/* Code by
               __            __                       __         
              /\ \__        /\ \                     /\ \        
   __     _ __\ \ ,_\       \ \ \___      __      ___\ \ \/'\    
 /'__`\  /\`'__\ \ \/        \ \  _ `\  /'__`\   /'___\ \ , <    
/\ \L\.\_\ \ \/ \ \ \_        \ \ \ \ \/\ \L\.\_/\ \__/\ \ \\`\  
\ \__/.\_\\ \_\  \ \__\        \ \_\ \_\ \__/.\_\ \____\\ \_\ \_\
 \/__/\/_/ \/_/   \/__/  _______\/_/\/_/\/__/\/_/\/____/ \/_/\/_/
                        /\______\                                
                        \/______/                                
*/

#include <bits>
using namespace std;



int main() {
ios::sync_with_stdio(0);
cin.tie(0);





return 0;
}