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 CPP):

Solution:
#include <string>
#include <iostream>
using namespace std;
int main() {
	string s;
	cin >> s;
	int n = s.size();
	bool ok = true;
	if (s[0] == '0' || s[n - 1] == '1') ok = false;
	for (int i = 0; i < n - 1; ++i) {
		if (s[i] != s[n - i - 2]) ok = false;
	}
	if (!ok) cout << -1 << endl;
	else {
		int pre = 1, cur = 2;
		for (int i = n - 2; i >= 0; --i) {
			cout << pre << ' ' << cur << endl;
			if (s[i] == '1') pre = cur;
			++cur;
		}
	}
	return 0;
}