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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
using namespace std;

typedef long long ll;
#define MOD 998244353

int main() {
  ll n;
  cin >> n;
  vector<ll> d(n);
  vector<ll> c(n, 0);
  ll maxd = -1;
  for (int i = 0; i < n; i++) {
    cin >> d[i];
    c[d[i]]++;
    if (maxd < d[i]) {
      maxd = d[i];
    }
  }
  ll ans = 1;
  if (c[0] != 1) {
    cout << 0 << endl;
    return 0;
  }
  for (int i = 1; i <= maxd; i++) {
    if (c[i] == 0) {
      ans = 0;
    }
    for (int j = 0; j < c[i]; j++) {
      ans *= c[i - 1];
      ans %= MOD;
    }
  }
  cout << ans%MOD << endl;
  return 0;
}