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.IO;
using System.Linq;
using System.Collections.Generic;

class Program
{
    static int[] dx = new int[] { 0, 0, 1, -1 };
    static int[] dy = new int[] { 1, -1, 0, 0 };
    const int INF = 1010101010;

    static void Solve()
    {
        var s = sc.Str();

        var used = new bool[30];

        if (s == "zyxwvutsrqponmlkjihgfedcba")
        {
            pr.WriteLine(-1);
            return;
        }

        foreach (var c in s)
            used[c - 'a'] = true;

        if (s.Length == 'z' - 'a' + 1)
        {
            for (var i = s.Length - 2; 0 <= i; i--)
            {
                if (s[i] < s[i + 1])
                {
                    pr.Write(s.Substring(0, i));
                    pr.WriteLine((char)s.Substring(i + 1).Where(c => s[i] < c).Min());
                    break;
                }
            }
        }
        else
        {
            pr.Write(s);
            pr.WriteLine((char)('a' + Array.IndexOf(used, false)));
        }
    }

    class Node : IComparable
    {
        public int Id;
        public int Cost;

        public int CompareTo(object obj)
        {
            return ((Node)obj).Cost - Cost;
        }

        public override string ToString()
        {
            return $"Id: {this.Id} - Cost: {this.Cost}";
        }
    }

    class Edge
    {
        public int To;
        public int Cost;
    }

    static double F(double prev, double next, double t)
    {
        return Math.Pow(Math.Exp((next - prev) / t), 2);
    }

    static int[,] Mul(int[,] a, int[,] b)
    {
        var ret = new int[a.GetLength(0), b.GetLength(1)];
        for (int i = 0; i < a.GetLength(0); i++)
            for (int j = 0; j < b.GetLength(1); j++)
                for (int k = 0; k < a.GetLength(1); k++)
                    ret[i, j] += a[i, k] * b[k, j];

        return ret;
    }

    static int[,] Pow(int[,] a, int n)
    {
        var b = new int[a.GetLength(1), a.GetLength(0)];

        var f = n % 2 == 1;

        for (int i = 0; i < a.GetLength(0); i++)
            b[i, i] = 1;

        while (n > 0)
        {
            if (n % 2 == 1)
                b = Mul(a, b);


            n >>= 1;
        }

        return b;
    }

    class Coord
    {
        public int x;
        public int y;
    }

    static void Main(string[] args)
    {
        pr.AutoFlush = true;
        Solve();
        pr.Flush();
        // Console.ReadKey();
    }

    static Scanner sc = new Scanner();
    static Printer pr = new Printer();
}

class Heap<T> where T : IComparable
{
    private List<T> _heap;
    private int _last;
    private int _cnt;
    private IComparer<T> _comparer;

    public Heap()
    {
        _heap = new List<T>();
        _last = 0;
    }

    public Heap(IEnumerable<T> e)
    {
        _heap = new List<T>(e);
        _cnt = _last = _heap.Count();

        for (int i = _last / 2; 0 <= i; i--)
            Heapify(i);
    }

    public Heap(IComparer<T> comparer)
    {
        _comparer = comparer;
    }

    public Heap(IEnumerable<T> e, IComparer<T> comparer) : this(e)
    {
        _comparer = comparer;
    }

    private int Compare(T a, T b)
    {
        if (_comparer == null)
            return a.CompareTo(b);
        else
            return _comparer.Compare(a, b);
    }

    public bool Empty()
    {
        return _last == 0;
    }

    public void Enqueue(T item)
    {
        if (_last < _cnt)
        {

            _heap[_last++] = item;
        }
        else
        {
            _heap.Add(item);
            _cnt++;
            _last++;
        }

        var i = _last - 1;

        while (0 < i)
        {
            if (0 <= Compare(_heap[(i - 1) / 2], _heap[i]))
                break;
            swap((i - 1) / 2, i);
            i = (i - 1) / 2;
        }
    }

    public T Dequeue()
    {
        if (_last == 0)
            throw new Exception("Empty");

        var ret = _heap[0];
        _heap[0] = _heap[--_last];

        Heapify(0);

        return ret;
    }

    public T Peek()
    {
        return _heap[0];
    }

    public int Count()
    {
        return _last;
    }

    private void Heapify(int i)
    {
        var max = i;
        if (i * 2 + 1 < _last && Compare(_heap[max], _heap[i * 2 + 1]) < 0)
            max = i * 2 + 1;
        if (i * 2 + 2 < _last && Compare(_heap[max], _heap[i * 2 + 2]) < 0)
            max = i * 2 + 2;

        if (max == i)
            return;

        swap(i, max);

        Heapify(max);
    }

    private void swap(int a, int b)
    {
        var t = _heap[a];
        _heap[a] = _heap[b];
        _heap[b] = t;
    }
}

#region IO
class Scanner
{
    private int _i = 0;
    private string[] line = new string[0];

    private T[] Enumerate<T>(int n, Func<T> f)
    {
        T[] ret = new T[n];
        for (int i = 0; i < n; i++)
            ret[i] = f();
        return ret;
    }

    public string Str()
    {
        if (line.Length <= _i)
        {
            line = Console.ReadLine().Split(' ');
            _i = 0;
        }

        return line[_i++];
    }

    public int Int() => int.Parse(Str());
    public long Long() => long.Parse(Str());
    public double Double() => double.Parse(Str());
    public int[] Int(int n) => Enumerate(n, Int);
    public long[] Long(int n) => Enumerate(n, Long);
    public double[] Double(int n) => Enumerate(n, Double);
    public string[] Str(int n) => Enumerate(n, Str);
}

class Printer : StreamWriter
{
    public Printer() : base(Console.OpenStandardOutput())
    {
        AutoFlush = false;
    }
}
#endregion