text stringlengths 198 433k | conversation_id int64 0 109k |
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
M-kun has the following three cards:
* A red card with the integer A.
* A green card with the integer B.
* A blue card with the integer C.
He is a genius magician who can do the following operation at most K times:
* Choose one of the three cards and multiply the written integer by 2.
His magic is successful if both of the following conditions are satisfied after the operations:
* The integer on the green card is strictly greater than the integer on the red card.
* The integer on the blue card is strictly greater than the integer on the green card.
Determine whether the magic can be successful.
Constraints
* 1 \leq A, B, C \leq 7
* 1 \leq K \leq 7
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
A B C
K
Output
If the magic can be successful, print `Yes`; otherwise, print `No`.
Examples
Input
7 2 5
3
Output
Yes
Input
7 4 2
3
Output
No
Submitted Solution:
```
a,b,c = map(int, input().split())
k = int(input())
t = 0
while(a>=b):
b = 2*b
t +=1
while(b>=c):
c = 2*c
t +=1
if(t<=k):
print("Yes")
else:
print("No")
```
Yes
| 101,800 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
M-kun has the following three cards:
* A red card with the integer A.
* A green card with the integer B.
* A blue card with the integer C.
He is a genius magician who can do the following operation at most K times:
* Choose one of the three cards and multiply the written integer by 2.
His magic is successful if both of the following conditions are satisfied after the operations:
* The integer on the green card is strictly greater than the integer on the red card.
* The integer on the blue card is strictly greater than the integer on the green card.
Determine whether the magic can be successful.
Constraints
* 1 \leq A, B, C \leq 7
* 1 \leq K \leq 7
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
A B C
K
Output
If the magic can be successful, print `Yes`; otherwise, print `No`.
Examples
Input
7 2 5
3
Output
Yes
Input
7 4 2
3
Output
No
Submitted Solution:
```
a, b, c = map(int, input().split())
k = int(input())
for i in range(k):
if(a >= b): b *= 2
elif(b >= c): c *= 2
if(a < b < c): print("Yes")
else: print("No")
```
Yes
| 101,801 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
M-kun has the following three cards:
* A red card with the integer A.
* A green card with the integer B.
* A blue card with the integer C.
He is a genius magician who can do the following operation at most K times:
* Choose one of the three cards and multiply the written integer by 2.
His magic is successful if both of the following conditions are satisfied after the operations:
* The integer on the green card is strictly greater than the integer on the red card.
* The integer on the blue card is strictly greater than the integer on the green card.
Determine whether the magic can be successful.
Constraints
* 1 \leq A, B, C \leq 7
* 1 \leq K \leq 7
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
A B C
K
Output
If the magic can be successful, print `Yes`; otherwise, print `No`.
Examples
Input
7 2 5
3
Output
Yes
Input
7 4 2
3
Output
No
Submitted Solution:
```
R,G,B = map(int, input().split())
K = int(input())
while R >= G:
G *= 2
K -= 1
while G >= B:
B *= 2
K -= 1
print('Yes' if K >= 0 else 'No')
```
Yes
| 101,802 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
M-kun has the following three cards:
* A red card with the integer A.
* A green card with the integer B.
* A blue card with the integer C.
He is a genius magician who can do the following operation at most K times:
* Choose one of the three cards and multiply the written integer by 2.
His magic is successful if both of the following conditions are satisfied after the operations:
* The integer on the green card is strictly greater than the integer on the red card.
* The integer on the blue card is strictly greater than the integer on the green card.
Determine whether the magic can be successful.
Constraints
* 1 \leq A, B, C \leq 7
* 1 \leq K \leq 7
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
A B C
K
Output
If the magic can be successful, print `Yes`; otherwise, print `No`.
Examples
Input
7 2 5
3
Output
Yes
Input
7 4 2
3
Output
No
Submitted Solution:
```
A,B,C=map(int,input().split())
K=int(input())
for i in range(K):
if A>=B:
B*=2
continue
C*=2
if A<B<C:
print('Yes')
else:
print('No')
```
Yes
| 101,803 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
M-kun has the following three cards:
* A red card with the integer A.
* A green card with the integer B.
* A blue card with the integer C.
He is a genius magician who can do the following operation at most K times:
* Choose one of the three cards and multiply the written integer by 2.
His magic is successful if both of the following conditions are satisfied after the operations:
* The integer on the green card is strictly greater than the integer on the red card.
* The integer on the blue card is strictly greater than the integer on the green card.
Determine whether the magic can be successful.
Constraints
* 1 \leq A, B, C \leq 7
* 1 \leq K \leq 7
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
A B C
K
Output
If the magic can be successful, print `Yes`; otherwise, print `No`.
Examples
Input
7 2 5
3
Output
Yes
Input
7 4 2
3
Output
No
Submitted Solution:
```
a, b, c = map(int, input().split())#赤midoriao
k = int(input())
#赤＜緑＜青
if a < b and b<c:
print("Yes")
else:
while a>=b:
b = b*2
k-=1
#print(b)
while b>=c or k>0:
c = c*2
k-=1
if a < b and b<c:
print("Yes")
else:
print("No")
```
No
| 101,804 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
M-kun has the following three cards:
* A red card with the integer A.
* A green card with the integer B.
* A blue card with the integer C.
He is a genius magician who can do the following operation at most K times:
* Choose one of the three cards and multiply the written integer by 2.
His magic is successful if both of the following conditions are satisfied after the operations:
* The integer on the green card is strictly greater than the integer on the red card.
* The integer on the blue card is strictly greater than the integer on the green card.
Determine whether the magic can be successful.
Constraints
* 1 \leq A, B, C \leq 7
* 1 \leq K \leq 7
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
A B C
K
Output
If the magic can be successful, print `Yes`; otherwise, print `No`.
Examples
Input
7 2 5
3
Output
Yes
Input
7 4 2
3
Output
No
Submitted Solution:
```
A,B,C = list(map(int,input().split()))
K = int(input())
flag= 0
for i in range(K):
if A>=B:
B *=2
if C <= B:
C *=2
if C >B and B>A:
flag = 1
break
if flag == 0:
print("No")
else:
print("Yes")
```
No
| 101,805 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
M-kun has the following three cards:
* A red card with the integer A.
* A green card with the integer B.
* A blue card with the integer C.
He is a genius magician who can do the following operation at most K times:
* Choose one of the three cards and multiply the written integer by 2.
His magic is successful if both of the following conditions are satisfied after the operations:
* The integer on the green card is strictly greater than the integer on the red card.
* The integer on the blue card is strictly greater than the integer on the green card.
Determine whether the magic can be successful.
Constraints
* 1 \leq A, B, C \leq 7
* 1 \leq K \leq 7
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
A B C
K
Output
If the magic can be successful, print `Yes`; otherwise, print `No`.
Examples
Input
7 2 5
3
Output
Yes
Input
7 4 2
3
Output
No
Submitted Solution:
```
R,G,B = map(int,input().split())
K = int(input())
for i in range(K):
if G < R:
G *= 2
elif B <= G:
B *= 2
# print('Green: ' + str(G) + ' blue:' + str(B))
if R < G and G < B:
print('Yes')
else:
print('No')
```
No
| 101,806 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
M-kun has the following three cards:
* A red card with the integer A.
* A green card with the integer B.
* A blue card with the integer C.
He is a genius magician who can do the following operation at most K times:
* Choose one of the three cards and multiply the written integer by 2.
His magic is successful if both of the following conditions are satisfied after the operations:
* The integer on the green card is strictly greater than the integer on the red card.
* The integer on the blue card is strictly greater than the integer on the green card.
Determine whether the magic can be successful.
Constraints
* 1 \leq A, B, C \leq 7
* 1 \leq K \leq 7
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
A B C
K
Output
If the magic can be successful, print `Yes`; otherwise, print `No`.
Examples
Input
7 2 5
3
Output
Yes
Input
7 4 2
3
Output
No
Submitted Solution:
```
import itertools
abc = list(map(int, input().split()))
K = int(input())
tmp = [0, 1, 2, 3]
ans = 'No'
for i in itertools.permutations(tmp, 3):
if sum(i) == K:
tmpabc = []
for j in range(3):
tmpabc.append(abc[j] * (2 ** i[j]))
if tmpabc[0] < tmpabc[1] and tmpabc[1] < tmpabc[2]:
ans = 'Yes'
break
print(ans)
```
No
| 101,807 |
Provide a correct Python 3 solution for this coding contest problem.
We have N balls. The i-th ball has an integer A_i written on it.
For each k=1, 2, ..., N, solve the following problem and print the answer.
* Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For each k=1,2,...,N, print a line containing the answer.
Examples
Input
5
1 1 2 1 2
Output
2
2
3
2
3
Input
4
1 2 3 4
Output
0
0
0
0
Input
5
3 3 3 3 3
Output
6
6
6
6
6
Input
8
1 2 1 4 2 1 4 1
Output
5
7
5
7
7
5
7
5
"Correct Solution:
```
n=int(input())
l=list(map(int,input().split()))
from collections import *
c=Counter(l)
a=sum(i*(i-1)//2 for i in c.values())
for i in l: print(a-c[i]+1)
```
| 101,808 |
Provide a correct Python 3 solution for this coding contest problem.
We have N balls. The i-th ball has an integer A_i written on it.
For each k=1, 2, ..., N, solve the following problem and print the answer.
* Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For each k=1,2,...,N, print a line containing the answer.
Examples
Input
5
1 1 2 1 2
Output
2
2
3
2
3
Input
4
1 2 3 4
Output
0
0
0
0
Input
5
3 3 3 3 3
Output
6
6
6
6
6
Input
8
1 2 1 4 2 1 4 1
Output
5
7
5
7
7
5
7
5
"Correct Solution:
```
from collections import Counter
N = int(input())
A = list(map(int, input().split()))
ans = 0
c = Counter(A)
for v in c.values():
ans += v*(v-1)//2
for i in A:
print(ans - (c[i] - 1))
```
| 101,809 |
Provide a correct Python 3 solution for this coding contest problem.
We have N balls. The i-th ball has an integer A_i written on it.
For each k=1, 2, ..., N, solve the following problem and print the answer.
* Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For each k=1,2,...,N, print a line containing the answer.
Examples
Input
5
1 1 2 1 2
Output
2
2
3
2
3
Input
4
1 2 3 4
Output
0
0
0
0
Input
5
3 3 3 3 3
Output
6
6
6
6
6
Input
8
1 2 1 4 2 1 4 1
Output
5
7
5
7
7
5
7
5
"Correct Solution:
```
import collections
N = int(input())
A = list(map(int,input().split()))
C = collections.Counter(A)
ans = 0
for i in C.values():
ans += int(0.5* i * (i-1))
for j in A:
print(ans-C[j]+1)
```
| 101,810 |
Provide a correct Python 3 solution for this coding contest problem.
We have N balls. The i-th ball has an integer A_i written on it.
For each k=1, 2, ..., N, solve the following problem and print the answer.
* Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For each k=1,2,...,N, print a line containing the answer.
Examples
Input
5
1 1 2 1 2
Output
2
2
3
2
3
Input
4
1 2 3 4
Output
0
0
0
0
Input
5
3 3 3 3 3
Output
6
6
6
6
6
Input
8
1 2 1 4 2 1 4 1
Output
5
7
5
7
7
5
7
5
"Correct Solution:
```
N = int(input())
A = list(map(int,input().split()))
C = [0] * (N + 1)
for i in A:
C[i] += 1
ans = 0
for i in C:
ans += i * (i - 1) // 2
for i in range(N):
print(ans - C[A[i]] + 1)
```
| 101,811 |
Provide a correct Python 3 solution for this coding contest problem.
We have N balls. The i-th ball has an integer A_i written on it.
For each k=1, 2, ..., N, solve the following problem and print the answer.
* Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For each k=1,2,...,N, print a line containing the answer.
Examples
Input
5
1 1 2 1 2
Output
2
2
3
2
3
Input
4
1 2 3 4
Output
0
0
0
0
Input
5
3 3 3 3 3
Output
6
6
6
6
6
Input
8
1 2 1 4 2 1 4 1
Output
5
7
5
7
7
5
7
5
"Correct Solution:
```
from collections import Counter
n=int(input())
a=list(map(int,input().split()))
c=Counter(a)
s=0
for key in c:
s+=c[key]*(c[key]-1)//2
for item in a:
print(s-c[item]+1)
```
| 101,812 |
Provide a correct Python 3 solution for this coding contest problem.
We have N balls. The i-th ball has an integer A_i written on it.
For each k=1, 2, ..., N, solve the following problem and print the answer.
* Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For each k=1,2,...,N, print a line containing the answer.
Examples
Input
5
1 1 2 1 2
Output
2
2
3
2
3
Input
4
1 2 3 4
Output
0
0
0
0
Input
5
3 3 3 3 3
Output
6
6
6
6
6
Input
8
1 2 1 4 2 1 4 1
Output
5
7
5
7
7
5
7
5
"Correct Solution:
```
n = int(input())
A = list(map(int, input().split()))
import collections
c = collections.Counter(A)
ans = sum([j*(j-1)//2 for j in c.values()])
for x in A:
print(ans-(c[x]-1))
```
| 101,813 |
Provide a correct Python 3 solution for this coding contest problem.
We have N balls. The i-th ball has an integer A_i written on it.
For each k=1, 2, ..., N, solve the following problem and print the answer.
* Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For each k=1,2,...,N, print a line containing the answer.
Examples
Input
5
1 1 2 1 2
Output
2
2
3
2
3
Input
4
1 2 3 4
Output
0
0
0
0
Input
5
3 3 3 3 3
Output
6
6
6
6
6
Input
8
1 2 1 4 2 1 4 1
Output
5
7
5
7
7
5
7
5
"Correct Solution:
```
N = int(input())
A = list(map(int, input().split()))
B = [0 for i in range(N)]
for a in A:
B[a-1] += 1
s = 0
for b in B:
s += b * (b-1) // 2
for a in A:
print(s - (B[a-1]-1))
```
| 101,814 |
Provide a correct Python 3 solution for this coding contest problem.
We have N balls. The i-th ball has an integer A_i written on it.
For each k=1, 2, ..., N, solve the following problem and print the answer.
* Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For each k=1,2,...,N, print a line containing the answer.
Examples
Input
5
1 1 2 1 2
Output
2
2
3
2
3
Input
4
1 2 3 4
Output
0
0
0
0
Input
5
3 3 3 3 3
Output
6
6
6
6
6
Input
8
1 2 1 4 2 1 4 1
Output
5
7
5
7
7
5
7
5
"Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
b = {}
for x in a:
b.setdefault(x, 0)
b[x] += 1
ans = 0
for x in b.values():
ans += x * (x - 1) // 2
for x in a:
print(ans - b[x] + 1)
```
| 101,815 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N balls. The i-th ball has an integer A_i written on it.
For each k=1, 2, ..., N, solve the following problem and print the answer.
* Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For each k=1,2,...,N, print a line containing the answer.
Examples
Input
5
1 1 2 1 2
Output
2
2
3
2
3
Input
4
1 2 3 4
Output
0
0
0
0
Input
5
3 3 3 3 3
Output
6
6
6
6
6
Input
8
1 2 1 4 2 1 4 1
Output
5
7
5
7
7
5
7
5
Submitted Solution:
```
import collections as cl
N = int(input())
A = list(map(int,input().split()))
cn = cl.Counter(A)
sumC = sum([n*(n-1)//2 for n in cn.values()])
for k in range(N):
print(sumC - cn[A[k]] +1)
```
Yes
| 101,816 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N balls. The i-th ball has an integer A_i written on it.
For each k=1, 2, ..., N, solve the following problem and print the answer.
* Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For each k=1,2,...,N, print a line containing the answer.
Examples
Input
5
1 1 2 1 2
Output
2
2
3
2
3
Input
4
1 2 3 4
Output
0
0
0
0
Input
5
3 3 3 3 3
Output
6
6
6
6
6
Input
8
1 2 1 4 2 1 4 1
Output
5
7
5
7
7
5
7
5
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
b = [0]*n
for i in range(n):
b[a[i]-1] += 1
c = sum([(i*(i-1))//2 for i in b])
for i in a:
print(c-(b[i-1]-1))
```
Yes
| 101,817 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N balls. The i-th ball has an integer A_i written on it.
For each k=1, 2, ..., N, solve the following problem and print the answer.
* Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For each k=1,2,...,N, print a line containing the answer.
Examples
Input
5
1 1 2 1 2
Output
2
2
3
2
3
Input
4
1 2 3 4
Output
0
0
0
0
Input
5
3 3 3 3 3
Output
6
6
6
6
6
Input
8
1 2 1 4 2 1 4 1
Output
5
7
5
7
7
5
7
5
Submitted Solution:
```
from collections import Counter
N = int(input())
A = list(map(int, input().split()))
C = Counter(A)
x = 0
for i in C:
x += C[i] * (C[i] - 1) // 2
for a in A:
print(x - (C[a] - 1))
```
Yes
| 101,818 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N balls. The i-th ball has an integer A_i written on it.
For each k=1, 2, ..., N, solve the following problem and print the answer.
* Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For each k=1,2,...,N, print a line containing the answer.
Examples
Input
5
1 1 2 1 2
Output
2
2
3
2
3
Input
4
1 2 3 4
Output
0
0
0
0
Input
5
3 3 3 3 3
Output
6
6
6
6
6
Input
8
1 2 1 4 2 1 4 1
Output
5
7
5
7
7
5
7
5
Submitted Solution:
```
n = int(input())
lis = list(map(int, input().split()))
ban = [0] * n
tmp = 0
for i in lis:
ban[i-1] += 1
for i in ban:
tmp += i*(i-1)//2
for i in lis:
print(tmp+(1-ban[i-1]))
```
Yes
| 101,819 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N balls. The i-th ball has an integer A_i written on it.
For each k=1, 2, ..., N, solve the following problem and print the answer.
* Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For each k=1,2,...,N, print a line containing the answer.
Examples
Input
5
1 1 2 1 2
Output
2
2
3
2
3
Input
4
1 2 3 4
Output
0
0
0
0
Input
5
3 3 3 3 3
Output
6
6
6
6
6
Input
8
1 2 1 4 2 1 4 1
Output
5
7
5
7
7
5
7
5
Submitted Solution:
```
def main():
import sys
input = sys.stdin.readline
n=int(input())
a=list(map(int,input().split()))
dic={}
for i in a:
if i in dic:
dic[i]+=1
else:
dic[i]=1
for i in list(dic):
if dic[i]==1:
dic.pop(i)
sum=0
for j in dic:
k=dic[j]
if k>1:
sum+=k*(k-1)//2
for i in range(n):
ans=0
if not dic:
ans=0
else:
k=dic[a[i]]
l=k-1
if k>1:
ans=sum-k*(k-1)//2+l*(l-1)//2
print(ans)
if __name__ == '__main__':
main()
```
No
| 101,820 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N balls. The i-th ball has an integer A_i written on it.
For each k=1, 2, ..., N, solve the following problem and print the answer.
* Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For each k=1,2,...,N, print a line containing the answer.
Examples
Input
5
1 1 2 1 2
Output
2
2
3
2
3
Input
4
1 2 3 4
Output
0
0
0
0
Input
5
3 3 3 3 3
Output
6
6
6
6
6
Input
8
1 2 1 4 2 1 4 1
Output
5
7
5
7
7
5
7
5
Submitted Solution:
```
import math
import collections
def combinations_count(n, r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
N = int(input())
A = list(map(int, input().split()))
for i in range(N):
result = 0
pop = A.pop(i)
c = collections.Counter(A)
for k, v in c.items():
if v > 1:
result = result + combinations_count(v, 2)
A.insert(i, pop)
print(result)
```
No
| 101,821 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N balls. The i-th ball has an integer A_i written on it.
For each k=1, 2, ..., N, solve the following problem and print the answer.
* Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For each k=1,2,...,N, print a line containing the answer.
Examples
Input
5
1 1 2 1 2
Output
2
2
3
2
3
Input
4
1 2 3 4
Output
0
0
0
0
Input
5
3 3 3 3 3
Output
6
6
6
6
6
Input
8
1 2 1 4 2 1 4 1
Output
5
7
5
7
7
5
7
5
Submitted Solution:
```
import math
N = int(input())
A = list(map(int, input().split()))
ans = 0
C = list(set(A))
M = len(C)
t = []
anst = 0
for i in range(M):
t.append(A.count(C[i]))
temp = A.count(C[i])
if temp >=2:
anst += temp*(temp-1)/2
#print(t)
#print(anst)
#print(jisyo[1])
for i in range(N):
#print(t[C.index(A[i])])
print(int(anst-t[C.index(A[i])]+1))
```
No
| 101,822 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N balls. The i-th ball has an integer A_i written on it.
For each k=1, 2, ..., N, solve the following problem and print the answer.
* Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq N
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
For each k=1,2,...,N, print a line containing the answer.
Examples
Input
5
1 1 2 1 2
Output
2
2
3
2
3
Input
4
1 2 3 4
Output
0
0
0
0
Input
5
3 3 3 3 3
Output
6
6
6
6
6
Input
8
1 2 1 4 2 1 4 1
Output
5
7
5
7
7
5
7
5
Submitted Solution:
```
import collections
n=int(input())
a=list(map(int,input().split()))
c = collections.Counter(a)
a1=len(list(set(a)))
total=0
for j in range(a1):
x=c.most_common()[j][1]
total+=x*(x-1)/2
print('total',total)
for i in range(n):
ans=total-a.count(a[i])+1
print(int(ans))
```
No
| 101,823 |
Provide a correct Python 3 solution for this coding contest problem.
How many ways are there to choose two distinct positive integers totaling N, disregarding the order?
Constraints
* 1 \leq N \leq 10^6
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
4
Output
1
Input
999999
Output
499999
"Correct Solution:
```
N=int(input())
if N%2==0:
print((N-1)//2)
else:
print(N//2)
```
| 101,824 |
Provide a correct Python 3 solution for this coding contest problem.
How many ways are there to choose two distinct positive integers totaling N, disregarding the order?
Constraints
* 1 \leq N \leq 10^6
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
4
Output
1
Input
999999
Output
499999
"Correct Solution:
```
n=int(input())
from math import factorial
print((n-1)//2)
```
| 101,825 |
Provide a correct Python 3 solution for this coding contest problem.
How many ways are there to choose two distinct positive integers totaling N, disregarding the order?
Constraints
* 1 \leq N \leq 10^6
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
4
Output
1
Input
999999
Output
499999
"Correct Solution:
```
n=int(input())
if n%2==0:n=n/2-1
else:n=n//2
print(int(n))
```
| 101,826 |
Provide a correct Python 3 solution for this coding contest problem.
How many ways are there to choose two distinct positive integers totaling N, disregarding the order?
Constraints
* 1 \leq N \leq 10^6
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
4
Output
1
Input
999999
Output
499999
"Correct Solution:
```
n=int(input())
print(int(n/2)-1 if n%2==0 else int((n-1)/2))
```
| 101,827 |
Provide a correct Python 3 solution for this coding contest problem.
How many ways are there to choose two distinct positive integers totaling N, disregarding the order?
Constraints
* 1 \leq N \leq 10^6
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
4
Output
1
Input
999999
Output
499999
"Correct Solution:
```
n = int(input())
print(int(n / 2) - (1 - (n % 2)))
```
| 101,828 |
Provide a correct Python 3 solution for this coding contest problem.
How many ways are there to choose two distinct positive integers totaling N, disregarding the order?
Constraints
* 1 \leq N \leq 10^6
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
4
Output
1
Input
999999
Output
499999
"Correct Solution:
```
n = int(input())
print(max(0,((n-1)//2)))
```
| 101,829 |
Provide a correct Python 3 solution for this coding contest problem.
How many ways are there to choose two distinct positive integers totaling N, disregarding the order?
Constraints
* 1 \leq N \leq 10^6
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
4
Output
1
Input
999999
Output
499999
"Correct Solution:
```
N = int(input())
print(N // 2 - 1 + N % 2)
```
| 101,830 |
Provide a correct Python 3 solution for this coding contest problem.
How many ways are there to choose two distinct positive integers totaling N, disregarding the order?
Constraints
* 1 \leq N \leq 10^6
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
4
Output
1
Input
999999
Output
499999
"Correct Solution:
```
N=int(input());
print((N-1)//2);
```
| 101,831 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
How many ways are there to choose two distinct positive integers totaling N, disregarding the order?
Constraints
* 1 \leq N \leq 10^6
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
4
Output
1
Input
999999
Output
499999
Submitted Solution:
```
n = int(input())
c = n//2
if(n%2 == 0):c-=1
print(c)
```
Yes
| 101,832 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
How many ways are there to choose two distinct positive integers totaling N, disregarding the order?
Constraints
* 1 \leq N \leq 10^6
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
4
Output
1
Input
999999
Output
499999
Submitted Solution:
```
import math
N=int(input())
ans=int(math.ceil(N/2.0)-1)
print(ans)
```
Yes
| 101,833 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
How many ways are there to choose two distinct positive integers totaling N, disregarding the order?
Constraints
* 1 \leq N \leq 10^6
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
4
Output
1
Input
999999
Output
499999
Submitted Solution:
```
n = int(input())
print((n+1)//2 -1)
```
Yes
| 101,834 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
How many ways are there to choose two distinct positive integers totaling N, disregarding the order?
Constraints
* 1 \leq N \leq 10^6
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
4
Output
1
Input
999999
Output
499999
Submitted Solution:
```
N=int(input())
print([0 if N<3 else (N-1)//2][0])
```
Yes
| 101,835 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
How many ways are there to choose two distinct positive integers totaling N, disregarding the order?
Constraints
* 1 \leq N \leq 10^6
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
4
Output
1
Input
999999
Output
499999
Submitted Solution:
```
N = int(input())
if N % 2 == 0:
ans = N / 2 - 1
else:
ans = (N -1) / 2
print(ans)
```
No
| 101,836 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
How many ways are there to choose two distinct positive integers totaling N, disregarding the order?
Constraints
* 1 \leq N \leq 10^6
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
4
Output
1
Input
999999
Output
499999
Submitted Solution:
```
a=int(input())
#b=int(input())
#c=int(input())
#d=int(input())
print(int((a-2)/2))
```
No
| 101,837 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
How many ways are there to choose two distinct positive integers totaling N, disregarding the order?
Constraints
* 1 \leq N \leq 10^6
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
4
Output
1
Input
999999
Output
499999
Submitted Solution:
```
n=int(input())
if n%2==0:
print(n//2)
else:
print(n//2-1)
```
No
| 101,838 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
How many ways are there to choose two distinct positive integers totaling N, disregarding the order?
Constraints
* 1 \leq N \leq 10^6
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the answer.
Examples
Input
4
Output
1
Input
999999
Output
499999
Submitted Solution:
```
a = int(input())
value = 0
if a%2 == 0:
value = a/2-1
else:
value = a/2
print(value)
```
No
| 101,839 |
Provide a correct Python 3 solution for this coding contest problem.
A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 \leq i \leq N+1) at coordinate D_i = D_{i-1} + L_{i-1}.
How many times will the ball make a bounce where the coordinate is at most X?
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 100
* 1 \leq X \leq 10000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
L_1 L_2 ... L_{N-1} L_N
Output
Print the number of times the ball will make a bounce where the coordinate is at most X.
Examples
Input
3 6
3 4 5
Output
2
Input
4 9
3 3 3 3
Output
4
"Correct Solution:
```
n,x=map(int,input().split())
*l,=map(int,input().split())
s=[0]
for i in range(n):
s.append(s[i]+l[i])
print(sum(t<=x for t in s))
```
| 101,840 |
Provide a correct Python 3 solution for this coding contest problem.
A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 \leq i \leq N+1) at coordinate D_i = D_{i-1} + L_{i-1}.
How many times will the ball make a bounce where the coordinate is at most X?
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 100
* 1 \leq X \leq 10000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
L_1 L_2 ... L_{N-1} L_N
Output
Print the number of times the ball will make a bounce where the coordinate is at most X.
Examples
Input
3 6
3 4 5
Output
2
Input
4 9
3 3 3 3
Output
4
"Correct Solution:
```
n,x=map(int,input().split())
l=[int(x) for x in input().split()]
ans=1
s=0
for ll in l:
s+=ll
if s <= x:
ans+=1
print(ans)
```
| 101,841 |
Provide a correct Python 3 solution for this coding contest problem.
A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 \leq i \leq N+1) at coordinate D_i = D_{i-1} + L_{i-1}.
How many times will the ball make a bounce where the coordinate is at most X?
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 100
* 1 \leq X \leq 10000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
L_1 L_2 ... L_{N-1} L_N
Output
Print the number of times the ball will make a bounce where the coordinate is at most X.
Examples
Input
3 6
3 4 5
Output
2
Input
4 9
3 3 3 3
Output
4
"Correct Solution:
```
n,x=map(int,input().split())
l=list(map(int,input().split()))
d=[sum(l[:i+1]) for i in range(len(l))]
print(sum([a<=x for a in d])+1)
```
| 101,842 |
Provide a correct Python 3 solution for this coding contest problem.
A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 \leq i \leq N+1) at coordinate D_i = D_{i-1} + L_{i-1}.
How many times will the ball make a bounce where the coordinate is at most X?
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 100
* 1 \leq X \leq 10000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
L_1 L_2 ... L_{N-1} L_N
Output
Print the number of times the ball will make a bounce where the coordinate is at most X.
Examples
Input
3 6
3 4 5
Output
2
Input
4 9
3 3 3 3
Output
4
"Correct Solution:
```
n,x=map(int,input().split())
s=list(map(int,input().split()))
t,c=0,1
for i in s:
if(t+i>x):
break
else:
t+=i
c+=1
print(c)
```
| 101,843 |
Provide a correct Python 3 solution for this coding contest problem.
A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 \leq i \leq N+1) at coordinate D_i = D_{i-1} + L_{i-1}.
How many times will the ball make a bounce where the coordinate is at most X?
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 100
* 1 \leq X \leq 10000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
L_1 L_2 ... L_{N-1} L_N
Output
Print the number of times the ball will make a bounce where the coordinate is at most X.
Examples
Input
3 6
3 4 5
Output
2
Input
4 9
3 3 3 3
Output
4
"Correct Solution:
```
N,X = map(int,input().split())
L = list(map(int,input().split()))
I = 0
A = 1
for i in L:
I+=i
if I <= X:
A += 1
print(A)
```
| 101,844 |
Provide a correct Python 3 solution for this coding contest problem.
A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 \leq i \leq N+1) at coordinate D_i = D_{i-1} + L_{i-1}.
How many times will the ball make a bounce where the coordinate is at most X?
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 100
* 1 \leq X \leq 10000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
L_1 L_2 ... L_{N-1} L_N
Output
Print the number of times the ball will make a bounce where the coordinate is at most X.
Examples
Input
3 6
3 4 5
Output
2
Input
4 9
3 3 3 3
Output
4
"Correct Solution:
```
n, x = map(int, input().split())
d = [0]
for l in map(int, input().split()):
d.append(d[-1] + l)
print(sum(dx <= x for dx in d))
```
| 101,845 |
Provide a correct Python 3 solution for this coding contest problem.
A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 \leq i \leq N+1) at coordinate D_i = D_{i-1} + L_{i-1}.
How many times will the ball make a bounce where the coordinate is at most X?
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 100
* 1 \leq X \leq 10000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
L_1 L_2 ... L_{N-1} L_N
Output
Print the number of times the ball will make a bounce where the coordinate is at most X.
Examples
Input
3 6
3 4 5
Output
2
Input
4 9
3 3 3 3
Output
4
"Correct Solution:
```
n,x=map(int,input().split())
l=list(map(int,input().split()))
c=1
t=0
for s in l:
t+=s
if t<=x:
c+=1
print(c)
```
| 101,846 |
Provide a correct Python 3 solution for this coding contest problem.
A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 \leq i \leq N+1) at coordinate D_i = D_{i-1} + L_{i-1}.
How many times will the ball make a bounce where the coordinate is at most X?
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 100
* 1 \leq X \leq 10000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
L_1 L_2 ... L_{N-1} L_N
Output
Print the number of times the ball will make a bounce where the coordinate is at most X.
Examples
Input
3 6
3 4 5
Output
2
Input
4 9
3 3 3 3
Output
4
"Correct Solution:
```
n, x = map(int, input().split())
l = list(map(int, input().split()))
ans = 1
d = 0
for i in l:
d = d + i
if d <= x: ans += 1
print(ans)
```
| 101,847 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 \leq i \leq N+1) at coordinate D_i = D_{i-1} + L_{i-1}.
How many times will the ball make a bounce where the coordinate is at most X?
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 100
* 1 \leq X \leq 10000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
L_1 L_2 ... L_{N-1} L_N
Output
Print the number of times the ball will make a bounce where the coordinate is at most X.
Examples
Input
3 6
3 4 5
Output
2
Input
4 9
3 3 3 3
Output
4
Submitted Solution:
```
n,x=map(int,input().split())
ll=list(map(int,input().split()))
ans=1
now=0
for l in ll:
now+=l
if now<=x:
ans+=1
print(ans)
```
Yes
| 101,848 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 \leq i \leq N+1) at coordinate D_i = D_{i-1} + L_{i-1}.
How many times will the ball make a bounce where the coordinate is at most X?
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 100
* 1 \leq X \leq 10000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
L_1 L_2 ... L_{N-1} L_N
Output
Print the number of times the ball will make a bounce where the coordinate is at most X.
Examples
Input
3 6
3 4 5
Output
2
Input
4 9
3 3 3 3
Output
4
Submitted Solution:
```
ans=0
n,x=map(int,input().split())
l=list(map(int,input().split()))
d=0
for i in l:
d+=i
if d<=x:ans+=1
print(ans+1)
```
Yes
| 101,849 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 \leq i \leq N+1) at coordinate D_i = D_{i-1} + L_{i-1}.
How many times will the ball make a bounce where the coordinate is at most X?
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 100
* 1 \leq X \leq 10000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
L_1 L_2 ... L_{N-1} L_N
Output
Print the number of times the ball will make a bounce where the coordinate is at most X.
Examples
Input
3 6
3 4 5
Output
2
Input
4 9
3 3 3 3
Output
4
Submitted Solution:
```
N,X=list(map(int,input().split()))
i=list(map(int,input().split()))
d=1
a=0
for s in i:
a+=s
if a<=X:
d+=1
print(d)
```
Yes
| 101,850 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 \leq i \leq N+1) at coordinate D_i = D_{i-1} + L_{i-1}.
How many times will the ball make a bounce where the coordinate is at most X?
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 100
* 1 \leq X \leq 10000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
L_1 L_2 ... L_{N-1} L_N
Output
Print the number of times the ball will make a bounce where the coordinate is at most X.
Examples
Input
3 6
3 4 5
Output
2
Input
4 9
3 3 3 3
Output
4
Submitted Solution:
```
n,x=map(int,input().split())
l=list(map(int,input().split()))
ans,d=1,0
for i in l:
d+=i
if d<=x:
ans+=1
else:
break
print(ans)
```
Yes
| 101,851 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 \leq i \leq N+1) at coordinate D_i = D_{i-1} + L_{i-1}.
How many times will the ball make a bounce where the coordinate is at most X?
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 100
* 1 \leq X \leq 10000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
L_1 L_2 ... L_{N-1} L_N
Output
Print the number of times the ball will make a bounce where the coordinate is at most X.
Examples
Input
3 6
3 4 5
Output
2
Input
4 9
3 3 3 3
Output
4
Submitted Solution:
```
N, X = map(int, input().split())
L = list(map(int, input().split()))
D =[0]
K = 0
for i in range(2, N+1):
D.append(D[i-2] + L[i-1])
D.append(D[(N+1)-2]+L[(N)-1])
k = [i for i in D if i <= X ]
print(len(k))
```
No
| 101,852 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 \leq i \leq N+1) at coordinate D_i = D_{i-1} + L_{i-1}.
How many times will the ball make a bounce where the coordinate is at most X?
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 100
* 1 \leq X \leq 10000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
L_1 L_2 ... L_{N-1} L_N
Output
Print the number of times the ball will make a bounce where the coordinate is at most X.
Examples
Input
3 6
3 4 5
Output
2
Input
4 9
3 3 3 3
Output
4
Submitted Solution:
```
n, x = map(int, input().split())
l = list(map(int, input().split()))
res = 0
for i in range(n):
res += l[i]
if x < res:
break
print(i+1)
```
No
| 101,853 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 \leq i \leq N+1) at coordinate D_i = D_{i-1} + L_{i-1}.
How many times will the ball make a bounce where the coordinate is at most X?
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 100
* 1 \leq X \leq 10000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
L_1 L_2 ... L_{N-1} L_N
Output
Print the number of times the ball will make a bounce where the coordinate is at most X.
Examples
Input
3 6
3 4 5
Output
2
Input
4 9
3 3 3 3
Output
4
Submitted Solution:
```
n,x = map(int,input().split())
l = list(map(int,input().split()))
d = 0
count = 1
for i in range(n):
d += l[i]
count += 1
if x <= d:
print(count)
break
```
No
| 101,854 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A ball will bounce along a number line, making N + 1 bounces. It will make the first bounce at coordinate D_1 = 0, and the i-th bounce (2 \leq i \leq N+1) at coordinate D_i = D_{i-1} + L_{i-1}.
How many times will the ball make a bounce where the coordinate is at most X?
Constraints
* 1 \leq N \leq 100
* 1 \leq L_i \leq 100
* 1 \leq X \leq 10000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
L_1 L_2 ... L_{N-1} L_N
Output
Print the number of times the ball will make a bounce where the coordinate is at most X.
Examples
Input
3 6
3 4 5
Output
2
Input
4 9
3 3 3 3
Output
4
Submitted Solution:
```
N, A=map(int, input().split())
L= list(map(int, input().split()))
X=0
count=0
for i in range(N+1):
if (X<A or X==A):
X=X+L[i]
count=count+1
else:
print(count)
break
```
No
| 101,855 |
Provide a correct Python 3 solution for this coding contest problem.
There are N dishes of cuisine placed in front of Takahashi and Aoki. For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.
When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.
Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat. Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".
Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Output
Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Examples
Input
3
10 10
20 20
30 30
Output
20
Input
3
20 10
20 20
20 30
Output
20
Input
6
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
Output
-2999999997
"Correct Solution:
```
n=int(input())
s=[]
for i in range(n):
a,b=map(int,input().split())
s.append([a+b,a,b])
s=sorted(s,key=lambda x: x[0],reverse=True)
tk,ao=0,0
for i in range(n):
if i%2==0:
tk+=s[i][1]
else:
ao+=s[i][2]
print(tk-ao)
```
| 101,856 |
Provide a correct Python 3 solution for this coding contest problem.
There are N dishes of cuisine placed in front of Takahashi and Aoki. For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.
When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.
Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat. Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".
Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Output
Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Examples
Input
3
10 10
20 20
30 30
Output
20
Input
3
20 10
20 20
20 30
Output
20
Input
6
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
Output
-2999999997
"Correct Solution:
```
N = int(input())
X = [list(map(int, input().split())) for i in range(N)]
X.sort(key=lambda x: x[0] + x[1], reverse=True)
ans = 0
for i, (a, b) in enumerate(X):
if i % 2 == 0:
ans += a
else:
ans -= b
print(ans)
```
| 101,857 |
Provide a correct Python 3 solution for this coding contest problem.
There are N dishes of cuisine placed in front of Takahashi and Aoki. For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.
When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.
Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat. Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".
Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Output
Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Examples
Input
3
10 10
20 20
30 30
Output
20
Input
3
20 10
20 20
20 30
Output
20
Input
6
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
Output
-2999999997
"Correct Solution:
```
N = int(input())
AB, ans = [], 0
for _ in range(N):
a, b = map(int, input().split())
AB.append([a+b, a, b])
AB = sorted(AB, reverse=True)
for i in range(N):
ans += (-1)**(i%2) * AB[i][i%2 + 1]
print(ans)
```
| 101,858 |
Provide a correct Python 3 solution for this coding contest problem.
There are N dishes of cuisine placed in front of Takahashi and Aoki. For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.
When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.
Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat. Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".
Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Output
Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Examples
Input
3
10 10
20 20
30 30
Output
20
Input
3
20 10
20 20
20 30
Output
20
Input
6
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
Output
-2999999997
"Correct Solution:
```
n=int(input())
l=[list(map(int,input().split())) for _ in range(n)]
l.sort(key=lambda x:x[0]+x[1],reverse=True)
print(sum([l[i][0] for i in range(n) if i % 2 == 0]) - sum([l[i][1] for i in range(n) if i % 2 == 1]))
```
| 101,859 |
Provide a correct Python 3 solution for this coding contest problem.
There are N dishes of cuisine placed in front of Takahashi and Aoki. For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.
When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.
Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat. Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".
Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Output
Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Examples
Input
3
10 10
20 20
30 30
Output
20
Input
3
20 10
20 20
20 30
Output
20
Input
6
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
Output
-2999999997
"Correct Solution:
```
N = int(input())
A, B = [], []
for _ in range(N):
a, b = map(int, input().split())
A.append(a + b)
B.append(b)
A.sort(reverse=True)
print(sum([ab for i, ab in enumerate(A) if i % 2 == 0]) - sum(B))
```
| 101,860 |
Provide a correct Python 3 solution for this coding contest problem.
There are N dishes of cuisine placed in front of Takahashi and Aoki. For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.
When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.
Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat. Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".
Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Output
Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Examples
Input
3
10 10
20 20
30 30
Output
20
Input
3
20 10
20 20
20 30
Output
20
Input
6
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
Output
-2999999997
"Correct Solution:
```
N=int(input())
AB=[list(map(int,input().split())) for i in range(N)]
b=-sum(AB[i][1] for i in range(N))
AB.sort(key=lambda x:x[0]+x[1],reverse=True)
for i in range(N):
if i%2==0:
b+=sum(AB[i])
print(b)
```
| 101,861 |
Provide a correct Python 3 solution for this coding contest problem.
There are N dishes of cuisine placed in front of Takahashi and Aoki. For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.
When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.
Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat. Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".
Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Output
Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Examples
Input
3
10 10
20 20
30 30
Output
20
Input
3
20 10
20 20
20 30
Output
20
Input
6
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
Output
-2999999997
"Correct Solution:
```
N = int(input())
e = [tuple(map(int, input().split())) for _ in range(N)]
e.sort(key=lambda x: x[0] + x[1], reverse=True)
ans = 0
for i in range(N):
if i % 2 == 0:
ans += e[i][0]
else:
ans -= e[i][1]
print(ans)
```
| 101,862 |
Provide a correct Python 3 solution for this coding contest problem.
There are N dishes of cuisine placed in front of Takahashi and Aoki. For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.
When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.
Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat. Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".
Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Output
Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Examples
Input
3
10 10
20 20
30 30
Output
20
Input
3
20 10
20 20
20 30
Output
20
Input
6
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
Output
-2999999997
"Correct Solution:
```
N = int(input())
AB = []
for _ in range(N):
A, B = map(int, input().split())
AB.append([A+B, A, B])
AB.sort()
result = [0, 0]
for i in range(N):
result[i%2] += AB[-1][i%2+1]
del AB[-1]
print(result[0] - result[1])
```
| 101,863 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N dishes of cuisine placed in front of Takahashi and Aoki. For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.
When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.
Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat. Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".
Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Output
Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Examples
Input
3
10 10
20 20
30 30
Output
20
Input
3
20 10
20 20
20 30
Output
20
Input
6
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
Output
-2999999997
Submitted Solution:
```
n=int(input())
ab=[list(map(int,input().split())) for _ in range(n)]
l=sorted([(a+b,a,b) for a,b in ab],reverse=True)
ans=sum([a for s,a,b in l[::2]])-sum([b for s,a,b in l[1::2]])
print(ans)
```
Yes
| 101,864 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N dishes of cuisine placed in front of Takahashi and Aoki. For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.
When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.
Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat. Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".
Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Output
Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Examples
Input
3
10 10
20 20
30 30
Output
20
Input
3
20 10
20 20
20 30
Output
20
Input
6
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
Output
-2999999997
Submitted Solution:
```
from collections import deque
n=int(input())
l=[list(map(int,input().split())) for i in range(n)]
l.sort(key = lambda x:x[0]+x[1],reverse=True)
ans=0
for i in range(n):
if i%2==0:
ans+=l[i][0]
else:
ans-=l[i][1]
print(ans)
```
Yes
| 101,865 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N dishes of cuisine placed in front of Takahashi and Aoki. For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.
When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.
Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat. Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".
Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Output
Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Examples
Input
3
10 10
20 20
30 30
Output
20
Input
3
20 10
20 20
20 30
Output
20
Input
6
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
Output
-2999999997
Submitted Solution:
```
n=int(input())
l=[None]*n
for i in range(n):
a,b=map(int,input().split())
l[i]=[a,b]
l.sort(key=lambda x:x[0]+x[1], reverse=True)
#print(l)
ans=0
for i in range(n):
if i%2:
ans-=l[i][1]
else:
ans+=l[i][0]
print(ans)
```
Yes
| 101,866 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N dishes of cuisine placed in front of Takahashi and Aoki. For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.
When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.
Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat. Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".
Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Output
Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Examples
Input
3
10 10
20 20
30 30
Output
20
Input
3
20 10
20 20
20 30
Output
20
Input
6
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
Output
-2999999997
Submitted Solution:
```
N = int(input())
AB = [0 for _ in range(N)]
SB = 0
for i in range(N):
A, B = map(int, input().split())
SB += B
AB[i] = A + B
AB.sort(reverse=True)
SAB = 0
for i in range(N):
if i % 2 == 0:
SAB += AB[i]
print(SAB-SB)
```
Yes
| 101,867 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N dishes of cuisine placed in front of Takahashi and Aoki. For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.
When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.
Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat. Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".
Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Output
Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Examples
Input
3
10 10
20 20
30 30
Output
20
Input
3
20 10
20 20
20 30
Output
20
Input
6
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
Output
-2999999997
Submitted Solution:
```
n = int(input())
taka = []
aoki = []
score = 0
for i in range(n):
t, a = map(int, input().split())
taka.append(t)
aoki.append(a)
for i in range(n):
maxT = max(taka)
maxA = max(aoki)
rm = 0
if (maxT > maxA):
rm = taka.index(maxT)
else:
rm = aoki.index(maxA)
if (i % 2 == 0):
score += taka.pop(rm)
aoki.pop(rm)
else:
taka.pop(rm)
score -= aoki.pop(rm)
print(score)
```
No
| 101,868 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N dishes of cuisine placed in front of Takahashi and Aoki. For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.
When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.
Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat. Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".
Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Output
Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Examples
Input
3
10 10
20 20
30 30
Output
20
Input
3
20 10
20 20
20 30
Output
20
Input
6
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
Output
-2999999997
Submitted Solution:
```
#coding:utf-8
###### input ######
n = int(input())
taka = []
aoki = []
for i in range(n):
t,a= map(int,input().split())
taka.append(t)
aoki.append(a)
###### main ######
res = 0
for i in range(n):
if i % 2 == 0: # turn TAKAHASHI
if max(taka) < max(aoki):
tmp = aoki.index(max(aoki))#[0]
else:
tmp = taka.index(max(taka))#[0]
print(tmp)
res+= taka[tmp]
taka[tmp] = 0
aoki[tmp] = 0
else:
if max(taka) > max(aoki):
tmp = taka.index(max(taka))#[0]
else:
tmp = aoki.index(max(aoki))#[0]
print(tmp)
res -= aoki[tmp]
taka[tmp] = 0
aoki[tmp] = 0
print(res)
```
No
| 101,869 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N dishes of cuisine placed in front of Takahashi and Aoki. For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.
When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.
Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat. Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".
Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Output
Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Examples
Input
3
10 10
20 20
30 30
Output
20
Input
3
20 10
20 20
20 30
Output
20
Input
6
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
Output
-2999999997
Submitted Solution:
```
n = int(input())
for i in range(n):
ab[i][0], ab[i][1] = map(int, input().split())
ab[i][2] = ab[i][0] + ab[i][1]
sorted(ab, key=lambda x: x[2])
print(sum(ab[0::2][0])-sum(ab[1::2][1]))
```
No
| 101,870 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N dishes of cuisine placed in front of Takahashi and Aoki. For convenience, we call these dishes Dish 1, Dish 2, ..., Dish N.
When Takahashi eats Dish i, he earns A_i points of happiness; when Aoki eats Dish i, she earns B_i points of happiness.
Starting from Takahashi, they alternately choose one dish and eat it, until there is no more dish to eat. Here, both of them choose dishes so that the following value is maximized: "the sum of the happiness he/she will earn in the end" minus "the sum of the happiness the other person will earn in the end".
Find the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Output
Print the value: "the sum of the happiness Takahashi earns in the end" minus "the sum of the happiness Aoki earns in the end".
Examples
Input
3
10 10
20 20
30 30
Output
20
Input
3
20 10
20 20
20 30
Output
20
Input
6
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000
Output
-2999999997
Submitted Solution:
```
def solve(n, xs, ys):
first_score = 0
second_score = 0
zs = sorted(zip(xs, ys))
for i in range(n):
if i % 2 == 0:
first_score += zs[i][0]
else:
second_score += zs[i][1]
res = first_score - second_score
return res
def main():
n = int(input())
xs = [0] * n
ys = [0] * n
for i in range(n):
xs[i], ys[i] = (int(z) for z in input().split())
res = solve(n, xs, ys)
print(res)
if __name__ == "__main__":
main()
```
No
| 101,871 |
Provide a correct Python 3 solution for this coding contest problem.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
"Correct Solution:
```
n = int(input())
if( n in {4,7,8,11,12,14,15,16} or n >= 18):
print('Yes')
else:
print('No')
```
| 101,872 |
Provide a correct Python 3 solution for this coding contest problem.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
"Correct Solution:
```
a=int(input())
print("Yes" if [4*x+7*y for x in range(101) for y in range(101)].count(a) else "No")
```
| 101,873 |
Provide a correct Python 3 solution for this coding contest problem.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
"Correct Solution:
```
x=int(input());print("No" if x<4 or 4<x<7 or 8<x<11 or x==13 or x==17 else "Yes")
```
| 101,874 |
Provide a correct Python 3 solution for this coding contest problem.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
"Correct Solution:
```
N = int(input())
for i in range(N//4+1):
if (N-4*i) % 7 == 0:
print("Yes")
exit()
print("No")
```
| 101,875 |
Provide a correct Python 3 solution for this coding contest problem.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
"Correct Solution:
```
N = int(input())
ans = "No"
for i in range(0,1+(N//7)):
if (N - 7*i)%4==0:
ans = "Yes"
break
print(ans)
```
| 101,876 |
Provide a correct Python 3 solution for this coding contest problem.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
"Correct Solution:
```
n = int(input())
print("Yes" if len([1 for i in range(100//4) for j in range(100//7) if i*4+j*7==n])>0 else "No")
```
| 101,877 |
Provide a correct Python 3 solution for this coding contest problem.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
"Correct Solution:
```
n=int(input())
if n<4 :
print("No")
elif n in {5, 6, 9, 10, 13, 17, 23}:
print("No")
else :
print("Yes")
```
| 101,878 |
Provide a correct Python 3 solution for this coding contest problem.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
"Correct Solution:
```
n = int(input())
ng = [1,2,3,5,6,9,10,13,17]
if n in ng:
print('No')
else:
print('Yes')
```
| 101,879 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
Submitted Solution:
```
N = int(input())
M = [4*i+7*j for i in range(30) for j in range(20)]
if N in M:
print("Yes")
else:
print("No")
```
Yes
| 101,880 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
Submitted Solution:
```
N=int(input())
a=[4*x+7*y for x in range(200) for y in range(200)]
ans="Yes" if N in a else "No"
print(ans)
```
Yes
| 101,881 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
Submitted Solution:
```
n=int(input())
if n <= 3 or n==5 or n==6 or n==9 or n==10 or n==13 or n==17:
print("No")
else:
print("Yes")
```
Yes
| 101,882 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
Submitted Solution:
```
n=int(input())
b=[]
for i in range(15):
for j in range(12):
b.append(i*4+j*7)
print("NYoe s"[n in b::2])
```
Yes
| 101,883 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
Submitted Solution:
```
n = int(input())
if n % 4 != 0 and n % 7 != 0 and n % 11 != 0:
print('Yes')
else:
print('No')
```
No
| 101,884 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
Submitted Solution:
```
if (N % 7) % 4 == 0 or (N % 4) % 7 == 0:
print("Yes")
else:
print("No")
```
No
| 101,885 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
Submitted Solution:
```
N = int(input())
#4*a + 7*b == N ???
counter = 0
for a in range(N//4):
for b in range(N//7):
if 4*a + 7*b == N:
counter += 1
print(counter)
```
No
| 101,886 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
La Confiserie d'ABC sells cakes at 4 dollars each and doughnuts at 7 dollars each. Determine if there is a way to buy some of them for exactly N dollars. You can buy two or more doughnuts and two or more cakes, and you can also choose to buy zero doughnuts or zero cakes.
Constraints
* N is an integer between 1 and 100, inclusive.
Input
Input is given from Standard Input in the following format:
N
Output
If there is a way to buy some cakes and some doughnuts for exactly N dollars, print `Yes`; otherwise, print `No`.
Examples
Input
11
Output
Yes
Input
40
Output
Yes
Input
3
Output
No
Submitted Solution:
```
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll MOD = 1e9 + 7;
const ll LINF = LLONG_MAX;
const int INF = INT_MAX;
int main() {
int n;
cin >> n;
for (int i = (0); i < (int)(30); i++) {
if ((n - 4 * i) % 7 == 0) {
cout << "Yes" << endl;
return 0;
}
if (i * 4 > n) break;
}
cout << "No" << endl;
}
```
No
| 101,887 |
Provide a correct Python 3 solution for this coding contest problem.
We have a tree with N vertices. The vertices are numbered 0 through N - 1, and the i-th edge (0 ≤ i < N - 1) comnnects Vertex a_i and b_i. For each pair of vertices u and v (0 ≤ u, v < N), we define the distance d(u, v) as the number of edges in the path u-v.
It is expected that one of the vertices will be invaded by aliens from outer space. Snuke wants to immediately identify that vertex when the invasion happens. To do so, he has decided to install an antenna on some vertices.
First, he decides the number of antennas, K (1 ≤ K ≤ N). Then, he chooses K different vertices, x_0, x_1, ..., x_{K - 1}, on which he installs Antenna 0, 1, ..., K - 1, respectively. If Vertex v is invaded by aliens, Antenna k (0 ≤ k < K) will output the distance d(x_k, v). Based on these K outputs, Snuke will identify the vertex that is invaded. Thus, in order to identify the invaded vertex no matter which one is invaded, the following condition must hold:
* For each vertex u (0 ≤ u < N), consider the vector (d(x_0, u), ..., d(x_{K - 1}, u)). These N vectors are distinct.
Find the minumum value of K, the number of antennas, when the condition is satisfied.
Constraints
* 2 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i < N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
a_0 b_0
a_1 b_1
:
a_{N - 2} b_{N - 2}
Output
Print the minumum value of K, the number of antennas, when the condition is satisfied.
Examples
Input
5
0 1
0 2
0 3
3 4
Output
2
Input
2
0 1
Output
1
Input
10
2 8
6 0
4 1
7 6
2 3
8 6
6 9
2 4
5 8
Output
3
"Correct Solution:
```
def main():
n = int(input())
ab = [list(map(int, input().split())) for _ in [0]*(n-1)]
g = [[] for _ in [0]*n]
[g[a].append(b) for a, b in ab]
[g[b].append(a) for a, b in ab]
for i in range(n):
if len(g[i]) > 2:
root = i
break
else:
print(1)
return
d = [-1]*n # 根からの距離
d[root] = 0
q = [root]
cnt = 0
while q: # BFS
cnt += 1
qq = []
while q:
i = q.pop()
for j in g[i]:
if d[j] == -1:
d[j] = cnt
qq.append(j)
q = qq
d2 = sorted([(j, i) for i, j in enumerate(d)])[::-1]
stock = [0]*n
ans = 0
for _, i in d2:
dist = d[i]
s = 0
cnt = 0
for j in g[i]:
if dist < d[j]:
s += stock[j]
cnt += 1
ans += max(cnt-s-1, 0)
s += max(cnt-s-1, 0)
if s > 0 or cnt > 1:
stock[i] = 1
print(ans)
main()
```
| 101,888 |
Provide a correct Python 3 solution for this coding contest problem.
We have a tree with N vertices. The vertices are numbered 0 through N - 1, and the i-th edge (0 ≤ i < N - 1) comnnects Vertex a_i and b_i. For each pair of vertices u and v (0 ≤ u, v < N), we define the distance d(u, v) as the number of edges in the path u-v.
It is expected that one of the vertices will be invaded by aliens from outer space. Snuke wants to immediately identify that vertex when the invasion happens. To do so, he has decided to install an antenna on some vertices.
First, he decides the number of antennas, K (1 ≤ K ≤ N). Then, he chooses K different vertices, x_0, x_1, ..., x_{K - 1}, on which he installs Antenna 0, 1, ..., K - 1, respectively. If Vertex v is invaded by aliens, Antenna k (0 ≤ k < K) will output the distance d(x_k, v). Based on these K outputs, Snuke will identify the vertex that is invaded. Thus, in order to identify the invaded vertex no matter which one is invaded, the following condition must hold:
* For each vertex u (0 ≤ u < N), consider the vector (d(x_0, u), ..., d(x_{K - 1}, u)). These N vectors are distinct.
Find the minumum value of K, the number of antennas, when the condition is satisfied.
Constraints
* 2 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i < N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
a_0 b_0
a_1 b_1
:
a_{N - 2} b_{N - 2}
Output
Print the minumum value of K, the number of antennas, when the condition is satisfied.
Examples
Input
5
0 1
0 2
0 3
3 4
Output
2
Input
2
0 1
Output
1
Input
10
2 8
6 0
4 1
7 6
2 3
8 6
6 9
2 4
5 8
Output
3
"Correct Solution:
```
import math
#import numpy as np
import queue
from collections import deque,defaultdict
import heapq
from sys import stdin,setrecursionlimit
#from scipy.sparse.csgraph import dijkstra
#from scipy.sparse import csr_matrix
ipt = stdin.readline
setrecursionlimit(10**7)
def main():
n = int(ipt())
way = [[] for i in range(n)]
for _ in [0]*(n-1):
a,b = map(int,ipt().split())
way[a].append(b)
way[b].append(a)
rt = -1
for i in range(n):
if len(way[i]) > 2:
rt = i
break
def dp(pp,np):
sum = 0
n0 = 0
for i in way[np]:
if i == pp:
continue
tmp = dp(np,i)
sum += tmp
if tmp == 0:
n0 += 1
if n0 > 1:
sum += n0-1
return sum
if rt == -1:
print(1)
exit()
else:
print(dp(-1,rt))
return
if __name__ == '__main__':
main()
```
| 101,889 |
Provide a correct Python 3 solution for this coding contest problem.
We have a tree with N vertices. The vertices are numbered 0 through N - 1, and the i-th edge (0 ≤ i < N - 1) comnnects Vertex a_i and b_i. For each pair of vertices u and v (0 ≤ u, v < N), we define the distance d(u, v) as the number of edges in the path u-v.
It is expected that one of the vertices will be invaded by aliens from outer space. Snuke wants to immediately identify that vertex when the invasion happens. To do so, he has decided to install an antenna on some vertices.
First, he decides the number of antennas, K (1 ≤ K ≤ N). Then, he chooses K different vertices, x_0, x_1, ..., x_{K - 1}, on which he installs Antenna 0, 1, ..., K - 1, respectively. If Vertex v is invaded by aliens, Antenna k (0 ≤ k < K) will output the distance d(x_k, v). Based on these K outputs, Snuke will identify the vertex that is invaded. Thus, in order to identify the invaded vertex no matter which one is invaded, the following condition must hold:
* For each vertex u (0 ≤ u < N), consider the vector (d(x_0, u), ..., d(x_{K - 1}, u)). These N vectors are distinct.
Find the minumum value of K, the number of antennas, when the condition is satisfied.
Constraints
* 2 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i < N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
a_0 b_0
a_1 b_1
:
a_{N - 2} b_{N - 2}
Output
Print the minumum value of K, the number of antennas, when the condition is satisfied.
Examples
Input
5
0 1
0 2
0 3
3 4
Output
2
Input
2
0 1
Output
1
Input
10
2 8
6 0
4 1
7 6
2 3
8 6
6 9
2 4
5 8
Output
3
"Correct Solution:
```
import sys
sys.setrecursionlimit(100000)
def dfs(v, p, links):
lv = links[v]
if len(lv) == 1:
return 0
cnt0 = 0
ret = 0
for l in lv:
if l == p:
continue
res = dfs(l, v, links)
ret += res
if res == 0:
cnt0 += 1
if cnt0:
ret += cnt0 - 1
return ret
def solve(n, links):
if n == 2:
return 1
for i, l in enumerate(links):
if len(l) > 2:
return dfs(i, None, links)
else:
return 1
n = int(input())
links = [set() for _ in range(n)]
for _ in range(n - 1):
a, b = map(int, input().split())
links[a].add(b)
links[b].add(a)
print(solve(n, links))
```
| 101,890 |
Provide a correct Python 3 solution for this coding contest problem.
We have a tree with N vertices. The vertices are numbered 0 through N - 1, and the i-th edge (0 ≤ i < N - 1) comnnects Vertex a_i and b_i. For each pair of vertices u and v (0 ≤ u, v < N), we define the distance d(u, v) as the number of edges in the path u-v.
It is expected that one of the vertices will be invaded by aliens from outer space. Snuke wants to immediately identify that vertex when the invasion happens. To do so, he has decided to install an antenna on some vertices.
First, he decides the number of antennas, K (1 ≤ K ≤ N). Then, he chooses K different vertices, x_0, x_1, ..., x_{K - 1}, on which he installs Antenna 0, 1, ..., K - 1, respectively. If Vertex v is invaded by aliens, Antenna k (0 ≤ k < K) will output the distance d(x_k, v). Based on these K outputs, Snuke will identify the vertex that is invaded. Thus, in order to identify the invaded vertex no matter which one is invaded, the following condition must hold:
* For each vertex u (0 ≤ u < N), consider the vector (d(x_0, u), ..., d(x_{K - 1}, u)). These N vectors are distinct.
Find the minumum value of K, the number of antennas, when the condition is satisfied.
Constraints
* 2 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i < N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
a_0 b_0
a_1 b_1
:
a_{N - 2} b_{N - 2}
Output
Print the minumum value of K, the number of antennas, when the condition is satisfied.
Examples
Input
5
0 1
0 2
0 3
3 4
Output
2
Input
2
0 1
Output
1
Input
10
2 8
6 0
4 1
7 6
2 3
8 6
6 9
2 4
5 8
Output
3
"Correct Solution:
```
# 大混乱したので乱択 # これ嘘じゃないのか？？？
def main():
import sys
sys.setrecursionlimit(500000)
N = int(input())
if N==2:
print(1)
exit()
E = [[] for _ in range(N)]
for _ in range(N-1):
a, b = map(int, input().split())
E[a].append(b)
E[b].append(a)
def dfs(v=0, p=-1, root=0):
cnt_child = 0
cnt_false = 0
res = 0
for u in E[v]:
if u!=p:
cnt_child += 1
d = dfs(u, v, root)
res += d
cnt_false += d == 0
return res + max(0, cnt_false - 1)
#for i in range(N):
# print(dfs(i, -1, i))
print(max(dfs(i, -1, i) for i in sorted(range(N), key=lambda x: -len(E[x]))[:1]))
main()
```
| 101,891 |
Provide a correct Python 3 solution for this coding contest problem.
We have a tree with N vertices. The vertices are numbered 0 through N - 1, and the i-th edge (0 ≤ i < N - 1) comnnects Vertex a_i and b_i. For each pair of vertices u and v (0 ≤ u, v < N), we define the distance d(u, v) as the number of edges in the path u-v.
It is expected that one of the vertices will be invaded by aliens from outer space. Snuke wants to immediately identify that vertex when the invasion happens. To do so, he has decided to install an antenna on some vertices.
First, he decides the number of antennas, K (1 ≤ K ≤ N). Then, he chooses K different vertices, x_0, x_1, ..., x_{K - 1}, on which he installs Antenna 0, 1, ..., K - 1, respectively. If Vertex v is invaded by aliens, Antenna k (0 ≤ k < K) will output the distance d(x_k, v). Based on these K outputs, Snuke will identify the vertex that is invaded. Thus, in order to identify the invaded vertex no matter which one is invaded, the following condition must hold:
* For each vertex u (0 ≤ u < N), consider the vector (d(x_0, u), ..., d(x_{K - 1}, u)). These N vectors are distinct.
Find the minumum value of K, the number of antennas, when the condition is satisfied.
Constraints
* 2 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i < N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
a_0 b_0
a_1 b_1
:
a_{N - 2} b_{N - 2}
Output
Print the minumum value of K, the number of antennas, when the condition is satisfied.
Examples
Input
5
0 1
0 2
0 3
3 4
Output
2
Input
2
0 1
Output
1
Input
10
2 8
6 0
4 1
7 6
2 3
8 6
6 9
2 4
5 8
Output
3
"Correct Solution:
```
import sys
readline = sys.stdin.readline
from collections import Counter
from random import randrange
def parorder(Edge, p):
N = len(Edge)
par = [0]*N
par[p] = -1
stack = [p]
order = []
visited = set([p])
ast = stack.append
apo = order.append
while stack:
vn = stack.pop()
apo(vn)
for vf in Edge[vn]:
if vf in visited:
continue
visited.add(vf)
par[vf] = vn
ast(vf)
return par, order
def getcld(p):
res = [[] for _ in range(len(p))]
for i, v in enumerate(p[1:], 1):
res[v].append(i)
return res
N = int(readline())
Edge = [[] for _ in range(N)]
Leaf = [0]*N
for _ in range(N-1):
a, b = map(int, readline().split())
Leaf[a] += 1
Leaf[b] += 1
Edge[a].append(b)
Edge[b].append(a)
Leaf = [i for i in range(N) if Leaf[i] == 1]
M = len(Leaf)
ANS = 10**9+7
for idx in [0] + [randrange(1, M) for _ in range(10)]:
root = Leaf[idx]
P, L = parorder(Edge, root)
C = getcld(P)
dp = [0]*N
countone = [0]*N
for l in L[::-1][:-1]:
p = P[l]
dp[l] += 1 + max(0, countone[l] - 1)
if dp[l] == 1:
countone[p] += 1
dp[p] += dp[l] - 1
dp[root] += 1 + max(0, countone[root] - 1)
ANS = min(ANS, dp[root])
print(ANS)
```
| 101,892 |
Provide a correct Python 3 solution for this coding contest problem.
We have a tree with N vertices. The vertices are numbered 0 through N - 1, and the i-th edge (0 ≤ i < N - 1) comnnects Vertex a_i and b_i. For each pair of vertices u and v (0 ≤ u, v < N), we define the distance d(u, v) as the number of edges in the path u-v.
It is expected that one of the vertices will be invaded by aliens from outer space. Snuke wants to immediately identify that vertex when the invasion happens. To do so, he has decided to install an antenna on some vertices.
First, he decides the number of antennas, K (1 ≤ K ≤ N). Then, he chooses K different vertices, x_0, x_1, ..., x_{K - 1}, on which he installs Antenna 0, 1, ..., K - 1, respectively. If Vertex v is invaded by aliens, Antenna k (0 ≤ k < K) will output the distance d(x_k, v). Based on these K outputs, Snuke will identify the vertex that is invaded. Thus, in order to identify the invaded vertex no matter which one is invaded, the following condition must hold:
* For each vertex u (0 ≤ u < N), consider the vector (d(x_0, u), ..., d(x_{K - 1}, u)). These N vectors are distinct.
Find the minumum value of K, the number of antennas, when the condition is satisfied.
Constraints
* 2 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i < N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
a_0 b_0
a_1 b_1
:
a_{N - 2} b_{N - 2}
Output
Print the minumum value of K, the number of antennas, when the condition is satisfied.
Examples
Input
5
0 1
0 2
0 3
3 4
Output
2
Input
2
0 1
Output
1
Input
10
2 8
6 0
4 1
7 6
2 3
8 6
6 9
2 4
5 8
Output
3
"Correct Solution:
```
"""
Writer: SPD_9X2
https://atcoder.jp/contests/apc001/tasks/apc001_e
厳密な照明は難しいが…
直径を取る
直径の端点からbfs
全ての頂点に関して、部分木に少なくとも一つのアンテナを持つかのフラグを管理
子の数をkとする。その内x個がtrueの場合、k-1-x個のアンテナを追加。自分のflagをtrueにする
子がfalseで、子が0 or 1つしかない場合のみfalse継続
簡単な木では最適になることを実験したがどうだろうか…？
"""
import sys
sys.setrecursionlimit(3*10**5)
from collections import deque
def NC_Dij(lis,start):
ret = [float("inf")] * len(lis)
ret[start] = 0
q = deque([start])
plis = [i for i in range(len(lis))]
while len(q) > 0:
now = q.popleft()
for nex in lis[now]:
if ret[nex] > ret[now] + 1:
ret[nex] = ret[now] + 1
plis[nex] = now
q.append(nex)
return ret,plis,now
N = int(input())
lis = [ [] for i in range(N) ]
for i in range(N-1):
a,b = map(int,input().split())
lis[a].append(b)
lis[b].append(a)
td,tp,stp = NC_Dij(lis,0)
ans = 0
def dfs(v,p):
x = 0
c = 0
retflag = False
for nex in lis[v]:
if nex != p:
c += 1
have = dfs(nex,v)
retflag = have or retflag
if have:
x += 1
if c-1-x > 0:
retflag = True
global ans
ans += max(0,c-1-x)
return retflag
dfs(stp,stp)
print (ans+1)
```
| 101,893 |
Provide a correct Python 3 solution for this coding contest problem.
We have a tree with N vertices. The vertices are numbered 0 through N - 1, and the i-th edge (0 ≤ i < N - 1) comnnects Vertex a_i and b_i. For each pair of vertices u and v (0 ≤ u, v < N), we define the distance d(u, v) as the number of edges in the path u-v.
It is expected that one of the vertices will be invaded by aliens from outer space. Snuke wants to immediately identify that vertex when the invasion happens. To do so, he has decided to install an antenna on some vertices.
First, he decides the number of antennas, K (1 ≤ K ≤ N). Then, he chooses K different vertices, x_0, x_1, ..., x_{K - 1}, on which he installs Antenna 0, 1, ..., K - 1, respectively. If Vertex v is invaded by aliens, Antenna k (0 ≤ k < K) will output the distance d(x_k, v). Based on these K outputs, Snuke will identify the vertex that is invaded. Thus, in order to identify the invaded vertex no matter which one is invaded, the following condition must hold:
* For each vertex u (0 ≤ u < N), consider the vector (d(x_0, u), ..., d(x_{K - 1}, u)). These N vectors are distinct.
Find the minumum value of K, the number of antennas, when the condition is satisfied.
Constraints
* 2 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i < N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
a_0 b_0
a_1 b_1
:
a_{N - 2} b_{N - 2}
Output
Print the minumum value of K, the number of antennas, when the condition is satisfied.
Examples
Input
5
0 1
0 2
0 3
3 4
Output
2
Input
2
0 1
Output
1
Input
10
2 8
6 0
4 1
7 6
2 3
8 6
6 9
2 4
5 8
Output
3
"Correct Solution:
```
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
from bisect import bisect_left, bisect_right
import random
from itertools import permutations, accumulate, combinations
import sys
import string
from copy import deepcopy
INF = 10 ** 20
sys.setrecursionlimit(2147483647)
def LI(): return list(map(int, sys.stdin.readline().split()))
def I(): return int(sys.stdin.readline())
def LS(): return sys.stdin.readline().split()
def S(): return sys.stdin.readline().strip()
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]
mod = 10 ** 9 + 7
n=I()
G=[[]for _ in range(n)]
r=-1
for _ in range(n-1):
a,b=LI()
G[a]+=[b]
G[b]+=[a]
if len(G[a])>2:
r=a
if len(G[b]) > 2:
r=b
visited=[0]*n
visited[r]=1
def f(x):
ret=0
cnt=0
for v in G[x]:
if visited[v]:
continue
visited[v] = 1
r=f(v)
ret+=r
if r==0:
cnt+=1
if cnt>1:
ret+=cnt-1
return ret
print(1 if r == -1 else f(r))
```
| 101,894 |
Provide a correct Python 3 solution for this coding contest problem.
We have a tree with N vertices. The vertices are numbered 0 through N - 1, and the i-th edge (0 ≤ i < N - 1) comnnects Vertex a_i and b_i. For each pair of vertices u and v (0 ≤ u, v < N), we define the distance d(u, v) as the number of edges in the path u-v.
It is expected that one of the vertices will be invaded by aliens from outer space. Snuke wants to immediately identify that vertex when the invasion happens. To do so, he has decided to install an antenna on some vertices.
First, he decides the number of antennas, K (1 ≤ K ≤ N). Then, he chooses K different vertices, x_0, x_1, ..., x_{K - 1}, on which he installs Antenna 0, 1, ..., K - 1, respectively. If Vertex v is invaded by aliens, Antenna k (0 ≤ k < K) will output the distance d(x_k, v). Based on these K outputs, Snuke will identify the vertex that is invaded. Thus, in order to identify the invaded vertex no matter which one is invaded, the following condition must hold:
* For each vertex u (0 ≤ u < N), consider the vector (d(x_0, u), ..., d(x_{K - 1}, u)). These N vectors are distinct.
Find the minumum value of K, the number of antennas, when the condition is satisfied.
Constraints
* 2 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i < N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
a_0 b_0
a_1 b_1
:
a_{N - 2} b_{N - 2}
Output
Print the minumum value of K, the number of antennas, when the condition is satisfied.
Examples
Input
5
0 1
0 2
0 3
3 4
Output
2
Input
2
0 1
Output
1
Input
10
2 8
6 0
4 1
7 6
2 3
8 6
6 9
2 4
5 8
Output
3
"Correct Solution:
```
#設定
import sys
input = sys.stdin.buffer.readline
sys.setrecursionlimit(10**7)
#ライブラリインポート
from collections import defaultdict
#入力受け取り
def getlist():
return list(map(int, input().split()))
class Graph(object):
def __init__(self):
self.graph = defaultdict(list)
def __len__(self):
return len(self.graph)
def add_edge(self, a, b):
self.graph[a].append(b)
def get_nodes(self):
return self.graph.keys()
#val = 0
def DFS(G, anstenna, edge_num, have, visit, node):
cnt = 0
for i in G.graph[node]:
if visit[i] != "Yes":
visit[i] = "Yes"
DFS(G, anstenna, edge_num, have, visit, i)
if have[i] == 1:
cnt += 1
anstenna[node] += anstenna[i]
if cnt < edge_num[node] - 1:
anstenna[node] += edge_num[node] - 1 - cnt
if anstenna[node] >= 1:
have[node] = 1
#処理内容
def main():
N = int(input())
G = Graph()
for i in range(N - 1):
a, b = getlist()
G.add_edge(a, b)
G.add_edge(b, a)
if N == 2:
print(1)
return
#DFS
anstenna = [0] * (N + 1)
have = [0] * (N + 1)
edge_num = [len(G.graph[i]) - 1 for i in range(N + 1)]
if max(edge_num) <= 1:
print(1)
return
visit = ["No"] * (N + 1)
visit[N] = "Yes"
s = None
for i in range(N):
if edge_num[i] >= 1:
s = i
break
G.add_edge(N, s)
G.add_edge(s, N)
edge_num[s] += 1
DFS(G, anstenna, edge_num, have, visit, N)
ans = anstenna[N]
if edge_num[s] == 2:
cnt = 0
for i in G.graph[s]:
if have[i] == 1:
cnt += 1
if cnt <= 2:
ans += 1
print(ans)
if __name__ == '__main__':
main()
```
| 101,895 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a tree with N vertices. The vertices are numbered 0 through N - 1, and the i-th edge (0 ≤ i < N - 1) comnnects Vertex a_i and b_i. For each pair of vertices u and v (0 ≤ u, v < N), we define the distance d(u, v) as the number of edges in the path u-v.
It is expected that one of the vertices will be invaded by aliens from outer space. Snuke wants to immediately identify that vertex when the invasion happens. To do so, he has decided to install an antenna on some vertices.
First, he decides the number of antennas, K (1 ≤ K ≤ N). Then, he chooses K different vertices, x_0, x_1, ..., x_{K - 1}, on which he installs Antenna 0, 1, ..., K - 1, respectively. If Vertex v is invaded by aliens, Antenna k (0 ≤ k < K) will output the distance d(x_k, v). Based on these K outputs, Snuke will identify the vertex that is invaded. Thus, in order to identify the invaded vertex no matter which one is invaded, the following condition must hold:
* For each vertex u (0 ≤ u < N), consider the vector (d(x_0, u), ..., d(x_{K - 1}, u)). These N vectors are distinct.
Find the minumum value of K, the number of antennas, when the condition is satisfied.
Constraints
* 2 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i < N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
a_0 b_0
a_1 b_1
:
a_{N - 2} b_{N - 2}
Output
Print the minumum value of K, the number of antennas, when the condition is satisfied.
Examples
Input
5
0 1
0 2
0 3
3 4
Output
2
Input
2
0 1
Output
1
Input
10
2 8
6 0
4 1
7 6
2 3
8 6
6 9
2 4
5 8
Output
3
Submitted Solution:
```
n = int(input())
g = [[] for _ in range(n)]
for i in range(n-1):
a,b = map(int,input().split())
g[a].append(b)
g[b].append(a)
ones = list(filter(lambda i:len(g[i])==1,range(n)))
if max([len(g[i]) for i in range(n)]) <= 2:
print(1)
exit()
def nbh(i):
inext = g[i][0]
def nbh_(xnext,x):
return g[xnext][0] ^ g[xnext][1] ^ x
while len(g[inext]) <= 2:
i,inext = inext,nbh_(inext,i)
return inext
edges = list(set([nbh(i) for i in ones]))
print(len(ones)-len(edges))
```
Yes
| 101,896 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a tree with N vertices. The vertices are numbered 0 through N - 1, and the i-th edge (0 ≤ i < N - 1) comnnects Vertex a_i and b_i. For each pair of vertices u and v (0 ≤ u, v < N), we define the distance d(u, v) as the number of edges in the path u-v.
It is expected that one of the vertices will be invaded by aliens from outer space. Snuke wants to immediately identify that vertex when the invasion happens. To do so, he has decided to install an antenna on some vertices.
First, he decides the number of antennas, K (1 ≤ K ≤ N). Then, he chooses K different vertices, x_0, x_1, ..., x_{K - 1}, on which he installs Antenna 0, 1, ..., K - 1, respectively. If Vertex v is invaded by aliens, Antenna k (0 ≤ k < K) will output the distance d(x_k, v). Based on these K outputs, Snuke will identify the vertex that is invaded. Thus, in order to identify the invaded vertex no matter which one is invaded, the following condition must hold:
* For each vertex u (0 ≤ u < N), consider the vector (d(x_0, u), ..., d(x_{K - 1}, u)). These N vectors are distinct.
Find the minumum value of K, the number of antennas, when the condition is satisfied.
Constraints
* 2 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i < N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
a_0 b_0
a_1 b_1
:
a_{N - 2} b_{N - 2}
Output
Print the minumum value of K, the number of antennas, when the condition is satisfied.
Examples
Input
5
0 1
0 2
0 3
3 4
Output
2
Input
2
0 1
Output
1
Input
10
2 8
6 0
4 1
7 6
2 3
8 6
6 9
2 4
5 8
Output
3
Submitted Solution:
```
# 大混乱したので乱択
from random import randint
def main():
import sys
sys.setrecursionlimit(500000)
N = int(input())
if N==2:
print(1)
exit()
E = [[] for _ in range(N)]
for _ in range(N-1):
a, b = map(int, input().split())
E[a].append(b)
E[b].append(a)
def dfs(v=0, p=-1, root=0):
cnt_child = 0
cnt_false = 0
res = 0
for u in E[v]:
if u!=p:
cnt_child += 1
d = dfs(u, v, root)
res += d
cnt_false += d == 0
return res + max(0, cnt_false - 1)
#for i in range(N):
# print(dfs(i, -1, i))
print(max(dfs(i, -1, i) for i in sorted(range(N), key=lambda x: -len(E[x]))[:5]))
main()
```
Yes
| 101,897 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a tree with N vertices. The vertices are numbered 0 through N - 1, and the i-th edge (0 ≤ i < N - 1) comnnects Vertex a_i and b_i. For each pair of vertices u and v (0 ≤ u, v < N), we define the distance d(u, v) as the number of edges in the path u-v.
It is expected that one of the vertices will be invaded by aliens from outer space. Snuke wants to immediately identify that vertex when the invasion happens. To do so, he has decided to install an antenna on some vertices.
First, he decides the number of antennas, K (1 ≤ K ≤ N). Then, he chooses K different vertices, x_0, x_1, ..., x_{K - 1}, on which he installs Antenna 0, 1, ..., K - 1, respectively. If Vertex v is invaded by aliens, Antenna k (0 ≤ k < K) will output the distance d(x_k, v). Based on these K outputs, Snuke will identify the vertex that is invaded. Thus, in order to identify the invaded vertex no matter which one is invaded, the following condition must hold:
* For each vertex u (0 ≤ u < N), consider the vector (d(x_0, u), ..., d(x_{K - 1}, u)). These N vectors are distinct.
Find the minumum value of K, the number of antennas, when the condition is satisfied.
Constraints
* 2 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i < N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
a_0 b_0
a_1 b_1
:
a_{N - 2} b_{N - 2}
Output
Print the minumum value of K, the number of antennas, when the condition is satisfied.
Examples
Input
5
0 1
0 2
0 3
3 4
Output
2
Input
2
0 1
Output
1
Input
10
2 8
6 0
4 1
7 6
2 3
8 6
6 9
2 4
5 8
Output
3
Submitted Solution:
```
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**6)
N = int(input())
G = [[] for _ in range(N)]
for _ in range(N-1):
a, b = map(int, input().split())
G[a].append(b)
G[b].append(a)
dp = [1] * N
def dfs(v, p):
cnt = 0
for c in G[v]:
if c == p:
continue
dfs(c, v)
if dp[c] == 1:
cnt += 1
dp[v] += dp[c] - 1
if cnt > 1:
dp[v] += cnt - 1
dfs(0, -1)
ans = [1] * N
def dfs2(v, p, par_val):
cnt = 0
for c in G[v]:
if c == p:
continue
if dp[c] == 1:
cnt += 1
ans[v] += dp[c] - 1
if p != -1:
if par_val == 1:
cnt += 1
ans[v] += par_val - 1
if cnt > 1:
ans[v] += cnt - 1
for c in G[v]:
if c == p:
continue
dfs2(c, v, ans[v] - (dp[c] - 1) - (1 if dp[c] == 1 and cnt > 1 else 0))
dfs2(0, -1, 0)
print(min(ans))
```
Yes
| 101,898 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a tree with N vertices. The vertices are numbered 0 through N - 1, and the i-th edge (0 ≤ i < N - 1) comnnects Vertex a_i and b_i. For each pair of vertices u and v (0 ≤ u, v < N), we define the distance d(u, v) as the number of edges in the path u-v.
It is expected that one of the vertices will be invaded by aliens from outer space. Snuke wants to immediately identify that vertex when the invasion happens. To do so, he has decided to install an antenna on some vertices.
First, he decides the number of antennas, K (1 ≤ K ≤ N). Then, he chooses K different vertices, x_0, x_1, ..., x_{K - 1}, on which he installs Antenna 0, 1, ..., K - 1, respectively. If Vertex v is invaded by aliens, Antenna k (0 ≤ k < K) will output the distance d(x_k, v). Based on these K outputs, Snuke will identify the vertex that is invaded. Thus, in order to identify the invaded vertex no matter which one is invaded, the following condition must hold:
* For each vertex u (0 ≤ u < N), consider the vector (d(x_0, u), ..., d(x_{K - 1}, u)). These N vectors are distinct.
Find the minumum value of K, the number of antennas, when the condition is satisfied.
Constraints
* 2 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i < N
* The given graph is a tree.
Input
Input is given from Standard Input in the following format:
N
a_0 b_0
a_1 b_1
:
a_{N - 2} b_{N - 2}
Output
Print the minumum value of K, the number of antennas, when the condition is satisfied.
Examples
Input
5
0 1
0 2
0 3
3 4
Output
2
Input
2
0 1
Output
1
Input
10
2 8
6 0
4 1
7 6
2 3
8 6
6 9
2 4
5 8
Output
3
Submitted Solution:
```
import sys
input = sys.stdin.readline
N = int(input())
adj = [[] for _ in range(N)]
for _ in range(N - 1):
a, b = map(int, input().split())
adj[a].append(b)
adj[b].append(a)
leaf = []
for i in range(N):
if len(adj[i]) == 1:
leaf.append(i)
if len(leaf) == 2:
print(1)
sys.exit()
par = {}
for v in leaf:
while True:
v_list = adj[v]
if len(v_list) == 1:
v_prev = v
v = v_list[0]
else:
v1, v2 = v_list
v, v_prev = v1 + v2 - v_prev, v
if len(adj[v]) > 2:
par[v] = 0
break
print(len(leaf) - len(par))
```
Yes
| 101,899 |
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