Problem Statement

You are given an integer sequence $A$ of length $N$. Perform the following operations in order to create a sequence $B$ of length $N$. ($\mathrm{XOR}$ denotes the bitwise exclusive OR.)

• Choose one non-negative integer $X$.
• For $i=1,2, \dots,N$, let $B_i=A_i \ \mathrm{XOR} \ X $.
• Sort $B$ in ascending order.
• For $i=1,2, \dots,N$, replace $B_i$ with $B_i \ \mathrm{XOR} \ X $.

How many sequences are possible as the final $B$? Find the answer modulo $998244353$. Here, two sequences $B$ and $B'$ of length $N$ are considered different if there exists an integer $i$ ($1 \le i \le N$) such that $B_i \neq B'_i$.

Input

$N$
$A_1$ $A_2$ $\dots$ $A_N$

Output

Print the number of sequences possible as the final $B$, modulo $998244353$.

Sample

3
0 0 1

2

3
1 0 2

4