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:
def Tree():
    S = input()
    N = len(S)

    if S[0] == "0" or S[-1] == "1":
        return []

    for i in range(N - 1):
        if S[i] != S[N - i - 2]:
            return []

    res = []
    path = S.count("1")
    for i in range(1, path + 1):
        res.append((i, i + 1))

    u = len(res) + 1
    v = 1
    for s in S[:-1]:
        if s == "1":
            v += 1
        else:
            u += 1
            res.append((v, u))

    return res


if __name__ == "__main__":
    tree = Tree()
    if tree:
        for x, y in tree:
            print(x, y)
    else:
        print(-1)