Kanye Dot Art

⠀⠀⢀⣠⣶⣶⣒⣢⡀⠀⠀⠀⢀⣀⣠⠤⢤⠤⣤⣀⡀⠀⠀⠀⢀⢴⣲⣖⡢⢄⠀⠀⠀ ⠀⢠⣾⡟⠁⠀⠀⠙⢿⢦⣖⣼⡳⣟⢿⡻⣝⢿⡹⣟⢦⣽⡆⢴⣷⠋⠀⠀⠙⢦⣳⡄⠀ ⠀⢽⢿⠀⠀⠀⠀⣠⣼⢿⣹⢲⡽⣚⡧⣟⢮⣏⢷⡭⢷⣎⢿⣻⢧⣀⠀⠀⠀⢈⣏⡷⠀ ⠀⠈⢻⣳⡤⣤⣾⣏⢷⣫⢞⣧⢻⡵⣻⢼⡳⣞⡽⣚⡷⢮⢷⣹⣎⢿⣷⣄⣤⣺⠟⠁⠀ ⠀⠀⠀⣰⣻⡿⣵⣺⠧⠿⣾⣜⣳⢽⣣⢯⣳⡝⣾⡹⣞⣽⡮⠷⢮⣟⣬⡷⣿⡅⠀⠀⠀ ⠀⠀⢠⣿⢯⣳⠟⢁⣴⣶⣮⢿⡝⣮⡳⣏⣶⣛⢶⡻⣼⢋⣒⣦⣄⠘⢷⡽⣺⡝⡄⠀⠀ ⠀⣰⢣⣏⣯⠏⢀⡎⠀⣿⣿⡆⣿⢧⡻⡵⢮⣝⢾⣹⡏⢸⡿⣿⣿⣃⠈⢷⣷⣻⡽⡄⠀ ⢠⣿⣟⣾⡏⠀⣾⣄⣼⣿⣽⠀⣿⢧⡻⣝⢯⡞⣧⢿⡇⠘⣿⡟⢿⣿⡆⠈⣷⣹⢿⣧⠀ ⣸⣿⣏⣿⠃⠀⣿⣿⠟⣿⠏⢠⣿⡞⣧⢟⡼⣳⡝⡾⣷⠀⢻⣧⣸⢿⡇⠀⢹⣟⠾⣿⡆ ⡿⣷⣏⣿⡇⠀⠹⡿⠶⠃⢀⣾⢳⡻⣼⣯⣗⣧⣟⡵⣻⣆⠀⠙⠿⠼⠃⠀⣼⣟⡻⡯⡇ ⡧⣷⡞⣽⢻⣦⣄⣀⣀⣠⣾⡯⠗⠉⣵⣾⣿⣿⡍⠙⠷⣯⢧⣄⣀⣀⣠⢾⡟⣼⢳⢿⡇ ⣷⣿⡝⣮⢷⡹⣎⠿⣽⡿⠋⠀⠀⠀⠉⠛⠛⠛⠁⠀⠀⠈⠻⣭⢿⡹⣏⠿⣜⢯⣻⣾⡇ ⠸⣽⣹⣎⢷⣫⡝⣯⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡗⣯⢻⡝⡾⣽⡟⠃ ⠀⠸⠽⣮⣳⣣⢟⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⡜⣧⡿⡽⠏⠀⠀ ⠀⠀⠀⠙⠣⣟⡮⡽⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡻⣙⠽⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠚⠬⠯⠷⠶⣒⣠⠤⢤⣤⣒⡶⠶⠿⠽⠚⠒⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠦⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⠎⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⠟⠈⠀⠤⠤⠤⠤⠒⠒⠉⠈⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠉⠒⠒⠔⠤⠤⠤⠢⠐⡿⣴⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡉⣾⠤⠤⠤⠤⠤⠠⠒⠙⡈⢄⠳⠈⠀⡄⣧⠸⠀⠋⠴⣀⠁⠚⠔⠤⠤⠤⠤⠤⡶⢻⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⠴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠢⣍⠹⠀⣸⠀⡜⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠢⠈⠀⠀⠀⠀ ⠀⠀⠃⡴⢀⠀⠁⠉⠁⠉⠉⠉⡈⣀⣀⠤⠤⠒⠑⠈⡀⣣⠸⠀⡟⣴⠀⠁⠊⠔⠤⡠⣀⠀⠋⠛⠉⠉⠉⠉⠀⠀⡀⠣⠈⠀⠀ ⠀⠏⣠⠀⠋⡴⣀⠉⠉⠀⠀⡀⣦⠹⠀⠀⠀⠀⠀⡀⠦⠘⢣⠁⣸⠋⡴⢀⠀⠀⠀⠀⠃⡾⣤⢀⠀⠀⠉⠈⣄⢧⠈⠀⢧⠈⠀ ⠁⢸⡀⠀⢠⠀⡿⣭⣮⢾⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⡀⡷⡟⣴⢀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⡿⣿⣍⠸⠀⢿⡀⠰⢻⠀ ⡇⠠⠀⠀⠁⠀⣄⢲⡐⢀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⠀⠀⠀⢄⠲⠤⠀⠀⢸⠀⠀⣷⠸ ⡇⠀⠀⠀⡀⠀⠀⠅⣉⢍⠐⠃⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠈⠗⣉⢍⠈⠀⠀⠀⠀⠀⡇⢸ ⡇⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⢀⠀⠀⠀⠀⠀⡇⢀ ⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠀ ⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡰⠀⠀ ⠀⠀⠀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀ ⠀⠀⠀⠀⡀⢦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡃⢦⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣤⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⣄⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠴⢀⠀⠀⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠹⠀⠀⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠀⠎⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠦⢝⠀⢀⠀⠀⠀⠁⠉⠛⠚⠔⠤⠧⣠⡀⣄⠼⠤⠢⠓⠙⠉⠈⠀⠀⠀⡀⠡⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠤⠠⣀⢀⠋⠟⣸⢦⠘⠀⠀⠀⠀⠀⠇⢤⣻⠙⠀⡀⣀⢄⠤⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡿⣿⣿⠀⠁⢺⡴⣤⣤⢦⠓⡟⠀⣧⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⡀⣄⣧⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣦⣿⣿⣿⢸⠀⠀⠀⠀⠢⠞⠀⠀⠀⠀⡀⣿⣿⣿⣼⣷⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠛⣿⣿⣿⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⣿⣿⣿⠋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣷⣿⣿⢯⠭⠿⠭⡚⣠⣀⢦⠽⠯⠽⠿⣿⣿⣾⣷⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⣿⣿⢻⠉⣀⣀⠀⠀⠀⠀⡀⡀⣉⢊⣿⣿⢻⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⠻⠛⠛⠿⣿⣹⣿⣿⣿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⡏⣿⣿⣿⣿⣾⢠⡄⣿⣿⣿⣿⣿⢿⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠁⣿⣿⣿⣽⣅⣭⠚⠓⣹⣬⣧⣿⣿⣿⢹⠀⠄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠾⠤⣿⣿⣿⣿⢠⠀⠀⣀⣀⢀⠀⡀⣷⣿⣿⣿⢼⠦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⢽⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⢸⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠛⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢸⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣏⢹⣙⢯⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⠻⡍⢎⠥⡙⣌⢣⡙⣌⢣⡙⢬⡑⢎⡼⣹⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣟⣿⣻⣟⣿⣻⣟⡿⣟⣿⣻⣟⡿⣿⣻⢿⣟⡿⣿⣻⢿⣟⡿⣟⡿⣿⣻⢿⣟⡿⣿⣻⢿⣟⡿⣿⣻⢿⡿⣟⡿⣿⢿⡿⣿ ⡎⢶⣹⢾⡽⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣧⡙⢎⡜⡱⣈⠦⡱⢌⢆⡙⢢⡙⢦⣛⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⢿⡽⣞⣷⣻⣞⡷⣯⢿⡽⣞⡷⣯⣟⡷⣯⢿⡾⣽⣳⣯⢿⡾⣽⢯⣟⡷⣯⢿⡾⣽⣳⣯⣟⣾⡽⣷⣻⢯⡿⣽⣻⡽⣯⣟⣿ ⡝⣢⢟⣯⡽⣛⠾⣵⣻⡞⣷⣻⣞⣷⢻⣞⣷⣻⣞⣷⣻⣞⣷⢻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣳⢟⡾⣳⢟⣾⣳⣟⣾⡷⣿⣞⣷⡿⣾⡜⣢⣼⣴⢡⣶⡕⣊⣶⣭⢆⡱⢎⡿⣞⣷⣻⣞⣷⣻⣞⡷⣯⣿⣽⣯⢿⣽⣞⣷⣯⢿⣽⣯⣿⣽⣻⣷⣯⣿⡽⣯⣿⣽⣳⣯⣿⣽⣯⣟⣾⣻⣽⣯⣟⣷⣯⣷⣻⣾⣽⣳⣟⣯⣟⣷⣻⡽⣷⣻⢾ ⡳⢌⠺⡔⢣⢍⠳⣌⠳⡝⣣⠟⡾⣞⣿⢺⣧⣟⢾⣵⣻⢮⣟⣟⣮⢷⣳⣟⣮⢷⣻⣞⣯⢷⡟⣯⣞⡵⣎⣶⣹⣞⣮⣽⢳⣯⡟⣽⣻⣥⣭⣟⣯⢿⡽⣻⡽⣯⢟⣤⣧⣏⡽⣿⢾⣷⢯⣿⣷⢯⣿⣻⣳⣛⡾⣟⣯⢟⡾⣽⣿⢯⡷⢯⣿⣷⣛⡾⣽⢿⣯⡻⣗⣯⣿⢷⣫⣟⣿⡽⣏⣷⣿⣽⣫⣿⡽⣳⢯⣿⡿⣽⢻⡾⣽⡿⣽⣳⣟⡿ ⡳⢌⡓⣌⢣⢊⠵⡨⢱⡘⢤⢋⣼⣱⠾⠿⠶⣯⣟⣞⡷⣻⡾⠚⢻⣯⡷⣾⢽⣫⢷⡾⣯⢯⡟⣷⠾⣽⢞⣳⣽⢾⡼⣽⡧⣿⣽⢻⣧⡟⣞⡟⣾⢯⡽⣷⣻⡽⣿⣻⢼⢯⡽⣞⡯⣿⣻⢾⣯⣟⣿⣳⡽⣭⢷⡟⣾⣫⣟⣽⣯⢷⡻⣏⣿⢾⣭⢷⢯⣿⢾⡽⣽⣺⣯⡟⣧⣟⡾⣿⡽⣾⣿⠾⣵⣯⢷⢯⡿⣼⠿⣭⠿⣵⢯⣿⢷⣻⢾⣽ ⡇⠎⡴⣈⠦⣉⠖⣡⢣⡼⠞⡩⠐⡄⢊⠔⡡⠔⠈⠭⣻⢿⡀⠀⠀⢹⣿⣳⢯⣯⢷⣻⣟⣷⣻⢟⡟⣧⢋⡕⢪⡙⡜⣩⠱⣉⠏⡣⢍⡛⢏⡜⣩⢋⠵⣉⢏⠳⢌⡻⢟⡾⣟⡷⣿⣻⣟⣿⣻⠾⣽⢷⣿⣻⢷⣿⣳⣷⢾⡷⣿⢾⣻⣟⡾⣿⢾⣟⡿⣯⢿⡾⣷⢿⡷⣿⣳⢿⣾⢿⣟⡿⣽⢿⣷⣻⢿⣻⡾⣟⡿⣟⣿⣻⢾⣟⣯⡟⣟⡾ ⡇⢭⠰⢌⠲⣡⣺⣶⢿⢀⠣⡐⢡⠘⡄⣾⢹⠛⣿⣦⡀⠑⢎⠳⣔⣫⣿⡽⣳⣟⣾⣳⣞⣷⣫⢿⡽⣦⢧⡘⢥⢒⡡⢆⠓⡬⡘⢥⢊⡜⢢⠜⡤⣉⠦⣑⠪⢜⢢⡑⢎⢼⣫⣽⡳⡷⣽⢮⢷⣻⣭⣟⡶⣯⢟⡾⣵⣫⢿⣹⢯⣟⣧⢿⡽⢯⣟⡾⣽⣏⡿⣽⣫⣟⣾⣳⢯⣟⣾⣛⡾⣽⣏⡿⣞⡽⣯⢷⣻⣽⣻⡽⣾⣽⣻⣞⣷⣻⣽⣻ ⡇⢎⡱⢊⡱⠼⣇⡟⣶⠊⠥⢐⡁⠒⡄⢻⡸⣶⣏⣿⢷⠀⠀⢳⠈⢿⣳⣛⡷⡽⣶⣛⣮⢷⣫⣟⢾⣝⣳⡝⢢⢃⠲⣉⠜⡰⣉⢆⠣⠜⣂⢣⢒⡡⠚⢤⡙⢢⠱⡘⣌⠲⡽⣶⣻⣽⣳⢯⣟⣧⣟⡾⣽⡽⣫⣟⡷⢯⡿⣭⣟⡾⣞⣯⡟⣟⡾⣽⣳⢯⣟⣳⡟⡾⣵⢯⣟⣞⣳⢯⣟⣳⢯⣻⡽⣛⡷⣯⢷⣳⢯⡽⡾⣵⣳⠿⣼⣳⡽⣞ ⡇⢎⡔⢣⠜⣡⣿⣰⢿⣰⣾⣶⡤⢇⡘⠌⢣⡘⠻⣷⡤⠁⠀⠀⡏⠄⠻⣽⢾⣹⢧⣟⠾⣭⢷⡞⣯⣞⢧⠛⢦⡉⢖⡡⢎⡱⣐⠪⣡⢋⠴⢡⢆⡱⣉⠖⢬⢡⢣⠱⢌⠳⣻⣵⡳⣷⢫⣟⡾⣵⠾⣽⡳⣟⡷⢯⣻⣏⡿⣵⢯⣻⢽⣺⡽⣏⣟⣳⢯⣟⣞⡷⣻⣽⣛⡾⣽⠾⣝⣟⡾⣽⣫⢷⣻⡽⣽⣳⢯⣯⣻⡽⣽⣳⢯⣟⢷⣫⡽⣯ ⡇⢎⡜⢢⡙⣴⣿⡛⡸⠉⠓⠁⠀⠀⠈⠑⠧⡙⠢⢄⣀⣀⠤⢚⠠⡉⠆⠹⣟⢮⡟⣞⣻⡽⣞⣽⣳⣎⠧⣙⠢⢍⡒⡌⠦⣑⠢⢓⠤⣃⠎⡥⢒⠴⢡⠚⡤⢃⠦⡙⠬⡱⡑⢮⢓⡏⠿⡜⣷⣫⣟⣳⢟⡽⣞⡯⢷⢾⣹⡽⢾⣹⣏⡷⢯⡽⣾⣹⢯⣞⡽⣞⡷⢯⡽⢯⣷⣻⡽⡾⣽⣳⢯⣟⣳⣟⣳⢯⣟⡾⣵⣻⣳⢯⣟⡾⢯⣷⢻⣳ ⡓⣌⠲⡡⢎⣿⠙⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠂⡤⠐⡌⢂⠥⠐⡩⠐⣹⢾⣹⡝⣧⢟⡮⣗⣳⣎⢷⣌⠳⣌⠒⡥⢓⠬⡱⣉⠖⣌⠲⡑⢎⡜⢢⡙⠴⣉⠦⡙⠴⣑⡘⢆⠣⡜⠱⣌⢣⢓⢾⡹⡾⣝⣳⡟⣯⢯⣳⡻⣏⡷⢾⣹⢯⢷⡳⢯⣳⢯⢾⣝⡾⣏⡿⣛⡶⣏⣷⢻⡵⣏⡿⣼⣳⣭⢟⣞⣧⣟⣳⡽⣭⡟⣾⢽⣻⡼⣯⢷ ⠇⡬⡑⢆⢣⡏⣩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢀⠣⠌⢂⠆⠱⣀⠣⠜⣯⣗⡻⡜⢬⡑⢮⠱⣞⢫⠞⣣⢌⠳⡘⣌⠲⡱⢌⠎⡔⢣⢍⠲⣌⠣⡜⡱⢌⡒⣍⠲⢤⡙⠬⡱⢌⠳⣄⠣⢎⠦⣽⡝⣯⣳⡽⣳⢯⣳⢻⣝⡾⣏⣟⢾⣫⡽⣏⡷⢯⣛⣮⢷⣫⡽⣏⣷⢻⡼⢯⣳⢯⡽⣶⢻⣼⣛⡾⣼⢞⣧⡟⣧⢿⣹⡞⣧⣟⠾⣽ ⡓⠴⡩⢜⣸⠑⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢆⠱⡈⢌⠒⡠⢍⡘⣿⣾⣱⣯⡾⣎⣦⠧⡟⢮⡘⡔⡊⢥⠓⣌⠱⡑⢪⠜⡌⢣⢊⠕⡢⢓⠬⡑⢎⠴⡨⡑⢦⡘⠥⢓⡌⢣⢆⡹⣘⣞⡶⣛⣧⢷⣫⢷⣫⢷⣛⣮⢷⣻⡼⣏⡾⣵⢯⡽⢯⡽⢮⣗⢯⣞⢷⣺⢯⡽⣏⣷⢫⣷⢫⣟⠶⣏⣷⣛⡾⣣⢿⣹⡞⣧⣟⣳⡞⣟⣳ ⡥⢣⡑⢎⣹⡌⠄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⡩⣤⣢⢅⣆⣣⠑⠎⣼⣿⡇⢹⣏⣯⡇⠚⠃⡀⢬⡗⡰⣉⢆⠣⠜⣢⠙⡔⢪⢌⡱⢊⠬⡑⢎⡒⢍⠲⡌⡱⡘⢤⢊⠕⠣⣌⢃⠦⡱⡹⣎⢷⣻⢼⡳⣏⢷⣫⠾⣝⡮⢷⣣⣟⢾⣹⡞⣽⢞⡯⣽⢻⡼⣏⡾⣏⡾⣳⡽⣞⠾⣝⣮⠿⣼⡻⣝⡶⣏⡷⣏⣟⡶⣻⡵⣞⢧⠿⣭⢷ ⡥⢣⠜⡢⠜⣯⡐⠢⣙⠢⢤⣀⣀⣄⠤⠤⢖⣻⣲⢓⠣⡍⡩⢍⢓⢋⣯⣿⣹⣛⡧⠝⢾⣵⡀⠀⣐⠃⣾⢵⡳⣌⠦⡙⡜⠤⣋⢌⠣⢆⡱⢊⠖⣩⠒⡜⣌⢣⠒⡥⣉⠖⡌⢎⡱⢂⢎⡒⢥⡑⢮⢻⡼⣳⡝⡜⣲⣭⢟⡽⣚⡯⢷⡞⣯⣳⢽⣣⢿⡹⣞⣽⢺⣭⢷⣫⠷⣝⣾⡹⢯⣻⡼⣻⢵⡻⣝⡾⣭⢷⡻⣼⢳⣻⡼⣏⣯⢿⣹⣞ ⡕⢪⠜⣡⢋⠴⡙⠧⣆⡹⢄⠒⡤⢂⢎⣱⣻⠛⢤⢊⣱⣴⣵⠾⠴⠿⠟⣭⣟⣟⣷⣠⣑⣤⣄⡉⢁⣼⡟⣮⢷⡹⢮⡱⢌⡓⠬⡌⡓⣌⠲⢩⠜⣄⠫⢔⠢⣅⠫⠔⣌⢚⡘⠦⢱⣉⠲⡘⢆⡍⢎⢷⡹⢧⡓⡼⢣⡛⡎⡴⢫⣽⢳⢯⣳⢽⡺⣵⣿⣿⡿⣞⡽⣎⡷⣭⢟⣽⢲⡟⣯⡳⣽⢳⢯⡽⣞⣵⢻⡞⣽⢳⢯⣳⡽⣞⡵⣯⢳⣞ ⡍⢦⡙⢤⢋⡒⣍⠚⡬⣙⠳⡓⢖⣳⣶⡷⡏⠘⢄⣶⢏⠏⠀⠙⢣⠀⠀⠀⠀⠉⠛⠯⣝⢞⡳⢏⠯⡹⠹⣌⠳⣏⢷⣛⡾⣌⠳⣌⠱⣌⠱⣃⠎⡴⣉⢎⡱⢢⡙⡜⢤⠣⡜⣡⢃⢆⢣⡙⠴⡘⢬⢺⡝⣧⠓⡜⣡⠓⣬⢳⣻⡜⣯⣳⢯⣞⡳⣽⣿⢯⣝⣮⢳⡝⣾⡱⣯⢞⣳⡽⣣⢿⣱⢯⣗⣻⡼⣞⢧⡿⣭⢯⣏⡷⡽⢮⡽⣞⡽⢮ ⡓⠦⣙⢢⠣⡜⢤⢋⠴⣈⠧⡙⢢⣿⣓⡏⡉⢉⣹⣺⠿⡀⠀⠀⢀⠑⢄⠀⠀⠀⠀⠀⠈⠑⢯⡜⢢⡑⢣⢌⡓⡌⡞⢧⡻⣜⡳⣎⠱⣌⠓⣌⡚⢤⢃⡎⡔⢣⠜⡘⢆⠳⡘⢤⢋⡌⢦⡉⢖⡩⢆⢣⡙⢦⡉⢖⡡⢋⡾⣭⡳⣝⢲⡙⡾⣜⣷⣹⢿⣾⣵⣮⣷⣿⣷⣟⡼⣫⢷⡹⣝⣮⣛⠾⣜⣧⢻⡼⣫⠾⣵⣫⢞⣵⡻⣝⢾⣱⢯⣛ ⡇⠳⡌⢆⠳⡘⢦⡉⢖⡡⢎⡱⢣⢿⣦⡇⠀⠀⡜⠉⠚⠁⠀⠀⢀⣄⠈⣆⠀⠀⠀⠀⠀⢀⣾⠙⣧⡘⢥⢊⠴⡱⢌⠳⣹⢭⠷⣍⡳⣌⣳⢼⡹⣎⠿⣼⡹⣆⠹⡘⣌⢣⢙⢢⠣⡜⢢⡙⢢⡑⢎⠦⡙⢤⡙⢢⡑⢯⡵⣣⠝⡤⢣⡝⣱⢯⡖⣯⣛⠾⣿⣿⣿⣿⣿⣿⣾⣱⢯⡝⣞⢶⣫⢟⡽⣎⡯⣗⢯⣻⢖⣯⣛⡶⣝⢯⣞⡽⢮⣳ ⡇⢳⠸⣌⢣⡑⢦⡉⢦⡑⠎⡔⣿⠘⠘⣧⠀⠈⣤⠔⢀⣀⣤⡞⠛⣽⠆⢹⢦⡀⠀⠀⠀⠸⢿⣞⣿⣿⣶⣏⡴⢑⢪⠱⣌⠺⡽⣭⣳⢏⡷⣫⡽⣭⢟⡾⣱⣏⢷⡹⣤⢣⠎⣆⠳⣌⠣⡜⣡⠚⣌⠲⣉⠦⣙⠢⣍⠳⣝⢣⠚⡔⢣⡞⣧⢟⡾⣱⣏⠿⣼⣿⣿⣿⣿⣿⣿⣷⣫⢾⣹⢞⡵⣫⣽⢺⡵⣫⢟⣼⢫⡶⣏⢾⣹⢞⣼⣹⢳⢧ ⡝⢢⢓⡌⢦⡙⢤⡙⠴⣈⠳⣸⡇⠈⡜⢛⡷⠀⢹⢾⣏⡉⢸⠉⢣⢻⡆⠀⣏⠛⢢⢄⣀⡠⣎⣾⡟⣻⡞⢹⣧⠍⣆⠓⣌⢣⢛⢶⣫⣞⣳⡽⣳⡝⣯⣞⢧⢯⣏⢷⣫⢏⡿⣬⠷⣬⢳⡜⣥⢫⡔⡣⢜⠢⣅⠳⣈⠳⣌⠲⡩⠜⣥⢻⡼⣏⣾⢳⢾⡹⢧⣻⢟⣿⢻⣏⢿⡹⢧⢯⡽⣺⣝⣳⢞⡧⣟⣵⣛⣮⢷⣹⡞⣽⢎⡿⣜⢧⡟⣞ ⡝⢢⢣⠜⡢⢍⠲⣌⠳⢌⡓⡜⣧⠀⢩⠀⠀⢇⠀⢯⠟⢷⣌⠦⠼⣼⣻⠀⠀⢉⣿⣎⣙⡛⠯⢥⣼⡵⡴⢿⡏⡜⢤⢋⡔⢪⠜⡪⢵⡞⣧⡻⣵⢻⣖⡻⣾⡹⢎⠶⣡⢛⡼⢧⡟⣧⡟⣾⣱⢯⣝⡳⣎⠷⣎⣷⡹⢶⡌⣧⣱⢻⡜⣯⣳⠽⣎⣟⢾⣹⡻⣜⢯⣞⡳⣞⡧⢿⣹⢮⡗⣷⢺⡵⣻⢼⡳⣎⡷⢮⣳⢧⡟⣮⢟⡼⣏⡾⣹⢞ ⡝⢢⠍⣎⠱⣊⠕⣢⠙⢦⠱⢼⣯⣳⣞⡆⠀⢚⡀⠈⢒⠀⢛⠵⠶⠛⠁⠀⣤⢿⡏⣷⢢⡙⣌⠣⢆⡙⣋⠦⡱⡘⢆⠣⡜⡡⢎⡱⢎⡽⣞⡵⣯⠷⣞⣽⢣⣟⢯⣳⡝⣮⣝⡳⣽⣣⣟⢶⣛⣮⢗⣯⢽⡻⣼⢺⣝⣧⣟⢶⣫⢗⣯⢳⣭⢿⣹⢮⣏⡷⣝⣯⢞⡾⣝⣮⡽⣻⢼⣳⢻⡼⣏⣾⢳⣏⢷⣫⢽⡳⣏⣾⡹⣎⡿⣼⢳⡽⣹⢮ ⡝⢢⠹⣄⠳⣌⠚⡤⢛⠤⣋⠦⡹⢟⡡⢿⡄⠀⠡⡀⠀⢳⠋⠀⠀⠒⡩⣼⠿⡱⡘⡽⡷⡧⢌⠳⣌⠲⡡⢎⡱⣉⢎⡱⢌⡱⢊⡴⣋⢾⣝⡾⣵⢻⣝⣮⢟⣾⣹⢶⡻⣵⣺⡝⣧⢷⣚⡯⣞⣵⣫⢞⣧⢿⣱⡟⣞⡶⣫⡗⣯⣞⡳⣟⢮⡗⣯⣞⢾⣹⠾⣜⣻⡼⣏⣶⢻⡵⣛⣮⢟⣵⡻⣜⢯⡞⣧⢯⡗⣯⠷⣮⢽⡳⣝⣮⢟⣼⣛⢮ ⡝⣌⠳⣌⠳⣌⠣⠵⣉⠶⣡⢚⡱⢊⡴⢣⠽⣮⣱⡗⣄⣀⣣⡀⢰⡯⢗⠣⣇⡱⢱⡘⣏⡝⣮⢓⠬⡱⡑⢎⠴⡡⢎⡔⢣⠜⣡⠶⣹⢞⣮⢳⡭⢳⡝⣮⢟⡶⣏⣾⢳⡽⣲⢟⡽⣺⡝⡾⣵⢞⣵⡻⣎⡷⢧⣻⡝⡾⣵⢫⢷⡺⣽⢺⣝⢾⡳⣞⣯⢳⡟⣭⢷⣹⢞⡵⣯⣝⡻⣼⢻⡼⣝⡯⣗⢯⡳⣏⣾⢳⡻⣝⡾⣽⡹⣎⡿⣼⣹⢞ ⡳⢌⠳⣌⠳⢌⢣⠓⡬⢒⠥⣊⠴⢣⠜⣡⢎⡹⢻⣶⢺⡒⢭⣻⣟⢫⡝⠷⣦⣧⣣⠞⡿⡱⠀⢻⡢⡕⣩⢎⢲⡑⡎⣜⡡⢞⡡⠞⣵⣫⢞⡧⣝⡣⢞⡱⢏⠾⣹⢎⡿⣜⣯⢾⣹⢧⡟⡽⣎⡿⣜⣳⡽⣞⢯⣳⢽⡳⣽⢫⣗⢯⣳⡻⣼⣳⢻⡵⣞⡻⣼⢫⡞⡵⢯⡞⣵⡺⣝⢧⣟⡽⣞⡵⣛⢾⡳⣝⡮⣏⢷⣏⢾⡵⣻⡝⣾⣱⢯⡞ ⡳⢌⠳⣌⠚⣌⠖⣩⠒⣍⠲⡡⢞⡡⢚⠥⣊⠴⣋⣿⠣⢮⣽⣫⠻⡧⡜⡱⢩⢛⣶⢾⠿⡧⢈⢹⣷⡑⢦⢊⠵⡘⡜⢤⠓⡎⠴⣋⠖⡭⣞⡽⢮⡝⣧⠹⣌⠳⣩⢞⡽⣳⢮⡳⣏⡾⣝⣳⡽⣺⢭⣳⢽⡺⣝⡮⢷⣫⢷⣛⣮⢟⡶⣻⢵⣫⢷⣫⢗⣻⡼⣿⣻⣽⣿⣿⣿⣳⢯⣞⢮⡷⣹⠾⡽⣧⣟⣾⣵⣛⠾⣼⡳⣝⣧⡻⢧⣛⣮⡽ ⡳⢌⠳⣌⠳⡌⢎⠥⣋⠴⡙⡔⢣⠜⣡⠞⡤⢓⡔⢪⠿⢿⠏⡁⣒⣿⡜⣡⠓⣬⢺⣴⠐⢳⠠⠈⣿⡘⢦⡉⡖⣩⠜⡢⠝⣌⠳⣌⠚⡴⣹⢞⡽⣹⣎⠷⣌⠳⢤⢋⡾⣱⢏⡿⣜⣳⢏⡷⣽⢳⣏⢷⣫⠷⣭⣻⢳⡽⣎⢷⡺⣝⡞⣱⢫⠞⣥⢋⡞⣱⢛⢶⡻⣟⡿⣿⢳⣝⡾⣎⡿⣼⢫⡟⣵⣿⣿⣿⣿⣞⢯⣳⡽⣹⢶⡻⣭⢟⡶⣹ ⣧⢫⣕⢪⡱⢬⣉⠶⡡⢎⡕⢪⡱⢊⡕⢪⠔⣣⣼⡿⢰⡕⠠⢀⢿⢏⠖⣡⢋⡔⣿⠜⠤⠋⠀⠐⡟⣗⢢⠕⡪⢔⡩⢒⡍⢆⠳⣌⠣⣕⢣⡟⣞⡳⣎⠟⡴⢩⢆⠫⡔⡍⡞⡱⢏⡾⣹⢚⡵⢋⡞⣧⢏⡿⣱⠏⣧⡙⢮⣳⡝⡞⢬⡑⢎⡼⢠⢧⡘⢦⡙⢦⡹⢜⡳⢭⢻⣜⡳⣽⢺⡵⢯⣛⢾⣹⢿⡟⣯⣝⡻⣖⡯⣽⢞⣳⢯⢾⣹⢳ ⣯⢗⡮⢷⡱⣎⠦⢳⣙⠲⡜⢣⠜⣡⢎⢣⡙⣴⡇⠐⠁⠀⠁⡞⣿⢨⠚⡥⣊⠴⣿⠀⠀⠀⠀⡐⣸⢏⠎⡼⡑⢎⡱⢣⠜⣪⠱⣌⠳⡌⢧⡛⣬⠳⡍⠞⣌⠣⢎⡱⢜⡰⢅⡛⢬⢣⡑⢎⠴⣋⠼⣌⠻⡜⣣⠝⡤⡙⣾⣿⠶⣉⠦⡙⢦⠸⡱⣾⣿⣢⠙⢦⠱⣉⠶⡩⢖⢮⡱⢫⢷⡹⣏⣞⢧⣛⣮⠽⡶⣭⢳⡝⣾⡱⢯⡳⣏⠷⣭⢻ ⡟⣮⢽⡳⡽⢮⣝⣣⢏⡷⣩⢎⠼⡡⢎⠲⡱⢼⡇⠀⠀⢀⠔⢠⠏⡆⢏⡴⡑⢎⠼⢧⠄⠠⢊⢔⠣⢎⣹⡴⢻⠦⣑⠣⢎⠥⡓⣌⠳⣌⢣⡜⢤⠓⣜⡩⢦⡙⢦⠱⣊⠴⣋⠜⣢⠣⡜⣩⠒⡥⢚⠤⢣⣙⣤⣯⣴⣷⡬⣡⢓⢬⣒⣭⡒⣍⠲⡍⢏⠥⣋⢦⣙⣤⣣⣱⣊⣶⣭⠟⠮⠷⠽⠮⠿⠼⠮⠿⠵⣯⣳⣛⢶⡻⣭⢷⡹⢯⣝⣳ ⡛⣜⣣⢟⡽⣳⢎⡷⣫⢞⡵⣎⢧⡱⢎⡣⢕⠪⡝⢖⡂⣁⠴⣉⢎⡱⢎⠴⣉⠮⡜⢪⡙⣍⠳⣌⣷⣟⣿⡷⢃⡳⢌⡓⢎⣱⠱⣌⠳⣌⠲⣘⠬⡙⢤⠓⢦⡙⢦⡛⣤⠓⣌⠞⡤⢓⠼⣄⠛⡔⢫⠜⣡⠾⡟⣯⡿⡦⢹⣆⣭⠞⠁⠀⠈⢧⣷⢛⣮⡖⠛⠒⠢⣀⢄⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⣒⠀⠈⣆⠘⣧⡟⣮⢷⡹⣮⢽⡳⣞⡵ ⡳⠸⣌⠻⣜⢧⡻⣜⢧⣛⢾⡹⢮⡝⣯⢳⣎⡱⢸⢡⠒⡥⢓⡌⢦⡑⢎⠲⡡⠞⣌⠣⡜⢤⢃⡏⢭⡓⢧⡘⢣⣜⣶⢿⢿⣿⠗⣌⠳⢌⠳⣌⠲⣉⡶⠭⢦⡙⢦⢻⡴⣫⡜⣬⠳⣍⠶⣬⡙⡌⣇⠺⣄⢳⣽⣮⣯⣴⠿⡿⠿⢤⢤⣠⣴⣾⣿⣿⣿⡗⠀⠀⡠⠊⠁⠊⠄⡠⢀⡀⠀⠀⠀⠀⣬⣁⡀⠀⡌⢧⠘⣿⡜⣧⢟⡼⢧⣻⢼⣹ ⡇⠳⣌⢳⡹⣎⢷⣫⢞⡽⢮⡝⣧⢻⣜⡳⣎⠷⣭⠖⣍⠲⣡⠚⡴⡘⣌⢣⠱⣉⢆⠳⡘⢆⡣⢜⢢⡙⢢⣽⣾⢟⣱⣮⣾⢋⠞⡤⢋⣌⠷⠚⠉⠀⠀⠀⠀⡿⢎⡳⣝⢧⡻⣜⢯⣝⡻⢶⡹⣜⠴⣏⠺⣿⣿⣿⣻⣏⣱⣬⣽⣌⠎⣿⣹⡿⡿⡿⣇⠮⣹⡛⡠⣀⠁⠐⠀⠀⠁⠂⢔⣠⣀⠀⠣⠀⠘⡶⠁⠈⢢⠈⢿⣎⡟⡾⣭⢳⣏⢾ ⣃⠓⡌⢆⡳⣝⢮⣓⢯⢞⣧⢻⣜⡳⣎⠷⣭⢻⣜⡻⣜⡳⢧⣛⠴⡱⣌⠶⣹⡜⣮⢳⡝⣮⢵⡫⢶⣹⣿⡿⣽⣿⡿⣟⣧⢏⣮⠕⢋⣠⡔⡮⢭⡕⠀⢀⡼⣍⢯⡳⣝⢮⡵⡹⣞⡼⣹⢧⡟⣾⠛⠋⠑⠊⠛⣿⠿⢷⡟⡛⣭⡷⣾⣿⢽⣷⣬⠱⣊⣶⡵⠋⠄⢡⠈⠐⠤⣀⠁⠤⠘⡷⠼⢮⡶⢄⣶⢒⠀⠀⠀⢓⠈⢷⣫⢷⣭⢷⡺⣝ ⡣⠜⡘⢬⠱⣎⠷⣹⢎⡷⢎⡷⢎⡷⢭⡻⣜⡳⣎⠷⣭⣛⡵⣫⣝⡳⣭⠻⣕⠾⣱⢏⡾⣱⢧⣛⢧⢿⡿⣽⢻⢧⡻⣜⡿⣯⣤⢾⡹⢧⣻⣹⠟⠀⣠⢎⡖⢬⢲⢻⡜⣧⢻⡵⣫⢞⡵⣫⡞⠓⠀⠀⠀⠀⠀⠣⠵⡀⠉⠉⠉⠳⣵⣾⣿⣋⣡⣟⢯⠎⠀⠀⡴⣉⣓⠖⠈⢀⡁⢲⣾⡀⢠⣤⣷⣉⢈⠎⣂⢄⠀⠀⢣⡈⢳⡿⣿⢯⣳⠽ ⡱⢈⠜⢢⡙⢬⡙⢥⡻⣜⣫⡜⣯⡜⣧⢻⡜⣵⢫⡝⡶⣹⣜⡳⣜⡳⣭⢻⡜⣏⢧⡻⣜⢧⡳⣭⢞⣣⡝⣮⢛⣶⠝⣁⣴⢻⣟⢮⣝⢧⡷⠋⢀⣴⢏⡷⣚⠦⣍⠮⣝⢮⡳⣝⣣⢟⣼⣱⣟⣾⣿⣿⣿⣿⣯⣥⡒⠻⣄⣀⣀⢀⣾⠓⢋⣏⣿⡿⠁⠀⣠⠾⢦⡱⠋⠀⡔⠁⠈⠚⡁⠈⡌⠉⢠⣾⠟⠒⠀⠁⠪⢂⠄⠳⠄⢻⡵⣫⢞⡽ ⡅⠊⠜⡠⠘⠤⡘⢢⡑⣎⠶⣙⢦⠽⣘⠧⣝⢎⢧⢫⡵⢣⢮⡕⣫⢼⡱⢧⣛⡼⢣⡟⣬⢳⠳⡞⢮⡵⣹⢲⠟⢁⢶⡹⣜⣳⢚⣦⠸⠋⣠⣖⢯⣧⢿⣞⣿⣻⣟⢮⡝⣎⢷⡹⣼⡾⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠙⢾⣿⠯⣿⣦⡾⠋⠁⢀⠔⠁⢂⠜⠁⠀⣰⣇⠀⢀⣴⣿⣿⣷⡶⣛⠇⠀⠀⠈⡦⠀⠀⣿⣪⡴⠄⢹⣳⣏⢾ ⠆⡉⠰⢁⢉⠰⢁⠒⡸⢌⡳⢭⢎⢯⣙⠞⣼⢪⡝⢶⡩⢏⠶⣩⣓⢮⡱⣓⠮⣜⢧⡹⣬⢓⢯⣙⡞⣴⠟⠁⣴⢫⢇⣛⢶⡭⠛⢁⡤⣮⡀⠩⡻⣮⢭⣻⣷⢿⡹⡲⡝⣎⢧⡟⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠡⠘⠀⠈⣅⡀⠀⠈⡥⠶⢄⠿⢦⣬⠋⠀⢀⡼⢏⣿⣾⡿⢿⣿⣿⣟⣳⣽⣷⠀⢀⣜⡑⠢⣀⠈⢮⡓⢦⣸⠘⣿⢎ ⡃⠄⠡⠂⠄⢂⠌⠢⡑⡍⣞⡱⣚⠼⣌⠻⣔⢣⢞⡣⡝⢮⡹⡱⢎⠶⣍⢧⡛⣜⢮⡱⢎⡝⣎⠶⣩⠋⠀⠸⢣⠯⠞⠋⢁⣠⡔⢯⣼⣟⢻⡆⠈⢻⣿⡷⣛⠮⣕⡳⣹⣼⣫⣾⣿⣿⣿⡿⣏⣹⡿⠛⠉⢭⣩⣿⣆⠀⠃⠬⠆⠀⠉⠀⠀⠀⠨⢀⠠⠬⢥⣙⡂⠛⠮⢽⡜⣯⢳⣇⣿⢻⡜⣶⠟⠻⣧⣉⣷⡎⠂⢙⣅⣺⢿⣦⣿⣦⣟⡞ ⡅⢈⠤⢁⡘⠠⢌⡱⢂⡗⢢⢳⢩⠞⡬⢳⡌⢳⡊⡵⡙⢦⢓⡝⢎⡳⡜⢦⡹⠜⣦⡙⢮⡜⣬⢳⡇⠀⠀⠀⠀⣀⡤⡖⣏⠶⣽⣿⢫⡜⣣⣿⣶⢿⡹⣵⣛⣯⢖⡵⢫⣿⣿⣿⢻⣿⣿⠀⠙⠉⠁⡐⢈⣹⣿⢯⣟⣷⣬⡀⢢⠀⠀⡀⡀⠀⠀⠀⠀⠐⠂⠤⣭⡷⠦⢅⡊⠉⣿⡿⣜⣣⢽⡎⠀⣴⣿⣿⣿⣷⣦⣼⢷⣿⣿⡁⠀⣹⣮⣝ ⠖⡠⢊⠴⣈⠳⣌⠲⡍⡜⢣⡙⢎⡱⢣⢇⡘⠡⢒⠠⠙⢠⠋⠜⣈⠳⢸⡑⢮⠹⣤⠛⢦⡱⢎⡱⢳⠴⣒⠶⣋⢧⢓⡭⣜⡿⣿⣡⣷⣾⡿⣛⠵⣫⢞⡵⣫⢞⡽⣴⣿⣿⣇⠛⠘⣿⡏⠀⠌⣀⣡⣶⣿⣿⣽⣻⣞⣷⣿⣿⣦⣄⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡒⠒⠿⠟⠧⠀⠉⠚⠄⠸⣿⣿⣿⣿⠳⢰⡿⣾⢮⣿⣿⣿⡿⡿⣞ ⡃⠠⢉⠂⠥⠓⠬⠱⠘⣈⠱⢌⢣⡱⢃⢎⠴⡡⢆⢂⡁⢂⠐⡠⢂⡜⠢⡝⣌⢓⢢⠛⡆⢧⡙⣬⠣⡝⡌⢧⢍⡲⢍⡲⣹⠿⡼⣟⢫⡕⢎⡥⡛⣔⠻⣼⢭⡟⣾⡱⣏⢿⣟⡦⡀⠹⢁⠈⠄⠈⢉⠀⠠⠴⢾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⠀⠘⠟⠻⡏⠁⢀⢎⣀⣾⢿⣿⡿⣏⡴⢛⡬ ⡁⠐⠠⠀⠀⡁⠂⠁⠠⠀⠀⠄⠂⠈⡅⢎⠲⡑⢎⠦⡑⢎⠲⣡⠣⡜⠱⣘⡌⢎⡌⢧⡙⠦⣱⢂⠧⢣⡙⢦⠚⡴⣉⠖⣡⠛⡴⡑⢎⡜⢪⠴⡙⡤⡯⡻⣮⠽⣖⡿⣼⢳⣎⢿⣳⢮⣀⠐⠈⡐⠀⠌⢐⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢔⡦⢄⡀⠀⠀⠘⢄⠑⠸⣄⠠⢸⡫⢿⡸⢹⠰⡉⠔ ⡥⢘⠠⢂⠄⡀⢀⠈⠀⠀⠁⠀⠈⠐⠘⠈⠥⡉⢆⢣⡙⡌⡓⢤⢃⠠⠁⠠⠈⠡⠘⠠⠘⡑⠄⡎⢎⡱⡘⢆⠫⡔⡱⢊⡥⢋⡴⣉⠖⡬⢃⠮⣱⢊⣾⣿⣿⢻⣜⡷⣭⠷⣞⡧⣏⢿⣹⢷⣦⡀⢌⣴⢿⡿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⡀⠠⠤⢤⡤⠤⠄⣀⡀⠀⠀⠈⠑⠮⣝⡒⢤⣀⠁⠢⢀⣱⠦⣀⠘⠋⠳⢦⡘⡄ ⠃⠌⠒⢡⠢⡐⠤⠀⠄⠂⠈⠀⠐⡀⠂⡌⠰⠰⢌⠒⡴⢡⡉⢖⡈⢆⠡⡀⠂⠐⠠⠐⠠⠐⡠⢘⠢⣡⠙⣌⠳⢌⡱⢣⡘⠥⣒⢡⠚⡴⣉⣞⣵⣿⣿⣳⣿⣻⢼⣳⡭⣟⢧⡟⠽⢮⣗⡯⣞⢿⣆⠀⡀⣤⣢⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡠⢊⠡⡖⢍⡁⠀⠀⠀⠉⠀⠒⠁⡒⠄⡀⠀⠈⠙⠲⣌⡝⢲⣦⣤⣀⢈⡑⣄⡠⠀⠹⡐ ⠅⡈⢐⠠⢂⠡⢊⠱⣈⠐⡠⢁⠆⡡⢊⠔⡩⠑⡌⢊⠔⡡⠜⢢⠉⢆⠱⢄⠣⢌⡱⢌⡑⡊⠴⣉⢒⡡⠚⣄⠣⢊⠴⢡⡘⢅⠆⢣⢩⡴⣻⣿⣿⣭⣉⠉⠉⣏⠷⣧⡟⣾⣹⣎⠱⣊⣬⣙⣋⣾⣭⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⢠⠇⢤⣘⢂⣉⣒⣌⠋⢔⠠⠄⡀⠀⠁⠨⡐⢄⠀⠀⠀⠉⠲⢿⣾⡽⣻⣟⡿⣷⣇⠀⠉ ⠐⡠⢃⣘⣄⣓⣈⣒⣄⣣⣐⠡⢊⡔⣡⣊⡔⢡⡘⢄⡊⣔⣉⣆⣉⣆⢃⣎⣑⣂⣒⡂⢆⣙⣐⡂⢆⢡⠣⠤⡙⢌⢂⠣⡘⢌⡸⣡⢾⣾⣿⣿⣿⣿⣿⣷⣶⡏⢧⡙⠿⣶⣫⡧⢓⠬⣛⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⢸⢰⠈⠙⠿⣄⡀⠈⠀⠀⠁⠢⢀⠁⠒⠄⢀⢠⡑⢄⠀⠀⠀⠀⠈⠙⢷⣭⣟⣧⡟⣷⡄ ⠠⢁⠒⣄⣼⣿⣿⣿⣿⣼⣯⣯⣿⣯⣷⣿⣿⣿⣽⣿⣿⣿⣽⣿⣿⣿⣿⣿⣽⠿⣿⣿⡾⣻⣷⡷⠎⢄⠃⢆⡑⡈⠆⡑⠌⣂⢶⣽⣿⣿⣿⣟⠿⢯⡍⠉⣿⠸⣂⢍⡶⢡⢍⠲⣉⠖⣡⢻⡖⢤⢋⠝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⡘⡼⠀⠀⠀⠈⡏⣔⠤⣀⠀⠀⠀⠁⠠⡀⠀⠀⠈⢄⢂⠀⠀⠀⠀⠀⠀⠑⡿⣶⢻⣗⡜ ⠠⢁⠸⣿⣿⣻⣯⣿⣿⣻⣿⣿⣫⣯⣽⣿⣿⣯⣯⣽⣿⣟⣟⣯⣱⣿⣿⣿⣆⠢⢄⠠⡐⠄⡐⢠⠉⡄⢊⠤⠐⢡⠘⢠⣱⣿⣿⣿⣷⣿⣯⣭⡤⠄⣀⡾⠁⠀⢩⣾⣿⠡⢎⡱⢌⡚⡤⢻⣿⡀⠈⢈⣑⣨⡧⡬⣝⢻⢿⣿⣿⣿⣿⣿⠃⠀⠀⠑⡙⣇⠀⠀⠀⠙⢆⡙⠲⣽⢢⣄⠀⠀⠀⠑⡨⠉⠈⡄⡆⠀⠀⠀⠀⠀⠀⢸⠯⣟⡾⣽ ⠐⡀⢢⣿⣹⣿⣿⣿⡛⣖⣟⣶⣲⣶⣾⣿⡄⠠⠀⠄⠂⠌⡈⠉⠌⠠⠀⠄⢂⢰⡈⡐⠤⠘⠠⢁⠂⠤⢁⠂⡉⠤⣸⢎⣽⣿⣿⣿⣿⡿⣿⡷⠤⡖⠋⣠⡖⠠⣿⣿⣿⠌⠓⢚⡔⠋⠰⣾⣿⣿⣤⣤⣯⣽⣶⣵⣮⣵⣮⣴⣩⣛⣿⠏⠀⠀⠀⠀⠑⠌⢳⡀⠀⠀⠀⠑⠢⢧⣀⢈⡯⠶⣄⡠⠂⠈⠀⣰⠸⡀⠀⠀⠀⠀⠀⠀⠱⡉⢿⡳ ⠀⡐⢀⣉⣍⣉⢉⣉⣉⡉⢉⣉⡉⢉⡈⢉⡀⡡⢈⣄⠉⣐⠠⢉⣀⠃⠌⡐⠂⡘⠿⣶⣄⡁⠒⠠⢈⠐⠠⢈⠐⡼⣱⣿⣿⣿⣿⣿⣿⡿⣷⡼⡟⣠⠞⣵⣃⣼⣿⣿⣿⡇⠀⠀⢽⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠢⡈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⡦⣀⠏⠀⠑⠐⡪⠭⢍⠢⡀⠀⠈⢄⠻ ⠀⠀⠨⠀⣶⡶⢾⣾⢷⣶⠶⣾⡷⣶⡾⢶⣶⠶⣶⡶⣶⡶⣶⣶⢸⠀⢂⠐⠠⠀⠄⠙⢟⠷⢪⣅⠠⠈⡐⠀⡟⢰⣿⣿⣿⣿⣿⣿⣿⣽⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣴⢞⡲⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣀⣤⡀⡀⠀⠀⠈⠢⡀⠁⠂⠄⢀⡀⠀⠀⠀⠀⢀⣰⠼⢟⢄⢀⣠⠋⢠⣶⡄⢱⣄⣂⠀⠈⢂ ⠀⠀⠀⠀⣿⣷⣾⣧⣸⣿⣀⣿⣆⣿⣧⣼⣿⣧⣿⣧⣼⣧⣹⣿⢸⠀⠀⠂⠁⠈⢀⠂⠈⠱⡘⠀⠑⢦⡀⠂⢣⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡮⢵⣿⣎⣿⣿⣿⣿⣿⣾⣻⠛⢿⣿⣿⡿⠋⠀⠀⠀⢰⠟⠹⣱⠈⢎⠀⠄⠀⠀⠀⠑⠠⡀⠀⠀⠉⠈⠉⠉⠁⠀⠀⠀⢰⠁⠻⣄⠈⠃⡠⢚⠓⠂⠀⠀⠈ ⠀⠈⠀⠀⠀⣼⠀⢸⢳⠀⣿⠃⢸⠀⡿⠆⢰⢳⠀⡟⡆⢸⡾⠀⢸⠀⠀⠁⠈⠀⡀⠐⠈⠀⠈⢺⣿⠾⢟⡶⣄⠑⢄⠉⠛⠿⢿⣿⣿⣿⣿⣿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡿⠟⠉⢀⠠⠀⠀⠀⠸⣄⠉⠁⢀⣎⡀⠀⠑⠄⣀⠀⢤⠐⠃⠈⠙⢷⣾⣶⣶⣶⣤⣤⣘⡀⠀⠀⠂⠄⠒⠁⠀⠀⠠⡀⠄ ⠀⠀⠀⠀⠀⡿⡀⢸⣸⠀⣿⠀⢼⠀⣽⡆⢸⣸⠀⡿⡇⠀⡇⠀⢸⠀⠀⢀⠀⠁⠀⠀⠐⠀⠁⠀⠈⢦⠀⠉⠙⠑⠢⡈⠢⢀⠀⠀⠈⠉⠙⠓⠚⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁⠒⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠑⣈⠤⣖⡉⠀⠀⡼⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡖⠒⢒⣲⣶⣴⣣⣤ ⠀⠀⠀⠀⣴⣧⣷⣼⣧⣴⣾⣤⣾⣦⣿⣦⣼⣷⡤⣷⣧⣤⢧⣤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⠶⣤⣌⣿⢷⣄⣑⣢⡀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⡤⠊⠀⠈⠻⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣿⢯⡷⢯⣟⡽ ⠀⠀⠀⠀⣿⡯⣇⡏⣅⢿⣁⣾⣿⣿⡇⢾⢸⣄⣇⡏⡇⣸⢸⣿⢨⠀⠀⠀⠀⠀⠀⠀⣠⠴⡶⣒⣛⠻⢅⠈⠻⢞⣼⢣⣯⡉⠉⠀⠉⢙⠒⢤⣀⣈⣐⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠉⠀⠀⠀⠀⠉⠀⠐⠀⠀⢀⡠⠾⠋⢀⠔⠹⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⠟⠋⢡⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣽⣻⡞⣽ ⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠴⠀⠀⠀⠀⢀⡔⠫⠱⢐⠎⠢⡉⠓⠚⠕⠀⠀⠉⠳⢮⣝⣳⢤⡀⠀⠙⠲⣬⠓⠦⣈⠉⠁⠀⠒⠒⠒⠠⠠⠤⣤⠀⠀⢀⠀⠀⢠⠔⢊⠉⡉⢉⠉⣴⡖⢁⠴⢅⣠⣧⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⡄⠙⠻⣿⣿⣿⣷⡏⠀ ⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⡀⠩⣉⣤⠴⠦⠧⡀⠀⠀⠀⠘⠛⣶⣤⣙⣧⣿⣺⣳⣄⣀⠀⠑⠦⡌⠓⢄⡀⠀⠀⠀⡖⠉⠀⠀⠀⠀⠀⠀⠀⡗⠐⣂⣡⡴⣺⣿⣿⠟⠙⠒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠙⢿⣿⣿⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠉⢻⣿⣆⣰⣿⣿⠁⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⢀⣠⡼⠟⠋⠉⠛⢿⣤⣀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣵⣾⣿⣿⡋⠁⠀⠀⣠⣉⣿⣿⣷⣶⣽⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⡿⠃⠘⠛⠛⠋⠁⠀⠉⠛⠛⠻⠎⠻⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⣴⣿⠿⠋⠁⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠈⠛⠿⣿⣷⡀⠀⠀ ⠀⠀⣼⣿⡇⣠⣤⣤⠤⢤⣤⠤⣿⡀⠀⠀⠀⣾⠧⢶⡦⠤⢤⣤⣤⡘⣿⣽⡄⠀ ⠀⣸⠟⣿⢸⣇⣀⣀⣴⣿⠿⠗⠚⠳⠄⠀⠴⠛⠲⠿⣿⣷⣀⣀⣀⣇⣿⠛⢷⠀ ⢰⡇⠀⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⣠⠴⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡀⠘⡇ ⣼⣠⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣄⠸ ⣿⠋⠁⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠀⠙⢇ ⠇⠀⢀⣤⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣧⣄⠀⠀ ⣧⣴⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣷⣤ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⡀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠓⠒⠒⠀⠸⣿⠿⠿⣿⣿⣿⣿⣿⡿⠿⠋⠉ ⠀⠀⠀⠈⠙⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⣛⠁⠀⠀⠀

⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠇⣿⣿⠹⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣁⣋⣟⣿⣿⣿⣿⣴⢀⠀⠀⠀⡿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠇⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⣿⣿⣿⣿⠻⠀⠀⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⢿⠟⣿⢻⣮⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣾⣠⣦⣿⡝⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣶⣠⠀⠀⢿⣝⣩⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⠿⠻⠛⡿⣿⣿⣿⣿⢿⠿⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣸⣷⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⢠⡇⣿⣿⣿⣿⣿⣧⣿⣿⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣠⢀⠀⡄⣿⣿⣿⣿⣿⠉⣿⣿⣾⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣾⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣩⣉⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⢿⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣿⣿⣾⣴⠀⠀⠀ �� ???..ekil os ti teg tnod uoy ti hcraes tnod uoy ti teg uoy nrop hcraes uoy .slobmys/sobmoc ijome ruoy teg dna no evom peed taht ton sti gniyrc pots gmo ekil ..tenretni eht no neve yeht era yhw ”etis siht no era sdik“

⠀⠀⠀⠀⠇⡬⣠⣀⣂⣀⠇⠀⠀⠋⠞⣡⣗⣈⠚⠒⠒⠓⠉⠋⠛⠓⠙⠉⠀⠋⠷⠾⠓⠀⠀⠃⠶⠒⠒⠓⠉⠈ ⠀⠀⠀⠀⠀⣄⠳⠘⠀⠀⡆⠛⡿⣹⠀⡃⠿⣯⠀⠀⠀⠀⡀⢱⠀⠀⠀⡀⢦⣟⡼⣌⡔⠸⠀⣿⠀⠀⠀⠀⠋⣴ ⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣷⣿⣿⢿⡮⣤⢠⠀⠀⠀⠀⠀⡄⠦⠛⠀⠀⠀⡄⡿⣽⠋⡟⡟⢴⠀⠀⠃⣰⠀⠀ ⠀⠂⡾⣀⣅⣇⢀⡇⠘⠀⠀⡄⣾⣠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠹⠀⠀⠀⠀⡀⣦⣿⣸⢠⠀⠀⡼⠀⠀⠀ ⠇⡞⣤⠲⠉⠈⠖⠒⢻⠀⠀⠀⢇⠀⠀⠀⠁⠊⡤⠀⠀⠀⡀⠐⠂⠀⡄⢦⠙⠀⠀⠀⠀⣞⠀⠀⠀⠇⢠⠀⠀⠀ ⠀⢤⠓⠉⠉⠈⠀⠀⡄⠘⠀⠀⡀⢠⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⡀⢆⠑⠈⡆⢀⠀⠀⠁⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣟⢈⠀⢣⠈⠀⠁⠟⣻⠈⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠁⠉⣄⠳⠈⠀⠁⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢨⠗⠤⣦⣓⢉⠈⣀⣿⢼⠑⠈⠀⠀⠀⠋⡼⢀⠀⠀⠉⡔⣠⠀⠁⠀⣀⢦⣘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣯⢻⡌⠲⠒⠙⠀⣁⢸⢸⢣⠀⣀⣀⣃⣷⠳⡀⢧⠬⣠⢀⠀⠀⠀⠀⢄⠀⠀⡀⠢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣆⣿⠷⠛⠉⢍⣋⠞⢸⡇⠀⠀⠀⡇⡄⠀⢧⠉⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⡄⣧⠛⢸⡀⠺⣂⠐⠀⠀⢸⡀⣧⣿⣤⠦⠓⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⡆⢸⠀⢀⠀⠀⠀⠀⢃⠉⡉⣋⢿⠟⣿⣿⣨⣀⢯⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠃⠷⠀⠇⠛⡿⣶⣷⣿⣽⣤⣤⣤⣦⣘⣦⣾⢤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⢚⠴⣤⣀⣀⠀⠀⠀⠀⣦⣿⠸⠀⠀⠀⣆⠘⠀⠀⠀⠉⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⣾⣠⠉⠋⠰⠀⠀⠁⠉⠋⠛⠓⣟⣿⣾⣶⣶⣶⢻⠀⠀⠀⣤⠀⠀⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⣿⣿⣼⠀⠀⣀⢀⠀⠟⡴⣁⣿⣶⣴⡥⢸⣷⣿⠈⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⢻⠓⠿⠻⠀⠀⡄⣱⢈⠀⠁⠋⡴⠀⡇⣿⢿⠖⠿⠿⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣾⡟⢹⠖⣠⣃⠰⠀⠀⠀⣁⣋⣙⠄⡿⣼⣤⢀⣀⣴⣧⣿⠉⠉⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣻⣿⠺⠛⡴⠁⠋⠟⡼⣷⣿⣿⠻⣿⣠⠀⠀⠁⠉⡏⣿⠀⣄⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⠿⠹⣇⣿⣶⢸⡀⣡⣟⣿⣿⢿⠰⠀⠅⡿⣸⣧⠙⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣷⣿⣿⣿⢿⣿⡼⢡⠀⠀⠟⣿⣿⣿⢾⠋⡿⣸⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣷⣻⣿⣿⣿⢻⠟⣿⣿⣿⣿⣼⣠⡀⣷⠻⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣤⣤⣷⣹⣀⡇⢸⠀⠀⠀⣆⢿⣿⠙⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢿⡈⢿⠂⠀⠀⠀⡀⣧⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⡌⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀

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⠋⡿⣿⣿⣿⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿ ⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣼⣻⣩⣋⣿⣿⣛⢛⣟⢻⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣿⣿⣿⣿⣴⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿ ⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠿⠿⠻⡿⣸⠀ ⣀⣧⢻⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠁⠋⠿⣿⣤⣠⣀⢀⠀⣀⣧⢿⠈ ⠀⡟⣾⣠⣀⣀⣀⣄⣧⣶⢿⠻⠙⠈⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡶⣤⣉⠋⠟⡶⣷⣨⠀⡇⢸⠀⠀⠀⠀⠀⠀⣿⢸ ⠇⣿⢠⠀⠀⠀⠀⠼⡣⠀⢹⡈⣀⣤⢶⠷⠛⡙⣍⢳⠀⠁⠈⠀⠀⠀⠀⠛⠙⠁⢟⠿⣴⣠⣣⠉⠉⣾⢀⠀⡟⢠⠀⠀⠀⠀⠀⠀⡏⢸ ⡇⣿⠀⠀⠀⠀⠀⣷⡄⠱⣄⠳⠈⠀⠀⠁⡞⣁⣼⣷⠻⡿⢴⠀⠀⠀⠀⣄⣧⣾⢠⢆⠹⠈⠀⠀⠀⠁⠋⡴⢀⠀⠀⠀⠀⠀⠎⢡⣿⢰ ⡄⣿⣜⠱⠀⠛⠉⡟⠙⠉⢌⠲⣑⣉⣉⢊⠖⡠⠀⠀⣧⢹⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⡀⣄⠤⠤⡤⣀⠀⠀⠀⠀⠀⠁⠊⡠⠃⡿⣱⠟ ⢻⣆⢿⡘⢦⠐⡇⣀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⠀⠀⠀⠀⠀⠀⡆⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠴⣀⠁⠟⣿⣿⣿⣿ ⣿⢿⣝⣷⠻⠈⡄⠲⡵⠉⠀⠀⠀⠀⠀⠀⠀⠊⠐⠏⣾⢀⠀⠀⠀⠀⠀⠀⠀⣄⣷⠻⠈⠀⠀⠀⠀⠀⠄⣀⠀⠀⠉⠟⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠻⠉⠀⠀⣀⢀⠀⠀⠀⠀⠉⠛⡿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⢿⠿⠻⠛⠛⠛⠿⠿⣾⣯⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠟⠿⠿⣶⣴⣤⠦⠒⠒⠓⠙⠀⠀⠀⠀⠂⠒⠖⠤⣤⣀⠀⠀⠀⣉⣛⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠉⠉⠁⠛⠛⠉⠉⠉⠉⠉⠁⠉⠉⠈⠀⠉⠉⠉⠉⠉⠛⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠤⠲⠓⠉⠀⠀⠈⠀⠀⡀⣀⠁⠉⠚⠴⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣰ ⠀⣄⠳⠉⠉⠉⠉⠉⠚⠒⠒⠛⠴⠦⠼⣤⣀⢤⢸⠀⠀⡆⣸⣤⢤⠧⠴⠦⠺⠒⠒⠒⠒⠓⠉⠉⠋⠴⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⠀⠀⠇⢰⠀⠀⠀⢸⠀⠀⡇⠈⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⠀⠀⠀⠀⡄⠳⠉⠁⠞⣠⠀⠀⠀⢀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢈⠀⠀⠀⠀⠀⠀⡀⣹⠀⠀⠀⠀⠀⠀⡇⡿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣄⠸⠀⠀⡀⢠⠀⠀⡇⠀⡄⣤⠀⠀⠇⢠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠉⠟⣿⠈⠀⣿⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⡟⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠟⠿⡿⣙⡋⣶⣠⢦⠺⡖⠹⠈⠀⠉⠛⡴⢦⠙⠉⠀⠉⠋⢶⠧⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⣤⣠⣀⠀⠀⠀⠀⠀⢧⠛⠙⣞⣤⣧⢻⠛⠛⡿⣼⣤⣳⠉⠋⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⡿⣿⣿⣤⣠⣀⣀⠄⠶⠶⡀⣀⣀⣄⡤⣿⣿⠿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⣰⢀⠁⣿⢹⠉⠋⠛⠙⠉⠀⠀⠛⠛⠓⠙⠉⡏⣿⠀⡀⣄⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠉⡿⣼⢀⠟⣿⣿⡛⢸⠀⠀⡇⢛⣿⣿⠻⣀⣧⢻⠉⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣷⢽⡤⣤⣀⣋⣼⠀⠁⠈⠀⣧⣉⣀⣤⢤⡿⣾⣶⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⠉⡏⣿⢿⠿⡧⣿⠿⠿⣸⣆⠿⠿⣿⢼⠿⡿⣿⢹⠉⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⡟⣿⣻⣟⠀⠀⣻⣟⣿⢻⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣻⣏⠈⠀⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢻⠀⣀⣿⣼⣤⣤⣧⣿⢀⠀⡟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠈⡇⢸⠀⠀⡇⢸⠀⡟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⡏⢸⠀⠀⡇⢹⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠁⡿⣿⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣿⢿⠈⠀ ⠀⡟⣿⢀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⡀⣿⢻⠀ ⠇⣿⢸⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⡇⣿⠸ ⡇⣿⠈⠀⠀⠀⠀⠁⣿⣿⠈⠀⠀⠀⠀⠁⣿⢸ ⡄⣿⢸⠀⠀⠀⠟⣿⣴⣦⣿⠻⠀⠀⠀⡇⣿⢠ ⠀⣧⣿⠘⠀⠀⣀⢀⠀⠀⡀⣀⠀⠀⠃⣿⣼⠀ ⠀⠀⣧⣿⠈⠀⠀⠀⠟⠻⠀⠀⠀⠁⣿⣼⠀⠀ ⠀⠀⡀⣿⢸⠀⠀⠀⡀⢀⠀⠀⠀⡇⣿⢀⠀⠀ ⠀⠀⠃⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠈⠀⠀ ⠀⠀⡟⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢻⠀⠀ ⠀⠁⣿⣿⣿⣿⣿⠿⠙⠋⠿⣿⣿⣿⣿⣿⠀⠀ ⠁⡿⣾⣀⠁⠈⠀⣀⣿⣿⣀⠀⠁⠈⣀⣷⢿⠈ ⡇⣿⢈⠀⡄⣴⠀⠀⣤⣤⠀⠀⣦⢠⠀⡁⣿⢸ ⡀⣷⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⣾⢀ ⠀⡀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⢀⠀

⠀⠀⠀⠀⠀⠀⣀⣸⢄⠑⠈⠀⠀⠀⠀⠀⠀⠁⠝⢀⠀⠀⠀⠀⠀⠀⠉⠟⣻⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⢼⠤⠤⠀⠿⡶⣤⣄⢤⠿⠘⠀⠤⠤⣹⢉⣿⣤⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣿⠀⠀⡆⢀⠀⠀⠁⣿⠖⠲⠒⠒⣶⢸⠀⠀⠀⣄⡄⣶⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡏⢹⠀⠀⠀⠀⠁⡽⠈⠀⠀⠀⠀⠀⡇⢠⢄⠑⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠟⣫⢿⠿⣸⠉⡖⣶⠴⡤⢣⠋⠓⠟⣴⠤⣤⣶⠱⠉⠯⠿⣻⢙⠉⠀⢄⠑⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⣿⣿⣶⣷⣿⣾⢀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣾⣷⣿⢿⠘⢄⠑⠀⠀⠀⠀ ⠀⠁⡏⣴⣀⠀⠀⡟⣿⢹⠉⠊⠒⠒⠒⠙⠛⠀⠀⠀⠳⠊⠒⠓⠒⠑⠉⡇⣿⢸⠀⠀⣄⢧⠉⠀⢄⠈⠀⠁ ⠀⣳⡾⠀⠀⠀⠋⣿⣼⣀⠋⠿⣿⣿⠶⡷⣸⠀⠀⠀⡇⢶⡶⣿⣿⠿⠘⣄⣷⢿⠈⠀⠀⠀⣿⠀⠀⢰⠀⠀ ⠀⠀⢹⠉⠛⠿⣿⣿⣠⣀⣀⢀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢳⠀⠀⠀⡀⣀⣀⣤⣿⢿⠻⠙⠉⣿⠈⠇⠀⠀⠀ ⠛⠈⣿⣿⣾⣴⣤⣿⠙⠀⠀⠀⠁⠋⡴⢀⠀⠁⡴⠘⠀⠀⢦⠙⠈⠀⠀⠀⠏⣿⣤⣦⣷⣿⣿⢠⡇⠉⠀⠉ ⣇⠀⡇⢀⠀⠀⠀⣿⣿⣟⣿⣬⣀⢿⠿⠿⠿⡼⠀⡆⠿⠿⠿⠿⣜⣤⣿⣿⣿⣿⠈⠀⠀⣀⣼⠀⡄⢠⠀⣤ ⠀⢧⡿⠿⠿⣿⣿⣿⣿⣿⣿⢻⠁⣿⣿⣩⣉⢠⠀⠀⣹⣍⣿⣿⢸⡏⣿⣿⣿⣿⣿⣿⠿⠿⢿⠚⠀⠀⠀⠀ ⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣤⣦⠈⠀⠀⣼⣤⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠃⠀⠀⠀ ⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢹⠀⠉⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣉⢈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣾⣤⢷⠻⠉⠀⠀⠀⠀⠀⠀⡟⣿⣟⣹⣿⣼⠳⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠀⠀⠀⡀⣧⢿⠻⠉⠀⠀⠀⣧⣿⡉⣋⠒⠓⠉⣆⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⠀⠀⠀⠋⣿⣿⣿⣿⣿⠛⠉⠂⢠⠀⠋⠿⠿⡸⢱⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠛⠟⡿⣿⣿⣿⣿⣿⣾⢁⣄⣳⢙⡀⣶⣿⣾⢠⡿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣿⣿⣿⣿⣿⣿⣿⣼⢀⡄⠸⡄⣿⠻⠙⠈⠁⠟⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣠⣀⠀⠀⣄⣷⣿⣾⣴⢀⠀⠀⠋⢰⠉⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠚⠴⣀⣀⢤⠷⠙⠀⠀⠀⠀⠀⠄⠦⠶⠶⠶⣤⢋⡼⣀⠀⡀⣬⣶⣿⣿⣿⣶⣴⢀⠏⡼⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠞⣠⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠁⠛⠛⠉⠈⠀⠀⠏⣰⠀⠀⠀⠀⣄⠲⠉⠈⠀⠀⠀⠀⣀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡾⣠⠀⠋⣔⣠⣄⣯⣸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡼⢀⠋⠔⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠁⠉⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⣷⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢰⠁⣿⢻⠔⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⣠⣄⣰⣄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠻⠀⠀⠀⠀⠀⠀⠀⠋⡴⠀⡞⣤⢀⠏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⢦⠙⠀⠀⠀⠀⠏⢠⠀⠀⠀⠂⡰⢀⠋⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⢄⣥⣟⢸⠀⠀⠀⠀⠀⠃⣿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢳⠘⠀⠀⠀⠀⡿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠛⡿⣿⣿⠸⠀⠀⠀⠀⠀⡏⣿⠻⣍⠲⠑⠉⠀⠀⠀⠀⠀⠀⠀⠋⠖⣶⢲⠉⣿⢬⠳⠈⡇⣿⣿⣿⠀⠁⠋⠚⠒⠒⠒⠒⠙⠈⣇⣿⣿⠻⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⡿⣶⣷⣿⣶⢶⠻⠉⠉⠉⠟⣿⣿⣿⣿⢿⠻⡛⣍⢭⠭⠭⠭⣤⣠⠀⠀⠀⠀⠀⡀⣄⠲⣄⡿⣿⣿⣾⣤⣀⠆⠲⠘⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⠈⠀⠀⠀⠀ ⠀⠀⠃⣴⠀⠀⠞⣠⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢠⡀⣀⢋⠞⠤⢤⠢⠛⠉⠀⠀⠀⠀⠋⡿⣿⣿⢠⠀⠀⠀⠉⠀⠀⠀⠷⠿⠿⠸⠑⡇⣿⣿⣿⢿⠀⠀⠀⠀ ⠀⠀⡇⠛⠛⠟⢠⠀⠀⠀⠀⠀⠀⣀⣤⣦⣶⣶⣶⣶⣤⢖⠴⡠⣀⢀⠀⠀⠀⠀⠀⡀⣀⠦⠷⣿⣿⣿⣿⣸⠀⠋⣸⣀⣸⠀⠀⠀⡄⣷⣿⢸⠁⡾⣿⣿⣿⣿⠸⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⢹⡿⣿⣿⠟⢠⠉⠛⠜⠉⠉⣏⣿⣿⠹⣟⣿⣿⣄⢸⠀⠀⠀ ⠀⠀⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣸⠀⠀⠀ ⠀⠀⡇⣾⣴⣦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣾⣧⣿⣿⣿⣿⣿⣿⣾⣷⢸⠀⠀⠀ ⠀⠀⠀⢧⠈⠀⣆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠀⣧⣯⣿⣿⣿⣿⢸⡇⢠⠀⠀⠀ ⠀⠀⠀⠀⢦⠙⠋⡿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢻⠉⠞⣷⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣦⣷⣿⣿⣿⢿⠴⡤⣀⣀⣀⣏⣿⣿⣿⢿⠿⠙⠈⠀⠀⠀⠀⠀⠀⡄⠹⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠏⠉⡟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣲⠒⠒⠒⠒⠤⣤⣦⣶⣿⣾⣠⠀⣆⠙⠀⠀⠀⠀⠀⠀⡀⢳⡟⣿⣾⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⢀⣦⣿⠻⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⡀⣷⢨⠀⠀⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠈⠀⡀⣦⣿⠻⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢫⠛⠛⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠋⣿⣿⣿⣿⣾⣤⣤⣀⣧⣿⣿⣾⣤⣠⣦⣷⢿⠻⠛⣟⣿⢻⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣶⣿⣿⠻⠈⠀⠀⣆⣿⠹⠀⠀⠀⠀⡀⣄⣦⣷⣿⣿⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣷⢿⠛⠛⡏⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣶⣶⣾⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠟⣿⣴⣠⢀⠀⠀⠀⠀⠀⠃⠚⠉⠁⠉⠋⠛⠿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇ ⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⣰ ⣀⢻⠶⠶⠲⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠀⠉⠛⠶⣧⣀⠀⠀⣆⠸ ⡇⢠⠀⠀⠤⢀⣸⣄⠦⠲⣛⢮⠀⠈⠀⠀⠓⠉⢞⡴⣦⢉⡴⠁⡼⠀⠀⠀⠁⣼ ⡇⠺⠈⠉⡏⠉⡢⠥⠭⡨⠔⣀⣷⢀⠀⠀⠀⣸⠀⢄⠠⠐⠤⣠⠀⠀⠁⠀⢟⢫ ⢻⢿⡘⠄⢹⠰⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⣦⠙⠀⠀⠀⠀⠀⠀⡠⠋⡿⣿⣿ ⣿⣿⣿⠻⠙⡈⠀⠀⠀⠉⠛⣴⢀⠀⠀⠀⠀⠀⡀⣭⠶⠓⠛⠛⠿⣯⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣹⣈⣃⣉⢉⠀⠀⠀⠀⠁⠀⠉⢉⠋⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣢⣈⢀⠋⡨⠭⠼⠤⠦⠤⠤⠇⢿⠘⠈⠀⠥⠐ ⠀⠐⠈⠃⠀⣦⣤⣀⠁⠀⠀⢀⠐⡀⢦⠿⢐⠃⢀⠀ ⡂⢁⠩⣀⠐⠄⠁⠔⢀⠀⠀⠠⡀⠂⠈⠠⠀⠰⠀⠀ ⠀⠀⠇⠘⠚⠵⢭⠲⠁⠁⠊⠠⠉⠄⡁⠠⡰⠀⠀⠀ ⠀⠀⠀⣦⡓⠛⠞⠃⠀⡁⢌⠛⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠃⡟⡻⢽⠭⠙⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠒⣤⡀⣀⣄⢻⠉⢋⢀⠁⠀⠈⠀ ⠀⠀⠀⠀⠃⡿⢠⡈⢀⠺⣴⣥⣷⠹⡉⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣿⣝⣎⠁⡋⣛⢟⡴⣄⣇⢂⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢿⠻⣿⢰⣃⣿⠹⠏⣠⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣤⣶⣶⡶⣾⣷⣀⠳⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡳⠀⠀⣄⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠾⢶⠑⠈⠀⠀⠟⠽⠚⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣶⠀⠋⣿⠿⠙⣄⠃⢛⡵⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⡂⣷⣿⣾⣰⠃⢇⡛⣋⡿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠊⠠⣄⠢⠈⠀⣈⠤⠤⢜⣀⣅⣤⣤⣠⡔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⡠⡔⣊⣔⠀⠀⠀⡀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡎⠟⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠈⠀⠀⠃⢠⡴⡎⠀⠀⠀⠀⠀⠀⠀⠁⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠅⠯⢠⠀⠀⠟⢁⠀⠀⠀⠀⠀⠋⠳⠈⠁⠿⠈⠀⠀⠀⠂⠙⠈⠀⠀ ⠀⠎⣤⣼⢢⠛⠟⣿⢿⣻⠖⠶⠨⡉⠀⣀⠄⣏⣾⢠⣄⠀⠉⢈⣧⣿⠸⠀ ⠀⢿⡼⠀⠀⠀⣀⣤⣤⣠⠀⢀⠀⠀⡀⠅⣿⣿⢋⡻⢰⠉⡄⢻⡼⣿⣿⠀ ⠀⣾⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣻⣿⡿⣿⣾⣿⣿⣿⣷⠀ ⠀⠄⠑⢻⠉⠀⠁⠉⠉⠈⠀⠀⠀⠀⡇⣄⣿⣿⣿⣿⣿⣿⠸⣖⣿⣿⡸⠀ ⠀⠀⠀⣀⣤⢢⠐⠄⣤⣷⣠⠣⠀⠀⡀⠢⣾⣦⣷⣿⣿⣿⢿⡿⣼⣤⠻⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠛⠰⠀⠀⠀⠄⠂⣷⣿⣬⣄⣷⣬⣄⠶⡛⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⣄⠦⡶⢿⠀⠀⠀⠀

⠀⠀⠁⠋⠒⠒⡷⢀⠀⠉⢴⠤⠤⠤⠠⠄⠀⠤⠤⠤⠦⢶⠲⠒⠛⠛⠚⠒⠚⢴⠢⠓⠉⠉⠉⠉⠛⠛⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀ ⠀⠞⣠⠀⠀⠀⡄⠸⠁⣏⠙⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢾⠘⠀⠀⠀⠀⠀⡆⣶⣤⣧⠄⠀⠀⡀⣟⢸⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⡖⣿⣹⣯⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠥⣋⡴⠀⠀⠀⠀⠀⠀⠁⠈⠂⡇⠼⠤⣧⠞⠇⢸⠀⠀⠀⠀⠀⠀ ⠏⣶⠙⠀⠀⠀⠀⠀⡆⣼⣀⠀⢄⠘⠀⠀⠀⠉⠊⠒⠤⣁⢿⡿⡄⠱⠋⠶⠘⠀⠀⠜⢀⠀⠀⠀⡅⠰⠁⢿⣼⠀⠀⠀⠀⠀⠀⠀ ⢆⠉⡀⢍⠢⠑⠉⠀⠀⡏⠲⠈⠀⡀⣸⢀⠀⠀⠀⠀⠀⡇⣿⣿⠀⠀⣄⡦⢐⠉⠉⢌⠒⠐⠛⠞⢒⡤⢀⡆⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⠀⡀⣹⢞⡠⠀⠀⠀⠀⠃⣤⠘⠀⠀⠁⠉⠉⡇⢀⣀⠃⢹⠚⠶⠶⣤⣄⣤⣢⢑⠈⠀⠀⠏⣽⠢⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠻⠚⡠⠀⠀⠀⠀⠀⠎⢠⠀⣇⢤⠣⡷⣙⣸⣆⠀⠃⡿⣿⠹⠀⠀⠁⠟⢿⠺⠈⡀⠧⡿⣿⣷⠹⡄⠛⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⠁⠔⣆⠈⠀⡄⠘⠀⡇⣷⠀⠈⠀⡇⣻⣏⣿⢻⠋⣰⣥⣼⠀⢉⠀⡷⣹⣌⣧⣿⢿⣺⣴⠀⠀⠀⠀⠀ ⠀⠀⠀⡆⢸⠀⠀⠀⠀⠄⢠⠀⠚⢸⠀⠀⢣⠉⡹⣿⠀⢸⠀⡇⣾⢷⣟⣿⣿⢿⡾⠒⡥⣟⢿⠻⣟⢹⠀⣇⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⠑⠈⠀⠀⠀⠋⡵⠀⡇⠈⠀⡆⡉⣤⣤⠢⢉⠀⡏⢠⠀⣄⣿⣿⣿⣿⠻⡿⣿⢹⣾⣶⣶⠸⡀⣿⢻⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠠⡀⢿⡿⠘⡀⢹⠉⠋⡚⢲⠀⠃⣿⣿⢰⠀⠀⡟⣼⣀⣤⣷⣿⣦⣶⣷⣿⠊⠀⡇⡗⣿⣻⣝⣭⠿⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⢧⠀⠈⠀⠀⠀⠀⠀⡆⣿⣸⠀⠀⠏⣾⢀⠀⠁⡿⣼⠀⠀⡔⠄⠀⠀⡄⡷⣿⣦⣷⣿⣿⣶⣶⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠿⡾⡀⠀⠀⠀⠀⠀⠀⠀⣦⢈⠀⠃⣿⢠⠀⠀⡿⣿⠁⠈⠀⢉⠈⠀⠉⡟⣿⣽⣿⢿⡿⣿⢿⠿⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⣁⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠢⡿⣸⠀⠀⡏⣿⣛⡖⠒⢓⣙⢛⠿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠢⠖⣶⣷⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠤⣀⢀⠀⠀⠂⠀⠄⢀⠋⢠⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⠜⠤⠦⠴⠠⡦⣨⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⢲⠉⠀⠀⠀⡿⣿⢿⠛⠈⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⡀⢳⠒⠒⠔⡸⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⣰⠀⣏⠐⠉⠉⣿⣿⣿⣿⣿⠿⠿⢠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⡼⣇⣠⠀⠀⡞⢀⣄⣷⣿⣿⣠⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⡾⣠⠎⢠⠀⠀⠎⢀⠀⠀⡀⣦⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠎⣠⠀⡼⢱⠀⠋⡴⢀⠀⠀⠀⠀⠁⣼⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢶⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⠃⢠⠀⠀⢤⠤⣠⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣹⠉⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⣠⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠟⠻⠘⢇⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⣀⣀⢄⠧⠴⠤⠛⠒⠓⠀⣼⠈⠀⠀⠀⠀⠀⠀⠀⠀⠖⢻⡞⣽⡟⣼⡷⢤⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠓⣽⣉⠄⡿⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣆⣸⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠄⠧⠄⠢⠓⠈⠁⢿⠒⡙⣿⠈⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠳⡉⢦⣙⣦⠉⠀⡀⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⠀⠀⠀⠀⠀⠀⠀⠁⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠾⣠⠀⣠⣀⣄⣧⢿⠀⠈⠀⠀⠀⠀⠀⠀⠋⠙⠈⠀⠀⠀⠁⠋⠔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢛⠛⠀⠀⠃⠉⠈⣶⣶⣶⠿⠛⠂⠒⠔⡷⢀⠀⣇⣀⠄⣀⣞⢤⠧⠮⠷⠙⠀⠀⠁⠟⠤⠤⠦⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⠻⡟⣽⣯⣿⢿⠿⠛⠙⣏⠀⠀⠀⡇⠀⠀⡀⠸⠀⡀⢹⠀⠇⣿⢾⠙⣄⠯⣠⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢡⠈⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⢸⠁⠋⡟⠀⠀⡄⠸⡟⣸⢀⡀⢃⢠⠀⠀⠀⠀⠋⡿ ⠀⠀⠀⠀⣤⣤⣷⡈⣷⣿⣾⢰⠀⣆⣻⢙⡋⣿⣹⣋⣿⣥⣿⣿⣿⢠⠀⠀⠀⠀⡆⣿⣿⣿⢻⠀⠀⡄⡖⠿⠀⠀⣇⠀⠀⠀⠀⠃⢨⠀ ⠀⠀⠀⠀⠀⠀⠶⠶⡦⣿⣿⠀⠀⠀⣼⡒⣉⣟⣿⣿⣶⣧⣿⣾⢠⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⢻⠈⠀⠀⡀⢦⠑⡀⢳⠉⠋⠟⣠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢸⠀⡁⣿⣿⠀⠀⡿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣴⢀⡀⠢⠈⠀⠀⠀⢄⣢⣬⠒⠁⢱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡏⢰⣧⠀⡏⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠀⠀⠀⡀⢏⠛⠉⠉⠉⡚⢤⠓⠉⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣼⠀⡇⠏⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠙⠀⠇⣿⣿⣿⣿⣿⠀⠀⠀⡀⢄⠢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⡆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡤⣶⣿⣿⣿⣿⢻⠉⠉⠉⠐⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⠀

⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡄⣿⣿⣷⣾⣴⣀⣧⣿⣼⢀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⣀⣷⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠙⠀⡀⣷⠻⠉⡄⣅⡿⣼⢀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣤⣀⣀⣀⣤⣶ ⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠛⠈⣀⣤⣶⣴⣠⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣾⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣴⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣷⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣴⣤⢶⠻⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⣿⣽⢀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⣾⣤⢀⠜⠀⠀⠀⠀⣀⣤⣶⠿⠛⠛⠛⠛⠛⠛⠟⠿⣿⣴⣠⡄⣿⠘⠀⠀⡦⢳⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠈⡀⣦⢷⠻⠙⠉⠈⠀⠀⠀⠀⠉⠋⠛⠿⡶⣴⣠⢀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⡀⣀⣀⢋⣼⢀⠀⣄⢿⠈⠀⡆⢿⠉⠈⠀⠁⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠆⠙⠀⠁⢸⠀⠀⠀⡀⣍⣾⣶⣤⣦⣴⣤⣤⣀⢀⠀⠀⠀⠀⠀⠋⠖⠲⠒⠛⠙⠈⠈⠀⠀⠀⠀⠀⠀⠁⡞⣠⣀⣄⣤⠤⡄⢷⠙⠋⣴⣀⣄⣧⣹⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣄⣀⠀⠀⠁⠞⣠⢀⠀⠀⠀⠀⠀⠁⠉⠉⠊⠒⠒⠴⡤⣀⢀⠀⠃⠛⠛⡙⢿⡉⢯⠛⠉⠉⠛⠶⣠⢀⠀⠀⠀⠀⠀⠀⡀⣷⢙⠉⠉⠛⡴⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀⠀⠀⠁⠚⠴⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣤⠦⠳⡏⣼⢀⠀⡁⣿⣾⠖⠶⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢴⠤⠤⡧⢀⠀⠀⠁⡼⢀⠀⠀⠀⠀⣇⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⣄⠢⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⢼⠤⠤⣿⠀⠀⠀⡿⢁⠋⠿⠢⠛⠓⡾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠈⣀⢦⠓⠈⠀⠀⠀⣀⢤⠲⠓⠉⠈⠀⠀⠀⡀⣿⣋⣶⣀⠀⠀⡇⣴⣤⣶⢶⠿⣽⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠞⡠⢀⠀⠀⡀⣄⠳⠈⡀⢤⠲⠉⠀⠀⠀⠀⠀⣀⣄⠲⠈⠀⡇⣸⠀⠀⠀⠆⣿⠀⠀⠀⠏⣾⣀⣄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⡼⢤⠳⠉⠈⠀⠉⡴⣀⠀⠀⠀⠀⡀⣄⠢⠘⠀⠀⠀⠀⠀⣇⠀⡿⠀⠀⠀⠀⠀⣿⢻⠈⠀⠀⠀⠀⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡷⠈⠀⠀⡀⣏⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⠀⣇⠈⠀⠀⠀⠃⣾⡀⣦⠻⠋⠟⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⢤⠤⡤⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠞⢠⠀⠀⠀⢳⠈⠀⠁⡿⢹⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⠒⠛⠓⠓⠒⠒⡗⠂⢒⡟⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀ ⣶⣤⡶⡧⡅⣮⠃⡇⠉⠈⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀ ⠛⡷⢨⡇⠃⢴⡇⡗⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀ ⣹⢍⢮⡗⡄⢨⡸⡇⡇⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⡠⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⣩⣈⢁⡇⠟⢩⡏⡗⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣻⠿⠛⡈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⣉⣀⣀⡅⣀⢀⠀⣇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣾⢀⠀⣆⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣠⠀⡇⡿⣿⣼⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢐⣆⠹⠉⠊⠒⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀ ⣿⢧⠀⡇⣹⣺⢣⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢆⠛⡿⣿⣋⠔⣠⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⣦⡄⠀⠇⠉⠉⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠄⣿⣯⣤⢀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⣤⠿⠸⡇⠀⡀⣗⢸⠀⠀⠀⠀⠀⠀⠀⠊⢠⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⢣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀ ⠉⣩⢻⡟⠍⢩⡯⢸⠀⠀⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⣾⣶⢳⠇⡃⣛⣟⢸⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀ ⣀⣛⢛⡾⠿⠻⣿⢸⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢩⠖⠠ ⠋⣾⢠⠀⠀⣄⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⠀⠀ ⣷⢠⠀⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀

⡆⠘⠀⠀⠀⠀⠀⠀⡀⢄⠤⠒⠙⠈⠈⠀⠀⣉⠋⠒⠤⣠⢀⠀⠀⠀⠀⠀⠀⠃⡰ ⠀⡀⢤⠠⠤⠤⠤⠤⠄⣰⣀⣈⠀⡀⢸⠀⠀⢸⡀⣀⣸⣀⢸⠀⠤⠤⠤⠤⡤⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⢀⠀⠀⠑⠀⠉⢰⠀⠀⢠⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⡹⠀⠀⠁⠈⠀⣆⢈⠀⠀⠀⠀⡎⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⠀⠀⡀⠀⠁⢸⡀⢀⠀⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠋⠛⠤⣿⢶⠙⣏⠈⠀⠀⠁⡶⠙⠀⠀⠀⡽⠋⡴⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⣤⣤⣠⢀⠀⠀⡆⠙⣉⢴⣧⢻⠛⡟⣼⡦⣹⠉⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠟⠶⣷⣾⣠⣀⢀⠀⠤⠠⡀⣀⢀⣧⣿⠶⠻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⢀⠁⡿⢴⠯⠿⠬⠸⠀⠇⠵⠿⠽⡦⣿⠈⡀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠿⣶⣿⠒⣤⣤⣮⢀⠁⠀⣷⣬⣤⢲⡟⣶⠿⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⢉⠋⣿⢿⠽⣧⠿⠿⣠⢷⠿⣿⠧⠿⣿⠛⡉⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⡿⣿⡷⠀⡇⡷⣿⡿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⠽⡿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣬⣶⣿⣿⣿⣿⣿⣶⣴⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠘⡇⢸⠀⠀⣸⠀⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⢸⠀⠇⢹⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⡀⣤⣷ ⣿⣿⣿⣶⢈⠀⠀⠀⠀⠀⠀⠀⠁⡜⢀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠀⠀⠀⠀⠀⡀ ⣿⣿⣰⠀⠀⣀⠤⠓⠉⠊⠖⠦⣑⠈⠆⠀⠀⠀⠀⠀⠊⢠⠀⠀⠀⡀⠀⠀⠀⠀ ⣿⣸⠀⠀⠀⠀⠀⠀⣄⠙⠀⠀⠀⠀⣀⠄⠢⠐⠉⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⡄⢈⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⡆⠈⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠲⣤⠺⠔⠤⠘⠄⠀⠀⠀⠈⠀ ⠀⠀⠀⠄⠤⠠⠔⠦⠤⠀⠀⠀⠀⠉⠁⠝⡈⠒⠛⡟⣿⠿⠙⢸⠀⢁⠀⠀⠆⠀ ⠀⠀⠀⠀⠀⡇⠛⢸⠀⠀⠀⠀⠀⠀⡐⠀⠀⠁⣿⣿⣿⣠⠀⡄⠘⠀⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣞⢈⠀⠀⠜⠐⠀⡌⠀⠀⠜⣀⣏⣴⣀⠠⠁⠎⢦⠙⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⢸⠟⠿⠹⠀⠃⢀⠀⡎⢤⢀⠀⠀⠀⡏⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⣿⣀⣠⣀⠸⡁⠀⠀⢋⡠⠧⠐⠀⡤⣦⡿⣻⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⣼⢣⠛⠟⢸⡀⢿⠿⣿⢼⢈⠀⠀⠃⡻⣴⣿⢹⠁⠀⠀⠀⠀ ⠀⠀⡀⠘⠀⠀⠀⡀⡦⣿⣶⢀⠀⣮⣿⣶⣶⣼⠛⠁⡀⢋⠿⣿⣿⡸⠀⠀⠀⠀ ⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠠⠀⠀⣇⢿⠿⠿⣿⣿⣳⠫⣧⣼⣣⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣆⠉⡉⣿⣿⣿⣿⣿⣡⡚⢆⢱⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣐⣉⣅⣞⣓⣼⡄⢿⡘⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢷⠑⣄⠉⡉⣦⢰⠀⠀⠀

⡄⣳⣿⣹⡟⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣾⣠ ⠃⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡞⣶⣾⣴⣀⠄⠄ ⡿⣿⣿⡇⣿⣿⣿⣹⣿⣿⣿⣿⠻⠈⠄⠄⠄⠄ ⠋⠟⠿⠿⠿⠻⣌⣿⣿⡎⣿⣿⣿⣾⡵⣭⡭⣍⣭⢮⠄⠄⠄⠄ ⡟⣿⣿⣿⣿⣿⣿⣿⡹⣷⣿⣾⣫⢟⣿⣿⣿⣿⣿⣿⣿⢿⠻⠄⠄ ⣶⣶⣿⣿⣿⣿⣿⣿⣿⢿⣎⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠄ ⠁⠈⠄⣇⣿⣿⣿⣿⣿⣿⢿⡎⣿⣿⣿⣼⣀⣀⣀⣀⣧⣿⣿⢠⠄ ⡀⣤⠄⡆⣶⣶⣿⣿⣿⣿⣿⢻⣅⣷⣿⢻⠈⠖⠶⠙⡟⣾⢉⠄⠄ ⡀⣚⣦⣷⣿⣿⢿⣙⣷⣿⣿⣿⣾⣫⡅⣷⠸⠄ ⠉⠟⡿⡇⢿⣜⣿⣿⣿⡶⣭⣿⣿⢿⣿⡇⡻⢨⠄ ⠋⡿⣿⣿⣿⣿⣿⣾⣤⢀⡄⡆⡽⣓⣭⣷⣿⣿⣿⣿⠘ ⠋⡿⣿⣿⣿⣿⢡⣀⣀⠄⠄⠋⠿⣿⡻⣪⣿⡄⣸⣧⣿⣿⣿ ⡟⣿⣿⣿⣿⣴⢀⠄⣱⠑⠞⡿⣿⣓⣛⣿⣿⡹⢇⠹⡇⣿⣿⣿ ⡏⣿⣿⣾⣭⢛⠛⠛⠛⡇⡄⠉⠄⢁⢦⣤⣥⣿⣴⠘⢩⡇⣿⣿⣿

⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣨⣶⡯⣥⣿⢏ ⣼⣿⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣿⣻⣿⣿ ⣿⣟⣀⣀⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣼⢹⡏⢿⣿⣿ ⡿⠿⠛⠛⠿⡑⣄⡀⠀⣤⠟⠛⠉⠉⠻⣿⡇⠘⣿⣿ ⠀⠰⠾⡿⠿⢾⡿⠁⢸⣷⠋⠿⠿⠿⠂⢸⣿⣾⣿⣿ ⠀⠀⠀⠀⠐⢿⢀⠀⠀⣙⠓⠀⠀⠀⠀⠹⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⡿⠨⠀⠀⣴⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿ ⠀⠀⠀⠀⠈⢰⣦⠠⢀⢠⠥⣀⠀⠀⠀⠀⣿⣿⣿⣿ ⡄⠀⠀⢀⣴⣿⠿⠿⠟⠿⢷⣦⡁⠀⠀⢠⠚⣿⣿⣿ ⣑⣄⣀⢸⠳⠤⢄⠠⠂⢀⡴⠞⣧⠀⢠⡎⠄⢿⣿⣿ ⣿⢻⡍⢸⣄⡀⠮⢬⣤⠔⢀⣠⣿⠀⢸⡇⠀⠀⠈⠙ ⡈⣿⠋⠈⣿⣿⡀⠆⠐⢲⣿⣿⡏⠀⣸⡇⠀⠀⠀⠀ ⠇⢻⣦⣄⣙⢿⣿⣿⣿⣾⣿⣋⣀⣀⣏⠇⠀⠀

⣿⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣀⣤⣄⣠⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣟⣤⣤⣤⣤⣤⣤⣤⣀⣀⣤⣤⣠⣀⣀⣀⣀⣀⣀⣿ ⣿⠀⠀⠀⠁⠟⠿⠿⠿⠿⠻⠙⠀⠀⠀⠇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠹⠀⠀⠀⠀⠋⡿⣿⣿⣿⢿⠻⠈⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠃⣾⣀⣀⣦⣿⣿⣿⣿⢿⠙⠛⡷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⣾⠲⠛⠙⠟⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⣿ ⣿⠀⠀⣿⠀⠀⠀⠀⠀⣦⣷⣿⣿⣿⢿⡿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠸⠀⢸⠀⠁⣟⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⠀⠀⠀⠀⣿ ⣿⠀⠀⣷⠈⠀⠀⠀⠀⠀⠀⣅⣿⣧⣨⠀⡀⢷⠻⠈⠀⠀⠀⠀⠀⠀⠁⡿⠀⢯⠚⣶⡥⣭⣿⣹⣧⣿⣿⣶⣀⢀⠀⡏⣰⠀⠀⠀⠀⣿ ⣿⠀⠀⡆⢾⠳⠍⢀⠄⡀⠈⡿⢠⡸⡀⠀⠀⡀⣧⣿⠶⠿⡰⠁⠚⠽⣁⣏⣲⣶⢤⣤⣀⢀⠀⡇⠁⣿⢉⠀⠀⠁⠿⣴⠳⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⢳⠀⡀⣄⠤⠲⠓⣯⠘⢹⠀⠀⠀⠁⠉⠈⠁⡰⠀⠁⠞⣠⢄⢢⠖⠤⣠⢀⠀⠀⠀⡇⡏⣰⠁⠛⠴⣠⡞⠀⡀⢳⠀⠀⠀⣿ ⣿⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⣀⣧⠙⠈⠁⠀⠀⡀⣧⢀⠀⡀⣦⠬⠤⠤⠒⠀⠄⠀⠀⠀⠁⣻⣾⡴⣠⠀⠀⠃⢸⠀⠀⡆⠸⠀⠀⣿ ⣿⠀⠀⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⢣⣄⠑⢄⠙⠚⣠⢄⠀⠀⠀⡀⠢⠒⠒⠑⠉⠋⠓⠔⡠⢀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢾⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⢫⠘⣆⣽⢈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⣞⢫⡠⠀⠀⠀⠀⠀⠀⠀⠇⢰⠀⠀⠀⠁⢸⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⣄⢽⠑⠀⠀⠀⠀⡩⢞⢸⠀⣆⡙⣀⠤⠦⠒⠒⠒⠒⠓⠿⣰⠀⣼⢦⠓⠈⠀⠀⠀⠀⠁⣰⠀⠀⠀⠀⡞⢀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⡀⣳⠹⠛⠴⡠⢀⠉⢺⠖⢴⡤⢯⠾⠶⠶⠒⠖⠶⡴⢄⠤⠲⢲⠑⠉⣄⠳⠙⠀⠋⡰⠀⠀⠀⠋⡴⢀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠁⠋⡿⣿⢹⠋⠴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡦⣿⣿⢹⠸⠁⠋⡴⢀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠋⠟⣿⣿⣿⣿⣿⣼⠢⠚⠔⠥⠿⠿⣿⣿⠩⠐⠀⠀⠀⠅⣿⠿⠿⠿⠽⠢⠓⠚⠀⣇⣿⣿⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠏⣾⣴⣠⡏⣿⣿⣿⣿⢻⡟⠛⠛⡛⣿⣿⣿⣶⣠⠀⠀⠀⠀⣄⣶⣿⣿⣿⢛⠛⠛⢿⠛⡙⣿⣿⢹⡄⢻⠈⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠆⣾⢀⠀⠋⣿⣿⣿⣿⣿⣠⣀⣀⣍⣭⣉⣉⠛⠹⠉⠉⠉⠉⠉⠉⣍⠻⣉⣀⣄⣤⣀⣀⣤⣤⣷⣿⣿⠻⠉⣆⠹⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⣄⠳⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⢿⠿⠛⠉⡅⣿⣿⣀⣧⢿⡟⢻⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⡀⢧⣯⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⣼⣦⣿⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⣧⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠁⣸⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣸⣧⣿⣸⠀⣏⣽⢛⡞⠀⠀⠀⠀⣣⣭⣷⣼⣧⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣵⣼⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡶⢹⠚⠶⠶⠙⡇⣶⣿⢿⣿⣿⠛⠙⠀⡏⣿⣿⣿⣿⣿⣿⡰⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣼⠀⠀⠀⡀⣧⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣿⠛⠈⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⡟⣼⠀⡀⣦⣻⣭⣶⣷⣿⣿⣿⣿⣿⢻⠉⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣫⡾⣠⠀⡇⣿⢸⣿⢿⠻⠛⠉⠈⣿ ⣿⠀⠀⠀⠀⠀⠀⣿⢠⠀⠀⠀⠀⣆⢷⠙⣈⣄⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣾⣶⣴⣀⢏⡿⣠⠀⠀⠀⡇⣼⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣅⢿⠀⠃⠙⠀⠀⠀⡀⠀⠀⠀⠀⠁⠋⠐⠀⠋⡾⣤⢀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡏⢰⠀⠀⣇⠹⠐⠀⠀⠀⠀⠀⠃⡿⢰⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⢰⣿ ⣿⠀⠀⠀⠀⠀⠀⣿⠘⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⡿⣿⠀⠉⠀⠀⠁⠰⡶⣿⠘⠀⠀⠀⢷⠈⠀⠀⠀⠀⠀⡇⢁⣿⣿⣿⣿⣿⣰⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠃⣼⠀⠀⠁⡿⣰⣀⣄⢤⠤⠤⠤⣤⣀⣆⢻⠈⠀⠀⡀⢿⠀⠀⠀⠀⠀⡿⡇⢸⣀⣄⣦⢒⠓⠉⣿ ⣿⠀⠀⠀⠀⠀⠀⣇⣿⠈⠀⠀⠁⡾⠀⠀⠁⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢿⠘⠀⠀⡀⢻⠈⠀⠀⠀⣿⡿⢀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⡆⣿⢹⠀⠁⡾⠀⠀⠋⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⠙⠀⠀⡀⢷⠈⠀⠇⣻⣾⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⣧⣿⠙⡼⠉⠟⡿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢿⠙⠁⡀⢷⠈⡏⣿⢀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠛⠛⠉⠉⠉⠛⠙⠛⡛⣿⣻⢛⠋⠛⠛⠋⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⡉⣿⣿⣿⢛⠛⠛⠙⠉⠉⠉⠉⠛⠛⣿

⠀⠀⠀⠀⠀⠀⠀⡃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⣾⣶⣤⣠⣀⢀⠀⠀⠀⠀⡁⣋⡿⣿⣿⣾⢠⠀⠀ ⠀⠀⠀⠿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣾⣴⣄⣷⣿⣿⣴⢀⠀⠀⠀ ⠀⠀⠀⣦⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣸⢀⠀⠀⠀⠁⣈⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣀⣦⣷⣿⢿⠛⠀⠀⠀⠀⠉⠀⠀⠀⠀⠃⡿⢿⠻⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠙⠀⠀⠀⠀ ⠀⠀⠀⡇⢸⠀⠉⣏⣿⣿⠿⡿⣿⣿⣿⠐⠀⠀⠀⡄⣤⣀⣀⣀⣤⣤⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⠰⠀⠀⠀ ⠀⠀⠉⡿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⣿⣾⢠⠀⠀⠀⠀ ⠃⡿⣿⣿⣿⣿⣿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⢘⠀⠁⠘⠀⠀ ⡄⣦⣿⣿⣿⣿⢻⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠛⣿⢸⠀⠀ ⠀⠀⡀⣄⣤⣶⣶⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠁⠈⣷⣿⣠⠄⠤⠤ ⢸⠀⠀⠀⠀⠀⠇⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢦⠓⠉⠞⣠⠀⠀⠁⠉⠛⠛⠓⣸⢠⡇⣿⠀⠀⠀⠀ ⣧⠻⠙⠈⠀⠀⡿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⡷⣿⣿⣿⢰⠁⣏⠘⡇⣿⡿⠠⠀⠀ ⡇⣿⣿⣿⣿⣿⣿⣽⠉⠉⠀⠉⠚⠒⠛⠛⠟⠿⠿⠿⣸⠀⠀⠀⠀⢿⠒⣴⣤⣤⣠⢀⠀⢠⡿⣿⣿⡿⢰⠀ ⡇⠈⣀⣄⣤⣷⣿⣾⠀⡇⣰⠀⠀⠀⡀⣦⣿⣿⣿⢶⢼⠀⠀⠀⠀⣄⠑⠀⠀⠀⠀⠁⠜⡟⣿⣿⣿⣼⠀⠀ ⡀⢳⠀⠀⠀⡇⣿⠀⠀⣧⠚⠒⠒⠔⠤⡤⣀⢀⠀⠏⢀⠀⠀⠀⠀⠀⠀⢄⠀⠁⠤⠏⣿⣿⣿⣿⣿⢀⠀⠀ ⠀⡀⢿⠻⠛⡟⣿⠀⠀⡀⢳⠈⠀⠀⠀⠀⠀⠁⠔⢀⠀⠀⠀⠀⠁⠉⠛⠿⡿⣿⠏⣿⣿⣿⣿⣿⢠⠀⠀⠀ ⠀⠀⣧⣿⣿⣿⣿⠙⠉⠉⠉⣉⠯⠉⠉⠉⠉⠛⠈⠀⠟⠿⠿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣾⢰⠀⠀⠀⠀ ⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣵⠟⠀⡇⣿⣿⣿⣿⣿⣹⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡴⢀⠀⠁⡀⣆⣿⣿⢀⠁⢸⠀⡀⠠⠀⠀ ⠀⠀⠀⠛⡛⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿⣼⢀⠁⠈⠁⠖⣤⠷⠒⣿⢸⠀⣹⠀⠀⠇⠀⠀⠀ ⠀⠀⠀⣹⣉⣿⣿⣿⢿⠈⠀⣀⣀⣤⣤⣦⣶⣿⣿⣿⣿⠛⠿⡾⠄⣨⠀⠀⡆⣧⣸⢸⠀⣇⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣁⣉⣯⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣿⣹⢀⠀⠀⢀⠀⠟⢿⣿⠀⢠⠀⠖⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⣻⣓⣛⣐⣆⣿⣿⢹⠀⠀⠀⠀⠀⡇⣿⣿⠀⣿⣿⢹⠀⠀⠀⠃⣿⣿⢠⠀⠀⠀⠛⠐⠀⠀⡤⢀⠀ ⠀⠀⠀⢣⠟⡿⠘⠀⣆⣿⣿⠹⠀⠀⠀⠀⡿⣿⣸⣧⣶⣿⣿⠈⠀⠀⡿⣿⣸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢦⠘⣂⠘⠀⠀⣇⣿⣿⠹⠀⠀⠁⣿⣿⢦⣄⠳⡟⣿⢻⠀⡏⣿⣿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠆⠔⠒⠛⠘⠀⣠⣄⣿⣿⠻⠀⡏⣿⢸⠀⠀⠀⡀⣧⣿⠿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠊⠤⠀⣀⢀⠀⣀⠀⠢⠈⠁⠔⡀⣀⣀⣀⢀⠢⠈⠀⠀ ⠀⠀⠀⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡨⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀ ⠀⠀⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀ ⠀⠁⢳⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠁⢀⠀ ⠁⠰⠀⠀⡀⣀⣤⠤⠤⠷⠛⠚⠒⠒⠓⠛⢹⠉⠛⠛⠟⠼⣤⣠⢣⠀ ⡇⠙⠀⠀⠀⠀⠊⠤⣀⢀⠀⠀⠀⠀⠀⠄⡂⣹⣀⢀⠀⠀⣀⠤⡓⠸ ⡇⠶⠶⠶⡶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠻⠀⠀⠀⠀⠀⠀⢡ ⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⡇ ⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣰⠀⠀⠀⠀⠀⠀⡌ ⠀⠀⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠎⢠⠀⠀⠀⠀⠀⠁⠔⠀ ⠀⠀⠀⠀⢀⠿⠛⠙⠉⠀⠀⠀⠁⠉⠛⡩⠀⠀⠀⠀⠉⠋⠹⢀⠀⠀ ⠀⠀⠀⠇⣠⣇⡍⣀⣀⣀⣀⣀⣄⣳⠉⡁⣰⣀⣀⣀⣇⣡⣰⠀⠀⠀ ⠀⠀⠀⠀⢈⠔⣷⠿⠾⠓⠛⠛⠐⡇⠀⣀⠄⠧⠔⠧⣠⢀⠀⠀⠀⠀ ⠀⠀⠀⡟⠀⠀⠀⣄⢹⠣⡏⢠⠀⡄⣹⠦⠑⡆⠁⠚⠳⠀⠀⠀⠀⠀ ⠀⠀⠃⣽⠻⠀⠀⠀⡇⠀⣄⠀⠀⠀⣸⠀⡇⠀⣄⠑⡖⢀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⣿⣛⣚⡒⣶⠶⠓⠛⡫⠛⠛⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠓⠈⠀⡄⠀⡀⢸⣇⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣴⣹⢙⠃⢳⠈⢻⢸⠃⣼⣤⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⠟⣸⣃⣿⠻⣌⡿⢠⡇⢽⠣⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢁⣻⢙⡟⣬⢠⡀⢠⠀⢱⠈⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣶⣴⣤⣦⡷⠿⠛⡉⠋⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠉⡿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠉⠋⠚⠗⣸⢀⠀⠀⡋⢶⠶⠶⠲⠒⠐⠂⠐⠂⠒⠒⠒⠒⡒⢶⠒⠛⠉⠉⠉⠉⠉⠉⠋⣞⠲⠓⠉⠉⠈⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠼⣠⢀⠀⠀⠀⢇⠀⠀⡄⢹⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣻⢈⠀⠀⢀⠀⠀⠀⡀⣀⣿⣿⣿⣷⣸⣈⣀⣀⣄⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠀⠀⠀⠀⠀⠀⡀⠻⠟⡿⣿⢻⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⢩⣼⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⡇⢹⠀⠉⠋⠈⠈⣥⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⠀⠀⠀⠀⠀⠀⡄⡤⣷⣿⠿⣿⣾⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣀⠇⠿⣤⢀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠐⠄⠦⣷⣈⣀⣀⣿⢠⡟⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣤⠱⠀⠀⠀⠀⠀⠀⠀⡀⣵⣀⠀⠀⡀⢦⠈⠀⠀⠀⠁⠉⠋⠒⠴⡠⢀⣿⠿⡿⡀⢳⠉⠏⠦⠸⠀⠀⠀⡼⢀⠀⠀⠀⠀⠀⡏⠀⠁⡟⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢳⠈⡀⢄⠢⠓⠉⠀⠀⠀⠀⡀⢿⠙⠀⠀⠀⣄⠼⡠⣀⣀⠀⠀⠀⠀⠀⠃⣿⣿⢸⠀⠀⣀⢦⡗⢉⠀⠀⠀⢦⠑⠉⠉⠉⠛⠽⢊⠔⣠⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠀⠇⢸⠀⡀⣷⠤⠛⠚⡤⢀⡀⢀⠀⠀⠃⢻⠈⠀⠀⠀⠀⠀⠀⠀⡇⣤⣤⢸⠀⠸⠀⠁⠋⠛⣟⣾⣶⢿⠽⡬⣠⣠⣀⢀⠀⠁⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢷⠀⠀⡅⠾⣠⠀⠀⠀⠀⠀⠀⠁⡰⠀⢳⠉⠀⠀⠃⠿⠿⠿⡟⠀⠀⢸⡏⢿⡾⣠⣤⣀⢀⠀⠁⠙⠀⣄⠦⠓⠈⠀⠏⣿⣿⠘⢆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢿⠞⣠⠀⠀⠀⠀⠀⠀⠀⠋⣠⠀⠀⡆⣘⣀⢧⣴⣿⡟⢀⡇⠀⠀⢿⣿⣿⣿⠙⠀⠀⠁⠟⣿⣿⣾⠳⠈⠀⣁⣿⣿⣿⣧⣿⠙⡀⠿⠻⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⣼⠀⠀⠀⠀⠀⠀⠀⠁⡞⣀⢹⠀⠀⠀⢳⠀⠀⠀⣿⢸⠀⡏⠀⠀⣿⣻⣋⣿⣿⢻⠈⡼⣀⣥⣾⢀⠁⢸⠀⣷⣿⣉⢤⣧⣿⣿⢿⣺⡶⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠖⣠⠀⠁⡏⠘⠀⠀⡆⠘⠀⡏⡯⢸⠀⣸⠀⠀⣿⣿⣿⡟⣿⣿⣿⢿⠛⡽⠉⠚⡵⣿⠿⠙⣍⣿⢸⠀⣤⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠋⣠⡀⢹⠀⠀⠀⣸⣆⢻⣿⢹⠀⢰⠀⠀⣟⢰⡀⣦⣿⣿⣿⣟⣿⠻⠈⠋⣿⣿⣼⣮⣿⣿⢿⠈⡆⣷⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢄⠳⠉⠀⠀⠁⠋⡴⣧⠈⠀⡇⠈⠀⠀⡄⠳⠈⠀⠀⣄⠿⠉⠋⣼⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣻⢛⣛⣀⣀⣄⢠⡉⣏⣿⣿⠻⠙⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⣆⣿⣿⢹⠀⡄⢲⠒⠒⠓⠒⣶⠀⠀⡟⣿⣿⣾⠀⠀⠀⠃⣿⣰⠀⣀⣤⣿⣿⣨⣦⣴⣷⣿⠉⠠⠀⠀⣸⣿⡟⢿⠳⣛⣟⣿⠿⠻⠙⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣦⠘⠀⠀⠐⠀⠀⠀⠀⠀⠀⣧⣿⣿⢀⠀⠀⠃⣿⣼⠀⠀⠀⠏⣿⣾⢠⠀⠁⡌⡄⠠⠀⠀⠀⢣⣿⣿⣶⣿⣿⣿⣶⣶⣶⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠟⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢰⠀⠀⠁⡿⣾⠀⠀⠀⠃⣿⣾⢀⠀⠀⡄⠀⠀⠀⠀⠀⠏⠿⣿⣾⠿⠿⣛⣿⣿⠿⠛⠙⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⣶⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⡟⣿⢠⠀⠀⠁⣿⣿⢶⡄⣤⠂⠒⠶⠰⠀⠇⡿⣿⣾⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣽⠉⠏⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⢹⠀⠀⠀⡿⣿⣿⠿⣭⣭⡍⣿⠹⠿⣿⣿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠤⡶⣶⣶⣿⣿⣿⣿⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢦⣙⢧⠘⢳⠈⠀⠁⢸⠏⢫⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡈⢰⢧⠀⢿⠀⣽⠟⢠⢧⠁⠉⠉⠉⠈⠀⠀ ⠀⠁⠞⣡⠾⣠⣀⣄⢿⠾⣠⣄⢦⠛⠈⠀⠀⡇⣴⠳⠈ ⠀⣽⣤⡶⠀⠀⠀⠃⣸⠀⠀⠀⢧⠀⣀⣤⠤⣤⠒⠁⢿ ⠀⡅⠻⠎⠙⠂⠀⡀⢱⠀⠀⠀⡀⢠⠀⠀⠀⠁⠆⣡⡾ ⠈⣿⣨⣤⣿⢤⠦⠹⡍⢩⠉⠉⡏⣼⠷⠬⣤⢶⠙⡟⢀ ⣷⣾⣴⣠⣄⢦⠛⢈⠁⠋⡴⣠⠀⠀⠀⣄⠦⠒⣟⣾⠀ ⠀⣇⢤⠳⠈⠀⠀⣧⣠⢷⠀⠀⠋⠠⠉⠚⠗⠼⣠⢀⠀ ⠀⡆⠙⠀⣧⠀⠀⡄⠀⡄⢰⠀⢁⡼⣀⠀⡥⢸⠀⠀⠀ ⠀⠀⡀⣄⡄⢳⠉⠀⠀⠀⠀⠉⡾⠂⠀⠒⡤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣄⠳⠖⣳⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠟⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠤⣤⣶⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷ ⣿⣿⣿⣿⣿⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣼⠀⡀⣄⠤⠲⠙⠈⠀⠀⠀⠀⠀⠁⠋⠛⡴⣠⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⣀⣦⠳⠛⠶⡤⣤⢀⣄⠦⠒⠑⠉⣸⠀⠀⠀⠀⠀⠀⠀⠀⠋⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠹⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⠦⠒⠛⠐⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⢀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠸⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠑⠈⠀⣆⠙⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢿⡶⣀⢧⠛⠔⡠⣀⢷⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠉⠉⠉⠈⠀⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠔⡤⣀⠀⠀⠏⣿⠛⠛⠈⠀⡇⠀⠀⡀⠸⠀⠀⠀⠀⢳⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣠⢀⡞⠀⠀⣀⠤⠢⠒⠒⠒⠒⠒⠑⠟⣻⠒⠶⠤⠤⠷⡿⣿⣿⣿⣿⣿⠾⡷⠸⠀⠀⡆⠘⠀⠀⠀⡄⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣴⢀⠀⠀⣆⠸⠀⠀⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⢰⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⣸⠀⠀⠀⠁⠋⠶⣿⣿⣿⣾⣳⠈⠀⠀⠀⠁⣟⠀⠀⡀⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠈⠀⠀⠀⡄⠐⢆⠀⠀⠀⡜⠀⠀⠀⠃⣼⢀⠀⠉⣾⣠⠀⠀⢇⠀⠁⠋⡔⣄⣶⠻⠈⡀⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡀⢸⠀⠟⠛⠛⠘⠀⠀⠀⠇⢠⠀⠀⠃⣿⣚⡴⣀⢀⠀⠀⠀⠀⡇⠩⣈⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⢹⡟⣿⣿⣿⣿⠘⠀⠀⣸⠀⠀⠀⡼⢀⠁⠈⠀⠀⠀⠀⠀⠉⡟⣿⢿⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⢸⣀⣀⣀⠀⢇⠀⠂⢀⠀⠀⠀⠁⠞⡠⣄⠷⠚⠒⠐⡤⣤⣶⢿⡿⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⢿⠈⠀⠀⠁⡏⠰⠀⢢⠙⠉⠋⡼⣿⠻⠞⣠⠀⠀⠀⠀⠀⠉⡷⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣹⠀⢿⠿⠿⣿⣿⠀⠀⠃⣿⣿⣿⣿⣿⣹⠉⠈⠀⠀⠀⠀⠟⢿⡾⣀⣧⣿⣿⠘⠀⠚⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠆⠘⠀⠀⠀⠀⠀⠀⡄⠳⣿⣿⣿⣿⣴⠀⠀⡇⣦⣿⣿⣿⣿⣿⣿⣴⠁⠉⠀⠀⣀⣀⠋⠟⡿⣿⣿⢿⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⢀⠀⠀⠀⡆⠉⣿⣸⣀⣀⣀⣿⠇⣿⢿⠛⠰⠀⠏⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⡿⣿⣿⠳⡽⠱⣇⣿⣹⣀⠓⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣀⣀⣄⣷⣿⣿⢿⠿⣿⣿⡿⣿⣾⠙⡆⢢⠟⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠛⠾⡿⣿⣿⣿⣿⣿⣿⣿⣸⠋⣿⢹⠋⣠⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⠑⡉⣀⣀⣀⣡⣖⢒⣟⡴⢀⣦⣿⢿⠈⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⡙⣟⠙⠀⣄⢳⠀⠀⡄⣷⣿⡟⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣽⢦⠙⡀⢳⠉⠉⠉⡀⣤⢠⠀⠀⠀⠀⠀

⡱⢎⠧⡹⢌⠧⡹⢌⠧⡹⢌⠧⡹⢌⡇⠯⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢱⡍⢮⡱⢍⢮⠱⡍⢮⡱⢍⠮⡱⡍⡞ ⡕⣋⠞⡱⣋⠞⣱⢋⡞⣡⢏⡚⢥⠫⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⠐⡀⡐⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡣⢇⡏⣎⠳⣙⠦⣙⢬⠳⣱⠹⡜ ⠮⣅⢯⡱⢍⡞⢥⡚⣬⡑⢮⡙⣎⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⡐⠀⢀⠀⠄⠨⠐⡂⣄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡱⡜⣬⠳⣩⠎⡕⡎⢧⡱⢣⡝ ⡳⡜⣆⢇⡏⡜⢦⡹⣄⡛⢦⡹⣌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⠐⡀⢂⠐⠀⡀⡀⠠⠐⡣⠲⠄⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡥⣛⢔⡣⡕⢮⡱⢎⢳⡘⡵⣘ ⣱⢃⡞⡲⡸⢍⡖⡱⢬⡙⢦⡓⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢂⠐⡀⠂⠌⠉⠀⠀⡁⠰⣄⠓⡂⡑⠢⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣩⠖⡱⢎⢣⢜⠪⣕⠺⣐⢣ ⢦⣋⠼⣡⠝⡼⣰⡙⢦⡙⢦⡹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢈⠠⠐⠠⠁⠌⠠⠦⠣⠙⠈⠀⠛⠀⢉⠠⠐⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣍⠧⣋⠞⡬⢳⡌⢧⡙⢦ ⡖⡥⣛⡔⣫⠲⢥⡚⣥⡙⢦⡙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠢⢠⡁⢎⡐⢌⡐⢢⠄⡄⣂⢠⢸⠀⣥⣓⢑⢌⠔⣈⠠⠀⠀⠀⠀⠀⠀⠀⠀⡙⢦⣋⡜⣎⡱⢣⠞⣥⢚⡥ ⡜⡥⢳⡘⢦⠛⢦⠹⡴⡙⢦⣙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⢨⢲⠢⢦⢰⡲⢌⡲⣕⡪⢷⠸⠛⠛⠕⠐⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡙⢦⢣⠞⣔⢣⣋⢞⡰⣃⠞ ⡸⣃⢇⡻⣘⠿⣘⠧⣃⠻⣄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠻⡄⠣⡛⡿⡛⣟⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢇⢟⡸⣘⢇⡸⡜⣤⢃⡟ ⡱⣃⠮⡱⢣⠞⡱⢪⠥⡛⡬⢎⡁⠀⠀⠀⠀⠀⠀⠀⠀⠒⡤⢤⣀⠀⠀⠀⠀⠉⠜⠱⢨⠔⡍⠒⡀⠀⠀⢀⣠⣴⣮⣶⡥⣒⠀⠆⠀⠀⠀⠀⠀⠀⠜⣊⢮⡱⢍⡎⠵⠳⣌⠞⣜ ⡱⢣⣍⠳⣍⠞⣱⢋⡼⢱⡙⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⣐⠂⢀⠀⠀⠀⠁⣴⠢⠄⠀⠀⠢⠁⢁⠠⠤⠄⠁⠁⠈⠀⠀⡀⢀⠀⠀⠀⠀⠹⣆⢧⣋⠼⣩⠳⣌⡛⢬ ⡱⢣⡜⡱⢎⡞⣡⠞⣜⢣⡝⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠐⢀⡬⠉⠂⠀⠀⠀⢀⢺⢁⠎⡀⠄⠀⠠⣄⠀⠀⢀⣦⠄⠀⢀⡀⠜⣀⠂⠀⠀⠀⠳⡜⢦⡙⣎⡱⣋⢖⡙⣎ ⡱⢣⡚⡥⢓⡼⢡⠞⡜⣢⠝⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⢡⡐⢏⠆⠀⠀⠀⠎⢎⣏⠒⡀⠈⢣⣤⠀⢐⣊⣃⠤⡐⠔⡨⠐⣁⠂⠌⠀⠀⢈⠷⣙⠶⣙⠦⡓⡭⢪⠕⣎ ⡱⢣⡹⢌⡳⡜⣣⢛⡬⣑⠞⡥⠁⠀⠀⠀⠀⠠⠀⢄⠠⠐⠨⠔⡡⢂⡉⢎⡀⠀⠀⠀⢎⠳⣌⠳⣈⠌⠹⢿⣽⡽⣰⣋⠷⡔⢎⡆⡱⠀⠄⠠⠀⠀⠈⡞⣥⡛⣬⠓⡽⣘⢇⡻⡰ ⡱⣃⠳⡥⢓⡱⢣⣙⢲⣉⠞⡄⠀⠀⠀⠀⠀⠀⠌⡐⢈⢂⠡⢂⡔⣢⡜⠦⠀⠀⠀⠐⣌⠳⡌⣓⢐⠊⠈⢿⣗⣦⣇⡟⣬⢻⣟⡬⡑⠌⢀⠀⠀⠀⠀⢙⢦⣙⢦⡛⡴⣩⠖⣱⢣ ⡱⣃⢏⠖⡭⣒⠳⣌⢧⢚⡜⠀⠀⠀⠀⠀⠀⠈⢀⠐⡀⢢⠡⢳⢴⠟⠂⠀⢀⡠⠀⢠⣤⢳⡶⣢⡀⣆⠀⠀⠘⣙⢮⡪⢱⠋⡎⡐⠡⢈⠀⠠⠀⠀⠀⠐⠼⣘⢦⠳⡱⢥⠺⣥⢚ ⡱⢎⢎⠞⣡⠇⣏⠲⣌⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠰⢡⢿⡱⠁⠀⠀⠀⠘⠓⠀⠀⠀⠉⠢⠉⠈⠈⠙⠀⣄⠠⢓⠕⣎⢝⡰⠡⡈⠄⠠⠀⠀⠀⠀⠀⠊⡝⢮⡱⣙⢎⡳⢆⢏ ⡱⣋⡜⢮⡑⡞⣌⠳⣌⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠣⢏⢶⣙⠄⡀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠋⠇⢀⠠⣴⢿⣦⢉⠼⡽⢏⡒⢡⠐⠠⠀⡀⠀⠀⠀⠀⠈⣝⠶⣱⢩⢖⡱⢫⡜ ⡱⢥⡚⢦⡙⢦⢍⡳⢜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐⠈⠲⢎⠇⠊⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠘⢃⢓⣹⡚⢌⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⣊⠷⣡⠏⡼⡘⣇⠞ ⣱⠣⡝⢦⣙⠮⣜⡡⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⠈⠀⠀⠀⠀⠀⠀⠤⡀⠈⠙⡶⠞⢖⠶⣄⠀⠀⠀⠀⠀⢕⠣⠅⠂⠍⠠⠈⠀⠀⠀⠀⠀⠀⠀⢎⡳⢥⡛⡴⣹⢰⣋ ⢖⡣⣝⢢⡝⢲⡸⣸⢩⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠐⠀⠀⠀⠀⠀⠀⠁⠐⠀⠁⠀⠁⠀⠌⠐⠁⠙⠢⠀⠀⠀⢠⠙⠜⢠⠑⠀⢀⠀⠀⠀⠀⠀⠀⢀⡩⢞⡱⣚⠴⣃⢧⡚ ⢎⡕⣪⠒⣜⢣⡱⢥⡓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠘⠲⢮⡍⢎⢒⣃⣐⠔⠦⡁⠀⠀⠀⢄⠣⠄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠰⣙⠮⡱⡍⣞⡡⢎⡵ ⢎⡲⢅⡻⢌⡳⣜⢣⠽⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠙⠁⠚⠑⠋⠀⡀⢳⡀⠀⠀⠈⢀⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣥⢫⡕⣭⢲⡙⡎⢖ ⢎⡖⣭⠲⣍⠶⠉⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰⣘⢦⢳⡘⢦⢣⡝⣘⢎ ⡎⡜⢢⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢪⢣⡝⡎⣧⠚⣥⠚ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠊⠱⣚⢬⠲⣍⡚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⡱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣐⠮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡰⡰⢎⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠀⠀⠤⠤⠤⠠⠀⠃⡘⢉⠭⠬⠤⠒⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣸⣤⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠻⠙⠀⠀⣇⢿⠉⠉⣏⢿⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠻⠀⠀⠀⠀⠀⠀⣧⠢⠀⠁⠚⡠⢦⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⣄⢿⠛⡿⣿⣴⣤⣧⣿⢙⣉⣉⢤⠻⠚⠀⠀⠀⠀⠀⡏⠀⢄⠳⠚⠖⡤⢀⠄⢣⠎⢀⠀⠀⠀⠀⡀⣀⠤⠓⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣴⣁⢿⠘⠀⡄⣷⢹⡉⣿⣿⣿⢿⠙⠀⠉⠛⠉⣸⠀⠞⣠⠀⠀⠀⠀⠀⠀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠙⠀⠀⠀⠀⠀ ⠀⠈⠃⣸⠀⡀⢻⠿⠶⠶⠛⣿⣰⣆⣿⣽⣿⣼⣠⠀⠀⡃⢀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠈⠀⠀⠀ ⡂⢻⡟⠀⠀⠀⣿⠋⠟⡽⣨⢀⠀⠀⣄⣷⣼⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠘⠀⠀ ⠀⣿⣼⠀⠁⠀⡇⣿⣿⣿⣿⢶⠳⠈⠉⠉⢸⠀⠀⠀⠀⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠀ ⠀⣧⣽⢋⡖⣤⣿⣿⣿⣿⣞⢴⣀⠀⣅⣾⣷⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢦⡘⢄⠳⠀⠀⠀⠀⠀⠀⠁⠈⢆⡀⢱ ⠀⡀⣸⢀⠀⠉⡟⢻⣌⢦⠑⠉⠋⠞⣲⠒⠒⢸⠀⠀⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⡄⠙⠀⢤⠀⠀⠀⠀⠀⣷⢸⠀⠈⡆ ⠀⠀⡄⡷⣾⣴⣠⠀⣅⠸⠀⡞⢀⠀⠀⠀⠇⢰⠀⠀⠀⡆⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠀⠀⠀⠀⠀⠆⣴⠀⠉⡀⢧ ⠀⠀⠀⡀⢢⠛⠞⡭⣄⠷⠟⢻⠀⠀⠀⠀⡅⠘⠀⠀⠀⠀⢳⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠴⣀⣀⣄⠷⡀ ⠀⠀⠀⠀⠀⠀⣀⣤⣤⣠⢀⡀⠹⠀⠎⣠⣀⣆⠾⠑⠈⠀⡀⠱⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠉⠉⠋⣶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠛⢀⠀⠀⠀⢣⠀⣀⠦⠑⡄⠙⡄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡍⣶⠬⣠⢦⠙⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⡆⠈⠀⠀⠀⣄⣙⠢⡈⠳⠈⠞⣧⠿⠧⠿⠀⠀⠀⠀⠀⠀⡍⠉⢏⠀⡀⠢⠉⠉⢿⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⠉⠉⠉⠉⡉⢫⣏⠲⣠⠁⡜⢀⠎⣇⠀⠀⠀⠀⠉⡔⣏⣸⣇⠀⠀⠀⣄⢸⡀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠁⡔⢀⠀⠀⣄⣘⣀⣀⢱⠉⠞⣠⠁⡔⢊⡴⢯⠺⠔⡠⢁⠔⢀⣁⣰⠀⠀⠀⠁⢺⠒⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠱⡀⠀⠀⠀⠀⠀⣆⠙⠋⡴⣠⣀⡤⢤⡤⢠⣀⠀⠀⠀⠃⣶⠳⠞⢠⠀⠀⠀⠋⡰⠀⠋⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠠⠒⠐⠤⠤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⡟⢶⠒⠒⠿⡠⣁⣎⡴⢀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣾⣤⣀⣤⣠⠀⢀⠀⡏⣾⣠⡀⣀⣷⣿⢸⠀⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣿⣿⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⢀⡀⡀⡀⡀⡀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⠀⣁⡟⢷⠙⠈⠀⠀⣀⠀⣤⣷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠟⣷⣸⠀⠀⠀⠀⠀⠀⠁⡟⣾⢀⠀⠀⠀⡀⣿⢸⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠛⠛⠾⠶⠶⠶⠶⠶⠷⠛⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⡿⢸⠏⣼⢀⠀⡀⣦⠻⠙⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠋⠟⣿⣸⡄⣷⠹⠀⠀⠀⠀⠃⡿⣴⠀⠀⠀⠀⠀⠀⣧⢻⠀⠀⠀⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⣾⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣤⣶⢿⠈⠀⠀⠀⠀⠀⣿⣶⣿⢀⠀⠀⠀⠀⠀⣄⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀ ⠀⠀⠋⡾⣠⠀⡟⢀⠀⡀⣦⠻⠀⠀⠋⣿⢠⠀⠀⠀⠀⠀⠀⠀⡇⣿⠈⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠻⠟⠿⠻⡿⠘⠀⡀⣧⠹⠛⠙⠈⠀⣾⠀⡄⢷⠙⠀⠀⠀⠀⠀⠀⡀⣦⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀ ⠛⡶⣠⠀⠀⠃⢠⠀⠀⠀⠀⣄⢻⡟⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢸⠀⠀⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣴⠠⠉⠉⠈⠀⠋⠟⣿⣿⢸⠿⠀⡂⣿⣿⣿⣿⣿⣧⢸⠀⠀⡏⣶⣵⣿⣿⢿⢿⠋⠿⢿⣟⢾⠻⠙⠈⠀⠀⠀⠀⡄⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣰⠀⠀⠀ ⢀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠏⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣠⠀⠀⣀⣿⣾⣧⣿⣟⣿⣿⣿⣿⠾⠷⣿⣿⢿⡶⣤⣤⢀⠁⡟⣿⠿⣶⣠⠀⣷⣾⣀⣆⠷⠙⠈⠀⣄⣤⢷⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⠈⠀⠀⠃⣿⢤⡇⣿⣿⣿⣿⣿⣿⠰⠀⣀⢀⠀⠀⠀⠋⠿⣿⣿⣨⢀⠀⠁⠋⡿⢸⠀⠀⠀⡀⣏⢿⠿⠿⡿⣴⣶⠿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡾⣠⠀⠀⠀⠀⠀⠀ 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⠀⠀⠘⡇⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⢿⠻⠛⠉⠉⠋⠛⠞⣶⣿⠻⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣤⣤⣩⣏⣿⣿⣾⣴⣀⣀⠀⠀⠀⠀⣧⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⣿⡟⡜⣷⢸⠀⠀⡇⣿⣿⣿⣿⣿⠘⠀⠀⡆⣿⢿⠀⡇⣿⣿⣿⣿⣿⣿⣿⣾⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠀⣼⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⣀⣿⣰⠀⠀⠀⣿⣿⠛⠀⡆⣿⣿⣿⣿⣿⣿⣀⠀⠀⠉⠟⠿⣿⣿⣾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⠀⠀⠀⡟⣿⣿⣿⣿⣿⢹⠀⠀⠀⣿⣿⠂⡟⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢛⠀⣆⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⢠⠀⠏⣿⢠⠀⠁⠈⡟⣿⣾⢀⠀⠁⣿⣿⣿⣿⣿⢩⠟⡿⣿⣿⣿⣿⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⢿⠈⠀⠀⠀⠀⠀⠀⠀⡆⣿⣶⡟⢸⠀⠀⡿⣿⣿⣿⣿⣿⣿⠀⠀⠁⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⢰⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠙⡄⢻⠀⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⢰⠀⠃⣾⢀⠛⠟⣿⣿⣿⣾⢀⠀⠋⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣯⢿⠘⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⠀⠃⣿⣸⡇⣿⣿⣿⣿⣿⣿⣿⣿⠁⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣄⢻⣏⠘⡆⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣸⠀⠟⣽⠿⣿⣿⣿⣤⣿⣿⢰⠀⠟⣿⣯⣿⣿⣿⣿⣿⣿⣿⣾⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠟⣾⣴⣀⢀⠀⠀⠀⠀⠀⠀⠀⡄⣿⡏⣿⠹⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⢷⣜⣶⠿⠈⣷⢸⠀⠀⠀⠀⠀⠀⠀⠟⣿⢻⢋⡿⣿⣿⣿⣨⡏⣼⠀⡇⣿⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣫⢸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠉⠛⠛⠟⣿⣿⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⣏⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⠁⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠘⣦⠻⡉⢿⡌⣿⠘⠀⠀⠀⠀⠋⠟⣽⣛⣿⣶⣿⣿⣿⣼⣶⣿⢰⠀⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠉⠀⠋⠛⡿⣻⠿⡿⣾⣴⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣤⢶⡶⣤⣤⣤⣄⣤⠳⠛⠟⡿⣿⣿⣿⣹⢉⠋⣿⣿⣿⢻⠟⣿⠀⡇⣺⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣶⣶⣥⣯⣿⣶⣠⠀⠀⠀⠀⠀⠀⣀⣄⣶⣷⣿⣿⣿⣿⣿⣿⡏⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣼⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣾⣠⢀⠀⠁⠟⡿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣦⡶⣶⣶⣴⣿⣿⣿⣿⣿⣿⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠁⣿⠀⠀⠁⠟⣿⣴⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⣯⣽⡿⣿⣿⣿⣿⣻⡏⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡟⢸⠋⡟⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣦⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡀⠱⠈⠀⠉⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠉⠉⠃⢾⢀⠀⠀⠀ ⠀⠀⠀⠈⢖⠠⠤⠠⠂⣐⠍⠁⠀⣧⠀⠊⠠⢂⠀⠄⠤⠤⣲⠁⠀⠀⠀⠀ ⠀⠊⡠⠁⠉⠉⠉⠀⠀⠒⠁⢄⢳⠀⡞⠠⠉⠀⠀⠀⠉⠉⠉⠈⣀⠢⠀⠀ ⡌⠀⠔⢋⠛⠈⡀⢦⠀⠀⠀⡀⠢⠻⢺⡠⠀⠀⠀⡼⢀⠀⠛⠑⢄⠈⢋⠀ ⢸⠀⠀⣄⣁⢈⠀⠊⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢣⠀⠁⣩⢠⠀⢀⡄⢸ ⠘⠀⠀⠀⠄⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡄⠤⠠⠀⠀⠀⢰ ⢂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀ ⠀⢄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠀⠀ ⠀⠀⠀⢇⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡧⠀⠀⠀⠀ ⠀⠀⠀⠸⠀⡀⠢⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢃⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠢⡁⠠⠀⠁⠉⠋⠒⠖⠠⠢⠂⠑⠉⠉⠀⠀⡩⢂⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣀⠋⠟⣸⢇⠊⠒⠑⡏⣇⠻⠙⡀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣠⢀⠁⠀⠀⣀⡄⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠁⢉⠈⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⣏⣿⢬⣤⡠⠀⡄⣤⣥⣿⣹⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⣖⣿⣿⣿⠿⠿⠿⣿⣿⣿⣲⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⡏⣿⣿⣿⣄⣿⣿⣿⢹⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣻⠓⣿⣿⢰⣤⠤⢠⡆⣿⣿⠚⡗⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢱⡇⣾⢠⠀⠀⠀⠀⠀⡄⣷⢸⡎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⡟⢀⠀⠀⠀⠀⠀⠀⠀⡀⢹⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠉⠛⠛⠛⠛⣹⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣩⣭⣿⣿⣿⣿⣿⣟⣛⣭⣽⣿ ⣿⢃⢎⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡿⣟⣿⢻⡽⣻⢽⣫⢟⡽⣫⠿⣝⢯⢻⡝⣯⢟⡿⣻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿ ⣿⢎⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣞⣷⣻⡭⣷⢻⡜⣮⢳⡹⢥⢫⡜⣎⠶⣡⢛⡜⣎⠳⡜⣥⢫⡜⣧⢻⡽⣫⢿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣷⣟⣷⣻⡼⣳⢽⣲⢫⣜⢲⢣⡙⣬⢣⡜⡬⣓⢥⡋⠶⣌⢳⣉⢦⢓⡼⣲⢏⡾⣭⢟⡾⣽⣻⣾⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣻⢷⣻⢞⣷⡹⢧⣋⢶⡹⡌⢧⢣⡙⣤⠣⣜⠲⣡⠞⣸⠱⢎⡱⠎⡜⢎⠶⣙⢎⡳⡝⣾⣹⢳⣿⣽⣿⢿⣿⣿⢷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣷⢯⣏⣗⣫⢲⣉⣆⡉⠄⢂⠉⠆⠂⠱⢀⠓⡈⠱⠠⠉⠆⢉⠂⠄⠑⡈⣄⣪⣴⣬⣵⣿⣴⣿⣷⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⡿⠿⢿⡿⢿⣿⣿⣿⣷⣶⣦⣌⣀⡀⢀⠀⢁⠀⡁⠐⢀⣠⣴⠾⡟⠿⡿⠿⠿⠟⡛⠛⢛⡛⢻⠻⣟⠿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢻⣿⣿⣿⣿⣿⡿⣽⣭⣷⣟⣮⣶⣶⣷⣶⣶⣶⣶⠶⣒⣴⣂⣧⣻⣿⣿⠿⡟⢠⠒⣤⡿⣟⣻⣄⣳⣘⣷⣾⢿⣶⣿⣷⣿⡿⠿⢿⣿⣾⣿⣷⣻⣯⣟⡾⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣿⣿⣿⣿⣿⣟⡿⣝⣻⢿⡿⣿⣷⣶⣿⡛⣛⢛⡛⢻⣍⣯⣿⣿⣿⡿⣏⠷⣉⢦⢉⠶⣹⠹⣟⣿⣿⣭⣯⡙⣏⠻⡙⢛⠛⡛⠻⢿⠿⡻⡝⢧⡻⣽⢯⣟⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢿⣏⡹⣎⠱⡎⢱⠉⢰⠀⠆⢁⡈⢆⠹⣈⠹⢿⣿⣿⣇⢿⣉⢶⢁⡎⡎⢶⢁⠿⣸⡎⣿⢷⡈⠷⢸⢀⠱⡈⠶⢀⠱⢀⠈⠱⠸⢇⢷⢹⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣻⣽⣟⡾⣵⢊⡕⡨⢄⠣⢄⠩⣐⠢⠜⣈⠦⡁⢎⣳⣿⣻⣼⣧⣻⣬⢣⡚⢬⢣⢏⢯⡳⢯⡿⣷⢌⠓⣌⠢⡑⠢⡑⢨⠐⢡⠊⡔⡱⢊⣜⣣⠷⣞⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⢻⣿⣟⣯⢿⡵⣯⡜⡵⢊⡕⢊⠔⡀⠣⠘⢄⠒⣩⣾⡿⢛⠛⠯⡛⢏⠁⠃⢈⠄⠁⠊⠼⠟⠛⠛⠛⠿⣶⠨⡐⠡⡁⠌⠄⡊⠤⢑⠰⡱⢩⢖⣭⢻⣽⣻⣿⣿⣿⣿⣿⣿⣿ ⣿⣻⣯⣿⣿⢯⣟⣷⣻⢼⣱⢋⡴⣁⠎⡤⣁⡮⢤⠆⡴⣩⢜⣳⣾⣶⣽⣾⣤⣃⣄⣚⣃⣔⣆⣮⣷⣿⢾⡷⣾⠷⣦⣥⡴⣬⡒⣌⢢⠅⣎⡱⣍⠾⣜⣯⣞⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣟⣯⣿⢾⡽⣞⣳⣯⢶⣽⣺⣵⢟⣹⣦⣿⣾⣷⣿⣿⣿⣿⠿⡿⠿⠿⢿⠿⠿⠟⠿⢻⠿⢿⢿⡿⣿⣿⣾⣷⣷⣧⡝⣞⢧⡻⣴⢳⡾⣏⣷⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡛⢛⣉⣉⣹⣿⣟⣽⣳⢯⣟⢮⣽⠏⣾⣿⣿⡿⢯⡽⣝⣮⣳⣬⣳⡽⡌⢇⡣⣌⢣⠛⡜⣥⢚⣥⣎⣷⣷⣮⢯⢟⣿⣿⣮⠹⣞⡵⣫⢗⣻⣽⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠉⣼⣿⣿⣿⣿⢻⣿⣷⣯⡞⡽⢮⣝⡞⣿⣿⣇⠞⣡⠏⡝⡮⡝⣭⣫⠔⡝⢘⠰⠈⢆⠙⣘⠰⣛⡮⣙⢣⠓⡜⢢⢎⣜⣿⣿⣿⡜⣞⡽⣾⣳⣿⣦⡀⠀⠀⠈⠉⠉⠉⠙⠛⠻ ⠀⠀⠘⣿⣿⢿⡯⣹⣿⣿⣳⡿⣽⢯⡞⣽⣻⣿⣿⣿⣷⣾⣷⣵⣯⣜⣙⣻⣛⣿⣻⣿⡻⣟⣻⠛⣏⠱⣌⣶⣽⣾⣿⣿⣿⣿⣿⣧⣻⣜⡿⣿⣿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣷⡄⢻⣿⣟⣿⡽⣯⣟⣳⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⢿⣽⣻⣯⣜⣭⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⢧⡿⣽⣿⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣀⣀⣀⣹⣿⣿⣿⣄⣿⣿⣷⣿⣷⣯⣷⣿⣾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣽⣾⣭⣿⣽⣿⣏⣿⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠉⠛⠛⣰⠀⠀⠀⠀⠀⠂⣴⣤⣀⣀⠀⠁⠛⠓⣿⣿⣰⠀ ⠀⠀⣇⣿⣿⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠟⣉⠉⠉⣈⢀⠀⠀ ⠀⠀⡇⡀⣅⣿⠻⠛⠟⠸⠀⠀⡶⣤⣦⣶⣶⣿⣿⣿⣿⢿⠐⠀ ⠀⠋⡿⣿⣿⣾⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣿⢠⠁⠀ ⡄⣶⣿⣿⢛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠻⡾⠀ ⠀⠀⠀⣀⣏⣾⠀⠀⠀⠀⠀⠀⠒⠉⠊⢠⠀⠁⠉⠋⠠⣿⠀⠀ ⡇⠿⠛⠙⣿⢠⠀⠀⠀⠁⠉⠉⠊⠀⠀⠧⣯⣿⣲⡒⠰⣿⡹⠘ ⡆⣈⣤⣧⣾⣠⢼⣀⠀⣦⣿⣶⢄⠀⠀⡄⠑⠀⠀⠃⡏⣿⣿⢀ ⠀⢃⠙⡏⢸⠀⢡⣀⣀⠀⠀⠊⢀⠀⠀⠁⠋⠛⠹⣿⣿⣿⢠⠀ ⠀⡀⣷⣿⢿⠛⠛⣛⠛⠛⠟⠹⠇⡿⣿⣽⣤⣿⣿⣿⣾⢠⠈⠀ ⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣠⠁⣀⣷⣸⣊⠀⠄⠀ ⠀⠀⡽⣯⣿⣹⣄⣤⣦⣶⣷⣿⣿⢋⠞⠔⢀⣆⣜⢸⢧⠀⠀⠀ ⠀⠀⣻⣛⣖⣿⠹⠀⠀⠀⡇⣾⣧⣛⠀⠀⠇⣿⢠⢸⡤⠀⠁⠐ ⠀⠀⢢⣷⠐⣆⣿⠘⠀⠀⡿⢽⡾⣿⠘⠀⣿⣸⠀⠀⣀⠀⠀⠀ ⠀⠀⡀⡐⢉⠂⣦⣿⠙⠃⣿⡀⡀⣦⢿⡟⣾⠠⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣸⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣩⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⣄⠦⠛⠙⠉⠉⠀⠉⠋⠟⣿⣷⠿⠙⠉⠈⠁⠉⠉⠋⠞⡤⣇⣿⣻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠃⣰⠀⠀⠀⠀⣿⣰⢀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⢷⠶⣿⣻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢸⠀⠀⠀⡤⠀⠀⠀⠀⠁⣾⢴⣤⣤⠤⠤⣤⣦⢹⠀⠀⠀⠀⡀⠀⣄⣰⠀⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣬⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠆⠀⠀⠀⠀⠁⠟⣥⢻⠛⠿⠠⠀⠇⠿⡿⣛⣖⢳⠈⠁⠉⠉⠟⣲⣒⣟⠿⠿⠀⠀⠃⠛⠙⡿⢨⠀⠀⡀⢤⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⠟⠿⣿⣿⣿⣿⣿⣾⠴⣠⣀⠀⠀⠀⠀⠀⣄⣶⣿⣶⣠⠀⠀⠀⠀⡀⣀⢤⡦⣿⣿⣿⣿⣿⠿⠛⠙⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠏⣿⣿⣶⣤⣤⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣤⣦⣶⣿⢿⠀⡀⢦⠙⠀⠀⠀⠀⠀ ⠀⠀⠁⠛⣾⣀⠀⠀⠀⠀⣿⣿⣸⠉⠉⠚⠒⠒⠒⠒⠙⠟⠸⠀⠀⠀⡆⠻⠞⠴⠦⠺⠒⠓⠉⠈⣷⣿⣿⠀⠀⠀⡀⣄⢻⠛⠀⡀⢃⠈⠀⠁⠀ ⠀⠆⣽⡏⢸⠀⠀⠀⠀⠋⣿⣾⣠⢀⠋⠿⡿⣿⢿⠻⡟⣼⢀⠀⠀⠀⠀⡇⢻⠟⣿⣿⣿⠻⠈⣀⣦⣿⣿⠙⠀⠀⠀⠀⡇⣿⠀⠀⡇⢸⠀⠀⠀ ⠀⠀⣀⣿⠀⠀⠀⠉⡏⣻⣿⢺⠶⡶⣶⣤⣤⣠⣀⢀⠃⢰⠀⠀⠀⠀⠀⡆⠘⠀⡀⣀⣄⣤⣦⠶⠲⡟⣿⣟⠹⠈⠀⠀⡀⣿⠒⠀⠈⠀⠀⠘⠀ ⠀⠀⠀⡇⠛⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⠀⠀⠀⠁⠀⠀⠀⣦⠙⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⣿⠸⠀⢸⠀⠀⠀⠀ ⠇⠻⠈⣧⣿⣿⣶⣤⣀⣇⣿⠻⠈⠀⠀⠀⠁⠋⠞⣠⠀⠀⠀⠇⣠⢣⠀⠀⠀⡄⢷⠙⠈⠀⠀⠀⠁⠟⣿⣸⣀⣤⣶⣿⣿⣿⢀⠀⢫⠘⠀⠁⠟ ⡀⣸⠀⡇⣸⢀⠀⠀⠀⡇⣿⣿⣽⣯⣿⣤⣠⣧⠿⠿⠿⠿⠿⣸⠀⡀⢿⠿⠿⠿⠿⡿⣤⣤⣿⣽⣭⣿⣿⢸⠀⠀⠀⡀⣇⣴⠀⠀⣦⢠⠀⡆⢠ ⠀⠆⠛⡏⢻⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⠹⠀⣿⣿⣿⣴⣤⣧⠀⠀⠀⡇⣤⣦⣿⣿⣿⠀⠃⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⡟⠙⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⠿⠿⡿⠀⠀⠀⡇⢿⠿⣿⣿⣿⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣀⣧⠀⠀⠀⡇⣠⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠰⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠘⠀⠀⡏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣀⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠁⠖⠦⠐⠈⠁⠉⠉⠉⠛⠛⠟⠿⠿⣿⣽⣤⣧⠦⠓⠙⠋⠽⠭⠭⠿⠿⠿⠿⠶⠶⠶⣤⣀⣄⠢⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠜⢀⠀⠀⠀⠄⡠⣀⢀⠀⠀⠀⠀⠀⣀⣄⣷⣮⣿⠿⣿⣾⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠱⠀⠀⠀⠀⠀⠀ ⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡟⣿⣿⢒⠒⠑⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀ ⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣸⠀⠀⠀⠀⠀⡀⢄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⠛⠙⠈⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⠿⠙ ⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⠈⠀⠀⠀⠀⠀⠏⣿⣾⣷⣿⣿⣿⣿ ⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⡏⢷⠀⠀⠀⠀⠏⣠⣞⢸⠀⡀⣀⣏⣰ ⠀⠀⠀⢢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢰⠋⢠⡄⠸⠀⠁⠟⢻⡟⢉⢸⠀⠋⡞⢠⠀ ⠀⠀⠀⠀⡄⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠋⡶⢑⠞⣠⠀⠀⢸⠋⡴⢁⣿⣿⣿⢻⡴⣠⠀⠀⠀ ⠀⠀⠀⠀⡎⠀⡀⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⡽⣋⠶⣠⠀⠀⠀⠏⣾⢀⠉⡼⣁⣼⣮⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢁⠀⠀⠀⠀⡁⢼⠲⠙⠀⠀⠀⠀⠀⠀⠀⡄⣿⣼⣤⣤⣀⠀⠁⠋⠒⠴⣠⢀⢸⠇⢡⢿⡿⠉⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡆⠈⠀⠀⠊⡴⢦⠒⡁⢌⠳⠙⠈⠀⠀⠀⠱⡄⢷⠈⠀⠄⡷⣿⠚⠒⠤⠤⠓⢋⣿⡿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢆⠈⡇⠀⠀⠀⠀⠀⡀⣤⣷⢿⠀⠀⠀⡀⢢⠈⣦⠻⠈⡇⣠⠀⠀⠀⠁⠟⣼⢁⡞⣮⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣧⣦⠻⠈⠀⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀⡄⠢⡈⣄⣶⠳⠛⠛⠜⣩⢊⡴⣩⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⣀⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠞⠓⠉⠉⡉⣉⠉⠓⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⠢⠙⠀⣈⢿⠻⠑⠈⠀⠁⠋⠒⠤⠤⡤⣦⠙⠀⠀⡀⣁⣼⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡇⠀⣿⣼⢀⠀⣀⣀⣀⢤⠳⠈⠀⠀⠀⣆⠀⠀⠋⣰⠀⠝⡤⠢⠐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⡞⣠⣀⡀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⠀⠀⠀⡇⢀⠁⠎⣄⢼⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡇⣿⣿⠈⠀⠁⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⣾⣮⢀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⢳⡀⢦⠙⡀⢻⣙⠿⠻⠛⠟⢸⠀⠀⠀⠀⣿⠔⢀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⠀⢧⠈⡇⠸⣽⣷⣿⣟⣿⣴⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⡀⣿⣬⢀⡇⡘⢀⣉⢉⠉⠋⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠤⠤⡷⢸⠂⡿⣠⣿⣹⠀⡀⣷⠀⠀⠏⢓⠉⠊⠒⠒⠤⠢⠙⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⢸⠁⣼⣧⠀⠀⡇⠀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⠠⠴⠚⠷⠿⠿⠿⠻⡾⡿⣿⣷⠿⡿⢿⠿⡿⣽⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣸⣀⣀⣉⣉⣉⣈⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣱⣀⣀⣀⣋⣛⣙⣈⣀⣀⣀⣇ ⢸⠀⡞⣠⣦⣿⣿⠻⠛⣷⠀⠀⠀⠀⠀⠀⠁⠀⡇⠲⠑⡟⣿⣿⣿⣿⠻⠀⠀⡇ ⢸⠀⢸⠀⠀⡀⣄⣾⣾⣤⠳⠈⠀⠀⠀⠀⡜⠃⡏⠒⡿⣾⣿⣾⣤⣀⣾⠀⠀⡇ ⢸⠀⣵⠢⠑⠉⠇⢨⢀⠀⡀⣴⣥⢰⠔⡺⣜⣥⣨⣀⠀⢁⣸⠀⠋⡶⢆⠈⠀⡇ ⢸⠀⡄⠈⠀⠀⣀⢄⠲⠈⡈⢀⡭⠀⡆⠀⠂⠀⠀⠀⠁⡾⢴⣠⠀⠸⠀⢇⠀⡇ ⢸⠀⠀⠆⠘⠀⠀⠀⡄⡙⡧⠰⠀⠀⠀⡀⠀⠁⠿⠜⢀⠀⠀⠀⠎⠀⠀⡇⠀⡇ ⢸⠀⠀⠀⡄⠻⠀⠁⡂⣧⠁⣫⣉⠭⠠⠁⠯⡹⡇⢤⠒⠈⠀⠃⢠⠀⠁⡰⠀⡇ ⢸⠀⠀⠀⠁⡟⣿⢊⠄⡀⢀⠀⡀⢀⠀⠀⠀⠀⡀⣀⠄⣷⠿⢙⠉⠔⢀⠀⠀⡇ ⢸⠀⠋⡾⣧⣿⣿⣹⣽⣉⣿⣿⣾⠀⠀⠀⣷⣿⣿⢉⠯⠉⣿⣿⢣⠈⠀⠀⠀⡇ ⢸⠆⢨⠋⡿⣿⣿⣩⣉⣟⣛⢛⠻⠛⠛⠛⢟⡛⣉⣁⣉⣄⣇⣿⠻⢌⠘⠀⠀⡇ ⢸⠀⡀⣷⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡿⣿⠉⣼⣷⠀⠀⡇ ⢸⠀⠀⡀⣿⣿⣿⣿⣷⣿⣤⣿⣵⣠⡀⣇⣷⣿⣿⣿⣿⣿⣿⣿⣿⢻⡰⠀⠀⡇ ⢸⠀⠀⠀⣇⣿⣿⣿⡿⣿⡿⣿⣧⠔⠤⠑⣤⢿⣿⢛⣙⣿⣿⣿⣿⡰⠀⠀⠀⡇ ⢸⠀⠀⠀⡇⣠⣤⣵⣶⣿⣿⣿⣿⠈⠀⡋⡿⣿⣿⣿⣿⣿⣾⣠⣧⣼⠻⠙⠉⡏ ⢸⠀⠀⠀⣿⠀⠀⠀⣄⠳⡀⣀⣤⣤⣴⣤⣤⣤⣤⣁⠞⣠⠀⠀⡇⣿⣿⣿⣿⣿ ⢸⠀⠀⠀⣿⠀⠀⠀⠀⡼⠀⣇⠸⠀⠀⠀⠃⣸⠀⣇⠈⠀⠀⠀⡏⡟⣿⣿⣿⣇ ⢸⠀⠀⠀⣧⠀⠀⠀⡎⠀⠁⡼⢤⠲⠒⡒⣄⢳⠀⠀⢣⠀⠀⠀⢸⣼⣦⣶⢉⡏ ⢸⠀⠀⠀⡇⢹⠀⠎⢀⠁⡼⢀⠀⠀⠀⠀⠀⡀⢷⠈⠀⢣⠀⠁⣿⢠⠀⠀⠀⡇ ⢸⠀⠀⠀⠀⣿⠟⢫⠾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠻⠉⢫⡏⣼⠀⠀⠀⠀⡇ ⢹⠉⠉⠉⠉⡍⣿⣩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⣯⣿⣽⠉⠉⠉⠉⠉⡏

⠀⠀⠠⠐⠁⠉⠛⠿⢟⡽⣊⠤⣀⠀⠀⣀⠀⠀⠀⡀⢆⠈⣿⠘⣇⡑⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠀⠀⡀⣿ ⠉⠉⠏⡿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢸⡇⢻⡃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠀⠀⠀⠋⠀⣇ ⡀⣧⣿⣿⣿⣿⣿⣼⠀⠀⠇⣠⣆⠀⠀⠀⠉⠋⠉⠉⠟⣿⣼⢀⠂⢽⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⡤⢡⠀⠋⡾⢸⠁⡟ ⠋⣿⣿⣿⣿⣿⣿⠉⡉⣏⡸⠹⠀⠋⠿⣾⣿⣿⣿⣿⣾⣹⠀⠀⠀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠔⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⡠⠀⠄⠃⡿⣭⣿⢿⢿⣿ ⣿⣿⣿⣿⣿⣿⣱⣋⢟⣿⣿⣻⡿⣿⣠⠟⣿⣿⣿⣻⠿⡿⢿⠙⡟⢨⠀⠀⠀⠀⠀⠀⠀⠀⠂⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠔⠡⣖⢌⠐⢣⠛⣿⣿⣿⣿⣿⢰⣿⣿ ⣧⣿⣿⣿⣿⣿⣿⣿⣿⣾⣅⣿⣿⢀⡟⣿⣿⣿⣿⢛⠘⡀⣿⣿⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣠⠒⡤⣁⢋⠟⡿⣿⣿⣿⣿⣿⣿⣿⠟⢿⡿ ⣯⣿⣿⣿⣿⣿⣿⣡⣼⢀⡿⣿⣿⡟⣿⣿⣿⣹⠉⡇⢻⡿⣿⢻⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠉⠖⡹⢫⠛⠟⡿⣿⢰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⣿⣿⣿⣿⣿⢸⡿⠀⡇⣿⣿⣿⣿⣿⣿⣰⠀⣏⡿⣿⣿⣿⠱⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠁⠙⠛⡿⣼⣏⣿⣿⣿⣯⣿⣾⣾⠙⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇ ⣿⣿⣿⣿⣿⣿⢿⣿⠀⡿⣿⣿⣿⣿⣿⣸⠀⠏⣿⣿⢻⡿⣨⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠛⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣞⡇⠂⣀⣀⣤⣥⣿⣦⣿⣧⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣹⢎⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠐⠀⠀⠁⠈⠉⠉⠈⠀⠀⣧⣿⣿⣇⣿⣿⣿⣿⣿⢃⢷⣣⢜⢩⠠⠀⠀⠀⠀⡀⢄⣶⣿⣿⣿⣿⣿ ⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣿⣨⣿⣿⢦⡙⠦⣊⠐⠈⠀⠀⠀⠀⠈⠁⠂⡀⠑⠌⠊⢣⠆⢋⢓⠶⣬⣤⣠⣄⣀⣀⣀⣤⢤⠶⣷⢠⡿⣿⣿⣿⣿⣿⣳⣹⢦⡜⠒⢈⠀⠀⠀⠀⠀⠀⠀⢤⣇⣿⣿⣿ ⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡅⣿⠿⣿⢲⣝⠣⢦⠔⢫⠔⠊⠁⠃⠄⠙⢢⡱⢆⡩⠜⢫⢽⣦⣈⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⣦⣿⣿⣿⢡⣻⢦⡙⢦⡙⢦⡈⠐⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿ ⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣾⣾⣷⣬⣹⣦⣵⣮⠿⡹⢞⡡⠜⡪⠕⣣⡙⢧⢏⡷⢤⠘⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣷⣿⣿⢞⣡⠜⢣⡄⢻⢄⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿ ⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣬⡜⢂⢠⡄⠀⣀⠠⢄⠡⡰⣯⢷⡩⢞⡡⠶⡙⢾⣹⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣹⠜⢣⠡⢠⠀⡄⢳⡈⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷ ⠀⠀⠁⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣌⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡡⣦⠿⣩⡼⡟⢼⡑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢺⡕⢃⠠⠀⠀⠀⠀⣄⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄ ⠀⠀⡇⣿⣾⢀⠀⣄⣷⣿⣿⣺⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡃⢦⡝⣽⡘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡂⠑⢀⠀⠀⠀⠀⠀⠀⣯⠿⠙⠈⠀⠀⠀⠂⡀⢇ ⠀⠀⣿⣾⢀⠀⠀⠀⡇⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡁⢬⡹⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢁⠠⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢿⠙⠀⠀⠀⠀⡏ ⠀⠀⡷⢸⠀⠀⠀⠀⡇⣼⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡔⡝⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠗⠟⠻⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣻⣷⢿⠻⠏⡟⢿ ⠀⠀⡆⣌⠐⠀⠀⠀⠀⢸⠘⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡌⡚⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣲⢴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣻⣿⢾⣤⣀⣀⣦ ⠀⠀⠀⢆⡘⠡⠀⠀⠀⢣⠁⡛⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠌⣿⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠘⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⢾⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠳⢌⠉⠀⡀⣧⡘⣦⡖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡝⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⢰⠀⠁⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣇⣿⣿⣿⢣⠙⠉⠋⡸ ⠀⠀⠀⠀⠀⠀⣄⡷⠻⠀⡀⣷⢿⠲⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡶⠘⠀⡿⣸⠐⠀⠀⠀⠀⠀⠀⠋⡴⣿⣿⣿⡿⣿⣿⢿⣿⣯⡷⣟⡴ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠳⠙⣿⠻⡀⢄⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡾⣠⠜⢀⠖⣾⡔⠈⠀⠁⠋⠛⠾⣤⢀⠇⣿⣿⣿⣿⣿⣿⣿⣾⣟⣾⣠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⢻⠈⡆⣿⠻⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⣿⢶⣁⠐⠀⠇⢾⣉⠟⣿⣾⣤⣀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣴⣟⣿⣼⢀⠀⠀ ⠀⠀⠀⠀⠁⠛⠛⠒⠀⠀⠀⠀⡀⣷⣿⣿⢿⣿⣿⣿⣿⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠁⠉⠛⠟⣿⣿⣿⣿⢊⠄⢀⠀⠀⡟⢿⣶⣠⢀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣼⠏⣷⣿⢀⠀⠁⠚ ⠀⠀⠀⡿⣾⣠⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⡿⣾⣿⣾⣏⣿⣠⠀⠁⠊⠟⡿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣿⣿⣿⣿⢋⣿⣿⣰⠀⠞⣣⢡ ⠀⠀⠇⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣷⣿⣿⣿⣿⢻⣷⣾⣝⣧⣾⣽⣦⣿⣿⣻⠆⠘⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⠀⣿⢿⠀⠇⣹⠟⣿⣼⡀⣄⢿⠈⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣾⢠⠃⡴⡕⢪⡰ ⠀⠀⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣾⡿⠦⣈⡖⢹⡄⢻⡈⣷⣿⣿⢰⠁⠂⠁⢀⠌⠂⠁⠀⣷⣿⣾⢿⣿⣿⢻⣇⣿⣿⣿⢠⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⠛⡾⢀⠒⠉⠀⠀ ⠀⠀⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢺⡅⣿⣿⣶⣍⠢⢄⡀⠀⣇⠰⡆⢿⡎⣿⣽⢈⡱⠆⢉⡰⠌⢃⠐⠳⡘⣬⣷⡙⣤⣷⣿⣿⣿⣿⣿⠂⠈⠀⠀⡄⠸⠀⠀⠀⠀⠀⡁⣿⣿⣿⣿⣟⣿⣾⢀⠀⠀⠀⢏⠟ ⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢽⡏⣼⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⢺⡔⡙⠤⢛⡾⣕⢊⡰⢓⣌⢶⠶⡾⣷⣿⠿⣿⣿⣿⣿⠸⡀⢢⠁⠀⣏⠙⠀⠀⠀⠀⡟⣿⣿⢷⣿⣿⣼⢀⠀⠁⠟⣵⣿⣴ ⠀⠀⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⣏⣿⣿⢶⣋⠞⣻⣧⡌⠲⢏⡷⠛⡄⡜⠣⢌⠲⠍⣛⣮⣷⣿⣿⣿⠛⢉⠛⡸⠀⣄⢿⠉⠉⡟⣿⣿⣾⣿⡿⣽⠻⠁⠟⣴⢋⣾⢀⠀ ⠀⠀⠀⣧⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠎⢣⣟⣿⣿⣷⣛⣆⠜⢪⡴⢙⣦⢛⣄⢺⡜⠳⢎⢡⡴⠎⣇⣯⣿⣿⣿⣿⣿⣿⠿⠿⠻⡿⣿⣿⣿⣿⣿⣯⣽⡾⣧⡾⣽⢃⡾⣠⠀⠁⡗ ⠀⠀⠀⠀⢆⠈⠀⠀⠀⠀⠀⠀⠁⡟⢦⢀⠀⠀⠋⠾⠶⠒⠈⠀⠃⡿⢮⣙⢿⣿⣿⣿⡿⣿⣼⠿⣏⣚⠗⣈⡿⢼⡒⠜⠣⣆⣻⡜⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣟⢰⠀⣿⣿⣼⢀⠀⠞⣻⣰ ⠀⠀⠀⠀⠀⠆⠘⠀⠀⠀⠀⠋⣳⡰⢀⠀⠀⠞⣠⠀⠀⠀⣆⠈⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⢽⢻⡿⣿⣴⠏⣁⠲⢎⣃⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣾⠀⡟⡾⢾⢸⠋⡳⣾⢠⠀ ⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠟⣬⡰⠀⠀⠀⡜⠀⠁⠟⣾⢶⠓⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣾⣱⣏⠖⣠⣀⣄⢤⡲⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⢾⢸⠏⣼⢀⣇⣷⣟⣴⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢿⠀⡞⢳⣀⠀⠀⠀⡄⠀⠏⣴⢀⠀⠋⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣵⢏⡼⢀⠀⠀⠉⠉⠀⠀⠀⠀⣀⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣾⡿⣞⣿⣼⠀⠀⡞⣟⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⡾⣜⠠⠀⠀⠀⠀⠀⠏⢠⠀⠀⠏⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡿⣠⠀⠀⠀⡀⣤⣠⣤⠀⠀⠄⣀⣀⢎⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣾⢀⠀⠟⣾⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⣹⢀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠇⣸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⠚⠤⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⡀⣁⢡⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⡿⢰⠀⠏⣾⢀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⣼⠐⠀⠀⠀⠀⠀⠁⣸⠀⠀⠋⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣰⢀⠀⠀⡀⢆⠻⠌⠙⣤⠀⠀⠀⠁⠋⡒⠉⣬⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⠀⠁⣿⢀⡇⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⣘⠀⠀⠀⠀⠀⠀⡇⢠⠀⠟⣿⣿⠃⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⠂⠀⠐⠀⠀⡂⣷⣿⡻⢟⠙⠀⠗⣼⣫⢾⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠀⡟⢸⠁⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⡴⠈⠀⠀⠀⠀⠁⠁⣼⠀⡞⣇⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣚⠡⣉⡙⠉⠉⢄⡸⣿⣿⣿⣿⢿⡹⣶⣿⣿⣿⣿⣼⣧⣧⣿⣿⣿⣿⡷⣿⣿⡏⣾⠀⡿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⣺⢌⠀⠀⠀⠀⠀⠰⡟⢸⠃⢠⡏⣿⣷⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠟⣾⣩⣚⠗⠉⠏⣽⣿⣿⣿⣿⣿⣿⢿⣛⣦⣿⣿⣿⣿⣞⣿⣿⣿⣷⣯⣿⢾⣿⢰⡟⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢒⢈⠀⠀⠀⠀⠀⢃⣿⢀⡇⣭⣢⢍⢣⡿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢯⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢿⣿⣿⣏⣿⣿⣯⣿⣿⣿⣽⡟⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡽⠎⠀⠀⠀⠀⠀⠀⡟⣸⠀⣾⠃⢆⢋⣿⣧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⢿⣾⣻⣿⢿⣯⣿⣿⣽⣻⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⢾⠃⢀⠀⠀⠀⠀⠁⣿⢸⡞⣀⠘⢣⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣈⣿⣿⣿⣳⣿⣿⣟⣿⣯⣿⣿⣿⣯⣿⣯⣟⣿⢿⣯⣿⣿⣻⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠼⢨⠱⠀⠀⠀⠀⡏⣿⢰⠀⢌⠃⣿⣿⣿⣿⣴⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⢯⣷⣿⣯⣱⢾⣯⡵⣿⢾⣟⣿⣽⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⣻⢌⠣⠀⠀⠀⠇⣿⣼⠉⡔⠋⣿⣯⣿⣽⢋⡾⣴⣠⢀⡄⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⡿⣶⣫⣵⣟⢺⣹⣿⣏⣻⣼⡟⣿⣾⣝⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⢻⣌⠐⠉⠛⠟⢿⣿⢹⠛⠿⣻⠿⣶⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣞⣿⣿⣽⢾⣻⣷⢟⣯⡽⣾⣛⢿⣽⡾⣟⣿⣻⣗⢯⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣄⣀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⡽⣿⣿⣿⣿⣽⣻⣷⣟⣯⡷⢯⣳⣽⢾⣿⡯⣿⣿⣞⡳⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣷⣿⣿⣿⣿⣏⣿⣿⣽⣿⣿⡾⣟⣿⢾⣿⣿⣿⣾⣟⣯⡷⣟⣳⣟⣳⡾⣟⢾⣿⢯⣿⣏⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠘⠂⠀⠀⠀⠀⠀⠁⠀⠊⠁⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⣿⣤⣷⣿⣿⣿⢿⣯⡾⣟⣿⣿⢾⣿⣯⣿⣿⣟⢯⣳⣽⡽⣾⡽⣻⣵⢾⣟⢯⣽⢯⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢌⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣵⣀⢀⠈⡁⣬⣷⣾⣶⣿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣟⣻⡿⣟⢯⣽⠿⣯⣝⡿⣯⡟⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⢻⠉⠀⠀⠀⠀⠀⠀⠁⠛⡛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣌⣀⣄⢦⠛⠉⠀⠀⠀⣿⣾⣴⣥⣀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰⠀⠀⠏⣿⣿⢿⠻⠈⡆⣀⣁⣛⣛⠣⣯⠿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠷⠟⡿⣿⣿⣿⣿⣰⣈⡷⠘⣆⣶⣴⡇⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠊⠖⡤⣷⣿⣿⣿⣴⢀⠀⢸⡄⣿⠿⠛⠟⣿⣿⣿⣿⣷⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠚⠤⡦⢲⠉⠀⠀⠀⡀⣦⢒⠓⠒⡵⢞⡤⣀⣦⣷⣿⣿⣾⣴⢁⡞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠔⢀⠀⠀⠀⠀⡀⢦⠘⠉⠒⠓⠉⠉⠉⡼⠀⠀⠀⡄⠢⠑⠈⠀⠀⡀⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⠃⠠⢁⡊⣴⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠁⠜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⣶⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠈⠀⠀⠀⠀⠀⠀⣮⠀⡿⢴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⢀⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢄⠑⠀⠀⠀⠁⡜⢀⡀⠀⠞⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠤⠯⣼⠀⠀⠀⠀⠃⣻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢳⠈⠀⠀⠇⣿⠘⠀⠀⠀⠀⠀⠀⠀⠓⠙⠈⠀⠀⠀⠀⠀ ⠀⠀⠁⠟⣿⣿⢿⠈⠀⠀⠁⡟⣿⡻⢍⠢⠒⠉⠉⠉⠁⠊⠴⣤⢠⡆⣳⠌⠑⣿⣿⣿⠊⠖⠤⠤⠤⠤⠂⠀⣿⣿⠻⠈⠀⠀⠀ ⠀⠁⡴⣀⣇⣰⣀⣄⠷⠿⣿⣿⣿⣿⣿⣿⢼⠤⠤⠡⠊⠒⠉⠈⠀⠀⠀⡁⠟⣿⣼⢀⠀⠀⣀⠀⠁⠛⠙⠀⡆⣿⣿⢿⠀⠀⠀ ⠀⡏⠛⠛⢰⠀⠀⠀⠀⣀⣤⣦⣶⣶⣶⣤⠀⠤⡀⢀⠀⠀⠀⣀⢄⠢⠿⣿⣿⣿⠀⠏⡸⣇⠀⠀⠀⣦⣿⠁⠾⣿⣿⣿⢸⠀⠀ ⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⡿⣿⢿⢹⠛⠿⠛⠛⣿⣿⢻⡟⣿⢸⢻⠀⠀ ⠀⣧⣿⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢸⠀⠀ ⠀⡀⠱⠀⢆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡀⣧⣿⣿⣿⣿⡁⢰⠀⠀ ⠀⠀⡀⢢⠟⣿⠻⠙⠉⠉⠉⠈⠁⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⡆⢸⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⡤⣿⣿⣿⣿⣼⠀⠀⠀ ⠀⠀⠀⠀⡀⣤⣶⣿⣽⢉⠉⠉⠏⣿⣿⣿⣾⢤⠱⠀⠀⠀⠀⠀⢆⠙⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣾⣶⣿⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠱⠀⡀⢣⠀⠀⠀⠀⠀⡀⣦⢸⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⡀⣦⢿⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠿⡿⠀⠀⠀⠀⠀⠀⠀⡄⠢⡷⣿⣿⣿⣬⣀⣀⣧⣿⣴⣀⣄⣦⢷⠻⡟⣿⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣷⠻⠉⠈⣧⢻⠈⠀⠀⠀⡀⣄⣤⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣶⣷⢾⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠁⠉⠉⠀⠄⡾⢤⠀⣤⠀⡠⡷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢣⠀ ⡄⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠞⢣⡄⠰⢄⡏⠐⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈ ⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⢸⠀⠀⠀⠋⢠⢢⠉⠒⠤⠤⠓⡹⠋⠋⠀⠁⠓⠒⠙⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣ ⠄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠁⢞⠑⠋⠽⣉⠉⠉⠉⢄⠀⠄⢀⠀⡀⣄⢷⢸⡀⠀⠀⡄⠙⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠤⠒⠒⠒⠓⠗⠤⡠⢁⠉⡏⣿⣀⠁⠟⠿⠻⣌⢸⠀⡇⣡⣛⣛⣈⣤⠻⠙⠉⠉⡞⠢⠒⠒⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠄⡏⠉⠹⣾⣴⣤⣧⣿⠿⡭⣤⣥⣭⣶⢀⠀⡀⡷⣾⣶⣶⠙⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠞⣤⣴⠀⢰⠀⠁⡏⣿⣿⢸⣇⣿⣿⣿⢿⠾⠿⠿⣿⢴⡯⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⣶⣠⠀⠀⡆⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣶⢸⡆⣷⣼⠏⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⠙⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⡿⣿⣿⣿⣬⢘⡇⣯⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣢⢄⡄⢠⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⢽⡯⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡙⣀⣿⣀⣀⣿⢀⠀⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠹⣇⠈⠀⣿⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⢸⠀⣿⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⣧⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠒⠤⠤⣀⣀⢀⠀⣀⣀⠤⠦⠓⠈⠀⠀⠀⠁⠞⠤⡤⣀⣀⣀⣀⣄⠤⠲⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠁⠞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⠀ ⠀⠀⠀⠀⠁⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠃⢩⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠋⣠⡀⣤⣤⣶⠶⠻⠛⠛⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠛⠿⢻⠀⠀⠀ ⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣭⣯⣿⢾⠶⠶⠶⠶⠷⠿⠿⢿⠛⠛⠟⠿⠿⣿⣿⣭⣤⣀⣀⠀⡀⢳⠀⠀ ⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠖⡤⣀⣀⠀⠀⠀⠠⠀⠀⠠⠀⠤⡂⣑⣯⣼⢤⣠⣀⣀⣀⣀⣀⣄⢤⠳⠉⡆⠸⠀ ⣿⣄⠢⠀⠀⠀⠀⠉⠋⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣾⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⢸⠀ ⣿⠿⠿⡿⣿⣿⣟⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢧⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈ ⢸⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣻⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰ ⠀⠀⠀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡵⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡰⠀ ⠀⠀⠀⠀⣄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠎⣢⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⢄⠣⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠴⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⡍⡿⣾⣿⣿⠿⠛⠛⠛⠛⠋⠛⠛⠛⠗⠾⣶⢶⠳⠛⠉⠉⠉⠉⠋⠓⠟⠿⣿⣷⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⢤⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⡀⣀⣀⣄⣷⠻⠀⠀⠀⣼⠀⠀⡀⣀⣀⠀⡃⢸⢁⡴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠢⠒⠒⢾⢿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⢤⣶⠑⠉⠉⠈⠁⠉⠋⡾⠴⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠊⠴⡠⣄⣷⣶⣿⣬⣶⠶⠶⠿⡿⣴⠀⠀⢸⠀⠀⠀⠀⠀⣃⣰⣀⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⡿⢠⠀⠀⠀⠀⢄⣷⡘⢦⠹⠀⣿⢰⠀⠀⠀⣧⣤⢦⠻⠉⠀⡆⠀⠀⠁⡏⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⣻⠈⠀⠀⠀⠀⠀⠀⣿⠀⣄⢳⣿⠀⠀⠀⠀⡇⠿⣠⢀⣄⢻⠀⢣⡾⣠⠀⡅⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣁⢮⠐⠀⠀⠀⠀⠀⣧⠘⠀⡄⢀⠀⠀⠀⠀⡇⣸⠀⠀⠀⣾⠀⠀⣄⠳⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⣠⡀⣧⣛⢭⠤⣀⣀⣀⣤⠶⠛⠉⠈⠀⠀⠖⣠⠀⠁⠈⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣽⣿⣏⣾⣠⣀⣀⣀⣂⣈⣤⣖⠿⠿⡷⣻⣍⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⣷⣿⠉⠉⠈⠀⠀⠆⢰⠀⠀⡀⣿⠈⣇⣿⢿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣻⠋⣴⢸⠀⠀⠿⠤⠤⠳⠈⣿⢀⡀⣿⣻⣯⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⣼⣄⣿⠛⢻⠈⡇⣤⢿⠛⡇⣿⣿⢠⠆⣿⡀⣀⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠏⢸⠟⣿⣠⢀⣞⣿⠽⡀⣦⠻⣿⣶⠀⠃⣼⢦⠳⠙⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣰⣧⣺⣷⠀⡇⣷⡏⣸⢤⠶⡟⣼⠀⠀⡞⣀⠦⠛⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣼⠀⣯⠟⠹⠋⡿⡴⣤⢠⠀⠀⡀⠀⠀⡆⢳⠉⠀⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⡛⣯⡻⢻⠋⠙⠈⠀⡆⣀⠀⠁⣟⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣴⣤⣀⣀⠀⠀⡀⣄⣦⣿⣶⣶⠶⠿⠿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⠀⡟⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢹⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣶⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡀⣷⣾⣶⣡⣄⣿⣼⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿ ⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⡀⣦⠿⠛⡟⣴⠀⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣠⠀⠀⠀⣄ ⠀⠀⡀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣴⢀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⡴⣬⣀⣄⢦⠷⠛⠉⠀⠀⠀⠀⠁⠉⠛⡾⣶⢹⠀⠀⡇⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣨⣤⢷⠙⠉⠀⠀⠀⠀⠀⠁⠋⠛⠾⣴⣠⠀⠎⢀⠀⠀⠀⠀⠆⣠⣄⣤⣤⣯⣴⣀⣧⠘⠀⣇⠸⠀⠀⣇⠸⠀⠀⠀⠀ ⠀⠀⠀⠆⠙⠁⢸⠀⠀⣁⣎⣶⣤⣦⣤⣤⣠⣀⠀⠀⠀⠉⠖⠲⠒⠓⠈⠈⠀⠀⠀⠀⠁⡞⣠⢄⠤⠤⣦⠹⡞⣠⣀⣧⣈⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣀⠀⠁⠜⣀⠀⠀⠀⠁⠋⠒⠒⠄⠤⡠⣀⠀⠀⠟⠶⠓⣿⡒⢶⠳⠚⡤⣠⠀⠀⠀⠀⠀⠀⣆⠳⠚⠖⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡸⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣁⢼⢠⠀⠃⡴⣠⣀⣤⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠳⠈⠀⠀⢄⠑⠈⠀⠀⠀⠀⠀⠀⠀⢺⠒⠖⢸⠀⠁⣸⠉⠚⠑⠉⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⠒⠑⡈⠤⠓⠈⠀⡀⢄⠢⠒⠙⠈⠀⠀⣧⣋⣰⢀⠀⡏⣤⣤⢷⡿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠏⣨⠀⠀⠀⡁⢾⠀⡀⢤⠒⠈⠀⠀⠀⡀⢦⠘⡇⢠⠀⠀⡄⢻⠀⠀⡶⢠⡀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⢀⡀⢤⠫⠔⢠⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠁⠰⡇⠀⠀⠀⠁⣾⢧⠘⠁⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⢤⠢⠖⢰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠊⣠⠀⡀⢱⠀⠁⡟⢸⠀⡀⣁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡀⣸⢄⠁⠈⠀⠉⠞⢙⠈⠀⠀⠊⠟⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠱⠀⡀⠀⠀⣴⠠⠄⣦⠀⠀⢠⣤⠂⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⡝⠛⠘⠞⠴⢢⠉⠉⡔⠦⠑⠂⠛⠹⡈⠢⠀⠀⠀⠀ ⠀⠃⣶⣤⣇⣾⠀⠉⠉⠉⠀⠀⠈⠉⠉⠀⣇⣼⣤⣦⡘⠂⠀⠀ ⠄⡖⠀⠃⡿⣩⢞⡶⠶⣖⠀⠀⡇⡦⢶⠳⣍⢿⠉⠀⡇⠀⢠⡄ ⠙⡇⣾⣤⣿⠉⠀⠉⠖⢀⠂⠱⠀⠢⠉⠀⠁⡟⣤⣷⣿⠀⡈⠁ ⠂⡏⠋⠛⣿⣿⣻⡇⣿⣼⢠⡀⣼⣿⣸⣏⣿⣿⠛⠙⡋⠈⢀⡀ ⠀⣇⣿⣿⣿⣿⣿⣿⣿⣉⠈⠀⣹⣿⢿⣿⣿⣿⣿⣿⣾⢠⠀⠀ ⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⢻⠋⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀ ⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡆⡀⣀⣀⠀⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠦⠙⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⡜⠳⠈⣯⠚⡷⢿⠂⠑⠉⠀⠀⠀⣇⠢⠈⠉⠐⣋⠣⠤⣀⠤⠒⠁⠀⠀⠀⠀⠀ ⠉⠀⣜⣇⠱⠄⣧⣚⢿⣿⠙⠂⠒⠸⠎⢀⠀⠀⠀⢆⠈⠀⠀⠀⠀⢀⠢⠀⠀⠀ ⣧⡏⠀⡇⣁⣛⣬⢀⣄⡷⢀⠀⠀⢣⢀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠄⠘⠀ ⡆⣺⠏⠓⣿⣿⣻⢔⠆⡿⠈⠀⠇⡀⠀⠀⠀⠀⠀⠀⡀⢵⠐⠈⠀⠀⠀⠀⣥⠡ ⠀⣡⠉⠟⢲⢌⠒⠚⡤⠀⢸⠀⠀⠈⠈⠀⠀⠀⠀⠀⡆⠀⠡⠄⠀⠀⠁⣮⠒⡕ ⠀⠀⣢⠓⠝⣫⡞⠀⠀⠉⢸⠀⠀⢡⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠤⢦⡜ ⠀⠀⠀⠀⡀⢀⠀⢃⡈⠀⡄⢌⠂⡈⠱⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢺⠶⡬⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢡⠀⡀⣂⠪⢋⠔⣦⡧⠸⠀⠀⠁⠳⢗⡀⠢⡚⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠃⡠⣀⣆⣈⣆⢋⠈⠊⠪⢬⠐⠤⢈⣁⡰⠀⠀⢺⡗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠀⠂⠒⢄⡠⠀⠀⢀⠀⠀⠀⡆⣏⢑⠈⠚⡡⠒⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣛⡻⡴⠴⣦⣠⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⢤⠤⠲⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⡴⣠⠀⢀⠀⠀⠀⠀⠀⠋⠗⠿⠯⠷⠺⠙⠀⠀⠀⠀⠀⠀⠀⣄⠦⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡤⢀⢀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣭⡿⢯⣫⣷⣟⣯⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠑⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠜⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢯⣹⢿⣳⣞⣽⠿⣳⣽⢻⠀⠀⠀⠀⠀⠀⠉⠛⠙⠈⠀⢆⠱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⢿⣳⣞⡽⣻⣷⣛⡽⣷⡞⣿⢿⠘⠀⠀⠀⡇⣹⠐⡠⣿⠀⠀⠀⢄⠑⠀⠀⠀⠀ ⠀⠀⠀⠁⡴⠐⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠏⣿⣿⣿⣻⣿⣟⡿⣿⡿⣟⣻⣿⣿⣿⣿⠙⠀⠀⡀⢳⡠⠇⣹⠉⠈⠀⠀⡀⢣⠈⠀⠀ ⠀⠀⠃⣰⠀⠃⠝⣣⣞⠭⣹⠼⣞⠭⠹⠀⠃⣿⣼⣦⣶⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣴⣷⣿⠘⠁⠉⡶⢿⣶⡭⠽⣣⣝⠮⠑⡀⢆⠘⠀ ⠀⠁⣰⠀⡜⢯⡜⢯⡖⢎⡳⡝⢧⣚⡝⢧⡟⣿⢠⠀⠉⠛⠛⠉⠉⠉⠉⠉⠛⠙⠉⠀⡆⣿⢿⠾⣩⢷⣋⢧⢭⡳⢬⡻⣍⢳⢫⠀⢧⠈ ⠀⡾⠘⡇⡼⢞⡱⢻⣥⣛⢧⡖⢪⡵⡞⢣⣿⣿⢿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣷⣿⡿⣿⣾⢳⣞⠮⣙⢶⡝⢫⣱⠷⣎⠭⢲⢸⠀⢻ ⣗⠣⠼⣴⣦⢷⣹⠷⣣⠵⣫⡴⣛⣲⡝⢳⣯⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣞⢧⡖⢝⣫⡴⢛⣱⡻⢦⣛⣍⡶⢘⠀⢼ ⡜⣹⠌⠣⢄⠐⣿⡳⢦⡹⢳⣭⠳⣮⡜⠽⣰⠀⠋⠼⢷⠸⠀⠀⠀⠀⠀⠀⠀⠗⡼⠳⠙⠀⣦⣛⣣⠶⢏⣥⡹⡶⠝⣮⠗⣩⡾⢀⠀⣺ ⢸⣇⠘⢁⡰⠏⣽⢯⣦⡝⡳⢎⢳⢯⣟⡳⠼⣼⢣⡞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⣘⣬⠷⢳⣻⣝⢮⣓⡳⣎⠹⣳⢯⡴⢀⠀⠀⣺ ⢸⠀⣧⡘⠟⢰⡀⣀⣽⣻⣾⣷⣶⢷⡹⠻⢖⡿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣾⣷⢿⡻⡝⡛⡾⣷⣶⣶⣟⡾⣀⢀⠀⠀⠀⠀⢺ ⢸⠀⠀⣄⢀⠀⠀⠀⡄⢻⠌⠢⡄⠐⡋⢿⠟⣾⣶⣷⣿⢸⠀⠀⠀⠀⠀⠀⠀⡇⣿⢻⡿⣶⣶⣿⢙⡈⠐⠤⡉⡞⢀⠞⡼⢦⠷⠙⠀⣻ ⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣠⣆⣿⣿⣿⢀⠁⠉⣏⣼⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣼⠀⠁⡉⣿⣀⣤⣤⣀⠀⡿⣈⠒⢌⠂⣇⠸⢺ ⣖⠈⠀⠀⠀⠀⠀⠁⠛⠿⠿⠿⡿⣿⣿⣿⣿⠿⡿⣿⣿⢨⠀⠀⠀⠀⠀⠀⠀⡅⣿⣿⣿⠿⣿⣿⣿⣿⢿⠿⠿⠻⣿⠄⠣⢁⢠⡏⢰⢼ ⠀⢳⠀⠀⠀⠀⠀⡄⣦⣴⣤⣤⣤⣀⣀⣄⣤⣤⣶⣷⣿⣿⢺⠀⠀⠀⠀⠀⡷⣿⣿⣶⣴⣤⣤⣤⣀⣀⣄⣤⣤⣶⣴⢷⠈⡰⠏⣰⠀⢼ ⠀⡀⡸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠛⠿⠿⠛⠛⠛⠉⠈⠀⠀⡀⢧⠟⣠⠀⠎⣠ ⠀⠀⡄⡝⠘⠀⠀⠀⠁⠛⠛⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣶⣴⣦⣶⣷⣿⣿⣿⢿⠛⠀⠀⠀⠀⠎⢠⠀ ⠀⠀⠀⡀⡣⠱⠀⠆⣿⣿⣶⣶⣶⣤⣶⣶⣿⣿⢿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣶⢠⠁⠓⠜⢀⠀⠀ ⠀⠀⠀⠀⠀⢆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⠿⠿⠈⠀⠀⠀⠀⠀⠀⣆⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠆⣾⣴⣧⣿⢸⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⢑⠪⠉⠀⠀⠀⠀⠀⠀⠀⡇⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢑⠩⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠤⡢⠓⠉⠉⠉⠈⠁⠀⠀⠀⠀⠉⠉⠉⠉⠛⠼⡬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣾⣶⣤⣤⣤⣀⠀⠀⠀⠀⢀⠀⡀⣁⡟⣿⣿⣯⣿⣰⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⠟⠿⠿⠿⠿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠚⡶⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⠿⠾⡧⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣶⣤⢀⠀⡀⣦⣷⣿⣴⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣷⣽⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣽⠀⠀⠀⠀⠀⠀⠁⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣄⣷⣿⣿⣿⠻⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⠻⠛⠛⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠛⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⢼⠀⠀⡐⣄⣶⣿⣽⢋⠛⠛⠿⠿⡿⣿⠀⠀⠀⠀⠀⡗⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢿⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣶⣿⣿⣿⣿⣿⣿⣿⣸⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀ ⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⢻⠀⠀⠀⠋⠀⠀⠀⠀ ⠁⣷⣿⣿⣿⣿⣿⣿⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⢻⠁⡟⣹⠀⠀⠀⠀ ⠀⠀⣄⣦⣿⣿⣿⣿⣿⣿⣿⠿⠿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣤⣦⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡆⣿⣿⣠⠀⡀⣀⣀⢀ ⣿⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣦⠳⠙⠉⠋⡴⢀⠀⠀⠀⠀⠉⠋⠛⠛⡏⣸⣆⠀⣿⣿⠀⠀⠀⠀⠀⠀ ⣇⠻⠉⠀⠀⠀⠀⠀⡟⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠈⠃⠟⡿⣿⣿⣿⣿⠀⡀⣧⠘⠀⣿⣿⠋⠸⠀⠀⠀⠀ ⡀⣿⣿⢿⠿⠛⠛⠛⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠋⠴⠀⠀⠀⡄⣧⣼⣄⣷⣿⣿⣿⢻⠚⠴⡤⢿⠃⣿⣿⣿⢡⠛⠀⠀⠀ ⠀⣾⣷⣟⣿⣿⣿⣿⣿⣿⢋⠛⠛⠈⠋⠞⠴⠤⠦⠿⣿⣿⣿⣿⣿⣾⢻⠀⠀⠀⠀⠀⡄⣾⡤⣤⣀⣀⣀⠀⠀⠀⠀⡰⡟⣿⣿⣿⣿⣾⠀⠀⠀ ⠀⢹⠀⡀⣀⣤⣦⣿⣿⣿⢰⠀⡃⣼⢀⠀⠀⠀⠀⣄⣶⣿⣿⣿⣿⢖⡷⠀⠀⠀⠀⠀⠀⣆⠛⠀⠀⠀⠀⠀⠀⠁⡼⠏⣿⣿⣿⣿⣿⢰⠀⠀⠀ ⠀⣧⠸⠀⠀⠀⠀⣿⣿⢸⠀⠀⣷⠀⠁⠉⠉⠉⠛⠒⠖⡤⣤⣀⠀⠁⡸⠀⠀⠀⠀⠀⠀⠀⡀⢦⠒⠈⠀⠒⠐⡋⡿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⢧⠙⠀⠀⠀⣿⣿⠈⠀⠀⡆⣽⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠠⠏⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀ ⠀⠀⡀⣿⣿⢿⠿⡿⣿⢸⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠂⠖⣠⠀⠀⠀⠀⠀⠁⠉⠛⠟⠿⣿⣿⣿⣿⠏⣽⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⣿⣿⣿⣿⣿⢿⠉⠉⠁⠀⠀⣀⢅⠩⠉⠉⠉⠋⠛⠻⠀⠀⠇⠿⡿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠚⠒⠒⠒⠒⠀⠀ ⠀⠀⠀⠀⣇⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⡇⣿⣿⣿⣿⣿⣴⢏⠀⠆⣟⣾⣿⣿⣿⣿⣿⣿⣠⠀⠀⠇⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣿⣾⢩⣿⣰⠀⠀⣤⢦⣷⣿⣿⣿⣰⣤⠣⠀⠀⡀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣽⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣾⣴⣠⢀⠀⠀⠉⠸⠀⡀⣿⣿⢸⠀⠋⣾⠀⠀⠀⡈⢀⠀⠀⠀ ⠀⠀⠀⠀⠛⠟⡿⣿⣿⣿⣿⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣛⣿⣿⣿⢠⠀⠀⠋⠀⠃⡾⣤⣦⠿⠶⡿⣿⢸⠀⣹⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⣽⣀⣥⣿⣿⣿⣿⢹⠀⠀⣀⣀⣤⣦⣶⣶⣷⣿⣿⣿⣿⣿⣿⣹⠉⠟⠿⢸⠖⣠⠀⠀⠀⡇⢶⣼⣆⢸⠀⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣶⣶⣶⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣷⣿⣿⢾⣴⣀⠀⠆⠰⠀⠁⠋⠉⠟⢰⡇⢸⠀⠀⣿⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⢿⠛⠛⠛⠛⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⡀⣷⣿⠛⠀⠀⠀⠀⠀⠀⡏⣿⣿⣾⠠⠀⢸⠀⣤⣤⠀⠀⠀⠀⠉⠀⠀⠀ ⠀⠀⠀⠀⣿⠷⠿⠿⠒⡀⣷⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠇⣿⣿⣸⠀⡇⣿⣿⢹⠀⠀⠀⠀⠁⣿⣿⣿⢀⠀⠀⢰⠀⠛⠲⠀⠀⠀⡄⣀⠀⠀⠀ ⠀⠀⠀⠀⣧⠏⠹⠿⠘⠀⡀⣷⣿⣿⢿⠈⠀⠀⠀⠀⠀⡏⣿⣿⣤⣦⣿⣿⣿⣿⠘⠀⠀⠀⡿⣿⣿⢸⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⣈⣤⣤⢈⠀⠀⠀⣷⣿⣿⢿⠈⠀⠀⠀⠀⣿⣿⣿⠋⡶⢹⡀⣿⣿⢻⠀⠀⠇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣄⢀⣀⣦⠀⠀⠁⡏⣿⣿⣿⢿⠈⠀⠀⠇⣿⣿⢰⣄⠀⡄⢶⣷⣿⣿⠸⠃⣾⣿⣿⢶⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠶⠤⠶⠺⠛⠀⡀⣠⢀⣧⣿⣿⣿⠈⠀⡿⣿⣾⠐⠀⠀⠀⠀⠀⣧⣿⣿⡿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣷⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⣧⣩⣓⣼⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠃⣶⣶⣶ ⠀⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⠀⠀⠀ ⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣠⠘⠀⠀⠀ ⠀⠀⠀⣎⠳⠈⠀⠀⠀⠀⠀⠉⠊⠴⣨⣀⣄⠧⠒⠐⠃⠚⠗⣠⢹⠀⢱⠀⠀⠀ ⠀⠀⠐⠎⠀⣁⢶⠤⠤⡤⣀⢀⠉⠒⠒⠑⠁⠀⠀⠋⡴⠤⡤⠱⡔⠄⠸⠀⠀⠀ ⠀⠀⠀⠀⠇⠀⠀⠔⠀⠀⠀⠀⠀⠍⢭⣖⢀⣎⣤⠆⠘⠀⠀⡀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠈⠀⠀⢵⠯⠀⠃⠓⠹⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⡈⠀⡁⠰⢀⠢⠀⠀⡀⠢⡇⢀⠀⢻⠀⡴⣁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠐⣔⢀⠀⠀⠀⠈⠀⠁⠐⡆⠈⠁⣸⢄⠧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠆⣈⣀⣀⢀⠸⠁⠚⡰⣖⣛⠐⠀⠂⠓⠒⠂⠒⠑⠃⡿⠾⠘⠀⠞⠤⠤⠂⠓ ⠀⠀⠀⠀⡀⠱⠀⠀⣇⣿⢻⠙⣿⡴⠀⠀⠀⡀⠑⠈⠀⠀⣆⣿⡸⢇⠋⢰⠀⠀⠚⡠ ⠀⠋⠴⠤⠤⡆⠘⠀⡀⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⠀⣀⡦⣿⣾⠠⠀⡎⠀⠀ ⠇⡼⠤⠐⠀⠤⢳⠀⠀⡆⠈⠀⠁⠞⣠⠀⠀⠀⠁⠀⡄⠢⠈⠀⠀⡎⢀⠀⠃⢠⠀⠀ ⠀⢄⠦⠀⠂⠘⡀⠘⠀⠀⠁⠔⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠤⠑⢀⠀⠀⡸⠀⠀⠀ ⠀⠀⠀⠀⡇⢸⠃⡖⠱⡨⣀⢧⠺⠁⠀⠀⠀⠉⡰⠀⠀⠋⠴⠀⠀⢄⠢⡤⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⢿⡝⠲⠒⡀⣇⡗⢇⠀⢀⠀⣶⠑⢄⠙⡠⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⢦⠷⠷⠿⣦⡀⠈⠒⠄⡀⠀⢳⡿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⣧⠀⣠⠀⠀⠀⢩⠀⣥⠛⣟⣿⠴⠢⠙⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠃⠙⠃⠚⣶⣶⣿⣽⣤⣤⣦⣌⣷⢤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⠴⣠⣀⠀⠀⠀⠀⡄⣿⠙⠉⠉⢏⠀⠀⠀⠐⠀⠚⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠟⡿⣾⢀⠄⡤⠁⠊⠴⠿⣾⣗⣼⣿⣘⣀⣀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢺⠗⠿⠀⠀⢶⣉⢉⠉⡔⠁⣿⢿⠛⠻⠸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⣿⡿⢿⡠⢁⢠⠀⠉⠋⠟⠙⣿⣼⣀⠀⣠⣇⢺⠓⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶⣿⣹⢉⠇⡿⣸⣄⣷⣿⣿⠙⠀⠀⠿⣾⢸⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣷⣿⣿⡿⢿⠵⠀⡃⣟⣿⣿⠙⠟⣸⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣶⣿⣿⢿⡿⣿⣾⣿⣠⣀⣦⠹⡇⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠹⡇⢹⠀⠀⡄⣷⢼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⢽⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀

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