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:
def main():
    s=input()
    n=len(s)
    res = []
    if s[0]=="0" or s[-1] == "1":
        print(-1)
        return 1
    m=n//2
    t=m
    for i in range(m,0,-1):
        if s[i-1] != s[n-i-1]:
            print(-1)
            return 1
        if i == m:
            if s[i-1]=="1":
                res.append([m,m+1])
                for j in range(m+2,n+1):
                    res.append([m+1,j])
            else:
                for j in range(m+1,n+1):
                    res.append([m,j])
        else:
            if s[i-1]=="1":
                res.append([t,i])
                t=i
            else:
                res.append([t,i])
    for sres in res:
        print(" ".join(map(str, sres)))


main()