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

typedef long long ll;
const int MAXN = 3001;
int prime[MAXN], flag[MAXN], d[MAXN], tot, mp[MAXN], inv[MAXN];
vector<int> p[MAXN];
int m;
const int mod = 998244353;

ll qpow(ll a, ll b)
{
    ll res = 1;
    while (b)
    {
        if (b & 1)
            res = res * a % mod;
        a = a * a % mod;
        b >>= 1;
    }
    return res;
}

void init()
{
    int n = 3000;
    d[1] = 1;
    for (int i = 2; i <= n; ++i)
    {
        if (!flag[i])
        {
            prime[++tot] = i;
            mp[i] = tot;
            d[i] = i;
        }
        for (int j = 1; j <= tot && prime[j] * i <= n; ++j)
        {
            flag[prime[j] * i] = 1;
            d[prime[j] * i] = prime[j];
            if (i % prime[j] == 0)
                break;
        }
    }

    for (int i = 1; i <= n; ++i)
        inv[i] = qpow(i, mod - 2);

    for (int i = 1; i <= tot; ++i)
        if (prime[i] <= 53)
            ++m;
}

void solve()
{
    int n;
    cin >> n;
    int S = 1 << m;
    vector<int> a(n + 1);
    for (int i = 1; i <= n; ++i)
    {
        cin >> a[i];
        int x = a[i], pg = 1;
        while (x != 1)
        {
            if (d[x] > prime[m - 1])
                pg = max(pg, d[x]);
            x /= d[x];
        }
        p[pg].push_back(a[i] / pg);
    }

    // O(n * 2 ^ m)
    int ans = 0;
    int k = 3000;
    vector<int> dp(S << 1);
    dp[0] = 1;
    for (int u = 1; u <= k; ++u)
    {
        if (p[u].empty())
            continue;
        for (int x : p[u])
        {
            int j = 0, y = x;
            while (y != 1)
            {
                j |= 1 << (mp[d[y]] - 1);
                y /= d[y];
            }

            if (u != 1)
                for (int i = S * 2 - 1; i >= 0; --i)
                {
                    if (i >> m & 1)
                        dp[i | j] = (dp[i | j] + 1ll * dp[i] * x * (u - 1) % mod) % mod;
                    else
                        dp[i | j | 1 << m] = (dp[i | j | 1 << m] + 1ll * dp[i] * x * u % mod) % mod;
                }
            else
                for (int i = S - 1; i >= 0; --i)
                    dp[i | j] = (dp[i | j] + 1ll * dp[i] * x) % mod;
        }
        for (int i = 0; i < S; ++i)
            dp[i] = (dp[i] + dp[i | 1 << m]) % mod, dp[i | 1 << m] = 0;
    }

    for (int i = 0; i < S; ++i)
    {
        dp[i] = dp[i];
        for (int j = 0; j < m; ++j)
            if (i >> j & 1)
                dp[i] = 1ll * dp[i] * inv[prime[j + 1]] % mod * (prime[j + 1] - 1) % mod;
        ans = (ans + dp[i]) % mod;
    }
    cout << ans << '\n';
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0), cout.tie(0);

    init();
    int t = 1;
    // cin >> t;
    while (t--)
    {
        solve();
    }
    return 0;
}