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 PYTHON):

Solution:
s = raw_input()
n=len(s)
pos=True
if s[0]!="1" or s[-1]!="0":
    pos=False
else:
    if n%2==0:
        for i in range(n/2 - 1):
            if s[i]!=s[n-i-2]:
                pos=False
                break
    else:
        for i in range((n-1)/2):
            if s[i]!=s[n-i-2]:
                pos=False

res_list = []
if pos==False:
    print -1
else:
    rep=1
    if n%2==0:
        for i in range(n/2):
            if s[i]=="1":
                res_list.append([rep,i+2])
                rep=i+2
            else:
                res_list.append([rep,i+2])
        for i in range(n/2-1):
            res_list.append([rep,i+n/2+2])
    else:
        for i in range((n-1)/2):
            if s[i]=="1":
                res_list.append([rep,i+2])
                rep=i+2
            else:
                res_list.append([rep,i+2])
        for i in range((n-1)/2):
            res_list.append([rep,i+(n-1)/2+2])

    for res in res_list:
        print str(res[0]) + " " + str(res[1])