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)

flag=True
if s[N-1]=='1':
        flag=False
if s[0]=='0' or s[N-2]=='0':
        flag=False


for i in range(N//2):
        if s[i]!=s[N-i-2]:
                flag=False
                break

if flag:
        ans = []
        prev = 0
        for i in range(N//2):
                if s[i]=='1':
                        for j in range(prev,i):
                                ans.append([i+1,j+1])
                        prev = i
        
        for i in range(prev,N-1):
                ans.append([N,i+1])
        
        for a in ans:
                print(*a)
else:
        print(-1)