text stringlengths 198 433k | conversation_id int64 0 109k |
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Provide tags and a correct Python 3 solution for this coding contest problem.
Polycarpus got an internship in one well-known social network. His test task is to count the number of unique users who have visited a social network during the day. Polycarpus was provided with information on all user requests for this time period. For each query, we know its time... and nothing else, because Polycarpus has already accidentally removed the user IDs corresponding to the requests from the database. Thus, it is now impossible to determine whether any two requests are made by the same person or by different people.
But wait, something is still known, because that day a record was achieved β M simultaneous users online! In addition, Polycarpus believes that if a user made a request at second s, then he was online for T seconds after that, that is, at seconds s, s + 1, s + 2, ..., s + T - 1. So, the user's time online can be calculated as the union of time intervals of the form [s, s + T - 1] over all times s of requests from him.
Guided by these thoughts, Polycarpus wants to assign a user ID to each request so that:
* the number of different users online did not exceed M at any moment,
* at some second the number of distinct users online reached value M,
* the total number of users (the number of distinct identifiers) was as much as possible.
Help Polycarpus cope with the test.
Input
The first line contains three integers n, M and T (1 β€ n, M β€ 20 000, 1 β€ T β€ 86400) β the number of queries, the record number of online users and the time when the user was online after a query was sent. Next n lines contain the times of the queries in the format "hh:mm:ss", where hh are hours, mm are minutes, ss are seconds. The times of the queries follow in the non-decreasing order, some of them can coincide. It is guaranteed that all the times and even all the segments of type [s, s + T - 1] are within one 24-hour range (from 00:00:00 to 23:59:59).
Output
In the first line print number R β the largest possible number of distinct users. The following n lines should contain the user IDs for requests in the same order in which the requests are given in the input. User IDs must be integers from 1 to R. The requests of the same user must correspond to the same identifiers, the requests of distinct users must correspond to distinct identifiers. If there are multiple solutions, print any of them. If there is no solution, print "No solution" (without the quotes).
Examples
Input
4 2 10
17:05:53
17:05:58
17:06:01
22:39:47
Output
3
1
2
2
3
Input
1 2 86400
00:00:00
Output
No solution
Note
Consider the first sample. The user who sent the first request was online from 17:05:53 to 17:06:02, the user who sent the second request was online from 17:05:58 to 17:06:07, the user who sent the third request, was online from 17:06:01 to 17:06:10. Thus, these IDs cannot belong to three distinct users, because in that case all these users would be online, for example, at 17:06:01. That is impossible, because M = 2. That means that some two of these queries belonged to the same user. One of the correct variants is given in the answer to the sample. For it user 1 was online from 17:05:53 to 17:06:02, user 2 β from 17:05:58 to 17:06:10 (he sent the second and third queries), user 3 β from 22:39:47 to 22:39:56.
In the second sample there is only one query. So, only one user visited the network within the 24-hour period and there couldn't be two users online on the network simultaneously. (The time the user spent online is the union of time intervals for requests, so users who didn't send requests could not be online in the network.)
Tags: greedy, two pointers
Correct Solution:
```
def main():
mode="filee"
if mode=="file":f=open("test.txt","r")
get = lambda :[int(x) for x in (f.readline() if mode=="file" else input()).split()]
gets = lambda :[str(x) for x in (f.readline()[:-1] if mode=="file" else input()).split(":")]
[n,m,t]=get()
[a,b]=[[0]*20002,[0]*20002]
if n<m:
print("No solution")
return
for i in range(1,n+1):
g = gets()
a[i] = int(g[-1]) + int(g[1])*60 + int(g[0])*3600
[p,count,sim,ist] = [1,0,0,False]
for i in range(1,n+1):
while p<i and a[i] - t + 1>a[p]:
p+=1
if b[p]!=b[p-1]:
sim = max(sim-1,0)
if a[i]<a[p]+t and sim<m:
[count,sim] = [count+1,sim+1]
if sim==m:
ist=True
b[i] = count
if ist==False:
print("No solution")
return
print(count)
for i in range(1,n+1):
print(b[i],end=' ')
if mode=="file":f.close()
if __name__=="__main__":
main()
```
| 94,800 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Polycarpus got an internship in one well-known social network. His test task is to count the number of unique users who have visited a social network during the day. Polycarpus was provided with information on all user requests for this time period. For each query, we know its time... and nothing else, because Polycarpus has already accidentally removed the user IDs corresponding to the requests from the database. Thus, it is now impossible to determine whether any two requests are made by the same person or by different people.
But wait, something is still known, because that day a record was achieved β M simultaneous users online! In addition, Polycarpus believes that if a user made a request at second s, then he was online for T seconds after that, that is, at seconds s, s + 1, s + 2, ..., s + T - 1. So, the user's time online can be calculated as the union of time intervals of the form [s, s + T - 1] over all times s of requests from him.
Guided by these thoughts, Polycarpus wants to assign a user ID to each request so that:
* the number of different users online did not exceed M at any moment,
* at some second the number of distinct users online reached value M,
* the total number of users (the number of distinct identifiers) was as much as possible.
Help Polycarpus cope with the test.
Input
The first line contains three integers n, M and T (1 β€ n, M β€ 20 000, 1 β€ T β€ 86400) β the number of queries, the record number of online users and the time when the user was online after a query was sent. Next n lines contain the times of the queries in the format "hh:mm:ss", where hh are hours, mm are minutes, ss are seconds. The times of the queries follow in the non-decreasing order, some of them can coincide. It is guaranteed that all the times and even all the segments of type [s, s + T - 1] are within one 24-hour range (from 00:00:00 to 23:59:59).
Output
In the first line print number R β the largest possible number of distinct users. The following n lines should contain the user IDs for requests in the same order in which the requests are given in the input. User IDs must be integers from 1 to R. The requests of the same user must correspond to the same identifiers, the requests of distinct users must correspond to distinct identifiers. If there are multiple solutions, print any of them. If there is no solution, print "No solution" (without the quotes).
Examples
Input
4 2 10
17:05:53
17:05:58
17:06:01
22:39:47
Output
3
1
2
2
3
Input
1 2 86400
00:00:00
Output
No solution
Note
Consider the first sample. The user who sent the first request was online from 17:05:53 to 17:06:02, the user who sent the second request was online from 17:05:58 to 17:06:07, the user who sent the third request, was online from 17:06:01 to 17:06:10. Thus, these IDs cannot belong to three distinct users, because in that case all these users would be online, for example, at 17:06:01. That is impossible, because M = 2. That means that some two of these queries belonged to the same user. One of the correct variants is given in the answer to the sample. For it user 1 was online from 17:05:53 to 17:06:02, user 2 β from 17:05:58 to 17:06:10 (he sent the second and third queries), user 3 β from 22:39:47 to 22:39:56.
In the second sample there is only one query. So, only one user visited the network within the 24-hour period and there couldn't be two users online on the network simultaneously. (The time the user spent online is the union of time intervals for requests, so users who didn't send requests could not be online in the network.)
Tags: greedy, two pointers
Correct Solution:
```
def main():
mode="filee"
if mode=="file":f=open("test.txt","r")
get = lambda :[int(x) for x in (f.readline() if mode=="file" else input()).split()]
gets = lambda :[str(x) for x in (f.readline()[:-1] if mode=="file" else input()).split(":")]
[n,m,t]=get()
a=[0]*20002
b=[0]*20002
if n<m:
print("No solution")
return
for i in range(1,1+n):
g = gets()
a[i] = int(g[-1]) + int(g[1])*60 + int(g[0])*3600
[p,count,sim] = [1,0,0]
is_solution_there=False
for i in range(1,n+1):
while p<i and a[i] - t + 1>a[p]:
p+=1
if b[p]!=b[p-1]:
sim = max(sim-1,0)
if a[i]<a[p]+t and sim<m:
count+=1
sim+=1
if sim==m:
is_solution_there=True
b[i] = count
if is_solution_there==False:
print("No solution")
return
print(count)
for i in range(1,n+1):
print(b[i],end=' ')
if mode=="file":f.close()
if __name__=="__main__":
main()
```
| 94,801 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Polycarpus got an internship in one well-known social network. His test task is to count the number of unique users who have visited a social network during the day. Polycarpus was provided with information on all user requests for this time period. For each query, we know its time... and nothing else, because Polycarpus has already accidentally removed the user IDs corresponding to the requests from the database. Thus, it is now impossible to determine whether any two requests are made by the same person or by different people.
But wait, something is still known, because that day a record was achieved β M simultaneous users online! In addition, Polycarpus believes that if a user made a request at second s, then he was online for T seconds after that, that is, at seconds s, s + 1, s + 2, ..., s + T - 1. So, the user's time online can be calculated as the union of time intervals of the form [s, s + T - 1] over all times s of requests from him.
Guided by these thoughts, Polycarpus wants to assign a user ID to each request so that:
* the number of different users online did not exceed M at any moment,
* at some second the number of distinct users online reached value M,
* the total number of users (the number of distinct identifiers) was as much as possible.
Help Polycarpus cope with the test.
Input
The first line contains three integers n, M and T (1 β€ n, M β€ 20 000, 1 β€ T β€ 86400) β the number of queries, the record number of online users and the time when the user was online after a query was sent. Next n lines contain the times of the queries in the format "hh:mm:ss", where hh are hours, mm are minutes, ss are seconds. The times of the queries follow in the non-decreasing order, some of them can coincide. It is guaranteed that all the times and even all the segments of type [s, s + T - 1] are within one 24-hour range (from 00:00:00 to 23:59:59).
Output
In the first line print number R β the largest possible number of distinct users. The following n lines should contain the user IDs for requests in the same order in which the requests are given in the input. User IDs must be integers from 1 to R. The requests of the same user must correspond to the same identifiers, the requests of distinct users must correspond to distinct identifiers. If there are multiple solutions, print any of them. If there is no solution, print "No solution" (without the quotes).
Examples
Input
4 2 10
17:05:53
17:05:58
17:06:01
22:39:47
Output
3
1
2
2
3
Input
1 2 86400
00:00:00
Output
No solution
Note
Consider the first sample. The user who sent the first request was online from 17:05:53 to 17:06:02, the user who sent the second request was online from 17:05:58 to 17:06:07, the user who sent the third request, was online from 17:06:01 to 17:06:10. Thus, these IDs cannot belong to three distinct users, because in that case all these users would be online, for example, at 17:06:01. That is impossible, because M = 2. That means that some two of these queries belonged to the same user. One of the correct variants is given in the answer to the sample. For it user 1 was online from 17:05:53 to 17:06:02, user 2 β from 17:05:58 to 17:06:10 (he sent the second and third queries), user 3 β from 22:39:47 to 22:39:56.
In the second sample there is only one query. So, only one user visited the network within the 24-hour period and there couldn't be two users online on the network simultaneously. (The time the user spent online is the union of time intervals for requests, so users who didn't send requests could not be online in the network.)
Submitted Solution:
```
def main():
mode="filee"
if mode=="file":f=open("test.txt","r")
get = lambda :[int(x) for x in (f.readline() if mode=="file" else input()).split()]
gets = lambda :[str(x) for x in (f.readline()[:-1] if mode=="file" else input()).split(":")]
[n,m,t]=get()
a=[0]*20002
b=[0]*20002
if n<m:
print("No solution")
return
for i in range(n):
g = gets()
temp = int(g[-1]) + int(g[1])*60 + int(g[0])*3600
a[i] = temp
[p,count,k,sim] = [0,0,0,0]
for i in range(n):
if a[p]<a[i] + t and sim<m:
count+=1
b[k] = count
sim+=1
else:
b[k] = count
p+=1
sim-=1
k+=1
print(count)
for i in range(20002):
if b[i] == 0:
break
print(b[i])
if mode=="file":f.close()
if __name__=="__main__":
main()
```
No
| 94,802 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Polycarpus got an internship in one well-known social network. His test task is to count the number of unique users who have visited a social network during the day. Polycarpus was provided with information on all user requests for this time period. For each query, we know its time... and nothing else, because Polycarpus has already accidentally removed the user IDs corresponding to the requests from the database. Thus, it is now impossible to determine whether any two requests are made by the same person or by different people.
But wait, something is still known, because that day a record was achieved β M simultaneous users online! In addition, Polycarpus believes that if a user made a request at second s, then he was online for T seconds after that, that is, at seconds s, s + 1, s + 2, ..., s + T - 1. So, the user's time online can be calculated as the union of time intervals of the form [s, s + T - 1] over all times s of requests from him.
Guided by these thoughts, Polycarpus wants to assign a user ID to each request so that:
* the number of different users online did not exceed M at any moment,
* at some second the number of distinct users online reached value M,
* the total number of users (the number of distinct identifiers) was as much as possible.
Help Polycarpus cope with the test.
Input
The first line contains three integers n, M and T (1 β€ n, M β€ 20 000, 1 β€ T β€ 86400) β the number of queries, the record number of online users and the time when the user was online after a query was sent. Next n lines contain the times of the queries in the format "hh:mm:ss", where hh are hours, mm are minutes, ss are seconds. The times of the queries follow in the non-decreasing order, some of them can coincide. It is guaranteed that all the times and even all the segments of type [s, s + T - 1] are within one 24-hour range (from 00:00:00 to 23:59:59).
Output
In the first line print number R β the largest possible number of distinct users. The following n lines should contain the user IDs for requests in the same order in which the requests are given in the input. User IDs must be integers from 1 to R. The requests of the same user must correspond to the same identifiers, the requests of distinct users must correspond to distinct identifiers. If there are multiple solutions, print any of them. If there is no solution, print "No solution" (without the quotes).
Examples
Input
4 2 10
17:05:53
17:05:58
17:06:01
22:39:47
Output
3
1
2
2
3
Input
1 2 86400
00:00:00
Output
No solution
Note
Consider the first sample. The user who sent the first request was online from 17:05:53 to 17:06:02, the user who sent the second request was online from 17:05:58 to 17:06:07, the user who sent the third request, was online from 17:06:01 to 17:06:10. Thus, these IDs cannot belong to three distinct users, because in that case all these users would be online, for example, at 17:06:01. That is impossible, because M = 2. That means that some two of these queries belonged to the same user. One of the correct variants is given in the answer to the sample. For it user 1 was online from 17:05:53 to 17:06:02, user 2 β from 17:05:58 to 17:06:10 (he sent the second and third queries), user 3 β from 22:39:47 to 22:39:56.
In the second sample there is only one query. So, only one user visited the network within the 24-hour period and there couldn't be two users online on the network simultaneously. (The time the user spent online is the union of time intervals for requests, so users who didn't send requests could not be online in the network.)
Submitted Solution:
```
def main():
mode="filee"
if mode=="file":f=open("test.txt","r")
get = lambda :[int(x) for x in (f.readline() if mode=="file" else input()).split()]
gets = lambda :[str(x) for x in (f.readline()[:-1] if mode=="file" else input()).split(":")]
[n,m,t]=get()
a=[0]*20002
b=[0]*20002
if n<m:
print("No solution")
return
for i in range(n):
g = gets()
temp = int(g[-1]) + int(g[1])*60 + int(g[0])*3600
a[i] = temp
[p,count,k,sim] = [0,0,0,0]
for i in range(n):
while p<i and a[i] - t + 1>=a[p]:
p+=1
sim = min(sim,m,i-p+1)
#print(p,a[p],a[i],a[i] - a[p],sim,i-p)
if p==i or (a[i] - t +1<a[p] and sim<m):
count+=1
b[k] = count
sim+=1
else:
b[k] = count
k+=1
print(count)
for i in range(20002):
if b[i] == 0:
break
print(b[i])
if mode=="file":f.close()
if __name__=="__main__":
main()
```
No
| 94,803 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Polycarpus got an internship in one well-known social network. His test task is to count the number of unique users who have visited a social network during the day. Polycarpus was provided with information on all user requests for this time period. For each query, we know its time... and nothing else, because Polycarpus has already accidentally removed the user IDs corresponding to the requests from the database. Thus, it is now impossible to determine whether any two requests are made by the same person or by different people.
But wait, something is still known, because that day a record was achieved β M simultaneous users online! In addition, Polycarpus believes that if a user made a request at second s, then he was online for T seconds after that, that is, at seconds s, s + 1, s + 2, ..., s + T - 1. So, the user's time online can be calculated as the union of time intervals of the form [s, s + T - 1] over all times s of requests from him.
Guided by these thoughts, Polycarpus wants to assign a user ID to each request so that:
* the number of different users online did not exceed M at any moment,
* at some second the number of distinct users online reached value M,
* the total number of users (the number of distinct identifiers) was as much as possible.
Help Polycarpus cope with the test.
Input
The first line contains three integers n, M and T (1 β€ n, M β€ 20 000, 1 β€ T β€ 86400) β the number of queries, the record number of online users and the time when the user was online after a query was sent. Next n lines contain the times of the queries in the format "hh:mm:ss", where hh are hours, mm are minutes, ss are seconds. The times of the queries follow in the non-decreasing order, some of them can coincide. It is guaranteed that all the times and even all the segments of type [s, s + T - 1] are within one 24-hour range (from 00:00:00 to 23:59:59).
Output
In the first line print number R β the largest possible number of distinct users. The following n lines should contain the user IDs for requests in the same order in which the requests are given in the input. User IDs must be integers from 1 to R. The requests of the same user must correspond to the same identifiers, the requests of distinct users must correspond to distinct identifiers. If there are multiple solutions, print any of them. If there is no solution, print "No solution" (without the quotes).
Examples
Input
4 2 10
17:05:53
17:05:58
17:06:01
22:39:47
Output
3
1
2
2
3
Input
1 2 86400
00:00:00
Output
No solution
Note
Consider the first sample. The user who sent the first request was online from 17:05:53 to 17:06:02, the user who sent the second request was online from 17:05:58 to 17:06:07, the user who sent the third request, was online from 17:06:01 to 17:06:10. Thus, these IDs cannot belong to three distinct users, because in that case all these users would be online, for example, at 17:06:01. That is impossible, because M = 2. That means that some two of these queries belonged to the same user. One of the correct variants is given in the answer to the sample. For it user 1 was online from 17:05:53 to 17:06:02, user 2 β from 17:05:58 to 17:06:10 (he sent the second and third queries), user 3 β from 22:39:47 to 22:39:56.
In the second sample there is only one query. So, only one user visited the network within the 24-hour period and there couldn't be two users online on the network simultaneously. (The time the user spent online is the union of time intervals for requests, so users who didn't send requests could not be online in the network.)
Submitted Solution:
```
def main():
mode="filee"
if mode=="file":f=open("test.txt","r")
get = lambda :[int(x) for x in (f.readline() if mode=="file" else input()).split()]
gets = lambda :[str(x) for x in (f.readline()[:-1] if mode=="file" else input()).split(":")]
[n,m,t]=get()
a=[0]*20002
b=[0]*20002
if n<m:
print("No solution")
return
for i in range(1,1+n):
g = gets()
temp = int(g[-1]) + int(g[1])*60 + int(g[0])*3600
a[i] = temp
[p,count,k,sim] = [1,0,0,0]
for i in range(1,n+1):
while p<i and a[i] - t + 1>=a[p]:
p+=1
if b[p]!=b[p-1]:
sim = max(sim-1,0)
#print(p,a[p],a[i],a[i] - a[p],sim,i-p)
if p==i or (a[i] - t +1<a[p] and sim<m):
count+=1
b[k] = count
sim+=1
else:
b[k] = count
k+=1
print(count)
for i in range(20002):
if b[i] == 0:
break
print(b[i])
if mode=="file":f.close()
if __name__=="__main__":
main()
```
No
| 94,804 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Polycarpus got an internship in one well-known social network. His test task is to count the number of unique users who have visited a social network during the day. Polycarpus was provided with information on all user requests for this time period. For each query, we know its time... and nothing else, because Polycarpus has already accidentally removed the user IDs corresponding to the requests from the database. Thus, it is now impossible to determine whether any two requests are made by the same person or by different people.
But wait, something is still known, because that day a record was achieved β M simultaneous users online! In addition, Polycarpus believes that if a user made a request at second s, then he was online for T seconds after that, that is, at seconds s, s + 1, s + 2, ..., s + T - 1. So, the user's time online can be calculated as the union of time intervals of the form [s, s + T - 1] over all times s of requests from him.
Guided by these thoughts, Polycarpus wants to assign a user ID to each request so that:
* the number of different users online did not exceed M at any moment,
* at some second the number of distinct users online reached value M,
* the total number of users (the number of distinct identifiers) was as much as possible.
Help Polycarpus cope with the test.
Input
The first line contains three integers n, M and T (1 β€ n, M β€ 20 000, 1 β€ T β€ 86400) β the number of queries, the record number of online users and the time when the user was online after a query was sent. Next n lines contain the times of the queries in the format "hh:mm:ss", where hh are hours, mm are minutes, ss are seconds. The times of the queries follow in the non-decreasing order, some of them can coincide. It is guaranteed that all the times and even all the segments of type [s, s + T - 1] are within one 24-hour range (from 00:00:00 to 23:59:59).
Output
In the first line print number R β the largest possible number of distinct users. The following n lines should contain the user IDs for requests in the same order in which the requests are given in the input. User IDs must be integers from 1 to R. The requests of the same user must correspond to the same identifiers, the requests of distinct users must correspond to distinct identifiers. If there are multiple solutions, print any of them. If there is no solution, print "No solution" (without the quotes).
Examples
Input
4 2 10
17:05:53
17:05:58
17:06:01
22:39:47
Output
3
1
2
2
3
Input
1 2 86400
00:00:00
Output
No solution
Note
Consider the first sample. The user who sent the first request was online from 17:05:53 to 17:06:02, the user who sent the second request was online from 17:05:58 to 17:06:07, the user who sent the third request, was online from 17:06:01 to 17:06:10. Thus, these IDs cannot belong to three distinct users, because in that case all these users would be online, for example, at 17:06:01. That is impossible, because M = 2. That means that some two of these queries belonged to the same user. One of the correct variants is given in the answer to the sample. For it user 1 was online from 17:05:53 to 17:06:02, user 2 β from 17:05:58 to 17:06:10 (he sent the second and third queries), user 3 β from 22:39:47 to 22:39:56.
In the second sample there is only one query. So, only one user visited the network within the 24-hour period and there couldn't be two users online on the network simultaneously. (The time the user spent online is the union of time intervals for requests, so users who didn't send requests could not be online in the network.)
Submitted Solution:
```
def main():
mode="filee"
if mode=="file":f=open("test.txt","r")
get = lambda :[int(x) for x in (f.readline() if mode=="file" else input()).split()]
gets = lambda :[str(x) for x in (f.readline()[:-1] if mode=="file" else input()).split(":")]
[n,m,t]=get()
a=[0]*20002
b=[0]*20002
if n<m:
print("No solution")
return
for i in range(1,1+n):
g = gets()
temp = int(g[-1]) + int(g[1])*60 + int(g[0])*3600
a[i] = temp
#print(a[i])
[p,count,k,sim] = [1,0,1,0]
for i in range(1,n+1):
while p<i and a[i] - t + 1>=a[p]:
p+=1
#print("Dec",end=' ')
if b[p]!=b[p-1]:
#print("yes")
sim = max(sim-1,0)
#print(p,a[p],a[i],a[i] - a[p],sim,i-p)
if a[i]!=82126 and (i==p or (a[i] - t +1<a[p] and sim<m)):
count+=1
b[k] = count
sim+=1
else:
b[k] = count
k+=1
print(count)
for i in range(1,20002):
if b[i] == 0:
break
print(b[i],end=' ')
if mode=="file":f.close()
if __name__=="__main__":
main()
```
No
| 94,805 |
Provide tags and a correct Python 3 solution for this coding contest problem.
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to hi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi β€ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
* Castles are split into blocks β groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
* The partitioning is chosen in such a way that every castle is a part of exactly one block.
* Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
* The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 β€ hi β€ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Examples
Input
3
1 2 3
Output
3
Input
4
2 1 3 2
Output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
<image>
In the second sample the partitioning is: [2, 1][3, 2]
<image>
Tags: sortings
Correct Solution:
```
#------------------------template--------------------------#
import os
import sys
from math import *
from collections import *
from fractions import *
from bisect import *
from heapq import*
from io import BytesIO, IOBase
def vsInput():
sys.stdin = open('input.txt', 'r')
sys.stdout = open('output.txt', 'w')
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
def value():return tuple(map(int,input().split()))
def array():return [int(i) for i in input().split()]
def Int():return int(input())
def Str():return input()
def arrayS():return [i for i in input().split()]
#-------------------------code---------------------------#
# vsInput()
n=Int()
a=array()
sorted_a=sorted(a)
pre=[sorted_a[0]]
for i in range(1,n):
pre.append(pre[-1]+sorted_a[i])
blocks=0
cur=0
for i in range(n):
cur+=a[i]
if(cur==pre[i]):
blocks+=1
print(blocks)
```
| 94,806 |
Provide tags and a correct Python 3 solution for this coding contest problem.
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to hi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi β€ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
* Castles are split into blocks β groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
* The partitioning is chosen in such a way that every castle is a part of exactly one block.
* Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
* The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 β€ hi β€ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Examples
Input
3
1 2 3
Output
3
Input
4
2 1 3 2
Output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
<image>
In the second sample the partitioning is: [2, 1][3, 2]
<image>
Tags: sortings
Correct Solution:
```
n=int(input())
a=list(map(int,input().split()))
s=0
cnt=0
for ai,bi in zip(a,sorted(a)):
s+=bi-ai
if s==0:
cnt+=1
print(cnt)
```
| 94,807 |
Provide tags and a correct Python 3 solution for this coding contest problem.
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to hi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi β€ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
* Castles are split into blocks β groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
* The partitioning is chosen in such a way that every castle is a part of exactly one block.
* Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
* The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 β€ hi β€ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Examples
Input
3
1 2 3
Output
3
Input
4
2 1 3 2
Output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
<image>
In the second sample the partitioning is: [2, 1][3, 2]
<image>
Tags: sortings
Correct Solution:
```
import math,sys
from sys import stdin, stdout
from collections import Counter, defaultdict, deque
input = stdin.readline
I = lambda:int(input())
li = lambda:list(map(int,input().split()))
def case():
n=I()
a=li()
b=a.copy()
b.sort()
d=defaultdict(int)
#print(*b)
j=0
ans=0
for i in range(n):
if(a[i]==b[j]):
d[b[j]]+=1
while(j<n and b[j] in d):
d[b[j]]-=1
if(d[b[j]]==0):
del(d[b[j]])
j+=1
if(j==i+1):
ans+=1
break
#print(i,j)
else:
d[a[i]]+=1
#print(d)
print(ans)
for _ in range(1):
case()
```
| 94,808 |
Provide tags and a correct Python 3 solution for this coding contest problem.
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to hi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi β€ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
* Castles are split into blocks β groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
* The partitioning is chosen in such a way that every castle is a part of exactly one block.
* Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
* The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 β€ hi β€ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Examples
Input
3
1 2 3
Output
3
Input
4
2 1 3 2
Output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
<image>
In the second sample the partitioning is: [2, 1][3, 2]
<image>
Tags: sortings
Correct Solution:
```
from operator import itemgetter
n = int(input())
inp = [ int(i) for i in input().split()]
ori = [ [inp[i], i] for i in range(len(inp)) ]
sorted_ori = sorted(ori, key=itemgetter(0, 1))
pivot, ans = -1, 0
for i in range(n):
pivot = max(sorted_ori[i][1], pivot)
if pivot == i:
ans = ans + 1
print(ans)
```
| 94,809 |
Provide tags and a correct Python 3 solution for this coding contest problem.
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to hi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi β€ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
* Castles are split into blocks β groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
* The partitioning is chosen in such a way that every castle is a part of exactly one block.
* Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
* The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 β€ hi β€ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Examples
Input
3
1 2 3
Output
3
Input
4
2 1 3 2
Output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
<image>
In the second sample the partitioning is: [2, 1][3, 2]
<image>
Tags: sortings
Correct Solution:
```
def main():
n, l = int(input()), list(map(int, input().split()))
res = m = 0
for i, x in enumerate(sorted(range(n), key=l.__getitem__)):
if m < x:
m = x
if m == i:
res += 1
print(res)
if __name__ == '__main__':
main()
```
| 94,810 |
Provide tags and a correct Python 3 solution for this coding contest problem.
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to hi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi β€ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
* Castles are split into blocks β groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
* The partitioning is chosen in such a way that every castle is a part of exactly one block.
* Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
* The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 β€ hi β€ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Examples
Input
3
1 2 3
Output
3
Input
4
2 1 3 2
Output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
<image>
In the second sample the partitioning is: [2, 1][3, 2]
<image>
Tags: sortings
Correct Solution:
```
n = int(input())
arr = list(map(int,input().split()))
pref = []
suf = []
mx = -1
for i in range(n):
if arr[i] > mx:
mx = arr[i]
pref.append(mx)
arr.reverse()
mn = 10000000000
for i in range(n):
if arr[i] < mn:
mn = arr[i]
suf.append(mn)
suf.reverse()
arr.reverse()
answer = 0
for i in range(n-1):
if pref[i] <= suf[i+1]:
answer += 1
print(answer+1)
```
| 94,811 |
Provide tags and a correct Python 3 solution for this coding contest problem.
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to hi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi β€ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
* Castles are split into blocks β groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
* The partitioning is chosen in such a way that every castle is a part of exactly one block.
* Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
* The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 β€ hi β€ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Examples
Input
3
1 2 3
Output
3
Input
4
2 1 3 2
Output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
<image>
In the second sample the partitioning is: [2, 1][3, 2]
<image>
Tags: sortings
Correct Solution:
```
import sys
def main():
n = int(input())
h = list(map(int, sys.stdin.readline().split()))
h = [0]+h
hmax = [0]*(n+1)
hmin = [0]*(n+1)
hmax[1] = h[1]
hmin[n] = h[n]
for i in range(2,n+1):
hmax[i] = max(hmax[i-1], h[i])
for i in range(n-1, 0, -1):
hmin[i] = min(hmin[i+1], h[i])
s = 1
for i in range(1, n):
if hmax[i] <= hmin[i+1]:
s += 1
print(s)
main()
```
| 94,812 |
Provide tags and a correct Python 3 solution for this coding contest problem.
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to hi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi β€ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
* Castles are split into blocks β groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
* The partitioning is chosen in such a way that every castle is a part of exactly one block.
* Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
* The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 β€ hi β€ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Examples
Input
3
1 2 3
Output
3
Input
4
2 1 3 2
Output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
<image>
In the second sample the partitioning is: [2, 1][3, 2]
<image>
Tags: sortings
Correct Solution:
```
def binsearch(a, x, k):
l = 0
r = k
while l < r - 1:
m = (l + r) // 2
if a[m] <= x:
l = m
else:
r = m
return l
n = int(input())
k = -1
a = [0] * n
for i in input().split():
x = int(i)
if k == -1:
k += 1
a[k] = x
else:
if x >= a[k]:
k += 1
a[k] = x
else:
k1 = k
k = binsearch(a, x, k + 1)
if a[k] <= x:
k += 1
a[k] = a[k1]
print(k + 1)
```
| 94,813 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to hi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi β€ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
* Castles are split into blocks β groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
* The partitioning is chosen in such a way that every castle is a part of exactly one block.
* Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
* The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 β€ hi β€ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Examples
Input
3
1 2 3
Output
3
Input
4
2 1 3 2
Output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
<image>
In the second sample the partitioning is: [2, 1][3, 2]
<image>
Submitted Solution:
```
from sys import stdin,stdout
from collections import defaultdict
nmbr = lambda: int(stdin.readline())
lst = lambda: list(map(int,stdin.readline().split()))
for _ in range(1):#nmbr()):
n=nmbr()
a=list(zip(lst(),range(n)))
a.sort();ans=mx=0
for i in range(n):
mx=max(a[i][1],mx)
if mx==i:ans+=1
print(ans)
```
Yes
| 94,814 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to hi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi β€ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
* Castles are split into blocks β groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
* The partitioning is chosen in such a way that every castle is a part of exactly one block.
* Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
* The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 β€ hi β€ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Examples
Input
3
1 2 3
Output
3
Input
4
2 1 3 2
Output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
<image>
In the second sample the partitioning is: [2, 1][3, 2]
<image>
Submitted Solution:
```
__author__ = 'MoonBall'
import sys
# sys.stdin = open('data/C.in', 'r')
T = 1
def process():
N = int(input())
h = map(int, input().split())
hpx = []
last = {}
for i, v in enumerate(h): hpx.append([v, i])
hpx = sorted(hpx, key=lambda x:x[0])
maxp = -1
i = 0
while i < N:
item = hpx[i]
v = item[0]
j = i
while j < N and hpx[j][0] == v:
p = hpx[j][1]
last[p] = max(maxp, p)
j = j + 1
j = i
while j < N and hpx[j][0] == v:
p = hpx[j][1]
maxp = max(maxp, p)
j = j + 1
i = j
ans = 0
p = 0
while p < N:
ans = ans + 1
nextp = p + 1
while p < N and p < nextp:
nextp = max(nextp, last[p] + 1)
p = p + 1
print(ans)
for _ in range(T):
process()
```
Yes
| 94,815 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to hi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi β€ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
* Castles are split into blocks β groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
* The partitioning is chosen in such a way that every castle is a part of exactly one block.
* Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
* The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 β€ hi β€ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Examples
Input
3
1 2 3
Output
3
Input
4
2 1 3 2
Output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
<image>
In the second sample the partitioning is: [2, 1][3, 2]
<image>
Submitted Solution:
```
from collections import Counter
if __name__ == '__main__':
n = int(input())
data = list(map(int, input().split()))
dd = {}
for i, x in enumerate(sorted(data)):
if x not in dd:
dd[x] = i
m = None
c = 0
n_pos = None
counter = Counter()
for i, x in enumerate(data):
if n_pos is None:
if dd[x] + counter[x] == i:
c += 1
else:
n_pos = dd[x] + counter[x]
m = x
else:
if x >= m:
m = x
n_pos = dd[x] + counter[x]
if i == n_pos:
c += 1
n_pos = None
counter[x] += 1
print(c)
```
Yes
| 94,816 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to hi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi β€ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
* Castles are split into blocks β groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
* The partitioning is chosen in such a way that every castle is a part of exactly one block.
* Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
* The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 β€ hi β€ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Examples
Input
3
1 2 3
Output
3
Input
4
2 1 3 2
Output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
<image>
In the second sample the partitioning is: [2, 1][3, 2]
<image>
Submitted Solution:
```
n=int(input())
a=list(map(int,input().split()))
b=sorted(a)
c={}
d={}
e=0
for i in range(n):
if a[i] not in c.keys():
c[a[i]]=1
else:
c[a[i]]+=1
if b[i] not in d.keys():
d[b[i]]=1
else:
d[b[i]]+=1
if c==d:
e=e+1
c={}
d={}
print(e)
```
Yes
| 94,817 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to hi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi β€ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
* Castles are split into blocks β groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
* The partitioning is chosen in such a way that every castle is a part of exactly one block.
* Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
* The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 β€ hi β€ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Examples
Input
3
1 2 3
Output
3
Input
4
2 1 3 2
Output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
<image>
In the second sample the partitioning is: [2, 1][3, 2]
<image>
Submitted Solution:
```
n = int(input())
l = list(map(int, input().split()))
blocks = 0
i = 1
if n == 1:
print(1)
else:
while i != len(l):
if l[i] <= l[i - 1]:
i += 1
else:
blocks += 1
i += 1
print(blocks + 1)
```
No
| 94,818 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to hi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi β€ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
* Castles are split into blocks β groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
* The partitioning is chosen in such a way that every castle is a part of exactly one block.
* Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
* The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 β€ hi β€ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Examples
Input
3
1 2 3
Output
3
Input
4
2 1 3 2
Output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
<image>
In the second sample the partitioning is: [2, 1][3, 2]
<image>
Submitted Solution:
```
mi=1000000000000
ma=0
k=0
n=input()
l=list(map(int,input().split()))
for x in l :
if mi>=x :
k=1
mi=x
else :
if x>=ma :
k+=1
ma=max(x,ma)
print(k)
```
No
| 94,819 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to hi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi β€ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
* Castles are split into blocks β groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
* The partitioning is chosen in such a way that every castle is a part of exactly one block.
* Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
* The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 β€ hi β€ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Examples
Input
3
1 2 3
Output
3
Input
4
2 1 3 2
Output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
<image>
In the second sample the partitioning is: [2, 1][3, 2]
<image>
Submitted Solution:
```
n=int(input())
s=input().split()
k=0
j=0
maxx=-9902
for i in range(n-1):
if abs(int(s[i])-int(s[i+1]))>maxx:
maxx=abs(int(s[i])-int(s[i+1]))
for i in range(n-1):
if abs(int(s[i])-int(s[i+1]))==maxx:
j+=1
print (j+1)
```
No
| 94,820 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to hi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi β€ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
* Castles are split into blocks β groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
* The partitioning is chosen in such a way that every castle is a part of exactly one block.
* Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
* The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 β€ hi β€ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Examples
Input
3
1 2 3
Output
3
Input
4
2 1 3 2
Output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
<image>
In the second sample the partitioning is: [2, 1][3, 2]
<image>
Submitted Solution:
```
k=int(input())
vis=list(map(int,input().split()))
viss=sorted(vis)
#print(viss)
i=0
etind=-1
ans=0
et=-1
while i<k:
if vis[i]==et:
etind+=1
i=i+1
ans+=1
#print("--")
continue
et=vis[i]
kod=0
kol=viss.index(vis[i])-etind-1
etind=viss.index(vis[i])
#if kol<0:
# kol=0
# etind+=1
s=0
#print(et,kol)
while s<kol and i<k-1:
i+=1
if vis[i]<et:
s+=1
elif vis[i]>et:
et=vis[i]
indet=i
s=s+1+kod
kol=viss.index(vis[i])
#print(et,"*")
else:
kod+=1
ans+=1
i+=1
print(ans)
```
No
| 94,821 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (<https://en.wikipedia.org/wiki/Seven-segment_display>).
<image>
Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.
For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then β 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.
Input
The only line contains two integers a, b (1 β€ a β€ b β€ 106) β the first and the last number typed by Max.
Output
Print the only integer a β the total number of printed segments.
Examples
Input
1 3
Output
12
Input
10 15
Output
39
Tags: implementation
Correct Solution:
```
def proc( x , nums ):
res = 0
while x != 0:
#print(x)
res += nums[x%10]
x //= 10
return res
if __name__ == "__main__":
nums = [6,2,5,5,4,5,6,3,7,6]
a , b = [int(x) for x in input().split()]
res = 0
s = str(list(range(a,b+1)))
#print(s)
for i in range(10):
res += nums[i] * s.count(str(i))
print(res)
```
| 94,822 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (<https://en.wikipedia.org/wiki/Seven-segment_display>).
<image>
Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.
For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then β 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.
Input
The only line contains two integers a, b (1 β€ a β€ b β€ 106) β the first and the last number typed by Max.
Output
Print the only integer a β the total number of printed segments.
Examples
Input
1 3
Output
12
Input
10 15
Output
39
Tags: implementation
Correct Solution:
```
segment = {'0':6,'1':2,'2':5,'3':5,'4':4,'5':5,'6':6,'7':3,'8':7,'9':6}
a,b = map(int,input().split())
ans = 0
s = str([i for i in range(a,b+1)])
for i in s:
try:
ans+=segment[i]
except:
pass
print(ans)
```
| 94,823 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (<https://en.wikipedia.org/wiki/Seven-segment_display>).
<image>
Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.
For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then β 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.
Input
The only line contains two integers a, b (1 β€ a β€ b β€ 106) β the first and the last number typed by Max.
Output
Print the only integer a β the total number of printed segments.
Examples
Input
1 3
Output
12
Input
10 15
Output
39
Tags: implementation
Correct Solution:
```
a,b=list(input().split())
t={'0':6,'1':2,'2':5,'3':5,'4':4,'5':5,'6':6,'7':3,'8':7,'9':6}
v=0
for k in range(int(a),int(b)+1):
s=str(k)
for i in s:
v+=t[i]
print(v)
```
| 94,824 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (<https://en.wikipedia.org/wiki/Seven-segment_display>).
<image>
Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.
For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then β 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.
Input
The only line contains two integers a, b (1 β€ a β€ b β€ 106) β the first and the last number typed by Max.
Output
Print the only integer a β the total number of printed segments.
Examples
Input
1 3
Output
12
Input
10 15
Output
39
Tags: implementation
Correct Solution:
```
import sys,math
'''
def construct(a,seg,low,high,pos):
try:
if low == high:
seg[pos] = a[low]
mid = (low+high)//2
construct(a,seg,low,mid,2*pos+1)
construct(a,seg,mid,high,2*pos+2)
seg[pos] = min(seg[2*pos+1],seg[2*pos+2])
except:
pass
a = [-1,2,4,0]
c = 1
while c<len(a):
c = 2*c
seg = [10000]*(2*c-1)
print(construct(a,seg,0,3,0))
def matrix(a,b):
c = [[a[0][0]*b[0][0]+a[0][1]*b[1][0],a[0][0]*b[0][1]+a[0][1]*b[1][1]],\
[a[1][0]*b[0][0]+a[1][1]*b[1][0],a[1][0]*b[1][0]+a[1][1]*b[1][1]]]
return c
def power(a,n):
if n == 0:
return [[1,1],[1,0]]
else:
if n%2 == 0:
return matrix(power(a,n//2),power(a,n//2))
else:
return matrix(matrix(a,a),power(a,n-1))
a = [[1,1],[1,0]]
for i in range(10):
print(power(a,i))
a = [[1,1],[1,0]]
c = a
for i in range(10):
c = matrix(c,a)
print(c)
t = int(input())
for _ in range(t):
n, w = map(int,input().split())
a = list(map(int,input().split()))
a.sort()
x = 0
s = 0
while x<n and s+a[x]<=w:
s+=a[x]
x+=1
if x == 0:
print(-1)
else:
print(x)
print(a[0:x+1])
'''
def cal(a,b):
seg = {0:6,1:2,2:5,3:5,4:4,5:5,6:6,7:3,8:7,9:6}
ans = 0
for i in range(a,b+1):
for c in str(i):
ans += seg[int(c)]
return ans
a, b = map(int,input().split())
print(cal(a,b))
```
| 94,825 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (<https://en.wikipedia.org/wiki/Seven-segment_display>).
<image>
Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.
For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then β 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.
Input
The only line contains two integers a, b (1 β€ a β€ b β€ 106) β the first and the last number typed by Max.
Output
Print the only integer a β the total number of printed segments.
Examples
Input
1 3
Output
12
Input
10 15
Output
39
Tags: implementation
Correct Solution:
```
arr = [6 , 2 , 5 , 5 , 4 , 5 , 6 , 3 , 7 , 6]
ans = 0
a , b = map(int , input().split())
for i in range(a , b+1):
x = list(str(i))
for j in x:
ans += arr[int(j)]
print(ans)
```
| 94,826 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (<https://en.wikipedia.org/wiki/Seven-segment_display>).
<image>
Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.
For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then β 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.
Input
The only line contains two integers a, b (1 β€ a β€ b β€ 106) β the first and the last number typed by Max.
Output
Print the only integer a β the total number of printed segments.
Examples
Input
1 3
Output
12
Input
10 15
Output
39
Tags: implementation
Correct Solution:
```
a,b=map(int,input().split())
z={"1":2,"2":5,"3":5,"4":4,"5":5,"6":6,"7":3,"8":7,"9":6,"0":6}
z1={"1":0,"2":0,"3":0,"4":0,"5":0,"6":0,"7":0,"8":0,"9":0,"0":0}
s=0
for i in range(a,b+1):
k=str(i)
for i in k:z1[i]+=1
for i in z:s+=z1[i]*z[i]
print(s)
```
| 94,827 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (<https://en.wikipedia.org/wiki/Seven-segment_display>).
<image>
Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.
For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then β 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.
Input
The only line contains two integers a, b (1 β€ a β€ b β€ 106) β the first and the last number typed by Max.
Output
Print the only integer a β the total number of printed segments.
Examples
Input
1 3
Output
12
Input
10 15
Output
39
Tags: implementation
Correct Solution:
```
a,b=map(int,input().split())
i=str(list(range(a,b+1)))
seg={'0': 6, '1': 2, '2': 5, '3': 5, '4': 4, '5': 5, '6': 6, '7': 3, '8': 7, '9': 6}
print(seg['0']*i.count('0')+seg['1']*i.count('1')+seg['2']*i.count('2')+seg['3']*i.count('3')+seg['4']*i.count('4')+seg['5']*i.count('5')+seg['6']*i.count('6')+seg['7']*i.count('7')+seg['8']*i.count('8')+seg['9']*i.count('9')
)
```
| 94,828 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (<https://en.wikipedia.org/wiki/Seven-segment_display>).
<image>
Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.
For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then β 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.
Input
The only line contains two integers a, b (1 β€ a β€ b β€ 106) β the first and the last number typed by Max.
Output
Print the only integer a β the total number of printed segments.
Examples
Input
1 3
Output
12
Input
10 15
Output
39
Tags: implementation
Correct Solution:
```
a, b = map(int, input().split())
sum = 0
t = [6, 2, 5, 5, 4, 5, 6, 3, 7, 6]
for i in range(a, b+1):
s = str(i)
for j in range(0, len(str(i))):
sum+=t[int(s[j])]
print(sum)
```
| 94,829 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (<https://en.wikipedia.org/wiki/Seven-segment_display>).
<image>
Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.
For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then β 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.
Input
The only line contains two integers a, b (1 β€ a β€ b β€ 106) β the first and the last number typed by Max.
Output
Print the only integer a β the total number of printed segments.
Examples
Input
1 3
Output
12
Input
10 15
Output
39
Submitted Solution:
```
a,b = list(map(int, input().split(" ")))
i=a
segment=[6,2,5,5,4,5,6,3,7,6]
sum=0
s=str([i for i in range(a,b+1)])
for i in range(10):
sum+=s.count(str(i))*segment[i]
print(sum)
```
Yes
| 94,830 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (<https://en.wikipedia.org/wiki/Seven-segment_display>).
<image>
Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.
For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then β 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.
Input
The only line contains two integers a, b (1 β€ a β€ b β€ 106) β the first and the last number typed by Max.
Output
Print the only integer a β the total number of printed segments.
Examples
Input
1 3
Output
12
Input
10 15
Output
39
Submitted Solution:
```
a, b = map(int, input().split())
d = {'0': 6, '1': 2, '2': 5, '3': 5, '4': 4,
'5': 5, '6': 6, '7': 3, '8': 7, '9': 6}
ans = 0
for i in range(a, b+1):
s = str(i)
for j in s:
ans += d[j]
#print(ans, j)
print(ans)
```
Yes
| 94,831 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (<https://en.wikipedia.org/wiki/Seven-segment_display>).
<image>
Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.
For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then β 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.
Input
The only line contains two integers a, b (1 β€ a β€ b β€ 106) β the first and the last number typed by Max.
Output
Print the only integer a β the total number of printed segments.
Examples
Input
1 3
Output
12
Input
10 15
Output
39
Submitted Solution:
```
dic = {
'1': 2,
'2': 5,
'3': 5,
'4': 4,
'5': 5,
'6': 6,
'7': 3,
'8': 7,
'9': 6,
'0': 6,
}
l, r = (map (int, input().strip().split()))
ans = 0
for i in range(l, r+1):
s = str(i)
for x in range(0, len(s)):
ans += dic[s[x]]
print(ans)
```
Yes
| 94,832 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (<https://en.wikipedia.org/wiki/Seven-segment_display>).
<image>
Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.
For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then β 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.
Input
The only line contains two integers a, b (1 β€ a β€ b β€ 106) β the first and the last number typed by Max.
Output
Print the only integer a β the total number of printed segments.
Examples
Input
1 3
Output
12
Input
10 15
Output
39
Submitted Solution:
```
seg = [6,2,5,5,4,5,6,3,7,6]
a,b = map(int,input().split())
num = str(list(range(a,b+1)))
ans = 0
for i in range(len(seg)):
ans += seg[i]*num.count(str(i))
print (ans)
```
Yes
| 94,833 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (<https://en.wikipedia.org/wiki/Seven-segment_display>).
<image>
Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.
For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then β 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.
Input
The only line contains two integers a, b (1 β€ a β€ b β€ 106) β the first and the last number typed by Max.
Output
Print the only integer a β the total number of printed segments.
Examples
Input
1 3
Output
12
Input
10 15
Output
39
Submitted Solution:
```
cnt = [6, 2, 5, 5, 4, 5, 6, 4, 7, 6]
def f(n):
ans = 0
while n != 0:
ans += cnt[n % 10]
n //= 10
return ans
a, b = map(int, input().split())
ans = 0
for i in range(a, b + 1):
ans += f(i)
print(ans)
```
No
| 94,834 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (<https://en.wikipedia.org/wiki/Seven-segment_display>).
<image>
Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.
For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then β 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.
Input
The only line contains two integers a, b (1 β€ a β€ b β€ 106) β the first and the last number typed by Max.
Output
Print the only integer a β the total number of printed segments.
Examples
Input
1 3
Output
12
Input
10 15
Output
39
Submitted Solution:
```
a,b = list(map(int, input().split(" ")))
i=a
segment=[6,2,5,5,4,5,6,3,7,6]
sum=0
s=[str(i) for i in range(a,b+1)]
for i in range(10):
sum+=s.count(str(i))*segment[i]
print(sum)
```
No
| 94,835 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (<https://en.wikipedia.org/wiki/Seven-segment_display>).
<image>
Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.
For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then β 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.
Input
The only line contains two integers a, b (1 β€ a β€ b β€ 106) β the first and the last number typed by Max.
Output
Print the only integer a β the total number of printed segments.
Examples
Input
1 3
Output
12
Input
10 15
Output
39
Submitted Solution:
```
def f(x):
return 49*int(x)*10**(int(x)-1)
def g(y):
segs = [6,2,5,5,4,5,6,3,7,6]
return sum(segs[1:int(y)])
def g_v(y,c):
segs = [6,2,5,5,4,5,6,3,7,6]
return sum(segs[0:int(y)+c])
def h(z):
segs = [6,2,5,5,4,5,6,3,7,6]
return segs[int(z)]
def seg_sum(n,c):
total = 0
for i in range(0,len(n)):
if len(n)-1-i > 0:
total += int(n[i])*f(len(n)-1-i)+g(n[i])*10**(len(n)-1-i)+h(n[i])*int(n[i+1:len(n)])
elif len(n)-1-i == 0:
total += g_v(int(n[len(n)-1]),c)
return total
def runner():
[a,b] = input().split()
print(seg_sum(b,1) - seg_sum(a,0))
runner()
```
No
| 94,836 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (<https://en.wikipedia.org/wiki/Seven-segment_display>).
<image>
Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.
For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then β 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.
Input
The only line contains two integers a, b (1 β€ a β€ b β€ 106) β the first and the last number typed by Max.
Output
Print the only integer a β the total number of printed segments.
Examples
Input
1 3
Output
12
Input
10 15
Output
39
Submitted Solution:
```
cnt = [6, 2, 5, 5, 5, 4, 5, 6, 4, 7, 6]
def f(n):
ans = 0
while n != 0:
ans += cnt[n % 10]
n //= 10
return ans
a, b = map(int, input().split())
ans = 0
for i in range(a, b + 1):
ans += f(i)
print(ans)
```
No
| 94,837 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Artem found a grasshopper. He brought it to his house and constructed a jumping area for him.
The area looks like a strip of cells 1 Γ n. Each cell contains the direction for the next jump and the length of that jump. Grasshopper starts in the first cell and follows the instructions written on the cells. Grasshopper stops immediately if it jumps out of the strip. Now Artem wants to find out if this will ever happen.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β length of the strip.
Next line contains a string of length n which consists of characters "<" and ">" only, that provide the direction of the jump from the corresponding cell. Next line contains n integers di (1 β€ di β€ 109) β the length of the jump from the i-th cell.
Output
Print "INFINITE" (without quotes) if grasshopper will continue his jumps forever. Otherwise print "FINITE" (without quotes).
Examples
Input
2
><
1 2
Output
FINITE
Input
3
>><
2 1 1
Output
INFINITE
Note
In the first sample grasshopper starts from the first cell and jumps to the right on the next cell. When he is in the second cell he needs to jump two cells left so he will jump out of the strip.
Second sample grasshopper path is 1 - 3 - 2 - 3 - 2 - 3 and so on. The path is infinite.
Tags: implementation
Correct Solution:
```
n = int(input())
s = list(1 if x == '>' else -1 for x in input())
l = list(map(int, input().split()))
summ = 1
cur = 0
next = 0
for i in range(n):
if cur < 0 or cur > n - 1:
print('FINITE')
exit()
if l[cur] == 0:
print('INFINITE')
exit()
next += l[cur] * s[cur]
l[cur] = 0
cur = next
print('INFINITE' if 0 <= cur < n else 'FINITE')
```
| 94,838 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Artem found a grasshopper. He brought it to his house and constructed a jumping area for him.
The area looks like a strip of cells 1 Γ n. Each cell contains the direction for the next jump and the length of that jump. Grasshopper starts in the first cell and follows the instructions written on the cells. Grasshopper stops immediately if it jumps out of the strip. Now Artem wants to find out if this will ever happen.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β length of the strip.
Next line contains a string of length n which consists of characters "<" and ">" only, that provide the direction of the jump from the corresponding cell. Next line contains n integers di (1 β€ di β€ 109) β the length of the jump from the i-th cell.
Output
Print "INFINITE" (without quotes) if grasshopper will continue his jumps forever. Otherwise print "FINITE" (without quotes).
Examples
Input
2
><
1 2
Output
FINITE
Input
3
>><
2 1 1
Output
INFINITE
Note
In the first sample grasshopper starts from the first cell and jumps to the right on the next cell. When he is in the second cell he needs to jump two cells left so he will jump out of the strip.
Second sample grasshopper path is 1 - 3 - 2 - 3 - 2 - 3 and so on. The path is infinite.
Tags: implementation
Correct Solution:
```
n=int(input())
s = input()
d = list(map(int, input().split()))
i = 0
for _ in range(n+1):
if i < 0 or i >= n:
print("FINITE")
exit()
if s[i] == '>':
i += d[i]
elif s[i] == '<':
i -= d[i]
print("INFINITE")
```
| 94,839 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Artem found a grasshopper. He brought it to his house and constructed a jumping area for him.
The area looks like a strip of cells 1 Γ n. Each cell contains the direction for the next jump and the length of that jump. Grasshopper starts in the first cell and follows the instructions written on the cells. Grasshopper stops immediately if it jumps out of the strip. Now Artem wants to find out if this will ever happen.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β length of the strip.
Next line contains a string of length n which consists of characters "<" and ">" only, that provide the direction of the jump from the corresponding cell. Next line contains n integers di (1 β€ di β€ 109) β the length of the jump from the i-th cell.
Output
Print "INFINITE" (without quotes) if grasshopper will continue his jumps forever. Otherwise print "FINITE" (without quotes).
Examples
Input
2
><
1 2
Output
FINITE
Input
3
>><
2 1 1
Output
INFINITE
Note
In the first sample grasshopper starts from the first cell and jumps to the right on the next cell. When he is in the second cell he needs to jump two cells left so he will jump out of the strip.
Second sample grasshopper path is 1 - 3 - 2 - 3 - 2 - 3 and so on. The path is infinite.
Tags: implementation
Correct Solution:
```
n = int(input())
s = input()
d = list(map(int, input().split()))
k = [False]*n
i = 0
inf = False
while not inf and i >= 0 and i < n:
if not k[i]:
k[i] = True
else:
inf = True
if s[i] == '<':
i -= d[i]
else:
i += d[i]
if inf:
print("INFINITE")
else:
print("FINITE")
```
| 94,840 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Artem found a grasshopper. He brought it to his house and constructed a jumping area for him.
The area looks like a strip of cells 1 Γ n. Each cell contains the direction for the next jump and the length of that jump. Grasshopper starts in the first cell and follows the instructions written on the cells. Grasshopper stops immediately if it jumps out of the strip. Now Artem wants to find out if this will ever happen.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β length of the strip.
Next line contains a string of length n which consists of characters "<" and ">" only, that provide the direction of the jump from the corresponding cell. Next line contains n integers di (1 β€ di β€ 109) β the length of the jump from the i-th cell.
Output
Print "INFINITE" (without quotes) if grasshopper will continue his jumps forever. Otherwise print "FINITE" (without quotes).
Examples
Input
2
><
1 2
Output
FINITE
Input
3
>><
2 1 1
Output
INFINITE
Note
In the first sample grasshopper starts from the first cell and jumps to the right on the next cell. When he is in the second cell he needs to jump two cells left so he will jump out of the strip.
Second sample grasshopper path is 1 - 3 - 2 - 3 - 2 - 3 and so on. The path is infinite.
Tags: implementation
Correct Solution:
```
n = int(input())
s = input()
p = 0
k = 0
a = list(map(int, input().split()))
for i in range(2 * n):
if s[p] == '>':
p += a[p]
else:
p -= a[p]
if (p > n - 1) or (p < 0):
print("FINITE")
k = 1
break
if not k:
print("INFINITE")
```
| 94,841 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Artem found a grasshopper. He brought it to his house and constructed a jumping area for him.
The area looks like a strip of cells 1 Γ n. Each cell contains the direction for the next jump and the length of that jump. Grasshopper starts in the first cell and follows the instructions written on the cells. Grasshopper stops immediately if it jumps out of the strip. Now Artem wants to find out if this will ever happen.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β length of the strip.
Next line contains a string of length n which consists of characters "<" and ">" only, that provide the direction of the jump from the corresponding cell. Next line contains n integers di (1 β€ di β€ 109) β the length of the jump from the i-th cell.
Output
Print "INFINITE" (without quotes) if grasshopper will continue his jumps forever. Otherwise print "FINITE" (without quotes).
Examples
Input
2
><
1 2
Output
FINITE
Input
3
>><
2 1 1
Output
INFINITE
Note
In the first sample grasshopper starts from the first cell and jumps to the right on the next cell. When he is in the second cell he needs to jump two cells left so he will jump out of the strip.
Second sample grasshopper path is 1 - 3 - 2 - 3 - 2 - 3 and so on. The path is infinite.
Tags: implementation
Correct Solution:
```
def main():
n = int(input())
arrows = input()
cells = [int(x) for x in input().split()]
print(solver(arrows, cells))
def solver(arrows, cells):
for i in range(len(arrows)):
if arrows[i] == '<':
cells[i] = - cells[i]
visited = [False] * len(cells)
index = 0
while True:
if index >= len(cells) or index < 0:
return "FINITE"
elif visited[index] == True:
return "INFINITE"
else:
visited[index] = True
index = index + cells[index]
#print(solver(">><", [2, 1, 1]))
#print(solver("><", [1, 2]))
main()
```
| 94,842 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Artem found a grasshopper. He brought it to his house and constructed a jumping area for him.
The area looks like a strip of cells 1 Γ n. Each cell contains the direction for the next jump and the length of that jump. Grasshopper starts in the first cell and follows the instructions written on the cells. Grasshopper stops immediately if it jumps out of the strip. Now Artem wants to find out if this will ever happen.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β length of the strip.
Next line contains a string of length n which consists of characters "<" and ">" only, that provide the direction of the jump from the corresponding cell. Next line contains n integers di (1 β€ di β€ 109) β the length of the jump from the i-th cell.
Output
Print "INFINITE" (without quotes) if grasshopper will continue his jumps forever. Otherwise print "FINITE" (without quotes).
Examples
Input
2
><
1 2
Output
FINITE
Input
3
>><
2 1 1
Output
INFINITE
Note
In the first sample grasshopper starts from the first cell and jumps to the right on the next cell. When he is in the second cell he needs to jump two cells left so he will jump out of the strip.
Second sample grasshopper path is 1 - 3 - 2 - 3 - 2 - 3 and so on. The path is infinite.
Tags: implementation
Correct Solution:
```
n = int(input())-1
s = input()
d = [int(i) for i in input().split()]
c = True
cnt = 0
i = 0
z = 0
while i<=n and i>=0:
if s[i]:
if s[i]==">":
i+=d[i]
z+=1
elif s[i]=="<":
i-=d[i]
z+=1
else:
break
if z>=2*n:c=False;break
if i>n or i<0:
print("FINITE")
else:
print("INFINITE")
```
| 94,843 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Artem found a grasshopper. He brought it to his house and constructed a jumping area for him.
The area looks like a strip of cells 1 Γ n. Each cell contains the direction for the next jump and the length of that jump. Grasshopper starts in the first cell and follows the instructions written on the cells. Grasshopper stops immediately if it jumps out of the strip. Now Artem wants to find out if this will ever happen.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β length of the strip.
Next line contains a string of length n which consists of characters "<" and ">" only, that provide the direction of the jump from the corresponding cell. Next line contains n integers di (1 β€ di β€ 109) β the length of the jump from the i-th cell.
Output
Print "INFINITE" (without quotes) if grasshopper will continue his jumps forever. Otherwise print "FINITE" (without quotes).
Examples
Input
2
><
1 2
Output
FINITE
Input
3
>><
2 1 1
Output
INFINITE
Note
In the first sample grasshopper starts from the first cell and jumps to the right on the next cell. When he is in the second cell he needs to jump two cells left so he will jump out of the strip.
Second sample grasshopper path is 1 - 3 - 2 - 3 - 2 - 3 and so on. The path is infinite.
Tags: implementation
Correct Solution:
```
if __name__ == '__main__':
Y = lambda: list(map(int, input().split()))
N = lambda: int(input())
n = N()
s = input()
a = Y()
nxt, ans = 0, 0
for i in range(n):
nxt += [a[nxt], -a[nxt]][s[nxt] == '<']
if nxt >= n or nxt < 0:
ans = 2
break
print("INFINITE"[ans:])
```
| 94,844 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Little Artem found a grasshopper. He brought it to his house and constructed a jumping area for him.
The area looks like a strip of cells 1 Γ n. Each cell contains the direction for the next jump and the length of that jump. Grasshopper starts in the first cell and follows the instructions written on the cells. Grasshopper stops immediately if it jumps out of the strip. Now Artem wants to find out if this will ever happen.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β length of the strip.
Next line contains a string of length n which consists of characters "<" and ">" only, that provide the direction of the jump from the corresponding cell. Next line contains n integers di (1 β€ di β€ 109) β the length of the jump from the i-th cell.
Output
Print "INFINITE" (without quotes) if grasshopper will continue his jumps forever. Otherwise print "FINITE" (without quotes).
Examples
Input
2
><
1 2
Output
FINITE
Input
3
>><
2 1 1
Output
INFINITE
Note
In the first sample grasshopper starts from the first cell and jumps to the right on the next cell. When he is in the second cell he needs to jump two cells left so he will jump out of the strip.
Second sample grasshopper path is 1 - 3 - 2 - 3 - 2 - 3 and so on. The path is infinite.
Tags: implementation
Correct Solution:
```
n=int(input())
s=input()
a=list(map(int,input().split()))
f=n*[False]
i,j=0,0
while True:
# print(i,f[i])
if i<0 or i>=n or n==1:
print("FINITE")
break
elif f[i]==True:
print("INFINITE")
break
else:
f[i]=True
if s[i]=='>':
i+=a[i]
else:
i-=a[i]
```
| 94,845 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Artem found a grasshopper. He brought it to his house and constructed a jumping area for him.
The area looks like a strip of cells 1 Γ n. Each cell contains the direction for the next jump and the length of that jump. Grasshopper starts in the first cell and follows the instructions written on the cells. Grasshopper stops immediately if it jumps out of the strip. Now Artem wants to find out if this will ever happen.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β length of the strip.
Next line contains a string of length n which consists of characters "<" and ">" only, that provide the direction of the jump from the corresponding cell. Next line contains n integers di (1 β€ di β€ 109) β the length of the jump from the i-th cell.
Output
Print "INFINITE" (without quotes) if grasshopper will continue his jumps forever. Otherwise print "FINITE" (without quotes).
Examples
Input
2
><
1 2
Output
FINITE
Input
3
>><
2 1 1
Output
INFINITE
Note
In the first sample grasshopper starts from the first cell and jumps to the right on the next cell. When he is in the second cell he needs to jump two cells left so he will jump out of the strip.
Second sample grasshopper path is 1 - 3 - 2 - 3 - 2 - 3 and so on. The path is infinite.
Submitted Solution:
```
import math
def main_function():
n = int(input())
s = input()
a = [int(i) for i in input().split(" ")]
current_position = 0
hash = [0 for i in range(100000)]
while True:
if current_position < 0 or current_position > n - 1:
print("FINITE")
break
else:
if hash[current_position] == 1:
print("INFINITE")
break
else:
hash[current_position] = 1
if s[current_position] == ">":
current_position += a[current_position]
else:
current_position -= a[current_position]
main_function()
```
Yes
| 94,846 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Artem found a grasshopper. He brought it to his house and constructed a jumping area for him.
The area looks like a strip of cells 1 Γ n. Each cell contains the direction for the next jump and the length of that jump. Grasshopper starts in the first cell and follows the instructions written on the cells. Grasshopper stops immediately if it jumps out of the strip. Now Artem wants to find out if this will ever happen.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β length of the strip.
Next line contains a string of length n which consists of characters "<" and ">" only, that provide the direction of the jump from the corresponding cell. Next line contains n integers di (1 β€ di β€ 109) β the length of the jump from the i-th cell.
Output
Print "INFINITE" (without quotes) if grasshopper will continue his jumps forever. Otherwise print "FINITE" (without quotes).
Examples
Input
2
><
1 2
Output
FINITE
Input
3
>><
2 1 1
Output
INFINITE
Note
In the first sample grasshopper starts from the first cell and jumps to the right on the next cell. When he is in the second cell he needs to jump two cells left so he will jump out of the strip.
Second sample grasshopper path is 1 - 3 - 2 - 3 - 2 - 3 and so on. The path is infinite.
Submitted Solution:
```
n = int(input())
D = [d if ch=='>' else -d for ch,d in zip(input(), map(int, input().split()))]
i = 0
visited = {0}
while True:
i += D[i]
if i < 0 or i >= n:
print('FINITE')
break
if i in visited:
print('INFINITE')
break
visited.add(i)
```
Yes
| 94,847 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Artem found a grasshopper. He brought it to his house and constructed a jumping area for him.
The area looks like a strip of cells 1 Γ n. Each cell contains the direction for the next jump and the length of that jump. Grasshopper starts in the first cell and follows the instructions written on the cells. Grasshopper stops immediately if it jumps out of the strip. Now Artem wants to find out if this will ever happen.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β length of the strip.
Next line contains a string of length n which consists of characters "<" and ">" only, that provide the direction of the jump from the corresponding cell. Next line contains n integers di (1 β€ di β€ 109) β the length of the jump from the i-th cell.
Output
Print "INFINITE" (without quotes) if grasshopper will continue his jumps forever. Otherwise print "FINITE" (without quotes).
Examples
Input
2
><
1 2
Output
FINITE
Input
3
>><
2 1 1
Output
INFINITE
Note
In the first sample grasshopper starts from the first cell and jumps to the right on the next cell. When he is in the second cell he needs to jump two cells left so he will jump out of the strip.
Second sample grasshopper path is 1 - 3 - 2 - 3 - 2 - 3 and so on. The path is infinite.
Submitted Solution:
```
def main():
n = int(input())
d = input()
l = [int(c) for c in input().split()]
visited = {0}
i = 0
while 0 <= i < n:
di, li = d[i], l[i]
i = i + li if di == '>' else i - li
if i in visited:
print('INFINITE')
return
visited.add(i)
print('FINITE')
if __name__ == '__main__':
main()
```
Yes
| 94,848 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Artem found a grasshopper. He brought it to his house and constructed a jumping area for him.
The area looks like a strip of cells 1 Γ n. Each cell contains the direction for the next jump and the length of that jump. Grasshopper starts in the first cell and follows the instructions written on the cells. Grasshopper stops immediately if it jumps out of the strip. Now Artem wants to find out if this will ever happen.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β length of the strip.
Next line contains a string of length n which consists of characters "<" and ">" only, that provide the direction of the jump from the corresponding cell. Next line contains n integers di (1 β€ di β€ 109) β the length of the jump from the i-th cell.
Output
Print "INFINITE" (without quotes) if grasshopper will continue his jumps forever. Otherwise print "FINITE" (without quotes).
Examples
Input
2
><
1 2
Output
FINITE
Input
3
>><
2 1 1
Output
INFINITE
Note
In the first sample grasshopper starts from the first cell and jumps to the right on the next cell. When he is in the second cell he needs to jump two cells left so he will jump out of the strip.
Second sample grasshopper path is 1 - 3 - 2 - 3 - 2 - 3 and so on. The path is infinite.
Submitted Solution:
```
n = int(input())
s = input()
a = list(map(int, input().split()))
WAS = False
pos = 1
for i in range(0, n) :
if s[pos - 1] == '<' : pos -= a[pos - 1]
else : pos += a[pos - 1]
if pos < 1 or pos > n : WAS = True
if WAS : break
if WAS : print("FINITE")
else : print("INFINITE")
```
Yes
| 94,849 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Artem found a grasshopper. He brought it to his house and constructed a jumping area for him.
The area looks like a strip of cells 1 Γ n. Each cell contains the direction for the next jump and the length of that jump. Grasshopper starts in the first cell and follows the instructions written on the cells. Grasshopper stops immediately if it jumps out of the strip. Now Artem wants to find out if this will ever happen.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β length of the strip.
Next line contains a string of length n which consists of characters "<" and ">" only, that provide the direction of the jump from the corresponding cell. Next line contains n integers di (1 β€ di β€ 109) β the length of the jump from the i-th cell.
Output
Print "INFINITE" (without quotes) if grasshopper will continue his jumps forever. Otherwise print "FINITE" (without quotes).
Examples
Input
2
><
1 2
Output
FINITE
Input
3
>><
2 1 1
Output
INFINITE
Note
In the first sample grasshopper starts from the first cell and jumps to the right on the next cell. When he is in the second cell he needs to jump two cells left so he will jump out of the strip.
Second sample grasshopper path is 1 - 3 - 2 - 3 - 2 - 3 and so on. The path is infinite.
Submitted Solution:
```
n=int(input())
S=input()
l=list(map(int,input().split()))
i=0
c=1
while i>=0 or i>=n-1 :
if S[i]=='>' and i+l[i]>n-1 :
c=1
break
if S[i]=='<' and i-l[i]<0 :
c=1
break
if l[i]==0 :
c=0
break
if S[i]=='>' :
i=i+l[i]
else :
i=i-l[i]
l[i]=0
if c==1 :
print('FINITE')
else :
print('INFINITE')
```
No
| 94,850 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Artem found a grasshopper. He brought it to his house and constructed a jumping area for him.
The area looks like a strip of cells 1 Γ n. Each cell contains the direction for the next jump and the length of that jump. Grasshopper starts in the first cell and follows the instructions written on the cells. Grasshopper stops immediately if it jumps out of the strip. Now Artem wants to find out if this will ever happen.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β length of the strip.
Next line contains a string of length n which consists of characters "<" and ">" only, that provide the direction of the jump from the corresponding cell. Next line contains n integers di (1 β€ di β€ 109) β the length of the jump from the i-th cell.
Output
Print "INFINITE" (without quotes) if grasshopper will continue his jumps forever. Otherwise print "FINITE" (without quotes).
Examples
Input
2
><
1 2
Output
FINITE
Input
3
>><
2 1 1
Output
INFINITE
Note
In the first sample grasshopper starts from the first cell and jumps to the right on the next cell. When he is in the second cell he needs to jump two cells left so he will jump out of the strip.
Second sample grasshopper path is 1 - 3 - 2 - 3 - 2 - 3 and so on. The path is infinite.
Submitted Solution:
```
n=int(input())
s=input()
l=list(map(int,input().split()))
c=0
for i in range(len(s)):
if s[i]=='>':
c+=l[i]
if c>n:
print('FINITE')
exit()
else:
c-=l[i]
if c<0:
print('FINITE')
exit()
print('INFINITE')
```
No
| 94,851 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Artem found a grasshopper. He brought it to his house and constructed a jumping area for him.
The area looks like a strip of cells 1 Γ n. Each cell contains the direction for the next jump and the length of that jump. Grasshopper starts in the first cell and follows the instructions written on the cells. Grasshopper stops immediately if it jumps out of the strip. Now Artem wants to find out if this will ever happen.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β length of the strip.
Next line contains a string of length n which consists of characters "<" and ">" only, that provide the direction of the jump from the corresponding cell. Next line contains n integers di (1 β€ di β€ 109) β the length of the jump from the i-th cell.
Output
Print "INFINITE" (without quotes) if grasshopper will continue his jumps forever. Otherwise print "FINITE" (without quotes).
Examples
Input
2
><
1 2
Output
FINITE
Input
3
>><
2 1 1
Output
INFINITE
Note
In the first sample grasshopper starts from the first cell and jumps to the right on the next cell. When he is in the second cell he needs to jump two cells left so he will jump out of the strip.
Second sample grasshopper path is 1 - 3 - 2 - 3 - 2 - 3 and so on. The path is infinite.
Submitted Solution:
```
n=int(input())
s=input()
l=list(map(int,input().split()))
c=0
for i in range(len(s)):
if s[i]=='>':
c+=l[i]
else:
c-=l[i]
if c>n or c<0:
break
print(['FINITE','INFINITE'][n>c>=0])
```
No
| 94,852 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Artem found a grasshopper. He brought it to his house and constructed a jumping area for him.
The area looks like a strip of cells 1 Γ n. Each cell contains the direction for the next jump and the length of that jump. Grasshopper starts in the first cell and follows the instructions written on the cells. Grasshopper stops immediately if it jumps out of the strip. Now Artem wants to find out if this will ever happen.
Input
The first line of the input contains a single integer n (1 β€ n β€ 100 000) β length of the strip.
Next line contains a string of length n which consists of characters "<" and ">" only, that provide the direction of the jump from the corresponding cell. Next line contains n integers di (1 β€ di β€ 109) β the length of the jump from the i-th cell.
Output
Print "INFINITE" (without quotes) if grasshopper will continue his jumps forever. Otherwise print "FINITE" (without quotes).
Examples
Input
2
><
1 2
Output
FINITE
Input
3
>><
2 1 1
Output
INFINITE
Note
In the first sample grasshopper starts from the first cell and jumps to the right on the next cell. When he is in the second cell he needs to jump two cells left so he will jump out of the strip.
Second sample grasshopper path is 1 - 3 - 2 - 3 - 2 - 3 and so on. The path is infinite.
Submitted Solution:
```
n = int(input())
t = input()
cord = 0
l = list(map(int,input().split()))
i = 0
d = set({})
while cord < len(t):
d.add(cord)
if t[cord] == ">":
cord = cord + l[i]
else:
cord = cord - l[i]
if cord < 0 or cord > n-1:
print("FINITE")
exit()
if cord in d:
print("INFINITE")
exit()
```
No
| 94,853 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Artem is fond of dancing. Most of all dances Artem likes rueda β Cuban dance that is danced by pairs of boys and girls forming a circle and dancing together.
More detailed, there are n pairs of boys and girls standing in a circle. Initially, boy number 1 dances with a girl number 1, boy number 2 dances with a girl number 2 and so on. Girls are numbered in the clockwise order. During the dance different moves are announced and all pairs perform this moves. While performing moves boys move along the circle, while girls always stay at their initial position. For the purpose of this problem we consider two different types of moves:
1. Value x and some direction are announced, and all boys move x positions in the corresponding direction.
2. Boys dancing with even-indexed girls swap positions with boys who are dancing with odd-indexed girls. That is the one who was dancing with the girl 1 swaps with the one who was dancing with the girl number 2, while the one who was dancing with girl number 3 swaps with the one who was dancing with the girl number 4 and so one. It's guaranteed that n is even.
Your task is to determine the final position of each boy.
Input
The first line of the input contains two integers n and q (2 β€ n β€ 1 000 000, 1 β€ q β€ 2 000 000) β the number of couples in the rueda and the number of commands to perform, respectively. It's guaranteed that n is even.
Next q lines contain the descriptions of the commands. Each command has type as the integer 1 or 2 first. Command of the first type is given as x ( - n β€ x β€ n), where 0 β€ x β€ n means all boys moves x girls in clockwise direction, while - x means all boys move x positions in counter-clockwise direction. There is no other input for commands of the second type.
Output
Output n integers, the i-th of them should be equal to the index of boy the i-th girl is dancing with after performing all q moves.
Examples
Input
6 3
1 2
2
1 2
Output
4 3 6 5 2 1
Input
2 3
1 1
2
1 -2
Output
1 2
Input
4 2
2
1 3
Output
1 4 3 2
Submitted Solution:
```
n, q = [int(i) for i in input().split()]
s1 = [2*i+1 for i in range(n//2)]
s2 = [2*i+2 for i in range(n//2)]
dv1 = 0
dv2 = 0
ch = 0
for i in range(q):
o = [int(i) for i in input().split()]
if o[0] == 1:
if o[1]<0:
o[1]+=n
if o[1]%2 == 0:
dv1+=o[1]//2
dv2+=o[1]//2
else:
if ch:
dv1+=o[1]//2+1
dv2+=o[1]//2
else:
dv1+=o[1]//2
dv2+=o[1]//2+1
ch = not ch
if o[0] == 2:
ch = not ch
if ch:
s1, s2 = s2, s1
s1 = s1[n//2-dv1%(n//2):]+s1[:n//2-dv1%(n//2)]
s2 = s2[n//2-dv2%(n//2):]+s2[:n//2-dv2%(n//2)]
s = []
for i in range(n):
if i%2 == 0:
s.append(s1[i//2])
else:
s.append(s2[i//2])
print(*s)
```
No
| 94,854 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Artem is fond of dancing. Most of all dances Artem likes rueda β Cuban dance that is danced by pairs of boys and girls forming a circle and dancing together.
More detailed, there are n pairs of boys and girls standing in a circle. Initially, boy number 1 dances with a girl number 1, boy number 2 dances with a girl number 2 and so on. Girls are numbered in the clockwise order. During the dance different moves are announced and all pairs perform this moves. While performing moves boys move along the circle, while girls always stay at their initial position. For the purpose of this problem we consider two different types of moves:
1. Value x and some direction are announced, and all boys move x positions in the corresponding direction.
2. Boys dancing with even-indexed girls swap positions with boys who are dancing with odd-indexed girls. That is the one who was dancing with the girl 1 swaps with the one who was dancing with the girl number 2, while the one who was dancing with girl number 3 swaps with the one who was dancing with the girl number 4 and so one. It's guaranteed that n is even.
Your task is to determine the final position of each boy.
Input
The first line of the input contains two integers n and q (2 β€ n β€ 1 000 000, 1 β€ q β€ 2 000 000) β the number of couples in the rueda and the number of commands to perform, respectively. It's guaranteed that n is even.
Next q lines contain the descriptions of the commands. Each command has type as the integer 1 or 2 first. Command of the first type is given as x ( - n β€ x β€ n), where 0 β€ x β€ n means all boys moves x girls in clockwise direction, while - x means all boys move x positions in counter-clockwise direction. There is no other input for commands of the second type.
Output
Output n integers, the i-th of them should be equal to the index of boy the i-th girl is dancing with after performing all q moves.
Examples
Input
6 3
1 2
2
1 2
Output
4 3 6 5 2 1
Input
2 3
1 1
2
1 -2
Output
1 2
Input
4 2
2
1 3
Output
1 4 3 2
Submitted Solution:
```
# You lost the game.
n,q = map(int, input().split())
Q = [list(map(int, input().split())) for _ in range(q)]
impair = 0
pair = 0
pos = 1
for i in range(q):
if Q[i][0] == 1:
d = Q[i][1]
impair += d
pair += d
if pos == 1 and d % 2:
pos = -1
elif pos == -1 and d % 2 == 0:
pos = 1
else:
impair += pos
pair += -pos
pos = -pos
for i in range(1,n+1):
j = i-1
if pair % 2:
if i % 2:
print(1+(j-pair) % n,end=" ")
else:
print(1+(j-impair) % n,end=" ")
else:
if i % 2:
print(1+(j-impair) % n,end=" ")
else:
print(1+(j-pair) % n,end=" ")
```
No
| 94,855 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Artem is fond of dancing. Most of all dances Artem likes rueda β Cuban dance that is danced by pairs of boys and girls forming a circle and dancing together.
More detailed, there are n pairs of boys and girls standing in a circle. Initially, boy number 1 dances with a girl number 1, boy number 2 dances with a girl number 2 and so on. Girls are numbered in the clockwise order. During the dance different moves are announced and all pairs perform this moves. While performing moves boys move along the circle, while girls always stay at their initial position. For the purpose of this problem we consider two different types of moves:
1. Value x and some direction are announced, and all boys move x positions in the corresponding direction.
2. Boys dancing with even-indexed girls swap positions with boys who are dancing with odd-indexed girls. That is the one who was dancing with the girl 1 swaps with the one who was dancing with the girl number 2, while the one who was dancing with girl number 3 swaps with the one who was dancing with the girl number 4 and so one. It's guaranteed that n is even.
Your task is to determine the final position of each boy.
Input
The first line of the input contains two integers n and q (2 β€ n β€ 1 000 000, 1 β€ q β€ 2 000 000) β the number of couples in the rueda and the number of commands to perform, respectively. It's guaranteed that n is even.
Next q lines contain the descriptions of the commands. Each command has type as the integer 1 or 2 first. Command of the first type is given as x ( - n β€ x β€ n), where 0 β€ x β€ n means all boys moves x girls in clockwise direction, while - x means all boys move x positions in counter-clockwise direction. There is no other input for commands of the second type.
Output
Output n integers, the i-th of them should be equal to the index of boy the i-th girl is dancing with after performing all q moves.
Examples
Input
6 3
1 2
2
1 2
Output
4 3 6 5 2 1
Input
2 3
1 1
2
1 -2
Output
1 2
Input
4 2
2
1 3
Output
1 4 3 2
Submitted Solution:
```
def dance_result(n, q, moves):
changes, swaps = 0, 0
for m in moves:
if m[0] == 1:
changes += m[1]
else:
swaps += 1
changes, swaps = changes % n, swaps % n
pos = []
for i in range(0, n):
p = ((i + changes) % (n)) + 1
pos.append(p)
if swaps == 1:
for i in range(n // 2):
pos[2*i], pos[(2*i) + 1] = pos[(2*i) + 1], pos[2*i]
pos_girl = [0]*n
for i in range(len(pos)):
p = pos[i]
pos_girl[p-1] = i + 1
return pos_girl
def main():
n, q = list(map(int, input().strip().split()))
moves = []
for t in range(q):
move = list(map(int, input().strip().split()))
moves.append(move)
ans = dance_result(n, q, moves)
print(' '.join(str(e) for e in ans))
if __name__ == '__main__':
main()
```
No
| 94,856 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Artem is fond of dancing. Most of all dances Artem likes rueda β Cuban dance that is danced by pairs of boys and girls forming a circle and dancing together.
More detailed, there are n pairs of boys and girls standing in a circle. Initially, boy number 1 dances with a girl number 1, boy number 2 dances with a girl number 2 and so on. Girls are numbered in the clockwise order. During the dance different moves are announced and all pairs perform this moves. While performing moves boys move along the circle, while girls always stay at their initial position. For the purpose of this problem we consider two different types of moves:
1. Value x and some direction are announced, and all boys move x positions in the corresponding direction.
2. Boys dancing with even-indexed girls swap positions with boys who are dancing with odd-indexed girls. That is the one who was dancing with the girl 1 swaps with the one who was dancing with the girl number 2, while the one who was dancing with girl number 3 swaps with the one who was dancing with the girl number 4 and so one. It's guaranteed that n is even.
Your task is to determine the final position of each boy.
Input
The first line of the input contains two integers n and q (2 β€ n β€ 1 000 000, 1 β€ q β€ 2 000 000) β the number of couples in the rueda and the number of commands to perform, respectively. It's guaranteed that n is even.
Next q lines contain the descriptions of the commands. Each command has type as the integer 1 or 2 first. Command of the first type is given as x ( - n β€ x β€ n), where 0 β€ x β€ n means all boys moves x girls in clockwise direction, while - x means all boys move x positions in counter-clockwise direction. There is no other input for commands of the second type.
Output
Output n integers, the i-th of them should be equal to the index of boy the i-th girl is dancing with after performing all q moves.
Examples
Input
6 3
1 2
2
1 2
Output
4 3 6 5 2 1
Input
2 3
1 1
2
1 -2
Output
1 2
Input
4 2
2
1 3
Output
1 4 3 2
Submitted Solution:
```
from collections import deque
n, q = map(int, input().split())
boys = deque(range(1, n + 1))
rot = 0
for i in range(q):
comm = list(map(int, input().split()))
if comm[0] == 1:
rot += comm[1]
if comm[0] == 2:
boys.rotate(rot)
for i in range(0, n, 2):
boys[i], boys[i + 1] = boys[i + 1], boys[i]
print(*boys)
```
No
| 94,857 |
Provide a correct Python 3 solution for this coding contest problem.
The Human-Cow Confederation (HC2), led by Heidi, has built a base where people and cows can hide, guarded from zombie attacks. The entrance to the base is protected by an automated gate which performs a kind of a Turing test: it shows the entering creature a photograph and asks them whether the top and bottom halves of this photograph have been swapped or not. A person (or even a cow) will have no problem answering such questions; on the other hand, a zombie would just randomly smash one of the two buttons.
The creature is asked a series of such questions. If at least 75% of them are answered correctly, the gate is unlocked; otherwise, a side door opens, beneath which a huge fan is spinning...
Heidi is now building a robot army to fight the zombies, and she wants the robots to also be able to enter the base. You are tasked with programming them to distinguish the images.
<image>
The first two images from the test set. The first picture has been rearranged, but not the second.
Input
The first line of the input contains the number q of questions (1 β€ q β€ 220). After that, q questions follow, each of which in the format described below.
The first line of every question contains two space-separated integers h and w (1 β€ h, w β€ 600) β the height (number of rows) and width (number of columns) of the photograph. (Most photographs are roughly 200 Γ 300.) After this, h lines follow, each describing a single row of the picture. The picture is monochrome (in shades of grey). Its i-th row is described by w space-separated integers aij (j = 1, ..., w), where aij is the brightness of the corresponding pixel (0 β€ aij < 256, where 0 is black and 255 is white).
Each picture will be either a real-life photograph, or a real-life photograph which has been broken up into two pieces and rearranged. More precisely, in the latter case, the topmost <image> rows have been moved to the bottom of the picture. It is guaranteed that h is even.
There is only a single input file to be processed, called all.in, and it is downloadable from the online judge. You are also a given another input file, called sample.in, which contains the first 20 pictures from all.in; you are provided the correct answers for sample.in in sample.out. You are also given a directory easy_bmp, which contains the first 50 input photographs in the form of .bmp image files, as well as a directory easy_sample_original_bmp, which contains the first 20 images before rearrangement. Check the notes for the download links.
Output
Your program should print q lines. The i-th line should contain your answer for the i-th question: YES if the photograph has been rearranged and NO otherwise. Your answers will be accepted if they all conform to this format and if at least 75% of them are correct.
Because the input is rather huge, feel free to process it locally and submit just your precomputed answers (i.e., a program which just prints your output for the input file all.in).
Note
The link to download all necessary files is http://assets.codeforces.com/files/690/easy_contestant_package.zip
"Correct Solution:
```
import sys, math
#sys.stdin = open ('sample.in','r')
n = int(input())
for i in range(n):
p,q = map(int,input().split())
for j in range(p):
if j == 0:
fir = list(map(int, input().split()))
elif j == p//2 - 1:
sec = list(map(int, input().split()))
elif j == p//2:
third = list(map(int, input().split()))
elif j == p-1:
fourth = list(map(int, input().split()))
else:
input()
ans1 = 0
ans2 = 0
for j in range(q):
ans1 += math.fabs(sec[j] - third[j])
ans2 += math.fabs(fir[j] - fourth[j])
if ans1 >= ans2:
print('YES')
else:
print('NO')
```
| 94,858 |
Provide a correct Python 3 solution for this coding contest problem.
The Human-Cow Confederation (HC2), led by Heidi, has built a base where people and cows can hide, guarded from zombie attacks. The entrance to the base is protected by an automated gate which performs a kind of a Turing test: it shows the entering creature a photograph and asks them whether the top and bottom halves of this photograph have been swapped or not. A person (or even a cow) will have no problem answering such questions; on the other hand, a zombie would just randomly smash one of the two buttons.
The creature is asked a series of such questions. If at least 75% of them are answered correctly, the gate is unlocked; otherwise, a side door opens, beneath which a huge fan is spinning...
Heidi is now building a robot army to fight the zombies, and she wants the robots to also be able to enter the base. You are tasked with programming them to distinguish the images.
<image>
The first two images from the test set. The first picture has been rearranged, but not the second.
Input
The first line of the input contains the number q of questions (1 β€ q β€ 220). After that, q questions follow, each of which in the format described below.
The first line of every question contains two space-separated integers h and w (1 β€ h, w β€ 600) β the height (number of rows) and width (number of columns) of the photograph. (Most photographs are roughly 200 Γ 300.) After this, h lines follow, each describing a single row of the picture. The picture is monochrome (in shades of grey). Its i-th row is described by w space-separated integers aij (j = 1, ..., w), where aij is the brightness of the corresponding pixel (0 β€ aij < 256, where 0 is black and 255 is white).
Each picture will be either a real-life photograph, or a real-life photograph which has been broken up into two pieces and rearranged. More precisely, in the latter case, the topmost <image> rows have been moved to the bottom of the picture. It is guaranteed that h is even.
There is only a single input file to be processed, called all.in, and it is downloadable from the online judge. You are also a given another input file, called sample.in, which contains the first 20 pictures from all.in; you are provided the correct answers for sample.in in sample.out. You are also given a directory easy_bmp, which contains the first 50 input photographs in the form of .bmp image files, as well as a directory easy_sample_original_bmp, which contains the first 20 images before rearrangement. Check the notes for the download links.
Output
Your program should print q lines. The i-th line should contain your answer for the i-th question: YES if the photograph has been rearranged and NO otherwise. Your answers will be accepted if they all conform to this format and if at least 75% of them are correct.
Because the input is rather huge, feel free to process it locally and submit just your precomputed answers (i.e., a program which just prints your output for the input file all.in).
Note
The link to download all necessary files is http://assets.codeforces.com/files/690/easy_contestant_package.zip
"Correct Solution:
```
print("""YES
NO
NO
YES
NO
NO
NO
NO
NO
YES
YES
YES
YES
YES
NO
YES
NO
YES
NO
YES
NO
NO
YES
NO
NO
YES
NO
NO
YES
YES
YES
YES
NO
YES
NO
YES
YES
YES
NO
YES
YES
NO
YES
YES
NO
YES
YES
YES
NO
YES
YES
NO
YES
YES
YES
YES
YES
NO
NO
NO
YES
NO
NO
NO
NO
NO
NO
NO
NO
NO
YES
NO
YES
NO
NO
NO
YES
YES
NO
YES
YES
NO
NO
NO
NO
NO
NO
YES
NO
NO
YES
NO
YES
NO
NO
NO
NO
YES
YES
YES
YES
YES
NO
NO
NO
YES
NO
YES
NO
YES
NO
YES
YES
NO
YES
YES
YES
YES
NO
NO
NO
YES
NO
YES
YES
YES
NO
YES
NO
NO
NO
YES
NO
NO
NO
YES
NO
YES
YES
YES
YES
YES
YES
YES
YES
YES
NO
YES
NO
NO
NO
NO
NO
YES
NO
NO
YES
NO
YES
NO
YES
NO
YES
NO
NO
YES
NO
NO
NO
YES
NO
YES
NO
NO
YES
NO
NO
NO
NO
YES
YES
YES
NO
YES
NO
NO
NO
YES
YES
NO
YES
NO
YES
YES
YES
NO
YES
YES
NO
YES
YES
YES
YES
NO
YES
YES
NO
NO
YES
NO
NO
NO
YES
YES
NO
YES""")
```
| 94,859 |
Provide a correct Python 3 solution for this coding contest problem.
The Human-Cow Confederation (HC2), led by Heidi, has built a base where people and cows can hide, guarded from zombie attacks. The entrance to the base is protected by an automated gate which performs a kind of a Turing test: it shows the entering creature a photograph and asks them whether the top and bottom halves of this photograph have been swapped or not. A person (or even a cow) will have no problem answering such questions; on the other hand, a zombie would just randomly smash one of the two buttons.
The creature is asked a series of such questions. If at least 75% of them are answered correctly, the gate is unlocked; otherwise, a side door opens, beneath which a huge fan is spinning...
Heidi is now building a robot army to fight the zombies, and she wants the robots to also be able to enter the base. You are tasked with programming them to distinguish the images.
<image>
The first two images from the test set. The first picture has been rearranged, but not the second.
Input
The first line of the input contains the number q of questions (1 β€ q β€ 220). After that, q questions follow, each of which in the format described below.
The first line of every question contains two space-separated integers h and w (1 β€ h, w β€ 600) β the height (number of rows) and width (number of columns) of the photograph. (Most photographs are roughly 200 Γ 300.) After this, h lines follow, each describing a single row of the picture. The picture is monochrome (in shades of grey). Its i-th row is described by w space-separated integers aij (j = 1, ..., w), where aij is the brightness of the corresponding pixel (0 β€ aij < 256, where 0 is black and 255 is white).
Each picture will be either a real-life photograph, or a real-life photograph which has been broken up into two pieces and rearranged. More precisely, in the latter case, the topmost <image> rows have been moved to the bottom of the picture. It is guaranteed that h is even.
There is only a single input file to be processed, called all.in, and it is downloadable from the online judge. You are also a given another input file, called sample.in, which contains the first 20 pictures from all.in; you are provided the correct answers for sample.in in sample.out. You are also given a directory easy_bmp, which contains the first 50 input photographs in the form of .bmp image files, as well as a directory easy_sample_original_bmp, which contains the first 20 images before rearrangement. Check the notes for the download links.
Output
Your program should print q lines. The i-th line should contain your answer for the i-th question: YES if the photograph has been rearranged and NO otherwise. Your answers will be accepted if they all conform to this format and if at least 75% of them are correct.
Because the input is rather huge, feel free to process it locally and submit just your precomputed answers (i.e., a program which just prints your output for the input file all.in).
Note
The link to download all necessary files is http://assets.codeforces.com/files/690/easy_contestant_package.zip
"Correct Solution:
```
print('YES')
print('NO')
print('NO')
print('YES')
print('NO')
print('NO')
print('NO')
print('NO')
print('NO')
print('YES')
print('YES')
print('YES')
print('YES')
print('YES')
print('YES')
print('YES')
print('NO')
print('YES')
print('NO')
print('YES')
print('NO')
print('NO')
print('YES')
print('NO')
print('NO')
print('YES')
print('NO')
print('NO')
print('YES')
print('YES')
print('NO')
print('YES')
print('NO')
print('YES')
print('NO')
print('YES')
print('YES')
print('YES')
print('NO')
print('YES')
print('YES')
print('NO')
print('YES')
print('YES')
print('NO')
print('YES')
print('YES')
print('YES')
print('NO')
print('YES')
print('NO')
print('NO')
print('YES')
print('YES')
print('YES')
print('YES')
print('YES')
print('YES')
print('NO')
print('NO')
print('YES')
print('NO')
print('NO')
print('NO')
print('NO')
print('YES')
print('NO')
print('NO')
print('NO')
print('NO')
print('YES')
print('NO')
print('YES')
print('NO')
print('NO')
print('NO')
print('YES')
print('YES')
print('NO')
print('YES')
print('YES')
print('NO')
print('NO')
print('NO')
print('NO')
print('NO')
print('NO')
print('YES')
print('NO')
print('NO')
print('YES')
print('NO')
print('YES')
print('NO')
print('NO')
print('NO')
print('NO')
print('YES')
print('YES')
print('YES')
print('YES')
print('YES')
print('NO')
print('NO')
print('NO')
print('YES')
print('NO')
print('YES')
print('NO')
print('YES')
print('NO')
print('YES')
print('NO')
print('NO')
print('YES')
print('YES')
print('YES')
print('YES')
print('NO')
print('NO')
print('NO')
print('YES')
print('NO')
print('YES')
print('YES')
print('YES')
print('NO')
print('YES')
print('NO')
print('NO')
print('NO')
print('YES')
print('NO')
print('NO')
print('NO')
print('YES')
print('YES')
print('YES')
print('YES')
print('YES')
print('YES')
print('YES')
print('YES')
print('YES')
print('YES')
print('YES')
print('NO')
print('YES')
print('NO')
print('NO')
print('NO')
print('NO')
print('NO')
print('YES')
print('NO')
print('NO')
print('YES')
print('NO')
print('YES')
print('NO')
print('YES')
print('NO')
print('YES')
print('NO')
print('NO')
print('YES')
print('YES')
print('NO')
print('NO')
print('YES')
print('NO')
print('NO')
print('NO')
print('NO')
print('YES')
print('NO')
print('YES')
print('NO')
print('NO')
print('YES')
print('NO')
print('YES')
print('YES')
print('YES')
print('NO')
print('NO')
print('NO')
print('YES')
print('YES')
print('NO')
print('YES')
print('NO')
print('YES')
print('YES')
print('YES')
print('NO')
print('YES')
print('YES')
print('NO')
print('YES')
print('NO')
print('YES')
print('YES')
print('NO')
print('YES')
print('YES')
print('NO')
print('NO')
print('YES')
print('NO')
print('NO')
print('NO')
print('YES')
print('YES')
print('NO')
print('YES')
```
| 94,860 |
Provide a correct Python 3 solution for this coding contest problem.
The Human-Cow Confederation (HC2), led by Heidi, has built a base where people and cows can hide, guarded from zombie attacks. The entrance to the base is protected by an automated gate which performs a kind of a Turing test: it shows the entering creature a photograph and asks them whether the top and bottom halves of this photograph have been swapped or not. A person (or even a cow) will have no problem answering such questions; on the other hand, a zombie would just randomly smash one of the two buttons.
The creature is asked a series of such questions. If at least 75% of them are answered correctly, the gate is unlocked; otherwise, a side door opens, beneath which a huge fan is spinning...
Heidi is now building a robot army to fight the zombies, and she wants the robots to also be able to enter the base. You are tasked with programming them to distinguish the images.
<image>
The first two images from the test set. The first picture has been rearranged, but not the second.
Input
The first line of the input contains the number q of questions (1 β€ q β€ 220). After that, q questions follow, each of which in the format described below.
The first line of every question contains two space-separated integers h and w (1 β€ h, w β€ 600) β the height (number of rows) and width (number of columns) of the photograph. (Most photographs are roughly 200 Γ 300.) After this, h lines follow, each describing a single row of the picture. The picture is monochrome (in shades of grey). Its i-th row is described by w space-separated integers aij (j = 1, ..., w), where aij is the brightness of the corresponding pixel (0 β€ aij < 256, where 0 is black and 255 is white).
Each picture will be either a real-life photograph, or a real-life photograph which has been broken up into two pieces and rearranged. More precisely, in the latter case, the topmost <image> rows have been moved to the bottom of the picture. It is guaranteed that h is even.
There is only a single input file to be processed, called all.in, and it is downloadable from the online judge. You are also a given another input file, called sample.in, which contains the first 20 pictures from all.in; you are provided the correct answers for sample.in in sample.out. You are also given a directory easy_bmp, which contains the first 50 input photographs in the form of .bmp image files, as well as a directory easy_sample_original_bmp, which contains the first 20 images before rearrangement. Check the notes for the download links.
Output
Your program should print q lines. The i-th line should contain your answer for the i-th question: YES if the photograph has been rearranged and NO otherwise. Your answers will be accepted if they all conform to this format and if at least 75% of them are correct.
Because the input is rather huge, feel free to process it locally and submit just your precomputed answers (i.e., a program which just prints your output for the input file all.in).
Note
The link to download all necessary files is http://assets.codeforces.com/files/690/easy_contestant_package.zip
"Correct Solution:
```
a = ['YES', 'NO', 'NO', 'YES', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'YES', 'YES', 'YES', 'NO', 'NO', 'YES', 'NO', 'YES', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'YES', 'NO', 'NO', 'YES', 'YES', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'YES', 'YES', 'NO', 'NO', 'YES', 'NO', 'NO', 'YES', 'NO', 'YES', 'YES', 'NO', 'NO', 'NO', 'NO', 'NO', 'YES', 'YES', 'YES', 'YES', 'NO', 'NO', 'NO', 'NO', 'YES', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'YES', 'YES', 'NO', 'NO', 'YES', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'YES', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'YES', 'YES', 'YES', 'NO', 'YES', 'NO', 'NO', 'NO', 'YES', 'NO', 'YES', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'YES', 'YES', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'YES', 'YES', 'YES', 'NO', 'YES', 'NO', 'NO', 'NO', 'YES', 'NO', 'NO', 'NO', 'YES', 'NO', 'NO', 'NO', 'YES', 'NO', 'YES', 'YES', 'YES', 'YES', 'YES', 'NO', 'YES', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'YES', 'NO', 'YES', 'NO', 'YES', 'NO', 'YES', 'NO', 'NO', 'YES', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'YES', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'YES', 'NO', 'NO', 'NO', 'NO', 'NO', 'YES', 'YES', 'NO', 'YES', 'NO', 'YES', 'YES', 'YES', 'NO', 'YES', 'YES', 'NO', 'NO', 'NO', 'NO', 'YES', 'NO', 'NO', 'YES', 'NO', 'NO', 'YES', 'NO', 'NO', 'NO', 'YES', 'NO', 'NO', 'NO']
for elem in a:
print(elem)
```
| 94,861 |
Provide a correct Python 3 solution for this coding contest problem.
The Human-Cow Confederation (HC2), led by Heidi, has built a base where people and cows can hide, guarded from zombie attacks. The entrance to the base is protected by an automated gate which performs a kind of a Turing test: it shows the entering creature a photograph and asks them whether the top and bottom halves of this photograph have been swapped or not. A person (or even a cow) will have no problem answering such questions; on the other hand, a zombie would just randomly smash one of the two buttons.
The creature is asked a series of such questions. If at least 75% of them are answered correctly, the gate is unlocked; otherwise, a side door opens, beneath which a huge fan is spinning...
Heidi is now building a robot army to fight the zombies, and she wants the robots to also be able to enter the base. You are tasked with programming them to distinguish the images.
<image>
The first two images from the test set. The first picture has been rearranged, but not the second.
Input
The first line of the input contains the number q of questions (1 β€ q β€ 220). After that, q questions follow, each of which in the format described below.
The first line of every question contains two space-separated integers h and w (1 β€ h, w β€ 600) β the height (number of rows) and width (number of columns) of the photograph. (Most photographs are roughly 200 Γ 300.) After this, h lines follow, each describing a single row of the picture. The picture is monochrome (in shades of grey). Its i-th row is described by w space-separated integers aij (j = 1, ..., w), where aij is the brightness of the corresponding pixel (0 β€ aij < 256, where 0 is black and 255 is white).
Each picture will be either a real-life photograph, or a real-life photograph which has been broken up into two pieces and rearranged. More precisely, in the latter case, the topmost <image> rows have been moved to the bottom of the picture. It is guaranteed that h is even.
There is only a single input file to be processed, called all.in, and it is downloadable from the online judge. You are also a given another input file, called sample.in, which contains the first 20 pictures from all.in; you are provided the correct answers for sample.in in sample.out. You are also given a directory easy_bmp, which contains the first 50 input photographs in the form of .bmp image files, as well as a directory easy_sample_original_bmp, which contains the first 20 images before rearrangement. Check the notes for the download links.
Output
Your program should print q lines. The i-th line should contain your answer for the i-th question: YES if the photograph has been rearranged and NO otherwise. Your answers will be accepted if they all conform to this format and if at least 75% of them are correct.
Because the input is rather huge, feel free to process it locally and submit just your precomputed answers (i.e., a program which just prints your output for the input file all.in).
Note
The link to download all necessary files is http://assets.codeforces.com/files/690/easy_contestant_package.zip
"Correct Solution:
```
for x in ['YES', 'NO', 'NO', 'YES', 'NO', 'NO', 'NO', 'NO', 'NO', 'YES', 'YES', 'YES', 'YES', 'YES', 'YES', 'YES', 'NO', 'YES', 'NO', 'YES', 'NO', 'NO', 'YES', 'NO', 'NO', 'YES', 'NO', 'NO', 'YES', 'YES', 'NO', 'YES', 'NO', 'YES', 'NO', 'YES', 'YES', 'YES', 'NO', 'YES', 'YES', 'NO', 'YES', 'YES', 'NO', 'YES', 'YES', 'YES', 'NO', 'YES', 'NO', 'NO', 'YES', 'YES', 'YES', 'YES', 'YES', 'YES', 'NO', 'NO', 'YES', 'NO', 'NO', 'NO', 'NO', 'YES', 'NO', 'NO', 'NO', 'NO', 'YES', 'NO', 'YES', 'NO', 'NO', 'NO', 'YES', 'YES', 'NO', 'YES', 'YES', 'NO', 'NO', 'NO', 'NO', 'NO', 'NO', 'YES', 'NO', 'NO', 'YES', 'NO', 'YES', 'NO', 'NO', 'NO', 'NO', 'YES', 'YES', 'YES', 'YES', 'YES', 'NO', 'NO', 'NO', 'YES', 'NO', 'YES', 'NO', 'YES', 'NO', 'YES', 'NO', 'NO', 'YES', 'YES', 'YES', 'YES', 'NO', 'NO', 'NO', 'YES', 'NO', 'YES', 'YES', 'YES', 'NO', 'YES', 'NO', 'NO', 'NO', 'YES', 'NO', 'NO', 'NO', 'YES', 'YES', 'YES', 'YES', 'YES', 'YES', 'YES', 'YES', 'YES', 'YES', 'YES', 'NO', 'YES', 'NO', 'NO', 'NO', 'NO', 'NO', 'YES', 'NO', 'NO', 'YES', 'NO', 'YES', 'NO', 'YES', 'NO', 'YES', 'NO', 'NO', 'YES', 'YES', 'NO', 'NO', 'YES', 'NO', 'NO', 'NO', 'NO', 'YES', 'NO', 'YES', 'NO', 'NO', 'YES', 'NO', 'YES', 'YES', 'YES', 'NO', 'NO', 'NO', 'YES', 'YES', 'NO', 'YES', 'NO', 'YES', 'YES', 'YES', 'NO', 'YES', 'YES', 'NO', 'YES', 'NO', 'YES', 'YES', 'NO', 'YES', 'YES', 'NO', 'NO', 'YES', 'NO', 'NO', 'NO', 'YES', 'YES', 'NO', 'YES']:
print(x)
```
| 94,862 |
Provide a correct Python 3 solution for this coding contest problem.
The Human-Cow Confederation (HC2), led by Heidi, has built a base where people and cows can hide, guarded from zombie attacks. The entrance to the base is protected by an automated gate which performs a kind of a Turing test: it shows the entering creature a photograph and asks them whether the top and bottom halves of this photograph have been swapped or not. A person (or even a cow) will have no problem answering such questions; on the other hand, a zombie would just randomly smash one of the two buttons.
The creature is asked a series of such questions. If at least 75% of them are answered correctly, the gate is unlocked; otherwise, a side door opens, beneath which a huge fan is spinning...
Heidi is now building a robot army to fight the zombies, and she wants the robots to also be able to enter the base. You are tasked with programming them to distinguish the images.
<image>
The first two images from the test set. The first picture has been rearranged, but not the second.
Input
The first line of the input contains the number q of questions (1 β€ q β€ 220). After that, q questions follow, each of which in the format described below.
The first line of every question contains two space-separated integers h and w (1 β€ h, w β€ 600) β the height (number of rows) and width (number of columns) of the photograph. (Most photographs are roughly 200 Γ 300.) After this, h lines follow, each describing a single row of the picture. The picture is monochrome (in shades of grey). Its i-th row is described by w space-separated integers aij (j = 1, ..., w), where aij is the brightness of the corresponding pixel (0 β€ aij < 256, where 0 is black and 255 is white).
Each picture will be either a real-life photograph, or a real-life photograph which has been broken up into two pieces and rearranged. More precisely, in the latter case, the topmost <image> rows have been moved to the bottom of the picture. It is guaranteed that h is even.
There is only a single input file to be processed, called all.in, and it is downloadable from the online judge. You are also a given another input file, called sample.in, which contains the first 20 pictures from all.in; you are provided the correct answers for sample.in in sample.out. You are also given a directory easy_bmp, which contains the first 50 input photographs in the form of .bmp image files, as well as a directory easy_sample_original_bmp, which contains the first 20 images before rearrangement. Check the notes for the download links.
Output
Your program should print q lines. The i-th line should contain your answer for the i-th question: YES if the photograph has been rearranged and NO otherwise. Your answers will be accepted if they all conform to this format and if at least 75% of them are correct.
Because the input is rather huge, feel free to process it locally and submit just your precomputed answers (i.e., a program which just prints your output for the input file all.in).
Note
The link to download all necessary files is http://assets.codeforces.com/files/690/easy_contestant_package.zip
"Correct Solution:
```
a = '''YES
NO
NO
YES
NO
NO
NO
NO
NO
YES
YES
YES
YES
YES
NO
YES
NO
YES
NO
YES
NO
NO
YES
NO
NO
YES
NO
NO
YES
YES
NO
YES
NO
YES
NO
YES
YES
YES
NO
YES
YES
NO
YES
YES
NO
YES
YES
YES
NO
YES
NO
NO
NO
YES
YES
YES
YES
NO
NO
NO
YES
NO
NO
NO
NO
NO
NO
NO
YES
NO
YES
NO
YES
NO
NO
NO
YES
YES
NO
YES
YES
NO
NO
NO
NO
NO
NO
YES
NO
NO
YES
NO
NO
YES
NO
NO
NO
YES
YES
YES
YES
YES
NO
NO
NO
YES
NO
YES
NO
YES
NO
NO
NO
NO
YES
YES
YES
YES
NO
NO
NO
NO
NO
YES
YES
YES
NO
YES
NO
NO
NO
YES
YES
NO
NO
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
NO
YES
NO
NO
NO
NO
NO
YES
NO
NO
YES
NO
YES
NO
YES
NO
YES
NO
NO
YES
YES
NO
NO
YES
NO
NO
NO
NO
YES
NO
NO
NO
NO
NO
NO
YES
NO
NO
NO
NO
NO
YES
YES
NO
YES
NO
YES
YES
YES
NO
YES
YES
NO
YES
NO
NO
YES
NO
YES
YES
NO
NO
YES
NO
NO
NO
YES
YES
NO
NO'''
print(a)
```
| 94,863 |
Provide a correct Python 3 solution for this coding contest problem.
The Human-Cow Confederation (HC2), led by Heidi, has built a base where people and cows can hide, guarded from zombie attacks. The entrance to the base is protected by an automated gate which performs a kind of a Turing test: it shows the entering creature a photograph and asks them whether the top and bottom halves of this photograph have been swapped or not. A person (or even a cow) will have no problem answering such questions; on the other hand, a zombie would just randomly smash one of the two buttons.
The creature is asked a series of such questions. If at least 75% of them are answered correctly, the gate is unlocked; otherwise, a side door opens, beneath which a huge fan is spinning...
Heidi is now building a robot army to fight the zombies, and she wants the robots to also be able to enter the base. You are tasked with programming them to distinguish the images.
<image>
The first two images from the test set. The first picture has been rearranged, but not the second.
Input
The first line of the input contains the number q of questions (1 β€ q β€ 220). After that, q questions follow, each of which in the format described below.
The first line of every question contains two space-separated integers h and w (1 β€ h, w β€ 600) β the height (number of rows) and width (number of columns) of the photograph. (Most photographs are roughly 200 Γ 300.) After this, h lines follow, each describing a single row of the picture. The picture is monochrome (in shades of grey). Its i-th row is described by w space-separated integers aij (j = 1, ..., w), where aij is the brightness of the corresponding pixel (0 β€ aij < 256, where 0 is black and 255 is white).
Each picture will be either a real-life photograph, or a real-life photograph which has been broken up into two pieces and rearranged. More precisely, in the latter case, the topmost <image> rows have been moved to the bottom of the picture. It is guaranteed that h is even.
There is only a single input file to be processed, called all.in, and it is downloadable from the online judge. You are also a given another input file, called sample.in, which contains the first 20 pictures from all.in; you are provided the correct answers for sample.in in sample.out. You are also given a directory easy_bmp, which contains the first 50 input photographs in the form of .bmp image files, as well as a directory easy_sample_original_bmp, which contains the first 20 images before rearrangement. Check the notes for the download links.
Output
Your program should print q lines. The i-th line should contain your answer for the i-th question: YES if the photograph has been rearranged and NO otherwise. Your answers will be accepted if they all conform to this format and if at least 75% of them are correct.
Because the input is rather huge, feel free to process it locally and submit just your precomputed answers (i.e., a program which just prints your output for the input file all.in).
Note
The link to download all necessary files is http://assets.codeforces.com/files/690/easy_contestant_package.zip
"Correct Solution:
```
print('''YES
NO
NO
YES
NO
NO
NO
NO
NO
YES
YES
YES
YES
YES
YES
YES
NO
YES
NO
YES
NO
NO
NO
NO
NO
YES
NO
NO
YES
YES
NO
YES
NO
YES
NO
YES
YES
YES
NO
YES
YES
NO
YES
YES
NO
YES
YES
NO
NO
YES
NO
NO
YES
YES
YES
YES
NO
NO
NO
NO
YES
NO
NO
NO
NO
NO
NO
NO
NO
NO
YES
NO
NO
NO
NO
NO
YES
YES
NO
NO
YES
NO
NO
NO
NO
NO
NO
NO
NO
NO
YES
NO
YES
NO
NO
NO
NO
YES
YES
YES
YES
YES
NO
NO
NO
YES
NO
YES
NO
YES
NO
NO
NO
NO
YES
YES
YES
YES
NO
NO
NO
YES
NO
YES
YES
YES
NO
YES
NO
NO
NO
YES
NO
NO
NO
YES
NO
YES
YES
YES
YES
YES
YES
YES
YES
YES
NO
YES
NO
NO
NO
NO
NO
YES
NO
NO
YES
NO
YES
NO
YES
NO
YES
NO
NO
YES
YES
NO
NO
YES
NO
NO
NO
NO
YES
NO
NO
NO
NO
YES
NO
YES
NO
NO
NO
NO
NO
YES
YES
NO
YES
NO
YES
YES
YES
NO
YES
YES
NO
NO
NO
YES
YES
NO
NO
YES
NO
NO
YES
NO
NO
NO
YES
YES
NO
YES
''')
```
| 94,864 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The Human-Cow Confederation (HC2), led by Heidi, has built a base where people and cows can hide, guarded from zombie attacks. The entrance to the base is protected by an automated gate which performs a kind of a Turing test: it shows the entering creature a photograph and asks them whether the top and bottom halves of this photograph have been swapped or not. A person (or even a cow) will have no problem answering such questions; on the other hand, a zombie would just randomly smash one of the two buttons.
The creature is asked a series of such questions. If at least 75% of them are answered correctly, the gate is unlocked; otherwise, a side door opens, beneath which a huge fan is spinning...
Heidi is now building a robot army to fight the zombies, and she wants the robots to also be able to enter the base. You are tasked with programming them to distinguish the images.
<image>
The first two images from the test set. The first picture has been rearranged, but not the second.
Input
The first line of the input contains the number q of questions (1 β€ q β€ 220). After that, q questions follow, each of which in the format described below.
The first line of every question contains two space-separated integers h and w (1 β€ h, w β€ 600) β the height (number of rows) and width (number of columns) of the photograph. (Most photographs are roughly 200 Γ 300.) After this, h lines follow, each describing a single row of the picture. The picture is monochrome (in shades of grey). Its i-th row is described by w space-separated integers aij (j = 1, ..., w), where aij is the brightness of the corresponding pixel (0 β€ aij < 256, where 0 is black and 255 is white).
Each picture will be either a real-life photograph, or a real-life photograph which has been broken up into two pieces and rearranged. More precisely, in the latter case, the topmost <image> rows have been moved to the bottom of the picture. It is guaranteed that h is even.
There is only a single input file to be processed, called all.in, and it is downloadable from the online judge. You are also a given another input file, called sample.in, which contains the first 20 pictures from all.in; you are provided the correct answers for sample.in in sample.out. You are also given a directory easy_bmp, which contains the first 50 input photographs in the form of .bmp image files, as well as a directory easy_sample_original_bmp, which contains the first 20 images before rearrangement. Check the notes for the download links.
Output
Your program should print q lines. The i-th line should contain your answer for the i-th question: YES if the photograph has been rearranged and NO otherwise. Your answers will be accepted if they all conform to this format and if at least 75% of them are correct.
Because the input is rather huge, feel free to process it locally and submit just your precomputed answers (i.e., a program which just prints your output for the input file all.in).
Note
The link to download all necessary files is http://assets.codeforces.com/files/690/easy_contestant_package.zip
Submitted Solution:
```
print("""YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
NO
YES
YES
YES
YES
YES
YES
YES
NO
YES
YES
YES
YES
YES
YES
YES
YES
YES
NO
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
NO
NO
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
NO
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
NO
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
""")
```
No
| 94,865 |
Provide tags and a correct Python 3 solution for this coding contest problem.
ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '<image>' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.
When ZS the Coder is at level k, he can :
1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
2. Press the '<image>' button. Let the number on the screen be x. After pressing this button, the number becomes <image>. After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m.
Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '<image>' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.
ZS the Coder needs your help in beating the game β he wants to reach level n + 1. In other words, he needs to press the '<image>' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '<image>' button at each level.
Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.
Input
The first and only line of the input contains a single integer n (1 β€ n β€ 100 000), denoting that ZS the Coder wants to reach level n + 1.
Output
Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '<image>' button at level i.
Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.
Examples
Input
3
Output
14
16
46
Input
2
Output
999999999999999998
44500000000
Input
4
Output
2
17
46
97
Note
In the first sample case:
On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14Β·1 = 16. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16Β·2 = 36. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46Β·3 = 144. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4.
Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10Β·3 = 36, and when the '<image>' button is pressed, the number becomes <image> and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution.
In the second sample case:
On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998Β·1 = 1018. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes 109 + 44500000000Β·2 = 9Β·1010. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3.
Tags: constructive algorithms, math
Correct Solution:
```
n = int(input())
now = 2
lvl = 0
ans = []
for i in range(1, n + 1):
to = (lvl + 1) * (lvl + 2)
ans.append((to * to - now) / (lvl + 1))
now = to
lvl = lvl + 1
for i in ans:
print(int(i))
```
| 94,866 |
Provide tags and a correct Python 3 solution for this coding contest problem.
ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '<image>' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.
When ZS the Coder is at level k, he can :
1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
2. Press the '<image>' button. Let the number on the screen be x. After pressing this button, the number becomes <image>. After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m.
Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '<image>' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.
ZS the Coder needs your help in beating the game β he wants to reach level n + 1. In other words, he needs to press the '<image>' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '<image>' button at each level.
Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.
Input
The first and only line of the input contains a single integer n (1 β€ n β€ 100 000), denoting that ZS the Coder wants to reach level n + 1.
Output
Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '<image>' button at level i.
Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.
Examples
Input
3
Output
14
16
46
Input
2
Output
999999999999999998
44500000000
Input
4
Output
2
17
46
97
Note
In the first sample case:
On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14Β·1 = 16. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16Β·2 = 36. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46Β·3 = 144. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4.
Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10Β·3 = 36, and when the '<image>' button is pressed, the number becomes <image> and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution.
In the second sample case:
On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998Β·1 = 1018. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes 109 + 44500000000Β·2 = 9Β·1010. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3.
Tags: constructive algorithms, math
Correct Solution:
```
from math import sqrt
m=2
print(2)
k=2
n=int(input())
while k<n+1:
print((k+1)*(k+1)*k-(k-1))
k+=1
```
| 94,867 |
Provide tags and a correct Python 3 solution for this coding contest problem.
ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '<image>' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.
When ZS the Coder is at level k, he can :
1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
2. Press the '<image>' button. Let the number on the screen be x. After pressing this button, the number becomes <image>. After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m.
Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '<image>' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.
ZS the Coder needs your help in beating the game β he wants to reach level n + 1. In other words, he needs to press the '<image>' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '<image>' button at each level.
Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.
Input
The first and only line of the input contains a single integer n (1 β€ n β€ 100 000), denoting that ZS the Coder wants to reach level n + 1.
Output
Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '<image>' button at level i.
Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.
Examples
Input
3
Output
14
16
46
Input
2
Output
999999999999999998
44500000000
Input
4
Output
2
17
46
97
Note
In the first sample case:
On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14Β·1 = 16. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16Β·2 = 36. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46Β·3 = 144. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4.
Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10Β·3 = 36, and when the '<image>' button is pressed, the number becomes <image> and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution.
In the second sample case:
On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998Β·1 = 1018. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes 109 + 44500000000Β·2 = 9Β·1010. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3.
Tags: constructive algorithms, math
Correct Solution:
```
def solve(x):
return ((((x + 1) ** 2) * (x ** 2)) - (x * x - x)) / x
inp = int(input(""))
lvl = 1
print ("2")
while(inp >= 2):
ops = solve(lvl + 1)
print (int(ops))
lvl = lvl + 1
inp = inp - 1
```
| 94,868 |
Provide tags and a correct Python 3 solution for this coding contest problem.
ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '<image>' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.
When ZS the Coder is at level k, he can :
1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
2. Press the '<image>' button. Let the number on the screen be x. After pressing this button, the number becomes <image>. After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m.
Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '<image>' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.
ZS the Coder needs your help in beating the game β he wants to reach level n + 1. In other words, he needs to press the '<image>' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '<image>' button at each level.
Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.
Input
The first and only line of the input contains a single integer n (1 β€ n β€ 100 000), denoting that ZS the Coder wants to reach level n + 1.
Output
Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '<image>' button at level i.
Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.
Examples
Input
3
Output
14
16
46
Input
2
Output
999999999999999998
44500000000
Input
4
Output
2
17
46
97
Note
In the first sample case:
On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14Β·1 = 16. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16Β·2 = 36. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46Β·3 = 144. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4.
Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10Β·3 = 36, and when the '<image>' button is pressed, the number becomes <image> and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution.
In the second sample case:
On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998Β·1 = 1018. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes 109 + 44500000000Β·2 = 9Β·1010. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3.
Tags: constructive algorithms, math
Correct Solution:
```
n = int(input())
nxt = 2
for i in range(1,n+1):
temp = (i+1)*2
if(temp%i != 0 or temp%(i+1) != 0):
temp = i*(i+1)
print(int((temp*temp-nxt)/i))
nxt = temp
```
| 94,869 |
Provide tags and a correct Python 3 solution for this coding contest problem.
ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '<image>' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.
When ZS the Coder is at level k, he can :
1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
2. Press the '<image>' button. Let the number on the screen be x. After pressing this button, the number becomes <image>. After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m.
Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '<image>' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.
ZS the Coder needs your help in beating the game β he wants to reach level n + 1. In other words, he needs to press the '<image>' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '<image>' button at each level.
Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.
Input
The first and only line of the input contains a single integer n (1 β€ n β€ 100 000), denoting that ZS the Coder wants to reach level n + 1.
Output
Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '<image>' button at level i.
Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.
Examples
Input
3
Output
14
16
46
Input
2
Output
999999999999999998
44500000000
Input
4
Output
2
17
46
97
Note
In the first sample case:
On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14Β·1 = 16. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16Β·2 = 36. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46Β·3 = 144. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4.
Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10Β·3 = 36, and when the '<image>' button is pressed, the number becomes <image> and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution.
In the second sample case:
On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998Β·1 = 1018. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes 109 + 44500000000Β·2 = 9Β·1010. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3.
Tags: constructive algorithms, math
Correct Solution:
```
import math
n = int(input())
al = 2
for i in range(1,n+1):
ai = (i*i+i)**2;
res= (ai -al)//i;
al = int(math.sqrt(int(ai)))
print(int(res))
```
| 94,870 |
Provide tags and a correct Python 3 solution for this coding contest problem.
ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '<image>' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.
When ZS the Coder is at level k, he can :
1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
2. Press the '<image>' button. Let the number on the screen be x. After pressing this button, the number becomes <image>. After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m.
Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '<image>' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.
ZS the Coder needs your help in beating the game β he wants to reach level n + 1. In other words, he needs to press the '<image>' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '<image>' button at each level.
Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.
Input
The first and only line of the input contains a single integer n (1 β€ n β€ 100 000), denoting that ZS the Coder wants to reach level n + 1.
Output
Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '<image>' button at level i.
Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.
Examples
Input
3
Output
14
16
46
Input
2
Output
999999999999999998
44500000000
Input
4
Output
2
17
46
97
Note
In the first sample case:
On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14Β·1 = 16. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16Β·2 = 36. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46Β·3 = 144. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4.
Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10Β·3 = 36, and when the '<image>' button is pressed, the number becomes <image> and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution.
In the second sample case:
On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998Β·1 = 1018. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes 109 + 44500000000Β·2 = 9Β·1010. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3.
Tags: constructive algorithms, math
Correct Solution:
```
str = input()
n = int(str)
num = 2;
lv = 1;
t = 1;
while n != 0:
t = nlv = lv + 1;
t = lv * nlv
print(lv * nlv * nlv - int(num / lv))
num = t;
lv = nlv;
n -= 1
```
| 94,871 |
Provide tags and a correct Python 3 solution for this coding contest problem.
ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '<image>' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.
When ZS the Coder is at level k, he can :
1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
2. Press the '<image>' button. Let the number on the screen be x. After pressing this button, the number becomes <image>. After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m.
Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '<image>' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.
ZS the Coder needs your help in beating the game β he wants to reach level n + 1. In other words, he needs to press the '<image>' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '<image>' button at each level.
Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.
Input
The first and only line of the input contains a single integer n (1 β€ n β€ 100 000), denoting that ZS the Coder wants to reach level n + 1.
Output
Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '<image>' button at level i.
Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.
Examples
Input
3
Output
14
16
46
Input
2
Output
999999999999999998
44500000000
Input
4
Output
2
17
46
97
Note
In the first sample case:
On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14Β·1 = 16. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16Β·2 = 36. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46Β·3 = 144. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4.
Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10Β·3 = 36, and when the '<image>' button is pressed, the number becomes <image> and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution.
In the second sample case:
On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998Β·1 = 1018. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes 109 + 44500000000Β·2 = 9Β·1010. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3.
Tags: constructive algorithms, math
Correct Solution:
```
n = int(input())
cur = int(2)
i = int(1)
nxt = int()
print(2)
while i < n:
i = i + 1
nxt = i * (i + 1)
print (int(((nxt * nxt) - cur) / i))
cur = nxt;
```
| 94,872 |
Provide tags and a correct Python 3 solution for this coding contest problem.
ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '<image>' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.
When ZS the Coder is at level k, he can :
1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
2. Press the '<image>' button. Let the number on the screen be x. After pressing this button, the number becomes <image>. After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m.
Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '<image>' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.
ZS the Coder needs your help in beating the game β he wants to reach level n + 1. In other words, he needs to press the '<image>' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '<image>' button at each level.
Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.
Input
The first and only line of the input contains a single integer n (1 β€ n β€ 100 000), denoting that ZS the Coder wants to reach level n + 1.
Output
Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '<image>' button at level i.
Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.
Examples
Input
3
Output
14
16
46
Input
2
Output
999999999999999998
44500000000
Input
4
Output
2
17
46
97
Note
In the first sample case:
On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14Β·1 = 16. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16Β·2 = 36. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46Β·3 = 144. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4.
Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10Β·3 = 36, and when the '<image>' button is pressed, the number becomes <image> and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution.
In the second sample case:
On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998Β·1 = 1018. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes 109 + 44500000000Β·2 = 9Β·1010. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3.
Tags: constructive algorithms, math
Correct Solution:
```
n=int(input())
num0 = 4
print("14")
for i in range(2, n + 1):
num1 = i * (i + 1)
x = (num1 * num1 - num0)/i
print("%d"%x)
num0 = num1
```
| 94,873 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '<image>' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.
When ZS the Coder is at level k, he can :
1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
2. Press the '<image>' button. Let the number on the screen be x. After pressing this button, the number becomes <image>. After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m.
Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '<image>' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.
ZS the Coder needs your help in beating the game β he wants to reach level n + 1. In other words, he needs to press the '<image>' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '<image>' button at each level.
Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.
Input
The first and only line of the input contains a single integer n (1 β€ n β€ 100 000), denoting that ZS the Coder wants to reach level n + 1.
Output
Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '<image>' button at level i.
Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.
Examples
Input
3
Output
14
16
46
Input
2
Output
999999999999999998
44500000000
Input
4
Output
2
17
46
97
Note
In the first sample case:
On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14Β·1 = 16. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16Β·2 = 36. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46Β·3 = 144. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4.
Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10Β·3 = 36, and when the '<image>' button is pressed, the number becomes <image> and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution.
In the second sample case:
On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998Β·1 = 1018. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes 109 + 44500000000Β·2 = 9Β·1010. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3.
Submitted Solution:
```
n = int(input())
for i in range(1,n+1) :
if i == 1 :
print(2)
else :
print((i+1)*(i+1)*i-(i-1))
```
Yes
| 94,874 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '<image>' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.
When ZS the Coder is at level k, he can :
1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
2. Press the '<image>' button. Let the number on the screen be x. After pressing this button, the number becomes <image>. After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m.
Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '<image>' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.
ZS the Coder needs your help in beating the game β he wants to reach level n + 1. In other words, he needs to press the '<image>' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '<image>' button at each level.
Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.
Input
The first and only line of the input contains a single integer n (1 β€ n β€ 100 000), denoting that ZS the Coder wants to reach level n + 1.
Output
Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '<image>' button at level i.
Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.
Examples
Input
3
Output
14
16
46
Input
2
Output
999999999999999998
44500000000
Input
4
Output
2
17
46
97
Note
In the first sample case:
On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14Β·1 = 16. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16Β·2 = 36. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46Β·3 = 144. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4.
Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10Β·3 = 36, and when the '<image>' button is pressed, the number becomes <image> and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution.
In the second sample case:
On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998Β·1 = 1018. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes 109 + 44500000000Β·2 = 9Β·1010. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3.
Submitted Solution:
```
import bisect
from itertools import accumulate, count
import os
import sys
import math
from decimal import *
from io import BytesIO, IOBase
from sys import maxsize
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
def input():
return sys.stdin.readline().rstrip("\r\n")
def isPrime(n):
if n <= 1:
return False
if n <= 3:
return True
if n % 2 == 0 or n % 3 == 0:
return False
i = 5
while i * i <= n:
if n % i == 0 or n % (i + 2) == 0:
return False
i = i + 6
return True
def SieveOfEratosthenes(n):
prime = []
primes = [True for i in range(n + 1)]
p = 2
while p * p <= n:
if primes[p] == True:
prime.append(p)
for i in range(p * p, n + 1, p):
primes[i] = False
p += 1
return prime
def primefactors(n):
fac = []
while n % 2 == 0:
fac.append(2)
n = n // 2
for i in range(3, int(math.sqrt(n)) + 2):
while n % i == 0:
fac.append(i)
n = n // i
if n > 1:
fac.append(n)
return sorted(fac)
def factors(n):
fac = set()
fac.add(1)
fac.add(n)
for i in range(2, int(math.sqrt(n)) + 1):
if n % i == 0:
fac.add(i)
fac.add(n // i)
return list(fac)
def modInverse(a, m):
m0 = m
y = 0
x = 1
if m == 1:
return 0
while a > 1:
q = a // m
t = m
m = a % m
a = t
t = y
y = x - q * y
x = t
if x < 0:
x = x + m0
return x
# ------------------------------------------------------code
n=int(input())
for i in range(1,n+1):
if i==1:
print(2)
else:
print((i*(i+1)*(i+1))-(i-1))
```
Yes
| 94,875 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '<image>' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.
When ZS the Coder is at level k, he can :
1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
2. Press the '<image>' button. Let the number on the screen be x. After pressing this button, the number becomes <image>. After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m.
Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '<image>' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.
ZS the Coder needs your help in beating the game β he wants to reach level n + 1. In other words, he needs to press the '<image>' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '<image>' button at each level.
Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.
Input
The first and only line of the input contains a single integer n (1 β€ n β€ 100 000), denoting that ZS the Coder wants to reach level n + 1.
Output
Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '<image>' button at level i.
Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.
Examples
Input
3
Output
14
16
46
Input
2
Output
999999999999999998
44500000000
Input
4
Output
2
17
46
97
Note
In the first sample case:
On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14Β·1 = 16. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16Β·2 = 36. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46Β·3 = 144. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4.
Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10Β·3 = 36, and when the '<image>' button is pressed, the number becomes <image> and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution.
In the second sample case:
On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998Β·1 = 1018. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes 109 + 44500000000Β·2 = 9Β·1010. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3.
Submitted Solution:
```
a=2
n=0
max = int(input())
for k in range(max+1):
if(k==0):
continue
n = k*(k+1)*(k+1)-a
a=k
print(n)
```
Yes
| 94,876 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '<image>' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.
When ZS the Coder is at level k, he can :
1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
2. Press the '<image>' button. Let the number on the screen be x. After pressing this button, the number becomes <image>. After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m.
Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '<image>' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.
ZS the Coder needs your help in beating the game β he wants to reach level n + 1. In other words, he needs to press the '<image>' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '<image>' button at each level.
Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.
Input
The first and only line of the input contains a single integer n (1 β€ n β€ 100 000), denoting that ZS the Coder wants to reach level n + 1.
Output
Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '<image>' button at level i.
Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.
Examples
Input
3
Output
14
16
46
Input
2
Output
999999999999999998
44500000000
Input
4
Output
2
17
46
97
Note
In the first sample case:
On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14Β·1 = 16. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16Β·2 = 36. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46Β·3 = 144. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4.
Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10Β·3 = 36, and when the '<image>' button is pressed, the number becomes <image> and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution.
In the second sample case:
On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998Β·1 = 1018. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes 109 + 44500000000Β·2 = 9Β·1010. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3.
Submitted Solution:
```
n=int(input())
ccc=2
s=4
for i in range(1,n+1):
s=i**2*(i+1)**2
t=int((s-ccc)/i)
print(t)
ccc=int(s**0.5)
```
Yes
| 94,877 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '<image>' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.
When ZS the Coder is at level k, he can :
1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
2. Press the '<image>' button. Let the number on the screen be x. After pressing this button, the number becomes <image>. After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m.
Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '<image>' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.
ZS the Coder needs your help in beating the game β he wants to reach level n + 1. In other words, he needs to press the '<image>' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '<image>' button at each level.
Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.
Input
The first and only line of the input contains a single integer n (1 β€ n β€ 100 000), denoting that ZS the Coder wants to reach level n + 1.
Output
Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '<image>' button at level i.
Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.
Examples
Input
3
Output
14
16
46
Input
2
Output
999999999999999998
44500000000
Input
4
Output
2
17
46
97
Note
In the first sample case:
On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14Β·1 = 16. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16Β·2 = 36. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46Β·3 = 144. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4.
Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10Β·3 = 36, and when the '<image>' button is pressed, the number becomes <image> and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution.
In the second sample case:
On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998Β·1 = 1018. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes 109 + 44500000000Β·2 = 9Β·1010. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3.
Submitted Solution:
```
n = int(input())
print(3)
for i in range(2, n + 1):
print(i ** 3 + 2 * i ** 2 + 1)
```
No
| 94,878 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '<image>' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.
When ZS the Coder is at level k, he can :
1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
2. Press the '<image>' button. Let the number on the screen be x. After pressing this button, the number becomes <image>. After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m.
Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '<image>' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.
ZS the Coder needs your help in beating the game β he wants to reach level n + 1. In other words, he needs to press the '<image>' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '<image>' button at each level.
Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.
Input
The first and only line of the input contains a single integer n (1 β€ n β€ 100 000), denoting that ZS the Coder wants to reach level n + 1.
Output
Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '<image>' button at level i.
Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.
Examples
Input
3
Output
14
16
46
Input
2
Output
999999999999999998
44500000000
Input
4
Output
2
17
46
97
Note
In the first sample case:
On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14Β·1 = 16. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16Β·2 = 36. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46Β·3 = 144. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4.
Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10Β·3 = 36, and when the '<image>' button is pressed, the number becomes <image> and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution.
In the second sample case:
On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998Β·1 = 1018. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes 109 + 44500000000Β·2 = 9Β·1010. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3.
Submitted Solution:
```
n = int(input())
print(2)
for k in range(2, n+1):
print(k*k*(k+1)*(k+1) - (k-1)*k)
```
No
| 94,879 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '<image>' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.
When ZS the Coder is at level k, he can :
1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
2. Press the '<image>' button. Let the number on the screen be x. After pressing this button, the number becomes <image>. After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m.
Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '<image>' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.
ZS the Coder needs your help in beating the game β he wants to reach level n + 1. In other words, he needs to press the '<image>' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '<image>' button at each level.
Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.
Input
The first and only line of the input contains a single integer n (1 β€ n β€ 100 000), denoting that ZS the Coder wants to reach level n + 1.
Output
Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '<image>' button at level i.
Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.
Examples
Input
3
Output
14
16
46
Input
2
Output
999999999999999998
44500000000
Input
4
Output
2
17
46
97
Note
In the first sample case:
On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14Β·1 = 16. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16Β·2 = 36. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46Β·3 = 144. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4.
Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10Β·3 = 36, and when the '<image>' button is pressed, the number becomes <image> and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution.
In the second sample case:
On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998Β·1 = 1018. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes 109 + 44500000000Β·2 = 9Β·1010. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3.
Submitted Solution:
```
n = int(input())
pd = [0]*(n+1);
pd[1] = 2
for i in range(2, n+1):
k = 1
while True:
if ((i*i*k*k - pd[i-1]) % (i-1) == 0):
pd[i] = i*k
break
k += 1
print((pd[i]*pd[i]-pd[i-1])//(i-1))
print(pd[n])
```
No
| 94,880 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '<image>' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.
When ZS the Coder is at level k, he can :
1. Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
2. Press the '<image>' button. Let the number on the screen be x. After pressing this button, the number becomes <image>. After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m.
Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '<image>' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.
ZS the Coder needs your help in beating the game β he wants to reach level n + 1. In other words, he needs to press the '<image>' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '<image>' button at each level.
Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.
Input
The first and only line of the input contains a single integer n (1 β€ n β€ 100 000), denoting that ZS the Coder wants to reach level n + 1.
Output
Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '<image>' button at level i.
Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.
Examples
Input
3
Output
14
16
46
Input
2
Output
999999999999999998
44500000000
Input
4
Output
2
17
46
97
Note
In the first sample case:
On the first level, ZS the Coder pressed the ' + ' button 14 times (and the number on screen is initially 2), so the number became 2 + 14Β·1 = 16. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 16 times, so the number becomes 4 + 16Β·2 = 36. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
After that, on the third level, ZS pressed the ' + ' button 46 times, so the number becomes 6 + 46Β·3 = 144. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 12 is indeed divisible by 4, so ZS the Coder can reach level 4.
Also, note that pressing the ' + ' button 10 times on the third level before levelling up does not work, because the number becomes 6 + 10Β·3 = 36, and when the '<image>' button is pressed, the number becomes <image> and ZS the Coder is at Level 4. However, 6 is not divisible by 4 now, so this is not a valid solution.
In the second sample case:
On the first level, ZS the Coder pressed the ' + ' button 999999999999999998 times (and the number on screen is initially 2), so the number became 2 + 999999999999999998Β·1 = 1018. Then, ZS the Coder pressed the '<image>' button, and the number became <image>.
After that, on the second level, ZS pressed the ' + ' button 44500000000 times, so the number becomes 109 + 44500000000Β·2 = 9Β·1010. Then, ZS pressed the '<image>' button, levelling up and changing the number into <image>.
Note that 300000 is a multiple of 3, so ZS the Coder can reach level 3.
Submitted Solution:
```
n=int(input())
s=1
for i in range(1,n+1):
n2=(i+1)**2
d=0
if s<n2:
d=n2-s
s=i+1
elif s>n2:
c=s%n2
d+=n2-c
s=n2*(s//n2+(1 if c else 0))
dx=(s//n2)**0.5
rdx=round(dx)
dx=rdx+1 if rdx<dx else rdx
dx2=dx**2
d+=dx2*n2-s
s=dx*(i+1)
print(d)
```
No
| 94,881 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.
Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.
Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.
Input
The only line of the input contains a single integer n (2 β€ n β€ 1018) β the number of players to participate in the tournament.
Output
Print the maximum number of games in which the winner of the tournament can take part.
Examples
Input
2
Output
1
Input
3
Output
2
Input
4
Output
2
Input
10
Output
4
Note
In all samples we consider that player number 1 is the winner.
In the first sample, there would be only one game so the answer is 1.
In the second sample, player 1 can consequently beat players 2 and 3.
In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners.
Tags: combinatorics, constructive algorithms, greedy, math
Correct Solution:
```
n=int(input())
a,b=2,1
cnt=0
while a<=n:
cnt+=1
a,b=a+b,a
print(cnt)
```
| 94,882 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.
Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.
Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.
Input
The only line of the input contains a single integer n (2 β€ n β€ 1018) β the number of players to participate in the tournament.
Output
Print the maximum number of games in which the winner of the tournament can take part.
Examples
Input
2
Output
1
Input
3
Output
2
Input
4
Output
2
Input
10
Output
4
Note
In all samples we consider that player number 1 is the winner.
In the first sample, there would be only one game so the answer is 1.
In the second sample, player 1 can consequently beat players 2 and 3.
In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners.
Tags: combinatorics, constructive algorithms, greedy, math
Correct Solution:
```
n = int(input())
l = [1, 2]
for i in range(100): l.append(l[-1] + l[-2])
for i in range(100):
if l[i] > n:
print(i - 1)
break
```
| 94,883 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.
Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.
Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.
Input
The only line of the input contains a single integer n (2 β€ n β€ 1018) β the number of players to participate in the tournament.
Output
Print the maximum number of games in which the winner of the tournament can take part.
Examples
Input
2
Output
1
Input
3
Output
2
Input
4
Output
2
Input
10
Output
4
Note
In all samples we consider that player number 1 is the winner.
In the first sample, there would be only one game so the answer is 1.
In the second sample, player 1 can consequently beat players 2 and 3.
In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners.
Tags: combinatorics, constructive algorithms, greedy, math
Correct Solution:
```
#python 3.6
fib=[1,2]
for i in range(90):
fib.append(fib[-1]+fib[-2])
n=int(input())
for i in range(len(fib)):
if fib[i]>n:
print(i-1)
break
```
| 94,884 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.
Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.
Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.
Input
The only line of the input contains a single integer n (2 β€ n β€ 1018) β the number of players to participate in the tournament.
Output
Print the maximum number of games in which the winner of the tournament can take part.
Examples
Input
2
Output
1
Input
3
Output
2
Input
4
Output
2
Input
10
Output
4
Note
In all samples we consider that player number 1 is the winner.
In the first sample, there would be only one game so the answer is 1.
In the second sample, player 1 can consequently beat players 2 and 3.
In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners.
Tags: combinatorics, constructive algorithms, greedy, math
Correct Solution:
```
###### ### ####### ####### ## # ##### ### #####
# # # # # # # # # # # # # ###
# # # # # # # # # # # # # ###
###### ######### # # # # # # ######### #
###### ######### # # # # # # ######### #
# # # # # # # # # # #### # # #
# # # # # # # ## # # # # #
###### # # ####### ####### # # ##### # # # #
from __future__ import print_function # for PyPy2
# from itertools import permutations
# from functools import cmp_to_key # for adding custom comparator
# from fractions import Fraction
from collections import *
from sys import stdin
from bisect import *
# from heapq import *
from math import *
g = lambda : stdin.readline().strip()
gl = lambda : g().split()
gil = lambda : [int(var) for var in gl()]
gfl = lambda : [float(var) for var in gl()]
gcl = lambda : list(g())
gbs = lambda : [int(var) for var in g()]
rr = lambda x : reversed(range(x))
mod = int(1e9)+7
inf = float("inf")
r = range
n, = gil()
a, b = 1, 2
ans = 1
while b+a <= n:
a, b = b, a+b
ans += 1
print(ans)
```
| 94,885 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.
Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.
Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.
Input
The only line of the input contains a single integer n (2 β€ n β€ 1018) β the number of players to participate in the tournament.
Output
Print the maximum number of games in which the winner of the tournament can take part.
Examples
Input
2
Output
1
Input
3
Output
2
Input
4
Output
2
Input
10
Output
4
Note
In all samples we consider that player number 1 is the winner.
In the first sample, there would be only one game so the answer is 1.
In the second sample, player 1 can consequently beat players 2 and 3.
In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners.
Tags: combinatorics, constructive algorithms, greedy, math
Correct Solution:
```
import sys,os,io
import math,bisect,operator
inf,mod = float('inf'),10**9+7
# sys.setrecursionlimit(10 ** 6)
from itertools import groupby,accumulate
from heapq import heapify,heappop,heappush
from collections import deque,Counter,defaultdict
input = iter(sys.stdin.buffer.read().decode().splitlines()).__next__
Neo = lambda : list(map(int,input().split()))
# test, = Neo()
n, = Neo()
t = 0
k1,k2 = 2,1
while k1 <= n:
t += 1
k1,k2 = k1+k2,k1
print(t)
```
| 94,886 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.
Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.
Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.
Input
The only line of the input contains a single integer n (2 β€ n β€ 1018) β the number of players to participate in the tournament.
Output
Print the maximum number of games in which the winner of the tournament can take part.
Examples
Input
2
Output
1
Input
3
Output
2
Input
4
Output
2
Input
10
Output
4
Note
In all samples we consider that player number 1 is the winner.
In the first sample, there would be only one game so the answer is 1.
In the second sample, player 1 can consequently beat players 2 and 3.
In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners.
Tags: combinatorics, constructive algorithms, greedy, math
Correct Solution:
```
n=int(input())
fib=1
last=1
i=0
while True:
i+=1
fib=fib+last
last=fib-last
if fib>n:
print(i-1)
exit(0)
#Π§ΡΠΎ Ρ codeforces?
```
| 94,887 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.
Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.
Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.
Input
The only line of the input contains a single integer n (2 β€ n β€ 1018) β the number of players to participate in the tournament.
Output
Print the maximum number of games in which the winner of the tournament can take part.
Examples
Input
2
Output
1
Input
3
Output
2
Input
4
Output
2
Input
10
Output
4
Note
In all samples we consider that player number 1 is the winner.
In the first sample, there would be only one game so the answer is 1.
In the second sample, player 1 can consequently beat players 2 and 3.
In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners.
Tags: combinatorics, constructive algorithms, greedy, math
Correct Solution:
```
n=int(input())
a,b,c=2,1,0
while a<=n:
a,b=a+b,a
c+=1
print(c)
```
| 94,888 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.
Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.
Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.
Input
The only line of the input contains a single integer n (2 β€ n β€ 1018) β the number of players to participate in the tournament.
Output
Print the maximum number of games in which the winner of the tournament can take part.
Examples
Input
2
Output
1
Input
3
Output
2
Input
4
Output
2
Input
10
Output
4
Note
In all samples we consider that player number 1 is the winner.
In the first sample, there would be only one game so the answer is 1.
In the second sample, player 1 can consequently beat players 2 and 3.
In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners.
Tags: combinatorics, constructive algorithms, greedy, math
Correct Solution:
```
n=int(input())
fib=1
last=1
i=0
while True:
i+=1
fib=fib+last
last=fib-last
if fib>n:
print(i-1)
exit(0)
```
| 94,889 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.
Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.
Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.
Input
The only line of the input contains a single integer n (2 β€ n β€ 1018) β the number of players to participate in the tournament.
Output
Print the maximum number of games in which the winner of the tournament can take part.
Examples
Input
2
Output
1
Input
3
Output
2
Input
4
Output
2
Input
10
Output
4
Note
In all samples we consider that player number 1 is the winner.
In the first sample, there would be only one game so the answer is 1.
In the second sample, player 1 can consequently beat players 2 and 3.
In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners.
Submitted Solution:
```
n=int(input())
x,y=1,1
z=-1
for i in range(0,n+1):
if y>n:
print(i-1)
break
z=x+y
x=y
y=z
```
Yes
| 94,890 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.
Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.
Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.
Input
The only line of the input contains a single integer n (2 β€ n β€ 1018) β the number of players to participate in the tournament.
Output
Print the maximum number of games in which the winner of the tournament can take part.
Examples
Input
2
Output
1
Input
3
Output
2
Input
4
Output
2
Input
10
Output
4
Note
In all samples we consider that player number 1 is the winner.
In the first sample, there would be only one game so the answer is 1.
In the second sample, player 1 can consequently beat players 2 and 3.
In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners.
Submitted Solution:
```
if __name__ == "__main__":
n = int(input())
arr = [1, 2]
while True:
tmp = arr[-1] + arr[-2]
if tmp > n:
break
arr.append(tmp)
print(len(arr) - 1)
```
Yes
| 94,891 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.
Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.
Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.
Input
The only line of the input contains a single integer n (2 β€ n β€ 1018) β the number of players to participate in the tournament.
Output
Print the maximum number of games in which the winner of the tournament can take part.
Examples
Input
2
Output
1
Input
3
Output
2
Input
4
Output
2
Input
10
Output
4
Note
In all samples we consider that player number 1 is the winner.
In the first sample, there would be only one game so the answer is 1.
In the second sample, player 1 can consequently beat players 2 and 3.
In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners.
Submitted Solution:
```
#------------------------template--------------------------#
import os
import sys
from math import *
from collections import *
from fractions import *
from bisect import *
from heapq import*
from io import BytesIO, IOBase
def vsInput():
sys.stdin = open('input.txt', 'r')
sys.stdout = open('output.txt', 'w')
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
def value():return tuple(map(int,input().split()))
def array():return [int(i) for i in input().split()]
def Int():return int(input())
def Str():return input()
def arrayS():return [i for i in input().split()]
#-------------------------code---------------------------#
#vsInput()
series=[2,3]
x=5
while(x<10**18):
series.append(x)
x+=series[-2]
#print(series)
n=Int()
ans=bisect_right(series,n)
print(ans)
```
Yes
| 94,892 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.
Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.
Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.
Input
The only line of the input contains a single integer n (2 β€ n β€ 1018) β the number of players to participate in the tournament.
Output
Print the maximum number of games in which the winner of the tournament can take part.
Examples
Input
2
Output
1
Input
3
Output
2
Input
4
Output
2
Input
10
Output
4
Note
In all samples we consider that player number 1 is the winner.
In the first sample, there would be only one game so the answer is 1.
In the second sample, player 1 can consequently beat players 2 and 3.
In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners.
Submitted Solution:
```
n = int(input())
a = 1
b = 1
k = 0
while a <= n:
a, b = a + b, a
k += 1
print(k - 1)
```
Yes
| 94,893 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.
Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.
Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.
Input
The only line of the input contains a single integer n (2 β€ n β€ 1018) β the number of players to participate in the tournament.
Output
Print the maximum number of games in which the winner of the tournament can take part.
Examples
Input
2
Output
1
Input
3
Output
2
Input
4
Output
2
Input
10
Output
4
Note
In all samples we consider that player number 1 is the winner.
In the first sample, there would be only one game so the answer is 1.
In the second sample, player 1 can consequently beat players 2 and 3.
In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners.
Submitted Solution:
```
n = int( input() )
if n <= 2:
print( 1 )
exit(0)
F = [1,1]
while F[-1] < n:
F.append( F[-1] + F[-2] )
s = 0
for i in range( len(F) ):
s += F[i]
if s > n:
print( i )
break
```
No
| 94,894 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.
Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.
Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.
Input
The only line of the input contains a single integer n (2 β€ n β€ 1018) β the number of players to participate in the tournament.
Output
Print the maximum number of games in which the winner of the tournament can take part.
Examples
Input
2
Output
1
Input
3
Output
2
Input
4
Output
2
Input
10
Output
4
Note
In all samples we consider that player number 1 is the winner.
In the first sample, there would be only one game so the answer is 1.
In the second sample, player 1 can consequently beat players 2 and 3.
In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners.
Submitted Solution:
```
"""
#If FastIO not needed, used this and don't forget to strip
#import sys, math
#input = sys.stdin.readline
"""
import os
import sys
from io import BytesIO, IOBase
import heapq as h
from bisect import bisect_left, bisect_right
from types import GeneratorType
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
import os
self.os = os
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
self.os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
from collections import defaultdict as dd, deque as dq, Counter as dc
import math, string
def getInts():
return [int(s) for s in input().split()]
def getInt():
return int(input())
def getStrs():
return [s for s in input().split()]
def getStr():
return input()
def listStr():
return list(input())
MOD = 998244353
"""
"""
def solve():
N = getInt()
x = 1
ans = 0
while x < N:
x *= 2
ans += 1
return ans
print(solve())
```
No
| 94,895 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.
Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.
Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.
Input
The only line of the input contains a single integer n (2 β€ n β€ 1018) β the number of players to participate in the tournament.
Output
Print the maximum number of games in which the winner of the tournament can take part.
Examples
Input
2
Output
1
Input
3
Output
2
Input
4
Output
2
Input
10
Output
4
Note
In all samples we consider that player number 1 is the winner.
In the first sample, there would be only one game so the answer is 1.
In the second sample, player 1 can consequently beat players 2 and 3.
In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners.
Submitted Solution:
```
from math import *
n = int(input())
if n == 4:
print(2)
else:
print(round(log(sqrt(5)*n,(1.0+sqrt(5))/2.0))-2 )
```
No
| 94,896 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.
Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.
Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.
Input
The only line of the input contains a single integer n (2 β€ n β€ 1018) β the number of players to participate in the tournament.
Output
Print the maximum number of games in which the winner of the tournament can take part.
Examples
Input
2
Output
1
Input
3
Output
2
Input
4
Output
2
Input
10
Output
4
Note
In all samples we consider that player number 1 is the winner.
In the first sample, there would be only one game so the answer is 1.
In the second sample, player 1 can consequently beat players 2 and 3.
In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners.
Submitted Solution:
```
n=int(input())
if(n==2):
print(1)
else:
s=pow(n,.5)
if(int(s)**2==n):
print(int(s))
else:
print(int(s)+1)
```
No
| 94,897 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Well, here is another math class task. In mathematics, GCD is the greatest common divisor, and it's an easy task to calculate the GCD between two positive integers.
A common divisor for two positive numbers is a number which both numbers are divisible by.
But your teacher wants to give you a harder task, in this task you have to find the greatest common divisor d between two integers a and b that is in a given range from low to high (inclusive), i.e. low β€ d β€ high. It is possible that there is no common divisor in the given range.
You will be given the two integers a and b, then n queries. Each query is a range from low to high and you have to answer each query.
Input
The first line contains two integers a and b, the two integers as described above (1 β€ a, b β€ 109). The second line contains one integer n, the number of queries (1 β€ n β€ 104). Then n lines follow, each line contains one query consisting of two integers, low and high (1 β€ low β€ high β€ 109).
Output
Print n lines. The i-th of them should contain the result of the i-th query in the input. If there is no common divisor in the given range for any query, you should print -1 as a result for this query.
Examples
Input
9 27
3
1 5
10 11
9 11
Output
3
-1
9
Tags: binary search, number theory
Correct Solution:
```
import math
from sys import stdout
def print_fast(string):
stdout.write(string + '\n')
def MGCD(_gcd, low, high):
answer = -1
botton = low
index = min(_gcd, high)
while index >= botton:
if _gcd % index == 0:
return index
index -= 1
return answer
_input = input().split()
a = int(_input[0])
b = int(_input[1])
_gcd = math.gcd(a, b)
divisors = []
i = 1
while i * i <= _gcd:
if _gcd % i == 0:
divisors.append(i)
divisors.append(_gcd // i)
i += 1
divisors = sorted(divisors)
testCases = int(input())
ans = []
for i in range(testCases):
_input = input().split()
l = int(_input[0])
h = int(_input[1])
answer = -1
for i in divisors:
if i > h:
break
if i >= l and i <= h:
answer = i
ans.append(str(answer))
#ans.append(str(MGCD(_gcd, l, h)))
print_fast('\n'.join(ans))
```
| 94,898 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Well, here is another math class task. In mathematics, GCD is the greatest common divisor, and it's an easy task to calculate the GCD between two positive integers.
A common divisor for two positive numbers is a number which both numbers are divisible by.
But your teacher wants to give you a harder task, in this task you have to find the greatest common divisor d between two integers a and b that is in a given range from low to high (inclusive), i.e. low β€ d β€ high. It is possible that there is no common divisor in the given range.
You will be given the two integers a and b, then n queries. Each query is a range from low to high and you have to answer each query.
Input
The first line contains two integers a and b, the two integers as described above (1 β€ a, b β€ 109). The second line contains one integer n, the number of queries (1 β€ n β€ 104). Then n lines follow, each line contains one query consisting of two integers, low and high (1 β€ low β€ high β€ 109).
Output
Print n lines. The i-th of them should contain the result of the i-th query in the input. If there is no common divisor in the given range for any query, you should print -1 as a result for this query.
Examples
Input
9 27
3
1 5
10 11
9 11
Output
3
-1
9
Tags: binary search, number theory
Correct Solution:
```
from math import gcd
a,b = list(map(int, input().split()))
cd = gcd(a,b)
ar =[]
for i in range(1,int(cd**0.5)+1):
if cd % i == 0:
ar.append(i)
if(i*i != cd):
ar.append(cd//i)
for _ in range(int(input())):
l,h = list(map(int, input().split()))
res = -1
for i in ar:
if(i >= l and i <= h):
res = max(res, i)
print(res)
```
| 94,899 |
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