Problem:
Score : 700 points

Problem Statement

You are given a string s of length n.
Does a tree with n vertices that satisfies the following conditions exist?

The vertices are numbered 1,2,..., n.

The edges are numbered 1,2,..., n-1, and Edge i connects Vertex u_i and v_i.

If the i-th character in s is 1, we can have a connected component of size i by removing one edge from the tree.

If the i-th character in s is 0, we cannot have a connected component of size i by removing any one edge from the tree.

If such a tree exists, construct one such tree.

Constraints

2 \leq n \leq 10^5

s is a string of length n consisting of 0 and 1.

Input

Input is given from Standard Input in the following format:

s

Output

If a tree with n vertices that satisfies the conditions does not exist, print -1.

If a tree with n vertices that satisfies the conditions exist, print n-1 lines.
The i-th line should contain u_i and v_i with a space in between.
If there are multiple trees that satisfy the conditions, any such tree will be accepted.

Sample Input 1

1111

Sample Output 1

-1

It is impossible to have a connected component of size n after removing one edge from a tree with n vertices.

Sample Input 2

1110

Sample Output 2

1 2
2 3
3 4

If Edge 1 or Edge 3 is removed, we will have a connected component of size 1 and another of size 3. If Edge 2 is removed, we will have two connected components, each of size 2.

Sample Input 3

1010

Sample Output 3

1 2
1 3
1 4

Removing any edge will result in a connected component of size 1 and another of size 3.

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

#if DEBUG
using System.Reflection;
using System.Threading.Tasks;
#endif

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Numerics;
using System.Globalization;

#if DEBUG
using System.Diagnostics;
#endif

namespace at103e
{
    class Program
    {
        static string _inputFilename = "input.txt";
        static string _outputFilename = "output.txt";
        static bool _useFileInput = false;
        const string _delim = "!";


        static void Main(string[] args)
        {
            StreamWriter file = null;
#if DEBUG
            var testNumber = 0;
            var timer = new Stopwatch();
            foreach (var test in GetTests())
            {

                timer.Start();

                var defaultColor = Console.ForegroundColor;
                Console.ForegroundColor = ConsoleColor.DarkYellow;
                Console.WriteLine($"<!-- TEST #{testNumber} -->");
                Console.ForegroundColor = defaultColor;
                Console.SetIn(test);


#else
            if (_useFileInput)
            {
                Console.SetIn(File.OpenText(_inputFilename));
                file = new StreamWriter(_outputFilename);
                Console.SetOut(file);
            }
#endif

                try
                {
#if DEBUG
                    Solution(testNumber);
#else
                Solution(0);
#endif
                }
                finally
                {
#if DEBUG
#else
                if (_useFileInput)
                {
                    file.Close();
                }
#endif
                }

#if DEBUG
                timer.Stop();

                Console.ForegroundColor = ConsoleColor.DarkYellow;
                Console.WriteLine($"<!-- TEST #{testNumber} FINISHED IN {timer.Elapsed.ToString(@"ss\:fff")}-->");
                Console.ForegroundColor = defaultColor;

                timer.Reset();
                testNumber++;
            }
#endif
        }



        static void Solution(int testNumber)
        {
            #region SOLUTION
            var s = Console.ReadLine();
            var n = s.Length;

            var g = new int[n];



            if (s[n - 1] != '0')
            {
                Console.WriteLine(-1);
                return;
            }

            if (n == 2)
            {
                if (s[0] != '1')
                {
                    Console.WriteLine(-1);
                    return;
                }

                Console.WriteLine("1 2");
                return;
            }

            var top = 1;
            //g[1] = 2;
            var nextTop = 2;
            var prev = 1;
            for (int i = 1; i < n; i++)
            {
                var next = s[i - 1];
                var last = s[n - 1 - i];
                if (next != last)
                {
                    Console.WriteLine(-1);
                    return;
                }

                if (i == 1 && next != '1')
                {
                    Console.WriteLine(-1);
                    return;
                }

                if (i - 1 == n - 1 - i )
                {
                    if (next == '1')
                    {
                        g[top - 1] = nextTop;
                        top = nextTop;
                        nextTop++;
                    }
                    else
                    {
                        g[nextTop - 1] = top;
                        nextTop++;
                    }

                    break;
                }
                else if (i - 1 + 1 == n - 1 - i)
                {
                    if (next == '1')
                    {
                        g[top - 1] = nextTop;
                        top = nextTop;
                        nextTop++;
                    }
                    else
                    {
                        g[nextTop - 1] = top;
                        nextTop++;
                    }

                    break;
                }
                else
                {
                    if (next == '1')
                    {
                        g[top - 1] = nextTop;
                        top = nextTop;
                        nextTop++;
                    }
                    else
                    {
                        g[nextTop - 1] = top;
                        nextTop++;
                    }

                }
            }

            while (nextTop <= n)
            {
                g[nextTop - 1] = top;
                nextTop++;
            }

            var sb = new StringBuilder();
            for (int i = 0; i < n; i++)
            {
                var p = g[i];
                if (p == 0)
                {
                    continue;
                }

                sb.AppendLine(string.Format("{0} {1}", i + 1, p));
            }

            Console.Write(sb);
            //var n = readInt();
            //var m = readInt();

            //var a = readIntArray();
            //var b = readIntArray();
            #endregion
        }

        static int ReadInt()
        {
            return int.Parse(Console.ReadLine());
        }

        static long ReadLong()
        {
            return long.Parse(Console.ReadLine());
        }

        static int[] ReadIntArray()
        {
            return Console.ReadLine().Split(' ').Where(i => !string.IsNullOrEmpty(i)).Select(i => int.Parse(i)).ToArray();
        }

        static long[] ReadLongArray()
        {
            return Console.ReadLine().Split(' ').Where(i => !string.IsNullOrEmpty(i)).Select(i => long.Parse(i)).ToArray();
        }

#if DEBUG
        static IEnumerable<TextReader> GetTests()
        {
            var tests = new List<string>();
            var resName = Assembly.GetCallingAssembly().GetManifestResourceNames()[0];
            using (var resource = new StreamReader(Assembly.GetCallingAssembly().GetManifestResourceStream(resName)))
            {
                while (true)
                {
                    var nextText = new StringBuilder();
                    var endOfFile = false;
                    while (true)
                    {
                        var line = resource.ReadLine();

                        endOfFile = line == null;
                        if (endOfFile)
                        {
                            break;
                        }

                        if (line.Equals(_delim, StringComparison.Ordinal))
                        {
                            break;
                        }

                        nextText.AppendLine(line);
                    }

                    yield return new StringReader(nextText.ToString());

                    if (endOfFile)
                    {
                        break;
                    }
                }
            }
        }
#endif
    }
}