⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠀⠈⠉⠁⠀⠀⠀⠉⠉⢹⣿⣷⡒⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣿⣿⣷⠀⠀⠈⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⡇⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣯⠀⣀⠀⠀⢀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡔⠃⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢸⣟⡴⣯⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣟⣠⠎⢤⣤⠾⣆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡀⠀⠀⠀⠀⣠⡴⡂⠀⠀⢱⢈⣾⣳⡭⠀⠀⢰⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⡀⠈⡾⣽⡻⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠌⡣⠀⠀⠀⠀⠸⣳⡇⠀⠀⠈⡀⡷⡯⠁⣾⠆⠈⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠊⠀⠁⡀⠏⡷⡃⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢠⠈⠌⠀⠸⡆⠀⠀⠀⠀⢱⠀⠀⢰⡤⠁⠘⠁⠀⠓⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠤⠜⠀⠀⠀⠀⡄⢣⠃⠀⠀⢸⠸⡀⠀⠀⠀⠀⠀⢠⠣⢇⠀⠀⠀⠇⠀⠀⠀⠀⠀⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⠠⠄⣀⣀⣀⡤⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⡃⢸⡜⠀⣦⠸⠀⠈⢢⡀⢀⢄⠢⡂⠁⠈⢗⣄⠀⢰⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⢤⠤⠂⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣀⢤⠄⡀⡇⠀⢱⡀⠀⠂⠇⠈⣿⡿⠒⢥⡈⠀⠀⠀⠀⢆⠑⠾⡄⠀⠀⠀⠀⣷⢛⣢⡀⠀⠀⠀⠀⠀⢀⢎⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⣟⢞⣇⢸⡠⡵⣄⠀⠸⡠⣿⡇⠀⠀⠈⠙⠒⠢⠘⢶⠗⠀⡀⠀⠀⠀⠀⡷⡳⣆⠕⢄⠀⠀⠀⠀⢈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣸⠙⢦⠈⠳⣄⠹⣬⣧⣴⣤⣄⠀⠀⠀⠀⢰⠆⢀⡇⠀⠀⠀⠀⢰⠉⠚⢌⠚⡄⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢸⣷⣮⡳⣠⢎⡝⠛⠾⣯⡗⡿⣷⠀⠀⠀⣸⠇⠪⡇⠀⠀⠀⠀⢘⠀⠲⠌⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⡈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠈⢹⠽⣿⢷⣅⡏⡂⣀⠀⡈⠢⢿⣽⠀⢠⢎⡏⢀⠞⡇⠀⠀⠀⠀⢸⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡢⢋⡰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⢒⣈⡠⠄⠀⢀⠚⠃⠹⣿⢝⢅⢎⠁⠂⠀⠐⠀⢠⡎⠩⠄⠦⠒⠐⠁⡆⠀⠀⠀⠀⣧⡔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡁⠔⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣤⠃⢁⢔⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⠀⠀⠀⠀⢹⢇⠻⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⢂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠘⣸⡀⢘⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⠄⠀⠀⠀⠈⠫⣢⣄⣉⠉⢀⣄⠀⠀⠀⠀⠀⠀⢀⠏⠒⠄⡱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠷⠗⠓⠚⠀⠀⠀⠑⠲⣔⠂⠤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣱⡀⠀⠀⠀⠀⠀⠈⠻⢽⣛⡿⣽⡇⠀⠀⠀⣠⠖⠁⠀⠀⠀⡘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⣇⠈⠒⢄⣀⠀⣀⡠⣴⡶⣿⣹⣏⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣯⣟⣷⠀⣀⣤⣦⣟⡷⡀⠀⠀⠘⠁⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀⠀⠀⢰⢀⠀⠀⠀⠀⠀⠀⠁⠌⡀⠤⣦⣶⣵⣿⣿⣽⣷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢾⣽⣣⡿⣯⡿⣿⣽⣾⡟⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠛⠳⠒⢒⣲⠖⢒⠒⣉⡀⠄⠺⠀⠀⠸⣔⢑⣄⡀⠀⠀⠀⠀⠀⠙⢮⠲⣿⣿⡿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣰⣯⢿⢶⣻⣽⢳⣻⢶⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠓⠂⠤⠀⠤⠄⣀⠀⠀⠉⠑⠂⠧⡀⠀⠀⠈⠙⠂⡈⠓⠀⠀⠀⠀⠀⠘⢁⣿⣿⣽⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣫⣾⣻⡼⣏⣿⣶⣿⣯⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠰⡢⣝⠶⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣽⢳⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠁⠀⠀⠀⡆⠀⠀⠀⠀⢠⣴⣾⣿⣿⢳⣿⣬⢻⣷⢲⢠⠀⢠⡄⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠕⠀⠀⠀⠀⠹⣆⣄⣀⣰⣿⣿⣿⡿⡽⣾⣹⢿⣲⡶⣾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠠⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣽⡳⣷⢫⣯⢷⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠐⢍⠉⠉⠒⠤⡀⠀⠀⠀⠀⡞⠁⠑⡄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣳⢻⣵⣻⣾⣿⡇⢀⠀⠀⠀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⢫⡑⠂⠽⣢⡀⠀⠈⠑⠠⣄⠞⠻⣄⠀⠈⠲⣿⡦⡀⢸⣿⣿⣿⣿⣿⣞⣵⣿⣿⣿⣿⣿⣿⣾⣧⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀ ⠀⢸⠁⠛⢦⡀⠈⠙⢦⡀⠀⠀⠀⠑⢄⠉⢆⠀⠀⣳⣻⣽⣺⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀ ⠀⠰⡳⡀⠀⠙⣄⠀⠀⠈⠦⡀⠀⠀⠀⠁⣩⣿⣳⣯⣗⣳⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠸⡱⣄⠀⠈⠦⢄⡀⢀⣈⣙⣤⣴⢾⣻⣼⣟⣷⡽⢯⣞⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠤⣀⠀⠱⠬⣭⣴⣦⢴⡾⢯⣟⣞⣧⢯⣟⡾⣽⣻⣼⣿⣻⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀

⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣻⣿⣼⣻⣽⡾⣟⢯⣧⣞⣟⢯⡾⢴⣦⣴⣭⠬⠱⠀⣀⠤ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣞⢯⡽⣷⣟⣼⣻⢾⣴⣤⣙⣈⢀⡀⢄⠦⠈⠀⣄⡱⠸⠀⠀ ⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣳⣗⣯⣳⣿⣩⠁⠀⠀⠀⡀⠦⠈⠀⠀⣄⠙⠀⡀⡳⠰⠀ ⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣺⣽⣻⣳⠀⠀⢆⠉⢄⠑⠀⠀⠀⡀⢦⠙⠈⡀⢦⠛⠁⢸⠀ ⠀⠀⠀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣄⣧⣾⣿⣿⣿⣿⣿⣿⣵⣞⣿⣿⣿⣿⣿⢸⡀⡦⣿⠲⠈⠀⣄⠻⠞⣄⠠⠑⠈⠀⡀⣢⠽⠂⡑⢫⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣤⣠⠀⠀⠀⢀⡇⣿⣾⣻⣵⢻⣳⣷⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⡄⠑⠁⡞⠀⠀⠀⠀⡀⠤⠒⠉⠉⢍⠐⠀⠀⠀ ⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣻⢷⣯⢫⣷⡳⣽⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⡀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⠠⠀⠀⠀⠀⠀⠀⠉⠋⠟⣾⡶⣲⢿⣹⣾⡽⡿⣿⣿⣿⣰⣀⣄⣆⠹⠀⠀⠀⠀⠕⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢠⠀⠀⠀⠀⠀⡄⢠⠀⢠⢲⣷⢻⣬⣿⢳⣿⣿⣾⣴⢠⠀⠀⠀⠀⡆⠀⠀⠀⠁⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢳⣽⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠶⣝⡢⠰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣯⣿⣶⣿⣏⡼⣻⣾⣫⠴⢠⠀⠀⠀⠀⠀⠀⠀⠀⡃⣽⣿⣿⢁⠘⠀⠀⠀⠀⠀⠓⡈⠂⠙⠈⠀⠀⡀⠧⠂⠑⠉⠀⠀⣀⠄⠤⠀⠤⠂⠓⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⡇⣿⣿⢶⣻⢳⣽⣻⢶⢿⣯⣰⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⡿⣿⣿⠲⢮⠙⠀⠀⠀⠀⠀⡀⣄⢑⣔⠸⠀⠀⠺⠄⡀⣉⠒⢒⠖⣲⢒⠒⠳⠛⠉⠉⠈⠀ ⠀⠀⠀⠀⠀⠀⡟⣾⣽⣿⡿⣯⡿⣣⣽⢾⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⣷⣽⣿⣿⣵⣶⣦⠤⡀⠌⠁⠀⠀⠀⠀⠀⠀⢀⢰⠀⠀⡀⠤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠁⠘⠀⠀⡀⡷⣟⣦⣤⣀⠀⣷⣟⣯⢸⠀⠀⠀⠀⠀⠀⠀⠁⠟⣏⣹⣿⡶⣴⡠⣀⠀⣀⢄⠒⠈⣇⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡘⠀⠀⠀⠁⠖⣠⠀⠀⠀⡇⣽⡿⣛⢽⠻⠈⠀⠀⠀⠀⠀⡀⣱⣀⣀⢀⠀⠀⠀⠀⠀⠀⣀⠤⠂⣔⠲⠑⠀⠀⠀⠚⠓⠗⠷⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡱⠄⠒⠏⢀⠀⠀⠀⠀⠀⠀⣄⢀⠉⣉⣄⣢⠫⠈⠀⠀⠀⠄⡞⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⠀⢘⡀⣸⠘⠀⣆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢂⠁⡈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣷⠻⢇⢹⠀⠀⠀⠀⢦⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠑⢔⢁⠃⣤⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠔⡁⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡔⣧⠀⠀⠀⠀⡆⠁⠐⠒⠦⠄⠩⡎⢠⠀⠐⠀⠂⠁⢎⢅⢝⣿⠹⠃⠚⢀⠀⠄⡠⣈⢒⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⡰⢋⡢⢤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠀⠀⢸⠀⠀⠀⠀⡇⠞⢀⡏⢎⢠⠀⣽⢿⠢⡈⠀⣀⡂⡏⣅⢷⣿⠽⢹⠈⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡈⡌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠌⠲⠀⢘⠀⠀⠀⠀⡇⠪⠇⣸⠀⠀⠀⣷⡿⡗⣯⠾⠛⡝⢎⣠⡳⣮⣷⢸⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⡄⠚⢌⠚⠉⢰⠀⠀⠀⠀⡇⢀⠆⢰⠀⠀⠀⠀⣄⣤⣴⣧⣬⠹⣄⠳⠈⢦⠙⣸⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢈⠀⠀⠀⠀⢄⠕⣆⡳⡷⠀⠀⠀⠀⡀⠀⠗⢶⠘⠢⠒⠙⠈⠀⠀⡇⣿⡠⠸⠀⣄⡵⡠⢸⣇⢞⣟⠈⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⢎⢀⠀⠀⠀⠀⠀⡀⣢⢛⣷⠀⠀⠀⠀⡄⠾⠑⢆⠀⠀⠀⠀⡈⢥⠒⡿⣿⠈⠇⠂⠀⡀⢱⠀⡇⡀⠄⢤⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠂⠤⢤⠀⠀⠀⠀⠀⡀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⠀⣄⢗⠈⠁⡂⠢⢄⢀⡀⢢⠈⠀⠸⣦⠀⡜⢸⡃⠀⠀⠀⠀⣀⠤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⡤⣀⣀⣀⠄⠠⠘⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠸⠀⡄⠀⠀⠀⠀⠀⠇⠀⠀⠀⢇⠣⢠⠀⠀⠀⠀⠀⡀⠸⢸⠀⠀⠃⢣⡄⠀⠀⠀⠀⠜⠤⡤⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠓⠀⠁⠘⠁⡤⢰⠀⠀⢱⠀⠀⠀⠀⡆⠸⠀⠌⠈⢠⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⡃⡷⠏⡀⠁⠀⠊⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠈⠆⣾⠁⡯⡷⡀⠈⠀⠀⡇⣳⠸⠀⠀⠀⠀⡣⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡻⣽⡾⠈⡀⣽⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡦⢰⠀⠀⡭⣳⣾⢈⢱⠀⠀⡂⡴⣠⠀⠀⠀⠀⡀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣆⠾⣤⢤⠎⣠⣟⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣯⡴⣟⢸⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⠃⡔⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⢀⠀⠀⣀⠀⣯⢻⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠙⠀⠀⠀⠀⡇⣿⣿⠿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⡷⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠒⠈⠀⠀⣷⣿⣿⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⡀⣧⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⡒⣷⣿⢹⠉⠉⠀⠀⠀⠁⠉⠈⠀⠒⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀