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 (2.7.1) (judge verdict: Wrong Answer)

S = gets.chomp
N = S.size
L = Rational(N, 2).ceil

if S[0] == '0' || S[-1] == '1'
  puts -1
  exit
end

cur = 0
sizes = []

1.upto(L) do |l|
  a = S[l - 1]
  b = S[N - l - 1]

  if a != b
    puts -1
    exit
  end

  if a == '0'
    sizes << cur if sizes.empty?
    cur = 1
  else
    if sizes.empty?
      cur += 1
    else
      sizes << l
    end
  end
end

sizes << cur if sizes.empty? && cur > 0

edges = Hash.new
roots = []
cur = 2

sizes.each_with_index do |size, i|
  if i == 0
    next if size == 1
    roots << 1

    (size - 1).times do
      edges[cur] = cur - 1
      cur += 1
    end
  else
    root = cur
    roots << root

    (size - 1).times do
      cur += 1
      edges[cur] = root
    end
  end
end

if cur > N
  puts -1
  exit
end

roots.each do |t|
  edges[t] = cur
end

edges.default = cur
ans = []

1.upto(N) do |u|
  next if cur == u
  v = edges[u]

  puts [u, v].sort.join(' ')
end