#pragma GCC optimize("O3") #include // clang-format off using namespace std; using ll = long long int; #define all(v) (v).begin(),(v).end() #define repeat(cnt,l) for(typename remove_const::type>::type cnt={};(cnt)<(l);++(cnt)) #define rrepeat(cnt,l) for(auto cnt=(l)-1;0<=(cnt);--(cnt)) #define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt)) #define upto(cnt,b,e,step) for(auto cnt=(b);(cnt)<=(e);(cnt)+=(step)) #define downto(cnt,b,e,step) for(auto cnt=(b);(e)<=(cnt);(cnt)-=(step)) const long long MD = 998244353; const long double PI = 3.1415926535897932384626433832795L; template inline ostream& operator <<(ostream &o, const pair p) { o << '(' << p.first << ':' << p.second << ')'; return o; } template inline T& chmax(T& to, const T& val) { return to = max(to, val); } template inline T& chmin(T& to, const T& val) { return to = min(to, val); } void bye(string s, int code = 0) { cout << s << endl; exit(code); } mt19937_64 randdev(8901016); template::value>::type* = nullptr> inline T rand(T l, T h, Random& rand = randdev) { return uniform_int_distribution(l, h)(rand); } template::value>::type* = nullptr> inline T rand(T l, T h, Random& rand = randdev) { return uniform_real_distribution(l, h)(rand); }template static ostream& operator<<(ostream& o, const std::vector& v) { o << "[ "; for(const auto& e : v) o< struct MyRangeFormat{ I b,e; MyRangeFormat(I _b, I _e):b(_b),e(_e){} }; template static ostream& operator<<(ostream& o, const MyRangeFormat& f) { o << "[ "; iterate(i,f.b,f.e) o<<*i<<' '; return o << ']'; } template struct MyMatrixFormat{ const I& p; long long n, m; MyMatrixFormat(const I& _p, long long _n, long long _m):p(_p),n(_n),m(_m){} }; template static ostream& operator<<(ostream& o, const MyMatrixFormat& f) { o<<'\n'; repeat(i,(f.n)) { repeat(j,f.m) o<(m,m+w)) #define FMTR(b,e) (MyRangeFormat(b,e)) #define FMTV(v) FMTR(v.begin(),v.end()) #define FMTM(m,h,w) (MyMatrixFormat(m,h,w)) #if defined(_WIN32) || defined(_WIN64) #define getc_x _getc_nolock #define putc_x _putc_nolock #elif defined(__GNUC__) #define getc_x getc_unlocked #define putc_x putc_unlocked #else #define getc_x getc #define putc_x putc #endif class MaiScanner { FILE* fp_; constexpr bool isvisiblechar(char c) noexcept { return (0x21<=(c)&&(c)<=0x7E); } public: inline MaiScanner(FILE* fp):fp_(fp){} template void input_integer(T& var) noexcept { var = 0; T sign = 1; int cc = getc_x(fp_); for (; cc < '0' || '9' < cc; cc = getc_x(fp_)) if (cc == '-') sign = -1; for (; '0' <= cc && cc <= '9'; cc = getc_x(fp_)) var = (var << 3) + (var << 1) + cc - '0'; var = var * sign; } inline int c() noexcept { return getc_x(fp_); } template::value, nullptr_t>::type = nullptr> inline MaiScanner& operator>>(T& var) noexcept { input_integer(var); return *this; } inline MaiScanner& operator>>(string& var) { int cc = getc_x(fp_); for (; !isvisiblechar(cc); cc = getc_x(fp_)); for (; isvisiblechar(cc); cc = getc_x(fp_)) var.push_back(cc); return *this; } template inline void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; } }; class MaiPrinter { FILE* fp_; public: inline MaiPrinter(FILE* fp):fp_(fp){} template void output_integer(T var) noexcept { if (var == 0) { putc_x('0', fp_); return; } if (var < 0) putc_x('-', fp_), var = -var; char stack[32]; int stack_p = 0; while (var) stack[stack_p++] = '0' + (var % 10), var /= 10; while (stack_p) putc_x(stack[--stack_p], fp_); } inline MaiPrinter& operator<<(char c) noexcept { putc_x(c, fp_); return *this; } template::value, nullptr_t>::type = nullptr> inline MaiPrinter& operator<<(T var) noexcept { output_integer(var); return *this; } inline MaiPrinter& operator<<(const char* str_p) noexcept { while (*str_p) putc_x(*(str_p++), fp_); return *this; } inline MaiPrinter& operator<<(const string& str) { const char* p = str.c_str(); const char* l = p + str.size(); while (p < l) putc_x(*p++, fp_); return *this; } template void join(IT begin, IT end, char sep = ' ') { for (bool b = 0; begin != end; ++begin, b = 1) b ? *this << sep << *begin : *this << *begin; } }; MaiScanner scanner(stdin); MaiPrinter printer(stdout); // clang-format on // max - min を固定して判定できないか? // 数直線上に ai, bi, avg(a,b) を置く。 // 尺取りで個数を管理する // int N; int A[200010], B[200010]; // // val, i vector> lis; bool check(int width) { const int n = (int)lis.size(); int tail = 0; map contains; repeat(head, n) { auto p = lis[head]; // LOG << "<" << p; contains[p.second] += 1; while (tail < n && lis[tail].first + width < p.first) { // LOG << ">" << lis[tail]; auto it = contains.find(lis[tail].second); it->second -= 1; if (it->second == 0) { contains.erase(it); } ++tail; } if ((int)contains.size() == N) { return true; } } return false; } int main() { scanner >> N; scanner.in(A, A+N); scanner.in(B, B+N); repeat(i, N) { lis.emplace_back(A[i], i); lis.emplace_back(B[i], i); lis.emplace_back((A[i] + B[i])/2, i); } sort(all(lis)); int ok = 1000000007; int ng = -1; while (ok - ng > 1) { int m = (ok + ng)/2; if (check(m)) ok = m; else ng = m; } cout << ok << endl; return 0; }