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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		char[] s = br.readLine().toCharArray();
		br.close();

		int n = s.length;
		if (s[0] == '0' || s[n - 2] == '0' || s[n - 1] == '1') {
			System.out.println(-1);
			return;
		}
		for (int i = 2; i <= n / 2; i++) {
			if (s[i - 1] != s[n - 1 - i]) {
				System.out.println(-1);
				return;
			}
		}

		PrintWriter pw = new PrintWriter(System.out);
		pw.println("1 " + n);
		int now = 1;
		for (int i = 2; i <= n / 2; i++) {
			pw.println(now + " " + i);
			if (s[i - 1] == '1') {
				now = i;
			}
		}
		for (int i = n / 2 + 1; i < n; i++) {
			pw.println(now + " " + i);
		}
		pw.flush();
	}
}