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;
using ll=long long;
const ll INF = 0x1fffffffffffffff;
int main(){
    ll n;
    cin>>n;
    vector<ll> d(n);
    for(ll i=0;i<n;i++)cin>>d[i];
    sort(d.begin(),d.end());
    ll ans=1,memo=1;
    vector<ll> m2(n-1,0);
    if(d[0]!=0)cout<<"0"<<endl;
	else if(d[0]==0&&d[1]==0)cout<<"0"<<endl;
    else{
        for(ll i=1;i<n;i++){
            if(d[i]==memo)m2[memo-1]++;
            else{
                memo++;
              if(memo==d[i])m2[memo-1]++;
            }
        }
        bool m3=true;
        for(ll i=1;i<memo;i++){
			ll a=m2[i];
			while(a>0){
       			ans=(ans*m2[i-1])%998244353;
        		a--;
    		}
        }
        if(m3)cout<<ans<<endl;
    }
}