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>
#include<string>
#include<algorithm>	
#include<cmath>
using namespace std;
int main() {
	long long n, a, sum = 0, num = 1, ans = 1; cin >> n;
	int test[123456], uiop[123456] = { 0 };
	for (int h = 0; h < n; h++) {
		cin >> test[h];
		if (h == 0 && test[h] == 0) {
			sum = 1;
		}
	}
	sort(test, test + n);
	if (sum == 0) {
		cout << 0 << endl; return 0;
	}
	for (int h = 1; h < n; h++) {
		if (test[h] == num) {
			uiop[num]++;
		}
		else if (test[h] == num + 1) {
			num++; uiop[num]++;
		}
	}
	for (int h = 1; h < num; h++) {
		ans = ans * pow(uiop[h], uiop[h + 1]);
		ans = ans % 998244353;
	}
	cout << ans % 998244353 << endl;
	cin >> n;
}