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{
	static long mod=998244353;
	public static void main(String[] args){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int[] d=new int[n];
		long count1=0;
		for(int i=0; i<n; i++){
			d[i]=sc.nextInt();
			if(d[i]==1){
				count1++;
			}
		}
		if(d[0]!=0){
			System.out.println(0);
			return;
		}
		Arrays.sort(d);
		long ans=1;
		int cc=2;
		long count=0;
		long count2=0;
		for(int i=1; i<n; i++){
			if(cc==d[i]){
				count++;
			}else if(cc+1==d[i]){
				count2=count;
				while(count>0){
					if((count & 1)==1){
						ans*=count1;
					}
					count>>=1;
					ans%=mod;
					count1*=count1;
					count1%=mod;
				}
				count1=count2;
				count=1;
				cc++;
			}
		}
		while(count>0){
			if((count & 1)==1){
				ans*=count1;
			}
			count>>=1;
			ans%=mod;
			count1*=count1;
			count1%=mod;
		}
		System.out.println(ans);
	}
}