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:
inp=[int(x) for x in list(input())]
length=len(inp)
x,y=(0,length-2)

if (not inp[0]==inp[length-2]==1) or inp[length-1]==1:
  print(-1)
  exit()

while x<y:
  if inp[x]!=inp[y]:
    print(-1)
    exit()
  else:
    x+=1
    y-=1

now=1
num=1
if length<=4:
  for x in inp:
    num+=1
    if x:
      print (now,num)
      now=num
    else:
      print (now,num)
    if num==length:
      break
else:
  for x in inp:
    num+=1
    if x:
      print (now,num)
      if num!=length-1:
        now=num
    else:
      print (now,num)
    if num==length:
      break