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<string>
#include <vector>
#include<queue>
#include<map>
#include<algorithm>
#include<iomanip>
#include<cmath>
#include<bitset>
using namespace std;
using vi = vector<int>;
using vii = vector<vi>;
using vs = vector<string>;
using pii = pair<int, int>;
#define rep(i,n) for(int i=0;i<n;i++)
#define rep2(i,m,n) for(int i=m;i<n;i++)
#define vsort(v) sort(v.begin(), v.end())
#define rv(v) reverse(v.begin(), v.end())
#define ll long long
#define PI 3.141592653589793
using vll = vector<ll>;
using Graph = vii;
const ll MOD = 998244353;

int main() {
	int n;
	cin >> n;
	vi d(n);
	vi s(n);
	int m = -1;
	rep(i, n) {
		cin >> d[i];
		s[d[i]]++;
		if (d[i] > m) m = d[i];
	}
	ll ans = (d[0] == 0) ? 1 : 0;
	for (int i = 1; i <= m; i++) {
		ans *= (ll)pow(s[i - 1], s[i]) % MOD;
	}
	cout << ans << endl;
	/*rep(i, m + 1) cout << s[i] << " ";*/
}