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 = [int(a) for a in list(input())]
L = len(S)

ok = True
if S[L-1] == 1 or S[0] == 0 or S[L-2] == 0:
    ok = False
for i in range(L-1):
    if S[i] != S[L-2-i]:
        ok = False

if not ok:
    print(-1)
else:
    graph = []
    p = 1
    go = True
    for i in range(1, L):
        if i <= L//2:
            graph.append((p, i+1))
            if go:
                p = i+1
            if S[i] == 1:            
                go = True
            else:
                go = False
        else:
            graph.append((p, i+1))
    
    for a, b in graph:
        print(a, b)