⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡶⠉⠀⠀⠀⠀⠀⠀⠉⠉⠶⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠖⠋⣀⣡⣈⠙⣦⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⢤⡀⠀⠀⠀⢀⡴⢉⣀⣤⣀⠉⢲⡀⠀
⠀⠀⠀⠀⠀⢀⡏⡰⠊⠁⠴⠉⢳⠈⢧⡼⢀⣀⣀⣀⣀⠴⡄⠀⣀⠤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢦⡜⠀⡎⠙⠆⠀⠙⣆⢳⡀
⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⣀⠄⣸⣀⠤⠃⠸⠼⢟⡏⠁⠠⢍⣀⡉⠒⠛⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣇⠤⣀⠀⠀⢸⡈⡇
⠀⠀⠀⠀⠀⢸⢸⠁⡠⠔⠋⠉⠁⠀⠀⠀⠀⣰⢫⣤⡀⣶⣦⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠬⣅⠈⣆⠀⢸⣇⡇
⠀⠀⠀⠀⠀⢘⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠮⠭⠀⠈⠹⠷⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠈⠀⡼⠀⡜⣸⠁
⠀⠀⠀⠀⡠⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠶⠒⠊⣁⢞⡱⣳⠀
⠀⠀⢀⠞⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠈⣡⠎⢀⣾⣒
⠀⠠⢾⣦⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠳⣀⣀⣀⡤⠚⠁⠀⠨⣿⠾
⠀⠀⢿⡷⡂⠀⠀⢸⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠀⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡁
⠀⠀⠸⣿⡷⠂⠀⢸⠀⠈⠑⠲⢤⣤⣤⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡴⠖⠉⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡇⠁
⠀⠀⠀⠹⣿⣇⠀⠸⡄⠀⠀⠀⠀⠉⠙⠶⠽⠉⠭⡍⠹⠯⠭⠿⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠅⠀
⠀⠀⠀⠀⢹⣼⣇⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡯⠀⠀
⠀⠀⠀⠀⠀⢳⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⡿⠁⠀⠀
⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢰⣾⡟⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠹⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⣴⣿⡿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⡗⠀⠀⠀⣼⣿⡏⠣⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⣶⣿⡇⠀⠀⠈⢷⡀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⡤⠾⢿⣿⡀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⣰⣾⣿⠇⠀⠀⠀⠀⠀⢣⡀⠀
⠀⠀⢀⡠⠴⠋⠀⠀⠀⠉⣿⣧⡄⠻⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣟⠁⠀⢀⣲⣿⡻⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠆⠀⠛⢿⣿⣷⣆⣀⡀⡀⡀⠀⡀⢀⠀⡠⣶⣶⡿⠛⠀⠀⣰⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⣆⠀⠀⠉⠙⠹⢿⣿⣿⣿⡦⣿⣿⣿⡿⠿⠏⠁⢀⣠⣾⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣽⣿⣦⣤⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⣴⣿⣟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣶⣤⣄⣠⣠⣤⣶⣿⡯⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠹⠿⠿⠽⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀