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:
#!/usr/bin/env python3
def f(s):
    n = len(s)
    if s[-1] == '1' or s[-2] == '0' or s[0] == '0':
        print(-1)
        return
    i,j = 0,n-2
    while i < j:
        if s[i] != s[j]:
            print(-1)
            return
        i+=1
        j-=1
    e = []
    k = 0
    for i, c in enumerate(s):
        if c == '1':
            if i == 0:
                k = 0
                continue
            for j in range(k+1): e.append((i-k+j, i+1))
            k = 0
        else: k += 1
    e.append((n-k, n))
    for u,v in e: print(u,v)
f(input())