Khada_Jhin is learning theoretical computer science.

Today, Jwong asked Khada_Jhin a question: for a string of length n consisting of 0 and 1, how many fundamentally different arrangements of grey code are there?

A permutation of length n is an array p = p_0p1p2...p_n - 1 consisting of n distinct integers from 0 to n - 1 in any order. A circular permutation is treated as a special permutation whose p₀ is always 0.

An arrangement of grey code is a circular permutation p = p_0p1p2...p_2ⁿ - 1, such that all p_i and p_i + 1 are just one digit different in binary. In particular, p_2ⁿ - 1 and p₀ also need to satisfy just one digit difference in binary.

But this question is so hard for Khada_Jhin, so Jwong simplifies the problem, now Khada_Jhin must compute for a string of length n consisting of 0, 1, how many fundamentally different arrangements of grey-like code?

We also define an arrangement of grey-like code as a circular permutation p = p_0p1p2...p_2ⁿ - 1, such that for all p_i and p_i + 1, the last n-1 bit of p_i must be the same as the first n-1 bit of p_i + 1 in binary.In particular, p_2ⁿ - 1 and p₀ also need to satisfy the last n-1 bit of p_2ⁿ - 1 must be the same as the first n-1 bit of p₀ in binary.

For example, when n = 2, the answer is equal to 1. Just one legal answer is 00, 01, 11, 10 in binary.

Now it becomes an easy question for Khada_Jhin, but he wants to check if he made a mistake, so please tell him what the answer is modulo 998244353.