text stringlengths 198 433k | conversation_id int64 0 109k |
|---|---|
Provide tags and a correct Python 3 solution for this coding contest problem.
The Saratov State University Olympiad Programmers Training Center (SSU OPTC) has n students. For each student you know the number of times he/she has participated in the ACM ICPC world programming championship. According to the ACM ICPC rules, each person can participate in the world championship at most 5 times.
The head of the SSU OPTC is recently gathering teams to participate in the world championship. Each team must consist of exactly three people, at that, any person cannot be a member of two or more teams. What maximum number of teams can the head make if he wants each team to participate in the world championship with the same members at least k times?
Input
The first line contains two integers, n and k (1 β€ n β€ 2000; 1 β€ k β€ 5). The next line contains n integers: y1, y2, ..., yn (0 β€ yi β€ 5), where yi shows the number of times the i-th person participated in the ACM ICPC world championship.
Output
Print a single number β the answer to the problem.
Examples
Input
5 2
0 4 5 1 0
Output
1
Input
6 4
0 1 2 3 4 5
Output
0
Input
6 5
0 0 0 0 0 0
Output
2
Note
In the first sample only one team could be made: the first, the fourth and the fifth participants.
In the second sample no teams could be created.
In the third sample two teams could be created. Any partition into two teams fits.
Tags: greedy, implementation, sortings
Correct Solution:
```
n, k = map(int, input().split())
y = list(map(int, input().split()))
diff=5-k
c=0
for i in y:
if i<=diff:
c+=1
print(c//3)
```
| 105,600 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Saratov State University Olympiad Programmers Training Center (SSU OPTC) has n students. For each student you know the number of times he/she has participated in the ACM ICPC world programming championship. According to the ACM ICPC rules, each person can participate in the world championship at most 5 times.
The head of the SSU OPTC is recently gathering teams to participate in the world championship. Each team must consist of exactly three people, at that, any person cannot be a member of two or more teams. What maximum number of teams can the head make if he wants each team to participate in the world championship with the same members at least k times?
Input
The first line contains two integers, n and k (1 β€ n β€ 2000; 1 β€ k β€ 5). The next line contains n integers: y1, y2, ..., yn (0 β€ yi β€ 5), where yi shows the number of times the i-th person participated in the ACM ICPC world championship.
Output
Print a single number β the answer to the problem.
Examples
Input
5 2
0 4 5 1 0
Output
1
Input
6 4
0 1 2 3 4 5
Output
0
Input
6 5
0 0 0 0 0 0
Output
2
Note
In the first sample only one team could be made: the first, the fourth and the fifth participants.
In the second sample no teams could be created.
In the third sample two teams could be created. Any partition into two teams fits.
Tags: greedy, implementation, sortings
Correct Solution:
```
a,b=map(int,input().split())
l=list(map(int,input().split()))
for i in range(b):
for j in range(len(l)):
l[j]+=1
l2=[]
l1=[]
for j in l:
if j<=5:
l1.append(j)
if len(l1)==3:
l2.append(l1)
l1=[]
print(len(l2))
```
| 105,601 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Saratov State University Olympiad Programmers Training Center (SSU OPTC) has n students. For each student you know the number of times he/she has participated in the ACM ICPC world programming championship. According to the ACM ICPC rules, each person can participate in the world championship at most 5 times.
The head of the SSU OPTC is recently gathering teams to participate in the world championship. Each team must consist of exactly three people, at that, any person cannot be a member of two or more teams. What maximum number of teams can the head make if he wants each team to participate in the world championship with the same members at least k times?
Input
The first line contains two integers, n and k (1 β€ n β€ 2000; 1 β€ k β€ 5). The next line contains n integers: y1, y2, ..., yn (0 β€ yi β€ 5), where yi shows the number of times the i-th person participated in the ACM ICPC world championship.
Output
Print a single number β the answer to the problem.
Examples
Input
5 2
0 4 5 1 0
Output
1
Input
6 4
0 1 2 3 4 5
Output
0
Input
6 5
0 0 0 0 0 0
Output
2
Note
In the first sample only one team could be made: the first, the fourth and the fifth participants.
In the second sample no teams could be created.
In the third sample two teams could be created. Any partition into two teams fits.
Tags: greedy, implementation, sortings
Correct Solution:
```
n,k = map(int,input().split())
l = list(map(int,input().split()))
count = 0
for i in l :
if i+k<= 5:
count+=1
print(count//3)
```
| 105,602 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Saratov State University Olympiad Programmers Training Center (SSU OPTC) has n students. For each student you know the number of times he/she has participated in the ACM ICPC world programming championship. According to the ACM ICPC rules, each person can participate in the world championship at most 5 times.
The head of the SSU OPTC is recently gathering teams to participate in the world championship. Each team must consist of exactly three people, at that, any person cannot be a member of two or more teams. What maximum number of teams can the head make if he wants each team to participate in the world championship with the same members at least k times?
Input
The first line contains two integers, n and k (1 β€ n β€ 2000; 1 β€ k β€ 5). The next line contains n integers: y1, y2, ..., yn (0 β€ yi β€ 5), where yi shows the number of times the i-th person participated in the ACM ICPC world championship.
Output
Print a single number β the answer to the problem.
Examples
Input
5 2
0 4 5 1 0
Output
1
Input
6 4
0 1 2 3 4 5
Output
0
Input
6 5
0 0 0 0 0 0
Output
2
Note
In the first sample only one team could be made: the first, the fourth and the fifth participants.
In the second sample no teams could be created.
In the third sample two teams could be created. Any partition into two teams fits.
Tags: greedy, implementation, sortings
Correct Solution:
```
n,k=map(int,input().split())
a=list(map(int,input().split()))
ans=0
for i in range(n):
if(a[i]+k<=5):
ans+=1
ans=ans//3
print(ans)
```
| 105,603 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Saratov State University Olympiad Programmers Training Center (SSU OPTC) has n students. For each student you know the number of times he/she has participated in the ACM ICPC world programming championship. According to the ACM ICPC rules, each person can participate in the world championship at most 5 times.
The head of the SSU OPTC is recently gathering teams to participate in the world championship. Each team must consist of exactly three people, at that, any person cannot be a member of two or more teams. What maximum number of teams can the head make if he wants each team to participate in the world championship with the same members at least k times?
Input
The first line contains two integers, n and k (1 β€ n β€ 2000; 1 β€ k β€ 5). The next line contains n integers: y1, y2, ..., yn (0 β€ yi β€ 5), where yi shows the number of times the i-th person participated in the ACM ICPC world championship.
Output
Print a single number β the answer to the problem.
Examples
Input
5 2
0 4 5 1 0
Output
1
Input
6 4
0 1 2 3 4 5
Output
0
Input
6 5
0 0 0 0 0 0
Output
2
Note
In the first sample only one team could be made: the first, the fourth and the fifth participants.
In the second sample no teams could be created.
In the third sample two teams could be created. Any partition into two teams fits.
Tags: greedy, implementation, sortings
Correct Solution:
```
# import sys
# sys.stdin=open("input1.in","r")
# sys.stdout=open("output2.out","w")
N,K=map(int,input().split())
L=list(map(int,input().split()))
count=0
for i in range(N):
L[i]=5-L[i]
if L[i]>=K:
count+=1
print(int(count/3))
```
| 105,604 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Saratov State University Olympiad Programmers Training Center (SSU OPTC) has n students. For each student you know the number of times he/she has participated in the ACM ICPC world programming championship. According to the ACM ICPC rules, each person can participate in the world championship at most 5 times.
The head of the SSU OPTC is recently gathering teams to participate in the world championship. Each team must consist of exactly three people, at that, any person cannot be a member of two or more teams. What maximum number of teams can the head make if he wants each team to participate in the world championship with the same members at least k times?
Input
The first line contains two integers, n and k (1 β€ n β€ 2000; 1 β€ k β€ 5). The next line contains n integers: y1, y2, ..., yn (0 β€ yi β€ 5), where yi shows the number of times the i-th person participated in the ACM ICPC world championship.
Output
Print a single number β the answer to the problem.
Examples
Input
5 2
0 4 5 1 0
Output
1
Input
6 4
0 1 2 3 4 5
Output
0
Input
6 5
0 0 0 0 0 0
Output
2
Note
In the first sample only one team could be made: the first, the fourth and the fifth participants.
In the second sample no teams could be created.
In the third sample two teams could be created. Any partition into two teams fits.
Tags: greedy, implementation, sortings
Correct Solution:
```
I=lambda:map(int,input().split())
_,k=I()
print(sum(x<=5-k for x in I())//3)
```
| 105,605 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Saratov State University Olympiad Programmers Training Center (SSU OPTC) has n students. For each student you know the number of times he/she has participated in the ACM ICPC world programming championship. According to the ACM ICPC rules, each person can participate in the world championship at most 5 times.
The head of the SSU OPTC is recently gathering teams to participate in the world championship. Each team must consist of exactly three people, at that, any person cannot be a member of two or more teams. What maximum number of teams can the head make if he wants each team to participate in the world championship with the same members at least k times?
Input
The first line contains two integers, n and k (1 β€ n β€ 2000; 1 β€ k β€ 5). The next line contains n integers: y1, y2, ..., yn (0 β€ yi β€ 5), where yi shows the number of times the i-th person participated in the ACM ICPC world championship.
Output
Print a single number β the answer to the problem.
Examples
Input
5 2
0 4 5 1 0
Output
1
Input
6 4
0 1 2 3 4 5
Output
0
Input
6 5
0 0 0 0 0 0
Output
2
Note
In the first sample only one team could be made: the first, the fourth and the fifth participants.
In the second sample no teams could be created.
In the third sample two teams could be created. Any partition into two teams fits.
Tags: greedy, implementation, sortings
Correct Solution:
```
n,k = map(int, input().split())
L = [int(i) for i in input().split()]
L.sort()
t = 0
for i in range(n):
if L[n-i-1] <= 5-k:
m = i
p = n - m
ans = int(p/3)
print(ans)
break
else:
t += 1
if t == n:
print(0)
```
| 105,606 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Saratov State University Olympiad Programmers Training Center (SSU OPTC) has n students. For each student you know the number of times he/she has participated in the ACM ICPC world programming championship. According to the ACM ICPC rules, each person can participate in the world championship at most 5 times.
The head of the SSU OPTC is recently gathering teams to participate in the world championship. Each team must consist of exactly three people, at that, any person cannot be a member of two or more teams. What maximum number of teams can the head make if he wants each team to participate in the world championship with the same members at least k times?
Input
The first line contains two integers, n and k (1 β€ n β€ 2000; 1 β€ k β€ 5). The next line contains n integers: y1, y2, ..., yn (0 β€ yi β€ 5), where yi shows the number of times the i-th person participated in the ACM ICPC world championship.
Output
Print a single number β the answer to the problem.
Examples
Input
5 2
0 4 5 1 0
Output
1
Input
6 4
0 1 2 3 4 5
Output
0
Input
6 5
0 0 0 0 0 0
Output
2
Note
In the first sample only one team could be made: the first, the fourth and the fifth participants.
In the second sample no teams could be created.
In the third sample two teams could be created. Any partition into two teams fits.
Tags: greedy, implementation, sortings
Correct Solution:
```
"""
βββ βββββββ βββ βββββββ βββββββ βββ ββββββ
βββββββββββββββ βββββββββββββββββββββββββββββ
ββββββ ββββββ ββββββββββββββββββββββββββββ
ββββββ ββββββ βββββββ βββββββββ βββ βββββββ
βββββββββββββββ βββββββββββββββββ βββ βββββββ
βββ βββββββ βββ ββββββββ βββββββ βββ ββββββ
"""
__author__ = "Dilshod"
n, k = map(int, input().split())
a = list(map(int ,input().split()))
a.sort()
cnt = 0
for i in range(0, n - 2, 3):
if a[i] + k <= 5 and a[i + 1] + k <= 5 and a[i + 2] + k <= 5:
cnt += 1
else:
break
print(cnt)
```
| 105,607 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Saratov State University Olympiad Programmers Training Center (SSU OPTC) has n students. For each student you know the number of times he/she has participated in the ACM ICPC world programming championship. According to the ACM ICPC rules, each person can participate in the world championship at most 5 times.
The head of the SSU OPTC is recently gathering teams to participate in the world championship. Each team must consist of exactly three people, at that, any person cannot be a member of two or more teams. What maximum number of teams can the head make if he wants each team to participate in the world championship with the same members at least k times?
Input
The first line contains two integers, n and k (1 β€ n β€ 2000; 1 β€ k β€ 5). The next line contains n integers: y1, y2, ..., yn (0 β€ yi β€ 5), where yi shows the number of times the i-th person participated in the ACM ICPC world championship.
Output
Print a single number β the answer to the problem.
Examples
Input
5 2
0 4 5 1 0
Output
1
Input
6 4
0 1 2 3 4 5
Output
0
Input
6 5
0 0 0 0 0 0
Output
2
Note
In the first sample only one team could be made: the first, the fourth and the fifth participants.
In the second sample no teams could be created.
In the third sample two teams could be created. Any partition into two teams fits.
Submitted Solution:
```
def solve(n,k,par):
par = sorted(par)
teams = 0
for i in range(0,n,3):
if(i+1<n and i+2<n):
pl1 = par[i]+k
pl2 = par[i+1]+k
pl3 = par[i+2]+k
if(pl1<=5 and pl2<=5 and pl3<=5):
teams+=1
print(teams)
if __name__ == "__main__":
n,k = map(int,input().split(" "))
par = list(map(int,input().split(" ")))
solve(n,k,par)
```
Yes
| 105,608 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Saratov State University Olympiad Programmers Training Center (SSU OPTC) has n students. For each student you know the number of times he/she has participated in the ACM ICPC world programming championship. According to the ACM ICPC rules, each person can participate in the world championship at most 5 times.
The head of the SSU OPTC is recently gathering teams to participate in the world championship. Each team must consist of exactly three people, at that, any person cannot be a member of two or more teams. What maximum number of teams can the head make if he wants each team to participate in the world championship with the same members at least k times?
Input
The first line contains two integers, n and k (1 β€ n β€ 2000; 1 β€ k β€ 5). The next line contains n integers: y1, y2, ..., yn (0 β€ yi β€ 5), where yi shows the number of times the i-th person participated in the ACM ICPC world championship.
Output
Print a single number β the answer to the problem.
Examples
Input
5 2
0 4 5 1 0
Output
1
Input
6 4
0 1 2 3 4 5
Output
0
Input
6 5
0 0 0 0 0 0
Output
2
Note
In the first sample only one team could be made: the first, the fourth and the fifth participants.
In the second sample no teams could be created.
In the third sample two teams could be created. Any partition into two teams fits.
Submitted Solution:
```
n, k = map(int, input().split())
b = list(map(int, input().split()))
kolvo = 0
chi = 0
chelovek = 0
for i in range(len(b)):
chi=0
while b[i] < 5:
b[i] += 1
chi += 1
if chi == k:
chelovek += 1
chi = 0
break
if chelovek == 3:
kolvo += 1
chelovek = 0
print(kolvo)
```
Yes
| 105,609 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Saratov State University Olympiad Programmers Training Center (SSU OPTC) has n students. For each student you know the number of times he/she has participated in the ACM ICPC world programming championship. According to the ACM ICPC rules, each person can participate in the world championship at most 5 times.
The head of the SSU OPTC is recently gathering teams to participate in the world championship. Each team must consist of exactly three people, at that, any person cannot be a member of two or more teams. What maximum number of teams can the head make if he wants each team to participate in the world championship with the same members at least k times?
Input
The first line contains two integers, n and k (1 β€ n β€ 2000; 1 β€ k β€ 5). The next line contains n integers: y1, y2, ..., yn (0 β€ yi β€ 5), where yi shows the number of times the i-th person participated in the ACM ICPC world championship.
Output
Print a single number β the answer to the problem.
Examples
Input
5 2
0 4 5 1 0
Output
1
Input
6 4
0 1 2 3 4 5
Output
0
Input
6 5
0 0 0 0 0 0
Output
2
Note
In the first sample only one team could be made: the first, the fourth and the fifth participants.
In the second sample no teams could be created.
In the third sample two teams could be created. Any partition into two teams fits.
Submitted Solution:
```
# coding=utf-8
# Created by TheMisfits
from sys import stdin
_input = stdin.readline
_int, _range = int, range
def solution():
n, k = [_int(i) for i in _input().split()]
arr = [_int(i) for i in _input().split()]
arr.sort()
ans = 0
for i in _range(2, n, 3):
if arr[i] + k <= 5:
ans += 1
print(ans)
solution()
```
Yes
| 105,610 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Saratov State University Olympiad Programmers Training Center (SSU OPTC) has n students. For each student you know the number of times he/she has participated in the ACM ICPC world programming championship. According to the ACM ICPC rules, each person can participate in the world championship at most 5 times.
The head of the SSU OPTC is recently gathering teams to participate in the world championship. Each team must consist of exactly three people, at that, any person cannot be a member of two or more teams. What maximum number of teams can the head make if he wants each team to participate in the world championship with the same members at least k times?
Input
The first line contains two integers, n and k (1 β€ n β€ 2000; 1 β€ k β€ 5). The next line contains n integers: y1, y2, ..., yn (0 β€ yi β€ 5), where yi shows the number of times the i-th person participated in the ACM ICPC world championship.
Output
Print a single number β the answer to the problem.
Examples
Input
5 2
0 4 5 1 0
Output
1
Input
6 4
0 1 2 3 4 5
Output
0
Input
6 5
0 0 0 0 0 0
Output
2
Note
In the first sample only one team could be made: the first, the fourth and the fifth participants.
In the second sample no teams could be created.
In the third sample two teams could be created. Any partition into two teams fits.
Submitted Solution:
```
import math
n, k = input().split()
n = int(n)
k = int(k)
list_of_years = list(map(int, input().split()))
# print(list_of_years)
count = 0
for i in list_of_years:
if 5 - i >= k:
count = count + 1
total_team = math.floor(count / 3)
print(total_team)
```
Yes
| 105,611 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Saratov State University Olympiad Programmers Training Center (SSU OPTC) has n students. For each student you know the number of times he/she has participated in the ACM ICPC world programming championship. According to the ACM ICPC rules, each person can participate in the world championship at most 5 times.
The head of the SSU OPTC is recently gathering teams to participate in the world championship. Each team must consist of exactly three people, at that, any person cannot be a member of two or more teams. What maximum number of teams can the head make if he wants each team to participate in the world championship with the same members at least k times?
Input
The first line contains two integers, n and k (1 β€ n β€ 2000; 1 β€ k β€ 5). The next line contains n integers: y1, y2, ..., yn (0 β€ yi β€ 5), where yi shows the number of times the i-th person participated in the ACM ICPC world championship.
Output
Print a single number β the answer to the problem.
Examples
Input
5 2
0 4 5 1 0
Output
1
Input
6 4
0 1 2 3 4 5
Output
0
Input
6 5
0 0 0 0 0 0
Output
2
Note
In the first sample only one team could be made: the first, the fourth and the fifth participants.
In the second sample no teams could be created.
In the third sample two teams could be created. Any partition into two teams fits.
Submitted Solution:
```
n=[int(x) for x in input().split()]
a=[int(x) for x in input().split()]
a=sorted(a)
count=0
if(len(a)>=3):
for i in range(len(a)):
if(a[i]==0 or a[i]==1):
count=count+1
print(count//3)
```
No
| 105,612 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Saratov State University Olympiad Programmers Training Center (SSU OPTC) has n students. For each student you know the number of times he/she has participated in the ACM ICPC world programming championship. According to the ACM ICPC rules, each person can participate in the world championship at most 5 times.
The head of the SSU OPTC is recently gathering teams to participate in the world championship. Each team must consist of exactly three people, at that, any person cannot be a member of two or more teams. What maximum number of teams can the head make if he wants each team to participate in the world championship with the same members at least k times?
Input
The first line contains two integers, n and k (1 β€ n β€ 2000; 1 β€ k β€ 5). The next line contains n integers: y1, y2, ..., yn (0 β€ yi β€ 5), where yi shows the number of times the i-th person participated in the ACM ICPC world championship.
Output
Print a single number β the answer to the problem.
Examples
Input
5 2
0 4 5 1 0
Output
1
Input
6 4
0 1 2 3 4 5
Output
0
Input
6 5
0 0 0 0 0 0
Output
2
Note
In the first sample only one team could be made: the first, the fourth and the fifth participants.
In the second sample no teams could be created.
In the third sample two teams could be created. Any partition into two teams fits.
Submitted Solution:
```
n, k = map(int, input().split())
d = list(map(int, input().split()))
u = []
for i in range(n):
if 5 - d[i] >= k:
u.append(5 - d[i])
m = len(u)
k = 3
n_f = 1
m_f = 1
for i in range(1, m + 1):
m_f *= i
mk_f = 1
for i in range(1, m - k + 1):
mk_f *= i
k_f = 1 * 2 * 3
print(int(m_f / (mk_f * k_f)))
```
No
| 105,613 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Saratov State University Olympiad Programmers Training Center (SSU OPTC) has n students. For each student you know the number of times he/she has participated in the ACM ICPC world programming championship. According to the ACM ICPC rules, each person can participate in the world championship at most 5 times.
The head of the SSU OPTC is recently gathering teams to participate in the world championship. Each team must consist of exactly three people, at that, any person cannot be a member of two or more teams. What maximum number of teams can the head make if he wants each team to participate in the world championship with the same members at least k times?
Input
The first line contains two integers, n and k (1 β€ n β€ 2000; 1 β€ k β€ 5). The next line contains n integers: y1, y2, ..., yn (0 β€ yi β€ 5), where yi shows the number of times the i-th person participated in the ACM ICPC world championship.
Output
Print a single number β the answer to the problem.
Examples
Input
5 2
0 4 5 1 0
Output
1
Input
6 4
0 1 2 3 4 5
Output
0
Input
6 5
0 0 0 0 0 0
Output
2
Note
In the first sample only one team could be made: the first, the fourth and the fifth participants.
In the second sample no teams could be created.
In the third sample two teams could be created. Any partition into two teams fits.
Submitted Solution:
```
n,k=map(int,input().split())
a=sorted(list(map(int,input().split())))
for i in range(len(a)):
if a[i]<=5-k:
i+=1
print(i//3)
```
No
| 105,614 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Saratov State University Olympiad Programmers Training Center (SSU OPTC) has n students. For each student you know the number of times he/she has participated in the ACM ICPC world programming championship. According to the ACM ICPC rules, each person can participate in the world championship at most 5 times.
The head of the SSU OPTC is recently gathering teams to participate in the world championship. Each team must consist of exactly three people, at that, any person cannot be a member of two or more teams. What maximum number of teams can the head make if he wants each team to participate in the world championship with the same members at least k times?
Input
The first line contains two integers, n and k (1 β€ n β€ 2000; 1 β€ k β€ 5). The next line contains n integers: y1, y2, ..., yn (0 β€ yi β€ 5), where yi shows the number of times the i-th person participated in the ACM ICPC world championship.
Output
Print a single number β the answer to the problem.
Examples
Input
5 2
0 4 5 1 0
Output
1
Input
6 4
0 1 2 3 4 5
Output
0
Input
6 5
0 0 0 0 0 0
Output
2
Note
In the first sample only one team could be made: the first, the fourth and the fifth participants.
In the second sample no teams could be created.
In the third sample two teams could be created. Any partition into two teams fits.
Submitted Solution:
```
import math
s = 0
n,k = map(int, input().split())
l =list(map(int,input().strip().split()))[:n]
l.sort()
for i in l:
f = i+k
if i<5 and f<=5:
s = s+1
if s>0 and s%3==0:
print(math.floor(s/3))
else:
print(0)
```
No
| 105,615 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.
Input
A single line contains two integers m and n (1 β€ m, n β€ 105).
Output
Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
6 1
Output
3.500000000000
Input
6 3
Output
4.958333333333
Input
2 2
Output
1.750000000000
Note
Consider the third test example. If you've made two tosses:
1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
<image>
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value
Tags: probabilities
Correct Solution:
```
m, n = map(int, input().split())
ans = 0
sump = 0
for i in range(1, m + 1):
p = pow(i / m, n) - sump
sump += p
ans += i * p
print(ans)
exit()
def f(x, y):
if y == 1:
return 1 / m
ans = 0.0
for i in range(1, x):
ans += f(i, y - 1) / m
ans += f(x, y - 1) * x / m
return ans
#for i in range(1, m + 1):
#for j in range(1, n + 1):
#print(f(i, j), end='\t')
#print()
def F():
ans = 0
for i in range(1, m + 1):
#print(i * f(i, n))
ans += i * f(i, n)
ans2 = 0
sump = 0
for i in range(1, m + 1):
p = pow(i / m, n) - sump
sump += p
ans2 += i * p
print('ans2', ans2)
print('ans ', ans)
return ans
L = 6
for i in range(1, L):
for j in range(1, L):
m, n = i, j
#print(m - F(), end=' ')
F()
print()
```
| 105,616 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.
Input
A single line contains two integers m and n (1 β€ m, n β€ 105).
Output
Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
6 1
Output
3.500000000000
Input
6 3
Output
4.958333333333
Input
2 2
Output
1.750000000000
Note
Consider the third test example. If you've made two tosses:
1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
<image>
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value
Tags: probabilities
Correct Solution:
```
import math
m, n = map(int,input().split())
e = 0
for i in range(1, m + 1):
e += i * (math.pow(i / m, n) - math.pow((i - 1) / m, n))
print(e)
```
| 105,617 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.
Input
A single line contains two integers m and n (1 β€ m, n β€ 105).
Output
Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
6 1
Output
3.500000000000
Input
6 3
Output
4.958333333333
Input
2 2
Output
1.750000000000
Note
Consider the third test example. If you've made two tosses:
1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
<image>
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value
Tags: probabilities
Correct Solution:
```
k=input()
m=int(k.split()[0])
n=int(k.split()[1])
q=0
for i in range(1,m):
q+=(i/m)**n
print(m-q)
```
| 105,618 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.
Input
A single line contains two integers m and n (1 β€ m, n β€ 105).
Output
Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
6 1
Output
3.500000000000
Input
6 3
Output
4.958333333333
Input
2 2
Output
1.750000000000
Note
Consider the third test example. If you've made two tosses:
1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
<image>
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value
Tags: probabilities
Correct Solution:
```
from math import *
m,n=map(int,input().split())
sum=0
for i in range(1,m):
sum+=pow(i/m,n)
ans=m-sum
print(ans)
```
| 105,619 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.
Input
A single line contains two integers m and n (1 β€ m, n β€ 105).
Output
Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
6 1
Output
3.500000000000
Input
6 3
Output
4.958333333333
Input
2 2
Output
1.750000000000
Note
Consider the third test example. If you've made two tosses:
1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
<image>
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value
Tags: probabilities
Correct Solution:
```
m , n = map(int , input().strip().split(' '))
ans = 0
for i in range(1 , m+1):
ans += i * (pow(i/m , n) - pow((i-1) / m , n))
print("%.9f" % ans)
```
| 105,620 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.
Input
A single line contains two integers m and n (1 β€ m, n β€ 105).
Output
Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
6 1
Output
3.500000000000
Input
6 3
Output
4.958333333333
Input
2 2
Output
1.750000000000
Note
Consider the third test example. If you've made two tosses:
1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
<image>
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value
Tags: probabilities
Correct Solution:
```
def dice_exp_max(faces, times):
def _prob_less_than_d(dots):
return (dots / faces) ** times
def _exp_max_d(dots):
return dots * (_prob_less_than_d(dots) - _prob_less_than_d(dots - 1))
return sum(_exp_max_d(dots) for dots in range(1, faces + 1))
m, n = map(int, input().split())
print(dice_exp_max(m, n))
```
| 105,621 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.
Input
A single line contains two integers m and n (1 β€ m, n β€ 105).
Output
Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
6 1
Output
3.500000000000
Input
6 3
Output
4.958333333333
Input
2 2
Output
1.750000000000
Note
Consider the third test example. If you've made two tosses:
1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
<image>
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value
Tags: probabilities
Correct Solution:
```
import math
if __name__ == '__main__':
m, n = [int(item) for item in input().split()]
res = 0
for i in range(1, m +1):
current = i* ( math.pow((i/m), n) - math.pow(((i - 1)/ m), n))
res += current
print(res)
```
| 105,622 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.
Input
A single line contains two integers m and n (1 β€ m, n β€ 105).
Output
Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
6 1
Output
3.500000000000
Input
6 3
Output
4.958333333333
Input
2 2
Output
1.750000000000
Note
Consider the third test example. If you've made two tosses:
1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
<image>
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value
Tags: probabilities
Correct Solution:
```
import math
import itertools
import collections
def getdict(n):
d = {}
if type(n) is list or type(n) is str:
for i in n:
if i in d:
d[i] += 1
else:
d[i] = 1
else:
for i in range(n):
t = ii()
if t in d:
d[t] += 1
else:
d[t] = 1
return d
def cdiv(n, k): return n // k + (n % k != 0)
def ii(): return int(input())
def mi(): return map(int, input().split())
def li(): return list(map(int, input().split()))
def lcm(a, b): return abs(a*b) // math.gcd(a, b)
def wr(arr): return ' '.join(map(str, arr))
def revn(n): return int(str(n)[::-1])
def prime(n):
if n == 2:
return True
if n % 2 == 0 or n <= 1:
return False
sqr = int(math.sqrt(n)) + 1
for d in range(3, sqr, 2):
if n % d == 0:
return False
return True
m, n = mi()
t = 0
for i in range(1, m):
t += (1 - i / m) ** n
print(m - t)
```
| 105,623 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.
Input
A single line contains two integers m and n (1 β€ m, n β€ 105).
Output
Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
6 1
Output
3.500000000000
Input
6 3
Output
4.958333333333
Input
2 2
Output
1.750000000000
Note
Consider the third test example. If you've made two tosses:
1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
<image>
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value
Submitted Solution:
```
import math
m,n = [int(i) for i in input().split()]
result = 0.0
count = m
while(count > 0):
parte1 = math.pow(count/m, n)
parte2 = math.pow((count-1)/m, n)
result += (parte1 - parte2)*count
count -= 1
print(result)
```
Yes
| 105,624 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.
Input
A single line contains two integers m and n (1 β€ m, n β€ 105).
Output
Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
6 1
Output
3.500000000000
Input
6 3
Output
4.958333333333
Input
2 2
Output
1.750000000000
Note
Consider the third test example. If you've made two tosses:
1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
<image>
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value
Submitted Solution:
```
m, n = map(int, input().split())
p_leq = [(i/m)**n for i in range(m+1)]
sol = 0
for i in range(1, m+1):
sol += i*(p_leq[i]-p_leq[i-1])
print(sol)
```
Yes
| 105,625 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.
Input
A single line contains two integers m and n (1 β€ m, n β€ 105).
Output
Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
6 1
Output
3.500000000000
Input
6 3
Output
4.958333333333
Input
2 2
Output
1.750000000000
Note
Consider the third test example. If you've made two tosses:
1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
<image>
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value
Submitted Solution:
```
import sys
import math
m,n = map(int, sys.stdin.readline().split())
C = 0
for i in range(1, m+1):
count = i * ((i/m)**n - ((i-1)/m)** n)
C = C + count
print(C)
```
Yes
| 105,626 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.
Input
A single line contains two integers m and n (1 β€ m, n β€ 105).
Output
Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
6 1
Output
3.500000000000
Input
6 3
Output
4.958333333333
Input
2 2
Output
1.750000000000
Note
Consider the third test example. If you've made two tosses:
1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
<image>
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value
Submitted Solution:
```
from math import pow
m , n = map(int,input().split())
ans = 0.0
for i in range(1,m+1):
ans += i * (pow(i/m,n)-pow((i-1.0)/m,n))
print('%.15f'%ans)
```
Yes
| 105,627 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.
Input
A single line contains two integers m and n (1 β€ m, n β€ 105).
Output
Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
6 1
Output
3.500000000000
Input
6 3
Output
4.958333333333
Input
2 2
Output
1.750000000000
Note
Consider the third test example. If you've made two tosses:
1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
<image>
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value
Submitted Solution:
```
m, n = map(int, input().split(" "))
ans = m
for i in range(1, m + 1):
ans -= (i/m)**n
print(ans)
```
No
| 105,628 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.
Input
A single line contains two integers m and n (1 β€ m, n β€ 105).
Output
Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
6 1
Output
3.500000000000
Input
6 3
Output
4.958333333333
Input
2 2
Output
1.750000000000
Note
Consider the third test example. If you've made two tosses:
1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
<image>
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value
Submitted Solution:
```
def main():
input_li = input().split(" ")
m = int(input_li[0])
n = int(input_li[1])
bunmo = m**n
limit = 2
if m > 10 and n > 10:
print((1 - ((m-1)**n)/bunmo)*m)
return 0
total = 1.0
for i in range(limit, m+1):
total = total+(((i**n) - ((i-1)**n)*i))
print(total/bunmo)
main()
```
No
| 105,629 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.
Input
A single line contains two integers m and n (1 β€ m, n β€ 105).
Output
Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
6 1
Output
3.500000000000
Input
6 3
Output
4.958333333333
Input
2 2
Output
1.750000000000
Note
Consider the third test example. If you've made two tosses:
1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
<image>
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value
Submitted Solution:
```
m,n=map(int,input().split())
ans = 0
powi = [0 for i in range(m+1)]
deno = pow(m,n)
for i in range(1,m+1):
powi[i] = pow(i/m,n)
print(powi)
for i in range(1,m+1):
ans += (powi[i] - powi[i-1])*i
print(ans)
```
No
| 105,630 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability <image>. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice n times.
Input
A single line contains two integers m and n (1 β€ m, n β€ 105).
Output
Output a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
6 1
Output
3.500000000000
Input
6 3
Output
4.958333333333
Input
2 2
Output
1.750000000000
Note
Consider the third test example. If you've made two tosses:
1. You can get 1 in the first toss, and 2 in the second. Maximum equals to 2.
2. You can get 1 in the first toss, and 1 in the second. Maximum equals to 1.
3. You can get 2 in the first toss, and 1 in the second. Maximum equals to 2.
4. You can get 2 in the first toss, and 2 in the second. Maximum equals to 2.
The probability of each outcome is 0.25, that is expectation equals to:
<image>
You can read about expectation using the following link: http://en.wikipedia.org/wiki/Expected_value
Submitted Solution:
```
m,n=map(int,input().split())
a=[0 for i in range(m+1)]
a[0]=1
ans=1
if(m==1):exit(print(1))
if(n==1):exit(print(((m)*(m+1))/(2*m)))
for i in range(1,m):
a[i]=a[i-1]+i*m
ans+=a[i]*(i+1)
print(ans/(m**n))
```
No
| 105,631 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].
By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?
Input
The single line of the input contains two integers a, b (1 β€ a, b β€ 107).
Output
Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).
Examples
Input
1 1
Output
0
Input
2 2
Output
8
Note
For the first sample, there are no nice integers because <image> is always zero.
For the second sample, the set of nice integers is {3, 5}.
Tags: math
Correct Solution:
```
from sys import stdin, stdout
from collections import Counter, defaultdict
import heapq
#range = xrange # not for python 3.0+
# main code
mod=10**9+7
ans=0
a,b=map(int,stdin.read().split())
for i in range(1,b):
#print val
val=a
t1=(val*(val+1))//2
t1%=mod
t1=(t1*b)%mod
temp=(t1*i)%mod
temp=(temp+((i*val)%mod))%mod
ans=(ans+temp)%mod
print(ans)
```
| 105,632 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].
By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?
Input
The single line of the input contains two integers a, b (1 β€ a, b β€ 107).
Output
Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).
Examples
Input
1 1
Output
0
Input
2 2
Output
8
Note
For the first sample, there are no nice integers because <image> is always zero.
For the second sample, the set of nice integers is {3, 5}.
Tags: math
Correct Solution:
```
MOD = int(1e9+7)
a, b = list(map(int, input().split()))
res = b * (b - 1) // 2 * (a + (1 + a) * a * b // 2)
print(res % MOD)
```
| 105,633 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].
By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?
Input
The single line of the input contains two integers a, b (1 β€ a, b β€ 107).
Output
Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).
Examples
Input
1 1
Output
0
Input
2 2
Output
8
Note
For the first sample, there are no nice integers because <image> is always zero.
For the second sample, the set of nice integers is {3, 5}.
Tags: math
Correct Solution:
```
a, b = (int(x) for x in input().split())
ans = b*(b-1)*a//2 + b*(b-1)*b*(1 + a)*a//4
print(ans % 1000000007)
```
| 105,634 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].
By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?
Input
The single line of the input contains two integers a, b (1 β€ a, b β€ 107).
Output
Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).
Examples
Input
1 1
Output
0
Input
2 2
Output
8
Note
For the first sample, there are no nice integers because <image> is always zero.
For the second sample, the set of nice integers is {3, 5}.
Tags: math
Correct Solution:
```
#input
a,b=map(int,input().split())
#variables
nicesum=(b*(b-1)//2)*(a*(a+1)//2)*b+(b*(b-1)//2)*a
#main
print(int(nicesum%1000000007))
```
| 105,635 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].
By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?
Input
The single line of the input contains two integers a, b (1 β€ a, b β€ 107).
Output
Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).
Examples
Input
1 1
Output
0
Input
2 2
Output
8
Note
For the first sample, there are no nice integers because <image> is always zero.
For the second sample, the set of nice integers is {3, 5}.
Tags: math
Correct Solution:
```
a, b = map(int, input().split())
print((b * (a * (a + 1) // 2) * (b * (b - 1) // 2 ) + a * b * (b - 1) // 2) % 1000000007)
```
| 105,636 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].
By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?
Input
The single line of the input contains two integers a, b (1 β€ a, b β€ 107).
Output
Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).
Examples
Input
1 1
Output
0
Input
2 2
Output
8
Note
For the first sample, there are no nice integers because <image> is always zero.
For the second sample, the set of nice integers is {3, 5}.
Tags: math
Correct Solution:
```
a,b = map(int, input().split())
sum = 0
mod = 1000000007
def c(i):
mi = i * b + i
ma = i * b * a + i
return ((mi+ma) * a)//2
sum = (((c(1) + c(b-1))*(b-1))//2)%mod
print(sum)
```
| 105,637 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].
By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?
Input
The single line of the input contains two integers a, b (1 β€ a, b β€ 107).
Output
Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).
Examples
Input
1 1
Output
0
Input
2 2
Output
8
Note
For the first sample, there are no nice integers because <image> is always zero.
For the second sample, the set of nice integers is {3, 5}.
Tags: math
Correct Solution:
```
a = input()
a = a.split()
a,b = int(a[0]),int(a[1])
k2 = b*(b-1)*a // 2
k = (b-1)*b//2 * b* (1+a)*a // 2
res = (k + k2) % 1000000007
print(res)
```
| 105,638 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].
By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?
Input
The single line of the input contains two integers a, b (1 β€ a, b β€ 107).
Output
Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).
Examples
Input
1 1
Output
0
Input
2 2
Output
8
Note
For the first sample, there are no nice integers because <image> is always zero.
For the second sample, the set of nice integers is {3, 5}.
Tags: math
Correct Solution:
```
a, b = map(int, input().split())
r1 = (b - 1) * b // 2
r2 = (a * b + 1 + b + 1) * a // 2
print((r1 * r2) % 1000000007)
```
| 105,639 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].
By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?
Input
The single line of the input contains two integers a, b (1 β€ a, b β€ 107).
Output
Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).
Examples
Input
1 1
Output
0
Input
2 2
Output
8
Note
For the first sample, there are no nice integers because <image> is always zero.
For the second sample, the set of nice integers is {3, 5}.
Submitted Solution:
```
#Collaborated with Rudransh singh and Bhumi patel
a, b = input().split(" ")
a = int(a)
b = int(b)
print((b * (b - 1) // 2) * (((a * (a + 1) // 2) * b) % 1000000007 + a) % 1000000007)
```
Yes
| 105,640 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].
By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?
Input
The single line of the input contains two integers a, b (1 β€ a, b β€ 107).
Output
Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).
Examples
Input
1 1
Output
0
Input
2 2
Output
8
Note
For the first sample, there are no nice integers because <image> is always zero.
For the second sample, the set of nice integers is {3, 5}.
Submitted Solution:
```
a,b=map(int,input().split())
dangbra=(b*(b-1)//2)*(a*(a+1)//2)*b+(b*(b-1)//2)*a
print(int(dangbra%1000000007))
```
Yes
| 105,641 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].
By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?
Input
The single line of the input contains two integers a, b (1 β€ a, b β€ 107).
Output
Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).
Examples
Input
1 1
Output
0
Input
2 2
Output
8
Note
For the first sample, there are no nice integers because <image> is always zero.
For the second sample, the set of nice integers is {3, 5}.
Submitted Solution:
```
a, b = map(int, input().split())
print((b * (b - 1) * b * a * (a + 1) // 4 + (b - 1) * b * a // 2) % (10 ** 9 + 7))
```
Yes
| 105,642 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].
By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?
Input
The single line of the input contains two integers a, b (1 β€ a, b β€ 107).
Output
Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).
Examples
Input
1 1
Output
0
Input
2 2
Output
8
Note
For the first sample, there are no nice integers because <image> is always zero.
For the second sample, the set of nice integers is {3, 5}.
Submitted Solution:
```
# Collaborated with no one
input1 = list(map(int, input().split(" ")))
a = input1[0]
b = input1[1]
quotient = b*(b-1)//2
remainder = a*(a+1)//2
answer = (quotient*((remainder*b)%(10**9+7)+a)%(10**9+7))
print(answer)
```
Yes
| 105,643 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].
By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?
Input
The single line of the input contains two integers a, b (1 β€ a, b β€ 107).
Output
Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).
Examples
Input
1 1
Output
0
Input
2 2
Output
8
Note
For the first sample, there are no nice integers because <image> is always zero.
For the second sample, the set of nice integers is {3, 5}.
Submitted Solution:
```
a,b=map(int,input().split())
print(b*(b-1)*a*(b*a+b+2)/4%(10**9+7))
```
No
| 105,644 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].
By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?
Input
The single line of the input contains two integers a, b (1 β€ a, b β€ 107).
Output
Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).
Examples
Input
1 1
Output
0
Input
2 2
Output
8
Note
For the first sample, there are no nice integers because <image> is always zero.
For the second sample, the set of nice integers is {3, 5}.
Submitted Solution:
```
#Created By Minsol Jeong
def N3():
a, b = [int(x) for x in input().split()]
mod = 10 ** 9 + 7
x = ((b * (b-1))/2) % mod
y = (a * (a+1)/2)% mod
sum = (x * ((y * b) % mod + a) % mod) % mod
print(sum)
if __name__=="__main__":
N3()
```
No
| 105,645 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].
By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?
Input
The single line of the input contains two integers a, b (1 β€ a, b β€ 107).
Output
Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).
Examples
Input
1 1
Output
0
Input
2 2
Output
8
Note
For the first sample, there are no nice integers because <image> is always zero.
For the second sample, the set of nice integers is {3, 5}.
Submitted Solution:
```
from sys import stdin, stdout
from collections import Counter, defaultdict
import heapq
#range = xrange # not for python 3.0+
# main code
mod=10**9+7
ans=0
a,b=map(int,stdin.read().split())
for i in range(1,b):
#print val
val=a
t1=(val*(val+1))/2
t1%=mod
t1=(t1*b)%mod
temp=(t1*i)%mod
temp=(temp+((i*val)%mod))%mod
ans=(ans+temp)%mod
print(ans)
```
No
| 105,646 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].
By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.
The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?
Input
The single line of the input contains two integers a, b (1 β€ a, b β€ 107).
Output
Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).
Examples
Input
1 1
Output
0
Input
2 2
Output
8
Note
For the first sample, there are no nice integers because <image> is always zero.
For the second sample, the set of nice integers is {3, 5}.
Submitted Solution:
```
a, b = map(int, input().split())
ans = ((a * a * b + 2 * a) * b * (b - 1) * (2 * b - 1)) // 12 + (a * b * b * (b - 1)) // 4
print(ans % 1000000007)
```
No
| 105,647 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Tomorrow Peter has a Biology exam. He does not like this subject much, but d days ago he learnt that he would have to take this exam. Peter's strict parents made him prepare for the exam immediately, for this purpose he has to study not less than minTimei and not more than maxTimei hours per each i-th day. Moreover, they warned Peter that a day before the exam they would check how he has followed their instructions.
So, today is the day when Peter's parents ask him to show the timetable of his preparatory studies. But the boy has counted only the sum of hours sumTime spent him on preparation, and now he wants to know if he can show his parents a timetable sΡhedule with d numbers, where each number sΡhedulei stands for the time in hours spent by Peter each i-th day on biology studies, and satisfying the limitations imposed by his parents, and at the same time the sum total of all schedulei should equal to sumTime.
Input
The first input line contains two integer numbers d, sumTime (1 β€ d β€ 30, 0 β€ sumTime β€ 240) β the amount of days, during which Peter studied, and the total amount of hours, spent on preparation. Each of the following d lines contains two integer numbers minTimei, maxTimei (0 β€ minTimei β€ maxTimei β€ 8), separated by a space β minimum and maximum amount of hours that Peter could spent in the i-th day.
Output
In the first line print YES, and in the second line print d numbers (separated by a space), each of the numbers β amount of hours, spent by Peter on preparation in the corresponding day, if he followed his parents' instructions; or print NO in the unique line. If there are many solutions, print any of them.
Examples
Input
1 48
5 7
Output
NO
Input
2 5
0 1
3 5
Output
YES
1 4
Tags: constructive algorithms, greedy
Correct Solution:
```
import sys
d, sumTime = map(int, input().split())
A = []
B = []
sumA = 0
sumB = 0
for i in range(d):
m, n = map(int, input().split())
A.append(m)
B.append(n)
sumA += m
sumB += n
if sumA > sumTime or sumB < sumTime:
print("NO")
sys.exit()
sumTime -= sumA
print("YES")
for i in range(d):
add = min(sumTime, B[i]-A[i])
A[i] += add
sumTime -= add
print(A[i],end = " ")
```
| 105,648 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Tomorrow Peter has a Biology exam. He does not like this subject much, but d days ago he learnt that he would have to take this exam. Peter's strict parents made him prepare for the exam immediately, for this purpose he has to study not less than minTimei and not more than maxTimei hours per each i-th day. Moreover, they warned Peter that a day before the exam they would check how he has followed their instructions.
So, today is the day when Peter's parents ask him to show the timetable of his preparatory studies. But the boy has counted only the sum of hours sumTime spent him on preparation, and now he wants to know if he can show his parents a timetable sΡhedule with d numbers, where each number sΡhedulei stands for the time in hours spent by Peter each i-th day on biology studies, and satisfying the limitations imposed by his parents, and at the same time the sum total of all schedulei should equal to sumTime.
Input
The first input line contains two integer numbers d, sumTime (1 β€ d β€ 30, 0 β€ sumTime β€ 240) β the amount of days, during which Peter studied, and the total amount of hours, spent on preparation. Each of the following d lines contains two integer numbers minTimei, maxTimei (0 β€ minTimei β€ maxTimei β€ 8), separated by a space β minimum and maximum amount of hours that Peter could spent in the i-th day.
Output
In the first line print YES, and in the second line print d numbers (separated by a space), each of the numbers β amount of hours, spent by Peter on preparation in the corresponding day, if he followed his parents' instructions; or print NO in the unique line. If there are many solutions, print any of them.
Examples
Input
1 48
5 7
Output
NO
Input
2 5
0 1
3 5
Output
YES
1 4
Tags: constructive algorithms, greedy
Correct Solution:
```
import os
import sys
debug = True
if debug and os.path.exists("input.in"):
input = open("input.in", "r").readline
else:
debug = False
input = sys.stdin.readline
def inp():
return (int(input()))
def inlt():
return (list(map(int, input().split())))
def insr():
s = input()
return s[:len(s) - 1] # Remove line char from end
def invr():
return (map(int, input().split()))
test_count = 1
if debug:
test_count = int(input())
for t in range(test_count):
if debug:
print("Test Case #", t + 1)
# Start code here
n, k = invr()
a = list()
min_total = 0
max_total = 0
for _ in range(n):
x, y = invr()
a.append((x, y))
min_total += x
max_total += y
if k < min_total or k > max_total:
print("NO")
else:
print("YES")
diff = k - min_total
ans = list()
for i in range(n):
ans.append(a[i][0] + min(a[i][1] - a[i][0], diff))
diff -= min(a[i][1] - a[i][0], diff)
print(" ".join(map(str, ans)))
```
| 105,649 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Tomorrow Peter has a Biology exam. He does not like this subject much, but d days ago he learnt that he would have to take this exam. Peter's strict parents made him prepare for the exam immediately, for this purpose he has to study not less than minTimei and not more than maxTimei hours per each i-th day. Moreover, they warned Peter that a day before the exam they would check how he has followed their instructions.
So, today is the day when Peter's parents ask him to show the timetable of his preparatory studies. But the boy has counted only the sum of hours sumTime spent him on preparation, and now he wants to know if he can show his parents a timetable sΡhedule with d numbers, where each number sΡhedulei stands for the time in hours spent by Peter each i-th day on biology studies, and satisfying the limitations imposed by his parents, and at the same time the sum total of all schedulei should equal to sumTime.
Input
The first input line contains two integer numbers d, sumTime (1 β€ d β€ 30, 0 β€ sumTime β€ 240) β the amount of days, during which Peter studied, and the total amount of hours, spent on preparation. Each of the following d lines contains two integer numbers minTimei, maxTimei (0 β€ minTimei β€ maxTimei β€ 8), separated by a space β minimum and maximum amount of hours that Peter could spent in the i-th day.
Output
In the first line print YES, and in the second line print d numbers (separated by a space), each of the numbers β amount of hours, spent by Peter on preparation in the corresponding day, if he followed his parents' instructions; or print NO in the unique line. If there are many solutions, print any of them.
Examples
Input
1 48
5 7
Output
NO
Input
2 5
0 1
3 5
Output
YES
1 4
Tags: constructive algorithms, greedy
Correct Solution:
```
d,hrs=[int(x) for x in input().split()]
hrs1 = hrs
a=[]
for i in range (d):
t=input().split()
a.append(t)
sum1=0
sum2 =0
for j in range (d):
sum1=int(a[j][0])+sum1
sum2=int(a[j][1])+sum2
count=0
if (sum1<= hrs <= sum2):
print("YES")
count=count+1
else:
print("NO")
b=[]
sum3=0
sum4=0
if (len (a)>=2) and (count==1):
for k in range (d-1,-1,-1):
sum3=int(a[k][0])+sum3
sum4=int(a[k][1])+sum4
m=[sum3,sum4]
b.append(m)
b.reverse()
c=[]
if count==1:
for g in range (d-1):
for n in range (int(a[g][0]),int(a[g][1])+1):
l=hrs-n
if(int(b[g+1][0])<=(l)<=int(b[g+1][1])):
hrs =l
c.append(n)
break
sum_5=sum(c)
op=hrs1-sum_5
c.append(op)
for lll in c:
print(lll,end=" ")
if (len (a) ==1)and (count ==1):
print (hrs1)
```
| 105,650 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Tomorrow Peter has a Biology exam. He does not like this subject much, but d days ago he learnt that he would have to take this exam. Peter's strict parents made him prepare for the exam immediately, for this purpose he has to study not less than minTimei and not more than maxTimei hours per each i-th day. Moreover, they warned Peter that a day before the exam they would check how he has followed their instructions.
So, today is the day when Peter's parents ask him to show the timetable of his preparatory studies. But the boy has counted only the sum of hours sumTime spent him on preparation, and now he wants to know if he can show his parents a timetable sΡhedule with d numbers, where each number sΡhedulei stands for the time in hours spent by Peter each i-th day on biology studies, and satisfying the limitations imposed by his parents, and at the same time the sum total of all schedulei should equal to sumTime.
Input
The first input line contains two integer numbers d, sumTime (1 β€ d β€ 30, 0 β€ sumTime β€ 240) β the amount of days, during which Peter studied, and the total amount of hours, spent on preparation. Each of the following d lines contains two integer numbers minTimei, maxTimei (0 β€ minTimei β€ maxTimei β€ 8), separated by a space β minimum and maximum amount of hours that Peter could spent in the i-th day.
Output
In the first line print YES, and in the second line print d numbers (separated by a space), each of the numbers β amount of hours, spent by Peter on preparation in the corresponding day, if he followed his parents' instructions; or print NO in the unique line. If there are many solutions, print any of them.
Examples
Input
1 48
5 7
Output
NO
Input
2 5
0 1
3 5
Output
YES
1 4
Tags: constructive algorithms, greedy
Correct Solution:
```
d, t = input().split()
d = int(d)
t = int(t)
minimum = 0
maximum = 0
min_list = []
max_list = []
ans = []
for i in range(d):
mi, ma = input().split()
mi = int(mi)
ma = int(ma)
min_list.append(mi)
max_list.append(ma)
minimum = minimum + mi
maximum = maximum + ma
def hours(days, hours):
if sum(min_list) == hours:
return min_list
else:
k = 0
while sum(min_list) < hours:
if min_list[k]<max_list[k]:
min_list[k] = min_list[k]+1
else:
k = k+1
return min_list
if minimum <= t <= maximum:
print('YES')
answer = hours(d, t)
print(*answer, sep=" ")
else:
print('NO')
```
| 105,651 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Tomorrow Peter has a Biology exam. He does not like this subject much, but d days ago he learnt that he would have to take this exam. Peter's strict parents made him prepare for the exam immediately, for this purpose he has to study not less than minTimei and not more than maxTimei hours per each i-th day. Moreover, they warned Peter that a day before the exam they would check how he has followed their instructions.
So, today is the day when Peter's parents ask him to show the timetable of his preparatory studies. But the boy has counted only the sum of hours sumTime spent him on preparation, and now he wants to know if he can show his parents a timetable sΡhedule with d numbers, where each number sΡhedulei stands for the time in hours spent by Peter each i-th day on biology studies, and satisfying the limitations imposed by his parents, and at the same time the sum total of all schedulei should equal to sumTime.
Input
The first input line contains two integer numbers d, sumTime (1 β€ d β€ 30, 0 β€ sumTime β€ 240) β the amount of days, during which Peter studied, and the total amount of hours, spent on preparation. Each of the following d lines contains two integer numbers minTimei, maxTimei (0 β€ minTimei β€ maxTimei β€ 8), separated by a space β minimum and maximum amount of hours that Peter could spent in the i-th day.
Output
In the first line print YES, and in the second line print d numbers (separated by a space), each of the numbers β amount of hours, spent by Peter on preparation in the corresponding day, if he followed his parents' instructions; or print NO in the unique line. If there are many solutions, print any of them.
Examples
Input
1 48
5 7
Output
NO
Input
2 5
0 1
3 5
Output
YES
1 4
Tags: constructive algorithms, greedy
Correct Solution:
```
d,sumtime = [int(i) for i in input().split()]
time = [0]*d
mintime,maxtime = 0,0
for i in range(d):
time[i] = [int(i) for i in input().split()]
mintime+=time[i][0]
maxtime+=time[i][1]
if sumtime<mintime or sumtime>maxtime:
print('NO')
else:
print('YES')
ans = [i[0] for i in time]
i = 0
while mintime<sumtime:
if ans[i]<time[i][1]:
ans[i]+=1
mintime+=1
else:
i+=1
print(*ans)
```
| 105,652 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Tomorrow Peter has a Biology exam. He does not like this subject much, but d days ago he learnt that he would have to take this exam. Peter's strict parents made him prepare for the exam immediately, for this purpose he has to study not less than minTimei and not more than maxTimei hours per each i-th day. Moreover, they warned Peter that a day before the exam they would check how he has followed their instructions.
So, today is the day when Peter's parents ask him to show the timetable of his preparatory studies. But the boy has counted only the sum of hours sumTime spent him on preparation, and now he wants to know if he can show his parents a timetable sΡhedule with d numbers, where each number sΡhedulei stands for the time in hours spent by Peter each i-th day on biology studies, and satisfying the limitations imposed by his parents, and at the same time the sum total of all schedulei should equal to sumTime.
Input
The first input line contains two integer numbers d, sumTime (1 β€ d β€ 30, 0 β€ sumTime β€ 240) β the amount of days, during which Peter studied, and the total amount of hours, spent on preparation. Each of the following d lines contains two integer numbers minTimei, maxTimei (0 β€ minTimei β€ maxTimei β€ 8), separated by a space β minimum and maximum amount of hours that Peter could spent in the i-th day.
Output
In the first line print YES, and in the second line print d numbers (separated by a space), each of the numbers β amount of hours, spent by Peter on preparation in the corresponding day, if he followed his parents' instructions; or print NO in the unique line. If there are many solutions, print any of them.
Examples
Input
1 48
5 7
Output
NO
Input
2 5
0 1
3 5
Output
YES
1 4
Tags: constructive algorithms, greedy
Correct Solution:
```
d, sumTime = map(int, input().split())
a = [(tuple(map(int, input().split()))) for _ in range(d)]
dp = [[False for _ in range(sumTime + 1)] for _ in range(d + 1)]
dp[0][0] = True
for day in range(1, d + 1):
minTime, maxTime = a[day - 1]
for time in range(sumTime + 1):
for today in range(minTime, maxTime + 1):
if time - today >= 0:
dp[day][time] |= dp[day - 1][time - today]
if not dp[d][sumTime]:
print('NO')
else:
print('YES')
ret = []
for day in range(d, 0, -1):
minTime, maxTime = a[day - 1]
for today in range(minTime, maxTime + 1):
if sumTime - today >= 0 and dp[day - 1][sumTime - today]:
ret.append(today)
sumTime -= today
break
else:
raise Exception('Cannot find answer')
print(' '.join(map(str, ret[::-1])))
```
| 105,653 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Tomorrow Peter has a Biology exam. He does not like this subject much, but d days ago he learnt that he would have to take this exam. Peter's strict parents made him prepare for the exam immediately, for this purpose he has to study not less than minTimei and not more than maxTimei hours per each i-th day. Moreover, they warned Peter that a day before the exam they would check how he has followed their instructions.
So, today is the day when Peter's parents ask him to show the timetable of his preparatory studies. But the boy has counted only the sum of hours sumTime spent him on preparation, and now he wants to know if he can show his parents a timetable sΡhedule with d numbers, where each number sΡhedulei stands for the time in hours spent by Peter each i-th day on biology studies, and satisfying the limitations imposed by his parents, and at the same time the sum total of all schedulei should equal to sumTime.
Input
The first input line contains two integer numbers d, sumTime (1 β€ d β€ 30, 0 β€ sumTime β€ 240) β the amount of days, during which Peter studied, and the total amount of hours, spent on preparation. Each of the following d lines contains two integer numbers minTimei, maxTimei (0 β€ minTimei β€ maxTimei β€ 8), separated by a space β minimum and maximum amount of hours that Peter could spent in the i-th day.
Output
In the first line print YES, and in the second line print d numbers (separated by a space), each of the numbers β amount of hours, spent by Peter on preparation in the corresponding day, if he followed his parents' instructions; or print NO in the unique line. If there are many solutions, print any of them.
Examples
Input
1 48
5 7
Output
NO
Input
2 5
0 1
3 5
Output
YES
1 4
Tags: constructive algorithms, greedy
Correct Solution:
```
string = input().split(' ')
d = int(string[0])
sumTime = int(string[1])
mins = []
maxs = []
for i in range(d):
string = input().split(' ')
mins.append(int(string[0]))
maxs.append(int(string[1]))
if not(sum(mins) <= sumTime <= sum(maxs)):
print('NO')
else:
days = maxs[:]
currentSum = sum(maxs)
for i in range(d):
old = days[i]
days[i] = max((days[i]-(currentSum-sumTime)), mins[i])
currentSum -= (old-days[i])
if currentSum == sumTime:
break
print('YES')
print(' '.join(str(item) for item in days))
```
| 105,654 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Tomorrow Peter has a Biology exam. He does not like this subject much, but d days ago he learnt that he would have to take this exam. Peter's strict parents made him prepare for the exam immediately, for this purpose he has to study not less than minTimei and not more than maxTimei hours per each i-th day. Moreover, they warned Peter that a day before the exam they would check how he has followed their instructions.
So, today is the day when Peter's parents ask him to show the timetable of his preparatory studies. But the boy has counted only the sum of hours sumTime spent him on preparation, and now he wants to know if he can show his parents a timetable sΡhedule with d numbers, where each number sΡhedulei stands for the time in hours spent by Peter each i-th day on biology studies, and satisfying the limitations imposed by his parents, and at the same time the sum total of all schedulei should equal to sumTime.
Input
The first input line contains two integer numbers d, sumTime (1 β€ d β€ 30, 0 β€ sumTime β€ 240) β the amount of days, during which Peter studied, and the total amount of hours, spent on preparation. Each of the following d lines contains two integer numbers minTimei, maxTimei (0 β€ minTimei β€ maxTimei β€ 8), separated by a space β minimum and maximum amount of hours that Peter could spent in the i-th day.
Output
In the first line print YES, and in the second line print d numbers (separated by a space), each of the numbers β amount of hours, spent by Peter on preparation in the corresponding day, if he followed his parents' instructions; or print NO in the unique line. If there are many solutions, print any of them.
Examples
Input
1 48
5 7
Output
NO
Input
2 5
0 1
3 5
Output
YES
1 4
Tags: constructive algorithms, greedy
Correct Solution:
```
import math
from collections import defaultdict
ml=lambda:map(int,input().split())
ll=lambda:list(map(int,input().split()))
ii=lambda:int(input())
ip=lambda:(input())
"""========main code==============="""
x,y=ml()
mn=0
mx=0
lol=[]
yo=[]
for _ in range(x):
a,b=ml()
mn+=a
mx+=b
yo.append(b)
lol.append(a)
if(sum(lol)<=y and sum(yo)>=y):
print("YES")
y-=sum(lol)
for i in range(len(lol)):
if(y>=0):
k=min(y,yo[i]-lol[i])
lol[i]+=k
y-=k
print(lol[i],end=" ")
else:
print("NO")
```
| 105,655 |
Provide tags and a correct Python 3 solution for this coding contest problem.
After a hard day Vitaly got very hungry and he wants to eat his favorite potato pie. But it's not that simple. Vitaly is in the first room of the house with n room located in a line and numbered starting from one from left to right. You can go from the first room to the second room, from the second room to the third room and so on β you can go from the (n - 1)-th room to the n-th room. Thus, you can go to room x only from room x - 1.
The potato pie is located in the n-th room and Vitaly needs to go there.
Each pair of consecutive rooms has a door between them. In order to go to room x from room x - 1, you need to open the door between the rooms with the corresponding key.
In total the house has several types of doors (represented by uppercase Latin letters) and several types of keys (represented by lowercase Latin letters). The key of type t can open the door of type T if and only if t and T are the same letter, written in different cases. For example, key f can open door F.
Each of the first n - 1 rooms contains exactly one key of some type that Vitaly can use to get to next rooms. Once the door is open with some key, Vitaly won't get the key from the keyhole but he will immediately run into the next room. In other words, each key can open no more than one door.
Vitaly realizes that he may end up in some room without the key that opens the door to the next room. Before the start his run for the potato pie Vitaly can buy any number of keys of any type that is guaranteed to get to room n.
Given the plan of the house, Vitaly wants to know what is the minimum number of keys he needs to buy to surely get to the room n, which has a delicious potato pie. Write a program that will help Vitaly find out this number.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 105) β the number of rooms in the house.
The second line of the input contains string s of length 2Β·n - 2. Let's number the elements of the string from left to right, starting from one.
The odd positions in the given string s contain lowercase Latin letters β the types of the keys that lie in the corresponding rooms. Thus, each odd position i of the given string s contains a lowercase Latin letter β the type of the key that lies in room number (i + 1) / 2.
The even positions in the given string contain uppercase Latin letters β the types of doors between the rooms. Thus, each even position i of the given string s contains an uppercase letter β the type of the door that leads from room i / 2 to room i / 2 + 1.
Output
Print the only integer β the minimum number of keys that Vitaly needs to buy to surely get from room one to room n.
Examples
Input
3
aAbB
Output
0
Input
4
aBaCaB
Output
3
Input
5
xYyXzZaZ
Output
2
Tags: greedy, hashing, strings
Correct Solution:
```
room = int(input())
desc = input().lower()
keys = desc[0::2]
way = desc[1::2]
keys_on_hands = ''
keys_to_buy = 0
for i in range(len(way)):
keys_on_hands += keys[i]
pos = keys_on_hands.find(way[i])
if pos == -1:
keys_to_buy += 1
else:
keys_on_hands = keys_on_hands[:pos] + keys_on_hands[pos+1:]
print('{0}'.format(keys_to_buy))
```
| 105,656 |
Provide tags and a correct Python 3 solution for this coding contest problem.
After a hard day Vitaly got very hungry and he wants to eat his favorite potato pie. But it's not that simple. Vitaly is in the first room of the house with n room located in a line and numbered starting from one from left to right. You can go from the first room to the second room, from the second room to the third room and so on β you can go from the (n - 1)-th room to the n-th room. Thus, you can go to room x only from room x - 1.
The potato pie is located in the n-th room and Vitaly needs to go there.
Each pair of consecutive rooms has a door between them. In order to go to room x from room x - 1, you need to open the door between the rooms with the corresponding key.
In total the house has several types of doors (represented by uppercase Latin letters) and several types of keys (represented by lowercase Latin letters). The key of type t can open the door of type T if and only if t and T are the same letter, written in different cases. For example, key f can open door F.
Each of the first n - 1 rooms contains exactly one key of some type that Vitaly can use to get to next rooms. Once the door is open with some key, Vitaly won't get the key from the keyhole but he will immediately run into the next room. In other words, each key can open no more than one door.
Vitaly realizes that he may end up in some room without the key that opens the door to the next room. Before the start his run for the potato pie Vitaly can buy any number of keys of any type that is guaranteed to get to room n.
Given the plan of the house, Vitaly wants to know what is the minimum number of keys he needs to buy to surely get to the room n, which has a delicious potato pie. Write a program that will help Vitaly find out this number.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 105) β the number of rooms in the house.
The second line of the input contains string s of length 2Β·n - 2. Let's number the elements of the string from left to right, starting from one.
The odd positions in the given string s contain lowercase Latin letters β the types of the keys that lie in the corresponding rooms. Thus, each odd position i of the given string s contains a lowercase Latin letter β the type of the key that lies in room number (i + 1) / 2.
The even positions in the given string contain uppercase Latin letters β the types of doors between the rooms. Thus, each even position i of the given string s contains an uppercase letter β the type of the door that leads from room i / 2 to room i / 2 + 1.
Output
Print the only integer β the minimum number of keys that Vitaly needs to buy to surely get from room one to room n.
Examples
Input
3
aAbB
Output
0
Input
4
aBaCaB
Output
3
Input
5
xYyXzZaZ
Output
2
Tags: greedy, hashing, strings
Correct Solution:
```
#_________________ Mukul Mohan Varshney _______________#
#Template
import sys
import os
import math
import copy
from math import gcd
from bisect import bisect
from io import BytesIO, IOBase
from math import sqrt,floor,factorial,gcd,log,ceil
from collections import deque,Counter,defaultdict
from itertools import permutations, combinations
import itertools
#define function
def Int(): return int(sys.stdin.readline())
def Mint(): return map(int,sys.stdin.readline().split())
def Lstr(): return list(sys.stdin.readline().strip())
def Str(): return sys.stdin.readline().strip()
def Mstr(): return map(str,sys.stdin.readline().strip().split())
def List(): return list(map(int,sys.stdin.readline().split()))
def Hash(): return dict()
def Mod(): return 1000000007
def Ncr(n,r,p): return ((fact[n])*((ifact[r]*ifact[n-r])%p))%p
def Most_frequent(list): return max(set(list), key = list.count)
def Mat2x2(n): return [List() for _ in range(n)]
def Lcm(x,y): return (x*y)//gcd(x,y)
def dtob(n): return bin(n).replace("0b","")
def btod(n): return int(n,2)
# Driver Code
def solution():
#for j in range(Int()):
n=Int()
a=Str()
m=len(a)
k=Hash()
i=0
count=0
while(i<m):
x=a[i].lower()
if(i%2==0):
if x in k:
k[x]+=1
else:
k[x]=1
else:
if x in k:
if(k[x]>0):
k[x]=k[x]-1
else:
count+=1
else:
count+=1
i+=1
print(count)
#Call the solve function
if __name__ == "__main__":
solution()
```
| 105,657 |
Provide tags and a correct Python 3 solution for this coding contest problem.
After a hard day Vitaly got very hungry and he wants to eat his favorite potato pie. But it's not that simple. Vitaly is in the first room of the house with n room located in a line and numbered starting from one from left to right. You can go from the first room to the second room, from the second room to the third room and so on β you can go from the (n - 1)-th room to the n-th room. Thus, you can go to room x only from room x - 1.
The potato pie is located in the n-th room and Vitaly needs to go there.
Each pair of consecutive rooms has a door between them. In order to go to room x from room x - 1, you need to open the door between the rooms with the corresponding key.
In total the house has several types of doors (represented by uppercase Latin letters) and several types of keys (represented by lowercase Latin letters). The key of type t can open the door of type T if and only if t and T are the same letter, written in different cases. For example, key f can open door F.
Each of the first n - 1 rooms contains exactly one key of some type that Vitaly can use to get to next rooms. Once the door is open with some key, Vitaly won't get the key from the keyhole but he will immediately run into the next room. In other words, each key can open no more than one door.
Vitaly realizes that he may end up in some room without the key that opens the door to the next room. Before the start his run for the potato pie Vitaly can buy any number of keys of any type that is guaranteed to get to room n.
Given the plan of the house, Vitaly wants to know what is the minimum number of keys he needs to buy to surely get to the room n, which has a delicious potato pie. Write a program that will help Vitaly find out this number.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 105) β the number of rooms in the house.
The second line of the input contains string s of length 2Β·n - 2. Let's number the elements of the string from left to right, starting from one.
The odd positions in the given string s contain lowercase Latin letters β the types of the keys that lie in the corresponding rooms. Thus, each odd position i of the given string s contains a lowercase Latin letter β the type of the key that lies in room number (i + 1) / 2.
The even positions in the given string contain uppercase Latin letters β the types of doors between the rooms. Thus, each even position i of the given string s contains an uppercase letter β the type of the door that leads from room i / 2 to room i / 2 + 1.
Output
Print the only integer β the minimum number of keys that Vitaly needs to buy to surely get from room one to room n.
Examples
Input
3
aAbB
Output
0
Input
4
aBaCaB
Output
3
Input
5
xYyXzZaZ
Output
2
Tags: greedy, hashing, strings
Correct Solution:
```
n = int(input())
b = input()
a = set()
d = dict()
count = 0
for i in range(2 * n - 2):
if i % 2 == 0:
if b[i] not in a:
a.add(b[i])
d[b[i]] = 1
else:
d[b[i]] += 1
else:
if b[i].lower() in a:
d[b[i].lower()] -= 1
if d[b[i].lower()] == 0:
a.remove(b[i].lower())
else:
count += 1
print(count)
```
| 105,658 |
Provide tags and a correct Python 3 solution for this coding contest problem.
After a hard day Vitaly got very hungry and he wants to eat his favorite potato pie. But it's not that simple. Vitaly is in the first room of the house with n room located in a line and numbered starting from one from left to right. You can go from the first room to the second room, from the second room to the third room and so on β you can go from the (n - 1)-th room to the n-th room. Thus, you can go to room x only from room x - 1.
The potato pie is located in the n-th room and Vitaly needs to go there.
Each pair of consecutive rooms has a door between them. In order to go to room x from room x - 1, you need to open the door between the rooms with the corresponding key.
In total the house has several types of doors (represented by uppercase Latin letters) and several types of keys (represented by lowercase Latin letters). The key of type t can open the door of type T if and only if t and T are the same letter, written in different cases. For example, key f can open door F.
Each of the first n - 1 rooms contains exactly one key of some type that Vitaly can use to get to next rooms. Once the door is open with some key, Vitaly won't get the key from the keyhole but he will immediately run into the next room. In other words, each key can open no more than one door.
Vitaly realizes that he may end up in some room without the key that opens the door to the next room. Before the start his run for the potato pie Vitaly can buy any number of keys of any type that is guaranteed to get to room n.
Given the plan of the house, Vitaly wants to know what is the minimum number of keys he needs to buy to surely get to the room n, which has a delicious potato pie. Write a program that will help Vitaly find out this number.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 105) β the number of rooms in the house.
The second line of the input contains string s of length 2Β·n - 2. Let's number the elements of the string from left to right, starting from one.
The odd positions in the given string s contain lowercase Latin letters β the types of the keys that lie in the corresponding rooms. Thus, each odd position i of the given string s contains a lowercase Latin letter β the type of the key that lies in room number (i + 1) / 2.
The even positions in the given string contain uppercase Latin letters β the types of doors between the rooms. Thus, each even position i of the given string s contains an uppercase letter β the type of the door that leads from room i / 2 to room i / 2 + 1.
Output
Print the only integer β the minimum number of keys that Vitaly needs to buy to surely get from room one to room n.
Examples
Input
3
aAbB
Output
0
Input
4
aBaCaB
Output
3
Input
5
xYyXzZaZ
Output
2
Tags: greedy, hashing, strings
Correct Solution:
```
n = int(input())
s = input()
need = 0
keys = {c: 0 for c in 'abcdefghijklmnopqrstuvwxyz'}
for c in s:
if c.islower():
keys[c] += 1
else:
c = c.lower()
if keys[c]:
keys[c] -= 1
else:
need += 1
print(need)
```
| 105,659 |
Provide tags and a correct Python 3 solution for this coding contest problem.
After a hard day Vitaly got very hungry and he wants to eat his favorite potato pie. But it's not that simple. Vitaly is in the first room of the house with n room located in a line and numbered starting from one from left to right. You can go from the first room to the second room, from the second room to the third room and so on β you can go from the (n - 1)-th room to the n-th room. Thus, you can go to room x only from room x - 1.
The potato pie is located in the n-th room and Vitaly needs to go there.
Each pair of consecutive rooms has a door between them. In order to go to room x from room x - 1, you need to open the door between the rooms with the corresponding key.
In total the house has several types of doors (represented by uppercase Latin letters) and several types of keys (represented by lowercase Latin letters). The key of type t can open the door of type T if and only if t and T are the same letter, written in different cases. For example, key f can open door F.
Each of the first n - 1 rooms contains exactly one key of some type that Vitaly can use to get to next rooms. Once the door is open with some key, Vitaly won't get the key from the keyhole but he will immediately run into the next room. In other words, each key can open no more than one door.
Vitaly realizes that he may end up in some room without the key that opens the door to the next room. Before the start his run for the potato pie Vitaly can buy any number of keys of any type that is guaranteed to get to room n.
Given the plan of the house, Vitaly wants to know what is the minimum number of keys he needs to buy to surely get to the room n, which has a delicious potato pie. Write a program that will help Vitaly find out this number.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 105) β the number of rooms in the house.
The second line of the input contains string s of length 2Β·n - 2. Let's number the elements of the string from left to right, starting from one.
The odd positions in the given string s contain lowercase Latin letters β the types of the keys that lie in the corresponding rooms. Thus, each odd position i of the given string s contains a lowercase Latin letter β the type of the key that lies in room number (i + 1) / 2.
The even positions in the given string contain uppercase Latin letters β the types of doors between the rooms. Thus, each even position i of the given string s contains an uppercase letter β the type of the door that leads from room i / 2 to room i / 2 + 1.
Output
Print the only integer β the minimum number of keys that Vitaly needs to buy to surely get from room one to room n.
Examples
Input
3
aAbB
Output
0
Input
4
aBaCaB
Output
3
Input
5
xYyXzZaZ
Output
2
Tags: greedy, hashing, strings
Correct Solution:
```
# coding=utf-8
if __name__ == '__main__':
n = int(input())
line = str(input())
cook = {'a': 0, 'b': 0, 'c': 0, 'd': 0, 'e': 0, 'f': 0, 'g': 0, 'h': 0, 'i': 0, 'j': 0, 'k': 0, 'l': 0, 'm': 0,
'n': 0, 'o': 0, 'p': 0, 'q': 0, 'r': 0, 's': 0, 't': 0, 'u': 0, 'v': 0, 'w': 0, 'x': 0, 'y': 0, 'z': 0}
tar = 0
for i in range(n - 1):
cook[line[2 * i]] += 1
if cook[line[2 * i + 1].lower()] > 0:
cook[line[2 * i + 1].lower()] -= 1
else:
tar += 1
print(tar)
```
| 105,660 |
Provide tags and a correct Python 3 solution for this coding contest problem.
After a hard day Vitaly got very hungry and he wants to eat his favorite potato pie. But it's not that simple. Vitaly is in the first room of the house with n room located in a line and numbered starting from one from left to right. You can go from the first room to the second room, from the second room to the third room and so on β you can go from the (n - 1)-th room to the n-th room. Thus, you can go to room x only from room x - 1.
The potato pie is located in the n-th room and Vitaly needs to go there.
Each pair of consecutive rooms has a door between them. In order to go to room x from room x - 1, you need to open the door between the rooms with the corresponding key.
In total the house has several types of doors (represented by uppercase Latin letters) and several types of keys (represented by lowercase Latin letters). The key of type t can open the door of type T if and only if t and T are the same letter, written in different cases. For example, key f can open door F.
Each of the first n - 1 rooms contains exactly one key of some type that Vitaly can use to get to next rooms. Once the door is open with some key, Vitaly won't get the key from the keyhole but he will immediately run into the next room. In other words, each key can open no more than one door.
Vitaly realizes that he may end up in some room without the key that opens the door to the next room. Before the start his run for the potato pie Vitaly can buy any number of keys of any type that is guaranteed to get to room n.
Given the plan of the house, Vitaly wants to know what is the minimum number of keys he needs to buy to surely get to the room n, which has a delicious potato pie. Write a program that will help Vitaly find out this number.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 105) β the number of rooms in the house.
The second line of the input contains string s of length 2Β·n - 2. Let's number the elements of the string from left to right, starting from one.
The odd positions in the given string s contain lowercase Latin letters β the types of the keys that lie in the corresponding rooms. Thus, each odd position i of the given string s contains a lowercase Latin letter β the type of the key that lies in room number (i + 1) / 2.
The even positions in the given string contain uppercase Latin letters β the types of doors between the rooms. Thus, each even position i of the given string s contains an uppercase letter β the type of the door that leads from room i / 2 to room i / 2 + 1.
Output
Print the only integer β the minimum number of keys that Vitaly needs to buy to surely get from room one to room n.
Examples
Input
3
aAbB
Output
0
Input
4
aBaCaB
Output
3
Input
5
xYyXzZaZ
Output
2
Tags: greedy, hashing, strings
Correct Solution:
```
from collections import Counter
n = int(input())
s = input()
keys = Counter()
buy = 0
for i in range(0, 2*n-2, 2):
keys[s[i]] += 1
room = s[i+1].lower()
if room not in keys or not keys[room]:
buy += 1
else:
keys[room] -= 1
print(buy)
```
| 105,661 |
Provide tags and a correct Python 3 solution for this coding contest problem.
After a hard day Vitaly got very hungry and he wants to eat his favorite potato pie. But it's not that simple. Vitaly is in the first room of the house with n room located in a line and numbered starting from one from left to right. You can go from the first room to the second room, from the second room to the third room and so on β you can go from the (n - 1)-th room to the n-th room. Thus, you can go to room x only from room x - 1.
The potato pie is located in the n-th room and Vitaly needs to go there.
Each pair of consecutive rooms has a door between them. In order to go to room x from room x - 1, you need to open the door between the rooms with the corresponding key.
In total the house has several types of doors (represented by uppercase Latin letters) and several types of keys (represented by lowercase Latin letters). The key of type t can open the door of type T if and only if t and T are the same letter, written in different cases. For example, key f can open door F.
Each of the first n - 1 rooms contains exactly one key of some type that Vitaly can use to get to next rooms. Once the door is open with some key, Vitaly won't get the key from the keyhole but he will immediately run into the next room. In other words, each key can open no more than one door.
Vitaly realizes that he may end up in some room without the key that opens the door to the next room. Before the start his run for the potato pie Vitaly can buy any number of keys of any type that is guaranteed to get to room n.
Given the plan of the house, Vitaly wants to know what is the minimum number of keys he needs to buy to surely get to the room n, which has a delicious potato pie. Write a program that will help Vitaly find out this number.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 105) β the number of rooms in the house.
The second line of the input contains string s of length 2Β·n - 2. Let's number the elements of the string from left to right, starting from one.
The odd positions in the given string s contain lowercase Latin letters β the types of the keys that lie in the corresponding rooms. Thus, each odd position i of the given string s contains a lowercase Latin letter β the type of the key that lies in room number (i + 1) / 2.
The even positions in the given string contain uppercase Latin letters β the types of doors between the rooms. Thus, each even position i of the given string s contains an uppercase letter β the type of the door that leads from room i / 2 to room i / 2 + 1.
Output
Print the only integer β the minimum number of keys that Vitaly needs to buy to surely get from room one to room n.
Examples
Input
3
aAbB
Output
0
Input
4
aBaCaB
Output
3
Input
5
xYyXzZaZ
Output
2
Tags: greedy, hashing, strings
Correct Solution:
```
from collections import defaultdict
n = int(input())
inp = input()
keys = defaultdict(lambda: 0)
res = 0
for i in range(0, 2*(n-1), 2):
keys[inp[i]] += 1
if keys[inp[i+1].lower()] > 0:
keys[inp[i+1].lower()] -= 1
else:
res += 1
print(res)
```
| 105,662 |
Provide tags and a correct Python 3 solution for this coding contest problem.
After a hard day Vitaly got very hungry and he wants to eat his favorite potato pie. But it's not that simple. Vitaly is in the first room of the house with n room located in a line and numbered starting from one from left to right. You can go from the first room to the second room, from the second room to the third room and so on β you can go from the (n - 1)-th room to the n-th room. Thus, you can go to room x only from room x - 1.
The potato pie is located in the n-th room and Vitaly needs to go there.
Each pair of consecutive rooms has a door between them. In order to go to room x from room x - 1, you need to open the door between the rooms with the corresponding key.
In total the house has several types of doors (represented by uppercase Latin letters) and several types of keys (represented by lowercase Latin letters). The key of type t can open the door of type T if and only if t and T are the same letter, written in different cases. For example, key f can open door F.
Each of the first n - 1 rooms contains exactly one key of some type that Vitaly can use to get to next rooms. Once the door is open with some key, Vitaly won't get the key from the keyhole but he will immediately run into the next room. In other words, each key can open no more than one door.
Vitaly realizes that he may end up in some room without the key that opens the door to the next room. Before the start his run for the potato pie Vitaly can buy any number of keys of any type that is guaranteed to get to room n.
Given the plan of the house, Vitaly wants to know what is the minimum number of keys he needs to buy to surely get to the room n, which has a delicious potato pie. Write a program that will help Vitaly find out this number.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 105) β the number of rooms in the house.
The second line of the input contains string s of length 2Β·n - 2. Let's number the elements of the string from left to right, starting from one.
The odd positions in the given string s contain lowercase Latin letters β the types of the keys that lie in the corresponding rooms. Thus, each odd position i of the given string s contains a lowercase Latin letter β the type of the key that lies in room number (i + 1) / 2.
The even positions in the given string contain uppercase Latin letters β the types of doors between the rooms. Thus, each even position i of the given string s contains an uppercase letter β the type of the door that leads from room i / 2 to room i / 2 + 1.
Output
Print the only integer β the minimum number of keys that Vitaly needs to buy to surely get from room one to room n.
Examples
Input
3
aAbB
Output
0
Input
4
aBaCaB
Output
3
Input
5
xYyXzZaZ
Output
2
Tags: greedy, hashing, strings
Correct Solution:
```
# bsdk idhar kya dekhne ko aaya hai, khud kr!!!
# import math
# from itertools import *
# import random
# import calendar
import datetime
# import webbrowser
n = int(input())
string = input()
keys = [0]*26
count = 0
for i in range(0, len(string), 2):
if string[i].upper() == string[i+1]:
continue
else:
if keys[ord(string[i+1].lower()) - 97] >= 1:
keys[ord(string[i + 1].lower()) - 97] -= 1
keys[ord(string[i]) - 97] += 1
else:
count += 1
keys[ord(string[i]) - 97] += 1
'''
if string[i+1].lower() in keys:
keys.remove(string[i+1].lower())
keys.append(string[i])
continue
else:
count += 1
keys.append(string[i])
'''
print(count)
```
| 105,663 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
After a hard day Vitaly got very hungry and he wants to eat his favorite potato pie. But it's not that simple. Vitaly is in the first room of the house with n room located in a line and numbered starting from one from left to right. You can go from the first room to the second room, from the second room to the third room and so on β you can go from the (n - 1)-th room to the n-th room. Thus, you can go to room x only from room x - 1.
The potato pie is located in the n-th room and Vitaly needs to go there.
Each pair of consecutive rooms has a door between them. In order to go to room x from room x - 1, you need to open the door between the rooms with the corresponding key.
In total the house has several types of doors (represented by uppercase Latin letters) and several types of keys (represented by lowercase Latin letters). The key of type t can open the door of type T if and only if t and T are the same letter, written in different cases. For example, key f can open door F.
Each of the first n - 1 rooms contains exactly one key of some type that Vitaly can use to get to next rooms. Once the door is open with some key, Vitaly won't get the key from the keyhole but he will immediately run into the next room. In other words, each key can open no more than one door.
Vitaly realizes that he may end up in some room without the key that opens the door to the next room. Before the start his run for the potato pie Vitaly can buy any number of keys of any type that is guaranteed to get to room n.
Given the plan of the house, Vitaly wants to know what is the minimum number of keys he needs to buy to surely get to the room n, which has a delicious potato pie. Write a program that will help Vitaly find out this number.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 105) β the number of rooms in the house.
The second line of the input contains string s of length 2Β·n - 2. Let's number the elements of the string from left to right, starting from one.
The odd positions in the given string s contain lowercase Latin letters β the types of the keys that lie in the corresponding rooms. Thus, each odd position i of the given string s contains a lowercase Latin letter β the type of the key that lies in room number (i + 1) / 2.
The even positions in the given string contain uppercase Latin letters β the types of doors between the rooms. Thus, each even position i of the given string s contains an uppercase letter β the type of the door that leads from room i / 2 to room i / 2 + 1.
Output
Print the only integer β the minimum number of keys that Vitaly needs to buy to surely get from room one to room n.
Examples
Input
3
aAbB
Output
0
Input
4
aBaCaB
Output
3
Input
5
xYyXzZaZ
Output
2
Submitted Solution:
```
#!/c/Python34/python
# coding: utf-8
def main():
N = int(input())
S = input()
count = 0
roomNum = 1
alpha = [0] * 26
for (i, s) in enumerate(S):
if roomNum == N:
break
if i % 2 == 0:
alpha[ord(s)-ord('a')] += 1
else:
if alpha[ord(s.lower())-ord('a')] == 0:
count += 1
else:
alpha[ord(s.lower())-ord('a')] -= 1
roomNum += 1
print(count)
if __name__ == '__main__':
main()
```
Yes
| 105,664 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
After a hard day Vitaly got very hungry and he wants to eat his favorite potato pie. But it's not that simple. Vitaly is in the first room of the house with n room located in a line and numbered starting from one from left to right. You can go from the first room to the second room, from the second room to the third room and so on β you can go from the (n - 1)-th room to the n-th room. Thus, you can go to room x only from room x - 1.
The potato pie is located in the n-th room and Vitaly needs to go there.
Each pair of consecutive rooms has a door between them. In order to go to room x from room x - 1, you need to open the door between the rooms with the corresponding key.
In total the house has several types of doors (represented by uppercase Latin letters) and several types of keys (represented by lowercase Latin letters). The key of type t can open the door of type T if and only if t and T are the same letter, written in different cases. For example, key f can open door F.
Each of the first n - 1 rooms contains exactly one key of some type that Vitaly can use to get to next rooms. Once the door is open with some key, Vitaly won't get the key from the keyhole but he will immediately run into the next room. In other words, each key can open no more than one door.
Vitaly realizes that he may end up in some room without the key that opens the door to the next room. Before the start his run for the potato pie Vitaly can buy any number of keys of any type that is guaranteed to get to room n.
Given the plan of the house, Vitaly wants to know what is the minimum number of keys he needs to buy to surely get to the room n, which has a delicious potato pie. Write a program that will help Vitaly find out this number.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 105) β the number of rooms in the house.
The second line of the input contains string s of length 2Β·n - 2. Let's number the elements of the string from left to right, starting from one.
The odd positions in the given string s contain lowercase Latin letters β the types of the keys that lie in the corresponding rooms. Thus, each odd position i of the given string s contains a lowercase Latin letter β the type of the key that lies in room number (i + 1) / 2.
The even positions in the given string contain uppercase Latin letters β the types of doors between the rooms. Thus, each even position i of the given string s contains an uppercase letter β the type of the door that leads from room i / 2 to room i / 2 + 1.
Output
Print the only integer β the minimum number of keys that Vitaly needs to buy to surely get from room one to room n.
Examples
Input
3
aAbB
Output
0
Input
4
aBaCaB
Output
3
Input
5
xYyXzZaZ
Output
2
Submitted Solution:
```
n = int(input())
s = input()
d = {}
res = 0
for x in s:
if x.islower():
d[x] = d.get(x, 0) + 1
else:
if d.get(x.lower(), 0) > 0:
d[x.lower()] -= 1
else:
res += 1
print(res)
```
Yes
| 105,665 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
After a hard day Vitaly got very hungry and he wants to eat his favorite potato pie. But it's not that simple. Vitaly is in the first room of the house with n room located in a line and numbered starting from one from left to right. You can go from the first room to the second room, from the second room to the third room and so on β you can go from the (n - 1)-th room to the n-th room. Thus, you can go to room x only from room x - 1.
The potato pie is located in the n-th room and Vitaly needs to go there.
Each pair of consecutive rooms has a door between them. In order to go to room x from room x - 1, you need to open the door between the rooms with the corresponding key.
In total the house has several types of doors (represented by uppercase Latin letters) and several types of keys (represented by lowercase Latin letters). The key of type t can open the door of type T if and only if t and T are the same letter, written in different cases. For example, key f can open door F.
Each of the first n - 1 rooms contains exactly one key of some type that Vitaly can use to get to next rooms. Once the door is open with some key, Vitaly won't get the key from the keyhole but he will immediately run into the next room. In other words, each key can open no more than one door.
Vitaly realizes that he may end up in some room without the key that opens the door to the next room. Before the start his run for the potato pie Vitaly can buy any number of keys of any type that is guaranteed to get to room n.
Given the plan of the house, Vitaly wants to know what is the minimum number of keys he needs to buy to surely get to the room n, which has a delicious potato pie. Write a program that will help Vitaly find out this number.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 105) β the number of rooms in the house.
The second line of the input contains string s of length 2Β·n - 2. Let's number the elements of the string from left to right, starting from one.
The odd positions in the given string s contain lowercase Latin letters β the types of the keys that lie in the corresponding rooms. Thus, each odd position i of the given string s contains a lowercase Latin letter β the type of the key that lies in room number (i + 1) / 2.
The even positions in the given string contain uppercase Latin letters β the types of doors between the rooms. Thus, each even position i of the given string s contains an uppercase letter β the type of the door that leads from room i / 2 to room i / 2 + 1.
Output
Print the only integer β the minimum number of keys that Vitaly needs to buy to surely get from room one to room n.
Examples
Input
3
aAbB
Output
0
Input
4
aBaCaB
Output
3
Input
5
xYyXzZaZ
Output
2
Submitted Solution:
```
n, s = int(input()), input()
a = [0] * 26
ans = 0
for i in range(len(s)):
if i & 1:
if a[ord(s[i]) - ord('A')] == 0:
a[ord(s[i]) - ord('A')] += 1
ans += 1
a[ord(s[i]) - ord('A')] -= 1
else:
a[ord(s[i]) - ord('a')] += 1
print(ans)
```
Yes
| 105,666 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
After a hard day Vitaly got very hungry and he wants to eat his favorite potato pie. But it's not that simple. Vitaly is in the first room of the house with n room located in a line and numbered starting from one from left to right. You can go from the first room to the second room, from the second room to the third room and so on β you can go from the (n - 1)-th room to the n-th room. Thus, you can go to room x only from room x - 1.
The potato pie is located in the n-th room and Vitaly needs to go there.
Each pair of consecutive rooms has a door between them. In order to go to room x from room x - 1, you need to open the door between the rooms with the corresponding key.
In total the house has several types of doors (represented by uppercase Latin letters) and several types of keys (represented by lowercase Latin letters). The key of type t can open the door of type T if and only if t and T are the same letter, written in different cases. For example, key f can open door F.
Each of the first n - 1 rooms contains exactly one key of some type that Vitaly can use to get to next rooms. Once the door is open with some key, Vitaly won't get the key from the keyhole but he will immediately run into the next room. In other words, each key can open no more than one door.
Vitaly realizes that he may end up in some room without the key that opens the door to the next room. Before the start his run for the potato pie Vitaly can buy any number of keys of any type that is guaranteed to get to room n.
Given the plan of the house, Vitaly wants to know what is the minimum number of keys he needs to buy to surely get to the room n, which has a delicious potato pie. Write a program that will help Vitaly find out this number.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 105) β the number of rooms in the house.
The second line of the input contains string s of length 2Β·n - 2. Let's number the elements of the string from left to right, starting from one.
The odd positions in the given string s contain lowercase Latin letters β the types of the keys that lie in the corresponding rooms. Thus, each odd position i of the given string s contains a lowercase Latin letter β the type of the key that lies in room number (i + 1) / 2.
The even positions in the given string contain uppercase Latin letters β the types of doors between the rooms. Thus, each even position i of the given string s contains an uppercase letter β the type of the door that leads from room i / 2 to room i / 2 + 1.
Output
Print the only integer β the minimum number of keys that Vitaly needs to buy to surely get from room one to room n.
Examples
Input
3
aAbB
Output
0
Input
4
aBaCaB
Output
3
Input
5
xYyXzZaZ
Output
2
Submitted Solution:
```
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,copy,functools
import random
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(): return [list(map(int, l.split())) for l in sys.stdin.readlines()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def pe(s): return print(str(s), file=sys.stderr)
def main():
n = I()
s = S()
r = 0
d = collections.defaultdict(int)
for i in range(n-1):
t = s[i*2]
u = chr(ord(s[i*2+1]) - ord('A') + ord('a'))
d[t] += 1
if d[u] > 0:
d[u] -= 1
else:
r += 1
return r
print(main())
```
Yes
| 105,667 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
After a hard day Vitaly got very hungry and he wants to eat his favorite potato pie. But it's not that simple. Vitaly is in the first room of the house with n room located in a line and numbered starting from one from left to right. You can go from the first room to the second room, from the second room to the third room and so on β you can go from the (n - 1)-th room to the n-th room. Thus, you can go to room x only from room x - 1.
The potato pie is located in the n-th room and Vitaly needs to go there.
Each pair of consecutive rooms has a door between them. In order to go to room x from room x - 1, you need to open the door between the rooms with the corresponding key.
In total the house has several types of doors (represented by uppercase Latin letters) and several types of keys (represented by lowercase Latin letters). The key of type t can open the door of type T if and only if t and T are the same letter, written in different cases. For example, key f can open door F.
Each of the first n - 1 rooms contains exactly one key of some type that Vitaly can use to get to next rooms. Once the door is open with some key, Vitaly won't get the key from the keyhole but he will immediately run into the next room. In other words, each key can open no more than one door.
Vitaly realizes that he may end up in some room without the key that opens the door to the next room. Before the start his run for the potato pie Vitaly can buy any number of keys of any type that is guaranteed to get to room n.
Given the plan of the house, Vitaly wants to know what is the minimum number of keys he needs to buy to surely get to the room n, which has a delicious potato pie. Write a program that will help Vitaly find out this number.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 105) β the number of rooms in the house.
The second line of the input contains string s of length 2Β·n - 2. Let's number the elements of the string from left to right, starting from one.
The odd positions in the given string s contain lowercase Latin letters β the types of the keys that lie in the corresponding rooms. Thus, each odd position i of the given string s contains a lowercase Latin letter β the type of the key that lies in room number (i + 1) / 2.
The even positions in the given string contain uppercase Latin letters β the types of doors between the rooms. Thus, each even position i of the given string s contains an uppercase letter β the type of the door that leads from room i / 2 to room i / 2 + 1.
Output
Print the only integer β the minimum number of keys that Vitaly needs to buy to surely get from room one to room n.
Examples
Input
3
aAbB
Output
0
Input
4
aBaCaB
Output
3
Input
5
xYyXzZaZ
Output
2
Submitted Solution:
```
n=int(input("enter no of rooms\n"))
string=input("enter string\n")
listkeys=[0]*26
count=0
q=2*n-2
#ans=ord(string[0])
#print(ans)
for i in range(0,q):
if(i%2==0):
#print(string[0])
k=ord(string[i])
#print(k)
k2=k-97
listkeys[k2]=listkeys[k2]+1
else :
k3=ord(string[i])
k4=k3+32
#print(k4-97)
if(listkeys[k4-97]>=1):
listkeys[k4-97]=listkeys[k4-97]-1
else :
count=count+1
print(count)
```
No
| 105,668 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
After a hard day Vitaly got very hungry and he wants to eat his favorite potato pie. But it's not that simple. Vitaly is in the first room of the house with n room located in a line and numbered starting from one from left to right. You can go from the first room to the second room, from the second room to the third room and so on β you can go from the (n - 1)-th room to the n-th room. Thus, you can go to room x only from room x - 1.
The potato pie is located in the n-th room and Vitaly needs to go there.
Each pair of consecutive rooms has a door between them. In order to go to room x from room x - 1, you need to open the door between the rooms with the corresponding key.
In total the house has several types of doors (represented by uppercase Latin letters) and several types of keys (represented by lowercase Latin letters). The key of type t can open the door of type T if and only if t and T are the same letter, written in different cases. For example, key f can open door F.
Each of the first n - 1 rooms contains exactly one key of some type that Vitaly can use to get to next rooms. Once the door is open with some key, Vitaly won't get the key from the keyhole but he will immediately run into the next room. In other words, each key can open no more than one door.
Vitaly realizes that he may end up in some room without the key that opens the door to the next room. Before the start his run for the potato pie Vitaly can buy any number of keys of any type that is guaranteed to get to room n.
Given the plan of the house, Vitaly wants to know what is the minimum number of keys he needs to buy to surely get to the room n, which has a delicious potato pie. Write a program that will help Vitaly find out this number.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 105) β the number of rooms in the house.
The second line of the input contains string s of length 2Β·n - 2. Let's number the elements of the string from left to right, starting from one.
The odd positions in the given string s contain lowercase Latin letters β the types of the keys that lie in the corresponding rooms. Thus, each odd position i of the given string s contains a lowercase Latin letter β the type of the key that lies in room number (i + 1) / 2.
The even positions in the given string contain uppercase Latin letters β the types of doors between the rooms. Thus, each even position i of the given string s contains an uppercase letter β the type of the door that leads from room i / 2 to room i / 2 + 1.
Output
Print the only integer β the minimum number of keys that Vitaly needs to buy to surely get from room one to room n.
Examples
Input
3
aAbB
Output
0
Input
4
aBaCaB
Output
3
Input
5
xYyXzZaZ
Output
2
Submitted Solution:
```
n = int(input())
seq = input()
ans = 0
seen = set()
for e in seq:
if e.islower():
seen.add(e)
else:
if e.lower() not in seen:
ans += 1
else:
seen.discard(e.lower())
print(ans)
```
No
| 105,669 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
After a hard day Vitaly got very hungry and he wants to eat his favorite potato pie. But it's not that simple. Vitaly is in the first room of the house with n room located in a line and numbered starting from one from left to right. You can go from the first room to the second room, from the second room to the third room and so on β you can go from the (n - 1)-th room to the n-th room. Thus, you can go to room x only from room x - 1.
The potato pie is located in the n-th room and Vitaly needs to go there.
Each pair of consecutive rooms has a door between them. In order to go to room x from room x - 1, you need to open the door between the rooms with the corresponding key.
In total the house has several types of doors (represented by uppercase Latin letters) and several types of keys (represented by lowercase Latin letters). The key of type t can open the door of type T if and only if t and T are the same letter, written in different cases. For example, key f can open door F.
Each of the first n - 1 rooms contains exactly one key of some type that Vitaly can use to get to next rooms. Once the door is open with some key, Vitaly won't get the key from the keyhole but he will immediately run into the next room. In other words, each key can open no more than one door.
Vitaly realizes that he may end up in some room without the key that opens the door to the next room. Before the start his run for the potato pie Vitaly can buy any number of keys of any type that is guaranteed to get to room n.
Given the plan of the house, Vitaly wants to know what is the minimum number of keys he needs to buy to surely get to the room n, which has a delicious potato pie. Write a program that will help Vitaly find out this number.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 105) β the number of rooms in the house.
The second line of the input contains string s of length 2Β·n - 2. Let's number the elements of the string from left to right, starting from one.
The odd positions in the given string s contain lowercase Latin letters β the types of the keys that lie in the corresponding rooms. Thus, each odd position i of the given string s contains a lowercase Latin letter β the type of the key that lies in room number (i + 1) / 2.
The even positions in the given string contain uppercase Latin letters β the types of doors between the rooms. Thus, each even position i of the given string s contains an uppercase letter β the type of the door that leads from room i / 2 to room i / 2 + 1.
Output
Print the only integer β the minimum number of keys that Vitaly needs to buy to surely get from room one to room n.
Examples
Input
3
aAbB
Output
0
Input
4
aBaCaB
Output
3
Input
5
xYyXzZaZ
Output
2
Submitted Solution:
```
input()
t = input()
keys = t[0::2]
rooms = t[1::2].lower()
currentKeys = set()
count = 0
for k,r in zip(keys, rooms):
currentKeys.add(k)
if r in currentKeys: currentKeys.remove(r)
else:
count += 1
print (count)
```
No
| 105,670 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
After a hard day Vitaly got very hungry and he wants to eat his favorite potato pie. But it's not that simple. Vitaly is in the first room of the house with n room located in a line and numbered starting from one from left to right. You can go from the first room to the second room, from the second room to the third room and so on β you can go from the (n - 1)-th room to the n-th room. Thus, you can go to room x only from room x - 1.
The potato pie is located in the n-th room and Vitaly needs to go there.
Each pair of consecutive rooms has a door between them. In order to go to room x from room x - 1, you need to open the door between the rooms with the corresponding key.
In total the house has several types of doors (represented by uppercase Latin letters) and several types of keys (represented by lowercase Latin letters). The key of type t can open the door of type T if and only if t and T are the same letter, written in different cases. For example, key f can open door F.
Each of the first n - 1 rooms contains exactly one key of some type that Vitaly can use to get to next rooms. Once the door is open with some key, Vitaly won't get the key from the keyhole but he will immediately run into the next room. In other words, each key can open no more than one door.
Vitaly realizes that he may end up in some room without the key that opens the door to the next room. Before the start his run for the potato pie Vitaly can buy any number of keys of any type that is guaranteed to get to room n.
Given the plan of the house, Vitaly wants to know what is the minimum number of keys he needs to buy to surely get to the room n, which has a delicious potato pie. Write a program that will help Vitaly find out this number.
Input
The first line of the input contains a positive integer n (2 β€ n β€ 105) β the number of rooms in the house.
The second line of the input contains string s of length 2Β·n - 2. Let's number the elements of the string from left to right, starting from one.
The odd positions in the given string s contain lowercase Latin letters β the types of the keys that lie in the corresponding rooms. Thus, each odd position i of the given string s contains a lowercase Latin letter β the type of the key that lies in room number (i + 1) / 2.
The even positions in the given string contain uppercase Latin letters β the types of doors between the rooms. Thus, each even position i of the given string s contains an uppercase letter β the type of the door that leads from room i / 2 to room i / 2 + 1.
Output
Print the only integer β the minimum number of keys that Vitaly needs to buy to surely get from room one to room n.
Examples
Input
3
aAbB
Output
0
Input
4
aBaCaB
Output
3
Input
5
xYyXzZaZ
Output
2
Submitted Solution:
```
n=int(input().strip())
l=input().strip()
result=0
d={}
for i in range(0,(n-1)*2,2):
if(l[i]==l[i+1].lower()):
continue
elif(d.get(l[i+1].lower(),0)):
d[l[i+1].lower()]-=1
else:
result+=1
d[l[i]]=1
print(result)
```
No
| 105,671 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.
A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.
Find the number of ways to choose a problemset for the contest.
Input
The first line contains four integers n, l, r, x (1 β€ n β€ 15, 1 β€ l β€ r β€ 109, 1 β€ x β€ 106) β the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 106) β the difficulty of each problem.
Output
Print the number of ways to choose a suitable problemset for the contest.
Examples
Input
3 5 6 1
1 2 3
Output
2
Input
4 40 50 10
10 20 30 25
Output
2
Input
5 25 35 10
10 10 20 10 20
Output
6
Note
In the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.
In the second example, two sets of problems are suitable β the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.
In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable.
Tags: bitmasks, brute force
Correct Solution:
```
n,l,r,x=map(int,input().split())
num=list(map(int,input().split()))
ans=0
for i in range(2**n):
st=bin(i)[2:]
st='0'*(n-len(st))+st
if st.count('1')>=2:
pt=[]
for i in range(len(st)):
if st[i]=='1':
pt.append(num[i])
if sum(pt)<=r and sum(pt)>=l and max(pt)-min(pt)>=x:
ans+=1
print(ans)
```
| 105,672 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.
A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.
Find the number of ways to choose a problemset for the contest.
Input
The first line contains four integers n, l, r, x (1 β€ n β€ 15, 1 β€ l β€ r β€ 109, 1 β€ x β€ 106) β the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 106) β the difficulty of each problem.
Output
Print the number of ways to choose a suitable problemset for the contest.
Examples
Input
3 5 6 1
1 2 3
Output
2
Input
4 40 50 10
10 20 30 25
Output
2
Input
5 25 35 10
10 10 20 10 20
Output
6
Note
In the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.
In the second example, two sets of problems are suitable β the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.
In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable.
Tags: bitmasks, brute force
Correct Solution:
```
import itertools
n,l,x1,r = map(int,input().split())
li = [int(i) for i in input().split()]
a =[]
for i in range(1,n+1):
x = itertools.combinations(li,i)
a+=x
count = 0
for j in a:
if(sum(list(j))<=x1 and sum(list(j))>=l):
if(max(j)-min(j)>=r):
count+=1
print(count)
```
| 105,673 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.
A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.
Find the number of ways to choose a problemset for the contest.
Input
The first line contains four integers n, l, r, x (1 β€ n β€ 15, 1 β€ l β€ r β€ 109, 1 β€ x β€ 106) β the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 106) β the difficulty of each problem.
Output
Print the number of ways to choose a suitable problemset for the contest.
Examples
Input
3 5 6 1
1 2 3
Output
2
Input
4 40 50 10
10 20 30 25
Output
2
Input
5 25 35 10
10 10 20 10 20
Output
6
Note
In the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.
In the second example, two sets of problems are suitable β the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.
In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable.
Tags: bitmasks, brute force
Correct Solution:
```
a = []
def fn(x,n,l,r,k) :
sum = 0
v = []
for j in range(n) :
if (1<<j)&x :
v.append(int(a[j]))
sum+=int(a[j])
if len(v)<2 :
return 0
else : return bool(v[len(v)-1]-v[0]>=k and sum >= l and sum <= r)
n ,l,r,k = input().split()
b = input().split()
for i in b :
a.append(int(i))
a.sort()
ans = 0
for i in range(1<<int(n)) :
ans = ans + int(fn(i,int(n),int(l),int(r),int(k)))
print(ans)
```
| 105,674 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.
A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.
Find the number of ways to choose a problemset for the contest.
Input
The first line contains four integers n, l, r, x (1 β€ n β€ 15, 1 β€ l β€ r β€ 109, 1 β€ x β€ 106) β the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 106) β the difficulty of each problem.
Output
Print the number of ways to choose a suitable problemset for the contest.
Examples
Input
3 5 6 1
1 2 3
Output
2
Input
4 40 50 10
10 20 30 25
Output
2
Input
5 25 35 10
10 10 20 10 20
Output
6
Note
In the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.
In the second example, two sets of problems are suitable β the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.
In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable.
Tags: bitmasks, brute force
Correct Solution:
```
import itertools
q=0
n, l, r, x=map(int,input().split())
c=list(map(int,input().split()))
for j in range(2,n+1):
for i in itertools.combinations(c,j):
if l<=sum(i)<=r and max(i)-min(i)>=x:
q+=1
print(q)
```
| 105,675 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.
A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.
Find the number of ways to choose a problemset for the contest.
Input
The first line contains four integers n, l, r, x (1 β€ n β€ 15, 1 β€ l β€ r β€ 109, 1 β€ x β€ 106) β the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 106) β the difficulty of each problem.
Output
Print the number of ways to choose a suitable problemset for the contest.
Examples
Input
3 5 6 1
1 2 3
Output
2
Input
4 40 50 10
10 20 30 25
Output
2
Input
5 25 35 10
10 10 20 10 20
Output
6
Note
In the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.
In the second example, two sets of problems are suitable β the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.
In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable.
Tags: bitmasks, brute force
Correct Solution:
```
# Description of the problem can be found at http://codeforces.com/problemset/problem/550/B
def b_f(l_v, c_v, c_i, l, h, l_p, h_p, x):
if c_i == len(l_v):
return 0
else:
n_l = l_v[c_i] if not l_p else min(l_v[c_i], l_p)
n_h = l_v[c_i] if not l_p else max(l_v[c_i], h_p)
return (1 if c_v + l_v[c_i] >= l and
c_v + l_v[c_i] <= h and
n_h - n_l >= x else 0) + (
b_f(l_v, c_v, c_i + 1, l, h, l_p, h_p, x) +
b_f(l_v, c_v + l_v[c_i], c_i + 1, l, h, n_l, n_h, x))
n, l, r, x = map(int, input().split())
l_v = list(map(int, input().split()))
print(b_f(l_v, 0, 0, l, r, None, None, x))
```
| 105,676 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.
A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.
Find the number of ways to choose a problemset for the contest.
Input
The first line contains four integers n, l, r, x (1 β€ n β€ 15, 1 β€ l β€ r β€ 109, 1 β€ x β€ 106) β the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 106) β the difficulty of each problem.
Output
Print the number of ways to choose a suitable problemset for the contest.
Examples
Input
3 5 6 1
1 2 3
Output
2
Input
4 40 50 10
10 20 30 25
Output
2
Input
5 25 35 10
10 10 20 10 20
Output
6
Note
In the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.
In the second example, two sets of problems are suitable β the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.
In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable.
Tags: bitmasks, brute force
Correct Solution:
```
IL = lambda: list(map(int, input().split()))
IS = lambda: input().split()
I = lambda: int(input())
S = lambda: input()
n, l, r, x = IL()
cArr = sorted(IL())
ans = 0
for i in range(1, 2**n):
csub = [cArr[j] for j in range(n) if i & 2**j]
if l <= sum(csub) <= r and csub[-1] - csub[0] >= x:
ans += 1
print(ans)
```
| 105,677 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.
A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.
Find the number of ways to choose a problemset for the contest.
Input
The first line contains four integers n, l, r, x (1 β€ n β€ 15, 1 β€ l β€ r β€ 109, 1 β€ x β€ 106) β the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 106) β the difficulty of each problem.
Output
Print the number of ways to choose a suitable problemset for the contest.
Examples
Input
3 5 6 1
1 2 3
Output
2
Input
4 40 50 10
10 20 30 25
Output
2
Input
5 25 35 10
10 10 20 10 20
Output
6
Note
In the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.
In the second example, two sets of problems are suitable β the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.
In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable.
Tags: bitmasks, brute force
Correct Solution:
```
n, l, r, x = map(int, input().split())
c = list(map(int, input().split()))
ans = 0
for i in range(2 ** n):
mask = bin(i)[2:].zfill(n)
temp = [c[j] for j in range(n) if int(mask[j])]
ans += (l <= sum(temp) <= r) and ((max(temp) - min(temp)) >= x)
print(ans)
```
| 105,678 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.
A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.
Find the number of ways to choose a problemset for the contest.
Input
The first line contains four integers n, l, r, x (1 β€ n β€ 15, 1 β€ l β€ r β€ 109, 1 β€ x β€ 106) β the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 106) β the difficulty of each problem.
Output
Print the number of ways to choose a suitable problemset for the contest.
Examples
Input
3 5 6 1
1 2 3
Output
2
Input
4 40 50 10
10 20 30 25
Output
2
Input
5 25 35 10
10 10 20 10 20
Output
6
Note
In the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.
In the second example, two sets of problems are suitable β the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.
In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable.
Tags: bitmasks, brute force
Correct Solution:
```
n, l, r, x = map(int, input().split())
arr = list(map(int, input().split()))
answer = 0
for i in range(2 ** n):
arr1 = []
for j in range(n):
if (i // 2 ** j) % 2 == 1:
arr1.append(arr[j])
if len(arr1) >= 2 and l <= sum(arr1) <= r and max(arr1) - min(arr1) >= x:
answer += 1
print(answer)
```
| 105,679 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.
A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.
Find the number of ways to choose a problemset for the contest.
Input
The first line contains four integers n, l, r, x (1 β€ n β€ 15, 1 β€ l β€ r β€ 109, 1 β€ x β€ 106) β the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 106) β the difficulty of each problem.
Output
Print the number of ways to choose a suitable problemset for the contest.
Examples
Input
3 5 6 1
1 2 3
Output
2
Input
4 40 50 10
10 20 30 25
Output
2
Input
5 25 35 10
10 10 20 10 20
Output
6
Note
In the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.
In the second example, two sets of problems are suitable β the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.
In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable.
Submitted Solution:
```
"""
Brandt Smith, Lemuel Gorion and Peter Haddad
codeforces.com
Problem 12455
"""
import sys
def set(mask, pos):
return mask | (1 << pos)
def isOn(mask, pos):
return mask & ( 1 << pos) > 0
n, l, r, x = map(int, input().split(' '))
dif = list(map(int, input().split(' ')))
count, mask = 0, 0
while mask <= 2**n:
summ, bit = [], 0
while bit < n:
if isOn(mask, bit):
summ.append(dif[bit])
bit += 1
if sum(summ) <= r and sum(summ) >= l and max(summ) - min(summ) >= x:
count += 1
mask += 1
print(count)
```
Yes
| 105,680 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.
A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.
Find the number of ways to choose a problemset for the contest.
Input
The first line contains four integers n, l, r, x (1 β€ n β€ 15, 1 β€ l β€ r β€ 109, 1 β€ x β€ 106) β the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 106) β the difficulty of each problem.
Output
Print the number of ways to choose a suitable problemset for the contest.
Examples
Input
3 5 6 1
1 2 3
Output
2
Input
4 40 50 10
10 20 30 25
Output
2
Input
5 25 35 10
10 10 20 10 20
Output
6
Note
In the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.
In the second example, two sets of problems are suitable β the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.
In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable.
Submitted Solution:
```
def s():
[n,l,r,x] = list(map(int,input().split(' ')))
l -= 1
r += 1
a = list(map(int,input().split(' ')))
s = 0
for i in range(1, 1<<n):
ind = 0
k = []
while i:
if i & 1:
k.append(a[ind])
ind += 1
i >>= 1
if max(k)-min(k) >= x and l < sum(k) < r:
s += 1
print(s)
s()
```
Yes
| 105,681 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.
A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.
Find the number of ways to choose a problemset for the contest.
Input
The first line contains four integers n, l, r, x (1 β€ n β€ 15, 1 β€ l β€ r β€ 109, 1 β€ x β€ 106) β the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 106) β the difficulty of each problem.
Output
Print the number of ways to choose a suitable problemset for the contest.
Examples
Input
3 5 6 1
1 2 3
Output
2
Input
4 40 50 10
10 20 30 25
Output
2
Input
5 25 35 10
10 10 20 10 20
Output
6
Note
In the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.
In the second example, two sets of problems are suitable β the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.
In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable.
Submitted Solution:
```
# Program to print all combination
# of size r in an array of size n
# The main function that prints
# all combinations of size r in
# arr[] of size n. This function
# mainly uses combinationUtil()
ans=0
n, l, w, x = map(int,input().split())
def printCombination(arr, n, r):
# A temporary array to
# store all combination
# one by one
data = [0]*r;
# Print all combination
# using temprary array 'data[]'
combinationUtil(arr, data, 0, n - 1, 0,r );
# arr[] ---> Input Array
# data[] ---> Temporary array to
# store current combination
# start & end ---> Staring and Ending
# indexes in arr[]
# index ---> Current index in data[]
# r ---> Size of a combination
# to be printed
def combinationUtil(arr, data, start,
end, index, r):
# Current combination is ready
# to be printed, print it
if (index == r):
# print('data=',data)
# print('l w ',l,w)
if l<=sum(data)<=w and (max(data)-min(data))>=x:
# for j in range(r):
# print(data[j], end = " ");
# print();
global ans
ans+=1
return;
# replace index with all possible elements.
#The condition "end-i+1 >= r-index"
# makes sure that including one element at index will make a combination
# with remaining elements at remaining positions
i = start;
while(i <= end and end - i + 1 >= r - index):
data[index] = arr[i];
combinationUtil(arr, data, i + 1,
end, index + 1, r);
i += 1;
# Driver Code
arr=list(map(int,input().split()))
#arr = [1,2,3,4,5];
for r in range(2,n+1):
#r = 3;
n = len(arr);
printCombination(arr, n, r);
# This code is contributed by mits
print(ans)
```
Yes
| 105,682 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.
A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.
Find the number of ways to choose a problemset for the contest.
Input
The first line contains four integers n, l, r, x (1 β€ n β€ 15, 1 β€ l β€ r β€ 109, 1 β€ x β€ 106) β the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 106) β the difficulty of each problem.
Output
Print the number of ways to choose a suitable problemset for the contest.
Examples
Input
3 5 6 1
1 2 3
Output
2
Input
4 40 50 10
10 20 30 25
Output
2
Input
5 25 35 10
10 10 20 10 20
Output
6
Note
In the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.
In the second example, two sets of problems are suitable β the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.
In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable.
Submitted Solution:
```
def check(j):
if sum(j)>=l and sum(j)<=r and (max(j)-min(j))>=x:
return 1
return 0
from itertools import combinations
n,l,r,x=list(map(int,input().split()))
c=list(map(int,input().rstrip().split()))
count=0
for i in range(2,n+1):
a=list(combinations(c,i))
for j in a:
if check(j):
count+=1
print(count)
```
Yes
| 105,683 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.
A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.
Find the number of ways to choose a problemset for the contest.
Input
The first line contains four integers n, l, r, x (1 β€ n β€ 15, 1 β€ l β€ r β€ 109, 1 β€ x β€ 106) β the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 106) β the difficulty of each problem.
Output
Print the number of ways to choose a suitable problemset for the contest.
Examples
Input
3 5 6 1
1 2 3
Output
2
Input
4 40 50 10
10 20 30 25
Output
2
Input
5 25 35 10
10 10 20 10 20
Output
6
Note
In the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.
In the second example, two sets of problems are suitable β the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.
In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable.
Submitted Solution:
```
n , l , r , x = map(int,input().split(' '))
list_num = list(map(int,input().split(' ')))
ans = 0
for m in range((1 << n)): # 2**n
mn = -9223372036854775807 # like integer min
mx = 9223372036854775807
count = 0
sum = 0
for i in range(n):
if m&(1<<i) != 0:
count +=1
sum += list_num[i]
mn = min(mn , list_num[i])
mx = min(mx , list_num[i])
if mx - mn >= x and sum >= l and sum <=r and count>= 2:
ans +=1
print(ans)
```
No
| 105,684 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.
A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.
Find the number of ways to choose a problemset for the contest.
Input
The first line contains four integers n, l, r, x (1 β€ n β€ 15, 1 β€ l β€ r β€ 109, 1 β€ x β€ 106) β the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 106) β the difficulty of each problem.
Output
Print the number of ways to choose a suitable problemset for the contest.
Examples
Input
3 5 6 1
1 2 3
Output
2
Input
4 40 50 10
10 20 30 25
Output
2
Input
5 25 35 10
10 10 20 10 20
Output
6
Note
In the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.
In the second example, two sets of problems are suitable β the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.
In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable.
Submitted Solution:
```
from itertools import combinations
n,l,x,r=map(int,input().split())
problems=[int(x) for x in input().split()]
result=0
for i in range(2,n+1):
for comb in combinations(problems, i):
summ = sum(comb)
mini = min(comb)
maxx = max(comb)
if summ>=l or summ<=r and maxx-mini>=x:
result += 1
print(result)
```
No
| 105,685 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.
A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.
Find the number of ways to choose a problemset for the contest.
Input
The first line contains four integers n, l, r, x (1 β€ n β€ 15, 1 β€ l β€ r β€ 109, 1 β€ x β€ 106) β the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 106) β the difficulty of each problem.
Output
Print the number of ways to choose a suitable problemset for the contest.
Examples
Input
3 5 6 1
1 2 3
Output
2
Input
4 40 50 10
10 20 30 25
Output
2
Input
5 25 35 10
10 10 20 10 20
Output
6
Note
In the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.
In the second example, two sets of problems are suitable β the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.
In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable.
Submitted Solution:
```
inp = input()
nums = [int(i) for i in inp.split(" ")]
inp1 = input()
nums1 = [int(j) for j in inp1.split(" ")]
l = nums[1]
r = nums[2]
x = nums[3]
def checker(array, x):
sums = []
used = []
for i in range(len(array)):
for j in range(len(array)):
if i == j:
continue
if [i,j] in used:
continue
if (array[i] - array[j] == x) or (array[j] - array[i] == x):
sums.append(array[i]+array[j])
used.append([i, j])
return sums
sums = checker(nums1, x)
c = 0
for k in sums:
if k >= l and k <= r:
c += 1
print(c)
```
No
| 105,686 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.
A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.
Find the number of ways to choose a problemset for the contest.
Input
The first line contains four integers n, l, r, x (1 β€ n β€ 15, 1 β€ l β€ r β€ 109, 1 β€ x β€ 106) β the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively.
The second line contains n integers c1, c2, ..., cn (1 β€ ci β€ 106) β the difficulty of each problem.
Output
Print the number of ways to choose a suitable problemset for the contest.
Examples
Input
3 5 6 1
1 2 3
Output
2
Input
4 40 50 10
10 20 30 25
Output
2
Input
5 25 35 10
10 10 20 10 20
Output
6
Note
In the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.
In the second example, two sets of problems are suitable β the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.
In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable.
Submitted Solution:
```
import re
s = input()
p1 = re.compile('[A-Z]*AB[A-Z]*BA[A-Z]*')
p2 = re.compile('[A-Z]*BA[A-Z]*AB[A-Z]*')
print('YES' if p1.match(s) or p2.match(s) else 'NO')
```
No
| 105,687 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya and Petya are playing a simple game. Vasya thought of number x between 1 and n, and Petya tries to guess the number.
Petya can ask questions like: "Is the unknown number divisible by number y?".
The game is played by the following rules: first Petya asks all the questions that interest him (also, he can ask no questions), and then Vasya responds to each question with a 'yes' or a 'no'. After receiving all the answers Petya should determine the number that Vasya thought of.
Unfortunately, Petya is not familiar with the number theory. Help him find the minimum number of questions he should ask to make a guaranteed guess of Vasya's number, and the numbers yi, he should ask the questions about.
Input
A single line contains number n (1 β€ n β€ 103).
Output
Print the length of the sequence of questions k (0 β€ k β€ n), followed by k numbers β the questions yi (1 β€ yi β€ n).
If there are several correct sequences of questions of the minimum length, you are allowed to print any of them.
Examples
Input
4
Output
3
2 4 3
Input
6
Output
4
2 4 3 5
Note
The sequence from the answer to the first sample test is actually correct.
If the unknown number is not divisible by one of the sequence numbers, it is equal to 1.
If the unknown number is divisible by 4, it is 4.
If the unknown number is divisible by 3, then the unknown number is 3.
Otherwise, it is equal to 2. Therefore, the sequence of questions allows you to guess the unknown number. It can be shown that there is no correct sequence of questions of length 2 or shorter.
Tags: math, number theory
Correct Solution:
```
def crivo():
n = 10000
pr = [True]*(n+1)
pr[0] = pr[1] = False
for i in range(2,n+1):
if(pr[i] and i*i<=n):
for j in range(i*i,n+1,i):
pr[j] = False
return pr;
l = crivo()
pr = []
for i in range(len(l)):
if(l[i]):
pr.append(i)
n = int(input())
res = []
i = 0
while pr[i]<=n:
k = pr[i]
while k<=n:
res.append(k)
k = k*pr[i]
i+=1
print(len(res))
print(" ".join([str(i) for i in res]))
```
| 105,688 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya and Petya are playing a simple game. Vasya thought of number x between 1 and n, and Petya tries to guess the number.
Petya can ask questions like: "Is the unknown number divisible by number y?".
The game is played by the following rules: first Petya asks all the questions that interest him (also, he can ask no questions), and then Vasya responds to each question with a 'yes' or a 'no'. After receiving all the answers Petya should determine the number that Vasya thought of.
Unfortunately, Petya is not familiar with the number theory. Help him find the minimum number of questions he should ask to make a guaranteed guess of Vasya's number, and the numbers yi, he should ask the questions about.
Input
A single line contains number n (1 β€ n β€ 103).
Output
Print the length of the sequence of questions k (0 β€ k β€ n), followed by k numbers β the questions yi (1 β€ yi β€ n).
If there are several correct sequences of questions of the minimum length, you are allowed to print any of them.
Examples
Input
4
Output
3
2 4 3
Input
6
Output
4
2 4 3 5
Note
The sequence from the answer to the first sample test is actually correct.
If the unknown number is not divisible by one of the sequence numbers, it is equal to 1.
If the unknown number is divisible by 4, it is 4.
If the unknown number is divisible by 3, then the unknown number is 3.
Otherwise, it is equal to 2. Therefore, the sequence of questions allows you to guess the unknown number. It can be shown that there is no correct sequence of questions of length 2 or shorter.
Tags: math, number theory
Correct Solution:
```
def SieveOfEratosthenes(n):
primes = []
prime = [True for i in range(n+1)]
p = 2
while (p * p <= n):
if (prime[p] == True):
for i in range(p * p, n+1, p):
prime[i] = False
p += 1
for p in range(2, n+1):
if prime[p]:
primes.append(p)
return primes
N = int(input())
primes = SieveOfEratosthenes(N)
newList = primes.copy()
for i in primes:
power = 2
while i ** power <= N:
newList.append(i ** power)
power += 1
print(len(newList))
print(*newList)
```
| 105,689 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya and Petya are playing a simple game. Vasya thought of number x between 1 and n, and Petya tries to guess the number.
Petya can ask questions like: "Is the unknown number divisible by number y?".
The game is played by the following rules: first Petya asks all the questions that interest him (also, he can ask no questions), and then Vasya responds to each question with a 'yes' or a 'no'. After receiving all the answers Petya should determine the number that Vasya thought of.
Unfortunately, Petya is not familiar with the number theory. Help him find the minimum number of questions he should ask to make a guaranteed guess of Vasya's number, and the numbers yi, he should ask the questions about.
Input
A single line contains number n (1 β€ n β€ 103).
Output
Print the length of the sequence of questions k (0 β€ k β€ n), followed by k numbers β the questions yi (1 β€ yi β€ n).
If there are several correct sequences of questions of the minimum length, you are allowed to print any of them.
Examples
Input
4
Output
3
2 4 3
Input
6
Output
4
2 4 3 5
Note
The sequence from the answer to the first sample test is actually correct.
If the unknown number is not divisible by one of the sequence numbers, it is equal to 1.
If the unknown number is divisible by 4, it is 4.
If the unknown number is divisible by 3, then the unknown number is 3.
Otherwise, it is equal to 2. Therefore, the sequence of questions allows you to guess the unknown number. It can be shown that there is no correct sequence of questions of length 2 or shorter.
Tags: math, number theory
Correct Solution:
```
n = int(input())
primes = []
is_prime = (n + 1) * [ True ]
is_prime[0] = is_prime[1] = False
pos = 0
while True:
while pos <= n and not is_prime[pos]:
pos += 1
if pos > n:
break
for i in range(2 * pos, n + 1, pos):
is_prime[i] = False
primes.append(pos)
pos += 1
def get_factors(x):
factors = []
for factor in primes:
if x % factor == 0:
factors.append(factor)
return factors
ask = []
for x in range(2, n + 1):
factors = get_factors(x)
if len(factors) == 1:
ask.append(x)
print(len(ask))
print(' '.join(map(str, ask)))
```
| 105,690 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya and Petya are playing a simple game. Vasya thought of number x between 1 and n, and Petya tries to guess the number.
Petya can ask questions like: "Is the unknown number divisible by number y?".
The game is played by the following rules: first Petya asks all the questions that interest him (also, he can ask no questions), and then Vasya responds to each question with a 'yes' or a 'no'. After receiving all the answers Petya should determine the number that Vasya thought of.
Unfortunately, Petya is not familiar with the number theory. Help him find the minimum number of questions he should ask to make a guaranteed guess of Vasya's number, and the numbers yi, he should ask the questions about.
Input
A single line contains number n (1 β€ n β€ 103).
Output
Print the length of the sequence of questions k (0 β€ k β€ n), followed by k numbers β the questions yi (1 β€ yi β€ n).
If there are several correct sequences of questions of the minimum length, you are allowed to print any of them.
Examples
Input
4
Output
3
2 4 3
Input
6
Output
4
2 4 3 5
Note
The sequence from the answer to the first sample test is actually correct.
If the unknown number is not divisible by one of the sequence numbers, it is equal to 1.
If the unknown number is divisible by 4, it is 4.
If the unknown number is divisible by 3, then the unknown number is 3.
Otherwise, it is equal to 2. Therefore, the sequence of questions allows you to guess the unknown number. It can be shown that there is no correct sequence of questions of length 2 or shorter.
Tags: math, number theory
Correct Solution:
```
primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997]
n = int(input())
x = int(n**0.5)
i = 0
a = []
for i in primes:
if i > n:
break
j = 1
while i*j <= n:
a.append(i*j)
j *= i
print(len(a))
for i in a:
print(i, end=' ')
```
| 105,691 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya and Petya are playing a simple game. Vasya thought of number x between 1 and n, and Petya tries to guess the number.
Petya can ask questions like: "Is the unknown number divisible by number y?".
The game is played by the following rules: first Petya asks all the questions that interest him (also, he can ask no questions), and then Vasya responds to each question with a 'yes' or a 'no'. After receiving all the answers Petya should determine the number that Vasya thought of.
Unfortunately, Petya is not familiar with the number theory. Help him find the minimum number of questions he should ask to make a guaranteed guess of Vasya's number, and the numbers yi, he should ask the questions about.
Input
A single line contains number n (1 β€ n β€ 103).
Output
Print the length of the sequence of questions k (0 β€ k β€ n), followed by k numbers β the questions yi (1 β€ yi β€ n).
If there are several correct sequences of questions of the minimum length, you are allowed to print any of them.
Examples
Input
4
Output
3
2 4 3
Input
6
Output
4
2 4 3 5
Note
The sequence from the answer to the first sample test is actually correct.
If the unknown number is not divisible by one of the sequence numbers, it is equal to 1.
If the unknown number is divisible by 4, it is 4.
If the unknown number is divisible by 3, then the unknown number is 3.
Otherwise, it is equal to 2. Therefore, the sequence of questions allows you to guess the unknown number. It can be shown that there is no correct sequence of questions of length 2 or shorter.
Tags: math, number theory
Correct Solution:
```
def gen_prime():
num = [0 for i in range(10**3+1)]
num[2] = 1
num[3] = 1
for i in range(4, 10**3+1):
isprime = True
for j in range(2, int(i**0.5)+1):
if num[j]:
if not i%j:
isprime = False
break
if isprime:
num[i] = 1
prime = []
for i in range(2, 10**3+1):
if num[i]:
prime.append(i)
return prime
import sys
def inp(): return sys.stdin.readline().strip()
t=1
#t=int(inp())
for _ in range(t):
#n,m =map(int, inp().split())
n=int(input())
primes=gen_prime()
ans=[]
a=0
for i in primes:
a=1
ii=i
while(ii<=n):
ans.append(ii)
ii=ii*i
print(len(ans))
print(*ans)
```
| 105,692 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya and Petya are playing a simple game. Vasya thought of number x between 1 and n, and Petya tries to guess the number.
Petya can ask questions like: "Is the unknown number divisible by number y?".
The game is played by the following rules: first Petya asks all the questions that interest him (also, he can ask no questions), and then Vasya responds to each question with a 'yes' or a 'no'. After receiving all the answers Petya should determine the number that Vasya thought of.
Unfortunately, Petya is not familiar with the number theory. Help him find the minimum number of questions he should ask to make a guaranteed guess of Vasya's number, and the numbers yi, he should ask the questions about.
Input
A single line contains number n (1 β€ n β€ 103).
Output
Print the length of the sequence of questions k (0 β€ k β€ n), followed by k numbers β the questions yi (1 β€ yi β€ n).
If there are several correct sequences of questions of the minimum length, you are allowed to print any of them.
Examples
Input
4
Output
3
2 4 3
Input
6
Output
4
2 4 3 5
Note
The sequence from the answer to the first sample test is actually correct.
If the unknown number is not divisible by one of the sequence numbers, it is equal to 1.
If the unknown number is divisible by 4, it is 4.
If the unknown number is divisible by 3, then the unknown number is 3.
Otherwise, it is equal to 2. Therefore, the sequence of questions allows you to guess the unknown number. It can be shown that there is no correct sequence of questions of length 2 or shorter.
Tags: math, number theory
Correct Solution:
```
def gen_prime():
num = [0 for i in range(10**3+1)]
num[2] = 1
num[3] = 1
for i in range(4, 10**3+1):
isprime = True
for j in range(2, int(i**0.5)+1):
if num[j]:
if not i%j:
isprime = False
break
if isprime:
num[i] = 1
prime = []
for i in range(2, 10**3+1):
if num[i]:
prime.append(i)
return prime
n = int(input())
prime = gen_prime()
div = []
i = 0
while i < len(prime):
for j in range(1, 10):
if prime[i]**j > n:
break
div.append(prime[i]**j)
i += 1
print(len(div))
for i in range(len(div)):
print(div[i], end = " ")
print()
```
| 105,693 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya and Petya are playing a simple game. Vasya thought of number x between 1 and n, and Petya tries to guess the number.
Petya can ask questions like: "Is the unknown number divisible by number y?".
The game is played by the following rules: first Petya asks all the questions that interest him (also, he can ask no questions), and then Vasya responds to each question with a 'yes' or a 'no'. After receiving all the answers Petya should determine the number that Vasya thought of.
Unfortunately, Petya is not familiar with the number theory. Help him find the minimum number of questions he should ask to make a guaranteed guess of Vasya's number, and the numbers yi, he should ask the questions about.
Input
A single line contains number n (1 β€ n β€ 103).
Output
Print the length of the sequence of questions k (0 β€ k β€ n), followed by k numbers β the questions yi (1 β€ yi β€ n).
If there are several correct sequences of questions of the minimum length, you are allowed to print any of them.
Examples
Input
4
Output
3
2 4 3
Input
6
Output
4
2 4 3 5
Note
The sequence from the answer to the first sample test is actually correct.
If the unknown number is not divisible by one of the sequence numbers, it is equal to 1.
If the unknown number is divisible by 4, it is 4.
If the unknown number is divisible by 3, then the unknown number is 3.
Otherwise, it is equal to 2. Therefore, the sequence of questions allows you to guess the unknown number. It can be shown that there is no correct sequence of questions of length 2 or shorter.
Tags: math, number theory
Correct Solution:
```
n = int(input())
MAX = 1001
bs = [True] * MAX
primes = []
def sieve():
bs[0] = False
bs[1] = False
for i in range(2, MAX):
if bs[i]:
for j in range(i * i, MAX, i):
bs[j] = False
primes.append(i)
def num_pfs(number):
pfs = set()
for p in primes:
if p * p > number:
break
if number % p == 0:
pfs.add(p)
while number % p == 0:
number //= p
if number != 1:
pfs.add(number)
return len(pfs)
q = []
sieve()
for i in range(2, n + 1):
if bs[i] or num_pfs(i) == 1:
q.append(i)
print(len(q))
print(' '.join(map(str, q)))
```
| 105,694 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya and Petya are playing a simple game. Vasya thought of number x between 1 and n, and Petya tries to guess the number.
Petya can ask questions like: "Is the unknown number divisible by number y?".
The game is played by the following rules: first Petya asks all the questions that interest him (also, he can ask no questions), and then Vasya responds to each question with a 'yes' or a 'no'. After receiving all the answers Petya should determine the number that Vasya thought of.
Unfortunately, Petya is not familiar with the number theory. Help him find the minimum number of questions he should ask to make a guaranteed guess of Vasya's number, and the numbers yi, he should ask the questions about.
Input
A single line contains number n (1 β€ n β€ 103).
Output
Print the length of the sequence of questions k (0 β€ k β€ n), followed by k numbers β the questions yi (1 β€ yi β€ n).
If there are several correct sequences of questions of the minimum length, you are allowed to print any of them.
Examples
Input
4
Output
3
2 4 3
Input
6
Output
4
2 4 3 5
Note
The sequence from the answer to the first sample test is actually correct.
If the unknown number is not divisible by one of the sequence numbers, it is equal to 1.
If the unknown number is divisible by 4, it is 4.
If the unknown number is divisible by 3, then the unknown number is 3.
Otherwise, it is equal to 2. Therefore, the sequence of questions allows you to guess the unknown number. It can be shown that there is no correct sequence of questions of length 2 or shorter.
Tags: math, number theory
Correct Solution:
```
def is_prime(n):
for i in range(2, n):
if ((n % i) == 0):
return 0
break
return 1
n = int(input())
if (n == 1):
print(0)
else:
q = []
for i in range(2, n + 1):
if (is_prime(i)):
q.append(i)
k = i
while(1):
k = k * i
if (k <= n):
q.append(k)
else:
break
print(len(q))
for i in q:
print(i, end=' ')
```
| 105,695 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya and Petya are playing a simple game. Vasya thought of number x between 1 and n, and Petya tries to guess the number.
Petya can ask questions like: "Is the unknown number divisible by number y?".
The game is played by the following rules: first Petya asks all the questions that interest him (also, he can ask no questions), and then Vasya responds to each question with a 'yes' or a 'no'. After receiving all the answers Petya should determine the number that Vasya thought of.
Unfortunately, Petya is not familiar with the number theory. Help him find the minimum number of questions he should ask to make a guaranteed guess of Vasya's number, and the numbers yi, he should ask the questions about.
Input
A single line contains number n (1 β€ n β€ 103).
Output
Print the length of the sequence of questions k (0 β€ k β€ n), followed by k numbers β the questions yi (1 β€ yi β€ n).
If there are several correct sequences of questions of the minimum length, you are allowed to print any of them.
Examples
Input
4
Output
3
2 4 3
Input
6
Output
4
2 4 3 5
Note
The sequence from the answer to the first sample test is actually correct.
If the unknown number is not divisible by one of the sequence numbers, it is equal to 1.
If the unknown number is divisible by 4, it is 4.
If the unknown number is divisible by 3, then the unknown number is 3.
Otherwise, it is equal to 2. Therefore, the sequence of questions allows you to guess the unknown number. It can be shown that there is no correct sequence of questions of length 2 or shorter.
Submitted Solution:
```
from math import sqrt, pow, log, log2, log10, exp
from copy import deepcopy
def read_ints():
return list(map(int, input().split()))
def read_int():
return read_ints()[0]
def read_floats():
return list(map(float, input().split()))
def read_float():
return read_floats()[0]
def one_dim_array(value, n):
return [deepcopy(value) for x in range(n)]
def two_dim_array(value, n, m):
return [[deepcopy(value) for x in range(m)] for x in range(n)]
def is_prime(n):
if n == 2:
return True
if n % 2 == 0:
return False
for i in range(3, int(sqrt(n)) + 1):
if n % i == 0:
return False
return True
def tf_to_yn(b):
return 'YES' if b else 'NO'
n = read_int()
res = []
for x in range(2, n + 1):
if is_prime(x):
e = x
while e <= n:
res.append(e)
e *= x
print(len(res))
print(' '.join(map(str,res)))
```
Yes
| 105,696 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya and Petya are playing a simple game. Vasya thought of number x between 1 and n, and Petya tries to guess the number.
Petya can ask questions like: "Is the unknown number divisible by number y?".
The game is played by the following rules: first Petya asks all the questions that interest him (also, he can ask no questions), and then Vasya responds to each question with a 'yes' or a 'no'. After receiving all the answers Petya should determine the number that Vasya thought of.
Unfortunately, Petya is not familiar with the number theory. Help him find the minimum number of questions he should ask to make a guaranteed guess of Vasya's number, and the numbers yi, he should ask the questions about.
Input
A single line contains number n (1 β€ n β€ 103).
Output
Print the length of the sequence of questions k (0 β€ k β€ n), followed by k numbers β the questions yi (1 β€ yi β€ n).
If there are several correct sequences of questions of the minimum length, you are allowed to print any of them.
Examples
Input
4
Output
3
2 4 3
Input
6
Output
4
2 4 3 5
Note
The sequence from the answer to the first sample test is actually correct.
If the unknown number is not divisible by one of the sequence numbers, it is equal to 1.
If the unknown number is divisible by 4, it is 4.
If the unknown number is divisible by 3, then the unknown number is 3.
Otherwise, it is equal to 2. Therefore, the sequence of questions allows you to guess the unknown number. It can be shown that there is no correct sequence of questions of length 2 or shorter.
Submitted Solution:
```
import math
isprime = [0]*1000010
prime = []
def seive():
isprime[1] = isprime[0] = 1
prime.append(2)
limit = int(math.sqrt(1000010))+2
for i in range(4,1000010,2):
isprime[i] = 1
for i in range(3,1000010,2):
if(not isprime[i]):
prime.append(i)
if(i <= limit):
for j in range(i*i,1000010,i*2):
isprime[j] = 1
seive()
n = int(input())
output_list = []
index = 0
while prime[index]<=n:
p = 1
x = pow(prime[index],p)
while(x<=n):
output_list.append(x)
p+=1
x = pow(prime[index],p)
index+=1
print(len(output_list))
for x in output_list:
print(x,end=" ")
print()
```
Yes
| 105,697 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya and Petya are playing a simple game. Vasya thought of number x between 1 and n, and Petya tries to guess the number.
Petya can ask questions like: "Is the unknown number divisible by number y?".
The game is played by the following rules: first Petya asks all the questions that interest him (also, he can ask no questions), and then Vasya responds to each question with a 'yes' or a 'no'. After receiving all the answers Petya should determine the number that Vasya thought of.
Unfortunately, Petya is not familiar with the number theory. Help him find the minimum number of questions he should ask to make a guaranteed guess of Vasya's number, and the numbers yi, he should ask the questions about.
Input
A single line contains number n (1 β€ n β€ 103).
Output
Print the length of the sequence of questions k (0 β€ k β€ n), followed by k numbers β the questions yi (1 β€ yi β€ n).
If there are several correct sequences of questions of the minimum length, you are allowed to print any of them.
Examples
Input
4
Output
3
2 4 3
Input
6
Output
4
2 4 3 5
Note
The sequence from the answer to the first sample test is actually correct.
If the unknown number is not divisible by one of the sequence numbers, it is equal to 1.
If the unknown number is divisible by 4, it is 4.
If the unknown number is divisible by 3, then the unknown number is 3.
Otherwise, it is equal to 2. Therefore, the sequence of questions allows you to guess the unknown number. It can be shown that there is no correct sequence of questions of length 2 or shorter.
Submitted Solution:
```
n=int(input())
a=[0]*(n+1)
b=[]
for i in range(2,n+1):
if a[i]: continue
ii=1
while ii*i<=n: ii*=i; b+=[ii]
j=i
while j<=n: a[j]=1; j+=i
print(len(b))
print(' '.join(map(str,b)))
```
Yes
| 105,698 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya and Petya are playing a simple game. Vasya thought of number x between 1 and n, and Petya tries to guess the number.
Petya can ask questions like: "Is the unknown number divisible by number y?".
The game is played by the following rules: first Petya asks all the questions that interest him (also, he can ask no questions), and then Vasya responds to each question with a 'yes' or a 'no'. After receiving all the answers Petya should determine the number that Vasya thought of.
Unfortunately, Petya is not familiar with the number theory. Help him find the minimum number of questions he should ask to make a guaranteed guess of Vasya's number, and the numbers yi, he should ask the questions about.
Input
A single line contains number n (1 β€ n β€ 103).
Output
Print the length of the sequence of questions k (0 β€ k β€ n), followed by k numbers β the questions yi (1 β€ yi β€ n).
If there are several correct sequences of questions of the minimum length, you are allowed to print any of them.
Examples
Input
4
Output
3
2 4 3
Input
6
Output
4
2 4 3 5
Note
The sequence from the answer to the first sample test is actually correct.
If the unknown number is not divisible by one of the sequence numbers, it is equal to 1.
If the unknown number is divisible by 4, it is 4.
If the unknown number is divisible by 3, then the unknown number is 3.
Otherwise, it is equal to 2. Therefore, the sequence of questions allows you to guess the unknown number. It can be shown that there is no correct sequence of questions of length 2 or shorter.
Submitted Solution:
```
import math
n = int(input())
m = 1
ans = []
def is_prime(number):
for i in range(2, int(math.sqrt(number))+1):
if number % i == 0:
return False
return True
for el in range(2, n + 1):
if is_prime(el):
candidate = el
while candidate <= n:
ans.append(str(candidate))
candidate *= el
print(len(ans))
print(" ".join(ans))
```
Yes
| 105,699 |
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