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>
using namespace std;
typedef pair<int,int> pii;

int n;
char str[100100];
vector<pii> ans;

int main() {
	scanf("%s",str+1);
	n=strlen(str+1);

	if(str[n]=='1' || str[1]=='0') {
		puts("-1");
		return 0;
	}

	int cur=1,c=2;
	for(int i=1;i<=n/2;i++) {
		if(str[n-i]!=str[i]) {
			puts("-1");
			return 0;
		}
		ans.push_back(pii(cur,c));
		if(str[i]=='1') cur=c;
		c++;
	}
	for(;c<=n;c++) ans.push_back(pii(cur,c));

	for(auto &it:ans)
		printf("%d %d\n",it.first,it.second);

	return 0;
}