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 = '0'
s += input()


def isPara(string, l, r):
    while l <= r:
        if s[l] != s[r]:
            return False
        l += 1
        r -= 1
    return True


def solve():
    N = len(s)-1
    if s[N] == '1' or s[1] == '0':
        print(-1)
        return
    if isPara(s, 1, N-1) == False:
        print(-1)
        return
    root = 1
    for i in range(2, N+1):
        print(str(root) + ' ' + str(i))
        if s[i-1] == '1':
            root = i


solve()