Buggy python submission (verdict: Time Limit Exceeded):
import sys

sys.setrecursionlimit(2*1000000)

N = int(input())
A = list(map(int, input().split(" ")))

dp_dict = {}

inf = -1*1000000000


def dp(i, j):
    if j == 1:
        return A[i]
    if i+2 >= N:
        return inf
    if N//2-j < i//2-1:
        return inf
    temp = max([dp(i+2, j-1)+A[i], dp(i+1, j)])
    dp_dict[(i, j)] = temp
    return temp


select = N//2
if select == 1:
    print(max(A))
else:
    print(dp(0, select))

Fixed submission:
N = int(input())
A = [0]+list(map(int, input().split(" ")))

dp_list = [{0, 0}, {0: 0, 1: A[1]}, {0: 0, 1: A[1] if A[1] > A[2] else A[2]}]

for i in range(3, N+1):
    b = (i-1)//2
    f = (i+1)//2
    dp_list.append({})
    for j in range(b, f+1):
        if j in dp_list[i-1]:
            dp_list[i][j] = dp_list[i-2][j-1]+A[i] if dp_list[i -
                                                              2][j-1]+A[i] > dp_list[i-1][j] else dp_list[i-1][j]
        else:
            dp_list[i][j] = dp_list[i-2][j-1]+A[i]

print(dp_list[-1][N//2])

Buggy python submission (verdict: Time Limit Exceeded):
import sys

sys.setrecursionlimit(2*1000000)

N = int(input())
A = list(map(int, input().split(" ")))

#dp_dict = {}


def dp(i, j):
    #print(i, j)
    if i >= N:
        return (-1*1000000000)
    if (N//2)-j < (i-1)//2:
        return (-1*1000000000)
    if j == 1:
        return A[i]
    # if (i, j) in dp_dict:
        # return dp_dict[(i, j)]
    else:
        temp = max([dp(i+2, j-1)+A[i], dp(i+1, j)])
        #dp_dict[(i, j)] = temp
        return temp


select = N//2
if select == 1:
    print(max(A))
else:
    print(dp(0, select))

Fixed submission:
N = int(input())
A = [0]+list(map(int, input().split(" ")))

dp_list = [{0, 0}, {0: 0, 1: A[1]}, {0: 0, 1: A[1] if A[1] > A[2] else A[2]}]

for i in range(3, N+1):
    b = (i-1)//2
    f = (i+1)//2
    dp_list.append({})
    for j in range(b, f+1):
        if j in dp_list[i-1]:
            dp_list[i][j] = dp_list[i-2][j-1]+A[i] if dp_list[i -
                                                              2][j-1]+A[i] > dp_list[i-1][j] else dp_list[i-1][j]
        else:
            dp_list[i][j] = dp_list[i-2][j-1]+A[i]

print(dp_list[-1][N//2])

Buggy python submission (verdict: Runtime Error):
import sys

sys.setrecursionlimit(2*1000000)

N = int(input())
A = list(map(int, input().split(" ")))



def dp(i, j):
    if i >= N:
        return (-1*1000000000)
    if (N//2)-j < (i-1)//2:
        return (-1*1000000000)
    if j == 1:
        return A[i]
	else:
        temp = max([dp(i+2, j-1)+A[i], dp(i+1, j)])
        dp_dict[(i, j)] = temp
        return temp


select = N//2
if select == 1:
    print(max(A))
else:
    print(dp(0, select))

Fixed submission:
N = int(input())
A = [0]+list(map(int, input().split(" ")))

dp_list = [{0, 0}, {0: 0, 1: A[1]}, {0: 0, 1: A[1] if A[1] > A[2] else A[2]}]

for i in range(3, N+1):
    b = (i-1)//2
    f = (i+1)//2
    dp_list.append({})
    for j in range(b, f+1):
        if j in dp_list[i-1]:
            dp_list[i][j] = dp_list[i-2][j-1]+A[i] if dp_list[i -
                                                              2][j-1]+A[i] > dp_list[i-1][j] else dp_list[i-1][j]
        else:
            dp_list[i][j] = dp_list[i-2][j-1]+A[i]

print(dp_list[-1][N//2])

Buggy python submission (verdict: Runtime Error):
N = int(input())
A = list(map(int, input().split(" ")))

dp_dict = {}


def dp(i, j):
    print(i, j)
    if i >= N:
        return (-1*10e+9)-1
    if j == 1:
        return A[i]
    if (i, j) in dp_dict:
        return dp_dict[(i, j)]
    else:
        temp = max([dp(i+2, j-1)+A[i], dp(i+1, j)])
        dp_dict[(i, j)] = temp
        return temp


print(dp(0, (N//2)))

Fixed submission:
N = int(input())
A = [0]+list(map(int, input().split(" ")))

dp_list = [{0, 0}, {0: 0, 1: A[1]}, {0: 0, 1: A[1] if A[1] > A[2] else A[2]}]

for i in range(3, N+1):
    b = (i-1)//2
    f = (i+1)//2
    dp_list.append({})
    for j in range(b, f+1):
        if j in dp_list[i-1]:
            dp_list[i][j] = dp_list[i-2][j-1]+A[i] if dp_list[i -
                                                              2][j-1]+A[i] > dp_list[i-1][j] else dp_list[i-1][j]
        else:
            dp_list[i][j] = dp_list[i-2][j-1]+A[i]

print(dp_list[-1][N//2])

Buggy python submission (verdict: Runtime Error):
N = int(input())
A = list(map(int, input().split(" ")))

dp_dict = {}


def dp(i, j):
    if i >= N:
        return -1*10e+9
    if (i+1)//2 > (N//2)-j+1:
        return -1*10e+9
    if j == 1:
        return A[i]
    if (i, j) in dp_dict:
        return dp_dict[(i, j)]
    else:
        temp = max([dp(i+2, j-1)+A[i], dp(i+1, j)])
        dp_dict[(i, j)] = temp
        return temp


print(dp(0, (N//2)))

Fixed submission:
N = int(input())
A = [0]+list(map(int, input().split(" ")))

dp_list = [{0, 0}, {0: 0, 1: A[1]}, {0: 0, 1: A[1] if A[1] > A[2] else A[2]}]

for i in range(3, N+1):
    b = (i-1)//2
    f = (i+1)//2
    dp_list.append({})
    for j in range(b, f+1):
        if j in dp_list[i-1]:
            dp_list[i][j] = dp_list[i-2][j-1]+A[i] if dp_list[i -
                                                              2][j-1]+A[i] > dp_list[i-1][j] else dp_list[i-1][j]
        else:
            dp_list[i][j] = dp_list[i-2][j-1]+A[i]

print(dp_list[-1][N//2])

Buggy python submission (verdict: Runtime Error):
N = int(input())
A = list(map(int, input().split(" ")))

dp_dict = {}


def dp(i, j):
    if j == 1:
        return A[i]
    # if (i-1)//2 > (N//2)-j:
        # return -1*10e+9
    if (N-1)-i < j:
        return -1*10e+9

    if (i, j) in dp_dict:
        return dp_dict[(i, j)]
    else:
        temp = max([dp(i+2, j-1)+A[i], dp(i+1, j)])
        dp_dict[(i, j)] = temp
        return temp


print(dp(0, N//2))

Fixed submission:
N = int(input())
A = [0]+list(map(int, input().split(" ")))

dp_list = [{0, 0}, {0: 0, 1: A[1]}, {0: 0, 1: A[1] if A[1] > A[2] else A[2]}]

for i in range(3, N+1):
    b = (i-1)//2
    f = (i+1)//2
    dp_list.append({})
    for j in range(b, f+1):
        if j in dp_list[i-1]:
            dp_list[i][j] = dp_list[i-2][j-1]+A[i] if dp_list[i -
                                                              2][j-1]+A[i] > dp_list[i-1][j] else dp_list[i-1][j]
        else:
            dp_list[i][j] = dp_list[i-2][j-1]+A[i]

print(dp_list[-1][N//2])

Buggy python submission (verdict: Runtime Error):
N = int(input())
A = list(map(int, input().split(" ")))


dp_dict = {}


def dp(i, j):
    if j == 1:
        return A[i]
    if (i-1)//2 > (N//2)-j:
        return -1*10e+9
    if (N-1)-i < j:
        return -1*10e+9

    if (i, j) in dp_dict:
        return dp_dict[(i, j)]
    else:
        temp = max([dp(i+2, j-1)+A[i], dp(i+1, j)])
        dp_dict[(i, j)] = temp
        return temp


print(dp(0, N//2))

Fixed submission:
N = int(input())
A = [0]+list(map(int, input().split(" ")))

dp_list = [{0, 0}, {0: 0, 1: A[1]}, {0: 0, 1: A[1] if A[1] > A[2] else A[2]}]

for i in range(3, N+1):
    b = (i-1)//2
    f = (i+1)//2
    dp_list.append({})
    for j in range(b, f+1):
        if j in dp_list[i-1]:
            dp_list[i][j] = dp_list[i-2][j-1]+A[i] if dp_list[i -
                                                              2][j-1]+A[i] > dp_list[i-1][j] else dp_list[i-1][j]
        else:
            dp_list[i][j] = dp_list[i-2][j-1]+A[i]

print(dp_list[-1][N//2])