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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val ans = solve()
    if (ans == null) {
        println(-1)
    } else {
        for (edge in ans!!) {
            println("${edge.first} ${edge.second}")
        }
    }
}

fun solve(): List<Pair<Int, Int>>? {
    val input = readLine()!!
    val n = input.length
    val bits = ("0" + input).map { it == '1' }.toBooleanArray()
    if (bits[n]) return null
    if (!bits[1]) return null
    for (i in 1..(n - 1)) {
        if (bits[i] && !bits[n - i]) return null
    }

    val edges = mutableListOf<Pair<Int, Int>>()
    var prev = 0
    for (i in 2..(n - 1)) {
        if (bits[i]) {
            if (prev == 0) {
                for (j in 1..(i - 1)) {
                    edges.add(Pair(j, i))
                }
            } else {
                edges.add(Pair(prev, i))
                for (j in (prev + 1)..(i - 1)) {
                    edges.add(Pair(j, i))
                }
            }
            prev = i
        }
    }
    edges.add(Pair(n - 1, n))

    return edges
}