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()
if S[-2]=="0":
    print(-1)
    exit()
for i in range(N-1):
    if S[i]!=S[N-2-i]:
        print(-1)
        exit()
ans=[]
nowzero=0
for i in range(N):
    if S[i]=="0":
        break
    nowzero+=1
if nowzero==N-1:
    for i in range(1,N):
        print(i,i+1)
    exit()
ans.append((1,2))
for i in range(N-2):
    if S[i]=="1":
        if i!=N-2 and S[i+1]=="0":
            nowzero=i+2
        ans.append((i+2,i+3))
    else:
        ans.append((nowzero,i+3))
for line in ans:
    print(line[0],line[1])