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().rstrip()
n = len(s)

# 1 and n-1 must be exist
if s[0] == "0" or s[-1] == "1":
    print(-1)
    exit()
# x and n-x must be exist at the same
for fs, bs in zip(s[:-1], s[:-1][::-1]):
    if fs != bs:
        print(-1)
        exit()

made = set()
node_num = 0
base = 0
for i, ch in enumerate(s[:-1]):
    if ch == "1" and i+1 not in made:
        node_num += 1
        print(node_num + 1, base + 1)
        base = node_num
        made.add(i+1)
        made.add(n-i-1)
    else:
        node_num += 1
        print(base + 1, node_num + 1)