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:
s=list(map(int,list(input())))
# s[0]=1,s[-1]=0,s[k]=s[n-k-1]は必要
def main(s):
  n=len(s)
  if s[0]!=1 or s[-1]!=0:return [[-1]]
  for k in range(n//2-1):
    if s[k]!=s[n-k-2]:return [[-1]]
  uv=[(1,2)]
  t=2
  i=3
  for x in s[1:-1]:
    uv.append((t,i))
    if x==1:
      t=i
    i+=1
  return uv
for x in main(s):
  print(*x,sep=' ')