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.IO;
using System.Linq;
using System.Runtime;
using System.Reflection;
using System.Diagnostics;
using System.Collections.Generic;
using System.Runtime.CompilerServices;
using System.Text;
using System.Text.RegularExpressions;
using static System.Math;

class P
{
    static void Main()
    {
        string s = Console.ReadLine();
        //対称である必要があって、下から攻めてく感じ 10^5なので、えー
        //作ることができないを作りたい
        //HLみたいな感じで木の枝を上一本だと見てあげる
        //端の0からやっていくにはそうしかない ないので
        List<Tuple<int, int>> vectors = new List<Tuple<int, int>>();
        if (s[0] != s[s.Length - 2] || s[0] == '0' || s[s.Length - 1] == '1') goto end;
        vectors.Add(new Tuple<int, int>(1, 2));
        int lastPoint = 2;
        for (int i = 1; i < s.Length / 2; i++)
        {
            if (s[i] != s[s.Length - i - 2]) goto end;
            vectors.Add(new Tuple<int, int>(lastPoint, i + 2));
            if (s[i] == '1') lastPoint = i + 2;
        }
        for (int i = s.Length / 2 + 2; i <= s.Length; i++)
        {
            vectors.Add(new Tuple<int, int>(lastPoint, i));
        }
        Console.WriteLine(string.Join("\n", vectors.Select(x => $"{x.Item1} {x.Item2}")));
        return;
        //真ん中の辺みたいなのがあって、そこで2つのシーケンスを繋げるとかしないと駄目
        //全部必要部分は構築したらあとはウニでいいかも?
        end:;
        Console.WriteLine("-1");
    }
}