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:
import sys
input = sys.stdin.readline
s = list(map(int, list(input())[: -1]))
if s[0] == 0 or s[-1] == 1:
  print(-1)
  exit(0)
n = len(s)
for i in range(n - 1):
  if s[i] != s[-2 - i]:
    print(-1)
    exit(0)
res = []
temp = []
s[-1] = 1
for i in range(n):
  if s[i] == 0 or i == 0:
    temp.append(i + 1)
  else:
    if len(res):
      p = res[-1][0]
      res.append((i + 1, p))
    if len(temp):
      while len(temp):
        res.append((i + 1, temp.pop()))
for _ in range(len(res)):
  print(*res.pop())