//EYEHEAD VERSION 4 POWERED BY BADCAT [URL: https://hmgc.ct.ws/]
//
//     /@@@@@@  /@@@@@@  /@@@@@   /@@@@@@  /@@@@@@  /@@@@@@@
//     /@   /@  /@////@  /@////@  /@/////  /@////@   ///@///
//     /@@@@    /@   /@  /@   /@  /@       /@   /@     /@
//     /@@@@@   /@@@@@@  /@   /@  /@       /@@@@@@     /@
//     /@   /@  /@////@  /@   /@  /@       /@////@     /@
// BY  /@@@@@@  /@   /@  /@@@@@   /@@@@@@  /@   /@     /@
//
//              (c)BADCAT FACTORY CO' LTD 2025
//  由洛谷BadCatFactory（即本OJ的badcat）自主制作，仅许使用，谢绝转载 


//                     大神Edsger Dijkstra
//
//                        #     #     #
//                        i     i     i
//                         i    i    i
//                          i   i   i
//                           i  i  i
//                            i i i
//                             iii
//
//                烧高香，拜大神，求AC！辟邪辟WA！ 

//import head files
// C
#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <unistd.h>
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
//#include <windows.h> //Microsoft Windows Lib
//#include <winternl.h> //Microsoft WinNT Lib

#if __cplusplus >= 201103L
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
#include <cstdalign>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif

// C++
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>

#if __cplusplus >= 201103L
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <typeindex>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#endif

//using namespace
using namespace std;

//defines
#define st short
#define li long
#define ll long long
#define fl float
#define db double
#define bl bool
#define ldb long double
#define vi void
#define cr char
#define cs const
#define sg string
#define im INT_MAX
#define iw INT_MIN
#define null NULL
#define endl '\n'
#define gl(a) getline(cin,a)
#define rt return
#define rn return 0
#define mx max
#define mi min
#define co cout
#define ci cin
#define fr for
#define wl while
#define endt '\0'
#define sortdown(a,b) sort(a,b),reverse(a,b)
#define m_func int main
#define it int
#define fst ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define mf_h it argc, cr** argv
#define te true
#define fe false
#define sq sqrt
#define sd signed
#define ce continue
#define bk break
#define inl inline 
#define sw switch
#define ca case
#define dt default
#define fd fixed
#define set_p setprecision
#define sk stack
#define ps push
#define qe queue
#define ep empty
#define ft front
#define bc back
#define pp pop
#define to top
#define su struct
#define ue unsigned
#define sz size
#define ee else
#define infinity 0x7fffffff
#define INF infinity
#define del delete
#define nptr nullptr
#define vect vector 

//functions
ll cf(ll a,ll b){ll x=1;fr(ll i=0;i<b;i++)x*=a;rt x;}//求次方 
inl bl is_p(ll a){if(a==1){rt fe;}bl x=te;fr(ll j=2;j<=sq(a);j++){if(a%j==0)x=fe;}rt x;}//判断质数 
it int_dx(it n){it s=0;wl(n){s=s*10+n%10;n/=10;}rt s;}//整数倒序 
bl str_hw(cr *str){it len=strlen(str);fr(it i=0,j=len-1;i<j;i++,j--){if(str[i]!=str[j])rt fe;}rt te;}//判断回文字符串 
bl int_hw(it n){it x=0,t=n;fr(it i=0;i<20;i++){if(n==0)bk;x*=10;x+=n%10;n/=10;}if(x==t)rt 1;rt 0;}//判断回文数 
it swap_int(it n){it x=0;fr(it i=0;i<20;i++){if(n==0)bk;x*=10;x+=n%10;n/=10;}rt x;}//反转整数 
it atoi(sg s,it r){it a=0;fr(it i=0;i<s.sz();i++){cr t=s[i];if(t>='0'&&t<='9')a=a*r+t-'0';ee a=a*r+t-'a'+10;}rt a;}//R进制转换10进制 

//vars, custom functions, structs and arrays 
cs ldb PI = 3.14159;
cs ldb E = 2.71828;
su vec2{ldb x,y;};
su vec3{ldb x,y,z;};
su vec2_int{it x,y;};
su vec3_int{it x,y,z;};

//classes and objects
//none

//main function
m_func(mf_h){
    fst;
    //begin
    
    //end
    rn;
}