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)


#include <stdio.h>
#include <math.h>
#define MAGIC 998244353
int main(){
	long n = 0;
	long d[100000] = {};
	long floor[100000] = {};
	long cnt = 0;
	long i=0; long j = 0;
	
	scanf("%ld",&n);
	
	for(i=0;i < n;i++){
		scanf("%ld",&d[i]);
	}
	
	for(i=0;i < n;i++){
		floor[d[i]]++;
	}

	if(floor[0] == 1){
			cnt = 1;
		for(i=0;i < n;i++){
			if(floor[i+1] == 0){
				break;
            }else{
            	for(j = 0;j < floor[i+1];j++){
					cnt = (cnt*(floor[i])) % MAGIC;
            	}
			}
		}
	}else{
		cnt = 0;
	}
	printf("%ld",cnt);	
	return 0;
}