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<stdio.h>
#include<string.h>
char s[100010];
int x[100010],k;
int main(){
	int n,i,k,M;
	scanf("%s",s+1);
	n=strlen(s+1);
	#define wa {puts("-1");return 0;}
	if(s[1]=='0'||s[n]=='1')wa
	for(i=1;i<n;i++){
		if(s[i]!=s[n-i])wa
	}
	k=0;
	for(i=1;i<n;i++){
		if(s[i]=='1')x[++k]=i;
	}
	M=k+1;
	for(i=1;i<=k;i++)printf("%d %d\n",i,i+1);
	for(i=2;i<=k;i++){
		n=x[i]-x[i-1]-1;
		while(n--)printf("%d %d\n",i,++M);
	}
}