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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
	static int r = 998244353;

	public static long mypow(long a, long b) {
		if (a == 1 || b == 0)
			return 1;
		long ans = 1;
		for (int i = 0; i < b; ++i) {
			ans *= a;
			ans %= r;
		}
		return ans;
	}

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		long len[] = new long[n];
		for (int i = 0; i < n; ++i) {
			int tmp = sc.nextInt();
			len[tmp]++;
		}
		sc.close();
		long num = len[1];
		long pre = num;
		long ans = 0;
		if (len[0] == 1) {
			ans = 1;
			for (int i = 2; i < n; ++i) {
				pre = len[i];
				long tmp = mypow(num, pre);
				ans *= tmp;
				ans %= r;
				num = len[i];
			}
		}
		System.out.println(ans);
	}
}