Problem Statement

You are given a sequence of non-negative integers $A = \left( A_1, A_2, \cdots, A_N \right)$ of length $N$.

Determine whether there exists a sequence $B$ satisfying the following conditions, and if one exists, show one example. Here, let $M$ be the length of $B$.

• $1 \leq B_i \leq N$
• $B_i \neq B_j$ whenever $1 \leq i < j \leq M$
• $A_{B_1} \oplus A_{B_2} \oplus \cdots \oplus A_{B_M} = 0$, where for non-negative integers $x,y$, $x \oplus y$ denotes the bitwise XOR of $x$ and $y$.

Input

$N$
$A_1\ \ A_2\ \ \cdots A_N$

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq A_i < 2^{60}$
• All inputs are integers.

Output

If no sequence $B$ satisfying the conditions exists, print -1 followed by a newline.
Otherwise, output in the following format.

$M$
$B_1\ \ B_2\ \ \cdots B_M$

Sample

4
2 0 2 4

2
1 3

1
2

3
2024 20 24

-1