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.
The Squareland national forest is divided into equal 1 Γ 1 square plots aligned with north-south and east-west directions. Each plot can be uniquely described by integer Cartesian coordinates (x, y) of its south-west corner.
Three friends, Alice, Bob, and Charlie are going to buy three distinct plots of land A, B, C in the forest. Initially, all plots in the forest (including the plots A, B, C) are covered by trees. The friends want to visit each other, so they want to clean some of the plots from trees. After cleaning, one should be able to reach any of the plots A, B, C from any other one of those by moving through adjacent cleared plots. Two plots are adjacent if they share a side.
<image> For example, A=(0,0), B=(1,1), C=(2,2). The minimal number of plots to be cleared is 5. One of the ways to do it is shown with the gray color.
Of course, the friends don't want to strain too much. Help them find out the smallest number of plots they need to clean from trees.
Input
The first line contains two integers x_A and y_A β coordinates of the plot A (0 β€ x_A, y_A β€ 1000). The following two lines describe coordinates (x_B, y_B) and (x_C, y_C) of plots B and C respectively in the same format (0 β€ x_B, y_B, x_C, y_C β€ 1000). It is guaranteed that all three plots are distinct.
Output
On the first line print a single integer k β the smallest number of plots needed to be cleaned from trees. The following k lines should contain coordinates of all plots needed to be cleaned. All k plots should be distinct. You can output the plots in any order.
If there are multiple solutions, print any of them.
Examples
Input
0 0
1 1
2 2
Output
5
0 0
1 0
1 1
1 2
2 2
Input
0 0
2 0
1 1
Output
4
0 0
1 0
1 1
2 0
Note
The first example is shown on the picture in the legend.
The second example is illustrated with the following image:
<image> | instruction | 0 | 19,456 | 23 | 38,912 |
Tags: implementation, math
Correct Solution:
```
def ii():
return int(input())
def mi():
return map(int, input().split())
def li():
return list(mi())
# A. Connect Three
a = [tuple(mi()) for i in range(3)]
a.sort()
up1 = a[1][1] >= a[0][1]
up2 = a[2][1] >= a[0][1]
ans = {a[0]}
x, y = a[0]
if up1 and up2:
while y < min(a[1][1], a[2][1]):
y += 1
ans.add((x, y))
while x < a[2][0]:
x += 1
ans.add((x, y))
hx, hy = a[2] if a[2][1] > a[1][1] else a[1]
while hy > y:
ans.add((hx, hy))
hy -= 1
else:
dn1 = a[1][1] <= a[0][1]
dn2 = a[2][1] <= a[0][1]
ans = {a[0]}
x, y = a[0]
if dn1 and dn2:
while y > max(a[1][1], a[2][1]):
y -= 1
ans.add((x, y))
while x < a[2][0]:
x += 1
ans.add((x, y))
lx, ly = a[2] if a[2][1] < a[1][1] else a[1]
while ly < y:
ans.add((lx, ly))
ly += 1
else:
x, y = a[0]
ans = {a[0]}
while x < a[2][0]:
x += 1
ans.add((x, y))
dy = 1 if a[1][1] <= a[0][1] else -1
xx, yy = a[1]
while yy != a[0][1]:
ans.add((xx, yy))
yy += dy
dy = 1 if a[2][1] <= a[0][1] else -1
xx, yy = a[2]
while yy != a[0][1]:
ans.add((xx, yy))
yy += dy
ans = sorted(ans)
print(len(ans))
print('\n'.join('%d %d' % (x, y) for x, y in ans))
``` | output | 1 | 19,456 | 23 | 38,913 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Squareland national forest is divided into equal 1 Γ 1 square plots aligned with north-south and east-west directions. Each plot can be uniquely described by integer Cartesian coordinates (x, y) of its south-west corner.
Three friends, Alice, Bob, and Charlie are going to buy three distinct plots of land A, B, C in the forest. Initially, all plots in the forest (including the plots A, B, C) are covered by trees. The friends want to visit each other, so they want to clean some of the plots from trees. After cleaning, one should be able to reach any of the plots A, B, C from any other one of those by moving through adjacent cleared plots. Two plots are adjacent if they share a side.
<image> For example, A=(0,0), B=(1,1), C=(2,2). The minimal number of plots to be cleared is 5. One of the ways to do it is shown with the gray color.
Of course, the friends don't want to strain too much. Help them find out the smallest number of plots they need to clean from trees.
Input
The first line contains two integers x_A and y_A β coordinates of the plot A (0 β€ x_A, y_A β€ 1000). The following two lines describe coordinates (x_B, y_B) and (x_C, y_C) of plots B and C respectively in the same format (0 β€ x_B, y_B, x_C, y_C β€ 1000). It is guaranteed that all three plots are distinct.
Output
On the first line print a single integer k β the smallest number of plots needed to be cleaned from trees. The following k lines should contain coordinates of all plots needed to be cleaned. All k plots should be distinct. You can output the plots in any order.
If there are multiple solutions, print any of them.
Examples
Input
0 0
1 1
2 2
Output
5
0 0
1 0
1 1
1 2
2 2
Input
0 0
2 0
1 1
Output
4
0 0
1 0
1 1
2 0
Note
The first example is shown on the picture in the legend.
The second example is illustrated with the following image:
<image> | instruction | 0 | 19,457 | 23 | 38,914 |
Tags: implementation, math
Correct Solution:
```
a=list(map(int,input().split()))
b=list(map(int,input().split()))
c=list(map(int,input().split()))
a, b, c = sorted([a,b,c])
ans = []
for i in range(min(a[1],b[1],c[1]),max(a[1],b[1],c[1])+1):
ans.append((b[0],i))
for i in range(a[0],b[0]+1):
ans.append((i,a[1]))
for i in range(b[0],c[0]+1):
ans.append((i,c[1]))
ans=set(ans)
print(len(ans))
for i in ans:
print(*i)
``` | output | 1 | 19,457 | 23 | 38,915 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Squareland national forest is divided into equal 1 Γ 1 square plots aligned with north-south and east-west directions. Each plot can be uniquely described by integer Cartesian coordinates (x, y) of its south-west corner.
Three friends, Alice, Bob, and Charlie are going to buy three distinct plots of land A, B, C in the forest. Initially, all plots in the forest (including the plots A, B, C) are covered by trees. The friends want to visit each other, so they want to clean some of the plots from trees. After cleaning, one should be able to reach any of the plots A, B, C from any other one of those by moving through adjacent cleared plots. Two plots are adjacent if they share a side.
<image> For example, A=(0,0), B=(1,1), C=(2,2). The minimal number of plots to be cleared is 5. One of the ways to do it is shown with the gray color.
Of course, the friends don't want to strain too much. Help them find out the smallest number of plots they need to clean from trees.
Input
The first line contains two integers x_A and y_A β coordinates of the plot A (0 β€ x_A, y_A β€ 1000). The following two lines describe coordinates (x_B, y_B) and (x_C, y_C) of plots B and C respectively in the same format (0 β€ x_B, y_B, x_C, y_C β€ 1000). It is guaranteed that all three plots are distinct.
Output
On the first line print a single integer k β the smallest number of plots needed to be cleaned from trees. The following k lines should contain coordinates of all plots needed to be cleaned. All k plots should be distinct. You can output the plots in any order.
If there are multiple solutions, print any of them.
Examples
Input
0 0
1 1
2 2
Output
5
0 0
1 0
1 1
1 2
2 2
Input
0 0
2 0
1 1
Output
4
0 0
1 0
1 1
2 0
Note
The first example is shown on the picture in the legend.
The second example is illustrated with the following image:
<image> | instruction | 0 | 19,458 | 23 | 38,916 |
Tags: implementation, math
Correct Solution:
```
xa, ya = map(int, input().split())
xb, yb = map(int, input().split())
xc, yc = map(int, input().split())
xs = [xa, xb, xc]
xs.sort()
ys = [ya, yb, yc]
ys.sort()
mx, my = xs[1], ys[1]
field = [[False]*1001 for _ in range(1001)]
for sx, sy in [(xa, ya), (xb, yb), (xc, yc)]:
for x in range(min(sx, mx), max(sx, mx)+1):
field[x][sy] = True
for y in range(min(sy, my), max(sy, my)+1):
field[mx][y] = True
ans = []
for x in range(1001):
for y in range(1001):
if field[x][y]:
ans.append((x, y))
print(len(ans))
for x, y in ans:
print(x, y)
``` | output | 1 | 19,458 | 23 | 38,917 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Squareland national forest is divided into equal 1 Γ 1 square plots aligned with north-south and east-west directions. Each plot can be uniquely described by integer Cartesian coordinates (x, y) of its south-west corner.
Three friends, Alice, Bob, and Charlie are going to buy three distinct plots of land A, B, C in the forest. Initially, all plots in the forest (including the plots A, B, C) are covered by trees. The friends want to visit each other, so they want to clean some of the plots from trees. After cleaning, one should be able to reach any of the plots A, B, C from any other one of those by moving through adjacent cleared plots. Two plots are adjacent if they share a side.
<image> For example, A=(0,0), B=(1,1), C=(2,2). The minimal number of plots to be cleared is 5. One of the ways to do it is shown with the gray color.
Of course, the friends don't want to strain too much. Help them find out the smallest number of plots they need to clean from trees.
Input
The first line contains two integers x_A and y_A β coordinates of the plot A (0 β€ x_A, y_A β€ 1000). The following two lines describe coordinates (x_B, y_B) and (x_C, y_C) of plots B and C respectively in the same format (0 β€ x_B, y_B, x_C, y_C β€ 1000). It is guaranteed that all three plots are distinct.
Output
On the first line print a single integer k β the smallest number of plots needed to be cleaned from trees. The following k lines should contain coordinates of all plots needed to be cleaned. All k plots should be distinct. You can output the plots in any order.
If there are multiple solutions, print any of them.
Examples
Input
0 0
1 1
2 2
Output
5
0 0
1 0
1 1
1 2
2 2
Input
0 0
2 0
1 1
Output
4
0 0
1 0
1 1
2 0
Note
The first example is shown on the picture in the legend.
The second example is illustrated with the following image:
<image> | instruction | 0 | 19,459 | 23 | 38,918 |
Tags: implementation, math
Correct Solution:
```
def doWay(x, y, x1, y1, x2, y2):
global answer
while x < x1 and x < x2:
x += 1
answer.add((x, y))
while y < y1 and y < y2:
y += 1
answer.add((x, y))
while x > x1 and x > x2:
x -= 1
answer.add((x, y))
while y > y1 and y > y2:
y -= 1
answer.add((x, y))
xy = list()
xy.append(tuple(map(int, input().split())))
xy.append(tuple(map(int, input().split())))
xy.append(tuple(map(int, input().split())))
answer = set(xy)
doWay(xy[0][0], xy[0][1], xy[1][0], xy[1][1], xy[2][0], xy[2][1])
doWay(xy[1][0], xy[1][1], xy[0][0], xy[0][1], xy[2][0], xy[2][1])
doWay(xy[2][0], xy[2][1], xy[0][0], xy[0][1], xy[1][0], xy[1][1])
print(len(answer))
for x, y in answer:
print(x, y)
``` | output | 1 | 19,459 | 23 | 38,919 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Squareland national forest is divided into equal 1 Γ 1 square plots aligned with north-south and east-west directions. Each plot can be uniquely described by integer Cartesian coordinates (x, y) of its south-west corner.
Three friends, Alice, Bob, and Charlie are going to buy three distinct plots of land A, B, C in the forest. Initially, all plots in the forest (including the plots A, B, C) are covered by trees. The friends want to visit each other, so they want to clean some of the plots from trees. After cleaning, one should be able to reach any of the plots A, B, C from any other one of those by moving through adjacent cleared plots. Two plots are adjacent if they share a side.
<image> For example, A=(0,0), B=(1,1), C=(2,2). The minimal number of plots to be cleared is 5. One of the ways to do it is shown with the gray color.
Of course, the friends don't want to strain too much. Help them find out the smallest number of plots they need to clean from trees.
Input
The first line contains two integers x_A and y_A β coordinates of the plot A (0 β€ x_A, y_A β€ 1000). The following two lines describe coordinates (x_B, y_B) and (x_C, y_C) of plots B and C respectively in the same format (0 β€ x_B, y_B, x_C, y_C β€ 1000). It is guaranteed that all three plots are distinct.
Output
On the first line print a single integer k β the smallest number of plots needed to be cleaned from trees. The following k lines should contain coordinates of all plots needed to be cleaned. All k plots should be distinct. You can output the plots in any order.
If there are multiple solutions, print any of them.
Examples
Input
0 0
1 1
2 2
Output
5
0 0
1 0
1 1
1 2
2 2
Input
0 0
2 0
1 1
Output
4
0 0
1 0
1 1
2 0
Note
The first example is shown on the picture in the legend.
The second example is illustrated with the following image:
<image> | instruction | 0 | 19,460 | 23 | 38,920 |
Tags: implementation, math
Correct Solution:
```
def main():
a = tuple(map(int, input().split()))
b = tuple(map(int, input().split()))
c = tuple(map(int, input().split()))
a, b, c = sorted((a, b, c))
(x1, y1) = a
(x2, y2) = b
(x3, y3) = c
dy2 = y2 - y1
dy3 = y3 - y1
sy2 = 1 if dy2 >= 0 else -1
sy3 = 1 if dy3 >= 0 else -1
ay2 = abs(dy2)
ay3 = abs(dy3)
c = 0
res = []
if sy2 == sy3:
for i in range(x1, x2 + 1):
c += 1
res.append((i, y1))
for i in range(1, max(ay2, ay3) + 1):
c += 1
res.append((x2, y1 + sy2 * i))
for i in range(x2 + 1, x3 + 1):
c += 1
res.append((i, y3))
else:
for i in range(x1, x3 + 1):
c += 1
res.append((i, y1))
for i in range(1, ay2 + 1):
c += 1
res.append((x2, y1 + sy2 * i))
for i in range(1, ay3 + 1):
c += 1
res.append((x3, y1 + sy3 * i))
print(c)
for (x, y) in res:
print(x, y)
main()
``` | output | 1 | 19,460 | 23 | 38,921 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Squareland national forest is divided into equal 1 Γ 1 square plots aligned with north-south and east-west directions. Each plot can be uniquely described by integer Cartesian coordinates (x, y) of its south-west corner.
Three friends, Alice, Bob, and Charlie are going to buy three distinct plots of land A, B, C in the forest. Initially, all plots in the forest (including the plots A, B, C) are covered by trees. The friends want to visit each other, so they want to clean some of the plots from trees. After cleaning, one should be able to reach any of the plots A, B, C from any other one of those by moving through adjacent cleared plots. Two plots are adjacent if they share a side.
<image> For example, A=(0,0), B=(1,1), C=(2,2). The minimal number of plots to be cleared is 5. One of the ways to do it is shown with the gray color.
Of course, the friends don't want to strain too much. Help them find out the smallest number of plots they need to clean from trees.
Input
The first line contains two integers x_A and y_A β coordinates of the plot A (0 β€ x_A, y_A β€ 1000). The following two lines describe coordinates (x_B, y_B) and (x_C, y_C) of plots B and C respectively in the same format (0 β€ x_B, y_B, x_C, y_C β€ 1000). It is guaranteed that all three plots are distinct.
Output
On the first line print a single integer k β the smallest number of plots needed to be cleaned from trees. The following k lines should contain coordinates of all plots needed to be cleaned. All k plots should be distinct. You can output the plots in any order.
If there are multiple solutions, print any of them.
Examples
Input
0 0
1 1
2 2
Output
5
0 0
1 0
1 1
1 2
2 2
Input
0 0
2 0
1 1
Output
4
0 0
1 0
1 1
2 0
Note
The first example is shown on the picture in the legend.
The second example is illustrated with the following image:
<image>
Submitted Solution:
```
def prov(y1, y2, y3):
if (abs(y1 - y2), abs(y1 - y3)) <= (abs(y2 - y1), abs(y2 - y3)) and (abs(y1 - y2), abs(y1 - y3)) <= (abs(y3 - y2), abs(y3 - y1)):
return y1
if(abs(y2 - y1), abs(y2 - y3)) <= (abs(y1 - y2), abs(y1 - y3)) and (abs(y2 - y1), abs(y2 - y3)) <= (abs(y3 - y2), abs(y3 - y1)):
return y2
if (abs(y3 - y2), abs(y3 - y1)) <= (abs(y1 - y2), abs(y1 - y3)) and (abs(y3 - y2), abs(y3 - y1)) <= (abs(y2 - y1), abs(y2 - y3)):
return y3
x1, y1 = list(map(int, input().split()))
x2, y2 = list(map(int, input().split()))
x3, y3 = list(map(int, input().split()))
arr = []
for i in range(max(y1, y2, y3) + 1):
arr.append([-1] * (max(x1, x2, x3) +1))
xj = prov(x1, x2, x3)
yi = prov(y1, y2, y3)
stx1 = min(x1, xj)
fix1 = max(x1, xj)
se = set()
for i in range(stx1, fix1+1):
se.add((i, y1))
sty1 = min(y1, yi)
fiy1= max(y1, yi)
for i in range(sty1, fiy1+1):
se.add((xj, i))
stx2 = min(x2, xj)
fix2 = max(x2, xj)
for i in range(stx2, fix2+1):
se.add((i, y2))
sty2 = min(y2, yi)
fiy2= max(y2, yi)
for i in range(sty2, fiy2+1):
se.add((xj, i))
stx3 = min(x3, xj)
fix3 = max(x3, xj)
for i in range(stx3, fix3+1):
se.add((i, y3))
sty3 = min(y3, yi)
fiy3= max(y3, yi)
for i in range(sty3, fiy3+1):
se.add((xj, i))
print(len(se))
se = list(se)
for i in range(len(se)):
print(se[i][0], se[i][1])
``` | instruction | 0 | 19,461 | 23 | 38,922 |
Yes | output | 1 | 19,461 | 23 | 38,923 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Squareland national forest is divided into equal 1 Γ 1 square plots aligned with north-south and east-west directions. Each plot can be uniquely described by integer Cartesian coordinates (x, y) of its south-west corner.
Three friends, Alice, Bob, and Charlie are going to buy three distinct plots of land A, B, C in the forest. Initially, all plots in the forest (including the plots A, B, C) are covered by trees. The friends want to visit each other, so they want to clean some of the plots from trees. After cleaning, one should be able to reach any of the plots A, B, C from any other one of those by moving through adjacent cleared plots. Two plots are adjacent if they share a side.
<image> For example, A=(0,0), B=(1,1), C=(2,2). The minimal number of plots to be cleared is 5. One of the ways to do it is shown with the gray color.
Of course, the friends don't want to strain too much. Help them find out the smallest number of plots they need to clean from trees.
Input
The first line contains two integers x_A and y_A β coordinates of the plot A (0 β€ x_A, y_A β€ 1000). The following two lines describe coordinates (x_B, y_B) and (x_C, y_C) of plots B and C respectively in the same format (0 β€ x_B, y_B, x_C, y_C β€ 1000). It is guaranteed that all three plots are distinct.
Output
On the first line print a single integer k β the smallest number of plots needed to be cleaned from trees. The following k lines should contain coordinates of all plots needed to be cleaned. All k plots should be distinct. You can output the plots in any order.
If there are multiple solutions, print any of them.
Examples
Input
0 0
1 1
2 2
Output
5
0 0
1 0
1 1
1 2
2 2
Input
0 0
2 0
1 1
Output
4
0 0
1 0
1 1
2 0
Note
The first example is shown on the picture in the legend.
The second example is illustrated with the following image:
<image>
Submitted Solution:
```
xa, ya = map(int, input().split())
xb, yb = map(int, input().split())
xc, yc= map(int, input().split())
srx = xa+xb+xc-min(xa, xb, xc)-max(xa, xb, xc)
sry = ya +yb+yc - min(ya, yb, yc)- max(ya, yb,yc)
l = max(xa, xb, xc)-min(xa, xb, xc)+max(ya, yb, yc)-min(ya, yb, yc)+1
print(l)
for i in range(min(xa, xb, xc), max(xa, xb, xc)+1):
print(i, sry)
if (ya!=sry):
i = ya
while (i!=sry):
print(xa, i)
i+=int((sry-ya)/abs(sry-ya))
if (yb!=sry):
i = yb
while (i!=sry):
print(xb, i)
i+=int((sry-yb)/abs(sry-yb))
if (yc!=sry):
i = yc
while (i!=sry):
print(xc, i)
i+=int((sry-yc)/abs(sry-yc))
``` | instruction | 0 | 19,462 | 23 | 38,924 |
Yes | output | 1 | 19,462 | 23 | 38,925 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Squareland national forest is divided into equal 1 Γ 1 square plots aligned with north-south and east-west directions. Each plot can be uniquely described by integer Cartesian coordinates (x, y) of its south-west corner.
Three friends, Alice, Bob, and Charlie are going to buy three distinct plots of land A, B, C in the forest. Initially, all plots in the forest (including the plots A, B, C) are covered by trees. The friends want to visit each other, so they want to clean some of the plots from trees. After cleaning, one should be able to reach any of the plots A, B, C from any other one of those by moving through adjacent cleared plots. Two plots are adjacent if they share a side.
<image> For example, A=(0,0), B=(1,1), C=(2,2). The minimal number of plots to be cleared is 5. One of the ways to do it is shown with the gray color.
Of course, the friends don't want to strain too much. Help them find out the smallest number of plots they need to clean from trees.
Input
The first line contains two integers x_A and y_A β coordinates of the plot A (0 β€ x_A, y_A β€ 1000). The following two lines describe coordinates (x_B, y_B) and (x_C, y_C) of plots B and C respectively in the same format (0 β€ x_B, y_B, x_C, y_C β€ 1000). It is guaranteed that all three plots are distinct.
Output
On the first line print a single integer k β the smallest number of plots needed to be cleaned from trees. The following k lines should contain coordinates of all plots needed to be cleaned. All k plots should be distinct. You can output the plots in any order.
If there are multiple solutions, print any of them.
Examples
Input
0 0
1 1
2 2
Output
5
0 0
1 0
1 1
1 2
2 2
Input
0 0
2 0
1 1
Output
4
0 0
1 0
1 1
2 0
Note
The first example is shown on the picture in the legend.
The second example is illustrated with the following image:
<image>
Submitted Solution:
```
def path(a,b):
x,y = a
fx,fy = b
f1,f2 = 1,1
if(fx < x):
f1 = -1
if(fy < y):
f2 = -1
p1,p2 = [],[]
for i in range(x,fx+f1,f1):
p1.append([i,y])
for i in range(y+f2,fy+f2,f2):
p1.append([fx,i])
for i in range(y,fy+f2,f2):
p2.append([x,i])
for i in range(x+f1,fx+f1,f1):
p2.append([i,fy])
return p1,p2
def merge(p1,p2):
p3 = p1[:]
for i in p2:
if i not in p3:
p3.append(i)
return p3
l = []
for i in range(3):
l.append(list(map(int,input().split())))
l.sort()
p1,p2 = path(l[0],l[1])
p3,p4 = path(l[1],l[2])
p5 = merge(p1,p3)
p6 = merge(p1,p4)
if(len(p6) < len(p5)):
p5 = p6[::]
p6 = merge(p2,p3)
if(len(p6) < len(p5)):
p5 = p6[::]
p6 = merge(p2,p4)
if(len(p6) < len(p5)):
p5 = p6[::]
print(len(p5))
for i in p5:
print(*i)
``` | instruction | 0 | 19,463 | 23 | 38,926 |
Yes | output | 1 | 19,463 | 23 | 38,927 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Squareland national forest is divided into equal 1 Γ 1 square plots aligned with north-south and east-west directions. Each plot can be uniquely described by integer Cartesian coordinates (x, y) of its south-west corner.
Three friends, Alice, Bob, and Charlie are going to buy three distinct plots of land A, B, C in the forest. Initially, all plots in the forest (including the plots A, B, C) are covered by trees. The friends want to visit each other, so they want to clean some of the plots from trees. After cleaning, one should be able to reach any of the plots A, B, C from any other one of those by moving through adjacent cleared plots. Two plots are adjacent if they share a side.
<image> For example, A=(0,0), B=(1,1), C=(2,2). The minimal number of plots to be cleared is 5. One of the ways to do it is shown with the gray color.
Of course, the friends don't want to strain too much. Help them find out the smallest number of plots they need to clean from trees.
Input
The first line contains two integers x_A and y_A β coordinates of the plot A (0 β€ x_A, y_A β€ 1000). The following two lines describe coordinates (x_B, y_B) and (x_C, y_C) of plots B and C respectively in the same format (0 β€ x_B, y_B, x_C, y_C β€ 1000). It is guaranteed that all three plots are distinct.
Output
On the first line print a single integer k β the smallest number of plots needed to be cleaned from trees. The following k lines should contain coordinates of all plots needed to be cleaned. All k plots should be distinct. You can output the plots in any order.
If there are multiple solutions, print any of them.
Examples
Input
0 0
1 1
2 2
Output
5
0 0
1 0
1 1
1 2
2 2
Input
0 0
2 0
1 1
Output
4
0 0
1 0
1 1
2 0
Note
The first example is shown on the picture in the legend.
The second example is illustrated with the following image:
<image>
Submitted Solution:
```
def solve(r, t):
if r < k:
for i in range(r, k + 1):
matrix[i][t] = 1
else:
for i in range(k, r + 1):
matrix[i][t] = 1
if t < l:
for i in range(t, l + 1):
matrix[k][i] = 1
else:
for i in range(l, t + 1):
matrix[k][i] = 1
(a, b), (m, n), (x, y) = map(int, input().split()), map(int, input().split()), map(int, input().split())
hmax, hmin, wmax, wmin = max((a, m, x)), min((a, m, x)), max((b, n, y)), min((b, n, y))
matrix = [[0 for i in range(wmax + 1)] for j in range(hmax + 1)]
print(hmax - hmin + wmax - wmin + 1)
k, l = (a + m + x) - (hmax + hmin), (b + n + y) - (wmax + wmin)
solve(a, b)
solve(m, n)
solve(x, y)
for i in range(len(matrix)):
for j in range(len(matrix[i])):
if matrix[i][j]:
print(i, j)
``` | instruction | 0 | 19,464 | 23 | 38,928 |
Yes | output | 1 | 19,464 | 23 | 38,929 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Squareland national forest is divided into equal 1 Γ 1 square plots aligned with north-south and east-west directions. Each plot can be uniquely described by integer Cartesian coordinates (x, y) of its south-west corner.
Three friends, Alice, Bob, and Charlie are going to buy three distinct plots of land A, B, C in the forest. Initially, all plots in the forest (including the plots A, B, C) are covered by trees. The friends want to visit each other, so they want to clean some of the plots from trees. After cleaning, one should be able to reach any of the plots A, B, C from any other one of those by moving through adjacent cleared plots. Two plots are adjacent if they share a side.
<image> For example, A=(0,0), B=(1,1), C=(2,2). The minimal number of plots to be cleared is 5. One of the ways to do it is shown with the gray color.
Of course, the friends don't want to strain too much. Help them find out the smallest number of plots they need to clean from trees.
Input
The first line contains two integers x_A and y_A β coordinates of the plot A (0 β€ x_A, y_A β€ 1000). The following two lines describe coordinates (x_B, y_B) and (x_C, y_C) of plots B and C respectively in the same format (0 β€ x_B, y_B, x_C, y_C β€ 1000). It is guaranteed that all three plots are distinct.
Output
On the first line print a single integer k β the smallest number of plots needed to be cleaned from trees. The following k lines should contain coordinates of all plots needed to be cleaned. All k plots should be distinct. You can output the plots in any order.
If there are multiple solutions, print any of them.
Examples
Input
0 0
1 1
2 2
Output
5
0 0
1 0
1 1
1 2
2 2
Input
0 0
2 0
1 1
Output
4
0 0
1 0
1 1
2 0
Note
The first example is shown on the picture in the legend.
The second example is illustrated with the following image:
<image>
Submitted Solution:
```
x1, y1 = map(int, input().split())
x2, y2 = map(int, input().split())
x3, y3 = map(int, input().split())
x = (x1 + x2 + x3) // 3
y = (y1 + y2 + y3) // 3
print(abs(x - x1) + abs(x - x2) + abs(x - x3) + abs(y - y1) + abs(y - y2) + abs(y - y3) + 1)
x0 = x1
y0 = y1
for j in range(abs(x - x1)):
if x > x1:
print(x0, y0)
x0 += 1
else:
print(x0, y0)
x0 -= 1
for j in range(abs(y - y1)):
if y > y1:
print(x0, y0)
y0 += 1
else:
print(x0, y0)
y0 -= 1
x0 = x2
y0 = y2
for j in range(abs(x - x2)):
if x > x2:
print(x0, y0)
x0 += 1
else:
print(x0, y0)
x0 -= 1
for j in range(abs(y - y2)):
if y > y2:
print(x0, y0)
y0 += 1
else:
print(x0, y0)
y0 -= 1
x0 = x3
y0 = y3
for j in range(abs(x - x3)):
if x > x3:
print(x0, y0)
x0 += 1
else:
print(x0, y0)
x0 -= 1
for j in range(abs(y - y3)):
if y > y3:
print(x0, y0)
y0 += 1
else:
print(x0, y0)
y0 -= 1
print(x, y)
``` | instruction | 0 | 19,465 | 23 | 38,930 |
No | output | 1 | 19,465 | 23 | 38,931 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Squareland national forest is divided into equal 1 Γ 1 square plots aligned with north-south and east-west directions. Each plot can be uniquely described by integer Cartesian coordinates (x, y) of its south-west corner.
Three friends, Alice, Bob, and Charlie are going to buy three distinct plots of land A, B, C in the forest. Initially, all plots in the forest (including the plots A, B, C) are covered by trees. The friends want to visit each other, so they want to clean some of the plots from trees. After cleaning, one should be able to reach any of the plots A, B, C from any other one of those by moving through adjacent cleared plots. Two plots are adjacent if they share a side.
<image> For example, A=(0,0), B=(1,1), C=(2,2). The minimal number of plots to be cleared is 5. One of the ways to do it is shown with the gray color.
Of course, the friends don't want to strain too much. Help them find out the smallest number of plots they need to clean from trees.
Input
The first line contains two integers x_A and y_A β coordinates of the plot A (0 β€ x_A, y_A β€ 1000). The following two lines describe coordinates (x_B, y_B) and (x_C, y_C) of plots B and C respectively in the same format (0 β€ x_B, y_B, x_C, y_C β€ 1000). It is guaranteed that all three plots are distinct.
Output
On the first line print a single integer k β the smallest number of plots needed to be cleaned from trees. The following k lines should contain coordinates of all plots needed to be cleaned. All k plots should be distinct. You can output the plots in any order.
If there are multiple solutions, print any of them.
Examples
Input
0 0
1 1
2 2
Output
5
0 0
1 0
1 1
1 2
2 2
Input
0 0
2 0
1 1
Output
4
0 0
1 0
1 1
2 0
Note
The first example is shown on the picture in the legend.
The second example is illustrated with the following image:
<image>
Submitted Solution:
```
def print_path(a, b, way='left'):
corner = a
if way == 'left':
for i in range(a[1], b[1]):
print(a[0], i + 1)
corner = a[0], i + 1
for i in range(corner[0], b[0]):
print(i + 1, corner[1])
else:
for i in range(a[0], b[0]):
print(i + 1, a[1])
corner = i + 1, a[1]
for i in range(corner[1], b[1]):
print(corner[0], i + 1)
a1, a2 = map(int, input().split())
b1, b2 = map(int, input().split())
c1, c2 = map(int, input().split())
points = sorted([(a1, a2), (b1, b2), (c1, c2)], key=lambda x: pow(x[0], 2) + pow(x[1], 2))
print(points)
a1, a2 = points[0]
b1, b2 = points[1]
c1, c2 = points[2]
if a1 <= b1 <= c1 and a2 <= b2 <= c2:
print(c1 - a1 + c2 - a2 + 1)
print(a1, a2)
print_path(points[0], points[1])
print_path(points[1], points[2])
else:
print(a1, a2)
print_path(points[0], points[2], 'right')
print('here')
if c1 <= b1 and c2 >= b2 >= a2:
print_path((c1, b2), points[1])
elif b2 < a2 and a1 <= b1 <= c1:
print_path(points[1], (b1, a2))
elif b1 < a1 and a2 <= b2 <= c2:
print_path(points[1], (a1, b2))
elif b2 > c2 and a1 <= b1 <= c1:
print_path((b1, c2), points[1])
``` | instruction | 0 | 19,466 | 23 | 38,932 |
No | output | 1 | 19,466 | 23 | 38,933 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Squareland national forest is divided into equal 1 Γ 1 square plots aligned with north-south and east-west directions. Each plot can be uniquely described by integer Cartesian coordinates (x, y) of its south-west corner.
Three friends, Alice, Bob, and Charlie are going to buy three distinct plots of land A, B, C in the forest. Initially, all plots in the forest (including the plots A, B, C) are covered by trees. The friends want to visit each other, so they want to clean some of the plots from trees. After cleaning, one should be able to reach any of the plots A, B, C from any other one of those by moving through adjacent cleared plots. Two plots are adjacent if they share a side.
<image> For example, A=(0,0), B=(1,1), C=(2,2). The minimal number of plots to be cleared is 5. One of the ways to do it is shown with the gray color.
Of course, the friends don't want to strain too much. Help them find out the smallest number of plots they need to clean from trees.
Input
The first line contains two integers x_A and y_A β coordinates of the plot A (0 β€ x_A, y_A β€ 1000). The following two lines describe coordinates (x_B, y_B) and (x_C, y_C) of plots B and C respectively in the same format (0 β€ x_B, y_B, x_C, y_C β€ 1000). It is guaranteed that all three plots are distinct.
Output
On the first line print a single integer k β the smallest number of plots needed to be cleaned from trees. The following k lines should contain coordinates of all plots needed to be cleaned. All k plots should be distinct. You can output the plots in any order.
If there are multiple solutions, print any of them.
Examples
Input
0 0
1 1
2 2
Output
5
0 0
1 0
1 1
1 2
2 2
Input
0 0
2 0
1 1
Output
4
0 0
1 0
1 1
2 0
Note
The first example is shown on the picture in the legend.
The second example is illustrated with the following image:
<image>
Submitted Solution:
```
s_1 = input().split(' ')
x_1 = int(s_1[0])
y_1 = int(s_1[1])
s_2 = input().split(' ')
x_2 = int(s_2[0])
y_2 = int(s_2[1])
s_3 = input().split(' ')
x_3 = int(s_3[0])
y_3 = int(s_3[1])
mas = [x_1,x_2,x_3]
mas_x = sorted([x_1,x_2,x_3])
m = [mas_x.index(mas[0]),mas_x.index(mas[1]),mas_x.index(mas[2])]
M = [0]*len(mas_x)
M[m[0]] = y_1
M[m[1]] = y_2
M[m[2]] = y_3
#print(m)
#mas_y = [y_1,y_2,y_3]
mas_y = M
#print(mas_x,M)
#print(mas_y)
X_1 = mas_x[0]
X_2 = mas_x[1]
X_3 = mas_x[2]
Y_1 = mas_y[0]
Y_2 = mas_y[1]
Y_3 = mas_y[2]
#print(X_1,X_2,X_3)
a = [[i ,Y_1] for i in range(X_1,X_2+1)]
b = [[Y_2,i] for i in range(min(X_1,X_2,X_3)+1,max(X_1,X_2,X_3))]
c =[]
if Y_1==Y_3:
c =[[i,Y_3] for i in range(X_2+1,X_3+1)]
else:
c = [[i,Y_3] for i in range(X_2,X_3+1)]
print(len(a)+len(b)+len(c))
for i in a:
print(i[0],i[1])
for j in b:
print(j[0],j[1])
for i in c:
print(i[0],i[1])
``` | instruction | 0 | 19,467 | 23 | 38,934 |
No | output | 1 | 19,467 | 23 | 38,935 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Squareland national forest is divided into equal 1 Γ 1 square plots aligned with north-south and east-west directions. Each plot can be uniquely described by integer Cartesian coordinates (x, y) of its south-west corner.
Three friends, Alice, Bob, and Charlie are going to buy three distinct plots of land A, B, C in the forest. Initially, all plots in the forest (including the plots A, B, C) are covered by trees. The friends want to visit each other, so they want to clean some of the plots from trees. After cleaning, one should be able to reach any of the plots A, B, C from any other one of those by moving through adjacent cleared plots. Two plots are adjacent if they share a side.
<image> For example, A=(0,0), B=(1,1), C=(2,2). The minimal number of plots to be cleared is 5. One of the ways to do it is shown with the gray color.
Of course, the friends don't want to strain too much. Help them find out the smallest number of plots they need to clean from trees.
Input
The first line contains two integers x_A and y_A β coordinates of the plot A (0 β€ x_A, y_A β€ 1000). The following two lines describe coordinates (x_B, y_B) and (x_C, y_C) of plots B and C respectively in the same format (0 β€ x_B, y_B, x_C, y_C β€ 1000). It is guaranteed that all three plots are distinct.
Output
On the first line print a single integer k β the smallest number of plots needed to be cleaned from trees. The following k lines should contain coordinates of all plots needed to be cleaned. All k plots should be distinct. You can output the plots in any order.
If there are multiple solutions, print any of them.
Examples
Input
0 0
1 1
2 2
Output
5
0 0
1 0
1 1
1 2
2 2
Input
0 0
2 0
1 1
Output
4
0 0
1 0
1 1
2 0
Note
The first example is shown on the picture in the legend.
The second example is illustrated with the following image:
<image>
Submitted Solution:
```
def func1(a,b,c,d,e):
j = max(c, d, e)
k = min(c, d, e)
print(j-k+1+abs(b-a))
for i in range(k,j+1):
print(str(a)+" "+str(i))
if a<b:
for i in range(a+1,b+1):
print(str(i)+" "+str(e))
else:
for i in range(b,a):
print(str(i)+" "+str(e))
def func2(a,b,c,d,e):
j = max(c, d, e)
k = min(c, d, e)
print(j-k+1+abs(b-a))
for i in range(k,j+1):
print(str(i)+" "+str(a))
if a<b:
for i in range(a+1,b+1):
print(str(e)+" "+str(i))
else:
for i in range(b,a):
print(str(e)+" "+str(i))
``` | instruction | 0 | 19,468 | 23 | 38,936 |
No | output | 1 | 19,468 | 23 | 38,937 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lunar New Year is approaching, and you bought a matrix with lots of "crosses".
This matrix M of size n Γ n contains only 'X' and '.' (without quotes). The element in the i-th row and the j-th column (i, j) is defined as M(i, j), where 1 β€ i, j β€ n. We define a cross appearing in the i-th row and the j-th column (1 < i, j < n) if and only if M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = 'X'.
The following figure illustrates a cross appearing at position (2, 2) in a 3 Γ 3 matrix.
X.X
.X.
X.X
Your task is to find out the number of crosses in the given matrix M. Two crosses are different if and only if they appear in different rows or columns.
Input
The first line contains only one positive integer n (1 β€ n β€ 500), denoting the size of the matrix M.
The following n lines illustrate the matrix M. Each line contains exactly n characters, each of them is 'X' or '.'. The j-th element in the i-th line represents M(i, j), where 1 β€ i, j β€ n.
Output
Output a single line containing only one integer number k β the number of crosses in the given matrix M.
Examples
Input
5
.....
.XXX.
.XXX.
.XXX.
.....
Output
1
Input
2
XX
XX
Output
0
Input
6
......
X.X.X.
.X.X.X
X.X.X.
.X.X.X
......
Output
4
Note
In the first sample, a cross appears at (3, 3), so the answer is 1.
In the second sample, no crosses appear since n < 3, so the answer is 0.
In the third sample, crosses appear at (3, 2), (3, 4), (4, 3), (4, 5), so the answer is 4. | instruction | 0 | 19,469 | 23 | 38,938 |
Tags: implementation
Correct Solution:
```
n = int(input())
s = []
for i in range(n):
ip = input()
s.append(ip)
count = 0
for i in range(1,n-1):
for j in range(1,n-1):
if s[i][j] == 'X' and s[i-1][j-1] == 'X' and s[i-1][j+1] == 'X' and s[i+1][j-1] == 'X' and s[i+1][j+1] == 'X':
count +=1
print(count)
``` | output | 1 | 19,469 | 23 | 38,939 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lunar New Year is approaching, and you bought a matrix with lots of "crosses".
This matrix M of size n Γ n contains only 'X' and '.' (without quotes). The element in the i-th row and the j-th column (i, j) is defined as M(i, j), where 1 β€ i, j β€ n. We define a cross appearing in the i-th row and the j-th column (1 < i, j < n) if and only if M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = 'X'.
The following figure illustrates a cross appearing at position (2, 2) in a 3 Γ 3 matrix.
X.X
.X.
X.X
Your task is to find out the number of crosses in the given matrix M. Two crosses are different if and only if they appear in different rows or columns.
Input
The first line contains only one positive integer n (1 β€ n β€ 500), denoting the size of the matrix M.
The following n lines illustrate the matrix M. Each line contains exactly n characters, each of them is 'X' or '.'. The j-th element in the i-th line represents M(i, j), where 1 β€ i, j β€ n.
Output
Output a single line containing only one integer number k β the number of crosses in the given matrix M.
Examples
Input
5
.....
.XXX.
.XXX.
.XXX.
.....
Output
1
Input
2
XX
XX
Output
0
Input
6
......
X.X.X.
.X.X.X
X.X.X.
.X.X.X
......
Output
4
Note
In the first sample, a cross appears at (3, 3), so the answer is 1.
In the second sample, no crosses appear since n < 3, so the answer is 0.
In the third sample, crosses appear at (3, 2), (3, 4), (4, 3), (4, 5), so the answer is 4. | instruction | 0 | 19,470 | 23 | 38,940 |
Tags: implementation
Correct Solution:
```
import sys
data = sys.stdin.read().splitlines()
n = int(data[0])
grid = [line for line in data[1:]]
cnt = 0
for i in range(1, n - 1):
for j in range(1, n - 1):
if grid[i][j] == grid[i - 1][j - 1] == grid[i - 1][j + 1] == grid[i + 1][j -
1] == grid[i + 1][j + 1] == 'X':
cnt += 1
print(cnt)
``` | output | 1 | 19,470 | 23 | 38,941 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lunar New Year is approaching, and you bought a matrix with lots of "crosses".
This matrix M of size n Γ n contains only 'X' and '.' (without quotes). The element in the i-th row and the j-th column (i, j) is defined as M(i, j), where 1 β€ i, j β€ n. We define a cross appearing in the i-th row and the j-th column (1 < i, j < n) if and only if M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = 'X'.
The following figure illustrates a cross appearing at position (2, 2) in a 3 Γ 3 matrix.
X.X
.X.
X.X
Your task is to find out the number of crosses in the given matrix M. Two crosses are different if and only if they appear in different rows or columns.
Input
The first line contains only one positive integer n (1 β€ n β€ 500), denoting the size of the matrix M.
The following n lines illustrate the matrix M. Each line contains exactly n characters, each of them is 'X' or '.'. The j-th element in the i-th line represents M(i, j), where 1 β€ i, j β€ n.
Output
Output a single line containing only one integer number k β the number of crosses in the given matrix M.
Examples
Input
5
.....
.XXX.
.XXX.
.XXX.
.....
Output
1
Input
2
XX
XX
Output
0
Input
6
......
X.X.X.
.X.X.X
X.X.X.
.X.X.X
......
Output
4
Note
In the first sample, a cross appears at (3, 3), so the answer is 1.
In the second sample, no crosses appear since n < 3, so the answer is 0.
In the third sample, crosses appear at (3, 2), (3, 4), (4, 3), (4, 5), so the answer is 4. | instruction | 0 | 19,471 | 23 | 38,942 |
Tags: implementation
Correct Solution:
```
n = int(input())
m = []
for _ in range(n):
tmp = input()
m.append(tmp)
# print(n,m[0][0])
res = 0
def check(i,j):
return m[i-1][j-1]=='X' and m[i-1][j+1]=='X' and m[i+1][j-1]== 'X' and m[i+1][j+1]=='X'
for i in range(1,n-1):
for j in range(1,n-1):
if m[i][j] == 'X' and check(i,j):
res+=1
# print(m[i][j],end='')
# print('')
print(res)
``` | output | 1 | 19,471 | 23 | 38,943 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lunar New Year is approaching, and you bought a matrix with lots of "crosses".
This matrix M of size n Γ n contains only 'X' and '.' (without quotes). The element in the i-th row and the j-th column (i, j) is defined as M(i, j), where 1 β€ i, j β€ n. We define a cross appearing in the i-th row and the j-th column (1 < i, j < n) if and only if M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = 'X'.
The following figure illustrates a cross appearing at position (2, 2) in a 3 Γ 3 matrix.
X.X
.X.
X.X
Your task is to find out the number of crosses in the given matrix M. Two crosses are different if and only if they appear in different rows or columns.
Input
The first line contains only one positive integer n (1 β€ n β€ 500), denoting the size of the matrix M.
The following n lines illustrate the matrix M. Each line contains exactly n characters, each of them is 'X' or '.'. The j-th element in the i-th line represents M(i, j), where 1 β€ i, j β€ n.
Output
Output a single line containing only one integer number k β the number of crosses in the given matrix M.
Examples
Input
5
.....
.XXX.
.XXX.
.XXX.
.....
Output
1
Input
2
XX
XX
Output
0
Input
6
......
X.X.X.
.X.X.X
X.X.X.
.X.X.X
......
Output
4
Note
In the first sample, a cross appears at (3, 3), so the answer is 1.
In the second sample, no crosses appear since n < 3, so the answer is 0.
In the third sample, crosses appear at (3, 2), (3, 4), (4, 3), (4, 5), so the answer is 4. | instruction | 0 | 19,472 | 23 | 38,944 |
Tags: implementation
Correct Solution:
```
n=int(input())
M=[input() for i in range(n)]
ANS=0
for i in range(1,n-1):
for j in range(1,n-1):
if M[i][j]==M[i-1][j-1]==M[i-1][j+1]==M[i+1][j-1]==M[i+1][j+1]=="X":
ANS+=1
print(ANS)
``` | output | 1 | 19,472 | 23 | 38,945 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lunar New Year is approaching, and you bought a matrix with lots of "crosses".
This matrix M of size n Γ n contains only 'X' and '.' (without quotes). The element in the i-th row and the j-th column (i, j) is defined as M(i, j), where 1 β€ i, j β€ n. We define a cross appearing in the i-th row and the j-th column (1 < i, j < n) if and only if M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = 'X'.
The following figure illustrates a cross appearing at position (2, 2) in a 3 Γ 3 matrix.
X.X
.X.
X.X
Your task is to find out the number of crosses in the given matrix M. Two crosses are different if and only if they appear in different rows or columns.
Input
The first line contains only one positive integer n (1 β€ n β€ 500), denoting the size of the matrix M.
The following n lines illustrate the matrix M. Each line contains exactly n characters, each of them is 'X' or '.'. The j-th element in the i-th line represents M(i, j), where 1 β€ i, j β€ n.
Output
Output a single line containing only one integer number k β the number of crosses in the given matrix M.
Examples
Input
5
.....
.XXX.
.XXX.
.XXX.
.....
Output
1
Input
2
XX
XX
Output
0
Input
6
......
X.X.X.
.X.X.X
X.X.X.
.X.X.X
......
Output
4
Note
In the first sample, a cross appears at (3, 3), so the answer is 1.
In the second sample, no crosses appear since n < 3, so the answer is 0.
In the third sample, crosses appear at (3, 2), (3, 4), (4, 3), (4, 5), so the answer is 4. | instruction | 0 | 19,473 | 23 | 38,946 |
Tags: implementation
Correct Solution:
```
n = int(input())
m = [ input() for i in range(n)]
c=0
for i in range(1,n-1):
for j in range(1,n-1):
if m[i][j] == 'X' and m[i-1][j-1]=='X' and m[i+1][j-1]=='X' and m[i-1][j+1]=='X' and m[i+1][j+1]=='X':
c+=1
print(c)
``` | output | 1 | 19,473 | 23 | 38,947 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lunar New Year is approaching, and you bought a matrix with lots of "crosses".
This matrix M of size n Γ n contains only 'X' and '.' (without quotes). The element in the i-th row and the j-th column (i, j) is defined as M(i, j), where 1 β€ i, j β€ n. We define a cross appearing in the i-th row and the j-th column (1 < i, j < n) if and only if M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = 'X'.
The following figure illustrates a cross appearing at position (2, 2) in a 3 Γ 3 matrix.
X.X
.X.
X.X
Your task is to find out the number of crosses in the given matrix M. Two crosses are different if and only if they appear in different rows or columns.
Input
The first line contains only one positive integer n (1 β€ n β€ 500), denoting the size of the matrix M.
The following n lines illustrate the matrix M. Each line contains exactly n characters, each of them is 'X' or '.'. The j-th element in the i-th line represents M(i, j), where 1 β€ i, j β€ n.
Output
Output a single line containing only one integer number k β the number of crosses in the given matrix M.
Examples
Input
5
.....
.XXX.
.XXX.
.XXX.
.....
Output
1
Input
2
XX
XX
Output
0
Input
6
......
X.X.X.
.X.X.X
X.X.X.
.X.X.X
......
Output
4
Note
In the first sample, a cross appears at (3, 3), so the answer is 1.
In the second sample, no crosses appear since n < 3, so the answer is 0.
In the third sample, crosses appear at (3, 2), (3, 4), (4, 3), (4, 5), so the answer is 4. | instruction | 0 | 19,474 | 23 | 38,948 |
Tags: implementation
Correct Solution:
```
def rlist(): return list(map(int, input().split()))
def rdi(): return int(input())
n = rdi()
line = list()
for i in range(n):
line.append(input())
cnt = 0
for i in range(1, n - 1):
for j in range(1, n - 1):
if line[i][j] == line[i - 1][j - 1] == line[i - 1][j + 1] == line[i + 1][j - 1] == line[i + 1][j + 1] == 'X':
cnt += 1
print(cnt)
``` | output | 1 | 19,474 | 23 | 38,949 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lunar New Year is approaching, and you bought a matrix with lots of "crosses".
This matrix M of size n Γ n contains only 'X' and '.' (without quotes). The element in the i-th row and the j-th column (i, j) is defined as M(i, j), where 1 β€ i, j β€ n. We define a cross appearing in the i-th row and the j-th column (1 < i, j < n) if and only if M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = 'X'.
The following figure illustrates a cross appearing at position (2, 2) in a 3 Γ 3 matrix.
X.X
.X.
X.X
Your task is to find out the number of crosses in the given matrix M. Two crosses are different if and only if they appear in different rows or columns.
Input
The first line contains only one positive integer n (1 β€ n β€ 500), denoting the size of the matrix M.
The following n lines illustrate the matrix M. Each line contains exactly n characters, each of them is 'X' or '.'. The j-th element in the i-th line represents M(i, j), where 1 β€ i, j β€ n.
Output
Output a single line containing only one integer number k β the number of crosses in the given matrix M.
Examples
Input
5
.....
.XXX.
.XXX.
.XXX.
.....
Output
1
Input
2
XX
XX
Output
0
Input
6
......
X.X.X.
.X.X.X
X.X.X.
.X.X.X
......
Output
4
Note
In the first sample, a cross appears at (3, 3), so the answer is 1.
In the second sample, no crosses appear since n < 3, so the answer is 0.
In the third sample, crosses appear at (3, 2), (3, 4), (4, 3), (4, 5), so the answer is 4. | instruction | 0 | 19,475 | 23 | 38,950 |
Tags: implementation
Correct Solution:
```
from sys import stdin,stdout
from itertools import combinations
from collections import defaultdict
def listIn():
return list((map(int,stdin.readline().strip().split())))
def stringListIn():
return([x for x in stdin.readline().split()])
def intIn():
return (int(stdin.readline()))
def stringIn():
return (stdin.readline())
if __name__=="__main__":
n=intIn()
count=0
arr=[]
for i in range(n):
temp=list(stringIn())
arr.append(temp)
for i in range(1,n-1):
for j in range(1,n-1):
if arr[i][j]==arr[i-1][j-1]==arr[i-1][j+1]==arr[i+1][j-1]==arr[i+1][j+1]=="X":
count+=1
print(count)
``` | output | 1 | 19,475 | 23 | 38,951 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Lunar New Year is approaching, and you bought a matrix with lots of "crosses".
This matrix M of size n Γ n contains only 'X' and '.' (without quotes). The element in the i-th row and the j-th column (i, j) is defined as M(i, j), where 1 β€ i, j β€ n. We define a cross appearing in the i-th row and the j-th column (1 < i, j < n) if and only if M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = 'X'.
The following figure illustrates a cross appearing at position (2, 2) in a 3 Γ 3 matrix.
X.X
.X.
X.X
Your task is to find out the number of crosses in the given matrix M. Two crosses are different if and only if they appear in different rows or columns.
Input
The first line contains only one positive integer n (1 β€ n β€ 500), denoting the size of the matrix M.
The following n lines illustrate the matrix M. Each line contains exactly n characters, each of them is 'X' or '.'. The j-th element in the i-th line represents M(i, j), where 1 β€ i, j β€ n.
Output
Output a single line containing only one integer number k β the number of crosses in the given matrix M.
Examples
Input
5
.....
.XXX.
.XXX.
.XXX.
.....
Output
1
Input
2
XX
XX
Output
0
Input
6
......
X.X.X.
.X.X.X
X.X.X.
.X.X.X
......
Output
4
Note
In the first sample, a cross appears at (3, 3), so the answer is 1.
In the second sample, no crosses appear since n < 3, so the answer is 0.
In the third sample, crosses appear at (3, 2), (3, 4), (4, 3), (4, 5), so the answer is 4. | instruction | 0 | 19,476 | 23 | 38,952 |
Tags: implementation
Correct Solution:
```
#A - CrossCounting
number = int(input())
mat = []
ans = 0
for i in range(number):
mat.append(' '.join(input()).split())
for i in range(1,number-1):
for j in range(1,number-1):
if mat[i][j] == "X":
if mat[i-1][j-1] == "X":
if mat[i-1][j+1] == "X":
if mat[i+1][j-1] == "X":
if mat[i+1][j+1] == "X":
ans+=1
print(ans)
``` | output | 1 | 19,476 | 23 | 38,953 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lunar New Year is approaching, and you bought a matrix with lots of "crosses".
This matrix M of size n Γ n contains only 'X' and '.' (without quotes). The element in the i-th row and the j-th column (i, j) is defined as M(i, j), where 1 β€ i, j β€ n. We define a cross appearing in the i-th row and the j-th column (1 < i, j < n) if and only if M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = 'X'.
The following figure illustrates a cross appearing at position (2, 2) in a 3 Γ 3 matrix.
X.X
.X.
X.X
Your task is to find out the number of crosses in the given matrix M. Two crosses are different if and only if they appear in different rows or columns.
Input
The first line contains only one positive integer n (1 β€ n β€ 500), denoting the size of the matrix M.
The following n lines illustrate the matrix M. Each line contains exactly n characters, each of them is 'X' or '.'. The j-th element in the i-th line represents M(i, j), where 1 β€ i, j β€ n.
Output
Output a single line containing only one integer number k β the number of crosses in the given matrix M.
Examples
Input
5
.....
.XXX.
.XXX.
.XXX.
.....
Output
1
Input
2
XX
XX
Output
0
Input
6
......
X.X.X.
.X.X.X
X.X.X.
.X.X.X
......
Output
4
Note
In the first sample, a cross appears at (3, 3), so the answer is 1.
In the second sample, no crosses appear since n < 3, so the answer is 0.
In the third sample, crosses appear at (3, 2), (3, 4), (4, 3), (4, 5), so the answer is 4.
Submitted Solution:
```
n = int(input())
a = [[x=='X' for x in input()] for _ in range(n)]
res = 0
for i in range(1,n-1):
for j in range(1,n-1):
if a[i][j] and a[i-1][j-1] and a[i-1][j+1] and a[i+1][j-1] and a[i+1][j+1]:
res += 1
print(res)
``` | instruction | 0 | 19,477 | 23 | 38,954 |
Yes | output | 1 | 19,477 | 23 | 38,955 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lunar New Year is approaching, and you bought a matrix with lots of "crosses".
This matrix M of size n Γ n contains only 'X' and '.' (without quotes). The element in the i-th row and the j-th column (i, j) is defined as M(i, j), where 1 β€ i, j β€ n. We define a cross appearing in the i-th row and the j-th column (1 < i, j < n) if and only if M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = 'X'.
The following figure illustrates a cross appearing at position (2, 2) in a 3 Γ 3 matrix.
X.X
.X.
X.X
Your task is to find out the number of crosses in the given matrix M. Two crosses are different if and only if they appear in different rows or columns.
Input
The first line contains only one positive integer n (1 β€ n β€ 500), denoting the size of the matrix M.
The following n lines illustrate the matrix M. Each line contains exactly n characters, each of them is 'X' or '.'. The j-th element in the i-th line represents M(i, j), where 1 β€ i, j β€ n.
Output
Output a single line containing only one integer number k β the number of crosses in the given matrix M.
Examples
Input
5
.....
.XXX.
.XXX.
.XXX.
.....
Output
1
Input
2
XX
XX
Output
0
Input
6
......
X.X.X.
.X.X.X
X.X.X.
.X.X.X
......
Output
4
Note
In the first sample, a cross appears at (3, 3), so the answer is 1.
In the second sample, no crosses appear since n < 3, so the answer is 0.
In the third sample, crosses appear at (3, 2), (3, 4), (4, 3), (4, 5), so the answer is 4.
Submitted Solution:
```
n=int(input())
l=[]
for i in range(n):
l.append(input())
c=0
for i in range(1,n-1):
for j in range(1,n-1):
if(l[i][j]=='X'):
if(l[i-1][j-1]=='X' and l[i-1][j+1]=='X' and l[i+1][j-1]=='X' and l[i+1][j+1]=='X'):
c+=1
print(c)
``` | instruction | 0 | 19,478 | 23 | 38,956 |
Yes | output | 1 | 19,478 | 23 | 38,957 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lunar New Year is approaching, and you bought a matrix with lots of "crosses".
This matrix M of size n Γ n contains only 'X' and '.' (without quotes). The element in the i-th row and the j-th column (i, j) is defined as M(i, j), where 1 β€ i, j β€ n. We define a cross appearing in the i-th row and the j-th column (1 < i, j < n) if and only if M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = 'X'.
The following figure illustrates a cross appearing at position (2, 2) in a 3 Γ 3 matrix.
X.X
.X.
X.X
Your task is to find out the number of crosses in the given matrix M. Two crosses are different if and only if they appear in different rows or columns.
Input
The first line contains only one positive integer n (1 β€ n β€ 500), denoting the size of the matrix M.
The following n lines illustrate the matrix M. Each line contains exactly n characters, each of them is 'X' or '.'. The j-th element in the i-th line represents M(i, j), where 1 β€ i, j β€ n.
Output
Output a single line containing only one integer number k β the number of crosses in the given matrix M.
Examples
Input
5
.....
.XXX.
.XXX.
.XXX.
.....
Output
1
Input
2
XX
XX
Output
0
Input
6
......
X.X.X.
.X.X.X
X.X.X.
.X.X.X
......
Output
4
Note
In the first sample, a cross appears at (3, 3), so the answer is 1.
In the second sample, no crosses appear since n < 3, so the answer is 0.
In the third sample, crosses appear at (3, 2), (3, 4), (4, 3), (4, 5), so the answer is 4.
Submitted Solution:
```
#!/usr/bin/env python
import os
import sys
from io import BytesIO, IOBase
#from bisect import bisect_left as bl #c++ lowerbound bl(array,element)
#from bisect import bisect_right as br #c++ upperbound br(array,element)
import math
def main():
n=int(input())
a=[input() for x in range(n)]
print(sum([a[x][y]=="X" and a[x][y+2]=="X" and a[x+1][y+1]=="X" and a[x+2][y]=="X" and a[x+2][y+2]=="X" for x in range(n-2) for y in range(n-2)]))
#-----------------------------BOSS-------------------------------------!
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# endregion
if __name__ == "__main__":
main()
``` | instruction | 0 | 19,479 | 23 | 38,958 |
Yes | output | 1 | 19,479 | 23 | 38,959 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lunar New Year is approaching, and you bought a matrix with lots of "crosses".
This matrix M of size n Γ n contains only 'X' and '.' (without quotes). The element in the i-th row and the j-th column (i, j) is defined as M(i, j), where 1 β€ i, j β€ n. We define a cross appearing in the i-th row and the j-th column (1 < i, j < n) if and only if M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = 'X'.
The following figure illustrates a cross appearing at position (2, 2) in a 3 Γ 3 matrix.
X.X
.X.
X.X
Your task is to find out the number of crosses in the given matrix M. Two crosses are different if and only if they appear in different rows or columns.
Input
The first line contains only one positive integer n (1 β€ n β€ 500), denoting the size of the matrix M.
The following n lines illustrate the matrix M. Each line contains exactly n characters, each of them is 'X' or '.'. The j-th element in the i-th line represents M(i, j), where 1 β€ i, j β€ n.
Output
Output a single line containing only one integer number k β the number of crosses in the given matrix M.
Examples
Input
5
.....
.XXX.
.XXX.
.XXX.
.....
Output
1
Input
2
XX
XX
Output
0
Input
6
......
X.X.X.
.X.X.X
X.X.X.
.X.X.X
......
Output
4
Note
In the first sample, a cross appears at (3, 3), so the answer is 1.
In the second sample, no crosses appear since n < 3, so the answer is 0.
In the third sample, crosses appear at (3, 2), (3, 4), (4, 3), (4, 5), so the answer is 4.
Submitted Solution:
```
M=[]
n=int(input())
for i in range(n):
M.append(list(input()))
count=0
for i in range(1,n-1):
for j in range(1,n-1):
if M[i][j]=="X" and M[i-1][j-1]=="X" and M[i-1][j+1]=="X" and M[i+1][j-1]=="X" and M[i+1][j+1]=="X":count+=1
print(count)
``` | instruction | 0 | 19,480 | 23 | 38,960 |
Yes | output | 1 | 19,480 | 23 | 38,961 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lunar New Year is approaching, and you bought a matrix with lots of "crosses".
This matrix M of size n Γ n contains only 'X' and '.' (without quotes). The element in the i-th row and the j-th column (i, j) is defined as M(i, j), where 1 β€ i, j β€ n. We define a cross appearing in the i-th row and the j-th column (1 < i, j < n) if and only if M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = 'X'.
The following figure illustrates a cross appearing at position (2, 2) in a 3 Γ 3 matrix.
X.X
.X.
X.X
Your task is to find out the number of crosses in the given matrix M. Two crosses are different if and only if they appear in different rows or columns.
Input
The first line contains only one positive integer n (1 β€ n β€ 500), denoting the size of the matrix M.
The following n lines illustrate the matrix M. Each line contains exactly n characters, each of them is 'X' or '.'. The j-th element in the i-th line represents M(i, j), where 1 β€ i, j β€ n.
Output
Output a single line containing only one integer number k β the number of crosses in the given matrix M.
Examples
Input
5
.....
.XXX.
.XXX.
.XXX.
.....
Output
1
Input
2
XX
XX
Output
0
Input
6
......
X.X.X.
.X.X.X
X.X.X.
.X.X.X
......
Output
4
Note
In the first sample, a cross appears at (3, 3), so the answer is 1.
In the second sample, no crosses appear since n < 3, so the answer is 0.
In the third sample, crosses appear at (3, 2), (3, 4), (4, 3), (4, 5), so the answer is 4.
Submitted Solution:
```
def answer():
n = int(input())
c=[]
i=0
while i<n:
c.append(list(input()))
i+=1
i=1
ans=0
while i<len(c)-1:
j=1
while j<len(c)-1:
if c[i][j]=="X":
if c[i-1][j+1]=="X" and c[i+1][j+1]=="X" and c[i-1][j+1]=="X" and c[i-1][j-1]=="X":
ans+=1
j+=1
i+=1
print(ans)
answer()
``` | instruction | 0 | 19,481 | 23 | 38,962 |
No | output | 1 | 19,481 | 23 | 38,963 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lunar New Year is approaching, and you bought a matrix with lots of "crosses".
This matrix M of size n Γ n contains only 'X' and '.' (without quotes). The element in the i-th row and the j-th column (i, j) is defined as M(i, j), where 1 β€ i, j β€ n. We define a cross appearing in the i-th row and the j-th column (1 < i, j < n) if and only if M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = 'X'.
The following figure illustrates a cross appearing at position (2, 2) in a 3 Γ 3 matrix.
X.X
.X.
X.X
Your task is to find out the number of crosses in the given matrix M. Two crosses are different if and only if they appear in different rows or columns.
Input
The first line contains only one positive integer n (1 β€ n β€ 500), denoting the size of the matrix M.
The following n lines illustrate the matrix M. Each line contains exactly n characters, each of them is 'X' or '.'. The j-th element in the i-th line represents M(i, j), where 1 β€ i, j β€ n.
Output
Output a single line containing only one integer number k β the number of crosses in the given matrix M.
Examples
Input
5
.....
.XXX.
.XXX.
.XXX.
.....
Output
1
Input
2
XX
XX
Output
0
Input
6
......
X.X.X.
.X.X.X
X.X.X.
.X.X.X
......
Output
4
Note
In the first sample, a cross appears at (3, 3), so the answer is 1.
In the second sample, no crosses appear since n < 3, so the answer is 0.
In the third sample, crosses appear at (3, 2), (3, 4), (4, 3), (4, 5), so the answer is 4.
Submitted Solution:
```
n = int(input())
matrix = []
for i in range(n):
x = input()
matrix.append(x)
cnt = 0
for i in range(1,n-1):
for j in range(1,n-1):
if(matrix[i-1][j-1] == 'X' and matrix[i+1][j-1] == 'X' and matrix[i-1][j+1] == 'X' and matrix[i+1][j+1] == 'X'):
cnt += 1
print(cnt)
``` | instruction | 0 | 19,482 | 23 | 38,964 |
No | output | 1 | 19,482 | 23 | 38,965 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lunar New Year is approaching, and you bought a matrix with lots of "crosses".
This matrix M of size n Γ n contains only 'X' and '.' (without quotes). The element in the i-th row and the j-th column (i, j) is defined as M(i, j), where 1 β€ i, j β€ n. We define a cross appearing in the i-th row and the j-th column (1 < i, j < n) if and only if M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = 'X'.
The following figure illustrates a cross appearing at position (2, 2) in a 3 Γ 3 matrix.
X.X
.X.
X.X
Your task is to find out the number of crosses in the given matrix M. Two crosses are different if and only if they appear in different rows or columns.
Input
The first line contains only one positive integer n (1 β€ n β€ 500), denoting the size of the matrix M.
The following n lines illustrate the matrix M. Each line contains exactly n characters, each of them is 'X' or '.'. The j-th element in the i-th line represents M(i, j), where 1 β€ i, j β€ n.
Output
Output a single line containing only one integer number k β the number of crosses in the given matrix M.
Examples
Input
5
.....
.XXX.
.XXX.
.XXX.
.....
Output
1
Input
2
XX
XX
Output
0
Input
6
......
X.X.X.
.X.X.X
X.X.X.
.X.X.X
......
Output
4
Note
In the first sample, a cross appears at (3, 3), so the answer is 1.
In the second sample, no crosses appear since n < 3, so the answer is 0.
In the third sample, crosses appear at (3, 2), (3, 4), (4, 3), (4, 5), so the answer is 4.
Submitted Solution:
```
n=int(input())
a=[]
for i in range(n):
a.append(list(input()))
print(a)
c=0
for i in range(1,n-1,1):
for j in range(1,n-1,1):
if(i+1>-1 and i+1<n and i-1>-1 and i-1<n and j+1>-1 and j+1<n and j-1>-1 and j-1<n):
if(a[i][j] == a[i+1][j+1] == a[i-1][j+1] == a[i+1][j-1] == a[i-1][j-1]=='X'):
c=c+1
print(c)
``` | instruction | 0 | 19,483 | 23 | 38,966 |
No | output | 1 | 19,483 | 23 | 38,967 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Lunar New Year is approaching, and you bought a matrix with lots of "crosses".
This matrix M of size n Γ n contains only 'X' and '.' (without quotes). The element in the i-th row and the j-th column (i, j) is defined as M(i, j), where 1 β€ i, j β€ n. We define a cross appearing in the i-th row and the j-th column (1 < i, j < n) if and only if M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = 'X'.
The following figure illustrates a cross appearing at position (2, 2) in a 3 Γ 3 matrix.
X.X
.X.
X.X
Your task is to find out the number of crosses in the given matrix M. Two crosses are different if and only if they appear in different rows or columns.
Input
The first line contains only one positive integer n (1 β€ n β€ 500), denoting the size of the matrix M.
The following n lines illustrate the matrix M. Each line contains exactly n characters, each of them is 'X' or '.'. The j-th element in the i-th line represents M(i, j), where 1 β€ i, j β€ n.
Output
Output a single line containing only one integer number k β the number of crosses in the given matrix M.
Examples
Input
5
.....
.XXX.
.XXX.
.XXX.
.....
Output
1
Input
2
XX
XX
Output
0
Input
6
......
X.X.X.
.X.X.X
X.X.X.
.X.X.X
......
Output
4
Note
In the first sample, a cross appears at (3, 3), so the answer is 1.
In the second sample, no crosses appear since n < 3, so the answer is 0.
In the third sample, crosses appear at (3, 2), (3, 4), (4, 3), (4, 5), so the answer is 4.
Submitted Solution:
```
n = int(input())
arr = []
for i in range(n):
arr.append(list(input()))
count = 0
if n <= 2:
print(0)
else:
for i in range(n - 1):
for j in range(1, n - 1):
if arr[i][j] == arr[i - 1][j - 1] == arr[i - 1][j + 1] == arr[i + 1][j - 1] == arr[i + 1][j + 1] == 'X':
count += 1
print(count)
``` | instruction | 0 | 19,484 | 23 | 38,968 |
No | output | 1 | 19,484 | 23 | 38,969 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sereja painted n points on the plane, point number i (1 β€ i β€ n) has coordinates (i, 0). Then Sereja marked each point with a small or large English letter. Sereja don't like letter "x", so he didn't use it to mark points. Sereja thinks that the points are marked beautifully if the following conditions holds:
* all points can be divided into pairs so that each point will belong to exactly one pair;
* in each pair the point with the lesser abscissa will be marked with a small English letter and the point with the larger abscissa will be marked with the same large English letter;
* if we built a square on each pair, the pair's points will be the square's opposite points and the segment between them will be the square's diagonal, then among the resulting squares there won't be any intersecting or touching ones.
Little Petya erased some small and all large letters marking the points. Now Sereja wonders how many ways are there to return the removed letters so that the points were marked beautifully.
Input
The first line contains integer n the number of points (1 β€ n β€ 105). The second line contains a sequence consisting of n small English letters and question marks β the sequence of letters, that mark points, in order of increasing x-coordinate of points. Question marks denote the points without letters (Petya erased them). It is guaranteed that the input string doesn't contain letter "x".
Output
In a single line print the answer to the problem modulo 4294967296. If there is no way to return the removed letters, print number 0.
Please, do not write the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
4
a???
Output
50
Input
4
abc?
Output
0
Input
6
abc???
Output
1
Submitted Solution:
```
def two(a,b):
if a=='?':
if b == '?':
return 1
else:
return 0
else:
if b =='?':
return 1
else:
return 0
def answer1(n,s):
if n & 1 ==1:
return 0
if n < 2:
return 0
kind = 0
ans = 0
start = 0
end = 1
while end < n :
a = s[start]
b = s[end]
p = two(a,b)
if p != 0:
kind = 0
if end - start > 1:
inner = answer1(end - start-1,s[start+1:end])
kind = inner
else:
kind = 1
if len(s[end+1:]) != 0:
right = answer1(n-end-1,s[end+1:])
kind *= right
ans += kind
end += 2
return ans
def finall(s,kind):
ch_nums = len(s.replace('?',''))
num = len(s) // 2 - ch_nums
ans = kind*(25**num)
ans = ans % 4294967296
return ans
n = int(input())
s = input()
kind = answer1(n,s)
ans = finall(s,kind)
print(ans)
``` | instruction | 0 | 19,730 | 23 | 39,460 |
No | output | 1 | 19,730 | 23 | 39,461 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N boxes arranged in a circle. The i-th box contains A_i stones.
Determine whether it is possible to remove all the stones from the boxes by repeatedly performing the following operation:
* Select one box. Let the box be the i-th box. Then, for each j from 1 through N, remove exactly j stones from the (i+j)-th box. Here, the (N+k)-th box is identified with the k-th box.
Note that the operation cannot be performed if there is a box that does not contain enough number of stones to be removed.
Constraints
* 1 β¦ N β¦ 10^5
* 1 β¦ A_i β¦ 10^9
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 β¦ A_N
Output
If it is possible to remove all the stones from the boxes, print `YES`. Otherwise, print `NO`.
Examples
Input
5
4 5 1 2 3
Output
YES
Input
5
6 9 12 10 8
Output
YES
Input
4
1 2 3 1
Output
NO
Submitted Solution:
```
#!/usr/bin/env python3
import sys
N = int(input())
A = list(map(int, input().split()))
S = N*(N+1) // 2
SA = sum(A)
if SA % S != 0:
print("NO")
sys.exit(0)
K = SA // S
# B = []
C = []
for i in range(N):
# B.append(A[i] - A[i-1] - K)
b = A[i] - A[i-1] - K
if (b > 0) or (-b % N != 0):
print("NO")
sys.exit(0)
C.append(-b//N)
print("YES")
``` | instruction | 0 | 20,155 | 23 | 40,310 |
Yes | output | 1 | 20,155 | 23 | 40,311 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N boxes arranged in a circle. The i-th box contains A_i stones.
Determine whether it is possible to remove all the stones from the boxes by repeatedly performing the following operation:
* Select one box. Let the box be the i-th box. Then, for each j from 1 through N, remove exactly j stones from the (i+j)-th box. Here, the (N+k)-th box is identified with the k-th box.
Note that the operation cannot be performed if there is a box that does not contain enough number of stones to be removed.
Constraints
* 1 β¦ N β¦ 10^5
* 1 β¦ A_i β¦ 10^9
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 β¦ A_N
Output
If it is possible to remove all the stones from the boxes, print `YES`. Otherwise, print `NO`.
Examples
Input
5
4 5 1 2 3
Output
YES
Input
5
6 9 12 10 8
Output
YES
Input
4
1 2 3 1
Output
NO
Submitted Solution:
```
#!/usr/bin/env python3
if __name__ == '__main__':
N = int(input())
A = list(map(int, input().split()))
q = (1+N)*N/2
mi = 1000000009
for i in range(0,N):
mi = min(mi, A[i])
p = mi//q
for i in range(0,N):
A[i] -= p * q
ans = False
while True:
mi = 0
ma = 0
for i in range(0,N):
if A[i] > A[ma]:
ma = i
if A[i] < A[mi]:
mi = i
if A[mi] < 0:
ans = False
break
elif A[ma] == 0:
ans = True
break
for i in range(0, N):
A[(ma+1+i)%N] -= i+1
# min(A) < 15
if ans:
print("YES")
else:
print("NO")
# 1 2 3 4 5
# 2 3 4 5 1
# 3 4 5 1 2
# 4 5 1 2 3
# 5 1 2 3 4
``` | instruction | 0 | 20,158 | 23 | 40,316 |
No | output | 1 | 20,158 | 23 | 40,317 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N boxes arranged in a circle. The i-th box contains A_i stones.
Determine whether it is possible to remove all the stones from the boxes by repeatedly performing the following operation:
* Select one box. Let the box be the i-th box. Then, for each j from 1 through N, remove exactly j stones from the (i+j)-th box. Here, the (N+k)-th box is identified with the k-th box.
Note that the operation cannot be performed if there is a box that does not contain enough number of stones to be removed.
Constraints
* 1 β¦ N β¦ 10^5
* 1 β¦ A_i β¦ 10^9
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 β¦ A_N
Output
If it is possible to remove all the stones from the boxes, print `YES`. Otherwise, print `NO`.
Examples
Input
5
4 5 1 2 3
Output
YES
Input
5
6 9 12 10 8
Output
YES
Input
4
1 2 3 1
Output
NO
Submitted Solution:
```
n,*a=map(int,open(0).read().split())
q,m=divmod(sum(a),n*-~n//2)
print('YNEOS'[any((y-x-q+m*7)%n or y-x>q for x,y in zip(a,a[1:]))::2])
``` | instruction | 0 | 20,160 | 23 | 40,320 |
No | output | 1 | 20,160 | 23 | 40,321 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Pavel made a photo of his favourite stars in the sky. His camera takes a photo of all points of the sky that belong to some rectangle with sides parallel to the coordinate axes.
Strictly speaking, it makes a photo of all points with coordinates (x, y), such that x_1 β€ x β€ x_2 and y_1 β€ y β€ y_2, where (x_1, y_1) and (x_2, y_2) are coordinates of the left bottom and the right top corners of the rectangle being photographed. The area of this rectangle can be zero.
After taking the photo, Pavel wrote down coordinates of n of his favourite stars which appeared in the photo. These points are not necessarily distinct, there can be multiple stars in the same point of the sky.
Pavel has lost his camera recently and wants to buy a similar one. Specifically, he wants to know the dimensions of the photo he took earlier. Unfortunately, the photo is also lost. His notes are also of not much help; numbers are written in random order all over his notepad, so it's impossible to tell which numbers specify coordinates of which points.
Pavel asked you to help him to determine what are the possible dimensions of the photo according to his notes. As there are multiple possible answers, find the dimensions with the minimal possible area of the rectangle.
Input
The first line of the input contains an only integer n (1 β€ n β€ 100 000), the number of points in Pavel's records.
The second line contains 2 β
n integers a_1, a_2, ..., a_{2 β
n} (1 β€ a_i β€ 10^9), coordinates, written by Pavel in some order.
Output
Print the only integer, the minimal area of the rectangle which could have contained all points from Pavel's records.
Examples
Input
4
4 1 3 2 3 2 1 3
Output
1
Input
3
5 8 5 5 7 5
Output
0
Note
In the first sample stars in Pavel's records can be (1, 3), (1, 3), (2, 3), (2, 4). In this case, the minimal area of the rectangle, which contains all these points is 1 (rectangle with corners at (1, 3) and (2, 4)). | instruction | 0 | 20,264 | 23 | 40,528 |
Tags: brute force, implementation, math, sortings
Correct Solution:
```
n = int(input())
a = [int(v) for v in input().split()]
a.sort()
ans = (a[-1] - a[n]) * (a[n - 1] - a[0])
for i in range(1, n):
ans = min(ans, (a[-1] - a[0]) * (a[i + n - 1] - a[i]))
print(ans)
``` | output | 1 | 20,264 | 23 | 40,529 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Pavel made a photo of his favourite stars in the sky. His camera takes a photo of all points of the sky that belong to some rectangle with sides parallel to the coordinate axes.
Strictly speaking, it makes a photo of all points with coordinates (x, y), such that x_1 β€ x β€ x_2 and y_1 β€ y β€ y_2, where (x_1, y_1) and (x_2, y_2) are coordinates of the left bottom and the right top corners of the rectangle being photographed. The area of this rectangle can be zero.
After taking the photo, Pavel wrote down coordinates of n of his favourite stars which appeared in the photo. These points are not necessarily distinct, there can be multiple stars in the same point of the sky.
Pavel has lost his camera recently and wants to buy a similar one. Specifically, he wants to know the dimensions of the photo he took earlier. Unfortunately, the photo is also lost. His notes are also of not much help; numbers are written in random order all over his notepad, so it's impossible to tell which numbers specify coordinates of which points.
Pavel asked you to help him to determine what are the possible dimensions of the photo according to his notes. As there are multiple possible answers, find the dimensions with the minimal possible area of the rectangle.
Input
The first line of the input contains an only integer n (1 β€ n β€ 100 000), the number of points in Pavel's records.
The second line contains 2 β
n integers a_1, a_2, ..., a_{2 β
n} (1 β€ a_i β€ 10^9), coordinates, written by Pavel in some order.
Output
Print the only integer, the minimal area of the rectangle which could have contained all points from Pavel's records.
Examples
Input
4
4 1 3 2 3 2 1 3
Output
1
Input
3
5 8 5 5 7 5
Output
0
Note
In the first sample stars in Pavel's records can be (1, 3), (1, 3), (2, 3), (2, 4). In this case, the minimal area of the rectangle, which contains all these points is 1 (rectangle with corners at (1, 3) and (2, 4)). | instruction | 0 | 20,265 | 23 | 40,530 |
Tags: brute force, implementation, math, sortings
Correct Solution:
```
n=int(input())
a=sorted(map(int,input().split()))
print(min([(a[n-1]-a[0])*(a[-1]-a[n])]+[(a[-1]-a[0])*(y-x)
for x,y in zip(a,a[n-1:])]))
``` | output | 1 | 20,265 | 23 | 40,531 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Pavel made a photo of his favourite stars in the sky. His camera takes a photo of all points of the sky that belong to some rectangle with sides parallel to the coordinate axes.
Strictly speaking, it makes a photo of all points with coordinates (x, y), such that x_1 β€ x β€ x_2 and y_1 β€ y β€ y_2, where (x_1, y_1) and (x_2, y_2) are coordinates of the left bottom and the right top corners of the rectangle being photographed. The area of this rectangle can be zero.
After taking the photo, Pavel wrote down coordinates of n of his favourite stars which appeared in the photo. These points are not necessarily distinct, there can be multiple stars in the same point of the sky.
Pavel has lost his camera recently and wants to buy a similar one. Specifically, he wants to know the dimensions of the photo he took earlier. Unfortunately, the photo is also lost. His notes are also of not much help; numbers are written in random order all over his notepad, so it's impossible to tell which numbers specify coordinates of which points.
Pavel asked you to help him to determine what are the possible dimensions of the photo according to his notes. As there are multiple possible answers, find the dimensions with the minimal possible area of the rectangle.
Input
The first line of the input contains an only integer n (1 β€ n β€ 100 000), the number of points in Pavel's records.
The second line contains 2 β
n integers a_1, a_2, ..., a_{2 β
n} (1 β€ a_i β€ 10^9), coordinates, written by Pavel in some order.
Output
Print the only integer, the minimal area of the rectangle which could have contained all points from Pavel's records.
Examples
Input
4
4 1 3 2 3 2 1 3
Output
1
Input
3
5 8 5 5 7 5
Output
0
Note
In the first sample stars in Pavel's records can be (1, 3), (1, 3), (2, 3), (2, 4). In this case, the minimal area of the rectangle, which contains all these points is 1 (rectangle with corners at (1, 3) and (2, 4)). | instruction | 0 | 20,266 | 23 | 40,532 |
Tags: brute force, implementation, math, sortings
Correct Solution:
```
n=int(input())
a=sorted(map(int,input().split()))
r=0
if n>1:r=min((a[n-1]-a[0])*(a[-1]-a[n]),(a[-1]-a[0])*min(y-x
for x,y in zip(a[1:],a[n:-1])))
print(r)
``` | output | 1 | 20,266 | 23 | 40,533 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Pavel made a photo of his favourite stars in the sky. His camera takes a photo of all points of the sky that belong to some rectangle with sides parallel to the coordinate axes.
Strictly speaking, it makes a photo of all points with coordinates (x, y), such that x_1 β€ x β€ x_2 and y_1 β€ y β€ y_2, where (x_1, y_1) and (x_2, y_2) are coordinates of the left bottom and the right top corners of the rectangle being photographed. The area of this rectangle can be zero.
After taking the photo, Pavel wrote down coordinates of n of his favourite stars which appeared in the photo. These points are not necessarily distinct, there can be multiple stars in the same point of the sky.
Pavel has lost his camera recently and wants to buy a similar one. Specifically, he wants to know the dimensions of the photo he took earlier. Unfortunately, the photo is also lost. His notes are also of not much help; numbers are written in random order all over his notepad, so it's impossible to tell which numbers specify coordinates of which points.
Pavel asked you to help him to determine what are the possible dimensions of the photo according to his notes. As there are multiple possible answers, find the dimensions with the minimal possible area of the rectangle.
Input
The first line of the input contains an only integer n (1 β€ n β€ 100 000), the number of points in Pavel's records.
The second line contains 2 β
n integers a_1, a_2, ..., a_{2 β
n} (1 β€ a_i β€ 10^9), coordinates, written by Pavel in some order.
Output
Print the only integer, the minimal area of the rectangle which could have contained all points from Pavel's records.
Examples
Input
4
4 1 3 2 3 2 1 3
Output
1
Input
3
5 8 5 5 7 5
Output
0
Note
In the first sample stars in Pavel's records can be (1, 3), (1, 3), (2, 3), (2, 4). In this case, the minimal area of the rectangle, which contains all these points is 1 (rectangle with corners at (1, 3) and (2, 4)). | instruction | 0 | 20,267 | 23 | 40,534 |
Tags: brute force, implementation, math, sortings
Correct Solution:
```
def main():
n = int(input())
a = [int(i) for i in input().split()]
a.sort()
x = a[n - 1] - a[0]
y = a[2 * n - 1] - a[n]
c1 = x * y
x = a[2 * n - 1] - a[0]
for i in range(1, n):
c1 = min(c1, x * (a[i + n - 1] - a[i]))
print(c1)
if __name__ == '__main__':
main()
``` | output | 1 | 20,267 | 23 | 40,535 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Pavel made a photo of his favourite stars in the sky. His camera takes a photo of all points of the sky that belong to some rectangle with sides parallel to the coordinate axes.
Strictly speaking, it makes a photo of all points with coordinates (x, y), such that x_1 β€ x β€ x_2 and y_1 β€ y β€ y_2, where (x_1, y_1) and (x_2, y_2) are coordinates of the left bottom and the right top corners of the rectangle being photographed. The area of this rectangle can be zero.
After taking the photo, Pavel wrote down coordinates of n of his favourite stars which appeared in the photo. These points are not necessarily distinct, there can be multiple stars in the same point of the sky.
Pavel has lost his camera recently and wants to buy a similar one. Specifically, he wants to know the dimensions of the photo he took earlier. Unfortunately, the photo is also lost. His notes are also of not much help; numbers are written in random order all over his notepad, so it's impossible to tell which numbers specify coordinates of which points.
Pavel asked you to help him to determine what are the possible dimensions of the photo according to his notes. As there are multiple possible answers, find the dimensions with the minimal possible area of the rectangle.
Input
The first line of the input contains an only integer n (1 β€ n β€ 100 000), the number of points in Pavel's records.
The second line contains 2 β
n integers a_1, a_2, ..., a_{2 β
n} (1 β€ a_i β€ 10^9), coordinates, written by Pavel in some order.
Output
Print the only integer, the minimal area of the rectangle which could have contained all points from Pavel's records.
Examples
Input
4
4 1 3 2 3 2 1 3
Output
1
Input
3
5 8 5 5 7 5
Output
0
Note
In the first sample stars in Pavel's records can be (1, 3), (1, 3), (2, 3), (2, 4). In this case, the minimal area of the rectangle, which contains all these points is 1 (rectangle with corners at (1, 3) and (2, 4)). | instruction | 0 | 20,268 | 23 | 40,536 |
Tags: brute force, implementation, math, sortings
Correct Solution:
```
n = int(input())
a = sorted(list(map(int, input().split())))
res = (a[n-1] - a[0])*(a[-1] - a[n])
for i in range(1, n):
if (a[-1] - a[0])*(a[n + i - 1] - a[i]) < res:
res = (a[-1] - a[0])*(a[n + i - 1] - a[i])
print(res)
``` | output | 1 | 20,268 | 23 | 40,537 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Pavel made a photo of his favourite stars in the sky. His camera takes a photo of all points of the sky that belong to some rectangle with sides parallel to the coordinate axes.
Strictly speaking, it makes a photo of all points with coordinates (x, y), such that x_1 β€ x β€ x_2 and y_1 β€ y β€ y_2, where (x_1, y_1) and (x_2, y_2) are coordinates of the left bottom and the right top corners of the rectangle being photographed. The area of this rectangle can be zero.
After taking the photo, Pavel wrote down coordinates of n of his favourite stars which appeared in the photo. These points are not necessarily distinct, there can be multiple stars in the same point of the sky.
Pavel has lost his camera recently and wants to buy a similar one. Specifically, he wants to know the dimensions of the photo he took earlier. Unfortunately, the photo is also lost. His notes are also of not much help; numbers are written in random order all over his notepad, so it's impossible to tell which numbers specify coordinates of which points.
Pavel asked you to help him to determine what are the possible dimensions of the photo according to his notes. As there are multiple possible answers, find the dimensions with the minimal possible area of the rectangle.
Input
The first line of the input contains an only integer n (1 β€ n β€ 100 000), the number of points in Pavel's records.
The second line contains 2 β
n integers a_1, a_2, ..., a_{2 β
n} (1 β€ a_i β€ 10^9), coordinates, written by Pavel in some order.
Output
Print the only integer, the minimal area of the rectangle which could have contained all points from Pavel's records.
Examples
Input
4
4 1 3 2 3 2 1 3
Output
1
Input
3
5 8 5 5 7 5
Output
0
Note
In the first sample stars in Pavel's records can be (1, 3), (1, 3), (2, 3), (2, 4). In this case, the minimal area of the rectangle, which contains all these points is 1 (rectangle with corners at (1, 3) and (2, 4)). | instruction | 0 | 20,269 | 23 | 40,538 |
Tags: brute force, implementation, math, sortings
Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
a.sort()
s1 = (a[n-1]-a[0])*(a[-1]-a[n])
tmp = a[-1] - a[0]
for i in range(1, n):
if tmp * (a[n+i-1]-a[i]) < s1:
s1 = tmp * (a[n+i-1]-a[i])
print(s1)
``` | output | 1 | 20,269 | 23 | 40,539 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Pavel made a photo of his favourite stars in the sky. His camera takes a photo of all points of the sky that belong to some rectangle with sides parallel to the coordinate axes.
Strictly speaking, it makes a photo of all points with coordinates (x, y), such that x_1 β€ x β€ x_2 and y_1 β€ y β€ y_2, where (x_1, y_1) and (x_2, y_2) are coordinates of the left bottom and the right top corners of the rectangle being photographed. The area of this rectangle can be zero.
After taking the photo, Pavel wrote down coordinates of n of his favourite stars which appeared in the photo. These points are not necessarily distinct, there can be multiple stars in the same point of the sky.
Pavel has lost his camera recently and wants to buy a similar one. Specifically, he wants to know the dimensions of the photo he took earlier. Unfortunately, the photo is also lost. His notes are also of not much help; numbers are written in random order all over his notepad, so it's impossible to tell which numbers specify coordinates of which points.
Pavel asked you to help him to determine what are the possible dimensions of the photo according to his notes. As there are multiple possible answers, find the dimensions with the minimal possible area of the rectangle.
Input
The first line of the input contains an only integer n (1 β€ n β€ 100 000), the number of points in Pavel's records.
The second line contains 2 β
n integers a_1, a_2, ..., a_{2 β
n} (1 β€ a_i β€ 10^9), coordinates, written by Pavel in some order.
Output
Print the only integer, the minimal area of the rectangle which could have contained all points from Pavel's records.
Examples
Input
4
4 1 3 2 3 2 1 3
Output
1
Input
3
5 8 5 5 7 5
Output
0
Note
In the first sample stars in Pavel's records can be (1, 3), (1, 3), (2, 3), (2, 4). In this case, the minimal area of the rectangle, which contains all these points is 1 (rectangle with corners at (1, 3) and (2, 4)). | instruction | 0 | 20,270 | 23 | 40,540 |
Tags: brute force, implementation, math, sortings
Correct Solution:
```
n=int(input())
a=list(map(int,input().split()))
a.sort()
k=12122121212121
for i in range(1,n):
k=min(k,a[i+n-1]-a[i])
k=k*(a[2*n-1]-a[0])
z=abs(a[0]-a[n-1])*abs(a[n]-a[2*n-1])
print(min(k,z))
``` | output | 1 | 20,270 | 23 | 40,541 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Pavel made a photo of his favourite stars in the sky. His camera takes a photo of all points of the sky that belong to some rectangle with sides parallel to the coordinate axes.
Strictly speaking, it makes a photo of all points with coordinates (x, y), such that x_1 β€ x β€ x_2 and y_1 β€ y β€ y_2, where (x_1, y_1) and (x_2, y_2) are coordinates of the left bottom and the right top corners of the rectangle being photographed. The area of this rectangle can be zero.
After taking the photo, Pavel wrote down coordinates of n of his favourite stars which appeared in the photo. These points are not necessarily distinct, there can be multiple stars in the same point of the sky.
Pavel has lost his camera recently and wants to buy a similar one. Specifically, he wants to know the dimensions of the photo he took earlier. Unfortunately, the photo is also lost. His notes are also of not much help; numbers are written in random order all over his notepad, so it's impossible to tell which numbers specify coordinates of which points.
Pavel asked you to help him to determine what are the possible dimensions of the photo according to his notes. As there are multiple possible answers, find the dimensions with the minimal possible area of the rectangle.
Input
The first line of the input contains an only integer n (1 β€ n β€ 100 000), the number of points in Pavel's records.
The second line contains 2 β
n integers a_1, a_2, ..., a_{2 β
n} (1 β€ a_i β€ 10^9), coordinates, written by Pavel in some order.
Output
Print the only integer, the minimal area of the rectangle which could have contained all points from Pavel's records.
Examples
Input
4
4 1 3 2 3 2 1 3
Output
1
Input
3
5 8 5 5 7 5
Output
0
Note
In the first sample stars in Pavel's records can be (1, 3), (1, 3), (2, 3), (2, 4). In this case, the minimal area of the rectangle, which contains all these points is 1 (rectangle with corners at (1, 3) and (2, 4)). | instruction | 0 | 20,271 | 23 | 40,542 |
Tags: brute force, implementation, math, sortings
Correct Solution:
```
n = int(input())
records = list(map(int,input().split()))
records.sort()
diffArr = []
for i in range(n+1):
if i == 0:
diffArr.append([records[n-1]-records[0],records[-1]-records[n]])
elif i == n:
diffArr.append([records[-1]-records[n],records[n-1]-records[0]])
else:
diffArr.append([records[n+i-1] - records[i],records[-1]-records[0]])
minDiff = min(diffArr, key = lambda t: t[0]*t[1])
print(minDiff[0]*minDiff[1])
``` | output | 1 | 20,271 | 23 | 40,543 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pavel made a photo of his favourite stars in the sky. His camera takes a photo of all points of the sky that belong to some rectangle with sides parallel to the coordinate axes.
Strictly speaking, it makes a photo of all points with coordinates (x, y), such that x_1 β€ x β€ x_2 and y_1 β€ y β€ y_2, where (x_1, y_1) and (x_2, y_2) are coordinates of the left bottom and the right top corners of the rectangle being photographed. The area of this rectangle can be zero.
After taking the photo, Pavel wrote down coordinates of n of his favourite stars which appeared in the photo. These points are not necessarily distinct, there can be multiple stars in the same point of the sky.
Pavel has lost his camera recently and wants to buy a similar one. Specifically, he wants to know the dimensions of the photo he took earlier. Unfortunately, the photo is also lost. His notes are also of not much help; numbers are written in random order all over his notepad, so it's impossible to tell which numbers specify coordinates of which points.
Pavel asked you to help him to determine what are the possible dimensions of the photo according to his notes. As there are multiple possible answers, find the dimensions with the minimal possible area of the rectangle.
Input
The first line of the input contains an only integer n (1 β€ n β€ 100 000), the number of points in Pavel's records.
The second line contains 2 β
n integers a_1, a_2, ..., a_{2 β
n} (1 β€ a_i β€ 10^9), coordinates, written by Pavel in some order.
Output
Print the only integer, the minimal area of the rectangle which could have contained all points from Pavel's records.
Examples
Input
4
4 1 3 2 3 2 1 3
Output
1
Input
3
5 8 5 5 7 5
Output
0
Note
In the first sample stars in Pavel's records can be (1, 3), (1, 3), (2, 3), (2, 4). In this case, the minimal area of the rectangle, which contains all these points is 1 (rectangle with corners at (1, 3) and (2, 4)).
Submitted Solution:
```
n=int(input())
CO=list(map(int,input().split()))
CO.sort()
area=(CO[n-1]-CO[0])*(CO[2*n-1]-CO[n])
for i in range(n+1):
areax=(CO[i+n-1]-CO[i])*(CO[2*n-1]-CO[0])
if areax<area:
area=areax
print(area)
``` | instruction | 0 | 20,272 | 23 | 40,544 |
Yes | output | 1 | 20,272 | 23 | 40,545 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pavel made a photo of his favourite stars in the sky. His camera takes a photo of all points of the sky that belong to some rectangle with sides parallel to the coordinate axes.
Strictly speaking, it makes a photo of all points with coordinates (x, y), such that x_1 β€ x β€ x_2 and y_1 β€ y β€ y_2, where (x_1, y_1) and (x_2, y_2) are coordinates of the left bottom and the right top corners of the rectangle being photographed. The area of this rectangle can be zero.
After taking the photo, Pavel wrote down coordinates of n of his favourite stars which appeared in the photo. These points are not necessarily distinct, there can be multiple stars in the same point of the sky.
Pavel has lost his camera recently and wants to buy a similar one. Specifically, he wants to know the dimensions of the photo he took earlier. Unfortunately, the photo is also lost. His notes are also of not much help; numbers are written in random order all over his notepad, so it's impossible to tell which numbers specify coordinates of which points.
Pavel asked you to help him to determine what are the possible dimensions of the photo according to his notes. As there are multiple possible answers, find the dimensions with the minimal possible area of the rectangle.
Input
The first line of the input contains an only integer n (1 β€ n β€ 100 000), the number of points in Pavel's records.
The second line contains 2 β
n integers a_1, a_2, ..., a_{2 β
n} (1 β€ a_i β€ 10^9), coordinates, written by Pavel in some order.
Output
Print the only integer, the minimal area of the rectangle which could have contained all points from Pavel's records.
Examples
Input
4
4 1 3 2 3 2 1 3
Output
1
Input
3
5 8 5 5 7 5
Output
0
Note
In the first sample stars in Pavel's records can be (1, 3), (1, 3), (2, 3), (2, 4). In this case, the minimal area of the rectangle, which contains all these points is 1 (rectangle with corners at (1, 3) and (2, 4)).
Submitted Solution:
```
N=int(input())
A=list(map(int,input().split()))
A.sort()
s=(A[N-1]-A[0])*(A[2*N-1]-A[N])
for i in range(1,N):
s=min(s,(A[N-1+i]-A[i])*(A[2*N-1]-A[0]))
print(s)
``` | instruction | 0 | 20,273 | 23 | 40,546 |
Yes | output | 1 | 20,273 | 23 | 40,547 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pavel made a photo of his favourite stars in the sky. His camera takes a photo of all points of the sky that belong to some rectangle with sides parallel to the coordinate axes.
Strictly speaking, it makes a photo of all points with coordinates (x, y), such that x_1 β€ x β€ x_2 and y_1 β€ y β€ y_2, where (x_1, y_1) and (x_2, y_2) are coordinates of the left bottom and the right top corners of the rectangle being photographed. The area of this rectangle can be zero.
After taking the photo, Pavel wrote down coordinates of n of his favourite stars which appeared in the photo. These points are not necessarily distinct, there can be multiple stars in the same point of the sky.
Pavel has lost his camera recently and wants to buy a similar one. Specifically, he wants to know the dimensions of the photo he took earlier. Unfortunately, the photo is also lost. His notes are also of not much help; numbers are written in random order all over his notepad, so it's impossible to tell which numbers specify coordinates of which points.
Pavel asked you to help him to determine what are the possible dimensions of the photo according to his notes. As there are multiple possible answers, find the dimensions with the minimal possible area of the rectangle.
Input
The first line of the input contains an only integer n (1 β€ n β€ 100 000), the number of points in Pavel's records.
The second line contains 2 β
n integers a_1, a_2, ..., a_{2 β
n} (1 β€ a_i β€ 10^9), coordinates, written by Pavel in some order.
Output
Print the only integer, the minimal area of the rectangle which could have contained all points from Pavel's records.
Examples
Input
4
4 1 3 2 3 2 1 3
Output
1
Input
3
5 8 5 5 7 5
Output
0
Note
In the first sample stars in Pavel's records can be (1, 3), (1, 3), (2, 3), (2, 4). In this case, the minimal area of the rectangle, which contains all these points is 1 (rectangle with corners at (1, 3) and (2, 4)).
Submitted Solution:
```
import functools
import time
from collections import Counter
def timer(func):
@functools.wraps(func)
def wrapper(*args, **kwargs):
stime = time.perf_counter()
res = func(*args, **kwargs)
elapsed = time.perf_counter() - stime
print(f"{func.__name__} in {elapsed:.4f} secs")
return res
return wrapper
class solver:
# @timer
def __init__(self):
pass
def __call__(self):
n = int(input())
a = list(map(int, input().strip().split()))
a.sort()
ans = 10**18
for i in range(n + 1):
x1 = a[i]
x2 = a[i + n - 1]
y1 = a[0] if i > 0 else a[n]
y2 = a[-1] if i < n else a[n - 1]
ans = min(ans, (x2 - x1) * (y2 - y1))
print(ans)
solver()()
``` | instruction | 0 | 20,274 | 23 | 40,548 |
Yes | output | 1 | 20,274 | 23 | 40,549 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pavel made a photo of his favourite stars in the sky. His camera takes a photo of all points of the sky that belong to some rectangle with sides parallel to the coordinate axes.
Strictly speaking, it makes a photo of all points with coordinates (x, y), such that x_1 β€ x β€ x_2 and y_1 β€ y β€ y_2, where (x_1, y_1) and (x_2, y_2) are coordinates of the left bottom and the right top corners of the rectangle being photographed. The area of this rectangle can be zero.
After taking the photo, Pavel wrote down coordinates of n of his favourite stars which appeared in the photo. These points are not necessarily distinct, there can be multiple stars in the same point of the sky.
Pavel has lost his camera recently and wants to buy a similar one. Specifically, he wants to know the dimensions of the photo he took earlier. Unfortunately, the photo is also lost. His notes are also of not much help; numbers are written in random order all over his notepad, so it's impossible to tell which numbers specify coordinates of which points.
Pavel asked you to help him to determine what are the possible dimensions of the photo according to his notes. As there are multiple possible answers, find the dimensions with the minimal possible area of the rectangle.
Input
The first line of the input contains an only integer n (1 β€ n β€ 100 000), the number of points in Pavel's records.
The second line contains 2 β
n integers a_1, a_2, ..., a_{2 β
n} (1 β€ a_i β€ 10^9), coordinates, written by Pavel in some order.
Output
Print the only integer, the minimal area of the rectangle which could have contained all points from Pavel's records.
Examples
Input
4
4 1 3 2 3 2 1 3
Output
1
Input
3
5 8 5 5 7 5
Output
0
Note
In the first sample stars in Pavel's records can be (1, 3), (1, 3), (2, 3), (2, 4). In this case, the minimal area of the rectangle, which contains all these points is 1 (rectangle with corners at (1, 3) and (2, 4)).
Submitted Solution:
```
n = int(input())
arr = sorted(list(map(int,input().split())))
ans = (arr[n-1]-arr[0])*(arr[2*n-1]-arr[n])
for i in range(1,n):
ans = min(ans,(arr[i+n-1]-arr[i])*(arr[2*n-1]-arr[0]))
print(ans)
``` | instruction | 0 | 20,275 | 23 | 40,550 |
Yes | output | 1 | 20,275 | 23 | 40,551 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pavel made a photo of his favourite stars in the sky. His camera takes a photo of all points of the sky that belong to some rectangle with sides parallel to the coordinate axes.
Strictly speaking, it makes a photo of all points with coordinates (x, y), such that x_1 β€ x β€ x_2 and y_1 β€ y β€ y_2, where (x_1, y_1) and (x_2, y_2) are coordinates of the left bottom and the right top corners of the rectangle being photographed. The area of this rectangle can be zero.
After taking the photo, Pavel wrote down coordinates of n of his favourite stars which appeared in the photo. These points are not necessarily distinct, there can be multiple stars in the same point of the sky.
Pavel has lost his camera recently and wants to buy a similar one. Specifically, he wants to know the dimensions of the photo he took earlier. Unfortunately, the photo is also lost. His notes are also of not much help; numbers are written in random order all over his notepad, so it's impossible to tell which numbers specify coordinates of which points.
Pavel asked you to help him to determine what are the possible dimensions of the photo according to his notes. As there are multiple possible answers, find the dimensions with the minimal possible area of the rectangle.
Input
The first line of the input contains an only integer n (1 β€ n β€ 100 000), the number of points in Pavel's records.
The second line contains 2 β
n integers a_1, a_2, ..., a_{2 β
n} (1 β€ a_i β€ 10^9), coordinates, written by Pavel in some order.
Output
Print the only integer, the minimal area of the rectangle which could have contained all points from Pavel's records.
Examples
Input
4
4 1 3 2 3 2 1 3
Output
1
Input
3
5 8 5 5 7 5
Output
0
Note
In the first sample stars in Pavel's records can be (1, 3), (1, 3), (2, 3), (2, 4). In this case, the minimal area of the rectangle, which contains all these points is 1 (rectangle with corners at (1, 3) and (2, 4)).
Submitted Solution:
```
if __name__ == "__main__":
n = int(input())
data = map(int, input().split())
s = sorted(data)
print((s[n-1] - s[0]) * (s[2*n - 1] - s[n]))
``` | instruction | 0 | 20,276 | 23 | 40,552 |
No | output | 1 | 20,276 | 23 | 40,553 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pavel made a photo of his favourite stars in the sky. His camera takes a photo of all points of the sky that belong to some rectangle with sides parallel to the coordinate axes.
Strictly speaking, it makes a photo of all points with coordinates (x, y), such that x_1 β€ x β€ x_2 and y_1 β€ y β€ y_2, where (x_1, y_1) and (x_2, y_2) are coordinates of the left bottom and the right top corners of the rectangle being photographed. The area of this rectangle can be zero.
After taking the photo, Pavel wrote down coordinates of n of his favourite stars which appeared in the photo. These points are not necessarily distinct, there can be multiple stars in the same point of the sky.
Pavel has lost his camera recently and wants to buy a similar one. Specifically, he wants to know the dimensions of the photo he took earlier. Unfortunately, the photo is also lost. His notes are also of not much help; numbers are written in random order all over his notepad, so it's impossible to tell which numbers specify coordinates of which points.
Pavel asked you to help him to determine what are the possible dimensions of the photo according to his notes. As there are multiple possible answers, find the dimensions with the minimal possible area of the rectangle.
Input
The first line of the input contains an only integer n (1 β€ n β€ 100 000), the number of points in Pavel's records.
The second line contains 2 β
n integers a_1, a_2, ..., a_{2 β
n} (1 β€ a_i β€ 10^9), coordinates, written by Pavel in some order.
Output
Print the only integer, the minimal area of the rectangle which could have contained all points from Pavel's records.
Examples
Input
4
4 1 3 2 3 2 1 3
Output
1
Input
3
5 8 5 5 7 5
Output
0
Note
In the first sample stars in Pavel's records can be (1, 3), (1, 3), (2, 3), (2, 4). In this case, the minimal area of the rectangle, which contains all these points is 1 (rectangle with corners at (1, 3) and (2, 4)).
Submitted Solution:
```
n = int(input())
a = sorted(map(int, input().split()))
best = (a[n - 1] - a[0]) * (a[2 * n - 1] - a[n])
for i in range(1, n - 1):
best = min(best, (a[n + i] - a[i]) * (a[2 * n - 1] - a[0]))
print(best)
``` | instruction | 0 | 20,277 | 23 | 40,554 |
No | output | 1 | 20,277 | 23 | 40,555 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pavel made a photo of his favourite stars in the sky. His camera takes a photo of all points of the sky that belong to some rectangle with sides parallel to the coordinate axes.
Strictly speaking, it makes a photo of all points with coordinates (x, y), such that x_1 β€ x β€ x_2 and y_1 β€ y β€ y_2, where (x_1, y_1) and (x_2, y_2) are coordinates of the left bottom and the right top corners of the rectangle being photographed. The area of this rectangle can be zero.
After taking the photo, Pavel wrote down coordinates of n of his favourite stars which appeared in the photo. These points are not necessarily distinct, there can be multiple stars in the same point of the sky.
Pavel has lost his camera recently and wants to buy a similar one. Specifically, he wants to know the dimensions of the photo he took earlier. Unfortunately, the photo is also lost. His notes are also of not much help; numbers are written in random order all over his notepad, so it's impossible to tell which numbers specify coordinates of which points.
Pavel asked you to help him to determine what are the possible dimensions of the photo according to his notes. As there are multiple possible answers, find the dimensions with the minimal possible area of the rectangle.
Input
The first line of the input contains an only integer n (1 β€ n β€ 100 000), the number of points in Pavel's records.
The second line contains 2 β
n integers a_1, a_2, ..., a_{2 β
n} (1 β€ a_i β€ 10^9), coordinates, written by Pavel in some order.
Output
Print the only integer, the minimal area of the rectangle which could have contained all points from Pavel's records.
Examples
Input
4
4 1 3 2 3 2 1 3
Output
1
Input
3
5 8 5 5 7 5
Output
0
Note
In the first sample stars in Pavel's records can be (1, 3), (1, 3), (2, 3), (2, 4). In this case, the minimal area of the rectangle, which contains all these points is 1 (rectangle with corners at (1, 3) and (2, 4)).
Submitted Solution:
```
n = 2*int(input())
arr = [int(i) for i in input().split()]
arr.sort()
first = (arr[0],arr[n//2])
last = (arr[n//2-1],arr[n-1])
#print(first,last)
print(abs(first[0]-last[0]) * abs(first[1]-last[1]))
``` | instruction | 0 | 20,278 | 23 | 40,556 |
No | output | 1 | 20,278 | 23 | 40,557 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Pavel made a photo of his favourite stars in the sky. His camera takes a photo of all points of the sky that belong to some rectangle with sides parallel to the coordinate axes.
Strictly speaking, it makes a photo of all points with coordinates (x, y), such that x_1 β€ x β€ x_2 and y_1 β€ y β€ y_2, where (x_1, y_1) and (x_2, y_2) are coordinates of the left bottom and the right top corners of the rectangle being photographed. The area of this rectangle can be zero.
After taking the photo, Pavel wrote down coordinates of n of his favourite stars which appeared in the photo. These points are not necessarily distinct, there can be multiple stars in the same point of the sky.
Pavel has lost his camera recently and wants to buy a similar one. Specifically, he wants to know the dimensions of the photo he took earlier. Unfortunately, the photo is also lost. His notes are also of not much help; numbers are written in random order all over his notepad, so it's impossible to tell which numbers specify coordinates of which points.
Pavel asked you to help him to determine what are the possible dimensions of the photo according to his notes. As there are multiple possible answers, find the dimensions with the minimal possible area of the rectangle.
Input
The first line of the input contains an only integer n (1 β€ n β€ 100 000), the number of points in Pavel's records.
The second line contains 2 β
n integers a_1, a_2, ..., a_{2 β
n} (1 β€ a_i β€ 10^9), coordinates, written by Pavel in some order.
Output
Print the only integer, the minimal area of the rectangle which could have contained all points from Pavel's records.
Examples
Input
4
4 1 3 2 3 2 1 3
Output
1
Input
3
5 8 5 5 7 5
Output
0
Note
In the first sample stars in Pavel's records can be (1, 3), (1, 3), (2, 3), (2, 4). In this case, the minimal area of the rectangle, which contains all these points is 1 (rectangle with corners at (1, 3) and (2, 4)).
Submitted Solution:
```
n = int(input())
a = [int(x) for x in input().split()]
a.sort()
top = [a[0], a[-1]]
right = [a[n - 1], a[n]]
print(abs((top[0] - right[0])*(top[1] - right[1])))
``` | instruction | 0 | 20,279 | 23 | 40,558 |
No | output | 1 | 20,279 | 23 | 40,559 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Like any unknown mathematician, Yuri has favourite numbers: A, B, C, and D, where A β€ B β€ C β€ D. Yuri also likes triangles and once he thought: how many non-degenerate triangles with integer sides x, y, and z exist, such that A β€ x β€ B β€ y β€ C β€ z β€ D holds?
Yuri is preparing problems for a new contest now, so he is very busy. That's why he asked you to calculate the number of triangles with described property.
The triangle is called non-degenerate if and only if its vertices are not collinear.
Input
The first line contains four integers: A, B, C and D (1 β€ A β€ B β€ C β€ D β€ 5 β
10^5) β Yuri's favourite numbers.
Output
Print the number of non-degenerate triangles with integer sides x, y, and z such that the inequality A β€ x β€ B β€ y β€ C β€ z β€ D holds.
Examples
Input
1 2 3 4
Output
4
Input
1 2 2 5
Output
3
Input
500000 500000 500000 500000
Output
1
Note
In the first example Yuri can make up triangles with sides (1, 3, 3), (2, 2, 3), (2, 3, 3) and (2, 3, 4).
In the second example Yuri can make up triangles with sides (1, 2, 2), (2, 2, 2) and (2, 2, 3).
In the third example Yuri can make up only one equilateral triangle with sides equal to 5 β
10^5. | instruction | 0 | 20,420 | 23 | 40,840 |
Tags: binary search, implementation, math, two pointers
Correct Solution:
```
import sys
input = sys.stdin.readline
def sum1(x):
k = min(d, c + x - 1, b + x - 1)
if k < c:
return 0
else:
return (c - b + 1) * (k - c + 1)
def sum2(x):
k = min(d, c + x - 1)
l = max(b + x, c)
if k < l:
return(0)
else:
return (c + x) * (k - l + 1) - (k + l) * (k - l + 1) // 2
a, b, c, d = map(int, input().split())
res = 0
for x in range(a, b + 1):
res += sum1(x) + sum2(x)
print(res)
``` | output | 1 | 20,420 | 23 | 40,841 |
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