message stringlengths 2 67k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 463 109k | cluster float64 19 19 | __index_level_0__ int64 926 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Taro is going to play a card game. However, now he has only n cards, even though there should be 52 cards (he has no Jokers).
The 52 cards include 13 ranks of each of the four suits: spade, heart, club and diamond.
Note
解θͺ¬
Input
In the first line, the number of cards n (n β€ 52) is given.
In the following n lines, data of the n cards are given. Each card is given by a pair of a character and an integer which represent its suit and rank respectively. A suit is represented by 'S', 'H', 'C' and 'D' for spades, hearts, clubs and diamonds respectively. A rank is represented by an integer from 1 to 13.
Output
Print the missing cards. The same as the input format, each card should be printed with a character and an integer separated by a space character in a line. Arrange the missing cards in the following priorities:
* Print cards of spades, hearts, clubs and diamonds in this order.
* If the suits are equal, print cards with lower ranks first.
Example
Input
47
S 10
S 11
S 12
S 13
H 1
H 2
S 6
S 7
S 8
S 9
H 6
H 8
H 9
H 10
H 11
H 4
H 5
S 2
S 3
S 4
S 5
H 12
H 13
C 1
C 2
D 1
D 2
D 3
D 4
D 5
D 6
D 7
C 3
C 4
C 5
C 6
C 7
C 8
C 9
C 10
C 11
C 13
D 9
D 10
D 11
D 12
D 13
Output
S 1
H 3
H 7
C 12
D 8
Submitted Solution:
```
#!/usr/bin/python
n = int(input())
card = [[0 for i in range(13)] for i in range(4)]
print(len(card[0]))
for i in range(n):
a,b = (i for i in input().split())
b = int(b)-1
if a == 'S':
card[0][b] = 1
elif a == 'H':
card[1][b] = 1
elif a == 'C':
card[2][b] = 1
elif a == 'D':
card[3][b] = 1
for i in range(4):
for j in range(13):
if card[i][j] == 0:
if i == 0:
print('S ', end = '')
elif i == 1:
print('H ', end = '')
elif i == 2:
print('C ', end = '')
elif i == 3:
print('D ', end = '')
print(str(j + 1))
``` | instruction | 0 | 86,574 | 19 | 173,148 |
No | output | 1 | 86,574 | 19 | 173,149 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Taro is going to play a card game. However, now he has only n cards, even though there should be 52 cards (he has no Jokers).
The 52 cards include 13 ranks of each of the four suits: spade, heart, club and diamond.
Note
解θͺ¬
Input
In the first line, the number of cards n (n β€ 52) is given.
In the following n lines, data of the n cards are given. Each card is given by a pair of a character and an integer which represent its suit and rank respectively. A suit is represented by 'S', 'H', 'C' and 'D' for spades, hearts, clubs and diamonds respectively. A rank is represented by an integer from 1 to 13.
Output
Print the missing cards. The same as the input format, each card should be printed with a character and an integer separated by a space character in a line. Arrange the missing cards in the following priorities:
* Print cards of spades, hearts, clubs and diamonds in this order.
* If the suits are equal, print cards with lower ranks first.
Example
Input
47
S 10
S 11
S 12
S 13
H 1
H 2
S 6
S 7
S 8
S 9
H 6
H 8
H 9
H 10
H 11
H 4
H 5
S 2
S 3
S 4
S 5
H 12
H 13
C 1
C 2
D 1
D 2
D 3
D 4
D 5
D 6
D 7
C 3
C 4
C 5
C 6
C 7
C 8
C 9
C 10
C 11
C 13
D 9
D 10
D 11
D 12
D 13
Output
S 1
H 3
H 7
C 12
D 8
Submitted Solution:
```
from collections import OrderedDict
cards = OrderedDict()
cards['S'] = set()
cards['H'] = set()
cards['D'] = set()
cards['C'] = set()
n = int(input())
for _ in range(n):
suit, num = input().split()
num = int(num)
cards[suit].add(num)
for suit, nums in cards.items():
for num in range(1,14):
if num not in nums:
print(suit, num)
``` | instruction | 0 | 86,575 | 19 | 173,150 |
No | output | 1 | 86,575 | 19 | 173,151 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Taro is going to play a card game. However, now he has only n cards, even though there should be 52 cards (he has no Jokers).
The 52 cards include 13 ranks of each of the four suits: spade, heart, club and diamond.
Note
解θͺ¬
Input
In the first line, the number of cards n (n β€ 52) is given.
In the following n lines, data of the n cards are given. Each card is given by a pair of a character and an integer which represent its suit and rank respectively. A suit is represented by 'S', 'H', 'C' and 'D' for spades, hearts, clubs and diamonds respectively. A rank is represented by an integer from 1 to 13.
Output
Print the missing cards. The same as the input format, each card should be printed with a character and an integer separated by a space character in a line. Arrange the missing cards in the following priorities:
* Print cards of spades, hearts, clubs and diamonds in this order.
* If the suits are equal, print cards with lower ranks first.
Example
Input
47
S 10
S 11
S 12
S 13
H 1
H 2
S 6
S 7
S 8
S 9
H 6
H 8
H 9
H 10
H 11
H 4
H 5
S 2
S 3
S 4
S 5
H 12
H 13
C 1
C 2
D 1
D 2
D 3
D 4
D 5
D 6
D 7
C 3
C 4
C 5
C 6
C 7
C 8
C 9
C 10
C 11
C 13
D 9
D 10
D 11
D 12
D 13
Output
S 1
H 3
H 7
C 12
D 8
Submitted Solution:
```
for i in range(52):
for j in range(1,5):
for k in range(1,14):
cardlist[i] = [j, k]
luckcard = []
num = int(input())
for i in range(num):
card[i] = [int(x) for x in input().split() if x.isdigit()]
count = 1
while True:
if card[i] == cardlist[count]:
break
else:
luckcard.append(card[i])
count += 1
luckcard.replace("S","0").replace("H","1").replace("C","2").replace("D","3")
luckcard.sort()
for i in range(52-n):
luckcard[i][0].replace("0","S").replace("1","H").replace("2","C").replace("3","D")
print("{0} {1}".format(luckcard[0],luckcard[1]))
``` | instruction | 0 | 86,576 | 19 | 173,152 |
No | output | 1 | 86,576 | 19 | 173,153 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card.
The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty.
Suppose Ciel and Jiro play optimally, what is the score of the game?
Input
The first line contain an integer n (1 β€ n β€ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 β€ si β€ 100) β the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 β€ ck β€ 1000) β the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.
Output
Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally.
Examples
Input
2
1 100
2 1 10
Output
101 10
Input
1
9 2 8 6 5 9 4 7 1 3
Output
30 15
Input
3
3 1 3 2
3 5 4 6
2 8 7
Output
18 18
Input
3
3 1000 1000 1000
6 1000 1000 1000 1000 1000 1000
5 1000 1000 1000 1000 1000
Output
7000 7000
Note
In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10.
In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3. | instruction | 0 | 86,984 | 19 | 173,968 |
Tags: games, greedy, sortings
Correct Solution:
```
chef_sum = 0
ramsay_sum = 0
odds_mids = []
for n in range(int(input())):
c, *c_list = map(int, input().split())
if c%2 == 1:
odds_mids.append(c_list.pop(c//2))
for index,element in enumerate(c_list):
if index < len(c_list)/2:
chef_sum += element
else:
ramsay_sum += element
odds_mids.sort(reverse = True)
for index, element in enumerate(odds_mids):
if index%2 == 0:
chef_sum += element
else:
ramsay_sum += element
print(chef_sum, ramsay_sum)
``` | output | 1 | 86,984 | 19 | 173,969 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card.
The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty.
Suppose Ciel and Jiro play optimally, what is the score of the game?
Input
The first line contain an integer n (1 β€ n β€ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 β€ si β€ 100) β the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 β€ ck β€ 1000) β the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.
Output
Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally.
Examples
Input
2
1 100
2 1 10
Output
101 10
Input
1
9 2 8 6 5 9 4 7 1 3
Output
30 15
Input
3
3 1 3 2
3 5 4 6
2 8 7
Output
18 18
Input
3
3 1000 1000 1000
6 1000 1000 1000 1000 1000 1000
5 1000 1000 1000 1000 1000
Output
7000 7000
Note
In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10.
In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3. | instruction | 0 | 86,985 | 19 | 173,970 |
Tags: games, greedy, sortings
Correct Solution:
```
from functools import reduce
n = int(input())
cards = [list(map(int, input().split()[1:])) for i in range(n)]
mid = sorted((c[len(c) >> 1] for c in cards if len(c) & 1 == 1), reverse=True)
add = lambda x=0, y=0: x + y
a, b = reduce(add, mid[::2] or [0]), reduce(add, mid[1::2] or [0])
for c in cards:
m = len(c) >> 1
a += reduce(add, c[:m] or [0])
b += reduce(add, c[m + (len(c) & 1):] or [0])
print(a, b)
``` | output | 1 | 86,985 | 19 | 173,971 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card.
The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty.
Suppose Ciel and Jiro play optimally, what is the score of the game?
Input
The first line contain an integer n (1 β€ n β€ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 β€ si β€ 100) β the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 β€ ck β€ 1000) β the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.
Output
Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally.
Examples
Input
2
1 100
2 1 10
Output
101 10
Input
1
9 2 8 6 5 9 4 7 1 3
Output
30 15
Input
3
3 1 3 2
3 5 4 6
2 8 7
Output
18 18
Input
3
3 1000 1000 1000
6 1000 1000 1000 1000 1000 1000
5 1000 1000 1000 1000 1000
Output
7000 7000
Note
In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10.
In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3. | instruction | 0 | 86,986 | 19 | 173,972 |
Tags: games, greedy, sortings
Correct Solution:
```
n=int(input())
s1,s2=0,0
tab = []
for i in range(n):
c = list(map(int,input().split()))
for j in range(1,c[0]+1):
if(j*2<=c[0]): s1+=c[j]
else: s2+=c[j]
if(c[0] & 1):
s2-=c[(c[0]+1)//2]
tab.append(c[(c[0]+1)//2])
if(len(tab)):
tab.sort()
tab.reverse()
for i in range(len(tab)):
if(i & 1): s2+=tab[i]
else: s1+=tab[i]
print(s1,s2)
``` | output | 1 | 86,986 | 19 | 173,973 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card.
The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty.
Suppose Ciel and Jiro play optimally, what is the score of the game?
Input
The first line contain an integer n (1 β€ n β€ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 β€ si β€ 100) β the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 β€ ck β€ 1000) β the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.
Output
Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally.
Examples
Input
2
1 100
2 1 10
Output
101 10
Input
1
9 2 8 6 5 9 4 7 1 3
Output
30 15
Input
3
3 1 3 2
3 5 4 6
2 8 7
Output
18 18
Input
3
3 1000 1000 1000
6 1000 1000 1000 1000 1000 1000
5 1000 1000 1000 1000 1000
Output
7000 7000
Note
In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10.
In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3. | instruction | 0 | 86,987 | 19 | 173,974 |
Tags: games, greedy, sortings
Correct Solution:
```
odd = []
first, second = 0, 0
for i in range(int(input())):
pile = list(map(int, input().split()))
s, pile = pile[0], pile[1:]
sh = s >> 1
if (s & 1) == 0:
first += sum(pile[:sh])
second += sum(pile[sh:])
else:
first += sum(pile[:sh])
second += sum(pile[sh+1:])
odd.append(pile[sh])
odd = sorted(odd, reverse=True)
first += sum(odd[::2])
second += sum(odd[1::2])
print(first, second)
``` | output | 1 | 86,987 | 19 | 173,975 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card.
The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty.
Suppose Ciel and Jiro play optimally, what is the score of the game?
Input
The first line contain an integer n (1 β€ n β€ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 β€ si β€ 100) β the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 β€ ck β€ 1000) β the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.
Output
Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally.
Examples
Input
2
1 100
2 1 10
Output
101 10
Input
1
9 2 8 6 5 9 4 7 1 3
Output
30 15
Input
3
3 1 3 2
3 5 4 6
2 8 7
Output
18 18
Input
3
3 1000 1000 1000
6 1000 1000 1000 1000 1000 1000
5 1000 1000 1000 1000 1000
Output
7000 7000
Note
In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10.
In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3. | instruction | 0 | 86,988 | 19 | 173,976 |
Tags: games, greedy, sortings
Correct Solution:
```
#!/usr/bin/env python3
odd, even = [], []
player1_turn = True
player1 = player2 = 0
pile_number = int(input())
for _ in range(pile_number):
n, *pile = tuple(map(int, input().split()))
if n % 2 == 0:
even.append(pile)
else:
odd.append(pile)
for pile in even:
n = len(pile)
player1 += sum(pile[:n//2])
player2 += sum(pile[n//2:])
for pile in sorted(odd, reverse=True, key=lambda x: x[len(x)//2]):
n = len(pile)
top, middle, bottom = pile[:n//2], pile[n//2], pile[n//2+1:]
player1 += sum(top)
player2 += sum(bottom)
if player1_turn:
player1 += middle
player1_turn = not player1_turn
else:
player2 += middle
player1_turn = not player1_turn
print(player1, player2)
``` | output | 1 | 86,988 | 19 | 173,977 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card.
The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty.
Suppose Ciel and Jiro play optimally, what is the score of the game?
Input
The first line contain an integer n (1 β€ n β€ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 β€ si β€ 100) β the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 β€ ck β€ 1000) β the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.
Output
Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally.
Examples
Input
2
1 100
2 1 10
Output
101 10
Input
1
9 2 8 6 5 9 4 7 1 3
Output
30 15
Input
3
3 1 3 2
3 5 4 6
2 8 7
Output
18 18
Input
3
3 1000 1000 1000
6 1000 1000 1000 1000 1000 1000
5 1000 1000 1000 1000 1000
Output
7000 7000
Note
In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10.
In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3. | instruction | 0 | 86,989 | 19 | 173,978 |
Tags: games, greedy, sortings
Correct Solution:
```
n = int(input())
c = [list(map(int, input().split())) for _ in range(n)]
a, b = 0, 0
d = []
for i in range(n):
if len(c[i]) % 2:
a += sum(c[i][1:c[i][0]//2+1])
b += sum(c[i][c[i][0]//2+1:])
else:
a += sum(c[i][1:c[i][0]//2+1])
b += sum(c[i][c[i][0]//2+2:])
d.append(c[i][c[i][0]//2+1])
d.sort(reverse=True)
print(a+sum(d[0::2]), b+sum(d[1::2]))
``` | output | 1 | 86,989 | 19 | 173,979 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card.
The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty.
Suppose Ciel and Jiro play optimally, what is the score of the game?
Input
The first line contain an integer n (1 β€ n β€ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 β€ si β€ 100) β the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 β€ ck β€ 1000) β the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.
Output
Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally.
Examples
Input
2
1 100
2 1 10
Output
101 10
Input
1
9 2 8 6 5 9 4 7 1 3
Output
30 15
Input
3
3 1 3 2
3 5 4 6
2 8 7
Output
18 18
Input
3
3 1000 1000 1000
6 1000 1000 1000 1000 1000 1000
5 1000 1000 1000 1000 1000
Output
7000 7000
Note
In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10.
In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3. | instruction | 0 | 86,990 | 19 | 173,980 |
Tags: games, greedy, sortings
Correct Solution:
```
#!/usr/bin/env pypy
rr= lambda: input().strip()
rri= lambda: int(rr())
rrm= lambda: [int(x) for x in rr().split()]
def sol(n):
cm=[]
res1=0
res2=0
for i in range(n):
x=rrm()
if x[0]%2==1:
cm.append(x[x[0]//2+1])
res1+=sum(x[1:x[0]//2+1])
res2+=sum(x[(x[0]+1)//2+1:])
cm.sort(reverse=True)
for i,v in enumerate(cm):
if i%2==0:
#print(v)
res1+=v
else:
res2+=v
return str(res1)+" "+str(res2)
T=1
for _ in range(T):
n=rri()
ans=sol(n)
print(ans)
``` | output | 1 | 86,990 | 19 | 173,981 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card.
The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty.
Suppose Ciel and Jiro play optimally, what is the score of the game?
Input
The first line contain an integer n (1 β€ n β€ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 β€ si β€ 100) β the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 β€ ck β€ 1000) β the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.
Output
Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally.
Examples
Input
2
1 100
2 1 10
Output
101 10
Input
1
9 2 8 6 5 9 4 7 1 3
Output
30 15
Input
3
3 1 3 2
3 5 4 6
2 8 7
Output
18 18
Input
3
3 1000 1000 1000
6 1000 1000 1000 1000 1000 1000
5 1000 1000 1000 1000 1000
Output
7000 7000
Note
In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10.
In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3. | instruction | 0 | 86,991 | 19 | 173,982 |
Tags: games, greedy, sortings
Correct Solution:
```
n = int(input())
a,b = 0,0
l = []
for _ in range(n):
inpt = list(map(int,input().split()))[1:]
li = len(inpt)
if li%2:
l.append(inpt[li//2])
a += sum((inpt[:li//2]))
b += sum((inpt[(li + 1)//2:]))
l.sort(reverse=True)
a += sum(l[::2])
b += sum(l[1::2])
print(a, b)
``` | output | 1 | 86,991 | 19 | 173,983 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card.
The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty.
Suppose Ciel and Jiro play optimally, what is the score of the game?
Input
The first line contain an integer n (1 β€ n β€ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 β€ si β€ 100) β the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 β€ ck β€ 1000) β the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.
Output
Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally.
Examples
Input
2
1 100
2 1 10
Output
101 10
Input
1
9 2 8 6 5 9 4 7 1 3
Output
30 15
Input
3
3 1 3 2
3 5 4 6
2 8 7
Output
18 18
Input
3
3 1000 1000 1000
6 1000 1000 1000 1000 1000 1000
5 1000 1000 1000 1000 1000
Output
7000 7000
Note
In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10.
In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3.
Submitted Solution:
```
import sys
from functools import reduce
for n in sys.stdin:
n = int(n)
cards = [list(map(int, input().split()[1:])) for i in range(n)]
mid = []
a, b = 0, 0
add = lambda x=0, y=0: x + y
for c in cards:
s = len(c)
m = s >> 1
a += reduce(add, c[:m] or [0])
b += reduce(add, c[m + (s & 1):] or [0])
if s & 1 == 1:
mid.append(c[m])
mid.sort(reverse=True)
j = True
for c in mid:
if j:
a += c
else:
b += c
j = not j
print(a, b)
``` | instruction | 0 | 86,992 | 19 | 173,984 |
Yes | output | 1 | 86,992 | 19 | 173,985 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card.
The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty.
Suppose Ciel and Jiro play optimally, what is the score of the game?
Input
The first line contain an integer n (1 β€ n β€ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 β€ si β€ 100) β the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 β€ ck β€ 1000) β the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.
Output
Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally.
Examples
Input
2
1 100
2 1 10
Output
101 10
Input
1
9 2 8 6 5 9 4 7 1 3
Output
30 15
Input
3
3 1 3 2
3 5 4 6
2 8 7
Output
18 18
Input
3
3 1000 1000 1000
6 1000 1000 1000 1000 1000 1000
5 1000 1000 1000 1000 1000
Output
7000 7000
Note
In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10.
In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3.
Submitted Solution:
```
import sys
from functools import reduce
for n in sys.stdin:
n = int(n)
cards = [list(map(int, input().split()[1:])) for i in range(n)]
mid = []
a, b = 0, 0
add = lambda x=0, y=0: x + y
for c in cards:
s = len(c)
m = s >> 1
if s & 1 == 0:
a += reduce(add, c[:m])
b += reduce(add, c[m:])
else:
a += reduce(add, c[:m] or [0])
b += reduce(add, c[m + 1:] or [0])
mid.append(c[m])
mid.sort(reverse=True)
j = True
for c in mid:
if j:
a += c
else:
b += c
j = not j
print(a, b)
``` | instruction | 0 | 86,993 | 19 | 173,986 |
Yes | output | 1 | 86,993 | 19 | 173,987 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card.
The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty.
Suppose Ciel and Jiro play optimally, what is the score of the game?
Input
The first line contain an integer n (1 β€ n β€ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 β€ si β€ 100) β the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 β€ ck β€ 1000) β the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.
Output
Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally.
Examples
Input
2
1 100
2 1 10
Output
101 10
Input
1
9 2 8 6 5 9 4 7 1 3
Output
30 15
Input
3
3 1 3 2
3 5 4 6
2 8 7
Output
18 18
Input
3
3 1000 1000 1000
6 1000 1000 1000 1000 1000 1000
5 1000 1000 1000 1000 1000
Output
7000 7000
Note
In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10.
In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3.
Submitted Solution:
```
from functools import reduce
n = int(input())
cards = [list(map(int, input().split()[1:])) for i in range(n)]
mid = [c[len(c) >> 1] for c in cards if len(c) & 1 == 1]
a, b = 0, 0
add = lambda x=0, y=0: x + y
for c in cards:
m = len(c) >> 1
a += reduce(add, c[:m] or [0])
b += reduce(add, c[m + (len(c) & 1):] or [0])
mid.sort(reverse=True)
a += reduce(add, mid[::2] or [0])
b += reduce(add, mid[1::2] or [0])
print(a, b)
``` | instruction | 0 | 86,994 | 19 | 173,988 |
Yes | output | 1 | 86,994 | 19 | 173,989 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card.
The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty.
Suppose Ciel and Jiro play optimally, what is the score of the game?
Input
The first line contain an integer n (1 β€ n β€ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 β€ si β€ 100) β the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 β€ ck β€ 1000) β the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.
Output
Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally.
Examples
Input
2
1 100
2 1 10
Output
101 10
Input
1
9 2 8 6 5 9 4 7 1 3
Output
30 15
Input
3
3 1 3 2
3 5 4 6
2 8 7
Output
18 18
Input
3
3 1000 1000 1000
6 1000 1000 1000 1000 1000 1000
5 1000 1000 1000 1000 1000
Output
7000 7000
Note
In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10.
In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3.
Submitted Solution:
```
rr= lambda: input().strip()
rri= lambda: int(rr())
rrm= lambda: [int(x) for x in rr().split()]
def sol(n):
cm=[]
res1=0
res2=0
for i in range(n):
x=rrm()
if x[0]%2==1:
cm.append(x[x[0]//2+1])
res1+=sum(x[1:x[0]//2+1])
res2+=sum(x[(x[0]+1)//2+1:])
cm.sort(reverse=True)
for i,v in enumerate(cm):
if i%2==0:
#print(v)
res1+=v
else:
res2+=v
return str(res1)+" "+str(res2)
T=1
for _ in range(T):
n=rri()
ans=sol(n)
print(ans)
``` | instruction | 0 | 86,995 | 19 | 173,990 |
Yes | output | 1 | 86,995 | 19 | 173,991 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card.
The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty.
Suppose Ciel and Jiro play optimally, what is the score of the game?
Input
The first line contain an integer n (1 β€ n β€ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 β€ si β€ 100) β the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 β€ ck β€ 1000) β the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.
Output
Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally.
Examples
Input
2
1 100
2 1 10
Output
101 10
Input
1
9 2 8 6 5 9 4 7 1 3
Output
30 15
Input
3
3 1 3 2
3 5 4 6
2 8 7
Output
18 18
Input
3
3 1000 1000 1000
6 1000 1000 1000 1000 1000 1000
5 1000 1000 1000 1000 1000
Output
7000 7000
Note
In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10.
In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3.
Submitted Solution:
```
n = int(input())
ar = list()
til = list()
for i in range(n) :
line = input()
pui = line.split()
til.append(int(pui[0]))
del(pui[0])
por = [int(j) for j in pui]
ar.append(por)
time = sum(til)
f1 = 0
f2 = 0
t = 1
while t <= time :
if t%2 == 1 :
m = 0
for i in range(len(ar)) :
if len(ar[i])!=0 and ar[i][0] > m :
m = ar[i][0]
ind = i
f1 = f1 + m
del(ar[ind][0])
else :
m = 0
for i in range(len(ar)) :
if len(ar[i])!=0 and ar[i][len(ar[i])-1] > m :
m = ar[i][len(ar[i])-1]
ind = i
elif len(ar[i])!=0 and ar[i][len(ar[i])-1] == m :
if len(ar[ind]) > len(ar[i]) :
ind = i
f2 = f2 + m
del(ar[ind][-1])
t = t+1
print(f1, f2)
``` | instruction | 0 | 86,996 | 19 | 173,992 |
No | output | 1 | 86,996 | 19 | 173,993 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card.
The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty.
Suppose Ciel and Jiro play optimally, what is the score of the game?
Input
The first line contain an integer n (1 β€ n β€ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 β€ si β€ 100) β the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 β€ ck β€ 1000) β the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.
Output
Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally.
Examples
Input
2
1 100
2 1 10
Output
101 10
Input
1
9 2 8 6 5 9 4 7 1 3
Output
30 15
Input
3
3 1 3 2
3 5 4 6
2 8 7
Output
18 18
Input
3
3 1000 1000 1000
6 1000 1000 1000 1000 1000 1000
5 1000 1000 1000 1000 1000
Output
7000 7000
Note
In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10.
In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3.
Submitted Solution:
```
rr= lambda: input().strip()
rri= lambda: int(rr())
rrm= lambda: [int(x) for x in rr().split()]
def sol(n):
cm=[]
res1=0
res2=0
for i in range(n):
x=rrm()
if x[0]%2==1:
cm.append(x[x[0]//2+1])
res1+=sum(x[1:x[0]//2+1])
res2+=sum(x[(x[0]+1)//2+1:])
for i,v in enumerate(cm):
if i%2==0:
#print(v)
res1+=v
else:
res2+=v
return str(res1)+" "+str(res2)
T=1
for _ in range(T):
n=rri()
ans=sol(n)
print(ans)
``` | instruction | 0 | 86,997 | 19 | 173,994 |
No | output | 1 | 86,997 | 19 | 173,995 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card.
The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty.
Suppose Ciel and Jiro play optimally, what is the score of the game?
Input
The first line contain an integer n (1 β€ n β€ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 β€ si β€ 100) β the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 β€ ck β€ 1000) β the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.
Output
Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally.
Examples
Input
2
1 100
2 1 10
Output
101 10
Input
1
9 2 8 6 5 9 4 7 1 3
Output
30 15
Input
3
3 1 3 2
3 5 4 6
2 8 7
Output
18 18
Input
3
3 1000 1000 1000
6 1000 1000 1000 1000 1000 1000
5 1000 1000 1000 1000 1000
Output
7000 7000
Note
In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10.
In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3.
Submitted Solution:
```
def main(args):
nPiles = int(input())
piles = []
for i in range (nPiles):
line = list(map(int, input().split(' ')))
piles.append(line[1:])
ciel = 0
jiro = 0
turn = 1
while piles:
if turn%2 != 0:
ciel += piles[0][0]
del piles[0][0]
turn += 1
if not piles[0]:
del piles[0]
elif turn%2 == 0:
jiro += piles[0][-1]
del piles[0][-1]
turn += 1
if not piles[0]:
del piles[0]
print(ciel, jiro)
return 0
if __name__ == '__main__':
import sys
sys.exit(main(sys.argv))
``` | instruction | 0 | 86,998 | 19 | 173,996 |
No | output | 1 | 86,998 | 19 | 173,997 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card.
The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty.
Suppose Ciel and Jiro play optimally, what is the score of the game?
Input
The first line contain an integer n (1 β€ n β€ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 β€ si β€ 100) β the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 β€ ck β€ 1000) β the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile.
Output
Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally.
Examples
Input
2
1 100
2 1 10
Output
101 10
Input
1
9 2 8 6 5 9 4 7 1 3
Output
30 15
Input
3
3 1 3 2
3 5 4 6
2 8 7
Output
18 18
Input
3
3 1000 1000 1000
6 1000 1000 1000 1000 1000 1000
5 1000 1000 1000 1000 1000
Output
7000 7000
Note
In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10.
In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3.
Submitted Solution:
```
# -*- coding: utf-8 -*-
"""
Created on Sat Nov 2 12:17:43 2019
@author: Saurav Sihag
"""
rr= lambda: input().strip()
rri= lambda: int(rr())
rrm= lambda: [int(x) for x in rr().split()]
def sol(n):
cm=[]
res=0
for i in range(n):
x=rrm()
if x[0]%2==1:
cm.append(x[x[0]//2+1])
res+=sum(x[1:x[0]//2+1])
for i,v in enumerate(cm):
if i%2==0:
#print(v)
res+=v
return res
T=1
for _ in range(T):
n=rri()
ans=sol(n)
print(ans)
``` | instruction | 0 | 86,999 | 19 | 173,998 |
No | output | 1 | 86,999 | 19 | 173,999 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kevin and Nicky Sun have invented a new game called Lieges of Legendre. In this game, two players take turns modifying the game state with Kevin moving first. Initially, the game is set up so that there are n piles of cows, with the i-th pile containing ai cows. During each player's turn, that player calls upon the power of Sunlight, and uses it to either:
1. Remove a single cow from a chosen non-empty pile.
2. Choose a pile of cows with even size 2Β·x (x > 0), and replace it with k piles of x cows each.
The player who removes the last cow wins. Given n, k, and a sequence a1, a2, ..., an, help Kevin and Nicky find the winner, given that both sides play in optimal way.
Input
The first line of the input contains two space-separated integers n and k (1 β€ n β€ 100 000, 1 β€ k β€ 109).
The second line contains n integers, a1, a2, ... an (1 β€ ai β€ 109) describing the initial state of the game.
Output
Output the name of the winning player, either "Kevin" or "Nicky" (without quotes).
Examples
Input
2 1
3 4
Output
Kevin
Input
1 2
3
Output
Nicky
Note
In the second sample, Nicky can win in the following way: Kevin moves first and is forced to remove a cow, so the pile contains two cows after his move. Next, Nicky replaces this pile of size 2 with two piles of size 1. So the game state is now two piles of size 1. Kevin then removes one of the remaining cows and Nicky wins by removing the other. | instruction | 0 | 87,083 | 19 | 174,166 |
Tags: games, math
Correct Solution:
```
from functools import reduce
def gao(x,y):
if x==1:
return 1
if x==2:
return (~y&1)*2
if x==3:
return y&1
if x&1:
return 0
if ~y&1:
return 1
l=len(bin(x))-bin(x).rfind('1')-1
if x>>l==3:
l+=1
return 2-l%2
n,k=map(int,input().split())
s=reduce(lambda x,y:x^gao(y,k),map(int,[0]+input().split()))
if s:
print('Kevin')
else:
print('Nicky')
``` | output | 1 | 87,083 | 19 | 174,167 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kevin and Nicky Sun have invented a new game called Lieges of Legendre. In this game, two players take turns modifying the game state with Kevin moving first. Initially, the game is set up so that there are n piles of cows, with the i-th pile containing ai cows. During each player's turn, that player calls upon the power of Sunlight, and uses it to either:
1. Remove a single cow from a chosen non-empty pile.
2. Choose a pile of cows with even size 2Β·x (x > 0), and replace it with k piles of x cows each.
The player who removes the last cow wins. Given n, k, and a sequence a1, a2, ..., an, help Kevin and Nicky find the winner, given that both sides play in optimal way.
Input
The first line of the input contains two space-separated integers n and k (1 β€ n β€ 100 000, 1 β€ k β€ 109).
The second line contains n integers, a1, a2, ... an (1 β€ ai β€ 109) describing the initial state of the game.
Output
Output the name of the winning player, either "Kevin" or "Nicky" (without quotes).
Examples
Input
2 1
3 4
Output
Kevin
Input
1 2
3
Output
Nicky
Note
In the second sample, Nicky can win in the following way: Kevin moves first and is forced to remove a cow, so the pile contains two cows after his move. Next, Nicky replaces this pile of size 2 with two piles of size 1. So the game state is now two piles of size 1. Kevin then removes one of the remaining cows and Nicky wins by removing the other. | instruction | 0 | 87,084 | 19 | 174,168 |
Tags: games, math
Correct Solution:
```
f = lambda: map(int, input().split())
n, k = f()
s = 0
for a in f():
d = 0
while a & 1 << d == 0: d += 1
t = (a == 3 << d) ^ (d & 1)
x = a & 1 if a < 4 else 0 if a & 1 else 2 - t
y = a if a < 3 else a & 1 ^ 1
s ^= x if k & 1 else y
print('Kevin' if s else 'Nicky')
# Made By Mostafa_Khaled
``` | output | 1 | 87,084 | 19 | 174,169 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kevin and Nicky Sun have invented a new game called Lieges of Legendre. In this game, two players take turns modifying the game state with Kevin moving first. Initially, the game is set up so that there are n piles of cows, with the i-th pile containing ai cows. During each player's turn, that player calls upon the power of Sunlight, and uses it to either:
1. Remove a single cow from a chosen non-empty pile.
2. Choose a pile of cows with even size 2Β·x (x > 0), and replace it with k piles of x cows each.
The player who removes the last cow wins. Given n, k, and a sequence a1, a2, ..., an, help Kevin and Nicky find the winner, given that both sides play in optimal way.
Input
The first line of the input contains two space-separated integers n and k (1 β€ n β€ 100 000, 1 β€ k β€ 109).
The second line contains n integers, a1, a2, ... an (1 β€ ai β€ 109) describing the initial state of the game.
Output
Output the name of the winning player, either "Kevin" or "Nicky" (without quotes).
Examples
Input
2 1
3 4
Output
Kevin
Input
1 2
3
Output
Nicky
Note
In the second sample, Nicky can win in the following way: Kevin moves first and is forced to remove a cow, so the pile contains two cows after his move. Next, Nicky replaces this pile of size 2 with two piles of size 1. So the game state is now two piles of size 1. Kevin then removes one of the remaining cows and Nicky wins by removing the other. | instruction | 0 | 87,085 | 19 | 174,170 |
Tags: games, math
Correct Solution:
```
f = lambda: map(int, input().split())
n, k = f()
s = 0
for a in f():
d = 0
while a & 1 << d == 0: d += 1
t = (a == 3 << d) ^ (d & 1)
x = a & 1 if a < 4 else 0 if a & 1 else 2 - t
y = a if a < 3 else a & 1 ^ 1
s ^= x if k & 1 else y
print('Kevin' if s else 'Nicky')
``` | output | 1 | 87,085 | 19 | 174,171 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kevin and Nicky Sun have invented a new game called Lieges of Legendre. In this game, two players take turns modifying the game state with Kevin moving first. Initially, the game is set up so that there are n piles of cows, with the i-th pile containing ai cows. During each player's turn, that player calls upon the power of Sunlight, and uses it to either:
1. Remove a single cow from a chosen non-empty pile.
2. Choose a pile of cows with even size 2Β·x (x > 0), and replace it with k piles of x cows each.
The player who removes the last cow wins. Given n, k, and a sequence a1, a2, ..., an, help Kevin and Nicky find the winner, given that both sides play in optimal way.
Input
The first line of the input contains two space-separated integers n and k (1 β€ n β€ 100 000, 1 β€ k β€ 109).
The second line contains n integers, a1, a2, ... an (1 β€ ai β€ 109) describing the initial state of the game.
Output
Output the name of the winning player, either "Kevin" or "Nicky" (without quotes).
Examples
Input
2 1
3 4
Output
Kevin
Input
1 2
3
Output
Nicky
Note
In the second sample, Nicky can win in the following way: Kevin moves first and is forced to remove a cow, so the pile contains two cows after his move. Next, Nicky replaces this pile of size 2 with two piles of size 1. So the game state is now two piles of size 1. Kevin then removes one of the remaining cows and Nicky wins by removing the other. | instruction | 0 | 87,086 | 19 | 174,172 |
Tags: games, math
Correct Solution:
```
G_EVEN = {0:0, 1:1, 2:2}
G_ODD = {0:0, 1:1, 2:0, 3:1}
def grundy(k, ai):
if k % 2:
if ai <= 3:
return G_ODD[ai]
elif ai % 2:
return 0
else:
p = 0
j = ai
while not j & 1:
p += 1
j >>= 1
if j == 3:
return 2 if p % 2 else 1
else:
return 1 if p % 2 else 2
return 1 + p % 2
else:
if ai <= 2:
return G_EVEN[ai]
else:
return ~ai & 1
def nim_sum(ns):
s = 0
for ni in ns:
s ^= ni
return s
def winner(k, a):
return bool(nim_sum(grundy(k, ai) for ai in a))
if __name__ == '__main__':
n, k = map(int, input().split())
a = list(map(int, input().split()))
print("Kevin" if winner(k, a) else "Nicky")
``` | output | 1 | 87,086 | 19 | 174,173 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kevin and Nicky Sun have invented a new game called Lieges of Legendre. In this game, two players take turns modifying the game state with Kevin moving first. Initially, the game is set up so that there are n piles of cows, with the i-th pile containing ai cows. During each player's turn, that player calls upon the power of Sunlight, and uses it to either:
1. Remove a single cow from a chosen non-empty pile.
2. Choose a pile of cows with even size 2Β·x (x > 0), and replace it with k piles of x cows each.
The player who removes the last cow wins. Given n, k, and a sequence a1, a2, ..., an, help Kevin and Nicky find the winner, given that both sides play in optimal way.
Input
The first line of the input contains two space-separated integers n and k (1 β€ n β€ 100 000, 1 β€ k β€ 109).
The second line contains n integers, a1, a2, ... an (1 β€ ai β€ 109) describing the initial state of the game.
Output
Output the name of the winning player, either "Kevin" or "Nicky" (without quotes).
Examples
Input
2 1
3 4
Output
Kevin
Input
1 2
3
Output
Nicky
Note
In the second sample, Nicky can win in the following way: Kevin moves first and is forced to remove a cow, so the pile contains two cows after his move. Next, Nicky replaces this pile of size 2 with two piles of size 1. So the game state is now two piles of size 1. Kevin then removes one of the remaining cows and Nicky wins by removing the other. | instruction | 0 | 87,087 | 19 | 174,174 |
Tags: games, math
Correct Solution:
```
def grundy(n, k):
if k % 2 == 0:
if n <= 2:
return n
else:
return n % 2 == 0
else:
if n <= 4:
return [0, 1, 0, 1, 2][n]
elif n % 2 == 1:
return 0
else:
return 2 if grundy(n // 2, k) == 1 else 1
if __name__ == "__main__":
n, k = map(int, input().split())
xList = map(int, input().split())
res = 0
for x in xList:
res ^= grundy(x, k)
print("Kevin" if res else "Nicky")
``` | output | 1 | 87,087 | 19 | 174,175 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kevin and Nicky Sun have invented a new game called Lieges of Legendre. In this game, two players take turns modifying the game state with Kevin moving first. Initially, the game is set up so that there are n piles of cows, with the i-th pile containing ai cows. During each player's turn, that player calls upon the power of Sunlight, and uses it to either:
1. Remove a single cow from a chosen non-empty pile.
2. Choose a pile of cows with even size 2Β·x (x > 0), and replace it with k piles of x cows each.
The player who removes the last cow wins. Given n, k, and a sequence a1, a2, ..., an, help Kevin and Nicky find the winner, given that both sides play in optimal way.
Input
The first line of the input contains two space-separated integers n and k (1 β€ n β€ 100 000, 1 β€ k β€ 109).
The second line contains n integers, a1, a2, ... an (1 β€ ai β€ 109) describing the initial state of the game.
Output
Output the name of the winning player, either "Kevin" or "Nicky" (without quotes).
Examples
Input
2 1
3 4
Output
Kevin
Input
1 2
3
Output
Nicky
Note
In the second sample, Nicky can win in the following way: Kevin moves first and is forced to remove a cow, so the pile contains two cows after his move. Next, Nicky replaces this pile of size 2 with two piles of size 1. So the game state is now two piles of size 1. Kevin then removes one of the remaining cows and Nicky wins by removing the other. | instruction | 0 | 87,088 | 19 | 174,176 |
Tags: games, math
Correct Solution:
```
def solve(x, k):
if k%2 == 0:
if x <= 2:
return x;
return (x+1)%2
else:
if x == 3 or x == 1:
return 1
if x%2 == 1:
return 0
if x == 0 or x == 2:
return 0
twos = 1
while x%2 == 0:
twos += 1
x //= 2
if x == 3:
twos += 1
return (twos%2)+1
(n, k) = map(int, input().split())
A = list(map(int, input().split()))
x = 0
for a in A:
x ^= solve(a,k)
if x == 0:
print("Nicky")
else:
print("Kevin")
``` | output | 1 | 87,088 | 19 | 174,177 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kevin and Nicky Sun have invented a new game called Lieges of Legendre. In this game, two players take turns modifying the game state with Kevin moving first. Initially, the game is set up so that there are n piles of cows, with the i-th pile containing ai cows. During each player's turn, that player calls upon the power of Sunlight, and uses it to either:
1. Remove a single cow from a chosen non-empty pile.
2. Choose a pile of cows with even size 2Β·x (x > 0), and replace it with k piles of x cows each.
The player who removes the last cow wins. Given n, k, and a sequence a1, a2, ..., an, help Kevin and Nicky find the winner, given that both sides play in optimal way.
Input
The first line of the input contains two space-separated integers n and k (1 β€ n β€ 100 000, 1 β€ k β€ 109).
The second line contains n integers, a1, a2, ... an (1 β€ ai β€ 109) describing the initial state of the game.
Output
Output the name of the winning player, either "Kevin" or "Nicky" (without quotes).
Examples
Input
2 1
3 4
Output
Kevin
Input
1 2
3
Output
Nicky
Note
In the second sample, Nicky can win in the following way: Kevin moves first and is forced to remove a cow, so the pile contains two cows after his move. Next, Nicky replaces this pile of size 2 with two piles of size 1. So the game state is now two piles of size 1. Kevin then removes one of the remaining cows and Nicky wins by removing the other. | instruction | 0 | 87,089 | 19 | 174,178 |
Tags: games, math
Correct Solution:
```
f = lambda: map(int, input().split())
n, k = f()
s = 0
for a in f():
d = 0
while a % (2 << d) == 0: d += 1
x = a & 1 if a < 4 else 0 if a & 1 else 1 if (a == 3 << d) ^ (d & 1) else 2
y = a if a < 3 else a & 1 ^ 1
s ^= x if k & 1 else y
print('Kevin' if s else 'Nicky')
``` | output | 1 | 87,089 | 19 | 174,179 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kevin and Nicky Sun have invented a new game called Lieges of Legendre. In this game, two players take turns modifying the game state with Kevin moving first. Initially, the game is set up so that there are n piles of cows, with the i-th pile containing ai cows. During each player's turn, that player calls upon the power of Sunlight, and uses it to either:
1. Remove a single cow from a chosen non-empty pile.
2. Choose a pile of cows with even size 2Β·x (x > 0), and replace it with k piles of x cows each.
The player who removes the last cow wins. Given n, k, and a sequence a1, a2, ..., an, help Kevin and Nicky find the winner, given that both sides play in optimal way.
Input
The first line of the input contains two space-separated integers n and k (1 β€ n β€ 100 000, 1 β€ k β€ 109).
The second line contains n integers, a1, a2, ... an (1 β€ ai β€ 109) describing the initial state of the game.
Output
Output the name of the winning player, either "Kevin" or "Nicky" (without quotes).
Examples
Input
2 1
3 4
Output
Kevin
Input
1 2
3
Output
Nicky
Note
In the second sample, Nicky can win in the following way: Kevin moves first and is forced to remove a cow, so the pile contains two cows after his move. Next, Nicky replaces this pile of size 2 with two piles of size 1. So the game state is now two piles of size 1. Kevin then removes one of the remaining cows and Nicky wins by removing the other.
Submitted Solution:
```
def solve(x, k):
if k%2 == 0:
if x == 0:
return 0;
return (x+1)%2+1
else:
if x == 3 or x == 1:
return 1
if x%2 == 1:
return 0
if x == 0 or x == 2:
return 0
twos = 1
while x%2 == 0:
twos += 1
x //= 2
if x == 3:
twos += 1
return (twos%2)+1
(n, k) = map(int, input().split())
A = list(map(int, input().split()))
x = 0
for a in A:
x ^= solve(a,k)
if x == 0:
print("Nicky")
else:
print("Kevin")
``` | instruction | 0 | 87,090 | 19 | 174,180 |
No | output | 1 | 87,090 | 19 | 174,181 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kevin and Nicky Sun have invented a new game called Lieges of Legendre. In this game, two players take turns modifying the game state with Kevin moving first. Initially, the game is set up so that there are n piles of cows, with the i-th pile containing ai cows. During each player's turn, that player calls upon the power of Sunlight, and uses it to either:
1. Remove a single cow from a chosen non-empty pile.
2. Choose a pile of cows with even size 2Β·x (x > 0), and replace it with k piles of x cows each.
The player who removes the last cow wins. Given n, k, and a sequence a1, a2, ..., an, help Kevin and Nicky find the winner, given that both sides play in optimal way.
Input
The first line of the input contains two space-separated integers n and k (1 β€ n β€ 100 000, 1 β€ k β€ 109).
The second line contains n integers, a1, a2, ... an (1 β€ ai β€ 109) describing the initial state of the game.
Output
Output the name of the winning player, either "Kevin" or "Nicky" (without quotes).
Examples
Input
2 1
3 4
Output
Kevin
Input
1 2
3
Output
Nicky
Note
In the second sample, Nicky can win in the following way: Kevin moves first and is forced to remove a cow, so the pile contains two cows after his move. Next, Nicky replaces this pile of size 2 with two piles of size 1. So the game state is now two piles of size 1. Kevin then removes one of the remaining cows and Nicky wins by removing the other.
Submitted Solution:
```
f = lambda: map(int, input().split())
n, k = f()
s = 0
for a in f():
d = 0
while a % (2 << d) == 0: d += 1
x = a & 1 if a < 4 else 0 if a & 1 else (a == 3 << d) ^ (d & 1)
y = a if a < 3 else a & 1 ^ 1
s ^= x if k & 1 else y
print('Kevin' if s else 'Nicky')
``` | instruction | 0 | 87,091 | 19 | 174,182 |
No | output | 1 | 87,091 | 19 | 174,183 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kevin and Nicky Sun have invented a new game called Lieges of Legendre. In this game, two players take turns modifying the game state with Kevin moving first. Initially, the game is set up so that there are n piles of cows, with the i-th pile containing ai cows. During each player's turn, that player calls upon the power of Sunlight, and uses it to either:
1. Remove a single cow from a chosen non-empty pile.
2. Choose a pile of cows with even size 2Β·x (x > 0), and replace it with k piles of x cows each.
The player who removes the last cow wins. Given n, k, and a sequence a1, a2, ..., an, help Kevin and Nicky find the winner, given that both sides play in optimal way.
Input
The first line of the input contains two space-separated integers n and k (1 β€ n β€ 100 000, 1 β€ k β€ 109).
The second line contains n integers, a1, a2, ... an (1 β€ ai β€ 109) describing the initial state of the game.
Output
Output the name of the winning player, either "Kevin" or "Nicky" (without quotes).
Examples
Input
2 1
3 4
Output
Kevin
Input
1 2
3
Output
Nicky
Note
In the second sample, Nicky can win in the following way: Kevin moves first and is forced to remove a cow, so the pile contains two cows after his move. Next, Nicky replaces this pile of size 2 with two piles of size 1. So the game state is now two piles of size 1. Kevin then removes one of the remaining cows and Nicky wins by removing the other.
Submitted Solution:
```
f = lambda: map(int, input().split())
n, k = f()
s = 0
for a in f():
d = 0
while a % (2 << d) == 0: d += 1
x = a & 1 if a < 4 else 0 if a & 1 else 2 - (a == 3 << d) ^ (d & 1)
y = a if a < 3 else a & 1 ^ 1
s ^= x if k & 1 else y
print('Kevin' if s else 'Nicky')
``` | instruction | 0 | 87,092 | 19 | 174,184 |
No | output | 1 | 87,092 | 19 | 174,185 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kevin and Nicky Sun have invented a new game called Lieges of Legendre. In this game, two players take turns modifying the game state with Kevin moving first. Initially, the game is set up so that there are n piles of cows, with the i-th pile containing ai cows. During each player's turn, that player calls upon the power of Sunlight, and uses it to either:
1. Remove a single cow from a chosen non-empty pile.
2. Choose a pile of cows with even size 2Β·x (x > 0), and replace it with k piles of x cows each.
The player who removes the last cow wins. Given n, k, and a sequence a1, a2, ..., an, help Kevin and Nicky find the winner, given that both sides play in optimal way.
Input
The first line of the input contains two space-separated integers n and k (1 β€ n β€ 100 000, 1 β€ k β€ 109).
The second line contains n integers, a1, a2, ... an (1 β€ ai β€ 109) describing the initial state of the game.
Output
Output the name of the winning player, either "Kevin" or "Nicky" (without quotes).
Examples
Input
2 1
3 4
Output
Kevin
Input
1 2
3
Output
Nicky
Note
In the second sample, Nicky can win in the following way: Kevin moves first and is forced to remove a cow, so the pile contains two cows after his move. Next, Nicky replaces this pile of size 2 with two piles of size 1. So the game state is now two piles of size 1. Kevin then removes one of the remaining cows and Nicky wins by removing the other.
Submitted Solution:
```
f = lambda: map(int, input().split())
n, k = f()
s = 0
for a in f():
d = 0
while a % (2 << d) == 0: d += 1
x = a & 1 if a < 4 else 0 if a & 1 else 1 + (a == 3 << d) ^ (d & 1 ^ 1)
y = a if a < 3 else a & 1 ^ 1
s ^= x if k & 1 else y
print('Kevin' if s else 'Nicky')
``` | instruction | 0 | 87,093 | 19 | 174,186 |
No | output | 1 | 87,093 | 19 | 174,187 |
Provide tags and a correct Python 3 solution for this coding contest problem.
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 β€ n β€ 350000) is given.
Each game is represented by a pair of scores a, b (1 β€ a, b β€ 109) β the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3. | instruction | 0 | 87,190 | 19 | 174,380 |
Tags: math, number theory
Correct Solution:
```
import os
import sys
from io import BytesIO, IOBase
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------------------
def RL(): return map(int, sys.stdin.readline().rstrip().split())
def RLL(): return list(map(int, sys.stdin.readline().rstrip().split()))
def N(): return int(input())
def comb(n, m): return factorial(n) / (factorial(m) * factorial(n - m)) if n >= m else 0
def perm(n, m): return factorial(n) // (factorial(n - m)) if n >= m else 0
def mdis(x1, y1, x2, y2): return abs(x1 - x2) + abs(y1 - y2)
mod = 998244353
INF = float('inf')
from math import factorial
from collections import Counter, defaultdict, deque
from heapq import heapify, heappop, heappush
from math import pow
# ------------------------------
def main():
for _ in range(N()):
a, b = RL()
mt = a*b
res = round(pow(mt, 1/3))
if res**3==mt and a%res==0 and b%res==0:
print('Yes')
else:
print('No')
if __name__ == "__main__":
main()
``` | output | 1 | 87,190 | 19 | 174,381 |
Provide tags and a correct Python 3 solution for this coding contest problem.
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 β€ n β€ 350000) is given.
Each game is represented by a pair of scores a, b (1 β€ a, b β€ 109) β the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3. | instruction | 0 | 87,191 | 19 | 174,382 |
Tags: math, number theory
Correct Solution:
```
import os
import sys
from io import BytesIO, IOBase
from collections import Counter
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
def input(): return sys.stdin.readline().rstrip("\r\n")
def gcd(a, b):
if a == 0:
return b
return gcd(b % a, a)
def lcm(a, b):
return (a * b) / gcd(a, b)
def main():
for _ in range(int(input())):
# n=int(input())
# a=list(map(int, input().split()))
a,b=map(int, input().split())
k=a*b
f=0
# l=0
# r=k+1
# f=0
# while(l<=r):
# mid=(l+r)//2
# tr=mid*mid*mid
# if tr==k:
# f=mid
# break
# if tr>k:
# r=mid-1
# else:
# l=mid+1
root=round(k**(1/3))
if root*root*root==k:
f=root
if f:
if (a%f)==(b%f)==0:
print('YES')
else:
print('NO')
else:
print('NO')
return
if __name__=="__main__":
main()
``` | output | 1 | 87,191 | 19 | 174,383 |
Provide tags and a correct Python 3 solution for this coding contest problem.
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 β€ n β€ 350000) is given.
Each game is represented by a pair of scores a, b (1 β€ a, b β€ 109) β the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3. | instruction | 0 | 87,192 | 19 | 174,384 |
Tags: math, number theory
Correct Solution:
```
import os, sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
for _ in range(int(input())):
a, b = map(int, input().split())
q = a * b
t = round(q ** (1 / 3))
if t * t * t == q and a % t == b % t == 0:
print('YES')
else:
print('NO')
``` | output | 1 | 87,192 | 19 | 174,385 |
Provide tags and a correct Python 3 solution for this coding contest problem.
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 β€ n β€ 350000) is given.
Each game is represented by a pair of scores a, b (1 β€ a, b β€ 109) β the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3. | instruction | 0 | 87,193 | 19 | 174,386 |
Tags: math, number theory
Correct Solution:
```
import os
import sys
from math import ceil, pow
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
def main():
for _ in range(int(input())):
a, b = map(int, input().split())
if (a * b == (ceil(pow(a * b, 1 / 3)) ** 3)):
temp = ceil(pow(a * b, 1 / 3))
if ((a % temp) == (b % temp) == 0):
print("Yes")
continue
print("No")
if __name__ == "__main__":
main()
``` | output | 1 | 87,193 | 19 | 174,387 |
Provide tags and a correct Python 3 solution for this coding contest problem.
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 β€ n β€ 350000) is given.
Each game is represented by a pair of scores a, b (1 β€ a, b β€ 109) β the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3. | instruction | 0 | 87,194 | 19 | 174,388 |
Tags: math, number theory
Correct Solution:
```
# ---------------------------iye ha aam zindegi---------------------------------------------
import math
import heapq, bisect
import sys
from collections import deque, defaultdict
from fractions import Fraction
mod = 10 ** 9 + 7
mod1 = 998244353
# ------------------------------warmup----------------------------
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# -------------------game starts now----------------------------------------------------import math
class TreeNode:
def __init__(self, k, v):
self.key = k
self.value = v
self.left = None
self.right = None
self.parent = None
self.height = 1
self.num_left = 1
self.num_total = 1
class AvlTree:
def __init__(self):
self._tree = None
def add(self, k, v):
if not self._tree:
self._tree = TreeNode(k, v)
return
node = self._add(k, v)
if node:
self._rebalance(node)
def _add(self, k, v):
node = self._tree
while node:
if k < node.key:
if node.left:
node = node.left
else:
node.left = TreeNode(k, v)
node.left.parent = node
return node.left
elif node.key < k:
if node.right:
node = node.right
else:
node.right = TreeNode(k, v)
node.right.parent = node
return node.right
else:
node.value = v
return
@staticmethod
def get_height(x):
return x.height if x else 0
@staticmethod
def get_num_total(x):
return x.num_total if x else 0
def _rebalance(self, node):
n = node
while n:
lh = self.get_height(n.left)
rh = self.get_height(n.right)
n.height = max(lh, rh) + 1
balance_factor = lh - rh
n.num_total = 1 + self.get_num_total(n.left) + self.get_num_total(n.right)
n.num_left = 1 + self.get_num_total(n.left)
if balance_factor > 1:
if self.get_height(n.left.left) < self.get_height(n.left.right):
self._rotate_left(n.left)
self._rotate_right(n)
elif balance_factor < -1:
if self.get_height(n.right.right) < self.get_height(n.right.left):
self._rotate_right(n.right)
self._rotate_left(n)
else:
n = n.parent
def _remove_one(self, node):
"""
Side effect!!! Changes node. Node should have exactly one child
"""
replacement = node.left or node.right
if node.parent:
if AvlTree._is_left(node):
node.parent.left = replacement
else:
node.parent.right = replacement
replacement.parent = node.parent
node.parent = None
else:
self._tree = replacement
replacement.parent = None
node.left = None
node.right = None
node.parent = None
self._rebalance(replacement)
def _remove_leaf(self, node):
if node.parent:
if AvlTree._is_left(node):
node.parent.left = None
else:
node.parent.right = None
self._rebalance(node.parent)
else:
self._tree = None
node.parent = None
node.left = None
node.right = None
def remove(self, k):
node = self._get_node(k)
if not node:
return
if AvlTree._is_leaf(node):
self._remove_leaf(node)
return
if node.left and node.right:
nxt = AvlTree._get_next(node)
node.key = nxt.key
node.value = nxt.value
if self._is_leaf(nxt):
self._remove_leaf(nxt)
else:
self._remove_one(nxt)
self._rebalance(node)
else:
self._remove_one(node)
def get(self, k):
node = self._get_node(k)
return node.value if node else -1
def _get_node(self, k):
if not self._tree:
return None
node = self._tree
while node:
if k < node.key:
node = node.left
elif node.key < k:
node = node.right
else:
return node
return None
def get_at(self, pos):
x = pos + 1
node = self._tree
while node:
if x < node.num_left:
node = node.left
elif node.num_left < x:
x -= node.num_left
node = node.right
else:
return (node.key, node.value)
raise IndexError("Out of ranges")
@staticmethod
def _is_left(node):
return node.parent.left and node.parent.left == node
@staticmethod
def _is_leaf(node):
return node.left is None and node.right is None
def _rotate_right(self, node):
if not node.parent:
self._tree = node.left
node.left.parent = None
elif AvlTree._is_left(node):
node.parent.left = node.left
node.left.parent = node.parent
else:
node.parent.right = node.left
node.left.parent = node.parent
bk = node.left.right
node.left.right = node
node.parent = node.left
node.left = bk
if bk:
bk.parent = node
node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1
node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right)
node.num_left = 1 + self.get_num_total(node.left)
def _rotate_left(self, node):
if not node.parent:
self._tree = node.right
node.right.parent = None
elif AvlTree._is_left(node):
node.parent.left = node.right
node.right.parent = node.parent
else:
node.parent.right = node.right
node.right.parent = node.parent
bk = node.right.left
node.right.left = node
node.parent = node.right
node.right = bk
if bk:
bk.parent = node
node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1
node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right)
node.num_left = 1 + self.get_num_total(node.left)
@staticmethod
def _get_next(node):
if not node.right:
return node.parent
n = node.right
while n.left:
n = n.left
return n
avl=AvlTree()
#-----------------------------------------------binary seacrh tree---------------------------------------
class SegmentTree1:
def __init__(self, data, default='z', func=lambda a, b: min(a ,b)):
"""initialize the segment tree with data"""
self._default = default
self._func = func
self._len = len(data)
self._size = _size = 1 << (self._len - 1).bit_length()
self.data = [default] * (2 * _size)
self.data[_size:_size + self._len] = data
for i in reversed(range(_size)):
self.data[i] = func(self.data[i + i], self.data[i + i + 1])
def __delitem__(self, idx):
self[idx] = self._default
def __getitem__(self, idx):
return self.data[idx + self._size]
def __setitem__(self, idx, value):
idx += self._size
self.data[idx] = value
idx >>= 1
while idx:
self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
idx >>= 1
def __len__(self):
return self._len
def query(self, start, stop):
if start == stop:
return self.__getitem__(start)
stop += 1
start += self._size
stop += self._size
res = self._default
while start < stop:
if start & 1:
res = self._func(res, self.data[start])
start += 1
if stop & 1:
stop -= 1
res = self._func(res, self.data[stop])
start >>= 1
stop >>= 1
return res
def __repr__(self):
return "SegmentTree({0})".format(self.data)
# -------------------game starts now----------------------------------------------------import math
class SegmentTree:
def __init__(self, data, default=0, func=lambda a, b: a + b):
"""initialize the segment tree with data"""
self._default = default
self._func = func
self._len = len(data)
self._size = _size = 1 << (self._len - 1).bit_length()
self.data = [default] * (2 * _size)
self.data[_size:_size + self._len] = data
for i in reversed(range(_size)):
self.data[i] = func(self.data[i + i], self.data[i + i + 1])
def __delitem__(self, idx):
self[idx] = self._default
def __getitem__(self, idx):
return self.data[idx + self._size]
def __setitem__(self, idx, value):
idx += self._size
self.data[idx] = value
idx >>= 1
while idx:
self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
idx >>= 1
def __len__(self):
return self._len
def query(self, start, stop):
if start == stop:
return self.__getitem__(start)
stop += 1
start += self._size
stop += self._size
res = self._default
while start < stop:
if start & 1:
res = self._func(res, self.data[start])
start += 1
if stop & 1:
stop -= 1
res = self._func(res, self.data[stop])
start >>= 1
stop >>= 1
return res
def __repr__(self):
return "SegmentTree({0})".format(self.data)
# -------------------------------iye ha chutiya zindegi-------------------------------------
class Factorial:
def __init__(self, MOD):
self.MOD = MOD
self.factorials = [1, 1]
self.invModulos = [0, 1]
self.invFactorial_ = [1, 1]
def calc(self, n):
if n <= -1:
print("Invalid argument to calculate n!")
print("n must be non-negative value. But the argument was " + str(n))
exit()
if n < len(self.factorials):
return self.factorials[n]
nextArr = [0] * (n + 1 - len(self.factorials))
initialI = len(self.factorials)
prev = self.factorials[-1]
m = self.MOD
for i in range(initialI, n + 1):
prev = nextArr[i - initialI] = prev * i % m
self.factorials += nextArr
return self.factorials[n]
def inv(self, n):
if n <= -1:
print("Invalid argument to calculate n^(-1)")
print("n must be non-negative value. But the argument was " + str(n))
exit()
p = self.MOD
pi = n % p
if pi < len(self.invModulos):
return self.invModulos[pi]
nextArr = [0] * (n + 1 - len(self.invModulos))
initialI = len(self.invModulos)
for i in range(initialI, min(p, n + 1)):
next = -self.invModulos[p % i] * (p // i) % p
self.invModulos.append(next)
return self.invModulos[pi]
def invFactorial(self, n):
if n <= -1:
print("Invalid argument to calculate (n^(-1))!")
print("n must be non-negative value. But the argument was " + str(n))
exit()
if n < len(self.invFactorial_):
return self.invFactorial_[n]
self.inv(n) # To make sure already calculated n^-1
nextArr = [0] * (n + 1 - len(self.invFactorial_))
initialI = len(self.invFactorial_)
prev = self.invFactorial_[-1]
p = self.MOD
for i in range(initialI, n + 1):
prev = nextArr[i - initialI] = (prev * self.invModulos[i % p]) % p
self.invFactorial_ += nextArr
return self.invFactorial_[n]
class Combination:
def __init__(self, MOD):
self.MOD = MOD
self.factorial = Factorial(MOD)
def ncr(self, n, k):
if k < 0 or n < k:
return 0
k = min(k, n - k)
f = self.factorial
return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD
# --------------------------------------iye ha combinations ka zindegi---------------------------------
def powm(a, n, m):
if a == 1 or n == 0:
return 1
if n % 2 == 0:
s = powm(a, n // 2, m)
return s * s % m
else:
return a * powm(a, n - 1, m) % m
# --------------------------------------iye ha power ka zindegi---------------------------------
def sort_list(list1, list2):
zipped_pairs = zip(list2, list1)
z = [x for _, x in sorted(zipped_pairs)]
return z
# --------------------------------------------------product----------------------------------------
def product(l):
por = 1
for i in range(len(l)):
por *= l[i]
return por
# --------------------------------------------------binary----------------------------------------
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
# --------------------------------------------------binary----------------------------------------
def countdig(n):
c = 0
while (n > 0):
n //= 10
c += 1
return c
def countGreater( arr,n, k):
l = 0
r = n - 1
# Stores the index of the left most element
# from the array which is greater than k
leftGreater = n
# Finds number of elements greater than k
while (l <= r):
m = int(l + (r - l) / 2)
if (arr[m] >= k):
leftGreater = m
r = m - 1
# If mid element is less than
# or equal to k update l
else:
l = m + 1
# Return the count of elements
# greater than k
return (n - leftGreater)
# --------------------------------------------------binary------------------------------------
for i in range(int(input())):
a,b=map(int,input().split())
c=a*b
l=int(c**(1./3)+0.5)
if l**3==a*b and a%l==0 and b%l==0:
print("YES")
else:
print("NO")
``` | output | 1 | 87,194 | 19 | 174,389 |
Provide tags and a correct Python 3 solution for this coding contest problem.
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 β€ n β€ 350000) is given.
Each game is represented by a pair of scores a, b (1 β€ a, b β€ 109) β the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3. | instruction | 0 | 87,195 | 19 | 174,390 |
Tags: math, number theory
Correct Solution:
```
import sys
n = int(input())
ans = []
arr = sys.stdin.read().split()
d = {}
for i in range(1,1001):
d[i**3] = i
for i in range(n):
a, b = int(arr[i<<1]), int(arr[i<<1|1])
if a == b:
if a in d:
ans.append('Yes')
else:
ans.append('No')
continue
if a > b: a, b = b, a
x = d.get(a*a//b,-1)
if x == -1:
ans.append('No')
continue
if a % (x*x):
ans.append('No')
continue
y = a //(x*x)
if x * x * y == a and x * y * y == b: ans.append('Yes')
else: ans.append('No')
print('\n'.join(ans))
``` | output | 1 | 87,195 | 19 | 174,391 |
Provide tags and a correct Python 3 solution for this coding contest problem.
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 β€ n β€ 350000) is given.
Each game is represented by a pair of scores a, b (1 β€ a, b β€ 109) β the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3. | instruction | 0 | 87,196 | 19 | 174,392 |
Tags: math, number theory
Correct Solution:
```
#Code by Sounak, IIESTS
#------------------------------warmup----------------------------
import os
import sys
import math
from io import BytesIO, IOBase
from fractions import Fraction
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
#-------------------game starts now-----------------------------------------------------
for t in range (int(input())):
a,b=map(int,input().split())
p=a*b
#print(p)
c=int(round(p**(1./3)))
#print (c)
if c**3==p and a%c==0 and b%c==0:
print("Yes")
else:
print("No")
``` | output | 1 | 87,196 | 19 | 174,393 |
Provide tags and a correct Python 3 solution for this coding contest problem.
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 β€ n β€ 350000) is given.
Each game is represented by a pair of scores a, b (1 β€ a, b β€ 109) β the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3. | instruction | 0 | 87,197 | 19 | 174,394 |
Tags: math, number theory
Correct Solution:
```
import os
import sys
from io import BytesIO, IOBase
from collections import Counter
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
def input(): return sys.stdin.readline().rstrip("\r\n")
n = int(input())
output = []
for i in range(1, n + 1):
a, b = map(int, input().split())
p = a * b
root = round(p ** (1 / 3))
ok = root * root * root == p and a % root == b % root == 0
output.append('Yes' if ok else 'No')
print('\n'.join(output))
``` | output | 1 | 87,197 | 19 | 174,395 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 β€ n β€ 350000) is given.
Each game is represented by a pair of scores a, b (1 β€ a, b β€ 109) β the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
Submitted Solution:
```
#------------------------template--------------------------#
import os
import sys
from math import *
from collections import *
from fractions import *
from bisect import *
from heapq import*
from io import BytesIO, IOBase
def vsInput():
sys.stdin = open('input.txt', 'r')
sys.stdout = open('output.txt', 'w')
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
def value():return tuple(map(int,input().split()))
def array():return [int(i) for i in input().split()]
def Int():return int(input())
def Str():return input()
def arrayS():return [i for i in input().split()]
#-------------------------code---------------------------#
# vsInput()
def PrimeFactors(n):
factors=[]
while(n%2==0):
factors.append(2)
n//=2
for i in range(3,int(sqrt(n))+1,2):
while(n%i==0):
factors.append(i)
n//=i
if(n>1):
factors.append(n)
return factors
for _ in range(Int()):
a,b=value()
root=ceil((a*b)**(1/3))
# print(root)
ok="No"
if(root**3==a*b and a%root==0 and b%root==0):
ok="Yes"
print(ok)
``` | instruction | 0 | 87,198 | 19 | 174,396 |
Yes | output | 1 | 87,198 | 19 | 174,397 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 β€ n β€ 350000) is given.
Each game is represented by a pair of scores a, b (1 β€ a, b β€ 109) β the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
Submitted Solution:
```
import sys
input = sys.stdin.readline
print = sys.stdout.write
cbrt = {i**3:i for i in range(1001)}
n = int(input())
all_res = []
for _ in range(n):
a, b = map(int, input().split())
if a == b:
all_res.append('Yes' if a in cbrt else 'No')
continue
if a > b:
a, b = b, a
r = cbrt.get(a * a // b, 0)
if r == 0 or a % (r * r) > 0:
all_res.append('No')
continue
y = a //(r * r)
if r * r * y == a and r * y * y == b:
all_res.append('Yes')
else:
all_res.append('No')
print('\n'.join(all_res))
``` | instruction | 0 | 87,199 | 19 | 174,398 |
Yes | output | 1 | 87,199 | 19 | 174,399 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 β€ n β€ 350000) is given.
Each game is represented by a pair of scores a, b (1 β€ a, b β€ 109) β the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
Submitted Solution:
```
import sys,os,io
from sys import stdin
from math import log, gcd, ceil
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
from bisect import bisect_left , bisect_right
import math
def ii():
return int(input())
def li():
return list(map(int,input().split()))
if(os.path.exists('input.txt')):
sys.stdin = open("input.txt","r") ; sys.stdout = open("output.txt","w")
else:
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
no = "No"
yes = "Yes"
def solve():
a,b = li()
x = (pow(a*b,1/3))
x=round(x)
if x*x*x==a*b and a%x==b%x==0:
print(yes)
else:
print(no)
t = 1
t = int(input())
for _ in range(t):
solve()
``` | instruction | 0 | 87,200 | 19 | 174,400 |
Yes | output | 1 | 87,200 | 19 | 174,401 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 β€ n β€ 350000) is given.
Each game is represented by a pair of scores a, b (1 β€ a, b β€ 109) β the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
Submitted Solution:
```
import os
import sys
from io import BytesIO, IOBase
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 inp():
return sys.stdin.readline().rstrip()
def mpint():
return map(int, inp().split(' '))
def itg():
return int(inp())
# ############################## import
# ############################## main
def solve():
"""
The answer is True iff
their exist x, y is Z+ s.t.
xy^2 = a && yx^2 = b
-> x = (b^2 / a)^(1/3)
"""
a, b = mpint()
x = round((b * b // a) ** (1 / 3))
if not x:
return False
y = round((a // x) ** 0.5)
return a == x * y * y and b == y * x * x
def main():
# solve()
# print(solve())
for _ in range(itg()):
# print(solve())
# solve()
print("Yes" if solve() else "No")
# print("YES" if solve() else "NO")
DEBUG = 0
URL = 'https://codeforces.com/problemset/problem/833/A'
if __name__ == '__main__':
if DEBUG == 1:
import requests # ImportError: cannot import name 'md5' from 'sys' (unknown location)
from ACgenerator.Y_Test_Case_Runner import TestCaseRunner
runner = TestCaseRunner(main, URL, 1)
inp = runner.input_stream
print = runner.output_stream
runner.checking()
elif DEBUG == 2:
main()
else:
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
main()
# Please check!
``` | instruction | 0 | 87,201 | 19 | 174,402 |
Yes | output | 1 | 87,201 | 19 | 174,403 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 β€ n β€ 350000) is given.
Each game is represented by a pair of scores a, b (1 β€ a, b β€ 109) β the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
Submitted Solution:
```
from math import log, exp
n = int(input())
for v in range(n):
a, b = map(int, input().split())
d = exp(log(a * b) / 3) * 10 ** 5 // 10 ** 5
if int(d) == d and a >= d and b >= d and a % d == 0 and b % d == 0:
print('Yes')
else:
print('No')
``` | instruction | 0 | 87,202 | 19 | 174,404 |
No | output | 1 | 87,202 | 19 | 174,405 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 β€ n β€ 350000) is given.
Each game is represented by a pair of scores a, b (1 β€ a, b β€ 109) β the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
Submitted Solution:
```
n=int(input())
eps=1e-9
def getAns(c):
L=1
R=c
while(L<=R):
mid = (L + R) // 2
if mid*mid*mid>c:
R = mid - 1
elif mid*mid*mid<c:
L = mid + 1
elif mid*mid*mid==c:
return True
#print(mid)
return False
for i in range(n):
raw = input().split()
a=int(raw[0])
b=int(raw[1])
c=a*b
#print(c)
if(getAns(c)):
print('Yes')
else:
print('No')
``` | instruction | 0 | 87,203 | 19 | 174,406 |
No | output | 1 | 87,203 | 19 | 174,407 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 β€ n β€ 350000) is given.
Each game is represented by a pair of scores a, b (1 β€ a, b β€ 109) β the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
Submitted Solution:
```
runs = int(input())
for idx in range(runs):
u, v = map(int, input().split(' '))
prod = u*v
if round(prod**(1/3))**3 == prod: print("Yes")
else: print("No")
``` | instruction | 0 | 87,204 | 19 | 174,408 |
No | output | 1 | 87,204 | 19 | 174,409 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 β€ n β€ 350000) is given.
Each game is represented by a pair of scores a, b (1 β€ a, b β€ 109) β the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
Submitted Solution:
```
if __name__ == "__main__":
n = int(input())
while n > 0:
a, b = map(int, input().split())
x = a * b
if int(round(x ** (1. / 3))) ** 3 == x:
print("Yes")
else:
print("No")
n -= 1
``` | instruction | 0 | 87,205 | 19 | 174,410 |
No | output | 1 | 87,205 | 19 | 174,411 |
Provide a correct Python 3 solution for this coding contest problem.
Ataru Oafoot of Aizu Gakuen University High School decided to play with a slot machine.
When you insert a medal on this machine, three reels will start spinning and each reel will stop automatically. In a normal game (normal game), 3 medals are inserted, and when the symbols are aligned, the following medals are obtained according to the symbols.
<image>
A special service will be started depending on how the patterns are aligned. A big bonus starts when you have 3 of 7 symbols, and you can play 5 bonus games. Also, when you have 3 BAR symbols, the regular bonus will start and you can play 3 bonus games.
If you have 3 star symbols, the free game will start and you will not be able to get medals, but you can start the next game without inserting medals.
During the bonus game, if you insert 2 medals per game, you will automatically get 3 grape patterns and 15 medals.
Oafoot started playing on the machine with 100 medals. After playing for a while, it ended in a normal game. How many medals did you have left?
Create a program that inputs play information and outputs the number of medals left at hand. The play information is given as the number of big bonuses b, the number of regular bonuses r, the number of grapes aligned during a normal game g, the number of cherries aligned c, the number of stars aligned s, and the total number of games t.
Note that t includes the number of bonus games. Also, medals will not disappear in the middle of the game.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a zero line. Each dataset is given in the following format:
b r g c s t
b, r, g, c, and s are integers greater than or equal to 0 and less than 200, and t is an integer less than or equal to 1000.
The number of datasets does not exceed 120.
Output
For each input dataset, the number of medals remaining at hand is output on one line.
Example
Input
3 2 30 3 26 226
9 0 18 3 20 118
5 5 12 2 15 203
7 4 19 2 22 197
7 4 24 4 17 209
0 0 0 0 0 0
Output
127
793
414
629
617 | instruction | 0 | 87,433 | 19 | 174,866 |
"Correct Solution:
```
# Aizu Problem 0229: Big Hit
import sys, math, os, bisect
# read input:
PYDEV = os.environ.get('PYDEV')
if PYDEV=="True":
sys.stdin = open("sample-input.txt", "rt")
while True:
b, r, g, c, s, t = [int(_) for _ in input().split()]
if t == 0:
break
print(100 + 95 * b + 63 * r + 7 * g + 2 * c - 3 * (t - s))
``` | output | 1 | 87,433 | 19 | 174,867 |
Provide a correct Python 3 solution for this coding contest problem.
Ataru Oafoot of Aizu Gakuen University High School decided to play with a slot machine.
When you insert a medal on this machine, three reels will start spinning and each reel will stop automatically. In a normal game (normal game), 3 medals are inserted, and when the symbols are aligned, the following medals are obtained according to the symbols.
<image>
A special service will be started depending on how the patterns are aligned. A big bonus starts when you have 3 of 7 symbols, and you can play 5 bonus games. Also, when you have 3 BAR symbols, the regular bonus will start and you can play 3 bonus games.
If you have 3 star symbols, the free game will start and you will not be able to get medals, but you can start the next game without inserting medals.
During the bonus game, if you insert 2 medals per game, you will automatically get 3 grape patterns and 15 medals.
Oafoot started playing on the machine with 100 medals. After playing for a while, it ended in a normal game. How many medals did you have left?
Create a program that inputs play information and outputs the number of medals left at hand. The play information is given as the number of big bonuses b, the number of regular bonuses r, the number of grapes aligned during a normal game g, the number of cherries aligned c, the number of stars aligned s, and the total number of games t.
Note that t includes the number of bonus games. Also, medals will not disappear in the middle of the game.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a zero line. Each dataset is given in the following format:
b r g c s t
b, r, g, c, and s are integers greater than or equal to 0 and less than 200, and t is an integer less than or equal to 1000.
The number of datasets does not exceed 120.
Output
For each input dataset, the number of medals remaining at hand is output on one line.
Example
Input
3 2 30 3 26 226
9 0 18 3 20 118
5 5 12 2 15 203
7 4 19 2 22 197
7 4 24 4 17 209
0 0 0 0 0 0
Output
127
793
414
629
617 | instruction | 0 | 87,434 | 19 | 174,868 |
"Correct Solution:
```
while 1:
b, r, g, c, s, t = map(int, input().split())
if t == 0:
break
ans = 100
ans += (15 - 2) * (5*b) + (15 - 3) * b
t -= 6*b
ans += (15 - 2) * (3*r) + (15 - 3) * r
t -= 4*r
ans += (7 - 3) * g
t -= g
ans += (2 - 3) * c
t -= c
t -= s
ans += (0 - 3) * t
print(ans)
``` | output | 1 | 87,434 | 19 | 174,869 |
Provide a correct Python 3 solution for this coding contest problem.
Ataru Oafoot of Aizu Gakuen University High School decided to play with a slot machine.
When you insert a medal on this machine, three reels will start spinning and each reel will stop automatically. In a normal game (normal game), 3 medals are inserted, and when the symbols are aligned, the following medals are obtained according to the symbols.
<image>
A special service will be started depending on how the patterns are aligned. A big bonus starts when you have 3 of 7 symbols, and you can play 5 bonus games. Also, when you have 3 BAR symbols, the regular bonus will start and you can play 3 bonus games.
If you have 3 star symbols, the free game will start and you will not be able to get medals, but you can start the next game without inserting medals.
During the bonus game, if you insert 2 medals per game, you will automatically get 3 grape patterns and 15 medals.
Oafoot started playing on the machine with 100 medals. After playing for a while, it ended in a normal game. How many medals did you have left?
Create a program that inputs play information and outputs the number of medals left at hand. The play information is given as the number of big bonuses b, the number of regular bonuses r, the number of grapes aligned during a normal game g, the number of cherries aligned c, the number of stars aligned s, and the total number of games t.
Note that t includes the number of bonus games. Also, medals will not disappear in the middle of the game.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a zero line. Each dataset is given in the following format:
b r g c s t
b, r, g, c, and s are integers greater than or equal to 0 and less than 200, and t is an integer less than or equal to 1000.
The number of datasets does not exceed 120.
Output
For each input dataset, the number of medals remaining at hand is output on one line.
Example
Input
3 2 30 3 26 226
9 0 18 3 20 118
5 5 12 2 15 203
7 4 19 2 22 197
7 4 24 4 17 209
0 0 0 0 0 0
Output
127
793
414
629
617 | instruction | 0 | 87,435 | 19 | 174,870 |
"Correct Solution:
```
while True:
b, r, g, c, s, t = map(int, input().split())
if b + r + g + c + s + t == 0:
break
normal_game = t - b * 5 - r * 3
bonus_game = b * 5 + r * 3
print(100 + bonus_game * 16 + 15 * b + 15 * r + 7 * g + 2 * c + 3 * s - t * 3)
``` | output | 1 | 87,435 | 19 | 174,871 |
Provide a correct Python 3 solution for this coding contest problem.
Ataru Oafoot of Aizu Gakuen University High School decided to play with a slot machine.
When you insert a medal on this machine, three reels will start spinning and each reel will stop automatically. In a normal game (normal game), 3 medals are inserted, and when the symbols are aligned, the following medals are obtained according to the symbols.
<image>
A special service will be started depending on how the patterns are aligned. A big bonus starts when you have 3 of 7 symbols, and you can play 5 bonus games. Also, when you have 3 BAR symbols, the regular bonus will start and you can play 3 bonus games.
If you have 3 star symbols, the free game will start and you will not be able to get medals, but you can start the next game without inserting medals.
During the bonus game, if you insert 2 medals per game, you will automatically get 3 grape patterns and 15 medals.
Oafoot started playing on the machine with 100 medals. After playing for a while, it ended in a normal game. How many medals did you have left?
Create a program that inputs play information and outputs the number of medals left at hand. The play information is given as the number of big bonuses b, the number of regular bonuses r, the number of grapes aligned during a normal game g, the number of cherries aligned c, the number of stars aligned s, and the total number of games t.
Note that t includes the number of bonus games. Also, medals will not disappear in the middle of the game.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a zero line. Each dataset is given in the following format:
b r g c s t
b, r, g, c, and s are integers greater than or equal to 0 and less than 200, and t is an integer less than or equal to 1000.
The number of datasets does not exceed 120.
Output
For each input dataset, the number of medals remaining at hand is output on one line.
Example
Input
3 2 30 3 26 226
9 0 18 3 20 118
5 5 12 2 15 203
7 4 19 2 22 197
7 4 24 4 17 209
0 0 0 0 0 0
Output
127
793
414
629
617 | instruction | 0 | 87,436 | 19 | 174,872 |
"Correct Solution:
```
while 1:
b, r, g, c, s, t = map(int, input().split())
if [b, r, g, c, s, t] == [0, 0, 0, 0, 0, 0]:
break
medal = 100
bonus = b * 5 + r * 3
normal = t - bonus - s
medal = medal + b * 15 + r * 15 + bonus * 15 + g * 7 + c * 2
medal = medal - normal * 3 - bonus * 2
print(medal)
``` | output | 1 | 87,436 | 19 | 174,873 |
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