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;
random_device rng;
mt19937 rd(rng());
unordered_map<int, int> mp;
vector<long long> v;
const int mod = 998244353;
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    int tmp;
    cin >> tmp;
    mp[tmp]++;
  }
  for (auto p : mp) v.push_back(p.second);
  sort(v.begin(), v.end());
  if (v.size() == 1) return cout << 1 << '\n', 0;
  long long ans = 0;
  if (v[v.size() - 1] > v[v.size() - 2]) ans++;
  for (int i = 0; i < v.size(); ++i)
    ans += v[i] * (v.size() - i - 1), ans %= mod;
  cout << ans << '\n';
}
