⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠻⢿⣏⡿⢓⣶⠦⣤⣀⠀⠀⠀⠀⠀⣰⡆⢀⣴⡇⣀⣴⣦⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⢿⣥⡶⢋⣩⡿⢦⣀⣀⣼⣻⣷⣿⣾⣿⣿⣿⣿⣟⣷⣶⣶⣀⡴⣶⢂⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣏⣁⡴⢛⡽⢛⡿⠞⣿⣾⣿⡯⣯⣟⢷⣥⣿⣿⣯⣥⢦⡿⣫⣼⢀⣠⡄⠀⢀⣀⣀⣀⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣲⣿⣤⣏⣀⣼⡃⠀⠀⠉⠓⠮⢽⣿⣿⣻⡉⢹⡟⢷⡯⢿⡿⣷⠷⣾⠛⣏⠉⣇⠸⡇⣹⣀⣧⣽⠿⠟⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣟⣉⣉⣥⡞⣫⣛⢮⣿⠿⢿⡿⠷⣶⣶⣤⡈⣿⣇⠀⣇⠘⡇⠘⡇⢸⠀⢸⠀⢸⣄⡽⠞⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣀⡶⠶⣦⣿⡷⠟⣻⣝⣿⣷⣹⢟⢽⣿⣿⣿⢯⡙⠋⠉⢹⣦⣿⣤⣧⣴⣧⣾⣦⣼⣷⣿⠟⠻⡟⠉⣙⠟⢒⡶⣦⣀⡀⠀⠀⠀ ⠀⠀⠀⢰⠦⣿⠉⡏⣏⡹⣷⡿⠿⣶⣄⣹⣬⣭⣭⣽⣿⠻⣿⣿⣿⠤⠽⢿⠒⠿⣤⣉⠻⣿⠈⠉⠉⣽⠟⢋⡤⢠⡞⠁⠰⠃⣰⠎⣽⣨⠍⣷⡀⠀⠀ ⠀⠀⣀⣿⡼⣟⣦⢹⢿⣿⣧⠶⠚⢷⡿⢿⡿⠿⢿⡿⠿⠶⠛⠛⠛⠛⠶⣶⣀⠀⠀⢹⡆⠀⠀⢀⣰⠇⣰⠀⢰⠇⢀⡾⠁⡀⠋⣤⠇⢰⠇⢸⢿⡄⠀ ⠀⠀⣿⣼⣿⡝⣍⣞⣿⠀⠙⠦⣤⣈⣁⣈⣁⣤⡤⠷⠖⠚⠋⠉⠉⠙⠓⠓⠈⠙⠃⢸⢇⠀⢀⣾⡿⢶⣄⣀⣙⣀⣘⣅⠸⠃⡼⠃⡤⢛⡴⣈⡶⢻⠀ ⠀⢸⣿⣸⢦⠷⣭⢨⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡴⠿⠛⢁⣾⡟⠀⠀⠀⠉⠉⠉⠉⢹⡄⣴⠀⠸⠃⣈⢁⣏⡆⣸⡇ ⠀⢈⣟⣧⣜⡟⣯⢳⢹⡹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠉⠀⢀⣀⣤⣴⣾⠿⠤⠤⣤⣀⣀⡀⢀⣀⣼⠇⡀⣰⠆⠰⢋⣈⡼⢰⣻⡇ ⠀⣸⡿⣮⡷⣙⣚⣟⠃⢭⢹⣿⡲⠶⠤⢤⣤⣤⣴⣶⣶⣿⣿⣧⣀⠀⠀⣠⣶⣿⣿⣿⣿⡿⢻⣿⡟⡿⢷⡭⣿⠯⠵⣃⣞⣵⣱⠀⡤⠉⠛⠁⢞⣽⣇ ⠀⣿⠷⠬⣭⣍⣉⡉⠙⠛⠛⠻⣿⣦⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡇⠀⠉⠛⠶⠿⠴⠶⠛⠿⠾⢦⣬⠧⠾⣴⠛⠛⠿⠋⢹⣿ ⢸⣿⣤⣤⣀⣤⡭⠿⠿⠛⠀⠀⠈⠻⢿⣶⣤⣌⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡤⠶⠚⢹⣿ ⠀⣿⣇⣀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢿⣿⣿⣿⠿⢿⣿⣿⣿⡿⠿⠟⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠯⠭⢤⣤⣠⣤⣀⣀⣀⣼⡟ ⠀⠸⣷⣬⠭⠤⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠃ ⠀⠀⠙⣿⣗⣶⣒⣿⠇⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢀⣀⣤⣽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠺⠶⣶⣒⠲⠶⠒⠒⠒⢶⣿⠇⠀ ⠀⠀⠀⠈⠻⣿⣿⣤⣤⣤⣤⣤⣤⣴⣾⠿⢋⣴⣿⠿⣛⣫⣭⣽⣶⣶⠿⣿⣿⣶⣶⣶⣶⣬⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⣤⣿⠏⠀⠀ ⠀⢀⣠⣴⣾⠟⠁⠉⠉⠉⢉⣉⣙⣿⣶⣴⣿⠋⠀⣾⣿⠛⢉⣁⣤⣶⣿⣟⣻⣿⣆⣤⣤⣭⣽⣿⣿⣆⠀⠀⠀⠀⠘⠿⣿⡋⠙⠛⠛⢛⣿⠋⠀⠀⠀ ⢸⣿⠋⠁⣾⣧⣿⠃⠀⣾⣟⣻⣿⡿⢀⣹⣧⣀⠀⠙⠛⢛⡿⠛⢩⣵⡿⣿⣯⣁⢿⣿⣯⣭⢉⣩⣬⣿⣷⣄⡀⠀⠀⠀⠀⠉⠉⠛⣶⡿⠃⠀⠀⠀⠀ ⠈⠛⠿⠿⠿⢿⣿⣶⣤⣭⣿⡿⠿⠿⠟⠛⠙⠛⠿⠿⠿⢿⣿⠀⣀⡙⣿⣤⣭⣿⣷⠀⣼⡿⠟⣋⣩⣀⣈⡙⠿⣷⣦⣤⣤⣤⣤⣾⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣿⠿⠿⠏⠉⠉⠁⠀⠙⢿⣶⣿⣿⣿⡿⣃⣾⣧⣾⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣷⠆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠷⣿⣟⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣀⣈⣿⣾⣿⠶⠾⠿⠶⠶⣶⣶⣶⣦⣶⡿⠋⠁⠉⠻⣷⣦⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢋⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⣀⣤⣤⡀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠙⣿⣆⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀