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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
public class Main
{
    public static void main(String[] args)
    {
        int count = 0;
        boolean sw = false;
        int max = Integer.MIN_VALUE;
        int min = Integer.MAX_VALUE;
        double dMax = Double.MIN_VALUE;
        double dMin = Double.MAX_VALUE;
        //StringBuilder answer=new StringBuilder();
        //input
        Scanner sc = new Scanner(System.in);
        int n=sc.nextInt();
        List<Integer> d = new ArrayList<>();
        Map<Integer,Integer> countMap = new HashMap<>();
        for (int i=0;i<n;++i)
        {
            int dd=sc.nextInt();
            d.add(dd);
            if (dd > max)
            {
                max = dd;
            }

            if (countMap.get(dd) == null)
            {
                countMap.put(dd,1);
            }else
            {
                int a = countMap.get(dd);
                ++a;
                countMap.put(dd,a);
            }

            if (i!=0 && dd == 0)
            {
                System.out.println(0);
                sc.close();
                System.exit(0);
            }
        }

        for (int i = 0;i < max;++i)
        {
            if (!d.contains(i))
            {
                System.out.println(0);
                sc.close();
                System.exit(0);
            }
        }

        List<Integer> list = new ArrayList<>();
        int b = -1;//上の頂点数
        for (int i=1;i<=max;++i)
        {
            //System.out.println("i = "+i);
            if (countMap.get(i) == null)
            {
                System.out.println(0);
                sc.close();
                System.exit(0);
            }else
            {
                int a = countMap.get(i);//その深さの頂点数
                if (b == -1)
                {
                    int c = i-1;
                    b = countMap.get(c);
                }
                double c = Math.pow((double)b,(double)a);
                //System.out.println("a = "+a+" b = "+b+" c = "+c);
                list.add((int)c);
                b = a;
            }
        }

        int ans = 1;
        for (int a:list)
        {
            ans *= a;
        }

        System.out.println(ans);
        sc.close();
    }
}