⠀⢠⣿⠧⠀⠀⠀⠀⣰⡟⠀⢀⣿⠉⣟⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢋⣝⢂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢏⡄⠀⠀⠀⠀⠀⠀⠀⢿⡟⡄⠀
⠠⣾⣿⣃⣤⡤⣖⢽⡷⠷⠻⣾⠿⠶⢿⠶⠲⢬⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣻⠏⡄⠀⠀⠀⠀⠀⠷⠶⢿⠗⠐⠚⢿⡔⠶⠴⠲⢤⣤⣖⣼⣇⣳⣀
⣻⣿⡟⠋⠐⠀⠀⡈⢧⠀⢰⣿⡒⠰⠿⡳⠺⣼⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡛⣇⠒⠀⠀⠀⠀⠀⠀⢀⣿⡆⠀⠀⠸⣿⡀⠀⠃⠀⠀⠀⡼⡿⠹⡟
⡜⢹⢇⠀⠀⢀⣄⢹⡇⡆⣼⡇⠀⠀⢰⣣⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠹⢷⠀⠀⠀⠀⠀⠀⠀⢘⡗⠀⠀⠀⠀⠺⣎⠀⠀⠀⠀⠀⠁⣷⡇⢰
⠃⢸⡽⠀⠀⠀⢸⣸⡟⠀⣿⡁⠀⠀⠨⣿⡄⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⡄⢹⣌⣯⠀⠀⠀⠀⠀⠀⠀⣽⡟⠀⠀⠀⠀⠐⣟⣅⠀⠀⠀⠀⠀⢻⠀⠀
⠁⢸⡻⠀⠀⠀⠀⣼⣧⣆⣧⠀⠀⠀⠀⠙⡽⡆⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⢽⣼⡎⠃⠀⠀⠀⠀⠀⣶⡿⠀⠀⠀⠀⠀⠀⠈⣻⡠⢄⠀⠀⠀⡽⡇⠀
⠀⠈⣹⣳⠤⣖⣛⣽⣿⣭⣿⣅⣄⣀⣀⡙⠻⣦⣀⢿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣽⡇⠀⠀⠀⠀⠀⢰⣿⠅⠄⢊⣀⣄⣤⣤⣠⣸⣿⣭⣙⣺⡷⢬⡇⠀
⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⣿⣷⣿⣷⡬⠻⠂⠀⠀⠀⠀⠀⠀⢸⣿⡒⠀⠀⠀⠠⢂⣾⣣⣶⣿⡿⠿⠟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀
⣿⡿⠿⢋⣵⡆⢰⢹⣿⣷⣻⣏⠟⣿⢷⣤⡈⠙⠛⢷⡔⣲⠤⠀⠀⠀⠀⠀⣺⡯⠃⠀⠀⢀⣴⡏⠙⠋⠁⠀⣤⣶⣿⣿⣿⣿⣏⣟⣿⡌⠢⢭⡻⠿⣿
⡟⠁⠀⣀⣩⣿⣄⢺⣿⣿⣿⣿⣿⣾⣿⣿⣷⡄⠀⠀⠓⡌⣽⣧⡀⠀⠀⣴⡿⠁⠀⠀⣠⡿⠋⠀⠀⠀⠀⣀⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⠄⣹⣿⠀⠈
⠀⠀⠀⣿⣿⡿⠟⣾⣿⣿⣿⣿⡿⠛⢿⣿⣿⠀⠀⠀⠀⠀⠙⢿⣞⠈⣰⡜⠎⠀⣰⣾⠏⠁⠀⠀⠀⠀⠀⣿⣿⡿⠟⢻⣿⣿⣿⣿⡿⢛⡷⣿⣿⠇⠀
⠀⠀⠀⢿⣏⠀⠀⠀⠙⢛⠛⠋⠀⠀⠀⣻⠿⠁⠀⠀⠀⠀⠀⠀⠘⢻⣿⢋⣴⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠉⠛⠛⠋⠁⠈⣿⣛⠟⠀⠀
⠀⠀⠀⠈⠙⠮⣀⢤⠄⠀⠀⠅⠶⣶⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣤⡾⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⠤⢤⡄⠠⢀⠠⣴⣒⠾⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿
⢧⢊⡙⢶⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⢋⢶
⠎⡔⢨⢂⠍⡛⠛⠶⢴⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⡖⠺⢏⠱⠌⢎⡡⢺
⠘⡌⢢⠍⡘⣅⢋⡒⠥⡘⢌⢛⡛⠳⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⠛⠭⡑⢢⠑⣌⠱⣈⢱⣮⢢⡁⢿
⢡⠚⠤⣙⠰⢌⠢⣜⣶⡿⠶⡾⠛⠛⡋⣻⡿⠛⠋⠙⠰⠖⠤⢀⢀⠀⠀⠀⠀⣀⣀⠀⠠⠤⠶⠚⠉⠡⣿⠏⢙⠉⠹⡶⠷⢷⣮⣤⡓⢌⢺⢽⡂⠜⣼
⠢⣉⠲⢌⠲⠌⣵⣿⠋⠐⢿⣣⣍⡣⢐⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⠈⠀⠀⠀⠀⠀⠊⣿⠣⠄⠣⣔⣱⣶⣿⠆⠙⢻⣶⢙⣮⡱⢉⢾
⡦⢡⠚⠤⢋⡌⢻⣿⠃⠀⠀⠀⠉⠙⠋⠙⠛⠑⠒⠶⠶⠶⣦⣤⣄⣀⠀⠀⠀⠀⣀⣢⣀⣢⣠⠤⠤⠾⠟⠻⠛⠛⣉⠋⠀⠁⠀⠀⣼⡷⢾⣘⢿⡈⢾
⡡⢃⠎⣅⠣⡘⡰⣿⡇⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠙⠷⣦⣴⠟⠉⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⣟⣷⡬⣽⣿⠨⣽
⡅⡎⣘⠤⣑⣬⣅⣿⡷⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣹⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢈⣿⢤⡉⠿⢛⡰⢼
⠧⠿⠻⢛⡋⠥⠤⣭⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠿⠍⠙⡛⠦⢴⣻