message stringlengths 2 16.2k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 575 109k | cluster float64 16 16 | __index_level_0__ int64 1.15k 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves permutations. He is making a permutation of length N.
Since he hates the integer K, his permutation will satisfy the following:
* Let the permutation be a_1, a_2, ..., a_N. For each i = 1,2,...,N, |a_i - i| \neq K.
Among the N! permutations of length N, how many satisfies this condition?
Since the answer may be extremely large, find the answer modulo 924844033(prime).
Constraints
* 2 ≦ N ≦ 2000
* 1 ≦ K ≦ N-1
Input
The input is given from Standard Input in the following format:
N K
Output
Print the answer modulo 924844033.
Examples
Input
3 1
Output
2
Input
4 1
Output
5
Input
4 2
Output
9
Input
4 3
Output
14
Input
425 48
Output
756765083
Submitted Solution:
```
import itertools
import numpy
a = input().split(" ")
N = int(a[0])
K = int(a[1])
l = list([i+1 for i in range(N)])
it = itertools.permutations(l,N)
itNum = numpy.array(list(it))
lNum = numpy.array(l)
isK = itNum - lNum
ans = 0
for i in isK:
if not(K in i or -K in i):
ans += 1
print(ans%924844033)
``` | instruction | 0 | 10,669 | 16 | 21,338 |
No | output | 1 | 10,669 | 16 | 21,339 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves permutations. He is making a permutation of length N.
Since he hates the integer K, his permutation will satisfy the following:
* Let the permutation be a_1, a_2, ..., a_N. For each i = 1,2,...,N, |a_i - i| \neq K.
Among the N! permutations of length N, how many satisfies this condition?
Since the answer may be extremely large, find the answer modulo 924844033(prime).
Constraints
* 2 ≦ N ≦ 2000
* 1 ≦ K ≦ N-1
Input
The input is given from Standard Input in the following format:
N K
Output
Print the answer modulo 924844033.
Examples
Input
3 1
Output
2
Input
4 1
Output
5
Input
4 2
Output
9
Input
4 3
Output
14
Input
425 48
Output
756765083
Submitted Solution:
```
import itertools
def isContainedValueK(tup, k):
for i, t in enumerate(tup):
if t - (i + 1) == k or t - (i + 1) == -k:
return True
return False
n, k = map(int, input().split())
r = [i for i in range(1, n + 1)]
cnt = 0
for tup in itertools.permutations(r, n):
if not isContainedValueK(tup, k):
cnt += 1
print(cnt)
``` | instruction | 0 | 10,670 | 16 | 21,340 |
No | output | 1 | 10,670 | 16 | 21,341 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke received N intervals as a birthday present. The i-th interval was [-L_i, R_i]. It is guaranteed that both L_i and R_i are positive. In other words, the origin is strictly inside each interval.
Snuke doesn't like overlapping intervals, so he decided to move some intervals. For any positive integer d, if he pays d dollars, he can choose one of the intervals and move it by the distance of d. That is, if the chosen segment is [a, b], he can change it to either [a+d, b+d] or [a-d, b-d].
He can repeat this type of operation arbitrary number of times. After the operations, the intervals must be pairwise disjoint (however, they may touch at a point). Formally, for any two intervals, the length of the intersection must be zero.
Compute the minimum cost required to achieve his goal.
Constraints
* 1 ≤ N ≤ 5000
* 1 ≤ L_i, R_i ≤ 10^9
* All values in the input are integers.
Input
The input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the minimum cost required to achieve his goal.
Examples
Input
4
2 7
2 5
4 1
7 5
Output
22
Input
20
97 2
75 25
82 84
17 56
32 2
28 37
57 39
18 11
79 6
40 68
68 16
40 63
93 49
91 10
55 68
31 80
57 18
34 28
76 55
21 80
Output
7337
Submitted Solution:
```
import sys
readline = sys.stdin.readline
readlines = sys.stdin.readlines
import numpy as np
N = int(readline())
LR = [tuple(int(x) for x in line.split()) for line in readlines()]
"""
・奇数個のとき：中央にどれかを固定。
・偶数のとき：原点で左右に分けるとしてよい。
・基本的に長さで内側から昇順（奇数のときの中央は謎）。→ソートしてdpできる。
・左に置いた個数をもってdp更新。また、中央を使ったかも同時に持って。
・偶数のときは、中央に1つ置いた状態から始める。
・大きい区間から外側に入れていく。
"""
LR.sort(key = lambda x: -x[1]-x[0])
INF = 10**15
dp_0 = np.full(N+1,INF,np.int64) # 左に置いた個数 → コスト。中央未確定。
dp_1 = np.full(N+1,INF,np.int64) # 左に置いた個数 → コスト。中央確定。
if N&1:
dp_0[0] = 0
else:
dp_1[0] = 0
for n,(L,R) in enumerate(LR):
length = R + L
prev_0 = dp_0
prev_1 = dp_1
dp_0 = np.full(N+1,INF,np.int64)
dp_1 = np.full(N+1,INF,np.int64)
x = np.arange(n+1,dtype=np.int64) # もともと左側にあった個数
# 左側に置く場合
np.minimum(prev_0[:n+1] + R + x * length, dp_0[1:n+2], out=dp_0[1:n+2])
np.minimum(prev_1[:n+1] + R + x * length, dp_1[1:n+2], out=dp_1[1:n+2])
# 右側に置く場合
np.minimum(prev_0[:n+1] + L + (n-x) * length, dp_0[:n+1], out=dp_0[:n+1])
np.minimum(prev_1[:n+1] + L + (n-x) * length, dp_1[:n+1], out=dp_1[:n+1])
# 中央に置く場合
np.minimum(prev_0[:n+1] + (N-1)//2 * length, dp_1[:n+1], out = dp_1[:n+1])
answer = dp_1[N//2]
print(answer)
``` | instruction | 0 | 11,520 | 16 | 23,040 |
No | output | 1 | 11,520 | 16 | 23,041 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke received N intervals as a birthday present. The i-th interval was [-L_i, R_i]. It is guaranteed that both L_i and R_i are positive. In other words, the origin is strictly inside each interval.
Snuke doesn't like overlapping intervals, so he decided to move some intervals. For any positive integer d, if he pays d dollars, he can choose one of the intervals and move it by the distance of d. That is, if the chosen segment is [a, b], he can change it to either [a+d, b+d] or [a-d, b-d].
He can repeat this type of operation arbitrary number of times. After the operations, the intervals must be pairwise disjoint (however, they may touch at a point). Formally, for any two intervals, the length of the intersection must be zero.
Compute the minimum cost required to achieve his goal.
Constraints
* 1 ≤ N ≤ 5000
* 1 ≤ L_i, R_i ≤ 10^9
* All values in the input are integers.
Input
The input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the minimum cost required to achieve his goal.
Examples
Input
4
2 7
2 5
4 1
7 5
Output
22
Input
20
97 2
75 25
82 84
17 56
32 2
28 37
57 39
18 11
79 6
40 68
68 16
40 63
93 49
91 10
55 68
31 80
57 18
34 28
76 55
21 80
Output
7337
Submitted Solution:
```
import sys
readline = sys.stdin.readline
readlines = sys.stdin.readlines
import numpy as np
N = int(readline())
LR = [tuple(int(x) for x in line.split()) for line in readlines()]
"""
・奇数個のとき：中央にどれかを固定。
・偶数のとき：原点で左右に分けるとしてよい。
・基本的に長さで内側から昇順（奇数のときの中央は謎）。→ソートしてdpできる。
・左に置いた個数をもってdp更新。また、中央を使ったかも同時に持って。
・偶数のときは、中央に1つ置いた状態から始める。
・大きい区間から外側に入れていく。
"""
LR.sort(key = lambda x: -x[1]-x[0])
if N%2 == 1:
raise Exception
INF = 10**15
dp_0 = np.full(N+1,INF,np.int64) # 左に置いた個数 → コスト。中央未確定。
dp_1 = np.full(N+1,INF,np.int64) # 左に置いた個数 → コスト。中央確定。
if N&1:
dp_0[0] = 0
else:
dp_1[0] = 0
for n,(L,R) in enumerate(LR):
length = R + L
prev_0 = dp_0
prev_1 = dp_1
dp_0 = np.full(N+1,INF,np.int64)
dp_1 = np.full(N+1,INF,np.int64)
x = np.arange(n+1,dtype=np.int64) # もともと左側にあった個数
# 左側に置く場合
np.minimum(prev_0[:n+1] + R + x * length, dp_0[1:n+2], out=dp_0[1:n+2])
np.minimum(prev_1[:n+1] + R + x * length, dp_1[1:n+2], out=dp_1[1:n+2])
# 右側に置く場合
np.minimum(prev_0[:n+1] + L + (n-x) * length, dp_0[:n+1], out=dp_0[:n+1])
np.minimum(prev_1[:n+1] + L + (n-x) * length, dp_1[:n+1], out=dp_1[:n+1])
# 中央に置く場合
np.minimum(prev_0[:n+1] + (N-1)//2 * length, dp_1[:n+1], out = dp_1[:n+1])
answer = dp_1[N//2]
print(answer)
``` | instruction | 0 | 11,521 | 16 | 23,042 |
No | output | 1 | 11,521 | 16 | 23,043 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke received N intervals as a birthday present. The i-th interval was [-L_i, R_i]. It is guaranteed that both L_i and R_i are positive. In other words, the origin is strictly inside each interval.
Snuke doesn't like overlapping intervals, so he decided to move some intervals. For any positive integer d, if he pays d dollars, he can choose one of the intervals and move it by the distance of d. That is, if the chosen segment is [a, b], he can change it to either [a+d, b+d] or [a-d, b-d].
He can repeat this type of operation arbitrary number of times. After the operations, the intervals must be pairwise disjoint (however, they may touch at a point). Formally, for any two intervals, the length of the intersection must be zero.
Compute the minimum cost required to achieve his goal.
Constraints
* 1 ≤ N ≤ 5000
* 1 ≤ L_i, R_i ≤ 10^9
* All values in the input are integers.
Input
The input is given from Standard Input in the following format:
N
L_1 R_1
:
L_N R_N
Output
Print the minimum cost required to achieve his goal.
Examples
Input
4
2 7
2 5
4 1
7 5
Output
22
Input
20
97 2
75 25
82 84
17 56
32 2
28 37
57 39
18 11
79 6
40 68
68 16
40 63
93 49
91 10
55 68
31 80
57 18
34 28
76 55
21 80
Output
7337
Submitted Solution:
```
import sys
readline = sys.stdin.readline
readlines = sys.stdin.readlines
import numpy as np
N = int(readline())
LR = [tuple(int(x) for x in line.split()) for line in readlines()]
"""
・奇数個のとき：中央にどれかを固定。
・偶数のとき：原点で左右に分けるとしてよい。
・基本的に長さで内側から昇順（奇数のときの中央は謎）。→ソートしてdpできる。
・左に置いた個数をもってdp更新。また、中央を使ったかも同時に持って。
・偶数のときは、中央に1つ置いた状態から始める。
・大きい区間から外側に入れていく。
"""
LR.sort(key = lambda x: -x[1]-x[0])
if N%2 == 1:
raise Exception
INF = 10**18
dp_0 = np.full(N+1,INF,np.int64) # 左に置いた個数 → コスト。中央未確定。
dp_1 = np.full(N+1,INF,np.int64) # 左に置いた個数 → コスト。中央確定。
if N&1:
dp_0[0] = 0
else:
dp_1[0] = 0
for n,(L,R) in enumerate(LR):
length = R + L
prev_0 = dp_0
prev_1 = dp_1
dp_0 = np.full(N+1,INF,np.int64)
dp_1 = np.full(N+1,INF,np.int64)
x = np.arange(n+1,dtype=np.int64) # もともと左側にあった個数
# 左側に置く場合
np.minimum(prev_0[:n+1] + R + x * length, dp_0[1:n+2], out=dp_0[1:n+2])
np.minimum(prev_1[:n+1] + R + x * length, dp_1[1:n+2], out=dp_1[1:n+2])
# 右側に置く場合
np.minimum(prev_0[:n+1] + L + (n-x) * length, dp_0[:n+1], out=dp_0[:n+1])
np.minimum(prev_1[:n+1] + L + (n-x) * length, dp_1[:n+1], out=dp_1[:n+1])
# 中央に置く場合
np.minimum(prev_0[:n+1] + (N-1)//2 * length, dp_1[:n+1], out = dp_1[:n+1])
answer = dp_1[N//2]
print(answer)
``` | instruction | 0 | 11,522 | 16 | 23,044 |
No | output | 1 | 11,522 | 16 | 23,045 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares lining up in a row, numbered 1 through N from left to right. Initially, all squares are white. We also have N-1 painting machines, numbered 1 through N-1. When operated, Machine i paints Square i and i+1 black.
Snuke will operate these machines one by one. The order in which he operates them is represented by a permutation of (1, 2, ..., N-1), P, which means that the i-th operated machine is Machine P_i.
Here, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P. Snuke has not decided what permutation P to use, but he is interested in the scores of possible permutations. Find the sum of the scores over all possible permutations for him. Since this can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 2 \leq N \leq 10^6
Input
Input is given from Standard Input in the following format:
N
Output
Print the sum of the scores over all possible permutations, modulo 10^9+7.
Examples
Input
4
Output
16
Input
2
Output
1
Input
5
Output
84
Input
100000
Output
341429644 | instruction | 0 | 14,844 | 16 | 29,688 |
"Correct Solution:
```
import sys
def I(): return int(sys.stdin.readline().rstrip())
N = I()
mod = 10**9+7
fac = [1]*(N+1)
for i in range(1,N+1):
fac[i] = (fac[i-1]*i) % mod
fac_inverse = [1]*(N+1)
for i in range(1,N+1):
fac_inverse[i] = pow(fac[i],mod-2,mod)
def nCr(n,r):
if n < r:
return 0
return (fac[n]*fac_inverse[r]*fac_inverse[n-r]) % mod
A = [0]*(N+1) # Ai = i回以下マシンを稼働することで、全て黒く塗られるような順列の個数
for i in range(N+1):
A[i] = (fac[i]*fac[N-1-i]*nCr(i-1,N-1-i)) % mod
ans = 0
for i in range(1,N):
ans += i*(A[i]-A[i-1])
ans %= mod
print(ans)
``` | output | 1 | 14,844 | 16 | 29,689 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares lining up in a row, numbered 1 through N from left to right. Initially, all squares are white. We also have N-1 painting machines, numbered 1 through N-1. When operated, Machine i paints Square i and i+1 black.
Snuke will operate these machines one by one. The order in which he operates them is represented by a permutation of (1, 2, ..., N-1), P, which means that the i-th operated machine is Machine P_i.
Here, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P. Snuke has not decided what permutation P to use, but he is interested in the scores of possible permutations. Find the sum of the scores over all possible permutations for him. Since this can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 2 \leq N \leq 10^6
Input
Input is given from Standard Input in the following format:
N
Output
Print the sum of the scores over all possible permutations, modulo 10^9+7.
Examples
Input
4
Output
16
Input
2
Output
1
Input
5
Output
84
Input
100000
Output
341429644 | instruction | 0 | 14,845 | 16 | 29,690 |
"Correct Solution:
```
import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")
n = int(input())
M = 10**9+7 # 出力の制限
N = n+3 # 必要なテーブルサイズ
g1 = [None] * (N+1) # 元テーブル
g2 = [None] * (N+1) #逆元テーブル
inverse = [None] * (N+1) #逆元テーブル計算用テーブル
g1[0] = g1[1] = g2[0] = g2[1] = 1
inverse[0], inverse[1] = [0, 1]
for i in range( 2, N + 1 ):
g1[i] = ( g1[i-1] * i ) % M
inverse[i] = ( -inverse[M % i] * (M//i) ) % M # ai+b==0 mod M <=> i==-b*a^(-1) <=> i^(-1)==-b^(-1)*aより
g2[i] = (g2[i-1] * inverse[i]) % M
def cmb(n, r, M):
if ( r<0 or r>n ):
return 0
r = min(r, n-r)
return (g1[n] * g2[r] * g2[n-r]) % M
ans = 0
prev = 0
# s = 0
for i in range((n+1)//2, n):
tmp = (cmb(i-1, n-i-1, M) * g1[i] * g1[n-1-i])
ans += tmp
# ans += i*(tmp-prev)
prev = tmp
# print(i, tmp, g1[i], g1[n-1-i])
ans %= M
i = n-1
ans = (i+1) * (cmb(i-1, n-i-1, M) * g1[i] * g1[n-1-i]) - ans
ans %= M
print(ans)
``` | output | 1 | 14,845 | 16 | 29,691 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares lining up in a row, numbered 1 through N from left to right. Initially, all squares are white. We also have N-1 painting machines, numbered 1 through N-1. When operated, Machine i paints Square i and i+1 black.
Snuke will operate these machines one by one. The order in which he operates them is represented by a permutation of (1, 2, ..., N-1), P, which means that the i-th operated machine is Machine P_i.
Here, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P. Snuke has not decided what permutation P to use, but he is interested in the scores of possible permutations. Find the sum of the scores over all possible permutations for him. Since this can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 2 \leq N \leq 10^6
Input
Input is given from Standard Input in the following format:
N
Output
Print the sum of the scores over all possible permutations, modulo 10^9+7.
Examples
Input
4
Output
16
Input
2
Output
1
Input
5
Output
84
Input
100000
Output
341429644 | instruction | 0 | 14,846 | 16 | 29,692 |
"Correct Solution:
```
import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")
n = int(input())
M = 10**9+7 # 出力の制限
N = n+3 # 必要なテーブルサイズ
g1 = [None] * (N+1) # 元テーブル
g2 = [None] * (N+1) #逆元テーブル
inverse = [None] * (N+1) #逆元テーブル計算用テーブル
g1[0] = g1[1] = g2[0] = g2[1] = 1
inverse[0], inverse[1] = [0, 1]
for i in range( 2, N + 1 ):
g1[i] = ( g1[i-1] * i ) % M
inverse[i] = ( -inverse[M % i] * (M//i) ) % M # ai+b==0 mod M <=> i==-b*a^(-1) <=> i^(-1)==-b^(-1)*aより
g2[i] = (g2[i-1] * inverse[i]) % M
def cmb(n, r, M):
if ( r<0 or r>n ):
return 0
r = min(r, n-r)
return (g1[n] * g2[r] * g2[n-r]) % M
ans = 0
prev = 0
# s = 0
for i in range((n+1)//2, n):
tmp = (cmb(i-1, n-i-1, M) * g1[i] * g1[n-1-i])
ans += i*(tmp-prev)
prev = tmp
# print(i, tmp, g1[i], g1[n-1-i])
ans %= M
print(ans)
``` | output | 1 | 14,846 | 16 | 29,693 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares lining up in a row, numbered 1 through N from left to right. Initially, all squares are white. We also have N-1 painting machines, numbered 1 through N-1. When operated, Machine i paints Square i and i+1 black.
Snuke will operate these machines one by one. The order in which he operates them is represented by a permutation of (1, 2, ..., N-1), P, which means that the i-th operated machine is Machine P_i.
Here, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P. Snuke has not decided what permutation P to use, but he is interested in the scores of possible permutations. Find the sum of the scores over all possible permutations for him. Since this can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 2 \leq N \leq 10^6
Input
Input is given from Standard Input in the following format:
N
Output
Print the sum of the scores over all possible permutations, modulo 10^9+7.
Examples
Input
4
Output
16
Input
2
Output
1
Input
5
Output
84
Input
100000
Output
341429644 | instruction | 0 | 14,848 | 16 | 29,696 |
"Correct Solution:
```
def inv(x, mod = 10 ** 9 + 7):
return pow(x, mod - 2, mod)
mod = 10 ** 9 + 7
N = int(input())
fact = [1]
for i in range(1, N):
fact.append(fact[-1] * i % mod)
inv_fact = [inv(fact[-1])]
for i in reversed(range(1, N)):
inv_fact.append(inv_fact[-1] * i % mod)
inv_fact = inv_fact[::-1]
ans = prev = 0
for k in range((N + 1) // 2, N):
cnt = fact[k - 1] * inv_fact[k * 2 - N] % mod * fact[k] % mod
ans += (cnt - prev + mod) * k
ans %= mod
prev = cnt
print(ans)
``` | output | 1 | 14,848 | 16 | 29,697 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares lining up in a row, numbered 1 through N from left to right. Initially, all squares are white. We also have N-1 painting machines, numbered 1 through N-1. When operated, Machine i paints Square i and i+1 black.
Snuke will operate these machines one by one. The order in which he operates them is represented by a permutation of (1, 2, ..., N-1), P, which means that the i-th operated machine is Machine P_i.
Here, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P. Snuke has not decided what permutation P to use, but he is interested in the scores of possible permutations. Find the sum of the scores over all possible permutations for him. Since this can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 2 \leq N \leq 10^6
Input
Input is given from Standard Input in the following format:
N
Output
Print the sum of the scores over all possible permutations, modulo 10^9+7.
Examples
Input
4
Output
16
Input
2
Output
1
Input
5
Output
84
Input
100000
Output
341429644 | instruction | 0 | 14,849 | 16 | 29,698 |
"Correct Solution:
```
n=int(input())
mod=10**9+7
fra=[1]*(n+2)
inv=[1]*(n+2)
t=1
for i in range(1,n+2):
t*=i
t%=mod
fra[i]=t
t=pow(fra[n+1],mod-2,mod)
for i in range(n+1,0,-1):
inv[i]=t
t*=i
t%=mod
ans=fra[n]
for i in range((n+1)//2,n):
ans-=fra[i-1]*inv[2*i-n]*fra[i]%mod
ans%=mod
print(ans)
``` | output | 1 | 14,849 | 16 | 29,699 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares lining up in a row, numbered 1 through N from left to right. Initially, all squares are white. We also have N-1 painting machines, numbered 1 through N-1. When operated, Machine i paints Square i and i+1 black.
Snuke will operate these machines one by one. The order in which he operates them is represented by a permutation of (1, 2, ..., N-1), P, which means that the i-th operated machine is Machine P_i.
Here, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P. Snuke has not decided what permutation P to use, but he is interested in the scores of possible permutations. Find the sum of the scores over all possible permutations for him. Since this can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 2 \leq N \leq 10^6
Input
Input is given from Standard Input in the following format:
N
Output
Print the sum of the scores over all possible permutations, modulo 10^9+7.
Examples
Input
4
Output
16
Input
2
Output
1
Input
5
Output
84
Input
100000
Output
341429644 | instruction | 0 | 14,850 | 16 | 29,700 |
"Correct Solution:
```
n = int(input())
fn,fk,mod = [1]*n,[1]*n,10**9+7
for i in range(n-1): fn[i+1] = (fn[i]*(i+2))%mod
def power(n,k):
if k==1: return n
elif k%2==0: return power((n**2)%mod,k//2)
else: return (n*power(n,k-1))%mod
def comb(n,k):
if n<k or k<0: return 0
elif k==0 or n==k: return 1
else: return (((fn[n-1]*fk[n-k-1])%mod)*fk[k-1])%mod
fk[-1] = power(fn[-1],mod-2)
for i in range(2,n+1): fk[-i] = (fk[-i+1]*(n+2-i))%mod
fn.append(1)
ans = fn[n-2]*(n-1)
for i in range(n-2,(n-1)//2,-1):
ans = (ans-comb(i-1,n-i-1)*fn[i-1]*fn[n-i-2])%mod
print(ans)
``` | output | 1 | 14,850 | 16 | 29,701 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares lining up in a row, numbered 1 through N from left to right. Initially, all squares are white. We also have N-1 painting machines, numbered 1 through N-1. When operated, Machine i paints Square i and i+1 black.
Snuke will operate these machines one by one. The order in which he operates them is represented by a permutation of (1, 2, ..., N-1), P, which means that the i-th operated machine is Machine P_i.
Here, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P. Snuke has not decided what permutation P to use, but he is interested in the scores of possible permutations. Find the sum of the scores over all possible permutations for him. Since this can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 2 \leq N \leq 10^6
Input
Input is given from Standard Input in the following format:
N
Output
Print the sum of the scores over all possible permutations, modulo 10^9+7.
Examples
Input
4
Output
16
Input
2
Output
1
Input
5
Output
84
Input
100000
Output
341429644
Submitted Solution:
```
# seishin.py
N = int(input())
MOD = 10**9 + 7
fact = [1]*(N+1)
rfact = [1]*(N+1)
for i in range(1, N+1):
fact[i] = r = i*fact[i-1] % MOD
rfact[i] = pow(r, MOD-2, MOD)
ans = cnt = 0
for K in range((N+1)//2, N):
res = fact[K]*fact[K-1]*rfact[2*K-N] % MOD
ans += (res - cnt) * K % MOD
cnt = res
ans %= MOD
print(ans)
``` | instruction | 0 | 14,852 | 16 | 29,704 |
Yes | output | 1 | 14,852 | 16 | 29,705 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares lining up in a row, numbered 1 through N from left to right. Initially, all squares are white. We also have N-1 painting machines, numbered 1 through N-1. When operated, Machine i paints Square i and i+1 black.
Snuke will operate these machines one by one. The order in which he operates them is represented by a permutation of (1, 2, ..., N-1), P, which means that the i-th operated machine is Machine P_i.
Here, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P. Snuke has not decided what permutation P to use, but he is interested in the scores of possible permutations. Find the sum of the scores over all possible permutations for him. Since this can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 2 \leq N \leq 10^6
Input
Input is given from Standard Input in the following format:
N
Output
Print the sum of the scores over all possible permutations, modulo 10^9+7.
Examples
Input
4
Output
16
Input
2
Output
1
Input
5
Output
84
Input
100000
Output
341429644
Submitted Solution:
```
characteristic=10**9+7
def plus(input1,input2):
return (input1+input2)%characteristic
def minus(input1,input2):
return (input1-input2)%characteristic
def times(input1,input2):
return (input1*input2)%characteristic
def exponen(input1,input2):
return pow(input1,input2,characteristic)
def divide(input1,input2):
return times(input1,exponen(input2,characteristic-2))
N=int(input())
Fact=[1 for i in range(N+1)]
Finv=[1 for i in range(N+1)]
for i in range(1,N+1):
Fact[i]=times(Fact[i-1],i)
Finv[i]=divide(1,Fact[i])
ans=0
SGL=[0 for i in range(N)]
for K in range(N):
if 2*K-N<0:
continue
SGL[K]=times(times(Fact[K],Finv[2*K-N]),Fact[K-1])
for K in range(1,N):
ans=plus(ans,times(SGL[K]-SGL[K-1],K))
print(ans)
``` | instruction | 0 | 14,853 | 16 | 29,706 |
Yes | output | 1 | 14,853 | 16 | 29,707 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares lining up in a row, numbered 1 through N from left to right. Initially, all squares are white. We also have N-1 painting machines, numbered 1 through N-1. When operated, Machine i paints Square i and i+1 black.
Snuke will operate these machines one by one. The order in which he operates them is represented by a permutation of (1, 2, ..., N-1), P, which means that the i-th operated machine is Machine P_i.
Here, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P. Snuke has not decided what permutation P to use, but he is interested in the scores of possible permutations. Find the sum of the scores over all possible permutations for him. Since this can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 2 \leq N \leq 10^6
Input
Input is given from Standard Input in the following format:
N
Output
Print the sum of the scores over all possible permutations, modulo 10^9+7.
Examples
Input
4
Output
16
Input
2
Output
1
Input
5
Output
84
Input
100000
Output
341429644
Submitted Solution:
```
P=10**9+7
def egcd(a, b):
(x, lastx) = (0, 1)
(y, lasty) = (1, 0)
while b != 0:
q = a // b
(a, b) = (b, a % b)
(x, lastx) = (lastx - q * x, x)
(y, lasty) = (lasty - q * y, y)
return (lastx, lasty, a)
def inv(x):
return egcd(x,P)[0]
N=int(input())
Fact=[0 for i in range(N+1)]
Finv=[0 for i in range(N+1)]
Fact[0]=1
Finv[0]=1
for i in range(N):
Fact[i+1]=((i+1)*Fact[i])%P
Finv[i+1]=(Finv[i]*inv(i+1))%P
SGN=[0 for i in range(N)]
ans=0
for k in range(N):
if 2*k-N>=0:
SGN[k]=(((Fact[k-1]*Fact[k])%P)*Finv[2*k-N])%P
ans=(ans+k*(SGN[k]-SGN[k-1]))%P
print(ans)
``` | instruction | 0 | 14,854 | 16 | 29,708 |
Yes | output | 1 | 14,854 | 16 | 29,709 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares lining up in a row, numbered 1 through N from left to right. Initially, all squares are white. We also have N-1 painting machines, numbered 1 through N-1. When operated, Machine i paints Square i and i+1 black.
Snuke will operate these machines one by one. The order in which he operates them is represented by a permutation of (1, 2, ..., N-1), P, which means that the i-th operated machine is Machine P_i.
Here, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P. Snuke has not decided what permutation P to use, but he is interested in the scores of possible permutations. Find the sum of the scores over all possible permutations for him. Since this can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 2 \leq N \leq 10^6
Input
Input is given from Standard Input in the following format:
N
Output
Print the sum of the scores over all possible permutations, modulo 10^9+7.
Examples
Input
4
Output
16
Input
2
Output
1
Input
5
Output
84
Input
100000
Output
341429644
Submitted Solution:
```
N = int(input()) - 1
LARGE = 10**9+7
def ex_euclid(x, y):
c0, c1 = x, y
a0, a1 = 1, 0
b0, b1 = 0, 1
while c1 != 0:
m = c0 % c1
q = c0 // c1
c0, c1 = c1, m
a0, a1 = a1, (a0 - q * a1)
b0, b1 = b1, (b0 - q * b1)
return c0, a0, b0
# precompute
fac_list = [1]*(N+1)
fac = 1
for i in range(1, N+1):
fac = (fac * i) % LARGE
fac_list[i] = fac
fac_inv_list = [1]*(N+1)
for i in range(N+1):
fac_inv_list[i] = pow(fac_list[i], LARGE-2, LARGE)
def nCr(n, r):
return (((fac_list[n] * fac_inv_list[r]) % LARGE) * fac_inv_list[n-r]) % LARGE
def pat(n, r):
return (((fac_list[n] * fac_inv_list[r]) % LARGE) * fac_inv_list[n-r]) % LARGE
pat = 0
score = 0
for k in range(N+1):
if k-1 >= N-k:
res = (((fac_list[k-1]*fac_list[k]) % LARGE) * fac_inv_list[k-1-N+k]) % LARGE
score = (score + (res - pat) * k) % LARGE
# print(k, pat, res)
pat = res
print(score)
``` | instruction | 0 | 14,855 | 16 | 29,710 |
Yes | output | 1 | 14,855 | 16 | 29,711 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares lining up in a row, numbered 1 through N from left to right. Initially, all squares are white. We also have N-1 painting machines, numbered 1 through N-1. When operated, Machine i paints Square i and i+1 black.
Snuke will operate these machines one by one. The order in which he operates them is represented by a permutation of (1, 2, ..., N-1), P, which means that the i-th operated machine is Machine P_i.
Here, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P. Snuke has not decided what permutation P to use, but he is interested in the scores of possible permutations. Find the sum of the scores over all possible permutations for him. Since this can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 2 \leq N \leq 10^6
Input
Input is given from Standard Input in the following format:
N
Output
Print the sum of the scores over all possible permutations, modulo 10^9+7.
Examples
Input
4
Output
16
Input
2
Output
1
Input
5
Output
84
Input
100000
Output
341429644
Submitted Solution:
```
def permutations(L):
if L == []:
return [[]]
else:
return [[h]+t for i,h in enumerate(L)
for t in permutations(L[:i]+L[i+1:])]
n = int(input())
perm_list = []
for i in range(n - 1):
perm_list.append(str(i+1))
perm_result = permutations(perm_list)
#print(perm_result)
score = 0
for p in perm_result:
m = [0] * n
for j in range(len(p)):
m[int(p[j])-1] = 1
m[int(p[j])] = 1
mini_score = 0
for i in range(n-1):
mini_score += m[i]
if mini_score == n-1:
score += j+1
break
print(score)
``` | instruction | 0 | 14,856 | 16 | 29,712 |
No | output | 1 | 14,856 | 16 | 29,713 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares lining up in a row, numbered 1 through N from left to right. Initially, all squares are white. We also have N-1 painting machines, numbered 1 through N-1. When operated, Machine i paints Square i and i+1 black.
Snuke will operate these machines one by one. The order in which he operates them is represented by a permutation of (1, 2, ..., N-1), P, which means that the i-th operated machine is Machine P_i.
Here, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P. Snuke has not decided what permutation P to use, but he is interested in the scores of possible permutations. Find the sum of the scores over all possible permutations for him. Since this can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 2 \leq N \leq 10^6
Input
Input is given from Standard Input in the following format:
N
Output
Print the sum of the scores over all possible permutations, modulo 10^9+7.
Examples
Input
4
Output
16
Input
2
Output
1
Input
5
Output
84
Input
100000
Output
341429644
Submitted Solution:
```
n = int(input())
p = 10**9 + 7
def fact(n, p):
n_ = [1]
for i in range(1, n+1):
n_.append((n_[-1]*i) % p)
return n
def invfact(n, f, p):
m = [pow(f[n], p-2, p)]
for i in range(n, 0, -1):
m.append(m[-1] * i % p)
return m
ans = 0
m = n - 1
f = fact(m, p)
rf = invfact(m, f, p)
rf.reverse()
perm = 0
for k in range((n+1)//2, n):
perm_ = f[k-1] * rf[2*k-n] %p * f[k] % p
ans += (perm_ - perm) %p * k % p
ans %= p
perm = perm_
print(ans)
``` | instruction | 0 | 14,857 | 16 | 29,714 |
No | output | 1 | 14,857 | 16 | 29,715 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares lining up in a row, numbered 1 through N from left to right. Initially, all squares are white. We also have N-1 painting machines, numbered 1 through N-1. When operated, Machine i paints Square i and i+1 black.
Snuke will operate these machines one by one. The order in which he operates them is represented by a permutation of (1, 2, ..., N-1), P, which means that the i-th operated machine is Machine P_i.
Here, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P. Snuke has not decided what permutation P to use, but he is interested in the scores of possible permutations. Find the sum of the scores over all possible permutations for him. Since this can be extremely large, compute the sum modulo 10^9+7.
Constraints
* 2 \leq N \leq 10^6
Input
Input is given from Standard Input in the following format:
N
Output
Print the sum of the scores over all possible permutations, modulo 10^9+7.
Examples
Input
4
Output
16
Input
2
Output
1
Input
5
Output
84
Input
100000
Output
341429644
Submitted Solution:
```
n = int(input())
p = 10**9 + 7
# def fact(n, p):
# n_ = 1
# yield n_
# for i in range(1, n+1):
# n_ = (n_*i) % p
# yield n_
# def invfact(n, f, p):
# m = pow(f[n], p-2, p)
# yield m
# for i in range(n, 0, -1):
# m = m * i % p
# yield m
def fact(n, p):
n_ = [1]
for i in range(1, n+1):
n_.append((n_[-1]*i) % p)
return n
def invfact(n, f, p):
m = [pow(f[n], p-2, p)]
for i in range(n, 0, -1):
m.append(m[-1] * i % p)
return m
ans = 0
m = n - 1
f = fact(m, p)
rf = invfact(m, f, p)
rf.reverse()
perm = 0
for k in range((n+1)//2, n):
perm_ = f[k-1] * rf[2*k-n] %p * f[k] % p
ans += (perm_ - perm) %p * k % p
ans %= p
perm = perm_
print(ans)
``` | instruction | 0 | 14,859 | 16 | 29,718 |
No | output | 1 | 14,859 | 16 | 29,719 |
Provide a correct Python 3 solution for this coding contest problem.
Let N be a positive integer.
There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}). Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements. Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').
Find the maximum possible score of a'.
Constraints
* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{3N}
Output
Print the maximum possible score of a'.
Examples
Input
2
3 1 4 1 5 9
Output
1
Input
1
1 2 3
Output
-1
Input
3
8 2 2 7 4 6 5 3 8
Output
5 | instruction | 0 | 15,812 | 16 | 31,624 |
"Correct Solution:
```
import heapq
N = int(input())
a = list(map(int, input().split()))
heap_left = []
left = 0
for i in range(N):
left += a[i]
heapq.heappush(heap_left, a[i])
lst_left = [left]
for i in range(N, 2 * N):
tmp = heapq.heappushpop(heap_left, a[i])
left = left - tmp + a[i]
lst_left += [left]
heap_right = []
right = 0
for i in range(2 * N, 3 * N):
right += a[i]
heapq.heappush(heap_right, -1 * a[i])
lst_right = [right]
for i in range(2 * N -1, N-1, -1):
tmp = heapq.heappushpop(heap_right, -1 * a[i])
right = right - (-1 * tmp) + a[i]
lst_right += [right]
# print (lst_left)
# print (lst_right)
ans = -1 * 10 ** 20
for i in range(N+1):
# print (lst_left[i], lst_right[-(i+1)])
ans = max(ans, lst_left[i]-lst_right[-(i+1)])
print (ans)
``` | output | 1 | 15,812 | 16 | 31,625 |
Provide a correct Python 3 solution for this coding contest problem.
Let N be a positive integer.
There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}). Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements. Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').
Find the maximum possible score of a'.
Constraints
* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{3N}
Output
Print the maximum possible score of a'.
Examples
Input
2
3 1 4 1 5 9
Output
1
Input
1
1 2 3
Output
-1
Input
3
8 2 2 7 4 6 5 3 8
Output
5 | instruction | 0 | 15,813 | 16 | 31,626 |
"Correct Solution:
```
import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda :sys.stdin.readline().rstrip()
from heapq import heapify,heappop,heappush
def resolve():
n=int(input())
A=list(map(int,input().split()))
P=[None]*(n+1); S=[None]*(n+1)
# prefix
Q=A[:n]
P[0]=sum(Q)
heapify(Q)
for i in range(1,n+1):
a=heappop(Q)
b=A[n+i-1]
P[i]=P[i-1]-a+max(a,b)
heappush(Q,max(a,b))
# suffix
Q=[-a for a in A[2*n:]]
S[-1]=sum(Q)
heapify(Q)
for i in range(n-1,-1,-1):
a=heappop(Q)
b=-A[n+i]
S[i]=S[i+1]-a+max(a,b)
heappush(Q,max(a,b))
print(max(*(p+s for p,s in zip(P,S))))
resolve()
``` | output | 1 | 15,813 | 16 | 31,627 |
Provide a correct Python 3 solution for this coding contest problem.
Let N be a positive integer.
There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}). Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements. Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').
Find the maximum possible score of a'.
Constraints
* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{3N}
Output
Print the maximum possible score of a'.
Examples
Input
2
3 1 4 1 5 9
Output
1
Input
1
1 2 3
Output
-1
Input
3
8 2 2 7 4 6 5 3 8
Output
5 | instruction | 0 | 15,814 | 16 | 31,628 |
"Correct Solution:
```
import heapq
n=int(input())
a1=[]
b1=[]
a2=[]
b2=[]
s=input().split()
for i in range(3*n):
if i<n:
a1.append(int(s[i]))
elif i>=2*n:
b1.append(-int(s[i]))
else:
a2.append(int(s[i]))
b2.append(-int(s[3*n-i-1]))
suma=[sum(a1)]
sumb=[sum(b1)]
heapq.heapify(a1)
heapq.heapify(b1)
for i in range(0,n):
heapq.heappush(a1,a2[i])
k=heapq.heappop(a1)
l=suma[-1]
suma.append(l+a2[i]-k)
for i in range(0,n):
heapq.heappush(b1,b2[i])
k=heapq.heappop(b1)
l=sumb[-1]
sumb.append(l+b2[i]-k)
ma=-1000000000000000
for i in range(n+1):
ma=max(ma,suma[i]+sumb[-i-1])
print(ma)
``` | output | 1 | 15,814 | 16 | 31,629 |
Provide a correct Python 3 solution for this coding contest problem.
Let N be a positive integer.
There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}). Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements. Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').
Find the maximum possible score of a'.
Constraints
* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{3N}
Output
Print the maximum possible score of a'.
Examples
Input
2
3 1 4 1 5 9
Output
1
Input
1
1 2 3
Output
-1
Input
3
8 2 2 7 4 6 5 3 8
Output
5 | instruction | 0 | 15,815 | 16 | 31,630 |
"Correct Solution:
```
import sys
from heapq import *
n, *a = map(int, sys.stdin.read().split())
def optimize(arr):
res = arr[:n]
heapify(res)
sum_arr = [sum(res)]
for x in arr[n:]:
y = heappop(res)
heappush(res, max(x, y))
sum_arr.append(sum_arr[-1] + max(0, x - y))
return sum_arr
def main():
left = a[:n*2]
right = [-x for x in a[n:]][::-1]
sum_left = optimize(left)
sum_right = optimize(right)
res = []
for i in range(n+1):
res.append(sum_left[i] + sum_right[n-i])
ans = max(res)
return ans
if __name__ == '__main__':
ans = main()
print(ans)
``` | output | 1 | 15,815 | 16 | 31,631 |
Provide a correct Python 3 solution for this coding contest problem.
Let N be a positive integer.
There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}). Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements. Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').
Find the maximum possible score of a'.
Constraints
* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{3N}
Output
Print the maximum possible score of a'.
Examples
Input
2
3 1 4 1 5 9
Output
1
Input
1
1 2 3
Output
-1
Input
3
8 2 2 7 4 6 5 3 8
Output
5 | instruction | 0 | 15,816 | 16 | 31,632 |
"Correct Solution:
```
import heapq
N = int(input())
A = list(map(int, input().split()))
R = A[:N]
B = [-a for a in A[2 * N:]]
heapq.heapify(R)
heapq.heapify(B)
R_sum = [sum(R)]
B_sum = [sum(B)]
for i in range(N, 2 * N):
heapq.heappush(R, A[i])
q = heapq.heappop(R)
R_sum.append(max(R_sum[-1], R_sum[-1] + A[i] - q))
for i in range(2 * N - 1, N - 1, -1):
heapq.heappush(B, -A[i])
q = heapq.heappop(B)
B_sum.append(max(B_sum[-1], B_sum[-1] - A[i] - q))
num = -float("inf")
for p, q in zip(R_sum, B_sum[::-1]):
num = max(num, p + q)
print(num)
``` | output | 1 | 15,816 | 16 | 31,633 |
Provide a correct Python 3 solution for this coding contest problem.
Let N be a positive integer.
There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}). Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements. Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').
Find the maximum possible score of a'.
Constraints
* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{3N}
Output
Print the maximum possible score of a'.
Examples
Input
2
3 1 4 1 5 9
Output
1
Input
1
1 2 3
Output
-1
Input
3
8 2 2 7 4 6 5 3 8
Output
5 | instruction | 0 | 15,817 | 16 | 31,634 |
"Correct Solution:
```
from heapq import *
n = int(input())
a = list(map(int, input().split()))
left = a[:n]
right = a[2*n:]
heapify(left)
l = [sum(left)]
r = [sum(right)]
sl = sum(left)
sr = sum(right)
for i in range(n):
k = heappop(left)
sl -= k
heappush(left, max(k, a[n+i]))
sl += max(k, a[n+i])
l.append(sl)
right = [-i for i in right]
heapify(right)
for i in range(n):
k = -heappop(right)
sr -= k
mini = min(k, a[2*n-1-i])
heappush(right, -mini)
sr += mini
r.append(sr)
r.reverse()
ans = -10**15
for i in range(n+1):
ans = max(l[i] - r[i], ans)
print(ans)
``` | output | 1 | 15,817 | 16 | 31,635 |
Provide a correct Python 3 solution for this coding contest problem.
Let N be a positive integer.
There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}). Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements. Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').
Find the maximum possible score of a'.
Constraints
* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{3N}
Output
Print the maximum possible score of a'.
Examples
Input
2
3 1 4 1 5 9
Output
1
Input
1
1 2 3
Output
-1
Input
3
8 2 2 7 4 6 5 3 8
Output
5 | instruction | 0 | 15,818 | 16 | 31,636 |
"Correct Solution:
```
import heapq
import sys
input = sys.stdin.readline
def solve():
n = int(input())
a = list(int(i) for i in input().split())
an = []
a2n = a[n:2*n]
a3n = []
for i in range(n):
heapq.heappush(an,a[i])
heapq.heappush(a3n,-1*a[i+2*n])
tmpsuman = sum(an)
tmpsuma3n = -1*sum(a3n)
suman = [tmpsuman]
suma3n = [tmpsuma3n]
for i in range(n):
tmp = a2n[i]
tmpsuman += tmp
heapq.heappush(an,tmp)
tmpsuman -= heapq.heappop(an)
suman.append(tmpsuman)
tmp = a2n[n-i-1]
tmpsuma3n += tmp
heapq.heappush(a3n,-1*tmp)
tmpsuma3n -= -1*heapq.heappop(a3n)
suma3n.append(tmpsuma3n)
ans = -1*float("INF")
for i in range(n+1):
ans = max(ans,suman[i]-suma3n[n-i])
print(ans)
solve()
``` | output | 1 | 15,818 | 16 | 31,637 |
Provide a correct Python 3 solution for this coding contest problem.
Let N be a positive integer.
There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}). Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements. Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').
Find the maximum possible score of a'.
Constraints
* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{3N}
Output
Print the maximum possible score of a'.
Examples
Input
2
3 1 4 1 5 9
Output
1
Input
1
1 2 3
Output
-1
Input
3
8 2 2 7 4 6 5 3 8
Output
5 | instruction | 0 | 15,819 | 16 | 31,638 |
"Correct Solution:
```
import heapq
n = int(input())
a = list(map(int, input().split()))
a1 = a[:n]
heapq.heapify(a1)
a1_sum = sum(a1)
a1_sums = [a1_sum]
for i in range(n, 2*n):
a1_min = heapq.heappop(a1) # pop the smallest value from a1
if a[i] > a1_min:
heapq.heappush(a1, a[i])
a1_sum = a1_sum - a1_min + a[i]
else:
heapq.heappush(a1, a1_min)
a1_sums.append(a1_sum)
a2 = a[-n:]
a2_sum = sum(a2)
a2_sums = [a2_sum]
a2_inv = [-aa for aa in a2]
heapq.heapify(a2_inv)
for i in range(2*n-1, n-1, -1):
a2_max = -heapq.heappop(a2_inv) # pop the largest value from a2
if a[i] < a2_max:
heapq.heappush(a2_inv, -a[i])
a2_sum = a2_sum - a2_max + a[i]
else:
heapq.heappush(a2_inv, -a2_max)
a2_sums.append(a2_sum)
a2_sums = a2_sums[::-1] # reverse order
ans = a1_sums[0] - a2_sums[0]
for a1_s, a2_s in zip(a1_sums, a2_sums):
ans = max(ans, a1_s-a2_s)
print(ans)
``` | output | 1 | 15,819 | 16 | 31,639 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let N be a positive integer.
There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}). Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements. Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').
Find the maximum possible score of a'.
Constraints
* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{3N}
Output
Print the maximum possible score of a'.
Examples
Input
2
3 1 4 1 5 9
Output
1
Input
1
1 2 3
Output
-1
Input
3
8 2 2 7 4 6 5 3 8
Output
5
Submitted Solution:
```
def f(a):
s=0;q=[]
for i in range(n):s+=a[i];heappush(q,a[i])
r=[s]
for i in range(n,2*n):s+=a[i];s-=heappushpop(q,a[i]);r+=[s]
return r
import sys;from heapq import*;n,*a=list(map(int,sys.stdin.read().split()));print(max(map(sum,zip(f(a),list(reversed(f(list(reversed([-e for e in a])))))))))
``` | instruction | 0 | 15,820 | 16 | 31,640 |
Yes | output | 1 | 15,820 | 16 | 31,641 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let N be a positive integer.
There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}). Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements. Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').
Find the maximum possible score of a'.
Constraints
* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{3N}
Output
Print the maximum possible score of a'.
Examples
Input
2
3 1 4 1 5 9
Output
1
Input
1
1 2 3
Output
-1
Input
3
8 2 2 7 4 6 5 3 8
Output
5
Submitted Solution:
```
import heapq
import bisect
n = int(input())
a = list(map(int, input().split()))
first_que = [a[i] for i in range(n)]
first_sum = sum(first_que)
heapq.heapify(first_que)
latter_que = [a[i] * -1 for i in range(2*n,3*n)]
latter_sum = sum(latter_que) * -1
heapq.heapify(latter_que)
ans = [0 for i in range(n+1)]
ans[0] = first_sum
for i in range(n,2*n):
heapq.heappush(first_que, a[i])
p = heapq.heappop(first_que)
first_sum += (a[i] - p)
ans[i-n+1] = first_sum
ans[-1] -= latter_sum
for i in range(2*n-1,n-1,-1):
heapq.heappush(latter_que,a[i]*(-1))
p = heapq.heappop(latter_que) * (-1)
latter_sum += (a[i] - p)
ans[i-n] -= latter_sum
print(max(ans))
``` | instruction | 0 | 15,821 | 16 | 31,642 |
Yes | output | 1 | 15,821 | 16 | 31,643 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let N be a positive integer.
There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}). Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements. Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').
Find the maximum possible score of a'.
Constraints
* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{3N}
Output
Print the maximum possible score of a'.
Examples
Input
2
3 1 4 1 5 9
Output
1
Input
1
1 2 3
Output
-1
Input
3
8 2 2 7 4 6 5 3 8
Output
5
Submitted Solution:
```
import heapq
n = int(input())
a = list(map(int,input().split()))
func = lambda p: p * (-1)
b = list(map(func,a[:]))
#print(a)
#print(b)
l = [0] * (3*n)
first = a[0:n]
second = b[2*n:3*n]
x = [0] * (3*n)
y = [0] * (3*n)
x[n-1] = sum(first)
y[2*n-1] = sum(second)
heapq.heapify(first)
heapq.heapify(second)
for i in range(n,2*n):
heapq.heappush(first, a[i])
s = first[0]
heapq.heappop(first)
x[i] = x[i-1] + a[i] - s
for i in range(n,2*n):
heapq.heappush(second, b[-i-1])
t = second[0]
heapq.heappop(second)
y[-i-2] = y[-i-1] + b[-i-1] - t
for i in range(n-1,2*n):
l[i] = x[i] + y[i]
#print(x)
#print(y)
#print(l)
print(max(l[n-1:2*n]))
``` | instruction | 0 | 15,822 | 16 | 31,644 |
Yes | output | 1 | 15,822 | 16 | 31,645 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let N be a positive integer.
There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}). Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements. Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').
Find the maximum possible score of a'.
Constraints
* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{3N}
Output
Print the maximum possible score of a'.
Examples
Input
2
3 1 4 1 5 9
Output
1
Input
1
1 2 3
Output
-1
Input
3
8 2 2 7 4 6 5 3 8
Output
5
Submitted Solution:
```
n=int(input())
import heapq
a=list(map(int,input().split()))
q=a[:n]
heapq.heapify(q)
x=[sum(q)]
for k in range(n,2*n):
v=heapq.heappushpop(q,a[k])
x.append(x[-1]+a[k]-v)
a=a[::-1]
q=[-v for v in a[:n]]
heapq.heapify(q)
y=[-sum(q)]
for k in range(n,2*n):
v=-heapq.heappushpop(q,-a[k])
y.append(y[-1]+a[k]-v)
print(max(v-w for v,w in zip(x,y[::-1])))
``` | instruction | 0 | 15,823 | 16 | 31,646 |
Yes | output | 1 | 15,823 | 16 | 31,647 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let N be a positive integer.
There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}). Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements. Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').
Find the maximum possible score of a'.
Constraints
* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{3N}
Output
Print the maximum possible score of a'.
Examples
Input
2
3 1 4 1 5 9
Output
1
Input
1
1 2 3
Output
-1
Input
3
8 2 2 7 4 6 5 3 8
Output
5
Submitted Solution:
```
import sys
fin = sys.stdin.readline
from heapq import heappop, heappush, heapify
class BSTNode(object):
"""A node in the vanilla BST tree."""
def __init__(self, parent, k):
"""Creates a node.
Args:
parent: The node's parent.
k: key of the node.
"""
self.key = k
self.parent = parent
self.left = None
self.right = None
def _str(self):
"""Internal method for ASCII art."""
label = str(self.key)
if self.left is None:
left_lines, left_pos, left_width = [], 0, 0
else:
left_lines, left_pos, left_width = self.left._str()
if self.right is None:
right_lines, right_pos, right_width = [], 0, 0
else:
right_lines, right_pos, right_width = self.right._str()
middle = max(right_pos + left_width - left_pos + 1, len(label), 2)
pos = left_pos + middle // 2
width = left_pos + middle + right_width - right_pos
while len(left_lines) < len(right_lines):
left_lines.append(' ' * left_width)
while len(right_lines) < len(left_lines):
right_lines.append(' ' * right_width)
if (middle - len(label)) % 2 == 1 and self.parent is not None and \
self is self.parent.left and len(label) < middle:
label += '.'
label = label.center(middle, '.')
if label[0] == '.': label = ' ' + label[1:]
if label[-1] == '.': label = label[:-1] + ' '
lines = [' ' * left_pos + label + ' ' * (right_width - right_pos),
' ' * left_pos + '/' + ' ' * (middle-2) +
'\\' + ' ' * (right_width - right_pos)] + \
[left_line + ' ' * (width - left_width - right_width) + right_line
for left_line, right_line in zip(left_lines, right_lines)]
return lines, pos, width
def __str__(self):
return '\n'.join(self._str()[0])
def find(self, k):
"""Finds and returns the node with key k from the subtree rooted at this
node.
Args:
k: The key of the node we want to find.
Returns:
The node with key k.
"""
if k == self.key:
return self
elif k < self.key:
if self.left is None:
return None
else:
return self.left.find(k)
else:
if self.right is None:
return None
else:
return self.right.find(k)
def find_min(self):
"""Finds the node with the minimum key in the subtree rooted at this
node.
Returns:
The node with the minimum key.
"""
current = self
while current.left is not None:
current = current.left
return current
def next_larger(self):
"""Returns the node with the next larger key (the successor) in the BST.
"""
if self.right is not None:
return self.right.find_min()
current = self
while current.parent is not None and current is current.parent.right:
current = current.parent
return current.parent
def insert(self, node):
"""Inserts a node into the subtree rooted at this node.
Args:
node: The node to be inserted.
"""
if node is None:
return
if node.key < self.key:
if self.left is None:
node.parent = self
self.left = node
else:
self.left.insert(node)
else:
if self.right is None:
node.parent = self
self.right = node
else:
self.right.insert(node)
def delete(self):
"""Deletes and returns this node from the BST."""
if self.left is None or self.right is None:
if self is self.parent.left:
self.parent.left = self.left or self.right
if self.parent.left is not None:
self.parent.left.parent = self.parent
else:
self.parent.right = self.left or self.right
if self.parent.right is not None:
self.parent.right.parent = self.parent
return self
else:
s = self.next_larger()
self.key, s.key = s.key, self.key
return s.delete()
def check_ri(self):
"""Checks the BST representation invariant around this node.
Raises an exception if the RI is violated.
"""
if self.left is not None:
if self.left.key > self.key:
raise RuntimeError("BST RI violated by a left node key")
if self.left.parent is not self:
raise RuntimeError("BST RI violated by a left node parent "
"pointer")
self.left.check_ri()
if self.right is not None:
if self.right.key < self.key:
raise RuntimeError("BST RI violated by a right node key")
if self.right.parent is not self:
raise RuntimeError("BST RI violated by a right node parent "
"pointer")
self.right.check_ri()
class MinBSTNode(BSTNode):
"""A BSTNode which is augmented to keep track of the node with the
minimum key in the subtree rooted at this node.
"""
def __init__(self, parent, key):
"""Creates a node.
Args:
parent: The node's parent.
k: key of the node.
"""
super(MinBSTNode, self).__init__(parent, key)
self.min = self
def find_min(self):
"""Finds the node with the minimum key in the subtree rooted at this
node.
Returns:
The node with the minimum key.
"""
return self.min
def insert(self, node):
"""Inserts a node into the subtree rooted at this node.
Args:
node: The node to be inserted.
"""
if node is None:
return
if node.key < self.key:
# Updates the min of this node if the inserted node has a smaller
# key.
if node.key < self.min.key:
self.min = node
if self.left is None:
node.parent = self
self.left = node
else:
self.left.insert(node)
else:
if self.right is None:
node.parent = self
self.right = node
else:
self.right.insert(node)
def delete(self):
"""Deletes this node itself.
Returns:
This node.
"""
if self.left is None or self.right is None:
if self is self.parent.left:
self.parent.left = self.left or self.right
if self.parent.left is not None:
self.parent.left.parent = self.parent
self.parent.min = self.parent.left.min
else:
self.parent.min = self.parent
# Propagates the changes upwards.
c = self.parent
while c.parent is not None and c is c.parent.left:
c.parent.min = c.min
c = c.parent
else:
self.parent.right = self.left or self.right
if self.parent.right is not None:
self.parent.right.parent = self.parent
return self
else:
s = self.next_larger()
self.key, s.key = s.key, self.key
return s.delete()
class BST(object):
"""A binary search tree."""
def __init__(self, klass = BSTNode):
"""Creates an empty BST.
Args:
klass (optional): The class of the node in the BST. Default to
BSTNode.
"""
self.root = None
self.klass = klass
def __str__(self):
if self.root is None: return '<empty tree>'
return str(self.root)
def find(self, k):
"""Finds and returns the node with key k from the subtree rooted at this
node.
Args:
k: The key of the node we want to find.
Returns:
The node with key k or None if the tree is empty.
"""
return self.root and self.root.find(k)
def find_min(self):
"""Returns the minimum node of this BST."""
return self.root and self.root.find_min()
def insert(self, k):
"""Inserts a node with key k into the subtree rooted at this node.
Args:
k: The key of the node to be inserted.
Returns:
The node inserted.
"""
node = self.klass(None, k)
if self.root is None:
# The root's parent is None.
self.root = node
else:
self.root.insert(node)
return node
def delete(self, k):
"""Deletes and returns a node with key k if it exists from the BST.
Args:
k: The key of the node that we want to delete.
Returns:
The deleted node with key k.
"""
node = self.find(k)
if node is None:
return None
if node is self.root:
pseudoroot = self.klass(None, 0)
pseudoroot.left = self.root
self.root.parent = pseudoroot
deleted = self.root.delete()
self.root = pseudoroot.left
if self.root is not None:
self.root.parent = None
return deleted
else:
return node.delete()
def next_larger(self, k):
"""Returns the node that contains the next larger (the successor) key in
the BST in relation to the node with key k.
Args:
k: The key of the node of which the successor is to be found.
Returns:
The successor node.
"""
node = self.find(k)
return node and node.next_larger()
def check_ri(self):
"""Checks the BST representation invariant.
Raises:
An exception if the RI is violated.
"""
if self.root is not None:
if self.root.parent is not None:
raise RuntimeError("BST RI violated by the root node's parent "
"pointer.")
self.root.check_ri()
class MinBST(BST):
"""An augmented BST that keeps track of the node with the minimum key."""
def __init__(self):
super(MinBST, self).__init__(MinBSTNode)
def height(node):
if node is None:
return -1
else:
return node.height
def update_height(node):
node.height = max(height(node.left), height(node.right)) + 1
class AVL(BST):
"""
AVL binary search tree implementation.
Supports insert, delete, find, find_min, next_larger each in O(lg n) time.
"""
def left_rotate(self, x):
y = x.right
y.parent = x.parent
if y.parent is None:
self.root = y
else:
if y.parent.left is x:
y.parent.left = y
elif y.parent.right is x:
y.parent.right = y
x.right = y.left
if x.right is not None:
x.right.parent = x
y.left = x
x.parent = y
update_height(x)
update_height(y)
def right_rotate(self, x):
y = x.left
y.parent = x.parent
if y.parent is None:
self.root = y
else:
if y.parent.left is x:
y.parent.left = y
elif y.parent.right is x:
y.parent.right = y
x.left = y.right
if x.left is not None:
x.left.parent = x
y.right = x
x.parent = y
update_height(x)
update_height(y)
def rebalance(self, node):
while node is not None:
update_height(node)
if height(node.left) >= 2 + height(node.right):
if height(node.left.left) >= height(node.left.right):
self.right_rotate(node)
else:
self.left_rotate(node.left)
self.right_rotate(node)
elif height(node.right) >= 2 + height(node.left):
if height(node.right.right) >= height(node.right.left):
self.left_rotate(node)
else:
self.right_rotate(node.right)
self.left_rotate(node)
node = node.parent
## find(k), find_min(), and next_larger(k) inherited from bst.BST
def insert(self, k):
"""Inserts a node with key k into the subtree rooted at this node.
This AVL version guarantees the balance property: h = O(lg n).
Args:
k: The key of the node to be inserted.
"""
node = super(AVL, self).insert(k)
self.rebalance(node)
def delete(self, k):
"""Deletes and returns a node with key k if it exists from the BST.
This AVL version guarantees the balance property: h = O(lg n).
Args:
k: The key of the node that we want to delete.
Returns:
The deleted node with key k.
"""
node = super(AVL, self).delete(k)
## node.parent is actually the old parent of the node,
## which is the first potentially out-of-balance node.
self.rebalance(node.parent)
N = int(fin())
a_list = [int(elem) for elem in fin().split()]
left, right = a_list[:N], a_list[N:]
thrown_away = [False] * (2 * N)
discarded_items = AVL(MinBSTNode)
# initialize
right_sum = sum(right)
for i, item in enumerate(right):
if i < N:
discarded_items.insert((item, i))
thrown_away[i] = True
right_sum -= item
else:
min_key = discarded_items.find_min().key
if item > min_key[0]:
discarded_items.delete(min_key)
old_item, old_idx = min_key
thrown_away[old_idx] = False
discarded_items.insert((item, i))
thrown_away[i] = True
right_sum += old_item - item
# move partitions and calculate a global maximum
left_sum = sum(left)
heapify(left)
max_score = left_sum - right_sum
for i, item in enumerate(right[:N]):
if not thrown_away[i]:
# update right
min_key = discarded_items.find_min().key
updated_item, updated_idx = min_key
discarded_items.delete(min_key)
right_sum += updated_item - item
thrown_away[updated_idx] = False
else:
# want to update discarded_items
discarded_items.delete((item, i))
# update left
if item > left[0]:
old_item = heappop(left)
heappush(left, item)
left_sum += item - old_item
max_score = max(max_score, left_sum - right_sum)
print(max_score)
``` | instruction | 0 | 15,824 | 16 | 31,648 |
No | output | 1 | 15,824 | 16 | 31,649 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let N be a positive integer.
There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}). Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements. Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').
Find the maximum possible score of a'.
Constraints
* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{3N}
Output
Print the maximum possible score of a'.
Examples
Input
2
3 1 4 1 5 9
Output
1
Input
1
1 2 3
Output
-1
Input
3
8 2 2 7 4 6 5 3 8
Output
5
Submitted Solution:
```
n=int(input())
a=list(map(int,input().split()))
import heapq as hq
f1=[0]*(3*n)
f1[n-1]=sum(a[:n])
h=a[:n]
hq.heapify(h)
su=f1[n-1]
for i in range(n,3*n):
cur=a[i]
x=hq.heappop(h)
if cur>x:
su-=x
su+=cur
hq.heappush(h,cur)
else:
hq.heappush(h,x)
f1[i]=su
f2=[0]*(3*n)
f2[2*n]=sum(a[2*n:])
su=f2[2*n]
h2=[]
hq.heapify(h2)
for i in a[2*n:]:
hq.heappush(h2,-i) #maxheap
for i in range(2*n-1,-1,-1):
cur=a[i]
x=-1*hq.heappop(h2)
if cur<x:
su-=x
su+=cur
hq.heappush(h2,cur)
else:
hq.heappush(h2,-x)
f2[i]=su
ans=-float('inf')
for i in range(n-1,2*n):
ans=max(ans,f1[i]-f2[i+1])
print(ans)
``` | instruction | 0 | 15,825 | 16 | 31,650 |
No | output | 1 | 15,825 | 16 | 31,651 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let N be a positive integer.
There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}). Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements. Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').
Find the maximum possible score of a'.
Constraints
* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{3N}
Output
Print the maximum possible score of a'.
Examples
Input
2
3 1 4 1 5 9
Output
1
Input
1
1 2 3
Output
-1
Input
3
8 2 2 7 4 6 5 3 8
Output
5
Submitted Solution:
```
N = int(input())
*A, = map(int,input().split())
q = []
for a in A[:N]:
heapq.heappush(q,a)
S1 = [sum(q)]
for a in A[N:N*2]:
if a>q[0]:
S1.append(S1[-1] + a - q[0])
heapq.heapreplace(q,a)
else:
S1.append(S1[-1])
q = []
for a in A[2*N:]:
heapq.heappush(q,-a)
S2 = [sum(q)]
for a in A[N:N*2][::-1]:
if a<-q[0]:
S2.append(S2[-1] - a - q[0])
heapq.heapreplace(q,-a)
else:
S2.append(S2[-1])
S2 = S2[::-1]
print(max(map(sum,zip(S1,S2))))
``` | instruction | 0 | 15,826 | 16 | 31,652 |
No | output | 1 | 15,826 | 16 | 31,653 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let N be a positive integer.
There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}). Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements. Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').
Find the maximum possible score of a'.
Constraints
* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_{3N}
Output
Print the maximum possible score of a'.
Examples
Input
2
3 1 4 1 5 9
Output
1
Input
1
1 2 3
Output
-1
Input
3
8 2 2 7 4 6 5 3 8
Output
5
Submitted Solution:
```
n=int(input())
l=list(map(int,input().split()))
a=(n*n)//2+1
b=sum(sorted(l[:a])[::-1][:-(a-n)])
c=sum(sorted(l[a:])[::-1][2*n-a:])
a-=1
d=sum(sorted(l[:a])[::-1][:-(a-n)])
e=sum(sorted(l[a:])[::-1][2*n-a:])
print(max(b-c,d-e))
``` | instruction | 0 | 15,827 | 16 | 31,654 |
No | output | 1 | 15,827 | 16 | 31,655 |
Provide a correct Python 3 solution for this coding contest problem.
There are N piles of candies on the table. The piles are numbered 1 through N. At first, pile i contains a_i candies.
Snuke and Ciel are playing a game. They take alternating turns. Snuke goes first. In each turn, the current player must perform one of the following two operations:
1. Choose a pile with the largest number of candies remaining, then eat all candies of that pile.
2. From each pile with one or more candies remaining, eat one candy.
The player who eats the last candy on the table, loses the game. Determine which player will win if both players play the game optimally.
Constraints
* 1≤N≤10^5
* 1≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 … a_N
Output
If Snuke will win, print `First`. If Ciel will win, print `Second`.
Examples
Input
2
1 3
Output
First
Input
3
1 2 1
Output
First
Input
3
1 2 3
Output
Second | instruction | 0 | 15,828 | 16 | 31,656 |
"Correct Solution:
```
n=int(input())
a=sorted(map(int,input().split()))[::-1]
j=i=0
for x in range(n):i+=a[i]>i;j+=a[j]>=i
print('SFeicrosntd'[(a[i-1]^i|j^i)&1::2])
``` | output | 1 | 15,828 | 16 | 31,657 |
Provide a correct Python 3 solution for this coding contest problem.
There are N piles of candies on the table. The piles are numbered 1 through N. At first, pile i contains a_i candies.
Snuke and Ciel are playing a game. They take alternating turns. Snuke goes first. In each turn, the current player must perform one of the following two operations:
1. Choose a pile with the largest number of candies remaining, then eat all candies of that pile.
2. From each pile with one or more candies remaining, eat one candy.
The player who eats the last candy on the table, loses the game. Determine which player will win if both players play the game optimally.
Constraints
* 1≤N≤10^5
* 1≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 … a_N
Output
If Snuke will win, print `First`. If Ciel will win, print `Second`.
Examples
Input
2
1 3
Output
First
Input
3
1 2 1
Output
First
Input
3
1 2 3
Output
Second | instruction | 0 | 15,829 | 16 | 31,658 |
"Correct Solution:
```
n = int(input())
a = [int(i) for i in input().split()]
a.sort(reverse=True)
a.append(0)
#after win=false first win = true
ans = False
for i in range(n):
if i+1>=a[i+1]:
ans=(((a[i]-i)%2)==0)
for j in range(i+1,n+1):
if a[j]<=i:
ans = ans or (((i-j)%2)==0)
break
break
if ans:
print("First")
else:
print("Second")
``` | output | 1 | 15,829 | 16 | 31,659 |
Provide a correct Python 3 solution for this coding contest problem.
There are N piles of candies on the table. The piles are numbered 1 through N. At first, pile i contains a_i candies.
Snuke and Ciel are playing a game. They take alternating turns. Snuke goes first. In each turn, the current player must perform one of the following two operations:
1. Choose a pile with the largest number of candies remaining, then eat all candies of that pile.
2. From each pile with one or more candies remaining, eat one candy.
The player who eats the last candy on the table, loses the game. Determine which player will win if both players play the game optimally.
Constraints
* 1≤N≤10^5
* 1≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 … a_N
Output
If Snuke will win, print `First`. If Ciel will win, print `Second`.
Examples
Input
2
1 3
Output
First
Input
3
1 2 1
Output
First
Input
3
1 2 3
Output
Second | instruction | 0 | 15,830 | 16 | 31,660 |
"Correct Solution:
```
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time
sys.setrecursionlimit(10**7)
inf = 10**10
mod = 10**9 + 7
def f():
n = int(input())
a = list(map(int, input().split()))
a.sort()
a.reverse()
i = j = 0
while i+1 < n and a[i+1] > j+1:
i += 1
j += 1
if (a[i] - j - 1) % 2 == 1:
return 'First'
k = 0
while i+1 < n and a[i+1] > j:
i += 1
k += 1
if k % 2 == 1:
return 'First'
return 'Second'
print(f())
``` | output | 1 | 15,830 | 16 | 31,661 |
Provide a correct Python 3 solution for this coding contest problem.
There are N piles of candies on the table. The piles are numbered 1 through N. At first, pile i contains a_i candies.
Snuke and Ciel are playing a game. They take alternating turns. Snuke goes first. In each turn, the current player must perform one of the following two operations:
1. Choose a pile with the largest number of candies remaining, then eat all candies of that pile.
2. From each pile with one or more candies remaining, eat one candy.
The player who eats the last candy on the table, loses the game. Determine which player will win if both players play the game optimally.
Constraints
* 1≤N≤10^5
* 1≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 … a_N
Output
If Snuke will win, print `First`. If Ciel will win, print `Second`.
Examples
Input
2
1 3
Output
First
Input
3
1 2 1
Output
First
Input
3
1 2 3
Output
Second | instruction | 0 | 15,831 | 16 | 31,662 |
"Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
a.sort(reverse = True)
a.append(0)
i = 0
j = 0
while i + 1 < a[i + 1]:
i += 1
j += 1
while i + 1 <= a[j]:
j += 1
if (j - i) % 2 == 0 or (a[i] - i) % 2 == 0:
print("First")
else:
print("Second")
``` | output | 1 | 15,831 | 16 | 31,663 |
Provide a correct Python 3 solution for this coding contest problem.
There are N piles of candies on the table. The piles are numbered 1 through N. At first, pile i contains a_i candies.
Snuke and Ciel are playing a game. They take alternating turns. Snuke goes first. In each turn, the current player must perform one of the following two operations:
1. Choose a pile with the largest number of candies remaining, then eat all candies of that pile.
2. From each pile with one or more candies remaining, eat one candy.
The player who eats the last candy on the table, loses the game. Determine which player will win if both players play the game optimally.
Constraints
* 1≤N≤10^5
* 1≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 … a_N
Output
If Snuke will win, print `First`. If Ciel will win, print `Second`.
Examples
Input
2
1 3
Output
First
Input
3
1 2 1
Output
First
Input
3
1 2 3
Output
Second | instruction | 0 | 15,832 | 16 | 31,664 |
"Correct Solution:
```
n=int(input())
a=sorted(map(int,input().split()))[::-1]
j=i=0
while i<n and a[i]>i:i+=1
while j<n and a[j]>=i:j+=1
print('SFeicrosntd'[(a[i-1]^i)&1|(j^i)&1::2])
``` | output | 1 | 15,832 | 16 | 31,665 |
Provide a correct Python 3 solution for this coding contest problem.
There are N piles of candies on the table. The piles are numbered 1 through N. At first, pile i contains a_i candies.
Snuke and Ciel are playing a game. They take alternating turns. Snuke goes first. In each turn, the current player must perform one of the following two operations:
1. Choose a pile with the largest number of candies remaining, then eat all candies of that pile.
2. From each pile with one or more candies remaining, eat one candy.
The player who eats the last candy on the table, loses the game. Determine which player will win if both players play the game optimally.
Constraints
* 1≤N≤10^5
* 1≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 … a_N
Output
If Snuke will win, print `First`. If Ciel will win, print `Second`.
Examples
Input
2
1 3
Output
First
Input
3
1 2 1
Output
First
Input
3
1 2 3
Output
Second | instruction | 0 | 15,833 | 16 | 31,666 |
"Correct Solution:
```
n = int(input())
a = list(map(int, input().split())) + [0]
a.sort(reverse=True)
for i in range(n):
if a[i + 1] <= i + 1:
y = a[i + 1:].count(i + 1)
x = i - a[i] - 1
if x % 2 == 0 and y % 2 == 0:
print('Second')
else:
print('First')
break
``` | output | 1 | 15,833 | 16 | 31,667 |
Provide a correct Python 3 solution for this coding contest problem.
There are N piles of candies on the table. The piles are numbered 1 through N. At first, pile i contains a_i candies.
Snuke and Ciel are playing a game. They take alternating turns. Snuke goes first. In each turn, the current player must perform one of the following two operations:
1. Choose a pile with the largest number of candies remaining, then eat all candies of that pile.
2. From each pile with one or more candies remaining, eat one candy.
The player who eats the last candy on the table, loses the game. Determine which player will win if both players play the game optimally.
Constraints
* 1≤N≤10^5
* 1≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 … a_N
Output
If Snuke will win, print `First`. If Ciel will win, print `Second`.
Examples
Input
2
1 3
Output
First
Input
3
1 2 1
Output
First
Input
3
1 2 3
Output
Second | instruction | 0 | 15,834 | 16 | 31,668 |
"Correct Solution:
```
import sys
n, *aaa = map(int, sys.stdin.read().split())
aaa.sort(reverse=True)
aaa.append(-1)
i = 0
while aaa[i + 1] > i + 1:
i += 1
j = i
while aaa[j] >= i + 1:
j += 1
if (aaa[i] - i) % 2 == 0 or (j - i) % 2 == 0:
ans = 0
else:
ans = 1
print(['First', 'Second'][ans])
``` | output | 1 | 15,834 | 16 | 31,669 |
Provide a correct Python 3 solution for this coding contest problem.
There are N piles of candies on the table. The piles are numbered 1 through N. At first, pile i contains a_i candies.
Snuke and Ciel are playing a game. They take alternating turns. Snuke goes first. In each turn, the current player must perform one of the following two operations:
1. Choose a pile with the largest number of candies remaining, then eat all candies of that pile.
2. From each pile with one or more candies remaining, eat one candy.
The player who eats the last candy on the table, loses the game. Determine which player will win if both players play the game optimally.
Constraints
* 1≤N≤10^5
* 1≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 … a_N
Output
If Snuke will win, print `First`. If Ciel will win, print `Second`.
Examples
Input
2
1 3
Output
First
Input
3
1 2 1
Output
First
Input
3
1 2 3
Output
Second | instruction | 0 | 15,835 | 16 | 31,670 |
"Correct Solution:
```
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
N,*A = map(int,read().split())
A.sort(reverse = True)
A.append(0)
i = 0
while A[i + 1] > i + 1:
i += 1
x = A[i] - (i + 1)
y = max(j for j in range(N) if A[j] > i) - i
answer = 'First' if x&1 or y&1 else 'Second'
print(answer)
``` | output | 1 | 15,835 | 16 | 31,671 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N piles of candies on the table. The piles are numbered 1 through N. At first, pile i contains a_i candies.
Snuke and Ciel are playing a game. They take alternating turns. Snuke goes first. In each turn, the current player must perform one of the following two operations:
1. Choose a pile with the largest number of candies remaining, then eat all candies of that pile.
2. From each pile with one or more candies remaining, eat one candy.
The player who eats the last candy on the table, loses the game. Determine which player will win if both players play the game optimally.
Constraints
* 1≤N≤10^5
* 1≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 … a_N
Output
If Snuke will win, print `First`. If Ciel will win, print `Second`.
Examples
Input
2
1 3
Output
First
Input
3
1 2 1
Output
First
Input
3
1 2 3
Output
Second
Submitted Solution:
```
n=int(input())
a=sorted(map(int,input().split()))[::-1]
j=i=0
while n:i+=a[i]>i;j+=a[j]>=i;n-=1
print('SFeicrosntd'[(a[i-1]^i|j^i)&1::2])
``` | instruction | 0 | 15,836 | 16 | 31,672 |
Yes | output | 1 | 15,836 | 16 | 31,673 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N piles of candies on the table. The piles are numbered 1 through N. At first, pile i contains a_i candies.
Snuke and Ciel are playing a game. They take alternating turns. Snuke goes first. In each turn, the current player must perform one of the following two operations:
1. Choose a pile with the largest number of candies remaining, then eat all candies of that pile.
2. From each pile with one or more candies remaining, eat one candy.
The player who eats the last candy on the table, loses the game. Determine which player will win if both players play the game optimally.
Constraints
* 1≤N≤10^5
* 1≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 … a_N
Output
If Snuke will win, print `First`. If Ciel will win, print `Second`.
Examples
Input
2
1 3
Output
First
Input
3
1 2 1
Output
First
Input
3
1 2 3
Output
Second
Submitted Solution:
```
N=int(input())
A=list(map(int,input().split()))
A.append(0)
A.sort()
winner=""
for i in range(N+1):
if A[N-i]>i:
if (A[N-i]-i)%2==0:
winner="First"
else:
winner="Second"
elif A[N-i]==i:
if (A[N-i+1]-A[N-i])%2==1:
winner="First"
break
else:
count=0
for j in range(N-i,-1,-1):
if A[j]==i:
count+=1
else:
break
if count%2==1:
winner="First"
else:
winner="Second"
break
else:
break
print(winner)
``` | instruction | 0 | 15,837 | 16 | 31,674 |
Yes | output | 1 | 15,837 | 16 | 31,675 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N piles of candies on the table. The piles are numbered 1 through N. At first, pile i contains a_i candies.
Snuke and Ciel are playing a game. They take alternating turns. Snuke goes first. In each turn, the current player must perform one of the following two operations:
1. Choose a pile with the largest number of candies remaining, then eat all candies of that pile.
2. From each pile with one or more candies remaining, eat one candy.
The player who eats the last candy on the table, loses the game. Determine which player will win if both players play the game optimally.
Constraints
* 1≤N≤10^5
* 1≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 … a_N
Output
If Snuke will win, print `First`. If Ciel will win, print `Second`.
Examples
Input
2
1 3
Output
First
Input
3
1 2 1
Output
First
Input
3
1 2 3
Output
Second
Submitted Solution:
```
n=int(input())
a=sorted(map(int,input().split()))[::-1]
j=i=0
for x in range(n):i+=a[i]>i;j+=a[j]>=i
print('SFeicrosntd'[(a[i-1]^i)&1|(j^i)&1::2])
``` | instruction | 0 | 15,838 | 16 | 31,676 |
Yes | output | 1 | 15,838 | 16 | 31,677 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N piles of candies on the table. The piles are numbered 1 through N. At first, pile i contains a_i candies.
Snuke and Ciel are playing a game. They take alternating turns. Snuke goes first. In each turn, the current player must perform one of the following two operations:
1. Choose a pile with the largest number of candies remaining, then eat all candies of that pile.
2. From each pile with one or more candies remaining, eat one candy.
The player who eats the last candy on the table, loses the game. Determine which player will win if both players play the game optimally.
Constraints
* 1≤N≤10^5
* 1≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 … a_N
Output
If Snuke will win, print `First`. If Ciel will win, print `Second`.
Examples
Input
2
1 3
Output
First
Input
3
1 2 1
Output
First
Input
3
1 2 3
Output
Second
Submitted Solution:
```
n=int(input())
a=sorted(map(int,input().split()))[::-1]
i=0
while i<n and a[i]>i:i+=1
j=i
while j<n and a[j]>=i:j+=1
print('SFeicrosntd'[(a[i-1]-i)&1 or (j-i)&1::2])
``` | instruction | 0 | 15,839 | 16 | 31,678 |
Yes | output | 1 | 15,839 | 16 | 31,679 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N piles of candies on the table. The piles are numbered 1 through N. At first, pile i contains a_i candies.
Snuke and Ciel are playing a game. They take alternating turns. Snuke goes first. In each turn, the current player must perform one of the following two operations:
1. Choose a pile with the largest number of candies remaining, then eat all candies of that pile.
2. From each pile with one or more candies remaining, eat one candy.
The player who eats the last candy on the table, loses the game. Determine which player will win if both players play the game optimally.
Constraints
* 1≤N≤10^5
* 1≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 … a_N
Output
If Snuke will win, print `First`. If Ciel will win, print `Second`.
Examples
Input
2
1 3
Output
First
Input
3
1 2 1
Output
First
Input
3
1 2 3
Output
Second
Submitted Solution:
```
n = int(input())
a = [int(i) for i in input().split()]
a.sort(reverse=True)
#after win=false first win = true
ans = False
for i in range(n):
if len(a)==1:
ans = ((a[i]%2)==1)
break
if len(a) == i+1:
ans = (((a[i]-i) % 2) == 0)
break
if i==a[i]:
for j in range(i-1,n):
if i>a[j]:
ans = (((j-i)%2)==1)
if i>=a[i+1]:
ans = ans or (((a[i]-i-1)%2)==1)
if i>=a[i+1] or i==a[i]:
break
if ans:
print("First")
else:
print("Second")
``` | instruction | 0 | 15,840 | 16 | 31,680 |
No | output | 1 | 15,840 | 16 | 31,681 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N piles of candies on the table. The piles are numbered 1 through N. At first, pile i contains a_i candies.
Snuke and Ciel are playing a game. They take alternating turns. Snuke goes first. In each turn, the current player must perform one of the following two operations:
1. Choose a pile with the largest number of candies remaining, then eat all candies of that pile.
2. From each pile with one or more candies remaining, eat one candy.
The player who eats the last candy on the table, loses the game. Determine which player will win if both players play the game optimally.
Constraints
* 1≤N≤10^5
* 1≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 … a_N
Output
If Snuke will win, print `First`. If Ciel will win, print `Second`.
Examples
Input
2
1 3
Output
First
Input
3
1 2 1
Output
First
Input
3
1 2 3
Output
Second
Submitted Solution:
```
# coding: utf-8
from __future__ import print_function
from __future__ import unicode_literals
from __future__ import division
from __future__ import absolute_import
import math
import string
import itertools
import fractions
import heapq
import collections
import re
import array
import bisect
def eat_all(al):
for i in range(len(al)):
al[i] -= 1
while True:
if al[0] == 0:
al.pop(0)
else:
break
return al
def step(turn, a_list):
if len(a_list) == 1:
if a_list[0] % 2 == 0:
return turn
else:
return (not turn)
if a_list[-1] % 2 != 0:
a_list.pop()
return step(not turn, a_list)
else:
a_list = eat_all(a_list)
a_list.pop()
if len(a_list) == 0:
return turn
return step(turn, a_list)
n = int(input())
a_list = [None] * n
inputs = input().split(" ")
for i in range(n):
a_list[i] = int(inputs[i])
a_list.sort()
win = step(1, a_list)
if win == 1:
print("First")
else:
print("Second")
``` | instruction | 0 | 15,841 | 16 | 31,682 |
No | output | 1 | 15,841 | 16 | 31,683 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N piles of candies on the table. The piles are numbered 1 through N. At first, pile i contains a_i candies.
Snuke and Ciel are playing a game. They take alternating turns. Snuke goes first. In each turn, the current player must perform one of the following two operations:
1. Choose a pile with the largest number of candies remaining, then eat all candies of that pile.
2. From each pile with one or more candies remaining, eat one candy.
The player who eats the last candy on the table, loses the game. Determine which player will win if both players play the game optimally.
Constraints
* 1≤N≤10^5
* 1≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 … a_N
Output
If Snuke will win, print `First`. If Ciel will win, print `Second`.
Examples
Input
2
1 3
Output
First
Input
3
1 2 1
Output
First
Input
3
1 2 3
Output
Second
Submitted Solution:
```
N=int(input())
L=list(map(int,input().split()))
s=0
for i in range(N):
s=s^L[i]
if s==0:
print("Second")
else:
print("First")
``` | instruction | 0 | 15,842 | 16 | 31,684 |
No | output | 1 | 15,842 | 16 | 31,685 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N piles of candies on the table. The piles are numbered 1 through N. At first, pile i contains a_i candies.
Snuke and Ciel are playing a game. They take alternating turns. Snuke goes first. In each turn, the current player must perform one of the following two operations:
1. Choose a pile with the largest number of candies remaining, then eat all candies of that pile.
2. From each pile with one or more candies remaining, eat one candy.
The player who eats the last candy on the table, loses the game. Determine which player will win if both players play the game optimally.
Constraints
* 1≤N≤10^5
* 1≤a_i≤10^9
Input
The input is given from Standard Input in the following format:
N
a_1 a_2 … a_N
Output
If Snuke will win, print `First`. If Ciel will win, print `Second`.
Examples
Input
2
1 3
Output
First
Input
3
1 2 1
Output
First
Input
3
1 2 3
Output
Second
Submitted Solution:
```
n=int(input())
a=sorted(map(int,input().split()))[::-1]
j=i=x=0
while x<n:i+=a[i]>i;j+=a[j]>=i,x+=1
print('SFeicrosntd'[(a[i-1]^i|j^i)&1::2])
``` | instruction | 0 | 15,843 | 16 | 31,686 |
No | output | 1 | 15,843 | 16 | 31,687 |
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