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

#include <climits>
#include <cmath>
#include <cstring>

#include <iomanip>

using namespace std;

#define FAST       			ios_base :: sync_with_stdio(false); cin.tie(NULL); 
#define endl "\n"

typedef long long int  ll;
typedef unsigned long long int ull;

#define MOD 998244353

ll power(ll a , ll p)
{
	ll result = 1;
	while(p != 0)
	{
		// checking if last bit is 1 or not 
		if(p & 1)
			result = ( (result%MOD) * (a%MOD) ) % MOD;
		
		a = ( (a%MOD) * (a%MOD) ) % MOD;
		p = p>>1;
	}

	return result;
}

int main()
{
	FAST;
	int n;
	cin >> n;
	
	ll arr[n];
	
	for(int i=0 ; i<n ; i++)
		cin >> arr[i];

	ll count[n+1] = {0};
	for(int i=0 ; i<n ; i++)
		count[arr[i]]++;

	if(count[0] != 1)
	{
		cout << "0";
		return 0;
	}

	ll tree = 1;
	ll op = 1;
	int temp = n-1;
	for(int i=1 ; i<=n ; i++)
	{
		if(count[i] == 0)
		{
		    //cout << temp << "--\n";
			if(temp == 0)
				break;
			cout << "0";
			return 0;
		}

		temp -= count[i];
		ll ans = power(op , count[i]);
		tree = ( (tree%MOD) * (ans%MOD))%MOD;
		op = count[i];
	}

	cout << tree;
	return 0;
}