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problem solution:
code:
#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
#include<cmath>
#include<queue>
#include<map>
#include<stack>
#include<set>
#include<ctime>
#define iss ios::sync_with_stdio(false)
using namespace std;
typedef unsigned long long ull;
typedef long long ll;
typedef pair<int,int>pii;
const int MAXN=1e5+5;
const int mod=998244353;
const int inf=0x3f3f3f;
const int p=73;
struct Complex
{
//a+bi
ll a, b;
Complex(ll _a, ll _b)
{
a = _a; b = _b;
}
};
Complex mul(Complex x, Complex y)
{
ll a = ((x.a*y.a - x.b*y.b)%mod + mod) % mod;
//ll a = ((x.a*y.a - 5*x.b*y.b)%mod + mod) % mod; //a+b\sqrt5_i
ll b = (x.a*y.b + x.b*y.a)%mod;
return Complex(a, b);
}
Complex cpow(Complex x, ll n)
{
Complex ret(1, 0);
while(n)
{
if(n&1) ret = mul(ret, x);
x = mul(x, x);
n >>= 1;
}
return ret;
}
ll mod_pow(ll x,ll n)
{
ll res=1;
while(n>0)
{
if(n&1) res=res*x%mod;
x=x*x%mod;
n>>=1;
}
return res;
}
int main()
{
int n;
cin>>n;
Complex a(1, 1);
Complex b(1,-1);
ll ans1=mod_pow(2,n);
Complex ans2= cpow(a, n);
Complex ans3= cpow(b, n);
ll ans=(ans1+ans2.a+ans3.a)%mod;
ans=ans*mod_pow(4,mod-2)%mod;
cout<<ans<<endl;
}