⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢰⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⠊⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢈⣽⣄⠀⠀⠣⠀⠀⠀⠀⢣⡀⠀⠈⣦⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⠈⠁⠘⢇⠀⠀⠀⠀⠀⢠⢸⠀⢰⣦⢻⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡆⡇⠠⣶⡄⠘⣦⡀⠀⠀⡄⠢⡘⡀⢸⢹⡆⢹⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢿⠂⣟⣿⡄⢼⣧⡤⠶⠶⠐⠋⠿⡾⠟⣧⣼⡆⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⣜⣧⣼⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡿⠛⢃⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠰⠛⠠⠀⠈⠀⠀⠈⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠊⠀⠢⠀⠠⡄⠁⠠⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⠀⠀⠀⠀⠀⡈⠀⢀⣤⣦⣤⣀⢀⢉⣦⣤⠶⠓⠉⠙⠲⢮⣗⠀⠀⠀⠀⣀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⠀⠀⠀⠀⣠⣮⣶⢿⠿⠋⠉⠁⠘⠉⠉⠀⠀⠀⠀⠀⠀⡴⠀⣹⣇⠈⠆⢸⣷⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡇⠈⠀⠖⣼⢼⡿⠏⠰⣀⠀⠀⢀⡀⠀⠀⠀⠀⢖⠤⣶⣾⣶⡀⠀⢹⡿⣌⠀⠹⢿⡺⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠋⢠⣟⣼⠁⠀⢠⠏⣹⣿⣿⡆⠀⠀⠀⠀⢸⠀⣿⣿⣿⣷⠀⢸⣗⠯⡁⠀⠈⠻⣿⡾⢳⣦⡀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠘⣿⣿⡀⠀⢸⡀⣿⣿⣿⣿⠀⠀⠀⠀⠸⡀⢻⡫⣸⡿⠀⣼⣿⠂⢉⣔⠎⢠⠈⠻⡟⠏⠺⣦⡀⠀⠀⠀⠀ ⠀⣆⠀⠀⠘⡷⣿⣧⡀⠘⢧⠹⡟⢍⣾⠀⣶⣯⡵⠀⠳⠤⠽⠟⠁⣰⡿⡫⡾⠟⠁⢀⠇⠀⠀⠹⡦⢷⣿⣵⡀⠀⠀⠀ ⠀⠘⡀⠀⠠⠀⢯⣻⣷⣄⡈⠑⠒⠚⠁⠀⠀⠈⠀⠀⠀⠀⢀⡠⣚⣿⡯⠋⢀⠀⣰⣿⣿⣷⣦⡀⠸⣬⣿⣮⡫⡲⠀⠀ ⠀⠀⠱⡀⠀⠀⠈⠏⠿⠷⡿⣶⣦⣤⣤⣀⣀⣠⣤⣴⣲⡯⣿⣞⠟⣍⠀⢠⠐⠿⣿⣿⣿⣿⣿⣿⣦⣹⣿⣿⡿⣏⡧⠀ ⠀⠀⠀⠈⢦⡀⠠⣶⡼⡄⠦⣜⢙⠋⠙⠛⢛⡻⠛⢉⣠⡾⠊⣠⣤⠼⠓⠉⠀⠀⠈⡿⠛⠉⠙⠛⠿⢿⣿⣿⡎⡏⠀⠀ ⠀⠀⠀⠀⢀⣾⣷⣦⣉⣿⣷⣽⣷⣿⣷⣴⣿⣿⢶⣿⣯⢿⡿⢿⡄⠀⠀⠀⠀⠀⠀⢰⠀⢀⡤⠔⠦⣤⣾⣿⢋⠀⠀⠀ ⠀⠀⠀⣠⣿⣿⣿⣿⡏⠙⠏⢻⢿⣿⠟⡻⡿⢛⢛⣹⡦⠙⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠓⠛⠁⠐⠒⣼⠿⡭⠛⠁⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⡟⠐⢷⣳⠃⠚⣳⣯⣭⢴⠿⡛⠉⠐⠀⠈⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤⣴⡦⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⡇⢸⢹⣿⠰⠚⣳⣀⣀⣤⣄⠠⡄⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠈⠹⣿⣿⡶⠀⠀ ⠀⣿⣿⣿⠛⠉⠉⢃⠈⢞⠻⣤⣬⣽⣻⣾⣿⠿⠻⣤⢩⠀⡀⠁⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠱⢄⢢⠀⠀⢿⣿⣟⠗⠆ ⠸⣿⠟⠁⠀⠀⠀⠘⢳⡌⠈⠂⢺⣿⣟⣷⡧⣤⠀⣿⣟⠀⠉⡀⠘⠀⠈⠂⠀⠐⢺⡀⠀⠀⠀⠀⢃⣁⡼⣿⣿⣿⡼⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠹⡇⠀⢹⢛⠇⠻⡍⡙⢻⠺⢶⠄⡀⠀⠀⠀⠀⠀⠁⠂⠀⠤⠀⣰⣿⠿⣿⣽⣿⣾⡯⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⡆⣤⠼⠸⣡⢁⡘⠇⢄⠉⠻⢗⡤⡀⠀⠀⠀⠀⣐⠄⣼⣿⠟⣰⣿⠿⢁⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠁⢿⣾⣷⣾⡸⢷⡆⠈⠐⠀⠐⠈⢛⠗⣤⣀⠀⠉⠓⠺⣿⣿⣿⣻⣢⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⣼⢻⠻⣿⢷⣷⡦⢴⠂⢄⠂⠀⠈⠙⠷⣢⣄⡴⢻⣿⡿⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠀⠀⠀⠼⡹⣇⡤⣸⢘⡜⢡⠀⠣⠄⠀⠀⠀⠀⠀⣨⢿⣿⡿⠉⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣴⣿⣿⡾⣸⡕⡀⠀⠀⠀⠀⠨⠦⢀⣼⢻⡟⠁⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏⠹⠯⠊⠉⠀⠀⠀⠀⠀⠀⠀⡎⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀