⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢁⣴⣾⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣄⢀⣠⣤⣠⠀⣀⡀⡀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⣶⣤⣼⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠻⠽⢿⠽⠿⡤⠿⠷⠇⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⢀⣠⣞⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠼ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠤⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⣛⡝⣫⢏⡵⢋⣽⣿⣿⣍⠻⣶⡘⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⡛⣽⣿⣿⣿⣿⣿⡷⣧⢚⡵⢪⡜⣿⣿⣿⣿⣿⠀⣸⠳⣜⣻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣙⢦⡹⢧⣿⣷⣿⣿⣿⣁⣽⢣⠞⡱⢎⣝⡹⠿⡿⢷⠺⣍⠳⣬⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⡙⢦⣙⢮⡱⢫⡝⣫⢛⡭⢲⡍⣞⣱⡿⢫⡜⣣⠝⣎⠳⣌⠳⣌⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⡹⢎⡜⢦⡹⡱⢎⡕⣫⢜⡣⡜⢦⡿⣘⢧⢚⡥⣛⢬⢳⡩⢳⣽⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣧⡫⣜⢣⠵⣙⠮⣜⢻⣿⣟⣿⡟⡵⣩⠖⣭⠲⣍⡚⣦⣽⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣭⣿⣿⣿⣿⣿⣿⣿⣾⣥⣟⣌⡳⣌⠳⣎⢻⠞⣏⠶⣡⣛⣴⡯⠶⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡿⣯⣟⣿⣯⣿⢻⡝⣯⢟⣿⣿⣯⣟⡻⢳⣞⣿⣾⣞⡛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⡿⣽⣳⣿⡞⣷⡹⢮⡝⡶⣫⢾⣿⣷⢿⣟⣿⣿⡽⣿⢿⣿⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⣿⡿⣷⡿⣇⠿⣶⢹⣇⢿⢱⡏⣿⣿⣏⡾⡹⣎⢷⡹⣎⢿⣿⣿⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣽⣻⣟⢻⢻⣮⣗⢮⣏⣳⣿⣿⣿⡱⣏⢷⡹⣎⢷⣛⢯⡻⣭⣛⡟⣷⢢⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣟⡾⣽⣏⢎⡳⠜⡮⢿⣶⣿⣿⣽⡳⣝⢮⡳⣝⢮⡳⣎⣷⣹⣶⣽⠾⡵⢯⠾⣵⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣯⣟⣿⡏⢮⡱⢫⣜⣿⣿⣿⡟⣧⢻⡜⣧⣻⣼⠷⣛⠟⣭⠳⡜⢦⡛⣜⢣⡛⡴⢫⡔⢮⡹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣟⡾⣽⣿⣿⣷⣷⣾⣿⣿⡹⢞⣱⣯⠾⣏⡝⢦⡛⣬⠛⡴⣋⡜⣣⠞⣬⢣⡝⣜⢣⠞⣥⠳⣍⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⣽⣿⡹⣍⠮⣽⣿⣶⡿⣻⠹⣌⠳⡜⣜⢣⡕⢮⡙⢶⠱⣎⠵⣚⠴⡣⢞⣌⢳⡚⡴⢫⡜⢣⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣾⣻⣱⢎⣵⣾⣿⣿⢔⣣⢛⡬⢳⡙⡜⢦⡙⢦⡙⣎⠳⣌⠳⣍⢞⡱⢭⡜⢦⡹⢜⡣⢞⡥⢻⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠷⢿⣽⣻⢾⣿⣷⣊⠞⡴⣋⡜⣣⠝⣜⢣⡝⢦⡹⣌⠳⣌⡳⣜⢪⡕⣣⠞⣡⠝⣎⠵⡣⢞⡥⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣿⣻⣟⣷⣙⠶⡱⢎⡕⣫⢜⢣⡚⣥⠳⣌⠳⣌⠳⣌⠳⡜⣥⢚⡥⣛⢬⡚⢵⢣⣚⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢳⣯⣟⣾⢻⣾⣑⢫⡜⡥⢎⢧⡙⢦⡛⣬⠳⡜⡳⣌⢳⡹⡔⣋⠶⣩⠖⣹⠪⣕⣺⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⣻⣯⢾⡽⣯⣟⢾⡽⣧⣞⡡⢏⠶⣙⢦⡙⢦⡛⣜⡱⢎⡓⠶⣹⣿⣷⡥⣛⠦⣛⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡶⣞⠻⣌⢳⡱⢎⡟⣿⣽⣯⣟⡾⣝⣯⢿⣾⣵⣩⠖⣭⠳⡜⢦⡙⢮⣍⠳⣍⠻⣍⠶⣡⣻⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠋⢹⣿⣯⡜⢣⡞⢱⣾⠋⠉⠉⠙⢻⣽⡞⣽⣮⡟⣯⣿⣷⣷⣽⣦⣽⣶⣬⣷⣬⣷⣾⣿⣿⣿⣽⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠞⠙⢦⡀⠈⠻⣷⣭⣶⠋⠁⠀⠀⠀⠀⠀⠉⠻⢷⣯⢾⣽⡺⣵⢯⢷⣻⠿⣽⡻⣟⣯⣿⣽⣟⣽⣛⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⡄⠀⠀⢙⣲⠶⣤⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠳⠿⢿⢾⠿⠗⠛⢋⣭⣼⣛⣳⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣇⠳⢄⡀⠈⠳⣟⣛⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⢀⣴⣿⣿⣻⣾⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠦⣝⠦⠤⠬⢤⡄⣬⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣟⣻⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⠒⠚⠚⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⣀⡀⣀⡀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠐⠒⠂⠉⠁⠁⠁⠉⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠉⠉⠢⡀⠀ ⠀⠀⠀⠀⠀⢀⡰⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠖⠒⡗⠂ ⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⠜⠀⠀ ⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡖⠐⠒⠒⠊⠉⢏⠅⠁⠀⠀⠀⠀⠀⠀⠀ ⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡄⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠑⢄⡀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠈⠁⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀