Harryxun/testdata huggingface dataset:
Buggy python submission (verdict: Runtime Error):
n=int(input())
mod=10**9+7
print((pow(10,n,mod)-2*pow(9,n,mod)+pow(8,n,mod)%mod)

Fixed submission:
n=int(input())
mod=10**9+7
print((pow(10,n,mod)-2*pow(9,n,mod)+pow(8,n,mod))%mod)
Buggy python submission (verdict: Runtime Error):
n,x,t=map(int,input().split())
    print(ceil(n/x)*t)

Fixed submission:
import os
import sys
from io import BytesIO, IOBase
from math import ceil
def main():
    n,x,t=map(int,input().split())
    print(ceil(n/x)*t)
# region fastio
BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")

if __name__ == "__main__":
    main()
Buggy python submission (verdict: Time Limit Exceeded):
x = int(input())
if x % 2 == 0:
    print(-1)
    exit()
s = 7
cnt = 1
while True:
    if s % x == 0:
        print(cnt)
        break
    s = s * 10 + 7
    cnt += 1


Fixed submission:
x = int(input())
cnt = 1
mod = 7

for i in range(x):
    if mod % x == 0:
        print(cnt)
        exit()
    mod = (10 * mod + 7) % x
    cnt += 1
print(-1)
Buggy python submission (verdict: Runtime Error):
a,b = input().split()
print(a * b)

Fixed submission:
a, b = map(int, input().split())

print(a*b)
Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())
a = list(map(int, input().split()))
a.sort(reverse = True)
sum = 1
for i in range(n):
    if(0 in a):
        print(0)
        break
    sum *= a[i]
    if(sum > 10 ** 18):
        print(-1)
        break
else:
    print(sum)


Fixed submission:
n = int(input())
a = list(map(int, input().split()))
a.sort(reverse = True)
sum = 1
if 0 in a:
    print(0)
else:
    for i in range(n):
        sum *= a[i]
        if(sum > 10 ** 18):
            print(-1)
            break
    else:
        print(sum)

Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())
a = list(map(int, input().split()))
a.sort(reverse = True)
sum = 1
for i in range(n):
    sum *= a[i]
    if(sum > 10 ** 18 and 0 not in  a):
        print(-1)
        break
else:
    print(sum)


Fixed submission:
n = int(input())
a = list(map(int, input().split()))
a.sort(reverse = True)
sum = 1
if 0 in a:
    print(0)
else:
    for i in range(n):
        sum *= a[i]
        if(sum > 10 ** 18):
            print(-1)
            break
    else:
        print(sum)

Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())
a = list(map(int,input().split()))
sum = 1
for i in range(n):
    sum *= a[i]

print(sum if sum <= 10 ** 18 else -1)


Fixed submission:
n = int(input())
a = list(map(int, input().split()))
a.sort(reverse = True)
sum = 1
if 0 in a:
    print(0)
else:
    for i in range(n):
        sum *= a[i]
        if(sum > 10 ** 18):
            print(-1)
            break
    else:
        print(sum)
Buggy python submission (verdict: Runtime Error):
s=input()
t=input()
print("Yes" s == t[:-1] else 'No')

Fixed submission:
s=input()
t=input()
print("Yes" if s == t[:-1] else 'No')
Buggy python submission (verdict: Runtime Error):
a, b, c, k = map(int, input().split())
if(k < a):
    pritn(k)
elif(a <= k <= a + b):
    print(a)
else:
    print(a - (k - (a + b)))


Fixed submission:
a, b, c, k = map(int, input().split())
if(k < a):
    print(k)
elif(k <= a + b):
    print(a)
else:
    print(a - (k - (a + b)))
Buggy python submission (verdict: Runtime Error):
import math
a, b, c, d = map(int, input().split())
if math.ceil(c / b) =< math.ceil(a / d):
  print("Yes")
else:
  print("No")


Fixed submission:
import math
a, b, c, d = map(int, input().split())
if math.ceil(c / b) <= math.ceil(a / d):
  print("Yes")
else:
  print("No")

Buggy python submission (verdict: Runtime Error):
import math
a, b, c, d = map(int, input().split())
if math(c / b) < math(a / d):
  print("Yes")
else:
  print("No")

Fixed submission:
import math
a, b, c, d = map(int, input().split())
if math.ceil(c / b) <= math.ceil(a / d):
  print("Yes")
else:
  print("No")

Buggy python submission (verdict: Runtime Error):
a, b, c, d = map(int, input().split())
while 1:
    c -= b
    if(c <= 0):
        print("Yes")
        break
    a -= d:
    if(a <= 0):
        print("No")
        break


Fixed submission:
import math
a, b, c, d = map(int, input().split())
if math.ceil(c / b) <= math.ceil(a / d):
  print("Yes")
else:
  print("No")

Buggy python submission (verdict: Runtime Error):
a, b, c, d = map(int, input().split())
while 1:
    c -= b
    if(a <= 0):
        print("Yes")
        break
    a -= d:
    if(d <= 0):
        print("No")
        break

Fixed submission:
import math
a, b, c, d = map(int, input().split())
if math.ceil(c / b) <= math.ceil(a / d):
  print("Yes")
else:
  print("No")
Buggy python submission (verdict: Runtime Error):
n, k = map(int, input().split())
count == 0
while n >= k:
  n = n // k
  count += 1
print(count)

Fixed submission:
n, k = map(int, input().split())
count = 0
while n >= k:
  n = n // k
  count += 1
print(count+1)
Buggy python submission (verdict: Runtime Error):
str = input()
for i in range(len(str)):
  str[i] = "x"
print(str)

Fixed submission:
str = input()
ans = ""
for i in range(len(str)):
  ans += "x"
print(ans)
Buggy python submission (verdict: Runtime Error):
a = int(input())
print(r**2)

Fixed submission:
r = int(input())
print(r**2)
Buggy python submission (verdict: Runtime Error):
a, s = input().split()
print(s if int(a) >= 3200 else "red")

Fixed submission:
a = int(input())
s = input()
print(s if a >= 3200 else "red")
Buggy python submission (verdict: Runtime Error):
r = int(input())
print(3 * a * a)

Fixed submission:
r = int(input())
print(3*r**2)

Buggy python submission (verdict: Runtime Error):
r = int(input())
print(3 * a**2)

Fixed submission:
r = int(input())
print(3*r**2)
Buggy python submission (verdict: Runtime Error):
import math
n, d = map(int, input().split())
print(math.ceil(n / (2d + 1)))

Fixed submission:
import math
n, d = map(int, input().split())
print(math.ceil(n / (2 * d + 1)))
Buggy python submission (verdict: Runtime Error):
a, b, c = input().split("/")
print("TBD" if b > 4 else "Heisei")

Fixed submission:
a, b, c = input().split("/")
print("TBD" if int(b) > 4 else "Heisei")
Buggy python submission (verdict: Runtime Error):
r = int(intput())
if r < 1200:
  print("ABC")
elif r < 2800:
  print("ARC")
else:
  print("AGC")

Fixed submission:
a = int(input())
print("AGC" if a >= 2800 else "ARC" if a >= 1200 else "ABC")
Buggy python submission (verdict: Runtime Error):
a = [input() for x in 3]
print(a[0][0] + a[1][1] + a[2][2])

Fixed submission:
a = [input() for x in range(3)]
print(a[0][0] + a[1][1] + a[2][2])
Buggy python submission (verdict: Runtime Error):
a, b, c = map(int, input().split())
print((a - b) % c)

Fixed submission:
a, b, c = [int(input()) for x in range(3)]
print((a - b) % c)
Buggy python submission (verdict: Runtime Error):
s = input()
print(s[::2]

Fixed submission:
s = input()
print(s[::2])
Buggy python submission (verdict: Runtime Error):
a = input()
print("Yes" if a == a.reverse() else "No")

Fixed submission:
a = input()
print("Yes" if a == a[::-1] else "No")
Buggy python submission (verdict: Runtime Error):
a, t = input().split()
print("H" if a == "H" and b =="H" or a == "D" and b == "D" else "D")

Fixed submission:
a, b = input().split()
print("H" if a == "H" and b =="H" or a == "D" and b == "D" else "D")
Buggy python submission (verdict: Runtime Error):
import math
n = int(input())
print(math.factrial(n) % (10**9 + 7))

Fixed submission:
import math
n = int(input())
print(math.factorial(n) % (10**9 + 7))

Buggy python submission (verdict: Runtime Error):
import math
a = int(input())
print(math.factorial(a) /( 10**9 + 7))

Fixed submission:
import math
n = int(input())
print(math.factorial(n) % (10**9 + 7))
Buggy python submission (verdict: Runtime Error):
a = list(map(int, input().split())).sorted()
print('Yes' if a[0] + a[1] == a[2] else 'No')

Fixed submission:
a = list(map(int, input().split()))
a = sorted(a)
print('Yes' if a[0] + a[1] == a[2] else 'No')
Buggy python submission (verdict: Time Limit Exceeded):
import itertools


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

MOD = 1000000007

l = []
for i in range(N):
    l.append(i)

C = itertools.combinations(l, 2)

a = 0
for c in C:
    a += A[c[0]] * A[c[1]] % MOD
    a %= MOD
print(a)

Fixed submission:
N = int(input())
A = list(map(int, input().split()))

MOD = 1000000007

a = 0
b = 0
for i in range(N):
    a += A[i] % MOD
    b += (A[i] ** 2) % MOD
a = a ** 2
ans = (a - b) * pow(2, MOD - 2, MOD) % MOD
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import itertools


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

MOD = 1000000007

l = []
for i in range(N):
    l.append(i)

C = itertools.combinations(l, 2)

a = 0
for c in C:
    a += A[c[0]] % MOD * A[c[1]] % MOD
a %= MOD
print(a)

Fixed submission:
N = int(input())
A = list(map(int, input().split()))

MOD = 1000000007

a = 0
b = 0
for i in range(N):
    a += A[i] % MOD
    b += (A[i] ** 2) % MOD
a = a ** 2
ans = (a - b) * pow(2, MOD - 2, MOD) % MOD
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import itertools


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

MOD = 1000000007

l = []
for i in range(N):
    l.append(i)

C = itertools.combinations(l, 2)

a = 0
for c in C:
    a += (A[c[0]] * A[c[1]]) % MOD
a %= MOD
print(a)

Fixed submission:
N = int(input())
A = list(map(int, input().split()))

MOD = 1000000007

a = 0
b = 0
for i in range(N):
    a += A[i] % MOD
    b += (A[i] ** 2) % MOD
a = a ** 2
ans = (a - b) * pow(2, MOD - 2, MOD) % MOD
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
N, K = list(map(int, input().split()))
A = list(map(int, input().split()))

c = N - K + 1
l = []

for i in range(K, N + 1):
    ans = 1
    for j in range(1, K + 1):
        ans *= A[i - j]
    l.append(ans)

for i in range(c - 1):
    if l[i] < l[i + 1]:
        print("Yes")
    else:
        print("No")

Fixed submission:
N, K = list(map(int, input().split()))
A = list(map(int, input().split()))

c = N - K
l = []

for j in range(K, N):
        l.append(A[j - K])
        l.append(A[j])

L = len(l)
for i in range(0, L, 2):
    if l[i + 1] > l[i]:
        print("Yes")
    else:
        print("No")

Buggy python submission (verdict: Time Limit Exceeded):
N, K = list(map(int, input().split()))
A = list(map(int, input().split()))

c = N - K + 1
l = []

for i in range(K, N + 1):
    ans = 1
    for j in range(1, K + 1):
        ans *= A[i - j]
    l.append(ans)

for i in range(c - 1):
    if l[i] < l[i + 1]:
        print("Yes")
    else:
        print("No")

Fixed submission:
N, K = list(map(int, input().split()))
A = list(map(int, input().split()))

c = N - K
l = []

for j in range(K, N):
        l.append(A[j - K])
        l.append(A[j])

L = len(l)
for i in range(0, L, 2):
    if l[i + 1] > l[i]:
        print("Yes")
    else:
        print("No")
Buggy python submission (verdict: Time Limit Exceeded):
N, K = list(map(int, input().split()))
A = list(map(int, input().split()))

l = [A[0]]
a = A[0] - 1
for _ in range(K):
    if A[a] not in l:
        l.append(A[a])
        a = A[a] - 1
    else:
        a = A[a]
        break
n = len(l)
b = 0
for i in range(n):
    if l[i] == a:
        del l[0:i]
        b = i
        break
T = len(l)
S = (K - b) % T
ans = l[S - 1]

print(ans)


Fixed submission:
N, K = list(map(int, input().split()))
A = list(map(int, input().split()))

l = [A[0]]
s = {A[0]}
a = A[0] - 1
for _ in range(K):
    if A[a] not in s:
        l.append(A[a])
        s.add(A[a])
        a = A[a] - 1
    else:
        a = A[a]
        break
n = len(l)
b = 0
for i in range(n):
    if l[i] == a:
        del l[0:i]
        b = i
        break
T = len(l)
S = (K - b) % T
ans = l[S - 1]

print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = list(map(int, input().split()))

for i in range(1, N + 1):
    print(A.count(i))

Fixed submission:
from collections import Counter


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

c = Counter(A)
for i in range(1, N + 1):
    print(c[i])
Buggy python submission (verdict: Time Limit Exceeded):
N, K = list(map(int, input().split()))
H = list(map(int, input().split()))

if K <= len(H):
    for i in range(K):
        H.remove(max(H))
else:
    H = [0]
ans = sum(H)
print(ans)

Fixed submission:
N, K = list(map(int, input().split()))
H = list(map(int, input().split()))

a = 0
b = 0
if N <= K:
    ans = 0
else:
    a = N - K

H.sort()
for i in range(a):
    b += H[i]
print(b)
Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
P = list(map(int, input().split()))

l = []
m = [P[0]]
for i in range(N):
    if P[i] <= min(m):
        m.append(P[i])
        continue
    else:
        l.append(i)
print(N - len(l))

Fixed submission:
N = int(input())
P = list(map(int, input().split()))

l = []
a = P[0]
for i in range(N):
    if P[i] <= a:
        a = P[i]
        continue
    else:
        l.append(i)
print(N - len(l))

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
P = list(map(int, input().split()))

l = []
for i in range(N):
    for j in range(i + 1):
        if P[i] <= P[j]:
            continue
        else:
            l.append(i)
            break
print(N - len(l))

Fixed submission:
N = int(input())
P = list(map(int, input().split()))

l = []
a = P[0]
for i in range(N):
    if P[i] <= a:
        a = P[i]
        continue
    else:
        l.append(i)
print(N - len(l))
Buggy python submission (verdict: Runtime Error):
    S = input()

    d = {"SUN": 7, "MON": 6, "TUE": 5, "WED": 4, "THU": 3, "FRI": 2, "SAT": 1}
    print(d[S])

Fixed submission:
S = input()

d = {"SUN": 7, "MON": 6, "TUE": 5, "WED": 4, "THU": 3, "FRI": 2, "SAT": 1}
print(d[S])
Buggy python submission (verdict: Time Limit Exceeded):
import itertools


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

C = list(itertools.permutations(V, N))
ans = 0
for c in C:
    a = c[0]
    for i in range(1, N):
        a = (a + c[i]) / 2
    ans = max(ans, a)
print(ans)

Fixed submission:
N = int(input())
V = list(map(int, input().split()))

C = sorted(V)

ans = 0
a = C[0]
for i in range(1, N):
    a = (a + C[i]) / 2
ans = max(ans, a)
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import itertools


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

C = list(itertools.permutations(V, N))
S = set(C)
ans = 0
for s in S:
    a = s[0]
    for i in range(1, N):
        a = (a + s[i]) / 2
    ans = max(ans, a)
print(ans)

Fixed submission:
N = int(input())
V = list(map(int, input().split()))

C = sorted(V)

ans = 0
a = C[0]
for i in range(1, N):
    a = (a + C[i]) / 2
ans = max(ans, a)
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import itertools


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

C = list(itertools.permutations(V, N))

n = len(C)
ans = 0
for c in C:
    for v in range(n):
        a = C[v][0]
        for i in range(1, N):
            a = (a + C[v][i]) / 2
        ans = max(ans, a)
print(ans)

Fixed submission:
N = int(input())
V = list(map(int, input().split()))

C = sorted(V)

ans = 0
a = C[0]
for i in range(1, N):
    a = (a + C[i]) / 2
ans = max(ans, a)
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
S = [None] * N
for i in range(N):
    S[i] = input()

C = []
for s in S:
    C.append(sorted(s))

ans = 0
for i in range(N - 1):
    for j in range(i + 1, N):
        if C[i] == C[j]:
            ans += 1

print(ans)

Fixed submission:
N = int(input())
S = [None] * N
for i in range(N):
    S[i] = input()

C = []
for s in S:
    T = tuple(sorted(s))
    C.append(T)

dic = {}
for i in range(N):
    if C[i] in dic:
        dic[C[i]] += 1
    else:
        dic[C[i]] = 1

ans = 0
for x in dic.values():
    ans += x * (x - 1) // 2
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = [None] * N
for i in range(N):
    A[i] = int(input())

b = max(A)

for i in range(N):
    if A[i] == b:
        a = A[i]
        A[i] = 0
        ans = max(A)
        print(ans)
        A[i] = a
    else:
        print(b)

Fixed submission:
N = int(input())
A = [None] * N
for i in range(N):
    A[i] = int(input())

l = sorted(A)
b = l[-1]
c = l[-2]

for i in range(N):
    if A[i] == b:
        print(c)
    else:
        print(b)

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = [None] * N
for i in range(N):
    A[i] = int(input())

for i in range(N):
    a = A[i]
    A[i] = 0
    ans = max(A)
    print(ans)
    A[i] = a

Fixed submission:
N = int(input())
A = [None] * N
for i in range(N):
    A[i] = int(input())

l = sorted(A)
b = l[-1]
c = l[-2]

for i in range(N):
    if A[i] == b:
        print(c)
    else:
        print(b)
Buggy python submission (verdict: Time Limit Exceeded):
L, R = list(map(int, input().split()))

a = 0
ans = 10 ** 9
for i in range(L, R):
    for j in range(i + 1, R + 1):
        a = (i * j) % 2019
        ans = min(a, ans)
print(ans)

Fixed submission:
L, R = list(map(int, input().split()))

a = 0
ans = 10 ** 9
r = min((L + 2018), R)

for i in range(L, r):
    n = min((i + 2019), R)
    for j in range(i + 1, n + 1):
        a = (i * j) % 2019
        # print(a)
        ans = min(a, ans)
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
N, M = list(map(int, input().split()))
L = [None] * M
R = [None] * M
for i in range(M):
    L[i], R[i] = list(map(int, input().split()))

l = [0] * N
for i in range(M):
    for j in range(L[i], R[i] + 1):
        l[j - 1] += 1
a = 0
for i in range(N):
    if l[i] == M:
        a += 1
print(a)

Fixed submission:
N, M = list(map(int, input().split()))
L = [None] * M
R = [None] * M
for i in range(M):
    L[i], R[i] = list(map(int, input().split()))

l = [L[0], R[0]] 
for i in range(1, M):
    if L[i] > l[0]:
        l[0] = L[i]
    if R[i] < l[1]:
        l[1] = R[i]

if l[0] <= l[1]:
    ans = l[1] - l[0] + 1
else:
    ans = 0
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
import itertools

N = int(input())
V = list(map(int, input().split()))
C = list(map(int, input().split()))

n = [i for i in range(N)]
ind = []
for i in range(1, N + 1):
    ind += list(itertools.combinations(n, i))

# print(ind)

M = len(ind)
ans = 0
for val in ind:
    X = 0
    Y = 0
    for v in val:
        X += V[v]
        Y += C[v]
        c = X - Y
    ans = max(ans, c)
print(ans)

Fixed submission:
N = int(input())
V = list(map(int, input().split()))
C = list(map(int, input().split()))

ans = 0
for i in range(N):
    X = V[i] - C[i]
    if X > 0:
        ans += X
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
N, W = list(map(int, input().split()))
w, v = [None] * N, [None] * N
for i in range(N):
    w[i], v[i] = list(map(int, input().split()))


dp = [[0] * (W + 1) for _ in range(N + 1)]
for i in range(1, N + 1):
    for j in range(W + 1):
        if w[i - 1] <= j:
            dp[i][j] = max(dp[i - 1][j], v[i - 1] + dp[i - 1][j - w[i - 1]])
        else:
            dp[i][j] = dp[i - 1][j]

ans = max(dp[N])
print(ans)
        

Fixed submission:
N, W = list(map(int, input().split()))
w, v = [None] * N, [None] * N
for i in range(N):
    w[i], v[i] = list(map(int, input().split()))


dp = [[0] * (W + 1) for _ in range(N + 1)]
for i in range(1, N + 1):
    for j in range(W + 1):
        if w[i - 1] <= j:
            dp[i][j] = max(dp[i - 1][j], v[i - 1] + dp[i - 1][j - w[i - 1]])
        else:
            dp[i][j] = dp[i - 1][j]

ans = max(dp[N])
print(ans)
Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
p = list(map(float, input().split()))

dp = [[0.0] * (N + 1) for _ in range(N + 1)]
dp[1][0] = 1 - p[0]
dp[1][1] = p[0]
for i in range(2, N + 1):
    for j in range(N + 1):
        if j == 0:
            dp[i][j] = dp[i - 1][j] * (1 - p[i - 1])
        else:
            dp[i][j] = dp[i - 1][j] * (1 - p[i - 1]) + dp[i - 1][j - 1] * p[i - 1]
M = N // 2 + 1
ans = 0
for i in range(M, N + 1):
    ans += dp[-1][i]
print(ans)

Fixed submission:
N = int(input())
p = list(map(float, input().split()))

dp = [[0.0] * (N + 1) for _ in range(N + 1)]
dp[1][0] = 1 - p[0]
dp[1][1] = p[0]
for i in range(2, N + 1):
    for j in range(N + 1):
        if j == 0:
            dp[i][j] = dp[i - 1][j] * (1 - p[i - 1])
        else:
            dp[i][j] = dp[i - 1][j] * (1 - p[i - 1]) + dp[i - 1][j - 1] * p[i - 1]
M = N // 2 + 1
ans = 0
for i in range(M, N + 1):
    ans += dp[-1][i]
print(ans)
Buggy python submission (verdict: Runtime Error):
n = int(input())
A = sorted(list(map(int, input().split())))
M = 10**6 + 1
L = [0]*M
ans = 0
for a in A:
    L[a] += 1
    if L[a] == 1:
        # k>=2として k*aは全て不適
        for i in range(2*a, M+1, a):
            L[i] += 2
# flagの数が答え
print(L.count(1))

Fixed submission:
n = int(input())
A = sorted(list(map(int, input().split())))
M = 10**6 + 1
L = [0]*M
for a in A:
    L[a] += 1
    if L[a] == 1:
        # k>=2として k*aは全て不適
        for i in range(2*a, M, a):
            L[i] += 2
# flagの数が答え
print(L.count(1))

Buggy python submission (verdict: Runtime Error):
n = int(input())
A = sorted(list(map(int, input().split())))
M = 2 * 10**5 + 1
L = [0]*M
ans = 0
for a in A:
    L[a] += 1
    if L[a] == 1:
        # k>=2として k*aは全て不適
        for i in range(2*a, M, a):
            L[i] += 2
# flagの数が答え
print(L.count(1))

Fixed submission:
n = int(input())
A = sorted(list(map(int, input().split())))
M = 10**6 + 1
L = [0]*M
for a in A:
    L[a] += 1
    if L[a] == 1:
        # k>=2として k*aは全て不適
        for i in range(2*a, M, a):
            L[i] += 2
# flagの数が答え
print(L.count(1))

Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())
A = sorted(list(map(int, input().split())))
flags = [1] * n
for i, a in enumerate(A):
    if flags[i]:
        for j, f in enumerate(flags[i+1:], i+1):
            if a == A[j]:
                flags[i] = 0
                flags[j] = 0
            if A[j] % a == 0:
                flags[j] = 0
print(sum(flags))

Fixed submission:
n = int(input())
A = sorted(list(map(int, input().split())))
M = 10**6 + 1
L = [0]*M
for a in A:
    L[a] += 1
    if L[a] == 1:
        # k>=2として k*aは全て不適
        for i in range(2*a, M, a):
            L[i] += 2
# flagの数が答え
print(L.count(1))

Buggy python submission (verdict: Time Limit Exceeded):
n = int(input())
A = sorted(list(map(int, input().split())))
flags = [1] * n
for i in range(1, n):
    for j in range(i):
        if A[i] == A[j]:
            flags[i] = 0
            flags[j] = 0
        if A[i] % A[j] == 0:
            flags[i] = 0
            break
print(sum(flags))

Fixed submission:
n = int(input())
A = sorted(list(map(int, input().split())))
M = 10**6 + 1
L = [0]*M
for a in A:
    L[a] += 1
    if L[a] == 1:
        # k>=2として k*aは全て不適
        for i in range(2*a, M, a):
            L[i] += 2
# flagの数が答え
print(L.count(1))