N=int(input())
A=[int(i) for i in input().split()]
B=[int(i) for i in input().split()]
X=[(A[i]+B[i])//2 for i in range(N)]
def solve(k):
    #max(C)-min(C)<=kとすることが可能かどうか
    for x in [A[0],B[0],X[0]]:
        MAX=x
        MIN=x
        for i in range(1,N):
            C=[]
            for y in [A[i],B[i],X[i]]:
                if max(MAX,y)-min(MIN,y)<=k:
                    MAX=max(MAX,y)
                    MIN=min(MIN,y)
                    C.append((max(MAX,y)-min(MIN,y),y))
            if len(C)==0:
                MAX=10**18
                MIN=-10**18
                break
            y=min(C)[1]
            MAX=max(MAX,y)
            MIN=min(MIN,y)
            
        if MAX-MIN<=k:
            return True
    return False
low=-1
high=1
while(not(solve(high))):
    high*=2
while(high-low>1):
    mid=(low+high)//2
    if solve(mid):
        high=mid
    else:
        low=mid
print(high)