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.math.BigInteger;
import java.util.Scanner;

class Solver {
	static final Solver INSTANCE = new Solver();

	void solve(Scanner sc) {
		int N = sc.nextInt();
		int[] count = new int[N];
		for (int i = 0; i < N; i++) {
			count[sc.nextInt()]++;
		}
		if (count[0] != 1) {
			System.out.println(0);
			return;
		}
		BigInteger multiply = BigInteger.ONE;
		BigInteger prev = BigInteger.valueOf(count[0]);
		BigInteger mod = BigInteger.valueOf(998244353);
		for (int i = 1; i < count.length; i++) {
			if (count[i] < 1) break;
			BigInteger pow = prev.modPow(prev = BigInteger.valueOf(count[i]), mod);
			multiply = multiply.multiply(pow).mod(mod);
		}
		System.out.println(multiply);
	}
}

class Main {
	public static void main(String... args) {
		Scanner in = new Scanner(System.in);

		Solver.INSTANCE.solve(in);

		in.close();
	}
}