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 sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")

s = input()
n = len(s)
if s[0]=="0" or s[-2]=="0" or s[-1]=="1":
    print("-1")
elif any(s[i]!=s[-2-i] for i in range(n-1)):
    print("-1")
else:
    i = 1
    ps = set([i])
    es = []
    for c in s[1:]:
        i += 1
        if c=="0":
            ps.add(i)
        else:
            for u in ps:
                es.append("%s %s" % (u,i))
            ps = set([i])
    for u in ps:
        if u!=n:
            es.append("%s %s" % (u, n))
    write("\n".join(es))