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;
class c
{
    static void Main()
    {
        Console.ReadLine();
        var d = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        long ans = 1;
        if (d[0] != 0) Console.WriteLine(0);
        else
        {
            d = d.Where((x, y) => y > 0).OrderBy(f => f).ToArray();
            if (d.Contains(0)) Console.WriteLine(0);
            else
            {
                var count = new int[d.Last() + 1];
                for (int i = 0; i < d.Length; i++)
                {
                    count[d[i]]++;
                }
                for (int i = 1; i < count.Length - 1; i++)
                {
                    ans *= (long)Math.Pow(count[i], count[i + 1]);
                    ans %= 998244353;
                }
                Console.WriteLine(ans);
            }
        }
    }
}