n = int(input())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
c = [(a[i]+b[i])//2 for i in range(n)]

dp = [[[0,0] for i in range(3)] for i in range(n)]

dp[0][0] = [a[0],a[0]]
dp[0][1] = [b[0],b[0]]
dp[0][2] = [c[0],c[0]]

for i in range(1, n):
  ai, bi,ci = a[i],b[i], c[i]
  for jj,j in enumerate([ai,bi,ci]):
    tmp = [10**10, -1, -1 ]
    tmp = min(tmp, [max(dp[i-1][0][0],j) - min(dp[i-1][0][1],j), max(dp[i-1][0][0],j ),min(dp[i-1][0][1],j) ])
    tmp = min(tmp, [max(dp[i-1][1][0],j) - min(dp[i-1][1][1],j), max(dp[i-1][1][0],j ),min(dp[i-1][1][1],j) ])
    tmp = min(tmp, [max(dp[i-1][2][0],j) - min(dp[i-1][2][1],j), max(dp[i-1][2][0],j ),min(dp[i-1][2][1],j) ])
    dp[i][jj] = tmp[1:]

ans = float("inf")
for i in range(3):
  ans = min(dp[-1][i][0] - dp[-1][i][1], ans)

print(ans)