⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⢶⠦⣧⡛⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⠁⢀⠀⠑⠼⢿⢑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀⠤⠀⠀⢀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠟⠋⠏⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⢯⢤⣄⣰⡷⠶⢾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣗⠦⢴⡏⡝⢖⣒⡽⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠈⠻⣍⢁⠂⣙⣛⣁⠀⢂⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⣰⡖⠄⠀⠀⣸⣧⣀⠉⠉⠁⡴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠉⠀⠀⠀⠀⠀⠸⣟⢼⣷⣶⣾⡷⠘⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⢀⡄⠀⢀⡀⠠⢀⠀⠀⠀⠔⠉⡎⠁⠘⣿⣿⣿⠃⠀⡖⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⢠⠀⣀⠀⠀⠀ ⠀⠀⣠⡱⡈⠔⡊⢩⡾⢁⡽⠃⠀⢀⣴⡄⠀⠠⠀⠀⡳⢀⡐⢸⣿⡇⢀⣠⢆⠆⠀⠱⡀⠀⠀⠐⡬⠰⢒⣣⡌⠬⠥⢬⡒⣈⢅⢏⠆⠀ ⢀⡐⢆⢿⣷⣾⣶⢻⣁⡟⣐⡤⢤⡯⢎⣃⡰⠁⠀⡡⢆⠀⢘⠆⣿⠡⠈⠀⢸⠑⠄⠀⠠⠀⠀⣐⢏⠚⢒⠏⡲⠤⢤⢔⣻⡏⠔⡦⠰⠀ ⠙⣞⢙⢾⡋⡡⡌⢹⡾⠨⠀⢰⢸⡇⣒⠎⠑⠀⡐⠁⡸⠀⢸⡐⢸⠀⠀⠀⢻⠀⠐⠄⠀⠑⡀⠤⡟⢂⣯⢊⠈⠋⢸⡆⡜⣷⡞⢦⡂⡄ ⠀⣠⢪⢶⡳⠶⠈⠛⠧⠡⣀⡞⢸⡇⣼⡕⠄⢰⣀⣀⡕⠀⠀⠀⢸⠀⠀⠀⠸⢀⣠⣸⡄⠐⣵⠴⠈⢙⠃⠸⠄⠤⣀⢳⡘⢼⡿⠶⠽⠊ ⠐⢊⡽⠋⠑⠤⡐⠃⣀⣒⣤⠟⣾⡥⣿⠼⣄⣼⣿⣿⣿⠳⠄⠀⣾⠈⢀⡴⣿⢫⣝⣻⣆⣼⣤⡧⢒⠒⠒⠂⠐⢂⢹⣘⣜⣢⢇⠲⡁⠀ ⢀⡞⠀⡰⣳⡀⠀⠉⢳⢫⡔⡩⢆⡳⠁⠀⣸⣿⣿⣿⣿⣷⣄⣀⣿⡆⣈⣴⣿⣿⣯⠹⣿⠃⡇⢡⡃⢘⠄⢣⣘⠔⠋⠈⣘⡭⢋⢬⠑⠀ ⠈⠺⢠⠅⢹⡽⢰⠀⠈⣯⣞⡕⠈⠘⠢⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡼⡚⡔⠀⠍⢩⠤⡖⡏⠀⠀⠉⡟⢧⣇⠣⠃⠀ ⠀⠀⠐⠂⠋⠀⠁⠘⠙⠫⡔⠒⠠⣀⠀⠐⡈⠿⣿⣿⣿⣿⡿⣯⠿⠿⣿⣿⣿⣿⣿⠿⠷⠱⠋⠀⠈⠁⠀⠀⢌⣠⡈⠀⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠰⠙⠦⠀⠀⢀⠰⡏⠛⠿⢏⡀⠀⠈⢱⡆⠀⠀⠀⡀⠀⠀⠀⠀⠊⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠉⠢⠀⣼⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀