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()
n = len(s)
comp = {i+1: True if st == '1' else False for i, st in enumerate(s)}
comp[0] = False

# feasibility check
feasible = True
for i in range(n//2 + 1):
    if i == 1 and not (comp[i] and comp[n-i]):
        feasible = False
        break
    elif comp[i] ^ comp[n-i]:
        feasible = False
        break

if not feasible:
    print(-1)
else:
    edge = []
    parent = n
    for i in reversed(range(1, n)):
        edge.append((i, parent))
        if comp[i]:
            parent = i
    for u, v in edge:
        print(u, v)