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 check(S):
    size = len(S)
    if S[0]=="0" or S[-1]=="1":
        return False
    else:
        for i in range(size-1):
            a, b = i, size-i-2
            if (S[a]=="1" and S[b]=="0") or (S[a]=="0" and S[b]=="1"):
                return False
        return True


S = input()
if check(S):
    N = len(S)
    l = [1]
    p = False
    for i in range(2, N+1):
        if p:
            l.append(i)
        else:
            print(l[-1], i)
        p = (S[i-1]=="1")
    for i in range(len(l)-1):
        print(l[i], l[i+1])
else:
    print(-1)