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:
def main():
    s=input()
    n=len(s)
    if s[n-1]=="1" or s[0]=="0":
        print(-1)
        return 0
    for i in range(n//2):
        if s[i]!=s[n-i-2]:
            print(-1)
            return 0
    t=[]
    now=1
    for i in range(n//2-1):
        t.append([now,i+2])
        if s[i]=="1":
            now=i+2
    t2=[[i+n//2,j+n//2] for i,j in t]
    if s[n//2-1]=="1":
        t.append([now,now+n//2])
    else:
        for i in range(len(t2)):
            if t2[i][0]==now+n//2:
                t2[i][0]=now
            if t2[i][1]==now+n//2:
                t2[i][1]=now
        t.append([now,now+n//2])
    if n%2==1:
        t.append([now,n])
    t+=t2
    for i,j in t:
        print(i,j)
main()