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)

require 'pp'
S=gets.chomp.split('')
N=S.size
# validate
if(S[-1]=="1")
	puts -1
	exit(0)
end
if(S[0] != "1" || S[-2] != "1")
	puts -1
	exit(0)
end
for i in 0..(S.size/2)
	if(S[i]!=S[S.size-2-i])
		puts -1
		exit(0)
	end
end
# const
prev_one = 1
prev = 1
for i in 1..((S.size*1.0/2).ceil-1)
	puts "1 #{i+1}"
end
now = (S.size*1.0/2).ceil+1
(S.size/2-1).downto(0){|i|
	case S[i]
	when "1"
		puts "#{prev_one} #{now}"
		prev_one = now
		prev = now
		now += 1
	when "0"
		puts "#{prev_one} #{now}"
		prev = now
		now += 1
	end
}