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:
#!/usr/bin/env python3


def solve(s):
    n = len(s)

    if s[0] != '1':
        print(-1)
        return
    if s[-1] != '0':
        print(-1)
        return
    for i in range((n - 1) // 2):
        if s[i] != s[n - 2 - i]:
            print(-1)
            return
    edges = [(1, 2)]
    s = s[: n // 2]
    p = 1
    if 3 < n and s[1] == '1':
        p = 2
    for i in range(1, n // 2):
        edges.append((p, i + 2))
        if s[i] == '1':
            p = i + 2
    for i in range(n // 2 + 1, n):
        edges.append((p, i + 1))

    for uv in edges:
        u, v = uv
        print('{} {}'.format(u, v))


def main():
    s = input()

    solve(s)


if __name__ == '__main__':
    main()