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 no():
    print(-1)
    exit()


s = input()
n = len(s)

if s[-1] == "1":
    no()

s = s[:-1]

if s != s[::-1]:
    no()

if s[0] == "0":
    no()

li = [0]
adj = [[] for _ in range(n + 1)]
for v, e in enumerate(s, 1):
    if e == "1":
        for u in li:
            adj[u].append(v)
        li = []

    li.append(v)

adj[n-1].append(n)

for u, vs in enumerate(adj[1:], 1):
    for v in vs:
        print(u, v)