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:
// ARC103C.cpp
#include <bits/stdc++.h>

using namespace std;

const int MAX_N = 1e5 + 200;

int n, fa[MAX_N];
char str[MAX_N];

int main()
{
    scanf("%s", str + 1), n = strlen(str + 1);
    if (str[1] == '0' || str[n] == '1')
        puts("-1"), exit(0);
    for (int i = 1, j = n - 1; i <= j; i++, j--)
        if (str[i] != str[j])
            puts("-1"), exit(0);
    int root = 1;
    for (int i = 2; i <= n; i++)
    {
        printf("%d %d\n", root, i);
        if (str[i - 1] == '1')
            root = i;
    }
    return 0;
}