Tr/ee

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

inputFormat

Input

Input is given from Standard Input in the following format:

s

outputFormat

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

样例

1110

1 2
2 3
3 4

</p>