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>
using namespace std;

int N;
string S;

int main()
{
    cin >> S;
    N = S.size();

    if(S[0] == '0' || S[N - 2] == '0' || S[N - 1] == '1')
    {
        cout << -1 << endl;
        return 0;
    }

    for(int i = 0; i < N - 1; i++)if(S[i] != S[N - 2 - i])
    {
        cout << -1 << endl;
        return 0;
    }

    int top = 1, next = 2;
    for(int i = 0; i < N - 1; i++)
    {
        cout << top << " " << next << endl;
        if(S[i] == '1')top = next;
        next++;
    }
    return 0;
}