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[0]=="0" or s[-1]=="1":
    print(-1)
    exit()
Ans = []
q = [0]
for i in range(1, N//2):
    c, cr = s[i], s[-2-i]
    if c!=cr:
        print(-1)
        exit()
    else:
        if c=="1":
            for u in q:
                Ans.append([u, i])
            q = [i]
        else:
            q.append(i)
i = N//2
if N%2==1:
    for u in q:
        Ans.append([u, i])
    for ans in Ans:
        print(ans[0]+1, ans[1]+1)
        print(N-ans[0], N-ans[1])
else:
    if len(q)==1:
        print(i, i+1)
        for ans in Ans:
            print(ans[0] + 1, ans[1] + 1)
            print(N - ans[0], N - ans[1])
    else:
        v = q.pop()
        for u in q:
            print(v+1, u+1)
            print(v+1, N-u)
        print(i, i+1)
        for ans in Ans:
            print(ans[0] + 1, ans[1] + 1)
            print(N - ans[0], N - ans[1])