Buggy python submission (verdict: Time Limit Exceeded):
import sys
#import copy
#import numpy as np
#import itertools
#import collections
#from collections import deque
#from scipy.sparse.csgraph import shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson
#from scipy.sparse import csr_matrix

sys.setrecursionlimit(10**6)
readline = sys.stdin.readline
#read = sys.stdin.buffer.read

inf = float('inf')

def main():
    # input
    N = int(readline())
    A = list(map(int, readline().split()))

    K = N//2
    DP = [[-inf] * (K)  for _ in range(N)]

    DP[0][0] = A[0]
    DP[1][0] = max(A[0], A[1])
    for i in range(2, N):
        i2 = i+1
        start = max(0, i2//2 - 1)
        end = min((i2 + 1)//2, K)
        for j in range(start, end):
            if j == 0:
                DP[i][j] = max(A[i], DP[i-1][j])
            else:
                DP[i][j] = max(DP[i-2][j-1] + A[i], DP[i-1][j])

    ans = DP[N-1][K-1]
    #print(DP)
    print(ans)


if __name__ == "__main__":
    main()


Fixed submission:
import sys
#import copy
#import numpy as np
#import itertools
#import collections
#from collections import deque
#from scipy.sparse.csgraph import shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson
#from scipy.sparse import csr_matrix

sys.setrecursionlimit(10**6)
readline = sys.stdin.readline
#read = sys.stdin.buffer.read

inf = float('inf')
#inf = pow(10, 10)

def main():
    # input
    N = int(readline())
    A = list(map(int, readline().split()))

    K = N//2
    DP0 = [-inf] * N
    DP1 = [-inf] * N
    DP2 = [-inf] * N

    DP2[0] = A[0]
    DP2[1] = max(A[0], A[1])
    DP1[:2] = [0] * 2
    DP0[:4] = [0] * 4
    for i in range(2, N):
        if i%2 == 0:
            DP2[i] = DP2[i-2] + A[i]
            DP1[i] = max(DP2[i-1], DP1[i-2] + A[i])
            DP0[i] = max(DP1[i-1], DP0[i-2] + A[i])
        else:
            DP2[i] = max(DP2[i-2] + A[i], DP2[i-1])
            DP1[i] = max(DP1[i-1], DP1[i-2] + A[i])
            DP0[i] = max(DP0[i-1], DP0[i-2] + A[i])

    if N%2 == 0:
        ans = DP2[N-1]
    else:
        ans = DP1[N-1]

    #print(DP0)
    #print(DP1)
    #print(DP2)
    print(ans)


if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys
#import copy
#import numpy as np
#import itertools
#import collections
#from collections import deque
#from scipy.sparse.csgraph import shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson
#from scipy.sparse import csr_matrix

sys.setrecursionlimit(10**6)
readline = sys.stdin.readline
#read = sys.stdin.buffer.read

inf = float('inf')

def main():
    # input
    N = int(readline())
    A = list(map(int, readline().split()))

    K = N//2
    DP = [[-inf] * (K)  for _ in range(N)]

    DP[0][0] = A[0]
    DP[1][0] = max(A[0], A[1])
    for i in range(2, N):
        i2 = i+1
        start = max(0, i2//2 - 1)
        end = min((i2 + 1)//2, K)
        for j in range(start, end):
            if j == 0:
                DP[i][j] = max(A[i], DP[i-1][j])
            else:
                DP[i][j] = max(DP[i-2][j-1] + A[i], DP[i-1][j])

    ans = DP[N-1][K-1]
    #print(DP)
    print(ans)


if __name__ == "__main__":
    main()


Fixed submission:
import sys
#import copy
#import numpy as np
#import itertools
#import collections
#from collections import deque
#from scipy.sparse.csgraph import shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson
#from scipy.sparse import csr_matrix

sys.setrecursionlimit(10**6)
readline = sys.stdin.readline
#read = sys.stdin.buffer.read

inf = float('inf')
#inf = pow(10, 10)

def main():
    # input
    N = int(readline())
    A = list(map(int, readline().split()))

    K = N//2
    DP0 = [-inf] * N
    DP1 = [-inf] * N
    DP2 = [-inf] * N

    DP2[0] = A[0]
    DP2[1] = max(A[0], A[1])
    DP1[:2] = [0] * 2
    DP0[:4] = [0] * 4
    for i in range(2, N):
        if i%2 == 0:
            DP2[i] = DP2[i-2] + A[i]
            DP1[i] = max(DP2[i-1], DP1[i-2] + A[i])
            DP0[i] = max(DP1[i-1], DP0[i-2] + A[i])
        else:
            DP2[i] = max(DP2[i-2] + A[i], DP2[i-1])
            DP1[i] = max(DP1[i-1], DP1[i-2] + A[i])
            DP0[i] = max(DP0[i-1], DP0[i-2] + A[i])

    if N%2 == 0:
        ans = DP2[N-1]
    else:
        ans = DP1[N-1]

    #print(DP0)
    #print(DP1)
    #print(DP2)
    print(ans)


if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys
#import copy
#import numpy as np
#import itertools
#import collections
#from collections import deque
#from scipy.sparse.csgraph import shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson
#from scipy.sparse import csr_matrix

sys.setrecursionlimit(10**6)
readline = sys.stdin.readline
#read = sys.stdin.buffer.read

inf = float('inf')

def main():
    # input
    N = int(readline())
    A = list(map(int, readline().split()))

    K = N//2
    DP = [[-inf] * (K)  for _ in range(N)]

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

    ans = DP[N-1][K-1]
    #print(DP)
    print(ans)


if __name__ == "__main__":
    main()


Fixed submission:
import sys
#import copy
#import numpy as np
#import itertools
#import collections
#from collections import deque
#from scipy.sparse.csgraph import shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson
#from scipy.sparse import csr_matrix

sys.setrecursionlimit(10**6)
readline = sys.stdin.readline
#read = sys.stdin.buffer.read

inf = float('inf')
#inf = pow(10, 10)

def main():
    # input
    N = int(readline())
    A = list(map(int, readline().split()))

    K = N//2
    DP0 = [-inf] * N
    DP1 = [-inf] * N
    DP2 = [-inf] * N

    DP2[0] = A[0]
    DP2[1] = max(A[0], A[1])
    DP1[:2] = [0] * 2
    DP0[:4] = [0] * 4
    for i in range(2, N):
        if i%2 == 0:
            DP2[i] = DP2[i-2] + A[i]
            DP1[i] = max(DP2[i-1], DP1[i-2] + A[i])
            DP0[i] = max(DP1[i-1], DP0[i-2] + A[i])
        else:
            DP2[i] = max(DP2[i-2] + A[i], DP2[i-1])
            DP1[i] = max(DP1[i-1], DP1[i-2] + A[i])
            DP0[i] = max(DP0[i-1], DP0[i-2] + A[i])

    if N%2 == 0:
        ans = DP2[N-1]
    else:
        ans = DP1[N-1]

    #print(DP0)
    #print(DP1)
    #print(DP2)
    print(ans)


if __name__ == "__main__":
    main()