⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠒⠀⠀⠒⠂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠄⠂⠠⢀⡀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡄⠀⠀⠀⠀⢀⠠⠐⠒⠐⠄
⢠⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⡀⠁⠉⠀⠀⠀⠀⠀⠈
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠰⠀⠀⠀⠀⠀⠀⠀⢨
⠘⠄⠤⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣼⣿⣿⠿⠿⠛⠻⠛⠛⠛⠙⠛⠛⠋⠩⠝⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢘⣿⡶⣶⠲⢶⣴⣦⡄⠁
⠀⠀⠇⠀⠀⠀⠠⠔⢈⠁⠁⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝⡾⣑⢎⡷⣏⡇⠀
⠀⠀⠏⠛⠓⠻⠷⠿⢿⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⣀⣠⣄⣤⣄⣀⣀⣀⠀⠸⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣽⡾⣝⣳⢎⡿⡥⠂⠀
⠀⠀⢰⠀⠀⠀⠀⠀⢘⠀⠀⠀⢿⣿⢰⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡽⣯⡽⢾⣹⡓⠀⠀
⠀⠀⢸⠀⠀⠀⠀⠀⠨⠀⡀⢠⡘⣿⠸⣿⣿⡟⣋⢿⣿⡿⠙⣿⣿⡿⣽⢻⣿⡿⢽⣷⡇⠀⠀⠀⠀⠀⠀⢠⣿⣟⣷⡻⣝⣧⢹⠀⠀
⠀⠀⠘⡀⠀⠀⠀⠀⠀⡄⠙⠀⣿⣿⠀⠈⠛⠂⠡⠾⠟⠁⠀⡨⠟⠓⣖⣋⡁⣤⣿⢿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣞⣷⡻⣽⡺⡥⠀⠀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⢹⣯⡦⣤⣦⣤⡄⣃⠀⠀⠀⢴⣛⣶⢏⣾⣿⣿⣿⣻⠁⠀⠀⠀⠀⠀⠀⣸⣿⢾⣳⣟⡷⡽⡁⠀⠀
⠀⠀⠀⠇⠀⠀⠀⠀⠀⢡⢸⣡⡍⢳⣿⣳⣭⡷⡤⠝⣤⣁⣀⣺⣿⢻⢾⣭⣿⣿⡿⠃⠀⠀⠀⠰⣭⣱⢀⣿⣿⣻⡽⣾⣝⣷⠁⠀⠀
⠀⠀⠀⢰⠀⠀⢀⢀⠀⢈⡆⠁⠀⠀⠸⣷⣻⢿⣿⣶⣼⣿⣿⣿⣯⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠉⠀⣼⣿⡷⣿⣽⣳⢯⠸⠀⠀⠀
⠀⠀⠀⠈⡄⠀⠀⢢⠳⡠⢼⠀⠀⠀⠀⢿⣶⣂⢿⣿⣏⢙⠈⠙⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣽⡷⣯⣟⠯⡆⠀⠀⠀
⠀⠀⠀⠀⠰⠀⠀⠀⡑⢝⢦⣇⠀⠀⠀⠘⣿⣿⣦⡹⢿⣶⣶⣶⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⣾⣿⣻⣞⢷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠇⠀⠶⡈⡎⣷⡾⣷⡀⠀⠀⣿⣿⣿⣿⣆⠈⣀⣈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⣷⣿⡎⡆⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠈⠮⠵⠵⠎⠵⠛⠛⠛⠛⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠽⣿⣟⢗⠜⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⡈⠎⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠀⠀⠉⠉⠉⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠀⠈⠀⠉⠉⠉⠉⠀⠀⠀⠀⠐⢰⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡰⢠⢒⡰⢂⡖⣐⠺⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢄⢢⡱⣘⢦⡜⣣⢮⡵⣫⡼⣧⢹⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢱⡰⢶⡖⣦⢤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣄⣤⣔⣦⣳⢦⣟⣮⣷⣻⣽⣞⣿⡽⣯⣿⣟⣿⠫⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢇⠢⡙⢤⠛⣼⢳⣻⢮⣝⡯⣽⣹⢮⡽⣭⣛⢮⣗⡻⣞⡽⣯⣻⠷⣯⢷⣻⢾⣽⣛⣷⣻⣞⢧⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⡵⣹⢦⣛⢦⣏⣷⣻⢮⡽⣶⣛⣮⢗⡷⣫⣟⡼⣝⣧⠿⣵⢯⡿⣭⢿⣭⣟⡾⣽⡞⣷⢏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣟⣯⣟⡿⣞⡷⣯⢿⡽⣞⣳⣭⢿⣹⣗⡾⣝⡾⣞⣻⡽⣾⡽⢯⣷⣛⡾⣽⣳⢿⢙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠪⠿⣽⣯⢿⡽⣯⢿⣽⣳⢯⣟⡷⡾⣝⣻⡼⣯⢷⣻⣗⣿⣻⢾⣽⣻⠷⡫⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠩⢟⢿⣽⣟⣾⣽⣟⣾⣽⡿⣽⣷⣻⣽⣯⣷⣻⣾⡽⡛⠎⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠉⠉⠙⠛⠛⡙⢩⠩⣅⠫⢖⡭⣿⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠣⡐⢍⠎⡼⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠱⡈⢎⡱⣝⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢑⠢⣑⢮⢿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠌⡒⡡⢞⣯⢯⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢢⠁⢧⡙⣮⣟⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠍⢦⡙⣮⢿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡘⢦⣙⣾⣋⠁⠀ ,⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀