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:
import sys

s = input()
n = len(s)
if s[0] == "0" or s[-1] == "1":
	print(-1)
	sys.exit()

possible = []
for i in range(n // 2):
	if s[i] != s[n - i - 2]:
		print(-1)
		sys.exit()

	if i > 0 and s[i] == "1":
		possible.append(i+1)

#print(possible)
l = len(possible)

edges = []

cnt = 0
for i in range(l):
	for j in range(cnt + 1, possible[i]):
		edges.append([j, possible[i]])
	if i != l - 1:
		edges.append([possible[i], possible[i+1]])
	else:
		edges.append([possible[i], possible[i] + 1])

	cnt = possible[i]

for i in range(cnt + 2, n + 1):
	edges.append([cnt + 1, i])

for e in edges:
	print(*e)