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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
	#include <boost/multiprecision/cpp_int.hpp>
	#include <boost/multiprecision/cpp_dec_float.hpp>
	using bll = boost::multiprecision::cpp_int;
	using bdouble = boost::multiprecision::cpp_dec_float_100;
#endif
#ifdef LOCAL_DEV
	void debug_impl() { std::cerr << std::endl; }
	template<typename Head, typename... Tail> void debug_impl(Head head, Tail... tail) { std::cerr << " " << head << (sizeof...(tail) ? "," : ""); debug_impl(tail...); }
	#define debug(...) std::cerr << std::boolalpha << "(" << #__VA_ARGS__ << ") ="; debug_impl(__VA_ARGS__); std::cerr << std::noboolalpha;
#else
	#define debug(...)
#endif
#ifdef LOCAL_TEST
	#define BOOST_STACKTRACE_USE_ADDR2LINE
	#define BOOST_STACKTRACE_ADDR2LINE_LOCATION /usr/local/opt/binutils/bin/addr2line
	#define _GNU_SOURCE
	#include <boost/stacktrace.hpp>
	template<typename T> class dvector : public std::vector<T> {
	public:
		dvector() : std::vector<T>() {}
		explicit dvector(size_t n, const T& value = T()) : std::vector<T>(n, value) {}
		dvector(const std::vector<T>& v) : std::vector<T>(v) {}
		dvector(const std::initializer_list<T> il) : std::vector<T>(il) {}
		dvector(const typename std::vector<T>::iterator first, const typename std::vector<T>::iterator last) : std::vector<T>(first, last) {}
		dvector(const std::string::iterator first, const std::string::iterator last) : std::vector<T>(first, last) {}
		T& operator[](size_t n) {
			try { return this->at(n); } catch (const std::exception& e) {
				std::cerr << boost::stacktrace::stacktrace() << std::endl; return this->at(n);
			}
		}
		const T& operator[](size_t n) const {
			try { return this->at(n); } catch (const std::exception& e) {
				std::cerr << boost::stacktrace::stacktrace() << std::endl; return this->at(n);
			}
		}
	};
	class dbool {
	private:
		bool boolvalue;
	public:
		dbool() : boolvalue(false) {}
		dbool(bool b) : boolvalue(b) {}
		dbool(const dbool &b) : boolvalue(b.boolvalue) {}
		operator bool&() { return boolvalue; }
		operator const bool&() const { return boolvalue; }
	};
	template<typename T> std::ostream& operator<<(std::ostream& s, const dvector<T>& v) {
		for (int i = 0, len = v.size(); i < len; ++i){ s << v[i]; if (i < len - 1) s << "\t"; } return s; }
	template<typename T> std::ostream& operator<<(std::ostream& s, const dvector< dvector<T> >& vv) {
		for (int i = 0, len = vv.size(); i < len; ++i){ s << vv[i] << std::endl; } return s; }
	template<typename T> std::ostream& operator<<(std::ostream& s, const std::set<T>& se) {
		s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}" << std::endl; return s; }
	template<typename T> std::ostream& operator<<(std::ostream& s, const std::multiset<T>& se) {
		s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}" << std::endl; return s; }
	template<typename T1, typename T2> std::ostream& operator<<(std::ostream& s, const std::map<T1, T2>& m) {
		s << "{" << std::endl; for (auto itr = m.begin(); itr != m.end(); ++itr){ s << "\t" << (*itr).first << " : " << (*itr).second << std::endl; } s << "}" << std::endl; return s; }
	template<typename T1, typename T2> std::ostream& operator<<(std::ostream& s, const std::pair<T1, T2>& p) { 
		return s << "(" << p.first << ", " << p.second << ")"; }
	#define vector dvector
	#define bool dbool
#endif
//#define int long long
using ll = long long;
//constexpr int INF = 1e9;//INT_MAX=(1<<31)-1=2147483647
constexpr ll INF = (ll)1e18;//(1LL<<63)-1=9223372036854775807
constexpr ll MOD = (ll)1e9 + 7;
constexpr double EPS = 1e-9;
constexpr int dx[4]={1,0,-1,0};
constexpr int dy[4]={0,1,0,-1};
#define p(var) std::cout<<var<<std::endl
#define rep(i, n)   for(ll i=0, i##_length=(n); i< i##_length; ++i)
#define repeq(i, n) for(ll i=1, i##_length=(n); i<=i##_length; ++i)
#define all(v) (v).begin(), (v).end()
#define uniq(v) (v).erase(unique((v).begin(), (v).end()), (v).end());
template<typename T> inline void pv(vector<T> &v) { for(ll i=0, N=v.size(); i<N; i++) std::cout << v[i] << " \n"[i==N-1]; }
template<typename T> inline T gcd(T a, T b) { return b ? gcd(b,a%b) : a; }
template<typename T> inline T lcm(T a, T b) { return a / gcd(a,  b) * b; }
template<typename T1, typename T2> inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
template<typename T1, typename T2> inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

/*-----8<-----template-----8<-----*/

/*-----8<-----library-----8<-----*/

constexpr ll N_MAX = 100000;
constexpr ll A_IB_I_MAX = 1000000000;

ll N;
vector<ll> A;
vector<ll> B;

void dfs(vector<vector<ll>> &g,ll v,ll p,ll depth,vector<ll> &seen){
	seen[v]=depth;
	for(ll nextv:g[v]){
		if(seen[nextv]!=-1)return;
		dfs(g,nextv,v,depth+1,seen);
	}
}

void solve() {
  	scanf("%lld", &N);
	A.assign(N, 0);
	rep(i, N) scanf("%lld", &A[i]);
	B.assign(N, 0);
	rep(i, N) scanf("%lld", &B[i]);

	//配置変え
	vector<pair<ll,ll>> C(N);
	rep(i,N){
		C[i].first=A[i];
		C[i].second=B[i];
	}
	sort(all(C));
	rep(i,N){
		A[i]=C[i].first;
		B[i]=C[i].second;
	}

	//最高形でも満たせないならNo
	vector<pair<ll,ll>> sortedApair(N),sortedBpair(N);
	rep(i,N){
		sortedApair[i].first=A[i];
		sortedApair[i].second=i;
		sortedBpair[i].first=B[i];
		sortedBpair[i].second=i;
	}
	vector<ll> sortedA=A,sortedB=B;
	sort(all(sortedA));
	sort(all(sortedB));
	sort(all(sortedApair));
	sort(all(sortedBpair));
	rep(i,N){
		if(sortedA[i]>sortedB[i]){p("No");return;}
	}
	
	debug(sortedApair);
	debug(sortedBpair);

	//猶予の検査 最初から都合の良い配置ならYes
	rep(i,N){
		ll j=lower_bound(all(sortedA),sortedB[i])-sortedA.begin();
		debug(j);
		if(i==j){
			if(sortedApair[i].second==sortedBpair[i].second){
				p("Yes");return;
			}
			continue;
		}
		j--;
		//ll l=sortedApair[i].second;
		//ll r=sortedApair[j].second;
		ll index=sortedBpair[i].second;
		//debug(l,r,A[index]);
		debug(i,j,index);
		if(i<=index && index<=j){
			p("Yes");return;
		}
		//if(l<=A[index] && A[index]<=r){
		//	p("Yes");return;
		//}
	}

	//ループ
	vector<vector<ll>> g(N);
	rep(i,N){
		g[i].push_back(sortedBpair[i].second);
	}
	debug(g);
	vector<ll> seen(N,-1);
	rep(i,N){
		if(seen[i]==-1){
			dfs(g,i,-1,0,seen);
		}
	}

	rep(i,N){
		if(seen[i]==N-1){
			p("No");return;
		}
	}
	p("Yes");
}

signed main() {
	solve();
	return 0;
}