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: Wrong Answer)

s = gets.chomp

if s[0]==?0 || s[-1]==?1
  #むり
  p -1
  exit
end

s = s[0..-2]

if !(s.size.times.map{|i| s[i]==s[-i-1]}.all?)
  #むり
  p -1
  exit
end

bitcnt = s.count("1")
bitcnt.times{|i|
  puts [i+1, i+2]*" "
}

used = 0
vidx = 0
nextnum = bitcnt+1
s.size.times{|i|
  if s[i]==?1
    w = i-used
    w.times{
      puts [vidx+1, nextnum]*" "
    }
    vidx += 1
    used = i+1
    nextnum += 1
  end
}