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, = map(int, open(0).readline().strip())
N = len(S)
ok = 1
for i in range(N-1):
    if S[i] != S[-2-i]:
        ok = 0
        break
if not ok or S[0] != 1 or S[-1] != 0:
    print(-1)
    exit(0)

E = []
V = [i+1 for i in range(N//2) if S[i]]
p = 1
for v in V:
    for i in range(p, v):
        E.append("%d %d\n" % (i, v))
    p = v

E.append("%d %d\n" % (p, p+1))
p += 1
for i in range(p+1, N+1):
    E.append("%d %d\n" % (p, i))
open(1, 'w').writelines(E)