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 <map>
#include <string>
#include <queue>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> P;
const ll mod = 998244353;
const ll INF = 1000000000000000;
ll n, g[100010];



ll pow(ll x, ll y)
{
	if (y == 0) return 1;
	if (y % 2)
	{
		return pow(x, y - 1) * x % mod;
	}
	else
	{
		ll yyy = pow(x, y / 2);
		return yyy * yyy % mod;
	}
}

ll div(ll x)
{
	return pow(x, mod - 2);
}



int main(void)
{
	
	cin >> n;

	ll d[100010];
	ll lar = 0;
	ll ans = 1;
	for (int i = 0; i < n; i++)
	{
		cin >> d[i];
		g[d[i]]++;
		lar = max(lar, d[i]);
	}
	sort(d, d + n);

	for (int i = 1; i <= lar; i++)
	{
		(ans *= pow(g[i - 1], g[i])) %= mod;
	}

	if (d[0] != 0 || g[0] != 1)
	{
		cout << 0 << endl;
	}
	else
	{
		cout << ans << endl;
	}


	int xxx;
	cin >> xxx;
}