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 {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		long HOGE = 998244353;

		long n = sc.nextLong();

		long[] counter = new long[200000];

		long max = 0;

		for (long i = 0; i < n; i++) {
			int tmp = sc.nextInt();

			if (tmp > max)
				max = tmp;

			counter[tmp]++;
		}

		long before = counter[0];
		long ans = 1;

		for (int i = 0; i < max + 1; i++) {
			if (counter[0] != 1) {
				ans = 0;
				break;
			}
			if (counter[i] == 0) {
				ans = 0;
			}
			//			System.out.println("b" + before + "c" + counter[i]);
			//			System.out.println(ans);

			ans = (long) Math.pow(before, counter[i]) % HOGE * ans;

			before = counter[i];
		}
		System.out.println(ans);

	}
}