⢀⢀⣠⣶⡶⠾⠿⠶⣶⣶⣤⣤⣤⠀⠀⠀⠀⢠⣤⣤⣴⣶⣶⣾⠿⠷⢶⣮⣖⠄
⠁⠛⠁⠀⠀⠀⠤⠤⠤⠤⠤⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠄⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠊⢹⣿⣿⣿⠙⡆⠀⠳⠀⠀⠀⠀⠀⠇⠀⡼⠋⣿⣿⣿⠉⠑⠄⠀⠀
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠴⠚⠁⠀⠀⡎⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀



⢀⢀⣠⣶⡶⠾⠿⠶⣶⣶⣤⣤⣤⠀⠀⠀⠀⢠⣤⣤⣴⣶⣶⣾⠿⠷⢶⣮⣖⠄
⠁⠛⠁⠀⠀⠀⠤⠤⠤⠤⠤⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠄⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠊⢹⣿⣿⣿⠙⡆⠀⠳⠀⠀⠀⠀⠀⠇⠀⡼⠋⣿⣿⣿⠉⠑⠄⠀⠀
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠴⠚⠁⠀⠀⡎⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀



⢀⢀⣠⣶⡶⠾⠿⠶⣶⣶⣤⣤⣤⠀⠀⠀⠀⢠⣤⣤⣴⣶⣶⣾⠿⠷⢶⣮⣖⠄
⠁⠛⠁⠀⠀⠀⠤⠤⠤⠤⠤⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠄⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠊⢹⣿⣿⣿⠙⡆⠀⠳⠀⠀⠀⠀⠀⠇⠀⡼⠋⣿⣿⣿⠉⠑⠄⠀⠀
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠴⠚⠁⠀⠀⡎⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀




⢀⢀⣠⣶⡶⠾⠿⠶⣶⣶⣤⣤⣤⠀⠀⠀⠀⢠⣤⣤⣴⣶⣶⣾⠿⠷⢶⣮⣖⠄
⠁⠛⠁⠀⠀⠀⠤⠤⠤⠤⠤⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠄⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠊⢹⣿⣿⣿⠙⡆⠀⠳⠀⠀⠀⠀⠀⠇⠀⡼⠋⣿⣿⣿⠉⠑⠄⠀⠀
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠴⠚⠁⠀⠀⡎⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀




⢀⢀⣠⣶⡶⠾⠿⠶⣶⣶⣤⣤⣤⠀⠀⠀⠀⢠⣤⣤⣴⣶⣶⣾⠿⠷⢶⣮⣖⠄
⠁⠛⠁⠀⠀⠀⠤⠤⠤⠤⠤⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠄⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠊⢹⣿⣿⣿⠙⡆⠀⠳⠀⠀⠀⠀⠀⠇⠀⡼⠋⣿⣿⣿⠉⠑⠄⠀⠀
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠴⠚⠁⠀⠀⡎⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀




⢀⢀⣠⣶⡶⠾⠿⠶⣶⣶⣤⣤⣤⠀⠀⠀⠀⢠⣤⣤⣴⣶⣶⣾⠿⠷⢶⣮⣖⠄
⠁⠛⠁⠀⠀⠀⠤⠤⠤⠤⠤⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠄⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠊⢹⣿⣿⣿⠙⡆⠀⠳⠀⠀⠀⠀⠀⠇⠀⡼⠋⣿⣿⣿⠉⠑⠄⠀⠀
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠴⠚⠁⠀⠀⡎⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀