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()
n = len(s)
flg = 1
lis = []
if s[-1] == '1':
    print('-1')
    flg = 0
else:
    for i in range(n//2):
        if s[i] == s[n-2-i]:
            lis.append(int(s[i]))
        else:
            print('-1')
            flg = 0
            break
if flg ==1:
    if lis[0] == 0:
        print('-1')
    else:
        posl = []
        for i in range(1,len(lis)):
            pos = i+1
            if lis[i]==1:
                posl.append(pos)
        old = 1
        for pos in posl:
            for i in range(old,pos):
                print('{} {}'.format(i,pos))
            old=pos
        print(('{} {}'.format(old,old+1)))
        for i in range(old+2,n+1):
            print(('{} {}'.format(old+1,i)))