Maid GIRL Emojis & Text

Copy & Paste Maid GIRL Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⣠⣾⠽⠛⠛⢻⠇⣠⠾⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡒⠒⣷⡋⠉⠉⠙⣿⡶⢾⣏⠀⠀⠀⢀⣾⣿⡅⣸⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠳⡀⠘⣷⡀⠀⠀⢊⣷⡿⣯⢶⣤⣴⣿⢿⣟⣷⡏⢸⡇⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠱⣴⣺⣀⣀⢔⣥⡟⡁⠘⡝⢾⣭⣭⠭⢿⡿⣆⢸⣆⠐⣿⣤⠒⡁⢠⣢⣄⣴⡒⣒⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡑⣿⠿⣷⣣⢻⢱⡇⠀⡇⢸⠯⣕⣤⡟⢿⡍⢿⠹⢆⠈⠉⠁⠈⢩⣭⠀⠉⠈⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣻⠛⡧⡏⢸⢸⢣⠀⡄⠀⡆⠠⣷⢳⠀⢻⡄⠃⢾⡄⠀⠀⠀⠈⠛⠛⠚⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣎⠟⢸⠀⡇⢸⡀⡌⢧⠁⢠⣻⣄⣸⣆⠆⠀⢣⠸⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⡇⡿⡇⢸⠀⡄⣞⣧⠉⣼⠑⡟⠀⣙⣶⣿⣿⠀⡆⢰⡷⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣀⠀⢠⡉⠓⢄⡀⢻⡇⠃⠈⣶⣿⣅⣸⡷⠛⠋⠀⢽⣿⠿⡏⢸⢠⡇⣸⣧⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⣄⡈⢙⣼⣏⢠⠀⢻⣟⢿⡿⢷⠀⠀⠀⠈⠉⠁⢀⣆⣼⠟⢇⢧⢣⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡌⣳⡟⣿⡄⢲⣽⠍⠁⠀⠀⠀⠀⠀⠀⠀⠈⣸⣞⠆⡎⢾⣧⡣⣾⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⡿⢹⡝⡟⣗⣿⣧⣀⠀⠀⠀⠀⠀⠀⢀⢾⣟⠝⢀⡇⠈⣯⡳⢍⢾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣇⡜⢠⣵⠟⢡⠼⣼⣩⣵⣶⣤⣠⢖⣥⡿⠮⠒⣺⣵⣶⣿⣿⣦⠳⠋⠳⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣋⠜⢋⣴⠛⢉⣩⡬⠙⣿⣿⠧⣿⣿⣿⣝⣧⣶⠶⠿⣶⣼⣿⣿⣿⣿⡆⠸⢀⢪⢿⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⢋⡠⠻⢻⣞⡿⠛⠛⣷⣿⣿⡍⠵⠺⣿⣿⣹⢧⣶⢣⣬⣿⣿⣿⣿⡿⢹⣄⢏⣾⡿⠜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡔⢛⣹⡋⡕⣠⣿⣧⠀⠀⣿⣦⣾⣿⣿⣿⣿⣦⣤⡞⡹⡗⣿⣼⣿⣍⣽⣿⣿⣿⣿⠃⣾⠙⠘⣟⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⢪⣡⣖⠥⠦⣞⡴⢿⣿⣿⡷⠌⡇⠉⠙⢻⣿⣿⣿⣟⠛⣇⡇⣧⡅⡟⠉⢪⣿⣿⣿⣿⠏⡄⣧⠟⣃⣺⠁⠀⠀⠀⠀⠀⠀ ⠀⢀⠔⣁⣴⠿⠋⠁⠀⠀⢀⠜⣁⣨⣵⣾⣾⣿⠀⠀⠀⠙⢿⣿⠂⠀⣿⣅⣇⢹⣸⠀⠀⢻⣿⣟⠁⠀⢸⢧⢾⡉⠀⠀⠀⠀⠀⠀⠀⠀ ⡴⠃⣰⡿⠁⠀⠀⠀⠀⠀⠈⠺⠿⢗⠃⣽⣿⣿⡄⠀⠀⠀⢀⣇⠀⠀⢿⣿⣿⣽⣿⡆⠀⠈⣇⠙⠀⠀⡾⠺⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⣦⠀⢸⡿⣿⣿⣿⡇⢀⡤⠏⠀⠀⢰⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⠀⠀⢿⣦⣸⠘⠀⠛⠹⢷⡏⠀⠀⠀⠀⣸⣿⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣴⣇⣿⣿⣿⣇⠀⠀⠀⠐⣼⣿⣿⣶⣤⣤⣦⣼⠀⠀⠀⢀⡴⣿⣿⣧⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣦⣀⡀⣀⣤⣒⣶⣿⣿⣿⣿⣡⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠀⠀⠰⠋⠀⣿⣿⣿⣷⡄⢱⠀⠀⠀⠀⠀⠀⠀ ⠻⡟⢛⣷⣿⣉⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⡼⣿⣿⣿⣿⣆⡀⣦⡀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⡇⠸⡀⠀⠀⡀⢻⣿⣿⣿⣿⡏⠀⠀⠀⡾⠀⣿⣿⣿⣿⣿⣷⣿⢿⡀⠀⠀⠀⠀ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⢸⡏⠈⢧⠀⠁⠀⠀⠱⡸⣿⣿⣿⡟⠀⠀⠀⡘⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣄⡀⢀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡿⢻⣿⣿⣿⣿⡟⣿⡄⢸⠀⠀⠀⠀⠀⠀⢿⣽⣿⠁⠀⠀⠀⠁⠀⣰⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣝⠚⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠈⣿⡟⠏⣇⠈⠻⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⠇⠀⠀⠀⠀⠀⣼⣿⡟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⠀⠐⡟⢿⣤⣿⡗⠖⡿⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⢸⣿⣷⡿⢻⣯⣽⣿⣿⣿⣿⣿⣿⣿ ⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⡇⢸⠚⠛⠋⢩⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⠇⠀⠀⠀⢸⣿⣿⣿⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠢⣀⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⠈⣧⠀⠀⢸⣧⡀⢷⡀⠀⠀⢀⠆⣴⣦⣀⢸⢇⡗⢲⣷⠞⢻⣿⣿⠀⢹⣯⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠐⠿⣬⠿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠈⠳⢄⣹⣤⠿⡾⣕⣀⣀⠤⢲⠛⣿⡏⠉⠁⣇⣻⣿⣂⢸⣿⡟⢀⣿⣸⣿⣿⣿⣿⣿⡿⠁ ⠀⠀⣀⡀⢨⠧⠻⣿⣿⣿⣿⣿⣧⢸⡀⠀⠀⠀⠀⠉⡿⠷⢷⡤⠈⠀⠀⢸⣄⣼⡇⠀⠐⢿⡧⡇⠹⣿⣿⢃⡾⢨⣿⣿⣿⣿⣿⣿⠃⠀ ⣖⠀⢀⣹⡉⢦⡈⠈⣿⣿⣿⣿⣿⣧⣿⢤⣄⣤⣴⣆⢘⣦⣸⣧⣀⣀⡠⡞⠻⣿⣿⠑⠤⠾⠋⢏⢹⣿⣇⡾⢧⣾⣿⣿⣿⣿⣿⠏⠀⠀ ⠘⠒⢻⡞⢹⠃⣷⠾⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣿⡟⣿⣿⠟⠀⠀⠀⠀⠸⣤⣼⣿⣄⠀⠀⢄⣀⠑⢿⣫⣷⣿⣿⣿⣿⣿⣿⠟⠀⡠⠀ ⢤⢤⠤⠽⣶⣯⣉⣤⡉⠻⢿⢿⠿⢿⣿⡿⠟⠛⠿⠿⠿⣇⠀⢀⠀⠀⡀⣰⢻⣯⣉⣿⣷⣦⣤⣬⣥⣿⣛⠻⠿⠿⠿⢿⡉⠀⣰⣾⣷⣾ ⠐⠒⠘⠛⠛⠛⠛⠛⠳⠶⢄⣀⣀⣀⣴⠧⠬⠤⠶⠒⠚⢿⣀⢘⠀⣜⡴⠉⠀⠈⠀⠀⠈⠙⠉⠀⠀⠠⠬⠭⠀⠃⠒⠊⠛⠛⠙⠓⠒⠒ ⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠉⠛⠒⠋⠀⢈⠀⣀⠀⠀⠀⠀⡄⢀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⡏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠘⣯⣼⣿⠟⣿⣿⠟⠁⣸⠁⠒⠠⢀⡀⠀⠠⠈⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡧⠖⠒⠒⠁⠉⠁⠀⠀⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⣴⡇⠀⢰⠀⠀⠀⢀⠀⡜⠀⠀⠹⡏⢁⣴⠛⠁⠀⢠⠇⠀⠀⠀⠀⠀⠜⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⢹⣒⣒⠶⠶⢦⡤⠝⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⠞⢠⡁⠀⢷⠀⠀⢀⠎⠸⠀⠀⠀⢀⣴⠋⠁⠀⠀⢀⠏⠈⠉⠀⠀⢀⣀⠀⠤⠐⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠸⡇⠀⠈⠆⢀⠇⠀⠁⠀⣼⢠⡞⡁⠀⠀⠀⢀⠏⠀⠀⠀⠚⠛⠂⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠀⠀⢀⣀⣀⣀⣀⠠⠄⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⡄⠀⠈⠚⠂⠀⠀⣴⣿⡎⠀⠀⠀⠀⠀⡞⠀⠀⠐⠒⠐⠀⠀⠀⠀⠈⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⢀⠀⠀⠤⠄⠒⠂⠨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⡀⢳⢀⣀⣠⠤⠤⠤⠤⠬⡇⠒⠈⠉⠀⠀⠀⠀⠀⠀⢀⠀⠘⣆⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠤⠂⠈⠙⠁⡀⠄⢂⠐⡀⠆⠐⣻⠀⠀⢀⡀⠄⠐⠂⠉⢀⣀⣀⣠⣼⣦⣤⣂⠐⠐⡈⠐⢂⠁⠒⠠⢁⠂⠌⢉⠑⢦⠀⣠⠤⠴⠾⢲⠶⠶⠤⠤⢤⣀⣀⠒⠀⠤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⠤⣌⣌⣠⠁⡐⠈⠄⢂⠐⡈⠄⣹⡖⠀⣀⣠⣦⣶⣿⣿⣭⣽⣶⣷⣽⣶⣬⣭⡳⣥⠀⠡⠀⠌⠠⢁⠂⠌⡀⠂⠌⢀⣾⣥⣶⣶⣿⣿⢿⡿⣿⣿⣿⣿⣮⣽⣿⣶⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠌⠐⡀⢂⠐⠠⢈⣷⣿⣿⣿⣟⡿⣽⣻⣿⣟⡷⣯⣟⣿⣿⣟⣿⣿⠇⠠⢁⠈⡐⠠⠈⠄⠠⢁⠂⣼⣿⣯⣷⣻⣿⣽⢯⣟⣷⣿⣟⣾⣽⣻⣟⡿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣌⡐⢀⠂⡈⠐⡀⠻⣿⣿⣿⣾⣿⣿⣽⣯⣿⣟⣷⣿⣾⣿⣿⣿⡿⠀⡁⠂⡐⠠⠁⠌⠠⠁⠂⠄⡈⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣷⣿⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠃⠐⠤⠀⠙⠛⠿⠿⣿⣿⣿⣿⠿⠿⠟⠛⢋⠉⡀⠄⢂⠐⠠⠐⠠⠁⠌⠠⠁⠌⠠⠐⡀⠈⠉⠛⠛⠟⠻⠟⠟⠻⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠐⠒⠂⠂⠂⠑⠀⠃⠈⠀⠃⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⠂⠀⠀⠀⠘⣧⠀⠀⣟⠛⠲⢤⡀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢹⡀ ⠀⡿⠀⠀⠀⠀⠀⠈⢷⡀⢻⡀⠀⠀⠙⢦⣰⠏⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⢀⣻⠞⠛⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠛⠓⠒⠓⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⡟⠀ ⠀⠘⣇⠀⠘⣿⠋⢹⠛⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⢳⠉⠀⣠⡾⠁⠀ ⣦⣤⣽⣆⢀⡇⠀⢸⡇⣾⡇⠀⠀⠀⠀⣿⣿⡷⠀⢸⡇⠐⠛⠛⣿⠀ ⠹⣦⠀⠀⠸⡇⠀⠸⣿⡿⠁⢀⡀⠀⠀⠿⠿⠃⠀⢸⠇⠀⢀⡾⠁⠀ ⠀⠈⡿⢠⢶⣡⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣴⣧⠆⠀⢻⡄⠀⠀ ⠀⢸⠃⠀⠘⠉⠀⠀⠀⠠⣄⡴⠲⠶⠴⠃⠀⠀⠀⠉⡀⠀⠀⢻⡄⠀ ⠀⠘⠒⠒⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠛⠒⠛⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠸⣟⠓⠒⠂⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⡇⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠻⡝⠦⡀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠉⠉⢉⠟⠀⠀⠀⣇⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⠀⠘⢆⠈⠒⠤⢤⣤⣔⠊⠁⠀⠀⠀⠀⠀⠀⢠⠎⠀⢀⡜⠋⢻⠀⠀⠈⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⡇⠀⠈⣢⡀⠀⠀⠀⠀⠉⠉⢀⣤⡆⠒⢄⠀⠘⠚⢏⣾⣅⠀⠀⣇⠀⠀⠀⠹⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡔⢻⡀⢩⡇⠙⠢⢄⡀⠀⠀⢀⠎⣿⠁⠀⠀⢣⠀⠀⠀⠑⡾⢄⣠⠞⠂⢦⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣎⢴⡾⢳⡈⣃⣀⡤⡾⠀⠀⠀⡘⢰⡟⠀⠀⠀⠈⡆⠀⠀⠀⠘⣆⠀⠀⠀⠀⠱⡀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⢁⡎⠀⠀⢹⡟⠁⢰⠁⠀⠀⠀⡇⠠⡇⠀⠀⠀⠀⢰⡀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠱⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⡏⠀⢠⢃⠃⠀⡇⠀⠀⠀⢰⣇⠀⠇⠀⠀⠀⠀⡘⢧⠀⠀⢠⡇⠸⡀⠀⠀⠀⠀⢣⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⠁⠀⢼⠸⠀⠀⣧⠀⠈⡇⠘⡿⡄⠀⠀⢰⠀⠀⠇⡸⠀⢀⡞⡇⢰⣇⠀⠀⠀⠀⠀⣆⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠸⡀⠀⣸⡀⠀⠀⢿⠣⢄⣹⣆⣳⣷⡀⠀⢸⠀⣸⣤⢷⡴⠾⣴⡷⠃⢸⠀⠀⠀⠀⠀⣾⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢣⡀⢻⠳⡀⠀⠸⣄⡤⠿⠛⠺⠭⠙⢄⡈⣶⠛⢛⣩⣦⣤⣄⡀⡀⠀⡇⠀⠀⠀⠀⢸⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⠺⠦⢸⠦⠤⣿⣤⣤⣶⣶⣶⣆⠀⠟⠛⠂⠘⢿⣿⣿⣿⣿⣷⣾⣷⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⠀⠀⢸⣿⣿⣿⣿⣿⣿⢢⡤⣴⣄⠀⠀⣾⣿⣛⢿⡟⠁⠁⠀⠀⠀⠀⣸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡄⠀⢰⠈⢻⡇⠀⠸⠛⣁⣺⠀⠀⢿⣤⣀⣀⠤⠴⠞⠁⠀⡇⠀⠀⠀⢀⣿⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠇⠀⢸⢿⡄⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠁⢸⠀⠀⢸⠀⢣⡀⠀⠀⠀⠰⣿⠛⢻⠟⠀⠀⠀⠀⠀⡎⠀⠀⣀⢰⣿⠏⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⡄⢸⠀⠀⠀⣇⠀⠙⠢⣀⠀⠀⠈⠉⠁⠀⠀⠀⢀⡠⡾⠁⢀⣔⣥⠟⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣧⠘⣧⠀⠀⠘⡄⠀⠀⠀⠑⠢⣄⣀⣀⣀⠤⠒⢉⣴⣡⡔⠫⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠳⢼⣷⣄⡄⠈⢢⣤⣀⠀⠀⣼⠀⠀⠀⠀⠀⠉⢡⠟⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⣠⡼⠁⣆⠀⠀⠀⢀⠴⠃⠀⢸⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀ ⠀⠀⠀⢠⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⡠⠞⡱⠁⢀⡜⡆⣠⡊⠁⠀⠀⠀⡞⠀⠈⢣⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀ ⠀⠀⠠⠃⠀⠀⠀⡰⣻⠃⠀⡠⠔⠋⠀⡸⡇⠀⣾⠓⠛⠳⣵⠀⠀⠀⣠⠁⠀⠀⠀⠣⡀⠈⠉⢒⠖⠒⢦⠀⠀⠀⠀⠀ ⠀⡀⠁⠀⠀⢀⡜⠀⡟⢲⡁⠀⠀⠀⣠⠃⠘⡾⠻⠀⠀⢀⡼⡆⣠⢾⠃⠀⠀⠀⠀⠀⠈⠢⡔⠁⠀⠀⠀⠑⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠤⠦⠶⠦⠤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠋⠁⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⠲⠤⣈⠙⠳⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠔⠛⠁⠀⣠⠤⡤⠟⠉⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠳⣄⠀⠀⠈⠙⠓⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠒⠚⡵⠋⠁⠀⠀⢠⠞⠀⣸⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠈⢦⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⢦⣤⡀ ⢀⣠⠶⠖⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⡟⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠹⡄⠈⢧⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢀⡼⠃ ⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢰⢷⡇⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠹⡄⠘⣆⠀⠀⠀⠀⠀⢿⠀⢀⡠⠤⠒⠋⠁⠀⢠⡾⠁⠀ ⠀⠀⠻⣖⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⡜⢸⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢱⡄⠹⡄⠀⠀⠀⠀⠈⣧⠉⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠱⣄⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠰⣷⣾⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⠀⠀⠀⠀⢳⠀⢧⠀⠀⠀⠀⠀⢹⡄⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⡜⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⢀⡏⢹⠀⠀⠀⠀⠀⠀⠀⢸⣿⡙⣆⠀⠀⠀⠀⢧⢸⡆⠀⠀⠀⠀⠈⡇⠐⠚⢥⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡝⣸⠀⠀⠀⠀⣼⠁⢀⣰⣿⢸⡀⠘⣇⡄⠀⠀⠀⠀⠀⠺⡷⢷⠿⠷⣦⠤⢄⣀⣏⣇⠀⠀⠀⠀⠀⢹⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠁⣿⠀⠀⠀⢠⣿⡞⠉⡏⠘⣾⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⣇⠈⢷⣀⠈⠳⣄⡀⠘⢾⠀⠀⠀⠀⠀⢸⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⢸⡿⣇⢰⣷⣶⣿⣧⣤⣹⣿⠙⣆⢶⢦⡀⠀⣹⣶⢾⣿⣿⣿⣾⣿⣆⠀⠀⠀⠀⠀⠀⢺⠙⢷⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡇⢸⠇⠀⠀⠀⢰⣷⡿⣾⢹⣿⣿⡿⢿⣿⠿⡆⠈⠻⠆⠙⠶⠏⠀⢸⣿⢿⡛⢿⣿⡛⢿⠀⠀⠀⠀⠀⣸⠀⣸⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠃⢸⠀⠀⠀⠀⠘⣿⡇⠀⢸⣿⠿⣿⣿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠹⠿⠟⣸⠇⢸⠀⠀⠀⠀⠀⣾⡤⠋⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢼⠘⡇⠀⠀⢻⣄⠈⠉⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠦⣴⣾⠏⠄⡾⠀⠀⠀⠀⢸⡏⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠀⣷⠀⠀⢸⣷⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣾⠇⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣽⢠⣿⡆⠀⢹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠃⢠⠇⠀⣸⣿⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣸⠹⣧⠀⠀⡿⣿⣯⣿⣷⣦⣄⣀⣀⣀⣀⠀⠀⠀⠀⣀⢀⣀⣀⣠⣴⣶⣿⣿⡇⢠⢿⠀⢰⣿⢣⡄⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠙⣇⠀⢧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣴⣏⣿⡴⣳⢋⣾⣇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⢦⠸⡟⢿⣟⢿⡿⣿⡟⢿⣿⠿⣿⡟⢻⣷⠔⢿⣿⣯⠛⢿⣯⡿⠟⠋⠙⠋⠞⠗⠋⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠛⠈⠳⠀⢉⣿⣿⣿⣯⣿⣦⣾⣿⣿⣇⠀⠀⢀⠴⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⠻⣿⣿⢸⣿⣿⣿⣿⣽⣿⡀⢠⠃⢀⣿⡖⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠿⣿⡿⠿⣿⣭⣽⣿⣿⣿⡇⢸⡀⠈⢰⡇⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⡇⠀⠀⠉⢹⣿⣾⣿⡃⠀⠀⠀⡼⠁⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣠⣇⣀⣀⣀⣈⣿⣿⣿⠁⠀⢀⡼⢁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠤⠖⢋⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣼⠟⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠙⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠀⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⢉⠘⣮⠁⠀⡖⢸⠀⠀⠁⣸⠖⢲⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⢄⠈⠰⢅⣸⣷⠴⠤⠦⠀⢔⡙⠈⡠⠓⣼⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠆⠀⠀⢱⣑⠖⢹⠁⠘⡄⠀⠀⠀⠀⠈⠑⠧⡀⣸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡓⢤⡀⠀⠀⡔⠁⠀⡆⠀⠀⢱⠆⠀⠀⠀⢤⡄⣠⡬⣾⣖⢺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣸⠈⠁⡞⠀⠀⠂⡇⠀⠀⠈⢿⡀⠀⠀⠈⣞⣇⡼⣿⢻⣷⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⢰⡁⢀⠀⠀⡇⠀⠀⠀⠘⡇⠀⢣⠀⠉⣿⠁⢻⡀⢷⣥⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⡇⠈⠀⢸⢘⡄⠀⡘⡀⠿⠀⠀⢆⠀⠣⣃⣼⣷⠸⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡇⡇⡄⠀⢸⣾⣷⠀⠱⣡⠀⢂⠀⢻⣆⡰⣟⠀⡏⡄⣿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡇⢣⡇⡇⢸⣏⣿⢧⠀⢩⡧⡏⢯⣭⣿⣷⣼⣤⣿⡇⣟⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⣷⠈⣧⢿⢹⣤⣼⣶⣳⡤⠽⠙⠞⠻⣟⢛⡇⡿⣸⣇⣿⣿⣇⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠃⢸⣆⢿⡟⣿⡿⣟⢛⠏⠀⠀⠀⠀⠀⢸⣉⠏⠌⣙⢻⠿⣟⣿⣮⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠂⢄⠀⠀⠀⠀⠀⠀⠀⢸⡹⠀⢸⠯⣾⣷⣹⠳⡄⠉⠐⠀⠀⠀⠀⠀⢸⣵⣺⠴⡥⢼⢀⣿⠻⣧⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢄⠀⠀⠑⠄⠀⠀⠀⠀⢀⣣⡇⠀⣿⠤⢬⡛⣿⠻⣿⠦⣀⡀⠀⠘⠁⣠⡜⡞⢠⠠⣄⡎⠠⡏⣄⠸⣣⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⢄⢀⣬⣦⢀⡀⠴⠓⢹⡇⡆⡿⠀⠐⠪⢹⡱⣹⣇⠀⠱⡍⢛⣿⡁⣸⠁⢺⢸⡟⡗⠢⡇⣷⣷⣙⢱⢄⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣧⣼⡆⠀⠀⠀⡾⡇⡇⣧⣴⠠⠄⢀⣣⢱⣿⡀⠀⠈⢾⣿⡻⣍⣴⣾⣸⣇⢌⢯⣿⢽⣾⠻⣮⢉⠙⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠉⠁⡇⠀⠀⡜⡟⣿⡇⣾⡿⠀⠀⠀⠨⣾⢹⡟⢄⠀⠀⠹⣱⠙⠿⣿⠏⠟⣌⣧⡿⢿⣿⢿⠷⡿⣦⠉⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠀⠀⠇⠀⡸⢰⡇⠛⣇⢻⣿⠀⠀⠉⠉⣿⡷⣴⠈⠣⡀⢀⠟⠋⠀⣾⢰⠀⢇⠠⣥⠈⢿⡍⠁⠉⠙⡢⣸⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⢰⠀⢀⠃⢸⢸⡇⣿⣹⠋⣆⠀⠀⡠⡿⡷⠙⡄⠀⢱⣼⠀⠀⢰⡿⡞⠀⢈⣇⢼⠀⠈⢡⠀⠀⠀⠘⡵⠟⢧⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸⠀⢸⢸⡇⡇⣳⣤⣿⠤⠾⠿⢶⣷⡑⢞⠒⢫⠃⠀⠀⡎⢷⣧⠈⠙⡖⠚⣀⠀⠘⡤⡀⠀⠀⠘⢶⠈⢣⠀⠀ ⠀⠀⠀⠀⡆⠀⢰⠀⠀⠘⡄⠘⡸⢳⠹⢏⠁⡀⠘⠄⠈⢂⠀⡝⣾⡆⡼⠀⠀⠸⠁⠘⠙⠷⣼⢿⡴⡝⠓⡄⡇⠡⠀⠀⠀⠀⢧⠐⠀⠀ ⠀⠀⠀⢠⠁⠀⡄⠀⠀⠀⠘⠀⠱⡿⢶⢸⠳⣬⣵⣦⣒⣛⣟⠤⠽⠣⠇⠀⠠⠇⠤⠔⠒⠈⣽⣿⣆⡗⠀⠉⠙⠄⡀⠀⠀⠀⠈⢀⠇⠀ ⠀⠀⠀⢸⠀⠀⠇⠀⠀⠀⠀⠀⠀⠱⠀⠑⠂⣿⠉⠀⠀⠈⢎⣇⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠇⠀⠛⠀⠀⠀⠀⠀⠀⠉⠑⠉⠉⠀⠀⠀ ⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢆⠀⠀⠀⠈⡏⠉⠉⠉⠉⡟⢉⡟⣦⣹⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠐⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡇⠀⢢⠀⠀⠀⢱⠀⢀⢀⠀⠓⢺⡁⢷⠔⠊⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢃⠈⠈⢄⠀⠀⠀⠀⠀⢀⢴⡥⣸⡇⠀⠀⢣⠀⠀⠀⠇⠀⠀⠱⠀⡇⢳⢸⠀⡐⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠣⡀⠀⠑⢄⣀⡀⡴⠙⡅⠓⣿⠹⡀⠀⠀⠳⡀⠀⠘⡄⠀⠀⢰⠁⠸⡎⡇⠁⠀⡏⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⣲⣶⣪⣶⣿⠀⠀⠘⢆⡏⡄⠁⠀⠀⠀⠑⡀⠀⢡⠀⠀⠸⠀⢰⠀⡇⠀⠀⡇⠘⡙⣝⢭⡔⣢⡤⢀⠀⠀⠀⠀⠀⠀ ⠀⠤⠤⠤⠐⢋⣹⠑⠺⣿⣽⡇⠀⠀⠀⠈⡇⢳⠀⢂⠀⠀⠀⠘⣄⠀⡆⠀⠀⠀⡌⠀⠃⠀⠀⠀⠀⣧⣧⣽⣿⣏⠽⡟⠱⣤⣴⣶⣦⣤ ⣶⣶⣶⣿⣿⣿⣿⡶⢶⡃⠨⣿⠯⠽⢶⣂⣻⣄⣆⡨⣶⡾⠀⠀⠈⢧⣹⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⡳⢴⡚⠳⣋⢿⢯⠟⣻⣿⣟⣻ ⣿⣉⡉⣩⣿⠟⠉⠉⠸⣻⣦⣼⣕⣦⣰⡕⢺⣟⡿⣵⣾⣃⠀⠀⠀⠈⢇⡆⠀⡀⠀⠀⠀⠀⠀⠀⣠⣋⡀⢠⠉⠻⣖⠽⢠⢵⠤⠟⣿⣿ ⠈⢙⣿⡿⣿⠀⠀⣠⠾⢽⠕⠀⠁⠦⢦⡏⠉⡛⢾⢾⣿⡯⣶⣖⡄⠀⠀⢻⠀⠁⠀⠀⠀⠀⠀⢜⡯⣄⠀⡘⠀⠀⠈⢧⡀⠑⣤⣿⣿⡿ ⠾⠟⠛⠉⢹⠀⣰⣃⣰⠽⢲⠒⠒⢤⢄⡸⡀⣀⣹⢸⡻⣟⣭⡗⡁⣰⣶⡀⡆⠀⠀⠀⠀⠀⢀⣼⠀⠉⡰⣁⡔⠊⣉⣠⠴⣄⠈⢆⠀⠀ ⠀⠀⠀⠀⢘⠀⠈⡵⠓⠁⠒⠉⠶⠾⢮⠈⠟⣧⠀⠇⡟⢏⡻⠟⠃⠉⠉⠀⢱⠀⠀⠀⠀⣴⠾⡀⡧⢂⠝⢉⢷⣞⡉⠀⠀⠀⠑⠄⠣⠀ ⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⢢⢄⠋⢷⠂⠀⠀⠀⠀⠀⠣⡀⠀⠀⢧⠃⠀⠀⠈⡄⡻⠞⠋⢀⡾⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣴⡇⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠘⡖⠀⠒⠚⠣⣀⢸⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣪⠝⡲⠦⣴⣖⣢⡔⠒⢤⣄⡽⣦⠴⡤⣀⠀⠀⠈⠙⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠑⣶⡟⣹⢺⡇⣷⢵⡮⠣⠇⠮⠓⠘⠒⠁⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⣀⠤⠐⠁⠀ ⠀⠀⠀⠀⠀⠈⠢⠄⢀⣀⠀⠠⠔⠊⠀⠀⠀⠀⣻⠜⡄⠆⠸⡰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡴⠒⠒⠒⠒⠒⠶⠦⠄⢹⣄⠀⠀⠑⠄⣀⡠⠤⠴⠒⠒⠒⠀⠀ ⢇⠀⠀⠀⠀⠀⠀⠐⠋⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀ ⠈⢆⠀⠀⠀⠀⡤⠤⣄⠀⠀⠀⠀⡤⠤⢄⠀⠀⠀⠀⠀⣠⠃⠀ ⠀⡀⠑⢄⡀⡜⠀⡜⠉⡆⠀⠀⠀⡎⠙⡄⠳⡀⢀⣀⣜⠁⠀⠀ ⠀⠹⣍⠑⠀⡇⠀⢣⣰⠁⠀⠀⠀⠱⣠⠃⠀⡇⠁⣠⠞⠀⠀⠀ ⠀⠀⠀⡇⠔⣦⠀⠀⠀⠈⣉⣀⡀⠀⠀⠰⠶⠖⠘⢧⠀⠀⠀⠀ ⠀⠀⠰⠤⠐⠤⣀⡀⠀⠈⠑⣄⡁⠀⡀⣀⠴⠒⠀⠒⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢯⡉⠁⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣞⡄⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢰⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⢹⠰⡀⠀⠀⡃⠑⢾⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⡀⠀⡆⠇⠀⠛⣄⠀⣇⣰⡿⣧⣤⣤⣬⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠀⠸⠐⣧⣈⢸⣄⢈⣷⣿⣿⢃⣿⣫⣴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡄⠐⡁⠈⢆⠈⠉⠻⣿⡿⡛⠉⣀⣤⣤⣤⣭⣿⡓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⠐⡆⠈⢳⣶⣶⢯⠊⣠⣾⣿⣿⣿⣿⡍⠉⠳⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢆⠀⠑⠀⡀⠙⡿⠁⣾⣿⣿⣿⣿⠝⠒⠢⢄⠀⠀⠑⢤⡀⠀⠀⠀ ⠀⠀⠀⠐⣤⣈⣦⣀⣀⠀⢀⡧⢤⣿⣿⣿⣿⣀⠄⠀⠀⠀⣣⣷⣦⡀⠈⠢⡀⠀ ⠀⠀⠀⠀⢣⡈⠙⢣⡀⢨⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣶⣶⣿⡆ ⠀⠀⢀⣐⣶⣛⠯⠖⠳⢼⠀⠀⠀⠀⡜⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠹⣁⠀⠀⣈⣩⠥⠀⠳⣦⠀⠀⣳⡿⢿⣿⣿⣿⣮⡻⢿⣿⣿⣿⣿⡫⣺⠀ ⠀⠀⠀⢈⣻⢛⡳⠤⠤⡾⣟⣒⠛⠯⡽⣍⠐⢌⡉⠙⠛⠛⠳⠬⠟⠋⠐⢊⠍⠀ ⠀⠀⡠⢐⡗⢁⡾⠋⣉⣬⠖⠒⠲⡤⠌⣂⠥⢀⡈⢣⡈⠀⠀⠀⠐⠪⢽⣋⠒⢄ ⡠⠊⠀⠛⠲⣿⡃⠜⡯⣴⢺⡛⠲⣵⢄⡀⠨⠁⠒⠒⠈⠀⠀⠀⠀⣀⣀⣉⡹⠂ ⠀⠀⠀⠀⠀⠘⡿⠀⢀⢿⢸⡇⠀⠀⠑⠪⡍⠒⠂⠀⠀⠀⠀⣠⠤⠐⠒⢾⡿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⠔⢈⢥⠐⠀⠀⠐⢄⠈⠐⢍⠐⠢⠄⢀⠀⠀⠀ ⢀⠤⠀⠒⠊⠉⠈⠀⡰⠁⠇⠀⠀⡆⠀⢂⢡⠀⠀⢣⠀⠀⢀⠠⢉⠆ ⠀⠣⡄⡀⠀⠀⠀⡰⠁⣾⠀⠀⠀⢡⠀⠀⢂⠆⠀⠀⡆⠈⠁⡠⠃⠀ ⠀⠀⠐⢬⠀⠀⢠⠁⡀⠟⠀⠀⠀⢸⣥⡀⠈⣴⠀⠀⢰⠐⡌⠀⠀⠀ ⠀⠀⠀⡏⡇⠀⣼⢲⢹⡀⣿⡀⠀⠸⢹⣉⣫⡘⠆⠀⢀⣄⠇⠀⠀⠀ ⠀⠀⠐⡇⠃⠀⣿⠞⣿⣿⡿⠘⠊⠒⠉⣿⣻⡗⡆⠀⢀⢸⡇⠀⠀⠀ ⠀⠀⠀⢰⢀⠀⣿⠀⠫⠉⠇⠀⠀⠀⠀⠃⠵⠃⠃⠀⢸⠁⡇⠀⠀⠀ ⠀⠀⠀⢸⣼⡀⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣠⡼⢰⢀⡇⢰⠁⠀⠀⠀ ⠀⠀⠀⠀⠃⠣⢸⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡷⡽⣾⡾⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⣩⣿⣾⣶⣿⡆⠠⢒⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢛⠛⠿⣿⡿⠀⢹⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣾⣤⣤⣿⣇⠠⡣⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⡤⠴⠞⠛⠉⣻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠁⠀⠀⠀⠈⠉⠉⠉⠙⠿⢍⣁⠀⠀⠀⠀⢀⡞⠉⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠴⠶⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⢀⡟⠀⣠⣿⡀⠀⠀⠀⠀⠀⠀ ⢀⣴⠒⡖⠒⠒⠒⠒⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡖⠉⠀⣠⠇⠀⠀⠀⠀⠀⠀ ⢸⣧⠉⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⢀⡴⠚⠉⠉⠑⠲⢤⡀⠀⠙⢦⠀⠉⣻⡦⠀⠀⠀⠀⠀ ⠀⢿⡀⠀⠀⠀⠀⡹⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠈⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠈⢷⡈⠳⣦⠀⠀⠀⠀⠀ ⠀⠈⣧⠀⠀⠀⢸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡔⠀⢳⡶⠃⠀⠀⠀⠀⠀ ⠀⠀⢹⡄⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⢀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡴⣲⠾⠑⠂⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⡼⠁⠀⠀⠀⠀⠀⢠⠟⠁⠀⡿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠸⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣶⠃⠀⠀⠀⠀⠀⢀⡎⠼⠃⠀⣇⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣠⠄⠘⡇⠀⠀⠀⠈⠛⠒⠤⡀⠀⠈⢧⠀⠈⠙⢲⣶⡴⠀ ⠀⠀⠀⠀⠀⠘⠷⣿⠤⠀⠀⠀⣼⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢧⠀⠤⢾⠁⠀⠀⢿⠀⠀⠀⢀⣤⣤⣶⣿⠤⣤⠬⠷⠤⢸⡟⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⡟⠀⠀⠀⠀⡟⠀⠀⠀⠀⡀⠀⠸⣄⣠⣾⣀⠀⠀⣼⢀⡖⠒⠾⢷⡶⢮⡙⢧⡇⠀⠀⠀⣸⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⣇⠀⠀⠀⣸⠁⠀⠀⠀⢠⡗⢤⣾⠿⣫⣾⢷⣄⢠⠟⠋⠀⠀⠀⣿⡷⣤⣿⡿⡇⠀⠀⢠⡿⠀⠀⠀⠀ ⠀⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠀⢿⠀⠀⣴⢃⡴⢾⡀⠀⠘⣷⣿⠁⢰⣿⣷⣤⣾⠂⠀⠀⠀⠀⠀⢹⣿⣿⣧⡀⢧⠀⠀⠈⢷⣄⡀⠀⠀ ⠀⠀⠘⠧⣄⠀⠀⠀⠀⠀⠀⠀⠸⡆⠚⠛⠉⠀⠀⠹⢄⠀⢿⡇⠀⠸⣿⣶⣿⣿⣶⡆⠀⠀⠀⠀⠢⠟⠛⠛⠡⢼⡄⢹⠖⠒⠋⠉⠀⠀ ⠀⠀⠀⠀⠈⠙⠳⢶⣤⡤⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠙⠚⣧⡀⠀⢹⣿⣿⡿⠿⠓⠀⠀⠀⠀⣀⡤⠴⠿⣧⡀⢹⡛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠧⢤⣤⠄⠀⠈⢧⡀⢦⣀⡀⠀⢶⡒⠉⠁⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⣴⠎⠁⠀⠀⠀⣬⣽⠟⢲⡲⠤⢄⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣅⣀⠀⠀⠀⢳⣼⡈⠙⠓⠶⣽⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠗⠀⠀⢀⣼⠟⢁⣴⡲⣭⡓⠤⣈⢉⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠈⣿⠀⣠⣄⠀⣙⡲⣤⣀⡀⠀⠀⠀⠀⠀⢀⡶⠻⣷⠶⠚⠋⠀⠀⣏⠳⡳⣄⠙⢦⣀⠙⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠁⠹⠟⠙⣿⠿⣄⣉⣴⣟⠉⠉⠙⠛⢧⡀⠙⠲⣄⡀⠀⠀⠸⡆⠙⣌⢳⣠⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡁⠀⢠⡿⡀⠉⠳⢶⣤⣤⡀⠉⣵⣦⠀⠙⣆⠀⠀⠹⣄⡽⠂⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣿⣿⣦⡏⡇⠋⣦⠀⢄⠙⢿⣿⣿⠛⠚⠷⢄⠈⢧⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠘⢿⣿⣿⣷⡇⠀⠈⠆⠈⢣⡈⢻⠉⠣⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠈⢿⣿⣿⡇⢀⣤⢤⣰⣶⣷⡟⢆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠘⣿⣿⣷⣿⣧⣨⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠙⢧⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠏⠀⢀⣷⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡆⠀⠀⠀⠀⣻⣿⣿⣿⣿⡟⠀⣠⠞⡁⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡠⠒⠈⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠢⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⠑⢄⠀⠀⠀⢀⡠⠒⠈⠉⡹⠋⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠑⢄⡰⠁⠀⠀⠀⣰⣁⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠬⠭⠒⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢀⡀⠤⢤⣤⣤⣤⡤⠀⠀⠀⣤⣤⣤⠄⣀⠀⠜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠭⣉⠉⠉⠀⠀⡅⠀⠘⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⡸⠘⣪⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⢀⣬⠔⠀⠙⠿⠟⠁⠀.⠤⠘⠿⠃⠠⠵⠂⠀⢃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⣀⠀⠀⠠⣀⣀⡀⠀⠀⠀⠀⠀⢀⠤⠂⠒⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⠄⣀⣀⣁⠠⠤⠐⠊⠁⠀⠀⢀⠀⡧⣧⣤⡜⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡆⠀⣠⡴⠁⢠⡄⠄⠒⠒⠂⠤⠤⠴⠀⠀⠀⣘⣄⠀⢀⡀⠀⠐⠂⠊⠑⠒⠒⠊⠁ ⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢇⡜⠀⡇⢠⡏⠀⠀⠀⠀⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠙⡔⠢⡀ ⠀⠀⠀⠀⠀⢴⠀⢸⠀⠀⠀⠉⠀⠈⢲⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢔⠀⠀⠀⠀⢝⡕⠄⣀⠈⡄ ⠀⠀⠀⠀⢰⠈⢢⡘⡀⠀⠀⠀⠀⠀⢠⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠈⠀⠀⠈⠑⢄ ⠀⠀⠀⠀⠈⡄⠀⠈⠈⠀⠀⠀⠀⠀⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣ ⠀⠀⠀⠀⠀⠐⢄⡠⠀⠀⠀⠀⠀⢀⠇⠀⡇⣠⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼ ⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⣘⣀⠀⢣⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⢋⠪⠆⣀⠔⠊⠉⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠜⢄⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠢⢄ ⠀⠀⠀⠀⣀⠠⠚⠒⠊⠀⠀⠀⠀⠀⠀⢀⠠⢊⠏⠛⠿⠯⠥⠤⠔⠊⠁⠀⠆⠁⠒⠠⢤⠤⠔⣛⠉⠀⠉⠒⠒⠄⡀ ⠀⠀⠀⡐⢀⣀⠀⠀⠀⣄⠤⠐⠂⠉⠉⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠈⠉⠐⠢⢄⢀⡀⠠⣈ ⠀⠀⠘⠒⠱⠀⢀⠀⢠⠁⠑⠢⢀⠔⠊⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠢⠀⠀⠀⠈⢆⢀⡸. ⠀⠀⠀⠀⢣⢤⣀⡀⡌⠀⠀⡔⠁⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠑⢄⠀⠈⣹⡅⡪⣪ ⠀⠀⠀⢠⡢⢃⢟⠰⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠈⢢⠀ ⠉⠈⠘ ⠀⠀⠀⠈⠵⠅⠊⠁⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠀⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢇ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢀⢜⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
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⠀⠀⠈⢶⡀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⡿⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠛⠋⠉⠉⠉⠉⠙⠒⠦⣄⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠘⣿⠶⣄⡀⠀⠀⠀⣰⠏⠀⢸⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⢀⣀⡤⠤⣄⣀⣀⠀⣀⡈⠙⠶⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⠳⣄⡉⠓⠦⣄⣇⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠪⣝⡛⠛⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠉⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⢳⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⡀⠀⠀⠀⠀⠈⢧⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣦⣄⣀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠰⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⣝⢦⡀⠀⠀⠀⠈⣷⣄⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠟⠋⠉⠁⠀⠀⠀⠙⢷⣤⣄⡘⢧⠀⠀⠐⣆⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠸⡇⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⡀⠉⠛⠒⠀⠀⠀⢻⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣰⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠙⢮⣇⠀⠀⢹⣄⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢻⡀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣦⣄⡀⠀⠀⠀⠀⠹⣄⠈⠳⢦⠀⠀⠀⠀⠘⠁⠀⣀⣤⣶⣶⣶⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡸⠙⢦⡀⠀⠀⢷⡀⠀⠀⠀⠀⠀⢳⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⢭⣗⣲⠀⠀⠀⠘⢧⣀⠀⣀⣀⣀⠀⠀⣠⣾⣿⡿⠿⠛⠛⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣇⣠⠇⠀⠀⠙⠦⣀⠈⠳⡄⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⡀⠀⣀⡼⠷⣬⣙⣀⣀⣠⠴⠛⠉⠉⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣸⡏⠻⣿⡿⡄⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠈⠙⠒⠿⢦⡀⠀⠀⠀⠀⠈⠧⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⣽⠛⢁⣠⣀⡈⢻⡽⠋⠀⣀⡤⠀⠀⠀⢤⡷⣿⡏⢸⠀⠀⠀⠀⠀⡟⠁⠙⠢⣿⡷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢠⡍⠲⢤⣀⠀⠀⠀⠈⢑⣶⠆⠀⠀⠀⠀ ⢼⠁⢠⠟⠀⠀⢩⠏⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢻⡇⠸⡄⠀⠀⠀⠀⠳⣄⣠⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣷⣴⡿⠁⠀⢦⡈⢻⡍⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⣾⠀⢸⣄⡀⠀⣇⣰⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠿⣆⣙⣦⣄⣀⣀⡠⠞⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠛⠉⠙⠿⠯⠼⠀⠀⠀⠙⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⠀⠘⣄⠉⠛⢻⠃⠀⠀⢀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠦⠤⣀⡀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⣀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢳⣄⠈⠓⠒⡇⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠓⠢⠤⣇⣠⠎⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠲⠦⢤⣤⣤⡤⠞⠙⢧⠀⡄⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⡏⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⢳⣄⣰⠶⣄⠀⠀⡇⢠⢶⡾⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠾⣇⣀⣏⡿⠋⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⣸⡇⠀⢰⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢀⣀⡤⡴⠧⢤⣀⣀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠔⠚⠛⠚⢿⡇⠀⣼⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣧⠔⣲⠒⠛⠓⠛⠳⠤⣀⡀⠉⠓⠢⢤⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠊⣡⠤⠤⠤⢤⠀⢳⠀⡇⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠙⢷⡶⢤⣤⣤⡤⠶⠚⢉⣻⣽⡿⠯⠤⣤⣄⡀⠀⠀⠈⠙⠲⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀ ⣰⠷⠋⠀⠀⠀⠀⠀⢀⣈⣷⣇⠀⠀⠀⢀⡏⣠⠶⠚⠉⠓⠲⢤⡀⠀⢀⡼⢳⡀⠀⠀⠙⢷⣠⠟⢷⠀⠸⣍⣨⡟⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⢀⡤⠞⠉⠁⠈⠹⣆⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⡭⠷⠊⠁⢈⡇⠀⠀⠀⠀⠉⠳⠦⣇⣀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀ ⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⡀⠀⠈⠧⣀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠳⣿⠛⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀ ⠀⠀⠀⠀⣿⠀⣠⠴⠒⡶⠃⠀⠀⠀⠈⠙⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠈⠑⠲⢤⣀⡀⠀⠀⠀⢀⣸⣷⠒⠛⠀⠀⠀⠀⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⣿⡾⠁⢀⡾⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠚⢉⣥⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⡠⠀⠉⠁⠀⣼⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠤⠶⠖⠉⡽⠀⠀⠈⠙⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠇⠀⠀⠀⠀⢻⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⣀⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡆⠀⠀⠀⠀⠀⠙⢦⡀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣂⡤⠶⠟⠛⠛⠛⠉⢾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⣠⠞⠋⠚⠋⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣤⡀⠀⠀⢠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠈⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣏⡀⠈⣏⣭⣶⡖⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⣢⠴⠟⠈⠁⠀⣠⢄⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠙⠿⢾⡷⣄⣀⠉⠻⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⠴⠋⠁⠀⠀⠀⠀⠀⢠⢟⠟⠀⠀⠀⠀⠀⠀⠸⡀⢀⡶⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠹⣌⠻⣝⢦⡈⢻⣄⠀⠀⠀ ⠀⢀⣀⡤⠴⠒⠉⣀⣀⣀⣀⣀⡀⠀⠀⠀⣿⡟⣠⠆⠀⠀⠀⠀⠀⠀⣷⠏⡇⠀⠀⠀⠀⢿⠘⣄⠀⠀⠀⠀⠀⠘⢆⠙⣧⣙⢦⣹⣧⠀⠀ ⠺⢿⡓⠈⠉⠉⠉⠉⣿⠁⠀⠈⠉⠓⢦⣄⣿⣰⠃⠀⠀⠀⠀⠀⠀⠀⣼⠄⢷⠀⠀⠀⠀⠘⣇⠙⣆⡀⠀⠀⠀⠀⠈⠀⠹⣿⣧⠳⣟⣧⡀ ⠀⠀⠉⠲⣄⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⠀⢿⠏⠀⠀⠀⠀⠀⢠⡄⠀⣿⠀⠈⢧⡀⠀⠀⣀⣼⣶⢻⣿⠶⠄⠀⠀⠀⠀⠀⠹⣿⡀⠹⠿⠁ ⠀⠀⠀⠀⠈⠳⢄⡀⠘⢆⠀⠀⠀⢀⡞⠀⡿⠀⠀⠀⠀⠀⠀⣼⣷⡀⣿⡄⠀⠈⢷⡀⠀⠀⢸⣷⣤⣿⣇⡀⠸⡄⠀⠠⡄⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠓⠤⣤⡼⠃⣀⡇⠀⠀⠀⠀⠀⢀⣿⣿⢻⡏⠀⠀⠀⠈⣇⠀⠀⣼⣿⣻⣽⣿⣇⡶⢹⠀⠀⢻⡀⠛⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣄⠀⠀⠀⢿⡇⠀⠀⠀⠀⢠⢿⣿⢸⣸⠁⠀⠀⠀⠀⢹⠀⣰⠏⠹⣿⣿⠉⢹⡇⠈⡆⠀⠈⣧⠀⢸⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠉⠁⢻⡇⠀⠀⠀⣴⠏⢹⣿⣿⡿⣿⡻⣟⠒⠀⣯⣤⠃⠀⠐⠿⠟⠂⠈⡇⢰⣇⠀⠀⢹⣰⠀⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢸⢳⠀⠀⠀⢹⡆⠸⣿⣙⣖⡟⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⡀⢿⡀⢀⢸⣿⠀⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⢦⠀⢸⠀⠀⠀⠀⠀⢳⡀⣜⣆⠈⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠘⡇⢸⣿⠿⠀⠈⠧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡵⡈⢧⡘⠀⠀⠀⠀⠀⠀⢧⡈⢻⠦⠤⠄⠀⠀⠀⠠⣄⣀⣀⡤⠄⠀⢰⡾⢡⡿⡄⣿⣿⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠳⡄⢳⡄⢀⠀⠈⢣⡀⠀⢳⡈⢧⡀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢀⣴⢿⣇⡎⠀⣿⡟⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠹⣄⢹⡄⣷⡉⢢⡹⡄⢠⣽⡏⣯⠉⠓⠲⠶⢤⣤⣤⣤⣴⢿⠟⢸⡿⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠘⡄⠻⣼⠛⠀⠈⠙⠦⣽⠟⠾⡆⠀⠀⠀⠀⢸⠀⠀⠀⠏⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣀⣤⠏⠀⠀⠁⠀⠀⠀⠀⠸⢦⣠⣤⣾⡿⠛⠻⢟⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣟⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠹⣆⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠈⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⢹⣆⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢻⡆⠀⠀⠈⠙⠲⠶⢤⣀⠀⣠⠎⠀⠀⠀⠀⢹⡀⢀⢻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⡇⢸⣼⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣇⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⡤⠴⠒⠒⠒⠦⢤⣄⣠⠴⠚⠋⠉⠀⠈⠙⢻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣠⠤⠖⠶⠖⢺⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠄⠠⠞⠉⠋⠁⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠺⠥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣀⡴⠻⣧⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣤⠴⠛⠀⠀⡀⠀⠀⠁⠀⠠⡄⠀⠀⠀⠀⡀⠀⠀⠀⠻⢦⣾⣋⡙⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⢱⢀⡶⠀⠀⠸⡄⠀⠀⠀⠀⠘⢌⠫⡳⣌⢳⡀⠀⠀ ⣤⡴⠶⠬⠥⠤⡤⠒⠀⠤⣀⠀⣿⣱⠂⠀⠀⠀⠀⠘⡏⣇⠀⠀⠀⢻⠱⡀⠀⠀⠀⠈⠢⠹⣦⡷⣿⣆⠀ ⠈⠳⢄⠀⠀⠀⡇⠀⠀⠀⢈⠛⣿⠃⠀⠀⠀⠀⡀⠀⡇⠘⡄⠀⠀⢀⣧⢽⣦⢄⠀⠀⠀⠀⠹⣧⠘⣿⠂ ⠀⠀⠀⠙⠦⡀⠳⣀⠀⠀⡸⠀⡇⠀⠀⠀⠀⢸⣧⣰⡧⠀⠘⣆⠀⠉⣿⣤⣿⣆⠀⡄⠀⢠⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⣈⠓⠒⠁⢰⡇⠀⠀⠀⢀⣾⣿⣽⠀⠀⠀⠸⠀⢀⠿⣿⣿⢿⣿⢹⠀⠈⣇⠙⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠓⠒⠀⢸⡇⠀⠀⣠⠟⣿⣿⣿⡦⣤⠄⢸⣀⠎⠀⣿⡿⠀⢃⢠⡇⠀⢹⡄⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢸⠃⠀⠀⢹⡀⢿⣷⣾⢛⡿⠀⠀⠀⠀⠀⠀⠀⠀⢾⡈⢧⠀⣸⡇⠘⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣦⡐⣄⢸⠀⠀⠀⠀⢣⠸⣦⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣧⢸⣄⣿⠃⠀⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⡈⢦⠀⠀⠀⣄⠀⢣⠸⡍⠉⠀⠀⠀⠓⠒⠊⠁⣠⣾⣴⠛⣾⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⣎⢳⣱⡔⢮⣦⠀⣵⡹⡑⠒⠢⠤⢤⡤⣤⣾⠟⣸⠃⠀⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠈⠂⠻⠉⠀⠈⠑⡿⠉⠳⠀⠀⠀⢸⡀⠀⢉⣀⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠒⠚⠁⠀⠀⠀⠀⠀⠈⠑⠚⠛⢧⡀⠙⢮⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠉⠳⢤⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠀⠀⢳⡀⠀⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⢧⠀⠀⠉⠑⠒⠤⠄⠐⠁⠀⠀⠀⡇⢠⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⣄⡠⠤⠤⠤⠤⢄⣀⡠⠔⠚⠉⠉⠛⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣄⡀⠀⠀⡠⢄⣀⣀⣠⣤⣤⡦⠀⠀ ⠀⠀⢀⣤⣄⠀⠀⢸⣿⣿⠟⠉⠀⠀⢂⠈⡠⠈⠙⠿⣿⣿⡇⠀⠀ ⢀⣼⣿⣿⠋⠀⠀⢸⡟⠁⠠⠊⢀⠔⡡⠊⢀⠆⢇⠀⡘⣿⠀⠀⠀ ⣾⣿⡿⠁⠀⠀⢀⡟⠀⣤⠃⣠⢣⢴⢁⡔⡙⡜⠈⡧⠅⢸⠀⠀⠀ ⣿⣿⠁⠀⠀⠐⢸⣷⡤⣦⣏⣟⣯⣠⠊⣰⠋⠤⠀⢩⡀⣘⠀⠀⠀ ⣿⣿⣇⠀⠀⠀⣼⣿⣧⢋⡼⣸⠏⠼⡿⣽⠩⣽⢻⡞⣷⣼⠀⠀⠀ ⠘⢿⣿⣦⣄⢬⣾⢯⡿⡯⡓⠛⠚⠳⠧⠯⠾⠿⣜⣣⡟⡜⡇⠀⠀ ⠀⠀⠙⠻⣿⣼⠘⢜⡼⣷⣌⡀⢠⡤⢤⠄⠀⢀⣽⣵⢿⣧⡸⡄⠀ ⠀⠀⠀⢠⠊⠢⠵⣘⣑⣺⢿⣦⣌⡒⢘⣠⣴⡾⢝⣥⠎⣼⡵⢁⠀ ⠀⠀⠀⠀⠄⢀⠀⡀⢊⢰⠳⣷⢙⠿⠟⢋⢴⢷⠀⠃⠔⡁⠛⠑⡀ ⠀⠀⠀⠸⠈⠠⠂⡐⢄⡆⢚⣉⡶⠤⠤⢻⡇⠘⡀⠚⠪⠴⠅⢂⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠒⠒⠈⠉⠙⠒⠲⣌⠉⢁⣀⢼⠷⠃⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢶⠲⣿⠋⠉⠉⠽⠛⣹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠑⠞⠒⠒⠒⠀⠀⣼⣦⣀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢆⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠄⠀⠀⠁⠀⢠⠀⠈⠑⢄⠀⡀⢄⡄⠀⢠⣿⣿⡧⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣆⠀⠀⠀⢀⠃⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⡘⡄⠁⢀⠟⠉⠁⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡖⠢⢤⣏⢆⠀⠀⡆⢀⡆⢀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠸⡀⠀⠀⠀⠓⠸⡀⠘⣆⡀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⡄⠀⠈⠝⢷⣼⡇⢸⠁⠀⠀⠀⡘⣾⠀⠀⠀⠀⠗⠦⠥⠤⡤⠂⠀⠀⡇⠀⣿⣄⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡤⠆⢀⡴⢿⡇⢸⠀⢸⡴⠊⠉⠙⠣⣀⠀⡀⠀⠀⣨⣿⣿⡶⣤⡆⢳⡀⣿⠀⠉⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡇⠀⡠⢲⠃⢃⠈⣦⣘⡷⢶⣶⣦⣄⠈⠁⠀⠀⣾⣏⢽⣿⣧⣟⡇⠀⡿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⠈⣰⠋⢳⠘⣤⢼⡈⣇⢿⡾⡟⡿⠃⠀⣀⡀⠀⠙⠓⠛⠋⣸⣵⠄⢸⣰⠃⠀⠀⠀⠀⢀⡠⠤⠤⢄⠀⠀⠀ ⠀⠀⠘⡤⠃⠀⢸⣿⠻⡀⢣⡈⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠾⢏⡿⠀⢸⢿⠀⠀⢠⣤⡔⠁⣀⢄⡀⠀⠙⡄⠀ ⠀⠀⠀⠀⠀⢠⣿⢿⡄⠀⢲⣯⡟⠁⠀⠀⠀⠒⠊⠉⠀⠀⠀⣀⣴⠾⣤⣴⢃⣼⠀⠀⠀⣽⠁⠀⢠⡜⠁⠀⠀⢰⠀ ⠀⠀⠀⠀⠀⠠⢷⡆⢱⣀⠈⢻⣏⣑⣶⠤⠤⣤⠤⠤⠤⠶⣏⠉⠀⢀⠿⣇⣴⠃⠀⠀⠀⠘⡄⠀⠀⠡⠄⠀⠀⡜⠀ ⠀⠀⠀⣷⡀⢰⠋⢻⢸⠈⠉⠉⠁⠀⠀⠀⣾⡿⠒⠤⢄⣰⡟⣷⣀⢸⣠⠏⢹⠀⣀⣠⠀⠀⠈⠢⠤⠤⠤⠤⠊⠀⠀ ⠀⠀⠀⡟⢳⣿⠀⠌⣸⠁⣀⣀⣀⣠⠴⠊⠉⢑⣒⠤⣤⣤⣶⣿⠾⣯⠉⠓⠻⣏⢁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⣷⠀⣿⣧⣾⡟⠋⡜⠉⠁⠀⠀⠸⣍⠉⢉⠉⣿⣿⣅⠀⢠⠃⠀⢸⡀⠈⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡾⠁⠈⡟⠁⡜⠀⠀⢀⡀⠀⠀⠘⡆⠁⡰⠋⢣⢹⠳⣮⠀⠀⠈⣷⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠁⡀⣀⡿⠞⠀⠀⠀⠈⡇⠀⠀⠀⠳⠞⠀⠀⠈⠻⠖⠁⠀⠀⠀⠈⢷⡄⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠻⢻⣿⠀⠀⠀⠀⠀⢰⡧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠀⠠⡀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠗⠙⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠉⠉⠑⢄⡈⠻⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠀⠀⢀⣾⠀⠀⠀⠀⠀⠈⠒⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠈⠏⠒⠤ ⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⡰⠛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⡅⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⡇⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠙⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠚⠋⠉⠉⠉⠉⢙⡟⠁⠀⠀⠀⣿⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡀⠘⢦⠈⠑⢦⣄⠀⠀⠀⢀⣠⡤⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⣲⡦⢿⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠈⠣⡀⠀⠈⠉⠛⠻⠿⠶⠤⣀⣀⠀⠀⠀⣀⠀⠀⠀⢀⡛⣀⣀⣒⣺⠀⠀⠀⡇⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⠀⠀⠀⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⡇⠈⠙⢦⠀⠀⠉⠙⢦⣸⠷⡆⠀⠀⢸⡀⠀⠀⠀⠀⢳⡱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠛⡆⠀⢉⠗⠈⠛⠦⣀⡀⠀⠀⠀⠀⣴⢡⣳⠁⠀⠀⠀⢳⡀⠀⠀⠀⠙⢦⢧⣀⣀⡴⠷⠄⣤⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠟⣠⣴⣿⡄⠺⢶⠀⠀⢀⣼⡇⠀⠀⠀⢰⠁⢸⣿⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠈⢧⠈⠉⠀⠀⠀⠈⢳⡀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣧⠞⣱⠏⠀⠱⣄⣼⡴⠚⢋⡏⠀⠀⠀⠀⡸⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⣰⢁⠀⠀⠀⡼⡹⠁⠀⡾⠀⠀⠀⠀⠀⡇⠀⢸⠁⠀⠀⠀⠀⠀⢸⢷⠀⠀⠀⠀⢀⠈⢧⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣷⠏⠀⠀⣸⢡⠇⠀⢰⡇⠀⠀⠀⠀⠀⣷⠀⠈⡆⠀⠀⠀⠀⠀⢸⠈⡇⠀⠀⠀⣸⡆⠘⡇⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢾⣿⠀⠀⠀⡇⣼⠀⠀⠸⡇⠀⠀⢶⠀⠀⡿⡄⠀⠀⠀⠀⡆⠀⠀⢸⠀⡇⠀⠀⢀⢟⡇⠀⣿⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣽⠀⠀⠈⡇⠁⠀⠀⢸⣿⡀⠀⠸⣇⠀⣧⢻⡀⠀⠀⠀⡇⠀⢀⡇⢠⡇⠀⣠⠟⢸⠃⡼⠙⡆⠀⠀⠀⠀⠀⠀⣹⡄⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡀⠀⢸⣷⠀⠀⠀⠀⣧⠙⠲⣄⣹⡧⣜⣦⣳⡀⠀⠀⡇⠀⣼⢶⡟⣻⠟⠛⢳⣾⠞⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⡀⠈⡏⢧⡀⠀⠀⢻⡀⣠⠴⠿⠿⠶⠿⠍⠙⢦⡀⢹⣴⠓⠛⠋⣵⣶⣶⣖⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢸⢳⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⢤⣹⡀⠙⣦⣀⠈⢿⣁⣀⣀⣤⣤⣤⣤⡄⠀⢹⡷⠿⠦⠨⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣧⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⣱⠋⠈⠉⢻⣽⣿⣿⣿⣿⣿⣿⣗⡀⠀⠀⢀⡀⠀⠀⠋⣳⣦⣾⡟⣿⣽⡿⠛⠟⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢨⣿⣿⡚⣿⢳⣿⡿⣽⢹⡖⠒⢾⡶⡄⠀⠘⠽⠯⠭⠴⢻⡏⠀⢀⡀⠀⠀⠀⠀⠀⣼⣹⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⣼⠀⠀⡴⠀⠸⣯⠁⠀⠐⠖⠊⢉⡹⡇⠀⠀⢿⣥⣄⣀⣀⣤⠤⠶⠟⠁⠀⢸⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣼⡇⠀⢰⡇⠀⢸⡿⣧⣀⡰⠶⠽⠟⠛⠁⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⡼⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡿⡏⡇⠀⡜⠀⠀⠀⡇⠸⡄⠀⠀⠀⠀⠀⠀⣠⣖⣤⣤⡤⡆⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣠⣏⣿⠃⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⡇⠀⠀⠀⣇⠀⠙⣆⠀⠀⠀⠀⠀⠛⣏⣀⣠⠞⠁⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⣰⢂⣟⡼⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⠀⡆⠀⣇⠀⠀⠀⢸⡄⠀⠈⠓⢦⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⡤⣿⠃⠀⢠⣞⣥⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣧⢧⠀⢿⣆⠀⠀⠀⢳⡀⠀⠀⠀⠈⠑⢦⣄⠀⠀⠀⠀⠀⣀⡴⠚⠁⣰⢃⣀⡾⣋⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢹⢦⡈⣿⣆⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠈⣻⠒⠒⠚⠉⠁⠀⠠⠾⠟⣻⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠙⠚⠯⣷⣴⣀⣀⣸⠿⠯⠤⠂⠀⣰⢿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠇⠈⣇⠀⠀⠀⠀⢀⡠⠚⠀⠀⠀⡇⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢩⡏⠀⠀⡘⢇⠀⣠⠖⠋⠀⠀⠀⠀⢸⠇⠀⠈⢣⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣠⢶⠏⠉⠉⠉⢉⡽⠛⠁⣠⡏⠀⢀⣼⣧⣼⣼⡉⣆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠳⡉⠙⠒⠶⠤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀ ⠀⠀⠀⡜⠁⠀⠀⠀⢀⡴⢣⡞⢀⣀⠴⠚⠁⠀⠀⢠⡏⢳⡀⡼⡟⠀⠀⠀⠈⢿⡄⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠙⢦⠀⠀⢀⡴⠋⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠂ ⠀⢀⠞⠀⠀⠀⠀⢀⡜⠁⢸⠏⢫⡀⠀⠀⠀⠀⢀⡜⠀⠀⣳⠃⡇⠀⠀⠀⣠⠟⡇⣀⡴⣫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠓⢶⣋⡀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢱⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⡌⠓⠦⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⠓⠲⠤⠤⣀⣀⣀⣀⣀⡀⠀⠈⠻⡕⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⠀⠉⠺⢽⡋⠑⠒⠤⣄⣀⣀⣐⡤⠤⠌⠓⠄⠀⠀⠀⠈⠉⠁⠈⠉⠁⠀⠀⠀⠀⠉⠓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠉⠳⣄⡀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣤⣤⣤⠤⠔⠦⠤⠒⠚⢉⡵⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⣶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢠⠞⠁⠀⢀⡜⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠳⡄⠀⠀⠀⠉⠳⢤⡐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⡰⠋⠀⠀⢠⠟⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⢧⠀⠀⠘⣆⠀⠀⢢⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⡼⠁⠀⠀⢠⠏⠀⠀⢀⡞⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⣇⠀⠀⠘⣆⠀⠀⢧⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠃⣠⠄⠀⣼⠁⠀⠀⢰⠏⠀⠀⠀⡼⠁⢀⡇⢠⢿⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⡀⠀⠀⠸⡄⠀⠘⣆⠀⠀⠀⠘⣆⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⠇⢠⠇⢠⠏⠀⠀⠀⢸⠁⠀⢸⠇⢸⢸⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠈⡇⠀⢻⠀⡇⠀⡀⠀⢣⠀⠀⢹⡄⠀⠀⠀⠹⡄⠀⠀⢰⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⡼⠀⠈⠀⠀⠀⠀⡏⠀⢠⢿⡀⣾⠘⠀⣇⠀⠀⡇⠀⠀⡆⠀⠀⠀⡇⠀⢸⠀⠁⠀⡇⠀⠀⠀⠀⠀⢳⠀⢆⠀⠀⡇⠀⢠⠟⢶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⣰⠃⠀⠀⠀⣴⠀⠀⠀⢠⠏⢸⣤⣿⠀⠀⢹⡄⠀⠸⠀⠀⢰⠀⠀⠀⠀⠀⣿⡇⠀⢀⠇⢀⠀⠀⠀⠀⠘⡆⠸⡄⣀⠁⠴⠃⡀⠈⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⢀⡏⠀⠀⠀⠀⣿⠀⠐⢒⡟⠉⢹⣽⠙⡗⠶⣿⣷⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⣿⡇⠀⢸⠀⢸⠀⠀⠀⠀⠀⠃⠀⣧⠘⡆⠀⠀⠈⠳⣜⠆⠀⠀⠀ ⠀⠀⠀⠐⠊⣁⣀⣤⠞⠀⣸⠀⠀⠀⠀⠀⢻⠀⠀⣸⠀⠀⢸⡟⠀⢷⠀⢸⡏⢧⡀⠀⠀⠸⡄⠀⠀⣀⣾⣿⣷⣶⣿⡀⢸⠀⠀⠀⠀⠀⠀⠀⡿⡄⠹⡄⠀⠀⠀⢱⡀⠀⠀⠀ ⠀⡠⠖⠊⣀⡴⠊⢁⡠⠺⠇⢠⢿⠀⠀⡇⢸⣄⣤⣷⣦⣤⣴⡇⠀⠈⡆⢸⡇⠈⢳⡀⠀⠀⡇⠀⠉⡼⢻⡿⣇⠞⠸⠉⡿⢦⡀⠀⠀⠀⠀⠀⡇⣷⠀⢳⡀⠀⠰⣄⢳⡀⠀⠀ ⠠⣤⣖⡉⠁⠔⠊⠁⠀⠀⠀⡿⠘⠀⠀⡇⣼⠿⣿⣿⠍⡹⢙⡿⣦⣄⠸⡜⡇⠀⠀⠱⣄⠀⡇⢀⡜⠁⣸⢡⡏⠀⡆⠠⠇⠀⠀⠀⠀⠀⡇⠀⡇⠈⠀⠈⠳⢦⣀⠀⠙⢷⡄⠀ ⠀⠀⠀⠉⠉⠓⠒⠀⠀⠀⢰⠇⡀⠀⢸⠉⢿⡗⢿⡟⠀⠃⡘⢹⡞⠟⠀⢳⣧⠀⠀⠀⠘⢆⢿⠼⣀⣶⣿⡿⢷⣿⣗⣶⣀⠀⠀⢸⠀⠀⢣⠀⡇⠀⢀⣀⣀⣀⣈⡉⠂⢈⣿⣄ ⠀⠀⠀⠀⠀⠀⢀⣴⢀⣠⠞⠀⡇⠀⢸⡀⠀⡷⠀⠻⢶⣤⡵⠿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢻⣷⠟⣿⡿⢣⠆⣸⣿⢛⣷⡶⠀⢸⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠾⣟⡿⠁⠀⢀⡇⠀⠈⣷⠀⣟⠀⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣿⣠⠉⠀⣣⡟⢀⣾⠇⠀⠈⣀⠀⢸⡆⡇⠀⠀⢀⣀⣴⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⠿⠧⠤⠶⠒⣾⡇⡇⢸⢸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣛⠳⠞⠻⠦⣾⠅⠀⠀⢠⠇⠀⡼⠸⠀⠀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣚⠁⠀⢧⠸⡄⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢠⠇⠀⠀⠀⡞⢀⢦⠃⢀⠀⠉⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡅⠀⠀⢸⡄⢇⠙⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢠⡆⠀⡼⢀⡞⢸⢀⡞⠀⠀⠀⠈⠻⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠤⢄⡀⠈⢧⠈⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⠏⢠⠏⣸⡽⠁⣜⠸⣼⢸⠧⠤⠤⠔⠒⠚⠛⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣀⡴⡞⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠀⡞⣴⡇⡼⢣⢣⡞⡹⢦⡹⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣼⣁⡴⢻⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡽⢡⡿⠁⢠⠋⣿⡇⠀⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⣹⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠋⢹⡟⢠⠞⠁⠀⠀⠀⣿⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣠⠴⠚⣽⠀⠠⡄⠀⠀⠀⠀⠀⠀⠠⠤⠖⠚⣹⠃⠀⡤⠋⢀⢏⡀⠀⡇⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠁⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢻⣯⣷⡤⠟⠀⠉⠉⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡙⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠈⡉⠒⢲⣤⣀⣀⣤⣴⣶⣶⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⡠⠄⠂⠈⢈⡉⠉⠛⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡿⠟⠁⠀⡠⠀⠀⠀⣠⠔⠀⡠⠚⠀⡄⠀⠀⠉⠻⣿⣿⣿⠁⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⢸⣿⠟⠃⠀⢀⠞⠀⠀⢠⠞⠁⣠⠊⠀⢀⣼⠁⣾⡀⠀⡄⠘⣿⡏⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣶⠏⠂⢠⢀⠎⠀⠀⡰⠃⢀⣼⠃⠀⡠⢋⠇⣰⠁⢿⡄⢸⡆⢹⣇⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⡎⣞⠀⣠⡾⢁⣾⢻⠃⣠⡞⠁⡜⡰⠃⠀⢸⡗⢒⡇⠈⣿⠀⠀⠀⠀ ⢰⣿⣿⣿⡏⠀⠀⠀⠀⢀⡠⠞⣿⠁⣄⣰⣼⢁⡝⢳⣷⡟⠁⣼⡴⠙⠀⣼⠟⠁⠀⠀⠸⢸⠀⡇⠀⠿⠀⠀⠀⠀ ⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⢰⣿⡏⢿⡟⢻⡿⢲⣿⡿⣿⣦⣤⣾⣿⣆⣁⣉⣀⡀⣸⢰⠀⠀⣾⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠘⣰⠈⠃⣾⡟⢡⡘⣿⡏⢸⡏⢩⣭⣽⡟⣿⣿⢻⣿⣼⣏⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣄⠀⠀⠀⡼⣏⣿⣿⣿⣿⣴⣿⣦⣼⣟⣠⣦⣄⣻⡇⣼⠇⣶⣬⣿⠁⣿⡇⢸⡿⢻⣿⡄⠀⠀⠀ ⠀⠀⠘⢿⣿⣿⣿⣷⣦⡞⢸⣿⡟⢿⣾⡿⣿⢦⡀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠻⠿⠿⢶⣬⣥⣿⣇⣾⠹⡗⠄⠀⠀ ⠀⠀⠀⠀⠙⠻⣿⣿⣿⡅⡿⠀⢧⠘⣇⣷⣝⣆⠉⠒⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢸⡿⣁⣼⣿⣿⣠⢸⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢻⡙⢷⡀⠈⠳⣿⡁⢻⣿⣷⡒⠀⠀⣿⠉⠉⣻⡏⠀⠀⠤⣴⣿⣟⡿⠋⣾⠛⣿⡜⣽⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⠶⣯⣀⡞⣁⡙⢻⣿⣿⣿⣦⣄⡀⠒⠒⠚⢀⣠⣴⣿⣯⣽⣋⣤⡾⠳⣴⣿⠿⢇⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢀⠭⡉⡿⠋⢹⣌⣿⣏⠻⣿⣷⣶⣿⣿⠋⢙⣿⡀⠀⢙⡏⠀⢠⠞⠙⣗⠢⡉⠀ ⠀⠀⠀⠀⠀⠀⠸⠀⢇⠀⠃⠀⠸⡀⠈⢇⠀⡇⠙⣿⣽⠤⡉⣛⣟⢋⡇⡴⢫⡾⢿⠀⢸⠀⡔⠁⡠⠀⠀⠇⠘⡆ ⠀⠀⠀⠀⠀⠀⢰⡇⠈⠂⢸⠶⡀⠑⣄⠘⡄⠘⣶⠟⠻⣦⣆⣠⣀⣀⣻⣷⠏⠀⢸⠀⠘⠴⢥⣎⣀⠔⣁⡴⠘⡏ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⠄⠜⠢⣈⡦⠗⠀⠸⢴⡶⡇⠈⠀⠙⠁⠠⢿⣦⠀⠈⠳⠄⣀⠀⠉⠉⠉⠀⣄⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡇⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⢀⣀⡴⠁⠀⠀⡇⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠱⡈⠲⢄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⡜⠀⠀⢀⡀⣹⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢇⠀⠘⢄⠀⠈⠒⠢⠶⣶⣆⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢠⡞⠉⠙⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣴⠐⠒⢄⠀⠈⠒⠫⡉⣿⣤⠀⠀⢱⠀⠀⠀⠀⠹⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠜⣇⠀⢸⠏⠉⠢⢄⡀⠀⠀⠀⠀⡰⢹⡟⠀⠀⠀⢣⡀⠀⠀⠈⢣⡸⣀⣀⡤⠧⠀⡄⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀ ⠀⡴⠁⣠⡾⡄⠸⠆⠀⠀⣠⡏⠀⠀⠀⢰⠃⣿⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠱⡀⠁⢆⠀⠀⠘⢆⠀⠀⠀⠀⢣⠀⠀⠀⠀ ⣸⠖⢡⠎⠀⠘⢤⣼⡞⠋⡽⠁⠀⠀⠀⡜⠀⢹⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⢣⠀⠀⠀ ⠉⢠⢃⠀⠀⢀⠞⡜⠀⢰⠃⠀⠀⠀⠀⡇⠀⢺⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⡄⢱⡀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠈⡆⠀⠀ ⠀⣿⡏⠀⠀⡸⢰⠁⠀⢸⠀⠀⢀⠀⠀⣿⠀⠘⠄⠀⠀⠀⠀⢸⠈⡄⠀⠀⢠⡇⠀⣇⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢱⠀⠀ ⠀⠿⡇⠀⠀⡇⠀⠀⠀⠸⡄⠀⠘⡆⠀⡏⣇⠀⠀⠀⢸⠀⠀⡞⢀⠇⠀⢠⠇⡇⢠⠻⡀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠘⡆⠀ ⠀⠀⡇⠀⠀⣷⠀⠀⠀⢸⡙⠦⣀⢹⣆⡰⣜⣄⠀⠀⢸⠀⢰⣧⡾⢲⡶⠫⣴⡧⠃⠀⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣇⠀ ⠀⠀⠹⡄⠀⡏⢦⠀⠀⠘⡇⢀⣠⠽⠷⠼⠭⠛⢦⡀⠘⣤⠟⠚⠛⣡⣶⣤⣭⡀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢻⠀ ⠀⠀⠀⠙⠦⣹⡀⠓⣄⡀⠸⣏⣀⣠⣤⣄⣀⣀⠀⢈⡷⠿⠦⠠⠿⣿⣿⣿⣿⣿⣷⣤⣾⡀⠀⠀⠀⠀⠈⢿⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠉⡰⠁⠀⠉⢯⣿⣿⣿⡿⢿⣿⡆⠀⠀⠀⠀⠀⠀⣩⣷⣶⣿⡿⠈⠟⢻⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠸⠀ ⠀⠀⠀⠀⠀⠀⣰⢁⠀⠀⡀⠚⢿⡍⠛⣻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⠁⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣇⡎⠀⢠⠃⠀⢸⡆⠀⠈⣉⡤⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⡆ ⠀⠀⠀⠀⠀⢸⣿⠇⠀⡎⠀⠀⠀⠸⡀⠈⠀⠀⠀⠀⠉⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⡾⣿⠀⢠⠃⠀⠀⢹⠀⠳⡀⠀⠀⠀⠀⠘⡟⠉⢙⡝⠁⠀⠀⠀⠀⠀⣸⠁⠀⠀⡠⢠⢿⡟⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⢿⡿⡀⢸⡀⠀⠀⠘⡄⠀⠈⠢⣀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⣀⣴⠇⠀⢀⣼⣡⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢧⣇⠈⣷⠀⠀⠀⢱⡀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⢀⣠⠔⠊⢡⠏⣠⠴⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡹⢆⠘⣷⡀⠀⠀⠱⣄⠀⡀⠀⠀⠀⢹⠒⠒⠊⠉⠀⠠⠴⠟⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠃⠀⠉⠙⠻⠶⠦⠤⠼⠛⠓⠊⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠐⠒⠈⠁⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠈⠒⢤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⠉⠚⡕⠒⣒⣖⣖⠖⠒⢍⠂⢱⠃⠀⠀⠀⠀ ⠀⠀⠀⢠⠈⠈⢀⣀⠀⠉⠈⠉⠀⢀⣀⠈⠈⢰⠀⠀⠀⠀ ⠀⠀⠀⠂⣀⡀⠉⠉⠑⠀⠀⠀⠀⠋⠉⠁⣀⣀⢣⣤⢢⣄ ⠀⠀⢸⠀⣒⠲⠀⠀⢄⡀⠠⠄⢀⣠⠀⠀⠗⣒⢸⠀⠷⡾ ⠀⠀⠀⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠀⠀⠂ ⠀⠰⠋⠉⣿⡞⠻⣆⣶⡶⠶⣶⣶⣶⡾⠏⠟⠋⠁⢀⠐⠀ ⢴⡀⠀⠀⢻⡝⣱⢛⡯⣄⣦⡿⣼⠁⠀⠀⠀⠀⠀⠈⡀⠀ ⢟⣷⣄⠀⠐⣽⣆⣧⠖⠻⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠈⢤⡆⡫⠿⣷⣾⠳⠆⠠⣂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀ ⠀⠀⠉⢇⡡⢊⣟⣄⢀⡧⠇⠀⠀⠀⠀⠀⢀⡀⠔⠁⠀⠀ ⠀⠀⠀⠀⠈⠁⠉⠉⠐⠒⠒⠒⠒⠂⠀⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⠖⠉⠒⢤⡀⠀⠀⠀⠀⢀⡤⠖⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⢁⠊⠀⣑⡄⠈⠙⠒⠒⠊⠁⠀⣊⠀⠑⡌⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠉⠑⢦⡀⠀ ⠀⠀⠀⣾⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⢿⢉⡁⠀⠀⠹⡄ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠈⣳⢄⣀⠀⠀⢧ ⠀⠀⠀⢸⡀⠀⠀⠀⠂⠌⣒⢄⠐⢍⡩⠆⡠⡔⠩⠐⠀⠀⠀⢀⡏⠀⠀⠀⠀⢸ ⠀⠀⠀⢀⣷⡀⠀⠀⠀⠈⠉⠉⠢⠠⠇⠰⠉⠉⠉⠀⠀⠀⢀⡜⠀⠀⠀⠀⢀⠏ ⠀⠀⢠⠎⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠀⠀⠀⠀⢠⠎⠀ ⠀⣰⠃⠀⠀⠀⠀⠉⠛⠯⢭⣀⣀⣒⣒⣀⣀⡩⠽⠓⠉⠀⠀⠀⠀⠀⡴⠃⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀ ⡞⡠⠂⡀⠀⠀⠀⡜⠀⠀⠀⠀⠉⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠹⣇⠀⣇⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀ ⠀⢸⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠈⣇⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡸⠀⠀⠀⠀ ⠀⠀⠈⠲⢖⣉⣫⣙⣷⠤⠤⠖⠒⠒⠒⠲⠤⢄⣀⣜⣍⣽⣉⣒⠴⠃⠀⠀⠀⠀
⠀⠀⠀⣀⣤⡶⠖⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⣶⣤⣤⣤⣤⣶⣶⡶⠟⠛⠛⠉⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⠿⠛⠉⠀⠀⢸⡆⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠿⠟⢛⣹⣿⣣⠴⣶⣾⡇⠀⠀⠀⣀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢼⣿⣿⣿⠋⠁⠀⠀⠐⠛⠋⠁⢀⣼⠟⠋⢧⣠⢴⣿⠋⢹⢻⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠷⣦⣤⣀⠀⠀⠀⠈⠁⠀⠀⠀⣠⠞⣁⠀⣿⠀⠹⣷⡀⠀⠀⠀⠀⠀ ⣤⡄⢀⣴⠟⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣄⡀⠀⠀⠀⣼⢿⡿⠋⠀⡏⠰⣦⢹⣧⠀⠀⠀⠀⠀ ⣿⢷⡾⠉⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⡀⠀⠻⢧⣄⣰⡇⠀⠙⣷⣿⡄⠀⠀⠀⠀ ⢀⡿⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢷⣶⣄⣀⠀⠀⠀⠀⠀⠀⣴⣿⣶⠄⠀⠀⠀⠈⠻⢷⣤⡀⠀⢸⡇⠀⠀⠘⢿⡄⠀⠀⠀⠀ ⢸⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠈⣹⣿⡷⣦⣤⣀⣼⣿⣿⡿⣠⣿⣿⡆⢀⣀⣀⠉⠻⣦⣼⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀ ⣼⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣾⠟⠋⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠻⣷⠀⠀⠀⠀⢻⡇⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⢨⣧⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⠛⠉⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣷⠀⠀⠀ ⠗⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠸⣷⡀⠀⢰⣶⣿⣶⣿⣿⣿⣿⡿⣿⣿⣿⡇⠈⠙⢿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⣧⡀⠀⠀⠀⠹⣷⡀⠘⠿⣿⣿⣿⣿⡿⠋⠀⢸⣿⣿⣷⣀⠀⠀⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠙⢷⣄⠀⠀⠀⠹⣷⡀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⣼⣿⠻⣿⣿⠏⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⢠⡆⠀⠀⠀⢸⡇⠀⠀⠀⠙⣷⣄⠀⠀⢹⣷⡄⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⣿⣿⣿⠿⠛⠁⠀⠀⢻⡇⠀⠀⠀⠀⢸⡇⠀⣀⠀⠀⣼⠃⠀⠀ ⠀⣄⠀⢸⣿⠀⠀⠀⢸⣷⠀⠀⠀⠀⠈⠻⣷⡀⠀⢻⣷⡘⣿⠉⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⠠⡦⠀⠀⠈⠀⢠⣿⠀⢠⡿⠀⠀⠀ ⠀⣿⡀⠀⣿⠀⢀⡀⠘⣿⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⡇⠀⠀⠀⠀⢸⣿⠀⣿⠃⠀⠀⠀ ⠀⢸⡇⠀⣿⣇⢹⡇⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⢀⣤⠀⢸⣿⢸⡏⠀⠀⠀⠀ ⠀⠸⣿⠀⢿⣿⠸⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣝⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠐⠀⠀⠒⠀⠀⣿⠁⠀⢸⣿⠀⠈⣿⢸⣧⠀⠀⠀⠀ ⠀⠀⢿⡄⢸⣿⡆⢿⠀⠈⣿⠀⠀⠀⠀⠀⠀⣴⣶⣄⡀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣸⡏⠀⠀⣿⣆⢿⣆⠀⠀⠀ ⠀⠀⢸⡇⢸⠟⣇⢸⡇⠀⢿⡇⠀⠀⠀⠀⢸⣿⣯⣿⣿⣶⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⣿⡇⠀⠀⣿⠹⣮⣿⣦⠀⠀ ⠀⠀⣸⣷⣿⡄⢿⡜⣧⠀⢸⣧⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⣿⡇⠀⠀⣿⠀⠙⢿⣿⣆⠀ ⠀⢰⣿⣿⠻⣿⡼⣧⣿⡄⠈⣿⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢹⠇⠀⢰⣿⠀⠀⠀⣿⠀⠀⠈⠻⣿⣧ ⢀⣾⡟⣿⠀⢻⣷⣽⣼⡇⠀⢸⣇⠀⠀⠀⠀⢠⣿⡿⣿⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⠀⠀⣾⡟⠀⠀⠀⣿⠀⠀⠀⠀⠙⠛ ⠋⠋⠀⣿⡀⠀⢻⣿⣿⣿⡀⠈⣿⠀⠀⠀⣠⣿⠟⠀⠈⠉⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃⣿⠀⠀⣿⡇⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡇⠀⠀⢻⣿⣿⣷⡀⣿⡇⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⡾⢠⡏⠀⢠⣿⡇⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠈⢿⡄⠀⠀⢻⣿⡏⠻⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⢸⡇⣼⣧⡶⢸⣿⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀ ⣧⡄⠀⠀⠈⠻⣦⣄⠀⠹⣿⣦⡘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⣼⢠⣿⣿⢁⣿⠃⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣦⡀⠀⠀⠈⠛⢷⣦⣌⠛⠿⣷⣿⣷⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠛⠁⠀⠀⠀⠀⡏⠸⣿⣷⠿⡏⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠙⢿⣦⡀⠀⠀⣦⣭⣿⣿⣶⣤⡀⠉⠉⠙⠛⠻⣿⢿⣶⣶⣶⣶⣿⣿⣟⣯⣤⣤⣤⣤⢤⡤⠴⣧⠀⠿⠋⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⢻⣧⡀⠙⢿⣦⣄⡀⠉⠻⢿⣿⣿⢿⣷⣦⠀⠀⢀⣽⣏⣙⣏⣉⣩⣇⣀⣸⣅⣀⣸⣄⣀⣠⣧⣀⣿⠻⢦⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⣿⣿⣦⣄⡙⢿⣟⠛⠷⠶⠮⣿⣿⡖⢀⣤⠞⠋⠀⣿⣀⣿⣀⣸⣇⣀⣽⣀⣀⣸⣁⣀⣸⣃⣀⣻⡀⠀⣹⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⣾⠏⠀⠉⠙⠛⠛⣿⠿⠶⣤⣤⣀⣴⠞⠉⠛⠲⢤⣄⡀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣄⣀⣀⡀⠀⠀⣀⣠⡤⠖⠒⠉⣁⠔⠋⣁⡰⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⢶⣂⣀⣀⣉⣀⡴⠛⠒⠒⠛⢶⠛⠯⠥⢵⡶⠟⠉⠁⠀⠀⢠⠞⠁⠀⢠⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠉⠁⠀⢀⣼⠏⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⢫⠀⠀⠀⣸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⡎⠀⠀⠀⠸⠟⢏⢀⠀⢠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⢠⠆⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢠⠁⠀⠀⠀⠆⠀⠀⠉⢀⠇⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠛⠀⠀⠀⠀⣀⡎⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡊⠀⢰⠀⠀⠘⢄⡀⢱⠎⠀⠀⠀⠀⠀⠀ ⣠⣔⣋⣤⡄⢒⣒⣘⢫⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀⠀⠀⠀⠁⠀⢸⡆⠀⠀⠀⠃⠈⢢⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠉⠉⣿⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠇⠀⢘⡏⠹⣧⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⣾⡆⠀⠀⠀⡄⠀⣾⡿⠀⢙⣧⣠⢤⣤⣀⡞⢸⡆⠀⠀⠈⠀⢸⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⣻⠁⢷⡄⠀⠀⢇⠀⣿⠀⠈⠉⠛⣆⠀⠀⠀⠏⠹⣇⠀⢰⡗⣄⠘⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢰⣠⣿⠖⠚⢧⠀⠀⢸⡀⢿⠀⢀⣴⠿⠿⣿⣶⣶⠧⣄⣿⠀⢸⡇⡼⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⢸⢹⣿⣧⣶⣞⣣⡀⠀⢧⢹⡀⠈⠁⠀⢺⣿⣿⣿⢂⡞⢹⠀⢸⣧⠃⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣄⠘⣿⣿⡋⠩⣿⣿⣿⠆⠸⣎⢷⢄⠀⠀⠈⠳⠿⠋⠈⠀⢸⠀⣼⣇⠀⠀⢹⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠻⡀⢿⣿⣟⠀⠙⠽⠿⠀⠈⠙⠛⠒⠀⠀⠈⠉⠁⠀⠀⠀⣸⠀⣿⢹⡀⡄⢸⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⢣⠘⣿⣏⢆⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢸⡇⠈⡿⡀⠘⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠨⣧⠈⡌⠎⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠘⢸⠃⢠⢿⣧⢀⡇⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠻⢆⢳⣦⠘⣦⣀⠀⠀⠀⠀⠀⠈⠙⠁⠀⣠⢾⣹⠂⠀⣼⠀⠘⢸⢹⡀⠹⡸⣷⣄⠀ ⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⢸⠘⡄⠹⣆⠱⡈⠑⠢⢤⣀⡀⠀⢀⣴⣿⠿⠋⣇⠸⠀⡇⢀⣨⣦⡆⠳⠄⠑⠘⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣇⠀⢹⡄⢳⡆⠀⠀⢨⣿⠛⠛⠉⠀⠀⠀⢿⣴⢿⠧⠝⠋⢋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⠀⠀⡇⠘⡿⠀⣀⡼⠛⠀⠀⠀⠀⠀⠀⠈⠀⠜⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠹⣀⡵⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⢤⡤⠴⠒⠚⠉⠁⡠⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⡜⠀⣸⡀⠀⠀⠀⠀⠀ ⢀⣴⣶⠶⠶⠒⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⡗⠋⣠⠇⠀⠀⠀⠀⠀ ⢸⡏⠈⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⢀⠔⠊⠉⠉⠒⠤⡀⠙⢆⠈⣹⠂⠀⠀⠀⠀ ⠀⢧⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠘⢆⠈⢧⣈⠇⠀⠀⠀⠀ ⠀⠸⣇⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⢀⡴⠅⠀⡄⠀⠀⠀⠀⠀⠀⠈⢣⠈⣇⠀⠀⠀⠀⠀ ⠀⠀⠹⡆⢀⠏⠀⠀⠀⠀⢠⠋⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠀⠀⠀⢀⠀⠀⠀⠘⡆⠸⣄⠀⠀⠀⠀ ⠀⠀⠀⠙⣾⢀⠀⠀⠀⢀⠇⠊⠀⡇⠀⠀⠀⠀⢺⠀⠀⣠⠄⠘⡆⠀⠀⠈⠑⠂⡄⠀⠹⡄⠈⣙⡶⠆⠀ ⠀⠀⠀⠀⠈⢹⠛⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠘⡄⢉⡇⠀⠀⡗⢀⣄⣰⣞⣛⢿⣵⠒⠉⠁⣿⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⠀⠀⢀⠇⠀⠀⠀⡦⣤⣿⣿⣿⣄⢀⠷⠋⠀⠀⣿⣍⣷⣿⠀⠀⢰⠇⠀⠀⠀ ⠀⠀⣀⡴⠋⠀⠀⠀⠀⢸⠀⢠⣎⡴⢦⠀⠘⣷⡏⠀⣿⣧⣼⡇⠀⠀⠀⠀⢿⣿⣯⡘⡀⠀⠘⣦⡀⠀⠀ ⠀⠀⠙⠦⣄⡀⠀⠀⠀⠈⡆⠋⠁⠀⠀⠳⢄⣻⠀⠀⣿⣾⣿⣷⡆⠀⠀⠀⠚⠉⣋⡀⢧⣸⠓⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⢭⣟⡃⢀⠀⠹⡄⢀⠀⠀⢀⡠⠼⠣⠀⠘⠟⠛⠉⠀⠀⢀⡴⠒⠚⠙⢣⣼⣏⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣉⠀⠀⠙⣼⡙⠒⠬⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⡾⠇⠀⠀⣰⠟⢡⡼⣗⠭⣉⢲⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣷⢀⣤⣈⣑⣢⣄⡀⠀⠀⠀⠀⣰⠻⣶⠖⠋⠁⠐⡙⣗⣌⠳⣌⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠋⣹⠟⠓⣤⠾⣍⡉⠉⠙⢦⣈⠓⢤⡀⠀⢣⠈⢎⠲⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣄⢰⣿⢠⠀⠙⢿⣶⣤⡾⣧⡀⠳⡀⠀⠓⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠙⢿⣿⣿⡇⠀⢣⠘⢄⠹⠟⠦⠀⠈⠀⢱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠘⣿⣿⡇⣠⢤⣴⣾⣾⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠹⣿⣿⣿⣶⣿⣿⣿⡄⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢹⣿⣿⣿⣿⣿⠃⠙⣄⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆⠀⠀⠀⣻⣿⣿⣿⡏⢀⡜⠃⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⠠⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⡤⠀⠀⢄⡄⠂⠈⠉⠀⠀⢈⠑⠠⠶⠯⠁⣸⣀⢠⠀⠀⠀⠀⠀ ⠀⠱⡀⠀⠀⠝⠀⠀⢰⠀⠀⠀⠄⠀⠀⢀⢠⢠⠿⠗⡈⠀⠀⠀⠀⠀ ⢂⠠⢱⡀⡈⣴⠀⠀⠀⠀⠀⢀⢸⠀⠀⠃⠂⢢⠀⠀⠁⠀⠀⠀⠀⠀ ⠈⣄⡀⡹⡇⠀⢀⠄⠚⢆⠀⠈⠉⣻⡯⣀⢰⢸⠓⠠⠇⠀⠀⠀⠀⠀ ⠀⠉⠀⡼⡰⠐⣼⢻⣶⣦⠁⠀⠞⢝⡿⢮⡀⠏⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠜⠀⣷⠃⢣⣉⡉⠁⠀⢉⠀⠀⠀⢞⠇⡼⠅⠠⣤⠊⠤⡀⠑⠀ ⠀⠀⠀⠘⣿⢇⠘⣧⣠⡀⢈⠀⠀⢤⠒⢉⠟⡰⠀⠀⢃⠀⠈⠀⢀⠇ ⠀⠀⡧⡘⢹⠠⠀⠀⠀⡰⠟⣑⠂⢎⣧⡼⢎⣄⠤⡆⠀⠑⠒⠒⠀⠀ ⠀⠀⡇⡿⣴⠓⡝⠉⠁⠰⡀⠁⣺⢏⠁⠆⠰⡈⠪⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠀⣸⠜⠀⠀⡀⠀⢰⠔⠀⠻⠝⠀⠀⠳⡀⠀⠳⡄⠀⠀⠀⠀ ⠀⠀⠈⣽⡇⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣸⠧⡀⠀⠀⠀ ⠀⠀⡠⠉⠑⠌⡢⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠢⣀⠀ ⢀⠔⠁⠀⠀⠀⡨⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢄⡀⠀⠀⠁⠈
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆。˚˙✧˖°📷 ༘ ⋆。˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧。⋆🌻⋆。‧˚⛷🧚‍♀️🛖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠤⣤⡤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⠤⠤⣄⣀⡠⠔⠒⠉⢁⣠⠀⠀⠀⠲⢶⣿⣷⣀⣤⡾⢿⣗⣲⠖⠂⠉⠉⢉⣉⡷⠶⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠒⠒⠤⢄⡀⠀⠉⠀⠀⠀⠘⠛⠋⣠⠔⢋⡉⠉⠛⠻⣿⣿⡚⠉⠛⠯⣀⠠⢤⠚⠁⠀⠀⠀⡜ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣈⣇⠀⠀⠀⠀⣀⠔⠋⢠⠎⠁⠀⠀⡠⠂⠀⡄⠙⣄⠈⠁⠺⢕⠢⣷⡀⠀⠀⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⢨⠟⢍⡉⠉⠉⠀⠀⢀⡎⠀⠀⣠⡞⠀⠀⠀⠈⣆⠈⠢⡀⠀⠀⠱⣄⠉⠢⢾⣁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠉⠀⠀⢨⠃⠂⠀⠀⡼⠀⠀⡰⢁⡇⠀⠀⠀⠀⢹⢳⢤⡙⣄⠀⠀⠘⣿⡋⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⠏⠀⠀⢀⣴⣧⡀⣼⡅⢸⡀⠀⠀⠀⠀⡌⢸⠀⢻⠙⠳⠀⠀⢻⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣤⣾⢤⡀⠀⣿⣿⡿⣿⠟⢿⢿⡇⠀⠀⢠⣾⣿⣧⣦⣤⣇⠀⠀⠢⣘⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡷⣿⠻⡄⠑⡄⢻⣿⠁⠈⠀⢸⠀⢿⣯⡠⠋⠈⡿⠉⢹⣿⣿⠀⠀⠀⢸⣿⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡇⠈⠈⠀⠀⠈⣾⣏⠣⠤⠤⠞⠀⠐⠋⠀⠀⢰⡅⠀⡼⣸⠟⣀⠤⠒⠉⢉⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡇⠀⠀⠀⠀⠀⠘⣿⡓⠀⠀⠀⠀⣀⡠⣀⠀⠀⠉⠉⢀⡿⠋⠁⠀⠀⠍⣹⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⢸⡿⣦⣀⣀⣺⣄⣀⡸⠂⠀⠀⣰⠿⠃⠀⠀⠀⢀⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠸⠆⠀⢸⠀⠈⢳⣶⠚⠉⡟⠉⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠧⠤⣾⠹⡦⠼⣇⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠖⠉⠀⣠⠇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠃⠀⠙⠒⠉⠀⠀⢤⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡞⠁⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠒⢤⠀⠀⠀ ⢱⡀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣃⠀⠀ ⠀⠑⢄⠀⠈⠲⢤⣀⣀⡠⠤⠒⠉⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢛⡿⠀⠀ ⠀⠀⠀⠑⠦⢄⡀⠀⠀⠀⢀⣀⠤⠊⠁⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠶⠧⠤⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⣀⠀⠀⠀⢀⡠⢴⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢀⠀⠀⠄⢀⠀⢠⡾⠋⣀⠰⣟⡷⠀⠈⠉⠛⠻⢿⣿⡻⢷⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⠂⢈⠀⠈⡀⠄⠂⣰⡟⠁⠀⠉⠙⣯⡟⠀⠠⠁⠄⡀⠀⠈⠛⠿⣯⡻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⡈⠀⠠⠀⠄⠁⠀⢀⣴⠏⠀⠀⠀⠀⠀⢸⡧⣄⠀⠁⠄⠰⠀⠠⠀⠄⠈⠙⢿⡝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠀⠐⡀⢀⠁⠠⠁⠀⠂⢴⡾⠁⠀⠀⠀⠀⠀⢀⣿⠀⣿⡀⠀⠐⠀⢻⡄⠀⠂⠐⠀⠀⠙⢿⣧⣤⣔⣦⣀⣀⢀⠀⠀⠀ ⠀⠀⡼⠃⠀⠀⠄⠀⡀⠄⡈⠄⣀⣤⠾⠛⠛⢷⣄⣀⣀⣀⣰⡟⠁⠀⣾⡅⠀⢀⠀⠀⢿⡀⠀⠈⢀⠁⣄⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛ ⣠⣼⠃⠀⠀⡁⠀⠐⠀⠀⣠⡼⠏⠁⠠⠄⡀⠀⠈⠉⠉⣽⡏⠀⠀⠀⣿⠆⠀⠠⠀⠀⠸⣧⠀⢠⡀⠀⠠⠑⡀⠈⢈⠠⠐⠀⠄⠠⢀⠀ ⣿⠃⠀⠀⢂⠀⠌⠀⠂⣴⠏⠀⠀⠄⠃⠀⠐⠰⢀⠀⣼⡟⠀⠠⠁⢸⣿⡇⠀⠀⠁⠀⠀⢿⣆⠀⢿⡀⠀⢁⠻⣄⠀⠀⠈⠀⠄⠀⣀⣤ ⡏⠀⢀⠂⠀⠄⠂⢀⣾⠋⠀⡀⢁⠂⠈⠀⠀⣴⠂⣲⣿⠃⠀⠄⠀⣾⣿⠁⠐⠀⡁⠀⠀⠘⣿⡄⠈⢷⡄⠀⠀⠙⢷⣤⡤⠶⠲⡛⠉⠀ ⢧⡀⠀⠀⠁⠄⢂⣼⠃⠀⠄⡀⠠⠈⠀⢁⣼⠃⣰⣟⡯⠀⠀⠀⣰⡟⣿⠀⢠⣀⠀⠀⠀⠁⣿⢿⣄⠀⠻⣦⠀⠀⠊⣷⠀⠀⠀⢱⢀⣶ ⠀⡹⠒⠳⡄⢀⣾⠃⠀⠌⠀⠄⠐⢀⢠⣾⠋⣠⣟⣾⣥⣄⠀⢠⡿⠁⣿⡄⠀⠀⠉⠐⠀⠄⣿⡆⢻⣄⠀⠙⢷⡀⠀⢹⡆⠀⠀⣸⣾⣟ ⣀⠀⠀⢀⡼⣾⠇⠀⠐⠈⡀⠐⠈⢀⣾⡇⣰⡟⣿⡃⣀⣉⣿⡟⠁⢀⣿⠈⠑⠢⠄⠀⠀⠀⣿⣷⠀⠙⢷⡄⠈⠻⣆⠈⣿⣀⣠⠟⢡⠾ ⠈⠣⣄⣾⣻⠏⠀⠀⠌⠀⠄⡁⠂⣾⠛⠋⠉⠀⠉⠻⠾⢶⠾⠋⠀⠀⠉⠻⢶⣄⣀⠁⣀⣀⣿⣿⠀⠀⢸⡟⢳⣄⡉⢿⣼⣿⣏⠀⠀⠀ ⠀⣠⢞⣹⡏⠀⠄⠁⡀⠌⠀⠄⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⢿⣽⡟⣿⡇⠀⣿⠃⠸⣯⠁⢻⣭⣿⣯⣥⣀⠀ ⠴⡃⢎⣿⠁⠄⡈⠄⠀⠐⠀⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠾⠿⣿⡁⠀⣿⠀⠀⣿⠀⢸⣇⢿⣿⣿⠏⠉ ⠡⡜⢻⡟⠀⡐⠀⡀⠌⢀⣶⢿⠁⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣼⣿⠀⠀⢻⠆⢸⡏⣾⣾⠃⠀⠀ ⡳⣌⢻⡇⠐⡀⠂⢀⠂⢸⡇⣿⣿⣶⣤⣙⣷⣟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⢸⠇⣸⣿⣿⣿⠀⠀⠀ ⠲⣌⢻⣧⠀⡄⢁⠠⠀⢸⡇⡧⠈⠉⠛⠿⠿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⣿⣟⡇⠘⠃⠐⢻⣿⣿⠀⠀⠀ ⡓⣌⢣⢿⡆⠂⡄⠠⠀⢸⣯⡗⠀⠀⠂⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣒⣛⣛⡋⢉⣴⢟⡸⣿⣆⠠⠀⠠⢸⣟⣷⠀⠀⠀ ⡱⣘⠦⡚⣿⣳⡴⠀⡁⠸⣿⣷⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠻⠟⠻⠿⣦⣿⣯⠆⣽⠇⣿⠀⠀⠀⢨⡿⣿⠀⠀⠀ ⡱⢎⡱⢣⠜⡻⣿⣄⡀⠁⢻⣇⡛⣷⣄⠀⠀⠀⠘⢿⣟⠶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠄⣾⣿⣿⣿⡏⣴⣨⣿⠀⠀⢸⣆⣿⣿⠀⠀⠀ ⡱⢎⠵⣋⠼⡱⢌⣝⣿⣦⠈⣿⠟⠋⠉⢛⣶⣄⣀⠀⠈⣩⣽⣯⣭⣄⡀⠀⣀⣀⣀⣤⣾⣿⣿⣿⣿⢃⣾⠗⡏⠀⢀⣼⣿⣿⣿⠀⠀⠀ ⡱⢎⠳⣌⠧⣓⣾⡿⣏⣿⣶⣿⣆⠀⠀⢾⡁⣬⠿⣿⡿⣿⡽⣾⣹⡟⣿⣿⡟⣿⣻⣟⣿⣿⣿⣿⣭⣾⡟⣜⣤⣴⣿⣿⣷⠿⠁⠀⠀⠀ ⡱⢋⡕⣊⣶⣿⢯⡿⣽⣞⣳⢯⣿⡆⠀⢸⡿⠁⣰⣿⣟⣳⣟⣳⢯⡽⣯⣿⣽⣳⣟⣾⣳⢿⣿⣿⡿⣏⣼⣾⣯⡽⠏⠉⠀⠀⠀⠀⠀⠀ ⡱⢩⢖⣵⡿⣽⢯⣟⡷⣯⣟⢿⣞⣿⣤⣿⢻⣷⣿⣿⣯⢷⣯⣟⣯⣟⡷⣻⣷⣻⣞⡷⣯⢿⣽⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣷⣾⢿⡽⣯⣟⡾⣽⣷⣻⢿⣾⡽⣿⣟⣿⣿⢷⣿⣯⣟⡾⣞⡷⣯⣟⣿⣻⣷⣯⢿⣽⣻⢾⣽⣿⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣼⢧⣄⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣠⣟⣿⣿⣦⣄⠀⠀⠀⠈⠈⠈⠀⠀⠀⠐⠐⠀⠂⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⢻⣿⣶⣻⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟ ⠠⠀⢻⣿⣿⣧⣙⠻⠿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠿⠋⠀⠀ ⠀⠀⠀⠻⣿⣿⣿⣷⣷⣬⡭⣙⢻⠿⣿⣷⣦⣤⣤⣤⣤⣴⣤⣤⣶⣶⣿⣿⣷⣿⣷⣿⣾⣿⣿⣿⡿⣿⣿⣷⣿⣾⣷⡿⢿⡿⣿⣶⣶⣤⣤⣤⣶⣶⡿⠿⠟⡛⢧⠐⠠⣄⣶ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡟⠛⢻⣿⣧⣛⠸⣃⡿⣿⣿⡟⠿⠿⣸⣧⠘⡄⠃⠄⢃⣤⣿⠃ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣟⠛⡛⣿⣿⣿⡿⠫⢅⠊⡔⠛⡿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⡟⡀⠀⠀⠘⢻⣿⣷⠈⠑⠛⠻⣿⣏⣲⡁⢎⡳⠈⠅⢺⣤⣿⠃⠀ ⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⢟⡻⢛⢂⠱⢿⣿⣏⠲⣁⠎⡘⢄⠣⡐⢌⡹⢿⣿⣿⣿⡟⢻⢋⠙⡉⠄⠠⠀⠌⢈⣿⣿⡇⠀⠀⠳⠿⠻⢿⣿⡀⠆⡉⠠⣽⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢳⡘⢦⡐⡁⠂⠌⠚⡹⢁⠓⡌⢆⡘⢤⠣⢜⢢⣽⣿⢫⠝⢦⡙⠢⠌⡐⠰⡈⠄⠡⠀⠂⠼⠟⠁⠀⠀⠀⠀⡀⠈⠹⣿⣦⣔⠙⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣿⣿⣿⣷⣷⣤⣂⠑⢦⡈⠔⣂⠹⣶⣙⣮⣿⢻⡌⢧⡚⣥⢎⠡⢊⡔⣿⠄⡁⠂⠡⠀⣀⣦⣼⣶⣾⣿⣿⣾⣷⣦⣜⣇⣟⣈⢿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠣⢄⢋⢿⣿⣿⢏⣳⢚⡧⢳⣼⢃⠎⣡⢺⣿⠀⠀⠀⢤⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠂⡜⢺⣿⣿⣏⢾⡹⣜⣻⡟⣌⠚⣤⣿⡇⠀⠀⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣾⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢌⡹⣿⣿⡞⣧⢻⣼⣿⡗⠤⡃⠔⡋⡄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠈⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⢣⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢦⢹⣿⣿⡜⡧⣏⣾⣿⡝⡼⢋⢆⡑⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣼⣿⡀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣷⠾⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⡿⣽⣳⡽⣾⡿⣿⣷⡩⢖⣬⢣⡔⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⣀⣶⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⣍⣙⠛⡛⢛⠛⢛⠛⣟⣿⣿⣿⣿⣿⣿⡿⣽⣳⣿⡻⣇⠻⣵⢻⣿⣏⢶⣫⢽⣹⣿⣿⣮⠣⠍⠛⠛⠛⠛⢉⡉⣤⣰⣶⣿⡿⢿⣿⢿⣿⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⣦⣸⣼⣿⣿⣿⣿⣿⣿⣿⡽⣏⣿⡱⢍⠳⣎⢿⡹⢮⣳⡟⣮⢳⣿⣿⣿⣿⣦⣴⣶⣶⣿⣿⣿⣿⡿⣏⠳⡜⢣⠞⣼⣿⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡿⣾⣟⣿⡿⣿⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢵⡚⢷⡈⠳⣬⢳⡹⢧⡳⣏⢷⡻⢿⣿⣿⣿⣿⣽⡿⢿⣻⣿⢶⣣⢓⡜⡛⠼⡳⠿⣛⣿⠄⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⢶⣩⠒⡭⣑⢮⡱⣙⢦⣽⣾⣿⠿⣛⠛⣿⣿⣿⣧⡛⢧⣛⢾⡣⢇⡫⣔⢫⠖⡑⣢⣽⣿⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⢾⣯⢿⣹⣿⣿⣿⣿⣿⣿⡽⣞⣧⠿⣷⢿⣿⣿⣿⣿⣿⣿⣏⣾⣶⡟⢋⠉⠻⣿⣿⣬⢣⡛⣜⡡⢖⡩⣻⣮⣴⣿⣟⣿⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⣟⣾⣟⡿⣜⢧⣳⠾⡽⣿⣿⣿⣿⣿⣿⣞⣿⣭⣿⢾⣽⣳⣿⣾⣿⣿⣿⠟⠀⠄⠈⠐⡀⣛⠿⡷⣙⠚⡅⠋⡔⠹⣿⢿⣿⣯⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣽⣷⡟⣿⣿⣿⣽⢻⡞⣧⡟⣵⢣⠛⣿⣿⣿⣿⣿⢳⣯⡟⣿⡞⣿⣿⣿⡟⠋⠁⠀⣤⠈⠀⡔⣴⣯⣶⣵⠈⠂⠀⠁⠀⢡⠐⣬⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣽⣻⣽⣿⢿⡿⣿⣿⣿⡿⢾⡵⢎⡳⢤⡩⢿⣿⣿⣿⣾⣿⣷⣯⣿⡿⠙⠀⠀⢀⠀⠀⠈⠀⠁⢉⠉⠉⠁⠃⠀⠀⢀⠢⢄⠂⡔⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣿⣾⣧⣿⣵⣯⣾⣽⣳⡞⣯⢞⡵⢎⡻⢽⣿⣿⣷⣿⣿⣿⡟⣁⠂⠠⠁⠀⠀⠀⠄⢀⠶⢠⠀⠄⡠⢀⠀⠀⠀⠂⠈⡐⢈⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣯⢿⡽⣯⡟⣿⣻⢯⡝⣧⢻⡜⣣⡙⢆⡞⣿⣿⣿⣿⢏⠴⣠⡀⠄⠂⠁⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢂⠱⣀⠐⢢⣿⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⣟⣷⣻⢷⣻⡾⣽⣞⣷⡹⢲⡝⡾⣜⣳⣿⣿⣿⣎⠶⡱⡉⢌⡑⢂⡐⠈⠃⠐⠠⠐⠀⠂⠌⠀⢄⡰⢉⠷⣎⡉⢶⣾⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⢻⡿⣿⣿⣾⣯⣿⣳⣟⣧⢟⡾⣽⣷⣯⣳⣯⣿⣿⣿⣿⣾⣽⣣⠽⡆⠜⡠⠒⡤⠘⠤⣁⠂⠆⣀⠢⣉⠶⣌⢃⠒⡀⠙⣼⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡹⣞⢧⡟⣯⢛⡿⢿⣿⣿⣾⣿⣾⣷⣯⣷⣯⣷⣿⡿⣟⠿⡿⢿⣿⣿⣷⣯⣼⣰⣥⣆⣍⠰⠠⢌⣰⣀⠒⡄⠓⠠⠈⢂⠄⢤⣾⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣳⡝⣮⢫⡝⡲⢏⢺⢡⠫⣝⢻⣿⣿⢿⢿⡻⣟⢯⡳⣝⢮⡛⣜⢣⢎⡝⡹⢛⡛⣛⠛⢋⣥⣶⣷⡾⠛⠁⠂⠐⠈⠀⠀⠌⡘⣦⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣳⠿⣜⣧⣾⣧⣭⣶⢃⠧⡘⢦⢩⢏⣻⣎⢷⣫⢷⡹⣎⣶⣹⣬⡓⢎⠴⣡⢃⠖⡠⢉⣂⢌⡉⢀⠀⣀⠀⠀⠀⢀⡀⠀⣌⣼⡟⠀⠀⠀⠀⠀⠀
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.  +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠖⠚⠉⠉⠉⠀⠠⣤⣄⡹⣷⣆⠈⠉⢉⣵⣶⣦⣄⣀⣤⣤⠤⠴⠶⠦⠤⠤⣤⣤⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣶⣒⣋⡉⠉⠉⠉⠉⠉⠓⠶⡤⠖⠉⠁⠀⠀⣤⣴⣶⠀⠀⢀⣠⠬⣝⣿⣿⣼⣶⣺⢿⣋⣻⣷⣾⣟⠁⠀⠀⠀⣀⡴⠶⠖⠋⠉⢹⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠁⠀⠀⠈⠉⠛⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢀⡤⠞⢁⣠⠤⠀⠈⠉⢛⡿⣿⣭⡀⠀⣋⡙⠦⣄⠀⠲⣎⠁⠀⠀⠀⠀⠀⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⠀⠀⠀⠀⠀⡠⠖⠋⢀⡔⠉⠀⠀⠀⢀⣴⠂⠀⣀⠀⢳⡄⠈⠉⠓⠮⣙⠢⣌⣦⠀⠀⠀⠀⡼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠘⣿⣖⠒⠒⠒⠒⠒⠋⠁⠀⢀⡞⠀⠀⠀⢀⣴⠊⠀⠀⠀⠙⢆⠀⠙⢆⠀⠀⠀⠈⠳⣄⠙⠳⣄⡀⡴⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⢰⠃⠈⠓⠦⣄⣀⠀⠀⠀⠀⡼⠁⠀⠀⢠⡞⡏⠀⠀⠀⠀⠀⢈⣷⣀⠈⢳⡀⠀⠀⠀⠘⣷⢤⣄⣉⣳⣶⣤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢠⠇⠈⠉⠀⠀⣰⡇⠀⠀⢠⠇⢰⠇⠀⠀⠀⠀⠀⠀⡇⢸⠷⣄⡹⣄⠀⠀⠀⢸⡏⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⡀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢠⡿⣇⠀⢰⡟⠀⢸⠀⠀⠀⠀⠀⠀⢠⡇⢸⠀⠘⣏⠙⠳⠄⠀⠀⢣⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣀⣿⡀⠀⠀⠀⣿⣺⣿⣿⣷⣿⣿⢷⣾⡇⠀⠀⠀⠀⣠⣿⣧⣏⣀⣀⣹⡄⠀⠐⢦⡀⠘⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡴⢺⡝⣾⠙⢦⡀⠀⣿⣻⡾⠋⢿⠁⠈⣧⠙⣇⣴⠄⠀⣴⠛⣿⣿⣿⣽⣻⣮⣧⠀⠀⠀⠙⠶⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡏⠻⡏⠙⡆⠀⠱⣄⠙⡿⣇⠀⠀⠀⠀⡜⠀⠿⢻⣦⠞⠁⠀⢸⠏⠀⠘⡏⣿⣿⠀⠀⠀⠀⢈⣟⣛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣸⠀⠉⠉⠀⠀⠀⠘⣶⣿⠙⢦⣀⣀⡼⠃⠀⠀⠟⠁⠀⠀⢠⣾⠀⠀⣸⢇⣿⠏⣀⣀⡴⠞⠋⣘⢸⣶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡳⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠓⠾⠃⢸⣿⠴⠛⠁⠀⢐⠚⢳⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡗⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣦⡀⠀⠀⠀⣤⠖⠋⠉⢲⠀⠀⠀⠀⢀⡴⣿⠁⠀⠀⠀⠀⠈⢁⡼⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢿⣔⣴⢤⣝⠦⣤⡤⠞⢀⡀⠀⣀⡬⠞⠁⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠄⠀⠠⡇⠀⠈⢻⣖⡖⠋⠉⣹⠋⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⣀⣰⠟⣦⣀⣠⣇⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠤⠖⠓⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣄⣁⣼⠀⠘⣌⣁⡼⠇⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠊⠁⠀⠀⡦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⢲⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡞⠁⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡾⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠓⢢⡄⠀⠀⠀⠀ ⠀⣷⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀ ⠀⠈⢧⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢗⣷⠀⠀⠀ ⠀⠀⠀⠑⢄⠀⠀⠀⠛⠒⠢⠤⠖⠛⠉⠀⠀⠀⣀⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡼⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠢⢤⣀⡀⠀⠀⠀⠀⣀⣤⠴⠚⠁⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣒⣦⣤⣤⣤⣤⣤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⢄⣀⡤⠤⡒⣋⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢙⣓⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚。⋆୨♡୧⋆ ˚。⋆
⠀⠀⠀⠀⢳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⠈⢵⣦⡤⢄⣀⠀⠀⠀⡀⠈⢦⡈⠉⠐⠒⠤⠂⠀⠀⠀⠙⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢇⠀⠈⠓⢄⡈⠉⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠤⠐⠦⠐⠒⣉⠅⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠜⠁⢀⠎⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠱⡀⠀⠀⠐⢤⣀⠤⠒⠉⠀⠀⠀⠀⠀⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡰⠃⠀⢠⠎⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠈⢆⠀⠘⡄⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀ ⠀⠀⠀⠀⠀⣠⠎⠀⠀⡜⠁⠀⢠⠃⠀⠀⡞⢀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠘⡄⠀⠘⡄⠀⢣⠀⠀⠘⣄⠀⠀⠀⠀⡸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠔⠀⡸⠀⡀⢠⠃⠀⠀⡜⠀⢸⢠⣿⠀⠀⠀⡀⠀⠀⠀⠀⢣⠀⡀⢱⠀⠀⠸⡀⠈⢇⠀⠀⠈⠆⠀⠀⢠⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠇⡰⠁⠃⠀⠀⢰⠁⢀⣏⢸⠇⠠⡀⠀⡇⠀⢠⠀⠀⢸⠀⢸⠈⠀⡆⠀⠁⠀⠘⡄⢀⠀⢸⠀⢠⠧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡰⠃⢠⠇⠀⠀⢰⠀⠀⢀⣎⣿⣾⡆⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⡀⠀⠀⠀⢡⠘⡄⡀⠐⠃⡀⢣⠀⠀⠀ ⠀⠀⠀⡀⠔⠋⣀⠀⡜⠀⠀⠀⢸⠀⠀⡟⠀⢸⡇⢏⠙⣿⢆⠀⠀⠀⡆⠀⠀⢠⣿⣇⣰⠀⠀⠀⠀⠀⠀⠀⣧⠹⡀⠀⠈⢳⠇⠀⠀ ⠀⣀⠤⠀⡲⠟⢁⢴⠃⣴⠀⢠⢸⡀⣰⣁⣀⣸⠀⠘⡄⢹⠈⢆⠀⠀⡇⠠⢒⣿⣿⣿⠿⠲⣧⡀⠀⠀⠀⠀⡏⡄⢣⠀⠀⣈⢆⠀⠀ ⠠⣤⣚⠉⠐⠊⠁⠀⢸⢹⠀⠸⣸⣿⣿⡏⠹⢻⣶⣄⢱⢸⠀⠈⢢⡀⠃⢠⠎⢸⣹⠃⠠⠠⠁⠀⢀⠀⢰⠀⡇⠁⠈⠳⢄⡈⠙⣧⠀ ⠀⠀⠀⠉⠉⠀⠀⠀⡞⠀⠀⡇⠹⡟⢿⡁⠀⢄⡇⠋⠀⢻⠀⠀⠀⠳⣼⣃⣼⣿⡟⠿⣿⣶⡄⠀⢸⠀⠀⠀⡇⠀⠠⠤⠤⠬⣁⡬⠧ ⠀⠀⠀⠀⢀⣾⣴⠞⠁⡀⠀⢣⡀⡿⠠⢍⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⢹⡋⠘⠠⣿⠙⣿⠀⠘⠀⠀⣀⠇⠀⠀⠀⣠⡾⠁⠀⠀ ⠀⠀⠀⠀⠰⠾⠥⠤⢴⡇⠀⠈⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠦⠾⣧⣾⠋⠀⢠⠃⢠⠛⠀⠀⣀⡭⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⠍⠀⢂⢃⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠃⠀⠀⡎⡠⡎⢠⠀⠉⢓⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠸⠘⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠇⡴⣁⡜⢠⢃⣧⣏⠀⠀⣀⣙⡧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⡇⣀⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣎⡜⡰⠻⣡⢷⣜⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢱⣃⠼⣽⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠞⡿⠁⡔⢹⡇⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠀⠙⠂⠀⠀⠀⠀⠀⠀⣀⣤⡖⠉⣸⢋⡜⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠦⠤⠔⠒⠉⠸⠀⢸⡀⠀⠀⠀⠀⠀⠉⠀⡼⣤⣼⣁⡜⠂⠤⢧⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠣⣈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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୨୧ ゚+。:.゚ヽ(*´∀`)ノ゚.:。+゚
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠢⠀⠂⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠠⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⢄⡙⢤⢞⡔⠁⠀⠀⠀ ⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢀⣳⡄⠉⠀⠀⠀⠀⠀ ⠀⠃⠁⢦⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⣋⠴⠞⡌⢪⠢⡤⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⡇⠀⠀⠀⠀⢠⠀⠀⡟⣁⡠⣶⢰⠈⢧⢰⡄⣀ ⠀⠀⠀⠀⠀⠀⢠⣴⠞⠁⠀⡄⠁⡦⡄⠀⠀⢸⠀⣤⠃⢿⡴⠇⣟⠀⢙⣧⢇⠀ ⠀⠀⠀⠀⠀⠀⠘⡅⡀⠀⢸⢧⠘⢱⣇⡀⠴⠩⠞⠏⠀⣴⡶⣶⢫⡄⠀⠣⢈⣂ ⠀⠀⠀⡀⠀⠀⠀⠐⣵⣄⣾⢈⣦⣴⢬⡄⠀⠀⠀⠀⢸⣾⡇⠛⠘⢃⠀⢀⡿⠀ ⠀⢀⠀⢡⠀⠀⠀⠀⠘⢅⣱⣿⣩⣷⡄⠀⠀⠀⠀⠀⠀⠙⠃⠡⡈⢺⡧⠚⠀⠀ ⢀⠆⠀⠀⠆⠀⠀⠀⠀⠀⠙⠿⡯⠠⠧⠂⠀⠀⠀⠀⠀⠀⠀⢀⠣⡀⠀⠑⠢⢄ ⠊⢀⠀⠀⠈⠄⠈⠢⡀⠀⠀⠀⠈⣲⠀⠀⠀⠀⠀⠀⠐⠀⠀⢅⡀⠀⣁⣒⣤⡀ ⠀⠈⠀⠀⠀⠈⣶⢦⢈⠒⢆⠙⠠⢄⡁⠢⡤⠤⢀⡠⠴⢦⣤⣆⢒⠉⠀⠑⢕⡾ ⠀⠀⠀⠀⠀⠀⠈⢦⠀⠈⠒⢌⠢⢀⠀⠉⠒⠓⠦⡧⢒⡺⠀⠀⠂⣈⠢⠀⠈⠀ ⠀⠀⠀⢸⡀⠀⠀⠀⠑⢠⠮⢍⣊⠀⢡⣂⡄⡀⠀⠈⠙⢖⡭⣐⠢⢠⠘⠃⠁⠀ ⠀⠀⠀⠈⢷⡀⠀⠀⠀⠘⠀⠠⠄⡕⠁⠀⠈⠉⠓⢦⢄⡀⠈⠲⡈⢦⡁⢢⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀ ⠀⡆⠤⠤⠤⠀⠂⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣡⠖⠀⠁⠀⠀⡠⠃ ⠀⠱⡀⠠⡀⠀⠀⠀⠀⠀⠐⠤⡒⡒⠒⠒⠒⢀⠁⠁⠀⠀⠀⢀⠔⠁⠘ ⠀⠀⠑⡀⠀⢁⡴⠆⠀⡐⠉⠢⡀⠑⢌⠉⠉⠩⡁⠢⡀⠀⠐⣧⡄⢀⠃ ⠀⠀⠀⠈⠠⡸⠀⠀⡠⡇⡇⠀⠘⢄⡀⠁⠂⠤⣐⢌⡺⠀⠀⠹⢇⠎⠀ ⠀⠀⠀⠀⠠⠁⢀⠔⣡⡄⢇⠀⠀⠀⠩⠂⠄⠀⠀⠀⠨⢃⢄⠀⢋⠀⠀ ⠀⠀⠀⠀⡗⠒⡳⠈⢸⣡⣌⣆⠰⡀⢀⢣⣀⣢⣀⠀⡠⡀⢩⠉⠘⡄⠀ ⠀⠀⠀⠀⡇⢀⢇⠀⣾⣤⢤⣄⡑⢵⡀⢎⣵⡀⢂⠀⢈⠘⢺⠀⠀⠏⠄ ⠀⠀⠀⠀⡇⢸⢸⣆⢳⡙⠪⠿⠂⠀⠙⠚⠻⠿⢾⠀⠌⢀⠞⡄⠀⠰⢸ ⠀⠀⠀⢴⠁⠸⠀⠘⠗⢧⡀⠀⠀⠀⠀⠀⠀⠀⠂⡞⣠⠘⠀⢡⠀⠀⠘ ⠀⠀⠀⡿⠀⠀⠇⠀⠘⣨⢅⠀⠀⠀⠀⠀⠀⠀⢘⣯⠣⢷⠀⢸⡄⠀⠀ ⠀⠀⢀⣷⠀⠀⠈⠄⠀⠁⠲⢵⠀⡀⠀⠀⡀⢴⠏⠁⠀⠀⠀⡼⠁⠀⠀ ⠀⠀⠸⡇⠀⠀⠀⠈⠢⠀⠀⢸⠀⠈⠀⠈⠀⢸⠀⠀⠀⡠⠊⠀⠀⠀⠀ ⠀⠀⠀⠐⠄⡀⠀⠀⠀⠈⠲⡃⠀⠀⠀⠀⠀⠀⠐⡠⠊⠀⠀⠀⠀⡠⠊ ⢀⠠⠐⠂⠈⠈⡀⠂⢠⠀⡀⠐⡄⠀⠀⠀⠀⡠⠊⠀⠀⢀⠄⠖⠈⠂⠠ ⠁⠀⠀⠀⠀⠀⠈⠂⠀⠑⠀⠁⠒⢄⣀⡠⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢍⠉⣩⡞⠋⠠⠃⠀⢻⠐⠲⠀⠀⠀⠒⡊⠁⢀⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⠏⢠⠀⡆⠀⠀⠈⠈⠀⠙⢄⢄⠀⠐⢀⠎⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⡺⢁⢃⡆⠐⠓⡀⠀⡁⡀⠀⢂⠢⠡⡡⡠⠉⠀⠈⠈⡄⠀ ⠀⠀⠀⠀⠀⠁⡙⠀⠂⣆⢡⠂⠘⢧⣀⡧⣀⡤⠤⠈⠁⢰⡱⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⢇⡛⢸⣆⣑⣓⢆⣤⠟⣉⣉⡑⢲⡄⠁⠈⠡⢁⠀⠀⠀⠨⠄ ⠀⠀⠀⠀⠀⠀⠘⡇⠘⣿⠿⠗⠋⠁⠘⣿⠿⡏⠿⣷⠀⢀⡇⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⢣⡆⢚⠀⠰⠀⠀⠀⢄⠀⠅⢤⡇⠀⢸⢡⢄⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠦⢺⠌⠀⢢⠀⡔⠒⡄⠀⠀⣠⠾⠁⠂⡶⠘⠢⡀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡫⡢⡯⠁⠒⠤⠤⡔⢪⠏⠜⠁⣬⠏⠉⠀⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⡠⠊⠪⣂⠁⢀⡴⡷⡫⢾⣡⠞⠁⠀⠀⢀⣰⠋⠀⠀⠀ ⡀⠀⠐⠲⠖⠈⠀⡔⠀⠀⠀⣘⢍⠪⣊⡴⠗⠋⠀⠀⠀⡀⠔⠁⠀⠈⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⣌⢠⡄⠶⠙⢸⡤⠞⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢂⠀
⣀⠴⠊⠉⠉⠁⠀⠀⠀⠀⢀⣀⣠⣭⣷⡶⡖⠛⣍⠉⢱⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠿⣿⡋⠉⠑⠃⠽⠫⢤⠖⢳⡀⠀⠀⠀ ⣤⡰⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠰⡷⢂⠠⣱⠀⠀⠀ ⡸⠀⠀⢸⠀⠀⠀⠀⠀⠒⡦⢤⣀⠀⣴⡦⣀⡈⠓⢄⡹⠀⠙⡅⠀⠀ ⡇⠀⠀⢸⠀⠀⠀⠀⠀⢸⠴⢋⣠⣿⣿⣿⣿⣿⠟⠀⠙⡄⠀⢱⠀⠀ ⠁⠀⠀⢸⠳⡄⠀⠱⡄⢿⣿⣿⠛⢿⣇⠈⣿⣿⣿⠂⠀⡇⠀⢸⠀⠀ ⠀⢠⠀⠈⡇⠈⢢⡀⠹⡜⣿⠇⠀⠈⣻⠿⠟⠉⢇⠀⠀⠇⡀⢸⠀⠀ ⢸⠸⡇⡀⣇⠀⠀⠙⢦⡹⡇⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⡇⡞⠀⠀ ⠈⡆⣧⡇⢸⠀⠀⠀⣀⠑⢿⡄⠀⠀⠀⠔⠀⠐⢀⡇⢸⠀⣗⣇⠀⠀ ⠀⣇⡿⣸⠘⡄⠀⠸⠿⠗⠀⠁⠀⠀⠀⠀⠀⠀⣼⠇⣸⠀⡟⢿⣆⠀ ⣰⢿⢳⣿⡆⢧⠀⠀⣰⢦⣀⣀⠀⠀⠀⠀⠀⣸⢿⠀⡟⠀⡇⠀⠹⠆ ⠀⢸⡀⢻⣷⣸⡀⠘⠃⠀⠀⠉⠀⠀⠀⢀⣴⢻⡸⢀⡇⢠⠇⠀⠀⠀ ⢤⠀⠳⣄⡻⣬⣧⡀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣤⣿⣽⢠⠏⠀⠀⠀⠀ ⣠⡳⣄⡀⢽⣶⣭⡉⠛⢳⢶⠶⠾⡯⢠⠀⡔⣇⡋⠾⠁⠀⠀⠀⠀⠀ ⣧⠟⠮⢿⣕⣚⣛⠬⢎⡙⠹⠭⠭⠋⠙⠉⠋⣃⠜⠂⢄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣖⠒⠋⠉⠉⠉⢉⣩⡷⣫⠟⠉⠀⣴⠋⠀⠀⠘⣯⡒⠢⢄⡤⣀⡀⠀⠀⠀⠀⠀⠠⣤⠤⠤⠟⠛⠉⠁⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢀⣴⣿⣫⠶⠃⠀⠀⣰⠃⠀⠀⠀⠀⢸⡙⣄⠀⠙⢦⡙⠢⣀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠀⠀⣰⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣴⣿⡿⠋⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⡇⠈⢦⠀⠀⢿⢦⡈⠳⣄⠀⠀⠀⠀⠙⡄⠀⠀⣴⡇⠘⡷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⢁⠀⢰⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢧⠙⢦⡈⠳⡀⠀⠀⠀⠀⠀⣴⠋⠀⠀⡇⠘⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠃⢰⠏⢠⡏⡄⠀⢠⠋⣧⡀⠀⠀⠀⠀⣦⠀⠀⠀⠈⢧⡀⠈⢣⡀⠙⣄⠙⢆⠀⠀⢀⡼⠋⠀⠀⠀⣇⠀⠈⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢛⡥⠊⢠⠏⢀⣾⠁⡇⠀⢸⠀⣇⣇⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢳⡀⠈⢟⣄⠈⢣⡈⢣⡠⠎⠀⠀⠀⠀⠀⠸⠀⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣛⡥⢶⠋⠀⢀⠏⢀⡞⠈⡇⢃⠀⢸⠀⢸⡼⡄⠀⠀⢠⣿⠀⢇⠀⠀⠀⠀⢧⠀⠸⡌⠄⠀⢳⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡾⠀⣸⡀⠀⢱⡈⡇⠸⠀⣸⠹⣽⣄⢀⣾⡟⢦⣸⠀⣤⡤⠖⠘⡆⠀⢳⠀⠀⢠⢧⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣰⢠⠃⢠⣿⠙⠲⣄⣳⣿⣀⢀⡇⠀⠈⢻⣿⡾⠤⠴⠿⠛⡿⣽⡠⡀⣻⠀⠈⡆⠀⠘⣏⣇⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡟⢾⠀⢸⢻⡄⢀⣀⡉⠉⠻⡿⠀⣀⣴⣿⠟⠁⢀⣀⣀⡄⢀⠁⠳⡕⣼⡄⠀⢳⠀⠀⢹⠘⡆⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣿⣷⠀⠀⠘⣦⣿⣿⣿⣿⣗⠰⠡⢔⡵⠟⠁⣶⣾⣿⣿⣿⣿⣿⣷⣤⣼⡇⣇⠀⢸⠀⠀⢸⡄⢸⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢨⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⢻⣿⠺⣿⣿⣿⠓⠚⠉⠀⠀⠐⠛⢿⣿⣿⡟⡿⡇⢸⡟⠁⣗⣿⠀⢸⠀⠀⢈⡇⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣆⠀⠀⢿⠃⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠈⣠⡁⠀⠀⢸⠁⣿⠀⠘⠀⠀⣿⣷⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣷⢹⡄⠈⣿⠀⠀⠀⠲⣴⠄⠀⠀⠀⠀⠀⠰⣄⠑⢄⠠⣀⠢⡀⡞⣰⡇⠀⠀⠀⢀⣿⣸⡆⡞⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢻⡳⣷⡀⠘⣄⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠈⠳⢤⠀⠀⠀⢨⣷⢿⠇⠀⠀⠀⢸⡟⠹⣿⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣥⠴⣾⢣⠀⠳⡀⠹⣆⠀⠀⠀⣤⠶⠿⠿⢦⡀⠀⠀⠀⠀⠀⠀⣀⡾⠃⡞⠀⣰⠂⠀⣿⠃⠘⠟⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⡦⣷⡀⠈⢦⣌⣳⣄⡀⠻⠅⠀⠀⠠⠇⠀⠀⠀⠀⣠⣶⡟⠁⡼⠁⡴⠁⠀⡼⣿⣄⣀⠀⠀⠙⢦⣀⣀⠀⠀⠀⢠⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢁⡷⣄⠘⣆⠀⠀⠉⠒⠦⢄⡀⠀⠀⣀⣤⠖⠋⣡⡾⠁⡼⢡⠎⠀⠀⡼⣱⣯⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⣰⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣣⠋⠻⣌⠳⣿⢣⡀⠀⢳⠀⠀⠈⠉⠉⢸⡄⢀⡼⡿⢁⠞⡁⠀⠀⠀⣼⣟⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⡴⠋⠳⣤⡉⠳⡄⠈⣇⠀⠀⠀⣀⣾⡷⢋⠞⣠⡿⡾⠁⢀⡴⣺⠕⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟⠁⠀⢠⠞⠀⠀⠀⠈⠻⣦⣹⣀⣘⣠⠴⢚⡿⣫⠔⠡⡾⠉⣴⡧⣶⠝⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡮⠥⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⡤⠔⠒⠒⣒⣶⠖⠋⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠹⣧⠈⢉⣴⢞⣡⡞⠁⣠⣾⣴⡾⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠠⠀⠀⠁⠤⠐⠒⠒⠋⠁⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⠀⠀⠀⢀⣠⢷⣛⣩⠖⢋⣠⣴⡾⠟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢀⣈⡧⢖⣪⠥⠒⣻⡇⢀⡴⣪⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠤⠖⢒⣯⠭⠒⠋⠁⠀⠀⢀⣿⢖⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀
⠀⠀⠘⡢⢄⣀⠀⠀⠀⠠⡠⠄⢀⣀⡀⠈⢦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⠈⠑⠌⠐⠒⠋⠈⠁⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⢀⡠⠀⠀ ⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢁⠔⠁⠀⠀ ⠀⠀⠀⠀⠠⠀⡠⠂⡠⠁⡐⠀⠀⠀⠀⠀⠀⠐⡈⠢⠀⠀⠢⡈⠀⠀⠀⢸⠀ ⠀⠀⠀⠔⠁⡐⠀⡐⠁⠰⢠⢰⠀⠀⠀⠀⠘⠀⠰⠀⢡⠈⡀⠈⢆⠀⠀⠆⠀ ⠀⠀⠀⠀⡠⠡⠐⠀⠠⠁⠌⡿⢀⠘⠀⠀⠀⠇⡇⠂⠀⠀⠰⢠⠈⠀⠼⠀⠀ ⠀⠀⠀⠀⠀⠆⠀⢸⠀⡞⢺⢳⢼⡄⠀⢠⠀⢀⣧⢸⢰⠀⠀⠃⡖⡈⠐⠵⠀ ⠠⡀⢔⠡⠘⣰⠀⢸⣴⡤⢼⡈⡌⠈⢄⢸⠐⢜⢿⠛⡒⠄⠀⡀⡷⠰⡀⠘⡄ ⠀⠁⠀⠀⢀⢣⢰⠹⡻⣉⣤⠙⠐⠆⠀⠢⣮⣾⠓⣶⣆⠀⠀⠁⡇⠀⠈⣁⠜ ⠀⠀⠠⠟⠥⡼⠀⣦⠇⠁⠀⠀⠀⠀⠀⠀⠀⢳⠥⠮⡞⠀⠄⡐⠀⡀⠞⠁⠀ ⠀⠀⠀⢰⡞⠀⠏⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡄⡘⡔⡱⠀⠑⣆⠀⠀ ⠀⠀⠀⠀⠈⠁⠸⢤⢘⢄⠀⠀⠀⠀⠀⠀⠀⠔⣑⢌⢚⣜⢼⡏⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢁⠇⠑⠀⠀⠀⢀⠠⡔⠪⠣⠂⠀⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠘⠀⠀⠀⠀⠸⡹⠗⠁⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣀⠠⠤⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⠠⠴⠊⠀⠀⠀⠀⠈⠐⢄⢀⢊⣃⠀⠀⠀ ⡞⠋⠍⡉⠁⠀⠀⠀⠀⠀⡠⠂⠀⢀⠄⠀⠄⡙⢅⢚⠄⠀⠀ ⠸⡀⠀⡊⠁⠀⠀⠀⠄⠀⠀⠀⡐⠁⠀⠀⠀⠈⠄⢢⠃⠀⠀ ⠀⢣⢠⠃⠀⠀⣔⢀⠀⠀⠀⠉⠁⠈⡀⠀⢀⠀⠈⡌⢄⠀⠀ ⠀⠀⠹⡦⠀⢰⠀⢸⠀⠀⠈⡄⢔⠀⠃⠀⣠⢤⣤⠴⠄⡞⠁ ⠀⠀⡠⠃⠀⢀⠀⡘⡀⠀⢢⢿⡿⢄⠗⠁⢹⣯⠾⠀⢰⠁⠀ ⠀⠪⢀⠀⠀⠘⡐⠊⠘⢄⡏⠸⣿⣿⡄⠀⠀⠛⡃⢆⡎⠃⠀ ⠀⠀⠀⠚⡥⠀⠣⡠⢄⣲⡈⠀⠉⠁⠀⢠⡊⠉⡩⢚⢆⠤⢄ ⠀⠀⠀⠀⠈⠁⠀⢹⡠⢌⢴⡤⢀⠀⢀⡞⢖⠊⠀⡹⣈⢪⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣮⣸⡏⠑⢦⣌⣦⡑⠄⠰⠃⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⠈⢻⣿⠀⣃⣠⣏⠂⠀⠘⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣿⣿⣾⣿⢇⠀⠀⠰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⣿⡟⠠⠃⢠⠁⠀⠀⠀⠀
⠀⠀⠀⠀⡠⠞⠁⠀⡀⢀⠀⣰⠏⠤⢿⡇⠈⠉⠛⠿⣟⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠖⠁⠀⠠⠐⠀⢠⡼⠃⠀⠀⢸⢇⡀⠐⢠⠀⠈⠑⠿⣦⡀⠀⠀⠀⠀⠀ ⠀⣠⠋⠀⠀⠌⢀⣀⡤⠿⢤⣀⣀⣠⠞⢈⡇⠀⠈⡷⠀⢀⠀⡉⠙⠛⠓⠶⠢⠦ ⣶⠁⠀⠄⠈⢀⡖⠋⢀⠂⣀⠈⣹⠃⠀⢸⡇⠀⠀⠸⡇⢠⡀⠐⢆⠀⠂⠀⠄⢀ ⡇⠀⢀⠂⣠⠟⠀⠐⠀⢀⡤⢲⡟⠀⠁⣿⠇⠀⠂⠀⣿⡄⢳⡀⠈⢷⡤⠖⡚⠉ ⠐⡤⢂⢠⡏⢀⠈⠐⢈⡼⣡⣿⣃⡀⣼⢫⡇⠐⠂⠀⣹⡽⣄⠹⣆⠈⣇⠀⣰⣾ ⢆⡀⣼⡟⠀⠀⡐⠈⣼⠧⠟⢧⣔⣻⠁⠸⣅⡀⠂⠀⣹⡇⠈⣧⣌⠳⣼⣴⠋⠘ ⢀⡼⡟⠀⡀⠁⢀⣺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡾⣟⣷⠀⡗⢸⡑⣿⣿⣦⣀ ⢊⣼⠇⠐⢀⠈⣴⡟⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣼⡇⠸⡇⣳⣿⠏⠀ ⢣⢾⡅⠂⠠⢘⣿⠻⢶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⡐⡇⢿⣿⠀⠀ ⢣⢚⣧⡀⢁⠸⣿⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠⣶⣷⣶⡋⣱⢞⣻⡇⠀⢸⣿⠁⠀ ⢣⢇⠞⣿⣄⠈⣿⢣⣄⠀⠀⢶⣦⣀⡀⠀⠈⠀⠉⢈⣿⣿⡎⣥⡟⠀⣴⣻⠀⠀ ⢣⢎⠽⣠⣿⢷⣸⡏⠉⣹⠶⣤⣬⢿⡽⣦⣤⡶⣴⣾⣿⣿⣣⡟⣃⣰⣿⡿⠀⠀ ⢣⢎⣳⡿⣽⢯⣟⣷⡀⣹⣋⣽⣯⢿⡽⣯⢷⡿⣽⣻⢿⣿⣿⣼⠿⠛⠉⠀⠀⠀ ⣧⣾⢿⡽⣯⡿⣾⣽⢿⣿⣿⣿⢯⡿⣽⢯⡿⣿⣳⢯⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣰⠶⢤⣍⡛⠶⣤⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣠⠶⠛⣩⡤⠶⢦⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡇⠀⠀⠈⢙⣶⠀⠉⠙⡏⢹⣿⠀⣿⣿⢀⡿⠉⠉⠀⢶⣏⠁⠀⠀⠈⡏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣧⣤⠴⠚⠉⠀⠀⠀⠀⠳⠾⠘⠶⠃⠻⠞⠁⠀⠀⠀⠀⠈⠙⠲⢤⣠⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢠⣶⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣄⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⣷⢀⣤⡶⠶⡶⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⢠⡇⠀⠟⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠛⠛⠓⣻⡟⠁⢻⡄⠹⡆⢻⡆ ⠀⠀⠀⠀⠀⠀⢸⡇⠠⠶⠚⢛⣻⡁⠀⠀⠀⢰⣄⠀⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⣠⡀⠀⠀⠀⢹⡛⠛⠲⠶⢸⣧⠀⣰⣇⣰⡇⣸⡇ ⠀⠀⠀⠀⠀⠀⠘⣇⠀⠶⠟⠋⠉⠀⠀⠀⠀⠀⠙⠛⠓⠛⠉⠁⠀⠉⠙⠛⠒⠛⠛⠁⠀⠀⠀⠈⠉⠛⠷⠆⣼⠏⠉⠉⠉⠙⢿⡋⠀ ⠀⠀⠀⠀⠀⠀⠀⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⣀⣿⣿⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⣯⣽⠏⠀⠀⠀⠀⣾⠁⠀ ⠀⠀⠀⠀⣠⠾⠋⠈⠻⢾⣎⣟⣻⣶⣶⢤⣤⣤⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣶⠾⣟⢻⣥⡿⠟⠁⠀⠀⠀⠀⣼⠃⠀⠀ ⠀⠀⠀⣰⠏⠀⠀⠀⠀⢰⢿⠟⣏⠀⢹⠛⢧⣼⣅⢿⣩⠿⠛⠻⣿⣏⣹⡉⢹⣈⣷⣨⣧⡼⠷⠛⠋⠁⠀⠀⠀⠀⣄⠀⡼⠃⠀⠀⠀ ⠀⢀⣰⡏⠀⠀⠀⠀⠀⣿⣸⣆⣻⣤⣿⣀⡏⢹⡝⢿⡇⠀⠀⠀⠈⢻⠈⠙⢿⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠃⠀⠀⠀⠀ ⠀⡿⣅⣇⠀⠀⠀⠀⠀⠘⠿⣤⠖⠛⢠⠟⠉⠛⢷⣜⣧⡀⠙⡟⣠⡟⢰⡶⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀ ⢀⣷⡙⢿⡀⠀⠀⠀⠀⢀⡀⢮⣷⡞⠛⠆⡞⠙⠻⣈⣷⣙⠛⠛⠛⠦⢼⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀ ⠸⣿⠓⢮⣿⣄⠀⠀⠀⠀⠙⢶⣼⡧⡞⠉⣻⣶⣿⠟⠛⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⢿⠶⠶⣏⣟⠳⣦⣄⣀⣀⣴⣿⠶⢛⣾⡿⠋⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀ ⠀⠈⠳⣤⢿⣹⠆⢸⠇⣉⣯⣵⣗⡶⣾⣿⢷⣶⣦⠀⠀⣠⡴⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⢿⡄⢸⠞⢉⣁⣤⣬⣽⣿⡇⠈⠋⠁⠀⣸⠃⡴⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⠞⠉⠁⣠⠖⢛⣯⣷⠀⠀⠀⠀⣯⠸⣇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣼⠁⣠⣾⡛⢮⣳⣄⣠⣤⠞⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠳⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠒⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢀⡤⠤⢄⠈⠙⠷⣦⣀⡀⠀⠀⠀⢀⣠⡴⠞⠋⢀⡠⠤⢄⡈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡰⠋⠀⠀⠀⣱⡀⠀⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⢠⡏⠀⠀⠀⠙⡄⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢰⣁⠤⠐⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⢤⣸⡄⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣠⣤⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠉⠻⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠖⠛⠂⠀⠀⠀⠈⢿⡄⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠰⠖⠛⠻⢿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠟⠛⠶⠄⠀⠀⠀⢿⣤⠤⠂⠀⠀⠀⠀⠈⢿⡀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣀⣀⣀⠀⠀⠀⠸⣧ ⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢀⡀⠐⠤⣀⠀⠀⠀⣤⠖⠒⠲⡄⠀⠀⠀⣀⠴⠂⢀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⢕⣦⠀⠙⠲⣤⠖⠁⠀⣶⠯⠄⠒⠉⠁⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⢈⣷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢆⡀⢀⣿⠀⢀⡄⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇ ⠀⠀⠀⠀⠀⣠⡾⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀ ⠀⠀⠀⠀⣴⠟⠀⠀⠀⠙⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀ ⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣒⡒⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⢒⣲⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀ ⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⢶⡦⠤⢤⣤⡤⠤⢴⠶⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀ ⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠲⠤⢀⣀⣠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⡰⠁⠀⢀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣷⡇⠀⠀⣧⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢻⣦⣤⣽⣦⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣄⠀⣀⡤⢤⡶⠦⣼⢷⣄⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⡾⣦⠶⣦⠤⣄⣀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⢧⣤⣤⣨⣦⣬⣷⡿⠷⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠳⠶⢦⣤⣴⣯⣼⣀⣼⣃⣀⣠⡼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣄⠖⡚ ⠀⠀⠀⠀⠀⠀⠀⠠⣶⠤⢀⡩⠛⠛⠻⡛⠉⠷⠒⠉⠁⡠⠊⠀⡞⠀ ⠀⠀⠀⠀⢀⠤⠒⠉⠀⢀⡞⠁⠀⠀⡰⠀⠀⢠⠂⠀⠰⢔⡀⠰⠀⠀ ⠀⠀⣠⠞⠁⠀⡐⠀⠀⡜⠀⠀⠀⠀⡇⠀⠀⡌⠀⠀⢆⠀⣠⠁⠀⠀ ⠠⠊⣥⣐⣒⣸⡁⠐⠀⠃⠀⢀⠀⣰⣇⠀⠀⠀⢸⠀⠀⢃⢡⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⢠⡄⠀⢈⠀⣷⠘⣆⣀⣄⡘⡇⠀⠘⠸⡇⠀⠀ ⠀⠀⠀⠀⠀⣯⠀⡀⣇⢱⡀⠘⠀⡇⠈⣩⣄⣀⡈⢻⠀⡗⡄⣿⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⣏⣷⣴⣷⡀⢃⣇⠉⠁⡾⣿⢯⢻⠀⡷⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⣧⢧⢨⣷⠜⠿⠏⠈⠾⠄⠀⠈⠉⠀⢸⢸⢳⠀⣽⠀⠀ ⠀⠀⠀⠀⠀⡿⠀⢎⢛⣃⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⢸⢀⣧⢹⠇⠀ ⠀⠀⠀⠀⣸⠃⠀⢸⠞⣦⢣⣀⠀⠀⠀⠐⢀⣴⡿⡀⡇⢘⠟⡈⡸⡄ ⠀⠀⠀⠀⠁⠀⠀⠈⢸⠈⡆⢦⠉⢐⡦⠴⠛⠁⢠⣥⠅⠞⣣⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢰⠸⡸⠔⠁⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡁⡤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠠⠄⠐⢒⣲⣖⠀⣤⣀⣀⠀⠠⠀⣀⣀ ⠀⠀⠀⠀⠀⡝⠓⠒⠠⢀⠉⠁⠀⠚⡃⢔⠠⠘⠻⠿⡓⢛⠅⡠⡒⠉⠀⡜ ⠀⠀⠀⠀⠀⠐⠄⠀⠀⢰⢖⠒⠒⠊⢠⠁⢀⡔⠁⠐⡈⢄⠈⠈⡙⠠⣔⠀ ⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⡌⠁⢀⡆⢠⢃⠀⠀⠀⡍⠢⡥⡀⠘⡏⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⢠⠁⡠⣼⢄⠀⣿⠿⠟⡾⣀⠀⣴⣷⣤⣥⠀⠢⣓⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡀⡋⠋⠂⠡⣿⢄⡀⠇⠹⠊⢀⠃⡸⡿⣀⠤⢛⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⡇⠀⠀⠀⢹⣅⠀⢠⠄⢢⠀⠉⣴⠋⠁⠐⡸⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠰⠈⢹⠉⢿⠓⡰⠈⠀⠀⡠⠊⠀⠀⠀ ⠀⢀⠄⠒⡂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠭⠇⠫⠕⠀⢀⠎⠀⠀⠀⠀⠀ ⠠⠁⡠⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⡀⠀⠀⠀ ⢣⠀⢄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀ ⠀⠁⢀⠑⠂⠀⠂⢈⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠂⠀ ⠀⠀⠀⠈⠀⠀⠈⠁⠀⠈⠢⡀⠀⠀⠀⠀⠀⢀⠠⠄⠖⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠰⠦⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠶⠒⠚⠉⠉⠉⠉⠉⠉⠙⠒⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣔⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠤⣄⣠⠤⠒⠚⠉⠁⠀⠀⠀⠀⠉⣽⣿⠀⠀⠀⠀⠀ ⠀⠀⢿⡏⠙⠒⠲⠶⠶⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢸⠀⠀⠀⠀⠀ ⠀⠀⠘⢧⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠴⠚⣩⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⠈⣦⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠲⣤⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣇⠀⠀⠀⠙⠳⠦⢄⣀⣀⣀⣀⠀⠀⠀⠀⢠⡾⡦⣄⠀⠉⠓⢮⣓⠒⠶⠶⠶⠤⠤⠴⠶⠿⠥⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠠⣖⣯⣿⣿⠀⠀⠀⢰⠏⢸⠁⠈⢳⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠐⠒⢄⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠚⣳⣶⣤⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⣶⣋⣧⠀⠀⠀⠀⢠⣿⠀⣸⠀⠀⠀⠹⣄⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠱⣄⠀⠰⣌⢷⡀⠀⠀⠀⠀⣹⣿⣧⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⢀⡾⠋⠀⠀⠀⠀⢀⡾⡿⢀⡿⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠓⠤⢄⣀⣀⠈⠳⣄⠙⢿⣧⠀⠀⠀⠀⠀⢹⣿⠇⢰⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠀⠀⠀⠀⠀⣠⠞⢠⠇⢸⡇⠀⠀⠀⠀⠀⠀⠈⢷⣤⡀⠀⠀⠠⠤⠤⠤⠿⠛⠁⠘⠳⣌⡻⣄⠀⠀⠀⠀⢨⣯⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢀⡴⠃⢀⡾⡀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢳⡙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠙⠻⢄⡀⠀⠀⠀⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⡴⠋⢀⡤⢺⢄⣇⢸⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣉⡲⣤⡀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠿⠵⢶⡞⠉⠀⢸⢸⢸⣼⡀⠘⣆⠀⠀⢰⡀⠀⠀⠀⠀⢷⡀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠘⡌⠉⠉⠉⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡏⠀⠀⠀⣿⣾⡤⠿⣧⠤⠼⣦⣀⠀⢷⡀⠀⠸⡆⠸⣷⣤⣤⣤⣷⣤⣤⡄⠀⠲⣄⠹⣄⠀⠀⢳⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡞⠀⠀⠀⠀⣿⣧⠀⠀⠈⠀⠀⠀⠙⢦⡈⢷⡀⠀⠸⡄⢹⡙⣆⠀⠈⢳⡀⠀⠀⠀⠈⠙⠺⢷⣄⢸⠀⠀⠀⠀⢸⡎⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢶⠛⣷⠀⠀⠀⣿⢿⣿⣛⢛⡟⣻⢶⡦⣄⠙⠦⣳⣄⠀⠹⡌⣷⣼⣦⠀⠀⢷⠀⠀⠀⠀⡞⠀⠀⠀⡜⠀⠀⠀⠀⠈⣇⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⠀⢸⣀⡄⠸⣿⡄⠻⣿⣮⡻⣿⣿⣇⡌⠀⠀⠈⠻⢶⢤⣽⣜⣿⣯⣷⣤⣌⡆⠀⠀⣼⠃⠀⠀⣼⢳⠀⠀⠀⠀⠀⢸⡀⠸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣿⠀⢘⣿⣷⡀⠹⣷⡀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠭⡿⢿⡇⠀⣰⠃⠀⠀⢰⠃⠈⣇⠀⠀⠀⠀⠀⣧⢀⢇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⣿⠀⠈⠋⠙⣝⣄⠹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⣇⢠⠋⠀⠀⢠⡏⠀⠀⢸⡀⠀⠀⠀⠀⠘⢸⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⡿⡆⠀⠀⠀⠹⣎⠳⣝⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠎⢀⣴⣎⢸⠁⠀⠀⠈⣧⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠠⢧⠀⠀⠀⠀⠸⡆⠘⣏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡔⣿⡀⢹⣼⡆⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢹⢀⣬⢷⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣾⣧⠏⠱⣾⣿⣧⠀⠀⠀⡻⣦⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⢿⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢸⠟⠳⡜⡟⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⣻⠟⠿⠀⠀⠀⠀⠉⠀⠀⠀⠇⡿⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⢹⡄⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⢻⡷⣄⣿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢹⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣸⡃⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠈⢻⠀⠈⠑⠦⣀⡀⠀⣀⡠⠞⠉⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠹⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠜⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡠⠴⠖⠊⠉⠉⠀⢀⠉⠓⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣺⠟⠙⠶⠤⣀⡀⠀⠀⠀⠀⠀ ⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠘⢿⡒⠢⢤⣀⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠘⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀ ⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠳⡄⠀⠈⠉⠙⠲⣿⡄⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⣠⠎⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⣠⠎⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⢀⠜⠁⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣰⡯⢶⡇⣀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⢿⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⠏⠀⠀⠀⠀⠀⣼⢁⡀⠠⠤⠤⠼⠇⠀⣼⡋⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⣀⣀⣴⣛⣁⡎⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠈⣢⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⠁⢀⡠⠝⠒⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⣀⣀⣠⠖⠁⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠑⢄⡠⠔⠒⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠚⠋⠉⠁⠀⠈⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠁⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡠⠀⠀⠀ ⠀⠀⠀⠀⣠⣆⡀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢀⠞⠙⢢⣠⢄⡠⠔⠋⡝⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣇⡠⠚⠀⠀⠀⠀ ⠀⠀⢠⡾⠋⠀⠈⠉⢢⣀⡼⠁⠀⠀⠀⢀⣀⣰⣇⡠⠴⠛⠛⢅⠀⠀⡜⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀ ⣀⣴⠋⠀⠀⠀⣀⡤⠞⢻⠃⠀⠀⠀⠀⡍⢻⣿⣿⣶⣄⠀⠀⠈⠆⢰⡷⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⡿⠃⠀⠀⠀⣾⣁⣤⠴⡟⠀⠀⠀⠀⣸⠀⣾⣿⣿⣿⣿⣷⡄⠀⠀⣾⡇⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⣠⣧⠀⠀⠀⠀⠀⠀ ⠉⢓⣶⣄⣰⠁⢿⡟⢸⠇⠀⠀⠀⢀⣿⣾⡿⢌⣉⡽⠟⠹⠇⠀⠀⢻⡇⢠⠁⣿⠀⠀⠀⠀⠀⠀⢠⠀⡼⠀⢀⠂⡟⢹⠀⠀⠀⠀⠀⠀ ⡇⣏⠉⠉⡏⠀⣼⠁⡜⠀⠀⠀⠀⣼⠹⣏⠳⣄⠀⠀⠀⠠⡄⠀⠀⠀⠸⣼⠀⡏⠉⠉⡗⠢⢄⣀⡏⣴⠃⢀⡎⢠⠃⠠⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠺⣅⣴⡇⣠⡇⠀⠀⠀⣀⠇⠀⢿⠀⠀⠙⠢⠤⠴⠛⠦⡀⢀⣴⣿⣷⣷⣤⣼⠃⠀⢀⠟⣿⠃⠀⢸⢀⣎⣐⣒⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⣠⡘⠀⠀⠀⠀⣿⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⡿⢿⣛⣻⣿⠿⢛⣿⣧⡠⠋⡴⢿⡄⠀⡞⡟⠁⢀⣀⣉⡥⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣷⣀⣀⠀⠀⣿⡀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠳⣌⠀⠀⠀⢀⣼⣿⣿⣡⠞⢀⡇⠀⠀⣿⠁⡴⠁⠀⠈⠓⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢿⣷⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣴⣿⣿⣾⡷⠃⠀⠘⣿⠀⢸⣿⡾⠉⠉⠀⠀⠀⠀⠉⠢⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⡈⢇⠙⠶⠤⣄⣀⣀⠀⠀⠀⠀⠀⣀⣤⢾⣃⡤⠟⠉⠀⠀⡄⢢⣿⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⢴⡊⢙⡏⠳⣜⢮⣣⡂⠀⠀⠀⠀⠉⣹⠉⠉⠉⣿⣾⡛⠢⣄⠀⠀⠀⠀⠈⣦⣿⡆⠀⡇⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡈⠟⠋⠉⠉⠳⢽⡻⣶⢄⡀⢀⣴⠵⠖⠀⠀⠀⠀⠸⡀⠙⣇⠀⠀⣠⠞⠁⢹⡇⠀⠃⠀⠸⡇⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢈⣿⠗⠛⠛⢤⣀⠀⠀⠀⠀⠀⠀⠉⣤⠚⣤⠞⠁⠀⠀⠘⣿⡤⠀⠀⠀⣧⡤⠶⣍⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡖⣛⡒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢖⣛⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢹⠁⠈⠙⣦⠉⠓⢶⢻⣿⢹⣿⢓⡖⠒⠋⢡⡞⠉⠀⢱⣳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠸⠤⠔⠊⠁⠀⠀⠘⠾⠙⠞⠙⠟⠀⠀⠀⠀⠉⠒⠤⠼⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠘⠛⠉⠉⠻⠆⠀⠀⠀⠀⠀⠀⠾⠋⠉⠙⠛⠀⠀⠀⠸⡆⢀⣠⣤⣄⡀⠀ ⠀⠀⠀⠀⠀⢸⠀⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠒⠒⣿⠋⢳⡄⢳⠹⡆ ⠀⠀⠀⠀⠀⣹⠐⢛⣉⣭⠄⠀⠀⠰⣦⣀⣀⣠⠴⢦⣄⣀⣀⣠⠄⠀⠀⢸⣍⣉⠓⢽⣤⣼⣥⣾⣤⠇ ⠀⠀⠀⠀⠀⠸⡆⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⢁⣟⠀⠀⠀⠈⡇⠀ ⠀⠀⠀⠀⠀⣰⣿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠀⠀⠀⢰⡇⠀ ⠀⠀⠀⣠⠞⠁⠙⢾⣼⣽⠷⣶⣶⢤⡤⣤⣤⣤⣤⣤⣤⣤⡤⣤⢴⠶⡖⣿⣿⠼⠛⠁⠀⠀⢀⠞⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⣼⢋⢹⡀⡎⢹⢾⣦⣷⠛⠉⠙⢷⠾⢦⡧⠼⠾⠛⠋⠉⠀⠀⠀⠀⠐⣤⠎⠀⠀⠀ ⢀⣾⣻⠀⠀⠀⠀⠹⣟⡭⠟⢹⠟⠾⣆⣻⡀⠰⡆⣸⢤⡄⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⢸⣇⠻⣄⠀⠀⠀⢀⡐⢷⡖⢛⣰⠉⣋⣹⣏⡛⠛⠣⠼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀ ⠘⣇⡙⣿⣦⣀⠀⠀⠉⣷⣟⣇⣨⣿⠟⠉⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠻⣌⣹⣣⠈⡟⢳⣞⣽⣥⣼⣟⣥⡄⠀⢀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀ ⠀⠀⠈⠛⢧⡀⡗⢋⣉⠭⣽⣿⡉⠛⠁⢀⠏⡴⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣏⠁⣠⠖⢹⣿⣇⠀⠀⠘⣄⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠳⠖⠛⠿⠿⣷⣖⣉⣁⣀⣀⣀⣀⣀⣀⣀⣤⠤⠴⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡠⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠲⢄⣀⠤⠃⠀⡠⠁⢀⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⢀⠀⠑⢤⣀⠞⢃⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⢠⠀⠀⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠻⡦⡀⠙⢤⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⢾⠁⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⣀⣽⡷⡆⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡆⠈⠳⢤⡀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣴⠞⠋⣡⣷⠿⡆⠑⡄⠱⣄⡀⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣴⠟⠋⠉⡄⢣⠀⠘⣆⠘⢆⠉⠑⠶⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⠘⡄⠀⣠⣴⣷⠈⡆⠀⠻⣇⠈⣧⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡐⢸⠀⣿⡏⠁⣿⡏⣆⡇⠀⠢⣿⡶⢻⠀⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⡿⠃⠀⠀⠀⣾⢰⠀⠘⡇⣾⠀⠀⠀⠀⢀⣿⠀⢀⣷⡇⠀⠘⠷⠞⠙⢠⡿⡁⠀⠀⣩⡧⠿⢥⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠉⡀⠀⠐⠒⠲⣿⢸⠲⠗⢷⣿⠀⠀⢀⣴⡞⣇⣴⢾⡟⠀⠀⢀⣴⣶⣶⣼⢧⣱⠀⠀⠈⢣⡀⠀⠳⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢱⠀⠀⢠⠀⡇⢿⠀⠀⠘⠘⣴⡖⠋⠋⠀⠉⠁⠀⠀⠀⢠⡿⣿⡇⢹⡿⠀⣿⡇⠀⠀⠀⢹⣶⠄⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣬⣿⣄⢸⣧⡇⢈⣶⣤⣾⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠸⡇⠀⠙⢻⠀⠀⠀⠘⡿⠆⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢿⢯⠻⠏⣷⣾⡿⢿⣏⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡃⠀⡇⠈⢦⢸⣤⠀⢠⡷⠀⠀⠀ ⠀⠀⢠⠄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠣⣠⣼⣿⣿⣤⣾⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠱⡄⠀⢻⣿⠒⠁⠁⠀⠀⠀ ⠀⢀⡎⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣟⠛⠀⢸⣃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⠉⠒⠤⢀⡀⠀ ⢀⡞⠀⠀⠀⠀⠀⢧⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠙⠢⣍⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠑⠢⢄⡀⠀⠀⠀⠈⠑ ⢺⠁⠀⠀⠀⠀⠀⠈⢧⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⡠⠮⡀⠀⠀⠀⠀⣈⣓⣶⣤⡀⠀ ⠀⠀⠀⠆⠀⠀⠀⠀⠀⢳⡤⣀⠀⠙⠦⣀⣀⣀⡠⣶⠒⠈⠉⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠊⠀⠀⠈⢁⡠⠔⠚⠓⢮⡛⢍⢉⣳ ⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡾⠷⠦⢄⠈⠉⠣⡀⠈⠙⠲⠦⣄⣀⡉⠲⣖⠒⠒⣊⣉⡽⠛⠛⠻⣖⣚⣛⡩⠥⣀⠀⠀⠀⠀⠙⢮⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠈⠓⠦⣈⠓⢤⡀⠀⠀⠈⠉⠛⠶⢿⣧⣄⣸⣄⠤⠤⢾⡿⠀⠀⠀⠐⠁⠉⢦⡀⠀⠀⠈⠁⠀ ⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⣈⣔⡊⡉⠒⢄⡀⠀⠀⠀⠀⠀⠉⠒⠯⣕⣒⠺⠅⣀⠀⠀⢀⠔⠢⠤⢱⡄⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠈⠳⠀⣤⠿⢤⡉⠉⣉⠈⠑⠨⣑⠢⣄⠀⠀⠀⠀⠀⠈⠛⢿⣲⣤⣉⠑⠣⢄⣀⠔⠊⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠉⠋⠳⣄⠔⠊⠉⠉⠓⠿⣶⣤⣀⠀⠀⠀⠀⠙⠢⣈⢉⡢⣄⡉⠓⢇⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢯⢦⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠒⠂⢀⡎⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡶⠤⣄⡀⠀⠈⠙⢏⡙⠻⣦⡀⠑⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠀⠒⡲⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠠⠔⡂⠀⠀⠈⠀⠀⠄⣀⠴⣅⡀⠀⠀⠀ ⠀⠀⠀⢀⠰⠒⠁⢠⡄⠀⠀⢢⢀⠀⢠⠀⠀⠓⢯⢭⡲⡀⠀ ⣤⠴⠬⢠⠀⠠⢀⣟⠄⠀⠀⠈⡾⠀⠀⢇⢄⠀⠀⠊⢪⡪⣆ ⠀⠑⢄⠸⡀⠀⡈⡏⠀⠀⢰⣀⡇⠡⠀⢺⣟⣇⢀⠀⡈⡇⠉ ⠀⠀⠀⠁⡮⣀⣁⡇⠀⢀⣾⣿⣀⡀⡃⡜⢿⡟⡏⡄⢱⠙⠀ ⠀⠀⠀⠀⢃⠀⠀⠇⠀⢃⢻⢿⡻⠀⠉⠀⠈⠀⢇⢃⢀⡆⠇ ⠀⠀⠀⠀⠈⡦⡣⡀⠀⡀⢎⠇⠀⠀⠠⠤⠂⣰⡻⣼⠞⠀⠀ ⠀⠀⠀⠀⠀⢹⠐⡱⡧⠺⢄⡯⡍⠐⢲⠒⠺⠹⠁⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢤⠐⠒⠀⠀⠀⠈⠒⠚⢍⠉⡂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠆⠀⠂⠤⢀⠐⠁⠘⡄⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⣀⡀⠀⢀⡀⠧⢟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠁⠀⠀⠈⠁⠀⠀⠀⢡⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠁⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⢕⠢⡀⠀⠀⢀⠠⠐⠀⠉⠁⠀⡝⠀⣀⣡⠀⠣⡀⠀⠀⠀⠀⠀ ⠀⠀⠇⠈⠢⠀⠉⠉⠒⠂⢀⡀⠤⡀⠸⢆⢠⡁⠈⡄⠀⠘⡦⡀⠀⠀⠀ ⠀⡀⢚⡀⣏⠁⢢⠄⠀⢠⢻⠇⠀⠐⠄⠀⠑⠇⠤⠒⠐⡀⠀⠀⠄⠀⠀ ⢰⢢⠋⠑⣼⠖⡙⠀⠀⠀⢸⠀⠀⠀⢁⠀⠀⠈⠄⠁⠀⠈⠄⠀⠈⡄⠀ ⠀⣷⠀⠰⡌⠀⠀⠀⠀⣇⠈⠀⠀⠀⠘⡆⠀⣸⠘⡀⠀⠀⠘⡀⠀⠰⠀ ⠀⠃⠀⡀⠀⠀⣆⠀⣆⢋⠄⠀⠀⠀⣆⣃⣠⢹⡐⠃⠀⠀⠀⣡⠀⠀⡄ ⠀⠘⡀⠙⠄⠀⢇⡨⠾⠽⠟⠦⡰⡜⢛⣪⣦⣍⡀⢸⠀⠀⠀⢸⠀⠀⠃ ⠀⠀⠈⠚⢪⠒⠨⣲⣶⡷⣶⡄⠋⠉⠈⣛⣿⣿⠛⠿⠂⠀⠀⢨⡆⠀⠀ ⠀⠀⠀⢀⢣⠀⡄⢹⡈⠹⠟⡃⠀⠀⠀⠈⠉⠈⠀⢸⠀⠀⠀⣼⠇⠀⢀ ⠀⠀⠀⢸⡇⢰⠀⢸⢡⠈⠁⠀⢀⣀⣀⡀⠀⠀⠀⡘⠀⠀⢠⡿⠀⠀⢸ ⠀⠀⠀⢸⠇⢀⠀⠘⡀⠢⢀⠀⠈⠣⠊⠀⠀⠀⣠⠃⢀⣢⠖⠁⠀⠀⠀ ⠀⠀⠀⠈⢲⠸⣄⠀⠡⠀⠀⠁⠂⡄⠀⠤⠒⣡⢢⠒⠙⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠌⠀⠛⠒⠦⠕⠚⠂⠀⡇⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠊⠀⠀⠀⢀⡀⠠⠄⠒⢱⠃⠀⠀⠀⠀⠀⡱⠀⠂⢄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠊⠉⠁⠀⠀⠀⠀⠀⠉⠁⠒⠦⢄⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣤⠀ ⠀⣶⠒⠦⠤⠤⠤⠤⠒⠒⠂⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠍⠉⠀⠀⠀⠀⠀⠀⠀⡼⠙⠀ ⠀⠘⣆⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠒⡹⠃⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⡄ ⠀⠀⠘⣆⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠑⠺⢄⣀⣀⣀⣀⡀⠀⠀⣀⣠⠊⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢸⠀ ⠀⠀⠀⠘⢆⠀⠀⠀⠈⢩⣖⣶⡆⠀⠀⢠⠋⡇⠱⡄⠀⠈⠳⣄⠀⠀⠈⠀⠤⡈⠉⠒⢄⠀⠀⠀⠀⠰⣯⣄⡀⠀⠀⡎⠀ ⠀⠀⠀⠀⠈⢦⡀⠀⠀⣞⡻⠁⠀⠀⢠⡇⢠⡇⠀⠈⢦⠀⠀⠈⠑⢄⡀⠀⠀⠘⢆⠀⢤⡱⡄⠀⠀⠀⣿⣿⡄⠀⡼⠁⠀ ⠀⠀⠀⠀⠀⠀⠙⠦⣤⠋⠀⠀⠀⢀⠾⡇⣼⠀⠀⠀⠀⠑⢤⡀⠀⠀⠈⠒⠠⢤⣀⡱⣄⡙⣷⠀⠀⠀⠀⢽⠇⡜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡴⠋⣸⠀⣿⠀⠀⠀⠀⠀⠈⢻⠢⢄⡀⠀⠀⠀⠀⠀⠀⡙⠺⣧⠀⠀⠀⠙⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⡠⠊⣠⠴⣅⣆⡏⢆⠀⠀⠀⠀⠀⠀⢣⠀⠈⠢⠀⠀⠀⠀⠀⠈⠑⠤⣍⣢⣄⡀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠐⠚⠛⢲⠏⠁⢠⣧⢻⣇⠈⢦⠀⠐⡄⠀⠀⡀⢧⠀⠀⢳⡀⠀⠀⠀⠘⢄⠀⠀⣆⠉⠉⠙⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠇⠀⠀⢸⡟⠈⠙⠋⠙⠳⣄⠹⡄⠀⢣⠘⡿⡒⠚⠻⡒⠀⠀⠑⠮⣦⡀⢸⠀⠀⠀⢸⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⡼⢢⠀⠀⣻⣿⣶⠶⣶⢶⣤⣌⠳⢽⣄⠀⢣⢳⣽⣄⠀⢱⠀⠀⠀⡴⠀⠈⣸⠀⠀⠀⠸⡄⢳⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⣤⠀⢻⡆⠻⣷⣟⣿⣿⡄⠀⠀⠙⠷⠬⢿⣿⣿⣷⣬⡆⠀⢰⠃⠀⢰⠻⡀⠀⠀⠀⢣⠀⡇ ⠀⠀⠀⠀⠀⠀⡼⠀⢰⡇⠀⠿⣷⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠙⡇⢠⠃⠀⢀⠇⠀⢧⠀⠀⠀⠘⡆⣴ ⠀⠀⠀⠀⠀⢾⡇⠀⠈⣧⠀⠀⠈⢿⠢⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣳⠏⢀⡄⠘⠀⠀⠸⡄⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⢠⣿⠀⠀⠀⠸⡄⠀⠀⠈⣆⠸⡝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⢞⣇⢹⣶⠀⠀⠀⡇⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢣⠀⠀⠀⢸⣴⡛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡞⠈⠻⠿⠂⠀⠀⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠈⢇⠀⠀⠈⠁⠹⣧⡘⡦⣄⠀⠀⠀⠀⠀⠀⢀⡴⣾⡏⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠈⡇⠈⠓⠤⣀⣀⣠⠔⠋⠀⡟⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃ ⠀⠀⠀⠀⠀⠀⠈⢒⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀ ⠀⠀⡀⠤⠒⠊⠉⠁⠀⢈⠉⠒⠢⢤⣀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⢀⠤⢲⠟⠉⠓⠢⠄⡀ ⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠙⢍⠁⠒⠀⢄⣡⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡔⠁⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⡌⢌⠢⠄⣀⡤⠐⠈⠁⠀⢀⠌⢀⠄⠇⠈⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣁⠠⡦⡀⠀⠀⢈⢴⠊⠠⡈⠙⢝⡄⢘⡀⠀⠉⢄⠀⠀⠀⠀⠀⠀⠀ ⢠⡪⠞⢌⣇⢤⠇⠀⡈⢾⠀⠀⠃⠀⠀⢊⠁⠀⠑⡀⠀⢣⠀⠀⠀⠀⠀⠀ ⠈⣾⠀⡘⠃⡈⠀⠀⡇⠠⠀⠀⠸⡆⠀⡀⢂⠀⠀⠰⠀⠀⠆⠀⠀⠀⠀⠀ ⠀⡇⠀⡟⠀⢣⡀⢆⠷⡀⠀⠀⣄⣆⣠⣁⠜⡀⠀⠀⣃⠀⢰⠀⠀⠀⠀⠀ ⠀⠘⡀⡷⡀⠸⡨⠚⠛⠓⢄⣶⢛⣾⣤⣁⡀⡇⠀⠀⢸⠀⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠌⠁⣿⣿⣿⣿⢌⣠⡈⢩⣿⣿⠟⠋⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠆⡀⢸⣅⣘⡥⠇⠈⠓⠀⠒⠊⠀⡇⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⡟⠀⠁⠈⠘⠄⠀⠀⢖⡲⠂⠀⠀⣰⠀⠠⣼⠏⠀⠀⠃⠀⠀⠀⠀ ⠀⠀⠀⠡⡄⣆⠀⢃⠀⠑⠠⣀⠀⣀⠤⢢⣃⠴⠟⠁⠀⠀⠀⠸⠀⠀⠀⠀ ⠀⠀⠀⢠⠋⠚⠦⠦⠵⠂⢀⢼⠀⠀⠈⡡⠉⢄⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀ ⠀⠀⠠⠁⠀⢀⠀⠀⢀⠔⡝⢠⢃⢔⠊⠀⢰⠀⠡⠄⢀⡀⠀⠀⠀⠑⠀⠀ ⠀⠐⠁⠀⡔⡬⡔⠈⠀⡘⢣⠋⠀⢈⡆⣠⠂⠀⠀⠐⢄⠔⠁⠑⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡊⠉⠉⠉⣩⡽⢾⠏⠁⢠⠎⠀⠀⢻⣕⠒⢤⠤⣀⠀⠀⠀⠀⠠⠀⠚⠋⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⣾⠿⠚⠁⠀⢀⠏⠀⠀⠀⠀⠌⢢⠀⠑⣬⡑⢄⠀⠀⠀⠘⢆⠀⠀⣠⠏⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⣀⠀⠀⣼⠀⠀⠀⠀⠀⠁⠀⠳⡀⠘⡝⢢⠑⢄⠀⠀⠈⠀⣠⠟⠀⢇⠱⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢟⢁⠞⢠⢣⠀⢀⢻⣤⠀⠀⠀⢰⠀⠀⠀⠡⡀⠘⣄⠑⢄⠣⡀⠀⡰⠋⠀⠀⢸⠀⠘⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⢔⣫⠖⠁⡞⢠⠿⢸⠀⢸⠀⣿⡄⠀⠀⣸⠀⡄⠀⠀⠹⡀⠸⢦⠈⢦⠑⡌⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⢁⠇⠀⡜⠀⡇⠀⢆⢀⠈⠀⡟⣷⡀⢠⡿⢄⠃⢠⣀⠤⢧⠀⢧⠀⠀⣇⠙⡄⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⢠⣆⠃⢸⡉⠲⢌⣻⣄⣰⠁⠈⢻⣿⠧⠴⠛⠻⢿⣠⢸⡄⠘⡄⠀⢻⣆⢱⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⠘⠀⢘⣧⣴⣦⣤⢈⠇⣠⣾⡿⣁⣤⣶⣴⣤⣄⠙⣼⡇⠀⢇⠀⢸⠘⡌⡆⠀⠀⠀⠀⠀⠀⠸⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠸⣿⠹⣿⣿⡮⠼⠋⠁⠀⠿⣿⣿⣿⣿⢹⡿⢩⣿⠀⢸⠀⢸⡆⢡⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡄⠀⢹⡃⠉⠉⠁⠀⠀⠀⠀⠀⠛⠋⠉⠍⠀⠀⡄⣸⠀⠈⠀⣾⡇⢘⡄⡀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢻⣾⡄⢹⡀⠀⠀⠪⡂⠀⠀⠀⠀⠳⣈⠂⠢⠐⢠⣧⡿⠀⠀⠀⡿⣼⣜⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣁⣬⡏⠳⡀⠳⡀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠁⠀⠀⡼⢫⠃⢠⠀⢰⡇⠸⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣾⢆⠈⢦⣙⣦⡀⠻⠀⠀⠨⠀⠀⠀⢀⣤⡾⢁⠎⡠⠃⢀⣿⣅⣀⡀⠑⣄⡀⠀⠀⠀⡜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣼⡧⡘⣦⠀⠈⡉⠒⠤⣀⠠⡴⠚⢡⡾⢁⠎⠘⠀⢀⣮⣿⠄⠀⠀⠉⠀⠀⠀⢠⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⡽⢮⡛⠷⡀⠸⡀⠀⠀⢀⣧⠔⡟⣡⣧⠂⢀⣠⡿⠟⠁⠀⠀⠀⠀⢀⣤⠖⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⣠⠊⠀⠀⠙⢧⣱⣀⣇⠠⢴⢟⡥⢊⡞⢩⣧⡴⠟⠋⠀⠀⠀⠀⠀⠀⣠⡞⠁⡀⠀⠀⠀⠀⠀⠀ ⠠⠤⠒⢒⣒⠶⠒⠉⠀⠀⡴⠁⠀⠀⠀⠀⠈⢷⣈⠭⣚⠵⢋⣠⣾⠾⠛⠉⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀ ⠀⠉⠁⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢆⣀⢤⣒⢿⡖⠊⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣞⠤⢄⣶⠾⠟⠊⠉⠀⣼⣷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀
⠀⢀⣠⡴⠞⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣳⣶⣤⣤⣶⡶⠿⢛⠋⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣿⣿⣿⣿⣿⣿⢭⣥⢀⣀⣼⡆⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⣼⣿⣿⡿⠋⠁⠀⠴⠟⠋⣩⡿⠻⣄⣠⣶⠛⡿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⣤⣀⠀⠀⠁⠀⠀⢠⣞⣡⢰⡇⠙⣧⠀⠀⠀⠀⠀ ⣶⣆⡾⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄⡀⠀⠻⣟⠁⢸⠈⢷⣸⡇⠀⠀⠀⠀ ⢉⡟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣄⣀⠀⠀⠀⠀⠀⣤⣦⡀⠀⠈⠙⠷⣄⡈⠉⣻⠀⠀⠻⣏⠀⠀⠀⠀ ⣸⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣩⣿⠶⢦⣤⣼⣿⣿⣣⣶⣶⣀⣤⡈⠛⢦⣇⠀⠀⠀⢻⡄⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠟⠁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠙⣇⠀⠀⠈⣧⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⣦⡀⠀⣤⣷⣤⣶⣿⣿⣿⣿⣿⠛⠻⢿⣿⣿⣿⣶⣦⡀⠀⠀⢻⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠙⢷⡄⠀⠀⠘⣷⡀⠻⣿⣿⣿⡿⠋⠀⢿⣿⣧⡀⠈⣿⣿⣿⣿⡟⠀⠀⠀⢸⠀⠀⠀⢸⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡀⠀⠙⣦⡀⠀⠘⣷⡀⣿⣿⣿⠀⠀⠀⠈⠻⣿⣿⣿⡿⠋⠻⣿⠁⠀⠀⠀⣾⠀⠀⠀⢸⡇⠀⠀ ⠀⡀⢰⣧⠀⠀⢸⡇⠀⠀⠈⠻⣦⡀⠸⣷⣸⡿⠃⠀⠀⠀⠀⠐⠟⠋⠉⠀⠀⠀⢸⡇⣀⠀⠀⠋⢠⡆⠀⣼⠀⠀⠀ ⠈⣇⠀⣿⠀⡀⠘⣧⠀⠀⠀⠀⠈⠻⣄⠹⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⢸⡇⢰⠇⠀⠀⠀ ⠀⢻⠀⣿⡆⣷⠀⣿⠀⠀⠀⠀⠀⠀⠙⢷⣜⣿⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⡇⠀⢠⡄⢸⣇⣿⠀⠀⠀⠀ ⠀⢸⡆⢹⣧⢹⡀⢸⡇⠀⠀⠀⠀⣠⣀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣼⠇⠀⣾⠃⠀⣯⢹⣆⠀⠀⠀ ⠀⠀⡇⣸⢿⡜⡇⠈⣇⠀⠀⠀⢰⣿⣿⣿⡦⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣿⠀⠀⡿⢿⣿⣆⠀⠀ ⠀⢠⣿⣿⡌⣧⣷⠀⢻⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⢸⡿⠀⠀⡇⠀⠻⣿⣆⠀ ⠀⣾⣿⠘⣿⣿⣿⡄⠸⡇⠀⠀⠀⢀⣾⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⢸⡇⠀⠀⡇⠀⠀⠘⠿⠆ ⠚⠋⢻⡀⠘⣿⣿⣧⠀⣿⠀⠀⣠⣾⠏⠈⠙⠛⠻⠗⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢣⡇⠀⣾⡇⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠸⣇⠀⠘⣿⣿⣧⣸⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⡾⢸⠃⠀⣿⠀⢀⡾⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠻⣦⡀⠘⢿⣆⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⢀⣇⣿⡿⣸⡏⢀⡾⠃⠀⠀⠀⠀⠀⠀ ⠙⢧⡀⠀⠈⠻⢶⣌⡛⠿⣾⣷⣤⣄⣀⣀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠁⠀⠀⢸⠹⣿⡿⣿⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⣌⠻⣦⣀⠀⠰⣾⣿⣷⣦⣄⠈⠉⠉⢻⣿⣿⣿⢿⡿⠿⡭⠤⢴⠶⠲⡖⢺⣄⠛⠁⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢹⣦⣈⠹⣷⣦⣤⣙⣻⣿⣿⠛⣀⡤⠚⣷⢺⡖⢲⡗⠲⡗⠒⣿⠒⢲⠗⢺⡉⠓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⡿⠋⠙⠛⠺⢿⠶⣤⣄⣉⡽⠚⠻⢤⣄⡈⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⢉⡡⠞⠁⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀
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