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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
class Program
{
	static void Main(string[] args)
	{
		// 整数の入力
		int n = int.Parse(Console.ReadLine());
      	string[] input = Console.ReadLine().Split(' ');
      	int[] counter = new int[n+1];
		for (int i = 0; i < n; i++) {
        	int num = int.Parse(input[i]);
          	counter[num]++;
        }
      	int res = counter[2] == 0 ? 0 : 1;
      	for (int i = 2; i <= n; i++) {
          	if (counter[i] == 0) break;
        	res *= counter[i-1] * (int)(System.Math.Pow(2, (double)(counter[i] - 1)));
        }
      	Console.WriteLine(res % 998244353);
      	
    }
}