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)
if s[-1] == '0' and s[0] == '1' and s[n - 2] == '1' and s[:n - 1] == s[n - 2 :: -1]:
    #s[i] = 「１辺を取り除いてi + 1頂点からなる連結成分を作れる」
    #連結成分のサイズは、1からn//2までチェックすれば十分
    #構成：各iに対し、iの次に1になっているbitを求める
    i = 0
    j = 1
    while j <= n - 2:
        if s[j] == '1':
            for k in range(i, j):
                print(k + 1, j + 1)
            i = j
            j = j + 1
        else:
            j += 1
    print(n - 1, n)

else:
    print(-1)