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°.✩┈┈∘*┈🌙┈*∘┈┈✩.°
⠀⠀⠀⠀⠀⠀⠀⠈⠡⠃⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⡼⣱⢢⠖⠀⠀⠀⠀⠀⠀⠈⢻⡉⠈⠉⠁⠋⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⣠⠏⠀⢀⡖⢾⡏⠀⠀⠀⠀⠀⠐⠒⠂⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣶⣶⣤⣀⠀⠈⠢⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣴⡾⠛⣆⠀⠀⠀⠀
⢀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⠀⣠⠞⠁⢀⣠⠞⢧⣾⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣶⣾⣿⣿⣿⣷⣦⣀⠀⠀⢀⡰⠋⢀⣴⣿⠟⠁⠀⢿⢻⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⡾⣷⡠⠖⠋⠀⠀⠀⣠⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣛⠉⠛⠛⠉⠛⠛⠻⠛⠷⢶⣿⣴⣾⡿⠋⠁⠀⠀⣇⠘⠞⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣖⣿⣿⣿⣯⣤⣤⣀⠀⠀⠀⠠⠀⠘⠦⠙⢹⣿⠴⠊⠀⠀⠀⢸⣤⠞⢁⣠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⣿⣿⣿⣿⠟⠛⣿⠀⢀⣀⠀⠀⠀⠀⣠⠖⣻⣿⣿⣿⣿⣿⡟⣏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠿⣦⡀⠀⠀⠀⠈⣿⣴⠟⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠁⠀⠀⠀⠙⣎⣠⣷⣾⣷⣿⣿⣿⣷⣼⣡⡶⣫⣿⣿⣿⣿⣿⣿⣭⣾⣾⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⡀⠱⡀⠛⠁⢀⣴⣶⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⣀⣀⣼⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⡿⢋⡿⠹⠿⠛⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⣀⣴⠋⠀⣼⡇⠻⣿⣷⡀⠱⡀⠀⠀⡇⠹⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣀⠤⢤⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣿⣿⡟⢻⣿⣿⣟⠀⣸⣷⡄⢠⡾⠛⣿⣿⣿⣧⢀⣠⡄⠀⣰⣿⠁⠀⢠⡿⠁⠀⢹⣿⣷⡀⠛⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⢿⣹⣏⠀⠀⡏⢿⣇⢈⡿⠉⠉⠛⣿⣿⣿⣿⠁⠀⠿⣻⣿⣿⣿⣿⣷⣸⡿⠁⠀⢠⣿⠁⡄⢠⢸⣿⣿⣷⠀⠀⠀⠈⠋⠀
⠀⠀⠀⠀⠀⠀⡔⠋⠃⠀⠀⢠⣿⣿⣿⣿⣿⡿⣿⡇⡄⡿⢻⣷⡶⢷⣾⣿⣿⣧⡀⠀⠠⣿⣿⢷⣿⣷⣦⣾⢿⣿⣿⣿⣿⣿⣟⣡⣀⣴⡿⠃⣼⡇⢸⢸⣿⣿⣿⣆⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣼⣿⣿⢻⣿⣿⡇⢿⣇⣿⠃⡾⠁⠀⠀⠀⠈⠻⣷⣝⢆⠀⢹⡃⡿⠙⣿⣿⣿⣀⣀⣵⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣠⣿⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀
⠉⠐⠐⠶⠦⠤⠤⢶⣿⡿⠹⢻⣿⣿⢸⡿⣿⣿⡘⣿⣿⣀⡃⠀⠀⠀⣠⣶⡶⣌⣿⡜⣆⠀⣿⡇⢠⡟⢻⣿⣿⣿⡟⡡⠛⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠿⠋⠀⠠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠰⢿⣿⠀⢳⠘⠿⣷⣽⣏⢙⣭⣄⡀⠀⠸⣟⣻⡾⠘⣿⡻⠀⡿⢷⡼⠀⣠⣿⣿⣿⣿⣷⣴⣟⠁⠀⠸⢿⣿⣿⣿⣿⣟⣯⣼⡶⠀⠀⠀⠀⠀⠀⠀
⣷⠂⠀⠀⠀⠀⢀⣿⣿⣷⠀⢠⡟⠙⣆⠈⠃⠀⠈⠛⢿⡋⠙⠳⣝⢦⡀⠈⠁⠀⠀⡇⠃⠀⠇⢸⣇⡴⢫⡟⢐⣿⣿⣿⣿⣗⠀⠀⠀⠘⣽⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠈⠈⣿⣿⣷⡟⠀⠀⠙⡄⣠⡧⠀⠀⠀⠉⠀⠀⠉⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⢁⣞⣠⡾⠛⣵⣿⣿⣿⣿⢞⣤⣾⢿⣿⠋⠉⢹⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀
⡿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⢿⣋⡁⠀⠐⠋⠩⠿⢿⣿⣿⡿⢣⣿⡇⠀⠀⠈⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⢸⢹⣿⣿⡇⠀⠀⣜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠶⣶⣶⡖⢂⣴⣿⢿⡏⣰⣿⣿⣯⣲⠃⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠃⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠶⠾⠷⣶⣬⣛⠻⣅⠀⣠⣿⣿⣿⣿⣿⣿⣣⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⠞⠣⡀⢠⡾⣿⣳⡍⠻⣷⣌⢿⣼⣿⣿⣿⡿⠿⠿⠯⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠉⢩⣿⣿⣿⡄⠀⠀⠀⠀⠀⣴⡾⠿⠽⠿⣿⣿⣷⣝⠲⡀⠀⠀⠀⠀⠈⠠⢴⣞⠚⢷⣽⡿⠁⠀⠘⣿⣯⣿⣽⣿⣿⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡀⠀⠀⠀⠀⠀⠀⣸⡿⣿⣿⣷⠄⠀⠀⠐⣾⠁⠀⠀⠀⠀⠀⠹⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⢫⢳⡘⣦⠀⠀⠀⠀⣹⡇⢇⣤⣾⣿⠀⠀⠉⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣧⠀⠀⠀⠀⠀⢀⡟⠁⢸⣿⣿⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⡎⠇⢸⠀⣀⣠⣴⣿⣷⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢿⣧⠀⠀⠀⢀⡞⠁⠀⠀⢿⣿⣿⣆⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣸⠇⠈⣠⣾⡋⢉⣙⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣤⣽⣿⣷⣦⣼⡇⠀⠀⠀⠘⣿⣿⣿⣇⠀⠈⠉⣄⣀⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣵⣋⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣟⣿⣙⠿⢿⣿⣶⣄⣀⣀⣹⣹⢿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⢙⣿⣿⡟⠛⠿⣷⣿⣿⣿⣿⣿⣿⡟⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣾⡏⠉⠛⠿⢿⣿⣶⣤⣀⣀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣭⣿⢿⣿⣿⣿⣿⣿⣿⢟⣿⠏⢀⡇⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⢙⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣹⣿⣿⢿⣿⡿⣷⣶⠦⠤⣶⣤⣶⣾⣿⣿⣿⣿⡿⠿⢿⣿⠿⠿⠿⠛⢋⣴⠟⢁⠴⠻⠀⠀⠀⠈⠛⠲⢤⣄⡀⠀⡀⠀⠀⠀
⠀⣀⣤⣾⣿⡿⠿⠛⠛⠋⢉⢩⣿⣷⣀⠀⠀⠀⢀⡿⠛⠹⣆⠀⠰⠏⠁⠀⠀⠀⢩⣿⣿⡿⠟⠻⣭⡀⠀⠀⠱⢤⣴⠶⠚⠋⠁⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀
⠾⣛⣋⣩⡤⠒⠒⣲⣷⣾⡏⠀⣿⣿⣏⢉⣽⠊⠉⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣖⠒⠒⠈⠁⠀⠀⠀⠀⢨⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠀⠀⠀⣸⣿⣿⣿⣿⣆⠘⣿⣿⠉⠀⠁⠀⠁⠀⠀⠀⠀⠻⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠸⣿⡝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⣿⣿⠛⣿⣿⣿⣿⠟⠛⢛⠷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠻⢷⣄⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⠛⠉⠀⠀⠀⠀⢠⠇⢰⢿⠙⣆⠉⠳⠦⣤⣀⣀⣀⣀⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⢹⣿⣭⢂⡀⢸⡆⠸⣿⣯⣛⢿⣿⣿⣷⣶⣦⣤⣽⡳⠶⠶⠒⠚⠛⢻⣀⡀⠀⠀⠀⠀⠀⠀⠀⢿⠋⣠⠋⠈⣧⠈⠳⣄⡀⢀⠀⠀⠠⠀⠀⠀⠀⠀⢠
✦✦✦✧✧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⠷⠀⠀⢀⣠⠴⢦
⢠⣶⡢⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⣠⡶⠋⡴⢃⡟
⠈⢷⣉⠢⣘⣟⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡤⠃⢀⡴⠋⣱⡷⣫⣶⠏⠀
⠀⠀⢻⡉⠙⠛⢦⠈⠙⠦⣄⠀⠀⠀⡖⠶⢤⣤⡄⢀⣀⣀⣀⡀⠀⢀⣀⣤⡀⢀⡴⡿⠁⣰⠟⠋⡀⠃⠀⠀
⠀⠀⠀⠙⢶⡦⠤⣝⣦⣄⠘⡷⣄⡀⠃⣼⣿⣿⣷⣿⠏⠉⠉⠁⠀⠙⠉⢀⡷⠋⢸⢃⠜⢁⣠⡾⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠷⣄⡀⠈⠑⢷⡄⢹⠇⠀⠿⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡿⠛⠉⣴⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⠒⠦⣝⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣣⣫⣴⣲⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠒⠂⢿⠀⠀⠘⠻⠇⢀⣀⠰⠿⠋⠀⠀⢀⣯⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⡟⠾⣧⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⣞⣷⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣨⡧⠘⠿⠦⣤⠀⢰⠄⠐⠃⠈⢿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⣶⡅⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠠⣿⡒⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⢂⣴⣞⣩⣼⣯⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠵⣌⣉⠛⢥⡭⠷⢦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⡾⠭⠿⣛⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢾⡉⠉⠉⠉⠉⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⣷⠆⠀⠲⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠛⢀⡄⢹⣇⠀⠀⠀⠀⢸⠀⠀⠀⢰⠀⠀⠀⢠⡄⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠲⡦⢀⣴⠒⠛⠋⠉⢠⣟⠀⠀⠀⠀⢀⠴⠀⠀⢸⡆⠀⠀⣸⡈⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢼⣿⡆⠀⠀⠀⢸⣆⣀⡀⢸⡋⠀⠀⣿⡿⡦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⠀⠙⠛⠞⠛⠛⠛⠉⠉⠙⣿⣿⠂⠃⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠰⠀⣠⡈⠈⡦⢶⡄⢀⣤⢀⠀⠀⠀⠀⠀⣀⣤⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠋⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀