#include <bits/stdc++.h>

using namespace std; const int maxn = 1e2 + 5, mod = 998244353, maxm = 4e3 + 5; typedef long long ll;

int n, a[maxn];

map<int, int> mp;

inline void add(int x)
{
	for (int i = 2; i * i <= x; i++) if (x % i == 0) while (x % i == 0) mp[i]++, x /= i;
	if (x != 1) mp[x]++;
}

inline int get(int x, int y) { int res = 0; while (x % y == 0) res++, x /= y; return res; }

int F[maxm * 2], U, G[maxm * 2], H[32][maxm * 2];


int main()
{
	scanf("%d", &n);
	for (int i = 1; i <= n; i++) scanf("%d", a + i), add(a[i]);
	for (int i = 1; i <= 32; i++) for (int l = 0; l <= i; l++) for (int r = l; r <= i; r++) H[i][l - (r - l) + maxm]++;
	int A = 1, B = 1;
	for (auto it = mp.begin(); it != mp.end(); it++)
	{
		int p = it->first;
		U = 0, F[maxm] = 1;
		for (int i = 1; i <= n; i++)
		{
			int g = get(a[i], p);
			if (!g) continue;
			A = (ll)A * (g + 1) * (g + 2) / 2 % mod;
			for (int y = -(U + g); y <= U + g; y++) G[y + maxm] = 0;
			for (int x = -g; x <= g; x++) for (int y = -U; y <= U; y++) G[x + y + maxm] = (G[x + y + maxm] + (ll)F[y + maxm] * H[g][x + maxm]) % mod;
			U += g; for (int y = -U; y <= U; y++) F[y + maxm] = G[y + maxm];
		}
		B = (ll)B * F[maxm] % mod;
	}
//	cerr << A << ' ' << B << endl;
	return 0 * printf("%lld\n", (ll)(mod - mod / 2) * (A + B) % mod);
}