you strive to join the secret "fraternity of digital Pythagoreans." This ancient society believes that the numbers rule the universe, and special, "perfect" numbers, store the key to the harmony of the world. To prove your value, you must pass the “test of perfection”.
rnThe program receives a sequence of natural numbers to the input, each on a new line. The input ends with the number 0. For each entered number (except 0), it is necessary to determine whether it is perfect.
rncertificate: the completed number & mdash; This is a natural number equal to the sum of all their own divisors (that is, all positive divisors, different from the number itself). For example, for the number 6, their own dividers are 1, 2 and 3. Their amount is 1 + 2 + 3 = 6, which means 6 & mdash; Perfect number.
Entires are supplied to the input of the program, each on a new line. The last number in the sequence is always 0. This number & mdash; A sign of the end of the input, and it is not necessary to process it.
For each number from the input sequence (except 0), the program must derive the word "yes" on a separate line, if the number is completed, and "no", if not.
6
28
12
1
0
Yes
Yes
No
no
EN
RU
EN
RU
def is_perfect(n):
"""
Проверяет, является ли число n совершенным.
"""
# Совершенные числа по определению больше 1.
if n <= 1:
return False
# Начинаем сумму с 1, так как 1 - делитель любого числа.
sum_of_divisors = 1
# Ищем делители до квадратного корня из n.
# Это эффективный способ, так как делители ходят парами.
# Например, для 28: (2, 14), (4, 7).
for i in range(2, int(n**0.5) + 1):
if n % i == 0:
sum_of_divisors += i
# Добавляем парный делитель, если он не равен самому корню
if i * i != n:
sum_of_divisors += n // i
# Сравниваем сумму делителей с исходным числом.
return sum_of_divisors == n
# Основной цикл программы
while True:
try:
number = int(input())
# Если ввели 0, завершаем программу.
if number == 0:
break
if is_perfect(number):
print("YES")
else:
print("NO")
except (ValueError, EOFError):
# Обработка некорректного ввода или конца файла
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