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<iostream>
#include<algorithm>
#include<cstring>
using namespace std;
const int N=100005;
char ss[N];
int n;
int X[N],Y[N];
int num=0;
int main()
{
	scanf("%s",ss+1);
	n=strlen(ss+1);
	if (ss[1]=='0'||ss[n]=='1')	{printf("-1\n");return 0;}
	for (int u=1;u<n;u++)
	{
		if (ss[u]!=ss[n-u])
		{
			printf("-1\n");
			return 0;
		}
	}
	printf("1 2\n");
	int tp=1,sum=2;
	for (int u=2;u<n;u++)
	{
		sum++;
		printf("%d %d\n",sum,tp);
		if (ss[u]=='1') tp=sum;
	}
	return 0;
}