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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

/*------------------------------------
........Bismillahir Rahmanir Rahim....
..........created by Abdul Aziz.......
------------------------------------*/
#include <iostream>
#include <algorithm>
#include <stdio.h>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <cstring>
#include <unordered_map>
#include <queue>
#define   mod  998244353
#define   int  long long 
#define   ld   long double
#define   pb   push_back
#define   vi  vector<int> 
#define   dbg(x)  cerr << #x << " = " << x << '\n'
#define   sz(x)  (int)x.size()
#define   all(a) (a.begin(),a.end())
#define   ff   first
#define   ss   second
#define   pii  pair<int,int> 
#define   lcm(a,b) (a*b)/__gcd(a,b) 
using namespace std;

inline void solve(){
    int n,mx=0; cin>>n; 
    map <int,int> cnt;
    while (n--){
        int a;cin>>a;
        cnt[a]++;
        mx=max(mx,a);
    }
    int ans=1; 
    if (cnt[0]>1 or cnt[0]==0) ans=0;
    for (int i=1;i<=mx;i++)
        ans = ans*(pow(i,cnt[i])-(cnt[i]==0));
    cout << ans << endl;
}

signed main()
{
    int n=1; // cin>>n;
    while (n--) solve();
    return 0;
}