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:
from bisect import bisect_right
s = list(map(int,list(input())))
s.insert(0,-1)
n = len(s)-1
flag = 0
if s[n]==1 or s[1]==0 or s[n-1]==0:
    flag = 1
else:
    for i in range(2,n-1):
        if s[i]!=s[n-i]:
            flag = 1
            break
if flag==1:
    print(-1)
else:
    print(n,n-1)
    A = [1,n-1]
    cur = 1
    for i in range(2,n-1):
        if s[i]==1:
            print(cur,i)
            cur = i
            A.append(i)
    print(cur,n-1)
    A = sorted(A)
    for i in range(2,n-1):
        if s[i]==0:
            ind = bisect_right(A,i)
            print(i,A[ind])