Jorking It Emojis & Text

hei guys, dot porn is actual asscheeks so heres Sunny's little tip for yall who can access sites like PH or Twitter even, use Yandex.ru/Yandex, its a Russian web browser, if the porn sites are blocked on your phone jus shlick it to the gifs, so uhh yeah, ha det ! ♡⁠˖⁠꒰⁠ᵕ⁠༚⁠ᵕ⁠⑅⁠꒱

🔞🍆

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

𓀐𓂸📹

⠀⠀⠀⡧⠈⠀⠀⠀⠁⡼⡁⣸⠀⠀⠀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢸⠁⠋⠞⣶⠶⡶⢶⠲⠓⠉⠈⡀⠣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠀⠀⠀⣿⣦⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠳⣌⠳⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠴⣩⠋⠖⠴⠤⢤⣤⠤⡶⢷⠙⠀⠃⠀⠀⠀ ⠀⠀⠏⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡷⠙⠀⠀⠀⠀⠀⠀⠟⣡⠞⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⡷⠀⠀⠀ ⠀⡞⢀⠀⠁⠚⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠀⠁⡟⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀ ⠃⢸⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀ ⡇⢈⠀⡇⢠⠀⡀⢡⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸ ⠀⢸⠀⡄⢹⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠘⠀⠀⠀⠀⠛⠀⠀⢸ ⠀⢧⠈⠀⡀⢤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠃⠷⠀⡿⠀⠀⢸ ⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⢠⠀⡟⢀ ⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠶⣠⠀⠀⠞⢀⠀ ⠀⠀⠀⠀⣼⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡼⠀⠀⠀ ⠀⠀⠀⡇⢸⠀⣀⠢⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡴⢀⠀⠀⠀⠀ ⠀⠀⠀⡇⢸⠀⠀⠀⡀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⠀⠀⠀⠀⡟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⠀⠀⠀ ⠀⠀⠀⠀⡄⠱⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡴⣤⢤⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⣻⠳⠈⠈⠀⠀⠀⠀⠀⠂⠖⠴⡤⣏⢠⠀⠀⠀⡄⡐⣀⣀⠀⠀⠀⠁⠉⠉⠁⠉⠉⠃⠜⡤⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣼⠀⠃⣿⣿⣯⣿⣦⠷⠛⠈⠀⡴⢀⠛⠒⠒⠒⠙⠀⠀⠋⠿⡿⣿⣿⣿⣿⣼⣿⣿⠸⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⢰⠀⡏⣿⢹⣿⣿⠀⠘⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣹⠀⣿⣿⢸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⣿⡏⣿⢸⠀⣿⣿⣣⣿⠰⠉⠞⠉⠞⡤⣤⠲⣿⣿⣿⣿⣿⣾⣿⣿⠿⣿⣷⢻⡇⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⡇⢸⣹⣿⣿⢰⠃⣿⣿⡿⣿⡟⣿⡴⢀⠀⠀⠀⠀⠀⣄⣦⣷⣿⣿⣥⣿⣿⣿⡌⣿⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⡇⢰⣷⢸⣿⠀⡟⣿⣿⣿⣿⣾⢁⠘⠀⠀⠀⠀⠀⠀⠀⠃⠉⢮⣦⠿⣶⢿⣧⢸⡇⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠈⡿⠸⡟⢠⣿⠁⣿⣧⣿⣾⣇⢿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣲⠻⣎⠹⣇⡘⢻⡇⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⢸⣧⢸⣿⡇⣸⡿⢀⡏⣼⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⡄⡹⡄⠹⢻⣷⡜⡇⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢿⡿⢸⣾⡇⢸⣿⠙⣿⢀⠇⢱⣼⢀⠀⠀⠀⠀⠀⠁⢻⠀⡯⠿⣿⢾⡟⠹⡆⡜⡏⠸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⣿⣿⢸⢸⡇⢻⣿⣇⣸⠀⣾⡅⠚⠟⠿⠿⠠⠄⠳⡏⣰⠈⣯⣿⣿⢿⣼⣧⠸⣧⣆⣹⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣷⢸⢸⡇⡇⣼⡟⢀⡇⢻⣯⣿⣿⣿⣿⠋⠐⠉⣇⠳⢿⡏⢸⠛⡌⣷⢯⢿⡆⠘⣿⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⡎⢸⢷⡇⣿⢸⣼⠀⠀⡁⣺⣀⣀⣀⣀⢀⠋⣇⣿⢊⣯⣿⢹⡧⢸⡇⣿⡇⠘⢫⣿⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢹⣧⡇⡿⣿⢸⢰⠀⠀⡇⣾⠙⠀⠀⠀⠀⣸⡇⢿⠀⣦⣿⣷⡇⢿⡴⣿⡄⢸⡇⣿⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⡜⣿⣿⣿⢸⠀⠀⠀⡇⢻⡝⢻⠉⠈⢿⢩⡍⣿⠸⠀⣧⡇⡇⢿⠀⣼⠀⢸⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣆⣿⣿⢸⠀⠀⠀⡇⢹⠀⡀⣧⣈⣿⣅⣉⣾⢠⠀⡇⡷⡟⡿⠀⢸⠇⢸⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠏⠀⠀⣿⠀⢀⡾⠛⠋⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡏⠀⠀⠀⣿⢀⣾⠁⠀⣰⠆⢹⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣧⠀⠀⢠⡟⢸⡇⠀⣰⠟⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣆⢀⣸⣇⣸⠃⢠⡏⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣶⠾⠟⠛⠉⠉⠉⠈⠉⠉⠛⠁⢾⠁⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⠾⠟⠛⠛⣻⣿⣙⡁⠀⠀⢾⣶⣾⣷⣿⣶⣄⠀⠀⠀⠀⠰⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣶⣶⠾⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⣿⣻⣟⣻⣿⡦⠀⠘⣿⣿⣛⡿⢶⡇⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⣿⣿⡗⠀⠀⠿⠉⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣿⡿⠁⠀⠀⠘⢦⣿⣿⠇⠟⠁⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠛⠆⠀⠀⠀⠀⠀⢀⢻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠿⣿⣭⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠶⢶⣶⣦⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣟⣯⣽⠟⠋⠀⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⠀⠉⠛⠷⣮⣍⣩⡍⢻⡟⠉⣉⢹⡏⠉⣿⣹⣷⣦⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢸⠇⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⢠⣠⡶⠀⠀⠀⠀⠘⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⡀⠀⠀⠀⠀⠀⠀⢹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣥⢠⣤⠼⠇⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡄⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠾⠷⠄⠀⠀⠀⢀⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠋⠀⠀⠀⠀⠀⠀⢰⣾⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣠⣿⣿⣶⣶⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠉⠛⢿⣿⣯⣿⡟⢿⠻⣿⢻⣿⢿⣿⣿⣿⣿⣿⠿⠟⠹⣟⢷⣄⠀⠀⠀⢀⣼⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠘⢷⣌⡻⠿⣿⣛⣿⣟⣛⣛⣋⣉⣉⣉⣀⡀⠀⠀⠈⠻⢿⣷⣶⣶⢛⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⠀⠀⠹⢯⣟⣛⢿⣿⣽⣅⣀⡀⠀⣀⡀⠀⠀⠀⠠⢦⣀⠰⡦⠀⢸⠀⣏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠷⠀⣸⠀⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠀⠀⢦⡀⡀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⠳⣝⠦⢄⠀⠀⠀⣟⣷⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⡀⠀⠀⠈⠙⠂⠀⠀⠀⢸⣿⡄⠀⠀⠘⢦⡙⢦⡀⠀⠀⠀⠀⢰⣷⣷⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢧⣤⣀⡀⠀⠀⠀⠀⠀⠀⢿⣷⣄⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⢿⡍⠛⠳⠶⣶⣤⣤⣤⣤⣤⣤⠼⠟⡟⢿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣷⣶⣶⣶⣶⣶⣶⣦⣀⣀⣀⣻⡀⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⢀⣼⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠀⠀⠈⠻⣿⡆⢹⣯⣽⣿⣿⠟⠋⠙⣿⣶⣿⣿⣿⣿⣾⣿⣿⣿⣟⠋⠉⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⠈⢻⣆⣿⠀⠀⠀⢁⣶⣿⠿⠟⠛⠷⣶⣽⣿⣿⣻⣏⠙⠃⣴⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⠀⠀⠉⠀⠀⠀⠀⠀⢹⣿⠀⣀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠉⠻⣿⣧⣿⢀⣰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⣤⣤⣤⣤⣤⣤⣾⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣅⣾⢿⣵⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⢹⣜⠷⠦⠤⠤⠤⠤⠤⠴⠶⠛⣉⣱⠿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠷⣦⣤⣤⣄⣠⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠟⠿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⠿⠻⠚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣸⠀⠀⠀ ⠉⠉⠉⠿⠿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⠀⠀⠀⠀ ⣤⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣾⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⣿⣶⣿⣾⣠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠻⠛⠙⠉⠀⠀⠀⠀⠀⠉⠈⠀⢿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⣄⣤⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣤⣷⣿⣿⣿⣿⣿⣿⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣶⣴⣠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣷⣿⣿⣿⣿⢿⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣷⣾⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢁⠟⠛⠛⣈⣧⣿⢿⠶⣶⠶⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⢿⡘⣾⢀⡟⣿⠿⠈⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣷⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⢠⢘⡿⣿⣿⣿⢿⠘⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢁⠟⡿⣶⣶⠶⠳⣍⣦⣿⣿⡘⣅⣶⣿⣶⣠⠁⢸⣇⣿⣿⣿⣿⢸⡀⠁⠍⠈⡑⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣶⣶⣴⣤⣠⣤⠃⣿⣴⣟⣿⣿⣿⢿⡙⢧⡘⣷⢿⡘⣷⠟⡿⢹⡀⣿⡘⣷⣿⣿⣿⢀⡇⣿⣿⣿⡘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⣦⣷⣿⣿⢂⠛⠛⠛⠛⠀⠻⡟⠿⠘⡇⣿⡇⣿⣿⣿⣿⣿⣿⢻⢧⡄⣿⢿⠀⣿⣿⣿⠸⣷⢸⠷⡛⣙⠘⠃⡆⣿⣿⣿⢿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠟⠿⡿⠈⣆⣿⠀⣧⣿⣿⢹⡆⣿⣿⣿⢿⡆⣿⡜⣿⣿⣿⣿⣿⣿⣿⡘⢸⣿⣿⠀⣧⣿⣶⣶⡀⠄⣿⣿⣿⢳⡌⢸⡁⣭⣭⢃⠀⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⣿⣿⣿⠸⣧⢿⡘⣍⣥⣋⠙⣄⣿⣾⣤⠈⣤⢿⣎⣿⣿⣿⣿⣿⣿⢸⢠⣿⣿⠀⠋⠿⣿⣿⣿⣿⣿⢿⠻⣛⢿⠈⡆⣿⣿⣶⠁⠟⠙⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣶⣴⣥⣬⣷⣿⡙⣄⣭⣩⠟⡄⣾⢁⣿⣿⣿⣾⢠⠻⢁⡛⣿⠉⣇⢿⣝⣷⣿⣿⣿⣾⠁⠀⣀⠃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢿⡛⣹⠈⡧⣿⣿⢿⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢠⠁⠋⠛⣟⠙⡀⣦⠀⣆⣴⣤⢩⠋⡓⣛⣿⣿⣿⠈⢰⡿⣿⣿⣿⠻⣀⣤⢶⣄⣤⢋⡴⢋⡿⣿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣦⣻⣿⣴⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢹⡆⣿⣿⣶⣀⣫⠟⠿⣿⣿⣿⣿⢃⡿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⢿⠘⡧⣰⡡⠟⣿⣿⠿⣿⣿⣿⣿⢿⣛⣍⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⣛⡛⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⠿⠿⠀⡟⣿⣿⣿⣿⣿⣿⢸⡿⣿⣿⣿⣿⣿⣿⢹⣧⣿⣿⣿⣿⣿⣿⠘⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣸⠃⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠻⣌⣷⣿⣿⣿⣿⢸⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⠸⣥⣭⣭⣬⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢻⡄⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠦⣙⣬⣶⣶⣶⡆⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⢸⣿⣿⣿⣿⣿⠻⣙⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣧⣿⣿⣸⣿⣿⣿⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⣸⢿⣿⠸⣧⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⢿⡙⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⣧⣿⢿⢿⣿⣿⣿⡘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢰⡙⣧⢻⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡇⣿⣿⣿⣿⣿⣿⣿⣿⠹⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⣆⣿⣿⣿⣿⣩⣿⡹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣼⡏⣿⠻⣌⢷⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣿⣿⣴⣩⣛⡛⣙⣬⣷⢻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣅⣟⣿⣿⣿⣿⣿⠻⣎⣿⣿⣿⣿⣿⣿⣿⣯⣾⢇⣼⠏⣿⣿⣿⣿⠻⣙⣤⣇⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢃⡿⣿⣿⣿⣿⣿⠻⣌⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣭⣽⣾⣶⣿⡿⣷⣿⣿⣿⣽⢟⣿⢥⣴⠋⣿⣿⣿⣿⣿⣿⣿⣿⠻⠙⣄⣧⣿⣿⣿⣿⣿⣿⣶⣥⣪⠒⠒⡖⣿⣿⣿⣿⣿⣯⣿⣿⢸⠛⣄⣷⣿⣿⣿⣿⣿⣿⣿⢿⠈⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⢶⠿⣛⠭⣦⣶⣿⣾⣿⣹⣠⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⣀⣧⣮⣿⣾⢀⣋⠞⠶⣭⣩⣛⣛⣟⣿⣾⣷⣿⣿⣿⢸⠏⠿⠙⣇⣿⣿⣿⣿⣿⣿⣿⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠿⡛⣌⣷⣿⣿⣿⣸⣸⠅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⣧⣰⠞⣥⢋⠽⣿⣿⣿⣿⣿⣿⣿⣿⡹⣦⣿⣿⢹⣇⣿⣿⡶⣿⣿⣿⣿⣿⣿⣿⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣧⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⡑⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣧⣿⣿⡆⣿⣴⠇⣿⣿⣿⣿⣿⣿⣿⢡⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡇⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⠘⢉⠋⡿⣿⣿⣿⣿⣿⣤⢃⡿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠋⣙⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣥⢚⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡿⣿⣿⣾⣶⣥⢋⠟⣿⣿⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡴⢏⣿⣿⣿⠿⡛⣝⣬⣦⣶⣶⣶⣶⣤⣩⢛⠿⣿⢡⢻⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣤⣋⣛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⣍⣶⣿⣿⣿⣿⣿⣼⢀⠉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡟⣿⠈⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢩⠛⡛⣛⣛⠛⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠇⣿⣿⢹⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣡⠟⡿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⠘⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢿⠈⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡆⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢋⡵⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⣿⣿⣿⣿⣿⢿⠙⡄⣷⣿⣿⣿⣿⣿⣿⣴⣫⣾⣡⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣼⢋⡴⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢿⠛⣍⣤⣶⣶⣶⣥⣩⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣧⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣰⡟⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢡⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠄⠀⡀⣀⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣿⣿⣿ ⣿⣿⣿⣿⣼⢋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠋⠀⢠⠃⠙⠉⠀⡀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣿ ⣿⣿⣿⣰⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣰⠀⠊⠃⠹⣼⠀⠀⠋⣿⣨⢉⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿ ⣿⣿⣰⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⣍⣶⣿⣿⣹⠀⠀⠃⡿⡟⢺⡇⠀⣿⣸⡏⣼⠻⠘⡀⣿⣿⣿⣿⣿⣿⣿⣶⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿ ⣿⣼⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡙⣦⢠⠀⠆⣿⣿⣿⢸⡀⠀⣿⣿⣄⣿⢀⣠⠀⣇⣾⣴⣩⣟⢛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷⣿ ⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⡟⣿⣿⣿⢸⠀⡇⣿⣰⡇⣾⠿⡠⠒⣡⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⡆⣿⢿⣿⢸⠀⣿⣹⠈⡿⢰⣸⠀⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⣆⣻⣿⢸⠀⣿⣿⢻⢠⣠⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠠⠁⣦⣰⠟⠠⡿⣾⢠⠀⠁⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿⡏⣿⣿⣿⠀⠀⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⢻⠟⣿⣻⣿⣽⣏⠟⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣀⣀⣷⣿⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣓⣌⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠀⠀⠀⡀⣷⠀⠀⠀⠀⣎⣿⣿⣿⣿⣿⣼⣤⣤⣷⣿⣿⣿⣿⣿⣿⣿⣾ ⡜⣿⣿⣿⣿⣿⣶⣿⣿⣿⣼⠀⠀⣀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣆⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⠁⠉⠋⠹⢀⢷⠿⡿⢿⡙⣧⣿⣿⣿⢸⡍⢀⡀⣷⣿⣿⣿⣿⣿⣿⢸ ⢻⣧⣿⣿⣿⣴⢩⣆⣿⣼⠏⠿⡼⠏⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠘⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⣿⣿⢻⡀⣧⣿⣿⣿⢿⣙⣷⣿⢸⣷⢻⠉⠉⣦⣿⣿⣿⣿⣿⢇ ⣿⡘⣿⣿⣿⠸⡇⢻⣀⡟⣿⣿⢃⣿⣿⣿⣴⢀⠤⠙⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢃⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣷⣿⣿⣿⣿⡹⣷⣿⣿⢿⠈⣌⣷⣿⣿⣶⠹⣧⣿⡘⣷⣿⣿⢿⡙⣇⣿⣿⣼⡏ ⣿⢿⡌⣿⣿⢃⡿⣼⡇⣶⣶⢸⡿⣿⣾⢡⠘⠀⠀⡀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠀⠀⠀⣄⣷⣿⣿⣿⠹⣧⣿⣿⢿⡌⠹⠧⣿⣿⣿⡘⣷⣿⠸⣁⣉⢁⢸⣿⣿⣿⢡⣿ ⣿⣿⢿⡜⣰⡆⣭⣸⡇⣧⣿⢸⣿⣴⢋⣿⣿⣾⢋⡿⣿⣿⣿⣿⣿⣾⣴⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠉⡟⡙⣦⣿⣿⣿⠹⣧⣓⣟⠘⡔⠸⡄⣿⣿⣿⡙⣶⢃⡿⣿⡧⠃⣿⣿⣰⡟⣿ ⣿⣿⣿⣿⠻⡀⣅⢸⡀⡟⣿⢸⢋⡿⣿⣿⣼⠏⣿⣿⣿⣿⣶⣥⣀⠗⡙⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣆⣿⣿⢻⣌⣿⣿⣿⡘⢸⣿⣿⠘⡷⠀⣧⣿⣿⣿⠻⡝⣷⣹⡼⠀⣿⣰⡏⣿⣿ ⣿⣿⣿⣿⣿⢻⡀⢠⣷⣿⣿⢃⢳⣝⣭⣤⠏⣿⣿⣿⣴⢋⡿⣹⠀⡀⣉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⢿⡙⣣⠟⢿⡙⣦⣿⢸⢈⣧⣿⣿⡻⢙⡁⣿⣿⣿⣿⣿⠻⣆⢠⠀⣰⡟⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠘⠛⡆⣿⣿⡇⣿⣿⣿⡉⣦⣶⣩⠟⣦⣿⣿⣴⢋⡿⣿⣿⣿⣴⣯⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⡂⣍⣦⣿⣿⣿⣿⢿⣌⣷⣿⢿⡻⢛⢫⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣴⢉⡼⠀⡿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢻⡆⢿⡙⣦⣿⣿⣿⢺⢃⠿⣿⣿⣿⢿⡴⢋⡿⣾⣵⣩⣚⠒⡙⣧⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⠂⣿⢿⡛⣭⣬⣶⣷⣿⡸⣄⣿⣿⣿⣿⣼⣿⣿⣿⣿⢸⣿⣿⣿⣴⢋⡰⠋⢿⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⣧⣿⢿⡙⣦⣷⢛⣿⣿⣿⣿⣵⢛⡋⣛⠟⠿⣿⣹⠀⠁⡉⡟⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡙⣧⣼⣋⣛⣟⢭⠩⠉⡌⣷⣿⣿⣿⣿⡿⣿⣿⣿⢿⡾⣡⢟⡴⢋⡰⡟⣿⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣭⠢⣙⣭⣤⣶⢃⡿⣿⣿⣾⣴⣥⣫⢛⠿⣿⣿⣿⣿⣿⣿⠛⣿⣾⣴⣢⣿⡙⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛⣝⣮⣷⣿⣿⣿⣿⠹⣦⣷⣿⣿⣿⣿⣶⣥⢋⠾⣥⢊⡡⢛⡿⣿⣿⡇⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠹⣆⣷⣿⣿⢿⠿⡛⣍⣭⠤⠿⠻⠚⠁⣍⣦⣶⣶⣶⣶⣶⣶⣶⣥⣩⣋⠛⠽⣤⢦⠶⠲⠓⣉⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡀⣭⣦⣶⣶⣶⡶⣥⣩⣋⠖⡴⣩⢛⠿⣿⣿⣿⣿⣸⣿⣰⡟⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⡉⣬⣶⣷⣿⣿⣿⣿⣿⣿⣀⠋⣶⣶⣶⣶⣤⠠⠗⠿⠛⡛⣙⣭⣬⣶⣶⣷⣿⠿⠿⠿⣿⢿⡛⣍⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣍⣷⢿⠽⡭⣫⣛⣛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠨⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⡁⣾⣿⣿⠿⡿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⠿⠻⣛⣍⣬⣶⣶⣶⣶⣶⣶⣶⣶⣴⣤⣩⣛⠛⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢠⣾⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣛⠟⡿⣿⣾⣴⣩⡙⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡄⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣾⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣋⢛⠿⣾⣴⣩⢋⡙⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣇⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢸⣇⢻⣇⠘⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣧⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠃⢠⣾⣇⣿⣿⢸⡏⣿⠹⣧⠻⠀⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢻⣆⣿⣿⣿⣿⣿⣾⣧⣿⣿⣴⠋⢠⡞⢣⡿⣿⣹⠏⣿⣿⣾⣶⣴⢡⣍⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣆⣿⣿⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠹⣦⣿⣿⣿⣡⠋⣿⣾⢱⠔⢀⡉⠛⠛⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⢿⠿⡻⣙⣀⣉⣭⣭⣭⣩⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡄⣿⠀⣿⢸⣷⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⡛⣛⣛⢛⠟⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡙⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣾⣷⣿⣿⢿⡌⠹⣧⢻⡇⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡆⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠦⡛⣍⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⣿⢿⡙⡈⣷⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡌⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣧⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣆⢿⠻⣍⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣆⠹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡐⠠⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠺⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⢀⠋⡟⠻⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣡⡟⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣡⢋⠟⣿⣿⣿⣿⣿⠿⡛⣌⣶⣶⣿⣿⣾⣴⢁⠟⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⣛⣝⣭⣬⣶⣶⣶⣶⣶⣶⣶⣽⣭⣭⣋⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣛⠟⠿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⢙⠉⣖⣷⣿⣿⣿⢐⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢄⠤⠤⠳⠀⠀⠀⠀⢹⡀⠰⡆⠘⢸⠁⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷⣿⣿⠿⠀⠀⠃⣘⣀⣄⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⢿⠈⠀⠀⢄⠻⠈⠀⡇⠻⠈⠀⢸⣇⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⡴⠀⠀⠁⠊⠀⠋⠒⡖⢶⠒⢲⡚⠑⠉⡈⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⠀⠀⡀⣦⠘⠀⣆⢻⠀⣇⡏⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠊⣠⠋⡴⢀⠀⡇⢛⠀⠀⢣⠀⠀⣀⣄⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⣄⠳⠈⣏⠸⡀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⡰⠁⡴⢀⠂⠀⠀⡏⠀⢦⠑⡈⠱⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠮⠒⠉⠀⢄⡄⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠀⠀⠀⠁⡴⢀⠀⠀⠀⡀⡀⢦⠙⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡀⢇⠘⠀⡀⠠⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⠀⠀⠀⡟⢈⠀⠀⠀⠀⡙⠀⠀⠀⠀⠄⠙⠓⠈⡙⠸⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡁⣿⠸⠀⠀⠀⠀⠀⠀ ⣀⠤⠤⠤⠤⠦⠲⡟⢀⠀⠀⠀⠀⠀⣷⠹⠃⠀⠀⠀⡄⡏⣟⣿⢠⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣁⣿⠈⠀⠀⠀⠀⠀ ⢿⠙⠉⠉⠉⠉⠃⢰⠀⠀⠀⠀⠀⠀⡇⣿⠻⢿⠛⠙⠃⢻⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀ ⣿⣿⠻⠈⠀⣀⣇⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢿⠈⠀⠀⠀ ⣿⣿⣿⣿⠿⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⡄⣳⣈⣁⣊⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⠻⡿⣿⣿⣿⣿⢿⣉⠀⠀ ⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇⠿⣲⠛⠛⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢻⡟⣿⣿⢿⠀⠀⠀⡈⣀⣤⣶⠤⠦⠗⠸⠀⠀⠀⠀⠀⠀⠀⠀⠁⡋⣞⣶⣳⠙⠛⡿⣲⠀⡄⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢹⠋⠾⣤⢥⠿⠶⠿⠚⡝⣤⠀⠀⠀⠀⠀⠀⠙⠉⣟⢋⠛⠟⡿⣶⣪⢐⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⣧⢾⣿⢻⠛⠟⣿⣴⠃⠛⠙⠉⠍⠉⠉⡃⣴⣧⣾⣴⣤⣠⢀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠃⠀⠀⠀⣀⣀⠀⠏⠀⡀⡁⣈⣀⣀⠀⠀⡄⠱⠈⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠀⠒⠑⠈⡀⣀⠀⠀⠀⡀⣢⠈⠀⠀⠀⠀⠀⡀⣀⣀⠁⠋⠔⠫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡿⣿⣿⣿⣿⣿⣿⣾⢀⡇⠻⠉⠉⡀⢄⠶⠛⠈⠀⠀⠀⢆⠀⠁⠈⠉⠉⠋⠟⡿⣼⢉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣹⠀⠁⡏⣿⣿⣿⢿⠿⠻⡛⣝⢨⠀⠀⠀⠀⣤⣤⣀⣄⣀⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣧⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠯⠙⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣤ ⣄⠳⠈⣄⣶⣿⣿⣿⣿⣿⣼⣶⣿⣿⣻⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠁⠚ ⠀⠀⣀⠢⠑⡉⣍⣶⣶⣷⣿⠻⡉⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣤⣤⣤⣤⣀⠀⠀⠀⠀⠄⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢤⡲⠙⣈⣤⣤⣥⣾⣶⣶⣷⣿⣿⣿⣿⣿⣿⣾⣶⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀

⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣿⣿⣿⣀⢀⠀⠁⠈⡀⢧⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠾⠾⣦⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⠀⠀⣄⣤⣠⠀⠀⠀⡀⣦⠻⠀⣆⠸ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⣴⠀⠀⣦⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⢨⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡀⢧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠸⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢼⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠀⠀⠀⠀⡄⣼⢹⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡄⢹⠀⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠀⡄⢹⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⢇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⢿⠛⠻⠟⠿⠟⠿⠿⠹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣗⣛⣿⣿⢿⠙⡄⣷⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⣷⣾⣶⢈⠏⠼⡇⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣰⠀⠀⠀⡇⠶⠙⣟⣽⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⣸⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣰⠀⠀⠀⠀⡏⡿⣿⣿⣽⣷⣿⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⡀⢧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⢸⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⣦⣿⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⣤⣾⢿⠉⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⣧⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠉⡏⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣷⣿⣿⡾⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠋⠞⡴⣤⣤⢻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡾⢠⠀⠀⠀⠀⠀⣀⢦⠙⠀⠀⠀⠀⠀⠀⠁⠋⠚⠖⠤⠤⣤⣤⣤⣤⠦⠓⡌⢸⠀⠀⠀⠀⠀⠀⣷⣿⣟⣻⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⠙⠈⠋⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⠈⠀⠀⠀⠀⠀⡆⣾⣟⣿⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣯⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⢧⣿⣾⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⠀⠀⠀⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣿⣿⠙⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⣷⣀⣧⡙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠀⠀⠀⠀⠀⠀⡷⢿⠈⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⡇⣸⢦⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠙⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠋⣸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⡈⣤⣷⢻⠤⠢⠒⠒⠒⠜⠠⠀⡀⣄⠦⠓⠛⠉⠉⠉⠉⠈⠀⠀⠀⡤⣅⢠⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠿⡧⣸⢦⠻⠉⠀⠀⠀⠀⠉⠋⠛⠽⠭⡯⣸⠄⠤⠢⠒⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢀⠀⠀⠀⠀⠀⠀⠁⠾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⠀⢸⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣿⢹⠈⠀⠀⠀⠀⡀⣀⢿⠻⠉⠈⠀⠀⠀⠉⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢷⠘⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣠⣀⣀⣄⠦⠻⠈⠀⠀⠇⣿⣿⣽⣿⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸⠀⢀⠀⠀⠁⠛⡿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⡇⣸⣷⣿⣿⢿⠋⠀⠀⠀⠀⠀⠀⠀⠏⠠⠈⠀⠏⣿⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣿⠀⠉⠟⠿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⢸⡀⣧⣿⣿⡟⢻⠀⠀⠀⠀⠀⠇⣱⡾⢁⠻⣿⣿⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣡⠏⣴⢃⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣧⠘⡇⣿⣜⣷⣿⢹⠈⠀⠁⠛⠀⡄⠋⣿⣿⣿⣿⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣾⠀⡜⢀⠞⣠⠁⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡎⡸⣤⠳⢿⣿⡄⣇⣿⢿⠉⣉⢉⠉⠉⣿⣿⣿⣿⣿⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⠀⠀⢃⡼⢀⠇⣡⣿⠀⡾⣧⠘⠀⠀⠉⠈⠀⠀⠈⠀⣇⣿⣄⠰⣧⣿⠀⠀⣷⣼⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠀⠁⡜⠀⠀⣹⣾⢀⡟⢀⠀⢸⠀⣦⡳⣿⣿⣿⣟⠈⡘⢀⠘⠀⡇⣼⠇⠀⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⡇⢸⠀⠆⣿⢰⠁⣰⠀⡟⢠⠄⠤⠠⠉⣉⣭⣯⣾⢀⠿⢿⠛⣿⢉⡴⠇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢻⠀⡆⢸⠀⠀⣧⠀⡇⠀⠏⣤⢤⠥⠿⡿⣿⢛⠛⣿⢠⠏⣿⣹⣿⣹⣿⠀⡟⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡆⢻⠀⠀⢇⠈⠀⡄⢹⠀⢻⣼⠀⠃⡿⣴⣠⠉⡟⣿⠛⠟⣿⣿⣾⣿⣬⢦⠿⣿⢿⠻⠛⠟⠿⠿⠿⠿⣿⡿⠿⠿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠀⠀⣆⠻⠈⠀⢣⠈⠀⡄⠹⣆⢿⠉⣿⣹⠚⡴⣀⣀⠁⣞⣿⣽⣿⢹⡞⣤⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠉⠉⠉⠏⣙⣧⢽⠳⣀⠀⠀⣀⠀⣀⣿⣨⢀⠀⠀⠋⠖⣠⠞⣩⣀⠀⠰⠋⡿⣿⣿⣿⣿⣾⣴⣶⣶⣶⣾⣶⣶⣶⣶⣷⣿ ⠀⠀⠂⠒⠒⠓⠒⠒⠇⠂⠷⠀⠚⠚⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⣀⢀⡀⣷⢮⠙⠀⠀⠁⠈⣇⣿⢤⠤⣡⢋⠛⡟⣴⣁⡏⠯⡿⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⠛⠾⠃⠷⠿⡿⢿⠿⠿⠿⠿⡿⢛⠿⠛⣿⠳⠈⠛⠀⠀⠀⠀⠀⡇⣈⡀⣛⣭⠲⣟⢯⣿⣿⣿⣾⠳⡚⢳⠟⣴⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢀⡀⣀⢀⡄⣰⣤⣰⣁⣈⣀⣀⣀⣀⣆⣤⣶⣷⢻⠒⣿⠛⠛⠛⠛⠛⡛⣿⠿⠿⣟⣿⣽⠀⠧⠿⣿⡿⣿⠙⠋⡿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

why are you here? do you realize what your are doing is wrong, this is disgusting and you should be so embarrassed get off your phone or what ever your using to see such things and pray for forgiveness to your lord if your an atheist i have nothing to say but your fucking stupid

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣶⢷⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠛⠿⠿⠛⠙⠀⠀⠀⠀⠀⠁⠛⠛⠛⠙⠈⠀⠀⠀⡄⣿⠉⠈⡀⣄⣿⠻⠀⠀⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠟⣾⢷⠿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⣿⣀⠀⠀⡀⣄⢷⠙⠈⠀⠀⣿⣼⣀⣀⣤⣧⢿⠻⠀⠀⡀⣤⣶⣶⣶⣶⣿⢰⠟⣾⣠⣀⣤⣤⣶⠿⠛⠀⠀⣿⠈⠀⠀⣄⣷⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣿⠙⠉⠉⠛⠿⣶⣤⣶⠿⠙⣦⢿⠻⠿⡿⣶⣤⣿⠘⠀⠀⠀⠀⠀⠀⡇⣾⠀⣆⢿⠙⠉⠛⠟⡿⣿⣼⠀⠀⡄⣦⢷⠿⠛⠛⣿⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣄⣤⣤⣀⢀⠀⠀⠀⡀⣤⣷⠻⣈⢀⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⡀⣄⣤⣀⣀⡟⣼⠀⠀⠀⠀⠀⠀⠀⠋⡿⣴⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⠻⠈⠀⠀⡇⢹⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀⠀⠃⡿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠁⠛⣿⣿⠈⠀⡇⣿⠀⠀⠀⠀⠀⡿⢰⠀⠀⠀⠀⠀⠀⠀⣿⢠⠀⠀⠀⠀⠀⠟⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⡾⢠⠛⢴⠟⣴⠀⠀⠀⣷⢈⣷⣏⣿⣾⢠⠀⡄⣿⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠁⡟⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡉⢿⠛⣿⠙⣯⠸⠀⠀⠇⣾⢧⡾⣸⠋⣿⠰⠀⠀⣿⠀⠀⠀⠁⣿⢠⠀⠀⠀⠀⠀⠀⠀⡏⢸⠀⠀⠀⠁⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣦⣹⣿⣐⡆⣻⠀⠀⠀⡏⢿⡀⢀⠀⣦⣻⠀⠀⠀⣿⠀⠀⠀⡇⣽⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠁⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⣿⣨⠀⠗⣤⠀⠀⠀⣿⣴⠀⠀⠀⣿⣸⠀⠀⠀⣿⠸⠀⠀⡀⣷⠹⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠟⠾⣴⣤⣤⣤⣶⠿⠛⠈⠁⡟⢰⠀⠀⠀⠀⢿⠀⠀⠀⣄⣷⠹⠈⠀⡀⣧⠻⠀⠀⠀⠀⠀⠀⣿⠀⠀⡟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠏⣾⣠⠀⠀⠀⠀⠆⠿⠿⣛⣦⡿⢨⠀⠀⠀⠀⡟⢠⠀⠀⠀⠀⠀⣄⣷⠻⠈⠀⣦⢻⠈⠀⠀⠀⠀⣿⠀⠃⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⣿⢀⠷⠙⠉⠈⠀⠀⡀⣀⣀⠀⡀⣷⡿⠰⠀⠀⣷⣿⠿⠛⠉⠀⠀⠀⠀⣀⣦⠻⠈⣄⢿⠘⠀⠀⠀⣿⠀⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⠦⠶⣤⣀⢀⡄⣷⠿⠳⠚⠀⠀⡁⢻⠀⠀⠀⡿⣿⣿⣿⣿⣿⠿⠛⠙⠈⠀⡀⣦⢿⡙⣿⠻⠛⠛⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣿⠘⠀⠀⠀⠀⠀⠀⣆⠳⠛⠈⠋⣾⢀⠀⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠛⠙⣟⣿⣠⣀⣀⣄⣷⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣰⣆⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠘⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⣿⠙⠀⠀⠀⠁⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠸⠀⡀⢦⠙⠈⠀⠀⠀⠛⠛⡟⣸⠀⠀⠀⠃⣸⣧⢻⠀⡀⣀⣀⣀⣀⣄⣤⣤⣧⣿⢷⠿⡻⣿⣿⣾⣴⣿⣽⣤⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣦⠙⠀⠀⠀⣀⢦⠶⡶⢠⠀⠀⠀⠀⠀⠇⣴⠀⠀⣧⢻⠀⠀⠀⠀⠀⠀⠀⠃⣾⢀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠻⠀⠀⡀⣄⣦⠷⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡾⠀⠀⠀⠀⣦⢻⠈⠀⠀⠀⠀⠏⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⢿⠘⠀⠀⠀⠀⡀⣄⣧⠹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⠳⠙⠏⠹⠉⠛⣴⣦⠶⡴⢀⠀⠀⠀⠀⠀⠀⣄⢷⠙⠀⠀⠏⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⣷⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢿⠟⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⢿⠙⠀⡀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠙⠉⠈⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⢿⠻⣯⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣤⣤⣶⢶⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣉⣛⠿⠾⠶⠿⠻⠛⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣵⣛⠟⠿⠿⠻⠛⣈⣦⢿⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⢃⣿⣿⣿⣿⣿⣿⣿⣿⠸⡀⣿⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⠀⠀⠀⠀⠀⠀⣿⢀⡄⣠⣀⣀⣀⣀⣀⣄⣤⣶⠀⡇⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⡿⢻⠈⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠋⠈⠀⠁⠛⠀⠀⠀⠀⡇⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⠀⠀⣄⢷⠘⠀⠀⠀⠀⠀⣧⢻⠀⠀⣶⢰⠀⡆⣾⢠⠀⠀⠁⡿⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠙⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⣦⢿⠙⠀⠀⠀⠀⠀⠀⠁⠋⡾⣠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣶⠷⠿⠿⠿⡶⣴⣠⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈ ⠀⠉⠉⠉⠛⠟⠿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀ ⡀⣄⣦⣿⣿⣴⣤⣧⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠛⠿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣼⠀⠀⠀⠀⣀⣦⣶⣷⣿⣿⢻⠈ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⣶⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⠿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠄⠀⠄⠀⠀⠀⠄⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⡉⢋⣿⠀⡇⢙⠀⠀⠀⠀⠀⢀⣀⠀⣄⣶⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀ ⠄⠀⠄⠁⠄⠁⡏⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⡾⣿⣛⡿⣶⣤⣧⠘⠉⣌⠳⠉⠋⠛⠙⠉⠛⠛⠉⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⠙⠄⠁⠄⡁⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠟⠶⡤⣤⣉⢟⡴⣠⢀⠀⠀⠀⡟⣸⠀⠀⡠⣷⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⡛⢯⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⠿⠉⠆⣿⣿⣿⢠⠀⠀⠁⠉⠉⠛⠟⠿⡿⣿⣿⣿⢿⠿⠿⣿⣴⣠⢀⠀⠀⠀⠀⠀⡏⣴⠀⠀⠀⠀⠀⣳⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣧⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠈⣆⣻⠏⣿⣿⣸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠁⠞⣤⢀⠀⠀⠉⠀⠀⠀⡄⠹⠀⡀⣄⣶⣿⣿⣿⡿⣴⠀⠏⣿⣿⣿⣿⢿⠻⠙⠈⠀⠀⠀⠀ ⣦⣿⠻⣌⣷⣿⡾⠀⣿⣿⣿⣿⣿⣽⣀⣿⣿⣿⣿⣿⣴⣠⠀⠀⠀⠀⠀⠟⣶⠳⣼⠀⠀⠀⠀⠀⣯⢠⠀⠀⠀⣷⠀⠀⠀⠀⡀⣤⣷⣿⠀⠀⣿⣽⣄⣶⣶⣶⣷⣶⣿⢿⠛⠙⠈ ⠀⡀⣦⢱⡾⣿⢣⠈⣶⣷⣹⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⡄⠻⡼⠉⠎⠀⠀⠀⠀⡟⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣄⢦⠓⡏⣻⣿⡿⣿⣿⣿⣿⡾⣠⠀⡁⣿ ⠀⠀⠀⡀⣿⣤⠀⣿⠈⡇⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⢈⢀⠀⠀⠀⡇⣾⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣟⣿⣶⣶⣿⣿⣿⣠⠀⠀⠁⣿⣥ ⢳⠀⠀⠀⣇⠀⠀⡇⣿⡿⣿⣿⣿⣾⣠⠀⠀⠆⠦⠘⠀⠀⠀⠀⠀⠀⠀⠀⢿⠰⠀⠀⠀⠀⠁⡿⢻⠀⠀⠀⡇⣿⠹⠀⠀⠀⠀⠀⡄⣣⢛⠙⠀⣀⣆⠻⡙⣀⢦⠓⠈⠀⡇⣿⣠ ⡀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⡿⢿⠈⠀⠀⠉⠟⣿⣿⣿⠻⠈⠋⡿⣿⣿⠹⠀⠀⠀⠀⠀⡄⠾⣄⠀⠀⠀⣄⣿⣿⠻⠀⣀⣤⡿⣿⠀ ⠀⠄⠀⠀⡆⠀⠀⠀⣿⡇⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡆⣿⡻⢷⠈⠀⡀⣷⠈ ⠀⠀⠇⠀⡀⠀⠀⠀⣧⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢁⣾⣠⣄⣶⠀⠀⠀⠀⠀⡄⣤⢤⠿⠙⠈⣇⣿⣻⢿⠀⠀⡀⣿ ⠀⠁⠐⠁⠀⠀⠀⠀⡇⠀⢿⠰⠀⠀⠀⠉⠋⠛⠖⠰⠀⠀⠀⠀⠀⡿⣿⣶⣶⣷⢉⣌⣦⣶⣶⣤⣤⣠⣁⠋⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠁⡞⢠⡌⣶⠿⣟⣿⣿⢹⠀⠀⡇ ⢿⡸⠀⡀⠸⠀⠀⠀⡇⠡⣸⠁⠋⠵⣿⣴⣀⠀⠀⠀⠀⠀⠀⠁⡾⣠⠀⠀⠀⠀⠀⣀⣤⢤⠲⠴⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡽⢈⠃⡼⠃⡽⠀⠆⣧⣿⣷⣿⣿⠀⠀⡄ ⣿⢸⠀⠀⢀⠀⠀⠀⡇⡿⢾⣠⠋⣴⢀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣫⡴⠟⣰⠋⣿⣵⡼⠀⡄⣿⡹⢰⣿⠀⠀⠀ ⡜⢻⠀⠀⠀⠀⠀⠀⡏⣰⠀⠏⣠⠀⠀⠟⠷⠐⠀⠀⠁⠞⣠⠤⠁⠘⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡴⢞⣡⡾⢥⡿⣤⢣⡾⢤⠩⠀⡇⣿⠸⣧⠘⠀⠀ ⣆⣇⠸⠀⡃⠀⠀⠀⡇⠀⡇⣰⠀⠀⠀⢰⡿⠡⠊⠛⣱⠘⠀⠞⣠⠀⠐⠁⠚⠀⠈⡋⠑⠜⢀⠀⠀⠀⠀⠂⠈⠀⠀⡤⢏⣠⡔⢞⣠⠃⡽⣉⠟⣿⢩⡯⢛⠀⡀⡆⢻⡀⢸⠀⠀ ⠀⣧⢿⠀⡇⠀⠀⠀⡄⠀⣼⢿⠈⠀⠋⡱⢞⣣⡼⢋⡰⠋⡴⢉⠀⠃⠞⣠⠋⡿⡵⢞⣠⠀⠀⠀⠀⠀⠀⠀⣆⠙⠋⡴⢀⠄⡤⢤⠤⣤⣤⣠⣀⠀⡀⣥⣿⢻⠘⠀⣿⠘⢰⠀⠀ ⠀⠀⡇⢻⡏⠀⠀⠀⠀⡇⢠⡇⢿⠏⣾⣡⠞⣯⣴⢋⡴⢂⡠⢃⠟⣠⢟⡶⣷⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢘⠀⠀⠀⠋⠶⠴⠷⠙⠀⠀⠀⠀⡅⣿⣿⣿⡿⣿⢰⠀⠀⠀ ⠀⠀⠀⣇⣿⢸⠀⠀⠀⡟⠀⡇⣟⣴⢸⡳⡘⢋⡵⢋⠟⠛⠟⠻⠖⣷⡿⣶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣟⠿⠿⠻⡛⢿⠉⠉⠟⣿⣿⣷⣿⣿⣿⠈⠀⠀⠉ ⠀⠀⠀⠀⣷⣿⠀⠀⠀⣻⠀⡀⣿⠀⢸⠀⣁⠞⣠⢄⠤⠤⠤⣤⣀⣀⠁⠘⠈⠀⠀⠟⠸⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⡄⢷⣿⣯⣶⣶⣶⣷⣿⣿⣾⣴⢀⠀⢿⣧⣶⠶⠶⡴⣄ ⠀⠀⠀⠀⡆⣿⠘⠀⠀⣤⠀⠀⢸⠀⢸⠁⡿⢠⠀⠀⠀⠀⠀⠀⠃⡴⣀⣀⣄⢷⡿⣾⢩⠀⠀⠀⠀⠀⠀⠀⡇⢻⠈⠀⠀⠀⣧⣴⣤⣤⣤⣤⣈⠀⠀⠀⠀⡀⣿⡆⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⢹⠀⠀⠀⠀⡇⢀⠀⣿⡟⣿⠹⠀⠀⠀⠀⠀⠀⣼⠁⠟⡿⣿⣿⣴⢏⣹⠉⠀⠀⠀⠀⠋⠙⡀⣆⢿⠀⠀⠀⡀⢿⠉⠉⠉⠋⣷⠻⠉⠀⠁⠛⡿⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⠘⠀⠀⠀⡄⠀⠀⣿⠀⣴⣶⣿⠿⠻⠛⠛⠛⣿⣿⣿⣶⣤⢋⡿⣴⣠⣆⣤⣤⠤⣤⢡⡌⢷⠛⣯⠘⠀⠀⠀⡇⡘⣀⣀⠀⡀⣸⣷⢷⣴⣠⡇⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⠀⠃⠈⠀⡇⢸⠀⠀⠀⣀⣀⣄⣭⣬⣈⣁⠛⠿⡿⣲⢶⠠⠛⠉⠉⠉⠋⠞⣴⢿⡀⣿⢮⣿⠂⠗⠿⡿⢸⠀⠀⠀⠀⢧⡀⣽⢷⠻⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⡇⢻⠇⠈⣷⠈⠀⠀⠀⠀⠁⡼⣻⣽⣀⣰⣀⠀⠀⠀⠁⡏⣿⣿⣀⣀⠀⠀⡆⣿⣿⢀⣦⠹⠀⠀⡀⢻⠀⠀⠀⠀⡇⠸⡇⡸⣿⣼⠀⠀⠀⠀⠀⠀ ⠴⢠⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⣿⡜⢿⡝⢹⠇⠷⠀⠀⡿⢀⣷⡘⣿⠳⠛⠛⠟⡿⣿⣾⣷⣄⠀⠀⠀⠀⠀⣿⣼⢸⠀⣇⠸⠀⠀⣿⠀⠀⠀⠀⡇⢸⠀⢷⣟⢰⠀⠀⠀⠀⠀⠀ ⠀⡀⠸⠀⠀⠀⠀⠀⣇⠸⠀⠀⡆⣾⣿⡀⣄⣠⡄⣿⠶⣼⠀⡄⣿⣿⠀⠀⠀⠀⠀⡄⢻⡇⢹⠀⠀⠀⠀⠀⣇⢸⢻⠀⠀⣧⠹⠀⣼⠀⠀⠀⠀⡇⢠⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠙⠀⠀⠀⠀⠀⣧⠈⠀⠀⢧⣎⢹⠀⠀⠀⣧⠸⢸⠀⠀⢿⣷⢹⠀⠀⠀⠀⠀⣧⡟⣿⠀⠀⠀⠀⠀⡄⢹⡇⠀⠀⡄⣿⢿⢠⠀⠀⠀⠀⡇⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢷⠈⠀⡀⢿⣆⠹⠀⠀⠀⣇⢻⠀⠀⣼⢻⣧⠸⠀⠀⠀⠀⡀⣿⡆⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⡏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⢳⠈⠀⡀⢳⠀⠀⠀⠀⠀⣦⠐⠀⣇⡄⢹⣄⠀⠀⠀⠀⠀⣆⠘⢸⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣇⣿⠀⠀⠀⠀⠃⢰⠀⠉⡟⠉⠉⠋⠂⠒⠒⠄⠤ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀⢷⠘⠀⡄⢻⠉⠀⠀⠀⠀⠀⠀⡄⢱⣆⠹⠈⠀⠀⠀⠀⠀⣀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢹⠉⠛⠛⠶⠶⠤⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣴⠀⠎⢃⡹⠛⣿⣿⣿⣿⣿⣶⣠⣀⢀⡀⠀⠀⠀⣀⣤⠲⠛⠈⡀⢦⡈⣀⢦⡘⠳⠈⣧⡘⢷⠣⠀⠀⣆⡌⢹⠀⡄⠱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣸⠀⠎⢠⡿⡿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠃⠏⠿⠘⠀⠀⠀⠀⠀⣀⣄⠳⠉⠀⠀⡄⠻⢆⠘⢇⡀⣽⠹⠀⠀⢣⡎⠘⠀⡀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣣⣴⠀⠃⢰⡇⣿⣿⣿⣿⣴⢁⠉⠉⠈⠈⠄⣠⢀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⡀⢤⠳⠉⡀⢧⡌⡱⢹⡆⡌⠸⠀⠀⢁⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣠⣿⣼⠀⠀⡼⠃⣿⣿⣿⣴⢀⠀⡇⢀⠁⣄⣶⢧⠬⡶⣒⣙⠉⠉⣉⢿⠻⠈⠀⠀⠀⠀⠀⡀⢦⠙⢷⡈⣿⠈⢷⡆⠘⠀⡀⡆⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠞⣧⢰⠀⣿⢀⠀⠇⢠⡟⣿⣿⢠⠀⠀⠀⡄⠹⡀⢦⠙⠉⡀⢠⠀⠀⣄⢷⣿⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⡀⣦⢹⡄⢹⡀⠘⢇⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⠡⡿⢿⡞⠀⠃⢠⠀⠀⣸⠁⣷⣴⢤⣶⠿⠛⠉⠉⣿⠘⠀⠀⣄⠳⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⣄⠹⡇⠀⢀⡀⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠖⡠⢿⡿⣿⣿⢠⠀⡟⠀⠀⠃⢠⡟⣼⠀⠀⠀⠀⣄⠳⣿⣶⣿⠠⠀⠀⡄⢹⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⡹⠸⠀⠀⢣⠀⠀⡇⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⣿⣿⣿⢸⠀⠇⢸⠀⠀⡾⠀⣾⢸⠉⠀⠀⠀⠀⠀⣧⠀⡄⢸⠀⠁⠗⢰⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⠀⠀⡇⢸⠀⡀⢸⠀⠀⠠⠈⠀ ⠀⠀⠁⡿⣿⣿⣿⣿⢐⠀⡟⠀⠀⠀⢀⠀⣿⣼⣀⢀⠀⠀⠀⠀⡀⢳⠛⢰⠀⢋⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠀⠀⢻⠀⠀⣿⠄⠀⠀⠀⠀ ⠀⠞⣿⣿⣿⣾⣠⣯⠀⠀⢸⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠁⠀⠀⠀⡀⢧⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣝⣭⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠆⠙⡇⠈⠀⣆⠀⠀⠀⠀⠀ ⡀⡠⣇⣿⣰⠁⠟⢸⠀⠀⢠⠀⠀⠀⠀⡇⣿⠀⠀⠀⠏⣸⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣾⣶⣤⣠⣉⢛⣛⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⣽⣷⢿⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⢠⠆⣠⣿⢸⠀⡄⠀⠀⠀⠀⠀⡇⣿⠀⠀⡞⣯⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣲⢙⠉⠋⠖⡴⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⡇⡸⣷⢣⠀⠸⠀⠀⠀⠀ ⠀⠎⢠⠀⠀⠀⣷⢸⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⡇⢧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣶⣠⣿⡆⣹⢻⡀⢱⢣⢸⠀⠀⠀⠀ ⠀⢠⠀⠀⠄⠓⡟⢀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠃⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠞⡥⢛⠛⠉⣤⠻⣯⣿⠈⡇⡘⢰⠀⠈⠀⠀ ⠇⠈⠀⠀⠀⠀⣆⠸⠸⠀⠀⠀⠀⠀⠀⠀⣿⡼⠀⠸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠋⠋⠾⡥⣛⠽⣺⣤⣧⣿⠀⢳⣧⣿⢿⠀⣤⠀⠀⢸⠀⠀ ⠀⢳⠀⠀⠀⠀⠃⢸⢸⠀⠀⠀⠀⠀⠀⠀⣻⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⢻⠞⣤⡠⢀⠀⠀⡏⣾⢘⡇⠘⣷⡧⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⢱⠀⠁⠋⡾⢸⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠁⠞⠡⠉⠟⣼⣠⠀⠁⠚⠶⣣⣟⢿⣷⣾⢀⡟⢠⡇⡾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠢⠀⠀⠋⠿⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣻⣝⣯⡴⢀⠀⠆⣫⡷⣼⣁⡧⠀⡀⣥⣿⡿⡶⣶⣾⢛⣠⠀⠁⣿⠀⡆⢸⠀⠀⠀⠀⠁⠀⠀ ⠀⡀⠀⠀⠀⡄⢷⡿⢃⠀⠀⠀⠀⡇⠀⠀⢸⠀⡆⠘⠀⠉⠉⠛⠉⠛⠖⡥⣯⢿⠟⠯⣶⡤⠒⣤⣹⢝⣠⠀⡀⡿⠘⠀⠀⡄⢀⠁⠋⣶⣜⠹⠁⡿⣾⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⣧⡟⠈⠀⠀⠀⡄⠈⠀⢻⠀⠀⢿⡽⣀⢇⡿⣿⢖⡭⣺⢴⣠⣀⠀⠀⠈⠀⠀⠀⣧⢌⠲⠘⡀⢾⠙⠀⡀⣂⣴⢀⡇⣧⡟⣨⡇⢸⠀⠁⢰⠀⠀⠀⠀⠂⠒⠀ ⠀⠀⠀⠀⠀⠂⠉⡏⣼⢸⠀⠀⠀⠀⢰⠀⣤⠀⠀⣹⡋⣿⣴⣴⡠⣀⢀⠋⠒⠶⠶⠳⡟⢋⠸⠀⠀⡀⢷⠀⡀⢦⡟⡄⠱⠀⠀⠀⠁⡟⣧⠀⢷⣾⢠⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣄⢷⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⣿⠛⠉⠉⠉⡽⢏⣻⢟⡿⣿⣿⣖⠀⠀⠀⠀⡜⢹⠀⠀⡄⢳⡀⢷⠲⠐⡿⣧⠀⠀⡇⢸⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⠀⠀⠀⡆⣾⠘⠀⠀⠀⠀⠀⠀⠀⠀⡆⣹⣤⣶⣭⣭⣭⣯⣽⣉⢉⣿⢉⠉⠋⡹⠈⠀⠏⢰⣇⠈⠀⠀⠀⠀⡀⢹⠃⢸⡏⠀⠀⡇⠀⠁⣸⠀⠀⠀⡾⠃⠠⠀⠀⠀ ⣄⠹⠃⠈⠀⢆⠘⠀⠀⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⠀⠀⣄⣦⡙⣀⣷⣙⣀⣀⠀⠀⠀⡀⣀⣟⠀⡀⢸⠀⠀⠀⠀⠀⡆⣼⠁⣸⠀⠀⡟⠀⡤⠀⠀⠀⡎⢁⡸⠀⠀⠀⠀ ⠀⣄⠻⣄⠳⠀⣄⠦⠟⢻⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⢿⠉⠀⠀⡀⣄⡻⣻⢿⠛⠖⠤⠤⠤⠤⣼⢤⡷⣮⠿⠙⠠⠀⠀⠀⣇⡇⢰⠀⠁⣸⠀⠀⠀⠀⡞⢡⡼⠀⠀⠀⠀⠀ ⠀⠀⡄⢳⡇⠀⠀⠈⠀⣀⣦⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢾⡘⣳⣈⣀⣀⢀⡀⠀⡄⠳⠀⠒⠐⠃⢀⠀⡀⣆⠀⣀⢶⠀⠀⠀⡄⣿⠀⠀⡏⠀⠀⠀⠁⡞⢁⡞⠤⠤⠯⠻⠈⠀ ⠀⠀⠀⡀⣦⠙⠀⣇⠻⠈⠀⡀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣽⠳⣄⠹⠀⠀⠀⠀⠀⠀⢧⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠋⢰⠀⠀⠃⡴⠏⣰⠋⠴⣠⢀⠀⠁⠛ ⠀⠀⠀⠀⠀⣄⠱⠀⢰⣄⠓⠈⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⣆⣻⢮⡘⢢⠀⠀⠀⠀⠀⠀⢆⠘⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⠄⢁⠟⢾⣠⢀⠀⠀⠀⠆⣴⣠ ⠀⠀⠀⠀⠀⠀⡀⢄⠙⠀⠂⢘⠀⠀⢦⠙⠀⠀⠀⠂⠘⠀⠀⠀⣄⣿⣽⠻⠈⠀⠀⠀⠀⠀⠀⣇⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠁⠐⠁⠟⣾⣠⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠳⡈⠳⠛⠈⡀⢧⠘⠀⠀⡄⠳⠈⠀⠀⡀⡳⢮⣟⠹⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠟⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢦⢓⣍⠳⠉⣀⠦⠙⠀⠀⣄⠲⠈⠀⠀⡄⣶⢙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⠀⠀⣀⣤⠲⠓⠉⡀⣤⠲⠑⠉⡈⢦⠓⠉⠀⡀⣄⢦⠶⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠔⣠⠀⠀⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠾⢤⠲⠒⣖⢽⠫⡛⢿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠆⢉⠀⠀⠀⠀⠀⠁⠞⠠⡇⢸⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠗⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠋⡿⢉⠉⡿⢉⠉⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠁⠋⠶⡤⣀⣀⣀⣀⣀⣀⣀⣄⢦⠶⠛⠉⠀⢦⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠤⣤⠀⠀⠀⠉⡇⢸⡄⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠳⡈⢷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⡶⣡⢉⠚⠶⠤⣠⣀⣀⣀⣀⣄⠤⣶⢳⠙⠀⠀⠸⠀⠀⠀ ⠀⠀⠋⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡳⠹⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⣡⠋⠾⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠳⢸⠀⠀⠀ ⠀⠏⣰⠀⠀⠀⠀⠚⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⢹⠀⠀⠀⠀⠀⠀⠃⡿⢿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠈⠀⠀ ⠃⢸⠀⠀⠀⠟⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⠀⠀⠀⠀⠃⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀ ⡇⠀⠀⠀⡟⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀ ⡅⠀⠀⠀⣼⠀⠀⡀⢤⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⡇⠈⠀⠀⢿⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿ ⡆⢸⠀⠀⡄⢻⠈⠀⠀⠀⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢳⠈⠀⠀⠀⠀⡆⢸⠀⠀⣿ ⠀⣷⠈⠀⠀⠀⣠⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡴⣽⠀⡇⢠⠀⠀⣾ ⠀⠀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⣤⠀⠀⠟⢠ ⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡴⢀⠀⠀⠟⣠⠀ ⠀⠀⠀⠀⣧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣤⣀⠀⠀⠀⠁⠞⢠⠀⠀ ⠀⠀⠀⠀⡇⡀⢤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣶⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⡀⢆⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠎⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠴⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⢀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠹⠀⠀⠀⠀⠀⡖⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡴⣄⣤⢦⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣄⡷⠨⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠖⠤⣾⢠⠀⠀⠀⠀⠆⣈⣄⠤⠦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠖⡴⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⣸⣀⢤⠇⠛⠛⠛⠛⠛⠉⠈⠀⢀⠀⠀⠁⡞⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠋⠛⠷⠿⠿⠿⠌⠿⠿⠹⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⣿⢀⠀⠁⣿⣿⣾⡟⣿⣼⣁⣦⠷⠻⠈⠀⣀⠀⠆⠶⠠⠀⠀⠦⠶⠈⠀⠁⠟⣿⣿⣿⣿⣽⣿⣿⣿⢸⣿⣿⣿⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⡇⣷⣿⢡⣿⣿⢰⠀⠈⡇⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⣿⣿⣿⠸⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡜⡇⣸⡟⣿⣿⠀⠀⣿⡿⣸⣇⣿⠘⠀⠁⠞⠀⠁⠛⠶⠶⠻⡏⣿⣿⣿⣿⣿⣿⣷⣿⣿⢿⠘⣿⣇⣿⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠃⢸⡇⢳⣿⣿⣼⠀⠀⣿⣿⢡⣿⣿⢁⠟⣽⢋⡴⣠⠀⠀⠀⠀⡄⣤⣷⣿⣿⣿⣿⣻⣾⣿⣿⣷⣿⠸⣾⢸⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⢸⡇⡇⣼⣿⢰⠀⡏⣿⣿⡿⣿⣿⣿⣿⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⣿⠀⣖⣿⢿⣷⢸⠀⢻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⡇⢰⠀⡿⢰⣿⠀⠀⣿⣿⣿⣾⣯⣿⣿⢠⠋⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⡈⢲⣦⢿⣶⣾⢿⡇⢿⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⡿⠸⠡⣾⠀⣿⠀⡇⣿⣶⣿⡟⣾⣧⢻⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣭⠻⡄⢻⠀⣧⠈⣧⠘⡇⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⣿⢸⡇⢸⠃⣿⠁⣿⢠⠁⣿⣸⠀⡏⣿⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⣬⡘⢻⡀⢿⡇⢸⡇⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⣇⢸⡇⢸⡇⢸⡇⢀⠀⡟⣾⠀⠇⣼⣇⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⠷⠫⠈⣆⠘⡀⢻⡇⡘⣿⡀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⣿⣾⣿⢸⡇⢰⡟⢠⡿⠻⠙⣿⢀⠀⡟⢡⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⠀⡏⡽⢿⣿⣴⠳⣯⠘⡀⡹⢨⣷⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⣿⢸⡇⠀⣿⠀⣿⣼⡇⣼⠀⡇⢸⡆⢁⠉⠛⠛⠛⠐⠀⠂⠙⠀⢸⢠⠀⣷⣿⣿⣿⢻⡾⣦⣿⠀⣇⠈⡇⣼⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⣿⢸⡇⠀⣿⠁⣿⢀⣿⠀⠀⡜⠃⡿⣻⠿⡭⢿⡿⠀⠀⠀⡀⢦⢹⡄⠸⡆⣸⣀⣀⣃⢿⠈⡌⢻⡆⢸⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⣧⢸⡇⠀⣿⡇⣿⠀⣼⠀⠆⢶⣿⡿⣿⣿⣿⣿⣿⠟⣴⠀⠻⠇⡹⢳⢯⠘⢻⠀⢻⠘⡄⢿⣷⣷⠀⢠⡇⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆⢸⡆⢸⣿⣿⣸⠇⢠⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠘⡆⡿⡱⡣⣧⢻⣷⡙⣿⢸⠀⣿⡏⡇⠸⠃⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣧⠘⢸⣿⣿⢸⡇⠀⠀⠀⠀⡇⢿⠙⠀⠀⠀⠀⠀⠁⢠⠀⣿⠸⡀⣹⣧⣧⢸⡇⢺⠚⣷⣿⠀⢿⠀⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⢹⣿⣿⣿⢸⠀⠀⠀⠀⠀⡟⣨⣦⢻⠀⠀⠀⠇⡟⠀⠁⣿⣸⠀⡀⡇⣸⢸⡇⢀⠀⡇⣼⠀⣿⠀⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡇⡿⣿⣿⢸⠀⠀⠀⠀⠀⣿⢄⠦⡶⢿⠚⠑⡏⢻⠲⠶⣿⣼⠀⠀⡇⢹⢸⡇⠇⠀⡇⢀⠀⣿⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠐⣧⣿⣿⢸⠀⠀⠀⠀⠀⣿⢸⠀⠀⡀⢧⠀⣇⢀⢃⠸⣾⢀⠀⠀⡆⣾⢸⣾⣿⠀⡇⠀⠃⣼⡇⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡇⢻⠿⠋⣻⣉⣿⣸⠀⠀⣤⣀⠀⠀⡈⣀⣤⡤⣧⣾⢻⣾⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣛⣷⣉⣿⣿⣦⢷⠙⠉⠉⠉⠉⠗⢋⠷⠹⠋⣟⠊⣷⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣿⣿⣿⣿⢰⠉⠀⣁⣟⣿⣾⢩⡟⢿⣧⣼⣇⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⣿⣿⣿⣿⠹⠋⠖⣶⣈⠄⠿⡻⣶⢳⡿⢥⣿⣾⣯⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⣿⢀⣆⣹⠈⠓⠟⠿⡿⣿⣿⠿⠼⡅⣯⣿⣿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣿⠿⠿⣿⣿⣿⣭⣿⣿⣿⣿⣿⠼⣿⣿⣟⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⣿⣿⣿⢻⠏⣿⣿⣷⣾⣿⣬⢯⡿⣿⣿⣷⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⣘⢀⠀⢀⠠⠉⡟⢫⠿⣿⣿⣿⣿⣾⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⣧⡻⢿⠀⡇⣿⣿⣿⣿⣿⣿⣿⣄⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⣼⣷⠙⣿⣨⢀⡟⣿⣿⢹⣇⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠿⣿⣿⣿⣿⢴⡧⣿⣿⣈⣀⣤⠀⠀⠀⠀⠀⠀⠀⣦⠘⠀⠀⠀⠀⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣷⣿⣿⣿⣽⣿⢿⣛⣿⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣧⠘⠀⠀⠀⡀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠃⣿⠁⠀⠃⣿⣿⠿⣿⣿⠀⡀⢡⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢰⠀⠀⠀⡄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡷⠀⠀⡸⣿⣿⢰⡇⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡜⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⠀⡇⢸⡇⢸⠀⣿⢸⣿⣿⣿⣿⡿⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⡇⢧⡀⢀⡇⣿⢸⣿⣿⢸⣿⣿⢿⣌⢤⠲⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡹⢹⡀⢳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⣶⠀⡘⡄⠁⠏⡟⣿⠁⣿⣿⢹⣇⣿⣿⣿⢃⠀⠀⣀⣄⠧⠷⠾⠶⠻⠙⠉⠀⠀⠀⠀⠀⠀⠀⡅⣸⠀⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⠀⠃⢻⢸⡆⣿⣿⣿⡇⣿⡟⣿⣿⣿⣿⣿⣹⠈⠀⠀⡀⣤⡶⠛⠂⠐⡉⣬⢻⠘⠀⠀⠀⠀⠋⣿⢻⡾⣴⣦⠶⠒⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢺⠀⡿⣇⢸⠀⣿⣿⣼⡇⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠉⠋⠟⣶⣤⣠⣀⣀⣀⣀⣄⠦⠷⠛⡿⣿⣤⣀⠀⠀⢀⠀⠀⠀⣀⢦⠻⠈⠀⠀ ⠀⠀⣿⠀⠀⢸⠇⣼⡇⢸⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢿⠾⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢾⠙⠀ ⠀⠀⣿⠀⠀⣤⡟⢀⡏⢸⠀⣿⣿⣿⡏⣿⣿⣿⣿⣴⣁⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣏⠈ ⠀⠀⡇⠀⠀⡿⣿⠀⣿⢸⠀⣿⣿⣿⣿⣿⣿⣴⠀⠋⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢘⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⢰ ⠀⠀⡇⠘⠀⣇⣼⠀⣿⢸⠀⣿⣿⣿⣿⣾⢀⠁⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠇⠈⡄⢸⠀⡇⢸⠇⣿⢀⠇⣿⣿⣿⣼⠀⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⢠⠀⠂⠐⠀⠀⠀⠀⠀⠀⡿⠀ ⡀⢻⠀⢸⠀⡇⢸⡆⣸⠀⡿⣿⣿⣼⠐⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀ ⠀⡄⡼⢸⠀⡇⢸⡿⢹⡿⣿⣿⣿⢰⠀⠃⢸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⣿⡿⣴⠀ ⠀⠀⢸⢸⠀⡇⣿⣿⣿⣿⣼⢠⣠⠀⠀⡀⣽⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠁⠋⡴⢀⠀⠀⠀⠀⠀⠀⠁⠋⠖⡤⣤⣀⠀⠀⠀ ⠀⠀⣧⢻⠀⡇⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠖⣠⢀⠀⠀⠀⠀⠁⠋⠒⠴⣀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⢸⠀⡇⣿⣱⠀⠀⠀⠀⠀⠀⠀⠏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⠒⠑⠉⠉⠛⢛⠛⠚⠒⠒⠒⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠀⡇⣸⡁⠸⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠁⠀⠀⡀⣉⠛⠾⣠⣋⣶⣠⣴⢀⡄⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⡿⠁⡾⢀⠀⠀⠀⠀⠀⡿⠀⠋⠛⠛⠟⠴⣷⣿⣿⡿⣿⣠⠀⡾⣠⠀⠀⠀⠀⡀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠈⣿⣼⠀⠀⠀⠀⠀⠀⠇⢱⠟⣿⣿⣿⠻⠈⡝⣼⣦⣿⢠⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠤⢷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠟⣸⠀⠀⠀⠀⠀⠀⠁⠞⣴⣠⠁⠀⠀⣀⣦⡿⣿⠀⣧⠸⠁⣿⠿⠙⠁⠈⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣼⠀⠀⠀⠀⠀⠀⠀⡿⣯⠨⠀⡛⢿⠙⠀⠄⡑⣧⠘⡀⢸⡇⣿⣿⣿⣷⢻⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⢈⠀⠀⠀⠀⠀⠀⠋⢻⠀⠇⠚⢀⠀⠀⠀⠀⡄⣷⢸⠀⢠⡆⣿⣧⣷⢠⣇⢿⠈⠀⠀⠀⠀⠀⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠏⢴⢀⠀⠀⠀⠀⠀⠀⣿⣿⠩⡟⠀⠀⠀⠀⠀⠋⠙⡇⢸⠇⢸⠀⣿⡟⡇⠀⠀⣷⢿⠈⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⣸⠀⠀⠀⠀⠀⠀⠁⡿⣃⣟⣿⣿⠴⣁⠉⠛⡴⣠⣄⣿⢿⡀⢸⠀⣿⣿⣸⠀⠀⡀⣻⢠⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⡿⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣾⣠⠀⠛⣴⣷⡟⠿⠻⠙⡏⣿⠀⢸⠀⣿⢸⢸⠀⠀⠀⣆⢻⠈⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣰⠀⠀⠀⠀⠀⠀⠇⣿⣶⣿⢀⠏⡴⢁⠛⠛⣽⣿⢮⣿⣷⣾⠀⢀⠀⣿⢁⢠⠀⠀⠀⠀⣧⢹⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡔⠀⠀⠀⠀⠀⠀⠁⡿⣰⡟⢋⡿⢻⠟⣿⢿⣯⢶⣡⡾⢀⡟⢠⠀⠠⠀⣾⡟⠀⠀⠀⠀⠀⡇⣿⠘⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⣰⡇⣿⣡⡟⣿⢟⣾⣠⢀⠃⣾⠀⠇⢸⠀⠀⠀⡇⢹⣰⠀⠁⠋⠾⡤⣦⣽⣷⠻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠏⣽⠋⣼⢋⣿⣾⣤⢀⠀⠋⠟⣴⠀⠃⣸⠀⠀⠀⠀⡟⡟⠟⡦⣠⠀⠀⠀⠀⡀⠧⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⢟⣣⡽⣾⣠⠀⠀⠋⠿⣴⢠⠀⠋⣠⠀⠀⠀⠀⡟⣿⣴⣀⠀⠀⠀⠀⠁⠋⡟⣴⣠⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⣿⣿⠿⣻⠓⠒⠶⣶⣤⢀⠁⠛⡴⢀⠀⠁⠛⠋⣶⣠⠀⠀⠀⠀⠀⡒⣶⣤⢠⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡀⢳⠀⠀⠀⢦⠘⠀⠀⢧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⣳⠀⠀⠀⣆⠸⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣇⠹⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⣀⢤⠲⠙⠉⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⠀⠀⠀⡄⡹⢤⠳⠋⠚⠖⠤⣤⣤⣤⡤⣦⢷⠾⠧⠒⠒⠒⠔⠬⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠀⠀⠀⠋⡖⢶⡘⣧⠘⠀⠀⠀⠀⠀⠁⠞⣠⠀⡸⢀⠀⠁⡟⢿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⡄⢸⠁⡾⢀⠀⠀⠀⠀⣠⠀⠀⠀⠉⠞⣠⠀⠀⡏⠿⠿⡿⣿⣽⣋⠚⠴⠦⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⠀ ⠀⠀⠀⠀⠀⣿⡟⢀⠀⠀⠀⠀⠀⠋⠔⠤⣀⢀⠀⠀⠀⠏⣷⣿⣿⣼⡉⣉⠈⠀⠀⠀⠀⡀⣄⠳⠈⠀⠀⠀⠀⠃⢠⠀⠀ ⠀⠀⠀⠀⠀⣧⢰⠀⠀⠀⠁⠋⡾⢀⠀⠀⠁⠈⠀⠀⠟⣾⣠⣟⣶⣠⣀⢀⣀⣀⢤⠲⠙⠈⠀⠀⣄⠳⠈⠀⠋⣰⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠉⠛⠟⡶⣤⣀⠁⠚⠖⡤⣠⠀⠀⡟⣼⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢾⠴⠤⣤⣤⣇⣰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⠀⠀⠀⠃⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠃⣼⠀⠀⠀⠁⠛⡾ ⠀⠀⠀⠀⠀⡿⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⡼⠀⠀⠋⠿⣠⣠⠀ ⠀⠀⠀⠀⠀⣿⠘⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⢀⠃⡾⣧⢠⠀⠁⠋ ⠀⠀⠀⠀⠇⣽⠋⠛⡔⠳⠛⠉⠉⠊⠒⠒⠀⠀⠀⠀⡀⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠋⣴⠁⢹⠚⠴⣠⠀ ⠀⠀⠀⠀⡏⢤⣧⠘⠀⡆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢟⠙⠉⠀⠀⠀⠉⠉⠈⠀⠀⠀⠇⢱⠁⣿⠿⣩⢀⠁⠋⠖⠤ ⠀⠀⠀⠀⢼⠁⡿⢨⠀⠆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⢀⡀⣀⣤⣤⣦⠶⠶⡶⢶⠻⠙⡿⡀⡇⣹⠀⡀⣀⣀⠀⠀⠀ ⠀⠀⠀⠃⢳⣰⣿⢠⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣸⠃⢰⠀⠀⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⢻⡀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠀⡿⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠤⠤⠲⠛⠖⠤⡠⣀⠃⣿⣿⣷⢿⡛⠻⠉⠋⠘⠀⠀⠀ ⠀⠀⡇⢀⡄⡀⢸⠀⠁⠉⠀⡄⠸⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠁⠚⠒⠑⠉⠉⠀⠃⣼⡇⣦⠸⡀⣀⢄⣤⣦⢛⠈⠀⠀ ⠀⠀⡾⣤⠤⠒⣗⠈⠀⡀⣄⣷⢹⢛⠘⠀⠀⠀⣿⢀⠀⠁⠁⠜⢀⠀⠉⠋⠐⡀⣀⢤⣲⣿⢳⢎⠈⠀⠀⠁⠖⣠⡆⠿⠾ ⢰⠏⢀⠀⠀⠀⠀⢦⠛⠀⠀⡀⠀⣀⣀⣀⣄⣤⣿⠈⠋⣻⣰⠂⠤⣀⢀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⠻⡾⢀⠀⠋⣴⢀⠀ ⠄⢹⠉⠉⠉⠉⠊⠒⣴⢦⠑⠈⠀⠀⠀⠀⠁⡟⣱⣷⣿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠑⣆⣿⣿⢿⠿⣦⣾⠙⠀⠀ ⡄⣤⣤⣦⠶⠓⢍⠲⠈⠀⡀⣤⣶⠽⠦⠓⡿⣿⠀⡇⣿⢋⣠⠀⠀⠀⠀⠀⠀⠎⠃⡏⣿⣿⢻⣴⣿⣏⣷⣿⢹⣼⠁⣿⠋ ⠀⠀⠀⠀⠀⠀⡀⣄⠦⠓⠉⠉⠜⠠⠉⣟⣾⢳⠃⣰⡏⣾⠞⡯⢻⠙⠙⠐⡇⢿⠉⠚⣒⣿⢿⠾⣿⢿⡀⣿⣿⢿⡼⢿⢧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣲⣟⣙⠈⠀⠀⣼⠿⣿⣿⣿⣿⣿⣿⣿⠖⣿⣿⢿⠛⠈⣿⣸⣿⣿⣴⠿⣘⣿⣿⠞⡇⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⠻⠈⢀⡟⣼⡇⣿⣿⣿⣿⣿⠙⣹⡀⣷⣿⣤⣿⢸⡀⣿⠸⣯⢿⣳⣯⢸⠇⣿ ⠀⠀⠀⠒⠚⠓⠓⠛⠙⠉⠉⠈⠀⠀⠀⠀⡀⣿⢿⣿⢸⡆⣿⣿⢀⣧⣹⣦⣿⠈⡏⣾⠘⡀⢿⠀⡇⢹⣿⣟⠘⣷⢸⡟⡇ ⠀⠂⠒⠶⠶⠤⣀⣀⠀⠀⠀⡀⣀⣀⣄⠷⡹⣇⣦⣿⣿⠈⣴⣸⠀⡀⣧⠘⡄⣿⣿⠀⣦⠀⣇⠀⠇⣿⣿⢠⣄⡿⢻⣸⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⡿⠹⣇⣿⢽⡀⣦⠘⠀⠀⣧⠙⣸⣿⠀⠀⠀⡀⠋⡿⣾⢒⠓⠉⡏⣰⠟⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⢽⣶⣿⢿⠿⣝⠿⠒⠒⡟⣀⣇⠛⠛⠛⠛⣒⢴⠤⣤⣤⣤⣿⡿⣼⢁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣷⢾⣕⣷⢽⠤⠤⠤⠤⡦⠓⠚⣴⣧⣿⣓⠉⠉⠉⠉⠋⡶⣶⢲⠶⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⣄⠳⢿⣧⣯⠻⠛⠉⠈⠀⠁⠉⡟⣴⣷⣙⣛⣶⣤⢀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⠿⠘⠀⡉⣛⢛⠛⡛⢙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⠞⠶⠶⠻⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⣿⣄⣿⢿⡿⣶⣠⣀⠉⠉⠞⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⠀⠀⠀⣇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣙⣋⣿⣾⢠⠀⠏⡶⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡁⣿⢥⠾⡥⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣆⣿⢸⣄⢿⡟⣼⢁⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣸⠀⠀⣯⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⢳⠛⡴⣀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⣦⠿⠿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀⠀⡀⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣰⠀⡀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢉⠀⠀⠀⣄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣠⠀⠀⠀⠀⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⡀⡀⢣⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠀⠀⠀⠀⠀⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⠀⠀⠀⠀⠀⠀⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⡼⢀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⡀⣏⢳⠈⠀⠀⠀⠋⡷⠙⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢨⠀⠀⠀⠀⠀⠋⡿⢻⠈⣦⠙⠀⡏⣠⠀⣄⢦⠓⠉⠀⠀⠉⠛⠖⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢾⠒⠒⠖⠶⡠⢀⢀⠀⢦⠘⣷⠿⢸⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠙⠈⠀⠀⠀⠀⠀⠀⠀⣇⣽⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣟⠹⠀⠀⠀⠀⠉⠋⡶⣿⣸⣍⠮⠓⠈⠀⠀⠀⠀⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠒⠴⣤⣀⣀⣄⣤⣤⣤⣤⣶⢤⣷⣾⣴⣦⣶⠦⡛⠛⠛⠛⠛⠛⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠞⠴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠋⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⠉⠉⠀⠀⠃⠶⣿⢸⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⡿⣿⠞⣤⣿⠛⠖⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⠀⡞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡷⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⡟⣠⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣶⢸⠀⡟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢦⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡹⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡼⣠⠀⠀⣁⣦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⠦⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣴⣟⢿⠷⠙⠀⠀⡄⡗⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⠳⠛⠛⠛⠛⠚⠶⡶⢷⠻⠙⠉⠀⠀⠀⠀⠁⠉⠟⠿⣴⣠⢀⠟⣰⣿⠀⣄⠳⠘⠀⡀⣹⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠋⣘⣒⣙⣈⣀⣀⢁⠋⠚⠴⠠⠏⢀⠇⣿⢸⠀⠀⣄⠦⠀⣍⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢿⠹⠈⣀⢀⡤⣀⢀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⡀⣟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡳⣜⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠃⡾⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⠙⠀⠀⠁⠉⠀⠀⠋⠀⠉⠀⢉⠉⠞⡴⣀⣀⢤⣷⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠷⠿⣿⣿⡿⣿⡿⣿⣿⣾⣠⠀⠀⠀⠀⠃⡿⢿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠚⣿⣾⣶⢙⡏⣿⣋⢹⠈⠀⠆⢠⠀⠀⡧⣿⣌⣿⣿⢿⠻⠙⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⡿⣿⣿⣿⣿⣿⣿⣿⢃⠐⠀⠀⠁⠞⠧⠻⠿⡿⣿⣿⣿⣿⣿⠻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣷⣿⣿⣿⣿⣿⡿⠸⠁⡿⣿⢀⡁⣧⣿⣓⣌⢿⣿⣿⣿⣿⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⠟⣿⣷⣿⣦⣼⣿⢻⠈⣠⣄⠦⣯⣾⣷⠀⢧⣿⡏⣿⣿⣷⣿⢿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣮⣿⠹⡄⡀⣿⣟⣿⠿⣿⣿⢹⡇⠸⡏⣿⣿⣿⣼⣧⣿⣿⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣉⣿⣿⢿⠿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣴⣶⣶⣿⣿⣿⣾⣴⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣺⣟⣿⣿⣿⣿⣿⣾⣶⣖⣶⣶⣶⣶⣿⣌⣷⠹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣾⣿⢻⡏⣭⣤⣣⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⣇⠻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢶⣿⠉⣟⣿⠋⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⡿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⠄⠶⡶⣷⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣄ ⣿⣿⣿⣿⣿⣿⣿⣶⣻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣾⢀⠀⠀⡀⣄⣦⠲⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠟⡶⣠⠀⠀⠀⠁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⠷⠛⠉⠋⠞⠶⣶⣨⣀⣦⠲⠙⠉⠈⠀⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⠲⠛⠉⠀⠀⠀⠀⠀⠀⠀⠛⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣠⣀⠁⠋⡴⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠲⠙⠈⠀⣯⠻⠈⠀⠀⠀⠁⠉⠈⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠾⣰⠀⣇⠻⠞⡤⣀⣀⣆⢹⠀⠀⣇⠘⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠖⡤⣠⢀⠀⠀⠗⣿⢛⠛⠉⠀⠀⡄⣼⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢄⢤⠄⠾⡤⣤⣿⣀⣀⢄⠲⠑⠉⠉⠉⠉⠉⠉⠉⠀⠀⠁⠏⡴⣡⢉⠉⠋⠛⠛⠛⡟⣿⣿⣿⣿⣿⢻⠉⠋⢿⠈⠀⠀⡀⢳⠀⠀⠀⠀⠀⡀⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠇⢸⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀⠤⡿⢴⣤⣀⣀⢀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣦⢹⠀⠀⠀⡄⢹⠀⠀⠀⠀⠀⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣰⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀⡤⢻⠀⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣗⣾⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⣸⠀⠀⠀⠀⠀⠁⠟⡶⣿⣿⣿⣿⣿⣶⢙⠀⠀⠀⠀⠀⠁⣟⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡟⢸⠀⠀⠀⠀⠀⢧⠈⣆⠸⠀⠀⠀⠁⡼⢀⠀⠀⠀⠁⡾⣰⢀⠀⠀⣇⣿⣴⢀⠀⡄⢻⠀⠀⠀⠁⡞⣦⢿⠿⠸⠀⠀⢦⠀⠀⠀⠀⠀⠅ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣀⣷⠀⠀⠁⠉⠀⠀⢀⠀⡀⠀⠀⠀⡏⢀⠀⠀⠀⠁⡿⢶⠡⠛⠖⡤⣠⢀⠀⠀⠀⠀⣿⠚⠖⡤⢀⠀⠀⠀⡀⣦⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠈⠁⡿⣿⣿⣿⣿⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⡟⢶⠴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⡇⢹⡿⣿⣿⣿⣿⣾⢵⠀⠀⠐⡏⠀⠀⠀⠀⠇⢠⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠃⠟⣼⣶⣷⢻⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡿⣿⣿⢸⣀⣀⣀⣀⠀⡄⢸⠀⠀⣾⠀⠀⠀⠀⣀⠀⠊⡴⣀⢦⠷⠛⠚⠒⠖⠶⣶⣶⣿⢽⠿⢿⣽⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⣏⠀⠀⣿⠈⠀⠀⠀⠃⡿⢿⠛⠀⠟⡤⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣾⣤⢻⠉⠉⠉⠛⡿⣿⠀⠀⠀⣇⢿⠿⡿⣿⡜⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠋⣹⣅⣾⣷⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⠀⣿⣿⣿⣿⢿⣿⣾⠀⠀⠀⡿⣿⣿⣿⣿⣿⣯⢹⠛⠿⠱⠈⠀⠀⠀⠀⡏⣿⣏⣴⠀⡀⣧⣿⣿⣿⠀⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⣝⣿⣿⣿⣿⣾⢠⠀⠀⠀⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠉⠋⠘⠀⠀⠀⠀⠋⠟⣻⣿⣿⣿⣿⠟⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠤⠤⣠⠀⠀⠀⠀⠀⢷⡁⣿⣿⣤⣤⣤⣄⣇⢸⠇⣿⣿⠹⠋⠿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠐⠀⠀⠀⠀⡆⡿⣿⣿⠛⠛⠛⠛⡿⢻⡏⣟⡿⣽⣈⡞⠈⡄⣿⣿⣾⣶⣴⣤⣷⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣤⣤⢿⡜⠹⣷⣽⣿⠘⡀⣧⣶⣴⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣷⣸⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⢇⠘⡤⣤⠷⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠁⡟⣿⢨⠋⡼⣆⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢷⠉⣀⣄⣤⣤⣤⣦⣴⣥⣽⣉⣯⣟⣴⣆⣿⣿⢿⠘⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠦⠲⠛⠒⠒⠷⣠⣀⣀⣷⠹⠀⠀⡀⣦⣽⣿⠹⣆⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⡮⢿⠙⠀⡀⣦⠹⠀⠀⠀⡀⣦⣿⠸⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠉⠁⠀⠈⠁⠀⠁⠈⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣈⢦⠙⠀⣆⢻⠍⠉⠉⠉⡀⣄⢠⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⠀⠀⠀⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠑⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⡀⢣⠀⠀⠀⠀⠀⣄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⡤⣠⣀⢄⠤⠦⠓⠚⠒⠁⢫⠈⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠈⠀⣄⠻⠐⠀⠀⠀⠀⡀⢦⠈⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠀⡄⠸⠀⠀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀ ⠀⠃⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠬⠤⢧⠀⠀⠀⠀⠀⠀⠀⣷⠈⠀⠀⠀ ⠀⡇⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠋⠿⠿⠹⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡏⢻⠀⠀⠀ ⠀⡇⢸⠀⣀⠤⠒⠈⠀⡀⠄⠢⠒⠇⠈⠀⠀⠀⠀⠀⡇⣿⣿⣿⣾⠀⠀⠀⠀⠊⠠⠀⠀⠀⠀⠁⠉⠛⠞⡴⣀⡠⠀⠀⠀ ⠀⡇⢰⠀⠀⠀⠀⡀⣊⠴⠢⠛⠘⠉⢏⠈⠀⠀⠀⠀⠀⣠⣆⣤⢀⠀⠉⠉⡀⠀⠀⠋⠖⡤⣠⣿⣼⣡⠉⠟⢀⠀⠀⠀⠀ ⠀⡎⠀⠀⠀⠀⠀⡿⢉⠞⡠⠀⠀⠀⠀⡀⠤⠓⠉⠀⠀⠀⠉⠊⠴⣠⠀⠀⠇⣶⣈⠀⠀⠀⠄⣦⣿⣿⣿⣿⠁⠜⢀⠀⠀ ⠁⢸⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡎⢅⣿⠹⠀⠀⠀⠀⡀⣧⣿⣿⣿⢿⠀⠀⠀ ⡄⢀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠤⠠⡀⣆⠘⢿⣿⣞⢀⠀⠀⠀⠓⠛⠛⣟⣷⣿⣼⢻⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡤⠑⠈⠀⠀⠀⠏⣰⡇⠀⠀⠀⠀⣄⠳⣯⣮⠿⡙⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠘⠀⠀⠀⠀⠀⠀⠉⠖⣩⠀⠀⠀⣁⣮⢶⣴⣠⠀⡇⣴⣠⢀⠀⠀⡀⣧⢿⣿⣿⣿⣼⣷⡇⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠷⠿⠾⠤⣀⠒⠈⠀⢇⠲⠔⢉⠀⠀⠀⠀⠀⡇⢻⠘⠀⠀⠀⠀⡏⣿⣿⣀⣧⣿⡆⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⡀⠢⡗⠙⠈⣄⢼⠷⠙⠀⠀⡄⣿⢘⠀⠆⣷⢻⣻⡇⣿⠘⡁⣿⠟⣿⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡳⢉⢉⡟⣿⢹⠀⠀⣆⢿⡘⢿⠏⣿⣾⡏⣿⢿⣽⣿⣿⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣷⣨⢴⠀⠀⠀⡄⣦⣷⣿⣿⣿⣿⣿⣿⣯⣴⣠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣸⠁⠛⠿⠶⣤⣤⣤⣤⣤⢤⠦⠓⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠛⠒⠒⠒⠒⠒⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠙⠀⠀⠀⠀⠀⠀⠀⠉⠖⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⠻⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠈⠀⠀⠀⠟⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠻⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠋⠀⠀⠀⣄⠢⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠂⢱⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣷⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠁⡞⢀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣷⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣦⠘⠀⠀⠀⠀⠀⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢳⡏⠘⠀⠀⠀⠀⡀⢤⠲⠀⠂⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠢⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢦⠘⠀⠀⠀⠀⠀⠉⠀⡀⣀⢄⠲⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⠀⠀⠀⠀⣀⢀⠤⠦⠒⠙⠉⡉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣰⣀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⣤⠹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠻⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⠤⠳⠘⠀⠀⠀⠀⠀⠗⣾⢀⠀⠀⡀⢧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⡤⢀⠀⠁⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢼⠀⠀⠀⠀⠀⠀⠀⠄⠤⠦⠶⠦⠶⠶⣹⠀⠀⠁⠖⡴⢀⠀⠀⠀⠀⠀⠄⣷⠀⠀⠀⠀⠀⠀⠀⠉⠚⠒⠒⡶⣰⢶⠀⠀⠁⠀⡇⢸⠀⠀⠀⠀⠀ ⠟⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⠀⣀⢀⠠⠀⠀⠀⠀⠀⠀⠁⠛⡞⢷⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠋⠶⢶⠲⠒⠒⠐⠒⠒⠖⡠⢀⠀⣿⠀⠀⠀⠀⠀⠀ ⣤⡱⠀⠀⠀⣄⠤⠲⠓⠉⠀⠀⡀⢳⠀⠄⠷⠚⠒⠒⠐⠀⠀⠀⠀⣤⢠⠀⠀⣀⣤⠠⠀⠀⠀⠒⠒⠙⠉⠛⠒⠒⠗⢯⣿⣰⠒⠙⠉⠈⠀⠀⠉⠋⠚⠴⠣⣼⢀⠀⠀⠀⠀⠀⠀ ⠀⡋⢶⠀⠀⠀⠀⠀⠀⡀⣄⠶⠙⡈⢠⠈⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠖⡭⣯⣺⠖⣦⠿⠻⠓⠘⠐⠀⠃⣚⢶⣤⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⣽⠒⠙⠈⠀⠁⠉⠉⠉⠉⠉⠈⣀⠶⣟⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠖⠷⡭⣚⢶⡴⣠⣀⢀⠀⠀⠀⣄⢠⡄⠠⠤⠤⣀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⢳⠈⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⠦⡓⢾⠙⠀⠋⣿⢺⣖⣶⠲⠛⠈⠋⠚⠷⣯⣚⠔⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣼⢀⠀⠀⠀⠀⣄⣟⣾⣤⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣶⠲⠛⠚⠶⠠⠀⣊⣓⢶⠶⠶⠶⠲⡗⢀⠀⠀⠀⠀⠀⠀⣇⢹⠀⠀⠁⡾⣀⣇⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⣹⣦⠤⠠⠀⠀⡀⠀⠉⠚⠶⠲⡟⢹⠈⠀⠀⠀⠉⠟⣴⣀⣃⣀⣁⠺⠀⣇⡙⢋⠛⠽⠬⠀⠂⠙⠈⠀⠀⠀⠀⠀⠉⠛⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣄⣤⣤⠳⠛⡿⢿⠿⠶⡤⢀⠀⡀⣭⣾⣤⢀⠀⠀⠀⡄⠇⣻⠛⡾⣤⢀⠀⠀⠀⣄⠻⠛⠴⢤⣤⣤⣤⣸⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠲⠙⠈⠀⠀⠀⡟⢦⠛⠐⠀⠁⠛⡾⣴⣯⣰⠀⠀⠀⠁⠚⠖⠶⣳⡉⢦⠙⠀⠀⠀⣇⠸⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠒⡟⣿⢨⠀⡀⢿⠟⣴⢀⠋⡴⢀⠀⠀⠁⠏⣲⠒⠴⠶⠿⣿⠤⣀⢶⠙⠀⡆⢸⣷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⠀⠀⡇⣹⠀⠟⢠⠀⠀⠀⠀⣧⠀⠀⠀⠁⠊⣴⣦⠿⠀⠀⡄⢳⠀⢠⡄⣻⣤⠦⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⠀⠀⡀⣷⡿⢸⠀⠀⠀⠀⠀⠀⡧⠘⡄⠀⠁⠀⠀⢠⠀⠀⠀⡄⢳⠀⠀⡄⠹⠀⠀⣧⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⣿⣿⢀⠀⠀⠀⠀⠀⠁⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⠸⡄⠀⣆⠙⠀⠀⣇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⡿⠀⠀⠟⢿⣿⢸⠀⠀⠀⠀⠀⠀⠻⡇⠉⠉⠈⠀⠀⠄⠷⣾⣥⣛⣿⢿⠙⠀⠀⣿⠈⠀⡄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⠀⠀⣿⣿⠁⢈⠛⠈⠀⠀⠋⣿⣾⣿⢹⠏⣽⢹⠀⠀⠀⣀⣄⣤⠶⡗⣿⡿⠀⣇⢸⠀⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⠀⠀⣿⣠⣧⢿⣿⣿⠳⠳⡀⣿⣷⣿⣽⣟⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠀⡆⣿⠀⡏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢈⠀⠀⣇⠘⡆⣿⣷⡏⡹⣸⠸⣇⣿⣴⣽⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⣼⠏⣽⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⠀⠀⠀⣷⠏⣻⣿⠈⣧⢿⢷⠀⣆⠐⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⠀⠇⢃⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⡀⣶⣶⣝⢪⡀⣿⠃⠀⠀⠀⡀⢷⠛⠿⠻⠿⠚⢻⠆⠷⠰⡯⣰⠀⠀⣤⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠻⠉⠀⠀⠀⣄⣶⡽⣻⠀⠀⠀⠀⡀⣄⣠⣀⡟⣁⡀⣀⣀⣀⢀⠀⠉⠀⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣽⣤⠠⠀⠀⠀⠀⣀⣄⠳⠙⠈⠁⠉⠒⡥⢸⡀⠠⠀⠀⠁⠚⡴⢁⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⠀⠀⠀⠀⠀⠁⠈⠀⠀⣀⢀⠀⠀⡶⠀⠀⠀⠀⣤⢀⠁⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⠀⠁⠛⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠷⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⠴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⠶⠓⠒⠒⠛⠛⠛⠛⠚⠴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠀⠁⠈⠀⠈⠀⠀⠀⠀⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⣆⠘⠀⠀⠁⠛⠰⠀⠀⠀⠀⠋⠚⡶⣷⣿⣿⣿⣿⣿⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⢧⠈⠀⠀⠀⠀⠀⠁⠞⣴⢀⠀⠀⡀⣷⣿⣿⣿⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⡛⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⠀⡀⢷⠈⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⠤ ⠀⠃⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⠟⡴⣠⢀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⡄⢻⠈⠀⠁⣼⠀⠀⠀⠀⠀⠀⠉⠟⡶⣤⣀⠀⠀ ⠀⡆⠈⣄⠦⠙⡄⣷⣿⣬⣤⣀⣀⣀⢁⠋⠚⠄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⣆⣼⢧⡿⠛⠸⠁⠋⠛⠴⣤⣉⠚⠴⣤⢀⠀⠀ ⠀⠀⢷⠙⠀⡀⢤⡶⣘⢦⠓⠉⠈⠀⡠⢀⠁⠉⠛⠛⠞⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠠⣇⠉⣾⣠⢀⠉⠖⡤⢀⠀⠀⠀⠀⠀⠀ ⠉⠋⡚⣶⠶⠒⠒⠀⠁⠉⠛⡴⣥⣯⣴⣤⣀⣀⣀⠀⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡏⣰⠉⠚⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣗⠛⠉⠀⠀⠀⠉⠛⡴⣀⠁⠟⣴⠀⠀⡄⢤⠶⠙⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣸⡄⣀⠀⠀⠀⠀⠀⠀⠉⠚⡴⣻⢀⠀ ⠀⠀⣋⣙⣈⣀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠋⠐⢧⠊⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡇⢸⠀⠀⠂⠴⢡⠋⠞⡤⣀⠀⠀⡇⠀⠀ ⠀⠇⢀⠀⣆⠾⠒⡛⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠞⢠⠀⠀⢦⡜⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠀⠀⠇⢠⡀⢲⠋⠛⠿⡽⣪⢖⠤⠤⠤⠶⠙⡇⠀⠀ ⠀⡼⠀⠀⠀⠀⠀⡟⣤⠱⠈⠀⠀⠀⠀⠀⠀⠀⠏⣰⠀⠀⠀⠀⠀⣄⡳⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣸⠀⠀⠃⣸⠁⠋⠛⡿⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀ ⡆⣿⠿⠸⠀⠀⠀⣧⠈⠀⣄⠦⠓⠉⠀⠀⠉⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⠀⠁⠟⣶⣤⣋⡾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀ ⠀⣇⣿⢠⠀⢦⠙⡇⢠⠀⠀⠀⠀⡀⣀⢤⡶⠙⠀⠀⠀⠀⠀⠀⠀⠁⠛⠞⣶⣶⠶⠙⠈⠀⠀⠀⠀⠀⠀⠖⣠⢁⠋⠞⣠⢀⠃⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡾⢀⠀⠀ ⠇⡀⢀⠄⠀⠃⣄⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣳⠙⠀⠾⠶⡤⣀⠀⠀⠀⠁⠞⣤⣳⣦⣤⢶⡽⣭⣭⣬⣤⣦⣳⠈⠀⠇⣠⠀⠀⠀⠀⠀⠀⠁⠞⣤⣁⠐⠀⠃⣾⢀⠀⠀⠀ ⡀⢿⠘⠀⠀⡀⢣⠉⢿⠉⠉⠀⠀⠀⠂⠙⠀⠀⠀⠀⣤⢻⠀⠀⠀⠀⠀⠁⠟⣼⢀⠀⡀⣦⠷⠻⡈⣀⠀⣀⢦⠙⠀⡀⢦⡘⠀⠀⠀⠀⠀⠀⠀⣠⠁⠞⣠⠁⠎⣷⠀⠀⠀⠀⠀ ⠀⣇⢹⠀⠀⠀⠀⣀⠀⠀⣇⢿⠈⠀⠀⣇⠻⠉⠉⠋⡼⢀⠀⠁⠉⠛⡿⣿⣰⠀⠀⠀⠀⠀⠀⣄⢹⠀⠀⠀⠀⡀⢦⠙⠀⣄⢦⠳⠉⠀⠀⠀⠀⠁⣋⠛⠿⣠⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⣾⠳⠈⠃⠉⠉⠚⠲⡗⣼⣀⢤⠶⣠⠀⠀⡞⣀⣀⣀⣆⣘⣀⣆⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠀⠀⠀⠀⠀⡀⣄⠲⠒⠛⡉⣉⣉⣋⣒⣖⡤⣀⠀⠀⠀⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⣶⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠈⠀⠀⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠃⣿⣟⣯⣶⣶⠰⠀⠁⠋⠚⡶⢀⠀⠀⣀⣥⡈⣄⣦⣛⣖⣮⠶⠿⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠐⠄⠤⠤⠤⣨⣛⢉⠈⠀⠀⡀⣤⠦⠓⣛⣌⣦⣷⢴⢤⠤⠤ ⠀⠀⠀⠀⠀⠀⠁⡾⡀⣦⣶⣴⣤⣠⣧⣨⠀⠀⠀⠀⠉⠛⠿⣿⢿⠿⠿⠿⠙⠈⠀⡄⣿⣿⣿⣻⣛⣝⣩⣭⣿⣻⠉⠀⠀⠀⠀⢳⣆⣘⣀⣤⠷⠳⠙⠈⠀⠀⣀⣄⠠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⣿⣾⠮⠳⣌⠧⠙⠉⡟⠀⠀⠁⠏⡿⣿⣴⣀⣀⠀⠀⠀⠀⠀⡀⣄⠦⡓⣭⣿⢸⠀⡀⣀⣀⣄⣦⣿⣶⠳⠙⠈⡆⠘⢆⠙⠈⠀⢰⠀⣀⢦⠳⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⡞⣷⣿⢀⢳⠐⡀⢧⡙⣄⣷⠀⠏⡿⣝⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣵⠹⠀⡀⢹⠀⢧⠉⡄⣿⢿⠟⠻⠉⠀⠀⡀⢀⠀⠀⠂⠀⠀ ⠀⠋⡾⣤⠂⡟⣸⠀⡸⠀⠁⡽⣹⢤⠲⠗⣿⡿⣾⢢⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣌⠘⠀⡆⠸⠀⣧⣤⣦⣿⣿⣹⣷⢾⠻⠙⠀⠀⠀⠀⠀⠀ ⡀⡃⢿⠀⠆⢧⢠⠇⢀⠀⡻⡸⣿⠉⢸⡏⣿⣴⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣆⠸⠀⢧⠡⠀⢧⠈⠀⣄⣷⡜⣳⡝⣿⣿⠻⠙⠀⠀⠀ ⠐⡿⣸⠀⠃⣷⢿⣸⠀⡏⡼⠀⣧⣿⠠⣿⣰⠤⠲⠽⠤⣸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⢦⠙⠀⠀⠀⠀⠀⠀⠀⡀⠸⡄⠘⡀⡽⠱⠀⢆⠙⠀⠀⢇⡘⣷⣠⣀⣄⣤⢶⠙⠀ ⡯⣿⢸⠀⠠⠀⣿⢀⠃⢹⢰⠀⡄⣿⠋⢰⠀⠀⠀⡀⢦⢧⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠟⣿⢳⠀⠀⠀⠀⠀⠀⠀⡆⠘⡄⠱⣇⡹⠀⠀⡄⠳⠀⠀⣆⡈⢳⠋⠜⣠⠀⠀⣀ ⣿⣿⢻⠠⠀⠀⣽⠀⡎⡇⠀⠘⠀⣿⣠⠀⠀⠀⠀⠀⠀⡏⣿⠘⠉⠀⠀⠀⠉⠉⠋⠘⣿⣿⣿⣿⡿⢿⠈⠀⠀⠀⠀⠀⠀⣆⠈⡁⣧⣿⠻⠀⠀⡀⣄⠙⠀⣧⠘⣧⢹⠀⠀⠀⡀ ⣿⣶⢠⠁⠀⠀⣾⠀⢸⠀⠀⢻⡏⣰⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣻⣾⣣⢻⠀⠀⠀⠀⠀⠀⠀⢧⡘⠀⣄⣷⢳⠀⠀⠀⡀⢤⠙⢇⠈⣇⠀⠀⠀⠀ ⠀⠀⠀⣸⠇⠀⢠⠇⢀⢸⠁⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⢾⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⠄⡙⣦⢿⠙⠀⠀⠄⡑⣯⣿⡜⠀⠀⠀⠀ ⠀⠀⠀⢰⠀⠀⠀⡇⠁⢸⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⢀⣏⣷⣾⣿⣿⣿⣻⣶⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠹⡀⢦⣐⡄⢱⠀⠀⡀⣄⣦⢸⠀⠀⠀⠐ ⠀⠀⠀⠀⢀⠁⠀⡇⡀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢴⠶⠴⡤⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢿⠈⡄⠑⡄⠳⠈⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣵⠳⠈⠀⠀⣄⠙⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣼⠳⠉⠉⡉⢿⠙⠀⠀⠀⠀⠀ ⠀⠘⠀⠀⠀⠀⠘⠀⠀⢠⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⠤⣤⠻⣏⣿⣿⣴⣀⠳⠀⠀⠀⠀ ⠀⣇⠙⠉⠀⠀⢸⠀⠀⠀⡆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠚⠐⠋⠚⠽⠋⠟⡿⢶⣿⣿⢞⠐⠀⠀⢀⠀⠀⠀ ⠈⡄⣼⡶⠛⠉⢹⠀⠀⠀⠀⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡿⣤⣫⣿⣿⣾⣿⣯⣶⣤⣁⠋⡿⣴⣠⠀⠀⠁⠋⠒⠀⠀⠀ ⢳⠸⣇⠈⠀⣄⣧⠈⠀⠀⠀⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⣿⣿⣻⣟⣶⣿⣉⠛⠾⣶⣤⣋⠔⠤⠤⡥⣭⣋⠒⠓⠘⠀⠀ ⡇⢯⠈⣷⠻⠙⡄⢸⠘⠀⡇⣇⣿⢻⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠄⠷⠸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠶⣶⣤⣤⣭⣤⣠⣀⠀⠀⠀⠀⢲⠛⠖⠤⣗⣘⣆⠘⠎⢀⠀⠀ ⠉⣹⢳⡀⣾⣿⢿⣟⢸⠀⡇⡀⣿⣿⠉⡿⠀⠀⣷⠛⠟⠿⠿⠻⠗⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠳⠈⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⡄⢷⠈⡀⠹⠀⡈⢷⠈⣞⢀⠀⠉⠈ ⡀⣧⡜⠙⡆⢿⣷⣿⣏⠘⡇⢸⣆⣿⣿⣶⢿⠿⡿⣿⣾⣤⡤⣩⣏⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠹⡄⠸⠀⡄⣿⢠⠁⡼⢀⠀ ⠀⠀⢧⣆⠘⣆⡘⢻⣸⢳⡇⢸⠀⣧⣿⣦⣽⣤⣤⣤⣤⣤⣤⣀⡄⠻⠀⠀⠢⠙⠀⠀⠀⠀⠀⠀⠀⡄⢷⠙⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢻⣏⠀⠃⣰⠁⡼⡀⠐⠀ ⠘⠀⡀⢳⢧⠀⢃⡄⢻⡄⡜⣿⠀⠀⣧⠸⣄⠓⠀⠀⠀⠀⠀⠀⢱⡀⢳⠈⠈⡀⣄⠳⠛⠈⠀⠀⠀⠀⡀⣷⠫⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣯⢿⣠⠀⡟⠀⠀⠀⠈ ⣿⠘⠀⡀⣳⢷⡄⠘⣇⠸⢆⣟⢹⠀⠀⣧⠘⡀⢦⠙⠀⠀⠁⠉⡏⠘⡀⣧⠈⠀⠀⠀⣄⣧⠾⠙⠀⠀⠀⠀⢧⢮⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠏⢠⠀⠀⠀⢁ ⣧⣿⠹⠀⡀⡹⢳⠁⠀⢧⠀⣆⡞⠘⣀⢤⢷⠙⠈⡀⣦⣙⢀⠀⠀⣦⠈⠀⢆⠘⠀⠀⠀⠀⣀⡳⢮⠙⠀⠀⠀⣦⡌⠳⠀⠀⠀⠀⠀⠀⠀⠁⠋⠖⣤⢾⢠⠃⡸⠀⠀⠀⠀⠀⡀ ⡄⣶⣿⢿⠙⡀⣱⣧⠘⡀⢸⠀⣆⢯⠀⠀⠀⢱⣄⡶⠽⡚⢯⠈⠀⠀⢧⠈⠀⡄⠳⠀⠀⠀⠀⠀⡀⡣⢮⠙⠀⠀⢇⡈⢳⠈⠖⠶⠴⡤⣠⣀⠀⠁⡼⠀⠏⣠⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣤⣷⢿⡙⢣⢯⠈⡆⠘⠀⢦⢿⠀⠀⡀⢱⠀⠀⣄⢦⣕⠺⠙⠈⢣⠀⠀⡀⢦⠙⠁⠀⠀⠀⠀⣄⡳⢮⠙⠀⢧⠈⢧⠈⠀⠀⠀⠀⠀⠋⣰⠀⠞⢀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣤⢷⣿⢫⠀⢆⠈⠀⣆⢻⠀⠀⡀⠱⠀⠀⠀⠀⣄⡳⣌⣦⠻⠀⠁⠋⡀⠳⣌⠓⠈⠀⠀⠀⢄⡙⠢⠈⢳⠀⢧⠈⠀⠀⠁⡴⢀⠀⡏⢀⠀⠀⡄⢸⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⡀⣄⠹⠀⣦⠈⠀⣄⢿⠈⠀⡄⠳⠀⠀⠒⠓⠛⡚⠲⡽⣷⣃⠈⠀⡀⣦⠻⢌⠑⠀⠀⠂⡈⠣⡌⣷⢹⠀⢧⠁⠞⣠⠀⠀⡎⢠⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠑⠀⠀⠀⠐⠈⠀⠀⡄⢱⠀⢇⠘⠀⡀⢷⠘⠀⡀⢣⠈⠀⠀⠀⠀⠀⡀⢤⢷⢎⠙⠀⠀⡄⣷⠻⢌⠐⠀⣄⠰⢦⡈⣧⠘⠋⣰⠀⠀⠁⠞⢀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢄⠑⠈⠀⡀⢦⠑⠈⡄⠻⠀⣄⠘⠀⠀⣆⠘⠀⠀⢆⠙⠀⠀⠀⠀⠀⠀⠀⣆⡝⠳⠀⠀⠀⣆⣿⠓⠈⠀⠀⠀⡆⠙⣼⢀⠀⠀⠋⡰⠀⠀⠀⠀⠋⠟⡿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠲⠉⠀⠀⣀⢤⡖⠻⠈⡄⠱⠀⠀⡀⠢⠈⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⡄⠱⢆⠙⠀⠀⡀⣶⣭⠷⠛⠞⡴⣠⠀⠁⠛⡼⢛⠛⠻⠾⠿⣷⣵⢸⣏⣿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡀⣄⢦⠛⢈⣏⠻⡟⠭⢻⠉⠙⣉⠤⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⠁⠋⠖⣩⢛⠟⠴⣤⣀⣅⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀ ⠠⠀⠀⠀⠀⠀⠃⠛⠙⡏⣶⣶⠙⡝⢤⣤⣤⠤⡦⣶⣶⠶⠶⡶⣿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠾⠴⠤⢧⣿⣾⣶⣴⣤⣠⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀ ⣄⢿⠿⡿⣿⣽⢀⣧⣿⣽⠮⠛⣿⣼⠲⠙⠈⠀⠀⠀⠀⠀⠀⠁⠚⡀⣄⢦⡛⣉⣤⣦⣶⣿⣭⢉⠟⡽⣩⣈⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀ ⡄⢀⣀⣤⣼⢆⣻⣿⣿⣿⣸⣤⣦⣷⣾⡶⣿⠿⠙⠀⠀⠀⠁⡼⠀⠀⠀⠀⠁⣉⣙⣭⠿⠿⡲⣙⡿⣻⠛⠜⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠉⠀ ⠀⠄⠻⠀⢸⠀⣷⢧⡿⣿⣽⠳⠈⡀⢦⠘⠀⣦⣿⢻⠀⠃⣰⠀⠀⠀⠁⠍⣫⠛⠉⠉⠀⡀⣄⡶⣶⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⣱⠋⡴⢀⠉ ⠀⠀⣇⢿⢛⠀⠃⡀⣿⣿⣿⡻⣿⠹⠀⣿⢸⠀⡆⣿⠀⣀⠀⠀⠀⠁⡟⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠶⡤⣀⠀⠀⠀⠁⠾⣠ ⠀⠀⡇⡀⣦⢹⠀⠀⡂⣷⣿⣿⣿⣿⠿⣿⣿⠉⠀⣿⠀⠸⠀⠀⠋⣿⣿⣿⣤⣠⣀⠀⠀⠀⣀⣀⣀⢤⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⡿⣩⣀⢉⣭⢀⠀⠀⠀⠁⠋⠖⣠⠀⠀ ⠀⠀⠀⠀⠏⣿⢳⠙⠀⠀⣄⣿⣿⣿⣿⣿⣿⣽⢀⣿⠀⢧⠁⠏⣿⣿⣿⣤⡤⣋⣀⣀⣀⢄⠤⠤⠤⠲⠓⠛⠛⠛⠘⠀⠀⠀⠀⠀⠃⡟⣿⣘⢧⠙⣀⣀⢤⠧⣬⣾⠹⠀⠀⠀⠀ ⠀⠀⠀⠆⣿⣿⠰⣆⠉⡀⠹⡀⣿⣿⣿⣿⣿⣿⠀⣿⠀⡿⡟⣿⣾⣠⢀⠀⠀⡠⢄⠵⠿⠴⣤⣀⣋⣾⣶⢀⠀⠀⠋⣗⣿⣿⣸⣆⣿⡟⣿⢿⠀⣧⢻⠀⠀⠀⢆⣇⣇⠘⠀⠀⠀ ⠀⠀⠀⠀⣧⣿⢹⠛⠛⠛⡟⢿⡞⣷⣼⣾⣿⣰⠀⣤⡦⣿⣾⣠⠀⠀⠀⠀⠁⢡⢟⣰⢀⠀⠐⡤⣉⠚⠒⠴⡤⣤⢀⠘⡀⣷⣿⡿⣿⣿⣿⣿⠀⠳⣽⠸⠀⠀⠀⣿⡟⢿⠀⠀⠀ ⠀⠀⠀⠀⡀⣧⣿⣿⣼⣷⣿⣿⢻⡿⢋⣿⢹⠉⠉⠉⠉⣼⠀⠀⠀⠀⠀⠀⠀⡿⣸⠀⠀⠋⠔⣡⣿⣿⠈⠀⠀⠀⠀⠤⠲⠙⣏⣿⣿⣿⣿⣿⠘⡇⡏⣿⠀⠀⠁⣿⢸⣾⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⣿⣿⣿⡏⣽⣿⣿⣾⣿⣶⣿⣿⣾⣣⣷⢸⠀⠀⠀⠀⠉⠈⡇⣿⠃⠶⣠⠀⠁⡿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⣦⣿⣯⣿⣿⣿⢹⣿⣸⣿⢸⠁⡿⣴⡇⢰⠀⠀⠉ ⢿⠈⠀⠀⠀⠀⡄⣼⣿⣿⣿⣿⣿⢸⢹⠀⡏⣿⢠⡿⣼⠀⠀⠃⠕⡨⣀⠀⡆⣿⠛⠉⠛⠿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⡀⣤⣠⣧⣿⣤⣦⣿⣿⢿⡟⣼⠀⡴⠋⠚⡤⣤ ⣿⢿⠘⠀⠀⠀⠀⢿⣟⣿⣿⣿⢼⢘⣿⣤⣦⢠⡞⣿⢠⠁⠋⡾⣠⣀⠀⠀⠃⣶⣷⣿⣿⣿⣶⣴⣤⣩⣎⢲⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⣿⢹⠈⣧⣿⣿⣷⠐⠃⡾⣀⠀⠀⠀ ⣿⡀⣧⠹⠀⠀⠀⣦⣿⣿⣿⣿⢈⣿⢩⠘⠀⡏⣯⣾⠟⣷⣿⢀⠀⠀⠀⠀⠀⠸⠀⠀⣀⣄⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢢⠙⣇⣿⣿⣺⣆⣿⣿⣿⣿⣿⠛⣰⠀⠀⠀⠀⠀ ⣿⠈⡄⣿⠹⡄⠈⠀⠃⡆⣿⣿⢸⣠⣆⣸⠃⣷⣿⢿⢰⡟⣰⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡉⣿⣿⣿⢿⠿⣿⡿⣿⣿⡿⣿⢿⠘⠀⠀⠀⠀ ⣿⢸⠀⡆⣿⠹⠀⠀⠀⠀⣆⣿⢸⠇⠀⢿⡿⣼⡇⣿⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠛⠛⠛⠟⠿⣶⣶⣶⣤⣤⣧⣿⢀⠀⡖⣷⣿⣿⣿⣿⣿⢹⣿⡄⣿⠘⠀⠀⠀ ⣿⣿⠀⠀⣧⣿⠘⠂⠀⠀⠀⣧⣿⡌⠀⣧⣿⠀⡇⣿⢹⠋⠛⠛⠛⠟⠿⠿⠿⡿⣿⣿⣿⣶⣤⣷⣿⣠⣀⣀⠉⠋⠀⠀⠀⠀⡤⣤⠀⠀⠉⡏⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿⠀⠀⠀ ⡈⣷⢹⠀⠀⣷⣿⠫⠀⠀⠀⠀⣷⢹⠀⣿⣾⠀⡀⣿⣿⣿⣿⣶⣷⣿⣾⣠⣀⣐⠀⡇⣿⠀⠀⠀⣦⠐⠀⡇⣴⣀⠀⠁⠈⠀⠃⠿⠘⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⣿⠸⠸⠀ ⢉⠛⣞⢿⠙⡄⣿⢻⠀⢠⠀⠀⡄⣻⠀⣧⠸⠀⠃⣿⣾⢀⠀⠀⡀⣀⢀⠀⠏⠸⠀⡇⣿⠀⠀⠙⠀⠀⠀⠇⡾⢰⠀⡀⢠⠀⡇⣿⢻⠛⡟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⢹⢸⠀ ⣷⣘⠅⠀⢀⠘⡀⣿⢱⠀⠀⠀⠀⣇⠸⡇⣿⡿⣤⣤⢠⠀⠀⠀⠁⡿⢚⠃⡿⢰⠀⡆⣴⠀⠀⣿⠻⠈⠉⠉⠋⠛⠿⠿⣿⣿⣿⣽⣩⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡆⡇⣿⠈⠀ ⠀⠀⠤⠤⢁⠨⠂⡀⡰⠐⠃⠀⠀⡀⣿⡏⣶⣷⢳⠛⡟⠀⠀⠛⡬⢠⠀⣿⢁⠉⠉⠋⠛⠛⠿⣿⣿⣿⣷⣿⣴⣯⣿⢹⠁⣿⣿⣿⠈⢳⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠿⡿⣼⢸⠀ ⠶⠶⠶⠶⠷⣿⠻⣹⠈⠀⠀⠡⠱⠈⡆⣹⡀⠀⣿⣿⣿⠉⠋⡟⢿⠿⡿⣿⣿⣿⣾⣶⣿⣴⣠⣣⢘⠀⡇⣿⠀⣷⣿⣿⡽⣍⣟⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣤⣷⢛⠉⠓ ⣤⠲⠙⠉⠀⡀⣿⣿⣽⣤⠿⠿⡀⢷⠐⣧⠘⠇⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⢙⠉⠉⠛⣿⢼⠦⣿⢿⠷⡆⣿⣤⠩⣿⣿⣿⣶⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣷⣾⣤⣦⣶⢲ ⠀⢹⡀⣄⢷⠙⢀⣼⣮⢿⡘⣷⣿⣻⢿⡿⣿⡝⣷⣴⣧⣿⢿⠘⠈⣇⣿⣿⣟⠘⡄⠸⣿⢿⠀⣿⣿⡿⠀⣿⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣟⣿⣼⠀⠀⠀⠀⠀ ⠀⡄⠘⠀⡠⣷⢿⠛⡈⡀⢷⠉⣧⣿⣿⣿⣿⣿⡈⢆⡌⣷⣿⣿⣿⡻⣿⣿⣿⣿⠉⢹⣿⣿⢸⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⡟⣿⣠⠁⠈⠀⠀⠀⠀ ⠀⠀⡄⠳⡀⡠⣷⣿⢿⠿⠉⡈⠁⣏⣿⣿⣿⣿⢿⠀⠟⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⣳⠛⡿⣴⢫⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⠳⡀⣧⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣡⣉⠛⠿⡿⣱⣟⣴⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⠳⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣿⣿⣿⠿⣿⣿⣿⣾⣿⣲⡙⢎⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⢿⡟⣿⣾⣤⡟⣏⣿⠟⣿⣿⣿⣿⣿⣿⣿⣻⣴⣠⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣟⣻⣉⣍⣿⢻⣉⣿⠻⣿⠿⠻⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠖⣶⠶⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣻⠀⠀⣄⠷⠝⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣦⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣡⠋⠞⣴⣤⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠋⢶⠓⠉⠀⠀⡀⣀⢀⠀⠁⠉⠛⠛⠛⢟⠿⣿⣿⣯⠤⣧⢾⠓⡙⠈⠁⠛⠶⠶⠶⠶⠿⠿⠿⠻⠛⠛⠟⠿⠶⣤⣀⣤⠶⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠋⡠⢀⠀⠀⡀⣁⣋⣚⣴⣤⣀⣀⣀⣀⣀⣀⣄⣦⣷⣿⢿⡻⡿⠋⠛⡿⣿⣿⣾⣴⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⡈⣷⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⣿⣿⢶⠖⠲⠲⠒⠓⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢀⠀⠀⠀⠀⠀⠀⡀⣄⠶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⠙⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⢿⠻⠈⠀ ⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⠻ ⠀⠀⠀⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣾⢁⠈⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣶⣶⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⡟⢧⠀⠀⠀⠀⠀⠁⡞⣀⣞⣷⠀⠀⡀⣀⣥⣿⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣼⠀⠏⢠⡄⠙⠀⠀⠀⠁⡿⢀⡏⢠⡇⠀⠀⠀⠃⡾⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣸⠁⠟⣰⠀⠀⣿⠀⠀⠏⣴⣧⣿⣿⠿⣸⠀⠋⡾⣤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠲⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠟⣼⠤⠻⣾⢀⠀⠀⠀⣽⠋⡾⢠⠀⣿⣿⣿⣏⢿⡶⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀⣄⠲⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠛⠾⣸⣫⢟⣶⢀⠀⠀⠀⠀⠏⣿⣨⠀⠉⡟⣠⡇⣰⣧⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⣄⠻⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠿⡿⣶⣶⣲⣴⣤⣠⠀⠀⠀⠁⠋⠚⡴⣀⣿⠀⡟⣠⣟⠛⣼⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠏⢸⠀⣀⢦⠛⠈⠀⠀⠀⠀⠀⠀⠀⠁⡀⣿⠹⠀⠀⠀⠁⠉⠛⠼⣠⣀⢀⠉⠀⠀⡶⠏⣰⡟⣿⣿⢿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠋⠴⣀⣀⣄⠤⠓⡙⣁⢧⠻⠘⠀⠀⠀⠀⡆⠘⡀⣷⠻⠈⠀⡀⣇⣿⢿⠴⣤⣀⣀⣀⢧⠹⣿⡿⣿⣿⣿⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⣄⡦⢿⣟⠘⠀⠀⠀⠀⣄⠱⠀⣄⢷⠙⠀⡇⣼⢀⠀⠀⠀⠀⠁⠟⣾⣀⠋⡾⣏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠶⢾⡝⠑⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⠀⠀⠀⠀⠀⠀⢆⠙⠀⣄⣶⡿⠙⠉⠈⠁⠋⠞⣤⢁⢟⡾⣠⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣤⠶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠒⠁⠀⣀⣤⣤⣦⢒⠖⠤⣠⢁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⡆⢷⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⣤⢤⠶⠓⠛⠛⠛⠛⠞⡧⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠦⠓⠈⠀⠀⣿⢿⠛⠙⠀⠀⠀⠀⠋⠛⠶⠤⣤⢤⣤⢷⠘⠀⠀⠀⠀⠀⣾⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇⢸⠀⣿⣿⣴⠀⠀⣤⣠⣤⣦⢶⠙⠀⠀⠀⠀⠀⡀⣷⠀⠀⠀⠋⡾⢀⠁⠾⡶⢹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢲⠒⠐⢻⠈⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠘⠀⠀⠀⠀⡀⠀⠀⡿⣠⠀⠀⡜⢧⠒⠉⡈⣀⣤⢤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡷⢠⠀⠀⠀⡙⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀⣿⠁⠋⡜⢀⡄⠹⡀⣀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠀⠀⡀⣿⣿⣿⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠄⣿⣴⣯⢀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⡆⠸⣄⢷⠙⠀⡀⣻⣉⢦⠿⠛⠉⠉⡏⢀⠀⠀⠀⠀⠀⡟⣩⠞⢠⠀⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⠀⠀⠀⣆⠙⠀⣄⢿⠀⡟⣻⣛⣿⣶⣿⢷⣼⠀⠀⠀⠀⠀⠀⡾⣠⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⠀⠀⠀⣆⠙⠉⣏⠀⣷⡌⣿⣥⣷⣿⣴⠀⠀⠀⠀⠀⠀⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢳⠈⠀⠀⣷⡋⢠⠀⡅⢻⠀⠁⡉⢉⠉⠋⠛⠘⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠤⢤⠤⠒⡟⣿⠸⠃⡟⢺⣧⣿⣿⣀⢀⢄⡟⢸⠀⠀⡇⢉⠀⠀⠁⠉⠋⠛⠖⠻⠈⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⣾⠀⡆⣿⣿⠀⠀⠀⣧⠀⠀⠃⣼⡀⣀⣀⢀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢹⠁⢹⠋⡾⢀⡄⢸⠀⠀⡿⠁⠋⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⣨⣆⣧⠾⣧⣾⣿⣿⡿⣷⠾⣷⣿⣿⣴⣿⣷⡿⣻⣿⣯⣿⣝⣯⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣼⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢯⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣾⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣦⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣶⣠⡂⢿⠀⡀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣠⠀⠀⠀⡆⢿⠀⠀⣆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠐⠀⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⠀⠀⠀⡇⢸⡆⠹⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠈⠀⠀⠀⠀⠀⠀⡆⢻⠀⣆⡹⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢣⠀⠀⠳⠀⠀⠀⠀⣷⠈⠀⣄⡻⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠴ ⠀⡀⢳⠀⡀⠻⠀⠀⠀⡇⢸⠁⠀⡆⠘⢆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡠⢀⠀ ⠀⠀⡀⢳⠀⡄⠱⠀⠀⠀⢳⡟⠀⠀⣿⣄⡽⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⣀⠀⠀⠀⠀ ⠀⠀⠀⡀⢷⠛⡟⣻⠾⠶⡶⣿⠀⠀⡞⠻⡀⢦⢟⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣟⣿⣴⢀⠀⠃⣿⠀⠀⢹⣄⢷⠙⡄⠻⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⡇⣿⢠⠀⠀⠀⡏⡆⠹⠀⣄⢦⠛⣏⢻⡄⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠰⡇⢠⠀⠀⠀⠀⠀⠁⡜⢀ ⠀⠀⠀⠀⣧⣸⠀⠀⠀⠏⢿⠿⣷⠁⠀⠀⠀⣄⣷⢹⣆⣿⢻⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠏⣰⠀⠀⠀⠁⢻⠟⣼⠀⠀ ⠀⠀⠀⠀⡀⢷⠈⠁⡞⣧⣼⢀⡀⣳⢦⠑⠈⠀⠀⡀⢦⣝⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣼⠀⠁⠞⢠⢠⠀⠀⠀⡟⣿⣿⠋⠘⠀ ⠀⠀⠀⠀⠀⠀⣄⣷⢸⡏⢠⠀⠀⡄⠳⠈⣄⢦⠳⠛⠙⠀⣄⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣟⣿⠾⣤⠁⠘⠀⠀⠁⠛⣿⣿⣶⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣷⢸⠀⠀⠀⠀⠀⣀⣤⠲⠛⡙⣍⣤⢶⡿⣿⡿⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣡⣟⣿⢛⠟⡴⣠⠀⠀⠁⡾⣹⠀⠀⠁⡞⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠉⠉⠈⠀⠀⠀⠁⢸⠀⣀⢤⠿⠻⣙⣍⣦⣶⠳⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣶⣶⣤⣀⣀⣀⢀⠀⠀⠀⠁⡞⢋⡟⠹⠁⡾⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢸⠀⠀⠀⡇⢸⠀⠀⠀⣷⣿⣶⣿⣾⢽⠪⡐⣀⢤⠶⠒⠉⠉⠀⠀⠀⠀⠁⠉⠛⡿⢿⠿⠿⠿⠛⠛⠉⠉⠉⠚⠖⡷⣾⣠⠀⣇⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⡇⢀⠀⠋⠖⣤⠀⠀⡆⢸⠀⣄⠢⠐⠀⠀⠀⠀⡁⣿⣽⣤⣤⣠⣀⣛⣒⣒⣒⢒⠓⠙⠉⠉⠉⠋⠛⠖⣠⠀⠀⠁⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡶⠋⡴⢀⠀⠀⠀⠀⠀⡄⠳⠈⠀⠀⠀⠀⠀⠋⡿⣷⣿⢸⠀⠋⡴⢀⠀⠀⠀⠀⠀⡀⣤⠲⠙⠀⠀⠀⠀⠀⠁⡿⣴⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⢸⠀⠀⠁⠊⠖⠶⠶⠲⠓⣍⠯⠲⠑⠋⡿⣵⢀⣆⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠦⠲⠒⠖⡴⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⡆⢸⠀⠏⣠⠀⠀⠀⠀⠀⠀⠀⣀⣄⠿⣶⢾⡹⠐⠀⣇⣿⣀⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣼⠄⣾⠀⠧⠀⡇⢸⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠚⠴⣤⣦⢹⠀⠀⠀⠀⠀⠋⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢿⠈⠈⠀⡇⠀⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠛⡴⣀⠀⠀⠀⠀⣁⢯⠛⠛⠞⡦⣿⢻⢚⠖⠶⠟⠾⠶⠽⠬⠤⠶⠓⣏⣿⢹⠀⡇⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⣴⢀⠀⠀⠀⠀⡀⣀⣁⣉⣛⣛⣟⠿⣿⠀⠀⠀⠀⡟⠀⠀⠀⣀⢦⠙⠀⠀⣆⢿⠈⡇⢨⡇⣿⠀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠟⢠⠀⠀⠀⠆⣤⣤⣀⣀⣀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠠⡀⢦⠛⠀⣆⢻⡀⠀⡏⠈⠀⡀⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⢠⠀⠀⠀⠁⠉⡟⠻⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⠀⡀⢳⠀⡀⠀⠀⣧⢹⠀⣿⢸⠀⠀⡀⣷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡸⠀⠀⠁⠍⣾⣶⣤⣄⢀⣀⢀⠀⠀⠁⠚⠠⠇⠿⠨⠿⢠⠀⠀⠀⠀⠀⠀⡄⢳⠀⠀⠀⠀⣧⡿⣾⢠⠀⠀⠀⠀⣦⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⢸⠀⠃⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⡼⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠇⡈⣷⢠⠀⠀⠀⠀⠀⠀⡄⣇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⣤⠒⠓⠛⠉⠉⠉⠙⠀⠀⠃⢠⠀⠯⡟⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⢸⠀⠀⠀⠀⠟⠿⣾⣠⠀⠀⠀⡗⠟⣿⣠⢛⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢇⠀⠀⠀⡇⡾⣠⠀⠀⠀⠀⠟⣴⣀⠋⡔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⣴⠀⠀⠀⠀⠀⠀⠁⠚⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⣼⠀⠀⠀⠀⠁⠋⠖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠉⠁⠉⠚⠴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⣤⣠⣄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⣹⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀⡄⠦⠻⠉⡟⣻⠀⠀⠇⠀⠠⠀⠀⠀⡁⣉⢀⡀⢅⢿⣿⣻⠀⠀⠀⣅⢹⣈⣀⣄⣤⣤⠶⣟⠰⡀⢸⠀⡀⢧⠈⠀⠀⠀⠀⣸⠋⣧⣗⠀⠀⠀⠀⣄⠽⠱⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⡿⣿⣿⠀⠀⡀⣁⠞⣡⣈⣒⢴⠥⣟⣿⣾⣴⣠⣀⣀⣀⣀⣀⣀⣃⣀⣧⠤⠳⠛⡉⠀⠀⢿⡄⣿⢾⣧⠘⠀⠀⡏⠇⢸⡇⡼⠀⠀⠀⠀⠀⣇⠸⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⣿⣠⣇⠻⡘⢧⡈⢋⣴⠋⠟⡿⣾⣤⢉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣦⣷⣿⢿⣻⣯⠻⢈⢭⢹⠉⠞⢻⡏⢹⣼⢻⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠊⠀⠀⠀⠀ ⠀⠁⠞⣤⢀⠀⠀⠀⣧⠒⣀⢉⣄⣳⣤⣠⠀⠀⣆⢇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠴⠦⠛⡒⣶⣤⣤⣠⣀⢀⠀⠀⡇⢸⠀⠀⣄⣳⢇⠘⠀⠀⠀⡇⢰⠂⠠⠀⠀⠀⠀⠀⠀ ⠏⣾⠠⠀⠀⠀⠀⠀⠂⠁⢬⣷⠀⡄⢹⠀⠀⠀⠀⠀⣄⠑⠈⠀⠀⠀⠁⠉⠚⠴⣤⣀⠀⠀⡄⠱⠈⠀⠉⠉⠈⠀⠿⣰⡆⢸⠀⠀⠀⡀⢿⢹⠀⠀⠀⡾⠹⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⢀⠀⠀⠀⠀⠀⠀⠏⡿⢔⣤⠼⠠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠋⠞⠴⣠⢀⠀⠀⠀⠀⠀⢃⠘⠋⣛⣒⢴⠳⠛⡴⣇⠛⠉⣀⠦⠙⠚⠔⣏⣤⢷⠙⡟⢀⡄⠹⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠋⡿⣾⢠⠀⠀⠃⠞⣀⠀⠀⠀⠀⠀⠁⠖⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⣶⢒⠖⠶⡤⣀⢀⠀⡀⣄⣷⢿⠘⡀⢳⠀⣰⠀⠀⣄⢱⠀⠀⡄⠳⠀⠀⠀⠀⠀⠀ ⢻⠀⠀⠀⠃⡵⢟⣿⢹⠀⠁⠟⣠⠀⠀⠀⠀⠁⠟⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢼⠀⡀⢸⠀⠀⠀⠀⡀⢧⠈⠀⡀⣶⠿⠙⠈⠀⠀ ⡆⠸⠁⠾⢋⡿⣿⣿⣿⠏⣿⢰⠁⠉⠉⠋⠾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣉⢈⠉⠘⠀⠐⠀⠀⠉⠀⠀⠀⢻⠼⣯⣿⠀⠀⠀⠀⠀⠀⣄⠛⠉⠈⡀⣤⡻⣬⠤ ⠀⢸⡏⡿⣿⣿⣿⣿⣿⣿⣶⠤⣤⣥⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⢲⠒⠒⠓⠉⠈⠀⡀⢄⠁⡟⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⠀⠀⠀⣄⠳ ⠀⣅⣿⣿⣿⣿⣿⣴⣠⠀⠀⠀⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⠤⠦⣷⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠀⠀⠀⠀ ⠃⡿⣿⣿⣴⣠⠀⠉⠛⠴⢀⠋⣴⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⣶⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀ ⣿⣾⣠⠀⠁⠞⡵⣼⢀⠉⠞⢠⠋⢸⠀⠀⠀⠁⠋⠒⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⣾⢀⠁⠟⣾⠤⣨⢁⡟⣴⠀⠏⣿⠀⠀⠀⠀⡦⠈⠀⠂⣦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀ ⢸⠃⣠⢀⠀⣿⠀⠏⢰⠁⡞⣧⣽⠃⡾⠛⠈⠁⠋⠛⠛⠙⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⢸⡆⠘⠀⠀⣄⣠⣟⠃⡼⢀⡇⣛⣿⠿⡿⣿⣾⣠⢀⠀⠀⡀⣤⢦⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⠀ ⢸⠀⢁⠈⠀⠁⣾⢿⣿⣿⠛⣸⣿⢀⣶⣿⣿⢻⠈⠀⠀⠀⠀⠋⠚⠒⡒⣉⣮⢶⠶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠀⠋ ⣿⠈⡄⠻⠴⠀⣧⣿⣿⣿⣿⣿⣻⠀⠀⡀⣤⣷⣿⠻⠉⠟⣼⣾⣤⣤⣤⣤⣷⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠒⣶⣿⡿⣸ ⣿⢿⠙⠉⠋⠛⡿⣿⣿⣿⣿⣼⣷⢻⠈⠀⡄⢽⡲⣿⣿⣿⠿⢿⠿⠽⠭⠻⠙⣟⣿⠸⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠻⠚⠓⠙⠋⠛⠓⠈⠉⠀⣄⣱⣿⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⢰⡄⣿⣿⠙⠀⡆⠹⠀⣀⣀⣤⣤⣦⣶⣿⣿⣿⣿⣿⣷⣾⣿⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠟⣻⣒⣖⣗⠳⠈⠀⠀⠀⢀⠷⠻⠍⣿⣼⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⢸⡄⣿⢻⠉⣿⣿⣿⠹⠀⣿⠘⠀⠀⡀⠩⠤⠶⠒⠛⠙⡉⣈⣀⢥⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⠛⠻⠉⢧⣿⠸⠀⠀⠀⠀⣷⣿⣿⣿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⣇⣿⣿⣿⣽⣧⣿⢻⣯⢿⠈⠀⠀⣧⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣴⠀⠀⠀⡀⣦⣿⣿⣿⣿⡟⣿⠙⠋⠛⠟⡾⣵⣯⣟⣿ ⣿⣿⣿⣿⣿⣼⣷⣿⣿⠀⡀⣿⣿⡏⢿⡀⣧⣿⣿⣿⢻⠀⠀⡂⢹⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢠⠀⠀⠋⠱⡟⣿⣿⣹⣄⣤⣶⣷⣿⣿⣭⣠⣀⣃⣿⣿⣿ ⣷⣿⣿⣿⣿⣿⡄⣷⣿⢸⠀⡄⣿⣿⣿⠀⡀⣷⣿⢾⣗⢿⠛⠉⣿⣄⠦⠒⠉⠉⠁⠞⢀⠀⠀⠀⠀⠀⠀⠀⠏⣾⢀⠁⠟⣿⢟⣿⣿⣿⣼⠀⣀⢤⠠⠁⡟⣠⣀⢀⠏⣿⣾⣯⣿ ⡄⣿⣿⣿⣿⣿⠀⡄⣿⢸⠀⠀⣧⣿⣿⠀⠀⡀⣷⢸⡀⣿⣷⣿⣿⢻⠙⠀⠀⣀⣄⢠⠀⠀⠀⠀⠀⠀⠀⠟⣾⢁⠟⣿⣿⣿⣿⣾⣡⡾⠀⠀⠀⠀⠁⡿⣼⠀⠁⡿⣿⣡⡿⣿⣿ ⠀⣇⣸⣧⣿⣿⠀⠀⣇⢸⠀⠀⡀⣿⣿⢸⠀⠀⡄⣿⠀⣧⠈⣧⣷⣿⣿⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠁⡟⣾⠏⣿⣿⣿⣿⣿⣴⢀⡟⢦⠀⠀⠤⠧⡿⣿⢛⡿⣿⣼⢁⡿⣿⣿⣿ ⠹⡀⣷⠀⣧⣿⠀⠀⡇⢸⠁⠀⠻⣇⣿⢸⠀⠀⠀⣧⠈⡀⢸⡏⡇⠀⣄⣦⣿⣻⢿⠿⠻⠀⠀⠀⠃⣴⡟⡿⣿⣿⣻⣿⣴⢀⠀⡏⣼⠀⠉⠋⠟⣿⣿⣵⣿⣾⣠⠃⣿⣿⣿⣴⢋ ⡄⠳⡎⠰⠀⣷⢹⠀⣿⠀⡇⢸⣧⡈⣿⢸⠀⠀⠘⡇⢸⠀⢧⣿⡇⠀⠀⠀⡀⣄⣷⣮⣿⣽⠹⠏⣰⡏⣿⣿⣿⣿⣴⢀⠀⠁⡿⣿⣿⣿⣿⣿⣿⣣⢿⣿⣴⠀⠋⣿⣿⣾⣠⠏⣿ ⠘⡀⢧⠻⠀⡀⣿⠘⣿⠀⡇⢀⠀⢧⣏⢸⠀⠘⣇⠈⢠⠀⡇⣰⡇⠀⠀⠀⠀⠋⠴⢀⡁⣿⣿⢠⠏⣿⣿⣿⣴⢀⠀⠀⠁⡟⣿⣾⣵⣿⣿⣷⣿⣷⣿⣭⠬⠶⣷⣶⣠⠀⠇⣻⣿ ⡄⠰⡀⣦⠸⠀⡆⢹⣿⠈⡇⠀⠸⡀⣿⢸⣧⢀⠀⣿⡌⠀⡇⠘⡇⠀⠀⠃⡿⣼⠀⠏⣿⣿⢠⠇⣿⣾⢠⢀⠀⠀⠀⠁⡿⣿⢡⠟⣿⣴⢁⡾⢈⣦⠻⠄⣦⣷⣉⠀⠂⠁⡿⣿⣿ ⠀⠀⠀⠑⣇⠈⠀⣇⣿⢸⡀⠇⣷⠸⡆⢘⡇⠈⠻⡀⢇⠀⡟⢸⡿⠀⠟⣼⣟⢡⡿⣿⣿⢠⠁⡿⣴⠀⠀⠀⠀⠀⠋⣿⣿⢿⣿⣴⢀⠁⡾⢟⣦⠻⡈⣷⢮⠻⡈⣄⠷⣿⣿⣿⣿ ⠀⠀⠀⡄⢹⢿⠀⡄⣿⢻⠈⡇⡀⣷⠀⢸⡄⢸⣄⢰⠀⠇⣿⢻⣿⡟⣩⠟⢿⣿⣿⣿⣰⠋⣿⢩⠋⠛⠟⠷⣿⣿⣷⣿⣿⣾⣤⣠⣥⣾⠿⢲⠀⡀⣦⡙⣮⣿⣿⠻⠯⡿⣾⣤⠀ ⠀⠀⠀⠀⡆⡔⠠⠀⣿⣄⢳⡄⠀⡄⢺⢠⠀⢹⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣶⣶⣴⣩⢛⡿⣿⣿⣿⣿⣾⣠⠀⠀⠃⡴⡞⢠⠉⠛⠟⡿⣿⣿⣱⡟⣶⢸⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠋⡴⢁⠈⠀⠁⠀⠀⠀⠀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡾⢁⠞⡠⣀⣀⣀⠀⠠⠠⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⢧⣌⠶⠐⠉⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡿⠀⠁⠞⣬⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⢾⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠁⣴⠃⢰⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⢸⠄⠀⠀⠀⠀⠀⠀⠀⠊⡆⢪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠇⢫⣾⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⢸⠐⠀⠀⠀⠀⠀⠀⠁⡿⣿⢯⠘⠉⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠀⡏⠀⡟⣿⢠⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣼⢀⠀⡀⢧⣀⢿⠁⠛⠒⠖⠤⠂⡒⣛⢭⠰⠀⢀⠀⣿⣠⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⣵⣼⠀⠀⠀⠃⣼⠃⡾⣠⠀⠀⠀⠀⠀⠀⠀⣀⢧⠘⠀⡏⢠⠀⠀⠀⢻⠈⠀⠀⠀⠀⠀⠀⠀⠛⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⣽⣼⢀⠀⠀⠁⡼⠃⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣷⠻⣰⠀⠀⠀⠀⠀⣄⢤⠤⡤⣤⣤⣠⣄⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡶⡿⠀⠀⠀⠀⡾⢉⡽⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠞⠶⠲⠓⠍⠨⠁⠈⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡟⢠⠀⠀⠀⡇⢤⡏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣾⢀⠀⠀⠀⣀⣄⠳⢘⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣸⠀⠀⠀⠇⣸⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⢀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⡇⢀⠀⠀⠀⡏⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡾⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⡆⡿⢸⠀⠉⠚⠓⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣿⠈⠀⠀⠁⢸⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠇⣾⢁⣸⡀⢿⠈⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⡾⣠⠀⠀⣀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠈⠀⠀⡀⣿⢀⠀⠀⡏⢸⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⢰⠇⣾⢀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠇⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠘⠀⠀⠀⡞⠘⠀⠇⣷⢿⣹⠹⠘⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⢸⡼⠏⣾⢀⠀⠀⠀⠀⠀⠀⠀⡇⢿⢿⡷⢾⠀⠀⠀⠀⡇⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢸⠀⠀⠀⣦⢿⠀⡏⡷⣳⠛⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣻⣟⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡞⣁⣿⢀⢠⠀⠀⠀⡟⣰⢦⡳⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢿⠀⠀⠀⠀⡇⠿⣫⢠⡀⣸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡟⣸⠀⠀⠀⠀⠀⣼⠀⠀⠀⣄⠲⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⡃⣿⣰⠀⠇⣏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣋⡸⠇⣸⠀⠀⠀⠀⠀⡏⢀⠧⠘⠀⠀⠀⣾⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⡀⣆⢿⠈⠀⣀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⢨⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣾⣿⢋⣷⠀⠀⠀⠀⠀⠋⢠⠀⡁⣤⠦⠓⡉⠈⠁⠀⢄⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⣦⢶⠙⠀⡄⠹⠀⠀⠀⠀⠀⠀⠋⡿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠀⣞⣾⣻⠐⠀⠀⠀⠀⠋⣾⠀⠀⠀⠘⠀⠀⠀⣀⣤⣤⠹⠈⢆⠑⠈⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠠⡓⢯⠈⠀⠀⠋⡵⣧⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⡵⡼⢀⡟⠸⠀⠀⠁⡿⣿⣿⠀⠀⠀⢿⠀⠀⠀⠀⠟⣨⣃⣯⠛⠀⢄⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣬⣿⣠⣤⡷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠋⡟⢞⣠⠀⠀⡀⢧⠀⠀⡇⣿⣿⣿⠀⠀⠀⣸⠀⠀⠀⠀⡀⢆⠻⡄⣤⣿⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠿⣴⠀⠀⡀⣿⢿⠛⠉⠀⠀⠁⠚⡴⣄⢀⠀⠀⠁⠛⡟⣼⣀⣆⣿⣷⣿⣄⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⡀⢷⠛⢀⡤⢿⠙⠀⠁ ⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣼⠀⠀⠀⠀⣆⡽⣷⣿⣻⣬⢶⠬⠷⠼⠭⣤⣷⣮⠹⣆⡽⢹⠀⣇⡟⣿⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡄⢦⠙⣁⣏⠻⡇ ⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡯⢁⠀⠀⠀⠁⠀⣿⠸⣆⣽⣧⠻⡀⠄⣷⠻⠀⠀⢧⣿⠀⡆⡾⢸⡄⢷⣼⠃⠀⠀⠀⡄⠘⡇⠈⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⡄ ⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⣿⡏⢣⣽⠛⠟⢠⢧⠙⡀⢫⡄⣷⠻⠈⣄⢳⠀⠀⣿⢸⠀⢧⣇⠛⡏⢸⡴⠀⠀⠀⠀⢿⠀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇⣹⣼⡼⠏⣴⢀⠀⡇⣿⣮⣟⠻⠈⣄⣦⠻⠀⢧⠈⣇⢸⠀⡆⣿⣻⡏⢰⠀⠀⠀⠀⠁⢿⠈⠀⢇⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⢀⠀⠀⠀⠀⡆⢿⡙⣧⣿⠹⠀⡀⢦⠙⢿⡏⢿⠀⠀⢹⢻⣸⠀⠀⠀⠐⠀⡟⣧⢤⠲⠘⠀⡀⢣⠈⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣆⣾⢻⠀⠀⣄⣿⣿⣸⠃⢸⣿⣿⢨⠀⠀⠀⠉⠞⣷⣿⠀⠀⢳⠋⠙⠀⢻⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣜⢷⠈⡀⡍⣿⢸⣆⢸⣿⢸⣿⣿⣿⣸⣇⠈⠀⠏⡿⢿⡿⣹⢧⡙⣿⠈⠀⠀⠀⠀⠀⠀ ⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⣄⠳⣈⣇⢸⠀⢸⣿⢿⣿⣿⣿⢹⠙⣧⠈⣆⣶⣦⢴⡋⣿⣎⣿⢿⠀⠀⠀⠀⠀⠀ ⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⠳⣎⣿⢿⠈⡇⣿⣿⣿⣟⣷⣿⣞⠸⢿⠈⡀⣅⣈⢻⡍⣾⣶⣘⠀⠀⠀⠀⠀⠀ ⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⣷⡜⣷⢹⡌⣿⣿⢾⣿⠀⣀⣿⣿⣌⣦⠹⢦⣎⡿⣜⢹⠀⢀⠈⠀⠀⠀⠀⠀ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⢶⡀⣦⢿⣿⣿⢹⣿⠙⠈⢀⣄⣷⠿⣜⢳⢛⡉⢉⡌⢠⠸⠀⠀⠀⠀⠀⠀

⠀⡄⠻⠀⠀⠀⠀⣷⠙⠀⠂⠀⡇⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣄⡽⠀⠀⠀⠀⣆⠻⠀⠀⡀⣀⣦⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⠘⠀⠀⠀⠀⣄⢠⠀⠀⠀⠀⡀⣦⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢷⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢿⠘⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠻⠉⠈⠀⠀⠀⠂⠒⠑⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⣸⠀⠀⠀⠀⡇⣸⢶⠙⠈⠀⠀⠀⠋⠛⠟⠿⠿⣿⣿⢽⠿⠛⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣦⠻⡈⣧⡟⣼⣠⣀⠀⠀⠀⠀⠀⠀⠀⣁⣿⣴⢀⣿⣐⣀⣀⣀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠈⠀⠀⠁⠟⡴⣤⢦⠘⣆⢿⠈⠀⠀⠀⠀⠀⠀⠀⠟⣴⢀⠀⡟⢀⠀⠀⠁⠟⣿⣿⠚⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀ ⠀⠀⠀⠀⠀⠀⡄⢻⠀⠃⡾⢀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠁⠋⡴⢀⠀⠀⠇⢿⠿⠿⠿⣿⣾⣰⣉⠋⠞⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢶⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠙⣿⢠⠀⠀⠀⠀⠀⠀⠀⠁⠉⠚⠶⡴⣠⢀⠀⠀⠀⠁⣿⣿⣿⣿⣾⣴⣤⣠⣀⢀⠀⠀⠀⠀⣀⢦⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⠀⠀⠀⠀⠀⠀⠁⡿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠁⡭⣟⣿⣿⣿⣿⠟⠿⠲⠛⠛⠙⠈⠀⠀⠀⠀⠀⣄⢷⠙⠀⠀⠀⠀⠀⡎⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⣼⠀⠀⠀⠀⠀⠋⠟⣾⢠⠀⠀⠀⠁⠋⠐⠀⠀⠇⣿⣴⢀⠏⣴⣤⢀⠀⠀⠀⠀⠀⡀⣄⢤⠲⠙⠉⠀⠀⠀⣄⢷⠙⠀⠉⡞⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢹⠉⠋⠟⡿⣶⣤⣀⠀⠁⠛⠖⡴⣤⠀⠀⠀⠃⣿⣠⠀⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢾⠶⣶⣶⣴⣤⣇⣾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣾⣤⣠⣀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⣿⣽⠀⠛⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠟⢠⠀⠀⠀⠀⠀⠀⠋ ⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⠀⠀⡏⣴⠀⠀⠀⠀⠉⠟⡿⣴ ⠀⠀⠀⠀⠀⠀⠀⡿⣾⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠏⣼⠀⠀⠀⠋⡿⣸⡄⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢹⡄⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⠀⠀⠏⣿⣿⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⣿⣦⡀⡀⢧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⠀⡟⣴⢃⣰⠀⠁⠋⠶⡤ ⠀⠀⠀⠀⠀⠀⡇⢿⠛⣿⣾⢠⣗⣿⠿⠺⠒⠒⠤⠤⠤⠀⠀⠀⠀⠀⠀⡆⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠀⡿⣠⠁⣿⠚⡴⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢤⣦⢻⠈⠀⡄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⠀⡏⣿⡿⣨⢀⠀⠀⠁⠛⠔⣤ ⠀⠀⠀⠀⠀⠀⣹⠀⠃⣿⢠⠀⠀⡟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡟⣠⣀⣤⣦⣶⠷⡿⣿⣛⣛⣙⣏⠻⠉⠉⠀⣿⡄⠀⣿⣤⢀⣄⢦⡶⣴⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢸⠟⣷⢿⠘⠀⠀⣃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣄⣶⠿⣿⠀⠀⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⠟⣠⡟⣸⠀⠀⠀⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣠⠀⣾⠀⠀⠀⠀⠀⣧⢸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠈⣄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣼⠀⡏⢸⠀⠀⠀⠀⠀⡄⢻⢠⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⠀⠀⠀⠀⠂⠒⠓⠙⠉⠁⠉⠛⠚⠴⣤⣀⠟⣿⣾⣿⢿⠙⣆⠙⠀⠀⠁⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠏⣠⢻⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⡏⣴⣿⣧⣈⣄⣶⣶⣽⠿⡿⣾⢠⠀⠀⠀⠀ ⠀⠀⠀⠇⢉⠈⢀⠀⣧⠈⠀⠂⠓⠙⠉⡁⣾⠁⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠁⠛⠴⡤⠤⠶⠶⠲⠛⠉⠏⣽⠁⣿⡄⢻⠀⠀⠀⠀⡀⣀⣦⠿⠻⠈⠀⠀ ⠀⠘⠀⡾⣤⣤⢤⠲⡓⢻⠀⠀⠀⡀⣄⣿⢹⠋⠛⠀⠀⠀⠀⠀⣿⢰⠀⠀⠁⠀⠋⣴⢀⠀⠀⠉⠋⠘⠀⠀⣀⣤⡶⡟⣾⠻⡌⠹⠀⠀⠀⠀⠛⡴⣠⡀⢷⠿⠾ ⠃⢠⠇⢠⠀⠀⠀⠀⠀⡅⢻⠁⠈⠀⠀⠄⣠⣄⣤⣤⠤⠤⠷⡦⣿⠈⠀⠃⣽⡿⢠⠋⠚⡤⣠⢀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⠻⠉⠟⣴⢀⠀⠁⡿⣴⢀⠀ ⡆⠉⣼⠀⠀⠀⠀⠀⠀⠀⡄⢯⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢿⠟⣻⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣷⢙⠉⠉⠟⣿⢀⠀⠀⠀ ⠀⡅⢛⠛⠛⠚⠒⠶⠷⠤⣠⣀⣀⣤⠿⠙⠉⠈⠀⠀⠀⠀⠟⣿⢦⣄⣿⣿⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠭⠭⠳⡉⣿⣿⣿⣿⣿⣹⣇⣹⢾⠁⠈⡀ ⠀⡄⣀⣄⣤⣶⠷⠻⠉⡄⠳⠈⠀⠀⡀⣄⣦⣿⢬⠦⠷⡿⣽⣿⠀⠄⣿⣿⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⠳⡏⣷⣿⣿⠿⣼⣇⣻⣧⣷⣿⣿⡋⣼⠀⡟⢻⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢦⠳⠙⠈⠀⠀⠋⠒⢀⠀⠭⣿⣿⣹⠀⡟⣀⣿⣿⠁⠚⠽⣉⠀⠁⠁⠀⠇⣿⠘⠀⣉⣭⣯⣿⢻⠛⡟⣿⠻⡀⣿⣿⣿⢻⡿⣷⣼⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⣛⢬⠳⠿⣤⣠⣀⠀⡀⠛⢹⡟⣿⢻⣿⡿⣿⣿⣿⣿⣸⠁⡟⣿⣿⣸⢀⠀⡇⣿⣾⣿⣿⣿⣷⠉⣧⣿⣿⣿⢹⡌⢳⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⣷⢿⠙⠀⠀⠀⣼⣧⣿⣾⣿⣿⣿⣿⣿⣿⣿⣼⣇⣿⣿⣿⣿⢿⠛⣿⣿⢸⣶⣿⣼⡀⣿⡿⣿⣿⣿⣿⢠⡇⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⢷⠻⠈⢀⡏⣿⢠⣿⣿⣿⣿⣿⣿⣾⢻⡏⣹⠀⣆⣿⢿⣰⣧⣿⢸⠀⣧⣿⠀⣯⣿⣾⡿⣿⣼⠀⡟⡿ ⠀⠀⠀⠀⠃⠛⠛⠛⠛⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠿⣟⣿⠀⡇⣿⣿⣼⢀⣧⣽⣦⣿⣿⠸⠀⣿⣿⠹⠀⣦⢻⠀⠀⣿⠀⣿⣏⢹⡀⣿⢸⠁⣿⡇ ⠀⠀⠀⠀⠁⡋⢛⡏⠺⣴⣤⣤⣤⣤⣤⢤⠥⠲⠒⠓⠛⠛⠖⣷⣿⣿⣿⠸⠀⣿⣿⢰⠀⡀⣿⢸⡀⣧⢻⡟⣿⣐⣷⠀⠀⣿⠀⠀⣯⡟⣻⣼⣤⢳⡟⢸⡏⢸⡇ ⠀⠀⡤⣠⣀⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡟⠘⡇⡀⣧⣿⢿⠐⣧⣷⠈⠀⠀⡄⣷⠘⠀⣇⣿⣼⠀⡄⠀⠀⡇⠀⠀⣿⣿⣼⠀⠀⠀⣷⣿⣾⢁⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⡟⢻⡀⣿⣿⢹⠀⡀⢧⠘⠀⠀⡀⣧⠹⡏⣇⣿⠀⠀⠀⠀⠀⠉⡿⣿⣾⠒⠒⠙⠉⡟⣼⠃⡿⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⢿⡷⣿⣿⣿⠿⠻⣯⠿⠛⠛⠙⣟⣠⣀⣿⠋⠉⠉⠉⠉⣻⣞⢶⠶⠤⠤⠤⣤⣿⢿⣿⣴⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⠻⡌⣿⣿⣻⣛⣉⣉⠉⠉⠉⣯⠸⠀⡅⣿⣿⣿⣽⣤⢀⠀⠀⠀⠀⠀⠃⡟⣿⣼⣋⠉⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣜⣷⣝⢦⣝⣿⠻⠉⠀⠀⠀⠀⡀⣤⠤⣠⢀⡁⣿⣿⣿⠿⠛⠛⠛⠛⡾⣠⣀⣤⣤⣠⣀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠙⣄⢶⣙⣘⣙⣮⢿⠻⠛⠉⠈⠀⠀⠁⠉⠟⣶⣠⣷⠻⠛⠖⡶⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⣀⣤⢤⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠁⡈⣀⣀⣁⣋⣙⠙⡛⡾⠉⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣹⠛⠞⡴⣤⢀⡿⣿⣶⣴⣠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠹⠀⠋⠛⠿⠿⠻⠈⠁⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠶⣤⣠⢀⠀⠀⠉⣭⣩⣿⠿⠿⠻⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡿⣶⣀⣀⣄⣄⣤⣭⣀⣤⣦⣶⣿⣬⣦⠷⠻⠟⠿⠿⠿⡭⣩⢈⠁⠉⠟⠿⡶⣶⣤⣤⣤⣆⣿⣿⣼⣠⣷⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⡀⣤⠶⡈⣄⣷⣻⣀⡋⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⡀⠀⡀⣷⢸⠛⡿⣾⣤⠶⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⢿⣿⣼⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠋⠰⠀⠁⡿⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠟⣠⠀⠀⡿⢠⠀ ⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠃⣾⢠⠀⠀⡟⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⠀⠀⠀⠀⠀⠟⣰⠀⠀⠋⡾⣤⠀⠀⠀ ⠈⠀⠀⠃⠈⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⠀⠀⠋⡾⢠⠀⠋⡟⣨⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣿⠿⠛⠈⠀⡄⢸⠀⠀⠀⠀⣇⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠙⠀⡟⣷⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣼⢀⠀⠀⠋⡾⣠⠋⠟⡿⣿⣿⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣀⣄⢳⠘⣇⠘⠀⠀⠀⠀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠷⣼⡀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣼⠀⠀⠋⡼⣠⠋⡿⣴⢀⡀⣧⣿⢠⠀⠀⠀⠀⠀ ⠀⠁⠁⠈⠈⠀⠀⠉⠋⣿⡿⣿⠘⠀⠀⠀⡀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⢱⠀⣆⢿⠙⠀⠀⠀⠀⠀⠉⡿⣴⣀⠀⠋⡾⣠⠋⡿⣶⢀⠉⠉⠉⠈⣇⢻⠀⠀⠀⠀⠀ ⠛⣟⡿⣿⣿⣿⣿⣾⣿⣿⡈⣷⣿⠻⠉⠉⠞⣤⢦⠹⠙⠀⠀⠀⠀⠀⠁⠋⠖⡤⢀⢀⡄⠙⠈⡀⣄⢶⠲⠛⠛⠿⣴⢁⠋⠿⡶⣡⠞⡤⣏⣠⠏⣿⣿⣿⣿⣿⡿⣿⠘⠀⠀⠀⠀ ⣎⣷⣿⣿⣿⣿⣿⢀⣀⣤⣶⠿⡛⣴⣺⣀⠀⠀⠀⡀⣄⢤⠻⠛⠛⠈⠀⠀⠀⠀⠀⠀⣄⣀⣄⣶⠷⠋⠟⡿⣯⣛⠴⣤⣤⢋⠞⣠⠀⡇⢉⠀⣷⡿⣼⣷⣟⣤⣿⣿⢹⠀⠀⠀⠀ ⢼⡇⣿⣿⣿⣿⣰⠀⠀⠀⠀⡀⣦⡻⣀⣿⢶⠻⠛⠉⠉⠛⠀⣀⣦⣿⣿⠹⠈⠀⠀⠀⠀⠀⠁⡿⣸⣄⣤⣧⣻⠋⠟⣤⣀⣄⠳⠘⠀⠀⠀⢤⠻⣶⣿⢿⡘⢦⣝⣦⣻⠸⠀⠀⠀ ⣶⡿⣿⣿⢀⣿⠀⠀⠀⠃⠈⠀⠇⣼⡆⣠⠀⠀⡀⣀⣄⣶⣿⣿⠙⣟⣿⣾⣷⢿⠻⠑⠀⠀⡟⣿⠀⠀⠀⡄⣿⣭⢉⠉⠀⠀⠀⡀⣄⠲⠀⠀⡀⣤⣦⣶⣷⠘⠀⠘⡀⢠⣄⠠⠀ ⠀⠁⣷⣿⠀⣿⠀⠀⠀⠀⣇⠿⣻⢀⠀⠷⠻⠙⠋⠛⠛⡿⣿⣽⢻⣿⣼⢤⡣⣿⣿⠀⠀⠀⣿⣿⠘⠀⠀⠀⣄⣿⣀⣀⢦⠹⠀⠀⠋⠾⣤⢀⠀⠀⠀⠀⡂⣿⡿⢻⠉⠀⠀⠀⠀ ⠀⡎⠸⣧⣿⢠⠀⠀⠁⠋⡿⣴⣹⠛⡿⣿⣿⣿⣿⣶⣶⣿⣿⢻⣉⣿⢸⠀⠀⣧⣿⠻⠀⠀⣧⣿⢸⠀⠀⠀⠀⡄⠹⠀⠀⡄⢻⡼⣠⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⢿⠛⠀⠀ ⠀⠀⣷⠘⣬⢢⠛⠿⣾⣥⢛⠛⠿⣿⣾⢀⣿⢸⠀⠀⠀⠀⣧⣿⣿⣼⢀⠀⠀⡀⣠⣦⠹⠀⠀⢳⣇⠀⠀⠀⠀⠀⣷⠀⠀⠀⡟⣿⠿⠛⠛⠿⠿⣾⣶⣶⣿⣿⣿⣿⢿⡈⣧⢻⠈ ⠀⠀⢿⢽⣿⠿⡿⠿⣿⣿⣿⣿⣿⣿⢀⠀⣧⢸⠀⠀⠀⠀⡄⣿⣿⣿⠈⠀⠀⡆⠸⠀⣆⠐⠀⡇⠸⠀⠀⠀⠀⠀⡄⠹⠀⠏⣿⣿⣶⣴⣠⣀⢀⠀⠀⠀⠀⣇⣿⣝⣿⣿⠀⣆⣿ ⠀⠀⣴⣤⣤⣶⣤⣶⣶⣶⣤⣤⣾⣿⠺⠀⡀⢷⠀⠀⠀⠀⠀⡆⣿⣽⢷⠙⠀⠇⢻⠈⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⡄⡷⣼⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⡄⣷⣹⣷⢻⠈⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢻⣬⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⠛⣈⢧⡘⣦⢿⠈⠀⠀⡄⢸⠀⠀⠁⠀⠀⠀⠀⡅⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⢠⠀⠀⣷⠻⣿⢻⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢐⠀⠉⠀⠀⠀⠃⣿⠿⠙⠀⣇⢸⣇⢻⠀⠀⣧⣧⣽⠳⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠋⠛⠿⣿⢨⠀⠀⠀⠀⣧⣿⣼⣷ ⠈⠀⠏⠿⠿⠿⡿⣿⣿⢿⣿⣿⣿⠀⠄⠻⠀⠀⠀⡀⢷⠙⣀⣦⣿⢿⠸⣷⢻⠐⠀⠀⣀⣦⠙⠀⡇⠹⠀⠀⠀⠀⠀⠀⡌⢃⠀⠀⠁⠁⠟⡿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⣦⢿⠟ ⠀⠀⣆⣿⣿⣿⣿⣿⣾⣶⣧⣿⣰⠀⠀⣿⠸⠀⠀⠀⡀⣦⢿⠨⡀⢷⢙⡆⣸⠀⠀⠀⠄⠀⣄⢹⡇⣼⠀⠀⠀⠀⠀⡇⢠⡇⠁⠟⣿⡾⣦⣿⣿⣿⡝⣷⣿⢿⠈⠀⠀⠀⠀⣆⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⣴⣠⠀⠀⠀⣿⣿⠈⠀⠀⠀⠀⣄⣷⠽⠀⣆⢿⡙⠀⠀⠀⠀⠀⠀⡄⣧⢸⠀⠀⠀⠀⠋⣰⠃⡿⣿⣽⣋⠯⠛⡟⣿⣿⣿⡙⣷⣿⣿⠈⠀⠀⠀⠀⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⣿⡰⣦⣿⢦⠀⠀⠀⠀⣿⣸⠀⡆⣤⢻⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠏⣠⠋⡿⣴⢀⣀⣀⣀⠀⠀⣧⣿⣿⣿⣿⣷⣿⢿⠈⠀⠀⠀⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡿⣧⠃⣿⡿⢻⠘⠀⠀⠀⣦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣸⣏⣿⡿⢛⠟⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⢿⣸⣷⣿⣿⠈⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠖⠶⠻⡏⣤⣀⢀⣀⣤⣿⣿⠹⠄⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⡿⣿⣿⣿⣿⣿⣷⢸⣆⢸⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⢻⡌⣿⣿⢿⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⢉⠂⠟⠻⠿⣤⣄⣿⣿⠻⠉⠀⡄⢋⠛⠛⠛⠛⠛⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⡼⣿⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⢹⡟⣿⣿⢿⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣰⠀⡟⣿⣿⠈⠀⣄⣿⣿⣿⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣴⠇⣼⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⢻⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢿⣿⣿⣿⡿⢻⠈⠀⡇⣿⢸⠆⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⢸⣿⣿⣿⣿⢋⠞⣶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣽⢲ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⡿⣿⢹⠈⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠟⡇⣿⣿⣿⣿⡛⣿⠿⠾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣎⣴⣥⢋⡟⣾⣤⣤⢤⣤⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣷⣿⣿⣿⣿⣿⣿⢻⣟⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⠟⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣻⣉⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡛⣽⣭⣶⣷⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⡄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣶⣶⣿⣿⣿⣿⣿⣿⣾⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣷ ⠁⠋⠙⠁⠉⠀⠈⠁⡐⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃⣿⣿⠀⠀⠀⡿⢧⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣼⣯⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢻⣿⣿⣿⠀⠀⡟⣼⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠻⠈⠉⠀⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⠀⠏⣿⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⠀⠀⠀⠀⠀⡇⡀⢿⡀⢹⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⣍⣿⠙⣿⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣆⠙⠉⠉⠉⠈⡀⢸⣇⢿⣧⣿⠀⠀⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⣿⣿⢀⡟⣿⣿⣿⣿⣿⣇⣿⣇⢠⠀⠀⠀⠁⠉⠒⠒⠴⠤⠤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣧⠸⢹⡿⣿⣿⢰⠀⠋⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡼⣠⣿⣿⢸⠏⣿⣿⣿⣿⣿⢹⣿⣾⡟⠀⠁⠚⡤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣽⣿⣿⣿⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠟⣴⣀⣀⣯⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⢻⢻⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠤⠲⠙⠀⠀⠀⠀⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠞⣤⢉⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠛⠿⣿⣴⣷⠟⣿⢿⡘⢷⠈⠀⠀⣿⣾⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⣿⣴⢦⡴⢋⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⢣⠙⠘⠀⠀⠀⠀⠀⡀⣧⣀⣷⣿⣿⠊⠀⡄⢢⡒⣷⡇⢸⠀⡇⣷⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀ ⢠⠀⠋⡿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⠤⠀⠀⠉⠉⠚⠀⡀⢷⡈⣦⣿⢿⠙⠀⠐⠉⡇⣼⠀⠃⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣧⣟⢿⣷⢥⠚⠴⣠⣀⢀⠀⠀⠀⠀⣄⠳⡈⣄⣶⣿⠿⡿⣾⠀⠃⣸⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠏⣷⣿⡟⡗⢏⠘⠀⡀⢀⠀⠀⠀⠀⠀⠀⣀⢦⠲⠙⣯⣾⢀⠁⡾⠀⠀⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠃⣿⢿⠙⣷⡞⣿⣿⡼⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠀⡇⢰⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠘⠀⣹⢤⡒⣽⣭⣯⣾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣇⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⢸⠀⡇⠘⠁⠋⣖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠢⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡄⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠄⣤⠤⡤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡟⣿⣟⠿⠼⢶⢨⠀⠀⠀⠇⠷⠐⠀⡏⢹⠀⠀⠀⡇⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣸⣷⣾⢰⢿⠏⣛⢝⠉⠀⠀⡄⡦⢀⠏⢡⡟⠹⠀⠀⠀⣦⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⢰⡀⢦⢹⣿⣄⣾⣼⣼⢧⠀⠤⠀⠏⢡⡿⣿⣿⢻⠈⠀⠀⣦⣿⣿⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡆⢸⣏⠸⠀⠁⣟⣿⢹⣹⢸⢰⡇⠷⠉⡿⢫⣿⣿⣿⣿⣿⣿⠻⠉⠀⣄⣷⣿⣿⣿⠻⠉⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠉⠈⠀⣄⢳⠙⠀⠀⢧⣷⢻⠈⡇⢘⡇⣿⣿⢿⠏⡄⠁⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠙⡉⣟⣿⣿⣿⣿⢿⠛⠉⠀⠀⠀ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⣀⣄⢶⠻⡈⢤⠳⡈⡧⣿⣿⠻⣎⠲⠚⡴⣿⡿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠈⣿⣿⣻⣯⣷⣿⣿⣿⣿⣶⣶⣤⠀ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⠙⠈⠀⡀⣤⣷⣿⢿⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⢸⣿⣿⣿⣿⣿⢿⡶⣶⠶⠲⠒⠖⠐ ⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠉⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣩⠁⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡜⢀⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣉⠛⡿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠙⠉⠈⠁⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣷⣿⣿⣿⣼⠀⠀⠀⠀⠀⠁⠉⠋ ⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⢏⣿⣿⣿⣿⣿⣿⣿⣿⢛⠚⠖⡶⣤⣤⣀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣦⣷⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠉⠉⠚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀

⠀⠀⠀⠀⠋⣴⠄⡠⢉⠊⠔⡡⣟⣤⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣀⣧⢻⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠚⣠⠀⠀⣀⠀⠀⠀⠁⣸⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠞⣠⠀⠀⠀⣧⠘⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠔⠀⠀⠀⠀⠀⠀ ⠀⡄⣸⣀⢄⠦⠓⠉⠀⠀⠀⡇⢿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⠀⡇⢿⠒⠒⠒⠙⠉⠉⠉⠓⠕⠭⣉⢉⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⢸⠀⠀⠀⠀⡁⢞⠿⠴⡷⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠹⠨⠄⠂⠒⣉⢦⣱⣀⠀⠀⠀⣀⢄⠦⠽⠼⠀⠀⠀ ⠀⡀⣀⣀⣦⠤⠦⢒⡟⣮⠈⡇⢹⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⣸⠀⡀⣀⢄⠦⣕⠳⢨⠀⠀⠀⠀⠀⠀⡄⢼⠛⠐⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡷⡜⠙⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⡸⢸⠀⠁⢤⠘⠀⠀⢦⡘⠳⠀⠀⠀⠀⠀⠏⣉⠯⠒⠒ ⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢿⣏⠦⠑⣈⠤⠒⠑⠈⠀⠀⠀⠀⠒⡠⠋⡠⠃⢲⡤⢀⠀⡀⠹⠀⠀⡄⡸⢳⠁⠊⠔⡠⣀⠀⠀⠀⠀ ⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠁⣿⡂⠀⠀⡀⣀⠤⠢⠒⠒⠒⠒⠒⠔⡠⠀⠀⡆⠀⠀⠀⠀⠀⡇⠉⠀⠀⡄⡠⢀⠀⠀⠀⠀⠀⠀⠉⠒ ⠓⠋⠛⢛⠉⠈⠀⠀⠀⠀⠊⣿⣡⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠃⡾⢰⠀⠀⠀⠀⠀⠀⠁⠊⠴⣸⠀⠀ ⠀⠀⡀⣀⢤⡒⣿⣌⣤⣶⠴⢁⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠁⠟⡩⢀⠄⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠦⠓⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⣆⢬⠐⠀⠀⠀⠀⠀⢄⠒⠉⠊⠖⣤⠹⠀⡁⣏⣿⢘⠀⠀ ⠠⠒⠈⠀⠀⠀⠀⠀⠀⠀⣄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⠀⠀⣄⠢⠓⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠋⡼⢹⣟⠀⡏ ⠀⠀⡀⢦⠒⠉⠀⠀⠀⠀⠀⡀⢤⠓⠉⠉⠀⠀⠀⠀⠀⠂⠚⠤⣠⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢸⣿⣉⠊⢳ ⠀⠀⠀⠀⠀⠀⣀⣀⠄⠤⠯⠴⠤⣀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠱⠀⠀⠀⠃⣴⣷⣿⡻⢿⢞⣧⢹⠉⠏⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⠈⠀⡃⠀⠀⡀⣷⢛⠞⣠⠀⠀⣿⣼ ⠀⠀⠀⠀⠀⠀⠛⠒⡴⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢬⡤⢣⠉⠀⡄⣿⠁⡴⢀⠏⣴⠀ ⠀⠀⠀⠤⠤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠉⣏⢿⠛⣿⡿⠀⠞⣠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣴⡠⣠⡇⡞⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⢀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣿⠚⣁⢫⠉⢿⡱⣈⣶⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡿⣿⢞⣤⣦⣷⣿⢰⣦⠷⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣰⠀⠀⠀⣸⡀⢤⢶⠙⣏⣹⣎⣷⣿⣿⣿⣿⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠋⠟⡿⣿⣿⣾⣠⠋⠔⠤⠤⠢⠙⠈⠀⠀⣀⣤⢶⡙⣦⣿⣿⣿⣿⢻⠀⠀⠀ ⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣠⠀⠃⢠⠁⠟⠩⠀⠉⡏⠻⠈⠀⠀⠀⡠⢦⣿⣿⣿⣿⣿⠺⠉⠀ ⠀⠀⠀⡇⣿⣿⣿⣿⣿⣾⣠⠀⠀⡟⠛⣿⣭⣊⣒⣄⣤⣀⣄⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⠈⠀⠀ ⠀⠀⠁⣿⣿⣿⣿⣿⣾⢀⠋⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠿⡿⣿⣿⣿⣿⣿⢻⠀⠀ ⠀⠀⡏⣿⣿⣿⣿⣻⠒⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢼⠀⡶⣶⣾⣤⣾⣤⣤⢀⣿⡿⣿⠀⠀ ⠀⠏⣿⣿⣿⣾⣿⣿⣻⣉⣉⢖⠶⠒⠈⠀⠀⠀⠁⠋⠑⢫⠟⠽⠺⡔⣤⣋⠏⠿⠻⣟⣿⣰⠀⠀ ⠀⣿⣿⣿⣿⠀⣆⣿⣿⣿⠻⠛⠌⠦⣾⢲⠈⠀⣟⢵⡿⣾⣷⢙⠍⠿⣯⣭⢻⡟⡟⣿⣶⣤⠦⠴ ⠃⣧⣿⣿⣸⠀⠀⡏⣶⣿⣿⣿⢿⠝⢉⠛⠒⡠⠀⣠⠀⠀⡀⠰⠀⡀⣀⣀⣀⣠⢀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⢹⠀⡜⣸⠉⣾⣷⢶⣎⣶⢸⢸⠁⠟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡇⣿⠘⢀⠯⣿⢉⡀⢄⡠⣏⡿⢾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣿⣿⡞⣷⣶⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡆⣬⣿⢸⡀⣤⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢢⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡀⠈⠀⠀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢦⡵⣾⡵⡇⠉⠟⢡⡜⢟⢠⡜⢹⡆⡔⢁⠞⠣⡈⠢⡒⢠⡅⠘⠀ ⠀⠀⢾⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢶⡷⢹⡾⠏⢹⡎⢲⡒⢭⣭⢀⠀⠀⣄⠫⠚⠖⡴⢠⠀ ⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣤⣤⢲⠻⠛⠉⡈⣀⣀⣀⣁⢉⠛⠀⠀⠀⠁ ⠀⠀⡇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⡀⣀⣄⠤⠤⠦⠒⠒⠛⠾⠴⠠ ⠀⠀⠀⣆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⣀⢤⠦ ⠀⠀⠀⠀⡄⠳⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠃⠈⠀⣿⣿⣿⣿⢸⠙⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢧⠘⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⠘⠀⠀⠀⠀⠀⢯⣿⣿⣿⣿⣿⣿⣿⠈⠳⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⣠⢤⠒⠙⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡆⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⠹⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣾⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠁⠉⡉⣮⣿⣿⣿⣿⣿⣿⣿⢻⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⡟⢓⣿⣜⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠒⠶⠲⣻⠈⠀⡀⣄⣿⣴⣿⣿⣿⣿⣿⣾⠙⠀ ⠀⠁⠞⡫⣼⢃⣳⣷⣼⣻⣸⢸⣾⢯⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⡇⢠⠀⠀⠀⢠⡖⢦⡱⣈⣄⢷⡟⣿⣛⣿⣿⢹⡇⠀ ⠞⢨⡾⣬⢜⣰⣾⢻⢡⣿⣿⣽⡆⣖⢹⣿⠀⠀⠀⠀⠉⠉⠏⠿⠀⠀⡌⠁⠀⠀⡿⠛⢻⡩⣈⣅⠦⠓⠙⣏⠻⠛⣶⣶⣷⣿⣿⢿⣸⠀ ⡆⡕⣜⡟⢸⡏⣾⡄⡥⣿⣴⣄⢤⡧⣵⣾⠁⠛⠶⣠⣀⣀⣀⠀⠀⠀⢻⢠⠁⠉⣟⣿⣸⠋⣛⣔⠭⠶⣶⣶⣶⠲⠙⠈⠀⡀⣦⣹⢩⣋ ⠀⡴⡜⣄⡽⢀⠀⠋⡴⢀⠀⠀⠁⡹⡟⣴⢀⠀⠀⠀⠋⠴⣤⣤⢤⠦⣳⠉⡏⠙⣄⣶⣠⢀⠀⠀⡀⣀⣀⣀⣄⣤⠶⣗⠙⠉⠌⠦⢤⡤ ⠀⠀⡆⣷⡿⢹⡔⢀⠀⠀⠀⠋⡶⣴⢀⠀⠀⠀⠀⠃⢸⠋⠾⣴⣋⣿⣿⣾⣶⣿⢿⠿⠛⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠤⠠⠀⠀ ⠀⠀⠀⠀⣿⣠⠀⠀⠀⠋⡿⢞⠴⢀⠀⠀⠀⠀⠀⡍⣿⣻⠟⡿⣿⣿⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀ ⠐⠀⠁⡟⢠⠀⠁⠟⡷⣴⣀⠀⠇⢪⠒⢴⠤⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠋⠒⠒⠒⠒⠦⠢⠐⠀⠄⠀ ⠀⠏⣾⢠⠀⠟⣾⣄⢀⠀⠀⠏⣻⠀⠁⠟⡿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⢰⠀⠃⣠⠀⠀⠀⠀⠀⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠈⣿⣀⣇⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠸⣯⣿⣿⣿⣿⣿⠚⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⣿⠈⠀⠀⠀⠀⠁⠛⠿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣹⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣄⣷⣿⣟⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⣿⣿⠛⠉⠛⠿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠀⣇⢸⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣋⢟⣿⣽⠉⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡁⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⣿⣾⣤⣟⣿⣿⣿⣴⣿⣿⣿⣿⣾⢀⡏⣴⣿⣿⣾⣽⣛⢟⣿⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠉⡼⢇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣾⢀⠀⣿⣿⣿⢠⡟⣿⣿⣿⣴⠀⠔⢷⠃⣿⣿⣿⣴⣤⣢⠋⡽⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⠀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢸⠀⠀⣇⣿⣻⡟⣼⣿⣿⣸⠀⠀⠀⡀⢦⣔⡤⣠⠀⠤⣷⣿⣶⣴⣏⣾⣿⣿⣿⣿⣿⣿⣿⣸⡄⠹⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣿⠻⠉⡏⣿⣿⣿⢿⣏⣿⢸⠀⠀⣄⠠⠀⠉⠀⠀⠀⠀⠀⠀⠛⡿⣿⣾⣯⣽⣿⣿⣿⣿⣿⢸⠀⡇⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣄⣶⣷⣿⣿⣿⣿⣿⣿⣼⢧⠀⠀⠀⠀⠀⠀⠀⠃⡿⢰⠀⠇⣿⣿⢛⡟⣿⣿⣿⢻⣿⣾⣿⢒⠒⡿⡸⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠉⠉⡟⣿⣿⣿⣿⣿⣻⣄⡷⠘⠀⣀⢦⠙⢀⠒⠔⣠⠀⠀⡳⣬⣠⣁⣟⡿⣿⣿⣿⣷⢟⣴⠂⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡄⠲⡈⢄⠹⠀⠀⠀⠀⠀⣀⣍⣟⣿⣿⣴⣀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣴⣀⠀⣉⣿⣿⣿⣿⢿⠿⠿⠻⠛⠙⠉⠉⠉⠛⠿⣿⣾⣿⣾⣀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣶⣠⠁⠋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣿⣿⣶⣤⣁⢚⡴⢀⠀⠃⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣶⣶⣶⠴⠤⣠⣀⠀⠀⠀⠃⣿⢩⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠏⣷⣿⣿⣿⣿⣾⣴⣠⣀⠀⠁⡿⣴⢀⠀⠀⠀⠀⠁⠀⠀⠁⠚⠴⡥⣉⣉⣛⣐⣏⢻⠀⠋⠛⠚⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⣸⡇⣿⣿⣿⣿⠀⠀⠀⣷⠈⡏⢹⠀⠀⠈⠀⠀⠀⠀⠀⠂⣸⠏⣿⣹⠚⡴⢋⡴⢀⡟⣾⢁⡰⠋⠿⡅⠾⡤⢦⠹⠀⠀⢸⠃⠀⠀⠀ ⡄⢹⡄⣿⣿⣾⣿⠻⠉⠋⣿⢰⡀⣄⢦⣤⢀⠀⠀⠀⠀⠀⠀⢹⡄⣶⣠⠋⡴⢃⠸⠏⣴⠏⣠⠟⢿⣠⡜⢃⡼⢷⡇⠈⠁⢸⡀⠈⠀⠀ ⠀⣄⠠⡄⣷⢿⡈⣄⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠚⡠⠁⠟⣼⠆⣠⠞⢁⡾⢯⢠⠎⢃⣰⠀⡼⡇⢾⣠⠀⠀⢸⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚｡⋆୨♡୧⋆ ˚｡⋆

⠀⠀⠀⠀⠀⠀⣏⢺⠒⠤⣀⢀⠉⠚⡴⣡⣟⣤⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡞⣀⣷⣻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡯⣠⠀⠒⠴⠤⣀⢀⠀⠀⣇⣸⠀⠀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣠⠀⠀⠀⣵⣹⣄⢦⠄⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠋⠖⣿⢉⠈⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⢀⠀⠀⠀⠀⠀⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠴⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡇⠀⠀⡀⣄⢤⠳⠙⠈⠀⠀⠀⠀⣿⢹⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡇⢧⠢⠒⠒⠒⠓⠙⠉⠉⠚⠒⠿⣭⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⡇⠀⠀⠀⠀⠀⠀⡀⣍⢯⠛⠴⠷⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⢸⠚⠐⠒⠒⠑⡉⣄⢦⣙⣀⢀⠀⠀⠀⠀⣀⢤⠦⠛⠒⠒⠒⠀⠀⠀ ⣀⣀⣤⠤⠴⠷⠛⠙⠉⡭⣀⡿⣿⠀⡇⣿⡜⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣿⣀⡀⢄⠤⠲⡓⣍⠦⡙⢦⠘⠀⠀⠀⠀⠀⠀⠀⡀⣧⢙⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣄⣦⡳⢹⡇⣸⢻⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⡾⣼⠀⠀⠀⠉⠀⠀⡀⢦⡙⢦⢙⠀⠀⠀⠀⠀⠀⠀⠀⡇⠹⣄⣠⣤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣿⡄⠻⡀⢦⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠏⢰⢸⠀⠁⡏⣠⢣⠈⠀⠀⡀⢧⡘⢳⠈⠀⠀⠀⠀⠀⠋⣽⠚⣒⠶⠤⠤ ⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣯⢦⠳⠉⣀⢤⠢⠓⠉⠈⠀⠀⠀⠀⠀⠉⠞⣠⠁⠞⢠⠃⢻⠴⣠⢀⠀⠀⢧⠈⠀⠀⠀⣦⡘⢷⠀⠁⠊⠖⡤⣀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡎⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⡇⠠⠀⡀⣤⠦⠒⠙⠉⣈⠀⠀⠀⠀⠀⠁⠋⠴⣠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢶⠞⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢺⡛⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣤⠦⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠖⡠⢀ ⢦⠒⠶⢽⠮⠒⠛⠉⠈⠀⠀⠀⠉⠞⣣⣴⠏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⡟⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠖⡤⣀⣸⠀⠀⠀ ⠀⠀⠀⠀⣀⣄⠦⡓⣿⣈⣤⣶⣻⠖⢠⠏⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠁⠿⣨⢀⠀⢦⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠳⠙⠙⠳⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⣵⠳⠈⠀⠀⠀⠀⠀⠀⠀⢶⠉⠀⠀⠀⠉⠞⣷⠈⣀⣄⢤⠧⡿⢠⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣶⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⡆⠛⢈⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⢀⠀⡀⢳⠀⠄⡤⣿⣸⢷⠈⠀⠃ ⣀⣄⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡴⠀⠀⠀⠀⠀⣀⢤⠶⠶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠛⡿⢀⢻⡿⢸⠀⣾ ⠀⠀⠀⡀⢤⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⡀⢤⠳⠙⠉⠈⠀⠀⠀⠀⠀⠉⠉⠓⠾⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣶⣿⣿⠀⣽⢀⠉⡞⢳ ⠀⠀⠀⠀⠀⠀⠀⣀⣄⠤⠤⠦⠶⠒⠛⠶⠤⠤⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠀⠀⠀⠀⠀⠋⠼⠿⢿⢿⡌⢻⣽⡼⡏⣠⣀⢀⠟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⠀⠀⣸⠀⠀⣠⣷⣿⣤⣠⠋⣸⣀⣀⣇⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⠈⠀⢳⠀⠀⠀⡀⣷⠿⣾⣠⠁⠀⠀⡿⣾⢠ ⠀⠀⠀⠀⠀⠀⠀⠃⠛⠖⠴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣉⣄⡤⢷⠙⠀⠀⡆⣿⢠⠞⣠⠀⠃⣾⢰⠀ ⠀⠀⠀⠂⠒⠒⠖⡴⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⠙⡀⣦⣽⠳⠈⣿⠏⢸⠀⠋⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢽⠷⡿⣻⣧⣿⣣⢸⡟⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣧⣸⣀⠀⠀⡇⢿⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⣿⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⠴⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣜⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡈⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣻⣖⢦⠓⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⢟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁⠚⣶⣤⣭⠿⠿⠿⠽⣤⣦⣳⠉⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⠞⣠⠀⠋⡿⣾⣶⢄⡢⣄⢷⠙⠀⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢰⠀⡇⢠⢀⠀⠐⠀⠀⢀⠀⣇⠸⡀⡅⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⢀⠀⠀⡆⠻⠀⠀⠄⢀⠀⠀⠉⡞⢀⠀⡀⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⢰⠀⠋⠴⠀⡄⣽⠶⠳⠚⠖⡷⣯⢀⠀⠀⠀⠀⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠋⡼⢀⠀⠀⠇⣹⠞⣡⡟⠣⠈⣇⠘⠀⢦⠙⠀⡆⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⢀⠀⠀⠀⠁⣿⡰⠋⣲⡓⠹⣦⡙⢳⠀⠀⡀⢦⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣾⠀⠀⠀⠀⠉⡾⢡⠟⢻⠛⠿⡟⠻⡀⣤⢳⠈⠀⠀⡀⣶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⢠⠀⠀⠀⠁⠞⣴⣿⣿⣿⣿⣸⣀⣦⣿⣿⠿⡸⢦⠙⠀⠀⡀⣷⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⢠⠀⠀⠀⠃⣹⠞⡿⣼⠇⣸⣿⢹⠀⡆⣿⣿⢷⣙⣀⣤⠳⠀⠀⠀⣷⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠿⣼⠋⣸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠇⣰⢁⠟⣾⠀⡅⢹⣿⡀⠻⠆⣿⣿⡘⣷⢿⠐⡀⢳⠀⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢹⣿⠀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠏⣰⠟⣾⣠⣦⠾⡿⣸⣶⠀⡏⠀⣧⣿⢸⠀⣧⢿⠈⡄⢹⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣴⣄⣿⠇⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣱⡿⣾⠀⠀⠀⠀⣿⢸⠀⠃⣸⠀⡇⣿⣿⠀⠀⣷⣿⠻⣏⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣁⣸⠀ ⠿⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⡟⣿⠁⠉⠈⠀⠇⣿⣾⠿⣿⠀⡄⣦⣿⣿⣧⠹⡄⣿⣿⣹⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⡼⠀⠀ ⢧⠈⡄⢤⠢⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠇⣿⢿⡀⣀⢇⠻⡿⣿⣿⣿⡿⠓⠙⠉⡀⣿⡟⣿⠺⣷⣿⣿⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢻⠁⡞⢀⠀⠀ ⡀⢷⠈⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⡿⣿⣠⠋⠞⣿⣩⣋⣻⣟⣿⢸⠀⡀⣀⣤⣦⣿⣿⠘⠀⣆⣿⢿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠿⠤⡤⢠⣯⣼⢀⠀⠀⠀ ⠀⡀⣧⣟⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣾⣠⠀⣧⣽⣻⣟⣿⢿⢻⠐⠀⠀⠀⠀⣿⣿⣼⠳⠈⣷⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⠁⡿⣰⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⣷⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣸⠀⠀⠁⠋⣞⣿⣿⣿⣼⠀⠀⠀⠀⣤⡷⣿⣿⢸⡀⣆⡿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣟⣾⢠⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⡀⣦⠱⠈⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣼⠀⠋⠞⣴⢀⠏⣼⣿⣾⠀⠀⠀⠀⠀⠀⡇⣿⣿⣷⠙⠀⡀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡞⣵⣞⣠⠀⠀⠀⠀⠉⠀⠇⣿ ⣿⣿⢿⠿⠘⠀⠁⣍⠦⠙⠛⠾⠴⡤⣤⣤⣷⣿⣶⡶⣿⠛⠉⠀⣿⢸⣿⢸⠀⠀⠀⠀⠀⠀⡃⣟⣿⠀⡍⢿⠛⣟⣿⢻⠛⠛⠙⠈⠀⠀⠀⠉⢚⠴⣀⠀⠀⠉⠛⠿⣿⣿⢸⡇⣿ ⣿⣿⣿⣿⢸⠀⡿⣿⣿⣿⢿⠛⠛⠍⠉⠉⠉⠈⠀⠀⠀⡀⣄⣦⣿⠙⡿⢀⠀⠀⠀⠉⠀⠀⡏⣿⣿⣬⣀⣁⣭⣯⣿⣿⣛⣛⣛⣿⣿⠿⣹⢉⠛⠛⠿⡿⣿⣿⣿⣿⣿⣿⢿⡀⣿ ⣿⣿⣿⣿⢹⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⣅⣶⣷⠘⠀⠀⠀⡆⢻⡿⣿⣿⡟⠛⠛⡿⣤⣤⣤⣤⣠⣀⣀⣀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿ ⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⣦⣷⠿⠿⡿⣿⢿⣿⠿⠿⠿⠿⣿⢹⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⣦⣿⣸⡄⣿⣿⣿⣿⣿⣿⣿⣿⠙⠉⠉⠈⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡇⢾⠤⠶⡿⢀⠈⠀⠀⠀⠀⠀⠃⣼⣁⣛⣛⠟⣷⣼⣀⢏⣽⢆⡴⠀⠋⣰⠎⣦⣴⣿⢹⠋⠿⣴⠀⠇⣿⢀⠀⡀⣿⡄⢷⠀⠀⣆⢹⠀⡀⣿⠀⡀⢻⠀⡇⠀⢸⠀⠀⠀⠀⠀ ⠀⡇⣿⠀⠃⣼⡀⠀⠀⠀⠀⠀⠀⡾⣤⣶⠴⡅⣫⣼⠀⡟⣰⠀⠀⠀⠏⣰⡞⣤⠳⠟⣴⣷⣨⣿⠀⠀⡇⣿⠀⠀⠀⡄⢹⡄⢻⠀⠀⣧⠈⠀⡆⢸⠀⣿⠀⡿⠀⢸⠀⠀⠀⠀⠀ ⠀⡀⣿⠿⡼⠀⠀⠀⠀⠀⠀⠀⠇⣿⠛⠶⡤⣁⣾⠀⡟⣰⠀⠀⠀⠏⣱⡾⠀⠀⠃⣿⠉⣿⢹⣿⠀⠀⡇⣿⠈⠀⠀⠀⣇⢸⣧⠸⠀⡀⢻⠉⠀⣷⠈⣇⠘⡧⠀⢹⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⣿⣀⢿⠀⠀⡞⢀⡏⣰⠀⠀⠀⠟⣵⡼⢀⠁⠟⣿⣿⣿⣿⣯⣹⠋⠛⡖⣶⢳⠉⠀⠀⠁⣿⠘⣷⠈⠀⣿⠉⣈⣦⣖⣷⢸⡇⠘⣿⠀⠀⠀⠀⠀ ⠀⠀⣿⢠⠀⠀⠀⠀⠀⠀⠀⡏⢹⠀⣿⠀⡏⢠⠇⣰⠀⠀⠀⡟⣽⡼⠀⠁⡟⣿⣿⣿⣿⣴⣠⣀⢀⠀⠀⠀⠀⡀⢧⠏⡃⢸⣧⡜⢿⠈⡁⣿⣿⣿⢿⡿⣿⡇⢸⣿⠀⠀⠀⠀⠀ ⠀⠇⣸⠀⠀⠀⠀⠀⠀⣼⠃⣾⣿⠀⣿⠇⣸⠃⣾⠀⠀⠀⠟⣿⡼⠁⠋⣞⣴⣠⢀⡀⢁⠀⠀⠀⠀⠀⠀⠁⠋⠙⠀⣆⣿⢿⠀⣧⣿⢻⠀⢳⡛⣿⢹⣧⣿⣿⢻⣿⠸⠀⠀⠀⠀ ⠀⠄⢀⠀⠀⠀⠀⠀⡀⢀⡿⢠⣿⠱⣿⣿⢠⡆⢠⠀⠀⡟⣿⡿⢶⣠⢀⠀⠀⠀⠀⠀⣿⠀⠁⠚⠶⠿⠶⣠⠀⡀⢧⠈⣠⣦⠻⠈⣧⣿⠹⠀⡀⣄⣶⣻⣿⣼⣿⡇⢹⠀⠀⠀⠀ ⢹⠸⠀⠀⠀⠁⠀⠁⢰⡇⣸⠀⣿⡇⣿⢰⠀⠀⠀⠀⠇⣿⣾⢉⠈⠀⠀⠀⠀⠀⠀⠀⣀⠰⠀⠋⡶⣠⠀⠀⠀⠀⠀⣷⠸⠀⡀⣦⠻⣎⣿⠹⠀⠀⠀⡄⣿⢿⣿⡈⣿⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⡼⠀⡟⠀⡿⢠⠇⣸⣿⣸⠀⠀⠀⠀⠃⣿⣿⣼⢀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠟⣾⢀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⡀⣦⣿⣿⠹⠀⠀⠀⡆⣿⣿⢻⣿⠈⠀⠀⠀ ⣸⠀⠀⠀⠇⠀⠃⣿⡇⣼⠁⣿⠇⣾⠀⠀⠀⠀⠀⡟⣿⣠⢀⡾⢀⠀⠀⠀⠀⠀⠁⠿⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠹⠉⠀⠀⠀⠀⠀⣄⣷⢹⠀⠀⠠⣧⣿⣿⣧⢸⠀⠀⠀ ⢠⠀⠀⠀⠸⠀⡄⣿⣿⢰⡟⢰⡿⢠⠀⠀⠀⠀⠃⣿⣸⠃⡼⠀⠀⠀⠀⠀⠀⠟⣿⢿⠈⠃⠈⠀⠁⠉⠀⠁⠉⠋⡿⣿⣦⣿⠈⠀⠀⠀⠀⠀⠀⣧⣯⠘⠀⠀⣧⣿⡷⢿⠀⠀⠀ ⠀⠀⠀⡏⢀⠀⡟⣿⣽⠇⣸⡏⣸⠀⠀⠀⠀⠁⡿⣼⠀⣰⠀⠀⠀⠀⠀⠀⡿⣻⣾⡶⣴⣀⣄⣠⣀⣀⣀⣀⢀⠀⡀⣀⢦⡿⢿⠘⠀⠀⠀⠀⠀⡀⣦⢻⠈⠁⡝⣿⡎⣿⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⣿⢹⣷⣿⠟⣿⢀⠀⠀⠀⠀⡏⢷⢠⡀⠀⠀⠀⠀⠀⠀⡆⣶⢶⠶⠶⡶⠤⠦⠶⠶⠶⠶⠶⠶⣤⢦⠶⠶⡶⣶⣶⢰⠀⠀⠀⠀⠀⠀⣆⢿⠀⣧⣎⢿⣿⢸⠀⠀ ⠀⠀⡇⢸⠀⡇⣼⣿⡆⣿⣏⢰⠀⠀⠀⠀⠇⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⢿⣷⣿⢹⠀⠀ ⠀⠀⡟⢀⠀⡇⢸⣇⠙⣿⣾⠀⠀⠀⠀⠀⣿⣏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡆⣸⣿⣿⠘⠀ ⠀⠀⣿⠛⠛⡾⢶⡟⣼⣤⢀⠀⠀⠀⠀⡇⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠜⠠⣷⣎⣿⢸⠀ ⠘⠋⣾⣠⡇⣿⢸⡇⢸⠀⠀⠀⠀⠀⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠸⠀⠀⠀⠀⠀⠀⡇⢿⠈⠀⣿⣿⠘⡀⢻⣧⢸⠀ ⡾⣠⠀⠀⡀⣀⠀⡇⢸⠀⠀⠀⠀⠀⠖⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⠀⣶⣤⢧⠈⣿⡼⣿⠀⣦⡞⣿⠀ ⠉⡾⢠⠉⡀⣀⠀⡇⢸⠐⠀⠀⠀⠀⠀⡟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣖⠠⠉⠉⠉⠍⠯⠛⠀⠀⣧⢹⣿⢸⠀⢻⣯⠘ ⣠⠁⡼⢀⠃⡼⠀⡇⢰⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠒⠤⠥⠦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡼⣠⢋⠶⡤⣠⣀⣀⣂⠛⠛⢸⠀⡇⣿⣿⢿⠀⣧⡼⣿ ⠀⡀⢳⠀⡆⢿⠈⡇⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠁⠟⠾⣶⣤⣠⣀⣀⣄⣶⣶⢷⠛⠒⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⠀⡇⢈⠋⠛⠶⠿⠻⠀⠀⣧⣿⠸⠀⣧⣿⣿⠘⡄⢸⣿ ⠁⠀⡀⢤⡠⣁⢸⡿⠀⠀⠀⠀⠀⠀⡏⢰⠀⠛⣿⣠⠀⠀⠀⠀⠁⠛⠛⠛⠙⠈⠀⠀⠀⣏⠙⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡏⣿⣿⣿⣰⣦⣿⢿⠸⠀⣿⣿⣿⣈⣿⣿⢹⠀⢀⣿ ⡀⣄⣤⣤⣯⣰⡇⢸⠀⠀⠀⠀⠀⠀⣿⠉⡟⣿⢠⠀⠀⠀⠋⠛⡾⣿⢶⠳⡏⣿⠻⠉⡿⣿⣽⠫⠈⠃⠚⠾⣶⣤⣤⣷⣽⣤⣧⣿⣿⡿⠻⣿⣿⢿⠿⣿⣿⣼⠀⣿⣷⣿⠀⠀⡇ ⡀⣅⠾⡠⢁⠞⣿⢸⠀⠀⠀⠀⠀⠀⣿⡿⣿⢹⠈⠀⠀⠇⣿⣿⣿⢠⠁⠉⣏⣿⣿⣿⣿⣿⣴⣦⢿⡀⢷⠀⠀⠀⠀⡄⣿⢸⡇⣿⣈⣧⣿⣿⣾⣶⣿⣀⣀⢀⠀⣿⡇⣿⠀⠀⡇ ⡀⢁⠋⠶⣢⠙⣿⢠⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⢿⠿⡿⣿⣿⣿⠻⡿⣿⣿⣿⣿⣿⣿⣿⠿⠀⡆⢹⡇⠘⠀⠀⠀⠀⡄⢷⠙⣄⣿⡄⣾⣷⠸⠀⠀⠀⠀⠀⠃⣿⡄⣿⠀⠀⡇ ⡴⣠⢀⠀⠀⠆⣿⢷⠙⠀⠁⠜⣾⠇⣾⣄⢶⡿⣬⣉⣭⣭⣿⣿⣿⣿⣾⣶⣿⣧⣹⢉⡟⣾⣰⠀⠀⣷⡼⣿⠀⠀⠀⠀⠀⡀⣷⠸⣟⢸⣿⡆⢻⠀⠀⠀⠀⠋⡿⣻⠀⣿⠀⠀⡇ ⠈⠀⠀⠀⠀⡇⢸⠀⢀⠀⡏⢠⢸⡇⢾⠷⠙⡘⣦⠻⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣴⣀⠀⠀⠀⠀⡇⢿⣿⠀⠀⠀⠀⠀⠀⡆⢿⣆⣿⣷⠘⣿⠉⠋⠿⣾⣠⡟⠀⠂⣿⠀⠀⡀ ⢸⠀⠀⠀⠀⡇⢸⠀⠀⠁⣸⠀⢠⡇⢸⠀⣀⣦⠷⡙⣯⠻⠈⠀⠀⠀⠀⠀⣇⣾⣿⠩⠉⠁⠉⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀⠀⠀⣇⠻⡟⡿⣿⣿⣾⣴⣀⠀⠏⣿⠀⡇⣿⠀⠀⠀ ⢿⠀⠀⠀⠀⡇⢸⠀⠀⡇⢠⠀⠀⡇⢾⠀⠀⠀⡄⣷⣽⣦⣷⠾⠿⠿⠿⠿⣿⣿⣿⣽⣦⣿⣿⠞⠀⠀⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣼⣇⢸⠀⠀⠁⣾⠀⠀⡟⣸⠀⠀⠇ ⡆⠈⠀⠀⠀⡇⠀⠀⠀⡜⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⣆⠻⡀⣧⠹⠀⠀⠀⡇⣸⣆⣿⣦⣿⣿⢰⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⣿⠀⡇⢸⠀⠁⡾⢀⠀⠃⣿⢠⠀⠀⡇ ⠀⢰⠀⠈⠀⡇⠀⠀⠀⢰⠀⠀⠀⡆⢿⠙⠈⠁⠈⠀⠀⣄⢻⠀⣇⠹⠀⠀⡇⢸⠀⣿⠀⠠⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢸⠀⡾⢠⠀⠃⣿⣾⠀⠀⠀⠀ ⠀⠂⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠃⣿⠉⣍⣦⢳⠈⠀⠀⡄⢿⠈⣧⠸⠀⡇⢸⠀⣇⠈⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡏⢃⡾⢀⠀⠃⡾⢇⢰⠀⠀⠀⠸ ⠀⠀⢣⠀⢀⡇⠸⠀⠃⠀⠀⠀⠀⠀⣿⢮⣓⣽⣤⢧⠘⠈⠀⡄⢻⠀⣷⠘⡿⢠⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⠀⣿⣾⢀⠉⠛⣾⢀⣰⠀⠀⠀⠀⢀

⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡇⠈⠀⠀⠀⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⣷⠘⠀⠀⠉⠉⠚⠖⠴⠤⠲⡟⢸⠀⡟⢸⠀⠀⠀⡇⠸⠀⠉⠞⠤⠤⣀⣀⣁⣠⢤⠤⠲⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⡟⠚⠴⣠⣀⠀⠀⠀⠀⠀⠁⣼⢀⠏⣠⣧⠘⠀⠀⠀⢻⠇⣰⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⣀⢤⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢐⠀⠀⠋⠖⣠⣇⠈⠀⠀⠀⠀⠀⠀⠀⠃⡼⠇⡾⢀⠀⠀⣇⠻⠈⠀⡇⡘⢸⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠦⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠏⣴⢀⠀⠀⠀⢳⠈⠀⠀⠀⠀⠀⠃⣹⠞⣷⠀⠁⠈⠀⡀⣸⣄⠳⠉⣿⣿⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⣴⢀⠀⠀⠀⠀⠀⠀⣀⢤⠳⠈⠀⠃⣿⣰⠀⡀⢻⡟⣿⠙⠀⢸⠀⠀⣄⣿⣨⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠢⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⢹⠋⠛⠛⣿⣿⣿⣿⣿⢸⠀⠀⠀⡀⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠙⠀⠀⠀⠀ ⠀⠀⠃⢰⠀⠀⠀⠀⠀⠉⠋⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⠻⠈⠋⠙⡟⣷⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠈⠀⠀ ⠀⠀⡇⠀⠉⠛⠟⠿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣴⣤⣀⣀⣠⣀⢀⠀⠀⡀⣦⣿⣿⢻⡀⣦⡿⣿⣿⣷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈ ⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠀⠀⡄⣷⢿⠈⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄ ⠀⠀⡟⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠙⠉⠉⠈⠏⣿⣿⠀⠀⠀⠀⣧⢿⠉⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡉⣤⣤⣿⣿⣿⣿⡿⣾⠀⠀⠀⠀⠀⣿⣸⢧⡈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠇⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠋⠞⠶⣤⣤⣤⣤⣤⣯⣿⣾⠉⡿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⣿⣿⠈⣄⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⣿⣾⣡⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠛⠿⣿⣿⠿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⣿⣼⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⣸⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣏⣿⡾⣤⣀⠀⡀⣿⣯⣸⠀⠀⠀⠀⠀⠀⠀⠂⣼⠀⠀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠟⡿⣶⣠⢂⠉⠀⠀⠀⠀⣄⣷⢸⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣰⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠁⠟⣶⣤⣀⢤⠦⠄⣤⢤⠢⠒⠒⠖⣤⢤⠢⠓⠉⠉⠊⠖⡠⢀⡀⢤⠤⠶⠤⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠁⣼⢀⠟⣽⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⢤⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠁⠉⠉⡏⣿⢛⡶⣠⣀⣀⢤⠤⠲⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡤⣤⣤⢦⠲⠛⠈⡆⣾⠟⠀⣾⠇⠀⠀⠛⠋⠁⣹⠃⠛⣟⠹⢹⠀⠀⠒⠴⡤⣤⣤⣤⠦⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠑⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠦⢸⣼⠇⢸⢸⠀⡆⣿⣿⡟⣇⠘⠀⠀⡀⡹⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⢧⢰⡇⣇⢰⠀⡇⣹⠿⣠⠀⣦⠻⠈⠀⡀⣧⢻⠇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠘⣾⠀⣧⡏⠿⣾⣧⡿⣿⠀⡄⠻⠈⣄⢿⠈⡀⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠆⠙⡿⣼⠀⠀⡇⣻⢸⠋⡟⣴⢹⠀⡟⣋⣇⠘⠙⡂⣿⡿⢹⣼⠻⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⢿⠉⠋⣿⣿⣾⣠⠀⠙⡇⡟⢸⣄⣷⢿⡘⢻⡀⣤⣶⢿⡏⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⣁⣟⣾⢠⠀⠋⡿⣿⣬⣀⢙⠝⡦⣿⣿⣿⢸⠀⠀⣄⣿⢀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡿⣼⢀⠀⡏⣿⣡⣀⢻⡿⣾⣿⣿⢿⡹⣼⣤⣷⠹⠀⡆⠸⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⡿⣾⣤⠃⡿⣿⣿⢻⣾⣿⣧⣿⢷⠙⡀⣦⢻⠈⢹⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⠃⣿⣾⢠⠋⡿⣨⣿⣵⣯⣿⢻⡿⣿⣿⣟⠻⠀⣤⢻⡆⠘⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢰⠀⠀⣸⡇⣸⢀⡿⢀⣿⣿⣿⡼⢀⡇⣿⣼⠀⣷⡎⡝⢹⠀⣧⠀⣆⠝⠳⠈⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣰⠀⠀⠇⢰⡄⢸⠀⣽⠁⣿⣿⣾⢟⠀⡇⣿⢸⠀⡇⢹⣆⣧⠀⡏⠠⡏⣤⠳⣌⠑⠈⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⢠⠀⠀⠋⣰⢧⠘⣧⠋⣸⡷⣿⣦⣷⡿⢿⣿⣿⠀⠀⡟⣿⢠⡇⠙⣽⠋⠖⡠⠀⣅⠻⣌⠳⠈⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⢀⠀⠀⠏⢹⠈⡀⣄⠤⣷⢛⣿⣠⠟⡿⣿⣹⣦⣿⠀⠃⣿⣾⠀⡇⣀⠀⠉⠛⠼⡠⣀⠀⣄⠳⡈⢦⠙⠀⠀⣄⠳⠈⠀⠀⠀⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠃⡰⠁⡴⢀⠀⣞⣟⠿⠻⡟⣸⠀⣿⣼⣿⣴⣄⢿⡟⢿⣿⣿⣿⠀⡟⠿⣿⣿⣿⢨⠀⠀⠀⠀⠀⣄⠳⡈⠢⠈⠀⠀⣄⠳⠈⠃⣰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠁⠞⣠⠀⠀⠏⣼⣧⣿⣿⣿⢸⠁⣿⢟⣸⠀⠏⣿⣿⣿⣿⣿⢺⠀⣿⣿⣿⣶⢀⠀⠀⠀⠀⠋⠖⠀⠀⣏⠳⡈⠳⠈⠀⠀⢤⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠋⡴⢯⠲⠙⠊⢀⣇⠈⣀⣒⣿⢀⡇⣿⣿⢿⡿⣾⣇⣾⣿⣿⣿⣿⠠⡃⣼⣀⠀⠂⠒⠶⡤⣀⢀⠀⠁⡿⢠⠀⣇⠻⣌⠳⠈⡟⢀⠀⠀⠀⠀⠀ ⢠⠀⠀⠀⠀⠀⠃⣰⠀⠀⠃⡴⢀⠇⣿⠀⠀⡟⣄⠦⢷⠈⠃⢻⠿⣿⣼⣧⣿⣿⠀⡇⢸⣇⣿⣿⣿⠳⡻⢻⠉⠉⠈⠁⠉⠋⠒⠴⠢⣙⣿⢽⡴⡦⢹⣄⠑⢏⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⣠⠀⠁⠟⣠⠀⠀⠀⡇⠀⠇⢸⠀⠀⠃⢾⡿⣽⣖⣸⢻⣿⣿⢸⠀⡆⢹⡇⣿⣼⣿⠀⣆⢿⡀⣮⣿⣼⠀⠀⠁⠉⠟⣽⣟⢻⠀⠀⣾⠿⡿⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠂⠈⠀⢀⠐⠋⡿⡏⠀⠀⠀⠀⡆⢹⡏⢻⠒⠒⡖⢤⣷⠀⡀⢸⣆⣷⣿⠀⠀⠀⣷⡏⣾⢀⡇⠸⠀⣸⠀⠀⠀⠁⠱⠁⠿⣿⣿⣿⣨⣉⢻⠈⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⠈⠁⠞⢲⠶⣿⠸⠙⠀⠀⠀⣷⡿⢻⠒⠒⠒⠒⣾⠁⡟⢠⠀⡄⣧⠀⠀⠀⡆⢹⢸⠀⡀⢸⠀⣧⠉⠈⠀⠁⡟⣿⣿⣿⣿⢻⣷⣿⣸⢸⣇⣏⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⡽⠉⠀⠀⡄⣷⣮⠐⠀⠀⡀⢷⣿⠘⠀⠀⠇⢹⡏⢀⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⠀⠀⢥⠉⡏⢿⡿⣿⢿⣿⣼⣷⣿⣷⣿⣸⣿⢻⢴⣤⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠳⡀⢻⡀⣀⢤⠦⡓⢯⠙⠀⠀⠀⡉⣛⣿⠴⠤⣤⣀⣃⣟⣤⠦⠳⠛⠈⠀⠀⠁⠋⠞⡶⣦⣲⣐⣀⣀⣀⣄⣥⢿⢿⡋⣿⠉⣿⣾⣰⢀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠘⡆⠸⠀⠀⠀⠀⠀⣂⣤⠦⡿⣶⣴⠀⠀⠀⠀⠤⠤⠶⠰⠀⠀⡗⣝⣧⣿⣿⣉⠉⠛⠖⠴⠤⠀⠀⠀⠁⠈⠀⡀⢦⣿⣠⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⠀⣧⠀⠀⠀⠀⠀⠀⠀⡞⢢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣝⢋⡼⣠⠀⠉⠊⠖⠤⠤⠶⠰⡀⢀⠙⠈⡀⢳⠀⠀⠀⠀⡆⢀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀

⠋⡿⣿⣿⣿⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿ ⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣼⣻⣩⣋⣿⣿⣛⢛⣟⢻⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣿⣿⣿⣿⣴⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿ ⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠿⠿⠻⡿⣸⠀ ⣀⣧⢻⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠁⠋⠿⣿⣤⣠⣀⢀⠀⣀⣧⢿⠈ ⠀⡟⣾⣠⣀⣀⣀⣄⣧⣶⢿⠻⠙⠈⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡶⣤⣉⠋⠟⡶⣷⣨⠀⡇⢸⠀⠀⠀⠀⠀⠀⣿⢸ ⠇⣿⢠⠀⠀⠀⠀⠼⡣⠀⢹⡈⣀⣤⢶⠷⠛⡙⣍⢳⠀⠁⠈⠀⠀⠀⠀⠛⠙⠁⢟⠿⣴⣠⣣⠉⠉⣾⢀⠀⡟⢠⠀⠀⠀⠀⠀⠀⡏⢸ ⡇⣿⠀⠀⠀⠀⠀⣷⡄⠱⣄⠳⠈⠀⠀⠁⡞⣁⣼⣷⠻⡿⢴⠀⠀⠀⠀⣄⣧⣾⢠⢆⠹⠈⠀⠀⠀⠁⠋⡴⢀⠀⠀⠀⠀⠀⠎⢡⣿⢰ ⡄⣿⣜⠱⠀⠛⠉⡟⠙⠉⢌⠲⣑⣉⣉⢊⠖⡠⠀⠀⣧⢹⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⡀⣄⠤⠤⡤⣀⠀⠀⠀⠀⠀⠁⠊⡠⠃⡿⣱⠟ ⢻⣆⢿⡘⢦⠐⡇⣀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⠀⠀⠀⠀⠀⠀⡆⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠴⣀⠁⠟⣿⣿⣿⣿ ⣿⢿⣝⣷⠻⠈⡄⠲⡵⠉⠀⠀⠀⠀⠀⠀⠀⠊⠐⠏⣾⢀⠀⠀⠀⠀⠀⠀⠀⣄⣷⠻⠈⠀⠀⠀⠀⠀⠄⣀⠀⠀⠉⠟⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠻⠉⠀⠀⣀⢀⠀⠀⠀⠀⠉⠛⡿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⢿⠿⠻⠛⠛⠛⠿⠿⣾⣯⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠟⠿⠿⣶⣴⣤⠦⠒⠒⠓⠙⠀⠀⠀⠀⠂⠒⠖⠤⣤⣀⠀⠀⠀⣉⣛⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠉⠉⠁⠛⠛⠉⠉⠉⠉⠉⠁⠉⠉⠈⠀⠉⠉⠉⠉⠉⠛⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⠀⠁⠒⠤⠢⠘⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠀⠀⡀⠉⡸⠀⠀⡀⢸⠀⠀⠀⠀⠣⠈⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠊⡴⠤⠦⠓⡌⠘⠀⠀⠁⠖⠤⣀⣀⡀⣋⢴⡠⣀⣀⣀⣀⣄⠢⠙⡇⠀⠀⠀⠀⠇⢀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠉⠀⠀⠀⠀⣄⢷⠈⠞⢀⠀⠀⠀⠋⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⢹⠛⠒⠒⡞⠀⠃⠙⡉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⢄⠙⠀⠀⠋⡷⣴⢦⠈⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣆⢻⠉⠒⢸⠀⠀⣄⡳⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠿⡩⠖⣠⢦⠙⣾⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⠀⠀⣱⠀⠀⢣⠀⠀⠀⠀⣿⣝⣽⠻⠉⠀⡇⠻⠀⠀⠀ ⠀⠀⠀⠀⢳⢆⠈⠀⠀⣦⢦⡷⢿⡟⣿⠲⠔⠤⠠⠔⣀⢢⠉⠞⠙⢻⠉⠉⡄⢾⠙⡇⢿⡶⢰⠁⠸⡄⢷⡛⣦⢿⠉⣿⢻⠀⠀ ⠀⠀⠀⠀⡄⠸⣄⠑⠀⠀⠀⠀⠀⣀⣄⢦⠑⠈⠀⠀⠀⠀⠀⠀⣇⣸⣀⣀⣆⠿⡘⡷⣾⠀⠀⡀⢸⠀⡀⢣⢷⣿⣿⢸⣆⢹⠀ ⠀⠀⠀⠀⠀⡆⠀⡀⢦⠈⠀⠀⠀⠀⠀⠀⠀⣄⠻⠘⠀⠀⠀⠀⡇⠁⠛⠙⠀⡀⣇⡟⢀⠀⠀⠀⣾⠙⠀⡀⣷⣿⣿⢻⠈⣧⠸ ⠀⠀⠀⠀⠀⠀⢱⠀⠀⡀⠣⠈⠀⠀⠀⠀⠀⠁⡞⣿⠘⠀⠀⠀⠸⡆⣷⣾⢠⠀⡄⣿⠀⠀⠀⠀⣼⡀⢦⠒⣤⣿⣆⢿⢢⡆⢻ ⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⢄⠙⠀⠀⠀⠋⡠⠞⣀⢱⠀⠀⡏⠉⠀⠀⠀⠀⠀⡇⣿⠀⠀⠁⠀⢸⠂⠀⠀⡀⣷⠘⢣⠘⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⡀⠻⠚⡤⢊⡤⠀⠀⠀⠀⠎⢀⡀⢤⠤⠑⠀⠀⡀⣄⠀⠀⡀⢳⢺⠑⠈⠀⠀⡄⢹⡆⢁⢸⡏ ⠀⠀⠀⠀⠀⠀⠀⡀⣻⢉⠭⠭⡩⡖⣶⣈⠀⠀⠀⠀⠀⠎⣧⣈⣀⠂⠭⣉⣄⠢⠙⠀⠀⠀⠀⠀⢸⠀⡀⠢⠈⠀⣿⠀⡏⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠱⠈⠀⠉⠀⠋⡴⠤⠓⠛⠟⡠⠏⣾⣤⡠⣀⣀⣀⢁⠬⡦⢿⠙⠀⠁⠏⢠⠀⠀⠀⣄⠹⣿⡇⠈⠃⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⣀⡄⠘⠀⡀⣿⢀⣎⣽⠀⠀⠉⠛⠀⠀⠉⣈⠠⠁⣾⣷⣤⣤⢶⠙⠀⠀⠀⡄⣿⡜⢫⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⣧⠋⢁⡾⣠⢀⣏⢾⡤⢀⠀⠛⣜⢹⠀⠀⠀⠀⠉⡉⢻⠀⠀⠀⣿⢠⡿⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠑⡄⣿⣿⢾⠤⠤⣮⠀⡆⢬⠤⣦⢶⣷⠶⠸⠀⠀⡀⣦⣿⠀⠀⠁⢰⠛⢰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣿⣿⠳⠋⡴⢀⠀⠀⢦⠉⠀⠁⣰⠀⠀⠀⠇⠒⠓⣏⠸⠀⡏⠞⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⡏⠈⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠃⣳⣄⠢⠙⠀⠀⠄⣠⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠀⢸⢆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⢠⡀⠸⠀⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⢻⡴⣄⢦⠛⠙⠉⠉⠉⠉⠛⠀⢣⠀⠁⢠⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡟⣡⠊⠔⣠⠀⠀⠉⠉⠀⠀⠀⢆⠑⢦⡿⠈⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⣾⣠⠀⠀⠁⠗⣀⠀⠀⣄⠳⠀⠀⠀⢄⣗⢹⠁⠟⡰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠙⠀⠁⠋⡟⠀⠀⠀⠀⠀⣀⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣄⣦⣷⣿⠻⠈⠀⠀⡏⣿⢰⠃⡿⢈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⣈⣤⠢⠙⠀⠀⠀⣆⢿⣧⠘⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣡⡘⠀⠄⣿⢃⠸⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠙⠉⠂⠀⡀⣦⣶⢾⣿⣿⢰⠇⣾⣤⣤⢦⠷⠻⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠻⠈⠀⣀⣻⣧⡸⠀⠀⡀⠀⠀⠀⢀⠀⢀⡁⡿⣸⠀⢀⠟⣸⠈⢇⠋⣼⠀⠀⠀⠀⠐⠀⠐ ⠀⣠⣄⣤⠦⡶⣴⣷⡻⣿⣾⣷⠿⠻⠛⠙⠙⠋⣉⣀⢀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⣄⣷⠛⣟⢹⣷⠘⠀⡀⠀⠁⠀⠀⠀⠀⡟⡞⢹⠀⠟⣿⣼⢀⡀⣿⢿⠾⠴⡥⠭⠿⠙⠠ ⠐⢀⠀⠉⠊⠖⣶⣶⣹⠉⠁⡾⣤⢰⡀⣿⣼⣷⣿⢿⠻⠛⠉⠉⠀⣀⢦⠙⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣾⠙⠂⠀⠀⠀⠀⠀⠁⢸⡀⡦⣶⣷⣿⢸⠀⠋⣿⣿⢿⡿⣨⣀⣈⣄⢻ ⠋⠟⡷⣹⠛⡴⣰⣃⣀⢧⡽⢈⠀⠀⠀⣠⢮⣠⠁⠛⠟⠿⣿⣿⣬⠶⠓⡙⣌⠳⠈⠀⠀⠀⠀⠀⠀⠀⣄⣶⣶⠾⠟⠛⠛⠚⡶⢻⠉⠉⠈⠀⣀⣤⡷⣿⣾⣟⣿⣿⣧⠻⢀⠀⡘ ⠀⠀⡏⣋⣷⠙⠛⠞⠳⡿⣿⢿⠀⠀⠀⠎⢫⠿⣿⣿⣿⣿⣶⣷⢿⠻⠛⡛⣿⠻⣟⠻⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⡏⣳⢯⡘⣀⣀⣤⣷⠿⣇⢱⣿⣿⣿⠀⡀⠻⠀⠀ ⠏⣴⢃⣦⠗⣰⡇⢻⣿⣿⣿⣿⠹⠘⠀⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣄⠳⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⣇⠘⠀⣀⠢⠙⠀⠀⣧⣸⠀⣿⣛⣙⢤⠶⡟⢹⠠ ⣦⠟⢢⠙⡀⢻⠀⣦⣲⢖⡷⣙⣷⢸⡏⠀⣆⣿⣿⣸⠀⠀⠀⡟⣠⣀⣀⣀⢤⠲⠉⠀⠀⡀⣦⠻⠈⠀⠀⠀⠀⠀⠉⠛⠾⡴⣠⣀⠦⠓⠚⡖⢶⠙⠀⢱⠀⣄⣿⣾⢿⠀⡄⣷⠈ ⠁⣼⠠⡓⢻⣽⠦⠒⠑⠉⠀⡀⣠⢻⣸⠀⠀⣧⣿⢀⠀⠀⡞⣿⠀⠀⠀⠀⠀⠀⡀⢣⠈⠀⠀⠀⣄⢦⠶⠿⣤⣠⢀⡀⣄⠤⠓⡉⣉⣭⠬⠢⠒⡉⢫⡀⢢⣷⣿⠿⣿⠈⠀⡇⣿ ⣶⠸⠀⠀⡥⣾⢶⠲⠓⡙⢮⠘⠀⡇⢨⠀⠀⡇⣸⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⠉⠟⣿⣹⠀⠀⠀⠀⠀⡀⢄⠤⠤⠤⡤⣳⣈⣀⣄⣷⣿⢿⠻⡈⣧⢸⠀⠀⣽⣷⣿⢸⠀⡇⢸ ⠛⣄⠳⣏⣺⠐⠤⠦⡒⢟⣈⣤⠙⠀⢻⠀⠀⡟⢀⠀⠀⠀⠀⣷⠀⠀⠀⠁⠿⡿⣾⣠⢞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⠀⠀⣿⣿⣿⣿⡻⣷⠈⠀⡆⡘⣷⢸⠀⡇⠰ ⣀⢸⡇⣀⢦⠚⠛⠖⡤⣀⣄⠹⠀⢂⣏⠈⠀⢸⠀⠀⠀⠀⠀⡄⠳⠋⠗⣿⣿⣻⠶⣠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⣷⣿⣿⣿⢖⣀⣿⣿⣿⣿⢰⠀⠀⢿⡀⢳⠀⡇⠀ ⠟⢸⠀⢆⠛⣕⡯⣼⠶⠼⠤⡄⠻⠀⡀⢷⡿⠀⠀⠀⠁⠉⠓⠛⠶⣾⣶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣶⣵⢡⠟⣿⣼⢦⠙⡀⣳⣯⣿⠐⠀⠀⡆⠘⡀⢹⡿⠈ ⣰⢻⠈⠀⡄⠹⡀⢲⠉⣏⠲⠙⡀⢹⠀⡄⣿⠀⠀⠏⣠⠋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣹⣉⣯⣾⣶⣥⣾⢀⠙⡌⠳⡀⢣⣷⢸⠀⠀⠀⢸⠀⡄⣿⢸ ⠀⡆⢹⠙⠈⡀⠳⠈⠀⣀⢹⡀⣷⣄⠻⠀⣇⠈⠃⢠⠏⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣩⣀⢒⠖⡤⣀⠀⠃⣴⢸⡀⢳⡀⣾⢠⠀⠀⠀⣇⠀⡇⡿⣿ ⢻⣝⡬⣀⣍⢿⠶⣤⣀⣀⣀⢄⡷⠈⡄⠸⡀⢹⡼⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠲⠙⠈⠀⠀⡸⠀⢸⠀⡀⢳⢸⠀⠀⠀⠀⡇⠀⡇⣸⣿ ⣷⣿⣿⣿⣼⠁⣛⣛⣟⢮⠳⠈⠀⢇⠻⣏⠈⣿⢸⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⢳⠀⠸⠀⠀⡆⢸⠀⠀⠀⠀⡇⠀⡇⢸⣿ ⠦⣽⣶⣿⢻⣿⣿⣿⣸⠀⠀⣄⠙⡘⡄⡘⣿⣀⢸⣸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠦⢶⠀⠀⠀⢸⠀⠀⠀⠀⡆⠀⡏⢳⣿ ⠀⣦⠻⡨⣦⣷⣿⣿⢀⠋⠸⠁⡟⢸⠀⢧⡏⠀⢇⢸⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠾⣶⡷⣾⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠸⣼⡟⣿ ⠀⠀⡄⢻⠀⠀⣄⣷⠇⣿⢹⡇⣆⠀⠀⡀⣷⠀⡇⢸⠀⣧⠈⠀⠀⠀⠀⠀⠁⠋⡿⣷⣸⣇⠿⣿⢿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢧⠀⠀⠀⠀⣿⣇⣿⣿ ⠀⠀⠀⣎⣻⠀⠁⣧⣿⣿⣿⡞⠈⠸⠀⠀⡅⠸⠀⢸⠀⠀⢧⠘⠀⠀⠀⠀⠟⣼⢀⠀⣉⣿⣿⣼⢀⠀⠀⠟⢉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⢸⠀⠀⠃⣰⡇⣿⣿ ⠀⠐⠀⠀⣧⠸⠂⡀⢻⣄⣷⢻⢷⢹⠀⠀⡾⢸⠀⢇⠘⠀⠀⣦⠻⠉⠀⠁⣿⢻⠟⡿⣾⣶⢀⠀⠒⠗⡾⣠⠀⠉⠞⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⠀⠀⡞⠀⡇⣧⣿ ⠀⠄⠀⠀⡄⣷⠌⠀⡤⢻⠀⣄⡳⣯⠹⠀⢸⣇⠈⠀⣧⠲⠈⠀⡄⣳⣬⡦⣿⣿⢚⣖⢲⠒⠒⠒⠒⣶⠒⠒⡽⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠏⢠⠀⡟⡇⣿ ⣤⠲⠙⢉⠀⡀⣿⠈⠀⡀⢷⠈⠀⡀⣤⢷⣏⡈⢱⠀⡀⢳⡀⢤⠓⠉⣍⡩⢹⡉⣚⢶⠶⠲⠔⠤⠤⠠⠀⠠⠀⡒⣒⣄⠤⠷⠫⠛⠑⠉⠀⠀⠀⠀⠀⢸⡆⠀⠃⣰⠀⠀⣹⡿⣿ ⠀⠀⠀⣀⣇⠿⡿⢻⠈⠀⠀⣄⠳⠈⠀⠀⡀⢦⡌⠘⠀⠉⢻⠚⠷⣾⣓⣛⢛⠛⠙⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⣤⢶⠿⠛⠈⠛⢰⠀⠃⡸⠀⠀⠏⣟⣿⣿ ⠀⠀⠀⠃⡿⣿⣿⣿⢿⠈⠀⠀⠀⣀⢦⠛⠈⠀⡇⣾⣠⢀⠀⠁⠉⠒⠶⠵⡤⣀⣀⣀⡀⣀⣀⣀⣀⠤⠦⠶⠒⠙⠉⠈⠀⠀⠀⠀⠀⠀⠁⠈⣀⣀⣦⠘⠁⣰⠀⠀⠁⣟⣿⣿⣿ ⠀⠀⠁⡛⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⣀⢯⣰⠀⠋⠿⣷⣉⠀⠀⠀⠀⣄⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⠑⠉⠀⠀⡀⣄⠦⠲⠝⣹⠀⠀⠀⡿⣿⣿⣿⣿ ⠃⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⠹⠀⠀⠀⠀⠃⣸⠋⣴⣤⣧⠘⣄⢴⠲⠙⠉⠀⠀⡀⢤⠲⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠠⠀⠀⠀⠀⠉⠛⠞⡿⣿⣿⣶⣦⣤⣀ ⡤⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⡇⣾⢀⠀⠀⠐⣦⠛⠉⠉⡛⣻⣄⠤⠲⠛⠙⠋⣙⢌⠤⠢⠛⠛⠛⠙⠉⠉⠉⠋⠛⠛⠛⠒⠀⠤⠤⡠⣁⣯⣿⡾⣴⣠⢀⠠⠀⠀⠄ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⢷⠙⠀⠀⠠⠀⠠⡄⠀⡄⣄⠻⠀⠄⠾⡙⢤⠲⣙⣀⣀⣇⣘⠳⣄⠳⠓⠙⠉⠀⠀⣳⣝⠿⠾⠿⡶⣤⣠⢀⠀⠀⠀⠁⠉⠉⠉⠟ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⣄⢠⠐⠈⠀⢈⡀⠀⠁⠀⣌⢷⠶⡶⣶⠳⠉⡀⣄⠿⠟⣶⡶⢷⡶⠶⠶⡬⣤⣠⣀⣀⠀⠀⠀⠀⠉⠋⠞⡤⡀⣀⠀⠈⠁⡟⣿ ⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠀⠀⠐⠀⠐⠀⠀⠂⠀⠐⠂⠀⠐⠀⠀⣂⣤⣐⣀⠐⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠖⡴⣠⢀⠀⠀⠀⠀⠀⠟⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠉⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⢠⠁⠼⣧⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠏⣠⠀⠀⡲⠟⡤⢤⠸⣀⣇⠸⠀⠀⠀⠄⠳⠋⡈⣀⣥⠮⠓⠙⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⣧⢨⠀⠀⠀⠀⡏⢺⡴⢀⠀⡞⢀⠀⠀⠀⠀⠀⣄⣝⠘⠀⣄⠳⣄⣷⠹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠞⣠⢁⡾⡤⣃⢴⠯⠺⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⡼⢀⠈⠋⠛⡴⢀⠀⠀⠀⠀⠀⠀⠀⡄⡸⠹⠀⡀⢹⠀⣄⢿⠈ ⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠋⡴⣀⢋⣴⠀⠋⣤⢀⠃⡰⠏⣳⠀⠀⠀⠀⠀⠀⠀⣷⠉⠈⡼⠀⠀⢆⣹⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡿⠈⠀⡇⠀⠀⣇⢾ ⠀⠀⠀⠀⠀⠁⡈⣁⣈⡄⢾⠒⡴⢶⠁⠟⢨⠀⠃⣼⠏⢠⡀⢳⠀⠀⠁⠉⠋⠖⡶⠰⣀⣦⠘⠀⠀⡀⢦⠳⠈⠀⠀⠀⠀⠀⠀⠀⠓⡏⢸⢸⠁⡸⠀⠀⡇⢸ ⠉⠀⠁⠋⠿⡿⣿⣀⣿⠀⢷⠈⠋⡿⣿⣠⠀⡀⣁⣞⢠⠃⠞⡦⢴⣀⣀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⣿⠽⠀⠀⠀⠀⠀⠀⠁⣾⢀⢻⡴⠀⠀⠉⣼⠀ ⣄⠀⠀⣅⣿⣧⢛⠛⠀⠉⡀⣧⢸⣀⣧⣤⠳⠟⣠⠀⠏⣰⠀⠀⠀⠀⠁⠛⠉⠈⠀⠀⠀⠀⠀⠀⣆⠳⠈⠀⠀⣧⢷⠀⠀⠀⠀⠋⡴⢀⡏⢠⠀⠀⠟⣠⠀⠀ ⠀⠀⠇⣿⡈⣦⣿⣿⠸⣄⠀⡇⣹⢸⡌⠀⠋⢰⠁⠟⣠⠀⠀⠀⠀⠧⣶⢶⣴⢠⠀⠀⠀⠀⠀⠀⠀⡀⢷⠈⠀⡀⣼⢸⠀⠃⡼⢀⠀⠎⢠⠀⠋⡴⢀⠀⠀⠀ ⠀⠀⡄⣠⠀⠀⢀⠀⠀⠀⠀⡇⣷⢠⢳⡰⢀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠻⠈⠀⠀⡄⢻⠀⠀⢸⢹⠟⣠⠀⠁⡔⢀⠋⡴⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠁⡾⡀⢸⠀⣀⠦⠓⡏⠀⠀⠁⠛⠿⡹⢿⠈⠀⠀⠀⠀⠁⠈⡀⢤⣶⣄⣤⣶⣿⠀⠀⢸⣾⢋⠠⠀⡜⠀⠟⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⢸⠀⢳⠈⠀⠀⠀⣧⢸⠎⣧⢟⡿⣿⣿⢀⠀⠀⠀⠀⡆⣀⣀⣀⣤⣤⣠⠇⣿⠀⠀⢁⢾⣳⠀⠀⢹⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣄⢤⠳⠈⡀⣽⢉⡏⣿⣿⣿⢰⠁⠋⠼⠦⠶⠓⠈⠀⢧⡟⠻⠈⡇⣿⠀⠀⡎⢀⠀⢦⠘⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⠀⠙⠀⠀⣇⠘⣿⣿⣿⣯⣾⣶⠦⡷⣜⠱⠀⠀⠀⣄⠸⠀⢻⢀⢀⡗⣼⠀⠎⢠⠦⠙⠀⢿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠶⢽⠈⠁⡾⣿⢹⡾⣾⣦⠙⠀⠀⡀⠀⡀⢣⠀⠀⠀⣧⠀⡇⠀⠀⡀⠀⡟⢠⠀⠀⡄⠱⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⢸⡇⣧⢹⡄⠀⡀⢠⠀⠀⠀⠀⡀⢸⠀⠀⡇⢹⣸⠀⠀⠋⡴⣷⠀⠀⠀⠀⡄⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢳⢹⠀⠀⣦⠐⠈⠀⠀⠀⠀⠀⠃⠀⡀⠀⠀⡆⣴⠀⠀⠎⢠⠀⡆⠘⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡈⣧⠨⠀⠀⠀⢆⠙⠀⠀⠀⠀⠀⢄⠙⠀⠀⠀⠀⠀⠆⢠⠀⠀⠀⣆⠙⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢿⣙⠈⠀⠀⠀⡀⠦⠘⠀⠀⠀⠀⡀⢤⠐⠀⠀⠀⠁⠉⠈⠀⠀⠀⡀⢦⠙⠀⠀⠀⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠉⣄⠦⠒⠓⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⠯⠲⠒⠙⠉⡉⢍⠺⠐⡍⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⠀⠀⠀⠀⠁⣸⢄⠯⠶⠓⠙⠈⠁⠋⠛⠾⠷⠟⡴⣀⠀⠀⠋⣰⢀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠞⣠⠋⡴⢀⠀⡀⣦⡻⣈⠀⠤⡠⣀⠀⠀⠀⠁⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠁⡏⢖⣠⢀⠀⠀⠀⠀⠀⡀⣦⠳⠈⠀⣥⠿⠛⠾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠤⠤⠤⠤⠤⠤⠤⡦⢸⠀⠀⠀⠀⠀⡀⣻⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⣋⣼⢀⠀⠀⠀⠀⠋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣇⠈⠦⠑⠀⡀⢢⠘⣀⠀⣽⣾⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⡞⠲⡗⠹⠀⠀⠀⠀⠀⠀⢹⠀⡄⠿⠀⠀⢀⠀⣀⣇⢀⠀⠀⠀⠀⠀⡏⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⢠⠀⠀⡀⢳⠈⠀⠀⠀⠀⣧⠘⠈⣆⠈⠁⠊⠀⠀⡿⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⢤⠳⠀⠀⠀⣇⠙⠉⠈⠀⡧⣷⢸⠀⢀⢀⠀⠀⡏⣸⠀⠀⠀⠃⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⠤⠀⠀⡆⠀⠀⠇⣴⣀⠀⠀⠀⡇⡇⢸⠀⠀⠀⠀⠟⣰⢀⠀⠀⠀⠏⢫⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣰⠀⠀⠀⠀⠀⡿⡌⢸⠀⠀⠁⡜⢀⠀⠀⠀⠀⠇⢿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡞⢠⠀⠀⠀⠀⠀⠁⣿⣀⣇⠉⠞⣠⠀⠀⠀⠀⠀⠀⡇⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⡰⠀⠀⠀⠀⠀⠀⠀⡇⣇⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠇⢯⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠃⠉⠟⣻⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⣽⣱⣳⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⡇⠘⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠃⣾⣷⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⠀⠀⢳⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡇⢹⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣶⠬⠶⠑⡌⠸⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⡀⣯⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣀⣧⠈⠀⡀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢯⠖⡤⣠⣀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⡰⢀⠀⠀⠀⠁⡚⢤⠳⠙⠉⠉⠉⠋⠚⠶⣲⠙⠈⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⣇⢼⠧⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠏⢸⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠻⠈⠀⠀⠀⡄⢹⠀⠀⠀⢧⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣄⠲⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢿⠈⠁⠀⠀⣧⠀⠀⠀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢤⠢⠒⠙⠈⠀⠀⠀⠀⠀⣆⡟⡞⠀⠀⡇⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠲⠈⠀⠀⠀⡀⣦⠻⠈⡀⠀⠀⠀⠀⠀⢻⠞⠻⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠢⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠀⠀⠀⠀⠀⣀⠦⠺⠓⠉⠉⠋⢠⠀⣇⠀⠋⠟⠘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢥⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠀⠀⠀⠀⠊⠴⣧⠀⡀⣇⢉⠀⠀⡤⣀⠀⡄⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⣀⠀⠀⠀⠀⠀⣀⣄⢤⠲⠙⠀⠀⠀⠀⠀⣾⠀⠀⠃⡵⠉⠋⣴⠀⠀⠀⡀⣀⢤⠳⠈⠀⠀⢺⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢇⠘⠀⠀⡇⢠⠀⠃⣸⠃⣸⣇⠴⣧⢰⠁⠋⠉⠞⠶⣷⠸⠃⢰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠋⠴⣠⠀⠀⠀⠀⡏⢰⠀⠀⡟⠀⠀⠀⢹⡀⠘⠀⠀⡾⡤⣤⣤⢤⢣⠀⠀⢇⣘⣧⢿⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣿⢈⠀⠀⠀⠁⠉⡶⢀⠀⠀⡏⢰⠀⠀⠁⡟⠉⢾⠑⠊⢿⠽⣩⠿⠋⠴⠦⠓⡏⢽⡼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠘⠀⠀⡀⣀⣀⣀⣀⣀⢀⠀⠀⠁⡞⢠⠀⠀⠀⡆⣾⣿⢀⠀⣀⢤⡢⣓⣼⢀⠀⠀⠑⣋⣴⣄⠧⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠲⠑⠉⠉⠉⠉⠉⠉⠒⠴⣀⠀⠀⠀⠀⠀⠀⠀⡄⠦⠑⠉⠀⠀⠀⣧⢺⡑⣯⣷⠳⠈⠀⡇⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⠓⠈⠀⢸⠀⣀⢦⢸⢧⠘⡏⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠓⢸⠀⠀⠀⠀⠀⣶⢤⠀

⠀⠀⠀⠀⠀⠀⠀⢒⠁⠀⠀⠀⢆⠸⠀⠀⡀⢄⠓⠒⠒⠁⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠂⠡⠤⡤⠙⠀⠀⠀⢠⠀⠀⠀⠀⡀⠡⠄⠐⡀⠣⠃⠑⠀⠀ ⡇⣀⠄⠠⠀⣀⣀⣀⠠⡀⠑⠀⠀⡄⠈⠀⠀⠀⠀⡀⠸⠀⠀⠀⢇⠸⢆⠀ ⠃⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠞⠲⢿⠘⠈⠀⠀⠃⢠⠀⠀⠀⠀⢸⠀⢸ ⡇⢰⠢⠀⠀⠀⠀⠀⠀⠀⡰⣰⢀⠀⡄⠥⢑⢁⠚⢺⠀⠀⠌⠀⠀⢰⠀⠘ ⡀⠑⠀⢀⠀⠀⠀⠀⠁⠔⣃⠈⢀⠀⠀⠃⢧⣹⣄⢸⠀⡠⠀⠀⠀⠀⠁⢠ ⠀⡀⠮⠐⠈⠀⠀⠁⢂⠤⣦⢻⠈⠀⠈⡅⡸⣧⢧⡘⠱⠀⠀⠀⠀⠁⠠⠀ ⠀⡏⠠⣀⣀⠄⠑⡀⠵⢼⡆⠈⠀⣣⠀⠀⢇⠀⣿⣠⡜⠀⠀⠀⠂⠠⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⢆⠈⠀⠀⡒⠢⠘⠒⠈⠀⠃⣤⡠⠀⠀⠀⠔⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠈⠈⠊⢵⡤⢢⡗⢩⠜⠴⠘⡠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⠴⠀⠁⢼⣧⣧⠰⠲⠄⠀⠁⢏⢸⠀⡇⠀⠀⣴⠠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣶⣧⢀⣟⠿⠺⠠⡗⣬⣿⢰⠀⡆⠚⠁⠥⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⢤⠖⢊⠐⠉⡌⢇⣰⠀⠄⣋⢠⡀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠈⠕⣌⢤⡱⠈⡀⠉⠛⡩⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⣠⡄⣤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠑⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⢀⠀⠀⠀⠀⡀⣀⣀⠀⠀⣷⣰⠤⠤⠦⠶⠒⡒⣙⣉⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣼⣷⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⡀⣦⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠻⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠙⠀⠀⠀⠀⠁⡞⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣷⢿⠙⠀⠀⠀⣷⣿⠉⠋⠛⡟⣿⠻⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢷⠘⠀⠀⠀⠀⠀⠀⠈⡆⡜⢦⠀⠋⠖⡤⠀⣄⠶⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⡀⣦⢿⠙⠛⡿⣿⣾⣤⣦⣷⣿⢹⠉⡀⣀⣤⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⣄⠦⠑⠉⠚⠶⣠⠀⠦⣆⠘⡗⢀⠀⠀⠀⠀⠀⠀⡀⣀⢤⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⣿⣴⣇⣹⠘⠀⠁⡏⣿⣿⣀⣄⣿⢿⣿⣿⢛⠈⠀⠀⠀⠀⠀⠇⣺⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⣠⠀⡇⣼⢤⠉⠀⠀⣄⣿⠿⡾⣿⣟⣿⣿⣿⣿⠻⠒⠤⣠⢦⡗⢠⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠙⠀⠀⠀⠀⠀⠀ ⠅⠇⠀⠏⣰⠀⠀⡄⣿⣶⣴⣤⣤⢿⣿⣼⠀⡄⣿⣿⡙⣿⣴⢀⠀⠀⠀⠀⡼⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠈⠀⠀⠀⠀ ⡀⡟⠘⣿⠀⠀⠀⠀⣿⠁⠻⠿⡽⣤⣀⠀⠀⠀⡀⣷⣾⣼⠀⠀⠀⠀⠀⠀⢸⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠀⠀⠀ ⠀⣇⢿⣾⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⢿⠛⠈⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠙⠀⠀ ⠀⡇⣿⢻⠐⡇⢹⠋⡏⣿⣿⣿⣿⣾⣸⡋⣖⢠⠷⡿⣿⢻⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡬⢶⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣌⢣⠀ ⠀⡀⣿⣙⠟⡴⣠⡄⣿⣾⣷⣻⢶⠼⣠⢀⠀⠀⠁⣛⣴⣤⠻⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠹⠀⡀⢳⠈⠀⠀⠀⠀⠀⠀⠉⠛⠐⡄⢠⠀⢻ ⠀⠀⣇⣨⠀⠀⠁⠋⡿⢻⡙⣄⢶⠛⠉⠉⠋⠞⣶⠒⠒⠒⣿⠀⠀⠀⠀⠀⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⠀⡄⠹⠀⠀⢤⠀⠀⠀⠀⠀⠀⡦⣿⢩⠉⠉⠀⡆ ⠀⠀⠀⢦⠟⠿⣯⢞⣤⢀⡄⢷⠘⠀⣃⣾⣠⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⠀⢹⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⠀⠀⠀⠀⠀⠀⠀⠃⠟⣸⢀⠀⡀⢆⠙ ⠀⠀⠀⠀⡄⣽⢀⠁⠁⠋⠞⣽⢈⠁⡇⢀⠀⠀⠀⠀⠀⡇⢈⠀⠀⠀⠀⠀⡇⠘⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⠒⡒⣗⠹⠈⡖ ⠀⠀⠀⠀⠀⡀⣦⡷⣽⢛⠉⡉⣭⣿⣶⠸⠀⠀⠀⠀⠉⡉⢻⠈⠀⠀⠀⠀⡀⢳⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣴⠀⠀⠀⠀⣅⢻⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⣀⣀⠀⠀⣇⠘⠀⠃⡠⢀⠀⡀⣵⠶⠙⠀⠀⠀⡄⢹⠀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠁⠉⠉⠋⡟⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠉⢰⠀⠀⠀⠀⡆⠈⡀⣄⠦⠙⠈⡄⠹⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⠺⠶⣤⣳⢈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣄⠷⡬⠳⠀⢦⠘⠀⠀⠁⠛⠛⠉⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⣦⣸⢀⢄⠙⠀⠀⣄⠧⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣦⡙⢦⠙⣄⠳⠋⣠⡆⣿⣰⣆⣿⢸⠀⠀⠀⠀⠀⠀⠁⡾⠛⠓⡟⠀⠀⡀⢦⠛⠚⡶⢿⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⢹⠉⠉⠉⠉⠉⠉⡍⠹⡋⢶⡤⢀⠁⡞⢠⠀⡞⠇⢠⠀⠀⠀⠀⠀⠋⡰⡏⣽⠀⡏⠀⠀⠀⠀⡄⢻⠀⡄⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⠀⠀⠃⡼⣀⡀⠀⡀⣧⣈⣠⣀⣧⢸⠀⠁⠞⣠⠀⠋⡴⠋⡾⠴⠿⠙⠒⠴⣠⠁⠞⢠⣀⣧⣰⠀⠀⠀⠀⠀⣿⠉⠋⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠄⣠⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⣉⣿⣶⠳⠋⡽⢋⡿⢋⠖⡴⣀⠀⠀⠀⠋⣻⠈⠀⠎⣠⠀⠀⠀⠀⠁⡞⢠⠀⠁⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠙⠀⠀⠀⠀⠀⠀⠀⡁⢿⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⣀⣏⣸⠀⠀⠀⠀⠁⠋⡿⠉⠁⠋⣰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠤⠤⠤⠤⡠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠹⣟⣼⠢⠖⠦⡿⣨⢀⠉⡞⣤⢀⠀⠀

⠈⣀⣀⢀⠉⠛⠟⡿⣶⢶⡤⣠⢀⠀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠇⠘⠁⠈⠚⠒⠒⠓⠟⣿⣿⣿⣿⣻⣉⣉⣀⣥⠍⠉⠛⠚⠁⠈⠀⢆ ⠀⠋⠟⣾⣴⣠⢀⠀⠀⠀⠀⠀⠀⠁⠉⠋⠙⠛⠚⠶⠵⠭⠠⠀⠀⢻⡛⢶⠶⠴⣤⣤⣤⣤⣤⢠⣄⢦⣷⣿⣿⣏⣿⣼⣤⣤⣿⣶⣍⠀ ⡾⣴⣆⠸⠀⠀⠋⠟⠿⣾⣿⣿⣾⣧⣽⣉⣉⠛⠛⣶⣟⠟⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣀⣦⣿⣠⠀⠀⠇⣼⣶⠷⠙ ⠀⠀⠀⢿⠚⣴⣠⣉⠛⠟⣾⣦⢀⠁⣾⣴⣤⣧⠀⠀⡏⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠁⡉⢦⠘⠀⡿⠀⠀⠀⣿ ⠀⠀⠁⣿⠟⠿⣿⣶⣤⣠⠀⠀⡇⣠⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⡇⣿⢻⢠⠀⣶⢿⠙⠙⣟ ⠋⡵⣿⣴⣧⣼⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡏⠀⠀⣯⣿⣿⣿⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡋⣾⣠⠁⠉⠈⣤⣦⣴⣀ ⢟⣺⢀⠋⣿⠀⠀⡟⢿⠈⠀⠁⢰⠀⠀⠀⠀⢸⠀⠏⣇⣿⣿⡽⠳⣿⠈⠀⠀⠀⠀⠁⠋⠛⠾⠤⠤⣿⣷⢀⠀⠀⠟⣶⣦⣿⠀⠀⠀⠏ ⣦⠻⡼⣠⣀⠀⠀⡀⣀⠉⠀⡜⠀⠀⠀⠀⠎⢀⠀⢸⡆⣿⣿⣿⠀⣧⢿⠀⠀⠀⠀⣀⣤⣤⠳⠒⠖⢠⡄⢻⠀⠇⣿⠀⠁⣟⢸⠀⠇⣴ ⠀⠀⠀⠀⠁⠛⠿⠴⠴⣦⣾⢀⠀⠀⠋⡴⢀⠀⠏⢸⠀⣧⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡀⢤⠙⠀⠀⡄⠳⡎⣻⠀⡏⣿⢀⠀⣇⠘ ⡾⠷⠈⠀⡿⣤⣧⠘⠀⡔⢋⠴⡧⣀⢀⠀⠀⠀⣹⢣⠀⠀⣷⣿⠈⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⠀⠀⣄⣷⣿⣴⢀⠀⠀⡆⢹ ⠀⡀⢹⠀⣧⠉⠋⢸⠁⡞⢶⠧⡿⠲⠓⠉⠉⠀⡀⣀⢲⠙⡛⣿⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⡆⣿⢻⠀⠁⠉⠀⠀⣧ ⠀⠟⢸⠀⡀⣶⣠⠀⠀⠀⠁⡴⠀⠀⠀⠀⡀⣄⠦⠙⠀⠀⣆⣿⡶⣦⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠿⣿⣾⠀⠀⡇ ⡇⣠⠀⠂⠟⠻⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠈⠀⠛⠙⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⣿⢸⠀⠀⣿ ⣼⠀⠏⠿⠛⢈⠀⠀⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⣷⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡅⣾⣠⢀⠀⠁⣟ ⠀⠛⣸⣆⣶⣿⠿⠓⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⣽⣷⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠃⠛⡟⠀⠁⠋⠟⣿⣠ ⠀⡄⣷⠻⡛⣾⣤⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⡄⣷⢹⡀⢦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⡇⣾⣀⠿⣿⣿⣿⣨⠀ ⠀⠀⡓⣕⣤⢀⠁⠛⠿⢾⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⡀⣦⠚⠘⣄⣷⠀⠀⠀⠀⠀⠀⠁⠞⢁⠟⣿⢹⠉⣾⣤⣖⣠⠀⠀ ⠀⠀⠀⣆⢷⠿⡈⣦⣭⢀⠀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠴⢥⡿⠀⠀⠀⠈⡇⢦⠙⠉⠉⠉⠛⡚⡷⣿⣿⣾⣴⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⣵⠲⣿⣿⠿⠻⡈⢦⠑⠀⠀⠀⠀⠀⠀⣀⣄⠿⣠⣀⣀⣄⠶⠲⡟⠀⣧⢐⣀⡿⣿⢻⡟⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣿⢸⠀⠁⣈⠤⠓⠛⠘⠀⠋⡟⢴⠀⠀⠀⠀⠀⠀⡀⢷⡆⠀⠟⣿⣿⣿⣟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃⡈⢏⡹⣀⣤⢿⡾⣷⣿⠻⠋⠛⣸⡿⢠⠀⠀⠀⠀⠀⠀⡇⢸⠇⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢟⣿⢻⣶⣷⠘⠀⣿⢻⠉⡈⣦⡷⣝⢿⢠⠀⠀⠀⠀⠀⠀⠀⡆⢽⡏⣿⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⣼⣤⢃⡟⣿⢠⡇⣾⡙⣝⣿⣿⠿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣨⣟⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⡉⣬⢠⠀⡇⢛⡻⠀⣀⠁⣤⣴⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⡳⢿⣾⣿⣿⢽⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠆⣿⣧⣿⢻⠟⢻⠈⢆⣿⠻⡿⣿⠿⡿⣶⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢹⡄⣷⣿⢾⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢄⠷⠙⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣈⠐⣋⡿⢶⡴⣥⣤⢯⣴⣠⢀⠀⠛⠔⠤⠤⠲⡙⣀⣤⡷⢽⠤⠤⠤⠦⡖⣿⣿⣿⣿⣿⣿⠙⠀⠀⣇⢸⣿⢹⠀⠀⠀⠀⠀⠀⠀ ⠙⠀⠀⠀⠀⠀⣄⢷⠙⠈⢠⡇⣿⣿⣿⣿⣿⢛⡾⣠⠀⠀⠏⣾⣠⢀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣯⢾⠀⠀⡀⣧⠻⠈⠀⠁⣏⣿⣿⣿⣿⣿⣿⠻⠀⡀⣿⡇⣿⠈⠀⠀⠀⠀⠀⠉ ⣿⢿⠙⠀⠀⠀⠀⠀⡀⢷⠻⡏⣿⣿⣿⣿⣿⣠⠀⠀⠀⡟⣼⢀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⣄⣿⠿⣠⢀⣄⣿⣿⣿⣿⣿⣿⢻⠀⣧⣸⣿⢸⢸⠈⠀⠋⡿⣿ ⣿⣿⣿⢿⠙⠈⠀⠀⠀⠀⡀⣽⣟⣿⣿⣿⢠⠀⠀⠃⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢻⠀⠀⡄⣷⣿⣿⣿⣿⣿⠹⡈⣿⡟⢿⣷⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⠛⠉⠀⡏⣴⣟⣿⣿⢰⠀⠀⠃⣷⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢻⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣼⠀⣋⣼⣠⠏⣿⣿⣼⠀⠀⠏⣱⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢻⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢶⣤⢁⠋⡿⣿⣿⣿⢾⠤⣧⣿⡷⣿⣰⠀⠋⠐⠙⠉⠈⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠁⠉⠉⠚⡙⣷⠿⣝⠻⠈⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣴⣠⢁⠋⠿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣳⣿⣿⠝⠭⢋⡽⣿⣧⣿⠿⡿⠀⠀⠀⠟⢿⠙⠀⠀⠧⠿⣽⣿⣭⢆⡙⠏⣿⣿⣿⣿⠙⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢹⠀⠀⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣶⣤⣤⣭⣪⣓⢸⠁⠸⠀⡟⣸⣿⣿⠻⠀⠀⣷⡚⣙⣍⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆⣿⣿ ⣾⣴⣆⠘⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠋⠀⠁⠟⣸⠃⣿⢀⡏⣻⠂⡟⣿⣿⢳⠈⡇⢿⢯⠛⠙⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⡀⣦ ⠀⠀⠀⣇⠸⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢃⣿⣾⢥⣿⣿⠛⣿⣿⡏⣿⣿⣿⣿⢿⡷⣿⣿⣿⣿⢹⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠣⠉⠀⠀ ⠀⠀⠀⠀⣆⠘⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡿⣷⢸⡟⣇⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣻⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⣄⢦⠛ ⠀⠁⠋⠖⡠⣄⠹⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡀⣦⠻⠈⡀ ⣷⢙⠀⠉⠋⠿⣿⠹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠈⠀⣄⢿ ⠀⣀⣄⣷⢻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣹⣆⣿⣿⣿⣿⣿⠀⣿⣿⢹⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣿⣶ ⠀⠀⠀⠀⡇⣮⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢻⣦⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⢰⣤⣐⠀ ⠀⠀⠀⠀⡀⢸⠀⣅⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣫⣽⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢷⠀⡇⡀⣷⢻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠏⣼⢀⠀⠀⠀⠀⠀⠏ ⠀⠀⠀⠀⠀⡇⠁⡏⠛⠒⣿⣁⣸⡇⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣶⢠⠇⣴⠀⠀⠀⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⠀⡾⠀⡇⢠⠁⣿⡇⢠⡇⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣄⢹⠉⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⢠⠀⡟⠀⠃⣷⡇⠘⡇⠈⠀⣄⣿⣬⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⢀⡏⠀⣿⢀⠀⡆⢹⠀⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠇⢰⠀⠃⢰⠀⣼⡄⠹⢦⠙⢄⠓⠈⡀⢦⠟⠻⣎⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣡⡾⢀⠏⢰⠃⣸⠀⠀⠀⣧⠸⠀⠀⠀⠀⠀⠀⡃ ⠀⠀⠀⣸⠀⠀⡞⠀⡇⢀⠀⣄⢦⡙⢦⠓⣈⢦⠓⡉⣤⣷⠙⠀⠠⡀⣄⣤⣶⣶⣷⣿⣿⣶⣶⣶⣶⣶⣤⣦⣿⣿⣿⣾⣫⠾⣡⠋⡴⢁⠟⣰⢻⠀⠀⠀⠀⣧⠘⠀⠀⠀⠀⠀⡅ ⠀⠀⠇⠀⠀⠇⢸⠀⣼⠀⠃⠀⠁⡜⣄⠢⣙⢄⠲⡉⣀⠤⣢⣷⠮⠻⠛⠉⠀⠀⠀⣆⢀⠀⠀⠀⠉⠉⠛⠿⠽⣻⢔⣧⣋⠖⣠⢋⠾⣠⠀⠀⡇⠸⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⡎⠀⠇⢸⠀⡇⠏⣰⠀⠀⠀⡀⢄⠲⡙⣌⠤⠒⠑⠉⠉⣉⣉⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣉⣉⠉⠒⠖⡠⢻⠞⣤⢳⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⡇⢸⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠤⠒⠒⠒⠒⠒⡑⣉⣈⣀⣀⣉⣉⣉⣉⣉⢉⠉⠉⠋⠛⡾⣶⢳⠈⠀⣄⠳⠀⠀⠀⢸⠀⠀⠏⠰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⠀⡆⢸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢧⠈⠀⡀⢷⠀⠁⢸⡀⡖⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⠀⡀⢸⡟⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⡆⣿⣿⣟⠀⠀⠀⠙⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠂⣿⣿⠀⠀⠀⠳⠀⢧⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⢀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⢄⠀⢠ ⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢸⠀⠀⠀⣷⠹⠀⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠀⠀⠀⡇⡄⠹⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⡄⠙⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠈⠀⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⡄⡱⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣄⣿⣿⣯⣽⣦⣿⢸⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⡆⣾⣵⣁⢿⡇⢸⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡰⠀⠀⠄⠭⡛⣿⣟⣿⢸⠀⠀⠀⠀⠀ ⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⠀⠀⠀⠄⣿⣿⣿⣟⣿⢸⠀⠀⠀⠀⠀ ⠀⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⡀⢧⠛⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⣿⡹⠀⠀⠀⠀⣷⣿⣿⣿⣿⢼⠀⠀⠀⠀⠀ ⠀⠹⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⣧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠀⠀⠀⡄⣿⡿⣿⣿⢸⠀⠀⠀⠀⠀ ⠉⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠉⠛⡿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⣧⣿⣿⣷⢸⠀⠀⠀⠀⠀ ⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡴⢀⠀⡀⣆⠳⠈⠀⠀⠀⠀⠀⠀⠁⠉⠊⠒⠒⠒⠉⠈⢸⠀⠀⠀⠀⡄⣿⣽⣿⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡟⢠⠀⠀⠀⠀⠀⠀⣄⠳⠈⠋⠖⠠⣀⠀⠀⠀⠀⠀⠀⠀⣀⡦⠈⠀⠀⠀⠀⣷⣗⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⡄⡿⣴⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⣤⣳⢬⠀⠀⠀⠀⠀⠀⠀⡄⠙⠀⠀⠀⠀⠇⠻⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⣤⠳⠉⠈⠀⠀⠀⠀⠀⡄⠳⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠋⡸⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠻⣀⣯⡹⢄⠤⠤⠢⢀⠀⡀⣄⠦⠻⠒⠒⠒⠂⠀⡀⢆⢀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⡀⢤⠢⠒⠒⠖⠤⡤⣦⣷⢸⠀⡀⣀⠄⠤⠓⠙⠀⠀⠀⠀⠀⠋⡴⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⡄⠙⠀⠀⠀⠀⠀⠉⠊⠖⡤⣤⠤⠓⠈⠀⠀⡇⣿⢿⠿⠶⠶⡤⢀⠀⠀⠀⠀⠀⠀⠇⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠘⡀⠀⠀⠋⡿⣼⢀⠀⠀⠀⠀⠀⠀⡀⢦⠙⣿⣇⣿⣿⠺⠸⠀⠀⠀⠀⠁⠰⠈⠀⡿⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣛⢿⠛⡷⣾⣧⣼⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⣧⠘⣇⣼⢿⢿⠈⠀⠀⠁⡰⡼⠏⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣰⠜⢁⠞⢥⠻⠙⠘⠀⠀⠀⠀⠀⠀⠁⠣⢦⡝⣼⡸⣿⢿⠘⠆⣠⠀⡏⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠤⠤⣦⣶⣤⣿⣸⠀⢃⡰⠁⣳⣸⢇⢧⠀⠀⠀⠈⠀⠉⡀⣿⢼⡰⢧⢸⢸⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢀⠃⢸⠀⡌⣸⠃⢰⠁⢰⡄⢦⣶⣷⡿⠙⣰⠉⠀⡟⢁⢰⡿⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⡇⠀⠀⢧⢠⡼⠀⡞⠑⣉⢋⠟⠽⡯⣸⡇⣿⣿⣾⡘⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⢈⠀⢱⠀⡀⠸⠇⡏⢀⠃⣾⣴⣁⣟⣹⠋⣿⣿⣿⣶⢛⡿⢻⠉⠋⠛⠛⠛⠟⠛⠛⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢧⠉⡌⠱⠀⣆⡈⣷⠛⣿⢚⠴⣀⣁⣞⣿⣿⣲⡖⣥⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⢶⠒⠒⠒⠒⢶⣖⣳⠩⠈⠀⠀⠀⣷⢙⠉⠉⠖⡠⠿⢒⠁⠍⠟⣶⣶⠶⡴⣤⣄⣤⣤⣤⣤⣤⣤⣶ ⠀⠀⣈⣘⣁⣉⡏⣙⢉⣉⣉⠟⠉⢉⠛⠀⠉⠀⠀⠀⠀⢾⣤⠶⠛⠯⡝⢿⠿⠿⡨⣧⢩⠞⢶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⢀⡆⣥⣴⣥⣠⣤⣠⣂⣴⣶⢿⣚⣿⠛⠛⠛⠛⣟⠻⣛⢿⡿⣀⣿⣿⢿⡿⠉⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠓⠚⠓⠛⠛⠘⠀⠃⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡀⣀⣄⠷⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢸⠀⠀⠀⡇⣐⣧⣧⠿⠛⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡏⢁⢸⠁⣶⣿⣾⣤⣿⠿⠿⠒⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣸⡇⠀⡟⠂⣿⠈⠀⠀⣀⠀⠀⡇⢸⡀⣇⢬⠶⠓⠉⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡞⠀⠀⠀⢿⢰⠀⣼⣿⣾⢿⠼⢀⠀⠏⠋⡴⠀⠀⡏⣾⣴⣤⣀⡏⣠⠤⠤⠒⠒⠒⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡵⣴⢀⠀⠀⠀⠀⣯⠀⡇⢿⣿⢻⡿⣿⠠⠀⣇⣸⢀⠀⠇⣠⠀⠀⠀⠞⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠒⠒⠊⠃⠛⠘⠀⠀⠀⣷⢉⠀⠀⠁⠋⠒⡖⣹⠉⡿⣿⣿⣧⣼⠀⠀⠿⠟⢸⠀⠸⣼⠀⠀⠀⡟⢈⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠆⠦⠘⡤⢤⠱⠀⠀⡄⠘⣀⣠⣀⠀⠀⠀⠀⡀⣤⣤⣿⡿⢸⠀⡏⢠⡏⡟⡟⠿⢻⠓⠚⡴⢀⢸⠀⠀⠀⠀⠁⠀⠀⠀ ⣄⢩⣭⣡⣉⣧⣽⣤⠀⠀⠀⢇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⠀⢁⠟⣿⣴⣤⣠⣀⠀⠦⠑⡔⠀⠀⠠⠀⠀⣤⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠃⡟⣷⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣾⣠⠀⠀⠀⠀⠀⠀⠋⡴⠀⠁⠈⠉⠒⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⡸⣦⣶⡀⣦⣸⣄⠳⠙⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠀⠀⠉⡔⢀⠀⠆⣶⣰⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠻⠈⠀⠀⠀⣄⠶⠓⣏⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⡧⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠾⣿⣼⣷⠺⠀⠀⠀⠀⠀⡀⣇⡼⣃⣿⣼⠀⠀⠀⡆⠿⠀⣫⣼⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⡈⣤⠤⠀⠀⠀⠀⠀⠒⠛⠛⣻⣿⢀⠀⠀⠀⠀⠇⣼⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⢳⠈⠀⠀⠀⠀⠀⡄⢤⡲⣿⡙⣄⠿⠓⠛⠙⠋⡴⢦⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠉⠏⡽⣿⠳⠈⠀⡀⣤⠳⠈⠀⡀⢦⠑⠈⠀⠀⣄⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠓⠈⠀⣄⠳⠈⠀⠀⣆⣈⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠢⠑⣉⠠⠀⠀⢏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠄⣦⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡆⠘⠀⠀⠀⠀⠀⠀⡀⢄⠤⠒⠙⠈⠈⠀⠀⣉⠋⠒⠤⣠⢀⠀⠀⠀⠀⠀⠀⠃⡰ ⠀⡀⢤⠠⠤⠤⠤⠤⠄⣰⣀⣈⠀⡀⢸⠀⠀⢸⡀⣀⣸⣀⢸⠀⠤⠤⠤⠤⡤⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⢀⠀⠀⠑⠀⠉⢰⠀⠀⢠⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⡹⠀⠀⠁⠈⠀⣆⢈⠀⠀⠀⠀⡎⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⠀⠀⡀⠀⠁⢸⡀⢀⠀⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠋⠛⠤⣿⢶⠙⣏⠈⠀⠀⠁⡶⠙⠀⠀⠀⡽⠋⡴⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⣤⣤⣠⢀⠀⠀⡆⠙⣉⢴⣧⢻⠛⡟⣼⡦⣹⠉⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠟⠶⣷⣾⣠⣀⢀⠀⠤⠠⡀⣀⢀⣧⣿⠶⠻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⢀⠁⡿⢴⠯⠿⠬⠸⠀⠇⠵⠿⠽⡦⣿⠈⡀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠿⣶⣿⠒⣤⣤⣮⢀⠁⠀⣷⣬⣤⢲⡟⣶⠿⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⢉⠋⣿⢿⠽⣧⠿⠿⣠⢷⠿⣿⠧⠿⣿⠛⡉⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⡿⣿⡷⠀⡇⡷⣿⡿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⠽⡿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣬⣶⣿⣿⣿⣿⣿⣶⣴⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠘⡇⢸⠀⠀⣸⠀⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⢸⠀⠇⢹⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡧⠙⡟⠀⡀⣀⠀⠉⠉⢉⢉⢉⢉⠉⠈⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠞⠂⣶⣯⠾⡴⣠⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣄⢤⠶⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠦⠛⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⢿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢸⠀⠀⠀⠀⠁⠛⠶⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠉⠈⠀⣔⢧⠙⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠟⣰⣅⣟⢿⠲⠛⠛⠉⠉⠈⠀⠀⠀⠀⠀⠁⠉⠟⡽⣥⣿⢼⠀⠀⠋⡾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠀⡄⢰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⢋⠾⣴⢀⠀⠀⠀⠀⡀⢀⠀⠀⠒⠒⠿⠿⣿⣻⣿⢿⣶⣧⢿⠟⣇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⡞⢋⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠛⣾⣭⢷⡿⣧⣛⢶⡑⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⡷⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣄⣶⡷⣾⢶⡶⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠀⠀⠀⠃⣿⠀⠀⠀⠀⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡄⢹⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠀⠀⠀⠂⣽⠀⠀⠀⠀⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠺⠙⠉⠀⣆⠸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⢿⠈⠀⣀⣀⣀⠄⠠⠤⠤⠤⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⣠⡇⣽⡉⢿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⣅⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⢰⠁⣿⣨⠀⠀⡀⣀⢤⠐⠀⠀⠀⠀⠖⡤⣤⣦⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⣰⠀⠀⡗⣾⣤⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⣷⠘⠀⠀⣀⢁⠋⠛⠟⠀⠦⠒⠝⠫⠒⠀⠀⡷⣾⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣴⠀⠀⠀⠀⠀⠀⠀⡀⣤⠶⠶⡤⣀⣧⠿⣟⣽⠻⠈⠀⡀⣇⢦⠛⠉⠉⣏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡟⣿⣨⣄⢤⣦⣶⠻⠉⡀⢹⠀⠀⠀⣀⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣷⣠⠀⠀⠀⠀⡀⣦⢿⡿⠀⠀⠀⠀⠀⣀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢻⡛⠸⠀⠃⠙⠉⠀⠀⣏⣾⠳⠉⠀⠀⠀⠀⠀⣦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠊⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢀⠀⡇⣿⣾⣿⠿⣻⣍⣤⣦⢷⠙⠈⠀⠐⠀⡄⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢳⠉⡆⣦⣠⣀⣀⡀⣀⣀⣤⣻⢈⡉⣦⠻⠀⠀⠀⠄⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⣄⣦⠷⠯⠛⠈⠀⠀⠀⠀⡀⢦⣙⠈⡀⢧⠘⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⠀⠀⣄⣦⣽⢾⠓⠈⠀⠀⠀⡄⢳⠈⠀⣆⠹⠀⠀⠀⠀⡄⢳⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⡀⢻⠀⡀⣄⠦⠲⠙⠉⣍⠻⠙⣿⠘⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠳⠈⠀⣸⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠱⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣾⣶⣤⣤⣤⣀⠀⠀⠀⠀⢀⠀⡀⣁⡟⣿⣿⣯⣿⣰⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⠟⠿⠿⠿⠿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠚⡶⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⠿⠾⡧⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣶⣤⢀⠀⡀⣦⣷⣿⣴⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣷⣽⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣽⠀⠀⠀⠀⠀⠀⠁⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣄⣷⣿⣿⣿⠻⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⠻⠛⠛⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠛⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⢼⠀⠀⡐⣄⣶⣿⣽⢋⠛⠛⠿⠿⡿⣿⠀⠀⠀⠀⠀⡗⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢿⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣶⣿⣿⣿⣿⣿⣿⣿⣸⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀ ⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⢻⠀⠀⠀⠋⠀⠀⠀⠀ ⠁⣷⣿⣿⣿⣿⣿⣿⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⢻⠁⡟⣹⠀⠀⠀⠀ ⠀⠀⣄⣦⣿⣿⣿⣿⣿⣿⣿⠿⠿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣤⣦⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡆⣿⣿⣠⠀⡀⣀⣀⢀ ⣿⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣦⠳⠙⠉⠋⡴⢀⠀⠀⠀⠀⠉⠋⠛⠛⡏⣸⣆⠀⣿⣿⠀⠀⠀⠀⠀⠀ ⣇⠻⠉⠀⠀⠀⠀⠀⡟⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠈⠃⠟⡿⣿⣿⣿⣿⠀⡀⣧⠘⠀⣿⣿⠋⠸⠀⠀⠀⠀ ⡀⣿⣿⢿⠿⠛⠛⠛⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠋⠴⠀⠀⠀⡄⣧⣼⣄⣷⣿⣿⣿⢻⠚⠴⡤⢿⠃⣿⣿⣿⢡⠛⠀⠀⠀ ⠀⣾⣷⣟⣿⣿⣿⣿⣿⣿⢋⠛⠛⠈⠋⠞⠴⠤⠦⠿⣿⣿⣿⣿⣿⣾⢻⠀⠀⠀⠀⠀⡄⣾⡤⣤⣀⣀⣀⠀⠀⠀⠀⡰⡟⣿⣿⣿⣿⣾⠀⠀⠀ ⠀⢹⠀⡀⣀⣤⣦⣿⣿⣿⢰⠀⡃⣼⢀⠀⠀⠀⠀⣄⣶⣿⣿⣿⣿⢖⡷⠀⠀⠀⠀⠀⠀⣆⠛⠀⠀⠀⠀⠀⠀⠁⡼⠏⣿⣿⣿⣿⣿⢰⠀⠀⠀ ⠀⣧⠸⠀⠀⠀⠀⣿⣿⢸⠀⠀⣷⠀⠁⠉⠉⠉⠛⠒⠖⡤⣤⣀⠀⠁⡸⠀⠀⠀⠀⠀⠀⠀⡀⢦⠒⠈⠀⠒⠐⡋⡿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⢧⠙⠀⠀⠀⣿⣿⠈⠀⠀⡆⣽⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠠⠏⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀ ⠀⠀⡀⣿⣿⢿⠿⡿⣿⢸⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠂⠖⣠⠀⠀⠀⠀⠀⠁⠉⠛⠟⠿⣿⣿⣿⣿⠏⣽⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⣿⣿⣿⣿⣿⢿⠉⠉⠁⠀⠀⣀⢅⠩⠉⠉⠉⠋⠛⠻⠀⠀⠇⠿⡿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠚⠒⠒⠒⠒⠀⠀ ⠀⠀⠀⠀⣇⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⡇⣿⣿⣿⣿⣿⣴⢏⠀⠆⣟⣾⣿⣿⣿⣿⣿⣿⣠⠀⠀⠇⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣿⣾⢩⣿⣰⠀⠀⣤⢦⣷⣿⣿⣿⣰⣤⠣⠀⠀⡀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣽⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣾⣴⣠⢀⠀⠀⠉⠸⠀⡀⣿⣿⢸⠀⠋⣾⠀⠀⠀⡈⢀⠀⠀⠀ ⠀⠀⠀⠀⠛⠟⡿⣿⣿⣿⣿⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣛⣿⣿⣿⢠⠀⠀⠋⠀⠃⡾⣤⣦⠿⠶⡿⣿⢸⠀⣹⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⣽⣀⣥⣿⣿⣿⣿⢹⠀⠀⣀⣀⣤⣦⣶⣶⣷⣿⣿⣿⣿⣿⣿⣹⠉⠟⠿⢸⠖⣠⠀⠀⠀⡇⢶⣼⣆⢸⠀⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣶⣶⣶⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣷⣿⣿⢾⣴⣀⠀⠆⠰⠀⠁⠋⠉⠟⢰⡇⢸⠀⠀⣿⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⢿⠛⠛⠛⠛⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⡀⣷⣿⠛⠀⠀⠀⠀⠀⠀⡏⣿⣿⣾⠠⠀⢸⠀⣤⣤⠀⠀⠀⠀⠉⠀⠀⠀ ⠀⠀⠀⠀⣿⠷⠿⠿⠒⡀⣷⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠇⣿⣿⣸⠀⡇⣿⣿⢹⠀⠀⠀⠀⠁⣿⣿⣿⢀⠀⠀⢰⠀⠛⠲⠀⠀⠀⡄⣀⠀⠀⠀ ⠀⠀⠀⠀⣧⠏⠹⠿⠘⠀⡀⣷⣿⣿⢿⠈⠀⠀⠀⠀⠀⡏⣿⣿⣤⣦⣿⣿⣿⣿⠘⠀⠀⠀⡿⣿⣿⢸⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⣈⣤⣤⢈⠀⠀⠀⣷⣿⣿⢿⠈⠀⠀⠀⠀⣿⣿⣿⠋⡶⢹⡀⣿⣿⢻⠀⠀⠇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣄⢀⣀⣦⠀⠀⠁⡏⣿⣿⣿⢿⠈⠀⠀⠇⣿⣿⢰⣄⠀⡄⢶⣷⣿⣿⠸⠃⣾⣿⣿⢶⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠶⠤⠶⠺⠛⠀⡀⣠⢀⣧⣿⣿⣿⠈⠀⡿⣿⣾⠐⠀⠀⠀⠀⠀⣧⣿⣿⡿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⡤⣀⣀⣀⢀⣀⣀⣦⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠒⠒⠙⠉⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡽⢉⠉⠀⠀⠀⣀⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠐⠀⠀⠀⠀⠀⠀⠀⠇⣿⣠⠀⡀⣄⢦⠛⠈⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢧⢹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠋⠚⡿⣿⣦⠻⠚⠑⠈⠀⠀⠀⡀⢻⠈⠀⠀⠀⠀⠀⡀⣷⠹⠈⠋⠴⣠⣀⣀⣀⣀⣄⠦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢟⠻⣿⢹⡟⣯⠚⣀⣠⠦⢿⠘⠀⠀⠀⡀⣦⠻⠉⠀⠀⠀⠀⠀⣧⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣧⢻⣟⣦⠐⣄⠤⠓⠈⡀⣄⠲⠙⠈⠀⠀⠀⣉⣞⠶⠒⠒⠛⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⢿⠈⠀⠀⠀⠇⠛⢷⣼⢧⣸⡖⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣶⢶⠙⠈⠀⣀⠀⠀⠀⡀⣀⣅⠹⠞⣠⠀⠀⠀⠈⡞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣀⢷⠀⠀⠀⡷⣿⠉⢻⡍⣜⠹⡀⢻⠉⠈⠀⠁⠋⠓⠛⠛⠛⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⣄⢤⠳⠈⠀⠀⠀⠀⡇⣿⢰⠀⠀⠀⠀⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⡇⢹⠈⠀⠀⣦⣶⣷⡙⢻⡏⠺⡴⣀⣦⣽⣼⢀⢀⠀⡀⢀⣧⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠀⠁⡞⣤⣤⠶⠙⠀⠀⡾⣿⣁⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⢿⣿⠀⠀⣀⢿⠸⣀⣄⢤⠲⠙⠉⠈⡀⠀⠀⠀⠀⠀⠀⡟⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⢀⠀⠀⠀⡀⢷⠈⣇⣌⣹⣗⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⠀⠀⠀⣄⣤⣦⣶⣤⣤⣦⢷⠿⠛⠛⠛⡚⣴⣀⢤⠦⠒⠒⠛⡿⢈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⠀⣸⠀⠀⠀⠀⠁⠀⣄⣶⣽⣬⣤⣤⠤⠦⠳⠉⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢠⡴⢀⠀⠀⠀⠀⠁⠟⣰⣿⠺⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⢸⠀⠀⠀⠁⣹⠈⠀⠀⠀⣀⢀⠀⠀⠀⠀⣀⢷⠈⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠛⣷⢿⣿⣳⠛⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⡇⢸⠀⠁⠘⡇⣸⣄⠲⠙⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⡞⠀⠀⠀⠀⠀⠀⠁⠞⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⢧⣾⣫⣴⣠⣤⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢺⡏⢘⠀⡿⢉⠀⢻⠀⠀⠁⢴⠲⠙⠀⠀⠀⠀⠀⠀⡇⠏⢸⠀⠀⠀⠀⠠⠁⣼⠀⠀⠀⠀⠀⠀⠀⠋⠛⠉⠉⠟⣿⣿⣿⢣⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⣸⣆⡦⣀⣇⠛⣿⠁⠞⢠⠀⠀⡀⣤⢷⠙⠀⠀⠀⠋⣴⢿⠶⠒⠳⠉⠀⡇⠀⠀⠀⠀⠀⠀⠁⡿⣭⡨⣄⣿⣿⡿⣿⣹⡇⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢿⠘⠀⠋⡿⣷⣿⣸⠀⠀⠀⠀⠀⠀⠀⡀⢄⠤⡤⢀⠀⢻⠀⠀⠀⡀⢤⡤⠷⠙⠏⠋⠋⠾⣠⣀⣀⣀⠇⠛⡿⣿⣿⣾⣤⣤⢦⠛⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⣏⣾⠿⣿⡟⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠷⠻⠛⠋⠞⡴⣦⣬⣦⣿⢻⠛⠘⠀⠀⠇⡿⣯⣿⣿⣇⠻⠶⠷⡯⣾⣶⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷⣿⠛⣿⣶⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠂⣝⣿⣿⣿⣷⠈⠀⣷⣿⣿⣿⡷⢿⡷⣿⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⣿⢻⠛⡟⣿⣿⢿⣻⢿⣿⢴⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⣿⣿⣿⣿⣿⣾⣶⣴⣠⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢶⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠆⠟⣬⠤⡠⣤⢀⠄⣤⡿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢷⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠁⠟⡨⣦⣘⢦⠙⠇⢠⠀⠀⠀⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⣿⢀⢤⠀⠀⠀⡇⡄⠘⠀⠀⠀⠀⠀⠀⠀⡏⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⡿⢀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠁⡼⠀⣄⠲⠟⡠⣀⣀⢤⠿⢹⠏⠻⠻⠀⠃⠔⠾⠤⠿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸ ⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⣏⠻⠉⠋⠞⣠⠀⠀⠀⠀⡀⢄⠂⠔⣠⢀⠀⠀⣀⣤⣷⣸⠀⠀⠀⠀⡀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⠉⠉⠉⠉⠉⠉⠚⠓⠴⣠⢀⠀⣟⣿⣴⣀⣁⣋⣛⣛⣌⠧⠰⠀⠀⠧⠴⠭⠭⠬⡤⣶⢻⠉⠀⠀⠀⠀⢻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣇⡀⢸⠀⠛⠿⠿⡿⣿⣿⠙⠉⡟⣿⣿⣿⣿⠛⢰⠀⠀⡇⠟⣿⣿⣿⢻⠀⡇⣿⣼⢤⠤⣠⠀⠀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⡿⠻⡾⠷⣼⣀⢀⠀⣿⣿⣟⢻⠓⠉⠉⠛⡽⣠⠀⠀⠀⠀⣦⣙⣈⣤⣥⠯⡷⣿⢹⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⡼⣀⣶⠀⡄⢸⠀⠁⠉⣿⣿⣿⣿⠈⡇⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣼⣀⣿⣿⣿⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠟⣿⢾⢠⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣼⠀⣿⣿⣿⢠⡟⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⠈⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠛⢸⠀⡇⡟⣿⡿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠠⠃⠘⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢸⠀⡟⡿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⠄⢠⡀⢀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣻⣄⣤⣷⣾⣶⣴⣿⣼⣀⢀⠃⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢻⠈⡇⢸⠀⠀⣧⢸⠀⠃⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢿⡉⢿⠀⠀⡇⣸⠃⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⠀⠀⡇⣿⣾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⢸⠀⡇⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠞⣠⢈⠀⠀⠀⠇⣿⣿⢿⣌⡼⡷⣷⡻⠣⡏⢳⠋⣏⢿⠈⡃⠈⣀⠳⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠴⣀⠀⠀⣄⠀⠀⠀⡿⣿⣿⣿⣿⡜⡻⣳⣯⢫⣦⡞⢼⣄⣿⣿⠨⢧⠀⠀⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠖⣥⢙⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠻⢯⣎⢞⠝⢿⡏⠘⡇⣿⢿⠘⢽⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠋⠴⠦⠓⠛⠟⠥⡴⣠⣀⠀⠀⠀⡀⣀⣤⠾⠓⠉⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⢿⣝⡹⣤⡱⣿⣯⠘⣿⣿⣿⡽⠻⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠋⡼⣋⡾⢠⠂⠐⡀⣱⣉⣉⣍⣭⢭⠯⠒⠒⠓⠉⡉⠉⠈⣀⣤⠢⠙⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠙⣄⣷⣿⡍⣿⣿⣿⣿⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠴⣀⠀⠀⠁⡟⣴⡿⣰⠀⠀⠋⠖⡤⣀⣀⣀⣀⣤⠦⣙⣌⠤⠓⠈⣀⣀⣄⣤⠦⠷⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡙⣾⣤⣦⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠁⠉⠞⡴⣠⠀⠀⠁⠉⠞⣠⣿⡿⣰⠃⡴⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠄⢻⣈⠣⠈⠀⠀⠀⠀⣄⠳⣈⣦⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠉⠋⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡤⣀⣉⠉⠚⠶⡤⣠⣀⠀⠀⡟⣿⣰⠀⡆⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣅⡷⢻⠀⠀⠀⠀⠀⠀⣄⠳⡙⣄⠷⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠒⠔⡤⣨⣀⣧⣿⢿⠿⠛⠙⠀⠃⣾⢠⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⡸⡟⣿⠀⠀⠀⠂⠿⠈⠀⡀⣤⢾⡓⣮⣿⣿⣿⣿⣿⣿⣿⣿⣬⣦⣶⣶⣿⣿ ⠄⡀⠀⠀⠀⠀⣆⠹⡀⣿⣿⣿⣿⣿⢿⣼⢀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⠛⠛⠛⠛⠛⡿⢹⢺⣯⣟⠀⠀⠀⠀⣄⢳⠈⠀⠀⡆⡘⣦⡿⣿⣿⣿⣿⣽⣤⣀⣤⠻⠈⠀⡀⣦ ⠀⠀⠀⠀⠀⠀⠀⣧⠹⡇⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⠀⠁⠟⣻⣾⣴⣠⣀⣀⣀⣀⠀⡀⣀⠀⠀⠀⠀⠀⠀⢆⠙⠀⠀⠀⢦⡌⣳⣯⣻⣿⣿⠻⠈⠉⣾⣿⠻⠈⡏ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⡿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⠛⠟⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⠀⠀⠀⢧⡘⢧⣿⣿⣿⣿⣿⣿⣿⡙⣧⣾⢁ ⠀⠀⠀⠀⠀⠀⠃⣸⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢶⣶⢘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠉⠀⣄⠱⣇⡿⣿⣬⡿⣻⣌⣦⣷⣼⣿ ⠀⠀⠀⠀⠀⠁⡿⠀⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⢀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠞⡤⢁⠮⠒⠓⠙⢦⣦⣿⣿⡼⣷⢷⠙⠘⠒⡗ ⠻⠛⠈⠀⠀⡿⣸⠀⣿⣼⠀⠃⠙⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠶⣤⣤⢦⡙⣈⢀⠀⠋⣾⢿⠛⣞⣿⣿⡈⢰⣆⢸⠀⠀ ⡀⣦⣿⢿⡟⣿⢸⠀⣿⢠⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⣄⣷⣿⣿⣿⡙⠛⣟⠿⡶ ⠀⠀⡆⣿⣿⣿⣿⡿⣸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⣿⣿⣿⢠⠀⡄⢿ ⠀⠀⠀⡟⣿⢹⣿⣿⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠊⠀⠉⠀⠀⠀⠋⣿⣿⣿⣿⣿⢻⠀⠀⡇ ⠀⠀⠀⣿⣿⣇⣻⣿⢣⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠈⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡼⣠⢀⣷⠉⠟⢻⠉⠛⡿⣿⣿⣿⣼⣤⣿⣿⡹⢻⡄ ⡇⠀⡇⣿⣿⡇⣿⣿⡟⠘⡇⢹⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣧⠈⠀⠀⠈⠀⣄⠦⠳⡟⣹⠈⠏⠿⡙⣉⠛⡿⣿⣿⣾⣥⣟⣿⢸⠀⣯⣿⣿⡿⠸ ⢩⠀⡇⣷⣿⡇⣿⣿⣿⢸⣿⠸⠀⢂⠈⠀⠀⠫⠴⡠⣄⢧⠘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⠈⠀⢸⠀⠀⡀⣁⣯⣶⣷⣿⣾⣶⣶⣶⣤⣧⣿⢿⣠⠇⣿⢾⠠⣇⣿⣿⢿⣿ ⠨⠀⢿⠟⣿⡇⣿⣿⢿⢆⢸⠀⠀⡃⣎⠛⡴⢁⠞⣡⠞⣠⠀⠀⠀⠏⠠⠀⢀⠀⠀⠀⠀⠀⠀⠃⣘⡇⢻⠀⠀⠀⢸⠀⣏⣿⣿⢿⠒⠒⠖⠴⣿⣿⣿⡼⣄⣿⢸⠀⡇⣾⣿⣿⣿ ⢶⠀⣿⣿⣿⡆⣷⣿⣿⡟⢽⠀⠀⠁⣼⢁⠞⣫⡴⢀⠀⠀⠁⠼⠉⣿⢸⠀⠀⠀⠀⠁⠉⠟⡿⣿⢸⡇⣿⠀⢸⠀⢸⠃⣿⣿⣿⣿⠉⠋⠖⡧⣿⣿⣸⢸⠀⣿⢸⠹⡄⣺⣿⣿⣿ ⠛⠀⣿⣿⣿⠦⡿⣿⣿⣿⣿⢋⡀⣟⠈⣭⠞⢠⠀⠀⠁⠞⣠⠒⣧⣿⢁⠸⠀⠁⠟⣿⣿⣿⣿⣿⢹⡇⣿⢹⢱⠀⢸⡿⣿⣿⣿⡟⣹⠀⠿⡇⣿⣿⠀⣇⠘⣿⢿⣿⠀⣿⣇⣿⣿ ⣿⢹⣀⣯⣿⢸⣖⣿⣻⣿⣿⠺⡏⣿⣴⣀⠀⠀⠀⠀⡿⢀⠃⠿⡿⣼⡜⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⣿⣿⣿⣿⣠⡀⣿⠀⣧⡌⣿⢸⠀⡀⢻⣿⣿⣿⠈⣿⡗⣿⣿ ⡇⣿⣿⣿⣿⢿⠀⣧⣾⣷⣿⣻⣀⣿⠀⠀⠀⠀⠀⠇⣿⠀⠃⣿⣾⣾⢃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣸⠹⣿⣿⣿⣸⠀⠀⣧⢸⡇⢹⣿⢨⠀⠀⡆⡿⣿⣿⢸⣄⡧⣿⣿ ⡇⣿⣿⣿⣿⣿⠛⠀⣷⡿⣿⣇⡞⣿⠘⠀⠀⠀⠀⡇⣿⣿⣿⣴⣏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣏⡿⣿⣿⢀⠀⠀⡄⣿⠀⣿⣿⢸⠀⠀⠀⣷⣿⣿⣿⠈⡄⣿⣿ ⠀⣿⣿⣿⣿⣿⢹⠀⠀⣧⣿⡸⣿⣿⢿⠉⠛⠟⡿⣿⣿⣶⢫⡴⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⣧⣿⣿⣥⣿⣿⠘⠀⠀⠀⣇⢻⣧⣿⢿⠀⠀⠀⡆⣿⣿⣿⢻⠀⣿⣿ ⠀⣇⣿⣿⣿⣿⣿⠨⠀⠀⣦⢿⣧⣿⣿⣿⣿⣿⣿⣻⣟⣤⢹⠀⡇⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣼⣠⠈⠃⣠⣿⣿⠹⣧⣿⢻⠀⠀⠀⡛⣿⡿⣿⣿⢿⠈⠀⠗⣇⣿⣿⣿⢹⣇⣿ ⠈⡀⣷⣿⣿⣿⣿⢻⠀⠀⠀⣇⣾⣿⣾⣠⣀⣀⢀⡇⣿⠙⣏⠛⡟⣿⣿⣿⡟⣼⣿⣿⣿⣾⣠⠀⠀⠀⡄⠀⣇⣿⣿⡿⣿⣿⠘⢻⠀⣿⡿⣿⣿⣿⣿⢹⠀⣧⣹⣿⣿⣿⣿⡯⣿ ⢿⠀⡆⣿⣿⣿⣿⣿⠿⠘⠂⡰⠀⣇⣿⠈⠀⠃⠁⣿⣿⣿⡄⢻⡄⣿⣿⣿⢸⢷⣾⣴⣀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⢹⡇⡟⣿⣿⣿⣿⣿⣿⣿⠸⡇⣿⣟⣿⣿⣿⣾⣿ ⣧⠹⠀⣆⣿⣿⣿⣿⣾⣷⠈⠀⠀⠀⣷⢻⠉⡗⣸⣿⣿⣿⢸⣷⢈⣿⣿⣿⢿⡎⠘⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣿⢿⣷⣿⣿⣿⣿ ⡀⣷⠸⠀⣧⣿⣿⣿⢿⡿⢻⠘⠈⠁⡈⣿⢻⡀⢻⣇⣿⣿⣿⡈⢻⡇⣿⣿⡇⠸⢀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡜⠈⣆⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡼⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠆⢿⢈⠀⠀⡀⣀⣀⣄⢠⠀⠀⠀⠀⠀⠄⢠⠀⠋⡖⣠⡀⡏⣿⣉⠶⠛⠈⠀⠀⠀⠀⠀⣄⠲⠙⠀⠀⣄⣦⠙⠀⠀⠀⣀⢷⠈⠀⠄⠈⠀⡀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢧⠉⠈⠀⠀⠀⠀⠀⠃⠈⠀⠆⠙⠀⠂⡴⢀⠁⠞⡤⢀⡏⣻⣯⠷⢛⠈⠀⠀⠀⠀⠀⠀⡀⠄⠶⠿⠿⡛⢿⠛⠉⠈⠀⣦⠙⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣧⣜⠦⠶⠶⠶⡶⣑⣭⠻⠉⡀⢷⠀⠀⠞⣠⠀⠃⠞⣳⣿⣵⣛⣉⣤⠷⠿⠿⠶⠶⠶⠲⠒⠙⡈⣦⡹⣄⣷⣿⣿⠻⠈⣆⠹⡄⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢤⠶⣝⠻⠈⠀⠀⠀⠀⡀⢦⣙⢬⠶⠛⠉⠁⠋⡾⣠⢋⡾⢂⡾⣿⣿⢿⠿⠉⣁⠈⠀⠀⠀⠀⠀⣄⢷⣟⢻⠀⣧⣿⣿⢿⠈⡄⢷⣏⠈⡄⠹⠀⡀⢳⠈ ⠀⠀⠀⠀⠀⡀⢤⠶⠙⡉⣈⣦⠿⠙⠀⠀⠀⠀⡀⣄⠦⠲⣙⣯⣻⠛⡾⣠⠀⡁⠟⣴⣀⣿⣠⣄⣦⣿⣹⢬⠦⠲⠓⠉⠈⡆⣷⠸⠀⣧⣿⣿⢺⠈⡄⣿⢰⠈⡀⢣⠈⡀⢦ ⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⣶⣾⣶⣷⣿⠻⠉⠀⠀⠀⠀⠀⠀⣅⣿⣠⠀⠀⠃⣼⢀⠁⡞⣠⠀⠀⠀⣄⣷⢿⠀⠀⠀⡀⣄⢷⣿⣿⠘⡀⣿⣿⢿⢻⠛⡿⣼⣤⣤⣦⣤⢤⠷ ⠀⠀⠀⠀⡀⣃⣿⣴⣤⣤⢦⠒⠓⠀⣀⣄⣷⢿⠛⠀⠀⠀⠀⡇⣼⠀⠀⠀⡟⠙⠟⣠⠀⠀⢧⠙⠛⠙⠛⣿⢠⠀⠀⠀⠀⠀⣷⣿⢠⠀⡇⣿⣿⣼⢀⡆⠰⠀⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⠃⣾⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣇⣿⢷⠛⣷⠈⡟⢸⠀⠀⠁⣿⣿⢠⠀⠀⠀⣧⣾⣥⣯⣾⣠⠀⠀⠀⠀⠀⠀⡀⣷⠸⠀⡇⣿⣿⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣿⡇⣼⣷⢿⣿⠘⠀⠀⡇⣿⣿⠀⠀⠀⠀⠀⣄⣡⢀⠀⠀⠀⠀⠀⠀⠀⠛⠉⡏⢹⠀⡇⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⢻⡇⣿⣿⢻⠀⠀⡇⣿⣿⠀⠀⠀⠀⠀⠀⣤⢠⠀⠀⠁⠼⣤⣠⣀⢀⠀⣏⣿⢀⡇⣿⣿⣿⣷⢿⠛⠙⠉⠈⠁⠉⠁ ⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⠀⣦⣿⣿⣿⣿⠈⠀⡄⣿⣿⢸⠛⠴⣤⣤⣤⠻⠀⠀⠀⡷⠉⠛⠿⠻⠞⣴⣧⢿⢀⡇⣿⣿⣿⡇⣿⣾⣿⣾⣿⣿⢸⠃ ⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠙⠟⣾⣆⢻⣦⢻⠀⠀⡇⣿⣿⢹⠉⠿⣿⢞⣠⠀⠀⠀⠀⢛⣛⠒⠐⠀⠀⣿⣿⠀⡇⣻⣿⣹⡇⣿⢸⣟⢿⡟⣿⣿⣠ ⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⢀⠀⣦⠛⣧⠹⠀⠀⣿⡻⣀⣀⢒⠄⠤⠠⠀⠀⠀⠀⠁⠋⠛⠚⠐⠀⣇⣸⠀⡆⣧⣿⢠⡇⣿⢃⣿⣆⢿⣿⢧⠘ ⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠘⠀⠀⡇⣴⠘⠀⠀⣦⢻⣷⠙⠀⣆⣿⢻⠁⠋⠛⠛⠙⠈⠀⠀⠟⣶⣤⣀⠀⠀⠃⣿⢸⠀⠁⣿⢸⠀⣿⢰⠀⠉⠟⣿⢸⡄⢻ ⠀⠀⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠀⠀⠀⡏⠻⢀⠀⠀⠀⣄⣿⣷⠹⠀⡀⣷⣿⣽⣳⣿⣛⣈⢦⠿⡛⢯⠙⠀⠀⠁⣿⣾⢀⠀⡟⣸⠀⡇⣿⠛⡾⣤⢀⡏⢰⠀⣠ ⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⠀⠀⠀⠏⣼⡀⢷⠘⠀⠀⠀⡀⣷⣿⠻⠀⠀⣄⣷⣿⣿⣻⣦⠻⣯⣿⣿⢿⠈⠁⣿⣿⢰⠀⡇⣽⠉⠟⡾⣠⢀⠀⠁⠏⣸⠀⠀⠿ ⠀⠀⡇⢼⠀⠀⠀⠁⠉⠉⠚⠖⠶⣿⣤⠦⠤⡿⣰⠀⠀⠀⣦⠻⠈⠀⠀⠀⣦⣿⢿⠙⠀⠀⣀⣀⣦⠹⡀⣷⣿⣼⡀⣦⡿⣿⣰⠁⠋⣿⣾⣤⣀⠀⠀⠀⠁⡟⣿⢻⠀⠀⣾ ⠀⠀⡇⣿⠋⠾⣤⣠⣸⠀⠀⠁⠉⣿⠀⠁⠞⣠⠀⠀⠀⠀⠋⠀⣀⠀⠀⠀⠀⡀⣶⣿⠻⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⡏⣿⣿⡶⣴⣀⢀⠀⠀⠀⠀⠀⠏⣴⣏⣿⣾⠀⠃⢿ ⠀⠀⡀⣾⣀⠀⠀⠏⢺⠗⠼⣠⣞⣼⠁⡾⢀⠀⠀⠀⠀⠏⣸⠀⠀⠀⠀⢦⠻⠈⠀⣇⣮⢶⠙⠉⠉⠉⠉⠉⠉⠉⠟⣶⣤⢀⠀⠀⠀⠀⠀⠀⠁⠋⡶⣡⠟⣰⡇⢰⠁⡟⢸ ⠀⠀⠀⢡⠛⠀⡇⣠⠃⣸⠀⡞⢀⢧⣼⠀⠀⠀⠉⠟⡶⣠⠀⠀⠀⠀⠀⠀⡀⣄⠶⡶⢙⠀⠀⣀⣀⣒⣀⣂⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣴⢋⠞⣴⢀⠇⣰⠁⡟⣠⢀ ⠀⠀⠀⡄⣇⠸⡄⠀⡜⠀⡞⢠⠃⡿⢺⠀⠊⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⢷⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠶⣤⢀⠀⣀⠀⠀⠀⠀⠁⡿⢸⠀⠁ ⠀⠀⠀⠀⡇⢸⠰⠂⠰⠆⢠⠀⣧⣸⣦⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣄⠦⠙⠉⠉⠉⠉⠉⠛⠛⠶⡴⣀⠀⠀⠀⠀⠀⠉⠈⠁⠋⠾⣿⣸⠀⠀⠀ ⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⡄⢲⠉⣏⣿⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠓⠉⠩⠀⠀⠀⠀⠀⣀⣉⣯⣶⠛⠉⠉⠈⠀⠀⠀⠀⠀⠋⡿⣾⣴⣠⢧⠛⣼⠀⠀⠀⡀ ⠀⠀⠀⠏⠿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⣷⣌⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠒⠶⡤⣀⢀⠀⡿⡴⣈⣄⢤⠤⠤⠧⣽⣀⣄⢶⠻⠈⠀⣏⢸⠀⠀⠀⠀ ⠀⠀⠃⣿⣿⢿⠙⠀⠀⠀⠀⠀⠉⠞⡴⣀⠀⠀⣀⠶⡙⣉⢤⠶⠶⠒⠛⠒⠒⣿⠞⠶⡶⣠⣀⠀⠀⠉⠋⠶⡤⣀⣟⣤⣳⢬⠳⠯⠈⡆⣄⢸⠀⠀⡀⣄⣾⣼⢣⠀⠀⠀⡽ ⠀⠃⣿⣿⣼⣶⣿⢿⠿⠿⡾⣰⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠶⠒⠉⠉⠉⠉⣯⠉⠉⠉⠉⠚⠶⡤⣀⠀⠀⠀⠀⣿⠈⠀⢿⠀⣧⣦⢻⠈⣇⠀⠀⠃⡿⣿⢰⡀⢀⠀⡀⣀ ⠃⣿⣿⣿⢹⠛⠿⣻⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣟⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡆⢻⠀⣇⠀⡇⠀⡇⢰⡇⠀⠏⣰⣏⢰⠀⠀⠀⠀⠀⠀ ⡆⣿⣼⠀⣏⣿⣾⣧⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡀⢯⠙⠈⠀⠀⠏⣠⠀⡀⠀⡆⠀⡄⠀⡟⡼⢁⡟⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⣆⢻⡟⣿⣽⠛⢳⣧⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠀⠀⠹⠀⣄⠶⠟⣴⠀⠀⠀⠀⠀⠀⠐⡇⣻⠟⣴⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣀⣀⠀⠀⡏⠼⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⢠⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀⠀⣤⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⢸⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⡴⢀⠀⠀⠀⠀⣁⣭⠿⠛⠛⠛⠛⠛⠛⠛⡿⣷⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠿⠛⠛⠛⠟⣿⣽⣧⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⣸⠀⠁⡋⠟⡴⣠⢀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠳⣟⣿⢿⠛⠙⠉⠀⠀⠁⠋⠛⠛⠛⠛⠉⠉⡟⡶⣿⣿⢬⢃⡿⢛⡟⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣿⡙⢂⡀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣀⣦⠧⣿⣿⣤⠀⠀⠉⠉⡈⣤⣶⠙⠀⠀⡄⣿⣧⢿⣷⣼⣠⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣶⢷⠙⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⣿⣰⠀⠄⣤⣀⢀⠀⠀⠀⠀⡀⣄⣤⠦⣿⠻⣷⣿⢹⠀⣿⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⠴⣤⣃⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⣇⣤⣦⣿⣿⣿⢠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠋⠴⣠⢀⠃⠀⠀⣾⠁⠛⠟⢿⠾⠶⠶⠛⠙⠀⠀⠀⠋⠟⣾⢿⣿⡛⠙⡟⣾⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⡤⢀⠀⠀⠀⡇⠁⡿⢿⣿⣿⣿⣿⣷⢿⡷⣿⣿⢿⠟⣿⣿⣿⣿⢉⣟⣿⣿⣿⢠⣼⣾⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡟⣼⣟⣿⣿⣿⣼⡏⠉⢟⣿⣿⣿⣿⣿⣿⣿⣄⣿⣠⣿⣾⣏⣌⡇⢿⢸⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⠃⣿⢀⣳⢸⡇⣇⢰⣼⢿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠼⣿⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠁⠋⣾⢁⠟⣰⠀⣸⡄⠀⣿⣹⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣟⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣷⣿⢉⣿⢸⡟⣄⢋⡿⣰⠀⡆⢀⠘⠀⣌⡁⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⡿⣿⣿⣿⠟⣸⡶⣆⣠⠀⠀⠀⠇⢰⠀⠁⡔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠲⠛⠈⠀⠀⠀⠀⣀⢦⡗⡯⢻⠀⠀⠀⠀⠀⠀⠀⡟⣋⣙⣉⣏⣐⣀⣀⣤⡢⠑⡈⢦⠷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢷⠻⠙⠉⠀⠀⠀⣇⢠⠀⠀⠀⠀⠀⠀⠇⣿⣚⣓⣙⠿⣠⢯⠙⠀⠀⠀⣀⠧⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠄⠤⣀⣀⢦⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡤⣤⠓⠀⡼⠀⠀⠀⠀⠀⠀⠀⣾⡀⢷⡴⣀⢤⠤⠤⡠⢦⠘⠇⠈⠀⣼⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡾⣓⠙⠋⠒⠴⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⢰⠀⠀⠀⠀⠀⠀⠇⢀⠀⡇⠘⠀⠀⠀⠀⠀⠀⣇⠈⢇⡏⢀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠙⠈⠀⠀⠀⠀⠀⠤⠒⠛⠈⠀⠀⠀⠀⠀⡏⠠⠀⠀⠀⠀⠀⠀⡜⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡄⣸⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣀⣀⢤⠲⠓⠛⠛⠤⡠⣀⣄⠦⠓⠉⠇⣼⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠃⣴⡿⢀⠀⠀⠀⠀⠀⠀⠇⢨⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠉⠉⠉⠉⠋⠗⢠⠀⠀⠀⠀⠀⠀⡋⣯⢀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⡇⢈⠀⠀⠀⠀⠀⠀⡏⠏⣰⠀⠀⠀⠀⠀⠀⠁⣸⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢾⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠁⠞⣣⢠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⣿⣠⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠇⢠⠀⠀⠀⠋⠞⣠⠂⡰⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⢤⠉⠙⠈⠀⠀⡆⠹⠁⠟⠽⣿⣻⣛⣉⣀⢤⠶⠙⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⡼⠀⠋⠴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣧⠭⣮⠀⠀⠋⡿⣟⣾⣠⠀⠀⠀⡞⣤⠳⠈⡀⣤⠳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⡇⠐⠀⠀⡟⢚⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠋⠞⠤⣡⠚⡴⣽⠻⠈⠏⣾⣾⣠⠀⠀⠀⠀⠀⢸⠀⠀⣆⠻⠀⡀⢧ ⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⡀⢄⡿⠛⠖⣸⢁⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡼⣉⠉⠚⡽⢀⠀⠀⡍⣿⣏⣿⡼⢀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⣄⢷⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⢼⡀⡄⠹⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⡥⣾⣠⠎⣠⠀⡀⢧⠿⣴⣤⣿⣿⣿⣀⠑⠉⠉⠀⠀⠁⡿⠈⠉⠀⠀⠀⣦⣿⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣰⠀⠀⠀⠀⢸⠀⠀⡄⠳⠈⠀⠀⠀⠀⡀⢤⠳⠉⠀⠀⠀⠁⡼⠀⠇⢨⠀⠀⠀⠀⢻⠹⠉⣽⢀⡀⣶⣒⢶⡥⣯⠻⣾⣀⣇⣸⣄⠿⠿⠀⡇⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡷⣴⠀⠀⠀⠀⠃⢰⠀⠀⠀⠀⣀⢦⠲⠙⠉⠉⠖⠴⠠⣀⣄⠦⡟⢀⠀⣆⠄⠀⠑⠀⡆⣿⢀⠀⣼⠀⠁⠉⠋⠖⠤⣷⡮⠳⠈⣆⢘⠀⡄⡼⠻⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠁⠋⠖⠶⠶⠲⠒⠙⠍⣈⣀⢶⠷⠿⠷⠿⣧⠀⢆⢎⠈⠀⡱⠠⠀⣸⠀⠀⣄⠶⡿⢠⠀⠀⠀⠁⠉⠈⣇⠾⣀⠀⠀⢸⣿⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢋⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠁⡿⣰⡢⣿⡌⠀⢣⣌⢞⠈⠀⠀⡏⢸⠀⠁⠉⠉⠉⠉⠀⠀⠇⣽⠉⣍⡿⠀⠀⠀⠀⢀⣿⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡽⠞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢷⣰⡾⠀⣆⢹⣿⠱⠀⣆⡜⡀⠀⡜⣼⠀⠇⣼⢀⡯⣿⡿⢨⠀⣀⢧⣿⣿⣏⠙⠈⠀⠀⡟⣤⠀⠀ ⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⢰⡏⢠⠀⠀⡆⡸⡄⠳⠀⠄⡈⡆⠇⢰⠋⣿⠟⠉⡏⣷⣿⠀⠀⠀⠀⣧⣩⣿⣿⢨⠀⡟⣾⣠⢀⠀ ⠀⠀⠀⢧⠈⠀⠀⠀⠀⠉⠟⣾⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡾⢡⠞⢠⠀⠀⠀⠀⣆⠸⠀⢢⠀⠀⠰⡇⠀⡄⣆⣷⡿⡿⣼⢀⠀⠀⠀⠀⡄⣷⡿⣾⢠⡟⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⠢⠙⠟⡴⣶⣠⠀⠀⠀⠁⠊⠶⣠⢁⡞⢀⠀⠀⠀⠟⣡⠊⣴⢀⠀⠀⠀⠀⠀⠀⣇⠉⠛⠚⠒⠒⡗⠺⠒⠓⠛⣍⣾⠗⠻⠙⠈⠁⠛⠾⣭⣯⢨⠇⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠳⠟⠾⣴⢀⠀⠀⠀⡿⠙⠉⠉⠒⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣠⠀⡀⢠⠀⠀⡀⢦⠒⡀⢦⣜⠷⣝⣤⢰⡏⣼⣯⣴⣀⣀⣇⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠒⠀⠀⠀⠀⡏⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠏⢠⠀⢀⠀⠀⠁⡿⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡽⢞⠀⠀⠀⠀⠀⣷⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣽⠞⢠⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢣⠀⠞⣤⢦⠙⠂⣗⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣍⠭⠓⠉⠀⠀⠀⠀⠀⠀⠀⠊⢠⠀⠀⠀⠉⠞⣠⠂⠛⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⡇⢀⠀⠀⡀⢦⠀⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢐⠀⡀⣤⣦⣷⠯⠚⠒⠓⠼⣧⠻⠛⠛⠖⡴⣀⠀⠀⡄⡶⣴⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡽⢿⡈⠹⠀⠀⠀⠀⡀⢦⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢦⠻⠉⠉⠉⠉⠊⡒⣀⣤⣧⣼⣦⣾⣷⣟⠀⠀⠀⠟⠿⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢤⣄⡳⢯⠑⠈⠀⠀⠀⠀⣀⢤⠤⠿⠘⠀⠀⠀⠀⠀⠀⠀⠁⠿⣩⢐⠀⠀⠈⠀⠀⠀⠀⡶⢀⠀⣇⡀⣾⠀⠀⠀⣤⡶⡖⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⠢⠒⠒⠒⠒⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠧⡙⠳⡄⣗⠘⠀⠀⠀⠀⠀⠀⣠⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢿⢷⡳⣭⣄⠲⠙⠟⠩⠋⠖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠁⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠋⠒⠒⠖⠴⣤⣠⣠⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣄⣤⣶⣒⣘⣀⣀⣀⣤⣤⠶⠻⠓⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠾⠴⡤⣤⣤⣤⣠⣀⣀⣀⣀⣤⣤⣤⣤⢤⠤⠤⠤⠲⠒⠒⠛⠛⠛⠉⠉⠉⠉⠉⠉⠈⠀⠋⠛⠿⠿⠴⠤⠷⠻⠛⠈⣦⣽⠀⠀ ⠀⠀⠀⠉⠛⠾⠵⣻⣶⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣉⣞⣷⢿⣥⣿⣾⣶⣤⣇⣿⠿⠻⣶⣿⠸⣷⢹⠀ ⠀⠟⣶⣶⣷⣛⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠟⠾⣤⣀⠀⠀⣆⡷⣿⣸⣠⠀⡇⣿⣿⣿⣿⣾⢰⠀⣧⢸ ⡟⢯⠶⠲⠖⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠚⠖⡶⣴⣫⣿⣸⠀⠀⠀⠀⡁⢦⠑⣮⢳⠀⠀⡄⣻⣯⣿⣿⢠⠀⠀⡇⢿ ⡧⣟⣿⠯⠙⡷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⣤⣠⣀⢀⠀⠁⠋⠞⣴⣤⣷⢸⠀⠀⠁⠛⣚⣷⡿⣿⡹⢮⠀⠀⡀⣤⣷⢀⠀⠀⠀⡏⣿ ⠀⣄⣷⣿⣛⣙⣦⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠶⣤⣀⠀⠀⠀⡇⢸⠀⠀⡼⢀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠋⡿⣾⣤ ⠀⠀⠀⣀⣤⢶⣛⡉⣯⠷⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠶⣤⣀⣀⣀⣄⣦⠶⠛⠈⠁⠍⢹⠀⡟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠧⠛⠀⠀⠀⠀⣄⢹⠀⠀ ⠉⠉⠉⠀⠀⠀⠀⠀⡀⣀⣤⣤⣿⣭⣿⣾⠶⠶⣤⣤⣿⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⢒⣏⠿⣾⠹⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⠻⠀⠀⠀⠀⡹⢻⠀ ⣀⣀⣄⣤⢤⠶⠲⠛⠛⠞⠴⣤⣠⣀⠁⠛⠚⠀⠀⠎⢠⠀⠀⠀⠀⡀⣤⠳⠀⠀⠀⠀⠀⠀⣧⣼⣠⢀⠀⡆⠻⠀⠀⠀⠀⠁⡾⣿⣿⣿⣿⠿⠙⠈⠀⡄⣿⢰ ⠀⠀⠀⠀⠉⠚⡴⣠⢀⠀⠀⠊⠴⣠⣀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⡅⢸⠃⠉⠟⠶⣴⢿⠘⠀⠋⣰⠀⣆⣿⣿⣿⣿⡾⣷⠛⠴⣠⠀ ⠀⠉⠞⡴⣀⠀⠀⠀⠀⠁⡞⢀⠀⠀⠀⠀⠀⠃⠞⠠⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀⣀⣄⢦⣹⣀⣄⠷⣸⠀⠀⠀⣿⣭⣟⠶⡤⣀⢀⠀⠀⠀ ⣴⢂⠑⠈⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠉⠚⡴⢀⠀⠀⠀⠀⠀⠀⡀⢻⠛⠀⠀⠀⠀⠀⠀⠏⣴⠀⠀⠀⠀⠀⣄⢻⠀⠀⢻⠋⠛⡾⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⣄⢦⠓⠈⠀⠀⡆⠀⠉⠒⡤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣼⢀⠀⠀⠀⠀⠀⠟⢠⠀⠀⠀⠀⠀⠀⠀⣟⠠⠀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣄⠳⠘⠤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣼⢀⠀⠀⠀⠀⠁⡾⢀⠀⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⠀⠀⠀⠀⠀⠀⡟⢠⠁⠞⠴⡤⠀⠀⠀⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀⡀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠄⠇⣼⠀⠀⠀⠀⠀⠀⠏⢻⠖⣠⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⣄⠻⠀⠀⠀⠀⠀⠀⠃⣾⢀⠀⠀⠀⠀⠀⠇⣼⢀⠀⠀⠀⠀⠋⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⡄⢧⠽⠯⠛⠛⠛⣿⢀⠀⠀⠀⠀⠀⠁⡾⢀⠀⠀⠀⠀⠋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠙⠀⠀⠀⠀⠀⠀⠀⠀⣄⣻⢙⠀⡏⣸⠀⠀⠀⠀⠀⠀⡿⢰⠀⠀⠀⠉⠟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⡻⢯⠈⠀⠀⠀⠀⠀⠀⠀⣄⠿⣸⠀⠀⠀⠀⠃⠙⡟⣠⠁⠾⣴⢦⡿⢠⠀⠀⠁⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣷⢿⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠘⠀⠀⠀⠁⣿⣰⠀⡇⢸⠀⠇⣟⠻⠚⡶⣤⢀⠿⡻⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡾⢰⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣧⠀⠀⠀⡇⣸⠀⠁⡿⢸⠀⡇⣿⣰⠀⠀⠀⠏⣾⣴⣡⡞⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⡿⢠⠀⠀⠀⠀⠀⠀⠀⣷⢸⠀⠀⡇⠀⠀⠀⡿⢀⠁⡼⢁⣿⣿⣾⢀⠀⠀⠀⠀⣀⠥⡽⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠀⠁⡾⠀⠀⠃⣿⢻⣾⠀⡇⣿⣾⢀⠀⠀⠀⠀⠀⠁⡿⢷⣯⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠃⣼⠧⣰⠀⠀⡇⣿⢀⠀⠀⠀⠀⠀⠄⣷⣿⠿⣯⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠋⡼⠃⣰⠀⠀⠀⡇⣽⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⢿⣏⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠀⠏⣴⠃⣼⠀⠀⠀⠀⠀⣛⠈⠁⠉⠀⠀⠀⠀⠤⠀⡀⣄⣶⣿⣹⣷⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢁⡾⣤⠹⣧⠀⠀⠀⠀⠀⠀⡀⠆⡟⣿⣿⠿⠿⠏⠾⠀⠀⠀⠀⠀⣀⣀⣇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⣴⠀⠀⡀⣆⠹⡄⣦⣐⠀⠀⠀⡏⢶⣝⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣹⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣠⠀⠀⠀⠀⠀⡀⠳⠛⠚⡠⡆⠀⣿⠀⡃⣽⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⣸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠁⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠻⣿⣾⣵⣾⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⣿⠀⠀⠀⠀⠀⠀⠀⡟⢉⠟⠻⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡘⣀⢈⠋⡾⢀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⡟⣼⣬⣦⣧⣿⣏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠶⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⣾⠀⠀⠀⠀⠀⡟⢲⠀⠀⠀⠀⡇⣿⢿⠿⣼⣭⢧⠚⠒⠓⠛⠐⠀⠀⠉⠛⠈⠀⠀⠀⠀⠀⠀⠋⡴⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⡟⣤⠸⠀⠀⠀⠀⡾⢀⣤⣯⣼⣤⢠⠀⠋⡨⢀⠀⣇⣿⣻⠒⠠⠀⠀⠀⠀⠁⠟⣠⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠏⣾⠀⠀⠀⠀⠟⢰⠁⢰⠀⠀⠀⡏⢀⠀⠀⣿⣾⢀⠟⣿⢀⠀⠀⠁⡾⣀⢀⠀⠀⠀⠀⠁⢿⣼⢀⠀⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠏⣿⣠⠀⠀⠀⠀⠏⢰⠋⣴⠀⠀⠀⠇⣼⠀⠀⠁⣼⠀⠀⣾⢀⠀⠀⡀⣿⢀⠀⠀⠀⠀⠀⠀⡟⣰⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠃⣿⡟⣰⠀⠀⠀⠀⣾⠀⠀⠀⡏⠀⠀⠇⠀⠀⠀⠀⠇⣸⠀⠀⠀⠀⠀⠀⠇⣼⠀⠀⠀⠀⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠀⠀⠀⠀⠀⡾⡤⣸⠀⠀⠀⠀⠃⢸⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡀⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢸⠀⠀⠀⠀⡿⢠⠀⠀⠀⣷⠈⠀⡄⠘⠀⠀⠀⣷⠀⠀⠀⠀⠀⠁⡾⢣⠙⠀⠀⠀⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠃⣾⠀⠀⠀⠀⡆⢻⠀⠀⣷⠈⠀⠀⡇⠀⠀⠀⠀⠋⣴⢀⠀⡀⣄⠦⠛⠛⠛⠞⡶⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⢠⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⣧⠸⠀⠀⢠⠀⠀⡇⠀⠀⠀⠞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠀⠀⠀⠀⢹⠃⣼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢇⠙⠀⠀⠀⠀⡇⠀⠋⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⢀⠀⠀⠀⠀⣿⡼⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣄⠻⠀⠀⠀⡏⠟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠛⠋⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⠁⠁⠘⠀⠈⣿⢀⠀⡼⠁⠛⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⣷⣾⠀⠇⢇⣤⠻⡾⠀⡟⢿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⡷⣶⣠⠀⣤⠿⡿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣇⠀⠀⠀⠀⠒⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⠿⡼⣧⢾⡴⡟⠈⠋⡾⢁⡞⣡⡾⢀⡞⣿⠀⢳⡔⣠⠋⠾⢻⡀⢶⠛⡟⢰⠀⢹⠀⠀ ⠀⠀⡇⠙⠛⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠲⢿⡛⣟⣾⢁⡞⢀⣿⠀⡏⢨⡄⠳⠛⠚⡴⢠⠀⡀⢲⠛⠉⡉⠋⠛⣾⠀⠀ ⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢦⡷⣝⠿⣿⠶⣠⣀⣀⢤⠦⠶⠒⠛⠋⠛⠚⡖⣴⣀⣀⢀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⣀⣄⣤⠤⢶⠷⠛⠛⠙⠀⠀⠀⠀⠁⠛⠚⠐⠀⠀⠀⠀⠃ ⠀⠀⠀⣧⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⢶⠶⠶⠒⠛⠛⠛⠶⡿⣴⣠ ⠀⠀⠀⡀⣷⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⠶⠷⠛ ⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠿⠿⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⡄⢳⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣷⠀⠀⠀⠀⠀⠀⡇⠘⠀⣿⣿⣿⣿⣿⣿⢉⠿⠚⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢧⠙⠀⠀⠀⡆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢀⠛⠀⠀⠀⠀⠀⠀⡁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⡄⠳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⣲⢦⠳⠉⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⠀⠀⡆⠸⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⣴⣥⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣧⣻⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠁⠚⠒⠒⠒⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠉⠀⠃⡿⢾⡟⣿⡘⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠼⠤⣤⢤⡿⢳⠙⠀⠀⠀⡄⣿⣾⣄⣿⣿⣿⣿⣿⣿⣼⢷⠈⠀ ⠀⠀⠁⠚⡯⣯⣰⢻⣱⣽⣿⣿⣿⣿⣿⡁⣼⢯⡈⢷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠇⣼⠀⠀⠀⠀⣄⠁⡖⢦⠛⣈⣀⣤⢷⠻⡟⣿⣛⣯⣷⣿⣿⠀⢻⠀ ⠁⠞⣠⠿⣧⣱⠋⣼⡿⡿⣾⡇⣟⣿⣷⡾⠟⣿⢸⡀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠀⠀⠀⡇⢠⠀⠀⠀⡟⢸⠏⠳⠞⠶⠶⠲⠙⠉⠀⣄⢷⠙⠀⣇⣿⣿⣿⣿⣿⣿⣿⠟⢰⠀ ⣣⠼⠟⣫⢣⡿⡄⢇⢣⢣⢩⡝⣿⣿⣿⠻⣉⣋⢟⡿⣿⠀⠀⠀⠉⠛⠚⠒⠒⡶⣤⠀⠀⠁⠸⠎⢠⠀⠀⣿⢻⣷⣶⠦⠲⠛⠛⠈⣀⣿⠻⡿⣿⣶⣤⣤⣤⣤⣤⣷⣿⣿⣧⠀⠒ ⡄⡴⢋⢡⡽⢸⠃⣿⣼⡀⣀⣏⣾⣠⠀⠀⡀⡇⣸⡏⣱⠋⠞⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⡇⢿⢰⠀⠋⠒⡟⣿⣿⠹⠚⡶⣤⣡⣉⣯⣿⣿⣽⣭⣦⠶⠳⠙⠀⠀⠀⣄⣶⠛⠚⠶ ⠀⡦⢣⣼⡀⢿⣨⠀⠀⠁⠞⣠⠀⠀⠀⠀⠃⣸⡏⣾⣠⢀⠀⠀⠀⠀⠁⠞⣤⣀⣀⣄⠤⡷⣻⠉⡄⢳⠈⣀⣧⣼⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣦⠶⣛⢛⠈⠀⠄⠦⡤⢤⣤ ⠀⠀⡀⢿⠿⣟⢿⠀⠏⣠⠀⠀⠀⠀⠀⠋⣿⣾⣠⠀⠀⠀⠀⠀⠀⠁⣾⠀⠁⠟⠾⣶⣿⣿⡿⣿⣿⣿⣿⢿⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⢒⠐⠀⠀⠀ ⠀⠀⠀⡀⣄⣿⣿⣾⢀⠀⠀⠀⠀⠁⠾⣡⣉⠐⠀⠀⠀⠀⠀⠀⠀⡇⢹⠟⣼⢀⠋⡿⣿⣿⣾⣡⢋⠿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠳⠛⠉⠀⠂ ⠀⠀⠀⠀⠀⡟⣰⠀⠀⠀⠀⠋⡟⣿⡶⣤⢀⠊⠐⠁⠀⠀⠉⠋⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠔⠤⠦⠁⡟⣠⠀⠀⠉⠟⡾⣿⣴⢀⠀⠀⡟⢚⠖⠶⡤⣤⣭⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣉⠋⠒⠒⠶⠴⠶⠤⠤⠶⠴⠤⠀⠀⠀ ⠀⠁⠟⣿⢰⠀⠁⠟⣿⣠⣠⠀⠀⠀⠁⡿⣸⠀⠀⠁⠟⡿⣾⢃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⡿⣿⢰⠀⠀⡇⣼⢀⠀⠀⠀⠀⠀⡇⣿⢿⠙⠟⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣥⣿⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⠙⠉⣿⣿⣀⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠁⣯⣿⣿⣿⣿⣿⣿⣿⠔⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⣿⢻⠀⠀⠀⠀⠀⠀⠀⠁⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣼⣀⣦⣿⣿⣹⣿⠀⣧⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣿⣿⠻⠈⠀⠀⠁⠛⠿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣿⣿⣿⣿⣿⣿⣿⠉⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⡿⣰⣆⣿⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡉⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣷⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⣁⠛⡿⣿⣿⣿⠛⠟⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡟⠘⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⣿⣿⣾⣤⣇⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣾⣠⠀⣾⣶⣷⣿⣻⣶⣿⣻⢛⡿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠁⠟⣰⢷⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣾⢀⠀⡇⣿⣿⣿⣰⠁⡟⣿⣿⣿⣿⣼⢀⠀⡷⢘⠁⡿⣿⣿⠿⣿⣾⣶⣸⢀⠏⡴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⡀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⢀⠀⠀⡇⣿⣿⣾⠃⡿⣿⣿⣿⣿⣰⠀⠀⢀⠀⣦⡝⣷⣽⣯⣾⠀⠉⠋⠟⣿⣿⢻⠞⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣇⠙⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠈⠀⠀⠀⣿⣿⢿⣿⣿⡆⣿⣿⣿⠀⠀⠀⠁⠈⠀⡄⢠⠀⠀⠀⠀⡀⣀⣶⣶⣴⣀⠋⡿⣞⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⣧⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣿⣿⠻⠉⠏⣿⣿⣿⣿⣿⠸⣏⣿⣿⠀⠀⠀⡀⣤⠀⠀⠓⠈⠀⠀⠀⠀⠈⠀⠀⠛⡿⣿⣿⣾⣡⣿⣥⣿⣿⣿⣿⣿⣿⣿⢠⠀⡇⢸⠁⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣾⠀⠀⠃⣿⣿⣿⢉⠏⣿⣿⣿⣿⣻⡟⣟⣿⣷⣼⠉⠉⡟⢿⣠⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣼⢷⠙⢿⠀⠀⠤⠲⠙⠀⠆⠐⠀⣇⣾⢀⠀⠁⡜⣷⣿⣦⣶⣷⣻⣿⣿⣿⣿⣿⣿⣡⡿⢠⠀⠏⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⠻⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⡉⣿⠸⠀⠃⠈⡀⠢⠙⡈⣀⢀⠀⠀⠀⠀⣄⠳⠛⠛⠛⡷⣿⣿⣿⣿⣾⣠⡇⣾⣰⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⣄⠶⠐⡀⣦⠐⠀⠀⠀⠀⠀⠀⠀⠁⣛⡿⣿⣿⣿⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣾⣤⣠⠀⡀⣧⣿⣿⣿⣿⣿⣿⠻⠛⠛⠛⠛⠙⠉⠉⠉⠉⠉⠛⠟⡿⣿⣾⣿⣿⣰⢀⠀⡟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣶⣠⠀⠉⠋⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣡⢋⡾⣠⠀⠀⠈⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣤⣠⢀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡿⣾⣤⣉⢋⠛⠶⣤⣀⠀⠀⠀⠃⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣷⣿⣿⣾⣴⣤⣤⣤⣤⣤⣀⢀⠀⠀⠀⠀⠀⠁⠉⣿⣿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⡿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⢀⠀⠀⠃⡿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠾⠤⣠⣁⢉⠋⠛⠐⠁⣿⠹⠀⠁⠛⠛⠛⠶⠷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠁⣿⢠⣿⣿⣿⣿⣿⣿⢀⠀⠀⠆⢿⠘⡀⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⢁⠟⡿⣼⣁⢟⣴⢁⠞⣠⠀⣿⠿⣴⠋⣼⢁⠛⠀⣷⠛⠾⠶⠛⠈⠀⠀⡇⠸⡀⠀⠀⠀⠀ ⡇⣿⠀⡇⣿⣿⣿⣿⣿⠈⠀⠀⠀⣿⣿⠀⣦⣿⠻⠋⠟⠰⠀⠀⠀⠀⠀⠀⠀⡇⢸⡄⣿⣿⣾⣰⠁⠞⣤⠉⠀⡏⣾⢠⠏⣠⠏⣽⣿⠀⡿⣠⠋⠻⡈⣷⠀⠀⡇⢸⠀⠀⠀⠀⠀ ⠀⣷⠹⡀⣷⣿⣿⣮⣿⣿⠻⠛⡿⣾⣠⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠈⣀⣀⠋⠞⣠⠁⠟⣠⠇⣼⢁⠞⢀⠟⣵⣾⢠⠏⢀⠟⣰⡇⢸⡇⠘⠋⡞⢰⠀⠸⠀⠀⠀ ⠀⡀⣤⠀⡄⣷⣿⢿⠉⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠻⡶⣠⠁⠟⣿⣴⠂⣰⠃⡴⠀⡾⣣⡾⢠⠇⢠⡟⢠⠀⡏⢠⡇⣾⢠⠀⠀⠀⢸⠀⠀⠀

⠀⠀⠁⠋⠒⠒⡷⢀⠀⠉⢴⠤⠤⠤⠠⠄⠀⠤⠤⠤⠦⢶⠲⠒⠛⠛⠚⠒⠚⢴⠢⠓⠉⠉⠉⠉⠛⠛⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀ ⠀⠞⣠⠀⠀⠀⡄⠸⠁⣏⠙⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢾⠘⠀⠀⠀⠀⠀⡆⣶⣤⣧⠄⠀⠀⡀⣟⢸⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⡖⣿⣹⣯⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠥⣋⡴⠀⠀⠀⠀⠀⠀⠁⠈⠂⡇⠼⠤⣧⠞⠇⢸⠀⠀⠀⠀⠀⠀ ⠏⣶⠙⠀⠀⠀⠀⠀⡆⣼⣀⠀⢄⠘⠀⠀⠀⠉⠊⠒⠤⣁⢿⡿⡄⠱⠋⠶⠘⠀⠀⠜⢀⠀⠀⠀⡅⠰⠁⢿⣼⠀⠀⠀⠀⠀⠀⠀ ⢆⠉⡀⢍⠢⠑⠉⠀⠀⡏⠲⠈⠀⡀⣸⢀⠀⠀⠀⠀⠀⡇⣿⣿⠀⠀⣄⡦⢐⠉⠉⢌⠒⠐⠛⠞⢒⡤⢀⡆⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⠀⡀⣹⢞⡠⠀⠀⠀⠀⠃⣤⠘⠀⠀⠁⠉⠉⡇⢀⣀⠃⢹⠚⠶⠶⣤⣄⣤⣢⢑⠈⠀⠀⠏⣽⠢⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠻⠚⡠⠀⠀⠀⠀⠀⠎⢠⠀⣇⢤⠣⡷⣙⣸⣆⠀⠃⡿⣿⠹⠀⠀⠁⠟⢿⠺⠈⡀⠧⡿⣿⣷⠹⡄⠛⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⠁⠔⣆⠈⠀⡄⠘⠀⡇⣷⠀⠈⠀⡇⣻⣏⣿⢻⠋⣰⣥⣼⠀⢉⠀⡷⣹⣌⣧⣿⢿⣺⣴⠀⠀⠀⠀⠀ ⠀⠀⠀⡆⢸⠀⠀⠀⠀⠄⢠⠀⠚⢸⠀⠀⢣⠉⡹⣿⠀⢸⠀⡇⣾⢷⣟⣿⣿⢿⡾⠒⡥⣟⢿⠻⣟⢹⠀⣇⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⠑⠈⠀⠀⠀⠋⡵⠀⡇⠈⠀⡆⡉⣤⣤⠢⢉⠀⡏⢠⠀⣄⣿⣿⣿⣿⠻⡿⣿⢹⣾⣶⣶⠸⡀⣿⢻⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠠⡀⢿⡿⠘⡀⢹⠉⠋⡚⢲⠀⠃⣿⣿⢰⠀⠀⡟⣼⣀⣤⣷⣿⣦⣶⣷⣿⠊⠀⡇⡗⣿⣻⣝⣭⠿⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⢧⠀⠈⠀⠀⠀⠀⠀⡆⣿⣸⠀⠀⠏⣾⢀⠀⠁⡿⣼⠀⠀⡔⠄⠀⠀⡄⡷⣿⣦⣷⣿⣿⣶⣶⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠿⡾⡀⠀⠀⠀⠀⠀⠀⠀⣦⢈⠀⠃⣿⢠⠀⠀⡿⣿⠁⠈⠀⢉⠈⠀⠉⡟⣿⣽⣿⢿⡿⣿⢿⠿⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⣁⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠢⡿⣸⠀⠀⡏⣿⣛⡖⠒⢓⣙⢛⠿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠢⠖⣶⣷⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣿⠀⠀⠀⠀⠀⠂⠛⠉⣞⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⢠⠀⠀⠀⠀⠀⠉⠉⠉⠉⠍⡭⣭⢩⣏⢻⠈⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⡋⣸⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⡗⣽⠚⠶⠤⡠⣀⣀⣀⣀⢀⠀⠀⡀⣀⣀⣀⣦⢹⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠁⡉⢧⠈⠀⠀⡈⢸⠀⠀⠀⠁⠿⣻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⠈⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠁⡿⢻⠛⠛⠟⡿⣛⣜⢷⠘⠈⣿⢸⠁⠛⠟⣾⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠢⠙⠈⠀ ⢀⣿⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⡀⣀⣅⡿⢿⠿⣿⢿⣶⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢁ ⠁⢰⠀⠀⠀⠀⡇⠈⠀⠀⠋⠞⡴⣠⣀⣀⣄⣤⡗⣘⢳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⣴ ⡤⠀⠀⠀⠀⠀⡁⢹⠁⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⡙⣉⠬⠢⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠒⠴⡤⣀⠀⠀ ⠀⠀⠀⠀⠀⡇⡏⣠⣷⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⣿⠙⡀⢦⠙⠀⡀⣀⠄⠤⠤⠠⠀⠁⠉⠚⠖⡤⣀⣠⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⡇⣰⠀⠀⣄⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⣀⣦⣷⢻⠛⡟⠻⠞⠶⡾⣴⣀⣀⣄⣀⠀⠀⠀⠄⠽⠤⠲⠉⠀⠀⠀⠋⡴ ⠸⠀⠀⠀⠀⡇⠀⠀⠀⠁⣾⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢦⠁⠉⡉⣿⣿⢉⣠⠀⠄⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⡀⢦⠙⡀⢆⠙⠟⢶⠠ ⠀⠀⠀⠀⠀⡇⢄⠻⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠾⠀⡟⣿⣰⣇⣿⣿⠻⠀⠀⠀⠀⠆⡽⣦⠒⠉⣀⣄⠤⠓⠈⡀⢿⠀⣇⣼⠀⠀ ⠀⠀⠀⠀⠀⡇⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣴⢀⠂⠙⣍⣿⣿⡟⠤⠀⠛⠒⡙⢮⠈⡀⣧⠺⠙⠀⣀⠤⣷⠐⡇⢠⠀⠀ ⠀⠀⠀⠀⠀⡇⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢫⣰⠀⠀⠀⠀⡀⣄⣷⢨⠀⠀⡀⢣⠈⣆⣿⠙⠀⣤⣤⢶⠻⠈⡀⠞⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⠀⠀⠀⠀⠀⠀⠀⡁⢹⠀⠀⠀⠀⣄⠙⡀⣤⣠⢤⠦⠓⠈⢋⡯⡿⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣶⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣰⠀⠀⠀⠀⠀⠀⠀⠁⡰⣼⠙⠈⠀⠀⠀⡀⣀⢀⠄⠤⠯⠺⡴⣀⢎⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠸⠀⠀⠀⠀⠀⠀⠀⠀⡟⣰⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢠⡀⣄⠦⠓⠙⠉⠉⠛⠽⣫⠖⣧⣠⣀⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⡄⢹⠀⠀⠀⠀⠀⠀⠁⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀⣆⣮⡙⣌⠠⠀⠿⡖⠾⠛⢈⠀⠀⠀⠘⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣿⣺⣴⣤⢤⠶⠿⠛⡛⣙⣉⢈⡄⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⠿⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⠀⠀⠁⡿⣿⣿⣾⣠⣀⣀⣧⣿⣿⣿⣿⣿⣶⣶⣴⣤⣤⣤⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠻⣸⣧⣾⣿⢸⠀⠋⡾⣠⣀⣃⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣴⢀⡾⢀⣥⢻⣾⣀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠀⠇⣼⠀⠀⠇⢠⠀⡇⣿⢀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⠀⠀⠃⣰⠀⠀⠀⣸⠠⠀⠀⢸⠀⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠁⡼⠀⠀⠀⡏⠀⠀⠀⠇⢨⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⡇⢰⠀⠀⠁⢸⠀⠀⠀⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⡿⠀⠀⠈⡽⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠏⢸⠀⠃⣿⣼⠀⠈⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠒⡼⣇⢸⠈⡿⣿⠀⠎⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠔⣠⠀⠀⠀⠀⠀⠁⠊⡴⢀⠀⠉⠚⡶⢁⡔⢀⡀⠇⣿⣿⢠⠎⢁⡼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠓⠀⠀⠀⠒⠓⠟⡿⣿⠛⠿⠿⣼⣀⢤⠓⡀⠀⠀⠀⣤⣀⣄⠷⢀⡀⠀⡇⢹⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⠉⡒⠛⠙⠓⡉⣉⣤⣶⣶⣿⢿⠛⡏⠻⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⣧⣽⣀⠀⣀⠂⠄⠩⠒⠒⠒⠀⡀⣀⣤⣦⣷⣷⢿⠛⠛⠉⠙⠀⠀⢦⠀⡀⢳⠈⠀⠀⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⠀⡄⠀⠁⠉⠋⡽⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣦⣤⣤⣶⣶⠿⠿⢻⠛⠙⣍⠧⠙⠈⡄⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠚⠤⡶⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠑⡈⣀⣄⣤⣶⣶⣿⣿⠿⡛⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠢⠈⠀⠀⠄⠳⠛⣉⣶⣭⣶⢷⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠿⠿⠿⠿⠿⠻⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⠈⠀⠀⣷⡲⣌⠣⣝⠾⣧⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀

⡀⣀⣀⡀⢀⢀⠀⠀⠀⠀⠁⠁⡿⣿⣿⢿⡛⣿⣿⢻⠙⡛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣦⣷⣿⣿⣿⣿⣾⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣶⢶⠶⠶⠶⠿ ⠀⠀⠀⠀⠀⡀⣠⣄⢠⠀⣷⣴⣿⣿⣿⣼⣤⣾⣽⣽⣧⣼⣧⣿⣼⣧⣵⣿⣾⣤⣧⣿⣼⠀⠀⠀⠀⠀⡀⣆⣴⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡤⣦⣿⣼⣤⠤⣤⢶⣤⡤⢤⡤⠶⣶⡴⠦⣶⢷⠛⡞⣷⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠋⠘⠀⠀⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⢹⠛⠉⠉⠀⣿⠀⠁⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣨⡄⣽⠀⠸⣧⠉⡟⣰⠀⡇⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣾⣶⢿⠛⣎⠙⢀⡿⣿⢠⠉⠟⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣤⠦⠺⡀⣦⣿⣿⡿⣿⣿⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠐⠀⠀⠀⠃⡿⣿⣿⣿⣿⠶⠷⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢻⠉⠉⠉⠟⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣾⣶⣧⣿⣿⣿⣿⣦⢿⠛⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠉⠟⣾⣯⣼⣧⣻⠀⡀⣧⣿⠸⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣹⠃⣿⢠⠀⣿⠘⠀⠁⣿⢻⠾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠋⡿⣿⢠⣟⣿⣴⠀⠀⣿⢻⠀⡦⣀⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⣦⣠⠃⣿⣿⠀⠀⠀⡆⣿⠀⠇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⢁⠸⠀⠀⠀⣿⠸⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⣿⣿⣿⡎⢠⠀⠀⠃⣾⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣷⣿⣿⢹⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠝⣿⣿⣿⣿⢟⣿⢹⣿⣼⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠟⣿⣿⣿⣾⣴⣠⣤⣤⣦⣶⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠞⠴⣦⣹⡇⣿⣠⡿⣾⠰⠀⠀⡄⢦⣿⢾⡛⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⠤⠶⠶⠒⠒⠚⠒⠒⠒⠒⠒⠒⠖⠾⠶⠤⣤⣠⢀⠀⠀⠀⠀⣧⡇⢠⠇⣴⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣯⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠟⣴⢦⠓⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⣤⠀⠀⠀⡀⣷⣿⡶⠓⠉⠈⠀⠀⠀⠀⠀⠀⡿⣶⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣥⣿⣿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣆⢳⠛⠈⠀⠀⠀⣷⠻⠈⡀⣀⢤⠶⠳⠙⠉⠉⣉⠏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡂⣿⡿⣿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠒⡟⣿⣮⠻⠈⠀⣆⢳⠙⠈⠀⠋⠀⡀⣀⠀⠉⡄⢹⠀⠧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⣴⣷⢿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣿⣧⣿⣿⢿⠻⠩⠈⡀⣀⣤⣶⢹⠈⠀⠀⠀⡆⢸⠀⠀⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⢷⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⡆⣿⣿⣿⣿⣴⣶⠶⠀⠀⠛⣸⣄⠦⠶⡤⢁⢻⠀⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢤⠶⠓⠉⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣏⣿⣀⣤⣤⣤⣀⠀⠀⠀⠋⡿⣿⢛⠛⠛⡿⣿⣻⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⠤⠤⠀⠀⠒ ⠀⠀⠀⠀⠀⠁⣿⢸⠀⠀⠀⠀⠀⠀⠃⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠷⡟⣾⢻⠀⠀⠀⠀⠀⠖⣶⣾⣥⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⢻⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⣷⡻⢻⠈⠇⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣄⣤⣤⣤⣦⢷⠙⠀⡀⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠲⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠟⣾⠻⠀⠀⣄⣤⢶⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢿⠙⠀⣀⢦⡝⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡿⣿⠛⡨⢷⠈⠀⠀⠀⠀⡀⣄⠦⠓⠉⠍⠭⠭⠶⠶⠿⠛⠛⠛⠿⡼⣤⡠⣀⣀⣀⣄⠳⠉⡀⣄⠲⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⡀⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣲⠙⠀⠀⠀⣀⣧⣿⣿⣿⠀⠀⠁⠟⡤⢷⠈⣀⢤⠳⠉⡀⢤⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢿⠘⠀⠀⠀⡀⣤⠲⠙⠈⠀⣄⣧⣿⢸⠆⣿⣾⠶⠙⣿⠀⠀⠀⡀⣄⠢⠓⣍⠳⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⣄⠦⠓⠉⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡀⣀⠤⠶⠲⠒⠒⠀⠀⠒⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣸⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣩⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⣄⠦⠛⠙⠉⠉⠀⠉⠋⠟⣿⣷⠿⠙⠉⠈⠁⠉⠉⠋⠞⡤⣇⣿⣻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠃⣰⠀⠀⠀⠀⣿⣰⢀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⢷⠶⣿⣻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢸⠀⠀⠀⡤⠀⠀⠀⠀⠁⣾⢴⣤⣤⠤⠤⣤⣦⢹⠀⠀⠀⠀⡀⠀⣄⣰⠀⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣬⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠆⠀⠀⠀⠀⠁⠟⣥⢻⠛⠿⠠⠀⠇⠿⡿⣛⣖⢳⠈⠁⠉⠉⠟⣲⣒⣟⠿⠿⠀⠀⠃⠛⠙⡿⢨⠀⠀⡀⢤⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⠟⠿⣿⣿⣿⣿⣿⣾⠴⣠⣀⠀⠀⠀⠀⠀⣄⣶⣿⣶⣠⠀⠀⠀⠀⡀⣀⢤⡦⣿⣿⣿⣿⣿⠿⠛⠙⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠏⣿⣿⣶⣤⣤⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣤⣦⣶⣿⢿⠀⡀⢦⠙⠀⠀⠀⠀⠀ ⠀⠀⠁⠛⣾⣀⠀⠀⠀⠀⣿⣿⣸⠉⠉⠚⠒⠒⠒⠒⠙⠟⠸⠀⠀⠀⡆⠻⠞⠴⠦⠺⠒⠓⠉⠈⣷⣿⣿⠀⠀⠀⡀⣄⢻⠛⠀⡀⢃⠈⠀⠁⠀ ⠀⠆⣽⡏⢸⠀⠀⠀⠀⠋⣿⣾⣠⢀⠋⠿⡿⣿⢿⠻⡟⣼⢀⠀⠀⠀⠀⡇⢻⠟⣿⣿⣿⠻⠈⣀⣦⣿⣿⠙⠀⠀⠀⠀⡇⣿⠀⠀⡇⢸⠀⠀⠀ ⠀⠀⣀⣿⠀⠀⠀⠉⡏⣻⣿⢺⠶⡶⣶⣤⣤⣠⣀⢀⠃⢰⠀⠀⠀⠀⠀⡆⠘⠀⡀⣀⣄⣤⣦⠶⠲⡟⣿⣟⠹⠈⠀⠀⡀⣿⠒⠀⠈⠀⠀⠘⠀ ⠀⠀⠀⡇⠛⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⠀⠀⠀⠁⠀⠀⠀⣦⠙⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⣿⠸⠀⢸⠀⠀⠀⠀ ⠇⠻⠈⣧⣿⣿⣶⣤⣀⣇⣿⠻⠈⠀⠀⠀⠁⠋⠞⣠⠀⠀⠀⠇⣠⢣⠀⠀⠀⡄⢷⠙⠈⠀⠀⠀⠁⠟⣿⣸⣀⣤⣶⣿⣿⣿⢀⠀⢫⠘⠀⠁⠟ ⡀⣸⠀⡇⣸⢀⠀⠀⠀⡇⣿⣿⣽⣯⣿⣤⣠⣧⠿⠿⠿⠿⠿⣸⠀⡀⢿⠿⠿⠿⠿⡿⣤⣤⣿⣽⣭⣿⣿⢸⠀⠀⠀⡀⣇⣴⠀⠀⣦⢠⠀⡆⢠ ⠀⠆⠛⡏⢻⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⠹⠀⣿⣿⣿⣴⣤⣧⠀⠀⠀⡇⣤⣦⣿⣿⣿⠀⠃⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⡟⠙⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⠿⠿⡿⠀⠀⠀⡇⢿⠿⣿⣿⣿⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣀⣧⠀⠀⠀⡇⣠⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠰⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠘⠀⠀⡏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣀⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠄⠤⠤⠤⠤⠤⠤⠤⠄⠠⣿⠀⠀⠀⠀⠀⠀⠀⡀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣫⡾⣠⠀⠀⠀⠀⠀⠀⢉⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠋⠉⠀⠀⠀⠷⣭⣤⠤⠀⠃⠟⣿⢀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⡆⢻⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⠀⣀⠸⠀⠀⠀⣦⠐⠀⠃⡖⣧⣰⠀⠀⠀⠀⠀⠀⠀⠃⣻⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠟⡾⣤⠦⣶⢻⠀⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⣄⣿⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣼⢀⠀⠀⠀⡀⢳⠈⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⣇⠈⠀⠁⠈⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠡⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣤⠳⠛⠈⠀⠀⠀⣇⠹⠀⠀⠀⠀⠀⡟⢿⡿⠀⠀⢀⡤⣀⠀⠀⠁⣿⢸⠀⠀⠀⠀⠁⠟⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠈⠀⠀⣄⢸⠀⠀⠀⡏⣾⢴⠤⠤⠀⠀⠇⣀⣿⠀⠀⠀⠀⠀⠀⠀⡟⣷⢀⠀⠀⠀⠀⡥⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠏⣴⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠁⡾⢠⠀⠀⠀⠀⠀⠁⡾⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣠⠀⠀⠀⠀⠀⠀⠀⣿⠈⣷⠈⠀⠀⠁⠛⣰⠀⠀⠀⠀⠀⠀⠀⡇⢯⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢠⠀⠀⠀⠀⠀⠀⠀⡇⣻⣤⡤⣻⠀⠛⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⣏⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠋⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⠟⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠀⠀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣯⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⢸⠀⠀⠀⣆⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⡾⣿⣫⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⢸⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢿⣡⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣸⠀⡇⠈⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⡞⣴⣻⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣴⠀⠀⡄⢹⠀⠀⠀⠀⢻⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢷⠈⠀⠀⠀⠀⠀⠀⠄⢹⠁⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣷⠒⠛⠙⠀⣆⠸⠀⠀⠀⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢷⠘⠀⠀⠀⠀⠀⠀⣿⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡀⢠⠀⣀⣤⠦⢿⠀⠀⠀⡆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠁⠉⡟⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣯⠾⡤⣠⢀⠀⡆⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠋⡼⣠⠀⠀⠀⠀⠀⠁⡚⢶⠛⠉⠈⠀⠀⠀⠀⠉⠋⠛⡿⢛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠀⠀⠀⡄⣷⢴⠷⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⣠⠀⠀⠀⠀⠀⠀⠇⣿⢀⠀⠀⣀⣄⣤⣤⣤⣤⣀⣀⠀⠀⠀⣀⣤⠤⠓⠙⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡄⠻⠃⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⠀⠀⠀⠀⠀⠀⠀⡀⣦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠻⠀⠀⠀⠀⠀⡇⢾⠀⠀⠀⠀⣆⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠲⠓⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣽⢳⠈⠙⠀⠀⡀⣿⠀⠀⠀⠀⠀⣧⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⠤⠲⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⡄⢳⢻⣧⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠤⠳⠙⠈⠀⠀⠀⠀⠀⣄⢷⠙⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⢸⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣄⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⠛⠈⠀⠀⠀⠀⠀⣄⢦⠛⠉⠈⠀⠀⠀⠀⠀⣿⣤⣀⣧⢬⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠓⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢻⠀⠀⠀⠀⠀⠀⠀⡀⣄⣿⣤⠲⠓⠛⠟⣰⠀⠀⡇⢹⠋⠖⣷⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢭⠯⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠋⠀⠀⠀⠀⠀⠉⠖⡤⣧⠸⠀⠀⣯⠙⠀⠀⠀⡤⣠⢀⠀⡀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡾⣤⣀⣀⣀⠀⡀⣀⣀⣤⢤⠦⠲⠛⠉⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠁⠞⣰⠀⠁⣼⠀⠀⠀⣀⣀⣄⢤⠲⠙⠀⠀⠀⠀⣿⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⠙⠀⠀⠀⠀⡇⢸⠀⠀⠃⣼⡀⣿⠤⣷⠛⠛⠛⠐⠀⠀⠀⠀⠁⡉⢿⠙⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⠀⠀⠀⡇⢸⠆⣾⠀⣴⢀⠀⣸⠛⠛⡽⢿⡷⣸⣀⣄⣧⢹⡟⣻⠙⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠁⠋⠴⣠⢀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⠃⣸⠀⠀⠀⡆⢹⠀⢿⠀⠀⠀⡟⣄⣠⣄⣠⣄⣤⢳⠐⠀⠀⣧⠘⡀⣛⣷⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠹⠀⠀⠀⠀⠃⣿⢀⠀⠀⠀⠀⠀⠀⠁⠟⣠⠀⠀⠀⠁⣾⢀⠀⠀⠀⠉⣿⠉⡟⠳⠙⠁⣿⠿⡽⣭⢻⠘⠏⠴⠦⠛⠉⡇⢻⠟⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠹⠀⠀⠀⠀⣄⣤⠤⠤⠤⠤⠤⣤⣠⠀⠀⠀⠀⠋⡼⢀⠀⠀⠀⠀⣷⡟⣿⣼⠀⣀⢤⣲⣛⣭⣭⣻⡶⢀⠀⠀⠀⣀⣥⣾⣦⠳⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⣠⠀⠀⠀⠀⠀⠀⡀⣠⣧⢹⠀⠀⠀⠀⠀⣀⣄⢷⠊⠀⠛⠛⡛⠿⣤⢀⠀⠀⣿⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢤⠢⠒⠛⠛⠛⠛⠛⠒⠖⠤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠲⠛⠈⠀⠀⠀⡆⣿⢤⠲⡛⣬⣵⢧⠘⠀⠀⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠲⠙⠀⠀⣿⠀⠀⡀⣤⡷⠸⣧⠙⠁⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠉⣿⠀⠀⠀⠀⡀⠀⠀⣟⣾⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⣚⡓⠛⡛⠛⠛⠛⠚⠓⢸⡅⢩⡍⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⣿⢸⡿⡟⡏⠂⢶⠸⠁⠀⢸⠀⠀⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀ ⣀⢁⡋⢈⡇⠀⣷⣘⡇⢰⢼⠶⠀⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀ ⠿⣭⣳⠈⡇⠘⣿⢀⡇⢠⢸⠁⠏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀ ⣹⡉⣉⢮⡷⠄⣤⠉⣸⠀⢸⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⣀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⣭⢄⣤⢀⡇⠙⡞⢀⣇⠘⢸⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⢛⠛⠙⠀⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀ ⣶⣶⠶⣦⡇⣦⡴⣁⣄⢠⢹⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡿⣿⣿⣾⣠⣀⣧⡘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠿⠙⠈⠀⠃⠛⠙⠛⠙⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣶⣶⣿⣼⢀⠀⠀⠀⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⣿⢀⠀⠀⡇⣾⣿⢿⠘⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠠⠀⡀⣿⠙⠋⠞⠤⡧⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀ ⣿⣼⠻⠀⡆⣸⣇⣹⢩⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢷⠟⡿⣿⢹⢋⠖⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⣾⢸⢸⠀⠃⢈⣀⠀⠀⣟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣠⠀⡇⣿⣷⣾⣤⢀⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠻⠉⠛⠀⡇⢤⡤⣦⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⠀⠀⡀⣦⡾⠀⠀⠀⠀⠀⠀⠀⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⢀⣇⣿⢨⡇⠀⠉⠈⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀ ⠚⡒⡒⢶⡶⠓⣛⣛⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀ ⣿⣿⣿⢸⡇⠀⣛⣃⣟⢸⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠀ ⣤⣥⣭⢩⡟⠛⣻⡉⣿⢸⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠋⠐ ⠀⣿⣿⣴⣠⣄⢦⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠾⣠⢀⠀ ⠿⣿⢠⠀⠀⠀⠀⡀⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀ ⣶⣸⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⠀⠀⠀⠀⠀

⠟⣿⣴⣠⢀⠀⠀⠀⠀⠀⠃⠚⠉⠁⠉⠋⠛⠿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇ ⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⣰ ⣀⢻⠶⠶⠲⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠀⠉⠛⠶⣧⣀⠀⠀⣆⠸ ⡇⢠⠀⠀⠤⢀⣸⣄⠦⠲⣛⢮⠀⠈⠀⠀⠓⠉⢞⡴⣦⢉⡴⠁⡼⠀⠀⠀⠁⣼ ⡇⠺⠈⠉⡏⠉⡢⠥⠭⡨⠔⣀⣷⢀⠀⠀⠀⣸⠀⢄⠠⠐⠤⣠⠀⠀⠁⠀⢟⢫ ⢻⢿⡘⠄⢹⠰⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⣦⠙⠀⠀⠀⠀⠀⠀⡠⠋⡿⣿⣿ ⣿⣿⣿⠻⠙⡈⠀⠀⠀⠉⠛⣴⢀⠀⠀⠀⠀⠀⡀⣭⠶⠓⠛⠛⠿⣯⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣹⣈⣃⣉⢉⠀⠀⠀⠀⠁⠀⠉⢉⠋⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿

⡤⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢤ ⢣⡀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⢀⡜ ⢸⡉⠒⠄⠀⠀⠀⢉⡙⢢⠀⠀⡔⢋⡉⠀⠀⠀⠠⠒⢉⡇ ⠀⠉⢖⠒⠀⠀⠀⣇⠀⣸⠀⠀⣇⠀⣸⠀⠀⠀⠒⡲⠉⠀ ⠀⠀⠀⠉⠙⠫⠤⠚⠉⠀⠀⠀⠀⠉⠓⠤⠝⠋⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠁⡿⣾⠀⠀⡿⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡄⣿⣏⣰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⢸⠀⡏⣷⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠀⠀⠀⠀⡃⢧⠈⠘⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⣍⢿⠋⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣬⠹⠀⠁⠈⡄⡘⢿⣟⣾⠀⠁⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⣸⡏⣿⣿⣿⣾⣟⣿⢸⠀⠀⠉⠒⠔⠤⠤⠤⣠⣀⣀⣀⣀⣀⣀⣄⠹⢻⣿⣿⢠⠃⡴⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠊⡶⢓⡿⣿⠏⣿⣿⣿⣿⢻⣿⣿⠉⠞⣠⢀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⠀⠀⡆⣿⣿⣿⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠞⡠⠉⠉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠁⠋⠟⡾⣳⠟⠻⢌⠙⠀⠀⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⢤⠴⢋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠐⠀⠀⠀⠀⣄⣈⣷⣿⠸⠀⣄⡒⢷⡏⠀⡏⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢁⠋⠒⠔⠠⠀⣄⠑⣄⣷⠻⠙⠋⡏⢠⠃⢠⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠀⡁⣿⣿⡿⣻⠀⠄⠠⠀⠀⠀⠀⢄⠢⡉⣯⣿⢠⠃⢰⠀⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠃⣾⠻⣯⡟⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡞⠀⠀⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢧⠀⣣⣄⡤⣓⣞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡆⠒⡖⠴⡤⢀⠀⠀⠀⠀⠀⠁⠋⠟⡻⢞⠲⠀⠀⠀⠋⠈⠀⢟⠀⠀⡀⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⡼⣷⣷⣃⠛⡛⠻⠈⠀⣤⢠⠎⣃⢻⠈⠀⡄⣿⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⢸⠀⣦⡿⣹⣟⣿⣇⠀⠀⠞⢏⣿⣿⢿⠙⠀⡄⣷⣿⣿⠹⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠷⠈⠀⡄⠿⢻⠀⡇⣄⣿⣿⠙⡄⣧⡿⣿⣿⣿⣿⣿⣿⢿⠹⡈⣧⣿⣿⢿⠻⠉⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⣀⢤⠶⡙⢬⠓⣄⣷⢿⡝⠺⣒⣷⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣾⣶⠴⠠ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⣄⠢⠉⠀⣄⣦⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣿⣿⣿⣿⣼⣤⢤⠠⠀⠀ ⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠉⠀⠀⠀⠀⠀⠀⠀⡀⢤⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣐⠃⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀ ⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠈⠀⠀⠀⠀⠀⠁⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣉⠟⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀ ⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⠋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢩⠉⠋⠚⠖⠴⡤ ⠀⠀⠀⠀⠀⣄⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⣀⢀⣀⠀⠀⠀⠀⡀⣀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣽⣧⢠⠀⡇⣿⣶⣤⣠⣀⣀⣀⣀⣀⣤⣷⣿⣿⠽⠠⠀⠀ ⠀⠀⠀⠀⡤⠦⠓⠻⠉⠀⠀⠀⠀⠀⡀⣤⠤⠠⠁⠛⠐⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣾⣷⣿⣠⣐⢻⠀⡄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣼⣤⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⡀⣀⢤⠶⠶⠛⠉⠈⠀⠀⠀⡁⣉⣿⣴⣄⢣⠌⠀⠦⠶⠤⠠⠀⠀⠀⠀⠄⠤⠀⠀⡆⣰⠋⡿⣷⠈⠀⡄⢻⠀⣇⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⠻⠙⠟⣴⣀⢀⠀⠀⡁⢹⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀⠃⡿⣴⢀⠀⣦⠙⠈⡄⢻⡀⣧⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠀⠁⠉⠟⡿⣾⣰⠀⠀⠀⠀⠈⠀⠋⢰⠀⠈⠀⠁⠟⣶⢀⠀⠀⠀⠀⣄⣿⠸⡇⢿⠙⣶⣟⢿⠙⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢛⡿⣩⣿⣿⣴⢀⠀⠀⠀⠀⠀⠁⠃⡘⠀⠀⠃⠿⣾⣠⠀⠀⠀⠀⠀⠁⠛⡶⣦⣷⣿⣿⠻⡈⠀⣄⢿⠘⠀⠀⠀⠀⠀⡟⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣤⣶⣿⢷⠻⠈⠀⠀⡀⣤⠀⠀⠀⠋⠟⠿⡿⣺⠖⠒⠒⠒⠒⠖⡶⣠⠀⡧⠸⠀⠀⣀⣦⣿⠘⠉⣿⣿⠸⠀⠀⠈⠀⣿⣿⣬⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣦⣧⣿⢋⡿⣸⠀⣄⢷⠿⠿⠿⠿⠶⡶⣤⣤⣁⣟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠻⠙⠈⠀⣆⣿⣿⣿⣿⢰⠀⠇⢸⠀⣿⣝⢟⠈ ⠀⠀⠀⠀⠀⠁⠋⠛⠒⠒⠒⠖⡶⣶⣶⡿⣴⣤⣀⡀⣤⣶⣳⢛⣛⠉⠉⠉⠛⠛⠞⡴⣤⢀⠀⠉⠐⠀⣀⣄⢤⠳⠙⠈⠀⠀⠃⡈⣀⣤⣤⣦⣿⣿⣿⣿⠀⠀⡇⠀⠀⣿⣠⡆⣠ ⠀⠀⠁⠚⡴⣣⠞⠀⠀⠀⠀⠀⠀⠟⣴⢀⠆⠶⠶⠺⠁⠉⠉⠉⡈⣀⣀⣁⢉⡿⢿⠿⠛⠭⣩⢋⠖⠶⣤⣤⣠⣠⣀⣄⢤⠦⡶⣷⠿⠩⠈⡟⣿⣿⣿⣿⠀⠀⡟⠀⠀⢠⠀⠀⠀ ⠀⠀⣠⠋⠴⡶⠲⠛⠙⠉⠉⠋⡾⣠⠀⠀⠁⠟⡿⣾⣴⣤⣤⣥⣭⣯⢿⠿⣴⣠⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣿⣶⣿⣾⣿⣿⠀⠁⣸⠀⠇⠀⠀⠀⠀ ⠀⠒⠀⠀⠀⠀⠀⠁⠋⡞⣶⣩⠟⣿⠛⠿⣿⣾⣶⣶⣶⣶⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⡌⢻⠀⣿⠀⡟⢠⠁⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣁⣋⠞⡴⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⡞⣿⣰⠏⣰⠀⡇⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣇⠛⣼⠀⠃⣼⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣧⠈⠀⡏⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⠋⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⡆⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢽⠀⠀⣿⠀⠀⠀⠀⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⠸⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⢿⠀⠀⠀⣿⠀⠀ ⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⣿⣿⢸⠀⠃⣿⠀⠀ ⠇⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣾⣿⣿⢸⠁⣿⣰⠀⠀ ⡀⣿⣿⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣷⣿⣧⣿⠃⡿⣾⠀⠀⠀ ⡄⣿⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣼⣿⣾⠀⣿⣿⢻⡿⣼⠀⠀⠀⠀ ⠀⣇⣿⣾⣿⢿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣾⠇⣿⢱⠻⡟⣿⣿⣼⠀⠀⠀⠀⠀ ⠀⡀⣦⣿⣿⣿⣿⣿⠿⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠁⣿⣼⡟⣿⣳⣿⣰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣧⣿⣿⣿⣿⣮⣷⣿⢯⠷⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⠀⠋⠶⠤⠶⠶⠲⣓⣙⠬⠤⠶⠲⠆⠶⠲⠒⠙⠉⠉⡇⣿⣿⡿⣽⡏⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⣦⣿⣷⣿⠻⣝⣯⣿⡟⣦⠻⠈⠀⠀⠀⠀⠀⠀⠋⠞⣫⠾⣤⢀⠀⠀⠀⠀⠀⠀⡀⣀⣤⠦⠓⠙⠀⠀⠀⠀⠀⣀⣇⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⣄⣶⣕⣾⡹⢧⡽⢷⠸⠀⠉⠚⠶⣠⠋⡴⣀⠀⠀⠁⠋⠶⠯⠾⠳⠈⠀⠀⠀⠀⠀⡀⣄⠶⠙⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠻⠈⣧⣿⣿⣵⣀⠀⠁⡾⣀⠀⠀⠀⠀⡇⢿⡿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠘⠀⡇⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⢿⠈⣧⣿⣸⠀⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⡇⣿⣿⣿⣿⣿⢰⠀⠀⠀⠉⠞⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⡀⣷⢿⢿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⠀⠉⠟⠿⣿⠹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡄⣿⣼⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀ ⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠘⣿⠃⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠍⣿⣹⣀⢄⠷⡙⣿⣿⣿⣸⣄⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠟⡇⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⢸⣿⡀⠋⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣶⣿⣿⣿⢿⠟⡿⣿⣿⣿⣿⢿⠈⡀⣷⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⣇⡿⣿⣷⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⣿⡟⣼⠆⠷⢸⠀⠉⣏⢻⠁⠋⠙⠈⠀⠁⠀⠀⠀⡄⣿⣿⣿⣿⣿⣭⣚⣒⣀⠀⠀⣄⣿⣿⣿⣿⠀⠀⣦⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⡀⣄⢦⡛⣙⣌⢤⠶⠿⠿⠿⠿⠿⠿⠀⣧⡀⣿⣿⢉⠈⡟⣿⣥⣿⣿⣿⣿⢸⡀⣷⢿⡙⢦⠘⠀⠀⡀⣦⣳⣀⠀⠀⠀⠀⠀⠁⠛⠖⣿⣿⣿⣿⢿⠿⠛⣿⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠡⠉⠉⠈⠀⡀⣤⡶⣿⢰⠀⡇⠛⣿⣿⣿⣿⣶⣽⣯⣻⣴⣤⢳⣼⠑⠀⣤⣿⢿⠙⠀⠀⠀⠀⠀⠀⠉⠛⠖⡴⣠⣀⠀⠹⣇⣿⣿⣸⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠟⣾⣵⣉⣉⠈⠀⠀⠀⣇⢰⠈⡇⣿⣿⣿⣿⣿⣉⣀⣀⠦⠙⠀⠀⣄⡳⢮⠀⡆⣿⣿⢷⠈⠀⠁⠟⡴⣀⢀⠀⠀⠀⠀⠀⣿⡏⣿⣿⢸⡆⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣸⢀⠀⣀⢠⣄⠠⠀⠀⡿⠛⣀⡇⣿⣿⡗⣿⣿⣿⢿⠛⠒⡄⢷⠛⠻⡙⣯⠻⠀⣇⣿⢿⣦⠿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⢻⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠁⠋⡶⢉⠉⠟⣦⣿⣿⣇⣿⣿⣾⣿⣿⢦⠻⠈⡀⣦⠹⡀⣧⢻⠈⣷⣿⢿⣾⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⡤⣀⠀⠀⣀⣷⣿⠀⣆⣿⡿⣿⡇⢻⡆⣿⢻⡈⣆⠻⠈⣗⢿⠘⣧⢿⡟⡿⣿⢿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⣿⣿⣿⣿⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢸⠀⣿⣇⣿⠀⣷⠘⣆⣼⣿⠘⡀⣷⠾⣦⣿⠻⣯⣿⣿⣿⣿⣿⣿⠩⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⠀⣿⡆⣿⢸⡇⢰⠄⣿⡜⣶⠹⡆⢻⠀⡀⣀⣦⣌⢻⣧⣿⣿⣷⣽⢻⠀⠀⠀⠀⠀⠁⠁⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⡇⠘⣿⢸⡇⠀⠀⡀⣷⢻⡈⢧⣿⠈⠀⠁⠉⠀⡆⠈⣿⣿⡘⣷⡟⢶⠀⠀⠀⠁⣸⡏⢉⣼⡏⣣⣿⣥⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢶⣆⢻⡀⢻⠁⠉⡉⣧⢿⠘⣇⣿⠙⣿⣻⣦⠷⢿⡏⣿⢹⡄⣿⠀⠁⠋⠙⡿⡿⣿⣿⢿⣻⡿⣾⡿⣿⣿⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⡆⠈⢤⣆⣨⣤⣷⠻⣄⣿⡌⣷⢸⠀⣦⣿⣿⣿⠙⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⠈⠀⠀⠀⣀⠀⡀⣄⢷⡙⣦⡰⣤⠀⠀⣇⣿⣻⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀

⠀⢀⠀⠀⠀⠂⠔⠤⣀⣀⠀⢀⠀⠉⠉⠀⠖⢠⠁⣞⠀⠉⠈⠐⠂⠀⣿⠐⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠹⠉⠉⠈⠻⠾⣠⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⢸⠀⠉⡀⣀⠀⡀⣋⠻⠙⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⠀⠀⠀⠀⠀⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⣴⠣⠓⠀⠀⠀⡇⣿⣿⣿⣿⠻⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢿⠤⡤⣀⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⡀⢾⠑⠉⠉⡆⣿⣿⣿⣿⣿⣿⣿⠭⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠆⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⡼⠟⠤⡾⢀⠄⢠⣁⣼⣀⣧⣿⣿⣿⣿⣾⣧⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠀⠀⠀⠃⡿⡴⢁⡞⢀⠀⠀⠁⡞⠀⠀⠀⡄⣷⣿⣸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⣴⣀⠋⡼⢀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⣅⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡾⢀⠀⠇⣠⢳⠀⠉⠞⣠⠀⠀⠀⠀⠀⠀⠀⡃⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣶⠷⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⢀⠀⠀⡄⠲⡖⡤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠁⠀⡔⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡎⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡸⣀⣋⠛⠈⡄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢀⠀⣀⣀⣀⣀⠤⠶⠲⠓⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠇⣾⣦⣿⠙⡉⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⣀⣀⣏⠼⠤⠧⠀⢸⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣤⢿⡴⢹⢿⡟⡀⣧⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⣽⣉⣉⣄⣿⢀⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⡄⣿⢀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⠚⠒⠙⠉⠈⠀⡀⢻⠙⡉⣀⣿⠈⠀⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠈⠀⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡀⢦⠙⣼⡄⠳⡎⣖⣿⢠⠀⠀⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠾⠈⣇⠺⡀⢷⠚⠓⠛⡟⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠿⣠⠀⠄⣠⠀⠀⡀⣆⣽⣐⠠⠙⠀⠀⠀⠀⠀⠀⠀⠀⠋⠶⠙⠈⠀⠀⠀⠀⠉⠛⠴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣉⠛⠛⠀⠀⠀⠙⠈⠀⣦⣶⣿⣿⠿⠻⠘⠒⠛⠒⠶⣹⢀⠀⠀⣿⣀⠤⡤⣀⢞⠤⠦⠿⠶⠿⠙⠀⠀⠀⠀⠋⠟⠤⠤⠤⠷⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⡿⣿⠉⠏⠾⣶⣷⢿⠿⠛⠙⠉⡈⣄⢳⠀⠀⠀⠀⣧⠀⠀⠀⡆⠘⠀⠀⡆⢸⠀⠀⣏⣼⠳⣈⣄⠦⠛⡼⣀⢀⠀⠀⠀⠀⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⡄⠸⠀⠀⠀⢧⠀⠀⠀⢧⢰⠀⣸⢸⢸⣄⠳⠉⣼⠀⠀⠀⠀⠀⠀⠀⡟ ⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠉⠛⠉⠋⠛⠀⠀⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⠀⠀⠀⠀⠀⢣⠉⠛⠿⡿⠘⠀⠀⠀⣷⡖⢸⢸⠀⠀⠁⡟⠀⠀⠀⠀⠀⠀⠃⡾⣶ ⠀⠀⠀⠀⠀⡄⣤⣦⣷⠉⣆⣿⣭⣞⣶⠀⠀⡄⣿⠒⠙⠓⣶⣻⠉⡋⣿⣬⣯⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⠘⠀⠀⡀⢢⣗⠟⠀⠀⠀⣇⠀⠀⠀⠀⠀⠁⣽⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠿⡿⠾⡟⣿⣿⠠⠀⠀⠀⣿⠳⣍⣥⣭⣿⣿⣿⣿⡶⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⣀⢦⠙⠀⡄⠹⠀⠀⠁⠟⣰⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⣤⣤⢰⠀⠀⠀⣿⠀⡀⣄⣿⣿⣼⣀⠀⠃⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣾⣠⢦⠙⠀⠀⠀⠀⡀⢦⠓⡪⢗⡬⣀⣄⠳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠇⣿⣧⢸⠀⠀⡿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣠⠀⠀⠀⡀⢄⠓⠈⠀⠀⠀⠀⣄⠦⣙⢌⠤⣄⠳⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⡿⣰⡀⢸⠀⡟⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠲⠈⠀⠀⠀⠀⠁⡟⠿⠻⠛⠛⠛⠾⡤⣀⠦⠓⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⣼⠀⠀⢸⡏⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠉⠀⠀⡟⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⢤⠲ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⠀⠀⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠒⣿⣿⣿⣿⣿⣿⣿⢻⠈⠀⠀⠀⠀⠈⠴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣤⣶⣶⣶⢶⠤⣤⢀⠀⠀

⠂⠀⠂⢳⡖⠔⠠⠀⠀⠐⠒⠒⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣦⣿⡹⣬⢻⣘⠀⠆⠂⠐⠇⠛⡿⣿ ⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣯⢹⠀⠀⠉⡿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠘⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣽⠉⣍⡤ ⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⣿⣿⣿⣿⢸ ⢻⢃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠯⣿⣿⣤⡄ ⣿⠘⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣻⡈⢋⢁⠈ ⣶⢸⠈⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⢧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣁⡮⣿ ⣀⢻⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡽⣿⣿ ⠀⡇⢳⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿ ⣿⣿⡞⠀⡏⣯⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢽⠀⣀⢻⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣙ ⢹⣏⢹⠘⢳⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⡆⠘⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣭ ⣠⣀⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢹⠀⠀⢧⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀ ⠀⠃⡈⢿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠂⠘⣇⠀⢰⠘⣆⡙⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿ ⠀⡀⣤⣄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡾⠀⢧⡁⡏⡇⢀⠀⡀⢦⡙⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣻ ⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢧⢰⠀⡀⠸⢱⣸⠀⠀⠀⠀⡀⢦⠳⢌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⢻ ⠀⠀⠀⠀⠀⡄⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢫⣰⠀⠀⠀⢁⡾⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠁⡿⣿⣷⣿ ⠀⠀⠀⠀⠀⠀⡀⣿⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡵⣞⢀⠀⠀⠀⠀⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠀⠀⠀⠀⠁⡟⢿⠘⣿⢿ ⠀⠂⠐⠀⠀⠀⠦⣦⢧⡙⠦⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣋⢴⣀⠀⠀⠀⠀⠀⠇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠈⠁⠟⣼⣿⢶⠶⣰⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣄⠳⡉⣅⠤⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⡠⣀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡼⢀⠀⣰⢁⠀⠀⠀ ⠀⠀⠄⠦⠒⠒⠉⠈⠀⠀⠀⠀⡀⣤⣳⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡷⣶⢾⠐⡶⠼⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠢⠗⠩⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⡶⣼⠀⢐⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠤⠲⠒⠙⠉⠉⠉⠀⠀⠁⠈⠀⠀⠀⣄⠠⣀⠤⠤⠀⠀⠀⠀⠀⠂⠐⠤⣠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣉⢈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣾⣤⢷⠻⠉⠀⠀⠀⠀⠀⠀⡟⣿⣟⣹⣿⣼⠳⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠀⠀⠀⡀⣧⢿⠻⠉⠀⠀⠀⣧⣿⡉⣋⠒⠓⠉⣆⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⠀⠀⠀⠋⣿⣿⣿⣿⣿⠛⠉⠂⢠⠀⠋⠿⠿⡸⢱⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠛⠟⡿⣿⣿⣿⣿⣿⣾⢁⣄⣳⢙⡀⣶⣿⣾⢠⡿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣿⣿⣿⣿⣿⣿⣿⣼⢀⡄⠸⡄⣿⠻⠙⠈⠁⠟⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣠⣀⠀⠀⣄⣷⣿⣾⣴⢀⠀⠀⠋⢰⠉⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠚⠴⣀⣀⢤⠷⠙⠀⠀⠀⠀⠀⠄⠦⠶⠶⠶⣤⢋⡼⣀⠀⡀⣬⣶⣿⣿⣿⣶⣴⢀⠏⡼⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠞⣠⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠁⠛⠛⠉⠈⠀⠀⠏⣰⠀⠀⠀⠀⣄⠲⠉⠈⠀⠀⠀⠀⣀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡾⣠⠀⠋⣔⣠⣄⣯⣸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡼⢀⠋⠔⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠁⠉⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⣷⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢰⠁⣿⢻⠔⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⣠⣄⣰⣄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠻⠀⠀⠀⠀⠀⠀⠀⠋⡴⠀⡞⣤⢀⠏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⢦⠙⠀⠀⠀⠀⠏⢠⠀⠀⠀⠂⡰⢀⠋⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⢄⣥⣟⢸⠀⠀⠀⠀⠀⠃⣿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢳⠘⠀⠀⠀⠀⡿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠛⡿⣿⣿⠸⠀⠀⠀⠀⠀⡏⣿⠻⣍⠲⠑⠉⠀⠀⠀⠀⠀⠀⠀⠋⠖⣶⢲⠉⣿⢬⠳⠈⡇⣿⣿⣿⠀⠁⠋⠚⠒⠒⠒⠒⠙⠈⣇⣿⣿⠻⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⡿⣶⣷⣿⣶⢶⠻⠉⠉⠉⠟⣿⣿⣿⣿⢿⠻⡛⣍⢭⠭⠭⠭⣤⣠⠀⠀⠀⠀⠀⡀⣄⠲⣄⡿⣿⣿⣾⣤⣀⠆⠲⠘⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⠈⠀⠀⠀⠀ ⠀⠀⠃⣴⠀⠀⠞⣠⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢠⡀⣀⢋⠞⠤⢤⠢⠛⠉⠀⠀⠀⠀⠋⡿⣿⣿⢠⠀⠀⠀⠉⠀⠀⠀⠷⠿⠿⠸⠑⡇⣿⣿⣿⢿⠀⠀⠀⠀ ⠀⠀⡇⠛⠛⠟⢠⠀⠀⠀⠀⠀⠀⣀⣤⣦⣶⣶⣶⣶⣤⢖⠴⡠⣀⢀⠀⠀⠀⠀⠀⡀⣀⠦⠷⣿⣿⣿⣿⣸⠀⠋⣸⣀⣸⠀⠀⠀⡄⣷⣿⢸⠁⡾⣿⣿⣿⣿⠸⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⢹⡿⣿⣿⠟⢠⠉⠛⠜⠉⠉⣏⣿⣿⠹⣟⣿⣿⣄⢸⠀⠀⠀ ⠀⠀⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣸⠀⠀⠀ ⠀⠀⡇⣾⣴⣦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣾⣧⣿⣿⣿⣿⣿⣿⣾⣷⢸⠀⠀⠀ ⠀⠀⠀⢧⠈⠀⣆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠀⣧⣯⣿⣿⣿⣿⢸⡇⢠⠀⠀⠀ ⠀⠀⠀⠀⢦⠙⠋⡿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢻⠉⠞⣷⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣦⣷⣿⣿⣿⢿⠴⡤⣀⣀⣀⣏⣿⣿⣿⢿⠿⠙⠈⠀⠀⠀⠀⠀⠀⡄⠹⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠏⠉⡟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣲⠒⠒⠒⠒⠤⣤⣦⣶⣿⣾⣠⠀⣆⠙⠀⠀⠀⠀⠀⠀⡀⢳⡟⣿⣾⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⢀⣦⣿⠻⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⡀⣷⢨⠀⠀⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠈⠀⡀⣦⣿⠻⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢫⠛⠛⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠋⣿⣿⣿⣿⣾⣤⣤⣀⣧⣿⣿⣾⣤⣠⣦⣷⢿⠻⠛⣟⣿⢻⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣶⣿⣿⠻⠈⠀⠀⣆⣿⠹⠀⠀⠀⠀⡀⣄⣦⣷⣿⣿⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣷⢿⠛⠛⡏⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣶⣶⣾⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠈⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⠀⠀⠀⠀⠀⡾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⣄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠃⣹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣧⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣿⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⡼⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢹⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⡿⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠲⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⢽⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⣿⠉⠋⠒⠒⠒⠓⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⢰⠀⠀⠁⠾⣠⢀⠀⠀⠀⠀⠀⠀⣀⠦⠙⠀⠀⠀⠀⠋⠖⡴⣀⣀⣀⣀⣀⢤⠳⠈⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠀⠃⣸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀ ⠀⠀⠀⠀⡇⢰⠀⠀⡼⠀⠀⠈⠉⠀⣄⠀⠀⠀⠀⠀⠀⠀⡀⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⡆⢹ ⠀⠀⠀⠀⣾⠀⠀⠀⢸⠀⠀⣶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠿⠈⣿ ⠀⠀⠀⠏⢠⠀⠀⠀⢳⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣴⢃⣼ ⠀⠀⠃⣰⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⠀ ⠀⠀⣼⠀⠀⠀⠀⠀⠀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣰⠀⠀ ⠀⡏⢀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣰⣇⠸⠀⠀ ⠛⣼⠀⠀⠀⠀⠀⠀⠀⡄⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⢀⠀⠀⢸⠀⠀ ⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠀⠀⢹⢸⠀ ⣄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀ ⠀⡀⢢⠙⠀⠀⠀⠀⠀⠀⠉⠉⡉⣿⠛⠛⠒⠚⠒⠒⠴⠀⠓⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀ ⠀⠀⠀⠀⣄⢾⠿⠛⠙⣀⢀⠀⡀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⣟⢲⠚⠤⠿⡤⢀⠀⠀⠀⠀ ⠀⠀⠀⠉⡼⣟⣧⣧⣸⢄⠳⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⠘⠁⠋⠟⡸⣀⢀⡞⢀⠏⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⣹⢸⡇⢸⠀⣼⣅⠻⠃⣿⠀⠀⠀⠀⠀⠀⡟⠴⣀⡇⣮⢀⠋⡼⢀⠇⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⣿⢀⡀⢸⠀⢸⡿⠀⣿⢰⠀⠀⠀⠀⠁⠛⣴⠤⠳⡍⢰⠇⣿⣧⠻⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣻⣹⠀⠀⡇⠈⢿⣟⠀⣿⠀⠀⠁⠚⡴⣀⠀⠀⠀⠀⡀⣄⡳⢹⠀⣷⣄⠱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣿⠸⠀⡄⢹⡇⣈⠀⣹⠀⠆⣠⢀⠀⠀⠁⠉⠋⠒⠒⠀⠀⣀⠦⡟⠘⡀⢷⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣆⢿⠈⠀⡇⠘⢰⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡷⠈⠀⠀⡄⢻⠀⠀⢧⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⢸⠀⡀⢿⠁⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⠉⠙⠀⡄⠙⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⡇⣱⣼⣆⠀⠀⠆⠇⠿⠿⠾⠀⠀⠀⠀⠀⡞⢿⡿⠳⠛⣏⠻⠀⡄⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢹⠛⣽⠇⢸⠀⢻⠀⠾⡇⣿⢾⣷⠉⠙⠀⠀⠀⠀⣷⣿⠩⣛⣿⡆⢸⠀⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⡀⢻⢸⠀⡇⣼⢶⠟⡛⢿⠾⣶⣀⠀⠀⠀⠁⠉⠉⡉⣿⢿⡴⣇⠀⡇⠘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⣶⠻⣿⢸⠀⣄⣷⠛⡉⣿⢀⠁⠉⠛⢾⢠⠀⠀⡀⣏⣿⣼⢠⠀⡇⢸⡇⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⡀⣄⢻⠀⠀⡀⢧⡇⣿⣄⣤⣠⣀⠀⠀⠀⠃⠞⣣⣼⠀⠀⠀⡇⢠⡏⣼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⣇⠀⠀⠀⡀⣧⣿⠘⠀⠀⠀⠁⠋⡴⣡⠞⣠⠀⠀⠀⠁⡼⠃⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⡆⢷⠊⠶⡴⣀⠉⠖⣠⠀⠀⠀⠀⠀⡶⢣⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠳⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠚⡤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⠤⠤⠶⠶⠶⠤⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

🎬👉👌💦

🎥🍆🍑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠹⢦⡤⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠞⠋⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⡀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⢀⣀⣀⣀⣱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠶⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠃⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⢻⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⣤⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠶⢤⣀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

.　 +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *

🔞🎬▶️

❤️❌❌❌🎥

🎬🍑🍆

😉👉👌📼

💦👄🎬🔞

🌐🍆🍑💦🎬

🍑🍆🎥

🍆🍑🎬

🍆🍑🎥⭐

🔞🎥

🎥🔥🔞

🇺🇸⭐🎥🍆🍑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣦⣿⠼⠀⠒⠒⠒⣐⣀⠤⠤⣤⣦⠶⡶⣷⠿⠿⠛⠛⡛⣙⢭⠭⣯⣾⣷⣿⣿⣿⣿⠿⠻⠛⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⠻⠈⠀⠀⠀⡠⣀⢀⠃⡵⢚⠰⠉⠀⠧⠚⠶⣒⢒⠒⣛⣛⣙⣉⣍⣭⣾⣿⣿⣭⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠈⠀⠀⠀⠀⠇⣶⠛⠚⠁⠊⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣷⣿⢿⣌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢿⠰⠀⠉⠛⡿⠀⣁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⠿⣟⣿⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣤⣿⣿⣴⣯⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣰⠀⠈⡧⣼⠀⡁⣨⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⣸⠀⠀⢠⡇⢼⠀⡀⠰⡇⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣶⣠ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠀⠀⠀⡅⢸⠀⡞⠁⡼⢋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣾⣠⠀⠀ ⠿⠿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⡆⢀⠆⢠⡀⡞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣤⠀⠀⠀⠀ ⣶⣿⣿⣿⣿⠿⠛⠉⠈⠉⠋⠛⠿⠿⠿⠿⠿⡿⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡿⣿⣿⣶⢀⠀⠚⠀⠀⠀ ⣀⣄⣤⣶⣶⣷⣿⣿⣶⣷⣷⣤⣤⣠⣀⣼⣀⣀⣏⣿⠻⠏⠿⠿⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⣿⣶⣤⢀⠀⠀⠆⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⡸⢸⠐⠁⠟⢹⢍⣿⣿⣶⣳⣾⣿⣴⠲⢕⠉⠀⠀⠀⠀⠁⠉⠛⡿⣿⣶⣪⣜⠹⠀⠀⠉⠞⠡⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠉⠚⠷⠿⢿⢿⠿⣶⣶⣴⣤⣀⠀⠀⡀⣯⣼⠀⠀⠄⡦⣝⣨⣀⣁⣁⡿⣿⣶⢷⠙⢂⣿⡉⠟⡾⢶⡶⣤⣤⣤⣤⣿⣿ ⠀⠀⠀⠛⠿⣿⣾⣶⣤⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⣄⠲⡉⡏⣽⠐⠉⡟⣯⠶⣠⣀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿ ⠋⠟⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿ ⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿