⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⣷⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⢟⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢵⣿⢯⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⢠⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢮⡵⢦⡶⠦⠭⠾⠷⢻⢷⣾⣿⣿⣿⣿⣿⡻⠽⠷⢬⡴⡶⠔⣊⣀⣀⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢬⡖⡶⣖⠆⠋⣌⢣⣛⢶⡲⢧⣦⣈⠻⢿⠟⣉⣠⢤⡴⣎⣿⡽⣧⢟⢞⡷⣎⡷⣑⢅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⢢⡕⢯⣞⡗⠁⢀⡞⣥⢳⡹⢮⣝⣿⣺⣭⣟⡶⣘⢲⣯⢿⣽⣯⢿⣽⣻⣞⢮⡹⣯⢷⣫⢖⡀⠑⡀⠀⠀⠀ ⠀⠀⢠⠀⠀⡲⢭⣻⠎⠀⢀⢯⡜⣶⣩⣝⣳⣞⣷⣻⢾⣽⡳⣌⢷⣯⢿⡽⣯⢿⣞⡷⣯⡗⡧⠹⣟⣷⣫⢖⡀⠐⠄⠀⠀ ⠀⢀⠁⠀⠰⣝⣳⡏⠀⠀⣼⣣⣟⣶⢳⢮⣷⣻⢾⡽⣿⣻⠷⣭⣟⡾⣯⣟⣿⣻⢾⣟⣷⣻⢵⠂⢹⣷⣻⢮⡕⢂⠘⡀⠀ ⠀⠎⠀⠠⣹⢎⡿⠀⠀⠰⣧⣟⡾⣿⠋⣷⢯⣟⣯⣿⣿⣿⢻⡼⣯⣟⣷⢿⣳⡿⠻⣟⣾⡽⣏⡎⠄⢻⣿⢯⡽⡒⠀⠐⠀ ⢠⠀⠀⠰⣭⣟⡇⠀⠀⣜⣳⢾⣟⠅⠀⠘⢿⣞⣯⣿⣿⣿⣳⣟⣷⣻⡾⣿⠟⠁⠀⢹⡷⣿⡽⢾⡂⠈⣿⣯⢷⡡⠃⠀⡄ ⡈⠀⠀⡱⢯⣾⠃⠀⠀⠴⣫⠿⠎⡀⡀⠀⠀⠻⣿⡿⣿⣿⣳⣞⣷⣻⡽⠋⠀⠀⣀⠀⠿⢷⣻⣏⡖⠀⢹⡾⣧⢃⠄⠀⣡ ⠇⠀⠀⣝⣯⢿⡁⠀⢠⢫⣽⣻⢶⣶⣳⢯⡷⣶⣾⣿⣟⡿⣳⣟⡾⣽⣷⣶⢯⣿⡶⣿⢿⣟⣷⣻⡼⠀⠘⣿⣳⢏⠄⠀⠰ ⡀⠀⡸⣜⡾⣿⠀⢀⠦⣳⠾⣽⣻⢶⢯⡿⣽⣳⣟⡾⡿⠁⠱⣯⢿⣽⣳⣯⣿⣳⣟⣯⡿⣞⣷⣻⡼⡁⠀⣿⣻⢞⡂⢀⠸ ⡇⢠⠱⣞⡽⣿⡀⢌⠞⣵⡻⣷⢯⣯⢟⣽⣳⣯⢿⡽⢁⢀⡀⢙⡿⣾⣽⢿⣟⡷⣯⡷⣟⡿⡾⣵⢻⡄⠀⣿⡽⣮⠱⠄⠼ ⢰⠀⡟⡼⣽⣻⡆⢌⡻⣖⡿⣽⣻⣼⣻⣞⡷⣯⢿⣿⣻⢯⡿⣟⣿⣯⢿⡿⣽⣻⢷⣻⢯⣿⣽⢯⠷⣌⠰⣿⣽⢣⡝⣌⢲ ⠀⣋⠼⣳⡝⣷⡏⣔⡹⡽⣿⣗⢻⢶⣛⡾⣽⢯⣟⣾⣽⣻⡽⣯⢿⡽⣯⣟⡷⣯⣟⡏⢫⣿⢯⣟⡽⢢⣱⡿⣞⡳⡜⡤⠇ ⠀⠱⢎⢷⣹⢯⣿⡆⡽⣳⡽⣾⣻⠏⢿⠿⠙⡛⠚⠓⢯⣿⡽⡏⠛⠙⠓⠋⠽⡷⢛⣷⡿⣯⣟⣾⡹⢥⣺⢿⣝⣳⡹⡜⠀ ⠀⠀⠪⡗⣯⣟⡾⣷⢱⢳⣽⣳⢯⡿⣷⣄⣴⡿⣦⠂⠈⠁⠉⠓⠰⣳⡿⣄⣠⣾⣟⣯⣟⣷⣻⢞⡧⣳⣿⣻⢾⣱⢳⠁⠀ ⠀⠀⠀⠙⣶⣯⣿⣽⣧⠛⣶⣯⣿⣽⢳⣯⣷⣿⣽⣷⢻⣶⣶⣶⣿⣿⣽⢻⣯⣷⢻⣾⣽⡞⣿⡏⣶⣿⣾⣽⢳⣯⠁⠀⠀ ⠀⠀⠀⠀⠑⣟⣾⣳⢿⣯⣗⠿⣾⣽⣻⣾⣻⢾⡽⣯⢿⣞⣷⣻⣞⡷⣯⡿⣾⣽⣻⣞⡿⣽⣳⣝⣾⢷⣯⣟⡷⣁⠀⠀⠀ ⠀⠀⠀⠠⠹⣜⡷⣿⣿⣾⣽⣟⡷⣯⣷⢿⡽⣯⢿⣽⣟⣾⢷⣻⣾⣻⢷⣟⣷⣯⡷⣿⣽⣳⣿⣾⣯⣿⣾⡿⡵⣃⠆⠀⠀ ⠀⠀⠀⠀⠁⠈⠘⠍⠻⡟⣿⢿⣿⣿⣾⣿⣽⣟⣯⣷⣿⣯⣿⣷⣿⣿⣿⣿⣾⣷⣿⣷⣿⣿⡿⡿⢟⠯⠓⠉⠂⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠩⠛⠽⣛⠿⢿⠿⡿⣿⢿⡿⣿⢿⢿⠻⣟⠻⠝⠫⠑⠃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀