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:
def main():
	s = input()
	if s[-1] == "1" or s[0] == "0":
		print(-1)
		return
	if s[0:-1][::-1] != s[:-1]:
		print(-1)
		return
	temp = 1
	init = []
	for i in range(1,int((len(s)+1)/2)):
		if s[i] == "1":
			for j in range(temp+1, i+2):
				print(temp, j, sep=" ")
			init += [temp]
			temp = i+2
	if temp != len(s):
		for j in range(temp+1, len(s)+1):
			print(temp, j, sep=" ")
	init += [temp]
	for i in range(len(init)-1):
		print(init[i], init[i+1], sep=" ")
	

main()