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()
eda = []
flag = False
N = len(S)
if S[-1] == '1':
  flag = True
if S[0] == '0':
  flag = True
if S[-2] == '0':
  flag = True
for k in range((N-1)//2):
  if S[k] != S[-k-2]:
    flag = True
  if S[k] == '1':
    eda.append(k+1)
if N%2 == 0:
  if S[N//2 -1] == '1':
    eda.append(N//2)
if flag:
  print(-1)
  exit()
ans = []
eda.reverse()
before = eda.pop()
while eda:
  after = eda.pop()
  for k in range(before, after):
    ans.append((k, after))
  before = after
ans.append((before, before+1))
for k in range(before+2, N+1):
  ans.append((before+1, k))
while ans:
  item = ans.pop()
  print(item[0], item[1])