Problem:
Score : 600 points

Problem Statement

Given are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N.
Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \leq B_i holds:

Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.

Constraints

2 \leq N \leq 10^5

1 \leq A_i,B_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N
B_1 B_2 ... B_N

Output

If the objective is achievable, print Yes; if it is not, print No.

Sample Input 1

3
1 3 2
1 2 3

Sample Output 1

Yes

We should swap the values of A_2 and A_3.

Sample Input 2

3
1 2 3
2 2 2

Sample Output 2

No

Sample Input 3

6
3 1 2 6 3 4
2 2 8 3 4 3

Sample Output 3

Yes

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
#define _overload3(_1, _2, _3, name, ...) name
#define _rep(i, n) repi(i, 0, n)
#define repi(i, a, b) for(int i = int(a), i##_len = (b); i < i##_len; ++i)
#define rep(...) _overload3(__VA_ARGS__, repi, _rep, )(__VA_ARGS__)
#define _repr(i, n) repri(i, n, 0)
/* loop in [n,m] step -1 */
#define repri(i, a, b) for(int i = int(a), i##_len = (b); i >= i##_len; --i)
/* loop in [n,0] step -1 or [n,m] step -1 */
#define repr(...) _overload3(__VA_ARGS__, repri, _repr, )(__VA_ARGS__)
#define all(x) (x).begin(), (x).end()
#define debug(x) cerr << #x << ": " << (x) << '\n'
#define endl '\n'
typedef vector<int> vint;
typedef pair<int, int> pint;
#define CPP_STR(x) CPP_STR_I(x)
#define CPP_CAT(x, y) CPP_CAT_I(x, y)
#define CPP_STR_I(args...) #args
#define CPP_CAT_I(x, y) x##y
#define ASSERT(expr...) assert((expr))

/* type annotation */
using i8 = int8_t;
using u8 = uint8_t;
using i16 = int16_t;
using u16 = uint16_t;
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;

using f32 = float;
using f64 = double;

constexpr i64 INF = 1'010'000'000'000'000'017LL;

constexpr i64 MOD = 1'000'000'007LL;

constexpr f64 EPS = 1e-12;

constexpr f64 PI = 3.14159265358979323846;

/* macros */
#define FOR(i, start, end)                             \
    for(i64 i = (start), CPP_CAT(i, xxxx_end) = (end); \
        i < CPP_CAT(i, xxxx_end); ++i)
#define REP(i, n) FOR(i, 0, n)
#define ALL(f, c, ...)                                               \
    (([&](decltype((c)) cccc) {                                      \
        return (f)(std::begin(cccc), std::end(cccc), ##__VA_ARGS__); \
    })(c))
template <typename C>
i64 SIZE(const C &c) {
    return static_cast<i64>(c.size());
}
template <typename T, size_t N>
i64 SIZE(const T (&)[N]) {
    return static_cast<i64>(N);
}
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())

/* marathon match */
#ifdef LOCAL
const i64 CYCLES_PER_SEC = 2800000000;
#else
const i64 CYCLES_PER_SEC = 2800000000;  // AtCoder
#endif

struct Timer {
    i64 start;

    Timer() { reset(); }

    void reset() { start = getCycle(); }

    inline double get() {
        return (double)(getCycle() - start) / CYCLES_PER_SEC * 1000;
    }

   private:
    inline i64 getCycle() {
        u32 low, high;
        __asm__ volatile("rdtsc" : "=a"(low), "=d"(high));
        return ((i64)low) | ((i64)high << 32);
    }
} timer;

class XorShift {
   public:
    unsigned int x, y, z, w;
    double nL[65536];

    XorShift() { init(); }

    void init() {
        x = 314159265;
        y = 358979323;
        z = 846264338;
        w = 327950288;
        double n = 1 / (double)(2 * 65536);
        for(int i = 0; i < 65536; i++) {
            nL[i] = log(((double)i / 65536) + n);
        }
    }

    inline unsigned int next() {
        unsigned int t = x ^ x << 11;
        x = y;
        y = z;
        z = w;
        return w = w ^ w >> 19 ^ t ^ t >> 8;
    }

    inline double nextLog() { return nL[next() & 0xFFFF]; }

    inline int nextInt(int m) { return (int)(next() % m); }

    int nextInt(int min, int max) { return min + nextInt(max - min + 1); }

    inline double nextDouble() { return (double)next() / ((long long)1 << 32); }
} rnd;

struct IoSetup {
    IoSetup() {
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(20);
        cerr << fixed << setprecision(20);
    }
} iosetup;

/* lambda recursion */
template <typename F>
class
#if defined(__has_cpp_attribute) && __has_cpp_attribute(nodiscard)
    [[nodiscard]]
#elif defined(__GNUC__) && __GNUC_PREREQ(3, 4)
__attribute__((warn_unused_result))
#endif  // defined(__has_cpp_attribute) && __has_cpp_attribute(nodiscard)
    FixPoint :
    F { public : explicit constexpr FixPoint(F &&f) noexcept :
            F(std::forward<F>(f)) {}

        template <typename... Args> constexpr decltype(auto)
        operator()(Args &&... args) const {
            return F::operator()(*this, std::forward<Args>(args)...);
}
}
;  // class FixPoint

template <typename F>
static inline constexpr decltype(auto) makeFixPoint(F &&f) noexcept {
    return FixPoint<F>{std::forward<F>(f)};
}

/* keep a max,min */
template <typename T, typename U, typename Comp = less<>>
bool chmax(T &xmax, const U &x, Comp comp = {}) {
    if(comp(xmax, x)) {
        xmax = x;
        return true;
    }
    return false;
}

template <typename T, typename U, typename Comp = less<>>
bool chmin(T &xmin, const U &x, Comp comp = {}) {
    if(comp(x, xmin)) {
        xmin = x;
        return true;
    }
    return false;
}

/* input,output operator for pair, vector and map */

/* input,output operator for pair and vector */
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
    os << p.first << " " << p.second;
    return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
    for(int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 != v.size() ? " " : "");
    }
    return os;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<vector<T>> &v) {
    for(int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 != v.size() ? "\n" : "");
    }
    return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
    for(T &in : v) is >> in;
    return is;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &mp) {
    os << "{";
    for(auto x = mp.begin(); x != mp.end(); ++x) {
        os << x->first << ":" << x->second << (x != prev(mp.end()) ? ", " : "");
    }
    os << "}";
    return os;
}

using std::to_string;

auto to_string(std::string s) -> std::string { return s; }

auto to_string(char c) -> std::string { return std::string{c}; }

auto to_string(const char *s) -> std::string {
    return to_string((std::string)s);
}

auto to_string(bool b) -> std::string { return (b ? "true" : "false"); }

template <typename T, typename U>
auto to_string(std::pair<T, U> p) -> std::string {
    return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <size_t N>
auto to_string(std::bitset<N> bs) -> std::string {
    std::string res{};
    for(size_t i = 0; i < N; i++)
        res.insert(res.begin(), bs.test(i) ? '1' : '0');
    return res;
}

template <typename T>
auto to_string(T v) -> std::string {
    bool flg = false;
    std::string res = "[";
    for(auto const &x : v) {
        if(flg)
            res += ", ";
        else
            flg = true;
        res += to_string(x);
    }
    res += "]";
    return res;
}

/* initialize vector. usage: auto v = make_v<int>(N,0); */
template <typename T>
vector<T> make_v(size_t a) {
    return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
    return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

/* fill vector. usage: fill_v(v,0); */
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
    t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
    for(auto &e : t) fill_v(e, v);
}

/* sum */
template <typename T>
T sum(vector<T> &v) {
    T ret = 0;
    for(T x : v) {
        ret += x;
    }
    return ret;
}
template <typename T>
auto sum(const T &a) {
    return a;
}
template <typename T, typename... A>
auto sum(const T &first, const A &... rest) {
    return sum(first) + sum(rest...);
}

int main() {
    auto end = [](string x) {
        cout << x << endl;
        exit(0);
    };
    i64 N;
    cin >> N;
    vector<i64> A(N), B(N);
    cin >> A;
    cin >> B;
    vector<i64> subA = A;

    sort(B.begin(), B.end());
    sort(subA.begin(), subA.end());
    REP(i, N) if(subA[i] > B[i]) end("No");

    UNIQUE(subA);
    vector<i64> idx(N + 1);
    if(subA.size() != A.size()) end("Yes");
    REP(i, N) idx[A[i]] = i;
    REP(i, N) {
        if(subA[i] == A[i]) end("Yes");
        i64 st = A[i];
        swap(A[i], A[idx[i]]);
        idx[A[i]] = idx[i], idx[i] = i;
    }
    end("No");
    return 0;
}