⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⣻⣛⢿⣳⢦⡀⠀⠀⢀⣀⣠⣤⢤⣤⣤⢤⡤⣤⡤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡹⣎⢷⡹⣎⢷⣫⢿⣶⡟⣯⢯⣝⢮⠷⣞⡼⣻⢵⣳⡽⣹⢯⣏⢿⡳⢦⣄⣀⣤⢴⠶⡶⢶⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣏⢷⡹⣎⢷⡹⣎⢷⡹⣾⣟⣼⢣⠿⣜⢯⣟⡼⣳⡟⣧⢳⡽⣧⣛⢿⣎⣿⣏⠾⡽⢿⣎⢿⡹⢧⣏⢷⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⣝⢮⡳⣝⢮⣷⣽⡾⣟⡟⣾⣱⡿⠿⡼⢯⣷⣽⣭⢻⡼⣣⢟⣵⢫⡞⣟⠶⣯⣛⡿⣝⣻⣧⢟⡳⣎⠿⡼⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢏⡾⣱⢏⣾⣿⢳⣻⣼⠟⣍⡳⢌⡳⢥⡃⢶⠨⡝⢻⢷⣽⣾⡼⠛⠉⠉⠉⠉⠉⠉⠉⠓⢿⣯⡷⣭⢻⡵⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡞⣧⣛⣾⢯⣳⠟⣥⢺⣾⣿⣿⣷⣶⣭⣎⣳⡘⣧⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣭⡳⣝⣳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⡿⣹⢾⣏⡹⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣗⡸⢃⣿⠀⠀⣠⣴⠾⠛⠛⠛⠛⠶⣤⡀⠀⢸⡶⣻⣜⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢞⣽⢯⡟⣤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⣾⠀⣴⠛⠀⠀⠀⠀⣤⣄⣄⡈⢻⡄⠈⣷⠗⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣾⠼⣿⡜⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⣿⢰⡏⠀⠀⠀⣀⠀⢀⣿⣿⣿⣮⣿⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣯⢿⣿⢰⠣⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢎⡞⢸⡇⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⣎⣿⣏⢎⡧⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⡽⠁⠀⢻⣄⠀⠀⠘⢿⣿⣿⣿⣿⣿⠋⢀⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡿⣿⣧⠼⠤⠿⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠀⠀⠀⠀⠻⢧⣄⡀⠀⠘⣛⣿⡿⠃⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣛⣿⠀⠀⠀⠀⢠⠀⠀⠉⠉⠛⠻⠿⣽⡻⠛⢿⣿⣻⣿⠷⠀⠀⠉⠙⠛⠋⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡖⣯⡇⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣝⣾⡇⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡮⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡽⣾⡿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣟⣿⣽⢷⣻⣿⢯⣿⣷⣶⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣶⡿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⣾⣻⢿⣯⢿⣾⡿⣞⣷⣿⢯⣟⣿⡿⣯⢿⣽⣯⢿⣽⣿⣻⢿⣿⡽⣯⣿⣷⣻⣿⡗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣽⣻⢾⣽⣻⡿⣿⣟⣾⣿⣻⣞⣿⢯⣟⣾⡿⣽⣻⣾⣟⣯⣿⡷⣯⣿⣯⣟⡷⣿⣳⣯⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⢿⣽⣻⢾⣽⣻⣞⡷⣿⡽⣯⣟⡿⣽⢿⡿⣯⣿⣾⣿⣽⣳⣿⣟⣾⣽⣿⣳⣿⣷⡿⣿⣟⡿⣽⣳⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⡿⣽⣻⢾⣽⣻⣾⡿⣯⣟⣷⣻⢷⣯⣟⣯⡿⣽⢯⣷⢯⡿⣽⢯⡿⣽⢯⡿⣽⢯⡷⣯⣟⡷⣯⢿⣽⣳⣯⢿⡄⠀⠀⠀⠀ ⠀⢀⣴⡿⣯⣟⣷⣻⣟⣾⣿⣽⣻⢷⣻⢾⣽⣻⢾⡽⣾⡽⣯⢿⣞⡿⣽⢯⡿⣽⢯⡿⣽⢯⡿⣽⢷⣯⣟⣿⣟⡾⣷⢯⣟⣷⡀⠀⠀⠀ ⣠⣿⢯⣟⣷⣻⣞⣷⡿⢹⣷⢯⣟⣯⣟⡿⣾⡽⣯⣟⡷⣿⣽⣻⣞⡿⣽⣻⣽⢯⡿⣽⢯⡿⣽⢯⣟⣾⡽⡟⣯⡿⣽⢯⣟⡾⣷⠀⠀⠀ ⢿⣯⢿⡾⣽⣳⡿⣯⣿⢿⣯⡿⣾⡽⣞⣿⣳⢿⣽⣞⣿⣳⢯⣷⣻⣽⢯⣷⢯⡿⣽⢯⡿⣽⢯⡿⣽⣞⣿⣁⣸⣿⡽⣯⢿⣽⣻⣆⠀⠀ ⠀⠉⠻⢟⣷⣿⣻⢷⣯⣿⣿⣽⣳⢿⣻⢾⣽⣻⢾⡽⣾⡽⣯⡷⣟⡾⣟⣾⣻⣽⢯⡿⣽⢯⡿⣽⢷⣯⣿⣟⣯⣿⣽⢯⡿⣞⡷⣿⡆⠀ ⠀⠀⠀⠀⠙⠾⣽⣻⢾⣽⣷⣯⣟⣯⣟⡿⣾⡽⣯⣟⡷⣟⡷⣟⣯⣟⣯⡷⣟⣾⣻⣽⢯⡿⣽⢯⡿⣾⣟⣾⣳⣯⢿⡿⣽⣻⡽⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⣟⣾⡽⣾⣽⣻⢷⣻⣽⢾⣻⣽⣻⣽⣳⣯⢷⣟⣯⡷⣟⣾⣻⣽⢯⡿⣽⣿⣻⣞⣷⡯⠿⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣻⣷⢯⣟⣯⣟⣾⣻⣽⢾⣽⣞⡷⣯⡿⣞⡷⣟⣯⡷⣟⣾⣻⣽⣷⡿⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⣮⣉⠯⣩⢛⡛⣛⢳⡛⠿⠾⠿⠿⠷⠿⢯⠿⢯⠷⠿⠿⠷⣻⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣏⡷⠋⠳⡗⡔⡣⢎⡱⢦⡙⢎⠵⣋⠼⣉⢮⡑⢮⡑⢮⡙⣬⡳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⠰⣏⠖⣩⠖⣱⢢⡙⢎⡲⡑⣎⠱⢦⡙⢦⣹⢆⡱⢺⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀⠀⠀⠐⣯⠘⣥⠚⣤⢣⡟⠓⠓⠓⠚⠛⣶⠛⣯⢱⠊⡕⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢾⡟⠀⠀⠀⠀⠀⠠⣏⡕⢪⡱⢊⡖⣯⠀⠀⠀⠀⠀⡧⢓⡬⢒⡭⢒⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢰⡇⢎⠳⣌⠳⡌⡷⠀⠀⠀⠀⠀⣯⠱⡌⢧⠸⡅⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⡩⢖⡌⡳⣘⡇⠀⠀⠀⠀⠀⡧⡓⣍⠲⡍⡼⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣬⠱⢎⠴⢣⣹⠃⠀⠀⠀⠀⢸⢇⠵⣊⡕⡚⠴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⡯⣘⠎⣕⣾⠀⠀⠀⠀⠀⣼⣎⠲⡅⣎⠹⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣮⣽⣭⣿⡭⠇⠀⠀⠀⠀⠀⠻⢭⣟⣳⣞⣛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣟⢮⣳⡇⠀⠀⠀⠀⠀⠀⠀⣀⣼⡽⣭⢿⣅⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣿⣿⠟⢒⠦⢤⡀⠀⣼⣿⣿⣿⣿⣿⠟⠉⠄⡚⠗⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣡⠔⡡⠂⣉⣬⣿⣿⣿⣿⣿⣿⣿⣶⣧⡎⣠⣴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⠛⠿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠨⣉⣙⡛⠛⠛⠛⠛⣉⡉⠽⠈⠁⠒⠀⠀⠀⠤⠠⠄⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⠀⠄⠠⠤⠀⠀⠀⠒⠁⠈⠽⡉⣉⠛⠛⠛⠛⡛⣙⣉⠨⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⣟⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⠿⠛⣉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣴⣠⡎⣧⣶⣿⣿⣿⣿⣿⣿⣿⣬⣉⠂⡡⠔⣡⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢢⠗⡚⠄⠉⠟⣿⣿⣿⣿⣿⣼⠀⡀⢤⠦⢒⠟⣿⣿⣷⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣅⢿⣭⡽⣼⣀⠀⠀⠀⠀⠀⠀⠀⡇⣳⢮⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣛⣞⣳⣟⢭⠻⠀⠀⠀⠀⠀⠇⡭⣿⣭⣽⣮⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠹⣎⡅⠲⣎⣼⠀⠀⠀⠀⠀⣾⣕⠎⣘⡯⣄⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠴⡚⡕⣊⠵⢇⢸⠀⠀⠀⠀⠃⣹⢣⠴⢎⠱⣬⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡼⡍⠲⣍⡓⡧⠀⠀⠀⠀⠀⡇⣘⡳⡌⢖⡩⡜⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡅⠸⢧⡌⠱⣯⠀⠀⠀⠀⠀⡷⡌⠳⣌⠳⢎⡇⢰⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢒⡭⢒⡬⢓⡧⠀⠀⠀⠀⠀⣯⡖⢊⡱⢪⡕⣏⠠⠀⠀⠀⠀⠀⡟⢾⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡕⠊⢱⣯⠛⣶⠛⠚⠓⠓⠓⡟⢣⣤⠚⣥⠘⣯⠐⠀⠀⠀⠁⡟⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢺⡱⢆⣹⢦⡙⢦⠱⣎⡑⡲⢎⡙⢢⣱⠖⣩⠖⣏⠰⠀⠀⠏⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡳⣬⡙⢮⡑⢮⡑⢮⣉⠼⣋⠵⢎⡙⢦⡱⢎⡣⡔⡗⠳⠋⡷⣏⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⣻⠷⠿⠿⠷⢯⠿⢯⠿⠷⠿⠿⠾⠿⡛⢳⣛⡛⢛⣩⠯⣉⣮⡽⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠓⡿⣷⣽⣻⣾⣟⡷⣯⣟⡷⣞⡿⣯⡷⣞⣽⢾⣽⣻⣾⣟⣯⣟⢯⣷⣻⣷⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠿⡯⣷⣞⣻⣿⣽⡿⢯⣽⣻⣾⣟⡷⣯⣟⢷⣯⣳⣽⣻⣽⣻⢾⣽⣻⢷⣻⣽⣾⡽⣾⣟⡿⢿⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠟⡽⣻⣽⡿⢿⣯⣳⣾⣟⣾⡿⢯⣽⡿⢯⣽⣻⣾⣟⡷⣯⣟⣯⣟⡷⣟⡷⣟⣯⡽⣾⡿⣟⣯⣟⣯⣷⣽⢾⣻⣽⠾⠙⠀⠀⠀⠀ ⠀⡆⣿⡷⣞⡿⢯⣽⣿⣯⣟⣿⣯⢷⣽⡿⢯⣽⡿⢯⣽⣻⣾⣟⡾⣟⡷⣯⡽⣾⡽⢾⣻⣽⢾⣻⢿⣳⣽⣿⣿⣯⢷⣻⣿⣷⢟⠻⠉⠀ ⠀⠀⣆⣻⣽⢿⣯⡽⣿⣸⣁⣿⣞⣽⡿⢯⣽⡿⢯⣽⡿⢯⣷⢯⣽⣻⣷⢯⣳⣿⣞⣽⢿⣳⣿⣞⡽⣾⡿⣯⢿⣿⣯⡿⣳⣽⡾⢿⣯⢿ ⠀⠀⠀⣷⡾⣟⢯⣽⡿⣯⡟⡽⣾⣟⢯⣽⡿⢯⣽⡿⢯⣽⣻⣽⡿⣞⣻⣽⣿⡷⣟⣯⡽⣾⡿⣟⣯⣟⢯⣷⢹⡿⣷⣞⣻⣷⣟⢯⣿⣠ ⠀⠀⠀⡀⣷⣟⢯⣷⡾⣟⣿⣟⣯⢷⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⣞⢿⣯⡽⣾⡽⢾⣻⣽⢾⣻⢷⣻⣽⣿⣾⣟⣻⣷⣟⣯⡿⣴⢀⠀ ⠀⠀⠀⠀⡄⢿⣯⣳⣽⢿⣯⡷⣟⣯⡷⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣷⢯⣽⡿⣯⣟⣯⢷⣻⣷⣟⣯⡿⣾⣻⣽⢾⣻⣽⡿⣼⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⣿⣳⣽⡿⣟⣿⡿⣷⣿⣳⣿⣽⣾⣟⣿⣳⣽⣿⣾⣿⣯⡿⢿⣽⡿⣟⣯⡽⣿⡷⣞⣻⣽⢾⣻⣽⢿⣾⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⣯⣳⣿⡷⣟⣯⣿⣯⡷⣿⣯⣟⣾⣻⣽⡿⣾⣟⢯⣿⣞⣻⣿⣾⣟⣿⡿⣻⣽⢾⣻⣽⢿⣾⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡗⣿⣻⣷⣿⣯⡽⣿⢿⣻⣿⣽⢿⣯⣽⢿⣯⡿⣿⣟⢯⣿⣷⣞⡿⣾⢿⣯⢿⣻⣾⣿⢿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⣿⡿⣶⣶⣴⣤⣤⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣤⣤⣶⣶⣷⣿⢯⣿⣻⢷⣽⣿⣟⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣶⡿⣾⡽⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣽⡮⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⢀⠀⠀⠀⠀⠀⠀⣀⠤⠑⠀⠀⠀⠀⠀⠀⠀⡇⣾⣝⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⠀⠀⠀⠀⠀⡇⣯⡖⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠁⠉⠋⠛⠙⠉⠀⠀⠷⣿⣻⣿⢿⠛⡻⣽⠿⠻⠛⠉⠉⠀⠀⢠⠀⠀⠀⠀⣿⣛⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠃⡿⣿⣛⠘⠀⡀⣄⢧⠻⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⠿⠤⠼⣧⣿⡿⢧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠆⢀⠋⣿⣿⣿⣿⣿⢿⠘⠀⠀⣄⢻⠀⠁⡽⠧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⡧⢎⣏⣿⣎⡽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⡇⢸⡞⢎⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠣⢰⣿⢿⣯⡟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⣿⣮⣿⣿⣿⢀⠀⣀⠀⠀⠀⡏⢰⣿⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⡜⣿⠼⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠗⣷⠈⡄⢻⡈⣄⣄⣤⠀⠀⠀⠀⠛⣴⠀⣾⣉⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣤⡟⢯⣽⢞⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⣜⣻⡶⢸⠀⡀⣤⠶⠛⠛⠛⠛⠾⣴⣠⠀⠀⣿⢃⡸⣗⣷⣿⣿⣿⣿⣿⣿⣿⣿⣴⡹⣏⢾⣹⡿⣟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣳⣝⡳⣭⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠺⣧⡘⣳⣎⣭⣶⣷⣿⣿⣾⢺⣥⠟⣳⢯⣾⣛⣧⡞⢯⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⡵⢻⣭⡷⣯⢿⠓⠉⠉⠉⠉⠉⠉⠉⠛⡼⣾⣽⢷⢻⡝⠨⢶⡃⢥⡳⢌⡳⣍⠟⣼⣻⢳⣿⣾⢏⣱⡾⢏⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⡼⠿⣎⡳⢟⣧⣻⣝⡿⣛⣯⠶⣟⡞⢫⣵⢟⣣⡼⢻⣭⣽⣷⢯⡼⠿⡿⣱⣾⡟⣟⡾⣽⣷⢮⣝⡳⢮⣝⡯⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣄⢷⣏⢧⡹⢿⣎⢿⡽⠾⣏⣿⣎⢿⣛⣧⡽⢳⣧⡟⣳⡼⣟⢯⣜⠿⢣⣼⣟⣾⡹⢷⣎⡹⢷⣎⡹⢷⣏⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣄⢶⡶⠶⢴⣤⣀⣄⢦⡳⢿⣏⢯⣹⡽⣳⢵⣻⡼⣞⠷⢮⣝⢯⣯⡟⣶⢿⣫⢷⣎⡹⢷⣎⡹⢿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡤⣤⡤⢤⣤⣤⢤⣤⣠⣀⢀⠀⠀⡀⢦⣳⢿⣛⣻⢾⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀