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: Wrong Answer)

using System;

public class AtCoder
{
    public static void Main()
    {
        string[] s;
        s = NextS();

        int n = s[0].Length;
        if (n == 2)
        {
            if (s[0] == "10") Console.WriteLine("1 2");
            else Console.WriteLine(-1);
            return;
        }            
        if (n == 3)
        {
            if(s[0] == "110")
            {
                Console.WriteLine("1 2");
                Console.WriteLine("2 3");
            }
            else Console.WriteLine(-1);
            return;
        }
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = int.Parse(s[0].Substring(i,1));

        bool f = true;
        for (int i = 1; i < n - 2; i++)
        {
            if (a[i] != a[n - 2 - i]) f = false;
        }
        if (!f || a[0] == 0 || a[n - 2] == 0 || a[n - 1] == 1)
        {           
            Console.WriteLine(-1);
            return;
        }

        int x = 2;
        int y = 2;
        Console.WriteLine("1 2");
        for(int i=1; i<n-1; i++)
        {
            Console.WriteLine(x + " " + (y + 1));
            if (a[i] == 1)
            {
                x++;
                y++;
            }
            else
            {
                y++;
            }
        }            
    }

    public static void DebugWL(object x) { System.Diagnostics.Debug.WriteLine(x); }
    public static string[] NextS() { return Console.ReadLine().Trim().Split(' '); }
}