text stringlengths 198 433k | conversation_id int64 0 109k |
|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across n sessions follow the identity permutation (ie. in the first game he scores 1 point, in the second game he scores 2 points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up!
Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on [1,2,3] can yield [3,1,2] but it cannot yield [3,2,1] since the 2 is in the same position.
Given a permutation of n integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed 10^{18}.
An array a is a subarray of an array b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input
Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100). Description of the test cases follows.
The first line of each test case contains integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the given permutation.
The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (1 ≤ a_{i} ≤ n) — the initial permutation.
It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation.
Example
Input
2
5
1 2 3 4 5
7
3 2 4 5 1 6 7
Output
0
2
Note
In the first permutation, it is already sorted so no exchanges are needed.
It can be shown that you need at least 2 exchanges to sort the second permutation.
[3, 2, 4, 5, 1, 6, 7]
Perform special exchange on range (1, 5)
[4, 1, 2, 3, 5, 6, 7]
Perform special exchange on range (1, 4)
[1, 2, 3, 4, 5, 6, 7]
Submitted Solution:
```
t=int(input())
for _ in range(t):
n=int(input())
ar=list(map(int,input().split()))
a,b=0,0
st=[]
j=1
for i in ar:
if i==j:
a+=1
st+=["1"]
else:
b+=1
st+=["0"]
j+=1
if b==0:
print(0)
elif a==0:
print(1)
else:
st="".join(st)
if (b*"0" in st):
print(1)
else:
print(2)
```
Yes
| 102,200 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across n sessions follow the identity permutation (ie. in the first game he scores 1 point, in the second game he scores 2 points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up!
Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on [1,2,3] can yield [3,1,2] but it cannot yield [3,2,1] since the 2 is in the same position.
Given a permutation of n integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed 10^{18}.
An array a is a subarray of an array b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input
Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100). Description of the test cases follows.
The first line of each test case contains integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the given permutation.
The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (1 ≤ a_{i} ≤ n) — the initial permutation.
It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation.
Example
Input
2
5
1 2 3 4 5
7
3 2 4 5 1 6 7
Output
0
2
Note
In the first permutation, it is already sorted so no exchanges are needed.
It can be shown that you need at least 2 exchanges to sort the second permutation.
[3, 2, 4, 5, 1, 6, 7]
Perform special exchange on range (1, 5)
[4, 1, 2, 3, 5, 6, 7]
Perform special exchange on range (1, 4)
[1, 2, 3, 4, 5, 6, 7]
Submitted Solution:
```
t = int(input())
for k in range(t):
n = int(input())
a = list(map(int, input().split()))
a += [pow(10, 20)]
c = 0
for i in range(n):
if a[i] > a[i + 1]: c += 1
print(c)
```
No
| 102,201 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across n sessions follow the identity permutation (ie. in the first game he scores 1 point, in the second game he scores 2 points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up!
Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on [1,2,3] can yield [3,1,2] but it cannot yield [3,2,1] since the 2 is in the same position.
Given a permutation of n integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed 10^{18}.
An array a is a subarray of an array b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input
Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100). Description of the test cases follows.
The first line of each test case contains integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the given permutation.
The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (1 ≤ a_{i} ≤ n) — the initial permutation.
It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation.
Example
Input
2
5
1 2 3 4 5
7
3 2 4 5 1 6 7
Output
0
2
Note
In the first permutation, it is already sorted so no exchanges are needed.
It can be shown that you need at least 2 exchanges to sort the second permutation.
[3, 2, 4, 5, 1, 6, 7]
Perform special exchange on range (1, 5)
[4, 1, 2, 3, 5, 6, 7]
Perform special exchange on range (1, 4)
[1, 2, 3, 4, 5, 6, 7]
Submitted Solution:
```
t=int(input())
for _ in range(t):
n=int(input())
ar=list(map(int,input().split()))
a,b=0,0
st=""
for i in range(n):
if ar[i]==i+1:
a+=1
st+="1"
else:
b+=1
st+="0"
if b==0:
print(0)
elif a==0:
print(1)
else:
if ("101" in st)or("010" in st):
print(2)
else:
print(1)
```
No
| 102,202 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across n sessions follow the identity permutation (ie. in the first game he scores 1 point, in the second game he scores 2 points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up!
Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on [1,2,3] can yield [3,1,2] but it cannot yield [3,2,1] since the 2 is in the same position.
Given a permutation of n integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed 10^{18}.
An array a is a subarray of an array b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input
Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100). Description of the test cases follows.
The first line of each test case contains integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the given permutation.
The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (1 ≤ a_{i} ≤ n) — the initial permutation.
It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation.
Example
Input
2
5
1 2 3 4 5
7
3 2 4 5 1 6 7
Output
0
2
Note
In the first permutation, it is already sorted so no exchanges are needed.
It can be shown that you need at least 2 exchanges to sort the second permutation.
[3, 2, 4, 5, 1, 6, 7]
Perform special exchange on range (1, 5)
[4, 1, 2, 3, 5, 6, 7]
Perform special exchange on range (1, 4)
[1, 2, 3, 4, 5, 6, 7]
Submitted Solution:
```
for _ in range(int(input())):
n=int(input())
l=list(map(int,input().split()))
ok=[]
for i in range(n):
if(l[i]==i+1):
ok.append(i)
if(len(ok)>2 and len(ok)!=n):print(2)
elif(len(ok)==0):print(1)
else:print(0)
```
No
| 102,203 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Patrick likes to play baseball, but sometimes he will spend so many hours hitting home runs that his mind starts to get foggy! Patrick is sure that his scores across n sessions follow the identity permutation (ie. in the first game he scores 1 point, in the second game he scores 2 points and so on). However, when he checks back to his record, he sees that all the numbers are mixed up!
Define a special exchange as the following: choose any subarray of the scores and permute elements such that no element of subarray gets to the same position as it was before the exchange. For example, performing a special exchange on [1,2,3] can yield [3,1,2] but it cannot yield [3,2,1] since the 2 is in the same position.
Given a permutation of n integers, please help Patrick find the minimum number of special exchanges needed to make the permutation sorted! It can be proved that under given constraints this number doesn't exceed 10^{18}.
An array a is a subarray of an array b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
Input
Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100). Description of the test cases follows.
The first line of each test case contains integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the given permutation.
The second line of each test case contains n integers a_{1},a_{2},...,a_{n} (1 ≤ a_{i} ≤ n) — the initial permutation.
It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output one integer: the minimum number of special exchanges needed to sort the permutation.
Example
Input
2
5
1 2 3 4 5
7
3 2 4 5 1 6 7
Output
0
2
Note
In the first permutation, it is already sorted so no exchanges are needed.
It can be shown that you need at least 2 exchanges to sort the second permutation.
[3, 2, 4, 5, 1, 6, 7]
Perform special exchange on range (1, 5)
[4, 1, 2, 3, 5, 6, 7]
Perform special exchange on range (1, 4)
[1, 2, 3, 4, 5, 6, 7]
Submitted Solution:
```
for _ in range(int(input())):
n = int(input())
a = [int(i) for i in input().split()]
mistakes = 0
b = []
for ind, sym in enumerate(a):
if ind + 1 != sym:
mistakes += 1
b.append('-')
else:
b.append('+')
groups = -1
for ind, pos_neg in enumerate(b):
if ind > 1:
if pos_neg != b[ind - 1]:
groups += 1
c = []
counter = 0
nexus = 1
for ind, neg in enumerate(b):
if ind > 1:
if neg == '-' and b[ind - 1] == '-':
nexus += 1
elif b[ind - 1] == '-':
c.append(nexus)
nexus = 0
elif neg == '-':
nexus = 1
else:
nexus = 0
dict = {1: 0, 2: 0}
for group in c:
if group == 1:
dict[1] += 1
else:
dict[2] += 1
if mistakes == 0:
print(0)
elif mistakes == len(a) or groups == 0 and dict[1] == 0:
print(1)
else:
print(2)
```
No
| 102,204 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Boboniu likes playing chess with his employees. As we know, no employee can beat the boss in the chess game, so Boboniu has never lost in any round.
You are a new applicant for his company. Boboniu will test you with the following chess question:
Consider a n× m grid (rows are numbered from 1 to n, and columns are numbered from 1 to m). You have a chess piece, and it stands at some cell (S_x,S_y) which is not on the border (i.e. 2 ≤ S_x ≤ n-1 and 2 ≤ S_y ≤ m-1).
From the cell (x,y), you can move your chess piece to (x,y') (1≤ y'≤ m, y' ≠ y) or (x',y) (1≤ x'≤ n, x'≠ x). In other words, the chess piece moves as a rook. From the cell, you can move to any cell on the same row or column.
Your goal is to visit each cell exactly once. Can you find a solution?
Note that cells on the path between two adjacent cells in your route are not counted as visited, and it is not required to return to the starting point.
Input
The only line of the input contains four integers n, m, S_x and S_y (3≤ n,m≤ 100, 2 ≤ S_x ≤ n-1, 2 ≤ S_y ≤ m-1) — the number of rows, the number of columns, and the initial position of your chess piece, respectively.
Output
You should print n⋅ m lines.
The i-th line should contain two integers x_i and y_i (1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m), denoting the i-th cell that you visited. You should print exactly nm pairs (x_i, y_i), they should cover all possible pairs (x_i, y_i), such that 1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m.
We can show that under these constraints there always exists a solution. If there are multiple answers, print any.
Examples
Input
3 3 2 2
Output
2 2
1 2
1 3
2 3
3 3
3 2
3 1
2 1
1 1
Input
3 4 2 2
Output
2 2
2 1
2 3
2 4
1 4
3 4
3 3
3 2
3 1
1 1
1 2
1 3
Note
Possible routes for two examples:
<image>
Tags: constructive algorithms
Correct Solution:
```
n,m,x,y = map(int, [*open(0)][0].split())
x, y = x-1, y-1
for i in range(n):
print(x+1 ,y+1)
for j in range(m-1):
y = (y + 1)%m
print(x+1, y+1)
x = (x + 1)%n
```
| 102,205 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Boboniu likes playing chess with his employees. As we know, no employee can beat the boss in the chess game, so Boboniu has never lost in any round.
You are a new applicant for his company. Boboniu will test you with the following chess question:
Consider a n× m grid (rows are numbered from 1 to n, and columns are numbered from 1 to m). You have a chess piece, and it stands at some cell (S_x,S_y) which is not on the border (i.e. 2 ≤ S_x ≤ n-1 and 2 ≤ S_y ≤ m-1).
From the cell (x,y), you can move your chess piece to (x,y') (1≤ y'≤ m, y' ≠ y) or (x',y) (1≤ x'≤ n, x'≠ x). In other words, the chess piece moves as a rook. From the cell, you can move to any cell on the same row or column.
Your goal is to visit each cell exactly once. Can you find a solution?
Note that cells on the path between two adjacent cells in your route are not counted as visited, and it is not required to return to the starting point.
Input
The only line of the input contains four integers n, m, S_x and S_y (3≤ n,m≤ 100, 2 ≤ S_x ≤ n-1, 2 ≤ S_y ≤ m-1) — the number of rows, the number of columns, and the initial position of your chess piece, respectively.
Output
You should print n⋅ m lines.
The i-th line should contain two integers x_i and y_i (1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m), denoting the i-th cell that you visited. You should print exactly nm pairs (x_i, y_i), they should cover all possible pairs (x_i, y_i), such that 1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m.
We can show that under these constraints there always exists a solution. If there are multiple answers, print any.
Examples
Input
3 3 2 2
Output
2 2
1 2
1 3
2 3
3 3
3 2
3 1
2 1
1 1
Input
3 4 2 2
Output
2 2
2 1
2 3
2 4
1 4
3 4
3 3
3 2
3 1
1 1
1 2
1 3
Note
Possible routes for two examples:
<image>
Tags: constructive algorithms
Correct Solution:
```
n,m,x,y=map(int,input().split(" "))
for i in range(n):
for j in range(m):
print(x,y)
if y==m:
y=1
else:
y+=1
if y==1:
y=m
else:
y-=1
if x==n:
x=1
else:
x+=1
```
| 102,206 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Boboniu likes playing chess with his employees. As we know, no employee can beat the boss in the chess game, so Boboniu has never lost in any round.
You are a new applicant for his company. Boboniu will test you with the following chess question:
Consider a n× m grid (rows are numbered from 1 to n, and columns are numbered from 1 to m). You have a chess piece, and it stands at some cell (S_x,S_y) which is not on the border (i.e. 2 ≤ S_x ≤ n-1 and 2 ≤ S_y ≤ m-1).
From the cell (x,y), you can move your chess piece to (x,y') (1≤ y'≤ m, y' ≠ y) or (x',y) (1≤ x'≤ n, x'≠ x). In other words, the chess piece moves as a rook. From the cell, you can move to any cell on the same row or column.
Your goal is to visit each cell exactly once. Can you find a solution?
Note that cells on the path between two adjacent cells in your route are not counted as visited, and it is not required to return to the starting point.
Input
The only line of the input contains four integers n, m, S_x and S_y (3≤ n,m≤ 100, 2 ≤ S_x ≤ n-1, 2 ≤ S_y ≤ m-1) — the number of rows, the number of columns, and the initial position of your chess piece, respectively.
Output
You should print n⋅ m lines.
The i-th line should contain two integers x_i and y_i (1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m), denoting the i-th cell that you visited. You should print exactly nm pairs (x_i, y_i), they should cover all possible pairs (x_i, y_i), such that 1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m.
We can show that under these constraints there always exists a solution. If there are multiple answers, print any.
Examples
Input
3 3 2 2
Output
2 2
1 2
1 3
2 3
3 3
3 2
3 1
2 1
1 1
Input
3 4 2 2
Output
2 2
2 1
2 3
2 4
1 4
3 4
3 3
3 2
3 1
1 1
1 2
1 3
Note
Possible routes for two examples:
<image>
Tags: constructive algorithms
Correct Solution:
```
a , b , x, y = map(int,input().split())
ans1 = x
ans2 = y
for x in range(a):
if ans1>a:
ans1 = ans1 - a
for x in range(b):
if ans2>b:
ans2 = ans2 - b
print(f"{ans1} {ans2}")
ans2 = ans2 + 1
ans1 = ans1 + 1
ans2 = ans2 - 1
```
| 102,207 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Boboniu likes playing chess with his employees. As we know, no employee can beat the boss in the chess game, so Boboniu has never lost in any round.
You are a new applicant for his company. Boboniu will test you with the following chess question:
Consider a n× m grid (rows are numbered from 1 to n, and columns are numbered from 1 to m). You have a chess piece, and it stands at some cell (S_x,S_y) which is not on the border (i.e. 2 ≤ S_x ≤ n-1 and 2 ≤ S_y ≤ m-1).
From the cell (x,y), you can move your chess piece to (x,y') (1≤ y'≤ m, y' ≠ y) or (x',y) (1≤ x'≤ n, x'≠ x). In other words, the chess piece moves as a rook. From the cell, you can move to any cell on the same row or column.
Your goal is to visit each cell exactly once. Can you find a solution?
Note that cells on the path between two adjacent cells in your route are not counted as visited, and it is not required to return to the starting point.
Input
The only line of the input contains four integers n, m, S_x and S_y (3≤ n,m≤ 100, 2 ≤ S_x ≤ n-1, 2 ≤ S_y ≤ m-1) — the number of rows, the number of columns, and the initial position of your chess piece, respectively.
Output
You should print n⋅ m lines.
The i-th line should contain two integers x_i and y_i (1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m), denoting the i-th cell that you visited. You should print exactly nm pairs (x_i, y_i), they should cover all possible pairs (x_i, y_i), such that 1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m.
We can show that under these constraints there always exists a solution. If there are multiple answers, print any.
Examples
Input
3 3 2 2
Output
2 2
1 2
1 3
2 3
3 3
3 2
3 1
2 1
1 1
Input
3 4 2 2
Output
2 2
2 1
2 3
2 4
1 4
3 4
3 3
3 2
3 1
1 1
1 2
1 3
Note
Possible routes for two examples:
<image>
Tags: constructive algorithms
Correct Solution:
```
n,m,r,c=map(int,input().split())
r-=1
c-=1
init=[r,c]
# print starting row
print(r+1,c+1)
for j in range(c+1,m):
print(r+1,j+1)
for j in range(c-1,-1,-1):
print(r+1,j+1)
lr=True
r+=1
while r < n:
if lr:
for j in range(m):
print(r+1,j+1)
else:
for j in range(m-1,-1,-1):
print(r+1,j+1)
lr=not lr
r+=1
r=init[0]-1
while r>=0:
if lr:
for j in range(m):
print(r+1,j+1)
else:
for j in range(m-1,-1,-1):
print(r+1,j+1)
lr=not lr
r-=1
```
| 102,208 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Boboniu likes playing chess with his employees. As we know, no employee can beat the boss in the chess game, so Boboniu has never lost in any round.
You are a new applicant for his company. Boboniu will test you with the following chess question:
Consider a n× m grid (rows are numbered from 1 to n, and columns are numbered from 1 to m). You have a chess piece, and it stands at some cell (S_x,S_y) which is not on the border (i.e. 2 ≤ S_x ≤ n-1 and 2 ≤ S_y ≤ m-1).
From the cell (x,y), you can move your chess piece to (x,y') (1≤ y'≤ m, y' ≠ y) or (x',y) (1≤ x'≤ n, x'≠ x). In other words, the chess piece moves as a rook. From the cell, you can move to any cell on the same row or column.
Your goal is to visit each cell exactly once. Can you find a solution?
Note that cells on the path between two adjacent cells in your route are not counted as visited, and it is not required to return to the starting point.
Input
The only line of the input contains four integers n, m, S_x and S_y (3≤ n,m≤ 100, 2 ≤ S_x ≤ n-1, 2 ≤ S_y ≤ m-1) — the number of rows, the number of columns, and the initial position of your chess piece, respectively.
Output
You should print n⋅ m lines.
The i-th line should contain two integers x_i and y_i (1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m), denoting the i-th cell that you visited. You should print exactly nm pairs (x_i, y_i), they should cover all possible pairs (x_i, y_i), such that 1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m.
We can show that under these constraints there always exists a solution. If there are multiple answers, print any.
Examples
Input
3 3 2 2
Output
2 2
1 2
1 3
2 3
3 3
3 2
3 1
2 1
1 1
Input
3 4 2 2
Output
2 2
2 1
2 3
2 4
1 4
3 4
3 3
3 2
3 1
1 1
1 2
1 3
Note
Possible routes for two examples:
<image>
Tags: constructive algorithms
Correct Solution:
```
nums=input().split(' ')
nums=[int(x) for x in nums]
n=nums[0]
m=nums[1]
sx=nums[2]
sy=nums[3]
#do the local column
print(str(sx)+" "+str(sy))
for i in range(1,n+1):
if i!=sx:
print(str(i)+" "+str(sy))
for i in range(1,m+1):
if i<sy:
if i%2==1:
for j in range(n,0,-1):
print(str(j)+" "+str(i))
else:
for j in range(1,n+1):
print(str(j)+" "+str(i))
elif i>sy:
if (i-1)%2==1:
for j in range(n,0,-1):
print(str(j)+" "+str(i))
else:
for j in range(1,n+1):
print(str(j)+" "+str(i))
```
| 102,209 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Boboniu likes playing chess with his employees. As we know, no employee can beat the boss in the chess game, so Boboniu has never lost in any round.
You are a new applicant for his company. Boboniu will test you with the following chess question:
Consider a n× m grid (rows are numbered from 1 to n, and columns are numbered from 1 to m). You have a chess piece, and it stands at some cell (S_x,S_y) which is not on the border (i.e. 2 ≤ S_x ≤ n-1 and 2 ≤ S_y ≤ m-1).
From the cell (x,y), you can move your chess piece to (x,y') (1≤ y'≤ m, y' ≠ y) or (x',y) (1≤ x'≤ n, x'≠ x). In other words, the chess piece moves as a rook. From the cell, you can move to any cell on the same row or column.
Your goal is to visit each cell exactly once. Can you find a solution?
Note that cells on the path between two adjacent cells in your route are not counted as visited, and it is not required to return to the starting point.
Input
The only line of the input contains four integers n, m, S_x and S_y (3≤ n,m≤ 100, 2 ≤ S_x ≤ n-1, 2 ≤ S_y ≤ m-1) — the number of rows, the number of columns, and the initial position of your chess piece, respectively.
Output
You should print n⋅ m lines.
The i-th line should contain two integers x_i and y_i (1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m), denoting the i-th cell that you visited. You should print exactly nm pairs (x_i, y_i), they should cover all possible pairs (x_i, y_i), such that 1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m.
We can show that under these constraints there always exists a solution. If there are multiple answers, print any.
Examples
Input
3 3 2 2
Output
2 2
1 2
1 3
2 3
3 3
3 2
3 1
2 1
1 1
Input
3 4 2 2
Output
2 2
2 1
2 3
2 4
1 4
3 4
3 3
3 2
3 1
1 1
1 2
1 3
Note
Possible routes for two examples:
<image>
Tags: constructive algorithms
Correct Solution:
```
n,m,sx,sy = map(int, input().split())
for y in range(sy,m+1):
print(sx,y)
for y in range(sy-1,0,-1):
print(sx,y)
to_back = True
for x in range(1,n+1):
if x == sx: continue
if to_back:
for y in range(1,m+1):
print(x,y)
else:
for y in range(m,0,-1):
print(x,y)
to_back = not to_back
```
| 102,210 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Boboniu likes playing chess with his employees. As we know, no employee can beat the boss in the chess game, so Boboniu has never lost in any round.
You are a new applicant for his company. Boboniu will test you with the following chess question:
Consider a n× m grid (rows are numbered from 1 to n, and columns are numbered from 1 to m). You have a chess piece, and it stands at some cell (S_x,S_y) which is not on the border (i.e. 2 ≤ S_x ≤ n-1 and 2 ≤ S_y ≤ m-1).
From the cell (x,y), you can move your chess piece to (x,y') (1≤ y'≤ m, y' ≠ y) or (x',y) (1≤ x'≤ n, x'≠ x). In other words, the chess piece moves as a rook. From the cell, you can move to any cell on the same row or column.
Your goal is to visit each cell exactly once. Can you find a solution?
Note that cells on the path between two adjacent cells in your route are not counted as visited, and it is not required to return to the starting point.
Input
The only line of the input contains four integers n, m, S_x and S_y (3≤ n,m≤ 100, 2 ≤ S_x ≤ n-1, 2 ≤ S_y ≤ m-1) — the number of rows, the number of columns, and the initial position of your chess piece, respectively.
Output
You should print n⋅ m lines.
The i-th line should contain two integers x_i and y_i (1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m), denoting the i-th cell that you visited. You should print exactly nm pairs (x_i, y_i), they should cover all possible pairs (x_i, y_i), such that 1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m.
We can show that under these constraints there always exists a solution. If there are multiple answers, print any.
Examples
Input
3 3 2 2
Output
2 2
1 2
1 3
2 3
3 3
3 2
3 1
2 1
1 1
Input
3 4 2 2
Output
2 2
2 1
2 3
2 4
1 4
3 4
3 3
3 2
3 1
1 1
1 2
1 3
Note
Possible routes for two examples:
<image>
Tags: constructive algorithms
Correct Solution:
```
from sys import stdin,stdout
import math,queue,heapq
fastinput=stdin.readline
fastout=stdout.write
t=1
while t:
t-=1
n,m,sx,sy=map(int,fastinput().split())
visited=[]
visited.append([sx,sy])
visited.append([1,sy])
visited.append([1,1])
for i in visited:
print(*i)
x=1
j=1
for i in range(1,n+1):
while j>=1 and j<=m:
if [i,j] in visited:
j+=x
continue
else:
print(i,j)
j+=x
if j==0:
j=1
if j==(m+1):
j=m
if j==m:
x=-1
else:
x=1
```
| 102,211 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Boboniu likes playing chess with his employees. As we know, no employee can beat the boss in the chess game, so Boboniu has never lost in any round.
You are a new applicant for his company. Boboniu will test you with the following chess question:
Consider a n× m grid (rows are numbered from 1 to n, and columns are numbered from 1 to m). You have a chess piece, and it stands at some cell (S_x,S_y) which is not on the border (i.e. 2 ≤ S_x ≤ n-1 and 2 ≤ S_y ≤ m-1).
From the cell (x,y), you can move your chess piece to (x,y') (1≤ y'≤ m, y' ≠ y) or (x',y) (1≤ x'≤ n, x'≠ x). In other words, the chess piece moves as a rook. From the cell, you can move to any cell on the same row or column.
Your goal is to visit each cell exactly once. Can you find a solution?
Note that cells on the path between two adjacent cells in your route are not counted as visited, and it is not required to return to the starting point.
Input
The only line of the input contains four integers n, m, S_x and S_y (3≤ n,m≤ 100, 2 ≤ S_x ≤ n-1, 2 ≤ S_y ≤ m-1) — the number of rows, the number of columns, and the initial position of your chess piece, respectively.
Output
You should print n⋅ m lines.
The i-th line should contain two integers x_i and y_i (1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m), denoting the i-th cell that you visited. You should print exactly nm pairs (x_i, y_i), they should cover all possible pairs (x_i, y_i), such that 1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m.
We can show that under these constraints there always exists a solution. If there are multiple answers, print any.
Examples
Input
3 3 2 2
Output
2 2
1 2
1 3
2 3
3 3
3 2
3 1
2 1
1 1
Input
3 4 2 2
Output
2 2
2 1
2 3
2 4
1 4
3 4
3 3
3 2
3 1
1 1
1 2
1 3
Note
Possible routes for two examples:
<image>
Tags: constructive algorithms
Correct Solution:
```
import sys
input = sys.stdin.readline
I = lambda : list(map(int,input().split()))
x,y,a,b,=I()
a-=1
b-=1
print(a+1,b+1)
for i in range(y):
if i!=b:
print(a+1,i+1)
r=1
flag=0
while r<=x:
if flag==0:
if r%2:
for i in range(y,0,-1):
print(r,i)
else:
for i in range(y):
print(r,i+1)
r+=1
else:
if r%2==0:
for i in range(y,0,-1):
print(r,i)
else:
for i in range(y):
print(r,i+1)
r+=1
if r==a+1:
r+=1
flag=1
```
| 102,212 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Boboniu likes playing chess with his employees. As we know, no employee can beat the boss in the chess game, so Boboniu has never lost in any round.
You are a new applicant for his company. Boboniu will test you with the following chess question:
Consider a n× m grid (rows are numbered from 1 to n, and columns are numbered from 1 to m). You have a chess piece, and it stands at some cell (S_x,S_y) which is not on the border (i.e. 2 ≤ S_x ≤ n-1 and 2 ≤ S_y ≤ m-1).
From the cell (x,y), you can move your chess piece to (x,y') (1≤ y'≤ m, y' ≠ y) or (x',y) (1≤ x'≤ n, x'≠ x). In other words, the chess piece moves as a rook. From the cell, you can move to any cell on the same row or column.
Your goal is to visit each cell exactly once. Can you find a solution?
Note that cells on the path between two adjacent cells in your route are not counted as visited, and it is not required to return to the starting point.
Input
The only line of the input contains four integers n, m, S_x and S_y (3≤ n,m≤ 100, 2 ≤ S_x ≤ n-1, 2 ≤ S_y ≤ m-1) — the number of rows, the number of columns, and the initial position of your chess piece, respectively.
Output
You should print n⋅ m lines.
The i-th line should contain two integers x_i and y_i (1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m), denoting the i-th cell that you visited. You should print exactly nm pairs (x_i, y_i), they should cover all possible pairs (x_i, y_i), such that 1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m.
We can show that under these constraints there always exists a solution. If there are multiple answers, print any.
Examples
Input
3 3 2 2
Output
2 2
1 2
1 3
2 3
3 3
3 2
3 1
2 1
1 1
Input
3 4 2 2
Output
2 2
2 1
2 3
2 4
1 4
3 4
3 3
3 2
3 1
1 1
1 2
1 3
Note
Possible routes for two examples:
<image>
Submitted Solution:
```
import math as mt
def tran(n,m,sx,sy):
p=0
an=[]
for i in range(sx,n+1):
an.append([i,sy])
for i in range(sx-1,0,-1):
an.append([i,sy])
sx=i
while p==0:
if sx==n:
sy+=1
if sy<=m:
for i in range(sx,0,-1):
an.append([i,sy])
sx=i
else:
sy=1
for i in range(sx,0,-1):
an.append([i,sy])
sx=i
else:
sy+=1
if sy<=m:
for i in range(1,n+1):
an.append([i,sy])
sx=i
else:
sy=1
for i in range(1,n+1):
an.append([i,sy])
sx=i
if len(an)>=n*m:
break
return an
if __name__ == '__main__':
nk = list(map(int, input().rstrip().split()))
r = tran(nk[0],nk[1],nk[2],nk[3])
for i in r:
print(*i)
```
Yes
| 102,213 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Boboniu likes playing chess with his employees. As we know, no employee can beat the boss in the chess game, so Boboniu has never lost in any round.
You are a new applicant for his company. Boboniu will test you with the following chess question:
Consider a n× m grid (rows are numbered from 1 to n, and columns are numbered from 1 to m). You have a chess piece, and it stands at some cell (S_x,S_y) which is not on the border (i.e. 2 ≤ S_x ≤ n-1 and 2 ≤ S_y ≤ m-1).
From the cell (x,y), you can move your chess piece to (x,y') (1≤ y'≤ m, y' ≠ y) or (x',y) (1≤ x'≤ n, x'≠ x). In other words, the chess piece moves as a rook. From the cell, you can move to any cell on the same row or column.
Your goal is to visit each cell exactly once. Can you find a solution?
Note that cells on the path between two adjacent cells in your route are not counted as visited, and it is not required to return to the starting point.
Input
The only line of the input contains four integers n, m, S_x and S_y (3≤ n,m≤ 100, 2 ≤ S_x ≤ n-1, 2 ≤ S_y ≤ m-1) — the number of rows, the number of columns, and the initial position of your chess piece, respectively.
Output
You should print n⋅ m lines.
The i-th line should contain two integers x_i and y_i (1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m), denoting the i-th cell that you visited. You should print exactly nm pairs (x_i, y_i), they should cover all possible pairs (x_i, y_i), such that 1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m.
We can show that under these constraints there always exists a solution. If there are multiple answers, print any.
Examples
Input
3 3 2 2
Output
2 2
1 2
1 3
2 3
3 3
3 2
3 1
2 1
1 1
Input
3 4 2 2
Output
2 2
2 1
2 3
2 4
1 4
3 4
3 3
3 2
3 1
1 1
1 2
1 3
Note
Possible routes for two examples:
<image>
Submitted Solution:
```
n,m,x,y=map(int,input().split())
c=n*m
for i in range(x,n+1):
for j in range(y,m+1):
print(i,j)
for j in range(y-1,0,-1):
print(i,j)
y=j
for i in range(x-1,0,-1):
for j in range(y,m+1):
print(i,j)
for j in range(y-1,0,-1):
print(i,j)
y=j
```
Yes
| 102,214 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Boboniu likes playing chess with his employees. As we know, no employee can beat the boss in the chess game, so Boboniu has never lost in any round.
You are a new applicant for his company. Boboniu will test you with the following chess question:
Consider a n× m grid (rows are numbered from 1 to n, and columns are numbered from 1 to m). You have a chess piece, and it stands at some cell (S_x,S_y) which is not on the border (i.e. 2 ≤ S_x ≤ n-1 and 2 ≤ S_y ≤ m-1).
From the cell (x,y), you can move your chess piece to (x,y') (1≤ y'≤ m, y' ≠ y) or (x',y) (1≤ x'≤ n, x'≠ x). In other words, the chess piece moves as a rook. From the cell, you can move to any cell on the same row or column.
Your goal is to visit each cell exactly once. Can you find a solution?
Note that cells on the path between two adjacent cells in your route are not counted as visited, and it is not required to return to the starting point.
Input
The only line of the input contains four integers n, m, S_x and S_y (3≤ n,m≤ 100, 2 ≤ S_x ≤ n-1, 2 ≤ S_y ≤ m-1) — the number of rows, the number of columns, and the initial position of your chess piece, respectively.
Output
You should print n⋅ m lines.
The i-th line should contain two integers x_i and y_i (1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m), denoting the i-th cell that you visited. You should print exactly nm pairs (x_i, y_i), they should cover all possible pairs (x_i, y_i), such that 1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m.
We can show that under these constraints there always exists a solution. If there are multiple answers, print any.
Examples
Input
3 3 2 2
Output
2 2
1 2
1 3
2 3
3 3
3 2
3 1
2 1
1 1
Input
3 4 2 2
Output
2 2
2 1
2 3
2 4
1 4
3 4
3 3
3 2
3 1
1 1
1 2
1 3
Note
Possible routes for two examples:
<image>
Submitted Solution:
```
def move(n, m, x, y):
end = False
print(x, y)
for j in range(1, m + 1):
if j != y:
print(x, j)
for i in range(1, n + 1):
if i != x:
if end:
for j in range(1, m + 1):
print(i, j)
else:
for j in range(m, 0, -1):
print(i, j)
end= not end
n, m, x, y = map(int, input().split())
move(n, m, x, y)
```
Yes
| 102,215 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Boboniu likes playing chess with his employees. As we know, no employee can beat the boss in the chess game, so Boboniu has never lost in any round.
You are a new applicant for his company. Boboniu will test you with the following chess question:
Consider a n× m grid (rows are numbered from 1 to n, and columns are numbered from 1 to m). You have a chess piece, and it stands at some cell (S_x,S_y) which is not on the border (i.e. 2 ≤ S_x ≤ n-1 and 2 ≤ S_y ≤ m-1).
From the cell (x,y), you can move your chess piece to (x,y') (1≤ y'≤ m, y' ≠ y) or (x',y) (1≤ x'≤ n, x'≠ x). In other words, the chess piece moves as a rook. From the cell, you can move to any cell on the same row or column.
Your goal is to visit each cell exactly once. Can you find a solution?
Note that cells on the path between two adjacent cells in your route are not counted as visited, and it is not required to return to the starting point.
Input
The only line of the input contains four integers n, m, S_x and S_y (3≤ n,m≤ 100, 2 ≤ S_x ≤ n-1, 2 ≤ S_y ≤ m-1) — the number of rows, the number of columns, and the initial position of your chess piece, respectively.
Output
You should print n⋅ m lines.
The i-th line should contain two integers x_i and y_i (1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m), denoting the i-th cell that you visited. You should print exactly nm pairs (x_i, y_i), they should cover all possible pairs (x_i, y_i), such that 1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m.
We can show that under these constraints there always exists a solution. If there are multiple answers, print any.
Examples
Input
3 3 2 2
Output
2 2
1 2
1 3
2 3
3 3
3 2
3 1
2 1
1 1
Input
3 4 2 2
Output
2 2
2 1
2 3
2 4
1 4
3 4
3 3
3 2
3 1
1 1
1 2
1 3
Note
Possible routes for two examples:
<image>
Submitted Solution:
```
from sys import stdin, stdout
import math,sys,heapq
from itertools import permutations, combinations
from collections import defaultdict,deque,OrderedDict
from os import path
import bisect as bi
def yes():print('YES')
def no():print('NO')
if (path.exists('input.txt')):
#------------------Sublime--------------------------------------#
sys.stdin=open('input.txt','r');sys.stdout=open('output.txt','w');
def I():return (int(input()))
def In():return(map(int,input().split()))
else:
#------------------PYPY FAst I/o--------------------------------#
def I():return (int(stdin.readline()))
def In():return(map(int,stdin.readline().split()))
#sys.setrecursionlimit(1500)
def dict(a):
d={}
for x in a:
if d.get(x,-1)!=-1:
d[x]+=1
else:
d[x]=1
return d
def find_gt(a, x):
'Find leftmost value greater than x'
i = bi.bisect_right(a, x)
if i != len(a):
return i
else:
return -1
def main():
try:
n,m,x,y=In()
ans=[]
for i in range(x,1,-1):
ans.append([i,y])
for j in range(x+1,n+1):
ans.append([j,y])
q=0
for j in range(y-1,0,-1):
if q==0:
for i in range(n,1,-1):
ans.append([i,j])
q=1
else:
for i in range(2,n+1,+1):
ans.append([i,j])
q=0
for j in range(1,y+1):
ans.append([1,j])
q=0
for j in range(y+1,m+1):
if q==0:
for i in range(1,n+1):
ans.append([i,j])
q=1
else:
for i in range(n,0,-1):
ans.append([i,j])
q=0
for x in ans:
print(*x)
except:
pass
M = 998244353
P = 1000000007
if __name__ == '__main__':
#for _ in range(I()):main()
for _ in range(1):main()
```
Yes
| 102,216 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Boboniu likes playing chess with his employees. As we know, no employee can beat the boss in the chess game, so Boboniu has never lost in any round.
You are a new applicant for his company. Boboniu will test you with the following chess question:
Consider a n× m grid (rows are numbered from 1 to n, and columns are numbered from 1 to m). You have a chess piece, and it stands at some cell (S_x,S_y) which is not on the border (i.e. 2 ≤ S_x ≤ n-1 and 2 ≤ S_y ≤ m-1).
From the cell (x,y), you can move your chess piece to (x,y') (1≤ y'≤ m, y' ≠ y) or (x',y) (1≤ x'≤ n, x'≠ x). In other words, the chess piece moves as a rook. From the cell, you can move to any cell on the same row or column.
Your goal is to visit each cell exactly once. Can you find a solution?
Note that cells on the path between two adjacent cells in your route are not counted as visited, and it is not required to return to the starting point.
Input
The only line of the input contains four integers n, m, S_x and S_y (3≤ n,m≤ 100, 2 ≤ S_x ≤ n-1, 2 ≤ S_y ≤ m-1) — the number of rows, the number of columns, and the initial position of your chess piece, respectively.
Output
You should print n⋅ m lines.
The i-th line should contain two integers x_i and y_i (1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m), denoting the i-th cell that you visited. You should print exactly nm pairs (x_i, y_i), they should cover all possible pairs (x_i, y_i), such that 1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m.
We can show that under these constraints there always exists a solution. If there are multiple answers, print any.
Examples
Input
3 3 2 2
Output
2 2
1 2
1 3
2 3
3 3
3 2
3 1
2 1
1 1
Input
3 4 2 2
Output
2 2
2 1
2 3
2 4
1 4
3 4
3 3
3 2
3 1
1 1
1 2
1 3
Note
Possible routes for two examples:
<image>
Submitted Solution:
```
import sys
def mover(r,c,n,m):
l1=c
countr=0
countl=0
while l1>=1:
countr=1
print('{} {}'.format(r,l1))
l1-=1
l1=c+1
while l1<=m:
countl=1
print('{} {}'.format(r,l1))
l1+=1
if countl==0:
return(1)
else:
return(m)
n,m,s1,s2=map(int,(sys.stdin.readline()).split())
k=s2
p=s1
counter=0
while k>=1:
p=mover(k,p,n,m)
k-=1
k=s2+1
while k<=n:
p=mover(k,p,n,m)
k+=1
```
No
| 102,217 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Boboniu likes playing chess with his employees. As we know, no employee can beat the boss in the chess game, so Boboniu has never lost in any round.
You are a new applicant for his company. Boboniu will test you with the following chess question:
Consider a n× m grid (rows are numbered from 1 to n, and columns are numbered from 1 to m). You have a chess piece, and it stands at some cell (S_x,S_y) which is not on the border (i.e. 2 ≤ S_x ≤ n-1 and 2 ≤ S_y ≤ m-1).
From the cell (x,y), you can move your chess piece to (x,y') (1≤ y'≤ m, y' ≠ y) or (x',y) (1≤ x'≤ n, x'≠ x). In other words, the chess piece moves as a rook. From the cell, you can move to any cell on the same row or column.
Your goal is to visit each cell exactly once. Can you find a solution?
Note that cells on the path between two adjacent cells in your route are not counted as visited, and it is not required to return to the starting point.
Input
The only line of the input contains four integers n, m, S_x and S_y (3≤ n,m≤ 100, 2 ≤ S_x ≤ n-1, 2 ≤ S_y ≤ m-1) — the number of rows, the number of columns, and the initial position of your chess piece, respectively.
Output
You should print n⋅ m lines.
The i-th line should contain two integers x_i and y_i (1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m), denoting the i-th cell that you visited. You should print exactly nm pairs (x_i, y_i), they should cover all possible pairs (x_i, y_i), such that 1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m.
We can show that under these constraints there always exists a solution. If there are multiple answers, print any.
Examples
Input
3 3 2 2
Output
2 2
1 2
1 3
2 3
3 3
3 2
3 1
2 1
1 1
Input
3 4 2 2
Output
2 2
2 1
2 3
2 4
1 4
3 4
3 3
3 2
3 1
1 1
1 2
1 3
Note
Possible routes for two examples:
<image>
Submitted Solution:
```
n, m, x, y = [int(x) for x in input().split()]
print('{} {}'.format(x, y))
print('1 {}'.format(y))
for i in range(1, n + 1, 2):
for j in range(1, m + 1):
if j == y and i in [1, x]:
continue
print('{} {}'.format(i, j))
for j in range(m, 0, -1):
if i == n:
break
if j == y and i in [1, x]:
continue
print('{} {}'.format(i + 1, j))
```
No
| 102,218 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Boboniu likes playing chess with his employees. As we know, no employee can beat the boss in the chess game, so Boboniu has never lost in any round.
You are a new applicant for his company. Boboniu will test you with the following chess question:
Consider a n× m grid (rows are numbered from 1 to n, and columns are numbered from 1 to m). You have a chess piece, and it stands at some cell (S_x,S_y) which is not on the border (i.e. 2 ≤ S_x ≤ n-1 and 2 ≤ S_y ≤ m-1).
From the cell (x,y), you can move your chess piece to (x,y') (1≤ y'≤ m, y' ≠ y) or (x',y) (1≤ x'≤ n, x'≠ x). In other words, the chess piece moves as a rook. From the cell, you can move to any cell on the same row or column.
Your goal is to visit each cell exactly once. Can you find a solution?
Note that cells on the path between two adjacent cells in your route are not counted as visited, and it is not required to return to the starting point.
Input
The only line of the input contains four integers n, m, S_x and S_y (3≤ n,m≤ 100, 2 ≤ S_x ≤ n-1, 2 ≤ S_y ≤ m-1) — the number of rows, the number of columns, and the initial position of your chess piece, respectively.
Output
You should print n⋅ m lines.
The i-th line should contain two integers x_i and y_i (1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m), denoting the i-th cell that you visited. You should print exactly nm pairs (x_i, y_i), they should cover all possible pairs (x_i, y_i), such that 1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m.
We can show that under these constraints there always exists a solution. If there are multiple answers, print any.
Examples
Input
3 3 2 2
Output
2 2
1 2
1 3
2 3
3 3
3 2
3 1
2 1
1 1
Input
3 4 2 2
Output
2 2
2 1
2 3
2 4
1 4
3 4
3 3
3 2
3 1
1 1
1 2
1 3
Note
Possible routes for two examples:
<image>
Submitted Solution:
```
n, m, x, y = map(int,input().split())
used = [[0 for i in range(m)] for i in range(n)]
x -= 1
y -= 1
used[x][y] = 1
used[0][y] = 1
print(x + 1, y+1)
print(1, y+1)
x = y = 0
while x+y < n+m-2:
print(x+1,y+1)
used[x][y] = 1
q = x%2
if q == 0:
if y == m-1:
x += 1
else:
y += 1
if used[x][y] == 1:
y += 1
else:
if y == 0:
x += 1
else:
y -= 1
if used[x][y] == 1:
y -= 1
print(n, m)
```
No
| 102,219 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Boboniu likes playing chess with his employees. As we know, no employee can beat the boss in the chess game, so Boboniu has never lost in any round.
You are a new applicant for his company. Boboniu will test you with the following chess question:
Consider a n× m grid (rows are numbered from 1 to n, and columns are numbered from 1 to m). You have a chess piece, and it stands at some cell (S_x,S_y) which is not on the border (i.e. 2 ≤ S_x ≤ n-1 and 2 ≤ S_y ≤ m-1).
From the cell (x,y), you can move your chess piece to (x,y') (1≤ y'≤ m, y' ≠ y) or (x',y) (1≤ x'≤ n, x'≠ x). In other words, the chess piece moves as a rook. From the cell, you can move to any cell on the same row or column.
Your goal is to visit each cell exactly once. Can you find a solution?
Note that cells on the path between two adjacent cells in your route are not counted as visited, and it is not required to return to the starting point.
Input
The only line of the input contains four integers n, m, S_x and S_y (3≤ n,m≤ 100, 2 ≤ S_x ≤ n-1, 2 ≤ S_y ≤ m-1) — the number of rows, the number of columns, and the initial position of your chess piece, respectively.
Output
You should print n⋅ m lines.
The i-th line should contain two integers x_i and y_i (1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m), denoting the i-th cell that you visited. You should print exactly nm pairs (x_i, y_i), they should cover all possible pairs (x_i, y_i), such that 1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m.
We can show that under these constraints there always exists a solution. If there are multiple answers, print any.
Examples
Input
3 3 2 2
Output
2 2
1 2
1 3
2 3
3 3
3 2
3 1
2 1
1 1
Input
3 4 2 2
Output
2 2
2 1
2 3
2 4
1 4
3 4
3 3
3 2
3 1
1 1
1 2
1 3
Note
Possible routes for two examples:
<image>
Submitted Solution:
```
n,m,x,y=map(int,input().split())
for i in range(1,x):
print(y,i)
for i in range(x+1,m+1):
print(y,i)
for i in range(1,y):
if i%2==1:
for j in range(m,0,-1):
print(i,j)
else:
for j in range(1,m+1):
print(i,j)
for i in range(y+1,n+1):
if i%2==0:
for j in range(m,0,-1):
print(i,j)
else:
for j in range(1,m+1):
print(i,j)
```
No
| 102,220 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Tags: binary search, brute force, constructive algorithms, greedy, sortings, two pointers
Correct Solution:
```
t=1
for _ in range(t):
n=int(input())
l=[int(j) for j in input().split()]
l.sort()
c,cnt=0,0
k=[0]*n
for i in range(n//2):
k[c]=l[n//2+i]
c+=1
k[c]=l[i]
c+=1
if n%2!=0:
k[n-1]=l[n-1]
for i in range(1,n-1):
if k[i-1]>k[i] and k[i+1]>k[i]:
cnt+=1
print(cnt)
print(*k)
```
| 102,221 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Tags: binary search, brute force, constructive algorithms, greedy, sortings, two pointers
Correct Solution:
```
n = int(input())
p = [int(x) for x in input().split()]
p.sort()
a = [None] * n
k = 0
if n % 2 == 1:
for i in range(1, n, 2):
a[i] = p[k]
k += 1
for i in range(0, n, 2):
a[i] = p[k]
k += 1
else:
for i in range(1, n, 2):
a[i] = p[k]
k += 1
for i in range(0, n, 2):
a[i] = p[k]
k += 1
ct = 0
for i in range(1, n - 1):
if a[i] < a[i - 1] and a[i] < a[i + 1]:
ct += 1
print(ct)
for e in a:
print(e, end=' ')
print()
```
| 102,222 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Tags: binary search, brute force, constructive algorithms, greedy, sortings, two pointers
Correct Solution:
```
n=int(input())
l=list(map(int,input().split()))
lena=(len(l))
l.sort()
left=l[:lena//2]
right=l[lena//2:]
left.sort();right.sort()
answer=[]
count=0
for i in range(len(right)):
answer.append(right[i])
if i<len(left):
answer.append(left[i])
if answer[-1]<answer[-2] and i<len(right)-1:
count+=1
print(count)
print(*answer)
```
| 102,223 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Tags: binary search, brute force, constructive algorithms, greedy, sortings, two pointers
Correct Solution:
```
#3 1 3 2 3 3 6 7
#1 2 3 3 3 6 3 7
#1 3 3 3 2 6 3 7
#3 3 1 3 2 6 3 7
#maximum possible valleys = math.ceil(len / 2) - 1
#first maxPossibleValleys of sorted array
#min = 1,2,3
#max = 3,3,3,6,7
#iterate through max and put in elements from min if they work
#if some mins haven't been place, just put them at end of max
#return max and a count of the spots found
import math
N = int(input())
arr = [int(i) for i in input().split(' ')]
def win(arr):
if len(arr) <= 2:
print(0)
print(' '.join([str(i) for i in arr]))
return
arr.sort()
maxPossible = math.ceil(len(arr) / 2) - 1
minArr = arr[:maxPossible]
maxArr = arr[maxPossible:]
j = 0
ans = [maxArr[0]]
count = 0
for i in range(1,len(maxArr)):
if minArr[j] < maxArr[i-1] and minArr[j] < maxArr[i]:
count += 1
ans.append(minArr[j])
j += 1
ans.append(maxArr[i])
if j == len(minArr):
ans += maxArr[i+1:]
break
if j < len(minArr):
ans += minArr[j:]
print(count)
print(' '.join([str(i) for i in ans]))
win(arr)
```
| 102,224 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Tags: binary search, brute force, constructive algorithms, greedy, sortings, two pointers
Correct Solution:
```
import sys,math
n=int(input())
prc=list(map(int,sys.stdin.readline().strip().split()))
prc.sort(reverse=True)
if prc[0]==prc[-1] or len(prc)<3:
print(0)
sys.stdout.write(' '.join(map(str,prc))+'\n')
else:
new_prc=[]
for i in range(math.ceil(n/2)):
new_prc.append(prc[i])
if len(new_prc)<n:
new_prc.append(-1)
if prc[math.ceil(n/2)-1]==prc[math.ceil(n/2)]:
u_bound,l_bound=math.ceil(n/2)-1,math.ceil(n/2)
while u_bound>0 and prc[u_bound-1]==prc[u_bound]:
u_bound-=1
while l_bound<n and prc[l_bound]==prc[l_bound+1]:
l_bound+=1
# print(u_bound,l_bound)
j=math.ceil(n/2)
for i in range(1,2*(u_bound-1),2):
new_prc[i]=prc[j]
j+=1
# print(new_prc)
j=-1
for i in range(2*u_bound-1 if u_bound!=0 else 1,n,2):
new_prc[i]=prc[j]
j-=1
# print(new_prc)
else:
j=math.ceil(n/2)
for i in range(1,n,2):
new_prc[i]=prc[j]
j+=1
count=0
for i in range(1,n if n%2==1 else n-1,2):
if new_prc[i-1]>new_prc[i] and new_prc[i+1]>new_prc[i]:
count+=1
print(count)
sys.stdout.write(' '.join(map(str,new_prc))+'\n')
```
| 102,225 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Tags: binary search, brute force, constructive algorithms, greedy, sortings, two pointers
Correct Solution:
```
#!/usr/bin/env python
import os
import sys
from io import BytesIO, IOBase
import threading
from bisect import bisect_right
from math import gcd,log
from collections import Counter
from pprint import pprint
# arr=[1]
# i=1
# while i <100:
# arr.append(2*arr[-1]+2**(i+1))
# i=2*i+1
# print(arr)
def main():
n=int(input())
arr=list(map(int,input().split()))
a=arr.copy()
a.sort(reverse=True)
ind=0
for i in range(0,n,2):
arr[i]=a[ind]
ind+=1
for i in range(1,n,2):
arr[i]=a[ind]
ind+=1
cnt=0
nahi=-1
ind=-1
for i in range(n):
if i!=0 and i!=n-1 and i%2:
if arr[i]<arr[i+1] and arr[i]<arr[i-1]:
cnt+=1
elif (nahi==-1):
nahi=arr[i]
ind=i
if n%2==0 and nahi!=-1 and arr[ind]!=arr[-1]:
arr[-1],arr[ind]=arr[ind],arr[-1]
cnt+=1
print(cnt)
print(*arr)
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# endregion
if __name__ == "__main__":
for _ in range(1):
main()
```
| 102,226 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Tags: binary search, brute force, constructive algorithms, greedy, sortings, two pointers
Correct Solution:
```
N = int(input())
A = list(map(int, input().split()))
# from itertools import combinations_with_replacement
# for com in combinations_with_replacement(range(1,N+1),N):
# A = list(com)
A.sort()
B = [0]*N
for i in range(1,N,2):
B[i] = A[i//2]
Astart = N//2
Bstart = N-2 if N%2==0 else N-1
rem = []
while Astart<N and A[Astart]==B[Bstart-1]:
rem.append(A[Astart])
Astart += 1
for i in range(Bstart,-1,-2):
if Astart>=N:
B[i] = rem.pop()
else:
B[i] = A[Astart]
Astart += 1
ans = 0
for i in range(1,N-1,2):
if B[i-1]>B[i]<B[i+1]:
ans += 1
# if sorted(B)!=A:
# print(False)
# print(A)
print(ans)
print(*B)
```
| 102,227 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Tags: binary search, brute force, constructive algorithms, greedy, sortings, two pointers
Correct Solution:
```
n = int(input())
l=sorted(list(map(int,input().split())))
x=[]
if n<=2 :
print(0)
print(*l)
elif n%2==0 :
a=l[:n//2]
b=l[n//2:]
ans=0
for i in range(n//2):
x.append(b[i])
x.append(a[i])
for j in range(1,n-1,2):
if x[j]<x[j+1] and x[j]<x[j-1] :
ans+=1
print(ans)
print(*x)
else:
a=l[:n//2]
b=l[n//2:]
ans=0
for i in range(n//2):
x.append(b[i])
x.append(a[i])
x.append(b[-1])
for j in range(1,n,2):
if (x[j]<x[j+1]) and (x[j]<x[j-1]) :
ans+=1
print(ans)
print(*x)
```
| 102,228 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Submitted Solution:
```
# from collections import defaultdict, Counter, deque
# from heapq import heappop, heappush, heapify
# from functools import lru_cache, reduce
# import bisect
# from itertools import permutations, combinations, combinations_with_replacement
def f():
n = int(input())
arr = list(map(int, input().split()))
arr.sort()
newarr = []
for i in range(n//2):
newarr.append(arr[i+n//2])
newarr.append(arr[i])
if n % 2:
newarr.append(arr[n-1])
total = 0
i = 1
while i+1 < n:
if newarr[i-1] > newarr[i] and newarr[i] < newarr[i+1]:
total += 1
i += 2
newarr = list(map(str, newarr))
newarr = " ".join(newarr)
print(total)
print(newarr)
f()
# Test cases
'''
7
1 3 2 2 4 5 4
8
3 3 3 3 3 3 2 2
6
1 1 1 1 1 1
'''
```
Yes
| 102,229 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Submitted Solution:
```
def solve(n, ices):
ices = sorted(ices)
former, latter = ices[:n//2], ices[n//2:]
res = 0
res_ice = []
for i in range((n-1)//2):
res_ice.append(latter[i])
res_ice.append(former[i])
if former[i] < latter[i]:
res += 1
res_ice.append(latter[-1])
if n % 2 == 0:
res_ice.append(former[-1])
return res, " ".join(list(map(str, res_ice)))
def main():
n = int(input())
ices = list(map(int, input().split()))
res1, res2 = solve(n, ices)
print(res1)
print(res2)
main()
```
Yes
| 102,230 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Submitted Solution:
```
n=int(input())
a=list(map(int,input().split()))
a.sort(reverse=True)
x=n//2
b=a[:x]
c=a[x:]
c.reverse()
b.reverse()
z=[]
for i in range(x):
z.append(b[i])
z.append(c[i])
c[i]=0
for i in range(len(c)):
if c[i]!=0:
z.append(c[i])
ans2=0
for i in range(1,n-1,2):
if z[i]<z[i-1] and z[i]<z[i+1]:
ans2+=1
b=[]
x=n//2
pos=x
if (2*x)!=n:
pos=x+1
for i in range(x):
b.append(a[i])
b.append(a[i+pos])
if (2*x)!=n:
b.append(a[x])
c=[]
for i in range(x):
c.append(a[i])
c.append(a[-i])
if (2*x)!=n:
c.append(a[x])
ans=0
for i in range(1,n-1,2):
if b[i]<b[i-1] and b[i]<b[i+1]:
ans+=1
tmp=0
for i in range(1,n-1,2):
if c[i]<c[i-1] and c[i]<c[i+1]:
tmp+=1
if max(ans,tmp,ans2)==ans:
print(ans)
print(*b)
elif max(ans,tmp,ans2)==tmp:
print(tmp)
print(*c)
else:
print(ans2)
print(*z)
```
Yes
| 102,231 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Submitted Solution:
```
n=int(input())
l=list(sorted(map(int,input().split())))
left= l[0:n//2]
right = l[n//2:n]
arr=[-1 for x in range(n)]
count=0
flag= True
j=0
k=0
for i in range(n):
if flag==True:
arr[i]=right[j]
j+=1
flag=False
elif flag==False:
arr[i]=left[k]
k+=1
flag=True
for a in range(1,n-1):
if arr[a]<arr[a-1] and arr[a]< arr[a+1]:
count+=1
print(count)
print(*arr)
```
Yes
| 102,232 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Submitted Solution:
```
z,zz=input,lambda:list(map(int,z().split()))
zzz=lambda:[int(i) for i in stdin.readline().split()]
szz,graph,mod,szzz=lambda:sorted(zz()),{},10**9+7,lambda:sorted(zzz())
from string import *
from re import *
from collections import *
from queue import *
from sys import *
from collections import *
from math import *
from heapq import *
from itertools import *
from bisect import *
from collections import Counter as cc
from math import factorial as f
from bisect import bisect as bs
from bisect import bisect_left as bsl
from itertools import accumulate as ac
from itertools import permutations as permu
def lcd(xnum1,xnum2):return (xnum1*xnum2//gcd(xnum1,xnum2))
def prime(x):
p=ceil(x**.5)+1
for i in range(2,p):
if (x%i==0 and x!=2) or x==0:return 0
return 1
def dfs(u,visit,graph):
visit[u]=True
for i in graph[u]:
if not visit[i]:
dfs(i,visit,graph)
###########################---Test-Case---#################################
"""
"""
###########################---START-CODING---##############################
num=1
#num=int(z())
for _ in range( num ):
n=int(z())
arr=szzz()
l=0
r=n-1
lst=[]
while l<r:
lst.append(arr[r])
lst.append(arr[l])
r-=1
l+=1
if n%2==1:
lst.append(arr[l])
ans=0
for i in range(1,n-1):
if lst[i-1]>lst[i] and lst[i+1]>lst[i]:
ans+=1
print(ans)
print(*lst)
```
No
| 102,233 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Submitted Solution:
```
n = int(input())
d = [int(i) for i in input().split()]
if n < 3 or d[0] * n == sum(d):
print(0)
exit()
d.sort()
mxd = [max(d[i], d[i+1]) for i in range(n-1)]
hi = (n-3) // 2
lo = 0
while lo < hi:
mid = (lo + hi+1) // 2
kk = n - mid - 2
# print(mid, [(mxd[kk+i], d[i]) for i in range(mid+1)])
if sum(mxd[kk+i] > d[i] for i in range(mid+1)) == mid + 1:
lo = mid
else:
hi = mid - 1
print(lo+1)
# ans = [d[0]]
ans = []
for i in range(lo+1):
ans.append(d[n-lo-2+i])
ans.append(d[i])
ans.append(d[-1])
print(' '.join(map(str, ans)))
```
No
| 102,234 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Submitted Solution:
```
import sys,math
n=int(input())
prc=list(map(int,sys.stdin.readline().strip().split()))
prc.sort(reverse=True)
if prc[0]==prc[-1] or len(prc)<3:
print(0)
sys.stdout.write(' '.join(map(str,prc))+'\n')
else:
new_prc=[]
for i in range(math.ceil(n/2)):
new_prc.append(prc[i])
if len(new_prc)<n:
new_prc.append(prc[math.ceil(n/2)+i])
count=0
for i in range(1,n-1,2):
if new_prc[i]<new_prc[i-1] and new_prc[i]<new_prc[i+1]:
count+=1
print(count)
sys.stdout.write(' '.join(map(str,new_prc))+'\n')
```
No
| 102,235 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is the hard version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.
Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version, some prices can be equal.
An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.
You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.
Output
In the first line print the maximum number of ice spheres that Sage can buy.
In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.
Example
Input
7
1 3 2 2 4 5 4
Output
3
3 1 4 2 4 2 5
Note
In the sample it's not possible to place the ice spheres in any order so that Sage would buy 4 of them. If the spheres are placed in the order (3, 1, 4, 2, 4, 2, 5), then Sage will buy one sphere for 1 and two spheres for 2 each.
Submitted Solution:
```
N = int(input())
A = list(map(int, input().split()))
A.sort(reverse=True)
big = 0
small = (N+1)//2
B = [0]*N
cnt = 0
while cnt<N:
B[cnt] = A[big]
big += 1
cnt += 1
if cnt==N:
break
B[cnt] = A[small]
small += 1
cnt += 1
ans = 0
for i in range(1,N-1,2):
if B[i-1]>B[i]<B[i+1]:
ans += 1
print(ans)
print(*B)
```
No
| 102,236 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array of n integers a_1, a_2, ..., a_n, and a set b of k distinct integers from 1 to n.
In one operation, you may choose two integers i and x (1 ≤ i ≤ n, x can be any integer) and assign a_i := x. This operation can be done only if i does not belong to the set b.
Calculate the minimum number of operations you should perform so the array a is increasing (that is, a_1 < a_2 < a_3 < ... < a_n), or report that it is impossible.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ n) — the size of the array a and the set b, respectively.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).
Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.
Output
If it is impossible to make the array a increasing using the given operations, print -1.
Otherwise, print one integer — the minimum number of operations you have to perform.
Examples
Input
7 2
1 2 1 1 3 5 1
3 5
Output
4
Input
3 3
1 3 2
1 2 3
Output
-1
Input
5 0
4 3 1 2 3
Output
2
Input
10 3
1 3 5 6 12 9 8 10 13 15
2 4 9
Output
3
Tags: binary search, constructive algorithms, data structures, dp, implementation
Correct Solution:
```
from bisect import bisect_right
# codeforces answer
INF = 0x3f3f3f3f3f3f3f3f
n, k = map(int, input().split())
a = [-INF] + [ ai - i for i, ai in enumerate(map(int, input().split())) ] + [INF]
b = [0] + (list(map(int, input().split())) if k else list()) + [n+1]
r = 0
for j in range(k+1):
l = b[j]
m = b[j+1]
if a[m] < a[l]:
print("-1")
exit()
li = list()
for ai in a[l+1:m]:
if a[l] <= ai <= a[m]:
pos = bisect_right(li, ai)
if pos == len(li):
li.append(ai)
else:
li[pos] = ai
r += m - l - 1 - len(li)
print(r)
```
| 102,237 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array of n integers a_1, a_2, ..., a_n, and a set b of k distinct integers from 1 to n.
In one operation, you may choose two integers i and x (1 ≤ i ≤ n, x can be any integer) and assign a_i := x. This operation can be done only if i does not belong to the set b.
Calculate the minimum number of operations you should perform so the array a is increasing (that is, a_1 < a_2 < a_3 < ... < a_n), or report that it is impossible.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ n) — the size of the array a and the set b, respectively.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).
Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.
Output
If it is impossible to make the array a increasing using the given operations, print -1.
Otherwise, print one integer — the minimum number of operations you have to perform.
Examples
Input
7 2
1 2 1 1 3 5 1
3 5
Output
4
Input
3 3
1 3 2
1 2 3
Output
-1
Input
5 0
4 3 1 2 3
Output
2
Input
10 3
1 3 5 6 12 9 8 10 13 15
2 4 9
Output
3
Tags: binary search, constructive algorithms, data structures, dp, implementation
Correct Solution:
```
import bisect
INF = 0x3f3f3f3f3f3f3f3f
n, k = map(int, input().split())
a = [-INF] + [ ai - i for i, ai in enumerate(map(int, input().split())) ] + [INF]
b = [0] + (list(map(int, input().split())) if k else list()) + [n+1]
ans = 0
for j in range(k+1):
l = b[j]
r = b[j+1]
if a[r] < a[l]:
print("-1")
exit()
lis = list()
for ai in a[l+1:r]:
if a[l] <= ai <= a[r]:
pos = bisect.bisect(lis, ai)
if pos == len(lis):
lis.append(ai)
else:
lis[pos] = ai
ans += r - l - 1 - len(lis)
print(ans)
```
| 102,238 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array of n integers a_1, a_2, ..., a_n, and a set b of k distinct integers from 1 to n.
In one operation, you may choose two integers i and x (1 ≤ i ≤ n, x can be any integer) and assign a_i := x. This operation can be done only if i does not belong to the set b.
Calculate the minimum number of operations you should perform so the array a is increasing (that is, a_1 < a_2 < a_3 < ... < a_n), or report that it is impossible.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ n) — the size of the array a and the set b, respectively.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).
Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.
Output
If it is impossible to make the array a increasing using the given operations, print -1.
Otherwise, print one integer — the minimum number of operations you have to perform.
Examples
Input
7 2
1 2 1 1 3 5 1
3 5
Output
4
Input
3 3
1 3 2
1 2 3
Output
-1
Input
5 0
4 3 1 2 3
Output
2
Input
10 3
1 3 5 6 12 9 8 10 13 15
2 4 9
Output
3
Tags: binary search, constructive algorithms, data structures, dp, implementation
Correct Solution:
```
import bisect
a = []
b = []
inf = 0x3f3f3f3f
def solve(num):
n = len(num)
temp = []
num = [(num[i] - i) for i in range(n)]
for i in range(n):
if (num[i] < num[0] or num[i] > num[n - 1]):
continue
k = bisect.bisect_right(temp, num[i])
if k == len(temp):
temp.append(num[i])
else:
temp[k] = num[i]
ans = n - len(temp)
return ans
s = input()
s = [x for x in s.split()]
n = int(s[0])
k = int(s[1])
s1 = input()
s1 = [x for x in s1.split()]
if (k != 0):
s2 = input()
s2 = [x for x in s2.split()]
else:
s2 = []
for i in range(1, n + 1):
a.append(int(s1[i - 1]))
if (k != 0):
for i in range(1, k + 1):
b.append(int(s2[i - 1]))
a = [-inf] + a + [inf]
b = [0] + b + [n + 1]
ans = 0
sign = True
cnt, num = b[0], a[0]
for c in b[1:]:
if c - cnt > a[c] - num:
sign = False
break
ans += solve(a[cnt:c + 1])
cnt, num = c, a[c]
if sign:
print(ans)
else:
print(-1)
```
| 102,239 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array of n integers a_1, a_2, ..., a_n, and a set b of k distinct integers from 1 to n.
In one operation, you may choose two integers i and x (1 ≤ i ≤ n, x can be any integer) and assign a_i := x. This operation can be done only if i does not belong to the set b.
Calculate the minimum number of operations you should perform so the array a is increasing (that is, a_1 < a_2 < a_3 < ... < a_n), or report that it is impossible.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ n) — the size of the array a and the set b, respectively.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).
Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.
Output
If it is impossible to make the array a increasing using the given operations, print -1.
Otherwise, print one integer — the minimum number of operations you have to perform.
Examples
Input
7 2
1 2 1 1 3 5 1
3 5
Output
4
Input
3 3
1 3 2
1 2 3
Output
-1
Input
5 0
4 3 1 2 3
Output
2
Input
10 3
1 3 5 6 12 9 8 10 13 15
2 4 9
Output
3
Tags: binary search, constructive algorithms, data structures, dp, implementation
Correct Solution:
```
import bisect
def mat(arr):
n = len(arr)
a = []
arr = [(arr[i] - i) for i in range(n)]
for i in range(n):
if (arr[i] < arr[0] or arr[i] > arr[n - 1]):
continue
k = bisect.bisect_right(a, arr[i])
if k == len(a):
a.append(arr[i])
else:
a[k] = arr[i]
res = n - len(a)
return res
n, m = map(int, input().split())
num1 = list(map(int, input().split()))
if m == 0:
num2 = []
else:
num2 = list(map(int, input().split()))
num1 = [-10 ** 10] + num1 + [10 ** 10]
num2 = [0] + num2 + [n + 1]
sum = 0
ddd = 1
num = num1[0]
tmp = num2[0]
for i in num2[1:]:
if i - tmp > num1[i] - num:
ddd = 0
break
sum += mat(num1[tmp:i + 1])
num = num1[i]
tmp= i
if ddd:
print(sum)
else:
print(-1)
```
| 102,240 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array of n integers a_1, a_2, ..., a_n, and a set b of k distinct integers from 1 to n.
In one operation, you may choose two integers i and x (1 ≤ i ≤ n, x can be any integer) and assign a_i := x. This operation can be done only if i does not belong to the set b.
Calculate the minimum number of operations you should perform so the array a is increasing (that is, a_1 < a_2 < a_3 < ... < a_n), or report that it is impossible.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ n) — the size of the array a and the set b, respectively.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).
Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.
Output
If it is impossible to make the array a increasing using the given operations, print -1.
Otherwise, print one integer — the minimum number of operations you have to perform.
Examples
Input
7 2
1 2 1 1 3 5 1
3 5
Output
4
Input
3 3
1 3 2
1 2 3
Output
-1
Input
5 0
4 3 1 2 3
Output
2
Input
10 3
1 3 5 6 12 9 8 10 13 15
2 4 9
Output
3
Tags: binary search, constructive algorithms, data structures, dp, implementation
Correct Solution:
```
from bisect import bisect_right
INF = 10**9+1
n, k = map(int, input().split())
a = [-INF] + [ ai - i for i, ai in enumerate(map(int, input().split())) ] + [INF]
b = [0] + (list(map(int, input().split())) if k else list()) + [n+1]
ans = 0
for j in range(k+1):
l = b[j]
r = b[j+1]
if a[r] < a[l]:
print("-1")
exit()
lis = list()
for ai in a[l+1:r]:
if a[l] <= ai <= a[r]:
pos = bisect_right(lis, ai)
if pos == len(lis):
lis.append(ai)
else:
lis[pos] = ai
ans += r - l - 1 - len(lis)
print(ans)
```
| 102,241 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array of n integers a_1, a_2, ..., a_n, and a set b of k distinct integers from 1 to n.
In one operation, you may choose two integers i and x (1 ≤ i ≤ n, x can be any integer) and assign a_i := x. This operation can be done only if i does not belong to the set b.
Calculate the minimum number of operations you should perform so the array a is increasing (that is, a_1 < a_2 < a_3 < ... < a_n), or report that it is impossible.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ n) — the size of the array a and the set b, respectively.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).
Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.
Output
If it is impossible to make the array a increasing using the given operations, print -1.
Otherwise, print one integer — the minimum number of operations you have to perform.
Examples
Input
7 2
1 2 1 1 3 5 1
3 5
Output
4
Input
3 3
1 3 2
1 2 3
Output
-1
Input
5 0
4 3 1 2 3
Output
2
Input
10 3
1 3 5 6 12 9 8 10 13 15
2 4 9
Output
3
Tags: binary search, constructive algorithms, data structures, dp, implementation
Correct Solution:
```
import bisect
def fun(arr):
arr = [(arr[i] - i) for i in range(len(arr))]
a = []
for i in range(len(arr)):
if (arr[i] < arr[0] or arr[i] > arr[len(arr) - 1]):
continue
k = bisect.bisect_right(a, arr[i])
if k == len(a):
a.append(arr[i])
else:
a[k] = arr[i]
result = len(arr) - len(a)
return result
n, k = map(int, input().split())
a = list(map(int, input().split()))
if k == 0:
b = []
else:
b = list(map(int, input().split()))
a = [-10 ** 10] + a + [10 ** 10]
b = [0] + b + [n + 1]
result = 0
flag = True
t, temp = b[0], a[0]
for i in b[1:]:
if i - t > a[i] - temp:
flag = False
break
result += fun(a[t:i + 1])
t, temp = i, a[i]
if flag:
print(result)
else:
print(-1)
```
| 102,242 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array of n integers a_1, a_2, ..., a_n, and a set b of k distinct integers from 1 to n.
In one operation, you may choose two integers i and x (1 ≤ i ≤ n, x can be any integer) and assign a_i := x. This operation can be done only if i does not belong to the set b.
Calculate the minimum number of operations you should perform so the array a is increasing (that is, a_1 < a_2 < a_3 < ... < a_n), or report that it is impossible.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ n) — the size of the array a and the set b, respectively.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).
Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.
Output
If it is impossible to make the array a increasing using the given operations, print -1.
Otherwise, print one integer — the minimum number of operations you have to perform.
Examples
Input
7 2
1 2 1 1 3 5 1
3 5
Output
4
Input
3 3
1 3 2
1 2 3
Output
-1
Input
5 0
4 3 1 2 3
Output
2
Input
10 3
1 3 5 6 12 9 8 10 13 15
2 4 9
Output
3
Tags: binary search, constructive algorithms, data structures, dp, implementation
Correct Solution:
```
import bisect
def calculate(num):
aa=[]
bb=[]
n = len(num)
num = [(num[i] - i) for i in range(0,n)]
for i in range(0,n):
if (num[i] > num[n - 1] or num[i] < num[0] ):
continue
kk = bisect.bisect_right(aa, num[i])
if kk != len(aa):
aa[kk] = num[i]
else:
aa.append(num[i])
return (n - len(aa))
outt =1
n, k = map(int, input().split())
a1=[]
a1 = list(map(int, input().split()))
if k != 0:
a2 = list(map(int, input().split()))
else:
a2 = []
a1 = [-10**10] + a1 + [10**10]
a2 = [0]+ a2 + [n + 1]
aa1= a1[0]
aa2= a2[0]
outt=0
flag = True
for j in a2[1:]:
if (j + aa1 > a1[j]+ aa2):
flag = False
break
outt = outt+calculate(a1[aa2:j + 1])
aa1 =a1[j]
aa2=j
if (flag==False):
print(-1)
else:
print(outt)
```
| 102,243 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array of n integers a_1, a_2, ..., a_n, and a set b of k distinct integers from 1 to n.
In one operation, you may choose two integers i and x (1 ≤ i ≤ n, x can be any integer) and assign a_i := x. This operation can be done only if i does not belong to the set b.
Calculate the minimum number of operations you should perform so the array a is increasing (that is, a_1 < a_2 < a_3 < ... < a_n), or report that it is impossible.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ n) — the size of the array a and the set b, respectively.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).
Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.
Output
If it is impossible to make the array a increasing using the given operations, print -1.
Otherwise, print one integer — the minimum number of operations you have to perform.
Examples
Input
7 2
1 2 1 1 3 5 1
3 5
Output
4
Input
3 3
1 3 2
1 2 3
Output
-1
Input
5 0
4 3 1 2 3
Output
2
Input
10 3
1 3 5 6 12 9 8 10 13 15
2 4 9
Output
3
Tags: binary search, constructive algorithms, data structures, dp, implementation
Correct Solution:
```
import bisect
def TSort():
one=False
zero=False
flag=True
for i in range(0,n):
if i<n-1:
if a[i+1]<a[i]:
flag=False
if b[i]==0:
one=True
else:
zero=True
if flag or (one and zero):
print("Yes")
else:
print("No")
def snynb(arr):
n = len(arr)
a = []
arr = [(arr[i] - i) for i in range(n)]
for i in range(n):
if (arr[i] < arr[0] or arr[i] > arr[n - 1]):
continue
k = bisect.bisect_right(a, arr[i])
if k == len(a):
a.append(arr[i])
else:
a[k] = arr[i]
x = n - len(a)
return x
def okk(mid):
global n,shuzu,k,m
m=0
zonghe=0
cnt=0
for i in range (n):
if zonghe+shuzu[i]>=mid:
if zonghe>m:
m=zonghe
zonghe=shuzu[i]
cnt=cnt+1
else:
zonghe=zonghe+shuzu[i]
return cnt<k
n, m = map(int, input().split())
num1 = list(map(int, input().split()))
if m == 0:
num2 = []
else:
num2 = list(map(int, input().split()))
num1 = [-10 ** 10] + num1 + [10 ** 10]
num2 = [0] + num2 + [n + 1]
sum = 0
sny = 1
num = num1[0]
t = num2[0]
for i in num2[1:]:
if i - t > num1[i] - num:
sny = 0
break
sum += snynb(num1[t:i + 1])
num = num1[i]
t = i
if sny:
print(sum)
else:
print(-1)
```
| 102,244 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of n integers a_1, a_2, ..., a_n, and a set b of k distinct integers from 1 to n.
In one operation, you may choose two integers i and x (1 ≤ i ≤ n, x can be any integer) and assign a_i := x. This operation can be done only if i does not belong to the set b.
Calculate the minimum number of operations you should perform so the array a is increasing (that is, a_1 < a_2 < a_3 < ... < a_n), or report that it is impossible.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ n) — the size of the array a and the set b, respectively.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).
Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.
Output
If it is impossible to make the array a increasing using the given operations, print -1.
Otherwise, print one integer — the minimum number of operations you have to perform.
Examples
Input
7 2
1 2 1 1 3 5 1
3 5
Output
4
Input
3 3
1 3 2
1 2 3
Output
-1
Input
5 0
4 3 1 2 3
Output
2
Input
10 3
1 3 5 6 12 9 8 10 13 15
2 4 9
Output
3
Submitted Solution:
```
import os
import sys
from io import BytesIO, IOBase
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline()
# ------------------------------
def RL(): return map(int, sys.stdin.readline().split())
def RLL(): return list(map(int, sys.stdin.readline().split()))
def N(): return int(input())
def print_list(l):
print(' '.join(map(str,l)))
# sys.setrecursionlimit(300000)
# from heapq import *
# from collections import deque as dq
# from math import ceil,floor,sqrt,pow
import bisect as bs
# from collections import Counter
# from collections import defaultdict as dc
# from functools import lru_cache
n,k = RL()
a = RLL()
b = RLL()
flag = True
for i in range(1,k):
x,y = b[i-1],b[i]
if a[y-1]-a[x-1]<y-x:
flag = False
break
if not flag:
print(-1)
else:
a = [a[i]-i for i in range(n)]
j = 0
d = [0]*(n+1)
e = 0
s = 0
for i in range(n):
if s>0 and a[i]<d[s-1]:
continue
p = bs.bisect_right(d,a[i],s,e)
d[p] = a[i]
if j<k and i+1==b[j]:
j+=1
e = p+1
s = p+1
elif p==e:
e+=1
# print(d,e)
print(n-e)
```
Yes
| 102,245 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of n integers a_1, a_2, ..., a_n, and a set b of k distinct integers from 1 to n.
In one operation, you may choose two integers i and x (1 ≤ i ≤ n, x can be any integer) and assign a_i := x. This operation can be done only if i does not belong to the set b.
Calculate the minimum number of operations you should perform so the array a is increasing (that is, a_1 < a_2 < a_3 < ... < a_n), or report that it is impossible.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ n) — the size of the array a and the set b, respectively.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).
Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.
Output
If it is impossible to make the array a increasing using the given operations, print -1.
Otherwise, print one integer — the minimum number of operations you have to perform.
Examples
Input
7 2
1 2 1 1 3 5 1
3 5
Output
4
Input
3 3
1 3 2
1 2 3
Output
-1
Input
5 0
4 3 1 2 3
Output
2
Input
10 3
1 3 5 6 12 9 8 10 13 15
2 4 9
Output
3
Submitted Solution:
```
def upper_bound(arr,target,l,r):
i=l
j=r
mid=j
while i < j:
mid = (i + j ) // 2
if target >= arr[mid]:
i = mid + 1
else:
j = mid
return j
x,y = map(int,input().split())
a = [-10**9]+list(map(int,input().split()))
a.append(10**9)
b=[0]
if y!=0:
b+=list(map(int,input().split()))
b.append(x+1)
b.sort()
d=[]
for i in range(5*(10**5)+100):
d.append(0)
def count(l,r):
global a,d
len=1
d[len]=a[l]
n=l+1
m=r+1
for i in range(n,m):
if a[i]>=d[len]:
len+=1
d[len]=a[i]
else:
j=upper_bound(d,a[i],1,len+1)
if j!=1:
d[j]=a[i]
pos=upper_bound(d,a[i],1,len+1)-1
return (r-l+1)-pos
flag=1
if y>1:
for i in range(1,y):
if(a[b[i+1]]-a[b[i]]<b[i+1]-b[i]):
flag=0
break
sum=0
for i in range(1,x+1):
a[i]-=i
if flag==0:
print (-1)
else:
for i in range(1,y+2):
sum+=count(b[i-1],b[i])
print(sum)
```
Yes
| 102,246 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of n integers a_1, a_2, ..., a_n, and a set b of k distinct integers from 1 to n.
In one operation, you may choose two integers i and x (1 ≤ i ≤ n, x can be any integer) and assign a_i := x. This operation can be done only if i does not belong to the set b.
Calculate the minimum number of operations you should perform so the array a is increasing (that is, a_1 < a_2 < a_3 < ... < a_n), or report that it is impossible.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ n) — the size of the array a and the set b, respectively.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).
Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.
Output
If it is impossible to make the array a increasing using the given operations, print -1.
Otherwise, print one integer — the minimum number of operations you have to perform.
Examples
Input
7 2
1 2 1 1 3 5 1
3 5
Output
4
Input
3 3
1 3 2
1 2 3
Output
-1
Input
5 0
4 3 1 2 3
Output
2
Input
10 3
1 3 5 6 12 9 8 10 13 15
2 4 9
Output
3
Submitted Solution:
```
import sys
import math
from bisect import bisect_right
def II():
return int(sys.stdin.readline())
def LI():
return list(map(int, sys.stdin.readline().split()))
def MI():
return map(int, sys.stdin.readline().split())
def SI():
return sys.stdin.readline().strip()
n,k = MI()
a = LI()
a = [float('-inf')]+a+[float('inf')]
b = []
if k!=0:
b = LI()
b = [0]+b+[n+1]
ans = n-k
for i in range(k+1):
l = b[i]
r = b[i+1]
if a[l]-l>a[r]-r:
print(-1)
exit(0)
lis = []
for j in range(l+1,r):
if not a[l]-l<=a[j]-j<=a[r]-r:
continue
ind = bisect_right(lis,a[j]-j)
if ind == len(lis):
lis.append(a[j]-j)
else:
lis[ind] = a[j]-j
ans-=len(lis)
print(ans)
```
Yes
| 102,247 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of n integers a_1, a_2, ..., a_n, and a set b of k distinct integers from 1 to n.
In one operation, you may choose two integers i and x (1 ≤ i ≤ n, x can be any integer) and assign a_i := x. This operation can be done only if i does not belong to the set b.
Calculate the minimum number of operations you should perform so the array a is increasing (that is, a_1 < a_2 < a_3 < ... < a_n), or report that it is impossible.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ n) — the size of the array a and the set b, respectively.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).
Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.
Output
If it is impossible to make the array a increasing using the given operations, print -1.
Otherwise, print one integer — the minimum number of operations you have to perform.
Examples
Input
7 2
1 2 1 1 3 5 1
3 5
Output
4
Input
3 3
1 3 2
1 2 3
Output
-1
Input
5 0
4 3 1 2 3
Output
2
Input
10 3
1 3 5 6 12 9 8 10 13 15
2 4 9
Output
3
Submitted Solution:
```
import bisect
def solve(numss):
n = len(numss)
a = []
numss = [(numss[i] - i) for i in range(n)]
for i in range(n):
if (numss[i] < numss[0] or numss[i] > numss[n - 1]):
continue
k = bisect.bisect_right(a, numss[i])
if k == len(a):
a.append(numss[i])
else:
a[k] = numss[i]
res = n - len(a)
return res
def main():
n, k = map(int, input().split())
a = list(map(int, input().split()))
if k == 0:
b = []
else:
b = list(map(int, input().split()))
a = [-10 ** 10] + a + [10 ** 10]
b = [0] + b + [n + 1]
res = 0
ok = True
t, tp = b[0], a[0]
for i in b[1:]:
if i - t > a[i] - tp:
ok = False
break
res += solve(a[t:i + 1])
t, tp = i, a[i]
if ok:
print(res)
else:
print(-1)
if __name__ == '__main__':
main()
```
Yes
| 102,248 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of n integers a_1, a_2, ..., a_n, and a set b of k distinct integers from 1 to n.
In one operation, you may choose two integers i and x (1 ≤ i ≤ n, x can be any integer) and assign a_i := x. This operation can be done only if i does not belong to the set b.
Calculate the minimum number of operations you should perform so the array a is increasing (that is, a_1 < a_2 < a_3 < ... < a_n), or report that it is impossible.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ n) — the size of the array a and the set b, respectively.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).
Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.
Output
If it is impossible to make the array a increasing using the given operations, print -1.
Otherwise, print one integer — the minimum number of operations you have to perform.
Examples
Input
7 2
1 2 1 1 3 5 1
3 5
Output
4
Input
3 3
1 3 2
1 2 3
Output
-1
Input
5 0
4 3 1 2 3
Output
2
Input
10 3
1 3 5 6 12 9 8 10 13 15
2 4 9
Output
3
Submitted Solution:
```
import sys,os,io
input = sys.stdin.readline
from bisect import bisect_right
N, K = map(int, input().split())
A = [-float('inf')]+list(map(int, input().split()))+[float('inf')]
if K:
B = [0]+list(map(int, input().split()))+[N+1]
else:
B = [0,N+1]
ans = N-K
for k in range(K+1):
left, right = B[k], B[k+1]
if A[left]>=A[right]:
print(-1)
break
lis = []
for i in range(left+1,right):
if not A[left]-left<=A[i]-i<=A[right]-right:
continue
ind = bisect_right(lis,A[i]-i)
if ind == len(lis):
lis.append(A[i]-i)
else:
lis[ind] = A[i]-i
ans -= len(lis)
else:
print(ans)
```
No
| 102,249 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of n integers a_1, a_2, ..., a_n, and a set b of k distinct integers from 1 to n.
In one operation, you may choose two integers i and x (1 ≤ i ≤ n, x can be any integer) and assign a_i := x. This operation can be done only if i does not belong to the set b.
Calculate the minimum number of operations you should perform so the array a is increasing (that is, a_1 < a_2 < a_3 < ... < a_n), or report that it is impossible.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ n) — the size of the array a and the set b, respectively.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).
Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.
Output
If it is impossible to make the array a increasing using the given operations, print -1.
Otherwise, print one integer — the minimum number of operations you have to perform.
Examples
Input
7 2
1 2 1 1 3 5 1
3 5
Output
4
Input
3 3
1 3 2
1 2 3
Output
-1
Input
5 0
4 3 1 2 3
Output
2
Input
10 3
1 3 5 6 12 9 8 10 13 15
2 4 9
Output
3
Submitted Solution:
```
maxn=1e6+10
a=list()
l=list()
b=list()
b1=list()
lasb=0
ban=list()
for i in range(1000010):
ban.append(0)
l.append(0)
s1=input()
w=s1.split(' ')
n=int(w[0])
k=int(w[1])
a.append(0)
b.append(0)
s2=input()
w2=s2.split(' ')
for i in range(n):
a.append(int(w2[i]))
if k!=0:
s3 = input()
w3 = s3.split(' ')
for i in range(k):
b1.append(int(w3[i]))
b1.sort()
for i in range(k):
b.append(b1[i])
ban[b1[i]]=1
f=True
for i in range(2,k+1):
if a[b[i-1]]-b[i-1]>a[b[i]]-b[i]:
print(-1)
f=False
if f:
e = 0
for i in range(1, n + 1):
a[i] -= i
for i in range(1, n + 1):
if e == 0 or a[i] >= l[e]:
e = e + 1
l[e] = a[i]
if (ban[i] == 1):
lasb = e
else:
flag = False
c = list()
for k in range(e):
c.append(l[k + 1])
for v in range(e):
if l[v] > a[i]:
break
p = v+1
if p <= lasb:
continue
l[p] = a[i]
if ban[i] == 1:
lasb = p
e = p
print(n - e)
```
No
| 102,250 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of n integers a_1, a_2, ..., a_n, and a set b of k distinct integers from 1 to n.
In one operation, you may choose two integers i and x (1 ≤ i ≤ n, x can be any integer) and assign a_i := x. This operation can be done only if i does not belong to the set b.
Calculate the minimum number of operations you should perform so the array a is increasing (that is, a_1 < a_2 < a_3 < ... < a_n), or report that it is impossible.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ n) — the size of the array a and the set b, respectively.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).
Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.
Output
If it is impossible to make the array a increasing using the given operations, print -1.
Otherwise, print one integer — the minimum number of operations you have to perform.
Examples
Input
7 2
1 2 1 1 3 5 1
3 5
Output
4
Input
3 3
1 3 2
1 2 3
Output
-1
Input
5 0
4 3 1 2 3
Output
2
Input
10 3
1 3 5 6 12 9 8 10 13 15
2 4 9
Output
3
Submitted Solution:
```
import bisect
one, two = map(int, input().split())
arr = list(map(int, input().split()))
if two == 0:
second = list()
else:
second = list(map(int, input().split()))
res = 0
second = [0] + second + [one + 1]
count = second[0]
num = arr[0]
arr = [-10 ** 10] + arr + [10 ** 10]
flag = 1
def judge(num):
n = len(num)
ls = list()
num = [(num[i] - i) for i in range(n)]
for i in range(n):
if (num[i] < num[0] or num[i] > num[n - 1]):
continue
k = bisect.bisect_right(ls, num[i])
if k == len(ls):
ls.append(num[i])
else:
ls[k] = num[i]
ans = n - len(ls)
return ans
for j in second[1:]:
if j - count > arr[j] - num:
flag = 0
break
res += judge(arr[count:j + 1])
count, num = j, arr[j]
if flag:
print(res)
else:
print(-1)
```
No
| 102,251 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of n integers a_1, a_2, ..., a_n, and a set b of k distinct integers from 1 to n.
In one operation, you may choose two integers i and x (1 ≤ i ≤ n, x can be any integer) and assign a_i := x. This operation can be done only if i does not belong to the set b.
Calculate the minimum number of operations you should perform so the array a is increasing (that is, a_1 < a_2 < a_3 < ... < a_n), or report that it is impossible.
Input
The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ n) — the size of the array a and the set b, respectively.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).
Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.
Output
If it is impossible to make the array a increasing using the given operations, print -1.
Otherwise, print one integer — the minimum number of operations you have to perform.
Examples
Input
7 2
1 2 1 1 3 5 1
3 5
Output
4
Input
3 3
1 3 2
1 2 3
Output
-1
Input
5 0
4 3 1 2 3
Output
2
Input
10 3
1 3 5 6 12 9 8 10 13 15
2 4 9
Output
3
Submitted Solution:
```
import sys, math
import io, os
#data = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
from bisect import bisect_left as bl, bisect_right as br, insort
from heapq import heapify, heappush, heappop
from collections import defaultdict as dd, deque, Counter
from itertools import permutations,combinations
def data(): return sys.stdin.readline().strip()
def mdata(): return list(map(int, data().split()))
def outl(var) : sys.stdout.write(' '.join(map(str, var))+'\n')
def out(var) : sys.stdout.write(str(var)+'\n')
#from decimal import Decimal
#from fractions import Fraction
#sys.setrecursionlimit(100000)
INF = 10**9
mod = int(1e9)+7
def CeilIndex(A, l, r, key):
while (r - l > 1):
m = l + (r - l) // 2
if (A[m] >= key):
r = m
else:
l = m
return r
def LongestIncreasingSubsequenceLength(A, size, s, e):
tailTable = [0 for i in range(e-s+1)]
ind = [0 for i in range(e-s+1)]
len = 0
tailTable[0] = A[s]
ind[0] = s
len = 1
for i in range(s+1, e):
if A[s]+i-s<=A[i]<=A[e]+i-e :
if (A[i] > tailTable[len - 1]):
if i-ind[len-1]<=A[i]-tailTable[len - 1]:
tailTable[len] = A[i]
ind[len] = i
len += 1
else:
ind1=CeilIndex(tailTable, -1, len - 1, A[i])
if i-ind[ind1]<=A[i]-tailTable[ind1 - 1]:
tailTable[ind1] = A[i]
ind[ind1]=i
return len-1
n,k=mdata()
a=[-INF]+mdata()+[INF]
b=[0]
if k:
b+=sorted(mdata())
b+=[n+1]
for i in range(k+1):
if a[b[i+1]]-a[b[i]]<b[i+1]-b[i]:
out(-1)
exit()
ans=0
for i in range(k+1):
ans+=b[i+1]-b[i]-1-LongestIncreasingSubsequenceLength(a,n+2,b[i],b[i+1])
out(ans)
```
No
| 102,252 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique).
Input
The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow.
Each test case consists of a single integer number x (1 ≤ x ≤ 50).
Output
Output t answers to the test cases:
* if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number;
* otherwise print -1.
Example
Input
4
1
5
15
50
Output
1
5
69
-1
Tags: brute force, greedy, math
Correct Solution:
```
resList = []
testCount = int(input())
for test in range(testCount):
num = int(input())
sum = 0
numStr=""
if(num>45):
resList.append(str(-1))
elif(len(str(num)) == 1):
resList.append(str(num))
else:
for i in reversed(range(1,10)):
if(num == 0):
break
elif(num < i):
sum = sum + num
numStr += str(num)
break
sum = sum + i
num = num - i
numStr += str(i)
resList.append(numStr[::-1])
for res in resList:
print(res)
```
| 102,253 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique).
Input
The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow.
Each test case consists of a single integer number x (1 ≤ x ≤ 50).
Output
Output t answers to the test cases:
* if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number;
* otherwise print -1.
Example
Input
4
1
5
15
50
Output
1
5
69
-1
Tags: brute force, greedy, math
Correct Solution:
```
def suma(n):
s=0
while n!=0 :
s=s+n%10
n=n//10
return s
te=int(input())
for i in range(te):
num=int(input())
res="987654321"
if num>45:
print("-1")
else:
for i in range(100):
if res[-1]=="0":
res=res[:-1]
if suma(int(res))==num:
print(res[::-1])
break
res=str(int(res)-1)
```
| 102,254 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique).
Input
The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow.
Each test case consists of a single integer number x (1 ≤ x ≤ 50).
Output
Output t answers to the test cases:
* if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number;
* otherwise print -1.
Example
Input
4
1
5
15
50
Output
1
5
69
-1
Tags: brute force, greedy, math
Correct Solution:
```
for _ in range (int(input())):
n=int(input())
if n==43:
print("13456789")
continue
elif n==44:
print("23456789")
continue
elif n==45:
print("123456789")
continue
s=set()
curr=9
num=0
copy=n
ch=1
while n>9:
if curr<1:
ch=0
break
num=num*10+curr
s.add(curr)
n-=curr
curr-=1
if ch==0:
print(-1)
elif n in s:
num=num*10+curr
s.add(curr)
n-=curr
curr-=1
if n in s:
print(-1)
else:
num=num*10+n
num=str(num)
num=num[::-1]
print(num)
else:
num=num*10+n
num=str(num)
num=num[::-1]
print(num)
```
| 102,255 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique).
Input
The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow.
Each test case consists of a single integer number x (1 ≤ x ≤ 50).
Output
Output t answers to the test cases:
* if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number;
* otherwise print -1.
Example
Input
4
1
5
15
50
Output
1
5
69
-1
Tags: brute force, greedy, math
Correct Solution:
```
t = int(input())
for _ in range(t):
x = int(input())
if x > 45:
print(-1)
else:
l = 0
while l*(l+1)//2+((9-l)*l) < x:
l += 1
s = []
for i in range(10-l, 10):
s += [i]
while sum(s)>x:
s[0] -= 1
for i in s:
print(i, end='')
print()
```
| 102,256 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique).
Input
The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow.
Each test case consists of a single integer number x (1 ≤ x ≤ 50).
Output
Output t answers to the test cases:
* if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number;
* otherwise print -1.
Example
Input
4
1
5
15
50
Output
1
5
69
-1
Tags: brute force, greedy, math
Correct Solution:
```
# cook your dish here
from sys import stdin, stdout
import math
from itertools import permutations, combinations
from collections import defaultdict
from collections import Counter
from bisect import bisect_left
import sys
from queue import PriorityQueue
import operator as op
from functools import reduce
import re
mod = 1000000007
input = sys.stdin.readline
def L():
return list(map(int, stdin.readline().split()))
def In():
return map(int, stdin.readline().split())
def I():
return int(stdin.readline())
def printIn(ob):
return stdout.write(str(ob) + '\n')
def powerLL(n, p):
result = 1
while (p):
if (p & 1):
result = result * n % mod
p = int(p / 2)
n = n * n % mod
return result
def ncr(n, r):
r = min(r, n - r)
numer = reduce(op.mul, range(n, n - r, -1), 1)
denom = reduce(op.mul, range(1, r + 1), 1)
return numer // denom
def SieveOfEratosthenes(n):
# Create a boolean array "prime[0..n]" and initialize
# all entries it as true. A value in prime[i] will
# finally be false if i is Not a prime, else true.
prime_list = []
prime = [True for i in range(n+1)]
p = 2
while (p * p <= n):
# If prime[p] is not changed, then it is a prime
if (prime[p] == True):
prime_list.append(p)
# Update all multiples of p
for i in range(p * p, n+1, p):
prime[i] = False
p += 1
return prime_list
def get_divisors(n):
for i in range(1, int(n / 2) + 1):
if n % i == 0:
yield i
yield n
# -------------------------------------
def myCode():
n = I()
if n<=9:
print(n)
elif n>=10 and n<=17:
for i in ("12345678"):
if int(i)+9 == n:
print(i+str(9))
break
elif n>=18 and n<=24:
for i in ("1234567"):
if int(i)+8+9 == n:
print(i+str(89))
break
elif n>=25 and n<=30:
for i in ("123456"):
if int(i)+7+8+9 == n:
print(i+str(789))
break
elif n>=31 and n<=35:
for i in ("12345"):
if int(i)+6+7+8+9 == n:
print(i+str(6789))
break
elif n>=36 and n<=39:
for i in ("1234"):
if int(i)+5+6+7+8+9 == n:
print(i+str(56789))
break
elif n>=40 and n<=42:
for i in ("123"):
if int(i)+4+5+6+7+8+9 == n:
print(i+str(456789))
break
elif n>=43 and n<=44:
for i in ("12"):
if int(i)+3+4+5+6+7+8+9 == n:
print(i+str(3456789))
break
elif n==45:
print(123456789)
else:
print(-1)
def main():
for t in range(I()):
myCode()
if __name__ == '__main__':
# print(int(math.log2(10)))
main()
```
| 102,257 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique).
Input
The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow.
Each test case consists of a single integer number x (1 ≤ x ≤ 50).
Output
Output t answers to the test cases:
* if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number;
* otherwise print -1.
Example
Input
4
1
5
15
50
Output
1
5
69
-1
Tags: brute force, greedy, math
Correct Solution:
```
import collections
from collections import defaultdict
for _ in range(int(input())):
n=int(input())
#s=input()
#n,q=[int(x) for x in input().split()]
if n>45:
print(-1)
continue
if n<10:
print(n)
continue
z = list(range(9,0,-1))
s = 0
ans=[]
for x in z:
if s+x<=n:
ans.append(x)
s+=x
ans=[str(x) for x in ans]
ans.sort()
print("".join(ans))
```
| 102,258 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique).
Input
The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow.
Each test case consists of a single integer number x (1 ≤ x ≤ 50).
Output
Output t answers to the test cases:
* if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number;
* otherwise print -1.
Example
Input
4
1
5
15
50
Output
1
5
69
-1
Tags: brute force, greedy, math
Correct Solution:
```
'''input
1
46
'''
T = int(input())
while T:
dig = 9
ans = ''
x = int(input())
dig = list(range(9,0,-1))
if(x > 45):
print(-1)
T -= 1
continue
for i in dig:
if(x >= i):
ans += str(i)
x -= i
print(ans[::-1])
T -= 1
```
| 102,259 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique).
Input
The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow.
Each test case consists of a single integer number x (1 ≤ x ≤ 50).
Output
Output t answers to the test cases:
* if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number;
* otherwise print -1.
Example
Input
4
1
5
15
50
Output
1
5
69
-1
Tags: brute force, greedy, math
Correct Solution:
```
"""
pppppppppppppppppppp
ppppp ppppppppppppppppppp
ppppppp ppppppppppppppppppppp
pppppppp pppppppppppppppppppppp
pppppppppppppppppppppppppppppppp
pppppppppppppppppppppppp
ppppppppppppppppppppppppppppppppppppppppppppppp pppppppppppppppppppp
pppppppppppppppppppppppppppppppppppppppppppppppp ppppppppppppppppppppp
ppppppppppppppppppppppppppppppppppppppppppppppppp pppppppppppppppppppppp
ppppppppppppppppppppppppppppppppppppppppppppppp pppppppppppppppppppppppp
pppppppppppppppppppppppppppppppppppppppppppppp pppppppppppppppppppppppppp
ppppppppppppppppppppppppppppppppppppppppppppp pppppppppppppppppppppppppppp
pppppppppppppppppppppppppppppppp pppppppppppppppppppppppppppppppp
pppppppppppppppppppppppppppp pppppppppppppppppppppppppppppppppppppppppppppp
ppppppppppppppppppppppppppp pppppppppppppppppppppppppppppppppppppppppppppppp
pppppppppppppppppppppppp pppppppppppppppppppppppppppppppppppppppppppppppppp
ppppppppppppppppppppppp ppppppppppppppppppppppppppppppppppppppppppppppppp
pppppppppppppppppppppp ppppppppppppppppppppppppppppppppppppppppppppppp
ppppppppppppppppppppp ppppppppppppppppppppppppppppppppppppppppppppp
pppppppppppppppppppppppp
pppppppppppppppppppppppppppppppp
pppppppppppppppppppppp pppppppp
ppppppppppppppppppppp ppppppp
ppppppppppppppppppp ppppp
pppppppppppppppppppp
"""
import sys
from functools import lru_cache, cmp_to_key
from heapq import merge, heapify, heappop, heappush, nsmallest
from math import ceil, floor, gcd, fabs, factorial, fmod, sqrt, inf
from collections import defaultdict as dd, deque, Counter as C
from itertools import combinations as comb, permutations as perm
from bisect import bisect_left as bl, bisect_right as br, bisect
from time import perf_counter
from fractions import Fraction
from decimal import Decimal
# sys.setrecursionlimit(pow(10, 6))
# sys.stdin = open("input.txt", "r")
# sys.stdout = open("output.txt", "w")
mod = pow(10, 9) + 7
# mod2 = 998244353
def data(): return sys.stdin.readline().strip()
def out(var): sys.stdout.write(str(var)+"\n")
def outa(*var, end="\n"): sys.stdout.write(' '.join(map(str, var)) + end)
def l(): return list(sp())
def sl(): return list(ssp())
def sp(): return map(int, data().split())
def ssp(): return map(str, data().split())
def l1d(n, val=0): return [val for i in range(n)]
def l2d(n, m, val=0): return [l1d(n, val) for j in range(m)]
for _ in range(int(data())):
x = int(data())
if x > 45:
out(-1)
continue
answer = []
temp = 9
while x:
if x >= temp:
answer.append(str(temp))
x -= temp
temp -= 1
else:
answer.append(str(x))
break
out(''.join(answer[::-1]))
```
| 102,260 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique).
Input
The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow.
Each test case consists of a single integer number x (1 ≤ x ≤ 50).
Output
Output t answers to the test cases:
* if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number;
* otherwise print -1.
Example
Input
4
1
5
15
50
Output
1
5
69
-1
Submitted Solution:
```
import copy
import math
t = int(input())
for case in range(t):
n = int(input())
s =""
k = 9
if(n>45):
print(-1)
continue
while(n>0):
if n>=k:
n-=k
s+=str(k)
k-=1
else:
s+=str(n)
break
print(s[::-1])
```
Yes
| 102,261 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique).
Input
The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow.
Each test case consists of a single integer number x (1 ≤ x ≤ 50).
Output
Output t answers to the test cases:
* if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number;
* otherwise print -1.
Example
Input
4
1
5
15
50
Output
1
5
69
-1
Submitted Solution:
```
t = int(input())
while t:
t -= 1;
n = int(input())
if n>45:
print(-1)
continue
x = 0
i = 9
j = 0
while n:
z = min(n, i)
i-=1
x = x + z*(10**j)
n -= z
j += 1
print(x)
```
Yes
| 102,262 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique).
Input
The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow.
Each test case consists of a single integer number x (1 ≤ x ≤ 50).
Output
Output t answers to the test cases:
* if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number;
* otherwise print -1.
Example
Input
4
1
5
15
50
Output
1
5
69
-1
Submitted Solution:
```
def main():
n = int(input())
output = []
for i in range(n):
x = int(input())
y = x
for i in range(9, 0, -1):
if x - i >= 0:
output.append(i)
x -= i
if sum(output) != y:
print(-1)
else:
print("".join(sorted([str(x) for x in output])))
output = []
if __name__ == "__main__":
main()
```
Yes
| 102,263 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique).
Input
The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow.
Each test case consists of a single integer number x (1 ≤ x ≤ 50).
Output
Output t answers to the test cases:
* if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number;
* otherwise print -1.
Example
Input
4
1
5
15
50
Output
1
5
69
-1
Submitted Solution:
```
def f(x):
s=0
for i in range(10):
if x>=sum(range(i,10)):
s = sum(range(i,10))
break
if x == s:
return "".join(map(str,range(i,10)))
return "".join(map(str, sorted([x-s]+list(range(i,10)))))
t = int(input())
for _ in range(t):
x = int(input())
if x>45:
print(-1)
elif x==45:
print(123456789)
elif x<10:
print(x)
else:
print(f(x))
```
Yes
| 102,264 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique).
Input
The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow.
Each test case consists of a single integer number x (1 ≤ x ≤ 50).
Output
Output t answers to the test cases:
* if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number;
* otherwise print -1.
Example
Input
4
1
5
15
50
Output
1
5
69
-1
Submitted Solution:
```
t = int(input())
for i in range(t):
n = int(input())
e = [46,47,48,49,50]
if int(n/10)==0:
print(n)
elif n in e:
print(-1)
elif n>9 and n<18:
s=n%9
print(s*(10**1)+9)
elif n>17 and n<25:
s=n%17
print(s*(10**2)+89)
elif n>24 and n<31:
s=n%24
print(s*(10**3)+789)
elif n>30 and n<36:
s=n%30
print(s*(10**4)+6789)
elif n>35 and n<40:
s=n%35
print(s*(10**5)+56789)
elif n>39 and n<43:
s=n%39
print(s*(10**6)+456789)
elif n==44:
print(23456789)
else:
print(123456789)
```
No
| 102,265 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique).
Input
The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow.
Each test case consists of a single integer number x (1 ≤ x ≤ 50).
Output
Output t answers to the test cases:
* if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number;
* otherwise print -1.
Example
Input
4
1
5
15
50
Output
1
5
69
-1
Submitted Solution:
```
class var:
list = 50 * [-1]
def sod(n):
s = 0
for j in range(len(n)):
s += ord(n[j]) - 48
return s
def f(s):
val = sod(s)
if val <= 50:
if var.list[val - 1] == -1 or int(s) < var.list[val - 1]:
var.list[val - 1] = int(s)
for j in range(10):
if chr(j + 48) not in s:
f(s + chr(j + 48))
#for j in range(10):
#f(chr(j + 48))
#print(var.list)
List = [1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 29, 39, 49, 59, 69, 79, 89, 189, 289, 389, 489, 589, 689, 789, 1789, 2789, 3789, 4789, 5789, 6789, 16789, 26789, 36789, 46789, 56789, 156789, 256789, 356789, 456789, 1456789, 2456789, 3456789, 13456789, 23456789, 123456789, -1, -1, -1, -1, 0]
for _ in range(int(input())):
print(List[int(input()) - 1])
```
No
| 102,266 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique).
Input
The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow.
Each test case consists of a single integer number x (1 ≤ x ≤ 50).
Output
Output t answers to the test cases:
* if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number;
* otherwise print -1.
Example
Input
4
1
5
15
50
Output
1
5
69
-1
Submitted Solution:
```
from math import *
sInt = lambda: int(input())
mInt = lambda: map(int, input().split())
lInt = lambda: list(map(int, input().split()))
t = sInt()
for _ in range(t):
n = sInt()
if n>17:
print(-1)
elif n==1:
print(n)
else:
a = n//2-1
print(a,end='')
print(n-a)
```
No
| 102,267 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a positive number x. Find the smallest positive integer number that has the sum of digits equal to x and all digits are distinct (unique).
Input
The first line contains a single positive integer t (1 ≤ t ≤ 50) — the number of test cases in the test. Then t test cases follow.
Each test case consists of a single integer number x (1 ≤ x ≤ 50).
Output
Output t answers to the test cases:
* if a positive integer number with the sum of digits equal to x and all digits are different exists, print the smallest such number;
* otherwise print -1.
Example
Input
4
1
5
15
50
Output
1
5
69
-1
Submitted Solution:
```
t = int(input())
for test in range(0,t):
n = int(input())
if n>45:
print(-1)
elif len(str(n))==1:
print(n)
else:
s = ''
big = 9
while(len(str(n))>1):
n = n-big
s = s+str(big)
big = big-1
if n<=big:
s = s+str(n)
s = s[::-1]
print(int(s))
else:
k = n-big
s = s+str(big)+str(k)
s = s[::-1]
print(int(s))
```
No
| 102,268 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5).
Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b.
Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple.
When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.
Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).
Output
For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.
Example
Input
3
3
6
9
Output
0
1
1
Note
The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1.
Tags: binary search, brute force, math, number theory
Correct Solution:
```
import io,os, math
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
# python3 15.py<in>op
t = int(input())
for _ in range(t):
n = int(input())
ans = 0
i = 3
while((((i*i) + 1)//2) <=n):
ans+=1
i+=2
print(ans)
```
| 102,269 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5).
Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b.
Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple.
When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.
Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).
Output
For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.
Example
Input
3
3
6
9
Output
0
1
1
Note
The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1.
Tags: binary search, brute force, math, number theory
Correct Solution:
```
import math
t=int(input())
for _ in range (t):
n=int(input())
count=-1
k=1
i=1
z=int(math.sqrt(((n-1)/2)+0.25)-0.5)
print(z)
```
| 102,270 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5).
Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b.
Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple.
When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.
Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).
Output
For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.
Example
Input
3
3
6
9
Output
0
1
1
Note
The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1.
Tags: binary search, brute force, math, number theory
Correct Solution:
```
import bisect
from itertools import accumulate
import os
import sys
import math
from decimal import *
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
def input():
return sys.stdin.readline().rstrip("\r\n")
def isPrime(n):
if n <= 1:
return False
if n <= 3:
return True
if n % 2 == 0 or n % 3 == 0:
return False
i = 5
while i * i <= n:
if n % i == 0 or n % (i + 2) == 0:
return False
i = i + 6
return True
def SieveOfEratosthenes(n):
prime = []
primes = [True for i in range(n + 1)]
p = 2
while p * p <= n:
if primes[p] == True:
prime.append(p)
for i in range(p * p, n + 1, p):
primes[i] = False
p += 1
return prime
def primefactors(n):
fac = []
while n % 2 == 0:
fac.append(2)
n = n // 2
for i in range(3, int(math.sqrt(n)) + 2):
while n % i == 0:
fac.append(i)
n = n // i
if n > 1:
fac.append(n)
return sorted(fac)
def factors(n):
fac = set()
fac.add(1)
fac.add(n)
for i in range(2, int(math.sqrt(n)) + 1):
if n % i == 0:
fac.add(i)
fac.add(n // i)
return list(fac)
def modInverse(a, m):
m0 = m
y = 0
x = 1
if m == 1:
return 0
while a > 1:
q = a // m
t = m
m = a % m
a = t
t = y
y = x - q * y
x = t
if x < 0:
x = x + m0
return x
# ------------------------------------------------------code
for _ in range(int(input())):
n = int(input())
count = 0
i=3
while(i*i<=2*n-1):
count+=1
i+=2
print(count)
```
| 102,271 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5).
Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b.
Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple.
When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.
Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).
Output
For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.
Example
Input
3
3
6
9
Output
0
1
1
Note
The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1.
Tags: binary search, brute force, math, number theory
Correct Solution:
```
import math
for i in range(int(input())):
n=int(input())
print(math.floor(((math.sqrt(2*n-1)+1)//2)-1))
```
| 102,272 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5).
Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b.
Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple.
When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.
Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).
Output
For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.
Example
Input
3
3
6
9
Output
0
1
1
Note
The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1.
Tags: binary search, brute force, math, number theory
Correct Solution:
```
t=int(input())
for i in range(t):
n=int(input())
m=int(pow(2*n-1,0.5))
ans=(m+1)//2
print(ans-1)
```
| 102,273 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5).
Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b.
Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple.
When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.
Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).
Output
For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.
Example
Input
3
3
6
9
Output
0
1
1
Note
The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1.
Tags: binary search, brute force, math, number theory
Correct Solution:
```
t=int(input())
for i in range(t):
n=int(input())
m=int((2*n-1)**(1/2))
k=int((m-1)/2)
print(k)
```
| 102,274 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5).
Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b.
Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple.
When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.
Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).
Output
For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.
Example
Input
3
3
6
9
Output
0
1
1
Note
The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1.
Tags: binary search, brute force, math, number theory
Correct Solution:
```
import sys
input = sys.stdin.readline
t=int(input())
for _ in range(t):
n=int(input())
i=3
ans=0
#print(i*i-1)
while i<=n and ((i*i-1)//2)<=n:
#print('ads',_)
if (i*i-1)%2==0 and (i*i-1)//2>=i and i*i-(i*i-1)//2<=n:
#print(i,(i*i-1)//2)
ans+=1
i+=1
print(ans)
```
| 102,275 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5).
Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b.
Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple.
When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.
Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).
Output
For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.
Example
Input
3
3
6
9
Output
0
1
1
Note
The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1.
Tags: binary search, brute force, math, number theory
Correct Solution:
```
def answer(n):
l=int(((2*n)-1)**0.5)
c=0
for i in range(3,l+1,2):
c+=1
print(c)
t=int(input())
for i in range(t):
n=int(input())
answer(n)
```
| 102,276 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5).
Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b.
Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple.
When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.
Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).
Output
For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.
Example
Input
3
3
6
9
Output
0
1
1
Note
The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1.
Submitted Solution:
```
import sys
import math
import bisect
from sys import stdin, stdout
from math import gcd, floor, sqrt, log2, ceil
from collections import defaultdict as dd
from bisect import bisect_left as bl, bisect_right as br
from bisect import insort
from collections import Counter
from collections import deque
from heapq import heappush,heappop,heapify
from itertools import permutations,combinations
from itertools import accumulate as ac
mod = int(1e9)+7
#mod = 998244353
ip = lambda : int(stdin.readline())
inp = lambda: map(int,stdin.readline().split())
ips = lambda: stdin.readline().rstrip()
out = lambda x : stdout.write(str(x)+"\n")
t = int(input())
for _ in range(t) :
n = ip()
ans = 0
i = 3
while i*i<= 2*n -1:
ans += 1
i += 2
print(ans)
```
Yes
| 102,277 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5).
Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b.
Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple.
When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.
Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).
Output
For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.
Example
Input
3
3
6
9
Output
0
1
1
Note
The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1.
Submitted Solution:
```
import math
def solve(n,ans):
odd = int(math.ceil(n/2))
low = 0
high = odd
k = -1
while low <= high:
mid = (low+high)//2
sq = pow(2*mid+1,2)
b = sq//2
if b+1 <= n:
low = mid+1
k = mid
else:
high = mid-1
ans.append(str(k))
def main():
t = int(input())
ans = []
for i in range(t):
n = int(input())
solve(n,ans)
print('\n'.join(ans))
main()
```
Yes
| 102,278 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5).
Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b.
Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple.
When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.
Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).
Output
For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.
Example
Input
3
3
6
9
Output
0
1
1
Note
The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1.
Submitted Solution:
```
k = int(((10**9)*2 - 1)**0.5)
dp = [0]*(k+1)
for a in range(1,k+1):
if (a**2)%2!=0:
if a**2 - 1>0:
dp[a] = dp[a-1] + 1
else:
dp[a] = dp[a-1]
else:
dp[a] = dp[a-1]
#print(dp)
for _ in range(int(input())):
n = int(input())
n = int((2*n - 1)**0.5)
ans = dp[n]
print(ans)
```
Yes
| 102,279 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5).
Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b.
Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple.
When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.
Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).
Output
For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.
Example
Input
3
3
6
9
Output
0
1
1
Note
The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1.
Submitted Solution:
```
import os
import sys
from io import BytesIO, IOBase
import math
import itertools
import bisect
import heapq
def main():
pass
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
def binary(n):
return (bin(n).replace("0b", ""))
def decimal(s):
return (int(s, 2))
def pow2(n):
p = 0
while (n > 1):
n //= 2
p += 1
return (p)
def primeFactors(n):
l = []
while n % 2 == 0:
l.append(2)
n = n / 2
for i in range(3, int(math.sqrt(n)) + 1, 2):
while n % i == 0:
l.append(i)
n = n / i
if n > 2:
l.append(int(n))
return (l)
def isPrime(n):
if (n == 1):
return (False)
else:
root = int(n ** 0.5)
root += 1
for i in range(2, root):
if (n % i == 0):
return (False)
return (True)
def maxPrimeFactors(n):
maxPrime = -1
while n % 2 == 0:
maxPrime = 2
n >>= 1
for i in range(3, int(math.sqrt(n)) + 1, 2):
while n % i == 0:
maxPrime = i
n = n / i
if n > 2:
maxPrime = n
return int(maxPrime)
def countcon(s, i):
c = 0
ch = s[i]
for i in range(i, len(s)):
if (s[i] == ch):
c += 1
else:
break
return (c)
def lis(arr):
n = len(arr)
lis = [1] * n
for i in range(1, n):
for j in range(0, i):
if arr[i] > arr[j] and lis[i] < lis[j] + 1:
lis[i] = lis[j] + 1
maximum = 0
for i in range(n):
maximum = max(maximum, lis[i])
return maximum
def isSubSequence(str1, str2):
m = len(str1)
n = len(str2)
j = 0
i = 0
while j < m and i < n:
if str1[j] == str2[i]:
j = j + 1
i = i + 1
return j == m
def maxfac(n):
root = int(n ** 0.5)
for i in range(2, root + 1):
if (n % i == 0):
return (n // i)
return (n)
def p2(n):
c=0
while(n%2==0):
n//=2
c+=1
return c
def seive(n):
primes=[True]*(n+1)
primes[1]=primes[0]=False
for i in range(2,n+1):
if(primes[i]):
for j in range(i+i,n+1,i):
primes[j]=False
p=[]
for i in range(0,n+1):
if(primes[i]):
p.append(i)
return(p)
def ncr(n, r, p):
num = den = 1
for i in range(r):
num = (num * (n - i)) % p
den = (den * (i + 1)) % p
return (num * pow(den,
p - 2, p)) % p
def denofactinverse(n,m):
fac=1
for i in range(1,n+1):
fac=(fac*i)%m
return (pow(fac,m-2,m))
def numofact(n,m):
fac = 1
for i in range(1, n + 1):
fac = (fac * i) % m
return(fac)
for _ in range(0,int(input())):
n=int(input())
t=2*n-1
t=int(t**0.5)
#print(t)
print(math.ceil(t/2)-1)
```
Yes
| 102,280 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5).
Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b.
Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple.
When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.
Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).
Output
For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.
Example
Input
3
3
6
9
Output
0
1
1
Note
The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1.
Submitted Solution:
```
import math
for _ in range(int(input())):
n=int(input())
s=math.floor(math.sqrt(2*n))//2
print(s)
```
No
| 102,281 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5).
Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b.
Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple.
When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.
Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).
Output
For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.
Example
Input
3
3
6
9
Output
0
1
1
Note
The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1.
Submitted Solution:
```
import sys
import os.path
if(os.path.exists('input_file.txt')):
sys.stdin = open("input_file.txt", "r")
sys.stdout = open("output_file.txt", "w")
mod=1000000007
def factorial(a):
ans=1
for i in range(1,a+1):
ans=(ans*i)%mod
return ans
#perfectsuare, other shorthanded
for _ in range(int(input())):
n=int(input())
ans=int((2*n+1)**.5)
if ans%2==0: print((ans//2)-1)
else:print(ans//2)
```
No
| 102,282 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5).
Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b.
Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple.
When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.
Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).
Output
For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.
Example
Input
3
3
6
9
Output
0
1
1
Note
The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1.
Submitted Solution:
```
import math
i=2
x=int(999999999**0.5)+100
dp=[0,0]
ans=0
a=0
b=0
c=0
while(i<=x):
a=i
b=(a*a-1)//2
c=b+1
if a*a+b*b==c*c:
ans+=1
dp.append(ans)
i+=1
x=len(dp)
for _ in range(int(input())):
n=int(input())
print(dp[math.ceil(n**0.5)])
```
No
| 102,283 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of the Pythagorean triple is (3, 4, 5).
Vasya studies the properties of right triangles, and he uses a formula that determines if some triple of integers is Pythagorean. Unfortunately, he has forgotten the exact formula; he remembers only that the formula was some equation with squares. So, he came up with the following formula: c = a^2 - b.
Obviously, this is not the right formula to check if a triple of numbers is Pythagorean. But, to Vasya's surprise, it actually worked on the triple (3, 4, 5): 5 = 3^2 - 4, so, according to Vasya's formula, it is a Pythagorean triple.
When Vasya found the right formula (and understood that his formula is wrong), he wondered: how many are there triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean both according to his formula and the real definition? He asked you to count these triples.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.
Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).
Output
For each test case, print one integer — the number of triples of integers (a, b, c) with 1 ≤ a ≤ b ≤ c ≤ n such that they are Pythagorean according both to the real definition and to the formula Vasya came up with.
Example
Input
3
3
6
9
Output
0
1
1
Note
The only Pythagorean triple satisfying c = a^2 - b with 1 ≤ a ≤ b ≤ c ≤ 9 is (3, 4, 5); that's why the answer for n = 3 is 0, and the answer for n = 6 (and for n = 9) is 1.
Submitted Solution:
```
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
import math
t=int(input())
for _ in range(t):
n=int(input())
ans=0
for i in range(2,n+1):
x=2*i+1
s=math.sqrt(x)
if int(s+0.5)**2==x:
ans+=1
print(ans)
```
No
| 102,284 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are an upcoming movie director, and you have just released your first movie. You have also launched a simple review site with two buttons to press — upvote and downvote.
However, the site is not so simple on the inside. There are two servers, each with its separate counts for the upvotes and the downvotes.
n reviewers enter the site one by one. Each reviewer is one of the following types:
* type 1: a reviewer has watched the movie, and they like it — they press the upvote button;
* type 2: a reviewer has watched the movie, and they dislike it — they press the downvote button;
* type 3: a reviewer hasn't watched the movie — they look at the current number of upvotes and downvotes of the movie on the server they are in and decide what button to press. If there are more downvotes than upvotes, then a reviewer downvotes the movie. Otherwise, they upvote the movie.
Each reviewer votes on the movie exactly once.
Since you have two servers, you can actually manipulate the votes so that your movie gets as many upvotes as possible. When a reviewer enters a site, you know their type, and you can send them either to the first server or to the second one.
What is the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to?
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.
Then the descriptions of t testcases follow.
The first line of each testcase contains a single integer n (1 ≤ n ≤ 50) — the number of reviewers.
The second line of each testcase contains n integers r_1, r_2, ..., r_n (1 ≤ r_i ≤ 3) — the types of the reviewers in the same order they enter the site.
Output
For each testcase print a single integer — the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to.
Example
Input
4
1
2
3
1 2 3
5
1 1 1 1 1
3
3 3 2
Output
0
2
5
2
Note
In the first testcase of the example you can send the only reviewer to either of the servers — they'll downvote anyway. The movie won't receive any upvotes.
In the second testcase of the example you can send all reviewers to the first server:
* the first reviewer upvotes;
* the second reviewer downvotes;
* the last reviewer sees that the number of downvotes is not greater than the number of upvotes — upvote themselves.
There are two upvotes in total. Alternatevely, you can send the first and the second reviewers to the first server and the last reviewer — to the second server:
* the first reviewer upvotes on the first server;
* the second reviewer downvotes on the first server;
* the last reviewer sees no upvotes or downvotes on the second server — upvote themselves.
Tags: greedy
Correct Solution:
```
for i in range(int(input())): n=int(input()); print(n-input().split().count('2'))
```
| 102,285 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are an upcoming movie director, and you have just released your first movie. You have also launched a simple review site with two buttons to press — upvote and downvote.
However, the site is not so simple on the inside. There are two servers, each with its separate counts for the upvotes and the downvotes.
n reviewers enter the site one by one. Each reviewer is one of the following types:
* type 1: a reviewer has watched the movie, and they like it — they press the upvote button;
* type 2: a reviewer has watched the movie, and they dislike it — they press the downvote button;
* type 3: a reviewer hasn't watched the movie — they look at the current number of upvotes and downvotes of the movie on the server they are in and decide what button to press. If there are more downvotes than upvotes, then a reviewer downvotes the movie. Otherwise, they upvote the movie.
Each reviewer votes on the movie exactly once.
Since you have two servers, you can actually manipulate the votes so that your movie gets as many upvotes as possible. When a reviewer enters a site, you know their type, and you can send them either to the first server or to the second one.
What is the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to?
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.
Then the descriptions of t testcases follow.
The first line of each testcase contains a single integer n (1 ≤ n ≤ 50) — the number of reviewers.
The second line of each testcase contains n integers r_1, r_2, ..., r_n (1 ≤ r_i ≤ 3) — the types of the reviewers in the same order they enter the site.
Output
For each testcase print a single integer — the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to.
Example
Input
4
1
2
3
1 2 3
5
1 1 1 1 1
3
3 3 2
Output
0
2
5
2
Note
In the first testcase of the example you can send the only reviewer to either of the servers — they'll downvote anyway. The movie won't receive any upvotes.
In the second testcase of the example you can send all reviewers to the first server:
* the first reviewer upvotes;
* the second reviewer downvotes;
* the last reviewer sees that the number of downvotes is not greater than the number of upvotes — upvote themselves.
There are two upvotes in total. Alternatevely, you can send the first and the second reviewers to the first server and the last reviewer — to the second server:
* the first reviewer upvotes on the first server;
* the second reviewer downvotes on the first server;
* the last reviewer sees no upvotes or downvotes on the second server — upvote themselves.
Tags: greedy
Correct Solution:
```
for _ in range(int(input())):
n=int(input())
l=list(map(int,input().split()))
d={1:0,2:0,3:0}
for i in l:
d[i]+=1
print(d[1]+d[3])
```
| 102,286 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are an upcoming movie director, and you have just released your first movie. You have also launched a simple review site with two buttons to press — upvote and downvote.
However, the site is not so simple on the inside. There are two servers, each with its separate counts for the upvotes and the downvotes.
n reviewers enter the site one by one. Each reviewer is one of the following types:
* type 1: a reviewer has watched the movie, and they like it — they press the upvote button;
* type 2: a reviewer has watched the movie, and they dislike it — they press the downvote button;
* type 3: a reviewer hasn't watched the movie — they look at the current number of upvotes and downvotes of the movie on the server they are in and decide what button to press. If there are more downvotes than upvotes, then a reviewer downvotes the movie. Otherwise, they upvote the movie.
Each reviewer votes on the movie exactly once.
Since you have two servers, you can actually manipulate the votes so that your movie gets as many upvotes as possible. When a reviewer enters a site, you know their type, and you can send them either to the first server or to the second one.
What is the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to?
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.
Then the descriptions of t testcases follow.
The first line of each testcase contains a single integer n (1 ≤ n ≤ 50) — the number of reviewers.
The second line of each testcase contains n integers r_1, r_2, ..., r_n (1 ≤ r_i ≤ 3) — the types of the reviewers in the same order they enter the site.
Output
For each testcase print a single integer — the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to.
Example
Input
4
1
2
3
1 2 3
5
1 1 1 1 1
3
3 3 2
Output
0
2
5
2
Note
In the first testcase of the example you can send the only reviewer to either of the servers — they'll downvote anyway. The movie won't receive any upvotes.
In the second testcase of the example you can send all reviewers to the first server:
* the first reviewer upvotes;
* the second reviewer downvotes;
* the last reviewer sees that the number of downvotes is not greater than the number of upvotes — upvote themselves.
There are two upvotes in total. Alternatevely, you can send the first and the second reviewers to the first server and the last reviewer — to the second server:
* the first reviewer upvotes on the first server;
* the second reviewer downvotes on the first server;
* the last reviewer sees no upvotes or downvotes on the second server — upvote themselves.
Tags: greedy
Correct Solution:
```
from sys import stdin
input = stdin.readline
def solution():
N = int(input())
R = list(map(int, input().split()))
print(sum(r in [1, 3] for r in R))
if __name__ == '__main__':
T = int(input())
for _ in range(T):
solution()
```
| 102,287 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are an upcoming movie director, and you have just released your first movie. You have also launched a simple review site with two buttons to press — upvote and downvote.
However, the site is not so simple on the inside. There are two servers, each with its separate counts for the upvotes and the downvotes.
n reviewers enter the site one by one. Each reviewer is one of the following types:
* type 1: a reviewer has watched the movie, and they like it — they press the upvote button;
* type 2: a reviewer has watched the movie, and they dislike it — they press the downvote button;
* type 3: a reviewer hasn't watched the movie — they look at the current number of upvotes and downvotes of the movie on the server they are in and decide what button to press. If there are more downvotes than upvotes, then a reviewer downvotes the movie. Otherwise, they upvote the movie.
Each reviewer votes on the movie exactly once.
Since you have two servers, you can actually manipulate the votes so that your movie gets as many upvotes as possible. When a reviewer enters a site, you know their type, and you can send them either to the first server or to the second one.
What is the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to?
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.
Then the descriptions of t testcases follow.
The first line of each testcase contains a single integer n (1 ≤ n ≤ 50) — the number of reviewers.
The second line of each testcase contains n integers r_1, r_2, ..., r_n (1 ≤ r_i ≤ 3) — the types of the reviewers in the same order they enter the site.
Output
For each testcase print a single integer — the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to.
Example
Input
4
1
2
3
1 2 3
5
1 1 1 1 1
3
3 3 2
Output
0
2
5
2
Note
In the first testcase of the example you can send the only reviewer to either of the servers — they'll downvote anyway. The movie won't receive any upvotes.
In the second testcase of the example you can send all reviewers to the first server:
* the first reviewer upvotes;
* the second reviewer downvotes;
* the last reviewer sees that the number of downvotes is not greater than the number of upvotes — upvote themselves.
There are two upvotes in total. Alternatevely, you can send the first and the second reviewers to the first server and the last reviewer — to the second server:
* the first reviewer upvotes on the first server;
* the second reviewer downvotes on the first server;
* the last reviewer sees no upvotes or downvotes on the second server — upvote themselves.
Tags: greedy
Correct Solution:
```
# cook your dish here
for _ in range(int(input())):
n = int(input())
r = list(map(int,input().split()))
ans = 0
for x in r:
if x == 1 or x == 3:
ans += 1
print(ans)
```
| 102,288 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are an upcoming movie director, and you have just released your first movie. You have also launched a simple review site with two buttons to press — upvote and downvote.
However, the site is not so simple on the inside. There are two servers, each with its separate counts for the upvotes and the downvotes.
n reviewers enter the site one by one. Each reviewer is one of the following types:
* type 1: a reviewer has watched the movie, and they like it — they press the upvote button;
* type 2: a reviewer has watched the movie, and they dislike it — they press the downvote button;
* type 3: a reviewer hasn't watched the movie — they look at the current number of upvotes and downvotes of the movie on the server they are in and decide what button to press. If there are more downvotes than upvotes, then a reviewer downvotes the movie. Otherwise, they upvote the movie.
Each reviewer votes on the movie exactly once.
Since you have two servers, you can actually manipulate the votes so that your movie gets as many upvotes as possible. When a reviewer enters a site, you know their type, and you can send them either to the first server or to the second one.
What is the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to?
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.
Then the descriptions of t testcases follow.
The first line of each testcase contains a single integer n (1 ≤ n ≤ 50) — the number of reviewers.
The second line of each testcase contains n integers r_1, r_2, ..., r_n (1 ≤ r_i ≤ 3) — the types of the reviewers in the same order they enter the site.
Output
For each testcase print a single integer — the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to.
Example
Input
4
1
2
3
1 2 3
5
1 1 1 1 1
3
3 3 2
Output
0
2
5
2
Note
In the first testcase of the example you can send the only reviewer to either of the servers — they'll downvote anyway. The movie won't receive any upvotes.
In the second testcase of the example you can send all reviewers to the first server:
* the first reviewer upvotes;
* the second reviewer downvotes;
* the last reviewer sees that the number of downvotes is not greater than the number of upvotes — upvote themselves.
There are two upvotes in total. Alternatevely, you can send the first and the second reviewers to the first server and the last reviewer — to the second server:
* the first reviewer upvotes on the first server;
* the second reviewer downvotes on the first server;
* the last reviewer sees no upvotes or downvotes on the second server — upvote themselves.
Tags: greedy
Correct Solution:
```
for _ in range(int(input())):
n= int(input())
arr= list(map(int, input().split()))
res = 0
for i in arr:
if i ==1 or i==3:
res+= 1
print(res)
```
| 102,289 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are an upcoming movie director, and you have just released your first movie. You have also launched a simple review site with two buttons to press — upvote and downvote.
However, the site is not so simple on the inside. There are two servers, each with its separate counts for the upvotes and the downvotes.
n reviewers enter the site one by one. Each reviewer is one of the following types:
* type 1: a reviewer has watched the movie, and they like it — they press the upvote button;
* type 2: a reviewer has watched the movie, and they dislike it — they press the downvote button;
* type 3: a reviewer hasn't watched the movie — they look at the current number of upvotes and downvotes of the movie on the server they are in and decide what button to press. If there are more downvotes than upvotes, then a reviewer downvotes the movie. Otherwise, they upvote the movie.
Each reviewer votes on the movie exactly once.
Since you have two servers, you can actually manipulate the votes so that your movie gets as many upvotes as possible. When a reviewer enters a site, you know their type, and you can send them either to the first server or to the second one.
What is the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to?
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.
Then the descriptions of t testcases follow.
The first line of each testcase contains a single integer n (1 ≤ n ≤ 50) — the number of reviewers.
The second line of each testcase contains n integers r_1, r_2, ..., r_n (1 ≤ r_i ≤ 3) — the types of the reviewers in the same order they enter the site.
Output
For each testcase print a single integer — the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to.
Example
Input
4
1
2
3
1 2 3
5
1 1 1 1 1
3
3 3 2
Output
0
2
5
2
Note
In the first testcase of the example you can send the only reviewer to either of the servers — they'll downvote anyway. The movie won't receive any upvotes.
In the second testcase of the example you can send all reviewers to the first server:
* the first reviewer upvotes;
* the second reviewer downvotes;
* the last reviewer sees that the number of downvotes is not greater than the number of upvotes — upvote themselves.
There are two upvotes in total. Alternatevely, you can send the first and the second reviewers to the first server and the last reviewer — to the second server:
* the first reviewer upvotes on the first server;
* the second reviewer downvotes on the first server;
* the last reviewer sees no upvotes or downvotes on the second server — upvote themselves.
Tags: greedy
Correct Solution:
```
t = int(input())
while t > 0:
t -= 1
n = int(input())
reviewer = [int(i) for i in input().strip().split(" ")]
countLikes = 0
countDisLikes = 0
for r in reviewer:
if r == 1:
countLikes += 1
elif r == 2:
countDisLikes += 1
else:
# if r == 3:
# if countLikes >= countDisLikes:
countLikes += 1
# else:
# countDisLikes += 1
print(f"{countLikes}")
```
| 102,290 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are an upcoming movie director, and you have just released your first movie. You have also launched a simple review site with two buttons to press — upvote and downvote.
However, the site is not so simple on the inside. There are two servers, each with its separate counts for the upvotes and the downvotes.
n reviewers enter the site one by one. Each reviewer is one of the following types:
* type 1: a reviewer has watched the movie, and they like it — they press the upvote button;
* type 2: a reviewer has watched the movie, and they dislike it — they press the downvote button;
* type 3: a reviewer hasn't watched the movie — they look at the current number of upvotes and downvotes of the movie on the server they are in and decide what button to press. If there are more downvotes than upvotes, then a reviewer downvotes the movie. Otherwise, they upvote the movie.
Each reviewer votes on the movie exactly once.
Since you have two servers, you can actually manipulate the votes so that your movie gets as many upvotes as possible. When a reviewer enters a site, you know their type, and you can send them either to the first server or to the second one.
What is the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to?
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.
Then the descriptions of t testcases follow.
The first line of each testcase contains a single integer n (1 ≤ n ≤ 50) — the number of reviewers.
The second line of each testcase contains n integers r_1, r_2, ..., r_n (1 ≤ r_i ≤ 3) — the types of the reviewers in the same order they enter the site.
Output
For each testcase print a single integer — the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to.
Example
Input
4
1
2
3
1 2 3
5
1 1 1 1 1
3
3 3 2
Output
0
2
5
2
Note
In the first testcase of the example you can send the only reviewer to either of the servers — they'll downvote anyway. The movie won't receive any upvotes.
In the second testcase of the example you can send all reviewers to the first server:
* the first reviewer upvotes;
* the second reviewer downvotes;
* the last reviewer sees that the number of downvotes is not greater than the number of upvotes — upvote themselves.
There are two upvotes in total. Alternatevely, you can send the first and the second reviewers to the first server and the last reviewer — to the second server:
* the first reviewer upvotes on the first server;
* the second reviewer downvotes on the first server;
* the last reviewer sees no upvotes or downvotes on the second server — upvote themselves.
Tags: greedy
Correct Solution:
```
from sys import stdin,stdout
stdin.readline
def mp(): return list(map(int, stdin.readline().strip().split()))
def it():return int(stdin.readline().strip())
from collections import defaultdict as dd,Counter as C,deque
from math import ceil,gcd,sqrt,factorial
for _ in range(it()):
n = it()
l = mp()
u = 0
for i in range(n):
if l[i] == 1 or l[i] == 3:
u += 1
print(u)
```
| 102,291 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are an upcoming movie director, and you have just released your first movie. You have also launched a simple review site with two buttons to press — upvote and downvote.
However, the site is not so simple on the inside. There are two servers, each with its separate counts for the upvotes and the downvotes.
n reviewers enter the site one by one. Each reviewer is one of the following types:
* type 1: a reviewer has watched the movie, and they like it — they press the upvote button;
* type 2: a reviewer has watched the movie, and they dislike it — they press the downvote button;
* type 3: a reviewer hasn't watched the movie — they look at the current number of upvotes and downvotes of the movie on the server they are in and decide what button to press. If there are more downvotes than upvotes, then a reviewer downvotes the movie. Otherwise, they upvote the movie.
Each reviewer votes on the movie exactly once.
Since you have two servers, you can actually manipulate the votes so that your movie gets as many upvotes as possible. When a reviewer enters a site, you know their type, and you can send them either to the first server or to the second one.
What is the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to?
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.
Then the descriptions of t testcases follow.
The first line of each testcase contains a single integer n (1 ≤ n ≤ 50) — the number of reviewers.
The second line of each testcase contains n integers r_1, r_2, ..., r_n (1 ≤ r_i ≤ 3) — the types of the reviewers in the same order they enter the site.
Output
For each testcase print a single integer — the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to.
Example
Input
4
1
2
3
1 2 3
5
1 1 1 1 1
3
3 3 2
Output
0
2
5
2
Note
In the first testcase of the example you can send the only reviewer to either of the servers — they'll downvote anyway. The movie won't receive any upvotes.
In the second testcase of the example you can send all reviewers to the first server:
* the first reviewer upvotes;
* the second reviewer downvotes;
* the last reviewer sees that the number of downvotes is not greater than the number of upvotes — upvote themselves.
There are two upvotes in total. Alternatevely, you can send the first and the second reviewers to the first server and the last reviewer — to the second server:
* the first reviewer upvotes on the first server;
* the second reviewer downvotes on the first server;
* the last reviewer sees no upvotes or downvotes on the second server — upvote themselves.
Tags: greedy
Correct Solution:
```
t = int(input())
for _ in range(t):
n = int(input())
ans = 0
a = [int(i) for i in input().split()]
for i in a:
if i == 1 or i == 3:
ans += 1
print(ans)
```
| 102,292 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are an upcoming movie director, and you have just released your first movie. You have also launched a simple review site with two buttons to press — upvote and downvote.
However, the site is not so simple on the inside. There are two servers, each with its separate counts for the upvotes and the downvotes.
n reviewers enter the site one by one. Each reviewer is one of the following types:
* type 1: a reviewer has watched the movie, and they like it — they press the upvote button;
* type 2: a reviewer has watched the movie, and they dislike it — they press the downvote button;
* type 3: a reviewer hasn't watched the movie — they look at the current number of upvotes and downvotes of the movie on the server they are in and decide what button to press. If there are more downvotes than upvotes, then a reviewer downvotes the movie. Otherwise, they upvote the movie.
Each reviewer votes on the movie exactly once.
Since you have two servers, you can actually manipulate the votes so that your movie gets as many upvotes as possible. When a reviewer enters a site, you know their type, and you can send them either to the first server or to the second one.
What is the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to?
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.
Then the descriptions of t testcases follow.
The first line of each testcase contains a single integer n (1 ≤ n ≤ 50) — the number of reviewers.
The second line of each testcase contains n integers r_1, r_2, ..., r_n (1 ≤ r_i ≤ 3) — the types of the reviewers in the same order they enter the site.
Output
For each testcase print a single integer — the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to.
Example
Input
4
1
2
3
1 2 3
5
1 1 1 1 1
3
3 3 2
Output
0
2
5
2
Note
In the first testcase of the example you can send the only reviewer to either of the servers — they'll downvote anyway. The movie won't receive any upvotes.
In the second testcase of the example you can send all reviewers to the first server:
* the first reviewer upvotes;
* the second reviewer downvotes;
* the last reviewer sees that the number of downvotes is not greater than the number of upvotes — upvote themselves.
There are two upvotes in total. Alternatevely, you can send the first and the second reviewers to the first server and the last reviewer — to the second server:
* the first reviewer upvotes on the first server;
* the second reviewer downvotes on the first server;
* the last reviewer sees no upvotes or downvotes on the second server — upvote themselves.
Submitted Solution:
```
t = int(input().rstrip())
for _ in range(t):
n = int(input().rstrip())
list1 = list(map(int, input().rstrip().split(" ")))
max1 = 0
count1 = 0
count2 = 0
for i in list1:
if i == 1:
count1 += 1
max1 = max([max1, count1])
elif i == 3:
count1 += 1
print(count1)
```
Yes
| 102,293 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are an upcoming movie director, and you have just released your first movie. You have also launched a simple review site with two buttons to press — upvote and downvote.
However, the site is not so simple on the inside. There are two servers, each with its separate counts for the upvotes and the downvotes.
n reviewers enter the site one by one. Each reviewer is one of the following types:
* type 1: a reviewer has watched the movie, and they like it — they press the upvote button;
* type 2: a reviewer has watched the movie, and they dislike it — they press the downvote button;
* type 3: a reviewer hasn't watched the movie — they look at the current number of upvotes and downvotes of the movie on the server they are in and decide what button to press. If there are more downvotes than upvotes, then a reviewer downvotes the movie. Otherwise, they upvote the movie.
Each reviewer votes on the movie exactly once.
Since you have two servers, you can actually manipulate the votes so that your movie gets as many upvotes as possible. When a reviewer enters a site, you know their type, and you can send them either to the first server or to the second one.
What is the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to?
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.
Then the descriptions of t testcases follow.
The first line of each testcase contains a single integer n (1 ≤ n ≤ 50) — the number of reviewers.
The second line of each testcase contains n integers r_1, r_2, ..., r_n (1 ≤ r_i ≤ 3) — the types of the reviewers in the same order they enter the site.
Output
For each testcase print a single integer — the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to.
Example
Input
4
1
2
3
1 2 3
5
1 1 1 1 1
3
3 3 2
Output
0
2
5
2
Note
In the first testcase of the example you can send the only reviewer to either of the servers — they'll downvote anyway. The movie won't receive any upvotes.
In the second testcase of the example you can send all reviewers to the first server:
* the first reviewer upvotes;
* the second reviewer downvotes;
* the last reviewer sees that the number of downvotes is not greater than the number of upvotes — upvote themselves.
There are two upvotes in total. Alternatevely, you can send the first and the second reviewers to the first server and the last reviewer — to the second server:
* the first reviewer upvotes on the first server;
* the second reviewer downvotes on the first server;
* the last reviewer sees no upvotes or downvotes on the second server — upvote themselves.
Submitted Solution:
```
def ints():
return list(map(int, input().split()))
def case():
n, = ints()
r = ints()
return n - r.count(2)
t, = ints()
for i in range(t):
print(case())
```
Yes
| 102,294 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are an upcoming movie director, and you have just released your first movie. You have also launched a simple review site with two buttons to press — upvote and downvote.
However, the site is not so simple on the inside. There are two servers, each with its separate counts for the upvotes and the downvotes.
n reviewers enter the site one by one. Each reviewer is one of the following types:
* type 1: a reviewer has watched the movie, and they like it — they press the upvote button;
* type 2: a reviewer has watched the movie, and they dislike it — they press the downvote button;
* type 3: a reviewer hasn't watched the movie — they look at the current number of upvotes and downvotes of the movie on the server they are in and decide what button to press. If there are more downvotes than upvotes, then a reviewer downvotes the movie. Otherwise, they upvote the movie.
Each reviewer votes on the movie exactly once.
Since you have two servers, you can actually manipulate the votes so that your movie gets as many upvotes as possible. When a reviewer enters a site, you know their type, and you can send them either to the first server or to the second one.
What is the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to?
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.
Then the descriptions of t testcases follow.
The first line of each testcase contains a single integer n (1 ≤ n ≤ 50) — the number of reviewers.
The second line of each testcase contains n integers r_1, r_2, ..., r_n (1 ≤ r_i ≤ 3) — the types of the reviewers in the same order they enter the site.
Output
For each testcase print a single integer — the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to.
Example
Input
4
1
2
3
1 2 3
5
1 1 1 1 1
3
3 3 2
Output
0
2
5
2
Note
In the first testcase of the example you can send the only reviewer to either of the servers — they'll downvote anyway. The movie won't receive any upvotes.
In the second testcase of the example you can send all reviewers to the first server:
* the first reviewer upvotes;
* the second reviewer downvotes;
* the last reviewer sees that the number of downvotes is not greater than the number of upvotes — upvote themselves.
There are two upvotes in total. Alternatevely, you can send the first and the second reviewers to the first server and the last reviewer — to the second server:
* the first reviewer upvotes on the first server;
* the second reviewer downvotes on the first server;
* the last reviewer sees no upvotes or downvotes on the second server — upvote themselves.
Submitted Solution:
```
from collections import Counter
from itertools import permutations
def getlist():
return list(map(int,input().split()))
def main():
t = int(input())
for num in range(t):
n = int(input())
arr = getlist()
count = Counter(arr)
down = count[2]
print(n-down)
main()
```
Yes
| 102,295 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are an upcoming movie director, and you have just released your first movie. You have also launched a simple review site with two buttons to press — upvote and downvote.
However, the site is not so simple on the inside. There are two servers, each with its separate counts for the upvotes and the downvotes.
n reviewers enter the site one by one. Each reviewer is one of the following types:
* type 1: a reviewer has watched the movie, and they like it — they press the upvote button;
* type 2: a reviewer has watched the movie, and they dislike it — they press the downvote button;
* type 3: a reviewer hasn't watched the movie — they look at the current number of upvotes and downvotes of the movie on the server they are in and decide what button to press. If there are more downvotes than upvotes, then a reviewer downvotes the movie. Otherwise, they upvote the movie.
Each reviewer votes on the movie exactly once.
Since you have two servers, you can actually manipulate the votes so that your movie gets as many upvotes as possible. When a reviewer enters a site, you know their type, and you can send them either to the first server or to the second one.
What is the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to?
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.
Then the descriptions of t testcases follow.
The first line of each testcase contains a single integer n (1 ≤ n ≤ 50) — the number of reviewers.
The second line of each testcase contains n integers r_1, r_2, ..., r_n (1 ≤ r_i ≤ 3) — the types of the reviewers in the same order they enter the site.
Output
For each testcase print a single integer — the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to.
Example
Input
4
1
2
3
1 2 3
5
1 1 1 1 1
3
3 3 2
Output
0
2
5
2
Note
In the first testcase of the example you can send the only reviewer to either of the servers — they'll downvote anyway. The movie won't receive any upvotes.
In the second testcase of the example you can send all reviewers to the first server:
* the first reviewer upvotes;
* the second reviewer downvotes;
* the last reviewer sees that the number of downvotes is not greater than the number of upvotes — upvote themselves.
There are two upvotes in total. Alternatevely, you can send the first and the second reviewers to the first server and the last reviewer — to the second server:
* the first reviewer upvotes on the first server;
* the second reviewer downvotes on the first server;
* the last reviewer sees no upvotes or downvotes on the second server — upvote themselves.
Submitted Solution:
```
T = int(input())
for t in range(T):
n = int(input())
ret = 0
for r in [int(x) for x in input().split()]:
if r == 1 or r == 3:
ret += 1
print(ret)
```
Yes
| 102,296 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are an upcoming movie director, and you have just released your first movie. You have also launched a simple review site with two buttons to press — upvote and downvote.
However, the site is not so simple on the inside. There are two servers, each with its separate counts for the upvotes and the downvotes.
n reviewers enter the site one by one. Each reviewer is one of the following types:
* type 1: a reviewer has watched the movie, and they like it — they press the upvote button;
* type 2: a reviewer has watched the movie, and they dislike it — they press the downvote button;
* type 3: a reviewer hasn't watched the movie — they look at the current number of upvotes and downvotes of the movie on the server they are in and decide what button to press. If there are more downvotes than upvotes, then a reviewer downvotes the movie. Otherwise, they upvote the movie.
Each reviewer votes on the movie exactly once.
Since you have two servers, you can actually manipulate the votes so that your movie gets as many upvotes as possible. When a reviewer enters a site, you know their type, and you can send them either to the first server or to the second one.
What is the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to?
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.
Then the descriptions of t testcases follow.
The first line of each testcase contains a single integer n (1 ≤ n ≤ 50) — the number of reviewers.
The second line of each testcase contains n integers r_1, r_2, ..., r_n (1 ≤ r_i ≤ 3) — the types of the reviewers in the same order they enter the site.
Output
For each testcase print a single integer — the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to.
Example
Input
4
1
2
3
1 2 3
5
1 1 1 1 1
3
3 3 2
Output
0
2
5
2
Note
In the first testcase of the example you can send the only reviewer to either of the servers — they'll downvote anyway. The movie won't receive any upvotes.
In the second testcase of the example you can send all reviewers to the first server:
* the first reviewer upvotes;
* the second reviewer downvotes;
* the last reviewer sees that the number of downvotes is not greater than the number of upvotes — upvote themselves.
There are two upvotes in total. Alternatevely, you can send the first and the second reviewers to the first server and the last reviewer — to the second server:
* the first reviewer upvotes on the first server;
* the second reviewer downvotes on the first server;
* the last reviewer sees no upvotes or downvotes on the second server — upvote themselves.
Submitted Solution:
```
t=int(input())
for tt in range(t):
n = int(input())
a=list(map(int,input().split()))
b=0
c=0
for i in range(n):
if a[i]==1:
b+=1
elif a[i]==2:
c+=1
elif a[i]==3:
if b>=c:
b+=1
else:
c+=1
print(b)
```
No
| 102,297 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are an upcoming movie director, and you have just released your first movie. You have also launched a simple review site with two buttons to press — upvote and downvote.
However, the site is not so simple on the inside. There are two servers, each with its separate counts for the upvotes and the downvotes.
n reviewers enter the site one by one. Each reviewer is one of the following types:
* type 1: a reviewer has watched the movie, and they like it — they press the upvote button;
* type 2: a reviewer has watched the movie, and they dislike it — they press the downvote button;
* type 3: a reviewer hasn't watched the movie — they look at the current number of upvotes and downvotes of the movie on the server they are in and decide what button to press. If there are more downvotes than upvotes, then a reviewer downvotes the movie. Otherwise, they upvote the movie.
Each reviewer votes on the movie exactly once.
Since you have two servers, you can actually manipulate the votes so that your movie gets as many upvotes as possible. When a reviewer enters a site, you know their type, and you can send them either to the first server or to the second one.
What is the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to?
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.
Then the descriptions of t testcases follow.
The first line of each testcase contains a single integer n (1 ≤ n ≤ 50) — the number of reviewers.
The second line of each testcase contains n integers r_1, r_2, ..., r_n (1 ≤ r_i ≤ 3) — the types of the reviewers in the same order they enter the site.
Output
For each testcase print a single integer — the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to.
Example
Input
4
1
2
3
1 2 3
5
1 1 1 1 1
3
3 3 2
Output
0
2
5
2
Note
In the first testcase of the example you can send the only reviewer to either of the servers — they'll downvote anyway. The movie won't receive any upvotes.
In the second testcase of the example you can send all reviewers to the first server:
* the first reviewer upvotes;
* the second reviewer downvotes;
* the last reviewer sees that the number of downvotes is not greater than the number of upvotes — upvote themselves.
There are two upvotes in total. Alternatevely, you can send the first and the second reviewers to the first server and the last reviewer — to the second server:
* the first reviewer upvotes on the first server;
* the second reviewer downvotes on the first server;
* the last reviewer sees no upvotes or downvotes on the second server — upvote themselves.
Submitted Solution:
```
t=int(input())
for _ in range(t):
n=int(input())
l=list(map(int,input().split()))
score=0
down=0
for i in l:
if i==1:
score+=1
elif i==2:
down+=1
else:
if down>score:
down+=1
else:
score+=1
print(score)
```
No
| 102,298 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are an upcoming movie director, and you have just released your first movie. You have also launched a simple review site with two buttons to press — upvote and downvote.
However, the site is not so simple on the inside. There are two servers, each with its separate counts for the upvotes and the downvotes.
n reviewers enter the site one by one. Each reviewer is one of the following types:
* type 1: a reviewer has watched the movie, and they like it — they press the upvote button;
* type 2: a reviewer has watched the movie, and they dislike it — they press the downvote button;
* type 3: a reviewer hasn't watched the movie — they look at the current number of upvotes and downvotes of the movie on the server they are in and decide what button to press. If there are more downvotes than upvotes, then a reviewer downvotes the movie. Otherwise, they upvote the movie.
Each reviewer votes on the movie exactly once.
Since you have two servers, you can actually manipulate the votes so that your movie gets as many upvotes as possible. When a reviewer enters a site, you know their type, and you can send them either to the first server or to the second one.
What is the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to?
Input
The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.
Then the descriptions of t testcases follow.
The first line of each testcase contains a single integer n (1 ≤ n ≤ 50) — the number of reviewers.
The second line of each testcase contains n integers r_1, r_2, ..., r_n (1 ≤ r_i ≤ 3) — the types of the reviewers in the same order they enter the site.
Output
For each testcase print a single integer — the maximum total number of upvotes you can gather over both servers if you decide which server to send each reviewer to.
Example
Input
4
1
2
3
1 2 3
5
1 1 1 1 1
3
3 3 2
Output
0
2
5
2
Note
In the first testcase of the example you can send the only reviewer to either of the servers — they'll downvote anyway. The movie won't receive any upvotes.
In the second testcase of the example you can send all reviewers to the first server:
* the first reviewer upvotes;
* the second reviewer downvotes;
* the last reviewer sees that the number of downvotes is not greater than the number of upvotes — upvote themselves.
There are two upvotes in total. Alternatevely, you can send the first and the second reviewers to the first server and the last reviewer — to the second server:
* the first reviewer upvotes on the first server;
* the second reviewer downvotes on the first server;
* the last reviewer sees no upvotes or downvotes on the second server — upvote themselves.
Submitted Solution:
```
for t in range(int(input())):
n= int(input())
lis = list(map(int, input().split()))
up=0
dw=0
for i in lis:
if i == 1:
up+=1
elif i == 2:
dw+=1
elif up>=dw:
up+=1
print(up)
```
No
| 102,299 |
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