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()

D = {}
for i in range(N - 1):
    D[i + 1] = S[i]
for i in range(1, N):
    if D[i] != D[N - i]:
        print(-1)
        exit()

# 構築
T = [[] for i in range(N)]

next = 1
mark = 0
for i in range(N):
    child = mark + 1
    if S[i] == "0":
        next += 1
    else:
        for n in range(next):
            T[mark].append(child)
            child += 1
        next = 1
        mark = child - 1

for i in range(N):
    for t in T[i]:
        print(i + 1, t + 1)