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 solve(s):
    if s[-1] == '1':
        return False
    if s[0] == '0':
        return False
    half = s[:len(s) // 2]
    if half != s[-2:(len(s) - 3) // 2:-1]:
        return False
    head = 1
    master = 1
    buf = []
    for i, c in enumerate(half):
        if c == '0':
            buf.append('{} {}'.format(master, i + 2))
        else:
            buf.append('{} {}'.format(head, i + 2))
            head = master = i + 2
    for i in range(len(half), len(s) - 1):
        buf.append('{} {}'.format(master, i + 2))
    return buf


res = solve(input())
if res == False:
    print(-1)
else:
    print('\n'.join(res))