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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question. Suppose you are given a positive integer a. You want to choose some integer b...
instruction
0
3,384
22
6,768
Yes
output
1
3,384
22
6,769
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question. Suppose you are given a positive integer a. You want to choose some integer b...
instruction
0
3,385
22
6,770
Yes
output
1
3,385
22
6,771
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question. Suppose you are given a positive integer a. You want to choose some integer b...
instruction
0
3,386
22
6,772
Yes
output
1
3,386
22
6,773
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question. Suppose you are given a positive integer a. You want to choose some integer b...
instruction
0
3,387
22
6,774
Yes
output
1
3,387
22
6,775
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question. Suppose you are given a positive integer a. You want to choose some integer b...
instruction
0
3,388
22
6,776
No
output
1
3,388
22
6,777
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question. Suppose you are given a positive integer a. You want to choose some integer b...
instruction
0
3,389
22
6,778
No
output
1
3,389
22
6,779
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question. Suppose you are given a positive integer a. You want to choose some integer b...
instruction
0
3,390
22
6,780
No
output
1
3,390
22
6,781
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question. Suppose you are given a positive integer a. You want to choose some integer b...
instruction
0
3,391
22
6,782
No
output
1
3,391
22
6,783
Provide tags and a correct Python 3 solution for this coding contest problem. A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not. The next prime number after x is the smallest prime number greater than x. For example, the nex...
instruction
0
3,847
22
7,694
Tags: brute force Correct Solution: ``` import math def isPrime(n1): if n1 == 0 or n1 == 1: return False s = int(math.sqrt(n1)) for i in range(2, s+1): if n1 % i == 0: return False return True m, n = map(int, input().split()) ans, i, x = m, m+1, [] while i <= n: if isPri...
output
1
3,847
22
7,695
Provide tags and a correct Python 3 solution for this coding contest problem. A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not. The next prime number after x is the smallest prime number greater than x. For example, the nex...
instruction
0
3,848
22
7,696
Tags: brute force Correct Solution: ``` data = list(map(int, input().split())) def eratosthenes(n): # n - число, до которого хотим найти простые числа sieve = list(range(n + 1)) sieve[1] = 0 # без этой строки итоговый список будет содержать единицу for i in sieve: if i > 1: for j...
output
1
3,848
22
7,697
Provide tags and a correct Python 3 solution for this coding contest problem. A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not. The next prime number after x is the smallest prime number greater than x. For example, the nex...
instruction
0
3,849
22
7,698
Tags: brute force Correct Solution: ``` from math import sqrt n, m = map(int, input().split()) def isprime(nn): if nn % 2 == 0: return False for i in range(3, int(sqrt(nn))+1): if nn % i == 0: return False return True for i in range(n+1, m+1): if isprime(i): if i...
output
1
3,849
22
7,699
Provide tags and a correct Python 3 solution for this coding contest problem. A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not. The next prime number after x is the smallest prime number greater than x. For example, the nex...
instruction
0
3,850
22
7,700
Tags: brute force Correct Solution: ``` import math num = input().split() def pcheck(num): num = int(num) for i in range(2, int(math.sqrt(num))+1): if num%i == 0: return False #RETURN FALSE FOR NON PRIME NUMBER return True for i in range(int(num[0])+1, int(num[1])+1): ...
output
1
3,850
22
7,701
Provide tags and a correct Python 3 solution for this coding contest problem. A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not. The next prime number after x is the smallest prime number greater than x. For example, the nex...
instruction
0
3,851
22
7,702
Tags: brute force Correct Solution: ``` def isPrime(num): if num > 1: for i in range(2, num): if num % i == 0: return False return True def nextPrime(num): num += 1 while not isPrime(num): num += 1 return num if __name__ == '__main__': d1, d2 =...
output
1
3,851
22
7,703
Provide tags and a correct Python 3 solution for this coding contest problem. A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not. The next prime number after x is the smallest prime number greater than x. For example, the nex...
instruction
0
3,852
22
7,704
Tags: brute force Correct Solution: ``` def answer(): a = [int(x) for x in input().split()] m = a[0] n = a[1] if m==2: if n==3: return "YES" else: return "NO" elif m==3: if n==5: return "YES" else: return "NO" if m%...
output
1
3,852
22
7,705
Provide tags and a correct Python 3 solution for this coding contest problem. A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not. The next prime number after x is the smallest prime number greater than x. For example, the nex...
instruction
0
3,853
22
7,706
Tags: brute force Correct Solution: ``` def main(): n, m = map(int,input().split(" ")) if m <= n: print("NO") return; for num in range(n+1,100): d = 2 f = 1 while d*d <= num: if num % d == 0: f = 0 break d += 1 ...
output
1
3,853
22
7,707
Provide tags and a correct Python 3 solution for this coding contest problem. A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not. The next prime number after x is the smallest prime number greater than x. For example, the nex...
instruction
0
3,854
22
7,708
Tags: brute force Correct Solution: ``` def calc(n, m): for i in range(n+1, m+1): is_prime = True if i < 2: is_prime = False for j in range(2, i): if i % j == 0: is_prime = False break if is_prime: #print(i) ...
output
1
3,854
22
7,709
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not. The next prime number after x is the smallest pr...
instruction
0
3,855
22
7,710
Yes
output
1
3,855
22
7,711
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not. The next prime number after x is the smallest pr...
instruction
0
3,856
22
7,712
Yes
output
1
3,856
22
7,713
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not. The next prime number after x is the smallest pr...
instruction
0
3,857
22
7,714
Yes
output
1
3,857
22
7,715
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not. The next prime number after x is the smallest pr...
instruction
0
3,858
22
7,716
Yes
output
1
3,858
22
7,717
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not. The next prime number after x is the smallest pr...
instruction
0
3,859
22
7,718
No
output
1
3,859
22
7,719
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not. The next prime number after x is the smallest pr...
instruction
0
3,860
22
7,720
No
output
1
3,860
22
7,721
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not. The next prime number after x is the smallest pr...
instruction
0
3,861
22
7,722
No
output
1
3,861
22
7,723
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not. The next prime number after x is the smallest pr...
instruction
0
3,862
22
7,724
No
output
1
3,862
22
7,725
Provide a correct Python 3 solution for this coding contest problem. For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Input n An integer n (1 ≤ n ≤ 1000000000). Output The number of totatives in a line. Examples Input 6 ...
instruction
0
4,141
22
8,282
"Correct Solution: ``` n = num = int(input()) i=2 while i * i <= n: if n % i ==0: num = num // i * (i - 1) while n % i == 0: n //= i i += 1 if n != 1 : num = num // n * (n - 1) print(num) ```
output
1
4,141
22
8,283
Provide a correct Python 3 solution for this coding contest problem. For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Input n An integer n (1 ≤ n ≤ 1000000000). Output The number of totatives in a line. Examples Input 6 ...
instruction
0
4,142
22
8,284
"Correct Solution: ``` def is_prime(x): # Perform prime number discrimination for odd numbers of 3 or more. return pow(2, x - 1, x) == 1 def solve(): n = int(input()) ans = n if n % 2 == 0: ans -= ans // 2 while n % 2 == 0: n //= 2 d = 3 while d <= n ** 0.5: ...
output
1
4,142
22
8,285
Provide a correct Python 3 solution for this coding contest problem. For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Input n An integer n (1 ≤ n ≤ 1000000000). Output The number of totatives in a line. Examples Input 6 ...
instruction
0
4,143
22
8,286
"Correct Solution: ``` n = int(input()) def prime_factor(n): factor = [] for i in range(2, int(n ** 0.5) + 1): while (n % i == 0): factor.append(i) n //= i if n != 1: factor.append(n) return factor def Euler_phi(n): divisors = prime_factor(n) divisors = set(divisors) res = n for factor in divisors: ...
output
1
4,143
22
8,287
Provide a correct Python 3 solution for this coding contest problem. For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Input n An integer n (1 ≤ n ≤ 1000000000). Output The number of totatives in a line. Examples Input 6 ...
instruction
0
4,144
22
8,288
"Correct Solution: ``` import sys,math n=m=int(input()) c=0 def factorint(N): i=2 fct=[] while i**2<=N: if N%i!=0: i+=1 else: N//=i fct.append(i) if N>1: fct.append(N) return fct l1=factorint(n) l2=list(set(l1)) #print(l1) #print(l2) if l...
output
1
4,144
22
8,289
Provide a correct Python 3 solution for this coding contest problem. For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Input n An integer n (1 ≤ n ≤ 1000000000). Output The number of totatives in a line. Examples Input 6 ...
instruction
0
4,145
22
8,290
"Correct Solution: ``` def factorize(n): a = [] while n % 2 == 0: a.append(2) n //= 2 f = 3 while f * f <= n: if n % f == 0: a.append(f) n //= f else: f += 2 if n != 1: a.append(n) return a def factorize2(n): plist ...
output
1
4,145
22
8,291
Provide a correct Python 3 solution for this coding contest problem. For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Input n An integer n (1 ≤ n ≤ 1000000000). Output The number of totatives in a line. Examples Input 6 ...
instruction
0
4,146
22
8,292
"Correct Solution: ``` def soi(n): #?´??????°????§£?????¢?????´????????? i=2 while True: if i*i>n: return n if n%i==0: return i i+=1 a=int(input()) ans=a count=1 i=2 # ??????????????° while True: temp=soi(a) if a==1: #?´??????°??????????????° ...
output
1
4,146
22
8,293
Provide a correct Python 3 solution for this coding contest problem. For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Input n An integer n (1 ≤ n ≤ 1000000000). Output The number of totatives in a line. Examples Input 6 ...
instruction
0
4,147
22
8,294
"Correct Solution: ``` import sys,bisect,math from functools import reduce sys.setrecursionlimit(15000) N = int(sys.stdin.readline()) def phi(N): n = N s = set() for i in range(2,math.floor(pow(N,0.5))+1): while n%i==0: s.add(i) n = n//i if n != 1: s.add(n) a1 = reduce(lambda a,b: a*b,[e...
output
1
4,147
22
8,295
Provide a correct Python 3 solution for this coding contest problem. For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Input n An integer n (1 ≤ n ≤ 1000000000). Output The number of totatives in a line. Examples Input 6 ...
instruction
0
4,148
22
8,296
"Correct Solution: ``` #!/usr/bin/env python # -*- coding: utf-8 -*- """ input: 1000000 output: 400000 """ import sys def min_prime_factor(n): k = 2 while True: if pow(k, 2) > n: return n if not n % k: return k k += 1 def phi(n): ans = n while True:...
output
1
4,148
22
8,297
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Input n An integer n (1 ≤ n ≤ 1000000000). Output T...
instruction
0
4,149
22
8,298
Yes
output
1
4,149
22
8,299
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Input n An integer n (1 ≤ n ≤ 1000000000). Output T...
instruction
0
4,150
22
8,300
Yes
output
1
4,150
22
8,301
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Input n An integer n (1 ≤ n ≤ 1000000000). Output T...
instruction
0
4,151
22
8,302
Yes
output
1
4,151
22
8,303
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Input n An integer n (1 ≤ n ≤ 1000000000). Output T...
instruction
0
4,152
22
8,304
Yes
output
1
4,152
22
8,305
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Input n An integer n (1 ≤ n ≤ 1000000000). Output T...
instruction
0
4,153
22
8,306
No
output
1
4,153
22
8,307
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Input n An integer n (1 ≤ n ≤ 1000000000). Output T...
instruction
0
4,154
22
8,308
No
output
1
4,154
22
8,309
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Input n An integer n (1 ≤ n ≤ 1000000000). Output T...
instruction
0
4,155
22
8,310
No
output
1
4,155
22
8,311
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Input n An integer n (1 ≤ n ≤ 1000000000). Output T...
instruction
0
4,156
22
8,312
No
output
1
4,156
22
8,313
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two positive integers a and b. There are two possible operations: 1. multiply one of the numbers by some prime p; 2. divide one of the numbers on its prime factor p. Wha...
instruction
0
4,173
22
8,346
No
output
1
4,173
22
8,347
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two positive integers a and b. There are two possible operations: 1. multiply one of the numbers by some prime p; 2. divide one of the numbers on its prime factor p. Wha...
instruction
0
4,174
22
8,348
No
output
1
4,174
22
8,349
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two positive integers a and b. There are two possible operations: 1. multiply one of the numbers by some prime p; 2. divide one of the numbers on its prime factor p. Wha...
instruction
0
4,175
22
8,350
No
output
1
4,175
22
8,351
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given two positive integers a and b. There are two possible operations: 1. multiply one of the numbers by some prime p; 2. divide one of the numbers on its prime factor p. Wha...
instruction
0
4,176
22
8,352
No
output
1
4,176
22
8,353
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Alex decided to try his luck in TV shows. He once went to the quiz named "What's That Word?!". After perfectly answering the questions "How is a pseudonym commonly referred to in the Internet?" ...
instruction
0
4,185
22
8,370
No
output
1
4,185
22
8,371
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Alex decided to try his luck in TV shows. He once went to the quiz named "What's That Word?!". After perfectly answering the questions "How is a pseudonym commonly referred to in the Internet?" ...
instruction
0
4,186
22
8,372
No
output
1
4,186
22
8,373
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Alex decided to try his luck in TV shows. He once went to the quiz named "What's That Word?!". After perfectly answering the questions "How is a pseudonym commonly referred to in the Internet?" ...
instruction
0
4,187
22
8,374
No
output
1
4,187
22
8,375
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Alex decided to try his luck in TV shows. He once went to the quiz named "What's That Word?!". After perfectly answering the questions "How is a pseudonym commonly referred to in the Internet?" ...
instruction
0
4,188
22
8,376
No
output
1
4,188
22
8,377
Provide tags and a correct Python 3 solution for this coding contest problem. Let's consider all integers in the range from 1 to n (inclusive). Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a, b), wher...
instruction
0
4,351
22
8,702
Tags: greedy, implementation, math, number theory Correct Solution: ``` length = int(input()) tests = [''] * length for i in range(length): tests[i] = int(input()) for i in tests: if i % 2 == 0: print(int(i / 2)) else: print(int((i - 1) / 2)) ```
output
1
4,351
22
8,703
Provide tags and a correct Python 3 solution for this coding contest problem. Let's consider all integers in the range from 1 to n (inclusive). Among all pairs of distinct integers in this range, find the maximum possible greatest common divisor of integers in pair. Formally, find the maximum value of gcd(a, b), wher...
instruction
0
4,352
22
8,704
Tags: greedy, implementation, math, number theory Correct Solution: ``` from math import sqrt from math import floor def solve(): n = int(input()) print(n//2) for cnt in range(int(input())): solve() ```
output
1
4,352
22
8,705