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 Python (3.8.2) (judge verdict: Wrong Answer)

import sys
input = sys.stdin.readline

#l = list(map(int, input().split()))
#import numpy as np
#arr = np.array([int(i) for i in input().split()])
'''
a,b=[],[]
for i in range():
    A, B = map(int, input().split())
    a.append(A)   
    b.append(B)'''

n=int(input())
d=list(map(int,input().split()))
import collections
ans=1
dd=collections.Counter(d)
dd=sorted(dd.items())
#print(dd)
if dd[0][1]!=1:
    print(0)
    sys.exit()
for i in range(max(d)+1):
    if i not in dd:
        print(0)
        sys.exit()

for i in range(max(d)):#0~n-1
    ans*=dd[i][1]**dd[i+1][1]
    if ans>998244353:
        ans%=998244353
print(ans)