#include <bits/stdc++.h>

using namespace std;

#define rep(i, s, e) for (int i = s; i <= e; ++i)
#define drep(i, s, e) for (int i = s; i >= e; --i)
#define file(a) freopen(#a".in", "r", stdin), freopen(#a".out", "w", stdout)
#define pv(a) cout << #a << " = " << a << endl
#define pa(a, l, r) cout << #a " : "; rep(_, l, r) cout << a[_] << ' '; cout << endl

const int P = 998244353;

const int N = 1e2 + 10;
const int M = 30;

int read() {
  int x = 0, f = 1; char c = getchar();
  for (; c < '0' || c > '9'; c = getchar()) if (c == '-') f = -1;
  for (; c >= '0' && c <= '9'; c = getchar()) x = x * 10 + c - 48;
  return x * f;
}

int inc(int a, int b) { return (a += b) >= P ? a - P : a; }
int dec(int a, int b) { return (a -= b) < 0 ? a + P : a; }
int mul(int a, int b) { return 1ll * a * b % P; }
void add(int &a, int b) { (a += b) >= P ? a -= P : 1; }
void sub(int &a, int b) { (a -= b) < 0 ? a += P : 1; }
int qpow(int a, int b) { int res = 1; for (; b; b >>= 1, a = mul(a, a)) if (b & 1) res = mul(res, a); return res; }

int n, a[N], c[N], ans = 1, same = 1;

struct node {
  int dat[2 * N * M];
  int& operator [] (int i) { return dat[i + N * M]; }
} f[N];

void work(int d) {
  rep(i, 1, n) {
    c[i] = 0;
    while (!(a[i] % d)) ++ c[i], a[i] /= d;
    ans = mul(ans, (c[i] + 1) * (c[i] + 2) / 2);
  }
  int lim = *max_element(c + 1, c + n + 1);
  f[0][0] = 1;
  rep(i, 1, n) rep(j, -i * lim, i * lim) f[i][j] = 0;
  rep(i, 1, n) rep(j, -i * lim, i * lim) rep(d, -c[i], c[i]) {
    add(f[i][j + d], mul(f[i - 1][j], (c[i] - abs(j)) / 2 + 1));
  }
  same = mul(same, f[n][0]);
}

int main() {
  n = read();
  rep(i, 1, n) a[i] = read();
  rep(i, 1, n) {
    for (int d = 2; d * d <= a[i]; ++ d) {
      if (!(a[i] % d)) work(d);
    }
    if (a[i] > 1) work(a[i]);
  }
  ans = mul(inc(ans, same), (P + 1) / 2);
  printf("%d\n", ans);
  return 0;
}