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 python

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

    if s[0] != '1' or s[-1] != '0':
        print(-1)
        return
    for i in range(n // 2):
        if s[i] != s[-(i + 2)]:
            print(-1)
            return

    v = [i + 1 if c == '1' else 0 for (i, c) in enumerate(s)]
    v[-1] = n

    last = n
    for i, x in reversed(list(enumerate(v))):
        if x != 0:
            v[i] = last
            last = x
        else:
            v[i] = last

    for i, x in enumerate(v[:-1]):
        print(i + 1, x)


if __name__ == '__main__':
    solve()