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



Sample input:
4
0 1 1 2


Sample output:
2

Submission status: Wrong Answer

Solution code:
N=int(input())
D=list(map(int, input().split()))
D=sorted(D)
p=998244353
edge=[0]*(N)

ans=1
for i in range(N):
    d=D[i]
    if i==0:
        if d==0:
            edge[0]+=1
            continue
        else:
            print(0)
            exit()
    if d==0:
        print(0)
        exit()
    if edge[d-1]==0:
        print(0)
        exit()
    else:
        edge[d]+=1
        ans*=edge[d-1]
        ans%=p

print(ans%p)

Submission status: Wrong Answer

Solution code:
N=int(input())
D=list(map(int, input().split()))
D=sorted(D)
p=998244353
edge=[0]*(N)

ans=1
for i in range(N):
    d=D[i]
    if i==0:
        if d==0:
            edge[0]+=1
            continue
        else:
            print(0)
            exit()
    if d==0:
        print(0)
        exit()
    if edge[d-1]==0:
        print(0)
        exit()
    else:
        edge[d]+=1
        ans*=edge[d-1]
        ans%=p

print(ans)

Submission status: Wrong Answer

Solution code:
N=int(input())
D=list(map(int, input().split()))
D=sorted(D)
p=998244353
edge=[0]*(N)

ans=1
for i in range(N):
    d=D[i]
    if i==0:
        if d==0:
            edge[0]+=1
            continue
        else:
            print(0)
            exit()
    if edge[d-1]==0:
        print(0)
        exit()
    else:
        edge[d]+=1
        ans*=edge[d-1]
        ans%=p

print(ans)

Submission status: Wrong Answer

Solution code:
print(0)

Submission status: Wrong Answer

Solution code:
from collections import Counter
n = int(input())
l = sorted(list(map(int,input().split())))
c = Counter(l)
mod = 998244353
if l.count(0) != 1:
    print(0)
    exit()
ans = 1
for i in l[1:]:
    ans *= c[i-1]
    ans %= mod
print(ans)

Submission status: Wrong Answer

Solution code:
from collections import Counter
n = int(input())
l = sorted(list(map(int,input().split())))
c = Counter(l)
mod = 998244353
if n == 1:
    if l[0] == 0:
        print(1)
    else:
        print(0)
    exit()
ans = 1
for i in l[1:]:
    ans *= c[i-1]
    ans %= mod
print(ans)

Submission status: Wrong Answer

Solution code:
from collections import Counter
n = int(input())
l = sorted(list(map(int,input().split())))
c = Counter(l)
mod = 998244353

ans = 1
for i in l[1:]:
    ans *= c[i-1]
    ans %= mod
print(ans)

Submission status: Wrong Answer

Solution code:
from collections import Counter
n = int(input())
l = sorted(list(map(int,input().split())))
c = Counter(l)
if l.count(0) != 1:
    print(0)
else:
    ans = 1
    for i in l[1:]:
        ans *= c[i-1]
    print(ans)

Submission status: Wrong Answer

Solution code:
n = int(input())
d = list(map(int,input().split()))
m = 998244353
import collections
c = collections.Counter(d)
if c[0] == 1:
    ans = 1
else:
    ans = 0
d = sorted(d)
for i in range(1,n):
    ans *= c[d[i]-1]
    ans %= m
print(ans)

Submission status: Wrong Answer

Solution code:
n=int(input())
d=list(map(int,input().split()))
mod=998244353
from collections import Counter

c=dict(Counter(d))
c=sorted(c.items(),key=lambda x: x[0])


if c[0][0]!=0:
    print(0)
    exit(0)

if c[0][1]!=1:
    print(0)
    exit(0)

for i in range(1,len(c)):
    if c[i][0]!=c[i-1][0]+1:
        print(0)
        exit(0)

ans=1
for i in range(1,len(c)):
    ans*=c[i-1][1]**(c[i][1])

print(ans%mod)

Submission status: Wrong Answer

Solution code:
n=int(input())
d=list(map(int,input().split()))
mod=998244353
from collections import Counter

c=dict(Counter(d))
c=sorted(c.items(),key=lambda x: x[0])


if c[0][0]!=0 or (c[0][0]==0 and c[0][1]!=1):
    print(0)
    exit(0)

ans=1
for i in range(1,len(c)):
    if c[i][1]==0 or c[i][0]!=c[i-1][0]+1:
        ans=0
        break
    elif c[i][0]!=1:
        ans*=c[i-1][1]**(c[i][1])

print(ans%mod)

Submission status: Wrong Answer

Solution code:
n=int(input())
d=list(map(int,input().split()))
mod=998244353
from collections import Counter

c=dict(Counter(d))
c=sorted(c.items(),key=lambda x: x[0])


if c[0][0]!=0 or (c[0][0]==0 and c[0][1]!=1):
    print(0)
    exit(0)

ans=1
for i in range(len(c)):
    if c[i][0]!=0 and c[i][1]==0:
        ans=0
        break
    elif i>1 and c[i][0]!=c[i-1][0]+1:
        ans=0
        break
    elif c[i][0]!=1 and c[i][0]!=0:
        ans*=c[i-1][1]**(c[i][1])

print(ans%mod)

Submission status: Wrong Answer

Solution code:
n=int(input())
d=list(map(int,input().split()))
mod=998244353
from collections import Counter

c=dict(Counter(d))
c=sorted(c.items(),key=lambda x: x[0])



if c[0][0]==0 and c[0][1]!=1:
    print(0)
    exit(0)

ans=1
for i in range(len(c)):
    if c[i][0]!=0 and c[i][1]==0:
        ans=0
        break
    elif c[i][0]!=1 and c[i][0]!=0:
        ans*=c[i-1][1]**(c[i][1])

print(ans%mod)

Submission status: Wrong Answer

Solution code:
N = int(input())
D = list(map(int, input().split()))

from collections import Counter
import sys

C = Counter(D)

if C[0] != 1:
    print(0)
elif D[0] != 0:
    print(0)
else:
    CL = sorted(C.items())
    num_prev = -1
    val_prev = 1
    ans = 1
    for item in CL:
        num = item[0]
        val = item[1]
        if num != num_prev + 1:
            print(0)
            sys.exit()
        else:
            ans *= val_prev**val
            num_prev = num
            val_prev = val
    print(ans)

Submission status: Wrong Answer

Solution code:
N = int(input())
D = list(map(int, input().split()))

from collections import Counter
import sys

C = Counter(D)

if C[0] != 1:
    print(0)
else:
    CL = sorted(C.items())
    num_prev = -1
    val_prev = 1
    ans = 1
    for item in CL:
        num = item[0]
        val = item[1]
        if num != num_prev + 1:
            print(0)
            sys.exit()
        else:
            ans *= val_prev**val
            num_prev = num
            val_prev = val
    print(ans)

Submission status: Wrong Answer

Solution code:
import sys
import heapq
import re
from itertools import permutations
from bisect import bisect_left, bisect_right
from collections import Counter, deque
from math import factorial, sqrt, ceil, gcd
from functools import lru_cache, reduce
from decimal import Decimal
from operator import mul

INF = 1 << 60
MOD = 1000000007
sys.setrecursionlimit(10 ** 7)


# UnionFind
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

# ダイクストラ
def dijkstra_heap(s, edge, n):
    #始点sから各頂点への最短距離
    d = [10**20] * n
    used = [True] * n #True:未確定
    d[s] = 0
    used[s] = False
    edgelist = []
    for a,b in edge[s]:
        heapq.heappush(edgelist,a*(10**6)+b)
    while len(edgelist):
        minedge = heapq.heappop(edgelist)
        #まだ使われてない頂点の中から最小の距離のものを探す
        if not used[minedge%(10**6)]:
            continue
        v = minedge%(10**6)
        d[v] = minedge//(10**6)
        used[v] = False
        for e in edge[v]:
            if used[e[1]]:
                heapq.heappush(edgelist,(e[0]+d[v])*(10**6)+e[1])
    return d

# 素因数分解
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr

# 組合せnCr
def combinations_count(n, r):
    if n < r:
        return 0
    r = min(r, n - r)
    numer = reduce(mul, range(n, n - r, -1), 1)
    denom = reduce(mul, range(1, r + 1), 1)
    return numer // denom

# 2数の最小公倍数
def lcm(x, y):
    return (x * y) // gcd(x, y)

# リストの要素の最小公倍数
def lcm_list(numbers):
    return reduce(lcm, numbers, 1)

# リストの要素の最大公約数
def gcd_list(numbers):
    return reduce(gcd, numbers)

# 素数判定
def is_prime(n):
    if n <= 1:
        return False
    p = 2
    while True:
        if p ** 2 > n:
            break
        if n % p == 0:
            return False
        p += 1
    return True


# limit以下の素数を列挙
def eratosthenes(limit):
    A = [i for i in range(2, limit+1)]
    P = []

    while True:
        prime = min(A)
        
        if prime > sqrt(limit):
            break
            
        P.append(prime)
            
        i = 0
        while i < len(A):
            if A[i] % prime == 0:
                A.pop(i)
                continue
            i += 1
            
    for a in A:
        P.append(a)
            
    return P

# 同じものを含む順列
def permutation_with_duplicates(L):

    if L == []:
        return [[]]

    else:
        ret = []

        # set（集合）型で重複を削除、ソート
        S = sorted(set(L))

        for i in S:

            data = L[:]
            data.remove(i)

            for j in permutation_with_duplicates(data):
                ret.append([i] + j)

        return ret

def make_divisors(n):
    lower_divisors , upper_divisors = [], []
    i = 1
    while i*i <= n:
        if n % i == 0:
            lower_divisors.append(i)
            if i != n // i:
                upper_divisors.append(n//i)
        i += 1
    return lower_divisors + upper_divisors[::-1]

# ここから書き始める
n = int(input())
d = sorted(list(map(int, input().split())))


cnt = [0 for i in range(n)]
for i in d:
    if i >= n:
        print(0)
        sys.exit()
    cnt[i] += 1
# print("cnt =", cnt)

ans = 1
flag = True
for i in range(n):
    if i == 0:
        if cnt[i] != 1:
            ans = 0
            break
    elif cnt[i] == 0:
        flag = False
    elif not flag:
        ans = 0
        break
    else:
        ans *= cnt[i - 1] ** cnt[i]

print(ans % 998244353)

# ans = 1
# cnt1 = 0
# cnt2 = 0
# for i in range(n):
#     if i == 0:
#         if d[i] > 0:
#             ans = 0
#             break
#         else:
#             cnt2 += 1
#     else:
#         if d[i] > d[i - 1] + 1:
#             ans = 0
#             break
#         elif d[i] == d[i - 1] + 1:
#             if cnt1 > 0:
#                 ans *= cnt1 ** cnt2
#             cnt1 = cnt2
#             cnt2 = 1
#         else:
#             cnt2 += 1
# # if cnt1 > 0:
# ans *= cnt1 ** cnt2
# print(ans)

Submission status: Wrong Answer

Solution code:
import sys
import heapq
import re
from itertools import permutations
from bisect import bisect_left, bisect_right
from collections import Counter, deque
from math import factorial, sqrt, ceil, gcd
from functools import lru_cache, reduce
from decimal import Decimal
from operator import mul

INF = 1 << 60
MOD = 1000000007
sys.setrecursionlimit(10 ** 7)


# UnionFind
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

# ダイクストラ
def dijkstra_heap(s, edge, n):
    #始点sから各頂点への最短距離
    d = [10**20] * n
    used = [True] * n #True:未確定
    d[s] = 0
    used[s] = False
    edgelist = []
    for a,b in edge[s]:
        heapq.heappush(edgelist,a*(10**6)+b)
    while len(edgelist):
        minedge = heapq.heappop(edgelist)
        #まだ使われてない頂点の中から最小の距離のものを探す
        if not used[minedge%(10**6)]:
            continue
        v = minedge%(10**6)
        d[v] = minedge//(10**6)
        used[v] = False
        for e in edge[v]:
            if used[e[1]]:
                heapq.heappush(edgelist,(e[0]+d[v])*(10**6)+e[1])
    return d

# 素因数分解
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr

# 組合せnCr
def combinations_count(n, r):
    if n < r:
        return 0
    r = min(r, n - r)
    numer = reduce(mul, range(n, n - r, -1), 1)
    denom = reduce(mul, range(1, r + 1), 1)
    return numer // denom

# 2数の最小公倍数
def lcm(x, y):
    return (x * y) // gcd(x, y)

# リストの要素の最小公倍数
def lcm_list(numbers):
    return reduce(lcm, numbers, 1)

# リストの要素の最大公約数
def gcd_list(numbers):
    return reduce(gcd, numbers)

# 素数判定
def is_prime(n):
    if n <= 1:
        return False
    p = 2
    while True:
        if p ** 2 > n:
            break
        if n % p == 0:
            return False
        p += 1
    return True


# limit以下の素数を列挙
def eratosthenes(limit):
    A = [i for i in range(2, limit+1)]
    P = []

    while True:
        prime = min(A)
        
        if prime > sqrt(limit):
            break
            
        P.append(prime)
            
        i = 0
        while i < len(A):
            if A[i] % prime == 0:
                A.pop(i)
                continue
            i += 1
            
    for a in A:
        P.append(a)
            
    return P

# 同じものを含む順列
def permutation_with_duplicates(L):

    if L == []:
        return [[]]

    else:
        ret = []

        # set（集合）型で重複を削除、ソート
        S = sorted(set(L))

        for i in S:

            data = L[:]
            data.remove(i)

            for j in permutation_with_duplicates(data):
                ret.append([i] + j)

        return ret

def make_divisors(n):
    lower_divisors , upper_divisors = [], []
    i = 1
    while i*i <= n:
        if n % i == 0:
            lower_divisors.append(i)
            if i != n // i:
                upper_divisors.append(n//i)
        i += 1
    return lower_divisors + upper_divisors[::-1]

# ここから書き始める
n = int(input())
d = sorted(list(map(int, input().split())))

m = max(d)
cnt = [0 for i in range(m + 1)]
for i in d:
    cnt[i] += 1
# print("cnt =", cnt)

ans = 1
flag = True
for i in range(m + 1):
    if i == 0:
        if cnt[i] != 1:
            ans = 0
            break
    elif cnt[i] == 0:
        flag = False
    elif not flag:
        ans = 0
        break
    elif cnt[i] >= 1:
        ans *= cnt[i - 1] ** cnt[i]

print(ans % 998244353)

# ans = 1
# cnt1 = 0
# cnt2 = 0
# for i in range(n):
#     if i == 0:
#         if d[i] > 0:
#             ans = 0
#             break
#         else:
#             cnt2 += 1
#     else:
#         if d[i] > d[i - 1] + 1:
#             ans = 0
#             break
#         elif d[i] == d[i - 1] + 1:
#             if cnt1 > 0:
#                 ans *= cnt1 ** cnt2
#             cnt1 = cnt2
#             cnt2 = 1
#         else:
#             cnt2 += 1
# # if cnt1 > 0:
# ans *= cnt1 ** cnt2
# print(ans)

Submission status: Wrong Answer

Solution code:
import sys
import heapq
import re
from itertools import permutations
from bisect import bisect_left, bisect_right
from collections import Counter, deque
from math import factorial, sqrt, ceil, gcd
from functools import lru_cache, reduce
from decimal import Decimal
from operator import mul

INF = 1 << 60
MOD = 1000000007
sys.setrecursionlimit(10 ** 7)


# UnionFind
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

# ダイクストラ
def dijkstra_heap(s, edge, n):
    #始点sから各頂点への最短距離
    d = [10**20] * n
    used = [True] * n #True:未確定
    d[s] = 0
    used[s] = False
    edgelist = []
    for a,b in edge[s]:
        heapq.heappush(edgelist,a*(10**6)+b)
    while len(edgelist):
        minedge = heapq.heappop(edgelist)
        #まだ使われてない頂点の中から最小の距離のものを探す
        if not used[minedge%(10**6)]:
            continue
        v = minedge%(10**6)
        d[v] = minedge//(10**6)
        used[v] = False
        for e in edge[v]:
            if used[e[1]]:
                heapq.heappush(edgelist,(e[0]+d[v])*(10**6)+e[1])
    return d

# 素因数分解
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr

# 組合せnCr
def combinations_count(n, r):
    if n < r:
        return 0
    r = min(r, n - r)
    numer = reduce(mul, range(n, n - r, -1), 1)
    denom = reduce(mul, range(1, r + 1), 1)
    return numer // denom

# 2数の最小公倍数
def lcm(x, y):
    return (x * y) // gcd(x, y)

# リストの要素の最小公倍数
def lcm_list(numbers):
    return reduce(lcm, numbers, 1)

# リストの要素の最大公約数
def gcd_list(numbers):
    return reduce(gcd, numbers)

# 素数判定
def is_prime(n):
    if n <= 1:
        return False
    p = 2
    while True:
        if p ** 2 > n:
            break
        if n % p == 0:
            return False
        p += 1
    return True


# limit以下の素数を列挙
def eratosthenes(limit):
    A = [i for i in range(2, limit+1)]
    P = []

    while True:
        prime = min(A)
        
        if prime > sqrt(limit):
            break
            
        P.append(prime)
            
        i = 0
        while i < len(A):
            if A[i] % prime == 0:
                A.pop(i)
                continue
            i += 1
            
    for a in A:
        P.append(a)
            
    return P

# 同じものを含む順列
def permutation_with_duplicates(L):

    if L == []:
        return [[]]

    else:
        ret = []

        # set（集合）型で重複を削除、ソート
        S = sorted(set(L))

        for i in S:

            data = L[:]
            data.remove(i)

            for j in permutation_with_duplicates(data):
                ret.append([i] + j)

        return ret

def make_divisors(n):
    lower_divisors , upper_divisors = [], []
    i = 1
    while i*i <= n:
        if n % i == 0:
            lower_divisors.append(i)
            if i != n // i:
                upper_divisors.append(n//i)
        i += 1
    return lower_divisors + upper_divisors[::-1]

# ここから書き始める
n = int(input())
d = sorted(list(map(int, input().split())))

m = max(d)
cnt = [0 for i in range(m + 1)]
for i in d:
    cnt[i] += 1
print("cnt =", cnt)

ans = 1
flag = True
for i in range(m + 1):
    if i == 0:
        if cnt[i] != 1:
            ans = 0
            break
    elif cnt[i] == 0:
        flag = False
    elif not flag:
        ans = 0
        break
    elif cnt[i] >= 1:
        ans *= cnt[i - 1] ** cnt[i]

print(ans % 998244353)

# ans = 1
# cnt1 = 0
# cnt2 = 0
# for i in range(n):
#     if i == 0:
#         if d[i] > 0:
#             ans = 0
#             break
#         else:
#             cnt2 += 1
#     else:
#         if d[i] > d[i - 1] + 1:
#             ans = 0
#             break
#         elif d[i] == d[i - 1] + 1:
#             if cnt1 > 0:
#                 ans *= cnt1 ** cnt2
#             cnt1 = cnt2
#             cnt2 = 1
#         else:
#             cnt2 += 1
# # if cnt1 > 0:
# ans *= cnt1 ** cnt2
# print(ans)

Submission status: Wrong Answer

Solution code:
import sys
import heapq
import re
from itertools import permutations
from bisect import bisect_left, bisect_right
from collections import Counter, deque
from math import factorial, sqrt, ceil, gcd
from functools import lru_cache, reduce
from decimal import Decimal
from operator import mul

INF = 1 << 60
MOD = 1000000007
sys.setrecursionlimit(10 ** 7)


# UnionFind
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

# ダイクストラ
def dijkstra_heap(s, edge, n):
    #始点sから各頂点への最短距離
    d = [10**20] * n
    used = [True] * n #True:未確定
    d[s] = 0
    used[s] = False
    edgelist = []
    for a,b in edge[s]:
        heapq.heappush(edgelist,a*(10**6)+b)
    while len(edgelist):
        minedge = heapq.heappop(edgelist)
        #まだ使われてない頂点の中から最小の距離のものを探す
        if not used[minedge%(10**6)]:
            continue
        v = minedge%(10**6)
        d[v] = minedge//(10**6)
        used[v] = False
        for e in edge[v]:
            if used[e[1]]:
                heapq.heappush(edgelist,(e[0]+d[v])*(10**6)+e[1])
    return d

# 素因数分解
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr

# 組合せnCr
def combinations_count(n, r):
    if n < r:
        return 0
    r = min(r, n - r)
    numer = reduce(mul, range(n, n - r, -1), 1)
    denom = reduce(mul, range(1, r + 1), 1)
    return numer // denom

# 2数の最小公倍数
def lcm(x, y):
    return (x * y) // gcd(x, y)

# リストの要素の最小公倍数
def lcm_list(numbers):
    return reduce(lcm, numbers, 1)

# リストの要素の最大公約数
def gcd_list(numbers):
    return reduce(gcd, numbers)

# 素数判定
def is_prime(n):
    if n <= 1:
        return False
    p = 2
    while True:
        if p ** 2 > n:
            break
        if n % p == 0:
            return False
        p += 1
    return True


# limit以下の素数を列挙
def eratosthenes(limit):
    A = [i for i in range(2, limit+1)]
    P = []

    while True:
        prime = min(A)
        
        if prime > sqrt(limit):
            break
            
        P.append(prime)
            
        i = 0
        while i < len(A):
            if A[i] % prime == 0:
                A.pop(i)
                continue
            i += 1
            
    for a in A:
        P.append(a)
            
    return P

# 同じものを含む順列
def permutation_with_duplicates(L):

    if L == []:
        return [[]]

    else:
        ret = []

        # set（集合）型で重複を削除、ソート
        S = sorted(set(L))

        for i in S:

            data = L[:]
            data.remove(i)

            for j in permutation_with_duplicates(data):
                ret.append([i] + j)

        return ret

def make_divisors(n):
    lower_divisors , upper_divisors = [], []
    i = 1
    while i*i <= n:
        if n % i == 0:
            lower_divisors.append(i)
            if i != n // i:
                upper_divisors.append(n//i)
        i += 1
    return lower_divisors + upper_divisors[::-1]

# ここから書き始める
n = int(input())
d = sorted(list(map(int, input().split())))

m = max(d)
cnt = [0 for i in range(m + 1)]
for i in d:
    cnt[i] += 1
# print("cnt =", cnt)

ans = 1
flag = True
for i in range(m + 1):
    if i == 0:
        if cnt[i] != 1:
            ans = 0
            break
    elif cnt[i] == 0:
        flag = False
    elif not flag:
        ans = 0
        break
    elif cnt[i] >= 1:
        ans *= cnt[i - 1] ** cnt[i]

print(ans)

# ans = 1
# cnt1 = 0
# cnt2 = 0
# for i in range(n):
#     if i == 0:
#         if d[i] > 0:
#             ans = 0
#             break
#         else:
#             cnt2 += 1
#     else:
#         if d[i] > d[i - 1] + 1:
#             ans = 0
#             break
#         elif d[i] == d[i - 1] + 1:
#             if cnt1 > 0:
#                 ans *= cnt1 ** cnt2
#             cnt1 = cnt2
#             cnt2 = 1
#         else:
#             cnt2 += 1
# # if cnt1 > 0:
# ans *= cnt1 ** cnt2
# print(ans)