Problem Statement

How many sets $S$ consisting of non-negative integers between $0$ and $2^N-1$ (inclusive) satisfy the following condition? Print the count modulo $998244353$.

• Every non-empty subset $T$ of $S$ satisfies at least one of the following:
• The number of elements in $T$ is odd.
  • The $\mathrm{XOR}$ of the elements in $T$ is not zero.

What is $\mathrm{XOR}$? The bitwise $\mathrm{XOR}$ of non-negative integers $A$ and $B$, $A \oplus B$, is defined as follows: When $A \oplus B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if exactly one of the digits in that place of $A$ and $B$ is $1$, and $0$ otherwise. For example, we have $3 \oplus 5 = 6$ (in base two: $011 \oplus 101 = 110$). Generally, the bitwise $\mathrm{XOR}$ of $k$ non-negative integers $p_1, p_2, p_3, \dots, p_k$ is defined as $(\dots ((p_1 \oplus p_2) \oplus p_3) \oplus \dots \oplus p_k)$. We can prove that this value does not depend on the order of $p_1, p_2, p_3, \dots, p_k$.

Constraints

• $1 \le N \le 2 \times 10^5$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.