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

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
printV = lambda x: print(*x, sep="\n")
printH = lambda x: print(" ".join(map(str,x)))
def IS(): return sys.stdin.readline()[:-1]
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LII(rows_number): return [II() for _ in range(rows_number)]
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]

def main():
	n = II()
	a = LI()
	a = [0]+a
	dp_t = [[-10**9-1 for _ in range(n//2+2)] for _ in range(n+1)]
	dp_f = [[-10**9-1 for _ in range(n//2+2)] for _ in range(n+1)]
	dp_f[0][0]=0
	for i in range(1,n+1):
		dp_f[i][(i-1)//2]=max(dp_f[i-1][(i-1)//2], dp_t[i-1][(i-1)//2])
		dp_t[i][(i-1)//2]=dp_f[i-1][(i-1)//2-1]+a[i]
		dp_f[i][(i-1)//2+1]=max(dp_f[i-1][(i-1)//2+1], dp_t[i-1][(i-1)//2+1])
		dp_t[i][(i-1)//2+1]=dp_f[i-1][(i-1)//2]+a[i]
	print(max(dp_t[n][n//2],dp_f[n][n//2]))
if __name__ == '__main__':
	main()

Fixed submission:
import sys
from collections import defaultdict

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
printV = lambda x: print(*x, sep="\n")
printH = lambda x: print(" ".join(map(str,x)))
def IS(): return sys.stdin.readline()[:-1]
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LII(rows_number): return [II() for _ in range(rows_number)]
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]

def main():
	n = II()
	a = LI()
	a = [0]+a
	dp_t = defaultdict(lambda: -10**18)
	dp_f =  defaultdict(lambda: -10**18)
	dp_f[(0,0)]=0
	for i in range(1,n+1):
		dp_f[(i,(i-1)//2)]=max(dp_f[(i-1,(i-1)//2)], dp_t[(i-1,(i-1)//2)])
		dp_t[(i,(i-1)//2)]=dp_f[(i-1,(i-1)//2-1)]+a[i]
		dp_f[(i,(i-1)//2+1)]=max(dp_f[(i-1,(i-1)//2+1)], dp_t[(i-1,(i-1)//2+1)])
		dp_t[(i,(i-1)//2+1)]=dp_f[(i-1,(i-1)//2)]+a[i]
	print(max(dp_t[(n,n//2)],dp_f[(n,n//2)]))
if __name__ == '__main__':
	main()

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

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
printV = lambda x: print(*x, sep="\n")
printH = lambda x: print(" ".join(map(str,x)))
def IS(): return sys.stdin.readline()[:-1]
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LII(rows_number): return [II() for _ in range(rows_number)]
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]

def main():
	n = II()
	a = LI()
	a = [0]+a
	dp = [[[-10**9,-10**9] for _ in range(n//2+2)] for _ in range(n+1)]
	dp[1][1][1]=a[1]
	for i in range(0,2):
		dp[i][0]=[0,0]
	for i in range(1,n+1):
		dp[i][(i-1)//2][0]=max(dp[i-1][(i-1)//2][0], dp[i-1][(i-1)//2][1])
		dp[i][(i-1)//2][1]=max(dp[i-1][(i-1)//2-1][0]+a[i], dp[i-2][(i-1)//2-1][0]+a[i])
		dp[i][i//2][0]=max(dp[i-1][i//2][0], dp[i-1][i//2][1])
		dp[i][i//2][1]=max(dp[i-1][i//2-1][0]+a[i], dp[i-2][i//2-1][0]+a[i])
		dp[i][(i+1)//2][1]=max(dp[i-1][(i+1)//2-1][0]+a[i], dp[i-2][(i+1)//2-1][0]+a[i])
	print(max(dp[n][n//2]))
if __name__ == '__main__':
	main()

Fixed submission:
import sys
from collections import defaultdict

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
printV = lambda x: print(*x, sep="\n")
printH = lambda x: print(" ".join(map(str,x)))
def IS(): return sys.stdin.readline()[:-1]
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LII(rows_number): return [II() for _ in range(rows_number)]
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]

def main():
	n = II()
	a = LI()
	a = [0]+a
	dp_t = defaultdict(lambda: -10**18)
	dp_f =  defaultdict(lambda: -10**18)
	dp_f[(0,0)]=0
	for i in range(1,n+1):
		dp_f[(i,(i-1)//2)]=max(dp_f[(i-1,(i-1)//2)], dp_t[(i-1,(i-1)//2)])
		dp_t[(i,(i-1)//2)]=dp_f[(i-1,(i-1)//2-1)]+a[i]
		dp_f[(i,(i-1)//2+1)]=max(dp_f[(i-1,(i-1)//2+1)], dp_t[(i-1,(i-1)//2+1)])
		dp_t[(i,(i-1)//2+1)]=dp_f[(i-1,(i-1)//2)]+a[i]
	print(max(dp_t[(n,n//2)],dp_f[(n,n//2)]))
if __name__ == '__main__':
	main()

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

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
printV = lambda x: print(*x, sep="\n")
printH = lambda x: print(" ".join(map(str,x)))
def IS(): return sys.stdin.readline()[:-1]
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LII(rows_number): return [II() for _ in range(rows_number)]
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]

def main():
	n = II()
	a = LI()
	a = [0]+a
	dp = [[[-10**9,-10**9] for _ in range(n//2+2)] for _ in range(n+1)]
	dp[1][1][1]=a[1]
	for i in range(0,2):
		dp[i][0]=[0,0]
	for i in range(1,n+1):
		if i-1 >= 3:
			dp[i][(i-1)//2][0]=max(dp[i-1][(i-1)//2][0], dp[i-1][(i-1)//2][1])
			dp[i][(i-1)//2][1]=max(dp[i-1][(i-1)//2-1][0]+a[i], dp[i-2][(i-1)//2-1][0]+a[i])
		if i >= 2:
			dp[i][i//2][0]=max(dp[i-1][i//2][0], dp[i-1][i//2][1])
			dp[i][i//2][1]=max(dp[i-1][i//2-1][0]+a[i], dp[i-2][i//2-1][0]+a[i])
		if i >= 2:
			dp[i][(i+1)//2][1]=max(dp[i-1][(i+1)//2-1][0]+a[i], dp[i-2][(i+1)//2-1][0]+a[i])
	print(max(dp[n][n//2]))
if __name__ == '__main__':
	main()

Fixed submission:
import sys
from collections import defaultdict

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
printV = lambda x: print(*x, sep="\n")
printH = lambda x: print(" ".join(map(str,x)))
def IS(): return sys.stdin.readline()[:-1]
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LII(rows_number): return [II() for _ in range(rows_number)]
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]

def main():
	n = II()
	a = LI()
	a = [0]+a
	dp_t = defaultdict(lambda: -10**18)
	dp_f =  defaultdict(lambda: -10**18)
	dp_f[(0,0)]=0
	for i in range(1,n+1):
		dp_f[(i,(i-1)//2)]=max(dp_f[(i-1,(i-1)//2)], dp_t[(i-1,(i-1)//2)])
		dp_t[(i,(i-1)//2)]=dp_f[(i-1,(i-1)//2-1)]+a[i]
		dp_f[(i,(i-1)//2+1)]=max(dp_f[(i-1,(i-1)//2+1)], dp_t[(i-1,(i-1)//2+1)])
		dp_t[(i,(i-1)//2+1)]=dp_f[(i-1,(i-1)//2)]+a[i]
	print(max(dp_t[(n,n//2)],dp_f[(n,n//2)]))
if __name__ == '__main__':
	main()

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

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
printV = lambda x: print(*x, sep="\n")
printH = lambda x: print(" ".join(map(str,x)))
def IS(): return sys.stdin.readline()[:-1]
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LII(rows_number): return [II() for _ in range(rows_number)]
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]

def main():
	n = II()
	a = LI()
	a = [0]+a
	dp = [[[-10**9,-10**9] for _ in range(n//2+2)] for _ in range(n+1)]
	dp[1][1][1]=a[1]
	for i in range(0,n+1):
		dp[i][0]=[0,0]
	for i in range(1,n+1):
		if i-1 >= 3:
			dp[i][(i-1)//2][0]=max(dp[i-1][(i-1)//2][0], dp[i-1][(i-1)//2][1])
			dp[i][(i-1)//2][1]=max(dp[i-1][(i-1)//2-1][0]+a[i], dp[i-2][(i-1)//2-1][0]+a[i])
		if i >= 2:
			dp[i][i//2][0]=max(dp[i-1][i//2][0], dp[i-1][i//2][1])
			dp[i][i//2][1]=max(dp[i-1][i//2-1][0]+a[i], dp[i-2][i//2-1][0]+a[i])
		if i >= 2:
			dp[i][(i+1)//2][1]=max(dp[i-1][(i+1)//2-1][0]+a[i], dp[i-2][(i+1)//2-1][0]+a[i])
	print(max(dp[n][n//2]))
if __name__ == '__main__':
	main()

Fixed submission:
import sys
from collections import defaultdict

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
printV = lambda x: print(*x, sep="\n")
printH = lambda x: print(" ".join(map(str,x)))
def IS(): return sys.stdin.readline()[:-1]
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LII(rows_number): return [II() for _ in range(rows_number)]
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]

def main():
	n = II()
	a = LI()
	a = [0]+a
	dp_t = defaultdict(lambda: -10**18)
	dp_f =  defaultdict(lambda: -10**18)
	dp_f[(0,0)]=0
	for i in range(1,n+1):
		dp_f[(i,(i-1)//2)]=max(dp_f[(i-1,(i-1)//2)], dp_t[(i-1,(i-1)//2)])
		dp_t[(i,(i-1)//2)]=dp_f[(i-1,(i-1)//2-1)]+a[i]
		dp_f[(i,(i-1)//2+1)]=max(dp_f[(i-1,(i-1)//2+1)], dp_t[(i-1,(i-1)//2+1)])
		dp_t[(i,(i-1)//2+1)]=dp_f[(i-1,(i-1)//2)]+a[i]
	print(max(dp_t[(n,n//2)],dp_f[(n,n//2)]))
if __name__ == '__main__':
	main()

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

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
printV = lambda x: print(*x, sep="\n")
printH = lambda x: print(" ".join(map(str,x)))
def IS(): return sys.stdin.readline()[:-1]
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LII(rows_number): return [II() for _ in range(rows_number)]
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]

def main():
	n = II()
	a = LI()
	a = [0]+a
	dp = [[[-10**9,-10**9] for _ in range(n//2+2)] for _ in range(n+1)]
	dp[1][1][1]=a[1]
	for i in range(0,n+1):
		dp[i][0]=[0,0]
	for i in range(1,n+1):
		if i-1 >= 3:
			dp[i][(i-1)//2][0]=max(dp[i-1][(i-1)//2][0], dp[i-1][(i-1)//2][1])
			dp[i][(i-1)//2][1]=max(dp[i-1][(i-1)//2-1][0]+a[i], dp[i-2][(i-1)//2-1][0]+a[i])
		if i >= 2:
			dp[i][i//2][0]=max(dp[i-1][i//2][0], dp[i-1][i//2][1])
			dp[i][i//2][1]=max(dp[i-1][i//2-1][0]+a[i], dp[i-2][i//2-1][0]+a[i])
		if i >= 2:
			dp[i][(i+1)//2][1]=max(dp[i-1][(i+1)//2-1][0]+a[i], dp[i-2][(i+1)//2-1][0]+a[i])
	print(max(dp[n][n//2]))
if __name__ == '__main__':
	main()

Fixed submission:
import sys
from collections import defaultdict

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
printV = lambda x: print(*x, sep="\n")
printH = lambda x: print(" ".join(map(str,x)))
def IS(): return sys.stdin.readline()[:-1]
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LII(rows_number): return [II() for _ in range(rows_number)]
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]

def main():
	n = II()
	a = LI()
	a = [0]+a
	dp_t = defaultdict(lambda: -10**18)
	dp_f =  defaultdict(lambda: -10**18)
	dp_f[(0,0)]=0
	for i in range(1,n+1):
		dp_f[(i,(i-1)//2)]=max(dp_f[(i-1,(i-1)//2)], dp_t[(i-1,(i-1)//2)])
		dp_t[(i,(i-1)//2)]=dp_f[(i-1,(i-1)//2-1)]+a[i]
		dp_f[(i,(i-1)//2+1)]=max(dp_f[(i-1,(i-1)//2+1)], dp_t[(i-1,(i-1)//2+1)])
		dp_t[(i,(i-1)//2+1)]=dp_f[(i-1,(i-1)//2)]+a[i]
	print(max(dp_t[(n,n//2)],dp_f[(n,n//2)]))
if __name__ == '__main__':
	main()