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:
vs = [int(i) for i in input().strip()]
n = (len(vs) - 2)//2
def main(vs):
    if vs[0] != 1:
        print(-1)
        return -1
    if vs[-1] != 0:
        print(-1)
        return -1
    if vs[-2] != 1:
        print(-1)
        return -1
    for i in range(n):
        if vs[i+1] != vs[-2-i-1]:
            print(-1)
            return

    temp = 1
    for i in range(n+1 if len(vs) % 2 == 0 else n+2):
        print(1, temp+1)
        temp += 1
    temptemp = temp
    temp = 1
    for i in range(n):
        x = 1+n-i
        if vs[n-i] == 1:
            print(temptemp, temptemp+1)
            temp = temptemp
            temptemp += 1
        else:
            print(temp, temptemp+1) 
            temptemp += 1

main(vs)