Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = list(map(int,input().split()))

DP = [[-10**18 for i in range((N+1)//2)] for i in range(N)]

DP[0][0] = A[0]
#for i in range(1,N):
#    DP[i][0] = max(DP[i-1][0],A[i])

#for i in range(1,N//2-1):
#    DP[2*i][i] = DP[2*(i-1)][i-1] + A[2*i]

for i in range(1,N):
    for j in range((i+1)//2-1,(i+2)//2):
        if j == 0:
            DP[i][0] = max(DP[i-1][0],A[i])
        else:
            DP[i][j] = max(DP[i-1][j],DP[i-2][j-1]+A[i])

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


Fixed submission:
from collections import defaultdict

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

DP = defaultdict(lambda: -10**18)

DP[(0,0)] = A[0]

for i in range(1,N):
    for j in range((i+1)//2-1,(i+2)//2):
        if j == 0:
            DP[(i,0)] = max(DP[(i-1,0)],A[i])
        else:
            DP[(i,j)] = max(DP[(i-1,j)],DP[(i-2,j-1)]+A[i])

print(DP[(N-1,N//2-1)])

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = list(map(int,input().split()))

DP = [[-10**9 for i in range((N+1)//2)] for i in range(N)]

DP[0][0] = A[0]
for i in range(1,N):
    DP[i][0] = max(DP[i-1][0],A[i])

for i in range(1,N//2-1):
    DP[2*i][i] = DP[2*(i-1)][i-1] + A[2*i]

for i in range(3,N):
    for j in range(i//2-2,(i+1)//2):
        DP[i][j] = max(DP[i-1][j],DP[i-2][j-1]+A[i])

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


Fixed submission:
from collections import defaultdict

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

DP = defaultdict(lambda: -10**18)

DP[(0,0)] = A[0]

for i in range(1,N):
    for j in range((i+1)//2-1,(i+2)//2):
        if j == 0:
            DP[(i,0)] = max(DP[(i-1,0)],A[i])
        else:
            DP[(i,j)] = max(DP[(i-1,j)],DP[(i-2,j-1)]+A[i])

print(DP[(N-1,N//2-1)])

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = list(map(int,input().split()))

DP = [[-10**9 for i in range((N+1)//2)] for i in range(N)]

DP[0][0] = A[0]
for i in range(1,N):
    DP[i][0] = max(DP[i-1][0],A[i])

for i in range(1,N//2-1):
    DP[2*i][i] = DP[2*(i-1)][i-1] + A[2*i]

for i in range(3,N):
    for j in range(N//2-(N-i+1)//2-1,(i+1)//2):
        DP[i][j] = max(DP[i-1][j],DP[i-2][j-1]+A[i])

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


Fixed submission:
from collections import defaultdict

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

DP = defaultdict(lambda: -10**18)

DP[(0,0)] = A[0]

for i in range(1,N):
    for j in range((i+1)//2-1,(i+2)//2):
        if j == 0:
            DP[(i,0)] = max(DP[(i-1,0)],A[i])
        else:
            DP[(i,j)] = max(DP[(i-1,j)],DP[(i-2,j-1)]+A[i])

print(DP[(N-1,N//2-1)])

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = list(map(int,input().split()))

DP = [[-10**9 for i in range((N+1)//2)] for i in range(N)]

DP[0][0] = A[0]
for i in range(1,N):
    DP[i][0] = max(DP[i-1][0],A[i])

for i in range(1,N//2-1):
    DP[2*i][i] = DP[2*(i-1)][i-1] + A[2*i]

for i in range(3,N):
    for j in range(1,(i+1)//2):
        DP[i][j] = max(DP[i-1][j],DP[i-2][j-1]+A[i])

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


Fixed submission:
from collections import defaultdict

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

DP = defaultdict(lambda: -10**18)

DP[(0,0)] = A[0]

for i in range(1,N):
    for j in range((i+1)//2-1,(i+2)//2):
        if j == 0:
            DP[(i,0)] = max(DP[(i-1,0)],A[i])
        else:
            DP[(i,j)] = max(DP[(i-1,j)],DP[(i-2,j-1)]+A[i])

print(DP[(N-1,N//2-1)])

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = list(map(int,input().split()))

for i in range(N):
    A[i] = [A[i],i]
    #A[i][0]:number,A[i][1]:index

A.sort(reverse = True)

sum = A[0][0]
index = [A[0][1]]
cnt = 1

for i in range(1,N):
    if A[i][1]+1 not in index and A[i][1]-1 not in index:
        sum += A[i][0]
        index.append(A[i][1])
        cnt += 1
        if cnt == N//2:
            break

print(sum)


Fixed submission:
from collections import defaultdict

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

DP = defaultdict(lambda: -10**18)

DP[(0,0)] = A[0]

for i in range(1,N):
    for j in range((i+1)//2-1,(i+2)//2):
        if j == 0:
            DP[(i,0)] = max(DP[(i-1,0)],A[i])
        else:
            DP[(i,j)] = max(DP[(i-1,j)],DP[(i-2,j-1)]+A[i])

print(DP[(N-1,N//2-1)])

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = list(map(int,input().split()))

for i in range(N):
    A[i] = [A[i],i]
    #A[i][0]:number,A[i][1]:index

A.sort(reverse = True)

sum = A[0][0]
index = [A[0][1]]
cnt = 1

for i in range(1,N):
    if A[i][1]+1 not in index and A[i][1]-1 not in index:
        sum += A[i][0]
        index.append(A[i][1])
        if len(index) == N//2:
            break

print(sum)


Fixed submission:
from collections import defaultdict

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

DP = defaultdict(lambda: -10**18)

DP[(0,0)] = A[0]

for i in range(1,N):
    for j in range((i+1)//2-1,(i+2)//2):
        if j == 0:
            DP[(i,0)] = max(DP[(i-1,0)],A[i])
        else:
            DP[(i,j)] = max(DP[(i-1,j)],DP[(i-2,j-1)]+A[i])

print(DP[(N-1,N//2-1)])