Problem: 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.

Examples

Input

1111


Output

-1


Input

1110


Output

1 2
2 3
3 4


Input

1010


Output

1 2
1 3
1 4

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.*;
import java.util.*;

class Main {
    private static final Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {

        int[] s = sc.nextLine().chars().map(c -> c - '0').toArray();

        boolean ok = s[0] == 1 && s[s.length-1] == 0;
        for (int i = 0; i < s.length-1; i++) {
            if (s[i] != s[s.length-2-i]) ok = false;
        }

        if (!ok) {
            System.out.println(-1);
        }
        else {
            ArrayList<Edge> edges = new ArrayList<>();
            Stack<Integer> children = new Stack<>();
            for (int v = 1; v <= s.length; v++) {
                if (s[v-1] == 1 || v == s.length) {
                    while (!children.empty()) {
                        edges.add(new Edge(v, children.pop()));
                    }
                }
                children.push(v);
            }

            for (Edge e : edges) {
                System.out.printf("%d %d\n", e.u, e.v);
            }
        }

        sc.close();
    }
}

class Edge {
    public int u, v;
    Edge(int u, int v) {
        this.u = u;
        this.v = v;
    }
}