⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢌⡲⡹⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡐⢀⠂⡐⠀⠄⢀⠀⡀⡐⠌⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⢆⡳⣱⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠆⢐⡀⠡⠈⢀⠂⡐⢌⢢⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡱⢈⠖⣱⣾⣿⣿⣿⣿⣿⣿⢿⡿⠸⣻⣿⣿⣿⣿ ⠀⠀⠀⠀⠁⠈⠀⠒⠠⠊⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⢠⠉⡎⣵⣿⣿⣿⣿⣿⡿⠟⢭⡇⠘⣿⣯⠿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠄⢊⠔⣏⡯⣿⣿⣿⣟⡀⠀⡸⠀⠀⢸⠻⢧⣻⠼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢡⠈⢢⠘⠤⢻⢿⣫⣿⣿⢷⡄⠁⠀⠀⠀⢫⠐⠈⢃ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣻⣳⠦⣄⠀⡀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⡁⠆⣌⣰⣌⣸⣷⣾⣿⣿⣻⣯⢿⡄⠀⠀⠀⠐⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢯⢿⣎⣷⢻⢿⡿⣯⢷⣄⠀⠀⠀⠀⢼⡇⠀⠀⠀⢠⢐⣱⣿⣿⣿⣿⣟⣿⣾⣟⣷⣿⣻⢾⡄⠀⠀⠀⠘⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⣟⣾⢩⡽⣺⢽⣯⡿⣯⢿⣿⣿⢷⣶⣦⣤⣦⣤⣤⣾⣿⣿⣿⡿⣿⣹⣾⡿⣯⡳⣿⣞⣿⡽⣯⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢨⠷⣛⣶⢾⡾⣾⣿⡮⣗⣫⣿⡻⢿⡷⣿⣿⠿⡿⣿⢿⣻⡯⣿⣿⣿⢿⡿⣽⢧⣿⣻⢷⣿⢏⣳⢃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠀⠀⠹⣯⢚⢷⣭⣦⡱⣟⡿⣞⣼⢴⣻⣟⣿⣿⣿⢿⣧⣷⢯⣳⣿⡻⣞⡿⣱⣿⡿⢟⣻⡿⣋⢮⠵⣫⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⡈⢽⣞⡿⣤⡟⣿⣮⣞⠯⡏⢸⣖⣿⡍⣏⣿⣟⡿⣎⣽⡿⣟⣿⡿⣽⣿⠟⡡⢍⣎⠳⣧⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⢻⣎⡻⡝⠻⣽⣳⣭⢂⣿⣾⣿⣙⣾⣽⣿⣷⣿⣾⣻⢽⣻⣿⣁⣿⡷⢉⠢⢑⠪⡐⣏⠶⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠙⢿⣅⢀⣺⣳⡛⡥⣿⣯⣿⢟⣻⣾⡻⢿⢳⣻⣷⣮⣧⣭⣾⠏⠐⠂⢁⠂⡑⠸⣌⡻⣥⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣯⢻⣩⠿⡵⡌⠞⢻⡿⡌⠓⣀⠻⣿⣿⣼⣿⠟⠡⠀⠂⠐⠀⠠⢁⠓⣬⢳⡭⠄⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠂⡀⠄⠠⢈⠳⣧⣇⣞⡾⡯⠁⣉⢈⣩⣿⡻⣷⣿⣴⣿⠃⡐⠀⠀⠀⠀⠈⠐⠠⡉⢶⣩⢞⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⠑⡌⢂⠖⣨⠻⣿⡹⢙⣡⣪⣹⡹⠿⠭⠽⣯⡿⡁⠂⠀⠀⠀⠀⠀⠀⠀⢡⡘⢦⡝⡾⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠑⡌⡑⢎⠥⣛⠼⣯⣟⢬⣟⣮⡡⡤⣐⣿⡟⠡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⡙⢦⣝⡳⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣⡐⡉⢆⢣⡙⢮⢵⡺⢿⡭⢉⣒⣾⣿⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠊⣕⢣⡞⣽⢣⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡅⡘⠤⣂⠝⡬⢲⡹⢏⣧⠀⠀⢀⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠩⢆⢧⣛⡼⣣⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢄⡑⢊⠴⣉⠖⣣⢝⡹⣎⠆⠀⢸⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠤⡙⢬⢲⣙⢾⣹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢌⢣⠚⣔⣋⠶⣩⠶⣹⡆⠀⢸⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢢⠙⣬⢓⢮⡳⡅⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠊⠴⣉⠶⣌⠳⣥⢛⡴⡃⠀⢨⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⢢⡙⣤⢛⣎⠷⡅⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠌⡓⣌⠶⣌⢳⢬⡓⡞⡇⠀⢸⡑⢂⠀⠀⠀⠀⠀⠀⠀⠀⠡⡐⡡⢜⡢⢏⡼⡹⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠱⢌⠶⣩⠞⣦⢹⡜⠁⠀⠐⡍⢆⠀⠀⠀⠀⠀⠀⠀⠠⠁⢆⠱⣊⠵⣋⡞⡁⠀⠀⠀⠀