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<iostream>
#include<stdio.h>
#include<string.h>
using namespace std;
char s[120000];
int fa[120000],p,n;
int a[120000];
int main(){
	scanf("%s",s+1);
	n=strlen(s+1);
	for(int i=1;i<=n;i++)a[i]=s[i]=='1';
	if(a[n]==1||a[1]==0){
		printf("-1\n");
		return 0;
	}
	for(int i=1;i<=n;i++){
		if(a[n-i]!=a[i]){
			printf("-1\n");
			return 0;
		}
		if(a[i]==1){
			for(int j=p;j<i;j++)fa[j]=i;
			p=i;
		}
	} 
	for(int i=p;i<=n;i++)fa[i]=n;
	for(int i=1;i<n;i++){
		printf("%d %d\n",i,fa[i]);
	}
}