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:
#ライブラリインポート
from collections import defaultdict

#入力受け取り
def getlist():
	return list(map(int, input().split()))

#処理内容
def main():
	s = list(input())
	N = len(s)
	judge = "Yes"
	if s[0] == "0":
		judge = "No"
	if s[N - 1] == "1":
		judge = "No"
	for i in range(N - 2):
		if s[i] != s[N - 2 - i]:
			judge = "No"
	if judge == "No":
		print(-1)
		return

	c = 1
	d = N
	for i in range(N - 1):
		if s[i] == "1":
			print(c, c + 1)
			c += 1
		else:
			print(c, d)
			d -= 1

if __name__ == '__main__':
	main()