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 = list(input())
n = len(s)
if s[n - 1] == "1" or s[0] == "0":
    print(-1)
    exit()
for i in range((n - 1) // 2):
    if not s[i] == s[n - 2 - i]:
        print(-1)
        exit()
l = n - s.count("0") + 1
x = [0] * l
j = 0
for i in range(n // 2):
    if s[i] == "1":
        j += 1
    else:
        x[j] += 1
        x[l - 1 - j] += 1
        if j == l - 1 - j and n % 2 == 0 and i == (n - 1) // 2:
            x[j] -= 1
for i in range(l - 1):
    print(i + 1, i + 2)
k = n - s.count("0") + 2
for i in range(l):
    for _ in range(x[i]):
        print(i + 1, k)
        k += 1