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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#define MOD 998244353
#define MAX 100005
#include <stdio.h>
#include <string.h>
#include <math.h>
int nivel[MAX];
int max(int a, int b){
	return a > b ? a: b;
}
long long int ans = 1;
int main(){
	memset(nivel, 0, sizeof(int) * MAX);
	int n, maxl = 0, read;
	scanf("%d", &n);
	for(int i = 0; i < n; ++i){
		scanf("%d", &read);
		maxl = max(maxl, read);
		nivel[read]++;
	}
	for(int i = 1; i <= maxl; ++i){
		ans = (ans * (int)round(pow(nivel[i-1], nivel[i]))) % MOD;
	}
	printf("%lld\n", ans);
}