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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>

using namespace std;

int N, D[100005];

int C[100005];

long long int MOD = 98244353;


int main(void) {

	cin >> N;

	for (int i = 1; i <= N; i++) {
		cin >> D[i];
		C[D[i]]++;
	}

	if (D[1] != 0 || C[0]!=1) { cout << 0 << endl;  return 0; }

	//for (int i = 2; i <= N; i++) { if (D[i] == 0) { cout << 0 << endl; return 0; } }

	long long int ans = 1;

	for (int d = 1; d <= N-1; d++) {
		for (int j = 1; j <= C[d]; j++) {
			ans *= C[d - 1];
			ans %= MOD;
		}
	}

	cout << ans << endl;

	return 0;
}