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;

//第二回全国統一プログラミング王決定戦予選
//B Counting of Trees
public class Main {
	static final int DIV = 998244353;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = Integer.parseInt(sc.next());
		int[] arrD = new int[N];
		int[] countD = new int[N];
		int maxD = 0;
		for (int i = 0; i < N; i++) {
			arrD[i] = Integer.parseInt(sc.next());
			countD[arrD[i]]++;
			maxD = Math.max(maxD, arrD[i]);
			if (i == 0 && arrD[i] != 0) {
				System.out.println(0);
				sc.close();
				return;
			}
			if (i != 0 && arrD[i] == 0) {
				System.out.println(0);
				sc.close();
				return;
			}

		}
		sc.close();

		for (int i = 1; i < maxD; i++) {
			if (countD[i] == 0) {
				System.out.println(0);
				return;
			}
		}

		long ans = arrD[1];
		for (int i = 2; i < N; i++) {
			ans *= arrD[i];
			ans %= DIV;
		}
		System.out.println(ans);
	}
}