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()

S = '0' + s
N = len(s)


# 葉から順に構築
def f():
    res = []
    r = 1
    C = []
    for i in range(2, N + 1):
        if S[i] == '0':
            C.append(i)
        else:
            res.append((r, i))
            r = i
            for c in C:
                res.append((r, c))
            C = []
    for c in C:
        res.append((r, c))
    return res


ans = (
    '-1' if S[1] == '0' or S[N] == '1' or any(
        S[i] != S[N - i]
        for i in range(1, N)
    ) else
    '\n'.join(
        '{} {}'.format(u, v)
        for u, v in f()
    )
)

print(ans)