⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠂⠢⠉⢉⠩⢍⢫⡝⣹⠶⡴⢦⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠁⠀⠠⠐⠠⠁⡈⠄⢣⠘⢦⡙⣖⣫⢽⣫⢷⣯⢿⡷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠌⠐⠠⠁⡐⢀⠐⠠⢉⠆⡱⢎⡼⢣⡟⣾⣹⢯⣿⣟⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⡄⠀⡘⢀⠘⠠⢀⠀⠄⠘⡀⠘⡄⢣⢜⡸⣇⢿⣸⣟⣿⣧⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢮⠀⢡⠀⡇⣼⠀⡜⢁⡴⠊⠀⠄⡈⢀⠂⠄⠡⢘⢂⠎⡵⢪⢷⡹⣾⣷⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⣅⠈⢷⣼⠷⠛⠛⢛⣿⣏⠂⢍⠢⡐⢀⠂⠠⢈⠐⠨⢌⡚⡜⣣⠟⣫⡷⠟⠛⠠⡀⠀⠉⠛⢿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⡘⠦⣌⣿⠟⠛⠢⣄⣴⡿⣛⡼⡇⠀⠑⡜⢄⠠⠁⠠⠈⡅⢲⠘⣼⢫⣾⠛⢷⣤⣠⣾⢿⣢⠀⠀⠀⠙⢿⣿⣧⠀⠀⠀ ⠀⠠⣰⠙⢶⣿⡟⠀⣄⣠⣿⣿⣾⡵⣯⡇⠀⠀⠸⡜⡄⠈⠄⡑⠌⢦⢩⣧⣿⡇⡇⠀⠈⣿⣿⣶⡽⡆⠀⠀⠀⠈⣿⣿⣆⠀⠀ ⠀⢠⣋⣝⡟⠘⣷⣼⣿⣿⣯⣿⣿⣿⡷⠁⠀⠀⠀⢰⡀⠌⡐⠌⡜⢢⠽⡞⢹⣧⣼⣷⣿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠸⣿⣿⡄⠀ ⠀⢸⢮⣽⠣⡀⠈⠛⠿⢿⣷⡿⠿⠋⠀⠀⠀⢄⠀⠀⡇⢢⢑⠪⡜⣡⢛⣧⠀⠛⢿⣿⣿⣯⣿⠟⠁⠀⠀⠀⠀⠀⠂⢿⣿⡇⠀ ⠀⣟⡶⡾⠀⠓⣀⠠⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣏⠲⣌⠳⡸⢥⣻⢰⠀⠀⠀⠈⠉⠉⠀⢀⡀⠤⠤⠰⣀⠀⠂⢸⣿⣷⠀ ⢤⣿⣻⠇⠊⠁⠀⠀⠀⠀⠀⠉⠂⢄⠀⠀⠔⠀⠀⠀⢹⠲⣌⢳⣙⢮⣽⠸⡄⠀⠀⠀⢀⢐⠌⠀⠀⠀⠀⠠⠀⠉⠢⠈⣿⣿⠠ ⠀⠿⠁⡄⠐⡈⠀⠀⠀⠀⠀⠀⠀⢂⠢⡀⠀⠀⠀⠀⣸⠳⣜⣣⢏⡾⣼⠀⢈⣢⣤⡔⡕⠁⠀⠀⠀⠀⠀⠀⠈⡐⠈⢎⠹⡿⠀ ⠸⣞⢹⡀⢃⠄⠀⠀⠀⠀⠀⠀⠀⠈⡄⢻⣙⡶⣢⣄⢯⡻⣜⢧⣻⡼⡽⣶⣟⡿⣿⢀⠀⠂⠄⠀⠀⠀⠀⠀⠠⢀⠡⡈⠆⣡⠀ ⢠⣿⣦⡙⠤⡈⠄⡀⠀⠀⠀⡀⠄⠡⠑⣸⣟⡼⣣⢟⡮⣗⢯⣞⣧⢿⣽⣳⢯⣟⣿⢠⡌⣡⠊⡄⢠⠀⠄⡠⢁⠎⡰⣡⣛⣼⠀ ⠘⣻⣿⣽⣳⡜⣴⢢⡱⣌⡳⣜⣜⣣⣟⣼⣯⠾⣝⢯⡾⣽⣛⣮⣟⢾⣳⢯⣿⢾⣻⣯⡵⣧⣳⡜⣦⠱⣌⣔⣣⢞⣵⡟⣾⠇⠀ ⠀⠈⢷⡝⢿⣿⣿⣷⣿⣷⣿⣿⣾⣿⣿⣟⣾⣻⢷⣶⣟⡷⣯⢷⣻⣶⣿⣿⣽⣿⣻⣿⣿⣿⣿⣿⣷⣿⣿⣾⣽⣿⢿⡛⠍⠀⠀ ⠀⠀⠀⠉⠣⣭⣛⣛⡻⣟⣿⣿⣻⣽⣾⣽⡾⣽⣻⡿⣿⣿⣽⣿⣿⣿⢿⣳⣿⣾⢿⣷⣿⣻⣞⣯⡭⣟⣻⣙⡭⣼⠞⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣾⢿⣟⣾⣷⡿⣟⣯⣿⢿⣽⣿⣻⣽⡿⣿⣟⣯⣿⣿⣻⣾⢿⡽⣞⡝⡺⣔⢣⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟⣯⣿⡟⣿⣾⡟⣿⣯⣿⣿⢻⣾⣿⢻⣿⡟⣿⢻⣷⣿⣽⡞⢻⡜⢱⡜⢱⡎⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⢯⣟⡷⣯⢿⣽⢾⣟⣾⢿⣯⡿⣟⣯⣿⣟⣯⡷⢯⠳⠍⢣⡜⣣⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⢽⣫⢟⡾⣻⢾⣽⣻⢾⣽⣻⠽⠾⡙⠎⢉⡡⢴⣩⠷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⠶⢫⡼⣤⣍⣂⣁⣠⣤⣤⣴⠾⢳⠫⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀