message stringlengths 2 22.8k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 16 109k | cluster float64 1 1 | __index_level_0__ int64 32 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N cities on a number line. The i-th city is located at coordinate x_i.
Your objective is to visit all these cities at least once.
In order to do so, you will first set a positive integer D.
Then, you will depart from coordinate X and perform Move 1 and Move 2 below, as many times as you like:
* Move 1: travel from coordinate y to coordinate y + D.
* Move 2: travel from coordinate y to coordinate y - D.
Find the maximum value of D that enables you to visit all the cities.
Here, to visit a city is to travel to the coordinate where that city is located.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq X \leq 10^9
* 1 \leq x_i \leq 10^9
* x_i are all different.
* x_1, x_2, ..., x_N \neq X
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_N
Output
Print the maximum value of D that enables you to visit all the cities.
Examples
Input
3 3
1 7 11
Output
2
Input
3 81
33 105 57
Output
24
Input
1 1
1000000000
Output
999999999
Submitted Solution:
```
import math
N,X=map(int,input().split())
L=list(map(int,input().split()))
L.append(X)
L=sorted(L)
m=L[1]-L[0]
for i in range(N):
m=math.gcd(m,L[i+1]-L[i])
print(m)
``` | instruction | 0 | 4,870 | 1 | 9,740 |
Yes | output | 1 | 4,870 | 1 | 9,741 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N cities on a number line. The i-th city is located at coordinate x_i.
Your objective is to visit all these cities at least once.
In order to do so, you will first set a positive integer D.
Then, you will depart from coordinate X and perform Move 1 and Move 2 below, as many times as you like:
* Move 1: travel from coordinate y to coordinate y + D.
* Move 2: travel from coordinate y to coordinate y - D.
Find the maximum value of D that enables you to visit all the cities.
Here, to visit a city is to travel to the coordinate where that city is located.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq X \leq 10^9
* 1 \leq x_i \leq 10^9
* x_i are all different.
* x_1, x_2, ..., x_N \neq X
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_N
Output
Print the maximum value of D that enables you to visit all the cities.
Examples
Input
3 3
1 7 11
Output
2
Input
3 81
33 105 57
Output
24
Input
1 1
1000000000
Output
999999999
Submitted Solution:
```
from math import gcd
N, O = map(int, input().split())
X = list(map(int, input().split()))
X.append(O)
X.sort()
diff = [x-y for x, y in zip(X[1:], X[:-1])]
# print(diff)
for i in range(N-1):
diff[i+1] = gcd(diff[i], diff[i+1])
print(diff[N-1])
``` | instruction | 0 | 4,871 | 1 | 9,742 |
No | output | 1 | 4,871 | 1 | 9,743 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N cities on a number line. The i-th city is located at coordinate x_i.
Your objective is to visit all these cities at least once.
In order to do so, you will first set a positive integer D.
Then, you will depart from coordinate X and perform Move 1 and Move 2 below, as many times as you like:
* Move 1: travel from coordinate y to coordinate y + D.
* Move 2: travel from coordinate y to coordinate y - D.
Find the maximum value of D that enables you to visit all the cities.
Here, to visit a city is to travel to the coordinate where that city is located.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq X \leq 10^9
* 1 \leq x_i \leq 10^9
* x_i are all different.
* x_1, x_2, ..., x_N \neq X
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_N
Output
Print the maximum value of D that enables you to visit all the cities.
Examples
Input
3 3
1 7 11
Output
2
Input
3 81
33 105 57
Output
24
Input
1 1
1000000000
Output
999999999
Submitted Solution:
```
def gcd(a,b):
if b == 0:
return a
return gcd(b, a%b)
def gcd_list(l):
# print(l)
if len(l) == 1:
return l[0]
temp = [gcd(l[0],l[1])]
n = 0
while(n<len(l)-2):
# print(temp)
temp.append( gcd(temp[n], l[n+2]) )
n = n+1
# print(temp)
return(temp[len(temp)-1])
n, start = map(int, input().split(" "))
li = list(map(int, input().split(" ")))
diff = min(li) - start
if(len(li) == 1):
print(diff)
else:
li.append(start)
diff = min(li) - start
for i in range(len(li)):
li[i] = li[i] - start - diff
# print(li)
print(gcd_list(li))
``` | instruction | 0 | 4,872 | 1 | 9,744 |
No | output | 1 | 4,872 | 1 | 9,745 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N cities on a number line. The i-th city is located at coordinate x_i.
Your objective is to visit all these cities at least once.
In order to do so, you will first set a positive integer D.
Then, you will depart from coordinate X and perform Move 1 and Move 2 below, as many times as you like:
* Move 1: travel from coordinate y to coordinate y + D.
* Move 2: travel from coordinate y to coordinate y - D.
Find the maximum value of D that enables you to visit all the cities.
Here, to visit a city is to travel to the coordinate where that city is located.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq X \leq 10^9
* 1 \leq x_i \leq 10^9
* x_i are all different.
* x_1, x_2, ..., x_N \neq X
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_N
Output
Print the maximum value of D that enables you to visit all the cities.
Examples
Input
3 3
1 7 11
Output
2
Input
3 81
33 105 57
Output
24
Input
1 1
1000000000
Output
999999999
Submitted Solution:
```
N, X = map(int, input().split())
L = [int(i) for i in input().split()]
def gcd(x, y):
while(y > 0):
x, y = y, x%y
return int(x)
l = X - L[0]
L.sort()
if N > 1:
D = [L[i] - L[i-1] for i in range(1, N)]
for i in range(N-1):
l = gcd(l, D[i])
print(l)
``` | instruction | 0 | 4,873 | 1 | 9,746 |
No | output | 1 | 4,873 | 1 | 9,747 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N cities on a number line. The i-th city is located at coordinate x_i.
Your objective is to visit all these cities at least once.
In order to do so, you will first set a positive integer D.
Then, you will depart from coordinate X and perform Move 1 and Move 2 below, as many times as you like:
* Move 1: travel from coordinate y to coordinate y + D.
* Move 2: travel from coordinate y to coordinate y - D.
Find the maximum value of D that enables you to visit all the cities.
Here, to visit a city is to travel to the coordinate where that city is located.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq X \leq 10^9
* 1 \leq x_i \leq 10^9
* x_i are all different.
* x_1, x_2, ..., x_N \neq X
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_N
Output
Print the maximum value of D that enables you to visit all the cities.
Examples
Input
3 3
1 7 11
Output
2
Input
3 81
33 105 57
Output
24
Input
1 1
1000000000
Output
999999999
Submitted Solution:
```
n,X = map(int,input().split())
x = list(map(int,input().split()))
x.append(X)
x.sort()
a=[]
for i in range(n-1):
a.append(x[i+1]-x[i])
def gcd(m,n):
while n!=0:
s = m%n
m = n
n = s
return m
ans=min(a)
for j in a:
if j%min(a) != 0:
ans = gcd(j,ans)
print(ans)
``` | instruction | 0 | 4,874 | 1 | 9,748 |
No | output | 1 | 4,874 | 1 | 9,749 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation aix + biy + ci = 0, where ai and bi are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.
Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).
Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.
Input
The first line contains two space-separated integers x1, y1 ( - 106 β€ x1, y1 β€ 106) β the coordinates of your home.
The second line contains two integers separated by a space x2, y2 ( - 106 β€ x2, y2 β€ 106) β the coordinates of the university you are studying at.
The third line contains an integer n (1 β€ n β€ 300) β the number of roads in the city. The following n lines contain 3 space-separated integers ( - 106 β€ ai, bi, ci β€ 106; |ai| + |bi| > 0) β the coefficients of the line aix + biy + ci = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).
Output
Output the answer to the problem.
Examples
Input
1 1
-1 -1
2
0 1 0
1 0 0
Output
2
Input
1 1
-1 -1
3
1 0 0
0 1 0
1 1 -3
Output
2
Note
Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):
<image> <image> | instruction | 0 | 5,407 | 1 | 10,814 |
Tags: geometry
Correct Solution:
```
x, y = map(int, input().split())
u, v = map(int, input().split())
s = 0
for i in range(int(input())):
a, b, c = map(int, input().split())
s += (a * x + b * y + c > 0) ^ (a * u + b * v + c > 0)
print(s)
``` | output | 1 | 5,407 | 1 | 10,815 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation aix + biy + ci = 0, where ai and bi are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.
Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).
Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.
Input
The first line contains two space-separated integers x1, y1 ( - 106 β€ x1, y1 β€ 106) β the coordinates of your home.
The second line contains two integers separated by a space x2, y2 ( - 106 β€ x2, y2 β€ 106) β the coordinates of the university you are studying at.
The third line contains an integer n (1 β€ n β€ 300) β the number of roads in the city. The following n lines contain 3 space-separated integers ( - 106 β€ ai, bi, ci β€ 106; |ai| + |bi| > 0) β the coefficients of the line aix + biy + ci = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).
Output
Output the answer to the problem.
Examples
Input
1 1
-1 -1
2
0 1 0
1 0 0
Output
2
Input
1 1
-1 -1
3
1 0 0
0 1 0
1 1 -3
Output
2
Note
Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):
<image> <image> | instruction | 0 | 5,408 | 1 | 10,816 |
Tags: geometry
Correct Solution:
```
x1,y1=[int(i) for i in input().split()]
x2,y2=[int(i) for i in input().split()]
n=int(input())
r=0
for i in range(n):
a,b,c = [int(i) for i in input().split()]
if (a*x1+b*y1+c)*(a*x2+b*y2+c)<0:
r+=1
print(r)
``` | output | 1 | 5,408 | 1 | 10,817 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation aix + biy + ci = 0, where ai and bi are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.
Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).
Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.
Input
The first line contains two space-separated integers x1, y1 ( - 106 β€ x1, y1 β€ 106) β the coordinates of your home.
The second line contains two integers separated by a space x2, y2 ( - 106 β€ x2, y2 β€ 106) β the coordinates of the university you are studying at.
The third line contains an integer n (1 β€ n β€ 300) β the number of roads in the city. The following n lines contain 3 space-separated integers ( - 106 β€ ai, bi, ci β€ 106; |ai| + |bi| > 0) β the coefficients of the line aix + biy + ci = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).
Output
Output the answer to the problem.
Examples
Input
1 1
-1 -1
2
0 1 0
1 0 0
Output
2
Input
1 1
-1 -1
3
1 0 0
0 1 0
1 1 -3
Output
2
Note
Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):
<image> <image> | instruction | 0 | 5,409 | 1 | 10,818 |
Tags: geometry
Correct Solution:
```
x,y = map(int,input().split())
x1,y1 = map(int,input().split())
n=int(input())
ans=0
for i in range(n):
a,b,c=map(int,input().split())
if((a*x+b*y+c)*(a*x1+b*y1+c)<0): ans+=1
print(ans)
``` | output | 1 | 5,409 | 1 | 10,819 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation aix + biy + ci = 0, where ai and bi are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.
Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).
Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.
Input
The first line contains two space-separated integers x1, y1 ( - 106 β€ x1, y1 β€ 106) β the coordinates of your home.
The second line contains two integers separated by a space x2, y2 ( - 106 β€ x2, y2 β€ 106) β the coordinates of the university you are studying at.
The third line contains an integer n (1 β€ n β€ 300) β the number of roads in the city. The following n lines contain 3 space-separated integers ( - 106 β€ ai, bi, ci β€ 106; |ai| + |bi| > 0) β the coefficients of the line aix + biy + ci = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).
Output
Output the answer to the problem.
Examples
Input
1 1
-1 -1
2
0 1 0
1 0 0
Output
2
Input
1 1
-1 -1
3
1 0 0
0 1 0
1 1 -3
Output
2
Note
Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):
<image> <image> | instruction | 0 | 5,410 | 1 | 10,820 |
Tags: geometry
Correct Solution:
```
x1,y1=map(int,input().split())
x2,y2=map(int,input().split())
a1=y1-y2
b1=x2-x1
c1=x2*(y2-y1)-y2*(x2-x1)
def intersect(a2,b2,c2):
global a1,b1,c1,x1,y1,x2,y2
if(a1*b2==a2*b1):
return False
x=(b1*c2-b2*c1)/(a1*b2-b1*a2)
y=(a1*c2-c1*a2)/(b1*a2-a1*b2)
if(min(x1,x2)<=x<=max(x1,x2) and min(y1,y2)<=y<=max(y1,y2)):
return True
return False
m=int(input())
ans=0
for i in range(m):
a2,b2,c2=map(int,input().split())
if(intersect(a2,b2,c2)):
ans+=1
print(ans)
``` | output | 1 | 5,410 | 1 | 10,821 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation aix + biy + ci = 0, where ai and bi are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.
Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).
Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.
Input
The first line contains two space-separated integers x1, y1 ( - 106 β€ x1, y1 β€ 106) β the coordinates of your home.
The second line contains two integers separated by a space x2, y2 ( - 106 β€ x2, y2 β€ 106) β the coordinates of the university you are studying at.
The third line contains an integer n (1 β€ n β€ 300) β the number of roads in the city. The following n lines contain 3 space-separated integers ( - 106 β€ ai, bi, ci β€ 106; |ai| + |bi| > 0) β the coefficients of the line aix + biy + ci = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).
Output
Output the answer to the problem.
Examples
Input
1 1
-1 -1
2
0 1 0
1 0 0
Output
2
Input
1 1
-1 -1
3
1 0 0
0 1 0
1 1 -3
Output
2
Note
Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):
<image> <image> | instruction | 0 | 5,411 | 1 | 10,822 |
Tags: geometry
Correct Solution:
```
#!/usr/bin/env python3
x1, y1 = (int(x) for x in input().split())
x2, y2 = (int(x) for x in input().split())
n = int(input())
ans = 0
for i in range(n):
a, b, c = (int(x) for x in input().split())
point1 = a*x1 + b*y1 + c
point2 = a*x2 + b*y2 + c
if point1 * point2 < 0:
ans += 1
print(ans)
``` | output | 1 | 5,411 | 1 | 10,823 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation aix + biy + ci = 0, where ai and bi are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.
Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).
Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.
Input
The first line contains two space-separated integers x1, y1 ( - 106 β€ x1, y1 β€ 106) β the coordinates of your home.
The second line contains two integers separated by a space x2, y2 ( - 106 β€ x2, y2 β€ 106) β the coordinates of the university you are studying at.
The third line contains an integer n (1 β€ n β€ 300) β the number of roads in the city. The following n lines contain 3 space-separated integers ( - 106 β€ ai, bi, ci β€ 106; |ai| + |bi| > 0) β the coefficients of the line aix + biy + ci = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).
Output
Output the answer to the problem.
Examples
Input
1 1
-1 -1
2
0 1 0
1 0 0
Output
2
Input
1 1
-1 -1
3
1 0 0
0 1 0
1 1 -3
Output
2
Note
Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):
<image> <image> | instruction | 0 | 5,412 | 1 | 10,824 |
Tags: geometry
Correct Solution:
```
def getMinSteps(x1, y1, x2, y2, n, lines):
min_steps = 0
for i in range(n):
a = lines[i][0]
b = lines[i][1]
c = lines[i][2]
if (a*x1+b*y1+c)*(a*x2+b*y2+c) < 0:
min_steps+=1
return min_steps
x1, y1 = [int(x) for x in input().split()]
x2, y2 = [int(x) for x in input().split()]
n = int(input())
lines = []
for i in range(n):
line = [int(x) for x in input().split()]
lines.append((line[0], line[1], line[2]))
print(getMinSteps(x1, y1, x2, y2, n, lines))
``` | output | 1 | 5,412 | 1 | 10,825 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation aix + biy + ci = 0, where ai and bi are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.
Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).
Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.
Input
The first line contains two space-separated integers x1, y1 ( - 106 β€ x1, y1 β€ 106) β the coordinates of your home.
The second line contains two integers separated by a space x2, y2 ( - 106 β€ x2, y2 β€ 106) β the coordinates of the university you are studying at.
The third line contains an integer n (1 β€ n β€ 300) β the number of roads in the city. The following n lines contain 3 space-separated integers ( - 106 β€ ai, bi, ci β€ 106; |ai| + |bi| > 0) β the coefficients of the line aix + biy + ci = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).
Output
Output the answer to the problem.
Examples
Input
1 1
-1 -1
2
0 1 0
1 0 0
Output
2
Input
1 1
-1 -1
3
1 0 0
0 1 0
1 1 -3
Output
2
Note
Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):
<image> <image> | instruction | 0 | 5,413 | 1 | 10,826 |
Tags: geometry
Correct Solution:
```
hx, hy = map(int, input().split())
ux, uy = map(int, input().split())
n = int(input())
count = 0
for i in range(n):
a,b,c = map(int, input().split())
h = a*hx + b*hy + c
u = a*ux + b*uy + c
if h*u<0:
count += 1
print(count)
``` | output | 1 | 5,413 | 1 | 10,827 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation aix + biy + ci = 0, where ai and bi are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.
Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).
Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.
Input
The first line contains two space-separated integers x1, y1 ( - 106 β€ x1, y1 β€ 106) β the coordinates of your home.
The second line contains two integers separated by a space x2, y2 ( - 106 β€ x2, y2 β€ 106) β the coordinates of the university you are studying at.
The third line contains an integer n (1 β€ n β€ 300) β the number of roads in the city. The following n lines contain 3 space-separated integers ( - 106 β€ ai, bi, ci β€ 106; |ai| + |bi| > 0) β the coefficients of the line aix + biy + ci = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).
Output
Output the answer to the problem.
Examples
Input
1 1
-1 -1
2
0 1 0
1 0 0
Output
2
Input
1 1
-1 -1
3
1 0 0
0 1 0
1 1 -3
Output
2
Note
Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):
<image> <image> | instruction | 0 | 5,414 | 1 | 10,828 |
Tags: geometry
Correct Solution:
```
h1, h2 = list(map(int,input().split()))
u1, u2 = list(map(int,input().split()))
pasos = 0
for i in int(input())*'_':
a, b, c= list(map(int,input().split()))
if (a * h1 + b * h2 + c) * (a * u1 + b * u2 + c) < 0:
pasos+=1
print(pasos)
``` | output | 1 | 5,414 | 1 | 10,829 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation aix + biy + ci = 0, where ai and bi are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.
Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).
Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.
Input
The first line contains two space-separated integers x1, y1 ( - 106 β€ x1, y1 β€ 106) β the coordinates of your home.
The second line contains two integers separated by a space x2, y2 ( - 106 β€ x2, y2 β€ 106) β the coordinates of the university you are studying at.
The third line contains an integer n (1 β€ n β€ 300) β the number of roads in the city. The following n lines contain 3 space-separated integers ( - 106 β€ ai, bi, ci β€ 106; |ai| + |bi| > 0) β the coefficients of the line aix + biy + ci = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).
Output
Output the answer to the problem.
Examples
Input
1 1
-1 -1
2
0 1 0
1 0 0
Output
2
Input
1 1
-1 -1
3
1 0 0
0 1 0
1 1 -3
Output
2
Note
Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):
<image> <image>
Submitted Solution:
```
homex,homey = (int(x) for x in input().split(" "))
univx,univy = (int(x) for x in input().split(" "))
n = int(input())
step = 0
for i in range(0,n):
a,b,c = (int(x) for x in input().split(" "))
homearea = ((a*homex + b*homey + c) < 0)
univarea = ((a*univx + b*univy + c) < 0)
if homearea != univarea:
step += 1
print(step)
``` | instruction | 0 | 5,415 | 1 | 10,830 |
Yes | output | 1 | 5,415 | 1 | 10,831 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation aix + biy + ci = 0, where ai and bi are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.
Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).
Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.
Input
The first line contains two space-separated integers x1, y1 ( - 106 β€ x1, y1 β€ 106) β the coordinates of your home.
The second line contains two integers separated by a space x2, y2 ( - 106 β€ x2, y2 β€ 106) β the coordinates of the university you are studying at.
The third line contains an integer n (1 β€ n β€ 300) β the number of roads in the city. The following n lines contain 3 space-separated integers ( - 106 β€ ai, bi, ci β€ 106; |ai| + |bi| > 0) β the coefficients of the line aix + biy + ci = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).
Output
Output the answer to the problem.
Examples
Input
1 1
-1 -1
2
0 1 0
1 0 0
Output
2
Input
1 1
-1 -1
3
1 0 0
0 1 0
1 1 -3
Output
2
Note
Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):
<image> <image>
Submitted Solution:
```
#import sys
#sys.stdin = open('input.txt', 'r')
#sys.stdout = open('output.txt', 'w')
def norm(a, b, c, d):
if (b * c >= 0):
return a * abs(c) <= abs(b) <= d * abs(c)
return -a * abs(c) >= abs(b) >= -d * abs(c)
x1, y1 = map(int, input().split())
x2, y2 = map(int, input().split())
a2 = y2 - y1
b2 = x1 - x2
c2 = 0 - a2 * x1 - b2 * y1
n = int(input())
ans = 0
for i in range(n):
a1, b1, c1 = map(int, input().split())
if (norm(min(x1, x2), (c2 * b1 - c1 * b2), (a1 * b2 - a2 * b1), max(x1, x2)) and norm(min(y1, y2), (c2 * a1 - c1 * a2), (a2 * b1 - a1 * b2), max(y1, y2))):
ans += 1
print(ans)
``` | instruction | 0 | 5,416 | 1 | 10,832 |
Yes | output | 1 | 5,416 | 1 | 10,833 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation aix + biy + ci = 0, where ai and bi are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.
Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).
Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.
Input
The first line contains two space-separated integers x1, y1 ( - 106 β€ x1, y1 β€ 106) β the coordinates of your home.
The second line contains two integers separated by a space x2, y2 ( - 106 β€ x2, y2 β€ 106) β the coordinates of the university you are studying at.
The third line contains an integer n (1 β€ n β€ 300) β the number of roads in the city. The following n lines contain 3 space-separated integers ( - 106 β€ ai, bi, ci β€ 106; |ai| + |bi| > 0) β the coefficients of the line aix + biy + ci = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).
Output
Output the answer to the problem.
Examples
Input
1 1
-1 -1
2
0 1 0
1 0 0
Output
2
Input
1 1
-1 -1
3
1 0 0
0 1 0
1 1 -3
Output
2
Note
Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):
<image> <image>
Submitted Solution:
```
x1,y1 = map(int,input().split())
x2,y2 = map(int,input().split())
n = int(input())
s = 0
for i in range(n):
a,b,c = map(int,input().split())
if ((((a * x1) + (b * y1) + c) * ((a * x2) + (b * y2) + c)) < 0):
s = s + 1
print(s)
``` | instruction | 0 | 5,417 | 1 | 10,834 |
Yes | output | 1 | 5,417 | 1 | 10,835 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation aix + biy + ci = 0, where ai and bi are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.
Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).
Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.
Input
The first line contains two space-separated integers x1, y1 ( - 106 β€ x1, y1 β€ 106) β the coordinates of your home.
The second line contains two integers separated by a space x2, y2 ( - 106 β€ x2, y2 β€ 106) β the coordinates of the university you are studying at.
The third line contains an integer n (1 β€ n β€ 300) β the number of roads in the city. The following n lines contain 3 space-separated integers ( - 106 β€ ai, bi, ci β€ 106; |ai| + |bi| > 0) β the coefficients of the line aix + biy + ci = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).
Output
Output the answer to the problem.
Examples
Input
1 1
-1 -1
2
0 1 0
1 0 0
Output
2
Input
1 1
-1 -1
3
1 0 0
0 1 0
1 1 -3
Output
2
Note
Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):
<image> <image>
Submitted Solution:
```
xhome, yhome = [int(x) for x in input().split()]
xuni, yuni = [int(x) for x in input().split()]
n_roads = int(input())
n_steps = 0
for i in range(n_roads):
a, b, c = [int(x) for x in input().split()]
hline = (a*xhome) + (b*yhome) + c
uline = (a*xuni) + (b*yuni) + c
if hline * uline < 0:
n_steps += 1
print(n_steps)
``` | instruction | 0 | 5,418 | 1 | 10,836 |
Yes | output | 1 | 5,418 | 1 | 10,837 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation aix + biy + ci = 0, where ai and bi are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.
Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).
Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.
Input
The first line contains two space-separated integers x1, y1 ( - 106 β€ x1, y1 β€ 106) β the coordinates of your home.
The second line contains two integers separated by a space x2, y2 ( - 106 β€ x2, y2 β€ 106) β the coordinates of the university you are studying at.
The third line contains an integer n (1 β€ n β€ 300) β the number of roads in the city. The following n lines contain 3 space-separated integers ( - 106 β€ ai, bi, ci β€ 106; |ai| + |bi| > 0) β the coefficients of the line aix + biy + ci = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).
Output
Output the answer to the problem.
Examples
Input
1 1
-1 -1
2
0 1 0
1 0 0
Output
2
Input
1 1
-1 -1
3
1 0 0
0 1 0
1 1 -3
Output
2
Note
Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):
<image> <image>
Submitted Solution:
```
x1, y1 = map(int, input().split())
x2, y2 = map(int, input().split())
n = int(input())
steps = 0
for i in range(n):
a, b, c = map(int, input().split())
if ((a*x1 + b*y1 + c < 0) != (a*x2 + a*y2 + c < 0)):
steps += 1
print(steps)
``` | instruction | 0 | 5,419 | 1 | 10,838 |
No | output | 1 | 5,419 | 1 | 10,839 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation aix + biy + ci = 0, where ai and bi are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.
Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).
Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.
Input
The first line contains two space-separated integers x1, y1 ( - 106 β€ x1, y1 β€ 106) β the coordinates of your home.
The second line contains two integers separated by a space x2, y2 ( - 106 β€ x2, y2 β€ 106) β the coordinates of the university you are studying at.
The third line contains an integer n (1 β€ n β€ 300) β the number of roads in the city. The following n lines contain 3 space-separated integers ( - 106 β€ ai, bi, ci β€ 106; |ai| + |bi| > 0) β the coefficients of the line aix + biy + ci = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).
Output
Output the answer to the problem.
Examples
Input
1 1
-1 -1
2
0 1 0
1 0 0
Output
2
Input
1 1
-1 -1
3
1 0 0
0 1 0
1 1 -3
Output
2
Note
Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):
<image> <image>
Submitted Solution:
```
from __future__ import division
def line(p1, p2):
A = (p1[1] - p2[1])
B = (p2[0] - p1[0])
C = (p1[0]*p2[1] - p2[0]*p1[1])
return [A, B, -C]
def intersection(L1, L2):
D = L1[0] * L2[1] - L1[1] * L2[0]
Dx = L1[2] * L2[1] - L1[1] * L2[2]
Dy = L1[0] * L2[2] - L1[2] * L2[0]
if D != 0:
x = Dx / D
y = Dy / D
return (x,y)
else:
return False
def is_on(a, b, c):
return (collinear(a, b, c)
and (within(a[0], c[0], b[0]) if a[0] != b[0] else
within(a[1], c[1], b[1])))
def collinear(a, b, c):
return (b[0] - a[0]) * (c[1] - a[1]) == (c[0] - a[0]) * (b[1] - a[1])
def within(p, q, r):
return p <= q <= r or r <= q <= p
def main():
x1, y1 = map(int,input().split())
x2, y2 = map(int,input().split())
path = line([x1, y1],[x2,y2])
n = int(input())
roads = []
count = 0
intersection_points = []
for _ in range(n):
temp = list(map(int,input().split()))
road = [temp[0], temp[1], -temp[2]]
intersection_point = intersection(road, path)
#print(intersection_point)
if intersection_point:
if intersection_point in intersection_points:
count += 1
elif is_on([x1, y1], [x2, y2], intersection_point):
count += 1
intersection_points.append(intersection_point)
print(count)
if __name__ == '__main__':
main()
``` | instruction | 0 | 5,420 | 1 | 10,840 |
No | output | 1 | 5,420 | 1 | 10,841 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation aix + biy + ci = 0, where ai and bi are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.
Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).
Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.
Input
The first line contains two space-separated integers x1, y1 ( - 106 β€ x1, y1 β€ 106) β the coordinates of your home.
The second line contains two integers separated by a space x2, y2 ( - 106 β€ x2, y2 β€ 106) β the coordinates of the university you are studying at.
The third line contains an integer n (1 β€ n β€ 300) β the number of roads in the city. The following n lines contain 3 space-separated integers ( - 106 β€ ai, bi, ci β€ 106; |ai| + |bi| > 0) β the coefficients of the line aix + biy + ci = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).
Output
Output the answer to the problem.
Examples
Input
1 1
-1 -1
2
0 1 0
1 0 0
Output
2
Input
1 1
-1 -1
3
1 0 0
0 1 0
1 1 -3
Output
2
Note
Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):
<image> <image>
Submitted Solution:
```
#498A
[x1,y1] = list(map(int,input().split()))
[x2,y2] = list(map(int,input().split()))
n = int(input())
c = 0
for i in range(n):
[a,b,c] = list(map(int,input().split()))
if (a*x1+b*x2+c)*(a*x2+b*y2+c) < 0:
c += 1
print(c)
``` | instruction | 0 | 5,421 | 1 | 10,842 |
No | output | 1 | 5,421 | 1 | 10,843 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Crazy Town is a plane on which there are n infinite line roads. Each road is defined by the equation aix + biy + ci = 0, where ai and bi are not both equal to the zero. The roads divide the plane into connected regions, possibly of infinite space. Let's call each such region a block. We define an intersection as the point where at least two different roads intersect.
Your home is located in one of the blocks. Today you need to get to the University, also located in some block. In one step you can move from one block to another, if the length of their common border is nonzero (in particular, this means that if the blocks are adjacent to one intersection, but have no shared nonzero boundary segment, then it are not allowed to move from one to another one in one step).
Determine what is the minimum number of steps you have to perform to get to the block containing the university. It is guaranteed that neither your home nor the university is located on the road.
Input
The first line contains two space-separated integers x1, y1 ( - 106 β€ x1, y1 β€ 106) β the coordinates of your home.
The second line contains two integers separated by a space x2, y2 ( - 106 β€ x2, y2 β€ 106) β the coordinates of the university you are studying at.
The third line contains an integer n (1 β€ n β€ 300) β the number of roads in the city. The following n lines contain 3 space-separated integers ( - 106 β€ ai, bi, ci β€ 106; |ai| + |bi| > 0) β the coefficients of the line aix + biy + ci = 0, defining the i-th road. It is guaranteed that no two roads are the same. In addition, neither your home nor the university lie on the road (i.e. they do not belong to any one of the lines).
Output
Output the answer to the problem.
Examples
Input
1 1
-1 -1
2
0 1 0
1 0 0
Output
2
Input
1 1
-1 -1
3
1 0 0
0 1 0
1 1 -3
Output
2
Note
Pictures to the samples are presented below (A is the point representing the house; B is the point representing the university, different blocks are filled with different colors):
<image> <image>
Submitted Solution:
```
px,py = map(int,input().split())
qx,qy = map(int,input().split())
n,s= int(input()),0
for _ in range(n):
a,b,c = map(int,input().split())
if not a:
x,y = -c/b,0
else:
x,y = 0,-c/a
s += ((px-x)*a+(py-y)*b)*((qx-x)*a+(qy-y)*b)<0
print(s)
# C:\Users\Usuario\HOME2\Programacion\ACM
``` | instruction | 0 | 5,422 | 1 | 10,844 |
No | output | 1 | 5,422 | 1 | 10,845 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In Berland there are n cities and n - 1 bidirectional roads. Each road connects some pair of cities, from any city you can get to any other one using only the given roads.
In each city there is exactly one repair brigade. To repair some road, you need two teams based in the cities connected by the road to work simultaneously for one day. Both brigades repair one road for the whole day and cannot take part in repairing other roads on that day. But the repair brigade can do nothing on that day.
Determine the minimum number of days needed to repair all the roads. The brigades cannot change the cities where they initially are.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 200 000) β the number of cities in Berland.
Each of the next n - 1 lines contains two numbers ui, vi, meaning that the i-th road connects city ui and city vi (1 β€ ui, vi β€ n, ui β vi).
Output
First print number k β the minimum number of days needed to repair all the roads in Berland.
In next k lines print the description of the roads that should be repaired on each of the k days. On the i-th line print first number di β the number of roads that should be repaired on the i-th day, and then di space-separated integers β the numbers of the roads that should be repaired on the i-th day. The roads are numbered according to the order in the input, starting from one.
If there are multiple variants, you can print any of them.
Examples
Input
4
1 2
3 4
3 2
Output
2
2 2 1
1 3
Input
6
3 4
5 4
3 2
1 3
4 6
Output
3
1 1
2 2 3
2 4 5
Note
In the first sample you can repair all the roads in two days, for example, if you repair roads 1 and 2 on the first day and road 3 β on the second day. | instruction | 0 | 5,457 | 1 | 10,914 |
Tags: *special, dfs and similar, graphs, greedy, trees
Correct Solution:
```
import sys
import threading
from collections import defaultdict
def put():
return map(int, input().split())
def dfs(i, p, m):
cnt = 1
z = 0
for j in tree[i]:
if j==p: continue
if cnt==m: cnt+=1
index = edge_index[(i,j)]
ans[cnt].append(index)
z = max(dfs(j,i,cnt), z)
cnt+=1
return max(z,cnt-1)
def solve():
l = dfs(1,0,0)
print(l)
for i in range(1, l+1):
print(len(ans[i]), *ans[i])
n = int(input())
edge_index = defaultdict()
ans = [[] for i in range(n+1)]
tree = [[] for i in range(n+1)]
for i in range(n-1):
x,y = put()
edge_index[(x,y)]=i+1
edge_index[(y,x)]=i+1
tree[x].append(y)
tree[y].append(x)
max_recur_size = 10**5*2 + 1000
max_stack_size = max_recur_size*500
sys.setrecursionlimit(max_recur_size)
threading.stack_size(max_stack_size)
thread = threading.Thread(target=solve)
thread.start()
``` | output | 1 | 5,457 | 1 | 10,915 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In Berland there are n cities and n - 1 bidirectional roads. Each road connects some pair of cities, from any city you can get to any other one using only the given roads.
In each city there is exactly one repair brigade. To repair some road, you need two teams based in the cities connected by the road to work simultaneously for one day. Both brigades repair one road for the whole day and cannot take part in repairing other roads on that day. But the repair brigade can do nothing on that day.
Determine the minimum number of days needed to repair all the roads. The brigades cannot change the cities where they initially are.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 200 000) β the number of cities in Berland.
Each of the next n - 1 lines contains two numbers ui, vi, meaning that the i-th road connects city ui and city vi (1 β€ ui, vi β€ n, ui β vi).
Output
First print number k β the minimum number of days needed to repair all the roads in Berland.
In next k lines print the description of the roads that should be repaired on each of the k days. On the i-th line print first number di β the number of roads that should be repaired on the i-th day, and then di space-separated integers β the numbers of the roads that should be repaired on the i-th day. The roads are numbered according to the order in the input, starting from one.
If there are multiple variants, you can print any of them.
Examples
Input
4
1 2
3 4
3 2
Output
2
2 2 1
1 3
Input
6
3 4
5 4
3 2
1 3
4 6
Output
3
1 1
2 2 3
2 4 5
Note
In the first sample you can repair all the roads in two days, for example, if you repair roads 1 and 2 on the first day and road 3 β on the second day.
Submitted Solution:
```
from copy import deepcopy
def C():
n = int(input())
graph = []
lines = []
road_counter = [0 for i in range(n+1)]
for i in range(n-1):
items = []
items.append(i+1)
inp = input().split(' ')
road_counter[int(inp[0])] += 1
items.append(int(inp[0]))
road_counter[int(inp[1])] += 1
items.append(int(inp[1]))
graph.append(items)
# items.append([x for x in input().split(' ')])
# for i in items:
# road_counter[i] += 1
print(graph)
sum_days = 0
while graph:
sum_today = 0
line = ""
cur_graph = deepcopy(graph) #Π·Π°Π½ΡΡΡΠ΅ Π³ΠΎΡΠΎΠ΄Π° Π² ΡΠ΅ΠΊΡΡΠΈΠΉ Π΄Π΅Π½Ρ
used = [0 for i in range(n+1)]
while cur_graph:
index = find_max(road_counter, used)
if(index != 0):
adjacent_pair = find_adjacent(cur_graph,index,graph)
line += str(adjacent_pair[1]) + " "
graph = adjacent_pair[2]
cur_graph = del_concerned(cur_graph,adjacent_pair[0],index)
used[index] = 1
used[adjacent_pair[0]] = 1
road_counter[index] -= 1
road_counter[adjacent_pair[0]] -= 1
sum_today += 1
lines.append(str(sum_today) + " " + line)
sum_days += 1
print(sum_days)
for i in lines:
print(i)
return()
def find_adjacent(full_list = [], x = int, start_list = []):
for i in full_list:
if(i[1] == x):
start_list.remove(i)
return [i[2],i[0], start_list]
elif(i[2] == x):
start_list.remove(i)
return [i[1],i[0], start_list]
def del_concerned(full_list = [], x = int, ind = int):
returned_list = deepcopy(full_list)
for i in full_list:
if(i[2] == x or i[1] == x or i[2] == ind or i[1] == ind):
returned_list.remove(i)
return returned_list
def find_max(roads_number = [], used = []):
index_r = 0
max_val = 0
for i in range(roads_number.__len__()):
if(roads_number[i] > max_val and used[i] != 1):
max_val = roads_number[i]
index_r = i
return index_r
C()
``` | instruction | 0 | 5,458 | 1 | 10,916 |
No | output | 1 | 5,458 | 1 | 10,917 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In Berland there are n cities and n - 1 bidirectional roads. Each road connects some pair of cities, from any city you can get to any other one using only the given roads.
In each city there is exactly one repair brigade. To repair some road, you need two teams based in the cities connected by the road to work simultaneously for one day. Both brigades repair one road for the whole day and cannot take part in repairing other roads on that day. But the repair brigade can do nothing on that day.
Determine the minimum number of days needed to repair all the roads. The brigades cannot change the cities where they initially are.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 200 000) β the number of cities in Berland.
Each of the next n - 1 lines contains two numbers ui, vi, meaning that the i-th road connects city ui and city vi (1 β€ ui, vi β€ n, ui β vi).
Output
First print number k β the minimum number of days needed to repair all the roads in Berland.
In next k lines print the description of the roads that should be repaired on each of the k days. On the i-th line print first number di β the number of roads that should be repaired on the i-th day, and then di space-separated integers β the numbers of the roads that should be repaired on the i-th day. The roads are numbered according to the order in the input, starting from one.
If there are multiple variants, you can print any of them.
Examples
Input
4
1 2
3 4
3 2
Output
2
2 2 1
1 3
Input
6
3 4
5 4
3 2
1 3
4 6
Output
3
1 1
2 2 3
2 4 5
Note
In the first sample you can repair all the roads in two days, for example, if you repair roads 1 and 2 on the first day and road 3 β on the second day.
Submitted Solution:
```
#!/usr/bin/python3
n = int(input())
degrees = [0 for i in range(n)]
max_deg = 0
adj = [list() for i in range(n)]
roads = []
for i in range(n-1):
f,t = map(int, input().split())
f -= 1
t -= 1
degrees[f] += 1
degrees[t] += 1
max_deg = max(max_deg, degrees[f], degrees[t])
roads.append((f, t))
adj[f].append(t)
adj[t].append(f)
days = max_deg
print(days)
repd = set()
for day in range(days):
used = set()
rep = []
for i, road in enumerate(roads):
f, t = road
if t in used or f in used:
continue
if i in repd:
continue
used.add(f)
used.add(t)
rep.append(i)
repd.add(i)
print(len(rep), end=' ')
for r in rep:
print(r+1, end=' ')
print()
``` | instruction | 0 | 5,459 | 1 | 10,918 |
No | output | 1 | 5,459 | 1 | 10,919 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In Berland there are n cities and n - 1 bidirectional roads. Each road connects some pair of cities, from any city you can get to any other one using only the given roads.
In each city there is exactly one repair brigade. To repair some road, you need two teams based in the cities connected by the road to work simultaneously for one day. Both brigades repair one road for the whole day and cannot take part in repairing other roads on that day. But the repair brigade can do nothing on that day.
Determine the minimum number of days needed to repair all the roads. The brigades cannot change the cities where they initially are.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 200 000) β the number of cities in Berland.
Each of the next n - 1 lines contains two numbers ui, vi, meaning that the i-th road connects city ui and city vi (1 β€ ui, vi β€ n, ui β vi).
Output
First print number k β the minimum number of days needed to repair all the roads in Berland.
In next k lines print the description of the roads that should be repaired on each of the k days. On the i-th line print first number di β the number of roads that should be repaired on the i-th day, and then di space-separated integers β the numbers of the roads that should be repaired on the i-th day. The roads are numbered according to the order in the input, starting from one.
If there are multiple variants, you can print any of them.
Examples
Input
4
1 2
3 4
3 2
Output
2
2 2 1
1 3
Input
6
3 4
5 4
3 2
1 3
4 6
Output
3
1 1
2 2 3
2 4 5
Note
In the first sample you can repair all the roads in two days, for example, if you repair roads 1 and 2 on the first day and road 3 β on the second day.
Submitted Solution:
```
def get():
s = input().split()
return int(s[0]), int(s[1])
def main2():
cities = dict()
n = int(input())
# days counter
dc = 0
for i in range(1, n):
ui, vi = get()
if ui not in cities.keys():
cities[ui] = [[i, vi]]
elif vi not in cities.keys():
cities[vi] = [[i, ui]]
elif len(cities[vi]) > len(cities[ui]):
cities[ui].append([i, vi])
else:
cities[vi].append([i, ui])
result = ""
# ΠΏΠΎΠΊΠ° Π½Π΅ Π²ΡΠ΅ Π΄ΠΎΡΠΎΠ³ΠΈ ΠΏΠΎΡΠΈΠ½Π΅Π½Ρ
while len(cities) > 0:
busy = set()
repaired = set()
# Π΄Π»Ρ ΠΊΠ°ΠΆΠ΄ΠΎΠ³ΠΎ Π³ΠΎΡΠΎΠ΄Π° Π² ΡΠ»ΠΎΠ²Π°ΡΠ΅
for city in list(cities):
# Π·Π°Π±Π»ΠΎΠΊΠΈΡΠΎΠ²Π°Π½ ΠΊΠ»ΡΡ
if city in busy:
continue
flag = False
a = 0
for i in cities[city]:
if i[1] not in busy:
a = i
flag = True
break
if not flag:
continue
repaired.add(a[0])
busy.add(a[1])
busy.add(city)
if len(cities[city]) == 1:
cities.pop(city)
else:
cities[city].remove(a)
result += "\n" + str(len(repaired))
for r in repaired:
result += " " + str(r)
dc += 1
result = str(dc) + result
print(result)
main2()
``` | instruction | 0 | 5,460 | 1 | 10,920 |
No | output | 1 | 5,460 | 1 | 10,921 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In Berland there are n cities and n - 1 bidirectional roads. Each road connects some pair of cities, from any city you can get to any other one using only the given roads.
In each city there is exactly one repair brigade. To repair some road, you need two teams based in the cities connected by the road to work simultaneously for one day. Both brigades repair one road for the whole day and cannot take part in repairing other roads on that day. But the repair brigade can do nothing on that day.
Determine the minimum number of days needed to repair all the roads. The brigades cannot change the cities where they initially are.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 200 000) β the number of cities in Berland.
Each of the next n - 1 lines contains two numbers ui, vi, meaning that the i-th road connects city ui and city vi (1 β€ ui, vi β€ n, ui β vi).
Output
First print number k β the minimum number of days needed to repair all the roads in Berland.
In next k lines print the description of the roads that should be repaired on each of the k days. On the i-th line print first number di β the number of roads that should be repaired on the i-th day, and then di space-separated integers β the numbers of the roads that should be repaired on the i-th day. The roads are numbered according to the order in the input, starting from one.
If there are multiple variants, you can print any of them.
Examples
Input
4
1 2
3 4
3 2
Output
2
2 2 1
1 3
Input
6
3 4
5 4
3 2
1 3
4 6
Output
3
1 1
2 2 3
2 4 5
Note
In the first sample you can repair all the roads in two days, for example, if you repair roads 1 and 2 on the first day and road 3 β on the second day.
Submitted Solution:
```
from sys import stdin, stdout
import math,sys,heapq
from itertools import permutations, combinations
from collections import defaultdict,deque,OrderedDict
from os import path
import bisect as bi
def yes():print('YES')
def no():print('NO')
if (path.exists('input.txt')):
#------------------Sublime--------------------------------------#
sys.stdin=open('input.txt','r');sys.stdout=open('output.txt','w');
def I():return (int(input()))
def In():return(map(int,input().split()))
else:
#------------------PYPY FAst I/o--------------------------------#
def I():return (int(stdin.readline()))
def In():return(map(int,stdin.readline().split()))
def dict(a):
d={}
for x in a:
if d.get(x,-1)!=-1:
d[x]+=1
else:
d[x]=1
return d
def find_gt(a, x):
'Find leftmost value greater than x'
i = bi.bisect_right(a, x)
if i != len(a):
return i
else:
return -1
def dfs(d,n):
parent=[-1]*(n+1)
visit=[False]*(n+1)
q=deque()
q.append(1)
parent[1]=0
while q:
temp=q.popleft()
if visit[temp]==False:
for x in d[temp]:
if visit[x]==False:
q.appendleft(x)
if parent[x]==-1:
parent[x]=temp
visit[temp]=True
parent.pop(0)
return(parent)
def main():
try:
n=I()
d=defaultdict(list)
path={}
for x in range(n-1):
a,b=In()
if a>b:
a,b=b,a
d[a].append(b)
d[b].append(a)
path[(a,b)]=x+1
parent=dfs(d,n)
#print(parent)
ans=[]
j=0
for x in range(n):
temp=[]
done=set()
for i in range(1,n):
if ((i+1) not in done) and (parent[i] not in done) and (parent[i]!=-1):
a=i+1
b=parent[i]
if a>b:
a,b=b,a
temp.append(path[(a,b)])
done.add(i+1)
done.add(parent[i])
parent[i]=-1
#print(done)
j+=1
if len(temp)==0:
break
ans.append(temp)
print(len(ans))
for x in range(len(ans)):
print(len(ans[x]),*ans[x])
except:
pass
M = 998244353
P = 1000000007
if __name__ == '__main__':
#for _ in range(I()):main()
for _ in range(1):main()
``` | instruction | 0 | 5,461 | 1 | 10,922 |
No | output | 1 | 5,461 | 1 | 10,923 |
Provide a correct Python 3 solution for this coding contest problem.
Emergency Evacuation
The Japanese government plans to increase the number of inbound tourists to forty million in the year 2020, and sixty million in 2030. Not only increasing touristic appeal but also developing tourism infrastructure further is indispensable to accomplish such numbers.
One possible enhancement on transport is providing cars extremely long and/or wide, carrying many passengers at a time. Too large a car, however, may require too long to evacuate all passengers in an emergency. You are requested to help estimating the time required.
The car is assumed to have the following seat arrangement.
* A center aisle goes straight through the car, directly connecting to the emergency exit door at the rear center of the car.
* The rows of the same number of passenger seats are on both sides of the aisle.
A rough estimation requested is based on a simple step-wise model. All passengers are initially on a distinct seat, and they can make one of the following moves in each step.
* Passengers on a seat can move to an adjacent seat toward the aisle. Passengers on a seat adjacent to the aisle can move sideways directly to the aisle.
* Passengers on the aisle can move backward by one row of seats. If the passenger is in front of the emergency exit, that is, by the rear-most seat rows, he/she can get off the car.
The seat or the aisle position to move to must be empty; either no other passenger is there before the step, or the passenger there empties the seat by moving to another position in the same step. When two or more passengers satisfy the condition for the same position, only one of them can move, keeping the others wait in their original positions.
The leftmost figure of Figure C.1 depicts the seat arrangement of a small car given in Sample Input 1. The car have five rows of seats, two seats each on both sides of the aisle, totaling twenty. The initial positions of seven passengers on board are also shown.
The two other figures of Figure C.1 show possible positions of passengers after the first and the second steps. Passenger movements are indicated by fat arrows. Note that, two of the passengers in the front seat had to wait for a vacancy in the first step, and one in the second row had to wait in the next step.
Your task is to write a program that gives the smallest possible number of steps for all the passengers to get off the car, given the seat arrangement and passengers' initial positions.
<image>
Figure C.1
Input
The input consists of a single test case of the following format.
$r$ $s$ $p$
$i_1$ $j_1$
...
$i_p$ $j_p$
Here, $r$ is the number of passenger seat rows, $s$ is the number of seats on each side of the aisle, and $p$ is the number of passengers. They are integers satisfying $1 \leq r \leq 500$, $1 \leq s \leq 500$, and $1 \leq p \leq 2rs$.
The following $p$ lines give initial seat positions of the passengers. The $k$-th line with $i_k$ and $j_k$ means that the $k$-th passenger's seat is in the $i_k$-th seat row and it is the $j_k$-th seat on that row. Here, rows and seats are counted from front to rear and left to right, both starting from one. They satisfy $1 \leq i_k \leq r$ and $1 \leq j_k \leq 2s$. Passengers are on distinct seats, that is, $i_k \ne= i_l$ or $j_k \ne j_l$ holds if $k \ne l$.
Output
The output should be one line containing a single integer, the minimum number of steps required for all the passengers to get off the car.
Sample Input 1
5 2 7
1 1
1 2
1 3
2 3
2 4
4 4
5 2
Sample Output 1
9
Sample Input 2
500 500 16
1 1
1 2
1 999
1 1000
2 1
2 2
2 999
2 1000
3 1
3 2
3 999
3 1000
499 500
499 501
499 999
499 1000
Sample Output 2
1008
Example
Input
5 2 7
1 1
1 2
1 3
2 3
2 4
4 4
5 2
Output
9 | instruction | 0 | 5,751 | 1 | 11,502 |
"Correct Solution:
```
r, s, p = map(int, input().split())
ps = [None] * p
for k in range(p):
i, j = map(int, input().split())
if j <= s:
j -= 1
ps[k] = r + 1 - i + abs(s - j)
ans = 0
for t, p in enumerate(sorted(ps)[::-1]):
ans = max(ans, t + p)
print(ans)
``` | output | 1 | 5,751 | 1 | 11,503 |
Provide a correct Python 3 solution for this coding contest problem.
Emergency Evacuation
The Japanese government plans to increase the number of inbound tourists to forty million in the year 2020, and sixty million in 2030. Not only increasing touristic appeal but also developing tourism infrastructure further is indispensable to accomplish such numbers.
One possible enhancement on transport is providing cars extremely long and/or wide, carrying many passengers at a time. Too large a car, however, may require too long to evacuate all passengers in an emergency. You are requested to help estimating the time required.
The car is assumed to have the following seat arrangement.
* A center aisle goes straight through the car, directly connecting to the emergency exit door at the rear center of the car.
* The rows of the same number of passenger seats are on both sides of the aisle.
A rough estimation requested is based on a simple step-wise model. All passengers are initially on a distinct seat, and they can make one of the following moves in each step.
* Passengers on a seat can move to an adjacent seat toward the aisle. Passengers on a seat adjacent to the aisle can move sideways directly to the aisle.
* Passengers on the aisle can move backward by one row of seats. If the passenger is in front of the emergency exit, that is, by the rear-most seat rows, he/she can get off the car.
The seat or the aisle position to move to must be empty; either no other passenger is there before the step, or the passenger there empties the seat by moving to another position in the same step. When two or more passengers satisfy the condition for the same position, only one of them can move, keeping the others wait in their original positions.
The leftmost figure of Figure C.1 depicts the seat arrangement of a small car given in Sample Input 1. The car have five rows of seats, two seats each on both sides of the aisle, totaling twenty. The initial positions of seven passengers on board are also shown.
The two other figures of Figure C.1 show possible positions of passengers after the first and the second steps. Passenger movements are indicated by fat arrows. Note that, two of the passengers in the front seat had to wait for a vacancy in the first step, and one in the second row had to wait in the next step.
Your task is to write a program that gives the smallest possible number of steps for all the passengers to get off the car, given the seat arrangement and passengers' initial positions.
<image>
Figure C.1
Input
The input consists of a single test case of the following format.
$r$ $s$ $p$
$i_1$ $j_1$
...
$i_p$ $j_p$
Here, $r$ is the number of passenger seat rows, $s$ is the number of seats on each side of the aisle, and $p$ is the number of passengers. They are integers satisfying $1 \leq r \leq 500$, $1 \leq s \leq 500$, and $1 \leq p \leq 2rs$.
The following $p$ lines give initial seat positions of the passengers. The $k$-th line with $i_k$ and $j_k$ means that the $k$-th passenger's seat is in the $i_k$-th seat row and it is the $j_k$-th seat on that row. Here, rows and seats are counted from front to rear and left to right, both starting from one. They satisfy $1 \leq i_k \leq r$ and $1 \leq j_k \leq 2s$. Passengers are on distinct seats, that is, $i_k \ne= i_l$ or $j_k \ne j_l$ holds if $k \ne l$.
Output
The output should be one line containing a single integer, the minimum number of steps required for all the passengers to get off the car.
Sample Input 1
5 2 7
1 1
1 2
1 3
2 3
2 4
4 4
5 2
Sample Output 1
9
Sample Input 2
500 500 16
1 1
1 2
1 999
1 1000
2 1
2 2
2 999
2 1000
3 1
3 2
3 999
3 1000
499 500
499 501
499 999
499 1000
Sample Output 2
1008
Example
Input
5 2 7
1 1
1 2
1 3
2 3
2 4
4 4
5 2
Output
9 | instruction | 0 | 5,752 | 1 | 11,504 |
"Correct Solution:
```
#!/usr/bin/python3
import array
from fractions import Fraction
import functools
import itertools
import math
import os
import sys
def main():
R, S, P = read_ints()
A = []
for _ in range(P):
i, j = read_ints()
i -= 1
j -= 1
A.append((i, j))
print(solve(R, S, P, A))
def solve(R, S, P, A):
q = [0] * (R + S + 1)
for i, j in A:
x = S - j if j < S else j - S + 1
q[R - 1 - i + x] += 1
of = 0
for i in range(R + S + 1):
c = q[i] + of
if c > 0:
q[i] = 1
of = c - 1
if of > 0:
return R + S + 1 + of
while q and q[-1] == 0:
del q[-1]
return len(q)
###############################################################################
# AUXILIARY FUNCTIONS
DEBUG = 'DEBUG' in os.environ
def inp():
return sys.stdin.readline().rstrip()
def read_int():
return int(inp())
def read_ints():
return [int(e) for e in inp().split()]
def dprint(*value, sep=' ', end='\n'):
if DEBUG:
print(*value, sep=sep, end=end)
if __name__ == '__main__':
main()
``` | output | 1 | 5,752 | 1 | 11,505 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You successfully found poor Arkady near the exit of the station you've perfectly predicted. You sent him home on a taxi and suddenly came up with a question.
There are n crossroads in your city and several bidirectional roads connecting some of them. A taxi ride is a path from some crossroads to another one without passing the same crossroads twice. You have a collection of rides made by one driver and now you wonder if this driver can be a robot or they are definitely a human.
You think that the driver can be a robot if for every two crossroads a and b the driver always chooses the same path whenever he drives from a to b. Note that a and b here do not have to be the endpoints of a ride and that the path from b to a can be different. On the contrary, if the driver ever has driven two different paths from a to b, they are definitely a human.
Given the system of roads and the description of all rides available to you, determine if the driver can be a robot or not.
Input
Each test contains one or more test cases. The first line contains a single integer t (1 β€ t β€ 3 β
10^5) β the number of test cases.
The first line of each test case contains a single integer n (1 β€ n β€ 3 β
10^5) β the number of crossroads in the city.
The next line contains a single integer q (1 β€ q β€ 3 β
10^5) β the number of rides available to you.
Each of the following q lines starts with a single integer k (2 β€ k β€ n) β the number of crossroads visited by the driver on this ride. It is followed by k integers c_1, c_2, ..., c_k (1 β€ c_i β€ n) β the crossroads in the order the driver visited them. It is guaranteed that all crossroads in one ride are distinct.
It is guaranteed that the sum of values k among all rides of all test cases does not exceed 3 β
10^5.
It is guaranteed that the sum of values n and the sum of values q doesn't exceed 3 β
10^5 among all test cases.
Output
Output a single line for each test case.
If the driver can be a robot, output "Robot" in a single line. Otherwise, output "Human".
You can print each letter in any case (upper or lower).
Examples
Input
1
5
2
4 1 2 3 5
3 1 4 3
Output
Human
Input
1
4
4
3 1 2 3
3 2 3 4
3 3 4 1
3 4 1 2
Output
Robot
Note
In the first example it is clear that the driver used two different ways to get from crossroads 1 to crossroads 3. It must be a human.
In the second example the driver always drives the cycle 1 β 2 β 3 β 4 β 1 until he reaches destination.
Submitted Solution:
```
1
``` | instruction | 0 | 5,824 | 1 | 11,648 |
No | output | 1 | 5,824 | 1 | 11,649 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The circle line of the Roflanpolis subway has n stations.
There are two parallel routes in the subway. The first one visits stations in order 1 β 2 β β¦ β n β 1 β 2 β β¦ (so the next stop after station x is equal to (x+1) if x < n and 1 otherwise). The second route visits stations in order n β (n-1) β β¦ β 1 β n β (n-1) β β¦ (so the next stop after station x is equal to (x-1) if x>1 and n otherwise). All trains depart their stations simultaneously, and it takes exactly 1 minute to arrive at the next station.
Two toads live in this city, their names are Daniel and Vlad.
Daniel is currently in a train of the first route at station a and will exit the subway when his train reaches station x.
Coincidentally, Vlad is currently in a train of the second route at station b and he will exit the subway when his train reaches station y.
Surprisingly, all numbers a,x,b,y are distinct.
Toad Ilya asks you to check if Daniel and Vlad will ever be at the same station at the same time during their journey. In other words, check if there is a moment when their trains stop at the same station. Note that this includes the moments when Daniel or Vlad enter or leave the subway.
Input
The first line contains five space-separated integers n, a, x, b, y (4 β€ n β€ 100, 1 β€ a, x, b, y β€ n, all numbers among a, x, b, y are distinct) β the number of stations in Roflanpolis, Daniel's start station, Daniel's finish station, Vlad's start station and Vlad's finish station, respectively.
Output
Output "YES" if there is a time moment when Vlad and Daniel are at the same station, and "NO" otherwise. You can print each letter in any case (upper or lower).
Examples
Input
5 1 4 3 2
Output
YES
Input
10 2 1 9 10
Output
NO
Note
In the first example, Daniel and Vlad start at the stations (1, 3). One minute later they are at stations (2, 2). They are at the same station at this moment. Note that Vlad leaves the subway right after that.
Consider the second example, let's look at the stations Vlad and Daniel are at. They are:
* initially (2, 9),
* after 1 minute (3, 8),
* after 2 minutes (4, 7),
* after 3 minutes (5, 6),
* after 4 minutes (6, 5),
* after 5 minutes (7, 4),
* after 6 minutes (8, 3),
* after 7 minutes (9, 2),
* after 8 minutes (10, 1),
* after 9 minutes (1, 10).
After that, they both leave the subway because they are at their finish stations, so there is no moment when they both are at the same station. | instruction | 0 | 5,829 | 1 | 11,658 |
Tags: implementation, math
Correct Solution:
```
list1=list(map(int,input().split()))
list2=[]
flag=0
for i in range(list1[0]):
list2.append(i+1)
if(list1[1]==list1[3]):
print('YES')
for j in range(list1[0]):
a=list1[1]+j
if a>list1[0]:
a=a-list1[0]
if(list2[a-1]==list2[list1[3]-j-1]):
flag=1
break
if(list2[a-1]==list1[2] or list2[list1[3]-j-1]==list1[4]):
break
if flag==1:
print('YES')
elif flag==0:
print('NO')
``` | output | 1 | 5,829 | 1 | 11,659 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The circle line of the Roflanpolis subway has n stations.
There are two parallel routes in the subway. The first one visits stations in order 1 β 2 β β¦ β n β 1 β 2 β β¦ (so the next stop after station x is equal to (x+1) if x < n and 1 otherwise). The second route visits stations in order n β (n-1) β β¦ β 1 β n β (n-1) β β¦ (so the next stop after station x is equal to (x-1) if x>1 and n otherwise). All trains depart their stations simultaneously, and it takes exactly 1 minute to arrive at the next station.
Two toads live in this city, their names are Daniel and Vlad.
Daniel is currently in a train of the first route at station a and will exit the subway when his train reaches station x.
Coincidentally, Vlad is currently in a train of the second route at station b and he will exit the subway when his train reaches station y.
Surprisingly, all numbers a,x,b,y are distinct.
Toad Ilya asks you to check if Daniel and Vlad will ever be at the same station at the same time during their journey. In other words, check if there is a moment when their trains stop at the same station. Note that this includes the moments when Daniel or Vlad enter or leave the subway.
Input
The first line contains five space-separated integers n, a, x, b, y (4 β€ n β€ 100, 1 β€ a, x, b, y β€ n, all numbers among a, x, b, y are distinct) β the number of stations in Roflanpolis, Daniel's start station, Daniel's finish station, Vlad's start station and Vlad's finish station, respectively.
Output
Output "YES" if there is a time moment when Vlad and Daniel are at the same station, and "NO" otherwise. You can print each letter in any case (upper or lower).
Examples
Input
5 1 4 3 2
Output
YES
Input
10 2 1 9 10
Output
NO
Note
In the first example, Daniel and Vlad start at the stations (1, 3). One minute later they are at stations (2, 2). They are at the same station at this moment. Note that Vlad leaves the subway right after that.
Consider the second example, let's look at the stations Vlad and Daniel are at. They are:
* initially (2, 9),
* after 1 minute (3, 8),
* after 2 minutes (4, 7),
* after 3 minutes (5, 6),
* after 4 minutes (6, 5),
* after 5 minutes (7, 4),
* after 6 minutes (8, 3),
* after 7 minutes (9, 2),
* after 8 minutes (10, 1),
* after 9 minutes (1, 10).
After that, they both leave the subway because they are at their finish stations, so there is no moment when they both are at the same station. | instruction | 0 | 5,830 | 1 | 11,660 |
Tags: implementation, math
Correct Solution:
```
from sys import stdin
# stdin=open('input.txt')
def input():
return stdin.readline().strip()
# from sys import stdout
# stdout=open('input.txt',mode='w+')
# def print1(x, end='\n'):
# stdout.write(str(x) +end)
# a, b = map(int, input().split())
# l = list(map(int, input().split()))
# # CODE BEGINS HERE.................
n, a, x, b, y = map(int, input().split())
flag = (a == b)
while not flag and a != x and b != y:
if a == n:
a = 1
else:
a += 1
if b == 1:
b = n
else:
b -= 1
if a == b:
flag = True
break
if flag:
print('YES')
else:
print('NO')
# # CODE ENDS HERE....................
# stdout.close()
``` | output | 1 | 5,830 | 1 | 11,661 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The circle line of the Roflanpolis subway has n stations.
There are two parallel routes in the subway. The first one visits stations in order 1 β 2 β β¦ β n β 1 β 2 β β¦ (so the next stop after station x is equal to (x+1) if x < n and 1 otherwise). The second route visits stations in order n β (n-1) β β¦ β 1 β n β (n-1) β β¦ (so the next stop after station x is equal to (x-1) if x>1 and n otherwise). All trains depart their stations simultaneously, and it takes exactly 1 minute to arrive at the next station.
Two toads live in this city, their names are Daniel and Vlad.
Daniel is currently in a train of the first route at station a and will exit the subway when his train reaches station x.
Coincidentally, Vlad is currently in a train of the second route at station b and he will exit the subway when his train reaches station y.
Surprisingly, all numbers a,x,b,y are distinct.
Toad Ilya asks you to check if Daniel and Vlad will ever be at the same station at the same time during their journey. In other words, check if there is a moment when their trains stop at the same station. Note that this includes the moments when Daniel or Vlad enter or leave the subway.
Input
The first line contains five space-separated integers n, a, x, b, y (4 β€ n β€ 100, 1 β€ a, x, b, y β€ n, all numbers among a, x, b, y are distinct) β the number of stations in Roflanpolis, Daniel's start station, Daniel's finish station, Vlad's start station and Vlad's finish station, respectively.
Output
Output "YES" if there is a time moment when Vlad and Daniel are at the same station, and "NO" otherwise. You can print each letter in any case (upper or lower).
Examples
Input
5 1 4 3 2
Output
YES
Input
10 2 1 9 10
Output
NO
Note
In the first example, Daniel and Vlad start at the stations (1, 3). One minute later they are at stations (2, 2). They are at the same station at this moment. Note that Vlad leaves the subway right after that.
Consider the second example, let's look at the stations Vlad and Daniel are at. They are:
* initially (2, 9),
* after 1 minute (3, 8),
* after 2 minutes (4, 7),
* after 3 minutes (5, 6),
* after 4 minutes (6, 5),
* after 5 minutes (7, 4),
* after 6 minutes (8, 3),
* after 7 minutes (9, 2),
* after 8 minutes (10, 1),
* after 9 minutes (1, 10).
After that, they both leave the subway because they are at their finish stations, so there is no moment when they both are at the same station. | instruction | 0 | 5,831 | 1 | 11,662 |
Tags: implementation, math
Correct Solution:
```
n, a, x, b, y = (int(i)-1 for i in input().split())
n += 1
while True:
if a == b:
print('YES')
break
if a == x or b == y:
print('NO')
break
a = (a+1) % n
b = (b-1) % n
``` | output | 1 | 5,831 | 1 | 11,663 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The circle line of the Roflanpolis subway has n stations.
There are two parallel routes in the subway. The first one visits stations in order 1 β 2 β β¦ β n β 1 β 2 β β¦ (so the next stop after station x is equal to (x+1) if x < n and 1 otherwise). The second route visits stations in order n β (n-1) β β¦ β 1 β n β (n-1) β β¦ (so the next stop after station x is equal to (x-1) if x>1 and n otherwise). All trains depart their stations simultaneously, and it takes exactly 1 minute to arrive at the next station.
Two toads live in this city, their names are Daniel and Vlad.
Daniel is currently in a train of the first route at station a and will exit the subway when his train reaches station x.
Coincidentally, Vlad is currently in a train of the second route at station b and he will exit the subway when his train reaches station y.
Surprisingly, all numbers a,x,b,y are distinct.
Toad Ilya asks you to check if Daniel and Vlad will ever be at the same station at the same time during their journey. In other words, check if there is a moment when their trains stop at the same station. Note that this includes the moments when Daniel or Vlad enter or leave the subway.
Input
The first line contains five space-separated integers n, a, x, b, y (4 β€ n β€ 100, 1 β€ a, x, b, y β€ n, all numbers among a, x, b, y are distinct) β the number of stations in Roflanpolis, Daniel's start station, Daniel's finish station, Vlad's start station and Vlad's finish station, respectively.
Output
Output "YES" if there is a time moment when Vlad and Daniel are at the same station, and "NO" otherwise. You can print each letter in any case (upper or lower).
Examples
Input
5 1 4 3 2
Output
YES
Input
10 2 1 9 10
Output
NO
Note
In the first example, Daniel and Vlad start at the stations (1, 3). One minute later they are at stations (2, 2). They are at the same station at this moment. Note that Vlad leaves the subway right after that.
Consider the second example, let's look at the stations Vlad and Daniel are at. They are:
* initially (2, 9),
* after 1 minute (3, 8),
* after 2 minutes (4, 7),
* after 3 minutes (5, 6),
* after 4 minutes (6, 5),
* after 5 minutes (7, 4),
* after 6 minutes (8, 3),
* after 7 minutes (9, 2),
* after 8 minutes (10, 1),
* after 9 minutes (1, 10).
After that, they both leave the subway because they are at their finish stations, so there is no moment when they both are at the same station. | instruction | 0 | 5,832 | 1 | 11,664 |
Tags: implementation, math
Correct Solution:
```
flag = True
n,a,x,b,y = list(map(int,input().split()))
for i in range(min((x-a)%n, (b-y)%n)):
a = a+1
b = b-1
if a>n:
a = 1
if b==0:
b = n
if a==b:
print("YES")
flag = False
break
if flag:
print("NO")
``` | output | 1 | 5,832 | 1 | 11,665 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The circle line of the Roflanpolis subway has n stations.
There are two parallel routes in the subway. The first one visits stations in order 1 β 2 β β¦ β n β 1 β 2 β β¦ (so the next stop after station x is equal to (x+1) if x < n and 1 otherwise). The second route visits stations in order n β (n-1) β β¦ β 1 β n β (n-1) β β¦ (so the next stop after station x is equal to (x-1) if x>1 and n otherwise). All trains depart their stations simultaneously, and it takes exactly 1 minute to arrive at the next station.
Two toads live in this city, their names are Daniel and Vlad.
Daniel is currently in a train of the first route at station a and will exit the subway when his train reaches station x.
Coincidentally, Vlad is currently in a train of the second route at station b and he will exit the subway when his train reaches station y.
Surprisingly, all numbers a,x,b,y are distinct.
Toad Ilya asks you to check if Daniel and Vlad will ever be at the same station at the same time during their journey. In other words, check if there is a moment when their trains stop at the same station. Note that this includes the moments when Daniel or Vlad enter or leave the subway.
Input
The first line contains five space-separated integers n, a, x, b, y (4 β€ n β€ 100, 1 β€ a, x, b, y β€ n, all numbers among a, x, b, y are distinct) β the number of stations in Roflanpolis, Daniel's start station, Daniel's finish station, Vlad's start station and Vlad's finish station, respectively.
Output
Output "YES" if there is a time moment when Vlad and Daniel are at the same station, and "NO" otherwise. You can print each letter in any case (upper or lower).
Examples
Input
5 1 4 3 2
Output
YES
Input
10 2 1 9 10
Output
NO
Note
In the first example, Daniel and Vlad start at the stations (1, 3). One minute later they are at stations (2, 2). They are at the same station at this moment. Note that Vlad leaves the subway right after that.
Consider the second example, let's look at the stations Vlad and Daniel are at. They are:
* initially (2, 9),
* after 1 minute (3, 8),
* after 2 minutes (4, 7),
* after 3 minutes (5, 6),
* after 4 minutes (6, 5),
* after 5 minutes (7, 4),
* after 6 minutes (8, 3),
* after 7 minutes (9, 2),
* after 8 minutes (10, 1),
* after 9 minutes (1, 10).
After that, they both leave the subway because they are at their finish stations, so there is no moment when they both are at the same station. | instruction | 0 | 5,833 | 1 | 11,666 |
Tags: implementation, math
Correct Solution:
```
if __name__ == '__main__':
n, a, x, b, y = map(int, input().split())
a -= 1
b -= 1
x -= 1
y -= 1
while a != x and b != y:
a = (a + 1) % n
b = (b - 1) % n
if a == b:
print("YES")
exit(0)
print("NO")
``` | output | 1 | 5,833 | 1 | 11,667 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The circle line of the Roflanpolis subway has n stations.
There are two parallel routes in the subway. The first one visits stations in order 1 β 2 β β¦ β n β 1 β 2 β β¦ (so the next stop after station x is equal to (x+1) if x < n and 1 otherwise). The second route visits stations in order n β (n-1) β β¦ β 1 β n β (n-1) β β¦ (so the next stop after station x is equal to (x-1) if x>1 and n otherwise). All trains depart their stations simultaneously, and it takes exactly 1 minute to arrive at the next station.
Two toads live in this city, their names are Daniel and Vlad.
Daniel is currently in a train of the first route at station a and will exit the subway when his train reaches station x.
Coincidentally, Vlad is currently in a train of the second route at station b and he will exit the subway when his train reaches station y.
Surprisingly, all numbers a,x,b,y are distinct.
Toad Ilya asks you to check if Daniel and Vlad will ever be at the same station at the same time during their journey. In other words, check if there is a moment when their trains stop at the same station. Note that this includes the moments when Daniel or Vlad enter or leave the subway.
Input
The first line contains five space-separated integers n, a, x, b, y (4 β€ n β€ 100, 1 β€ a, x, b, y β€ n, all numbers among a, x, b, y are distinct) β the number of stations in Roflanpolis, Daniel's start station, Daniel's finish station, Vlad's start station and Vlad's finish station, respectively.
Output
Output "YES" if there is a time moment when Vlad and Daniel are at the same station, and "NO" otherwise. You can print each letter in any case (upper or lower).
Examples
Input
5 1 4 3 2
Output
YES
Input
10 2 1 9 10
Output
NO
Note
In the first example, Daniel and Vlad start at the stations (1, 3). One minute later they are at stations (2, 2). They are at the same station at this moment. Note that Vlad leaves the subway right after that.
Consider the second example, let's look at the stations Vlad and Daniel are at. They are:
* initially (2, 9),
* after 1 minute (3, 8),
* after 2 minutes (4, 7),
* after 3 minutes (5, 6),
* after 4 minutes (6, 5),
* after 5 minutes (7, 4),
* after 6 minutes (8, 3),
* after 7 minutes (9, 2),
* after 8 minutes (10, 1),
* after 9 minutes (1, 10).
After that, they both leave the subway because they are at their finish stations, so there is no moment when they both are at the same station. | instruction | 0 | 5,834 | 1 | 11,668 |
Tags: implementation, math
Correct Solution:
```
n, a, x, b, y = map(int,input().split())
while a != x and b != y:
a += 1
b -= 1
if a > n:a = 1
if b <= 0:b = n
if a == b:
print("YES")
exit()
print("NO")
``` | output | 1 | 5,834 | 1 | 11,669 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The circle line of the Roflanpolis subway has n stations.
There are two parallel routes in the subway. The first one visits stations in order 1 β 2 β β¦ β n β 1 β 2 β β¦ (so the next stop after station x is equal to (x+1) if x < n and 1 otherwise). The second route visits stations in order n β (n-1) β β¦ β 1 β n β (n-1) β β¦ (so the next stop after station x is equal to (x-1) if x>1 and n otherwise). All trains depart their stations simultaneously, and it takes exactly 1 minute to arrive at the next station.
Two toads live in this city, their names are Daniel and Vlad.
Daniel is currently in a train of the first route at station a and will exit the subway when his train reaches station x.
Coincidentally, Vlad is currently in a train of the second route at station b and he will exit the subway when his train reaches station y.
Surprisingly, all numbers a,x,b,y are distinct.
Toad Ilya asks you to check if Daniel and Vlad will ever be at the same station at the same time during their journey. In other words, check if there is a moment when their trains stop at the same station. Note that this includes the moments when Daniel or Vlad enter or leave the subway.
Input
The first line contains five space-separated integers n, a, x, b, y (4 β€ n β€ 100, 1 β€ a, x, b, y β€ n, all numbers among a, x, b, y are distinct) β the number of stations in Roflanpolis, Daniel's start station, Daniel's finish station, Vlad's start station and Vlad's finish station, respectively.
Output
Output "YES" if there is a time moment when Vlad and Daniel are at the same station, and "NO" otherwise. You can print each letter in any case (upper or lower).
Examples
Input
5 1 4 3 2
Output
YES
Input
10 2 1 9 10
Output
NO
Note
In the first example, Daniel and Vlad start at the stations (1, 3). One minute later they are at stations (2, 2). They are at the same station at this moment. Note that Vlad leaves the subway right after that.
Consider the second example, let's look at the stations Vlad and Daniel are at. They are:
* initially (2, 9),
* after 1 minute (3, 8),
* after 2 minutes (4, 7),
* after 3 minutes (5, 6),
* after 4 minutes (6, 5),
* after 5 minutes (7, 4),
* after 6 minutes (8, 3),
* after 7 minutes (9, 2),
* after 8 minutes (10, 1),
* after 9 minutes (1, 10).
After that, they both leave the subway because they are at their finish stations, so there is no moment when they both are at the same station. | instruction | 0 | 5,835 | 1 | 11,670 |
Tags: implementation, math
Correct Solution:
```
n, a, x, b, y = map(int, input().split())
m1 = []
m2 = []
while a != x:
m1.append(a)
a += 1
if a > n:
a = 1
while b != y:
m2.append(b)
b -= 1
if b < 1:
b = n
m1.append(a)
m2.append(b)
b = False
for i in range(min(len(m1), len(m2))):
if m1[i] == m2[i]:
b = True
break
if b:
print('YES')
else:
print('NO')
``` | output | 1 | 5,835 | 1 | 11,671 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The circle line of the Roflanpolis subway has n stations.
There are two parallel routes in the subway. The first one visits stations in order 1 β 2 β β¦ β n β 1 β 2 β β¦ (so the next stop after station x is equal to (x+1) if x < n and 1 otherwise). The second route visits stations in order n β (n-1) β β¦ β 1 β n β (n-1) β β¦ (so the next stop after station x is equal to (x-1) if x>1 and n otherwise). All trains depart their stations simultaneously, and it takes exactly 1 minute to arrive at the next station.
Two toads live in this city, their names are Daniel and Vlad.
Daniel is currently in a train of the first route at station a and will exit the subway when his train reaches station x.
Coincidentally, Vlad is currently in a train of the second route at station b and he will exit the subway when his train reaches station y.
Surprisingly, all numbers a,x,b,y are distinct.
Toad Ilya asks you to check if Daniel and Vlad will ever be at the same station at the same time during their journey. In other words, check if there is a moment when their trains stop at the same station. Note that this includes the moments when Daniel or Vlad enter or leave the subway.
Input
The first line contains five space-separated integers n, a, x, b, y (4 β€ n β€ 100, 1 β€ a, x, b, y β€ n, all numbers among a, x, b, y are distinct) β the number of stations in Roflanpolis, Daniel's start station, Daniel's finish station, Vlad's start station and Vlad's finish station, respectively.
Output
Output "YES" if there is a time moment when Vlad and Daniel are at the same station, and "NO" otherwise. You can print each letter in any case (upper or lower).
Examples
Input
5 1 4 3 2
Output
YES
Input
10 2 1 9 10
Output
NO
Note
In the first example, Daniel and Vlad start at the stations (1, 3). One minute later they are at stations (2, 2). They are at the same station at this moment. Note that Vlad leaves the subway right after that.
Consider the second example, let's look at the stations Vlad and Daniel are at. They are:
* initially (2, 9),
* after 1 minute (3, 8),
* after 2 minutes (4, 7),
* after 3 minutes (5, 6),
* after 4 minutes (6, 5),
* after 5 minutes (7, 4),
* after 6 minutes (8, 3),
* after 7 minutes (9, 2),
* after 8 minutes (10, 1),
* after 9 minutes (1, 10).
After that, they both leave the subway because they are at their finish stations, so there is no moment when they both are at the same station. | instruction | 0 | 5,836 | 1 | 11,672 |
Tags: implementation, math
Correct Solution:
```
import sys
n, a, x, b, y = [int(x) for x in input().split()]
while a!=x and b!=y:
a+= 1
if a==n+1:
a = 1
b -= 1
if b==0:
b = n
if a==b:
print('YES')
sys.exit()
print('NO')
``` | output | 1 | 5,836 | 1 | 11,673 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The circle line of the Roflanpolis subway has n stations.
There are two parallel routes in the subway. The first one visits stations in order 1 β 2 β β¦ β n β 1 β 2 β β¦ (so the next stop after station x is equal to (x+1) if x < n and 1 otherwise). The second route visits stations in order n β (n-1) β β¦ β 1 β n β (n-1) β β¦ (so the next stop after station x is equal to (x-1) if x>1 and n otherwise). All trains depart their stations simultaneously, and it takes exactly 1 minute to arrive at the next station.
Two toads live in this city, their names are Daniel and Vlad.
Daniel is currently in a train of the first route at station a and will exit the subway when his train reaches station x.
Coincidentally, Vlad is currently in a train of the second route at station b and he will exit the subway when his train reaches station y.
Surprisingly, all numbers a,x,b,y are distinct.
Toad Ilya asks you to check if Daniel and Vlad will ever be at the same station at the same time during their journey. In other words, check if there is a moment when their trains stop at the same station. Note that this includes the moments when Daniel or Vlad enter or leave the subway.
Input
The first line contains five space-separated integers n, a, x, b, y (4 β€ n β€ 100, 1 β€ a, x, b, y β€ n, all numbers among a, x, b, y are distinct) β the number of stations in Roflanpolis, Daniel's start station, Daniel's finish station, Vlad's start station and Vlad's finish station, respectively.
Output
Output "YES" if there is a time moment when Vlad and Daniel are at the same station, and "NO" otherwise. You can print each letter in any case (upper or lower).
Examples
Input
5 1 4 3 2
Output
YES
Input
10 2 1 9 10
Output
NO
Note
In the first example, Daniel and Vlad start at the stations (1, 3). One minute later they are at stations (2, 2). They are at the same station at this moment. Note that Vlad leaves the subway right after that.
Consider the second example, let's look at the stations Vlad and Daniel are at. They are:
* initially (2, 9),
* after 1 minute (3, 8),
* after 2 minutes (4, 7),
* after 3 minutes (5, 6),
* after 4 minutes (6, 5),
* after 5 minutes (7, 4),
* after 6 minutes (8, 3),
* after 7 minutes (9, 2),
* after 8 minutes (10, 1),
* after 9 minutes (1, 10).
After that, they both leave the subway because they are at their finish stations, so there is no moment when they both are at the same station.
Submitted Solution:
```
numberOfStations, danielS, danielE, vladS, vladE = input().split()
numberOfStations = int(numberOfStations)
danielS = int(danielS)
danielE = int(danielE)
vladE = int(vladE)
vladS = int(vladS)
i=0
meet=False
while True:
if danielS == vladS:
meet=True
break
if danielS == danielE or vladS == vladE:
break
if danielS == numberOfStations:
danielS=1
else:
danielS+=1
if vladS == 1:
vladS=numberOfStations
else:
vladS-=1
print("YES" if meet else "NO")
``` | instruction | 0 | 5,837 | 1 | 11,674 |
Yes | output | 1 | 5,837 | 1 | 11,675 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The circle line of the Roflanpolis subway has n stations.
There are two parallel routes in the subway. The first one visits stations in order 1 β 2 β β¦ β n β 1 β 2 β β¦ (so the next stop after station x is equal to (x+1) if x < n and 1 otherwise). The second route visits stations in order n β (n-1) β β¦ β 1 β n β (n-1) β β¦ (so the next stop after station x is equal to (x-1) if x>1 and n otherwise). All trains depart their stations simultaneously, and it takes exactly 1 minute to arrive at the next station.
Two toads live in this city, their names are Daniel and Vlad.
Daniel is currently in a train of the first route at station a and will exit the subway when his train reaches station x.
Coincidentally, Vlad is currently in a train of the second route at station b and he will exit the subway when his train reaches station y.
Surprisingly, all numbers a,x,b,y are distinct.
Toad Ilya asks you to check if Daniel and Vlad will ever be at the same station at the same time during their journey. In other words, check if there is a moment when their trains stop at the same station. Note that this includes the moments when Daniel or Vlad enter or leave the subway.
Input
The first line contains five space-separated integers n, a, x, b, y (4 β€ n β€ 100, 1 β€ a, x, b, y β€ n, all numbers among a, x, b, y are distinct) β the number of stations in Roflanpolis, Daniel's start station, Daniel's finish station, Vlad's start station and Vlad's finish station, respectively.
Output
Output "YES" if there is a time moment when Vlad and Daniel are at the same station, and "NO" otherwise. You can print each letter in any case (upper or lower).
Examples
Input
5 1 4 3 2
Output
YES
Input
10 2 1 9 10
Output
NO
Note
In the first example, Daniel and Vlad start at the stations (1, 3). One minute later they are at stations (2, 2). They are at the same station at this moment. Note that Vlad leaves the subway right after that.
Consider the second example, let's look at the stations Vlad and Daniel are at. They are:
* initially (2, 9),
* after 1 minute (3, 8),
* after 2 minutes (4, 7),
* after 3 minutes (5, 6),
* after 4 minutes (6, 5),
* after 5 minutes (7, 4),
* after 6 minutes (8, 3),
* after 7 minutes (9, 2),
* after 8 minutes (10, 1),
* after 9 minutes (1, 10).
After that, they both leave the subway because they are at their finish stations, so there is no moment when they both are at the same station.
Submitted Solution:
```
n, a, x, b, y = map(int, input().split())
def get_next_positive(a):
return a%n+1
def get_next_negative(b):
return n if b == 1 else b-1
while a != x and b != y:
a = get_next_positive(a)
b = get_next_negative(b)
if a == b:
print("YES")
exit(0)
print("NO")
``` | instruction | 0 | 5,838 | 1 | 11,676 |
Yes | output | 1 | 5,838 | 1 | 11,677 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The circle line of the Roflanpolis subway has n stations.
There are two parallel routes in the subway. The first one visits stations in order 1 β 2 β β¦ β n β 1 β 2 β β¦ (so the next stop after station x is equal to (x+1) if x < n and 1 otherwise). The second route visits stations in order n β (n-1) β β¦ β 1 β n β (n-1) β β¦ (so the next stop after station x is equal to (x-1) if x>1 and n otherwise). All trains depart their stations simultaneously, and it takes exactly 1 minute to arrive at the next station.
Two toads live in this city, their names are Daniel and Vlad.
Daniel is currently in a train of the first route at station a and will exit the subway when his train reaches station x.
Coincidentally, Vlad is currently in a train of the second route at station b and he will exit the subway when his train reaches station y.
Surprisingly, all numbers a,x,b,y are distinct.
Toad Ilya asks you to check if Daniel and Vlad will ever be at the same station at the same time during their journey. In other words, check if there is a moment when their trains stop at the same station. Note that this includes the moments when Daniel or Vlad enter or leave the subway.
Input
The first line contains five space-separated integers n, a, x, b, y (4 β€ n β€ 100, 1 β€ a, x, b, y β€ n, all numbers among a, x, b, y are distinct) β the number of stations in Roflanpolis, Daniel's start station, Daniel's finish station, Vlad's start station and Vlad's finish station, respectively.
Output
Output "YES" if there is a time moment when Vlad and Daniel are at the same station, and "NO" otherwise. You can print each letter in any case (upper or lower).
Examples
Input
5 1 4 3 2
Output
YES
Input
10 2 1 9 10
Output
NO
Note
In the first example, Daniel and Vlad start at the stations (1, 3). One minute later they are at stations (2, 2). They are at the same station at this moment. Note that Vlad leaves the subway right after that.
Consider the second example, let's look at the stations Vlad and Daniel are at. They are:
* initially (2, 9),
* after 1 minute (3, 8),
* after 2 minutes (4, 7),
* after 3 minutes (5, 6),
* after 4 minutes (6, 5),
* after 5 minutes (7, 4),
* after 6 minutes (8, 3),
* after 7 minutes (9, 2),
* after 8 minutes (10, 1),
* after 9 minutes (1, 10).
After that, they both leave the subway because they are at their finish stations, so there is no moment when they both are at the same station.
Submitted Solution:
```
n,a,x,b,y=map(int,input().split())
ans=0
curr=a
t=205
dan=[]
while(curr!=x):
dan.append(curr)
if(curr+1>n):
curr=1
else:
curr+=1
dan.append(x)
vlad=[]
curr=b
while(curr!=y):
vlad.append(curr)
if(curr-1==0):
curr=n
else:
curr-=1
vlad.append(y)
l=min(len(vlad),len(dan))
for i in range(l):
if(vlad[i]==dan[i]):
ans=1
#print(dan,vlad)
if(ans==1):
print("YES")
else:
print("NO")
``` | instruction | 0 | 5,839 | 1 | 11,678 |
Yes | output | 1 | 5,839 | 1 | 11,679 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The circle line of the Roflanpolis subway has n stations.
There are two parallel routes in the subway. The first one visits stations in order 1 β 2 β β¦ β n β 1 β 2 β β¦ (so the next stop after station x is equal to (x+1) if x < n and 1 otherwise). The second route visits stations in order n β (n-1) β β¦ β 1 β n β (n-1) β β¦ (so the next stop after station x is equal to (x-1) if x>1 and n otherwise). All trains depart their stations simultaneously, and it takes exactly 1 minute to arrive at the next station.
Two toads live in this city, their names are Daniel and Vlad.
Daniel is currently in a train of the first route at station a and will exit the subway when his train reaches station x.
Coincidentally, Vlad is currently in a train of the second route at station b and he will exit the subway when his train reaches station y.
Surprisingly, all numbers a,x,b,y are distinct.
Toad Ilya asks you to check if Daniel and Vlad will ever be at the same station at the same time during their journey. In other words, check if there is a moment when their trains stop at the same station. Note that this includes the moments when Daniel or Vlad enter or leave the subway.
Input
The first line contains five space-separated integers n, a, x, b, y (4 β€ n β€ 100, 1 β€ a, x, b, y β€ n, all numbers among a, x, b, y are distinct) β the number of stations in Roflanpolis, Daniel's start station, Daniel's finish station, Vlad's start station and Vlad's finish station, respectively.
Output
Output "YES" if there is a time moment when Vlad and Daniel are at the same station, and "NO" otherwise. You can print each letter in any case (upper or lower).
Examples
Input
5 1 4 3 2
Output
YES
Input
10 2 1 9 10
Output
NO
Note
In the first example, Daniel and Vlad start at the stations (1, 3). One minute later they are at stations (2, 2). They are at the same station at this moment. Note that Vlad leaves the subway right after that.
Consider the second example, let's look at the stations Vlad and Daniel are at. They are:
* initially (2, 9),
* after 1 minute (3, 8),
* after 2 minutes (4, 7),
* after 3 minutes (5, 6),
* after 4 minutes (6, 5),
* after 5 minutes (7, 4),
* after 6 minutes (8, 3),
* after 7 minutes (9, 2),
* after 8 minutes (10, 1),
* after 9 minutes (1, 10).
After that, they both leave the subway because they are at their finish stations, so there is no moment when they both are at the same station.
Submitted Solution:
```
n, a, x, b, y = map(int, input().split())
while a != x and b != y:
a = a % n + 1
b = (b - 1 - 1 + n) % n + 1
if a == b:
print("YES")
exit()
print("NO")
``` | instruction | 0 | 5,840 | 1 | 11,680 |
Yes | output | 1 | 5,840 | 1 | 11,681 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The circle line of the Roflanpolis subway has n stations.
There are two parallel routes in the subway. The first one visits stations in order 1 β 2 β β¦ β n β 1 β 2 β β¦ (so the next stop after station x is equal to (x+1) if x < n and 1 otherwise). The second route visits stations in order n β (n-1) β β¦ β 1 β n β (n-1) β β¦ (so the next stop after station x is equal to (x-1) if x>1 and n otherwise). All trains depart their stations simultaneously, and it takes exactly 1 minute to arrive at the next station.
Two toads live in this city, their names are Daniel and Vlad.
Daniel is currently in a train of the first route at station a and will exit the subway when his train reaches station x.
Coincidentally, Vlad is currently in a train of the second route at station b and he will exit the subway when his train reaches station y.
Surprisingly, all numbers a,x,b,y are distinct.
Toad Ilya asks you to check if Daniel and Vlad will ever be at the same station at the same time during their journey. In other words, check if there is a moment when their trains stop at the same station. Note that this includes the moments when Daniel or Vlad enter or leave the subway.
Input
The first line contains five space-separated integers n, a, x, b, y (4 β€ n β€ 100, 1 β€ a, x, b, y β€ n, all numbers among a, x, b, y are distinct) β the number of stations in Roflanpolis, Daniel's start station, Daniel's finish station, Vlad's start station and Vlad's finish station, respectively.
Output
Output "YES" if there is a time moment when Vlad and Daniel are at the same station, and "NO" otherwise. You can print each letter in any case (upper or lower).
Examples
Input
5 1 4 3 2
Output
YES
Input
10 2 1 9 10
Output
NO
Note
In the first example, Daniel and Vlad start at the stations (1, 3). One minute later they are at stations (2, 2). They are at the same station at this moment. Note that Vlad leaves the subway right after that.
Consider the second example, let's look at the stations Vlad and Daniel are at. They are:
* initially (2, 9),
* after 1 minute (3, 8),
* after 2 minutes (4, 7),
* after 3 minutes (5, 6),
* after 4 minutes (6, 5),
* after 5 minutes (7, 4),
* after 6 minutes (8, 3),
* after 7 minutes (9, 2),
* after 8 minutes (10, 1),
* after 9 minutes (1, 10).
After that, they both leave the subway because they are at their finish stations, so there is no moment when they both are at the same station.
Submitted Solution:
```
n, a, x, b, y = map(int, input().split())
# p1 = a
# p2 = b
while True:
if a == b:
print('YES')
exit()
elif a == x or b == y:
print('NO')
exit()
a = a + 1 if x < n else 1
b = b - 1 if x > 1 else n
``` | instruction | 0 | 5,841 | 1 | 11,682 |
No | output | 1 | 5,841 | 1 | 11,683 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The circle line of the Roflanpolis subway has n stations.
There are two parallel routes in the subway. The first one visits stations in order 1 β 2 β β¦ β n β 1 β 2 β β¦ (so the next stop after station x is equal to (x+1) if x < n and 1 otherwise). The second route visits stations in order n β (n-1) β β¦ β 1 β n β (n-1) β β¦ (so the next stop after station x is equal to (x-1) if x>1 and n otherwise). All trains depart their stations simultaneously, and it takes exactly 1 minute to arrive at the next station.
Two toads live in this city, their names are Daniel and Vlad.
Daniel is currently in a train of the first route at station a and will exit the subway when his train reaches station x.
Coincidentally, Vlad is currently in a train of the second route at station b and he will exit the subway when his train reaches station y.
Surprisingly, all numbers a,x,b,y are distinct.
Toad Ilya asks you to check if Daniel and Vlad will ever be at the same station at the same time during their journey. In other words, check if there is a moment when their trains stop at the same station. Note that this includes the moments when Daniel or Vlad enter or leave the subway.
Input
The first line contains five space-separated integers n, a, x, b, y (4 β€ n β€ 100, 1 β€ a, x, b, y β€ n, all numbers among a, x, b, y are distinct) β the number of stations in Roflanpolis, Daniel's start station, Daniel's finish station, Vlad's start station and Vlad's finish station, respectively.
Output
Output "YES" if there is a time moment when Vlad and Daniel are at the same station, and "NO" otherwise. You can print each letter in any case (upper or lower).
Examples
Input
5 1 4 3 2
Output
YES
Input
10 2 1 9 10
Output
NO
Note
In the first example, Daniel and Vlad start at the stations (1, 3). One minute later they are at stations (2, 2). They are at the same station at this moment. Note that Vlad leaves the subway right after that.
Consider the second example, let's look at the stations Vlad and Daniel are at. They are:
* initially (2, 9),
* after 1 minute (3, 8),
* after 2 minutes (4, 7),
* after 3 minutes (5, 6),
* after 4 minutes (6, 5),
* after 5 minutes (7, 4),
* after 6 minutes (8, 3),
* after 7 minutes (9, 2),
* after 8 minutes (10, 1),
* after 9 minutes (1, 10).
After that, they both leave the subway because they are at their finish stations, so there is no moment when they both are at the same station.
Submitted Solution:
```
d = tuple(map(int, input().split()))
n = d[0]
a = d[1]
x = d[2]
b = d[3]
y = d[4]
if a < x:
if b < y:
if a < b or y < x:
if (a < b and (a - b) % 2 == 0) or ((n - a + b) % 2 == 0):
print('YES')
else:
print('NO')
else:
print('NO')
else:
if (b < x and b > a) and (b - a) % 2 == 0:
print('YES')
else:
print('NO')
else:
if b > y:
if (x > b or a < y) and (b-a)%2==0:
print('YES')
else:
print('NO')
else:
if (b<a and (n-a+b)%2==0) or (b-a)%2==0:
print('YES')
else:
print('NO')
``` | instruction | 0 | 5,842 | 1 | 11,684 |
No | output | 1 | 5,842 | 1 | 11,685 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The circle line of the Roflanpolis subway has n stations.
There are two parallel routes in the subway. The first one visits stations in order 1 β 2 β β¦ β n β 1 β 2 β β¦ (so the next stop after station x is equal to (x+1) if x < n and 1 otherwise). The second route visits stations in order n β (n-1) β β¦ β 1 β n β (n-1) β β¦ (so the next stop after station x is equal to (x-1) if x>1 and n otherwise). All trains depart their stations simultaneously, and it takes exactly 1 minute to arrive at the next station.
Two toads live in this city, their names are Daniel and Vlad.
Daniel is currently in a train of the first route at station a and will exit the subway when his train reaches station x.
Coincidentally, Vlad is currently in a train of the second route at station b and he will exit the subway when his train reaches station y.
Surprisingly, all numbers a,x,b,y are distinct.
Toad Ilya asks you to check if Daniel and Vlad will ever be at the same station at the same time during their journey. In other words, check if there is a moment when their trains stop at the same station. Note that this includes the moments when Daniel or Vlad enter or leave the subway.
Input
The first line contains five space-separated integers n, a, x, b, y (4 β€ n β€ 100, 1 β€ a, x, b, y β€ n, all numbers among a, x, b, y are distinct) β the number of stations in Roflanpolis, Daniel's start station, Daniel's finish station, Vlad's start station and Vlad's finish station, respectively.
Output
Output "YES" if there is a time moment when Vlad and Daniel are at the same station, and "NO" otherwise. You can print each letter in any case (upper or lower).
Examples
Input
5 1 4 3 2
Output
YES
Input
10 2 1 9 10
Output
NO
Note
In the first example, Daniel and Vlad start at the stations (1, 3). One minute later they are at stations (2, 2). They are at the same station at this moment. Note that Vlad leaves the subway right after that.
Consider the second example, let's look at the stations Vlad and Daniel are at. They are:
* initially (2, 9),
* after 1 minute (3, 8),
* after 2 minutes (4, 7),
* after 3 minutes (5, 6),
* after 4 minutes (6, 5),
* after 5 minutes (7, 4),
* after 6 minutes (8, 3),
* after 7 minutes (9, 2),
* after 8 minutes (10, 1),
* after 9 minutes (1, 10).
After that, they both leave the subway because they are at their finish stations, so there is no moment when they both are at the same station.
Submitted Solution:
```
n, a, x, b, y = list(map(int, input().split()))
flag= 0
if a == b:
flag = 1
for q in range(min(abs(x-a), abs(y-b))):
if a == b:
flag = 1
break
a = a+1
if a > n:
a = 1
b = b-1
if b < 1:
b = n
if a == b:
flag = 1
break
if flag == 1:
print("YES")
else:
print("NO")
``` | instruction | 0 | 5,843 | 1 | 11,686 |
No | output | 1 | 5,843 | 1 | 11,687 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The circle line of the Roflanpolis subway has n stations.
There are two parallel routes in the subway. The first one visits stations in order 1 β 2 β β¦ β n β 1 β 2 β β¦ (so the next stop after station x is equal to (x+1) if x < n and 1 otherwise). The second route visits stations in order n β (n-1) β β¦ β 1 β n β (n-1) β β¦ (so the next stop after station x is equal to (x-1) if x>1 and n otherwise). All trains depart their stations simultaneously, and it takes exactly 1 minute to arrive at the next station.
Two toads live in this city, their names are Daniel and Vlad.
Daniel is currently in a train of the first route at station a and will exit the subway when his train reaches station x.
Coincidentally, Vlad is currently in a train of the second route at station b and he will exit the subway when his train reaches station y.
Surprisingly, all numbers a,x,b,y are distinct.
Toad Ilya asks you to check if Daniel and Vlad will ever be at the same station at the same time during their journey. In other words, check if there is a moment when their trains stop at the same station. Note that this includes the moments when Daniel or Vlad enter or leave the subway.
Input
The first line contains five space-separated integers n, a, x, b, y (4 β€ n β€ 100, 1 β€ a, x, b, y β€ n, all numbers among a, x, b, y are distinct) β the number of stations in Roflanpolis, Daniel's start station, Daniel's finish station, Vlad's start station and Vlad's finish station, respectively.
Output
Output "YES" if there is a time moment when Vlad and Daniel are at the same station, and "NO" otherwise. You can print each letter in any case (upper or lower).
Examples
Input
5 1 4 3 2
Output
YES
Input
10 2 1 9 10
Output
NO
Note
In the first example, Daniel and Vlad start at the stations (1, 3). One minute later they are at stations (2, 2). They are at the same station at this moment. Note that Vlad leaves the subway right after that.
Consider the second example, let's look at the stations Vlad and Daniel are at. They are:
* initially (2, 9),
* after 1 minute (3, 8),
* after 2 minutes (4, 7),
* after 3 minutes (5, 6),
* after 4 minutes (6, 5),
* after 5 minutes (7, 4),
* after 6 minutes (8, 3),
* after 7 minutes (9, 2),
* after 8 minutes (10, 1),
* after 9 minutes (1, 10).
After that, they both leave the subway because they are at their finish stations, so there is no moment when they both are at the same station.
Submitted Solution:
```
n, a, x, b, y = (int(el) for el in input().split())
s =[i + 1 for i in range(n)]
p = a
v = b
meet = False
while p <= x and v >= y:
if p == v:
meet = True
break
p += 1
v -= 1
if meet:
print('YES')
else:
print('NO')
``` | instruction | 0 | 5,844 | 1 | 11,688 |
No | output | 1 | 5,844 | 1 | 11,689 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In this problem we assume the Earth to be a completely round ball and its surface a perfect sphere. The length of the equator and any meridian is considered to be exactly 40 000 kilometers. Thus, travelling from North Pole to South Pole or vice versa takes exactly 20 000 kilometers.
Limak, a polar bear, lives on the North Pole. Close to the New Year, he helps somebody with delivering packages all around the world. Instead of coordinates of places to visit, Limak got a description how he should move, assuming that he starts from the North Pole. The description consists of n parts. In the i-th part of his journey, Limak should move ti kilometers in the direction represented by a string diri that is one of: "North", "South", "West", "East".
Limak isnβt sure whether the description is valid. You must help him to check the following conditions:
* If at any moment of time (before any of the instructions or while performing one of them) Limak is on the North Pole, he can move only to the South.
* If at any moment of time (before any of the instructions or while performing one of them) Limak is on the South Pole, he can move only to the North.
* The journey must end on the North Pole.
Check if the above conditions are satisfied and print "YES" or "NO" on a single line.
Input
The first line of the input contains a single integer n (1 β€ n β€ 50).
The i-th of next n lines contains an integer ti and a string diri (1 β€ ti β€ 106, <image>) β the length and the direction of the i-th part of the journey, according to the description Limak got.
Output
Print "YES" if the description satisfies the three conditions, otherwise print "NO", both without the quotes.
Examples
Input
5
7500 South
10000 East
3500 North
4444 West
4000 North
Output
YES
Input
2
15000 South
4000 East
Output
NO
Input
5
20000 South
1000 North
1000000 West
9000 North
10000 North
Output
YES
Input
3
20000 South
10 East
20000 North
Output
NO
Input
2
1000 North
1000 South
Output
NO
Input
4
50 South
50 North
15000 South
15000 North
Output
YES
Note
Drawings below show how Limak's journey would look like in first two samples. In the second sample the answer is "NO" because he doesn't end on the North Pole.
<image> | instruction | 0 | 6,257 | 1 | 12,514 |
Tags: geometry, implementation
Correct Solution:
```
n = int(input())
coord = 0
for i in range(n):
ai, bi = input().split()
ai = int(ai)
if (coord == 0 and bi != 'South'):
print("NO")
break
if (coord == 20000 and bi != 'North'):
print("NO")
break
if (bi == 'North'):
coord -= ai
if (coord < 0):
print("NO")
break
elif (bi == 'South'):
coord += ai
if (coord > 20000):
print("NO")
break
else:
if (coord != 0):
print("NO")
else:
print("YES")
``` | output | 1 | 6,257 | 1 | 12,515 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In this problem we assume the Earth to be a completely round ball and its surface a perfect sphere. The length of the equator and any meridian is considered to be exactly 40 000 kilometers. Thus, travelling from North Pole to South Pole or vice versa takes exactly 20 000 kilometers.
Limak, a polar bear, lives on the North Pole. Close to the New Year, he helps somebody with delivering packages all around the world. Instead of coordinates of places to visit, Limak got a description how he should move, assuming that he starts from the North Pole. The description consists of n parts. In the i-th part of his journey, Limak should move ti kilometers in the direction represented by a string diri that is one of: "North", "South", "West", "East".
Limak isnβt sure whether the description is valid. You must help him to check the following conditions:
* If at any moment of time (before any of the instructions or while performing one of them) Limak is on the North Pole, he can move only to the South.
* If at any moment of time (before any of the instructions or while performing one of them) Limak is on the South Pole, he can move only to the North.
* The journey must end on the North Pole.
Check if the above conditions are satisfied and print "YES" or "NO" on a single line.
Input
The first line of the input contains a single integer n (1 β€ n β€ 50).
The i-th of next n lines contains an integer ti and a string diri (1 β€ ti β€ 106, <image>) β the length and the direction of the i-th part of the journey, according to the description Limak got.
Output
Print "YES" if the description satisfies the three conditions, otherwise print "NO", both without the quotes.
Examples
Input
5
7500 South
10000 East
3500 North
4444 West
4000 North
Output
YES
Input
2
15000 South
4000 East
Output
NO
Input
5
20000 South
1000 North
1000000 West
9000 North
10000 North
Output
YES
Input
3
20000 South
10 East
20000 North
Output
NO
Input
2
1000 North
1000 South
Output
NO
Input
4
50 South
50 North
15000 South
15000 North
Output
YES
Note
Drawings below show how Limak's journey would look like in first two samples. In the second sample the answer is "NO" because he doesn't end on the North Pole.
<image> | instruction | 0 | 6,258 | 1 | 12,516 |
Tags: geometry, implementation
Correct Solution:
```
from math import sin
def mp(): return map(int,input().split())
def lt(): return list(map(int,input().split()))
def pt(x): print(x)
def ip(): return input()
def it(): return int(input())
def sl(x): return [t for t in x]
def spl(x): return x.split()
def aj(liste, item): liste.append(item)
def bin(x): return "{0:b}".format(x)
def listring(l): return ' '.join([str(x) for x in l])
def ptlist(l): print(' '.join([str(x) for x in l]))
n = it()
s = 10000
r = 0
deg = 0
bl = True
for _ in range(n):
a,b = input().split()
c = int(a)
if s == 10000 and b != "South":
bl = False
elif s == -10000 and b != "North":
bl = False
else:
if b == "North":
if s + c > 10000:
bl = False
else:
s += c
if b == "South":
if s - c < -10000:
bl = False
else:
s -= c
if bl:
if s == 10000:
pt("YES")
else:
pt("NO")
else:
pt("NO")
``` | output | 1 | 6,258 | 1 | 12,517 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In this problem we assume the Earth to be a completely round ball and its surface a perfect sphere. The length of the equator and any meridian is considered to be exactly 40 000 kilometers. Thus, travelling from North Pole to South Pole or vice versa takes exactly 20 000 kilometers.
Limak, a polar bear, lives on the North Pole. Close to the New Year, he helps somebody with delivering packages all around the world. Instead of coordinates of places to visit, Limak got a description how he should move, assuming that he starts from the North Pole. The description consists of n parts. In the i-th part of his journey, Limak should move ti kilometers in the direction represented by a string diri that is one of: "North", "South", "West", "East".
Limak isnβt sure whether the description is valid. You must help him to check the following conditions:
* If at any moment of time (before any of the instructions or while performing one of them) Limak is on the North Pole, he can move only to the South.
* If at any moment of time (before any of the instructions or while performing one of them) Limak is on the South Pole, he can move only to the North.
* The journey must end on the North Pole.
Check if the above conditions are satisfied and print "YES" or "NO" on a single line.
Input
The first line of the input contains a single integer n (1 β€ n β€ 50).
The i-th of next n lines contains an integer ti and a string diri (1 β€ ti β€ 106, <image>) β the length and the direction of the i-th part of the journey, according to the description Limak got.
Output
Print "YES" if the description satisfies the three conditions, otherwise print "NO", both without the quotes.
Examples
Input
5
7500 South
10000 East
3500 North
4444 West
4000 North
Output
YES
Input
2
15000 South
4000 East
Output
NO
Input
5
20000 South
1000 North
1000000 West
9000 North
10000 North
Output
YES
Input
3
20000 South
10 East
20000 North
Output
NO
Input
2
1000 North
1000 South
Output
NO
Input
4
50 South
50 North
15000 South
15000 North
Output
YES
Note
Drawings below show how Limak's journey would look like in first two samples. In the second sample the answer is "NO" because he doesn't end on the North Pole.
<image> | instruction | 0 | 6,259 | 1 | 12,518 |
Tags: geometry, implementation
Correct Solution:
```
import math as mt
import sys,string,bisect
input=sys.stdin.readline
from collections import deque,defaultdict
L=lambda : list(map(int,input().split()))
Ls=lambda : list(input().split())
M=lambda : map(int,input().split())
I=lambda :int(input())
def dist(x,y,c,d):
return mt.sqrt((x-c)**2+(y-d)**2)
def circle(x1, y1, x2,y2, r1, r2):
distSq = (((x1 - x2)* (x1 - x2))+ ((y1 - y2)* (y1 - y2)))**(.5)
if (distSq + r2 <= r1):
return True
else:
return False
n=I()
x=0
d=0
for i in range(n):
dis,dire=input().split()
dis=int(dis)
if(dire[0]=='S'):
x+=dis
if(dire[0]=="N"):
x-=dis
if(x==0 or x==20000):
if(dire[0]=='E' or dire[0]=='W'):
print("NO")
d=1
break
if(x<0):
print("NO")
d=1
break
if(x>20000):
print("NO")
d=1
break
if(x==0 and d==0):
print("YES")
elif(d==0):
print("NO")
``` | output | 1 | 6,259 | 1 | 12,519 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In this problem we assume the Earth to be a completely round ball and its surface a perfect sphere. The length of the equator and any meridian is considered to be exactly 40 000 kilometers. Thus, travelling from North Pole to South Pole or vice versa takes exactly 20 000 kilometers.
Limak, a polar bear, lives on the North Pole. Close to the New Year, he helps somebody with delivering packages all around the world. Instead of coordinates of places to visit, Limak got a description how he should move, assuming that he starts from the North Pole. The description consists of n parts. In the i-th part of his journey, Limak should move ti kilometers in the direction represented by a string diri that is one of: "North", "South", "West", "East".
Limak isnβt sure whether the description is valid. You must help him to check the following conditions:
* If at any moment of time (before any of the instructions or while performing one of them) Limak is on the North Pole, he can move only to the South.
* If at any moment of time (before any of the instructions or while performing one of them) Limak is on the South Pole, he can move only to the North.
* The journey must end on the North Pole.
Check if the above conditions are satisfied and print "YES" or "NO" on a single line.
Input
The first line of the input contains a single integer n (1 β€ n β€ 50).
The i-th of next n lines contains an integer ti and a string diri (1 β€ ti β€ 106, <image>) β the length and the direction of the i-th part of the journey, according to the description Limak got.
Output
Print "YES" if the description satisfies the three conditions, otherwise print "NO", both without the quotes.
Examples
Input
5
7500 South
10000 East
3500 North
4444 West
4000 North
Output
YES
Input
2
15000 South
4000 East
Output
NO
Input
5
20000 South
1000 North
1000000 West
9000 North
10000 North
Output
YES
Input
3
20000 South
10 East
20000 North
Output
NO
Input
2
1000 North
1000 South
Output
NO
Input
4
50 South
50 North
15000 South
15000 North
Output
YES
Note
Drawings below show how Limak's journey would look like in first two samples. In the second sample the answer is "NO" because he doesn't end on the North Pole.
<image> | instruction | 0 | 6,260 | 1 | 12,520 |
Tags: geometry, implementation
Correct Solution:
```
n=int(input())
b=0
currentPos=0
for i in range(n):
k,dir=input().split()
k=int(k)
if currentPos==0 and dir!='South':
b=1
elif currentPos==20000 and dir!='North':
b=1
elif dir=='North' and currentPos-k<0:
b=1
elif dir=='South' and currentPos+k>20000:
b=1
else:
if dir=='North':
currentPos-=k
elif dir=='South':
currentPos+=k
#print(currentPos)
if currentPos!=0:
b=1
if b==0:
print('YES')
else:
print('NO')
``` | output | 1 | 6,260 | 1 | 12,521 |
Provide tags and a correct Python 3 solution for this coding contest problem.
In this problem we assume the Earth to be a completely round ball and its surface a perfect sphere. The length of the equator and any meridian is considered to be exactly 40 000 kilometers. Thus, travelling from North Pole to South Pole or vice versa takes exactly 20 000 kilometers.
Limak, a polar bear, lives on the North Pole. Close to the New Year, he helps somebody with delivering packages all around the world. Instead of coordinates of places to visit, Limak got a description how he should move, assuming that he starts from the North Pole. The description consists of n parts. In the i-th part of his journey, Limak should move ti kilometers in the direction represented by a string diri that is one of: "North", "South", "West", "East".
Limak isnβt sure whether the description is valid. You must help him to check the following conditions:
* If at any moment of time (before any of the instructions or while performing one of them) Limak is on the North Pole, he can move only to the South.
* If at any moment of time (before any of the instructions or while performing one of them) Limak is on the South Pole, he can move only to the North.
* The journey must end on the North Pole.
Check if the above conditions are satisfied and print "YES" or "NO" on a single line.
Input
The first line of the input contains a single integer n (1 β€ n β€ 50).
The i-th of next n lines contains an integer ti and a string diri (1 β€ ti β€ 106, <image>) β the length and the direction of the i-th part of the journey, according to the description Limak got.
Output
Print "YES" if the description satisfies the three conditions, otherwise print "NO", both without the quotes.
Examples
Input
5
7500 South
10000 East
3500 North
4444 West
4000 North
Output
YES
Input
2
15000 South
4000 East
Output
NO
Input
5
20000 South
1000 North
1000000 West
9000 North
10000 North
Output
YES
Input
3
20000 South
10 East
20000 North
Output
NO
Input
2
1000 North
1000 South
Output
NO
Input
4
50 South
50 North
15000 South
15000 North
Output
YES
Note
Drawings below show how Limak's journey would look like in first two samples. In the second sample the answer is "NO" because he doesn't end on the North Pole.
<image> | instruction | 0 | 6,261 | 1 | 12,522 |
Tags: geometry, implementation
Correct Solution:
```
from sys import *
from math import *
n=int(stdin.readline())
m=[]
for i in range(n):
a = list(stdin.readline().split())
m.append(a)
x=0
f=0
for i in range(n):
if x==0 and m[i][1]!="South":
f=1
break
if x==20000 and m[i][1]!="North":
f=1
break
if m[i][1]=="South":
x+=int(m[i][0])
if x>20000:
f=1
break
if m[i][1]=="North":
x-=int(m[i][0])
if x<0:
f=1
break
if x!=0 or f==1:
print("NO")
else:
print("YES")
``` | output | 1 | 6,261 | 1 | 12,523 |
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