⠀⠀⠀⠀⠀⠀⠀⢍⠯⡽⢭⡻⢭⣛⡭⢯⡽⣩⠯⣝⡭⢯⡝⣯⡝⣯⣽⣭⠯⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠷⠿⣏⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⢚⡹⢧⣛⡥⣏⢿⣷⡚⣥⢻⡼⣙⢮⣝⡶⠛⠉⠀⠀⠀⠀⠀⠈⠑⠒⠒⠤⢀⡀⠀⠀⣀⠀⠀⠈⠉⠛⠿⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡱⣏⢮⢏⡿⣿⣵⣫⣼⣹⠞⠁⠔⠂⠐⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠈⠑⠢⣄⠀⠀⠐⠍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡝⢮⣻⢾⡿⠿⠟⠁⠀⠀⢀⠊⠑⢢⡀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠀⠑⢄⠀⠠⠀⢄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣧⢟⠉⠀⠀⠔⠉⠈⢀⢀⣤⡀⠀⠘⢄⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⡀⡀⠀⠈⠪⡢⡀⠱⣄⠱⡄⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡗⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣫⠏⠀⠀⡜⠀⠀⡰⠟⠉⠉⢣⠀⠀⠈⢣⠀⠀⠀⠀⢄⢈⢆⠀⡐⠄⠀⠘⡀⠈⠢⡌⠀⠈⠌⢂⠈⢢⠈⢆⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⣼⢣⠀⠀⠀⠀⠀⠀⠀⡰⣱⡏⠀⠄⡸⠀⡀⢸⠀⠀⠀⠀⠸⡄⢣⠐⡀⢷⣆⠀⠀⡘⠀⠎⢆⠐⢌⢂⠀⡁⠀⠀⠘⢆⠀⠀⠀⠡⠀⠱⡈⢇⠄⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⣼⢣⣋⠀⠀⠀⠀⠀⠰⡱⡹⠀⠰⢀⢃⠃⢡⡇⠀⠀⠀⠀⠀⢻⡀⠀⠀⠈⢻⡌⢄⠁⠀⠈⠌⢂⠈⡆⠁⠀⠀⠀⠀⠈⠦⠀⠀⢄⠡⠀⢡⠈⣎⠆⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿ ⡿⣸⢇⡧⠄⠀⠀⠀⠀⣇⢃⠇⠀⡄⠸⠀⠀⡀⡇⠀⠀⠀⠀⠀⠸⡃⠀⠀⠀⠘⣿⠀⠀⠀⢀⠘⡘⡄⠸⡀⡀⠀⢀⠄⢃⠘⣃⠀⠸⠣⢃⠸⠀⠸⡘⢀⠀⠀⢿⣿⣿⣿⣿⣿⣿ ⡷⣙⣮⢳⡍⡀⠀⠀⠀⡇⢸⠀⠀⠃⡇⠀⠀⣧⡇⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠡⠸⣧⠀⠀⠎⠀⠈⠰⡀⢱⠈⠀⠄⠀⠀⠡⠈⠀⠂⠘⣄⠀⠀⠀⢣⠀⠉⠄⠸⣿⣿⣿⣿⣿⣿ ⣝⡳⣎⠷⣎⠥⡀⠀⠀⠀⡈⠀⠐⢠⠁⡄⡆⣿⣧⠤⠖⢤⡀⠀⠀⠸⡀⠣⠀⡇⠁⢻⡄⠸⠀⠀⠀⠀⢣⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠘⡄⡆⠐⡀⣿⣿⣿⣿⣿⣿ ⢧⣻⣘⡻⣬⢳⢥⢂⠀⠀⡇⠀⠈⠈⠐⠀⠀⢷⣿⠀⡔⠀⢱⠀⠀⠀⢣⠀⠢⠃⠀⠘⣷⠀⠀⠀⠀⠀⠈⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠇⢰⠀⠁⢸⣿⣿⣿⣿⣿ ⢧⡳⣜⡳⢭⣫⢎⠧⣆⠀⣇⠀⠀⠀⠀⠀⠀⣼⣸⠀⠙⠒⠁⠀⠀⠀⠈⣷⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⠀⠀⢸⢸⠀⠀⢸⣿⣿⣿⣿⣿ ⣧⢳⡣⣝⠳⣎⡝⠾⣌⢇⣫⡄⠀⠀⠀⠀⠀⣟⡌⡏⠒⠒⣒⣦⣤⣄⡀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⡄⠀⠘⡼⠀⠀⣸⣿⣿⣿⣿⣿ ⢧⡛⣴⢋⠷⣸⢘⠯⣜⢮⡘⡇⠰⠀⠀⠀⠀⢹⣇⠘⠔⠉⣀⡠⠤⠤⣍⡳⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⡇⠀⠀⡇⠀⡇⡿⠿⠛⠛⠛⠿ ⢧⡹⠢⢏⡳⢥⣋⢞⡱⢎⡒⣹⠀⡆⠀⠀⠀⢸⣿⡀⡔⠉⠀⠰⠆⠀⠀⠀⡎⣿⡄⠀⠀⢆⠀⣄⠀⠀⣦⢰⡄⠀⠀⠀⡀⠀⠀⠀⠀⢠⢠⡇⢇⣰⠤⠢⢅⢰⢠⡇⠀⠀⠀⠀⠀ ⢧⡹⣱⢋⣜⢣⢎⢧⡙⢮⡑⣸⢃⢘⠄⠀⠀⠈⣿⡁⠐⠤⣀⣠⠤⠔⠊⢀⠇⠘⣟⢄⣧⣸⢆⡏⢣⡀⢩⢿⠸⡄⠀⢠⢻⣤⡇⠀⡠⢻⡘⢱⡜⢁⠔⣆⠈⡇⣼⢘⡒⠦⣤⣄⣀ ⡣⢕⡣⢋⡼⡌⢞⡢⡝⢦⡙⣼⢈⣎⡌⢜⢄⠀⢸⠁⠀⠀⠀⠀⠀⠀⠐⢸⠀⠀⠙⡌⠻⡟⠈⢿⠀⠱⣼⠈⠀⠹⡄⡌⠈⠉⣧⠞⠁⣸⠁⡘⢠⡞⡄⠀⠀⡿⢡⡶⠞⠋⠉⠀⠀ ⢇⠫⡔⢎⡲⢩⠖⣡⢋⢦⡹⠛⡡⠀⠱⠄⠩⢢⢀⣃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠘⠀⠈⠀⠀⠉⠀⠀⠀⠈⠇⠀⠀⠁⠀⠀⠃⢰⠁⣞⠹⡍⠀⣰⣳⡯⠵⠶⠒⠒⠒⠒ ⡍⢖⡩⢎⡱⢃⡞⡡⢏⠞⢠⠊⠀⠀⠀⠀⢀⣀⣙⣟⢆⠀⠀⠀⠀⠀⠀⠈⠲⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡸⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢎⡱⡘⢦⢃⠯⢴⣩⠃⣀⠇⠀⠀⠀⠀⠀⠈⠛⢒⠒⢬⣭⢅⣒⠂⠤⢄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠗⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢢⠱⡘⢆⡭⠾⠤⡏⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣹⣦⠀⠉⢽⠉⠁⠀⡀⠀⠀⠉⠉⠉⠙⠛⠩⠖⠀⠀⠀⠀⠀⠀⣠⣾⠧⠴⠒⠒⣒⣊⣩⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢂⡷⠚⠁⡀⠀⠀⠀⣸⢇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣧⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⡚⠩⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠘⢯⡿⢧⣠⠀⠀⠀⠀⠀⠈⠉⠛⠫⠵⣒⡎⢳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⣞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠙⣧⣽⣷⠀⢠⠀⢠⠀⠀⠀⢠⣾⣵⣷⣶⠚⠛⠛⠒⠒⠒⠈⠁⠁⠒⠒⠒⠒⠒⠒⠒⠂⣤⣤⣤⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⠹⡜⢿⡆⠀⠀⠀⠀⠀⠀⠀⢀⡬⠷⣨⡽⠧⠿⠚⠚⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣍⡍⠆⢷⡀⠀⠀⠀⠀⡠⠔⠚⠉⠉⠉⢁⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣢⢙⡢⣀⠔⠉⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠈⠉⠁⠉⠉⠉⠉⠉⠁⠒⠒⠚⠓⠚⠤⠤⠅⣀⣀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⢀⠈⠙⠪⡶⠵⠾⣛⠛⠓⠒⠒⠒⠂⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠈⠢⣄⠀⠉⠑⠢⢄⠀⠀⠀⠀⠀⠀⠉⠉⠒⠢⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠤⠤⣄⡑⠄⠓⢄⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢖⡦⢤⣀⡀⠀⠀⠀⠀⠀⠈⠙⠻⣒⡤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠣⠔⡩⠢⣄⠀⡳⣄⡀⠀⠀⠀⠙⠢⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣍⣓⠦⣄⡀⠀⠀⠀⠀⠱⠙⠽⣝⡢⣀