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.*;

public class Main {
    static int mod = 998244353;
    static long pow(long a,int n) {
        long res=1;
        while (n>0) {
            if ((n-n/2*2)==1) {
                res=res*a%mod;
            }
            a=a*a%mod;
            n>>=1;
        }
        return res;
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        int[] D = new int[N];
        int[] map = new int[N+100];
        for (int i=0;i<N;i++) {
            D[i] = Integer.parseInt(sc.next());
            map[D[i]]++;
        }
        long ans = 1L;
        for (int i=1;i<N+100;i++) {
            if (map[i]==0) {
                break;
            } else {
                ans = ans*pow(map[i-1], map[i])%mod;
            }
        }
        if (D[0]!=0) {
            System.out.println(0);
        } else {
            System.out.println(ans);
        }
    }
}