#include<bits/stdc++.h>

using namespace std;

#define ll long long

#define sp ios_base::sync_with_stdio(false),cin.tie(NULL),cout.tie(NULL)

#define cps CLOCKS_PER_SEC

#define mod (ll)1000000007

#define f first

#define s second

#define debug1(x) cerr<<x<<"\n"

#define debug2(x,y) cerr<<x<<" "<<y<<"\n"

#define debug3(x,y,z) cerr<<x<<" "<<y<<" "<<z<<"\n"

#define nl cerr<<"\n";

#define pq priority_queue

#define inf 0x3f3f3f3f

#define test cerr<<"abcd\n";

#define pi pair<ll,ll>

#define pii pair<int,pi>

#define pb push_back

#define mxn 200005

ll a[mxn],l1[mxn],l2[mxn],r1[mxn],r2[mxn];

unordered_map<ll,ll> mp1,mp2;

#define error(args...) { string _s = #args; replace(_s.begin(), _s.end(), ',', ' '); stringstream _ss(_s); istream_iterator<string> _it(_ss); err(_it, args); }

void err(istream_iterator<string> it) {}

template<typename T, typename... Args>

void err(istream_iterator<string> it, T a, Args... args) {

cout << *it << " =: " << a << endl;

err(++it, args...);

}

template <typename T1, typename T2>

inline std::ostream& operator << (std::ostream& os, const std::pair<T1, T2>& buf) {

return os << "(" << buf.first << ": " << buf.second << ")";

}

template<typename T>

inline std::ostream &operator << (std::ostream & os,const std::vector<T>& v) {

bool first = true;

os << "[";

for(unsigned int i = 0; i < v.size(); i++) {

if(!first) os << ", ";

os << v[i];

first = false;

}

return os << "]";

}

template<typename T>

inline std::ostream &operator << (std::ostream & os,const std::set<T>& v) {

bool first = true;

os << "{";

for (typename std::set<T>::const_iterator ii = v.begin(); ii != v.end(); ++ii) {

if(!first) os << ", ";

os << *ii;

first = false;

}

return os << "}";

}

template<typename T1, typename T2>

inline std::ostream &operator << (std::ostream & os,const std::map<T1, T2>& v) {

bool first = true;

os << "{";

for (typename std::map<T1, T2>::const_iterator ii = v.begin(); ii != v.end(); ++ii) {

if(!first) os << ", ";

os << *ii ;

first = false;

}

return os << "}";

}

template<typename T>

inline std::ostream &operator << (std::ostream & os,const vector<vector<T>>& v) {

os << '\n';

for (auto &u: v) os << u << '\n';

return os;

}

#define dbg1(x) cout << #x << ": " << x << endl;

#define dbg2(x, y) cout << #x << ": " << x << " | " << #y << ": " << y << endl;

#define dbg3(x, y, z) cout << #x << ": " << x << " | " << #y << ": " << y << " | " << #z << ": " << z << endl;

#define dbg4(a, b, c, d) cout << #a << ": " << a << " | " << #b << ": " << b << " | " << #c << ": " << c << " | " << #d << ": " << d << endl;

#define dbg5(a, b, c, d, e) cout << #a << ": " << a << " | " << #b << ": " << b << " | " << #c << ": " << c << " | " << #d << ": " << d << " | " << #e << ": " << e << endl;

#define dbg6(a, b, c, d, e, f) cout << #a << ": " << a << " | " << #b << ": " << b << " | " << #c << ": " << c << " | " << #d << ": " << d << " | " << #e << ": " << e << " | " << #f << ": " << f << endl;

#define dbg(...) fprintf(stderr, __VA_ARGS__)

#define dbgv(x) cout << #x << " = " << x << endl

#define dbga(arr, len) {cout << #arr << " = "; for (int _ = 0; _ < len; _++)\

cout << arr[_] << " "; cout << endl;}

#define dbgi(it) {cout << #it << " = "; for (const auto& _ : it)\

cout << _ << " "; cout << endl;}

void showstack(stack <int> s)

}

int main(){

}