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().strip()
n = len(s)
s = {i + 1 for i in range(n) if s[i] == '1'}

if n in s or 1 not in s or any(n - x not in s for x in s):
    print(-1)
else:
    s = sorted(s)
    c = 1
    e = []
    for i in range(1, len(s)):
        while c < s[i]:
            e.append((c, s[i]))
            c += 1
    e.append((c, n))
    e = [str(u) + ' ' + str(v) for u, v in e]
    print(*e, sep='\n')