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:
import bisect
s = input()
if s[-1] == "1" or s[0] == "0":
    print(-1)
    exit()

for i in range((len(s) - 1) // 2):
    # print(i,len(s)- i - 2)
    if s[i] != s[len(s) - i -2]:
        print(-1)
        exit()

sd = s[:-1] + '1'
plist = [i for i, v in enumerate(sd) if v == '1']
# print(plist)
for i,v in enumerate(s[:-1]):
    r = bisect.bisect(plist,i)
    print(i+1,plist[r] + 1)