「サンリオキャラクター」アスキーアート૮(○・ꙍ・○)ა【コピペ◎】

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　　⢠⠔⠚⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⠏⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡀⠀⠀⠀⡇⠀⠀⢀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢧⠀⠀⠀⢳⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢀⡀⠀⠀
⠀⠀⠀⠀⠑⡶⠀⠀⠙⠛⠻⠿⣿⣿⣿⣿⠷⠶⠒⠚⠉⠉⠉⠓⡄
⠀⠀⠀⠀⡼⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡴⠲⢤⠇⠀⠀⠀⠀⣆⡸⠂⠀⠀⠐⠀⠀⠀⢶⣤⣀⣀⡤⠞⠁
⠀⢧⡀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢈⡷⠒⢆⠀⠀⠀
⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀
⢰⠒⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀
⠀⠙⠲⠞⠓⠢⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠳⠤⠖⠃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣺⣿⣿⣷⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣼⢾⠕⠊⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣰⣦⣶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠅⠀⠀⠀⠀⠀⠈⠙⢿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠔⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣶⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⡀⠀⠀⠀⠀
⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀
⠀⣀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠀
⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⢠⣤⣤⡆⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀
⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⠛⣿⠁⠀⠀⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⢀⣼⣿⣦⣄⡀⣸⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⡟⣿⣦⡀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠟⠋⢀⣼⡿⠛⠛⠁⠀⠀⠉⠙⢿⣦⠀⠀⠀⠀⠀⠀⢻⣿⣶⣶⣤⣤⣶⣾⡿⠃⠀
⠀⠀⠊⠻⢿⣶⣤⣤⣤⣴⣾⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⡀⢠⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠲⣽⣷⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⢁⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⣿⣿⠀⠀⠀⣀⠀⠀⠀⣴⣾⣟⣉⣁⠀⠉⠝⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣻⡇⠀⠀⠀⠀⠾⣿⡄⠀⠀⠀⣿⣮⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠿⠿⣷⣾⣿⠿⠿⠻⠿⣿⣦⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣇⣠⣾⠆⠀⠀⢹⣿⡄⠀⠀⢹⣿⡆⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠛⠛⠋⠁⠀⠀⠀⠀⢻⣷⠀⠀⠘⠛⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢴⣦⣄⣀⣀⣀⣀⣤⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⣤⣄⣀⠀⠀⠉⠙⠛⠛⢿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⡿⠿⠿⢾⣷⡾⢿⠿⠿⠟⢁⣀⣤⣿⣧⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠉⠉⠛⠻⢿⣦⡀⠀⠀⠀⠀⠙⠿⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠛⠛⠻⣿⣧⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣾⡏⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⢶⣶⣤⣄⣀⣀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡻⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀
⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠹⣿⣷⣄⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣆⠀⠀⠀⠀⢀⣠⣼⡿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣶⣶⡾⠿⠛⠛⠻⠿⠷⠶⣶⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⠾⠿⠿⠟⠛⠛⠙⠿⣷⣶⣶⣶⡿⠛⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⡇⠀⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠁⣤⣤⠀⠉⠉⠛⠷⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣾⠋⢀⣴⣶⣾⣿⣿⣿⣿⣿⣶⣦⡀⠈⢻⣆⠀⠀⠀⠀
⠀⠀⠀⣾⢃⣠⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⣄⡀⢻⡆⠀⠀⠀
⠀⠀⣸⡿⢋⡁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢈⡙⢾⣇⠀⠀⠀
⢀⣾⠋⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠙⢷⡄⠀
⣾⡇⠀⣼⠀⠀⠀⠛⠀⠀⡀⢲⡶⢀⡀⠀⠛⠀⠀⠀⢿⠀⢸⣷⠀
⠸⣧⡀⢹⡄⢀⣀⠀⠀⠈⠧⠞⠑⠖⠃⠀⠀⢀⣀⢀⡿⢀⣼⠇⠀
⠀⠈⠙⢻⡿⠉⠉⢳⣄⣀⡀⠀⠀⢀⣀⣀⡞⠉⠉⢻⡟⠛⠁⠀⠀
⠀⠀⠀⠀⠻⠶⠶⠾⠉⠛⠛⠛⠛⠛⠛⠉⠻⠶⠶⠟⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠄⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠀⡣⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠠⠊⠀⠉⠰⠀⠀⠀⢸⠇⠀⢠⠘⠁⠘⢢⡀⠀⠀⠀⠀⠀⠐⠒⢄⠀⣠⠼⠃⠀⡰⠊⠉⠀⢉⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡆⠀⠀⠀⠀⠃⠀⠀⣼⠀⠀⠈⠙⠆⡰⠉⠁⢀⣤⢤⡄⠀⠀⠀⠈⠤⠁⠀⠀⣜⡁⡐⠁⠀⠀⠈⢂⠘⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢀⣠⠬⠵⠒⠒⣾⠖⣶⡧⣄⣀⠀⠀⠀⠀⠀⠀⣼⠀⠱⠀⠀⠀⠀⢀⠀⢻⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣴⡯⣖⠺⣍⢻⡙⢯⡹⢜⣓⡒⠮⣍⡳⢤⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠠⠀⣸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣮⣳⢌⡇⡞⢥⡚⡼⢤⢋⡳⢦⣙⠳⣿⡀⣰⠇⠀⠀⠀⠀⠀⡠⠁⢠⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⠉⡄⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠾⠷⢼⣵⠮⠧⣷⣦⣭⠿⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⣊⠁⠀⠋⣒⡄⠀⠀⠘⠲⣄⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⢤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢱⢀⠏⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡠⢎⠰⢆⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠠⡤⠤⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠁⠀⠸⢅⡈⢀⣈⡵⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠶⠶⢤⡀⢠⠏⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣶⡄⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢱⡰⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢐⠁⠂⠀⠀⠙⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⡾⣧⣀⣸⡆⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠀
⠀⠀⠀⠀⠘⣆⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣠⠖⠛⠓⣆⢠⠔⠃⠈⠢⠄
⠀⠀⢀⡀⠀⠙⣦⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣾⠀⠉⢊⢰⠋⠁
⠀⣠⠆⠸⣄⠀⠈⠳⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠊⣴⠋⠀⠀⠀⠁⠀⠀
⠘⠃⠄⢰⠄⠃⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠊⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢸⡁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠅⣀⠼⠁⠳⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⣾⠀⠐⠲⠀⡴⠊⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢇⡀⣀⢀⡀⣀⢀⡀⣀⢀⡀⣀⢀⡀⣀⠀⣀⢀⡀⢀⡀⣀⠀⣀⢀⡀⢀⡀⣀⠀⣀⢈⠀⡀⢀⡀⡇⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣿⣿⣿⣿⣿⡷⣄⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣠⡴⠖⠋⠀⠈⠉⠛⠛⠛⠛⠛⠉⠀⠈⠛⠶⣄⡀⠀⠀
⢀⡴⠋⠀⠀⣰⠅⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⢰⡄⠀⠈⠻⣦⠀
⣾⠁⠀⠀⢰⠇⠀⠀⠉⠀⢀⠘⡗⣀⠀⠉⠀⠀⢷⡀⠀⠀⢸⡆
⠳⣄⣀⣠⡟⠀⠀⠀⠀⠀⠈⠊⠙⠋⠀⠀⠀⠀⠈⢳⡶⠴⠞⠁
⠀⠀⢩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀
⠀⠀⣾⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣿⠀⠀
⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁⠀⠀
⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀
⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢳⣀⣴⠋⠉⠉⠉⠉⠉⠉⠳⢤⡼⠃

⠀⠀⠀⢠⡞⠉⠳⠤⠶⠶⢶⣶⣤⣾⣿⣷⡄⠀⠀⠀
⠀⠀⠀⢨⠇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣇⠀⠀⠀
⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⡆⠀⠀
⠀⠀⣾⠀⠀⢴⡄⢀⠀⠀⠀⢀⠀⢠⡄⠀⠀⣿⠀⠀
⠀⠀⠸⣄⠀⠀⠀⠈⠒⠚⠓⠚⠁⠀⠀⠀⣠⠏⠀⠀
⠀⠀⠀⠈⠓⠦⢤⣄⣀⣀⣀⣀⣠⡤⠴⠞⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣷⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠉⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠉⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣶⣤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠻⣷⣄⠀⠀
⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⢠⣶⡆⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢰⣶⡄⠀⠸⣷⡀⠀⠀⠀⠀⠈⠻⣦⠀
⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀⠻⣿⠃⠀⢤⡄⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣏⣀⣴⣿⣦⣤⣼⣇⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠉⠉⠉⠉⠙⠛⠻⣶⣄⠀⠀⠀⠀⠀⢹⣷⣤⣤⣤⣶⠿⠃
⠀⠀⠀⠀⠙⠿⣦⣤⣤⣶⢿⣗⠀⠀⠀⠀⠀⠀⣼⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⣀⠀⠀⢸⡇⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣼⡏⠀⠀⠘⢷⣦⣴⣿⣦⣟⡃⣀⣤⡀⠀⠀⠀⠀⠀⣀⣤⣿⡾⠋⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠄⠀⠀⠀⠀⠀⠉⠉⠉⠛⣿⣦⣯⠀⢀⣤⠀⠀⣾⠟⠉⠁⠀⠀⠀⠀⠀⡈⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣤⣀⡀⠀⠀⢀⣀⣠⣿⠋⣡⡄⠘⠋⠀⠀⢻⣧⣀⣀⣀⣠⣤⣶⠿⠁⢸⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⡀⠀⠈⠙⠛⠛⠛⠛⣿⣟⠀⠀⠙⠃⠀⣀⡀⠀⣠⣽⠟⠉⠉⠉⠁⠀⠀⠀⣈⣿⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠛⠛⢷⣄⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣤⣴⣿⣶⠿⠛⠉⠀⠀⠀⠀⠀⢠⣶⠟⠛⠛⠻⣷⡀⠀
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠸⣷⠀
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀
⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⣾⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣤⣶⠿⣿⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣴⡿⣷⣤⣀⣤⣴⠿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠟⢀⣀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠟⠛⠛⠓⠙⠚⢡⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢫⣍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡶⠛⣶⡼⠃⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⠀⣀⣿⠀⠀⠘⠋⠀⣀⠀⠀⠀⠀⠀⠀⣠⡿⠙⣽⣷⣦⡀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡀⠀⠀⠈⠛⠃⠀⢾⠇⠀⠰⠾⠁⠀⠈⠻⢿⣿⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡳⡤⢀⡀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⣬⣽⣿⣶⣶⣶⣟⠙⠳⣦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⠟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⡏⠉⠉⠉⠉⠉⠛⠛⠻⠿⣽⣿⣿⣿⡛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⡟⠉⠀⠀⠀⢰⡶⣤⣄⣀⣀⣀⣀⣀⠀⠀⠈⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠒⠒⠒⠒⠛⠛⠀⠈⠉⠉⠉⠙⠓⠒⠲⠶⠖⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠋⠉⠉⠉⠛⠿⢷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣴⡿⠁⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠶⠆⠀⣰⡆⠀⠀⠀⠀⠀⢸⣿⣿⣦⣀⠀⠀⠀⠀⠀
⠀⢀⣴⣶⠿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣶⣤⣀⠀
⢰⣿⣿⠌⠁⠈⠽⣷⣶⣶⣤⣄⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢰⣿⠙⢿⣿⣿⣿⣿⣿⣿⡇
⢿⣏⡉⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⠿⣟⢛⡻⣷⣤⠀⠀⠀⣸⡟⠀⠀⠙⢿⣿⣿⣿⣿⠇
⠈⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠵⢈⣿⡆⠀⣠⣿⠃⠀⠀⠀⠈⠙⠛⠛⠁⠀
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣰⣿⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣽⣿⣿⣶⣶⣴⣤⣤⣶⡿⠟⠛⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠻⣿⣿⣿⡿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣷⡀⠀⠀⠐⠻⡄⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢷⣿⣧⠀⣈⡝⠃⠈⠉⠉⠉⠲⢦⣀⣀⣤⣶⣖⣿⣿⣷⠀
⠀⠀⠀⠀⠀⠀⠉⣻⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠈⠉⠛⠛⠋⠀⠀
⠀⠀⠀⣴⠲⡄⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀
⢠⡞⠓⠉⢰⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡴⣄⣀⡀
⠀⠛⠒⠒⠋⠀⠀⠿⠀⠀⢠⣄⠀⠀⠀⠀⠀⢾⠆⠀⠸⣄⠈⠳⠭⠼⠃
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⠋⠀⠀⠲⠒⠀⠀⣀⣄⣤⣼⣶⢶⡤⣄⠀
⠀⠀⠀⣴⡊⢯⢽⢷⡴⠖⠐⠒⠓⠶⢦⣄⡴⠋⠁⠀⠀⠀⠉⢷⡁⠎⢧
⠀⠀⠀⢷⡁⢠⣤⣏⠀⠀⠀⠀⠀⠀⠀⣻⣇⠀⠀⠀⠀⠀⠀⣸⠇⢉⡞
⠀⠀⠀⣴⣷⣶⣶⣿⣶⣤⣤⣤⣤⣴⣾⣿⣿⣷⣶⣶⣶⣶⣿⣷⣶⣿⡦
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠷⠿⣿⡆⠀⢠⣿⣿
⠀⠀⠀⠀⣀⣴⠟⠉⠀⠀⠀⠉⢿⣼⣿⠃
⠀⢠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢿
⢠⣿⡿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣹⠀⣰⡄⠀⠀⠀⣶⠀⢸⡁
⠀⠀⠀⠀⣿⠀⠀⠀⠘⠛⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠈⠻⣶⣤⣤⣤⣤⣴⡶⠛

⠀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣏⡿⡇⠀⠀⢀⡀⢀⡤⣠⡀⠀⠀⠀⠀⠀⠀⠀
⠀⢻⣳⣇⢀⡤⠾⠙⠈⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀
⠀⠀⢙⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⡀⠀⠀
⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣽⣷⡄
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠳⢷⣿
⠀⠀⠻⠀⠀⣠⡀⠀⠀⠀⠀⢀⣄⠀⠘⠃⠀⠀⠀
⠀⢠⡇⠀⠀⠛⠃⠀⠰⠶⠀⠚⠛⠀⠀⢷⠀⠀⠀
⠀⠀⠳⢤⣀⡀⣤⣄⡀⠀⣀⣤⣄⣀⡴⠋⠀⠀⠀
⠀⠀⠀⠀⠈⢹⣿⢏⣿⣿⢿⡽⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠛⠛⠉⠈⠙⠛⠃

⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀
⢈⣿⣿⣿⡄⠀⢰⡄⡾⢰⠆⠀⠀⣠⣾⣿⣿⠇
⠀⠹⣿⣿⣷⠟⠀⠁⠀⠀⠘⠙⠻⣿⠿⠟⠁⠀
⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀
⠀⠀⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀
⠀⠀⣽⠃⠄⢤⣤⠀⢀⠀⠰⣶⠀⠀⠹⠃⠀⠀
⠀⢸⣇⣬⣤⡀⠇⠀⠈⠀⠀⠂⢰⡞⠛⢿⠄⠀
⠀⠈⢿⣀⣠⡿⣶⠶⡶⠖⠶⠞⠟⠳⠶⠞⠁⠀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣰⣦⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣾⣿⣷⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⡿⣷⣡⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⠀⢀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣷⣿⡧⡆⠀⠀⠀⠀⣔⣦⣜⢼⡿⣯⣂⣀⢴⣿⡿⢿⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⢿⣿⣿⣈⣟⡇⠀⢀⢠⣄⣷⠟⠻⠿⠛⠊⠉⠉⠚⢹⣿⣖⣀⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀
⠀⠈⣾⣿⣿⣿⣏⡧⣢⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣾⣔⢄⡀⢀⣠⣲⣼⣷⣶⣿⣿⣾⣾⣿⣤⣒⢄⠀
⠀⠀⠘⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣿⣿⣟⣛⣿⣿⣾⡟⣶⣿⣾⣿⡿⡿⠇
⠀⠀⠀⠣⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⠟⡻⢿⣿⣿⣿⡿⢿⣟⠻⠟⠃⠀⠀
⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠻⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣏⡉⠀⠀⠀⠀⠀⢿⡿⠃⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠰⣿⣕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢟⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠩⢿⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⣟⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢉⡻⢿⣿⣿⣿⣿⣶⣶⣶⣶⡦⠀⠀⣶⣶⣶⣾⣿⣿⣿⣿⣷⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢠⣦⣷⣿⣿⣿⣿⣿⣯⣟⡿⣿⢿⣷⡆⢀⣼⣿⣿⣻⣯⣿⣿⣿⣿⣾⣯⣔⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡠⣷⣿⣿⣟⣯⢿⣽⣿⣿⣿⣿⣿⣿⢯⣟⡿⣿⢿⣻⣾⣿⡿⣿⣻⣽⣷⣻⢿⣿⣿⣶⣅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣺⣾⠟⠉⠻⣿⣯⣿⣿⣿⣟⡷⣯⣟⣾⢿⣽⣻⣽⢿⣽⣻⢾⣽⡷⣿⣿⣿⣿⣟⣾⡿⠛⢿⣮⡢⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣿⠁⠀⠀⠀⢨⣿⣿⣿⣻⣞⣿⡽⣾⢯⣿⢾⣽⡾⣯⡷⣟⣯⡷⣿⣳⣯⢿⣿⣿⡁⠀⠀⠀⢻⣷⣇⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡄⠀⠀⢠⣿⣿⣿⣾⣷⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣿⣿⣷⠀⠀⠀⢸⣿⢺⠀⠀⠀⠀⠀⠀⠀
⠙⠹⣿⠶⢦⣼⣿⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠛⠛⠛⠛⠿⣿⣇⣠⣴⣿⢟⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⡅⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡁⣿⡇⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣿⣏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣤⣤⣤⣶⠿⠟⠋⠀⠀⠀⠀⠀⣼⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣻⣏⣀⣤⣄⣀⣀⣀⣀⣀⣀⣼⣿⣀⣀⣀⣀⣀⣀⣀⣠⣿⣟⡫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀　　(Ｙ)――-、
　　／　　　　 ＼
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　｜　_人_人_人_　|
　 ＼(_ ●　　●)ノ
　　 _＞―-＝-イ
　 (| 　　　　　＼
　　ヽ　　　＼／)
　　 (_　＿＿)￣
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⠀　　＿＿_(Ｙ)
　 ／　　　　＼
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　L人_人_人_人　ヽ_
　人●　　●　)　　)
（＿＞―ﾟ―＜~　　 )
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　￣T￣￣　　　＼
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　　|＿＿＿＿／￣
　　(_／

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣺⡭⠵⠚⠋⠉⠉⣹⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡽⠟⠉⠁⠀⠀⠀⠀⣤⣾⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⡽⠛⠁⠀⠀⢠⢤⡀⠀⣠⣞⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣫⡴⠋⠀⠀⠀⠰⣖⠋⠈⠉⡿⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡿⠋⠀⠀⠀⠀⠀⠀⢸⣆⣤⣄⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡴⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣞⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣾⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⢾⠞⠀⠀⠀⢀⣀⣠⠖⣶⣀⣠⣤⣼⣵⣳⣦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⢯⠏⠀⠀⠀⠀⢸⣥⡿⠚⠉⠁⠀⠀⠀⠀⠈⠉⠑⠺⢭⡒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⢟⠏⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡞⡿⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣸⢻⠁⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣧⡏⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢹⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣮⡠⢿⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢀⣤⣀⣠⣦⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣸⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⣿⠀⠀⡽⠃⠀⠹⣆⢀⣀⣀⡴⠒⣻⡉⠉⠁⠀⠉⠉⠉⠓⠒⢦⣀⡀⠀⢰⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⡟⠛⠳⠇⠀⠀⠀⠈⢻⣀⡉⠀⠈⠻⠛⠀⠀⠀⠀⠀⠀⠀⣿⡗⢸⣥⣴⣿⡟⠀⠀⣀⣠⠤⢴⣒⣒⣒⣲⣦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢲⣤⣤⣀⠀⠈⠳⠤⠴⠂⠀⢀⣴⣿⣿⣿⣿⣷⣶⣾⡽⠖⠋⠉⠉⠉⠉⠉⠉⠓⠺⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠈⠻⠭⠿⠟⠛⢿⣿⣿⣿⣿⡟⡟⢹⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⡄⠀⠀⢻⡀⠀⠀⢸⠀⠘⣯⣿⡟⣽⠖⣃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣾⡄⠀⠀⠀⠀⠀⢀⡜⠁⠀⢧⠀⠀⠀⢳⡀⠀⣸⠀⠀⣿⣿⣧⣿⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡝⣦⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣯⣇⠀⠀⠀⠀⠀⡏⣀⡴⠦⢾⣇⠀⠀⠀⢳⣄⡟⠀⠀⣿⣷⣯⡷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣶⠹⣷⣶⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢹⣿⡀⠀⠀⠀⠀⣷⠋⠀⠀⡼⢹⣤⣤⡤⠶⣿⡤⠤⣤⣿⠁⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣼⠦⠴⠟⠒⠖⢿⣬⡇⠀⡼⠳⡼⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢳⢿⡀⠀⠀⠀⢳⡀⢀⡼⠓⠒⠻⣶⣼⠿⠉⠿⠿⠿⣿⣀⣼⡋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠾⠋⠁⠀⠰⠿⠀⢀⡶⠊⠀⠉⢻⡇⢀⡇⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢯⢧⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⢼⣇⠀⠀⠀⠀⠀⠀⣀⣤⡼⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⢠⡞⠀⠈⣧⣧⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⢿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣄⣠⣄⠀⠀⣾⠰⣶⡦⠀⠀⠤⠤⢏⣠⠞⠁⢠⣀⢀⡴⠋⠀⢠⣴⣣⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢯⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⡗⠹⣬⡟⠻⠧⣤⣈⣀⣠⡤⠶⠾⠭⠛⠀⠀⠀⠹⠿⠤⣤⣀⣸⠟⡟⢧⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠳⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢸⡯⠥⣄⡞⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠏⠀⢸⣶⢻⣦⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣞⢦⡀⠀⠀⠀⠀⠀⠘⢿⠛⠻⠷⣄⠀⠀⠀⠀⠀⡾⠁⠀⠙⠶⠦⣄⣀⣀⣀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢻⠀⠀⢸⣇⣿⣻⠭⠽⠿⢿⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⢤⡀⠀⠀⠀⠀⣿⣧⣄⡟⠃⠀⠀⠀⠀⠀⠷⣤⣼⡗⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢸⡦⠤⠾⠃⠀⠀⠀⠀⣠⣞⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢆⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⣴⡇⠀⠀⢠⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⡴⣫⡏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢽⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠖⠋⠛⠒⠛⢦⡀⠀⠀⠀⢀⣼⠧⢤⡤⠞⠁⠀⠀⢀⣤⢺⡿⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢝⡶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣠⠴⠞⠁⠀⠀⠀⢀⣀⠴⣞⡿⠚⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠪⢵⣖⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⣖⣮⡽⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢉⣓⠒⠯⠽⠿⣗⢒⠖⠂⠦⠤⠄⠤⠴⢖⣒⠲⠾⠿⠯⢟⢒⠛⣛⣉⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⣐⣦⣥⣼⣶⢶⡶⣦⣬⣴⣀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠒⣵⡀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⢰⣭⣅⣦⣵⡾⠟⡫⠍⢦⠱⡐⢆⠲⣁⠎⣩⠙⡛⢷⣦⣕⡀⡀⠀⢠⣪⠭⠭⠵⠚⠀⠀⢻⡡⡀⠀⠀
⠀⠀⠀⠀⠠⣀⣿⣧⣿⠛⡥⠘⣆⠱⣉⠦⢡⠓⡬⢑⠢⣍⠰⠩⢜⠢⢌⡹⢻⣮⣢⠘⢜⣆⠀⠀⠀⠀⠀⠀⠉⠒⣅⠂
⠀⠀⠀⢰⢹⣏⣽⡦⢡⢋⠴⣉⠤⢓⡰⢌⠣⢜⡰⢉⠲⢄⡋⡕⢊⡱⢊⠴⡁⠞⣷⣵⣼⣹⠀⠀⠀⠀⠀⢀⡴⡚⠕⠁
⠀⠀⠀⠀⠱⣽⡟⣐⠣⣌⠲⢌⡒⠥⢒⠬⡑⠦⢌⠣⣑⠪⠔⣌⠣⡔⡩⢢⠍⡜⠤⢿⡟⣇⣤⣤⣶⣄⠀⡾⠘⠀⠀⠀
⠀⠀⠀⠀⣖⣿⠰⢡⠒⡤⢓⠢⡜⢌⡃⠖⣉⠦⣉⠖⡡⢎⡑⢢⡑⠦⢱⠡⡚⢌⡜⢌⣿⣹⢈⢧⠣⠫⢓⡣⠃⠀⠀⠀
⠀⠀⠀⢰⢸⡧⣉⠦⡙⢤⢃⠣⠜⢢⢡⢋⡔⠢⣅⠚⡰⢡⢊⠥⡘⡜⢢⠱⢡⠎⡰⢊⢼⣇⡿⡜⡌⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⢸⡇⢲⠰⣉⠆⢎⡡⢋⢆⠣⡒⠬⣑⢢⡙⡰⢃⣜⣦⠱⡘⢢⡍⠲⢌⡱⢊⢼⡏⢱⢣⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⢺⡏⢆⠓⡤⢋⠆⡥⢋⠤⣣⣅⠓⣤⣿⢷⣵⣼⠞⠷⣧⣼⡿⢿⣅⣎⣴⢃⣾⡻⡏⡅⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⣸⡗⣌⠣⢒⡉⢖⡰⣉⢆⣿⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣴⣶⡍⢛⠛⣿⣿⢿⣕⣢⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢻⡷⢨⠜⡡⢚⣤⢚⡟⠋⣱⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⣸⣾⠟⢉⡽⢧⢣⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⢌⣾⢃⢇⢪⠱⣟⠉⠋⠁⠀⠈⠛⠁⠀⠀⠀⢠⣀⣀⡰⠆⠀⣀⣤⠞⠉⢻⡀⣻⠲⡼⡘⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠔⣥⡟⢣⢊⡔⣊⡑⡛⠷⠶⠶⡶⣤⣤⣤⣤⣤⣤⡤⠤⠤⠶⡾⠋⠁⠀⠀⠀⠀⠻⣷⢞⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⢾⡗⣨⢑⠢⢜⢠⢒⣩⣜⣥⡷⠟⠋⠁⠀⠀⠀⠀⠙⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⣀⡼⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢬⣻⣷⢊⡱⢊⢦⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣀⣤⡾⢫⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠨⢸⣇⢎⡴⡿⠉⢷⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡋⣿⢻⠋⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠑⠝⣿⡿⢯⡔⠘⢷⣀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⢟⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠣⢻⣾⣽⣷⡞⡹⢛⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣔⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠚⠋⠿⣶⣭⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢣⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣤⡀⠀⢀⡴⢏⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠈⣸⠷⢾⡫⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⣧⣀⣀⣠⡴⡾⣏⠀⠀⠀⣠⣴⠃⠀⠀⢧⡃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠓⠂⠈⠈⠊⢓⣒⠚⠝⠋⠙⣒⠦⠖⢞⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠉⠉⠻⣯⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠹⣯⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⢀⣀⡀⠀⠈⠻⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⣀⣀⣀⣾⠟⢛⣿⣂⣀⣀⣸⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⣠⣶⣶⣢⣄⣀⣀⠀⠀⠀⠀⠀⠀⢀⣿⡏⣿⣏⢉⡛⠃⠰⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⣿⣖⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣧⡄⠹⣿⡿⠿⢿⣶⠀⠀⠀⠀⣸⣿⣀⣼⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⢋⠍⡰⢀⢃⠒⡐⢂⠆⡐⠢⡐⢄⡉⡙⠡⡐⢶⣤⣿⣿⠀⠀⣀⣰⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⡉⢄⢊⠰⡈⠔⣁⠊⠤⡑⢨⠐⡡⠡⠌⢂⡐⢁⠣⡐⠤⢉⠻⢿⣿⠿⢟⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠤⠑⡈⢢⠡⠌⠒⡠⢑⠰⢈⠂⠥⡐⢡⠘⠤⡈⠆⡡⠐⢡⠊⡔⡈⠹⣧⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣖⣦⣤⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠰⣁⠊⡅⡘⢠⠒⢨⠑⡠⢃⠂⡅⢊⡐⠡⢂⡘⠤⢁⠎⢄⠩⡐⠰⢠⠡⡁⠜⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠉⠙⠛⢿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⡘⠰⣀⠒⡠⠑⢂⡘⢠⠁⡒⠌⡐⠌⡂⠰⢁⠆⠌⡰⠁⡌⢂⠆⣁⢃⠢⡐⡁⠎⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠠⠡⡑⠠⠌⢄⡑⠂⠤⠡⠌⠰⠈⠤⠑⡈⠅⠢⠌⠰⢀⠣⠄⠡⠂⡄⠊⠔⡠⠡⡘⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⡌⡁⠆⡑⡈⢄⠠⢃⢂⡑⡈⢅⢊⠰⡁⠆⣁⠣⣈⠱⠈⡔⡈⢅⠊⢄⡉⠄⡁⠒⡠⠌⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠰⠄⡁⠎⡐⢀⠂⢒⠠⢂⠰⢀⠊⠄⢒⡈⠔⡠⢒⠠⠌⡑⢠⠒⣈⠰⠠⢐⡈⠄⢡⠐⣀⢺⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⣿⠏⠀⠀
⠀⠀⢀⣤⣤⣀⠀⠀⣿⣿⣰⠃⡘⠤⠑⡈⠌⠄⢣⡌⠐⡡⠘⡈⣼⣇⡂⡁⠆⡰⢰⣌⠄⠢⢄⠡⢊⠄⣂⠩⠄⠂⠤⢸⣿⠀⠀⠀⠀⠀⢠⣦⣄⣀⣠⡿⢷⣤⣤⣴⠿⢷⣄⣀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠃⠀⠀⠀
⠀⠀⢸⡇⠈⠙⠻⠟⠛⠉⣿⠀⢆⠑⡈⡐⡈⢌⢸⣷⣥⣀⣣⣶⠟⠛⠷⣶⣶⠾⠛⠻⣮⣔⣨⣾⣇⠒⣀⠒⡨⠘⢠⠙⣿⠀⠀⢠⣄⣤⠾⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠻⣷⣴⣶⡄⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀
⠀⠀⢸⡧⠀⠀⠀⠀⠀⢰⡇⠌⡰⠐⣴⣥⣐⣬⡾⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣍⠈⢿⣔⣀⣂⡄⡑⢠⠊⣿⡄⠀⣾⠃⢠⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⡄⢻⣇⡀⣀⣀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀
⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠻⣦⠁⢆⣈⣿⠉⣡⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠙⠋⠉⢻⣧⠂⠜⡸⢷⡚⠁⠀⠘⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⠇⠀⠉⣛⠋⢻⣷⣿⡟⠁⠀⠀⠀⠀⠀⠀
⠙⢿⣤⣤⣀⠀⠀⠀⣠⣤⣤⠼⢷⡶⣿⠋⠀⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⣠⡾⠃⢌⠂⡅⠌⡛⢷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣿⣷⡀⣸⠏⢿⣤⠈⠼⣧⡈⣦⡀⠀⠀⠀⠀⠀⠀⠀⢦⣀⠀⣀⡾⠃⠀⠀⠀⠀⢀⣠⡾⠛⢩⢁⢂⠉⠄⠂⡔⣦⠁⡌⣿⣦⣄⣀⣀⠀⠀⠀⠀⠉⠓⠶⠚⠋⠀⠀⠀⣀⣠⣴⡶⠟⠉⠀⠸⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣉⣽⡖⢈⢻⣎⠄⡙⢛⠛⠻⢦⣤⣄⣀⣀⣀⣀⣀⣉⣉⣁⣠⣤⣤⠴⠶⢿⣏⡡⠂⢍⠂⠆⡈⢌⠠⢃⠐⡘⣷⡶⢿⡄⣉⣭⡿⠟⠛⠛⠻⣶⡶⠶⣒⣻⠟⠛⠛⢯⣭⡟⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣿⡏⠰⠈⠄⠻⣧⡈⢄⠣⡘⠠⠄⢩⣽⠟⠉⠉⠻⢭⣉⡤⠶⠋⠀⠀⠀⠀⠈⠻⣮⡄⡉⠆⡑⢠⠒⡀⠆⡐⢸⡇⠘⣷⠟⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣦⠽⣇⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣿⡄⢃⠡⢘⠠⡙⢿⡄⢢⠑⡂⢡⣾⠃⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠻⣶⡈⡐⡁⢲⣅⣒⣈⣾⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢿⣄⢻⡄⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠹⢿⣾⣶⡿⠁⠤⢉⢿⣆⠡⠘⣸⡏⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠻⣶⡠⢁⣿⠋⣹⠟⠉⠀⠀⠀⠀⠀⣠⢾⣤⣀⡶⠛⢲⣦⣤⠶⣯⣴⠾⢿⣾⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣧⠉⡄⢣⡾⢻⣧⢧⣿⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠙⣷⠏⣾⠁⠀⠀⠀⠀⠀⢀⡞⠻⣤⣀⠍⣟⠛⡛⢉⣷⣰⣯⣄⣂⣽⣿⣶⣤⣤⣀⣀⣀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣾⣿⣇⣻⠈⠳⣌⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⡼⠛⢾⡙⢷⣄⠀⠀⠀⣰⡿⠀⠀⠈⠉⠛⠳⢬⡶⠟⣿⠀⢹⡌⢹⡎⢻⣿⣿⡛⢿⢛⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣴⡾⠋⠀⠀⠀⣿⠀⠉⢻⣶⣾⣿⡇⠀⠀⠀⠀⠀⠀⡿⠐⢨⡏⠀⠈⣷⢀⢻⡄⠉⠓⠿⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣧⠠⣄⢻⣦⣿⣴⣠⣿⡏⢹⣿⠀⠀⠀⠀⠀⠀⢸⣅⣊⢴⡇⠀⠀⠛⠛⠉⠀⢀⡴⢾⣀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠿⠛⠛⠛⠁⠁⣸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣠⡶⠋⠀⠀⢉⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣼⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛⢶⣦⣄⣀⣀⡀⠀⠀⠀⣀⣀⣠⣴⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠉⡿⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⢐⣾⠀⠀⠉⢉⣹⣿⣿⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣟⠛⠛⠉⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣄⣤⣴⣾⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⢤⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⣉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠾⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀／￣＼／￣＼
　｜　●｜●　｜
　 >――＾ー―<
　( 〇　　　〇 )
　 ＼＿＼／＿／
　 〈/ ￣<･L_)><|
　 (⌒＞ーイ￣)
　　￣　　　￣

⠀⠀⠀⠀⢀⣴⠶⠿⠶⣦⣄⠀⠀⠀⣴⠾⠛⠛⠷⣦⡀
⠀⠀⠀⣾⠋⠀⠄⠀⠀⠄⠈⣧⢀⡟⠀⠀⠄⠀⠀⠀⢻⡄
⠀⠀⢸⠃⠀⠀⠂⠀⠐⣀⡀⠘⣿⠀⣀⣀⠂⠐⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠐⠂⠐⢸⣿⣿⠀⣿⠀⣿⣿⡇⠐⠀⠀⠀⣿
⠀⠀⢸⡀⠀⠈⠁⠀⠀⠙⠁⢠⠻⡀⠈⠉⠀⠈⠀⠀⢀⣿
⠀⠀⣰⢿⡀⠐⡀⠀⠀⠂⣠⠟⣄⠻⣤⣀⠂⠐⢀⣤⡿⣷
⠀⠀⣿⢤⡌⠛⠶⠶⠾⠛⢠⡜⢣⡜⢢⣍⡉⢉⢉⡄⢸⠘⣇
⠀⢰⡇⡇⢞⢯⢵⡪⢝⡣⢕⡪⢕⡪⢕⡪⢕⢢⡹⢳⣗⠆⣿
⠀⠈⣧⡑⡺⡳⠮⢎⡱⢎⡱⢎⡱⢎⡱⢎⠱⡆⠳⢺⢝⢠⡟
⠀⠀⢻⣄⠲⢆⡸⠘⣷⣌⠣⢜⡣⠜⢃⣴⠟⡨⢱⠇⣠⡿
⠀⣾⠛⡉⠿⣶⣬⣁⣂⣈⣛⣦⣡⣾⣋⣀⣁⣬⣴⣟⠁
⠘⣯⠰⢎⡱⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠙⣶
⠀⠈⠻⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠁⣿⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡄⢡⢌⡛⣿
⠀⠀⠀⠀⣿⣤⣶⣄⣈⣴⣌⣡⡟⠀⠻⣄⠊⠱⢊⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠿⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠀⠀⣀⣴⣾⣿⠿⠿⠿⠿⠿⣿⣷⣤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⢀⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣧⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⡀⠈⣿⣿⠁⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⢀⣿⡏⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠛⠋⢀⣼⣿⣷⠀⢻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣽⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⣿⡆⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀
⠀⠀⠀⠀⠀⢀⣾⣿⡟⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠈⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀
⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠉⠛⠿⣿⣿⣶⣶⣾⣿⡿⠟⠋⠀⠀⠀⠀⠙⢿⣷⣦⣄⣀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣧⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⢀⣴⠟⢛⡛⢷⣆⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⠿⠟⠛⠉⠀⢿⣿⡄⠀⠀
⠀⠀⠀⠀⢸⣿⣿⢸⡇⠀⠈⠁⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⢶⣦⡀⠀⢸⣿⡇⠀⠀
⠀⠀⠀⠀⠀⣿⣿⡘⣧⡀⠀⠖⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠐⠂⠈⢿⡄⢸⣿⡇⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣷⡈⠙⠻⠛⠋⠀⢴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢻⣆⠀⠀⠀⠀⣼⠇⣾⣿⠃⠀⠀
⠀⢀⣤⣤⣼⣿⡟⢿⣿⣦⣀⠀⠀⠀⠈⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠀⠻⢷⣬⡴⠟⢋⣼⣿⡟⠀⠀⠀
⠀⠸⣿⣿⠿⠟⠁⠀⠙⠿⣿⣿⣶⣤⣄⣀⡀⠙⢿⣿⣷⣄⠀⠀⢀⣤⣾⣿⡿⠛⠁⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣀⣀⡀⠀
⣴⣾⣿⡿⠀⠀⠀⠀⠀⣠⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣭⣤⣤⣤⣴⣶⣶⣿⣿⡿⠟⠋⠘⠿⢿⣿⣿⠀
⣿⣿⣅⠀⠀⠀⠀⠀⣴⣿⠟⠁⣼⣿⣿⣿⣿⣿⠉⠉⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡟⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣧⣄
⠈⢿⣿⣷⣄⠀⢀⣾⣿⠏⠀⢰⣿⣿⣿⣿⣿⠇⠀⢀⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⠘⣿⣧⡀⠀⠀⠀⠀⠀⢙⣿⣿
⠀⠀⠙⠿⣿⣿⣿⡿⢃⣠⣤⣿⣿⣿⣿⣿⣿⣶⡄⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡀⠹⣿⣧⠀⠀⠀⢀⣤⣿⣿⠏
⠀⠀⠀⠀⢀⣿⣿⠁⣾⣿⠿⣿⣿⣿⣿⠃⠙⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠹⣿⣧⣶⣾⣿⡿⠛⠁⠀
⠀⠀⠀⢰⣿⡿⣿⣿⣿⡿⠀⠈⠛⠛⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⡋⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠘⣿⣷⡈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣿⣿⣿⣿⣿⣷⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⣿⣷⣦⣄⡀⠀⠀⣀⣤⣶⣿⡿⠋⠀⠈⣿⣿⣆⢠⣴⣶⣦⣄⠀⢀⣴⣶⣦⣀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⠿⠛⡉⠀⠀⠀⠀⠈⠿⣿⣿⡿⠛⠿⣿⣿⣿⡿⠛⠿⣿⣿⣿⠟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠉⠉⠉⠛⢷⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣤⡶⠾⠻⠶⣶⣄⡀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀
⠀⠀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠙⢿⣦⣿⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀
⠀⣼⡟⠀⠀⠀⠀⠀⠀⢀⣠⣄⡈⢿⣿⠀⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀
⢠⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠈⣿⡀⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀
⠘⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⢠⣿⢷⣄⡀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣦⡀⠀⠀⠀
⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠙⠻⠷⠶⠶⠶⠶⠟⠋⠁⠀⠙⣷⠀⠀⠀
⠀⠀⠙⣷⣤⣀⡀⠀⠀⣀⣠⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⢸⡇⠀⢹⡇⠀⠀
⠀⠀⢸⡏⠉⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠁⠀⣸⡇⠀⠀
⠀⠀⢸⡇⠀⣰⡆⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⣰⣿⣁⠀⠀
⠀⠀⠈⣿⡀⠙⠃⠙⠁⠀⠀⣤⣄⣀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣠⣾⠟⠉⢻⣧⣀
⠀⠀⠀⠘⣿⣄⡀⠀⠀⠀⠀⠈⠉⠙⠛⠷⢶⣴⡟⣁⣠⣤⡶⠾⢿⣯⠀⠀⠀⢀⣽⠟
⠀⠀⠀⠀⣾⠟⠻⠷⣦⣤⣤⣤⣤⣴⡶⠶⠶⠛⠛⠉⠉⠀⠀⠀⣀⣹⣷⣀⣠⡿⠋⠀
⠀⠀⠀⣰⡿⠀⠀⠀⠀⣹⡏⠀⠀⠀⠀⢀⣀⣠⡤⠤⠶⠒⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀
⠀⠀⠀⠻⣷⣤⣀⠀⢠⣿⡤⠴⠖⠚⠋⠉⢁⣀⣤⠤⠴⢾⡿⠙⠛⠋⠙⠿⠟⣿⡆⠀
⠀⠀⠀⠀⠀⠉⠛⠻⣿⣯⣠⠤⠶⠒⠛⠉⠉⠁⠀⣀⣀⣼⡇⠀⠀⠀⠀⠀⢀⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⣀⣀⣠⣤⣴⡶⠾⢿⡿⠋⠙⣷⣄⠀⠀⢀⣠⣾⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠛⢛⣉⠉⠁⣠⣄⣠⡿⠁⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣴⠟⠻⠷⠿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠛⠛⠛⠛⠛⠻⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣠⣶⣿⡿⠿⠿⠿⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡄⠀⣿⣿⠇⠀⢀⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠇⢰⣿⡟⠀⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠋⢀⣾⣿⡇⠀⠈⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⢿⣷⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀
⠀⠀⠀⠀⠀⢀⣾⣿⠟⠉⠻⣿⣶⣄⣀⡀⠀⢀⣀⣀⣤⣶⣿⠿⠋⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠃⠀⠀
⠀⠀⠀⠀⢠⣿⣿⠃⢀⡠⠤⠀⢩⡛⠿⠿⢿⣿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠙⠿⣷⣤⣤⣀⣀⣀⣀⣠⣤⣴⣾⡿⢿⣿⡄⠀⠀
⠀⠀⠀⠀⣾⣿⡇⢠⠋⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠛⢛⣉⠁⠀⠀⢻⣿⡄⠀
⠀⠀⠀⠀⣿⣿⠁⣮⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠉⢢⡀⠀⣿⣷⠀
⠀⠀⠀⠀⣿⣿⠀⠘⢦⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢹⠀⢸⣿⡄
⠀⠀⠀⠀⢹⣿⣇⠀⠀⠉⠉⠉⠉⠀⢴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⡼⠀⣸⣿⠇
⠀⠀⢠⣴⣤⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠈⠲⠤⠤⠴⠊⠀⢠⣿⡿⠀
⠀⢀⣸⣿⡟⠛⠿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀
⠀⢿⣿⠛⠃⠀⠀⠀⠈⠙⠻⢿⣷⣦⣤⣄⣀⣀⠀⠉⠻⣷⣦⡀⠀⣀⣴⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠁⠀⠀
⣾⣿⠿⠃⠀⠀⠀⠀⠀⠀⢠⣾⣿⠛⠛⠻⠿⠿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⠿⠟⠁⠀⠀⠀⠀
⠙⢿⣦⣄⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⢠⣶⣾⣯⡉⠉⠛⣛⣿⣟⠛⠛⠛⠛⠛⢿⣿⡿⠿⢿⣿⣶⣶⣤⣀⠀⠀⠀⠀
⠀⠀⠙⠻⣿⣶⣦⣤⣼⣿⣿⡀⠀⢀⣠⣤⡀⠀⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠉⠙⠻⣷⣄⠀⠀
⠀⠀⣴⣾⡿⠿⣿⣿⡿⠛⠻⣷⣶⣿⠟⠛⣿⡆⢻⣿⣿⡿⠟⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⢠⣴⣾⡿⠀⠀
⠀⠀⣿⡏⠀⠀⠈⠉⠁⠀⠀⠈⠛⠁⠀⠀⣿⣿⠀⠈⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⣀⣸⣿⠁⠀⠀⠀
⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣾⡿⠿⠋⠀⠀⠀⠀
⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠻⣷⣤⣄⣀⣀⣀⣀⣤⣶⣿⠟⠁⠀⠀⠀⠀⢹⣿⠏⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⣠⣴⣾⣶⣄⠀⠀⢀⣤⣦⣄⡀⠀⢨⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠛⠉⠈⠻⣷⣾⡿⠟⠉⠛⠿⢿⠿⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠉⠀⠀⠀⠀⠀⠒⠐⠈⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠻⢾⣶⣄⠳
⠀⠀⠀⢀⣴⣟⣭⣶⣶⣶⣯⣷⣤⣝⣿⣷⣴
⠀⠀⣴⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢷⣿⠾
⠀⢰⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢷⠀⣠⣀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡎⣞⣶⣿
⠀⣿⣿⣿⣿⣿⢿⣿⢟⣛⣃⠿⣿⣿⣿⣿⣿⣿⣿
⠀⢻⡹⣿⣿⣿⡹⣳⠁⠀⣠⢟⠉⠓⣭⠿⣿⢇⡇
⠀⠀⣇⣿⣿⢟⡞⠉⡭⢶⣞⢝⡆⠀⠀⠙⣜⢻
⢀⡿⣿⣿⣿⣾⠀⠀⠻⡿⠀⠈⠀⠀⠀⠀⠹⡌⡇
⣏⠿⠿⢿⡗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠇
⠉⠉⢽⡾⠛⠋⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⣾⠉⢌⢔⡂⢹⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠹⣄⠑⢑⠂⣸⣀⣤⣤⣀⣀⡤⠀⠉⣙⡄
⠀⠀⠀⠀⠙⠓⠟⠒⠂⠀⠀⠀⠙⠋⠉⠉

⠀⠀⠀⠀⠀⠀⣠⠾⣛⢷⡀⣴⠃
⠀⠀⠀⠀⠀⠀⣙⣦⠻⠗⣻⠷⠶⠶⢶⣄
⠀⠀⢀⣤⣤⣾⠁⠀⠉⠉⠉⠀⠀⠀⠀⠙⣧⣤⣦
⠀⠀⣿⣺⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⡌⣧
⠀⠀⠿⣴⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣧⠏
⠀⠀⠀⢻⣀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⣰⣋
⠀⠀⢠⠟⣬⣛⢉⣤⣉⠻⢦⣴⠟⢁⣈⣉⢭⣴⡘⣷
⠀⠀⡟⠋⠉⠉⣿⣇⣸⢌⣿⣿⡇⣿⣈⣿⠘⠋⠉⠙⣇⡀
⠰⠻⡗⠀⠀⠀⠈⠛⠉⠉⠓⠶⠛⠉⠛⠋⠀⠀⠀⠋⣿
⠀⣤⣷⠂⠀⠀⠀⠀⠀⠈⣻⢙⠋⠀⠀⠀⠀⠀⠀⢸⠏⠃
⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠙⠿⣦⣤⣀⣀⡰⡶⡀⣀⣀⣤⡶⠛
⠀⠀⠀⠀⠀⠀⣼⠁⣤⡤⣵⢸⣷⣤⣤⠻⡄
⠀⠀⠀⣴⣦⢰⢏⠀⠀⣠⡏⢸⢷⡀⠀⢰⣿⢀⡶⣆
⠀⠀⢸⠁⢠⣿⡸⠀⠛⢿⣧⣏⣼⠈⠀⢿⢸⡟⡔⣿
⠀⠀⢸⡀⡸⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠠⠎⣿
⠀⠀⠈⠻⠿⠛⠙⠳⣦⣤⣤⣤⣤⣤⣴⠿⠛⠿⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢵⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣷⣿⠿⠛⢾⣔⠀⠀⠀⠀⣀⣤⣤⣤⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣿⠛⠹⣿⠀⠀⠀⠀⠹⣿⡢⠀⣐⣿⠛⠙⠛⠿⣷⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠋⠀⠀⠈⠀⠀⠀⠀⠀⠸⣿⣂⣼⠃⠀⠀⠀⠀⠈⢿⣮
⠀⠀⡀⣠⣦⣰⠀⠀⢉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣀⠀⠀⠀⠀⠀⠈⣿⠐
⠀⢤⣿⠟⠁⠙⣿⣶⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢼⣿⠀⠀⠀⠀⠀⢸⣿⡄
⠐⣿⠁⠀⠀⠀⠀⠻⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⣿⣧
⣯⣿⠀⠀⠀⠀⠀⣾⡿⠛⠃⠀⠀⠀⠀⠀⠀⢠⣶⣦⣤⣾⡿⠀⠀⠀⠀⠀⠀⠙⢿⣶⡢
⠯⣿⠀⠀⠀⠀⠀⢿⣦⢀⣀⣥⣾⣷⡀⠀⢠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀
⠀⢟⣿⣄⠀⠀⠀⠀⠙⠟⠋⠉⠀⠈⠛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣖
⠀⠀⠐⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣶⡀⢀⡠⠖⠈⠉⠑⡹⣿⢀
⠀⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⣿⠀⠀⠀⠀⠀⠀⠀⣿⣾⣒⠠
⠀⠨⣿⠃⠀⠀⠀⠀⢀⣶⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⣸⠀⠀⠀⠀⠀⠀⠛⣿⡇
⠀⡫⣿⠀⠀⢀⣀⣄⣿⣿⣿⡿⠀⠸⡇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠣⡿⡀⠖⠁⠀⠀⢸⣿⣿⣧⣭⣼⠁⠤⣀⣀⡤⠆⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢻⢼⡠
⠀⠰⣿⣇⠀⠀⠀⠀⠀⠙⠿⠿⠟⠋⠀⠀⠀⠀⠀⡀⠀⢰⣦⠀⠀⠀⣠⣶⣾⣷⣶⣄⠀⣼⡿⠃⠀⠁
⣪⢞⡭⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣠⣿⠻⢶⠾⠟⠀⠀⣽⣿⠀⠀⠀⠊⢿⣿⣿⠍
⠀⠀⠀⣹⣧⣭⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⣿⠃⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⣀⡀
⠀⠀⠠⣮⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣶⣿⡶⠀⠀⢸⣿⠁⠀⠀⠀⠘⡠
⠀⠀⠐⠈⠀⠐⠭⣿⣦⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠂⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣿⠉⠀⠀⠀⠀⢠⠿⠃⠁⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠰⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⡾⠀⠀⠀⢀⢼⠌⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⠁⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠃⠈⣿⠄⠀⠀⠀⠂⠀⣠⡞⠈
⠀⠀⠀⠀⠀⣶⣷⣶⢄⡾⡏⠀⠀⣀⣀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⣄⣴⣶⣅⠘⠀⠀⣿⠰⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣌⣿⠀⠈⣿⡧⠀⠀⠀⠘⠿⣿⣶⣾⣿⠃⠀⠀⠀⠀⠀⣵⣿⠃⠀⢿⣿⠀⠀⣿⢐
⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠇⠀⠀⢸⣿⡆⣰⡏⡀
⠀⠀⠀⠀⢺⠄⠀⠀⠀⢻⣿⡅⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⢿⡟
⠀⠀⠀⠀⢏⣷⣤⢤⣾⢿⡐⢹⣿⣿⣶⣦⡤⣤⣐⣒⣒⣒⣒⣠⡿⢿⣤⣀⣀⣿⣫⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠛⠿⠿⠿⠿⠛⠂⠈⠀⠘⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣷⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⡋⢡⡔⠢⢠⡈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⢠⡜⠱⠃⡊⠱⢎⡱⠄⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢁⡢⢜⠅⣼⣿⣿⠃⡪⢕⡪⢄⡠⢄⡈⠛⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢀⡱⢎⡱⢰⣿⡿⢁⡪⢕⡪⢕⠊⣠⣤⠢⢜⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡕⡊⢱⢪⢸⠟⡔⡪⢕⡢⢔⠊⣾⣿⡿⢠⡜⠣⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡙⠀⠟⡩⢢⡜⢇⡨⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠟⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⢰⣦⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⢈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠁⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⡁⠀⠠⠄⠀⠀⣀⣀⣤⣀⣀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣴⠶⠿⠿⠷⣦⣄⠀⢀⠀⠐⠂⡀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠠⠀⠀⠀⠂⣀⣶⠟⠋⠉⠀⠀⠀⠈⠙⠿⣦⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠁⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⡀⠀⠈⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠠⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢀⣤⣶⣦⣿⡇⠀⠂⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠐⠀⢿⣿⣿⣿⣷⣤
⠀⠀⣾⣿⠛⡩⠀⣿⡇⠂⠠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⢻⠀⠈⠀⠀⡇⠀⠀⠀⢀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⠠⢆⣀⠻⣷
⠀⣾⡿⢠⡕⠪⠀⣿⠄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⢸⣿⠀⠸⢇⡐⢻⣷
⢰⣿⠁⠑⣁⣀⣀⣿⡀⠁⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⣿⠀⡀⢀⠀⣿⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣾⣷⣶⠘⠈⣿
⢸⣿⠨⠻⣿⠿⠟⣿⡇⠂⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡀⠀⢀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡀⠀⠂⢸⣿⢠⡩⢩⡢⢸⣿
⢸⣿⠨⢕⡪⢕⡂⣿⣇⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢀⠀⠀⠀⣿⡿⡘⢣⡜⠣⣼⣿
⢸⣿⠐⢪⢕⠸⠕⢹⣿⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠁⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⣿⣧⣤⣀⠪⠅⣿⡏
⠀⣿⡄⡂⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠀⠛⠷⣦⣤⣤⣤⣶⠾⠟⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠉⠛⠛⠿⠿⡶⠶⠿⠛⠋⠀⠀⠀⠀⠀⠀⢰⣿⠛⠿⠿⠃⣼⣿
⠀⠹⣿⠈⢄⡩⢄⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⡜⡣⠊⣼⣿⠃
⠀⠀⠹⣿⣄⠊⠃⣀⣿⣿⠀⢀⠀⠐⠀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀⠂⠠⠀⠀⢠⣿⣶⣶⣶⣿⠟
⠀⠀⠀⠀⠛⠿⠿⠟⠉⣿⣦⣶⣿⣿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣿⣿⣷⣾⡿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠋⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⣀⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠺⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣤⣀⣀⡀⠀⠀⠀⣀⣀⣴⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⠗⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣅
⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢿⣆
⠀⠀⠀⠀⠀⣼⣿⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠌⣤⡀⠀⠀⢿⣆
⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⡀⣶⡆⠈⠀⠀⡈⢰⣦⡀⠀⢀⣡⣶⡄⠀⠀⠀⢰⣦⣀⠀⣀⣀⣶⣶⠠⠀⠀⡀⣿⣄⠀⢀⣀⣴⣄⠀⠄⠀⠀⠁⣿⡇⠀⠀⠀⣿⡆
⠀⠀⠀⢀⣿⠇⠀⠀⠀⠐⠀⣿⠃⠀⠀⠀⠁⠀⠙⠿⠿⠿⠿⠋⡀⠂⠀⠀⠀⠙⠻⠿⠿⠿⠛⠀⠂⠀⠀⠀⠀⠛⠿⠿⠿⠛⡁⠀⠀⠀⠀⠄⣿⡇⠀⠀⠀⢸⣿⡀
⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⢸⣿⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠈⡠⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠠⠊⠀⠛⢿⣦
⠀⣴⣿⠃⠀⠂⠀⠀⠀⠐⣸⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠂⠀⠀⠀⠀⣿⣧
⠀⣿⠃⠄⠂⠀⠀⠀⠄⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⡀⠀⠠⠀⢸⣿
⠸⣿⠀⠀⠀⠀⣿⠃⡀⠀⣿⡟⢁⡀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣷⣦⣤⣾⣿⠿⠀⠀⠀⠀⠀⠀⠘⣿⣶⣶⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⡀⢸⣿
⠀⣿⣧⠂⠄⠀⣿⡆⠁⠀⣿⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠅⣿⡇⢀⣿⡟⠀⠀⢀⣿⡟
⠀⠈⢿⣷⣄⣈⠀⠛⢿⣿⣿⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠋⢀⣠⣶⣿⠟
⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣧⠡⢀⠀⠀⡀⠠⠀⠀⠀⠀⠠⠠⠄⡀⠈⠀⠀⠀⡀⠀⣼⣿⣿⡄⠡⠄⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢄⠀⠀⠀⣀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⢿⣷⣄⠀⠀⠀⢀⣴⣶⣤⣀⣀⣀⣀⣤⣾⣿⠃⠈⢿⣶⣤⣀⣥⣶⣷⡀⠀⠂⠀⠐⢀⣴⣿⣿⣶⣶⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⠟⠉⠙⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠿⣿⣿⣿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⢢⢜⡢⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡐⡨⢀⣾⡧⡑⠹⠾⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠠⠢⠢⠸⠋⢔⢆⢁⣶⠐⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠿⠶⠐⠓⠒⠃⠜⠣⡉⢡⠢⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢠⠇⠀⠀⠀⣠⡶⠛⠉⠛⠻⣦⡀⠀⠀⠀⠀⢀⡶⠛⠉⠉⠉⠛⢶⡀⠀⠀⢿
⠀⠀⠀⠀⣿⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⡇
⠀⣠⡶⠓⡟⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠛⠳⣄
⢰⠃⠂⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⢠⣿⣿⠀⣸⠀⠀⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠸⠣⠸⡄
⣿⠨⠍⠉⡇⠀⠀⢿⠀⠀⠀⠀⠀⠀⠛⠉⠀⡟⠀⠀⣿⠀⠙⠋⠀⠀⠀⠀⠀⢀⡏⠀⠀⣿⢙⡋⠁⡇
⢸⡀⢡⣤⣧⠀⠀⠀⢷⣀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠷⣄⠀⠀⠀⠀⣀⣴⠋⠀⠀⠀⣿⣤⡅⠀⡇⠠
⠀⢷⡀⠀⣩⣤⡀⠀⠀⠈⠛⠻⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⣠⠶⠶⣄⠃⢖⠅⣼⠀⠂
⠀⠀⠉⣹⠁⠀⢹⣤⡶⠶⠶⠶⠶⠶⠾⠿⠻⠛⠛⠛⠛⠛⠛⠛⠛⠻⠷⠶⠶⡏⠀⠀⠈⣷⣶⡛
⠀⢀⡾⠁⠀⠀⠈⠉⢷⠶⠶⠶⠶⠿⣻⠛⠛⠛⠛⣟⠛⠛⠛⢿⠛⠿⠶⠶⡾⠉⠀⠀⠀⠀⠀⠉⣷
⠀⣿⠀⠀⠀⠀⠀⠀⢾⡶⠶⠶⠶⢀⡏⡜⡣⢎⠃⡏⡪⢅⡨⠈⡇⠛⠛⠋⢷⡀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠀⠀⣀⡿⠀⠀⠀⢸⠀⢪⠕⢪⡀⢃⡣⢌⡕⠀⡟⠀⠀⠀⢸⠀⠀⢀⡀⠀⠀⠀⣾
⠀⠈⢷⣄⠀⠀⠀⠀⠉⠀⡀⠀⠀⣘⣆⠢⢸⢆⡘⢱⡆⢪⡕⣰⠣⣄⣀⣼⠃⠙⠛⠋⢠⣤⡶⠛
⠀⠀⠀⠀⠉⠛⣿⠀⠀⠀⠙⠿⠟⠁⠈⠷⣤⣑⠘⠑⢃⣈⡶⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⡾⠛⠻⣦⣀⣀⣀⠈⠉⠉⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⣠⠶⠷⢾⠀⠀⠀⠘⠁⠀⠈⢷⣀⡾⠀⠀⠈⢷⣤⠾⠁⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣤⡶⠟⢀⠄⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠙⠶⣤⣤⠶⠛⠶⠶⠾⠋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠁⠈⠁⠀⠈