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:
// practice with kaiboy
import java.io.*;
import java.util.*;

public class Main extends PrintWriter {
	Main() { super(System.out); }
	Scanner sc = new Scanner(System.in);
	public static void main(String[] $) {
		Main o = new Main(); o.main(); o.flush();
	}

	void main() {
		byte[] cc = (" " + sc.next()).getBytes();
		int n = cc.length - 1;
		if (cc[n] != '0' || cc[1] != '1' || cc[n - 1] != '1') {
			println(-1);
			return;
		}
		for (int i = 2, j = n - 2; i < j; i++, j--)
			if (cc[i] != cc[j]) {
				println(-1);
				return;
			}
		int i = 1;
		for (int j = 2; j <= n / 2; j++)
			if (cc[j] == '1' || j == n / 2)
				while (i < j) {
					println(i + " " + j);
					i++;
				}
		if (cc[i] == '1') {
			i++;
			println(i - 1 + " " + i);
		}
		for (int j = i + 1; j <= n; j++)
			println(i + " " + j);
	}
}