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.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		String s = sc.next();
		boolean flag = true;
		if(s.charAt(0) != '1' || s.charAt(s.length() - 2) != '1' || s.charAt(s.length() - 1) != '0')
			flag = false;
		if(flag) {
			for(int i = 1; i < s.length() / 2; i++) {
				if(s.charAt(i) != s.charAt(s.length() - 2 - i)) {
					flag = false;
					break;
				}
			}
		}
		if(flag) {
			List<Node> node = new ArrayList<>();
			int from = 1;
			for(int i = 1; i < s.length(); i++) {
				if(s.charAt(i) == '1') {
					from = i + 2;
					node.add(new Node(1, i + 1));
					node.add(new Node(1, i + 2));
					break;
				} else {
					node.add(new Node(1, i + 1));
				}
			}
			for(int i = from - 1; i < s.length() - 1; i++) {
				node.add(new Node(from, i + 2));
				if(s.charAt(i) != '0') {
					from = i + 2;
				}
			}
			for(Node e : node) {
				System.out.println(e.getFrom() + " " + e.getTo());
			}
		} else {
			System.out.println(-1);
		}

	}
}

class Node {
	private int from;
	private int to;

	protected Node(int from, int to) {
		super();
		this.from = from;
		this.to = to;
	}

	public int getFrom() {
		return from;
	}

	public void setFrom(int from) {
		this.from = from;
	}

	public int getTo() {
		return to;
	}

	public void setTo(int to) {
		this.to = to;
	}

}