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)
flag=False
for i in range(n//2):
    if s[i]!=s[-i-2]:
        flag=True
        break
if flag or s[0]=="0" or s[-1]=="1":
    print(-1)
elif n==2:
    print("2 1")
elif n==3:
    print("2 1")
    print("3 2")
else:
    print("2 1")
    head=2
    for i in range(3,n//2+2):
        print(str(i)+" "+str(head))
        if s[i-2]=="1":
            head=i
    i+=1
    while i<=n:
        print(str(i)+" "+str(head))
        i+=1