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 <iostream>
#include <vector>
#include <algorithm>
#include <cmath>

using namespace std;

//int func(vector<int> &m) { return  }

int main(){
    long long int N;
    cin >> N;
    vector<int> D(N);
    for(int i=0;i<N;++i) cin >> D[i];
    int count = 1;
    if(D[0]>0){
        cout << 0 << endl;
        return 0;
    } 
    else{
        long long int d_max = *max_element(D.begin(),D.end());
        vector<long long int> num(d_max);
        
        for (int i = 1; i < N; ++i)
        {
            int a = D[i];
            num[a-1]++;
        }
        for (int i = 1; i < d_max; ++i)
        {
            count *= pow(num[i-1],num[i]);
        }
        cout << count << endl;
        
        
        return 0;
    }

    
    
}