You are given an integer x represented as a product of n its prime divisors p_1 ⋅ p_2, ⋅ … ⋅ p_n. Let S be the set of all positive integer divisors of x (including 1 and x itself).

We call a set of integers D good if (and only if) there is no pair a ∈ D, b ∈ D such that a ≠ b and a divides b.

Find a good subset of S with maximum possible size. Since the answer can be large, print the size of the subset modulo 998244353.

Input

The first line contains the single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of prime divisors in representation of x.

The second line contains n integers p_1, p_2, ..., p_n (2 ≤ p_i ≤ 3 ⋅ 10^6) — the prime factorization of x.

Output

Print the maximum possible size of a good subset modulo 998244353.

Examples

Input


3
2999999 43 2999957


Output


3


Input


6
2 3 2 3 2 2


Output


3

Note

In the first sample, x = 2999999 ⋅ 43 ⋅ 2999957 and one of the maximum good subsets is \{ 43, 2999957, 2999999 \}.

In the second sample, x = 2 ⋅ 3 ⋅ 2 ⋅ 3 ⋅ 2 ⋅ 2 = 144 and one of the maximum good subsets is \{ 9, 12, 16 \}.
#include <bits/stdc++.h>
using namespace std;
const int N = 200005, MOD = 998244353;
int n, p, ret = N;
long long ans = 1, inv[N];
map<int, int> ma;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> p;
    ma[p]++;
  }
  int ret = N, sz = ma.size() - 1;
  for (auto &v : ma) {
    ret = min(ret, v.second);
  }
  inv[1] = 1;
  for (int i = 2; i < N; i++) {
    inv[i] = MOD - MOD / i * inv[MOD % i] % MOD;
    if (i <= sz) {
      (ans *= inv[i]) %= MOD;
    }
    if (i <= ret) {
      (ans *= inv[i]) %= MOD;
    }
  }
  for (int i = 2; i <= ret + sz; i++) {
    (ans *= i) %= MOD;
  }
  cout << ans;
}
