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()
if s[0] == "0" or s[-1] == "1":
    print(-1)
    exit()
n = len(s)
if n == 2:
    if s == "10":
        print(1, 2)
        exit()
    else:
        print(-1)
        exit()

m = n // 2
tmp = m + 1
ANS = []
for i in reversed(range(1, m + 1)):
    j = n - i
    if s[i - 1] == "1" and s[j - 1] == "1":
        ANS.append((tmp, i))
        tmp = i
    elif s[i - 1] == "0" and s[j - 1] == "0":
        ANS.append((tmp, i))
    else:
        print(-1)
        exit()
for i in range(m + 2, n + 1):
    ANS.append((m + 1, i))

for a, b in ANS:
    print(a, b)