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.io.IOException;

public class Main{
    public static void main(String[] args){
        int count = 0;
        long[] input = null;
        long[] box = null;
        BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));
        try{
            String str = bufferedReader.readLine();
            String str2 = bufferedReader.readLine();
            String[] st = str2.split(" ");
            count = Integer.parseInt(str);
            input = new long[count];
            box = new long[count+1];
            int c = 0;
            for(String s: st){
                int a = Integer.parseInt(s);
                input[c] = a;
                box[a]++;
                c++;
            }
        } catch (IOException e){
            e.printStackTrace();
        }
        if(box[0] != 1L || input[0] != 0L){
            System.out.println(0);
        } else{
            long ans = 1;
            for(int i = 1;i < count;i++){
                ans = (ans % 998244353L) * ((long)Math.pow(box[i],box[i+1]) % 998244353L) % 998244353L;
                if(ans == 0L){
                    break;
                }
            }
            System.out.println("" + ans);
        }

    }
}