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.Linq;
using System.Numerics;
using System;

public class Hello
{
    public const int MOD = 998244353;
    public static void Main()
    {

        var n = int.Parse(Console.ReadLine().Trim());
        string[] line = Console.ReadLine().Trim().Split(' ');
        var a = Array.ConvertAll(line, int.Parse);
        var amax = a.Max();
        var b = new int[amax + 1];
        for (int i = 0; i < n; i++) b[a[i]]++;
        getAns(b);
    }
    static void getAns(int[] b)
    {
        BigInteger ans = 1;
        if (b[0] != 1) { Console.WriteLine(0); return; }
        for (int i = 1; i < b.Length; i++)
        {
            if (b[i] == 0) { Console.WriteLine(0); return; }
            else
            {
                ans *= BigInteger.ModPow(i, b[i], MOD);
                ans %= MOD;
            }
        }
        Console.WriteLine(ans);
    }
}