⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠈⠁⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡠⠒⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⠛⠊⠊⠀⠀⢀⠀⠀⠀⠀⠀⢠⣠⠀⠀⠀⠀⡰⢅⡐⠦⣦⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⢠⣚⡞⠀⠀⠀⣐⣢⠱⣠⡀⢀⠀⠈⠀⠓⢌⡬⡊⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⡀⠀⠀⠀⠀⣰⣷⠏⢸⠇⡀⣵⢿⢁⣾⠯⢣⣔⢓⢌⢴⢀⠩⡏⠾⠀⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡎⠀⢀⠖⣵⣟⣿⡇⠀⠀⢳⣼⢯⣿⢾⡟⠁⢨⣽⠈⢆⠈⢈⣴⡁⠒⢀⢡⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢠⣾⠿⢿⡇⠀⣈⢔⣼⣻⣿⣀⣀⣀⡾⡿⡿⠊⠘⣿⣀⣼⣯⣯⣪⣤⢮⠪⠊⠂⠀⠺⢜⡗⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣻⠕⣋⢾⡿⠐⠑⢻⣧⡝⢯⢿⣯⢏⣻⣇⠀⠉⠀⣾⢿⣤⣼⠻⣟⢻⣷⠘⠦⢀⢀⠠⡀⠈⠪⡣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡯⠐⠞⣲⡾⠳⢢⣾⣿⠅⣴⡿⣞⢿⡾⣿⡄⠀⠈⣯⠿⣿⣹⣻⠧⠙⣿⣦⣔⠝⢝⡔⢕⢄⠀⡼⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣲⣪⣟⣤⣾⠟⣔⣄⣼⣽⣏⠀⠀⠙⠋⠁⠈⠉⠁⠀⠀⠀⠀⠋⠀⠁⠀⢈⣿⠟⣣⢀⠀⠁⠀⠀⢈⠷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣫⡾⠋⣽⢫⣻⣼⡖⠙⢻⣾⣙⡄⠀⠀⠀⠀⠀⣰⠀⠄⠀⣠⣄⠀⠀⠀⠀⠨⣟⡏⣷⣦⠞⡁⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠰⣿⢛⣿⢠⣿⠟⡽⣯⡣⠀⢸⢿⡿⣿⠀⠀⠀⠀⠀⠙⠋⠓⠚⠛⠁⠀⠀⠀⠀⢠⡟⢘⢉⢱⣷⢩⢲⡄⠀⢠⢃⠟⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⢷⣜⣷⣛⣤⠿⣹⠀⣻⣿⣧⠀⠀⠀⠀⣠⣶⣷⣿⣶⣤⠄⠀⠀⢀⣴⣿⢗⣧⢪⠛⣄⠇⠙⣢⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠉⠛⠸⣿⣥⣰⣻⢿⣔⡼⡨⢆⣿⣷⣿⣷⣄⠀⠀⠉⠙⠿⠾⠀⠀⠀⠀⣠⣾⣟⡿⢀⡉⡽⠦⣂⡀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⢀⠰⣶⣰⡿⣿⣿⣿⣺⣼⣽⣜⠁⠳⠙⣿⣾⡿⠑⠦⣀⠀⠀⠀⠀⢀⣠⠞⢻⣿⡜⢷⣧⣀⠑⠣⢭⣦⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣻⣿⣟⣽⣻⢿⣮⠻⠾⣷⣧⣐⢩⣿⡇⠁⠀⢌⠙⠲⠐⠚⠉⠀⠀⢹⣿⡿⣦⡹⠽⠇⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡻⠿⡆⡐⣿⡟⠛⠋⠀⠀⣀⣯⣽⢿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣗⢻⣮⡙⠷⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢂⠀⠂⠀⡈⠈⢻⣃⣤⣶⣿⣿⣿⣿⣿⠋⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣸⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠄⠀⢀⣄⣰⣤⣶⣾⣿⣿⣿⣿⣿⡟⣿⣷⠀⠙⣷⣤⡀⠀⠀⠀⠀⠀⣰⣿⠃⢿⣻⣽⣷⣿⣵⣿⠟⠷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀ ⣁⣠⣤⣾⣿⣿⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣴⡀⠘⡿⣶⣮⠁⠀⣠⡾⠏⠁⢰⣿⡿⣟⡯⣿⠟⠀⠀⠀⠀⠈⢹⢿⣪⠔⡤⣤⡀⠀ ⣿⣿⣾⢺⡯⡿⣸⣿⣿⣿⣿⣾⣿⣿⡟⢿⣻⣿⣿⠷⢒⣿⡮⣻⣦⣿⠿⡀⡀⣺⣿⡻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⣷⣾⣧⣿⣶⠯⡢ ⣯⣿⠟⡿⣿⢁⣿⣿⣿⣯⣿⣷⣿⡳⣿⣽⣿⣿⣿⠀⢺⣟⣿⣆⣿⢸⣿⣧⣾⣿⣿⣿⣿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢿⠿⣣⠀⠈ ⣿⣿⡾⢿⣿⣿⣿⢹⡗⠋⢩⣻⣿⣿⣿⣿⣿⢿⣿⣇⢺⢾⣿⣹⢻⣧⡀⣿⣯⣿⣿⣿⣿⣮⢹⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣼⠀⡇⠀⠀ ⣾⣿⠂⠸⣿⠟⡻⡿⢿⢢⣿⣿⣌⡿⣟⢿⣿⣯⣿⣿⣀⢹⣿⡷⢿⣧⡹⣿⣿⣿⣿⣻⢿⣽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀ ⣿⡏⣔⠅⡿⡐⢀⢳⠰⠹⣿⢿⣿⢿⣟⣯⣿⣿⣾⣿⣾⣽⣟⡷⣜⣿⣬⣿⣿⣿⢻⡯⣿⣿⠊⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀ ⣿⣧⣶⡶⡶⢂⠦⡞⣷⠱⣟⣾⣿⣿⡎⡜⣿⣿⣿⣿⣿⠾⣿⡓⣼⡿⢿⣿⣿⢯⣿⣼⣾⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀ ⣿⣿⣿⡶⡷⠧⢣⣷⣿⠿⣷⣿⣿⣿⣶⢴⠟⣿⣿⣿⣷⢻⣗⣵⢿⣧⠟⠻⣿⣿⠷⠤⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀ ⣿⣿⣿⣷⣷⣼⣿⣿⣿⡆⣿⣿⢿⣿⡟⢛⡜⣿⣿⣿⣿⣸⣿⣕⣽⣫⠏⢤⣻⡅⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢆⡄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣷⢾⡓⢿⣿⣿⣿⡻⣿⠟⣿⣜⠋⠀⢹⣿⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⣾⢥⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡶⡾⣚⣿⣟⣾⡿⣿⡶⣿⡿⠶⣶⣷⣿⡷⠶⠿⡶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠐⢷⡟⡏⠁⠀⠀