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>
using namespace std;

int main()
{
  int n;
  int node_nums[1000100] = {0};

  cin >> n;
  int value;
  int max_depth = 0;
  for (int i = 0; i < n; ++i)
  {
    cin >> value;
    if (i == 0 && value != 0)
    {
      cout << 0 << endl;
      return 0;
    }
    node_nums[value]++;
    if (value > max_depth)
    {
      max_depth = value;
    }
  }

  int result = 1;
  for (int i = 1; i <= max_depth; ++i)
  {
    for (int j = 0; j < node_nums[i]; ++j)
    {
      result *= node_nums[i - 1];
      result %= 998244353;
    }
  }
  cout << result << endl;
  return 0;
}