⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡤⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣞⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣴⡶⣶⣲⣦⣦⣤⣄⣀⠀⠀⠀⠀⢸⣝⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⣟⣿⣽⣟⣷⣷⣾⣺⢼⣣⢫⡛⡲⣄⡀⠈⠳⢓⣄⠀⠈⠙⣦⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣾⣯⢿⡾⣵⢷⡩⡣⢧⠫⢲⡀⠀⠈⠑⡄⠀⢘⣻⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣻⣷⣿⣿⣾⣿⡿⣿⣿⢿⣿⡽⣯⠮⢪⡺⡡⡋⡐⠬⣢⣀⣀⠅⠀⣸⣞⢃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣿⢿⣟⣿⣿⣟⣿⣾⣿⣽⣿⣿⡿⣿⣷⢿⢽⣓⡵⢕⠌⣵⠋⡉⡉⢤⠀⠀⣼⢇⣧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⣿⢹⣿⣿⣿⣻⣿⣟⣿⣻⢿⣯⣿⢿⣯⢿⢻⡱⣟⡧⡑⠔⢗⡀⠢⠘⠠⣇⠸⣂⢳⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢾⡧⠠⣯⡾⣿⣻⣾⣽⣷⣷⣣⢋⢞⡛⢕⣃⣭⣞⡷⢌⣆⢑⠪⣰⠃⠑⡡⢪⠀⠫⣺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⣿⠣⣀⣿⡿⣿⠿⠿⠫⡳⣻⣯⡿⠬⢱⡾⡿⡻⠑⡊⢪⢝⡷⢷⡩⡆⢂⠑⣕⠀⠀⠈⠻⣄⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡳⡓⣥⡾⠋⡉⢀⠐⡀⠂⡨⢱⢕⠍⣪⣬⡑⠊⢄⠐⠠⠀⠄⠈⡉⠑⢮⢄⠡⡨⠀⠀⠀⠀⢘⠄⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡵⡁⣯⠂⠄⠔⠠⠀⢂⠐⠠⠨⣴⢯⣿⡷⡃⢆⠠⡈⢐⠀⢊⠆⠰⢂⠜⢷⣀⢵⡠⠄⠊⣀⠔⠀⣼⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢜⠀⣿⠈⢌⡐⢀⠡⡀⠄⠡⠐⣃⣷⠋⠈⢳⠰⠀⠄⠠⠈⢿⠈⢊⢒⣵⡿⠁⠄⢀⣴⠚⣁⣴⢾⢛⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠑⢄⣿⣆⠨⠐⠄⢄⠠⣈⣦⣿⣿⠇⢀⠁⡀⢇⢱⣪⣀⠊⢈⠛⠈⢾⣿⡇⠈⡀⡞⡦⣞⠿⡱⣓⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣦⡿⣿⣿⣷⣷⣿⡾⡛⣏⣿⢿⡟⠀⠄⠂⠰⡈⡆⢢⣻⣻⡟⣻⢿⣮⠿⢜⢄⡁⢱⠭⡼⡋⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣟⣿⢿⣽⣿⢪⡥⣮⢟⣿⢻⡟⣆⠐⠠⣅⠑⢌⡇⢢⡵⠳⢡⡟⡻⢙⢃⠕⡐⠥⢤⡙⢜⢯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠹⢾⣗⡟⢇⠒⡠⢕⣿⣢⣿⣽⡔⣠⡏⢒⡱⡡⡘⡎⢠⠘⠨⠂⠢⠱⡁⢘⡔⠀⠙⠆⠱⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⢀⢈⢀⠁⠂⢅⣧⣿⣽⣟⣿⣽⣿⠅⢄⢮⡣⡜⣳⠀⠢⠁⠌⠨⠀⠊⠀⠀⠀⠌⠃⠀⣽⡗⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⣧⢢⠁⠂⣸⣳⢻⡽⡹⡻⣚⣝⢓⣓⠽⠎⡾⢨⢣⢁⠅⢂⠨⢊⠠⠁⢘⡂⠀⠀⣠⡿⣡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠨⠀⣛⣨⣧⣾⣸⣷⣾⡿⣺⡿⢼⣏⢞⢢⡆⢶⠀⢵⠀⣅⠀⠈⠈⣀⣴⣟⡽⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⢨⢀⡘⣙⣋⢙⣘⣁⣈⣁⢨⣥