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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠒⠒⠲⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀
⣶⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠁⠀⠈⠉⠉⠉⠓⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀
⠘⢷⣶⡾⠿⠭⣙⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠙⡆⠀⠀⠀⠀⠀⠀⠈⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⡀⠀⠀⠀⠀⢀⠞⠁⠈⠑⠢⠤⣀⣀⡀⠀⠀⠀⠀⣀⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢳⠀⠀⠀⢠⣯⢴⣶⣖⣺⣿⢲⣦⡬⣍⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣈⢧⡀⠀⠸⣷⣾⣡⣿⣇⣼⣏⣨⡷⢛⣯⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣯⣓⠂⣼⡿⢷⣾⣉⣀⣉⠉⠳⠟⣿⠴⡿⢻⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣷⣶⠤⣄⠀⠉⠙⣲⢄⠀⠀⠻⣿⣿⣿⡜⣷⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⠀⠀⠉⠲⣤⣼⣾⣷⡄⠀⠈⠁⢈⣇⣁⠀⠀⠀⠀⠀⠀⣰⠋⠈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡟⠻⣿⡿⣆⢀⣄⢀⣼⠿⣟⠛⠛⡄⠀⠀⣸⡏⣹⠀⠀⠀⠀⢀⡴⠁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣦⡙⠒⠻⣄⡽⡏⣻⡟⢻⣿⢻⣤⠻⣿⣾⣿⣿⢁⣿⡆⠀⠀⣠⡞⠁⢀⣾⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠛⠿⠶⣾⣤⣿⣧⣟⣎⣉⣉⢙⣶⣿⣿⡿⠹⣾⣿⣿⡆⠀⢻⠀⢠⡿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠛⠛⠃⢰⠋⠀⣾⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⡀⠀⠀⠀⣀⡼⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ඞSUSSY
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠈⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠾⣟⣻⣽⣯⣯⣷⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⡀⠀⠀⢀⣾⣟⣥⡾⠟⠛⠉⠉⠉⣙⡿⣿⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣭⠥⠤⢬⡍⠻⣿⣦⣀⣼⡇⢻⣿⡀⠀⠀⠀⣠⣤⣽⣿⡏⢠⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠁⠀⠀⠀⠀⠘⠂⣼⣿⣿⣻⣿⣦⡙⠻⠷⠶⠶⠿⠿⠛⣉⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣟⡋⠛⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⠳⣤⠀⠀⠀⠀⢀⣤⣾⣿⣿⠛⢁⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⠛⢻⣯⡿⢿⡏⠉⣽⣟⣡⣤⣾⣵⣿⣿⣟⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠛⢛⣋⣤⣤⣤⣴⣟⡥⠤⣿⣿⣿⣿⣿⣿⠿⢛⣿⣿⡿⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣡⣤⣴⡿⠿⠿⣿⣿⡟⠻⣧⠀⠀⢿⣿⣿⣿⠋⡀⠀⠉⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣿⡟⠙⠉⠤⣤⡀⠀⠀⠀⠀⣠⡞⠃⠀⠀⠀⣿⣧⣿⣿⣶⣶⢶⣤⣶⣿⣯⣿⣿⡿⢸⢻⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠁⠐⢤⡀⠀⠙⢢⣤⣴⠟⠉⠙⠛⠛⣿⣿⠿⣿⢿⣿⣟⣵⣾⣿⣷⣾⣿⣿⣿⣧⢸⡙⣷⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡜⢧⣧⣀⣭⣿⠿⢻⣏⡈⠛⢶⣄⠀⠴⡿⠋⢁⣤⣿⣿⣿⣿⣿⣿⣿⣷⡄⣽⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣾⣿⢽⣿⣿⣿⣦⣿⣶⢾⡿⠿⡟⠛⢿⡛⠋⣿⣠⡿⣿⡇⢈⣿⣿⣷⣿⣿⣿⣿⣿⠏⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢨⣭⡻⣆⣿⢻⡄⢹⠛⠻⣾⠷⣶⡭⠶⢶⣿⠖⠛⣻⡇⢨⣿⢸⣿⡇⣿⣿⣿⠉⣿⣿⣛⣿⣻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢀⡿⣧⠙⣿⡀⢿⢸⡗⠲⣧⠠⣿⡤⠴⣾⣿⠀⠀⣿⡇⠸⣿⠈⣿⣧⣿⣿⣿⣶⣿⢟⣿⣿⣿⣿⣿⣿⣿⣟⢶⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢻⡀⠹⡇⣤⠀⢳⠀⢻⡄⢼⣇⠀⠽⣿⠀⠀⠻⣧⠀⢿⣇⢸⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⢇⣭⣷⣦⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠈⣷⢀⡇⣿⠀⣼⠀⢸⡇⠘⡇⠀⠀⢿⣧⠀⠀⣻⡇⢘⣿⣮⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠻⢿⡿⠁⠀⠻⣮⠙⢶⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⣷⣍⣾⣧⡟⢡⣿⠀⢸⠇⠀⣧⠀⠀⢘⣿⠀⠀⠉⣧⠈⡩⣿⡇⣸⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⣻⣶⡄⠀⣹⣧⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⣶⣿⣿⣿⣿⡇⢸⠁⠀⣎⠀⠀⣿⡄⠀⠈⣿⡀⢸⣄⣿⡀⠀⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣴⣿⣿⣿⠿⠛⠀⣿⣿⠀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣋⣼⣿⣿⣿⠋⢿⣷⣰⡀⠀⢻⣗⢦⣸⣷⣀⣾⣿⣷⣾⣿⣿⣷⣾⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣧⠀⢇⡈⠻⢍⡠⣦⣴⣿⣿⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣿⣿⣿⠟⠁⠀⠈⢻⣿⣿⣾⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣯⣿⠶⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠱⠶⣦⣶⡶⠟⠉⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠀⠀⠀⠁⠀⠀⠀⠀⡹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠛⢦⣤⡀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⡇⠂⢘⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣤⣾⣿⣷⣦⡄⢹⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠏⢹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠃⠀⠀⠀⣈⢻⣿⣿⣿⣽⣵⣿⡿⡷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⢠⡼⣿⠁⢸⣿⣿⣿⣷⣌⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⣤⡾⠛⠻⣿⣿⣿⣿⣧⡛⠀⠀⠀⠀⠀⢀⣤⣴⣾⡿⠀⠀⠀⠀⢰⣤⣿⡟⠛⢻⡿⠋⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⣧⠀⠛⣿⣿⢛⣫⣴⣿⠃⠀⠀⠀⠀⣠⣶⣿⠛⠙⣦⠀⢻⣿⣿⣿⣿⣧⣿⡐⣤⡀⠀⠈⢻⡏⢁⣠⣴⡟⣀⣴⣿⣿⠟⠀⠀⢸⡇⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣄⣸⡇⠹⣦⣾⣋⣤⣴⡿⠟⠁⠀⠀⠀⢀⡾⣿⣿⣤⣀⣀⣠⣤⣿⣿⣿⣿⣿⠿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠁⠀⠀⠀⢸⠃⢠⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⢻⣿⣾⣿⠿⠈⠉⠀⠀⠀⠀⠀⠀⠀⢸⠇⠃⠙⣿⡉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⢸⢠⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣬⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣻⣿⠟⠁⢀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠿⣇⠀⣠⣏⣶⣿⣤⣶⣿⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠃⠀⠊⠉⣡⣾⣿⣿⣿⣿⣿⣿⢻⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣤⣶⣿⣿⡉⠙⢛⣿⣿⣿⣿⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⠿⠿⠿⠟⠛⠛⠛⠿⠶⠿⠿⠟⠛⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣹⡟⢀⣹⣧⠀⠉⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣭⣽⣍⣉⣈⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠻⠿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
💎💙🌊🌌🧊🌀🔵🐬🦋🌠🧿💦💧📘🌐⛲🐳🔹🐟🌃🟦🌧️🌨️🫐📖🧢🔷🥶🐋💤🧵🌧️💎💙📨💎🌊🌌🆒🦈🌏♿🌨🆓🥣👔🦕🔽👖👤👥🔃⬇️✈️🌐🖱️🌊🐚🎏🧺🌀🌊💎🚰❄🇫🇲⚗📥🌦️🛏️⤵️🇲🇩🇳🇮📤📧📪🇬🇹🇪🇪🏴🇹🇩🇪🇺
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢧⠀⠀⣠⡶⠖⠒⠚⠋⠁⠀⠀⠀⠈⠙⠛⠒⠒⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣷⣿⣋⠀⠀⠀⠀⠀⠀⠿⢯⣉⡉⠙⠓⢦⣄⠀⠀⠀⠉⠛⠶⠦⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⡀⠈⠛⠶⠤⠤⠶⠤⣄⡀⠈⠉⠉⠓⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡇⢀⣠⢤⡀⠀⠀⠀⠀⠉⠓⠶⢤⣤⣤⣤⣾⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⢰⣶⣶⣤⡀⠀⠈⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣧⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⣭⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡁⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠲⢤⡀⠀⠀⠀
⠀⠀⣿⡀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠲⣦⣀⠀⠀⠘⠿⣯⣉⠓⠲⠤⣀⠀⠘⠿⣭⣷⣦⡀⠀⠀⠀⠀
⠀⠤⢧⣝⣒⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠶⢦⣌⡙⠓⠒⠚⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣘⡏⠑⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣤⣤⣤⣀⠀⢀⣠⡤⠔⠒⠚⠉
⠉⠉⠉⠙⠳⢦⣄⠀⠀⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠼⠛⠉⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠈⠛⣶⡯⠏⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⡵⠋⠁⠀⠀⠀⠀⠀⣠⡾⠋⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣆⠀⠀⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡽⠋⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⢠
⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢼⡿⠙⣄⣀⣀⣀⠤⣴⢶⠚⠉⠉⠉⢹⣿⡏⠉⠉⠙⣓⣲⡶⢮⣀⠀⠀⠀⠀⢀⣤⡾⠿⠛⠛⠛⠉⠉
⡽⠋⠑⠦⢄⣀⣀⠀⠀⠀⣀⣸⠆⠀⢀⣈⡉⠀⠀⠀⣻⣾⠧⠶⠒⠶⠚⠛⠲⠶⣤⣤⣹⣾⠃⠀⠈⠓⡖⠚⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠓⣦⡤⠤⠤⣀⣉⢩⠿⡍⠁⠀⠀⠀⣿⡿⠇⠀⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠷⡄⠰⣏⡽⠃⠀⣹⣀⣀⣀⣀⣤⣤⠖⠚
⣼⠁⠀⠀⠀⠀⠈⠉⠛⠓⠒⠿⠟⢛⡻⣄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣴⠋⠉⠁⠉⠉⠛⠲⢿⣽⡀⠀
⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠨⡷⣄⣤⢿⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠀⠀⣴⠷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠉⠛
⠀⠀⠉⠓⠒⠦⠤⠴⠒⠒⠉⠁⠀⠀⠀⠀⠈⠈⠟⢯⡀⠈⠉⠒⠢⠤⣤⠤⠤⠴⠒⠋⠹⣍⣇⣠⠞⠁⠀⠈⠙⢦⣉⣿⠗⠒⠒⠶⠤⠤
⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣀⣸⣽⣃⣀⣀⣀⣤⡴⠚⠉⠹⡟⢢⣄⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⢸⠋⢱⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⢹⣿⣿⣿⠓⣦⣄⣀⠙⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠇⢠⡏⠀⠀⠈⣳⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢹⣦⡀⠀⢻⡿⠃⣴⠟⠀⠉⠉⠛⠀⠀⠀⠀
⠀⠀⠀⠀⠑⠦⣀⣀⣀⣀⠀⠈⠉⠒⠤⣤⠃⠀⠑⠄⠀⠀⠀⠀⣠⠞⠁⠀⠙⠀⠀⠀⣠⡾⠁⠙⠲⠾⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡞⠀⠀⣰⠟⠀⢀⣿⡿⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠔⠋⠀⠀⢰⣏⡤⠖⠉⠛⣇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢰⡀⠀⣶⣠⡀⣠⣒⣠⣆⣴⢀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣹⣼⣴⣾⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣾⣅⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣸⣾⣿⣿⣿⣏⠙⢛⡀⣴⣿⡟⣉⣔⠚⠋⠀⢸⣿⠿⣿⣿⣿⣿⣶⣤⣄⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣦⣾⣿⣿⠟⠋⠈⢛⣠⣼⣿⣿⣿⣄⠉⠟⠚⠚⠳⢠⣭⠀⠈⠉⢉⣽⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⡀⣠⣴⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⢩⣿⣿⠙⠻⢿⣶⣶⣦⣤⣤⣤⣶⣶⡾⠟⢋⣁⣙⡋⠿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣨⣾⣿⡟⠛⣿⣿⢿⣿⠀⡿⢗⠖⣡⣿⡟⢙⠓⠶⡄⣄⡍⠉⣩⣽⣿⣿⡍⡴⡷⡛⢙⢉⢻⢶⡀⠙⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣤⣾⠟⠅⣸⡟⠀⡶⠀⢀⣿⣟⢂⣍⠉⠀⢢⢪⣵⣿⠿⡋⠈⣿⣯⡠⡧⡤⠉⠩⢬⠍⠽⢦⡄⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣿⣿⡟⠛⠛⢁⣴⠜⢻⣿⡀⢩⣠⣾⣿⡁⠹⠟⢛⢺⣴⣿⠟⣁⣴⡿⠇⠉⢻⣷⣤⠈⠉⣀⡹⡕⠙⠈⣡⣤⣼⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⣿⣿⣿⣧⠐⠙⠘⢂⣴⣿⣿⠟⠛⢛⣿⡟⢿⣷⣶⣾⡿⣻⣥⠔⢻⢨⠸⠚⢣⣌⠻⣿⣶⣦⣈⣤⣶⣶⡿⠟⠛⠻⣿⣿⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣴⠿⣿⣶⣼⣿⣷⣶⡾⠟⠛⢩⣿⠀⣶⣸⣿⠀⢠⣿⣿⢿⣿⡇⠱⡤⠀⢀⠌⠐⠈⢡⣤⣼⣿⣿⣿⣯⣍⠀⠀⠋⠉⠀⢻⣿⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣼⣿⡆⠘⣿⣿⠘⣿⣆⠰⢶⡖⢿⣿⠀⢹⣿⡟⢠⣾⡿⢁⡈⠹⣿⣬⡖⠉⢸⣵⣶⣿⣿⣿⣭⣴⣶⣷⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⠟⠛⠃⣰⣿⣿⠀⠻⣿⣧⡼⠁⢸⣿⡀⢺⣿⢣⣿⣟⢰⡯⣷⠆⠈⣻⣿⣿⣿⣿⣿⣿⡿⠿⢿⡋⠉⠉⣿⣿⡿⠋⠉⠁⣶⣤⣤⠘⢿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀
⣿⣶⣶⣾⣿⣿⣿⣈⣀⣬⣿⣧⣧⣠⣿⣷⣾⣿⣿⡏⢈⣉⣀⣴⣷⣿⠟⠋⣹⣿⣿⡏⠀⠀⢠⣿⣹⢀⣼⣿⣿⣷⣶⣶⣤⣄⣁⠉⠋⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀
⣿⣿⣉⣿⣿⠉⠉⠉⣉⣿⣿⢟⠋⢉⣹⣿⠟⣻⡟⠛⠛⢛⠿⣿⣿⠿⣷⣦⣾⣿⣿⣿⣄⣀⣀⣩⣿⣿⣿⣏⡀⡐⢊⡍⣉⡙⠻⠿⣷⣶⣄⣾⣿⣿⣷⣄⠀⠀⠀⠀
⠈⣿⣿⣿⣶⣶⣶⣶⣿⣯⣁⣀⠛⣴⣿⠇⢀⣿⣧⣀⣡⣀⣀⣸⣿⣆⠁⠉⠉⠛⢿⣿⣿⣿⣿⡿⠟⢋⣈⠙⣿⣷⣜⠧⠍⣋⣀⣴⣶⣾⠿⣿⣿⣧⡟⢿⣷⡀⠀⠀
⠀⠈⣿⣧⡀⢀⣿⡿⠉⣉⡉⠻⢿⣿⡿⠿⠟⢻⣿⡟⢋⠛⠉⠉⢻⣿⡿⠿⢿⢿⣾⣿⣧⠀⠹⢿⣦⡉⠿⣥⡁⠙⢿⣷⣾⠿⠋⣉⣂⣴⣴⣄⠙⢿⣿⣯⣿⣷⡦⠀
⠀⠀⠈⢿⣿⣾⣟⣄⣀⣉⠑⠂⢸⣿⠁⡾⠗⠘⢻⣿⡘⣭⠲⠶⠀⢻⣿⡠⣶⣤⡀⢿⣿⣇⠀⡎⠻⣿⣄⠋⣁⣴⣾⡿⣿⣷⡈⢣⣬⢨⡘⠚⣳⣆⠙⢿⢿⣿⣿⡆
⠀⠀⠀⠀⠹⣿⣿⣉⠛⠛⠿⣶⣾⣿⣤⣶⣶⣶⣦⣿⣧⣀⣤⣴⣶⣶⣿⣧⡘⣙⣈⣈⣻⣿⣆⣀⣤⣼⣿⣿⡿⢋⣥⣤⠸⠻⣿⣆⣘⠾⠐⠆⢎⣴⣶⣾⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣀⡈⣿⡏⡉⢉⣰⣌⡉⢿⣿⡟⢋⡀⡀⡈⢽⣿⡿⠿⠟⠛⢻⣿⣿⠟⣋⣉⢹⣿⣷⠸⠏⠋⠦⣄⠈⢻⣷⡄⠉⣴⣿⠋⣡⣦⣀⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⢿⣿⣿⣿⣿⣿⣤⣍⠁⠀⠹⣿⡄⠛⢦⡆⠐⣿⣧⠘⣻⣷⡀⢿⣿⡌⢿⡻⠀⢘⣿⣧⠘⣟⢙⣁⣠⣤⣽⣿⣶⣿⢣⡾⡋⣃⠄⣝⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠛⢻⣿⣿⣶⣴⣿⣿⣮⣤⣤⣀⡙⣿⡀⠿⠋⢁⠀⢻⣇⣠⣶⣾⠿⢿⣿⣧⣴⡿⠟⠛⢋⣉⠛⠛⣿⣦⢁⠅⡂⠀⡲⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠁⠈⠉⢯⡙⡟⢻⠿⣿⣿⣷⡾⣿⠿⠿⢿⣿⠟⢉⣤⣡⠄⠙⢿⣿⡠⡿⣻⢭⠘⢾⢠⠌⢿⣷⣇⠸⣆⡯⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠃⠘⡇⠈⢻⠿⢿⣷⣤⣄⡀⣿⠷⢾⢧⠴⢽⠄⠛⣿⣇⠾⢸⠉⢩⠍⠩⢅⡀⢻⣿⣮⠁⡷⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠸⠀⠀⠙⠻⣿⣾⣿⣷⣄⡀⠛⣘⡃⣄⠙⣿⡄⢻⣀⡒⡇⠒⣀⣀⣀⣼⣿⣧⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣤⣿⣿⣿⣦⣘⠜⠃⣠⣹⣿⣦⠚⢑⣴⣿⠿⢛⣛⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⣁⠀⠹⢿⣿⣿⡿⠟⠻⠻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⣉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⣭⡴⡟⠉⠟⢴⢈⠻⣿⣷⣾⣿⣿⣿⡿⠿⢛⣋⣉⡥⡇⠞⠟⠃⠄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢃⠐⠁⠒⠓⠂⠖⠒⠚⢀⠀⠉⠉⠉⠉⡀⠀⠰⠚⠹⠡⠀⠐⠆⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⠷⠀⠀⢀⣠⠴⢦
⢠⣶⡢⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⣠⡶⠋⡴⢃⡟
⠈⢷⣉⠢⣘⣟⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡤⠃⢀⡴⠋⣱⡷⣫⣶⠏⠀
⠀⠀⢻⡉⠙⠛⢦⠈⠙⠦⣄⠀⠀⠀⡖⠶⢤⣤⡄⢀⣀⣀⣀⡀⠀⢀⣀⣤⡀⢀⡴⡿⠁⣰⠟⠋⡀⠃⠀⠀
⠀⠀⠀⠙⢶⡦⠤⣝⣦⣄⠘⡷⣄⡀⠃⣼⣿⣿⣷⣿⠏⠉⠉⠁⠀⠙⠉⢀⡷⠋⢸⢃⠜⢁⣠⡾⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠷⣄⡀⠈⠑⢷⡄⢹⠇⠀⠿⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡿⠛⠉⣴⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⠒⠦⣝⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣣⣫⣴⣲⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠒⠂⢿⠀⠀⠘⠻⠇⢀⣀⠰⠿⠋⠀⠀⢀⣯⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⡟⠾⣧⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⣞⣷⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣨⡧⠘⠿⠦⣤⠀⢰⠄⠐⠃⠈⢿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⣶⡅⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠠⣿⡒⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⢂⣴⣞⣩⣼⣯⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠵⣌⣉⠛⢥⡭⠷⢦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⡾⠭⠿⣛⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢾⡉⠉⠉⠉⠉⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⣷⠆⠀⠲⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠛⢀⡄⢹⣇⠀⠀⠀⠀⢸⠀⠀⠀⢰⠀⠀⠀⢠⡄⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠲⡦⢀⣴⠒⠛⠋⠉⢠⣟⠀⠀⠀⠀⢀⠴⠀⠀⢸⡆⠀⠀⣸⡈⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢼⣿⡆⠀⠀⠀⢸⣆⣀⡀⢸⡋⠀⠀⣿⡿⡦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⠀⠙⠛⠞⠛⠛⠛⠉⠉⠙⣿⣿⠂⠃⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠰⠀⣠⡈⠈⡦⢶⡄⢀⣤⢀⠀⠀⠀⠀⠀⣀⣤⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠋⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
˗ ˏ ˋ ★ˎˊ ˗ ༺𝓜𝓮𝓻𝓻𝔂༻༺𝓒𝓱𝓻𝓲𝓼𝓽𝓶𝓪𝓼༻ ˗ ˏ ˋ ★ˎˊ ˗