Problem:
Score : 300 points

Problem Statement

Gotou just received a dictionary. However, he doesn't recognize the language used in the dictionary. He did some analysis on the dictionary and realizes that the dictionary contains all possible diverse words in lexicographical order.

A word is called diverse if and only if it is a nonempty string of English lowercase letters and all letters in the word are distinct. For example, atcoder, zscoder and agc are diverse words while gotou and connect aren't diverse words.

Given a diverse word S, determine the next word that appears after S in the dictionary, i.e. the lexicographically smallest diverse word that is lexicographically larger than S, or determine that it doesn't exist.

Let X = x_{1}x_{2}...x_{n} and Y = y_{1}y_{2}...y_{m} be two distinct strings. X is lexicographically larger than Y if and only if Y is a prefix of X or x_{j} > y_{j} where j is the smallest integer such that x_{j} \neq y_{j}.

Constraints

1 \leq |S| \leq 26

S is a diverse word.

Input

Input is given from Standard Input in the following format:

S

Output

Print the next word that appears after S in the dictionary, or -1 if it doesn't exist.

Sample Input 1

atcoder

Sample Output 1

atcoderb

atcoderb is the lexicographically smallest diverse word that is lexicographically larger than atcoder. Note that atcoderb is lexicographically smaller than b.

Sample Input 2

abc

Sample Output 2

abcd

Sample Input 3

zyxwvutsrqponmlkjihgfedcba

Sample Output 3

-1

This is the lexicographically largest diverse word, so the answer is -1.

Sample Input 4

abcdefghijklmnopqrstuvwzyx

Sample Output 4

abcdefghijklmnopqrstuvx

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using static System.Math;

namespace CompetitionPrograming2
{
    public sealed class Program : BaseProgram
    {
        public static void Main(string[] _) { using (new SetConsole()) { Solve(); } }
        public static void Solve()
        {
            var str = GetString();
            var a = AtoZ().Except(str).OrderBy(x => x).ToArray();
            if (a.Length <= 0)
            {
                var tmp = str.NextPermutation();
                if (tmp != null)
                {
                    var tmpArray = tmp.ToArray();
                    var count = 0;
                    for (int i = 0; i < tmpArray.Length; i++)
                    {
                        if (tmpArray[i] != str[i])
                        {
                            break;
                        }
                        count++;
                    }
                    Write(string.Concat(tmp.Take(count + 1))); return;
                }
                Write(-1); return;
            }
            Write(str + a[0]);
        }
    }
    public abstract class BaseProgram
    {
        protected readonly static long divisor = 1000000007;
        protected static void Write(object obj) => Console.WriteLine(obj);
        protected static string GetString()
        {
            var str = Console.ReadLine();
            if (str == null) { throw new NullReferenceException("標準入力がnullです Solveメソッド内の解答コードが間違っています"); }
            return str;
        }
        protected static T GetNumber<T>() where T : IComparable, IComparable<T>, IConvertible, IEquatable<T>, IFormattable
        {
            var str = GetString();
            var t = typeof(T);
            try
            {
                if ((t == typeof(byte)))
                {
                    return (T)(object)str.ToByte();
                }
                else if (t == typeof(int))
                {
                    return (T)(object)str.ToInt();
                }
                else if (t == typeof(long))
                {
                    return (T)(object)str.ToLong();
                }
                else if (t == typeof(double))
                {
                    return (T)(object)str.ToDouble();
                }
                else if (t == typeof(decimal))
                {
                    return (T)(object)str.ToDecimal();
                }
                else if (t == typeof(BigInteger))
                {
                    return (T)(object)str.ToBigInteger();
                }
            }
            catch (OverflowException)
            {
                throw new OverflowException("より大きい数値型を指定してください");
            }
            throw new NotSupportedException();
        }
        protected static T[] GetArray<T>() where T : IComparable, IComparable<T>, IConvertible, IEquatable<T>
        {
            return GetString().ToArray<T>();
        }
        protected static List<T> GetList<T>() where T : IComparable, IComparable<T>, IConvertible, IEquatable<T>
        {
            return GetString().ToList<T>();
        }
        protected static TResult[] GetArray<TResult>(Func<string, TResult> selector)
        {
            return (TResult[])(object)GetString().Split().Select(selector).ToArray();
        }
        protected static void Swap<T>(ref T item1, ref T item2)
        {
            var tmp = item1;
            item1 = item2;
            item2 = tmp;
        }
        protected static IEnumerable<char> AtoZ()
        {
            for (char i = 'a'; i <= 'z'; i++)
            {
                yield return i;
            }
        }
        protected sealed class SetConsole : IDisposable
        {
            readonly StreamWriter sw = new StreamWriter(Console.OpenStandardOutput());
            public SetConsole()
            {
                sw.AutoFlush = false;
                Console.SetOut(sw);
            }
            public void Dispose()
            {
                Console.Out.Flush();
                sw.AutoFlush = true;
                Console.SetOut(sw);
            }
        }
    }
    public static class ExtentionsLibrary
    {
        public static T[] NextPermutation<T>(this IEnumerable<T> collection) where T : IComparable
        {
            var array = collection.ToArray();
            int? exchangingNumIndex = null;
            for (int i = 1; i < array.Length; i++)
            {
                if (array[i - 1].CompareTo(array[i]) >= 0) { continue; }

                exchangingNumIndex = i - 1;
            }

            if (exchangingNumIndex == null) { return null; }

            for (int j = array.Length - 1; j >= 0; j--)
            {
                if (array[(int)exchangingNumIndex].CompareTo(array[j]) >= 0) { continue; }

                var tmp = array[j];
                array[j] = array[(int)exchangingNumIndex];
                array[(int)exchangingNumIndex] = tmp;
                array = array.Take((int)exchangingNumIndex + 1).Concat(array.Skip((int)exchangingNumIndex + 1).Reverse()).ToArray();
                break;
            }
            return array;
        }
        public static IEnumerable<T[]> Permutations<T>(this IEnumerable<T> collection) where T : IComparable
        {
            var next = collection.NextPermutation();

            while (next != null)
            {
                yield return next;

                next = next.NextPermutation();
            }
        }
        public static long Gcd(this long a, long b)
        {
            if (a < b) { return Gcd(b, a); }
            long tmp;
            do
            {
                tmp = a % b;
                a = b;
                b = tmp;
            } while (tmp != 0);
            return a;
        }
        public static IEnumerable<Tuple<long, int>> Factorize(this long n)
        {
            yield return Tuple.Create(1L, 1);
            var rootN = Math.Sqrt(n);
            for (long i = 2; i <= rootN; i++)
            {
                if (n % i != 0) { continue; }

                var count = 1;
                n /= i;
                while (n % i == 0)
                {
                    n /= i;
                    count++;
                }
                yield return Tuple.Create(i, count);
            }
            if (n != 1) { yield return Tuple.Create(n, 1); }
        }
        public static T[,] CopyArray<T>(this T[,] array)
        {
            var firstDimentionLength = array.GetLength(0);
            var secondDimentionLength = array.GetLength(1);
            var newDArray = new T[firstDimentionLength, secondDimentionLength];
            Array.Copy(array, newDArray, firstDimentionLength * secondDimentionLength);
            return newDArray;
        }
        public static T[] ToArray<T>(this string str) where T : IComparable, IComparable<T>, IConvertible, IEquatable<T>
        {
            if (typeof(T) == typeof(string)) { return (T[])(object)str.Split(); }

            return str.ConvertEnumerator<T>().ToArray();
        }
        public static List<T> ToList<T>(this string str) where T : IComparable, IComparable<T>, IConvertible, IEquatable<T>
        {
            if (typeof(T) == typeof(string)) { return (List<T>)(object)str.Split().ToList(); }

            return str.ConvertEnumerator<T>().ToList();
        }
        public static IEnumerable<T> ConvertEnumerator<T>(this string str) where T : IComparable, IComparable<T>, IConvertible, IEquatable<T>
        {
            var t = typeof(T);
            if (t == typeof(byte))
            {
                return (IEnumerable<T>)str.Split().Select(byte.Parse);
            }
            if (t == typeof(int))
            {
                return (IEnumerable<T>)str.Split().Select(int.Parse);
            }
            if (t == typeof(long))
            {
                return (IEnumerable<T>)str.Split().Select(long.Parse);
            }
            if (t == typeof(double))
            {
                return (IEnumerable<T>)str.Split().Select(double.Parse);
            }
            if (t == typeof(decimal))
            {
                return (IEnumerable<T>)str.Split().Select(decimal.Parse);
            }
            if (t == typeof(BigInteger))
            {
                return (IEnumerable<T>)str.Split().Select(BigInteger.Parse);
            }
            throw new NotSupportedException();
        }
        public static byte ToByte(this string str) => byte.Parse(str);
        public static byte ToByte(this char chr) => byte.Parse(chr.ToString());
        public static int ToInt(this string str) => int.Parse(str);
        public static int ToInt(this char chr) => int.Parse(chr.ToString());
        public static long ToLong(this string str) => long.Parse(str);
        public static double ToDouble(this string str) => double.Parse(str);
        public static decimal ToDecimal(this string str) => decimal.Parse(str);
        public static BigInteger ToBigInteger(this string str) => BigInteger.Parse(str);
        public static DateTime ToDateTime(this string str) => DateTime.Parse(str);
        public static string StringJoin(this object[] array, string separator = "") => string.Join(separator, array);
        public static string StringJoin<T>(this IEnumerable<T> collection, string separator = "") => string.Join(separator, collection.Select(c => c.ToString()));
        public static int LowerBound<T>(this IReadOnlyList<T> a, T v) => LowerBound(a, v, Comparer<T>.Default);
        public static int LowerBound<T>(this IReadOnlyList<T> a, T v, Comparer<T> cmp)
        {
            var l = 0;
            var r = a.Count - 1;
            while (l <= r)
            {
                var mid = l + (r - l) / 2;
                var result = cmp.Compare(a[mid], v);
                if (result == -1)
                {
                    l = mid + 1;
                }
                else
                {
                    r = mid - 1;
                }
            }
            return l;
        }
        public static int UpperBound<T>(this IReadOnlyList<T> a, T v) => UpperBound(a, v, Comparer<T>.Default);
        public static int UpperBound<T>(this IReadOnlyList<T> a, T v, Comparer<T> cmp)
        {
            var l = 0;
            var r = a.Count - 1;
            while (l <= r)
            {
                var mid = l + (r - l) / 2;
                var res = cmp.Compare(a[mid], v);
                if (res <= 0) l = mid + 1;
                else r = mid - 1;
            }
            return l;
        }
    }

    public struct Mint
    {
        public static long MOD = (long)1e9 + 7;

        /// <summary>
        /// 0以上MOD未満の整数
        /// </summary>
        public long Value;

        public Mint(long val)
        {
            Value = val % MOD;
            if (Value < 0) Value += MOD;
        }

        private static Mint Ctor(long val)
        {
            return new Mint() { Value = val };
        }

        public static Mint operator +(Mint a, Mint b)
        {
            long res = a.Value + b.Value;
            if (res > MOD) res -= MOD;
            return Ctor(res);
        }
        public static Mint operator -(Mint a, Mint b)
        {
            long res = a.Value - b.Value;
            if (res < 0) res += MOD;
            return Ctor(res);
        }

        public static Mint operator *(Mint a, Mint b)
        {
            long res = a.Value * b.Value;
            if (res > MOD) res %= MOD;
            return Ctor(res);
        }

        public static Mint operator /(Mint a, Mint b)
        {
            return a * Inv(b);
        }

        public static Mint Pow(Mint a, long n)
        {
            if (n == 0) return new Mint(1);
            Mint b = Pow(a, n >> 1);
            b *= b;
            if ((n & 1) == 1) b *= a;
            return b;
        }

        public static Mint Inv(Mint n)
        {
            long a = n.Value;
            long b = MOD;

            long x = 1;
            long u = 0;
            while (b != 0)
            {
                long k = a / b;
                long _x = u;
                u = x - k * u;
                x = _x;

                long _a = a;
                a = b;
                b = _a - (k * b);
            }

            return new Mint(x);
        }

        public override string ToString()
        {
            return Value.ToString();
        }

        public static implicit operator Mint(long a) { return new Mint(a); }
        public static explicit operator long(Mint a) { return a.Value; }
        public static Mint Choose(long n, long k)
        {
            Mint numerator = 1, denominator = 1;
            for (int i = 0; i < k; i++)
            {
                numerator *= n - i;
                denominator *= i + 1;
            }
            return numerator / denominator;
        }
    }
    public sealed class Settings
    {
        public enum Priority : byte
        {
            Smaller = 0,
            Larger = 1
        }
    }
}