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.*;
//import java.math.BigDecimal;

public class Main{
    public static void main(String args[]){

        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        int[] m = new int[n];
        long answer = 1;
        //BigDecimal answer = BigDecimal.valueOf(1);

        if(sc.nextInt() != 0) answer = 0;
        //if(sc.nextInt() != 0) answer = BigDecimal.valueOf(0);
        else m[0]++;
        for(int i = 1; i < n; i++){
            int x;
            if((x = sc.nextInt()) == 0){
                answer = 0;
                //answer = BigDecimal.valueOf(0);
                break;
            }
            m[x]++;
        }

        for(int i = 1; i < n; i++){
            //answer *= ((long)Math.pow(m[i-1], m[i]) % 998244353);
            //answer = answer.multiply(BigDecimal.valueOf(Math.pow(m[i-1], m[i])));
            for(int j = 0; j < m[i]; j++){
                answer *= m[i-1] % 998244353;
            }
        }

        //System.out.println(answer % 998244353);
        //System.out.println(answer.remainder(BigDecimal.valueOf(998244353)).toBigInteger());
        System.out.println(answer);

    }

}