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[n-1] == '1':
    print(-1)
    exit(0)
if s[0] == '0' or s[n-2] == '0':
    print(-1)
    exit(0)
for i in range(n-1):
    if s[i] != s[n-2-i]:
        print(-1)
        exit(0)

#rebuild tree

#record all size
ss = []

for i in range(n-1,-1,-1):
    if s[i] == '1':
        ss.append(i+1)


now_no = 1
now_siz = n
for siz in ss:
    others = now_siz - siz - 1
    for i in range(1,others+1):
        print(now_no,now_no+i)
    print(now_no,now_no+others+1)
    now_no += others+1
    now_siz = siz