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<cstdio>
#include<cstring>
char S[1001000];
int a[100100],n;
int main(){
	scanf("%s",S+1);
	n=strlen(S+1);
	for(int i=1;i<=n;i++)a[i]=S[i]-'0';
	if(a[n]==1||a[1]==0)return puts("-1"),0;
	for(int i=1;i<n;i++)
		if(a[i]!=a[n-i])return puts("-1"),0;
	int root=1;
	for(int i=1;i<n;i++){
		printf("%d %d\n",root,i+1);
		if(a[i]==1) root=i+1;
	}	
}