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
input = sys.stdin.readline

S = '-' + input().rstrip()
N = len(S) - 1

def solve(S):
    if S[1] == '0':
        return None
    if S[N] == '1':
        return None
    prev = 1
    graph = []
    for n in range(1,N//2 + 1):
        if S[n] != S[N-n]:
            return None
        if S[n] == '0':
            continue
        for i in range(prev,n):
            graph.append('{} {}'.format(i,n))
        prev = n
    for i in range(prev,N):
        graph.append('{} {}'.format(i,N))
    return graph

graph = solve(S)

if graph is None:
    print(-1)
else:
    print('\n'.join(graph))