Buggy python submission (verdict: Runtime Error):
n=int(input())
a=list(map(int,input().split()))
import numpy as np
dp=np.full((3,n+1),-pow(10,15))
dp[1,1]=a[0]
for i in range(2,n+1):
    #l,r=max(1,n//2-(n-i+1)//2),(i+1)//2+1
    l,r=max(1,i//2-1),(i+1)//2+1
    if i%3==2:
        now,pre,prepre=2,1,0
    elif i%3==0:
        now,pre,prepre=0,2,1
    elif i%3==1:
        now,pre,prepre=1,0,2
    dp[now,l:r]=np.maximum(dp[pre,l:r],dp[prepre,l-1:r-1]+a[i-1])
print(dp[now,n//2])

Fixed submission:
from collections import defaultdict

n=int(input())
a=list(map(int,input().split()))
#n=2*pow(10,5)
#a=range(1,pow(10,5)+1)
# dp[i][j]:i番目の数字の中からj個数字を取った時の最大。(i//2)-1<=j<=(i+1)//2
# 求めるのはdp[n][n//2]
dp=defaultdict(lambda:-pow(10,18))
dp[(1,1)]=a[0]
for i in range(2,n+1): #i番目の数字はa[i-1]
      for j in range(i//2-1,(i+1)//2+1):
            if j==1:
                  dp[(i,j)]=max(dp[(i-1,1)],a[i-1])
            elif j==0:
                  dp[(i,j)]=0
            else:
                  dp[(i,j)]=max(dp[(i-2,j-1)]+a[i-1],dp[(i-1,j)])
print(dp[(n,n//2)])

Buggy python submission (verdict: Runtime Error):
n=int(input())
a=list(map(int,input().split()))
import numpy as np
dp=np.zeros((3,n+1),np.int64)
dp[:,0]=0
dp[1,1]=a[0]
for i in range(2,n+1):
    l,r=n//2-(n-i+1)//2,i//2+1
    if i%3==2:
      now,pre,prepre=2,1,0
    elif i%3==0:
      now,pre,prepre=0,2,1
    elif i%3==1:
      now,pre,prepre=1,0,2
    dp[now,l:r]=np.maximum(dp[pre,l:r],dp[prepre,l-1:r-1]+a[i-1])
print(dp[now,n//2])

Fixed submission:
from collections import defaultdict

n=int(input())
a=list(map(int,input().split()))
#n=2*pow(10,5)
#a=range(1,pow(10,5)+1)
# dp[i][j]:i番目の数字の中からj個数字を取った時の最大。(i//2)-1<=j<=(i+1)//2
# 求めるのはdp[n][n//2]
dp=defaultdict(lambda:-pow(10,18))
dp[(1,1)]=a[0]
for i in range(2,n+1): #i番目の数字はa[i-1]
      for j in range(i//2-1,(i+1)//2+1):
            if j==1:
                  dp[(i,j)]=max(dp[(i-1,1)],a[i-1])
            elif j==0:
                  dp[(i,j)]=0
            else:
                  dp[(i,j)]=max(dp[(i-2,j-1)]+a[i-1],dp[(i-1,j)])
print(dp[(n,n//2)])

Buggy python submission (verdict: Runtime Error):
n=int(input())
a=list(map(int,input().split()))
import numpy as np
dp=np.full((n+1,n+1),-pow(10,15))
dp[:,0]=0
dp[1,1]=a[0]
for i in range(2,n+1):
    dp[i,1:]=np.maximum(dp[i-1,1:],dp[i-2,:-1]+a[i-1])
print(dp[n,n//2])

Fixed submission:
from collections import defaultdict

n=int(input())
a=list(map(int,input().split()))
#n=2*pow(10,5)
#a=range(1,pow(10,5)+1)
# dp[i][j]:i番目の数字の中からj個数字を取った時の最大。(i//2)-1<=j<=(i+1)//2
# 求めるのはdp[n][n//2]
dp=defaultdict(lambda:-pow(10,18))
dp[(1,1)]=a[0]
for i in range(2,n+1): #i番目の数字はa[i-1]
      for j in range(i//2-1,(i+1)//2+1):
            if j==1:
                  dp[(i,j)]=max(dp[(i-1,1)],a[i-1])
            elif j==0:
                  dp[(i,j)]=0
            else:
                  dp[(i,j)]=max(dp[(i-2,j-1)]+a[i-1],dp[(i-1,j)])
print(dp[(n,n//2)])

Buggy python submission (verdict: Time Limit Exceeded):
n=int(input())
a=list(map(int,input().split()))
import math
dp=[[-math.inf]*(n+1) for _ in range(n+1)]
dp[0][0]=0
dp[1][0]=0
dp[1][1]=a[0]
for i in range(2,n+1):
    for j in range(n//2-(n-i+1)//2,i//2+1):
        dp[i][j]=max(dp[i-1][j],dp[i-2][j-1]+a[i-1])
print(dp[n][n//2])


Fixed submission:
from collections import defaultdict

n=int(input())
a=list(map(int,input().split()))
#n=2*pow(10,5)
#a=range(1,pow(10,5)+1)
# dp[i][j]:i番目の数字の中からj個数字を取った時の最大。(i//2)-1<=j<=(i+1)//2
# 求めるのはdp[n][n//2]
dp=defaultdict(lambda:-pow(10,18))
dp[(1,1)]=a[0]
for i in range(2,n+1): #i番目の数字はa[i-1]
      for j in range(i//2-1,(i+1)//2+1):
            if j==1:
                  dp[(i,j)]=max(dp[(i-1,1)],a[i-1])
            elif j==0:
                  dp[(i,j)]=0
            else:
                  dp[(i,j)]=max(dp[(i-2,j-1)]+a[i-1],dp[(i-1,j)])
print(dp[(n,n//2)])

Buggy python submission (verdict: Runtime Error):
import numpy as np
n=int(input())
a=list(map(int,input().split()))
# dp[i][j]:i番目の数字の中からj個数字を取った時の最大。(i//2)-1<=j<=(i+1)//2
# 求めるのはdp[n][n//2]
dp=np.full((n+1,n+1),-1e+9)
dp[1,1]=a[0]
for i in range(2,n+1): #i番目の数字はa[i-1]
      for j in range(i//2-1,(i+1)//2+1):
            dp[i,j]=max(dp[i-2,j-1]+a[i-1],dp[i-1,j])
print(int(dp[n,n//2]))

Fixed submission:
from collections import defaultdict

n=int(input())
a=list(map(int,input().split()))
#n=2*pow(10,5)
#a=range(1,pow(10,5)+1)
# dp[i][j]:i番目の数字の中からj個数字を取った時の最大。(i//2)-1<=j<=(i+1)//2
# 求めるのはdp[n][n//2]
dp=defaultdict(lambda:-pow(10,18))
dp[(1,1)]=a[0]
for i in range(2,n+1): #i番目の数字はa[i-1]
      for j in range(i//2-1,(i+1)//2+1):
            if j==1:
                  dp[(i,j)]=max(dp[(i-1,1)],a[i-1])
            elif j==0:
                  dp[(i,j)]=0
            else:
                  dp[(i,j)]=max(dp[(i-2,j-1)]+a[i-1],dp[(i-1,j)])
print(dp[(n,n//2)])

Buggy python submission (verdict: Runtime Error):
import numpy as np
n=int(input())
a=list(map(int,input().split()))
# dp[i][j]:i番目の数字の中からj個数字を取った時の最大。(i//2)-1<=j<=(i+1)//2
# 求めるのはdp[n][n//2]
dp=np.zeros((n+1,(n+1)//2+1),np.int64)
dp[1,1]=a[0]
for i in range(2,n+1): #i番目の数字はa[i-1]
      for j in range(max(0,i//2-1),(i+1)//2+1):
            dp[i,j]=max(dp[i-2,j-1]+a[i-1],dp[i-1,j])
print(dp[n,n//2])

Fixed submission:
from collections import defaultdict

n=int(input())
a=list(map(int,input().split()))
#n=2*pow(10,5)
#a=range(1,pow(10,5)+1)
# dp[i][j]:i番目の数字の中からj個数字を取った時の最大。(i//2)-1<=j<=(i+1)//2
# 求めるのはdp[n][n//2]
dp=defaultdict(lambda:-pow(10,18))
dp[(1,1)]=a[0]
for i in range(2,n+1): #i番目の数字はa[i-1]
      for j in range(i//2-1,(i+1)//2+1):
            if j==1:
                  dp[(i,j)]=max(dp[(i-1,1)],a[i-1])
            elif j==0:
                  dp[(i,j)]=0
            else:
                  dp[(i,j)]=max(dp[(i-2,j-1)]+a[i-1],dp[(i-1,j)])
print(dp[(n,n//2)])

Buggy python submission (verdict: Runtime Error):
import numpy as np
n=int(input())
a=list(map(int,input().split()))
# dp[i][j]:i番目の数字の中からj個数字を取った時の最大。(i//2)-1<=j<=(i+1)//2
# 求めるのはdp[n][n//2]
dp=np.zeros((n+1,n+1),np.int64)
dp[1,1]=a[0]
dp[2,1]=max(a[:2])
for i in range(2,n+1): #i番目の数字はa[i-1]
      for j in range(max(0,i//2-1),(i+1)//2+1):
            dp[i,j]=max(dp[i-2,j-1]+a[i-1],dp[i-1,j])
print(dp[n,n//2])

Fixed submission:
from collections import defaultdict

n=int(input())
a=list(map(int,input().split()))
#n=2*pow(10,5)
#a=range(1,pow(10,5)+1)
# dp[i][j]:i番目の数字の中からj個数字を取った時の最大。(i//2)-1<=j<=(i+1)//2
# 求めるのはdp[n][n//2]
dp=defaultdict(lambda:-pow(10,18))
dp[(1,1)]=a[0]
for i in range(2,n+1): #i番目の数字はa[i-1]
      for j in range(i//2-1,(i+1)//2+1):
            if j==1:
                  dp[(i,j)]=max(dp[(i-1,1)],a[i-1])
            elif j==0:
                  dp[(i,j)]=0
            else:
                  dp[(i,j)]=max(dp[(i-2,j-1)]+a[i-1],dp[(i-1,j)])
print(dp[(n,n//2)])