⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣢⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠤⡶⠞⠙⡏⠉⠉⠹⠯⡭⢓⡲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⡟⠀⠈⠒⣺⠟⡱⢄⠀⢀⣀⡀⠀⠉⠢⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣵⡥⠔⠓⠒⠠⣞⢴⣫⣴⠚⣿⣏⠞⠑⠿⣺⣟⢶⣄⡈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⡼⠟⠡⠴⠶⠲⠤⠬⣆⣹⡿⣟⣫⡞⠀⠙⠳⣦⡙⢷⡵⣽⣷⣾⣤⣀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠋⠀⠀⠀⠀⢀⣀⣀⡤⣴⣖⡲⡒⢲⣏⠙⢲⣤⡙⢿⣆⠙⢾⣆⠀⠈⢗⠦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⣠⡴⡾⣹⠉⢱⢸⣧⠹⣏⠺⣮⣆⢻⣆⠀⠘⣟⢷⡻⣆⠈⠻⡄⠀⢹⣦⡈⠑⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⣠⡞⠁⢧⣿⣿⢼⠀⣿⢩⢣⣹⡤⠝⡿⡞⡟⡄⠀⠘⡤⢝⡽⡜⢷⡵⡑⢾⣿⣿⣤⡀⠑⠀⠀ ⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⣠⣎⢸⡟⠀⣸⣼⣏⣞⣇⢻⡀⢣⠛⣷⣠⡼⣿⡷⣶⡀⠀⢣⣄⣻⡱⠀⠹⣆⢀⠱⣟⣎⠉⠉⠁⠀ ⠀⠀⣠⠜⠁⠀⠀⠀⠀⢀⡔⢹⢸⡜⡇⡄⣿⣼⢷⣼⣽⢮⢧⠀⠻⠾⠋⣷⣿⣿⢸⡟⠁⢸⢣⣶⢸⣄⠀⠘⣆⠙⢞⢯⢧⠀⠀⠀ ⠀⡴⠃⠀⠀⠀⠀⠀⣠⠋⠀⠸⡸⣇⢱⣣⢿⣏⢸⢺⣿⠀⠙⠃⠀⠀⠀⠝⠫⠾⠗⠀⠀⠈⣺⣹⡸⠹⣦⠀⠸⣄⠸⣯⠫⢇⠀⠀ ⢰⠃⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⢣⣿⡄⣷⣷⣿⡬⠿⠾⠂⡄⠀⠀⠀⠀⠴⠾⠗⠀⠀⠀⠀⢙⣵⠇⣤⡹⡆⠘⣿⣇⢹⣿⣼⠀⠀ ⣿⠀⠀⠀⠀⠀⠋⠳⣄⠀⠀⠀⠀⠹⣷⣹⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⡸⣿⣻⢨⡿⣾⣼⡿⣿⠀⠀ ⠈⠳⣄⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⢨⣿⠿⣿⡆⠀⠀⠀⠰⠤⠔⠒⠉⠀⠀⠀⢀⡄⣼⣿⣿⣿⣿⣇⢹⢙⣼⠁⠈⡿⢂⠏⠀⠀ ⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠈⠓⣶⣞⣿⢸⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠏⢸⣿⣿⣿⣿⣷⠹⡾⠸⠃⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠘⡆⢹⣾⣿⣿⣿⣿⣿⣶⣤⣀⣀⣤⣾⡿⠁⢀⣘⣿⡝⢿⣿⢯⡣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠇⢧⠘⡽⠑⠙⣟⠻⣯⢟⠛⠛⡿⡿⠋⢀⢿⣯⢉⠍⠉⠓⣿⠈⠳⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⠷⣤⡀⢸⠀⡇⠀⠣⢸⡸⠙⠈⡄⠀⣻⠀⠀⣜⠇⡇⠘⠀⠀⢀⣱⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⣒⠀⠙⣻⢸⢣⠀⢀⠴⠁⢸⠀⣔⡾⢃⡤⢪⠏⢰⠁⢀⣤⠒⣹⠛⠁⠉⠉⠙⢶⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠉⢂⡇⡜⣿⠒⠯⠒⣹⣿⡄⡟⡴⠋⣠⠏⣠⣿⡶⢹⢃⡾⡁⠀⢀⢦⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣠⣾⡞⣈⠁⢐⠎⣰⣿⡟⢹⡟⡡⠞⣡⡾⢋⠞⢀⠇⡾⡹⠀⢠⠏⡎⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠺⣷⠋⢰⢿⡿⢁⣞⠏⢀⣴⠏⡠⠋⠀⡾⢠⠇⡇⢀⠏⡸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⣸⣸⡇⡾⣠⣶⢟⣡⠎⠀⠀⢰⡇⢸⢸⠁⠈⢀⠇⠀⠀⣰⠀⠀⢱⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⣟⣿⣿⠿⣫⠴⠋⠀⠀⠀⠀⢺⠀⠼⢸⠀⠀⡼⠀⠀⠀⢿⡀⠀⣸⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠻⡨⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⣆⢹⠘⠆⢰⡇⠀⠀⠀⠈⢣⡀⢿⡤⠟⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣷⣥⢸⠃⠀⣠⠴⢒⣉⣭⣭⣴⣾⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢿⢸⡠⢊⣡⠖⠉⠀⢿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡎⣴⠏⠁⠐⠀⠀⢸⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣄⠀⠀⢆⢳⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⡟⢸⣿⡄⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠑⠂⠀⠉⠳⣦⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣾⠃⠀⠀⢷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠘⣿⠏⠀⠀⠀⠈⣧⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠘⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁