#include <algorithm>
#include <iostream>
#include <vector>
#include <math.h>
#include <set>
#include <map>
#include <string>
#include <stack>
#include <queue>
#include <iomanip>
#include <numeric>
#include <tuple>
#include <bitset>
#include <complex>
#include <unistd.h>
#include <cassert>
#include <cctype>
#include <random>
#define _USE_MATH_DEFINES
#define _GLIBCXX_DEBUG
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> plglg;
typedef pair<double, ll> pdlg;
typedef tuple<int, int, int> tiii;
typedef tuple<ll, ll, ll> tlglglg;
typedef tuple<double, double, double> tddd;
typedef complex<double> xy_t;
int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};
double pi = 3.141592653589793;
ll mod = 998244353;
int intmax = 2147483647;
int intmin = -2147483648;
ll llmax = 9223372036854775807;
ll llmin = -9223372036854775807;
int iinf = intmax / 8;
ll inf = llmax / 8;
double eps = 1e-11;

ll multiply(ll x, ll y) {
    return (x % mod) * (y % mod) % mod;
}

ll gcd(ll a, ll b) {
    return b != 0 ? gcd(b, a % b) : a;
}

int main() {
    ll N;
    cin >> N;
    ll a[N];
    for (int i = 0; i < N; i++) {
        cin >> a[i];
    }
    sort(a, a + N);
    ll ans = 1;
    for (int i = 0; i < N; i++) {
        ans = multiply(ans, gcd(a[i], i));
    }
    cout << ans << endl;
}
