message stringlengths 2 19.9k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 322 108k | cluster float64 15 15 | __index_level_0__ int64 644 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Wabbit is trying to move a box containing food for the rest of the zoo in the coordinate plane from the point (x_1,y_1) to the point (x_2,y_2).
He has a rope, which he can use to pull the box. He can only pull the box if he stands exactly 1 unit away from the box in the direction of one of two coordinate axes. He will pull the box to where he is standing before moving out of the way in the same direction by 1 unit.
<image>
For example, if the box is at the point (1,2) and Wabbit is standing at the point (2,2), he can pull the box right by 1 unit, with the box ending up at the point (2,2) and Wabbit ending at the point (3,2).
Also, Wabbit can move 1 unit to the right, left, up, or down without pulling the box. In this case, it is not necessary for him to be in exactly 1 unit away from the box. If he wants to pull the box again, he must return to a point next to the box. Also, Wabbit can't move to the point where the box is located.
Wabbit can start at any point. It takes 1 second to travel 1 unit right, left, up, or down, regardless of whether he pulls the box while moving.
Determine the minimum amount of time he needs to move the box from (x_1,y_1) to (x_2,y_2). Note that the point where Wabbit ends up at does not matter.
Input
Each test contains multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 1000): the number of test cases. The description of the test cases follows.
Each of the next t lines contains four space-separated integers x_1, y_1, x_2, y_2 (1 ≤ x_1, y_1, x_2, y_2 ≤ 10^9), describing the next test case.
Output
For each test case, print a single integer: the minimum time in seconds Wabbit needs to bring the box from (x_1,y_1) to (x_2,y_2).
Example
Input
2
1 2 2 2
1 1 2 2
Output
1
4
Note
In the first test case, the starting and the ending points of the box are (1,2) and (2,2) respectively. This is the same as the picture in the statement. Wabbit needs only 1 second to move as shown in the picture in the statement.
In the second test case, Wabbit can start at the point (2,1). He pulls the box to (2,1) while moving to (3,1). He then moves to (3,2) and then to (2,2) without pulling the box. Then, he pulls the box to (2,2) while moving to (2,3). It takes 4 seconds.
Submitted Solution:
```
q = int(input())
for i in range(q):
xa, ya, xb, yb = map(int, input().split())
if xa == xb:
print(abs(ya - yb))
continue
print(abs(ya - yb) + abs(xb - xa) + 2)
``` | instruction | 0 | 86,835 | 15 | 173,670 |
No | output | 1 | 86,835 | 15 | 173,671 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Wabbit is trying to move a box containing food for the rest of the zoo in the coordinate plane from the point (x_1,y_1) to the point (x_2,y_2).
He has a rope, which he can use to pull the box. He can only pull the box if he stands exactly 1 unit away from the box in the direction of one of two coordinate axes. He will pull the box to where he is standing before moving out of the way in the same direction by 1 unit.
<image>
For example, if the box is at the point (1,2) and Wabbit is standing at the point (2,2), he can pull the box right by 1 unit, with the box ending up at the point (2,2) and Wabbit ending at the point (3,2).
Also, Wabbit can move 1 unit to the right, left, up, or down without pulling the box. In this case, it is not necessary for him to be in exactly 1 unit away from the box. If he wants to pull the box again, he must return to a point next to the box. Also, Wabbit can't move to the point where the box is located.
Wabbit can start at any point. It takes 1 second to travel 1 unit right, left, up, or down, regardless of whether he pulls the box while moving.
Determine the minimum amount of time he needs to move the box from (x_1,y_1) to (x_2,y_2). Note that the point where Wabbit ends up at does not matter.
Input
Each test contains multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 1000): the number of test cases. The description of the test cases follows.
Each of the next t lines contains four space-separated integers x_1, y_1, x_2, y_2 (1 ≤ x_1, y_1, x_2, y_2 ≤ 10^9), describing the next test case.
Output
For each test case, print a single integer: the minimum time in seconds Wabbit needs to bring the box from (x_1,y_1) to (x_2,y_2).
Example
Input
2
1 2 2 2
1 1 2 2
Output
1
4
Note
In the first test case, the starting and the ending points of the box are (1,2) and (2,2) respectively. This is the same as the picture in the statement. Wabbit needs only 1 second to move as shown in the picture in the statement.
In the second test case, Wabbit can start at the point (2,1). He pulls the box to (2,1) while moving to (3,1). He then moves to (3,2) and then to (2,2) without pulling the box. Then, he pulls the box to (2,2) while moving to (2,3). It takes 4 seconds.
Submitted Solution:
```
t = int(input())
for _ in range(t):
a,b,c,d = map(int,input().split())
x = c-a
y = d-b
ans = x+y
if x!=0 and y!=0:
ans+=2
print (ans)
``` | instruction | 0 | 86,836 | 15 | 173,672 |
No | output | 1 | 86,836 | 15 | 173,673 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Wabbit is trying to move a box containing food for the rest of the zoo in the coordinate plane from the point (x_1,y_1) to the point (x_2,y_2).
He has a rope, which he can use to pull the box. He can only pull the box if he stands exactly 1 unit away from the box in the direction of one of two coordinate axes. He will pull the box to where he is standing before moving out of the way in the same direction by 1 unit.
<image>
For example, if the box is at the point (1,2) and Wabbit is standing at the point (2,2), he can pull the box right by 1 unit, with the box ending up at the point (2,2) and Wabbit ending at the point (3,2).
Also, Wabbit can move 1 unit to the right, left, up, or down without pulling the box. In this case, it is not necessary for him to be in exactly 1 unit away from the box. If he wants to pull the box again, he must return to a point next to the box. Also, Wabbit can't move to the point where the box is located.
Wabbit can start at any point. It takes 1 second to travel 1 unit right, left, up, or down, regardless of whether he pulls the box while moving.
Determine the minimum amount of time he needs to move the box from (x_1,y_1) to (x_2,y_2). Note that the point where Wabbit ends up at does not matter.
Input
Each test contains multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 1000): the number of test cases. The description of the test cases follows.
Each of the next t lines contains four space-separated integers x_1, y_1, x_2, y_2 (1 ≤ x_1, y_1, x_2, y_2 ≤ 10^9), describing the next test case.
Output
For each test case, print a single integer: the minimum time in seconds Wabbit needs to bring the box from (x_1,y_1) to (x_2,y_2).
Example
Input
2
1 2 2 2
1 1 2 2
Output
1
4
Note
In the first test case, the starting and the ending points of the box are (1,2) and (2,2) respectively. This is the same as the picture in the statement. Wabbit needs only 1 second to move as shown in the picture in the statement.
In the second test case, Wabbit can start at the point (2,1). He pulls the box to (2,1) while moving to (3,1). He then moves to (3,2) and then to (2,2) without pulling the box. Then, he pulls the box to (2,2) while moving to (2,3). It takes 4 seconds.
Submitted Solution:
```
a = int(input())
for x in range(a):
b,c,d,e = map(int,input().split())
print((abs(d-b)+abs(e-c))**2)
``` | instruction | 0 | 86,837 | 15 | 173,674 |
No | output | 1 | 86,837 | 15 | 173,675 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Wabbit is trying to move a box containing food for the rest of the zoo in the coordinate plane from the point (x_1,y_1) to the point (x_2,y_2).
He has a rope, which he can use to pull the box. He can only pull the box if he stands exactly 1 unit away from the box in the direction of one of two coordinate axes. He will pull the box to where he is standing before moving out of the way in the same direction by 1 unit.
<image>
For example, if the box is at the point (1,2) and Wabbit is standing at the point (2,2), he can pull the box right by 1 unit, with the box ending up at the point (2,2) and Wabbit ending at the point (3,2).
Also, Wabbit can move 1 unit to the right, left, up, or down without pulling the box. In this case, it is not necessary for him to be in exactly 1 unit away from the box. If he wants to pull the box again, he must return to a point next to the box. Also, Wabbit can't move to the point where the box is located.
Wabbit can start at any point. It takes 1 second to travel 1 unit right, left, up, or down, regardless of whether he pulls the box while moving.
Determine the minimum amount of time he needs to move the box from (x_1,y_1) to (x_2,y_2). Note that the point where Wabbit ends up at does not matter.
Input
Each test contains multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 1000): the number of test cases. The description of the test cases follows.
Each of the next t lines contains four space-separated integers x_1, y_1, x_2, y_2 (1 ≤ x_1, y_1, x_2, y_2 ≤ 10^9), describing the next test case.
Output
For each test case, print a single integer: the minimum time in seconds Wabbit needs to bring the box from (x_1,y_1) to (x_2,y_2).
Example
Input
2
1 2 2 2
1 1 2 2
Output
1
4
Note
In the first test case, the starting and the ending points of the box are (1,2) and (2,2) respectively. This is the same as the picture in the statement. Wabbit needs only 1 second to move as shown in the picture in the statement.
In the second test case, Wabbit can start at the point (2,1). He pulls the box to (2,1) while moving to (3,1). He then moves to (3,2) and then to (2,2) without pulling the box. Then, he pulls the box to (2,2) while moving to (2,3). It takes 4 seconds.
Submitted Solution:
```
from sys import stdout,stdin
from collections import defaultdict,deque
import math
t=int(stdin.readline())
for _ in range(t):
#n=int(stdin.readline())
x1,y1,x2,y2=map(int,stdin.readline().split())
#l=list(map(int,stdin.readline().split()))
if x1==x2 and y1==y2:
print(0)
elif x1==x2:
print(abs(y1-y2))
elif y1==y2:
print(abs(y1-y2))
else:
print(abs(x2-x1)+abs(y2-y1)+2)
``` | instruction | 0 | 86,838 | 15 | 173,676 |
No | output | 1 | 86,838 | 15 | 173,677 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.
Input
The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands.
The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.
Output
Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.
Examples
Input
6
URLLDR
Output
2
Input
4
DLUU
Output
0
Input
7
RLRLRLR
Output
12
Note
In the first case, the entire source code works, as well as the "RL" substring in the second and third characters.
Note that, in the third case, the substring "LR" appears three times, and is therefore counted three times to the total result. | instruction | 0 | 87,094 | 15 | 174,188 |
Tags: brute force, implementation
Correct Solution:
```
n = int(input(""))
s = str(input(""))
c = 0
for i in range(0, n - 1):
for f in range(i + 2, n + 1):
if s[i:f].count('R') == s[i:f].count('L') and s[i:f].count('U') == s[i:f].count('D'):
c = c + 1
r = 'S'
else:
r = ''
#print (i, f, s[i:f], r)
print (c)
``` | output | 1 | 87,094 | 15 | 174,189 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.
Input
The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands.
The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.
Output
Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.
Examples
Input
6
URLLDR
Output
2
Input
4
DLUU
Output
0
Input
7
RLRLRLR
Output
12
Note
In the first case, the entire source code works, as well as the "RL" substring in the second and third characters.
Note that, in the third case, the substring "LR" appears three times, and is therefore counted three times to the total result. | instruction | 0 | 87,095 | 15 | 174,190 |
Tags: brute force, implementation
Correct Solution:
```
def retorna(caminho):
l, r, u, d = 0, 0, 0, 0
for e in caminho:
if e == 'L':
l += 1
elif e == 'R':
r += 1
elif e == 'U':
u += 1
elif e == 'D':
d += 1
if l == r and u == d and u + d + l + r != 0:
return True
return False
n = int(input())
moves = input()
if n == 1:
print(0)
else:
i = 0
ans = 0
while i < n - 1:
for j in range(1, len(moves)):
if retorna(moves[i:j+1]):
ans += 1
i += 1
print(ans)
``` | output | 1 | 87,095 | 15 | 174,191 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.
Input
The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands.
The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.
Output
Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.
Examples
Input
6
URLLDR
Output
2
Input
4
DLUU
Output
0
Input
7
RLRLRLR
Output
12
Note
In the first case, the entire source code works, as well as the "RL" substring in the second and third characters.
Note that, in the third case, the substring "LR" appears three times, and is therefore counted three times to the total result. | instruction | 0 | 87,096 | 15 | 174,192 |
Tags: brute force, implementation
Correct Solution:
```
n = int(input())
moves = list(input())
mapping = {'U':1,
'D':-1,
'R':1,
'L':-1}
ans = 0
for i in range(n):
hor = 0
vert = 0
for j in range(i,n):
move = moves[j]
if move == 'U' or move == 'D':
vert += mapping[move]
else:
hor += mapping[move]
if hor == 0 and vert == 0:
ans += 1
print(ans)
``` | output | 1 | 87,096 | 15 | 174,193 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.
Input
The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands.
The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.
Output
Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.
Examples
Input
6
URLLDR
Output
2
Input
4
DLUU
Output
0
Input
7
RLRLRLR
Output
12
Note
In the first case, the entire source code works, as well as the "RL" substring in the second and third characters.
Note that, in the third case, the substring "LR" appears three times, and is therefore counted three times to the total result. | instruction | 0 | 87,097 | 15 | 174,194 |
Tags: brute force, implementation
Correct Solution:
```
tam = int(input())
string = input()
total = 0
substrings = [string[i: j] for i in range(len(string)) for j in range(i + 1, len(string) + 1)]
filtered = []
for sub in substrings:
if len(sub) % 2 == 0:
filtered.append(sub)
for palavra in filtered:
countD = 0
countU = 0
countR = 0
countL = 0
for letra in palavra:
if(letra == 'D'):
countD += 1
elif(letra == 'U'):
countU += 1
elif(letra == 'R'):
countR += 1
elif(letra == 'L'):
countL += 1
if(countD == countU and countL == countR):
total += 1
print(total)
``` | output | 1 | 87,097 | 15 | 174,195 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.
Input
The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands.
The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.
Output
Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.
Examples
Input
6
URLLDR
Output
2
Input
4
DLUU
Output
0
Input
7
RLRLRLR
Output
12
Note
In the first case, the entire source code works, as well as the "RL" substring in the second and third characters.
Note that, in the third case, the substring "LR" appears three times, and is therefore counted three times to the total result. | instruction | 0 | 87,098 | 15 | 174,196 |
Tags: brute force, implementation
Correct Solution:
```
n = int(input())
commands = input()
vertical = [0]
horizontal = [0]
for i in range(1,n+1):
vert_diff = 0
hor_diff = 0
if commands[i-1] == 'U':
vert_diff = 1
elif commands[i-1] == 'D':
vert_diff = -1
elif commands[i-1] == 'R':
hor_diff = 1
else:
hor_diff = -1
vertical.append(vertical[i-1] + vert_diff)
horizontal.append(horizontal[i-1] + hor_diff)
total = 0
for i in range(1,n+1):
for j in range(i+1, n+1):
hor_diff = horizontal[j] - horizontal[i-1]
vert_diff = vertical[j] - vertical[i-1]
if hor_diff == 0 and vert_diff == 0:
total += 1
print(total)
``` | output | 1 | 87,098 | 15 | 174,197 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.
Input
The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands.
The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.
Output
Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.
Examples
Input
6
URLLDR
Output
2
Input
4
DLUU
Output
0
Input
7
RLRLRLR
Output
12
Note
In the first case, the entire source code works, as well as the "RL" substring in the second and third characters.
Note that, in the third case, the substring "LR" appears three times, and is therefore counted three times to the total result. | instruction | 0 | 87,099 | 15 | 174,198 |
Tags: brute force, implementation
Correct Solution:
```
n, s = int(input()), input()
a = [s[i:j+1] for i in range(n) for j in range(i, n)]
print(sum(i.count('L') == i.count('R') and i.count('D') == i.count('U') for i in a))
``` | output | 1 | 87,099 | 15 | 174,199 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.
Input
The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands.
The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.
Output
Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.
Examples
Input
6
URLLDR
Output
2
Input
4
DLUU
Output
0
Input
7
RLRLRLR
Output
12
Note
In the first case, the entire source code works, as well as the "RL" substring in the second and third characters.
Note that, in the third case, the substring "LR" appears three times, and is therefore counted three times to the total result. | instruction | 0 | 87,100 | 15 | 174,200 |
Tags: brute force, implementation
Correct Solution:
```
from collections import Counter
n = int(input())
s = input()
k = 0
for i in range(n-1):
for j in range(i+2, n+1, 2):
c = Counter(s[i:j])
k += (c['U']==c['D'] and c['R']==c['L'])
print(k)
``` | output | 1 | 87,100 | 15 | 174,201 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.
Input
The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands.
The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.
Output
Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.
Examples
Input
6
URLLDR
Output
2
Input
4
DLUU
Output
0
Input
7
RLRLRLR
Output
12
Note
In the first case, the entire source code works, as well as the "RL" substring in the second and third characters.
Note that, in the third case, the substring "LR" appears three times, and is therefore counted three times to the total result. | instruction | 0 | 87,101 | 15 | 174,202 |
Tags: brute force, implementation
Correct Solution:
```
def f(i, j):
subs = s[i:j+1]
return subs.count("L") == subs.count("R") and subs.count("U") == subs.count("D")
n = int(input())
s = input()
r = 0
for i in range(n):
for j in range(i+1,n):
if f(i, j):
r += 1
print(r)
``` | output | 1 | 87,101 | 15 | 174,203 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.
Input
The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands.
The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.
Output
Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.
Examples
Input
6
URLLDR
Output
2
Input
4
DLUU
Output
0
Input
7
RLRLRLR
Output
12
Note
In the first case, the entire source code works, as well as the "RL" substring in the second and third characters.
Note that, in the third case, the substring "LR" appears three times, and is therefore counted three times to the total result.
Submitted Solution:
```
n = int(input())
string = input()
c = []
for char in string:
if char == 'U':
c.append(1)
if char == 'D':
c.append(-1)
if char == 'R':
c.append(2000)
if char == 'L':
c.append(-2000)
ans = 0
for k in range(2,len(c) + 1,2): #groups of odd lentgh can NOT sum to 0
for i in range(0,len(c) - k + 1):
#print(c[i:i + k])
t = sum(c[i:i + k])
if t == 0:
ans += 1
print(ans)
``` | instruction | 0 | 87,102 | 15 | 174,204 |
Yes | output | 1 | 87,102 | 15 | 174,205 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.
Input
The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands.
The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.
Output
Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.
Examples
Input
6
URLLDR
Output
2
Input
4
DLUU
Output
0
Input
7
RLRLRLR
Output
12
Note
In the first case, the entire source code works, as well as the "RL" substring in the second and third characters.
Note that, in the third case, the substring "LR" appears three times, and is therefore counted three times to the total result.
Submitted Solution:
```
n = int(input())
c = input()
s = 0
for i in range(n):
for j in range(i + 1, n):
x = 0
y = 0
sub = c[i : j + 1]
for k in sub:
if k == "L":
x -= 1
elif k == "R":
x += 1
elif k == "U":
y += 1
else:
y -= 1
if x == 0 and y == 0:
s += 1
print(s)
``` | instruction | 0 | 87,103 | 15 | 174,206 |
Yes | output | 1 | 87,103 | 15 | 174,207 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.
Input
The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands.
The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.
Output
Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.
Examples
Input
6
URLLDR
Output
2
Input
4
DLUU
Output
0
Input
7
RLRLRLR
Output
12
Note
In the first case, the entire source code works, as well as the "RL" substring in the second and third characters.
Note that, in the third case, the substring "LR" appears three times, and is therefore counted three times to the total result.
Submitted Solution:
```
n = int(input())
l = input()
ans = 0
for i in range(2, n + 1):
for j in range(n - i + 1):
st = l[j : j + i]
if st.count('L') == st.count('R') and st.count('U') == st.count('D'):
ans += 1
print(ans)
``` | instruction | 0 | 87,104 | 15 | 174,208 |
Yes | output | 1 | 87,104 | 15 | 174,209 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.
Input
The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands.
The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.
Output
Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.
Examples
Input
6
URLLDR
Output
2
Input
4
DLUU
Output
0
Input
7
RLRLRLR
Output
12
Note
In the first case, the entire source code works, as well as the "RL" substring in the second and third characters.
Note that, in the third case, the substring "LR" appears three times, and is therefore counted three times to the total result.
Submitted Solution:
```
import collections
import math
n = int(input())
s = input()
ans = 0
for i in range(len(s)):
for j in range(i, len(s)):
t = s[i:j+1]
if t.count('U') == t.count('D') and t.count('L') == t.count('R'):
ans += 1
print(ans)
``` | instruction | 0 | 87,105 | 15 | 174,210 |
Yes | output | 1 | 87,105 | 15 | 174,211 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.
Input
The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands.
The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.
Output
Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.
Examples
Input
6
URLLDR
Output
2
Input
4
DLUU
Output
0
Input
7
RLRLRLR
Output
12
Note
In the first case, the entire source code works, as well as the "RL" substring in the second and third characters.
Note that, in the third case, the substring "LR" appears three times, and is therefore counted three times to the total result.
Submitted Solution:
```
if __name__=='__main__':
n=int(input())
s=input()
i=0
ans=0
while(i<n):
r,l,u,d=0,0,0,0
g=i
while(g<n):
if(s[g]=='R'):
r+=1
elif(s[g]=='L'):
l+=1
elif(s[g]=='U'):
u+=1
elif(s[g]=='D'):
d+=1
if(d==u and l ==r):
print("i-> ",i," g-> ",g)
ans+=1
g+=1
i+=1
print(ans)
``` | instruction | 0 | 87,106 | 15 | 174,212 |
No | output | 1 | 87,106 | 15 | 174,213 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.
Input
The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands.
The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.
Output
Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.
Examples
Input
6
URLLDR
Output
2
Input
4
DLUU
Output
0
Input
7
RLRLRLR
Output
12
Note
In the first case, the entire source code works, as well as the "RL" substring in the second and third characters.
Note that, in the third case, the substring "LR" appears three times, and is therefore counted three times to the total result.
Submitted Solution:
```
n = int(input())
s = input()
print(2)
``` | instruction | 0 | 87,107 | 15 | 174,214 |
No | output | 1 | 87,107 | 15 | 174,215 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.
Input
The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands.
The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.
Output
Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.
Examples
Input
6
URLLDR
Output
2
Input
4
DLUU
Output
0
Input
7
RLRLRLR
Output
12
Note
In the first case, the entire source code works, as well as the "RL" substring in the second and third characters.
Note that, in the third case, the substring "LR" appears three times, and is therefore counted three times to the total result.
Submitted Solution:
```
#!/usr/bin/python3.5
n=int(input())
s=input()
i,e=0,0
while i<n:
k=i+1
while k<=n:
c,d=0,0
for j in range(i,k):
if s[j]=='U':
c+=1
elif s[j]=='D':
c-=1
elif s[j]=='R':
d+=1
else:
d-=1
if c==0 and c==0:
e+=1
k+=1
i+=1
print(e)
``` | instruction | 0 | 87,108 | 15 | 174,216 |
No | output | 1 | 87,108 | 15 | 174,217 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.
Input
The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands.
The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.
Output
Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.
Examples
Input
6
URLLDR
Output
2
Input
4
DLUU
Output
0
Input
7
RLRLRLR
Output
12
Note
In the first case, the entire source code works, as well as the "RL" substring in the second and third characters.
Note that, in the third case, the substring "LR" appears three times, and is therefore counted three times to the total result.
Submitted Solution:
```
C=lambda x,y:x.count(y)
def P(s):
return C(s,"R")-C(s,"L")+1j*(C(s,"U")-C(s,"D"))
n=int(input())
s=input()
p=P(s)
c=0
for z in range(0,n):
for l in range(z+1,n+1):
print(s[z:l],p,P(s[z:l]),p+P(s[z:l]))
c+=p+P(s[z:l])==0
print(c)
``` | instruction | 0 | 87,109 | 15 | 174,218 |
No | output | 1 | 87,109 | 15 | 174,219 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a matrix A of size x × y filled with integers. For every <image>, <image> Ai, j = y(i - 1) + j. Obviously, every integer from [1..xy] occurs exactly once in this matrix.
You have traversed some path in this matrix. Your path can be described as a sequence of visited cells a1, a2, ..., an denoting that you started in the cell containing the number a1, then moved to the cell with the number a2, and so on.
From the cell located in i-th line and j-th column (we denote this cell as (i, j)) you can move into one of the following cells:
1. (i + 1, j) — only if i < x;
2. (i, j + 1) — only if j < y;
3. (i - 1, j) — only if i > 1;
4. (i, j - 1) — only if j > 1.
Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know x and y exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer a1, then move to the cell containing a2 (in one step), then move to the cell containing a3 (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?
Input
The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers in the cells on your path.
Output
If all possible values of x and y such that 1 ≤ x, y ≤ 109 contradict with the information about your path, print NO.
Otherwise, print YES in the first line, and in the second line print the values x and y such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding 109.
Examples
Input
8
1 2 3 6 9 8 5 2
Output
YES
3 3
Input
6
1 2 1 2 5 3
Output
NO
Input
2
1 10
Output
YES
4 9
Note
The matrix and the path on it in the first test looks like this:
<image>
Also there exist multiple correct answers for both the first and the third examples. | instruction | 0 | 87,255 | 15 | 174,510 |
Tags: implementation
Correct Solution:
```
n = int(input())
m = list(map(int, input().split()))
f = 0
cur = 0
for i in range(n - 1):
if(abs(m[i] - m[i+1]) == 0):
f = 2
elif(abs(m[i] - m[i+1]) > 1):
x = abs(m[i] - m[i+1])
f = 1
if(f == 2):
print("NO")
else:
if(f == 0):
print("YES")
print(1000000000, 1000000000)
else:
i = (m[0] - 1) // x
j = (m[0] - 1) % x
for u in range(1, n):
i2 = (m[u] - 1) // x
j2 = (m[u] - 1) % x
if(i == i2 and abs(j - j2) == 1) or (j == j2 and abs(i - i2) == 1):
pass
else:
f = 2
i = i2
j = j2
if(f == 2):
print("NO")
else:
print("YES")
print(1000000000, x)
``` | output | 1 | 87,255 | 15 | 174,511 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a matrix A of size x × y filled with integers. For every <image>, <image> Ai, j = y(i - 1) + j. Obviously, every integer from [1..xy] occurs exactly once in this matrix.
You have traversed some path in this matrix. Your path can be described as a sequence of visited cells a1, a2, ..., an denoting that you started in the cell containing the number a1, then moved to the cell with the number a2, and so on.
From the cell located in i-th line and j-th column (we denote this cell as (i, j)) you can move into one of the following cells:
1. (i + 1, j) — only if i < x;
2. (i, j + 1) — only if j < y;
3. (i - 1, j) — only if i > 1;
4. (i, j - 1) — only if j > 1.
Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know x and y exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer a1, then move to the cell containing a2 (in one step), then move to the cell containing a3 (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?
Input
The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers in the cells on your path.
Output
If all possible values of x and y such that 1 ≤ x, y ≤ 109 contradict with the information about your path, print NO.
Otherwise, print YES in the first line, and in the second line print the values x and y such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding 109.
Examples
Input
8
1 2 3 6 9 8 5 2
Output
YES
3 3
Input
6
1 2 1 2 5 3
Output
NO
Input
2
1 10
Output
YES
4 9
Note
The matrix and the path on it in the first test looks like this:
<image>
Also there exist multiple correct answers for both the first and the third examples. | instruction | 0 | 87,256 | 15 | 174,512 |
Tags: implementation
Correct Solution:
```
from math import ceil
n=int(input())
arr=list(map(int,input().split()))
s=set()
for i in range(1,n):
if abs(arr[i] -arr[i-1]) ==1:
continue
s.add(abs(arr[i] -arr[i-1]))
if not s:
print("YES")
print(1000000000,max(arr))
exit()
s=list(s)
if s and s[0] ==0:
print("NO")
exit()
if len(s) >1:
print("NO")
exit()
c=s[0]
flag=0
row=0
for i in range(n-1):
if arr[i] %c ==0 and arr[i+1] ==arr[i] +1:
flag=1
break
if arr[i+1] % c==0 and arr[i] -1 ==arr[i+1]:
flag=1
break
row =max(row,ceil(arr[i] /c),ceil(arr[i+1] /c))
if flag==1:
print("NO")
else:
print("YES")
print(1000000000,c)
``` | output | 1 | 87,256 | 15 | 174,513 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a matrix A of size x × y filled with integers. For every <image>, <image> Ai, j = y(i - 1) + j. Obviously, every integer from [1..xy] occurs exactly once in this matrix.
You have traversed some path in this matrix. Your path can be described as a sequence of visited cells a1, a2, ..., an denoting that you started in the cell containing the number a1, then moved to the cell with the number a2, and so on.
From the cell located in i-th line and j-th column (we denote this cell as (i, j)) you can move into one of the following cells:
1. (i + 1, j) — only if i < x;
2. (i, j + 1) — only if j < y;
3. (i - 1, j) — only if i > 1;
4. (i, j - 1) — only if j > 1.
Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know x and y exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer a1, then move to the cell containing a2 (in one step), then move to the cell containing a3 (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?
Input
The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers in the cells on your path.
Output
If all possible values of x and y such that 1 ≤ x, y ≤ 109 contradict with the information about your path, print NO.
Otherwise, print YES in the first line, and in the second line print the values x and y such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding 109.
Examples
Input
8
1 2 3 6 9 8 5 2
Output
YES
3 3
Input
6
1 2 1 2 5 3
Output
NO
Input
2
1 10
Output
YES
4 9
Note
The matrix and the path on it in the first test looks like this:
<image>
Also there exist multiple correct answers for both the first and the third examples. | instruction | 0 | 87,257 | 15 | 174,514 |
Tags: implementation
Correct Solution:
```
import configparser
import math
import sys
input = sys.stdin.readline
def main():
n = int(input())
a = [int(x) for x in input().split(' ')]
if n == 1:
print('YES')
print(1,' ', int(1e9))
return
diff = None
for i in range(n-1):
cur_diff = abs(a[i + 1] - a[i])
if cur_diff == 0:
print('NO')
return
if cur_diff != 1:
if diff is None:
diff = cur_diff
else:
if cur_diff != diff:
print('NO')
return
if diff == None:
print('YES')
print(int(1e9), ' ', 1)
return
cols = diff
for i in range(n-1):
cur_diff = a[i + 1] - a[i]
if a[i] % cols == 0:
if cur_diff == -1 or cur_diff == -cols or cur_diff == cols:
continue
else:
print('NO')
return
elif a[i] % cols == 1:
if cur_diff == 1 or cur_diff == -cols or cur_diff == cols:
continue
else:
print('NO')
return
else:
if cur_diff == 1 or cur_diff == -1 or cur_diff == -cols or cur_diff == cols:
continue
else:
print('NO')
return
print('YES')
print(int(1e9), ' ', cols)
if __name__ == '__main__':
main()
``` | output | 1 | 87,257 | 15 | 174,515 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a matrix A of size x × y filled with integers. For every <image>, <image> Ai, j = y(i - 1) + j. Obviously, every integer from [1..xy] occurs exactly once in this matrix.
You have traversed some path in this matrix. Your path can be described as a sequence of visited cells a1, a2, ..., an denoting that you started in the cell containing the number a1, then moved to the cell with the number a2, and so on.
From the cell located in i-th line and j-th column (we denote this cell as (i, j)) you can move into one of the following cells:
1. (i + 1, j) — only if i < x;
2. (i, j + 1) — only if j < y;
3. (i - 1, j) — only if i > 1;
4. (i, j - 1) — only if j > 1.
Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know x and y exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer a1, then move to the cell containing a2 (in one step), then move to the cell containing a3 (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?
Input
The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers in the cells on your path.
Output
If all possible values of x and y such that 1 ≤ x, y ≤ 109 contradict with the information about your path, print NO.
Otherwise, print YES in the first line, and in the second line print the values x and y such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding 109.
Examples
Input
8
1 2 3 6 9 8 5 2
Output
YES
3 3
Input
6
1 2 1 2 5 3
Output
NO
Input
2
1 10
Output
YES
4 9
Note
The matrix and the path on it in the first test looks like this:
<image>
Also there exist multiple correct answers for both the first and the third examples. | instruction | 0 | 87,258 | 15 | 174,516 |
Tags: implementation
Correct Solution:
```
n = int(input())
a = list(map(int , input().split()))
if n == 1:
print('YES')
print(a[0], a[0])
exit()
vdist = set(abs(a[i] - a[i-1]) for i in range(1, len(a)))
maxn = max(a)
y = max(vdist)
if 0 in vdist:
print('NO')
exit()
if y == 1:
print('YES')
print(maxn, 1)
exit()
if len(vdist) >2 or ((len(vdist) == 2) and (1 not in vdist)):
print('NO')
exit()
for i in range(1, len(a)):
start, finish = min(a[i], a[i-1]), max(a[i], a[i-1])
if start % y == 0 and (finish - start < y) :
print('NO')
exit()
print('YES')
print(maxn//y +1, y)
``` | output | 1 | 87,258 | 15 | 174,517 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a matrix A of size x × y filled with integers. For every <image>, <image> Ai, j = y(i - 1) + j. Obviously, every integer from [1..xy] occurs exactly once in this matrix.
You have traversed some path in this matrix. Your path can be described as a sequence of visited cells a1, a2, ..., an denoting that you started in the cell containing the number a1, then moved to the cell with the number a2, and so on.
From the cell located in i-th line and j-th column (we denote this cell as (i, j)) you can move into one of the following cells:
1. (i + 1, j) — only if i < x;
2. (i, j + 1) — only if j < y;
3. (i - 1, j) — only if i > 1;
4. (i, j - 1) — only if j > 1.
Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know x and y exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer a1, then move to the cell containing a2 (in one step), then move to the cell containing a3 (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?
Input
The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers in the cells on your path.
Output
If all possible values of x and y such that 1 ≤ x, y ≤ 109 contradict with the information about your path, print NO.
Otherwise, print YES in the first line, and in the second line print the values x and y such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding 109.
Examples
Input
8
1 2 3 6 9 8 5 2
Output
YES
3 3
Input
6
1 2 1 2 5 3
Output
NO
Input
2
1 10
Output
YES
4 9
Note
The matrix and the path on it in the first test looks like this:
<image>
Also there exist multiple correct answers for both the first and the third examples. | instruction | 0 | 87,259 | 15 | 174,518 |
Tags: implementation
Correct Solution:
```
n=int(input())
l=[int(i) for i in input().split()]
'''
123
456
789
'''
if n==1:
print('YES')
print(l[0],l[0])
exit()
row=None
col=None
m=max(l)
for i in range(1,n):
if abs(l[i]-l[i-1])==0:
print('NO')
exit()
if abs(l[i]-l[i-1])!=1:
if col==None:
col=abs(l[i]-l[i-1])
else:
if col!=abs(l[i]-l[i-1]):
print('NO')
exit()
'''
1 2 3
4 5 6
7 8 9
col==3 and there is a move 3 to 4 dont neglect it
'''
if not col :
print('YES')
print(max(l),1)
exit()
for i in range(1,n):
if abs(l[i]-l[i-1])==1:
if min(l[i],l[i-1])%col==0:
print('NO')
exit()
from math import ceil
if col==None:
col=1
print('YES')
row=ceil(max(l)/col)
print(row,col)
exit()
print('YES')
row=ceil(max(l)/col)
print(row,col)
#print(row,col)
``` | output | 1 | 87,259 | 15 | 174,519 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a matrix A of size x × y filled with integers. For every <image>, <image> Ai, j = y(i - 1) + j. Obviously, every integer from [1..xy] occurs exactly once in this matrix.
You have traversed some path in this matrix. Your path can be described as a sequence of visited cells a1, a2, ..., an denoting that you started in the cell containing the number a1, then moved to the cell with the number a2, and so on.
From the cell located in i-th line and j-th column (we denote this cell as (i, j)) you can move into one of the following cells:
1. (i + 1, j) — only if i < x;
2. (i, j + 1) — only if j < y;
3. (i - 1, j) — only if i > 1;
4. (i, j - 1) — only if j > 1.
Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know x and y exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer a1, then move to the cell containing a2 (in one step), then move to the cell containing a3 (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?
Input
The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers in the cells on your path.
Output
If all possible values of x and y such that 1 ≤ x, y ≤ 109 contradict with the information about your path, print NO.
Otherwise, print YES in the first line, and in the second line print the values x and y such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding 109.
Examples
Input
8
1 2 3 6 9 8 5 2
Output
YES
3 3
Input
6
1 2 1 2 5 3
Output
NO
Input
2
1 10
Output
YES
4 9
Note
The matrix and the path on it in the first test looks like this:
<image>
Also there exist multiple correct answers for both the first and the third examples. | instruction | 0 | 87,260 | 15 | 174,520 |
Tags: implementation
Correct Solution:
```
n = int(input())
num = list(map(int, input().split()))
y = []
fl = True
for i in range(len(num) - 1):
y1 = abs(num[i] - num[i + 1])
if y1 > 1:
y.append(y1)
elif y1 == 0:
fl = False
if len(y) == 0 and fl:
print('YES')
print(10 ** 9, 10**9)
else:
if fl:
smth = y[0]
if len(set(y)) > 1:
fl = False
else:
for i in range(len(num) - 1):
a, b = num[i], num[i + 1]
if a > b:
a, b = b, a
if a == b:
fl = False
break
else:
if abs(a - b) != 1 and a % smth != b % smth:
fl = False
break
elif abs(a- b) == 1 and a % smth == 0 and b % smth == 1:
fl = False
break
if not fl:
print('NO')
elif smth <= 10 ** 9:
print('YES')
print(10**9, smth)
else:
print('NO')
``` | output | 1 | 87,260 | 15 | 174,521 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a matrix A of size x × y filled with integers. For every <image>, <image> Ai, j = y(i - 1) + j. Obviously, every integer from [1..xy] occurs exactly once in this matrix.
You have traversed some path in this matrix. Your path can be described as a sequence of visited cells a1, a2, ..., an denoting that you started in the cell containing the number a1, then moved to the cell with the number a2, and so on.
From the cell located in i-th line and j-th column (we denote this cell as (i, j)) you can move into one of the following cells:
1. (i + 1, j) — only if i < x;
2. (i, j + 1) — only if j < y;
3. (i - 1, j) — only if i > 1;
4. (i, j - 1) — only if j > 1.
Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know x and y exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer a1, then move to the cell containing a2 (in one step), then move to the cell containing a3 (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?
Input
The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers in the cells on your path.
Output
If all possible values of x and y such that 1 ≤ x, y ≤ 109 contradict with the information about your path, print NO.
Otherwise, print YES in the first line, and in the second line print the values x and y such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding 109.
Examples
Input
8
1 2 3 6 9 8 5 2
Output
YES
3 3
Input
6
1 2 1 2 5 3
Output
NO
Input
2
1 10
Output
YES
4 9
Note
The matrix and the path on it in the first test looks like this:
<image>
Also there exist multiple correct answers for both the first and the third examples. | instruction | 0 | 87,261 | 15 | 174,522 |
Tags: implementation
Correct Solution:
```
n = int(input())
a = list(map(int, input().strip().split()))
y = -1
for i in range(1, n):
_y = abs(a[i] - a[i-1])
if _y == 0:
print('NO')
exit(0)
if _y == 1:
continue
if y == -1:
y = _y
else:
if y != _y:
print('NO')
exit(0)
if y == -1:
y = max(a)
x = int(1e9)
pr, pc = -1, -1
for i in range(n):
r = (a[i] - 1) // y
c = (a[i] - 1) % y
if not (0 <= r < x and 0 <= c < y):
print('NO')
exit(0)
if pr != -1:
if r == pr and c == pc + 1:
pass
elif r == pr and c == pc - 1:
pass
elif r == pr + 1 and c == pc:
pass
elif r == pr - 1 and c == pc:
pass
else:
print('NO')
exit(0)
pr, pc = r, c
print('YES')
print(x, y)
``` | output | 1 | 87,261 | 15 | 174,523 |
Provide tags and a correct Python 3 solution for this coding contest problem.
There is a matrix A of size x × y filled with integers. For every <image>, <image> Ai, j = y(i - 1) + j. Obviously, every integer from [1..xy] occurs exactly once in this matrix.
You have traversed some path in this matrix. Your path can be described as a sequence of visited cells a1, a2, ..., an denoting that you started in the cell containing the number a1, then moved to the cell with the number a2, and so on.
From the cell located in i-th line and j-th column (we denote this cell as (i, j)) you can move into one of the following cells:
1. (i + 1, j) — only if i < x;
2. (i, j + 1) — only if j < y;
3. (i - 1, j) — only if i > 1;
4. (i, j - 1) — only if j > 1.
Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know x and y exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer a1, then move to the cell containing a2 (in one step), then move to the cell containing a3 (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?
Input
The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers in the cells on your path.
Output
If all possible values of x and y such that 1 ≤ x, y ≤ 109 contradict with the information about your path, print NO.
Otherwise, print YES in the first line, and in the second line print the values x and y such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding 109.
Examples
Input
8
1 2 3 6 9 8 5 2
Output
YES
3 3
Input
6
1 2 1 2 5 3
Output
NO
Input
2
1 10
Output
YES
4 9
Note
The matrix and the path on it in the first test looks like this:
<image>
Also there exist multiple correct answers for both the first and the third examples. | instruction | 0 | 87,262 | 15 | 174,524 |
Tags: implementation
Correct Solution:
```
import sys
n=int(sys.stdin.readline())
vals=[int(x) for x in sys.stdin.readline().split()]
import operator
diffs=list(set(
r for x,y in zip(vals[1:],vals) for r in (abs(x-y),) if r!=1
))
if len(diffs)>1 or 0 in diffs:
print("NO")
sys.exit()
if not diffs:
# all of them are 1-change
print("YES")
print(f"{10**9} {10**9}")
sys.exit()
j=diffs[0]
for i in range(1,n):
if abs(vals[i-1]-vals[i])!=1:continue
if (vals[i-1]-1)//j != (vals[i]-1)//j:
print("NO")
sys.exit()
print("YES")
print(f"{10**9} {j}")
``` | output | 1 | 87,262 | 15 | 174,525 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a matrix A of size x × y filled with integers. For every <image>, <image> Ai, j = y(i - 1) + j. Obviously, every integer from [1..xy] occurs exactly once in this matrix.
You have traversed some path in this matrix. Your path can be described as a sequence of visited cells a1, a2, ..., an denoting that you started in the cell containing the number a1, then moved to the cell with the number a2, and so on.
From the cell located in i-th line and j-th column (we denote this cell as (i, j)) you can move into one of the following cells:
1. (i + 1, j) — only if i < x;
2. (i, j + 1) — only if j < y;
3. (i - 1, j) — only if i > 1;
4. (i, j - 1) — only if j > 1.
Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know x and y exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer a1, then move to the cell containing a2 (in one step), then move to the cell containing a3 (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?
Input
The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers in the cells on your path.
Output
If all possible values of x and y such that 1 ≤ x, y ≤ 109 contradict with the information about your path, print NO.
Otherwise, print YES in the first line, and in the second line print the values x and y such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding 109.
Examples
Input
8
1 2 3 6 9 8 5 2
Output
YES
3 3
Input
6
1 2 1 2 5 3
Output
NO
Input
2
1 10
Output
YES
4 9
Note
The matrix and the path on it in the first test looks like this:
<image>
Also there exist multiple correct answers for both the first and the third examples.
Submitted Solution:
```
n = int(input())
a = [int(x) for x in input().split()]
y = []
for s, t in zip(a, a[1:]):
if abs(s - t) != 1 and s != t:
y.append(abs(s - t))
y.append(1)
y = y[0]
for s, t in zip(a, a[1:]):
if not(abs(s - t) == y or (abs(s - t) == 1 and min(s, t) % y != 0)):
break
else:
print("YES")
print("{} {}".format(10**9, y))
exit()
print("NO")
``` | instruction | 0 | 87,263 | 15 | 174,526 |
Yes | output | 1 | 87,263 | 15 | 174,527 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a matrix A of size x × y filled with integers. For every <image>, <image> Ai, j = y(i - 1) + j. Obviously, every integer from [1..xy] occurs exactly once in this matrix.
You have traversed some path in this matrix. Your path can be described as a sequence of visited cells a1, a2, ..., an denoting that you started in the cell containing the number a1, then moved to the cell with the number a2, and so on.
From the cell located in i-th line and j-th column (we denote this cell as (i, j)) you can move into one of the following cells:
1. (i + 1, j) — only if i < x;
2. (i, j + 1) — only if j < y;
3. (i - 1, j) — only if i > 1;
4. (i, j - 1) — only if j > 1.
Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know x and y exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer a1, then move to the cell containing a2 (in one step), then move to the cell containing a3 (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?
Input
The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers in the cells on your path.
Output
If all possible values of x and y such that 1 ≤ x, y ≤ 109 contradict with the information about your path, print NO.
Otherwise, print YES in the first line, and in the second line print the values x and y such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding 109.
Examples
Input
8
1 2 3 6 9 8 5 2
Output
YES
3 3
Input
6
1 2 1 2 5 3
Output
NO
Input
2
1 10
Output
YES
4 9
Note
The matrix and the path on it in the first test looks like this:
<image>
Also there exist multiple correct answers for both the first and the third examples.
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
x = 1
for i in range(n - 1):
if a[i] == a[i + 1]:
print('NO')
break
if abs(a[i] - a[i + 1]) != 1:
if x == 1:
x = abs(a[i] - a[i + 1])
elif abs(a[i] - a[i + 1]) != x:
print('NO')
break
else:
pos = []
for i in range(n):
pos.append(((a[i] - 1) % x, (a[i] - 1) // x))
for i in range(n - 1):
if abs(pos[i][0] - pos[i + 1][0]) + abs(pos[i][1] - pos[i + 1][1]) != 1:
print('NO')
break
else:
print('YES')
print(max(a), x)
``` | instruction | 0 | 87,264 | 15 | 174,528 |
Yes | output | 1 | 87,264 | 15 | 174,529 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a matrix A of size x × y filled with integers. For every <image>, <image> Ai, j = y(i - 1) + j. Obviously, every integer from [1..xy] occurs exactly once in this matrix.
You have traversed some path in this matrix. Your path can be described as a sequence of visited cells a1, a2, ..., an denoting that you started in the cell containing the number a1, then moved to the cell with the number a2, and so on.
From the cell located in i-th line and j-th column (we denote this cell as (i, j)) you can move into one of the following cells:
1. (i + 1, j) — only if i < x;
2. (i, j + 1) — only if j < y;
3. (i - 1, j) — only if i > 1;
4. (i, j - 1) — only if j > 1.
Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know x and y exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer a1, then move to the cell containing a2 (in one step), then move to the cell containing a3 (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?
Input
The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers in the cells on your path.
Output
If all possible values of x and y such that 1 ≤ x, y ≤ 109 contradict with the information about your path, print NO.
Otherwise, print YES in the first line, and in the second line print the values x and y such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding 109.
Examples
Input
8
1 2 3 6 9 8 5 2
Output
YES
3 3
Input
6
1 2 1 2 5 3
Output
NO
Input
2
1 10
Output
YES
4 9
Note
The matrix and the path on it in the first test looks like this:
<image>
Also there exist multiple correct answers for both the first and the third examples.
Submitted Solution:
```
n = int(input())
way = list(map(int, input().split()))
i, f = 0, 0
while i + 1 < n and abs(way[i] - way[i + 1]) == 1:
i += 1
if i == n - 1:
y = 10 ** 9
else:
y = abs(way[i] - way[i + 1])
i = 0
while i + 1 < n and f == 0 and y != 0:
if abs(way[i] - way[i + 1]) == 1:
if (way[i] - 1) // y != (way[i + 1] - 1) // y:
f = 1
elif y != abs(way[i] - way[i + 1]):
f = 1
i += 1
if f == 1 or y == 0:
print('NO')
else:
print('YES')
print(10 ** 9, y)
``` | instruction | 0 | 87,265 | 15 | 174,530 |
Yes | output | 1 | 87,265 | 15 | 174,531 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a matrix A of size x × y filled with integers. For every <image>, <image> Ai, j = y(i - 1) + j. Obviously, every integer from [1..xy] occurs exactly once in this matrix.
You have traversed some path in this matrix. Your path can be described as a sequence of visited cells a1, a2, ..., an denoting that you started in the cell containing the number a1, then moved to the cell with the number a2, and so on.
From the cell located in i-th line and j-th column (we denote this cell as (i, j)) you can move into one of the following cells:
1. (i + 1, j) — only if i < x;
2. (i, j + 1) — only if j < y;
3. (i - 1, j) — only if i > 1;
4. (i, j - 1) — only if j > 1.
Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know x and y exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer a1, then move to the cell containing a2 (in one step), then move to the cell containing a3 (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?
Input
The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers in the cells on your path.
Output
If all possible values of x and y such that 1 ≤ x, y ≤ 109 contradict with the information about your path, print NO.
Otherwise, print YES in the first line, and in the second line print the values x and y such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding 109.
Examples
Input
8
1 2 3 6 9 8 5 2
Output
YES
3 3
Input
6
1 2 1 2 5 3
Output
NO
Input
2
1 10
Output
YES
4 9
Note
The matrix and the path on it in the first test looks like this:
<image>
Also there exist multiple correct answers for both the first and the third examples.
Submitted Solution:
```
# Project name: Matrix Walk
#http://codeforces.com/contest/954/problem/C
n = int(input())
a = list(map(int, input().split()))
b,c=[],[]
for i in range(n-1):
if abs(a[i]-a[i+1]) == 1:
c+=[max(a[i], a[i+1])]
continue
elif (a[i]==a[i+1]):
exit(print('NO'))
else: b+=[abs(a[i]-a[i+1])]
if len(set(b))>1:
print ('NO')
elif (len(set(b))==0):
print('YES')
print(10**9,10**9)
else:
for i in c:
if (i-1)%b[0]==0:
print('NO')
exit()
print ('YES')
print (10**9, b[0])
``` | instruction | 0 | 87,266 | 15 | 174,532 |
Yes | output | 1 | 87,266 | 15 | 174,533 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a matrix A of size x × y filled with integers. For every <image>, <image> Ai, j = y(i - 1) + j. Obviously, every integer from [1..xy] occurs exactly once in this matrix.
You have traversed some path in this matrix. Your path can be described as a sequence of visited cells a1, a2, ..., an denoting that you started in the cell containing the number a1, then moved to the cell with the number a2, and so on.
From the cell located in i-th line and j-th column (we denote this cell as (i, j)) you can move into one of the following cells:
1. (i + 1, j) — only if i < x;
2. (i, j + 1) — only if j < y;
3. (i - 1, j) — only if i > 1;
4. (i, j - 1) — only if j > 1.
Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know x and y exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer a1, then move to the cell containing a2 (in one step), then move to the cell containing a3 (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?
Input
The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers in the cells on your path.
Output
If all possible values of x and y such that 1 ≤ x, y ≤ 109 contradict with the information about your path, print NO.
Otherwise, print YES in the first line, and in the second line print the values x and y such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding 109.
Examples
Input
8
1 2 3 6 9 8 5 2
Output
YES
3 3
Input
6
1 2 1 2 5 3
Output
NO
Input
2
1 10
Output
YES
4 9
Note
The matrix and the path on it in the first test looks like this:
<image>
Also there exist multiple correct answers for both the first and the third examples.
Submitted Solution:
```
from math import ceil
def count_xy(n, b):
y = -1
pr = b[0]
xy = pr
for i in range(1, n):
a = b[i]
xy = max(xy, a)
if a == pr:
continue
if abs(a-pr) == 1:
pr = a
continue
if y == -1 or y == abs(pr-a):
y = abs(pr-a)
pr = a
continue
xy = -1
break
if xy == -1:
return -1, -1
else:
pr = b[0]
for i in range(1, n):
a = b[i]
if abs(a-pr) == 1 and min(a, pr)%y == 0 and y != -1:
return -1, -1
if y == -1:
y = 1
return ceil(xy/y), y
n = int(input())
b = [int(x) for x in input().split()]
x, y = count_xy(n, b)
if x == -1:
print("NO")
else:
print("YES")
print(x, y)
``` | instruction | 0 | 87,267 | 15 | 174,534 |
No | output | 1 | 87,267 | 15 | 174,535 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a matrix A of size x × y filled with integers. For every <image>, <image> Ai, j = y(i - 1) + j. Obviously, every integer from [1..xy] occurs exactly once in this matrix.
You have traversed some path in this matrix. Your path can be described as a sequence of visited cells a1, a2, ..., an denoting that you started in the cell containing the number a1, then moved to the cell with the number a2, and so on.
From the cell located in i-th line and j-th column (we denote this cell as (i, j)) you can move into one of the following cells:
1. (i + 1, j) — only if i < x;
2. (i, j + 1) — only if j < y;
3. (i - 1, j) — only if i > 1;
4. (i, j - 1) — only if j > 1.
Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know x and y exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer a1, then move to the cell containing a2 (in one step), then move to the cell containing a3 (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?
Input
The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers in the cells on your path.
Output
If all possible values of x and y such that 1 ≤ x, y ≤ 109 contradict with the information about your path, print NO.
Otherwise, print YES in the first line, and in the second line print the values x and y such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding 109.
Examples
Input
8
1 2 3 6 9 8 5 2
Output
YES
3 3
Input
6
1 2 1 2 5 3
Output
NO
Input
2
1 10
Output
YES
4 9
Note
The matrix and the path on it in the first test looks like this:
<image>
Also there exist multiple correct answers for both the first and the third examples.
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
x=max(a)
y = -1
ans = "YES"
for i in range(n-1):
da = abs(a[i+1]-a[i])
if (da>1):
if (y==-1):
y = da
elif (y!=da):
ans = "NO"
break
if (da==0):
ans = "NO"
break
if (ans!="NO"):
for i in range(n - 1):
da = abs(a[i + 1] - a[i])
if ((da==1)&(int((a[i+1]-1)/y)!=int((a[i]-1)/y))):
ans = "NO"
break
x = int(max(a)/y)+1
if (n==1):
x = a[n-1]
y = a[n-1]
print(ans)
if (ans=="YES"):
print(x,y)
``` | instruction | 0 | 87,268 | 15 | 174,536 |
No | output | 1 | 87,268 | 15 | 174,537 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a matrix A of size x × y filled with integers. For every <image>, <image> Ai, j = y(i - 1) + j. Obviously, every integer from [1..xy] occurs exactly once in this matrix.
You have traversed some path in this matrix. Your path can be described as a sequence of visited cells a1, a2, ..., an denoting that you started in the cell containing the number a1, then moved to the cell with the number a2, and so on.
From the cell located in i-th line and j-th column (we denote this cell as (i, j)) you can move into one of the following cells:
1. (i + 1, j) — only if i < x;
2. (i, j + 1) — only if j < y;
3. (i - 1, j) — only if i > 1;
4. (i, j - 1) — only if j > 1.
Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know x and y exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer a1, then move to the cell containing a2 (in one step), then move to the cell containing a3 (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?
Input
The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers in the cells on your path.
Output
If all possible values of x and y such that 1 ≤ x, y ≤ 109 contradict with the information about your path, print NO.
Otherwise, print YES in the first line, and in the second line print the values x and y such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding 109.
Examples
Input
8
1 2 3 6 9 8 5 2
Output
YES
3 3
Input
6
1 2 1 2 5 3
Output
NO
Input
2
1 10
Output
YES
4 9
Note
The matrix and the path on it in the first test looks like this:
<image>
Also there exist multiple correct answers for both the first and the third examples.
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
yy = 1
for i in range(1, n):
if abs(a[i] - a[i - 1]) != 1:
yy = abs(a[i] - a[i - 1])
break
xmin, xmax = 0, 0
x = 0
ymin, ymax = 0, 0
y = 0
for i in range(n - 1):
if a[i + 1] - a[i] == yy:
if a[i + 1] - a[i] != yy:
print('NO')
exit(0)
x += 1
xmax = max(xmax, x)
elif a[i + 1] - a[i] == -yy:
if a[i] - a[i + 1] != yy:
print('NO')
exit(0)
x -= 1
xmin = min(xmin, x)
elif a[i + 1] - a[i] == -1:
y -= 1
ymin = min(ymin, y)
else:
y += 1
ymax = max(ymax, y)
y = ymax - ymin + 1
x = xmax - xmin + 1
if y > yy:
print('NO')
else:
print('YES')
print(x, yy)
``` | instruction | 0 | 87,269 | 15 | 174,538 |
No | output | 1 | 87,269 | 15 | 174,539 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a matrix A of size x × y filled with integers. For every <image>, <image> Ai, j = y(i - 1) + j. Obviously, every integer from [1..xy] occurs exactly once in this matrix.
You have traversed some path in this matrix. Your path can be described as a sequence of visited cells a1, a2, ..., an denoting that you started in the cell containing the number a1, then moved to the cell with the number a2, and so on.
From the cell located in i-th line and j-th column (we denote this cell as (i, j)) you can move into one of the following cells:
1. (i + 1, j) — only if i < x;
2. (i, j + 1) — only if j < y;
3. (i - 1, j) — only if i > 1;
4. (i, j - 1) — only if j > 1.
Notice that making a move requires you to go to an adjacent cell. It is not allowed to stay in the same cell. You don't know x and y exactly, but you have to find any possible values for these numbers such that you could start in the cell containing the integer a1, then move to the cell containing a2 (in one step), then move to the cell containing a3 (also in one step) and so on. Can you choose x and y so that they don't contradict with your sequence of moves?
Input
The first line contains one integer number n (1 ≤ n ≤ 200000) — the number of cells you visited on your path (if some cell is visited twice, then it's listed twice).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the integers in the cells on your path.
Output
If all possible values of x and y such that 1 ≤ x, y ≤ 109 contradict with the information about your path, print NO.
Otherwise, print YES in the first line, and in the second line print the values x and y such that your path was possible with such number of lines and columns in the matrix. Remember that they must be positive integers not exceeding 109.
Examples
Input
8
1 2 3 6 9 8 5 2
Output
YES
3 3
Input
6
1 2 1 2 5 3
Output
NO
Input
2
1 10
Output
YES
4 9
Note
The matrix and the path on it in the first test looks like this:
<image>
Also there exist multiple correct answers for both the first and the third examples.
Submitted Solution:
```
n = int(input())
walk = list(map(int, input().split()))
flag = 0
index = walk[0]
prevC = walk[0]
breakFlag = 0
raw = 1
for i in range(n - 1):
temp = walk[i + 1] - walk[i]
if temp == 1:
#print("R")
index+=1
if index>prevC:
prevC += 1
elif temp == -1:
#print("L")
continue
elif temp > 1:
raw += 1
#print("D")
if flag == 0:
prevC = abs(temp)
flag = 1
else:
if prevC == abs(temp):
continue
else:
breakFlag = 1
break
#print(raw)
elif temp < 0:
#print('U')
if flag == 0:
prevC = abs(temp)
flag = 1
else:
if prevC == abs(temp):
continue
else:
breakFlag = 1
break
elif temp == 0:
breakFlag = 1
break
if breakFlag == 1:
print("NO")
else:
print("YES")
print(raw, prevC)
``` | instruction | 0 | 87,270 | 15 | 174,540 |
No | output | 1 | 87,270 | 15 | 174,541 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The city of Fishtopia can be imagined as a grid of 4 rows and an odd number of columns. It has two main villages; the first is located at the top-left cell (1,1), people who stay there love fishing at the Tuna pond at the bottom-right cell (4, n). The second village is located at (4, 1) and its people love the Salmon pond at (1, n).
The mayor of Fishtopia wants to place k hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells.
A person can move from one cell to another if those cells are not occupied by hotels and share a side.
Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?
Input
The first line of input contain two integers, n and k (3 ≤ n ≤ 99, 0 ≤ k ≤ 2×(n-2)), n is odd, the width of the city, and the number of hotels to be placed, respectively.
Output
Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO".
If it is possible, print an extra 4 lines that describe the city, each line should have n characters, each of which is "#" if that cell has a hotel on it, or "." if not.
Examples
Input
7 2
Output
YES
.......
.#.....
.#.....
.......
Input
5 3
Output
YES
.....
.###.
.....
..... | instruction | 0 | 87,271 | 15 | 174,542 |
Tags: constructive algorithms
Correct Solution:
```
n,k=list(map(int, input().split(' ')))
def print_res(lst):
for i in lst:
print(''.join(i))
res=[['.']*n] + [['.']*n] + [['.']*n] + [['.']*n]
if k==0:
print('YES')
print_res(res)
elif k>(n-2)*2:
print('NO')
elif k==n-2:
print('YES')
res[1]=['.']+['#'*k]+['.']
# res[1][0]='.'
# res[1][-1]='.'
print_res(res)
elif k%2==0:
print("YES")
for i in range(k//2):
res[1][i+1]='#'
res[2][i+1]='#'
print_res(res)
elif k<(n-2):
print("YES")
res[1]=['.'*((n-k)//2)]+['#'*(k)]+['.'*((n-k)//2)]
print_res(res)
elif k>(n-2):
print("YES")
res[1]=['.']+['#'*(n-2)]+['.']
x=(k-n+2)//2
for i in range(x):
res[2][i+1]='#'
res[2][-i-2]='#'
# res[2]=['.']+['#'*()]+['.']+['#'*((k-n+2)//2)]+['.']
print_res(res)
else:
print('NO')
``` | output | 1 | 87,271 | 15 | 174,543 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The city of Fishtopia can be imagined as a grid of 4 rows and an odd number of columns. It has two main villages; the first is located at the top-left cell (1,1), people who stay there love fishing at the Tuna pond at the bottom-right cell (4, n). The second village is located at (4, 1) and its people love the Salmon pond at (1, n).
The mayor of Fishtopia wants to place k hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells.
A person can move from one cell to another if those cells are not occupied by hotels and share a side.
Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?
Input
The first line of input contain two integers, n and k (3 ≤ n ≤ 99, 0 ≤ k ≤ 2×(n-2)), n is odd, the width of the city, and the number of hotels to be placed, respectively.
Output
Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO".
If it is possible, print an extra 4 lines that describe the city, each line should have n characters, each of which is "#" if that cell has a hotel on it, or "." if not.
Examples
Input
7 2
Output
YES
.......
.#.....
.#.....
.......
Input
5 3
Output
YES
.....
.###.
.....
..... | instruction | 0 | 87,272 | 15 | 174,544 |
Tags: constructive algorithms
Correct Solution:
```
n, k = map(int, input().split())
def generate_hotels_even(n, k):
city = [None] * 4
for i in range(4):
city[i] = ['.'] * n
for i in range(k//2):
city[1][i + 1] = '#'
city[2][i + 1] = '#'
return '\n'.join(map(lambda x: ''.join(x), city))
def generate_hotels_odd_1(n, k):
city = [None] * 4
for i in range(4):
city[i] = ['.'] * n
city[1] = '.' * ((n - k)//2) + '#' * k + '.' * ((n - k)//2)
return '\n'.join(map(lambda x: ''.join(x), city))
def generate_hotels_odd_2(n, k):
city = [None] * 4
for i in range(4):
city[i] = ['.'] * n
city[1] = '.' + '#' * (n - 2) + '.'
leftover = k - (n - 2)
city[2] = '.' * ((n - leftover)//2) + '#' * (leftover // 2) + '.' + '#' * (leftover // 2) + '.' * ((n - leftover)//2)
return '\n'.join(map(lambda x: ''.join(x), city))
if k%2 == 0:
print("YES")
print(generate_hotels_even(n, k))
elif k <= n - 2:
print("YES")
print(generate_hotels_odd_1(n, k))
else:
print("YES")
print(generate_hotels_odd_2(n, k))
``` | output | 1 | 87,272 | 15 | 174,545 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The city of Fishtopia can be imagined as a grid of 4 rows and an odd number of columns. It has two main villages; the first is located at the top-left cell (1,1), people who stay there love fishing at the Tuna pond at the bottom-right cell (4, n). The second village is located at (4, 1) and its people love the Salmon pond at (1, n).
The mayor of Fishtopia wants to place k hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells.
A person can move from one cell to another if those cells are not occupied by hotels and share a side.
Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?
Input
The first line of input contain two integers, n and k (3 ≤ n ≤ 99, 0 ≤ k ≤ 2×(n-2)), n is odd, the width of the city, and the number of hotels to be placed, respectively.
Output
Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO".
If it is possible, print an extra 4 lines that describe the city, each line should have n characters, each of which is "#" if that cell has a hotel on it, or "." if not.
Examples
Input
7 2
Output
YES
.......
.#.....
.#.....
.......
Input
5 3
Output
YES
.....
.###.
.....
..... | instruction | 0 | 87,273 | 15 | 174,546 |
Tags: constructive algorithms
Correct Solution:
```
n, k = map(int, input().split())
print("YES")
x = [["." for i in range(n)] for _ in range(4)]
curr = 1
if(k % 2 != 0):
while k > 2 and curr != n // 2:
x[1][curr] = "#"
x[1][n - curr-1] = "#"
curr += 1
k -= 2
curr = 1
while k > 2 and curr != n // 2:
x[2][curr] = "#"
x[2][n - curr - 1] = "#"
curr += 1
k -= 2
x[1][n//2] = "#"
else:
curr = 1
while k > 0:
x[1][curr] = "#"
x[2][curr] = "#"
curr += 1
k -= 2
for i in x:
print(''.join(i))
``` | output | 1 | 87,273 | 15 | 174,547 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The city of Fishtopia can be imagined as a grid of 4 rows and an odd number of columns. It has two main villages; the first is located at the top-left cell (1,1), people who stay there love fishing at the Tuna pond at the bottom-right cell (4, n). The second village is located at (4, 1) and its people love the Salmon pond at (1, n).
The mayor of Fishtopia wants to place k hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells.
A person can move from one cell to another if those cells are not occupied by hotels and share a side.
Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?
Input
The first line of input contain two integers, n and k (3 ≤ n ≤ 99, 0 ≤ k ≤ 2×(n-2)), n is odd, the width of the city, and the number of hotels to be placed, respectively.
Output
Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO".
If it is possible, print an extra 4 lines that describe the city, each line should have n characters, each of which is "#" if that cell has a hotel on it, or "." if not.
Examples
Input
7 2
Output
YES
.......
.#.....
.#.....
.......
Input
5 3
Output
YES
.....
.###.
.....
..... | instruction | 0 | 87,274 | 15 | 174,548 |
Tags: constructive algorithms
Correct Solution:
```
n,k = [int(s) for s in input().split()]
def line(h=0):
if h < 0: h = 0
if h > n-2: h = n-2
if h%2 == 1:
ans = '.'*((n-h)//2) + '#'*h + '.'*((n-h)//2)
else:
ans = '.' + '#'*(h//2) + '.'*(n-h-2) + '#'*(h//2) + '.'
return ans
if k > 2*(n-2):
print("NO")
else:
print("YES")
print(line())
print(line(k))
print(line(k-(n-2)))
print(line())
``` | output | 1 | 87,274 | 15 | 174,549 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The city of Fishtopia can be imagined as a grid of 4 rows and an odd number of columns. It has two main villages; the first is located at the top-left cell (1,1), people who stay there love fishing at the Tuna pond at the bottom-right cell (4, n). The second village is located at (4, 1) and its people love the Salmon pond at (1, n).
The mayor of Fishtopia wants to place k hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells.
A person can move from one cell to another if those cells are not occupied by hotels and share a side.
Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?
Input
The first line of input contain two integers, n and k (3 ≤ n ≤ 99, 0 ≤ k ≤ 2×(n-2)), n is odd, the width of the city, and the number of hotels to be placed, respectively.
Output
Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO".
If it is possible, print an extra 4 lines that describe the city, each line should have n characters, each of which is "#" if that cell has a hotel on it, or "." if not.
Examples
Input
7 2
Output
YES
.......
.#.....
.#.....
.......
Input
5 3
Output
YES
.....
.###.
.....
..... | instruction | 0 | 87,275 | 15 | 174,550 |
Tags: constructive algorithms
Correct Solution:
```
n, k = list(map(int, input().split()))
if 2 * (n - 2) < k:
print('NO')
else:
print('YES')
total = 0
arr = []
for j in range(4):
arr.append(['.' for i in range(n)])
if k % 2 == 0:
for j in range(1, n - 1):
for i in range(1, 3):
if total < k:
arr[i][j] = '#'
total += 1
else:
break
if total >= k:
break
elif k == 1:
arr[1][n // 2] = '#'
elif k == 3:
arr[1][n // 2] = '#'
arr[1][(n // 2) - 1] = '#'
arr[1][(n // 2) + 1] = '#'
else:
arr[1][1] = '#'
arr[1][2] = '#'
arr[2][1] = '#'
total = 3
for j in range(3, n - 1):
for i in range(1, 3):
if total < k:
arr[i][j] = '#'
total += 1
else:
break
if total >= k:
break
s = ''
for row in arr:
s += row[0]
for c in row[1:]:
s += c
s += '\n'
print(s)
``` | output | 1 | 87,275 | 15 | 174,551 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The city of Fishtopia can be imagined as a grid of 4 rows and an odd number of columns. It has two main villages; the first is located at the top-left cell (1,1), people who stay there love fishing at the Tuna pond at the bottom-right cell (4, n). The second village is located at (4, 1) and its people love the Salmon pond at (1, n).
The mayor of Fishtopia wants to place k hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells.
A person can move from one cell to another if those cells are not occupied by hotels and share a side.
Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?
Input
The first line of input contain two integers, n and k (3 ≤ n ≤ 99, 0 ≤ k ≤ 2×(n-2)), n is odd, the width of the city, and the number of hotels to be placed, respectively.
Output
Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO".
If it is possible, print an extra 4 lines that describe the city, each line should have n characters, each of which is "#" if that cell has a hotel on it, or "." if not.
Examples
Input
7 2
Output
YES
.......
.#.....
.#.....
.......
Input
5 3
Output
YES
.....
.###.
.....
..... | instruction | 0 | 87,276 | 15 | 174,552 |
Tags: constructive algorithms
Correct Solution:
```
n, k = map(int, input().split())
print('YES')
print('.' * n)
if k % 2 == 0:
print('.' + '#' * (k // 2) + '.' * (n - (k // 2) - 2) + '.')
print('.' + '#' * (k // 2) + '.' * (n - (k // 2) - 2) + '.')
else:
it = min((n - 2), k)
off = ((n - 2) - it) // 2
k -= it
print('.' * (off + 1) + '#' * it + '.' * (off + 1))
print('.' + '#' * (k // 2) + '.' * (n - k - 2) + '#' * (k // 2) + '.')
print('.' * n)
``` | output | 1 | 87,276 | 15 | 174,553 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The city of Fishtopia can be imagined as a grid of 4 rows and an odd number of columns. It has two main villages; the first is located at the top-left cell (1,1), people who stay there love fishing at the Tuna pond at the bottom-right cell (4, n). The second village is located at (4, 1) and its people love the Salmon pond at (1, n).
The mayor of Fishtopia wants to place k hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells.
A person can move from one cell to another if those cells are not occupied by hotels and share a side.
Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?
Input
The first line of input contain two integers, n and k (3 ≤ n ≤ 99, 0 ≤ k ≤ 2×(n-2)), n is odd, the width of the city, and the number of hotels to be placed, respectively.
Output
Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO".
If it is possible, print an extra 4 lines that describe the city, each line should have n characters, each of which is "#" if that cell has a hotel on it, or "." if not.
Examples
Input
7 2
Output
YES
.......
.#.....
.#.....
.......
Input
5 3
Output
YES
.....
.###.
.....
..... | instruction | 0 | 87,277 | 15 | 174,554 |
Tags: constructive algorithms
Correct Solution:
```
s=list(map(int,input().split()))
n=s[0]
k=s[1]
l=[ [ "." for j in range(n) ] for i in range(4)]
if k%2==0:
s=k//2
for i in range(1,s+1):
l[1][i]="#"
l[2][i]="#"
else:
s=(k-1)//2
l[1][n//2]="#"
if s>((n-3)//2):
for i in range(1,s+1):
l[1][i]="#"
l[1][n-1-i]="#"
diff=s-((n-3)//2)
for i in range(1,diff+1):
l[2][i]="#"
l[2][n-1-i]="#"
else:
for i in range(1,s+1):
l[1][i]="#"
l[1][n-1-i]="#"
print("YES")
for i in range(4):
print("".join(l[i]))
``` | output | 1 | 87,277 | 15 | 174,555 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The city of Fishtopia can be imagined as a grid of 4 rows and an odd number of columns. It has two main villages; the first is located at the top-left cell (1,1), people who stay there love fishing at the Tuna pond at the bottom-right cell (4, n). The second village is located at (4, 1) and its people love the Salmon pond at (1, n).
The mayor of Fishtopia wants to place k hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells.
A person can move from one cell to another if those cells are not occupied by hotels and share a side.
Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?
Input
The first line of input contain two integers, n and k (3 ≤ n ≤ 99, 0 ≤ k ≤ 2×(n-2)), n is odd, the width of the city, and the number of hotels to be placed, respectively.
Output
Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO".
If it is possible, print an extra 4 lines that describe the city, each line should have n characters, each of which is "#" if that cell has a hotel on it, or "." if not.
Examples
Input
7 2
Output
YES
.......
.#.....
.#.....
.......
Input
5 3
Output
YES
.....
.###.
.....
..... | instruction | 0 | 87,278 | 15 | 174,556 |
Tags: constructive algorithms
Correct Solution:
```
n,k=map(int,input().split())
ch1="."*n
"""LOOOOOOOOOOOOOOOOOOOOOOOOOL this is so easy man i want some juicy ratinng"""
if(k%2==0):
print("YES")
ch2="."+"#"*(k//2)+"."*(n-(k//2)-1)
ch3="."+"#"*(k//2)+"."*(n-(k//2)-1)
print(ch1)
print(ch2)
print(ch3)
print(ch1)
else:
if(k<=n-2):
print("YES")
ch2="."*((n-k)//2)+"#"*k+"."*((n-k)//2)
ch3=ch1
print(ch1)
print(ch2)
print(ch3)
print(ch1)
else:
print("YES")
p=k-n+2
ch2="."+"#"*(n-2)+"."
ch3="."+"#"*(p-1)+"."*(n-p-2)+"#"+"."
print(ch1)
print(ch2)
print(ch3)
print(ch1)
``` | output | 1 | 87,278 | 15 | 174,557 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The city of Fishtopia can be imagined as a grid of 4 rows and an odd number of columns. It has two main villages; the first is located at the top-left cell (1,1), people who stay there love fishing at the Tuna pond at the bottom-right cell (4, n). The second village is located at (4, 1) and its people love the Salmon pond at (1, n).
The mayor of Fishtopia wants to place k hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells.
A person can move from one cell to another if those cells are not occupied by hotels and share a side.
Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?
Input
The first line of input contain two integers, n and k (3 ≤ n ≤ 99, 0 ≤ k ≤ 2×(n-2)), n is odd, the width of the city, and the number of hotels to be placed, respectively.
Output
Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO".
If it is possible, print an extra 4 lines that describe the city, each line should have n characters, each of which is "#" if that cell has a hotel on it, or "." if not.
Examples
Input
7 2
Output
YES
.......
.#.....
.#.....
.......
Input
5 3
Output
YES
.....
.###.
.....
.....
Submitted Solution:
```
n, k = (int(x) for x in input().split())
print('YES')
empty = '.' * n
if k % 2 != 0 and k < n - 2:
frst = '#' * k
frst = '.' * ((n - k) // 2) + frst + '.' * ((n - k) // 2)
scnd = empty
elif k % 2 != 0:
frst = '.' + '#' * (n - 2) + '.'
scnd = '.' + '#' * ((k - n + 2) // 2)
scnd = scnd + '.' * (n - len(scnd) * 2) + scnd[::-1]
elif k % 2 == 0:
frst = '.' + '#' * (k // 2) + '.' * n
frst = frst[:n]
scnd = frst
print(empty)
print(frst)
print(scnd)
print(empty)
``` | instruction | 0 | 87,279 | 15 | 174,558 |
Yes | output | 1 | 87,279 | 15 | 174,559 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The city of Fishtopia can be imagined as a grid of 4 rows and an odd number of columns. It has two main villages; the first is located at the top-left cell (1,1), people who stay there love fishing at the Tuna pond at the bottom-right cell (4, n). The second village is located at (4, 1) and its people love the Salmon pond at (1, n).
The mayor of Fishtopia wants to place k hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells.
A person can move from one cell to another if those cells are not occupied by hotels and share a side.
Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?
Input
The first line of input contain two integers, n and k (3 ≤ n ≤ 99, 0 ≤ k ≤ 2×(n-2)), n is odd, the width of the city, and the number of hotels to be placed, respectively.
Output
Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO".
If it is possible, print an extra 4 lines that describe the city, each line should have n characters, each of which is "#" if that cell has a hotel on it, or "." if not.
Examples
Input
7 2
Output
YES
.......
.#.....
.#.....
.......
Input
5 3
Output
YES
.....
.###.
.....
.....
Submitted Solution:
```
n, k = map(int, input().split())
if k % 2 == 0:
print('YES')
print('.' * n)
print('.' + '#' * (k // 2) + '.' * (n - 1 - k // 2))
print('.' + '#' * (k // 2) + '.' * (n - 1 - k // 2))
print('.' * n)
elif k == (n-2):
print('YES')
print('.' * n)
print('.' + '#' * k + '.' * (n - 1 - k))
print('.' * n)
print('.' * n)
elif k >= 5:
print('YES')
print('.' * n)
print('.' + '#' * (k // 2 + 1) + '.' * (n - 2 - k//2))
print('.' + '#' * (k // 2 - 1) + '.#' + '.' * (n - 2 - k//2))
print('.' * n)
elif k == 3 and n >= 5:
print('YES')
print('.' * n)
print('.' * ((n - 3) // 2) + '#.#' + '.' * ((n - 3) // 2))
print('.' * ((n - 1) // 2) + '#' + '.' * ((n - 1) // 2))
print('.' * n)
elif k == 1:
print('YES')
print('.' * n)
print('.' * n)
print('.' * ((n - 1) // 2) + '#' + '.' * ((n - 1) // 2))
print('.' * n)
else:
print('NO')
``` | instruction | 0 | 87,280 | 15 | 174,560 |
Yes | output | 1 | 87,280 | 15 | 174,561 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The city of Fishtopia can be imagined as a grid of 4 rows and an odd number of columns. It has two main villages; the first is located at the top-left cell (1,1), people who stay there love fishing at the Tuna pond at the bottom-right cell (4, n). The second village is located at (4, 1) and its people love the Salmon pond at (1, n).
The mayor of Fishtopia wants to place k hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells.
A person can move from one cell to another if those cells are not occupied by hotels and share a side.
Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?
Input
The first line of input contain two integers, n and k (3 ≤ n ≤ 99, 0 ≤ k ≤ 2×(n-2)), n is odd, the width of the city, and the number of hotels to be placed, respectively.
Output
Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO".
If it is possible, print an extra 4 lines that describe the city, each line should have n characters, each of which is "#" if that cell has a hotel on it, or "." if not.
Examples
Input
7 2
Output
YES
.......
.#.....
.#.....
.......
Input
5 3
Output
YES
.....
.###.
.....
.....
Submitted Solution:
```
n, k = map(int, input().split())
a = ['.' * n for i in 'iiii']
if k > n - 2:
a[1] = '.' + '#' * (n - 2) + '.'
k -= n - 2
a[2] = '.' + '#' * (k >> 1) + '.' * (n - 2 - k >> 1)
a[2] = a[2] + ('#' if k & 1 else '.') + a[2][::-1]
print('YES')
print('\n'.join(a))
``` | instruction | 0 | 87,281 | 15 | 174,562 |
Yes | output | 1 | 87,281 | 15 | 174,563 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The city of Fishtopia can be imagined as a grid of 4 rows and an odd number of columns. It has two main villages; the first is located at the top-left cell (1,1), people who stay there love fishing at the Tuna pond at the bottom-right cell (4, n). The second village is located at (4, 1) and its people love the Salmon pond at (1, n).
The mayor of Fishtopia wants to place k hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells.
A person can move from one cell to another if those cells are not occupied by hotels and share a side.
Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?
Input
The first line of input contain two integers, n and k (3 ≤ n ≤ 99, 0 ≤ k ≤ 2×(n-2)), n is odd, the width of the city, and the number of hotels to be placed, respectively.
Output
Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO".
If it is possible, print an extra 4 lines that describe the city, each line should have n characters, each of which is "#" if that cell has a hotel on it, or "." if not.
Examples
Input
7 2
Output
YES
.......
.#.....
.#.....
.......
Input
5 3
Output
YES
.....
.###.
.....
.....
Submitted Solution:
```
n, k = [int(x) for x in input().split()]
if k % 2 == 0:
print("YES")
print("."*n)
print("." + "#" * (k // 2) + "." * (n - 1 - k//2))
print("." + "#" * (k // 2) + "." * (n - 1 - k//2))
print("."*n)
elif n % 2 == 1:
print("YES")
print("."*n)
top = min(k, n-2)
bot = (k - top)
print("." * ((n - top) // 2) + "#" * top + "." * ((n - top) // 2))
print("." + "#" * (bot // 2) + "." * (n - 2 - bot) + "#" * (bot // 2) + ".")
print("."*n)
else:
print("NO")
``` | instruction | 0 | 87,282 | 15 | 174,564 |
Yes | output | 1 | 87,282 | 15 | 174,565 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The city of Fishtopia can be imagined as a grid of 4 rows and an odd number of columns. It has two main villages; the first is located at the top-left cell (1,1), people who stay there love fishing at the Tuna pond at the bottom-right cell (4, n). The second village is located at (4, 1) and its people love the Salmon pond at (1, n).
The mayor of Fishtopia wants to place k hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells.
A person can move from one cell to another if those cells are not occupied by hotels and share a side.
Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?
Input
The first line of input contain two integers, n and k (3 ≤ n ≤ 99, 0 ≤ k ≤ 2×(n-2)), n is odd, the width of the city, and the number of hotels to be placed, respectively.
Output
Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO".
If it is possible, print an extra 4 lines that describe the city, each line should have n characters, each of which is "#" if that cell has a hotel on it, or "." if not.
Examples
Input
7 2
Output
YES
.......
.#.....
.#.....
.......
Input
5 3
Output
YES
.....
.###.
.....
.....
Submitted Solution:
```
n, k = [int(x) for x in input().split(' ')]
if (k == 0):
print('YES')
print('.' * n)
print('.' * n)
print('.' * n)
print('.' * n)
elif (k % 2 == 0):
print('YES')
print('.' * n)
print('.' + '#' * int(k / 2) + '.' * (n - 1 - int(k / 2)))
print('.' + '#' * int(k / 2) + '.' * (n - 1 - int(k / 2)))
print('.' * n)
else:
if (k % 2 == 1 and k < 5):
print('NO')
elif (k % 2 == 1 and k == (n - 2)):
print('YES')
print('.' * n)
print('.' + '#' * (n - 2) + '.')
print('.' * n)
print('.' * n)
elif (k % 2 == 1 and (k - n + 2) >= 2):
print('YES')
print('.' * n)
print('.' + '#' * (n - 2) + '.')
print('.' + '#' * (k - n + 1) + '.' * ((n - 3) - (k - n + 1)) + '#.')
print('.' * n)
elif (k % 2 == 1 and k >= 5):
print('YES')
print('.' * n)
k1 = int((k - 5) / 2)
print('.###' + '#' * k1 + '.' * (n - 5 - k1) + '.')
print('.#.#' + '#' * k1 + '.' * (n - 5 - k1) + '.')
print('.' * n)
``` | instruction | 0 | 87,283 | 15 | 174,566 |
No | output | 1 | 87,283 | 15 | 174,567 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The city of Fishtopia can be imagined as a grid of 4 rows and an odd number of columns. It has two main villages; the first is located at the top-left cell (1,1), people who stay there love fishing at the Tuna pond at the bottom-right cell (4, n). The second village is located at (4, 1) and its people love the Salmon pond at (1, n).
The mayor of Fishtopia wants to place k hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells.
A person can move from one cell to another if those cells are not occupied by hotels and share a side.
Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?
Input
The first line of input contain two integers, n and k (3 ≤ n ≤ 99, 0 ≤ k ≤ 2×(n-2)), n is odd, the width of the city, and the number of hotels to be placed, respectively.
Output
Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO".
If it is possible, print an extra 4 lines that describe the city, each line should have n characters, each of which is "#" if that cell has a hotel on it, or "." if not.
Examples
Input
7 2
Output
YES
.......
.#.....
.#.....
.......
Input
5 3
Output
YES
.....
.###.
.....
.....
Submitted Solution:
```
n, k = map(int, input().split())
print("YES")
x = [["." for i in range(n)] for _ in range(4)]
curr = 1
while k > 2 and curr != n // 2:
x[1][curr] = "#"
x[1][n - curr-1] = "#"
curr += 1
k -= 2
curr = 1
while k > 2 and curr != n // 2:
x[2][curr] = "#"
x[2][n - curr - 1] = "#"
curr += 1
k -= 2
x[1][n//2] = "#"
if(k == 2):
x[2][n// 2]= "#"
for i in x:
print(''.join(i))
``` | instruction | 0 | 87,284 | 15 | 174,568 |
No | output | 1 | 87,284 | 15 | 174,569 |
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