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;
using System.IO;
using System.Diagnostics;

class Myon
{
    public Myon() { }
    public static int Main()
    {
        new Myon().calc();
        return 0;
    }

    Scanner cin;
    Func cin2;
    void calc()
    {
        cin = new Scanner();
        cin2 = new Func();
        int N=cin.nextInt();
        int[] a=cin.ArrayInt(N,0);
        long ans=1;
        long mod=998244353;
        long count =1;
        long before =1;
        Array.Sort(a);
        for(int i=0;i<N;i++)
        {
            if(i<a[i]){ans=0;break;}
            if(i>0&&a[i-1]==a[i]){count++;}
            else if(i>0&&a[i-1]!=a[i]&&a[i]-a[i-1]==1){ans*=(long)Math.Pow(before,count);before=count;count=1;}
            else if(i>0&&a[i]-a[i-1]>1){ans=0;break;}
            ans%=mod;
            
        }
        ans*=(long)Math.Pow(before,count);
        ans%=mod;
        if(a[0]!=0)ans=0;
        Console.WriteLine(ans);
        
    }
}



class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return next();
        i = 0;
        return s[i++];
    }

    public int nextInt()
    {
        return int.Parse(next());
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextInt() + add;
        }
        return Array;
    }

    public long nextLong()
    {
        return long.Parse(next());
    }

    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextLong() + add;
        }
        return Array;
    }

    public double nextDouble()
    {
        return double.Parse(next());
    }


    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextDouble() + add;
        }
        return Array;
    }
}

class Answer
{
    public void Int2DArrayAns(int[,]x,char c)
    {
        for(int i=0;i<x.GetLength(0);i++)
        {
            for(int j=0;j<x.GetLength(1)-1;j++)
            {
                Console.Write(x[i,j]);
                Console.Write(c);
            }
            Console.WriteLine(x[i,x.GetLength(1)-1]);
        }
    }
    public void Char2DArrayAns(char[,]x,char c)
    {
        for(int i=0;i<x.GetLength(0);i++)
        {
            for(int j=0;j<x.GetLength(1)-1;j++)
            {
                Console.Write(x[i,j]);
                Console.Write(c);
            }
            Console.WriteLine(x[i,x.GetLength(1)-1]);
        }
    }
}

class Func
{
    public long GCDLong(long a, long b)
    {
        while(a!=0)
        {
          long t=a;
          a=b%a;
          b= t;
        }
      
        return b;        
    }
}