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: Accepted)

#include<bits/stdc++.h>
#define endl "\n"
#define pb push_back
#define ll long long
#define ld long double
#define d1(x)  cerr << #x << "--> " << x << endl
#define d2(x, y)  cerr << #x << "--> " << x << " | " << #y << "--> " << y <<endl
#define d3(x, y,z)  cerr << #x << "--> " << x << " | " << #y << "--> " << y <<" | " << #z << "--> "<< z<< endl
#define vpll vector<pair<ll,ll>>
#define F first
#define S second
using namespace std;

ll mode=pow(10,9)+7;
bool cmp(pair<ll,ll> x, pair<ll, ll> y){
	return x.S<y.S;
}


int main(){ 
    
    #ifndef ONLINE_JUDGE
	//freopen("input.txt", "r", stdin);
	#endif
	
	ios::sync_with_stdio(0);
    cin.tie(0);
	
	ll n;
	cin>>n;
	ll a[n];
	ll f[n]={0};
	for (int i=0;i<n;i++){
		cin>>a[i];
		f[a[i]]++;
	}
	ll ans=1;
	for (int i=1;i<n;i++){
		ans=(ans%998244353*f[a[i]-1]%998244353)%998244353;
	}
	if (f[0]!=1 || a[0]!=0){
		cout<<0<<endl;
	}
	else{
		cout<<ans<<endl;
	}
		
 	return 0;
}