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<bits/stdc++.h>
#define fail {puts("-1");return 0;}
using namespace std;
char s[100005];
int main()
{
    int n;
    scanf("%s",s+1);
    n=strlen(s+1);
    for(int i=1;i<=n/2;i++)if(s[i]!=s[n-i])fail
    if(s[1]=='0'||s[n]=='1')fail
    int now=2;
    printf("1 2\n");
    for(int i=2;i<n;i++)
    {
        printf("%d %d\n",now,i+1);
        if(s[i]=='1')now=i+1;
    }
    return 0;
}