get { return StrArr.Select(double.Parse).ToArray(); } }
    public string[] StrArr { get { return Str.Split(); } }
    bool eq<T, U>() { return typeof(T).Equals(typeof(U)); }
    T ct<T, U>(U a) { return (T)Convert.ChangeType(a, typeof(T)); }
    T cv<T>(string s) { return eq<T, int>()    ? ct<T, int>(int.Parse(s))
                             : eq<T, long>()   ? ct<T, long>(long.Parse(s))
                             : eq<T, double>() ? ct<T, double>(double.Parse(s))
                             : eq<T, char>()   ? ct<T, char>(s[0])
                                               : ct<T, string>(s); }
    public void Multi<T>(out T a) { a = cv<T>(Str); }
    public void Multi<T, U>(out T a, out U b)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); }
    public void Multi<T, U, V>(out T a, out U b, out V c)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); }
    public void Multi<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]); }
    public void Multi<T, U, V, W, X, Y, Z>(out T a, out U b, out V c, out W d, out X e, out Y f, out Z g)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]);  g = cv<Z>(ar[6]);}
}
class mymath
{
    public static long Mod = 1000000007;
    public static bool isprime(long a)
    {
        if (a < 2) return false;
        for (long i = 2; i * i <= a; i++) if (a % i == 0) return false;
        return true;
    }
    public static bool[] sieve(int n)
    {
        var p = new bool[n + 1];
        for (int i = 2; i <= n; i++) p[i] = true;
        for (int i = 2; i * i <= n; i++) if (p[i]) for (int j = i * i; j <= n; j += i) p[j] = false;
        return p;
    }
    public static List<int> getprimes(int n)
    {
        var prs = new List<int>();
        var p = sieve(n);
        for (int i = 2; i <= n; i++) if (p[i]) prs.Add(i);
        return prs;
    }
    public static long[][] E(int n)
    {
        var ret = new long[n][];
        for (int i = 0; i < n; i++) { ret[i] = new long[n]; ret[i][i] = 1; }
        return ret;
    }
    public static long[][] pow(long[][] A, long n)
    {
        if (n == 0) return E(A.Length);
        var t = pow(A, n / 2);
        if ((n & 1) == 0) return mul(t, t);
        return mul(mul(t, t), A);
    }
    public static double dot(double[] x, double[] y)
    {
        int n = x.Length;
        double ret = 0;
        for (int i = 0; i < n; i++) ret += x[i] * y[i];
        return ret;
    }
    public static long dot(long[] x, long[] y)
    {
        int n = x.Length;
        long ret = 0;
        for (int i = 0; i < n; i++) ret = (ret + x[i] * y[i]) % Mod;
        return ret;
    }
    public static T[][] trans<T>(T[][] A)
    {
        int n = A[0].Length, m = A.Length;
        var ret = new T[n][];
        for (int i = 0; i < n; i++) { ret[i] = new T[m]; for (int j = 0; j < m; j++) ret[i][j] = A[j][i]; }
        return ret;
    }
    public static double[] mul(double[][] A, double[] x)
    {
        int n = A.Length;
        var ret = new double[n];
        for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
        return ret;
    }
    public static long[] mul(long[][] A, long[] x)
    {
        int n = A.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
        return ret;
    }
    public static long[][] mul(long[][] A, long[][] B)
    {
        int n = A.Length;
        var Bt = trans(B);
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]);
        return ret;
    }
    public static long[] add(long[] x, long[] y)
    {
        int n = x.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = (x[i] + y[i]) % Mod;
        return ret;
    }
    public static long[][] add(long[][] A, long[][] B)
    {
        int n = A.Length;
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = add(A[i], B[i]);
        return ret;
    }
    public static long pow(long a, long b)
    {
        if (a >= Mod) return pow(a % Mod, b);
        if (a == 0) return 0;
        if (b == 0) return 1;
        var t = pow(a, b / 2);
        if ((b & 1) == 0) return t * t % Mod;
        return t * t % Mod * a % Mod;
    }
    public static long inv(long a) { return pow(a, Mod - 2); }
    public static long gcd(long a, long b)
    {
        while (b > 0) { var t = a % b; a = b; b = t; }
        return a;
    }
    // a x + b y = gcd(a, b)
    public static long extgcd(long a, long b, out long x, out long y)
    {
        long g = a; x = 1; y = 0;
        if (b > 0) { g = extgcd(b, a % b, out y, out x); y -= a / b * x; }
        return g;
    }
    public static long lcm(long a, long b) { return a / gcd(a, b) * b; }
    public static long comb(int n, int r)
    {
        if (n < 0 || r < 0 || r > n) return 0;
        if (n - r < r) r = n - r;
        if (r == 0) return 1;
        if (r == 1) return n;
        int[] numer = new int[r], denom = new int[r];
        for (int k = 0; k < r; k++) { numer[k] = n - r + k + 1; denom[k] = k + 1; }
        for (int p = 2; p <= r; p++)
        {
            int piv = denom[p - 1];
            if (piv > 1)
            {
                int ofst = (n - r) % p;
                for (int k = p - 1; k < r; k += p) { numer[k - ofst] /= piv; denom[k] /= piv; }
            }
        }
        long ret = 1;
        for (int k = 0; k < r; k++) if (numer[k] > 1) ret = ret * numer[k] % Mod;
        return ret;
    }
}