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 PYTHON):

Solution:
def check_str(s):
    n = len(s) - 1
    if (s[1] != 1) or (s[-1] != 0):
        return False
    else:
        for i in range(1, n / 2):
            if s[i] != s[n - i]:
                return False
    return True

def solve():
    s = [int(_) for _ in raw_input()]
    s.insert(0,0)
    if not check_str(s):
        print '-1'
        return
    sub = []
    for i in range(len(s)):
        if s[i] == 1:
            sub.append(i)
    ## Create tree caterpillar type
    ## body
    body_leng = len(sub) + 1
    for i in range(1, body_leng):
        print str(i) + ' ' + str(i+1)
    ## legs
    cnt = body_leng
    for i in range(1, body_leng - 1):
        num_legs = sub[i] - sub[i-1] - 1
        for j in range(cnt + 1, cnt + num_legs + 1):
            print str(i+1) + ' ' + str(j)
        cnt += num_legs

if __name__ == '__main__':
    solve()