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.
String can be called correct if it consists of characters "0" and "1" and there are no redundant leading zeroes. Here are some examples: "0", "10", "1001".
You are given a correct string s.
You can perform two different operations on this string:
1. swap any pair of adjacent characters (for example, "101" <image> "110");
2. replace "11" with "1" (for example, "110" <image> "10").
Let val(s) be such a number that s is its binary representation.
Correct string a is less than some other correct string b iff val(a) < val(b).
Your task is to find the minimum correct string that you can obtain from the given one using the operations described above. You can use these operations any number of times in any order (or even use no operations at all).
Input
The first line contains integer number n (1 ≤ n ≤ 100) — the length of string s.
The second line contains the string s consisting of characters "0" and "1". It is guaranteed that the string s is correct.
Output
Print one string — the minimum correct string that you can obtain from the given one.
Examples
Input
4
1001
Output
100
Input
1
1
Output
1
Note
In the first example you can obtain the answer by the following sequence of operations: "1001" <image> "1010" <image> "1100" <image> "100".
In the second example you can't obtain smaller answer no matter what operations you use.
Submitted Solution:
```
n=int(input())
s=input()
count=0
for i in s:
if(i=='0'):
count+=1
print('1'+'0'*count)
```
No
| 13,900 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
String can be called correct if it consists of characters "0" and "1" and there are no redundant leading zeroes. Here are some examples: "0", "10", "1001".
You are given a correct string s.
You can perform two different operations on this string:
1. swap any pair of adjacent characters (for example, "101" <image> "110");
2. replace "11" with "1" (for example, "110" <image> "10").
Let val(s) be such a number that s is its binary representation.
Correct string a is less than some other correct string b iff val(a) < val(b).
Your task is to find the minimum correct string that you can obtain from the given one using the operations described above. You can use these operations any number of times in any order (or even use no operations at all).
Input
The first line contains integer number n (1 ≤ n ≤ 100) — the length of string s.
The second line contains the string s consisting of characters "0" and "1". It is guaranteed that the string s is correct.
Output
Print one string — the minimum correct string that you can obtain from the given one.
Examples
Input
4
1001
Output
100
Input
1
1
Output
1
Note
In the first example you can obtain the answer by the following sequence of operations: "1001" <image> "1010" <image> "1100" <image> "100".
In the second example you can't obtain smaller answer no matter what operations you use.
Submitted Solution:
```
n = int(input())
s = input()
z = 0
o = 0
for c in s:
if c == '0':
z += 1
else:
o += 1
ans = None
if o >= 1:
ans = 1 << z
else:
ans = 0
s = ""
while ans > 0:
s = str(ans % 2) + s
ans //= 2
print(s)
```
No
| 13,901 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
String can be called correct if it consists of characters "0" and "1" and there are no redundant leading zeroes. Here are some examples: "0", "10", "1001".
You are given a correct string s.
You can perform two different operations on this string:
1. swap any pair of adjacent characters (for example, "101" <image> "110");
2. replace "11" with "1" (for example, "110" <image> "10").
Let val(s) be such a number that s is its binary representation.
Correct string a is less than some other correct string b iff val(a) < val(b).
Your task is to find the minimum correct string that you can obtain from the given one using the operations described above. You can use these operations any number of times in any order (or even use no operations at all).
Input
The first line contains integer number n (1 ≤ n ≤ 100) — the length of string s.
The second line contains the string s consisting of characters "0" and "1". It is guaranteed that the string s is correct.
Output
Print one string — the minimum correct string that you can obtain from the given one.
Examples
Input
4
1001
Output
100
Input
1
1
Output
1
Note
In the first example you can obtain the answer by the following sequence of operations: "1001" <image> "1010" <image> "1100" <image> "100".
In the second example you can't obtain smaller answer no matter what operations you use.
Submitted Solution:
```
n = int(input())
s = input()
c = 2
j = 0
for i in s:
if i == 1:
c += 1
if n == 1:
print(1)
elif n % 2 == 0:
print(1, end='')
while j < (n - c):
print(0, end = '')
j += 1
else:
print(1, end='')
while j < (n - c):
print(0, end = '')
j += 1
print(1, end='')
```
No
| 13,902 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
String can be called correct if it consists of characters "0" and "1" and there are no redundant leading zeroes. Here are some examples: "0", "10", "1001".
You are given a correct string s.
You can perform two different operations on this string:
1. swap any pair of adjacent characters (for example, "101" <image> "110");
2. replace "11" with "1" (for example, "110" <image> "10").
Let val(s) be such a number that s is its binary representation.
Correct string a is less than some other correct string b iff val(a) < val(b).
Your task is to find the minimum correct string that you can obtain from the given one using the operations described above. You can use these operations any number of times in any order (or even use no operations at all).
Input
The first line contains integer number n (1 ≤ n ≤ 100) — the length of string s.
The second line contains the string s consisting of characters "0" and "1". It is guaranteed that the string s is correct.
Output
Print one string — the minimum correct string that you can obtain from the given one.
Examples
Input
4
1001
Output
100
Input
1
1
Output
1
Note
In the first example you can obtain the answer by the following sequence of operations: "1001" <image> "1010" <image> "1100" <image> "100".
In the second example you can't obtain smaller answer no matter what operations you use.
Submitted Solution:
```
n = int(input())
B = input()
z = 0
for c in B:
z += c == '0'
print('1'+'0'*z)
```
No
| 13,903 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Allen is playing Number Clicker on his phone.
He starts with an integer u on the screen. Every second, he can press one of 3 buttons.
1. Turn u → u+1 \pmod{p}.
2. Turn u → u+p-1 \pmod{p}.
3. Turn u → u^{p-2} \pmod{p}.
Allen wants to press at most 200 buttons and end up with v on the screen. Help him!
Input
The first line of the input contains 3 positive integers: u, v, p (0 ≤ u, v ≤ p-1, 3 ≤ p ≤ 10^9 + 9). p is guaranteed to be prime.
Output
On the first line, print a single integer ℓ, the number of button presses. On the second line, print integers c_1, ..., c_ℓ, the button presses. For 1 ≤ i ≤ ℓ, 1 ≤ c_i ≤ 3.
We can show that the answer always exists.
Examples
Input
1 3 5
Output
2
1 1
Input
3 2 5
Output
1
3
Note
In the first example the integer on the screen changes as 1 → 2 → 3.
In the second example the integer on the screen changes as 3 → 2.
Submitted Solution:
```
u, v, p = [int(x) for x in input().split()]
def egcd(a, b):
if a == 0:
return (b, 0, 1)
else:
g, y, x = egcd(b % a, a)
return (g, x - (b // a) * y, y)
def modinv(a, m):
g, x, y = egcd(a, m)
if g != 1:
raise Exception('modular inverse does not exist')
else:
return x % m
def moves(x, p):
return [(x + 1) % p, (x + p -1) % p, (modinv(x, p) if x else x)]
q = [u]
parent = {u: None}
depth = {u: 0}
res = []
q2 = [v]
parent2 = {v: None}
depth2 = {v: 0}
res2 = []
ans = None
while q:
node = q.pop(0)
if node in parent2:
ans = node
break
for i, child in enumerate(moves(node, p)):
if child not in parent:
parent[child] = (node, i + 1)
depth[child] = depth[node] + 1
q.append(child)
node2 = q2.pop(0)
if node2 in parent:
ans = node2
break
for i, child in enumerate(moves(node2, p)):
if child not in parent2:
parent2[child] = (node2, i + 1)
depth2[child] = depth2[node2] + 1
q2.append(child)
left = ans
while parent[left] is not None:
left, val = parent[left]
res.append(val)
res = res[::-1]
right = ans
while parent2[right] is not None:
right, val = parent2[right]
res.append(val)
print(len(res))
print(" ".join(map(str, res)))
```
No
| 13,904 |
Provide a correct Python 3 solution for this coding contest problem.
When you asked some guy in your class his name, he called himself S, where S is a string of length between 3 and 20 (inclusive) consisting of lowercase English letters. You have decided to choose some three consecutive characters from S and make it his nickname. Print a string that is a valid nickname for him.
Constraints
* 3 \leq |S| \leq 20
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print your answer.
Examples
Input
takahashi
Output
tak
Input
naohiro
Output
nao
"Correct Solution:
```
# A
S = input()
print(S[0:3])
```
| 13,905 |
Provide a correct Python 3 solution for this coding contest problem.
When you asked some guy in your class his name, he called himself S, where S is a string of length between 3 and 20 (inclusive) consisting of lowercase English letters. You have decided to choose some three consecutive characters from S and make it his nickname. Print a string that is a valid nickname for him.
Constraints
* 3 \leq |S| \leq 20
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print your answer.
Examples
Input
takahashi
Output
tak
Input
naohiro
Output
nao
"Correct Solution:
```
S = input()
nik = S[0:3]
print(nik)
```
| 13,906 |
Provide a correct Python 3 solution for this coding contest problem.
When you asked some guy in your class his name, he called himself S, where S is a string of length between 3 and 20 (inclusive) consisting of lowercase English letters. You have decided to choose some three consecutive characters from S and make it his nickname. Print a string that is a valid nickname for him.
Constraints
* 3 \leq |S| \leq 20
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print your answer.
Examples
Input
takahashi
Output
tak
Input
naohiro
Output
nao
"Correct Solution:
```
s = str(input())
nikname = s[0:3]
print(nikname)
```
| 13,907 |
Provide a correct Python 3 solution for this coding contest problem.
When you asked some guy in your class his name, he called himself S, where S is a string of length between 3 and 20 (inclusive) consisting of lowercase English letters. You have decided to choose some three consecutive characters from S and make it his nickname. Print a string that is a valid nickname for him.
Constraints
* 3 \leq |S| \leq 20
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print your answer.
Examples
Input
takahashi
Output
tak
Input
naohiro
Output
nao
"Correct Solution:
```
S = input()
name = S[0:3]
print(name)
```
| 13,908 |
Provide a correct Python 3 solution for this coding contest problem.
When you asked some guy in your class his name, he called himself S, where S is a string of length between 3 and 20 (inclusive) consisting of lowercase English letters. You have decided to choose some three consecutive characters from S and make it his nickname. Print a string that is a valid nickname for him.
Constraints
* 3 \leq |S| \leq 20
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print your answer.
Examples
Input
takahashi
Output
tak
Input
naohiro
Output
nao
"Correct Solution:
```
S = input()
print(S[:3:])
```
| 13,909 |
Provide a correct Python 3 solution for this coding contest problem.
When you asked some guy in your class his name, he called himself S, where S is a string of length between 3 and 20 (inclusive) consisting of lowercase English letters. You have decided to choose some three consecutive characters from S and make it his nickname. Print a string that is a valid nickname for him.
Constraints
* 3 \leq |S| \leq 20
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print your answer.
Examples
Input
takahashi
Output
tak
Input
naohiro
Output
nao
"Correct Solution:
```
# coding:utf-8
s = input()
print(s[:3])
```
| 13,910 |
Provide a correct Python 3 solution for this coding contest problem.
When you asked some guy in your class his name, he called himself S, where S is a string of length between 3 and 20 (inclusive) consisting of lowercase English letters. You have decided to choose some three consecutive characters from S and make it his nickname. Print a string that is a valid nickname for him.
Constraints
* 3 \leq |S| \leq 20
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print your answer.
Examples
Input
takahashi
Output
tak
Input
naohiro
Output
nao
"Correct Solution:
```
name = input().strip()
print(name[:3])
```
| 13,911 |
Provide a correct Python 3 solution for this coding contest problem.
When you asked some guy in your class his name, he called himself S, where S is a string of length between 3 and 20 (inclusive) consisting of lowercase English letters. You have decided to choose some three consecutive characters from S and make it his nickname. Print a string that is a valid nickname for him.
Constraints
* 3 \leq |S| \leq 20
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print your answer.
Examples
Input
takahashi
Output
tak
Input
naohiro
Output
nao
"Correct Solution:
```
S = input() #ここで標準入力
print (S[0:3])
```
| 13,912 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
When you asked some guy in your class his name, he called himself S, where S is a string of length between 3 and 20 (inclusive) consisting of lowercase English letters. You have decided to choose some three consecutive characters from S and make it his nickname. Print a string that is a valid nickname for him.
Constraints
* 3 \leq |S| \leq 20
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print your answer.
Examples
Input
takahashi
Output
tak
Input
naohiro
Output
nao
Submitted Solution:
```
s = list(str(input()))
print("".join(s[0:3]))
```
Yes
| 13,913 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
When you asked some guy in your class his name, he called himself S, where S is a string of length between 3 and 20 (inclusive) consisting of lowercase English letters. You have decided to choose some three consecutive characters from S and make it his nickname. Print a string that is a valid nickname for him.
Constraints
* 3 \leq |S| \leq 20
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print your answer.
Examples
Input
takahashi
Output
tak
Input
naohiro
Output
nao
Submitted Solution:
```
n = input();
print(n[0:3])
```
Yes
| 13,914 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
When you asked some guy in your class his name, he called himself S, where S is a string of length between 3 and 20 (inclusive) consisting of lowercase English letters. You have decided to choose some three consecutive characters from S and make it his nickname. Print a string that is a valid nickname for him.
Constraints
* 3 \leq |S| \leq 20
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print your answer.
Examples
Input
takahashi
Output
tak
Input
naohiro
Output
nao
Submitted Solution:
```
x=list(input())
print(x[0]+x[1]+x[2])
```
Yes
| 13,915 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
When you asked some guy in your class his name, he called himself S, where S is a string of length between 3 and 20 (inclusive) consisting of lowercase English letters. You have decided to choose some three consecutive characters from S and make it his nickname. Print a string that is a valid nickname for him.
Constraints
* 3 \leq |S| \leq 20
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print your answer.
Examples
Input
takahashi
Output
tak
Input
naohiro
Output
nao
Submitted Solution:
```
x = input()
print(x[0:3])
```
Yes
| 13,916 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
When you asked some guy in your class his name, he called himself S, where S is a string of length between 3 and 20 (inclusive) consisting of lowercase English letters. You have decided to choose some three consecutive characters from S and make it his nickname. Print a string that is a valid nickname for him.
Constraints
* 3 \leq |S| \leq 20
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print your answer.
Examples
Input
takahashi
Output
tak
Input
naohiro
Output
nao
Submitted Solution:
```
import math
N, K = map(int, input().split(" "))
A = list(map(int, input().split(" ")))
for i in range(min(math.ceil(math.log(N)+5), K)):
B = [0] * N
for n, A_n in enumerate(A):
B_min = max(0, n-A_n)
b_max = min(N-1, n+A_n)
B[B_min] += 1
if b_max+1 < N:
B[b_max+1] -= 1
sum = 0
for n in range(len(A)):
sum += B[n]
A[n] = sum
print(" ".join(list(map(str, A))))
```
No
| 13,917 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
When you asked some guy in your class his name, he called himself S, where S is a string of length between 3 and 20 (inclusive) consisting of lowercase English letters. You have decided to choose some three consecutive characters from S and make it his nickname. Print a string that is a valid nickname for him.
Constraints
* 3 \leq |S| \leq 20
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print your answer.
Examples
Input
takahashi
Output
tak
Input
naohiro
Output
nao
Submitted Solution:
```
def main():
n,k = map(int,input().split())
A = list(map(int,input().split()))
k = min(50,k)
dp = [[0]*n for _ in range(k+1)]
for i in range(n):
dp[0][i] = A[i]
flag = False
for i in range(1,k+1):
pos = [0]*n
neg = [0]*n
for j in range(n):
pwr = dp[i-1][j]
pos[max(0,j-pwr)]+=1
neg[min(n-1,j+pwr)]+=1
ac_pos = 0
ac_neg = 0
for j in range(n):
ac_pos += pos[j]
ac_neg += neg[j]
pos[j] = ac_pos
neg[j] = ac_neg
if pos[0]==n and neg[n-2]==0:
flag = True
break
dp[i][0] = pos[0]
for j in range(1,n):
dp[i][j] = pos[j] - neg[j-1]
if flag:
for j in range(n-1):
print(n, end=" ")
print(n)
else:
for j in range(n-1):
print(dp[i][j], end=" ")
print(dp[i][n-1])
main()
```
No
| 13,918 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
When you asked some guy in your class his name, he called himself S, where S is a string of length between 3 and 20 (inclusive) consisting of lowercase English letters. You have decided to choose some three consecutive characters from S and make it his nickname. Print a string that is a valid nickname for him.
Constraints
* 3 \leq |S| \leq 20
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print your answer.
Examples
Input
takahashi
Output
tak
Input
naohiro
Output
nao
Submitted Solution:
```
name = input()
print(name[0:2])
```
No
| 13,919 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
When you asked some guy in your class his name, he called himself S, where S is a string of length between 3 and 20 (inclusive) consisting of lowercase English letters. You have decided to choose some three consecutive characters from S and make it his nickname. Print a string that is a valid nickname for him.
Constraints
* 3 \leq |S| \leq 20
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print your answer.
Examples
Input
takahashi
Output
tak
Input
naohiro
Output
nao
Submitted Solution:
```
a = list(map(int,input().split()))
b = list(map(int,input().split()))
c = int(input())
aa = a[0]+a[1]*c
bb = b[0]+b[1]*c
d = aa-bb
e = a[1]-b[1]
if aa > bb:
if d % e == 0:
print("YES")
else:
print("NO")
elif aa == bb:
print("YES")
else:
print("NO")
```
No
| 13,920 |
Provide a correct Python 3 solution for this coding contest problem.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
"Correct Solution:
```
from bisect import bisect
def main():
n,k,*a=map(int,open(0).read().split())
a.sort()
i=bisect(a,0)
a,b=a[i:],a[i-1::-1]
n,m=len(a),len(b)
ok=10**18
ng=-ok
while ok-ng>1:
x=(ok+ng)//2
s=0
if x>=0:
s+=n*m
t=0
i=n
for y in a:
while i and a[i-1]*y>x:
i-=1
t+=i
if y*y<=x:
t-=1
s+=t//2
t=0
i=m
for y in b:
while i and b[i-1]*y>x:
i-=1
t+=i
if y*y<=x:
t-=1
s+=t//2
else:
i=m
for y in a:
while i and b[i-1]*y<=x:
i-=1
s+=m-i
if s>=k:
ok=x
else:
ng=x
print(ok)
main()
```
| 13,921 |
Provide a correct Python 3 solution for this coding contest problem.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
"Correct Solution:
```
import sys
input=sys.stdin.readline
n,k=map(int,input().split())
a=list(map(int,input().split()))
ap,an=[],[]
zeronum=0
for i in range(n):
if a[i]>0:
ap.append(a[i])
elif a[i]<0:
an.append(-a[i])
else:
zeronum+=1
np,nn=len(ap),len(an)
def fminus(x):
j=0
cnt=0
for i in range(np):
cnt+=j
while j<nn and an[j]*ap[i]>=x:
j+=1
cnt+=1
return cnt
def fplus(x,length,lis):
r=length-1
cnt=0
for l in range(length):
while lis[r]*lis[l]>x:
if r==l:
break
r-=1
if r==l:
break
elif lis[r]*lis[l]<=x:
cnt+=r-l
return cnt
if np*nn<k<=np*nn+zeronum*(zeronum-1)//2+zeronum*(np+nn):
print(0)
else:
#print(ap)
#print(an)
if k<=np*nn:
an.sort(reverse=True)
ap.sort()
ng=10**18
ok=0
while ng-ok>1:
mid=(ok+ng)//2
if fminus(mid)>=k:
ok=mid
else:
ng=mid
print(-ok)
else:
an.sort()
ap.sort()
k-=np*nn+zeronum*(zeronum-1)//2+zeronum*(np+nn)
#print(k)
ok=10**18
ng=0
#print(ok,ng)
while ok-ng>1:
mid=(ok+ng)//2
if fplus(mid,nn,an)+fplus(mid,np,ap)>=k:
ok=mid
else:
ng=mid
print(ok)
```
| 13,922 |
Provide a correct Python 3 solution for this coding contest problem.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
"Correct Solution:
```
import sys
readline = sys.stdin.readline
def count(A, B, x):
N = len(A)
M = len(B)
res = 0
r = -1
for l in range(N):
a = A[l]
while r < M-1 and B[r+1]*a <= x:
r += 1
res += r+1
return res
def count2(A, x):
res = 0
for a in A:
if a*a <= x:
res += 1
return res
N, K = map(int, readline().split())
A = list(map(int, readline().split()))
Am = []
Ap = []
minus = 0
zero = 0
plus = 0
for a in A:
if a < 0:
minus += 1
Am.append(-a)
elif a == 0:
zero += 1
else:
plus += 1
Ap.append(a)
ms = minus*plus
zs = ms + zero*(minus+plus) + zero*(zero-1)//2
Am.sort()
Ap.sort()
Amr = Am[::-1]
Apr = Ap[::-1]
if K <= ms:
K = ms+1-K
ok = max(max(Am+[0]), max(Ap+[0]))**2
ng = 0
while abs(ok-ng)>1:
med = (ok+ng)//2
if count(Amr, Ap, med) >= K:
ok = med
else:
ng = med
ans = -ok
elif K <= zs:
ans = 0
else:
K -= zs
ok = max(max(Am+[0]), max(Ap+[0]))**2
ng = 0
while abs(ok-ng)>1:
med = (ok+ng)//2
if (count(Amr, Am, med) + count(Apr, Ap, med) - count2(Am, med) - count2(Ap, med))//2 >= K:
ok = med
else:
ng = med
ans = ok
print(ans)
```
| 13,923 |
Provide a correct Python 3 solution for this coding contest problem.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
"Correct Solution:
```
n,k=list(map(int,input().split()))
a=list(map(int,input().split()))
am=[]
ap=[]
zc=0
for i in a:
if i<0:
am.append(i)
elif i>0:
ap.append(i)
else:
zc+=1
am.sort()
ap.sort()
#print(am,ap)
def count(n,m,p,z):
mx=-10**20
lm=len(m)
lp=len(p)
if n==0:
if z or (lm and lp):
return (lm*lp+(lm+lp)*z+(z*(z-1))//2,0 if z else m[-1]*p[0])
else:
return (0,0)
elif n<0:
r=0
j=0
for i in m:
while j<len(p) and i*p[j]>n:
j+=1
if j<len(p) and mx<i*p[j]:
mx=i*p[j]
r+=len(p)-j
return (r,mx)
else:
if z or (lm and lp):
mx=0 if z else m[-1]*p[0]
r=lm*lp+(lm+lp)*z+(z*(z-1))//2
j=lp-1
for i in range(lp):
while j>i and p[i]*p[j]>n:
j-=1
if j>i and p[i]*p[j]>mx:
mx=p[i]*p[j]
r+=j-i
if i==j:
break
j=lm-1
for i in range(lm):
while j>i and m[i]*m[j]<=n:
j-=1
if i>j:
j=i
if j<lm-1 and m[i]*m[j+1]>mx:
mx=m[i]*m[j+1]
r+=lm-j-1
return (r,mx)
r=10**18
t=0
s=set()
while True:
ret=count(t,am,ap,zc)
#if r<100:
# print(t,ret)
if ret[0]<k:
s.add(t)
t+=r
r=(r+1)//2
elif ret[0]==k:
print(ret[1])
break
else:
if t in s:
print(ret[1])
break
s.add(t)
t-=r
r=(r+1)//2
```
| 13,924 |
Provide a correct Python 3 solution for this coding contest problem.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
"Correct Solution:
```
import bisect
n, k = map(int, input().split())
a = sorted(map(int, input().split()))
def count(t):
c = 0
for x in a:
if x == 0:
c += len(a) - 1 if t >= 0 else 0
elif x > 0:
c += bisect.bisect_left(a, (t // x) + 1) - (x * x <= t)
else:
c += len(a) - bisect.bisect_left(a, -(t // -x)) - (x * x <= t)
return c
lo = -1000000000000000001
hi = 1000000000000000001
while hi - lo > 1:
mid = (lo + hi) // 2
if count(mid) < k * 2:
lo = mid
else:
hi = mid
print(hi)
```
| 13,925 |
Provide a correct Python 3 solution for this coding contest problem.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
"Correct Solution:
```
from bisect import *
from math import ceil
N, K = map(int, input().split())
A = list(map(int, input().split()))
Ap = []
Am = []
for a in A:
if a >= 0:
Ap.append(a)
elif a < 0:
Am.append(a)
p = len(Ap)
m = len(Am)
Ap.sort()
Am.sort(reverse=True)
U = 10 ** 18
L = - 10 ** 18
while U - L > 1:
mid = (U+L)//2
cnt = 0
if mid >= 0:
cnt += p*m
i = p
t = 0
for a in Ap:
while i and Ap[i-1] * a > mid:
i -= 1
t += i
if a*a <= mid:
t -= 1
cnt += t//2
i = m
t = 0
for a in Am:
while i and Am[i-1] * a > mid:
i -= 1
t += i
if a*a <= mid:
t -= 1
cnt += t//2
else:
i = m
for a in Ap:
while i and Am[i-1] * a <= mid:
i -= 1
cnt += m - i
if cnt < K:
L = mid
else:
U = mid
print(U)
```
| 13,926 |
Provide a correct Python 3 solution for this coding contest problem.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
"Correct Solution:
```
n, k = map(int, input().split())
a = list(map(int, input().split()))
plus, zero, minus = [], [], []
for x in a:
if x > 0:
plus.append(x)
elif x == 0:
zero.append(x)
else:
minus.append(x)
m, z, p = len(minus), len(zero), len(plus)
mm, zz, pp = m * p, z * (m + p) + (z * (z - 1)) // 2, (m * (m-1)) // 2 + (p * (p-1)) // 2
plus.sort()
plus2 = plus[::-1]
minus.sort()
minus2 = minus[::-1]
#print(mm, zz, pp)
if mm + zz >= k and mm < k:
print(0)
elif mm >= k:
ok, ng = -10**19, 0
while ng-ok > 1:
x = (ng+ok)//2
res = 0
l = 0
for c in plus:
if l == m:
res += m
elif minus[l] * c >= x:
res += l
else:
while minus[l] * c < x:
l += 1
if l == m:
break
res += l
if res < k:
ok = x
else:
ng = x
print(ng-1)
else:
ok, ng = 0, 10**19
while ng-ok > 1:
x = (ng+ok)//2
lm, lp = 0, 0
res = 0
for c in minus:
if c*c < x:
res -= 1
if lm == m:
res += m
elif minus2[lm] * c >= x:
res += lm
else:
while minus2[lm] * c < x:
lm += 1
if lm == m:
break
res += lm
for c in plus2:
if c*c < x:
res -= 1
if lp == p:
res += p
elif plus[lp] * c >= x:
res += lp
else:
while plus[lp] * c < x:
lp += 1
if lp == p:
break
res += lp
res //= 2
res += zz + mm
#print(x, res)
if res < k:
ok = x
else:
ng = x
print(ng-1)
```
| 13,927 |
Provide a correct Python 3 solution for this coding contest problem.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
"Correct Solution:
```
N,K = map(int,input().split())
A_s = list(map(int,input().split()))
minus = [-x for x in A_s if x < 0]
plus = [x for x in A_s if x >= 0]
minus.sort()
plus.sort()
def cnt(x):
ans = 0
if x < 0:
r = 0
x = -x
for num in minus[::-1]:
while r < len(plus) and plus[r] * num < x:
r += 1
ans += len(plus) - r
return ans
r = 0
for num in minus[::-1]:
if num * num <= x: ans -= 1
while r < len(minus) and minus[r] * num <= x:
r += 1
ans += r
r = 0
for num in plus[::-1]:
if num * num <= x: ans -= 1
while r < len(plus) and plus[r] * num <= x:
r += 1
ans += r
ans //= 2
ans += len(minus) * len(plus)
return ans
top = 2 * (10**18) + 2
bottom = 0
while top - bottom > 1:
mid = (top + bottom) // 2
if cnt(mid-10**18-1) < K:
bottom = mid
else:
top = mid
print(int(top-10**18-1))
```
| 13,928 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
Submitted Solution:
```
def solve():
from bisect import bisect_left, bisect_right
N, K = map(int, input().split())
As = list(map(int, input().split()))
As.sort()
negAs = [-A for A in As[::-1]]
A2s = [A*A for A in As]
A2s.sort()
pstvBs = []
numB0= 0
ngtvBs = []
for A in As:
if A > 0:
pstvBs.append(A)
elif A == 0:
numB0 += 1
else:
ngtvBs.append(A)
def isOK(x):
if x >= 0:
dire = 1
else:
dire = -1
num = 0
# 正
iA = 0
for B in pstvBs[::-dire]:
key = x//B
while iA < N and As[iA] <= key:
iA += 1
num += iA
# ゼロ
if x >= 0:
num += N*numB0
# 負
iA = 0
for B in ngtvBs[::dire]:
key = x//(-B)
while iA < N and negAs[iA] <= key:
iA += 1
num += iA
i = bisect_right(A2s, x)
num -= i
num //= 2
return num >= K
ng, ok = -(10**18)-1, 10**18+1
while abs(ok-ng) > 1:
mid = (ng+ok) // 2
if isOK(mid):
ok = mid
else:
ng = mid
print(ok)
solve()
```
Yes
| 13,929 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
Submitted Solution:
```
from bisect import bisect_left, bisect_right
N, K = map(int, input().split())
As = sorted(map(int, input().split()))
l = - (10 ** 18 + 10)
r = 10 ** 18 + 10
while True:
mid = (l + r) // 2
count = 0
for i, A in enumerate(As):
if A > 0:
count += bisect_right(As, mid//A, lo = i+1) - (i+1)
elif A < 0:
count += N - bisect_left(As, -((-mid)//A), lo = i+1)
else:
if mid >= 0:
count += N - i - 1
if count < K:
l = mid
else:
r = mid
if r - l == 1:
break
print(r)
```
Yes
| 13,930 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
Submitted Solution:
```
N,K=map(int,input().split())
A=list(map(int,input().split()))
m,p=[],[]
for a in A:
if a<0:
m.append(a)
elif a>0:
p.append(a)
M,P=len(m),len(p)
Z=N-M-P
m.sort()
p.sort()
if M*P<K<=N*(N-1)//2-M*(M-1)//2-P*(P-1)//2:
print(0)
elif K<=M*P:
l,r=-10**18-1,0
while l+1<r:
t=(l+r)//2
x=0
mi=0
for pi in range(P):
while mi<M and m[mi]*p[pi]<=t:
mi+=1
x+=mi
if K<=x:
r=t
else:
l=t
print(r)
else:
l,r=0,10**18+1
K-=M*P+Z*(Z-1)//2+Z*(M+P)
m.reverse()
while l+1<r:
t=(l+r)//2
x=0
mi,pi=0,0
for mj in range(M-1,-1,-1):
while mi<M and m[mi]*m[mj]<=t:
mi+=1
x+=mi-(1 if mj<mi else 0)
for pj in range(P-1,-1,-1):
while pi<P and p[pi]*p[pj]<=t:
pi+=1
x+=pi-(1 if pj<pi else 0)
if K<=x//2:
r=t
else:
l=t
print(r)
```
Yes
| 13,931 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
Submitted Solution:
```
import sys
input = sys.stdin.readline
N, K = map(int, input().split())
A = [int(i) for i in input().split()]
p = []
m = []
zero = 0
for i in range(N) :
if A[i] > 0 :
p.append(A[i])
elif A[i] < 0 :
m.append(-A[i])
else :
zero += 1
p.sort()
m.sort()
ng, ok = -(10 ** 18)-1, 10 ** 18+1
while ok - ng > 1 :
mid = (ok + ng) // 2
s = 0
if mid < 0 :
j = 0
for i in range(len(m) - 1, -1, -1) :
while j < len(p) and m[i] * p[j] < -mid :
j += 1
s += len(p) - j
else :
j = len(p) - 1
for i in range(len(p)) :
while j >= 0 and p[i] * p[j] > mid :
j -= 1
s += max(0, j - i)
j = len(m) - 1
for i in range(len(m)) :
while j >= 0 and m[i] * m[j] > mid :
j -= 1
s += max(0, j - i)
s += (len(p) + len(m)) * zero + len(p) * len(m) + zero * (zero - 1) // 2
if s < K :
ng = mid
else :
ok = mid
print(ok)
```
Yes
| 13,932 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
Submitted Solution:
```
N,K = map(int,input().split())
A = list(map(int,input().split()))
A = sorted(A)
mi = 0
zero = 0
for a in A:
if a<0:
mi+=1
elif a==0:
zero+=1
else:
break
plu = N-mi-zero
A_mi = A[0:mi:]
A_mi_rev = A_mi[::-1]
A_plu = A[mi+zero::]
A_plu_rev = A_plu[::-1]
num_mi = plu*mi
num_zero = (plu+mi)*zero+(zero*(zero-1))//2
r = max(A[-1]**2+10,A[0]**2+10)
l = A[0]*A[-1]-10
while l+1!=r:
m = (l+r)//2
num = 0
if m>0:
num+=num_mi+num_zero
if num>=K:
r=m
continue
cou=0
for i in range(0,plu):
while True:
if cou>=plu-i-1:
num+=plu-i-1
break
x = A_plu_rev[i]*A_plu[cou]
if x<m:
cou+=1
else:
num+=cou
break
if num>=K:
break
if num>=K:
r=m
continue
cou = 0
for i in range(0,mi):
while True:
if cou>=mi-i-1:
num+=mi-i-1
break
x = A_mi[i]*A_mi_rev[cou]
if x<m:
cou+=1
else:
num+=cou
break
if num>=K:
break
if num>=K:
r=m
else:
l=m
elif m==0:
num+=num_mi
if num>=K:
r=m
else:
l=m
else:
cou = 0
for a in A_mi_rev:
while True:
if cou==plu:
num+=cou
break
x = a*A_plu_rev[cou]
if x<m:
cou+=1
else:
num+=cou
break
if num>=K:
break
if num>=K:
r = m
else:
l = m
print(l)
```
No
| 13,933 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
Submitted Solution:
```
import sys
from bisect import bisect_left
import numpy as np
from math import ceil
def main():
read = sys.stdin.read
N, K, *A = map(int, read().split())
A.sort()
m = bisect_left(A, 0)
z = bisect_left(A, 1) - m
p = N - m - z
M = m * p
Z = z * (N - z) + z * (z - 1) // 2
if K <= M:
left = A[0] * A[-1] - 1
right = 0
minuses = np.array(A[:m], np.int64)
pluses = np.array(A[-p:], np.int64)
while left + 1 < right:
mid = ceil((left + right) / 2)
a = (p - np.searchsorted(pluses, np.ceil(mid / minuses), side='left')).sum()
if a < K:
left = mid
else:
right = mid
print(right)
elif K <= M + Z:
print(0)
else:
print(1)
if __name__ == '__main__':
main()
```
No
| 13,934 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
Submitted Solution:
```
import bisect
n,k=map(int,input().split())
A=list(map(int,input().split()))
A.sort()
x=bisect.bisect_left(A,0,lo=0,hi=len(A))
y=bisect.bisect_right(A,0,lo=0,hi=len(A))
AN=x
A0=y-x
AP=n-y
if x!=0:
An=A[:x]
else:
An=[]
Ann=An[::-1]
Annn=[0]*AN
for i in range(AN):
Annn[i]=Ann[i]*(-1)
if y!=n:
App=A[-n+y:]
Ap=App[::-1]
else:
Ap=[]
if k<=AN*AP:
ok=An[0]*Ap[0]-1
ng=0
while ng-ok>1:
mid=(ok+ng)//2
c=0
for i in range(AN):
c=c+AP-bisect.bisect_left(App,((-1)*mid+(-1)*An[i]-1)//((-1)*An[i]),lo=0,hi=AP)
if c<k:
ok=mid
else:
ng=mid
ans=ok+1
print(ans)
elif k<=n*(n-1)//2-AN*(AN-1)//2-AP*(AP-1)//2:
print(0)
else:
k=n*(n-1)//2-k+1
if AN>0 and AP>0:
ok=max(An[0]**2,Ap[0]**2)
elif AN>0:
ok=An[0]**2
else:
ok=Ap[0]**2
ng=0
while ok-ng>1:
mid=(ok+ng)//2
c=0
for i in range(AN):
c=c+max(0,AN-i-1-bisect.bisect_left(Annn,(mid+Annn[AN-i-1]-1)//Annn[AN-i-1],lo=0,hi=AN))
for i in range(AP):
c=c+max(0,AP-i-1-bisect.bisect_left(App,(mid+App[AP-i-1]-1)//App[AP-i-1],lo=0,hi=AP))
if c<k:
ok=mid
else:
ng=mid
ans=ok-1
print(ans)
```
No
| 13,935 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
Submitted Solution:
```
n,k = map(int,input().split())
a = list(map(int,input().split()))
a.sort()
p = []
z = []
m = []
for i in range(n):
if a[i] > 0:
p.append(a[i])
elif a[i] == 0:
z.append(a[i])
else:
m.append(a[i])
nb1 = a[0]*a[n-1]
nb2 = max(a[0]*a[1],a[n-1]*a[n-2])
p1 = len(p)
z1 = len(z)
m1 = len(m)
#print(p,m)
#print(p1,z1,m1)
def sytr(x,p,z,m,p1,z1,m1):
ans = 0
ans2 = 0
ans3 = -10**18
if x > 0:
m.sort(reverse=True)
p.sort()
ans += p1*m1 + (p1+m1)*z1 + (z1-1)*z1//2
ans2 += ans
now = 0
#print(p)
now1 = p1-1
now2 = 0
now3 = p1-1
if p1 > 1:
while now < now1:
if p[now]*p[now1] > x:
now1 -= 1
else:
ans3 = max(ans3,p[now]*p[now1])
ans += now1-now
now += 1
while now2 < now3:
if p[now2]*p[now3] >= x:
now3 -= 1
else:
ans2 += now3 - now2
now2 += 1
if m1 > 1:
now = 0
now1 = m1-1
now2 = 0
now3 = m1-1
while now < now1:
if m[now]*m[now1] > x:
now1 -= 1
else:
ans3 = max(ans3,m[now]*m[now1])
ans += now1 - now
now += 1
while now2 < now3:
if m[now2]*m[now3] >= x:
now3 -= 1
else:
ans2 += now3 - now2
now2 += 1
elif x == 0:
p.sort()
m.sort()
if p1 > 0 and m1 > 0:
ans3 = p[0]*m[m1-1]
if z1 > 0:
ans3 = 0
ans += p1*m1
ans2 += (p1+m1)*z1 + ans
else:
p.sort(reverse=True)
m.sort()
now = 0
now1 = m1-1
now2 = 0
now3 = m1-1
if p1 > 0 and m1 > 0:
while now < p1 and now1 >= 0:
if p[now]*m[now1] > x:
now1 -= 1
else:
ans3 = max(ans3,p[now]*m[now1])
ans += now1+1
now += 1
while now2 < p1 and now3 >= 0:
if p[now2]*m[now3] >= x:
now3 -= 1
else:
ans2 += now3+1
now2 += 1
return [ans,ans2,ans3]
while nb1 + 1 < nb2:
#print(nb1,nb2)
x = (nb1+nb2)//2
#print(sytr(x,p,z,m,p1,z1,m1))
if max(sytr(x,p,z,m,p1,z1,m1)[0],sytr(x,p,z,m,p1,z1,m1)[1]) < k:
nb1 = x
elif min(sytr(x,p,z,m,p1,z1,m1)[0],sytr(x,p,z,m,p1,z1,m1)[1]) > k:
nb2 = x
else:
if abs(sytr(x,p,z,m,p1,z1,m1)[1]-sytr(x,p,z,m,p1,z1,m1)[0]) == 0:
x = sytr(x,p,z,m,p1,z1,m1)[2]
break
else:
break
print(x)
```
No
| 13,936 |
Provide a correct Python 3 solution for this coding contest problem.
The weather in Takahashi's town changes day by day, in the following cycle: Sunny, Cloudy, Rainy, Sunny, Cloudy, Rainy, ...
Given is a string S representing the weather in the town today. Predict the weather tomorrow.
Constraints
* S is `Sunny`, `Cloudy`, or `Rainy`.
Input
Input is given from Standard Input in the following format:
S
Output
Print a string representing the expected weather tomorrow, in the same format in which input is given.
Examples
Input
Sunny
Output
Cloudy
Input
Rainy
Output
Sunny
"Correct Solution:
```
w = ["Sunny", "Cloudy", "Rainy"]
s = input()
print(w[(w.index(s) + 1) % 3])
```
| 13,937 |
Provide a correct Python 3 solution for this coding contest problem.
The weather in Takahashi's town changes day by day, in the following cycle: Sunny, Cloudy, Rainy, Sunny, Cloudy, Rainy, ...
Given is a string S representing the weather in the town today. Predict the weather tomorrow.
Constraints
* S is `Sunny`, `Cloudy`, or `Rainy`.
Input
Input is given from Standard Input in the following format:
S
Output
Print a string representing the expected weather tomorrow, in the same format in which input is given.
Examples
Input
Sunny
Output
Cloudy
Input
Rainy
Output
Sunny
"Correct Solution:
```
s = input()
l=['Sunny','Cloudy','Rainy']*2
print(l[l.index(s) + 1])
```
| 13,938 |
Provide a correct Python 3 solution for this coding contest problem.
The weather in Takahashi's town changes day by day, in the following cycle: Sunny, Cloudy, Rainy, Sunny, Cloudy, Rainy, ...
Given is a string S representing the weather in the town today. Predict the weather tomorrow.
Constraints
* S is `Sunny`, `Cloudy`, or `Rainy`.
Input
Input is given from Standard Input in the following format:
S
Output
Print a string representing the expected weather tomorrow, in the same format in which input is given.
Examples
Input
Sunny
Output
Cloudy
Input
Rainy
Output
Sunny
"Correct Solution:
```
w = {'Sunny':'Cloudy', 'Cloudy':'Rainy', 'Rainy':'Sunny'}
print(w[input()])
```
| 13,939 |
Provide a correct Python 3 solution for this coding contest problem.
The weather in Takahashi's town changes day by day, in the following cycle: Sunny, Cloudy, Rainy, Sunny, Cloudy, Rainy, ...
Given is a string S representing the weather in the town today. Predict the weather tomorrow.
Constraints
* S is `Sunny`, `Cloudy`, or `Rainy`.
Input
Input is given from Standard Input in the following format:
S
Output
Print a string representing the expected weather tomorrow, in the same format in which input is given.
Examples
Input
Sunny
Output
Cloudy
Input
Rainy
Output
Sunny
"Correct Solution:
```
t = ['Sunny', 'Cloudy', 'Rainy', 'Sunny']
print(t[t.index(input())+1])
```
| 13,940 |
Provide a correct Python 3 solution for this coding contest problem.
The weather in Takahashi's town changes day by day, in the following cycle: Sunny, Cloudy, Rainy, Sunny, Cloudy, Rainy, ...
Given is a string S representing the weather in the town today. Predict the weather tomorrow.
Constraints
* S is `Sunny`, `Cloudy`, or `Rainy`.
Input
Input is given from Standard Input in the following format:
S
Output
Print a string representing the expected weather tomorrow, in the same format in which input is given.
Examples
Input
Sunny
Output
Cloudy
Input
Rainy
Output
Sunny
"Correct Solution:
```
di = {'Sunny':'Cloudy','Cloudy':'Rainy','Rainy':'Sunny'}
print(di[input()])
```
| 13,941 |
Provide a correct Python 3 solution for this coding contest problem.
The weather in Takahashi's town changes day by day, in the following cycle: Sunny, Cloudy, Rainy, Sunny, Cloudy, Rainy, ...
Given is a string S representing the weather in the town today. Predict the weather tomorrow.
Constraints
* S is `Sunny`, `Cloudy`, or `Rainy`.
Input
Input is given from Standard Input in the following format:
S
Output
Print a string representing the expected weather tomorrow, in the same format in which input is given.
Examples
Input
Sunny
Output
Cloudy
Input
Rainy
Output
Sunny
"Correct Solution:
```
s = input()
print({"Sunny":"Cloudy","Cloudy":"Rainy","Rainy":"Sunny"}[s])
```
| 13,942 |
Provide a correct Python 3 solution for this coding contest problem.
The weather in Takahashi's town changes day by day, in the following cycle: Sunny, Cloudy, Rainy, Sunny, Cloudy, Rainy, ...
Given is a string S representing the weather in the town today. Predict the weather tomorrow.
Constraints
* S is `Sunny`, `Cloudy`, or `Rainy`.
Input
Input is given from Standard Input in the following format:
S
Output
Print a string representing the expected weather tomorrow, in the same format in which input is given.
Examples
Input
Sunny
Output
Cloudy
Input
Rainy
Output
Sunny
"Correct Solution:
```
S = input()
li = ['Sunny','Cloudy','Rainy','Sunny']
print(li[li.index(S)+1])
```
| 13,943 |
Provide a correct Python 3 solution for this coding contest problem.
The weather in Takahashi's town changes day by day, in the following cycle: Sunny, Cloudy, Rainy, Sunny, Cloudy, Rainy, ...
Given is a string S representing the weather in the town today. Predict the weather tomorrow.
Constraints
* S is `Sunny`, `Cloudy`, or `Rainy`.
Input
Input is given from Standard Input in the following format:
S
Output
Print a string representing the expected weather tomorrow, in the same format in which input is given.
Examples
Input
Sunny
Output
Cloudy
Input
Rainy
Output
Sunny
"Correct Solution:
```
S=input()
l=["Sunny", "Cloudy", "Rainy" ]
print(l[ ((l.index(S))+1 )%3 ])
```
| 13,944 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The weather in Takahashi's town changes day by day, in the following cycle: Sunny, Cloudy, Rainy, Sunny, Cloudy, Rainy, ...
Given is a string S representing the weather in the town today. Predict the weather tomorrow.
Constraints
* S is `Sunny`, `Cloudy`, or `Rainy`.
Input
Input is given from Standard Input in the following format:
S
Output
Print a string representing the expected weather tomorrow, in the same format in which input is given.
Examples
Input
Sunny
Output
Cloudy
Input
Rainy
Output
Sunny
Submitted Solution:
```
a = ["Rainy","Cloudy","Sunny"]
b = input()
print(a[a.index(b)-1])
```
Yes
| 13,945 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The weather in Takahashi's town changes day by day, in the following cycle: Sunny, Cloudy, Rainy, Sunny, Cloudy, Rainy, ...
Given is a string S representing the weather in the town today. Predict the weather tomorrow.
Constraints
* S is `Sunny`, `Cloudy`, or `Rainy`.
Input
Input is given from Standard Input in the following format:
S
Output
Print a string representing the expected weather tomorrow, in the same format in which input is given.
Examples
Input
Sunny
Output
Cloudy
Input
Rainy
Output
Sunny
Submitted Solution:
```
ls={"Sunny":"Cloudy", "Cloudy":"Rainy", "Rainy":"Sunny"}
print(ls[input()])
```
Yes
| 13,946 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The weather in Takahashi's town changes day by day, in the following cycle: Sunny, Cloudy, Rainy, Sunny, Cloudy, Rainy, ...
Given is a string S representing the weather in the town today. Predict the weather tomorrow.
Constraints
* S is `Sunny`, `Cloudy`, or `Rainy`.
Input
Input is given from Standard Input in the following format:
S
Output
Print a string representing the expected weather tomorrow, in the same format in which input is given.
Examples
Input
Sunny
Output
Cloudy
Input
Rainy
Output
Sunny
Submitted Solution:
```
l=["Sunny","Cloudy","Rainy"]
S=input()
print(l[l.index(S)-2])
```
Yes
| 13,947 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The weather in Takahashi's town changes day by day, in the following cycle: Sunny, Cloudy, Rainy, Sunny, Cloudy, Rainy, ...
Given is a string S representing the weather in the town today. Predict the weather tomorrow.
Constraints
* S is `Sunny`, `Cloudy`, or `Rainy`.
Input
Input is given from Standard Input in the following format:
S
Output
Print a string representing the expected weather tomorrow, in the same format in which input is given.
Examples
Input
Sunny
Output
Cloudy
Input
Rainy
Output
Sunny
Submitted Solution:
```
s = input()
L = ['Sunny', 'Cloudy', 'Rainy']
print(L[(L.index(s)+1)%3])
```
Yes
| 13,948 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The weather in Takahashi's town changes day by day, in the following cycle: Sunny, Cloudy, Rainy, Sunny, Cloudy, Rainy, ...
Given is a string S representing the weather in the town today. Predict the weather tomorrow.
Constraints
* S is `Sunny`, `Cloudy`, or `Rainy`.
Input
Input is given from Standard Input in the following format:
S
Output
Print a string representing the expected weather tomorrow, in the same format in which input is given.
Examples
Input
Sunny
Output
Cloudy
Input
Rainy
Output
Sunny
Submitted Solution:
```
arr ={"Sunny":"Cloudy","Cloudy":"Rain","Rain":""Cloudy"}
S = input()
print(arr[S])
```
No
| 13,949 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The weather in Takahashi's town changes day by day, in the following cycle: Sunny, Cloudy, Rainy, Sunny, Cloudy, Rainy, ...
Given is a string S representing the weather in the town today. Predict the weather tomorrow.
Constraints
* S is `Sunny`, `Cloudy`, or `Rainy`.
Input
Input is given from Standard Input in the following format:
S
Output
Print a string representing the expected weather tomorrow, in the same format in which input is given.
Examples
Input
Sunny
Output
Cloudy
Input
Rainy
Output
Sunny
Submitted Solution:
```
import sys
input = sys.stdin.readline
s=input()
if s == "Sunny":
print("Cloudy")
elif s == "Cloudy":
print("Rainy")
else:
print("Sunny")
```
No
| 13,950 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The weather in Takahashi's town changes day by day, in the following cycle: Sunny, Cloudy, Rainy, Sunny, Cloudy, Rainy, ...
Given is a string S representing the weather in the town today. Predict the weather tomorrow.
Constraints
* S is `Sunny`, `Cloudy`, or `Rainy`.
Input
Input is given from Standard Input in the following format:
S
Output
Print a string representing the expected weather tomorrow, in the same format in which input is given.
Examples
Input
Sunny
Output
Cloudy
Input
Rainy
Output
Sunny
Submitted Solution:
```
import sys
def main():
N = sys.stdin.readline()
w = ['Sunny', 'Cloudy', 'Rainy']
i = w.index(N)
print(w[(i+1)%3])
if __name__=='__main__':
main()
```
No
| 13,951 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The weather in Takahashi's town changes day by day, in the following cycle: Sunny, Cloudy, Rainy, Sunny, Cloudy, Rainy, ...
Given is a string S representing the weather in the town today. Predict the weather tomorrow.
Constraints
* S is `Sunny`, `Cloudy`, or `Rainy`.
Input
Input is given from Standard Input in the following format:
S
Output
Print a string representing the expected weather tomorrow, in the same format in which input is given.
Examples
Input
Sunny
Output
Cloudy
Input
Rainy
Output
Sunny
Submitted Solution:
```
S = input()
if S == 'Sunny':
print("くもり")
S =='Cloudy'
print("雨")
else:
print("晴れ")
```
No
| 13,952 |
Provide a correct Python 3 solution for this coding contest problem.
We have a tree with N vertices numbered 1 to N. The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i. Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:
* For any two vertices painted in the same color, the distance between them is an even number.
Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq u_i < v_i \leq N
* 1 \leq w_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
u_1 v_1 w_1
u_2 v_2 w_2
.
.
.
u_{N - 1} v_{N - 1} w_{N - 1}
Output
Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain `0` if Vertex i is painted white and `1` if it is painted black.
If there are multiple colorings that satisfy the condition, any of them will be accepted.
Examples
Input
3
1 2 2
2 3 1
Output
0
0
1
Input
5
2 5 2
2 3 10
1 3 8
3 4 2
Output
1
0
1
0
1
"Correct Solution:
```
N, = map(int, input().split())
import sys
sys.setrecursionlimit(10**6)
d = [set() for _ in range(N+1)]
Cs = [0 for _ in range(N+1)]
for _ in range(N-1):
u, v, p = map(int, input().split())
d[u].add((v, p))
d[v].add((u, p))
def it(v, p):
for u, c in d[v]:
if u == p:
continue
Cs[u] = int(not Cs[v]) if c%2 else Cs[v]
it(u, v)
it(1, None)
for i in range(1, N+1):
print(Cs[i])
```
| 13,953 |
Provide a correct Python 3 solution for this coding contest problem.
We have a tree with N vertices numbered 1 to N. The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i. Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:
* For any two vertices painted in the same color, the distance between them is an even number.
Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq u_i < v_i \leq N
* 1 \leq w_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
u_1 v_1 w_1
u_2 v_2 w_2
.
.
.
u_{N - 1} v_{N - 1} w_{N - 1}
Output
Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain `0` if Vertex i is painted white and `1` if it is painted black.
If there are multiple colorings that satisfy the condition, any of them will be accepted.
Examples
Input
3
1 2 2
2 3 1
Output
0
0
1
Input
5
2 5 2
2 3 10
1 3 8
3 4 2
Output
1
0
1
0
1
"Correct Solution:
```
n=int(input())
edges=[[] for i in range(n)]
import sys
sys.setrecursionlimit(10**7)
for i in range(n-1):
a,s,w=map(int,input().split())
edges[a-1].append([s-1,w]);edges[s-1].append([a-1,w])
colors=[-1]*n
colors[0]=1
def dfs(now):
for to,cost in edges[now]:
if colors[to]==-1:
colors[to]=(cost+colors[now])%2
dfs(to)
dfs(0)
print(*colors,sep="\n")
```
| 13,954 |
Provide a correct Python 3 solution for this coding contest problem.
We have a tree with N vertices numbered 1 to N. The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i. Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:
* For any two vertices painted in the same color, the distance between them is an even number.
Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq u_i < v_i \leq N
* 1 \leq w_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
u_1 v_1 w_1
u_2 v_2 w_2
.
.
.
u_{N - 1} v_{N - 1} w_{N - 1}
Output
Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain `0` if Vertex i is painted white and `1` if it is painted black.
If there are multiple colorings that satisfy the condition, any of them will be accepted.
Examples
Input
3
1 2 2
2 3 1
Output
0
0
1
Input
5
2 5 2
2 3 10
1 3 8
3 4 2
Output
1
0
1
0
1
"Correct Solution:
```
(n,),*t=[map(int,t.split())for t in open(0)]
*e,=eval('[],'*-~n)
q=[(1,0)]
f=[-1]*n
for v,w,c in t:e[v]+=(w,c),;e[w]+=(v,c),
for v,c in q:
f[v-1]=c&1
for w,d in e[v]:q+=[(w,c+d)]*(f[w-1]<0)
print(*f)
```
| 13,955 |
Provide a correct Python 3 solution for this coding contest problem.
We have a tree with N vertices numbered 1 to N. The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i. Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:
* For any two vertices painted in the same color, the distance between them is an even number.
Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq u_i < v_i \leq N
* 1 \leq w_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
u_1 v_1 w_1
u_2 v_2 w_2
.
.
.
u_{N - 1} v_{N - 1} w_{N - 1}
Output
Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain `0` if Vertex i is painted white and `1` if it is painted black.
If there are multiple colorings that satisfy the condition, any of them will be accepted.
Examples
Input
3
1 2 2
2 3 1
Output
0
0
1
Input
5
2 5 2
2 3 10
1 3 8
3 4 2
Output
1
0
1
0
1
"Correct Solution:
```
n=int(input())
q=[[] for i in range(n+1)]
for i in range(n-1):
a,b,c=map(int,input().split())
q[a].append((b,c))
q[b].append((a,c))
l=[-1]*n
s=[(1,0)]
while s:
a,w=s.pop()
l[a-1]=w%2
for b,c in q[a]:
if l[b-1]==-1:
s.append((b,w+c))
for i in l:
print(i)
```
| 13,956 |
Provide a correct Python 3 solution for this coding contest problem.
We have a tree with N vertices numbered 1 to N. The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i. Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:
* For any two vertices painted in the same color, the distance between them is an even number.
Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq u_i < v_i \leq N
* 1 \leq w_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
u_1 v_1 w_1
u_2 v_2 w_2
.
.
.
u_{N - 1} v_{N - 1} w_{N - 1}
Output
Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain `0` if Vertex i is painted white and `1` if it is painted black.
If there are multiple colorings that satisfy the condition, any of them will be accepted.
Examples
Input
3
1 2 2
2 3 1
Output
0
0
1
Input
5
2 5 2
2 3 10
1 3 8
3 4 2
Output
1
0
1
0
1
"Correct Solution:
```
N = int(input())
adj = [[] for _ in range(N)]
for i in range(N-1):
u,v,w = map(int,input().split())
u,v = u-1, v-1
w %= 2
adj[u].append((v,w))
adj[v].append((u,w))
color = [None]*N
color[0] = False
stack = [0]
while stack:
u = stack.pop()
for v,w in adj[u]:
if color[v] is None:
color[v] = (w%2) ^ color[u]
stack.append(v)
for c in color:
print(1 if c else 0)
```
| 13,957 |
Provide a correct Python 3 solution for this coding contest problem.
We have a tree with N vertices numbered 1 to N. The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i. Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:
* For any two vertices painted in the same color, the distance between them is an even number.
Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq u_i < v_i \leq N
* 1 \leq w_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
u_1 v_1 w_1
u_2 v_2 w_2
.
.
.
u_{N - 1} v_{N - 1} w_{N - 1}
Output
Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain `0` if Vertex i is painted white and `1` if it is painted black.
If there are multiple colorings that satisfy the condition, any of them will be accepted.
Examples
Input
3
1 2 2
2 3 1
Output
0
0
1
Input
5
2 5 2
2 3 10
1 3 8
3 4 2
Output
1
0
1
0
1
"Correct Solution:
```
def solve():
from collections import deque
n,*l=map(int,open(0).read().split())
con=[[] for _ in range(n)]
dist=[-1]*n
dist[0]=0
for a,b,c in zip(*[iter(l)]*3):
con[a-1].append((b-1,c%2))
con[b-1].append((a-1,c%2))
stk=deque([0])
while stk:
cur=stk.pop()
for nxt,d in con[cur]:
if dist[nxt]<0:
stk.append(nxt)
dist[nxt]=(dist[cur]+d)%2
print(*dist,sep="\n")
if __name__=="__main__":
solve()
```
| 13,958 |
Provide a correct Python 3 solution for this coding contest problem.
We have a tree with N vertices numbered 1 to N. The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i. Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:
* For any two vertices painted in the same color, the distance between them is an even number.
Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq u_i < v_i \leq N
* 1 \leq w_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
u_1 v_1 w_1
u_2 v_2 w_2
.
.
.
u_{N - 1} v_{N - 1} w_{N - 1}
Output
Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain `0` if Vertex i is painted white and `1` if it is painted black.
If there are multiple colorings that satisfy the condition, any of them will be accepted.
Examples
Input
3
1 2 2
2 3 1
Output
0
0
1
Input
5
2 5 2
2 3 10
1 3 8
3 4 2
Output
1
0
1
0
1
"Correct Solution:
```
import sys
sys.setrecursionlimit(10**9)
n = int(input())
T = [[] for _ in range(n)]
for _ in range(n-1):
u,v,w = map(int,input().split())
u -= 1
v -= 1
w %= 2
T[u].append((v,w))
T[v].append((u,w))
ans = [0]*n
def dfs(u,p=-1,c=0):
for v,w in T[u]:
if v == p: continue
nc = (c+1)%2 if w else c
ans[v] = nc
dfs(v,u,nc)
dfs(0)
print("\n".join(map(str,ans)))
```
| 13,959 |
Provide a correct Python 3 solution for this coding contest problem.
We have a tree with N vertices numbered 1 to N. The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i. Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:
* For any two vertices painted in the same color, the distance between them is an even number.
Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq u_i < v_i \leq N
* 1 \leq w_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
u_1 v_1 w_1
u_2 v_2 w_2
.
.
.
u_{N - 1} v_{N - 1} w_{N - 1}
Output
Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain `0` if Vertex i is painted white and `1` if it is painted black.
If there are multiple colorings that satisfy the condition, any of them will be accepted.
Examples
Input
3
1 2 2
2 3 1
Output
0
0
1
Input
5
2 5 2
2 3 10
1 3 8
3 4 2
Output
1
0
1
0
1
"Correct Solution:
```
N=int(input())
links=[set() for _ in [0]*N]
for i in range(1,N):
u,v,w=map(int,input().split())
u-=1
v-=1
links[u].add((v,w))
links[v].add((u,w))
ans=[-1]*N
q=[(0,0,-1)]
while q:
v,d,p=q.pop()
if d%2==0:
ans[v]=0
else:
ans[v]=1
for u,w in links[v]:
if u==p:
continue
q.append((u,w+d,v))
print('\n'.join(map(str,ans)))
```
| 13,960 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a tree with N vertices numbered 1 to N. The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i. Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:
* For any two vertices painted in the same color, the distance between them is an even number.
Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq u_i < v_i \leq N
* 1 \leq w_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
u_1 v_1 w_1
u_2 v_2 w_2
.
.
.
u_{N - 1} v_{N - 1} w_{N - 1}
Output
Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain `0` if Vertex i is painted white and `1` if it is painted black.
If there are multiple colorings that satisfy the condition, any of them will be accepted.
Examples
Input
3
1 2 2
2 3 1
Output
0
0
1
Input
5
2 5 2
2 3 10
1 3 8
3 4 2
Output
1
0
1
0
1
Submitted Solution:
```
n=int(input())
path=[[] for i in range(n)]
for i in range(n-1):
a,b,c=map(int, input().split())
path[a-1].append([b-1,c%2])
path[b-1].append([a-1,c%2])
ans=[-1]*n
ans[0]=0
q=[0]
while q:
nq=[]
for k in q:
for i,j in path[k]:
if ans[i]==-1:
ans[i]=(ans[k]+j)%2
nq.append(i)
q=nq[:]
for i in ans:print(str(i))
```
Yes
| 13,961 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a tree with N vertices numbered 1 to N. The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i. Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:
* For any two vertices painted in the same color, the distance between them is an even number.
Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq u_i < v_i \leq N
* 1 \leq w_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
u_1 v_1 w_1
u_2 v_2 w_2
.
.
.
u_{N - 1} v_{N - 1} w_{N - 1}
Output
Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain `0` if Vertex i is painted white and `1` if it is painted black.
If there are multiple colorings that satisfy the condition, any of them will be accepted.
Examples
Input
3
1 2 2
2 3 1
Output
0
0
1
Input
5
2 5 2
2 3 10
1 3 8
3 4 2
Output
1
0
1
0
1
Submitted Solution:
```
N = int(input())
E = [[] for _ in range(N)]
for _ in range(N-1):
u,v,w = map(int,input().split())
u -= 1
v -= 1
E[u].append((v,w))
E[v].append((u,w))
color = [-1 for _ in range(N)]
stack = [u]
color[u] = 0
while stack:
u = stack.pop()
for v,w in E[u]:
if color[v] == -1:
stack.append(v)
if w % 2 == 0:
color[v] = color[u]
else:
color[v] = (color[u] + 1) % 2
for i in range(N):
print(color[i])
```
Yes
| 13,962 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a tree with N vertices numbered 1 to N. The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i. Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:
* For any two vertices painted in the same color, the distance between them is an even number.
Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq u_i < v_i \leq N
* 1 \leq w_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
u_1 v_1 w_1
u_2 v_2 w_2
.
.
.
u_{N - 1} v_{N - 1} w_{N - 1}
Output
Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain `0` if Vertex i is painted white and `1` if it is painted black.
If there are multiple colorings that satisfy the condition, any of them will be accepted.
Examples
Input
3
1 2 2
2 3 1
Output
0
0
1
Input
5
2 5 2
2 3 10
1 3 8
3 4 2
Output
1
0
1
0
1
Submitted Solution:
```
import sys
sys.setrecursionlimit(pow(10, 7))
def dfs(v, c):
color[v] = c
for x in glaph[v]:
u, w = x[0], x[1]
if color[u] != -1:
continue
if w%2 == 0:
dfs(u, c)
else:
dfs(u, 1-c)
n = int(input())
color = [-1]*n
glaph = [[]*n for _ in range(n)]
for _ in range(n-1):
u,v,w = map(int, input().split())
glaph[u-1].append((v-1, w))
glaph[v-1].append((u-1, w))
dfs(v=0, c=0)
for i in color:
print(i)
```
Yes
| 13,963 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a tree with N vertices numbered 1 to N. The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i. Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:
* For any two vertices painted in the same color, the distance between them is an even number.
Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq u_i < v_i \leq N
* 1 \leq w_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
u_1 v_1 w_1
u_2 v_2 w_2
.
.
.
u_{N - 1} v_{N - 1} w_{N - 1}
Output
Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain `0` if Vertex i is painted white and `1` if it is painted black.
If there are multiple colorings that satisfy the condition, any of them will be accepted.
Examples
Input
3
1 2 2
2 3 1
Output
0
0
1
Input
5
2 5 2
2 3 10
1 3 8
3 4 2
Output
1
0
1
0
1
Submitted Solution:
```
import math
import sys
sys.setrecursionlimit(30000)
N=int(input())
edges=[[] for i in range(N+1)]
d=[-1 for i in range(N+1)]
for i in range(1,N):
u,v,w=[int(i) for i in input().split()]
edges[u].append([v,w])
edges[v].append([u,w])
def kyori(u):
for v,w in edges[u]:
if d[v]==-1:
d[v]=d[u]+w
kyori(v)
d[1]=0
kyori(1)
for i in d[1:]:
if i%2==0:
print(1)
else:
print(0)
```
Yes
| 13,964 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a tree with N vertices numbered 1 to N. The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i. Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:
* For any two vertices painted in the same color, the distance between them is an even number.
Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq u_i < v_i \leq N
* 1 \leq w_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
u_1 v_1 w_1
u_2 v_2 w_2
.
.
.
u_{N - 1} v_{N - 1} w_{N - 1}
Output
Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain `0` if Vertex i is painted white and `1` if it is painted black.
If there are multiple colorings that satisfy the condition, any of them will be accepted.
Examples
Input
3
1 2 2
2 3 1
Output
0
0
1
Input
5
2 5 2
2 3 10
1 3 8
3 4 2
Output
1
0
1
0
1
Submitted Solution:
```
N, M = map(int, input().split())
X = [0] * M
Y = [0] * M
Z = [0] * M
for i in range(M):
X[i], Y[i], Z[i] = map(int, input().split())
X1 = list(set(X))
print(N-len(X1))
```
No
| 13,965 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a tree with N vertices numbered 1 to N. The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i. Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:
* For any two vertices painted in the same color, the distance between them is an even number.
Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq u_i < v_i \leq N
* 1 \leq w_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
u_1 v_1 w_1
u_2 v_2 w_2
.
.
.
u_{N - 1} v_{N - 1} w_{N - 1}
Output
Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain `0` if Vertex i is painted white and `1` if it is painted black.
If there are multiple colorings that satisfy the condition, any of them will be accepted.
Examples
Input
3
1 2 2
2 3 1
Output
0
0
1
Input
5
2 5 2
2 3 10
1 3 8
3 4 2
Output
1
0
1
0
1
Submitted Solution:
```
n = int(input())
g = [[] for _ in range(n)]
for _ in range(n-1):
u,v,w = map(int,input().split())
g[u-1].append((v-1,w))
g[v-1].append((u-1,w))
ans = [0] * n
for i in range(n):
for c in g[i]:
if c[1] % 2 == 0:
if ans[i] % 2 == 0:
ans[c[0]] = 0
else:
ans[c[0]] = 1
else:
if ans[i] % 2 == 0:
ans[c[0]] = 1
else:
ans[c[0]] = 0
for i in ans:
print(i)
```
No
| 13,966 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a tree with N vertices numbered 1 to N. The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i. Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:
* For any two vertices painted in the same color, the distance between them is an even number.
Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq u_i < v_i \leq N
* 1 \leq w_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
u_1 v_1 w_1
u_2 v_2 w_2
.
.
.
u_{N - 1} v_{N - 1} w_{N - 1}
Output
Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain `0` if Vertex i is painted white and `1` if it is painted black.
If there are multiple colorings that satisfy the condition, any of them will be accepted.
Examples
Input
3
1 2 2
2 3 1
Output
0
0
1
Input
5
2 5 2
2 3 10
1 3 8
3 4 2
Output
1
0
1
0
1
Submitted Solution:
```
N = int(input())
adj_list = { i: [] for i in range(N+1) }
for _ in range(N-1):
u,v,w = map(int, input().split())
adj_list[u].append([v,w])
adj_list[v].append([u,w])
res = [None] * N
visited = [False] * (N+1)
def dfs(node, c, w):
res[node-1] = c
visited[node] = True
for nei, nw, in adj_list[node]:
if not visited[nei]:
if (w+nw)%2 == 0:
dfs(nei, 0, w+nw)
else:
dfs(nei, 1, w+nw)
dfs(1, 0, 0)
for r in res: print(r)
```
No
| 13,967 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a tree with N vertices numbered 1 to N. The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i. Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:
* For any two vertices painted in the same color, the distance between them is an even number.
Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq u_i < v_i \leq N
* 1 \leq w_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
u_1 v_1 w_1
u_2 v_2 w_2
.
.
.
u_{N - 1} v_{N - 1} w_{N - 1}
Output
Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain `0` if Vertex i is painted white and `1` if it is painted black.
If there are multiple colorings that satisfy the condition, any of them will be accepted.
Examples
Input
3
1 2 2
2 3 1
Output
0
0
1
Input
5
2 5 2
2 3 10
1 3 8
3 4 2
Output
1
0
1
0
1
Submitted Solution:
```
from collections import deque
N = int(input())
Graph = [[] for i in range(N)]
for i in range(N-1):
u,v,w = map(int, input().split())
Graph[u-1].append((v-1, w))
Graph[v-1].append((u-1, w))
used = [0]*N
Q = deque([0])
used[0] = 1
ans = [0]*N
while Q:
i = Q.popleft()
j = ans[i]
for uv, w in Graph[i]:
if used[uv]:
continue
if w%2 != 0:
ans[uv] = 1
else:
ans[uv] = j
Q.append(uv)
used[uv] = 1
print(*ans)
```
No
| 13,968 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.
Eating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death. As he wants to live, he cannot eat one in such a situation. Eating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.
Find the maximum number of tasty cookies that Takahashi can eat.
Constraints
* 0 \leq A,B,C \leq 10^9
* A,B and C are integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the maximum number of tasty cookies that Takahashi can eat.
Examples
Input
3 1 4
Output
5
Input
5 2 9
Output
10
Input
8 8 1
Output
9
"Correct Solution:
```
A,B,C = map(int,input().split())
c = min(C,A+B+1)
print(B+c)
```
| 13,969 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.
Eating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death. As he wants to live, he cannot eat one in such a situation. Eating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.
Find the maximum number of tasty cookies that Takahashi can eat.
Constraints
* 0 \leq A,B,C \leq 10^9
* A,B and C are integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the maximum number of tasty cookies that Takahashi can eat.
Examples
Input
3 1 4
Output
5
Input
5 2 9
Output
10
Input
8 8 1
Output
9
"Correct Solution:
```
a,b,c=map(int,input().split())
if a+b>=c:
print(b+c)
else:
print(a+2*min(b,c)+1)
```
| 13,970 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.
Eating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death. As he wants to live, he cannot eat one in such a situation. Eating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.
Find the maximum number of tasty cookies that Takahashi can eat.
Constraints
* 0 \leq A,B,C \leq 10^9
* A,B and C are integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the maximum number of tasty cookies that Takahashi can eat.
Examples
Input
3 1 4
Output
5
Input
5 2 9
Output
10
Input
8 8 1
Output
9
"Correct Solution:
```
a,b,c = map(int,input().split())
ans = b + min(c,a+b+1)
print(ans)
```
| 13,971 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.
Eating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death. As he wants to live, he cannot eat one in such a situation. Eating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.
Find the maximum number of tasty cookies that Takahashi can eat.
Constraints
* 0 \leq A,B,C \leq 10^9
* A,B and C are integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the maximum number of tasty cookies that Takahashi can eat.
Examples
Input
3 1 4
Output
5
Input
5 2 9
Output
10
Input
8 8 1
Output
9
"Correct Solution:
```
a, b, c = list(map(int, input().split()))
ans = min([c, a+b+1]) + b
print(ans)
```
| 13,972 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.
Eating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death. As he wants to live, he cannot eat one in such a situation. Eating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.
Find the maximum number of tasty cookies that Takahashi can eat.
Constraints
* 0 \leq A,B,C \leq 10^9
* A,B and C are integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the maximum number of tasty cookies that Takahashi can eat.
Examples
Input
3 1 4
Output
5
Input
5 2 9
Output
10
Input
8 8 1
Output
9
"Correct Solution:
```
(A,B,C) = map(int,input().split())
print(B+min(C,A+B+1))
```
| 13,973 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.
Eating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death. As he wants to live, he cannot eat one in such a situation. Eating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.
Find the maximum number of tasty cookies that Takahashi can eat.
Constraints
* 0 \leq A,B,C \leq 10^9
* A,B and C are integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the maximum number of tasty cookies that Takahashi can eat.
Examples
Input
3 1 4
Output
5
Input
5 2 9
Output
10
Input
8 8 1
Output
9
"Correct Solution:
```
A,B,C=map(int,input().split())
c=min(A+B+1,C)
print(B+c)
```
| 13,974 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.
Eating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death. As he wants to live, he cannot eat one in such a situation. Eating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.
Find the maximum number of tasty cookies that Takahashi can eat.
Constraints
* 0 \leq A,B,C \leq 10^9
* A,B and C are integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the maximum number of tasty cookies that Takahashi can eat.
Examples
Input
3 1 4
Output
5
Input
5 2 9
Output
10
Input
8 8 1
Output
9
"Correct Solution:
```
a,b,c=map(int,input().split())
if a+b>=c-1:
print(b+c)
else:
print(a+b+b+1)
```
| 13,975 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.
Eating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death. As he wants to live, he cannot eat one in such a situation. Eating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.
Find the maximum number of tasty cookies that Takahashi can eat.
Constraints
* 0 \leq A,B,C \leq 10^9
* A,B and C are integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the maximum number of tasty cookies that Takahashi can eat.
Examples
Input
3 1 4
Output
5
Input
5 2 9
Output
10
Input
8 8 1
Output
9
"Correct Solution:
```
a,b,c = map(int, input().split())
ans=b*2
ans+=a+1
ans = min(ans,b+c)
print(ans)
```
| 13,976 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.
Eating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death. As he wants to live, he cannot eat one in such a situation. Eating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.
Find the maximum number of tasty cookies that Takahashi can eat.
Constraints
* 0 \leq A,B,C \leq 10^9
* A,B and C are integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the maximum number of tasty cookies that Takahashi can eat.
Examples
Input
3 1 4
Output
5
Input
5 2 9
Output
10
Input
8 8 1
Output
9
Submitted Solution:
```
a,b,c=map(int,input().split())
if c>a+b:
print(a+b+1+b)
else:
print(b+c)
```
Yes
| 13,977 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.
Eating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death. As he wants to live, he cannot eat one in such a situation. Eating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.
Find the maximum number of tasty cookies that Takahashi can eat.
Constraints
* 0 \leq A,B,C \leq 10^9
* A,B and C are integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the maximum number of tasty cookies that Takahashi can eat.
Examples
Input
3 1 4
Output
5
Input
5 2 9
Output
10
Input
8 8 1
Output
9
Submitted Solution:
```
a,b,c=map(int,input().split())
print(b+min(c,(a+b)+1))
```
Yes
| 13,978 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.
Eating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death. As he wants to live, he cannot eat one in such a situation. Eating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.
Find the maximum number of tasty cookies that Takahashi can eat.
Constraints
* 0 \leq A,B,C \leq 10^9
* A,B and C are integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the maximum number of tasty cookies that Takahashi can eat.
Examples
Input
3 1 4
Output
5
Input
5 2 9
Output
10
Input
8 8 1
Output
9
Submitted Solution:
```
A,B,C=map(int,input().split())
ans=B+min(A+B+1,C)
print(ans)
```
Yes
| 13,979 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.
Eating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death. As he wants to live, he cannot eat one in such a situation. Eating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.
Find the maximum number of tasty cookies that Takahashi can eat.
Constraints
* 0 \leq A,B,C \leq 10^9
* A,B and C are integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the maximum number of tasty cookies that Takahashi can eat.
Examples
Input
3 1 4
Output
5
Input
5 2 9
Output
10
Input
8 8 1
Output
9
Submitted Solution:
```
A, B, C = map(int, input().split())
print(min(B + C, B + A + B + 1))
```
Yes
| 13,980 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.
Eating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death. As he wants to live, he cannot eat one in such a situation. Eating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.
Find the maximum number of tasty cookies that Takahashi can eat.
Constraints
* 0 \leq A,B,C \leq 10^9
* A,B and C are integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the maximum number of tasty cookies that Takahashi can eat.
Examples
Input
3 1 4
Output
5
Input
5 2 9
Output
10
Input
8 8 1
Output
9
Submitted Solution:
```
a,b,c=map(int,input().split())
if(a+b>=c):
print(b+c)
else:
print(2*b+a)
```
No
| 13,981 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.
Eating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death. As he wants to live, he cannot eat one in such a situation. Eating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.
Find the maximum number of tasty cookies that Takahashi can eat.
Constraints
* 0 \leq A,B,C \leq 10^9
* A,B and C are integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the maximum number of tasty cookies that Takahashi can eat.
Examples
Input
3 1 4
Output
5
Input
5 2 9
Output
10
Input
8 8 1
Output
9
Submitted Solution:
```
a=input()
A,B,C=a.split(' ')
A=int(A)
B=int(B)
C=int(C)
count=0
for i in range(C):
count+=1
if B!=0:
count+=1
B-=1
elif A!=0:
A-=1
else:
break
for i in range(B):
count+=1
print(count)
```
No
| 13,982 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.
Eating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death. As he wants to live, he cannot eat one in such a situation. Eating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.
Find the maximum number of tasty cookies that Takahashi can eat.
Constraints
* 0 \leq A,B,C \leq 10^9
* A,B and C are integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the maximum number of tasty cookies that Takahashi can eat.
Examples
Input
3 1 4
Output
5
Input
5 2 9
Output
10
Input
8 8 1
Output
9
Submitted Solution:
```
a, b, c = map(int,input().split())
if a + b >= c:
print(b+c)
else:
x = c - (a + 1)
if x <= b:
print(a + x + c)
else:
print(a + b + x)
```
No
| 13,983 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.
Eating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death. As he wants to live, he cannot eat one in such a situation. Eating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.
Find the maximum number of tasty cookies that Takahashi can eat.
Constraints
* 0 \leq A,B,C \leq 10^9
* A,B and C are integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the maximum number of tasty cookies that Takahashi can eat.
Examples
Input
3 1 4
Output
5
Input
5 2 9
Output
10
Input
8 8 1
Output
9
Submitted Solution:
```
A,B,C=int(input())
if A+B >= C:
print(B+C)
else:
print(A+2*B+1)
```
No
| 13,984 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate 0. Aoki has N segments. The i-th segment is [L_i,R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).
The game has N steps. The i-th step proceeds as follows:
* First, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.
* Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.
After N steps are performed, Takahashi will return to coordinate 0 and the game ends.
Let K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?
Constraints
* 1 ≤ N ≤ 10^5
* -10^5 ≤ L_i < R_i ≤ 10^5
* L_i and R_i are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above. It is guaranteed that K is always an integer when L_i,R_i are integers.
Examples
Input
3
-5 1
3 7
-4 -2
Output
10
Input
3
1 2
3 4
5 6
Output
12
Input
5
-2 0
-2 0
7 8
9 10
-2 -1
Output
34
"Correct Solution:
```
from itertools import accumulate
N = int(input())
L, R = [0], [0]
for i in range(N):
li, ri = map(int, input().split())
L.append(li)
R.append(ri)
L.sort(reverse=True)
R.sort()
L = list(accumulate(L))
R = list(accumulate(R))
ans = 0
for k in range(N+1):
ans = max(ans, 2*(L[k]-R[k]))
print(ans)
```
| 13,985 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate 0. Aoki has N segments. The i-th segment is [L_i,R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).
The game has N steps. The i-th step proceeds as follows:
* First, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.
* Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.
After N steps are performed, Takahashi will return to coordinate 0 and the game ends.
Let K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?
Constraints
* 1 ≤ N ≤ 10^5
* -10^5 ≤ L_i < R_i ≤ 10^5
* L_i and R_i are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above. It is guaranteed that K is always an integer when L_i,R_i are integers.
Examples
Input
3
-5 1
3 7
-4 -2
Output
10
Input
3
1 2
3 4
5 6
Output
12
Input
5
-2 0
-2 0
7 8
9 10
-2 -1
Output
34
"Correct Solution:
```
N = int(input())
L,R = [],[]
for i in range(N):
l,r = map(int,input().split())
L.append(l)
R.append(r)
# 原点を追加
L.append(0)
R.append(0)
# 左端点は降順に、右端点は昇順にソート
L.sort(reverse=True)
R.sort()
Ans = 0
for i in range(N+1):
if L[i] > R[i]:
Ans += (L[i] - R[i])*2
print(Ans)
```
| 13,986 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate 0. Aoki has N segments. The i-th segment is [L_i,R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).
The game has N steps. The i-th step proceeds as follows:
* First, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.
* Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.
After N steps are performed, Takahashi will return to coordinate 0 and the game ends.
Let K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?
Constraints
* 1 ≤ N ≤ 10^5
* -10^5 ≤ L_i < R_i ≤ 10^5
* L_i and R_i are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above. It is guaranteed that K is always an integer when L_i,R_i are integers.
Examples
Input
3
-5 1
3 7
-4 -2
Output
10
Input
3
1 2
3 4
5 6
Output
12
Input
5
-2 0
-2 0
7 8
9 10
-2 -1
Output
34
"Correct Solution:
```
def main():
import heapq
n = int(input())
ab = [tuple(map(int, input().split())) for _ in [0]*n]
# 1周目
d = dict()
for a, b in ab:
d[(a, b)] = d.get((a, b), 0)+1
left, right = [(b, a) for a, b in ab], [(-a, b) for a, b in ab]
heapq.heapify(left)
heapq.heapify(right)
ans1 = 0
now = 0
for i in range(n):
while left:
a, b = heapq.heappop(left)
a, b = b, a
if d[(a, b)] > 0:
d[(a, b)] -= 1
if b < now:
ans1 += now-b
now = b
elif now < a:
ans1 += a-now
now = a
break
while right:
a, b = heapq.heappop(right)
a, b = -a, b
if d[(a, b)] > 0:
d[(a, b)] -= 1
if now < a:
ans1 += a-now
now = a
elif b < now:
ans1 += now-b
now = b
break
ans1 += abs(now)
# 2周目
d = dict()
for a, b in ab:
d[(a, b)] = d.get((a, b), 0)+1
left, right = [(b, a) for a, b in ab], [(-a, b) for a, b in ab]
heapq.heapify(left)
heapq.heapify(right)
ans2 = 0
now = 0
for i in range(n):
while right:
a, b = heapq.heappop(right)
a, b = -a, b
if d[(a, b)] > 0:
d[(a, b)] -= 1
if now < a:
ans2 += a-now
now = a
elif b < now:
ans2 += now-b
now = b
break
while left:
a, b = heapq.heappop(left)
a, b = b, a
if d[(a, b)] > 0:
d[(a, b)] -= 1
if b < now:
ans2 += now-b
now = b
elif now < a:
ans2 += a-now
now = a
break
ans2 += abs(now)
print(max(ans1, ans2))
main()
```
| 13,987 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate 0. Aoki has N segments. The i-th segment is [L_i,R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).
The game has N steps. The i-th step proceeds as follows:
* First, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.
* Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.
After N steps are performed, Takahashi will return to coordinate 0 and the game ends.
Let K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?
Constraints
* 1 ≤ N ≤ 10^5
* -10^5 ≤ L_i < R_i ≤ 10^5
* L_i and R_i are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above. It is guaranteed that K is always an integer when L_i,R_i are integers.
Examples
Input
3
-5 1
3 7
-4 -2
Output
10
Input
3
1 2
3 4
5 6
Output
12
Input
5
-2 0
-2 0
7 8
9 10
-2 -1
Output
34
"Correct Solution:
```
from heapq import heappop, heappush
N = int(input())
QL = []
QR = []
for i in range(N):
L, R = map(int, input().split())
heappush(QL, (-L, i))
heappush(QR, (R, i))
QL1 = QL[:]
QR1 = QR[:]
deta = set()
x = 0
ans = 0
for i in range(N):
if i % 2 == 0:
for _ in range(N):
if QL1[0][1] not in deta:
break
heappop(QL1)
L, i = heappop(QL1)
deta.add(i)
L = -L
if x < L:
ans += L - x
x = L
else:
for _ in range(N):
if QR1[0][1] not in deta:
break
heappop(QR1)
R, i = heappop(QR1)
deta.add(i)
if x > R:
ans += x - R
x = R
ans += abs(x)
x = 0
ans1 = 0
deta = set()
for i in range(N):
if i % 2:
for _ in range(N):
if QL[0][1] not in deta:
break
heappop(QL)
L, i = heappop(QL)
deta.add(i)
L = -L
if x < L:
ans1 += L - x
x = L
else:
for _ in range(N):
if QR[0][1] not in deta:
break
heappop(QR)
R, i = heappop(QR)
deta.add(i)
if x > R:
ans1 += x - R
x = R
ans1 += abs(x)
print(max(ans1, ans))
```
| 13,988 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate 0. Aoki has N segments. The i-th segment is [L_i,R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).
The game has N steps. The i-th step proceeds as follows:
* First, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.
* Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.
After N steps are performed, Takahashi will return to coordinate 0 and the game ends.
Let K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?
Constraints
* 1 ≤ N ≤ 10^5
* -10^5 ≤ L_i < R_i ≤ 10^5
* L_i and R_i are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above. It is guaranteed that K is always an integer when L_i,R_i are integers.
Examples
Input
3
-5 1
3 7
-4 -2
Output
10
Input
3
1 2
3 4
5 6
Output
12
Input
5
-2 0
-2 0
7 8
9 10
-2 -1
Output
34
"Correct Solution:
```
N = int(input())
L = [0]*N
R = [0]*N
for i in range(N):
L[i],R[i] = map(int,input().split(" "))
L.sort(reverse=True)
R.sort()
ans = 0
acc = 0
for i in range(N):
ans = max(ans,acc+2*L[i])
acc += (2*(L[i]-R[i]))
ans = max(ans,acc)
acc = 0
for i in range(N):
ans = max(ans,acc+2*(-R[i]))
acc += (2*(L[i]-R[i]))
ans = max(ans,acc)
print(ans)
```
| 13,989 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate 0. Aoki has N segments. The i-th segment is [L_i,R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).
The game has N steps. The i-th step proceeds as follows:
* First, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.
* Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.
After N steps are performed, Takahashi will return to coordinate 0 and the game ends.
Let K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?
Constraints
* 1 ≤ N ≤ 10^5
* -10^5 ≤ L_i < R_i ≤ 10^5
* L_i and R_i are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above. It is guaranteed that K is always an integer when L_i,R_i are integers.
Examples
Input
3
-5 1
3 7
-4 -2
Output
10
Input
3
1 2
3 4
5 6
Output
12
Input
5
-2 0
-2 0
7 8
9 10
-2 -1
Output
34
"Correct Solution:
```
import sys
input = sys.stdin.readline
N = int(input())
Ls = []
Rs = []
l0 = 0
r0 = 0
for i in range(N):
l, r = map(int, input().split())
Ls.append((l, i))
Rs.append((r, i))
if l > 0:
l0 += 1
if r < 0:
r0 += 1
Ls.sort(reverse=True)
Rs.sort()
used = [False]*N
if l0 > r0:
toright = True
else:
toright = False
l = 0
r = 0
ans = 0
now = 0
for _ in range(N):
if toright:
while True:
nl, ind = Ls[l]
if used[ind]:
l += 1
else:
used[ind] = True
break
if nl-now > 0:
ans += nl - now
now = nl
toright = False
else:
while True:
nr, ind = Rs[r]
if used[ind]:
r += 1
else:
used[ind] = True
break
if now-nr > 0:
ans += now-nr
now = nr
toright = True
ans += abs(now)
print(ans)
```
| 13,990 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate 0. Aoki has N segments. The i-th segment is [L_i,R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).
The game has N steps. The i-th step proceeds as follows:
* First, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.
* Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.
After N steps are performed, Takahashi will return to coordinate 0 and the game ends.
Let K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?
Constraints
* 1 ≤ N ≤ 10^5
* -10^5 ≤ L_i < R_i ≤ 10^5
* L_i and R_i are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above. It is guaranteed that K is always an integer when L_i,R_i are integers.
Examples
Input
3
-5 1
3 7
-4 -2
Output
10
Input
3
1 2
3 4
5 6
Output
12
Input
5
-2 0
-2 0
7 8
9 10
-2 -1
Output
34
"Correct Solution:
```
from collections import deque
N=int(input())
Sec=[]
Left1,Right1=[],[]
for i in range(N):
l,r=map(int,input().split())
Sec.append((l,r))
Left1.append((l,i))
Right1.append((r,i))
Left1.sort()
Right1.sort(reverse=True)
Left2=Left1[:]
Right2=Right1[:]
Used=[False]*N
pos=0
n=0
ans1=0
f_l,f_r=0,0
while Left1 or Right1:
if n%2==0:
if not Left1:
n+=1
continue
l,i=Left1[-1]
if Used[i]:
Left1.pop()
continue
if pos<l:
ans1+=l-pos
pos=l
Used[i]=True
Left1.pop()
f_l=0
else:
if f_l==1:
Left1.pop()
f_l=0
else:
f_l=1
n+=1
elif n%2==1:
if not Right1:
n+=1
continue
r,i=Right1[-1]
if Used[i]:
Right1.pop()
continue
if r<pos:
ans1+=pos-r
pos=r
Used[i]=True
Right1.pop()
f_r=0
else:
if f_r==1:
Right1.pop()
f_r=0
else:
f_r=1
n+=1
ans1+=abs(pos)
n=0
ans2=0
Used=[False]*N
f_l,f_r=0,9
pos=0
while Left2 or Right2:
if n%2==1:
if not Left2:
n+=1
continue
l,i=Left2[-1]
if Used[i]:
Left2.pop()
continue
if pos<l:
ans2+=l-pos
pos=l
Used[i]=True
Left2.pop()
f_l=0
else:
if f_l==1:
Left2.pop()
f_l=0
else:
f_l=1
n+=1
elif n%2==0:
if not Right2:
n+=1
continue
r,i=Right2[-1]
if Used[i]:
Right2.pop()
continue
if r<pos:
ans2+=pos-r
pos=r
Used[i]=True
Right2.pop()
f_r=0
else:
if f_r==1:
Right2.pop()
f_r=0
else:
f_r=1
n+=1
ans2+=abs(pos)
print(max(ans1,ans2))
```
| 13,991 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate 0. Aoki has N segments. The i-th segment is [L_i,R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).
The game has N steps. The i-th step proceeds as follows:
* First, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.
* Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.
After N steps are performed, Takahashi will return to coordinate 0 and the game ends.
Let K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?
Constraints
* 1 ≤ N ≤ 10^5
* -10^5 ≤ L_i < R_i ≤ 10^5
* L_i and R_i are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above. It is guaranteed that K is always an integer when L_i,R_i are integers.
Examples
Input
3
-5 1
3 7
-4 -2
Output
10
Input
3
1 2
3 4
5 6
Output
12
Input
5
-2 0
-2 0
7 8
9 10
-2 -1
Output
34
"Correct Solution:
```
N = int(input())
sect = []
sect_l = []
sect_r = []
for i in range(N):
l,r = map(int,input().split())
sect_l.append((l,r,i))
sect_r.append((r,l,i))
sect.append((l,r))
sect_l.sort()
sect_r.sort()
sect_r.reverse()
ans_l,ans_r = 0,0
if sect_r[N-1][0] < 0:
used = [False for i in range(N)]
L = [x for x in sect_l]
R = [x for x in sect_r]
next = 'L'
cur = 0
cnt = 0
while cnt < N:
if next == 'R':
while True:
l,r,i = L.pop()
if not used[i]:
used[i] = True
break
if not (l <= cur and cur <= r):
ans_l += abs(cur - l)
cur = l
next = 'L'
cnt += 1
else:
while True:
r,l,i = R.pop()
if not used[i]:
used[i] = True
break
if not (l <= cur and cur <= r):
ans_l += abs(cur - r)
cur = r
next = 'R'
cnt += 1
ans_l += abs(cur)
if sect_l[N-1][0] > 0:
used = [False for i in range(N)]
L = [x for x in sect_l]
R = [x for x in sect_r]
next = 'R'
cur = 0
cnt = 0
while cnt < N:
if next == 'R':
while True:
l,r,i = L.pop()
if not used[i]:
used[i] = True
break
if not (l <= cur and cur <= r):
ans_r += abs(cur - l)
cur = l
next = 'L'
cnt += 1
else:
while True:
r,l,i = R.pop()
if not used[i]:
used[i] = True
break
if not (l <= cur and cur <= r):
ans_r += abs(cur - r)
cur = r
next = 'R'
cnt += 1
ans_r += abs(cur)
print(max(ans_l,ans_r))
```
| 13,992 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate 0. Aoki has N segments. The i-th segment is [L_i,R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).
The game has N steps. The i-th step proceeds as follows:
* First, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.
* Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.
After N steps are performed, Takahashi will return to coordinate 0 and the game ends.
Let K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?
Constraints
* 1 ≤ N ≤ 10^5
* -10^5 ≤ L_i < R_i ≤ 10^5
* L_i and R_i are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above. It is guaranteed that K is always an integer when L_i,R_i are integers.
Examples
Input
3
-5 1
3 7
-4 -2
Output
10
Input
3
1 2
3 4
5 6
Output
12
Input
5
-2 0
-2 0
7 8
9 10
-2 -1
Output
34
Submitted Solution:
```
from itertools import accumulate
N = int(input())
L, R = [0], [0]
for i in range(N):
li, ri = map(int, input().split())
L.append(li)
R.append(ri)
L = list(accumulate(sorted(L, reverse=True)))
R = list(accumulate(sorted(R)))
ans = 0
for k in range(N):
ans = max(ans, 2*(L[k] - R[k]))
print(ans)
```
Yes
| 13,993 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate 0. Aoki has N segments. The i-th segment is [L_i,R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).
The game has N steps. The i-th step proceeds as follows:
* First, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.
* Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.
After N steps are performed, Takahashi will return to coordinate 0 and the game ends.
Let K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?
Constraints
* 1 ≤ N ≤ 10^5
* -10^5 ≤ L_i < R_i ≤ 10^5
* L_i and R_i are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above. It is guaranteed that K is always an integer when L_i,R_i are integers.
Examples
Input
3
-5 1
3 7
-4 -2
Output
10
Input
3
1 2
3 4
5 6
Output
12
Input
5
-2 0
-2 0
7 8
9 10
-2 -1
Output
34
Submitted Solution:
```
from operator import itemgetter
from collections import deque
N = int(input())
L = [[0,0]]
for i in range(N):
l,r = map(int,input().split())
L.append([l,r])
Q = sorted(L)
R = sorted(L,key=itemgetter(1))
ans = 0
suma=0
for i in range(N//2+1):
suma +=2*(Q[-i-1][0]-R[i][1])
if suma>ans:
ans = suma
print(ans)
```
Yes
| 13,994 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate 0. Aoki has N segments. The i-th segment is [L_i,R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).
The game has N steps. The i-th step proceeds as follows:
* First, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.
* Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.
After N steps are performed, Takahashi will return to coordinate 0 and the game ends.
Let K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?
Constraints
* 1 ≤ N ≤ 10^5
* -10^5 ≤ L_i < R_i ≤ 10^5
* L_i and R_i are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above. It is guaranteed that K is always an integer when L_i,R_i are integers.
Examples
Input
3
-5 1
3 7
-4 -2
Output
10
Input
3
1 2
3 4
5 6
Output
12
Input
5
-2 0
-2 0
7 8
9 10
-2 -1
Output
34
Submitted Solution:
```
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
from heapq import heappop,heappush
from copy import deepcopy
n = int(readline())
lr = list(map(int,read().split()))
hq_left = []
hq_right = []
for i in range(n):
l,r = lr[i*2:i*2+2]
heappush(hq_left,(-1*l,i))
heappush(hq_right,(r,i))
hq_left_origin = deepcopy(hq_left)
hq_right_origin = deepcopy(hq_right)
done = [0] * n
ans = -1*10**5
now = 10**5
while(len(hq_left)>0)&(len(hq_right)>0):
while(hq_left):
l,ind_l = hq_left[0]
l *= -1
if(done[ind_l] == 1):
heappop(hq_left)
else:
break
else:
break
while(hq_right):
r,ind_r = hq_right[0]
if(done[ind_r] == 1):
heappop(hq_right)
else:
break
else:
break
if( l-now > now-r):
if(l > now):
ans += l-now
now = l
done[ind_l] = 1
heappop(hq_left)
else:
if(now > r):
ans += now-r
now = r
done[ind_r] = 1
heappop(hq_right)
ans += abs(now)
ans2 = -1*10**5
now = -1 * 10**5
hq_left = deepcopy(hq_left_origin)
hq_right = deepcopy(hq_right_origin)
done = [0] * n
while(len(hq_left)>0)&(len(hq_right)>0):
while(hq_left):
l,ind_l = hq_left[0]
l *= -1
if(done[ind_l] == 1):
heappop(hq_left)
else:
break
else:
break
while(hq_right):
r,ind_r = hq_right[0]
if(done[ind_r] == 1):
heappop(hq_right)
else:
break
else:
break
if( l-now > now-r):
if(l > now):
ans2 += l-now
now = l
done[ind_l] = 1
heappop(hq_left)
else:
if(now > r):
ans2 += now-r
now = r
done[ind_r] = 1
heappop(hq_right)
ans2 += abs(now)
print(max(ans,ans2))
```
Yes
| 13,995 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate 0. Aoki has N segments. The i-th segment is [L_i,R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).
The game has N steps. The i-th step proceeds as follows:
* First, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.
* Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.
After N steps are performed, Takahashi will return to coordinate 0 and the game ends.
Let K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?
Constraints
* 1 ≤ N ≤ 10^5
* -10^5 ≤ L_i < R_i ≤ 10^5
* L_i and R_i are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above. It is guaranteed that K is always an integer when L_i,R_i are integers.
Examples
Input
3
-5 1
3 7
-4 -2
Output
10
Input
3
1 2
3 4
5 6
Output
12
Input
5
-2 0
-2 0
7 8
9 10
-2 -1
Output
34
Submitted Solution:
```
from operator import itemgetter
n = int(input())
lr = [list(map(int, input().split())) for i in range(n)] + [[0, 0]]
l_sort = sorted(lr, key=itemgetter(0), reverse=True)
r_sort = sorted(lr, key=itemgetter(1))
ans = 0
sigma = 0
for i in range(n // 2 + 1):
sigma += 2 * (l_sort[i][0] - r_sort[i][1])
if sigma > ans:
ans = sigma
print(ans)
```
Yes
| 13,996 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate 0. Aoki has N segments. The i-th segment is [L_i,R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).
The game has N steps. The i-th step proceeds as follows:
* First, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.
* Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.
After N steps are performed, Takahashi will return to coordinate 0 and the game ends.
Let K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?
Constraints
* 1 ≤ N ≤ 10^5
* -10^5 ≤ L_i < R_i ≤ 10^5
* L_i and R_i are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above. It is guaranteed that K is always an integer when L_i,R_i are integers.
Examples
Input
3
-5 1
3 7
-4 -2
Output
10
Input
3
1 2
3 4
5 6
Output
12
Input
5
-2 0
-2 0
7 8
9 10
-2 -1
Output
34
Submitted Solution:
```
#!usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
res = list(sys.stdin.readline())
if res[-1] == "\n":
return res[:-1]
return res
def IR(n):
return [I() for i in range(n)]
def LIR(n):
return [LI() for i in range(n)]
def SR(n):
return [S() for i in range(n)]
def LSR(n):
return [LS() for i in range(n)]
sys.setrecursionlimit(1000000)
mod = 1000000007
def solve():
n = I()
p = LIR(n)
p.sort(key = lambda x : max(x[0],min(0,x[1])))
x = 0
ans = 0
l = 0
r = n-1
while l <= r:
a,b = p[l]
l += 1
if x < a:
ans += a-x
x = a
elif b < x:
ans += x-b
x = b
if l > r:
break
a,b = p[r]
r -= 1
if x < a:
ans += a-x
x = a
elif b < x:
ans += x-b
x = b
m = ans+abs(x)
x = 0
ans = 0
l = 0
r = n-1
while l <= r:
a,b = p[r]
r -= 1
if x < a:
ans += a-x
x = a
elif b < x:
ans += x-b
x = b
a,b = p[l]
l += 1
if x < a:
ans += a-x
x = a
elif b < x:
ans += x-b
x = b
if l > r:
break
ans += abs(x)
print(max(m,ans))
return
#Solve
if __name__ == "__main__":
solve()
```
No
| 13,997 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate 0. Aoki has N segments. The i-th segment is [L_i,R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).
The game has N steps. The i-th step proceeds as follows:
* First, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.
* Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.
After N steps are performed, Takahashi will return to coordinate 0 and the game ends.
Let K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?
Constraints
* 1 ≤ N ≤ 10^5
* -10^5 ≤ L_i < R_i ≤ 10^5
* L_i and R_i are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above. It is guaranteed that K is always an integer when L_i,R_i are integers.
Examples
Input
3
-5 1
3 7
-4 -2
Output
10
Input
3
1 2
3 4
5 6
Output
12
Input
5
-2 0
-2 0
7 8
9 10
-2 -1
Output
34
Submitted Solution:
```
# coding: utf-8
import sys
import math
import fractions
import heapq
import collections
import re
import array
import bisect
from collections import Counter, defaultdict
def array2d(dim1, dim2, init=None):
return [[init for _ in range(dim2)] for _ in range(dim1)]
def move(p, l, r):
if p < l:
p = l
elif p > r:
p = r
return p
def main():
N = int(input())
hl = []
hr = []
md = (0, 0, 0, 0)
for i in range(N):
l, r = map(int, input().split())
heapq.heappush(hl, (l, r, i))
heapq.heappush(hr, (-r, l, i))
d = abs(move(0, l, r))
# sys.stderr.write("{} -> {}\n".format(str((l, r)), d))
if d > md[0]:
md = (d, i, l, r)
# sys.stderr.write(str(md) + "\n")
used = [False] * N
ans = md[0]
used[md[1]] = True
p = move(0, md[2], md[3])
if p > 0:
mode = 1 # right
else:
mode = 0 # left / center?
while hr and hl:
# sys.stderr.write("pos: {}\n".format(p))
if mode == 0:
if len(hr) == 0:
mode = 1
continue
r, l, i = heapq.heappop(hr)
# sys.stderr.write("r: {}\n".format(str((l, -r, i))))
# sys.stderr.write(" used: {}\n".format(used[i]))
if not used[i]:
used[i] = True
r = -r
np = move(p, l, r)
ans += abs(p-np)
p = np
mode = 1
else:
if len(hl) == 0:
mode = 0
continue
l, r, i = heapq.heappop(hl)
# sys.stderr.write("l: {}\n".format(str((l, r, i))))
# sys.stderr.write(" used: {}\n".format(used[i]))
if not used[i]:
used[i] = True
np = move(p, l, r)
ans += abs(p-np)
p = np
mode = 0
ans += abs(p)
return ans
if __name__ == "__main__":
print(main())
```
No
| 13,998 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi and Aoki will play a game with a number line and some segments. Takahashi is standing on the number line and he is initially at coordinate 0. Aoki has N segments. The i-th segment is [L_i,R_i], that is, a segment consisting of points with coordinates between L_i and R_i (inclusive).
The game has N steps. The i-th step proceeds as follows:
* First, Aoki chooses a segment that is still not chosen yet from the N segments and tells it to Takahashi.
* Then, Takahashi walks along the number line to some point within the segment chosen by Aoki this time.
After N steps are performed, Takahashi will return to coordinate 0 and the game ends.
Let K be the total distance traveled by Takahashi throughout the game. Aoki will choose segments so that K will be as large as possible, and Takahashi walks along the line so that K will be as small as possible. What will be the value of K in the end?
Constraints
* 1 ≤ N ≤ 10^5
* -10^5 ≤ L_i < R_i ≤ 10^5
* L_i and R_i are integers.
Input
Input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the total distance traveled by Takahashi throughout the game when Takahashi and Aoki acts as above. It is guaranteed that K is always an integer when L_i,R_i are integers.
Examples
Input
3
-5 1
3 7
-4 -2
Output
10
Input
3
1 2
3 4
5 6
Output
12
Input
5
-2 0
-2 0
7 8
9 10
-2 -1
Output
34
Submitted Solution:
```
#!usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
res = list(sys.stdin.readline())
if res[-1] == "\n":
return res[:-1]
return res
def IR(n):
return [I() for i in range(n)]
def LIR(n):
return [LI() for i in range(n)]
def SR(n):
return [S() for i in range(n)]
def LSR(n):
return [LS() for i in range(n)]
sys.setrecursionlimit(1000000)
mod = 1000000007
def solve():
n = I()
p = LIR(n)
p.sort(key = lambda x : max(x[0],min(0,x[1])))
if p[0][1] < p[-1][0]:
p = p[::-1]
x = 0
ans = 0
l = 0
r = n-1
while l <= r:
a,b = p[l]
l += 1
if x < a:
ans += a-x
x = a
elif b < x:
ans += x-b
x = b
if l > r:
break
a,b = p[r]
r -= 1
if x < a:
ans += a-x
x = a
elif b < x:
ans += x-b
x = b
ans += abs(x)
print(ans)
return
#Solve
if __name__ == "__main__":
solve()
```
No
| 13,999 |
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