You have been given an array $$A$$ of size $$N$$. Now, let's call the weight of a subsequence the xor of all elements it contains.The weight of a subsequence containing $$0$$ elements is $$0$$. Now, you need to find the summation of xor of each subsequence $$ \times $$ the length of the subsequence over all $$2^N$$ subsequences of the given array $$A$$.

As the answer can be rather large, print it Modulo $$ 998244353 $$

Can you do it ?

Input Format :

The first line contains a single integer $$N$$ denoting the size of the given array $$A$$. The next line contains $$N$$ integers, where the $$i^{th}$$ integer denotes $$A[i]$$.

Output Format:

Print a single integer denoting the answer. As the answer can be rather large, print it Modulo $$ 998244353 $$

Input Constraints :

$$ 1 \le N \le 5 \cdot 10^5 $$

$$ 0 \le A[i] \le 10^{18} $$

Note that the Expected Output Feature for Custom Invocation is not supported for this contest.