#include<bits/stdc++.h>
using namespace std;

#define int long long

#define rep(i,n) for(int i=0;i<(n);i++)
#define pb push_back
#define all(v) (v).begin(),(v).end()
#define fi first
#define se second
typedef vector<int>vint;
typedef pair<int,int>pint;
typedef vector<pint>vpint;

template<typename A,typename B>inline void chmin(A &a,B b){if(a>b)a=b;}
template<typename A,typename B>inline void chmax(A &a,B b){if(a<b)a=b;}

template<int32_t mod>
struct ModInt{
	int32_t a;
	inline int32_t normalize(int64_t x){
		x%=mod;
		if(x<0)x+=mod;
		return x;
	}
	ModInt(const int64_t a=0):a(normalize(a)){}

	ModInt& operator+=(const ModInt &x){
		a+=x.a;
		if(a>=mod)a-=mod;
		return *this;
	}
	ModInt& operator-=(const ModInt &x){
		a-=x.a;
		if(a<0)a+=mod;
		return *this;
	}
	ModInt& operator*=(const ModInt &x){
		a=(int64_t)a*x.a%mod;
		return *this;
	}
	ModInt& operator/=(const ModInt &x){
		*this*=x.inv();
		return *this;
	}

	ModInt operator+(const ModInt x){return ModInt(*this)+=x;}
	ModInt operator-(const ModInt x){return ModInt(*this)-=x;}
	ModInt operator*(const ModInt x){return ModInt(*this)*=x;}
	ModInt operator/(const ModInt x){return ModInt(*this)/=x;}
	bool operator==(const ModInt x){return a==x.a;}
	bool operator!=(const ModInt x){return a!=x.a;}

	ModInt operator-(){return ModInt(0)-ModInt(*this);}
	ModInt pow(int64_t ex)const{
		int64_t x=a;
		int64_t res=1;
		while(ex){
			if(ex&1)res=res*x%mod;
			x=x*x%mod;
			ex>>=1;
		}
		return ModInt(res);
	}
	ModInt inv()const{return pow(mod-2);}
};

template<int32_t mod>
istream& operator>>(istream& in,ModInt<mod>& a){
	return (in>>a.a);
}
template<int32_t mod>
ostream& operator<<(ostream& out,const ModInt<mod>& a){
	return (out<<a.a);
}
using mint=ModInt<998244353>;

int gcd(int a,int b){
	return b?gcd(b,a%b):a;
}

int N;
int A[111111];

signed main(){
	cin>>N;
	rep(i,N)cin>>A[i];
	sort(A,A+N);

	mint ans=1;
	for(int i=0;i<N;i++)ans*=gcd(A[i],i);
	cout<<ans<<endl;
	return 0;
}