message stringlengths 2 44.5k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 42 109k | cluster float64 5 5 | __index_level_0__ int64 84 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.
If there are several answers, you can print any.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.
The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).
Output
For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.
Otherwise, print "YES" and any possible such representation.
Example
Input
5
64
32
97
2
12345
Output
YES
2 4 8
NO
NO
NO
YES
3 5 823
Submitted Solution:
```
def isPrime(n):
if n == 2 or n == 3: return True
if n % 2 == 0 or n < 2: return False
for i in range(3, int(n ** 0.5) + 1, 2):
if n % i == 0:
return False
return True
t = int(input())
for _ in range(t):
f = 0
n = int(input())
if isPrime(n):
print("NO")
continue
for i in range(2, int(n ** 0.5) + 1):
if n % i == 0:
if not isPrime(n // i):
m = n // i
for j in range(2, int(m ** 0.5) + 1):
if m % j == 0 and i != j != (m // j) != i:
print("YES")
print(i, j, m // j)
f = 1
break
if f:
break
if not f:
print("NO")
``` | instruction | 0 | 5,171 | 5 | 10,342 |
Yes | output | 1 | 5,171 | 5 | 10,343 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.
If there are several answers, you can print any.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.
The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).
Output
For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.
Otherwise, print "YES" and any possible such representation.
Example
Input
5
64
32
97
2
12345
Output
YES
2 4 8
NO
NO
NO
YES
3 5 823
Submitted Solution:
```
# ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
# ░░░░░░░▄▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▄░░░░░░
# ░░░░░░█░░▄▀▀▀▀▀▀▀▀▀▀▀▀▄░░█░░░░░
# ░░░░░░█░█░░▀░░░░░░░░▀░░█░█░░░░░
# ░░░░░░█░█░░░▀░░░░░░▀░░░█░█░░░░░
# ░░░░░░█░█░░░░▀░░░░▀░░░░█░█░░░░░
# ░░░░░░█░█▄░░░░▀░░▀░░░░▄█░█░░░░░
# ░░░░░░█░█░░░░░░██░░░░░░█░█░░░░░
# ░░░░░░█░▀░░░░░░░░░░░░░░▀░█░░░░░
# ░░░░░░█░░░░░░░░░░░░░░░░░░█░░░░░
# ░░░░░░█░░░░░░░░░░░░░░░░░░█░░░░░
# ░░░░░░▀░░░░░░░░░░░░░░░░░░▀░░░░░
# ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
import math
for i in range(int(input())):
n = int(input())
l = []
p =math.sqrt(n)
p = int(p)
i=2
while len(l)<2 and i<p:
if n%i==0:
l.append(i)
n=n//i
i+=1
if len(l)==2 and n not in l:
print("YES")
print(*l,n)
else:
print("NO")
``` | instruction | 0 | 5,172 | 5 | 10,344 |
Yes | output | 1 | 5,172 | 5 | 10,345 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.
If there are several answers, you can print any.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.
The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).
Output
For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.
Otherwise, print "YES" and any possible such representation.
Example
Input
5
64
32
97
2
12345
Output
YES
2 4 8
NO
NO
NO
YES
3 5 823
Submitted Solution:
```
import math
for i in range(int(input())):
x = int(input())
a,b=[2,3] if x%2 ==0 else [3,5]
while b <= int(math.sqrt(x)):
if x%(a*b) == 0:
c = int(x/(a*b))
if c != a and c != b:
print("YES")
print(f"{a} {b} {c}");break
else:
print("NO");break
b+=1;
else:
print("NO")
``` | instruction | 0 | 5,174 | 5 | 10,348 |
No | output | 1 | 5,174 | 5 | 10,349 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.
If there are several answers, you can print any.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.
The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).
Output
For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.
Otherwise, print "YES" and any possible such representation.
Example
Input
5
64
32
97
2
12345
Output
YES
2 4 8
NO
NO
NO
YES
3 5 823
Submitted Solution:
```
t = int(input())
for _ in range(t):
n = int(input())
factors = []
for factor in range (2, 1000000000):
if n < factor:
break
if n % factor == 0:
factors.append(factor)
n = n // factor
if len(factors) == 2:
break
if len(factors) == 2:
factors.append(n)
print('YES')
print(' '.join(map(str, factors)))
else:
print('NO')
``` | instruction | 0 | 5,175 | 5 | 10,350 |
No | output | 1 | 5,175 | 5 | 10,351 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.
If there are several answers, you can print any.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.
The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).
Output
For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.
Otherwise, print "YES" and any possible such representation.
Example
Input
5
64
32
97
2
12345
Output
YES
2 4 8
NO
NO
NO
YES
3 5 823
Submitted Solution:
```
# _1294c
##########
def productOfThreeNumbers(n, answer=(1, )):
lengthOfAnswer = len(answer)
if lengthOfAnswer == 3:
if n > answer[-1]:
return f'YES\n{answer[1]} {answer[2]} {int(n)}'
return 'NO'
for i in range(answer[-1]+1, int(n**(1/(4-lengthOfAnswer)))):
if not n%i:
return productOfThreeNumbers(n/i, answer+(i, ))
return 'NO'
nTestCases = int(input())
testCases = [int(input()) for x in range(nTestCases)]
[print(productOfThreeNumbers(testCase)) for testCase in testCases]
``` | instruction | 0 | 5,176 | 5 | 10,352 |
No | output | 1 | 5,176 | 5 | 10,353 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Phoenix loves playing with bits — specifically, by using the bitwise operations AND, OR, and XOR. He has n integers a_1, a_2, ..., a_n, and will perform q of the following queries:
1. replace all numbers a_i where l ≤ a_i ≤ r with a_i AND x;
2. replace all numbers a_i where l ≤ a_i ≤ r with a_i OR x;
3. replace all numbers a_i where l ≤ a_i ≤ r with a_i XOR x;
4. output how many distinct integers a_i where l ≤ a_i ≤ r.
For each query, Phoenix is given l, r, and x. Note that he is considering the values of the numbers, not their indices.
Input
The first line contains two integers n and q (1 ≤ n ≤ 2 ⋅ 10^5; 1 ≤ q ≤ 10^5) — the number of integers and the number of queries, respectively.
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i < 2^{20}) — the integers that Phoenix starts with.
The next q lines contain the queries. For each query, the first integer of each line is t (1 ≤ t ≤ 4) — the type of query.
If t ∈ \{1, 2, 3\}, then three integers l_i, r_i, and x_i will follow (0 ≤ l_i, r_i, x_i < 2^{20}; l_i ≤ r_i).
Otherwise, if t=4, two integers l_i and r_i will follow (0 ≤ l_i ≤ r_i < 2^{20}).
It is guaranteed that there is at least one query where t=4.
Output
Print the answer for each query where t=4.
Examples
Input
5 6
5 4 3 2 1
1 2 3 2
4 2 5
3 2 5 3
4 1 6
2 1 1 8
4 8 10
Output
3
2
1
Input
6 7
6 0 2 3 2 7
1 0 4 3
2 6 8 4
4 0 7
3 2 5 3
1 0 1 2
4 0 3
4 2 7
Output
5
1
2
Note
In the first example:
* For the first query, 2 is replaced by 2 AND 2 = 2 and 3 is replaced with 3 AND 2 = 2. The set of numbers is \{1, 2, 4, 5\}.
* For the second query, there are 3 distinct numbers between 2 and 5: 2, 4, and 5.
* For the third query, 2 is replaced by 2 XOR 3 = 1, 4 is replaced by 4 XOR 3 = 7, and 5 is replaced by 5 XOR 3 = 6. The set of numbers is \{1, 6, 7\}.
* For the fourth query, there are 2 distinct numbers between 1 and 6: 1 and 6.
* For the fifth query, 1 is replaced by 1 OR 8 = 9. The set of numbers is \{6, 7, 9\}.
* For the sixth query, there is one distinct number between 8 and 10: 9.
Submitted Solution:
```
a=20
b=10
print(a+b)
``` | instruction | 0 | 5,268 | 5 | 10,536 |
No | output | 1 | 5,268 | 5 | 10,537 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Input
The input contains a single integer a (1 ≤ a ≤ 18257).
Output
Print a single integer output (1 ≤ output ≤ 2·109).
Examples
Input
2
Output
13
Submitted Solution:
```
#!/usr/bin/env python
from __future__ import division, print_function
import math
import os
import sys
from fractions import *
from sys import *
from io import BytesIO, IOBase
from itertools import *
from collections import *
# sys.setrecursionlimit(10**5)
if sys.version_info[0] < 3:
from __builtin__ import xrange as range
from future_builtins import ascii, filter, hex, map, oct, zip
# sys.setrecursionlimit(10**6)
# 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")
def print(*args, **kwargs):
"""Prints the values to a stream, or to sys.stdout by default."""
sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
at_start = True
for x in args:
if not at_start:
file.write(sep)
file.write(str(x))
at_start = False
file.write(kwargs.pop("end", "\n"))
if kwargs.pop("flush", False):
file.flush()
if sys.version_info[0] < 3:
sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
def inp(): return sys.stdin.readline().rstrip("\r\n") # for fast input
def out(var): sys.stdout.write(str(var)) # for fast output, always take string
def lis(): return list(map(int, inp().split()))
def stringlis(): return list(map(str, inp().split()))
def sep(): return map(int, inp().split())
def strsep(): return map(str, inp().split())
def fsep(): return map(float, inp().split())
def inpu(): return int(inp())
# -----------------------------------------------------------------
def regularbracket(t):
p = 0
for i in t:
if i == "(":
p += 1
else:
p -= 1
if p < 0:
return False
else:
if p > 0:
return False
else:
return True
# -------------------------------------------------
def binarySearchCount(arr, n, key):
left = 0
right = n - 1
count = 0
while (left <= right):
mid = int((right + left) / 2)
# Check if middle element is
# less than or equal to key
if (arr[mid] <= key):
count = mid + 1
left = mid + 1
# If key is smaller, ignore right half
else:
right = mid - 1
return count
# ------------------------------reverse string(pallindrome)
def reverse1(string):
pp = ""
for i in string[::-1]:
pp += i
if pp == string:
return True
return False
# --------------------------------reverse list(paindrome)
def reverse2(list1):
l = []
for i in list1[::-1]:
l.append(i)
if l == list1:
return True
return False
def mex(list1):
# list1 = sorted(list1)
p = max(list1) + 1
for i in range(len(list1)):
if list1[i] != i:
p = i
break
return p
def sumofdigits(n):
n = str(n)
s1 = 0
for i in n:
s1 += int(i)
return s1
def perfect_square(n):
s = math.sqrt(n)
if s == int(s):
return True
return False
# -----------------------------roman
def roman_number(x):
if x > 15999:
return
value = [5000, 4000, 1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1]
symbol = ["F", "MF", "M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"]
roman = ""
i = 0
while x > 0:
div = x // value[i]
x = x % value[i]
while div:
roman += symbol[i]
div -= 1
i += 1
return roman
def soretd(s):
for i in range(1, len(s)):
if s[i - 1] > s[i]:
return False
return True
# print(soretd("1"))
# ---------------------------
def countRhombi(h, w):
ct = 0
for i in range(2, h + 1, 2):
for j in range(2, w + 1, 2):
ct += (h - i + 1) * (w - j + 1)
return ct
def countrhombi2(h, w):
return ((h * h) // 4) * ((w * w) // 4)
# ---------------------------------
def binpow(a, b):
if b == 0:
return 1
else:
res = binpow(a, b // 2)
if b % 2 != 0:
return res * res * a
else:
return res * res
# -------------------------------------------------------
def binpowmodulus(a, b, m):
a %= m
res = 1
while (b > 0):
if (b & 1):
res = res * a % m
a = a * a % m
b >>= 1
return res
# -------------------------------------------------------------
def coprime_to_n(n):
result = n
i = 2
while (i * i <= n):
if (n % i == 0):
while (n % i == 0):
n //= i
result -= result // i
i += 1
if (n > 1):
result -= result // n
return result
# -------------------prime
def prime(x):
if x == 1:
return False
else:
for i in range(2, int(math.sqrt(x)) + 1):
if (x % i == 0):
return False
else:
return True
def luckynumwithequalnumberoffourandseven(x, n, a):
if x >= n and str(x).count("4") == str(x).count("7"):
a.append(x)
else:
if x < 1e12:
luckynumwithequalnumberoffourandseven(x * 10 + 4, n, a)
luckynumwithequalnumberoffourandseven(x * 10 + 7, n, a)
return a
def luckynuber(x, n, a):
p = set(str(x))
if len(p) <= 2:
a.append(x)
if x < n:
luckynuber(x + 1, n, a)
return a
#------------------------------------------------------interactive problems
def interact(type, x):
if type == "r":
inp = input()
return inp.strip()
else:
print(x, flush=True)
#------------------------------------------------------------------zero at end of factorial of a number
def findTrailingZeros(n):
# Initialize result
count = 0
# Keep dividing n by
# 5 & update Count
while (n >= 5):
n //= 5
count += n
return count
#-----------------------------------------------merge sort
# Python program for implementation of MergeSort
def mergeSort(arr):
if len(arr) > 1:
# Finding the mid of the array
mid = len(arr) // 2
# Dividing the array elements
L = arr[:mid]
# into 2 halves
R = arr[mid:]
# Sorting the first half
mergeSort(L)
# Sorting the second half
mergeSort(R)
i = j = k = 0
# Copy data to temp arrays L[] and R[]
while i < len(L) and j < len(R):
if L[i] < R[j]:
arr[k] = L[i]
i += 1
else:
arr[k] = R[j]
j += 1
k += 1
# Checking if any element was left
while i < len(L):
arr[k] = L[i]
i += 1
k += 1
while j < len(R):
arr[k] = R[j]
j += 1
k += 1
#-----------------------------------------------lucky number with two lucky any digits
res = set()
def solve(p, l, a, b,n):#given number
if p > n or l > 10:
return
if p > 0:
res.add(p)
solve(p * 10 + a, l + 1, a, b,n)
solve(p * 10 + b, l + 1, a, b,n)
# problem
"""
n = int(input())
for a in range(0, 10):
for b in range(0, a):
solve(0, 0)
print(len(res))
"""
#-----------------------------------------------
# endregion------------------------------
"""
def main():
n = inpu()
cnt=0
c = n
if n % 7 == 0:
print("7" * (n // 7))
else:
while(c>0):
c-=4
cnt+=1
if c%7==0 and c>=0:
#print(n,n%4)
print("4"*(cnt)+"7"*(c//7))
break
else:
if n % 4 == 0:
print("4" * (n // 4))
else:
print(-1)
if __name__ == '__main__':
main()
"""
"""
def main():
n,t = sep()
arr = lis()
i=0
cnt=0
min1 = min(arr)
while(True):
if t>=arr[i]:
cnt+=1
t-=arr[i]
i+=1
else:
i+=1
if i==n:
i=0
if t<min1:
break
print(cnt)
if __name__ == '__main__':
main()
"""
# Python3 program to find all subsets
# by backtracking.
# In the array A at every step we have two
# choices for each element either we can
# ignore the element or we can include the
# element in our subset
def subsetsUtil(A, subset, index,d):
print(*subset)
s = sum(subset)
d.append(s)
for i in range(index, len(A)):
# include the A[i] in subset.
subset.append(A[i])
# move onto the next element.
subsetsUtil(A, subset, i + 1,d)
# exclude the A[i] from subset and
# triggers backtracking.
subset.pop(-1)
return d
def subsetSums(arr, l, r,d, sum=0):
if l > r:
d.append(sum)
return
subsetSums(arr, l + 1, r,d, sum + arr[l])
# Subset excluding arr[l]
subsetSums(arr, l + 1, r,d, sum)
return d
"""
def main():
t = inpu()
for _ in range(t):
n = inpu()
arr=[]
subset=[]
i=0
l=[]
for j in range(26):
arr.append(3**j)
if __name__ == '__main__':
main()
"""
def main():
n = int(input())
cnt=1
if n==1:
print(1)
else:
for i in range(1,n):
cnt+=i*12
print(cnt)
if __name__ == '__main__':
main()
``` | instruction | 0 | 5,293 | 5 | 10,586 |
Yes | output | 1 | 5,293 | 5 | 10,587 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Input
The input contains a single integer a (1 ≤ a ≤ 18257).
Output
Print a single integer output (1 ≤ output ≤ 2·109).
Examples
Input
2
Output
13
Submitted Solution:
```
#star noumber problem
# 1 13....
n=int(input())
k=6*n;k1=n-1;ans=k*k1
print(ans+1)
``` | instruction | 0 | 5,294 | 5 | 10,588 |
Yes | output | 1 | 5,294 | 5 | 10,589 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Input
The input contains a single integer a (1 ≤ a ≤ 18257).
Output
Print a single integer output (1 ≤ output ≤ 2·109).
Examples
Input
2
Output
13
Submitted Solution:
```
n=int(input())
a=3*n-2
b=n-1
print(int((a*(a+1))/2 + ((b*(b+1))/2)*3))
``` | instruction | 0 | 5,295 | 5 | 10,590 |
Yes | output | 1 | 5,295 | 5 | 10,591 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Input
The input contains a single integer a (1 ≤ a ≤ 18257).
Output
Print a single integer output (1 ≤ output ≤ 2·109).
Examples
Input
2
Output
13
Submitted Solution:
```
n = int(input())
print((2*n-2)*n*3+1)
``` | instruction | 0 | 5,296 | 5 | 10,592 |
Yes | output | 1 | 5,296 | 5 | 10,593 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Input
The input contains a single integer a (1 ≤ a ≤ 18257).
Output
Print a single integer output (1 ≤ output ≤ 2·109).
Examples
Input
2
Output
13
Submitted Solution:
```
n = int(input())
z = [1,12]
for i in range(2,n):
z.append(z[-1]*2)
s = 0
if n==1:
s = 1
elif n==4:
s = 73
elif n==5:
s = 121
else:
s = sum(z)
print(s)
``` | instruction | 0 | 5,297 | 5 | 10,594 |
No | output | 1 | 5,297 | 5 | 10,595 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Input
The input contains a single integer a (1 ≤ a ≤ 18257).
Output
Print a single integer output (1 ≤ output ≤ 2·109).
Examples
Input
2
Output
13
Submitted Solution:
```
_ = input()
print(13)
``` | instruction | 0 | 5,298 | 5 | 10,596 |
No | output | 1 | 5,298 | 5 | 10,597 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Input
The input contains a single integer a (1 ≤ a ≤ 18257).
Output
Print a single integer output (1 ≤ output ≤ 2·109).
Examples
Input
2
Output
13
Submitted Solution:
```
__author__ = 'MARI'
def main():
a = int(input())
print(1 + 6*(a*(a+1)//2-1))
if __name__ == '__main__':
import sys
argv = sys.argv
main()
``` | instruction | 0 | 5,299 | 5 | 10,598 |
No | output | 1 | 5,299 | 5 | 10,599 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Input
The input contains a single integer a (1 ≤ a ≤ 18257).
Output
Print a single integer output (1 ≤ output ≤ 2·109).
Examples
Input
2
Output
13
Submitted Solution:
```
n = int(input())
if(n%2 == 0):
print((12*(n-1)) + 1)
else:
print((12*n)+1)
``` | instruction | 0 | 5,300 | 5 | 10,600 |
No | output | 1 | 5,300 | 5 | 10,601 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let p (i) be the i-th prime number from the smallest. For example, 7 is the fourth prime number from the smallest, 2, 3, 5, 7, so p (4) = 7.
Given n, the sum of p (i) from i = 1 to n s
s = p (1) + p (2) + .... + p (n)
Create a program that outputs. For example, when n = 9, s = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 = 100.
Input
Given multiple datasets. Each dataset is given the integer n (n ≤ 10000). When n is 0, it is the last input. The number of datasets does not exceed 50.
Output
For n in each dataset, print s on one line.
Example
Input
2
9
0
Output
5
100
Submitted Solution:
```
import itertools
n=104730;a=list(range(n));a[:2]=0,0
for i in range(2,97):
a[i*2::i]=[0]*len(a[i*2::i])
p=list(itertools.compress(range(n),a))
for e in iter(input,'0'):print(sum(p[:int(e)]))
``` | instruction | 0 | 5,727 | 5 | 11,454 |
No | output | 1 | 5,727 | 5 | 11,455 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let p (i) be the i-th prime number from the smallest. For example, 7 is the fourth prime number from the smallest, 2, 3, 5, 7, so p (4) = 7.
Given n, the sum of p (i) from i = 1 to n s
s = p (1) + p (2) + .... + p (n)
Create a program that outputs. For example, when n = 9, s = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 = 100.
Input
Given multiple datasets. Each dataset is given the integer n (n ≤ 10000). When n is 0, it is the last input. The number of datasets does not exceed 50.
Output
For n in each dataset, print s on one line.
Example
Input
2
9
0
Output
5
100
Submitted Solution:
```
from itertools import *
n=range(104730);a=list(n)
for i in range(2,315):a[i*2::i]=[0]*len(a[i*2::i])
p=list(compress(n,a))
for e in iter(input,'0'):print(sum(p[:int(e)+1])-1)
``` | instruction | 0 | 5,728 | 5 | 11,456 |
No | output | 1 | 5,728 | 5 | 11,457 |
Provide a correct Python 3 solution for this coding contest problem.
Given two non-negative decimal integers $a$ and $b$, calculate their AND (logical conjunction), OR (logical disjunction) and XOR (exclusive disjunction) and print them in binary representation of 32 bits.
Constraints
* $0 \leq a, b \leq 2^{32} - 1$
Input
The input is given in the following format.
$a \; b$
Output
Print results of AND, OR and XOR in a line respectively.
Example
Input
8 10
Output
00000000000000000000000000001000
00000000000000000000000000001010
00000000000000000000000000000010 | instruction | 0 | 5,796 | 5 | 11,592 |
"Correct Solution:
```
a,b = map(int,input().split())
MASK = (1 << 32)-1
print("{:032b}".format(a & b))
print("{:032b}".format(a | b))
print("{:032b}".format(a ^ b))
``` | output | 1 | 5,796 | 5 | 11,593 |
Provide a correct Python 3 solution for this coding contest problem.
Given two non-negative decimal integers $a$ and $b$, calculate their AND (logical conjunction), OR (logical disjunction) and XOR (exclusive disjunction) and print them in binary representation of 32 bits.
Constraints
* $0 \leq a, b \leq 2^{32} - 1$
Input
The input is given in the following format.
$a \; b$
Output
Print results of AND, OR and XOR in a line respectively.
Example
Input
8 10
Output
00000000000000000000000000001000
00000000000000000000000000001010
00000000000000000000000000000010 | instruction | 0 | 5,797 | 5 | 11,594 |
"Correct Solution:
```
#前問題の解答参照
a,b = map(int, input().split( ))
##<<左桁ずらし
print("{:032b}".format(a&b))
print("{:032b}".format(a|b))
print("{:032b}".format(a^b))
``` | output | 1 | 5,797 | 5 | 11,595 |
Provide a correct Python 3 solution for this coding contest problem.
Given two non-negative decimal integers $a$ and $b$, calculate their AND (logical conjunction), OR (logical disjunction) and XOR (exclusive disjunction) and print them in binary representation of 32 bits.
Constraints
* $0 \leq a, b \leq 2^{32} - 1$
Input
The input is given in the following format.
$a \; b$
Output
Print results of AND, OR and XOR in a line respectively.
Example
Input
8 10
Output
00000000000000000000000000001000
00000000000000000000000000001010
00000000000000000000000000000010 | instruction | 0 | 5,798 | 5 | 11,596 |
"Correct Solution:
```
a, b = (int(x) for x in input().split())
print('{0:032b}'.format(a & b))
print('{0:032b}'.format(a | b))
print('{0:032b}'.format(a ^ b))
``` | output | 1 | 5,798 | 5 | 11,597 |
Provide a correct Python 3 solution for this coding contest problem.
Given two non-negative decimal integers $a$ and $b$, calculate their AND (logical conjunction), OR (logical disjunction) and XOR (exclusive disjunction) and print them in binary representation of 32 bits.
Constraints
* $0 \leq a, b \leq 2^{32} - 1$
Input
The input is given in the following format.
$a \; b$
Output
Print results of AND, OR and XOR in a line respectively.
Example
Input
8 10
Output
00000000000000000000000000001000
00000000000000000000000000001010
00000000000000000000000000000010 | instruction | 0 | 5,799 | 5 | 11,598 |
"Correct Solution:
```
a, b = map(int, input().split())
print(f'{a & b:032b}')
print(f'{a | b:032b}')
print(f'{a ^ b:032b}')
``` | output | 1 | 5,799 | 5 | 11,599 |
Provide a correct Python 3 solution for this coding contest problem.
Given two non-negative decimal integers $a$ and $b$, calculate their AND (logical conjunction), OR (logical disjunction) and XOR (exclusive disjunction) and print them in binary representation of 32 bits.
Constraints
* $0 \leq a, b \leq 2^{32} - 1$
Input
The input is given in the following format.
$a \; b$
Output
Print results of AND, OR and XOR in a line respectively.
Example
Input
8 10
Output
00000000000000000000000000001000
00000000000000000000000000001010
00000000000000000000000000000010 | instruction | 0 | 5,800 | 5 | 11,600 |
"Correct Solution:
```
if __name__ == "__main__":
a, b = map(lambda x: int(x), input().split())
mask = (1 << 32) - 1
print(f"{(a & b) & mask:032b}")
print(f"{(a | b) & mask:032b}")
print(f"{(a ^ b) & mask:032b}")
``` | output | 1 | 5,800 | 5 | 11,601 |
Provide a correct Python 3 solution for this coding contest problem.
Given two non-negative decimal integers $a$ and $b$, calculate their AND (logical conjunction), OR (logical disjunction) and XOR (exclusive disjunction) and print them in binary representation of 32 bits.
Constraints
* $0 \leq a, b \leq 2^{32} - 1$
Input
The input is given in the following format.
$a \; b$
Output
Print results of AND, OR and XOR in a line respectively.
Example
Input
8 10
Output
00000000000000000000000000001000
00000000000000000000000000001010
00000000000000000000000000000010 | instruction | 0 | 5,801 | 5 | 11,602 |
"Correct Solution:
```
a,b = (int(x) for x in input().split())
MAX = (1 << 32) - 1
print("{:032b}".format(a & b))
print("{:032b}".format(a | b))
print("{:032b}".format(a ^ b))
``` | output | 1 | 5,801 | 5 | 11,603 |
Provide a correct Python 3 solution for this coding contest problem.
Given two non-negative decimal integers $a$ and $b$, calculate their AND (logical conjunction), OR (logical disjunction) and XOR (exclusive disjunction) and print them in binary representation of 32 bits.
Constraints
* $0 \leq a, b \leq 2^{32} - 1$
Input
The input is given in the following format.
$a \; b$
Output
Print results of AND, OR and XOR in a line respectively.
Example
Input
8 10
Output
00000000000000000000000000001000
00000000000000000000000000001010
00000000000000000000000000000010 | instruction | 0 | 5,802 | 5 | 11,604 |
"Correct Solution:
```
a,b=map(int,input().split())
print(format(a&b,'032b'))
print(format(a|b,'032b'))
print(format(a^b,'032b'))
``` | output | 1 | 5,802 | 5 | 11,605 |
Provide a correct Python 3 solution for this coding contest problem.
Given two non-negative decimal integers $a$ and $b$, calculate their AND (logical conjunction), OR (logical disjunction) and XOR (exclusive disjunction) and print them in binary representation of 32 bits.
Constraints
* $0 \leq a, b \leq 2^{32} - 1$
Input
The input is given in the following format.
$a \; b$
Output
Print results of AND, OR and XOR in a line respectively.
Example
Input
8 10
Output
00000000000000000000000000001000
00000000000000000000000000001010
00000000000000000000000000000010 | instruction | 0 | 5,803 | 5 | 11,606 |
"Correct Solution:
```
a,b=map(int,input().split())
print(f'{a&b:032b}\n{a|b:032b}\n{a^b:032b}')
``` | output | 1 | 5,803 | 5 | 11,607 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given two non-negative decimal integers $a$ and $b$, calculate their AND (logical conjunction), OR (logical disjunction) and XOR (exclusive disjunction) and print them in binary representation of 32 bits.
Constraints
* $0 \leq a, b \leq 2^{32} - 1$
Input
The input is given in the following format.
$a \; b$
Output
Print results of AND, OR and XOR in a line respectively.
Example
Input
8 10
Output
00000000000000000000000000001000
00000000000000000000000000001010
00000000000000000000000000000010
Submitted Solution:
```
a, b = map(int, input().split())
print('{:032b}'.format(a & b))
print('{:032b}'.format(a | b))
print('{:032b}'.format(a ^ b))
``` | instruction | 0 | 5,804 | 5 | 11,608 |
Yes | output | 1 | 5,804 | 5 | 11,609 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given two non-negative decimal integers $a$ and $b$, calculate their AND (logical conjunction), OR (logical disjunction) and XOR (exclusive disjunction) and print them in binary representation of 32 bits.
Constraints
* $0 \leq a, b \leq 2^{32} - 1$
Input
The input is given in the following format.
$a \; b$
Output
Print results of AND, OR and XOR in a line respectively.
Example
Input
8 10
Output
00000000000000000000000000001000
00000000000000000000000000001010
00000000000000000000000000000010
Submitted Solution:
```
def main():
bm = 0xffffffff
a,b = map(int, input().split())
an = (a & b) & bm
o = (a | b) & bm
xo = (a ^ b) & bm
print(format(an, "032b"))
print(format(o, "032b"))
print(format(xo, "032b"))
main()
``` | instruction | 0 | 5,805 | 5 | 11,610 |
Yes | output | 1 | 5,805 | 5 | 11,611 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given two non-negative decimal integers $a$ and $b$, calculate their AND (logical conjunction), OR (logical disjunction) and XOR (exclusive disjunction) and print them in binary representation of 32 bits.
Constraints
* $0 \leq a, b \leq 2^{32} - 1$
Input
The input is given in the following format.
$a \; b$
Output
Print results of AND, OR and XOR in a line respectively.
Example
Input
8 10
Output
00000000000000000000000000001000
00000000000000000000000000001010
00000000000000000000000000000010
Submitted Solution:
```
a, b = map(int, input().split())
print("{:032b}".format(a & b))
print("{:032b}".format(a | b))
print("{:032b}".format(a ^ b))
``` | instruction | 0 | 5,806 | 5 | 11,612 |
Yes | output | 1 | 5,806 | 5 | 11,613 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given two non-negative decimal integers $a$ and $b$, calculate their AND (logical conjunction), OR (logical disjunction) and XOR (exclusive disjunction) and print them in binary representation of 32 bits.
Constraints
* $0 \leq a, b \leq 2^{32} - 1$
Input
The input is given in the following format.
$a \; b$
Output
Print results of AND, OR and XOR in a line respectively.
Example
Input
8 10
Output
00000000000000000000000000001000
00000000000000000000000000001010
00000000000000000000000000000010
Submitted Solution:
```
def out(n):
mask = 2**32 -1
print(format(n&mask,"032b"))
a,b = map(int,input().split())
out(a&b)
out(a|b)
out(a^b)
``` | instruction | 0 | 5,807 | 5 | 11,614 |
Yes | output | 1 | 5,807 | 5 | 11,615 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Boboniu likes bit operations. He wants to play a game with you.
Boboniu gives you two sequences of non-negative integers a_1,a_2,…,a_n and b_1,b_2,…,b_m.
For each i (1≤ i≤ n), you're asked to choose a j (1≤ j≤ m) and let c_i=a_i\& b_j, where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Note that you can pick the same j for different i's.
Find the minimum possible c_1 | c_2 | … | c_n, where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
Input
The first line contains two integers n and m (1≤ n,m≤ 200).
The next line contains n integers a_1,a_2,…,a_n (0≤ a_i < 2^9).
The next line contains m integers b_1,b_2,…,b_m (0≤ b_i < 2^9).
Output
Print one integer: the minimum possible c_1 | c_2 | … | c_n.
Examples
Input
4 2
2 6 4 0
2 4
Output
2
Input
7 6
1 9 1 9 8 1 0
1 1 4 5 1 4
Output
0
Input
8 5
179 261 432 162 82 43 10 38
379 357 202 184 197
Output
147
Note
For the first example, we have c_1=a_1\& b_2=0, c_2=a_2\& b_1=2, c_3=a_3\& b_1=0, c_4 = a_4\& b_1=0.Thus c_1 | c_2 | c_3 |c_4 =2, and this is the minimal answer we can get. | instruction | 0 | 5,958 | 5 | 11,916 |
Tags: bitmasks, brute force, dp, greedy
Correct Solution:
```
n, m = [int(i) for i in input().split(" ")]
a = [int(i) for i in input().split(" ")]
b = [int(i) for i in input().split(" ")]
ab = [b.copy() for i in a]
result = 0b1111111111
def isTrue(a, s):
return (a >> s) & 1
for s in range(9, -1, -1):
new_ab = [None for i in ab]
possible = True
for i, ca in enumerate(a):
if isTrue(ca, s):
res = [cb for cb in ab[i] if not isTrue(cb, s)]
if len(res) != 0:
new_ab[i] = res
else:
possible = False
break
else:
new_ab[i] = ab[i]
if possible:
result ^= 1 << s
ab = new_ab
print(result)
``` | output | 1 | 5,958 | 5 | 11,917 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Boboniu likes bit operations. He wants to play a game with you.
Boboniu gives you two sequences of non-negative integers a_1,a_2,…,a_n and b_1,b_2,…,b_m.
For each i (1≤ i≤ n), you're asked to choose a j (1≤ j≤ m) and let c_i=a_i\& b_j, where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Note that you can pick the same j for different i's.
Find the minimum possible c_1 | c_2 | … | c_n, where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
Input
The first line contains two integers n and m (1≤ n,m≤ 200).
The next line contains n integers a_1,a_2,…,a_n (0≤ a_i < 2^9).
The next line contains m integers b_1,b_2,…,b_m (0≤ b_i < 2^9).
Output
Print one integer: the minimum possible c_1 | c_2 | … | c_n.
Examples
Input
4 2
2 6 4 0
2 4
Output
2
Input
7 6
1 9 1 9 8 1 0
1 1 4 5 1 4
Output
0
Input
8 5
179 261 432 162 82 43 10 38
379 357 202 184 197
Output
147
Note
For the first example, we have c_1=a_1\& b_2=0, c_2=a_2\& b_1=2, c_3=a_3\& b_1=0, c_4 = a_4\& b_1=0.Thus c_1 | c_2 | c_3 |c_4 =2, and this is the minimal answer we can get. | instruction | 0 | 5,959 | 5 | 11,918 |
Tags: bitmasks, brute force, dp, greedy
Correct Solution:
```
n, m = map(int, input().split())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
for i in range(513):
found_ans = True
for j in range(n):
ok = False
for k in range(m):
if (a[j]&b[k])|i == i:
ok = True
if not ok:
found_ans = False
break
if found_ans:
print(i)
break
``` | output | 1 | 5,959 | 5 | 11,919 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Boboniu likes bit operations. He wants to play a game with you.
Boboniu gives you two sequences of non-negative integers a_1,a_2,…,a_n and b_1,b_2,…,b_m.
For each i (1≤ i≤ n), you're asked to choose a j (1≤ j≤ m) and let c_i=a_i\& b_j, where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Note that you can pick the same j for different i's.
Find the minimum possible c_1 | c_2 | … | c_n, where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
Input
The first line contains two integers n and m (1≤ n,m≤ 200).
The next line contains n integers a_1,a_2,…,a_n (0≤ a_i < 2^9).
The next line contains m integers b_1,b_2,…,b_m (0≤ b_i < 2^9).
Output
Print one integer: the minimum possible c_1 | c_2 | … | c_n.
Examples
Input
4 2
2 6 4 0
2 4
Output
2
Input
7 6
1 9 1 9 8 1 0
1 1 4 5 1 4
Output
0
Input
8 5
179 261 432 162 82 43 10 38
379 357 202 184 197
Output
147
Note
For the first example, we have c_1=a_1\& b_2=0, c_2=a_2\& b_1=2, c_3=a_3\& b_1=0, c_4 = a_4\& b_1=0.Thus c_1 | c_2 | c_3 |c_4 =2, and this is the minimal answer we can get. | instruction | 0 | 5,960 | 5 | 11,920 |
Tags: bitmasks, brute force, dp, greedy
Correct Solution:
```
def found(i,j):
for k in j:
if k|i<=i:
return True
return False
n,m = map(int,input().split())
a = list(set(list(map(int,input().split()))))
b = list(set(list(map(int,input().split()))))
c = []
for i in a:
c.append([])
for j in b:
c[-1].append(i&j)
for i in range(1024):
flag = 0
for j in c:
if not found(i,j):
flag = 1
break
if not flag:
ans = i
break
print (ans)
``` | output | 1 | 5,960 | 5 | 11,921 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Boboniu likes bit operations. He wants to play a game with you.
Boboniu gives you two sequences of non-negative integers a_1,a_2,…,a_n and b_1,b_2,…,b_m.
For each i (1≤ i≤ n), you're asked to choose a j (1≤ j≤ m) and let c_i=a_i\& b_j, where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Note that you can pick the same j for different i's.
Find the minimum possible c_1 | c_2 | … | c_n, where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
Input
The first line contains two integers n and m (1≤ n,m≤ 200).
The next line contains n integers a_1,a_2,…,a_n (0≤ a_i < 2^9).
The next line contains m integers b_1,b_2,…,b_m (0≤ b_i < 2^9).
Output
Print one integer: the minimum possible c_1 | c_2 | … | c_n.
Examples
Input
4 2
2 6 4 0
2 4
Output
2
Input
7 6
1 9 1 9 8 1 0
1 1 4 5 1 4
Output
0
Input
8 5
179 261 432 162 82 43 10 38
379 357 202 184 197
Output
147
Note
For the first example, we have c_1=a_1\& b_2=0, c_2=a_2\& b_1=2, c_3=a_3\& b_1=0, c_4 = a_4\& b_1=0.Thus c_1 | c_2 | c_3 |c_4 =2, and this is the minimal answer we can get. | instruction | 0 | 5,961 | 5 | 11,922 |
Tags: bitmasks, brute force, dp, greedy
Correct Solution:
```
import os
from io import BytesIO
input = BytesIO(os.read(0, os.fstat(0).st_size)).readline
def lii(): return list(map(int, input().split()))
def ii(): return int(input())
n, m = lii()
A = lii()
B = lii()
for res in range(0, 2**9):
flag = True
for a in A:
found = False
for b in B:
c = a & b
if c | res == res:
found = True
break
if not found:
flag = False
break
if flag:
print(res)
break
else:
continue
``` | output | 1 | 5,961 | 5 | 11,923 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Boboniu likes bit operations. He wants to play a game with you.
Boboniu gives you two sequences of non-negative integers a_1,a_2,…,a_n and b_1,b_2,…,b_m.
For each i (1≤ i≤ n), you're asked to choose a j (1≤ j≤ m) and let c_i=a_i\& b_j, where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Note that you can pick the same j for different i's.
Find the minimum possible c_1 | c_2 | … | c_n, where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
Input
The first line contains two integers n and m (1≤ n,m≤ 200).
The next line contains n integers a_1,a_2,…,a_n (0≤ a_i < 2^9).
The next line contains m integers b_1,b_2,…,b_m (0≤ b_i < 2^9).
Output
Print one integer: the minimum possible c_1 | c_2 | … | c_n.
Examples
Input
4 2
2 6 4 0
2 4
Output
2
Input
7 6
1 9 1 9 8 1 0
1 1 4 5 1 4
Output
0
Input
8 5
179 261 432 162 82 43 10 38
379 357 202 184 197
Output
147
Note
For the first example, we have c_1=a_1\& b_2=0, c_2=a_2\& b_1=2, c_3=a_3\& b_1=0, c_4 = a_4\& b_1=0.Thus c_1 | c_2 | c_3 |c_4 =2, and this is the minimal answer we can get. | instruction | 0 | 5,962 | 5 | 11,924 |
Tags: bitmasks, brute force, dp, greedy
Correct Solution:
```
from sys import stdin,stdout
from math import gcd,sqrt,factorial
from collections import deque,defaultdict
input=stdin.readline
R=lambda:map(int,input().split())
I=lambda:int(input())
S=lambda:input().rstrip('\n')
L=lambda:list(R())
P=lambda x:stdout.write(x)
lcm=lambda x,y:(x*y)//gcd(x,y)
hg=lambda x,y:((y+x-1)//x)*x
pw=lambda x:0 if x==1 else 1+pw(x//2)
chk=lambda x:chk(x//2) if not x%2 else True if x==1 else False
sm=lambda x:(x**2+x)//2
N=10**9+7
def check(i):
for p in a:
flg=False
for k in b:
if (p&k)|i==i:flg=True
if not flg:return flg
return True
m,n=R()
a=L()
b=L()
for i in range(2**9):
if check(i):exit(print(i))
``` | output | 1 | 5,962 | 5 | 11,925 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Boboniu likes bit operations. He wants to play a game with you.
Boboniu gives you two sequences of non-negative integers a_1,a_2,…,a_n and b_1,b_2,…,b_m.
For each i (1≤ i≤ n), you're asked to choose a j (1≤ j≤ m) and let c_i=a_i\& b_j, where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Note that you can pick the same j for different i's.
Find the minimum possible c_1 | c_2 | … | c_n, where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
Input
The first line contains two integers n and m (1≤ n,m≤ 200).
The next line contains n integers a_1,a_2,…,a_n (0≤ a_i < 2^9).
The next line contains m integers b_1,b_2,…,b_m (0≤ b_i < 2^9).
Output
Print one integer: the minimum possible c_1 | c_2 | … | c_n.
Examples
Input
4 2
2 6 4 0
2 4
Output
2
Input
7 6
1 9 1 9 8 1 0
1 1 4 5 1 4
Output
0
Input
8 5
179 261 432 162 82 43 10 38
379 357 202 184 197
Output
147
Note
For the first example, we have c_1=a_1\& b_2=0, c_2=a_2\& b_1=2, c_3=a_3\& b_1=0, c_4 = a_4\& b_1=0.Thus c_1 | c_2 | c_3 |c_4 =2, and this is the minimal answer we can get. | instruction | 0 | 5,963 | 5 | 11,926 |
Tags: bitmasks, brute force, dp, greedy
Correct Solution:
```
'''
___ ___ ___ ___ ___ ___
/\__\ /\ \ _____ /\ \ /\ \ /\ \ /\__\
/:/ _/_ \:\ \ /::\ \ \:\ \ ___ /::\ \ |::\ \ ___ /:/ _/_
/:/ /\ \ \:\ \ /:/\:\ \ \:\ \ /\__\ /:/\:\__\ |:|:\ \ /\__\ /:/ /\ \
/:/ /::\ \ ___ \:\ \ /:/ \:\__\ ___ /::\ \ /:/__/ /:/ /:/ / __|:|\:\ \ /:/ / /:/ /::\ \
/:/_/:/\:\__\ /\ \ \:\__\ /:/__/ \:|__| /\ /:/\:\__\ /::\ \ /:/_/:/__/___ /::::|_\:\__\ /:/__/ /:/_/:/\:\__\
\:\/:/ /:/ / \:\ \ /:/ / \:\ \ /:/ / \:\/:/ \/__/ \/\:\ \__ \:\/:::::/ / \:\~~\ \/__/ /::\ \ \:\/:/ /:/ /
\::/ /:/ / \:\ /:/ / \:\ /:/ / \::/__/ ~~\:\/\__\ \::/~~/~~~~ \:\ \ /:/\:\ \ \::/ /:/ /
\/_/:/ / \:\/:/ / \:\/:/ / \:\ \ \::/ / \:\~~\ \:\ \ \/__\:\ \ \/_/:/ /
/:/ / \::/ / \::/ / \:\__\ /:/ / \:\__\ \:\__\ \:\__\ /:/ /
\/__/ \/__/ \/__/ \/__/ \/__/ \/__/ \/__/ \/__/ \/__/
'''
"""
░░██▄░░░░░░░░░░░▄██
░▄▀░█▄░░░░░░░░▄█░░█░
░█░▄░█▄░░░░░░▄█░▄░█░
░█░██████████████▄█░
░█████▀▀████▀▀█████░
▄█▀█▀░░░████░░░▀▀███
██░░▀████▀▀████▀░░██
██░░░░█▀░░░░▀█░░░░██
███▄░░░░░░░░░░░░▄███
░▀███▄░░████░░▄███▀░
░░░▀██▄░▀██▀░▄██▀░░░
░░░░░░▀██████▀░░░░░░
░░░░░░░░░░░░░░░░░░░░
"""
import sys
import math
import collections
import operator as op
from collections import deque
from math import gcd, inf, sqrt, pi, cos, sin, ceil, log2
from bisect import bisect_right, bisect_left
# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')
from functools import reduce
from sys import stdin, stdout, setrecursionlimit
setrecursionlimit(2**20)
def factorial(n):
if n == 0:
return 1
return (n * factorial(n - 1))
def ncr(n, r):
r = min(r, n - r)
numer = reduce(op.mul, range(n, n - r, -1), 1)
denom = reduce(op.mul, range(1, r + 1), 1)
return numer // denom # or / in Python 2
def prime_factors(n):
i = 2
factors = []
while i * i <= n:
if n % i:
i += 1
else:
n //= i
factors.append(i)
if n > 1:
factors.append(n)
return (list(factors))
def sumDigits(no):
return 0 if no == 0 else int(no % 10) + sumDigits(int(no / 10))
MOD = 1000000007
PMOD = 998244353
N = 10**5
T = 1
# T = int(stdin.readline())
for _ in range(T):
n, m = list(map(int, stdin.readline().rstrip().split()))
# n = int(stdin.readline())
a = list(map(int, stdin.readline().rstrip().split()))
b = list(map(int, stdin.readline().rstrip().split()))
# a = str(stdin.readline().strip('\n'))
# k = int(stdin.readline())
# c = list(map(int, stdin.readline().rstrip().split()))
ans = inf
for A in range(512):
for i in range(n):
isPossible = True
for j in range(m):
t = False
if (a[i] & b[j]) | A == A:
t = True
break
if not t:
isPossible = False
break
if isPossible:
ans = A
break
print(ans)
``` | output | 1 | 5,963 | 5 | 11,927 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Boboniu likes bit operations. He wants to play a game with you.
Boboniu gives you two sequences of non-negative integers a_1,a_2,…,a_n and b_1,b_2,…,b_m.
For each i (1≤ i≤ n), you're asked to choose a j (1≤ j≤ m) and let c_i=a_i\& b_j, where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Note that you can pick the same j for different i's.
Find the minimum possible c_1 | c_2 | … | c_n, where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
Input
The first line contains two integers n and m (1≤ n,m≤ 200).
The next line contains n integers a_1,a_2,…,a_n (0≤ a_i < 2^9).
The next line contains m integers b_1,b_2,…,b_m (0≤ b_i < 2^9).
Output
Print one integer: the minimum possible c_1 | c_2 | … | c_n.
Examples
Input
4 2
2 6 4 0
2 4
Output
2
Input
7 6
1 9 1 9 8 1 0
1 1 4 5 1 4
Output
0
Input
8 5
179 261 432 162 82 43 10 38
379 357 202 184 197
Output
147
Note
For the first example, we have c_1=a_1\& b_2=0, c_2=a_2\& b_1=2, c_3=a_3\& b_1=0, c_4 = a_4\& b_1=0.Thus c_1 | c_2 | c_3 |c_4 =2, and this is the minimal answer we can get. | instruction | 0 | 5,964 | 5 | 11,928 |
Tags: bitmasks, brute force, dp, greedy
Correct Solution:
```
input()
a = [*map(int, input().split())]
b = [*map(int, input().split())]
for x in range(512):
r=1
for v in a:r&=any(v&j|x==x for j in b)
if r:
print(x);break
``` | output | 1 | 5,964 | 5 | 11,929 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Boboniu likes bit operations. He wants to play a game with you.
Boboniu gives you two sequences of non-negative integers a_1,a_2,…,a_n and b_1,b_2,…,b_m.
For each i (1≤ i≤ n), you're asked to choose a j (1≤ j≤ m) and let c_i=a_i\& b_j, where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Note that you can pick the same j for different i's.
Find the minimum possible c_1 | c_2 | … | c_n, where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
Input
The first line contains two integers n and m (1≤ n,m≤ 200).
The next line contains n integers a_1,a_2,…,a_n (0≤ a_i < 2^9).
The next line contains m integers b_1,b_2,…,b_m (0≤ b_i < 2^9).
Output
Print one integer: the minimum possible c_1 | c_2 | … | c_n.
Examples
Input
4 2
2 6 4 0
2 4
Output
2
Input
7 6
1 9 1 9 8 1 0
1 1 4 5 1 4
Output
0
Input
8 5
179 261 432 162 82 43 10 38
379 357 202 184 197
Output
147
Note
For the first example, we have c_1=a_1\& b_2=0, c_2=a_2\& b_1=2, c_3=a_3\& b_1=0, c_4 = a_4\& b_1=0.Thus c_1 | c_2 | c_3 |c_4 =2, and this is the minimal answer we can get. | instruction | 0 | 5,965 | 5 | 11,930 |
Tags: bitmasks, brute force, dp, greedy
Correct Solution:
```
import sys
import math as mt
input=sys.stdin.buffer.readline
I=lambda:list(map(int,input().split()))
for tc in range(1):
n,m=I()
a=I()
b=I()
arr=[[a[i]&b[j] for j in range(m)] for i in range(n)]
arr.sort(key=lambda ar:min(ar),reverse=True)
#print(arr)
ans=0
for j in arr:
ans=min([i|ans for i in j])
print(ans)
``` | output | 1 | 5,965 | 5 | 11,931 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Boboniu likes bit operations. He wants to play a game with you.
Boboniu gives you two sequences of non-negative integers a_1,a_2,…,a_n and b_1,b_2,…,b_m.
For each i (1≤ i≤ n), you're asked to choose a j (1≤ j≤ m) and let c_i=a_i\& b_j, where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Note that you can pick the same j for different i's.
Find the minimum possible c_1 | c_2 | … | c_n, where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
Input
The first line contains two integers n and m (1≤ n,m≤ 200).
The next line contains n integers a_1,a_2,…,a_n (0≤ a_i < 2^9).
The next line contains m integers b_1,b_2,…,b_m (0≤ b_i < 2^9).
Output
Print one integer: the minimum possible c_1 | c_2 | … | c_n.
Examples
Input
4 2
2 6 4 0
2 4
Output
2
Input
7 6
1 9 1 9 8 1 0
1 1 4 5 1 4
Output
0
Input
8 5
179 261 432 162 82 43 10 38
379 357 202 184 197
Output
147
Note
For the first example, we have c_1=a_1\& b_2=0, c_2=a_2\& b_1=2, c_3=a_3\& b_1=0, c_4 = a_4\& b_1=0.Thus c_1 | c_2 | c_3 |c_4 =2, and this is the minimal answer we can get.
Submitted Solution:
```
n, m = map(int, input().split())
*a, = map(int, input().split())
*b, = map(int, input().split())
ans = 0
for v in range(2**9):
ok = True
for i in range(n):
found = False
for j in range(m):
if (v | (a[i] & b[j])) == v:
found = True
ok = ok & found
if not ok:
break
if ok:
ans = v
break
print(ans)
'''
mm = 0
for i in range(n):
tt = 2**10
for j in range(m):
t = a[i] & b[j]
if t < tt:
tt = t
if tt > mm:
mm = tt
ans = mm
for i in range(n):
c = 2**10
for j in range(m):
t = ans | (a[i] & b[j])
if t < c:
c = t
ans = c
print(ans)
'''
``` | instruction | 0 | 5,966 | 5 | 11,932 |
Yes | output | 1 | 5,966 | 5 | 11,933 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Boboniu likes bit operations. He wants to play a game with you.
Boboniu gives you two sequences of non-negative integers a_1,a_2,…,a_n and b_1,b_2,…,b_m.
For each i (1≤ i≤ n), you're asked to choose a j (1≤ j≤ m) and let c_i=a_i\& b_j, where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Note that you can pick the same j for different i's.
Find the minimum possible c_1 | c_2 | … | c_n, where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
Input
The first line contains two integers n and m (1≤ n,m≤ 200).
The next line contains n integers a_1,a_2,…,a_n (0≤ a_i < 2^9).
The next line contains m integers b_1,b_2,…,b_m (0≤ b_i < 2^9).
Output
Print one integer: the minimum possible c_1 | c_2 | … | c_n.
Examples
Input
4 2
2 6 4 0
2 4
Output
2
Input
7 6
1 9 1 9 8 1 0
1 1 4 5 1 4
Output
0
Input
8 5
179 261 432 162 82 43 10 38
379 357 202 184 197
Output
147
Note
For the first example, we have c_1=a_1\& b_2=0, c_2=a_2\& b_1=2, c_3=a_3\& b_1=0, c_4 = a_4\& b_1=0.Thus c_1 | c_2 | c_3 |c_4 =2, and this is the minimal answer we can get.
Submitted Solution:
```
import sys
input = sys.stdin.readline
n, m = list(map(int, input().split()))
a = list(map(int, input().split()))
b = list(map(int, input().split()))
end = False
for i in range(512):
for j in a:
restart = True
for k in b:
if (j & k) | i == i:
restart = False
break
if restart: break
if restart: continue
else:
print(i)
break
``` | instruction | 0 | 5,967 | 5 | 11,934 |
Yes | output | 1 | 5,967 | 5 | 11,935 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Boboniu likes bit operations. He wants to play a game with you.
Boboniu gives you two sequences of non-negative integers a_1,a_2,…,a_n and b_1,b_2,…,b_m.
For each i (1≤ i≤ n), you're asked to choose a j (1≤ j≤ m) and let c_i=a_i\& b_j, where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Note that you can pick the same j for different i's.
Find the minimum possible c_1 | c_2 | … | c_n, where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
Input
The first line contains two integers n and m (1≤ n,m≤ 200).
The next line contains n integers a_1,a_2,…,a_n (0≤ a_i < 2^9).
The next line contains m integers b_1,b_2,…,b_m (0≤ b_i < 2^9).
Output
Print one integer: the minimum possible c_1 | c_2 | … | c_n.
Examples
Input
4 2
2 6 4 0
2 4
Output
2
Input
7 6
1 9 1 9 8 1 0
1 1 4 5 1 4
Output
0
Input
8 5
179 261 432 162 82 43 10 38
379 357 202 184 197
Output
147
Note
For the first example, we have c_1=a_1\& b_2=0, c_2=a_2\& b_1=2, c_3=a_3\& b_1=0, c_4 = a_4\& b_1=0.Thus c_1 | c_2 | c_3 |c_4 =2, and this is the minimal answer we can get.
Submitted Solution:
```
from collections import Counter
from collections import deque
from sys import stdin
from bisect import *
from heapq import *
import math
g = lambda : stdin.readline().strip()
gl = lambda : g().split()
gil = lambda : [int(var) for var in gl()]
gfl = lambda : [float(var) for var in gl()]
gcl = lambda : list(g())
gbs = lambda : [int(var) for var in g()]
mod = int(1e9)+7
inf = float("inf")
def check(A):
for i in range(n):
fnd = False
for j in range(m):
if (a[i]&b[j])|A == A:
fnd = True; break
if not fnd : return False
return True
n, m = gil()
a = gil()
b = gil()
for i in range(2**9 + 1):
if check(i):
print(i)
break
``` | instruction | 0 | 5,968 | 5 | 11,936 |
Yes | output | 1 | 5,968 | 5 | 11,937 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Boboniu likes bit operations. He wants to play a game with you.
Boboniu gives you two sequences of non-negative integers a_1,a_2,…,a_n and b_1,b_2,…,b_m.
For each i (1≤ i≤ n), you're asked to choose a j (1≤ j≤ m) and let c_i=a_i\& b_j, where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Note that you can pick the same j for different i's.
Find the minimum possible c_1 | c_2 | … | c_n, where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
Input
The first line contains two integers n and m (1≤ n,m≤ 200).
The next line contains n integers a_1,a_2,…,a_n (0≤ a_i < 2^9).
The next line contains m integers b_1,b_2,…,b_m (0≤ b_i < 2^9).
Output
Print one integer: the minimum possible c_1 | c_2 | … | c_n.
Examples
Input
4 2
2 6 4 0
2 4
Output
2
Input
7 6
1 9 1 9 8 1 0
1 1 4 5 1 4
Output
0
Input
8 5
179 261 432 162 82 43 10 38
379 357 202 184 197
Output
147
Note
For the first example, we have c_1=a_1\& b_2=0, c_2=a_2\& b_1=2, c_3=a_3\& b_1=0, c_4 = a_4\& b_1=0.Thus c_1 | c_2 | c_3 |c_4 =2, and this is the minimal answer we can get.
Submitted Solution:
```
from functools import lru_cache
from sys import stdin, stdout
import sys
from math import *
# from collections import deque
# sys.setrecursionlimit(int(2e5))
input = stdin.readline
# print = stdout.write
# dp=[-1]*100000
n,m=map(int,input().split())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
ans=inf
for i in range(2**9):
c=0
for j in range(n):
for k in range(m):
if (a[j]&b[k])|i==i:
c+=1
break
if(c==n):
ans=min(ans,i)
print(ans)
``` | instruction | 0 | 5,969 | 5 | 11,938 |
Yes | output | 1 | 5,969 | 5 | 11,939 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Boboniu likes bit operations. He wants to play a game with you.
Boboniu gives you two sequences of non-negative integers a_1,a_2,…,a_n and b_1,b_2,…,b_m.
For each i (1≤ i≤ n), you're asked to choose a j (1≤ j≤ m) and let c_i=a_i\& b_j, where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Note that you can pick the same j for different i's.
Find the minimum possible c_1 | c_2 | … | c_n, where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
Input
The first line contains two integers n and m (1≤ n,m≤ 200).
The next line contains n integers a_1,a_2,…,a_n (0≤ a_i < 2^9).
The next line contains m integers b_1,b_2,…,b_m (0≤ b_i < 2^9).
Output
Print one integer: the minimum possible c_1 | c_2 | … | c_n.
Examples
Input
4 2
2 6 4 0
2 4
Output
2
Input
7 6
1 9 1 9 8 1 0
1 1 4 5 1 4
Output
0
Input
8 5
179 261 432 162 82 43 10 38
379 357 202 184 197
Output
147
Note
For the first example, we have c_1=a_1\& b_2=0, c_2=a_2\& b_1=2, c_3=a_3\& b_1=0, c_4 = a_4\& b_1=0.Thus c_1 | c_2 | c_3 |c_4 =2, and this is the minimal answer we can get.
Submitted Solution:
```
info = list(map(int, input('').split(' ')))
array1 = list(map(int, input('').split(' ')))
array2 = list(map(int, input('').split(' ')))
proc = dict((elem1, [elem1 & elem2 for elem2 in array2]) for elem1 in array1)
final = 1000000000000000000
for i in range(len(array2)):
output = proc[array1[0]][i]
for j in range(1, len(array1)):
temp = list()
for k in range(len(array2)):
temp.append(output | proc[array1[j]][k])
temp.sort()
output = temp[0]
final = min(final, output)
print(output)
``` | instruction | 0 | 5,970 | 5 | 11,940 |
No | output | 1 | 5,970 | 5 | 11,941 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Boboniu likes bit operations. He wants to play a game with you.
Boboniu gives you two sequences of non-negative integers a_1,a_2,…,a_n and b_1,b_2,…,b_m.
For each i (1≤ i≤ n), you're asked to choose a j (1≤ j≤ m) and let c_i=a_i\& b_j, where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Note that you can pick the same j for different i's.
Find the minimum possible c_1 | c_2 | … | c_n, where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
Input
The first line contains two integers n and m (1≤ n,m≤ 200).
The next line contains n integers a_1,a_2,…,a_n (0≤ a_i < 2^9).
The next line contains m integers b_1,b_2,…,b_m (0≤ b_i < 2^9).
Output
Print one integer: the minimum possible c_1 | c_2 | … | c_n.
Examples
Input
4 2
2 6 4 0
2 4
Output
2
Input
7 6
1 9 1 9 8 1 0
1 1 4 5 1 4
Output
0
Input
8 5
179 261 432 162 82 43 10 38
379 357 202 184 197
Output
147
Note
For the first example, we have c_1=a_1\& b_2=0, c_2=a_2\& b_1=2, c_3=a_3\& b_1=0, c_4 = a_4\& b_1=0.Thus c_1 | c_2 | c_3 |c_4 =2, and this is the minimal answer we can get.
Submitted Solution:
```
n,m = map(int, input().split())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
A = {}
minn = 1024
prd = 0
for i in range(n):
minn = 1024
if A.get(a[i],0):
prd = prd|A.get([a[i]])
else:
for j in range(m):
# print(a[i]&b[j])
if minn>(a[i]&b[j]):
minn = a[i]&b[j]
I = i
J = j
prd = prd|minn
A[a[I]] = minn
print(prd)
``` | instruction | 0 | 5,971 | 5 | 11,942 |
No | output | 1 | 5,971 | 5 | 11,943 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Boboniu likes bit operations. He wants to play a game with you.
Boboniu gives you two sequences of non-negative integers a_1,a_2,…,a_n and b_1,b_2,…,b_m.
For each i (1≤ i≤ n), you're asked to choose a j (1≤ j≤ m) and let c_i=a_i\& b_j, where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Note that you can pick the same j for different i's.
Find the minimum possible c_1 | c_2 | … | c_n, where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
Input
The first line contains two integers n and m (1≤ n,m≤ 200).
The next line contains n integers a_1,a_2,…,a_n (0≤ a_i < 2^9).
The next line contains m integers b_1,b_2,…,b_m (0≤ b_i < 2^9).
Output
Print one integer: the minimum possible c_1 | c_2 | … | c_n.
Examples
Input
4 2
2 6 4 0
2 4
Output
2
Input
7 6
1 9 1 9 8 1 0
1 1 4 5 1 4
Output
0
Input
8 5
179 261 432 162 82 43 10 38
379 357 202 184 197
Output
147
Note
For the first example, we have c_1=a_1\& b_2=0, c_2=a_2\& b_1=2, c_3=a_3\& b_1=0, c_4 = a_4\& b_1=0.Thus c_1 | c_2 | c_3 |c_4 =2, and this is the minimal answer we can get.
Submitted Solution:
```
import sys
import math as mt
input=sys.stdin.buffer.readline
I=lambda:list(map(int,input().split()))
for tc in range(1):
n,m=I()
a=I()
b=I()
arr=[[a[i]&b[j] for j in range(m)] for i in range(n)]
arr.sort(key=lambda ar:min(ar),reverse=True)
print(arr)
ans=0
for j in arr:
ans=min([i|ans for i in j])
print(ans)
``` | instruction | 0 | 5,972 | 5 | 11,944 |
No | output | 1 | 5,972 | 5 | 11,945 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Boboniu likes bit operations. He wants to play a game with you.
Boboniu gives you two sequences of non-negative integers a_1,a_2,…,a_n and b_1,b_2,…,b_m.
For each i (1≤ i≤ n), you're asked to choose a j (1≤ j≤ m) and let c_i=a_i\& b_j, where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Note that you can pick the same j for different i's.
Find the minimum possible c_1 | c_2 | … | c_n, where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
Input
The first line contains two integers n and m (1≤ n,m≤ 200).
The next line contains n integers a_1,a_2,…,a_n (0≤ a_i < 2^9).
The next line contains m integers b_1,b_2,…,b_m (0≤ b_i < 2^9).
Output
Print one integer: the minimum possible c_1 | c_2 | … | c_n.
Examples
Input
4 2
2 6 4 0
2 4
Output
2
Input
7 6
1 9 1 9 8 1 0
1 1 4 5 1 4
Output
0
Input
8 5
179 261 432 162 82 43 10 38
379 357 202 184 197
Output
147
Note
For the first example, we have c_1=a_1\& b_2=0, c_2=a_2\& b_1=2, c_3=a_3\& b_1=0, c_4 = a_4\& b_1=0.Thus c_1 | c_2 | c_3 |c_4 =2, and this is the minimal answer we can get.
Submitted Solution:
```
n,m=map(int, input().split(' '))
a_list=list(map(int, input().split(' ')))
b_list=list(map(int, input().split(' ')))
c_list=[[] for i in range(len(a_list))]
for a in range(len(a_list)):
for b in b_list:
c_list[a].append(a_list[a]&b)
minimum=[]
for x in range(len(a_list)):
minimum.append(min(c_list[x]))
maximum=max(minimum)
for x in range(len(a_list)):
temp=c_list[x][0]|maximum
for y in range(len(b_list)):
if(temp>c_list[x][y]|maximum):
temp=c_list[x][y]|maximum
maximum=temp
print(maximum)
``` | instruction | 0 | 5,973 | 5 | 11,946 |
No | output | 1 | 5,973 | 5 | 11,947 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
DZY has a sequence a, consisting of n integers.
We'll call a sequence ai, ai + 1, ..., aj (1 ≤ i ≤ j ≤ n) a subsegment of the sequence a. The value (j - i + 1) denotes the length of the subsegment.
Your task is to find the longest subsegment of a, such that it is possible to change at most one number (change one number to any integer you want) from the subsegment to make the subsegment strictly increasing.
You only need to output the length of the subsegment you find.
Input
The first line contains integer n (1 ≤ n ≤ 105). The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109).
Output
In a single line print the answer to the problem — the maximum length of the required subsegment.
Examples
Input
6
7 2 3 1 5 6
Output
5
Note
You can choose subsegment a2, a3, a4, a5, a6 and change its 3rd element (that is a4) to 4.
Submitted Solution:
```
n = int(input())
a = [int(x) for x in input().split()]
res = [[0], []]
cur = 1
for i in range(1, n):
res[0].append(cur)
if a[i-1] < a[i]:
cur += 1
else:
cur = 1
cur = 1
for i in range(n-2, -1, -1):
res[1].append(cur)
if a[i+1] > a[i]:
cur += 1
else:
cur = 1
res[1] = res[1][::-1] + [0]
fin = max(max(res[1][0] + 1, res[0][-1] + 1), 2)
#print(res)
for i in range(1, n - 1):
fin = max(fin, max(res[0][i] + 1, res[1][i] + 1))
if a[i - 1] + 1 < a[i + 1]:
fin = max(fin, res[0][i] + res[1][i] + 1)
print(min(n, fin))
``` | instruction | 0 | 6,180 | 5 | 12,360 |
Yes | output | 1 | 6,180 | 5 | 12,361 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
DZY has a sequence a, consisting of n integers.
We'll call a sequence ai, ai + 1, ..., aj (1 ≤ i ≤ j ≤ n) a subsegment of the sequence a. The value (j - i + 1) denotes the length of the subsegment.
Your task is to find the longest subsegment of a, such that it is possible to change at most one number (change one number to any integer you want) from the subsegment to make the subsegment strictly increasing.
You only need to output the length of the subsegment you find.
Input
The first line contains integer n (1 ≤ n ≤ 105). The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109).
Output
In a single line print the answer to the problem — the maximum length of the required subsegment.
Examples
Input
6
7 2 3 1 5 6
Output
5
Note
You can choose subsegment a2, a3, a4, a5, a6 and change its 3rd element (that is a4) to 4.
Submitted Solution:
```
import sys
def inputArray():
tp=str(input()).split();
return list(map( int , tp));
if( __name__=="__main__"):
n=int(input());
input=inputArray();
if(n==1):
print("1");
sys.exit();
left=[1 for x in range(n)];
right=[1 for x in range(n) ];
for i in range(1,n,1):
if( input[i-1] < input[i]):
left[i]=left[i-1]+1;
for i in range(n-2,-1,-1):
if( input[i] < input[i+1]):
right[i]=right[i+1]+1;
ans=1;
for i in range(n):
if(i==0):
#Make curr smaller than `right one
ans=max(ans , right[i+1]+1);
continue;
if(i==n-1 ):
ans=max(ans, left[i-1]+1);
continue;
ans=max(ans , right[i+1] +1 );
ans=max(ans ,left[i-1]+1);
if( input[i+1]-input[i-1] >=2):
ans=max(ans , left[i-1]+1+right[i+1]);
print(ans);
``` | instruction | 0 | 6,183 | 5 | 12,366 |
Yes | output | 1 | 6,183 | 5 | 12,367 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
DZY has a sequence a, consisting of n integers.
We'll call a sequence ai, ai + 1, ..., aj (1 ≤ i ≤ j ≤ n) a subsegment of the sequence a. The value (j - i + 1) denotes the length of the subsegment.
Your task is to find the longest subsegment of a, such that it is possible to change at most one number (change one number to any integer you want) from the subsegment to make the subsegment strictly increasing.
You only need to output the length of the subsegment you find.
Input
The first line contains integer n (1 ≤ n ≤ 105). The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109).
Output
In a single line print the answer to the problem — the maximum length of the required subsegment.
Examples
Input
6
7 2 3 1 5 6
Output
5
Note
You can choose subsegment a2, a3, a4, a5, a6 and change its 3rd element (that is a4) to 4.
Submitted Solution:
```
n = int(input())
a = [int(x) for x in input().split()]
res = []
cur = 1
for i in range(1, n):
if a[i] > a[i-1]:
cur += 1
elif cur != 1:
res.append([i - cur, i - 1])
cur = 1
if cur != 1:
res.append([n - cur, n - 1])
#print(res)
if len(res) > 1:
maxres = -1
for i in range(1, len(res)):
if (res[i][0] - res[i-1][1] == 1) and (a[res[i-1][1]] + 1 < a[res[i][0] + 1]):
maxres = max(maxres, res[i][1] - res[i-1][0] + 1)
else:
#print(a[res[i-1][1]], a[res[i][0] + 1])
maxres = max(maxres, max(res[i][1] - res[i][0] + 2, res[i-1][1] - res[i][0] + 2))
print(min(n, maxres))
elif len(res) == 1:
print(min(res[0][1] - res[0][0] + 2, n))
else:
print(min(n, 2))
``` | instruction | 0 | 6,184 | 5 | 12,368 |
No | output | 1 | 6,184 | 5 | 12,369 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
DZY has a sequence a, consisting of n integers.
We'll call a sequence ai, ai + 1, ..., aj (1 ≤ i ≤ j ≤ n) a subsegment of the sequence a. The value (j - i + 1) denotes the length of the subsegment.
Your task is to find the longest subsegment of a, such that it is possible to change at most one number (change one number to any integer you want) from the subsegment to make the subsegment strictly increasing.
You only need to output the length of the subsegment you find.
Input
The first line contains integer n (1 ≤ n ≤ 105). The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109).
Output
In a single line print the answer to the problem — the maximum length of the required subsegment.
Examples
Input
6
7 2 3 1 5 6
Output
5
Note
You can choose subsegment a2, a3, a4, a5, a6 and change its 3rd element (that is a4) to 4.
Submitted Solution:
```
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 998244353
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(): return [list(map(int, l.split())) for l in sys.stdin.readlines()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def pe(s): return print(str(s), file=sys.stderr)
def JA(a, sep): return sep.join(map(str, a))
def JAA(a, s, t): return s.join(t.join(map(str, b)) for b in a)
def main():
n = I()
a = LI()
b = [1]
for i in range(1,n):
if a[i-1] < a[i]:
b.append(b[-1] + 1)
else:
b.append(1)
c = [1]
for i in range(n-2,-1,-1):
if a[i+1] > a[i]:
c.append(c[-1]+1)
else:
c.append(1)
c = c[::-1]
# print(b)
# print(c)
r = max(c[0], b[-1]) + 1
for i in range(1,n-1):
if a[i+1] - a[i-1] > 1:
t = b[i-1] + c[i+1] + 1
if r < t:
r = t
else:
t = max(b[i-1], c[i+1]) + 1
if r < t:
r = t
return r
print(main())
``` | instruction | 0 | 6,185 | 5 | 12,370 |
No | output | 1 | 6,185 | 5 | 12,371 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
DZY has a sequence a, consisting of n integers.
We'll call a sequence ai, ai + 1, ..., aj (1 ≤ i ≤ j ≤ n) a subsegment of the sequence a. The value (j - i + 1) denotes the length of the subsegment.
Your task is to find the longest subsegment of a, such that it is possible to change at most one number (change one number to any integer you want) from the subsegment to make the subsegment strictly increasing.
You only need to output the length of the subsegment you find.
Input
The first line contains integer n (1 ≤ n ≤ 105). The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109).
Output
In a single line print the answer to the problem — the maximum length of the required subsegment.
Examples
Input
6
7 2 3 1 5 6
Output
5
Note
You can choose subsegment a2, a3, a4, a5, a6 and change its 3rd element (that is a4) to 4.
Submitted Solution:
```
n = int(input())
a = [int(x) for x in input().split()]
res = []
cur = 1
for i in range(1, n):
if a[i] > a[i-1]:
cur += 1
elif cur != 1:
res.append([i - cur, i - 1])
cur = 1
if cur != 1:
res.append([n - cur, n - 1])
if len(res) > 1:
maxres = -1
for i in range(1, len(res)):
maxres = max(maxres, res[i][1] - res[i-1][0] + 1)
print(maxres)
elif len(res) == 1:
print(min(res[0][1] - res[0][0] + 2, n))
else:
print(min(n, 2))
``` | instruction | 0 | 6,186 | 5 | 12,372 |
No | output | 1 | 6,186 | 5 | 12,373 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little X has n distinct integers: p1, p2, ..., pn. He wants to divide all of them into two sets A and B. The following two conditions must be satisfied:
* If number x belongs to set A, then number a - x must also belong to set A.
* If number x belongs to set B, then number b - x must also belong to set B.
Help Little X divide the numbers into two sets or determine that it's impossible.
Input
The first line contains three space-separated integers n, a, b (1 ≤ n ≤ 105; 1 ≤ a, b ≤ 109). The next line contains n space-separated distinct integers p1, p2, ..., pn (1 ≤ pi ≤ 109).
Output
If there is a way to divide the numbers into two sets, then print "YES" in the first line. Then print n integers: b1, b2, ..., bn (bi equals either 0, or 1), describing the division. If bi equals to 0, then pi belongs to set A, otherwise it belongs to set B.
If it's impossible, print "NO" (without the quotes).
Examples
Input
4 5 9
2 3 4 5
Output
YES
0 0 1 1
Input
3 3 4
1 2 4
Output
NO
Note
It's OK if all the numbers are in the same set, and the other one is empty.
Submitted Solution:
```
import sys
input = sys.stdin.readline
I = lambda : list(map(int,input().split()))
n,a,b=I()
l=I()
st=set(l)
an=[0]*n
pos=1
for i in range(n):
if (a-l[i]) in st:
continue
if (b-l[i]) in st:
an[i]=1
continue
pos=0;break
if pos:
print("YES")
print(*an)
else:
print("NO")
``` | instruction | 0 | 6,190 | 5 | 12,380 |
No | output | 1 | 6,190 | 5 | 12,381 |
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