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 = [int(x) for x in input()]
N = len(S)
if S[0] == 0 or S[-1] == 1 or any(S[i] != S[-i - 2] for i in range(N - 1)):
    print(-1)
    quit()

edge = [(1, 2)]
root, now = 2, 3
for i in range(1, N // 2 + 1):
    edge.append((root, now))
    if S[i] == 1:
        root = now
    now += 1
while now <= N:
    edge.append((root, now))
    now += 1
for s, t in edge:
    print(s, t)