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=[int(c) for c in input()]
N=len(S)
r=all([S[i]==S[N-i-2] for i in range(N//2)]) and S[0] and not S[-1]
t=[(1,2)]
e=2
for i in range(1,(N-1)//2):
    t.append((e,i+2))
    if S[i]:
        e=i+2
f=1
if N%2==0:
    t.append((e,N-e+1))
    if S[N//2-1]:
        f=0
for i in range(0,(N-1)//2):
    t.append([e if t[i][j]==e and f else (N-e+1 if t[i][j]==N-t[i][j]+1 and f else N-t[i][j]+1) for j in range(2)])
if r:
    print(*[str(l[0])+" "+str(l[1]) for l in t],sep='\n')
else:
    print(-1)