message stringlengths 2 16.2k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 575 109k | cluster float64 16 16 | __index_level_0__ int64 1.15k 217k |
|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
We have a board with a 2 \times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \times 2 or 2 \times 1 square.
Then, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors. Here, it is not always necessary to use all three colors.
Find the number of such ways to paint the dominoes, modulo 1000000007.
The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:
* Each domino is represented by a different English letter (lowercase or uppercase).
* The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.
Constraints
* 1 \leq N \leq 52
* |S_1| = |S_2| = N
* S_1 and S_2 consist of lowercase and uppercase English letters.
* S_1 and S_2 represent a valid arrangement of dominoes.
Input
Input is given from Standard Input in the following format:
N
S_1
S_2
Output
Print the number of such ways to paint the dominoes, modulo 1000000007.
Examples
Input
3
aab
ccb
Output
6
Input
1
Z
Z
Output
3
Input
52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn
Output
958681902 | instruction | 0 | 23,671 | 16 | 47,342 |
"Correct Solution:
```
n = int(input())
s1 = input()
s2 = input()
mod = 10**9+7
dp = [-1] * (n)
if s1[0] == s2[0]:
dp[0] = 1
else:
dp[0] = 2
for i in range(n-1):
if dp[i] == -1:
continue
if s1[i] == s2[i]:
dp[i+1] = (dp[i] * 2) % mod
continue
if i+2 >= n:
break
if s1[i+2] == s2[i+2]:
dp[i+2] = dp[i]
else:
dp[i+2] = (dp[i] * 3) % mod
ans = dp[-1] if dp[-1] != -1 else dp[-2]
print((ans * 3) % mod)
# print(dp)
``` | output | 1 | 23,671 | 16 | 47,343 |
Provide a correct Python 3 solution for this coding contest problem.
We have a board with a 2 \times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \times 2 or 2 \times 1 square.
Then, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors. Here, it is not always necessary to use all three colors.
Find the number of such ways to paint the dominoes, modulo 1000000007.
The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:
* Each domino is represented by a different English letter (lowercase or uppercase).
* The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.
Constraints
* 1 \leq N \leq 52
* |S_1| = |S_2| = N
* S_1 and S_2 consist of lowercase and uppercase English letters.
* S_1 and S_2 represent a valid arrangement of dominoes.
Input
Input is given from Standard Input in the following format:
N
S_1
S_2
Output
Print the number of such ways to paint the dominoes, modulo 1000000007.
Examples
Input
3
aab
ccb
Output
6
Input
1
Z
Z
Output
3
Input
52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn
Output
958681902 | instruction | 0 | 23,672 | 16 | 47,344 |
"Correct Solution:
```
N=int(input())
S=str(input())
T=str(input())
mod=10**9+7
answer=1
if S[0]==T[0]:
answer=3
else:
answer=6
for i in range(1,N):
if S[i]==T[i]:
if S[i-1]==T[i-1]:
answer=(answer*2)%mod
else:
if not S[i]==S[i-1]:
if S[i-1]==T[i-1]:
answer=(answer*2)%mod
else:
answer=(answer*3)%mod
print(answer)
``` | output | 1 | 23,672 | 16 | 47,345 |
Provide a correct Python 3 solution for this coding contest problem.
We have a board with a 2 \times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \times 2 or 2 \times 1 square.
Then, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors. Here, it is not always necessary to use all three colors.
Find the number of such ways to paint the dominoes, modulo 1000000007.
The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:
* Each domino is represented by a different English letter (lowercase or uppercase).
* The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.
Constraints
* 1 \leq N \leq 52
* |S_1| = |S_2| = N
* S_1 and S_2 consist of lowercase and uppercase English letters.
* S_1 and S_2 represent a valid arrangement of dominoes.
Input
Input is given from Standard Input in the following format:
N
S_1
S_2
Output
Print the number of such ways to paint the dominoes, modulo 1000000007.
Examples
Input
3
aab
ccb
Output
6
Input
1
Z
Z
Output
3
Input
52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn
Output
958681902 | instruction | 0 | 23,673 | 16 | 47,346 |
"Correct Solution:
```
n = int(input())
s1 = input()
s2 = input()
mod = 10**9 + 7
if s1[0] == s2[0]:
ans = 3
q = 1
else:
ans = 6
q = -1
for i in range(1, n):
x = s1[i]
y = s2[i]
if x == y:
if q == 0:
q = 1
elif q == 1:
ans *= 2
else:
if q == -1:
q = 0
elif q == 0:
ans *= 3
q = -1
else:
ans *= 2
q = -1
ans %= mod
print(ans%mod)
``` | output | 1 | 23,673 | 16 | 47,347 |
Provide a correct Python 3 solution for this coding contest problem.
We have a board with a 2 \times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \times 2 or 2 \times 1 square.
Then, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors. Here, it is not always necessary to use all three colors.
Find the number of such ways to paint the dominoes, modulo 1000000007.
The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:
* Each domino is represented by a different English letter (lowercase or uppercase).
* The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.
Constraints
* 1 \leq N \leq 52
* |S_1| = |S_2| = N
* S_1 and S_2 consist of lowercase and uppercase English letters.
* S_1 and S_2 represent a valid arrangement of dominoes.
Input
Input is given from Standard Input in the following format:
N
S_1
S_2
Output
Print the number of such ways to paint the dominoes, modulo 1000000007.
Examples
Input
3
aab
ccb
Output
6
Input
1
Z
Z
Output
3
Input
52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn
Output
958681902 | instruction | 0 | 23,674 | 16 | 47,348 |
"Correct Solution:
```
N = int(input())
S1 = input()
S2 = input()
result = 3
if N != 1:
i=1
while i < N:
if S1[i-1] == S2[i-1]:
result *= 2
elif S1[i-1] != S1[i]:
if S1[i] != S2[i]:
result *= 3
elif i == 1:
result *= 2
i += 1
print(result%1000000007)
``` | output | 1 | 23,674 | 16 | 47,349 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a board with a 2 \times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \times 2 or 2 \times 1 square.
Then, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors. Here, it is not always necessary to use all three colors.
Find the number of such ways to paint the dominoes, modulo 1000000007.
The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:
* Each domino is represented by a different English letter (lowercase or uppercase).
* The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.
Constraints
* 1 \leq N \leq 52
* |S_1| = |S_2| = N
* S_1 and S_2 consist of lowercase and uppercase English letters.
* S_1 and S_2 represent a valid arrangement of dominoes.
Input
Input is given from Standard Input in the following format:
N
S_1
S_2
Output
Print the number of such ways to paint the dominoes, modulo 1000000007.
Examples
Input
3
aab
ccb
Output
6
Input
1
Z
Z
Output
3
Input
52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn
Output
958681902
Submitted Solution:
```
n = int(input())
s1 = input()
s2 = input()
cnt = 1
i = 0
while i <= n-1:
if i == 0:
if s1[i] == s2[i]:
cnt *= 3
s = 0
else:
cnt *= 6
i += 1
s = 1
elif s1[i] == s2[i]:
if s == 0:
cnt *= 2
else:
cnt *= 1
s = 0
else:
if s == 0:
cnt *= 2
else:
cnt *= 3
s = 1
i += 1
i += 1
print(cnt % (10**9+7))
``` | instruction | 0 | 23,675 | 16 | 47,350 |
Yes | output | 1 | 23,675 | 16 | 47,351 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a board with a 2 \times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \times 2 or 2 \times 1 square.
Then, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors. Here, it is not always necessary to use all three colors.
Find the number of such ways to paint the dominoes, modulo 1000000007.
The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:
* Each domino is represented by a different English letter (lowercase or uppercase).
* The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.
Constraints
* 1 \leq N \leq 52
* |S_1| = |S_2| = N
* S_1 and S_2 consist of lowercase and uppercase English letters.
* S_1 and S_2 represent a valid arrangement of dominoes.
Input
Input is given from Standard Input in the following format:
N
S_1
S_2
Output
Print the number of such ways to paint the dominoes, modulo 1000000007.
Examples
Input
3
aab
ccb
Output
6
Input
1
Z
Z
Output
3
Input
52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn
Output
958681902
Submitted Solution:
```
mod = 10**9+7
N = int(input())
s1 = input()
s2 = input()
ans = 1
cur = 0
i = 0
while i < N:
if s1[i] == s2[i]:
ans *= 3-cur
ans %= mod
i += 1
cur = 1
else:
if cur == 2:
ans *= 3
else:
ans *= (3-cur)*(2-cur)
ans %= mod
i += 2
cur = 2
print(ans)
``` | instruction | 0 | 23,676 | 16 | 47,352 |
Yes | output | 1 | 23,676 | 16 | 47,353 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a board with a 2 \times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \times 2 or 2 \times 1 square.
Then, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors. Here, it is not always necessary to use all three colors.
Find the number of such ways to paint the dominoes, modulo 1000000007.
The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:
* Each domino is represented by a different English letter (lowercase or uppercase).
* The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.
Constraints
* 1 \leq N \leq 52
* |S_1| = |S_2| = N
* S_1 and S_2 consist of lowercase and uppercase English letters.
* S_1 and S_2 represent a valid arrangement of dominoes.
Input
Input is given from Standard Input in the following format:
N
S_1
S_2
Output
Print the number of such ways to paint the dominoes, modulo 1000000007.
Examples
Input
3
aab
ccb
Output
6
Input
1
Z
Z
Output
3
Input
52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn
Output
958681902
Submitted Solution:
```
MOD = 10 ** 9 + 7
n = int(input())
s1 = input()
s2 = input()
ans = 1
index =0
if s1[0] == s2[0]:
ans *= 3
index = 1
else:
ans *= 3 * 2
index = 2
while index < n:
if s1[index-1] == s2[index-1]:
ans *= 2
if s1[index] == s2[index]:
index += 1
else:
index += 2
else:
if s1[index] == s2[index]:
index += 1
else:
ans *= 3
index += 2
ans %= MOD
print(ans)
``` | instruction | 0 | 23,677 | 16 | 47,354 |
Yes | output | 1 | 23,677 | 16 | 47,355 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a board with a 2 \times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \times 2 or 2 \times 1 square.
Then, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors. Here, it is not always necessary to use all three colors.
Find the number of such ways to paint the dominoes, modulo 1000000007.
The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:
* Each domino is represented by a different English letter (lowercase or uppercase).
* The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.
Constraints
* 1 \leq N \leq 52
* |S_1| = |S_2| = N
* S_1 and S_2 consist of lowercase and uppercase English letters.
* S_1 and S_2 represent a valid arrangement of dominoes.
Input
Input is given from Standard Input in the following format:
N
S_1
S_2
Output
Print the number of such ways to paint the dominoes, modulo 1000000007.
Examples
Input
3
aab
ccb
Output
6
Input
1
Z
Z
Output
3
Input
52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn
Output
958681902
Submitted Solution:
```
n=int(input())
l1=[str(x) for x in input()]
l2=[str(x) for x in input()]
if l1[0]==l2[0]:
pat=3
typ='lon'
else:
pat=6
typ='lat'
for i in range(1,n):
if l1[i]!=l1[i-1]:
if typ=='lon':
if l1[i]==l2[i]:
pat *= 2
else:
pat *= 2
typ='lat'
else:
if l1[i]==l2[i]:
typ='lon'
else:
pat *= 3
print(pat%(10**9+7))
``` | instruction | 0 | 23,678 | 16 | 47,356 |
Yes | output | 1 | 23,678 | 16 | 47,357 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a board with a 2 \times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \times 2 or 2 \times 1 square.
Then, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors. Here, it is not always necessary to use all three colors.
Find the number of such ways to paint the dominoes, modulo 1000000007.
The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:
* Each domino is represented by a different English letter (lowercase or uppercase).
* The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.
Constraints
* 1 \leq N \leq 52
* |S_1| = |S_2| = N
* S_1 and S_2 consist of lowercase and uppercase English letters.
* S_1 and S_2 represent a valid arrangement of dominoes.
Input
Input is given from Standard Input in the following format:
N
S_1
S_2
Output
Print the number of such ways to paint the dominoes, modulo 1000000007.
Examples
Input
3
aab
ccb
Output
6
Input
1
Z
Z
Output
3
Input
52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn
Output
958681902
Submitted Solution:
```
n = int(input())
s1 = input()
s2 = input()
mod = 10**9+7
dp = [-1] * (n)
if s1[0] == s2[0]:
dp[0] = 1
else:
dp[0] = 2
for i in range(n-1):
if dp[i] == -1:
continue
if s1[i] == s2[i]:
dp[i+1] = (dp[i] * 2) % mod
continue
if i+2 > n:
continue
if s1[i+2] == s2[i+2]:
dp[i+2] = dp[i]
else:
dp[i+2] = (dp[i] * 3) % mod
ans = dp[-1] if dp[-1] != -1 else dp[-2]
print((ans * 3) % mod)
# print(dp)
``` | instruction | 0 | 23,679 | 16 | 47,358 |
No | output | 1 | 23,679 | 16 | 47,359 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a board with a 2 \times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \times 2 or 2 \times 1 square.
Then, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors. Here, it is not always necessary to use all three colors.
Find the number of such ways to paint the dominoes, modulo 1000000007.
The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:
* Each domino is represented by a different English letter (lowercase or uppercase).
* The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.
Constraints
* 1 \leq N \leq 52
* |S_1| = |S_2| = N
* S_1 and S_2 consist of lowercase and uppercase English letters.
* S_1 and S_2 represent a valid arrangement of dominoes.
Input
Input is given from Standard Input in the following format:
N
S_1
S_2
Output
Print the number of such ways to paint the dominoes, modulo 1000000007.
Examples
Input
3
aab
ccb
Output
6
Input
1
Z
Z
Output
3
Input
52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn
Output
958681902
Submitted Solution:
```
N = int(input())
S1 = input()
S2 = input()
i = 1
if S1[0] == S2[0]:
ans = 3
state = 0
else:
i+= 1
ans = 6
state = 1
while N -1 > i:
if S1[i] == S1[i+1] and state == 0:
ans *= 2
i+=2
state = 1
elif S1[i] == S1[i+1] and state == 1:
ans *= 3
i+=2
elif S1[i] != S1[i+1] and state == 0:
ans *= 2
i+= 1
elif S1[i] != S1[i+1] and state == 1:
ans *= 1
i+=1
state = 0
ans %= 10**9+7
print(ans)
``` | instruction | 0 | 23,680 | 16 | 47,360 |
No | output | 1 | 23,680 | 16 | 47,361 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a board with a 2 \times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \times 2 or 2 \times 1 square.
Then, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors. Here, it is not always necessary to use all three colors.
Find the number of such ways to paint the dominoes, modulo 1000000007.
The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:
* Each domino is represented by a different English letter (lowercase or uppercase).
* The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.
Constraints
* 1 \leq N \leq 52
* |S_1| = |S_2| = N
* S_1 and S_2 consist of lowercase and uppercase English letters.
* S_1 and S_2 represent a valid arrangement of dominoes.
Input
Input is given from Standard Input in the following format:
N
S_1
S_2
Output
Print the number of such ways to paint the dominoes, modulo 1000000007.
Examples
Input
3
aab
ccb
Output
6
Input
1
Z
Z
Output
3
Input
52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn
Output
958681902
Submitted Solution:
```
N = int(input())
S1 = input()
S2 = input()
MOD = 1000000007
if S1[0] == S2[0]:
ans = 3
pre = 1
else:
ans = 6
pre = 2
for i in range(1, N):
if S1[i] == S1[i - 1]: continue
if S1[i] == S2[i]:
if pre == 1:
ans *= 2
pre = 1
else:
if ans==1:
ans *= 2
else:
ans *=3
pre = 2
ans %= MOD
print(ans)
``` | instruction | 0 | 23,681 | 16 | 47,362 |
No | output | 1 | 23,681 | 16 | 47,363 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a board with a 2 \times N grid. Snuke covered the board with N dominoes without overlaps. Here, a domino can cover a 1 \times 2 or 2 \times 1 square.
Then, Snuke decided to paint these dominoes using three colors: red, cyan and green. Two dominoes that are adjacent by side should be painted by different colors. Here, it is not always necessary to use all three colors.
Find the number of such ways to paint the dominoes, modulo 1000000007.
The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:
* Each domino is represented by a different English letter (lowercase or uppercase).
* The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.
Constraints
* 1 \leq N \leq 52
* |S_1| = |S_2| = N
* S_1 and S_2 consist of lowercase and uppercase English letters.
* S_1 and S_2 represent a valid arrangement of dominoes.
Input
Input is given from Standard Input in the following format:
N
S_1
S_2
Output
Print the number of such ways to paint the dominoes, modulo 1000000007.
Examples
Input
3
aab
ccb
Output
6
Input
1
Z
Z
Output
3
Input
52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn
Output
958681902
Submitted Solution:
```
mod = 1000000007
n = int(input())
up = input()
dw = input()
arrays = 1
j = 0
justBefore = None
if up[j] == dw[j]:
arrays *= 3
j += 1
justBefore = "T"
else:
arrays *= 6
j += 2
justBefore = "Y"
while(j != len(up)-1):
if len(up)<3:break
if justBefore == "T":
if up[j] == dw[j]:
arrays *= 2
arrays%=1000000007
j += 1
justBefore = "T"
else:
arrays *= 2
arrays%=1000000007
j += 2
justBefore = "Y"
else:
if up[j] == dw[j]:
arrays *= 1
arrays%=1000000007
j += 1
justBefore = "T"
else:
arrays *= 3
arrays%=1000000007
j += 2
justBefore = "Y"
print(arrays)
``` | instruction | 0 | 23,682 | 16 | 47,364 |
No | output | 1 | 23,682 | 16 | 47,365 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke found N strange creatures. Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.
Every creature can absorb another creature whose size is at most twice the size of itself. When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B. Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.
Snuke has been watching these creatures merge over and over and ultimately become one creature. Find the number of the possible colors of this creature.
Constraints
* 2 \leq N \leq 100000
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 … A_N
Output
Print the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.
Examples
Input
3
3 1 4
Output
2
Input
5
1 1 1 1 1
Output
5
Input
6
40 1 30 2 7 20
Output
4 | instruction | 0 | 23,683 | 16 | 47,366 |
"Correct Solution:
```
N = int(input())
As = list(map(int, input().split()))
As.sort()
s = 0
ans = 0
for i in range(len(As)-1):
s += As[i]
if s * 2 >= As[i+1]:
ans += 1
else:
ans = 0
ans += 1
print(ans)
``` | output | 1 | 23,683 | 16 | 47,367 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke found N strange creatures. Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.
Every creature can absorb another creature whose size is at most twice the size of itself. When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B. Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.
Snuke has been watching these creatures merge over and over and ultimately become one creature. Find the number of the possible colors of this creature.
Constraints
* 2 \leq N \leq 100000
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 … A_N
Output
Print the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.
Examples
Input
3
3 1 4
Output
2
Input
5
1 1 1 1 1
Output
5
Input
6
40 1 30 2 7 20
Output
4 | instruction | 0 | 23,684 | 16 | 47,368 |
"Correct Solution:
```
#累積和で毎回sumしない
N=int(input())
A=sorted(map(int,input().split()))
b=0
c=0
for n in range(N-1):
b += A[n]
if b*2 >= A[n+1]:
c+=1
else:
c=0
print(c+1)
``` | output | 1 | 23,684 | 16 | 47,369 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke found N strange creatures. Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.
Every creature can absorb another creature whose size is at most twice the size of itself. When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B. Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.
Snuke has been watching these creatures merge over and over and ultimately become one creature. Find the number of the possible colors of this creature.
Constraints
* 2 \leq N \leq 100000
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 … A_N
Output
Print the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.
Examples
Input
3
3 1 4
Output
2
Input
5
1 1 1 1 1
Output
5
Input
6
40 1 30 2 7 20
Output
4 | instruction | 0 | 23,685 | 16 | 47,370 |
"Correct Solution:
```
n = int(input())
ai = [int(i) for i in input().split()]
ai.sort()
tmp = ai[0]
num = 0
for i in range(1,n):
if 2*tmp >= ai[i]:
num += 1
else:
num = 0
tmp += ai[i]
print(num+1)
``` | output | 1 | 23,685 | 16 | 47,371 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke found N strange creatures. Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.
Every creature can absorb another creature whose size is at most twice the size of itself. When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B. Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.
Snuke has been watching these creatures merge over and over and ultimately become one creature. Find the number of the possible colors of this creature.
Constraints
* 2 \leq N \leq 100000
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 … A_N
Output
Print the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.
Examples
Input
3
3 1 4
Output
2
Input
5
1 1 1 1 1
Output
5
Input
6
40 1 30 2 7 20
Output
4 | instruction | 0 | 23,686 | 16 | 47,372 |
"Correct Solution:
```
import sys
def input(): return sys.stdin.readline().strip()
n=int(input())
a=sorted(map(int,input().split()))
c=0
for i in range(n-1):
if a[i]*2<a[i+1]:
c=i+1
a[i+1]+=a[i]
print(n-c)
``` | output | 1 | 23,686 | 16 | 47,373 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke found N strange creatures. Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.
Every creature can absorb another creature whose size is at most twice the size of itself. When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B. Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.
Snuke has been watching these creatures merge over and over and ultimately become one creature. Find the number of the possible colors of this creature.
Constraints
* 2 \leq N \leq 100000
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 … A_N
Output
Print the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.
Examples
Input
3
3 1 4
Output
2
Input
5
1 1 1 1 1
Output
5
Input
6
40 1 30 2 7 20
Output
4 | instruction | 0 | 23,687 | 16 | 47,374 |
"Correct Solution:
```
n=int(input())
i=list(map(int,input().split()))
i.sort()
temp=1
size=i[0]
for k in range(1,n):
if size*2>=i[k]:
temp+=1
size+=i[k]
else:
temp=1
size+=i[k]
print(temp)
``` | output | 1 | 23,687 | 16 | 47,375 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke found N strange creatures. Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.
Every creature can absorb another creature whose size is at most twice the size of itself. When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B. Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.
Snuke has been watching these creatures merge over and over and ultimately become one creature. Find the number of the possible colors of this creature.
Constraints
* 2 \leq N \leq 100000
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 … A_N
Output
Print the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.
Examples
Input
3
3 1 4
Output
2
Input
5
1 1 1 1 1
Output
5
Input
6
40 1 30 2 7 20
Output
4 | instruction | 0 | 23,688 | 16 | 47,376 |
"Correct Solution:
```
N = int(input())
A = list(map(int, input().split()))
A.sort()
tmp = A[0]
ans = 1
for i in range(1, N):
if tmp*2 >= A[i]:
tmp += A[i]
ans += 1
else:
tmp += A[i]
ans = 1
print(ans)
``` | output | 1 | 23,688 | 16 | 47,377 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke found N strange creatures. Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.
Every creature can absorb another creature whose size is at most twice the size of itself. When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B. Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.
Snuke has been watching these creatures merge over and over and ultimately become one creature. Find the number of the possible colors of this creature.
Constraints
* 2 \leq N \leq 100000
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 … A_N
Output
Print the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.
Examples
Input
3
3 1 4
Output
2
Input
5
1 1 1 1 1
Output
5
Input
6
40 1 30 2 7 20
Output
4 | instruction | 0 | 23,689 | 16 | 47,378 |
"Correct Solution:
```
n=int(input())
a=[int(j) for j in input().split()]
a.sort()
tmp=0
ans=n
c=1
for i in range(n-1):
tmp+=a[i]
if tmp*2<a[i+1]:
ans-=c
c=1
else:
c+=1
print(ans)
``` | output | 1 | 23,689 | 16 | 47,379 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke found N strange creatures. Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.
Every creature can absorb another creature whose size is at most twice the size of itself. When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B. Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.
Snuke has been watching these creatures merge over and over and ultimately become one creature. Find the number of the possible colors of this creature.
Constraints
* 2 \leq N \leq 100000
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 … A_N
Output
Print the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.
Examples
Input
3
3 1 4
Output
2
Input
5
1 1 1 1 1
Output
5
Input
6
40 1 30 2 7 20
Output
4 | instruction | 0 | 23,690 | 16 | 47,380 |
"Correct Solution:
```
n=int(input())
l=sorted(list(map(int,input().split())))
ans,s=1,0
for u in l:
if 2*s>=u:ans+=1
else:ans=1
s+=u
print(ans)
``` | output | 1 | 23,690 | 16 | 47,381 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke found N strange creatures. Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.
Every creature can absorb another creature whose size is at most twice the size of itself. When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B. Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.
Snuke has been watching these creatures merge over and over and ultimately become one creature. Find the number of the possible colors of this creature.
Constraints
* 2 \leq N \leq 100000
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 … A_N
Output
Print the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.
Examples
Input
3
3 1 4
Output
2
Input
5
1 1 1 1 1
Output
5
Input
6
40 1 30 2 7 20
Output
4
Submitted Solution:
```
N = int(input())
A = list(map(int,input().split()))
A.sort()
tmp = 0
out = 0
for i in range(N):
if tmp*2 < A[i]:
out = i
tmp += A[i]
print(N - out)
``` | instruction | 0 | 23,691 | 16 | 47,382 |
Yes | output | 1 | 23,691 | 16 | 47,383 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke found N strange creatures. Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.
Every creature can absorb another creature whose size is at most twice the size of itself. When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B. Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.
Snuke has been watching these creatures merge over and over and ultimately become one creature. Find the number of the possible colors of this creature.
Constraints
* 2 \leq N \leq 100000
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 … A_N
Output
Print the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.
Examples
Input
3
3 1 4
Output
2
Input
5
1 1 1 1 1
Output
5
Input
6
40 1 30 2 7 20
Output
4
Submitted Solution:
```
n = int(input())
arr = list(map(int,input().split()))
arr.sort()
outs = -1
c = 0
for i in range(n-1):
c += arr[i]
if 2*c < arr[i+1]:
outs = i
if outs >= 0:
print(n - 1 - outs)
else:
print(n)
``` | instruction | 0 | 23,692 | 16 | 47,384 |
Yes | output | 1 | 23,692 | 16 | 47,385 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke found N strange creatures. Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.
Every creature can absorb another creature whose size is at most twice the size of itself. When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B. Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.
Snuke has been watching these creatures merge over and over and ultimately become one creature. Find the number of the possible colors of this creature.
Constraints
* 2 \leq N \leq 100000
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 … A_N
Output
Print the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.
Examples
Input
3
3 1 4
Output
2
Input
5
1 1 1 1 1
Output
5
Input
6
40 1 30 2 7 20
Output
4
Submitted Solution:
```
N = int(input())
A = [int(_) for _ in input().split()]
A.sort()
result = 0
t = 0
for a in A:
if a <= t * 2:
t += a
result += 1
else:
t += a
result = 1
print(result)
``` | instruction | 0 | 23,693 | 16 | 47,386 |
Yes | output | 1 | 23,693 | 16 | 47,387 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke found N strange creatures. Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.
Every creature can absorb another creature whose size is at most twice the size of itself. When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B. Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.
Snuke has been watching these creatures merge over and over and ultimately become one creature. Find the number of the possible colors of this creature.
Constraints
* 2 \leq N \leq 100000
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 … A_N
Output
Print the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.
Examples
Input
3
3 1 4
Output
2
Input
5
1 1 1 1 1
Output
5
Input
6
40 1 30 2 7 20
Output
4
Submitted Solution:
```
N=int(input())
l= list(map(int,input().split()))
l.sort()
S=0
ans=0
for i in range(N-1):
S+=l[i]
if S*2<l[i+1]:
ans=i+1
print(N-ans)
``` | instruction | 0 | 23,694 | 16 | 47,388 |
Yes | output | 1 | 23,694 | 16 | 47,389 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke found N strange creatures. Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.
Every creature can absorb another creature whose size is at most twice the size of itself. When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B. Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.
Snuke has been watching these creatures merge over and over and ultimately become one creature. Find the number of the possible colors of this creature.
Constraints
* 2 \leq N \leq 100000
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 … A_N
Output
Print the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.
Examples
Input
3
3 1 4
Output
2
Input
5
1 1 1 1 1
Output
5
Input
6
40 1 30 2 7 20
Output
4
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split()))
a.sort()
ans = 0
for i in range(n - 1, -1, -1):
if a[i] <= a[i - 1] * 2:
ans += 1
print(ans)
``` | instruction | 0 | 23,695 | 16 | 47,390 |
No | output | 1 | 23,695 | 16 | 47,391 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke found N strange creatures. Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.
Every creature can absorb another creature whose size is at most twice the size of itself. When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B. Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.
Snuke has been watching these creatures merge over and over and ultimately become one creature. Find the number of the possible colors of this creature.
Constraints
* 2 \leq N \leq 100000
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 … A_N
Output
Print the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.
Examples
Input
3
3 1 4
Output
2
Input
5
1 1 1 1 1
Output
5
Input
6
40 1 30 2 7 20
Output
4
Submitted Solution:
```
import bisect
N = int(input())
A = [int(x) for x in input().split()]
A.sort()
mx = max(A)
ind = bisect.bisect_left(A,mx//2)
print(N-ind)
``` | instruction | 0 | 23,696 | 16 | 47,392 |
No | output | 1 | 23,696 | 16 | 47,393 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke found N strange creatures. Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.
Every creature can absorb another creature whose size is at most twice the size of itself. When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B. Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.
Snuke has been watching these creatures merge over and over and ultimately become one creature. Find the number of the possible colors of this creature.
Constraints
* 2 \leq N \leq 100000
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 … A_N
Output
Print the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.
Examples
Input
3
3 1 4
Output
2
Input
5
1 1 1 1 1
Output
5
Input
6
40 1 30 2 7 20
Output
4
Submitted Solution:
```
n=int(input())
i=list(map(int,input().split()))
i.sort()
temp=1
size=i[0]
for k in range(1,n):
if size*2>=i[k]:
temp+=1
size+=i[k]
else:
temp=1
print(temp)
``` | instruction | 0 | 23,697 | 16 | 47,394 |
No | output | 1 | 23,697 | 16 | 47,395 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke found N strange creatures. Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.
Every creature can absorb another creature whose size is at most twice the size of itself. When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B. Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.
Snuke has been watching these creatures merge over and over and ultimately become one creature. Find the number of the possible colors of this creature.
Constraints
* 2 \leq N \leq 100000
* 1 \leq A_i \leq 10^9
* A_i is an integer.
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 … A_N
Output
Print the number of the possible colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.
Examples
Input
3
3 1 4
Output
2
Input
5
1 1 1 1 1
Output
5
Input
6
40 1 30 2 7 20
Output
4
Submitted Solution:
```
N = int(input())
A = list(map(int, input().split()))
A = sorted(A)
wa = A[0] # i - 1 までの和
cnt = 1 # i 番目の生き物より小さかったのに、i 番目の生き物を食べれるやつの数
for i in range(1, N):
if 2 * wa >= A[i]:
cnt += 1
else:
cnt = 1
wa += A[i]
print(cnt)
``` | instruction | 0 | 23,698 | 16 | 47,396 |
No | output | 1 | 23,698 | 16 | 47,397 |
Provide a correct Python 3 solution for this coding contest problem.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the permutation written into the blocks of step N was (a_1, a_2, ..., a_{2N-1}).
Find the integer written into the block of step 1.
Constraints
* 2≤N≤10^5
* (a_1, a_2, ..., a_{2N-1}) is a permutation of (1, 2, ..., 2N-1).
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{2N-1}
Output
Print the integer written into the block of step 1.
Examples
Input
4
1 6 3 7 4 5 2
Output
4
Input
2
1 2 3
Output
2 | instruction | 0 | 23,699 | 16 | 47,398 |
"Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
def check(mid):
if a[n - 1] >= mid and (a[n - 2] >= mid or a[n] >= mid):
return True
elif a[n - 1] < mid and (a[n - 2] < mid or a[n] < mid):
return False
l = n - 1
while l > 0:
if (a[l] < mid) ^ (a[l - 1] < mid):
l -= 1
else:
break
r = n - 1
while r < n * 2 - 2:
if (a[r] < mid) ^ (a[r + 1] < mid):
r += 1
else:
break
if l == 0 and r == n * 2 - 1:
return bool((n & 1) ^ (a[n - 1] < mid))
if abs(n - 1 - l) < abs(n - 1 - r):
return a[l] >= mid
else:
return a[r] >= mid
ok = 0
ng = n * 2
while ng - ok > 1:
mid = (ok + ng) // 2
if check(mid):
ok = mid
else:
ng = mid
print(ok)
``` | output | 1 | 23,699 | 16 | 47,399 |
Provide a correct Python 3 solution for this coding contest problem.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the permutation written into the blocks of step N was (a_1, a_2, ..., a_{2N-1}).
Find the integer written into the block of step 1.
Constraints
* 2≤N≤10^5
* (a_1, a_2, ..., a_{2N-1}) is a permutation of (1, 2, ..., 2N-1).
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{2N-1}
Output
Print the integer written into the block of step 1.
Examples
Input
4
1 6 3 7 4 5 2
Output
4
Input
2
1 2 3
Output
2 | instruction | 0 | 23,700 | 16 | 47,400 |
"Correct Solution:
```
N=int(input())
a=list(map(int,input().split()))
def cond(n):
L=(0,-1)
for i in range(1,N):
if a[i]>=n and a[i-1]>=n:
L=(i,1)
elif a[i]<n and a[i-1]<n:
L=(i,0)
R=(2*N-1,-1)
for i in range(2*N-3,N-2,-1):
if a[i]>=n and a[i+1]>=n:
R=(i,1)
elif a[i]<n and a[i+1]<n:
R=(i,0)
if L[1]==-1 and R[1]==-1:
return a[0]>=n
elif L[1]==-1:
return R[1]==1
elif R[1]==-1:
return L[1]==1
elif L[1]==R[1]:
return R[1]==1
else:
if L[1]==0:
return N-1-L[0]>R[0]-(N-1)
else:
return N-1-L[0]<R[0]-(N-1)
start=1
end=2*N-1
while end-start>1:
test=(end+start)//2
if cond(test):
start=test
else:
end=test
if cond(end):
print(end)
else:
print(start)
``` | output | 1 | 23,700 | 16 | 47,401 |
Provide a correct Python 3 solution for this coding contest problem.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the permutation written into the blocks of step N was (a_1, a_2, ..., a_{2N-1}).
Find the integer written into the block of step 1.
Constraints
* 2≤N≤10^5
* (a_1, a_2, ..., a_{2N-1}) is a permutation of (1, 2, ..., 2N-1).
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{2N-1}
Output
Print the integer written into the block of step 1.
Examples
Input
4
1 6 3 7 4 5 2
Output
4
Input
2
1 2 3
Output
2 | instruction | 0 | 23,701 | 16 | 47,402 |
"Correct Solution:
```
# def makelist(n, m):
# return [[0 for i in range(m)] for j in range(n)]
N = int(input())
a = [0] + list(map(int, input().split()))
def check(n):
b = [False]*(len(a))
for i in range(1, len(a)):
if a[i] >= n:
b[i] = True
else:
b[i] = False
r = int(1e9)
l = int(1e9)
rb = b[N]
lb = b[N]
for i in range(1, N):
if lb == b[N-i]:
l = i
break
else:
lb = b[N-i]
for i in range(1, N):
if rb == b[N+i]:
r = i
break
else:
rb = b[N+i]
if r == int(1e9) and l == int(1e9):
if N % 2 == 1:
return b[N]
else:
return not b[N]
else:
if r < l:
return rb
else:
return lb
# 条件を満たす最小の値を返す
def binarySearch(small, big):
mid = (big + small) // 2
if big - small <= 1:
if check(small): return small
else: return big
else:
if not check(mid):
return binarySearch(small, mid)
else:
return binarySearch(mid, big)
print(binarySearch(2, 2*N-2))
``` | output | 1 | 23,701 | 16 | 47,403 |
Provide a correct Python 3 solution for this coding contest problem.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the permutation written into the blocks of step N was (a_1, a_2, ..., a_{2N-1}).
Find the integer written into the block of step 1.
Constraints
* 2≤N≤10^5
* (a_1, a_2, ..., a_{2N-1}) is a permutation of (1, 2, ..., 2N-1).
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{2N-1}
Output
Print the integer written into the block of step 1.
Examples
Input
4
1 6 3 7 4 5 2
Output
4
Input
2
1 2 3
Output
2 | instruction | 0 | 23,702 | 16 | 47,404 |
"Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
l, r = 1, n * 2
while r - l > 1:
m = (l + r) // 2
li = [0] * (2 * n - 1)
for i in range(2 * n - 1):
if a[i] >= m:
li[i] = 1
t = li[n - 1]
for i in range(n - 1):
if ((t + li[n + i] + i) & 1 == 0):
if li[n + i] & 1:
l = m
else:
r = m
break
if((t + li[n - i - 2] + i) & 1 == 0):
if li[n - i - 2] & 1:
l = m
else:
r = m
break
else:
if (n + t) & 1:
r = m
else:
l = m
print(l)
``` | output | 1 | 23,702 | 16 | 47,405 |
Provide a correct Python 3 solution for this coding contest problem.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the permutation written into the blocks of step N was (a_1, a_2, ..., a_{2N-1}).
Find the integer written into the block of step 1.
Constraints
* 2≤N≤10^5
* (a_1, a_2, ..., a_{2N-1}) is a permutation of (1, 2, ..., 2N-1).
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{2N-1}
Output
Print the integer written into the block of step 1.
Examples
Input
4
1 6 3 7 4 5 2
Output
4
Input
2
1 2 3
Output
2 | instruction | 0 | 23,703 | 16 | 47,406 |
"Correct Solution:
```
n = int(input())
A = list(map(int, input().split()))
l = 1
r = 2*n
while l < r-1:
mid = (l+r)//2
B = []
C = []
for i in range(0,2*n-1):
B.append(A[i] >= mid)
C.append(0)
for i in range(1,2*n-1):
if B[i-1] == B[i]:
C[i] = 1
for i in range(0,2*n-2):
if B[i+1] == B[i]:
C[i] = 1
mi = 2*n
ans = False
for i in range(0,2*n-1):
if C[i] == 1:
if abs(i-n+1) < mi:
mi = abs(i-n+1)
ans = B[i]
if mi == 2*n: #specialfall
ans = ((n+1)%2)^B[n-1]
if ans == True:
l = mid
else:
r = mid
print(l)
``` | output | 1 | 23,703 | 16 | 47,407 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the permutation written into the blocks of step N was (a_1, a_2, ..., a_{2N-1}).
Find the integer written into the block of step 1.
Constraints
* 2≤N≤10^5
* (a_1, a_2, ..., a_{2N-1}) is a permutation of (1, 2, ..., 2N-1).
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{2N-1}
Output
Print the integer written into the block of step 1.
Examples
Input
4
1 6 3 7 4 5 2
Output
4
Input
2
1 2 3
Output
2
Submitted Solution:
```
N=int(input())
a=list(map(int,input().split()))
def cond(n):
L=(0,-1)
for i in range(1,N):
if a[i]>=n and a[i-1]>=n:
L=(i,1)
elif a[i]<n and a[i-1]<n:
L=(i,0)
R=(2*N-1,-1)
for i in range(2*N-3,N-2,-1):
if a[i]>=n and a[i+1]>=n:
R=(i,1)
elif a[i]<n and a[i+1]<n:
R=(i,0)
if L[1]==-1 and R[1]==-1:
return a[0]>=n
elif L[1]==-1:
return R[1]==1
elif R[1]==-1:
return L[1]==1
else:
if L[1]==0:
return N-1-L[0]>R[0]-(N-1)
else:
return N-1-L[0]<R[0]-(N-1)
start=1
end=2*N-1
while end-start>1:
test=(end+start)//2
if cond(test):
start=test
else:
end=test
if cond(end):
print(end)
else:
print(start)
``` | instruction | 0 | 23,704 | 16 | 47,408 |
No | output | 1 | 23,704 | 16 | 47,409 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the permutation written into the blocks of step N was (a_1, a_2, ..., a_{2N-1}).
Find the integer written into the block of step 1.
Constraints
* 2≤N≤10^5
* (a_1, a_2, ..., a_{2N-1}) is a permutation of (1, 2, ..., 2N-1).
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{2N-1}
Output
Print the integer written into the block of step 1.
Examples
Input
4
1 6 3 7 4 5 2
Output
4
Input
2
1 2 3
Output
2
Submitted Solution:
```
import math
from functools import reduce
from collections import deque
import sys
sys.setrecursionlimit(10**7)
from statistics import median
def s(generator, splitter, mapper):
return [ mapper(s) for s in generator().split(splitter) ]
# スペース区切りの入力を読み込んで数値リストにして返します。
def get_nums_l():
return [ int(s) for s in input().split(" ")]
# 改行区切りの入力をn行読み込んで数値リストにして返します。
def get_nums_n(n):
return [ int(input()) for _ in range(n)]
n = int(input())
nums = get_nums_l()
while len(nums) > 1:
print(nums)
new_nums = []
for i in range(1, len(nums)-1):
new_nums.append(median(nums[i-1:i+2]))
nums = new_nums
print(nums[0])
``` | instruction | 0 | 23,705 | 16 | 47,410 |
No | output | 1 | 23,705 | 16 | 47,411 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.
<image>
A pyramid with N=4 steps
Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:
* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.
<image>
Writing integers into the blocks
Afterwards, he erased all integers written into the blocks. Now, he only remembers that the permutation written into the blocks of step N was (a_1, a_2, ..., a_{2N-1}).
Find the integer written into the block of step 1.
Constraints
* 2≤N≤10^5
* (a_1, a_2, ..., a_{2N-1}) is a permutation of (1, 2, ..., 2N-1).
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{2N-1}
Output
Print the integer written into the block of step 1.
Examples
Input
4
1 6 3 7 4 5 2
Output
4
Input
2
1 2 3
Output
2
Submitted Solution:
```
n = int(input())
print(n)
``` | instruction | 0 | 23,707 | 16 | 47,414 |
No | output | 1 | 23,707 | 16 | 47,415 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct. He is sorting this sequence in increasing order. With supernatural power, he can perform the following two operations on the sequence in any order:
* Operation 1: choose 2 consecutive elements, then reverse the order of those elements.
* Operation 2: choose 3 consecutive elements, then reverse the order of those elements.
Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.
Constraints
* 1 ≦ N ≦ 10^5
* 0 ≦ A_i ≦ 10^9
* If i ≠ j, then A_i ≠ A_j.
* All input values are integers.
Input
The input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the minimum number of times Operation 1 that Snuke has to perform.
Examples
Input
4
2
4
3
1
Output
1
Input
5
10
8
5
3
2
Output
0 | instruction | 0 | 24,637 | 16 | 49,274 |
"Correct Solution:
```
import bisect
import copy
n = int(input())
L = []
zahyou = []
for i in range(n):
L.append(int(input()))
C = copy.deepcopy(L)
C.sort()
for i in range(n):
t = L[i]
k = bisect.bisect_left(C,t)
zahyou.append(k)
ans = 0
for i in range(n):
if zahyou[i]%2 != i%2:
ans += 1
print(ans//2)
``` | output | 1 | 24,637 | 16 | 49,275 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct. He is sorting this sequence in increasing order. With supernatural power, he can perform the following two operations on the sequence in any order:
* Operation 1: choose 2 consecutive elements, then reverse the order of those elements.
* Operation 2: choose 3 consecutive elements, then reverse the order of those elements.
Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.
Constraints
* 1 ≦ N ≦ 10^5
* 0 ≦ A_i ≦ 10^9
* If i ≠ j, then A_i ≠ A_j.
* All input values are integers.
Input
The input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the minimum number of times Operation 1 that Snuke has to perform.
Examples
Input
4
2
4
3
1
Output
1
Input
5
10
8
5
3
2
Output
0 | instruction | 0 | 24,638 | 16 | 49,276 |
"Correct Solution:
```
#%%
n = int(input())
a = [[] for i in range(n)]
for i in range(n):
tmp = [int(input()), i]
a[i] = tmp
b = sorted(a)
#print(b)
c = []
ans = 0
for i in range(n):
c.append(b[i][1])
ans += (i - c[i])%2
ans //= 2
print(ans)
``` | output | 1 | 24,638 | 16 | 49,277 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct. He is sorting this sequence in increasing order. With supernatural power, he can perform the following two operations on the sequence in any order:
* Operation 1: choose 2 consecutive elements, then reverse the order of those elements.
* Operation 2: choose 3 consecutive elements, then reverse the order of those elements.
Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.
Constraints
* 1 ≦ N ≦ 10^5
* 0 ≦ A_i ≦ 10^9
* If i ≠ j, then A_i ≠ A_j.
* All input values are integers.
Input
The input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the minimum number of times Operation 1 that Snuke has to perform.
Examples
Input
4
2
4
3
1
Output
1
Input
5
10
8
5
3
2
Output
0 | instruction | 0 | 24,639 | 16 | 49,278 |
"Correct Solution:
```
import copy
n = int(input())
nums = []
for i in range(n):
nums.append(int(input()))
taiou = {}
reprica = copy.copy(nums)
reprica.sort()
for i, r in enumerate(reprica):
taiou[r] = i
ans = 0
for i, num in enumerate(nums):
if i % 2 != taiou[num] % 2:
ans += 1
print(ans // 2)
``` | output | 1 | 24,639 | 16 | 49,279 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct. He is sorting this sequence in increasing order. With supernatural power, he can perform the following two operations on the sequence in any order:
* Operation 1: choose 2 consecutive elements, then reverse the order of those elements.
* Operation 2: choose 3 consecutive elements, then reverse the order of those elements.
Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.
Constraints
* 1 ≦ N ≦ 10^5
* 0 ≦ A_i ≦ 10^9
* If i ≠ j, then A_i ≠ A_j.
* All input values are integers.
Input
The input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the minimum number of times Operation 1 that Snuke has to perform.
Examples
Input
4
2
4
3
1
Output
1
Input
5
10
8
5
3
2
Output
0 | instruction | 0 | 24,640 | 16 | 49,280 |
"Correct Solution:
```
n = int(input())
nums = [[int(input()), i] for i in range(n)]
nums.sort()
ans = 0
for i in range(n):
if abs (i - nums[i][1]) % 2 == 1:
ans += 1
print(ans // 2)
``` | output | 1 | 24,640 | 16 | 49,281 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct. He is sorting this sequence in increasing order. With supernatural power, he can perform the following two operations on the sequence in any order:
* Operation 1: choose 2 consecutive elements, then reverse the order of those elements.
* Operation 2: choose 3 consecutive elements, then reverse the order of those elements.
Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.
Constraints
* 1 ≦ N ≦ 10^5
* 0 ≦ A_i ≦ 10^9
* If i ≠ j, then A_i ≠ A_j.
* All input values are integers.
Input
The input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the minimum number of times Operation 1 that Snuke has to perform.
Examples
Input
4
2
4
3
1
Output
1
Input
5
10
8
5
3
2
Output
0 | instruction | 0 | 24,641 | 16 | 49,282 |
"Correct Solution:
```
n=int(input())
a=[int(input()) for _ in range(n)]
aa=a.copy()
aa.sort()
import bisect
a=[bisect.bisect_left(aa,x) for x in a]
ans=0
for i in range(n):
if (i-a[i])%2==0:
pass
else:
ans+=1
print(ans//2)
``` | output | 1 | 24,641 | 16 | 49,283 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct. He is sorting this sequence in increasing order. With supernatural power, he can perform the following two operations on the sequence in any order:
* Operation 1: choose 2 consecutive elements, then reverse the order of those elements.
* Operation 2: choose 3 consecutive elements, then reverse the order of those elements.
Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.
Constraints
* 1 ≦ N ≦ 10^5
* 0 ≦ A_i ≦ 10^9
* If i ≠ j, then A_i ≠ A_j.
* All input values are integers.
Input
The input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the minimum number of times Operation 1 that Snuke has to perform.
Examples
Input
4
2
4
3
1
Output
1
Input
5
10
8
5
3
2
Output
0 | instruction | 0 | 24,642 | 16 | 49,284 |
"Correct Solution:
```
N, *A = map(int, open(0).read().split())
B = sorted(A)
dic = {B[i]:i for i in range(N)}
ans = sum((i+1)%2==dic[n]%2 for i,n in enumerate(A))
print(ans//2)
``` | output | 1 | 24,642 | 16 | 49,285 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct. He is sorting this sequence in increasing order. With supernatural power, he can perform the following two operations on the sequence in any order:
* Operation 1: choose 2 consecutive elements, then reverse the order of those elements.
* Operation 2: choose 3 consecutive elements, then reverse the order of those elements.
Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.
Constraints
* 1 ≦ N ≦ 10^5
* 0 ≦ A_i ≦ 10^9
* If i ≠ j, then A_i ≠ A_j.
* All input values are integers.
Input
The input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the minimum number of times Operation 1 that Snuke has to perform.
Examples
Input
4
2
4
3
1
Output
1
Input
5
10
8
5
3
2
Output
0 | instruction | 0 | 24,643 | 16 | 49,286 |
"Correct Solution:
```
import bisect
n=int(input())
l=[]
e=[]
for i in range(n//2):
j=int(input())
e.append(j)
l.append(j)
j=int(input())
l.append(j)
if n%2==1:
j=int(input())
e.append(j)
l.append(j)
l.sort()
e.sort()
res=0
for i in range(0,n,2):
if e[min(len(e)-1,bisect.bisect_left(e,l[i]))]!=l[i]:
res+=1
print(res)
``` | output | 1 | 24,643 | 16 | 49,287 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct. He is sorting this sequence in increasing order. With supernatural power, he can perform the following two operations on the sequence in any order:
* Operation 1: choose 2 consecutive elements, then reverse the order of those elements.
* Operation 2: choose 3 consecutive elements, then reverse the order of those elements.
Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.
Constraints
* 1 ≦ N ≦ 10^5
* 0 ≦ A_i ≦ 10^9
* If i ≠ j, then A_i ≠ A_j.
* All input values are integers.
Input
The input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the minimum number of times Operation 1 that Snuke has to perform.
Examples
Input
4
2
4
3
1
Output
1
Input
5
10
8
5
3
2
Output
0 | instruction | 0 | 24,644 | 16 | 49,288 |
"Correct Solution:
```
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time
sys.setrecursionlimit(10**7)
inf = 10**9
n = int(input())
a = [[int(input()),_] for _ in range(n)]
a.sort()
r = 0
for i in range(0,n,2):
if a[i][1] % 2 == 1:
r += 1
print(r)
``` | output | 1 | 24,644 | 16 | 49,289 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct. He is sorting this sequence in increasing order. With supernatural power, he can perform the following two operations on the sequence in any order:
* Operation 1: choose 2 consecutive elements, then reverse the order of those elements.
* Operation 2: choose 3 consecutive elements, then reverse the order of those elements.
Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.
Constraints
* 1 ≦ N ≦ 10^5
* 0 ≦ A_i ≦ 10^9
* If i ≠ j, then A_i ≠ A_j.
* All input values are integers.
Input
The input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the minimum number of times Operation 1 that Snuke has to perform.
Examples
Input
4
2
4
3
1
Output
1
Input
5
10
8
5
3
2
Output
0
Submitted Solution:
```
N=int(input())
A=[int(input()) for i in range(N)]
P=0
B=sorted(list(set(A)))
C=0
E=dict()
for i in range(N):
E[B[i]]=E.get(B[i],0)+1
D=dict()
for i in range(N):
if E[B[i]]&1:
D[B[i]]=C
C+=1
else:
D[B[i]]=-1
for i in range(N):
if (i&1)!=(D[A[i]]&1) and D[A[i]]!=-1:
P+=1
print(P>>1)
``` | instruction | 0 | 24,645 | 16 | 49,290 |
Yes | output | 1 | 24,645 | 16 | 49,291 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct. He is sorting this sequence in increasing order. With supernatural power, he can perform the following two operations on the sequence in any order:
* Operation 1: choose 2 consecutive elements, then reverse the order of those elements.
* Operation 2: choose 3 consecutive elements, then reverse the order of those elements.
Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.
Constraints
* 1 ≦ N ≦ 10^5
* 0 ≦ A_i ≦ 10^9
* If i ≠ j, then A_i ≠ A_j.
* All input values are integers.
Input
The input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the minimum number of times Operation 1 that Snuke has to perform.
Examples
Input
4
2
4
3
1
Output
1
Input
5
10
8
5
3
2
Output
0
Submitted Solution:
```
import bisect
n = int(input())
a = [int(input()) for _ in range(n)]
b = list(a)
b.sort()
s, t = 0, 0
for i in range(n):
x = bisect.bisect_left(b, a[i])
if i % 2 == 0 and x % 2 == 1:
s += 1
elif i % 2 == 1 and x % 2 == 0:
t += 1
print(max(s, t))
``` | instruction | 0 | 24,646 | 16 | 49,292 |
Yes | output | 1 | 24,646 | 16 | 49,293 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct. He is sorting this sequence in increasing order. With supernatural power, he can perform the following two operations on the sequence in any order:
* Operation 1: choose 2 consecutive elements, then reverse the order of those elements.
* Operation 2: choose 3 consecutive elements, then reverse the order of those elements.
Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.
Constraints
* 1 ≦ N ≦ 10^5
* 0 ≦ A_i ≦ 10^9
* If i ≠ j, then A_i ≠ A_j.
* All input values are integers.
Input
The input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the minimum number of times Operation 1 that Snuke has to perform.
Examples
Input
4
2
4
3
1
Output
1
Input
5
10
8
5
3
2
Output
0
Submitted Solution:
```
N = int(input())
A = [[int(input()),i] for i in range(N)]
Asort = sorted(A)
ans = 0
for key,val in enumerate(Asort):
if abs(key-val[1])%2==1:
ans += 1
print(ans//2)
``` | instruction | 0 | 24,647 | 16 | 49,294 |
Yes | output | 1 | 24,647 | 16 | 49,295 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct. He is sorting this sequence in increasing order. With supernatural power, he can perform the following two operations on the sequence in any order:
* Operation 1: choose 2 consecutive elements, then reverse the order of those elements.
* Operation 2: choose 3 consecutive elements, then reverse the order of those elements.
Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.
Constraints
* 1 ≦ N ≦ 10^5
* 0 ≦ A_i ≦ 10^9
* If i ≠ j, then A_i ≠ A_j.
* All input values are integers.
Input
The input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the minimum number of times Operation 1 that Snuke has to perform.
Examples
Input
4
2
4
3
1
Output
1
Input
5
10
8
5
3
2
Output
0
Submitted Solution:
```
n = int(input())
a = [int(input()) for i in range(n)]
even_num = set((a[i] for i in range(0,n) if i % 2 == 0))
a.sort()
odd_num = set((a[i] for i in range(0, n) if i % 2 == 1))
count = len(even_num & odd_num)
print(count)
``` | instruction | 0 | 24,648 | 16 | 49,296 |
Yes | output | 1 | 24,648 | 16 | 49,297 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct. He is sorting this sequence in increasing order. With supernatural power, he can perform the following two operations on the sequence in any order:
* Operation 1: choose 2 consecutive elements, then reverse the order of those elements.
* Operation 2: choose 3 consecutive elements, then reverse the order of those elements.
Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.
Constraints
* 1 ≦ N ≦ 10^5
* 0 ≦ A_i ≦ 10^9
* If i ≠ j, then A_i ≠ A_j.
* All input values are integers.
Input
The input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the minimum number of times Operation 1 that Snuke has to perform.
Examples
Input
4
2
4
3
1
Output
1
Input
5
10
8
5
3
2
Output
0
Submitted Solution:
```
N=int(input())
A=[int(input()) for i in range(N)]
odd =[A[i] for i in range(N) if i%2 ==0]
even=[A[i] for i in range(N) if i%2 ==1]
A.sort()
odd.sort()
even.sort()
ans=0
for i in range(0,N,2):
if A[i]!=odd[i//2]:
ans+=1
tmp=0
for i in range(1,N,2):
if A[i]!=even[i//2]:
tmp+=1
print(max(ans,tmp))
``` | instruction | 0 | 24,649 | 16 | 49,298 |
No | output | 1 | 24,649 | 16 | 49,299 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke got an integer sequence of length N from his mother, as a birthday present. The i-th (1 ≦ i ≦ N) element of the sequence is a_i. The elements are pairwise distinct. He is sorting this sequence in increasing order. With supernatural power, he can perform the following two operations on the sequence in any order:
* Operation 1: choose 2 consecutive elements, then reverse the order of those elements.
* Operation 2: choose 3 consecutive elements, then reverse the order of those elements.
Snuke likes Operation 2, but not Operation 1. Find the minimum number of Operation 1 that he has to perform in order to sort the sequence in increasing order.
Constraints
* 1 ≦ N ≦ 10^5
* 0 ≦ A_i ≦ 10^9
* If i ≠ j, then A_i ≠ A_j.
* All input values are integers.
Input
The input is given from Standard Input in the following format:
N
A_1
:
A_N
Output
Print the minimum number of times Operation 1 that Snuke has to perform.
Examples
Input
4
2
4
3
1
Output
1
Input
5
10
8
5
3
2
Output
0
Submitted Solution:
```
def nibutan2(array,value,left,right,first = True):
if first:
if array[left]>value:
return 0
elif array[right]<value:
return len(array)
if right-left<=1:
return right
else:
i=(left+right)//2
if array[i]>value:
return nibutan(array,value,left,i,False)
elif array[i]<value:
return nibutan(array,value,i,right,False)
N=int(input())
A=[]
B=[]
for i in range(N):
if i%2==0:
A.append(int(input()))
else:
B.append(int(input()))
A.sort()
B.sort()
count=0
for i in range(len(A)):
c=nibutan2(B,A[i],0,len(B)-1)
count+=abs(c-i)
print(count)
``` | instruction | 0 | 24,650 | 16 | 49,300 |
No | output | 1 | 24,650 | 16 | 49,301 |
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