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;
using System.IO;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Threading.Tasks;
using System.Text.RegularExpressions;
using Debug = System.Diagnostics.Debug;
using System.Runtime.CompilerServices;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;

class Program
{
    static void Main(string[] args)
    {
        ulong N = ulong.Parse(Console.ReadLine());
        string []input = Console.ReadLine().Split();
        long[] D = new long[N];
        for(ulong i = 0; i < N; i++)
        {
            D[i] = long.Parse(input[i]);
        }
        Array.Sort(D);
        ulong ans = 1;
        ulong count = 1;
        ulong temp =1;
        for (ulong i = 1; i < N; i++)
        {
            if (D[i]==0 || D[0] != 0) { ans = 0; }
            if (i>1&&D[i - 1] != D[i]) {
                ans =ans * (ulong)(Math.Pow(temp, (i - count)) % 998244353) % 998244353;
                temp = (ulong)i - count;
                count = (ulong)i;
            }
            
        }
        ans = ans * (ulong)(Math.Pow(temp, (N - count)) % 998244353) % 998244353;
        Console.WriteLine(ans% 998244353);
    }
    
}