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()
n = len(S)
m = n // 2
if S[0] == '0' or S[-1] == '1':
  print(-1)
  quit()

ans = [[1, 2]]
node = 1
now = 3
for i in range(m):
  if S[i] != S[n-i-2]:
    print(-1)
    quit()
  else:
    if i == 0:
      continue
    ans.append([node, now])
    if S[i] == '0':
      now += 1
    else:
      node = now
      now += 1

for i in range(now, n+1):
  ans.append([node, i])

for a in ans:
  print(*a)