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 N 100007
using namespace std;
char s[N];
int x[N];
int main(){
    scanf("%s",s+1);
    int n=strlen(s+1);
    if(s[1]=='0'){puts("-1");return 0;}
    if(s[n]=='1'){puts("-1");return 0;}
    for(int i=1;i<n;++i)
        if(s[i]!=s[n-i]){puts("-1");return 0;}
    int k=0;
    for(int i=1;i<=n;++i)
        if(s[i]=='1')x[++k]=i;
    for(int i=1;i<=k;++i)printf("%d %d\n",i,i+1);
    for(int i=2,id=k+1;i<=k;++i)
        for(int j=x[i]-x[i-1]-1;j>0;--j)printf("%d %d\n",i,++id);
}