⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡺⠉⠉⠁⠢⠀⠀⠀⠆⠀⠔⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣣⣀⡀⣀⣀⣀⠀⠘⠈⠪⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡾⣟⢳⣾⡿⠭⣞⣿⣳⡀⢀⡇⡠⡀⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣲⡾⣿⣿⢯⣷⡷⢯⣟⡾⣍⠯⣱⣙⣦⣍⠻⡿⢦⢧⣻⣽⣯⣿⣻⠿⡽⡔⢢⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣹⢷⡾⣾⢯⣿⡿⣞⢙⣾⡽⣞⣽⣳⠯⠟⣀⣯⣟⣾⣿⣟⣶⣶⣶⠥⣾⣶⠿⠛⡝⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡻⣯⣿⣯⢿⣿⡽⣞⣾⣷⡵⣢⢤⢼⣲⢾⣟⡾⣹⣟⣿⣞⣧⣿⣚⣛⣉⣀⣠⡜⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣽⣾⣭⣿⡞⣿⡽⡾⣷⣻⡽⣯⣻⣯⢿⡾⣽⡷⣹⣾⣿⣾⣷⣯⣷⢿⣫⣮⡁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡼⣟⡿⣿⡼⣧⣟⣇⣣⢿⣿⢣⣟⣇⡻⢿⣧⢿⡧⣿⣿⣼⣛⣻⡼⣟⢤⡻⡣⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡿⣽⣻⣽⣟⣾⣤⣮⣷⣿⣿⡼⣇⣠⣶⣿⣿⣷⣯⣿⣳⢿⡝⡿⣯⢭⡤⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡿⣷⣟⣿⣿⡟⡽⣿⡿⠙⠋⠟⡾⠜⣿⣟⢜⣿⣽⣸⣽⡿⣿⣻⢟⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⡿⢳⣿⡈⠉⠉⠀⠀⠀⠀⠀⠀⢀⣼⣿⠛⠉⢵⣿⣽⣯⡥⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡷⠋⠀⠻⣗⠀⠀⠀⢀⣉⣀⠄⠀⢀⡾⠋⠀⠰⢛⣿⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠈⠁⠀⡀⠈⠀⠑⢤⣀⠈⢀⠠⠒⣏⡳⠄⠀⠀⠀⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⡁⢀⢴⠟⠯⢼⡷⢶⣦⣟⣟⣻⣿⣿⣿⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⢐⣶⣾⢦⣤⣤⠄⠒⠉⠒⠠⠼⢥⣠⡙⢮⡝⡿⣷⣯⣿⣞⡋⠳⢶⣦⣤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣤⡤⠤⢰⣾⣿⣳⣻⣿⣿⣞⣿⣿⣿⡄⣠⠀⠀⠀⠀⠈⠙⢇⣤⢍⣵⣿⣿⣤⡈⢹⣧⣮⠟⠉⠐⣿⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠄⠂⠻⣿⢷⣠⣘⣿⣿⣷⣫⣿⣿⣾⣿⣿⣿⣏⣏⢣⡀⠀⠀⠀⣌⠳⣶⣭⡝⠫⠄⢉⣴⣿⠋⠁⠀⠀⢠⡏⡄⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠀⠀⠀⠈⠛⠻⣽⣿⣿⣿⣿⣿⣿⣿⡻⣯⡱⢺⣿⣿⡿⢦⠘⣧⡘⡷⡉⠨⡀⣠⣒⠍⢹⣿⣦⡀⠀⢀⢢⠃⠀⠸⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠱⣄⠀⢀⣠⣾⣿⣿⣿⣿⡿⠿⠯⠿⢿⣷⣾⣽⡟⢫⠁⠀⠘⡄⡟⣧⠰⣈⣵⡼⠿⡵⠀⣾⠻⢿⣿⣷⣾⣜⠀⡄⢶⣿⣼⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠙⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⡡⡇⢀⣤⡱⣇⣽⣳⡟⠉⠀⠀⠀⢰⡇⠀⠀⢩⡿⢟⢿⢷⣶⣾⣿⡿⠿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡔⢃⣈⣽⣿⠟⠋⠀⠀⠄⣤⣄⠀⣾⠀⢀⢜⣹⠃⢀⣉⡛⡟⠛⢟⣿⣤⣽⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⣾⣿⡿⠏⠀⠀⠀⠀⠀⠀⠉⠁⢸⣇⠔⡡⢎⣿⣶⣶⣤⣶⣧⠴⣾⣿⠟⠛⠛⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢋⠥⣾⡆⠀⠀⠀⠀⠠⠀⠀⢀⣿⠅⡎⡱⣼⠛⠚⠛⢻⣾⣷⣿⣶⠟⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢰⡌⢢⢱⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣯⠘⢰⢱⡟⠀⠀⠀⠀⣿⣿⣿⠁⠀⢱⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣯⣶⣲⣦⣤⣄⣀⡀⠀⢀⣿⢉⠎⡥⣞⠃⠀⠀⠀⠀⠘⣿⠃⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡿⣿⡷⣫⢽⡩⢯⠽⣷⣾⣿⣮⣜⣰⡽⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⠓⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⡿⠋⠉⠹⠿⢟⣻⣿⢷⣻⣿⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⢢⡀⠀⠀⢧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣭⡆⡼⠁⠀⠀⡇⠀⠀⠀⡏⢀⡀⠀⢫⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠘⣸⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠛⠉⣰⠃⠀⠀⢀⠃⠀⠀⠀⢿⠸⣿⣦⢄⡙⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢄⢸⣿⣿⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠎⠀⢀⣴⣇⠀⠀⣠⣼⡄⠀⠀⠀⢺⠀⠈⠙⠿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠈⣶⣿⣿⠉⠪⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠠⣃⣤⣾⣿⡿⣣⣾⣯⣿⣿⣿⣦⢤⢲⣿⣧⠀⠀⠀⠈⠉⠻⡝⢂⠀⠀⠀⠀⠀⠀⠀⠸⡟⢅⡀⣀⣼⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠟⠋⡜⠀⠉⠉⠁⢠⠃⠑⠛⠾⠟⢻⣿⣧⣀⠀⠀⠀⠀⠘⡄⠱⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀