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;
#define INF 1LL<<62
#define inf 998244353

ll ch[100010];
int main() {
	ll n;
	cin>>n;
	for(ll i=0;i<n;i++){
		ll now;
		cin>>now;
		ch[now]++;
		if(i==0&&now!=0){
			cout << 0;
			return 0;
		}
	}
	if(ch[0]!=1){
		cout << 0;
		return 0;
	}
	ll cnt=ch[0];
	ll ans=1;
	for(ll i=1;;i++){
		ans*=pow(ch[i-1],ch[i]);
		ans%=inf;
		cnt+=ch[i];
		if(cnt==n){
			break;
		}
	}
	cout <<ans;
	// your code goes here
	return 0;
}