text stringlengths 198 433k | conversation_id int64 0 109k |
|---|---|
Provide a correct Python 3 solution for this coding contest problem.
Takahashi wants to be a member of some web service.
He tried to register himself with the ID S, which turned out to be already used by another user.
Thus, he decides to register using a string obtained by appending one character at the end of S as his ID.
He is now trying to register with the ID T. Determine whether this string satisfies the property above.
Constraints
* S and T are strings consisting of lowercase English letters.
* 1 \leq |S| \leq 10
* |T| = |S| + 1
Input
Input is given from Standard Input in the following format:
S
T
Output
If T satisfies the property in Problem Statement, print `Yes`; otherwise, print `No`.
Examples
Input
chokudai
chokudaiz
Output
Yes
Input
snuke
snekee
Output
No
Input
a
aa
Output
Yes
"Correct Solution:
```
s = input()
if s == input()[:-1]:
print("Yes")
else:
print("No")
```
| 98,400 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi wants to be a member of some web service.
He tried to register himself with the ID S, which turned out to be already used by another user.
Thus, he decides to register using a string obtained by appending one character at the end of S as his ID.
He is now trying to register with the ID T. Determine whether this string satisfies the property above.
Constraints
* S and T are strings consisting of lowercase English letters.
* 1 \leq |S| \leq 10
* |T| = |S| + 1
Input
Input is given from Standard Input in the following format:
S
T
Output
If T satisfies the property in Problem Statement, print `Yes`; otherwise, print `No`.
Examples
Input
chokudai
chokudaiz
Output
Yes
Input
snuke
snekee
Output
No
Input
a
aa
Output
Yes
"Correct Solution:
```
s = input()
t = input()
r = 'Yes' if s == t[:-1] else 'No'
print(r)
```
| 98,401 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi wants to be a member of some web service.
He tried to register himself with the ID S, which turned out to be already used by another user.
Thus, he decides to register using a string obtained by appending one character at the end of S as his ID.
He is now trying to register with the ID T. Determine whether this string satisfies the property above.
Constraints
* S and T are strings consisting of lowercase English letters.
* 1 \leq |S| \leq 10
* |T| = |S| + 1
Input
Input is given from Standard Input in the following format:
S
T
Output
If T satisfies the property in Problem Statement, print `Yes`; otherwise, print `No`.
Examples
Input
chokudai
chokudaiz
Output
Yes
Input
snuke
snekee
Output
No
Input
a
aa
Output
Yes
"Correct Solution:
```
print("YNeos"[input() != input()[:-1]::2])
```
| 98,402 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi wants to be a member of some web service.
He tried to register himself with the ID S, which turned out to be already used by another user.
Thus, he decides to register using a string obtained by appending one character at the end of S as his ID.
He is now trying to register with the ID T. Determine whether this string satisfies the property above.
Constraints
* S and T are strings consisting of lowercase English letters.
* 1 \leq |S| \leq 10
* |T| = |S| + 1
Input
Input is given from Standard Input in the following format:
S
T
Output
If T satisfies the property in Problem Statement, print `Yes`; otherwise, print `No`.
Examples
Input
chokudai
chokudaiz
Output
Yes
Input
snuke
snekee
Output
No
Input
a
aa
Output
Yes
"Correct Solution:
```
S,T = input(),input()
print('Yes' if S==T[:-1] else 'No')
```
| 98,403 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi wants to be a member of some web service.
He tried to register himself with the ID S, which turned out to be already used by another user.
Thus, he decides to register using a string obtained by appending one character at the end of S as his ID.
He is now trying to register with the ID T. Determine whether this string satisfies the property above.
Constraints
* S and T are strings consisting of lowercase English letters.
* 1 \leq |S| \leq 10
* |T| = |S| + 1
Input
Input is given from Standard Input in the following format:
S
T
Output
If T satisfies the property in Problem Statement, print `Yes`; otherwise, print `No`.
Examples
Input
chokudai
chokudaiz
Output
Yes
Input
snuke
snekee
Output
No
Input
a
aa
Output
Yes
"Correct Solution:
```
s=input();print('NYoe s'[s==input()[:len(s)]::2])
```
| 98,404 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi wants to be a member of some web service.
He tried to register himself with the ID S, which turned out to be already used by another user.
Thus, he decides to register using a string obtained by appending one character at the end of S as his ID.
He is now trying to register with the ID T. Determine whether this string satisfies the property above.
Constraints
* S and T are strings consisting of lowercase English letters.
* 1 \leq |S| \leq 10
* |T| = |S| + 1
Input
Input is given from Standard Input in the following format:
S
T
Output
If T satisfies the property in Problem Statement, print `Yes`; otherwise, print `No`.
Examples
Input
chokudai
chokudaiz
Output
Yes
Input
snuke
snekee
Output
No
Input
a
aa
Output
Yes
"Correct Solution:
```
print("Yes") if input()==input()[:-1] else print("No")
```
| 98,405 |
Provide a correct Python 3 solution for this coding contest problem.
Takahashi wants to be a member of some web service.
He tried to register himself with the ID S, which turned out to be already used by another user.
Thus, he decides to register using a string obtained by appending one character at the end of S as his ID.
He is now trying to register with the ID T. Determine whether this string satisfies the property above.
Constraints
* S and T are strings consisting of lowercase English letters.
* 1 \leq |S| \leq 10
* |T| = |S| + 1
Input
Input is given from Standard Input in the following format:
S
T
Output
If T satisfies the property in Problem Statement, print `Yes`; otherwise, print `No`.
Examples
Input
chokudai
chokudaiz
Output
Yes
Input
snuke
snekee
Output
No
Input
a
aa
Output
Yes
"Correct Solution:
```
a=input()
b=input()
if a==b[0:-1]:
print('Yes')
else:
print('No')
```
| 98,406 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi wants to be a member of some web service.
He tried to register himself with the ID S, which turned out to be already used by another user.
Thus, he decides to register using a string obtained by appending one character at the end of S as his ID.
He is now trying to register with the ID T. Determine whether this string satisfies the property above.
Constraints
* S and T are strings consisting of lowercase English letters.
* 1 \leq |S| \leq 10
* |T| = |S| + 1
Input
Input is given from Standard Input in the following format:
S
T
Output
If T satisfies the property in Problem Statement, print `Yes`; otherwise, print `No`.
Examples
Input
chokudai
chokudaiz
Output
Yes
Input
snuke
snekee
Output
No
Input
a
aa
Output
Yes
Submitted Solution:
```
s,d=[input(),input()]
print("Yes") if s==d[:-1] else print("No")
```
Yes
| 98,407 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi wants to be a member of some web service.
He tried to register himself with the ID S, which turned out to be already used by another user.
Thus, he decides to register using a string obtained by appending one character at the end of S as his ID.
He is now trying to register with the ID T. Determine whether this string satisfies the property above.
Constraints
* S and T are strings consisting of lowercase English letters.
* 1 \leq |S| \leq 10
* |T| = |S| + 1
Input
Input is given from Standard Input in the following format:
S
T
Output
If T satisfies the property in Problem Statement, print `Yes`; otherwise, print `No`.
Examples
Input
chokudai
chokudaiz
Output
Yes
Input
snuke
snekee
Output
No
Input
a
aa
Output
Yes
Submitted Solution:
```
S = input()
T = input()
print("Yes") if S == T[:-1] else print("No")
```
Yes
| 98,408 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi wants to be a member of some web service.
He tried to register himself with the ID S, which turned out to be already used by another user.
Thus, he decides to register using a string obtained by appending one character at the end of S as his ID.
He is now trying to register with the ID T. Determine whether this string satisfies the property above.
Constraints
* S and T are strings consisting of lowercase English letters.
* 1 \leq |S| \leq 10
* |T| = |S| + 1
Input
Input is given from Standard Input in the following format:
S
T
Output
If T satisfies the property in Problem Statement, print `Yes`; otherwise, print `No`.
Examples
Input
chokudai
chokudaiz
Output
Yes
Input
snuke
snekee
Output
No
Input
a
aa
Output
Yes
Submitted Solution:
```
k = input()
s = input()
print("Yes" if s[:-1] == k else "No")
```
Yes
| 98,409 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi wants to be a member of some web service.
He tried to register himself with the ID S, which turned out to be already used by another user.
Thus, he decides to register using a string obtained by appending one character at the end of S as his ID.
He is now trying to register with the ID T. Determine whether this string satisfies the property above.
Constraints
* S and T are strings consisting of lowercase English letters.
* 1 \leq |S| \leq 10
* |T| = |S| + 1
Input
Input is given from Standard Input in the following format:
S
T
Output
If T satisfies the property in Problem Statement, print `Yes`; otherwise, print `No`.
Examples
Input
chokudai
chokudaiz
Output
Yes
Input
snuke
snekee
Output
No
Input
a
aa
Output
Yes
Submitted Solution:
```
S = input()
T = input()
print('Yes' if S[:] == T[:-1] else 'No')
```
Yes
| 98,410 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi wants to be a member of some web service.
He tried to register himself with the ID S, which turned out to be already used by another user.
Thus, he decides to register using a string obtained by appending one character at the end of S as his ID.
He is now trying to register with the ID T. Determine whether this string satisfies the property above.
Constraints
* S and T are strings consisting of lowercase English letters.
* 1 \leq |S| \leq 10
* |T| = |S| + 1
Input
Input is given from Standard Input in the following format:
S
T
Output
If T satisfies the property in Problem Statement, print `Yes`; otherwise, print `No`.
Examples
Input
chokudai
chokudaiz
Output
Yes
Input
snuke
snekee
Output
No
Input
a
aa
Output
Yes
Submitted Solution:
```
S = input()
T = input()
if len(S)+1 == len(T):
print('Yes')
else:
print('No')
```
No
| 98,411 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi wants to be a member of some web service.
He tried to register himself with the ID S, which turned out to be already used by another user.
Thus, he decides to register using a string obtained by appending one character at the end of S as his ID.
He is now trying to register with the ID T. Determine whether this string satisfies the property above.
Constraints
* S and T are strings consisting of lowercase English letters.
* 1 \leq |S| \leq 10
* |T| = |S| + 1
Input
Input is given from Standard Input in the following format:
S
T
Output
If T satisfies the property in Problem Statement, print `Yes`; otherwise, print `No`.
Examples
Input
chokudai
chokudaiz
Output
Yes
Input
snuke
snekee
Output
No
Input
a
aa
Output
Yes
Submitted Solution:
```
a, b = input(), input()
if a==b[:len(a)]:
print("Yes")
else:
print("NO")
```
No
| 98,412 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi wants to be a member of some web service.
He tried to register himself with the ID S, which turned out to be already used by another user.
Thus, he decides to register using a string obtained by appending one character at the end of S as his ID.
He is now trying to register with the ID T. Determine whether this string satisfies the property above.
Constraints
* S and T are strings consisting of lowercase English letters.
* 1 \leq |S| \leq 10
* |T| = |S| + 1
Input
Input is given from Standard Input in the following format:
S
T
Output
If T satisfies the property in Problem Statement, print `Yes`; otherwise, print `No`.
Examples
Input
chokudai
chokudaiz
Output
Yes
Input
snuke
snekee
Output
No
Input
a
aa
Output
Yes
Submitted Solution:
```
S = input()
T = input()
if S[:-len(S)-1] == T:
print("Yes")
else:
print("No")
```
No
| 98,413 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Takahashi wants to be a member of some web service.
He tried to register himself with the ID S, which turned out to be already used by another user.
Thus, he decides to register using a string obtained by appending one character at the end of S as his ID.
He is now trying to register with the ID T. Determine whether this string satisfies the property above.
Constraints
* S and T are strings consisting of lowercase English letters.
* 1 \leq |S| \leq 10
* |T| = |S| + 1
Input
Input is given from Standard Input in the following format:
S
T
Output
If T satisfies the property in Problem Statement, print `Yes`; otherwise, print `No`.
Examples
Input
chokudai
chokudaiz
Output
Yes
Input
snuke
snekee
Output
No
Input
a
aa
Output
Yes
Submitted Solution:
```
import re
s=input()
t=input()
if(re.search(s,t)):
print("Yes")
else:
print("No")
```
No
| 98,414 |
Provide a correct Python 3 solution for this coding contest problem.
Niwango has N cards, numbered 1,2,\ldots,N. He will now arrange these cards in a row.
Niwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below. To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.
* To the immediate right of Card 1 (if any) is NOT Card a_1.
* To the immediate right of Card 2 (if any) is NOT Card a_2.
* \vdots
* To the immediate right of Card N (if any) is NOT Card a_N.
Constraints
* 2 \leq N \leq 10^{5}
* 1 \leq a_i \leq N
* a_i \neq i
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 \ldots a_N
Output
If no arrangements satisfy the conditions, print `-1`. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:
b_1 b_2 \ldots b_N
Here, b_i represents the i-th card from the left.
Examples
Input
4
2 3 4 1
Output
1 3 2 4
Input
2
2 1
Output
-1
Input
13
2 3 4 5 6 7 8 9 10 11 12 13 12
Output
1 3 2 4 6 5 7 9 8 10 12 11 13
"Correct Solution:
```
import sys
from itertools import permutations
readline = sys.stdin.readline
from itertools import accumulate
from collections import Counter
from bisect import bisect as br, bisect_left as bl
class PMS:
#1-indexed
def __init__(self, A, B, issum = False):
#Aに初期状態の要素をすべて入れる,Bは値域のリスト
self.X, self.comp = self.compress(B)
self.size = len(self.X)
self.tree = [0] * (self.size + 1)
self.p = 2**(self.size.bit_length() - 1)
self.dep = self.size.bit_length()
CA = Counter(A)
S = [0] + list(accumulate([CA[self.X[i]] for i in range(self.size)]))
for i in range(1, 1+self.size):
self.tree[i] = S[i] - S[i - (i&-i)]
if issum:
self.sumtree = [0] * (self.size + 1)
Ssum = [0] + list(accumulate([CA[self.X[i]]*self.X[i] for i in range(self.size)]))
for i in range(1, 1+self.size):
self.sumtree[i] = Ssum[i] - Ssum[i - (i&-i)]
def compress(self, L):
#座圧
L2 = list(set(L))
L2.sort()
C = {v : k for k, v in enumerate(L2, 1)}
# 1-indexed
return L2, C
def leng(self):
#今入っている個数を取得
return self.count(self.X[-1])
def count(self, v):
#v(Bの元)以下の個数を取得
i = self.comp[v]
s = 0
while i > 0:
s += self.tree[i]
i -= i & -i
return s
def less(self, v):
#v(Bの元である必要はない)未満の個数を取得
i = bl(self.X, v)
s = 0
while i > 0:
s += self.tree[i]
i -= i & -i
return s
def leq(self, v):
#v(Bの元である必要はない)以下の個数を取得
i = br(self.X, v)
s = 0
while i > 0:
s += self.tree[i]
i -= i & -i
return s
def add(self, v, x):
#vをx個入れる,負のxで取り出す,iの個数以上取り出すとエラーを出さずにバグる
i = self.comp[v]
while i <= self.size:
self.tree[i] += x
i += i & -i
def get(self, i):
# i番目の値を取得
if i <= 0:
return -1
s = 0
k = self.p
for _ in range(self.dep):
if s + k <= self.size and self.tree[s+k] < i:
s += k
i -= self.tree[s]
k //= 2
return self.X[s]
def gets(self, v):
#累積和がv以下となる最大のindexを返す
v1 = v
s = 0
k = self.p
for _ in range(self.dep):
if s + k <= self.size and self.sumtree[s+k] < v:
s += k
v -= self.sumtree[s]
k //= 2
if s == self.size:
return self.leng()
return self.count(self.X[s]) + (v1 - self.countsum(self.X[s]))//self.X[s]
def addsum(self, i, x):
#sumを扱いたいときにaddの代わりに使う
self.add(i, x)
x *= i
i = self.comp[i]
while i <= self.size:
self.sumtree[i] += x
i += i & -i
def countsum(self, v):
#v(Bの元)以linema下のsumを取得
i = self.comp[v]
s = 0
while i > 0:
s += self.sumtree[i]
i -= i & -i
return s
def getsum(self, i):
#i番目までのsumを取得
x = self.get(i)
return self.countsum(x) - x*(self.count(x) - i)
N = int(readline())
A = list(map(int, readline().split()))
if N <= 8:
ans = True
for k in permutations(range(1, N+1)):
for i in range(N-1):
if k[i+1] == A[k[i]-1]:
break
else:
break
else:
ans = False
if not ans:
print(-1)
else:
print(*k)
else:
dim = [0]*(N+1)
for i in range(N):
a = A[i]
dim[a] += 1
T = PMS(list(range(2, N+1)), list(range(2, N+1)))
L = [1]
for i in range(N-7):
k = T.get(1)
if A[L[-1]-1] == k:
k = T.get(2)
L.append(k)
T.add(k, -1)
rem = [T.get(i) for i in range(1, 7)]
for k in permutations(rem):
if A[L[-1]-1] == k[0]:
continue
for i in range(5):
if k[i+1] == A[k[i]-1]:
break
else:
ans = L + list(k)
break
else:
L = L + list(k)
ok = -1
ng = N-5
while abs(ok-ng) > 1:
med = (ok+ng)//2
C = Counter()
for l in L[med:]:
C[A[l-1]] += 1
k, v = C.most_common()[0]
if v == N-med-1 and k in L[med:]:
ng = med
else:
ok = med
C = Counter()
for l in L[ng:]:
C[A[l-1]] += 1
k, _ = C.most_common()[0]
L = L[:ng] + [k]
S = set(range(1, N+1))
for l in L:
S.remove(l)
S = list(S)
T = PMS(S, S)
LS = len(S)
for _ in range(LS):
k = T.get(1)
if A[L[-1]-1] == k:
k = T.get(2)
L.append(k)
T.add(k, -1)
ans = L
print(*ans)
```
| 98,415 |
Provide a correct Python 3 solution for this coding contest problem.
Niwango has N cards, numbered 1,2,\ldots,N. He will now arrange these cards in a row.
Niwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below. To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.
* To the immediate right of Card 1 (if any) is NOT Card a_1.
* To the immediate right of Card 2 (if any) is NOT Card a_2.
* \vdots
* To the immediate right of Card N (if any) is NOT Card a_N.
Constraints
* 2 \leq N \leq 10^{5}
* 1 \leq a_i \leq N
* a_i \neq i
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 \ldots a_N
Output
If no arrangements satisfy the conditions, print `-1`. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:
b_1 b_2 \ldots b_N
Here, b_i represents the i-th card from the left.
Examples
Input
4
2 3 4 1
Output
1 3 2 4
Input
2
2 1
Output
-1
Input
13
2 3 4 5 6 7 8 9 10 11 12 13 12
Output
1 3 2 4 6 5 7 9 8 10 12 11 13
"Correct Solution:
```
import sys
from collections import defaultdict
from heapq import heappop, heappush
from itertools import permutations
from operator import itemgetter
# ある条件に当てはまらない限り、i番目に置く数字 xi は、
# それまで使ってない中で最も小さい数字か、
# またはその次に小さい数字（x[i-1]の右に最も小さい数字を置けない場合）
#
# ある条件: 以下の条件を満たす、未使用の数 k がある
# 残っているk以外の全ての数字が、kを共通して右側に置けない数として指定している
# ＝kを先頭に持ってこない限り、kを置ける機会が無い
#
# ただし残りが少なく（3以下）なってくると例外的なものが出てくるため、それ以降は全探索
def fill_remainings(ans, aaa, x, remainings):
"""
xを先頭にして残りを昇順に追加
ただしxの次の要素のみ、aaa[x]で禁止されていた場合はその次と入れ替える
remainingsにはxを含め3要素以上残っていることが前提
"""
ans.append(x)
i = len(ans)
while remainings:
k = heappop(remainings)
if k != x:
ans.append(k)
if aaa[x] == ans[i]:
ans[i], ans[i + 1] = ans[i + 1], ans[i]
def solve(n, aaa):
if n == 2:
return [-1]
in_degrees = defaultdict(lambda: 0)
for i, a in enumerate(aaa, start=1):
in_degrees[a] += 1
in_degrees = dict(in_degrees)
# 少なくとも残り個数がこれ+1になるまでは「ある条件」には当てはまらない
# ただし減少することはあるため、直前に再チェック必要
curr_max = max(in_degrees.values())
remainings = list(range(1, n + 1))
aaa.insert(0, 0)
ans = []
banned = -1
for i in range(n - 3):
if curr_max == n - i - 1:
curr_x, curr_max = max(in_degrees.items(), key=itemgetter(1))
if curr_max == n - i - 1:
fill_remainings(ans, aaa, curr_x, remainings)
return ans
top = heappop(remainings)
if top == banned:
ans.append(heappop(remainings))
heappush(remainings, top)
else:
ans.append(top)
banned = aaa[ans[-1]]
# 確定した数字の入り次数を削減
if banned in in_degrees:
if in_degrees[banned] == 1:
del in_degrees[banned]
else:
in_degrees[banned] -= 1
in_degrees.pop(ans[-1], 0)
remainings.sort()
for i, j, k in permutations(remainings):
if i != banned and j != aaa[i] and k != aaa[j]:
ans += [i, j, k]
break
return ans
n, *aaa = map(int, sys.stdin.buffer.read().split())
print(*solve(n, aaa))
```
| 98,416 |
Provide a correct Python 3 solution for this coding contest problem.
Niwango has N cards, numbered 1,2,\ldots,N. He will now arrange these cards in a row.
Niwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below. To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.
* To the immediate right of Card 1 (if any) is NOT Card a_1.
* To the immediate right of Card 2 (if any) is NOT Card a_2.
* \vdots
* To the immediate right of Card N (if any) is NOT Card a_N.
Constraints
* 2 \leq N \leq 10^{5}
* 1 \leq a_i \leq N
* a_i \neq i
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 \ldots a_N
Output
If no arrangements satisfy the conditions, print `-1`. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:
b_1 b_2 \ldots b_N
Here, b_i represents the i-th card from the left.
Examples
Input
4
2 3 4 1
Output
1 3 2 4
Input
2
2 1
Output
-1
Input
13
2 3 4 5 6 7 8 9 10 11 12 13 12
Output
1 3 2 4 6 5 7 9 8 10 12 11 13
"Correct Solution:
```
import sys
from itertools import permutations
n = int(input())
a = [0] + list(map(int, input().split()))
if n == 2:
print(-1)
sys.exit()
used = [False for _ in range(n+1)]
hate = dict()
for x in a[1:]:
if x in hate:
hate[x] += 1
else:
hate[x] = 1
cur = 1
ng = 0
ans = []
while len(ans) < n-3:
if len(hate) == 2:
worst = False
for k, v in hate.items():
if v == n - len(ans) - 1 and not used[k]:
worst = k
break
if worst:
ans.append(k)
used[k] = True
ng = a[k]
hate[a[k]] -= 1
if hate[a[k]] == 0:
del hate[a[k]]
continue
while used[cur]:
cur += 1
if cur == ng:
cur_copy = cur+1
while used[cur_copy]:
cur_copy += 1
ans.append(cur_copy)
used[cur_copy] = True
ng = a[cur_copy]
hate[ng] -= 1
if hate[ng] == 0:
del hate[ng]
else:
ans.append(cur)
used[cur] = True
ng = a[cur]
hate[ng] -= 1
if hate[ng] == 0:
del hate[ng]
yet = [i for i in range(1, n+1) if not used[i]]
for p in permutations(yet):
if p[0] != ng and p[1] != a[p[0]] and p[2] != a[p[1]]:
ans += list(p)
break
print(*ans)
```
| 98,417 |
Provide a correct Python 3 solution for this coding contest problem.
Niwango has N cards, numbered 1,2,\ldots,N. He will now arrange these cards in a row.
Niwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below. To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.
* To the immediate right of Card 1 (if any) is NOT Card a_1.
* To the immediate right of Card 2 (if any) is NOT Card a_2.
* \vdots
* To the immediate right of Card N (if any) is NOT Card a_N.
Constraints
* 2 \leq N \leq 10^{5}
* 1 \leq a_i \leq N
* a_i \neq i
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 \ldots a_N
Output
If no arrangements satisfy the conditions, print `-1`. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:
b_1 b_2 \ldots b_N
Here, b_i represents the i-th card from the left.
Examples
Input
4
2 3 4 1
Output
1 3 2 4
Input
2
2 1
Output
-1
Input
13
2 3 4 5 6 7 8 9 10 11 12 13 12
Output
1 3 2 4 6 5 7 9 8 10 12 11 13
"Correct Solution:
```
"""
Writer: SPD_9X2
https://atcoder.jp/contests/dwacon6th-prelims/tasks/dwacon6th_prelims_d
左からおいていくことを考える
残ったカード全てから嫌われている場合、もう置くしかない
貪欲に置いていき、残りカード全てから嫌われてしまったら置く？
そうなるとただの実装難問題だが…
for i in range(N)
if 残りのカード全てから嫌われてしまっているカードがあったら置く。
elif 辞書順最小のカードが置けたら置く
elif 辞書順2番目のカードが存在したら置く。
else -1?
なのか？？
3枚以上なら絶対置くことが可能そうに見える
残りのカード全てから嫌われてしまっている、判定はどうすればよいと？
嫌われてる辞書(残存するカードのみ)を作っておき、len(辞書) == 2 で、1でない方が嫌われ者
elif 以降はheapqを使うのが良さそう
おいてるフラグ配列を管理しておき、置いてないが出るまでpop
置けない場合は、もう1つ出るまでpopし、置いて最初の奴を戻す
何が問題なんだ…？
この方法だとqueueが空になってしまうけど構成不可能ではない、ケースが存在する
N==2で-1は正しかった
互いに嫌いな2個が最後に残るとまずい
→最後の3つを全探索するか？
→これが丸そう
"""
def allserch(dnt,x,y,z):
ret = []
if dnt != x and a[x] != y and a[y] != z:
ret.append([x,y,z])
if dnt != x and a[x] != z and a[z] != y:
ret.append([x,z,y])
if dnt != y and a[y] != x and a[x] != z:
ret.append([y,x,z])
if dnt != y and a[y] != z and a[z] != x:
ret.append([y,z,x])
if dnt != z and a[z] != x and a[x] != y:
ret.append([z,x,y])
if dnt != z and a[z] != y and a[y] != x:
ret.append([z,y,x])
ret.sort()
return ret[0]
import heapq
import sys
N = int(input())
a = list(map(int,input().split()))
if N == 2:
print (-1)
sys.exit()
for i in range(N):
a[i] -= 1
ans = []
dont = None
hq = []
for i in range(N):
heapq.heappush(hq,i)
usable = [True] * N
dic = {}
for i in range(N):
if a[i] not in dic:
dic[a[i]] = 1
else:
dic[a[i]] += 1
for loop in range(N-3):
flag = True
if len(dic) == 2:
maxind = None
for i in dic:
if maxind == None:
maxind = i
elif dic[i] > dic[maxind]:
maxind = i
if dic[maxind] == (N-loop-1) and usable[maxind]:
nc = maxind
flag = False
if flag:
while (not usable[hq[0]]):
heapq.heappop(hq)
fi = heapq.heappop(hq)
if dont != fi:
nc = fi
else:
while (not usable[hq[0]]):
heapq.heappop(hq)
sec = heapq.heappop(hq)
heapq.heappush(hq,fi)
nc = sec
#print (nc,a[nc])
ans.append(nc+1)
usable[nc] = False
dic[a[nc]] -= 1
dont = a[nc]
if dic[a[nc]] == 0:
del dic[a[nc]]
pas = []
while len(hq) > 0:
now = heapq.heappop(hq)
if usable[now]:
pas.append(now)
rec = allserch(dont,pas[0],pas[1],pas[2])
for i in range(3):
rec[i] += 1
ans += rec
print (*ans)
```
| 98,418 |
Provide a correct Python 3 solution for this coding contest problem.
Niwango has N cards, numbered 1,2,\ldots,N. He will now arrange these cards in a row.
Niwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below. To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.
* To the immediate right of Card 1 (if any) is NOT Card a_1.
* To the immediate right of Card 2 (if any) is NOT Card a_2.
* \vdots
* To the immediate right of Card N (if any) is NOT Card a_N.
Constraints
* 2 \leq N \leq 10^{5}
* 1 \leq a_i \leq N
* a_i \neq i
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 \ldots a_N
Output
If no arrangements satisfy the conditions, print `-1`. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:
b_1 b_2 \ldots b_N
Here, b_i represents the i-th card from the left.
Examples
Input
4
2 3 4 1
Output
1 3 2 4
Input
2
2 1
Output
-1
Input
13
2 3 4 5 6 7 8 9 10 11 12 13 12
Output
1 3 2 4 6 5 7 9 8 10 12 11 13
"Correct Solution:
```
import sys
input = sys.stdin.readline
N=int(input())
A=[0]+list(map(int,input().split()))
if N==2 and A==[0,2,1]:
print(-1)
sys.exit()
C=[0]*(N+1)
for i in range(1,N+1):
if A[i]!=i:
C[A[i]]+=1
import heapq
H=[]
for i in range(1,N+1):
H.append((-C[i],i))
heapq.heapify(H)
NOUSE=list(range(N,0,-1))
USELIST=[0]*(N+1)
ANS=[0]
for rest in range(N-1,2,-1):
#print(ANS,NOUSE,H,rest)
if -H[0][0]==rest and rest!=0:
x,y=heapq.heappop(H)
ANS.append(y)
C[y]=0
C[A[y]]-=1
USELIST[y]=1
else:
for i in range(len(NOUSE)-1,-1,-1):
if USELIST[NOUSE[i]]==0 and A[ANS[-1]]!=NOUSE[i]:
x=NOUSE.pop(i)
ANS.append(x)
USELIST[x]=1
C[x]=0
C[A[x]]-=1
break
while C[H[0][1]]!=-H[0][0]:
x,y=heapq.heappop(H)
heapq.heappush(H,(-C[y],y))
while NOUSE and USELIST[NOUSE[-1]]==1:
NOUSE.pop()
NOUSE=[i for i in range(N+1) if USELIST[i]==0]
from itertools import permutations
REST=list(permutations(sorted(NOUSE[1:])))
if len(REST)==2:
for x,y in REST:
if A[ANS[-1]]!=x and A[x]!=y:
ANS.extend([x,y])
break
else:
for x,y,z in REST:
if A[ANS[-1]]!=x and A[x]!=y and A[y]!=z:
ANS.extend([x,y,z])
break
print(*ANS[1:])
```
| 98,419 |
Provide a correct Python 3 solution for this coding contest problem.
Niwango has N cards, numbered 1,2,\ldots,N. He will now arrange these cards in a row.
Niwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below. To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.
* To the immediate right of Card 1 (if any) is NOT Card a_1.
* To the immediate right of Card 2 (if any) is NOT Card a_2.
* \vdots
* To the immediate right of Card N (if any) is NOT Card a_N.
Constraints
* 2 \leq N \leq 10^{5}
* 1 \leq a_i \leq N
* a_i \neq i
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 \ldots a_N
Output
If no arrangements satisfy the conditions, print `-1`. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:
b_1 b_2 \ldots b_N
Here, b_i represents the i-th card from the left.
Examples
Input
4
2 3 4 1
Output
1 3 2 4
Input
2
2 1
Output
-1
Input
13
2 3 4 5 6 7 8 9 10 11 12 13 12
Output
1 3 2 4 6 5 7 9 8 10 12 11 13
"Correct Solution:
```
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
from bisect import bisect_right, bisect_left
import random
from itertools import permutations, accumulate, combinations, product
import sys
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor, gamma, log
from operator import mul
from functools import reduce
sys.setrecursionlimit(2147483647)
INF = 10 ** 20
def LI(): return list(map(int, sys.stdin.buffer.readline().split()))
def I(): return int(sys.stdin.buffer.readline())
def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()
def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]
mod = 10 ** 9 + 7
class BIT:
def __init__(self, size):
self.bit = [0] * size
self.size = size
self.total = 0
def add(self, i, w):
x = i + 1
self.total += w
while x <= self.size:
self.bit[x - 1] += w
x += x & -x
return
def sum(self, i):
res = 0
x = i + 1
while x:
res += self.bit[x - 1]
x -= x & -x
return res
def search(self, k):
if k > self.total:
return -1
if k == 0:
return 0
step = 1 << (self.size.bit_length() - 1)
now_index = 0
ret = 0
while step:
if now_index + step < self.size and ret + self.bit[now_index + step - 1] < k:
ret += self.bit[now_index + step - 1]
now_index += step
step >>= 1
# now_indexを伸ばしいって、sumがk以上に達する直前まで伸ばし続けるならreturnのところでnow_index - 1。
# その場合、bit.sum(now_index - 1) <= k < bit.sum(now_index)
# 達してすぐのindexであれば-1しない
return now_index
n = I()
A = LI()
if n == 2:
if A[0] == 2 and A[1] == 1:
print(-1)
elif A[0] != 2:
print(1, 2)
else:
print(2, 1)
exit()
bit = BIT(n + 1)
for i in range(1, n + 1):
bit.add(i, 1)
ans = []
pre = -1
for j in range(n - 1):
x = bit.search(1)
if x == pre:
x = bit.search(2)
bit.add(x, -1)
ans += [x]
pre = A[x - 1]
last_x = bit.search(1)
bit.add(last_x, -1)
if A[ans[-1] - 1] != last_x:
ans += [last_x]
print(*ans)
exit()
cnt = 0
for k in range(n - 2, -1, -1):
if A[ans[k] - 1] == last_x:
x = ans.pop()
bit.add(x, 1)
cnt += 1
else:
break
if cnt == 1:
last3 = []
for a, b, c in permutations((ans.pop(), x, last_x)):
if A[ans[-1] - 1] != a and A[a - 1] != b and A[b - 1] != c:
last3 += [[a, b, c]]
print(*ans + min(last3))
exit()
ans += [last_x]
x = bit.search(1)
if x == A[ans[-1] - 1]:
x = bit.search(2)
bit.add(x, -1)
ans += [x]
for l in range(cnt - 1):
x = bit.search(1)
bit.add(x, -1)
ans += [x]
print(*ans)
```
| 98,420 |
Provide a correct Python 3 solution for this coding contest problem.
Niwango has N cards, numbered 1,2,\ldots,N. He will now arrange these cards in a row.
Niwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below. To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.
* To the immediate right of Card 1 (if any) is NOT Card a_1.
* To the immediate right of Card 2 (if any) is NOT Card a_2.
* \vdots
* To the immediate right of Card N (if any) is NOT Card a_N.
Constraints
* 2 \leq N \leq 10^{5}
* 1 \leq a_i \leq N
* a_i \neq i
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 \ldots a_N
Output
If no arrangements satisfy the conditions, print `-1`. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:
b_1 b_2 \ldots b_N
Here, b_i represents the i-th card from the left.
Examples
Input
4
2 3 4 1
Output
1 3 2 4
Input
2
2 1
Output
-1
Input
13
2 3 4 5 6 7 8 9 10 11 12 13 12
Output
1 3 2 4 6 5 7 9 8 10 12 11 13
"Correct Solution:
```
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
import itertools
from collections import deque
from heapq import heappop, heappush, heapify
from collections import defaultdict
N = int(readline())
A = list(map(lambda x: int(x) - 1,read().split())) + [-1]
def test(A,B):
for x,y in zip(B, B[1:]):
if A[x] == y:
return False
return True
def solve_small(cand, A, ng_first = -1):
for p in itertools.permutations(cand):
if p[0] == ng_first:
continue
if test(A, p):
return p
return False
if N <= 6:
p = solve_small(range(N), A)
if not p:
print(-1)
exit()
print(' '.join(str(x+1) for x in p))
exit()
in_deg = [0] * (N+10)
for x in A:
in_deg[x] += 1
q = [(-x, i) for i,x in enumerate(in_deg)] # in_deg最大の人を分かるようにしたい
heapify(q)
se = set(q)
def greedy(rest,A,ng_first):
B = []
ng = ng_first
while len(rest) >= 4:
x = rest[0]; y = rest[1]
if ng == x:
B.append(y)
rest.popleft()
rest.popleft()
rest.appendleft(x)
else:
B.append(x)
rest.popleft()
ng = A[B[-1]]
return B
rest = deque(range(N))
B = []
prev = N
n = N
for _ in range(N-4):
while q[0] not in se:
heappop(q)
if -q[0][0] == n - 1:
v = q[0][1]
B.append(v)
rest.remove(v)
B += greedy(rest, A, A[B[-1]])
break
x = rest[0]; y = rest[1]
if A[prev] == x:
B.append(y)
rest.popleft()
rest.popleft()
rest.appendleft(x)
else:
B.append(x)
rest.popleft()
prev = B[-1]
v = A[B[-1]]
se.remove((-in_deg[v],v))
in_deg[v] -= 1
se.add((-in_deg[v],v))
n -= 1
if len(B) < N:
B += list(solve_small(rest, A, A[B[-1]]))
print(' '.join(str(x+1) for x in B))
```
| 98,421 |
Provide a correct Python 3 solution for this coding contest problem.
Niwango has N cards, numbered 1,2,\ldots,N. He will now arrange these cards in a row.
Niwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below. To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.
* To the immediate right of Card 1 (if any) is NOT Card a_1.
* To the immediate right of Card 2 (if any) is NOT Card a_2.
* \vdots
* To the immediate right of Card N (if any) is NOT Card a_N.
Constraints
* 2 \leq N \leq 10^{5}
* 1 \leq a_i \leq N
* a_i \neq i
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 \ldots a_N
Output
If no arrangements satisfy the conditions, print `-1`. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:
b_1 b_2 \ldots b_N
Here, b_i represents the i-th card from the left.
Examples
Input
4
2 3 4 1
Output
1 3 2 4
Input
2
2 1
Output
-1
Input
13
2 3 4 5 6 7 8 9 10 11 12 13 12
Output
1 3 2 4 6 5 7 9 8 10 12 11 13
"Correct Solution:
```
from itertools import permutations
from heapq import *
import sys
sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
# smallで作った数列のチェック
def check_s(res, ngi):
if res[0] == ngi: return False
for i in range(len(res) - 1):
if res[i + 1] == ng[res[i]]:
return False
return True
# nが小さいときの全探索用
def small(remain, ngi):
for res in permutations(remain):
if check_s(res, ngi): return res
return [-2]
# 使った数を消しながら最小の数を返す
def delpop():
while 1:
i = heappop(hp)
if not used[i]: return i
# 次の数を選ぶ
def next_i(ngi, cr):
i = delpop()
if i == ngi:
ii = delpop()
heappush(hp, i)
i = ii
ngj = ng[i]
if used[ngj]: return i
if indeg[ngj] < cr - 1: return i
heappush(hp, i)
return ngj
def main():
# 頂点iを追加しても、残りの頂点でハミルトンパスが存在するかチェックしながら
# 残りが4点になるまで小さい順に頂点を選んでいく
ans = []
ngi = -1
cnt_remain = n
for _ in range(n - 4):
i = next_i(ngi, cnt_remain)
ans.append(i)
used[i] = True
cnt_remain -= 1
ngi = ng[i]
indeg[ngi] -= 1
# 4点以下の残りについては愚直に探す
remain = []
while hp:
i=heappop(hp)
if used[i]:continue
remain.append(i)
ans += small(remain, ngi)
ans = [x + 1 for x in ans]
print(*ans)
n = II()
ng = LI1()
hp = list(range(n))
heapify(hp)
used = [False] * n
indeg = [0] * n
for k in ng: indeg[k] += 1
main()
```
| 98,422 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Niwango has N cards, numbered 1,2,\ldots,N. He will now arrange these cards in a row.
Niwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below. To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.
* To the immediate right of Card 1 (if any) is NOT Card a_1.
* To the immediate right of Card 2 (if any) is NOT Card a_2.
* \vdots
* To the immediate right of Card N (if any) is NOT Card a_N.
Constraints
* 2 \leq N \leq 10^{5}
* 1 \leq a_i \leq N
* a_i \neq i
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 \ldots a_N
Output
If no arrangements satisfy the conditions, print `-1`. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:
b_1 b_2 \ldots b_N
Here, b_i represents the i-th card from the left.
Examples
Input
4
2 3 4 1
Output
1 3 2 4
Input
2
2 1
Output
-1
Input
13
2 3 4 5 6 7 8 9 10 11 12 13 12
Output
1 3 2 4 6 5 7 9 8 10 12 11 13
Submitted Solution:
```
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
import itertools
from collections import deque
from heapq import heappop, heappush, heapify
from collections import defaultdict
N = int(readline())
A = list(map(lambda x: int(x) - 1,read().split())) + [-1]
def test(A,B):
for x,y in zip(B, B[1:]):
if A[x] == y:
return False
return True
def solve_small(cand, A, ng_first = -1):
for p in itertools.permutations(cand):
if p[0] == ng_first:
continue
if test(A, p):
return p
return False
if N <= 4:
p = solve_small(range(N), A)
if not p:
print(-1)
exit()
print(' '.join(str(x+1) for x in p))
exit()
in_deg = [0] * (N+10)
for x in A:
in_deg[x] += 1
q = [(-x, i) for i,x in enumerate(in_deg)] # in_deg最大の人を分かるようにしたい
heapify(q)
se = set(q)
def greedy(rest,A,ng_first):
B = []
ng = ng_first
while len(rest) >= 4:
x = rest[0]; y = rest[1]
if ng == x:
B.append(y)
rest.popleft()
rest.popleft()
rest.appendleft(x)
else:
B.append(x)
rest.popleft()
ng = A[B[-1]]
return B
rest = deque(range(N))
B = []
prev = N
n = N
for _ in range(N-4):
while q[0] not in se:
heappop(q)
if -q[0][0] == n - 1:
v = q[0][1]
B.append(v)
rest.remove(v)
B += greedy(rest, A, A[B[-1]])
break
x = rest[0]; y = rest[1]
if A[prev] == x:
B.append(y)
rest.popleft()
rest.popleft()
rest.appendleft(x)
else:
B.append(x)
rest.popleft()
prev = B[-1]
v = A[B[-1]]
se.remove((-in_deg[v],v))
in_deg[v] -= 1
se.add((-in_deg[v],v))
if len(B) < N:
B += list(solve_small(rest, A, A[B[-1]]))
print(' '.join(str(x+1) for x in B))
```
No
| 98,423 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Niwango has N cards, numbered 1,2,\ldots,N. He will now arrange these cards in a row.
Niwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below. To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.
* To the immediate right of Card 1 (if any) is NOT Card a_1.
* To the immediate right of Card 2 (if any) is NOT Card a_2.
* \vdots
* To the immediate right of Card N (if any) is NOT Card a_N.
Constraints
* 2 \leq N \leq 10^{5}
* 1 \leq a_i \leq N
* a_i \neq i
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 \ldots a_N
Output
If no arrangements satisfy the conditions, print `-1`. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:
b_1 b_2 \ldots b_N
Here, b_i represents the i-th card from the left.
Examples
Input
4
2 3 4 1
Output
1 3 2 4
Input
2
2 1
Output
-1
Input
13
2 3 4 5 6 7 8 9 10 11 12 13 12
Output
1 3 2 4 6 5 7 9 8 10 12 11 13
Submitted Solution:
```
from heapq import heappush,heappop,heapify
import sys
import itertools
N=int(input())
A=[0]+list(map(int,input().split()))
if N==2:
print(-1)
sys.exit()
if N==3:
for u in itertools.permutations(range(1,4)):
for i in range(2):
if A[u[i]]!=u[i+1]:
continue
else:
break
else:
print(*u)
sys.exit()
else:
print(-1)
sys.exit()
ans=[1]
lsls=[i for i in range(2,N+1)]
heapify(lsls)
for i in range(N-2):
u=heappop(lsls)
if A[ans[-1]]!=u:
ans.append(u)
else:
ans.append(heappop(lsls))
heappush(lsls,u)
u=lsls[0]
U=0
if A[ans[-1]]!=u:
ans.append(u)
else:
for i in range(N-3,-1,-1):
if A[ans[i]]!=u:
if i==N-3:
if A[u]!=ans[i+1]:
ans=ans[:i+1]+[u]+ans[i+1:]
break
else:
U=ans[N-3]
else:
if A[u]!=ans[i+1]:
ans=ans[:i+1]+[u]+ans[i+1:]
else:
ans=ans[:i+1]+[u,ans[i+2],ans[i+1]]+ans[i+3:]
break
else:
if U!=0:
ans=[U,u]
lsls=[]
for i in range(1,N+1):
if i!=U and i!=u:
lsls.append(i)
heapify(lsls)
for i in range(N-3):
u=heappop(lsls)
if A[ans[-1]]!=u:
ans.append(u)
else:
ans.append(heappop(lsls))
heappush(lsls,u)
u=lsls[0]
ans.append(u)
else:
ans=[u]
lsls=[i for i in range(1,u)]+[i for i in range(u+1,N+1)]
heapify(lsls)
for i in range(N-2):
u=heappop(lsls)
if A[ans[-1]]!=u:
ans.append(u)
else:
ans.append(heappop(lsls))
heappush(lsls,u)
u=lsls[0]
ans.append(u)
print(*ans)
```
No
| 98,424 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Niwango has N cards, numbered 1,2,\ldots,N. He will now arrange these cards in a row.
Niwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below. To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.
* To the immediate right of Card 1 (if any) is NOT Card a_1.
* To the immediate right of Card 2 (if any) is NOT Card a_2.
* \vdots
* To the immediate right of Card N (if any) is NOT Card a_N.
Constraints
* 2 \leq N \leq 10^{5}
* 1 \leq a_i \leq N
* a_i \neq i
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 \ldots a_N
Output
If no arrangements satisfy the conditions, print `-1`. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:
b_1 b_2 \ldots b_N
Here, b_i represents the i-th card from the left.
Examples
Input
4
2 3 4 1
Output
1 3 2 4
Input
2
2 1
Output
-1
Input
13
2 3 4 5 6 7 8 9 10 11 12 13 12
Output
1 3 2 4 6 5 7 9 8 10 12 11 13
Submitted Solution:
```
import sys
N = int(input())
a = list(map(int,input().split()))
A = []
for i in range(N):
A.append([a[i],i+1])
flag = True
for i in range(N-2):
if A[i][0] == A[i+1][1]:
t = A[i+2]
A[i+2] = A[i+1]
A[i+1] = t
for i in range(N+1):
if i == N:
print (-1)
sys.exit()
elif A[-1][1] == A[-2][0]:
flag = False
for j in range(N-1):
j = N-2-j
if A[j][0] != A[-1][1]:
A.insert(j+1,A[-1])
del A[-1]
flag = True
break
if not flag:
A.insert(0,A[-1])
del A[-1]
else:
break
ans = []
for i in range(N):
ans.append(A[i][1])
print (" ".join(map(str,ans)))
```
No
| 98,425 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Niwango has N cards, numbered 1,2,\ldots,N. He will now arrange these cards in a row.
Niwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below. To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.
* To the immediate right of Card 1 (if any) is NOT Card a_1.
* To the immediate right of Card 2 (if any) is NOT Card a_2.
* \vdots
* To the immediate right of Card N (if any) is NOT Card a_N.
Constraints
* 2 \leq N \leq 10^{5}
* 1 \leq a_i \leq N
* a_i \neq i
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 \ldots a_N
Output
If no arrangements satisfy the conditions, print `-1`. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:
b_1 b_2 \ldots b_N
Here, b_i represents the i-th card from the left.
Examples
Input
4
2 3 4 1
Output
1 3 2 4
Input
2
2 1
Output
-1
Input
13
2 3 4 5 6 7 8 9 10 11 12 13 12
Output
1 3 2 4 6 5 7 9 8 10 12 11 13
Submitted Solution:
```
import heapq
n = int(input())
ukeire = [0]*n
A = list(map(int, input().split()))
if n==2 and A == [2, 1]:
print(-1)
else:
for i in range(n):
a = A[i]
if i+1 != a:
ukeire[a-1] += 1
f = 1
if n-1 in ukeire:
f = ukeire.index(n-1) + 1
can = [i+1 for i in range(n) if i != f-1]
heapq.heapify(can)
L = [f]
while can:
t = heapq.heappop(can)
if A[L[-1]-1] == t:
if can:
s = heapq.heappop(can)
L.append(s)
heapq.heappush(can, t)
else:
k = L[-1]
L = L[:-1] + [t] + [k]
else:
L.append(t)
print(*L)
```
No
| 98,426 |
Provide a correct Python 3 solution for this coding contest problem.
There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \ldots, 999999, 1000000.
Among them, some K consecutive stones are painted black, and the others are painted white.
Additionally, we know that the stone at coordinate X is painted black.
Print all coordinates that potentially contain a stone painted black, in ascending order.
Constraints
* 1 \leq K \leq 100
* 0 \leq X \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K X
Output
Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.
Examples
Input
3 7
Output
5 6 7 8 9
Input
4 0
Output
-3 -2 -1 0 1 2 3
Input
1 100
Output
100
"Correct Solution:
```
k,x = map(int,input().split())
for i in range(x-k+1,x+k):
print(i,end=' ')
```
| 98,427 |
Provide a correct Python 3 solution for this coding contest problem.
There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \ldots, 999999, 1000000.
Among them, some K consecutive stones are painted black, and the others are painted white.
Additionally, we know that the stone at coordinate X is painted black.
Print all coordinates that potentially contain a stone painted black, in ascending order.
Constraints
* 1 \leq K \leq 100
* 0 \leq X \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K X
Output
Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.
Examples
Input
3 7
Output
5 6 7 8 9
Input
4 0
Output
-3 -2 -1 0 1 2 3
Input
1 100
Output
100
"Correct Solution:
```
a,b =map(int,input().split())
x = list(range(b-a+1, b+a))
print(*x)
```
| 98,428 |
Provide a correct Python 3 solution for this coding contest problem.
There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \ldots, 999999, 1000000.
Among them, some K consecutive stones are painted black, and the others are painted white.
Additionally, we know that the stone at coordinate X is painted black.
Print all coordinates that potentially contain a stone painted black, in ascending order.
Constraints
* 1 \leq K \leq 100
* 0 \leq X \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K X
Output
Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.
Examples
Input
3 7
Output
5 6 7 8 9
Input
4 0
Output
-3 -2 -1 0 1 2 3
Input
1 100
Output
100
"Correct Solution:
```
a,b=map(int,input().split())
for i in range(a*2-1):
print(b-a+1+i,end=' ')
```
| 98,429 |
Provide a correct Python 3 solution for this coding contest problem.
There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \ldots, 999999, 1000000.
Among them, some K consecutive stones are painted black, and the others are painted white.
Additionally, we know that the stone at coordinate X is painted black.
Print all coordinates that potentially contain a stone painted black, in ascending order.
Constraints
* 1 \leq K \leq 100
* 0 \leq X \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K X
Output
Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.
Examples
Input
3 7
Output
5 6 7 8 9
Input
4 0
Output
-3 -2 -1 0 1 2 3
Input
1 100
Output
100
"Correct Solution:
```
k,x=map(int,input().split())
for i in range(2*k-1):
print(x+1-k+i,end=" ")
```
| 98,430 |
Provide a correct Python 3 solution for this coding contest problem.
There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \ldots, 999999, 1000000.
Among them, some K consecutive stones are painted black, and the others are painted white.
Additionally, we know that the stone at coordinate X is painted black.
Print all coordinates that potentially contain a stone painted black, in ascending order.
Constraints
* 1 \leq K \leq 100
* 0 \leq X \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K X
Output
Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.
Examples
Input
3 7
Output
5 6 7 8 9
Input
4 0
Output
-3 -2 -1 0 1 2 3
Input
1 100
Output
100
"Correct Solution:
```
k, x = map(int, input().split())
print(*[i for i in range(x-(k-1), x+k)])
```
| 98,431 |
Provide a correct Python 3 solution for this coding contest problem.
There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \ldots, 999999, 1000000.
Among them, some K consecutive stones are painted black, and the others are painted white.
Additionally, we know that the stone at coordinate X is painted black.
Print all coordinates that potentially contain a stone painted black, in ascending order.
Constraints
* 1 \leq K \leq 100
* 0 \leq X \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K X
Output
Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.
Examples
Input
3 7
Output
5 6 7 8 9
Input
4 0
Output
-3 -2 -1 0 1 2 3
Input
1 100
Output
100
"Correct Solution:
```
K,X=input().split()
K=int(K)
X=int(X)
print(*[i+X-K+1 for i in range(2*K-1)])
```
| 98,432 |
Provide a correct Python 3 solution for this coding contest problem.
There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \ldots, 999999, 1000000.
Among them, some K consecutive stones are painted black, and the others are painted white.
Additionally, we know that the stone at coordinate X is painted black.
Print all coordinates that potentially contain a stone painted black, in ascending order.
Constraints
* 1 \leq K \leq 100
* 0 \leq X \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K X
Output
Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.
Examples
Input
3 7
Output
5 6 7 8 9
Input
4 0
Output
-3 -2 -1 0 1 2 3
Input
1 100
Output
100
"Correct Solution:
```
K, X = map(int, input().split())
print(*list(range(X-(K-1), X+(K-1)+1)))
```
| 98,433 |
Provide a correct Python 3 solution for this coding contest problem.
There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \ldots, 999999, 1000000.
Among them, some K consecutive stones are painted black, and the others are painted white.
Additionally, we know that the stone at coordinate X is painted black.
Print all coordinates that potentially contain a stone painted black, in ascending order.
Constraints
* 1 \leq K \leq 100
* 0 \leq X \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K X
Output
Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.
Examples
Input
3 7
Output
5 6 7 8 9
Input
4 0
Output
-3 -2 -1 0 1 2 3
Input
1 100
Output
100
"Correct Solution:
```
k,x = map(int,input().split())
for i in range(x-k+1,x+k):
print(i)
```
| 98,434 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \ldots, 999999, 1000000.
Among them, some K consecutive stones are painted black, and the others are painted white.
Additionally, we know that the stone at coordinate X is painted black.
Print all coordinates that potentially contain a stone painted black, in ascending order.
Constraints
* 1 \leq K \leq 100
* 0 \leq X \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K X
Output
Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.
Examples
Input
3 7
Output
5 6 7 8 9
Input
4 0
Output
-3 -2 -1 0 1 2 3
Input
1 100
Output
100
Submitted Solution:
```
k,n=map(int,input().split())
for i in range(k*2-1):
print(n-k+i+1)
```
Yes
| 98,435 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \ldots, 999999, 1000000.
Among them, some K consecutive stones are painted black, and the others are painted white.
Additionally, we know that the stone at coordinate X is painted black.
Print all coordinates that potentially contain a stone painted black, in ascending order.
Constraints
* 1 \leq K \leq 100
* 0 \leq X \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K X
Output
Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.
Examples
Input
3 7
Output
5 6 7 8 9
Input
4 0
Output
-3 -2 -1 0 1 2 3
Input
1 100
Output
100
Submitted Solution:
```
K,X=map(int, input().split())
for x in range(X-K+1,X+K):
print(x,"",end="")
```
Yes
| 98,436 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \ldots, 999999, 1000000.
Among them, some K consecutive stones are painted black, and the others are painted white.
Additionally, we know that the stone at coordinate X is painted black.
Print all coordinates that potentially contain a stone painted black, in ascending order.
Constraints
* 1 \leq K \leq 100
* 0 \leq X \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K X
Output
Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.
Examples
Input
3 7
Output
5 6 7 8 9
Input
4 0
Output
-3 -2 -1 0 1 2 3
Input
1 100
Output
100
Submitted Solution:
```
k,x = map(int,input().split())
tmp = [i for i in range(x-k+1, x+k)]
print(*tmp)
```
Yes
| 98,437 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \ldots, 999999, 1000000.
Among them, some K consecutive stones are painted black, and the others are painted white.
Additionally, we know that the stone at coordinate X is painted black.
Print all coordinates that potentially contain a stone painted black, in ascending order.
Constraints
* 1 \leq K \leq 100
* 0 \leq X \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K X
Output
Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.
Examples
Input
3 7
Output
5 6 7 8 9
Input
4 0
Output
-3 -2 -1 0 1 2 3
Input
1 100
Output
100
Submitted Solution:
```
k, x = map(int, input().split())
a = range(x - k + 1, x + k)
print(*a)
```
Yes
| 98,438 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \ldots, 999999, 1000000.
Among them, some K consecutive stones are painted black, and the others are painted white.
Additionally, we know that the stone at coordinate X is painted black.
Print all coordinates that potentially contain a stone painted black, in ascending order.
Constraints
* 1 \leq K \leq 100
* 0 \leq X \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K X
Output
Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.
Examples
Input
3 7
Output
5 6 7 8 9
Input
4 0
Output
-3 -2 -1 0 1 2 3
Input
1 100
Output
100
Submitted Solution:
```
i = list(map(int,input().split()))
K = i[0]
X = i[1]
print(list(range(X-K+1,X+K)))
```
No
| 98,439 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \ldots, 999999, 1000000.
Among them, some K consecutive stones are painted black, and the others are painted white.
Additionally, we know that the stone at coordinate X is painted black.
Print all coordinates that potentially contain a stone painted black, in ascending order.
Constraints
* 1 \leq K \leq 100
* 0 \leq X \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K X
Output
Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.
Examples
Input
3 7
Output
5 6 7 8 9
Input
4 0
Output
-3 -2 -1 0 1 2 3
Input
1 100
Output
100
Submitted Solution:
```
K,X=map(int,input().split())
M=[]
for i in range (X-K+1,X+K):
M.append(i)
M.sort()
print(''.join(map(str,M)))
```
No
| 98,440 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \ldots, 999999, 1000000.
Among them, some K consecutive stones are painted black, and the others are painted white.
Additionally, we know that the stone at coordinate X is painted black.
Print all coordinates that potentially contain a stone painted black, in ascending order.
Constraints
* 1 \leq K \leq 100
* 0 \leq X \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K X
Output
Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.
Examples
Input
3 7
Output
5 6 7 8 9
Input
4 0
Output
-3 -2 -1 0 1 2 3
Input
1 100
Output
100
Submitted Solution:
```
k,x = map(int,input().split())
p = [x-k+1+i for i in range(2*k-1)]
print(q)
```
No
| 98,441 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are 2000001 stones placed on a number line. The coordinates of these stones are -1000000, -999999, -999998, \ldots, 999999, 1000000.
Among them, some K consecutive stones are painted black, and the others are painted white.
Additionally, we know that the stone at coordinate X is painted black.
Print all coordinates that potentially contain a stone painted black, in ascending order.
Constraints
* 1 \leq K \leq 100
* 0 \leq X \leq 100
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K X
Output
Print all coordinates that potentially contain a stone painted black, in ascending order, with spaces in between.
Examples
Input
3 7
Output
5 6 7 8 9
Input
4 0
Output
-3 -2 -1 0 1 2 3
Input
1 100
Output
100
Submitted Solution:
```
k, x = (int(i) for i in input().split())
arr = []
for i in range(-k + 1, 0):
for j in range(0, k + 1):
arr.append(i + j + x)
sorted_list = sorted(list(set(arr)))
if (k == 1):
result = x
result = " ".join(map(str, sorted_list))
print(result)
```
No
| 98,442 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:
* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.
There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.
Input
Input is given from Standard Input in the following format:
N X
S_1 S_2 \ldots S_{N}
Output
Print the answer.
Examples
Input
2 19
3 7
Output
3
Input
5 82
22 11 6 5 13
Output
288
Input
10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009
Output
279669259
"Correct Solution:
```
mod = 10**9+7
n,m = map(int,input().split())
s = list(map(int,input().split()))
s.sort()
s = [None] + s
dp = [[0 for i in range(m+1)] for j in range(n+1)]
dp[1] = [i % s[1] for i in range(m+1)]
for i in range(2,n+1):
for j in range(m+1):
dp[i][j] = (dp[i-1][j] * (i-1) + dp[i-1][j%s[i]]) % mod
print(dp[n][m])
```
| 98,443 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:
* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.
There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.
Input
Input is given from Standard Input in the following format:
N X
S_1 S_2 \ldots S_{N}
Output
Print the answer.
Examples
Input
2 19
3 7
Output
3
Input
5 82
22 11 6 5 13
Output
288
Input
10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009
Output
279669259
"Correct Solution:
```
n, x = map(int, input().split())
a = list(map(int, input().split()))
a.sort()
MOD = 10 ** 9 + 7
S = [0] * (x+1)
T = [0] * (x+1)
S[x] = 1
for i in range(n-1, -1, -1):
T = [0] * (x + 1)
for j in range(x+1):
S[j] %= MOD
T[j] += S[j] * i % MOD
T[j % a[i]] += S[j]
S, T = T, S
print(sum(i * S[i] % MOD for i in range(a[0]) ) % MOD)
```
| 98,444 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:
* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.
There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.
Input
Input is given from Standard Input in the following format:
N X
S_1 S_2 \ldots S_{N}
Output
Print the answer.
Examples
Input
2 19
3 7
Output
3
Input
5 82
22 11 6 5 13
Output
288
Input
10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009
Output
279669259
"Correct Solution:
```
MOD = 10**9 + 7
N, X = map(int, input().split())
Ss = list(map(int, input().split()))
Ss.sort(reverse=True)
minS = Ss[-1]
D = {X: 1}
for i, S in enumerate(Ss[:-1]):
D2 = {}
for x, num in D.items():
D2[x] = (D2.get(x, 0) + num*(N-1-i)) % MOD
D2[x%S] = (D2.get(x%S, 0) + num) % MOD
D = D2
ans = 0
for x, num in D.items():
ans += (x%minS) * num % MOD
ans %= MOD
print(ans)
```
| 98,445 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:
* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.
There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.
Input
Input is given from Standard Input in the following format:
N X
S_1 S_2 \ldots S_{N}
Output
Print the answer.
Examples
Input
2 19
3 7
Output
3
Input
5 82
22 11 6 5 13
Output
288
Input
10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009
Output
279669259
"Correct Solution:
```
N,X=map(int,input().split())
S=list(map(int,input().split()))
pr=10**9+7
b={X:1}
S.sort(reverse=1)
def ir(k,v):
global d
if k in d:
d[k]=(d[k]+v)%pr
else:
d[k]=v
for i in range(N):
t=S[i]
n=N-i-1
d={}
for k,v in b.items():
ir(k%t,v)
ir(k,v*n)
b=d
a=0
for k,v in b.items():
a=(a+k*v)%pr
print(a)
```
| 98,446 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:
* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.
There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.
Input
Input is given from Standard Input in the following format:
N X
S_1 S_2 \ldots S_{N}
Output
Print the answer.
Examples
Input
2 19
3 7
Output
3
Input
5 82
22 11 6 5 13
Output
288
Input
10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009
Output
279669259
"Correct Solution:
```
#!usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
res = list(sys.stdin.readline())
if res[-1] == "\n":
return res[:-1]
return res
def IR(n):
return [I() for i in range(n)]
def LIR(n):
return [LI() for i in range(n)]
def SR(n):
return [S() for i in range(n)]
def LSR(n):
return [LS() for i in range(n)]
sys.setrecursionlimit(1000000)
mod = 1000000007
# 挿入dp
def solve():
n,x = LI()
s = LI()
s.sort()
dp = [[0]*(x+1) for i in range(n+1)] # dp[i][j] := スタート時点の値がjの時に最初のi個の順列すべてを試し、えられる総和
for j in range(x+1):
dp[0][j] = j # dpの定義より明らか
for i in range(n):
si = s[i]
ni = i+1
nd = dp[i][j%si] # 先頭にsiを挿入 (スタートの値がj%siとなる)
nd += i*dp[i][j] # 先頭以外にsiを挿入 (スタートの値も間の値も変わらない)
dp[ni][j] += nd
if dp[ni][j] >= mod:
dp[ni][j] %= mod
print(dp[n][x])
return
#Solve
if __name__ == "__main__":
solve()
```
| 98,447 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:
* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.
There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.
Input
Input is given from Standard Input in the following format:
N X
S_1 S_2 \ldots S_{N}
Output
Print the answer.
Examples
Input
2 19
3 7
Output
3
Input
5 82
22 11 6 5 13
Output
288
Input
10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009
Output
279669259
"Correct Solution:
```
mod=10**9+7
N,X=map(int,input().split())
S=[int(i) for i in input().split()]
S.sort(reverse=True)
Factorial=[1]*(N+1)
for i in range(1,N+1):
Factorial[i]=Factorial[i-1]*(i)%mod
def power(x,y):
if y==0:
return 1
elif y==1:
return x%mod
elif y%2==0:
return power(x,y//2)**2%mod
else:
return ((power(x,y//2)**2)*x)%mod
inv=[0]*(N+1)
for i in range(N+1):
inv[i]=power(i,mod-2)
dp=[[0]*(X+1) for i in range(N+1)]
for x in range(X+1):
dp[N][x]=x
for i in range(N)[::-1]:
for x in range(X+1):
dp[i][x]=dp[i+1][x%S[i]]+(N-i-1)*dp[i+1][x]
dp[i][x]%=mod
print((dp[0][X])%mod)
```
| 98,448 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:
* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.
There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.
Input
Input is given from Standard Input in the following format:
N X
S_1 S_2 \ldots S_{N}
Output
Print the answer.
Examples
Input
2 19
3 7
Output
3
Input
5 82
22 11 6 5 13
Output
288
Input
10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009
Output
279669259
"Correct Solution:
```
N,X = map(int,input().split())
S = list(map(int,input().split()))
S.sort()
mod = 10**9+7
dp = [[x]+[0]*N for x in range(X+1)]
for x in range(X+1):
for n in range(1,N+1):
dp[x][n] = (dp[x%S[n-1]][n-1] + (n-1)*dp[x][n-1])%mod
print(dp[X][N])
```
| 98,449 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:
* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.
There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.
Input
Input is given from Standard Input in the following format:
N X
S_1 S_2 \ldots S_{N}
Output
Print the answer.
Examples
Input
2 19
3 7
Output
3
Input
5 82
22 11 6 5 13
Output
288
Input
10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009
Output
279669259
"Correct Solution:
```
from collections import defaultdict
inpl = lambda: list(map(int,input().split()))
M = 10**9 + 7
N, X = inpl()
S = sorted(inpl())
P = defaultdict(lambda: -1)
def ModuloOperations(i, x):
if i == 0:
return x
else:
if P[(i,x)] < 0:
P[(i,x)] = (ModuloOperations(i-1,x)*(i-1) + ModuloOperations(i-1, x % S[i-1])) % M
return P[(i,x)]
print(ModuloOperations(N,X))
```
| 98,450 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:
* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.
There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.
Input
Input is given from Standard Input in the following format:
N X
S_1 S_2 \ldots S_{N}
Output
Print the answer.
Examples
Input
2 19
3 7
Output
3
Input
5 82
22 11 6 5 13
Output
288
Input
10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009
Output
279669259
Submitted Solution:
```
MOD = 10**9 + 7
N,X = map(int,input().split())
S = list(map(int,input().split()))
S.sort()
S = [None] + S
dp = [[0 for i in range(X+1)] for j in range(N+1)]
dp[1] = [i % S[1] for i in range(X+1)]
for n in range(2, N+1):
for x in range(X+1):
dp[n][x] = (dp[n-1][x] * (n-1) + dp[n-1][x%S[n]]) % MOD
print(dp[N][X])
```
Yes
| 98,451 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:
* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.
There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.
Input
Input is given from Standard Input in the following format:
N X
S_1 S_2 \ldots S_{N}
Output
Print the answer.
Examples
Input
2 19
3 7
Output
3
Input
5 82
22 11 6 5 13
Output
288
Input
10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009
Output
279669259
Submitted Solution:
```
N,X=map(int,input().split())
S=list(map(int,input().split()))
S.sort()
mod=10**9+7
dp=[[0 for i in range(10**5+1)] for j in range(N)]
for i in range(10**5+1):
dp[0][i]=i%S[0]
for i in range(1,N):
for j in range(10**5+1):
dp[i][j]=(i*dp[i-1][j]+dp[i-1][j%S[i]])%mod
print(dp[N-1][X])
```
Yes
| 98,452 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:
* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.
There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.
Input
Input is given from Standard Input in the following format:
N X
S_1 S_2 \ldots S_{N}
Output
Print the answer.
Examples
Input
2 19
3 7
Output
3
Input
5 82
22 11 6 5 13
Output
288
Input
10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009
Output
279669259
Submitted Solution:
```
def examA():
ABC =LI(); ABC.sort()
if ABC[0]==ABC[-1]:
print("Yes")
else:
print("No")
return
def examB():
N = I()
S = SI()
red = S.count("R")
if red>N//2:
print("Yes")
else:
print("No")
return
def examC():
N,Q = LI()
S = SI()
T = [LSI()for _ in range(Q)]
l = -1; r = N
while(r-l>1):
cur = (r+l)//2
now = copy.deepcopy(cur)
flag = False
for t,d in T:
if S[now]==t:
if d=="R":
now += 1
else:
now -= 1
if now==N:
flag = True
break
if now==-1:
break
if flag:
r = cur
else:
l = cur
R = r
l = -1; r = N
while(r-l>1):
cur = (r+l)//2
now = copy.deepcopy(cur)
flag = False
for t,d in T:
if S[now]==t:
if d=="R":
now += 1
else:
now -= 1
if now==-1:
flag = True
break
if now==N:
break
if flag:
l = cur
else:
r = cur
L = l
ans = max(0,R-L-1)
print(ans)
return
def examD():
N, X = LI()
S = LI()
S.sort(reverse=True)
dp = [[0]*(X+1)for _ in range(N+1)]
dp[0][X] = 1
for i in range(N):
s = S[i]
for j in range(X+1):
dp[i+1][j%s] += dp[i][j]
dp[i+1][j%s] %= mod
for j in range(X+1):
dp[i+1][j] += dp[i][j]*(N-i-1)
dp[i+1][j] %= mod
#print(dp)
ans = 0
for i,d in enumerate(dp[-1]):
ans += d*i
ans %= mod
print(ans)
return
def examE():
ans = 0
print(ans)
return
def examF():
ans = 0
print(ans)
return
import sys,copy,bisect,itertools,heapq,math
from heapq import heappop,heappush,heapify
from collections import Counter,defaultdict,deque
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))
def LSI(): return list(map(str,sys.stdin.readline().split()))
def LS(): return sys.stdin.readline().split()
def SI(): return sys.stdin.readline().strip()
global mod,mod2,inf,alphabet
mod = 10**9 + 7
mod2 = 998244353
inf = 10**18
alphabet = [chr(ord('a') + i) for i in range(26)]
if __name__ == '__main__':
examD()
"""
"""
```
Yes
| 98,453 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:
* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.
There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.
Input
Input is given from Standard Input in the following format:
N X
S_1 S_2 \ldots S_{N}
Output
Print the answer.
Examples
Input
2 19
3 7
Output
3
Input
5 82
22 11 6 5 13
Output
288
Input
10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009
Output
279669259
Submitted Solution:
```
from collections import defaultdict
n,x = map(int,input().split())
a = list(map(int,input().split()))
a.sort(reverse=True)
mod = 10**9+7
dp = [defaultdict(int) for i in range(n+1)]
dp[0][x] = 1
for i in range(1,n+1):
for j in dp[i-1].keys():
k = j%a[i-1]
dp[i][j] = (dp[i][j]+dp[i-1][j]*(n-i))%mod
dp[i][k] = (dp[i][k]+dp[i-1][j])%mod
ans = 0
for i,x in dp[n].items():
ans = (ans+i*x)%mod
print(ans)
```
Yes
| 98,454 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:
* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.
There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.
Input
Input is given from Standard Input in the following format:
N X
S_1 S_2 \ldots S_{N}
Output
Print the answer.
Examples
Input
2 19
3 7
Output
3
Input
5 82
22 11 6 5 13
Output
288
Input
10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009
Output
279669259
Submitted Solution:
```
mod = 10**9+7
n,m = map(int,input().split())
s = list(map(int,input().split()))
s.sort()
s = [None] + s
dp = [[0 for i in range(m+1)] for j in range(n+1)]
dp[1] = [i % s[1] for i in range(m+1)]
for i in range(2,n+1):
for j in range(m+1):
dp[i][j] = (dp[i-1][j] * (i-1) + dp[n-1][j%s[i]]) % mod
print(dp[n][m])
```
No
| 98,455 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:
* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.
There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.
Input
Input is given from Standard Input in the following format:
N X
S_1 S_2 \ldots S_{N}
Output
Print the answer.
Examples
Input
2 19
3 7
Output
3
Input
5 82
22 11 6 5 13
Output
288
Input
10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009
Output
279669259
Submitted Solution:
```
N, X = map(int, input().split())
S = list(map(int, input().split()))
numbers = S[:]
def dps(numbers, x):
if len(numbers) == 1:
return x % numbers[0]
ret = 0
for i, n in enumerate(numbers):
x_mod = x % n
if x_mod == 0:
ret += x_mod
ret += dps(numbers[0:i] + numbers[i+1:], x_mod)
return ret
ans = dps(numbers, X)
ans = ans % (10 ** 9 + 7)
print(ans)
```
No
| 98,456 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:
* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.
There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.
Input
Input is given from Standard Input in the following format:
N X
S_1 S_2 \ldots S_{N}
Output
Print the answer.
Examples
Input
2 19
3 7
Output
3
Input
5 82
22 11 6 5 13
Output
288
Input
10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009
Output
279669259
Submitted Solution:
```
import math
N, X = map(int, input().split())
Ss = sorted(list(map(int, input().split())))
memo = {}
MOD = 10 ** 9 + 7
def mod(x, ss):
if (x, tuple(ss)) in memo:
print('hit')
return memo[(x, tuple(ss))]
if len(ss) == 1:
return x % ss[0]
if x < ss[0]:
res = x * math.factorial(len(ss))
memo[(x, tuple(ss))] = res
return res
total = 0
for s in ss:
ss2 = ss[:]
ss2.remove(s)
total = (total + mod(x % s, ss2)) % MOD
memo[(x, tuple(ss))] = total
return total
print(mod(X, Ss))
```
No
| 98,457 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:
* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.
There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.
Constraints
* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.
Input
Input is given from Standard Input in the following format:
N X
S_1 S_2 \ldots S_{N}
Output
Print the answer.
Examples
Input
2 19
3 7
Output
3
Input
5 82
22 11 6 5 13
Output
288
Input
10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009
Output
279669259
Submitted Solution:
```
import numpy as np
N, X = map(int, input().split())
S = list(map(int, input().split()))
MOD = 1000000007
numbers = S[:]
numbers.sort()
dp = np.zeros((N+1, X+1), dtype=int)
dp = np.arange(X+1)
dp_n = []
for n in numbers:
dp_n = np.zeros((X+1), dtype=np.int64)
dp_n += [dp[x % n] for x in range(X+1)]
dp_n = dp_n % MOD
dp_n += dp * i % MOD
dp_n = dp_n % MOD
dp = dp_n
print(int(dp_n[X]) % MOD)
```
No
| 98,458 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.
Constraints
* The length of S is 2 or 3.
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
If the length of S is 2, print S as is; if the length is 3, print S after reversing it.
Examples
Input
abc
Output
cba
Input
ac
Output
ac
"Correct Solution:
```
a = input()
if(len(a)==2):
print(a)
else:
print(a[::-1])
```
| 98,459 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.
Constraints
* The length of S is 2 or 3.
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
If the length of S is 2, print S as is; if the length is 3, print S after reversing it.
Examples
Input
abc
Output
cba
Input
ac
Output
ac
"Correct Solution:
```
s=input()
if len(s)==2:
print(s)
else:
s=list(reversed(s))
print(*s,sep="")
```
| 98,460 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.
Constraints
* The length of S is 2 or 3.
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
If the length of S is 2, print S as is; if the length is 3, print S after reversing it.
Examples
Input
abc
Output
cba
Input
ac
Output
ac
"Correct Solution:
```
s = input()
print(s if len(s) == 2 else s[::-1])
```
| 98,461 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.
Constraints
* The length of S is 2 or 3.
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
If the length of S is 2, print S as is; if the length is 3, print S after reversing it.
Examples
Input
abc
Output
cba
Input
ac
Output
ac
"Correct Solution:
```
a=input()
if len(a)==3:
print(a[2]+a[1]+a[0])
else:
print(a)
```
| 98,462 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.
Constraints
* The length of S is 2 or 3.
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
If the length of S is 2, print S as is; if the length is 3, print S after reversing it.
Examples
Input
abc
Output
cba
Input
ac
Output
ac
"Correct Solution:
```
str = input()
if len(str) == 3:
str = str[::-1]
print(str)
```
| 98,463 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.
Constraints
* The length of S is 2 or 3.
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
If the length of S is 2, print S as is; if the length is 3, print S after reversing it.
Examples
Input
abc
Output
cba
Input
ac
Output
ac
"Correct Solution:
```
S = list(input())
if len(S) == 3:
S = S[::-1]
print(''.join(S))
```
| 98,464 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.
Constraints
* The length of S is 2 or 3.
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
If the length of S is 2, print S as is; if the length is 3, print S after reversing it.
Examples
Input
abc
Output
cba
Input
ac
Output
ac
"Correct Solution:
```
s=input()
print((s,s[::-1])[len(s)==3])
```
| 98,465 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.
Constraints
* The length of S is 2 or 3.
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
If the length of S is 2, print S as is; if the length is 3, print S after reversing it.
Examples
Input
abc
Output
cba
Input
ac
Output
ac
"Correct Solution:
```
s=str(input())
n=len(s)
if n==2:
print(s)
else:
print(s[::-1])
```
| 98,466 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.
Constraints
* The length of S is 2 or 3.
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
If the length of S is 2, print S as is; if the length is 3, print S after reversing it.
Examples
Input
abc
Output
cba
Input
ac
Output
ac
Submitted Solution:
```
l = input()
if len(l) ==3:
print(l[::-1])
else:
print(l)
```
Yes
| 98,467 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.
Constraints
* The length of S is 2 or 3.
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
If the length of S is 2, print S as is; if the length is 3, print S after reversing it.
Examples
Input
abc
Output
cba
Input
ac
Output
ac
Submitted Solution:
```
s=input()
S=list(s)
if len(S)==2:
print(s)
else:
print(S[2]+S[1]+S[0])
```
Yes
| 98,468 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.
Constraints
* The length of S is 2 or 3.
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
If the length of S is 2, print S as is; if the length is 3, print S after reversing it.
Examples
Input
abc
Output
cba
Input
ac
Output
ac
Submitted Solution:
```
tmp = input()
if len(tmp) == 3:
print(tmp[::-1])
else:
print(tmp)
```
Yes
| 98,469 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.
Constraints
* The length of S is 2 or 3.
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
If the length of S is 2, print S as is; if the length is 3, print S after reversing it.
Examples
Input
abc
Output
cba
Input
ac
Output
ac
Submitted Solution:
```
s=input();print(s if len(s)<3 else s[::-1])
```
Yes
| 98,470 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.
Constraints
* The length of S is 2 or 3.
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
If the length of S is 2, print S as is; if the length is 3, print S after reversing it.
Examples
Input
abc
Output
cba
Input
ac
Output
ac
Submitted Solution:
```
S = input()
listed_S = list[S]
if len(listed_S)==2:
print(S)
elif len(listed_S)==3:
print(S[::-1])
```
No
| 98,471 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.
Constraints
* The length of S is 2 or 3.
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
If the length of S is 2, print S as is; if the length is 3, print S after reversing it.
Examples
Input
abc
Output
cba
Input
ac
Output
ac
Submitted Solution:
```
from collections import deque
n = int(input())
listx = [int(input()) for i in range(n)]
listx.sort()
listx = deque(listx)
listy = deque([])
ans=0
x=listx.popleft()
listy.appendleft(x)
x=listx.pop()
listy.append(x)
ans+=int(listy[1])-int(listy[0])
while len(listx)>=1:
abs1=abs(listx[0]-listy[-1])
abs2=abs(listx[-1]-listy[0])
if abs1 < abs2:
x=listx.pop()
listy.appendleft(x)
ans+=abs2
else:
x=listx.popleft()
listy.append(x)
ans+=abs1
if listy[0] > listy[-1]:
listy.reverse()
print(ans)
```
No
| 98,472 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.
Constraints
* The length of S is 2 or 3.
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
If the length of S is 2, print S as is; if the length is 3, print S after reversing it.
Examples
Input
abc
Output
cba
Input
ac
Output
ac
Submitted Solution:
```
s = input()
if len(s) == 2:
s = s[::-1]
print(s)
```
No
| 98,473 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length 2 or 3 consisting of lowercase English letters. If the length of the string is 2, print it as is; if the length is 3, print the string after reversing it.
Constraints
* The length of S is 2 or 3.
* S consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
If the length of S is 2, print S as is; if the length is 3, print S after reversing it.
Examples
Input
abc
Output
cba
Input
ac
Output
ac
Submitted Solution:
```
import sys
# 関数 solve は，もちろん，問題に応じて書き換える
def solve(S):
x = S
if len(S) == 2:
return S
elif len(S) == 3 :
return x[2] + x[1] + x[0]
# ここから下は，入力・出力形式が同じであれば，変えなくて良い．
def readQuestion():
line = sys.stdin.readline().rstrip()
return int(line)
def main():
n = readQuestion()
answer = solve(n)
print(answer)
if __name__ == '__main__':
main()
```
No
| 98,474 |
Provide a correct Python 3 solution for this coding contest problem.
In "Takahashi-ya", a ramen restaurant, basically they have one menu: "ramen", but N kinds of toppings are also offered. When a customer orders a bowl of ramen, for each kind of topping, he/she can choose whether to put it on top of his/her ramen or not. There is no limit on the number of toppings, and it is allowed to have all kinds of toppings or no topping at all. That is, considering the combination of the toppings, 2^N types of ramen can be ordered.
Akaki entered Takahashi-ya. She is thinking of ordering some bowls of ramen that satisfy both of the following two conditions:
* Do not order multiple bowls of ramen with the exactly same set of toppings.
* Each of the N kinds of toppings is on two or more bowls of ramen ordered.
You are given N and a prime number M. Find the number of the sets of bowls of ramen that satisfy these conditions, disregarding order, modulo M. Since she is in extreme hunger, ordering any number of bowls of ramen is fine.
Constraints
* 2 \leq N \leq 3000
* 10^8 \leq M \leq 10^9 + 9
* N is an integer.
* M is a prime number.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of the sets of bowls of ramen that satisfy the conditions, disregarding order, modulo M.
Examples
Input
2 1000000007
Output
2
Input
3 1000000009
Output
118
Input
50 111111113
Output
1456748
Input
3000 123456791
Output
16369789
"Correct Solution:
```
N, M = map(int, input().split())
fact = [1]*(N+1)
rfact = [1]*(N+1)
for i in range(1, N+1):
fact[i] = r = (i * fact[i-1]) % M
rfact[i] = pow(r, M-2, M)
memo = {}
def f(N, K):
if (N, K) in memo:
return memo[N, K]
if K == 0:
return N == 0
elif K == 1 or N == K:
return 1
r = memo[N, K] = (f(N-1, K-1) + K*f(N-1, K)) % M
return r
S = [1]
rev2 = pow(2, M-2, M)
base = pow(2, N, M)
ans = 0
S = [1]
for K in range(N+1):
r = (fact[N] * rfact[K] * rfact[N-K]) % M
r = (r * pow(2, pow(2, N - K, M-1), M)) % M
b = 1
v = 0
T = [0]*(K+2)
for L in range(K):
T[L+1] = s = (S[L] + (L+1)*S[L+1]) % M
v += s * b
b = (b * base) % M
v += b
T[K+1] = 1
S = T
r = (r * v) % M
if K % 2:
ans -= r
else:
ans += r
ans %= M
base = (base * rev2) % M
print(ans)
```
| 98,475 |
Provide a correct Python 3 solution for this coding contest problem.
In "Takahashi-ya", a ramen restaurant, basically they have one menu: "ramen", but N kinds of toppings are also offered. When a customer orders a bowl of ramen, for each kind of topping, he/she can choose whether to put it on top of his/her ramen or not. There is no limit on the number of toppings, and it is allowed to have all kinds of toppings or no topping at all. That is, considering the combination of the toppings, 2^N types of ramen can be ordered.
Akaki entered Takahashi-ya. She is thinking of ordering some bowls of ramen that satisfy both of the following two conditions:
* Do not order multiple bowls of ramen with the exactly same set of toppings.
* Each of the N kinds of toppings is on two or more bowls of ramen ordered.
You are given N and a prime number M. Find the number of the sets of bowls of ramen that satisfy these conditions, disregarding order, modulo M. Since she is in extreme hunger, ordering any number of bowls of ramen is fine.
Constraints
* 2 \leq N \leq 3000
* 10^8 \leq M \leq 10^9 + 9
* N is an integer.
* M is a prime number.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of the sets of bowls of ramen that satisfy the conditions, disregarding order, modulo M.
Examples
Input
2 1000000007
Output
2
Input
3 1000000009
Output
118
Input
50 111111113
Output
1456748
Input
3000 123456791
Output
16369789
"Correct Solution:
```
from collections import defaultdict
class Combinatorics:
def __init__(self, N, mod):
'''
Preprocess for calculating binomial coefficients nCr (0 <= r <= n, 0 <= n <= N)
over the finite field Z/(mod)Z.
Input:
N (int): maximum n
mod (int): a prime number. The order of the field Z/(mod)Z over which nCr is calculated.
'''
self.mod = mod
self.fact = {i: None for i in range(N+1)} # n!
self.inverse = {i: None for i in range(1, N+1)} # inverse of n in the field Z/(MOD)Z
self.fact_inverse = {i: None for i in range(N+1)} # inverse of n! in the field Z/(MOD)Z
# preprocess
self.fact[0] = self.fact[1] = 1
self.fact_inverse[0] = self.fact_inverse[1] = 1
self.inverse[1] = 1
for i in range(2, N+1):
self.fact[i] = i * self.fact[i-1] % self.mod
q, r = divmod(self.mod, i)
self.inverse[i] = (- (q % self.mod) * self.inverse[r]) % self.mod
self.fact_inverse[i] = self.inverse[i] * self.fact_inverse[i-1] % self.mod
def binom(self, n, r):
'''
Calculate nCr = n! /(r! (n-r)!) % mod
'''
if n < r or n < 0 or r < 0:
return 0
else:
return self.fact[n] * (self.fact_inverse[r] * self.fact_inverse[n-r] % self.mod) % self.mod
N, M = map(int, input().split())
com = Combinatorics(N, M)
ans = 0
# Preprocess
# calculate 2**n and 2**(2**n)
pow2 = [0] * (N*N // 4 + 1)
pow_pow2 = [0] * (N+1)
pow2[0] = 1; pow_pow2[0] = 2
for i in range(1, N*N // 4 + 1):
pow2[i] = (pow2[i-1] * 2) % M
for i in range(1, N+1):
pow_pow2[i] = pow(pow_pow2[i-1], 2, M)
# (#ways to order i ramens, with each of n toppings chosen at most once)
ways2 = {n: defaultdict(int) for n in range(N+1)}
for n in range(N+1):
ways = 0 # (#ways to choose n toppings, with each topping chosen at most once)
temp = 0
if n >= 1:
for i in range(n+1):
ways2[n][i] = (ways2[n][i] + ways2[n-1][i]) % M # n-th topping is not used
if i >= 1: ways2[n][i] = (ways2[n][i] + ways2[n-1][i-1]) % M # only n-th topping is used in an order
ways2[n][i] = (ways2[n][i] + (i*ways2[n-1][i]) % M) % M # n-th topping is chosen with another topping
temp = (temp + (ways2[n][i] * pow2[(N-n)*i]) % M) % M # degree of freedom on each order is 2**(N-n)
else: # n = 0
ways2[n][0] = 1
temp += ways2[n][0]
ways = (temp * pow_pow2[N-n]) % M
if n % 2 == 0:
ans = (ans + (com.binom(N, n) * ways) % M) % M
else:
ans = (ans - (com.binom(N, n) * ways) % M) % M
print(ans)
```
| 98,476 |
Provide a correct Python 3 solution for this coding contest problem.
In "Takahashi-ya", a ramen restaurant, basically they have one menu: "ramen", but N kinds of toppings are also offered. When a customer orders a bowl of ramen, for each kind of topping, he/she can choose whether to put it on top of his/her ramen or not. There is no limit on the number of toppings, and it is allowed to have all kinds of toppings or no topping at all. That is, considering the combination of the toppings, 2^N types of ramen can be ordered.
Akaki entered Takahashi-ya. She is thinking of ordering some bowls of ramen that satisfy both of the following two conditions:
* Do not order multiple bowls of ramen with the exactly same set of toppings.
* Each of the N kinds of toppings is on two or more bowls of ramen ordered.
You are given N and a prime number M. Find the number of the sets of bowls of ramen that satisfy these conditions, disregarding order, modulo M. Since she is in extreme hunger, ordering any number of bowls of ramen is fine.
Constraints
* 2 \leq N \leq 3000
* 10^8 \leq M \leq 10^9 + 9
* N is an integer.
* M is a prime number.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of the sets of bowls of ramen that satisfy the conditions, disregarding order, modulo M.
Examples
Input
2 1000000007
Output
2
Input
3 1000000009
Output
118
Input
50 111111113
Output
1456748
Input
3000 123456791
Output
16369789
"Correct Solution:
```
# coding: utf-8
# Your code here!
import sys
sys.setrecursionlimit(10**6)
readline = sys.stdin.readline #文字列入力のときは注意
n,MOD = [int(i) for i in readline().split()]
SIZE=3001; #MOD=10**9+7 #998244353 #ここを変更する
SIZE += 1
inv = [0]*SIZE # inv[j] = j^{-1} mod MOD
fac = [0]*SIZE # fac[j] = j! mod MOD
finv = [0]*SIZE# finv[j] = (j!)^{-1} mod MOD
inv[1] = 1
fac[0] = fac[1] = 1
finv[0] = finv[1] = 1
for i in range(2,SIZE):
inv[i] = MOD -(MOD//i)*inv[MOD%i]%MOD
fac[i] = fac[i-1]*i%MOD
finv[i]= finv[i-1]*inv[i]%MOD
def choose(n,r): # nCk mod MOD の計算
if 0 <= r <= n:
return (fac[n]*finv[r]%MOD)*finv[n-r]%MOD
else:
return 0
"""
make the table of Sterling numbers of the second kind
Sterling[ball][box]
SIZE = n
Sterling2 = [[0]*(SIZE+1) for _ in range(SIZE+1)]
Sterling2[0][0] = Sterling2[1][1] = 1
for i in range(2,SIZE+1):
for k in range(1,i+1):
Sterling2[i][k] = (Sterling2[i-1][k-1] + k*Sterling2[i-1][k])%MOD
"""
SIZE = n+1
f = [[0]*(SIZE) for _ in range(SIZE)]
f[0][0] = 1
for i in range(1,SIZE):
f[i][0] = 1
for k in range(1,i+1):
f[i][k] = (f[i-1][k] + f[i-1][k-1] + k*f[i-1][k])%MOD
#print(f)
#pow(2,n-s,MOD-1)
pp = [1]*SIZE
for i in range(1,SIZE):
pp[i] = 2*pp[i-1]%(MOD-1)
def size(s):
"""
for b in range(n+1):
res += f[s][b]*pow(2,b*(n-s),MOD)
"""
res = 0
p = 1
e = pow(2,(n-s),MOD)
for b in range(SIZE):
res += f[s][b]*p
p *= e
p %= MOD
return res*pow(2,pp[n-s],MOD)%MOD
#for i in range(n+1):
# print(size(i))
ans = 0
sgn = 1
for j in range(n+1):
ans += sgn*choose(n,j)*size(j)
ans %= MOD
sgn *= -1
print(ans)
```
| 98,477 |
Provide a correct Python 3 solution for this coding contest problem.
In "Takahashi-ya", a ramen restaurant, basically they have one menu: "ramen", but N kinds of toppings are also offered. When a customer orders a bowl of ramen, for each kind of topping, he/she can choose whether to put it on top of his/her ramen or not. There is no limit on the number of toppings, and it is allowed to have all kinds of toppings or no topping at all. That is, considering the combination of the toppings, 2^N types of ramen can be ordered.
Akaki entered Takahashi-ya. She is thinking of ordering some bowls of ramen that satisfy both of the following two conditions:
* Do not order multiple bowls of ramen with the exactly same set of toppings.
* Each of the N kinds of toppings is on two or more bowls of ramen ordered.
You are given N and a prime number M. Find the number of the sets of bowls of ramen that satisfy these conditions, disregarding order, modulo M. Since she is in extreme hunger, ordering any number of bowls of ramen is fine.
Constraints
* 2 \leq N \leq 3000
* 10^8 \leq M \leq 10^9 + 9
* N is an integer.
* M is a prime number.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of the sets of bowls of ramen that satisfy the conditions, disregarding order, modulo M.
Examples
Input
2 1000000007
Output
2
Input
3 1000000009
Output
118
Input
50 111111113
Output
1456748
Input
3000 123456791
Output
16369789
"Correct Solution:
```
n, m = map(int, input().split())
MOD = m
list_size = n+2
f_list = [1] * list_size
f_r_list = [1] * list_size
for i in range(list_size - 1):
f_list[i + 1] = int((f_list[i] * (i + 1)) % MOD)
f_r_list = [pow(x, MOD-2, MOD) for x in f_list]
def comb(N, r):
if N < r or r < 0:
return 0
else:
return (((f_list[N] * f_r_list[N - r]) % MOD) * f_r_list[r]) % MOD
st = [[0 for _ in range(n+1)] for _ in range(n+1)]
st[0][0] = 1
for i in range(1, n+1):
st[i][0] = 1
for j in range(1, i+1):
st[i][j] = (st[i-1][j-1] + (j+1) * st[i-1][j]) % MOD
ans = 0
for i in range(n+1):
res = (comb(n, i) * pow(2, pow(2, n-i, MOD-1), MOD)) % MOD
tmp = 0
for j in range(i+1):
tmp += st[i][j] * pow(2, (n-i) * j, MOD)
tmp %= MOD
res *= tmp
res %= MOD
if i%2 == 0:
ans += res
else:
ans -= res
ans %= MOD
print(ans)
```
| 98,478 |
Provide a correct Python 3 solution for this coding contest problem.
In "Takahashi-ya", a ramen restaurant, basically they have one menu: "ramen", but N kinds of toppings are also offered. When a customer orders a bowl of ramen, for each kind of topping, he/she can choose whether to put it on top of his/her ramen or not. There is no limit on the number of toppings, and it is allowed to have all kinds of toppings or no topping at all. That is, considering the combination of the toppings, 2^N types of ramen can be ordered.
Akaki entered Takahashi-ya. She is thinking of ordering some bowls of ramen that satisfy both of the following two conditions:
* Do not order multiple bowls of ramen with the exactly same set of toppings.
* Each of the N kinds of toppings is on two or more bowls of ramen ordered.
You are given N and a prime number M. Find the number of the sets of bowls of ramen that satisfy these conditions, disregarding order, modulo M. Since she is in extreme hunger, ordering any number of bowls of ramen is fine.
Constraints
* 2 \leq N \leq 3000
* 10^8 \leq M \leq 10^9 + 9
* N is an integer.
* M is a prime number.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of the sets of bowls of ramen that satisfy the conditions, disregarding order, modulo M.
Examples
Input
2 1000000007
Output
2
Input
3 1000000009
Output
118
Input
50 111111113
Output
1456748
Input
3000 123456791
Output
16369789
"Correct Solution:
```
N, M = map(int, input().split())
fact = [1]*(N+1)
rfact = [1]*(N+1)
for i in range(1, N+1):
fact[i] = r = (i * fact[i-1]) % M
rfact[i] = pow(r, M-2, M)
S = [1]
rev2 = pow(2, M-2, M)
base = pow(2, N, M)
ans = 0
S = [1]
for K in range(N+1):
res = (fact[N] * rfact[K] * rfact[N-K]) % M
res = (res * pow(2, pow(2, N - K, M-1), M)) % M
b = 1
v = 0
T = [0]*(K+2)
for L in range(K):
T[L+1] = s = (S[L] + (L+1)*S[L+1]) % M
v += s * b
b = (b * base) % M
v += b
T[K+1] = 1
S = T
res = (res * v) % M
if K % 2:
ans -= res
else:
ans += res
ans %= M
base = (base * rev2) % M
print(ans)
```
| 98,479 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In "Takahashi-ya", a ramen restaurant, basically they have one menu: "ramen", but N kinds of toppings are also offered. When a customer orders a bowl of ramen, for each kind of topping, he/she can choose whether to put it on top of his/her ramen or not. There is no limit on the number of toppings, and it is allowed to have all kinds of toppings or no topping at all. That is, considering the combination of the toppings, 2^N types of ramen can be ordered.
Akaki entered Takahashi-ya. She is thinking of ordering some bowls of ramen that satisfy both of the following two conditions:
* Do not order multiple bowls of ramen with the exactly same set of toppings.
* Each of the N kinds of toppings is on two or more bowls of ramen ordered.
You are given N and a prime number M. Find the number of the sets of bowls of ramen that satisfy these conditions, disregarding order, modulo M. Since she is in extreme hunger, ordering any number of bowls of ramen is fine.
Constraints
* 2 \leq N \leq 3000
* 10^8 \leq M \leq 10^9 + 9
* N is an integer.
* M is a prime number.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of the sets of bowls of ramen that satisfy the conditions, disregarding order, modulo M.
Examples
Input
2 1000000007
Output
2
Input
3 1000000009
Output
118
Input
50 111111113
Output
1456748
Input
3000 123456791
Output
16369789
Submitted Solution:
```
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor
from operator import mul
from functools import reduce
from pprint import pprint
INF = 10 ** 20
def LI(): return list(map(int, sys.stdin.readline().split()))
def I(): return int(sys.stdin.readline())
def LS(): return sys.stdin.readline().split()
def S(): return sys.stdin.readline().strip()
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]
n, mod = LI()
fac = [1] * (n + 1)
inv = [1] * (n + 1)
for j in range(1, n + 1):
fac[j] = fac[j-1] * j % mod
inv[n] = pow(fac[n], mod-2, mod)
for j in range(n-1, -1, -1):
inv[j] = inv[j+1] * (j+1) % mod
def comb(n, r):
if r > n or n < 0 or r < 0:
return 0
return fac[n] * inv[n - r] * inv[r] % mod
sterling = [[0] * (n + 1) for _ in range(n + 1)]
sterling[0][0] = 1
# n個の区別できるものをk個の(n個以下)の区別不可能なグループに分けることに(i, j)が対応
# n >= k
for i in range(1, n + 1):
for j in range(i + 1):
sterling[i][j] = sterling[i - 1][j] * (j + 1)
if j:
sterling[i][j] += sterling[i - 1][j - 1]
sterling[i][j] %= mod
ans = pow(2, pow(2, n, mod), mod)
for l in range(1, n + 1):
ret = 0
for k in range(l + 1):
cumsum = (sterling[l - 1][k - 1] + (k + 1) * sterling[l - 1][k]) % mod
cumsum = cumsum * pow(pow(2, n - l, mod), k, mod) % mod
cumsum = cumsum * pow(2, pow(2, n - l, mod), mod) % mod
cumsum = cumsum * comb(n, l) % mod
ret += cumsum
if l % 2:
ans -= ret
else:
ans += ret
ans %= mod
print(ans)
```
No
| 98,480 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In "Takahashi-ya", a ramen restaurant, basically they have one menu: "ramen", but N kinds of toppings are also offered. When a customer orders a bowl of ramen, for each kind of topping, he/she can choose whether to put it on top of his/her ramen or not. There is no limit on the number of toppings, and it is allowed to have all kinds of toppings or no topping at all. That is, considering the combination of the toppings, 2^N types of ramen can be ordered.
Akaki entered Takahashi-ya. She is thinking of ordering some bowls of ramen that satisfy both of the following two conditions:
* Do not order multiple bowls of ramen with the exactly same set of toppings.
* Each of the N kinds of toppings is on two or more bowls of ramen ordered.
You are given N and a prime number M. Find the number of the sets of bowls of ramen that satisfy these conditions, disregarding order, modulo M. Since she is in extreme hunger, ordering any number of bowls of ramen is fine.
Constraints
* 2 \leq N \leq 3000
* 10^8 \leq M \leq 10^9 + 9
* N is an integer.
* M is a prime number.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of the sets of bowls of ramen that satisfy the conditions, disregarding order, modulo M.
Examples
Input
2 1000000007
Output
2
Input
3 1000000009
Output
118
Input
50 111111113
Output
1456748
Input
3000 123456791
Output
16369789
Submitted Solution:
```
import sys
sys.setrecursionlimit(10 ** 6)
input = sys.stdin.readline
def main():
def com(com_n, com_r):
return fac[com_n] * inv[com_r] * inv[com_n - com_r] % md
n, md = map(int, input().split())
# combinationの準備
n_max = n+3
fac = [1]
inv = [1] * (n_max + 1)
k_fac_inv = 1
for i in range(1, n_max + 1):
k_fac_inv = k_fac_inv * i % md
fac.append(k_fac_inv)
k_fac_inv = pow(k_fac_inv, md - 2, md)
for i in range(n_max, 1, -1):
inv[i] = k_fac_inv
k_fac_inv = k_fac_inv * i % md
# スターリング数発展の作成
stir = [[1] * (n + 1) for _ in range(n + 1)]
si1 = stir[0]
for i in range(1, n + 1):
si = stir[i]
for j in range(1, i):
si[j] = si1[j] * (j + 1) + si1[j - 1]
si1 = si
# 本体
ans = 0
pm = 1
for m in range(n + 1):
a = 0
e2 = pow(2, n - m)
for k in range(m + 1):
a = (a + stir[m][k] * pow(e2, k, md)) % md
ans = (ans + pm * a * pow(2, e2, md) * com(n, m)) % md
pm *= -1
print(ans)
main()
```
No
| 98,481 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In "Takahashi-ya", a ramen restaurant, basically they have one menu: "ramen", but N kinds of toppings are also offered. When a customer orders a bowl of ramen, for each kind of topping, he/she can choose whether to put it on top of his/her ramen or not. There is no limit on the number of toppings, and it is allowed to have all kinds of toppings or no topping at all. That is, considering the combination of the toppings, 2^N types of ramen can be ordered.
Akaki entered Takahashi-ya. She is thinking of ordering some bowls of ramen that satisfy both of the following two conditions:
* Do not order multiple bowls of ramen with the exactly same set of toppings.
* Each of the N kinds of toppings is on two or more bowls of ramen ordered.
You are given N and a prime number M. Find the number of the sets of bowls of ramen that satisfy these conditions, disregarding order, modulo M. Since she is in extreme hunger, ordering any number of bowls of ramen is fine.
Constraints
* 2 \leq N \leq 3000
* 10^8 \leq M \leq 10^9 + 9
* N is an integer.
* M is a prime number.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of the sets of bowls of ramen that satisfy the conditions, disregarding order, modulo M.
Examples
Input
2 1000000007
Output
2
Input
3 1000000009
Output
118
Input
50 111111113
Output
1456748
Input
3000 123456791
Output
16369789
Submitted Solution:
```
N,M = list(map(int,input().split()))
table = [1,1]
while len(table) <= N:
temp = 1
for i in range(len(table)-1):
table[i+1] += temp
temp = table[i+1]- temp
table[i+1] = M
table.append(1)
S = [1]
rev2 = pow(2, M-2, M)
base = pow(2, N, M)
ans = 0
S = [1]
for K in range(N+1):
res = table[K] % M
res = (res * pow(2, pow(2, N - K, M-1), M)) % M
b = 1
v = 0
T = [0]*(K+2)
for L in range(K):
T[L+1] = s = (S[L] + (L+1)*S[L+1]) % M
v += s * b
b = (b * base) % M
v += b
T[K+1] = 1
S = T
res = (res * v) % M
if K % 2:
ans -= res
else:
ans += res
ans %= M
base = (base * rev2) % M
print(ans)
```
No
| 98,482 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In "Takahashi-ya", a ramen restaurant, basically they have one menu: "ramen", but N kinds of toppings are also offered. When a customer orders a bowl of ramen, for each kind of topping, he/she can choose whether to put it on top of his/her ramen or not. There is no limit on the number of toppings, and it is allowed to have all kinds of toppings or no topping at all. That is, considering the combination of the toppings, 2^N types of ramen can be ordered.
Akaki entered Takahashi-ya. She is thinking of ordering some bowls of ramen that satisfy both of the following two conditions:
* Do not order multiple bowls of ramen with the exactly same set of toppings.
* Each of the N kinds of toppings is on two or more bowls of ramen ordered.
You are given N and a prime number M. Find the number of the sets of bowls of ramen that satisfy these conditions, disregarding order, modulo M. Since she is in extreme hunger, ordering any number of bowls of ramen is fine.
Constraints
* 2 \leq N \leq 3000
* 10^8 \leq M \leq 10^9 + 9
* N is an integer.
* M is a prime number.
Input
Input is given from Standard Input in the following format:
N M
Output
Print the number of the sets of bowls of ramen that satisfy the conditions, disregarding order, modulo M.
Examples
Input
2 1000000007
Output
2
Input
3 1000000009
Output
118
Input
50 111111113
Output
1456748
Input
3000 123456791
Output
16369789
Submitted Solution:
```
import numpy as np
from collections import defaultdict
class Combinatorics:
def __init__(self, N, mod):
'''
Preprocess for calculating binomial coefficients nCr (0 <= r <= n, 0 <= n <= N)
over the finite field Z/(mod)Z.
Input:
N (int): maximum n
mod (int): a prime number. The order of the field Z/(mod)Z over which nCr is calculated.
'''
self.mod = mod
self.fact = {i: None for i in range(N+1)} # n!
self.inverse = {i: None for i in range(1, N+1)} # inverse of n in the field Z/(MOD)Z
self.fact_inverse = {i: None for i in range(N+1)} # inverse of n! in the field Z/(MOD)Z
# preprocess
self.fact[0] = self.fact[1] = 1
self.fact_inverse[0] = self.fact_inverse[1] = 1
self.inverse[1] = 1
for i in range(2, N+1):
self.fact[i] = i * self.fact[i-1] % self.mod
q, r = divmod(self.mod, i)
self.inverse[i] = (- (q % self.mod) * self.inverse[r]) % self.mod
self.fact_inverse[i] = self.inverse[i] * self.fact_inverse[i-1] % self.mod
def binom(self, n, r):
'''
Calculate nCr = n! /(r! (n-r)!) % mod
'''
if n < r or n < 0 or r < 0:
return 0
else:
return self.fact[n] * (self.fact_inverse[r] * self.fact_inverse[n-r] % self.mod) % self.mod
N, M = map(int, input().split())
com = Combinatorics(N, M)
ans = 0
# Preprocess
# calculate 2**n and 2**(2**n)
pow2 = np.power(2, np.array(range(N*N // 4 + 1)))
pow_pow2 = [0] * (N+1)
pow_pow2[0] = 2
for i in range(1, N*N // 4 + 1):
pow2[i] = (pow2[i-1] * 2) % M
for i in range(1, N+1):
pow_pow2[i] = pow(pow_pow2[i-1], 2, M)
# (#ways to order i ramens, with each of n toppings chosen at most once)
ways2 = {n: defaultdict(int) for n in range(N+1)}
for n in range(N+1):
ways = 0 # (#ways to choose n toppings, with each topping chosen at most once)
temp = 0
if n >= 1:
for i in range(n+1):
ways2[n][i] = (ways2[n][i] + ways2[n-1][i]) % M # n-th topping is not used
if i >= 1: ways2[n][i] = (ways2[n][i] + ways2[n-1][i-1]) % M # only n-th topping is used in an order
ways2[n][i] = (ways2[n][i] + (i*ways2[n-1][i]) % M) % M # n-th topping is chosen with another topping
temp = (temp + (ways2[n][i] * pow2[(N-n)*i]) % M) % M # degree of freedom on each order is 2**(N-n)
else: # n = 0
ways2[n][0] = 1
temp += ways2[n][0]
ways = (temp * pow_pow2[N-n]) % M
if n % 2 == 0:
ans = (ans + (com.binom(N, n) * ways) % M) % M
else:
ans = (ans - (com.binom(N, n) * ways) % M) % M
print(ans)
```
No
| 98,483 |
Provide a correct Python 3 solution for this coding contest problem.
Ringo has a string S.
He can perform the following N kinds of operations any number of times in any order.
* Operation i: For each of the characters from the L_i-th through the R_i-th characters in S, replace it with its succeeding letter in the English alphabet. (That is, replace `a` with `b`, replace `b` with `c` and so on.) For `z`, we assume that its succeeding letter is `a`.
Ringo loves palindromes and wants to turn S into a palindrome. Determine whether this is possible.
Constraints
* 1 \leq |S| \leq 10^5
* S consists of lowercase English letters.
* 1 \leq N \leq 10^5
* 1 \leq L_i \leq R_i \leq |S|
Input
Input is given from Standard Input in the following format:
S
N
L_1 R_1
L_2 R_2
:
L_N R_N
Output
Print `YES` if it is possible to turn S into a palindrome; print `NO` if it is impossible.
Examples
Input
bixzja
2
2 3
3 6
Output
YES
Input
abc
1
2 2
Output
NO
Input
cassert
4
1 2
3 4
1 1
2 2
Output
YES
"Correct Solution:
```
import sys
from operator import sub
sys.setrecursionlimit(100000)
def dfs(s, visited):
visited.add(s)
for v in links[s]:
if v not in visited:
dfs(v, visited)
def solve():
checked = set()
for i in range(ls // 2 + 1):
if i in checked:
continue
visited = set()
dfs(i, visited)
inner_total = sum(sd[k] for k in visited) % 26
if inner_total != 0:
return False
checked.update(visited)
return True
s = input()
sl = list(map(ord, s))
sd = list(map(sub, sl + [97], [97] + sl))
ls = len(s)
lsd = len(sd)
n = int(input())
links = [set() for _ in range(lsd)]
for i in range((ls + 1) // 2):
links[i].add(ls - i)
links[ls - i].add(i)
for a, b in (map(int, input().split()) for _ in range(n)):
links[a - 1].add(b)
links[b].add(a - 1)
print('YES' if solve() else 'NO')
```
| 98,484 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into S to obtain a correct bracket sequence.
Here, a correct bracket sequence is defined as follows:
* `()` is a correct bracket sequence.
* If X is a correct bracket sequence, the concatenation of `(`, X and `)` in this order is also a correct bracket sequence.
* If X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.
* Every correct bracket sequence can be derived from the rules above.
Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.
Constraints
* The length of S is N.
* 1 ≤ N ≤ 100
* S consists of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of `(` and `)` into S.
Examples
Input
3
())
Output
(())
Input
6
)))())
Output
(((()))())
Input
8
))))((((
Output
(((())))(((())))
"Correct Solution:
```
N = int(input())
S = input()
s = S[:]
while '()' in s:
s = s.replace('()', '')
ans = '(' * s.count(')') + S + ')' * s.count('(')
print(ans)
```
| 98,485 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into S to obtain a correct bracket sequence.
Here, a correct bracket sequence is defined as follows:
* `()` is a correct bracket sequence.
* If X is a correct bracket sequence, the concatenation of `(`, X and `)` in this order is also a correct bracket sequence.
* If X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.
* Every correct bracket sequence can be derived from the rules above.
Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.
Constraints
* The length of S is N.
* 1 ≤ N ≤ 100
* S consists of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of `(` and `)` into S.
Examples
Input
3
())
Output
(())
Input
6
)))())
Output
(((()))())
Input
8
))))((((
Output
(((())))(((())))
"Correct Solution:
```
N=int(input())
S=input()
a=[0]
for c in S:
a.append(a[-1]+(1 if c=='(' else -1))
k=-min(a)
l=S.count('(')+k-S.count(')')
ans='('*k+S+')'*l
print(ans)
```
| 98,486 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into S to obtain a correct bracket sequence.
Here, a correct bracket sequence is defined as follows:
* `()` is a correct bracket sequence.
* If X is a correct bracket sequence, the concatenation of `(`, X and `)` in this order is also a correct bracket sequence.
* If X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.
* Every correct bracket sequence can be derived from the rules above.
Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.
Constraints
* The length of S is N.
* 1 ≤ N ≤ 100
* S consists of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of `(` and `)` into S.
Examples
Input
3
())
Output
(())
Input
6
)))())
Output
(((()))())
Input
8
))))((((
Output
(((())))(((())))
"Correct Solution:
```
input()
t=s=input()
p,q=o="()"
while o in s:s=s.replace(o,"")
print(p*s.count(q)+t+q*s.count(p))
```
| 98,487 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into S to obtain a correct bracket sequence.
Here, a correct bracket sequence is defined as follows:
* `()` is a correct bracket sequence.
* If X is a correct bracket sequence, the concatenation of `(`, X and `)` in this order is also a correct bracket sequence.
* If X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.
* Every correct bracket sequence can be derived from the rules above.
Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.
Constraints
* The length of S is N.
* 1 ≤ N ≤ 100
* S consists of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of `(` and `)` into S.
Examples
Input
3
())
Output
(())
Input
6
)))())
Output
(((()))())
Input
8
))))((((
Output
(((())))(((())))
"Correct Solution:
```
N = int(input())
X = input()
L, R = 0, 0
for x in X:
if x == "(":
R += 1
else:
if R == 0:
L += 1
else:
R -= 1
print(L*"("+X+R*")")
```
| 98,488 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into S to obtain a correct bracket sequence.
Here, a correct bracket sequence is defined as follows:
* `()` is a correct bracket sequence.
* If X is a correct bracket sequence, the concatenation of `(`, X and `)` in this order is also a correct bracket sequence.
* If X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.
* Every correct bracket sequence can be derived from the rules above.
Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.
Constraints
* The length of S is N.
* 1 ≤ N ≤ 100
* S consists of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of `(` and `)` into S.
Examples
Input
3
())
Output
(())
Input
6
)))())
Output
(((()))())
Input
8
))))((((
Output
(((())))(((())))
"Correct Solution:
```
N = int(input())
S = input()
R=0;L=0
for i in range(N):
if S[i] == ')':
if L == 0:
R+=1
else:
L -= 1
else:
L += 1
Answer = '(' * R + S + ')' * L
print(Answer)
```
| 98,489 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into S to obtain a correct bracket sequence.
Here, a correct bracket sequence is defined as follows:
* `()` is a correct bracket sequence.
* If X is a correct bracket sequence, the concatenation of `(`, X and `)` in this order is also a correct bracket sequence.
* If X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.
* Every correct bracket sequence can be derived from the rules above.
Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.
Constraints
* The length of S is N.
* 1 ≤ N ≤ 100
* S consists of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of `(` and `)` into S.
Examples
Input
3
())
Output
(())
Input
6
)))())
Output
(((()))())
Input
8
))))((((
Output
(((())))(((())))
"Correct Solution:
```
n=int(input())
s=input()
l=0
r=0
for c in s:
if c=='(':
r+=1
elif c==')':
if r>0:
r-=1
else:
l+=1
print('('*l+s+')'*r)
```
| 98,490 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into S to obtain a correct bracket sequence.
Here, a correct bracket sequence is defined as follows:
* `()` is a correct bracket sequence.
* If X is a correct bracket sequence, the concatenation of `(`, X and `)` in this order is also a correct bracket sequence.
* If X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.
* Every correct bracket sequence can be derived from the rules above.
Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.
Constraints
* The length of S is N.
* 1 ≤ N ≤ 100
* S consists of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of `(` and `)` into S.
Examples
Input
3
())
Output
(())
Input
6
)))())
Output
(((()))())
Input
8
))))((((
Output
(((())))(((())))
"Correct Solution:
```
n=int(input())
s=input()
a=b=0
k=0
for i in range(n):
if s[i]=="(":
a+=1
else:
b+=1
if a<b:
k+=1
a+=1
s=k*("(")+s
if a>b:
s+=")"*(a-b)
print(s)
```
| 98,491 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a string S of length N consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into S to obtain a correct bracket sequence.
Here, a correct bracket sequence is defined as follows:
* `()` is a correct bracket sequence.
* If X is a correct bracket sequence, the concatenation of `(`, X and `)` in this order is also a correct bracket sequence.
* If X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.
* Every correct bracket sequence can be derived from the rules above.
Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.
Constraints
* The length of S is N.
* 1 ≤ N ≤ 100
* S consists of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of `(` and `)` into S.
Examples
Input
3
())
Output
(())
Input
6
)))())
Output
(((()))())
Input
8
))))((((
Output
(((())))(((())))
"Correct Solution:
```
input();s=input();r=l=0
for c in s:r=max(r-1+2*(c=='('),0)
for c in s[::-1]:l=max(l-1+2*(c==')'),0)
print(l*'('+s+')'*r)
```
| 98,492 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length N consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into S to obtain a correct bracket sequence.
Here, a correct bracket sequence is defined as follows:
* `()` is a correct bracket sequence.
* If X is a correct bracket sequence, the concatenation of `(`, X and `)` in this order is also a correct bracket sequence.
* If X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.
* Every correct bracket sequence can be derived from the rules above.
Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.
Constraints
* The length of S is N.
* 1 ≤ N ≤ 100
* S consists of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of `(` and `)` into S.
Examples
Input
3
())
Output
(())
Input
6
)))())
Output
(((()))())
Input
8
))))((((
Output
(((())))(((())))
Submitted Solution:
```
n=int(input())
s=input()
X=[0]
r=0
for i in range(n):
if s[i]=="(":
r+=1
else:
r-=1
X.append(r)
left=-min(X)
right=X[-1]+left
print("("*left+s+")"*right)
```
Yes
| 98,493 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length N consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into S to obtain a correct bracket sequence.
Here, a correct bracket sequence is defined as follows:
* `()` is a correct bracket sequence.
* If X is a correct bracket sequence, the concatenation of `(`, X and `)` in this order is also a correct bracket sequence.
* If X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.
* Every correct bracket sequence can be derived from the rules above.
Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.
Constraints
* The length of S is N.
* 1 ≤ N ≤ 100
* S consists of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of `(` and `)` into S.
Examples
Input
3
())
Output
(())
Input
6
)))())
Output
(((()))())
Input
8
))))((((
Output
(((())))(((())))
Submitted Solution:
```
n=int(input())
s=input()
a=0
l=0
for i in range(n):
if s[i]=='(':
a+=1
else:
a-=1
if a<0:
l+=1
a+=1
print('('*l+s+')'*a)
```
Yes
| 98,494 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length N consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into S to obtain a correct bracket sequence.
Here, a correct bracket sequence is defined as follows:
* `()` is a correct bracket sequence.
* If X is a correct bracket sequence, the concatenation of `(`, X and `)` in this order is also a correct bracket sequence.
* If X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.
* Every correct bracket sequence can be derived from the rules above.
Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.
Constraints
* The length of S is N.
* 1 ≤ N ≤ 100
* S consists of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of `(` and `)` into S.
Examples
Input
3
())
Output
(())
Input
6
)))())
Output
(((()))())
Input
8
))))((((
Output
(((())))(((())))
Submitted Solution:
```
n = int(input())
s = input()
i = 0
k = 0
while i < len(s):
if s[i] == "(":
k += 1
else:
if k > 0:
k -= 1
else:
s = "(" + s
i += 1
i += 1
print(s+")"*k)
```
Yes
| 98,495 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length N consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into S to obtain a correct bracket sequence.
Here, a correct bracket sequence is defined as follows:
* `()` is a correct bracket sequence.
* If X is a correct bracket sequence, the concatenation of `(`, X and `)` in this order is also a correct bracket sequence.
* If X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.
* Every correct bracket sequence can be derived from the rules above.
Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.
Constraints
* The length of S is N.
* 1 ≤ N ≤ 100
* S consists of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of `(` and `)` into S.
Examples
Input
3
())
Output
(())
Input
6
)))())
Output
(((()))())
Input
8
))))((((
Output
(((())))(((())))
Submitted Solution:
```
n = int(input())
s = input()
a=0
b=0
c=0
for c in s:
if c=='(':
a+=1
else:
if a>0:
a-=1
else:
b+=1
s+=')'*a
s = '('*b+s
print(s)
```
Yes
| 98,496 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length N consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into S to obtain a correct bracket sequence.
Here, a correct bracket sequence is defined as follows:
* `()` is a correct bracket sequence.
* If X is a correct bracket sequence, the concatenation of `(`, X and `)` in this order is also a correct bracket sequence.
* If X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.
* Every correct bracket sequence can be derived from the rules above.
Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.
Constraints
* The length of S is N.
* 1 ≤ N ≤ 100
* S consists of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of `(` and `)` into S.
Examples
Input
3
())
Output
(())
Input
6
)))())
Output
(((()))())
Input
8
))))((((
Output
(((())))(((())))
Submitted Solution:
```
n = int(input())
s = input()
lv = [0] * n
lvi = 0
for i,v in enumerate(s):
if v == '(' :
lvi += 1
else:
lvi -= 1
lv[i] = lvi
l = min(lv)
r = -lv[-1] + l
print('('*(-l) + s + ')'*(-r))
```
No
| 98,497 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length N consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into S to obtain a correct bracket sequence.
Here, a correct bracket sequence is defined as follows:
* `()` is a correct bracket sequence.
* If X is a correct bracket sequence, the concatenation of `(`, X and `)` in this order is also a correct bracket sequence.
* If X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.
* Every correct bracket sequence can be derived from the rules above.
Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.
Constraints
* The length of S is N.
* 1 ≤ N ≤ 100
* S consists of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of `(` and `)` into S.
Examples
Input
3
())
Output
(())
Input
6
)))())
Output
(((()))())
Input
8
))))((((
Output
(((())))(((())))
Submitted Solution:
```
N = int(input())
S = input()
ss = S.replace(')(', ') (').split()
ans = ''
for s in ss:
a = s.count('(')
b = s.count(')')
ans = '(' * (b - a) + ans + s + ')' * (a - b)
print(ans)
```
No
| 98,498 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a string S of length N consisting of `(` and `)`. Your task is to insert some number of `(` and `)` into S to obtain a correct bracket sequence.
Here, a correct bracket sequence is defined as follows:
* `()` is a correct bracket sequence.
* If X is a correct bracket sequence, the concatenation of `(`, X and `)` in this order is also a correct bracket sequence.
* If X and Y are correct bracket sequences, the concatenation of X and Y in this order is also a correct bracket sequence.
* Every correct bracket sequence can be derived from the rules above.
Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.
Constraints
* The length of S is N.
* 1 ≤ N ≤ 100
* S consists of `(` and `)`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the lexicographically smallest string among the shortest correct bracket sequences that can be obtained by inserting some number of `(` and `)` into S.
Examples
Input
3
())
Output
(())
Input
6
)))())
Output
(((()))())
Input
8
))))((((
Output
(((())))(((())))
Submitted Solution:
```
n=int(input())
s=input()
stack=[]
for c in s:
if len(stack)>0 and stack[-1]=='(' and c==')':
stack.pop()
else:
stack.append(c)
if len(stack)==0:
print(s)
else:
l=0
r=0
for c in stack:
if c==')':
l+=1
else:
r+=1
print('('*l+s+')'*r)
```
No
| 98,499 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.