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 <algorithm>
#include <functional>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <cstdio>
#include <cmath>
#include <tuple>
#define rep(i, n) for(i = 0; i < n; i++)
using namespace std;

int powmod(int a, int n, int mod) {
	if (n == 0) return 1;
	if (n % 2 == 0) return powmod((a * a) % mod, n / 2, mod);
	return (a * powmod(a, n - 1, mod)) % mod;
}

int n;
int d;
int maxd;
int cnt[100000];

signed main() {
	int i;
	
	cin >> n;
	rep(i, n) {
		cin >> d;
		maxd = max(maxd, d);
		cnt[d]++;
	}
	
	int mod = 998244353;
	int ans = 1;
	rep(i, maxd) {
		ans *= powmod(cnt[i], cnt[i + 1], mod);
		ans %= mod;
	}
	cout << ans << endl;
	return 0;
}