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 PYTHON3):

Solution:
s = input()

if s[0] == '0' or s[-2] == '0' or s[-1] == '1':  # 's' should be like "1xx...x0"
    print(-1)
elif s[:-1] != s[-2::-1]:
    print(-1)
else:
    half = len(s) // 2
    one_indices = [i+1 for i in range(1, half) if s[i] == '1'] # not including 0 or larger than n//2

    parents = [0] * (len(s) + 1)
    parent_index = 1
    for index in one_indices:
        for i in range(parent_index, index):
            parents[i] = index
        parent_index = index

    root = parent_index + 1
    parents[parent_index] = root
    for index in range(root + 1, len(s) + 1):
        parents[index] = root

    for node, parent in enumerate(parents):
        if parent == 0: # This means node is 0 or the root of the tree.
            continue
        print(node, parent)