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.Linq;
using System.Collections.Generic;
class ProgramB
    {
        static void Main(string[] args)
        {
            string input = Console.ReadLine();
            long n = long.Parse(input);

            long[] d = new long [n];
            long[] d_num = new long[n];
            long sum = 1;

            string[] input_d = Console.ReadLine().Split();


            for(long i = 0;i < n;i++)
            {
                d[i] = long.Parse(input_d[i]);
                
                if(d[0] != 0 || (i > 0 && d[i] == 0))
                {
                    Console.WriteLine("0");
                    return;
                }
                d_num[d[i]]++;
            }

            for(long i = 1;i <= d.Max();i++)
            {
                if(d_num[i] == 0)
                {
                    Console.WriteLine("0");
                    return;
                }
                long temp = (long)(Math.Pow(d_num[i - 1], d_num[i]));
                sum = sum * temp;
                if(sum >= 998244353)
                    sum = sum % 998244353;

            }

            Console.WriteLine(sum);

        }
    }