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.Scanner;

public class Main {
	
	static long mod = 998244353L;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int n = Integer.parseInt(sc.next());
		
		int []d = new int [n];
		int []p = new int [100001];
		
		long ans = 1;
		int max = -1;
		
		for(int i = 0 ; i < n ;i++) {
			d[i] = Integer.parseInt(sc.next());
			p[d[i]]++;
			max = Math.max(d[i], max);
		}
		
		if(d[0] != 0 || p[0] != 1) {
			System.out.println(0);
			return;
		}
		
		for(int i = 1 ; i <= max ; i++) {
			ans = ans * Modpow((long)p[i-1],(long)p[i]) % mod ;
			System.out.println(ans);
		}
		
		System.out.println(ans);	
	}
	
	static long Modpow(long a, long n) {
		long res = 1;
		while(n > 0) {
			if((n & 1) == 1) {
				res = res * a % mod;
			}
			a = a * a % mod;
			n >>= 1;
		}
		return res;
	}
}