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 $p_1, p_2, p_3, \dots, p_k$.
  

Input

Input is given from Standard Input in the following format:
N

Output

Print the answer.

Constraints

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

Sample Input 1

2

Sample Output 1

15

Sets such as $\lbrace 0,2,3 \rbrace, \lbrace 1 \rbrace$, and $\lbrace \rbrace$ satisfy the condition.
On the other hand, $\lbrace 0,1,2,3 \rbrace$ does not.
This is because the subset $\lbrace 0,1,2,3 \rbrace$ of $\lbrace 0,1,2,3 \rbrace$ has an even number of elements, whose bitwise $\mathrm{XOR}$ is 0.

Sample Input 2

146

Sample Output 2

743874490

见题面 Input 部分

见题面 Output 部分