⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠛⠛⠒⠒⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠶⠒⠒⠲⠶⠦⢤⣼⡃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣴⠛⠻⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⣠⠿⢦⡴⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⠈⠉⠻⣦⠟⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀
⠀⢀⣀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀
⢰⡏⠈⢳⣟⠁⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢸⡟⠉⣿⣿⣧⣨⠇⢀⣀⣀⡀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠛⠚⠋⠉⠳⢦⡀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⢀⠙⠿⢿⣿⣿⣯⠞⠋⠁⠈⠉⠳⢦⡄⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢀⡇⠀⠀⠀⠀⠀⣤⠞⠉⠉⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⢠⡀⠙⣦⠀⣸⠃⠀⢰⠋⠉⠳⠋⠉⠙⡆⠀
⠀⠀⠀⠀⢀⠤⠤⣄⡀⠈⠛⠚⠋⣷⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢛⣿⣁⠀⢸⣦⡟⠀⠀⠸⣆⠀⠀⠀⠀⡼⠃⠀
⠀⠀⠀⠀⡏⠀⠀⠀⠵⠒⠲⢤⠀⠹⡆⠀⠀⢸⠇⢀⣤⡤⠤⣄⠀⠀⢠⠄⣄⠀⠀⢰⣿⠿⣿⣀⣸⡟⠀⠀⠀⠀⠈⠓⢤⡴⠊⠀⠀⠀
⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢨⠇⠀⠙⢦⡀⢸⡄⠀⣻⣴⣶⡶⠀⠀⣬⠭⠅⡆⠀⠈⣴⠟⠉⠉⢻⣦⡶⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠳⡄⠀⣀⡤⠖⠉⠀⠀⠀⠀⠙⢦⣿⣤⣛⣿⠿⢧⣄⠀⠈⠒⣒⣡⡤⢾⡇⠀⢠⣴⣟⣯⡛⠛⠃⠀⠀⠀⢠⡏⠉⠳⠖⠲
⠀⠀⠀⣀⣀⡀⠹⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣽⠿⣇⠀⠀⠹⡗⠚⣋⡭⠤⠤⣤⣷⡀⠀⢻⢿⣄⡿⠀⠀⠀⠀⠀⠀⠳⡀⠀⢀⡠
⡴⠚⠻⠇⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣿⠋⢉⣛⣿⠀⠀⢹⠟⠉⠀⠀⠀⠀⠈⠳⣶⠟⠀⠀⠀⡰⠒⠓⢆⠀⠀⠀⠘⠒⠉⠀
⠹⢄⣀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠲⣶⠀⠀⠺⣥⣽⣦⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡇⠀⠀⢨⡧⣄⡀⠀⠀⠀⠀
⠀⠀⠈⠉⠁⠀⠀⣀⣀⡞⠉⠙⡆⠀⣧⣴⣄⠹⣦⣀⣀⣸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠃⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠏⠁⠈⠀⠀⠀⡀⠀⠈⠀⠙⠳⠦⣬⣭⣽⣿⣆⠀⠀⠀⠀⠀⣤⠀⠀⣹⡇⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⡼⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢧⣄⣀⣀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠁⠀⠀⠀⠀⣰⠏⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠛⣉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⣀⣤⠞⠛⠶⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢠⠋⠉⠉⠒⠲⢤⣀⣠⡀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡠⠖⠋⠉⠀⠀⠀⠀⠉⠉⠢⣄⠀⠀⠀⢀⠼⠤⠇⠀
⠀⠀⠀⣀⠔⠊⠁⠀⢨⠏⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠀⠀⠱⣄⡴⠃⠀⠀⠀⠀
⢸⣉⠿⣁⠀⠀⠀⢀⡇⠀⠀⠀⠀⢿⣽⣿⣼⡠⠤⢄⣀⠀⠀⢱⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠑⢦⡀⢸⠀⠀⠀⡠⠒⠒⠚⠛⠉⠀⢠⣀⡌⠳⡀⡌⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠉⣆⠀⢰⠁⣀⣀⠀⠀⣀⠀⠈⡽⣧⢀⡷⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡤⢄⠀⠈⠢⣸⣄⢽⣞⡂⠀⠈⠁⣀⡜⠁⣩⡷⠿⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢯⣁⡸⠀⠀⠀⡬⣽⣿⡀⠙⣆⡸⠛⠠⢧⠀⡿⠯⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⡤⠤⣵⠁⢸⣻⡤⠏⠀⠀⠀⠀⢹⠀⠀⠀⡊⠱⣀⠀⠀⠀
⠀⠀⢀⠜⠀⢘⠀⠀⠱⠲⢜⣢⣤⣧⠀⠀⠀⠀⠀⢴⠇⠀⠀⠀⠧⠠⠜⠀⠀⠀
⠀⠀⠘⠤⠤⠚⠀⠀⠀⠀⠀⠀⢸⠁⠁⠀⣀⠎⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⡴⠤⠄⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠆
⢾⣷⢤⣀⣀⣀⣀⠀⠀⣾⣦⠀⠀⠴⣿⣄⡠⠖⠉⣷⠀
⠀⠸⡄⠀⠀⠀⠈⠙⡖⠒⢿⠛⠒⢲⠷⣏⠀⠀⠀⢹⠀
⠀⠀⢳⡀⠀⠀⠀⠀⠉⠀⠈⠀⢀⡬⠤⡈⠑⣄⢀⠜⠀
⠀⠀⠀⢳⡤⠤⠀⠀⠀⠀⠀⠀⢇⢆⡰⡾⠀⠈⣇⠀⠀
⠀⠀⠀⢸⡇⣀⡀⢀⡤⣺⣍⡙⠚⠿⣻⠗⣫⣶⣸⠀⠀
⠀⠶⢶⡚⠉⠁⢇⡎⠀⢸⣠⠏⠀⠀⢠⡜⠧⢇⡟⠀⠀
⠀⠀⠀⠧⠤⡀⠘⣧⡀⠀⠀⠀⠸⣓⡾⢀⡠⠞⢀⠀⠀
⢠⢤⡀⠀⠀⣓⡶⢜⡯⠵⠶⠒⠊⢹⣮⡍⠀⢰⣃⠔⢁
⠸⢦⣯⡶⡯⠷⠀⠈⠙⠦⠦⡄⣀⣀⣯⣁⣠⠞⠙⠋⠁
⠀⠀⠀⠀⢹⢀⠀⠀⠀⠀⢀⡼⠓⢮⣙⡸⠁⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣸⡇⠀⠀⠘⠯⡀⠴⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠳⠤⠤⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀