Problem:
Score : 300 points

Problem Statement

Given is an integer sequence D_1,...,D_N of N elements. Find the number, modulo 998244353, of trees with N vertices numbered 1 to N that satisfy the following condition:

For every integer i from 1 to N, the distance between Vertex 1 and Vertex i is D_i.

Notes

A tree of N vertices is a connected undirected graph with N vertices and N-1 edges, and the distance between two vertices are the number of edges in the shortest path between them.

Two trees are considered different if and only if there are two vertices x and y such that there is an edge between x and y in one of those trees and not in the other.

Constraints

1 \leq N \leq 10^5

0 \leq D_i \leq N-1

Input

Input is given from Standard Input in the following format:

N
D_1 D_2 ... D_N

Output

Print the answer.

Sample Input 1

4
0 1 1 2

Sample Output 1

2

For example, a tree with edges (1,2), (1,3), and (2,4) satisfies the condition.

Sample Input 2

4
1 1 1 1

Sample Output 2

0

Sample Input 3

7
0 3 2 1 2 2 1

Sample Output 3

24

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

int main() {
  int N;
  cin >> N;
  vector<int> D(N), cnt(N);
  for (int i = 0, d; cin >> d; i++) {
    D.at(i) = d;
    cnt.at(d)++;
  }
  if (D.at(0) || !cnt.at(0)) return cout << 0 << "\n", 0;
  long ans = 1;
  int mx = *max_element(D.begin(), D.end());
  for (long i = 1; i <= mx; i++) {
    long tmp = cnt.at(i);
    while (tmp--) {
      ans *= cnt.at(i - 1);
      ans %= 998244353;
    }
  }
  cout << ans << "\n";
}