Problem:
Score : 800 points

Problem Statement

Given is a positive even number N.

Find the number of strings s of length N consisting of A, B, and C that satisfy the following condition:

s can be converted to the empty string by repeating the following operation:

Choose two consecutive characters in s and erase them. However, choosing AB or BA is not allowed.

For example, ABBC satisfies the condition for N=4, because we can convert it as follows: ABBC → (erase BB) → AC → (erase AC) → (empty).

The answer can be enormous, so compute the count modulo 998244353.

Constraints

2 \leq N \leq 10^7

N is an even number.

Input

Input is given from Standard Input in the following format:

N

Output

Print the number of strings that satisfy the conditions, modulo 998244353.

Sample Input 1

2

Sample Output 1

7

Except AB and BA, all possible strings satisfy the conditions.

Sample Input 2

10

Sample Output 2

50007

Sample Input 3

1000000

Sample Output 3

210055358

Solution in JavaScript (node.js v5.12) (judge verdict: Accepted)

"use strict";
var GET=(function(){function f(s){return new g(s);}function g(s){this._s=s.trim().split("\n");this._y=0;}g.prototype.a=function(f){var s=this._s, y=this._y, r;if(typeof s[y]==="string")s[y]=s[y].split(" ").reverse();r=s[y].pop();if(!s[y].length)this._y++;return f?r:+r;};g.prototype.l=function(f){var s=this._s[this._y++].split(" ");return f?s:s.map(a=>+a);};g.prototype.m=function(n,f){var r=this._s.slice(this._y,this._y+=n).map(a=>a.split(" "));return f?r:r.map(a=>a.map(a=>+a));};g.prototype.r=function(n,f){var r=this._s.slice(this._y,this._y+=n);return f?r:r.map(a=>+a);};return f;})();
var o=GET(require("fs").readFileSync("/dev/stdin","utf8"));
function xArray(v){var a=arguments,l=a.length,r="Array(a["+--l+"]).fill(0).map(x=>{return "+v+";})";while(--l)r="Array(a["+l+"]).fill(0).map(x=>"+r+")";return eval(r);}

var mod = 998244353;
function mul(a,b){return ((a>>16)*b%mod*65536+(a&65535)*b)%mod;}
function pow(a,n){for(var r=1;n;a=mul(a,a),n>>=1)if(n&1)r=mul(a,r);return r;}

console.log(main());
function main(){
  var n = o.a();
  var ans = pow(3,n);
  var fac = 2, m = n/2;
  var inv = [];
  inv.length = m+2;
  inv[0] = inv[1] = 1;
  for(var i = 0; i < m;){
    ans -= fac;
    fac = mul(mul(fac,(n-i)*2),inv[++i]);
    inv[i+1] = mod-mul(inv[mod%(i+1)|0],(mod/(i+1)|0));
  }
  ans%=mod;
  return ans<0?ans+mod:ans;
}