//#pragma GCC optimize("Ofast")
//#pragma GCC optimize ("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//THESE ARE LAST DITCH EFFORTS!!!

#include <bits/stdc++.h>

using namespace std;

const int mod = 998244353;

typedef long long ll;

ll addmod(ll a, ll b, ll m){
    if(a >= m - b) return a + b - m;
    return a + b;
}

ll mulmod(ll a, ll b, ll m){
    ll ans = 0;
    while(b){
        if(b & 1) ans = addmod(ans, a, m);
        a = addmod(a, a, m);
        b >>= 1;
    }
    return ans;
}

ll fexp(ll a, ll b, ll n){
    ll r = 1;
    while(b){
        if(b & 1) r = mulmod(r, a, n);
        a = mulmod(a, a, n);
        b >>= 1;
    }
    return r;
}

bool miller(ll a, ll n){
    if (a >= n) return true;
    ll s = 0, d = n - 1;
    while(d % 2 == 0 && d) d >>= 1, s++;
    ll x = fexp(a, d, n);
    if (x == 1 || x == n - 1) return true;
    for (int r = 0; r < s; r++, x = mulmod(x,x,n)){
        if (x == 1) return false;
        if (x == n - 1) return true;
    }
    return 0;
}

bool isprime(ll n){
    if(n == 1) return false;
    int base[] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37};
    for (int i = 0; i < 12; ++i) if (!miller(base[i], n)) return false;
    return true;
}

ll pollard(ll n){
    ll x, y, d, c = 1;
    if (n % 2 == 0) return 2;
    while(true){
        y = x = 2;
        while(true){
            x = addmod(mulmod(x,x,n), c, n);
            y = addmod(mulmod(y,y,n), c, n);
            y = addmod(mulmod(y,y,n), c, n);
            d = __gcd(abs(x-y), n);
            if (d == n) break;
            else if (d > 1) return d;
        }
        c++;
    }
}

void factor(ll n, vector<ll>& v){
    if (n == 1 || isprime(n)) return v.push_back(n);
    ll f = pollard(n);
    factor(f, v), factor(n/f, v);
    sort(v.begin(), v.end());
}

int main() {
    ios_base::sync_with_stdio(false);
    //cin.tie(nullptr);
    map<long long, long long> cnt;
    int n;
    cin >> n;
    while(n--) {
        long long x;
        cin >> x;
        vector<long long> f;
        factor(x, f);
        for(auto e : f) {
            cnt[e]++;
        }
    }
    long long ans = 1;
    for(auto e : cnt) {
        ans = (ans * (e.second + 1)) % mod;
    }
    cout << ans << "\n";
    return 0;
}