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 <bits/stdc++.h>
#define Int int64_t

using namespace std;

int main() {
	string s;
	cin >> s;

	int n = s.size();
	bool ok = (s[0] == '1') && (s.back() == '0');
	for (int i = 0; i < n - 1; ++i) {
		ok = ok && (s[i] == s[n - 2 - i]);
	}

	if (!ok) {
		cout << "-1\n";
		return 0;
	}

	vector<pair<int, int>> ans;
	int r = n;
	for (int i = n - 1; i > 0; --i) {
		ans.emplace_back(r, i);
		if (s[i - 1] == '1') { r = i; }
	}
	
	for (auto p : ans) {
		cout << p.first << " " << p.second << endl;
	}

	return 0;
}