message stringlengths 2 28.7k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 21 109k | cluster float64 7 7 | __index_level_0__ int64 42 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
BerPhone X is almost ready for release with n applications being preinstalled on the phone. A category of an application characterizes a genre or a theme of this application (like "game", "business", or "education"). The categories are given as integers between 1 and n, inclusive; the i-th application has category c_i.
You can choose m β the number of screens and s β the size of each screen. You need to fit all n icons of the applications (one icon representing one application) meeting the following requirements:
* On each screen, all the icons must belong to applications of the same category (but different screens can contain icons of applications of the same category);
* Each screen must be either completely filled with icons (the number of icons on the screen is equal to s) or almost filled with icons (the number of icons is equal to s-1).
Your task is to find the minimal possible number of screens m.
Input
The first line contains an integer t (1 β€ t β€ 10 000) β the number of test cases in the input. Then t test cases follow.
The first line of each test case contains an integer n (1 β€ n β€ 2β
10^6) β the number of the icons. The second line contains n integers c_1, c_2, ..., c_n (1 β€ c_i β€ n), where c_i is the category of the i-th application.
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 2β
10^6.
Output
Print t integers β the answers to the given test cases in the order they follow in the input. The answer to a test case is an integer m β the minimum number of screens on which all n icons can be placed satisfying the given requirements.
Example
Input
3
11
1 5 1 5 1 5 1 1 1 1 5
6
1 2 2 2 2 1
5
4 3 3 1 2
Output
3
3
4
Note
In the first test case of the example, all the icons can be placed on three screens of size 4: a screen with 4 icons of the category 1, a screen with 3 icons of the category 1, and a screen with 4 icons of the category 5.
Submitted Solution:
```
import sys
import os
from io import BytesIO, IOBase
from types import GeneratorType
from collections import defaultdict
BUFSIZE = 8192
import math
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")
t=int(input())
for i in range(t):
#n=int(input())
#b=list(map(int,input().split()))
n=int(input())
c=list(map(int,input().split()))
d=defaultdict(lambda:0)
for j in c:
d[j]+=1
cnt=[]
for j in d:
cnt.append(d[j])
cnt.sort()
mi=cnt[0]+1
ans=float("inf")
i=1
while(i<=mi):
curr=0
poss=1
for j in cnt:
if j>=((i-1)*math.ceil(j/i)):
curr+=math.ceil(j/i)
else:
poss=0
break
if poss:
ans=min(ans,curr)
i+=1
print(ans)
``` | instruction | 0 | 101,329 | 7 | 202,658 |
Yes | output | 1 | 101,329 | 7 | 202,659 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
BerPhone X is almost ready for release with n applications being preinstalled on the phone. A category of an application characterizes a genre or a theme of this application (like "game", "business", or "education"). The categories are given as integers between 1 and n, inclusive; the i-th application has category c_i.
You can choose m β the number of screens and s β the size of each screen. You need to fit all n icons of the applications (one icon representing one application) meeting the following requirements:
* On each screen, all the icons must belong to applications of the same category (but different screens can contain icons of applications of the same category);
* Each screen must be either completely filled with icons (the number of icons on the screen is equal to s) or almost filled with icons (the number of icons is equal to s-1).
Your task is to find the minimal possible number of screens m.
Input
The first line contains an integer t (1 β€ t β€ 10 000) β the number of test cases in the input. Then t test cases follow.
The first line of each test case contains an integer n (1 β€ n β€ 2β
10^6) β the number of the icons. The second line contains n integers c_1, c_2, ..., c_n (1 β€ c_i β€ n), where c_i is the category of the i-th application.
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 2β
10^6.
Output
Print t integers β the answers to the given test cases in the order they follow in the input. The answer to a test case is an integer m β the minimum number of screens on which all n icons can be placed satisfying the given requirements.
Example
Input
3
11
1 5 1 5 1 5 1 1 1 1 5
6
1 2 2 2 2 1
5
4 3 3 1 2
Output
3
3
4
Note
In the first test case of the example, all the icons can be placed on three screens of size 4: a screen with 4 icons of the category 1, a screen with 3 icons of the category 1, and a screen with 4 icons of the category 5.
Submitted Solution:
```
from collections import Counter as CO
t=int(input())
for _ in range(t):
n=int(input())
arr=list(map(int,input().split()))
freq=dict(CO(arr))
l=[]
for k in freq:
l+=[freq[k]]
ls=list(set(l))
fact=[2]
for i in ls:
for j in range(1,int(i**.5)+1):
if(i%j==0):
fact+=[j,i//j]
fact=list(set(fact))
fact.sort(reverse=True)
#print(fact)
#print(ls)
for i in fact:
flag=0
for j in ls:
if((i-j%i)<=j//i+1 or j%i==0 ):
pass
else:
#print(i,j)
flag=1
break
if(flag==0):
ans=i
break
co=0
for j in l:
if(j%ans==0):
co+=j//ans
else:
co+=j//ans+1
print(co)
``` | instruction | 0 | 101,330 | 7 | 202,660 |
No | output | 1 | 101,330 | 7 | 202,661 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
BerPhone X is almost ready for release with n applications being preinstalled on the phone. A category of an application characterizes a genre or a theme of this application (like "game", "business", or "education"). The categories are given as integers between 1 and n, inclusive; the i-th application has category c_i.
You can choose m β the number of screens and s β the size of each screen. You need to fit all n icons of the applications (one icon representing one application) meeting the following requirements:
* On each screen, all the icons must belong to applications of the same category (but different screens can contain icons of applications of the same category);
* Each screen must be either completely filled with icons (the number of icons on the screen is equal to s) or almost filled with icons (the number of icons is equal to s-1).
Your task is to find the minimal possible number of screens m.
Input
The first line contains an integer t (1 β€ t β€ 10 000) β the number of test cases in the input. Then t test cases follow.
The first line of each test case contains an integer n (1 β€ n β€ 2β
10^6) β the number of the icons. The second line contains n integers c_1, c_2, ..., c_n (1 β€ c_i β€ n), where c_i is the category of the i-th application.
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 2β
10^6.
Output
Print t integers β the answers to the given test cases in the order they follow in the input. The answer to a test case is an integer m β the minimum number of screens on which all n icons can be placed satisfying the given requirements.
Example
Input
3
11
1 5 1 5 1 5 1 1 1 1 5
6
1 2 2 2 2 1
5
4 3 3 1 2
Output
3
3
4
Note
In the first test case of the example, all the icons can be placed on three screens of size 4: a screen with 4 icons of the category 1, a screen with 3 icons of the category 1, and a screen with 4 icons of the category 5.
Submitted Solution:
```
from collections import Counter
from math import ceil
t = int(input())
for _ in range(0,t):
n = int(input())
ss = [int(i) for i in input().split()]
c = Counter(ss)
aa = sorted([int(i) for i in c.values()])
maxx = 10**9+7
check = list(set(sorted(aa)))
ll = check[0]
if len(check)>=2 and check[1]-check[0] == 1:
ll = check[1]
for i in range(1,ll+1):
val = True
pos = []
for ii in aa:
if ii%i == 0 or ii%i == i-1:
pos.append(ceil(ii/i))
continue
else:
val = False
break
if val:
maxx = min(maxx,sum(pos))
print(maxx)
``` | instruction | 0 | 101,331 | 7 | 202,662 |
No | output | 1 | 101,331 | 7 | 202,663 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
BerPhone X is almost ready for release with n applications being preinstalled on the phone. A category of an application characterizes a genre or a theme of this application (like "game", "business", or "education"). The categories are given as integers between 1 and n, inclusive; the i-th application has category c_i.
You can choose m β the number of screens and s β the size of each screen. You need to fit all n icons of the applications (one icon representing one application) meeting the following requirements:
* On each screen, all the icons must belong to applications of the same category (but different screens can contain icons of applications of the same category);
* Each screen must be either completely filled with icons (the number of icons on the screen is equal to s) or almost filled with icons (the number of icons is equal to s-1).
Your task is to find the minimal possible number of screens m.
Input
The first line contains an integer t (1 β€ t β€ 10 000) β the number of test cases in the input. Then t test cases follow.
The first line of each test case contains an integer n (1 β€ n β€ 2β
10^6) β the number of the icons. The second line contains n integers c_1, c_2, ..., c_n (1 β€ c_i β€ n), where c_i is the category of the i-th application.
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 2β
10^6.
Output
Print t integers β the answers to the given test cases in the order they follow in the input. The answer to a test case is an integer m β the minimum number of screens on which all n icons can be placed satisfying the given requirements.
Example
Input
3
11
1 5 1 5 1 5 1 1 1 1 5
6
1 2 2 2 2 1
5
4 3 3 1 2
Output
3
3
4
Note
In the first test case of the example, all the icons can be placed on three screens of size 4: a screen with 4 icons of the category 1, a screen with 3 icons of the category 1, and a screen with 4 icons of the category 5.
Submitted Solution:
```
def function(lis):
lis_item = []
lis_item_freq = []
for i in lis:
if i in lis_item:
lis_item_freq[lis_item.index(i)] += 1
else:
lis_item.append(i)
lis_item_freq.append(0)
lis_item_freq[lis_item.index(i)] += 1
least_occured = min(lis_item_freq)
max_possible = least_occured # it can be least_occured - 1
for i in lis_item_freq:
if i%max_possible < max_possible-1 and i%max_possible !=0:
#print("yes")
max_possible -= 1
if max_possible+1 in lis_item_freq:
max_possible += 1
summ = 0
for i in lis_item_freq:
summ += i//max_possible
if i%max_possible!=0:
summ+=1
print(summ)
# print(lis_item)
# print(lis_item_freq)
t = int(input())
for i in range(t):
length = int(input())
value = input().split()
function(value)
``` | instruction | 0 | 101,332 | 7 | 202,664 |
No | output | 1 | 101,332 | 7 | 202,665 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
BerPhone X is almost ready for release with n applications being preinstalled on the phone. A category of an application characterizes a genre or a theme of this application (like "game", "business", or "education"). The categories are given as integers between 1 and n, inclusive; the i-th application has category c_i.
You can choose m β the number of screens and s β the size of each screen. You need to fit all n icons of the applications (one icon representing one application) meeting the following requirements:
* On each screen, all the icons must belong to applications of the same category (but different screens can contain icons of applications of the same category);
* Each screen must be either completely filled with icons (the number of icons on the screen is equal to s) or almost filled with icons (the number of icons is equal to s-1).
Your task is to find the minimal possible number of screens m.
Input
The first line contains an integer t (1 β€ t β€ 10 000) β the number of test cases in the input. Then t test cases follow.
The first line of each test case contains an integer n (1 β€ n β€ 2β
10^6) β the number of the icons. The second line contains n integers c_1, c_2, ..., c_n (1 β€ c_i β€ n), where c_i is the category of the i-th application.
It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 2β
10^6.
Output
Print t integers β the answers to the given test cases in the order they follow in the input. The answer to a test case is an integer m β the minimum number of screens on which all n icons can be placed satisfying the given requirements.
Example
Input
3
11
1 5 1 5 1 5 1 1 1 1 5
6
1 2 2 2 2 1
5
4 3 3 1 2
Output
3
3
4
Note
In the first test case of the example, all the icons can be placed on three screens of size 4: a screen with 4 icons of the category 1, a screen with 3 icons of the category 1, and a screen with 4 icons of the category 5.
Submitted Solution:
```
from collections import defaultdict as dd
t=int(input())
while t:
n=int(input())
d=dd(int)
l=list(map(int,input().split()))
for i in l:
d[i]+=1
li=[]
for i in d:
li.append(d[i])
mx=1000000000000000000
si=li[0]
ll=[]
mi=10000000000000000000000
for m in range(1,min(li)+1):
cou=dd(int)
lol=0
lo=0
for i in li:
#print(m,i)
if(i==1):
#print("lol")
cou[m]+=1
elif(i%m==0 and m!=1):
cou[m]+=i//m
else:
ex=i%m
if(m==1):
ex=i//2
cou[m+1]+=ex
i-=ex*(m+1)
cou[m]+=i//m
lol=1
else:
if(i//m>=ex):
cou[m+1]+=ex
i-=ex*(m+1)
cou[m]+=i//m
lol=1
else:
cou[m-1]+=m-ex
i-=(m-ex)*(m-1)
cou[m]+=i//m
lo=1
if((cou[m]+cou[m+1]+cou[m-1])<mi and lol!=lo):
mi=(cou[m]+cou[m+1]+cou[m-1])
#print(d,mi)
print(mi)
t-=1
``` | instruction | 0 | 101,333 | 7 | 202,666 |
No | output | 1 | 101,333 | 7 | 202,667 |
Provide tags and a correct Python 3 solution for this coding contest problem.
As the boat drifts down the river, a wood full of blossoms shows up on the riverfront.
"I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."
"What is it like?"
"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?"
There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.
The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers.
According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.
You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.
Note that you can choose arbitrary n and m under the constraints below, they are not given in the input.
Input
The first and only line of input contains four space-separated integers a, b, c and d (1 β€ a, b, c, d β€ 100) β the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.
Output
In the first line, output two space-separated integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns in the grid respectively.
Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.
In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).
Examples
Input
5 3 2 1
Output
4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD
Input
50 50 1 1
Output
4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Input
1 6 4 5
Output
7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD
Note
In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.
<image> | instruction | 0 | 101,776 | 7 | 203,552 |
Tags: constructive algorithms, graphs
Correct Solution:
```
a = list(map(int, input().split()))
ab = [['A']*25+['B']*25 for i in range(25)]
cd = [['C']*25+['D']*25 for i in range(25)]
print (50, 50)
for i in range(4):
a[i] -= 1
si, sj = 26, 26
while a[0] > 0:
cd[si-25][sj] = 'A'
a[0] -= 1
sj += 2
if sj == 50:
sj = 26
si += 2
si, sj = 26, 0
while a[1] > 0:
cd[si-25][sj] = 'B'
a[1] -= 1
sj += 2
if sj == 26:
sj = 0
si += 2
si, sj = 0,0
while a[2] > 0:
ab[si][sj] = 'C'
a[2] -= 1
sj += 2
if sj == 24:
sj = 0
si += 2
si, sj = 0, 26
while a[3] > 0:
ab[si][sj] = 'D'
a[3] -= 1
sj += 2
if sj == 50:
sj = 26
si += 2
for i in ab:
print (''.join(i))
for i in cd:
print (''.join(i))
``` | output | 1 | 101,776 | 7 | 203,553 |
Provide tags and a correct Python 3 solution for this coding contest problem.
As the boat drifts down the river, a wood full of blossoms shows up on the riverfront.
"I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."
"What is it like?"
"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?"
There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.
The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers.
According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.
You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.
Note that you can choose arbitrary n and m under the constraints below, they are not given in the input.
Input
The first and only line of input contains four space-separated integers a, b, c and d (1 β€ a, b, c, d β€ 100) β the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.
Output
In the first line, output two space-separated integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns in the grid respectively.
Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.
In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).
Examples
Input
5 3 2 1
Output
4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD
Input
50 50 1 1
Output
4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Input
1 6 4 5
Output
7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD
Note
In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.
<image> | instruction | 0 | 101,777 | 7 | 203,554 |
Tags: constructive algorithms, graphs
Correct Solution:
```
a = [int(x) - 1 for x in input().split()]
n = m = 48
colors = "ABCD"
side = n // 2
ans = [[0] * n for _ in range(n)]
for i, color in enumerate(colors):
for dx in range(side):
for dy in range(side):
x, y = dx + side * (i & 1), dy + side * (i // 2)
ans[x][y] = color
new_i = (i + 1) % 4
if 0 < min(dx, dy) and max(dx, dy) < side - 1 and a[new_i] and dx & 1 and dy & 1:
ans[x][y] = colors[new_i]
a[new_i] -= 1
print(n, m)
print(*(''.join(row) for row in ans), sep='\n')
``` | output | 1 | 101,777 | 7 | 203,555 |
Provide tags and a correct Python 3 solution for this coding contest problem.
As the boat drifts down the river, a wood full of blossoms shows up on the riverfront.
"I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."
"What is it like?"
"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?"
There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.
The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers.
According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.
You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.
Note that you can choose arbitrary n and m under the constraints below, they are not given in the input.
Input
The first and only line of input contains four space-separated integers a, b, c and d (1 β€ a, b, c, d β€ 100) β the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.
Output
In the first line, output two space-separated integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns in the grid respectively.
Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.
In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).
Examples
Input
5 3 2 1
Output
4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD
Input
50 50 1 1
Output
4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Input
1 6 4 5
Output
7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD
Note
In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.
<image> | instruction | 0 | 101,778 | 7 | 203,556 |
Tags: constructive algorithms, graphs
Correct Solution:
```
import sys
A,B,C,D = map(int,input().split())
board = [['A']*50 for i in range(33)]
for i in range(24,33):
for j in range(50):
board[i][j] ='B'
A -= 1
for i in range(1,24,2):
for j in range(1,50,2):
# Bλ 1κ° λ¨κ²¨λκΈ°
if B > 1:
board[i][j] = 'B'
B -= 1
elif C > 0:
board[i][j] = 'C'
C -= 1
elif D > 0:
board[i][j] = 'D'
D -= 1
board[23][49] = 'B'
for i in range(25,33,2):
for j in range(1,50,2):
if A > 0:
board[i][j] = 'A'
A -= 1
sys.stdout.write("33 50\n")
for i in range(33):
sys.stdout.write(''.join(board[i]))
if i != 32:
sys.stdout.write('\n')
``` | output | 1 | 101,778 | 7 | 203,557 |
Provide tags and a correct Python 3 solution for this coding contest problem.
As the boat drifts down the river, a wood full of blossoms shows up on the riverfront.
"I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."
"What is it like?"
"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?"
There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.
The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers.
According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.
You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.
Note that you can choose arbitrary n and m under the constraints below, they are not given in the input.
Input
The first and only line of input contains four space-separated integers a, b, c and d (1 β€ a, b, c, d β€ 100) β the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.
Output
In the first line, output two space-separated integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns in the grid respectively.
Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.
In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).
Examples
Input
5 3 2 1
Output
4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD
Input
50 50 1 1
Output
4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Input
1 6 4 5
Output
7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD
Note
In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.
<image> | instruction | 0 | 101,779 | 7 | 203,558 |
Tags: constructive algorithms, graphs
Correct Solution:
```
a, b, c, d = map(int, input().split())
res = [['A'] * 50 for i in range(25)] + \
[['B'] * 50 for i in range(25)]
a, b = a - 1, b - 1
for i in range(0, 24, 2):
for j in range(0, 50, 2):
if b > 0:
b -= 1
res[i][j] = 'B'
elif c > 0:
c -= 1
res[i][j] = 'C'
elif d > 0:
d -= 1
res[i][j] = 'D'
if a > 0:
a -= 1
res[i + 26][j] = 'A'
print(50, 50)
for i in res:
print(''.join(i))
``` | output | 1 | 101,779 | 7 | 203,559 |
Provide tags and a correct Python 3 solution for this coding contest problem.
As the boat drifts down the river, a wood full of blossoms shows up on the riverfront.
"I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."
"What is it like?"
"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?"
There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.
The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers.
According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.
You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.
Note that you can choose arbitrary n and m under the constraints below, they are not given in the input.
Input
The first and only line of input contains four space-separated integers a, b, c and d (1 β€ a, b, c, d β€ 100) β the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.
Output
In the first line, output two space-separated integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns in the grid respectively.
Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.
In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).
Examples
Input
5 3 2 1
Output
4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD
Input
50 50 1 1
Output
4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Input
1 6 4 5
Output
7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD
Note
In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.
<image> | instruction | 0 | 101,780 | 7 | 203,560 |
Tags: constructive algorithms, graphs
Correct Solution:
```
a,b,c,d = map(int,input().split())
if a + b + c + d == 4:
print(1,4)
print("ABCD")
else:
print(50,50)
ans = [[""]*50 for i in range(50)]
if a == 1:
for i in range(50):
for j in range(50):
ans[i][j] = "A"
for i in range(0,50,2):
for j in range(0,50,2):
b -= 1
ans[i][j] = "B"
if b == 0:
break
if b == 0:
break
for i in range(15,50,2):
for j in range(0,50,2):
c -= 1
ans[i][j] = "C"
if c == 0:
break
if c == 0:
break
for i in range(30,50,2):
for j in range(0,50,2):
d -= 1
ans[i][j] = "D"
if d == 0:
break
if d == 0:
break
elif b == 1:
for i in range(50):
for j in range(50):
ans[i][j] = "B"
for i in range(0,50,2):
for j in range(0,50,2):
a -= 1
ans[i][j] = "a"
if a == 0:
break
if a == 0:
break
for i in range(15,50,2):
for j in range(0,50,2):
c -= 1
ans[i][j] = "C"
if c == 0:
break
if c == 0:
break
for i in range(30,50,2):
for j in range(0,50,2):
d -= 1
ans[i][j] = "D"
if d == 0:
break
if d == 0:
break
else:
b -= 1
a -= 1
for i in range(50):
for j in range(50):
ans[i][j] = "A"
for i in range(0,50,2):
for j in range(0,50,2):
b -= 1
ans[i][j] = "B"
if b == 0:
break
if b == 0:
break
for i in range(12,50,2):
for j in range(0,50,2):
c -= 1
ans[i][j] = "C"
if c == 0:
break
if c == 0:
break
for i in range(24,50,2):
for j in range(0,50,2):
d -= 1
ans[i][j] = "D"
if d == 0:
break
if d == 0:
break
for i in range(35,50):
for j in range(50):
ans[i][j] = "B"
for i in range(37,50,2):
for j in range(0,50,2):
a -= 1
ans[i][j] = "A"
if a == 0:
break
if a == 0:
break
for i in range(50):
for j in range(50):
print(ans[i][j],end="")
print()
``` | output | 1 | 101,780 | 7 | 203,561 |
Provide tags and a correct Python 3 solution for this coding contest problem.
As the boat drifts down the river, a wood full of blossoms shows up on the riverfront.
"I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."
"What is it like?"
"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?"
There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.
The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers.
According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.
You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.
Note that you can choose arbitrary n and m under the constraints below, they are not given in the input.
Input
The first and only line of input contains four space-separated integers a, b, c and d (1 β€ a, b, c, d β€ 100) β the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.
Output
In the first line, output two space-separated integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns in the grid respectively.
Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.
In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).
Examples
Input
5 3 2 1
Output
4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD
Input
50 50 1 1
Output
4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Input
1 6 4 5
Output
7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD
Note
In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.
<image> | instruction | 0 | 101,781 | 7 | 203,562 |
Tags: constructive algorithms, graphs
Correct Solution:
```
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 998244353
dd = [(0,-1),(1,0),(0,1),(-1,0)]
ddn = [(0,-1),(1,-1),(1,0),(1,1),(0,1),(-1,-1),(-1,0),(-1,1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def main():
a,b,c,d = LI()
r = [['']*50 for _ in range(50)]
for i in range(50):
for j in range(50):
if i < 25:
if j < 25:
r[i][j] = 'A'
else:
r[i][j] = 'B'
else:
if j < 25:
r[i][j] = 'C'
else:
r[i][j] = 'D'
for i in range(a-1):
j = (i // 12) * 2
k = (i % 12) * 2
r[j][k+26] = 'A'
for i in range(b-1):
j = (i // 12) * 2
k = (i % 12) * 2
r[j][k] = 'B'
for i in range(c-1):
j = (i // 12) * 2
k = (i % 12) * 2
r[j+26][k+26] = 'C'
for i in range(d-1):
j = (i // 12) * 2
k = (i % 12) * 2
r[j+26][k] = 'D'
return '50 50\n' + '\n'.join(map(lambda x: ''.join(x), r))
print(main())
``` | output | 1 | 101,781 | 7 | 203,563 |
Provide tags and a correct Python 3 solution for this coding contest problem.
As the boat drifts down the river, a wood full of blossoms shows up on the riverfront.
"I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."
"What is it like?"
"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?"
There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.
The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers.
According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.
You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.
Note that you can choose arbitrary n and m under the constraints below, they are not given in the input.
Input
The first and only line of input contains four space-separated integers a, b, c and d (1 β€ a, b, c, d β€ 100) β the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.
Output
In the first line, output two space-separated integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns in the grid respectively.
Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.
In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).
Examples
Input
5 3 2 1
Output
4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD
Input
50 50 1 1
Output
4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Input
1 6 4 5
Output
7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD
Note
In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.
<image> | instruction | 0 | 101,782 | 7 | 203,564 |
Tags: constructive algorithms, graphs
Correct Solution:
```
FIFTY = 50
TWENTY_FIVE = 25
TWELVE = 12
grid = [['X' for _ in range(FIFTY)] for _ in range(FIFTY)]
def construct(n, mark, bg, base_i, base_j):
for i in range(TWENTY_FIVE):
for j in range(TWENTY_FIVE):
grid[base_i + i][base_j + j] = bg
for i in range(n):
grid[base_i + 2 * (i // TWELVE) + 1][base_j + 2 * (i % TWELVE) + 1] = mark
def main():
a, b, c, d = map(int, input().split())
construct(a - 1, 'A', 'B', 0, 0)
construct(b - 1, 'B', 'C', TWENTY_FIVE, 0)
construct(c - 1, 'C', 'D', 0, TWENTY_FIVE)
construct(d - 1, 'D', 'A', TWENTY_FIVE, TWENTY_FIVE)
print(FIFTY, FIFTY)
for row in grid:
print(''.join(row))
if __name__ == '__main__':
main()
``` | output | 1 | 101,782 | 7 | 203,565 |
Provide tags and a correct Python 3 solution for this coding contest problem.
As the boat drifts down the river, a wood full of blossoms shows up on the riverfront.
"I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."
"What is it like?"
"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?"
There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.
The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers.
According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.
You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.
Note that you can choose arbitrary n and m under the constraints below, they are not given in the input.
Input
The first and only line of input contains four space-separated integers a, b, c and d (1 β€ a, b, c, d β€ 100) β the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.
Output
In the first line, output two space-separated integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns in the grid respectively.
Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.
In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).
Examples
Input
5 3 2 1
Output
4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD
Input
50 50 1 1
Output
4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Input
1 6 4 5
Output
7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD
Note
In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.
<image> | instruction | 0 | 101,783 | 7 | 203,566 |
Tags: constructive algorithms, graphs
Correct Solution:
```
a, b, c, d = map(int, input().strip().split())
def fill(s, st, ch, cnt):
ri, ci = st, 0
while cnt > 0:
s[ri][ci] = ch
cnt -= 1
ci += 2
if ci >= 50:
ri += 3
ci = 0
dat = dict()
dat.update({'A': a, 'B': b, 'C': c, 'D': d})
dat = sorted(dat.items(), key=lambda kv : kv[1])
mf = dat[3]
lf = dat[0]
res = list()
for i in range(30):
res.append(list(lf[0] * 50))
for i in range(20):
res.append(list(mf[0] * 50))
fill(res, 0, dat[3][0], dat[3][1] - 1)
fill(res, 1, dat[2][0], dat[2][1])
fill(res, 2, dat[1][0], dat[1][1])
fill(res, 31, dat[0][0], dat[0][1] - 1)
print(50, 50)
for e_ in res:
print(''.join(map(str, e_)))
``` | output | 1 | 101,783 | 7 | 203,567 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
As the boat drifts down the river, a wood full of blossoms shows up on the riverfront.
"I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."
"What is it like?"
"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?"
There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.
The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers.
According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.
You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.
Note that you can choose arbitrary n and m under the constraints below, they are not given in the input.
Input
The first and only line of input contains four space-separated integers a, b, c and d (1 β€ a, b, c, d β€ 100) β the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.
Output
In the first line, output two space-separated integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns in the grid respectively.
Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.
In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).
Examples
Input
5 3 2 1
Output
4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD
Input
50 50 1 1
Output
4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Input
1 6 4 5
Output
7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD
Note
In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.
<image>
Submitted Solution:
```
data = input()
def main():
counters = [int(x) for x in data.split(' ')]
codes = {
0: 'A',
1: 'B',
2: 'C',
3: 'D',
}
counters[0] -= 1
counters[3] -= 1
completed = []
row = []
for flower in range(1, 4):
rows, row = fill_grid(row, 'A', codes[flower], counters[flower])
completed += rows
if row:
completed.append(''.join(row) + 'A' * (50 - len(row)))
completed.append('A' * 50)
completed.append('D' * 50)
row = []
rows, row = fill_grid(row, 'D', 'A', counters[0])
completed += rows
if row:
completed.append(''.join(row) + 'D' * (50 - len(row)))
completed.append('D' * 50)
print('{} 50'.format(len(completed)))
for row in completed:
print(row)
def fill_grid(row, grid, flower, counter):
completed = []
while counter > 0:
counter -= 1
row.append(flower)
row.append(grid)
if len(row) == 50:
completed.append(''.join(row))
completed.append(''.join([grid] * 50))
row = []
return completed, row
if __name__ == '__main__':
main()
``` | instruction | 0 | 101,784 | 7 | 203,568 |
Yes | output | 1 | 101,784 | 7 | 203,569 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
As the boat drifts down the river, a wood full of blossoms shows up on the riverfront.
"I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."
"What is it like?"
"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?"
There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.
The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers.
According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.
You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.
Note that you can choose arbitrary n and m under the constraints below, they are not given in the input.
Input
The first and only line of input contains four space-separated integers a, b, c and d (1 β€ a, b, c, d β€ 100) β the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.
Output
In the first line, output two space-separated integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns in the grid respectively.
Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.
In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).
Examples
Input
5 3 2 1
Output
4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD
Input
50 50 1 1
Output
4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Input
1 6 4 5
Output
7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD
Note
In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.
<image>
Submitted Solution:
```
a,b,c,d=map(int,input().split())
m=[]
for i in range(50):
m.append([0]*50)
for i in range(0,25,2):
for j in range(0,25,2):
if a==1:
break
a-=1
m[i][j]='A'
if a==1:
break
for i in range(25):
for j in range(25):
if m[i][j]==0:
m[i][j]='B'
for i in range(0,25,2):
for j in range(26,50,2):
if b==1:
break
b-=1
m[i][j]='B'
if b==1:
break
for i in range(25):
for j in range(25,50):
if m[i][j]==0:
m[i][j]='C'
for i in range(26,50,2):
for j in range(25,50,2):
if c==1:
break
c-=1
m[i][j]='C'
if c==1:
break
for i in range(25,50):
for j in range(25,50):
if m[i][j]==0:
m[i][j]='D'
for i in range(25,50,2):
for j in range(0,24,2):
if d==1:
break
d-=1
m[i][j]='D'
if d==1:
break
for i in range(25,50):
for j in range(0,25):
if m[i][j]==0:
m[i][j]='A'
print(50,50)
for i in range(50):
for j in range(50):
print(m[i][j],end="")
print()
``` | instruction | 0 | 101,785 | 7 | 203,570 |
Yes | output | 1 | 101,785 | 7 | 203,571 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
As the boat drifts down the river, a wood full of blossoms shows up on the riverfront.
"I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."
"What is it like?"
"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?"
There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.
The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers.
According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.
You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.
Note that you can choose arbitrary n and m under the constraints below, they are not given in the input.
Input
The first and only line of input contains four space-separated integers a, b, c and d (1 β€ a, b, c, d β€ 100) β the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.
Output
In the first line, output two space-separated integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns in the grid respectively.
Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.
In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).
Examples
Input
5 3 2 1
Output
4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD
Input
50 50 1 1
Output
4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Input
1 6 4 5
Output
7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD
Note
In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.
<image>
Submitted Solution:
```
a,b,c,d=map(int,input().split())
r=[['A' for i in range(50)] for j in range(50)]
flag=0
print(50,50)
for i in range(0,8,2):
for j in range(0,50,2):
r[i][j]='D'
d-=1
if(d==0):
flag=1
break
if(flag==1):
break
flag=0
for i in range(8,16,2):
for j in range(0,50,2):
r[i][j]='C'
c-=1
if(c==0):
flag=1
break
if(flag==1):
break
for i in range(49,32,-1):
for j in range(50):
r[i][j]='B'
a-=1
b-=1
flag=0
if(a!=0):
for i in range(34,50,2):
for j in range(0,50,2):
r[i][j]='A'
a-=1
if(a==0):
flag=1
break
if(flag==1):
break
flag=0
if(b!=0):
for i in range(16,50,2):
for j in range(0,50,2):
r[i][j]='B'
b-=1
if(b==0):
flag=1
break
if(flag==1):
break
for i in r:
for j in i:
print(j,end="")
print()
``` | instruction | 0 | 101,786 | 7 | 203,572 |
Yes | output | 1 | 101,786 | 7 | 203,573 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
As the boat drifts down the river, a wood full of blossoms shows up on the riverfront.
"I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."
"What is it like?"
"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?"
There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.
The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers.
According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.
You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.
Note that you can choose arbitrary n and m under the constraints below, they are not given in the input.
Input
The first and only line of input contains four space-separated integers a, b, c and d (1 β€ a, b, c, d β€ 100) β the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.
Output
In the first line, output two space-separated integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns in the grid respectively.
Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.
In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).
Examples
Input
5 3 2 1
Output
4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD
Input
50 50 1 1
Output
4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Input
1 6 4 5
Output
7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD
Note
In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.
<image>
Submitted Solution:
```
a,b,c,d = list(map(int ,input().split()))
pole = []
for row in range (40):
pole.append(['A']*50)
for row in range (10):
pole.append(['D']*50)
for i in range(b):
pole[(i // 25) *2 ][(i %25) *2] = 'B'
for i in range(c):
pole[ 7 + (i // 25) *2 ][(i %25) *2] = 'C'
for i in range(d-1):
pole[ 14 + (i // 25) *2 ][(i %25) *2] = 'D'
for i in range(a-1):
pole[41 + (i // 25) *2 ][(i %25) *2] = 'A'
print('50 50')
for row in range(50):
print(''.join(pole[row]))
``` | instruction | 0 | 101,787 | 7 | 203,574 |
Yes | output | 1 | 101,787 | 7 | 203,575 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
As the boat drifts down the river, a wood full of blossoms shows up on the riverfront.
"I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."
"What is it like?"
"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?"
There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.
The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers.
According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.
You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.
Note that you can choose arbitrary n and m under the constraints below, they are not given in the input.
Input
The first and only line of input contains four space-separated integers a, b, c and d (1 β€ a, b, c, d β€ 100) β the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.
Output
In the first line, output two space-separated integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns in the grid respectively.
Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.
In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).
Examples
Input
5 3 2 1
Output
4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD
Input
50 50 1 1
Output
4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Input
1 6 4 5
Output
7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD
Note
In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.
<image>
Submitted Solution:
```
# https://codeforces.com/problemset/problem/989/C
def create(bk, fr, num):
a = [[bk for _ in range(50)] for _ in range(12)]
flg = True
for i in range(0, 12, 2):
for j in range(0, 50, 2):
if num == 0:
flg = False
break
a[i][j] = fr
num -= 1
if flg == False:
break
return a
a, b, c, d = list(map(int, input().split()))
a -= 1
b -= 1
c -= 1
d -= 1
ans = []
ans.extend(create('A', 'B', b))
ans.extend(create('B', 'C', c))
ans.extend(create('C', 'D', d))
ans.extend(create('D', 'A', a))
for x in ans:
for y in x:
print(y, end='')
print()
``` | instruction | 0 | 101,788 | 7 | 203,576 |
No | output | 1 | 101,788 | 7 | 203,577 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
As the boat drifts down the river, a wood full of blossoms shows up on the riverfront.
"I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."
"What is it like?"
"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?"
There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.
The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers.
According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.
You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.
Note that you can choose arbitrary n and m under the constraints below, they are not given in the input.
Input
The first and only line of input contains four space-separated integers a, b, c and d (1 β€ a, b, c, d β€ 100) β the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.
Output
In the first line, output two space-separated integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns in the grid respectively.
Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.
In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).
Examples
Input
5 3 2 1
Output
4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD
Input
50 50 1 1
Output
4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Input
1 6 4 5
Output
7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD
Note
In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.
<image>
Submitted Solution:
```
line = input()
flowers = line.split('\n')[0]
flowers = flowers.split(' ')
a = int(flowers[3])
ind = 3
for i in range(3):
if int(flowers[i]) < a:
a = int(flowers[i])
ind = i
b = int(flowers[3])
index = (ind+2)%4
field = [[0 for x in range(50)] for y in range(50)]
def makerect(field,n,index):
for i in range(50):
for j in range(50):
if field[i][j] == 0:
field[i][j] = chr(n+65)
req = int(flowers[n]) - 1
k = 49
l = 1
while(req > 0):
field[k][l] = chr(index + 65)
req -= 1
l = l + 2
if(l > 49):
l = 1
k = k-2
m = 48
while(m > k-2 and int(flowers[ind]) != 1):
for j in range(50):
field[m][j] = chr(index+65)
m = m - 2
return field
def makefield(field,flowers,ind,index):
for k in range(4):
if k == index:
if int(flowers[ind]) == 1:
a = int(flowers[k])
else:
a = int(flowers[k]) - 1
else:
a = int(flowers[k])
j = k
i = 0
while a > 0 :
field[i][j] = chr(k+65)
j = j + 4
a = a - 1
if(j > 49):
i = i + 2
j = k
return
makefield(field,flowers,ind,index)
field = makerect(field,ind,index)
for i in range(50):
for j in range(50):
print(field[i][j],end = "")
print()
``` | instruction | 0 | 101,789 | 7 | 203,578 |
No | output | 1 | 101,789 | 7 | 203,579 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
As the boat drifts down the river, a wood full of blossoms shows up on the riverfront.
"I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."
"What is it like?"
"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?"
There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.
The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers.
According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.
You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.
Note that you can choose arbitrary n and m under the constraints below, they are not given in the input.
Input
The first and only line of input contains four space-separated integers a, b, c and d (1 β€ a, b, c, d β€ 100) β the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.
Output
In the first line, output two space-separated integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns in the grid respectively.
Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.
In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).
Examples
Input
5 3 2 1
Output
4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD
Input
50 50 1 1
Output
4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Input
1 6 4 5
Output
7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD
Note
In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.
<image>
Submitted Solution:
```
#input = open('t.txt').readline
count = list(map(int, input().split()))
flower = 'ABCD'
a = []
last = -1
if all(x == 0 for x in count):
print('0 0')
exit()
while True:
best = 0
best_count = -1
for i in range(4):
if i != last and count[i] > best_count:
best = i
best_count = count[i]
a.append(flower[best]*2)
count[best] -= 1
if count[best] == 0:
break
last = best
i = 0
sep = flower[best]*2
while i < 4:
pair = flower[i]+flower[best]
for j in range(count[i]):
a.append(pair)
a.append(sep)
i += 1
print(str(len(a))+' 2')
print('\n'.join(a))
``` | instruction | 0 | 101,790 | 7 | 203,580 |
No | output | 1 | 101,790 | 7 | 203,581 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
As the boat drifts down the river, a wood full of blossoms shows up on the riverfront.
"I've been here once," Mino exclaims with delight, "it's breathtakingly amazing."
"What is it like?"
"Look, Kanno, you've got your paintbrush, and I've got my words. Have a try, shall we?"
There are four kinds of flowers in the wood, Amaranths, Begonias, Centaureas and Dianthuses.
The wood can be represented by a rectangular grid of n rows and m columns. In each cell of the grid, there is exactly one type of flowers.
According to Mino, the numbers of connected components formed by each kind of flowers are a, b, c and d respectively. Two cells are considered in the same connected component if and only if a path exists between them that moves between cells sharing common edges and passes only through cells containing the same flowers.
You are to help Kanno depict such a grid of flowers, with n and m arbitrarily chosen under the constraints given below. It can be shown that at least one solution exists under the constraints of this problem.
Note that you can choose arbitrary n and m under the constraints below, they are not given in the input.
Input
The first and only line of input contains four space-separated integers a, b, c and d (1 β€ a, b, c, d β€ 100) β the required number of connected components of Amaranths, Begonias, Centaureas and Dianthuses, respectively.
Output
In the first line, output two space-separated integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns in the grid respectively.
Then output n lines each consisting of m consecutive English letters, representing one row of the grid. Each letter should be among 'A', 'B', 'C' and 'D', representing Amaranths, Begonias, Centaureas and Dianthuses, respectively.
In case there are multiple solutions, print any. You can output each letter in either case (upper or lower).
Examples
Input
5 3 2 1
Output
4 7
DDDDDDD
DABACAD
DBABACD
DDDDDDD
Input
50 50 1 1
Output
4 50
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ABABABABABABABABABABABABABABABABABABABABABABABABAB
BABABABABABABABABABABABABABABABABABABABABABABABABA
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Input
1 6 4 5
Output
7 7
DDDDDDD
DDDBDBD
DDCDCDD
DBDADBD
DDCDCDD
DBDBDDD
DDDDDDD
Note
In the first example, each cell of Amaranths, Begonias and Centaureas forms a connected component, while all the Dianthuses form one.
<image>
Submitted Solution:
```
a, b, c, d = map(int, input().split())
m = [['D']*50 for i in range(50)]
for i in range(a):
m[0][i] = 'A'
for i in range(b):
m[1][i] = 'B'
for i in range(c):
m[2][i] = 'C'
print(50,50)
for line in m:
print(''.join(line))
``` | instruction | 0 | 101,791 | 7 | 203,582 |
No | output | 1 | 101,791 | 7 | 203,583 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n Γ m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that:
1. All cells in a set have the same color.
2. Every two cells in a set share row or column.
Input
The first line of input contains integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns correspondingly.
The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black.
Output
Output single integer β the number of non-empty sets from the problem description.
Examples
Input
1 1
0
Output
1
Input
2 3
1 0 1
0 1 0
Output
8
Note
In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets. | instruction | 0 | 102,587 | 7 | 205,174 |
Tags: combinatorics, math
Correct Solution:
```
def twopmo(n):
return (1<<n)-n-1
n,m = [int(x) for x in input().split()]
numzr = [0 for i in range(n)]
numzc = [0 for i in range(m)]
matrix = [[] for j in range(n)]
for i in range(n):
matrix[i] = [int(x) for x in input().split()]
for i in range(n):
for j in range(m):
if matrix[i][j]==1:
numzc[j]+=1
numzr[i]+=1
ans = n*m
for i in range(n):
ans = ans + twopmo(numzr[i]) + twopmo(m-numzr[i])
for i in range(m):
ans = ans + twopmo(numzc[i]) + twopmo(n-numzc[i])
print(ans)
``` | output | 1 | 102,587 | 7 | 205,175 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n Γ m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that:
1. All cells in a set have the same color.
2. Every two cells in a set share row or column.
Input
The first line of input contains integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns correspondingly.
The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black.
Output
Output single integer β the number of non-empty sets from the problem description.
Examples
Input
1 1
0
Output
1
Input
2 3
1 0 1
0 1 0
Output
8
Note
In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets. | instruction | 0 | 102,588 | 7 | 205,176 |
Tags: combinatorics, math
Correct Solution:
```
numRows, numCols = [int(i) for i in input().split()]
arr = []
total = 0
for _ in range(numRows):
arr.append([int(i) for i in input().split()])
for row in range(numRows):
numOnes = sum([arr[row][col] for col in range(numCols)])
numZeroes = numCols - numOnes
total += (2**numZeroes - 1) + (2**numOnes - 1)
for col in range(numCols):
numOnes = sum([arr[row][col] for row in range(numRows)])
numZeroes = numRows - numOnes
total += (2**numZeroes - 1) + (2**numOnes - 1)
total -= numRows * numCols
print(total)
``` | output | 1 | 102,588 | 7 | 205,177 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n Γ m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that:
1. All cells in a set have the same color.
2. Every two cells in a set share row or column.
Input
The first line of input contains integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns correspondingly.
The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black.
Output
Output single integer β the number of non-empty sets from the problem description.
Examples
Input
1 1
0
Output
1
Input
2 3
1 0 1
0 1 0
Output
8
Note
In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets. | instruction | 0 | 102,589 | 7 | 205,178 |
Tags: combinatorics, math
Correct Solution:
```
n, m = map(int, input().split())
a = [list(map(int, input().split())) for i in range(n)]
col = [[0, 0] for i in range(m)]
row = [[0, 0] for i in range(n)]
for i in range(n):
summa = sum(a[i])
row[i] = [summa, m - summa]
for i in range(m):
summa = 0
for j in range(n):
summa += a[j][i]
col[i] = [summa, n - summa]
res = 0
for i in row:
res += (2 ** i[0]) + (2 ** i[1]) - 2
for i in col:
res += (2 ** i[0]) + (2 ** i[1]) - 2
res -= n *m
print(res)
``` | output | 1 | 102,589 | 7 | 205,179 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n Γ m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that:
1. All cells in a set have the same color.
2. Every two cells in a set share row or column.
Input
The first line of input contains integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns correspondingly.
The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black.
Output
Output single integer β the number of non-empty sets from the problem description.
Examples
Input
1 1
0
Output
1
Input
2 3
1 0 1
0 1 0
Output
8
Note
In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets. | instruction | 0 | 102,590 | 7 | 205,180 |
Tags: combinatorics, math
Correct Solution:
```
#B. Rectangles
#Problem number 844: Rectangles
n,m = [int(i) for i in input().split()]
#each element of the row and of the column will contain a pair ('number_of_whites', 'number_of_blacks')
rows = [[0,0] for i in range(n)]
columns = [[0,0] for i in range(m)]
#read row by row
for i in range(n):
row = [int(element) for element in input().split()]
for j in range(m):
if row[j] == 0: #white
rows[i][0] += 1
columns[j][0] += 1
else:
rows[i][1] += 1
columns[j][1] += 1
#count individual sets
number_of_sets = n*m
for count in rows:
if count[0] > 0:
number_of_sets += 2**count[0] - 1 - count[0] #total number of subsets - empty subset - individual subsets(counted since the beginning)
if count[1] > 0:
number_of_sets += 2**count[1] - 1 - count[1]
for count in columns:
if count[0] > 0:
number_of_sets += 2**count[0] - 1 - count[0] #total number of subsets - empty subset - individual subsets(counted since the beginning)
if count[1] > 0:
number_of_sets += 2**count[1] - 1 - count[1]
print(number_of_sets)
``` | output | 1 | 102,590 | 7 | 205,181 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n Γ m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that:
1. All cells in a set have the same color.
2. Every two cells in a set share row or column.
Input
The first line of input contains integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns correspondingly.
The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black.
Output
Output single integer β the number of non-empty sets from the problem description.
Examples
Input
1 1
0
Output
1
Input
2 3
1 0 1
0 1 0
Output
8
Note
In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets. | instruction | 0 | 102,591 | 7 | 205,182 |
Tags: combinatorics, math
Correct Solution:
```
n, m = [int(x) for x in input().split()]
l = []
for i in range(n):
temp = list(map(int, input().split()))
l.append(temp)
s = n * m
for i in range(n):
c0 = 0
c1 = 0
for j in range(m):
if l[i][j] == 0: c0 += 1
else: c1 += 1
s += ((2 ** c0) - 1 - c0)
s += ((2 ** c1) - 1 - c1)
for i in range(m):
c0 = 0
c1 = 0
for j in range(n):
if l[j][i] == 0: c0 += 1
else: c1 += 1
s += ((2 ** c0) - 1 - c0)
s += ((2 ** c1) - 1 - c1)
print(s)
``` | output | 1 | 102,591 | 7 | 205,183 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n Γ m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that:
1. All cells in a set have the same color.
2. Every two cells in a set share row or column.
Input
The first line of input contains integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns correspondingly.
The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black.
Output
Output single integer β the number of non-empty sets from the problem description.
Examples
Input
1 1
0
Output
1
Input
2 3
1 0 1
0 1 0
Output
8
Note
In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets. | instruction | 0 | 102,592 | 7 | 205,184 |
Tags: combinatorics, math
Correct Solution:
```
h, w = map(int, input().split())
grid = []
ans = 0
for i in range(h):
grid.append(input().split())
for i in range(h):
whiterun = 0
blackrun = 0
for x in range(w):
if grid[i][x] == '0':
ans += 2**whiterun
whiterun += 1
else:
ans += 2**blackrun
blackrun += 1
for i in range(w):
whiterun = 0
blackrun = 0
for x in range(h):
if grid[x][i] == '0':
ans += (2**whiterun)-1
whiterun += 1
else:
ans += (2**blackrun)-1
blackrun += 1
print(ans)
``` | output | 1 | 102,592 | 7 | 205,185 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n Γ m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that:
1. All cells in a set have the same color.
2. Every two cells in a set share row or column.
Input
The first line of input contains integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns correspondingly.
The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black.
Output
Output single integer β the number of non-empty sets from the problem description.
Examples
Input
1 1
0
Output
1
Input
2 3
1 0 1
0 1 0
Output
8
Note
In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets. | instruction | 0 | 102,593 | 7 | 205,186 |
Tags: combinatorics, math
Correct Solution:
```
import sys
input = sys.stdin.readline
def solve():
n, m = map(int, input().split())
a = [list(map(int, input().split())) for i in range(n)]
r = 0
for i in a:
c = i.count(0)
r += 2**c - 1 + 2**(m - c) - 1
for i in range(m):
c = 0
for j in range(n):
c += a[j][i] == 0
r += 2**c - 1 + 2**(n - c) - 1
print(r - n * m)
solve()
``` | output | 1 | 102,593 | 7 | 205,187 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n Γ m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that:
1. All cells in a set have the same color.
2. Every two cells in a set share row or column.
Input
The first line of input contains integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns correspondingly.
The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black.
Output
Output single integer β the number of non-empty sets from the problem description.
Examples
Input
1 1
0
Output
1
Input
2 3
1 0 1
0 1 0
Output
8
Note
In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets. | instruction | 0 | 102,594 | 7 | 205,188 |
Tags: combinatorics, math
Correct Solution:
```
(n,m)=map(int,input().split());
l=[];
for i in range(n):
ll=list(map(int,input().split()));
l.append(ll);
s=0;
for x in l:
c1=x.count(1);
c0=x.count(0);
s=s+2**c1+2**c0-2;
for i in range(m):
c0=0;
c1=0;
for j in range(n):
if(l[j][i]==0):
c0+=1;
if(l[j][i]==1):
c1+=1;
s=s+2**c0+2**c1-2;
s=s-m*n;
print(s);
``` | output | 1 | 102,594 | 7 | 205,189 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n Γ m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that:
1. All cells in a set have the same color.
2. Every two cells in a set share row or column.
Input
The first line of input contains integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns correspondingly.
The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black.
Output
Output single integer β the number of non-empty sets from the problem description.
Examples
Input
1 1
0
Output
1
Input
2 3
1 0 1
0 1 0
Output
8
Note
In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets.
Submitted Solution:
```
n, m = map(int, input().split())
g, v = [list(map(int, input().split())) for i in range(n)], -n * m
for si in map(sum, g):
v += 2 ** si - 1 + 2 ** (m - si) - 1
for sj in (sum(g[i][j] for i in range(n)) for j in range(m)):
v += 2 ** sj - 1 + 2 ** (n - sj) - 1
print(v)
``` | instruction | 0 | 102,595 | 7 | 205,190 |
Yes | output | 1 | 102,595 | 7 | 205,191 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n Γ m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that:
1. All cells in a set have the same color.
2. Every two cells in a set share row or column.
Input
The first line of input contains integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns correspondingly.
The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black.
Output
Output single integer β the number of non-empty sets from the problem description.
Examples
Input
1 1
0
Output
1
Input
2 3
1 0 1
0 1 0
Output
8
Note
In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets.
Submitted Solution:
```
import math
def choose(n, k):
return math.factorial(n) / (math.factorial(k) * math.factorial(n - k))
class CodeforcesTask844BSolution:
def __init__(self):
self.result = ''
self.n_m = []
self.board = []
def read_input(self):
self.n_m = [int(x) for x in input().split(" ")]
for x in range(self.n_m[0]):
self.board.append([int(x) for x in input().split(" ")])
def process_task(self):
white_row_sums = [sum(row) for row in self.board]
black_row_sums = [self.n_m[1] - row for row in white_row_sums]
white_col_sums = [0] * self.n_m[1]
for x in range(self.n_m[1]):
for y in range(self.n_m[0]):
white_col_sums[x] += self.board[y][x]
black_col_sums = [self.n_m[0] - row for row in white_col_sums]
subsets = white_row_sums + black_row_sums + white_col_sums + black_col_sums
sub_cnt = 0
for ss in subsets:
sub_cnt += 2 ** ss - 1
self.result = str(int(sub_cnt - self.n_m[0] * self.n_m[1]))
def get_result(self):
return self.result
if __name__ == "__main__":
Solution = CodeforcesTask844BSolution()
Solution.read_input()
Solution.process_task()
print(Solution.get_result())
``` | instruction | 0 | 102,596 | 7 | 205,192 |
Yes | output | 1 | 102,596 | 7 | 205,193 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n Γ m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that:
1. All cells in a set have the same color.
2. Every two cells in a set share row or column.
Input
The first line of input contains integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns correspondingly.
The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black.
Output
Output single integer β the number of non-empty sets from the problem description.
Examples
Input
1 1
0
Output
1
Input
2 3
1 0 1
0 1 0
Output
8
Note
In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets.
Submitted Solution:
```
a = input().split()
n,m = int(a[0]), int(a[1])
c1 = [0]*m
r =0
for i in range(n):
k = list(map(int,input().split()))
s1=0
for j in range(m):
if(k[j]==1):
s1+=1
c1[j]+=1
r += 2**s1 + 2**(m-s1) - 2
for i in c1:
r+= 2**i + 2**(n-i) - 2
r-=(n*m)
print(r)
``` | instruction | 0 | 102,597 | 7 | 205,194 |
Yes | output | 1 | 102,597 | 7 | 205,195 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n Γ m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that:
1. All cells in a set have the same color.
2. Every two cells in a set share row or column.
Input
The first line of input contains integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns correspondingly.
The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black.
Output
Output single integer β the number of non-empty sets from the problem description.
Examples
Input
1 1
0
Output
1
Input
2 3
1 0 1
0 1 0
Output
8
Note
In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets.
Submitted Solution:
```
import sys
inf = float('inf')
ip = lambda : sys.stdin.readline().rstrip()
split = lambda : ip().split(' ')
ip1 = lambda : map(int,split())
arr = lambda : list(ip1())
arr1 = lambda n : [arr() for _ in range(n)]
mod = 998244353
n,m=ip1()
a=arr1(n)
ans=n*m
for i in range(n):
ct=0
for j in range(m):
if a[i][j]:
ct+=1
ct2=m-ct
ans += 2**ct + 2**ct2 - 2 - ct-ct2
for j in range(m):
ct=0
for i in range(n):
if a[i][j]:
ct+=1
ct2=n-ct
ans += 2**ct + 2**ct2 - 2-ct-ct2
print(ans)
``` | instruction | 0 | 102,598 | 7 | 205,196 |
Yes | output | 1 | 102,598 | 7 | 205,197 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n Γ m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that:
1. All cells in a set have the same color.
2. Every two cells in a set share row or column.
Input
The first line of input contains integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns correspondingly.
The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black.
Output
Output single integer β the number of non-empty sets from the problem description.
Examples
Input
1 1
0
Output
1
Input
2 3
1 0 1
0 1 0
Output
8
Note
In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets.
Submitted Solution:
```
n,m = map(int, input().split())
grid = []
for i in range(n):
row = [int(x) for x in input().split()]
grid.append(row)
numCells = n * m
whiteRow = []
blackRow = []
whiteCol = []
blackCol = []
for row in grid:
whiteRow.append(len([x for x in row if x == 0]))
blackRow.append(len([x for x in row if x == 1]))
for i in range(m):
col = [row[i] for row in grid]
whiteCol.append(len([x for x in col if x == 0]))
blackCol.append(len([x for x in col if x == 1]))
total = 0
x1 = [x for x in whiteRow if x >= 2]
x2 = [x for x in whiteCol if x >= 2]
x3 = [x for x in blackRow if x >= 2]
x4 = [x for x in blackCol if x >= 2]
print(numCells + len(x1)+ len(x2) + len(x3) + len(x4))
``` | instruction | 0 | 102,599 | 7 | 205,198 |
No | output | 1 | 102,599 | 7 | 205,199 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n Γ m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that:
1. All cells in a set have the same color.
2. Every two cells in a set share row or column.
Input
The first line of input contains integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns correspondingly.
The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black.
Output
Output single integer β the number of non-empty sets from the problem description.
Examples
Input
1 1
0
Output
1
Input
2 3
1 0 1
0 1 0
Output
8
Note
In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets.
Submitted Solution:
```
n, m = map(int, input().split())
matrix = [list(map(int, input().split())) for _ in range(n)]
result = n * m
for i in range(n):
if matrix[i].count(0):
result += matrix[i].count(0) - 1
if matrix[i].count(1):
result += matrix[i].count(1) - 1
for i in range(m):
zero_counter, one_counter = 0, 0
for j in range(n):
if matrix[j][i] == 0:
zero_counter += 1
else:
one_counter += 1
if zero_counter:
result += zero_counter - 1
if one_counter:
result += one_counter - 1
print(result)
``` | instruction | 0 | 102,600 | 7 | 205,200 |
No | output | 1 | 102,600 | 7 | 205,201 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n Γ m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that:
1. All cells in a set have the same color.
2. Every two cells in a set share row or column.
Input
The first line of input contains integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns correspondingly.
The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black.
Output
Output single integer β the number of non-empty sets from the problem description.
Examples
Input
1 1
0
Output
1
Input
2 3
1 0 1
0 1 0
Output
8
Note
In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets.
Submitted Solution:
```
import math
def choose(n, k):
return math.factorial(n) / (math.factorial(k) * math.factorial(n - k))
class CodeforcesTask844BSolution:
def __init__(self):
self.result = ''
self.n_m = []
self.board = []
def read_input(self):
self.n_m = [int(x) for x in input().split(" ")]
for x in range(self.n_m[0]):
self.board.append([int(x) for x in input().split(" ")])
def process_task(self):
white_row_sums = [sum(row) for row in self.board]
black_row_sums = [self.n_m[1] - row for row in white_row_sums]
white_col_sums = [0] * self.n_m[1]
for x in range(self.n_m[1]):
for y in range(self.n_m[0]):
white_col_sums[x] += self.board[y][x]
black_col_sums = [self.n_m[0] - row for row in white_col_sums]
subsets = white_row_sums + black_row_sums + white_col_sums + black_col_sums
sub_cnt = 0
for ss in subsets:
for x in range(2, ss + 1):
sub_cnt += choose(ss, x)
self.result = str(int(sub_cnt + self.n_m[0] * self.n_m[1]))
def get_result(self):
return self.result
if __name__ == "__main__":
Solution = CodeforcesTask844BSolution()
Solution.read_input()
Solution.process_task()
print(Solution.get_result())
``` | instruction | 0 | 102,601 | 7 | 205,202 |
No | output | 1 | 102,601 | 7 | 205,203 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n Γ m table. Each cell of the table is colored white or black. Find the number of non-empty sets of cells such that:
1. All cells in a set have the same color.
2. Every two cells in a set share row or column.
Input
The first line of input contains integers n and m (1 β€ n, m β€ 50) β the number of rows and the number of columns correspondingly.
The next n lines of input contain descriptions of rows. There are m integers, separated by spaces, in each line. The number equals 0 if the corresponding cell is colored white and equals 1 if the corresponding cell is colored black.
Output
Output single integer β the number of non-empty sets from the problem description.
Examples
Input
1 1
0
Output
1
Input
2 3
1 0 1
0 1 0
Output
8
Note
In the second example, there are six one-element sets. Additionally, there are two two-element sets, the first one consists of the first and the third cells of the first row, the second one consists of the first and the third cells of the second row. To sum up, there are 8 sets.
Submitted Solution:
```
n,m = list(map(int,input().split()))
ans = 0
c1,c0 = 0,0
for i in range(n):
arr = list(map(int,input().split()))
c1 = arr.count(1)
c0 = m-c1
ans+=((2**c1)-1)
ans+=((2**c0)-1)
print(ans)
``` | instruction | 0 | 102,602 | 7 | 205,204 |
No | output | 1 | 102,602 | 7 | 205,205 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive.
Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that:
1. for every i: b_i and g_i are integers between 1 and k, inclusive;
2. there are no two completely identical pairs, i.e. no two indices i, j (i β j) such that b_i = b_j and g_i = g_j at the same time;
3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β g_i for every i;
4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β b_{i + 1} and g_i β g_{i + 1} hold.
Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second):
Bad color choosing:
* (1, 2), (2, 3), (3, 2), (1, 2) β contradiction with the second rule (there are equal pairs);
* (2, 3), (1, 1), (3, 2), (1, 3) β contradiction with the third rule (there is a pair with costumes of the same color);
* (1, 2), (2, 3), (1, 3), (2, 1) β contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same).
Good color choosing:
* (1, 2), (2, 1), (1, 3), (3, 1);
* (1, 2), (3, 1), (2, 3), (3, 2);
* (3, 1), (1, 2), (2, 3), (3, 2).
You have to find any suitable color choosing or say that no suitable choosing exists.
Input
The only line of the input contains two integers n and k (2 β€ n, k β€ 2 β
10^5) β the number of pairs and the number of colors.
Output
If it is impossible to find any suitable colors choosing, print "NO".
Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β colors of costumes of man and woman in the i-th pair, respectively.
You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.
Examples
Input
4 3
Output
YES
3 1
1 3
3 2
2 3
Input
10 4
Output
YES
2 1
1 3
4 2
3 4
4 3
3 2
2 4
4 1
1 4
3 1
Input
13 4
Output
NO | instruction | 0 | 102,924 | 7 | 205,848 |
Tags: constructive algorithms, implementation
Correct Solution:
```
n, k = map(int, input().split())
i = 1
if k*(k-1) < n:
print("NO")
else:
print("YES")
l = 0
j = 0
while l < n//2:
l += 1
j += 1
if i == j:
j += 1
if j > k:
i += 1
j = i+1
print(i,j)
print(j,i)
j += 1
if i == j:
j += 1
if j > k:
i += 1
j = i+1
if n % 2 == 1:
print(i, j)
``` | output | 1 | 102,924 | 7 | 205,849 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive.
Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that:
1. for every i: b_i and g_i are integers between 1 and k, inclusive;
2. there are no two completely identical pairs, i.e. no two indices i, j (i β j) such that b_i = b_j and g_i = g_j at the same time;
3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β g_i for every i;
4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β b_{i + 1} and g_i β g_{i + 1} hold.
Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second):
Bad color choosing:
* (1, 2), (2, 3), (3, 2), (1, 2) β contradiction with the second rule (there are equal pairs);
* (2, 3), (1, 1), (3, 2), (1, 3) β contradiction with the third rule (there is a pair with costumes of the same color);
* (1, 2), (2, 3), (1, 3), (2, 1) β contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same).
Good color choosing:
* (1, 2), (2, 1), (1, 3), (3, 1);
* (1, 2), (3, 1), (2, 3), (3, 2);
* (3, 1), (1, 2), (2, 3), (3, 2).
You have to find any suitable color choosing or say that no suitable choosing exists.
Input
The only line of the input contains two integers n and k (2 β€ n, k β€ 2 β
10^5) β the number of pairs and the number of colors.
Output
If it is impossible to find any suitable colors choosing, print "NO".
Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β colors of costumes of man and woman in the i-th pair, respectively.
You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.
Examples
Input
4 3
Output
YES
3 1
1 3
3 2
2 3
Input
10 4
Output
YES
2 1
1 3
4 2
3 4
4 3
3 2
2 4
4 1
1 4
3 1
Input
13 4
Output
NO | instruction | 0 | 102,925 | 7 | 205,850 |
Tags: constructive algorithms, implementation
Correct Solution:
```
from collections import *
from math import *
k,n = map(int,input().split())
K = k
ans = []
for i in range(1,n+1):
for j in range(i+1,n+1):
if(k <= 0):
break
ans.append([i,j])
ans.append([j,i])
k -= 2
if(len(ans) >= K):
print("YES")
for i in range(K):
print(*ans[i])
else:
print("NO")
``` | output | 1 | 102,925 | 7 | 205,851 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive.
Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that:
1. for every i: b_i and g_i are integers between 1 and k, inclusive;
2. there are no two completely identical pairs, i.e. no two indices i, j (i β j) such that b_i = b_j and g_i = g_j at the same time;
3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β g_i for every i;
4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β b_{i + 1} and g_i β g_{i + 1} hold.
Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second):
Bad color choosing:
* (1, 2), (2, 3), (3, 2), (1, 2) β contradiction with the second rule (there are equal pairs);
* (2, 3), (1, 1), (3, 2), (1, 3) β contradiction with the third rule (there is a pair with costumes of the same color);
* (1, 2), (2, 3), (1, 3), (2, 1) β contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same).
Good color choosing:
* (1, 2), (2, 1), (1, 3), (3, 1);
* (1, 2), (3, 1), (2, 3), (3, 2);
* (3, 1), (1, 2), (2, 3), (3, 2).
You have to find any suitable color choosing or say that no suitable choosing exists.
Input
The only line of the input contains two integers n and k (2 β€ n, k β€ 2 β
10^5) β the number of pairs and the number of colors.
Output
If it is impossible to find any suitable colors choosing, print "NO".
Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β colors of costumes of man and woman in the i-th pair, respectively.
You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.
Examples
Input
4 3
Output
YES
3 1
1 3
3 2
2 3
Input
10 4
Output
YES
2 1
1 3
4 2
3 4
4 3
3 2
2 4
4 1
1 4
3 1
Input
13 4
Output
NO | instruction | 0 | 102,926 | 7 | 205,852 |
Tags: constructive algorithms, implementation
Correct Solution:
```
m,k = map(int,input().strip().split())
maxp = k*(k-1)
mp = {}
if m>maxp:
print("NO")
else:
l = 1
h = 2
print("YES")
i = 0
while i<m:
if str(l)+" "+str(h) not in mp:
print(l,h)
i+=1
if i>=m:
break
print(h,l)
i+=1
mp[str(l)+" "+str(h)] = 1
mp[str(h)+" "+str(l)] = 1
h+=1
if h==l:
h+=1
if h>k:
h = 1
l+=1
``` | output | 1 | 102,926 | 7 | 205,853 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive.
Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that:
1. for every i: b_i and g_i are integers between 1 and k, inclusive;
2. there are no two completely identical pairs, i.e. no two indices i, j (i β j) such that b_i = b_j and g_i = g_j at the same time;
3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β g_i for every i;
4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β b_{i + 1} and g_i β g_{i + 1} hold.
Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second):
Bad color choosing:
* (1, 2), (2, 3), (3, 2), (1, 2) β contradiction with the second rule (there are equal pairs);
* (2, 3), (1, 1), (3, 2), (1, 3) β contradiction with the third rule (there is a pair with costumes of the same color);
* (1, 2), (2, 3), (1, 3), (2, 1) β contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same).
Good color choosing:
* (1, 2), (2, 1), (1, 3), (3, 1);
* (1, 2), (3, 1), (2, 3), (3, 2);
* (3, 1), (1, 2), (2, 3), (3, 2).
You have to find any suitable color choosing or say that no suitable choosing exists.
Input
The only line of the input contains two integers n and k (2 β€ n, k β€ 2 β
10^5) β the number of pairs and the number of colors.
Output
If it is impossible to find any suitable colors choosing, print "NO".
Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β colors of costumes of man and woman in the i-th pair, respectively.
You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.
Examples
Input
4 3
Output
YES
3 1
1 3
3 2
2 3
Input
10 4
Output
YES
2 1
1 3
4 2
3 4
4 3
3 2
2 4
4 1
1 4
3 1
Input
13 4
Output
NO | instruction | 0 | 102,927 | 7 | 205,854 |
Tags: constructive algorithms, implementation
Correct Solution:
```
n,k=map(int,input().split())
if(n>(k*(k-1))):
print('NO')
else:
print('YES')
arr=[0]*(k+1)
for i in range(1,k):
arr[i]=i+1
arr[-1]=1
ansarr=[]
count=0
index=1
while(count<n):
ansarr.append(index)
ansarr.append(arr[index])
arr[index]+=1
if(arr[index]>k):
arr[index]=1
index+=1
count+=1
if(index>k):
index=1
print(*ansarr)
``` | output | 1 | 102,927 | 7 | 205,855 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive.
Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that:
1. for every i: b_i and g_i are integers between 1 and k, inclusive;
2. there are no two completely identical pairs, i.e. no two indices i, j (i β j) such that b_i = b_j and g_i = g_j at the same time;
3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β g_i for every i;
4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β b_{i + 1} and g_i β g_{i + 1} hold.
Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second):
Bad color choosing:
* (1, 2), (2, 3), (3, 2), (1, 2) β contradiction with the second rule (there are equal pairs);
* (2, 3), (1, 1), (3, 2), (1, 3) β contradiction with the third rule (there is a pair with costumes of the same color);
* (1, 2), (2, 3), (1, 3), (2, 1) β contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same).
Good color choosing:
* (1, 2), (2, 1), (1, 3), (3, 1);
* (1, 2), (3, 1), (2, 3), (3, 2);
* (3, 1), (1, 2), (2, 3), (3, 2).
You have to find any suitable color choosing or say that no suitable choosing exists.
Input
The only line of the input contains two integers n and k (2 β€ n, k β€ 2 β
10^5) β the number of pairs and the number of colors.
Output
If it is impossible to find any suitable colors choosing, print "NO".
Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β colors of costumes of man and woman in the i-th pair, respectively.
You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.
Examples
Input
4 3
Output
YES
3 1
1 3
3 2
2 3
Input
10 4
Output
YES
2 1
1 3
4 2
3 4
4 3
3 2
2 4
4 1
1 4
3 1
Input
13 4
Output
NO | instruction | 0 | 102,928 | 7 | 205,856 |
Tags: constructive algorithms, implementation
Correct Solution:
```
n,k=map(int,input().rstrip().split(" "))
if((k*k-k)<n):
print("NO")
exit()
print("YES")
prev1=0;prev2=0
c=0;
for i in range(1,k+1):
for j in range(i+1,k+1):
curr1=i;curr2=j
if(prev1==curr1 or prev2==curr2):
curr1,curr2=curr2,curr1
print(curr1,curr2)
c+=1
if(c==n):
exit()
curr1,curr2=curr2,curr1
print(curr1,curr2)
c+=1
if(c==n):
exit()
``` | output | 1 | 102,928 | 7 | 205,857 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive.
Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that:
1. for every i: b_i and g_i are integers between 1 and k, inclusive;
2. there are no two completely identical pairs, i.e. no two indices i, j (i β j) such that b_i = b_j and g_i = g_j at the same time;
3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β g_i for every i;
4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β b_{i + 1} and g_i β g_{i + 1} hold.
Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second):
Bad color choosing:
* (1, 2), (2, 3), (3, 2), (1, 2) β contradiction with the second rule (there are equal pairs);
* (2, 3), (1, 1), (3, 2), (1, 3) β contradiction with the third rule (there is a pair with costumes of the same color);
* (1, 2), (2, 3), (1, 3), (2, 1) β contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same).
Good color choosing:
* (1, 2), (2, 1), (1, 3), (3, 1);
* (1, 2), (3, 1), (2, 3), (3, 2);
* (3, 1), (1, 2), (2, 3), (3, 2).
You have to find any suitable color choosing or say that no suitable choosing exists.
Input
The only line of the input contains two integers n and k (2 β€ n, k β€ 2 β
10^5) β the number of pairs and the number of colors.
Output
If it is impossible to find any suitable colors choosing, print "NO".
Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β colors of costumes of man and woman in the i-th pair, respectively.
You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.
Examples
Input
4 3
Output
YES
3 1
1 3
3 2
2 3
Input
10 4
Output
YES
2 1
1 3
4 2
3 4
4 3
3 2
2 4
4 1
1 4
3 1
Input
13 4
Output
NO | instruction | 0 | 102,929 | 7 | 205,858 |
Tags: constructive algorithms, implementation
Correct Solution:
```
def main():
n, k = map(int, input().split())
if n > k * (k - 1):
print('NO')
return
print('YES')
printed = 0
i = 0
while printed < n:
first = i % k
second = (i + i // k + 1) % k
print(first + 1, second + 1)
printed += 1
i += 1
main()
``` | output | 1 | 102,929 | 7 | 205,859 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive.
Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that:
1. for every i: b_i and g_i are integers between 1 and k, inclusive;
2. there are no two completely identical pairs, i.e. no two indices i, j (i β j) such that b_i = b_j and g_i = g_j at the same time;
3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β g_i for every i;
4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β b_{i + 1} and g_i β g_{i + 1} hold.
Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second):
Bad color choosing:
* (1, 2), (2, 3), (3, 2), (1, 2) β contradiction with the second rule (there are equal pairs);
* (2, 3), (1, 1), (3, 2), (1, 3) β contradiction with the third rule (there is a pair with costumes of the same color);
* (1, 2), (2, 3), (1, 3), (2, 1) β contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same).
Good color choosing:
* (1, 2), (2, 1), (1, 3), (3, 1);
* (1, 2), (3, 1), (2, 3), (3, 2);
* (3, 1), (1, 2), (2, 3), (3, 2).
You have to find any suitable color choosing or say that no suitable choosing exists.
Input
The only line of the input contains two integers n and k (2 β€ n, k β€ 2 β
10^5) β the number of pairs and the number of colors.
Output
If it is impossible to find any suitable colors choosing, print "NO".
Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β colors of costumes of man and woman in the i-th pair, respectively.
You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.
Examples
Input
4 3
Output
YES
3 1
1 3
3 2
2 3
Input
10 4
Output
YES
2 1
1 3
4 2
3 4
4 3
3 2
2 4
4 1
1 4
3 1
Input
13 4
Output
NO | instruction | 0 | 102,930 | 7 | 205,860 |
Tags: constructive algorithms, implementation
Correct Solution:
```
# Legends Always Come Up with Solution
# Author: Manvir Singh
import os
import sys
from io import BytesIO, IOBase
def main():
n,k=map(int,input().split())
if (k-1)*k<n:
print("NO")
else:
print("YES")
z=0
for i in range(2,k+1):
for j in range(1,i):
print(j,i)
z+=1
if z==n:
return
print(i,j)
z+=1
if z==n:
return
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
if __name__ == "__main__":
main()
``` | output | 1 | 102,930 | 7 | 205,861 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive.
Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that:
1. for every i: b_i and g_i are integers between 1 and k, inclusive;
2. there are no two completely identical pairs, i.e. no two indices i, j (i β j) such that b_i = b_j and g_i = g_j at the same time;
3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β g_i for every i;
4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β b_{i + 1} and g_i β g_{i + 1} hold.
Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second):
Bad color choosing:
* (1, 2), (2, 3), (3, 2), (1, 2) β contradiction with the second rule (there are equal pairs);
* (2, 3), (1, 1), (3, 2), (1, 3) β contradiction with the third rule (there is a pair with costumes of the same color);
* (1, 2), (2, 3), (1, 3), (2, 1) β contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same).
Good color choosing:
* (1, 2), (2, 1), (1, 3), (3, 1);
* (1, 2), (3, 1), (2, 3), (3, 2);
* (3, 1), (1, 2), (2, 3), (3, 2).
You have to find any suitable color choosing or say that no suitable choosing exists.
Input
The only line of the input contains two integers n and k (2 β€ n, k β€ 2 β
10^5) β the number of pairs and the number of colors.
Output
If it is impossible to find any suitable colors choosing, print "NO".
Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β colors of costumes of man and woman in the i-th pair, respectively.
You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.
Examples
Input
4 3
Output
YES
3 1
1 3
3 2
2 3
Input
10 4
Output
YES
2 1
1 3
4 2
3 4
4 3
3 2
2 4
4 1
1 4
3 1
Input
13 4
Output
NO | instruction | 0 | 102,931 | 7 | 205,862 |
Tags: constructive algorithms, implementation
Correct Solution:
```
'''
Auther: ghoshashis545 Ashis Ghosh
College: jalpaiguri Govt Enggineering College
'''
from os import path
import sys
from functools import cmp_to_key as ctk
from collections import deque,defaultdict as dd
from bisect import bisect,bisect_left,bisect_right,insort,insort_left,insort_right
from itertools import permutations
from datetime import datetime
from math import ceil,sqrt,log,gcd
def ii():return int(input())
def si():return input()
def mi():return map(int,input().split())
def li():return list(mi())
abc='abcdefghijklmnopqrstuvwxyz'
abd={'a': 0, 'b': 1, 'c': 2, 'd': 3, 'e': 4, 'f': 5, 'g': 6, 'h': 7, 'i': 8, 'j': 9, 'k': 10, 'l': 11, 'm': 12, 'n': 13, 'o': 14, 'p': 15, 'q': 16, 'r': 17, 's': 18, 't': 19, 'u': 20, 'v': 21, 'w': 22, 'x': 23, 'y': 24, 'z': 25}
mod=1000000007
#mod=998244353
inf = float("inf")
vow=['a','e','i','o','u']
dx,dy=[-1,1,0,0],[0,0,1,-1]
def bo(i):
return ord(i)-ord('a')
def solve():
n,k=mi()
a=[]
for i in range(1,k+1):
for j in range(i+1,k+1):
a.append([i,j])
a.append([j,i])
if(len(a)>=n):
print('YES')
for i in range(n):
print(*a[i])
exit(0)
print("NO")
if __name__ =="__main__":
solve()
``` | output | 1 | 102,931 | 7 | 205,863 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive.
Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that:
1. for every i: b_i and g_i are integers between 1 and k, inclusive;
2. there are no two completely identical pairs, i.e. no two indices i, j (i β j) such that b_i = b_j and g_i = g_j at the same time;
3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β g_i for every i;
4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β b_{i + 1} and g_i β g_{i + 1} hold.
Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second):
Bad color choosing:
* (1, 2), (2, 3), (3, 2), (1, 2) β contradiction with the second rule (there are equal pairs);
* (2, 3), (1, 1), (3, 2), (1, 3) β contradiction with the third rule (there is a pair with costumes of the same color);
* (1, 2), (2, 3), (1, 3), (2, 1) β contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same).
Good color choosing:
* (1, 2), (2, 1), (1, 3), (3, 1);
* (1, 2), (3, 1), (2, 3), (3, 2);
* (3, 1), (1, 2), (2, 3), (3, 2).
You have to find any suitable color choosing or say that no suitable choosing exists.
Input
The only line of the input contains two integers n and k (2 β€ n, k β€ 2 β
10^5) β the number of pairs and the number of colors.
Output
If it is impossible to find any suitable colors choosing, print "NO".
Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β colors of costumes of man and woman in the i-th pair, respectively.
You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.
Examples
Input
4 3
Output
YES
3 1
1 3
3 2
2 3
Input
10 4
Output
YES
2 1
1 3
4 2
3 4
4 3
3 2
2 4
4 1
1 4
3 1
Input
13 4
Output
NO
Submitted Solution:
```
n,k=map(int,input().split())
if(n>(k*(k-1))):
print('NO')
else:
ans=[0 for i in range(n)]
for i in range(len(ans)):
ans[i]=(i+1)%k
if(ans[i]==0):
ans[i]=k
count=1
temp=[0 for i in range(len(ans))]
for i in range(len(ans)):
if(i%k==0):
temp[i]=count+1
count+=1
else:
temp[i]=temp[i-1]+1
if(temp[i]>k):
temp[i]%=k
print('YES')
for i in range(n):
print(ans[i],temp[i])
``` | instruction | 0 | 102,932 | 7 | 205,864 |
Yes | output | 1 | 102,932 | 7 | 205,865 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive.
Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that:
1. for every i: b_i and g_i are integers between 1 and k, inclusive;
2. there are no two completely identical pairs, i.e. no two indices i, j (i β j) such that b_i = b_j and g_i = g_j at the same time;
3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β g_i for every i;
4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β b_{i + 1} and g_i β g_{i + 1} hold.
Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second):
Bad color choosing:
* (1, 2), (2, 3), (3, 2), (1, 2) β contradiction with the second rule (there are equal pairs);
* (2, 3), (1, 1), (3, 2), (1, 3) β contradiction with the third rule (there is a pair with costumes of the same color);
* (1, 2), (2, 3), (1, 3), (2, 1) β contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same).
Good color choosing:
* (1, 2), (2, 1), (1, 3), (3, 1);
* (1, 2), (3, 1), (2, 3), (3, 2);
* (3, 1), (1, 2), (2, 3), (3, 2).
You have to find any suitable color choosing or say that no suitable choosing exists.
Input
The only line of the input contains two integers n and k (2 β€ n, k β€ 2 β
10^5) β the number of pairs and the number of colors.
Output
If it is impossible to find any suitable colors choosing, print "NO".
Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β colors of costumes of man and woman in the i-th pair, respectively.
You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.
Examples
Input
4 3
Output
YES
3 1
1 3
3 2
2 3
Input
10 4
Output
YES
2 1
1 3
4 2
3 4
4 3
3 2
2 4
4 1
1 4
3 1
Input
13 4
Output
NO
Submitted Solution:
```
import math
n,k=map(int,input().split())
if n>k*(k-1):
print("NO")
else:
print("YES")
count,ok=0,False
for i in range(math.ceil(n/k)):
for j in range(k):
count+=1
if (j+i+2)%k==0:
print(j+1,k)
else:
print(j+1,(j+1+i+1)%k)
if count==n:
ok=True
break
if ok==True:
break
``` | instruction | 0 | 102,933 | 7 | 205,866 |
Yes | output | 1 | 102,933 | 7 | 205,867 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive.
Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that:
1. for every i: b_i and g_i are integers between 1 and k, inclusive;
2. there are no two completely identical pairs, i.e. no two indices i, j (i β j) such that b_i = b_j and g_i = g_j at the same time;
3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β g_i for every i;
4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β b_{i + 1} and g_i β g_{i + 1} hold.
Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second):
Bad color choosing:
* (1, 2), (2, 3), (3, 2), (1, 2) β contradiction with the second rule (there are equal pairs);
* (2, 3), (1, 1), (3, 2), (1, 3) β contradiction with the third rule (there is a pair with costumes of the same color);
* (1, 2), (2, 3), (1, 3), (2, 1) β contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same).
Good color choosing:
* (1, 2), (2, 1), (1, 3), (3, 1);
* (1, 2), (3, 1), (2, 3), (3, 2);
* (3, 1), (1, 2), (2, 3), (3, 2).
You have to find any suitable color choosing or say that no suitable choosing exists.
Input
The only line of the input contains two integers n and k (2 β€ n, k β€ 2 β
10^5) β the number of pairs and the number of colors.
Output
If it is impossible to find any suitable colors choosing, print "NO".
Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β colors of costumes of man and woman in the i-th pair, respectively.
You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.
Examples
Input
4 3
Output
YES
3 1
1 3
3 2
2 3
Input
10 4
Output
YES
2 1
1 3
4 2
3 4
4 3
3 2
2 4
4 1
1 4
3 1
Input
13 4
Output
NO
Submitted Solution:
```
from sys import stdin
n,k=map(int,stdin.readline().strip().split())
mx=(k*(k-1))
if mx<n:
print("NO")
exit(0)
x=0
print("YES")
for i in range(1,k):
for j in range(i+1,k+1):
print(i,j)
x+=1
if x==n:
exit(0)
print(j,i)
x+=1
if x==n:
exit(0)
``` | instruction | 0 | 102,934 | 7 | 205,868 |
Yes | output | 1 | 102,934 | 7 | 205,869 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive.
Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that:
1. for every i: b_i and g_i are integers between 1 and k, inclusive;
2. there are no two completely identical pairs, i.e. no two indices i, j (i β j) such that b_i = b_j and g_i = g_j at the same time;
3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β g_i for every i;
4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β b_{i + 1} and g_i β g_{i + 1} hold.
Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second):
Bad color choosing:
* (1, 2), (2, 3), (3, 2), (1, 2) β contradiction with the second rule (there are equal pairs);
* (2, 3), (1, 1), (3, 2), (1, 3) β contradiction with the third rule (there is a pair with costumes of the same color);
* (1, 2), (2, 3), (1, 3), (2, 1) β contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same).
Good color choosing:
* (1, 2), (2, 1), (1, 3), (3, 1);
* (1, 2), (3, 1), (2, 3), (3, 2);
* (3, 1), (1, 2), (2, 3), (3, 2).
You have to find any suitable color choosing or say that no suitable choosing exists.
Input
The only line of the input contains two integers n and k (2 β€ n, k β€ 2 β
10^5) β the number of pairs and the number of colors.
Output
If it is impossible to find any suitable colors choosing, print "NO".
Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β colors of costumes of man and woman in the i-th pair, respectively.
You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.
Examples
Input
4 3
Output
YES
3 1
1 3
3 2
2 3
Input
10 4
Output
YES
2 1
1 3
4 2
3 4
4 3
3 2
2 4
4 1
1 4
3 1
Input
13 4
Output
NO
Submitted Solution:
```
n, k = map(int, input().split())
if n > k*(k-1):
print("NO")
else:
print("YES")
cnt = 0
for delta in range(k):
for c in range(1, k+1):
if cnt < n:
cnt +=1
print(c, 1+(c+delta)%k)
else:
break
``` | instruction | 0 | 102,935 | 7 | 205,870 |
Yes | output | 1 | 102,935 | 7 | 205,871 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive.
Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that:
1. for every i: b_i and g_i are integers between 1 and k, inclusive;
2. there are no two completely identical pairs, i.e. no two indices i, j (i β j) such that b_i = b_j and g_i = g_j at the same time;
3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i β g_i for every i;
4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i β b_{i + 1} and g_i β g_{i + 1} hold.
Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second):
Bad color choosing:
* (1, 2), (2, 3), (3, 2), (1, 2) β contradiction with the second rule (there are equal pairs);
* (2, 3), (1, 1), (3, 2), (1, 3) β contradiction with the third rule (there is a pair with costumes of the same color);
* (1, 2), (2, 3), (1, 3), (2, 1) β contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same).
Good color choosing:
* (1, 2), (2, 1), (1, 3), (3, 1);
* (1, 2), (3, 1), (2, 3), (3, 2);
* (3, 1), (1, 2), (2, 3), (3, 2).
You have to find any suitable color choosing or say that no suitable choosing exists.
Input
The only line of the input contains two integers n and k (2 β€ n, k β€ 2 β
10^5) β the number of pairs and the number of colors.
Output
If it is impossible to find any suitable colors choosing, print "NO".
Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i β colors of costumes of man and woman in the i-th pair, respectively.
You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.
Examples
Input
4 3
Output
YES
3 1
1 3
3 2
2 3
Input
10 4
Output
YES
2 1
1 3
4 2
3 4
4 3
3 2
2 4
4 1
1 4
3 1
Input
13 4
Output
NO
Submitted Solution:
```
n, k = map(int, input().split())
flg = [[True for _ in range(k + 1)] for _ in range(k + 1)]
ans = [[1, 2]]
flg[1][2] = False
for pair in range(1, n):
ok = False
for b in range(1, k + 1):
for g in range(1, k + 1):
if flg[b][g] and b != g and b != ans[pair - 1][0] and g != ans[pair - 1][1]:
ans.append([b, g])
flg[b][g] = False
ok = True
break
if ok:
break
if not ok:
print("NO")
exit(0)
print("YES")
for a in ans:
print(a[0], a[1])
``` | instruction | 0 | 102,936 | 7 | 205,872 |
No | output | 1 | 102,936 | 7 | 205,873 |
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