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:
import sys

readline = sys.stdin.readline
MOD = 10 ** 9 + 7
INF = float('INF')
sys.setrecursionlimit(10 ** 5)


def main():
    S = "*" + input()
    N = len(S) - 1

    if S[N] == "1":
        return print(-1)
    if S[1] == "0":
        return print(-1)

    edge = []
    cur_u = 1
    cur_v = 2

    for i in range(1, N // 2 + 1):
        if S[i] != S[N - i]:
            return print(-1)

        edge.append([cur_u, cur_v])
        if S[i] == "1":
            cur_u = cur_v
        cur_v += 1

    for i in range(cur_v, N + 1):
        edge.append([cur_u, i])

    for i in range(N - 1):
        print(*edge[i])


if __name__ == '__main__':
    main()