⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡛⠉⠉⠉⠉⠀⠀⠀⠀⠙⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠤⠤⠄⢄⣀⣀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠛⠙⠻⢄⣀⠀⠀⠀⠀⠀⠀⠀⢹⣂⣀⣀⣀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠤⠀⠂⠀⠀⠀⠯⠷⢦⣤⣀⠙⢦⣄⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⣬⠭⠿⢿⣦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡀⠀⠀⠀⠻⣿⣧⡀⠀⠀⠀⢀⡤⠟⠃⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠋⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣶⢷⡄⢣⣶⢤⣄⠀⠈⢫⡙⢆⣠⠞⠉⠀⠀⠰⠦⠴⠥⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠴⠊⠉⡩⠍⠉⠉⢉⣉⠛⠲⣄⠀⠀⠈⠳⠬⠷⠀⢀⢣⠘⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣀⣤⣴⠾⠒⠚⠛⠉⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠠⠖⠛⠉⡹⠋⠙⣓⣷⡤⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣠⠦⢴⠓⠋⠉⠁⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠿⢓⣚⡞⠿⠿⠿⠭⣉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⡴⠯⠷⠴⣿⠤⣤⣀⡀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡞⠃⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣶⡠⠤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⢠⣐⠤⠿⠒⠒⠚⠛⠃⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠰⠀⠀⢱⡀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠫⢉⢦⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠒⠀⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠄⠀⢸⡄⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠄⢀⢹⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠘⠳⣄⠈⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣸⠁⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢀⠠⡛⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠤⠖⠒⣒⡾⣧⠀⠀⠙⢿⣿⣈⡳⢄⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢀⠀⠂⠐⡽⠄⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⡀⣿⠃⠀⠀⠀⠀ ⢀⠤⠒⠉⠁⠀⠀⣠⣾⡥⠖⠻⣆⠰⣦⠀⠻⣦⡉⠓⠛⠤⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣒⣨⡶⠃⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣷⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⢔⠟⠁⠀⠀⡀⠀⠘⢷⡈⠻⢦⣜⢿⣶⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⡠⠊⠁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⣀⠙⣿⣷⣝⣶⣄⡘⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣀⣰⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⠙⠛⡗⠀⠀⠀⠀⠀⠀⢀⡞⠙⠶⣄⡙⢿⣛⠻⠿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⣿⡿⠉⠁⠈⠀⠈⢻⣾⣦⠦⣀⡀⢠⠄⠀⡞⡫⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⢠⣴⣦⠀⠀⢠⡟⠀⠀⠀⠈⠙⢲⣭⢳⡄⠀⠉⠛⣦⣤⡄⣠⣤⣤⣴⣴⣾⡝⡟⡏⣿⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣯⣿⣿⣽⣷⣿⣷⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠟⠒⠉⠀⣿⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠆⠀⠀⠀⠉⣉⡽⠿⠃⠘⠂⢷⣿⣷⠃⠀⠀⠀⠀⠀⣼⢟⢻⣿⠓⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣯⡽⢖⡀⢀⠀⠈⡠⣷⠃⠀⠀⠀⠀⠀⣸⣯⠽⢒⢳⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠋⠉⠀⠀⠻⡄⢀⢴⡼⠁⠀⠀⠀⠀⠀⣴⣷⡿⠿⡫⣽⢻⢛⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⡽⠁⠀⠀⠀⠀⠀⣴⣟⢯⣳⣼⣶⠿⠛⠋⠁⠈⠛⠢⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠉⠀⠀⠀⠀⠈⠙⠶⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢾⡟⠁⠀⠀⠀⠀⠀⣼⢣⡴⢯⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠶⣤⣤⠟⠒⠩⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⠉⢳⠞⠀⠀⠀⠀⠀⢀⣾⠳⢟⠡⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀ ⠀⠀⠀⠀⠀⠙⢾⠅⣻⣄⢀⣀⡀⠉⠙⠂⠀⠀⠀⠀⣀⣀⡤⠔⠊⠋⠉⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣠⣏⠀⠠⣠⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⡔⣸⠋⢈⠗⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⡴⠃⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓