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 = input()
l = len(s)

if s[0] != '1' or s[-2] != '1' or s[-1] != '0':
  print('-1')
  exit()
if s[:-1] != s[:-1][::-1]:
  print('-1')
  exit()

# 1頂点に全部ついた状態から始める
e = [l] + [-1] * (l-1)
now = 0
h = (l-1) // 2
for i in range(h, 0, -1):
  c = s[i]
  if c == '0':
    continue
  # now の木から子をi個取り出して繋げる
  e[now] = l - i
  e[l-i-1] = l
  now = l-i-1

for i, a in enumerate(e):
  for j in range(i+2, a+1):
    print(i+1, j)