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 <math.h>
#include <algorithm>
#include <string>
#include <string.h>
#include <queue>
#include <vector>
#include <set>
#include <map>
#include <tuple>
#include <stdlib.h>
using namespace std;
#define PI 3.14159265358979
typedef long long int ll;


int main()
{
	ll N, D, maxi = 0; cin >> N;
	ll ans = 1;
	bool flag = true;
	ll c[100001] = {};
	for (ll i = 0; i < N; i++)
	{
		cin >> D;
		maxi = (D>maxi?D:maxi);
		c[D]++;
	}
	for (ll i = 0; i <= maxi; i++)
	{
		if (c[i] == 0)flag = false;
		if (flag&&i > 1) {
			for (int j = 0; j < c[i]; j++)
			{
				ans *= c[i-1];
				ans %= 998244353;
			}
		}
	}
	if (c[0]>1)flag = false;
	cout << (flag?ans:0);
}