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:
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)

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())))

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
ans *= cnt1 ** cnt2
print(ans)

Submission status: Wrong Answer

Solution code:
#import sys
#import numpy as np
import math
#import itertools
#from fractions import Fraction
#import itertools
from collections import deque
from collections import Counter
#import heapq
#from fractions  import gcd
#input=sys.stdin.readline
#import bisect

Mod=998244353

n=int(input())
d=list(map(int,input().split()))
c=Counter(d)
ans=1
for i in c:
  if i==0:
    if c[i]!=1:
      print(0)
      exit()
  else:
    if i-1 not in c:
      print(0)
      exit()
    else:
      ans*=pow(c[i-1],c[i],Mod)
      ans%=Mod
print(ans)

Submission status: Wrong Answer

Solution code:
#import sys
#import numpy as np
import math
#import itertools
#from fractions import Fraction
#import itertools
from collections import deque
from collections import Counter
#import heapq
#from fractions  import gcd
#input=sys.stdin.readline
#import bisect

Mod=998244353
M=10**7 #書き換え
fac=[0]*M
finv=[0]*M
inv=[0]*M

#finvに逆元、facに階乗のmod
def COMinit():
  fac[0]=fac[1]=1
  finv[0]=finv[1]=1
  inv[1]=1
  for i in range(2,M):
    fac[i]=(fac[i-1]*i%Mod)%Mod
    inv[i]=Mod-inv[Mod%i]*(Mod//i) %Mod
    finv[i]=(finv[i-1]*inv[i]%Mod)%Mod
def COM(n,k):
  if n<k:
    return 0
  if n<0 or k<0:
    return 0
  return (fac[n]*(finv[k]*finv[n-k]%Mod)%Mod)%Mod

COMinit()

n=int(input())
d=list(map(int,input().split()))
c=Counter(d)
ans=1
for i in c:
  if i==0:
    if c[i]!=1:
      print(0)
      exit()
  else:
    if i-1 not in c:
      print(0)
      exit()
    else:
      ans*=pow(c[i-1],c[i],Mod)
      ans%=Mod
print(ans)

Submission status: Wrong Answer

Solution code:
from collections import Counter

N = input()
D_list = list(map(int, input().split()))

max_D = max(D_list)
cnt_dic = dict(Counter(D_list))

if (D_list[0] == 0) & (cnt_dic.get(0) == 1):
    ans = 1
    for n in range(1, max_D + 1):
        ans *= cnt_dic.get(n - 1, 0)  ** cnt_dic.get(n, 1)
    print(ans)
else: 
    print(0)

Submission status: Wrong Answer

Solution code:
N=int(input())
D=list(map(int,input().split()))
mod=998244353
D.sort(reverse=True)
d=D.pop(-1)
if d!=0:
  print(0);exit()

ans=1
l=1
k=1
bef=0
while len(D)!=0:
  d=D.pop(-1)
  if d==0:
    print(0);exit()
  
  if bef==d:
    l+=1
  elif bef+1==d:
    k=l
    l=1
  else:
    print(0);exit()
    
  ans*=k
  ans%=mod
  bef=d
print(ans)

Submission status: Wrong Answer

Solution code:
N=int(input())
D=list(map(int,input().split()))
mod=998244353
D.sort()

bef=1
l=1
ans=1
for i,d in enumerate(D):
  if i==0:
    if d!=0:
      print(0);exit()
  elif d==0:
    print(0);exit()
  else :
    if D[i-1]==d:
      l+=1
    elif D[i-1]+1!=d:
      print(0);exit()
    else:
      bef=l
      l=1
    ans*=bef
    ans%=mod
    

print(ans)

Submission status: Wrong Answer

Solution code:
N=int(input())
D=list(map(int,input().split()))
mod=998244353
D.sort()

bef=1
l=1
ans=1
for i,d in enumerate(D):
  if i==0:
    if d!=0:
      print(0);exit()
  elif d==0:
    print(0);exit()
  
  else :
    if D[i-1]==d:
      l+=1
    else:
      bef=l
      l=1
    ans*=bef
    ans%=mod
    
print(ans)

Submission status: Wrong Answer

Solution code:
import collections 
N=int(input())
D=list(map(int,input().split()))
mod=998244353
D.sort()
E=collections.Counter(D)

bef=1
ans=1
for i in range(len(E.items())):
  e=list(E.items())[i]
  if i==0:
    if e[0]!=0 or e[1]!=1:
      print(0);exit()
  else:
    if i!=e[0]:
      print(0);exit()
  
    ans*=pow(bef,e[1],mod)
    ans%=mod
    bef=e[1]
print(ans)

Submission status: Wrong Answer

Solution code:
# -*- coding: utf-8 -*-
"""
Created on Sat Jun 20 09:37:56 2020

@author: NEC-PCuser
"""

N = int(input())

D = list(map(int, input().split()))


if D[0] != 0:
    print(0)
else:
    n_count = [0] * 100000
    for i in range(N):
        n_count[D[i]] += 1
        
    count = 1
    ans = 1
    for j in range(1, len(n_count)):
        count += n_count[j]
        if n_count[j] == 0:
            break
        else:
            ans = ans * (n_count[j - 1] ** n_count[j])
    if (count != N):
        print(0)
    else:
        print(ans)

Submission status: Wrong Answer

Solution code:
# -*- coding: utf-8 -*-
"""
Created on Sat Jun 20 09:37:56 2020

@author: NEC-PCuser
"""

N = int(input())

D = list(map(int, input().split()))


if D[0] != 0:
    print(0)
else:
    n_count = [0] * 100000
    for i in range(N):
        n_count[D[i]] += 1
        
    count = 1
    ans = 1
    for j in range(1, len(n_count)):
        count += n_count[j]
        if n_count[j] == 0:
            break
        else:
            ans = ans * (n_count[j - 1] ** n_count[j])
    print(ans)

Submission status: Wrong Answer

Solution code:
N=int(input())
D=list(map(int,input().split()))
MOD=998244353
goal=-1
tree=[0]*(N)
ans=1
for i in range(N):
    a=D[i]
    goal=max(a,goal)
    tree[a]+=1
if tree[0]==1:
    for i in range(1,goal+1):
        ans*=pow(tree[i-1],tree[i],MOD)
        ans%=MOD
    print(ans)
else:
    print(0)

Submission status: Wrong Answer

Solution code:
import sys
from collections import Counter

input = sys.stdin.readline

N = int(input())
ans = 1
mod = 998244353
D = list(map(int, input().split()))
if D[0] != 0:
    print(0)
    exit()
D = sorted(Counter(D).items())
tmp = D[0][1]
stream = 0
for n, i in D:
    if stream != n:
        print(0)
        exit()
    if n == 0 and i == 1:
        stream += 1
        continue
    else:
        print(0)
        exit()
    ans *= pow(tmp, i)
    ans %= mod
    tmp = i
    stream += 1
print(ans)

Submission status: Wrong Answer

Solution code:
import sys
from collections import Counter

input = sys.stdin.readline

N = int(input())
ans = 1
mod = 998244353
D = list(map(int, input().split()))
if D[0] != 0:
    print(0)
    exit()
D = sorted(Counter(D).items())
tmp = D[0][1]
stream = 0
for n, i in D:
    if stream != n:
        print(0)
        exit()
    if n == 0:
        stream += 1
        continue
    ans *= pow(tmp, i)
    ans %= mod
    tmp = i
    stream += 1
print(ans)

Submission status: Wrong Answer

Solution code:
import sys
from collections import Counter

input = sys.stdin.readline

N = int(input())
ans = 1
mod = 998244353
D = sorted(Counter(list(map(int, input().split()))).items())
tmp = D[0][1]
stream = 0
for n, i in D:
    if stream != n:
        print(0)
        exit()
    if n == 0:
        stream += 1
        continue
    ans *= pow(tmp, i)
    ans %= mod
    tmp = i
    stream += 1
print(ans)

Submission status: Wrong Answer

Solution code:
import sys
from collections import Counter

input = sys.stdin.readline

N = int(input())
ans = 1
mod = 998244353
D = sorted(Counter(list(map(int, input().split()))).items())
tmp = D[0][1]
stream = 0
for n, i in D:
    if stream != n:
        exit()
    if n == 0:
        stream += 1
        continue
    ans *= pow(tmp, i)
    ans %= mod
    tmp = i
    stream += 1
print(ans)

Submission status: Wrong Answer

Solution code:
import sys
from collections import Counter

input = sys.stdin.readline

N = int(input())
ans = 1
mod = 998244353
D = sorted(Counter(list(map(int, input().split()))).items())
tmp = D[0][1]
stream = -1
for n, i in D:
    if stream + 1 != n:
        print(0)
        exit()
    if n == 0:
        continue
    ans *= pow(tmp, i)
    ans %= mod
    tmp = i
    stream += 1
print(ans)

Submission status: Wrong Answer

Solution code:
# -*- coding: utf-8 -*-

#############
# Libraries #
#############

import sys
input = sys.stdin.readline

import math
#from math import gcd
import bisect
import heapq
from collections import defaultdict
from collections import deque
from collections import Counter
from functools import lru_cache


#############
# Constants #
#############

MOD = 10**9+7
INF = float('inf')
AtoZ = "abcdefghijklmnopqrstuvwxyz"

#############
# Functions #
#############

######INPUT######
def I(): return int(input().strip())
def S(): return input().strip()
def IL(): return list(map(int,input().split()))
def SL(): return list(map(str,input().split()))
def ILs(n): return list(int(input()) for _ in range(n))
def SLs(n): return list(input().strip() for _ in range(n))
def ILL(n): return [list(map(int, input().split())) for _ in range(n)]
def SLL(n): return [list(map(str, input().split())) for _ in range(n)]

######OUTPUT######
def P(arg): print(arg); return
def Y(): print("Yes"); return
def N(): print("No"); return
def E(): exit()
def PE(arg): print(arg); exit()
def YE(): print("Yes"); exit()
def NE(): print("No"); exit()

#####Shorten#####
def DD(arg): return defaultdict(arg)


#####Inverse#####
def inv(n): return pow(n, MOD-2, MOD)

######Combination######
kaijo_memo = []
def kaijo(n):
  if(len(kaijo_memo) > n):
    return kaijo_memo[n]
  if(len(kaijo_memo) == 0):
    kaijo_memo.append(1)
  while(len(kaijo_memo) <= n):
    kaijo_memo.append(kaijo_memo[-1] * len(kaijo_memo) % MOD)
  return kaijo_memo[n]

gyaku_kaijo_memo = []
def gyaku_kaijo(n):
  if(len(gyaku_kaijo_memo) > n):
    return gyaku_kaijo_memo[n]
  if(len(gyaku_kaijo_memo) == 0):
    gyaku_kaijo_memo.append(1)
  while(len(gyaku_kaijo_memo) <= n):
    gyaku_kaijo_memo.append(gyaku_kaijo_memo[-1] * pow(len(gyaku_kaijo_memo),MOD-2,MOD) % MOD)
  return gyaku_kaijo_memo[n]

def nCr(n,r):
  if(n == r):
    return 1
  if(n < r or r < 0):
    return 0
  ret = 1
  ret = ret * kaijo(n) % MOD
  ret = ret * gyaku_kaijo(r) % MOD
  ret = ret * gyaku_kaijo(n-r) % MOD
  return ret

######Factorization######
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

#####MakeDivisors######
def make_divisors(n):
  divisors = []
  for i in range(1, int(n**0.5)+1):
    if n % i == 0:
      divisors.append(i)
      if i != n // i: 
        divisors.append(n//i)
  divisors.sort()
  return divisors

#####MakePrimes######
def make_primes(N):
  max = int(math.sqrt(N))
  seachList = [i for i in range(2,N+1)]
  primeNum = []
  while seachList[0] <= max:
    primeNum.append(seachList[0])
    tmp = seachList[0]
    seachList = [i for i in seachList if i % tmp != 0]
  primeNum.extend(seachList)
  return primeNum

#####GCD#####
def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

#####LCM#####
def lcm(a, b):
    return a * b // gcd (a, b)

#####BitCount#####
def count_bit(n):
  count = 0
  while n:
    n &= n -1
    count += 1
  return count

#####ChangeBase#####
def base_10_to_n(X, n):
  if X//n:
    return base_10_to_n(X//n, n)+[X%n]
  return [X%n]

def base_n_to_10(X, n):
  return sum(int(str(X)[-i-1])*n**i for i in range(len(str(X))))

#####IntLog#####
def int_log(n, a):
  count = 0
  while n>=a:
    n //= a
    count += 1
  return count

#############
# Main Code #
#############
N = I()
A = IL()
M = max(A)
dic = DD(int)
for a in A:
  dic[a] += 1
if dic[0] != 1 and A[0] != 0:
  print(0)
  exit()
else:
  ans = 1
  for i in range(M):
    ans *= pow(dic[i],dic[i+1])
    ans %= 998244353

print(ans)

Submission status: Wrong Answer

Solution code:
mod = 998244353
n = int(input())
d = list(map(int, input().split()))
d.sort()

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

max_d = max(d)
cnt = [0] * (max_d + 1)

for num in d:
    cnt[num] += 1

if cnt[0] > 1:
    print(0)
    exit(0)

ans = 1

for i in range(1, len(cnt)):
    ans *= pow(cnt[i - 1], cnt[i], mod)
    ans %= mod

print(ans)

Submission status: Wrong Answer

Solution code:
# -*- coding: utf-8 -*-

#############
# Libraries #
#############

import sys
input = sys.stdin.readline

import math
#from math import gcd
import bisect
import heapq
from collections import defaultdict
from collections import deque
from collections import Counter
from functools import lru_cache


#############
# Constants #
#############

MOD = 10**9+7
INF = float('inf')
AtoZ = "abcdefghijklmnopqrstuvwxyz"

#############
# Functions #
#############

######INPUT######
def I(): return int(input().strip())
def S(): return input().strip()
def IL(): return list(map(int,input().split()))
def SL(): return list(map(str,input().split()))
def ILs(n): return list(int(input()) for _ in range(n))
def SLs(n): return list(input().strip() for _ in range(n))
def ILL(n): return [list(map(int, input().split())) for _ in range(n)]
def SLL(n): return [list(map(str, input().split())) for _ in range(n)]

######OUTPUT######
def P(arg): print(arg); return
def Y(): print("Yes"); return
def N(): print("No"); return
def E(): exit()
def PE(arg): print(arg); exit()
def YE(): print("Yes"); exit()
def NE(): print("No"); exit()

#####Shorten#####
def DD(arg): return defaultdict(arg)


#####Inverse#####
def inv(n): return pow(n, MOD-2, MOD)

######Combination######
kaijo_memo = []
def kaijo(n):
  if(len(kaijo_memo) > n):
    return kaijo_memo[n]
  if(len(kaijo_memo) == 0):
    kaijo_memo.append(1)
  while(len(kaijo_memo) <= n):
    kaijo_memo.append(kaijo_memo[-1] * len(kaijo_memo) % MOD)
  return kaijo_memo[n]

gyaku_kaijo_memo = []
def gyaku_kaijo(n):
  if(len(gyaku_kaijo_memo) > n):
    return gyaku_kaijo_memo[n]
  if(len(gyaku_kaijo_memo) == 0):
    gyaku_kaijo_memo.append(1)
  while(len(gyaku_kaijo_memo) <= n):
    gyaku_kaijo_memo.append(gyaku_kaijo_memo[-1] * pow(len(gyaku_kaijo_memo),MOD-2,MOD) % MOD)
  return gyaku_kaijo_memo[n]

def nCr(n,r):
  if(n == r):
    return 1
  if(n < r or r < 0):
    return 0
  ret = 1
  ret = ret * kaijo(n) % MOD
  ret = ret * gyaku_kaijo(r) % MOD
  ret = ret * gyaku_kaijo(n-r) % MOD
  return ret

######Factorization######
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

#####MakeDivisors######
def make_divisors(n):
  divisors = []
  for i in range(1, int(n**0.5)+1):
    if n % i == 0:
      divisors.append(i)
      if i != n // i: 
        divisors.append(n//i)
  divisors.sort()
  return divisors

#####MakePrimes######
def make_primes(N):
  max = int(math.sqrt(N))
  seachList = [i for i in range(2,N+1)]
  primeNum = []
  while seachList[0] <= max:
    primeNum.append(seachList[0])
    tmp = seachList[0]
    seachList = [i for i in seachList if i % tmp != 0]
  primeNum.extend(seachList)
  return primeNum

#####GCD#####
def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

#####LCM#####
def lcm(a, b):
    return a * b // gcd (a, b)

#####BitCount#####
def count_bit(n):
  count = 0
  while n:
    n &= n -1
    count += 1
  return count

#####ChangeBase#####
def base_10_to_n(X, n):
  if X//n:
    return base_10_to_n(X//n, n)+[X%n]
  return [X%n]

def base_n_to_10(X, n):
  return sum(int(str(X)[-i-1])*n**i for i in range(len(str(X))))

#####IntLog#####
def int_log(n, a):
  count = 0
  while n>=a:
    n //= a
    count += 1
  return count

#############
# Main Code #
#############
N = I()
A = IL()
M = max(A)
dic = DD(int)
for a in A:
  dic[a] += 1
if dic[0] != 1:
  print(0)
  exit()
else:
  ans = 1
  for i in range(M):
    ans *= pow(dic[i],dic[i+1])
    ans %= 998244353

print(ans)

Submission status: Wrong Answer

Solution code:
mod = 998244353
n = int(input())
d = list(map(int, input().split()))
d.sort()

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

max_d = max(d)
cnt = [0] * (max_d + 1)

for num in d:
    cnt[num] += 1

if cnt[0] > 1:
    print(0)
    exit(0)

ans = 1

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

print(ans)

Submission status: Wrong Answer

Solution code:
# -*- coding: utf-8 -*-

#############
# Libraries #
#############

import sys
input = sys.stdin.readline

import math
#from math import gcd
import bisect
import heapq
from collections import defaultdict
from collections import deque
from collections import Counter
from functools import lru_cache


#############
# Constants #
#############

MOD = 10**9+7
INF = float('inf')
AtoZ = "abcdefghijklmnopqrstuvwxyz"

#############
# Functions #
#############

######INPUT######
def I(): return int(input().strip())
def S(): return input().strip()
def IL(): return list(map(int,input().split()))
def SL(): return list(map(str,input().split()))
def ILs(n): return list(int(input()) for _ in range(n))
def SLs(n): return list(input().strip() for _ in range(n))
def ILL(n): return [list(map(int, input().split())) for _ in range(n)]
def SLL(n): return [list(map(str, input().split())) for _ in range(n)]

######OUTPUT######
def P(arg): print(arg); return
def Y(): print("Yes"); return
def N(): print("No"); return
def E(): exit()
def PE(arg): print(arg); exit()
def YE(): print("Yes"); exit()
def NE(): print("No"); exit()

#####Shorten#####
def DD(arg): return defaultdict(arg)


#####Inverse#####
def inv(n): return pow(n, MOD-2, MOD)

######Combination######
kaijo_memo = []
def kaijo(n):
  if(len(kaijo_memo) > n):
    return kaijo_memo[n]
  if(len(kaijo_memo) == 0):
    kaijo_memo.append(1)
  while(len(kaijo_memo) <= n):
    kaijo_memo.append(kaijo_memo[-1] * len(kaijo_memo) % MOD)
  return kaijo_memo[n]

gyaku_kaijo_memo = []
def gyaku_kaijo(n):
  if(len(gyaku_kaijo_memo) > n):
    return gyaku_kaijo_memo[n]
  if(len(gyaku_kaijo_memo) == 0):
    gyaku_kaijo_memo.append(1)
  while(len(gyaku_kaijo_memo) <= n):
    gyaku_kaijo_memo.append(gyaku_kaijo_memo[-1] * pow(len(gyaku_kaijo_memo),MOD-2,MOD) % MOD)
  return gyaku_kaijo_memo[n]

def nCr(n,r):
  if(n == r):
    return 1
  if(n < r or r < 0):
    return 0
  ret = 1
  ret = ret * kaijo(n) % MOD
  ret = ret * gyaku_kaijo(r) % MOD
  ret = ret * gyaku_kaijo(n-r) % MOD
  return ret

######Factorization######
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

#####MakeDivisors######
def make_divisors(n):
  divisors = []
  for i in range(1, int(n**0.5)+1):
    if n % i == 0:
      divisors.append(i)
      if i != n // i: 
        divisors.append(n//i)
  divisors.sort()
  return divisors

#####MakePrimes######
def make_primes(N):
  max = int(math.sqrt(N))
  seachList = [i for i in range(2,N+1)]
  primeNum = []
  while seachList[0] <= max:
    primeNum.append(seachList[0])
    tmp = seachList[0]
    seachList = [i for i in seachList if i % tmp != 0]
  primeNum.extend(seachList)
  return primeNum

#####GCD#####
def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

#####LCM#####
def lcm(a, b):
    return a * b // gcd (a, b)

#####BitCount#####
def count_bit(n):
  count = 0
  while n:
    n &= n -1
    count += 1
  return count

#####ChangeBase#####
def base_10_to_n(X, n):
  if X//n:
    return base_10_to_n(X//n, n)+[X%n]
  return [X%n]

def base_n_to_10(X, n):
  return sum(int(str(X)[-i-1])*n**i for i in range(len(str(X))))

#####IntLog#####
def int_log(n, a):
  count = 0
  while n>=a:
    n //= a
    count += 1
  return count

#############
# Main Code #
#############
N = I()
A = IL()
M = max(A)
dic = DD(int)
for a in A:
  dic[a] += 1
if dic[0] != 1:
  print(0)
  exit()
else:
  ans = 1
  for i in range(M):
    ans *= pow(dic[i],dic[i+1])
print(ans)