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)

a = readline.chomp.split("").map(&:to_i)
s = a.size
k = [0, *a]
r = k.zip(k.reverse).all?{|(i,j)| i == j}
unless a[0] == 1 && a[s-2] == 1 && a[s-1] == 0 && r
    puts -1
    exit
end

pc = 2
nc = 2
res = []
res << [1, 2]
a[1..s-2].each{|k|
    if k == 0
        nc += 1
        res << [nc - 1, nc]
    else
        res << [pc, pc + 1]
        nc = pc + 1
        pc = pc + 1
    end
}

res.each{|(i, j)|
    puts "#{i} #{j}"
}