message stringlengths 2 44.5k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 276 109k | cluster float64 23 23 | __index_level_0__ int64 552 217k |
|---|---|---|---|---|---|
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Petya loves playing with squares. Mum bought him a square 2n Γ 2n in size. Petya marked a cell inside the square and now he is solving the following task.
The task is to draw a broken line that would go along the grid lines and that would cut the square into two equal parts. The cutting line should not have any common points with the marked cell and the resulting two parts should be equal up to rotation.
Petya wants to determine whether it is possible to cut the square in the required manner given the sizes of the square side and the coordinates of the marked cell. Help him.
Input
The first line contains three space-separated integers 2n, x and y (2 β€ 2n β€ 100, 1 β€ x, y β€ 2n), representing the length of a square's side and the coordinates of the marked cell. It is guaranteed that 2n is even.
The coordinates of the marked cell are represented by a pair of numbers x y, where x represents the number of the row and y represents the number of the column. The rows and columns are numbered by consecutive integers from 1 to 2n. The rows are numbered from top to bottom and the columns are numbered from the left to the right.
Output
If the square is possible to cut, print "YES", otherwise print "NO" (without the quotes).
Examples
Input
4 1 1
Output
YES
Input
2 2 2
Output
NO
Note
A sample test from the statement and one of the possible ways of cutting the square are shown in the picture:
<image> | instruction | 0 | 37,799 | 23 | 75,598 |
Tags: implementation, math
Correct Solution:
```
"""
Square must be far enough from the center to allow for a line that wouldn't touch it
4 rows in the middle are touched:
2 in the center are fully touched
2 on the edges are touched only except for the first and last cells
"""
def solution(double_n, x, y):
n = double_n // 2
if x in (n, n + 1) and y in (n, n + 1):
return "NO"
return "YES"
if __name__ == "__main__":
double_n, x, y = map(int, input().rstrip().split(" "))
print(solution(double_n, x, y))
``` | output | 1 | 37,799 | 23 | 75,599 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Petya loves playing with squares. Mum bought him a square 2n Γ 2n in size. Petya marked a cell inside the square and now he is solving the following task.
The task is to draw a broken line that would go along the grid lines and that would cut the square into two equal parts. The cutting line should not have any common points with the marked cell and the resulting two parts should be equal up to rotation.
Petya wants to determine whether it is possible to cut the square in the required manner given the sizes of the square side and the coordinates of the marked cell. Help him.
Input
The first line contains three space-separated integers 2n, x and y (2 β€ 2n β€ 100, 1 β€ x, y β€ 2n), representing the length of a square's side and the coordinates of the marked cell. It is guaranteed that 2n is even.
The coordinates of the marked cell are represented by a pair of numbers x y, where x represents the number of the row and y represents the number of the column. The rows and columns are numbered by consecutive integers from 1 to 2n. The rows are numbered from top to bottom and the columns are numbered from the left to the right.
Output
If the square is possible to cut, print "YES", otherwise print "NO" (without the quotes).
Examples
Input
4 1 1
Output
YES
Input
2 2 2
Output
NO
Note
A sample test from the statement and one of the possible ways of cutting the square are shown in the picture:
<image> | instruction | 0 | 37,800 | 23 | 75,600 |
Tags: implementation, math
Correct Solution:
```
n, x, y = [int(i) for i in input().split()]
n = n//2
if (x==n or x==n+1) and (y==n or y==n+1):
print('NO')
else:
print('YES')
``` | output | 1 | 37,800 | 23 | 75,601 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Petya loves playing with squares. Mum bought him a square 2n Γ 2n in size. Petya marked a cell inside the square and now he is solving the following task.
The task is to draw a broken line that would go along the grid lines and that would cut the square into two equal parts. The cutting line should not have any common points with the marked cell and the resulting two parts should be equal up to rotation.
Petya wants to determine whether it is possible to cut the square in the required manner given the sizes of the square side and the coordinates of the marked cell. Help him.
Input
The first line contains three space-separated integers 2n, x and y (2 β€ 2n β€ 100, 1 β€ x, y β€ 2n), representing the length of a square's side and the coordinates of the marked cell. It is guaranteed that 2n is even.
The coordinates of the marked cell are represented by a pair of numbers x y, where x represents the number of the row and y represents the number of the column. The rows and columns are numbered by consecutive integers from 1 to 2n. The rows are numbered from top to bottom and the columns are numbered from the left to the right.
Output
If the square is possible to cut, print "YES", otherwise print "NO" (without the quotes).
Examples
Input
4 1 1
Output
YES
Input
2 2 2
Output
NO
Note
A sample test from the statement and one of the possible ways of cutting the square are shown in the picture:
<image> | instruction | 0 | 37,801 | 23 | 75,602 |
Tags: implementation, math
Correct Solution:
```
k=input().split(" ")
n=int(k[0])
x=int(k[1])
y=int(k[2])
n/=2
if (x==n or x==n+1)and(y==n or y==n+1):
print("NO")
else:
print("YES")
``` | output | 1 | 37,801 | 23 | 75,603 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya loves playing with squares. Mum bought him a square 2n Γ 2n in size. Petya marked a cell inside the square and now he is solving the following task.
The task is to draw a broken line that would go along the grid lines and that would cut the square into two equal parts. The cutting line should not have any common points with the marked cell and the resulting two parts should be equal up to rotation.
Petya wants to determine whether it is possible to cut the square in the required manner given the sizes of the square side and the coordinates of the marked cell. Help him.
Input
The first line contains three space-separated integers 2n, x and y (2 β€ 2n β€ 100, 1 β€ x, y β€ 2n), representing the length of a square's side and the coordinates of the marked cell. It is guaranteed that 2n is even.
The coordinates of the marked cell are represented by a pair of numbers x y, where x represents the number of the row and y represents the number of the column. The rows and columns are numbered by consecutive integers from 1 to 2n. The rows are numbered from top to bottom and the columns are numbered from the left to the right.
Output
If the square is possible to cut, print "YES", otherwise print "NO" (without the quotes).
Examples
Input
4 1 1
Output
YES
Input
2 2 2
Output
NO
Note
A sample test from the statement and one of the possible ways of cutting the square are shown in the picture:
<image>
Submitted Solution:
```
n=list(map(int,input().split()))
d=n[0]
e=n[1]
f=n[2]
if (e==d//2 or e==d//2+1) and(f==d//2 or f==d//2+1):
print("NO")
else:
print("YES")
``` | instruction | 0 | 37,802 | 23 | 75,604 |
Yes | output | 1 | 37,802 | 23 | 75,605 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya loves playing with squares. Mum bought him a square 2n Γ 2n in size. Petya marked a cell inside the square and now he is solving the following task.
The task is to draw a broken line that would go along the grid lines and that would cut the square into two equal parts. The cutting line should not have any common points with the marked cell and the resulting two parts should be equal up to rotation.
Petya wants to determine whether it is possible to cut the square in the required manner given the sizes of the square side and the coordinates of the marked cell. Help him.
Input
The first line contains three space-separated integers 2n, x and y (2 β€ 2n β€ 100, 1 β€ x, y β€ 2n), representing the length of a square's side and the coordinates of the marked cell. It is guaranteed that 2n is even.
The coordinates of the marked cell are represented by a pair of numbers x y, where x represents the number of the row and y represents the number of the column. The rows and columns are numbered by consecutive integers from 1 to 2n. The rows are numbered from top to bottom and the columns are numbered from the left to the right.
Output
If the square is possible to cut, print "YES", otherwise print "NO" (without the quotes).
Examples
Input
4 1 1
Output
YES
Input
2 2 2
Output
NO
Note
A sample test from the statement and one of the possible ways of cutting the square are shown in the picture:
<image>
Submitted Solution:
```
l=input().split(" ")
n=int(l[0])
x=int(l[1])
y=int(l[2])
h=n/2
if( (x==h)&(y==h) ) :
print("NO")
elif(( x==h)&(y==h+1 )):
print("NO")
elif( (x==h+1)&(y==h) ):
print("NO")
elif((x==h+1)&(y==h+1) ):
print("NO")
else: print("YES")
``` | instruction | 0 | 37,803 | 23 | 75,606 |
Yes | output | 1 | 37,803 | 23 | 75,607 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya loves playing with squares. Mum bought him a square 2n Γ 2n in size. Petya marked a cell inside the square and now he is solving the following task.
The task is to draw a broken line that would go along the grid lines and that would cut the square into two equal parts. The cutting line should not have any common points with the marked cell and the resulting two parts should be equal up to rotation.
Petya wants to determine whether it is possible to cut the square in the required manner given the sizes of the square side and the coordinates of the marked cell. Help him.
Input
The first line contains three space-separated integers 2n, x and y (2 β€ 2n β€ 100, 1 β€ x, y β€ 2n), representing the length of a square's side and the coordinates of the marked cell. It is guaranteed that 2n is even.
The coordinates of the marked cell are represented by a pair of numbers x y, where x represents the number of the row and y represents the number of the column. The rows and columns are numbered by consecutive integers from 1 to 2n. The rows are numbered from top to bottom and the columns are numbered from the left to the right.
Output
If the square is possible to cut, print "YES", otherwise print "NO" (without the quotes).
Examples
Input
4 1 1
Output
YES
Input
2 2 2
Output
NO
Note
A sample test from the statement and one of the possible ways of cutting the square are shown in the picture:
<image>
Submitted Solution:
```
n,x,y=map(int,input().split())
n//=2
print("NO" if (x==n or x==n+1) and (y==n or y==n+1) else "YES")
``` | instruction | 0 | 37,804 | 23 | 75,608 |
Yes | output | 1 | 37,804 | 23 | 75,609 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya loves playing with squares. Mum bought him a square 2n Γ 2n in size. Petya marked a cell inside the square and now he is solving the following task.
The task is to draw a broken line that would go along the grid lines and that would cut the square into two equal parts. The cutting line should not have any common points with the marked cell and the resulting two parts should be equal up to rotation.
Petya wants to determine whether it is possible to cut the square in the required manner given the sizes of the square side and the coordinates of the marked cell. Help him.
Input
The first line contains three space-separated integers 2n, x and y (2 β€ 2n β€ 100, 1 β€ x, y β€ 2n), representing the length of a square's side and the coordinates of the marked cell. It is guaranteed that 2n is even.
The coordinates of the marked cell are represented by a pair of numbers x y, where x represents the number of the row and y represents the number of the column. The rows and columns are numbered by consecutive integers from 1 to 2n. The rows are numbered from top to bottom and the columns are numbered from the left to the right.
Output
If the square is possible to cut, print "YES", otherwise print "NO" (without the quotes).
Examples
Input
4 1 1
Output
YES
Input
2 2 2
Output
NO
Note
A sample test from the statement and one of the possible ways of cutting the square are shown in the picture:
<image>
Submitted Solution:
```
n, x, y = map(int, input().split())
m = n // 2
if m + 1 >= x >= m and m + 1 >= y >= m:
print("NO")
else:
print("YES")
``` | instruction | 0 | 37,805 | 23 | 75,610 |
Yes | output | 1 | 37,805 | 23 | 75,611 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya loves playing with squares. Mum bought him a square 2n Γ 2n in size. Petya marked a cell inside the square and now he is solving the following task.
The task is to draw a broken line that would go along the grid lines and that would cut the square into two equal parts. The cutting line should not have any common points with the marked cell and the resulting two parts should be equal up to rotation.
Petya wants to determine whether it is possible to cut the square in the required manner given the sizes of the square side and the coordinates of the marked cell. Help him.
Input
The first line contains three space-separated integers 2n, x and y (2 β€ 2n β€ 100, 1 β€ x, y β€ 2n), representing the length of a square's side and the coordinates of the marked cell. It is guaranteed that 2n is even.
The coordinates of the marked cell are represented by a pair of numbers x y, where x represents the number of the row and y represents the number of the column. The rows and columns are numbered by consecutive integers from 1 to 2n. The rows are numbered from top to bottom and the columns are numbered from the left to the right.
Output
If the square is possible to cut, print "YES", otherwise print "NO" (without the quotes).
Examples
Input
4 1 1
Output
YES
Input
2 2 2
Output
NO
Note
A sample test from the statement and one of the possible ways of cutting the square are shown in the picture:
<image>
Submitted Solution:
```
a,b,c=map(int,input().split())
if a!=2*b and a!=2*c:
print("YES")
else:
print("NO")
``` | instruction | 0 | 37,806 | 23 | 75,612 |
No | output | 1 | 37,806 | 23 | 75,613 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya loves playing with squares. Mum bought him a square 2n Γ 2n in size. Petya marked a cell inside the square and now he is solving the following task.
The task is to draw a broken line that would go along the grid lines and that would cut the square into two equal parts. The cutting line should not have any common points with the marked cell and the resulting two parts should be equal up to rotation.
Petya wants to determine whether it is possible to cut the square in the required manner given the sizes of the square side and the coordinates of the marked cell. Help him.
Input
The first line contains three space-separated integers 2n, x and y (2 β€ 2n β€ 100, 1 β€ x, y β€ 2n), representing the length of a square's side and the coordinates of the marked cell. It is guaranteed that 2n is even.
The coordinates of the marked cell are represented by a pair of numbers x y, where x represents the number of the row and y represents the number of the column. The rows and columns are numbered by consecutive integers from 1 to 2n. The rows are numbered from top to bottom and the columns are numbered from the left to the right.
Output
If the square is possible to cut, print "YES", otherwise print "NO" (without the quotes).
Examples
Input
4 1 1
Output
YES
Input
2 2 2
Output
NO
Note
A sample test from the statement and one of the possible ways of cutting the square are shown in the picture:
<image>
Submitted Solution:
```
n,x,y=map(int,input().split())
p=int(n/2)+2
if n==2:
print('NO')
elif n%2==0 and y in range(int(n/2),p) and x not in range(int(n/2),p):
print('YES')
elif n%2==0 and x in range(int(n/2),p) and y not in range(int(n/2),p):
print('YES')
else:
print('NO')
``` | instruction | 0 | 37,807 | 23 | 75,614 |
No | output | 1 | 37,807 | 23 | 75,615 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya loves playing with squares. Mum bought him a square 2n Γ 2n in size. Petya marked a cell inside the square and now he is solving the following task.
The task is to draw a broken line that would go along the grid lines and that would cut the square into two equal parts. The cutting line should not have any common points with the marked cell and the resulting two parts should be equal up to rotation.
Petya wants to determine whether it is possible to cut the square in the required manner given the sizes of the square side and the coordinates of the marked cell. Help him.
Input
The first line contains three space-separated integers 2n, x and y (2 β€ 2n β€ 100, 1 β€ x, y β€ 2n), representing the length of a square's side and the coordinates of the marked cell. It is guaranteed that 2n is even.
The coordinates of the marked cell are represented by a pair of numbers x y, where x represents the number of the row and y represents the number of the column. The rows and columns are numbered by consecutive integers from 1 to 2n. The rows are numbered from top to bottom and the columns are numbered from the left to the right.
Output
If the square is possible to cut, print "YES", otherwise print "NO" (without the quotes).
Examples
Input
4 1 1
Output
YES
Input
2 2 2
Output
NO
Note
A sample test from the statement and one of the possible ways of cutting the square are shown in the picture:
<image>
Submitted Solution:
```
n,x,y=map(int,input().split())
if x==1:
if y==1:
if n>x:
if (n**2)//2>=4:
print("YES")
else:
print("NO")
else:
print("NO")
elif y==n:
if n>1:
if (n**2)//2>=4:
print("YES")
else:
print("NO")
else:
print("NO")
else:
if (n**2)//2>=6:
print("YES")
else:
print("NO")
elif x==n:
if y==1 or y==n:
if n>1:
if (n**2)//2>=4:
print("YES")
else:
print("NO")
else:
print("NO")
else:
if (n**2)//2>=6:
print("YES")
else:
print("NO")
else:
if y==1 or y==n:
if (n**2)//2>=6:
print("YES")
else:
print("NO")
else:
if (n**2)//2>=9:
print("YES")
else:
print("NO")
``` | instruction | 0 | 37,808 | 23 | 75,616 |
No | output | 1 | 37,808 | 23 | 75,617 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya loves playing with squares. Mum bought him a square 2n Γ 2n in size. Petya marked a cell inside the square and now he is solving the following task.
The task is to draw a broken line that would go along the grid lines and that would cut the square into two equal parts. The cutting line should not have any common points with the marked cell and the resulting two parts should be equal up to rotation.
Petya wants to determine whether it is possible to cut the square in the required manner given the sizes of the square side and the coordinates of the marked cell. Help him.
Input
The first line contains three space-separated integers 2n, x and y (2 β€ 2n β€ 100, 1 β€ x, y β€ 2n), representing the length of a square's side and the coordinates of the marked cell. It is guaranteed that 2n is even.
The coordinates of the marked cell are represented by a pair of numbers x y, where x represents the number of the row and y represents the number of the column. The rows and columns are numbered by consecutive integers from 1 to 2n. The rows are numbered from top to bottom and the columns are numbered from the left to the right.
Output
If the square is possible to cut, print "YES", otherwise print "NO" (without the quotes).
Examples
Input
4 1 1
Output
YES
Input
2 2 2
Output
NO
Note
A sample test from the statement and one of the possible ways of cutting the square are shown in the picture:
<image>
Submitted Solution:
```
n_2, x, y = map(int, input(). split(' '))
if n_2 - x > 2:
print("YES")
else:
print("NO")
``` | instruction | 0 | 37,809 | 23 | 75,618 |
No | output | 1 | 37,809 | 23 | 75,619 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers n and k.
You need to construct k regular polygons having same [circumcircle](https://en.wikipedia.org/wiki/Circumscribed_circle), with distinct number of sides l between 3 and n.
<image> Illustration for the first example.
You can rotate them to minimize the total number of distinct points on the circle. Find the minimum number of such points.
Input
The only line of input contains two integers n and k (3 β€ n β€ 10^{6}, 1 β€ k β€ n-2), the maximum number of sides of a polygon and the number of polygons to construct, respectively.
Output
Print a single integer β the minimum number of points required for k polygons.
Examples
Input
6 2
Output
6
Input
200 50
Output
708
Note
In the first example, we have n = 6 and k = 2. So, we have 4 polygons with number of sides 3, 4, 5 and 6 to choose from and if we choose the triangle and the hexagon, then we can arrange them as shown in the picture in the statement.
Hence, the minimum number of points required on the circle is 6, which is also the minimum overall possible sets.
Submitted Solution:
```
def findTriangles(n):
num = n
# prthe number of triangles
# having two side common
print(num, end = " ")
# prthe number of triangles
# having no side common
print(num * (num - 4) * (num - 5) // 6)
# Driver code
# initialize the number
# of sides of a polygon
n = 6;
findTriangles(n)
``` | instruction | 0 | 37,821 | 23 | 75,642 |
No | output | 1 | 37,821 | 23 | 75,643 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three multisets of pairs of colored sticks:
* R pairs of red sticks, the first pair has length r_1, the second pair has length r_2, ..., the R-th pair has length r_R;
* G pairs of green sticks, the first pair has length g_1, the second pair has length g_2, ..., the G-th pair has length g_G;
* B pairs of blue sticks, the first pair has length b_1, the second pair has length b_2, ..., the B-th pair has length b_B;
You are constructing rectangles from these pairs of sticks with the following process:
1. take a pair of sticks of one color;
2. take a pair of sticks of another color different from the first one;
3. add the area of the resulting rectangle to the total area.
Thus, you get such rectangles that their opposite sides are the same color and their adjacent sides are not the same color.
Each pair of sticks can be used at most once, some pairs can be left unused. You are not allowed to split a pair into independent sticks.
What is the maximum area you can achieve?
Input
The first line contains three integers R, G, B (1 β€ R, G, B β€ 200) β the number of pairs of red sticks, the number of pairs of green sticks and the number of pairs of blue sticks.
The second line contains R integers r_1, r_2, ..., r_R (1 β€ r_i β€ 2000) β the lengths of sticks in each pair of red sticks.
The third line contains G integers g_1, g_2, ..., g_G (1 β€ g_i β€ 2000) β the lengths of sticks in each pair of green sticks.
The fourth line contains B integers b_1, b_2, ..., b_B (1 β€ b_i β€ 2000) β the lengths of sticks in each pair of blue sticks.
Output
Print the maximum possible total area of the constructed rectangles.
Examples
Input
1 1 1
3
5
4
Output
20
Input
2 1 3
9 5
1
2 8 5
Output
99
Input
10 1 1
11 7 20 15 19 14 2 4 13 14
8
11
Output
372
Note
In the first example you can construct one of these rectangles: red and green with sides 3 and 5, red and blue with sides 3 and 4 and green and blue with sides 5 and 4. The best area of them is 4 Γ 5 = 20.
In the second example the best rectangles are: red/blue 9 Γ 8, red/blue 5 Γ 5, green/blue 2 Γ 1. So the total area is 72 + 25 + 2 = 99.
In the third example the best rectangles are: red/green 19 Γ 8 and red/blue 20 Γ 11. The total area is 152 + 220 = 372. Note that you can't construct more rectangles because you are not allowed to have both pairs taken to be the same color.
Submitted Solution:
```
import sys, math
import io, os
#data = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
from bisect import bisect_left as bl, bisect_right as br, insort
from heapq import heapify, heappush, heappop
from collections import defaultdict as dd, deque, Counter
#from itertools import permutations,combinations
def data(): return sys.stdin.readline().strip()
def mdata(): return list(map(int, data().split()))
def outl(var) : sys.stdout.write('\n'.join(map(str, var))+'\n')
def out(var) : sys.stdout.write(str(var)+'\n')
from decimal import Decimal
from fractions import Fraction
#sys.setrecursionlimit(100000)
INF = float('inf')
mod = int(1e9)+7
from types import GeneratorType
def bootstrap(f, stack=[]):
def wrappedfunc(*args, **kwargs):
if stack:
return f(*args, **kwargs)
else:
to = f(*args, **kwargs)
while True:
if type(to) is GeneratorType:
stack.append(to)
to = next(to)
else:
stack.pop()
if not stack:
break
to = stack[-1].send(to)
return to
return wrappedfunc
@bootstrap
def recur(r,g,b):
if (r+b+g)==r or (r+b+g)==g or (r+b+g)==b:
yield 0
return
if dp[r][g][b]:
yield dp[r][g][b]
return
if r>0 and g>0:
dp[r][g][b]=max(dp[r][g][b],R[r-1]*G[g-1]+(yield recur(r-1,g-1,b)))
if r>0 and b>0:
dp[r][g][b]=max(dp[r][g][b],R[r-1]*B[b-1]+(yield recur(r-1,g,b-1)))
if b>0 and g>0:
dp[r][g][b]=max(dp[r][g][b],B[b-1]*G[g-1]+(yield recur(r,g-1,b-1)))
yield dp[r][g][b]
r,g,b=mdata()
R=sorted(mdata())
G=sorted(mdata())
B=sorted(mdata())
dp=[[[0]*(b+1) for i in range(g+1)] for i in range(r+1)]
out(recur(r,g,b))
``` | instruction | 0 | 37,901 | 23 | 75,802 |
Yes | output | 1 | 37,901 | 23 | 75,803 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three multisets of pairs of colored sticks:
* R pairs of red sticks, the first pair has length r_1, the second pair has length r_2, ..., the R-th pair has length r_R;
* G pairs of green sticks, the first pair has length g_1, the second pair has length g_2, ..., the G-th pair has length g_G;
* B pairs of blue sticks, the first pair has length b_1, the second pair has length b_2, ..., the B-th pair has length b_B;
You are constructing rectangles from these pairs of sticks with the following process:
1. take a pair of sticks of one color;
2. take a pair of sticks of another color different from the first one;
3. add the area of the resulting rectangle to the total area.
Thus, you get such rectangles that their opposite sides are the same color and their adjacent sides are not the same color.
Each pair of sticks can be used at most once, some pairs can be left unused. You are not allowed to split a pair into independent sticks.
What is the maximum area you can achieve?
Input
The first line contains three integers R, G, B (1 β€ R, G, B β€ 200) β the number of pairs of red sticks, the number of pairs of green sticks and the number of pairs of blue sticks.
The second line contains R integers r_1, r_2, ..., r_R (1 β€ r_i β€ 2000) β the lengths of sticks in each pair of red sticks.
The third line contains G integers g_1, g_2, ..., g_G (1 β€ g_i β€ 2000) β the lengths of sticks in each pair of green sticks.
The fourth line contains B integers b_1, b_2, ..., b_B (1 β€ b_i β€ 2000) β the lengths of sticks in each pair of blue sticks.
Output
Print the maximum possible total area of the constructed rectangles.
Examples
Input
1 1 1
3
5
4
Output
20
Input
2 1 3
9 5
1
2 8 5
Output
99
Input
10 1 1
11 7 20 15 19 14 2 4 13 14
8
11
Output
372
Note
In the first example you can construct one of these rectangles: red and green with sides 3 and 5, red and blue with sides 3 and 4 and green and blue with sides 5 and 4. The best area of them is 4 Γ 5 = 20.
In the second example the best rectangles are: red/blue 9 Γ 8, red/blue 5 Γ 5, green/blue 2 Γ 1. So the total area is 72 + 25 + 2 = 99.
In the third example the best rectangles are: red/green 19 Γ 8 and red/blue 20 Γ 11. The total area is 152 + 220 = 372. Note that you can't construct more rectangles because you are not allowed to have both pairs taken to be the same color.
Submitted Solution:
```
#writing my first dp program
def solu(i,j,k):
if(dp[i][j][k]!=-1):
return dp[i][j][k]
best=0
if(i<r and j<g):
best=max(best,R[i]*G[j]+solu(i+1,j+1,k))
if(j<g and k<b):
best=max(best,B[k]*G[j]+solu(i,j+1,k+1))
if(k<b and i<r):
best=max(best,R[i]*B[k]+solu(i+1,j,k+1))
dp[i][j][k]=best
return dp[i][j][k]
r,g,b=map(int,input().split())
R=list(map(int,input().split()))
G=list(map(int,input().split()))
B=list(map(int,input().split()))
area=0
R=sorted(R,reverse=True)
G=sorted(G,reverse=True)
B=sorted(B,reverse=True)
dp=[[[-1 for j in range(201)] for k in range(201)] for l in range(201)]
ans=solu(0,0,0)
print(ans)
``` | instruction | 0 | 37,902 | 23 | 75,804 |
Yes | output | 1 | 37,902 | 23 | 75,805 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three multisets of pairs of colored sticks:
* R pairs of red sticks, the first pair has length r_1, the second pair has length r_2, ..., the R-th pair has length r_R;
* G pairs of green sticks, the first pair has length g_1, the second pair has length g_2, ..., the G-th pair has length g_G;
* B pairs of blue sticks, the first pair has length b_1, the second pair has length b_2, ..., the B-th pair has length b_B;
You are constructing rectangles from these pairs of sticks with the following process:
1. take a pair of sticks of one color;
2. take a pair of sticks of another color different from the first one;
3. add the area of the resulting rectangle to the total area.
Thus, you get such rectangles that their opposite sides are the same color and their adjacent sides are not the same color.
Each pair of sticks can be used at most once, some pairs can be left unused. You are not allowed to split a pair into independent sticks.
What is the maximum area you can achieve?
Input
The first line contains three integers R, G, B (1 β€ R, G, B β€ 200) β the number of pairs of red sticks, the number of pairs of green sticks and the number of pairs of blue sticks.
The second line contains R integers r_1, r_2, ..., r_R (1 β€ r_i β€ 2000) β the lengths of sticks in each pair of red sticks.
The third line contains G integers g_1, g_2, ..., g_G (1 β€ g_i β€ 2000) β the lengths of sticks in each pair of green sticks.
The fourth line contains B integers b_1, b_2, ..., b_B (1 β€ b_i β€ 2000) β the lengths of sticks in each pair of blue sticks.
Output
Print the maximum possible total area of the constructed rectangles.
Examples
Input
1 1 1
3
5
4
Output
20
Input
2 1 3
9 5
1
2 8 5
Output
99
Input
10 1 1
11 7 20 15 19 14 2 4 13 14
8
11
Output
372
Note
In the first example you can construct one of these rectangles: red and green with sides 3 and 5, red and blue with sides 3 and 4 and green and blue with sides 5 and 4. The best area of them is 4 Γ 5 = 20.
In the second example the best rectangles are: red/blue 9 Γ 8, red/blue 5 Γ 5, green/blue 2 Γ 1. So the total area is 72 + 25 + 2 = 99.
In the third example the best rectangles are: red/green 19 Γ 8 and red/blue 20 Γ 11. The total area is 152 + 220 = 372. Note that you can't construct more rectangles because you are not allowed to have both pairs taken to be the same color.
Submitted Solution:
```
# @author --> ajaymodi
# optimized approach with memoization (dp)
import sys
# sys.stdin=open("input.in","r")
# sys.stdout=open("output.out","w")
input=lambda : sys.stdin.readline().strip()
char = [chr(i) for i in range(97,123)]
CHAR = [chr(i) for i in range(65,91)]
mp = lambda:list(map(int,input().split()))
INT = lambda:int(input())
rn = lambda:range(INT())
from math import ceil,sqrt,factorial,gcd
r,g,b = mp()
rl = sorted(mp(),reverse=True)
gl = sorted(mp(),reverse=True)
bl = sorted(mp(),reverse=True)
def solve(i,j,k):
if dp_table[i][j][k] != -1:
return dp_table[i][j][k]
ans = 0
if i < r and j < g:
ans = max(solve(i+1,j+1,k) + rl[i]*gl[j],ans)
if i < r and k < b:
ans = max(solve(i+1,j,k+1) + rl[i]*bl[k],ans)
if j < g and k < b:
ans = max(solve(i,j+1,k+1) + gl[j]*bl[k],ans)
dp_table[i][j][k] = ans
return dp_table[i][j][k]
dp_table = [[[-1 for i in range(b+1)] for j in range(g+1)] for k in range(r+1)]
res = solve(0,0,0)
print(res)
``` | instruction | 0 | 37,903 | 23 | 75,806 |
Yes | output | 1 | 37,903 | 23 | 75,807 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three multisets of pairs of colored sticks:
* R pairs of red sticks, the first pair has length r_1, the second pair has length r_2, ..., the R-th pair has length r_R;
* G pairs of green sticks, the first pair has length g_1, the second pair has length g_2, ..., the G-th pair has length g_G;
* B pairs of blue sticks, the first pair has length b_1, the second pair has length b_2, ..., the B-th pair has length b_B;
You are constructing rectangles from these pairs of sticks with the following process:
1. take a pair of sticks of one color;
2. take a pair of sticks of another color different from the first one;
3. add the area of the resulting rectangle to the total area.
Thus, you get such rectangles that their opposite sides are the same color and their adjacent sides are not the same color.
Each pair of sticks can be used at most once, some pairs can be left unused. You are not allowed to split a pair into independent sticks.
What is the maximum area you can achieve?
Input
The first line contains three integers R, G, B (1 β€ R, G, B β€ 200) β the number of pairs of red sticks, the number of pairs of green sticks and the number of pairs of blue sticks.
The second line contains R integers r_1, r_2, ..., r_R (1 β€ r_i β€ 2000) β the lengths of sticks in each pair of red sticks.
The third line contains G integers g_1, g_2, ..., g_G (1 β€ g_i β€ 2000) β the lengths of sticks in each pair of green sticks.
The fourth line contains B integers b_1, b_2, ..., b_B (1 β€ b_i β€ 2000) β the lengths of sticks in each pair of blue sticks.
Output
Print the maximum possible total area of the constructed rectangles.
Examples
Input
1 1 1
3
5
4
Output
20
Input
2 1 3
9 5
1
2 8 5
Output
99
Input
10 1 1
11 7 20 15 19 14 2 4 13 14
8
11
Output
372
Note
In the first example you can construct one of these rectangles: red and green with sides 3 and 5, red and blue with sides 3 and 4 and green and blue with sides 5 and 4. The best area of them is 4 Γ 5 = 20.
In the second example the best rectangles are: red/blue 9 Γ 8, red/blue 5 Γ 5, green/blue 2 Γ 1. So the total area is 72 + 25 + 2 = 99.
In the third example the best rectangles are: red/green 19 Γ 8 and red/blue 20 Γ 11. The total area is 152 + 220 = 372. Note that you can't construct more rectangles because you are not allowed to have both pairs taken to be the same color.
Submitted Solution:
```
import sys
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
ns = lambda: readline().rstrip()
ni = lambda: int(readline().rstrip())
nm = lambda: map(int, readline().split())
nl = lambda: list(map(int, readline().split()))
r, g, b = nm()
R = nl()
G = nl()
B = nl()
dp = [[[-1 for i in range(b+1)] for i in range(g+1)] for i in range(r+1)]
R.sort(reverse=True)
G.sort(reverse=True)
B.sort(reverse=True)
R.insert(0, 0)
G.insert(0, 0)
B.insert(0, 0)
dp[0][0][0], ans = 0, 0
for i in range(0, r+1):
for j in range(0, g+1):
for k in range(0, b+1):
if i==0 and j==0 and k==0:continue
if i and j and dp[i - 1][j - 1][k] != -1:
dp[i][j][k] = max(dp[i][j][k], dp[i - 1][j - 1][k] + R[i] * G[j])
if k and j and dp[i][j - 1][k - 1] != -1:
dp[i][j][k] = max(dp[i][j][k], dp[i][j - 1][k - 1] + B[k] * G[j])
if i and k and dp[i - 1][j][k - 1] != -1:
dp[i][j][k] = max(dp[i][j][k], dp[i - 1][j][k - 1] + R[i] * B[k])
ans = max(ans, dp[i][j][k])
print(ans)
``` | instruction | 0 | 37,904 | 23 | 75,808 |
Yes | output | 1 | 37,904 | 23 | 75,809 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three multisets of pairs of colored sticks:
* R pairs of red sticks, the first pair has length r_1, the second pair has length r_2, ..., the R-th pair has length r_R;
* G pairs of green sticks, the first pair has length g_1, the second pair has length g_2, ..., the G-th pair has length g_G;
* B pairs of blue sticks, the first pair has length b_1, the second pair has length b_2, ..., the B-th pair has length b_B;
You are constructing rectangles from these pairs of sticks with the following process:
1. take a pair of sticks of one color;
2. take a pair of sticks of another color different from the first one;
3. add the area of the resulting rectangle to the total area.
Thus, you get such rectangles that their opposite sides are the same color and their adjacent sides are not the same color.
Each pair of sticks can be used at most once, some pairs can be left unused. You are not allowed to split a pair into independent sticks.
What is the maximum area you can achieve?
Input
The first line contains three integers R, G, B (1 β€ R, G, B β€ 200) β the number of pairs of red sticks, the number of pairs of green sticks and the number of pairs of blue sticks.
The second line contains R integers r_1, r_2, ..., r_R (1 β€ r_i β€ 2000) β the lengths of sticks in each pair of red sticks.
The third line contains G integers g_1, g_2, ..., g_G (1 β€ g_i β€ 2000) β the lengths of sticks in each pair of green sticks.
The fourth line contains B integers b_1, b_2, ..., b_B (1 β€ b_i β€ 2000) β the lengths of sticks in each pair of blue sticks.
Output
Print the maximum possible total area of the constructed rectangles.
Examples
Input
1 1 1
3
5
4
Output
20
Input
2 1 3
9 5
1
2 8 5
Output
99
Input
10 1 1
11 7 20 15 19 14 2 4 13 14
8
11
Output
372
Note
In the first example you can construct one of these rectangles: red and green with sides 3 and 5, red and blue with sides 3 and 4 and green and blue with sides 5 and 4. The best area of them is 4 Γ 5 = 20.
In the second example the best rectangles are: red/blue 9 Γ 8, red/blue 5 Γ 5, green/blue 2 Γ 1. So the total area is 72 + 25 + 2 = 99.
In the third example the best rectangles are: red/green 19 Γ 8 and red/blue 20 Γ 11. The total area is 152 + 220 = 372. Note that you can't construct more rectangles because you are not allowed to have both pairs taken to be the same color.
Submitted Solution:
```
import sys
r, g, b = map(int, sys.stdin.readline().split())
list_stick = [sorted(list(map(int, sys.stdin.readline().split()))) for _ in range(3)]
res = 0
i = [0, 1, 2]
while (not list_stick[0]) + (not list_stick[1]) + (not list_stick[2])<2:
i.sort(key = lambda x: list_stick[x][-1] if list_stick[x] else 0)
if list_stick[i[0]] and list_stick[i[1]] and list_stick[i[0]][-1] == list_stick[i[1]][-1]:
if len(list_stick[i[0]]) > len(list_stick[i[1]]):
temp = i[0]
i[0] = i[1]
i[1] = temp
res += list_stick[i[-1]].pop()*list_stick[i[-2]].pop()
print(res)
``` | instruction | 0 | 37,905 | 23 | 75,810 |
No | output | 1 | 37,905 | 23 | 75,811 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three multisets of pairs of colored sticks:
* R pairs of red sticks, the first pair has length r_1, the second pair has length r_2, ..., the R-th pair has length r_R;
* G pairs of green sticks, the first pair has length g_1, the second pair has length g_2, ..., the G-th pair has length g_G;
* B pairs of blue sticks, the first pair has length b_1, the second pair has length b_2, ..., the B-th pair has length b_B;
You are constructing rectangles from these pairs of sticks with the following process:
1. take a pair of sticks of one color;
2. take a pair of sticks of another color different from the first one;
3. add the area of the resulting rectangle to the total area.
Thus, you get such rectangles that their opposite sides are the same color and their adjacent sides are not the same color.
Each pair of sticks can be used at most once, some pairs can be left unused. You are not allowed to split a pair into independent sticks.
What is the maximum area you can achieve?
Input
The first line contains three integers R, G, B (1 β€ R, G, B β€ 200) β the number of pairs of red sticks, the number of pairs of green sticks and the number of pairs of blue sticks.
The second line contains R integers r_1, r_2, ..., r_R (1 β€ r_i β€ 2000) β the lengths of sticks in each pair of red sticks.
The third line contains G integers g_1, g_2, ..., g_G (1 β€ g_i β€ 2000) β the lengths of sticks in each pair of green sticks.
The fourth line contains B integers b_1, b_2, ..., b_B (1 β€ b_i β€ 2000) β the lengths of sticks in each pair of blue sticks.
Output
Print the maximum possible total area of the constructed rectangles.
Examples
Input
1 1 1
3
5
4
Output
20
Input
2 1 3
9 5
1
2 8 5
Output
99
Input
10 1 1
11 7 20 15 19 14 2 4 13 14
8
11
Output
372
Note
In the first example you can construct one of these rectangles: red and green with sides 3 and 5, red and blue with sides 3 and 4 and green and blue with sides 5 and 4. The best area of them is 4 Γ 5 = 20.
In the second example the best rectangles are: red/blue 9 Γ 8, red/blue 5 Γ 5, green/blue 2 Γ 1. So the total area is 72 + 25 + 2 = 99.
In the third example the best rectangles are: red/green 19 Γ 8 and red/blue 20 Γ 11. The total area is 152 + 220 = 372. Note that you can't construct more rectangles because you are not allowed to have both pairs taken to be the same color.
Submitted Solution:
```
import sys
r, g, b = map(int, sys.stdin.readline().split())
list_stick = [sorted(list(map(int, sys.stdin.readline().split()))) for _ in range(3)]
res = 0
i = [0, 1, 2]
while (not list_stick[0]) + (not list_stick[1]) + (not list_stick[2])<2:
i.sort(key = lambda x: list_stick[x][-1] if list_stick[x] else 0)
res += list_stick[i[-1]].pop()*list_stick[i[-2]].pop()
print(res)
``` | instruction | 0 | 37,906 | 23 | 75,812 |
No | output | 1 | 37,906 | 23 | 75,813 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three multisets of pairs of colored sticks:
* R pairs of red sticks, the first pair has length r_1, the second pair has length r_2, ..., the R-th pair has length r_R;
* G pairs of green sticks, the first pair has length g_1, the second pair has length g_2, ..., the G-th pair has length g_G;
* B pairs of blue sticks, the first pair has length b_1, the second pair has length b_2, ..., the B-th pair has length b_B;
You are constructing rectangles from these pairs of sticks with the following process:
1. take a pair of sticks of one color;
2. take a pair of sticks of another color different from the first one;
3. add the area of the resulting rectangle to the total area.
Thus, you get such rectangles that their opposite sides are the same color and their adjacent sides are not the same color.
Each pair of sticks can be used at most once, some pairs can be left unused. You are not allowed to split a pair into independent sticks.
What is the maximum area you can achieve?
Input
The first line contains three integers R, G, B (1 β€ R, G, B β€ 200) β the number of pairs of red sticks, the number of pairs of green sticks and the number of pairs of blue sticks.
The second line contains R integers r_1, r_2, ..., r_R (1 β€ r_i β€ 2000) β the lengths of sticks in each pair of red sticks.
The third line contains G integers g_1, g_2, ..., g_G (1 β€ g_i β€ 2000) β the lengths of sticks in each pair of green sticks.
The fourth line contains B integers b_1, b_2, ..., b_B (1 β€ b_i β€ 2000) β the lengths of sticks in each pair of blue sticks.
Output
Print the maximum possible total area of the constructed rectangles.
Examples
Input
1 1 1
3
5
4
Output
20
Input
2 1 3
9 5
1
2 8 5
Output
99
Input
10 1 1
11 7 20 15 19 14 2 4 13 14
8
11
Output
372
Note
In the first example you can construct one of these rectangles: red and green with sides 3 and 5, red and blue with sides 3 and 4 and green and blue with sides 5 and 4. The best area of them is 4 Γ 5 = 20.
In the second example the best rectangles are: red/blue 9 Γ 8, red/blue 5 Γ 5, green/blue 2 Γ 1. So the total area is 72 + 25 + 2 = 99.
In the third example the best rectangles are: red/green 19 Γ 8 and red/blue 20 Γ 11. The total area is 152 + 220 = 372. Note that you can't construct more rectangles because you are not allowed to have both pairs taken to be the same color.
Submitted Solution:
```
t=input()
r=list(map(int,input().split()))
g=list(map(int,input().split()))
b=list(map(int,input().split()))
r.sort()
g.sort()
b.sort()
li=[r,g,b]
ans=0
def get_area(li):
if(len(li)==2):
return li[0].pop()*li[1].pop()
else:
if(li[0][-1]==li[1][-1]==li[2][-1]):
li.sort(key=lambda x:len(x),reverse=True)
return li[0].pop()*li[1].pop()
if(li[0][-1]==min(li[0][-1],li[1][-1],li[2][-1])):
return li[1].pop()*li[2].pop()
if (li[1][-1] == min(li[0][-1], li[1][-1], li[2][-1])):
return li[0].pop()*li[2].pop()
if (li[2][-1] == min(li[0][-1], li[1][-1], li[2][-1])):
return li[0].pop()*li[1].pop()
while(len(li)>=2):
ans+=get_area(li)
tr=[]
for i in li:
if(i==[]):
tr.append(i)
for i in tr:
li.remove(i)
print(ans)
``` | instruction | 0 | 37,907 | 23 | 75,814 |
No | output | 1 | 37,907 | 23 | 75,815 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three multisets of pairs of colored sticks:
* R pairs of red sticks, the first pair has length r_1, the second pair has length r_2, ..., the R-th pair has length r_R;
* G pairs of green sticks, the first pair has length g_1, the second pair has length g_2, ..., the G-th pair has length g_G;
* B pairs of blue sticks, the first pair has length b_1, the second pair has length b_2, ..., the B-th pair has length b_B;
You are constructing rectangles from these pairs of sticks with the following process:
1. take a pair of sticks of one color;
2. take a pair of sticks of another color different from the first one;
3. add the area of the resulting rectangle to the total area.
Thus, you get such rectangles that their opposite sides are the same color and their adjacent sides are not the same color.
Each pair of sticks can be used at most once, some pairs can be left unused. You are not allowed to split a pair into independent sticks.
What is the maximum area you can achieve?
Input
The first line contains three integers R, G, B (1 β€ R, G, B β€ 200) β the number of pairs of red sticks, the number of pairs of green sticks and the number of pairs of blue sticks.
The second line contains R integers r_1, r_2, ..., r_R (1 β€ r_i β€ 2000) β the lengths of sticks in each pair of red sticks.
The third line contains G integers g_1, g_2, ..., g_G (1 β€ g_i β€ 2000) β the lengths of sticks in each pair of green sticks.
The fourth line contains B integers b_1, b_2, ..., b_B (1 β€ b_i β€ 2000) β the lengths of sticks in each pair of blue sticks.
Output
Print the maximum possible total area of the constructed rectangles.
Examples
Input
1 1 1
3
5
4
Output
20
Input
2 1 3
9 5
1
2 8 5
Output
99
Input
10 1 1
11 7 20 15 19 14 2 4 13 14
8
11
Output
372
Note
In the first example you can construct one of these rectangles: red and green with sides 3 and 5, red and blue with sides 3 and 4 and green and blue with sides 5 and 4. The best area of them is 4 Γ 5 = 20.
In the second example the best rectangles are: red/blue 9 Γ 8, red/blue 5 Γ 5, green/blue 2 Γ 1. So the total area is 72 + 25 + 2 = 99.
In the third example the best rectangles are: red/green 19 Γ 8 and red/blue 20 Γ 11. The total area is 152 + 220 = 372. Note that you can't construct more rectangles because you are not allowed to have both pairs taken to be the same color.
Submitted Solution:
```
r,g,b=map(int,input().split())
R=list(map(int,input().split()))
G=list(map(int,input().split()))
B=list(map(int,input().split()))
area=0
R.sort()
G.sort()
B.sort()
cr=r-1
cg=g-1
cb=b-1
while(1):
if((cr<0 and cg<0)or(cr<0 and cb<0)or(cg<0 and cb<0)):
break
if(cr<0 and cg>=0 and cb>=0):
area+=G[cg]*B[cb]
cg-=1
cb-=1
elif(cr>=0 and cg<0 and cb>=0):
area+=R[cr]*B[cb]
cr-=1
cb-=1
elif(cr>=0 and cg>=0 and cb<0):
area+=R[cr]*G[cg]
cr-=1
cg-=1
elif(max(R[cr],G[cg],B[cb])==R[cr]):
if(max(G[cg],B[cb])==G[cg]):
area+=R[cr]*G[cg]
cr-=1
cg-=1
else:
area+=R[cr]*B[cb]
cr-=1
cb-=1
elif(max(R[cr],G[cg],B[cb])==G[cg]):
if(max(R[cr],B[cb])==R[cr]):
area+=G[cg]*R[cr]
cg-=1
cr-=1
else:
area+=G[cg]*B[cb]
cg-=1
cb-=1
else:
if(max(R[cr],G[cg])==R[cr]):
area+=B[cb]*R[cr]
cb-=1
cr-=1
else:
area+=B[cb]*G[cg]
cb-=1
cg-=1
print(area)
``` | instruction | 0 | 37,908 | 23 | 75,816 |
No | output | 1 | 37,908 | 23 | 75,817 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have two positive integers w and h. Your task is to count the number of rhombi which have the following properties:
* Have positive area.
* With vertices at integer points.
* All vertices of the rhombi are located inside or on the border of the rectangle with vertices at points (0, 0), (w, 0), (w, h), (0, h). In other words, for all vertices (xi, yi) of the rhombus the following conditions should fulfill: 0 β€ xi β€ w and 0 β€ yi β€ h.
* Its diagonals are parallel to the axis.
Count the number of such rhombi.
Let us remind you that a rhombus is a quadrilateral whose four sides all have the same length.
Input
The first line contains two integers w and h (1 β€ w, h β€ 4000) β the rectangle's sizes.
Output
Print a single number β the number of sought rhombi.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout streams or the %I64d specifier.
Examples
Input
2 2
Output
1
Input
1 2
Output
0
Note
In the first example there exists only one such rhombus. Its vertices are located at points (1, 0), (2, 1), (1, 2), (0, 1). | instruction | 0 | 37,959 | 23 | 75,918 |
Tags: brute force, math
Correct Solution:
```
import sys
import math
#import random
#sys.setrecursionlimit(10000000)
input = sys.stdin.readline
############ ---- USER DEFINED INPUT FUNCTIONS ---- ############
def inp():
return(int(input()))
def inara():
return(list(map(int,input().split())))
def insr():
s = input()
return(list(s[:len(s) - 1]))
def invr():
return(map(int,input().split()))
################################################################
############ ---- THE ACTUAL CODE STARTS BELOW ---- ############
w,h=invr()
if w>h:
w,h=h,w
ans=0
for i in range(1,w+1):
for j in range(1,h+1):
if w-2*i+1>0 and h-2*j+1>0:
ans+=(w-2*i+1)*(h-2*j+1)
print(ans)
``` | output | 1 | 37,959 | 23 | 75,919 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have two positive integers w and h. Your task is to count the number of rhombi which have the following properties:
* Have positive area.
* With vertices at integer points.
* All vertices of the rhombi are located inside or on the border of the rectangle with vertices at points (0, 0), (w, 0), (w, h), (0, h). In other words, for all vertices (xi, yi) of the rhombus the following conditions should fulfill: 0 β€ xi β€ w and 0 β€ yi β€ h.
* Its diagonals are parallel to the axis.
Count the number of such rhombi.
Let us remind you that a rhombus is a quadrilateral whose four sides all have the same length.
Input
The first line contains two integers w and h (1 β€ w, h β€ 4000) β the rectangle's sizes.
Output
Print a single number β the number of sought rhombi.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout streams or the %I64d specifier.
Examples
Input
2 2
Output
1
Input
1 2
Output
0
Note
In the first example there exists only one such rhombus. Its vertices are located at points (1, 0), (2, 1), (1, 2), (0, 1). | instruction | 0 | 37,960 | 23 | 75,920 |
Tags: brute force, math
Correct Solution:
```
import sys
input = sys.stdin.readline
w, h = map(int, input().split())
maxW = w//2
maxH = h//2
ans = 0
for i in range(1, maxW+1):
for j in range(1, maxH+1):
ans += (w-(i*2)+1)*(h-(j*2)+1)
print(ans)
``` | output | 1 | 37,960 | 23 | 75,921 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have two positive integers w and h. Your task is to count the number of rhombi which have the following properties:
* Have positive area.
* With vertices at integer points.
* All vertices of the rhombi are located inside or on the border of the rectangle with vertices at points (0, 0), (w, 0), (w, h), (0, h). In other words, for all vertices (xi, yi) of the rhombus the following conditions should fulfill: 0 β€ xi β€ w and 0 β€ yi β€ h.
* Its diagonals are parallel to the axis.
Count the number of such rhombi.
Let us remind you that a rhombus is a quadrilateral whose four sides all have the same length.
Input
The first line contains two integers w and h (1 β€ w, h β€ 4000) β the rectangle's sizes.
Output
Print a single number β the number of sought rhombi.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout streams or the %I64d specifier.
Examples
Input
2 2
Output
1
Input
1 2
Output
0
Note
In the first example there exists only one such rhombus. Its vertices are located at points (1, 0), (2, 1), (1, 2), (0, 1). | instruction | 0 | 37,961 | 23 | 75,922 |
Tags: brute force, math
Correct Solution:
```
x, y = map(int, input().split())
x = x**2
y = y**2
ans = (x//4)*(y//4)
print(ans)
``` | output | 1 | 37,961 | 23 | 75,923 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have two positive integers w and h. Your task is to count the number of rhombi which have the following properties:
* Have positive area.
* With vertices at integer points.
* All vertices of the rhombi are located inside or on the border of the rectangle with vertices at points (0, 0), (w, 0), (w, h), (0, h). In other words, for all vertices (xi, yi) of the rhombus the following conditions should fulfill: 0 β€ xi β€ w and 0 β€ yi β€ h.
* Its diagonals are parallel to the axis.
Count the number of such rhombi.
Let us remind you that a rhombus is a quadrilateral whose four sides all have the same length.
Input
The first line contains two integers w and h (1 β€ w, h β€ 4000) β the rectangle's sizes.
Output
Print a single number β the number of sought rhombi.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout streams or the %I64d specifier.
Examples
Input
2 2
Output
1
Input
1 2
Output
0
Note
In the first example there exists only one such rhombus. Its vertices are located at points (1, 0), (2, 1), (1, 2), (0, 1). | instruction | 0 | 37,962 | 23 | 75,924 |
Tags: brute force, math
Correct Solution:
```
try:
import math
w,h=list(map(int,input().split(" ")))
s1=0
s2=0
for i in range(2,w+1,2):
s1+=w-i+1
for i in range(2,h+1,2):
s2+=h-i+1
print(s1*s2)
except:
pass
``` | output | 1 | 37,962 | 23 | 75,925 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have two positive integers w and h. Your task is to count the number of rhombi which have the following properties:
* Have positive area.
* With vertices at integer points.
* All vertices of the rhombi are located inside or on the border of the rectangle with vertices at points (0, 0), (w, 0), (w, h), (0, h). In other words, for all vertices (xi, yi) of the rhombus the following conditions should fulfill: 0 β€ xi β€ w and 0 β€ yi β€ h.
* Its diagonals are parallel to the axis.
Count the number of such rhombi.
Let us remind you that a rhombus is a quadrilateral whose four sides all have the same length.
Input
The first line contains two integers w and h (1 β€ w, h β€ 4000) β the rectangle's sizes.
Output
Print a single number β the number of sought rhombi.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout streams or the %I64d specifier.
Examples
Input
2 2
Output
1
Input
1 2
Output
0
Note
In the first example there exists only one such rhombus. Its vertices are located at points (1, 0), (2, 1), (1, 2), (0, 1). | instruction | 0 | 37,963 | 23 | 75,926 |
Tags: brute force, math
Correct Solution:
```
data = [int(i) for i in input().split()]
w = data[0]
h = data[1]
if w < 2 or h < 2:
print(0)
else:
res = 0
for i in range(2, w + 1, 2):
for j in range(2, h + 1, 2):
res = res + (w - i + 1) * (h - j + 1)
print(res)
``` | output | 1 | 37,963 | 23 | 75,927 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have two positive integers w and h. Your task is to count the number of rhombi which have the following properties:
* Have positive area.
* With vertices at integer points.
* All vertices of the rhombi are located inside or on the border of the rectangle with vertices at points (0, 0), (w, 0), (w, h), (0, h). In other words, for all vertices (xi, yi) of the rhombus the following conditions should fulfill: 0 β€ xi β€ w and 0 β€ yi β€ h.
* Its diagonals are parallel to the axis.
Count the number of such rhombi.
Let us remind you that a rhombus is a quadrilateral whose four sides all have the same length.
Input
The first line contains two integers w and h (1 β€ w, h β€ 4000) β the rectangle's sizes.
Output
Print a single number β the number of sought rhombi.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout streams or the %I64d specifier.
Examples
Input
2 2
Output
1
Input
1 2
Output
0
Note
In the first example there exists only one such rhombus. Its vertices are located at points (1, 0), (2, 1), (1, 2), (0, 1). | instruction | 0 | 37,964 | 23 | 75,928 |
Tags: brute force, math
Correct Solution:
```
#!/usr/bin/env python3
w, h = map(int, input().split())
w_edge = h_edge = 0
for i in range(2, w + 1, 2):
w_edge += (w - i + 1)
for i in range(2, h + 1, 2):
h_edge += (h - i + 1)
print(w_edge * h_edge)
``` | output | 1 | 37,964 | 23 | 75,929 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have two positive integers w and h. Your task is to count the number of rhombi which have the following properties:
* Have positive area.
* With vertices at integer points.
* All vertices of the rhombi are located inside or on the border of the rectangle with vertices at points (0, 0), (w, 0), (w, h), (0, h). In other words, for all vertices (xi, yi) of the rhombus the following conditions should fulfill: 0 β€ xi β€ w and 0 β€ yi β€ h.
* Its diagonals are parallel to the axis.
Count the number of such rhombi.
Let us remind you that a rhombus is a quadrilateral whose four sides all have the same length.
Input
The first line contains two integers w and h (1 β€ w, h β€ 4000) β the rectangle's sizes.
Output
Print a single number β the number of sought rhombi.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout streams or the %I64d specifier.
Examples
Input
2 2
Output
1
Input
1 2
Output
0
Note
In the first example there exists only one such rhombus. Its vertices are located at points (1, 0), (2, 1), (1, 2), (0, 1). | instruction | 0 | 37,965 | 23 | 75,930 |
Tags: brute force, math
Correct Solution:
```
w, h = map(int, input().split())
if w < 2 or h < 2:
print(0)
else:
ans = 0
for x in range(2, w + 1, 2):
for y in range(2, h + 1, 2):
ans += (w + 1 - x) * (h + 1 - y)
print(ans)
``` | output | 1 | 37,965 | 23 | 75,931 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have two positive integers w and h. Your task is to count the number of rhombi which have the following properties:
* Have positive area.
* With vertices at integer points.
* All vertices of the rhombi are located inside or on the border of the rectangle with vertices at points (0, 0), (w, 0), (w, h), (0, h). In other words, for all vertices (xi, yi) of the rhombus the following conditions should fulfill: 0 β€ xi β€ w and 0 β€ yi β€ h.
* Its diagonals are parallel to the axis.
Count the number of such rhombi.
Let us remind you that a rhombus is a quadrilateral whose four sides all have the same length.
Input
The first line contains two integers w and h (1 β€ w, h β€ 4000) β the rectangle's sizes.
Output
Print a single number β the number of sought rhombi.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout streams or the %I64d specifier.
Examples
Input
2 2
Output
1
Input
1 2
Output
0
Note
In the first example there exists only one such rhombus. Its vertices are located at points (1, 0), (2, 1), (1, 2), (0, 1). | instruction | 0 | 37,966 | 23 | 75,932 |
Tags: brute force, math
Correct Solution:
```
h, w = map(int, input().split())
x, y = h % 2, w % 2
print(((h + x) * (h - x) * (w + y) * (w - y)) // 16)
``` | output | 1 | 37,966 | 23 | 75,933 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have two positive integers w and h. Your task is to count the number of rhombi which have the following properties:
* Have positive area.
* With vertices at integer points.
* All vertices of the rhombi are located inside or on the border of the rectangle with vertices at points (0, 0), (w, 0), (w, h), (0, h). In other words, for all vertices (xi, yi) of the rhombus the following conditions should fulfill: 0 β€ xi β€ w and 0 β€ yi β€ h.
* Its diagonals are parallel to the axis.
Count the number of such rhombi.
Let us remind you that a rhombus is a quadrilateral whose four sides all have the same length.
Input
The first line contains two integers w and h (1 β€ w, h β€ 4000) β the rectangle's sizes.
Output
Print a single number β the number of sought rhombi.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout streams or the %I64d specifier.
Examples
Input
2 2
Output
1
Input
1 2
Output
0
Note
In the first example there exists only one such rhombus. Its vertices are located at points (1, 0), (2, 1), (1, 2), (0, 1).
Submitted Solution:
```
def solve(h,b):
maxH = h//2
maxW = b//2
A = [maxH**2, maxH*(maxH + 1)][h % 2]
B = [maxW**2, maxW*(maxW + 1)][b % 2]
return A*B
w,h = map(int, input().split())
print(solve(w,h))
``` | instruction | 0 | 37,967 | 23 | 75,934 |
Yes | output | 1 | 37,967 | 23 | 75,935 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have two positive integers w and h. Your task is to count the number of rhombi which have the following properties:
* Have positive area.
* With vertices at integer points.
* All vertices of the rhombi are located inside or on the border of the rectangle with vertices at points (0, 0), (w, 0), (w, h), (0, h). In other words, for all vertices (xi, yi) of the rhombus the following conditions should fulfill: 0 β€ xi β€ w and 0 β€ yi β€ h.
* Its diagonals are parallel to the axis.
Count the number of such rhombi.
Let us remind you that a rhombus is a quadrilateral whose four sides all have the same length.
Input
The first line contains two integers w and h (1 β€ w, h β€ 4000) β the rectangle's sizes.
Output
Print a single number β the number of sought rhombi.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout streams or the %I64d specifier.
Examples
Input
2 2
Output
1
Input
1 2
Output
0
Note
In the first example there exists only one such rhombus. Its vertices are located at points (1, 0), (2, 1), (1, 2), (0, 1).
Submitted Solution:
```
w,h = map(int,input().split())
cw,ch = 0,0
for i in range(2,w+1,2):
cw += 1+w-i
for i in range(2,h+1,2):
ch += 1+h-i
print(cw*ch)
``` | instruction | 0 | 37,968 | 23 | 75,936 |
Yes | output | 1 | 37,968 | 23 | 75,937 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have two positive integers w and h. Your task is to count the number of rhombi which have the following properties:
* Have positive area.
* With vertices at integer points.
* All vertices of the rhombi are located inside or on the border of the rectangle with vertices at points (0, 0), (w, 0), (w, h), (0, h). In other words, for all vertices (xi, yi) of the rhombus the following conditions should fulfill: 0 β€ xi β€ w and 0 β€ yi β€ h.
* Its diagonals are parallel to the axis.
Count the number of such rhombi.
Let us remind you that a rhombus is a quadrilateral whose four sides all have the same length.
Input
The first line contains two integers w and h (1 β€ w, h β€ 4000) β the rectangle's sizes.
Output
Print a single number β the number of sought rhombi.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout streams or the %I64d specifier.
Examples
Input
2 2
Output
1
Input
1 2
Output
0
Note
In the first example there exists only one such rhombus. Its vertices are located at points (1, 0), (2, 1), (1, 2), (0, 1).
Submitted Solution:
```
#!/usr/bin/env python
from __future__ import division, print_function
import math
import os
import sys
from fractions import *
from sys import stdin,stdout
from io import BytesIO, IOBase
from itertools import accumulate
from collections import deque
#sys.setrecursionlimit(10**5)
def inp(): return sys.stdin.readline().rstrip("\r\n") # for fast input
def out(var): sys.stdout.write(str(var)) # for fast output, always take string
def lis(): return list(map(int, inp().split()))
def stringlis(): return list(map(str, inp().split()))
def sep(): return map(int, inp().split())
def strsep(): return map(str, inp().split())
def fsep(): return map(float, inp().split())
def inpu(): return int(inp())
if sys.version_info[0] < 3:
from __builtin__ import xrange as range
from future_builtins import ascii, filter, hex, map, oct, zip
#sys.setrecursionlimit(10**6)
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
def print(*args, **kwargs):
"""Prints the values to a stream, or to sys.stdout by default."""
sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
at_start = True
for x in args:
if not at_start:
file.write(sep)
file.write(str(x))
at_start = False
file.write(kwargs.pop("end", "\n"))
if kwargs.pop("flush", False):
file.flush()
if sys.version_info[0] < 3:
sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
#-----------------------------------------------------------------
def regularbracket(t):
p=0
for i in t:
if i=="(":
p+=1
else:
p-=1
if p<0:
return False
else:
if p>0:
return False
else:
return True
#-------------------------------------------------
def binarySearchCount(arr, n, key):
left = 0
right = n - 1
count = 0
while (left <= right):
mid = int((right + left) / 2)
# Check if middle element is
# less than or equal to key
if (arr[mid] <= key):
count = mid+1
left = mid + 1
# If key is smaller, ignore right half
else:
right = mid - 1
return count
#------------------------------reverse string(pallindrome)
def reverse1(string):
pp=""
for i in string[::-1]:
pp+=i
if pp==string:
return True
return False
#--------------------------------reverse list(paindrome)
def reverse2(list1):
l=[]
for i in list1[::-1]:
l.append(i)
if l==list1:
return True
return False
def mex(list1):
#list1 = sorted(list1)
p = max(list1)+1
for i in range(len(list1)):
if list1[i]!=i:
p = i
break
return p
def sumofdigits(n):
n = str(n)
s1=0
for i in n:
s1+=int(i)
return s1
def perfect_square(n):
s = math.sqrt(n)
if s==int(s):
return True
return False
#-----------------------------roman
def roman_number(x):
if x>15999:
return
value=[5000,4000,1000,900,500,400,100,90,50,40,10,9,5,4,1]
symbol = ["F","MF","M","CM","D","CD","C","XC","L","XL","X","IX","V","IV","I"]
roman=""
i=0
while x>0:
div = x//value[i]
x = x%value[i]
while div:
roman+=symbol[i]
div-=1
i+=1
return roman
def soretd(s):
for i in range(1,len(s)):
if s[i-1]>s[i]:
return False
return True
#print(soretd("1"))
#---------------------------
def countRhombi(h, w):
ct = 0
for i in range(2, h + 1, 2):
for j in range(2, w + 1, 2):
ct += (h - i + 1) * (w - j + 1)
return ct
#---------------------------------
def binpow(a,b):
if b==0:
return 1
else:
res=binpow(a,b//2)
if b%2!=0:
return res*res*a
else:
return res*res
#-------------------------------------------------------
def binpowmodulus(a,b,m):
a %= m
res = 1
while (b > 0):
if (b & 1):
res = res * a % m
a = a * a % m
b >>= 1
return res
#-------------------------------------------------------------
def coprime_to_n(n):
result = n
i=2
while(i*i<=n):
if (n % i == 0):
while (n % i == 0):
n //= i
result -= result // i
i+=1
if (n > 1):
result -= result // n
return result
#-------------------prime
def prime(x):
if x==1:
return False
else:
for i in range(2,int(math.sqrt(x))+1):
if(x%i==0):
return False
else:
return True
def luckynumwithequalnumberoffourandseven(x,n,a):
if x >= n and str(x).count("4") == str(x).count("7"):
a.append(x)
else:
if x < 1e12:
luckynumwithequalnumberoffourandseven(x * 10 + 4,n,a)
luckynumwithequalnumberoffourandseven(x * 10 + 7,n,a)
return a
#def mapu(): return map(int,input().split())
#endregion------------------------------
"""
def main():
x,y,n = sep()
c = (Fraction(x,y).limit_denominator(n))
# print(type(c))
# print(c)
c = str(c)
if "/" in c:
print(c)
else:
print(c+"/"+"1")
if __name__ == '__main__':
main()
"""
if __name__ == '__main__':
a,b = sep()
print(countRhombi(a,b))
``` | instruction | 0 | 37,969 | 23 | 75,938 |
Yes | output | 1 | 37,969 | 23 | 75,939 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have two positive integers w and h. Your task is to count the number of rhombi which have the following properties:
* Have positive area.
* With vertices at integer points.
* All vertices of the rhombi are located inside or on the border of the rectangle with vertices at points (0, 0), (w, 0), (w, h), (0, h). In other words, for all vertices (xi, yi) of the rhombus the following conditions should fulfill: 0 β€ xi β€ w and 0 β€ yi β€ h.
* Its diagonals are parallel to the axis.
Count the number of such rhombi.
Let us remind you that a rhombus is a quadrilateral whose four sides all have the same length.
Input
The first line contains two integers w and h (1 β€ w, h β€ 4000) β the rectangle's sizes.
Output
Print a single number β the number of sought rhombi.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout streams or the %I64d specifier.
Examples
Input
2 2
Output
1
Input
1 2
Output
0
Note
In the first example there exists only one such rhombus. Its vertices are located at points (1, 0), (2, 1), (1, 2), (0, 1).
Submitted Solution:
```
import sys
import math
import itertools
import functools
import collections
import operator
import fileinput
import copy
ORDA = 97 # a
def ii(): return int(input())
def mi(): return map(int, input().split())
def li(): return [int(i) for i in input().split()]
def lcm(a, b): return abs(a * b) // math.gcd(a, b)
def revn(n): return str(n)[::-1]
def dd(): return collections.defaultdict(int)
def ddl(): return collections.defaultdict(list)
def sieve(n):
if n < 2: return list()
prime = [True for _ in range(n + 1)]
p = 3
while p * p <= n:
if prime[p]:
for i in range(p * 2, n + 1, p):
prime[i] = False
p += 2
r = [2]
for p in range(3, n + 1, 2):
if prime[p]:
r.append(p)
return r
def divs(n, start=2):
r = []
for i in range(start, int(math.sqrt(n) + 1)):
if (n % i == 0):
if (n / i == i):
r.append(i)
else:
r.extend([i, n // i])
return r
def divn(n, primes):
divs_number = 1
for i in primes:
if n == 1:
return divs_number
t = 1
while n % i == 0:
t += 1
n //= i
divs_number *= t
def prime(n):
if n == 2: return True
if n % 2 == 0 or n <= 1: return False
sqr = int(math.sqrt(n)) + 1
for d in range(3, sqr, 2):
if n % d == 0: return False
return True
def convn(number, base):
newnumber = 0
while number > 0:
newnumber += number % base
number //= base
return newnumber
def cdiv(n, k): return n // k + (n % k != 0)
def ispal(s):
for i in range(len(s) // 2 + 1):
if s[i] != s[-i - 1]:
return False
return True
w, h = mi()
ans = 0
for i in range(2, w * 2 // 2 + 1, 2):
for j in range(2, h * 2 // 2 + 1, 2):
ans += (w - i + 1) * (h - j + 1)
print(ans)
``` | instruction | 0 | 37,970 | 23 | 75,940 |
Yes | output | 1 | 37,970 | 23 | 75,941 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have two positive integers w and h. Your task is to count the number of rhombi which have the following properties:
* Have positive area.
* With vertices at integer points.
* All vertices of the rhombi are located inside or on the border of the rectangle with vertices at points (0, 0), (w, 0), (w, h), (0, h). In other words, for all vertices (xi, yi) of the rhombus the following conditions should fulfill: 0 β€ xi β€ w and 0 β€ yi β€ h.
* Its diagonals are parallel to the axis.
Count the number of such rhombi.
Let us remind you that a rhombus is a quadrilateral whose four sides all have the same length.
Input
The first line contains two integers w and h (1 β€ w, h β€ 4000) β the rectangle's sizes.
Output
Print a single number β the number of sought rhombi.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout streams or the %I64d specifier.
Examples
Input
2 2
Output
1
Input
1 2
Output
0
Note
In the first example there exists only one such rhombus. Its vertices are located at points (1, 0), (2, 1), (1, 2), (0, 1).
Submitted Solution:
```
"""
Template written to be used by Python Programmers.
Use at your own risk!!!!
Owned by adi0311(rating - 5 star at CodeChef and Specialist at Codeforces).
"""
import sys
from functools import lru_cache, cmp_to_key
from heapq import merge, heapify, heappop, heappush, nlargest, nsmallest, _heapify_max, _heapreplace_max
from math import ceil, floor, gcd, fabs, factorial, fmod, sqrt, inf, log
from collections import defaultdict as dd, deque, Counter as c
from itertools import combinations as comb, permutations as perm
from bisect import bisect_left as bl, bisect_right as br, bisect
from fractions import Fraction
# sys.setrecursionlimit(2*pow(10, 6))
# sys.stdin = open("input.txt", "r")
# sys.stdout = open("output.txt", "w")
mod = pow(10, 9) + 7
mod2 = 998244353
def data(): return sys.stdin.readline().strip()
def out(var): sys.stdout.write(str(var))
def outln(var): sys.stdout.write(str(var)+"\n")
def l(): return list(sp())
def sl(): return list(ssp())
def sp(): return map(int, data().split())
def ssp(): return map(str, data().split())
def l1d(n, val=0): return [val for i in range(n)]
def l2d(n, m, val=0): return [l1d(n, val) for j in range(m)]
w, h = sp()
answer = 0
t = 0
for i in range(33):
t += pow(2, i)
if w - t <= 0 or h - t <= 0:
break
answer += (w - t) * (h - t)
outln(answer)
``` | instruction | 0 | 37,971 | 23 | 75,942 |
No | output | 1 | 37,971 | 23 | 75,943 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have two positive integers w and h. Your task is to count the number of rhombi which have the following properties:
* Have positive area.
* With vertices at integer points.
* All vertices of the rhombi are located inside or on the border of the rectangle with vertices at points (0, 0), (w, 0), (w, h), (0, h). In other words, for all vertices (xi, yi) of the rhombus the following conditions should fulfill: 0 β€ xi β€ w and 0 β€ yi β€ h.
* Its diagonals are parallel to the axis.
Count the number of such rhombi.
Let us remind you that a rhombus is a quadrilateral whose four sides all have the same length.
Input
The first line contains two integers w and h (1 β€ w, h β€ 4000) β the rectangle's sizes.
Output
Print a single number β the number of sought rhombi.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout streams or the %I64d specifier.
Examples
Input
2 2
Output
1
Input
1 2
Output
0
Note
In the first example there exists only one such rhombus. Its vertices are located at points (1, 0), (2, 1), (1, 2), (0, 1).
Submitted Solution:
```
try:
w,h=list(map(int,input().split(" ")))
if w<2 or h<2:
print(0)
else:
if w!=2 and h!=2:
s=(w-1)*(h-1)
else:
k=max(w,h)
s=k-1
print(s)
except:
pass
``` | instruction | 0 | 37,972 | 23 | 75,944 |
No | output | 1 | 37,972 | 23 | 75,945 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have two positive integers w and h. Your task is to count the number of rhombi which have the following properties:
* Have positive area.
* With vertices at integer points.
* All vertices of the rhombi are located inside or on the border of the rectangle with vertices at points (0, 0), (w, 0), (w, h), (0, h). In other words, for all vertices (xi, yi) of the rhombus the following conditions should fulfill: 0 β€ xi β€ w and 0 β€ yi β€ h.
* Its diagonals are parallel to the axis.
Count the number of such rhombi.
Let us remind you that a rhombus is a quadrilateral whose four sides all have the same length.
Input
The first line contains two integers w and h (1 β€ w, h β€ 4000) β the rectangle's sizes.
Output
Print a single number β the number of sought rhombi.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout streams or the %I64d specifier.
Examples
Input
2 2
Output
1
Input
1 2
Output
0
Note
In the first example there exists only one such rhombus. Its vertices are located at points (1, 0), (2, 1), (1, 2), (0, 1).
Submitted Solution:
```
m,n=map(int,input().split())
s=0
for i in range(1,min(m,n)):
s+=(m-1)*(n-1)
print(s)
``` | instruction | 0 | 37,973 | 23 | 75,946 |
No | output | 1 | 37,973 | 23 | 75,947 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have two positive integers w and h. Your task is to count the number of rhombi which have the following properties:
* Have positive area.
* With vertices at integer points.
* All vertices of the rhombi are located inside or on the border of the rectangle with vertices at points (0, 0), (w, 0), (w, h), (0, h). In other words, for all vertices (xi, yi) of the rhombus the following conditions should fulfill: 0 β€ xi β€ w and 0 β€ yi β€ h.
* Its diagonals are parallel to the axis.
Count the number of such rhombi.
Let us remind you that a rhombus is a quadrilateral whose four sides all have the same length.
Input
The first line contains two integers w and h (1 β€ w, h β€ 4000) β the rectangle's sizes.
Output
Print a single number β the number of sought rhombi.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use cin, cout streams or the %I64d specifier.
Examples
Input
2 2
Output
1
Input
1 2
Output
0
Note
In the first example there exists only one such rhombus. Its vertices are located at points (1, 0), (2, 1), (1, 2), (0, 1).
Submitted Solution:
```
w,h=map(int,input().split())
x=h//2
y=w//2
x=(x*(x+1))//2
y=(y*(y+1))//2
if(w%2==0):
e=h//2-1
y+=((e)*(e+1))//2
else:
y*=2
if(h%2==0):
e=h//2-1
x+=((e)*(e+1))//2
else:
x*=2
print(x*y)
``` | instruction | 0 | 37,974 | 23 | 75,948 |
No | output | 1 | 37,974 | 23 | 75,949 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A country called Flatland is an infinite two-dimensional plane. Flatland has n cities, each of them is a point on the plane.
Flatland is ruled by king Circle IV. Circle IV has 9 sons. He wants to give each of his sons part of Flatland to rule. For that, he wants to draw four distinct straight lines, such that two of them are parallel to the Ox axis, and two others are parallel to the Oy axis. At that, no straight line can go through any city. Thus, Flatland will be divided into 9 parts, and each son will be given exactly one of these parts. Circle IV thought a little, evaluated his sons' obedience and decided that the i-th son should get the part of Flatland that has exactly ai cities.
Help Circle find such four straight lines that if we divide Flatland into 9 parts by these lines, the resulting parts can be given to the sons so that son number i got the part of Flatland which contains ai cities.
Input
The first line contains integer n (9 β€ n β€ 105) β the number of cities in Flatland. Next n lines each contain two space-separated integers: xi, yi ( - 109 β€ xi, yi β€ 109) β the coordinates of the i-th city. No two cities are located at the same point. The last line contains nine space-separated integers: <image>.
Output
If there is no solution, print a single integer -1.
Otherwise, print in the first line two distinct real space-separated numbers: x1, x2 β the abscissas of the straight lines that are parallel to the Oy axis. And in the second line print two distinct real space-separated numbers: y1, y2 β the ordinates of the straight lines, parallel to the Ox. If there are multiple solutions, print any of them.
When the answer is being checked, a city is considered to lie on a straight line, if the distance between the city and the line doesn't exceed 10 - 6. Two straight lines are considered the same if the distance between them doesn't exceed 10 - 6.
Examples
Input
9
1 1
1 2
1 3
2 1
2 2
2 3
3 1
3 2
3 3
1 1 1 1 1 1 1 1 1
Output
1.5000000000 2.5000000000
1.5000000000 2.5000000000
Input
15
4 4
-1 -3
1 5
3 -4
-4 4
-1 1
3 -3
-4 -5
-3 3
3 2
4 1
-4 2
-2 -5
-3 4
-1 4
2 1 2 1 2 1 3 2 1
Output
-3.5000000000 2.0000000000
3.5000000000 -1.0000000000
Input
10
-2 10
6 0
-16 -6
-4 13
-4 -2
-17 -10
9 15
18 16
-5 2
10 -5
2 1 1 1 1 1 1 1 1
Output
-1
Note
The solution for the first sample test is shown below:
<image>
The solution for the second sample test is shown below:
<image>
There is no solution for the third sample test.
Submitted Solution:
```
n=int(input())
x=set()
y=set()
a=dict()
for l in range(n):
m=list(map(int,input().split()))
if m[0] not in a:
a[m[0]]=[m[1]]
x.add(m[0]+1)
else:
if min(a[m[0]])>m[1]:
y.add(m[1]+1)
a[m[0]].append(m[1])
elif max(a[m[0]])<m[1]:
y.add(m[1])
a[m[0]].append(m[1])
else:
y.add(m[1]+1)
y.add(m[1])
a[m[0]].append(m[1])
x.discard(max(list(x)))
print(len(y)+len(x))
for h in (y):
print('y',h)
for u in (x):
print('x',u)
``` | instruction | 0 | 37,991 | 23 | 75,982 |
No | output | 1 | 37,991 | 23 | 75,983 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's assume that we are given a matrix b of size x Γ y, let's determine the operation of mirroring matrix b. The mirroring of matrix b is a 2x Γ y matrix c which has the following properties:
* the upper half of matrix c (rows with numbers from 1 to x) exactly matches b;
* the lower half of matrix c (rows with numbers from x + 1 to 2x) is symmetric to the upper one; the symmetry line is the line that separates two halves (the line that goes in the middle, between rows x and x + 1).
Sereja has an n Γ m matrix a. He wants to find such matrix b, that it can be transformed into matrix a, if we'll perform on it several (possibly zero) mirrorings. What minimum number of rows can such matrix contain?
Input
The first line contains two integers, n and m (1 β€ n, m β€ 100). Each of the next n lines contains m integers β the elements of matrix a. The i-th line contains integers ai1, ai2, ..., aim (0 β€ aij β€ 1) β the i-th row of the matrix a.
Output
In the single line, print the answer to the problem β the minimum number of rows of matrix b.
Examples
Input
4 3
0 0 1
1 1 0
1 1 0
0 0 1
Output
2
Input
3 3
0 0 0
0 0 0
0 0 0
Output
3
Input
8 1
0
1
1
0
0
1
1
0
Output
2
Note
In the first test sample the answer is a 2 Γ 3 matrix b:
001
110
If we perform a mirroring operation with this matrix, we get the matrix a that is given in the input:
001
110
110
001
| instruction | 0 | 38,017 | 23 | 76,034 |
Tags: implementation
Correct Solution:
```
n, m = map(int, input().split())
a = [list(map(int, input().split())) for _ in range(n)]
def pol(x, y):
if y % 2 != 0:
return False
l, r = 0, y - 1
while l < r:
if a[l][x] != a[r][x]:
return False
l += 1
r -= 1
return True
result = 1
for i in range(m):
j = n
while pol(i, j):
j //= 2
result = max(result, j)
print(result)
``` | output | 1 | 38,017 | 23 | 76,035 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's assume that we are given a matrix b of size x Γ y, let's determine the operation of mirroring matrix b. The mirroring of matrix b is a 2x Γ y matrix c which has the following properties:
* the upper half of matrix c (rows with numbers from 1 to x) exactly matches b;
* the lower half of matrix c (rows with numbers from x + 1 to 2x) is symmetric to the upper one; the symmetry line is the line that separates two halves (the line that goes in the middle, between rows x and x + 1).
Sereja has an n Γ m matrix a. He wants to find such matrix b, that it can be transformed into matrix a, if we'll perform on it several (possibly zero) mirrorings. What minimum number of rows can such matrix contain?
Input
The first line contains two integers, n and m (1 β€ n, m β€ 100). Each of the next n lines contains m integers β the elements of matrix a. The i-th line contains integers ai1, ai2, ..., aim (0 β€ aij β€ 1) β the i-th row of the matrix a.
Output
In the single line, print the answer to the problem β the minimum number of rows of matrix b.
Examples
Input
4 3
0 0 1
1 1 0
1 1 0
0 0 1
Output
2
Input
3 3
0 0 0
0 0 0
0 0 0
Output
3
Input
8 1
0
1
1
0
0
1
1
0
Output
2
Note
In the first test sample the answer is a 2 Γ 3 matrix b:
001
110
If we perform a mirroring operation with this matrix, we get the matrix a that is given in the input:
001
110
110
001
| instruction | 0 | 38,018 | 23 | 76,036 |
Tags: implementation
Correct Solution:
```
mtxSize = list(map(int, input().split()))
rows = mtxSize[0]
inArray = []
for i in range(rows):
inputs = list(map(int, input().split()))
inArray.append(inputs)
bRows = rows
revArray = inArray[::-1]
while(rows%2 == 0):
if inArray == revArray:
rows //= 2
bRows = rows
del(inArray[rows:])
del(revArray[:rows])
else:
break
print(bRows)
``` | output | 1 | 38,018 | 23 | 76,037 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's assume that we are given a matrix b of size x Γ y, let's determine the operation of mirroring matrix b. The mirroring of matrix b is a 2x Γ y matrix c which has the following properties:
* the upper half of matrix c (rows with numbers from 1 to x) exactly matches b;
* the lower half of matrix c (rows with numbers from x + 1 to 2x) is symmetric to the upper one; the symmetry line is the line that separates two halves (the line that goes in the middle, between rows x and x + 1).
Sereja has an n Γ m matrix a. He wants to find such matrix b, that it can be transformed into matrix a, if we'll perform on it several (possibly zero) mirrorings. What minimum number of rows can such matrix contain?
Input
The first line contains two integers, n and m (1 β€ n, m β€ 100). Each of the next n lines contains m integers β the elements of matrix a. The i-th line contains integers ai1, ai2, ..., aim (0 β€ aij β€ 1) β the i-th row of the matrix a.
Output
In the single line, print the answer to the problem β the minimum number of rows of matrix b.
Examples
Input
4 3
0 0 1
1 1 0
1 1 0
0 0 1
Output
2
Input
3 3
0 0 0
0 0 0
0 0 0
Output
3
Input
8 1
0
1
1
0
0
1
1
0
Output
2
Note
In the first test sample the answer is a 2 Γ 3 matrix b:
001
110
If we perform a mirroring operation with this matrix, we get the matrix a that is given in the input:
001
110
110
001
| instruction | 0 | 38,019 | 23 | 76,038 |
Tags: implementation
Correct Solution:
```
n, m = map(int, input().split())
a = []
for i in range(n):
a.append(list(map(int, input().split())))
while n and n % 2 == 0 and a[:n//2] == a[n-1:n//2-1:-1]:
n //= 2
print(n)
``` | output | 1 | 38,019 | 23 | 76,039 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's assume that we are given a matrix b of size x Γ y, let's determine the operation of mirroring matrix b. The mirroring of matrix b is a 2x Γ y matrix c which has the following properties:
* the upper half of matrix c (rows with numbers from 1 to x) exactly matches b;
* the lower half of matrix c (rows with numbers from x + 1 to 2x) is symmetric to the upper one; the symmetry line is the line that separates two halves (the line that goes in the middle, between rows x and x + 1).
Sereja has an n Γ m matrix a. He wants to find such matrix b, that it can be transformed into matrix a, if we'll perform on it several (possibly zero) mirrorings. What minimum number of rows can such matrix contain?
Input
The first line contains two integers, n and m (1 β€ n, m β€ 100). Each of the next n lines contains m integers β the elements of matrix a. The i-th line contains integers ai1, ai2, ..., aim (0 β€ aij β€ 1) β the i-th row of the matrix a.
Output
In the single line, print the answer to the problem β the minimum number of rows of matrix b.
Examples
Input
4 3
0 0 1
1 1 0
1 1 0
0 0 1
Output
2
Input
3 3
0 0 0
0 0 0
0 0 0
Output
3
Input
8 1
0
1
1
0
0
1
1
0
Output
2
Note
In the first test sample the answer is a 2 Γ 3 matrix b:
001
110
If we perform a mirroring operation with this matrix, we get the matrix a that is given in the input:
001
110
110
001
| instruction | 0 | 38,020 | 23 | 76,040 |
Tags: implementation
Correct Solution:
```
n,m=map(int,input().split())
l=[]
for i in range(n):l.append("".join(list(map(str,input().split()))))
if n&1:print(n)
else:
while 1:
if l[:n//2]!=l[n//2:n][::-1]:print(n);break
n//=2
``` | output | 1 | 38,020 | 23 | 76,041 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's assume that we are given a matrix b of size x Γ y, let's determine the operation of mirroring matrix b. The mirroring of matrix b is a 2x Γ y matrix c which has the following properties:
* the upper half of matrix c (rows with numbers from 1 to x) exactly matches b;
* the lower half of matrix c (rows with numbers from x + 1 to 2x) is symmetric to the upper one; the symmetry line is the line that separates two halves (the line that goes in the middle, between rows x and x + 1).
Sereja has an n Γ m matrix a. He wants to find such matrix b, that it can be transformed into matrix a, if we'll perform on it several (possibly zero) mirrorings. What minimum number of rows can such matrix contain?
Input
The first line contains two integers, n and m (1 β€ n, m β€ 100). Each of the next n lines contains m integers β the elements of matrix a. The i-th line contains integers ai1, ai2, ..., aim (0 β€ aij β€ 1) β the i-th row of the matrix a.
Output
In the single line, print the answer to the problem β the minimum number of rows of matrix b.
Examples
Input
4 3
0 0 1
1 1 0
1 1 0
0 0 1
Output
2
Input
3 3
0 0 0
0 0 0
0 0 0
Output
3
Input
8 1
0
1
1
0
0
1
1
0
Output
2
Note
In the first test sample the answer is a 2 Γ 3 matrix b:
001
110
If we perform a mirroring operation with this matrix, we get the matrix a that is given in the input:
001
110
110
001
| instruction | 0 | 38,021 | 23 | 76,042 |
Tags: implementation
Correct Solution:
```
n, m = map(int, input().split())
mat = [input() for _ in range(n)]
while n > 1 and n % 2 == 0:
if mat[:n] != list(reversed(mat[:n])):
break
n //= 2
if n == 1:
if len(set(mat)) > 1:
n = 2
break
print(n)
``` | output | 1 | 38,021 | 23 | 76,043 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's assume that we are given a matrix b of size x Γ y, let's determine the operation of mirroring matrix b. The mirroring of matrix b is a 2x Γ y matrix c which has the following properties:
* the upper half of matrix c (rows with numbers from 1 to x) exactly matches b;
* the lower half of matrix c (rows with numbers from x + 1 to 2x) is symmetric to the upper one; the symmetry line is the line that separates two halves (the line that goes in the middle, between rows x and x + 1).
Sereja has an n Γ m matrix a. He wants to find such matrix b, that it can be transformed into matrix a, if we'll perform on it several (possibly zero) mirrorings. What minimum number of rows can such matrix contain?
Input
The first line contains two integers, n and m (1 β€ n, m β€ 100). Each of the next n lines contains m integers β the elements of matrix a. The i-th line contains integers ai1, ai2, ..., aim (0 β€ aij β€ 1) β the i-th row of the matrix a.
Output
In the single line, print the answer to the problem β the minimum number of rows of matrix b.
Examples
Input
4 3
0 0 1
1 1 0
1 1 0
0 0 1
Output
2
Input
3 3
0 0 0
0 0 0
0 0 0
Output
3
Input
8 1
0
1
1
0
0
1
1
0
Output
2
Note
In the first test sample the answer is a 2 Γ 3 matrix b:
001
110
If we perform a mirroring operation with this matrix, we get the matrix a that is given in the input:
001
110
110
001
| instruction | 0 | 38,022 | 23 | 76,044 |
Tags: implementation
Correct Solution:
```
n, m = [int(i) for i in input().split()]
a = [input().split() for i in range(n)]
while n%2==0:
if a[:n//2] == a[n//2:n][::-1]:
n //= 2
else:
break
print(n)
``` | output | 1 | 38,022 | 23 | 76,045 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's assume that we are given a matrix b of size x Γ y, let's determine the operation of mirroring matrix b. The mirroring of matrix b is a 2x Γ y matrix c which has the following properties:
* the upper half of matrix c (rows with numbers from 1 to x) exactly matches b;
* the lower half of matrix c (rows with numbers from x + 1 to 2x) is symmetric to the upper one; the symmetry line is the line that separates two halves (the line that goes in the middle, between rows x and x + 1).
Sereja has an n Γ m matrix a. He wants to find such matrix b, that it can be transformed into matrix a, if we'll perform on it several (possibly zero) mirrorings. What minimum number of rows can such matrix contain?
Input
The first line contains two integers, n and m (1 β€ n, m β€ 100). Each of the next n lines contains m integers β the elements of matrix a. The i-th line contains integers ai1, ai2, ..., aim (0 β€ aij β€ 1) β the i-th row of the matrix a.
Output
In the single line, print the answer to the problem β the minimum number of rows of matrix b.
Examples
Input
4 3
0 0 1
1 1 0
1 1 0
0 0 1
Output
2
Input
3 3
0 0 0
0 0 0
0 0 0
Output
3
Input
8 1
0
1
1
0
0
1
1
0
Output
2
Note
In the first test sample the answer is a 2 Γ 3 matrix b:
001
110
If we perform a mirroring operation with this matrix, we get the matrix a that is given in the input:
001
110
110
001
| instruction | 0 | 38,023 | 23 | 76,046 |
Tags: implementation
Correct Solution:
```
n, m = map(int, input().split())
mat = [input() for _ in range(n)]
ans = n
while ans > 1 and ans % 2 == 0:
if mat[:ans] == list(reversed(mat[:ans])):
ans //= 2
else:
break
if ans == 1:
if len(set(mat)) > 1:
ans = 2
break
print(ans)
``` | output | 1 | 38,023 | 23 | 76,047 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's assume that we are given a matrix b of size x Γ y, let's determine the operation of mirroring matrix b. The mirroring of matrix b is a 2x Γ y matrix c which has the following properties:
* the upper half of matrix c (rows with numbers from 1 to x) exactly matches b;
* the lower half of matrix c (rows with numbers from x + 1 to 2x) is symmetric to the upper one; the symmetry line is the line that separates two halves (the line that goes in the middle, between rows x and x + 1).
Sereja has an n Γ m matrix a. He wants to find such matrix b, that it can be transformed into matrix a, if we'll perform on it several (possibly zero) mirrorings. What minimum number of rows can such matrix contain?
Input
The first line contains two integers, n and m (1 β€ n, m β€ 100). Each of the next n lines contains m integers β the elements of matrix a. The i-th line contains integers ai1, ai2, ..., aim (0 β€ aij β€ 1) β the i-th row of the matrix a.
Output
In the single line, print the answer to the problem β the minimum number of rows of matrix b.
Examples
Input
4 3
0 0 1
1 1 0
1 1 0
0 0 1
Output
2
Input
3 3
0 0 0
0 0 0
0 0 0
Output
3
Input
8 1
0
1
1
0
0
1
1
0
Output
2
Note
In the first test sample the answer is a 2 Γ 3 matrix b:
001
110
If we perform a mirroring operation with this matrix, we get the matrix a that is given in the input:
001
110
110
001
| instruction | 0 | 38,024 | 23 | 76,048 |
Tags: implementation
Correct Solution:
```
import sys
import math
from collections import defaultdict
import itertools
MAXNUM = math.inf
MINNUM = -1 * math.inf
def getInt():
return int(sys.stdin.readline().rstrip())
def getInts():
return map(int, sys.stdin.readline().rstrip().split(" "))
def getString():
return sys.stdin.readline().rstrip()
def printOutput(ans):
sys.stdout.write()
pass
def solve(grid):
if len(grid) % 2 == 1:
return len(grid)
x = len(grid)
while x % 2 == 0:
x //= 2
for k in range(x, len(grid) + 1):
seq = [i for i in range(k)]
cur = 0
total = 0
for line in grid:
# print(k, grid[cur], line)
if line == grid[seq[cur]]:
total += 1
cur += 1
if cur == len(seq):
seq = [i for i in reversed(seq)]
cur = 0
else:
break
if total == len(grid) and cur == 0:
return k
return len(grid)
def readinput():
n, m = getInts()
grid = []
for _ in range(n):
grid.append(getString())
print(solve(grid))
readinput()
``` | output | 1 | 38,024 | 23 | 76,049 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's assume that we are given a matrix b of size x Γ y, let's determine the operation of mirroring matrix b. The mirroring of matrix b is a 2x Γ y matrix c which has the following properties:
* the upper half of matrix c (rows with numbers from 1 to x) exactly matches b;
* the lower half of matrix c (rows with numbers from x + 1 to 2x) is symmetric to the upper one; the symmetry line is the line that separates two halves (the line that goes in the middle, between rows x and x + 1).
Sereja has an n Γ m matrix a. He wants to find such matrix b, that it can be transformed into matrix a, if we'll perform on it several (possibly zero) mirrorings. What minimum number of rows can such matrix contain?
Input
The first line contains two integers, n and m (1 β€ n, m β€ 100). Each of the next n lines contains m integers β the elements of matrix a. The i-th line contains integers ai1, ai2, ..., aim (0 β€ aij β€ 1) β the i-th row of the matrix a.
Output
In the single line, print the answer to the problem β the minimum number of rows of matrix b.
Examples
Input
4 3
0 0 1
1 1 0
1 1 0
0 0 1
Output
2
Input
3 3
0 0 0
0 0 0
0 0 0
Output
3
Input
8 1
0
1
1
0
0
1
1
0
Output
2
Note
In the first test sample the answer is a 2 Γ 3 matrix b:
001
110
If we perform a mirroring operation with this matrix, we get the matrix a that is given in the input:
001
110
110
001
Submitted Solution:
```
def f(c):
n = len(c)
if (n % 2 == 1):
return n
for i in range(n):
if c[i] != c[n - i - 1]:
return n
return f(c[:n // 2])
n, m = map(int, input().split())
c = [input() for i in range(n)]
print(f(c))
``` | instruction | 0 | 38,025 | 23 | 76,050 |
Yes | output | 1 | 38,025 | 23 | 76,051 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's assume that we are given a matrix b of size x Γ y, let's determine the operation of mirroring matrix b. The mirroring of matrix b is a 2x Γ y matrix c which has the following properties:
* the upper half of matrix c (rows with numbers from 1 to x) exactly matches b;
* the lower half of matrix c (rows with numbers from x + 1 to 2x) is symmetric to the upper one; the symmetry line is the line that separates two halves (the line that goes in the middle, between rows x and x + 1).
Sereja has an n Γ m matrix a. He wants to find such matrix b, that it can be transformed into matrix a, if we'll perform on it several (possibly zero) mirrorings. What minimum number of rows can such matrix contain?
Input
The first line contains two integers, n and m (1 β€ n, m β€ 100). Each of the next n lines contains m integers β the elements of matrix a. The i-th line contains integers ai1, ai2, ..., aim (0 β€ aij β€ 1) β the i-th row of the matrix a.
Output
In the single line, print the answer to the problem β the minimum number of rows of matrix b.
Examples
Input
4 3
0 0 1
1 1 0
1 1 0
0 0 1
Output
2
Input
3 3
0 0 0
0 0 0
0 0 0
Output
3
Input
8 1
0
1
1
0
0
1
1
0
Output
2
Note
In the first test sample the answer is a 2 Γ 3 matrix b:
001
110
If we perform a mirroring operation with this matrix, we get the matrix a that is given in the input:
001
110
110
001
Submitted Solution:
```
n, m = map(int, input().split())
a = []
for i in range(n):
a.append(list(map(int, input().split())))
def ok(ar1, ar2):
l = len(ar1)
for i in range(l):
if ar1[i] != ar2[l-i-1]:
return False
return True
def process(ar):
if len(ar)%2 == 1:
return len(ar)
if ok(ar[:len(ar)//2], ar[len(ar)//2:]):
return process(ar[:len(ar)//2])
else:
return len(ar)
s = process(a)
print(s)
``` | instruction | 0 | 38,026 | 23 | 76,052 |
Yes | output | 1 | 38,026 | 23 | 76,053 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's assume that we are given a matrix b of size x Γ y, let's determine the operation of mirroring matrix b. The mirroring of matrix b is a 2x Γ y matrix c which has the following properties:
* the upper half of matrix c (rows with numbers from 1 to x) exactly matches b;
* the lower half of matrix c (rows with numbers from x + 1 to 2x) is symmetric to the upper one; the symmetry line is the line that separates two halves (the line that goes in the middle, between rows x and x + 1).
Sereja has an n Γ m matrix a. He wants to find such matrix b, that it can be transformed into matrix a, if we'll perform on it several (possibly zero) mirrorings. What minimum number of rows can such matrix contain?
Input
The first line contains two integers, n and m (1 β€ n, m β€ 100). Each of the next n lines contains m integers β the elements of matrix a. The i-th line contains integers ai1, ai2, ..., aim (0 β€ aij β€ 1) β the i-th row of the matrix a.
Output
In the single line, print the answer to the problem β the minimum number of rows of matrix b.
Examples
Input
4 3
0 0 1
1 1 0
1 1 0
0 0 1
Output
2
Input
3 3
0 0 0
0 0 0
0 0 0
Output
3
Input
8 1
0
1
1
0
0
1
1
0
Output
2
Note
In the first test sample the answer is a 2 Γ 3 matrix b:
001
110
If we perform a mirroring operation with this matrix, we get the matrix a that is given in the input:
001
110
110
001
Submitted Solution:
```
mtxSize = list(map(int, input().split()))
rows = mtxSize[0]
inArray = []
for i in range(rows):
inputs = list(map(int, input().split()))
inArray.append(inputs)
revArray = inArray[::-1]
while(rows%2 == 0):
if inArray == revArray:
rows //= 2
del(inArray[rows:])
del(revArray[:rows])
else:
break
print(rows)
``` | instruction | 0 | 38,027 | 23 | 76,054 |
Yes | output | 1 | 38,027 | 23 | 76,055 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's assume that we are given a matrix b of size x Γ y, let's determine the operation of mirroring matrix b. The mirroring of matrix b is a 2x Γ y matrix c which has the following properties:
* the upper half of matrix c (rows with numbers from 1 to x) exactly matches b;
* the lower half of matrix c (rows with numbers from x + 1 to 2x) is symmetric to the upper one; the symmetry line is the line that separates two halves (the line that goes in the middle, between rows x and x + 1).
Sereja has an n Γ m matrix a. He wants to find such matrix b, that it can be transformed into matrix a, if we'll perform on it several (possibly zero) mirrorings. What minimum number of rows can such matrix contain?
Input
The first line contains two integers, n and m (1 β€ n, m β€ 100). Each of the next n lines contains m integers β the elements of matrix a. The i-th line contains integers ai1, ai2, ..., aim (0 β€ aij β€ 1) β the i-th row of the matrix a.
Output
In the single line, print the answer to the problem β the minimum number of rows of matrix b.
Examples
Input
4 3
0 0 1
1 1 0
1 1 0
0 0 1
Output
2
Input
3 3
0 0 0
0 0 0
0 0 0
Output
3
Input
8 1
0
1
1
0
0
1
1
0
Output
2
Note
In the first test sample the answer is a 2 Γ 3 matrix b:
001
110
If we perform a mirroring operation with this matrix, we get the matrix a that is given in the input:
001
110
110
001
Submitted Solution:
```
n, m = [int(x) for x in input().split()]
a = [input() for i in range(n)]
k = 0
while (True):
if n%2: break
br = False
for i in range(n//2):
if a[i] != a[n-i-1]:
br = True
break
if br: break
k += 1
n //= 2
print(n)
``` | instruction | 0 | 38,028 | 23 | 76,056 |
Yes | output | 1 | 38,028 | 23 | 76,057 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's assume that we are given a matrix b of size x Γ y, let's determine the operation of mirroring matrix b. The mirroring of matrix b is a 2x Γ y matrix c which has the following properties:
* the upper half of matrix c (rows with numbers from 1 to x) exactly matches b;
* the lower half of matrix c (rows with numbers from x + 1 to 2x) is symmetric to the upper one; the symmetry line is the line that separates two halves (the line that goes in the middle, between rows x and x + 1).
Sereja has an n Γ m matrix a. He wants to find such matrix b, that it can be transformed into matrix a, if we'll perform on it several (possibly zero) mirrorings. What minimum number of rows can such matrix contain?
Input
The first line contains two integers, n and m (1 β€ n, m β€ 100). Each of the next n lines contains m integers β the elements of matrix a. The i-th line contains integers ai1, ai2, ..., aim (0 β€ aij β€ 1) β the i-th row of the matrix a.
Output
In the single line, print the answer to the problem β the minimum number of rows of matrix b.
Examples
Input
4 3
0 0 1
1 1 0
1 1 0
0 0 1
Output
2
Input
3 3
0 0 0
0 0 0
0 0 0
Output
3
Input
8 1
0
1
1
0
0
1
1
0
Output
2
Note
In the first test sample the answer is a 2 Γ 3 matrix b:
001
110
If we perform a mirroring operation with this matrix, we get the matrix a that is given in the input:
001
110
110
001
Submitted Solution:
```
mtxSize = list(map(int, input().split()))
rows = mtxSize[0]
inArray = []
for i in range(rows):
inputs = list(map(int, input().split()))
inArray.append(inputs)
bRows = 0
same = 1
if rows%2 == 0:
for i in range(1,rows):
if inArray[i] == inArray[0]:
same += 1
bRows = rows // same
else:
for i in range(2, rows):
if rows%i == 0:
notPrime = rows
for i in range(1,rows):
if inArray[i] == inArray[0]:
same += 1
bRows = rows // same
break
else:
bRows = rows
print(bRows)
``` | instruction | 0 | 38,029 | 23 | 76,058 |
No | output | 1 | 38,029 | 23 | 76,059 |
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