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)

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

namespace AtCoder
{
    class Program
    {
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        static IEnumerable<int[]> Solve(string S)
        {
            int N = S.Length;
            if (S.Last() != '0') { return null; }
            if (S.First() != '1') { return null; }
            for (int i = 0; i < N - 2 - i; ++i)
            {
                if (S[i] != S[N - 2 - i]) { return null; }
            }
            var set = new List<int> { 0 };
            for (int i = 1; i < N; ++i) { if (S[i] == '1') { set.Add(i + 1); } }
            set.Add(N);
            var edges = new List<int[]>();
            for (int i = 1; i < set.Count; ++i)
            {
                for (int j = set[i - 1] + 1; j < set[i]; ++j)
                {
                    edges.Add(new int[] { j, set[i] });
                }
                if (i + 1 < set.Count)
                {
                    edges.Add(new int[] { set[i], set[i + 1] });
                }
            }
            return edges;
        }
        static void Main(string[] args)
        {
            var edges = Solve(Read());
            if (edges == null)
            {
                Console.WriteLine(-1);
            }
            else
            {
                foreach (var edge in edges) { Console.WriteLine(string.Join(" ", edge)); }
            }
        }
    }
}