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)
if s[-1]=="1":
    print(-1)
    exit()

if s[0]=="0":
    print(-1)
    exit()

data=[]
for i in range(0,n-1):
    if s[i]=="1":
        data.append(i+1)
        if s[n-2-i]=="0":
            print(-1)
            exit()
m=len(data)
edge=[]
for i in range(1,m):
    edge.append((i,i+1))
index=m+1
for i in range(1,m):
    if i!=1:
        size=data[-i]
        nextsize=data[-i-1]
        E=size-1-nextsize
        count=0
        while E>count:
            edge.append((i,index))
            index+=1
            count+=1
    else:
        size=n
        nextsize=data[-2]
        E=size-1-nextsize
        count=0
        while E>count:
            edge.append((i,index))
            index+=1
            count+=1

for i in range(n-1):
    u,v=edge[i]
    print(u,v)