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.Linq;
using System.Collections.Generic;
using Debug = System.Diagnostics.Trace;
using SB = System.Text.StringBuilder;
using System.Numerics;
using static System.Math;
using Number = System.Int64;
namespace Program {
    public class Solver {
        Random rnd = new Random(0);
        public void Solve() {
            // R = N + D
            // R - N = D
            // N = a_0, a_1, ..., a_k
            // R = a_k, a_k-1,.., a_0
            // R-N = (a_k-a_0)*10^0 +(a_0-a_k)*10^k + ...
            // R-N = (a_k-a_0)*(10^k-1) + (a_k-1 - a_1)*10*(10^{k-2}-1) + (a_{k-2} - a_2)*10^2*(10^k^{k-4}-1)
            // b_i = (a_{k-i} - a_i) -9~9
            // -9 * (10^k - 1) + 9 * (10^{k-1}-1)
            // 
            var ans = 0L;
            var coef = new int[50, 2];
            for (int i = 0; i < 10; i++)
                for (int j = 0; j < 10; j++) {
                    if (i != 0) { coef[(i - j) + 25, 0]++; }
                    coef[(i - j) + 25, 1]++;
                }
            for (int v = -9; v <= 9; v++) {
                //                Debug.WriteLine($"{v} {coef[v + 25, 0]} {coef[v + 25, 1]}");
            }
            var D = rl;
            foreach (var k in Rep(17)) {
                var co = Enumerate(k / 2 + 1, x => (long)(BigInteger.Pow(10, x) * (BigInteger.Pow(10, k - 2 * x) - 1)));
                var max = Enumerate(k / 2 + 2, x => co.Skip(x).Sum() * 9);
                Func<int, long, long> dfs = null;
                dfs = (i, d) => {
                    Debug.WriteLine($"{i} {d}");
                    if (k - i > i) {
                        var ret = 0L;
                        for (int v = -9; v <= 9; v++) {
                            var nd = d + v * co[i];
                            if (nd <= max[i + 1] && -max[i + 1] <= nd) {
                                Debug.WriteLine(v);
                                var add = dfs(i + 1, nd);
                                if (i == 0) add *= coef[v + 25, 0];
                                else add *= coef[v + 25, 1];
                                ret += add;
                            }

                        }
                        return ret;
                    } else {
                        if (d == 0) {
                            if (k % 2 == 0) return 10;
                            else return 1;
                        } else return 0;
                    }
                };
                ans += dfs(0, D);
            }
            Console.WriteLine(ans);
        }

        const long INF = 1L << 60;
        int ri => sc.Integer();
        long rl => sc.Long();
        double rd => sc.Double();
        string rs => sc.Scan();
        public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());

        static IEnumerable<int> Rep(int n) => Enumerable.Range(0, n);
        static IEnumerable<int> RRep(int n) => Enumerable.Range(0, n).Reverse();
        static T[] Enumerate<T>(int n, Func<int, T> f) {
            var a = new T[n];
            for (int i = 0; i < a.Length; ++i) a[i] = f(i);
            return a;
        }
        static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
    }
}
#region main
static class Ex {
    static public string AsString(this IEnumerable<char> ie) { return new string(ie.ToArray()); }
    static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") {
        return string.Join(st, ie);
    }
    static public void Main() {
        Console.SetOut(new Program.IO.Printer(Console.OpenStandardOutput()) { AutoFlush = true });
        var solver = new Program.Solver();
        solver.Solve();
        Console.Out.Flush();
    }
}
#endregion
#region Ex
namespace Program.IO {
    using System.IO;
    using System.Text;
    using System.Globalization;

    public class Printer : StreamWriter {
        public override IFormatProvider FormatProvider => CultureInfo.InvariantCulture;
        public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
    }

    public class StreamScanner {
        public StreamScanner(Stream stream) { str = stream; }

        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;

        private byte read() {
            if (isEof) return 0;
            if (ptr >= len) {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0) {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }

        public char Char() {
            byte b = 0;
            do b = read(); while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }
        public string Scan() {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
            return sb.ToString();
        }
        public string ScanLine() {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n' && b != 0; b = (char)read()) if (b != '\r') sb.Append(b);
            return sb.ToString();
        }
        public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
        public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
        public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
}

#endregion