#include <bits/stdc++.h>
#define pii pair<int, int>
#define MP make_pair
#define fi first
#define se second
using namespace std;
mt19937 rnd(time(0));
const int mod = 998244353, base = 3000;
int n, a[105], pri[10005];
vector<pii> vec[105];
map<int, int> mp;
int f[105][6005], g[100];
int tot, ans1 = 1, ans2 = 1;
int qmod(int x)
{
	if (x >= mod) x -= mod;
	return x; 
}
int ksm(int a, int b = mod - 2)
{
	int ret = 1;
	for (; b; b >>= 1, a = 1ll * a * a % mod) if (b & 1) ret = 1ll * ret * a % mod;
	return ret;
}
int calc(int x)
{
	return 1ll * x * (x + 1) / 2 % mod;
}
int main()
{
	cin >> n;
//	n = 100;
	for (int i = 1; i <= n; i++)
	{
		cin >> a[i];
//		a[i] = rnd() % 100 + 1;
//		cout << a[i] << " ";
		int tmp = a[i];
		for (int j = 2; j * j <= tmp; j++)
		{
			if (tmp % j == 0)
			{
				int now = 0;
				while (tmp % j == 0) tmp /= j, now++;
				if (mp.find(j) == mp.end()) mp[j] = ++tot, pri[tot] = j;
				vec[i].push_back(MP(mp[j], now));
			}
		}
		if (tmp > 1)
		{
			if (mp.find(tmp) == mp.end()) mp[tmp] = ++tot, pri[tot] = tmp;
			vec[i].push_back(MP(mp[tmp], 1));
		}
		for (auto x : vec[i]) ans1 = 1ll * ans1 * calc(x.se + 1) % mod;
	}
	for (int i = 1; i <= tot; i++)
	{
		memset(f, 0, sizeof(f));
		f[0][base] = 1;
		int lst = 0;
		for (int j = 1; j <= n; j++)
		{
			int tmp = a[j], c = 0;
			while (tmp % pri[i] == 0) c++, tmp /= pri[i];
			if (c == 0) continue;
			for (int k = 0; k <= 60; k++) g[k] = 0;
			for (int k = 0; k <= c; k++)
			{
				for (int l = 0; l <= k; l++)
				{
					g[k - l - l + 30]++;
				}
			}
			for (int k = -3000; k <= 3000; k++) if (f[lst][k + base])
			{
				for (int l = -30; l <= 30; l++) if (g[l + 30])
				{
					f[j][k + base + l] = qmod(f[j][k + base + l] + 1ll * f[lst][k + base] * g[l + 30] % mod);
				}
			}
			lst = j;
		}
		ans2 = 1ll * ans2 * f[lst][base] % mod;
	}
	printf("%d\n", 1ll * qmod(ans1 + ans2) * ksm(2) % mod);
	return 0;
}