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 math

s = input()

N = len(s)
s = "#" + s
possible = 1
if s[-1] == "1" or s[1] == "0":
  possible = 0
for i in range(1,math.floor(N/2)):
  if s[i] != s[N - i]:
    possible = 0

if not possible:
  print(-1)
elif N == 2:
  if s[1] == "1" and s[2] == "0":
    print(1, 2)
  else:
    print(-1)
elif N == 3:
  if s[1] == "1" and s[2] == "1":
    print(1,2)
    print(2,3)
  else:
    print(-1)
else:
  destination = [1] * (N+1)
  dest_change = [0] * (N+1)
  root = 2
  max_bit = math.floor(N/2)
  for i in range(max_bit, -1, -1):
    if s[i] == "1":
      #destination = destination[:root+1] + [root]*(i-1) + destination[root+i:]
      dest_change[root + 1] = dest_change[root + 1] + 1
      dest_change[root + i] = dest_change[root + i] - 1
      root += 1
  for i in range(1,N+1):
    destination[i] = destination[i - 1] + dest_change[i]
  for i in range(2,N+1):
    print(i, destination[i])