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:
# coding: utf-8
# Your code here!

ss=input()
ans=0

if ss[-1]=="1":
    ans=-1
s=ss[:-1]
#print(s)
gans=[]

c=1
for i in range(len(s)):
    if i==0 and s[i]=="0":
        ans=-1
        break
    if s[i] != s[len(s)-i-1]:
        ans=-1
        break
    
    if s[i]=="1":
        gans.append([c, i+2])
        c=i+2
    else:
        gans.append([i+2,c])


if ans==-1:
    print(ans)
else:
    for i in gans:
        print(*i)