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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll mod = 998244353;
const int N = 100000 + 5;
int a[N];
 
ll mul_pow(ll x,ll y){
	ll ans = 1;
	while(y){
		if(y&1)
			ans = (ans*x) % mod;
		x = (x*x)%mod;
		y>>=1;
	}
	return ans;
}
 
int main()
{
	int n;
	cin >> n;
	int maxn = 0;
	int flag = 0;
	for(int i = 0; i < n; i++){
		int x;
		cin >> x;
		if(i == 0 && x != 0)
			flag = 1;
		a[x]++;
		maxn = max(maxn,x);
	}
	long long sum = 1;
	if(a[0] == 0 && flag)
		cout << 0 << endl;
	else{
		for(int i = 1; i <= maxn; i++){
			if(a[i-1] == 0){
				sum = 0;
				break;
			}
			sum = sum * mul_pow(a[i-1],a[i])%mod;
		}
		cout << sum << endl;
	}
	return 0;
 }