Fluttershy W Glasses :) Emojis & Text

⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣀⠀⠜⣁⣤⣀⠋⠉⢣⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⠮⠙⠂⠀⢨⠋⠉⡩⠋⠁⠘⠣⠿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠤⡠⡮⠋⠁⠀⠀⠀⢀⠇⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠓⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⡰⠁⠀⠈⢵⡀⠀⠀⠀⠀⢸⢀⡎⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⢠⠁⠀⠀⠀⠈⠾⠀⠙⠒⠦⣇⡜⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠸⡎⡀⠀⠀⠀⠀⢀⠄⢀⠀⡾⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡋⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⢇⡇⠀⠀⠀⠀⠸⠀⠸⢼⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⣃⠴⠊⠀⠀ ⠀⠀⠀⢸⢠⠀⠀⠔⠁⠀⣎⡙⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⣠⠴⠋⡉⠀⠀⠀⠈⢳⡀⠀⠀⠸⠀⠀⠀⠀ ⠀⠀⠀⠈⡜⠀⠀⠂⢀⠂⠉⢁⡇⠀⠀⢾⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢶⣄⠀⠀⠀⠛⡟⠳⣦⠃⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⡇⠀⠀⠘⢄⠠⣸⡇⠀⠀⠈⡿⡀⠀⠀⠀⠀⢀⡴⠋⣁⠠⡄⣻⠀⠀⠀⠀⡵⢶⣮⠻⣭⡄⠀⠀⠀⡇⠀⠀⠻⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢠⠀⠀⠀⠀⠀⣿⢹⡀⠀⠀⢱⠀⢀⠐⠒⣶⣿⣶⡾⠛⢛⣿⣾⢤⣤⣤⣤⣤⣾⡷⠒⠒⠒⠲⢦⣴⣅⠀⣘⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢛⡀⠀⠀⠀⠀⢳⣆⢃⠀⠀⠀⢧⠬⠽⠟⠻⡟⡆⣄⣠⡾⣿⡿⠀⣻⡟⢻⡿⠟⡀⠀⠀⠀⠀⡴⣿⠃⡴⠏⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠃⠀⠀⠀⠀⠸⡘⡌⢆⠀⠀⠘⣆⠀⠰⣻⢿⡵⡹⣿⣿⠟⠁⢠⡟⠀⠀⠳⣱⡀⠀⠀⢀⡼⢁⡏⡜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢦⣀⠀⠒⠁⢀⡀⠀⠀⢇⠱⡈⢆⠀⠀⠈⢧⠑⢥⣈⠣⠤⣄⣠⡤⠶⠋⢰⡄⠈⢀⣠⠯⢤⣤⣾⠤⢞⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡶⠎⠓⠀⠀⠀⠀⠘⠡⢢⢜⠀⢡⠈⢆⠀⠀⠀⠳⡀⠈⠙⠲⢀⣤⠀⠀⢀⢾⠙⠓⣞⠁⠀⣰⠋⠀⡠⠓⠤⢄⣀⠀⠀⠀⠀⠀⠀ ⠀⢠⠒⠛⠽⣛⠢⠶⣤⣀⠀⠀⠘⡇⠀⢣⠀⢣⠀⠀⠀⠙⣄⠀⠀⡄⠈⠉⠛⠃⠀⠱⣄⠈⢳⡴⠃⠀⡰⠁⠀⠀⠀⠀⠈⠁⠐⠂⠀⠀ ⠀⢠⠉⠒⠤⡀⢉⠐⢠⠖⠀⠀⠀⢻⡀⠀⢣⠀⠱⡀⠀⠀⠈⣆⢠⠃⠀⠀⠀⠀⠀⠀⠈⢣⡀⠙⣆⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣵⡄⡀⢨⡟⠁⠀⠀⠀⠀⠀⠈⣗⠀⠀⢃⠀⠘⡄⠀⠀⠘⡞⠂⠀⠤⠀⣀⠀⠀⠀⣸⠙⢆⠈⢳⡷⠆⠒⠊⠉⠉⠉⠒⠒⠀⠤⠄ ⠀⠀⠈⠷⣌⠊⡗⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠈⡄⠀⠘⡄⠀⠀⢹⡒⠠⢄⡀⠀⣩⠖⠉⠁⠀⠉⠱⣖⢳⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⢾⡢⢀⠀⠀⠀⠠⣴⡋⢻⡄⠀⢸⡀⠀⢱⠀⠀⠸⡇⠀⠀⠈⠑⢷⣄⠀⠀⠀⠀⠀⠀⠙⠞⢃⡤⣢⡍⠁⠒⢂⣤⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠈⢻⡆⣧⠀⠀⡇⠀⠀⡇⠀⢰⡇⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⣴⢋⡴⢣⠴⡣⢚⡽⠟⣀⣴ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣬⠷⣾⠀⠀⠀⠀⠀⠇⠀⣼⡁⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠉⠐⠋⣞⡴⢉⣴⣿⠟⠁ ⣀⠈⡉⠁⠐⠛⠡⠖⣤⢀⡀⣼⡵⣜⡵⢀⠿⠀⠀⡀⠀⠀⡇⣐⠞⠶⠯⣤⣤⣔⣸⠯⢙⣛⠰⠖⣀⡤⠄⣀⡀⢀⢼⠿⣰⣽⡿⠋⠀⠀ ⠈⠻⣦⡀⠀⠀⠀⠀⠒⠛⠉⠻⠙⢗⣀⠖⠁⠀⢀⠇⠀⢠⠻⠚⠂⠀⠀⠀⠈⠉⠛⠿⠷⣶⣬⣅⣒⠤⢉⡐⠀⠅⢕⣾⡿⠛⠒⠒⠀⠀ ⠀⠀⠈⠫⣢⡀⠀⠀⠀⠀⠀⢀⢣⠀⠀⠀⠀⢠⢎⣠⢢⢁⡀⠂⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠉⠛⠻⠷⣶⣦⣴⣿⠋⠁⠀⠐⡊⠅⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⣄⣀⣰⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠤⠒⠉⠳⢄⠱⡀⠀⠀⢨⠇⠀⡌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣞⡁⠀⢀⣀⡀⠀⠡⣱⠴⠊⠹⠀⠀⢹⠀⣷⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡜⠁⣀⡀⠀⠄⠀⠈⣁⡾⠁⠀⠀⠀⠀⠀⠸⠀⢹⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡾⠒⠉⢀⣀⣀⣀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡇⠀⡰⠋⠀⠀⢸⣭⡛⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡏⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⡇⠀⠀⠀⣸⣏⢳⠀⠀⠀⢀⣀⠤⠴⠿⠂⣸⠀⠀⣘⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⡄⠘⣆⠀⠘⠛⢻⣿⡇⠀⠰⠋⠀⠀⠀⠀⣠⠃⠀⢠⣿⢹⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣄⠈⠳⣄⠀⢈⡿⠃⠀⠀⠀⠀⠀⠀⡴⠃⠀⢠⢋⠇⡼⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⢄⡈⠓⢬⡓⠤⣼⣀⣀⣤⡴⡞⠀⠀⠠⢃⠎⢀⡗⢊⣉⣉⣙⣷⣖⣊⡉⠉⠁⠒⠢⡀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠲⣄⠈⠳⢄⠀⠀⠀⡟⠀⠀⡰⠁⡜⠀⢸⠙⢷⡔⠚⣉⡭⣿⡀⠈⠑⣄⠀⠀⠈⢢⡀⠀⠀⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠑⢄⢠⡇⠀⡰⠁⢠⠁⢀⡆⠀⠀⢈⣏⣤⣶⣿⠇⠀⠀⠘⡄⠀⠀⠀⢡⠀⠀⢨⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⢳⡄⠈⢿⡇⠀⡅⠀⠸⠀⣼⣀⣀⣠⣾⣵⠟⠉⣹⠀⠀⠀⠀⢻⠀⠀⠀⢸⠀⠀⡼⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⢸⡉⠈⢁⡜⢹⠀⢸⡿⡀⡄⠀⡇⠀⣇⠠⣭⣽⣶⠋⠀⢠⠇⠀⠀⠀⠀⡟⠀⠀⢀⠎⠀⡰⠁⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⣄⠉⠓⠉⠀⢀⡧⠊⠀⠹⣷⠀⠸⡀⠘⢆⣿⣿⡟⢇⠀⠘⠙⣆⠀⠀⣸⠁⠀⢀⠎⢀⡔⠁⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⡏⠙⢦⣵⣄⠀⢉⣩⡇⠸⡄⠀⠀⠸⡀⣴⠃⠀⡠⢃⡴⠋⠀⣠⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠇⠉⠉⠉⡇⡇⠀⡇⠀⠀⠀⡿⠃⠀⡜⡡⠋⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣸⠀⠀⠀⠀⣿⠁⢠⠃⠀⠀⢰⠇⠀⡼⡞⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢀⠇⠀⠀⠀⢸⠏⠀⡜⠀⠀⠀⠘⣧⡀⡇⢧⠀⠉⠑⠒⠀⢉⣉⣉⣉⡉⠓⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⡞⠀⠀⠀⠀⣸⠤⢴⠁⠀⠀⠀⢀⡏⠉⠓⠒⠷⠶⠒⠚⠉⠁⠀⠀⠀⠀⠙⢦⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠺⠤⠤⠤⠤⠴⠋⠀⠈⠓⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⡀⠀⢀⣠⣤⣴⣶⣶⡦⠤⢤⣤⣀⣀⣼⠀⠀⡽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠫⣯⠙⡟⢿⣿⣿⡿⠁⠀⢠⣾⣿⣿⣿⡿⠀⠀⢹⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣷⣧⡀⢱⠈⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⢸⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⡄⢀⣀⣠⣿⣿⣿⠿⢿⣷⣤⡀⠈⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⡇⣾⣿⣦⣀⣿⡄⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⠿⢯⣷⢄⠀⠀⠀⠀⡄⢻⣿⣯⣻⣿⡧⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⠟⠁⠀⠚⢻⣦⣱⣄⠀⠀⢣⠈⠛⣽⣿⠿⠭⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠻⣿⣿⠀⠀⠈⠂⠀⠀⢀⣄⣠⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠄⢠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⣠⣤⣶⣶⣾⣶⣶⣦⣄⠀⠀⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠴⠯⠤⠤⢶⢾⣿⣿⣿⣿⣿⠏⠷⣄⢀⣀⣀⣀⡀⣼⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠸⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠈⠉⣡⣾⣿⠏⠀⢰⣿⠉⣩⠀⠉⢙⣿⡿⠛⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢻⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣿⣿⡿⠋⠀⢀⣾⡿⠀⣉⣀⣇⠘⠋⣿⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠘⢯⡀⠀⢀⣾⣿⠇⣴⠨⣿⣿⡯⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⠻⢦⣾⣿⠏⠀⠈⢈⣝⡟⠁⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢄⣀⡀⠀⠀⠉⠁⠀⠰⣄⠀⠁⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠃⠀⠀⣸⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢹⠁⠀⢠⠶⠤⠤⢴⡾⢦⡀⠀⠀⣼⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠇⠀⠀⢸⡄⠀⠀⠀⠙⢆⠙⢦⡀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢰⣿⡿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡟⢻⡀⠀⠀⠀⠈⢳⡀⢳⡀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⢀⣼⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⡇⠀⢧⠀⠀⠀⠀⠀⢷⠀⢳⠀⠀⠀⠈⢧⠀⠀⠀⠀⢀⣿⣿⡏⢀⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢸⠇⠀⠸⡆⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠘⣧⠀⠀⠀⢸⣿⣿⡷⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣾⠀⠀⠀⣧⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢸⡆⠀⠀⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⣿⠀⠀⠀⠀⣏⣀⣸⠇⠀⠀⠀⠀⠀⣷⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⣤⣤⣤⡤⠴⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠈⠉⢿⣄⣀⣠⣤⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠗⢤⡀⠀⠀⠀⠀⠀⠀⠀⣰⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠴⠖⢏⣉⣉⣹⠀⠀⢹⢦⡀⠀⠀⡰⣆⢠⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡶⠋⠁⢀⡴⠚⠉⠀⠀⠁⠀⠘⡎⣷⣄⠀⠇⢸⡎⢀⡇⣤⣄⠀⠀⢀⡤⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⢛⡠⠶⢶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣶⠀⢸⠀⢸⣾⠞⢹⡤⠚⠁⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡗⠉⠀⠀⣾⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣧⠀⢀⡾⠁⠐⠋⠀⢀⣴⣋⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⠀⡔⠉⢻⠀⠸⡏⢍⣿⣖⠺⡷⠤⠆⠀⠀⢹⣾⡀⣾⠖⡆⠀⠠⠔⠋⠁⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⠀⣇⠀⠈⠣⡀⠙⢌⣿⣿⣿⠇⠀⠀⠀⠀⠀⢿⣿⡼⠀⣧⢤⡄⡠⠴⠮⠥⣄⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢷⣜⣆⠀⢀⡅⠀⠀⠈⠉⠀⢀⡴⠀⠀⠀⠀⢸⡇⡇⠈⠁⣼⣁⣤⠤⠒⢊⠥⠒⠊⠉⠉⠉⠉⠙⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣷⣬⣳⠤⠴⠤⡖⠊⢁⣿⠀⠀⠀⠀⠈⡿⠁⠀⢚⣏⠵⠈⢲⣊⠥⠒⠒⠒⠒⠤⢄⡀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣌⠑⢆⢠⠇⢠⡞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢘⡏⠉⠉⠉⠑⢦⡀⠀⠈⠓⣄⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡾⠳⠀⡏⠇⢈⡟⣴⠋⠀⡼⣄⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⡆⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢫⡻⠤⠔⢃⡶⢋⡞⢁⠤⠊⠀⢸⠦⡌⠀⠀⣖⣀⣨⣦⡀⠀⢀⣎⡀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠁⠀⡾⠊⣁⠠⠤⢒⣻⡟⠀⠀⡴⠃⠀⠀⢳⠙⡄⠀⠀⢳⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡎⠀⢀⡜⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡡⠊⠀⣠⠖⠋⣼⣤⠀⢸⢳⠀⠀⠀⠀⡇⠸⡀⠀⠀⣇⠀⠀⠀⣠⠋⠀⠀⢀⠞⢀⡠⠋⡜⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡾⠓⢶⠀⢻⢙⣖⠈⠛⠦⡄⠀⠀⢸⠀⡇⠀⠀⢸⡀⢀⡼⠁⠀⣠⣖⡡⠔⢉⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠝⠶⠟⠀⢸⢿⡀⠀⠀⢠⠃⠀⠀⡜⠀⡇⠀⠀⠈⡇⡾⠁⡰⡻⠊⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣱⣄⣠⡏⠀⠀⠰⠧⣴⠁⠀⠀⢀⡇⢷⣸⠀⡁⠀⠀⠛⠲⠴⠒⠒⠒⣲⣦⣑⢲⡦⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠙⠲⠧⠤⠤⠤⠤⠔⠒⠊⠉⠁⢀⡄⠈⠹⡌⢇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⢤⣜⠡⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡴⠛⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠬⣷⠄⠀⠀⠀⠀⢰⣆⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠐⢿⣬⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⢠⣤⡀⠀⠙⣆⠀⠀⠀⠀⠙⠀⠀⠀⠀ ⠀⠀⣸⡄⠀⠀⠀⢀⡏⠀⠀⣀⡀⠀⠀⠀⠛⠀⠀⠈⣯⠀⠀⢞⣛⣯⡉⠀⠀⠀⣸⢦⣄⡀ ⠀⠺⢿⡿⠛⠀⠀⢸⡇⠀⡀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⢉⡏⠁⠀⠈⠛⡾⠋⠀ ⠀⢀⠈⠁⠀⠀⢀⣹⡷⣶⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⢦⡄⠀⠰⠋⣹⡷⠛⠁⠀⠀⠀⠀⠀⣠⣤⡤⠤⣄⠀⠀⠀⠸⣧⡀⠀⣴⠛⣦⠀⠀⠀ ⠈⠻⠟⠁⠀⠀⠘⠋⠻⢶⣤⣀⠀⠀⠀⠾⠡⠸⣇⠀⠀⠀⠀⠀⠀⠈⠳⣆⡿⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⠏⠃⠀⠀⠀⠀⠀⠀⠀⠙⣇⣸⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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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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⢤⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀ ⠀⢿⣿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⢿⡿⠁ ⠀⢸⠀⠁⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⡿⠃⠀⢸⡀⠀ ⠀⢸⠀⠀⠀⠈⣎⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣟⡀⡇⠀⠀⠀⡇⠀ ⠀⢸⠀⠀⠀⠀⢸⣄⠹⣿⣿⣿⣦⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢠⣾⣿⣿⣿⣿⣫⣾⡇⠀⠀⠀⣷⠀ ⠀⣾⠀⠀⠀⠀⠘⡜⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⢽⠁⠀⠀⠀⣿⠀ ⠀⢸⠀⠀⠀⠀⠰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⣄⡀⠀⠀⣿⠀ ⠀⢸⡆⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⠀⢰⣿⠀ ⢳⡸⣿⣤⣄⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⢴⣿⣳⠀ ⠠⣽⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣡⠏ ⠤⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠄ ⠀⠰⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠄ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠊⢻⠈⢿⣿⣿⣿⣿⣿⣿⡏⠙⢻⡇⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡏⠘⡇⠀⠀⠸⡄⠈⣿⣿⣿⣿⣿⡏⠀⠀⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣶⣶⣤⣀⠡⠀⠈⢻⣿⣿⣿⠀⢀⣤⣶⣶⣦⣄⣿⣿⣿⡟⠛⢻⣿⣿⣧⠀ ⠴⠛⠁⠈⣿⡀⠉⢻⣿⣿⣿⣿⢹⣾⣿⣿⣿⡆⠀⠀⠙⢿⡄⠀⢿⣽⣿⣿⡏⣿⣿⣿⡟⠀⢀⣾⠇⠀⠉⠛ ⠀⠀⠀⠀⠈⣷⡀⠈⢿⣿⣇⠘⠘⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡽⠛⣣⣿⣿⠃⢀⣾⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠟⠙⢦⣌⡻⣿⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣥⡶⠋⠛⠧⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⣿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢟⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣬⣁⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⢓⢤⣀⠀⠀⠀⠶⠿⠷⠀⠀⠀⣀⣤⣾⣿⢿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢃⡞⣰⠈⠓⢦⢄⣀⠀⣀⣠⣴⠞⠁⢸⠇⣿⡀⣿⠿⣿⣿⣿⣿⣿⣷⡄⠀ ⠀⠀⠀⣿⣿⣿⠟⠋⠉⠉⠉⠣⣼⠃⣟⠂⣄⠈⠳⡍⠉⢉⡾⠁⠀⠀⡿⣸⡟⠋⠀⠀⠈⠉⠹⣿⣿⣿⡇⠀ ⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣦⠙⢇⠀⠉⣶⢿⠀⡿⣆⠈⠁⣰⣇⣿⣧⡀⠀⠀⠀⠀⠀⠈⣿⣿⠇⠀ ⠀⠀⠀⣿⣧⠀⠀⠀⠀⢠⠴⠶⢾⣿⠆⡌⠆⣰⣧⡄⣤⣠⣿⡀⣰⢻⣷⣮⣉⡀⠀⠀⠒⠲⠆⣰⣿⣿⠀⠀ ⠀⠀⠀⢻⣿⡈⠙⠛⠛⠛⣀⣐⣤⣶⣿⣯⠈⠀⠘⣿⣷⣿⠏⡟⠁⣸⣿⣿⣿⡟⠻⠥⠴⠶⠾⢻⣿⣿⣆⠀ ⠀⠀⠀⣸⣿⣟⠒⠠⠄⠂⣠⣿⣿⣿⣿⣿⡄⠀⠀⢻⣷⣿⠀⠀⠀⣿⣿⣿⣿⣿⣄⠀⠀⢀⣴⣿⣿⣿⡏⠀ ⠀⠀⢠⣿⣿⢿⣷⣦⣤⣾⣿⣿⠙⢿⣿⣿⣷⡀⠀⣸⣿⡿⡄⠀⢰⣿⣿⡿⢋⣿⣿⣷⣶⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠘⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣷⠀⣟⣽⣾⣿⢠⣿⡿⠋⣰⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⡆⠀ ⠀⠀⢠⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⡿⣿⣿⣿⣿⣿⡿⢋⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⣿⣿⠇⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀⣠⡾⢛⣦⣄⣰⠶⣆⣾⡙⣶⡤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⢤⣀⣿⡄⡟⠁⡇⢸⡅⠈⡿⠀⣿⡏⠹⡿⠀⢿⡏⠙⣆⠀⠀ ⠀⠀⢠⡖⢲⡸⡅⠈⣿⠇⢷⡇⢸⡇⠀⣇⠀⡇⠀⢻⣷⠀⢷⠀⣼⠀⢰⠇⠀⠀ ⠀⠀⠘⣧⠀⣇⢧⠀⢸⡄⠸⡇⢸⣷⠀⢿⠀⣷⠀⡿⢹⠀⢸⣤⡇⠀⣾⠓⢦⠀ ⢠⡞⠳⡿⣄⡸⣼⡆⢸⡇⠀⡇⠀⣿⡄⢸⠀⢹⢰⡇⢸⡆⠘⣿⠁⢀⡏⠀⣼⠀ ⠘⣧⠀⣟⠉⣧⢹⡇⠸⡇⠀⣷⠀⣿⡇⢸⡇⠸⣿⠀⣼⡇⢠⡏⠀⢸⠃⢰⠇⠀ ⠀⠘⡆⢹⡀⠸⡆⢷⠀⡇⠀⢻⠀⢸⣿⢸⡇⢀⡏⢰⣿⡇⣸⠁⠀⣾⠀⣿⣄⠀ ⢀⣴⢿⡄⢧⠀⢹⣼⡀⣻⣀⣘⣧⣀⣿⣼⣇⣼⣅⣾⣸⣧⡏⠀⠀⡏⢸⣧⠈⢳ ⣾⠁⣿⣷⡘⣦⡴⠿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣤⣰⡇⣿⡟⠀⢸ ⢹⡄⠙⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠟⠁⠀⣼ ⠀⢻⡄⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⡏ ⠀⠀⢻⡄⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢸⠇ ⠀⠀⠀⢻⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠈⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⠀⠀⠀⢻⡄⢰⣿⡏⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⣱⡄⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢸⡇⠘⠿⡿⠿⠁⠀⠀⣶⡀⢐⣶⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⣼⠁⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀ ⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⣿⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡾⠋⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢤⣀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠞⠁⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠙⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠚⠀⠀⠀⠀⠀⣰⠃⢠⡏⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠈⠛⠓⠶⠤⠤⠤⢤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡽⠀⢸⠀⠀⠀⠀⠸⡄⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⢸⠀⠀⠀⠀⠀⢻⡀⢿⡀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠀⢸⡄⠀⠀⠀⠀⠀⠻⣌⢷⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⣸⡇⠀⢸⠀⠀⠀⠀⠙⠳⣿⣆⡀⠀⠀⠀⡟⣦⠀⠀⢀⡠⠖⠁⢨⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⡤⠞⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠠⣦⣩⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⡉⠉⠓⠀⢸⠃⠈⢧⡰⠋⠀⠀⢀⡾⣧⠀⠀⠀⠀⠀⠀⠀⢹⡖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⠀⠈⢹⣹⡄⢸⣻⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⢀⣠⣌⡃⠀⢀⡴⠊⠀⢹⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠶⠦⣠⣠⠷⢷⡈⣿⢷⠀⠀⠀⠀⠀⣿⡄⠀⠀⢹⠀⠀⠀⠉⠙⢿⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⢸⠀⣠⡟⠀⠀⠈⢧⢸⡞⣷⡀⠀⠀⠀⢹⣷⠀⠀⢸⡆⠀⣀⣀⡀⠀⠙⢦⡀⢸⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⣿⣰⠏⠀⠀⣀⡤⠬⢷⣽⡌⢧⡀⠀⠀⠈⣯⣇⠀⠀⣷⣶⣶⣦⣬⣭⣿⣆⡙⢿⡄⠀⠀⠀⠀⠀⡀⢸⡇⠀⠀⠒⠚⠉⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠋⣀⣴⣾⣿⣾⣿⣷⡛⠻⠤⠻⣦⣀⠀⠘⣜⢦⣶⣿⢽⣿⣿⣿⣟⣿⢿⣿⣷⣯⣤⠀⠀⠀⢰⡇⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⣀⣿⣼⣿⡿⣿⢛⡻⣿⣿⣏⠀⠀⠀⠈⠉⠉⠙⠻⠎⠛⠂⠈⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡷⠀⠀⢸⠃⢸⡷⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⣽⣿⣿⣗⠀⣿⣿⢿⣿⢷⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠘⠻⢧⣠⠏⡸⡏⠀⠀⠀⠀⣾⠀⢨⡇⠙⣆⠀⠀⠀⢸⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣦⠀⢀⡈⢁⣀⣡⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⠰⠞⠃⠋⢸⡇⠀⠀⠀⢀⡇⠀⢸⡇⠀⢹⡄⠀⠀⡟⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⢸⠘⢧⠀⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⣀⢸⡃⠀⠀⢰⣸⠀⠀⢸⡇⠀⣾⠁⠀⠸⠃⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⢸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⢸⠁⠀⠀⢰⡏⠀⢠⣸⠟⣼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠁⠀⠘⣾⢎⠗⠀⠀⢰⡆⠀⠀⡆⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⣴⠃⠀⠀⠸⣿⠀⠀⠀⠀⢸⡇⠀⢰⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⡙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⡜⠁⠀⠀⢀⢠⡇⠀⠀⢀⠀⠘⡇⢀⡟⡇⢀⠄⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⢳⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣈⡿⠀⠈⠀⠀⠀⠀⠈⣼⠀⠀⠀⣿⠀⠀⣷⣼⣹⢃⡼⠀⠀ ⠀⠀⠀⠀⠈⣇⠀⠀⢸⠀⠀⠀⠀⠀⣀⠈⠙⠒⠶⠤⢶⣶⡖⠋⠉⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⡀⢰⡇⠀⣤⣼⢳⣷⠀⢸⣿⡿⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢀⣴⠟⢉⣼⡇⠀⠀⠀⠀⠀⠀⣠⢞⣡⠄⠀⠀⠀⠀⡼⡇⣼⣀⢸⡿⠷⠤⠽⠾⠷⠷⠀⠀⠀⠀⠀ ⠀⡆⠀⠀⠀⠘⡇⢀⣼⠹⡄⠀⠀⣀⡬⢶⣾⠟⢁⡾⠟⠋⠀⠀⠀⠀⠀⠀⠛⠋⢹⡏⠀⠀⠀⣠⡿⠁⣷⠋⠈⣙⣷⡀⠀⠀⠀⠀⠀⠈⠙⠲⣤⠀ ⠀⢳⡀⠀⠀⠀⢻⡀⡿⡆⢠⢾⡿⠋⣠⠞⢁⡴⢋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⣠⠴⠊⠁⠀⠀⠉⣠⠞⠉⣠⠝⢦⣀⢀⡤⠋⠉⠉⠀⠀⠣ ⠀⠀⠹⡄⢀⠀⠀⠻⣅⡀⣰⠏⠀⡴⠃⢠⣿⠞⠉⠉⠉⠓⢦⡀⢠⣤⣤⡤⠚⢓⡾⠉⠀⠀⠀⠀⠀⣠⠟⠁⢀⡼⠃⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠚⣳⣤⣀⡈⠙⣧⣀⡞⠁⠀⡞⣀⡤⠖⠦⣄⠀⠀⠙⢶⣀⡐⠙⠲⣏⠀⠀⠀⠀⠀⣠⠞⠁⠀⣰⡮⠂⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⠁⠀⠤⡉⠉⠛⠋⠁⠀⢠⠏⠁⠀⠀⠀⠀⠉⠲⣄⣠⣿⣁⣲⡤⠈⢳⡀⠀⢀⡼⠁⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⠀⡰⠃⠀⠀⢀⠘⢾⡄⢠⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⠜⣱⠃⠤⠤⠀⠀⠀⠘⢦⡟⢀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠑⢄⡉⠉⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢒⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠙⣦⡀⢰⠃⠘⣇⠀⠀⠀⠀⢀⣠⡤⠶⠒⠒⠒⠶⢦⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⢦⡀⣧⢰⠋⢳⣼⢠⡟⠻⣄⣀⡴⠞⠯⣁⠀⠀⠒⠢⢄⣉⠛⢽⡛⠷⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠹⣿⣼⠀⠀⢿⡟⢀⠀⠙⣏⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠑⢦⣙⢧⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠹⣿⠀⠀⢸⠃⢺⠀⠀⠈⠓⠶⣤⡀⠀⠀⠱⣄⠀⠀⠀⠀⢹⡶⣽⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢿⠀⠀⢸⡇⠸⡆⠀⠀⠀⠀⠀⠉⠳⣄⢲⣌⣦⠀⠀⠀⠀⢷⠈⢿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠦⣷⠀⠀⢸⠂⠀⢸⣷⡀⠙⠀⠀⠀⠀⠀⠀⠀⠙⢷⣯⠛⢦⣀⠀⠀⠘⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠸⣇⠀⠈⢠⠶⣾⡏⢷⠀⠀⣳⣦⠤⠤⠤⣤⣄⣀⣹⣄⣷⠼⣿⡦⣄⡸⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⠂⠀⡏⠀⢹⢳⠘⣇⠀⠚⠛⠀⠀⠀⣀⣼⣿⡇⠀⠐⣾⣿⠀⠀⠉⠉⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⡏⠙⢷⡇⠀⢸⠘⣆⠘⢧⣄⠀⠀⠀⠐⣿⠗⣛⡃⠀⠀⢈⣉⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢖⣺⢿⣛⠟⠓⠦⣤⣀⠀⠀⠀⣳⣷⠀⠀⠋⠀⣾⠀⠈⢶⣿⡞⠟⠒⠀⠀⠀⠘⢿⣿⠓⣦⠼⠟⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡶⠋⢁⣴⠿⡪⠝⠊⢉⣉⠩⣍⣙⠳⣄⣸⡇⠈⢳⡀⠀⠀⢻⢇⠀⠀⢱⣳⡄⠈⠒⣶⠶⠶⠦⠾⠟⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⢋⣠⣴⡿⢡⠎⢀⡠⠊⠁⠄⣐⣶⠶⢿⣾⣿⠿⣄⣖⠛⠃⠀⢾⡘⡄⠀⣀⢡⣷⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡵⣻⣻⣹⢁⠏⢠⠎⢠⠂⢠⠜⠉⠀⢀⡾⣿⣿⠀⠈⠙⠢⣄⡀⠸⡇⠸⣄⡟⡞⢿⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠏⢠⡇⡇⡇⡞⠀⡎⣠⠁⢠⠏⠀⠀⠀⢸⡇⢸⣿⢀⠀⠀⠀⠀⠀⠀⢷⠀⣹⠁⢹⣾⡞⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⣾⢹⢸⢠⡇⢰⠁⠃⠀⡞⠀⠀⠀⠀⣀⣧⠀⠃⠈⣇⠀⠀⠀⠀⠀⢸⣠⠏⠀⠖⠛⠉⠙⣧⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⢸⠘⢸⠀⢸⢸⣀⢠⠇⠀⠀⠸⡏⠁⠹⠀⠀⠀⢘⣧⣄⠀⠀⠀⢾⡋⠀⠀⠀⢀⠀⠀⢸⡄⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠇⡀⠀⢸⠀⢸⡀⢹⢸⠀⠀⠀⠀⡇⠀⠀⢀⣀⡴⢿⠋⠉⠉⠙⠛⠛⠛⠒⠚⣻⠋⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⡇⠀⢸⠀⠀⠇⢿⣿⠀⠀⠀⠀⡧⠀⠀⠀⠈⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⢸⠃⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⡇⠀⢸⡀⡇⠀⢸⠹⣇⠀⠀⢰⠇⠀⠀⠀⠀⢧⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡟⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣰⡇⠀⢸⠀⣧⡃⣸⠄⠈⠀⠀⣽⠀⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢀⡞⠲⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢣⡇⠀⢸⣶⣿⡃⣿⠀⠀⠀⠀⠘⢧⣀⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠃⣸⠁⡘⢸⡿⢹⣰⠏⠀⠀⠀⠀⠀⠀⠈⠙⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠇⣠⢧⡟⠁⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣯⢾⡿⠋⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠿⠋⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⣀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡗⠋⠁⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢻⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⡇⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⡞⠀⢸⠀⢀⡟⡆⠀⠀⠀⢀⠀⠀⢃⠀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⠃⠀⢀⡇⠘⡇⠀⠀⠀⠀⠀⢰⡟⠀⢰⠃⠀⢸⠀⡸⠀⣇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⢸⡄⠀⣸⠀⠀⡇⠀⠀⠀⠀⢠⠛⠃⢀⡟⠀⠀⢸⢠⠃⠀⢸⠀⠀⠀⡇⠀⠀⠘⡆⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⣼⢳⠀⡆⢀⣀⡇⠠⣏⣀⠀⢱⠀⠀⠀⣰⠏⢰⠀⡜⠀⠀⠀⣸⡎⣠⠔⢻⢀⣠⣼⡷⠶⢤⣤⣁⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠇⢀⣷⣿⣿⣿⣿⣾⣄⠙⠣⡘⡆⠀⢰⠏⠀⣼⡜⠀⠀⠀⢀⡿⠛⢁⣠⣾⣿⠿⠛⠓⠒⠿⢧⣝⢳⣦⠀⢸⠀ ⠀⠀⠀⠀⢸⣴⣿⣿⠟⠁⠀⣈⣽⣿⣷⡄⠀⢹⣤⠃⠀⠀⠟⠀⠀⠀⠀⠘⠃⣠⡿⢛⣡⣶⣾⣿⣷⣦⣄⠀⠉⢳⣝⣿⣩⠀ ⠀⠀⠀⠀⣼⣿⣿⠃⠀⢠⣾⣿⣿⣿⣿⣿⣆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⢰⣿⣿⣿⣷⣿⣾⡟⢿⣷⠀⠀⢻⡜⣿⠀ ⠀⠀⠀⠀⣿⣿⡏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⣿⣿⣟⣷⡀⢸⡆⠀⢸⡇⣹⡷ ⠀⠀⠀⢻⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⣯⣿⠟⡛⠓⣾⠁⠀⣼⣷⠟⠁ ⠀⠀⠀⠀⣇⠙⠿⣦⡈⢿⡛⢷⠁⢠⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣟⣀⡀⠰⠂⠀⡠⠋⠀⠈⢁⡞⠀⠀ ⠀⠀⠀⠀⠸⡄⠀⠀⠁⠈⠛⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⣀⠀⠀⠀⠈⠉⠛⠒⠒⠋⠀⠀⠀⢀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠒⠶⠾⠍⠛⠛⣛⠻⣾⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⣀⣠⣌⣙⣛⡏⢧⠀⠀⠀⠀⠀⢶⣖⣚⣉⣀⣠⠄⠀⠀⠀ ⠀⠀⢠⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡴⠒⠉⠉⠀⠀⠀⠀⠀⠉⠻⡄⠀⠀⠙⠁⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⣄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠙⠲⢦⣬⠵⠟⠦⣄⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠤⣴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⢳⣦⠀⠀⠉⠓⠲⠭⢅⣀⡀⠀⠀⠀⠀⠙⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣿⡳⠒⠒⣀⣀⡤⠤⠀⠀⠀ ⠀⠀⠀⠀⢀⠏⢻⡀⠀⣠⠷⣦⡀⠀⠀⡿⣍⠙⠓⠒⠶⠦⠤⣤⡤⠤⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⠁⡴⢋⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⢠⠞⣧⡴⠁⠀⠀⠙⠒⣤⡷⠌⣳⣄⢀⡴⠳⣄⣴⡷⠤⢤⣤⣤⣤⠤⠤⠤⣤⣴⣿⣾⣤⠚⡄⠀⠀⡆⠀⠀⠀ ⠀⠀⠀⠀⠠⠃⠀⠈⠀⠀⠀⠀⡰⠋⣩⡾⠛⠉⠙⠉⠀⢠⠟⠽⠳⠤⣤⣀⣀⡤⠔⠒⠉⠉⠀⠀⠁⠉⠢⡙⠆⠀⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⣼⠟⠀⠀⠀⠀⠀⢀⣈⣧⣀⣤⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠲⠄⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⡏⠀⢀⣠⣤⡶⠾⠛⠉⢹⠋⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠸⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⢻⡄⠀⠀ ⢀⠀⠀⠀⠀⡞⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⢧⠀⠀ ⠀⠀⠀⠀⢰⢁⠀⣇⠀⠀⠀⠀⠀⠈⠀⠐⣄⡀⠀⠀⠤⢤⠊⢮⠢⡄⠀⠘⡇⠀ ⡀⠀⠀⠀⡎⡜⣄⣌⣆⠤⡂⡄⠀⠀⠆⢄⠙⡛⠲⡔⢳⢊⠁⢛⣾⠁⠀⠀⠁⠀ ⠁⠀⠀⠀⣧⣁⣈⡳⡀⠑⠜⠾⢔⡤⣘⡀⠉⠻⢍⡉⠉⠀⠺⡑⢼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠿⣽⣿⡀⠀⠒⠒⠂⠀⠉⠢⢴⣵⣶⣻⣷⣦⣬⢺⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⢃⠀⡿⡯⣻⠀⠀⠀⠀⠀⠀⠰⣿⣽⣻⣽⡍⠛⣿⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡆⠐⠪⠽⠉⠀⠀⠀⠀⠀⠀⠀⠀⣻⡥⠚⣀⡀⠁⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠉⢀⢜⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠰⡲⣟⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠏⠀⠀⠀⠀⠀⠀ ⢠⡀⡀⠱⣄⠹⢇⡑⠠⡀⠘⠏⠙⠽⠀⠀⠀⠀⠀⠀⡀⡴⠋⠀⠀⢀⠄⣀⠀⡆ ⠀⢳⣿⡦⣄⣁⣦⠤⡝⣫⣑⠤⣀⣀⡀⠠⠤⠐⠈⢡⡮⠀⠀⢀⣴⡫⠔⠉⠢⣱ ⠀⠀⠈⠉⠉⣁⠤⡰⠒⡩⡽⠋⢩⣿⠄⠠⠄⠄⢊⠩⠒⠒⢻⣍⣴⣤⡀⢀⣀⠀ ⠀⠀⠀⢠⠎⠀⢠⠁⡴⡱⠀⠀⠈⠅⠀⢀⠠⠂⠁⠀⠀⠀⡘⠘⠀⢀⠀⠁⠀⠑

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢘⡆⠀⠀⠀⣀⣤⣤⣤⣂⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣆⠀⢀⢔⣾⣯⣶⣿⣿⣿⣿⣿⠛⠉⢉⠞⢀⣾⠀⠀⠀ ⠀⠀⠀⠉⠉⢹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⡟⠀⠀⠀ ⢀⣄⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⡀⠀ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄ ⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⠕⠀⠀ ⠘⠁⢸⣿⣿⣿⣿⣿⣿⡟⠏⠀⢰⣿⣿⣿⣿⣿⠈⢿⣿⣿⣷⡈⠂⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⡏⣀⣈⣥⣄⢻⣿⣿⣿⣿⣐⠈⣿⣿⣿⡧⠔⠀⠀ ⠀⠀⠈⠙⢿⡿⢿⣿⢧⠀⠁⢀⠠⠀⠟⠁⠈⠉⠛⠋⢿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⠐⡶⠝⢀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠢⣸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⠤⠍⠡⢄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⠀⠀⡖⠒⠋⠁⠀⠀⠀⠰⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠎⠐⠠⢇⡀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠈⠑⠂⠽⠮⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡀⡠⠔⠒⠐⠉⠙⣆⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠐⠿⠃⠀ ⠀⣄⠀⠀⢸⠀⢀⡀⠀⠸⠀⠘⡃⠠⣳⣖⠀⢀⣦⣀ ⠈⠻⠉⠀⣿⣤⢘⠉⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠙⠀ ⢼⡦⠀⢊⢿⡋⠀⠀⠀⡴⢴⠒⠄⠀⠘⢄⢠⠛⡄⠀ ⠀⠁⠀⠀⠀⠉⢱⠂⠀⠀⠺⠂⠀⠀⠀⠀⢻⣰⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡾⠻⣤⢤⡤⢷⡦⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢩⡇⣠⠛⣆⠉⠲⣝⢦⠀⠈⠙⢳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⠥⠤⣀⣀⢸⡗⠁⢀⡾⣆⠀⠈⢮⣧⠀⠀⢸⡇⢹⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⣀⣀⣀⣀⣈⣙⣧⠴⠋⠀⢸⣆⡀⠈⢻⡀⠀⡼⠁⣼⣴⠋⠹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠚⠉⠉⠁⠀⠀⠀⠈⣷⡀⣀⡴⠃⠹⠍⠓⠚⠧⢴⣃⣴⡿⠁⠀⠀⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢀⣤⣔⠚⠉⠉⠉⣩⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⡀⢸⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣤⠞⠛⠤⣌⡙⢦⡀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⣼⠁⢸⡇⠙⢧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠙⢦⣿⡁⠀⠀⠀⠀⠀⠀⠀⣴⣸⣳⣷⣧⣾⡵⠂⠼⠁⠀⢸⣧⠀⢸⡹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⣀⣤⣤⣤⡀⢸⠟⣷⡄⠀⠀⠀⠀⢠⣼⢿⣿⠏⠙⢿⡇⠀⠀⠀⠀⠀⣿⡁⢣⣨⡇⠸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢟⣁⢠⡟⠛⢺⠀⣿⣿⠀⠀⠀⣰⡿⣿⢸⣿⣇⠀⣼⠃⠀⠀⠀⢀⣼⠁⢣⠈⣿⠀⠀⢧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢠⡿⠋⠉⣹⣿⠀⠀⢸⡄⠘⡿⠀⠀⢠⡿⠀⢻⡈⢿⣿⣿⡟⠀⠀⠀⢀⡾⢹⠀⢸⣠⠏⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠉⠉⠉⠉⠛⠶⣤⣀⠈⢷⣀⡉⣉⣡⡤⢶⣯⠿⠋⠁⠀⠀⢸⠁⠀⠀⢳⣄⣨⡿⠁⠀⠀⠀⢸⠀⢸⢀⡼⠃⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡈⠉⠉⠀⠀⢸⡄⠀⠐⠀⠀⠀⠘⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⠆⢸⣀⡼⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⢀⡇⠀⠀⠀⢀⣠⠴⠖⠒⠉⠉⠒⠲⠤⣀⠀⠙⣦⠀⠀⠀⠀⠙⠦⣄⣠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢏⡴⠟⠁⠀⠀⣀⣀⣀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⡇⢸⡇⠀⢀⠔⢉⡤⠞⠉⠉⠉⠉⠉⠑⠶⣌⡙⢆⠈⢷⡀⠀⠀⠀⠀⠈⠉⠓⠶⠶⢤⣄⣀⣀⣠⠴⣶⡿⠟⠉⠀⠀⣠⡶⠋⠁⠀⢸⢷⡀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢀⡇⠘⣇⡴⠁⣴⠋⠀⠀⠀⣀⣠⡤⠤⣤⣀⡀⠙⢮⡳⡀⢳⣤⠶⠖⠒⠶⠶⢤⣄⣀⠀⠀⣀⡼⠀⣼⠋⠀⠀⠀⣴⠞⠁⢻⣿⡆⡰⠋⠈⡇⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠘⡇⠀⢿⠀⡼⠁⠀⠀⡴⠚⠁⠀⠀⠀⠀⠀⠉⠳⢆⠹⣽⠋⢻⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢻⣦⣀⠀⠀⠛⢯⣉⣁⡴⠟⠁⠀⢀⣽⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡀⠘⣷⡇⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣍⠉⠉⠉⠉⠁⠀⠀⠀⣠⠋⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡄⠈⢧⠀⠈⢷⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢷⡇⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⣀⡴⠊⠁⣠⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠳⡀⠈⢇⠀⠀⠙⢦⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⢄⢿⣠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣖⣊⣁⣀⠤⢞⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠳⡄⠈⠳⣄⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣇⡞⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣀⣠⠴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠙⢦⡀⠈⠳⣄⠀⠀⠈⠛⠦⣄⡀⠀⠀⠀⣴⠞⠾⠧⠚⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢠⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠑⢄⠀⠈⠳⢄⡀⠀⣀⡼⠛⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠛⠒⠲⠦⠤⢾⡇⠀⠀⠀⢸⢿⠁⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡗⠦⣄⠀⠀⠀⠀⠀⠈⢷⡤⣤⡀⠙⢦⡀⠀⢙⡿⠋⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⢹⡄⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⣾⡄⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡇⠀⠈⠳⣤⡤⠴⢖⠛⣏⠀⠈⢳⠀⠀⠙⣳⠏⠀⠀⣠⠞⠋⠀⠀⠀⠀⢀⡴⠋⢹⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣋⠉⠉⠓⣤⡽⣿⠀⢸⠀⠸⡀⠀⠘⣇⠀⢰⠏⠀⣤⠞⠁⠀⠀⠀⠀⠀⢀⡾⠁⠀⢸⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢸⡆⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀ ⣠⠾⢥⣀⠈⠁⢀⡜⠉⠀⢸⠀⢸⠀⠀⡇⠀⠀⣿⢠⠏⢠⡞⠁⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠘⣇⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⡇⠀⠀⠀⠀⠀⢯⣇⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀ ⣿⠀⠀⣟⢳⣠⠏⠀⠀⢠⡟⠀⡞⠀⠀⡇⠀⢸⡛⠟⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠈⢷⡄⠀⡇⠀⠀⠀⠀⠀⠸⣽⡄⠀⠀⠀⠀⠈⢳⡀⠀⠀ ⢸⡄⠀⠈⠛⠻⢦⣀⣀⡼⠁⣸⠃⠀⠀⡇⠀⡾⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠙⢦⣧⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⢀⣳⠄⠀ ⠀⠹⢦⣀⠀⠀⠀⣠⣾⡁⢠⠃⠀⠀⢰⠁⡼⠃⠀⠀⠀⣿⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣄⣀⣀⣀⣀⣼⢿⣀⣀⣀⣀⣀⣀⣀⣻⣉⣒⢒⣚⣉⣉⣁⡀⠀ ⠀⠀⠀⠉⠙⠒⠚⠉⠉⠉⠙⠒⠦⣤⣇⡼⠁⠀⠀⠀⠀⢸⠦⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⢲⣯⣟⣹⣛⣟⣛⣿⣻⣽⣘⣏⣋⣉⣉⣉⣝⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠤⣦⢴⠟⠋⠁⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⢴⣾⡙⣻⡷⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠘⢿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠆⠀⠀⢰⣿⣦⠤⠔⠀⢹⣧⣀⣀⠀⠀⠀⠈⠀⡀⠀⠀⠀ ⠀⠀⣸⣆⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣀⡀⠀⠀⠀⠀⠾⠂⠀⠀⠀⢻⡏⠀⠀⢾⡛⠻⣯⣉⠁⠀⠀⠀⢀⡿⣤⣀⡀ ⠠⣴⣟⣻⡷⢶⠀⠀⠀⣾⠀⠀⠀⢰⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠀⠈⠛⠛⠛⣿⠛⠂⠀⠐⠻⣷⣼⠟⠉ ⠀⠀⠹⡿⠀⠀⠀⠀⠀⣿⣠⣀⣒⠀⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠔⠀⠀⠀⠀⠈⠋⠀⠀ ⠀⣠⠀⠀⠀⠀⠀⢀⣤⣿⠟⣿⡉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡿⢶⣤⡀⠀⠘⠟⢁⣿⡞⠛⠉⠀⠀⠀⠀⠀⠀⠀⣰⣤⣤⡶⠤⣤⣄⠀⠀⠀⠀⠺⣧⡀⠀⠀⣴⠟⢿⡆⠀⠀⠀ ⠛⢷⣾⠋⠀⠀⠀⠀⣾⠛⢷⣤⣀⡀⠀⠀⠀⠀⠀⣼⠋⡁⢻⡀⢀⠀⠉⠀⠀⠀⠀⠀⠈⢻⣤⠀⣿⠐⢸⡇⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣷⠄⠀⠀⠀⠁⠀⢀⣸⡷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡏⠀⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣼⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣠⡤⠒⠒⠒⠒⠒⢢⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠚⣻⠟⢋⡡⠤⠐⠂⠉⠁⣠⠔⠛⠛⠲⣄⣠⠞⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⢕⠊⠁⠀⠀⠀⠀⡤⠊⠀⠀⠀⠀⢀⡼⠁⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⡯⣾⠋⠀⠀⠀⠀⣠⠊⠀⠀⣀⠴⠒⠉⠉⠀⠀⠀⡷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠋⢠⠇⠀⠀⠀⠀⣴⡷⡞⡠⠞⠁⠀⠀⠀⠀⠀⠀⢠⠃⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠀⠀⣀⣤⡞⢉⣰⠟⠁⠀⢀⣀⡠⣤⣶⣧⡠⠋⠀⣼⠁⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡼⠓⠚⢻⣟⢻⠁⢾⡿⣶⣶⡏⠉⢹⣇⡸⠉⠉⠀⠀⡞⢿⠀⠀⠀⠀⣠⠞⠉⠀⢠⠇⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢼⠋⠓⠢⢾⣿⡟⠀⠘⣇⢿⣿⢻⣦⣾⡿⠃⠀⠀⠀⢰⠃⣼⡄⠀⢀⡞⠁⠀⢀⡴⢋⡤⠖⠋⠁⢀⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⡀⢰⠋⠉⠀⠀⠀⠙⠾⢿⣿⠿⠛⠁⠀⠀⠀⢠⠏⢀⣿⡇⢀⡎⣀⡀⢠⣾⠟⠉⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠿⣧⣀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⣼⣿⡇⣾⠞⠁⣿⠋⠀⠀⠀⣀⠴⠋⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣈⡛⣷⣤⣄⣀⡀⠀⣀⣀⡠⠝⠛⠒⡾⠋⣼⣿⣿⣧⡏⠀⣰⢃⣀⣀⣤⠾⠷⠾⠭⣭⣥⣄⡀⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀ ⠀⢰⡏⠁⠀⠀⠉⠉⠁⠀⢸⠏⠁⠀⠀⠀⢀⡞⢀⣾⣿⣿⠿⡟⠀⣰⠟⠉⢈⡇⠀⠀⠀⠀⠀⣠⣟⠙⠻⣦⡄⣀⣀⠙⣆⠀⠀⠀⠀ ⠀⠀⠙⠶⢤⣀⣀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣸⣷⣿⣿⣿⠏⢰⠃⠀⠀⠀⣠⣎⡤⠴⠒⠒⠛⠻⢄⠀⠑⡄⠘⣿⡌⢯⠛⢾⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢉⠽⢻⡇⠀⠀⠀⠀⠀⣿⣿⠿⣿⡏⠀⡼⠀⠀⠴⣞⠉⠉⠙⣏⡉⠑⠢⡀⠀⢣⠀⠸⡀⠸⣿⡈⣆⠈⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⣸⡇⠀⠀⠀⠀⠀⣿⡏⠀⣿⠀⢰⠃⠀⢀⣠⣟⣠⣴⠚⠀⠙⢦⠀⠘⢆⠀⢇⠀⣇⠀⣿⡇⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠸⠀⠀⢹⡆⢸⠈⠉⠉⠉⣧⡀⠈⣇⠀⠀⠈⣧⠀⠘⡆⢸⠀⢻⠀⢸⣧⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠻⣾⠀⠀⠀⡄⠹⡇⠀⣿⠀⠀⠀⢸⡀⡀⢣⢸⠀⠘⠀⢸⡟⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣤⡀⢀⠀⠀⢢⠀⠀⠈⠃⠀⣰⠃⠀⠃⢀⡇⠀⠀⠀⠀⡇⡽⢸⠀⠀⡇⠀⢸⡇⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢹⣿⠀⠀⠀⢧⣀⣠⠤⢾⣇⠀⠀⠀⢼⠤⣀⠀⠀⢠⣇⡇⢸⣄⠀⡇⠀⣿⣧⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢸⢸⠀⠀⠀⠸⣦⡀⠀⠈⠈⢢⣄⡀⠀⠀⠘⡆⠀⢸⣿⠃⢸⣿⠀⡃⢠⣿⣿⣸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⡞⢸⠀⠀⠀⠀⢷⠏⠁⠀⠀⢀⣿⠉⠀⠀⠀⢧⠀⠋⢸⠀⢸⢹⠀⡇⢸⣿⡏⢿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢠⠇⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⠀⠀⢸⡆⢸⣿⡄⡇⢸⣿⣇⠈⠻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⡜⠀⡾⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⡿⠀⠀⠀⠀⠈⡇⠀⠘⣷⢸⠘⣷⡇⢸⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⣰⠃⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢧⠀⠀⠹⣿⡀⠈⠻⣄⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⣰⠇⠀⣸⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠃⠀⠀⠈⠛⠯⠝⠛⠿⠷⠖⠂ ⠀⠀⠀⠀⠀⠳⠦⠤⠤⠴⠚⠁⠀⣰⠏⠀⠀⠀⠀⠀⢰⠗⠒⠒⠚⠹⣇⣀⠀⠀⣀⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣄⣀⣀⣤⡤⠞⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠔⣉⡀⠂⠀⠌⢁⢲⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢁⠂⠀⠤⠤⠔⠁⡀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢸⡌⢀⣷⠆⠀⣌⣟⢢⣀⣶⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠸⡅⠺⣿⣶⠀⠉⢿⡿⡏⢱⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⢣⠀⠻⠁⢀⡰⠀⠀⢁⠆⢬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⡄⢠⠉⢠⡪⢂⠂⣿⡛⢳⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⠙⠀⠸⢆⣰⠕⢠⠂⡘⠀⣱⠞⠀⡁⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠓⢚⠀⠐⢸⡍⢀⠃⢸⡙⠏⠁⠀⢴⢍⡙⠃⠐⠒⠂⠀⠈⠢⠉⠰⡠⡀ ⠀⠀⠀⠀⠀⠑⠤⠼⣧⡘⢄⠈⠂⠤⢄⠒⠈⠀⠀⠀⠀⠀⢈⡆⠀⣠⠀⠀⠃⢡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠷⠶⠤⠄⡲⠶⡤⢉⡉⠑⠂⠅⣊⠩⠍⢀⠤⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠛⠁⠀⠀⠈⠉⠁⠉⠉⠉⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⡚⠛⠉⠉⠉⠛⠓⠦⣄⡀⠀⢀⣠⢞⡥⠴⠾⠷⠶⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⣤⠽⠛⢉⣀⡤⠤⠶⠶⠶⠶⠤⢤⣀⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣠⠞⠉⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠟⠦⣄⡀⠀⠀⠀⣸⢇⡞⢁⢴⣫⠤⠶⠒⠒⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⠀⠀⠀⡿⠀⠀⠈⠉⠛⠛⢛⣵⣾⣴⡗⣩⠴⠒⠛⠒⠦⣄⡀⠀⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⠳⡄⠀⠀⠀⠀⠀⢻⠢⡀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⠻⡅⠀⠀⢀⠀⠀⠀⠙⠲⣄⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠙⢦⡀⠀⠀⠀⣸⠀⢱ ⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣿⠀⠀⡴⢦⡀⢻⣦⠀⠈⢧⠀⠀⠀⠀⠈⢧⡀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠙⠲⢶⡶⠁⠀⢈ ⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⡇⠀⣼⠁⠀⠙⡄⢿⣇⠀⠈⣧⠀⠀⠀⠀⠀⢳⡄⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⣸ ⠀⠀⢰⡏⠙⣧⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⢹⠘⣿⡄⠀⡟⢧⡀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃ ⠀⠀⠸⡇⠀⠘⢧⡀⠀⠀⣷⠀⢷⣀⣀⣠⠃⠀⠀⣙⣾⠧⣤⣝⡲⣤⣀⠀⠘⣷⣤⡀⠀⠀⠀⠈⠓⢤⣀⡀⠀⠀⠀⠀⢀⣠⣴⠞⠁⠀ ⠀⠀⠀⢻⡄⠀⠈⠳⣄⠀⣻⡄⠀⠀⣌⡙⢷⣤⣾⣯⣤⡀⠀⠈⢳⡄⠉⠙⠓⠛⠦⣽⣷⣤⣄⣀⠀⠀⠀⠉⠉⠛⣛⣩⠽⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠹⣆⠀⠀⢈⡿⠋⣧⠀⠠⣬⣛⣿⡿⢃⣤⠶⠿⣦⡀⠀⢻⡄⠀⠀⠀⣼⢏⣨⣽⣦⠉⠉⠙⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣦⡟⠀⢠⣏⠃⠀⠈⢙⡟⢠⣿⣧⣀⣀⡿⢧⠀⠈⣷⠀⠀⣼⣳⢻⡅⢀⣿⡇⠀⠀⢸⣿⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢸⠙⢦⠀⠀⢸⡇⢸⣇⣽⣿⡿⠀⢸⠀⠀⢸⡆⢀⡏⣿⣠⣿⡏⠈⡿⠀⠀⠀⣇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠈⢧⡈⠳⣄⠈⠓⢬⡿⢻⡿⠃⠀⡾⠀⢀⣠⣧⡼⢧⣿⣙⡟⠀⣰⠃⠀⢀⣠⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠑⢄⠈⠳⣄⠀⠈⠙⠛⠛⠛⠓⠚⢩⡅⠀⠶⠀⠈⠉⠛⠛⠓⠒⠋⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⢳⡀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠴⠂⠀⠀⠀⠀⣰⡛⣆⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⣧⠀⢸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁⣡⠼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡦⣄⡀⢀⣀⣤⣏⡀⣸⠉⠉⠙⣿⠓⠒⠶⠶⠶⠶⠶⠶⣖⠒⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡽⣋⡽⣾⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢋⡞⠁⠀⠀⠙⣦⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣣⠞⠀⠀⠀⢠⠀⢸⡏⠀⠀⠀⠀⠀⢠⡆⠀⠀⢻⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⠴⢶⣾⣯⡉⠁⠀⠀⠀⣠⠏⢀⡾⠓⠶⢤⣀⠀⠀⠀⡇⠀⠀⢈⣧⣸⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⢋⡥⠞⠋⠉⠉⠉⢙⣓⣲⠖⠋⣿⠶⠋⠀⠀⠀⠀⠈⢷⠀⠀⣷⠀⠀⠀⢻⡏⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⢏⡴⠉⠀⠀⢀⣴⡖⣻⠟⠛⠻⣆⣠⡬⠤⠥⣤⡀⠀⠀⢀⡾⠀⣀⣿⠀⠀⠀⠈⢷⡀⠀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⣾⠀⠀⠀⠀⠘⠦⣝⡛⠶⢤⣤⣟⣁⠤⠶⠶⢶⣿⢀⣤⠟⠛⣽⠋⢻⡇⣄⠀⣾⠻⣷⢤⣿⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⢿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⢿⠈⣿⠀⠀⠀⠀⠈⠻⡅⠀⣀⡸⠆⠈⣿⠉⢳⡇⠀⠘⣦⣀⣤⡼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⣾⣠⠿⢤⣤⠴⢊⣩⡙⣿⣄⣻⣄⣀⣀⡿⢤⣤⣄⣠⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠦⣭⣓⡒⢶⣶⣶⡶⠟⠉⠉⠲⣤⣤⠖⠋⠉⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠤⡒⠒⠒⠒⠤⢀⢀⡠⠪⠄⠃⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢢⠀⢀⠔⡊⠅⠒⠀⠉⠉⠁⠐⠠⣈⠢⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠓⠠⢀⣀⢼⣔⡕⢌⣒⣀⠐⠢⢄⠀⠀⠀⠀⠀⠑⡈⠢⡀⠀⠀⠀⢄⠀ ⠀⠀⡎⠀⠀⠀⠰⠉⠉⢳⠁⢀⠀⠁⠢⡀⠁⢂⠀⠀⠀⠀⠈⢂⠘⢆⠀⠀⠸⠡ ⠀⠀⢡⠀⠀⠀⡇⠠⠑⢌⢷⠀⢡⠀⠀⠈⢆⠀⠑⢄⠀⠀⠀⠀⠑⠠⠭⠞⠁⢠ ⠀⢰⠉⢆⠀⠀⡇⡇⠀⢈⠘⢇⢸⠣⡀⠀⠈⣆⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⢀⠄ ⠀⠈⡄⠈⠢⡀⣇⠈⢀⠢⣄⣔⣉⠉⢪⡑⠂⠼⢕⣤⣀⡀⠉⠒⠒⢒⡲⠞⠁⠀ ⠀⠀⠈⠢⣀⠝⢹⠄⠲⢽⢛⣔⠊⣷⠀⢱⠀⢀⣾⠔⢳⡀⠉⣿⣻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡎⠀⠈⢆⠀⢸⢸⣭⣿⠁⡇⠀⡆⡈⣇⣷⠉⡇⠀⢨⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠈⠢⡑⢄⠙⠹⠧⠤⠥⢐⠓⠅⠓⠣⠼⠤⠐⠉⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣇⠀⠀⠀⠐⡄⢣⠀⠀⠀⠀⠈⠐⠒⠀⠀⢀⠬⢂⡴⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢦⢄⣀⣠⣇⡸⠐⢲⠂⠠⠤⠤⠤⡄⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢱⠗⠝⠛⠣⡀⡸⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠼⠊⠀⢀⠀⣏⠀⠀⠀⢰⠀⠰⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⡲⠝⠛⠛⢂⣤⠔⡯⠜⠀⠉⠑⡄⢸⠀⠀⢷⠁⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣜⠊⠀⠀⡲⠽⣉⢙⠔⣒⣒⣢⠀⡴⢥⠼⡄⠀⡨⣄⢸⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⢟⡀⠀⠀⠀⠁⠒⢻⢹⠀⠀⣉⣪⠀⡼⠂⢟⠱⠇⠘⡤⠤⠃⠀⠀⠀⠀⠀⠀⠀ ⠈⠪⢂⡤⢤⣤⠤⠚⠫⣑⠩⠒⡾⠓⠓⠒⠉⠁⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⢛⢍⢃⠉⠒⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠤⣄⣤⡀⠀⢀⡴⢅⢐⣀⡤⡱⠛⢂⠀⢩⡗⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⢄⠙⠌⢢⡎⠁⠀⠀⠀⡜⠠⢀⣀⠀⠈⠁⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠣⣌⠉⠓⢴⡅⢣⢰⠻⠇⠉⢰⠀⠀⠀⠀⣠⠇⠀⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡭⠒⠼⣍⠢⢻⡀⢳⡆⠈⠺⢯⠿⠛⡌⢀⠎⢸⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣳⢖⣻⡶⡵⠼⡤⣲⣀⡠⠄⢢⠁⡌⡐⠹⠀⠀⠀ ⠀⠀⣀⠤⠒⠒⠒⠢⢼⠁⣥⣼⠉⢱⠀⣸⢃⡴⠁⠀⠀⢸⠀⠠⠀⢳⣭⢱⡄ ⢠⠞⠁⠀⡠⢒⠎⢛⡾⠇⠪⠋⢒⣎⠀⣿⠀⠀⠀⠈⠑⢮⢆⡡⡁⠭⣅⣾⠇ ⣯⠀⠀⡘⡰⢹⠀⠀⠉⠁⠢⠀⠀⢒⣩⠳⡢⠤⠴⠞⠐⠒⠋⠉⠑⠒⠋⠁⠀ ⣯⡀⠀⢃⠐⢌⠢⣀⠀⠀⠀⠈⢢⠀⣀⠠⢁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣕⢄⠀⠑⠢⠁⣐⣫⠶⢒⠲⠒⠉⣉⠭⠐⠊⠹⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⢬⣩⢭⠤⠮⠑⢊⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

(\ (\ („• ֊ •„) ━O━O━━━━━━━━━ ・:。𝐢𝐧𝐯𝐢𝐭𝐚𝐭𝐢𝐨𝐧「 ✉️ 」・:三 ━━━━━━━━━━━━━ https://discord.gg/mylittlepony𝜗𝜚౨ৎ𝜗𝜚౨ৎ౨ৎ🎀

⢀⡀⠀⠀⣰⣿⣿⠙⠁⠀⢸⠀⠀⠀⠀⠀⠈⠁⠀⢸⠇⠀⠀⠀⠈⠈⠻⢯⢷⡴⣤⣀⠀⣠⠙⠋⠙⢦⠀⠀⠀⢹⡷⠀⠀⠀⠉⠙⠿⣇ ⡿⠃⢠⣴⢿⣿⡏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⠉⠁⠀⠀⠀⠈⠳⡄⡄⠀⢷⡀⠀⠀⠀⠀⠀⠈ ⠈⣿⣿⣷⣾⢿⠃⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠈⢷⡀⠀⠀⠀⠀⠀ ⠀⠻⠿⠿⡿⢸⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠐⠤⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣀⣀⠤⠤⠀⠀⠀⠳⡄⠀⠙⠒⠶⣿⡿⢂ ⠀⠀⠀⢰⠁⡞⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠔⢊⣩⣤⡴⠒⠒⠒⠒⠂⠤⣽⣦⣀⣠⠖⣁⠴⣫ ⠀⠀⠀⢸⣾⡇⠀⠆⠀⠀⡇⣷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⢋⣿⡾⠛⠉⠀⠐⠂⠈⠛⠛⠉⣿⣾⣟⣡⣴⣾⣿⣟⡁ ⠀⠀⠀⡾⣿⡇⠀⠀⠀⢰⣧⣿⠄⠀⠀⠀⠀⠀⢸⠀⠀⢀⡤⠖⣋⣥⢴⡾⠍⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠾⠿⠛⣿⢻⣿⣿ ⠀⠀⠀⠉⣿⣿⢧⣀⠀⣼⣩⠟⠀⠀⠀⠀⠀⠀⣸⠤⢚⣥⣶⣿⣯⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣀⣠⣴⣏⣸⣿⠇ ⠀⠀⠀⠀⢸⣿⠶⣤⣙⡟⠣⢤⣀⣀⠀⠀⠀⠀⣿⡴⣿⣷⣾⣿⠏⢀⣶⡄⠀⠀⠀⢀⣶⢲⡄⠀⠀⠀⠀⠀⣼⠷⠶⠛⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⠟⠒⠝⠟⠳⢶⣦⣤⣬⣭⣭⣭⣽⣿⣿⣿⣿⡇⠀⡟⠉⣻⠀⠀⠀⡸⠳⢴⠇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠘⡟⣿⣠⡇⠀⠛⠒⠒⠰⠃⠀⢸⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡞⠉⣀⣤⡀⠀⠀⢀⣠⡄⠈⠉⠒⢄⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢠⣄⠀⠀⠀⠀⣰⢤⠀⠀⠀⢰⠇⡇⠀⠉⠙⠀⠠⠀⠈⠛⠛⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣯⣼⡇⠀⠀⠀⡿⠤⡇⠀⠀⣾⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡏⠓⠶⠆⠀⣇⣀⠀⣀⡇⠀⠱⠔⠋⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣠⡄⠀⠉⠀⣠⣤⡀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⠛⠁⠠⠤⠄⠉⠋⠁⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣇⠤⠂⠠⣱⣆⣁⡙⣑⡀⣠⡤⣤⣤⣤⣄⣄⡐⠇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⠿⣏⣏⣀⡼⣤⣿⡿⣿⠌⠁⢀⡂⢁⣀⡰⢡⠉⠩⡒⢄⡀⠀⠀⠀ ⠿⢿⡿⣅⠀⢸⢣⠁⡙⠩⣰⣿⣾⢷⡤⠛⠛⠒⡞⠉⠉⠒⠛⢳⠹⢶⣻⣆⣀⠀ ⡿⠅⣰⠋⢹⣿⡀⢳⠃⢱⢻⠛⠚⡯⡇⠀⠲⢶⣶⠀⠀⣀⣀⢰⣧⠄⢹⠋⢽⠁ ⠣⢬⣣⢄⣾⣇⣧⡜⠀⡏⠁⠀⢠⣿⣀⣆⡀⣿⣿⠀⢀⠀⠀⢸⡇⠃⢹⠉⢻⠀ ⠀⠃⠀⢹⣿⣿⣸⣇⠀⡇⠀⠀⢸⣿⠀⣷⠈⡟⣿⠀⡌⠀⣸⣾⡇⣿⣾⠀⢸⣇ ⠂⡀⠀⣸⣿⣿⣿⡏⡇⡇⠀⢠⢨⠉⠁⠙⠚⠃⠻⠦⠿⠠⠿⠯⠷⢿⡏⠀⣾⣿ ⠀⠂⢊⣿⣿⣿⡿⡇⣿⣧⠀⢸⣾⠗⠓⠒⠯⠀⠀⠀⠀⠀⠤⠴⣶⡼⡀⠀⣿⣿ ⠀⠀⣸⣼⣿⡏⡇⣿⣿⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠥⠐⠛⠛ ⠀⢠⡇⣿⣿⣇⡇⣿⣿⣿⡆⣧⣟⢧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠁⠀⠀⠀⠀ ⠀⣞⢱⣿⣿⣿⡇⡇⢿⣿⣿⣧⣿⢄⠁⠀⠀⠀⠀⠀⠀⠉⢀⣵⠀⠀⠀⠀⠀⠀ ⡼⢁⣾⣿⣿⣿⡇⡇⠘⣿⣿⣿⣿⣦⣈⡂⠄⣀⢀⣠⣴⣾⣿⡏⠀⠀⢀⣀⢠⡤ ⠃⢸⣿⣿⡟⠩⠁⠉⠉⠈⣻⣿⣿⣿⣿⣿⣿⢷⠞⣉⣉⣙⣿⠁⠀⠀⣸⠀⠈⡝ ⢀⣿⣿⣿⠇⠃⠀⠀⠀⠀⠈⢦⠙⣿⠻⠦⣳⣿⡤⠙⡄⢳⡄⠀⠀⠀⣿⠀⠀⠃ ⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⢳⣹⠀⠀⢫⡤⣜⠀⢹⡜⠀⠀⠀⠀⡿⡆⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⣵⣶⣿⣿⠉⢍⢠⡈⠻⠶⣬⡙⢷⣮⠙⠿⣿⣷⣶⣄⠀⠀⢀⣠⢖⡡⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠒⠤⠄⣈⡑⠢⠤⢀⡴⠛⣵⣿⣿⠟⠉⢹⡶⠈⣌⢻⡄⠀⠘⣿⣷⣹⣷⣄⠹⣿⠛⢻⣷⣶⡯⠶⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⠟⢲⡞⠁⣼⣿⣿⠏⠀⢠⢸⣇⡀⣿⡎⢿⣆⠸⡌⠻⣿⣿⣿⣧⠈⢷⡀⡿⣝⣧⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⢀⡞⠀⣼⣿⡿⢃⠀⣠⠏⣼⣿⡇⢿⣧⢘⣿⣿⣧⠀⠙⠿⣿⣿⣷⡈⢷⡀⠘⣞⢧⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣷⡾⢡⢤⣯⣿⢣⢎⣾⡟⢠⣿⡿⣿⢸⡏⢿⣿⣿⣿⣷⡀⠘⣿⣿⣿⣷⡈⢷⡀⠘⣯⣳⣦⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣧⡟⣟⣾⣯⡟⣼⢻⢃⣿⡿⠁⠸⡌⣿⡀⠻⣟⣿⣿⣿⣄⠈⢿⣿⣿⣿⣌⢿⣄⠘⢷⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⢹⣿⣿⢿⢱⡇⢸⣿⡿⠁⠀⣀⣷⣿⣧⠀⠙⢦⡙⠻⣿⣷⣦⣻⣿⣿⣿⣎⣿⣦⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢧⣿⣿⡿⠈⢸⢇⣿⣿⣡⠔⠊⠁⠀⢳⣿⡆⠀⠀⠙⢦⡈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣧⡀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣼⣿⣿⣯⢇⣿⣸⣿⠁⠀⢀⠀⣀⠀⠀⠻⣿⡄⠀⠀⠀⢛⣽⢧⣤⣌⡿⣿⣿⣿⣿⣿⣿⣆⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⢿⣿⡇⣸⠃⢀⣾⣿⣿⣦⡀⠀⠀⠙⢿⡄⠀⠀⢼⣅⣼⣿⣿⡿⣯⣽⣿⢻⣿⣿⣿⣷⡀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⡇⣿⢙⣿⣏⣠⣿⣿⡇⠀⠀⠀⠈⠻⣆⠀⠸⡿⢿⣿⣿⠇⢹⠿⣿⡈⣿⣿⣿⣿⣿⣷⣾⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⠸⣿⣷⣿⣿⡇⢿⠿⢿⡟⡋⠀⠀⠀⠀⠀⠈⠣⡀⠑⢤⣤⣶⠀⠀⠀⣿⡇⣿⣿⣿⣿⢹⡟⠿⣿⣿⣷⣤⡀⠀ ⠀⠀⢠⣿⣿⠏⣿⣿⣿⢀⣿⡏⣿⠉⠛⠊⠳⣤⣶⠇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⣷⣷⡀⠀⠈⠉⠉⠙⠓ ⢀⣴⣿⣿⠃⠀⣿⣿⣿⢸⣿⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⡏⠿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠋⣸⡿⠁⠀⠀⣿⣿⣿⣿⣿⡄⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⣿⣿⣿⣿⣦⣤⠟⠋⠉⠒⢦⡀⠀⠀ ⡴⠏⠀⠀⠀⠀⣿⡿⠋⢹⣿⣇⠘⣇⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⣿⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠁⠀⠀⢸⣿⣿⡄⢹⡄⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠀⠀⠀⠀⠈⣿⠻⣿⣟⣿⣄⠀⠀⠀⠉⢲⡤⢄⡀⠀⠀⠀⡠⠞⡟⠀⣠⠀⠀⣾⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡄⠈⠻⣿⣿⠓⠤⠀⠀⠀⠙⠦⣈⠉⠒⠉⢀⡞⢀⠜⠁⠀⣸⠟⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⢂⠀⠀⠀⠘⠆⠀⠀⠉⠓⣄⠀⠀⠀⠀⠀⠀⠉⢲⣤⣞⡊⠁⠀⠀⠚⠁⢰⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣇⠀⠈⢆⢀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⢠⠋⠘⡄⠈⠢⡀⠀⠀⢀⠇⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⡟⣆⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⢠⠃⠰⠲⡜⡆⠀⠈⠢⣠⠎⠀⣿⡟⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡄⠀⠀ ⠀⠀⠀⣿⣿⠁⣿⣦⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠃⠀⠘⠂⠃⠸⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⣿⣿⠀⣿⣿⣷⡄⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢠⣿⠀⠀ ⠀⠀⠀⣿⣿⠀⢻⣿⣿⣿⣦⣄⠀⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⢀⡜⢁⠄⠀⠀⢸⣿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠿⠿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⡀⠀⢀⣠⣤⣶⣶⣶⣷⣶⣶⣿⣿⣷⣶⣶⣶⣶⣮⣝⡻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡤⠔⠒⢤⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡜⠉⠀⠀⠀⠀⢳⠀⢀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠀⠀⠀⠀⠀⠀⠈⡇⣼⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⣇⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⡇⢀⣀⣀⣀⣀⣀⠀⡿⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⡆⠀⠀⠀⠀⠀ ⡇⠘⠙⠻⠛⠛⠛⠃⢧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡽⡄⠀⠀⠀⠠ ⡇⠀⠀⠛⠛⠙⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠠⠁ ⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣠⠄⠻⣿⣿⣿⣿⣿⣿⠹⣷⠠⠤⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⠓⢤⠆⠀ ⢣⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢀⠴⠋⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇⠻⡇⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⠞⠀⠀ ⠈⡆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡼⣧⠀⠻⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⢱⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⢿⠀⠀⢙⣀⠀⠀⠀⢿⣿⣿⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠙⠒⠦⠤⣼⣿⣿⣿⣿⣿⣿⣿⢻⡏⠀⢀⣤⣖⣲⣭⡶⠀⠀⠀⠀⠀⠙⢿⣞⠀⠼⠶⣾⣭⣤⣀⠈⢿⣿⡞⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡿⣻⣿⣿⣿⣿⣿⢸⠀⣠⣾⡿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠈⠉⠛⣿⣦⣿⡇⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠃⢿⣿⣿⣿⣿⣿⠸⠴⢫⣱⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣧⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠀⢸⠙⣿⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡰⠊⠉⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣂⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠘⡇⣿⣿⠟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡆⠀⠘⢾⣿⣸⢻⣷⡄⠀⠀⠀⠀⣀⣀⠀⣿⠀⣀⡀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢿⡟⢙⢿⣆⠀⠀⠀⣴⠁⡸⠀⡼⠋⣱⠃⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢸⣷⣤⣘⡛⣦⣀⠠⠃⠀⡇⡼⠀⣼⢁⡴⠊⣹⠀⠴⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⡾⠀⣿⠙⣿⣯⠈⢿⣇⠀⡿⠃⠀⠷⠟⢠⠞⢁⡠⢤⡄⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⡈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢠⡿⣿⡆⠀⠛⠈⠀⠀⠀⠀⡄⠛⠚⣡⣴⣾⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡀⠠⠊⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠋⠁⠀⡿⢿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣠⣤⣯⠽⠛⣇⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⡿⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣇⠈⢧⢠⠏⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠈⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢸⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣆⣨⢋⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠘⣿⣿⡗⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⠒⠒⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢠⡴⠚⠛⠛⢦⡀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢀⣿⣤⠤⠤⣤⣼⣇⡀⢀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠼⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀ ⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀ ⠀⠀⡇⠀⠀⠀⠀⢠⣖⠀⠀⣿⢸⠀⠀⢸⠈⡇⠀⣤⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⢀⡇⠀⡶⠶⠶⣼⣹⣦⠤⠗⠸⣤⣤⣼⠀⣧⣠⡿⣧⣤⣤⡀⠀⢠⡇⠀ ⢀⡾⠁⠀⣽⠀⣼⠋⠙⢻⣷⡀⠀⠀⠀⠀⠀⢠⣾⢿⣷⣦⠸⡇⠀⠈⢧⠀ ⢸⠁⠀⣼⠁⠀⣧⠀⣀⡾⢻⡇⠀⠀⠀⠀⠀⣿⠀⠀⡿⣿⠀⠳⡄⠀⠈⣇ ⠘⣇⠀⣿⢦⡤⠼⣿⠿⠿⠋⠀⢀⠀⠀⡀⠀⠙⠿⢿⠿⣯⠤⣤⢿⡇⢠⡏ ⠀⠈⢧⢸⡆⠳⣤⣸⠂⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⢼⣁⡴⠋⡼⢰⠏⠀ ⠀⠀⠺⠞⠀⠀⠀⠙⠶⢤⣀⡀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠉⠀⠀⠹⠿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢿⣿⣿⣶⣄⠀⠀⠀⣀⣠⣠⣠⣀⣤⣤⣤⣤⣤⣬⣤⣄⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⣿⠶⣦⣀⠀⠸⡆⠀⠙⠛⠏⣻⣷⣴⣾⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠛⠛⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣴⣧⣞⣴⠉⢷⣦⣵⡀⠀⣠⣴⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⠀⠈⢡⣶⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢻⡿⣿⣵⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣾⡿⣿⣿⡿⣿⣷⡶⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⣀⠀⠙⢻⣿⢿⣿⣿⣿⣯⡸⡌⢧⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠸⢣⣤⣿⣾⣿⣿⣧⢿⣿⣜⣷⣿⡀⢻⡙⢳⣯⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣀⣹⡿⡿⣿⡟⣠⣽⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣯⣿⣿⣿⣿⣿⣿⣴⣿⣏⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣻⣭⣿⣭⣷⣿⣿⢯⠹⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣾⣩⣿⣏⢹⣿⣿⣿⡿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢻⣤⣿⣿⣧⣸⣿⣿⣿⡿⣥⠾⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣟⠡⠏⣶⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢻⣇⢿⣞⣿⢻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⢿⣿⠿⣦⠿⣮⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣾⣿⣸⣷⡷⢜⣻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⡴⠶⠖⣶⡶⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣻⡟⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣯⡁⠲⣤⠿⣏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠉⠁⠀⠈⠙⢶⣌⢷⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠛⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣤⣦⣽⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡿⣷⣯⣻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣨⠘⢛⢿⣿⣿⢦⣛⣚⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠿⠛⠀⠠⣤⣾⣿⣿⣿⣖⠿⣏⣥⣽⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣤⣤⡴⠶⠶⠶⠶⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⠀⠀⡀⣾⣿⡛⢿⣿⣿⣯⡷⠿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⡆⠀⠀⠀⠀⠀⢻⣿⣿⣿⢻⣿⣿⣿⣏⣿⢠⣤⣶⣽⣾⣷⣽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣏⣯⡟⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠉⠉⠉⠉⠉⠛⠿⠶⠾⠷⣦⣽⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡋⠉⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⠠⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣀⡶⠄⠐⠂⢳⣤⠖⠋⠉⠙⠉⢦⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡸⢷⠒⠤⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣾⣁⡤⠀⠀⣨⠚⢻⣖⣲⣶⣦⡄⢲⡷⠴⠒⡞⠛⣻⠛⠟⠳⡛⢿⠿⣷⣴⣀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣩⡏⠀⢀⣸⡷⢤⣼⣿⣿⢿⣿⣇⠀⠁⠀⠀⠘⡄⠀⠀⠀⠀⢱⠘⡄⠀⠈⢫⡚⢵⡤⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠟⠋⠀⠀⢸⣏⠛⠓⠻⢿⣿⠖⠋⣿⣿⣻⣾⣿⠅⠀⣤⣶⣾⣟⣁⣠⡿⠿⠿⢿⣅⣙⣶⣶⣔⠛⣄⣈⢻⣷⡀⠀⠀⠀⠀ ⠛⠛⢿⣿⠟⢦⣀⠀⢀⣿⠸⣆⠀⢀⠏⠀⢢⣰⣿⣿⣾⡿⢿⣶⠖⠋⠁⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠉⢻⡛⠛⠿⣦⣹⡳⣤⣄⠀⠀ ⣶⣶⠋⠁⢠⡿⠛⣿⣿⣿⡀⠙⣦⣾⠖⢒⣶⢿⡿⠯⢭⣍⣿⣿⣀⣒⣢⣤⣤⣼⣧⡄⠀⠀⣀⣀⣀⠀⢀⣸⣇⠀⠀⢈⣏⡷⢻⣿⡇⠀ ⡟⠉⠠⣠⡿⠁⠀⣿⣿⣹⣇⠀⢸⡇⠀⢸⣿⣸⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢉⣿⣿⡇⠀⠀⠐⠒⠒⠒⠀⣿⣿⠫⡤⢤⣧⣀⣀⣻⠇⠀ ⠓⠤⣀⡟⠣⣄⢠⣿⣿⡇⣿⣄⡾⠀⠀⣸⠀⠀⠀⠀⠀⣼⣿⣇⣀⣇⠀⠀⣸⣿⣿⡇⠀⠀⡄⠀⠀⠀⡄⣿⣿⠀⣧⠀⣿⠁⠈⣿⡆⠀ ⠀⢀⡞⠋⠑⠺⣿⣿⣿⣷⢸⣿⡇⠀⠀⣿⠀⠀⠀⠀⠘⣿⣿⠋⠉⣯⡙⠛⣿⣿⣿⣧⠀⠀⡇⠀⠀⢠⣇⣿⣿⣤⣿⣀⣿⠀⠀⢸⣷⠀ ⠆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⣿⣧⢀⠀⣧⠀⠀⠀⠀⠀⣿⣿⡄⠀⣿⡇⠀⣿⡇⡟⣿⠀⢸⡇⠀⠀⣾⣿⣿⣿⢰⣿⣿⣿⠀⠀⢸⣿⣴ ⡶⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⢸⠀⣼⠀⠀⠀⡀⢰⠛⠛⠛⠒⠓⠷⠤⣿⡇⠇⣿⡄⢸⡇⠀⢠⣿⣿⢿⣇⣾⣿⣷⡏⠀⠀⣼⣿⣿ ⠀⠠⠂⠀⣔⣼⣿⣿⣿⣿⣿⣿⡇⢸⣇⣿⠀⠀⠀⣧⢨⡇⡀⢀⠀⠀⠀⣀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡟⠁⠀⠀⣿⣿⣿ ⠀⠀⠂⠚⢀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡄⠀⠉⣿⣿⡿⠿⠛⠛⠻⠷⢶⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⢶⣶⣖⣾⠇⠀⠀⢰⣿⣿⣿ ⠀⠀⠀⠀⣸⠟⣿⣿⣿⡿⡇⠘⣧⣼⣿⣿⡇⠀⠀⢸⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡿⣼⠀⢀⣸⣿⣿⣿ ⠀⠀⠀⢀⡿⢾⣿⣿⣿⡇⡇⠀⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠚⠉⠉⠉⠉⠉ ⠀⠀⠀⣾⠃⣾⣿⣿⣿⠉⡇⠀⣿⣿⣿⣿⣿⡀⢰⢤⣿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⢀⣿⣿⣿⣿⣼⡇⠀⡇⣿⣿⣿⣿⣧⣸⡿⣿⡇⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢚⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⡇⢸⣿⣿⣿⣿⣿⣇⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠉⠀⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⢿⣿⣿⣿⣿⣿⣾⣿⡀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠃⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠈⢿⣿⣿⣿⣿⣏⣿⣷⣤⣄⣈⣑⢲⣤⣀⣀⣀⣤⢶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣀⡤⢴⣶⡿ ⡏⠀⣀⣿⣿⣿⣿⣿⠛⢻⠗⠐⠉⠉⠑⠚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠼⠟⠋⠋⠉⠉⣿⣿⡟⠀⠀⠀⠀⠀⡟⠀⠀⠀⣏⢷ ⠁⠀⣼⣿⣿⣿⣿⡇⢀⠇⠀⠀⠀⠀⠀⠀⠈⢺⡟⢿⣿⣿⣿⣿⣿⠿⢿⠿⢛⢻⡟⠲⣶⡲⠤⣤⠞⢻⠃⠀⠀⠀⠀⢰⡇⠀⠀⠀⢻⠨ ⠀⢰⣿⣿⣿⣿⣿⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠉⢻⣿⠛⠿⢷⣦⣲⡿⠿⡧⠤⠛⣷⠀⢻⣆⡎⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠸⠀ ⢀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠈⣿⠁⠀⠀⠈⡿⠋⠉⢻⡆⠀⠸⣧⠀⡟⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⣧ ⣾⣿⣿⣿⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣸⣆⠀⠀⠀⢙⣿⠿⢿⣄⡀⠀⢻⡶⠁⠀⠀⠀⠀⠀⠀⢸⠻⣧⠀⠀⠀⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡴⠋⡉⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣶⣶⠶⠾⠿⠿⢿⣦⣦⡙⢶⣶⢦⣄⠀⣦⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠛⠛⢿⡁⠀⠀⠀⠀⠀⠠⢀⡈⠛⠲⠿⢿⣟⠛⠻⣶⡦⢄⡀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣈⣟⣳⣤⣄⣀⡤⠞⠁⠀⠀⠀⣀⠀⠀⠈⠂⠀⢀⣠⠤⠤⠤⠠⠤⠤⢄⣈⣻⠿⢿⣆⣙⠛⠃⣬⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠙⡿⠀⠈⣏⠀⠀⠀⠒⠈⣉⡭⠶⠒⡒⠋⠉⠉⠀⠀⠀⠀⠀⠐⠤⡀⠈⠉⠓⠲⢬⣉⠻⣤⣩⣙⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣻⡤⠀⠀⡠⠛⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠙⠀⣾⠏⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⠀⠈⣷⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡾⠀⢠⣿⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⣴⡟⣿⠁⣰⠋⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⣿⢷⡤⢄⣠⡶⣾⣿⣴⠏⠀⣿⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠘⠿⣷⣶⡶⣿⣺⣿⣿⣧⣀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠿⣿⡇⠈⠉⠀⡿⠉⠁⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡏⠙⠒⢒⣾⠃⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⣇⠀⠀⡀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⢠⢿⠿⣤⠀⢸⠁⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢹⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣰⡞⠀⢹⡀⢠⣿⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡇⢀⡾⡏⠀⢸⡆⡿⠀⣴⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣰⠇⠤⠀⠹⣄⠀⠀⠀⢻⣆⠀⠀⢀⣸⡿⠁⠀⢸⣧⢿⡿⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⡸⣻⠀⠀⠀⢳⠃⢠⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⣿⣶⡶⠿⠦⡌⠛⠶⠤⠼⠏⠓⠤⠾⠃⠀⣀⣴⣿⣿⣿⣇⡇⠀⢀⡄⠀⡀⠀⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⣷⠇⠀⠀⠀⢸⡇⡞⡟⢹⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠋⡠⠖⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠉⠉⠉⢸⣿⢀⣠⢾⠀⠀⢱⣄⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⡟⣷⡇⡏⠀⢀⡏⠀⠀⠀⠀⠀⣤⣤⣾⣿⡟⠀⡞⢁⣠⣶⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⣼⣿⣯⣄⡼⠀⠀⢸⡟⣆⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⣻⡇⠻⡇⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣏⢹⣿⡟⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⣙⣬⣿⣿⣷⣤⣄⣸⠁⠹⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢠⣿⣷⣤⢃⡞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠻⢿⣿⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠉⠉⠁⠉⠉⠀⠀⠉⠙⠳⣤⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠟⡇⠀⠀⠀⠀⠀⡼⣼⡿⣾⡜⠁⢸⡄⠀⠀⠀⠀⠀⠀⠹⣦⣄⡈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠆⢀⣴⣿⡿⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠃⠀⠶ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⢃⢏⠁⣿⣇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣭⣍⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣠⠞⣹⡏⢁⣀⣤⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⣰⠃⡼⢸⠀⡟⠘⢦⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣽⡭⠭⠽⣶⠶⢤⣤⠴⢶⣶⠟⠁⠀⠿⣦⣽⣵⠟⠛⠁⠀⠀⢠⣤⠶⣤⡀⠀⠀⠀⠀⠙⡿⢂⡀ ⠀⠀⠀⢼⠃⠀⠀⠀⡰⠃⡸⠃⡿⠀⣷⠀⠀⠉⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣀⡈⠓⢮⡙⣿⣿⠀⠀⠀⠀⠀⠀⢈⣾⡧⠀⠀⢠⡿⡃⠀⠈⠙⣧⡀⠀⠀⠀⢡⣀⠋ ⠀⠀⠀⡼⠀⠀⢀⡜⠁⣰⠃⢰⠇⠀⠙⣆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠲⣤⢀⣀⣀⡴⢾⠁⠀⣠⡿⠿⠿⡷⣦⠀⠀⠀⢰⢻⡇⠀⠀⠀⣾⣋⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⣄⣀ ⠀⠀⢰⠃⠀⣠⠏⢀⡜⠁⠀⡼⠀⠀⠀⠈⠓⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠙⠾⣆⣾⠋⠀⠀⠀⠀⢹⣧⠀⠀⠈⠛⠃⠀⠀⠀⢻⣯⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠈⣿ ⠀⢠⠏⢠⠞⠁⣠⠟⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠓⣢⠄⠙⢷⣶⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⠶⠛⠋⠀⠀⠀⠀⠀⠉ ⣠⢏⣴⣁⡤⠞⠁⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢀⣠⣄⣙⣦⡀⠀⠀⠀⠀⠙⠳⣶⠒⠉⠁⠀⠀⠈⠻⣦⣤⢀⠀⢀⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠁⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢠⣾⢿⣪⠿⠀⣿⡿⡷⢤⣄⣤⡤⠴⠴⠋⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⢾⡿⣿⣆⣉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣀⣀⣰⣛⣱⣿⠶⠶⢾⣯⣼⡇⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⠀⣠⣤⡼⢿⣿⣧⣨⣿⣶⣄⣀⣀⣀⣀⡀⠀⠀⣀⡀⣴⡙⠻⠶ ⠀⠀⠀⠀⢀⣀⣴⠇⠀⡴⣻⠟⠋⠉⠀⠀⢁⣰⣯⣖⢾⣶⠛⠁⢠⣴⡶⠿⣿⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡻⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⢹⢿⡟⣿⣏⠀⠈⠙⠶⢄

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⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⡇⠀⢰⢰⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢏⠉⠁⠀⠀⠀⠀ ⠀⠀⢰⠀⡇⢀⠀⠡⣧⡀⠀⣧⠀⠀⡀⠇⠀⠀⠀⡆⠀⢀⠀⠀⠀ ⠀⠀⠘⠐⣷⢸⡀⠀⠀⡉⠀⣇⡱⠁⡀⢻⠀⠀⠀⢱⠈⠁⠀⠀⠀ ⠀⠀⡌⡰⠊⢋⣧⡀⠀⢧⠀⡇⢀⠈⠢⣸⠀⠀⠀⢸⠀⠀⣀⠄⠀ ⠀⠀⡗⣡⣶⣼⡟⠕⢄⣘⣂⡽⣿⣿⣿⣮⣤⡀⢠⢸⠀⠉⢸⠀⠀ ⠀⠸⡿⠍⠷⠿⡵⠀⠀⠀⠀⠀⢸⡙⣭⣛⠋⠀⡀⢸⢣⠀⢸⠀⠀ ⠀⠀⡏⡆⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠶⢼⠀⢠⠃⢸⡸⠀⠂⠀⠀ ⠀⠀⡇⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠀⡟⠁⢠⠀⡄⠀ ⠀⠀⢃⠀⡅⠂⠄⡀⠀⠀⠀⢀⠀⠀⢐⠇⠈⠀⢀⠃⢠⠀⣴⣇⠂ ⠀⠀⢸⠀⣇⠀⠀⠀⡩⢙⡏⠀⠀⣀⣌⠀⠀⡰⣘⣰⠏⠷⠿⡁⠀ ⠘⠄⠀⢇⠏⠴⢊⢋⡔⠁⡀⠀⠀⣠⡂⠄⠊⢘⠡⢊⠂⢄⠐⠀⠑ ⠀⠈⡲⢤⠵⠥⠁⡮⠐⠠⢈⢢⡍⡲⡀⠀⡀⠀⠴⠁⠀⠀⠡⠀⠀ ⠀⠈⠀⠈⡢⠀⢠⠀⠀⠀⠀⠙⠃⠀⠈⠪⠠⠊⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣠⡶⢦⣄⠀⠀⠀⠀⠀⠀⠀⣠⡶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡟⢀⡀⠙⣷⡀⠀⠀⠀⢀⡾⢋⡤⡙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⠇⠙⣄⠘⠧⠤⠤⠤⣾⢡⠏⠀⢱⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡟⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡏⠀⢀⡖⠲⣄⠀⠀⠀⣀⠤⠊⠁⠀⢣⡀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣠⠤⠞⠀⠀⠈⠑⠦⠊⠁⠀⠀⠀⠀⠀⠙⠒⡂⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⢀⡇⢱⠀⢱⣶⡄⠀⢠⣤⣤⡄⠀⠀⣴⣶⡆⠀⠰⠥⡀⠘⣧⠀⠀⠀⢀⣀⣀⡀ ⢸⡇⡞⠀⠈⠋⠁⠀⢈⣩⣭⣁⠀⠀⠉⠉⠀⠀⠀⢠⢇⣤⡿⠀⣠⡶⠛⠉⢸⠃ ⠘⠷⠿⣤⣄⣀⡀⠀⠹⣏⣠⠟⠁⠀⠀⣀⣀⣤⡶⠟⠋⠁⢀⡾⠋⠀⠀⠀⢸⡄ ⠀⠀⠀⠀⠀⠉⠉⡟⠛⠒⠒⠒⠚⠛⠋⠉⠁⠈⠻⣦⠀⠀⢸⢇⡠⡄⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⡄⠀⠀⠀⣤⠀⠀⠀⠘⣧⠀⢸⠉⠀⠧⠴⠲⣸⡇ ⠀⠀⠀⠀⣾⠛⢷⣧⡀⢀⣸⡇⠀⣀⢤⣿⠞⠛⢻⡄⢹⣆⣿⠀⠀⠀⠀⣠⡟⠀ ⠀⠀⠀⠀⢹⡆⠀⢿⡈⠉⠸⡟⠊⠁⢸⡇⠀⠀⣸⡇⢈⡟⠁⠀⢀⣠⡾⠋⠀⠀ ⠀⠀⠀⠀⠀⠻⠶⠾⠷⠶⠶⠷⠶⠶⠾⠧⠤⠾⠿⠴⠾⠷⠶⠛⠋⠁⠀⠀⠀⠀