Arctic Fox Dot Art

Copy & Paste Arctic Fox Dot Art Emojis & Symbols

⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⡄⠀⠀⠀⠀ ⠀⠀⠀⡇⢠⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠋⠁⡀⠀⣇⠀⠀⠀⠀ ⠀⠀⠀⡇⠈⡇⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⡴⠃⠀⢸⡀⠀⠀⠀ ⠀⠀⠀⡇⠀⠸⡄⠀⠈⠣⣀⡤⠴⠒⠒⠒⠲⠤⣄⡀⠀⠀⣠⠃⠀⠀⠀⣠⠇⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠳⣀⡤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⡠⠃⠀⠀⠀⣠⠇⠀⠀⠀⢠⠃⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⡎⠀⠀⠀⠀ ⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀ ⠀⠯⣄⡀⠀⠀⠋⠉⠉⠉⠳⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠉⠑⣄⠀⠀⠠⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠙⢦⡀⠀⠀⠀⠀ ⣠⣞⡥⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠧⣄⡀⠀ ⠀⠀⠀⣇⣀⣀⣀⡀⠀⠀⠀⡀⠀⠀⢷⠏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠖⠒⠃⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢧⣀⣀⠼⡄⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⢸⠤⠤⡄⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⣆⣀⣀⣀⠤⠒⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠔⠋⠙⣄⣠⠞⢧⣀⣀⣰⣄⣀⣀⣀⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠖⠦⠼⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣁⠙⠛⠛⠛⠉⠉⠉⠉⠉⣁⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⢻⣷⣀⡤⢰⣿⣗⢚⡳⠈⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢸⣆⣛⣿⣷⣿⣿⣿⣤⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢘⣿⣿⣿⣿⣿⠇⣿⡟⠀⠻⣿⠓⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣯⣁⣈⣧⡿⠀⠀⠀⣉⡴⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣿⣿⣿⣿⣿⠏⠁⠀⠲⠖⠉⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠘⣹⣿⣿⡟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⣶⣬⣀⠀⣾⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠛⣿⣿⣿⣿⣿⣿⣶⣾⡏⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣿⣿⣷⣾⠀⢿⣿⣿⣿⣿⣿⡛⢿⣧⠙⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⢿⣿⣿⣿⣿⣿⣶⢿⠇⠈⡧⠀⠀⠀⢰⣿⣿⣶⣰⣀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⡿⣏⣼⣾⣃⡀⠀⠀⠐⣄⣿⣿⣿⣿⣿⣗⠂⠀⢀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣷⣀⢻⣿⠄⡀⡄⠈⣿⣿⣿⣿⣿⡛⢣⣦⠙⢷⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡆⢰⣿⣿⣿⣿⣿⣾⡏⣼⣷⡜⠀⢻⣿⣿⡟⢻⣿⡄⢻⠀⢰⠆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢉⣀⢸⣿⢹⣿⣿⡟⣿⣗⡍⠈⠁⢀⠘⣿⣿⣿⣼⣿⣷⡀⢂⡈⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣠⣶⣾⣿⡏⣼⠃⢿⣿⠉⠇⣿⡉⠁⠀⣴⠀⠠⣹⣿⠿⣿⣿⣿⡟⠀⢹⡄⠈⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣧⡘⠻⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⠟⠋⣡⣤⣴⣾⣿⣿⣿⠟⢠⣿⠀⡿⠁⠀⢰⣿⡇⠀⢰⣿⣦⠀⢣⣿⠷⡇⢿⡿⠁⠘⣎⢱⡄⠀⠀⣸⣿⣿⡿⠿⠿⣿⣿⣿⠿⠟ ⣿⣿⣿⣿⣿⣿⣦⠈⠃⣀⣤⣴⣿⣿⣿⣿⠟⠀⠛⠿⣟⣿⣿⣿⡉⠸⠊⣼⣿⡇⠁⠀⠀⣼⣿⠇⠀⣿⣿⣿⣷⢺⡇⢠⠑⢀⡀⠀⠀⠿⠅⠉⠀⠀⠁⢠⡄⠀⠀⠀⠀⠀⠁⠀⠀ ⣿⣿⣷⣈⣛⣛⣉⣰⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠽⢋⣉⡴⣂⠀⠴⠿⠏⠁⠀⢀⡘⠛⠐⠀⠴⠿⠿⣿⣿⡾⠆⠀⠀⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣰⣾⠿⠃⢠⣽⠀⢙⣃⣀⠤⠤⣇⣀⣀⣀⣀⣠⣭⠭⣥⡖⠀⠀⠲⠾⢷⠖⣰⣦⣷⣶⣄⠙⠉⠀⠉⠻⣄⡀⠀⠀⠀⠀⠀⠀ ⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠒⠿⠉⣁⣉⣠⠤⢤⣬⣹⣿⣿⢷⣷⠶⣦⡉⣹⣿⡿⠉⠈⠠⠄⠀⠀⠀⠀⠰⢤⡄⣤⣾⣦⠀⢀⣀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀
⠀⢄⠢⡐⢢⢘⡰⢌⢢⢑⢢⠱⢌⢢⠱⢌⢢⠱⡌⢦⡑⢎⠴⡡⠎⡴⠡⠎⡴⠡⢎⠴⠡⠎⡴⢁⠎⡴⠡⢎⡰⢡⠎⡰⢂⠒⡄⠂⠄⡀ ⠈⡄⢢⠑⢢⡁⢒⠌⣂⠎⠤⢃⠎⢤⠋⡤⢃⠞⣶⣆⣈⣤⣶⠔⡄⡀⡕⠀⠰⣉⠲⢌⢃⠳⣐⠩⠜⣠⠋⡤⡑⢆⡡⢃⠎⡱⢀⠣⠐⡀ ⠐⡨⢄⡉⢆⡘⢄⠃⢆⠌⡃⢎⡘⠤⠓⡄⢣⠂⣿⣽⣿⣿⡗⣣⠉⠀⠀⠀⠀⢆⡑⡊⢌⡒⠌⡬⠑⡄⠣⠔⡡⠒⡄⢣⠘⡄⠣⡐⠡⠀ ⠀⡁⠂⢌⠐⡈⠆⡉⠆⡘⡐⠢⠘⡄⢣⠘⡄⠃⣿⣿⣿⢯⡋⡧⠀⠀⠀⠀⠈⠢⡐⢡⠒⠌⡒⠤⢉⠔⡉⠆⢡⠃⡘⢀⠃⠌⠡⠐⡁⠂ ⠀⠠⠃⠄⣀⠃⠄⠠⠘⠠⢀⠃⠄⠠⠀⠄⡘⢃⣿⣿⣧⣤⡿⠛⠀⠀⠀⠀⠀⠀⠀⠃⡘⠠⠀⠄⠄⠠⢀⠘⡀⠄⠠⢀⠘⡀⠣⢀⠀⡀ ⠈⡔⠡⢂⠤⠈⡄⠡⠌⡁⠂⡌⠤⠁⠌⡐⢈⠘⣿⣿⣿⣻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠔⡨⠐⡄⠒⡠⠘⣀⠂⡂⢄⢁⠂⠄⡀ ⠐⣈⠡⢂⠰⠁⡄⠡⡐⢠⠡⡐⢂⠡⢂⠰⡀⢎⣿⣿⣿⣮⣗⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⢈⠂⣁⠒⡀⢂⠁⠂⠄⢊⠐⠀ ⡘⣄⠡⢊⠄⡉⢄⠁⡘⢄⠳⡘⠤⠋⠔⢃⠉⢋⢿⣿⣿⣿⣿⡺⡁⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⡠⢎⠰⣁⢊⠱⡈⠆⠌⡐ ⠸⢄⠋⠖⠨⠑⠊⠁⠉⠦⣁⠀⡡⢀⠆⡴⡘⢦⡘⣿⣿⣿⣿⢶⡹⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡑⢊⠡⠌⢂⠱⢈⠒⡰⢀ ⠐⠢⠌⡐⢢⠁⢆⠡⡈⢒⢀⠣⢌⡡⢚⠤⡑⢦⡘⠄⢿⣿⣿⣿⢒⡵⢀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡑⡌⢦⡑⢎⡐⠁⠂ ⡘⣄⠒⡤⢡⡘⢤⠣⡜⢢⢍⠲⡅⢎⡱⢈⠱⠠⢌⠱⡈⠙⣿⣿⣿⣧⢃⡆⣠⠀⢈⢸⠀⢁⠒⠀⠀⠀⠀⠀⠀⠁⡑⢈⠀⠌⠠⠘⠠⠁ ⠴⣈⠳⣌⢣⠜⣢⠓⣌⠣⢎⡱⢜⡸⣐⠣⣌⡑⢢⠡⠌⡁⢿⣻⣿⣿⣿⠽⠱⠁⠀⢰⢫⡆⣳⡀⢃⠀⠀⠀⠀⠀⠐⠄⡈⠄⠡⠈⠄⠁ ⢸⢡⢳⡌⡞⣬⢡⠋⣴⠉⡖⢱⠊⣴⢡⠓⣤⣽⣮⣷⣿⣷⣿⡟⡎⢹⣾⡞⠀⡔⠂⠁⠓⠚⢩⢻⡅⠀⡄⠀⠀⠀⠈⡔⠐⢨⡄⠃⡌⠀ ⢢⢋⡦⣭⠒⣥⠋⠜⠄⢋⡔⢣⠚⡤⢋⡢⣽⣾⣿⣿⠿⣼⠑⡣⠁⢰⡗⠑⠀⣿⡆⠆⠛⡜⢳⠧⠁⠀⠀⠀⠀⠀⠡⠄⠁⠂⠄⠂⠠⠀ ⣤⡍⣾⣿⣷⣦⢡⣄⡚⢴⢨⢃⠃⠀⠉⠛⡝⠯⡍⠐⢡⡯⠇⠁⠀⣼⠛⠈⢸⣿⣿⣞⡄⠁⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡙⣉⠳⡘⢆⠣⢆⡙⢆⠣⠆⠀⠀⠠⣬⡒⢃⣐⠖⠫⠉⣀⣀⠐⠀⠀⡸⣉⢈⣉⠗⠈⢤⣼⡭⣤⣤⣤⡀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠠⢃⠩⠌⢓⡌⡸⢌⡣⠭⣔⡲⠉⣧⣐⡯⠟⡩⢛⠻⡻⠿⢯⣕⣭⠉⠁⠈⠀⠀⠀⠀⠀⠠⠈⣽⣇⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⡆⢀⠀⣀⡀⡀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠃⣌⣳⣿⠿⡿⢿⣿⣏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⠀⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣿⣿⠡⠊⣤⠠⢹⣿⣧⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡬⡂⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠠⠷⠶⢇⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⠛⢷⣶⣤⡂⠉⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣤⣦⣶⣿⣿⣿⣿⣦⢀⣸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣾⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡟⠉⣽⣿⣿⣿⣿⣷⣀⣰⣿⣿⣿⣿⣿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⣊⣿⣿⣿⣿⠋⢻⣿⣿⣿⣿⡿⠁⣤⣾⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣵⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡮⡀⢴⣶⣶⣶⣶⣶⣶⣦⠶⠀⡀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⣩⣿⠁⢺⣿⣿⣿⣿⡹⠿⠿⣿⡿⠛⢻⣿⣿⣿⢆⠸⣿⣿⣿⣿⣿⣿⣿⣄⠀⡇⣴⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢘⣿⣿⣿⣦⣼⣿⣷⠠⠉⢿⢙⣿⣷⡀⣄⣥⣴⣿⣿⣿⣿⣿⣖⠀⠾⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⢿⣿⣿⣿⣿⣿⣿⡴⠂⠺⣷⢾⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⡆⢠⣿⣿⡟⢙⣅⣀⣀⢀⡀⠀⠀ ⣾⣿⣿⣿⣆⠰⣌⠀⡇⣿⣿⣿⣿⣷⠸⣿⣿⠏⣿⣿⣏⠜⢂⣰⡎⣼⣿⣿⣿⣿⣿⣏⠛⣿⣿⣿⣿⣧⢹⣿⡿⠁⠺⣿⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣌⡛⢰⠉⡿⠟⣿⣿⣄⡻⣿⡄⡏⢸⡿⡆⠀⢨⠁⣿⣿⣿⠛⣿⣿⣿⣤⣾⠻⠻⢿⣿⣼⣥⡆⠿⢅⢲⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⠟⣿⣿⣿⣿⡆⣔⡔⣡⣿⣿⣿⡇⣸⡇⣿⣷⣌⡇⠀⠈⢠⣿⣿⡟⢡⣿⣿⣿⣿⣿⣶⣷⣿⣿⢻⣿⣤⣾⣶⣴⣿⡟⠫⢙⢻⣿ ⣿⣯⡀⠠⢀⣼⣿⣿⣷⣈⣼⣿⣿⡿⠿⢛⣡⡇⣿⣿⡆⠅⠀⠀⣼⣿⣿⢁⠚⠻⢛⣏⣙⣋⡙⠻⣿⣿⡀⣤⣿⣿⣿⣿⣿⠸⠸⠠⢂⣿ ⣿⣿⣏⣰⣄⣿⣿⣿⣿⡿⠛⣋⣤⢖⠟⠻⠟⠇⢿⣿⣿⠀⠀⢠⣿⣷⡮⢨⣿⣻⣿⠿⣿⡿⢿⡿⢿⣿⢷⣸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿ ⣿⣿⢿⢿⠿⠿⠿⠿⠟⠑⢼⣏⢉⠅⠈⣦⡉⠇⢸⣿⣿⠀⠀⢉⣿⡺⠠⢹⣷⢑⣴⣾⣾⣷⣆⠑⣾⣿⠆⣼⡶⡶⢻⡫⢟⢝⠝⡻⣿⣿ ⣿⣿⣷⣶⣶⣶⣴⣦⣔⣀⠂⠁⠀⠁⠀⠀⠀⠀⠙⠻⡍⠀⠀⠘⠙⢃⠀⠀⠁⠈⠻⠿⠷⠛⠛⠋⠋⠁⠀⢭⠀⠨⡈⡘⣯⣃⣤⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⣦⣤⣠⣀⠀⣀⣀⡀⡀⣠⣤⣶⣶⣦⣶⣶⣴⣤⣤⣀⣤⣤⣭⣽⣿⣾⣢⣿⣬⣿⣾⣖⢯⡿⢭⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢽⣿⣿⣿⣭⣢⣯⣽⣛⣋⡾⢷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢿⣿⡗⣿⣿⣿⣟⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡞⠛⡿⣿⣿⣿⣿⣿⣿⡿⢋⣦⣭⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣏⣴⣿⣿⣒⣶⣾⣿⣿ ⣿⣧⣌⣙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣋⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
AI Story Generator
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⠀⠀⠀⠀⠀⠀⠀⣶⣶⡶⠾⢾⣿⣿⣿⣿⣿⣿⣷⠄⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⢉⣿⣿⣿⣿⣿⣷⣦⣷⣶⣾⠗⠻⠳⣶⣿⣷⣶⡦⠀⠀⠀⠈⢾⣾⣾⣿⣿⣿⡆⣿⡇ ⠀⠀⠀⣀⣀⠀⢀⢁⣀⣠⣤⣬⣛⠿⢿⡿⠿⠿⠟⠂⠘⠘⠛⡉⠭⠍⡻⢿⣿⢿⣛⣄⢀⠈⢻⣿⣿⣿⣿⣿⢹⣿⣿⣿⣎⠀⠀⡽⣿⣿⣿⡗⠀⠀⠀⠀⠀⠈⠀⢇⢱⠏⡁⣿⡇ ⠀⠐⢿⣿⡏⢀⣾⣥⡬⠛⠿⡻⣿⣿⣾⣶⣾⣿⣶⣾⣶⣿⣿⣮⣾⡞⢈⣆⡃⠺⣿⣿⣾⣦⣠⠙⢟⣿⡿⢉⡶⣝⢿⣿⣿⡄⠀⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠶⡂⢣⣇⢻⡇ ⠀⠀⠀⠁⠀⣤⠥⠺⢿⣥⣢⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡻⢿⡓⡪⣾⣷⠄⠹⣿⣿⣿⣿⣦⡆⢠⣾⡇⡃⣹⡢⣿⣿⠅⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠨⠠⠱⣙⢸⡇ ⠀⠀⠀⠀⢠⣿⠊⠩⢁⠨⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢅⡡⠤⠀⠀⠦⣾⣿⣿⡀⢹⣿⣿⣿⣿⢿⡀⠻⣿⣷⣼⣿⣾⣧⡆⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠑⠀⠛⣬⡇ ⠀⠀⠀⠀⢸⣿⣧⢁⣀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡒⠈⡀⣹⣶⣿⣿⣿⣯⠅⠸⣪⢾⠟⠊⡰⠐⣌⠻⣿⣿⣿⣿⣇⠀⠹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇ ⠀⠀⠀⠀⢩⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣚⣿⣿⣿⣿⣿⣿⣗⠠⠽⠀⢊⣾⣧⣾⣿⣷⠸⣿⣿⣿⣿⡄⠈⢬⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠄⡠⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣄⢢⢻⡯⣥⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣿⣿⣿⢿⡿⠛⠫⢍⣿⣿⣿⣿⣿⣿⠿⠋⠻⢿⢿⣿⠧⢟⣻⣿⣿⣿⣿⡻⢃⠂⠐⢿⣿⣿⣿⡿⣷⣜⣿⣿⣿⣿⣿⣮⣦⣧⣭⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣿⣿⣿⣥⣴⣄⠀⠀⣿⢻⣿⣿⣿⡏⠀⠀⠀⣠⣴⣶⣾⣷⣬⣿⣿⣿⣿⣿⠧⣄⠀⣾⣿⣿⣿⣷⡙⣿⣿⢽⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣻⣿⣿⣿⡆⠙⣡⣿⣷⣿⣿⣿⣿⣍⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣯⠠⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⠑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣰⣄⠀⢠⡇ ⠀⠀⠀⣰⣿⣿⣿⡙⡁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣟⣿⣿⣿⣿⣿⣿⣿⡇⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⣸⣿⣿⣆⠸⡇ ⠀⠀⠀⣻⣿⣿⣿⡓⠶⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⠥⣎⠍⠸⢿⡿⠟⠋⠀⠀⠈⠻⣿⣿⡟⣿⣿⣿⡇⠀⠀⠀⠀⠽⣿⣿⣿⡖⡀ ⠀⠀⠠⢄⣻⣿⣿⣿⣧⢅⢏⠁⠀⠀⠙⣿⣿⣿⠋⠔⠊⢩⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣰⡄⠀⠀⠀⠂⠂⠀⠀⠀⠙⢏⣿⣼⣿⣿⠀⠀⠀⠀⠀⠈⠛⣿⣿⠁⠆ ⠀⠀⠀⠾⣿⣿⣿⣿⣷⣥⣌⠲⡄⢀⠮⠙⢋⠈⠁⢐⢸⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⢇⣀⣼⣾⣿⣄⡀⠀⠘⣿⣿⣿⡿⠀⠀⠀⠀⠀⣰⢛⣿⣌⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡽⡡⡢⢥⣷⠇⢄⠕⢙⠑⡀⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣛⣿⣿⣿⣧⠀⠀⠙⣿⡝⠀⠀⠀⠀⠀⠀⣿⠿⠿⣧⣿⡀ ⠀⠀⠀⠀⢒⣿⣿⣿⣿⣿⣿⣿⣉⢞⠕⡁⢨⢾⠧⢰⣠⠋⣼⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢀⡎⣿⣿⠀⠀⠀⠀⠀⠀⠃⠸⣻⣿⣿⡇ ⠀⠀⠀⠂⠿⢿⣿⣿⣿⣿⡿⣫⢖⣵⣟⡬⡃⡸⠣⠻⠓⣸⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡯⢌⡋⡟⠈⡆⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⡇ ⠀⠀⠁⠐⠊⠽⣿⣿⣿⣿⣷⣭⣦⣞⡾⢋⠉⠑⠅⣈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⢿⣔⡃⠃⠀⠀⠀⠀⢠⡹⣿⣿⣿⣿⡇ ⠀⠀⠀⠂⠀⣈⣻⣿⣿⣿⣿⣿⡿⢿⡯⠟⠀⣡⠝⠹⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣤⠕⠀⠀⠀⠀⠘⠧⣿⣿⣿⣿⡇ ⠀⠀⠀⠐⡀⠉⠰⢻⣿⣿⣿⣿⣷⣿⡬⡺⠫⡢⡴⠂⢯⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡯⣷⠠⠀⠀⠀⢈⢻⡟⢿⣿⡇ ⠀⠀⠀⠐⡇⠀⠼⣿⣿⣿⣿⣿⣿⣋⢄⢬⡾⡂⢀⢌⠸⣿⣼⣏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡪⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣏⣄⣀⣤⣄⠢⠙⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣷⡞⠐⡴⣗⣠⠃⣽⣷⣷⣧⣻⣿⣿⡹⣿⣍⣻⣿⣿⣿⣿⣿⣿⢪⡠⠊⢘⣿⣔⡩⣜⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣚⣿⣿⣿⠓⠈⢉⡄ ⠀⠀⠀⢀⠂⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣼⣏⡅⠼⣳⣖⢏⢸⣿⡿⣽⢹⡝⡷⣻⣿⡟⢿⣿⣿⣿⣿⢷⠛⣯⠂⠙⢻⣿⣿⣶⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣾⣿⡇ ⠀⠀⠀⣾⣿⣤⣤⠶⣀⢚⡹⣿⣿⣿⣿⣿⣯⡨⠞⠡⠈⣠⣽⣯⣿⣸⣧⢱⣿⣬⣿⡿⣾⣿⣿⣿⣿⣄⡈⠭⣪⣶⣿⣿⣿⣿⣯⣽⣿⣿⣯⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠸⣿⣿⣿⣿⣷⣮⠰⠩⠽⢽⣿⣿⣿⣿⣭⣞⣶⣟⠟⠝⣸⠝⢿⡜⣼⡌⡝⡼⣧⣿⣿⣿⣿⣿⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢐⣶⡄⢹⣿⣿⣿⣿⣿⣿⡄⠄⠱⠈⣽⣿⣿⣿⣿⣿⣣⣣⠞⢍⢌⠊⢋⢾⡄⣇⠇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⢿⡦⠬⠻⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⢤⡰⠁⠻⢿⣿⣿⣿⣿⣟⡁⣩⠮⡀⠀⠀⣄⣽⣄⢣⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⡿⢻⣿⣿⣿⣿⣟⠞⡙⢬⡕⣴⣼⣿⣿⣿⣿⣿⣿⡇ ⠀⣿⣿⣿⣿⣿⡷⢹⣿⣿⣿⢾⣾⢁⣠⣤⣿⣿⣿⣿⣿⢻⠕⣄⢜⣄⠀⠀⡨⣾⢿⣯⠀⡁⣿⠟⣻⣿⣿⣿⣿⣿⠝⠝⢒⢀⠄⣛⣿⣿⣿⣿⣮⣺⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⣻⣿⣿⣿⣿⣿⡮⣿⣻⣿⣧⡭⠬⢼⣿⣿⣿⣿⣿⣿⢃⡾⡑⣾⣿⠂⢤⣾⣿⣿⣿⠀⡞⣡⣿⣿⣿⣿⣿⣿⢁⠊⠠⠒⢑⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣛⣻⣿⠇ ⠀⣽⣿⣿⣷⣦⣀⢹⣷⣥⣟⣛⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠨⣿⣿⣶⣿⣿⣿⣿⣷⠀⡤⡡⡿⢿⣿⣿⣿⣻⡠⠤⠀⠡⡭⣥⣴⣿⣿⣿⣿⣿⡿⠿⡛⠙⠁⠄⣒⣩⠅⠀⢩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠛⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠉⠻⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢡⣀⠈⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠠⢤⣀⠀⠀⠈⢳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠈⠀⡁⢻⡓⠘⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠾⠄⠀⠀⠀⣿⣿⣟⡲⣤⡀⠀⠀⠀⠀⣰⣯⣤⠎⠰⡇⠀⣳⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠰⠦⣤⣀⠀⠈⠏⢿⡑⣌⡟⣦⡀⠀⣴⡟⠾⠓⠒⠒⠦⡀⢹⣇⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣸⣾⣿⣿⣦⣄⡀⠈⣿⡈⣻⡏⢽⣾⢻⠁⢀⠀⠀⢀⣠⣝⣭⣿⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡍⠉⠵⢾⡗⠉⢧⢀⠻⣷⣿⣇⡾⠃⠘⠀⣄⠐⠀⠶⢟⣿⣿⣿⠀⠀⣿⣿⡱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⣦⡀⠸⢯⠃⠈⠟⠀⠇⠀⠻⠃⠀⠀⢸⡿⠛⢰⣾⣿⣿⣿⠋⠀⣸⣿⡿⢽⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⡙⢶⡮⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⢀⣾⢹⣿⠋⠛⠀⢠⣥⣿⡄⠘⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠉⠈⠀⠀⠀⠀⢸⣅⣿⠿⠂⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⣀⣀⣀⣼⡿⠻⠀⠁⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⣿⣍⣭⣉⠀⠀⠭⠖⢦⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡆⠀⠀⠀⠀⠀⣸⣿⡶⡶⢤⣄⣀⣸⢧⠀⠀⠀⠑⣦⣀⢪⡑⠦⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠾⡟⠀⠀⠀⠀⣠⣿⡿⠿⠷⠚⠉⠁⢉⠻⢽⣟⣀⠀⠀⠙⣦⡙⣷⡈⠣⡀⠸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠃⠀⠀⢠⣴⣿⡉⠉⠀⠀⠀⠀⠐⠛⠓⠀⠘⠛⠿⣶⡄⢹⣷⡜⣧⠀⠈⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⢹⡆⢿⡆⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠙⢦⠻⡹⡌⢧⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⣸⣷⣻⣷⣄⣤⠴⠒⠀⠠⠴⠤⠆⠀⠀⢦⣀⠀⠀⢳⡿⢿⡏⠳⣶⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣁⣀⠀⠀⣀⣀⣼⣯⣽⣿⠙⠿⠛⣠⣴⡄⠀⠀⠀⠐⠀⠀⢠⢹⠀⠀⠀⠓⢸⢧⠀⢹⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⣽⣿⣿⠞⠋⠙⠛⠋⠿⢁⣠⣴⣋⣡⡤⠤⠤⠤⠤⠤⠤⣀⡈⢳⡇⠀⠀⠀⠸⣿⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣉⠀⠀⢀⣀⣤⣶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢤⡀⠀⠀⢹⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢧⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣽⣯⣿⣭⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣽⣿⣿⣿ ⣿⣿⣿⣟⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⣻⣿⣿⡟ ⣿⣿⣿⣷⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⢐⣾⣿⣿⠃ ⡇⣿⣿⣿⠭⠥⠄⠈⠻⣷⣦⣤⣶⣦⣤⣤⣴⣶⣤⣴⣿⠋⠀⠠⠭⢭⣿⣿⣿⠀ ⡇⢻⣿⣿⣿⣶⢖⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣲⣾⣿⣿⣿⡏⠀ ⡇⠈⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⡟⠀⠀ ⡇⠀⢸⣟⢜⣿⣿⡿⣟⠟⠉⠉⠛⣿⣿⣿⣟⠋⠁⠈⠙⣻⢿⣿⣿⡸⣿⠁⠀⠀ ⡇⠀⣸⣿⣿⡿⠋⠉⠁⣀⣐⠢⣄⢸⣿⣿⠀⣠⢖⣂⣀⠈⠉⠛⢿⣿⣿⣄⠀⠀ ⡇⣼⣿⣿⣿⡷⡋⢰⠟⠻⣽⣷⢿⣿⣿⣿⣿⣷⣿⣿⠟⢳⡈⠹⣾⣿⣿⣿⣆⠀ ⡇⢾⣿⣿⣿⣏⠀⢸⣶⠀⠀⠀⠀⣿⣿⣿⠻⣆⠀⠀⢀⣼⡇⢈⢿⣿⣿⣿⣧⠀ ⡇⢻⣿⣿⣿⣯⢂⣼⣿⣷⣷⣇⣼⣿⣿⣿⠅⢸⣾⣷⣿⣿⣆⣠⣿⣿⣿⣿⡷⠀ ⡇⢪⢿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⡿⠭⠅⠀⡄⡿⠉⠙⢿⣿⣿⣿⣿⣿⡿⡁⠀ ⡇⠀⠞⣿⣿⣿⣿⣿⣧⠈⢿⣿⡏⣿⣶⣿⠄⣧⠃⠀⢀⣵⣿⣿⣿⣿⡏⠇⠀⠀ ⡇⠀⠀⠘⠹⡟⣿⣿⣿⣷⣾⣿⣿⣬⠽⢭⡴⠁⠀⣰⣿⣿⣿⣿⢻⠿⠃⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠙⢿⢿⣿⣿⣿⢠⢉⠉⠉⠀⠀⡆⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣼⣼⢸⣰⣸⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢁⠧⡩⡗⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⠁⡱⣛⣖⡌⣊⠓⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⣧⡁⢈⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠰⣯⠒⠀⣺⠿⠫⣃⢤⡁⣊⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡒⡉⡀⠆⠱⣑⡆⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣁⠙⡠⠈⠁⠈⠓⢹⠕⢜⡫⡙⡃⠡⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⡄⠁⠢⠀⠑⠀⠀⠈⠐⢌⠀⢄⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⠃⠓⠉⠀⠀⠀⠀⠀⠀⠁⠄⠛⣽⣧⠁⠋⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠫⣎⣛⢠⠁⠀⠀⠀⠀⠀⠀⠡⢤⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡸⠩⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⢮⢁⣎⣯⣊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⡔⠒⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠐⡀⢤⠐⢨⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⢭⠁⠀⠸⠩⡀⢙⠂⠀⡀⠀⠀⠀⠀⠀⠃⡀⡙⡱⠫⠸⡓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢪⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⢔⡯⠀⠀⠀⢂⠀⠁⠘⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠤⠃⠀⠀⠈⢐⡟⣉⠀⡑⡄⠐⢀⠀⠀⠀⠀⠘⠄⠁⢶⣸⣅⠶⣀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡖⠖⠁⠀⠀⠀⠀⠀⠀⠀⣴⠵⡽⡱⢽⠁⠀⠀⠀⠘⡀⠐⠂⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣈⣋⠀⠀⠀⠀⠚⡑⠀⢶⡁⡅⢆⢀⠀⠄⠀⠀⠀⠀⠀⠀⠡⠳⣿⣅⠓⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢹⠁⠀⠀⠀⠀⠀⠀⡀⢀⡣⢛⠕⠉⠠⣙⠀⠀⠀⠀⠀⢣⠀⠈⠅⠸⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡜⠠⠀⠀⠀⠀⠄⠛⡁⠊⢳⣶⠁⢀⠀⠄⠈⢀⠀⠀⠀⠀⠀⠑⠯⣷⠖⣦⣶⣮⡵⣀⠀⠀⠀⠀⠂⠠⠶⢒⠀⠀⠀⠀⠀⠀⠀⣆⡀⠀⠀⠀⠀⠀⠀⡠⢁⠔⡀⡽⡋⠀⠀⢄⠅⠀⠀⠀⠀⠀⠀⠇⠠⠡⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢈⠀⠀⠀⠀⠀⠀⢁⠀⡄⢔⠫⣇⠧⡂⠑⠠⠀⢒⠒⠁⠐⠈⠀⠀⠘⣠⣾⣧⡷⡿⣿⢾⣗⣾⣶⣦⡤⡾⡶⠦⢶⠷⣆⣬⣗⡷⡇⢒⡐⠢⠀⠄⠀⠨⢅⢮⡄⠆⠡⠀⠀⡨⡈⠀⠀⠀⠀⠀⠀⠀⠡⠇⢁⡠⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠠⠀⠀⠀⠀⠀⠀⠈⠄⠀⠃⠄⠘⠴⠧⣀⠄⢂⣔⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠁⠀⠀⠀⠁⠀⠂⠀⠉⠀⡙⠀⠁⠈⠑⠀⠀⠉⠁⠋⠀⠀⢉⢜⢹⠃⠀⠚⠄⣔⡍⠀⠀⠀⠀⠀⠀⠀⠀⢸⡐⢂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠮⣔⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠈⠙⠧⣳⢂⠋⠷⢧⣉⣖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠈⠉⠷⠂⠁⠹⣟⣟⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⡧⢀⢀⣠⣤⣀⣄⣄⡠⡀⣸⣧⠞⠓⠛⠟⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠖⠑⡤⡑⢴⠅⣂⠂⠒⣊⡁⠄⢂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡰⡡⠊⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⡿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠓⠕⡸⣀⡒⠄⣄⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣶⡁⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀⠤⢩⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡨⡖⢫⢦⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠐⠂⠀⠐⢹⣀⠪⠀⠊⠛⠛⠓⢲⡷⠉⠉⠁⠏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢒⢊⣌⣥⠋⢅⠡⡠⣔⣊⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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≽^•⩊•^≼ .°˖⋆ ℧ 𓃗 .°˖⋆°❀⋆.ೃ࿔*:・١٥٧٤♡ᡣ𐭩ྀིྀིྀ ⋆˚࿔ 𝐧𝐚𝐦𝐞 𝜗𝜚˚⋆ (⸝⸝⸝O﹏ O⸝⸝⸝)˚˖𓍢ִ໋🍃˚.⛰️⋆☁️ฅ^•ﻌ•^ฅ˗ˏˋ 𓅰 ˎˊ˗‎‧₊˚✧ (๑>؂•̀๑) ^•ﻌ•^ฅε(´。•᎑•`)っ 💕(⚈₋₍⚈)ʕ·ᴥ·ʔ>^•-•^<( ͠° ͟ʖ ͡°) sussy?˚˖𓍢ִ໋🦢˚ദ്ദി ˉ͈̀꒳ˉ͈́ )✧˚₊‧ ꒰ა ☆ ໒꒱ ‧₊˚ִֶָ𓂃 ࣪˖ ִֶָ🐇་༘࿐ ⠀⠀⠀⠀⠀⢿⣿⣿⣦⠀⠀⢿⣿⡄⠀⠀⠀⠛⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⣿⣿⣷⣿⣿⣿⣗⣀⣀⣤⣤⣴⣖⣒⣒⣼⠿⠽⠿⠶⠖⠒⠛⠟⠛⠻⠋⡉⣀ ⣦⣤⢠⣄⠀⠸⣿⣿⣿⣯⣠⣟⣻⣶⣄⠀⠀⠀⣻⣿⣿⣿⣿⣦⡀⠀⠀⣀⠀⣀⣀⣤⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣉⣉⣩⣤⣤⣴⣶⣶⡶⠿⠷⣶⣿⣿⣾⣿⣿⡿⠿ ⣿⣿⣿⣽⣄⠠⢿⣿⣿⣞⣿⣿⣿⣿⣟⡀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢫⡉⠉⠁⠀⢷⠀⠀⡇⠀⠀⠀⢁⣿⣿⣿⣿⣿⣥⢼ ⣼⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⢿⣿⣿⣿⣿⣯⣿⡿⠇⢸⠸⣷⣬⢿⣼⣿⣦⣿⣿⣿⣿⣿⣿⣷⣶⣼⣦⣤⣷⣀⣀⣀⣘⣢⣴⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿ ⡚⠛⢿⣿⢿⢿⢿⡿⣿⣿⡿⡾⣿⣻⣟⣿⢻⡟⠿⣿⣿⣿⣿⣿⣿⢽⠉⢹⠉⠛⠝⢸⣿⣿⣿⣻⣯⣿⣿⣿⣛⣏⣹⣀⣀⣀⣏⣇⣀⣇⣆⣀⣤⣤⣤⣯⣽⣿⣿⣯⣿⣿⣿⣿⣿ ⣿⣿⡯⠹⠽⠿⠿⠿⠿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣾⣶⣼⣤⣤⣤⣤⣤⣀⣀⣴⣏⣿⣙⣒⣼⣃⣀⣈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⣿⠿⣿⠿⡿⠿⣿⣿⡿ ⣿⣿⣶⣀⣀⡀⢭⠉⠁⠀⠈⠉⠉⢻⠉⠉⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣶⣶⣦⣤⣴⣿⣿⣥ ⣿⣿⣿⡷⠒⠒⠛⠓⠸⠧⢀⣀⣀⣈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⠻⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠸⣿⣿⣿⡤⠤⠒⠒⣟⣋⣩⣽⡤⠤⣿⡤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠙⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠸⣿⣏⣿⣿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⢀⣀⣴⣾⣶⣴⣿⣭⣷⣾⣿⣿⣿⣿⣧⣤⡀⠀⠀⠋⠉⠉⠙⠛⠻⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⡿⠿⢛⠿⠛⠛⡹⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⠙⠛⠻⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢰⠃⠀⠀⠀⠂⠀⠀⠻⢿⣿⣾⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣴⣶⠶⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⠆⠀⠀⠀⠀⣀⣼⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠏⠀⠀⠀⠀⠀⣠⡾⠓⣡⡾⠋⠀⢾⣿⣿⣿⠟⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠀⠀⢀⣴⡿⠋⣠⣾⠋⠀⠀⠀⠀⠉⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣼⡠⠴⡿⠋⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣿⡱⠊⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡴⠟⢡⢯⣧⣞⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀🐅🐅🐅🐅🐅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡿⠙⢿⣄⠀⠀⠀⠀⠀⠀⣿⠖⠚⠉⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡇⠀⣀⡹⣷⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⠞⠛⠛⠛⠛⠛⠶⣦⣄⠀⠀⠀⠀ ⣿⡷⠋⠀⠀⢨⣿⣾⠟⠿⠾⠿⠷⠶⣶⣤⣀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀ ⢻⡇⠀⠀⢀⣴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀ ⢸⣇⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷ ⠘⣿⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡏ ⠀⢩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⣿⠀⠀⠀⣀⡤⠔⠒⠒⠉⠉⠉⠓⠒⠲⠤⣀⠀⢠⣶⠟⠃ ⠀⢸⡇⠀⠀⠀⠀⡔⠊⠲⡀⠀⠈⢧⣀⢰⣶⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⣧⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⡅⠀ ⠀⠸⣇⠀⠀⠀⠀⣷⣦⠔⠃⠀⠀⠀⠀⢸⣿⣿⡖⠒⠾⠿⠿⣿⡆⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀ ⠀⠀⢻⣆⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⡌⠉⠋⠁⠀⠀⢀⣶⣿⣄⣀⣀⣀⣙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇ ⠀⢀⣠⣿⠧⠒⠋⠙⠛⠓⠠⠤⣀⣀⠎⠀⠀⠀⠀⠀⠀⠘⡄⠉⠉⠉⠉⠉⠉⠛⠛⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇ ⢰⣿⡋⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠻⠿⠿⠿⢷⡆⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏ ⠀⠙⢻⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇ ⠀⠀⠈⠛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀ ⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀ ⠀⠀⠀⠀⠙⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⣤⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣰⡿⠟⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⢀⣼⣿⠄⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⣀⣠⠤⠄⣤⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡙⠻⠶⣶⡾⠥⠔⠒⠒⣲⡾⠛⠉⠉⢿⡍⠙⣷⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⢸⡇⠀⠀⠀⠀⣿⠃⠀⠀⠀⢸⡇⠀⢹⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠈⣷⠀⠀⠀⢸⡿⠀⠀⠀⠀⢸⡇⠀⠈⣿⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢀⣿⠀⠀⢀⣿⠃⠀⠀⠀⠀⠺⣷⣶⣶⣿⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⢿⣿⣤⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⠻⢶⣄⡀⠀⠀⠀⢀⣤⠶⠛⠛⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⣙⣿⣦⣤⣴⣿⣁⠀⠀⣸⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣡⣾⣿⣿⣿⣿⣿⣿⣿⣷⣌⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣄⡈⢻⣿⡟⢁⣠⣾⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠘⣿⠃⣿⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠛⣰⠿⣆⠛⠁⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣦⠀⠘⠛⠋⠀⣴⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⠾⢿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⠟⠋⣁⣠⣤⣤⡶⠶⠶⣤⣄⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣮⣉⣉⣉⣤⣴⣶⣿⣿⣋⡥⠄⠀⠀⠀⠀⠉⢻⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣁⣤⣀⣀⣤⣤⣤⣤⣄⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠉⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠐⣶⠄⢼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠧⠀⠀⠸⣿⣷⡦⣄⠀⠀⠀⢠⣿⡤⠀⡇⠘⡆⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠐⣦⣤⠀⠙⠹⣕⢼⣷⣄⣠⡿⠛⠉⠉⠒⣄⣿⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠚⢻⣿⡷⢦⠀⢿⣼⣏⣺⠟⡇⠀⠀⢀⣶⣶⣾⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⡀⠸⣗⠈⠷⠘⠏⢻⠇⠀⠀⣿⠆⣤⣾⣿⡿⠃⢸⣿⣷⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⢲⠎⠃⠀⠀⠀⠀⠀⠀⠺⠁⢰⢿⡿⠋⠃⠠⡽⣷⡈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⢀⣷⡟⠃⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⢶⣷⣲⡛⠉⠰⠦⢄⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣆⠀⠀⠀⠀⣿⣷⡦⢤⣀⣰⣦⡀⠀⠓⣤⡘⣕⢤⡀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡏⠀⠀⠀⣼⠿⠛⠛⠉⠀⣠⡙⠫⣤⣀⠀⢱⣌⢧⠙⢦⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠰⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣄⢿⣞⢇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢀⣷⣿⣦⣠⠤⠈⠡⠬⠤⠀⠀⢄⡀⠈⢳⡿⣯⢳⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣥⣄⣀⣠⣤⣿⣿⡿⠙⢃⡤⠶⠀⠀⠀⠀⠀⢠⣧⠀⠀⠁⣿⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠏⠀⠀⠀⣈⣤⠾⠗⠒⠒⠉⠉⠉⠑⠒⠠⢿⡀⠀⠀⢻⢢⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
𖧷⇝☾☁︎︎☽⇜𖧷
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛🟧🟧⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬛🟧🟧⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛🟧🟧⬛⬛⬛⬛⬛⬛⬛🟧🟧⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛🟧⬜🟧🟧⬛🟧🟧🟧🟧🟧🟧⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛🟧⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛🟧⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬜⬛⬛🟧🟧⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬛🟧🟧🟧⬜⬛⬛🟧🟧🟧🟧🟧⬛⬛⬛⬛🟧⬛🟧🟧🟧🟧🟧⬛⬜⬜⬜ ⬜⬛🟧🟧🟧⬛⬛⬛⬛🟧🟧🟧🟧⬛⬛⬜⬛🟧⬛🟧🟧🟧🟧🟧🟧⬛⬜⬜ ⬜⬛🟧🟧🟧⬛⬛⬜⬛🟧🟧🟧🟧🟧⬛⬛🟧⬛🟧🟧🟧🟧🟧🟧🟧🟧⬛⬜ ⬜⬛⬛⬜🟧🟧⬛⬛🟧🟧🟧🟧🟧🟧🟧🟧⬜⬛🟧⬛⬛⬛⬛⬛🟧🟧⬛⬜ ⬛⬛⬛⬛⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧⬜⬛🟧⬛⬛🟧🟧🟧🟧⬛⬛⬛⬛ ⬛⬜⬜⬜⬛⬛⬜⬜⬜⬜🟧🟧🟧🟧⬜⬛⬛⬛🟧🟧🟧🟧🟧🟧🟧🟧⬛⬛ ⬛⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬛⬛⬛⬛⬛🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬛ ⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬛ ⬛⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬛ ⬛⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬛ ⬛⬜⬜⬜⬜⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬛⬜ ⬜⬛⬜⬜🟧🟧🟧⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬛⬜ ⬜⬛⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬛⬜⬜ ⬜⬜⬛🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬛⬜⬜⬜ ⬜⬜⬜⬛⬛🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
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⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡿⣿⠏⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣇⠀⠀⠀⢀⡀⠵⠤⠤⠤⣀⣀⡀⠤⠐⠒⠒⣶⣶⡆⠀ ⠀⢻⣆⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢈⢽⠁⠀ ⠀⠀⠣⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⡴⡣⠃⠀⠀ ⠀⠀⡸⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣁⠔⠁⠀⠀⠀ ⠀⠀⠧⡛⠛⠒⠀⢹⠚⠛⡇⠒⠠⠿⢿⣸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢱⠒⢠⣀⠒⣊⡀⠤⠤⡔⠊⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡘⠐⠿⢿⠀⢿⡿⠁⠀⢣⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠇⠀⠀⣌⠀⣘⡄⠀⠀⠈⡇⠉⠉⠑⠢⡀⠀⠀ ⠀⠀⠀⡸⠀⠀⠀⠈⠑⠂⠈⠀⠀⠀⠘⡄⡀⠀⢀⣵⠀⠀ ⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠉⠁⠻⢄⣇⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⠟⠛⠛⠳⣯⡓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡿⠋⠀⠀⠀⠀⠀⠻⣮⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⢴⣿⣭⣭⣟⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⡀⠀⠀⠘⢷⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣻⠟⠁⠀⠀⠈⠻⢦⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡾⠁⠀⠀⠀⠀⢠⡿⠀⠠⠀⠈⢷⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣳⠏⠀⠀⠀⠀⠀⠀⠈⠹⣦⡓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣾⠁⠀⠀⠀⠀⢀⣿⠃⢀⠁⠠⡀⠈⣷⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣯⡟⠀⠀⠀⣤⠀⠀⠀⠀⠀⠈⠻⣮⡣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣼⠃⠀⠀⠀⠀⠀⣼⡟⢀⠠⠐⠀⢡⠀⠘⣷⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⠃⠀⣴⠀⠹⣷⡀⠀⠀⠀⠀⠀⠈⢷⣜⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⢰⣿⠀⠄⠂⠐⡈⠀⢃⠀⢹⣎⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⣿⠀⠀⠏⠀⡀⠻⣷⡀⠀⠀⠀⠀⠀⠈⢻⣌⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡿⠀⠀⠀⠀⠀⠀⣸⡟⠀⠰⠀⠂⠡⢀⠸⡀⠈⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣟⡏⠀⣠⠂⠐⠀⡀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠙⣧⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⣿⠇⡂⠁⠄⡁⠐⠠⠀⢡⠀⠸⣏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⣟⠀⠠⠁⠀⠄⡈⢿⣆⠐⠀⠀⠀⠀⠀⠈⢿⡜⢦⣀⣤⢴⣖⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠈⡐⠀⠌⠐⠠⠘⡆⠀⢿⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⡯⠀⢂⠠⠁⠠⠀⠌⢿⣆⠀⠀⠀⠀⠀⠀⣀⣿⣾⡿⠛⠋⠉⠉⢹⡄⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣠⣐⡀⠁⠌⠠⢁⠀⢣⠀⠸⣏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⢃⠐⠀⠄⠠⠁⡐⠈⡈⣿⡆⠀⠀⢀⣴⠿⠛⠉⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢟⠛⢻⡧⠐⠈⡐⠠⢀⠂⠆⠀⣿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠂⢈⠀⢂⠐⠀⢂⠐⢸⣧⠀⠀⠀⠀⠀⠐⠀⢸⡁⠀⠀⠀⠀⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣴⣤⡀⠂⢂⠀⡃⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⡇⠀⠀⠡⠀⠂⠄⠂⢡⣾⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠉⠉⣿⡇⠀⠡⠀⢸⠀⠈⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡿⣿⠀⠠⠁⠐⠠⠐⠠⡘⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢈⠐⠠⠈⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠀⠀⡃⢀⠂⠀⣿⡿⠛⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢀⠈⠄⠐⡀⠀⢼⡾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⡇⠀⡇⠀⡀⠂⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⢀⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⢿⡄⠢⠐⠠⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣧⠀⠰⠀⠠⠐⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⢿⣄⠂⠐⠀⠀⣼⢧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⣿⠀⠘⠄⠐⠀⠌⢠⡿⠀⠀⠀⠀⣀⣤⣦⣶⣤⣴⠏⠀⣀⣤⣴⣶⣶⣶⣦⣤⡀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠜⣿⡀⠈⠀⢠⣿⣿⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣇⠀⠻⡀⠈⠀⣿⠃⠀⠀⢠⣾⣿⣿⡿⢿⣿⠏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⢿⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣿⣀⣴⣿⣿⣿⣿⣿⣭⣟⢦⣀⣀⣀⠀⠀ ⠀⠀⠀⢻⣻⣆⠀⠱⣀⢩⣿⠀⠀⠀⠠⠟⠋⠁⠀⣰⠃⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠙⣿⣿⠁⠀⢹⣿⡿⠿⣯⡻⡆ ⠀⠀⠀⠈⢻⣻⣦⠀⠉⢸⡗⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠈⠛⠿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⣀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡶⠀⣿⣿⡀⠐⠈⢁⠠⠀⣼⣇⡇ ⠀⠀⠀⠀⠀⠙⢽⡷⣦⣽⡇⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣝⣿⡼⣿⣧⡐⠈⣠⣤⢾⣫⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⠇⠘⣧⠀⠀⠀⠀⠀⢀⣾⣧⣄⣀⢀⣀⣠⣾⠋⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣻⡇⠀⠘⢿⣿⣛⡿⠷⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⠳⣶⣤⡴⣾⢿⡹⢮⡝⣯⢻⣽⣿⣿⣄⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⣀⣠⣤⠿⢻⡞⣷⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣷⣿⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠹⣷⡹⣎⢷⡹⢧⣻⣼⠿⣿⣄⠉⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣽⣧⣤⣀⣀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣯⣞⣭⣻⣟⣷⡀⢀⠛⢿⡄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠻⣧⡈⠐⢈⣡⣾⠏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣯⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣓⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠛⠋⠁⠀⠀⠀⠀⠀⠀⠶⠛⠉⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣺⣿⣿⣻⢦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣧⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡿⠀⠘⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⢿⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠖⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢶⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠒⠒⠖⠶⠦⠤⠤⢤⡤⣤⠤⣤⢤⡤⣤⢤⡤⠤⠤⠤⠴⠶⠒⠒⠒⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣦⣄⡉⠻⢿⣿⣿⣿⡿⠛⣉⣤⣤⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⠦⠀⠙⠛⠋⠀⠾⣿⣿⠇⣸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠈⠻⢷⡄⠀⢠⡾⠟⠁⠀⠙⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣧⠀⣼⠀⠀⠀⠀⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⣤⠏⣀⠹⣤⣾⣿⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠙⣿⣧⣤⣴⣿⠋⠀⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠰⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣁⡀⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠛⠛⢉⣉⣉⠛⠻⣷⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡏⠀⠀⠑⠶⠶⠶⠛⠋⠉⠀⠀⠴⢚⣻⣿⣿⣿⣿⣶⡄⠻⣿⣿⣿⣿⣿ ⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠾⠛⠿⠿⠛⠛⠛⠛⠻⠀⢻⣿⣿⣿⣿ ⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢾⣧⡾⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⢷⣾⢿⣧⢞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⣾⣥⣭⡍⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣟⡼⠻⢿⠇⣹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⢟⡥⡿⠗⢷⡔⣶⣿⡇⢿⣿⠉⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠛⠀⠀⠀⣼⢧⣿⡟⣁⣾⣍⠀⠐⢒⣩⣭⣤⡌⠿⢛⣩⣭⣉⣛⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡏⣼⢫⣾⣿⠟⠛⢠⣶⠿⠋⢉⣿⠃⢀⣀⡽⠟⣿⣛⠳⢄⢁⡰⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⡀⢱⣿⣿⣧⡤⢠⣿⢡⣎⣠⠞⣡⣴⠿⠿⣰⡿⠋⢹⣇⣼⢠⠙⣾⣿⣷⣦⡀⠀⠀ ⠀⠀⠀⠀⠹⣿⡈⢿⣿⡟⢀⢾⣿⣌⣩⣤⡾⠋⠀⡔⢰⣿⠀⣶⠞⡿⠋⢸⣧⢹⣿⣿⣿⡷⠀⠀ ⠀⠀⠀⠀⠀⢈⣽⣬⢻⣿⢸⣮⠙⠛⠛⠋⠁⠀⣼⣧⠘⣿⣄⠀⢾⠁⠀⢸⣿⣆⢣⡙⠻⡷⣄⠀ ⠀⠀⢀⣤⣶⠿⠟⣡⣿⣫⠞⠉⠀⠀⠀⠀⠀⠀⢿⣿⣷⠊⠙⠳⣌⢣⡀⠘⢿⡿⣿⣿⣦⠁⣸⡄ ⠀⢀⣿⠃⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠈⣾⡗⠀⠈⠁⠈⠻⡇⢧⣿⡇ ⠀⣿⡿⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⢠⠑⣾⡏⠀ ⠀⠙⠁⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⢀⣾⡾⠟⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠀⠀⠀⠰⠞⠋⠀⠀⠀⠀
⢀⣴⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠇⠈⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣀⣀⠀⠀ ⠀⣯⣧⠀⠀⠀⠀⠀⠀⠤⠔⠒⠛⠉⠉⠛⠛⠒⠶⢤⣠⠴⠒⠋⠉⠉⠀⠀⠀⠈⢿⣿⣿⡿⠀⠀ ⠀⠸⣿⣧⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⠁⠀⠀ ⠀⠀⠹⣟⠧⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢠⣾⣱⠇⠀⠀⠀ ⠀⠀⠀⠙⢦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⡴⠋⣰⠋⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠋⣠⡞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⢣⣾⣿⣧⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⢀⣤⣤⡄⠸⣦⠶⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠿⠛⠛⠒⠉⠉⠁⣿⠟⠒⠚⣷⠈⠉⠒⠤⢸⣿⣿⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠲⢤⣀⣀⠀⠀⠹⣄⣀⣠⠎⠀⠀⠀⠀⠀⣀⣠⡴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⣹⣤⡆⠀⠀⣤⣀⣖⠒⠒⠈⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠰⢺⣿⣿⣿⠀⠀⣿⣿⡿⠋⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠁⠉⡟⠀⠀⢻⡛⠁⠀⠀⠀⠀⢳⣠⠶⠾⠧⠤⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⣴⡃⠀⠀⣀⣧⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⠁⠻⠓⢄⡇⠀⠳⡄⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣤⣄⡀⠀⢰⣿⢿⡄⠀⠀ ⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠉⠉⠉⠙⠿⣅⡀⢧⡀⠀ ⠀⠀⠀⠀⠀⠙⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠖⠒⠛⠉⠀⠀⠀⠀⠀⠀⠪⠽⠾⠷⠴
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣣⣴⠟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣤⣾⣿⢟⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⡁⣿⠋⡴⠿⢋⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡿⠷⣭⣶⣿⣷⢨⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣯⡞⣰⢟⠻⢿⡟⢀⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⢟⣠⢞⡥⠾⣷⡔⣦⣼⣿⡏⣹⣿⡏⠃⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠷⠭⠀⠉⠀⠀⣽⡇⣼⣿⡿⠁⣼⠟⠇⢀⣀⣠⠤⠞⠛⣛⡛⠛⣿⣿⠿⠿⠿⠿⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡿⢱⣿⠟⣡⣴⣾⣿⣇⠀⢀⣠⣶⣿⣿⣿⣿⠒⠋⠐⠶⣿⣿⣷⣶⣤⣈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⠁⣿⢣⣾⣿⡿⠛⠉⠙⣴⣿⠟⡋⠁⢀⣾⠟⠀⣀⣄⡴⠟⣋⣭⣭⣍⠛⠳⠀⢮⡹⣶⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⢻⣧⠀⠃⣿⣿⣿⣇⣠⠖⣼⡿⢡⡞⢁⣴⡿⢋⣤⣾⠿⠿⢀⣾⡿⠋⠉⣿⢀⣾⠀⡄⢻⣾⣿⣿⣷⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣧⠀⢿⣿⣿⣿⢁⠀⣿⣧⡘⠛⢋⣡⣴⡿⠋⠀⣰⢂⣾⡟⠀⣴⣴⢟⣼⡟⢠⣿⡄⢻⣿⣿⣿⣿⡷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⠧⠌⢿⣿⣿⠈⣦⠻⣿⣿⣿⣿⡿⠏⠀⠀⣰⣇⠸⣿⡇⠀⠛⢁⡾⠃⠀⢸⣿⣧⠘⣏⠻⣿⣿⣇⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣿⣷⢆⣿⣿⢂⣿⡇⠀⠈⠉⠁⠀⠀⠀⢰⣿⣿⣄⠻⢿⣦⡀⠸⣇⠀⠀⠘⣿⣿⣷⣌⣷⣌⠙⡿⢹⡄⠀ ⠀⠀⠀⣠⣤⣶⡿⠿⠛⣡⣾⢟⣵⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠓⠀⠉⠛⢦⡙⢧⡀⠀⠹⣿⠻⣿⣿⣿⢧⠀⢸⣿⠀ ⠀⠀⢠⣿⠏⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠀⠀⠀⢻⣾⡿⠀⠀⠈⠂⠀⠻⣿⡇⣧⣾⣿⠇ ⠀⣠⣿⣿⠀⠀⢾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠁⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠰⡌⣇⣼⣿⠟⠀ ⠀⠻⣿⡃⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⢰⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣶⡀⠀⠀⠀⠀⠀⠠⡿⠁⣿⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⢫⠑⠦⢤⣤⣤⠤⠶⠷⢦⣜⠀⠀⠀⣀⣠⣤⣾⠟⠀⠀ ⠀⠀⠈⢧⠀⠀⠈⢁⣐⣒⣒⢤⡈⠳⠔⣫⡽⠚⣻⠏⠀⠀⠀ ⠀⠀⠀⠘⣗⠤⣀⣠⠑⢴⣿⠇⣹⠀⠘⠃⢀⡴⠋⠀⣰⡇⠀ ⠀⠀⠀⠀⠘⡄⠀⢻⡀⢀⣠⣿⠅⠀⡠⠞⠉⠀⢀⣾⣿⣧⠀ ⠀⠀⠀⠀⠀⠘⡄⠀⠉⠓⠛⠀⠀⣾⠀⠀⣠⣴⣿⣿⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⣀⣸⠃⢀⠜⢟⣿⡿⢿⢿⣿⡇ ⠀⠀⠀⠀⠀⡰⠋⠀⠀⢰⠋⠀⠀⢠⠋⠀⠀⠓⠻⡱⢤⢫⡇ ⠀⠀⠀⠀⣰⠁⠀⠀⠀⢸⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠈⢰⡇ ⠀⠀⠀⠰⡅⠀⠀⠀⠀⠸⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡜⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢧⠀⠀⡀⠀⠀⠀⠀⠀⠀⡼⠁⠀ ⠀⠀⠀⠹⡀⠀⣄⠀⠀⠀⠈⣇⠀⡇⠀⠀⠀⠀⠀⡼⠁⠀⠀ ⠀⠀⠀⠀⢸⠢⣮⣀⡄⠀⠀⠘⡆⢱⠀⠀⠀⠀⢰⠃⠀⠀⠀ ⠀⡔⠂⠐⢺⡀⣿⣿⠇⠀⠀⠀⠈⢌⡆⠀⠀⠀⡿⠀⠀⠀⠀ ⠀⢣⠀⠀⠀⡇⣿⡿⠶⠶⠶⢤⣀⠀⠑⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠈⠣⡀⠀⡧⣿⠁⠀⠀⠀⠀⠀⠑⠢⡐⡄⠀⡇⠀⠀⠀⠀ ⣤⣴⣶⣾⣶⡇⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⢰⢀⠇⠀⠀⠀⠀ ⠈⠉⠁⠰⢭⣶⡿⠁⠉⠂⢄⡀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢴⣾⣿⡿⠿⠶⠾⠿⠿⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⣿⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣁⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡇⠀⠀⠀ ⠀⠀⠀⠹⣆⠈⠛⠷⢦⣤⣤⣴⣶⡾⠿⠿⠿⠿⢿⣷⣬⡀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⠟⠃⠀⠀⠀ ⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠐⠲⠶⠤⠤⠤⣤⣀⣀⠀⠙⠿⣦⢀⣴⠾⠛⣉⣥⡾⢿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⢶⣶⠶⠶⢶⣬⡙⢷⣄⠀⠈⠋⣡⣶⡿⠛⠁⢀⣼⠟⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⡷⣤⣀⠀⠀⢠⠙⢦⣴⣿⣿⣿⠆⢹⡇⠀⠀⠿⠃⠀⢀⣰⣿⠏⠀⠀⢀⣾⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⠀⠉⠙⢺⣏⠀⠀⠉⠙⣋⣡⣴⠿⠁⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⢠⣾⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⢿⣄⠀⠀⠀⠶⣿⣷⠖⠀⠀⣠⡾⠛⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠻⢷⣬⣿⣿⠍⠁⠀⢀⡾⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⠄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⣨⡽⠇⠀⢀⡴⡷⣧⡏⡿⣿⢿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⣠⡤⠶⠖⠚⠂⠀⣠⡟⠀⠈⢏⡿⢧⣧⣛⠸⢹⢻⢿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠉⠿⠹⢇⡻⣅⣬⣁⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠴⠈⣿⡇ ⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁ ⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀ ⠀⠀⠀⠀⠀⠉⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀ ⠀⠀⠀⠀⠀⢼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⢾⡥⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣄⠀⠀⠘⡧⣄⠀⠀⠀⠀⠀⠈⢷⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⢆⣀⡵⢩⠀⡀⠀⠀⠀⠀⠈⢷⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⣿⣼⣦⣷⠀⠀⠀⠀⠀⠈⢧⠀⢷⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀ ⠀⢠⠞⠛⠉⠛⠒⢾⡄⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢧⢸⡆⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠸⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣆⠀⠀⠀⠀⠀⣷⢸⣿⣿⡿⠟⠛⠛⠛⠷⠶⣤⣄⠀⠀⠈⢣⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣧⡀⠀⠀⠀⣿⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠱⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣤⡀⠀⣿⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⢱⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣤⣤⣤⣬⣿⣶⣿⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣧⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⣿⣿⠿⠟⢛⡻⠋⢠⣿⣿⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⢿⣶⣾⣿⣿⠟⠀⠀⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣈⣩⣭⣤⣤⣤⣤⣤⣤⣠⣼⣷⣶⣤⣤⣤⣤⣴⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠞⠛⣻⣧⣷⣾⣿⣿⣿⣿⣶⣶⣯⣤⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢠⠀⠀⠀⢔⣾⣷⠟⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢴⣿⣯⡻⣟⣵⣿⣿⣁⠨⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣽⡿⣹⣾⠷⡿⢿⣿⢿⣿⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⡠⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⠿⣽⣿⠁⢎⡀⢌⣠⠏⢻⡆⢸⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣻⢿⣿⣿⣿⣿⣷⡠⠀⠀⠀⠀⠀⠀ ⢸⣯⢿⣿⡿⡀⣘⠎⠙⢶⡀⠌⣿⠑⣿⣯⢿⡿⣿⣿⣯⣟⡿⣿⣿⡿⣿⣽⣟⡿⣭⣟⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⢸⢯⣿⣿⣷⡑⠑⠲⡄⡖⠛⠒⣼⣿⣿⣽⣯⣿⣿⣿⡷⣯⣿⣽⣳⢿⣽⣻⣾⣽⣿⣿⣿⣾⣿⣿⣿⣿⣧⠂⠀⠀⠀⠀ ⢸⣯⣿⣿⣿⠿⣧⣆⠻⣄⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀ ⠘⣷⣿⡙⠁⢀⣻⣿⣿⠛⠻⢿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⢽⣥⣷⠂⡀⢠⣿⣯⣑⣠⣾⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⠀⠀⠀ ⠀⠀⠙⣿⣿⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣻⠀⠀⠀ ⠀⠀⢰⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⣀⣀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀ ⠀⠀⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠈⠻⢿⣯⡻⢿⣿⣟⣿⣿⣿⠿⠿⠿⠟⢻⣿⣿⣿⣿⣿⢇⠀⠀ ⠀⢰⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣆⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣟⣿⣯⠆⠀ ⠀⠺⣧⣄⣠⣿⣿⡿⠛⠻⣿⡿⣿⣿⡇⢀⣠⣤⣤⣤⣅⣒⠀⠀⠀⠀⠀⠀⠀⣮⣶⡾⢿⢷⠖⣿⣿⣿⣿⣿⡹⣿⣧⠀ ⠀⠀⢸⣿⣿⣿⡿⠠⠤⣄⡈⠧⢿⣿⣯⠛⠛⠛⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡜⣿⡆ ⠀⢠⣿⣿⣿⣿⣿⣄⠀⠘⠮⠖⠈⢿⣿⣧⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⣽⣿⣸⠇ ⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣶⣽⣻⢿⣷⠦⠀⠀⠀⠀⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⡀⣠⠞⢉⣶⡤⢤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⣻⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣵⣶⣟⣳⢶⡄⠈⢻⣿⣿⣿⡿⣿⢿⠅⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣿⣿⣷⣾⠯⣿⣿⣿⣧⣀⠀⠀⠈⠙⠛⠿⢿⡿⣿⣏⣁⣀⣉⣙⣣⠀⣠⣿⣿⣿⣷⣿⣭⣶⣤⡆⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⣱⣻⣿⣿⣿⠋⠚⠻⠭⠷⣲⢤⣀⠀⠊⠛⢤⡈⣻⠋⠈⡽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⡿⠁⠀⠀⠀⢀⣠⣶⠞⠘⠯⡲⣄⣀⣽⣅⣀⡞⠀⢹⣿⣿⣿⣿⣿⡿⣿⡿⡅⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣾⣿⣿⡿⠁⠀⠀⠀⠀⠉⣼⣯⣽⣶⣴⣶⣿⣿⣿⣿⣻⣻⢷⣾⡟⢿⣿⣯⣷⡿⣿⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠿⢿⣿⣛⡶⣤⣀⣀⣀⣀⣀⣿⣿⣷⣿⣲⣌⡻⣛⣿⣿⣿⣿⡿⠟⡻⣿⣷⣿⣿⣧⣸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡄⢀⠙⢦⣀⠀⠀⠀⢀⢎⢀⠦⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢡⠨⣄⠈⠿⣕⣄⢀⡾⠊⠨⣸⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢞⠻⡗⢆⢷⢇⠛⢀⡀⢴⣶⡇⣸⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠢⠕⠈⠀⠈⠀⠞⢱⠿⠛⢠⢿⡙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢐⠆⠀⠀⠀⠀⠀⠀⠁⣄⣄⡼⢎⡀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⠀⠀⢰⣧⣤⠠⣆⡀⠫⡱⡢⡀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡤⡏⠈⠀⠐⠊⠙⠢⡸⣞⡌⠘⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⣴⡷⡤⢂⠁⠀⠀⢠⠈⠟⡞⢆⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⠞⠉⢙⣥⠮⠍⠒⠒⠠⠼⡀⠀⠇⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣦⡀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠈⠻⠾⢿⣍⠉⠉⠉⠉⠉⠉⠙⠛⠳⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣅⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠙⣇⢀⡤⠦⠤⠼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀ ⠀⠀⠀⣴⠋⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀ ⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢦⠀⣀⠀⠀⠀⠀⠀⢻⡇⠀⠀ ⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣰⢿⠀⠀⠀⠀⠀⠀⠀⢸⠳⣄⠉⠀⠀⠀⠀⠈⣧⠀⠀ ⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⡾⠀⢀⠀⢰⠁⢸⠀⡞⠀⠈⢶⣄⠀⠀⠀⠀⢹⡆⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣠⡶⢋⣠⣖⣴⣃⣰⠇⣠⣇⣠⣯⣾⠷⠶⣧⡀⢹⣦⠀⠀⠀⠈⣷⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠉⣠⠞⣫⣧⣬⡙⠁⠈⠉⠁⠀⠀⠘⣱⣿⣶⡌⢿⣼⣿⡇⡼⠀⠀⢹⡆ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢰⠇⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠈⢿⡿⠋⠀⠀⠀⢸⡇ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠘⠛⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⢹⡿⠃⠀⣼⡇⠀⠀⠀⠀⠀⣷ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢰⡏ ⢿⣆⠀⠀⡎⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⢀⣿⠁⠀⠀⠀⣼⣾⠃ ⠘⢿⣦⣸⣇⠀⠀⠀⢠⠀⠰⡟⠻⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠛⠁⠀⠀⠀⣼⠟⠁⠀ ⠀⠀⠀⠙⠿⣷⡀⠀⢸⣀⠀⣿⡀⠀⠀⠉⠉⠛⢛⣿⠶⠶⣶⡶⠶⠶⠚⠛⠉⢸⢀⡇⠀⣰⣣⠾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠳⠼⣿⣄⠹⡟⢶⣿⡶⠾⢿⣛⡋⠀⠀⠘⠻⢶⣤⣤⡤⠶⣿⣾⠷⠚⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⡿⠃⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⣉⠻⣶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⣾⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣴⠞⢉⣠⣴⢾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠉⠁⠀⠀⠁⠈⠉⠉⠀⠀⠈⠉⠓⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣿⠓⠲⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⢀⡞⠀⡴⠀⢠⠀⠠⡄⠀⠀⢰⠞⠛⠁⠈⠻⢤⣴⡄⢈⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢰⠇⠀⠀⡇⠀⣧⠀⠀⠸⡷⠄⠿⠿⠀⣼⣿⣅⣼⣷⢾⣷ ⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⣴⣿⠁⠀⣿⠀⠀⠀⡇⠀⢹⡄⠀⠈⠷⠤⢶⣄⣼⠏⣠⣍⠉⣿⡋⠁ ⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣠⡾⠁⣿⠀⠀⣿⠀⠀⢰⡇⠀⡾⢻⣄⠀⠀⠀⠀⠈⢷⣄⡙⠛⣀⣿⣇⠀ ⠀⠀⠀⠀⠀⠸⡇⠀⠀⣀⣴⠾⠋⠀⠀⢹⣆⠀⠹⣇⢀⡾⠀⣰⠃⠀⠹⣦⡀⠀⢸⡆⠀⠙⠳⠞⠛⠉⣿⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⡇⠀⠀⠀⠀⠀⠙⢷⣄⣹⣿⣥⠾⠃⠀⠀⠀⠈⠛⠶⣼⡇⠀⠀⠀⠀⠀⠐⡏⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⡇⠀⢀⣀⣀⣲⠀⠘⠛⠋⠉⠁⠀⠠⣤⣀⣀⡀⠀⠀⢸⡇⢸⠦⣤⡀⠀⠀⣇⠀ ⠀⠀⠀⠀⢀⡾⣰⠂⠀⢸⡇⠈⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠂⢸⠃⢸⡄⠀⢳⠀⠀⢻⠀ ⠀⠀⢀⣠⠞⣡⣿⠀⠀⢸⡅⠀⠀⠀⠀⠀⢀⣠⣄⠀⣀⣄⠀⠀⠀⠀⢸⣰⠆⠀⣿⠀⢸⡇⢀⡾⠀⠀⢸⠀ ⠒⠚⠋⠉⠉⠁⣿⠀⢀⣸⣇⠀⠀⠀⢀⣀⣿⠉⠹⣷⠃⢸⣄⡤⠤⡄⠈⠀⠀⣼⠇⠀⣼⡷⠟⠀⣠⣄⣾⠀ ⠀⠀⠀⠀⠀⠀⠹⣦⣈⢿⣽⣷⣤⣄⣿⡉⠻⣦⣀⣿⣆⣾⠏⢀⣴⣁⣀⢀⣴⣯⣤⣾⠋⢀⣀⣴⣿⠿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡿⣿⡋⠉⠛⢷⣿⠟⢛⠙⠻⣶⠛⠉⠀⣹⠟⠛⠛⠛⠛⠛⠉⠙⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣨⡽⠿⠿⠟⣿⠸⣿⣦⠄⢸⡶⠚⠛⢧⡀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣀⣀⣠⣤⢿⣧⣈⣛⣴⡿⠷⣤⡤⠜⠁⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠉⠉⡿⠉⣠⡾⠀⢹⡟⠙⣷⣄⣀⣹⠷⠶⠶⠶⠶⠶⠒⠚⢯⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠛⠛⢻⡁⣀⣾⣇⠀⣼⠛⠉⠉⠙⠳⣄⣠⣤⡶⠶⠦⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⣾⣿⣿⢻⡋⠛⠁⣀⣀⣤⠤⠀⠈⢡⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⣠⢴⡟⠋⠸⣿⣾⣷⢦⡈⠉⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⡁⣸⣇⠀⠈⣿⠛⢙⣶⣟⠛⢷⣄⣤⡴⠞⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⢋⡿⣦⣀⣽⣡⡿⠦⠉⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠐⠋⠉⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢳⡀⠀⠀⠀⠁⠒⠀⠀⠤⠄⣀⣀⣀⡀⠀⠠⣄ ⠀⠀⠀⢸⠁⢳⣴⠂⢀⣀⠀⣀⠀⠀⠀⠈⠑⠀⠀⠀⢀⡎ ⠀⠀⠀⢸⣤⡼⠁⢰⠁⠸⡇⢀⠇⠀⢔⠉⣷⠢⣠⣶⣿⠁ ⠀⠀⠀⣸⣿⠁⠀⠈⠁⠀⠉⠁⠐⣻⣫⠒⠯⡠⠛⣿⠃⠀ ⠀⠀⢰⣿⣿⣤⣤⡤⠤⣖⡂⠉⠉⠀⠈⢓⣄⠀⠈⡃⠀⠀ ⠀⠀⠀⢻⣧⣿⡋⣒⠂⠒⠁⡀⠀⢀⠈⠩⣀⣱⣼⠀⠀⠀ ⠀⠀⠀⠀⣯⣵⣙⢦⣀⠀⠀⠈⠉⠉⠀⠀⣐⣼⡿⠀⠀⠀ ⠀⠀⠀⠀⠻⣿⣋⣙⣛⣿⣶⣀⣲⣶⣾⣿⣿⡯⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⢿⡞⠛⣿⣿⢿⡟⢻⠛⠋⠁⠀⠀⠀⠀ ⢠⣀⠀⠀⠀⢠⣿⣿⣴⣪⣁⣸⠉⢣⣸⠀⠀⠀⠀⠀⠀⠀ ⠈⠒⠈⠩⠭⠿⢏⡙⠛⠛⠛⠛⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣇⡸⠀⠒⠒⠲⡀⡎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢿⡄⠀⠀⠀⠀⣠⡶⠛⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠈⢿⡀⠀⣠⡾⠋⠀⢀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠘⣧⡾⠋⠀⢀⣴⢿⡆⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡥⠀⢀⣀⣤⣤⣀⣴⠏⠀⠀⣰⠟⠁⢸⡇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢻⡷⠞⠋⠉⣼⢻⡟⠁⠀⢀⡾⠃⠀⠀⣼⣇⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣀⠈⠁⠀⠀⠀⣰⠟⠀⠀⣴⠟⠀⠀⠀⠀⠈⢉⣿⠃⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⡀⠀⠉⠻⣦⡀⠀⡾⠋⠀⢀⡾⠃⠀⠀⠀⢀⣀⣤⣞⣁⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣦⡀⠀⠈⠻⣆⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠉⢉⣽⠟⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠙⣧⡀⢸⡄⠀⠀⠀⠀⠐⠶⢾⣿⠀⢀⡟⠀⠀⢀⣠⣄⠀⠀⠀⠀ ⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢈⣷⣬⡷⠶⠖⠒⣻⣿⡟⠋⠁⢀⣾⡷⠖⠛⠋⠉⢹⠀⠀⠀⠀ ⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡁⠀⠀⢀⣤⠞⢋⡿⠀⠀⢴⣟⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣚⣸⣿⣿⣿⣿⠟⢉⣤⣤⣤⣌⠛⢶⡶⠋⠀⢀⡾⢧⣄⣀⣀⣉⣿⡶⠄⠀⠀⠀⣾⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⣿⣷⡈⣷⠀⢠⡾⠁⠀⠙⠿⣯⡉⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀ ⠀⠹⣿⣿⣿⠛⢉⠙⢿⣿⣿⢻⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⠃⣿⣴⠛⢿⡛⠛⠛⠛⠋⠁⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀ ⠀⠀⠙⢛⣰⣾⣿⣿⡄⢁⣶⣿⣿⣿⣿⣿⣌⡻⠿⣿⡿⠿⢃⣼⣿⠷⠖⠚⠋⠀⠀⠀⣀⣀⡀⠀⠀⢿⣅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⠷⠶⠶⠞⠛⠛⠋⠀⠀⠀⠀⣠⣶⠿⠛⠛⠛⠿⢶⣤⡙⢷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⣉⣉⣁⣀⣤⡤⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⣤⣶⣿⣿⣶⣦⣉⠻⣦⡙⢧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⡈⢿⡄⠹⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢿⡄⠘⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠹⣦⣸⣷⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣷⡟⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠸⡟⣿⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣤⣀⣠⡾⠋⠀⠀⣀⣤⡶⢿⣿⢿⣧⡈⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣀⣠⠶⠋⠁⣉⣁⣤⡴⠶⠛⠋⠁⠀⠈⢿⠀⠙⢿⣦⣈⠛⠿⠿⠿⠛⢁⣴⡿⢹⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⠛⠛⠛⠋⢻⣅⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠛⠿⢷⣶⣶⡾⠟⢻⠃⢸⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠓⠊⢉⠃⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⢄⠀⡀⠄⡪⠊⠀⠀⠀⠀⡘⣠⠀⠀⠀⠀ ⣿⣿⣷⣶⣎⠥⣔⣀⡠⠤⠄⠠⠃⠠⠑⠍⣠⣋⠀⠀⠀⠀⠀⢠⡏⠽⡀⠘⠀⠀ ⣿⣿⣿⣿⡿⠀⠟⣄⠤⠍⠒⠂⠉⠁⠈⠀⠀⠘⠑⢄⠀⠀⠐⢁⡇⡄⢡⠀⠀⠀ ⠛⠛⠋⠉⠀⠀⠀⠸⡑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⣼⠇⣆⣸⢤⣤⠜ ⢶⣶⣶⠖⠀⢀⣔⡈⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⠺⡖⡾⠁⠀ ⡋⠉⠀⠀⠠⡄⣋⠀⠠⠤⢀⠀⡶⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢼⢚⡻⠀⠠ ⢣⠀⠀⠀⠀⠁⡇⢀⡤⣧⣌⡄⢹⢿⠕⠀⡐⠈⣡⠇⠀⠀⠀⠀⠀⡿⡥⠃⠀⠀ ⢢⠡⡀⠀⠀⠀⡇⡿⢰⣿⣿⠀⠘⠀⠀⠀⠓⠚⣁⣠⣴⣶⠀⠀⠈⠚⠡⠄⣀⠀ ⠀⠣⡰⣉⠐⠀⢱⣇⠸⠫⢸⠄⠀⠀⠀⠘⠛⠋⠉⠉⠉⠀⠠⡰⠀⠀⣔⣀⠤⠊ ⠀⠀⠈⠂⡽⡥⠝⠟⠂⠑⠉⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⠵⢒⢖⣹⠈⠀ ⠀⠀⠀⠀⢑⡝⣢⠤⢀⠀⠀⠀⠀⠀⠤⠴⠀⠀⠀⠀⢀⡠⠾⠵⠓⠊⢋⣤⠃⠀⠀ ⠀⠀⡠⢊⠅⠂⠈⠁⠀⠈⠁⠒⠤⠤⠤⡄⠐⡶⠽⠃⠀⠀⠀⠀⠀⠛⠉⠁⠒⠠ ⠀⠀⠐⡙⢅⠐⣂⡀⠀⠀⠀⠀⠀⠻⡒⠊⡭⠉⠒⠈⠁⠒⠠⠄⠀⠀⠀⠀⢴⠒ ⠀⠀⠀⠈⢀⣑⠢⠄⠈⠀⠀⠠⠤⢀⣽⣶⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠⠃⠀
⠀⠀⠀⠀⠀⠀⢀⡴⠙⠦⢴⡒⠒⠒⠒⠠⠤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠳⡄⢀⡀⢨⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀ ⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⢀⠀⠀⠈⢷⠀⠀ ⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠈⣠⢞⠃⠀⠠⢀⢸⠱⣅⠀⠀⠘⡆⠀ ⠀⡇⠀⠀⠀⠀⠀⢀⣄⠤⣊⢴⣜⢴⡡⠣⢮⢶⠶⡌⣧⠀⠀⢹⠀ ⠀⡇⠀⠀⠀⠀⠀⢸⢀⠎⣾⣿⡆⠀⠀⠀⠀⣿⣿⠘⡧⠞⠀⠘⡆ ⢰⠀⠀⠀⠀⠀⠀⡌⠀⠀⠩⠿⠃⠀⠀⠀⠀⠙⠋⠀⡇⠀⠀⠀⡇ ⠘⣆⠀⠆⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣠⠇⠀⢀⣶⠃ ⠀⠙⠒⢶⡀⢰⡀⣇⠉⠓⠒⠤⡤⠤⡤⠤⠤⠔⠚⡅⢀⣢⠎⠁⠀ ⠀⠀⠀⠀⠈⠒⠓⢼⣵⠗⠛⠫⠥⠤⠭⠶⢶⡲⠗⠓⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⢰⠀⠀⠀⠀⠀⠈⠎⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠀⢸⠀⠀⠀⠄⠂⠀⡸⠈⣇⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣾⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠄⣀⠀⠀⠀⢀⠔⠁⠀⡽⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⣍⠀⠀⠀⠀⠀⣔⣶⠁⠢⠀⠀⠀⡠⠁⠀ ⠰⢶⣿⣏⠉⠉⠉⠀⠒⡠⠊⠀⢿⡿⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⢐⠁⠀⠀ ⠀⠀⠈⠙⠳⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⢈⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⣠⠆⡇⠀⠀⡉⢰⣦⣀⡀⠀⠀⠀⠘⡀⠀ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡔⠳⠃⠂⠁⠀⡰⡹⣁⣤⣧⡆⠑⢢⠀⠀⠃⠀ ⠀⠀⠀⠀⠀⠀⡆⠀⠀⡰⡁⣧⣿⠍⢻⢀⠔⠗⠑⠩⠂⠀⠡⠀⡗⡵⠄⢰⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⠐⠊⠃⣇⠙⢄⡰⠁⠀⠀⠀⠈⠤⠴⠇⠀⠇⠇⢀⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⡆⡿⡦⠀⠀⠀⠀⣀⠀⠀⠀⣜⢆⡴⢰⡔⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡐⢌⠢⠀⢀⡀⢀⣀⠄⠞⢡⡾⠥⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡣⠄⠀⠈⣄⡅⠂⠙⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⡠⠊⡜⠈⡄⢸⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣹⠀⠐⠀⠠⣸⠸⣘⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠯⢈⣀⣀⡀⢖⣃⣒⣷⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠉⠉⠛⠳⠀⠤⠓⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠼⠿⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠖⣫⣷⣿⡿⠂⠀⠀⠀⠀⡀⠈⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠘⠛⠋⠁⠀⣴⠶⢤⣤⡔⢻⣦⣶⣦⡉⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⠔⠋⠀⢀⣰⠀⠀⠀⢠⠤⢤⣼⣛⣿⣻⡿⠳⣷⣽⣿⣝⡿⢾⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⢾⢿⠀⠀⠀⢈⣧⣾⠛⣍⠁⠀⠀⠀⠀⣠⠈⠙⢿⢹⣿⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⢰⡏⣿⡇⢰⣿⡄⠀⠀⠀⠀⣿⣳⠀⢸⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠤⢀⡀⠀⠀⠀⠀⡾⠀⠀⠈⢧⠸⡇⠈⠛⠃⡀⠀⡀⣀⠈⠋⠀⢸⡄⢹⣿⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀ ⠀⠀⢀⠎⠁⠀⠀⠈⠑⠢⢄⣈⡇⠀⠀⣀⣜⣏⡇⠀⠀⡜⠉⠉⠀⠉⡇⠀⠀⠸⣧⣾⣏⡀⠤⠐⠚⠉⠁⠀⠀⠱⡀⠀ ⠀⢀⡎⠀⢠⠀⠀⠀⠀⠱⡄⠀⠙⢄⡀⠙⣿⢉⣇⠀⠀⣇⠀⠀⠀⢀⡇⠀⠀⡰⢛⡏⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⣇⠀ ⠀⡜⠀⠀⢸⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⠐⡏⠀⣹⠒⢦⡬⠵⢶⣾⣭⢤⡶⢿⠁⢸⡇⠀⠀⠀⠀⡠⡞⠀⠀⠀⠀⢸⠀ ⢰⠁⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠢⡀⠀⠀⡇⠀⢿⠑⠉⠻⢶⣄⡼⠥⠊⠀⣼⠀⡎⡇⠀⠀⠀⡔⠁⡇⠀⠀⠀⠀⠈⡆ ⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠁⢠⡀⢹⡘⢮⡇⠐⣠⣀⠏⠀⠀⠀⠀⣿⢰⢁⡇⠀⢀⠞⢀⡰⡇⠀⠀⠀⠀⠀⡇ ⠘⠀⠀⠀⠀⠀⠀⢸⣄⣈⣳⣄⡀⠀⠈⡇⢸⡃⠀⡇⠈⠛⡿⢼⡆⠀⠀⠀⣿⠈⢸⠁⣠⡦⠔⠉⠀⡇⠀⠀⠀⢀⣧⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠑⠢⢼⠀⡇⠀⠇⠀⠀⣷⠀⠀⠀⠀⠀⣟⠀⢾⠟⠉⠀⠀⠀⠀⠹⠤⢄⣀⡼⠃⠀ ⠀⠀⠠⣀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⢈⣷⣧⠀⡇⠀⡸⠈⣇⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⡎⢸⢻⠀⡀⢠⠃⠀⡸⡄⠀⠀⠀⢸⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⡜⢸⢀⠃⠈⠀⢀⠇⢱⡀⠀⠀⠀⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡇⠸⢸⠀⠀⠀⢸⠀⢸⣧⠀⠀⠀⢸⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡇⠀⣸⠀⠀⠀⡎⢀⣿⣿⣆⠀⠀⣸⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⣿⡇⠀⠀⠀⠁⣼⣿⣿⣿⡄⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠺⠟⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡄⠙⢿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⢳⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⢸⣇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⣠⠏⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡄⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣔⠚⠓⠒⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠊⠉⠁⠚⠋⢁⣖⣤⣔⢦⣮⣍⡢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠊⠥⢼⠆⠀⠀⣤⠾⡚⠛⠈⢙⠓⢏⣷⣁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡁⠀⢞⢻⢸⡗⠀⠀⠸⠇⢸⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⡠⠉⠈⠑⡢⠄⡁⠀⣼⣾⠀⠰⠁⠁⢡⠀⢸⣼⡃⠤⠐⠀⠉⠑⡀ ⠰⠁⢰⠀⡀⠈⢄⠈⠂⢼⢘⠤⣘⣤⣤⣂⣤⡎⡆⠀⠀⢀⡄⠀⠀⠃ ⠃⠀⠈⠀⠃⠀⠀⠠⢀⢸⢘⡏⠙⢲⠜⠊⣰⢢⠅⠀⡠⠁⡇⠀⠀⢸ ⠂⠀⠀⠀⠠⠐⠤⣀⠘⡈⠀⡇⠘⡧⠆⠀⢸⠊⡇⡴⠕⠁⡇⠀⠀⡼ ⠀⢄⠀⠀⠜⠀⠀⠀⠉⢣⡆⡅⢠⢣⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠈⠈⠀⠀⠀⠀⠠⣁⠁⡇⠆⢠⢂⠀⠀⡇⢃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠃⠀⠀⢸⡄⠀⢰⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣴⠀⠀⢃⣿⣷⡀⣼⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠃⠀⠀⣾⣿⠛⠳⠈⠋⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣼⣿⣿⡄⠀⣇⠀⢡⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⡜⣿⣿⣿⡇⠀⣿⡄⠘⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠞⠛⠉⣡⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡤⠶⠖⠛⣿⠋⣀⣴⣶⠿⠋⠱⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣽⠷⠶⣦⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠟⠛⠻⣧⡀⢀⣈⠉⠙⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢠⡟⠀⠀⢹⠀⠀⢷⠀⠀⠀⢸⣯⠀⠀⣠⢤⡀⠉⠙⣯⣽⠆⠠⡏⢀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟⠀⠀⣿⠀⠀⠀⢸⡇⠀⢸⡄⠀⠀⠈⣻⠿⠄⠻⠿⠃⢀⣴⣿⣷⣤⣴⣿⡛⣹⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⢰⡏⠀⠀⠀⢸⡇⠀⢸⣷⠀⠀⠀⠻⢦⣤⢶⣅⣀⣼⣯⢀⣀⡛⠋⢻⣟⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢸⣿⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⢰⡟⣧⠀⠀⠀⠀⠀⠀⠙⢻⣇⠀⠸⠯⠷⠀⢺⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⢸⣿⠀⠀⠸⣿⠀⠀⠀⣿⠁⠀⣼⠁⠘⣷⡀⠀⠀⠀⠀⡄⠀⠙⢷⣦⡀⣀⣶⡾⢿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣤⣾⠟⠋⠀⠀⠀⠀⢻⣧⡀⠀⢻⣷⣀⣼⠇⢀⣴⠏⠀⠀⠈⢿⣦⡀⠀⠀⣿⠀⠀⠀⠉⠛⠋⠁⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠹⢿⣦⣀⣹⣿⣋⣴⡿⠋⠀⠀⠀⠀⠀⠉⠻⢷⣄⣿⠀⡀⠀⠀⠀⠀⠀⠀⢻⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢠⣄⠀⠀⠾⠿⠿⠛⠛⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠀⣿⣀⣀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⢃⡄⠀⠀⢸⡇⠀⣤⣶⣶⣶⣶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣶⣤⣄⠀⢸⣿⠀⢿⠉⠙⢳⡄⠀⠀⢸⣇⠀ ⠀⠀⠀⠀⠀⠀⣼⠏⣼⡇⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢸⡏⠀⢸⡇⠀⠀⣿⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⣠⡾⢋⣴⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣿⢁⣶⠀⠀⣿⡇⠀⢸⡇⠀⣰⡇⠀⠀⠀⣿⠀ ⠠⣤⠶⠟⠛⠳⠛⢉⣿⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⣾⠟⠙⢿⣄⡟⠉⣿⠀⢀⣀⣀⠀⠙⠉⠁⠀⢸⣿⠀⠀⣼⣧⣼⠟⠀⢀⣀⢀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⢺⣿⢿⣦⡀⠀⠀⢰⡶⢦⣿⣆⠀⢸⣿⡅⠀⣿⡾⠋⠁⣹⠇⠀⠀⠀⣠⣿⠃⠀⣴⡿⠋⠀⠀⢠⣾⢏⣼⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣌⣻⣿⣽⣿⣶⣦⣼⣷⣄⠙⣿⣦⣼⣿⣷⣼⡟⠁⣀⣴⣯⣤⣤⣠⣴⣿⣷⣶⣿⣛⣁⣤⣤⣴⣿⠿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣽⠿⣿⡋⠉⠉⠻⢿⣿⣿⠏⠍⠉⠻⠿⡿⠟⠁⠀⠀⣨⡟⠉⠉⠉⠉⠉⠉⠛⠉⠉⠙⢶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠙⣻⣷⣶⣶⡾⣿⠁⣶⣿⣅⣀⠀⢻⣦⣶⠶⢾⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢱⡟⠋⠁⠀⠈⠁⢾⣦⠘⢛⣿⠏⢀⣿⣇⡀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣼⣿⣦⣤⣤⡶⠾⢟⡟⠷⣦⣴⣽⣿⡟⠛⠻⢷⣞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠈⠉⣽⠋⠀⣠⣾⠃⠀⢹⡿⠉⠻⣷⣤⣀⢀⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠻⠷⠾⢻⡇⠀⢀⣿⣇⠀⠀⣿⠾⠛⠉⠉⠛⢶⣄⠀⠀⣀⣠⣤⢤⣄⣀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⣷⣶⡟⣿⡿⣦⣼⠟⠀⠀⠀⠀⠀⠀⠙⠿⠟⣻⡟⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⢠⣾⣫⠿⣿⡇⣿⣇⠀⠀⢀⣤⠴⠶⠚⠛⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢀⣤⡶⣿⠉⠁⠘⢻⣷⣿⣿⡳⣦⡈⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢠⣿⠋⠀⣿⡀⠀⠀⢛⣿⠷⠙⢷⣼⡿⠛⢷⣆⠀⣀⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠡⡾⢻⣷⡀⠀⠾⣻⠀⣴⣟⠙⠷⠀⠈⠻⢿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠿⢛⣿⣷⣴⣧⣾⣏⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠘⠋⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀
╺⃝⃤₊˚⊹🦊🐾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠒⠒⠖⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢿⡟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠛⠀⣿⠀⣀⣀⣀⣀⡤⣄⣤⠤⠶⠶⠦⣤⣄⣸⣿⣿⣆⠠⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⢠⣾⣿⠾⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⠒⠓⢤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⡇⢀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⢳⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡼⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⢀⡦⣿⡏⠉⠉⠁⠈⡹⡖⢶⣦⠤⣀⠀⠀⡷⠊⠀⠀⠀⠀ ⠀⡠⠒⠘⠿⢋⠁⡄⠀⠀⢀⠠⠔⠚⡁⠀⣿⢸⣹⡁⠃⣸⣶⠀⢀⣶⡁⣇⡜⠈⡆⠸⠙⡶⠁⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⡆⠘⡤⠊⠁⠀⡇⠀⢻⣶⡿⢽⣿⣿⣿⠟⠻⣆⡼⢻⣿⣿⣿⢿⣷⡇⢰⣷⠀⠀⠀⠀⠀⠀ ⠐⢄⠀⠀⢀⡼⠁⠀⢻⠀⠀⠀⡄⠀⠀⢘⡇⠨⣽⡿⠿⠀⠀⠋⠀⠰⢿⡿⠟⢸⠿⠀⢸⠙⠧⠀⠀⠀⠀⠀ ⠀⠀⠉⠋⠁⠀⠀⠀⣾⣇⠀⠀⢰⠀⠀⡌⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡆⠀⡜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠏⢸⠀⠀⠈⡇⠀⢡⢧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠇⣰⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⢳⠀⠀⠸⣄⠘⣿⣶⣤⣄⣘⣉⣛⣦⡤⠔⢺⠏⠀⡼⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣦⠀⣠⣬⣦⣼⣿⣄⠈⠙⢢⣼⡍⢻⣦⣼⣇⣰⡽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠹⣿⣿⡿⣿⣿⣿⣿⣷⣄⡟⡏⠹⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣘⡍⢣⡀⠀⠀⠀⣼⡟⠛⠁⠈⢿⣿⣿⣯⣈⣷⣿⣼⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠧⠀⠀⠀⠃⠀⢙⣿⣷⣤⡟⠳⠶⠶⠶⠚⣿⣿⣿⣿⣿⡿⣻⣾⣿⣿⣿⠙⣯⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀ ⠸⣯⣥⠠⠄⠀⢀⣾⣿⣿⣿⠛⢦⡀⠀⠀⠀⣿⡛⣫⣿⣿⠿⠋⠀⢹⣏⢻⣄⡿⣶⠶⣿⣿⣿⣄⠀⠻⡁⠀ ⠀⠘⠓⠒⣲⣶⠻⠊⣿⣿⠃⠀⠈⢿⣦⣀⣸⣿⣿⢿⣿⡁⠀⠀⠀⢘⣿⣼⡇⠀⣿⡄⠹⢿⣿⣿⣇⢠⠛⣆ ⠀⠀⠀⠀⠛⠿⣤⣾⣿⠁⠀⠀⠀⠈⢻⣿⣿⠋⠀⢺⣿⡛⠛⠛⠛⢻⡟⢹⡇⢀⣿⣧⠈⢸⣿⣿⡏⠙⠛⠋ ⠀⠀⠀⠀⠀⠀⠈⠙⠾⣤⣄⠀⠀⣠⠟⢻⣯⠀⠀⠈⣿⡇⠀⠀⠀⠸⣗⠈⣷⡚⠃⢿⣦⡼⠟⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠞⠁⠀⣼⣇⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠀⠹⣧⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠷⣄⡰⢾⣿⣇⣀⡀⠀⠀⣿⡴⠆⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣤⢤⣬⣷⣾⡿⠤⣬⠽⠿⠿⡿⠧⣤⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⋆˚🐾˖°‧˚꒰🐾꒱༘⋆⨺⃝ ✮🌀๑˚ ༘ ೀ⋆。˚
⠀⢀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠟⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⢿⣿⣿⠿⠗⠀⠀⠉⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⡟⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⢿⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣿⡦⠶⠤⣤⣤⣄⣀⡀⠀⠀⠀⢀⣀⣤⠶⠶⠚⠛⠉⠉⠉⠹⣟⣿⣿⣿⣿⠇⠀⠀ ⠀⠸⣧⣿⡄⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠾⣍⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡽⡿⣿⡟⠀⠀⠀ ⠀⠀⢻⡞⣿⡀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⣿⠁⠀⠀⠀ ⠀⠀⠀⢻⡟⢿⡄⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⣴⠏⣸⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣆⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⣠⡾⠋⣽⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣠⡴⠋⢀⣾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠁⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⣰⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⢸⣆⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣁⠻⣿⣿⣿⣠⠤⠤⠖⠒⠒⣦⣭⣍⣉⣭⣕⠒⠶⠤⣀⡀⠀⢾⣿⣿⣿⠆⢸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠻⣯⣍⠉⠀⠀⠀⠀⠀⠀⠀⣟⠃⠀⠀⠈⣻⠁⠀⠀⠈⠉⠓⠚⠻⠿⠯⠤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣀⣀⠀⠀⠀⠘⢦⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠉⠉⣇⣴⡆⠀⠈⢀⣀⠀⡤⠤⠖⠒⠒⠛⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⣴⣾⣿⣿⣷⠀⠀⢸⣿⣿⣿⣖⠦⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠋⢠⢿⢿⣿⣿⠀⠀⠹⣿⣟⢿⠃⠀⠀⠀⠀⠸⡇⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢳⡋⠁⠀⠀⠀⠀⠀⠀⢿⣠⠞⠻⠿⠶⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠞⠓⣶⣤⡀⠐⡟⠙⢧⡀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠦⠇⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢠⣼⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣲⣤⣄⡀⠀⠈⢿⣧⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠛⠈⠙⠻⢿⣟⡃⠈⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⢉⠻⢦⣜⣷⣄⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⡤⣤⡀ ⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣶⣄⣀⣀⡀⣀⡀⠀⠀⠀⠀⣸⣤⣻⠻⣾⡇ ⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠳⣄⠀⠘⢿⢻⣿⣟⠇ ⠀⢠⣤⣤⣤⣾⣿⣿⣿⡟⠋⠀⠀⢉⡿⢿⠛⣿⡿⡑⡀⠘⣷⡀⢀⡏⠉⠀⠀ ⠀⠘⠿⢿⡿⠋⣱⡿⠋⠀⠀⠀⡌⠉⡧⠆⠿⠵⢼⡀⠱⡀⠈⠙⠛⢲⣶⠀⠀ ⠀⠀⠀⣿⡓⠊⠁⢀⠀⢀⡆⠀⡇⠀⡇⠀⢀⠀⠀⡇⠀⡇⠀⠈⠻⡏⠁⠀⠀ ⠀⠀⣰⠇⠉⢙⠏⠁⠀⢸⠁⢀⠷⡀⢣⠀⠸⠆⠀⡇⡸⢣⠀⢇⠀⣿⠀⠀⠀ ⡤⠞⢁⣠⠆⢸⠀⠀⢠⠏⠀⡜⠉⠑⠬⠆⠀⠀⠩⠗⠉⠀⢃⠘⡄⡿⠀⠀⠀ ⠙⠛⢹⠏⠀⢸⠀⣠⠋⣠⣾⣶⣶⣦⣄⠀⠀⠀⢨⣶⣶⣶⣬⣆⠹⣇⠀⠀⠀ ⢠⠖⠋⣀⣠⣼⣯⠤⠚⢏⠀⠣⣘⡫⠇⠀⠀⠀⠀⢎⣃⠇⠈⡟⣝⢾⠃⠀⠀ ⠈⠛⠛⢻⣿⣧⡘⡄⠰⢌⣢⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡱⠻⠾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣦⣀⢳⣎⣑⣦⡀⠀⠀⠁⠀⣀⣴⣿⣞⣳⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢉⡽⣿⠏⣾⠿⢷⣷⣿⣿⣿⣽⣿⡿⣽⣟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠋⢰⢿⠚⢿⡿⡿⠋⠘⢿⣟⣻⢽⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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