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.util.Map.Entry;

import javax.swing.text.Segment;
import javax.xml.ws.WebEndpoint;

import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;

import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;
 
public class Main //implements Runnable
{
//    static int dx[]={-1,0,1,0};
//    static int dy[]={0,-1,0,1};

    public static void main(String[] args)   throws Exception, IOException{        
        long mod=1000000007;
        Reader sc = new Reader(System.in);
        PrintWriter out=new PrintWriter(System.out);
        PriorityQueue<Integer> q=new PriorityQueue<>();
        
        int n=sc.nextInt();
        int d[]=new int[n+1];
        for (int i = 0; i < n; i++) {
			d[sc.nextInt()]++;
		}
		if(d[0]!=1)ret("0");

		int w=0;
        long a=1;
        for (int i = 0; i < d.length; i++) {
			w+=d[i];
			if(w==n)break;
			for (int j = 0; j < d[i+1]; j++) {
				a*=d[i];
				a%=998244353L;
			}
		}

        out.println(a);
     	out.flush();
    }
    
    static void ret(String ans) {
    	System.out.println(ans);
    	System.exit(0);
    }
    
    static boolean validpos(int x,int y,int r, int c){
        return x<r && 0<=x && y<c && 0<=y;
    }

    static void db(Object... os){
        System.err.println(Arrays.deepToString(os));
    }
}


class P {
	int x, y, d;
	P(int  x, int y, int d) {
	  this.x=x;
	  this.y=y;
	  this.d=d;
	}
}

//class P implements Comparable<P>{
//    int a,b;
//    P(int a, int b) {
//    	this.b=b;
//    	this.a=a;
//    }
//
//    public int compareTo(P p){
//        return p.a-a;//des
//    }
//}

class Reader
{ 
    private BufferedReader x;
    private StringTokenizer st;
    
    public Reader(InputStream in)
    {
        x = new BufferedReader(new InputStreamReader(in));
        st = null;
    }
    public String nextString() throws IOException
    {
        while( st==null || !st.hasMoreTokens() )
            st = new StringTokenizer(x.readLine());
        return st.nextToken();
    }
    public int nextInt() throws IOException
    {
        return Integer.parseInt(nextString());
    }
    public int[] nextIntArray(int size) throws IOException{
        int r[] = new int[size];
        for (int i = 0; i < size; i++) {
            r[i] = this.nextInt(); 
        }
        return r;
    }
    public long[] nextLongArray(int size) throws IOException{
        long r[] = new long[size];
        for (int i = 0; i < size; i++) {
            r[i] = this.nextLong(); 
        }
        return r;
    }
    public char[] getCharSet() throws IOException{
        return this.nextString().toCharArray();
    }    
    public long nextLong() throws IOException
    {
        return Long.parseLong(nextString());
    }
    public double nextDouble() throws IOException
    {
        return Double.parseDouble(nextString());
    }
}