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 <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <algorithm>
#include <time.h>
#include <string.h>
#include <vector>
#include <queue>
#include <map>
using namespace std;
inline int lowb(int x) {
	return x & -x;
}
int n, m, a[100005], b[100005] /*, p[], ans */;
struct EDGE {
	int to, dis;
};
long long ans= 1;
int main() {
	cin >> n;
	for(int i= 1; i <= n; i++) {
		cin >> a[i];
	}
	sort(a + 1, a + n + 1);
	b[0]= 1;
	for(int i= 1; i <= n; i++) {
		ans= 1ll * ans * b[a[i]] % 998244353, ++b[a[i] + 1];
	}
	if(b[0] > 1) {
		cout << 0 << endl;
	}
	else {
		cout << ans << endl;
	}
	return 0;
}