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.Scanner;

public class Main {
    public static void main(String[] args) {
        new Main().run();
    }

    private void run() {
        Scanner scanner = new Scanner(System.in);
        int N = scanner.nextInt();
//        int[] D = new int[N];
        long[] A = new long[10000000];
        long max = 0;
        for (int i = 0; i < N; i++) {
            long D = scanner.nextLong();
            A[Math.toIntExact(D)]++;
            max = Math.max(D, max);
        }
        long ans = 1;
//        for (int j = 0; j <= max; j++) {
        if (A[0] == 0) {
            System.out.println(0);
            return;
        }
//        }
        for (long j = 1; j <= max; j++) {
            long a = A[Math.toIntExact(j - 1)];
            long n = A[Math.toIntExact(j)];

            while(n-- > 0) {
                ans *= (long)a;
                ans %= (long)998244353;
            }

        }
        System.out.println(ans);
    }

    static long power(long a, long n) {
        //　結果の初期値
        long result = 1;
        // nが１の場合に計算
        if (1 <= n) {
            // aをn回掛ける
            for (long i = 0; i < n; ++i) {
                result = ((result % (long) 998244353) * (a % (long) 998244353)) % (long) 998244353;
            }
        }
        // 結果を戻す
        return result;
    }
}