Cylinder Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠴⠶⢶⡶⠒⠚⢻⡟⠛⠛⣻⠟⠛⢛⡿⠛⠛⣻⠖⠒⢶⡶⠶⢤⣤⣤⣀⣀
⠀⠀⠀⣀⣤⠶⠞⣻⠉⠉⢀⡼⠃⠀⣠⠞⠁⢀⣴⠋⠀⢠⡾⠁⠀⣰⠟⠀⢀⡼⠋⠀⣠⠟⠁⢀⣴⠋⠀⣨⡟⠙⠛⠶⢦⣄⡀
⢀⡴⠛⠉⠀⢠⡾⠃⠀⣰⠟⠀⢀⡼⠋⠀⣠⠞⠁⢀⣴⠋⠀⢠⡾⠁⠀⣰⠟⠀⢀⡾⠋⠀⣠⠟⠁⢀⡴⠋⠀⢠⡾⠁⠀⣈⠙⠷⣄
⣾⠀⠀⢀⣴⠋⠀⢠⡞⠁⠀⣰⠟⠀⢀⡼⠋⠀⣠⠞⠁⢀⣴⠋⠀⢠⡾⠁⠀⣴⠟⠀⢀⡾⠋⠀⣠⠞⠀⢀⡴⠋⠀⣠⡾⠁⠀⠀⢹
⣿⢦⣀⠚⠁⢀⣴⠋⠀⢠⡾⠁⠀⣰⠟⠀⢀⡼⠋⠀⣠⠞⠁⢀⣴⠋⠀⣠⡾⠁⠀⣰⠟⠀⢀⡾⠋⠀⣠⠟⠁⢀⣴⠋⠀⠀⢀⣠⢿
⣿⠀⠉⠛⠶⣬⣅⣀⡴⠋⠀⢠⡾⠁⠀⣴⠟⠀⢀⡼⠋⠀⣠⠟⠁⢀⣴⠋⠀⣠⡾⠁⠀⣴⠟⠀⢀⡾⠋⠀⠰⣟⣁⣤⡴⠞⠋⠁⢸
⣿⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠿⠶⣤⣾⣥⣄⣰⣟⣀⣀⣾⣋⣀⣠⣞⣁⣀⣴⣋⣀⣀⣾⣥⣤⣤⡿⠶⠶⠟⠛⠋⠉⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠉⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠈⠉⠛⠳⠶⢦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⠶⠶⠛⠋⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣽⣽⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣯⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣶⣶⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣶⣶⣶⣶⣦⣤⣤⣄⣀⡀
⠀⠀⢀⣤⣴⣶⡿⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⠿⣶⣦⣄⡀
⢠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷
⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿
⣿⡇⠈⠙⠻⠿⣷⣶⣦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⣶⣿⠿⠛⠋⠁⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⢿⣷⣶⣶⣶⣶⣶⣾⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾
⠀⠙⠿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⠿⠋
⠀⠀⠀⠀⠉⠛⠛⠿⠿⣷⣶⣶⣦⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣾⠿⠿⠛⠋⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⡿⠿⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠻⠿⠿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⣼⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡏⠛⠻⠿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⡿⠿⠛⠋⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣧⣤⣶⣶⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣷⣶⣦⣤⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⡇
⠀⠀⠀⠀⠀⢻⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣶⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⣀⡉⠈⢁⣀⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢰⣲⣦⣾⡇⣿⠭⣒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠂⠾⠶⠿⠔⠣⣇⠀⣀⣱⣵⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠺⣷⡖⠪⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠱⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⡇⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠇⡇⢰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⣇⢇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡰⢫⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣪⠔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢤⣔⡪⠕⠊⠅⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡠⡔⠂⢉⣀⡠⠞⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⣠⡴⠞⠳⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠋⠁⠘⡌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⢾⡇
⠀⠀⠀⠀⢀⣠⠤⠂⠀⢻⡿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠶⠋⠀⠠⠄⢲⣶⣤⣤⡤⣤⠀⠀⠴⠜⠻⠿⠟⡇
⠀⠀⠀⠘⣣⠙⡘⢃⣀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠢⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⢠⣀⣀⣀⣀⣀⣀⣀⣀⠠⠶⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢰⠀⠀⠀⢠⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣀⠀⠀⠀⢸⠀⠀⠀⢸⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣷⠀⠀⢸⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣸⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡿⠛⠁⠀⠀⠸⡀⠀⠀⢸⣿⡿⠟⠁⠀⠀⠐⠀⠀⠀⠀⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢠⠀⠀⠀⢴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⡇⠀⠀⠐⣚⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠈⠀⠀⣴⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⡇⠀⠀⠠⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⢿⣿⣶⣦⣄⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣤
⡇⠀⠀⠀⢼⢾⣿⡶⠁⠀⠀⡀⠀⠀⠀⣸⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠟⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿
⠁⠀⠀⠠⠤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠠⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⢠⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠐⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠁
⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠇⠀⠀⣙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⡇⠀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⡇⠀⢀⣺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⡇⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣏⣏⣼⣩⣽⣩⣿⣻⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠒⠒⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠙⠓⠒⠶⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠶⠖⠒⠛⠉⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠠⠀⠠⠀⠠⠀⠠⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠤⠀⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠲⠶⠤⠤⠤⠤⠤⠤⠴⠖⠒⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠄⡀⢀⢠⠀⢀⣀⠀⣀⡄⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠄⢹⡎⠸⠆⠼⠸⠺⣄⡇⢗⡸⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠞


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣶⡆⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⠿⢿⠿⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⢡⢊⠭⠙⣎⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⡘⣌⣀⣢⢎⣼⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣶⣾⣶⣾⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣿⣧⣴⡦⠈⠉⠈⠛⠃⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣷⡿⠋⠉⠉⠻⣿⣿⠆⠀⢀⣰⣶⣦⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⡃⠀⠀⠀⠀⢸⣿⡶⠀⠰⣿⠂⠈⢽⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣶⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷⣄⣀⣀⣠⣿⣿⠄⠀⠈⠹⠷⡶⠿⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣾⠋⠉⠙⢿⡷⠀⠀⠀⠀⣠⣴⣄⠀⣿⣿⡇⠀⣴⣄⡀⠿⠛⣿⡟⠻⠗⠀⠀⠀⠀⠀⡀⣾⣦⣿⣷⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⠀⠀⠀⣸⣟⠃⠀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢀⡀⠀⠀⢀⣴⣴⣶⣆⡀⠚⣿⡿⠋⠁⠈⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠿⣶⠾⡿⠉⠀⠰⣿⣿⣿⣿⠟⢉⣭⣭⣍⡙⢿⣿⣿⣿⡷⠄⠀⢾⡿⡋⣱⣿⡦⠿⣿⡇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⣤⣄⣶⣆⣠⣄⠀⠀⠀⢀⣀⣼⣿⣿⠃⣼⢋⡥⠤⣌⠻⣆⢹⣿⣿⣄⣀⠀⠘⠿⢶⡾⠟⠁⠺⠿⣿⣦⣀⣀⣴⣿⠿
⠀⠀⠀⣿⡀⢈⡷⠀⢰⣶⣿⠟⠛⠛⠿⣷⣶⡄⠀⠸⡿⣿⣿⣿⠸⣇⢸⡀⠀⣸⠀⣿⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠻⠛⢿⡟⠛⠟
⠀⠀⠀⠈⠙⠋⠀⠀⣶⣿⠇⠀⠀⠀⠀⢹⣿⣦⠀⠀⢀⣼⣿⣿⣆⠻⢦⣍⣉⣥⡾⢃⣼⣿⣿⣄⠀⠀⠀⠀⢰⣷⣾⣿⣶⣿⠆
⠀⣀⣀⡀⠀⠀⠀⠀⢨⣿⣧⡀⠀⠀⢀⣼⣿⡅⠀⠀⠈⠿⠿⢿⣿⣷⣦⣭⣭⣥⣴⣿⣿⡿⢿⠟⠀⠀⠐⢿⣿⠟⠉⠀⠉⠻⣿⡟
⢸⡋⠉⣿⠀⠀⠀⠀⠈⠉⣿⡿⣿⡿⢿⡯⠉⢠⡞⠛⢧⠀⠀⢼⣿⡿⠿⣿⣿⡿⠿⣿⣿⠄⠀⠀⠀⠀⠺⢿⣿⠀⠀⠀⠀⠀⣿⡿⠇
⠈⠛⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠘⢧⣤⠞⠀⠀⠀⠈⠁⠀⠛⠛⠃⠀⠈⠀⠀⠀⠀⠀⠂⠐⢿⢿⣦⣄⣀⣠⣾⡿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠻⣿⠛⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⡆⠀⣀⣸⣿⣿⣿⣀⡀⠀⣼⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣶⣿⣿⣿⠿⣛⣫⣭⣥⣶⣶⣮⣭⣭⣛⡻⢿⣿⣿⣷⣾⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⡿⣫⣴⣿⠿⠛⠋⠉⠉⠉⠉⠉⠛⠻⢿⣶⣌⡻⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣠⣾⣿⡿⢫⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣮⠻⣿⣿⣦⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡿⣱⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡹⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢱⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⢹⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣿⡇⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⣿⣿⣧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣿⡇⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⡹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠙⢿⣿⣷⣜⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠟⠙⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣷⣝⠻⣿⣶⣤⣄⣀⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠿⣿⣿⣿⣶⣭⣝⣛⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠃⠀⠉⢹⣿⣿⣿⠉⠁⠈⢿⣿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠈⡧⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣀⣴⢋⣿⠟⠉⠉⠉⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⣠⣾⠿⢿⣶⡀⠀⠀⢰⣤⣼⣧⣴⣎⢀⡀⢹⣏⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⢀⣀⣤⣠⡄⠀⢸⠉⠈⣳⠀⠀⠀⠀⣠⣤⣤⡀
⠀⢻⣿⣄⣰⣿⢇⣘⣿⠟⠉⠉⠉⠉⠛⢿⣥⣽⢿⣄⡀⠀⣀⣴⣿⠁⠀⠀⢀⣸⡾⠋⠉⠉⠙⢿⡬⠓⢒⣡⣤⣄⡀⣸⡏⠀⠈⢿⠄
⠀⠀⠙⠛⠛⠉⣈⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣧⡌⠉⠻⠛⠻⣩⣶⣶⣶⣄⠠⣿⠀⠀⠀⠀⠀⠈⣿⢢⣿⠋⠉⠹⣿⡜⢷⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠈⢙⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡀⠀⠀⠀⢰⣿⡏⠀⢹⣿⠖⢻⣄⠀⠀⠀⢀⣰⣏⠙⣿⣦⣀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠙⢻⣧⡀⠀⠀⠀⠀⢀⣰⣿⡅⠀⠀⠀⠀⠀⠻⢿⣶⡿⠟⠀⠈⠹⠟⢶⠲⠟⠓⠀⠀⠈⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠷⣶⣶⣶⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⢠⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠱⠰⠤⠄⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢄⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠒⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠈⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⢎⣣⡀⠀⠀⠀⠀⠰⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠚⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢱⡇⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢪⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠠⡐⠁⠀⠐⠲⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠈⠉⠀⠀⠀⠀⠀⠀⡰⠢⠤⠁
⠀⠀⠀⠀⠀⣬⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠓⢍⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁
⠀⠀⢀⠂⠒⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠢⠀⠔⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠊⢷⡀⠀⠀⠀⠠⠀⠰⠊⠐⠠⠤⣀⡰⠃⠻⠞⠙⣄⠠⠔⠊⠁
⠀⠉⠚⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠐
⠀⢀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠅⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠁⢃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠁⠀⠀⠀⢀⢄⡀⢀⠁⠀⠀⠀⠄⠂⠐⢄
⠀⠀⠀⠑⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣈⠅⠀⠀⢀⢀⣀⣄⠀⠀⠀⠔⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠐⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠁⠀⠀⢀⠈⠐⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⡀⡀⠀⠀⡠⠀⠀⣀⠤⠂⠒⠀⠉⠉⠁⠀⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢢
⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠇⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠁⠓⠒⠒⠒⠒⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢃
⠀⠀⠀⢻⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⢸⡠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠀⠀⠀⡰⠃
⠀⠀⠀⠀⢇⠄⠢⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠔⠈⢿⣿
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠐⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠈⠢⣀⡀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠢⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠐⠒⠂⠤⠤⠤⠤⠤⠤⠄⠒⠂⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠋⠉⠉⠀⠀⠀⠀⣀⣈⣉⣉⣉⣉⠙⠓⠒⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁⣀⡤⠴⠒⠖⠒⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠳⣤⣀⡀⠀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⡀⠈⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⢀⡴⠋⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⣴⠒⢦⡔⠛⣷⠀⠀⠀⠀⢶⡆⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢀⡴⠋⠀⠀⠀⠀⣀⢴⡄⠀⠀⠀⠀⠀⠙⠶⣤⣀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠳⣄⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⣰⡟⠀⣰⠟⠁⠀⠀⠀⢠⣞⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠇⠀⠀⠀⠈⢳⣄⠈⢷⡀
⠀⠀⠀⠀⠀⣴⠏⠀⣰⠏⠀⢀⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠀⢾⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠘⣷
⠀⠀⠀⠀⢰⡏⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢠⣶⠄⠀⠀⠀⠀⠀⠐⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣿⠀⠸⣧
⠀⠀⠀⠀⣿⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⡇⠀⢹⡆
⠀⠀⠀⢰⡟⠀⢰⡇⠀⠀⠀⠀⠀⢠⡴⢤⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠈⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⣾⠙⠶⠚⢳⠀⠀⠀⠈⣷⠀⠈⣧
⠀⠀⠀⢸⡇⠀⢸⠃⠀⢀⡀⠀⠀⢸⡄⠘⠋⣻⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠻⣄⢀⣴⠏⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⢸⡇⠀⣾⠇⠀⠻⠟⠀⠀⠀⠻⠶⠞⠉⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢰⣶⠀⣿⠀⠀⢹
⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⢾⣿⠀⣿⠀⠀⣾
⠀⠀⠀⢸⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⠟⠀⣿⠀⠀⣿
⠀⠀⠀⢸⡆⢸⣷⠀⠀⠀⢀⣴⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠔⢀⡿⠀⠀⣿
⠀⠀⠀⢸⡇⠀⣿⡄⠀⢾⡽⠋⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠈⠓⠦⣤⣄⣀⣀⣀⣀⣠⡴⠛⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢰⡇
⠀⠀⠀⠀⢷⡀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⣼
⠀⠀⠀⠀⠘⢧⡀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠀⠀⢠⡟⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠈⢷⣄⠈⠻⣆⡀⠀⠘⠟⠀⠀⠀⣠⣤⡴⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⣤⠖⢄⣀⡀⠀⠀⠙⠚⠀⢠⠏⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠈⠻⣦⡀⠀⠀⠀⠸⣧⣀⡁⣼⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠁⡽⠀⠀⠀⠀⢠⠏⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⠙⢦⣄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠸⠯⣽⣓⣶⣤⣄⠀⠀⠀⠀⠈⠳⠶⠚⠁⠀⠀⢀⡴⠋⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠛⢶⣄⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠶⠀⠀⠀⠀⢀⣠⡴⠋⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⠀⠀⠈⠻⢦⣄⡀⠀⠀⠻⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠋⢁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠉⠛⠳⠶⣶⣶⣦⣤⣤⣤⣤⣤⣤⡶⠾⠛⠉⠁⢀⣠⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⡀⠀⠦⠶⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣀⣤⣿⡉⢻⣷⣦⣄⣠⣶⣦⣾⠁⣠⡿⠀⣼⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⣴⢶⣮⣉⣥⣟⣿⣾⣿⠏⠀⡙⣿⣿⣿⣿⡟⢀⣼⣯⡞⠀⠀⢀⣾⣿⡄
⠀⠀⠀⠀⢠⣼⢶⡀⠀⠀⠀⣀⣤⡶⠉⠉⠉⠙⣿⣷⣿⣿⣿⠛⠁⢀⣤⣴⣾⠿⢛⣫⣴⣿⣿⣿⡇⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⣾⣿⣷⡧⢤⠂⠙⠛⠛⠙⠛⠛⠓⠚⠛⠋⢩⡵⠀⠀⠀⣴⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣸⡙⠿⠁
⠀⣄⠀⣠⣿⣿⣿⠧⣼⡗⠀⠀⠀⠀⣀⣀⣴⣾⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠙⠿⠿⠿⠿⠷⠂
⠀⠘⠻⠿⠿⠿⠋⠀⠀⠀⠤⢄⣴⣿⣿⣿⡿⠿⠿⠿⠿⢇⣀⣀⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠛⠛⠿⠟⠋
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⣶⣟⣿⣦⠀⠀⢀⣴⣛⡟⣶⡀⠀⠀⣴⠞⠛⢷⡄⠀⠀⣤⡼⢓⠿⣤⠀⠀⢠⣾⡿⢿⣦⠀⠀⢀⡲⠛⠛⢶⡀
⠀⠸⣟⡧⣟⣾⠀⠀⠘⣧⠚⡟⣼⠇⠀⠀⢿⣀⢀⣸⡇⠀⠀⠼⣍⡆⣳⠷⠀⠀⠸⣟⣤⣼⣽⠃⠀⠀⢧⠀⠀⣸⠃
⠀⠀⠉⠙⠉⠁⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⠙⠉⠋⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠉⠙
⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⢀⣠⢤⣤⡀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⢀⣠⣤⡀
⠀⠀⣾⠁⠀⠈⣗⠀⠀⣻⠁⠀⠘⣟⠀⠀⣾⢥⠈⡢⢿⠀⠀⢸⣿⡋⣻⣿⠀⠀⢐⡏⠀⠀⢹⡂⠀⠀⡏⠀⠀⢹⡆
⠀⠀⠙⠲⠤⠞⠁⠀⠀⠉⢷⠶⡾⠉⠀⠀⠘⠷⢽⠴⠋⠀⠀⠈⠻⠿⠿⠛⠀⠀⠀⠓⠦⠴⠛⠀⠀⠀⠙⠦⠴⠞

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣀⣸⠗⠛⠛⠺⣧⣀⠀⠀⠀⠀⣀⣸⡷⢿⣿⢾⣇⣀⠀⠀⠀⠀⢀⣴⠋⠉⠉⠙⣦⡀⠀⠀⠀⠀⣀⣸⠷⢺⡗⠾⣇⣀⠀⠀⠀⠀⣀⣼⡻⢿⡽⢟⣧⣀
⠀⢀⣽⠛⣶⠛⠛⣶⠛⣯⡀⠀⠀⢀⣽⠏⣾⡿⢿⣷⠹⣯⡀⠀⠀⠀⣎⠀⢱⡶⢶⡎⠀⢹⠀⠀⠀⢀⣹⢓⠊⠀⠀⠑⠞⣏⡀⠀⠀⢀⣿⣎⣀⡼⢧⣀⣱⢿⡀
⠀⠈⣻⡀⠻⣤⣤⠟⢀⣟⠁⠀⠀⠈⣻⣾⣯⣦⣾⣽⣶⣟⠁⠀⠀⠀⢇⠀⡸⠷⠾⢇⠀⣸⠀⠀⠀⠈⣹⡤⢄⠀⠀⡠⣥⣏⠁⠀⠀⠈⣷⢏⠉⢳⡞⠉⡹⣾⠁
⠀⠀⠉⢹⣦⣼⣧⢴⡏⠉⠀⠀⠀⠀⠉⢹⡷⣦⣴⢾⡏⠉⠀⠀⠀⠀⠈⠻⣄⣀⣀⣠⠟⠁⠀⠀⠀⠀⠉⢹⡶⢼⡧⢶⡏⠉⠀⠀⠀⠀⠉⢳⣵⣞⣳⣮⡟⠉
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⡀
⠀⠀⡀⣬⣾⣿⣿⣷⣥⢂⠀⠀⠀⠀⣀⣼⣛⣻⣟⣛⣧⣀⠀⠀⠀⠀⢠⡴⠟⢻⡟⠻⢶⡀⠀⠀⠀⠀⢰⣶⣴⣿⣿⣦⣶⡆⠀⠀⠀⠀⣰⡼⣟⡿⢿⣛⢷⣀
⠀⠐⣾⣿⠑⡤⢤⠊⣿⣷⠀⠀⠀⢀⣿⣸⣿⡿⢿⣿⣏⣿⣀⠀⠀⠐⣿⢷⡶⣻⣟⢶⡶⢿⡀⠀⠀⣀⣴⣿⠋⠀⠀⠙⣿⣦⣀⠀⠀⢐⣿⡼⢿⢗⡸⡿⢯⣿⡂
⠀⠠⢿⣿⡠⠓⠚⢄⣿⡿⠄⠀⠀⠈⣿⢹⣿⣷⣼⣿⡏⣿⠁⠀⠀⠈⣷⠀⣿⣽⣯⣾⢀⣿⠄⠀⠀⠙⠻⣿⣄⠀⠀⣠⣿⠟⠁⠀⠀⠨⣿⣳⣾⡮⠵⣷⣾⣿⠅
⠀⠀⠁⢛⢿⣿⣿⡿⡛⠌⠀⠀⠀⠀⠉⢻⣭⣽⣯⣭⡟⠉⠀⠀⠀⠀⠉⠿⣯⣤⣠⣽⡟⠃⠀⠀⠀⠀⠸⠿⠻⣿⣿⠟⠿⠇⠀⠀⠀⠀⠙⢷⣯⣷⣾⣭⡞⠋
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣀⣸⣷⠿⠿⣾⣇⣀⠀⠀⠀⠀⣀⡼⠛⢻⡟⠛⢧⣀⠀⠀⠀⠀⣠⡾⠛⢻⡟⠛⢷⣀⠀⠀⠀⠀⣠⡶⢟⣩⣍⡻⢶⣄⠀⠀⠀⠀⣀⡼⣳⣯⣽⣟⢧⣀
⠀⢀⣽⡟⣨⠗⠺⣅⣹⣯⡀⠀⠀⢀⡿⠛⢦⡼⢧⡴⠛⢿⡀⠀⠀⢰⡿⠀⢀⡼⢧⡀⠈⢿⡂⠀⠀⢠⡟⡰⠁⢠⡄⠈⣎⢻⡄⠀⠀⢀⡿⣾⣟⡽⢯⣻⣷⢿⡀
⠀⠈⣻⣏⢙⡦⢴⡋⣸⣟⠁⠀⠀⠈⣷⣤⠞⢳⡞⠳⣤⣾⠁⠀⠀⠨⣷⣤⠞⠳⠞⠳⣤⣾⠅⠀⠀⠘⣧⡱⡔⠉⠉⢢⢎⣽⠃⠀⠀⠈⣳⢿⣯⣳⣞⣽⣟⣾⠁
⠀⠀⠉⢹⡿⣶⣶⢿⡏⠉⠀⠀⠀⠀⠉⢳⣤⣼⣧⣤⡞⠉⠀⠀⠀⠀⠙⢷⣤⣄⣠⣤⡾⠉⠀⠀⠀⠀⠙⠷⣮⣑⣋⣵⠾⠋⠀⠀⠀⠀⠉⢳⣽⣿⣻⢭⡞⠉
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⡀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢰⣶⢟⣛⣛⡻⣶⡆⠀⠀⠀⠀⣀⣼⠿⢻⡟⠿⣧⣂⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⢰⣶⣿⠛⠛⣿⣶⡆⠀⠀⠀⠀⠰⣦⡶⢿⡿⢶⣴⠆
⠀⢈⣿⢱⢿⡷⢾⡿⡎⣿⡁⠀⠀⢐⣿⠧⢤⡼⢦⡤⠼⣿⡂⠀⠀⠠⣿⣿⣿⢟⡻⣿⣿⣿⡀⠀⠀⢈⣿⠛⠛⣤⣤⠛⠛⣿⡁⠀⠀⢀⣴⣏⡾⢋⡙⢷⣹⣧⡀
⠀⢈⣿⡸⣾⡷⢾⣳⢇⣿⡁⠀⠀⠨⣿⡄⢨⠷⠾⡅⢠⣿⠅⠀⠀⠈⣿⣿⣿⣮⣵⣿⣿⣿⠀⠀⠀⢈⣿⣤⣤⠛⠻⣤⣤⣿⡁⠀⠀⠈⠻⣏⢷⣌⣡⡾⣹⠟⠁
⠀⠀⠸⠿⣮⣭⣭⣵⠿⠇⠀⠀⠀⠀⠉⢻⣷⣤⣤⣾⡟⠍⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠸⠿⣿⣤⣤⣿⠿⠇⠀⠀⠀⠀⠰⠟⠳⣾⣷⠞⠿⠆
⠀⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣠⣼⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⣠⡾⠋⠉⠉⠙⢷⣄⠀⠀⠀⠀⢰⡶⠛⠋⠙⠛⣶⡆⠀⠀⠀⠀⣀⣸⡷⢿⡿⢿⣇⣀⠀⠀⠀⠀⣀⣼⢿⣛⣛⡿⣧⣀
⠀⢐⣿⣿⣿⠛⠛⣿⣿⣿⡂⠀⠀⢰⡟⠑⠢⡠⢤⠔⠊⢻⡆⠀⠀⢈⡿⠓⢲⡴⢦⡴⠏⢿⡁⠀⠀⢀⣽⣏⣀⡼⢧⣀⣹⣯⡀⠀⠀⢀⣿⢳⣯⡿⢿⣽⡞⣿⡀
⠀⠨⣿⣿⣿⣤⣤⣿⣿⣿⠅⠀⠀⠸⣧⡠⠔⠑⠊⠢⢄⣼⠇⠀⠀⢈⣷⠀⠈⢳⠞⠁⠀⣾⡁⠀⠀⠈⣻⣏⠉⢳⡞⠉⣹⣟⠁⠀⠀⠈⣿⡼⣟⣷⣾⣻⢧⣿⠁
⠀⠀⠙⢿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠙⢷⣄⣀⣀⣤⡾⠋⠀⠀⠀⠀⠸⠷⣤⣜⣧⣤⠾⠇⠀⠀⠀⠀⠉⢹⣷⣾⣷⢾⡏⠉⠀⠀⠀⠀⠉⢻⣾⣭⣭⣷⡟⠉
⠀⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⣩⠝⠉⠀⠀⠀⠀⠉⠛⢭⡙⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣉⣤⠤⠔⠊⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⠤⢭⣷⣤⣀
⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⢠⠖⠚⢉⣁⡽⠀⠀⢰⠋⢳⠀⠀⠀⠀⢀⡠⠖⡄⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠈⠒⠋⠉⠀⠀⠀⠀⢸⠀⣾⠀⠀⢀⠔⠋⣠⠖⠁⠀⠀⠀⠀⢸⢧⡀
⠀⠀⠀⠀⡰⠁⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠸⣀⠇⠀⠀⠘⠒⠋⠀⠀⠀⢸⡉⢣⠀⠸⡆⠱⡀
⠀⠀⠀⣰⠁⢰⠁⠀⠀⠀⣏⣉⣉⣉⣁⡵⠀⠀⢀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢣⠀⢣⡀⢱⡀
⠀⠀⢀⠇⡰⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠋⠉⠑⠒⠉⠉⠛⢆⡀⠀⠀⠀⠀⠀⠀⠑⠜⠁⠀⠈⠢⣇
⠀⠀⢸⠞⠁⠀⣇⠙⣄⠀⠀⠀⠀⢀⡴⡶⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡑⡄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠸⡄
⠀⠀⡏⠀⠀⠀⠈⢦⠘⢆⠀⠀⠀⢸⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⢀⡠⠚⢁⠼⠀⠀⠀⡇
⠀⠀⣇⠀⠀⠀⠀⠈⠓⠊⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢏⡠⠞⠁⠀⠀⠀⣼⡇
⠀⠀⢹⢆⠀⠀⠀⠀⠀⡠⢄⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠀⠀⠀⠀⠀⠀⠀⢀⡞⢰⠃
⠀⠀⢸⠈⢧⠀⠀⢀⡜⢁⡜⠀⠀⢸⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡯⠞⠀⠀⠀⠀⢠⠋⣳⢸⠀⢸
⠀⠀⠈⡆⠈⡇⠀⡞⢀⠞⠀⠀⠀⠀⠙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⠀⠀⠀⠀⢀⠏⢠⠃⠘⡄⡎
⠀⠀⠀⢹⠀⡇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⢄⣀⡤⠤⣀⡠⠔⡿⠀⠐⣏⠙⠦⡀⠀⠸⠤⠏⠀⠀⢹⠁
⠀⠀⠀⠀⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠁⠀⠀⠀⠉⠉⣀⣀⠀⠀⠑⢦⡈⣣⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⢣⠀⣞⢉⣉⣉⣉⡱⠀⠀⠀⡠⠊⢁⠇⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠉⠁⠀⡠⠖⣫⠋
⠀⠀⠀⠀⠀⠈⢣⡈⠉⠁⠀⠀⠀⠀⢠⡋⣠⠞⠁⠀⠀⠀⠀⠀⠀⢠⡇⢸⠀⠀⠀⠀⠀⠀⡜⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⡒⠢⠤⢤⣀⠉⠁⠀⠀⢰⡉⠲⢤⣀⠀⠈⠣⠞⠀⠀⠀⠀⠀⢰⡧⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠙⠢⣄⠀⠀⠉⠓⠤⣈⡵⠀⣠⠴⠒⠦⢤⡤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠽⠦⢤⣀⣀⣀⣠⡾⠥⠤⠒⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⡦⡀⠀⠀⠀⢀⣀⠀⡰
⠀⠀⠀⠀⠀⠊⠀⠂⠀⠀⠀⠐⠐⠐⠀⠂⠀⠀⠀⠀⠀⠀⡀⢡⠈⢂⠀⢀⠂⠀⡔⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠆⠀⠀⠐⠀⡜⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⢐⣒⡒⠂⠢⡀⡄⠁⡆⡜⠀⠀⢀⠔⢊⡁⠤⠔⠊⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⢀⡀⡁⠒⠟⣾⣶⣷⣀⣄⡬⠔⢊⡁⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠶⣤⡀⢂⠶⠾⠾⣿⡿⣷⠆⢖⣲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠁⠀⢉⣿⡇⠀⠀⠀⠀⢹⡄⠀⠀⠐⡷⠈⠦⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡐⠄⠘⠚⠠⣀⡀⣿⣦⡀⠀⠀⠀⢨⣷⡆⡢⣼⢃⢀⡅⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠂⣑⠀⠀⠠⢰⠙⠳⠉⠟⠿⡷⠤⣿⠏⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠐⠀⢰⠃


⠀⠀⠀⠀⢀⣴⠂⠰⣶⡆⠀⠀⠀⠀⡴⠙⢶⡁⠀⠀⠀⠀⠀⠀⣠⠖⠀⠐⣖⠀⠀⠀⠀⠀⢀⠞⠛⠙⠲⡄
⠀⠀⠀⠀⠨⠿⠖⠙⠋⠡⠀⠀⠀⠘⢄⡀⠀⡇⠀⠀⠀⠀⠀⠀⢻⡀⣀⢰⠇⢀⠀⠀⠀⠀⢹⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠁⠀⠀⠀⠀⠈⠛⠷⠶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢠⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⡕⡀⠀⡀⢀⠀⢀⡀⣤⣀⣀⣤⣤⣤⣤⣄⠊⠁⠀⢱⠀⠄⡀
⠀⠀⠀⠀⠘⠃⢁⠚⠀⠀⣱⣵⣾⣿⣿⣿⣿⣟⣾⣿⣿⣷⣄⣀⡀⠀⠀⠈⠘⠒⠄
⠀⠀⠀⠀⢠⠀⢸⡄⢁⡌⠸⠟⠛⠛⢉⣉⣁⠀⡀⠀⠀⠀⠀⠀⠈⠉⠛⠫⣉⠉⠓⠲⠤⣄⡀
⠀⠀⠀⠀⢹⠦⠌⠊⢣⡀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⣀⠀⠀⠀⠀⠀⠀⠂⢀⠁⠀⡢⣄⢀⣭⣷⡄
⠀⠀⠀⠀⠊⢢⡈⠀⠀⢹⠑⠂⢤⣾⡂⠀⠀⠀⢀⡶⣾⡗⠀⠐⠁⠤⣴⣒⠚⠇⣒⣿⡎⣮⣾⣧⠃
⠀⠀⠀⠀⢡⡀⣿⡢⣴⣼⣿⣦⡘⣿⣿⣌⢄⣀⠘⠿⡯⠆⢠⠜⠀⣸⣿⣿⣿⣿⣿⢹⡧⢂⠾⠇
⠀⠀⠀⠀⢀⠂⢛⡇⣿⠧⠸⣿⠦⣿⣡⣿⣧⡀⣙⣀⣢⠴⠊⡈⢤⡻⡛⠛⠻⢛⣽⣯⣿⣥⣀
⠀⠀⠀⢀⢐⠂⢠⣿⣿⢮⢆⠉⣲⣿⢿⣿⡿⠻⣾⣿⡖⢛⣛⣓⣶⡖⢶⡶⣶⣿⣿⣿⡇⢹⢿⡇
⠀⠀⠀⠀⢨⠀⠀⣿⣿⢀⣱⣶⣿⠁⠉⠍⣿⠀⠉⢨⡿⡊⠻⣿⡿⠠⠡⢉⣣⣽⣰⡿⢃⠄⢀⡇
⠀⠀⠀⠀⠘⠀⢄⡸⣿⣾⠿⢿⣿⣤⣼⣿⠃⠀⢀⡼⠿⠿⠟⠋⠀⠀⠀⠸⣿⣿⣟⣡⣾⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣠⣾⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⢸⣧⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣼⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢸⣿⢰⣿⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣄⢠⣴⣿⣟⢸⣿⢸⣿⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣠⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣿⢸⣿⠿⠿⠿⠿⢸⣿⣧⣴⠶⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢿⣯⣸⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠷⣦⣴⣿⡇⣿⣿⢰⣶⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣦⣤⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣇⣿⣿⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣉⣛⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣭⣍⡇⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⡍⣿⡇⣿⢙⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣼⡇⣿⢸⡇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡇⣿⢸⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠶⠾⠶⣷⢸⣿⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠻⣶⣿⣨⣿⠸⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠟⠻⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣛⣛⡛⣿⣾⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⣿⡇⣿⣶⣶⣶⣶⢸⣿⡟⠻⠶⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠋⠁⠻⣿⣯⢹⣿⢸⣿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢸⣿⠸⣿⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢸⡏⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢻⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠿⠃

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⢿⣿⢮⠻⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢮⡑⠌⠳⡀⠙⡄⢻⣿⠸⠟⣿⣿⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠯⣍⡙⠻⢮⡂⠀⠀⠀⠀⠀⢻⠀⠀⢿⡟⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣟⣛⡛⠛⠒⠢⠄⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢻⢫⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣛⣫⣭⣭⡥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢣⠞⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣛⡫⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡄⣤⢄⠀⠀⠀⠀⠁⣠⡾⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡠⣀⣤⠔⠂⠀⠀⠀⠀⠀⢸⡏⡟⠻⠜⠧⠘⠋⠀⠀⠀⠀⠐⣉⣴⠿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣾⠟⣉⠀⠀⠀⠀⠀⠀⡄⢠⣶⣶⡇⢸⡇⠀⠀⠀⠀⠀⠠⠔⠋⠉⠚
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡾⠋⢀⠀⠀⠀⠀⠀⠑⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣪⣭
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⡴⢣⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⣛⣛⣯⣭
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣣⡧⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠐⠢⠤⣤⣤⣬⣽⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣼⣷⠀⠀⣧⠀⠀⠀⠀⠀⠨⡳⣦⣬⣙⣲⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣿⣿⣴⡄⣿⣧⠘⣄⠈⢦⡐⢌⡳⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⣼⣦⡳⣿⣷⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠄⠀⠀⠀⠀⠈⠣⠍⠌⠄⠋⠉⢠⠀⢌⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡺⠁⠈⠂⠀⠨⡹⠀⠀⠀⢀⠄⢄⠀⠀⠈⠒⠂⠀⠈⢫⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣊⠉⠁⠀⢀⠤⡀⠀⢀⣀⠀⠀⠀⠀⠑⠀⠀⠀⠤⠒⠀⠀⠀⠀⠁⢄⡑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠈⠤⠃⣀⠀⠀⠑⠁⠀⠡⠼⠀⠀⠀⠀⠀⡔⠒⡀⠑⠚⠀⠀⠀⠀⠀⢀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡄⡄⠀⢸⠀⠑⡰⠀⠀⠀⠀⠀⠀⢀⡤⠒⠢⡁⠊⠀⠀⠀⠔⢠⠀⠀⠀⠣⠔⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⢸⢃⠀⠑⠁⠀⠀⠁⠉⠀⠀⠀⡠⠤⠤⢠⡊⠠⠠⠄⢘⠠⢀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⡆⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠔⠁⠀⠀⠀⠀⠀⠈⠢⡈⠢⠀⠀⠀⢀⠔⠊⡂⠀⢠⡒⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠊⢂⠀⠀⢘⣙⠀⠀⡎⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⠀⠀⠀⠀⠑⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠁⠁⠀⠀⠀⢀⠀⠀⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠱⠀⠀⢠⠒⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⢀⠤⡀⠀⠀⠀⢇⠰⠀⠒⡔⡄⠀⠀⠀⠀⠀⠀⠀⠀⡔⡠⠀⠀⠈⠒⠁⠀⠀⠱⡠⠃⢐
⠀⠀⠀⠀⠀⠀⠀⠰⢠⠀⠈⠒⠁⠀⠀⣀⠀⠀⠀⠀⢃⣈⠐⠤⢀⣀⣀⣀⠠⢊⠸⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠣⡀⠀⠀⠀⠘⠴⠁⠀⠀⠀⡄⢄⠈⠆⣀⠄⠂⢐⠀⠊⠀⠀⠀⢆⡁⢸⠀⠀⠀⣎⢱⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⡆⠀⠀⡎⢢⠀⠀⠀⡔⠱⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢔⢰⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⣀⠀⠀⠀⠈⠈⠁⠀⠰⣁⡑⠀⠐⡅⠠⠕⠀⠀⠀⢠⠂⠉⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⣈⣚⠠⠀⢤⠀⠀⠀⡀⠀⠀⠀⡀⠀⢈⡉⠀⠀⠀⡰⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡇⠀⠈⠚⠀⡠⠊⠀⠀⠀⠈⠁⢀⡡⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠛⠒⠀⠀⠀⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠰⠅⠀⠠⢁⠌⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠶⣒⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡤⡄⢴⢅⠊⠌⣁⢠⢀⡶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠸⣇⠀⢻⣷⠀⠠⠄⠀⠀⠀⠀⢀⠻
⠀⠀⠀⠀⢴⢖⡐⠠⢀⢠⣧⣦⠊⡔⠁⡇⠞⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⣤⣿⣄⣠⡏⠀⠀⠀⠡⠁⢄⠀⠀⢰⠢⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠑⠮⠗⣿⣾⣿⣿⣿⣓⠈⠂⠁⢀⠄⠀⠀⠀⣠⣴⡿⠉⠰⠀⠀⠀⠈⠛⠿⠯⠝⠉⠀⠀⠀⠀⠀⠀⠆⠀⠐⢀⠬⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠙⢟⣿⣭⣵⣾⡄⠀⠀⠀⠠⠃⣿⡗⡁⠈⠀⢱⠀⠀⠀⠀⠀⠀⠀⠘⠶⢄⣂⠄⡀⠀⢟⡆⢸⡂⢀⢀⠎⠐
⠀⠀⠀⡀⠀⠠⠠⢤⣌⠅⠀⠒⣈⣽⣽⡿⠟⢣⡆⠀⠀⠐⣇⢿⣷⠀⣠⣂⡜⠀⠀⣀⣤⢤⣄⠀⠀⠀⠀⠉⠗⡨⣰⣌⢟⡷⠇⡰⠃⠊
⠀⠀⠀⠀⠀⢀⠖⣠⣼⢆⣠⣾⠛⢹⡏⠐⠨⠀⠒⠄⠀⠀⠈⠺⠽⠿⠛⠉⠀⢠⡞⠁⠠⠓⣀⣷⠀⠀⡀⠠⡀⠄⡈⣿⣿⣿⣯⡡⠀⠀⡀
⠀⠀⠀⠀⠀⢃⣾⣧⠃⠈⣾⣷⠀⣼⡷⡈⠁⠀⣲⡁⠀⠀⠀⢀⣠⣤⣤⣀⠀⠸⣿⢳⡆⢹⣿⡟⠀⠀⠉⠂⠠⠀⠀⠁⠀⠀⠀⠉⠁⠈⠈⠁
⠀⠀⠀⠀⠀⠈⢛⣯⣴⣾⢫⠝⣷⣿⢳⡾⡞⠛⠻⠖⠀⠀⠀⣟⠁⣈⢙⣟⣦⠀⠉⠛⠓⠚⠉⠀⣠⣄⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⣺⡯⠊⠀⡀⠅⠌⠪⠑⢦⡜⢆⠀⠀⠀⠀⠈⣿⣦⣀⡰⢿⡟⠀⠀⠀⠀⠀⠀⠰⣝⣛⠉⠛⣋⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⣘⠀⠈⠑⠚⠛⠀⠀⠀⠀⠀⠈⠉⠛⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠧⠓⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠆⠀⠀⠄⠒⠀⠀⠀⡠⠤⠄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣴⡤⠤⢄⣀⣀⠀⠀⠀⠀⢀⡀⠈⣉⣀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡀⡜⣽⣿⣿⣿⡯⣥⣀⠞⣩⣴⡆⣿⡾⠚⡀⠀⠀⠆⡤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⣿⡛⠒⠀⠄⠜⣏⣉⠚⡿⠅⢈⡀⣿⠟⠃⢀⠀⠀⢠⣊⣷⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⢠⣾⣿⣯⣴⣶⠂⠀⠀⠈⠻⠿⠆⣠⣄⣤⡆⢰⣿⠀⢠⡿⢉⣗⠂⠁
⠀⠀⠀⠀⠀⡀⠰⠯⠀⠀⠀⠈⠋⠁⠺⠋⣉⠔⠂⠀⠀⠀⠀⢀⠈⢻⣾⣡⢿⠟⢠⡎⢠⡜⠋
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢤⠋⠀⠀⠀⠀⢀⣤⠶⡄⠁⡟⠔⣗⠬⠊⠀⠉⠁
⠀⠀⠀⢠⣄⠀⠘⠳⠦⣤⣀⡀⠀⠄⠁⠀⠀⠀⡀⢀⢎⢺⠋⢀⣤⠄⠂
⠀⠀⠀⠘⠻⣅⡀⠀⠀⠀⠈⠀⢁⠂⠀⠤⠄⠀⢀⡎⢸⠏⣰⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠄⡲⠶⢖⣀⣠⠀⠂⠚⠲⠘⠚⠁

⢿⣿⣷⣦⣀⠉⠪⡳⣤⡈⠳⣕⢄⠙⢿⣧⡀⠳⡱⡱⠱⢱⡱⢻⡀⠀⠇⡇⠘⡇⠀⢸⠀⠸⠈⢀⡟⢌⣎⠎⢎⢎⠞⢀⣼⡽⡿⡫⣪⠞⢁⣴⢞⠕⠋⣀⣴⣾⡿
⣄⡀⠉⠙⠿⣗⣤⡀⠙⠝⢦⡈⠢⡑⢀⠙⣟⣄⠑⠄⠀⠁⠳⠈⢇⠀⢠⢻⠀⡇⠀⠘⠀⡆⠀⣸⠁⠜⠈⠀⠠⠊⡠⣻⠫⠊⠈⠜⢁⡴⠫⠃⢁⣤⣺⠿⠋⣁⣴
⢈⠙⠳⢤⣀⠈⠙⠪⣖⠀⠀⠙⠲⣄⠀⠀⠈⠻⡢⡈⠀⠀⠀⠁⠘⡀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠃⠘⠀⠀⠀⢁⢔⠝⠁⠀⠀⣠⠴⠋⠀⠠⣲⠕⠋⠁⣀⣬⣾⡿
⢄⡀⠀⠀⠈⠛⠦⣄⡀⠉⠂⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠐⠈⠀⡠⠔⠪⠛⠋⠁⢀
⣦⣌⣉⠂⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⣈⣥
⠀⠀⠉⠙⠓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠚⠉⣁⣠
⠷⠶⢶⣤⣄⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⣚⣋⡭⠥
⣉⣀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠈⠁⠀⠀⢀⣀
⠓⠶⠶⠭⠥⠄⠂⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠉⠁
⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤
⠶⠶⢶⣒⡒⠬⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⣀⣀
⠉⠉⠀⠀⠀⢀⡀⠀⣀⣀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉
⣶⣖⣾⣿⡯⠷⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢶
⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢄⡀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠋⠁⠀⠀⢀⡤⠖⠋⠀⡀⠄⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⡀⠀⠀⠢⢄⠀⠀⠂⢄⡀⢀
⢁⣠⣴⡚⠉⢀⣠⢖⠏⠂⠀⣠⠖⠋⠀⠀⢀⣴⠕⠀⠀⠀⠀⡄⢠⠁⠀⢸⠀⠀⠀⠀⡃⠀⠈⡄⢁⠀⠀⠀⠀⠨⣦⡀⠀⠈⠻⣶⣄⠀⠀⠹⡲⣄⡀⠈⢓⠯⣷
⡿⠟⢉⣠⣶⡯⠛⢁⢠⣪⠞⢁⠔⡡⠀⣰⡻⠫⡢⠂⠀⠀⡼⢀⡏⠀⠐⣼⡄⡇⠀⢠⣇⠂⠀⢹⡀⢣⠀⠀⠀⢔⠝⣽⣕⢄⠈⢮⡫⣷⣕⡄⡈⠛⢽⣶⣤⡉⠻
⣤⣾⡿⠟⠉⣠⢔⡵⠛⢁⡴⡻⠊⣠⣾⡟⡕⡵⡱⠀⠀⡼⡱⣼⠁⡀⡆⡇⣿⡇⠀⢸⢸⢰⢀⠈⣧⢎⢧⣆⢆⠈⢮⢪⢻⣷⣷⣄⠙⢮⡻⣟⢮⡢⣄⠉⠻⢿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶⡦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⣤⣤⣤⣼⣄⣬⣿⣿⣯⣄⣀⣰⣇⣀⡀⠙⢷⡌⢹⣿⣶⣄
⢀⣀⣄⠀⣂⠠⠦⠄⠀⠤⠤⠤⡤⢠⡀⣉⣋⣉⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠋⠁⠐⠚⢛⡈⠉⠉⠉⠉
⠸⣍⠹⣉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣻⠋⣉⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠨⢡⠻⠁⠛⠉⠙⠫⣍⠛⠛⠛⠛⠓⢸⡥⡌⠻⠒⠀⠀⣿⡿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⣿
⠀⠀⠀⣦⣤⡤⣤⣤⣭⣥⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⠆⠋⣴⡾⣿⠀⠐⠛⠛⠛⠛⠋⠉⠁⣈⣿⣗⠛⡿⠂
⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠋⠙⠿⠿⠿⠿⠛⢻⣿⣿⣶⠰⡦⣡⡟⠛⠛⠛⠛⠛⠛⠉⠉⠙⣿⣿⣯⣵⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣤⣀⣤⣤⣿⣾⣷⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠉⠉⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠲⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣤⣠⣦⢠⣠⢤⣤⢴⣀⣴⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠈⠀⡄⠀⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠁⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠉⠀⠈⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠀⠀⠀⠀⢂⠀⢀⠔⠀⠀⠀⠀⠀⠀⠠

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢰⣮⡥⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢖⡎⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⣳⡚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡮⠭⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠭⠭⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣭⣭⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠩⠭⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠔⣛⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠬⠽⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠒⣎⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡶⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠭⣟⡉

⣤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣼⣷⣭⣿⣷⣵⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⢾⣏⣯⣴⣾⠿⡿⣿⣿⠟⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⠁⠍⠚⠀⢓⣀⣀⣀⣀⣀⣘⡉⡸⣽⣽⣛⣭⣼⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣷⡶⡥⢤⡔⢻⣋⣏⡏⡉⣸⣿⣽⣍⣽⣟⣻⣟⢻⢿⢿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢠⡤⢰⠠⣷⣷⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡞⠈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠟⠀⠐⠈⡥⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠹⠟⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢱⣼⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢼⣾⣯⣾⣧⣾⣿⣿⣿⣿⣿⣿⣿⠳⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠛⠿⡿⢿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣠⠘⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠺⡟⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠈⠃⢻⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢻⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠶⠶⣶⣦⣤⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⢸⡟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⠿⠿⠶⠶⢶⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢇⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠉⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣭⡛⠃
⠀⠀⠀⠀⣴⣿⡿⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⢀⣾⣿⡟⢀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀
⠀⢀⣾⣿⠏⢠⠏⠀⣼⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣷⣾⡀
⠀⣼⣿⡟⢠⡏⠀⣰⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡆
⢀⣿⣿⢁⣾⡇⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷
⢸⣿⣿⢸⣿⡇⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷
⢸⣿⣿⢸⣿⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⢸⣿⣿⢸⣿⡆⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⢸⣿⣿⡜⣿⣷⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠈⣿⣿⣧⣿⣿⣆⠘⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣿⣿⣦⣻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣙⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠘⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣮⣍⡛⠓⠒⠤⠤⢄⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⠿⠟⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣌⣀⣀⠀⠂⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣀⡴⣻⣿⣿⣿⣿⣿⠿⢛⣋⣭⠭⠭⠭⣿⣿⣿⣿⣿⣿⣿⣷⣤⡈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠘⣡⣾⣿⣿⡿⠟⢉⠴⠚⠉⠀⡀⠀⣀⣀⣀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣦⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠞⠀⣰⠀⠀⠀⣼⡿⣿⣿⠋⢀⠔⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠉⠓⠦⡀⠈⠙⣮⢻⣿⣧⠳⣄⠙⡄
⠀⠀⠀⠀⠀⠀⡜⠀⢰⡟⠀⠀⣼⠏⣼⡿⠁⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠈⣷⣿⣿⣧⠹⣆⠘⡄
⠀⠀⠀⠀⠀⢸⠀⠀⣿⠇⠂⢸⡏⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⣿⣿⣿⣇⢹⡀
⠀⠀⠀⠀⠀⡆⠀⢸⣿⢠⠀⣿⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢻⣿⣿⣿⣾⡧
⠀⠀⠀⠀⠀⢣⠀⢸⣿⢸⠀⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⡀⢸⣿⢸⠀⠃⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣾⣿⣿⣿⣿⡇⡀
⠀⠀⠀⠀⠀⠈⣷⠘⣿⡄⣇⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣿⣧⣏⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢻⣇⢻⣷⠘⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣟⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⡎⢿⣧⠀⢠⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢟⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡌⢻⣷⣌⣷⣄⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠞⣱⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣹⣿⣿⣿⣷⣄⡙⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠿⢛⣵⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠻⣿⣿⣿⣯⣟⢿⣦⣤⣈⡉⠛⠻⠿⣿⡿⠿⠿⣛⣫⣵⣾⣿⢟⣫⣿⡿⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠿⣛⣯⣷⣿⣟⠅⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣻⣿⣯⣿⣶⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⢀⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡁⠀⠀⠀⣴⣶⣾⣿⡿⠉⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣎⠀⠀⠰⢾⣾⣿⣿⣿⠇⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣿⣷⣷⢶⣿⣿⣿⣿⣿⣿⣗⢲⠀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠖⠶⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣯⣿⡇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣀⣄⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠟⠋⠁⠔⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⢹⠯⣿⣻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠀⢀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠐⠳⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⠈⠳⢮⣝⣋⢻⣿⣿⣿⣿⣿⣿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣴⢦⢤⣉⣉⣙⢓⣿⡿⣶⣶⡯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠛⠿⠿⠿⠿⠞⠋⠁





⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠀⠒⠒⠒⠒⠒⠂⠤⠤⡄⢀⠠⠤⣄⠀⢀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡅⠀⠀⠀⠉⠻⠉⠉⠉⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠥⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠃⠤⢤⡴⠶⠂⠀⠂⠀⠀⠠⡀
⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⢠⣶⡀
⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣖⠈⣿⣶⣾⢆⠜⠀⠀⠀⣴⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⡇
⠀⠀⠀⠀⣶⣶⢶⣦⣤⣤⣤⣤⣀⠀⠀⣀⣀⣀⣤⣤⣤⣤⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠈⢸⣿⣿⡀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠈⠿⣿⡏⠀⠸⣻⣿⡿⣿⣿⠀⠀⠀⠀⢀⣠⣤⣶⡶⠶⠿⠟
⠀⢐⣉⣈⣉⡛⠛⠛⠛⠿⠿⠿⠿⠿⠇⠀⠀⣀⣈⣈⣉⣀⡀⢺⣿⣿⡿⣿⢯⣤⣶⠾⠿⠛⠋⠉
⠀⠙⠛⠛⠿⠿⠿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣬⣭⣭⣭⣭⣽⣶⣾⠿⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⢷⡄
⢘⣷⡀
⠘⢷⡙⠢⣀
⠀⠈⣿⣄⠀⠉⠀⠀⣄
⠀⠀⠨⡆⠐⠄⡀⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠸⣀⠀⠀⠁⠒⢤⣀⠀⠈⠳⡄
⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠈⠑⢄⠀⠈⢆
⠀⠀⠀⠀⠈⣴⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠴⠒⡄⠀⣠⠞
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠉⣀⠴⣆⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢁⣠⡴⠖⠉⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢁⣀⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⣀⡤⠖⠉⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⢋⣡⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡤⠖⠛⠲⣄⣀⡠⠴⢛⣩⡴⠚⠙⢇
⠀⠀⠀⠀⠀⠀⠀⢾⣯⣅⣀⡀⢢⠴⠊⢩⡴⠚⠁⠀⠀⠀⠀⠼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣹⡷⡖⠇⢸⠇⠀⠀⠀⠀⠀⠀⢀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠀⢀⣠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠃⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⡄⠀⠀⠰⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⣀⠀⡆⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡄⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠙⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡟⠀⠀⣾⣿⡟⠁⠀⣰⣿⣿⠋⠀⢀⣴⣿⣿⠟⠁⠀⢀⣤⣶⣾⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣶⣤⣀⠀⠈⠙⢿⣿⣷⡄⠀⠈⢿⣿⣧⡀⠀⠹⣿⣿⡄
⡟⠀⠀⣼⣿⡟⠀⠀⣼⣿⡿⠁⠀⣠⣿⣿⠟⠁⠀⣠⣾⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣷⣤⡀⠀⠙⢿⣿⣦⠀⠀⢻⣿⣷⡀⠀⠹⣿⣿⡀
⠁⠀⣸⣿⡿⠀⠀⣼⣿⡿⠁⠀⣰⣿⡿⠃⠀⢠⣾⣿⡿⠋⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠈⠻⣿⣿⣄⠀⠈⢻⣿⣧⠀⠀⢹⣿⣷⡀⠀⢹⣿⣷
⠀⢀⣿⣿⠃⠀⢰⣿⣿⠁⠀⣰⣿⡿⠁⠀⣰⣿⣿⠋⠀⢀⣴⣿⣿⠿⠛⠉⠉⠁⠉⠉⠙⠻⢿⣿⣶⡄⠀⠈⢿⣿⣧⠀⠀⢻⣿⣧⠀⠀⢻⣿⣧⠀⠀⣿⣿
⠀⢸⣿⡟⠀⠀⣿⣿⡇⠀⢀⣿⣿⠃⠀⢰⣿⣿⠃⠀⢠⣿⣿⠟⠁⠀⣀⣤⣶⣶⣶⣦⣄⠀⠀⠙⢿⣿⣆⠀⠈⢿⣿⣇⠀⠀⣿⣿⡆⠀⠘⣿⣿⡄⠀⢸⣿
⠀⣿⣿⡇⠀⢠⣿⣿⠀⠀⢸⣿⡟⠀⠀⣿⣿⡇⠀⢠⣿⣿⠃⠀⢠⣾⣿⡿⠛⠛⠛⠿⣿⣿⣄⠀⠈⣿⣿⡆⠀⠈⣿⣿⡄⠀⢸⣿⣿⠀⠀⢿⣿⡇⠀⠈⣿
⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⣿⣿⡇⠀⢰⣿⣿⠀⠀⢸⣿⡟⠀⠀⣿⣿⡏⠀⢀⣤⡀⠀⠘⣿⣿⡄⠀⢸⣿⣿⠀⠀⣿⣿⡇⠀⠈⣿⣿⠀⠀⢸⣿⣷⠀⠀⣿
⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⣿⣿⡇⠀⠸⣿⣿⠀⠀⢸⣿⣇⠀⠀⣿⣿⣦⣀⣼⣿⡇⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⣿⣿⡇⠀⠀⣿⣿⠀⠀⢸⣿⣿⠀⠀⣿
⠀⣿⣿⡇⠀⠸⣿⣿⠀⠀⢹⣿⣇⠀⠀⣿⣿⡇⠀⠘⣿⣿⣄⠀⠈⠻⠿⡿⠿⠛⠀⠀⣼⣿⡿⠀⠀⣼⣿⡟⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⣸⣿⡇⠀⠀⣿
⠀⢹⣿⣧⠀⠀⣿⣿⡆⠀⠘⣿⣿⡄⠀⠸⣿⣿⡄⠀⠘⢿⣿⣶⣄⣀⠀⠀⠀⣀⣤⣾⣿⡟⠁⠀⣰⣿⣿⠁⠀⣸⣿⡿⠀⠀⣼⣿⡏⠀⠀⣿⣿⠇⠀⢰⣿
⠀⠘⣿⣿⡄⠀⠸⣿⣷⡀⠀⠹⣿⣷⡀⠀⠙⣿⣿⣦⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⡿⠟⠁⠀⢀⣼⣿⡿⠁⠀⣠⣿⣿⠃⠀⢰⣿⣿⠁⠀⣸⣿⡿⠀⠀⣼⣿
⡀⠀⢹⣿⣷⠀⠀⢻⣿⣷⡀⠀⠹⣿⣿⣄⠀⠈⠻⣿⣿⣦⣀⡀⠀⠀⠉⠉⠉⠀⠀⢀⣠⣶⣿⣿⠟⠀⠀⣴⣿⣿⠃⠀⢠⣿⣿⠇⠀⢠⣿⣿⠃⠀⢠⣿⣿
⣇⠀⠀⢻⣿⣧⠀⠀⢻⣿⣷⡀⠀⠘⢿⣿⣧⣄⠀⠈⠛⠿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⠟⠋⠀⠀⣠⣾⣿⠟⠁⠀⣠⣿⣿⠋⠀⢀⣾⣿⠏⠀⢀⣾⣿⠏
⣿⣆⠀⠀⢻⣿⣧⡀⠀⠙⣿⣿⣦⠀⠀⠙⢿⣿⣷⣤⣀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⣠⣴⣿⣿⠟⠃⠀⢀⣴⣿⡿⠃⠀⢠⣿⣿⠏⠀⢀⣾⣿⡟
⣿⣿⣷⢶⣶⣿⣿⣷⣶⣶⣾⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣶⣶⣶⣿⣿⣿⣶⣶⣾⣿⣿⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠋⠛⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣷⡀⢰⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣶⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣟⣿⣿⣛⣿⣻⣿⣿⣷⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⠿⠏⠙⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠒⠛⠛⠛⠉⠉⠉⠛⠛⠛⠓⠒⠶⠶⠶⢦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠤⣀⠀⠀⠀⠀⠀⠘⠦⣤⣉⣉⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⡀
⠀⠀⠀⠀⠀⣀⢴⡏⠀⠀⠀⠀⠀⠈⠢⣈⠑⣆⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⣠⠞⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢃⡤⠞⠋⠉⠉⠓⠦⣤⣀⣀⡤⠎⠀⠀⠉⠉⠉⠀⠀⠀⠹⡆⠀⠘⣏⠛⢦⣄⠀⠀⠀⠀⠈⠳⣄
⠀⠀⣼⠋⠀⡏⠀⠀⣠⠖⢋⡆⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢿⠀⠀⠈⠣⣄⠈⣧⠀⠀⠀⠀⠀⠘⣧
⠀⣼⠇⠀⠀⢹⠀⡞⣁⡴⡋⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⣠⣤⡶⠶⠶⠶⠶⠶⢶⣤⣄⣀⠀⠨⣙⠲⣄⠈⠳⣄⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⢹⡆
⢸⡏⠀⠀⢀⡞⠀⠉⠁⠚⠁⠀⠀⠀⠀⠀⡇⠀⣠⡴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠦⣌⠳⣌⢳⡀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡜⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⠏⠸
⣿⠀⢀⠀⠈⠢⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣠⠞⠁⠀⠀⠀⠀⠀⠀⡼⠃⡽⢠⠏
⢻⡄⠸⡆⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠁⢠⡖⢉⠇⠀⠀⠀⢰⣃⡼⠁⠘⡆⡰⢀
⠘⣷⠀⢷⡀⠀⢀⡴⠋⠀⠀⠀⣠⠴⠒⠂⡄⠀⠀⠈⠙⠓⠶⠦⣤⣤⣀⣀⣀⣤⣤⠤⠶⠚⠋⠉⠀⠀⠀⢠⡏⣠⠊⠀⠀⠀⠀⠀⠀⣀⡤⠞⢱⠃⣸
⠀⠸⣧⠘⢷⡀⡞⠀⠀⠀⡞⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢠⠞⠁⠀⢠⠃⢠⡟
⠀⠀⠘⢧⡈⢳⡹⣄⠀⣰⠇⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⡤⠖⢋⡽⠃⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣰⠋⢠⡟⠁
⠀⠀⠀⠈⠻⣆⠙⢮⡉⠁⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠻⠴⠚⠁⠀⠀⠀⠀⠀⠘⠳⠦⠤⠌⠃⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣸⠇⢀⡾⠃⣴⠏
⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣠⡤⠖⠋⠁⠀⠉⠉⠒⠶⠞⢋⡴⢛⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠦⣤⣤⠞⠉⠹⡄⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠔⢚⣩⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⡼⠁⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠶⠦⠤⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⠤⠴⠶⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡿⢿⣿⡿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣿⣿⣿⣿⣷⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣦⣾⣹⠟⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠉⠈⢻⣿⣧⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡁⣹⣿⣼⡿⣦⣾⡟⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠸⣿⣭⣿⣿⣦⣴⣾⣿⡛⣿⡟
⠀⠀⠀⠀⣠⣤⡶⠶⣦⣤⣹⣿⣿⣾⡁⣹⣿⡿⠁⠀⠀⢀⣴⡿⠛⢻⡏⠙⢻⣷⣿⣿⣿⣉⣿⣿⢛⣿⣿⡟⠁
⠀⠀⢠⡾⢿⣧⠶⠶⠶⣌⠻⣯⡙⠛⠛⠛⠉⠀⠀⠀⠀⣾⠟⠳⣦⣼⣷⣴⠟⠉⣿⡌⠙⠛⠿⠿⠛⠛⠁
⠀⠀⣿⢁⡟⢹⡿⠛⢶⣼⣷⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣿⣧⣠⣿⠷⠶⣾⡇⠀⣠⣤⣤⣤⣤⣀⠀⠀⠀⣀⣀
⠀⠀⣿⡈⣧⠘⣷⣤⠾⢡⡟⢸⣇⣴⣿⣟⣿⣦⡀⠀⠀⠹⣯⡀⢠⡿⠙⢿⣄⣠⣿⣷⡿⢿⡅⠀⠈⣹⡿⣷⡀⡞⢷⡬⢷
⠀⠀⠘⢷⣌⣻⡿⠶⠶⢋⣰⡟⢹⣷⣾⠉⢹⣶⣿⠀⠀⠀⠘⠻⢿⣧⣤⣾⠿⠋⢹⡿⠀⠀⣻⠶⢾⡋⠀⢸⣿⠙⠾⠵⠋
⠀⠀⠀⠀⠙⠛⠷⠶⣾⣟⣁⡀⠈⢷⣾⣟⣿⡶⠃⠀⠀⠀⠀⣰⡾⢿⣦⠀⠀⠀⢸⣷⡴⠶⠿⣤⡼⠷⢶⣴⣿
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠹⢷⣾⠟⠀⠀⠀⠀⢻⣦⡀⠀⣾⠆⠀⣠⣿⢏⣤⣤⣦⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⣽⣿⣿⠇⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠙⠻⠿⠿⠿⠟⢫⣽⣿⠋⠁⠀⠀⠀⠉⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡿⣯⣶⡿⠟⠛⠛⡿⢷⣦⡀⠀⠀⠀⣰⡟⢻⣩⠿⣧⠀⠀⠀⠀⠀⠀⢠⣿⠋⠻⣷⣶⣶⣶⣶⣤⠀⢀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⡿⠙⣷⡖⠚⣾⢧⡄⠙⣿⡄⠀⠀⢻⣉⡿⣜⢒⡿⠀⠀⠀⠀⠀⠀⢼⡏⠀⠀⣾⣿⡟⠉⢻⣿⣿⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢸⣃⣿⠟⢻⣦⢿⡶⢿⣷⠀⠀⠀⠛⠶⠾⢿⣷⡶⠿⠿⠶⣶⡄⢹⣧⠀⠀⢻⣿⣷⣤⣾⣿⠏⠀⠀⣿⠇
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠘⣿⡟⠻⣏⢻⡷⠿⣇⡼⠁⣸⡟⠀⠀⠀⠀⠀⣾⡟⠙⣷⣠⣄⣴⠟⠻⣿⣿⣦⡀⠀⠙⣿⠟⠛⠁⠀⢀⣼⠯
⠀⠀⠀⣠⣾⣿⣿⠋⠙⣿⣷⣝⣿⣄⠈⣿⠳⠒⠛⢷⣴⡟⠁⠀⠀⠀⠀⢰⣿⠀⢀⣿⠁⠈⣻⡄⠀⣿⡎⠙⠿⣦⣼⣿⣀⣀⣤⣶⠟⠋
⠀⠀⢰⣿⠁⠉⣿⣶⣶⡿⠛⢿⡎⠙⠻⢿⣶⣶⠿⠟⠉⠀⠀⠀⠀⠀⠀⠈⣿⡟⠋⠻⢶⡶⠟⠛⢻⣿⠃⠀⠀⠁⠉⠋⠛⠋⠉
⠀⠀⢸⣿⣷⠾⣿⣤⣿⣧⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣷⣷⣦⣼⣿⣦⣄⣸⣇⣀⣴⡟⠃
⠀⠀⠘⢿⣇⠀⣸⣿⠁⠈⣿⡿⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⠛⠙⢿⡟⠉⢹⣿⣿⣏⡉⠛⠙⠙⠉⠀⢠⣴⢶⣄
⠀⠀⠀⠈⠙⠿⢿⣿⡷⣾⣋⣁⠀⠀⠀⠀⠀⠀⢐⣿⡿⠿⣷⣶⠿⠿⣶⣾⠟⠛⣿⣗⠀⠀⠀⠀⠀⠸⣷⣴⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⣿⣿⣆⠀⠀⠀⠀⣺⣿⣅⣀⣼⡇⠀⠀⠈⣿⣦⣤⣿⣿⡀⣀⣾⣾⡿⠿⠿⣷⣤⠀⢠⠴⣶⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣍⣽⡿⣿⠀⠀⠀⠀⢘⣿⣿⠟⠛⢿⣦⣤⣾⡏⠉⢹⣿⣿⣼⡟⣡⡾⣿⠓⢶⣌⢻⣧⢾⡒⣭⠓⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣿⣿⡷⠋⠀⠀⠀⠀⠀⠻⢿⣧⣤⣾⡏⠀⢹⣿⣶⣿⠟⢫⣿⠀⣏⣰⡟⢻⡶⢿⠋⣿⡍⠙⠛⠋⠉⠻⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⡿⣿⣿⣿⡿⠟⠋⠀⠈⢿⣟⠻⣍⣙⣿⣤⠟⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣤⣍⣹⣧⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠁

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣠⣶⣋⣁⣂⡀⠀⠉⠉⢷⡔
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⠿⠻⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⣽⡷⠂⠄⠁⠂⠀⢢⡄⠉⠻⣿⡿⠿⢿⣟⡓⢻⣞⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣾⠇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠑⣤⣄⣨⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠺⢿⠋⠀⠀⠀⠀⠀⠀⡆⢀⠠⠈⠀⠀⠠⠉⠿⠿⢿⣿⣿⠆
⠀⠀⠀⠀⠠⠂⠐⠀⠀⠛⠛⠂⢀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣧⡀⠀⠀⠀⠀⠈⠁⣾⣧⣦⣤⣄⡁⢴⣶⣿⣿⣿⡟⠒
⠀⠀⠀⠀⢀⣴⣿⣁⡖⠀⠀⠀⠀⠙⠿⣷⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣼⣿⣧⠀⢀⣀⡀⢐⣴⡿⠛⢛⡿⣿⣿⣿⣷⣿⡿⠋⡈
⠀⠀⠀⠀⠀⣼⣿⣿⣿⡆⢀⣄⠀⠀⣾⡛⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡯⢶⣤⣟⣹⣻⣧⣿⣿⡗⠀⢀⣴⣿⣿⣿⣿⠠⠁
⠀⠀⠀⠀⢰⣄⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⠛⠀⠘⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢘⣻⣟⠻⠿⠟⠛⠛⢻⣿⣿⣿⣹⣆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠒⠰⢂⣽⣆⣀⣤⣄⡌⠉⣻⣡⣿⣿⡁⠀⠀⠀⠀⢀⣤⡾⠟⠉⠉⣻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠜⡃⠸⣿⠴⣿⣿⣿⣿⡿⡃⠀⠀⠀⠀⠀⢀⣾⡿⠃⢀⡀⢰⣿⣿⣿⡄⢀⡀⠀⠀⢤⡀⠀⠀⠀⢠⠎⠀⠀⠀⠐⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠄⠀⠁⠀⣠⠄⠀⠀⡀⠾⣿⣿⣏⣉⣿⣿⣿⠿⣿⣿⠋⠀⠀⠀⠀⠙⣷⡀⠀⢻⠀⠀⠀⠀⠀⠈⣹⠟⠀⠀⠀⠀⠀⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⡿⠛⠉⢹⣆⡀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠤⣄⣤⣔⠲⣿⠀⠀⠀⠀⠀⠀⠀⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠈⣀⠄⠀⣿⣿⣿⡷⠁⠀⠀⠀⢼⣿⣿⣍⣠⣤⣤⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⣀⣄⣤⣨⣵⣾⣿⣿⣿⣟⣠⣤⣾⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠟⠛⠉⢻⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠘⠒⠀⢀⣤⣴⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣟⣀⣠⣤⣤⣤⣤⣴⣶⣿⣷⣶⡶⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡽⠋⠁⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣙⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣯⠩⢿⣿⣿⣟⢷⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣠⣾⣿⣿⣿⠟⠉⠙⠉⠉⠉⠛⠻⠿⢿⣿⣆⠀⠀⠀⠀⠈⠉⠉⠱⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠀⣐⣀⣼⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠘⣿⢿⡇⠀⢃⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⡿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⡇⠀⠈⠃⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠰⠿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠘⠇⠀⢲⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣴⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣰⠸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡄⠀⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣟⣄⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⢛⣾⣷⣶⣴⣶⣿⣿⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠿⠿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠨⠿⠛⠿⠿⠿⠿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣼⣿⣿⡿⠿⠛⠛⠉⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁

⠀⡀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣷⡄⠻⣿⣿⣿⣖⣒⠒⠀⠀⠀⠀⠀⣤⣄
⢸⣿⡄⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⠍
⢸⣻⣿⠁⢂⡀⠀⠀⠀⠀⠈⠉⠛⠊⠉⢀⣀⣤⣀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂
⠘⢿⣿⣀⡞⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣛⣿⣷⣄⠀⠀⠀⠀⢠⣤⣄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠈⠛⠓⠿⣿⣷⣦⣄⡀⡀⠀⠀⠀⣾⣿⣽⣿⣿⣿⣿⣧⠀⠐⠲⠒⢻⣹⣿⣿⠗⢦⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡁⠀⠀⠀⣿⣇⣿⡮⢽⣿⣿⣿⡆⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈⠓⠄⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⣿⣿⢈⣶⣮⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣯⣙⣾⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣧⣽⣿⡿⢿⣤⣤⣤⣄⣀⣀⣀⣈⣉⣉⣭⣭⣽⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣦⣤⣴⣾⣿⣿⣿⣿⣷⣦⣤⣴⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠉⠛⠻⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠉⢀⣤⣶⣾⣿⣿⣿⣿⣷⣶⣄⡀⠙⢿⣿⣦
⠀⠀⠀⠀⠀⢀⣶⣶⣶⣿⣿⠃⢀⣴⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣦⠀⠙⣿⣷⣶⣶⣦
⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⠃⢀⣾⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⠀⠸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠙⢿⣿⡏⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⠀⣸⣿
⠀⠀⠀⠀⠀⣠⣴⣿⣿⣧⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⢻⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠏⠀⣼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠛⠛⠛⢻⣿⣦⡀⠙⢿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠟⠁⢀⣼⣿⠟⠛⠛⠋⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⣀⠈⠙⠛⠿⠿⠿⠿⠛⠋⠁⣠⣴⣿⣿⡇⠀⢀⣤⣄⠀⢀⣸⣿⣿⣿⣀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣷⠐⣿⣿⣿⡿⠿⠛⠛⠛⠛⠻⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠟⠉⠈⠉⢻⣿⣿⣿⣿⡟⠉⠁⠙⠻⡿⠟⠁⢠⣿⠟⠉⣠⣴⣾⣿⣿⣷⣶⣤⡈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠀⠀⠀⠀⠀⢰⣿⣿⣿⠏⢠⣾⣿⡿⠛⠋⠉⠛⠻⣿⣿⣦⠈⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡏⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠘⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⢿⣿⣧⡀⠀⠀⠀⠀⠀⣰⣿⣿⠇⢰⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣧⡈⠻⣿⣿⣶⣦⣤⣶⣾⣿⡿⠃⣠⣿⠿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣈⠉⠛⠛⠛⠛⠋⢁⣠⣾⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⠟⠿⣿⣶⣶⣾⡿⠟⢿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠸⣿⣿⡟⠀⠀⠀⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣴⡿⠟⠉⠀⠀⠀⢀⣀⣤⡤⠄
⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⠏⣠⣾⠟⠉⠀⠀⢀⣠⣴⡾⠟⠋⠁
⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⠟⢡⡾⠋⠁⠀⣀⡴⠞⠛⠉
⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⠏⣴⠏⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⢃⡾⠁⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⢇⡞⠀⠀⠀⢀⡴⠞⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡿⣼⠁⠀⢀⡴⠋⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻
⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⡇⡇⠀⢠⠏⠀⠀⠀⢉⣀⣀⡀⠀⠀⠉⠙⠲⢤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⡇⡇⠀⡞⠀⠀⣰⣾⣿⡿⠿⣿⣿⡦⣄⠀⠀⠀⠉⠳⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣷⣳⠀⢣⠀⢸⣿⣿⣿⣷⣖⣶⣝⣿⣮⢷⡀⠀⠀⠀⠀⠙⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣿⣿⣧⡈⢦⡈⠻⣭⣥⣹⣿⣿⣿⡞⣿⣧⢿⡀⠘⣆⠀⠀⠈⠻⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⢿⣿⣶⣿⣷⣶⣿⢿⣿⣿⣿⣿⣿⣿⠸⣧⠀⠸⣇⠀⠀⠀⠘⢦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣭⣿⣿⣭⣷⣿⡿⣻⣿⡏⣿⣿⠇⣿⠀⠀⢿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣼⣿⡿⣹⣿⣿⢀⣿⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣛⠛⠛⠛⠛⣛⣋⣭⣴⣾⣿⣿⡿⣱⣿⣿⡏⢸⣿⠀⠀⢸⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣴⣿⣿⡿⢀⣿⡟⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⡿⠁⣼⣿⠃⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣵⣾⣿⣿⣿⡿⠁⣼⣿⡏⠀⠀⠀⣼⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣥⣾⣿⣿⣿⣿⣿⠟⠀⣼⣿⡟⠀⠀⠀⢀⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢛⣩⣴⣾⣿⣿⣿⣿⣿⣿⡿⠋⢀⣼⣿⡿⠁⠀⠀⠀⣼⣿⣿⠁

⠀⠀⢀⣔⣶⣢⡄⠀⠀⣤⣖⣲⣄⠀⠀⣠⢶⣶⢦⠀⠀⢀⠔⣶⠢⡀⠀⠀⡠⡶⣖⣄⠀⠀⣠⠖⡒⢢⡀⠀⢀⠔⣒⡢⡄⠀⠀⡴⡖⡲⢄
⠀⠀⠸⡿⣤⢿⡏⠀⠈⣷⡧⢿⡿⠀⠀⢿⣼⣼⣼⠃⠀⠸⡛⣤⢛⠇⠀⠀⢟⣄⡼⡻⠀⠀⢣⠚⠜⣡⠃⠀⠸⡘⠯⢃⡏⠀⠈⣗⠢⠓⡾
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉
⠀⠀⢠⣾⠿⣷⡄⠀⢀⣶⣿⣻⣦⠀⠀⣴⢿⣿⢶⡀⠀⢠⡞⣿⢓⣆⠀⢀⣶⣿⢿⣦⠀⠀⣰⢎⣟⢲⡀⠀⢠⣞⣿⡳⣆⠀⢀⡶⣏⡹⢦
⠀⠀⠸⣾⣦⣿⠏⠀⠈⢷⣟⣻⡿⠀⠀⢻⣼⣾⣼⠃⠀⠸⣏⣷⣉⠟⠀⠘⢿⣧⣾⡿⠀⠀⢳⣈⣚⡴⠃⠀⠸⣜⣳⣳⠏⠀⠈⢷⣱⣋⡾
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉
⠀⠀⢠⣮⠿⣵⡆⠀⠀⣴⣯⣿⣦⠀⠀⣴⢿⢿⢷⡄⠀⢠⣊⠿⣑⡆⠀⠀⣶⠟⢯⣦⠀⠀⡴⢋⢏⡳⡀⠀⢠⢎⣭⡕⡆⠀⠀⠔⠏⡝⢢
⠀⠀⠘⢟⣶⡻⠇⠀⠀⠿⣗⣿⠟⠀⠀⠹⣼⣾⡼⠁⠀⠘⢍⣶⣩⠇⠀⠀⢿⣦⣜⠟⠀⠀⠱⣉⣚⡴⠁⠀⠘⢌⣓⡡⠇⠀⠀⠯⣁⣉⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣤⣶⣶⠶⠶⠶⠶⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀⠀⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⣻⠿⠛⠛⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⡞⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠀⡀⡁⠀⣉⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢸⣿⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⣿⡏⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃⢸⡟⠁⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⣠⣾⠇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⢀⣀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⣀⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠏⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠛⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣻⡶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣶⣬⣙⠻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⣉⣤⣴⣶⣾⠿⠿⠿⠿⠿⠿⢶⣶⣤⣄⡉⠛⠿⣿⣦⡈⠛⢦⡀
⠀⠀⠀⠀⠀⣠⣾⡿⢟⣡⣶⡿⠟⠋⠉⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠈⠙⠻⢷⣦⣈⠛⢿⣦⡀⠙⢦⡀
⠀⠀⠀⢀⣾⣿⠟⣵⣿⡿⠋⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠈⠻⣷⣄⠙⢿⣦⠀⠹⣆
⠀⠀⢠⣿⡿⢣⣾⣿⠋⣠⣴⣿⣿⣿⣿⣿⠿⠟⢛⣛⣛⣛⣛⡛⠿⢿⣿⣿⣷⣄⠀⠈⠻⣧⡈⢻⣧⡀⠘⣧
⠀⢠⣿⡿⢡⣿⣿⣷⣾⠟⣫⣿⡿⠛⣉⣴⣶⡿⠟⠛⠉⠉⠉⠛⠛⠶⣬⡙⢿⣿⣷⣄⠀⠙⣿⡄⠹⣷⡀⠘⣧
⢀⣿⣿⢡⣿⣿⣿⠟⢁⣾⡿⠋⣠⣾⡿⠛⠁⢀⣠⣴⣶⣶⣶⣶⣤⣀⠀⠙⢦⡙⣿⣿⣆⠀⠘⣿⡀⢻⣧⠀⢹
⣸⣿⣏⣾⣿⡿⠁⣰⡿⠋⣠⣾⣿⠏⠀⢀⣴⣿⡿⢟⣻⡭⠭⣝⣻⢿⣷⣆⠀⠻⡜⣿⣿⡆⠀⢹⣇⠘⣿⡄
⣿⣿⣿⣿⡟⠀⣼⡿⠁⣰⣿⣿⠃⠀⣰⣿⣿⢋⡔⢋⣠⣶⣶⣦⣌⠳⡝⣿⣧⠀⢻⢹⣿⣧⠀⠘⣿⠀⣿⡇
⣿⣿⣿⣿⠁⣸⡿⠁⣰⣿⣿⡏⠀⢰⣿⣿⢣⠏⢠⡿⣿⡿⢋⡙⢿⣧⢸⢸⣿⡇⢸⣿⣿⣿⠀⢀⣿⠀⣿⡇
⣿⣿⣿⡇⢠⣿⠃⠀⣿⣿⣿⠁⠀⣼⣿⣿⢸⠀⣿⡇⣿⣇⢇⠶⠿⢃⢞⣾⣿⠃⣼⣿⣿⠇⠀⣸⡇⢸⣿⡇⢸
⢿⣿⣿⠀⢸⣿⠀⢸⣿⣿⣿⠀⠀⢻⣿⣿⢸⡀⢹⣿⣝⢿⣷⣭⣭⣷⣿⡿⢃⣼⣿⣿⠏⠀⢠⡟⢠⣿⣿⣡⣿
⠸⣿⣿⠀⣿⡇⠀⢸⣿⣿⣿⡇⠀⠸⣿⣿⣆⢷⡀⠹⣿⣷⣯⣽⣿⣭⣥⣶⣿⣿⠟⠁⢀⣴⠟⣠⣿⣿⣿⣿⠃
⠀⢿⣿⠀⢿⡇⠀⠸⣿⣿⣿⣷⠀⠀⢻⣿⣿⣦⡙⢤⡀⠙⠛⠿⠿⠿⠿⠛⠋⠁⣀⣴⠟⣡⣾⣿⣿⣿⡿⠃
⠀⠈⣿⡆⢸⣿⠀⠀⢿⣿⣿⣿⣧⠀⠀⠹⣿⣿⣿⣦⣝⡓⠦⢤⣤⣤⣤⠴⠶⢛⣉⣴⣾⣿⣿⣿⡿⠋
⠀⠀⠘⣷⠀⢿⡄⠀⠘⣿⣿⣿⣿⣷⣄⠀⠈⠻⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⢀⡴⠂
⠀⠀⠀⠈⢧⠈⢷⡀⠀⠘⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠀⠀⢀⣠⣶⠏
⠀⠀⠀⠀⠀⠁⠈⢷⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠤⠶⠶⠶⠤⠤⢤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠙⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠙⠂⠀⠀⢦⡄⠀⠀⠀⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡴⠛⠉⠁⠀⠀⠀⠉⠙⠳⢦⡀⠀⠀⠛⠉⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣤⢤⣤⣄⡀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣅⡀⠀⠀⠈⠙⣦⣀⡴⠋⠀⢀⡀⠀⠀⠀⠈⠳⠀⠀⠀⢹⡄
⠀⠀⠀⠀⣿⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⡇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣷⠀⠘⢷⣄⣠⡴⠛⠻⡆⠀⠀⠀⠀⠲⣤⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠒⠶⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡶⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡇
⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠘⣇⢀⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⢦⡀⠀⠀⠀⣠⠤⠦⠤⠴⠞⠁⣾
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⢸⡇⠀⢀⡞⠁⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢀⣰⠟⠀⠀⠀⠀⠈⠳⠶⠟⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠶⢤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⢀⣀⢀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⢫⣾⣿⣧⡏⣏⡯⡿⡽⣍⣷⣤⠉⠛⠳⢶⣤⣄⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠟⠛⠛⠛⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⣠⣤⣀
⠀⠀⠀⣠⠔⠠⢠⢖⣭⡭⣕⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣩⡲⡖⣮⠳⡄
⠀⠀⣴⠄⠀⠀⣇⢾⣿⡿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣯⠿⡿⣭⢃⣧
⠀⠐⠀⠀⠀⠐⠉⠈⠙⠛⠁⠊⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠈⠉⠙⠉⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣶⣶⣾⣶⠀⡀⠀⠀⠠⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠠⢀⡤⣤⡢⠐⠀⠤⠀⠀⠀⠀⠤⠤⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣷⠂⡔⠂⡑⠢⡀⣦
⠀⠀⠀⠀⢠⡄⠀⡀⡏⢴⠆⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡅⠸⠟⢀⠇⣼⣿
⠀⠐⠀⠀⠀⠀⠀⠁⠙⠒⠒⠁⠂⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠈⠓⠒⠁⠴⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⣴⣿⢻⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢀⡴⣢⠤⠤⠤⣄⠐⠀⠀⠰⠿⠛⠃⠘⠛⠛⠛⠛⠛⠀⠘⠛⠛⠛⠟⠉⠀⠀⠀⡠⠒⣒⣒⠢⣄
⠀⠀⠀⠀⠎⡜⣱⡞⣿⢗⣎⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣰⣿⢙⡛⣽⡌⢇
⠀⠀⡀⠀⠀⡇⢯⣝⠄⣉⡻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢫⣥⡕⣢⣝⠇⡼
⠀⠸⠷⠀⠀⠛⠈⠙⠚⠋⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠂⠉⠓⠛⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣤⣤⣄⣀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣰⠿⠯⣏⠀⢈⡯⠿⢷⡀⠀⠀⠀⠀⣴⡿⢿⣏⠁⠀⠀⠈⣹⡿⢿⣦
⠀⠀⠀⣰⣿⣿⣿⡿⠿⢿⣿⣿⣿⡆⠀⠀⢰⣿⣀⣠⡟⠉⠙⣧⣀⣸⣷⠀⠀⢠⣾⠏⠀⠈⢿⣆⣠⣀⣴⡟⠀⠀⠻⣷
⠀⠀⠀⢺⣿⣿⣿⣇⠀⣬⣿⣿⣿⡇⠀⠀⢸⣷⠉⠙⣧⣀⣠⡟⠉⢳⣿⠀⠀⣼⡏⠀⠀⢀⣾⣿⠿⠿⣻⣧⠀⠀⠀⢻⣇
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠹⣦⣴⡏⠀⠉⣗⣤⡾⠁⠀⠀⣿⡿⠿⠿⢿⣿⣇⠀⢀⣽⣿⠿⠿⠿⢿⣷
⠀⠀⠀⠀⠈⠛⠿⢿⣿⡿⠿⠋⠀⠀⣄⣰⣄⣠⠈⠙⠻⠲⠚⠛⠉⠀⠀⠀⠀⢹⣧⠀⠀⠀⢻⣷⣿⣿⣿⡋⠀⠀⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⡿⠛⠛⢿⣷⠂⠀⠀⠀⢀⣠⣠⣠⣀⡀⠀⠻⣧⡀⣠⡿⠁⠀⠀⠘⣷⡀⣠⣾⠟
⠀⠀⠀⠀⠀⣠⣴⠶⠶⣦⣄⠀⠙⣿⣇⢀⠀⣸⣿⠃⠀⣀⣾⠿⣿⡋⢹⡿⢿⣶⡀⠈⠻⢿⣧⣤⣠⣠⣤⣼⡿⠛⠁
⠀⠀⠀⠀⣸⡟⢱⠒⠲⡎⢻⡆⠈⠉⡿⢿⡿⢿⠉⠁⢐⣾⡿⣤⣾⠟⠿⣧⡼⢿⣷⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⢻⣇⡸⠤⠤⢇⣼⡇⠀⠀⠀⠀⢀⠀⠀⠀⠐⣿⣤⣼⣧⣀⣠⣿⣦⣼⣿⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠙⠷⠶⡶⠿⠋⠀⠀⠀⣤⣷⣾⣾⣧⠆⠀⠻⣿⣄⣼⠛⢻⣧⣸⣿⠃⠀⠀⠀⢐⣾⡿⠋⠋⠉⠙⢽⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢀⣹⣿⠁⠀⠀⢹⣿⡁⠀⠘⠹⠻⢿⠿⠿⠛⠀⠀⠀⠀⠀⣺⣿⡏⠀⠀⠀⠀⠀⣹⣿⡗
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣄⠀⠞⣿⣄⣀⣠⣾⡷⠂⠀⣀⢀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡢⠀⠀⠀⣰⣿⣿⠃
⠀⠀⠀⠀⣾⣿⣿⡿⠿⣿⣿⣿⣆⠈⠁⠟⠻⠙⠋⠁⠀⢤⣿⣿⣻⡿⣤⠄⠀⠀⣠⣶⣶⣦⡄⠘⠿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠐⣿⣿⣿⣧⣤⣾⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠐⢾⣾⡁⢀⣷⣿⠖⠀⢸⣿⡏⠉⣿⣿⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠟⢀⣠⣴⡶⣶⢦⣦⣄⠀⠋⣻⢾⡿⢾⠙⠃⠀⠘⢿⣿⣾⣿⠟⠀⠀⣀⣄⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢠⣿⠿⡁⠀⡇⠀⣨⠿⣿⡄⠀⠀⠁⣀⣤⣤⣤⣄⡀⠀⠁⠀⢀⣰⡟⢿⣿⣬⣿⡿⢷⣆
⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣿⣃⣀⣈⡶⠛⣾⣁⣀⣸⣷⠀⠀⣴⣿⣿⠿⠿⣿⣿⣦⠀⠀⣲⣿⣿⠫⠊⠉⠑⠽⣿⣿⣆
⠀⠀⠀⠀⣼⡿⡛⢛⢿⣦⠀⣿⡇⠀⣨⠷⡶⠿⡀⠀⣸⣟⠀⢰⣿⣿⢱⡋⢙⢎⣿⣿⡄⠀⢺⣦⣿⣁⠀⠀⠀⢜⡷⣼⡗
⠀⠀⠀⠀⣿⣇⠄⠠⣸⣿⠀⠘⢿⣾⡁⠀⡇⠀⣈⣶⠿⠃⠀⠀⢿⣿⣷⣭⣭⣾⣿⡿⠀⠀⠘⢻⣏⣷⣯⠦⡵⣏⣹⡟
⠀⠀⠀⠀⠘⠻⠿⠿⠟⠁⠀⠀⠈⠘⠛⠻⠿⠟⠏⠋⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠋⠟⠿⠶⠿⠻⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⢿⣧⡀
⠀⠀⠀⠀⠀⣼⡿⠁⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠈⢻⣷⡀
⠀⠀⠀⠀⣾⡿⠁⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⣰⣿⣷⡄⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⢀⣼⡿⠁⠹⣿⣆⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠹⣿⣦⣀⠀⠀⣀⣴⣿⠇⠀⢀⣾⡟⠁⠀⠀⠘⢿⣦⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠈⠛⠻⠿⠿⠟⠋⠁⠀⢠⣿⠟⠀⠀⠀⠀⠀⠈⢿⣧⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠈⠛⢿⣷⣶⣤⣴⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⣀⡀⠀⠀⢀⣀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠉⠘⠁⠈⠉⡑⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⢞⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠐⠀⠀⠀⡁⣠⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠐⢀⠀⠀⠀⠀⠀⣠⣼⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⣀⣰⣄⣤⣶⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢰⠏⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣤⡤⠤⢤⣀⡀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⣂⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡏
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠂⠋⠉⠉⠁⠐⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣷⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⢿⣧⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿
⠀⠀⠀⢸⣇⣠⠀⠀⠀⠀⠀⠐⣀⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢻⣷⣚⣄⡁⠀⠀⠀⠀⠀⡀⢠⠇
⠀⠀⠀⠹⡛⠙⡿⢶⣶⣨⣶⣿⣿⣿⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣙⠻⣷⢀⠠⡄⠠⣄⣨⡴⠋
⠀⠀⠀⠀⠈⠢⣤⣛⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢠⣀⡄⠀⠀⢀⠀⠀⠀⠀⠈⠙⠻⠿⠛⠿⠶⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⢀⣀⣠⣠⢠⡔⢬⣿⣷⠰⡿⠛⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⡹⠁⢯⣥⢽⠏⠑⢻⣿⣿⣛⣏⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣉⢫⠱⣦⣾⣿⣋⠀⢠⣿⣿⡿⣿⣭⣙⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡚⠋⢟⠻⣳⣬⣸⣟⡃⣴⣿⠗⠙⠉⠀⠈⠉⢳⣦⣙⢦⡀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣭⣠⣿⣛⡡⣝⠻⣧⠼⠁⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠉⢷⣿⠛⠛⠻⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠂⠉⣉⣿⡿⣺⡿⠿⠆⣴⡻⠉⠈⠙⠻⢶⣤⣤⡄⢠⡆⠀⢿⡏⠀⠀⠀⠻⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡴⠦⠉⡽⣲⣿⣟⣲⢁⣿⣃⠆⠀⠀⠀⠀⠀⢿⣧⡈⢇⠠⣾⠃⠀⠀⠀⠀⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢷⢉⣿⣫⣍⡼⢷⣠⣿⠍⡀⠀⠀⠀⠈⠀⠈⠻⣿⣿⣼⠃⠀⠈⠁⠀⢀⡿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣩⠛⠻⡟⣿⢲⡇⠘⣿⣤⣆⠀⠀⠀⠀⡄⣀⣷⣿⠿⠛⠓⠂⠀⡀⣀⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠛⣤⣿⡼⢿⢿⣇⠀⠙⠻⠿⠿⠛⡛⠋⣉⣁⣤⣤⣖⣿⣿⣷⣾⠻⡜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣁⣋⣾⢹⣾⣿⣿⡶⣴⣶⣿⣿⣿⠿⣯⠷⣫⣼⡟⢾⣿⣾⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡼⠻⢛⣿⣿⣿⡿⣺⢷⣰⣟⣽⣛⢿⣿⣶⡖⠀⡝⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠍⢚⡡⢿⡵⣦⣻⣿⣿⣿⣿⡻⣶⠛⢍⠀⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⣿⠚⠟⠙⣷⡛⠉⣏⠐⢔⠧⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠜⠃⠈⠁⠀⠊

⠀⠀⣠⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠿⠿⠛⠛⠛⠛⠛⠋⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⢿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣄
⣠⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀
⣿⡿⠋⠀⠀⠀⠀⠀⣀⣴⣿⡿⠟⠋⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠈⠙⠻⣿⣷⣦⡀⠀⠀⠀⠀⠉⠻⣿⣿⣦
⠋⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠀⠀⠀⠀⢀⣤⣶⣿⠟⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⢿⣷⣦⣀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠈⠻⣿
⠀⠀⠀⢀⣴⣾⣿⠟⠁⠀⠀⠀⢀⣤⣾⡿⠟⠉⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠈⠛⢿⣷⣦⡀⠀⠀⠀⠉⠻⣿⣷⣄⠀⠀⠀⠀⠘
⠀⠀⣴⣿⡿⠛⠁⠀⠀⠀⣠⣴⣿⠟⠉⠀⠀⠀⣠⣴⡿⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣷⣤⡀⠀⠀⠈⠻⢿⣶⣄⠀⠀⠀⠈⠻⣿⣷⡀
⠀⣼⣿⡟⠀⠀⠀⢀⣠⣾⡿⠋⠁⠀⠀⣠⣴⡿⠛⠉⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣦⣄⠀⠀⠙⠻⣷⣄⡀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠘⣿⣷
⣰⣿⡟⠀⠀⠀⢠⣿⡟⠋⠀⠀⢀⣤⣾⠟⠉⠀⢀⣠⣶⠟⠋⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠙⠿⣦⣀⠀⠈⠙⢿⣦⣄⠀⠀⠈⢿⣷⠀⠀⠀⠹⣿⣧
⣿⡿⠁⠀⠀⢀⣿⡿⠀⠀⢀⣴⡿⠋⠁⠀⣀⣴⠿⠋⠀⢀⣴⠾⠋⠙⠛⠛⠉⠉⠉⠉⠙⠷⣤⡀⠈⠙⢷⣤⡀⠀⠉⠻⣷⡀⠀⠈⣿⣧⠀⠀⠀⢹⣿⣇
⣿⠁⠀⠀⠀⣼⣿⠁⠀⠀⣼⡿⠀⠀⣠⡾⠛⠁⢀⣠⡾⠛⠁⣠⡶⠛⠛⠛⠛⠛⠛⠛⠷⣄⠈⠛⢶⣄⡀⠉⠻⣶⡀⠀⢻⣧⠀⠀⠘⣿⣇⠀⠀⠀⢻⣿⡆
⠃⠀⠀⠀⣼⣿⠃⠀⠀⣰⣿⠁⠀⢰⡿⠀⢀⣶⠟⠁⣠⡴⠞⢁⣠⠞⣛⠛⠛⠛⣛⠛⢦⡈⠻⢦⣄⠈⠻⣦⠀⠹⣧⠀⠀⢿⣇⠀⠀⢹⣿⡆⠀⠀⠘⣿⣿
⠀⠀⠀⢰⣿⡏⠀⠀⢠⣿⠇⠀⢀⣿⠃⠀⣼⠇⢀⡾⠉⣠⠶⢋⣡⠞⣩⢭⣍⣭⢭⡑⢦⡙⠲⢤⠈⢷⠀⢹⡆⠀⢻⡆⠀⠘⣿⡄⠀⠀⢿⣷⠀⠀⠀⢹⣿
⠀⠀⠀⣾⣿⠁⠀⠀⣾⡟⠀⠀⣼⡏⠀⢰⡟⠀⣸⠃⢸⠃⡶⢫⠴⣚⠕⣵⣒⣊⡱⢝⡲⢍⢳⠘⡇⠸⣇⠈⣿⡀⠈⣿⡀⠀⢹⣷⠀⠀⠸⣿⡆⠀⠀⠘⣿
⠀⠀⢠⣿⡏⠀⠀⢰⣿⠃⠀⢰⣿⠀⢀⣿⠁⢠⡏⢀⡟⢠⠇⡾⡸⢰⢭⣺⣷⣿⣯⡵⢮⠸⡘⣆⢻⡄⢻⡄⠸⣧⠀⢹⣇⠀⠈⣿⡆⠀⠀⢿⣷⠀⠀⠀⢻
⠀⠀⣼⣿⠁⠀⠀⣾⡏⠀⠀⣾⡇⠀⢼⡇⠀⣿⠀⣾⠁⡏⢸⢱⠳⡷⣾⣿⡉⢹⣿⠶⢇⡗⡵⣸⢂⡷⢀⡗⠀⣿⠀⢀⣿⠀⠀⣽⡇⠀⠀⣸⣿⠀⠀⠀⣸
⠀⠀⢹⣿⡄⠀⠀⢹⣷⠀⠀⢹⣧⠀⠘⣷⠀⢹⡆⠸⣆⠹⡌⣧⢡⢱⠞⣻⣿⣿⣟⠿⣬⢸⢰⠇⡼⠁⡾⠁⣸⠇⠀⣼⠇⠀⢰⣿⠁⠀⢀⣿⡇⠀⠀⠀⣿
⠀⠀⠈⣿⣧⠀⠀⠈⣿⡆⠀⠈⣿⡄⠀⢻⡆⠀⢿⡀⢹⡀⣧⠸⢌⡓⢌⡪⠑⠚⠵⡩⢒⣩⠞⣠⡇⢸⠇⢠⡟⠀⢰⡟⠀⠀⣾⡇⠀⠀⣸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⢻⣿⡄⠀⠀⢹⣷⠀⠀⢸⣷⠀⠈⣿⡀⠘⣇⠈⢧⣌⠙⠦⣌⠳⡭⠭⠬⠭⠴⢋⡴⠚⢉⣴⠟⠀⣾⠃⢀⣿⠁⠀⣸⡿⠀⠀⢠⣿⡇⠀⠀⠀⣿⣿
⠀⠀⠀⠘⣿⣧⠀⠀⠈⣿⣇⠀⠀⢻⣇⠀⠸⣧⠀⠙⠷⣄⡈⠛⢦⣈⠓⠒⠒⠒⠒⠒⢋⣤⠞⠉⣀⣴⠞⠁⢀⣼⡇⠀⢠⣿⠃⠀⢀⣾⡟⠀⠀⠀⣸⣿⡏
⡆⠀⠀⠀⢹⣿⣆⠀⠀⠘⣿⡆⠀⠈⣿⣄⠀⠙⠻⣦⣀⠈⠛⢶⣄⠙⠛⠛⠛⠛⠛⠛⠋⢁⣤⠞⠋⠀⣠⣶⠟⠉⠀⣠⣿⠇⠀⠀⣼⣿⠁⠀⠀⢰⣿⡟
⣿⡄⠀⠀⠀⢻⣿⡄⠀⠀⠹⣿⡄⠀⠈⠻⣷⣄⡀⠈⠙⠷⣤⡀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⣀⣴⠿⠋⠀⢀⣤⣾⠟⠁⠀⠀⣸⣿⠃⠀⠀⢠⣿⡿
⣿⣷⡀⠀⠀⠀⢿⣿⡀⠀⠀⠻⢿⣦⣀⠀⠀⠙⠿⣦⣄⠀⠈⠛⢷⣶⣶⣶⣶⣶⣶⣶⣶⣶⠾⠋⠁⠀⣠⣴⠿⠋⠀⠀⢀⣴⣾⠟⠃⠀⠀⢀⣿⣿⠁
⢹⣿⣷⠀⠀⠀⠈⣿⣷⣄⠀⠀⠀⠙⠿⣷⣄⠀⠀⠈⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡿⠛⠁⠀⠀⣠⣶⡿⠛⠁⠀⠀⢀⣤⣾⡿⠃
⠀⢿⣿⣧⠀⠀⠀⠈⠛⢿⣷⣄⡀⠀⠀⠈⠻⢿⣶⣄⡀⠀⠈⠛⠛⠛⠛⠛⠻⠿⠛⠛⠛⠛⠛⠛⠁⠀⠀⣠⣴⣾⠿⠋⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⢠
⠀⠈⢿⣿⣷⣄⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠉⠻⢿⣶⣄⣀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣠⣴⣿⠟⠋⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⣠⣶⣿
⠀⠀⠀⠙⠿⣿⣷⣄⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⠀⠀⠀⠈⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠀⠀⠀⢀⣠⣴⣿⡿⠛⠁⠀⠀⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠉⠻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠛⠁⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋
⣷⣆⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣄⡀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⢀⣠⣶⣿⣿⠟⠁
⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⣶⠶⠚⠋⠉⠉⠛⠲⢶⣤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠁⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠈⠉⠙⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⡁⣀⣀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣄⣀⣀⡈⠙⢲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠛⠋⠉⠉⠉⠁⠀⣀⣠⣤⠴⠖⠒⢦⠀⠀⠀⠀⡤⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠀⣀⣀⡤⠴⠋⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⢳⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡟⠀⠀⠀⠀⣠⠞⠋⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⢿⢷⡀
⠀⠀⠀⠀⡴⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠸⣇⣠⡴⠋⠁⠀⠀⠀⣰⠞⢲⡄⠀⠀⢸⡄⠹⡄
⠀⠀⠀⡼⠁⢠⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠞⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⣆⠀⠹⡄⠀⠸⡇⠀⠹⡆
⠀⠀⣼⠁⠀⣸⠁⠀⠀⠀⠀⢸⡋⠀⠀⢀⣀⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢹⡄⠀⢻⡄⠀⢹⡄
⠀⢰⠇⠀⣰⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣴⡿⠿⠛⠓⠦⠤⠴⠚⠛⠯⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⡿⠀⠀⠙⠲⣄⢷
⠀⡟⢀⡞⠁⢀⡤⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⢻⡆
⢸⣷⠋⠀⠀⠘⢇⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⣠⠖⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢻
⣼⠁⠀⠀⠀⠀⠘⢧⠀⠘⣆⠀⠀⠀⠀⠀⢰⡇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠃⠀⠀⠀⠀⠀⢀⡴⠚⠁⢨⡇⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠈⢷⡀⢘⡇⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣠⠖⠋⠀⣠⠞⠉⠀⠀⠀⠀⢰
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠻⣄⡴⠋⠁⠀⠀⠀⠀⠀⣰⢿
⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢸
⢸⡇⢳⡀⠀⠀⠀⠀⠀⢀⡞⠉⢹⠄⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⠇⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣼⠁⠀⣿
⠀⡇⠀⠹⡄⠀⠀⠀⢠⠟⠀⣰⠏⠀⠀⠀⠀⣏⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠖⠋⠀⠀⠀⠀⠀⠀⢀⡟⠀⣸⠂⣿⠀⢀⡇
⠀⢻⠀⠀⢻⠀⠀⣠⠏⠀⣰⠃⠀⠀⠀⠀⠀⠉⠳⠿⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢠⠏⠀⢹⡀⢸⠃
⠀⠸⡇⠀⢸⠀⠀⠘⠦⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡏⠀⠀⣴⠖⢦⡀⠀⠀⠀⠀⣼⠁⢠⡟⠀⠀⠈⣧⡟
⠀⠀⢹⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣓⢶⣤⡴⠖⠓⠶⢤⣶⠚⢉⡼⠁⠀⠀⠻⢄⠀⠉⠢⣄⠀⠀⠙⠶⠛⠀⠀⠀⠀⢸⠁
⠀⠀⠀⢷⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢳⡄⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⢻⡀⠀⢀⡤⠤⠶⠶⠶⠶⠶⣤⠀⠀⠀⠀⠀⢀⣤⠞⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⣷⠀⠀⠀⠀⠀⠙⠲⠚⠁⠀⠀⢀⣠⠴⣾⠋
⠀⠀⠀⠀⠀⢧⠀⠸⢄⣤⣤⣤⣤⡤⠤⠞⠀⠀⠀⢀⡴⠋⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠀⣰⠃
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣤⣀⣀⣀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⣠⠶⢦⣄⡀⠀⠀⠀⠀⠸⣇⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣉⠉⠉⠛⠲⠦⣄⠀⠀⠀⠀⠀⠹⢤⣀⠈⠙⠓⠦⣄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠈⠙⠲⣤⣀⣸⠇⠀⢀⡴⠖⠒⠒⠶⢤⣤⡤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣌⣙⣦⣄⡀⠀⠀⠀⠀⠉⠁⣠⠞⠉⣀⣀⣤⠴⠞⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣓⣶⣶⣶⣶⣞⣛⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣴⣿⣿⣿⣿⡇⠈⢻⣦⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢹⣿⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀
⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⢿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣻⣧⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣛⣻⣭⣷⣾⠿⣫⣿⣿⣿⣿⣿⣿⡟⣿⣿
⠳⠾⠛⠓⠮⣝⣛⠿⢿⣿⣿⣿⣿⣿⣿⣽⣿⣛⣻⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣟⣿⣭⣵⣶⣿⣿⣿⣿⡿⢿⣛⡭⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠿⠿⠟⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⡴⠞⣉⠥⠖⠒⠒⠤⢍⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⡔⡰⢋⡴⠋⣀⠴⠒⠒⠓⠲⢤⡉⢢⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣾⠇⠀⡼⡹⢡⠏⣔⡝⠁⣤⠞⠋⠹⣷⣄⠹⡄⢳
⠀⠀⠀⠀⠀⠀⡎⠀⠀⢸⣿⠀⢰⢣⠇⡞⢸⡸⠀⣼⠁⠀⣰⣶⣬⣿⠀⡇⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⠀⢸⢸⠀⡇⢿⢁⠀⢿⠀⠀⠘⠛⠛⠁⠜⠁⠀⡠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⡀⡇⠀⡇⢸⢻⠀⢸⡞⡇⢳⠸⡌⣆⠈⢧⣀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡰
⠀⠀⡀⠀⠀⡇⢣⠀⢳⠈⡞⡇⠈⢷⣿⡄⢣⠙⢎⠢⣀⠈⠙⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⡴⠁⠀⠀⡠⠀⢠⠃⠀⠀⡰
⠀⠀⡇⠀⠀⢸⠸⡄⠘⡆⠱⡹⡄⠘⢿⣷⡄⠑⢤⡙⠢⢄⣀⠀⠀⠀⢀⣀⠤⠒⢁⠴⠊⠀⠀⢀⠔⠁⡰⠁⠀⠀⡰⠁
⠀⠀⠸⡀⠀⠀⢣⢳⡀⠘⣄⠱⡝⣆⠈⠻⣿⣦⣀⠉⠓⠲⠤⠭⠭⠭⠥⠤⠖⠊⠁⠀⠀⢀⠔⠁⣠⠎⠀⡀⢀⠜
⠀⠐⡄⢣⠀⢣⠈⢦⢳⡄⠘⢦⠘⢮⡳⣄⠈⠛⠿⣿⣶⣤⣤⣀⣀⣀⣀⡠⠤⢔⣊⠥⠊⢁⡠⠊⢁⡠⠊⡰⠋
⠀⠀⠹⡄⢣⠀⢣⠀⠳⡙⣦⡀⠳⣄⠙⠮⣗⢦⣄⡀⠉⠉⠛⠒⠒⠒⠒⠊⣉⣁⠠⠔⢊⣡⡤⠖⢉⠴⠋⠀⣀⠄
⠀⠀⠀⠙⡄⠱⡀⠑⣄⠘⢮⡻⣦⣀⠙⣦⣈⠑⠪⢝⣳⣶⣦⣤⣤⣤⣬⣭⣤⡶⠶⠟⢋⡡⠴⠊⠁⣀⡤⠊
⠀⠀⠀⠀⠈⢮⡻⣦⠈⠳⣄⠉⠪⣝⢷⣬⣛⠿⣶⣦⣤⣉⡉⠉⠉⠉⠁⠤⠤⠒⠒⠉⢁⣠⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠙⢾⣿⣦⡈⠓⢄⡈⠙⠪⢝⣻⢶⣯⣽⣛⣳⡶⠶⢶⡶⠶⠶⠶⠞⠛⠋⠉⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣻⢦⢌⡓⠦⣔⡨⢭⣒⡪⠭⢭⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣌⡓⠦⢍⣙⠒⠯⠭⣿⣓⣒⣒⣒⣒⣒⡚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠻⢷⣦⣬⣉⣙⠒⠒⠦⠤⠤⠄⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢭⣉⣛⠛⠿⠿⠷⠶⠶⠶⠶⠶⠿⠟⠓⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠂⠤⠤⠤⠤⠤⠒⠒⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀
⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡉⢳
⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⡞⡿⣡
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡋⡰⠱⣼⢡⣣
⢹⣿⣿⠟⣻⢟⡟⣛⢛⠛⣻⢟⡿⢻⠟⡻⢛⠿⣛⢛⡛⢛⠛⠚⠓⣲⠖⡒⢒⡶⢲⠶⡶⠶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⡴⠱⢡⠡⢀⡾⠁
⠀⠈⠻⣾⡴⣫⢎⠵⡫⢊⠕⡩⠞⡡⢊⠔⡡⢚⠕⢋⠔⠁⠐⡠⠊⡠⠊⡠⠪⠘⡡⢊⡴⣣⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⣡⠊⠠⠁⢆⡷⠋
⠀⠀⠀⠈⢿⣱⣋⣎⣔⣁⡔⠠⠎⡴⢡⠎⣰⠃⠐⢁⠄⢀⠊⠠⠋⠠⠊⠀⡠⠊⡠⢋⠔⣡⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⡙⢀⠀⠁⠇⣰⠟
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠓⠒⠒⠒⠶⠶⠶⠾⠶⠾⠤⠤⢤⣥⣿⠀⠀⠀⠀⠀⠀⣠⡾⠛⠑⠐⠁⠆⣨⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢠⡾⢋⡴⠁⠠⡀⣨⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢀⣴⠋⢰⢋⢠⠁⢁⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣴⡏⡔⠄⠃⠂⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⡱⡘⡀⡜⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠡⠐⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⠀⠀⠈⢣⣸⠁⠀⠀⣠⠴⠶⢦⡀⠀⣼⠖⠁
⠀⠀⠀⠀⠀⠀⢰⠏⠰⠶⠶⣭⡳⣄⠀⠀⠛⠀⠀⡴⣳⠋⠙⠋⡇⠀⠀⣠⣾⡟⡆
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠹⠞⢦⠀⠀⠀⢠⠇⡏⠀⠀⢀⠇⠀⢰⠇⢀⡼⠁⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⢇⠀⠀⢸⠀⠀⠀⢀⠞⠀⠀⣾⡴⠋⠀⢠⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⡀⠀⠘⡆⠀⠸⡇⠀⢠⠏⠀⠀⠀⠉⠀⠀⠀⢀⣠⠤⣴⣒⡶⣤
⠀⠀⠀⠀⠀⠀⣠⠤⣤⣀⠀⠀⠈⠙⠳⣤⣹⠀⠀⢧⢠⡏⠀⡤⡄⠀⠀⠀⣠⠞⡩⠞⠋⠉⠉⠉⢸⠇
⠀⠀⠀⠀⠀⠀⠙⠳⠶⠾⠷⠀⠀⠀⠀⠈⠛⠀⠀⠘⣾⡇⠀⣧⠇⠀⠀⣰⠃⠚⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠘⢿⣦⠘⠀⠀⠉⠀⠀⢰⠃⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⣠⠶⣋⡭⠵⠖⠀⠀⠈⠉⠓⢦⣄⠙⠀⠀⠀⠀⠀⢀⡏⠀⠀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⣼⢡⡟⠁⠀⠀⠀⠀⢀⣠⡴⠞⢛⣛⡀⠀⠀⠀⠀⠀⣸⣀⡴⠚⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠙⢮⣥⣀⣠⣤⠴⠞⠋⠁⠀⣼⣛⣛⣋⣳⣄⠀⠀⠀⠟⠁⠀⠀⣠⣖⣉⣉⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣛⣙⣻⣛⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠘⣦⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠈⠟⡀⠀⠀⠘⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⢰⡅⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣥⠀⠀⠀⡠⠁⠀⠀⠀⠀⡠⢲⠂⠤⣦⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⢾⠀⠑⢻⡄⠀⠐⠀⠀⠀⠀⡠⢊⠔⠉⠀⠉⠘⠀⠀⠀⠀⠀⡈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠎⠀⠀⠀⢀⠌⠀⠀⠀⡠⠊⠔⠁⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠂⠎⠀⠀⠀⢀⠂⠀⠀⢀⠜⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡌⠀⠀⠀⠠⠀⠀⠀⠠⢃⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢀⠀⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡌⡈⠀⠀⠀⠀⠁⠀⠀⠜⡠⠃⠀⠀⢀⠔⠁⠀⠀⢀⠄⢊⡡⠒⠄⡉⡬
⠀⠀⠀⠀⠀⠀⠀⡰⡸⠀⠀⠀⢀⠁⠀⢠⢎⠜⠀⠀⠀⡠⠀⠀⢀⠄⠊⡠⠐⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⢀⣷⠁⠀⠀⠀⠀⠀⠠⠢⠂⠀⠀⢀⠄⠀⡠⠂⡡⠐⠁⠀⠀⠀⠀⠨⠀⠁⠐⠀⠠
⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⡠⡡⠁⠀⠀⡀⢁⠴⡊⠔⠁⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠜⡇
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢀⠀⡰⠔⠀⠀⠀⢎⢔⠥⠊⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡩⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠏⠀⠀⢀⡦⠞⠁⠀⡀⠀⠀⠀⣀⡀⠤⠤⠒⢒⣊⣉⡹⢃⠀⡤⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠋⠀⠀⠰⠋⠀⢀⣄⡂⣔⠂⠩⠅⠐⠂⠉⠉⠁⠀⠀⠀⠑⣈⣫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣦⠦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢿⣫⣽⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⣫⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣽⣆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⢃⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣎⠁
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇
⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣿⣿⣿⡏⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧
⠀⠀⠀⠀⢸⣿⣿⣿⠇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⢿⣟⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣎⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⡻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⡻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⣫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣬⡻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣍⡛⠷⣦⣄⣀⠀⠀⠀⠀⠲⠶⠶⠶⢖⣂⣠⣴⡾⣿⣛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠠⠉⠙⠛⠿⠶⠶⠶⣤⡤⠤⠤⠶⠶⠒⠋⠉



⣿⡟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⣚⣯⣍⣉⠉⠉⠛⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣚⣉⣀⣠⠞⠁⠀⠀⠈⠙⠒⠋⠉⠉⠻⡟⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡞⠉⠈⠉⠀⢰⡆⠀⠑⠦⠀⠹⡄⠀⠀⠀⠻⢤⣈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣠⠞⠀⢤⡀⠀⠀⠘⠃⠀⠀⢀⣀⠀⠀⣠⠖⠀⠀⡄⠈⠳⡌⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡿⠉⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠰⠇⠀⠀⡇⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣇⠀⢀⠤⠖⠂⢀⡇⠀⢀⣽⠶⠒⠒⠒⠶⣄⠀⠘⠓⠂⠀⡀⠀⢧⡀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣰⠃⠀⠀⠀⠀⠀⠘⠀⢀⡟⠀⠀⠀⠀⠀⠀⠈⣧⠀⢀⡀⠀⠙⠆⠀⠙⣆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠀⠀⠲⠦⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠋⠀⡀⠀⠀⣹⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠀⢲⡀⠀⠀⠀⢦⡀⠈⣇⠀⠀⠀⠀⠀⠀⢀⡾⠀⠰⠋⠀⠀⣇⠀⢠⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡆⠀⠁⠀⣶⠀⠀⠁⠀⠘⠳⣄⣀⣀⣀⣤⠞⠁⡀⠀⢠⠞⠀⠈⠀⢸⡄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢧⣀⠀⢠⡇⠀⠀⠀⢲⠀⠀⣠⠍⠉⣉⣀⠀⠀⡇⠀⠀⠀⠲⡄⠀⠈⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠈⢳⡀⠀⢠⣀⠀⠈⠃⠐⠃⠀⠀⠈⠉⠀⠀⠀⡤⠀⠀⠀⠀⣠⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⢧⡀⠀⠈⠀⠀⠀⠰⣄⠀⠀⠲⡄⠀⠀⠸⠁⠀⠐⠲⢾⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢭⡛⠓⠦⣄⠀⠀⠘⢃⣀⡀⠙⠀⠀⠀⣠⠴⣲⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣬⣝⣓⣚⣉⣉⣉⣳⣶⣤⠾⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⡶⣦⡀
⠀⢰⣶⡒⠒⠛⠋⠉⢉⣁⡠⠴⢧⡀⠙⠳⢦⡄
⠀⢸⠈⠛⢿⣯⣉⡉⣶⣌⠀⢄⡀⠉⠓⢤⣼⡇
⠀⠸⣦⣀⠀⠀⢨⣿⠄⣛⣃⣠⣴⣷⡾⠛⢻⠁
⠀⠀⠘⡏⠉⢳⡖⠛⠛⢻⠉⢻⡅⠀⣹⣤⠼⠷⠖⢲⣶⣆
⠀⠀⠀⠸⣄⠀⢿⡄⠀⠈⣳⡴⠟⠋⠁⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⢈⣦⣀⣙⠓⠋⠁⠀⠈⠂⠀⠄⠠⠀⢸⠉⡿⢩⢫⣿⡆
⠀⢀⣴⣾⣿⣿⣿⣿⣿⣶⣆⡄⠀⠀⠀⠀⠀⠀⠸⣿⠷⣿⣿⣭⣧⠤⣄⡀
⠀⣾⣿⣿⣿⣷⣻⣿⣿⣿⣷⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⠬⣮⠟⠁⠠⠨⡛⠗⢶⣿⣿⣿⣶⡄
⠀⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣏⠓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠠⠨⢙⢿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⠙⠲⢤⣈⡁⠒⣤⣤⣤⣤⣄⡀⠀⠀⠈⠒⠐⠒⠁⠀⠹⠟⠛⠲⠦⠤⣄
⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣯⣿⣿⣿⣷⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠛⣿⣿⣿⣿⣿⣿⣵⣚⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠁⠙⠲⠭⢵⣶⣦⣤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠁
⢀⣀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⢀⡀
⠀⠈⠙⠲⢤⣀⠀⠀⠀⠠⣄⡉⠲⢄⠙⠢⣄
⢄⡀⠀⠀⠀⠈⠑⠢⣄⡀⠀⠉⠲⢤⡉⠂⠈⠑⢄
⠤⣄⣁⢦⣤⣀⠀⠀⠈⠙⠳⠦⣄⠀⠈⠓⠄⢀⡀
⠀⠀⠀⠉⠓⠛⠙⠒⠦⢄⡀⢀⣈⠙⠻⠿⣶⣤⣉⠲⢄⡀⢀⡀
⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⢄⣀⡈⠉⠒⠢⢄⡉⠛⠷⢦⣈⠐⠉⠢⢄
⠤⠬⢍⣉⡙⠛⠓⠶⠦⠤⣤⣀⡉⠉⠒⠢⠤⠀⠀⠐⢤⣌⡑⠢⠑⠢⢁
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣀
⠉⠉⠉⠉⠉⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⣒
⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠒⠒⠂⠐⠒⠒⠒⠩⠭⠭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⣀⠀⠄
⠤⠤⠤⠶⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠐⢊⣉⡉⠤⠀⠈⠉⠀⢀⠤⠔⠂
⠔⠒⣒⣀⡀⠄⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠟⠒⠉
⠉⠉⠁⠀⠀⠀⠀⢀⡴⠖⠛⠉⠉⠁
⠀⣀⡤⠴⠒⣊⡩⠥⠒⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡠⠔⡀
⠀⣤⡶⠞⠋⠁⠀⠀⠀⠀⠀⣀⡤⠒⠉⢀⡠⠖⣩⠔⠋
⠋⠁⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⠀⠀⠀⠀⠐⠊⠁
⠀⠀⢀⡠
⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠇⡟⢳⢼⠋⢸⡏⠁⡟⢻⠀⢸⠂⢸⡇⣿⣸⢸⡋⠱⣏⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣙⡆⡟⠋⢸⡉⢸⡏⠁⣇⣸⠀⢸⡀⢸⡇⡏⣿⢸⡋⢠⣝⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠈⠉⠈⠉⠁⠉⠉⠀⠈⠉⠉⠁⠁⠈⠈⠉⠁⠉⠁

⠀⠀⠀⠀⢀⣀⢀⣀⡀⠀⠀⢀⠀⡀⠀⡠⠔⢰⣦⣀⣀
⠀⠀⠀⠀⣿⢹⠉⠉⠉⠉⠉⠉⣿⣷⣋⠀⠀⢠⣼⣧⣤⣤⣤⡄⠀⠀⠀⣀⣀⣀⣀
⠀⠀⣠⣤⣿⡟⣄⣀⣀⣀⣤⠾⣛⣉⣀⣀⣀⣀⣛⣛⣂⠛⠻⠋⡉⠭⢭⣉⠉⢉⡉⠉⢉⠛⠓⢶⣦⣄⣀⣀
⠀⠀⣷⣼⣿⠃⠸⣒⣲⣿⠛⣛⢩⡉⣁⠀⠀⣩⣭⣽⣿⣿⣶⡾⠿⢿⣷⣄⠉⠋⠁⠀⣀⣉⠒⢤⣀⠈⠙⠻⢿⣦⡀
⠀⠀⡿⢻⣿⣿⣶⣿⣿⣿⣇⣿⡸⣇⢿⣸⣦⡻⠿⣿⣿⣿⠃⣾⣟⣷⡜⣿⡆⠀⢿⣭⣍⣉⡀⠠⢈⡑⠦⣄⡀⠈⠛⢷⣤⣀
⠀⠀⠙⠛⠛⠛⠃⠀⠀⠉⠙⠛⠛⠻⠿⠿⠿⠿⠛⠛⠙⣿⠛⢿⣿⣟⡗⣿⣧⣴⠚⣿⣿⣝⡻⠿⣶⣾⣭⣶⣌⣁⡀⣀⢉⣿⣿⣷⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣝⣛⣛⣵⣿⣿⠏⠀⣿⣿⣿⣿⣷⣶⣾⣿⢿⣛⡿⠿⠝⠛⠛⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠠⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⢻⠇⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⢀⣀⡃⠀⠸⡀⠀⠀⠀⠀⠀⠆⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⢀⡴⣊⠀⠈⣿⢆⣿⡇⠀⠀⣷⠀⠀⠀⠀⢀⠀⠀⢶⡀⠀⠀⡄
⠀⠀⠀⢀⡴⢀⠄⠁⠀⠀⠀⢀⣠⣠⣏⣾⣿⣿⣿⣵⣿⣿⣧⢀⠞⠛⠀⠀⠀⠀⠀⠰⢆⠘⣿⣄⣀⣀⠀⠀⠁
⠀⠀⢀⣿⣵⠏⠀⡄⠀⠀⠀⠈⢻⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣤⣤⣄⠀⠀⠀⠀⠀⠠⠕⡌⠻⣿⣿⡆⠀⠒
⠀⠀⢸⣿⣄⡁⠀⠣⢀⡀⠤⠊⠁⠀⢀⠈⠀⠈⠀⡠⠚⠋⠀⢀⠜⠝⢿⣶⣄⠲⡀⠀⣳⣼⣧⠀⠈⠉⠁⠀⡄⠀⡀
⠀⠀⠈⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⢸⣿⣿⣦⠀⣤⣔⣿⡿⠀⢀⡀
⠀⠀⠀⠀⠮⣻⢿⣷⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠟⣿⣿⡛⢾⣿⢷⡄
⠀⠀⠀⠱⣆⠀⠀⠫⠛⠻⠿⠿⠿⠶⠶⠶⠶⠒⠛⠛⠛⠉⠉⠉⠀⠀⠀⣠⡾⣫⣿⣿⡟⠀⠙⡄
⠀⠀⠀⠀⠈⠙⠒⠄⣀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠚⠉⠀⠙⠟⠉⠁⠀⠀⠈⠒⠂⠠⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠶⠶⠶⠶⠖⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠘⠃⠀⠐⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠉⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⠤⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠢⠄⠔⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠄⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠆⠀⠀⠀⠆⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⣀⡄
⠀⠀⠀⢀⠀⡉⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠑⠄⡀⠀⠐⠀⠐⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠉⠓⠀⠐⠷⢀⡀⠈
⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠁⠰⠄⠀⠀⠀⠀⠀⠀⠈⠀⠠⢀⠀⡠⠀⠀⠠⠂⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠀⢀⠘⠁
⠀⠀⠀⠀⠚⠀⠀⠉⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠤⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠐⠐⠋
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡙⢀⣤⡀⠀⠀⠀⠂⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠑
⠀⠀⠀⠀⠀⠀⢤⡀⠀⡀⢀⡀⠀⠰⠀⠀⠁⠈⠃⠀⠈⠀⠂⢶⡌⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠂⠀⠀⡈⠀⠀⠀⢹⡂⠠⢀⡾⠤⠀⠀⢤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣬⠓⡁⠂⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠱⣄⠀⠰⠀⠀⠀⠈⠁⠀⠀⠀⠤⠄⠀⠀⠀⠀⠓⠒⠈⢀⡰⠅⠀⠀⠀⣔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠳⣌⡓⢡⡄⠀⠀⠰⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⢤⠊⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡀⠀⠀⠄⠐⠀⠀⡀⢸⠍⢋⡄⠀⠀⠀⠀⠀⠙⠒⠂⠀⠒⠚⠁⠉⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⡀⠠⠀⠀⠀⠀⠀⠘⠓⠄⢈⠀⢴⣀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠃⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣁⠀⠀⠀⠀⠀⠀⠁⠀⢃⠀⢦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠈⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠈⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢀⡤⠚⠁⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⡄⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⠀⠀⠀⠀⣰⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣤⣴⣿⣿⣿⣿⡀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⣠⣦⣄⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣦
⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣆⣠⣤⣿⣿⣿⣄⣀⣴⣿⣦
⢀⣤⣤⣤⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣷⣾⣿⣆
⠉⠻⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⢠⣤⣼⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⣄
⢀⣤⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡏⠉
⠀⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⠃
⠀⠀⠀⠀⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⠻⠿⠋⠀⣿⣿⣿⡄⠀⠀⢠⣶⣶⣤⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠈⣿⣿⣿⣿⡿⠿⠟⢿⣿⣿⣿⣿⠀⣠⣾⣷⣄⣠⣴⣿⣿⣿⣿⣿⣷⣿⣿⣿⡏⠀⠙⠛⠁⠀⠀⣿⣿⣿⠁⠀⠀⠙⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠹⠿⠿⠛⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣾⣷⣄⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣼⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡇⠰⠁⠀⠀⠀⠀⠀⠀⠀⠉⢟⣿⣿⣿⣿⣷⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣤⣤⣶⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠉⠉⠹⣿⣿⣿⠇⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠛⣦⡀
⠀⢠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠻⣦⡀
⠀⠀⣿⠈⠉⠛⠻⢿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣶⣦⣄⣀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢶⣦⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡛⣧⡀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⢋⣤⠇⡏⣳⡄
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⡄⣸⣿⢸⣵⠋
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡴⢰⠇⡏⣣⠞⠁
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⠛⢩⣼⠃⠀⠀⠀⠀⠀⢀⣴⠟⢱⠀⡇⡞⢀⡼⠃
⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣤⣴⣶⢿⡿⣻⠋⣽⣡⡷⠖⢛⡟⠀⠀⠀⠀⢀⣴⡟⢡⠇⡟⢸⣣⠷⠋
⠀⠀⢸⣷⣠⣴⣶⣿⢿⢏⡟⢡⢏⣾⡤⠟⠋⠉⠀⠀⠀⣼⠃⠀⠀⢀⣴⣿⢋⡇⡼⠰⣣⠞⠁
⠀⠀⠈⠻⣿⡼⢱⢣⣧⠼⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣠⡾⠋⡞⢸⠁⣧⠞⠁
⠀⠀⠀⠀⠉⠛⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣠⡾⣋⣰⢰⠃⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣫⠀⡟⢇⡼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡇⢸⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠋

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠈⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⡀⢀⣠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠳⢤⡂⠀⠀⣄⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⡄⢤⠷⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡤⡻⣄⠐⠈⢷⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣔⣀⣤⠬⠶⠒⠃⣁⠆⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡛⢶⣄⡀⡉⠙⠛⠓⣾⣾⠾⢲⠾⠿⠿⠿⠟⠋⠉⠉⠉⠉⠁⠁⠀⢀⡠⠟⠀⡈⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡖⢊⠛⣷⡦⡤⣄⡉⡀⡀⢀⡠⠀⠀⠀⢀⡀⢀⣀⣀⣤⢴⠴⠋⠁⠀⢰⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣵⣀⡷⠀⠀⠀⠀⠀⠁⠀⠀⠐⠐⠛⠛⠉⠉⠉⢉⠀⢠⣀⣤⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠈⠹⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡘⠑⠚⠉⠁⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣫⣄⠈⠙⠛⠓⠗⠒⠳⠒⢸⣀⣣⠴⠋⠁⠀⠀⠀⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣈⡛⠞⠄⠉⠉⠐⠛⠙⠋⠉⠁⠀⠀⠀⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣮⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡶⠒⠛⠉⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣴⣳⡔⣄⡠⢠⣩⣈⣤⣰⣏⣠⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⡛⠛⠛⠛⠛⡯⡼⢟⣉⠙⢉⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡁⠀⠀⠀⣼⣿⢏⠚⠛⣂⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢋⠿⠵⢶⣶⣿⣿⡷⡷⣻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⣼⣿⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣇⠀⢿⣿⠀⠀⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢟⡨⣻⠀⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣄⢹⡆⠿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠁⢽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡌⢟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⣼⣷⡤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣾⠁


⣿⢿⠿⡿⡿⢟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣛⣻⣿⣟⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠉⡍⢠⠒⠭⡖
⠀⠀⠀⠀⣀⡤⠖⠒⠒⠒⠒⠀⠀⠁⠀⠀⠀⠐⠒⠒⠒⠒⣒⣒⠒⠒⠓⠚⠒⠚⠒⠒⠀⡤⠌⠉⠉⣉⡳⡀
⠀⠀⠠⢊⡽⠀⠀⠀⠀⠀⠀⢀⠀⢒⢸⡉⠉⠃⠀⠀⣴⡿⠓⢦⡙⢆⠈⠀⠀⠁⠀⠀⢀⠁⠀⠐⢸⢿⣽⡇
⠀⢀⠐⠋⠀⠀⠁⠀⠀⠠⠐⠐⠒⠉⠉⠀⠀⣀⠒⡾⡟⢢⢂⣎⣧⢸⠈⠀⠀⠠⠐⡨⠁⠀⠄⠀⢸⡽⣾⡇
⠀⠘⡃⣤⠀⠄⠀⠀⠀⡇⠀⢴⠒⢀⠀⠀⠀⠀⠀⢧⡏⢒⣿⢏⢹⠘⠀⠀⠀⠀⢀⣂⣀⣁⣀⣀⣘⣦⡽⠁
⠀⠀⠀⢈⣑⣒⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠒⠀⠀⢷⠉⡏⢃⡾⣠⡔⢶⣾⠿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠋⠛⠛⠉⠀⠀⠀⠓⠒⠋

⠀⠀⠀⠀⠀⠀⢰⣾⡿⠀⢠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⡰⢞⣡⠾⠛⣒⣒⣀⡀
⠀⠀⠀⣠⣦⠀⢸⣿⡇⢀⣾⡟⠁⣀⣴⣾⣿⣦⠀⠀⠀⠀⠀⠀⢰⣧⢨⡞⣡⠟⣃⣤⠿⠿⠭⣭⣭⣓
⠀⠀⠀⢻⣿⣆⠀⢿⡇⢸⡟⢠⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣶⣀⡇⠘⣽⠃⣸⠟⣃⣠⣔⡶⠶⣍⢉⠻⡄
⠀⢠⣄⠀⠙⢿⣦⡈⢷⡸⡡⢋⠴⠶⠿⠿⠿⢿⣿⣧⠀⠀⣤⣨⠘⣿⠐⡿⣸⡇⣠⢿⣟⡢⡉⢢⡈⢻⢷⣌⠂
⠀⠸⣿⣿⣦⣄⣈⡛⠒⣁⠀⠀⢝⡛⠷⣶⣤⣀⠈⠉⠀⠀⣈⡙⣧⢸⣄⢇⠻⣇⠀⠋⠹⣳⢸⡆⢿⡆⣄⢹⡄
⠀⠀⠀⠈⠉⠉⠉⢉⣩⡵⢹⠎⣆⠹⣦⡈⠻⣿⣷⡄⠀⠀⠙⠻⣌⢃⠻⠿⣦⣘⡾⠶⠞⢋⣼⡁⢸⠇⣿⢀⠁
⠀⠀⠹⣿⣿⣿⠿⠛⠉⣰⡟⢀⣿⠀⢻⣷⡀⠈⠿⠁⠀⠀⠈⠛⢙⠻⠷⣤⣤⣝⣛⣃⣈⣽⠟⢡⣿⠀⡟⠈
⠀⠀⠀⠈⠀⢀⣠⣴⣿⠟⠀⣼⣿⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠛⢙⡶⠶⡭⣉⣁⣬⣿⠞⣀⡼⡋⡸⠃
⠀⠀⠀⠀⠀⠙⠻⠟⠁⠀⣼⣿⡟⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠖⢺⡛⣠⠴⣟⠥⠊⠁

⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠉⠓⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⢶⣬⡙⠳⣤⠀⣄
⠀⠀⠀⣠⠞⢉⣤⠶⠚⠋⠉⠓⠒⢤⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠛⠛⠿⣶⣄⠙⢿⡄⢹⣧⠈⣧
⠀⠀⣰⠏⣰⠏⣠⠴⠒⠛⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⡶⠶⠶⢶⣄⠙⣧⢸⡇⢀⣿⠀⣿⡆⣆
⠀⢠⡟⣸⠇⣼⢃⡴⠖⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣁⣤⣶⠶⠦⣌⣳⣹⣸⢃⡾⠃⣰⡿⠀⣿
⠀⢸⡇⣿⢸⡇⣾⢡⣖⣂⡀⣀⣀⢠⣤⡀⣤⡄⣤⣤⠀⠀⠃⣼⠟⢁⣤⠶⢒⡲⠅⡂⡱⢭⠴⠾⠋⣠⣾⠇⡄
⠀⠘⣷⢹⣎⣿⡹⣧⣟⣛⣵⣿⢟⣾⡿⣹⣿⢧⣿⡟⠀⠀⢸⡏⢠⡿⠁⣴⠏⣴⢱⡘⣌⠓⠶⠶⠟⠛⢁⡼⠁
⠀⠀⠹⣧⡻⣮⡻⣾⣽⣿⣯⣵⣿⢟⣵⣿⢋⣾⡿⠁⠀⠀⠈⠇⢾⡇⢸⣟⠀⣿⠈⣷⡈⠻⠶⢶⡶⠾⢋⠁
⠀⠀⠀⠘⢿⣮⣻⢷⣿⣭⣭⣷⣾⠿⣻⣵⣿⠏⠀⠀⠀⠀⠀⠀⠘⣧⠘⣿⡀⢻⣧⡈⠻⢷⣦⣤⣤⠶⠋
⠀⠀⠀⠀⠀⠈⠛⠿⢶⣿⣿⣶⣾⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈⠳⣤⡙⠻⠶⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠢⠐⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠉⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⠤⠓⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⢂⡴⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣸⡵⠋
⠀⠀⠀⠀⡠⠁⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⡠⠐
⠀⢀⠎⢀⠔⠊
⠀⠂⠐⠁
⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⢩⡄⠀⡄⠈⣀⠀⠀⠀⠀⠀⠀⠈⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠁⠀⠀⣠⠆⠀⠠⠄⠀⠈⣄⣀⢀⣤⡴⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠄⠀⠀⠀⠀⠁⠶⠀⣠⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⡄⠀⣠⠀⠀⠖⠀⠀⠀⠄⢀⡾⢂⢀⡀⡀⡂⠀⠠⠒⡁⠐⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠚⠀⠀⠀⡀⠠⠈⢀⡔⠛⡒⠒⠀⠐⠀⠀⠒⠀⠀⢀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠑⠀⠐⠂⠐⠠⠄⠀⠁⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠈⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⢻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀
⠀⠀⠀⠀⠀⢠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀
⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀
⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧
⠀⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇
⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⢸⣿
⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⣼⣿
⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⢀⣿⣿
⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⠀⢀⣾⣿⡟
⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠟⠁⠀⣠⣿⣿⠟
⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣾⣿⣿⡿⠟⠋⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠛⠛⠉⠁⠀⢀⣠⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣦⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣴⣾⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁

⠀⠈⠒⠄⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠈⠂⢄⠀⠀⠈⠠⡀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠈⠂⢀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠑⠄⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠶⠒⠒⠈⢈⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡀⠀⠠⠤⠀⠒⠂⠈⠉⠉⠉⠀⠀⠀⠀⠀⡀⠤⠐⠊⡡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠔⠀⠀⠀⠀⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⣠⠞⠀⠀⠀⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢀⡠⠖⠉⠀⡠⠂⠀⠀⢀⠞⠁⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⢀⡤⠚⠁⠀⢀⠔⠋⠀⠀⢀⠔⠁⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⣿⣷⣶⣾⣾⡿⣾⣶⣶⣾⣿⣾⣾⣶⣶⣶⣶⣿⣶⣾⣷⣶⣾⣶⣶⣿⣶⣷⣾⣷⣿⣶⣶⣶⣾⣿⣶⣾⣷⣶⣶⣶⣾⣷⡷⣷⡾⢾⣾⢷⣶⣷⠾⠶⡿⠶⣷

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣽⣿⣿⣿⣻⣿⡿⣽⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣷⠹⣿⣿⣿⣿⣿⣿⡿⣿⡇⣿⣿⣿⣇⣿⣿⣿⢣⣿⡟⣼⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡌⢻⣿⣇⢻⢻⣟⣿⢿⡏⡇⣿⠃⣿⣿⣿⣸⡟⣾⢃⣾⡟⣼⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣽⣿⣿⣯⢻⣿⡄⢻⣿⡈⠄⣿⢹⠀⠁⡇⣿⠀⣿⣽⠇⣿⢱⠏⣼⠟⣼⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⢯⡻⣿⣧⠹⣿⡄⢻⣷⠀⠸⡎⠀⠀⠇⢻⢸⡇⡿⢸⠃⠏⣸⠏⣼⢋⡼⣣⣿⣿⢿⣿⣿⢟⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣝⣷⣝⠻⣷⣝⣟⢮⢳⡘⠿⡀⠛⠆⠀⠁⠀⠀⠀⠀⠘⠁⠁⠈⠈⢠⠏⡼⢁⠎⡴⡿⢛⣵⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣝⡿⣽⡿⣯⡳⣌⡙⠈⠳⡅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠊⣠⠞⢉⣴⡿⣻⣿⣿⣿⢟⣻⣿⣿
⣿⣿⣿⣿⣿⣿⠿⣶⣝⡻⢥⡈⠙⢦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢁⡴⢛⣵⠿⠛⢉⣭⣾⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣍⠛⠶⣍⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⣠⣴⠾⣛⣭⣶⣿⣿⣿⣿
⣿⣭⣟⣛⡿⠟⠻⠾⣭⣛⡢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠒⠉⣁⣾⣿⠿⢿⣿⣿
⣿⣿⠷⠿⣿⣽⣖⣂⡀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⣋⠩⠤⠶⠛⣛⣋⣭
⣿⣿⣿⣿⣶⣶⣦⣭⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠶⠚⣛⣻⣿⣿⣿
⣿⣿⣿⣯⣭⣭⣭⣭⠭⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠶⠶
⣟⣛⣛⣛⣛⣛⣛⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠚⠒⠒⠶⠾⠿⠿⢿
⣿⣿⣿⣿⣿⠯⠦⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣬⣛⣻⣿⣷⣶⣶⣶
⣿⣿⣿⣶⣶⡿⢛⣋⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡲⠦⣤⣍⣙⡛⠿⠿⣿
⣿⣿⣿⠿⢛⣋⣭⣴⣶⠟⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣉⡙⠲⢮⣭⣟⣻⠿⣶
⣭⣷⣶⣿⣿⠿⣛⣭⣶⣾⡿⢃⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠑⠦⣄⠲⣮⣝⣳⢶⣤⣉⡛⠿⣷
⣿⣿⣿⣿⣷⣿⣿⣿⣟⣽⣾⠋⣠⠖⠁⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢙⢦⣔⢌⡙⢦⣝⠿⣿⣿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⢞⠕⢀⡴⠁⢀⠎⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣄⢙⢮⡳⣌⠻⣿⣦⣝⢿⣮⣝⡿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣫⡶⣫⢖⢁⣴⠏⠀⣰⢃⡔⠀⢀⡞⠀⢰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠹⣷⣵⣿⣞⢷⣮⡻⣿⣿⣿⣿⣿⣶⣽⣻
⣿⣿⣿⣿⣿⣿⣿⣻⢞⣵⣿⡿⣡⣢⡾⣡⡿⣴⢃⣾⢁⠆⡏⢸⠃⡇⢀⢠⢰⠀⠀⢧⢠⢢⢻⣦⠹⣿⣿⣿⣷⣝⣿⣮⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣼⣿⡟⣵⣿⣿⢏⣾⠇⣾⢸⠇⣿⢠⡇⣼⢸⡘⡇⢸⡘⣏⣯⣧⢻⣧⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⣾⣿⣿⡟⣾⣿⣸⡏⣿⢸⣿⣼⣿⣿⢸⡇⣿⠈⣧⢻⣼⣿⣎⢿⣷⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢹⡏⣼⡇⣿⣿⣿⠈⣷⣿⡆⢿⣏⣿⣿⣿⣎⢿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣿⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣇⣿⣷⣿⣿⣿⡇⣿⣿⣷⢸⣿⣿⣿⣿⣿⣎⢿⣿⣮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⠤⠴⠶⠦⠤⠤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠋⠉⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠲⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⡠⢄⠀⠀⠀⠀⠘⠧⢭⣉⣳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⡾⠀⠀⠀⠀⠀⠑⢦⣙⡆⠀⣀⣤⣀⡀⠀⠀⠀⠀⢀⠤⣤⣀⣤⠴⠶⢤⡀⠀⠀⣀⡀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⢀⡴⠋⡼⠁⠀⢀⣀⠀⠀⠀⠀⠈⡰⠚⠁⠀⠀⠉⠓⠶⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢣⡙⠳⣄⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⢀⡾⠁⠘⡇⢀⠔⢋⡴⠁⠀⠀⠀⣸⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠒⠤⣀⠈⢧⠀⠀⠙⠢⠼⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⣼⠃⠀⢀⠟⠘⠚⠽⠂⠀⠀⠀⠀⡇⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠈⠉⠙⠓⠶⣌⡑⢌⠳⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⢠⡏⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⠃⠁⡀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡞⢸⡇
⠀⠀⠀⢸⡇⢀⡀⠈⠂⠤⣀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⠔⠁⣀⠀⠀⠀⠀⡜⢁⠇⡞⠀⠀⣷
⠀⠀⠀⠀⣷⠀⣇⠀⠀⠀⣸⠃⠀⠀⠀⢀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠋⠁⣠⠎⠉⠀⠀⠀⠸⠱⠋⠀⡵⡐⢠⡇
⠀⠀⠀⠀⠸⣇⠸⡄⠀⡔⠁⠀⡠⠀⠊⠁⠀⡀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⠧⠔⠀⠀⠀⠀⠀⣠⠖⠉⣰⠃⣾⠁
⠀⠀⠀⠀⠀⠙⣦⠹⣆⢇⠀⢀⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⡤⠖⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⣰⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣌⠫⡙⠋⠀⠀⠀⠀⠀⠘⠲⣄⠀⠸⠥⠖⠉⠀⠀⠀⠀⠐⠭⠭⠝⠂⠀⠀⢀⡀⢀⠀⠀⠀⢀⡇⢀⡼⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⠴⠚⠉⠉⠉⠉⠒⠒⣋⡴⢋⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠲⠴⠊⠁⠹⡄⠀⡞⠁⠀⠀⠀⠀⠀⠀⢀⣉⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠀⣀⣀⣠⡤⠶⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠒⠒⠚⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣞⢆⠀⠀⢀⣔⠱⠦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡲⢯⢚⡅⢠⠻⣌⡛⣚⠇
⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣛⣈⣤⢮⠱⠬⢭⠏⣀⢠⠀⡖⣶⣶⠂
⠀⠀⠀⠀⣠⣟⣿⣿⢄⠈⠻⠓⠄⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⠀⠀⢯⣺⣒⣺⢦⣟⢞⡿⢺⢹⣸⣴⠻⡬⠁
⠀⠀⠀⢠⣿⢸⣟⡷⠈⢁⡘⢩⢉⣇⠀⠀⠀⠀⠹⣻⢾⢴⣴⣉⡰⣌⣿⣿⣯⡗⣲⡎⣦⡼⢎⡑⠦⠋⠀⠀⠀⠀⡠
⠀⠀⠀⢨⣷⢸⣿⣿⠈⢣⠀⣤⡃⣞⠀⠀⠀⠀⠀⠈⠓⠯⢮⣏⣟⣷⣿⣿⣿⣿⣻⣿⠶⠙⠀⠀⢀⣠⠤⠀⠒⠈
⠀⠀⠀⠀⢿⣎⢿⣿⣇⢴⣺⣶⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⠟⢻⣿⣿⣿⡫⣗⣶⣶⡋
⠀⠀⠀⠀⠀⠘⠷⠽⢿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣞⡁⣀⠀⣈⣷⣳⡿⣿⣿⣿⣿⢀
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣤⠢⠤⠀⠙⠲⢶⣗⡖⠀⠉⠉⣠⣶⣾⣿⡿⡟⢋⠛⣾⡀
⠀⠀⠀⠀⠹⣡⣀⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠴⠠⣹⣼⡿⢄⣠⣿⠛⠏⣹⡟⠁⠆⢨⠰⠰⢷⡄
⠀⠀⠀⣠⣖⠻⣯⣭⣵⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢰⡏⣷⣿⠋⡟⣀⢿⣹⣯⠒⡉⣿⣿⡠⠝⠢⡘⢠⣤⠇
⠀⠀⣼⣿⠋⠁⠸⣿⠁⠙⢛⣿⣧⠀⠀⠀⠀⠀⠀⠘⣶⣿⣿⡯⠄⠄⣼⢿⣿⡬⣠⣿⣿⢥⣮⠡⣬⣔⣞⣧
⠀⢸⣿⣿⡀⠀⠀⣿⡆⠀⠨⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⢉⣷⣴⣾⣿⣿⡼⠾⢯⣭⣿⣋⣿⣽⣏⠙⠛⠓⠛⠁
⠀⠘⣟⣿⣧⣶⣾⣾⣧⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠞⠁⠥⢊⣙⡂⡿⣼⠉⢤⣊⣾⣦
⠀⠀⠈⠿⣿⣿⣿⠟⣻⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠸⣎⣷⠬⣧⠀⠐⠧⣙⣳⣾⢇
⠀⠀⠀⠀⠀⠉⠙⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡎⠷⠇⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⡠⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣧⡙⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣮⣽⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠙⠂⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣯⠊⢻⣿⣿⣿⠸⠀⡇⢹⢸⣿⣿⣿⠟⠀⢰⢿⣿⣿⠟⣴⡿⣫⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡙⢿⣷⡀⠹⣟⣿⠀⠁⠁⢸⢸⣿⣿⡏⠀⢠⠏⣾⡿⢣⡾⢋⣾⢟⣫⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣆⠙⢿⣄⠙⡞⣇⠀⠀⠀⢸⣿⣿⠀⠀⠈⢠⠋⡴⢋⣵⢟⣵⢟⢽⡯
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⣙⢷⣄⠙⢦⡈⠘⠄⠀⠀⠘⢻⠇⠀⠀⠀⠀⠊⡠⢋⠴⠋⠀⠐⠝⣋
⠀⠀⠀⠀⠀⠀⠀⢨⣁⠉⠛⠿⠿⣇⡈⠳⢄⠳⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣬⠷
⠀⠀⠀⠀⠀⠀⠀⠠⣬⣍⣒⠀⠀⠀⠈⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢉⣁⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠨⡥⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢠⠠⣦⠀⠀⠀⠀⠀⠐⠒⠭⠽⢷⣞⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠶⠶⠶⠤⠀⠀⠀⠀⠈⠟⠋⠙⣈⠀⣡⠀⠀⠀⠀⠀⠀⠨⠭⠽⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠯⠉⠉⠀⠀⠀⠀⠀⠀⠀⢰⠸⠟⠟⠀⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⢠⡴⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠭⣙⡓⠶⠿
⠀⠀⠀⠀⠀⠀⠀⢠⡴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡙⢦⣈⢷⣦⣄⡀⠉⠙⠲
⠀⠀⠀⠀⠀⠀⠀⠐⣋⢀⣠⡶⣀⠔⡀⢀⡴⠁⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠹⣄⠙⢷⣽⣿⣿⣷⣦⣿
⠀⠀⠀⠀⠀⠀⠀⢨⣿⢟⣭⢞⣵⣞⣵⠟⠀⠀⠀⠀⢰⠀⢸⠀⠀⠀⠘⣎⣆⠘⢷⣄⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢨⡷⣛⣵⣿⣿⡿⠃⣴⠃⡼⠀⠀⡿⠀⣾⢠⠀⡄⠀⢹⣞⣧⠈⢻⣷⣌⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⡟⢁⣼⣟⣼⢁⡾⢸⡇⣿⣿⢸⠀⣷⢀⢸⣿⣿⣷⡀⡹⣿⣿⣿⣿⣿