def main():
    import sys
    input = sys.stdin.read().split()
    idx = 0
    N = int(input[idx])
    idx += 1
    A = list(map(int, input[idx:idx+N]))
    idx += N
    B = list(map(int, input[idx:idx+N]))
    idx += N
    
    possible_x = None
    for i in range(N):
        a = A[i]
        b = B[i]
        m = (a + b) // 2
        current = {a, b, m}
        if possible_x is None:
            possible_x = current
        else:
            possible_x &= current
        if not possible_x:
            break
    
    if possible_x:
        print(0)
        return
    
    candidates = []
    for i in range(N):
        a = A[i]
        b = B[i]
        m = (a + b) // 2
        candidates.append((a, i))
        candidates.append((b, i))
        candidates.append((m, i))
    
    candidates.sort()
    
    freq = [0] * N
    count = 0
    min_length = float('inf')
    left = 0
    
    for right in range(len(candidates)):
        val, group = candidates[right]
        if freq[group] == 0:
            count += 1
        freq[group] += 1
        
        while count == N and left <= right:
            current_min = candidates[left][0]
            current_max = val
            current_length = current_max - current_min
            if current_length < min_length:
                min_length = current_length
            
            left_val, left_group = candidates[left]
            freq[left_group] -= 1
            if freq[left_group] == 0:
                count -= 1
            left += 1
    
    print(min_length)

if __name__ == '__main__':
    main()