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>
#include<algorithm>
#include<cmath>
#define MN 100005
using namespace std;
char ch[MN];int n;
int main(){
	scanf("%s",ch+1);n=strlen(ch+1);
	for(int i=1,j=n-1;i<=j;i++,j--)if(ch[i]!=ch[j])return 0*puts("-1");
	if(ch[n]=='1'||ch[1]=='0')return 0*puts("-1");	
	int lst=1;
    for(int i=2;i<=n;i++)if(ch[i]=='1'){
		printf("%d %d\n",i,lst);
		for(int j=lst+1;j<i;j++)printf("%d %d\n",i,j);
		lst=i;
    }printf("%d %d\n",n,n-1);
}