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 = "0" + input()
    ans = []
    f = True
    for i in range(len(s)//2):
        if s[i] != s[len(s)-1-i]:
            f = False
            break
    if s[1] == "0" or s[-2] == "0":
        f = False
    if f:
        ans = []
        p = len(s)-1
        for i in reversed(range(1, len(s)-1)):
            c = s[i]
            ans.append([i, p])
            if c == "1":
                p = i
        for u, v in ans:
            print(u, v)
    else:
        print(-1)

if __name__ == "__main__":
    main()