/***
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 *    $$$$$$$\  $$\ $$$$$$$\   $$$$$$$\ $$$$$$$\   $$$$$$\   $$$$$$$ |$$\ $$\  $$$$$$\  
 *    $$  __$$\ $$ |$$  __$$\ $$  _____|$$  __$$\ $$  __$$\ $$  __$$ |$$ |\__|$$  __$$\ 
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 *    $$ |  $$ |$$ |$$ |  $$ |\$$$$$$$\ $$ |  $$ |\$$$$$$  |\$$$$$$$ |$$ |$$ |\$$$$$$  |
 *    \__|  \__|\__|\__|  \__| \_______|\__|  \__| \______/  \_______|\__|$$ | \______/ 
 *                                                                  $$\   $$ |          
 *                                                                  \$$$$$$  |          
 *                                                                   \______/           
 */