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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {
    public static void main(String args[]) throws Exception{
        BufferedReader stdR = new BufferedReader(new InputStreamReader(System.in));
        int N = Integer.parseInt(stdR.readLine());
        String[] s = stdR.readLine().split(" ");
        int[] D = new int[N];
        for(int i = 0 ; i < N ; i++) {
            D[i] = Integer.parseInt(s[i]);
        }
        if(D[0] != 0) {
            System.out.println("0");
        }else {
            Arrays.sort(D);
            int[] jisuu = new int[D[N - 1] + 1];
            for(int i = 0 ; i < N ; i++) {
                jisuu[D[i]]++;
            }
            if(jisuu[0] != 1) {
                System.out.println(0);
            }else {
                long count = 1;
                for(int i = 1 ; i < jisuu.length ; i++) {
                    if(jisuu[i] == 0) {
                        count = 0;
                        break;
                    }else {
                        count *= Math.pow(jisuu[i - 1], jisuu[i]);
                        count %= 998244353;
                    }
                }
                System.out.println(count);
            }
        }
    }
}