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 OCaml (4.10.0) (judge verdict: Accepted)

Scanf.scanf "%s" (fun s ->
    let n = String.length s in
    let proc () =
        let rec loop i prev acc =
            if i = n - 1 then prev, acc else 
                let acc = (prev, i + 2) :: acc in
                if i >= n / 2 then loop (i + 1) prev acc else
                    if s.[i] <> s.[n - 2 - i] then prev, [] else
                    if s.[i] = '1' then loop (i + 1) (i + 2) acc
                                   else loop (i + 1) prev    acc
        in
        let prev, acc = loop 0 1 [] in
        if acc = [] then print_endline "-1" else
            List.iter (fun (a, b) -> Printf.printf "%d %d\n" a b) acc
    in
    if s.[n - 1] = '1' || s.[0] = '0' || s.[n - 2] = '0' then print_endline "-1" else proc ()
)