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 Ruby (2.3.3) (judge verdict: Accepted)

# frozen_string_literal: true

S = gets.strip

N = S.size
S1 = '0' + S

if S1 == S1.reverse && S[0] == '1'
  center = (N + 1) / 2
  i = 0
  (2..center).each do |j|
    if S1[j] == '1'
      puts "#{i} #{j}" if i != 0
      ((i + 1)...j).each do |k|
        puts "#{j} #{k}"
      end 
      i = j
    end
  end
  puts "#{i} #{N}" if i != 0
  ((i + 1)...N).each do |k|
    puts "#{N} #{k}"
  end
else  
  puts(-1)
end