⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢖⡒⠠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣚⡕⠊⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠑⠦⣈⢻⣙⠶⠒⠋⠉⠁⠀⠀⠀⠉⠙⠲⠖⠡⢺⡃⠀⠀⢀⠔⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⣠⠴⣲⠞⠉⠀⠀⢀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⣠⣟⡏⡑⠚⠉⣆⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠻⣤⠎⣁⡀⠤⡒⠒⠺⠶⣤⣀⡀⠀⠀⠀⠀⠀⠰⣋⠠⠀⠁⠀⠀⢩⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣞⡵⠞⠉⣔⣩⣤⣀⡀⠀⠀⠉⠛⢷⣤⡀⠀⠀⠀⠈⢳⠂⠀⢠⣀⢑⡆⡘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⢠⡴⠛⡡⠊⠉⠉⠙⠛⠢⣄⡀⠀⠈⠺⣖⣄⠀⠀⢸⡇⣠⢤⡋⣫⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⣣⣾⡏⠀⢠⢃⡠⢄⡀⠀⠀⠀⠀⡟⠲⣄⠀⠀⠓⣕⣄⣀⣽⣶⡟⠒⠏⠛⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠏⢸⣀⡴⡞⢡⠀⠀⢀⠙⠢⣄⢀⠃⣸⡈⢻⣄⣴⣾⣿⣟⣹⣏⢀⣤⢄⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣼⡿⣆⢸⡅⢠⣧⢠⠀⠀⡞⠀⠀⠀⡟⢢⠯⣷⡘⣭⠿⡟⠀⠹⣽⣡⣾⡾⠺⢶⢢⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⡟⢩⠏⢾⢧⣸⣘⡿⠤⠤⠽⠄⠀⢼⣡⠯⠀⠈⠳⣿⠀⠘⣆⠀⠘⣧⣊⣷⣤⣝⣫⠀⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣼⡿⠃⡄⢸⣿⢛⣿⣿⡆⠀⠀⠀⠀⠀⢾⣿⣿⣷⣦⣹⢦⣀⣘⣇⠀⠘⡞⢿⠜⠈⡏⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⣟⡇⠀⢧⢸⢹⢸⡋⠙⡇⠀⠀⠀⠀⠀⡿⠛⢶⡇⠙⣿⠖⣓⣾⣹⣇⠀⠘⡶⡄⠀⠘⠤⠬⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⡇⡇⠀⢸⣽⡼⠀⠽⠭⠃⠀⢀⡀⠀⣀⣷⣉⣢⡃⣰⣥⡾⠋⢠⡟⢹⡆⠀⠘⣴⡀⠀⠀⠀⣹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈⢿⡿⣄⠀⠙⢿⣄⠀⡠⣤⠴⢿⢿⠐⠋⢿⣽⡿⠚⢭⣁⠄⡼⣼⣷⣿⣟⡤⠤⢤⠃⡀⠤⣴⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣽⣿⣤⠄⣈⡿⣿⡟⠁⠀⠀⠱⣤⣴⣿⡩⠤⠔⢒⣲⣾⣿⣿⣟⣁⣀⣤⡶⠟⢉⡡⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⢭⡽⡿⠉⠀⠀⠈⠳⣶⠤⣸⡿⢻⣽⣫⠟⣛⣯⣉⠛⢿⠉⠓⠦⣭⠥⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⣴⠋⡆⠀⠀⠀⠀⠈⠷⣿⡇⠈⣻⡷⠛⠉⠀⠉⠻⣷⡱⣄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⠀⠀⠀⢀⣠⣾⠻⣾⠋⠀⡄⣴⡿⣷⡀⢡⢹⢾⢧⡀⠀⠀⠀⠀⠀⠀⢀⢶⣟⠄⠀⠈⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⡴⣋⣼⣽⣿⣟⣠⢲⣟⣿⣤⡿⡽⠀⡈⡇⠑⢝⢦⠀⠀⠀⠀⠀⡏⠙⢬⠗⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⣀⡀⢸⡵⣟⣽⣇⡿⣡⠃⠀⠉⠁⠘⠛⠃⠀⣷⠟⠆⠀⠙⢧⠀⠀⠀⠀⡇⠀⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡗⢊⡠⡏⠈⣿⡟⠁⣀⣀⠀⠀⠀⠀⠀⢀⡞⠀⠘⡄⠀⡜⠀⠀⠀⠀⡇⠀⢿⠀⠀⠀⠀ ⢰⠳⣦⣄⣀⣠⠤⠴⠻⣏⣧⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⢸⠇⠀⣿⣿⠘⠀⠀⠉⠒⠤⣄⡠⢾⢧⢀⣠⢴⠈⢣⠀⠀⠀⠀⡧⠀⢸⠀⠀⠀⠀ ⢸⣀⠞⠈⣠⡀⠀⠀⣤⡄⠙⢆⣀⠀⠀⠀⠀⠀⢱⡀⣤⣼⠀⢰⣿⣿⣿⠛⠁⠐⠲⠂⠾⣴⠛⠉⠡⣀⣨⣷⡿⠃⠀⠀⣰⠃⠀⡾⠀⠀⠀⠀ ⠀⡿⠀⣘⠷⠃⢰⣦⠙⠙⢀⢬⠧⠀⠀⠀⠀⠀⠸⣏⠁⡏⠉⢺⣿⢻⢹⣤⣀⠀⢀⣀⣼⠧⣤⣶⣯⠟⣻⡧⣤⠤⠔⠚⠁⢀⡜⠁⠀⠀⠀⠀ ⠀⣻⣀⡉⣤⢀⣀⢥⣴⣊⣧⡞⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⣶⠼⠿⢿⣿⡿⣿⣟⠛⠛⠋⠉⣀⣠⠴⠾⢁⣰⣀⣀⡀⠤⠖⠉⠀⠀⠀⠀⠀⠀ ⢸⣹⣉⡟⣿⢭⣿⣩⣷⣽⣿⢷⠤⡀⠀⠀⠀⠀⠀⠀⠀⢰⣉⣩⢿⠥⣀⡿⢿⢾⣩⣭⣉⣿⣋⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⠾⢧⡉⠻⡽⠁⠻⡟⢁⣞⡤⠗⠂⠀⠀⠀⠀⣠⠤⠼⣯⣟⢉⣑⡶⣋⣿⠏⢁⣙⡼⠿⢛⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠒⠤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⠦⠛⠉⠉⠉⠋⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⣙⣿⣧⣿⣿⣹⣷⣶⣧⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀