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 Ruby (2.3.3) (judge verdict: Accepted)

n=gets.chomp.to_i
d=gets.chomp.split(" ").map{|s| s.to_i}
if d.count(0)!=1 ||d[0]!=0
  p 0
  exit
end
d.sort!
i,j=0,0
t=Array.new(n,0)
while i!=n
  c=0
  while d[j]==i
    j+=1
    c+=1
  end
  t[i]=c
  i+=1
end
#p t
ans=[]
ans[0]=t[0]
for i in 1..n-1
  ans[i]=(t[i-1]**t[i])*ans[i-1]%998244353 if t[i]!=0
  ans[i]=0 if t[i]==0
end
#p ans
p ans[d.max]