⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣁⠀⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⢄⡀⠀⠀⠀⠀⠀⠀⠦⠂⢸⠰⠈⠢⠦⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠒⠃⠀⣀⢠⣡⠆⡄⠊⣭⠰⢋⠙⡠⠸⣰⡀⡠⠀⠮⠥⠣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢣⠇⣠⢼⠼⣟⠣⠀⢠⢀⠄⠼⠛⡿⢇⣇⡠⠠⡤⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣁⣿⣾⣽⣷⡶⢞⠨⢷⢶⣾⣿⣻⡅⠑⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡜⣉⠫⡒⣢⠑⢌⠳⡀⢣⠹⡄⢉⢫⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⠟⡘⠶⣗⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⣪⣦⣾⣾⣶⣿⣿⣷⣶⣷⣯⣌⣎⢇⠀⠀⠀⠀⠀⠀⠀⣀⢔⣷⠗⠘⢿⣻⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⢴⣿⣿⣷⡰⡘⡔⡼⣁⠇⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢎⡡⡆⡌⡔⣠⣿⣿⣿⠢⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠤⣿⣿⣿⣿⣷⣔⣩⣗⠛⠶⠞⠁⠀⠀⢀⢾⣽⣿⣿⣿⠿⠛⠛⠛⠒⠛⠛⠛⠿⣿⣿⣿⡾⣆⠀⠀⠀⠈⠓⢚⢛⠑⣊⣴⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣦⣷⣀⢀⡠⣔⣾⣟⣾⣿⣿⣭⣶⣿⣿⣿⣧⠰⣾⣿⣿⣿⣶⣭⣿⣿⣞⣯⣦⠤⣀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡤⢄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⢶⣟⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡠⡄⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⠇⠀⡽⡸⡿⣿⣿⣿⣿⣿⡽⢿⣷⠘⠟⠃⣾⣿⣿⣿⣧⣤⣤⣿⣿⣿⠀⣿⣿⣧⣤⣤⣿⣿⣿⣿⡇⠛⢣⢸⢿⡟⣽⡿⣿⣿⣿⣿⡟⠀⢭⠀⠻⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⡞⠋⠀⣠⡣⠁⠁⡿⣿⢿⣯⣛⢗⣮⡹⠶⣄⠀⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⠀⣿⣿⡟⠛⠛⣿⣿⣿⣿⡇⢀⠼⣎⢮⣱⣛⣕⣻⢿⣟⡏⠁⠀⢞⡀⠀⠉⠳⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡿⣝⢮⡽⣛⣛⠟⠛⠿⣖⣻⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⠀⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣘⡷⠞⢛⣛⠛⢿⣹⢮⡝⡇⠀⠀⠈⠺⢢⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⢴⠍⠀⠀⠀⠀⣠⢷⣫⢷⡹⢦⠃⠀⠔⠀⣜⣾⣿⣿⣿⣿⣇⣀⣠⣿⣿⣿⠀⣿⣿⣇⣤⣄⣿⣿⣿⣿⣏⣷⡆⠈⢄⠈⠫⢎⣻⣧⢻⡹⣄⠀⠀⠀⠀⠱⣢⠀⠀⠀⠀ ⠀⠀⣜⡌⠀⠀⠀⣠⡴⣏⡷⣹⡮⠃⡀⠄⠁⠀⠀⠈⠙⢿⣿⣿⣿⡟⠛⠛⣿⣿⣿⠀⣿⣿⡟⠛⠛⣿⣿⣿⣿⡿⠋⠂⠀⠀⠁⠀⠌⠢⢝⢯⣳⣭⢳⣄⡀⠀⠀⢡⡆⠀⠀⠀ ⠀⠀⠩⣣⢀⣠⢯⡗⣯⣳⢽⠏⣠⣿⡿⣶⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣿⣿⣿⠀⣿⣿⣷⣶⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠠⣿⣞⡿⣆⠫⡾⣜⡷⣺⠽⣄⢠⣣⠃⠀⠀⠀ ⠀⠀⠀⠑⠊⠽⣾⡹⢧⣏⣿⣶⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⣾⡿⣿⣷⣯⡳⣽⣣⢿⠇⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⡻⣽⢺⠟⠉⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⡾⣿⡀⠀⠈⠱⣟⡵⣫⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⢷⡻⡼⠋⠀⠀⠀⠈⠛⣿⣶⣶⣶⣆⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣴⣶⣶⡾⣽⡋⠀⠀⠀⠀⠙⢾⣱⢻⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢣⡟⡞⠉⠀⠀⠀⡔⠀⠀⠈⣭⣥⡍⣥⣥⡄⠀⠀⠂⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠈⠀⢁⢈⠉⠉⠉⠉⠉⠁⠁⠈⢀⠀⠀⠀⠉⠑⡞⣸⠂⠀⠀⠀⠀ ⠀⣴⠒⠈⣏⣮⣀⣀⡀⠀⡐⠀⠀⡀⢸⣇⣿⠇⡇⡿⢀⠀⡀⢀⢂⠀⠀⠈⠛⠻⢿⣿⠿⠛⠉⠀⠀⢀⠌⠀⠀⣿⣚⡯⣗⣿⣿⣿⡏⡞⠀⠀⢢⠀⣠⣀⣠⠟⡵⠀⠐⢤⢀⠀ ⡇⢳⡀⠐⠛⣦⣻⠿⠟⠒⠒⠲⠒⢒⠀⠂⠐⠂⠒⠰⢖⣖⠲⠒⠒⠗⠒⠒⠒⠒⢒⠒⠒⠒⠒⠒⠒⢊⠀⠉⠛⣛⡮⠁⠉⠀⠉⠈⠉⢉⠈⠨⠒⠛⠻⠿⠯⡝⠛⠀⢀⣸⠇⠀ ⠁⠀⠈⠀⠅⠔⠀⠀⠀⠀⠈⠀⠐⠀⢁⠢⢀⠀⠀⠀⠀⣸⠆⣠⠄⠀⠀⠀⠀⡀⣸⣼⡇⠀⠀⠀⠀⠀⢢⡆⠸⣏⠀⠀⠀⠀⡀⠔⡀⠔⠀⠀⠁⠀⠀⠀⠐⠀⢁⡀⠉⢁⠐⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠈⠁⣀⡈⠁⠐⠉⠀⠈⠀⠀⠁⠀⠁⠀⠀⠁⠉⠀⠀⠀⠀⠑⠀⢈⣁⣀⠀⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀