text stringlengths 198 433k | conversation_id int64 0 109k |
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Provide a correct Python 3 solution for this coding contest problem.
Takahashi is at an all-you-can-eat restaurant.
The restaurant offers N kinds of dishes. It takes A_i minutes to eat the i-th dish, whose deliciousness is B_i.
The restaurant has the following rules:
* You can only order one dish at a time. The dish ordered will be immediately served and ready to eat.
* You cannot order the same kind of dish more than once.
* Until you finish eating the dish already served, you cannot order a new dish.
* After T-0.5 minutes from the first order, you can no longer place a new order, but you can continue eating the dish already served.
Let Takahashi's happiness be the sum of the deliciousness of the dishes he eats in this restaurant.
What is the maximum possible happiness achieved by making optimal choices?
Constraints
* 2 \leq N \leq 3000
* 1 \leq T \leq 3000
* 1 \leq A_i \leq 3000
* 1 \leq B_i \leq 3000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N T
A_1 B_1
:
A_N B_N
Output
Print the maximum possible happiness Takahashi can achieve.
Examples
Input
2 60
10 10
100 100
Output
110
Input
3 60
10 10
10 20
10 30
Output
60
Input
3 60
30 10
30 20
30 30
Output
50
Input
10 100
15 23
20 18
13 17
24 12
18 29
19 27
23 21
18 20
27 15
22 25
Output
145
"Correct Solution:
```
N,T = map(int, input().split())
abl = []
for _ in range(N):
a,b = map(int, input().split())
abl.append((a,b))
abl.sort()
dp = [ [0]*6001 for _ in range(N+1) ]
for i in range(N):
a,b = abl[i]
for t in range(6001):
dp[i+1][t] = max(dp[i+1][t], dp[i][t])
if t < T: dp[i+1][t+a] = max(dp[i][t]+b, dp[i][t+a])
ans = max(dp[N])
print(ans)
```
| 6,400 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi is at an all-you-can-eat restaurant.
The restaurant offers N kinds of dishes. It takes A_i minutes to eat the i-th dish, whose deliciousness is B_i.
The restaurant has the following rules:
* You can only order one dish at a time. The dish ordered will be immediately served and ready to eat.
* You cannot order the same kind of dish more than once.
* Until you finish eating the dish already served, you cannot order a new dish.
* After T-0.5 minutes from the first order, you can no longer place a new order, but you can continue eating the dish already served.
Let Takahashi's happiness be the sum of the deliciousness of the dishes he eats in this restaurant.
What is the maximum possible happiness achieved by making optimal choices?
Constraints
* 2 \leq N \leq 3000
* 1 \leq T \leq 3000
* 1 \leq A_i \leq 3000
* 1 \leq B_i \leq 3000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N T
A_1 B_1
:
A_N B_N
Output
Print the maximum possible happiness Takahashi can achieve.
Examples
Input
2 60
10 10
100 100
Output
110
Input
3 60
10 10
10 20
10 30
Output
60
Input
3 60
30 10
30 20
30 30
Output
50
Input
10 100
15 23
20 18
13 17
24 12
18 29
19 27
23 21
18 20
27 15
22 25
Output
145
"Correct Solution:
```
n,t=map(int,input().split())
l=[list(map(int,input().split())) for i in range(n)]
l.sort()
dp=[[0]*(t) for i in range(n+1)]
for i in range(1,n+1):
for j in range(t):
if j-l[i-1][0]>=0:
dp[i][j]=max(dp[i-1][j-l[i-1][0]]+l[i-1][1],dp[i-1][j])
else:
dp[i][j]=dp[i-1][j]
ans=[]
for i in range(n):
ans.append(dp[i][-1]+l[i][1])
print(max(ans))
```
| 6,401 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi is at an all-you-can-eat restaurant.
The restaurant offers N kinds of dishes. It takes A_i minutes to eat the i-th dish, whose deliciousness is B_i.
The restaurant has the following rules:
* You can only order one dish at a time. The dish ordered will be immediately served and ready to eat.
* You cannot order the same kind of dish more than once.
* Until you finish eating the dish already served, you cannot order a new dish.
* After T-0.5 minutes from the first order, you can no longer place a new order, but you can continue eating the dish already served.
Let Takahashi's happiness be the sum of the deliciousness of the dishes he eats in this restaurant.
What is the maximum possible happiness achieved by making optimal choices?
Constraints
* 2 \leq N \leq 3000
* 1 \leq T \leq 3000
* 1 \leq A_i \leq 3000
* 1 \leq B_i \leq 3000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N T
A_1 B_1
:
A_N B_N
Output
Print the maximum possible happiness Takahashi can achieve.
Examples
Input
2 60
10 10
100 100
Output
110
Input
3 60
10 10
10 20
10 30
Output
60
Input
3 60
30 10
30 20
30 30
Output
50
Input
10 100
15 23
20 18
13 17
24 12
18 29
19 27
23 21
18 20
27 15
22 25
Output
145
"Correct Solution:
```
N, T = map(int, input().split())
a_list = []
for _ in range(N):
a, b = map(int, input().split())
a_list.append((a, b))
a_list.sort(key=lambda x: x[0])
dp = [[0 for _ in range(T + 3001)] for _ in range(N + 1)]
for i in range(1, N + 1):
a, b = a_list[i - 1]
for j in range(T + 3001):
dp[i][j] = dp[i - 1][j]
for j in range(T):
dp[i][j + a] = max(dp[i - 1][j + a], dp[i - 1][j] + b)
print(max(dp[-1]))
```
| 6,402 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi is at an all-you-can-eat restaurant.
The restaurant offers N kinds of dishes. It takes A_i minutes to eat the i-th dish, whose deliciousness is B_i.
The restaurant has the following rules:
* You can only order one dish at a time. The dish ordered will be immediately served and ready to eat.
* You cannot order the same kind of dish more than once.
* Until you finish eating the dish already served, you cannot order a new dish.
* After T-0.5 minutes from the first order, you can no longer place a new order, but you can continue eating the dish already served.
Let Takahashi's happiness be the sum of the deliciousness of the dishes he eats in this restaurant.
What is the maximum possible happiness achieved by making optimal choices?
Constraints
* 2 \leq N \leq 3000
* 1 \leq T \leq 3000
* 1 \leq A_i \leq 3000
* 1 \leq B_i \leq 3000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N T
A_1 B_1
:
A_N B_N
Output
Print the maximum possible happiness Takahashi can achieve.
Examples
Input
2 60
10 10
100 100
Output
110
Input
3 60
10 10
10 20
10 30
Output
60
Input
3 60
30 10
30 20
30 30
Output
50
Input
10 100
15 23
20 18
13 17
24 12
18 29
19 27
23 21
18 20
27 15
22 25
Output
145
"Correct Solution:
```
n,t = map(int,input().split())
ab = sorted([list(map(int, input().split())) for i in range(n)])
dp = [[0 for i in range(t+1)]for j in range(n+1)]
for i in range(n):
ti,vi = ab[i]
for j in range(t+1):
if j + ti <= t:
dp[i+1][j+ti] = max(dp[i+1][j+ti],dp[i][j]+vi)
dp[i+1][j] = max(dp[i][j],dp[i+1][j])
ans = 0
for i, (ti, vi) in enumerate(ab):
ans = max(ans, dp[i][t - 1] + vi)
print(ans)
```
| 6,403 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi is at an all-you-can-eat restaurant.
The restaurant offers N kinds of dishes. It takes A_i minutes to eat the i-th dish, whose deliciousness is B_i.
The restaurant has the following rules:
* You can only order one dish at a time. The dish ordered will be immediately served and ready to eat.
* You cannot order the same kind of dish more than once.
* Until you finish eating the dish already served, you cannot order a new dish.
* After T-0.5 minutes from the first order, you can no longer place a new order, but you can continue eating the dish already served.
Let Takahashi's happiness be the sum of the deliciousness of the dishes he eats in this restaurant.
What is the maximum possible happiness achieved by making optimal choices?
Constraints
* 2 \leq N \leq 3000
* 1 \leq T \leq 3000
* 1 \leq A_i \leq 3000
* 1 \leq B_i \leq 3000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N T
A_1 B_1
:
A_N B_N
Output
Print the maximum possible happiness Takahashi can achieve.
Examples
Input
2 60
10 10
100 100
Output
110
Input
3 60
10 10
10 20
10 30
Output
60
Input
3 60
30 10
30 20
30 30
Output
50
Input
10 100
15 23
20 18
13 17
24 12
18 29
19 27
23 21
18 20
27 15
22 25
Output
145
"Correct Solution:
```
import sys
input = sys.stdin.readline
N,T=map(int,input().split())
D=[tuple(map(int,input().split())) for i in range(N)]
D.sort()
DP=[0]*(T+1)
ANS=0
for i in range(N):
a,b=D[i]
for j in range(T,a-1,-1):
DP[j]=max(DP[j-a]+b,DP[j])
for j in range(i+1,N):
ANS=max(ANS,DP[T-1]+D[j][1])
print(ANS)
```
| 6,404 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi is at an all-you-can-eat restaurant.
The restaurant offers N kinds of dishes. It takes A_i minutes to eat the i-th dish, whose deliciousness is B_i.
The restaurant has the following rules:
* You can only order one dish at a time. The dish ordered will be immediately served and ready to eat.
* You cannot order the same kind of dish more than once.
* Until you finish eating the dish already served, you cannot order a new dish.
* After T-0.5 minutes from the first order, you can no longer place a new order, but you can continue eating the dish already served.
Let Takahashi's happiness be the sum of the deliciousness of the dishes he eats in this restaurant.
What is the maximum possible happiness achieved by making optimal choices?
Constraints
* 2 \leq N \leq 3000
* 1 \leq T \leq 3000
* 1 \leq A_i \leq 3000
* 1 \leq B_i \leq 3000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N T
A_1 B_1
:
A_N B_N
Output
Print the maximum possible happiness Takahashi can achieve.
Examples
Input
2 60
10 10
100 100
Output
110
Input
3 60
10 10
10 20
10 30
Output
60
Input
3 60
30 10
30 20
30 30
Output
50
Input
10 100
15 23
20 18
13 17
24 12
18 29
19 27
23 21
18 20
27 15
22 25
Output
145
Submitted Solution:
```
def main():
N, T = map(int, input().split())
ab = [tuple(map(int, input().split())) for i in range(N)]
ab.sort(key=lambda x: x[0])
t = ab[-1][0]
dp = [-1]*(T+t+1)
dp[0] = 0
for a, b in ab:
for i in range(T-1, -1, -1):
if dp[i] < 0:
continue
if dp[i+a] < dp[i]+b:
dp[i+a] = dp[i]+b
ans = max(dp)
print(ans)
main()
```
Yes
| 6,405 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi is at an all-you-can-eat restaurant.
The restaurant offers N kinds of dishes. It takes A_i minutes to eat the i-th dish, whose deliciousness is B_i.
The restaurant has the following rules:
* You can only order one dish at a time. The dish ordered will be immediately served and ready to eat.
* You cannot order the same kind of dish more than once.
* Until you finish eating the dish already served, you cannot order a new dish.
* After T-0.5 minutes from the first order, you can no longer place a new order, but you can continue eating the dish already served.
Let Takahashi's happiness be the sum of the deliciousness of the dishes he eats in this restaurant.
What is the maximum possible happiness achieved by making optimal choices?
Constraints
* 2 \leq N \leq 3000
* 1 \leq T \leq 3000
* 1 \leq A_i \leq 3000
* 1 \leq B_i \leq 3000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N T
A_1 B_1
:
A_N B_N
Output
Print the maximum possible happiness Takahashi can achieve.
Examples
Input
2 60
10 10
100 100
Output
110
Input
3 60
10 10
10 20
10 30
Output
60
Input
3 60
30 10
30 20
30 30
Output
50
Input
10 100
15 23
20 18
13 17
24 12
18 29
19 27
23 21
18 20
27 15
22 25
Output
145
Submitted Solution:
```
n,t=map(int,input().split())
ab=[list(map(int,input().split()))for _ in range(n)]
ab.sort()
dp=[6007*[0]for _ in range(n)]
ans=0
for i in range(n):
a,b=ab[i]
for j in range(6007):
if i==0:
if j>=a and j<t:dp[i][j]=b
elif j>=a and j-a<t:dp[i][j]=max(dp[i-1][j-a]+b,dp[i-1][j])
else:dp[i][j]=dp[i-1][j]
ans=max(ans,dp[i][j])
print(ans)
```
Yes
| 6,406 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi is at an all-you-can-eat restaurant.
The restaurant offers N kinds of dishes. It takes A_i minutes to eat the i-th dish, whose deliciousness is B_i.
The restaurant has the following rules:
* You can only order one dish at a time. The dish ordered will be immediately served and ready to eat.
* You cannot order the same kind of dish more than once.
* Until you finish eating the dish already served, you cannot order a new dish.
* After T-0.5 minutes from the first order, you can no longer place a new order, but you can continue eating the dish already served.
Let Takahashi's happiness be the sum of the deliciousness of the dishes he eats in this restaurant.
What is the maximum possible happiness achieved by making optimal choices?
Constraints
* 2 \leq N \leq 3000
* 1 \leq T \leq 3000
* 1 \leq A_i \leq 3000
* 1 \leq B_i \leq 3000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N T
A_1 B_1
:
A_N B_N
Output
Print the maximum possible happiness Takahashi can achieve.
Examples
Input
2 60
10 10
100 100
Output
110
Input
3 60
10 10
10 20
10 30
Output
60
Input
3 60
30 10
30 20
30 30
Output
50
Input
10 100
15 23
20 18
13 17
24 12
18 29
19 27
23 21
18 20
27 15
22 25
Output
145
Submitted Solution:
```
n,t=map(int,input().split())
l=[list(map(int,input().split())) for i in range(n)]
l.sort()
L=[]
for i in range(n):
L.append(l[i][1])
dp=[[0]*(t) for i in range(n+1)]
for i in range(1,n+1):
for j in range(t):
if j-l[i-1][0]>=0:
dp[i][j]=max(dp[i-1][j-l[i-1][0]]+l[i-1][1],dp[i-1][j])
else:
dp[i][j]=dp[i-1][j]
ans=[]
for i in range(n):
ans.append(dp[i][-1]+max(L[i:]))
print(max(ans))
```
Yes
| 6,407 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi is at an all-you-can-eat restaurant.
The restaurant offers N kinds of dishes. It takes A_i minutes to eat the i-th dish, whose deliciousness is B_i.
The restaurant has the following rules:
* You can only order one dish at a time. The dish ordered will be immediately served and ready to eat.
* You cannot order the same kind of dish more than once.
* Until you finish eating the dish already served, you cannot order a new dish.
* After T-0.5 minutes from the first order, you can no longer place a new order, but you can continue eating the dish already served.
Let Takahashi's happiness be the sum of the deliciousness of the dishes he eats in this restaurant.
What is the maximum possible happiness achieved by making optimal choices?
Constraints
* 2 \leq N \leq 3000
* 1 \leq T \leq 3000
* 1 \leq A_i \leq 3000
* 1 \leq B_i \leq 3000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N T
A_1 B_1
:
A_N B_N
Output
Print the maximum possible happiness Takahashi can achieve.
Examples
Input
2 60
10 10
100 100
Output
110
Input
3 60
10 10
10 20
10 30
Output
60
Input
3 60
30 10
30 20
30 30
Output
50
Input
10 100
15 23
20 18
13 17
24 12
18 29
19 27
23 21
18 20
27 15
22 25
Output
145
Submitted Solution:
```
def main():
e=enumerate
(n,t),*g=[list(map(int,t.split()))for t in open(0)]
d=[0]
g.sort()
dp=[]
d=[0]*t
for a,b in g:
p=d[:]
for i in range(a,t):
v=d[i-a]+b
if v>p[i]:p[i]=v
dp+=p,
d=p
a=m=0
for(*_,v),(_,w)in zip(dp[-2::-1],g[::-1]):
if w>m:m=w
if v+m>a:a=v+m
print(a)
main()
```
Yes
| 6,408 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi is at an all-you-can-eat restaurant.
The restaurant offers N kinds of dishes. It takes A_i minutes to eat the i-th dish, whose deliciousness is B_i.
The restaurant has the following rules:
* You can only order one dish at a time. The dish ordered will be immediately served and ready to eat.
* You cannot order the same kind of dish more than once.
* Until you finish eating the dish already served, you cannot order a new dish.
* After T-0.5 minutes from the first order, you can no longer place a new order, but you can continue eating the dish already served.
Let Takahashi's happiness be the sum of the deliciousness of the dishes he eats in this restaurant.
What is the maximum possible happiness achieved by making optimal choices?
Constraints
* 2 \leq N \leq 3000
* 1 \leq T \leq 3000
* 1 \leq A_i \leq 3000
* 1 \leq B_i \leq 3000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N T
A_1 B_1
:
A_N B_N
Output
Print the maximum possible happiness Takahashi can achieve.
Examples
Input
2 60
10 10
100 100
Output
110
Input
3 60
10 10
10 20
10 30
Output
60
Input
3 60
30 10
30 20
30 30
Output
50
Input
10 100
15 23
20 18
13 17
24 12
18 29
19 27
23 21
18 20
27 15
22 25
Output
145
Submitted Solution:
```
from operator import itemgetter
def cul(menu):
good = 0 # 美味しさ
time = 0 # 時間
for i in range(len(menu)):
if time >= T-1:
break
else:
good += menu[i][1]
time += menu[i][0]
return good
N,T = map(int,input().split())
menu = list()
for i in range(N):
menu.append(list(map(int,input().split())))
# 時間が少ない順に計算
menu.sort() # 時間が少ない順にソート
good_1 = cul(menu)
# 満足度が多い順に計算
menu.sort(key=itemgetter(1),reverse=True)
good_2 = cul(menu)
print(max(good_1,good_2))
# 満足度と時間を考えてソート
# menu_1 = dict()
# for i in range(len(menu)):
# if abs(menu[i][1]-menu[i][0]) not in menu_1:
# menu_1[abs(menu[i][1]-menu[i][0])] = menu[i]
# print(menu_1)
```
No
| 6,409 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi is at an all-you-can-eat restaurant.
The restaurant offers N kinds of dishes. It takes A_i minutes to eat the i-th dish, whose deliciousness is B_i.
The restaurant has the following rules:
* You can only order one dish at a time. The dish ordered will be immediately served and ready to eat.
* You cannot order the same kind of dish more than once.
* Until you finish eating the dish already served, you cannot order a new dish.
* After T-0.5 minutes from the first order, you can no longer place a new order, but you can continue eating the dish already served.
Let Takahashi's happiness be the sum of the deliciousness of the dishes he eats in this restaurant.
What is the maximum possible happiness achieved by making optimal choices?
Constraints
* 2 \leq N \leq 3000
* 1 \leq T \leq 3000
* 1 \leq A_i \leq 3000
* 1 \leq B_i \leq 3000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N T
A_1 B_1
:
A_N B_N
Output
Print the maximum possible happiness Takahashi can achieve.
Examples
Input
2 60
10 10
100 100
Output
110
Input
3 60
10 10
10 20
10 30
Output
60
Input
3 60
30 10
30 20
30 30
Output
50
Input
10 100
15 23
20 18
13 17
24 12
18 29
19 27
23 21
18 20
27 15
22 25
Output
145
Submitted Solution:
```
N, T = map(int, input().split())
AB = [list(map(int, input().split())) for _ in range(N)]
dp = [[[0] * T for _ in range(N + 1)] for _ in range(2)] # (最後の注文を使ったか, i未満までみた, T)
for i in range(1, N + 1):
a, b = AB[i-1]
for t in range(T):
if t-a>=0:
dp[0][i][t] = max(dp[0][i - 1][t], dp[0][i - 1][t-a] + b)
else:
dp[0][i][t] = dp[0][i - 1][t]
dp[1][i][t] = max(dp[1][i - 1][t], dp[0][i - 1][t] + b)
print(dp[1][N][T-1])
```
No
| 6,410 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi is at an all-you-can-eat restaurant.
The restaurant offers N kinds of dishes. It takes A_i minutes to eat the i-th dish, whose deliciousness is B_i.
The restaurant has the following rules:
* You can only order one dish at a time. The dish ordered will be immediately served and ready to eat.
* You cannot order the same kind of dish more than once.
* Until you finish eating the dish already served, you cannot order a new dish.
* After T-0.5 minutes from the first order, you can no longer place a new order, but you can continue eating the dish already served.
Let Takahashi's happiness be the sum of the deliciousness of the dishes he eats in this restaurant.
What is the maximum possible happiness achieved by making optimal choices?
Constraints
* 2 \leq N \leq 3000
* 1 \leq T \leq 3000
* 1 \leq A_i \leq 3000
* 1 \leq B_i \leq 3000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N T
A_1 B_1
:
A_N B_N
Output
Print the maximum possible happiness Takahashi can achieve.
Examples
Input
2 60
10 10
100 100
Output
110
Input
3 60
10 10
10 20
10 30
Output
60
Input
3 60
30 10
30 20
30 30
Output
50
Input
10 100
15 23
20 18
13 17
24 12
18 29
19 27
23 21
18 20
27 15
22 25
Output
145
Submitted Solution:
```
N,T = map(int,input().split())
AB = [tuple(map(int,input().split())) for i in range(N)]
dp = [[[0,0] for t in range(T)] for i in range(N+1)]
for i,(a,b) in enumerate(AB):
for t in range(T-1,-1,-1):
dp[i+1][t][0] = max(dp[i+1][t][0], dp[i][t][0])
dp[i+1][t][1] = max(dp[i+1][t][1], dp[i][t][1])
if t+a < T:
dp[i+1][t+a][0] = max(dp[i+1][t+a][0], dp[i][t][0] + b)
dp[i+1][t+a][1] = max(dp[i+1][t+a][1], dp[i][t][1] + b)
dp[i+1][t][1] = max(dp[i+1][t][1], dp[i][t][0] + b)
print(dp[-1][-1][-1])
```
No
| 6,411 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi is at an all-you-can-eat restaurant.
The restaurant offers N kinds of dishes. It takes A_i minutes to eat the i-th dish, whose deliciousness is B_i.
The restaurant has the following rules:
* You can only order one dish at a time. The dish ordered will be immediately served and ready to eat.
* You cannot order the same kind of dish more than once.
* Until you finish eating the dish already served, you cannot order a new dish.
* After T-0.5 minutes from the first order, you can no longer place a new order, but you can continue eating the dish already served.
Let Takahashi's happiness be the sum of the deliciousness of the dishes he eats in this restaurant.
What is the maximum possible happiness achieved by making optimal choices?
Constraints
* 2 \leq N \leq 3000
* 1 \leq T \leq 3000
* 1 \leq A_i \leq 3000
* 1 \leq B_i \leq 3000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N T
A_1 B_1
:
A_N B_N
Output
Print the maximum possible happiness Takahashi can achieve.
Examples
Input
2 60
10 10
100 100
Output
110
Input
3 60
10 10
10 20
10 30
Output
60
Input
3 60
30 10
30 20
30 30
Output
50
Input
10 100
15 23
20 18
13 17
24 12
18 29
19 27
23 21
18 20
27 15
22 25
Output
145
Submitted Solution:
```
N, T = map(int, input().split())
data = []
for i in range(N):
a, b = map(int, input().split())
data.append((a,b))
data.sort()
#print(data)
dp = [0] * T
ans = 0
for a, b in data:
ans = max(ans, dp[-1]+b)
if a < T:
eatable = dp[:T-a]
j = 0
for i in range(a, T, 1):
if dp[i] < eatable[j] + b:
dp[i] = eatable[j] + b
j += 1
print(ans)
```
No
| 6,412 |
Provide a correct Python 3 solution for this coding contest problem.
There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).
We will repeat the following operation as long as possible:
* Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.
We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq x_i, y_i \leq 10^5
* If i \neq j, x_i \neq x_j or y_i \neq y_j.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the maximum number of times we can do the operation.
Examples
Input
3
1 1
5 1
5 5
Output
1
Input
2
10 10
20 20
Output
0
Input
9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5
Output
16
"Correct Solution:
```
import sys
from collections import defaultdict
import queue
n = int(sys.stdin.readline())
graph = defaultdict(list)
X, Y = [[] for i in range(n)], [[] for i in range(n)]
atX, atY = defaultdict(list), defaultdict(list)
for i in range(n):
a, b = map(int, sys.stdin.readline().split())
a -= 1; b-= 1
X[i] = a; Y[i] = b
atX[X[i]].append(i)
atY[Y[i]].append(i)
visX = set(); visY = set()
found = [False]*n
ans = n*(-1)
for root in range(n):
if found[root]: continue
usedX, usedY = set(), set()
que = queue.Queue()
que.put(root)
found[root] = True
usedX.add(X[root])
usedY.add(Y[root])
while not que.empty():
cur = que.get()
toVisit = []
if X[cur] not in visX:
visX.add(X[cur])
for ele in atX[X[cur]]:
toVisit.append(ele)
if Y[cur] not in visY:
visY.add(Y[cur])
for ele in atY[Y[cur]]:
toVisit.append(ele)
for ele in toVisit:
if found[ele]: continue
found[ele] = True
usedX.add(X[ele])
usedY.add(Y[ele])
que.put(ele)
ans += len(usedX)*len(usedY)
print(ans)
```
| 6,413 |
Provide a correct Python 3 solution for this coding contest problem.
There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).
We will repeat the following operation as long as possible:
* Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.
We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq x_i, y_i \leq 10^5
* If i \neq j, x_i \neq x_j or y_i \neq y_j.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the maximum number of times we can do the operation.
Examples
Input
3
1 1
5 1
5 5
Output
1
Input
2
10 10
20 20
Output
0
Input
9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5
Output
16
"Correct Solution:
```
from itertools import*
from math import*
from collections import*
from heapq import*
from bisect import bisect_left,bisect_right
from copy import deepcopy
inf = float("inf")
mod = 10**9+7
from functools import reduce
import sys
sys.setrecursionlimit(10**7)
class UnionFind():
def __init__(self, N):
self.rank = [0] * N
self.par = [i for i in range(N)]
self.counter = [1] * N
def find(self, x):
if self.par[x] == x:
return x
else:
self.par[x] = self.find(self.par[x])
return self.par[x]
def unite(self, x, y):
x = self.find(x)
y = self.find(y)
if x != y:
z = self.counter[x] + self.counter[y]
self.counter[x], self.counter[y] = z, z
if self.rank[x] < self.rank[y]:
self.par[x] = y
else:
self.par[y] = x
if self.rank[x] == self.rank[y]:
self.rank[x] += 1
def size(self, x):
x = self.find(x)
return self.counter[x]
def same(self, x, y):
return self.find(x) == self.find(y)
N = int(input())
uf = UnionFind(N)
x_dict={}
y_dict={}
xy = []
for i in range(N):
x,y = map(int,input().split())
if x in x_dict:
uf.unite(i,x_dict[x])
else:
x_dict[x]=i
if y in y_dict:
uf.unite(i,y_dict[y])
else:
y_dict[y]=i
xy.append((x,y))
unite_dict={}
for i in range(N):
ur = uf.find(i)
unite_dict.setdefault(ur,[set(),set()])
unite_dict[ur][0].add(xy[i][0])
unite_dict[ur][1].add(xy[i][1])
p = 0
for k,v in unite_dict.items():
p +=len(v[0])*len(v[1])
print(p-N)
```
| 6,414 |
Provide a correct Python 3 solution for this coding contest problem.
There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).
We will repeat the following operation as long as possible:
* Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.
We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq x_i, y_i \leq 10^5
* If i \neq j, x_i \neq x_j or y_i \neq y_j.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the maximum number of times we can do the operation.
Examples
Input
3
1 1
5 1
5 5
Output
1
Input
2
10 10
20 20
Output
0
Input
9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5
Output
16
"Correct Solution:
```
# 長方形の4点のうち3点が必要なので自明からほど遠い
# x,yを2部グラフ、格子を辺とみなす
# 連結成分ごとに張られる......
n = int(input())
xy = [list(map(int, input().split())) for _ in range(n)]
mx =0
my = 0
for i in range(n):
mx = max(mx,xy[i][0])
my = max(my,xy[i][1])
*p, = range(mx+my+1)
rank = [1]*(mx+my+1)
for i in range(n):
xy[i][1] += mx
def root(x):
if x == p[x]:
return x
p[x] = y = root(p[x])
return y
def unite(x, y):
px = root(x); py = root(y)
if px == py:
return 0
rx = rank[px]; ry = rank[py]
if ry < rx:
p[py] = px
elif rx < ry:
p[px] = py
else:
p[py] = px
rank[px] += 1
return 1
for x,y in xy:
unite (x,y)
xp = [0]*(mx+my+1)
yp = [0]*(mx+my+1)
for i in range(mx+my+1):
if i<=mx:
xp[root(i)]+=1#p[i]では不十分
else:
yp[root(i)]+=1
ans = 0
for i in range(mx+my+1):
ans += xp[i]*yp[i]
ans -= n
print(ans)
```
| 6,415 |
Provide a correct Python 3 solution for this coding contest problem.
There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).
We will repeat the following operation as long as possible:
* Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.
We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq x_i, y_i \leq 10^5
* If i \neq j, x_i \neq x_j or y_i \neq y_j.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the maximum number of times we can do the operation.
Examples
Input
3
1 1
5 1
5 5
Output
1
Input
2
10 10
20 20
Output
0
Input
9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5
Output
16
"Correct Solution:
```
n = int(input())
xy = [list(map(int, input().split())) for _ in range(n)]
xtoy = {}
ytox = {}
for x, y in xy:
if x not in xtoy:
xtoy[x] = []
xtoy[x].append(y)
if y not in ytox:
ytox[y] = []
ytox[y].append(x)
ret = 0
while len(xtoy) > 0:
x = next(iter(xtoy))
xs = set()
ys = set()
xs.add(x)
q = [(x, None)]
while len(q) > 0:
(xx, yy) = q.pop(0)
if xx is not None:
for y in xtoy.pop(xx):
if y not in ys:
ys.add(y)
q.append((None, y))
if yy is not None:
for x in ytox.pop(yy):
if x not in xs:
xs.add(x)
q.append((x, None))
ret += len(xs) * len(ys)
print(ret - n)
```
| 6,416 |
Provide a correct Python 3 solution for this coding contest problem.
There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).
We will repeat the following operation as long as possible:
* Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.
We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq x_i, y_i \leq 10^5
* If i \neq j, x_i \neq x_j or y_i \neq y_j.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the maximum number of times we can do the operation.
Examples
Input
3
1 1
5 1
5 5
Output
1
Input
2
10 10
20 20
Output
0
Input
9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5
Output
16
"Correct Solution:
```
import sys
input = sys.stdin.readline
max_n = 10**5
ans = 0
n = int(input())
class UnionFind:
def __init__(self, n):
self.par = [i for i in range(n)]
self.sizea = [1 if _ < n//2 else 0 for _ in range(n)]
self.sizeb = [0 if _ < n//2 else 1 for _ in range(n)]
self.sizec = [1 for _ in range(n)]
self.rank = [0] * (n)
def find(self, x):
if self.par[x] == x:
return x
else:
self.par[x] = self.find(self.par[x])
return self.par[x]
def is_root(self, x):
if self.par[x] == x:
return True
else:
return False
def union(self, x, y):
x = self.find(x)
y = self.find(y)
if x != y:
if self.rank[x] < self.rank[y]:
x, y = y, x
if self.rank[x] == self.rank[y]:
self.rank[x] += 1
self.par[y] = x
self.sizea[x] += self.sizea[y]
self.sizeb[x] += self.sizeb[y]
self.sizec[x] += self.sizec[y]
else:
self.sizec[x] += 1
def get_size(self, x):
x = self.find(x)
return self.sizea[x],self.sizeb[x],self.sizec[x]
uf = UnionFind(2*max_n)
for _ in range(n):
x,y = map(int, input().split())
x -= 1
y += max_n - 1
uf.union(x, y)
for i in range(max_n):
if uf.is_root(i):
a,b,c = uf.get_size(i)
if a*b > 1:
ans += a*b -(c-1)
print(ans)
```
| 6,417 |
Provide a correct Python 3 solution for this coding contest problem.
There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).
We will repeat the following operation as long as possible:
* Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.
We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq x_i, y_i \leq 10^5
* If i \neq j, x_i \neq x_j or y_i \neq y_j.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the maximum number of times we can do the operation.
Examples
Input
3
1 1
5 1
5 5
Output
1
Input
2
10 10
20 20
Output
0
Input
9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5
Output
16
"Correct Solution:
```
# https://drken1215.hatenablog.com/entry/2019/06/23/004700
# https://atcoder.jp/contests/abc131/submissions/7975278
# https://tjkendev.github.io/procon-library/python/union_find/union_find.html
def main():
from collections import Counter
import sys
input = sys.stdin.readline
MX = 10 ** 5 + 10
*p, = [r for r in range(MX * 2)]
def root(x):
if x == p[x]:
return x
p[x] = y = root(p[x])
return y
def unite(x, y):
px = root(x)
py = root(y)
if px == py:
return 0
if px < py:
p[py] = px
else:
p[px] = py
return 1
n = int(input())
for _ in range(n):
x, y = (int(x) - 1 for x in input().split()) # [1,)->[0,)
unite(x, y + MX)
ctr_x = Counter(root(r) for r in range(MX))
ctr_y = Counter(root(r) for r in range(MX, MX * 2))
rs = set(ctr_x.keys())
rs.update(ctr_y.keys())
ans = sum(ctr_x[r] * ctr_y[r] for r in rs) - n
print(ans)
if __name__ == '__main__':
main()
```
| 6,418 |
Provide a correct Python 3 solution for this coding contest problem.
There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).
We will repeat the following operation as long as possible:
* Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.
We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq x_i, y_i \leq 10^5
* If i \neq j, x_i \neq x_j or y_i \neq y_j.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the maximum number of times we can do the operation.
Examples
Input
3
1 1
5 1
5 5
Output
1
Input
2
10 10
20 20
Output
0
Input
9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5
Output
16
"Correct Solution:
```
import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda :sys.stdin.readline().rstrip()
def resolve():
V=100005
n=int(input())
E=[[] for _ in range(V*2)]
for _ in range(n):
x,y=map(int,input().split())
y+=V
E[x].append(y)
E[y].append(x)
visited=[0]*(2*V)
def dfs(v):
if(visited[v]): return
visited[v]=1
cnt[v//V]+=1
for nv in E[v]: dfs(nv)
ans=[0]
for v in range(2*V):
if(visited[v]): continue
cnt=[0]*2 # 連結成分のx,yの個数
dfs(v)
ans[0]+=cnt[0]*cnt[1]
print(ans[0]-n)
resolve()
```
| 6,419 |
Provide a correct Python 3 solution for this coding contest problem.
There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).
We will repeat the following operation as long as possible:
* Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.
We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq x_i, y_i \leq 10^5
* If i \neq j, x_i \neq x_j or y_i \neq y_j.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the maximum number of times we can do the operation.
Examples
Input
3
1 1
5 1
5 5
Output
1
Input
2
10 10
20 20
Output
0
Input
9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5
Output
16
"Correct Solution:
```
import sys
sys.setrecursionlimit(10 ** 7)
def dfs(G, F, crr, pre, ret, st):
F[crr] = False
if crr < 10**5:
ret[0] += 1
else:
ret[1] += 1
for nxt in G[crr]:
if nxt == pre:
continue
p, q = crr, nxt
if q < p:
p, q = q, p
if not (p, q) in st:
st.add((p, q))
ret[2] += 1
if F[nxt]:
dfs(G, F, nxt, crr, ret, st)
def main():
n = int(input())
G = [[] for _ in range(2 * 10**5)]
for _ in range(n):
x, y = map(int, input().split())
x, y = x-1, y-1 + 10**5
G[x].append(y)
G[y].append(x)
F = [True]*(2* 10**5)
ans = 0
st = set()
for i in range(2 * 10**5):
if F[i] and len(G[i]) > 0:
tmp = [0]*3
dfs(G, F, i, -1, tmp, st)
ans += tmp[0] * tmp[1] - tmp[2]
print(ans)
if __name__ == "__main__":
main()
```
| 6,420 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).
We will repeat the following operation as long as possible:
* Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.
We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq x_i, y_i \leq 10^5
* If i \neq j, x_i \neq x_j or y_i \neq y_j.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the maximum number of times we can do the operation.
Examples
Input
3
1 1
5 1
5 5
Output
1
Input
2
10 10
20 20
Output
0
Input
9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5
Output
16
Submitted Solution:
```
import sys
sys.setrecursionlimit(10**7)
INF = 10 ** 18
MOD = 10 ** 9 + 7
def YesNo(x): return 'Yes' if x else 'No'
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x) - 1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def II(): return int(sys.stdin.readline())
def SI(): return input()
from collections import defaultdict
def main():
N = II()
xy = []
for _ in range(N):
xy.append(LI())
xy2g = defaultdict(int)
g2xy = defaultdict(set)
for x, y in xy:
y = -y
gx = xy2g[x]
gy = xy2g[y]
if gx != gy and gx != 0 and gy != 0: # merge
if len(g2xy[gx]) < len(g2xy[gy]):
gx, gy = gy, gx
for xy in g2xy[gy]:
xy2g[xy] = gx
g2xy[gx] |= g2xy[gy]
g2xy[gy].clear()
else:
g = gx or gy or x
xy2g[x] = xy2g[y] = g
g2xy[g] |= {x, y}
ans = -N
for xys in g2xy.values():
nx = 0
for xy in xys:
if xy > 0:
nx += 1
ny = len(xys) - nx
ans += nx * ny
return ans
print(main())
```
Yes
| 6,421 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).
We will repeat the following operation as long as possible:
* Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.
We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq x_i, y_i \leq 10^5
* If i \neq j, x_i \neq x_j or y_i \neq y_j.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the maximum number of times we can do the operation.
Examples
Input
3
1 1
5 1
5 5
Output
1
Input
2
10 10
20 20
Output
0
Input
9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5
Output
16
Submitted Solution:
```
from collections import deque
N = int(input())
V = set()
E = {}
for _ in range(N):
x,y = map(int, input().split())
y += 100010
V.add(x)
V.add(y)
if x not in E:
E[x] = [y]
else:
E[x].append(y)
if y not in E:
E[y] = [x]
else:
E[y].append(x)
#print(V)
#print(E)
## DFS
visited = [ False ] * 200020
willSearch = [ False ] * 200020
Q = deque()
ans = 0
for v in V:
if visited[v]:
continue
Q.append(v)
xcount, ycount = 0,0
edge_count = 0
while len(Q) > 0:
now = Q.pop()
visited[now] = True
if now > 100005:
ycount += 1
else:
xcount += 1
for nxt in E[now]:
edge_count += 1
if visited[nxt] or willSearch[nxt]:
continue
#print(v,now,nxt)
willSearch[nxt] = True
Q.append(nxt)
#print(v,xcount, ycount, edge_count)
ans += xcount * ycount
ans -= edge_count // 2
print(ans)
```
Yes
| 6,422 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).
We will repeat the following operation as long as possible:
* Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.
We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq x_i, y_i \leq 10^5
* If i \neq j, x_i \neq x_j or y_i \neq y_j.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the maximum number of times we can do the operation.
Examples
Input
3
1 1
5 1
5 5
Output
1
Input
2
10 10
20 20
Output
0
Input
9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5
Output
16
Submitted Solution:
```
# reference -> https://atcoder.jp/contests/abc131/submissions/10358162
import sys
sys.setrecursionlimit(100000)
# 再帰的に連結部分の辺の数を求める
# 同じ辺を2回ずつ数えるので、最終的には2で割る
def solve(x, x_set, y_set, x2y, y2x):
num_e = 0
if x in x2y:
x_set.add(x)
yl = x2y.pop(x)
num_e += len(yl)
for y in yl:
num_e += solve(y, y_set, x_set, y2x, x2y)
return num_e
N = int(input())
X2Y = {}
Y2X = {}
for i in range(N):
x, y = map(int, input().split())
if x in X2Y:
X2Y[x].append(y)
else:
X2Y[x] = [y]
if y in Y2X:
Y2X[y].append(x)
else:
Y2X[y] = [x]
ans = 0
while X2Y:
x = next(iter(X2Y)) # まだスタートに選んでいないxを取り出す
x_set = set() # 上のxと連結であるxの集合
y_set = set() # 上のxと連結であるyの集合
num_e = solve(x, x_set, y_set, X2Y, Y2X)
ans += len(x_set)*len(y_set) - num_e//2
print(ans)
```
Yes
| 6,423 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).
We will repeat the following operation as long as possible:
* Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.
We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq x_i, y_i \leq 10^5
* If i \neq j, x_i \neq x_j or y_i \neq y_j.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the maximum number of times we can do the operation.
Examples
Input
3
1 1
5 1
5 5
Output
1
Input
2
10 10
20 20
Output
0
Input
9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5
Output
16
Submitted Solution:
```
from collections import Counter
def main():
MAX = 10 ** 5 + 1
data = [-1] * (2 * MAX)
def find(x):
if data[x] < 0:
return x
else:
data[x] = find(data[x])
return data[x]
def union(x, y):
x, y = find(x), find(y)
if x != y:
if data[y] < data[x]:
x, y = y, x
data[x] += data[y]
data[y] = x
return (x != y)
N, *XY = map(int, open(0).read().split())
for x, y in zip(*[iter(XY)] * 2):
union(x, y + MAX)
X = Counter(find(i) for i in range(MAX))
Y = Counter(find(i) for i in range(MAX, MAX * 2))
res = sum(X[i] * Y[i] for i in range(MAX * 2))
print(res - N)
if __name__ == '__main__':
main()
```
Yes
| 6,424 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).
We will repeat the following operation as long as possible:
* Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.
We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq x_i, y_i \leq 10^5
* If i \neq j, x_i \neq x_j or y_i \neq y_j.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the maximum number of times we can do the operation.
Examples
Input
3
1 1
5 1
5 5
Output
1
Input
2
10 10
20 20
Output
0
Input
9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5
Output
16
Submitted Solution:
```
def solve():
N = int(input())
XY = [[int(i) for i in input().split()] for i in range(N)]
if N < 3: return 0
setY = set()
XYdict = {}
for x, y in XY:
setY.add(y)
if x not in XYdict:
XYdict[x] = set([y])
else:
XYdict[x].add(y)
ans = 0
for i in XYdict:
for j in XYdict:
if i == j: continue
_and = XYdict[i] & XYdict[j]
if len(_and) == 0: continue
xor = XYdict[i] ^ XYdict[j]
l = len(xor)
if l == 0: continue
ans += l
XYdict[i] |= xor
XYdict[j] |= xor
return ans
print(solve())
```
No
| 6,425 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).
We will repeat the following operation as long as possible:
* Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.
We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq x_i, y_i \leq 10^5
* If i \neq j, x_i \neq x_j or y_i \neq y_j.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the maximum number of times we can do the operation.
Examples
Input
3
1 1
5 1
5 5
Output
1
Input
2
10 10
20 20
Output
0
Input
9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5
Output
16
Submitted Solution:
```
N = int(input().strip())
X = {}
Y = {}
for _ in range(N):
x, y = map(int, input().strip().split())
if x not in X: X[x] = set()
X[x].add(y)
if y not in Y: Y[y] = set()
Y[y].add(x)
count = 0
for x, y_set in X.items():
if len(y_set) < 2:
continue
for y in y_set:
x_set = Y[y]
if len(x_set) < 2:
continue
for _x in x_set:
if x == _x:
continue
count += len(y_set - X[_x])
X[_x] = y_set | X[_x]
print(count)
```
No
| 6,426 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).
We will repeat the following operation as long as possible:
* Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.
We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq x_i, y_i \leq 10^5
* If i \neq j, x_i \neq x_j or y_i \neq y_j.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the maximum number of times we can do the operation.
Examples
Input
3
1 1
5 1
5 5
Output
1
Input
2
10 10
20 20
Output
0
Input
9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5
Output
16
Submitted Solution:
```
from collections import defaultdict
import sys
input = sys.stdin.readline
n = int(input())
xy = [list(map(int,input().split())) for i in range(n)]
graph = [[] for i in range(2*10**5+1)]
ans = 0
for x,y in xy:
y += 10**5
graph[x].append(y)
graph[y].append(x)
ans -= 1
vis = [0 for i in range(2*10**5+1)]
for i in range(1,2*10**5+1):
if vis[i]:
continue
stack = [i]
nx = 0
ny = 0
while stack:
x = stack.pop()
if x > 10**5:
ny += 1
else:
nx += 1
vis[x] = 1
for y in graph[x]:
if not vis[y]:
stack.append(y)
ans += nx*ny
print(ans)
```
No
| 6,427 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).
We will repeat the following operation as long as possible:
* Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.
We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq x_i, y_i \leq 10^5
* If i \neq j, x_i \neq x_j or y_i \neq y_j.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the maximum number of times we can do the operation.
Examples
Input
3
1 1
5 1
5 5
Output
1
Input
2
10 10
20 20
Output
0
Input
9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5
Output
16
Submitted Solution:
```
import sys
sys.setrecursionlimit(10**7)
INF = 10 ** 18
MOD = 10 ** 9 + 7
def YesNo(x): return 'Yes' if x else 'No'
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x) - 1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def II(): return int(sys.stdin.readline())
def SI(): return input()
from collections import defaultdict
def main():
N = II()
xy = []
for _ in range(N):
xy.append(LI())
x2g = defaultdict(int)
y2g = defaultdict(int)
g2y = defaultdict(set)
g2x = defaultdict(set)
for x, y in xy:
gx = x2g[x]
gy = y2g[y]
if gx > 0 and gy > 0: # merge
if len(g2x[gx]) + len(g2y[gx]) < len(g2x[gy]) + len(g2x[gy]):
gx, gy = gy, gx
for x in g2x[gy]:
x2g[x] = gx
for y in g2y[gy]:
y2g[y] = gx
g2y[gx] |= g2y[gy]
g2x[gx] |= g2x[gy]
g2y[gy] = set()
g2x[gy] = set()
elif gx > 0:
y2g[y] = gx
g2y[gx].add(y)
elif gy > 0:
x2g[x] = gy
g2x[gy].add(x)
else:
x2g[x] = x
y2g[y] = x
g2x[x].add(x)
g2y[x].add(y)
ans = -N
for g in g2x.keys():
if g2x[g]:
ans += len(g2x[g]) * len(g2y[g])
return ans
print(main())
```
No
| 6,428 |
Provide a correct Python 3 solution for this coding contest problem.
We conducted a survey on newspaper subscriptions. More specifically, we asked each of the N respondents the following two questions:
* Question 1: Are you subscribing to Newspaper X?
* Question 2: Are you subscribing to Newspaper Y?
As the result, A respondents answered "yes" to Question 1, and B respondents answered "yes" to Question 2.
What are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?
Write a program to answer this question.
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N
* 0 \leq B \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.
Examples
Input
10 3 5
Output
3 0
Input
10 7 5
Output
5 2
Input
100 100 100
Output
100 100
"Correct Solution:
```
N, A, B = map(int, input().split())
M = min(A, B)
m = max(0, (A + B) - N)
print(M, m)
```
| 6,429 |
Provide a correct Python 3 solution for this coding contest problem.
We conducted a survey on newspaper subscriptions. More specifically, we asked each of the N respondents the following two questions:
* Question 1: Are you subscribing to Newspaper X?
* Question 2: Are you subscribing to Newspaper Y?
As the result, A respondents answered "yes" to Question 1, and B respondents answered "yes" to Question 2.
What are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?
Write a program to answer this question.
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N
* 0 \leq B \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.
Examples
Input
10 3 5
Output
3 0
Input
10 7 5
Output
5 2
Input
100 100 100
Output
100 100
"Correct Solution:
```
n,a,b=map(int,input().split());t=min(a,b);print(t,max(max(a,b)-n+t,0))
```
| 6,430 |
Provide a correct Python 3 solution for this coding contest problem.
We conducted a survey on newspaper subscriptions. More specifically, we asked each of the N respondents the following two questions:
* Question 1: Are you subscribing to Newspaper X?
* Question 2: Are you subscribing to Newspaper Y?
As the result, A respondents answered "yes" to Question 1, and B respondents answered "yes" to Question 2.
What are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?
Write a program to answer this question.
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N
* 0 \leq B \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.
Examples
Input
10 3 5
Output
3 0
Input
10 7 5
Output
5 2
Input
100 100 100
Output
100 100
"Correct Solution:
```
n, a, b = map(int, input().split())
print(min(a, b), max((min(a, b) - (n - max(a, b)), 0)))
```
| 6,431 |
Provide a correct Python 3 solution for this coding contest problem.
We conducted a survey on newspaper subscriptions. More specifically, we asked each of the N respondents the following two questions:
* Question 1: Are you subscribing to Newspaper X?
* Question 2: Are you subscribing to Newspaper Y?
As the result, A respondents answered "yes" to Question 1, and B respondents answered "yes" to Question 2.
What are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?
Write a program to answer this question.
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N
* 0 \leq B \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.
Examples
Input
10 3 5
Output
3 0
Input
10 7 5
Output
5 2
Input
100 100 100
Output
100 100
"Correct Solution:
```
N, A, B = map(int, input().split(" "))
print(min(A, B), max(0, A + B - N))
```
| 6,432 |
Provide a correct Python 3 solution for this coding contest problem.
We conducted a survey on newspaper subscriptions. More specifically, we asked each of the N respondents the following two questions:
* Question 1: Are you subscribing to Newspaper X?
* Question 2: Are you subscribing to Newspaper Y?
As the result, A respondents answered "yes" to Question 1, and B respondents answered "yes" to Question 2.
What are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?
Write a program to answer this question.
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N
* 0 \leq B \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.
Examples
Input
10 3 5
Output
3 0
Input
10 7 5
Output
5 2
Input
100 100 100
Output
100 100
"Correct Solution:
```
n,a,b = map(int,input().split())
ma = min(a,b)
mi = max(ma - (n - max(a,b)), 0)
print(ma,mi)
```
| 6,433 |
Provide a correct Python 3 solution for this coding contest problem.
We conducted a survey on newspaper subscriptions. More specifically, we asked each of the N respondents the following two questions:
* Question 1: Are you subscribing to Newspaper X?
* Question 2: Are you subscribing to Newspaper Y?
As the result, A respondents answered "yes" to Question 1, and B respondents answered "yes" to Question 2.
What are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?
Write a program to answer this question.
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N
* 0 \leq B \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.
Examples
Input
10 3 5
Output
3 0
Input
10 7 5
Output
5 2
Input
100 100 100
Output
100 100
"Correct Solution:
```
N, A, B = map(int, input().split())
print(min(A, B), (A + B - N if A + B > N else 0))
```
| 6,434 |
Provide a correct Python 3 solution for this coding contest problem.
We conducted a survey on newspaper subscriptions. More specifically, we asked each of the N respondents the following two questions:
* Question 1: Are you subscribing to Newspaper X?
* Question 2: Are you subscribing to Newspaper Y?
As the result, A respondents answered "yes" to Question 1, and B respondents answered "yes" to Question 2.
What are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?
Write a program to answer this question.
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N
* 0 \leq B \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.
Examples
Input
10 3 5
Output
3 0
Input
10 7 5
Output
5 2
Input
100 100 100
Output
100 100
"Correct Solution:
```
n, a, b = map(int, input().split())
M = min(a, b)
m = max(0, a+b-n)
print(M, m)
```
| 6,435 |
Provide a correct Python 3 solution for this coding contest problem.
We conducted a survey on newspaper subscriptions. More specifically, we asked each of the N respondents the following two questions:
* Question 1: Are you subscribing to Newspaper X?
* Question 2: Are you subscribing to Newspaper Y?
As the result, A respondents answered "yes" to Question 1, and B respondents answered "yes" to Question 2.
What are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?
Write a program to answer this question.
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N
* 0 \leq B \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.
Examples
Input
10 3 5
Output
3 0
Input
10 7 5
Output
5 2
Input
100 100 100
Output
100 100
"Correct Solution:
```
N, A, B = map(int, input().split())
print(min(A, B), max(B-(N-A), 0))
```
| 6,436 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We conducted a survey on newspaper subscriptions. More specifically, we asked each of the N respondents the following two questions:
* Question 1: Are you subscribing to Newspaper X?
* Question 2: Are you subscribing to Newspaper Y?
As the result, A respondents answered "yes" to Question 1, and B respondents answered "yes" to Question 2.
What are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?
Write a program to answer this question.
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N
* 0 \leq B \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.
Examples
Input
10 3 5
Output
3 0
Input
10 7 5
Output
5 2
Input
100 100 100
Output
100 100
Submitted Solution:
```
n,x,y=map(int,input().split())
print(min(x,y),max(0,x+y-n))
```
Yes
| 6,437 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We conducted a survey on newspaper subscriptions. More specifically, we asked each of the N respondents the following two questions:
* Question 1: Are you subscribing to Newspaper X?
* Question 2: Are you subscribing to Newspaper Y?
As the result, A respondents answered "yes" to Question 1, and B respondents answered "yes" to Question 2.
What are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?
Write a program to answer this question.
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N
* 0 \leq B \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.
Examples
Input
10 3 5
Output
3 0
Input
10 7 5
Output
5 2
Input
100 100 100
Output
100 100
Submitted Solution:
```
N, A, B = tuple(map(int, input().split()))
print(min(A, B), max(0, (A + B) - N))
```
Yes
| 6,438 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We conducted a survey on newspaper subscriptions. More specifically, we asked each of the N respondents the following two questions:
* Question 1: Are you subscribing to Newspaper X?
* Question 2: Are you subscribing to Newspaper Y?
As the result, A respondents answered "yes" to Question 1, and B respondents answered "yes" to Question 2.
What are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?
Write a program to answer this question.
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N
* 0 \leq B \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.
Examples
Input
10 3 5
Output
3 0
Input
10 7 5
Output
5 2
Input
100 100 100
Output
100 100
Submitted Solution:
```
n,a,b = list(map(int, input().split()))
mx = min(a,b)
mn = max(a+b-n,0)
print(mx, mn)
```
Yes
| 6,439 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We conducted a survey on newspaper subscriptions. More specifically, we asked each of the N respondents the following two questions:
* Question 1: Are you subscribing to Newspaper X?
* Question 2: Are you subscribing to Newspaper Y?
As the result, A respondents answered "yes" to Question 1, and B respondents answered "yes" to Question 2.
What are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?
Write a program to answer this question.
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N
* 0 \leq B \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.
Examples
Input
10 3 5
Output
3 0
Input
10 7 5
Output
5 2
Input
100 100 100
Output
100 100
Submitted Solution:
```
n,a,b = map(int, input().split())
Max = min(a,b)
print(Max, max(a+b-n, 0))
```
Yes
| 6,440 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We conducted a survey on newspaper subscriptions. More specifically, we asked each of the N respondents the following two questions:
* Question 1: Are you subscribing to Newspaper X?
* Question 2: Are you subscribing to Newspaper Y?
As the result, A respondents answered "yes" to Question 1, and B respondents answered "yes" to Question 2.
What are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?
Write a program to answer this question.
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N
* 0 \leq B \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.
Examples
Input
10 3 5
Output
3 0
Input
10 7 5
Output
5 2
Input
100 100 100
Output
100 100
Submitted Solution:
```
from sys import stdin
N,A,B=[int(x) for x in stdin.readline().rstrip().split()]
if N==A and A==B and B==N:
print(N,N)
else:
if A>B:
if (A+B)>N:
print(B,A-B)
else:
print(B,0)
else:
if (A+B)>N:
print(A,B-A)
else:
print(A,0)
```
No
| 6,441 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We conducted a survey on newspaper subscriptions. More specifically, we asked each of the N respondents the following two questions:
* Question 1: Are you subscribing to Newspaper X?
* Question 2: Are you subscribing to Newspaper Y?
As the result, A respondents answered "yes" to Question 1, and B respondents answered "yes" to Question 2.
What are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?
Write a program to answer this question.
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N
* 0 \leq B \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.
Examples
Input
10 3 5
Output
3 0
Input
10 7 5
Output
5 2
Input
100 100 100
Output
100 100
Submitted Solution:
```
x, y, z = map(int,input().split())
print(min(y,z), max(0, x-y-z))
```
No
| 6,442 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We conducted a survey on newspaper subscriptions. More specifically, we asked each of the N respondents the following two questions:
* Question 1: Are you subscribing to Newspaper X?
* Question 2: Are you subscribing to Newspaper Y?
As the result, A respondents answered "yes" to Question 1, and B respondents answered "yes" to Question 2.
What are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?
Write a program to answer this question.
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N
* 0 \leq B \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.
Examples
Input
10 3 5
Output
3 0
Input
10 7 5
Output
5 2
Input
100 100 100
Output
100 100
Submitted Solution:
```
n, a, b = map(int, input().split())
print(min(a, b), (a+b) - n)
```
No
| 6,443 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We conducted a survey on newspaper subscriptions. More specifically, we asked each of the N respondents the following two questions:
* Question 1: Are you subscribing to Newspaper X?
* Question 2: Are you subscribing to Newspaper Y?
As the result, A respondents answered "yes" to Question 1, and B respondents answered "yes" to Question 2.
What are the maximum possible number and the minimum possible number of respondents subscribing to both newspapers X and Y?
Write a program to answer this question.
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N
* 0 \leq B \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print the maximum possible number and the minimum possible number of respondents subscribing to both newspapers, in this order, with a space in between.
Examples
Input
10 3 5
Output
3 0
Input
10 7 5
Output
5 2
Input
100 100 100
Output
100 100
Submitted Solution:
```
def main():
N, A, B = map(int, input().split())
if N == A and N == B:
# 全員が両方読んでいる場合
print(N, N)
return
max_result = max([A, B])
min_result = min([A, B])
if A + B > N:
# AとBの合計がNより大きい場合、最大は小さい方の数、最小は大ー小
print(min_result, max_result - min_result)
elif A + B <= N:
# AとBの合計がNより小さい場合、最大は小さい方の数、最小は0
print(min_result, 0)
main()
```
No
| 6,444 |
Provide a correct Python 3 solution for this coding contest problem.
In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east. A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i). Takahashi the king is interested in the following Q matters:
* The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.
Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.
Constraints
* N is an integer between 1 and 500 (inclusive).
* M is an integer between 1 and 200 \ 000 (inclusive).
* Q is an integer between 1 and 100 \ 000 (inclusive).
* 1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)
* 1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)
Input
Input is given from Standard Input in the following format:
N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q
Output
Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.
Examples
Input
2 3 1
1 1
1 2
2 2
1 2
Output
3
Input
10 3 2
1 5
2 8
7 10
1 7
3 10
Output
1
1
Input
10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10
Output
7
9
10
6
8
9
6
7
8
10
"Correct Solution:
```
N, M, Q = map(int, input().split())
train = [[0]*(N+1) for _ in range(N+1)]
for i in range(M):
a, b = map(int, input().split())
train[a][b] += 1
for i in range(1, N+1):
for j in range(1, N+1):
train[i][j] += train[i][j-1]
for i in range(Q):
ans = 0
l, r = map(int, input().split())
for j in range(l, r+1):
ans += train[j][r]-train[j][l-1]
print(ans)
```
| 6,445 |
Provide a correct Python 3 solution for this coding contest problem.
In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east. A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i). Takahashi the king is interested in the following Q matters:
* The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.
Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.
Constraints
* N is an integer between 1 and 500 (inclusive).
* M is an integer between 1 and 200 \ 000 (inclusive).
* Q is an integer between 1 and 100 \ 000 (inclusive).
* 1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)
* 1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)
Input
Input is given from Standard Input in the following format:
N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q
Output
Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.
Examples
Input
2 3 1
1 1
1 2
2 2
1 2
Output
3
Input
10 3 2
1 5
2 8
7 10
1 7
3 10
Output
1
1
Input
10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10
Output
7
9
10
6
8
9
6
7
8
10
"Correct Solution:
```
n,m,q=map(int,input().split())
t=[[0]*(1+n) for _ in range(1+n)]
for i in range(m):
l,r=map(int,input().split())
t[l][r]+=1
for i in range(n):
for j in range(n):
t[i+1][j+1]+=t[i+1][j]+t[i][j+1]-t[i][j]
for i in range(q):
p,q=map(int,input().split())
p-=1
print(t[q][q]-t[q][p]-t[p][q]+t[p][p])
```
| 6,446 |
Provide a correct Python 3 solution for this coding contest problem.
In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east. A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i). Takahashi the king is interested in the following Q matters:
* The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.
Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.
Constraints
* N is an integer between 1 and 500 (inclusive).
* M is an integer between 1 and 200 \ 000 (inclusive).
* Q is an integer between 1 and 100 \ 000 (inclusive).
* 1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)
* 1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)
Input
Input is given from Standard Input in the following format:
N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q
Output
Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.
Examples
Input
2 3 1
1 1
1 2
2 2
1 2
Output
3
Input
10 3 2
1 5
2 8
7 10
1 7
3 10
Output
1
1
Input
10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10
Output
7
9
10
6
8
9
6
7
8
10
"Correct Solution:
```
from itertools import accumulate
N, M, Q, *I = map(int, open(0).read().split())
LR, PQ = I[:2 * M], I[2 * M:]
M = [[0] * (N + 1) for _ in range(N + 1)]
for l, r in zip(*[iter(LR)] * 2):
M[l][r] += 1
A = [list(accumulate(reversed(a)))[::-1] for a in zip(*[accumulate(m) for m in M])]
for p, q in zip(*[iter(PQ)] * 2):
print(A[q][p])
```
| 6,447 |
Provide a correct Python 3 solution for this coding contest problem.
In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east. A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i). Takahashi the king is interested in the following Q matters:
* The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.
Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.
Constraints
* N is an integer between 1 and 500 (inclusive).
* M is an integer between 1 and 200 \ 000 (inclusive).
* Q is an integer between 1 and 100 \ 000 (inclusive).
* 1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)
* 1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)
Input
Input is given from Standard Input in the following format:
N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q
Output
Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.
Examples
Input
2 3 1
1 1
1 2
2 2
1 2
Output
3
Input
10 3 2
1 5
2 8
7 10
1 7
3 10
Output
1
1
Input
10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10
Output
7
9
10
6
8
9
6
7
8
10
"Correct Solution:
```
n,m,q=map(int,input().split())
tpos=[[0]*(n+1) for _ in range(n+1)]
for _ in range(m):
l,r=map(int,input().split())
tpos[l][r]+=1
for i in range(1,n+1):
for j in range(1,n+1):
tpos[i][j]=tpos[i][j]+tpos[i-1][j]+tpos[i][j-1]-tpos[i-1][j-1]
for _ in range(q):
l,r=map(int,input().split())
print(tpos[r][r]-tpos[l-1][r]-tpos[r][l-1]+tpos[l-1][l-1])
```
| 6,448 |
Provide a correct Python 3 solution for this coding contest problem.
In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east. A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i). Takahashi the king is interested in the following Q matters:
* The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.
Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.
Constraints
* N is an integer between 1 and 500 (inclusive).
* M is an integer between 1 and 200 \ 000 (inclusive).
* Q is an integer between 1 and 100 \ 000 (inclusive).
* 1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)
* 1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)
Input
Input is given from Standard Input in the following format:
N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q
Output
Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.
Examples
Input
2 3 1
1 1
1 2
2 2
1 2
Output
3
Input
10 3 2
1 5
2 8
7 10
1 7
3 10
Output
1
1
Input
10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10
Output
7
9
10
6
8
9
6
7
8
10
"Correct Solution:
```
import bisect
N,M,Q=map(int,input().split())
LR=[[0]*(N+1) for _ in range(N)]
for i in range(M):
l,r=map(int,input().split())
LR[l-1][r]+=1
for i in range(N):
for j in range(1,N+1):
LR[i][j]+=LR[i][j-1]
for _ in range(Q):
ans=0
p,q=map(int,input().split())
for i in range(p-1,q):
ans+=LR[i][q]-LR[i][p-1]
print(ans)
```
| 6,449 |
Provide a correct Python 3 solution for this coding contest problem.
In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east. A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i). Takahashi the king is interested in the following Q matters:
* The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.
Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.
Constraints
* N is an integer between 1 and 500 (inclusive).
* M is an integer between 1 and 200 \ 000 (inclusive).
* Q is an integer between 1 and 100 \ 000 (inclusive).
* 1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)
* 1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)
Input
Input is given from Standard Input in the following format:
N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q
Output
Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.
Examples
Input
2 3 1
1 1
1 2
2 2
1 2
Output
3
Input
10 3 2
1 5
2 8
7 10
1 7
3 10
Output
1
1
Input
10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10
Output
7
9
10
6
8
9
6
7
8
10
"Correct Solution:
```
N, M, Q = map(int, input().split())
G = [[0]*(N+1) for _ in range(N+1)]
for _ in range(M):
L, R = map(int, input().split())
G[L][R] += 1
for i in range(N+1):
for j in range(1, N+1):
G[i][j] += G[i][j-1]
for _ in range(Q):
p, q = map(int, input().split())
ans = 0
for i in range(p, q+1):
ans += G[i][q]
print(ans)
```
| 6,450 |
Provide a correct Python 3 solution for this coding contest problem.
In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east. A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i). Takahashi the king is interested in the following Q matters:
* The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.
Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.
Constraints
* N is an integer between 1 and 500 (inclusive).
* M is an integer between 1 and 200 \ 000 (inclusive).
* Q is an integer between 1 and 100 \ 000 (inclusive).
* 1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)
* 1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)
Input
Input is given from Standard Input in the following format:
N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q
Output
Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.
Examples
Input
2 3 1
1 1
1 2
2 2
1 2
Output
3
Input
10 3 2
1 5
2 8
7 10
1 7
3 10
Output
1
1
Input
10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10
Output
7
9
10
6
8
9
6
7
8
10
"Correct Solution:
```
N,M,Q = map(int,input().split())
LR = [[0 for _ in range(N)] for _ in range(N)]
for j in range(M):
l,r = map(int,input().split())
LR[l-1][r-1] += 1
for i in range(N):
for j in range(1,N):
LR[i][j] += LR[i][j-1]
for _ in range(Q):
p,q = map(int,input().split())
ans = 0
for i in range(q-p+1):
ans += LR[p+i-1][q-1]
print(ans)
```
| 6,451 |
Provide a correct Python 3 solution for this coding contest problem.
In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east. A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i). Takahashi the king is interested in the following Q matters:
* The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.
Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.
Constraints
* N is an integer between 1 and 500 (inclusive).
* M is an integer between 1 and 200 \ 000 (inclusive).
* Q is an integer between 1 and 100 \ 000 (inclusive).
* 1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)
* 1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)
Input
Input is given from Standard Input in the following format:
N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q
Output
Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.
Examples
Input
2 3 1
1 1
1 2
2 2
1 2
Output
3
Input
10 3 2
1 5
2 8
7 10
1 7
3 10
Output
1
1
Input
10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10
Output
7
9
10
6
8
9
6
7
8
10
"Correct Solution:
```
n,m,Q = map(int,input().split())
a = []
for i in range(n+1):
a.append([0]*(n+1))
s = a[:]
for i in range(m):
l,r = map(int,input().split())
a[l][r] += 1
for l in range(1,n+1):
for r in range(1,n+1):
s[l][r] = a[l][r] + s[l-1][r] + s[l][r-1] - s[l-1][r-1]
for i in range(Q):
p,q = map(int,input().split())
print(s[q][q] - s[p-1][q] - s[q][p-1] + s[p-1][p-1])
```
| 6,452 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east. A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i). Takahashi the king is interested in the following Q matters:
* The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.
Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.
Constraints
* N is an integer between 1 and 500 (inclusive).
* M is an integer between 1 and 200 \ 000 (inclusive).
* Q is an integer between 1 and 100 \ 000 (inclusive).
* 1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)
* 1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)
Input
Input is given from Standard Input in the following format:
N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q
Output
Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.
Examples
Input
2 3 1
1 1
1 2
2 2
1 2
Output
3
Input
10 3 2
1 5
2 8
7 10
1 7
3 10
Output
1
1
Input
10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10
Output
7
9
10
6
8
9
6
7
8
10
Submitted Solution:
```
N, M, Q = map(int, input().split())
lst = []
cnt = [0]*N
ans = [0]*Q
for i in range(M):
a, b = map(int, input().split())
lst.append([b, a, 't'])
for i in range(Q):
a, b = map(int, input().split())
lst.append([b, a+500, i])
lst.sort()
for i in lst:
if i[2] == 't':
cnt[i[1]-1] += 1
else:
ans[i[2]] = sum(cnt[i[1]-501:i[0]])
for j in ans:
print(j)
```
Yes
| 6,453 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east. A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i). Takahashi the king is interested in the following Q matters:
* The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.
Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.
Constraints
* N is an integer between 1 and 500 (inclusive).
* M is an integer between 1 and 200 \ 000 (inclusive).
* Q is an integer between 1 and 100 \ 000 (inclusive).
* 1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)
* 1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)
Input
Input is given from Standard Input in the following format:
N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q
Output
Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.
Examples
Input
2 3 1
1 1
1 2
2 2
1 2
Output
3
Input
10 3 2
1 5
2 8
7 10
1 7
3 10
Output
1
1
Input
10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10
Output
7
9
10
6
8
9
6
7
8
10
Submitted Solution:
```
N,M,Q = map(int,input().split())
s = [[0 for j in range(501)] for i in range(501)]
for _ in range(M):
L,R = map(int,input().split())
s[L][R] += 1
# 二次元累積和
for i in range(1,501):
for j in range(1,501):
s[i][j] += s[i-1][j] + s[i][j-1] - s[i-1][j-1]
# クエリに対してO(1)で求める
for _ in range(Q):
p,q = map(int,input().split())
print(s[q][q]-s[p-1][q]-s[q][p-1]+s[p-1][p-1])
```
Yes
| 6,454 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east. A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i). Takahashi the king is interested in the following Q matters:
* The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.
Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.
Constraints
* N is an integer between 1 and 500 (inclusive).
* M is an integer between 1 and 200 \ 000 (inclusive).
* Q is an integer between 1 and 100 \ 000 (inclusive).
* 1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)
* 1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)
Input
Input is given from Standard Input in the following format:
N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q
Output
Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.
Examples
Input
2 3 1
1 1
1 2
2 2
1 2
Output
3
Input
10 3 2
1 5
2 8
7 10
1 7
3 10
Output
1
1
Input
10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10
Output
7
9
10
6
8
9
6
7
8
10
Submitted Solution:
```
n,m,q=map(int,input().split())
t=[[0]*(1+n) for _ in range(1+n)]
for i in range(m):
l,r=map(int,input().split())
t[l][r]+=1
for i in range(n):
for j in range(n+1):
t[i+1][j]+=t[i][j]
for i in range(n+1):
for j in range(n):
t[i][j+1]+=t[i][j]
for i in range(q):
p,q=map(int,input().split())
print(t[q][q]-t[q][p-1]-t[p-1][q]+t[p-1][p-1])
```
Yes
| 6,455 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east. A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i). Takahashi the king is interested in the following Q matters:
* The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.
Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.
Constraints
* N is an integer between 1 and 500 (inclusive).
* M is an integer between 1 and 200 \ 000 (inclusive).
* Q is an integer between 1 and 100 \ 000 (inclusive).
* 1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)
* 1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)
Input
Input is given from Standard Input in the following format:
N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q
Output
Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.
Examples
Input
2 3 1
1 1
1 2
2 2
1 2
Output
3
Input
10 3 2
1 5
2 8
7 10
1 7
3 10
Output
1
1
Input
10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10
Output
7
9
10
6
8
9
6
7
8
10
Submitted Solution:
```
N, M, Q = map(int, input().split())
MAP = [[0] * N for i in range(N)]
for i in range(M):
L, R = map(int, input().split())
MAP[L-1][R-1] += 1
for r in range(N):
for l in range(N-1, 0, -1):
MAP[l-1][r] += MAP[l][r]
for r in range(N-1):
for l in range(N):
MAP[l][r+1] += MAP[l][r]
for i in range(Q):
p, q = map(int, input().split())
print(MAP[p-1][q-1])
```
Yes
| 6,456 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east. A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i). Takahashi the king is interested in the following Q matters:
* The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.
Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.
Constraints
* N is an integer between 1 and 500 (inclusive).
* M is an integer between 1 and 200 \ 000 (inclusive).
* Q is an integer between 1 and 100 \ 000 (inclusive).
* 1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)
* 1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)
Input
Input is given from Standard Input in the following format:
N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q
Output
Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.
Examples
Input
2 3 1
1 1
1 2
2 2
1 2
Output
3
Input
10 3 2
1 5
2 8
7 10
1 7
3 10
Output
1
1
Input
10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10
Output
7
9
10
6
8
9
6
7
8
10
Submitted Solution:
```
N,M,Q = [int(i) for i in input().split()]
LR = [[int(i), int(j)] for i, j in [input().split() for i in range(M)]]
LR = sorted(LR)
PQ = [[int(i), int(j)] for i, j in [input().split() for i in range(Q)]]
for p,q in PQ:
tmp = [p,-1]
LR.append(tmp)
LR = sorted(LR)
ind = LR.index(tmp)+1
tmpLR = LR[ind:]
LR.remove(tmp)
tmp = [N+1,q]
tmpLR.append(tmp)
tmpLR = sorted(tmpLR, key = lambda x:x[1])
ind = tmpLR.index(tmp)
tmpLR = tmpLR[:ind]
print(len(tmpLR))
```
No
| 6,457 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east. A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i). Takahashi the king is interested in the following Q matters:
* The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.
Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.
Constraints
* N is an integer between 1 and 500 (inclusive).
* M is an integer between 1 and 200 \ 000 (inclusive).
* Q is an integer between 1 and 100 \ 000 (inclusive).
* 1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)
* 1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)
Input
Input is given from Standard Input in the following format:
N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q
Output
Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.
Examples
Input
2 3 1
1 1
1 2
2 2
1 2
Output
3
Input
10 3 2
1 5
2 8
7 10
1 7
3 10
Output
1
1
Input
10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10
Output
7
9
10
6
8
9
6
7
8
10
Submitted Solution:
```
import numpy as np
n, m, q = map(int, input().split())
m_list = []
for i in range(m):
m_list.append(list(map(int, input().split())))
m_list = sorted(m_list)
q_list = []
for i in range(q):
q_list.append(list(map(int, input().split())))
train_map = np.array([[0 for i in range(n)] for ii in range(n)])
for m_ in m_list:
start, end = m_[0], m_[1]
train_map[:start, end-1:] += 1
for q_ in q_list:
q_s, q_e = q_[0]-1, q_[1]-1
print(train_map[q_s, q_e])
```
No
| 6,458 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east. A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i). Takahashi the king is interested in the following Q matters:
* The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.
Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.
Constraints
* N is an integer between 1 and 500 (inclusive).
* M is an integer between 1 and 200 \ 000 (inclusive).
* Q is an integer between 1 and 100 \ 000 (inclusive).
* 1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)
* 1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)
Input
Input is given from Standard Input in the following format:
N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q
Output
Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.
Examples
Input
2 3 1
1 1
1 2
2 2
1 2
Output
3
Input
10 3 2
1 5
2 8
7 10
1 7
3 10
Output
1
1
Input
10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10
Output
7
9
10
6
8
9
6
7
8
10
Submitted Solution:
```
n, m, q = map(int,input().split())
bord = [[0 for _j in range(n+1)] for _i in range(n+1)]
for _i in range(m):
left, right = map(int, input().split())
bord[left][right] += 1
result = []
for _i in range(q):
p, q = map(int, input().split())
c = 0
for i in range(p, q+1):
for j in range(p, q+1):
c += bord[i][j]
result.append(c)
print(*result)
```
No
| 6,459 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east. A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i). Takahashi the king is interested in the following Q matters:
* The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.
Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.
Constraints
* N is an integer between 1 and 500 (inclusive).
* M is an integer between 1 and 200 \ 000 (inclusive).
* Q is an integer between 1 and 100 \ 000 (inclusive).
* 1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)
* 1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)
Input
Input is given from Standard Input in the following format:
N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q
Output
Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.
Examples
Input
2 3 1
1 1
1 2
2 2
1 2
Output
3
Input
10 3 2
1 5
2 8
7 10
1 7
3 10
Output
1
1
Input
10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10
Output
7
9
10
6
8
9
6
7
8
10
Submitted Solution:
```
n,m,q=map(int,input().split())
a=[]
b=[]
for i in range(n):
a.append([0]*(n))
b.append([0]*(n))
#import numpy as np
#b=np.array(b)
#print(a)
for i in range(m):
l,r=map(int,input().split())
#print(a[(r-1):n,0:l])
a[r-1][l-1]+=1
for l in range(n):
for r in range(l,n):
temp=a[r][l]
for i in range(r,n):
for j in range(0,l+1):
b[i][j]+=temp
#b[r:n,0:l+1]+=temp
#print(a)
#print(b)
for i in range(q):
P,Q=map(int,input().split())
print(b[(Q-1)][(P-1)])
```
No
| 6,460 |
Provide a correct Python 3 solution for this coding contest problem.
You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N. Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.
Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:
* Add 2 to a_i.
* Add 1 to b_j.
Constraints
* 1 ≤ N ≤ 10 000
* 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 .. a_N
b_1 b_2 .. b_N
Output
If we can repeat the operation zero or more times so that the sequences a and b become equal, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 2 3
5 2 2
Output
Yes
Input
5
3 1 4 1 5
2 7 1 8 2
Output
No
Input
5
2 7 1 8 2
3 1 4 1 5
Output
No
"Correct Solution:
```
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
S=sum(b)-sum(a)
if S<0:print("No")
else:
cnt=0
for i in range(n):
cnt+=max((b[i]-a[i]+1)//2,0)
if cnt<=S:print('Yes')
else:print("No")
```
| 6,461 |
Provide a correct Python 3 solution for this coding contest problem.
You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N. Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.
Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:
* Add 2 to a_i.
* Add 1 to b_j.
Constraints
* 1 ≤ N ≤ 10 000
* 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 .. a_N
b_1 b_2 .. b_N
Output
If we can repeat the operation zero or more times so that the sequences a and b become equal, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 2 3
5 2 2
Output
Yes
Input
5
3 1 4 1 5
2 7 1 8 2
Output
No
Input
5
2 7 1 8 2
3 1 4 1 5
Output
No
"Correct Solution:
```
n=int(input())
a=[int(j) for j in input().split()]
b=[int(j) for j in input().split()]
tmp=0
if tmp<0:
print("No")
exit()
for i,j in zip(a,b):
if i>j:
tmp+=j-i
elif i<j:
tmp+=(j-i)//2
if tmp>=0:
print("Yes")
else:
print("No")
```
| 6,462 |
Provide a correct Python 3 solution for this coding contest problem.
You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N. Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.
Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:
* Add 2 to a_i.
* Add 1 to b_j.
Constraints
* 1 ≤ N ≤ 10 000
* 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 .. a_N
b_1 b_2 .. b_N
Output
If we can repeat the operation zero or more times so that the sequences a and b become equal, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 2 3
5 2 2
Output
Yes
Input
5
3 1 4 1 5
2 7 1 8 2
Output
No
Input
5
2 7 1 8 2
3 1 4 1 5
Output
No
"Correct Solution:
```
N = int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
plus=0;minus=0;co=0
for i in range(N):
c=a[i]-b[i]
if c < 0:
minus-=c
if c%2==1:
co+=1
elif c > 0:
plus+=c
print("Yes" if minus >= plus*2+co else "No")
```
| 6,463 |
Provide a correct Python 3 solution for this coding contest problem.
You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N. Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.
Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:
* Add 2 to a_i.
* Add 1 to b_j.
Constraints
* 1 ≤ N ≤ 10 000
* 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 .. a_N
b_1 b_2 .. b_N
Output
If we can repeat the operation zero or more times so that the sequences a and b become equal, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 2 3
5 2 2
Output
Yes
Input
5
3 1 4 1 5
2 7 1 8 2
Output
No
Input
5
2 7 1 8 2
3 1 4 1 5
Output
No
"Correct Solution:
```
N=int(input())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
A_sum=0
for i in range(N):
if A[i]>B[i]:
A_sum+=A[i]-B[i]
elif A[i]<B[i]:
A_sum-=(B[i]-A[i])//2
if A_sum<=0:
print("Yes")
else:
print("No")
```
| 6,464 |
Provide a correct Python 3 solution for this coding contest problem.
You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N. Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.
Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:
* Add 2 to a_i.
* Add 1 to b_j.
Constraints
* 1 ≤ N ≤ 10 000
* 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 .. a_N
b_1 b_2 .. b_N
Output
If we can repeat the operation zero or more times so that the sequences a and b become equal, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 2 3
5 2 2
Output
Yes
Input
5
3 1 4 1 5
2 7 1 8 2
Output
No
Input
5
2 7 1 8 2
3 1 4 1 5
Output
No
"Correct Solution:
```
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
count=0
for i in range(n):
if a[i]<=b[i]:
s=(b[i]-a[i])//2
count+=s
else:
s=a[i]-b[i]
count-=s
if count>=0:
print("Yes")
else:
print("No")
```
| 6,465 |
Provide a correct Python 3 solution for this coding contest problem.
You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N. Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.
Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:
* Add 2 to a_i.
* Add 1 to b_j.
Constraints
* 1 ≤ N ≤ 10 000
* 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 .. a_N
b_1 b_2 .. b_N
Output
If we can repeat the operation zero or more times so that the sequences a and b become equal, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 2 3
5 2 2
Output
Yes
Input
5
3 1 4 1 5
2 7 1 8 2
Output
No
Input
5
2 7 1 8 2
3 1 4 1 5
Output
No
"Correct Solution:
```
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
cnt=sum(b)-sum(a)
for i,j in zip(a,b):
if i<j:cnt-=(j-i+1)//2
print(['No','Yes'][cnt>=0])
```
| 6,466 |
Provide a correct Python 3 solution for this coding contest problem.
You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N. Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.
Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:
* Add 2 to a_i.
* Add 1 to b_j.
Constraints
* 1 ≤ N ≤ 10 000
* 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 .. a_N
b_1 b_2 .. b_N
Output
If we can repeat the operation zero or more times so that the sequences a and b become equal, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 2 3
5 2 2
Output
Yes
Input
5
3 1 4 1 5
2 7 1 8 2
Output
No
Input
5
2 7 1 8 2
3 1 4 1 5
Output
No
"Correct Solution:
```
N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
plus_2 = 0
minus = 0
for a, b in zip(A, B):
if a < b:
plus_2 += (b-a)//2
else:
minus += a-b
if plus_2 >= minus:
print('Yes')
else:
print('No')
```
| 6,467 |
Provide a correct Python 3 solution for this coding contest problem.
You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N. Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.
Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:
* Add 2 to a_i.
* Add 1 to b_j.
Constraints
* 1 ≤ N ≤ 10 000
* 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 .. a_N
b_1 b_2 .. b_N
Output
If we can repeat the operation zero or more times so that the sequences a and b become equal, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 2 3
5 2 2
Output
Yes
Input
5
3 1 4 1 5
2 7 1 8 2
Output
No
Input
5
2 7 1 8 2
3 1 4 1 5
Output
No
"Correct Solution:
```
n, *p = map(int, open(0).read().split())
s = sum(j - i - max(0, i - j) - max(0, j - i)%2 for i, j in zip(p, p[n:]))
print("Yes" if s >= 0 == s%2 else "No")
```
| 6,468 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N. Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.
Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:
* Add 2 to a_i.
* Add 1 to b_j.
Constraints
* 1 ≤ N ≤ 10 000
* 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 .. a_N
b_1 b_2 .. b_N
Output
If we can repeat the operation zero or more times so that the sequences a and b become equal, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 2 3
5 2 2
Output
Yes
Input
5
3 1 4 1 5
2 7 1 8 2
Output
No
Input
5
2 7 1 8 2
3 1 4 1 5
Output
No
Submitted Solution:
```
n = int(input())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
tot = 0
for i in range(0, n):
if a[i] < b[i]:
tot += (b[i] - a[i]) // 2
else:
tot -= a[i] - b[i]
print ("Yes" if tot >= 0 else "No")
```
Yes
| 6,469 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N. Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.
Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:
* Add 2 to a_i.
* Add 1 to b_j.
Constraints
* 1 ≤ N ≤ 10 000
* 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 .. a_N
b_1 b_2 .. b_N
Output
If we can repeat the operation zero or more times so that the sequences a and b become equal, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 2 3
5 2 2
Output
Yes
Input
5
3 1 4 1 5
2 7 1 8 2
Output
No
Input
5
2 7 1 8 2
3 1 4 1 5
Output
No
Submitted Solution:
```
n=int(input())
*A,=map(int,input().split())
*B,=map(int,input().split())
print("Yes" if sum(B)-sum(A) >= sum(max((a+b)%2,a-b) for a,b in zip(A,B)) else "No")
```
Yes
| 6,470 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N. Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.
Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:
* Add 2 to a_i.
* Add 1 to b_j.
Constraints
* 1 ≤ N ≤ 10 000
* 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 .. a_N
b_1 b_2 .. b_N
Output
If we can repeat the operation zero or more times so that the sequences a and b become equal, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 2 3
5 2 2
Output
Yes
Input
5
3 1 4 1 5
2 7 1 8 2
Output
No
Input
5
2 7 1 8 2
3 1 4 1 5
Output
No
Submitted Solution:
```
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
p=0
for i in range(n):
if a[i]<b[i]:
p+=(b[i]-a[i])//2
elif b[i]<a[i]:
p-=(a[i]-b[i])
if p>=0:
print('Yes')
else:
print('No')
```
Yes
| 6,471 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N. Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.
Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:
* Add 2 to a_i.
* Add 1 to b_j.
Constraints
* 1 ≤ N ≤ 10 000
* 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 .. a_N
b_1 b_2 .. b_N
Output
If we can repeat the operation zero or more times so that the sequences a and b become equal, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 2 3
5 2 2
Output
Yes
Input
5
3 1 4 1 5
2 7 1 8 2
Output
No
Input
5
2 7 1 8 2
3 1 4 1 5
Output
No
Submitted Solution:
```
n = int(input())
A = list(map(int,input().split()))
B = list(map(int,input().split()))
c = 0
for a,b in zip(A,B):
c += min((b-a)//2, b-a)
print('Yes' if c>=0 else 'No')
```
Yes
| 6,472 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N. Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.
Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:
* Add 2 to a_i.
* Add 1 to b_j.
Constraints
* 1 ≤ N ≤ 10 000
* 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 .. a_N
b_1 b_2 .. b_N
Output
If we can repeat the operation zero or more times so that the sequences a and b become equal, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 2 3
5 2 2
Output
Yes
Input
5
3 1 4 1 5
2 7 1 8 2
Output
No
Input
5
2 7 1 8 2
3 1 4 1 5
Output
No
Submitted Solution:
```
N = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
n = sum(b) - sum(a)
c = 0
for i in range(N):
if a[i] > b[i]:
c += a[i] - b[i]
elif a[i] < b[i]:
c += (b[i] - a[i] + 2 - 1) // 2
print('Yes' if n >= 0 and c <= n else 'No')
```
No
| 6,473 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N. Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.
Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:
* Add 2 to a_i.
* Add 1 to b_j.
Constraints
* 1 ≤ N ≤ 10 000
* 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 .. a_N
b_1 b_2 .. b_N
Output
If we can repeat the operation zero or more times so that the sequences a and b become equal, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 2 3
5 2 2
Output
Yes
Input
5
3 1 4 1 5
2 7 1 8 2
Output
No
Input
5
2 7 1 8 2
3 1 4 1 5
Output
No
Submitted Solution:
```
n = int(input())
A = list(map(int,input().split()))
B = list(map(int,input().split()))
x = sum(B) - sum(A)
cnt1 = 0
cnt2 = 0
for i in range(n):
if A[i] > B[i]:
cnt1 += (A[i] - B[i])
else:
cnt2 += (B[i] - A[i])//2
if min(cnt1, cnt2) <= x:
print('Yes')
else:
print('No')
```
No
| 6,474 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N. Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.
Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:
* Add 2 to a_i.
* Add 1 to b_j.
Constraints
* 1 ≤ N ≤ 10 000
* 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 .. a_N
b_1 b_2 .. b_N
Output
If we can repeat the operation zero or more times so that the sequences a and b become equal, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 2 3
5 2 2
Output
Yes
Input
5
3 1 4 1 5
2 7 1 8 2
Output
No
Input
5
2 7 1 8 2
3 1 4 1 5
Output
No
Submitted Solution:
```
N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
biggerA, biggerB = 0, 0
for i in range(N):
if A[i] > B[i]:
biggerA += A[i] - B[i]
elif A[i] < B[i]:
biggerB += B[i] - A[i]
if biggerA * 2 <= biggerB:
print('Yes')
else:
print('No')
```
No
| 6,475 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N. Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.
Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:
* Add 2 to a_i.
* Add 1 to b_j.
Constraints
* 1 ≤ N ≤ 10 000
* 0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 .. a_N
b_1 b_2 .. b_N
Output
If we can repeat the operation zero or more times so that the sequences a and b become equal, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 2 3
5 2 2
Output
Yes
Input
5
3 1 4 1 5
2 7 1 8 2
Output
No
Input
5
2 7 1 8 2
3 1 4 1 5
Output
No
Submitted Solution:
```
N = int(input())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
flag = "Yes"
for i in range(N):
A_max = max(a)
B_max = max(b)
if A_max > B_max:
flag = "No"
else:
del a[a.index(A_max)]
del b[b.index(B_max)]
print(flag)
```
No
| 6,476 |
Provide a correct Python 3 solution for this coding contest problem.
We have an N \times N square grid.
We will paint each square in the grid either black or white.
If we paint exactly A squares white, how many squares will be painted black?
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N^2
Inputs
Input is given from Standard Input in the following format:
N
A
Outputs
Print the number of squares that will be painted black.
Examples
Input
3
4
Output
5
Input
19
100
Output
261
Input
10
0
Output
100
"Correct Solution:
```
import math
n=int(input())
a=int(input())
print(n*n-a)
```
| 6,477 |
Provide a correct Python 3 solution for this coding contest problem.
We have an N \times N square grid.
We will paint each square in the grid either black or white.
If we paint exactly A squares white, how many squares will be painted black?
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N^2
Inputs
Input is given from Standard Input in the following format:
N
A
Outputs
Print the number of squares that will be painted black.
Examples
Input
3
4
Output
5
Input
19
100
Output
261
Input
10
0
Output
100
"Correct Solution:
```
x=int(input())
y=int(input())
print(x*x-y)
```
| 6,478 |
Provide a correct Python 3 solution for this coding contest problem.
We have an N \times N square grid.
We will paint each square in the grid either black or white.
If we paint exactly A squares white, how many squares will be painted black?
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N^2
Inputs
Input is given from Standard Input in the following format:
N
A
Outputs
Print the number of squares that will be painted black.
Examples
Input
3
4
Output
5
Input
19
100
Output
261
Input
10
0
Output
100
"Correct Solution:
```
#coding: utf-8
print(int(input())**2 - int(input()))
```
| 6,479 |
Provide a correct Python 3 solution for this coding contest problem.
We have an N \times N square grid.
We will paint each square in the grid either black or white.
If we paint exactly A squares white, how many squares will be painted black?
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N^2
Inputs
Input is given from Standard Input in the following format:
N
A
Outputs
Print the number of squares that will be painted black.
Examples
Input
3
4
Output
5
Input
19
100
Output
261
Input
10
0
Output
100
"Correct Solution:
```
n = int(input())
a = int(input())
x = n*n-a
print(x)
```
| 6,480 |
Provide a correct Python 3 solution for this coding contest problem.
We have an N \times N square grid.
We will paint each square in the grid either black or white.
If we paint exactly A squares white, how many squares will be painted black?
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N^2
Inputs
Input is given from Standard Input in the following format:
N
A
Outputs
Print the number of squares that will be painted black.
Examples
Input
3
4
Output
5
Input
19
100
Output
261
Input
10
0
Output
100
"Correct Solution:
```
N = int(input())
A = int(input())
Y = N**2 -A
print(Y)
```
| 6,481 |
Provide a correct Python 3 solution for this coding contest problem.
We have an N \times N square grid.
We will paint each square in the grid either black or white.
If we paint exactly A squares white, how many squares will be painted black?
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N^2
Inputs
Input is given from Standard Input in the following format:
N
A
Outputs
Print the number of squares that will be painted black.
Examples
Input
3
4
Output
5
Input
19
100
Output
261
Input
10
0
Output
100
"Correct Solution:
```
n=int(input())
s=int(input())
print(n*n-s)
```
| 6,482 |
Provide a correct Python 3 solution for this coding contest problem.
We have an N \times N square grid.
We will paint each square in the grid either black or white.
If we paint exactly A squares white, how many squares will be painted black?
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N^2
Inputs
Input is given from Standard Input in the following format:
N
A
Outputs
Print the number of squares that will be painted black.
Examples
Input
3
4
Output
5
Input
19
100
Output
261
Input
10
0
Output
100
"Correct Solution:
```
n=int(input())
a=int(input())
n=pow(n,2)
print(n-a)
```
| 6,483 |
Provide a correct Python 3 solution for this coding contest problem.
We have an N \times N square grid.
We will paint each square in the grid either black or white.
If we paint exactly A squares white, how many squares will be painted black?
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N^2
Inputs
Input is given from Standard Input in the following format:
N
A
Outputs
Print the number of squares that will be painted black.
Examples
Input
3
4
Output
5
Input
19
100
Output
261
Input
10
0
Output
100
"Correct Solution:
```
n=input()
x=int(input())
m=int(n)*int(n)
print(m-x)
```
| 6,484 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have an N \times N square grid.
We will paint each square in the grid either black or white.
If we paint exactly A squares white, how many squares will be painted black?
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N^2
Inputs
Input is given from Standard Input in the following format:
N
A
Outputs
Print the number of squares that will be painted black.
Examples
Input
3
4
Output
5
Input
19
100
Output
261
Input
10
0
Output
100
Submitted Solution:
```
#10:40
n = int(input())
a = int(input())
print ( n * n - a )
```
Yes
| 6,485 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have an N \times N square grid.
We will paint each square in the grid either black or white.
If we paint exactly A squares white, how many squares will be painted black?
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N^2
Inputs
Input is given from Standard Input in the following format:
N
A
Outputs
Print the number of squares that will be painted black.
Examples
Input
3
4
Output
5
Input
19
100
Output
261
Input
10
0
Output
100
Submitted Solution:
```
n = int(input())
A = int(input())
print(n*n - A)
```
Yes
| 6,486 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have an N \times N square grid.
We will paint each square in the grid either black or white.
If we paint exactly A squares white, how many squares will be painted black?
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N^2
Inputs
Input is given from Standard Input in the following format:
N
A
Outputs
Print the number of squares that will be painted black.
Examples
Input
3
4
Output
5
Input
19
100
Output
261
Input
10
0
Output
100
Submitted Solution:
```
n = int(input())
a = int(input())
print(int((n*n) - a))
```
Yes
| 6,487 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have an N \times N square grid.
We will paint each square in the grid either black or white.
If we paint exactly A squares white, how many squares will be painted black?
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N^2
Inputs
Input is given from Standard Input in the following format:
N
A
Outputs
Print the number of squares that will be painted black.
Examples
Input
3
4
Output
5
Input
19
100
Output
261
Input
10
0
Output
100
Submitted Solution:
```
N = int(input()) ** 2
A = int(input())
print(str(N - A))
```
Yes
| 6,488 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have an N \times N square grid.
We will paint each square in the grid either black or white.
If we paint exactly A squares white, how many squares will be painted black?
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N^2
Inputs
Input is given from Standard Input in the following format:
N
A
Outputs
Print the number of squares that will be painted black.
Examples
Input
3
4
Output
5
Input
19
100
Output
261
Input
10
0
Output
100
Submitted Solution:
```
N,A=map(int,input().split())
print((N*N)-A)
```
No
| 6,489 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have an N \times N square grid.
We will paint each square in the grid either black or white.
If we paint exactly A squares white, how many squares will be painted black?
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N^2
Inputs
Input is given from Standard Input in the following format:
N
A
Outputs
Print the number of squares that will be painted black.
Examples
Input
3
4
Output
5
Input
19
100
Output
261
Input
10
0
Output
100
Submitted Solution:
```
#from numpy import*
from scipy.sparse.csgraph import shortest_path #shortest_path(csgraph=graph)
#from scipy.sparse.csgraph import dijkstra
from scipy.sparse import csr_matrix
from collections import* #defaultdict Counter deque appendleft
from fractions import gcd
from functools import* #reduce
from itertools import* #permutations("AB",repeat=2) combinations("AB",2) product("AB",2) groupby accumulate
from operator import mul,itemgetter
from bisect import* #bisect_left bisect_right
from heapq import* #heapify heappop heappushpop
from math import factorial,pi
from copy import deepcopy
import sys
#input=sys.stdin.readline #危険！基本オフにしろ！
sys.setrecursionlimit(10**8)
def main():
n=int(input())
grid=[list(map(int,input().split()))for i in range(n)]
p=shortest_path(csgraph=csr_matrix(grid))
q=[list(i) for i in p]
if q!=grid:
print(-1)
else:
for i in range(n):
p[i][i]=float("inf")
ans=0
P=[min(p[i])for i in range(n)]
# print(p)
for i in range(n):
for j in range(i):
if i==j:
continue
if p[i][j]<P[i]+P[j]:
ans+=p[i][j]
print(int(ans))
```
No
| 6,490 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have an N \times N square grid.
We will paint each square in the grid either black or white.
If we paint exactly A squares white, how many squares will be painted black?
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N^2
Inputs
Input is given from Standard Input in the following format:
N
A
Outputs
Print the number of squares that will be painted black.
Examples
Input
3
4
Output
5
Input
19
100
Output
261
Input
10
0
Output
100
Submitted Solution:
```
a=int(input())
b=int(input())
print(a^2-b)
```
No
| 6,491 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have an N \times N square grid.
We will paint each square in the grid either black or white.
If we paint exactly A squares white, how many squares will be painted black?
Constraints
* 1 \leq N \leq 100
* 0 \leq A \leq N^2
Inputs
Input is given from Standard Input in the following format:
N
A
Outputs
Print the number of squares that will be painted black.
Examples
Input
3
4
Output
5
Input
19
100
Output
261
Input
10
0
Output
100
Submitted Solution:
```
a = input()
n = input()
a = int(a)
n = int(n)
print (n * n - a)
```
No
| 6,492 |
Provide a correct Python 3 solution for this coding contest problem.
There are four points: $A(x_1, y_1)$, $B(x_2, y_2)$, $C(x_3, y_3)$, and $D(x_4, y_4)$. Write a program which determines whether the line $AB$ and the line $CD$ are parallel. If those two lines are parallel, your program should prints "YES" and if not prints "NO".
Input
Input consists of several datasets. In the first line, you are given the number of datasets $n$ ($n \leq 100$). There will be $n$ lines where each line correspondgs to each dataset. Each dataset consists of eight real numbers:
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$ $x_4$ $y_4$
You can assume that $-100 \leq x_1, y_1, x_2, y_2, x_3, y_3, x_4, y_4 \leq 100$. Each value is a real number with at most 5 digits after the decimal point.
Output
For each dataset, print "YES" or "NO" in a line.
Example
Input
2
0.0 0.0 1.0 1.0 1.0 0.0 2.0 1.0
3.0 2.0 9.0 6.0 13.0 5.0 7.0 9.0
Output
YES
NO
"Correct Solution:
```
EPS = 10**-10
n = int(input())
pos = []
for _ in range(n):
pos.append(list(map(float, input().split())))
for i in range(n):
vec_ax = pos[i][2]-pos[i][0]
vec_ay = pos[i][3]-pos[i][1]
vec_bx = pos[i][6]-pos[i][4]
vec_by = pos[i][7]-pos[i][5]
if abs(vec_bx*vec_ay - vec_by*vec_ax) < EPS:
print("YES")
else:
print("NO")
```
| 6,493 |
Provide a correct Python 3 solution for this coding contest problem.
There are four points: $A(x_1, y_1)$, $B(x_2, y_2)$, $C(x_3, y_3)$, and $D(x_4, y_4)$. Write a program which determines whether the line $AB$ and the line $CD$ are parallel. If those two lines are parallel, your program should prints "YES" and if not prints "NO".
Input
Input consists of several datasets. In the first line, you are given the number of datasets $n$ ($n \leq 100$). There will be $n$ lines where each line correspondgs to each dataset. Each dataset consists of eight real numbers:
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$ $x_4$ $y_4$
You can assume that $-100 \leq x_1, y_1, x_2, y_2, x_3, y_3, x_4, y_4 \leq 100$. Each value is a real number with at most 5 digits after the decimal point.
Output
For each dataset, print "YES" or "NO" in a line.
Example
Input
2
0.0 0.0 1.0 1.0 1.0 0.0 2.0 1.0
3.0 2.0 9.0 6.0 13.0 5.0 7.0 9.0
Output
YES
NO
"Correct Solution:
```
def cross_product(a,b):
return (a.conjugate()*b).imag
N = int(input().strip())
for _ in range(N):
P = list(map(float,input().strip().split()))
for i in range(len(P)):
P[i] = int(P[i]*1000000.0)
z = complex(P[0]-P[2],P[1]-P[3])
w = complex(P[4]-P[6],P[5]-P[7])
if abs(cross_product(z,w)) < 1:
print("YES")
else:
print("NO")
```
| 6,494 |
Provide a correct Python 3 solution for this coding contest problem.
There are four points: $A(x_1, y_1)$, $B(x_2, y_2)$, $C(x_3, y_3)$, and $D(x_4, y_4)$. Write a program which determines whether the line $AB$ and the line $CD$ are parallel. If those two lines are parallel, your program should prints "YES" and if not prints "NO".
Input
Input consists of several datasets. In the first line, you are given the number of datasets $n$ ($n \leq 100$). There will be $n$ lines where each line correspondgs to each dataset. Each dataset consists of eight real numbers:
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$ $x_4$ $y_4$
You can assume that $-100 \leq x_1, y_1, x_2, y_2, x_3, y_3, x_4, y_4 \leq 100$. Each value is a real number with at most 5 digits after the decimal point.
Output
For each dataset, print "YES" or "NO" in a line.
Example
Input
2
0.0 0.0 1.0 1.0 1.0 0.0 2.0 1.0
3.0 2.0 9.0 6.0 13.0 5.0 7.0 9.0
Output
YES
NO
"Correct Solution:
```
import math
import cmath
def cross_product(a,b):
return (a.conjugate()*b).imag
n = int(input())
for i in range(n):
L = list(map(float,input().split()))
a,b,c,d = [complex(L[j*2],L[j*2+1]) for j in range(4)]
vec_A = b-a
vec_B = d-c
if abs(cross_product(vec_A,vec_B)) < 1e-11:
print('YES')
else:
print('NO')
```
| 6,495 |
Provide a correct Python 3 solution for this coding contest problem.
There are four points: $A(x_1, y_1)$, $B(x_2, y_2)$, $C(x_3, y_3)$, and $D(x_4, y_4)$. Write a program which determines whether the line $AB$ and the line $CD$ are parallel. If those two lines are parallel, your program should prints "YES" and if not prints "NO".
Input
Input consists of several datasets. In the first line, you are given the number of datasets $n$ ($n \leq 100$). There will be $n$ lines where each line correspondgs to each dataset. Each dataset consists of eight real numbers:
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$ $x_4$ $y_4$
You can assume that $-100 \leq x_1, y_1, x_2, y_2, x_3, y_3, x_4, y_4 \leq 100$. Each value is a real number with at most 5 digits after the decimal point.
Output
For each dataset, print "YES" or "NO" in a line.
Example
Input
2
0.0 0.0 1.0 1.0 1.0 0.0 2.0 1.0
3.0 2.0 9.0 6.0 13.0 5.0 7.0 9.0
Output
YES
NO
"Correct Solution:
```
E = 10 ** -10
def check(lst):
x1, y1, x2, y2, x3, y3, x4, y4 = lst
vabx, vaby = x2 - x1, y2 - y1
vcdx, vcdy = x4 - x3, y4 - y3
if abs(vabx * vcdy - vcdx * vaby) < E:
return True
else:
return False
n = int(input())
for _ in range(n):
plst = list(map(float, input().split()))
print("YES" if check(plst) else "NO")
```
| 6,496 |
Provide a correct Python 3 solution for this coding contest problem.
There are four points: $A(x_1, y_1)$, $B(x_2, y_2)$, $C(x_3, y_3)$, and $D(x_4, y_4)$. Write a program which determines whether the line $AB$ and the line $CD$ are parallel. If those two lines are parallel, your program should prints "YES" and if not prints "NO".
Input
Input consists of several datasets. In the first line, you are given the number of datasets $n$ ($n \leq 100$). There will be $n$ lines where each line correspondgs to each dataset. Each dataset consists of eight real numbers:
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$ $x_4$ $y_4$
You can assume that $-100 \leq x_1, y_1, x_2, y_2, x_3, y_3, x_4, y_4 \leq 100$. Each value is a real number with at most 5 digits after the decimal point.
Output
For each dataset, print "YES" or "NO" in a line.
Example
Input
2
0.0 0.0 1.0 1.0 1.0 0.0 2.0 1.0
3.0 2.0 9.0 6.0 13.0 5.0 7.0 9.0
Output
YES
NO
"Correct Solution:
```
n = int(input())
for _ in range(n):
x1, y1, x2, y2, x3, y3, x4, y4 = map(float, input().split())
abx = x2 - x1
aby = y2 - y1
cdx = x4 - x3
cdy = y4 - y3
if abs(aby * cdx) < 1e-10 and abs(cdy * abx) < 1e-10:
print(['NO', 'YES'][abs(abx - cdx) < 1e-10 or abs(aby - cdy) < 1e-10])
elif abs(aby * cdx - cdy * abx) < 1e-10:
print('YES')
else:
print('NO')
```
| 6,497 |
Provide a correct Python 3 solution for this coding contest problem.
There are four points: $A(x_1, y_1)$, $B(x_2, y_2)$, $C(x_3, y_3)$, and $D(x_4, y_4)$. Write a program which determines whether the line $AB$ and the line $CD$ are parallel. If those two lines are parallel, your program should prints "YES" and if not prints "NO".
Input
Input consists of several datasets. In the first line, you are given the number of datasets $n$ ($n \leq 100$). There will be $n$ lines where each line correspondgs to each dataset. Each dataset consists of eight real numbers:
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$ $x_4$ $y_4$
You can assume that $-100 \leq x_1, y_1, x_2, y_2, x_3, y_3, x_4, y_4 \leq 100$. Each value is a real number with at most 5 digits after the decimal point.
Output
For each dataset, print "YES" or "NO" in a line.
Example
Input
2
0.0 0.0 1.0 1.0 1.0 0.0 2.0 1.0
3.0 2.0 9.0 6.0 13.0 5.0 7.0 9.0
Output
YES
NO
"Correct Solution:
```
import math
def equal(x, y):
return math.fabs(x - y) <= 10 ** (-10)
def spam(_x1, _y1, _x2, _y2):
if _x1 > _x2:
return _x1, _y1, _x2, _y2
else:
return _x2, _y2, _x1, _y1
for i in range(int(input())):
x1, y1, x2, y2, x3, y3, x4, y4 = list(map(float, input().split()))
b1 = (x1 - x2, y1 - y2)
b2 = (x3 - x4, y3 - y4)
p = 0 if b2[0] != 0 else 1
q = 1 if b2[0] != 0 else 0
t = b1[p]/b2[p]
if equal(b1[q], b2[q] * t):
print('YES')
else:
print('NO')
```
| 6,498 |
Provide a correct Python 3 solution for this coding contest problem.
There are four points: $A(x_1, y_1)$, $B(x_2, y_2)$, $C(x_3, y_3)$, and $D(x_4, y_4)$. Write a program which determines whether the line $AB$ and the line $CD$ are parallel. If those two lines are parallel, your program should prints "YES" and if not prints "NO".
Input
Input consists of several datasets. In the first line, you are given the number of datasets $n$ ($n \leq 100$). There will be $n$ lines where each line correspondgs to each dataset. Each dataset consists of eight real numbers:
$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$ $x_4$ $y_4$
You can assume that $-100 \leq x_1, y_1, x_2, y_2, x_3, y_3, x_4, y_4 \leq 100$. Each value is a real number with at most 5 digits after the decimal point.
Output
For each dataset, print "YES" or "NO" in a line.
Example
Input
2
0.0 0.0 1.0 1.0 1.0 0.0 2.0 1.0
3.0 2.0 9.0 6.0 13.0 5.0 7.0 9.0
Output
YES
NO
"Correct Solution:
```
n = int(input())
for i in range(n):
x1, y1, x2, y2, x3, y3, x4, y4 = map(float, input().split())
v1x = x1 - x2
v1y = y1 - y2
v2x = x3 - x4
v2y = y3 - y4
if abs(v1x * v2y - v2x * v1y) < 10 ** -10 :
print("YES")
else:
print("NO")
```
| 6,499 |
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