message stringlengths 2 44.5k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 42 109k | cluster float64 5 5 | __index_level_0__ int64 84 217k |
|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
There is an integer sequence A of length N whose values are unknown.
Given is an integer sequence B of length N-1 which is known to satisfy the following:
B_i \geq \max(A_i, A_{i+1})
Find the maximum possible sum of the elements of A.
Constraints
* All values in input are integers.
* 2 \leq N \leq 100
* 0 \leq B_i \leq 10^5
Input
Input is given from Standard Input in the following format:
N
B_1 B_2 ... B_{N-1}
Output
Print the maximum possible sum of the elements of A.
Examples
Input
3
2 5
Output
9
Input
2
3
Output
6
Input
6
0 153 10 10 23
Output
53 | instruction | 0 | 3,122 | 5 | 6,244 |
"Correct Solution:
```
N=int(input())
B=list(map(int,input().split()))
A=[B[0],B[-1]]
for i in range(N-2):
A.append(min(B[i],B[i+1]))
print(sum(A))
``` | output | 1 | 3,122 | 5 | 6,245 |
Provide a correct Python 3 solution for this coding contest problem.
There is an integer sequence A of length N whose values are unknown.
Given is an integer sequence B of length N-1 which is known to satisfy the following:
B_i \geq \max(A_i, A_{i+1})
Find the maximum possible sum of the elements of A.
Constraints
* All values in input are integers.
* 2 \leq N \leq 100
* 0 \leq B_i \leq 10^5
Input
Input is given from Standard Input in the following format:
N
B_1 B_2 ... B_{N-1}
Output
Print the maximum possible sum of the elements of A.
Examples
Input
3
2 5
Output
9
Input
2
3
Output
6
Input
6
0 153 10 10 23
Output
53 | instruction | 0 | 3,123 | 5 | 6,246 |
"Correct Solution:
```
n=int(input())
a=list(map(int,input().split()))+[100000]
print(sum([a[0]]+[min(a[i],a[i+1])for i in range(n-1)]))
``` | output | 1 | 3,123 | 5 | 6,247 |
Provide a correct Python 3 solution for this coding contest problem.
There is an integer sequence A of length N whose values are unknown.
Given is an integer sequence B of length N-1 which is known to satisfy the following:
B_i \geq \max(A_i, A_{i+1})
Find the maximum possible sum of the elements of A.
Constraints
* All values in input are integers.
* 2 \leq N \leq 100
* 0 \leq B_i \leq 10^5
Input
Input is given from Standard Input in the following format:
N
B_1 B_2 ... B_{N-1}
Output
Print the maximum possible sum of the elements of A.
Examples
Input
3
2 5
Output
9
Input
2
3
Output
6
Input
6
0 153 10 10 23
Output
53 | instruction | 0 | 3,124 | 5 | 6,248 |
"Correct Solution:
```
n=int(input())
B=list(map(int,input().split()))
res=B[0]+B[n-2]
for i in range(n-2):
res += min(B[i],B[i+1])
print(res)
``` | output | 1 | 3,124 | 5 | 6,249 |
Provide a correct Python 3 solution for this coding contest problem.
There is an integer sequence A of length N whose values are unknown.
Given is an integer sequence B of length N-1 which is known to satisfy the following:
B_i \geq \max(A_i, A_{i+1})
Find the maximum possible sum of the elements of A.
Constraints
* All values in input are integers.
* 2 \leq N \leq 100
* 0 \leq B_i \leq 10^5
Input
Input is given from Standard Input in the following format:
N
B_1 B_2 ... B_{N-1}
Output
Print the maximum possible sum of the elements of A.
Examples
Input
3
2 5
Output
9
Input
2
3
Output
6
Input
6
0 153 10 10 23
Output
53 | instruction | 0 | 3,125 | 5 | 6,250 |
"Correct Solution:
```
n=int(input())
b=list(map(int,input().split()))
ans=b[0]+b[n-2]
for i in range(1,n-1):
ans+=min(b[i],b[i-1])
print(ans)
``` | output | 1 | 3,125 | 5 | 6,251 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is an integer sequence A of length N whose values are unknown.
Given is an integer sequence B of length N-1 which is known to satisfy the following:
B_i \geq \max(A_i, A_{i+1})
Find the maximum possible sum of the elements of A.
Constraints
* All values in input are integers.
* 2 \leq N \leq 100
* 0 \leq B_i \leq 10^5
Input
Input is given from Standard Input in the following format:
N
B_1 B_2 ... B_{N-1}
Output
Print the maximum possible sum of the elements of A.
Examples
Input
3
2 5
Output
9
Input
2
3
Output
6
Input
6
0 153 10 10 23
Output
53
Submitted Solution:
```
n = int(input())
b = list(map(int, input().split()))
a = [min(b[i],b[i+1]) for i in range(n-2)]
print(sum(a) + b[0] + b[-1])
``` | instruction | 0 | 3,126 | 5 | 6,252 |
Yes | output | 1 | 3,126 | 5 | 6,253 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is an integer sequence A of length N whose values are unknown.
Given is an integer sequence B of length N-1 which is known to satisfy the following:
B_i \geq \max(A_i, A_{i+1})
Find the maximum possible sum of the elements of A.
Constraints
* All values in input are integers.
* 2 \leq N \leq 100
* 0 \leq B_i \leq 10^5
Input
Input is given from Standard Input in the following format:
N
B_1 B_2 ... B_{N-1}
Output
Print the maximum possible sum of the elements of A.
Examples
Input
3
2 5
Output
9
Input
2
3
Output
6
Input
6
0 153 10 10 23
Output
53
Submitted Solution:
```
n = int(input())
b = [int(i) for i in input().split()]
print(b[0] + sum([min(b[i], b[i+1]) for i in range(n-2)]) + b[n-2])
``` | instruction | 0 | 3,127 | 5 | 6,254 |
Yes | output | 1 | 3,127 | 5 | 6,255 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is an integer sequence A of length N whose values are unknown.
Given is an integer sequence B of length N-1 which is known to satisfy the following:
B_i \geq \max(A_i, A_{i+1})
Find the maximum possible sum of the elements of A.
Constraints
* All values in input are integers.
* 2 \leq N \leq 100
* 0 \leq B_i \leq 10^5
Input
Input is given from Standard Input in the following format:
N
B_1 B_2 ... B_{N-1}
Output
Print the maximum possible sum of the elements of A.
Examples
Input
3
2 5
Output
9
Input
2
3
Output
6
Input
6
0 153 10 10 23
Output
53
Submitted Solution:
```
n,*bb = map(int, open(0).read().split())
ans = bb[0] + bb[-1]
for i in range(n-2):
ans += min(bb[i],bb[i+1])
print(ans)
``` | instruction | 0 | 3,128 | 5 | 6,256 |
Yes | output | 1 | 3,128 | 5 | 6,257 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is an integer sequence A of length N whose values are unknown.
Given is an integer sequence B of length N-1 which is known to satisfy the following:
B_i \geq \max(A_i, A_{i+1})
Find the maximum possible sum of the elements of A.
Constraints
* All values in input are integers.
* 2 \leq N \leq 100
* 0 \leq B_i \leq 10^5
Input
Input is given from Standard Input in the following format:
N
B_1 B_2 ... B_{N-1}
Output
Print the maximum possible sum of the elements of A.
Examples
Input
3
2 5
Output
9
Input
2
3
Output
6
Input
6
0 153 10 10 23
Output
53
Submitted Solution:
```
N=int(input())
B=list(map(int,input().split()))
a=B[0]+B[-1]
for i in range(N-2):
a+=min(B[i],B[i+1])
print(a)
``` | instruction | 0 | 3,129 | 5 | 6,258 |
Yes | output | 1 | 3,129 | 5 | 6,259 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is an integer sequence A of length N whose values are unknown.
Given is an integer sequence B of length N-1 which is known to satisfy the following:
B_i \geq \max(A_i, A_{i+1})
Find the maximum possible sum of the elements of A.
Constraints
* All values in input are integers.
* 2 \leq N \leq 100
* 0 \leq B_i \leq 10^5
Input
Input is given from Standard Input in the following format:
N
B_1 B_2 ... B_{N-1}
Output
Print the maximum possible sum of the elements of A.
Examples
Input
3
2 5
Output
9
Input
2
3
Output
6
Input
6
0 153 10 10 23
Output
53
Submitted Solution:
```
N = int(input())
B = list(map(int,input().split()))[::-1]
t = B[0]
ans = t
for k in range(1,N-1):
t = min(B[k],t)
ans += t
ans += t
print(ans)
``` | instruction | 0 | 3,130 | 5 | 6,260 |
No | output | 1 | 3,130 | 5 | 6,261 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is an integer sequence A of length N whose values are unknown.
Given is an integer sequence B of length N-1 which is known to satisfy the following:
B_i \geq \max(A_i, A_{i+1})
Find the maximum possible sum of the elements of A.
Constraints
* All values in input are integers.
* 2 \leq N \leq 100
* 0 \leq B_i \leq 10^5
Input
Input is given from Standard Input in the following format:
N
B_1 B_2 ... B_{N-1}
Output
Print the maximum possible sum of the elements of A.
Examples
Input
3
2 5
Output
9
Input
2
3
Output
6
Input
6
0 153 10 10 23
Output
53
Submitted Solution:
```
# -*- coding: utf-8 -*-
# 整数の入力
n = int(input())
# スペース区切りの整数の入力
a = map(int, input().split())
alist = list(a)
tmp = []
for i in range(n-1):
if i == 0:
tmp.append(alist[i])
tmp.append(alist[i])
else:
if i+2 < n and alist[i] > alist[i+1]:
tmp.append(alist[i+1])
else:
tmp.append(alist[i])
sum = 0
for i in tmp:
sum += int(i)
print(sum)
``` | instruction | 0 | 3,131 | 5 | 6,262 |
No | output | 1 | 3,131 | 5 | 6,263 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is an integer sequence A of length N whose values are unknown.
Given is an integer sequence B of length N-1 which is known to satisfy the following:
B_i \geq \max(A_i, A_{i+1})
Find the maximum possible sum of the elements of A.
Constraints
* All values in input are integers.
* 2 \leq N \leq 100
* 0 \leq B_i \leq 10^5
Input
Input is given from Standard Input in the following format:
N
B_1 B_2 ... B_{N-1}
Output
Print the maximum possible sum of the elements of A.
Examples
Input
3
2 5
Output
9
Input
2
3
Output
6
Input
6
0 153 10 10 23
Output
53
Submitted Solution:
```
N = int(input())
list_b = list(map(int,input().split()))
ans = 0
ans += list_b[0]
for i in range(N-1):
if (i != 0) and (i != N-2):
if (list_b[i] >= list_b[i-1]) and (list_b[i] <= list_b[i+1]):
ans += list_b[i]
elif (list_b[i] < list_b[i-1]) and (list_b[i] < list_b[i+1]):
ans += list_b[i]
else:
ans += list_b[i+1]
else:
ans += list_b[i]
print(ans)
``` | instruction | 0 | 3,132 | 5 | 6,264 |
No | output | 1 | 3,132 | 5 | 6,265 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is an integer sequence A of length N whose values are unknown.
Given is an integer sequence B of length N-1 which is known to satisfy the following:
B_i \geq \max(A_i, A_{i+1})
Find the maximum possible sum of the elements of A.
Constraints
* All values in input are integers.
* 2 \leq N \leq 100
* 0 \leq B_i \leq 10^5
Input
Input is given from Standard Input in the following format:
N
B_1 B_2 ... B_{N-1}
Output
Print the maximum possible sum of the elements of A.
Examples
Input
3
2 5
Output
9
Input
2
3
Output
6
Input
6
0 153 10 10 23
Output
53
Submitted Solution:
```
from functools import reduce
n=int(input())
b=list(map(int, input().split()))
b.extend([b[n-2],b[n-2]])
a=[]
j=0
for i in range(n):
if i < 2:
a.append(b[j])
continue
a.append(max(b[j], b[j+1]))
print(a)
if b[j+1] <= a[i]:
a[i-1]=min(b[j], b[j+1])
a[i]=min(b[j], b[j+1])
j+=1
print(reduce(lambda x,y: x+y, a))
``` | instruction | 0 | 3,133 | 5 | 6,266 |
No | output | 1 | 3,133 | 5 | 6,267 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino is planning to record N TV programs with recorders.
The TV can receive C channels numbered 1 through C.
The i-th program that she wants to record will be broadcast from time s_i to time t_i (including time s_i but not t_i) on Channel c_i.
Here, there will never be more than one program that are broadcast on the same channel at the same time.
When the recorder is recording a channel from time S to time T (including time S but not T), it cannot record other channels from time S-0.5 to time T (including time S-0.5 but not T).
Find the minimum number of recorders required to record the channels so that all the N programs are completely recorded.
Constraints
* 1≤N≤10^5
* 1≤C≤30
* 1≤s_i<t_i≤10^5
* 1≤c_i≤C
* If c_i=c_j and i≠j, either t_i≤s_j or s_i≥t_j.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N C
s_1 t_1 c_1
:
s_N t_N c_N
Output
When the minimum required number of recorders is x, print the value of x.
Examples
Input
3 2
1 7 2
7 8 1
8 12 1
Output
2
Input
3 4
1 3 2
3 4 4
1 4 3
Output
3
Input
9 4
56 60 4
33 37 2
89 90 3
32 43 1
67 68 3
49 51 3
31 32 3
70 71 1
11 12 3
Output
2 | instruction | 0 | 3,173 | 5 | 6,346 |
"Correct Solution:
```
n,c = [int(i) for i in input().split()]
A = [[0 for i in range(c)] for j in range(100000)]
for i in range(n):
s,t,c = [int(i) for i in input().split()]
for i in range(s-1,t):
A[i][c-1] = 1
ans = 0
for i in range(100000):
val = sum(A[i])
if val > ans:
ans = val
print(ans)
``` | output | 1 | 3,173 | 5 | 6,347 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino is planning to record N TV programs with recorders.
The TV can receive C channels numbered 1 through C.
The i-th program that she wants to record will be broadcast from time s_i to time t_i (including time s_i but not t_i) on Channel c_i.
Here, there will never be more than one program that are broadcast on the same channel at the same time.
When the recorder is recording a channel from time S to time T (including time S but not T), it cannot record other channels from time S-0.5 to time T (including time S-0.5 but not T).
Find the minimum number of recorders required to record the channels so that all the N programs are completely recorded.
Constraints
* 1≤N≤10^5
* 1≤C≤30
* 1≤s_i<t_i≤10^5
* 1≤c_i≤C
* If c_i=c_j and i≠j, either t_i≤s_j or s_i≥t_j.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N C
s_1 t_1 c_1
:
s_N t_N c_N
Output
When the minimum required number of recorders is x, print the value of x.
Examples
Input
3 2
1 7 2
7 8 1
8 12 1
Output
2
Input
3 4
1 3 2
3 4 4
1 4 3
Output
3
Input
9 4
56 60 4
33 37 2
89 90 3
32 43 1
67 68 3
49 51 3
31 32 3
70 71 1
11 12 3
Output
2 | instruction | 0 | 3,174 | 5 | 6,348 |
"Correct Solution:
```
N, C = map(int, input().split())
accu = [[0]*(10**5+10) for _ in range(C)]
for _ in range(N):
s, t, c = map(int, input().split())
accu[c-1][s] += 1
accu[c-1][t+1] -= 1
for i in range(C):
for j in range(1, 10**5+10):
accu[i][j] += accu[i][j-1]
ans = 0
for i in range(10**5+10):
tmp = 0
for j in range(C):
tmp += accu[j][i]>0
ans = max(ans, tmp)
print(ans)
``` | output | 1 | 3,174 | 5 | 6,349 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino is planning to record N TV programs with recorders.
The TV can receive C channels numbered 1 through C.
The i-th program that she wants to record will be broadcast from time s_i to time t_i (including time s_i but not t_i) on Channel c_i.
Here, there will never be more than one program that are broadcast on the same channel at the same time.
When the recorder is recording a channel from time S to time T (including time S but not T), it cannot record other channels from time S-0.5 to time T (including time S-0.5 but not T).
Find the minimum number of recorders required to record the channels so that all the N programs are completely recorded.
Constraints
* 1≤N≤10^5
* 1≤C≤30
* 1≤s_i<t_i≤10^5
* 1≤c_i≤C
* If c_i=c_j and i≠j, either t_i≤s_j or s_i≥t_j.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N C
s_1 t_1 c_1
:
s_N t_N c_N
Output
When the minimum required number of recorders is x, print the value of x.
Examples
Input
3 2
1 7 2
7 8 1
8 12 1
Output
2
Input
3 4
1 3 2
3 4 4
1 4 3
Output
3
Input
9 4
56 60 4
33 37 2
89 90 3
32 43 1
67 68 3
49 51 3
31 32 3
70 71 1
11 12 3
Output
2 | instruction | 0 | 3,175 | 5 | 6,350 |
"Correct Solution:
```
n,c=map(int,input().split())
a=[]
tf=0
for _ in range(n):
s,t,ch=map(int,input().split())
a+=[(ch,s,t)]
a=sorted(a)
flag=a[0][0]
ans=[0]*(10**5+1)
tf=0
for ch,s,t, in a:
if ch==flag and tf==s:ans[s]+=1
else:ans[s-1]+=1
ans[t]-=1
tf=t
flag=ch
for i in range(10**5):
ans[i+1]+=ans[i]
print(max(ans))
``` | output | 1 | 3,175 | 5 | 6,351 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino is planning to record N TV programs with recorders.
The TV can receive C channels numbered 1 through C.
The i-th program that she wants to record will be broadcast from time s_i to time t_i (including time s_i but not t_i) on Channel c_i.
Here, there will never be more than one program that are broadcast on the same channel at the same time.
When the recorder is recording a channel from time S to time T (including time S but not T), it cannot record other channels from time S-0.5 to time T (including time S-0.5 but not T).
Find the minimum number of recorders required to record the channels so that all the N programs are completely recorded.
Constraints
* 1≤N≤10^5
* 1≤C≤30
* 1≤s_i<t_i≤10^5
* 1≤c_i≤C
* If c_i=c_j and i≠j, either t_i≤s_j or s_i≥t_j.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N C
s_1 t_1 c_1
:
s_N t_N c_N
Output
When the minimum required number of recorders is x, print the value of x.
Examples
Input
3 2
1 7 2
7 8 1
8 12 1
Output
2
Input
3 4
1 3 2
3 4 4
1 4 3
Output
3
Input
9 4
56 60 4
33 37 2
89 90 3
32 43 1
67 68 3
49 51 3
31 32 3
70 71 1
11 12 3
Output
2 | instruction | 0 | 3,176 | 5 | 6,352 |
"Correct Solution:
```
n,c = map(int,input().split())
stc = [list(map(int,input().split())) for i in range(n)]
stc.sort()
R = [[stc[0][1],stc[0][2]]]
for s,t,c in stc[1:]:
for i in range(len(R)):
tr,cr = R[i][0],R[i][1]
if c == cr and tr <=s:
R[i] = [t,c]
break
if c!=cr and tr <s:
R[i] = [t,c]
break
else:
R.append([t,c])
print(len(R))
``` | output | 1 | 3,176 | 5 | 6,353 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino is planning to record N TV programs with recorders.
The TV can receive C channels numbered 1 through C.
The i-th program that she wants to record will be broadcast from time s_i to time t_i (including time s_i but not t_i) on Channel c_i.
Here, there will never be more than one program that are broadcast on the same channel at the same time.
When the recorder is recording a channel from time S to time T (including time S but not T), it cannot record other channels from time S-0.5 to time T (including time S-0.5 but not T).
Find the minimum number of recorders required to record the channels so that all the N programs are completely recorded.
Constraints
* 1≤N≤10^5
* 1≤C≤30
* 1≤s_i<t_i≤10^5
* 1≤c_i≤C
* If c_i=c_j and i≠j, either t_i≤s_j or s_i≥t_j.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N C
s_1 t_1 c_1
:
s_N t_N c_N
Output
When the minimum required number of recorders is x, print the value of x.
Examples
Input
3 2
1 7 2
7 8 1
8 12 1
Output
2
Input
3 4
1 3 2
3 4 4
1 4 3
Output
3
Input
9 4
56 60 4
33 37 2
89 90 3
32 43 1
67 68 3
49 51 3
31 32 3
70 71 1
11 12 3
Output
2 | instruction | 0 | 3,177 | 5 | 6,354 |
"Correct Solution:
```
N,C = map(int, input().split())
t_max = 2*10**5
c_imos = [[0]*t_max for t in range(C)]
# 前処理 : 同一チャンネルのときはくっつけられる
c_imos = [[0]*t_max for t in range(C)]
for i in range(N):
s,t,c = map(int, input().split())
c -= 1
s -= 1
# t -= 1
c_imos[c][s] += 1
c_imos[c][t] -= 1
ans = [0] * t_max
from itertools import accumulate
for c_ in c_imos:
acc = list(accumulate(c_))
ans = [a+min(1,b) for a,b in zip(ans,acc)]
print(max(ans))
``` | output | 1 | 3,177 | 5 | 6,355 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino is planning to record N TV programs with recorders.
The TV can receive C channels numbered 1 through C.
The i-th program that she wants to record will be broadcast from time s_i to time t_i (including time s_i but not t_i) on Channel c_i.
Here, there will never be more than one program that are broadcast on the same channel at the same time.
When the recorder is recording a channel from time S to time T (including time S but not T), it cannot record other channels from time S-0.5 to time T (including time S-0.5 but not T).
Find the minimum number of recorders required to record the channels so that all the N programs are completely recorded.
Constraints
* 1≤N≤10^5
* 1≤C≤30
* 1≤s_i<t_i≤10^5
* 1≤c_i≤C
* If c_i=c_j and i≠j, either t_i≤s_j or s_i≥t_j.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N C
s_1 t_1 c_1
:
s_N t_N c_N
Output
When the minimum required number of recorders is x, print the value of x.
Examples
Input
3 2
1 7 2
7 8 1
8 12 1
Output
2
Input
3 4
1 3 2
3 4 4
1 4 3
Output
3
Input
9 4
56 60 4
33 37 2
89 90 3
32 43 1
67 68 3
49 51 3
31 32 3
70 71 1
11 12 3
Output
2 | instruction | 0 | 3,178 | 5 | 6,356 |
"Correct Solution:
```
N, C = map(int, input().split())
X = [list(map(int, input().split())) for _ in range(N)]
LEN = 10 ** 5 + 7
d = [[0] * LEN for _ in range(C + 1)]
for s, t, c in X:
d[c][s] += 1
d[c][t + 1] -= 1
for i in range(C + 1):
for j in range(LEN - 1):
d[i][j + 1] += d[i][j]
x = [0] * LEN
for i in range(C + 1):
for j in range(LEN):
x[j] += int(d[i][j] > 0)
print(max(x))
``` | output | 1 | 3,178 | 5 | 6,357 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino is planning to record N TV programs with recorders.
The TV can receive C channels numbered 1 through C.
The i-th program that she wants to record will be broadcast from time s_i to time t_i (including time s_i but not t_i) on Channel c_i.
Here, there will never be more than one program that are broadcast on the same channel at the same time.
When the recorder is recording a channel from time S to time T (including time S but not T), it cannot record other channels from time S-0.5 to time T (including time S-0.5 but not T).
Find the minimum number of recorders required to record the channels so that all the N programs are completely recorded.
Constraints
* 1≤N≤10^5
* 1≤C≤30
* 1≤s_i<t_i≤10^5
* 1≤c_i≤C
* If c_i=c_j and i≠j, either t_i≤s_j or s_i≥t_j.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N C
s_1 t_1 c_1
:
s_N t_N c_N
Output
When the minimum required number of recorders is x, print the value of x.
Examples
Input
3 2
1 7 2
7 8 1
8 12 1
Output
2
Input
3 4
1 3 2
3 4 4
1 4 3
Output
3
Input
9 4
56 60 4
33 37 2
89 90 3
32 43 1
67 68 3
49 51 3
31 32 3
70 71 1
11 12 3
Output
2 | instruction | 0 | 3,179 | 5 | 6,358 |
"Correct Solution:
```
n, c = map(int, input().split())
stc = [list(map(int, input().split())) for _ in range(n)]
# 同チャンネルの連続する放送を一つにまとめる
stc.sort(key=lambda x: (x[2], x[0]))
imos = [0] * (10**5 + 1)
curr_c = 0
cuur_t = 0
for s, t, c in stc:
if curr_c == c and curr_t == s:
imos[s] += 1
else:
imos[s-1] += 1
imos[t] -= 1
curr_t = t
curr_c = c
rui = [0] * (10**5 + 1)
for i in range(10**5):
rui[i+1] = rui[i] + imos[i]
print(max(rui))
``` | output | 1 | 3,179 | 5 | 6,359 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino is planning to record N TV programs with recorders.
The TV can receive C channels numbered 1 through C.
The i-th program that she wants to record will be broadcast from time s_i to time t_i (including time s_i but not t_i) on Channel c_i.
Here, there will never be more than one program that are broadcast on the same channel at the same time.
When the recorder is recording a channel from time S to time T (including time S but not T), it cannot record other channels from time S-0.5 to time T (including time S-0.5 but not T).
Find the minimum number of recorders required to record the channels so that all the N programs are completely recorded.
Constraints
* 1≤N≤10^5
* 1≤C≤30
* 1≤s_i<t_i≤10^5
* 1≤c_i≤C
* If c_i=c_j and i≠j, either t_i≤s_j or s_i≥t_j.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N C
s_1 t_1 c_1
:
s_N t_N c_N
Output
When the minimum required number of recorders is x, print the value of x.
Examples
Input
3 2
1 7 2
7 8 1
8 12 1
Output
2
Input
3 4
1 3 2
3 4 4
1 4 3
Output
3
Input
9 4
56 60 4
33 37 2
89 90 3
32 43 1
67 68 3
49 51 3
31 32 3
70 71 1
11 12 3
Output
2 | instruction | 0 | 3,180 | 5 | 6,360 |
"Correct Solution:
```
N, C = map(int, input().split())
ch = [[False for i in range(100001)] for j in range(C+1)]
for i in range(N):
s, t, c = map(int, input().split())
for j in range(s, t+1):
ch[c][j] = True
ans = 0
for i in range(100001):
count = 0
for j in range(1, C+1):
if ch[j][i]:
count += 1
ans = max(count, ans)
print(ans)
``` | output | 1 | 3,180 | 5 | 6,361 |
Provide a correct Python 3 solution for this coding contest problem.
For a sequence of integers $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, eliminate all equivalent elements.
Constraints
* $1 \leq n \leq 100,000$
* $-1000,000,000 \leq a_i \leq 1,000,000,000$
* $a_0 \leq a_1 \leq ... \leq a_{n-1}$
Input
A sequence is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
Output
Print the sequence after eliminating equivalent elements in a line. Separate adjacency elements by a space character.
Example
Input
4
1 2 2 4
Output
1 2 4 | instruction | 0 | 3,313 | 5 | 6,626 |
"Correct Solution:
```
n=int(input())
S=set(map(int, input().split()))
print(*sorted(list(S)))
``` | output | 1 | 3,313 | 5 | 6,627 |
Provide a correct Python 3 solution for this coding contest problem.
For a sequence of integers $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, eliminate all equivalent elements.
Constraints
* $1 \leq n \leq 100,000$
* $-1000,000,000 \leq a_i \leq 1,000,000,000$
* $a_0 \leq a_1 \leq ... \leq a_{n-1}$
Input
A sequence is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
Output
Print the sequence after eliminating equivalent elements in a line. Separate adjacency elements by a space character.
Example
Input
4
1 2 2 4
Output
1 2 4 | instruction | 0 | 3,314 | 5 | 6,628 |
"Correct Solution:
```
n = input()
li = set([int(i) for i in input().split()])
li = sorted(li)
print(" ".join(map(str, li)))
``` | output | 1 | 3,314 | 5 | 6,629 |
Provide a correct Python 3 solution for this coding contest problem.
For a sequence of integers $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, eliminate all equivalent elements.
Constraints
* $1 \leq n \leq 100,000$
* $-1000,000,000 \leq a_i \leq 1,000,000,000$
* $a_0 \leq a_1 \leq ... \leq a_{n-1}$
Input
A sequence is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
Output
Print the sequence after eliminating equivalent elements in a line. Separate adjacency elements by a space character.
Example
Input
4
1 2 2 4
Output
1 2 4 | instruction | 0 | 3,315 | 5 | 6,630 |
"Correct Solution:
```
def main():
n = input()
s = sorted(set(map(int, input().split(" "))))
print(*s)
main()
``` | output | 1 | 3,315 | 5 | 6,631 |
Provide a correct Python 3 solution for this coding contest problem.
For a sequence of integers $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, eliminate all equivalent elements.
Constraints
* $1 \leq n \leq 100,000$
* $-1000,000,000 \leq a_i \leq 1,000,000,000$
* $a_0 \leq a_1 \leq ... \leq a_{n-1}$
Input
A sequence is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
Output
Print the sequence after eliminating equivalent elements in a line. Separate adjacency elements by a space character.
Example
Input
4
1 2 2 4
Output
1 2 4 | instruction | 0 | 3,316 | 5 | 6,632 |
"Correct Solution:
```
n = int(input())
b = list(map(int,input().split()))
a = list()
pre = 100100100
for bb in b:
if bb != pre:
a.append(bb)
pre = bb
print(a[0],end="")
for aa in a[1:]:
print(" {}".format(aa),end="")
print()
``` | output | 1 | 3,316 | 5 | 6,633 |
Provide a correct Python 3 solution for this coding contest problem.
For a sequence of integers $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, eliminate all equivalent elements.
Constraints
* $1 \leq n \leq 100,000$
* $-1000,000,000 \leq a_i \leq 1,000,000,000$
* $a_0 \leq a_1 \leq ... \leq a_{n-1}$
Input
A sequence is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
Output
Print the sequence after eliminating equivalent elements in a line. Separate adjacency elements by a space character.
Example
Input
4
1 2 2 4
Output
1 2 4 | instruction | 0 | 3,317 | 5 | 6,634 |
"Correct Solution:
```
n = int(input())
a = sorted(list(set((map(int, input().split())))))
print(*a)
``` | output | 1 | 3,317 | 5 | 6,635 |
Provide a correct Python 3 solution for this coding contest problem.
For a sequence of integers $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, eliminate all equivalent elements.
Constraints
* $1 \leq n \leq 100,000$
* $-1000,000,000 \leq a_i \leq 1,000,000,000$
* $a_0 \leq a_1 \leq ... \leq a_{n-1}$
Input
A sequence is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
Output
Print the sequence after eliminating equivalent elements in a line. Separate adjacency elements by a space character.
Example
Input
4
1 2 2 4
Output
1 2 4 | instruction | 0 | 3,318 | 5 | 6,636 |
"Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
a = sorted(set(a))
print(" ".join(map(str, a)))
``` | output | 1 | 3,318 | 5 | 6,637 |
Provide a correct Python 3 solution for this coding contest problem.
For a sequence of integers $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, eliminate all equivalent elements.
Constraints
* $1 \leq n \leq 100,000$
* $-1000,000,000 \leq a_i \leq 1,000,000,000$
* $a_0 \leq a_1 \leq ... \leq a_{n-1}$
Input
A sequence is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
Output
Print the sequence after eliminating equivalent elements in a line. Separate adjacency elements by a space character.
Example
Input
4
1 2 2 4
Output
1 2 4 | instruction | 0 | 3,319 | 5 | 6,638 |
"Correct Solution:
```
from sys import stdin
n = int(stdin.readline())
l = list(stdin.readline().split())
l = list(dict.fromkeys(l))
print(' '.join(l))
``` | output | 1 | 3,319 | 5 | 6,639 |
Provide a correct Python 3 solution for this coding contest problem.
For a sequence of integers $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, eliminate all equivalent elements.
Constraints
* $1 \leq n \leq 100,000$
* $-1000,000,000 \leq a_i \leq 1,000,000,000$
* $a_0 \leq a_1 \leq ... \leq a_{n-1}$
Input
A sequence is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
Output
Print the sequence after eliminating equivalent elements in a line. Separate adjacency elements by a space character.
Example
Input
4
1 2 2 4
Output
1 2 4 | instruction | 0 | 3,320 | 5 | 6,640 |
"Correct Solution:
```
def unique(li):
"""Returns a list of unique elements in ordered list li
>>> unique([1, 1])
[1]
>>> unique([1, 2])
[1, 2]
"""
return [li[i] for i in range(len(li)) if i == 0 or li[i] > li[i-1]]
def run():
n = int(input())
li = [int(x) for x in input().split()]
assert(n == len(li))
print(" ".join([str(x) for x in unique(li)]))
if __name__ == '__main__':
run()
``` | output | 1 | 3,320 | 5 | 6,641 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a sequence of integers $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, eliminate all equivalent elements.
Constraints
* $1 \leq n \leq 100,000$
* $-1000,000,000 \leq a_i \leq 1,000,000,000$
* $a_0 \leq a_1 \leq ... \leq a_{n-1}$
Input
A sequence is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
Output
Print the sequence after eliminating equivalent elements in a line. Separate adjacency elements by a space character.
Example
Input
4
1 2 2 4
Output
1 2 4
Submitted Solution:
```
n=int(input())
A=list(map(int,input().split()))
A=sorted(list(set(A)))
print(' '.join(map(str,A)))
``` | instruction | 0 | 3,321 | 5 | 6,642 |
Yes | output | 1 | 3,321 | 5 | 6,643 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a sequence of integers $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, eliminate all equivalent elements.
Constraints
* $1 \leq n \leq 100,000$
* $-1000,000,000 \leq a_i \leq 1,000,000,000$
* $a_0 \leq a_1 \leq ... \leq a_{n-1}$
Input
A sequence is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
Output
Print the sequence after eliminating equivalent elements in a line. Separate adjacency elements by a space character.
Example
Input
4
1 2 2 4
Output
1 2 4
Submitted Solution:
```
n = int(input())
a = sorted(list(set(list(map(int,input().split())))))
print (' '.join(map(str,a)))
``` | instruction | 0 | 3,322 | 5 | 6,644 |
Yes | output | 1 | 3,322 | 5 | 6,645 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a sequence of integers $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, eliminate all equivalent elements.
Constraints
* $1 \leq n \leq 100,000$
* $-1000,000,000 \leq a_i \leq 1,000,000,000$
* $a_0 \leq a_1 \leq ... \leq a_{n-1}$
Input
A sequence is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
Output
Print the sequence after eliminating equivalent elements in a line. Separate adjacency elements by a space character.
Example
Input
4
1 2 2 4
Output
1 2 4
Submitted Solution:
```
n = int(input())
A = list(map(int, input().split()))
B = [A[0]]
for i in A:
if B[-1] < i:
B.append(i)
print(*B)
``` | instruction | 0 | 3,323 | 5 | 6,646 |
Yes | output | 1 | 3,323 | 5 | 6,647 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a sequence of integers $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, eliminate all equivalent elements.
Constraints
* $1 \leq n \leq 100,000$
* $-1000,000,000 \leq a_i \leq 1,000,000,000$
* $a_0 \leq a_1 \leq ... \leq a_{n-1}$
Input
A sequence is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
Output
Print the sequence after eliminating equivalent elements in a line. Separate adjacency elements by a space character.
Example
Input
4
1 2 2 4
Output
1 2 4
Submitted Solution:
```
N = int(input())
A = list(map(int,input().split()))
print(*sorted(set(A)))
``` | instruction | 0 | 3,324 | 5 | 6,648 |
Yes | output | 1 | 3,324 | 5 | 6,649 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a sequence of integers $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, eliminate all equivalent elements.
Constraints
* $1 \leq n \leq 100,000$
* $-1000,000,000 \leq a_i \leq 1,000,000,000$
* $a_0 \leq a_1 \leq ... \leq a_{n-1}$
Input
A sequence is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
Output
Print the sequence after eliminating equivalent elements in a line. Separate adjacency elements by a space character.
Example
Input
4
1 2 2 4
Output
1 2 4
Submitted Solution:
```
# coding=utf-8
N = int(input())
A = list(map(int, input().split()))
print(' '.join(map(str, set(A))))
``` | instruction | 0 | 3,325 | 5 | 6,650 |
No | output | 1 | 3,325 | 5 | 6,651 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a sequence of integers $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, eliminate all equivalent elements.
Constraints
* $1 \leq n \leq 100,000$
* $-1000,000,000 \leq a_i \leq 1,000,000,000$
* $a_0 \leq a_1 \leq ... \leq a_{n-1}$
Input
A sequence is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
Output
Print the sequence after eliminating equivalent elements in a line. Separate adjacency elements by a space character.
Example
Input
4
1 2 2 4
Output
1 2 4
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split(' ')))
a = list(set(a))
print(' '.join(list(map(str, a))))
``` | instruction | 0 | 3,326 | 5 | 6,652 |
No | output | 1 | 3,326 | 5 | 6,653 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three integers a, b and x. Your task is to construct a binary string s of length n = a + b such that there are exactly a zeroes, exactly b ones and exactly x indices i (where 1 ≤ i < n) such that s_i ≠ s_{i + 1}. It is guaranteed that the answer always exists.
For example, for the string "01010" there are four indices i such that 1 ≤ i < n and s_i ≠ s_{i + 1} (i = 1, 2, 3, 4). For the string "111001" there are two such indices i (i = 3, 5).
Recall that binary string is a non-empty sequence of characters where each character is either 0 or 1.
Input
The first line of the input contains three integers a, b and x (1 ≤ a, b ≤ 100, 1 ≤ x < a + b).
Output
Print only one string s, where s is any binary string satisfying conditions described above. It is guaranteed that the answer always exists.
Examples
Input
2 2 1
Output
1100
Input
3 3 3
Output
101100
Input
5 3 6
Output
01010100
Note
All possible answers for the first example:
* 1100;
* 0011.
All possible answers for the second example:
* 110100;
* 101100;
* 110010;
* 100110;
* 011001;
* 001101;
* 010011;
* 001011.
Submitted Solution:
```
from collections import Counter
def A():
N = int(input())
c = Counter(input().split())
print(c.most_common(1)[0][1])
def B():
A, B, X = map(int, input().split())
s = ''.join(['0']*A) + ''.join(['1']*B)
i = 1
while X > 1:
s = s[:i] + '1' + s[i:-1]
i += 2
X -= 2
#if X == 0:
# s = s[1] + s[0] + s[2:]
print(s)
def C():
pass
def D():
pass
def E():
pass
B()
``` | instruction | 0 | 3,339 | 5 | 6,678 |
No | output | 1 | 3,339 | 5 | 6,679 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fibonacci strings are defined as follows:
* f1 = «a»
* f2 = «b»
* fn = fn - 1 fn - 2, n > 2
Thus, the first five Fibonacci strings are: "a", "b", "ba", "bab", "babba".
You are given a Fibonacci string and m strings si. For each string si, find the number of times it occurs in the given Fibonacci string as a substring.
Input
The first line contains two space-separated integers k and m — the number of a Fibonacci string and the number of queries, correspondingly.
Next m lines contain strings si that correspond to the queries. It is guaranteed that strings si aren't empty and consist only of characters "a" and "b".
The input limitations for getting 30 points are:
* 1 ≤ k ≤ 3000
* 1 ≤ m ≤ 3000
* The total length of strings si doesn't exceed 3000
The input limitations for getting 100 points are:
* 1 ≤ k ≤ 1018
* 1 ≤ m ≤ 104
* The total length of strings si doesn't exceed 105
Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.
Output
For each string si print the number of times it occurs in the given Fibonacci string as a substring. Since the numbers can be large enough, print them modulo 1000000007 (109 + 7). Print the answers for the strings in the order in which they are given in the input.
Examples
Input
6 5
a
b
ab
ba
aba
Output
3
5
3
3
1
Submitted Solution:
```
p=input().rstrip().split(' ')
A=int(p[0])
a='b'
b='a'
if A>2:
a='b'
b='a';
for i in range(2,A):
c=a+b;
b=a;
a=c;
if A==1:
C=list(a)
elif A==2:
C=list(b)
else:
C=list(c)
for i in range(0,int(p[1])):
s=input().rstrip()
t=len(s)
if t>len(C):
print(0%1000000007)
elif t==len(C):
if s==''.join(C):
print(1)
else:
print(0%1000000007)
else:
V=0;
for j in range(0,len(C)-t+1):
G=C[j:j+t]
if ''.join(G)==s:
V+=1;
print(V%1000000007)
``` | instruction | 0 | 3,646 | 5 | 7,292 |
No | output | 1 | 3,646 | 5 | 7,293 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Fibonacci strings are defined as follows:
* f1 = «a»
* f2 = «b»
* fn = fn - 1 fn - 2, n > 2
Thus, the first five Fibonacci strings are: "a", "b", "ba", "bab", "babba".
You are given a Fibonacci string and m strings si. For each string si, find the number of times it occurs in the given Fibonacci string as a substring.
Input
The first line contains two space-separated integers k and m — the number of a Fibonacci string and the number of queries, correspondingly.
Next m lines contain strings si that correspond to the queries. It is guaranteed that strings si aren't empty and consist only of characters "a" and "b".
The input limitations for getting 30 points are:
* 1 ≤ k ≤ 3000
* 1 ≤ m ≤ 3000
* The total length of strings si doesn't exceed 3000
The input limitations for getting 100 points are:
* 1 ≤ k ≤ 1018
* 1 ≤ m ≤ 104
* The total length of strings si doesn't exceed 105
Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.
Output
For each string si print the number of times it occurs in the given Fibonacci string as a substring. Since the numbers can be large enough, print them modulo 1000000007 (109 + 7). Print the answers for the strings in the order in which they are given in the input.
Examples
Input
6 5
a
b
ab
ba
aba
Output
3
5
3
3
1
Submitted Solution:
```
s=input()
a,b=map(int,s.split(' '))
f={1:'a',2:'b'}
for n in range(3,a+1):
g=f[n-1]+f[n-2]
f.update({n:g})
fn=str(f[a])
if 1<=a<=3000 and 1<=b<=3000 and len(fn)<=3000:
pass
else:
raise SystemExit
gg={}
for i in range(1,b+1):
hh=input()
gg.update({i:hh})
for z in range(1,b+1):
mm=str(gg[z])
print(fn.count(mm))
``` | instruction | 0 | 3,647 | 5 | 7,294 |
No | output | 1 | 3,647 | 5 | 7,295 |
Provide a correct Python 3 solution for this coding contest problem.
There are N positive integers arranged in a circle.
Now, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:
* Choose an integer i such that 1 \leq i \leq N.
* Let a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.
Here the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.
Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
Print the minimum number of operations required, or `-1` if the objective cannot be achieved.
Examples
Input
3
1 1 1
13 5 7
Output
4
Input
4
1 2 3 4
2 3 4 5
Output
-1
Input
5
5 6 5 2 1
9817 1108 6890 4343 8704
Output
25 | instruction | 0 | 3,996 | 5 | 7,992 |
"Correct Solution:
```
import heapq as h
n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
e6 = 10**6
q = [-b[i]*e6-i for i in range(n)]
h.heapify(q)
cnt = 0
while q:
w = -h.heappop(q)
v,i = w//e6, w%e6
u = b[(i-1)%n] + b[(i+1)%n]
if v < u or a[i] == v: continue
elif a[i] > v: print(-1); exit(0)
t = (v-a[i])//u
if not t: print(-1); exit(0)
cnt += t
b[i] -= t*u
if b[i] > a[i]:
h.heappush(q,-b[i]*e6-i)
print(cnt if a==b else -1)
``` | output | 1 | 3,996 | 5 | 7,993 |
Provide a correct Python 3 solution for this coding contest problem.
There are N positive integers arranged in a circle.
Now, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:
* Choose an integer i such that 1 \leq i \leq N.
* Let a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.
Here the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.
Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
Print the minimum number of operations required, or `-1` if the objective cannot be achieved.
Examples
Input
3
1 1 1
13 5 7
Output
4
Input
4
1 2 3 4
2 3 4 5
Output
-1
Input
5
5 6 5 2 1
9817 1108 6890 4343 8704
Output
25 | instruction | 0 | 3,997 | 5 | 7,994 |
"Correct Solution:
```
def main():
from sys import exit
n = int(input())
a = [int(e) for e in input().split()]
b = [int(e) for e in input().split()]
result = 0
q = [i for i in range(n) if b[i] != a[i]]
while len(q) != 0:
nq = []
c = 0
for i in q:
if i == 0 or i == n - 1:
j = b[(n + i - 1) % n] + b[(n + i + 1) % n]
else:
j = b[i - 1] + b[i + 1]
if j > b[i] - a[i]:
nq.append(i)
continue
c += 1
k = (b[i] - a[i]) // j
result += k
b[i] -= j * k
if a[i] != b[i]:
nq.append(i)
if c == 0 and len(nq) != 0:
print(-1)
exit()
q = nq
print(result)
main()
``` | output | 1 | 3,997 | 5 | 7,995 |
Provide a correct Python 3 solution for this coding contest problem.
There are N positive integers arranged in a circle.
Now, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:
* Choose an integer i such that 1 \leq i \leq N.
* Let a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.
Here the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.
Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
Print the minimum number of operations required, or `-1` if the objective cannot be achieved.
Examples
Input
3
1 1 1
13 5 7
Output
4
Input
4
1 2 3 4
2 3 4 5
Output
-1
Input
5
5 6 5 2 1
9817 1108 6890 4343 8704
Output
25 | instruction | 0 | 3,998 | 5 | 7,996 |
"Correct Solution:
```
from heapq import heappush,heappop
n,*t=map(int,open(0).read().split())
a=t[:n]
b=t[n:]
B=[]
for i,j in enumerate(b):heappush(B,(-j,i))
c=0
d=0
while B and d<2*10**6:
d+=1
y,i=heappop(B)
x,z=b[(i-1)%n],b[(i+1)%n]
t=(b[i]-a[i])//(x+z)
b[i]-=t*(x+z)
c+=t
if b[i]>a[i]:
heappush(B,(-b[i],i))
print([-1,c][a==b])
``` | output | 1 | 3,998 | 5 | 7,997 |
Provide a correct Python 3 solution for this coding contest problem.
There are N positive integers arranged in a circle.
Now, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:
* Choose an integer i such that 1 \leq i \leq N.
* Let a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.
Here the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.
Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
Print the minimum number of operations required, or `-1` if the objective cannot be achieved.
Examples
Input
3
1 1 1
13 5 7
Output
4
Input
4
1 2 3 4
2 3 4 5
Output
-1
Input
5
5 6 5 2 1
9817 1108 6890 4343 8704
Output
25 | instruction | 0 | 3,999 | 5 | 7,998 |
"Correct Solution:
```
from heapq import heapify, heappop, heappush
def solve(n, aaa, bbb):
q = [(-b, i) for i, b in enumerate(bbb) if b != aaa[i]]
heapify(q)
ans = 0
while q:
b, i = heappop(q)
b = -b - aaa[i]
d, b = divmod(b, bbb[(i - 1) % n] + bbb[(i + 1) % n])
if d == 0:
return -1
b += aaa[i]
bbb[i] = b
ans += d
if b != aaa[i]:
heappush(q, (-b, i))
return ans
n = int(input())
aaa = list(map(int, input().split()))
bbb = list(map(int, input().split()))
print(solve(n, aaa, bbb))
``` | output | 1 | 3,999 | 5 | 7,999 |
Provide a correct Python 3 solution for this coding contest problem.
There are N positive integers arranged in a circle.
Now, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:
* Choose an integer i such that 1 \leq i \leq N.
* Let a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.
Here the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.
Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
Print the minimum number of operations required, or `-1` if the objective cannot be achieved.
Examples
Input
3
1 1 1
13 5 7
Output
4
Input
4
1 2 3 4
2 3 4 5
Output
-1
Input
5
5 6 5 2 1
9817 1108 6890 4343 8704
Output
25 | instruction | 0 | 4,000 | 5 | 8,000 |
"Correct Solution:
```
###test
n=int(input())
A=list(map(int,input().split( )))
B=list(map(int,input().split( )))
count=0
flag=True
while flag:
flag=False
for i in range(-1,n-1):
tonari=B[i-1]+B[i+1]
tmp=(B[i]-A[i])//tonari
if tmp>0:
B[i]-=tonari*tmp
count+=tmp
flag=True
if A==B:
print(count)
else:
print(-1)
``` | output | 1 | 4,000 | 5 | 8,001 |
Provide a correct Python 3 solution for this coding contest problem.
There are N positive integers arranged in a circle.
Now, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:
* Choose an integer i such that 1 \leq i \leq N.
* Let a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.
Here the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.
Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
Print the minimum number of operations required, or `-1` if the objective cannot be achieved.
Examples
Input
3
1 1 1
13 5 7
Output
4
Input
4
1 2 3 4
2 3 4 5
Output
-1
Input
5
5 6 5 2 1
9817 1108 6890 4343 8704
Output
25 | instruction | 0 | 4,001 | 5 | 8,002 |
"Correct Solution:
```
def p_c():
N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
l = [-1] * N
for i in range(N):
l[i] = B[i - 1] + B[(i + 1) % N]
ans = 0
while 1:
f = False
for i in range(N):
if A[i] <= B[i] - l[i]:
f = True
n = (B[i] - A[i]) // l[i]
ans += n
B[i] -= n * l[i]
l[i - 1] -= n * l[i]
l[(i + 1) % N] -= n * l[i]
if not f:
break
if A != B:
print(-1)
else:
print(ans)
if __name__ == '__main__':
p_c()
``` | output | 1 | 4,001 | 5 | 8,003 |
Provide a correct Python 3 solution for this coding contest problem.
There are N positive integers arranged in a circle.
Now, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:
* Choose an integer i such that 1 \leq i \leq N.
* Let a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.
Here the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.
Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
Print the minimum number of operations required, or `-1` if the objective cannot be achieved.
Examples
Input
3
1 1 1
13 5 7
Output
4
Input
4
1 2 3 4
2 3 4 5
Output
-1
Input
5
5 6 5 2 1
9817 1108 6890 4343 8704
Output
25 | instruction | 0 | 4,002 | 5 | 8,004 |
"Correct Solution:
```
N=int(input())
A=[int(i) for i in input().split()]
B=[int(i) for i in input().split()]
ans=0
while(True):
flag=0
#print(B)
for i in range(N):
tmp=B[(i-1)%N]+B[(i+1)%N]
if B[i]>tmp and B[i]>A[i]:
beforeans=ans
if B[i]%tmp>=A[i]:
ans+=B[i]//tmp
B[i]%=tmp
else:
k=((A[i]-1-(B[i]%tmp))//tmp)+1
ans+=B[i]//tmp
B[i]%=tmp
#print(i,1,B)
ans-=k
B[i]+=k*tmp
#print(i,2,B)
if ans!=beforeans:
flag=1
if flag==0:
break
flag2=1
for i in range(N):
if A[i]!=B[i]:
flag2=0
break
if flag2:
print(ans)
else:
print(-1)
``` | output | 1 | 4,002 | 5 | 8,005 |
Provide a correct Python 3 solution for this coding contest problem.
There are N positive integers arranged in a circle.
Now, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:
* Choose an integer i such that 1 \leq i \leq N.
* Let a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.
Here the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.
Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
Print the minimum number of operations required, or `-1` if the objective cannot be achieved.
Examples
Input
3
1 1 1
13 5 7
Output
4
Input
4
1 2 3 4
2 3 4 5
Output
-1
Input
5
5 6 5 2 1
9817 1108 6890 4343 8704
Output
25 | instruction | 0 | 4,003 | 5 | 8,006 |
"Correct Solution:
```
words = lambda t : list(map(t, input().split()))
n = int(input())
a = words(int)
b = words(int)
def getNext(i):
if i == n-1:
return 0
else:
return i+1
def getPrev(i):
if i == 0:
return n-1
else:
return i-1
from collections import deque
q = deque()
def verify(i):
if b[i] != a[i] and b[i] - (b[getNext(i)] + b[getPrev(i)]) >= a[i]:
return True
else:
return False
for i in range(len(b)):
if b[i] >= a[i] and verify(i):
q.append(i)
ans = 0
succeed = True
while not len(q) == 0:
i = q.popleft()
ni = getNext(i)
pi = getPrev(i)
#print(i, b)
d = b[ni] + b[pi]
if b[i] % d == a[i] % d:
ans += b[i] // d - (a[i] // d)
b[i] = a[i]
else:
ans += b[i] // d
b[i] %= d
if b[i] < a[i]:
succeed = False
break
if verify(ni):
q.append(ni)
if verify(pi):
q.append(pi)
for i in range(len(b)):
if a[i] != b[i]:
succeed = False
break
if succeed:
print(ans)
else:
print(-1)
``` | output | 1 | 4,003 | 5 | 8,007 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N positive integers arranged in a circle.
Now, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:
* Choose an integer i such that 1 \leq i \leq N.
* Let a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.
Here the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.
Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
Print the minimum number of operations required, or `-1` if the objective cannot be achieved.
Examples
Input
3
1 1 1
13 5 7
Output
4
Input
4
1 2 3 4
2 3 4 5
Output
-1
Input
5
5 6 5 2 1
9817 1108 6890 4343 8704
Output
25
Submitted Solution:
```
import heapq
import os
import sys
if os.getenv("LOCAL"):
sys.stdin = open("_in.txt", "r")
sys.setrecursionlimit(10 ** 9)
INF = float("inf")
IINF = 10 ** 18
MOD = 10 ** 9 + 7
# MOD = 998244353
N = int(sys.stdin.buffer.readline())
A = list(map(int, sys.stdin.buffer.readline().split()))
B = list(map(int, sys.stdin.buffer.readline().split()))
# 逆から貪欲に操作可能
def solve():
heap = [(-b, i) for i, b in enumerate(B)]
heapq.heapify(heap)
ret = 0
while heap:
b, i = heapq.heappop(heap)
b *= -1
a = A[i]
if b < a:
return -1
if b == a:
continue
step = B[(i - 1) % N] + B[(i + 1) % N]
if (b - a) // step == 0:
return -1
cnt = (b - a) // step
ret += cnt
b -= cnt * step
B[i] = b
heapq.heappush(heap, (-b, i))
return ret
ans = solve()
print(ans)
``` | instruction | 0 | 4,004 | 5 | 8,008 |
Yes | output | 1 | 4,004 | 5 | 8,009 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N positive integers arranged in a circle.
Now, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:
* Choose an integer i such that 1 \leq i \leq N.
* Let a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.
Here the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.
Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
Print the minimum number of operations required, or `-1` if the objective cannot be achieved.
Examples
Input
3
1 1 1
13 5 7
Output
4
Input
4
1 2 3 4
2 3 4 5
Output
-1
Input
5
5 6 5 2 1
9817 1108 6890 4343 8704
Output
25
Submitted Solution:
```
N = int(input())
A = list(map(int,input().split()))
B = list(map(int,input().split()))
ans = 0
queue = []
# 山を探す
for i in range(N):
if B[i] > B[(i+1)%N] + B[(i-1)%N] and B[i] > A[i]:
queue.append(i)
# 山を崩す
while queue != []:
p = queue.pop(-1)
hoge = (B[p] - A[p])//(B[(p+1)%N]+B[(p-1)%N])
B[p] -= (B[(p+1)%N]+B[(p-1)%N])*hoge
ans += hoge
if B[(p+1)%N] > B[p] + B[(p+2)%N] and B[(p+1)%N] > A[(p+1)%N]:
queue.append((p+1)%N)
if B[(p-1)%N] > B[p] + B[(p-2)%N] and B[(p-1)%N] > A[(p-1)%N]:
queue.append((p-1)%N)
if A == B:
print(ans)
else:
print(-1)
``` | instruction | 0 | 4,005 | 5 | 8,010 |
Yes | output | 1 | 4,005 | 5 | 8,011 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N positive integers arranged in a circle.
Now, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:
* Choose an integer i such that 1 \leq i \leq N.
* Let a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.
Here the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.
Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
Print the minimum number of operations required, or `-1` if the objective cannot be achieved.
Examples
Input
3
1 1 1
13 5 7
Output
4
Input
4
1 2 3 4
2 3 4 5
Output
-1
Input
5
5 6 5 2 1
9817 1108 6890 4343 8704
Output
25
Submitted Solution:
```
#
import sys
import math
# ひとつ入力
n = int(input())
# initial state
a = [int(i) for i in input().split()]
# last state
b = [int(i) for i in input().split()]
answer = 0
answer_p = -1
while answer >= 0:
answer_p = answer
for i in range(n):
tmp = b[(i-1)%n] + b[(i+1)%n]
if 0 < tmp < b[i] and a[i] < b[i]:
res = (b[i]-a[i]) // (b[(i+1)%n]+b[(i-1)%n])
answer += res
b[i] -= res * (b[(i+1)%n]+b[(i-1)%n])
if answer == answer_p:
break
# print(a,b,answer)
for i in range(n):
if a[i] != b[i]:
print(-1)
exit()
print(answer)
``` | instruction | 0 | 4,006 | 5 | 8,012 |
Yes | output | 1 | 4,006 | 5 | 8,013 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N positive integers arranged in a circle.
Now, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:
* Choose an integer i such that 1 \leq i \leq N.
* Let a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.
Here the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.
Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
Print the minimum number of operations required, or `-1` if the objective cannot be achieved.
Examples
Input
3
1 1 1
13 5 7
Output
4
Input
4
1 2 3 4
2 3 4 5
Output
-1
Input
5
5 6 5 2 1
9817 1108 6890 4343 8704
Output
25
Submitted Solution:
```
import heapq
def naive():
N = int(input())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
hantei = [1]*N
for i,(x,y) in enumerate(zip(a,b)):
if x<y:
hantei[i] = 0
if x>y:
print(-1)
exit()
# a == b となるidxの数。これがNでwhileから抜ける
rest = sum(hantei)
t = []
for i,val in enumerate(b):
heapq.heappush(t, (-val,i))
res = 0
while rest < N:
now = heapq.heappop(t)
abc = -now[0]
idx = now[1]
newval = abc - b[(idx-1)%N] - b[(idx+1)%N]
b[idx] = newval
# print(b)
if a[idx] > newval:
res = -1
break
elif a[idx] == newval:
hantei[idx] = 0
rest += 1
res += 1
heapq.heappush(t, (-newval,idx))
print(res)
def naive2():
N = int(input())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
hantei = [1]*N
for i,(x,y) in enumerate(zip(a,b)):
if x<y:
hantei[i] = 0
if x>y:
print(-1)
exit()
# a == b となるidxの数。これがNでwhileから抜ける
rest = sum(hantei)
t = []
for i,val in enumerate(b):
if val==a[i] or val==1:
continue
heapq.heappush(t, (-val,i))
res = 0
while rest < N:
now = heapq.heappop(t)
abc = -now[0]
idx = now[1]
left = b[(idx-1)%N]
right = b[(idx+1)%N]
step = left+right
if abc <= step:
res = -1
break
sub_cnt = (abc-1)//step
if (abc-a[idx])%step==0 and (abc-a[idx])//step < sub_cnt:
res += (abc-a[idx])//step
hantei[idx] = 0
b[idx] = a[idx]
rest += 1
continue
if sub_cnt <= 0:
res = -1
break
diff = sub_cnt*step
b[idx] -= diff
# print(b)
if a[idx] > b[idx]:
res = -1
break
elif a[idx] == b[idx]:
hantei[idx] = 0
rest += 1
res += sub_cnt
continue
res += sub_cnt
heapq.heappush(t, (-b[idx],idx))
print(res)
naive2()
``` | instruction | 0 | 4,007 | 5 | 8,014 |
Yes | output | 1 | 4,007 | 5 | 8,015 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N positive integers arranged in a circle.
Now, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:
* Choose an integer i such that 1 \leq i \leq N.
* Let a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.
Here the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.
Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
Print the minimum number of operations required, or `-1` if the objective cannot be achieved.
Examples
Input
3
1 1 1
13 5 7
Output
4
Input
4
1 2 3 4
2 3 4 5
Output
-1
Input
5
5 6 5 2 1
9817 1108 6890 4343 8704
Output
25
Submitted Solution:
```
#import sys
#input = sys.stdin.readline
n = int(input())
a =[int(xi) for xi in input().split()]
b =[int(yi) for yi in input().split()]
cnt, prev_cnt = 0, -1
while cnt != prev_cnt:
prev_cnt = cnt
for i in range(n):
adj_sum = b[i - 1] + b[(i + 1) % n]
k = (b[i] - a[i]) // adj_sum
if k > 0:
b[i] -= k * adj_sum
cnt += k
print(cnt if a == b else -1)
``` | instruction | 0 | 4,008 | 5 | 8,016 |
No | output | 1 | 4,008 | 5 | 8,017 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.