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__▐▐█████▍▌▐▓▓▉ ◢▓▓█ ▼ ████
__ ▌██████▎ ▀▀▀ █▓▓▌ ▌ █████▌
_▐ ██████▊ ℳ ▀◥◤▀ ▲████▉
_▊ ███████◣ ′ ℳ ▃◢██████▐
_ ▉ ████████◣ ▃、 ◢███▊███
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⢋⣴⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠇⣶⣶⣦⣬⣥⣌⠙⣆⣸⣦⣿⣿⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡄⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡌⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⡘⣿⣿⣿⣿⡿⣿⢿⣿⣿⠿⣿⠄⠙⡁⣿⡘⢟⢉⣿⣿⣿⣿
⣿⣿⣿⠄⡿⠿⣿⣯⠐⠉⡄⣿⣿⣿⣿⣿⣶⡾⠫⢊⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣇⢋⡭⠟⣿⣷⣶⣿⣿⡿⠛⢩⢍⠕⢠⠾⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣙⡛⠿⢟⣩⣭⣅⡻⠂⢊⣴⡀⠈⠙⠻⠷⢹⣿⣿⣿⣿
⣿⡟⣡⣦⢹⣿⣿⢁⡺⠿⠻⠉⣀⣀⣀⠄⠿⢿⠶⠄⣴⡆⠈⠩⠠⡪
⣿⡇⢴⠾⡸⠿⠇⣉⣹⣿⣷⣿⣿⣿⣿⣿⠶⢠⣤⣬⣥⣮⣀⡦⢀⣐
⣿⣿⣦⣘⡁⠟⠄⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣾⣿
⣿⣿⣿⣿⣿⣿⣷⡘⢿⣿⠿⣋⣉⣉⠻⡿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣇⠀⢸⣿⣿⣦⣤⣄⣀⣴⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⢀⣼⣿⣿⣧⣿⣿⣿⡟⠉⢿⣿⡏⠉⢻⠂⡀⠀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣷⣦⣿⣏⠁⠀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀
⢠⣾⣿⡿⠋⠀⠈⠙⣿⣿⣿⡿⣿⡿⠿⠟⢿⣿⣿⣷⣄⠀
⠈⠿⡿⠃⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⠻⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠟⠃⠀
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆ ⣠⣶⣿⣶⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⣾⣿⣿⣧⠀⠻⣿⣿⠿⠉
⣰⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⠏
⠀⠈⠛⠿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⡀⣠⣾⡇⠀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⡇
⠀⣶⣿⣦⣜⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⣴⣺⣦⣙⣿⣷⣄
⠀⣯⡇⣻⣿⣿⣿⣿⣷⣾⣿⣬⣥⣭⣽⣿⣿⣧⣼⡇⣯⣇⣹⣿⣿⣿⣿⣧⠀⠀
⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗
⠀⠀⠀⠀⠀⣰⠋⡀⣠⠟⢁⣾⠇⠀⣀⣷⠀⠀⠓⣝⠂⠙⣆⢄⢻⡞⢢⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢸⢡⠃⢠⡞⠁⠀⣰⡟⠉⢦⣄⠀⠈⢆⠀⢻⣾⡄⢧⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⡇⡌⠀⡞⠀⢀⣴⡋⠀⠀⠀⣙⣷⡀⠘⡄⠘⣿⣧⢸⣼⣥⠀⠀
⣀⣀⣀⣀⣞⣰⠁⡇⠀⣧⢴⡛⠛⠁⠀⠀⠀⠉⠉⡙⡦⡇⠀⣿⣸⣼⣿⣇⣀⣀
⠳⢽⣷⠺⡟⡿⣯⡇⠰⣧⢩⣭⣥⠀⠀⠀⠀⢠⣭⣥⠁⡀⠀⣿⡟⣴⠶⢁⡨⠊
⠀⠀⠉⢳⢦⣅⠘⣿⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣏⣳⡇⢴⡞⠁⠀
⠀⠀⠀⣼⢸⡅⢹⣿⣿⣾⣟⠀⠀⠠⣀⢄⡠⠀⠀⠠⡚⣿⡿⣿⢻⠁⢹⣷⡀⠀
⠀⠀⠸⡏⠸⡇⢼⣿⡿⠟⠛⠓⣦⣄⣀⣀⣀⣀⡤⠴⠿⢿⡟⠛⠺⣦⣬⣗