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 rep(i,n) for(int i=0;i<(int)(n);i++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)
#define fs first
#define sc second
typedef pair<ll, ll> l_l;
#define EPS (1e-7)
#define INF (1e9)
#define PI (acos(-1))

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
  int n;
  cin>>n;
  vector<int>d(n);
  rep(i,n)cin>>d[i];
  if(d[0]!=0){
    cout<<0;
    return 0;
  }
  sort(d.begin(),d.end());
  vector<int>s(n);
  rep(i,n){
   s[d[i]]++;
  }
  ll ans=1;
  for(int i=1;i<n-1;i++){
    ans=ans*pow(s[i],s[i+1]);
  }
  cout<<ans<<endl;
}