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 (3.4.3) (judge verdict: Wrong Answer)

# -*- coding: utf-8 -*-
import sys
# from collections import defaultdict, deque
# from math import sqrt, gcd, factorial, tan, pi, sin, cos
def input(): return sys.stdin.readline()[:-1] # warning not \n
# def input(): return sys.stdin.buffer.readline()[:-1]

MOD = 998244353

def solve():
    n = int(input())
    d = [int(x) for x in input().split()]
    f = [0] * n
    for e in d:
        f[e] += 1
    
    ok = f[0] != 0
    z = 0
    ans = 1
    for i in range(1, n):
        if (f[i] == 0): z = 1
        if (z and f[i]): ok = 0
        ans *= pow(f[i-1], f[i], MOD)
        ans %= MOD
    print(ans * ok)




t = 1
# t = int(input())
for case in range(1,t+1):
    ans = solve()



"""
1 -> (1, 2) -> (2 ** 3, 3) -> (3, 1)

"""