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>
#define ll long long
#define pb push_back
#define mod 998244353
#define ff first
#define ss second
#define endl '\n'
using namespace std;
const ll inf=1e18;
/*ll power(ll x,ll y)
{
    ll res=1;
    while(y>0)
    {
        if(y%2==1)
            res=(res*x)%mod;
        x=(x*x)%mod;
        y=y/2;
    }
    return res;
}*/
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    ll n;
    cin>>n;
   vector<ll>v;
   ll i,m,s=0,a,b,c,r,k;
   for(i=0;i<n;i++)
   {
       cin>>m;
       v.pb(m);
       if(m==0)
        s++;
   }
   if(v[0]!=0 || s>1)
   {
       cout<<0<<endl;
       return 0;
   }
   ll arr[n+1]={0},arr1[n+1];
   arr[0]=1;
   fill(arr1,arr1+n+1,1);
   c=1;
   sort(v.begin(),v.end());
   for(i=1;i<n;i++)
   {
       a=(arr[v[i]-1]*arr1[v[i]-1])%mod;
       arr1[v[i]]=(arr1[v[i]]*a)%mod;
       arr[v[i]]++;
   }
   cout<<arr1[v[n-1]]<<endl;
}