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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp15
{
    class Class30
    {
        static void Main()
        {
            int N = int.Parse(Console.ReadLine());
            var d = Console.ReadLine().Split().Select(int.Parse).ToArray();
            Array.Sort(d);
            long ans = d.Count(x => x == 0);
            long last = 0;
            long count = 0;
            long lastcount = 1;
            for(int i = 0;i<N ;)
            {
                if (d[i] == last)
                {
                    count++;
                    i++;
                }
                else
                {
                    if(count == 0)
                    {
                        ans = 0;
                        break;
                    }
                    for(int k = 0; k < count; k++)
                    {
                        ans *= lastcount;
                        ans %= 998244353;
                    }

                    
                    lastcount = count;
                    count = 0;
                    last++;
                }
            }
            for (int j = 0; j < count; j++)
            {
                ans *= lastcount;
            ans %= 998244353;
            }
                
            Console.WriteLine(ans);
        }
    }
}