Content word Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣽⣿⣽⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣻⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⡏⠏⣿⣿⢹⣿⣿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣷⣽⣧⣷⣿⣿⣼⣿⣿⣭⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣻⣯⣿⣹⣿⣿⣿⣿⡿⣿⣿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣷
⠀⠀⠀⠀⢰⡿⣻⣽⣝⣿⡏⢹⣟⢻⣿⡏⣽⣯⣻⣿⣿⢏⢻⣿⣫⣿⢙⣯⣹⣏⢹⣿⡍⣿⣿⡏⣿⣯⢹⣿⣹⡆
⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⡇⢸⡉⣾⣿⡇⣽⣽⣿⣿⢏⣛⡀⢿⣿⣿⢸⣿⣿⣿⢸⣿⣿⡘⣿⣽⣿⣿⢨⣭⣿⡇
⠀⠀⠀⠀⠸⣷⣽⣛⣿⣿⣧⣼⣷⣜⣿⣧⣽⣿⣽⣯⣾⣿⣿⣬⣿⣿⣬⣿⣿⣯⣼⣿⣿⣷⣼⣿⣿⣯⣼⣿⣯⠇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣮⣼⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣗⣿⣿⣿⣛⣷⢟⣿⣿⣿⣺⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣟⣿⣿⣿⣭⣽⣽⣻⣿⣿⠭⢽⣿⣿⠿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⢹⣿⣷⣿⣿⣷⣿⣿⣿⣶⡮⣾⣿⣿⣿⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⢭⣾⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⣛⣻⣿⣿⣮⣭⣽⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣷⣾⣭⣍⣽⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠷⠲⠞⠛⠛⠋⠉


⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⣿⣿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠛⠛⠻⠿⣿⣿⣶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⣯⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⡿⠿⢿⣿⠿⣿⣿⢿⡿⠿⠿⢿⡿⠿⠿⢿⣿⠿⣿⡿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢠⣯⣿⣿⣿⣿⣿⣿⡇⣰⣿⣾⡏⢰⣿⡆⣿⠀⡈⠿⢸⣿⡇⢰⣿⡇⠘⣛⣿⣟⢀⠙⠇⣿⣿⡆⣾⣿⣿⣿⣿⣿⣿⣿⣽⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣈⢛⣹⣷⣈⢛⣡⣿⣀⣿⣆⣸⣿⣇⣸⣿⣇⣘⣛⣛⣿⣸⣷⣀⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠹⣿⠋⢹⣿⡟⠉⢿⣿⡏⣩⣭⠙⣿⠹⠏⣩⣿⡏⣭⣭⣽⣯⡍⢩⣽⡏⢹⡏⠙⢿⠉⣿⠋⣥⣍⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣟⣿⣿⡇⣤⠁⡤⢸⡿⢀⣋⡈⢿⡇⣤⡄⢸⣿⢀⣦⠸⣿⡇⢴⣾⣿⣿⡇⢸⣿⡇⢸⡇⢰⡌⠀⣿⠈⢿⡉⢹⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣿⣿⣷⣾⣷⣾⣿⣷⣾⣷⣿⣿⣾⣿⣾⣿⣷⣿⣷⣶⣶⣾⣿⣷⣾⣿⣷⣾⣷⣾⣿⣶⣿⣷⣶⣶⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣟⡿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣻⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣿⣿⠽⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠿⠿⠿⠿⠿⠿⠿⠿⠞⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⣢⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢀⡴⠉⠲⠀⠴⠒⠊⠉⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢀⡠⠤⠷⠤⢄⡀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⠀⠀⠀⣀⢄⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡄⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠉⠁⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡠⠤⠖⢂⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠈⡆⠀⠀⡴⠖⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⡀⠀⠀⠀⣿⡄⠀⠀⠘⡄⠀⠀⠘⡄⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠈⠉⢇⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢤⡀⠀⠀⢀⣾⠁⠀⠀⠘⣄⠀⠀⢻⣧⠀⠀⠀⢸⠀⠀⠀⠈⠢⡀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⢈⡷⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⣴⣇⠀⠀⠀⡇⠀⠀⠘⣿⡄⠀⠀⠀⠈⢦⣤⣌⣿⡄⠀⠀⠈⡇⠀⠀⠀⠀⢨⠏⠉⠉
⠀⠀⠀⠀⢠⠔⠋⠀⠀⠀⢠⣾⠉⠁⠀⢣⠀⠀⢹⣿⠀⠀⠀⢡⠀⠀⢀⣻⠿⢄⡀⠀⠀⠈⢿⡄⠹⣷⠀⠀⠀⢱⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠘⣿⣇⠀⠀⠈⠆⣠⣼⣿⡇⠀⠀⠘⡶⠊⠁⠀⠀⠀⠈⠢⡀⠀⠘⠃⠀⠈⠀⠀⠀⠘⡄⠀⢸
⠀⠀⠀⠀⣀⣼⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠸⣿⡏⢿⣧⠀⠀⠀⡇⠀⠀⣠⣤⣤⡀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠸⡄⢀⡠⠤⢄⡀
⠀⠉⠉⠀⠀⠀⢱⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⢻⠇⠈⢿⠀⠀⠀⢡⠀⡎⠀⠈⣿⣿⡄⠀⡇⠀⠀⠀⠀⣆⠀⠀⠀⠸⡄⠀⠘⣅
⠀⠀⠀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⠀⢀⣿⡿⠁⠀⡇⠀⠀⠀⠀⣿⣧⣀⡠⠔⠁⠀⠀⠈⠆
⠀⠀⠀⠀⠎⠈⠢⠤⠤⢄⠀⠀⠀⢿⣿⡆⠀⠀⠀⠸⣧⠀⠀⠀⢈⡆⠀⠉⠉⠉⠀⠀⢠⣷⡀⢀⡠⠔⠃⠈⠉⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠇⠀⠀⠘⣿⣷⠀⠀⠀⣀⡏⠓⠚⠿⣧⣀⠀⠀⠀⠀⣀⡴⠋⠉⠉⠁⠀⠀⠀⠀⠀⡠⠖⠒⠒⢤⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⡾⠀⠀⠀⠈⠛⠒⠊⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠙⠢⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⣀⣀⣀⠴⠋⠘⢦⣀⡠⠴⠚⠉⠉⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠉⠁⠀⡜⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⡀
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⣀⠤⠤⠤⠤⠤⠤⠤⠖⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡠⠊⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⢱⠒⠊⠉⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⠤⠾⣄⠀⠀⠀⠀⠀⠀⠈⠒⠒⠉⠈⠋⠑⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠴⠁⠈⠢⡀⠀⠸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣶⠀⠀⣶⠀⠀⣶⠀⠀⢰⣆⠀⠀⢰⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⢹⣿⣿⠉⣿⣟⠹⣿⣿⡋⢻⣿⣿⡏⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠛⠁⠀⠛⠀⠀⠀⠛⠀⠀⠈⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣼⣿⣿⣴⣿⣷⣼⣿⣿⣷⣼⣿⣿⣧⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣿⠿⣿⣶⠀⠿⣿⣿⠇⣰⣾⡿⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⡄⠀⣿⣿⠀⣿⣿⠀⣾⣿⡶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣿⣿⣶⣾⣿⠟⣴⣿⣿⡆⠻⣿⣷⣾⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣁⠀⠉⠉⢉⡅⠀⠈⣩⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣴⠘⡆⢀⠳⡀⣀⡖⠘⢳⡆⢠⡧⣤⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢫⡏⢹⠿⣸⣿⠿⢹⣧⡋⣿⡇⢘⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠟⢰⡇⣿⠁⠀⣿⠉⠂⢸⠃⢸⡇⣯⢸⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣸⡇⣸⢀⣿⣿⢰⣾⣿⠀⣿⠃⡏⢺⡇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡀⢁⣈⠀⠀⢉⡀⢀⣈⡁⠈⣁⣉⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢿⡾⢿⣿⣿⡾⢿⠿⠷⣿⣷⠿⠾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⢀⣿⡇⢸⡏⢻⣆⣿⠛⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⣿⡟⠈⢸⠀⣶⡄⢻⠀⣦⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣇⣸⣿⠀⣾⣻⡇⢸⣇⣸⡟⣿⠀⢸⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⠇⢸⡿⠡⠄⢸⠀⠿⠃⣼⠀⣿⠇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡟⢻⣿⣼⠟⢻⡇⢸⡟⢿⡀⣿⣤⡿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢰⡌⠸⠃⣵⡌⢸⠈⣬⠸⣿⠀⠋⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣸⠃⠀⣸⡅⠀⠹⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⢸⡁⠀⠀⠀⠀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠚⠉⠉⠉⠻⣦⠀⠙⣧⣀⣠⠟⠁⠀⠀⣠⠖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢰⣶⡄⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⢀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⣸⣿⡇⣤⡿⠟⢁⡀⠀⣻⣦⡔⠒⣶⡌⠙⠲⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣤⣄⠀⠀⠀⣿⣿⠀⠀⣴⡷⠈⢻⠋⣹⣿⢀⢀⣿⡇⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⢠⣤⣌⣉⠛⠂⠀⢻⣿⡄⠀⢿⡇⣠⠎⠀⣿⡇⠻⢾⠟⠀⠠⠞⣋⣁⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠙⠛⠀⠀⠉⠁⠀⢸⣿⠃⠀⡀⠀⠀⠐⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⢲⣄⠀⡀⣤⣄⢰⣏⠆⡈⠻⠆⢰⣿⣠⠊⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠠⠿⠏⣾⡟⠈⢹⠉⠙⢺⣿⠂⠀⣼⡿⠁⣼⣿⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢨⣿⡇⠀⡼⠀⠀⣿⡏⢀⠞⢹⡇⢰⣿⠃⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣤⠔⠁⠉⠛⠋⠀⠀⠀⠙⠛⠉⠀⠀⠀⠈⠻⠤⠾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⠀⣠⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢀⡴⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⢀⡾⣦⣶⠌⣻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣰⢋⣴⣿⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠰⠁⠀⢸⣦⠾⠁⡀
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⣁⣴⠿⣆⠀⠉⢻⡏⠀⠀⠀⠀⠀⠀⠀⢠⠏⡼⣡⣿⣿⢻⣷⠇⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠴⣦⡘⣿⣷⣾⠇
⠀⠀⠀⠀⣠⡴⠛⣉⣤⣾⢯⠙⣦⡞⠳⣶⠌⠠⠀⠀⠀⠀⠀⠀⠔⢁⠞⣰⣿⢻⣿⢸⣿⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠸⣷⣌⣻⠁
⠀⠀⡰⠛⣁⣤⡀⠹⠏⠻⣄⠀⠀⣻⠖⠁⡰⠃⠀⠀⠀⠀⠀⠀⢒⣩⣾⣿⣇⣼⣿⢼⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⣿⣄⠻⣿⠏⡜
⠀⠚⢠⣾⣏⢠⡉⠀⠀⠀⣹⠶⠂⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢹⡟⢡⣿⠏⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡔⠀⠹⣿⣷⣦⢀⡇⡀
⢀⣤⣦⣄⠙⢯⣉⡀⠀⠀⣀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡇⠛⢸⣷⢸⠏⡠⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢻⣄⠀⠙⠿⢟⡼⢡⠁
⠘⣷⣄⠙⢷⠀⠋⣡⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣾⡿⠀⡰⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣾⡄⠋⣡⢇⡆
⠀⠈⠛⠷⠚⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⣤⣀⠀⠀⠀⠀⣿⣿⠀⠋⠀⠊⠔⠁⠀⠀⠀⠀⢀⠀⢀⡤⠀⡤⡄⠀⠀⠘⠿⠿⠁⠐⠡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⡋⣵⡘⢿⣍⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡂⢨⡟⣧⠿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠙⢿⡾⣿⣄⠻⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣷⣷⣧⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡷⣦⣌⢻⣌⠻⣃⠵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣹⡾⠿⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠛⡫⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡿⣷⠰⣌⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠁⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢩⠚⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣿⣄⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⡀⣾⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢀⠄⢸⣵⣿⡄⠀⠹⣿⣷⠀⠀⠀⠀⠀⡠⠒⠉⠉⠉⠉⠛⠻⣿⣿⣦⣌⠑⢢⡀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⣾⣇⣿⣿⠛⢿⣿
⠀⠀⠀⠀⣴⠃⡴⢸⠈⢿⣿⡄⠀⢻⡟⠀⠀⠀⠀⢸⣀⣠⠴⠤⣄⠀⢠⣤⣴⠛⠻⣿⣿⣾⣷⠀⠀⠀⠀⠀⢀⡾⠃⠀⣴⡄⣿⠏⢻⣿⠀⢸⣿
⠀⠀⠀⣼⠃⡐⠁⠘⠀⠈⢿⣿⣤⡞⢁⠀⠀⠀⠀⢠⡟⠷⢤⡶⠟⠀⠀⡿⢿⣿⣦⣼⣿⠛⠛⠀⠀⠀⠀⢀⠞⠁⠀⠈⣿⣧⢸⡄⢸⣿⠀⢸⣿
⠀⣀⣾⠃⡼⢡⣿⡄⢧⠀⠈⢿⡟⣰⠃⠀⠀⠀⠀⠘⣇⣰⠖⢦⠐⢶⣿⣇⡀⠈⠙⢿⡿⠆⢲⠀⠀⠀⠀⠁⠀⣠⠀⠰⣿⣿⣜⡃⢸⣿⣤⣾⣿
⠀⠉⣠⡞⠁⠸⡟⢿⣾⡄⠀⠘⣰⠃⠀⠀⠀⠀⠀⠀⠈⣿⠛⢡⣤⣼⡛⠿⣿⣷⣿⡄⠀⠀⣸⠀⠀⠀⠀⠀⣾⣿⡄⠀⢻⢸⣿⠅⣸⣿⣿⣿⠃
⠀⠞⠋⠀⠀⠀⢹⠀⠙⣷⡀⢀⠇⠀⣠⠀⠀⠀⠀⢠⣴⣿⠀⠀⢿⣿⣷⣤⣈⡻⠿⢇⣠⠞⣿⠀⠀⠀⠀⠀⣿⣿⡁⠀⣸⠘⣿⠀⢹⡿⠛⠁
⠀⣠⣾⣄⠀⠀⠈⣧⠀⠘⢣⡞⢠⡞⠁⠀⠀⠀⠀⠀⠈⢰⣶⣷⣄⠀⠙⢿⣿⣿⢠⡏⠀⣼⡃⠀⠀⠀⠀⠀⡏⢻⡇⠀⣿⡀⢿⠀⠟⠀⣀⡴⠂
⠀⢹⡿⣿⣧⡀⠀⢸⣄⡴⠋⢠⡿⠀⠀⠀⠀⠀⠀⢲⣶⠞⢻⢿⣿⣷⣼⡇⢩⡴⠚⠀⢈⣹⡟⠀⠀⠀⠀⢸⣷⢾⣿⡀⣿⡇⠸⠃⢀⣼⠋
⠀⠀⣇⣘⣿⣿⡷⢸⡇⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠘⠛⢂⣾⣀⢙⣿⣿⣿⠀⢹⠀⠀⢈⡉⣹⠀⠀⠀⢀⣸⣇⣼⣿⡇⣿⡇⠀⢀⡾⠁
⠀⠛⣿⣍⠸⠏⣡⡿⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇⠀⠁⣠⠞⣀⠀⠘⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⠇⠋⢀⣴⠟
⠀⠀⠉⠉⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠒⠚⠛⠋⠉⠓⠚⠁⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠐⠂⠀⠀⠐⠀⠐⠐⠀⠀⠀⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠂⠃⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠐⠓⠆⠊⠁⠀⠀⠀⠀⠀⣴⣾⣶⣴⣶⣴⣆⣶⡿⣶⠀⠀⠀⠀⠀⢀⣠⡤⣠⣄⢸⣿⡀
⠀⠀⠀⢠⣴⣤⠀⢀⡔⠀⣤⢸⡟⠀⠀⠀⠻⢷⣧⣿⣧⣿⣿⣿⡿⠟⠀⠀⠀⢾⣿⣸⣿⢻⣿⢿⣧⣿⡇
⠀⠀⠀⣿⡁⣛⡠⠘⢛⠈⠉⣿⡷⠆⠀⠀⠸⠷⠿⠋⢙⣋⣈⣛⣃⡀⠀⠀⠀⠀⢻⣿⡟⢸⣿⣾⡿⢨⣥
⠀⠀⠀⠹⢷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠛⠛⠉⠉⠛⠛⠁⠀⠀⠀⠀⠀⣿⣿⠀⠙⠛⠁⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣠⣤⡄⢠⡆⣤⣀⡀⢀⠀⠀⠀⠀⠐⢦⡀⢸⠂⠀⠞
⠀⠀⠀⣠⣤⣰⣾⣧⣟⣾⣷⣶⣠⡀⠀⠀⢻⡏⣿⣸⣿⣾⣿⣧⣿⡇⠀⠀⠀⣠⣄⢡⣶⡄⣾⣷⢰⡄
⠀⠀⠀⢹⣿⢿⡿⠛⠋⠛⠛⠛⣿⠃⠀⠀⠘⣷⣿⠻⣏⠋⢁⣩⠙⠇⠀⠀⠀⢻⣿⣸⣿⡷⣿⣿⣿⣷⡟
⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⣡⡾⣿⡴⠛⡿⠞⠛⠂⠀⠀⠘⣿⡿⢉⢁⠠⣄⠀⠛
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠸⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀
⠀⠀⠀⢀⡀⣰⡿⣀⢰⣶⣶⡇⣾⡇⠀⠀⠰⣶⣿⢛⡉⢀⡄⣄⠀⣿⠀⠀⠀⢿⡿⣧⣰⣆⣤⣤⡄⣀
⠀⠀⠀⠘⣿⡏⣾⡋⣾⣹⣿⡷⣿⡇⠀⠀⢴⣿⣿⡉⠀⣼⢡⣿⣄⣿⠀⠀⠀⢸⣇⣿⢿⣇⣿⣟⣿⣿⡋
⠀⠀⠀⠀⣿⡷⢿⠄⠿⠹⠿⡷⣿⠇⠀⠀⠀⣿⠁⣷⣰⡟⣸⡿⣿⣿⠀⠀⠀⠘⠛⠋⠈⠻⠋⠿⠋⣿⡅
⠀⠀⠀⠀⢩⣤⡴⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⢸⠀⢿⣿⠇⡿⠁⠘⣿⠀⠀⠀⠀⠛⠛⠛⠛⠳⠶⢦⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠾⠿⠿⠿⠿⠿⠿⠿⠶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠤⠬⣍⡛⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⣡⣾⠫⠊⣀⣤⣤⣤⣴⣿⡉⠉⢩⣉⠄⠀⠿⠛⠛⠛⠦⠉⡗⢨⢻⣧⡀
⠀⠀⠀⠀⢀⡤⠞⠋⠀⠀⣴⡟⠸⣆⢈⠛⠿⠿⠿⣿⠿⠷⡶⠶⠶⠖⠒⠒⠛⠛⠛⠚⠛⢁⢀⡼⠉⣿⣆
⠀⠀⠀⢰⠟⠀⠀⠀⠀⣼⡇⠱⡀⠈⠳⠬⣐⡢⠄⠀⠀⣀⣀⣀⣀⣀⣀⠀⢀⡀⠤⢐⡬⠴⠋⠀⡰⠃⣿⡄
⠀⠀⠀⡿⠀⠀⠀⠀⠀⣿⠙⣄⠉⠲⢤⣀⡀⠉⠉⠓⠒⠒⠒⠦⠴⠖⠒⠒⠒⠚⠉⠁⢀⣠⠴⠊⢀⡜⢹⡇
⠀⠀⣼⡟⢻⠀⠀⠀⠀⣿⡀⠈⠑⠦⣄⡀⠉⠙⠒⠒⠶⠤⠤⠤⠤⠤⠤⠴⠖⠒⠒⠉⠉⣀⡤⠖⠉⠀⣾⠿⡄
⠀⣼⣿⠁⡾⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠈⠉⠓⠒⠒⠤⠤⠤⠤⠤⠤⠤⠤⠤⠒⠒⠋⠉⠀⠀⢀⣠⠶⣿⣆⣙⣦⣄⡀
⠰⡇⣿⣚⣃⣀⣀⡴⠟⢻⡇⠀⠀⡶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠁⣠⡿⠉⠉⡭⠯⣍⠓⠶⣄
⠀⠹⡌⠉⠉⠉⠉⠀⢐⣾⡇⠀⠀⣷⠀⠈⠉⠙⠓⠒⠲⠶⠶⠶⠶⠶⠶⠖⠒⠚⠋⠉⠁⢀⣠⠴⠋⣿⠇⠀⠀⡇⠀⠈⣧⡀⠈
⠀⢀⣿⡀⠀⡀⠀⠀⠀⠙⢧⠀⠀⣿⠀⠀⢰⠲⠤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠴⠒⠋⣉⠀⣴⡆⣿⡀⠀⠀⡇⠀⠀⣿⡇
⣰⠟⢿⣇⢘⡿⠋⠀⠀⠀⠀⢳⡀⢹⠀⠀⢸⠀⢠⣄⠀⣠⡀⠀⣤⡀⠀⢠⣴⣶⣦⡀⢸⣿⣼⣿⠁⣿⣇⠀⢰⡇⢀⡼⠃⠀⣸
⢿⠀⠀⠻⣆⠀⠀⠀⣀⣄⡀⠀⢳⢸⠀⠀⢸⠀⢸⣿⣰⣿⡇⢸⣿⡇⢠⣿⣿⢿⣿⡇⢸⣿⣿⣷⡄⣿⣿⣶⣶⠿⠟⠒⠚⢡⡏
⠈⢷⡀⠀⠙⢧⡀⡾⠋⠀⠙⢦⡈⣿⡀⠀⢸⡆⢸⣿⣿⣿⠃⢸⣿⡇⢸⣿⠁⠀⣩⡀⢸⣿⠛⠟⠁⣿⣿⡏⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠹⣆⠀⠀⠻⣽⣦⡀⢀⡴⣷⢻⡇⠀⠘⡇⢸⣿⣿⣿⠀⢸⣿⡇⢸⣿⣦⣴⣿⠇⠸⢋⣴⣿⠆⣿⣯⠙⠂⠀⣴⡾⠋
⠀⠀⠀⠘⣧⡀⠀⠈⣹⠿⠿⣞⠳⡜⡇⠀⠀⡇⢸⣿⡿⣿⣧⢸⣿⡇⠈⢿⣿⡿⠃⣀⢰⣿⣿⡿⢰⣿⡇⠀⣀⡴⠋
⠀⠀⠀⢠⣿⠿⣦⡸⣅⠀⠀⠈⣧⡇⡇⠀⠀⡇⠈⣿⡇⢻⣿⠀⠿⠇⠀⠀⣠⣶⣿⣿⠻⢿⣿⠀⢸⣿⡿⠟⠉
⠀⠀⠀⠀⢷⡀⠈⠻⣮⡳⢤⢞⡽⠁⣇⠀⠀⣧⠀⣉⣠⣄⠁⢠⣶⠀⣿⡇⠿⣿⣿⠁⠀⢸⣿⠀⢸⡏
⠀⠀⠀⠀⠀⠙⠳⣄⠀⠉⢻⣿⠀⠀⣿⠀⠀⣿⠀⣿⣿⣿⡇⢸⣿⠀⣿⡇⠀⢸⣿⠀⠀⢸⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣬⣿⠀⠀⢻⠀⠀⢻⠀⣿⣿⣿⣇⢸⣿⡀⣿⡇⠀⢸⣿⠀⠀⢸⡟⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⠀⠀⢸⠀⢿⣿⣿⡿⠈⣿⣿⣿⠇⠀⢸⡿⠀⢀⣠⠾⢃⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠘⠦⣄⣉⡉⠁⠀⠘⠿⠋⣀⣀⣠⡤⠖⠋⠁⣠⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠘⠳⢤⣄⡀⠀⠉⠉⠉⠙⠛⠛⠉⠉⠉⢀⣀⣤⠶⠛⠁⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠉⠙⠛⠓⠒⠒⠒⠒⠒⠛⠋⠉⠁⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢤⣤⠀⢀⡾⠒⠒⠶⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀⣀⣀⣀⢀⣀⢈⡛⠃⠀⠀⠛⠚⢙⣋⣛⣛⣙⠛⠛⠃⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠉⡉⡉⠈⣉⡈⢉⣉⠁⠀⣿⡃⢀⣶⣤⣾⢠⡤⣤⣤⠖⣶⡤⣴⣠⡴⢦⢰⡦
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⣠⣤⣤⣄⠀⣿⡇⢸⣿⠀⠈⣻⡃⢠⡤⠀⢠⠀⠀⠀⠀⠆⠠⠄⠀⣀⢀⢀⡈⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣦⠰⣿⡷⠾⠿⠂⣿⡇⢸⣿⠀⠨⣿⠆⢸⡗⠀⣯⢸⣟⣷⣾⠋⣾⣹⠞⡏⢿⠸⣏⠀⢨⠇⣻⠃
⠀⠀⠀⠀⢀⣀⠀⠙⠛⠛⠋⠀⠙⠛⠛⠋⠀⠛⠃⠘⠛⠀⢀⡽⡅⠐⡿⠀⠾⠘⠃⢠⡤⢠⣤⢥⣴⢀⡀⣀⠁⠀⠀⠀⣾⠀⣳
⠀⠀⠀⠀⠀⡀⠀⣤⠀⡄⠀⢉⠉⠉⠉⠉⠃⣠⡈⠉⣉⠉⣠⣟⡁⠀⡟⠀⣶⢶⡶⢶⣤⣶⣶⣤⣶⢺⡇⣾⠀⣶⣶⡄⣾⠀⠡⢠⣤⡀
⠀⠀⠀⠀⣟⣙⡃⣿⠀⣷⢼⡏⣿⢸⣟⢻⡇⣿⡇⣻⣿⣇⢈⣽⡆⢀⣿⡄⠛⠈⠃⠙⠀⠛⠛⠀⠛⠛⠃⠛⠈⠛⠛⠁⢩⠀⠀⢨⡭⡁
⠀⠰⠀⣠⣌⠉⣁⢉⣀⣁⡀⠉⠉⣀⡁⢈⣁⠈⠁⠈⠉⠁⠀⢷⡄⠀⠀⠀⠀⠛⠚⠚⠛⠘⠛⠃⢠⡁⠁⠈⠁⠉⠉⠀⢉⡀⠀⣘⣛⡁
⠀⠸⠈⢛⣛⠀⣤⣤⣠⣤⠠⡦⣄⣤⣠⣤⢤⣀⡤⢴⣤⠀⢈⡻⡅⠀⢸⣟⣷⢸⡟⢱⡟⣻⣤⣟⣻⡇⣿⣸⡇⣾⠛⡃⢻⡏⠀⢩⣿⡆⢸
⢤⡄⠘⠿⠟⠀⠃⠉⠙⠉⠈⠃⠘⠉⠋⠈⠛⠉⠁⠈⠉⠀⠈⠛⠃⠄⠸⠏⠁⡈⠁⠀⠉⣉⠀⠉⢩⠁⠍⠭⠅⠈⠉⡁⠈⠉⠀⢈⣸⡅⢸
⢘⡇⠰⣿⣶⠐⠖⠐⠒⠂⠀⠛⠑⠋⠓⠘⠃⠛⠙⠓⠛⠀⠀⠀⣶⣶⠀⠀⠘⠓⠛⠋⠛⠛⠀⣠⣶⠀⠀⠶⠆⠀⠈⠓⠛⠛⠃⠘⠋⠁
⢻⡁⠀⡾⠆⠀⣿⣷⠿⣿⡶⢿⣿⡆⠰⠿⢛⣿⣷⠀⣿⣷⠿⠃⣿⣿⣴⡿⠋⣰⣾⠛⢻⣶⠐⢿⣿⠿⠀⣿⡇⢸⣿⡾⢿⣷⠀⣼⡿⠷⣾
⢘⡆⣀⣩⣅⠀⣿⣇⠀⣿⡇⢸⣿⡇⢴⣿⣋⣽⣿⠀⣿⣿⠀⠀⣿⣿⠻⣿⣆⢻⣿⣛⣫⣍⠁⢺⣿⣄⠀⣿⡇⢸⣿⡇⢸⣿⠀⢻⣧⣤⣿
⠸⠇⢠⣴⣧⠀⢉⣁⣀⣉⣁⣀⣉⡁⠈⠉⠉⢉⣉⢀⡉⣁⠀⢀⣉⢉⠀⢉⠉⢀⠉⡉⠉⣁⡀⡈⢉⠉⣀⠉⢁⠈⡉⡀⠈⠉⠀⢶⣯⣤⣿
⠀⢀⠀⣭⣭⢠⠉⣉⣉⣁⠁⢀⣉⣁⢘⣓⠀⣀⣈⣀⠁⠀⣀⣈⡁⠈⠀⢻⠀⠛⠙⠛⠀⡉⠉⠙⠙⠉⠉⠉⢉⡙⠉⠅⠤⠀⠀⠀⠀⠡
⠀⢀⠀⢶⡟⢰⢸⣿⡋⣻⡇⢸⣿⠉⢸⣿⢰⣿⠉⢙⡁⣾⣿⠭⠿⠀⠀⢀⠀⠰⣿⣇⢸⡿⢰⡿⠃⣺⣿⡆⢿⡗⣴⣟⣶⢠⡞⢲⡆⢷⣰
⠀⠀⣴⣯⣿⢘⢨⣿⠛⠛⣁⠘⠋⢀⠘⠛⠀⠛⠛⠛⠁⠈⠛⠚⠛⠀⠀⣾⠀⣘⠛⠋⠈⠛⠈⠃⠀⠛⠛⡃⠘⠓⠈⠛⠛⠀⣿⣿⠇⣬⡿
⠀⠀⢀⣀⣀⣈⣀⣉⣀⡀⠀⣤⢀⣤⣠⣤⣠⣄⣄⣄⣤⣤⣄⣤⣠⡄⠀⢹⠀⠸⠀⣾⠲⣶⠆⣶⡴⣶⡾⡗⣟⢰⡦⠠⠦⠤⠴⠖⠶⢤
⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⢀⠉⠀⠉⠈⢈⡀⠁⠉⠁⠉⢠⣉⣨⢈⣁⠀⠺⠂⢻⠀⢰⢶⠄⣤⡤⢦⢠⡤⣦⣤⣤⡤⡶⣤⣤⡴⡴⡆
⠀⠀⠀⠀⠰⡿⠛⠿⠺⠉⠿⠐⠿⢺⠿⠺⠗⠛⠿⠺⠛⢆⡀⠀⢤⠤⠤⠄⠤⠠⠤⢤⠀⠀⠀⢀⡀⣀⠀⡉⠀⢀⣀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⣤⣄⣄⣀⢀⣄⢰⣠⢴⡄⣀⡀⠰⡇⢸⣿⣤⣤⡀⣠⣤⣤⢀⣤⣤⣤⡀⣤⣤⣤⣤⠀⣠⣤⣼⣿⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠛⠟⠙⠋⠙⠛⠉⠘⠘⠃⠿⠁⠀⡇⢸⣿⣀⣿⡇⣸⣿⠀⢠⣶⢚⣿⡇⣿⡏⢸⣿⠀⣿⡇⣹⣿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⠶⠒⠒⠲⠖⠒⠒⢈⡇⠈⠉⠙⠋⠀⣉⣉⢀⣈⠙⠋⢉⣁⣉⡁⠈⠋⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⡆⣤⢴⠴⠠⡇⠠⣶⡰⡇⣰⣦⣴⣶⣴⣾⣆⣶⣤⡆⣴⣿⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠉⢀⣉⣈⣁⣀⣀⣈⠉⠈⠉⠀⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠙⠉⠁






⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠠
⠈⠀⠀⠉⠀⠠⠀⠄⠀⠀⣀⠀⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠐⣆⠀⠀⠀⡀⠀⣀⠀⠀⢈⠀⠀⣀
⠀⠀⠀⠐⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀⢙⡄⢀⠒⠦⠤⢤⠀⠀⠀⠀⠘⠀⠀⠀⢹⠀⠀⢘⠝⠉⠀⠐⠂⠀⠀⠀⠀⠉⠢
⠀⠀⠀⠀⠀⠀⣇⣀⣀⣤⡖⠒⣶⣾⣿⣿⡇⢸⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣤⡊⠀⠀⢀⡠⠴⠒⠲⢤⣀⣠⠤
⠀⠀⠀⠀⠀⠀⢸⠿⠿⠟⠓⠛⠉⠉⠀⡰⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠐⠀⠀⠀⣾⠈⠎⠀⠀⢈⡏⠀⠀⠤⠤⠤⠄
⠀⠀⠀⠀⠀⡠⢼⣀⣀⣤⣤⣴⣶⣶⣿⣿⣦⡀⠀⠀⠀⢿⠀⠀⠀⠀⠄⠀⠀⠀⣧⣼⠀⠀⠀⣸⠀⠀⠸⠀⠀⠌
⠀⠀⠀⠀⠀⠁⣘⠿⠿⠟⢻⠿⠿⠍⠁⠀⢀⡿⡀⠀⠀⠘⠀⠠⠈⠈⠀⠀⠀⣸⠁⠘⠀⠀⠀⢟⠀⠀⠳⠶⠶⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠾⠀⣆⣀⣠⣼⣤⣶⣷⣿⣿⠛⠃⢧⠀⠀⢀⠀⡁⠃⠀⠀⠀⣰⢇⠀⠰⡄⠀⠀⠈⠂⠀⠀⠐⠢⡀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠛⠛⠋⠉⣩⠼⠂⠀⠄⢳⣄⠀⠀⠀⠀⣀⡤⠞⠃⠈⠀⠺⠿⢄⡀⠐⠀⠀⠀⠀⠀⣀⣵⡋⠙
⠀⠀⠀⠀⠀⠀⠀⣇⣀⣠⡤⠴⠒⠋⠁⠀⠀⠀⠀⠁⠨⠉⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠒⠒⢒⡾⠋⠁⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠠⠠⠈⠂⠀⠓⢄⢠⠤⣄⣀⡀⠀⠀⠀⠀⢰⠈⠉⠉⣷⣀⠤⠀⠀⠀⠄⠀⠈⠉⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⢀⣠⢤⣀⠀⠀⠀⢳⣤⣤⣤⡿⠀⠀⠀⠀⢸⣶⣶⣶⣿⠂⠀⠈⠀⠁⠀⠀⠈⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⠞⠁⠀⠀⠈⡆⠀⠀⡾⠿⠟⠻⡇⠀⠀⠀⠀⠘⠋⠉⠉⡇⠠⠤⠤⡄⠀⠀⢀⡏⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢠⠃⠀⠀⠀⠀⢀⠃⠀⠀⣥⣤⣤⣴⡇⠀⠀⠀⠀⣶⣶⣶⣶⠇⠀⢠⣴⠁⠀⠀⢸⣄⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⢀⠎⠀⠀⠀⡿⠿⠛⠻⠇⠀⠀⠀⠘⠋⠉⠉⡿⠀⠀⠈⢱⠂⠀⠄⣼⠘⠃
⠀⠀⠀⠀⠀⢀⠼⡆⠀⠀⠈⠢⠄⠤⠒⠁⠀⠀⠀⠾⢡⣤⣤⡄⠀⠀⣅⠀⣰⣶⣶⡾⠃⠀⠀⣶⠆⠀⠀⠀⣧⡄
⠀⠀⠀⠀⠀⠘⢠⠞⢄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠈⢿⠛⠛⠒⠚⠛⠛⠛⣋⡟⠳⠀⠀⠀⣀⡃⠀⠀⢰⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠙⠲⠤⠤⠤⠖⡞⢩⠃⠀⠀⠀⠊⢹⠲⠤⠤⠤⠶⠚⠁⠘⠀⠀⠀⠘⠋⠶⠤⠤⠼⠻⠆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⢶⠀⠀⢻⠀⡼⠁⣠⡄
⠀⢀⣄⠀⠀⢴⣦⠀⠀⠀⠘⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠙⠢⣄⡀⠀⠀⣀⡴⠋⠘⣇⠀⠈⠀⠠⠞⠉⠀⠀⠀⠀⢀⡀
⠀⠈⠙⠛⠶⢤⡈⠑⠀⠀⠀⠀⠳⡌⠓⠦⣄⣀⠀⢀⣀⠜⠁⠀⠀⠈⠉⠙⠉⠁⠀⠀⠀⠈⠲⣄⣀⣀⣀⣀⣠⠤⠖⣺⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣆⠀⠀⣨⠭⢭⠁⠀⣠⠤⠤⣤⡤⠖⠚⠛⠓⠲⢤⡀⢀⣀⣀⠉⠁⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠸⡄⢠⡇⠀⠈⢧⠀⡏⠀⢀⡇⠀⢀⣠⣤⣤⡀⠀⠈⣿⠀⠉⡇⠀⢀⡤⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢷⡒⠒⢷⠀⠀⢳⡼⠀⠀⠀⠘⣾⠇⠀⢸⠀⢠⠏⠀⠀⠈⢻⡄⠀⡟⠀⠀⡇⡰⠋⠀⠀⣧⣄⣠⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠘⣇⠀⠘⠃⠀⣰⡆⠀⠘⠀⠀⡟⠀⡏⠀⠀⠀⠀⠀⡇⠀⡇⠀⢸⠟⠁⠀⠀⠀⡇⡸⠃⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⢹⡄⠀⠀⢀⡏⢻⡄⠀⠀⢠⡇⠀⡇⠀⠀⠀⠀⢠⠇⢰⡇⠀⠀⠀⣠⣶⠀⠀⡿⠁⠀⡰⠃
⠀⠀⠀⠀⠀⠀⢴⠶⠭⠥⠤⣤⣀⣀⣧⠀⠀⣸⠁⠀⢷⡀⠀⢸⠀⠀⠹⣄⠀⢀⡠⠋⠀⢸⠀⠀⢀⡴⠃⣿⠀⠀⠀⢀⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡤⠇⠀⠀⠈⠷⠶⠛⢷⣄⠀⠈⠉⠉⠀⠀⣠⢾⣀⣠⠞⠀⠀⣿⠀⠀⢠⠞⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⣀⣀⣀⡀⠀⠀⠀⠙⠻⠶⠶⠶⠖⠋⠁⠈⠉⠁⠀⠀⢀⣿⣀⣠⠛⠒⠒⠒⠒⠺⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢠⠏⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⣠⠞⠉⠀⠀⠀⠉⠓⠦⣀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⢀⠀⠀⠀⠈⠳⣌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⣧⠀⠀⠀⠀⠈⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠂⣘⢸⣶⠄⠀⠀⠀⢀⡄⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠷⣶⡶⠂⠈⠁⠀⡔⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢴⣿⡏⣻⢻⣾⠃⠀⠀⠀⠀⠘⠛⠟⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣄⣤⣴⣍⡿⢳⠼⢼⣧⢠⢀⣀⠀⠀⠀⠀⠰⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⢻⠋⠁⠈⠹⠀⠀⠀⠀⠈⠉⣻⠆⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠛⣂⡄⡀⠀⢀⣄⣀⠀⠀⠀⠀⣴⢿⡆⠀⠀⢀⣠⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠷⣾⡉⠁⢀⣀⠤⣅⠀⠀⠁⠀⠹⣇⣴⠆⠈⢗⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠘⣿⣀⡞⢰⠀⠘⠓⠦⣄⣀⣰⠌⠙⠶⣄⣼⣇⢈⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠸⣧⣀⡷⢋⣿⣗⢼⠀⢰⣂⣠⣿⣿⡁⠀⠀⠀⢻⣶⠝⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈⢿⡇⡞⠻⡏⠀⠀⠘⣋⠀⣀⣽⣆⠀⠀⠀⠸⡄⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢲⣾⣞⣻⢾⠉⢀⠀⠰⣍⣯⠥⠭⠝⠂⠀⠀⠀⡃⠀⠀⠀⢀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠖⠙⠈⠉⠁⠀⠘⠀⠀⢃⣴⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⢀⡿⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⢰⣆⠀⢰⣿⢸⣀⠀⠀⠀⡀⡐⠈⡁⠙⠀⢻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡟⢀⠀⠀⠀⠀⡈⠀⠸⠁⡬⠉⠀⠀⠀⠋⢈⣇⠀⠀⠀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⠀⠈⢉⠄⠀⠀⣀⣿⠀⠀⢀⡇⠤⠄⠀⠀⠀⢻⣷⠛⠛⠋⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠤⢤⣈⣹⠁⠟⠃⠀⠀⠀⢀⡅⠀⠸⠛⢣⣀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣅⡿⠆⠀⠀⠀⠀⠻⢷⣾⣇⠀⢈⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠕⠁⠀⠀⠠⡌⠀⠀⠀⠀⠙⢿⣶⡦⠐⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠰⡿⠁⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢰⣟⡀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠙⢿⣷⡿⠙⠇⠀⠀⠀⠀⠀⠀⠀⢸⠇⢐⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠈⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠄⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠱⣄⠀⠀⢢⠀⢀⡴⠻⣿⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⢴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡶⠦⣤⣀⡘⠦⠀⣈⡷⠋⠀⠀⠙⢿⣄⣠⡏⠀⠀⣠⠂⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⡄⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⠛⠷⠶⠾⠷⠖⠚⡿⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢧⣃⣤⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡤⠶⠋⣿⡆⢀⡄⢀⣾⡿⠀⢀⡀⠀⠀⣤⣤⡄⠀⠀⠀⠀⣀⣿⡞⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣿⣧⣾⣧⣾⡿⢡⣾⡿⣿⣷⡀⢸⣿⡇⠀⠀⠀⣰⣿⠛⣿⣿⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠋⢻⣿⣿⠿⣿⡿⠁⠸⣿⣷⣿⡿⠃⠈⣿⣇⣴⡆⣴⣿⠃⠀⠈⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⢀⣾⠏⠉⠀⠉⠁⠀⠀⠈⠉⠉⠁⠀⠀⠿⠿⠻⣿⣿⠃⣀⣤⣾⣟⣫⡉⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠞⠁⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣹⠛⠁
⠀⠀⠀⠀⠀⠐⠚⠉⠁⠚⠋⠉⠉⠉⠉⠉⣩⡛⢷⣦⡀⠀⠀⢀⣀⣤⣤⣄⣀⡀⠀⠻⠛⠳⣤⡀⠀⠀⠀⠚⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣴⠏⣰⠗⠙⣷⣠⠞⣋⠭⠡⣶⠈⠹⣍⠃⣍⣉⠀⠀⠉⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡰⠃⠀⠀⢸⢣⣿⠇⠐⠳⠸⡇⠀⠈⠂⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠻⡀⠀⠀⠀⠐⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠙⠻⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⢿⣿⣿⡿⠿⠋⠉⠉⠙⠛⠉⠁⢠⠀⢀⡀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠁⠀⠀⠀⡴⠀⠀⠀⠲⢄⠀⡀⡀⠒⠦⣤⣄⠈⢰⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⢠⡄⠀⠀⠀⠀⠘⡿⣯⣛⢳⣄⠈⠙⠻⣄⣿⣿⣿⣷⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡄⠀⠙⢲⡝⣷⡀⠀⠈⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠀⠀⠀⠀⠀⠇⠀⠀⠀⣿⠼⣿⡀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣰⢇⡴⠃⠀⠀⠀⢻⣆⣹⡇⠀⠀⠀⠻⣿⡿⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢿⣿⣿⡇⠀⠀⠀⠀⢸⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⢼⣿⣿⠇⠀⠀⣀⣀⣜⣃⠹⡇⠀⢀⣀⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣆⢹⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠿⠿⠾⠟⠻⠿⠿⠛⢻⡿⢿⣿⣿⣿⣿⡿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣯⣤⣤⣤⠀⠀⠀⠀⠀⠀⣾⠁⣾⡟⠉⠈⠀⠀⠠⠁⢀⣠⣼⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣴⡟⢱⡟⠀⠀⠀⠀⢠⣾⣿⣿⠿⠿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⢐⣿⢘⣿⠃⠀⠀⠀⠠⣿⠟⠛⠫⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠺⣿⠀⠀⠀⠀⠀⢸⡷⢊⣿⠀⠀⠀⠀⢸⡟⠀⠀⠀⠱⠀⠰⢿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⡀⠀⠀⠀⠀⠸⣿⢈⣿⠀⠀⠀⠀⠸⣷⠀⠀⠀⣼⣿⣿⣿⣿⡋⠉⠀⠀⠀⠀⠀⣠⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣧⠀⢀⢹⣧⠀⠀⠀⠀⠀⠿⣎⠻⣆⠀⠀⠀⠀⢿⣆⠀⠰⠿⠿⢿⣿⣿⣿⣿⣶⣦⣀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣧⣼⣶⣿⣿⣷⣶⣶⣄⣀⣐⣻⣷⣿⣶⣶⣦⣄⠘⣿⣿⣶⣶⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣛⣙⡛⠛⠛⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡿⠿⡿⠌⠙⠛⠛⠋⠙⣭⠋⡍⠻⠿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⢴⡞⣧⢺⡛⣿⣿⣷⣄⡀⠀⠀⠈⢫⡈⣷⡀⣠⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣠⢋⢷⣛⡙⠋⠉⠉⠉⠁⠀⠀⠀⠀⢳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣭⠴⣭⠆⠀⠀⠀⣀⣠⣴⣧⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⣴⣿⣿⠟⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢨⠀⢀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⠐⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠈⠉⠉⠉⠐⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠈⠑⠠⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢀⣡⠄⠀⢀⠜⠁⠀⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠃⠀⠀⢀⠔⠂⠁⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠂⠀⠆⠀⠀⠀⠀⠀⠋⢀⠏⠀⠘⠃⠉⠀⠄⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⡄⠀⠀⢰⠁⠀⡠⠂⠀⠀⠰⠋⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠁⠀⠀⢠⢃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠄⢀⡤⠐⠒⠂⠸⠀⠀⠀⠊⡠⠀⠀⠰⠄⠄⢀⠸⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⡠⠁⢠⠃⠀⠀⠀⠀⢠⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠊⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠈⠀⠀⢀⡔⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠘⠀⠴⠃⢀⡄⠀⢀⡔⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⡦⠴⠃⠀⡫⠀⠀⢀⠂⠠⠠⠖⠉⠀⠛⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⢊⢁⠔⠁⡠⠃⠀⠈⠈⠀⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⢀⠠⠐⠂⠀⠀⠀⢄⠀⠀⠀⢠⠂⠀⠈⡀⠔⠊⠀⢠⠤⠄⠐⠪⠁
⠀⠀⠀⢀⡠⡄⠄⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠸⠁⠌⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⢀⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠠⠀⠀⢠
⠀⠀⠀⠀⠀⠘⠂⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡟
⠀⠀⠀⠀⠀⠀⢀⠎⠀⡠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⡠⠊⠀⠀⠂⠀⢀⠔⠀⠀⠀⠀⡠⠊⠀⡾
⠀⠀⠀⢠⡀⠀⠎⠀⡞⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠂⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠃⠀⠀⠁⣀⠞⠀⢀⡾⠁
⠀⠀⠀⠀⡀⢠⡀⡜⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠰⠀⠀⠇⢀⠞⠃⠀⠀⢠⠊⠀⠀⠀⢀⠴⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⡀⢀⡀⠀⠀⠀⠀⠂⠀⠀⣄⠀⠈⢀
⠀⠀⠀⠀⠀⠁⢀⠔⠁⠀⠀⠀⠀⢸⠀⠀⠀⢘⠀⠀⢀⠀⠀⡠⠀⠠⠀⠀⠀⠀⠀⢸⠁⣀⡀⠀⠀⠀⠀⠀⢻⡀⢀⠀⢰⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⣀⣤⡆⠀⠀⠘⠀⠀⠀⢆⡰⠀⠁⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠚⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠈⠀⠀⠀⠿⠀⠈⡾⠀⠀⠀⢸⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⢰⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⡀⠀⠀⡇⠀⠀⠀⠀⡗⡀⠀⠀⠀⢸⡄⠀⠀⠀⢂
⠀⠀⠀⢀⠀⠀⠸⠀⡄⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠁⠀⠀⡃⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⡈⡅⡠⠃⡔⠁⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠰⣤⠤⠤⠶⠋⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⡰⠁⠉⠴⠉⡀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⣼⠏
⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠖⢂⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠡⡀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡦⠻⣿⣿⠂⠀⠀⠀⠀⢦⡑⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠐⢻⣿⣦⣖⣮⠁⠀⠀⠀⠀⠀⢨⡟⠀⠀⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⠀⠀⣿⣿⡿⠛⠀⠀⠀⠀⠦⠀⣶⣿⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣷⠀⢀⣾⠿⣍⢔⣲⣒⣀⣀⣀⡘⠻⡏⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⢿⣷⣼⡇⠀⣈⠉⠛⠛⠛⢛⠿⠿⣦⢙⢀⣾⣿⣷⢲⡎
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠙⢿⣥⠶⣚⠀⠀⠀⠀⠔⣲⢶⣼⡿⠿⠛⠁⠁⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⡀⠀⢀⣸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⣀⡀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠛⠷⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠷⣷⣿⣿⠿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠻⠀⠈⢉⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣀⣀⢠⣤⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠁⠸⠿⠟⠀⠰⡿⠿⠶⠂⠀⠀⣿⠿⠟⠿⣿⣿⠷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶⡦⠀⣀⣾⣄⠀⠀⡀⠀⠀⢀⣼⡷⣤⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠤⠖⠋⠉⣷⢄⣠⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠰⠀⠀⠀⠘⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠒⠦⢄⣀⣀⡀⢀⣀
⠀⠀⠀⠀⡠⠄⠠⠴⠲⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠔⠀⠀⠀⠀⠈⠑⢦
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠒⣒⠒⠒⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⣀⠔⠒⠒⠂⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⠄⠀⠀⠀⡠⠊
⠀⠀⠀⠀⡰⠋⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⠂⠲⠃⢠⠎⡄⢀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⢀⠊⠀⡠⠄⠀⢀⠖⠀⠀⠀⢀⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⢈⠀⠈⠀⠀⡄⢀⡠⠄⠀⠠⠅⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢠⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠈⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡐⠀⠀⠀⠂⠀⠀⠀⠀⡰⠀⠀⠀⠐⠁⠔⠁⣠⠀⠀⠄⢡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡇⠒⠀⠪⠁⠀⠠⠂⠀⠰⠈⠀⠘⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡁⠔⢀⠔⠁⠀⠁⡁⡤
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠐⠁⠐⠀⠁⠀⠀⠀⠀⡀⠀⠰⠁⠀⠤⠂⠁⠀⠐⠀⠀⠁
⠀⠀⠈⡴⠐⡉⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠐⠜⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⢀⢴⠄
⠀⠀⠀⠀⠀⠀⡔⠁⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⢀⠔⠈⠀⠁⠀⠀⡠⠂⠀⠂⠀⠀⠤⠀⠀⠀⢀⠔⢁⡞
⠀⠀⠀⡄⠀⠈⠀⠎⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠊⠀⠀⢀⡔⠁⢀⡾
⠀⠀⠀⠀⠀⡅⡌⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁
⠀⠀⠀⠀⠀⠀⢃⠽⠉⠀⠀⠰⠁⠀⠀⡠⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢰⠁⠀⢲
⠀⠀⠀⠀⠀⡤⠁⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠄⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⣇⢠⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠛⠃⠀⠀⢁⠀⠀⠰⠂⠀⠰⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠀⠀⢹⡆⠀⡀⠀⠀⢸⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢰⠂⠀⠘⠀⠀⠈⠀⠀⠁⠀⠀⢸⡄⠀⠀⠅
⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⢸⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⢸⡇
⠀⠀⠀⡀⠀⠸⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠠⢁⡠⢁⠜⠀⠀⠀⢠⠟⠀⠀⠀⠀⠈⠦⠖⠒⠚⠁⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴⠋
⠀⠀⠆⠀⠈⠠⠄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠁⢀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠁

⡶⣶⢶⠶⡶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⠒⠂⠀⢀⡼⠤⠀⠀⠀⢀⡨⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⣠⠴⠟⠒⠒⡂⠋⠈⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣿⣀⣴⠞⠋⠀⠀⠀⠀⠀⠑⠒⠃⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠅⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⣠⣄⣰⠏⠀⠀⠀⠀⠘⣧⣰⠻⡶⣄⠀⠀⠀⠀⠀⠀⠀⣠⠟⢦⡤⢶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣧⢀⣴⣿⠋⠳⡀⠀⠀⠀⢠⡞⢉⣯⠻⡄⠀⠀⣠⠶⠦⠞⠃⠸⣟⠎⠳⢄⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠙⣦⣤⡴⠋⢰⡿⣌⣢⠈⠳⢮⣁⣀⣀⠀⠀⠀⠹⡗⢀⣀⣵⢶⣷⡾⠁⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣠⠴⣿⠁⠀⠀⠀⠘⢧⣀⡈⠑⠀⠀⠀⠀⠈⠑⠄⠀⠀⠉⠉⠁⠀⠸⣅⠙⠲⠦⢤⡴⢺⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⢀⣿⡄⠀⠀⠀⠀⣤⣻⡍⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣹⠇⢸⡄⠀⠀⡞⣰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⢸⣿⣇⠀⠀⠀⠀⠸⣟⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⢠⠘⣆⣿⣇⠀⡼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠀⢹⠀⠈⠙⠢⠀⣤⠀⠀⠀⢀⣿⣷⠀⠀⠀⣿⡆⢸⣿⣿⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⢄⠀⠀⣾⡇⠸⡀⠀⠀⠀⢠⣿⡆⠀⠀⢸⣿⣿⡂⠀⢠⣿⡇⢸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⣿⣦⣿⣷⠀⠙⢂⠀⠀⢸⣿⣇⠀⠀⣼⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡷⢦⡴⢄⣀⣿⣿⣿⣀⣀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣾⣧⣴⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠟⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠁⠊⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⢳⠤⣄⣀⣀⣤⠞⠀⠳⢤⣀⣀⣠⠴⢛⡇⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⢠⣀⠙⠢⠀⢸⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠚⠋⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⣄⠀⠀⢰⡇⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢠⡄⠀⠀⢸⡇⠀⡏⠈⢳⠀⠹⣆⣶⣬⡇⠀⢠⡟
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠘⡆⠻⡄⣶⣼⡇⠀⢷⣀⣼⢀⠀⠹⠇⠙⠃⠁⠸⡇⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠀⠖⠂⠀⠀⡇⠀⠹⡏⠻⠃⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠾⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀
⠀⠀⠀⠀⠀⠀⡤⠚⠁⠀⠀⠀⡀⠀⠈⠳⣄⠀⠀⢀⣠⡤⠴⠦⢤⣰⠃⠀⠰⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠡⠎⠀⠀⢸⣆⡴⠋⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⢸⡟⠀⠀⢰⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⣀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠀⠒⠒⠒⠒⠒⠀⠀⠄⡀⠀⠀⠀⠀⡠⢄⣀⡉⠐⠈⠀⠤⣤⣍⠙⠀⠀⠑⢄
⠀⠀⢀⠀⠒⠉⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣄⠀⠀⠀⢀⠴⠛⠁⡀⠈⢙⡁⠀⠒⠶⠌⢻⡀⠀⣀⠀⠀⠀⠀⡀
⠀⠐⠁⠘⣿⡀⣄⢻⠀⣴⣦⢸⡇⡄⣼⢀⣿⠃⠀⠀⠀⢠⠤⡂⠚⠀⠀⠈⢿⣶⣦⠤⠈⠂⠹⣦⡘⢿⣶⣶⡀⠈⢄
⠀⠀⠀⠀⠘⢷⣿⣾⢸⡇⢸⡏⣿⣿⠇⡼⠃⠀⠀⠀⢀⡊⢰⣿⠶⢔⢦⠶⡆⢻⡛⠁⠀⠇⢀⡹⣿⡛⢊⠻⠓⣤⣈
⠀⠀⠀⠀⠀⠈⠿⠹⠀⠛⠛⠀⠉⠘⢠⠁⠀⠀⢀⣴⡶⠀⠈⠁⠀⠀⠳⣤⣄⣤⢙⡤⣶⣷⣼⣟⣛⠛⠦⣑⢤⣚⣿⣇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠠⠀⡆⠺⣻⣿⡀⠀⠀⠐⠁⠀⢀⣠⠴⠶⠶⠤⠙⣝⢯⡉⠉⣛⣻⣶⣬⡛⣯⣻⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡵⠛⠒⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⠳⠯⠛⠉⠋⠑⣦⣙⣎⠛⠷⠿⠁⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡏⠘⢿⡹⣿⣴⣆⠐⠀⢸⡆⢍⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡥⠄⡀⠀⠀⠀⠀⠂⣉⠉⠻⠆⠀⠀⠀⠀⠘⠘⢸⡇⠘⣿⣍⣁⡠⢞⣣⢂⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⡿⠥⠴⠄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠖⠆⣼⡃⡀⣿⣧⣄⡻⠟⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⣄⣄⣼⣧⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⢳⢧⣧⡿⠋⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣁⠘⣽⣿⣦⠀⠀⠐⠀⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣼⣇⢠⠟⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠾⢣⠶⢿⠛⠹⣷⣦⡀⢶⣀⣠⡤⡾⢩⠀⠀⠀⠀⠀⣴⠃⣸⣟⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣽⣴⠉⢀⣼⡦⣳⣼⣿⣿⣦⠹⣞⡇⣀⠘⠀⠀⠀⢀⡾⠁⢈⣿⣿⠘⠂⣨⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⠋⡿⣷⡄⠉⢠⣜⡊⣙⣼⢟⣷⡄⠬⠥⠚⠀⠀⡐⠛⠁⠀⠈⠛⠛⠓⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠓⠀⠀⢬⠿⠞⠉⠞⠹⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⡓⣄⣀⣈⣴⣦⡒⠼⢻⡄⡀⠀⠀⠀⠀⠀⠀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⡿⠋⠓⠋⠑⢈⣭⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠘⣇⡀⣿⣿⢸⡇⢶⣀⣀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢀⠄⢀⠠⠀⠀⣿⣿⢸⡿⠋⠁⠀⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣳⠦⠡⠲⠠⠉⠀⡩⠀⢼⣿⠜⠃⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⠋⠀⡀⡄⠀⢄⠀⠘⠀⡹⠘⠃⠀⢠⡠⠂⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠤⠀⢀⠐⠄⠀⠐⠄⢀⡀⠵⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠢⣈⠀⠀⠀⠐⣀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠉⠁
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡀⠘⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠁⠀⠀⠀⠀⢠⠀⠀⠘⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠸⠈⠃⠀⠀⠀⠀⢀⠰⠀⠀⠀⠠⡀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⠀⠀⠀⠀⢀⠐⠒⠀⠀⠀⠀⠀⠔⡀⠀⡠⠀⠁⠀⠀⠲⠀⠀⠀⠀⣀⠀⠉⠀⠀⠀⠀⠐⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠠⠈⠀⠈⠢⠔⠊⠁⠀⠀⡀⠄⠂⠀⠀⢎⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⠀⠀⢀⠇⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠤⠀⠀⣀⡠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠠⠀⠉⠐⠢⢀⠀⢧
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠐⠂⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣎⠠⠂⠁⠀⡀⠀⠀⠀⠀⠈⠁⠀⠡⢄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⣀⣤⣄⣠⣬⣭⣷
⠀⠀⠀⠀⠀⡏⠡⠀⣀⣀⣀⣤⣄⣀⠀⠀⣠⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣇⠐⠋⠉⠉⠉⠀⠀⠀⣀⣀⠀⠀⠀⣀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡟⠛⠳⢦⣠⣄⡀⠴⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⠀⠀⠀⠀⣤⣾⣦⡐⠛⠉⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢷⣦⡀⠀⠈⠁⠀⣀⣤⣾⣷⣦⣤⣄⣀⣀⣤⣦⣴⣶⣾⣷⣷⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢿⠀⠄⠺⠦⠴⠶⠴⠶⣤⣤⡤⣤⣤⣤⣤⣠⣤⣄⣀⣀⣀⣈⣉⣉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣿⠛⢻⠖⠊⠈⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣭⣬⣭⣭⢽⠶⠶⠶⠦⢤⠄⢀⣀⠀⠀⠀⠈⠉⠛⠛⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⡤⣿⠶⠶⣦⣄⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠅⠀⠀⠀⠀⠀⠀⠉⠙⢩⣙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣦⢀⠀⠀⠀⠀⠀⠀⠀⣀⣭⢤⣄⣀⠀⠈⢇⠐
⠀⠀⠀⠀⠀⠀⣾⣿⣿⢀⠄⠠⡀⠀⠀⣴⠻⣿⣿⢿⢾⣽⣳⣲⢄⣖⡀
⠀⠀⠀⠀⠀⢷⣿⠙⢸⠁⠀⠀⠀⠀⡜⠾⢩⢿⠷⠦⢴⡯⣛⠿⣿⡿⠛⢷⣿⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢠⣷⡴⢩⣵⠛⡷⢾⢦⡏⣹⣏⢫⣶⣾⣿⣿⣷⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠲⠧⠀⠀⠀⠀⠘⡟⠞⠋⢠⠒⡇⢺⠉⢠⣶⡼⢹⣟⣿⣿⣷⡿⣿⢿⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣹⠁⡞⠐⡇⣯⠀⢶⢀⣜⢻⡦⣽⣟⣿⣿⡿⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠬⢀⡿⡗⠀⣤⠈⠁⡻⠿⢷⣬⠛⣿⣿⣿⣿⣇⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡂⢸⡇⢰⠄⢍⠁⢨⣉⣟⢠⡜⠓⢻⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣼⣂⣸⣁⣼⣿⣮⣤⣹⡗⢿⠈⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣋⢪⡿⣿⣏⠉⠃⢸⡇⢸⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠁⢢⠀⠀⠀⠀⠀⠺⣿⠋⠙⢻⣿⣿⣾⣾⣷⣤⣼⣧⣼⢿⡿⣿⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⡰⠃⠈⢢⣀⣘⣀⡀⣤⡀⠀⠀⣿⡀⠀⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣆⢷⡹⣧⡘⣿⡀
⠀⠀⠀⠀⠀⠀⡠⠋⠡⠄⠀⠀⠛⢉⣿⡗⠈⠁⠈⠉⠉⠁⠀⠀⠀⡟⠈⠻⣿⣿⣿⣿⣿⣾⣎⢳⣜⢿⣿⣇
⠀⠀⠀⠀⡔⠉⠀⠀⠀⡀⠂⣀⡴⠛⠛⠃⠀⠀⠀⠀⠀⠐⠀⠠⣸⠃⠀⣼⣿⠻⣝⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠡⠄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠠⢤⣄⣀⠀⣀⠘⢦⣴⠁⠀⠀⣘⣇⠀⠀⠈⣿⠋⠻⣿⢿⣿⣿⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⣠⣶⣶⣾⣾⣿⣿⣿⣤⣾⣿⣿⡇⡀⡤⢿⣤⣶⣤⣿⡀⠀⠘⢷⡈⠘⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣙⡛⠉⠙⠛⡛⢛⠿⢿⣿⣿⣷⣷⣧⢸⣿⣿⣿⣿⡇⠀⠀⠈⢹⡆⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠏⠳⠦⠤⠀⠀⠴⣿⣿⣿⣿⣿⠘⢿⣿⢁⣿⠁⠀⠀⠀⠀⠗⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⠀⢘⣿⢀⡿⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠀⠌⠈⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢴⣶⡒⠶⣿⡙⠻⣿⣍⠉⠻⣿⡙⢿⡖⢶⡶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠺⢿⣭⣉⡛⠷⢮⣝⡲⢬⣙⠳⢤⡉⠳⢤⡈⠳⣄⠹⡌⢧⢹⢸⢇⡟⣹⠖⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⢯⣛⡿⠷⠶⢤⠤⠭⡙⠳⠦⣬⣙⠳⢮⣝⡲⠬⡓⠤⣙⠢⠈⠃⠈⠀⠈⠈⠈⠐⠡⢞⡡⠞⣋⣷⢤⡀
⠀⠀⠀⠀⢀⣴⣿⠿⠀⠀⠈⢲⡀⠀⣰⠃⠀⣨⠉⠓⣤⣌⣙⣒⠦⢍⡓⠤⢁⠀⠁⠀⠀⢠⠞⠉⠉⠉⠳⡄⠀⠐⠈⠥⠴⠶⢛⣳⣄
⠀⠀⢀⣴⣫⠔⠢⣅⣠⡞⠉⠳⢄⡀⠉⠀⠠⠉⠁⢀⣼⠷⢻⣿⣷⢶⡌⠉⠂⠀⢀⡴⢲⡇⠀⠀⠀⠀⠀⢸⣀⣠⠞⠛⣯⡩⠭⠭⠭⣷⣄
⠀⢠⣾⣿⣶⣾⣿⣿⣿⣷⣄⠰⠞⣉⡦⠴⠞⣳⠖⠋⠁⠀⠘⣿⡏⠀⠈⠓⣲⡯⣍⡀⣨⢷⠴⠚⠓⢦⣤⣾⣾⡃⠀⣼⡿⠻⢏⣹⢷⠚⠙⢦
⢠⣿⣿⣿⣿⣿⣇⣤⡤⣉⡛⠳⢿⡀⣀⣴⣞⠁⢀⠀⠀⠀⣩⣿⡿⠀⢀⡟⠙⠲⡀⠉⠳⢤⣴⡶⠾⡿⠟⡻⠉⠀⠀⣘⣷⠀⠀⢙⣷⣯⣴⣾⣇
⣼⣿⣿⣿⣿⣷⠟⣽⣻⣯⣿⣷⣶⡉⠛⢿⣿⣿⣶⡄⠀⣴⣿⠓⠀⣠⣿⣤⣤⣠⠞⢀⣀⢤⣬⣻⣮⣄⠈⠀⠀⢀⣠⣿⣿⣤⣾⣿⡿⣿⣟⣿⣿
⣿⣿⡟⣷⡿⣿⢻⡼⣧⣷⣿⣶⣿⣿⣶⣄⣌⡙⠻⢿⣼⣧⣤⣤⣾⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⢬⣿⣿⢿⡟⣿⣾⣿⣿⣻⣯⣿⣿
⣿⣿⢿⣿⣷⣞⣚⣿⣿⣭⣿⣿⣿⢻⣿⣶⡬⠝⠳⣤⣈⣙⠻⢿⣿⣿⣿⣟⡷⠾⠿⠛⢛⣋⣭⣭⣷⣶⣾⣷⣿⣿⠿⣾⣝⣗⣯⣷⣿⣿⢾⣿⣿
⢹⣿⣾⣿⣷⣮⣿⣧⣿⣭⣻⣏⡽⣻⣿⣿⣿⣷⣄⡙⠻⣿⡷⢯⣤⡿⠉⣿⣀⡀⠝⠻⠿⠷⠶⠯⢿⣧⢾⣛⣿⣶⡿⣿⣿⣿⣷⣿⣿⣹⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡟⣿⣆⣤⣍⣳⣯⡳⣄⣈⠙⠛⠻⠶⣬⣵⣾⣿⠿⠷⠿⠯⠿⢶⣿⣟⣿⣞⢻⡿⣽⣿⣿⣿⠃
⠀⠀⠹⣿⡽⢿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣗⣺⠭⣿⡷⣷⣿⣾⣳⣾⣿⣦⣽⡷⠀⠀⠀⠈⠹⣿⣿⣿⣯⠭⠽⢿⣟⣒⣶⣭⣝⣛⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠻⣷⣾⣷⣺⣭⣿⣿⣿⣿⣭⢟⡻⢿⡲⢭⣓⢪⣽⣿⡿⠟⠋⠁⠀⠀⠀⡀⠀⠀⢸⣿⣛⣛⣯⣭⡿⢾⣛⣛⣿⣭⣭⣭⡽⠋
⠀⠀⠀⠀⠀⠈⠛⢿⣞⣛⡻⣍⣯⣭⣝⣿⣮⡓⣭⣷⡾⠟⠋⠁⠀⠀⠤⠀⠀⠀⡀⠀⠀⢀⣼⡿⣟⣻⠽⢗⣛⣭⠭⠴⣶⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣿⣽⣹⣯⣷⡿⣿⣭⠁⠄⠀⠀⠀⠒⡤⠀⠁⠀⠴⠀⣠⡶⣛⠽⣛⣭⠶⣚⡭⢵⣲⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣯⣶⣶⣖⢐⣠⣶⠖⠔⠐⠀⢢⣾⣷⣻⣵⣟⣯⣶⠿⠗⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⣀⠀⠐⠢⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠈⠉⢢⡠⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠒⠐⠢⣠⠊⣠⢀⣈
⠀⠀⠀⠀⠀⠄⠀⠂⠈⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠈⠱⡀
⠀⠀⠀⠀⠀⢀⠴⠊⢉⠭⠍⠐⠀⠀⠀⢀⠤⠤⠤⠤⠄⠤⠔⢂⠉⠩⢁⡒⠤⠤⠤⠤⠤⣀⠀⠀⠀⠢⠤⢄⠠⠒⠂⠀⠐⠲⢄
⠀⠀⠀⠀⢀⡏⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⢹⡷⠊⠀⠀⠀⠀⠈⠻⡀⠀⠀⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⡠⠜⢀⡠⢚⣍⠢⣄⠀⠀⠀⠀⡇⠀⠀⠀⢀⠊⠀⠀⣀⣤⣤⣄⠀⠀⠘⡀⠀⢸⢸⠀⠀⠀⠀⣀⠔⣊⣑⠦⡀⠀⠀⢀⠆
⠀⠀⢸⠀⢐⢡⠒⠁⠘⣿⣆⢃⠀⠀⠀⡇⠀⠀⠀⠄⠀⠀⣴⣿⠟⠉⠙⠆⠀⠀⣷⠀⠈⢸⠀⠀⠀⢰⢡⣾⠏⠀⠑⡌⠓⢐⠪⡐
⠀⢀⡬⠓⠈⢦⢣⠀⠀⠸⣿⡌⢒⣐⠢⠇⡀⠀⢠⠀⠀⠀⣿⠁⠀⠀⢠⠂⠀⠀⣿⠀⠀⠘⠤⢒⡐⢃⣿⡟⠀⠀⡰⣱⣿⠟⠑⡘⢆
⠀⡞⠀⠀⠀⠀⢣⠣⡀⠀⢹⣿⠃⠀⠑⢦⡅⠀⠘⠀⠀⠀⠙⠄⠀⠔⠁⠀⠀⢀⣿⠀⠀⣦⠊⠀⠈⣾⡟⠀⠀⡐⣴⣿⠋⠀⢀⢊⠜
⠀⡇⠀⠀⠀⠀⠀⢣⡱⡀⠀⠻⠀⠀⡀⠈⠁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠁⠀⡀⠀⠸⠁⠀⢄⣼⡿⠁⢀⠔⡱⠋⡄
⠀⠙⢤⣀⣀⠀⠀⠀⠱⡑⡀⠀⠀⢸⣷⡄⠀⠀⢠⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⢀⣾⡇⠀⠀⠀⢌⣾⡟⠁⡠⣡⠎⢀⠜
⠀⠀⠀⠀⠈⢣⠤⠀⠀⠱⡐⢄⣀⣸⣿⡿⠲⣶⣾⣿⡿⠻⣷⣶⣶⣾⣿⠟⢻⣿⣿⣶⠶⢻⣿⣧⣀⣀⣈⣹⠟⠟⢋⠜⠁⠀⡇
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠙⠪⣙⠛⣛⣃⠞⠢⠭⠤⠒⠒⠤⢭⣭⠥⠤⠒⠒⠠⠭⠥⠺⣜⣛⡻⢛⡁⣿⡷⠤⣂⠜⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠒⠒⠉⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠃⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⡄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠦⢑⡦⠤⠤⠀⢱⡀⠀⠀⠀⠀⠀⠒⠒⠄⠀⠀⠀⠀⡐⠤⠤⠂⠀⠑⠲⠤⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡤⠠⠆⠀⠀⠀⠀⠙⠢⠄⣀⣀⠠⠄⠀⠈⠓⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢡⠠⠁



⡶⣶⢶⠶⡶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⢶⣶⡶⢶⡶⢶⣶⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⢾⣽⣿⣿⣿⣿⣯⡗⠀⠀⠀⠀⢀⣤⠴⠿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠇⣀⠁⣀⣀
⠀⠀⢿⣿⡿⠁⠎⢻⣿⡿⠀⠀⠀⠀⣾⣿⣷⠰⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠉⠘⠃⠨⠄⠉⠁
⠀⠀⢫⢿⣿⠀⠀⢸⣿⣍⠁⠀⠀⢸⣏⠉⠀⠁⠈⠉⣽⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠘⣿⣤⣤⣼⡇⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⡖⣴⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄
⠀⠀⠀⠀⣀⣈⣉⣩⡅⠀⠀⠠⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⣿⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠄⠀⠀⠀⡀⢀⡀⢀⡀⣀⢀⢀⠀⢀⢀⢀⠀⣀⢀⠀⢀⠀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣀
⠀⠀⠀⠀⠀⣔⣆⠆⠀⠀⢶⣌⠉⠀⠀⠀⣱⢸⠀⠺⡇⣿⢾⢸⠇⢿⢸⢹⠀⢿⠈⡇⢸⠀⢻⡇⡟⡇⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠘⢹⠛⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⡀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣤⠄
⠀⠀⠀⣀⠀⢀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⢀⣾⣶⣶⣿⡎
⠀⠀⠀⠙⠁⠙⠛⠈⠋⠀⠀⢠⣤⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢶⣦⠿⠚⠿⣧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠱⠶⣿⡇
⠀⠀⠀⢠⣤⡀⢀⣀⡄⠀⠀⠈⣿⡆⠀⠀⠀⣸⡟⠀⠀⠀⣷⣶⠇⠀⠐⠀⠘⣷⣶⠀⠀⠀⠀⠀⢿⣿⡤⡀⠀⠁⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⢐⣂⣀⣉⣭⡅⠀⠀⠀⠘⠇⠀⠀⠀⠿⠁⠀⠀⠀⣶⣾⡀⠀⠀⠀⢀⣿⣶⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⢿⠀⠀⣿⠇
⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⢰⣿⢲⣶⣾⢿⡧⠉⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠈⣷⣶⡇
⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣉⡛⠈⠀⠀⠀⠀⣴⣶⡖⠀⣨⣭⣅⠀⠐⣶⣶⠆⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⢠
⠀⠀⠀⣰⠉⢳⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⠀⠀⠁⠤⠉⠠⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐
⠀⠀⠀⠺⠰⠉⠆⠀⠀⠀⠀⠀⣶⣏⣳⡖⠀⠀⠀⠀⠀⢀⣘⣁⠀⠀⠀⠀⠀⠀⠹⠺⠈⠁⠀⠀⠀⠀⠀⢨⡀⠗⣈⠂
⠀⠀⠀⠐⠿⠗⠃⠀⠀⠀⠀⠀⠁⠙⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠺⠏⠁⠀⠀⠀⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢘⣏⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡉⣯⠩⠀⠀⠀⠀⠀⠀⡑⣇⣿⡋⠀⠀⠀⠀⠀⣾⠃⢷⡄⠀⠀⠀⠀⠀⢸⠦⠿⠀⠀⠀⠀⠀⠀⠠⠛⡈⠓⠆
⠀⠀⠀⢓⣿⡀⠂⠀⠀⠀⠀⠨⠃⣇⡿⢡⠀⠀⠀⠀⠀⢻⠀⣾⠃⠀⠀⠀⠀⠀⡅⠀⠀⣏⠀⠀⠀⠀⠀⢐⠀⠁⠘⡂
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⢸⣁⡿⠀⠀⠀⠀⠀⠀⠹⣀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠴⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠰⣤⣤⡔⠢⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⢐⡀⠀⠀⠀⠀⠐⢀⡊⣒⠀⠀⠀⠀⠀⠀⠀⡤⢢⠄
⠀⠀⠀⢐⢠⢰⠂⠀⠀⠀⠀⠀⡜⠀⠂⠀⠀⠀⠀⢀⢀⡻⠻⡟⡀⠀⠀⠀⠀⠀⠈⠀⠃⠔⠀⠀⠀⠀⠀⢀⣄⣀⡀
⠀⠀⠈⢹⡸⢀⠁⠀⠀⠀⠀⠐⠢⢝⢡⠃⠀⠀⠀⠀⠀⢿⡘⣿⠀⠀⠀⠀⠀⠀⠀⡀⢀⠁⠀⠀⠀⠀⠀⠘⢖⣲⠗
⠀⠀⠀⢻⣒⣚⡗⠂⠀⠀⠀⠀⢶⣌⣰⠦⠀⠀⠀⢀⠁⠪⡄⠼⠉⠀⠀⠀⠀⠀⠀⢇⡼⢀
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⡀⢀⠁⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⢀⣄⡄⠀⠀⠀⠀⠀⠀⠀⢨⣡
⠀⠀⠐⡘⠁⠋⠪⠀⠀⠀⠀⠀⢈⠇⣺⠀⠀⠀⠀⠀⠀⠒⠐⠀⠠⠀⠀⠀⠀⠀⠼⠃⠷⠀⠀⠀⠀⠀⠀⠀⠚⠳
⠀⠘⠒⠄⠀⠀⠔⠀⠀⠀⠀⠀⣰⠐⡰⠀⠀⠀⠀⠀⠬⠀⠀⠈⠤⠀⠀⠀⠀⠈⢦⣛⣠⠆⠀⠀⠀⠀⠀⠀⠂⠘⠂
⠀⠈⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⢤⠔⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠚⠘⠆⠀⠀⠀⠀⠀⠀⠐⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⣶⣤⡴⡇⠀⠀⠀⠀⠀⠘⢡⠛⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡆⣖⠀⠀⠀⠀⠀⠠⠌⠀⠀⠠⠄
⠀⠀⠠⠄⣿⠅⠃⠀⠀⠀⠀⠀⢂⠸⠀⡂⠀⠀⠀⠄⠀⡌⠈⣄⠀⠀⠀⠀⠀⠀⣠⡞⠤⠀⠀⠀⠀⠀⠀⢴⡄⠀⣼
⠀⠀⠀⠶⠊⠛⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⠑⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣤⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣿⡿⡇
⠀⠀⠀⢰⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡶⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣴⣇
⠀⠀⠀⠀⠙⣿⣿⣿⣽⣿⣶⣤⣀⢀⠰⠃⠘⠆⠀⢀⣤⣶⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢻⣙⣻⣿⣿⣿⣿⣿⣷⡇⠡⠄⠸⣾⣿⣿⣿⣿⣿⣟⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠉⣵⣿⣿⣿⡽⣛⢵⡂⠙⠋⢐⡪⣝⢯⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠈⠷⠀⠀⡀⢀⣰⡄⠀⣸⢿⣿⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢰⢹⣿⣾⣿⣿⡏⣆⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡰⠂⠁⣠⣴⣿⠿⠋⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠶⠭⠭⠷⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⣵⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠸⢿⠿⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢢⢂
⠀⠀⠀⠈⠖⡼⢀⣃⡤⢠⡄⣀⠀⢄⡘⠃⠘⠃⣀⠀⢀⠠⡄⢰⣔⣇⢧⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢳⡧⠀⡄
⠀⠀⠀⠀⠘⡍⣑⡒⠽⡶⠳⢺⢧⣦⡍⠁⠈⢉⣴⡤⣟⠺⢳⡮⠔⡚⡉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⠮⢷⠢⠌
⠀⠀⠀⠀⠀⠀⠨⠦⠎⠑⠘⠋⢋⣹⡄⠀⠀⢠⣏⠙⠋⠋⠚⠹⠴⠏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣮⡯⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⣴⣤⣤⣤⣶⣦⣉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⡀⠀⠀⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢁⣛⡻⠿⠿⠿⢛⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⠀⢠⣀⣼⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢩⣙⣛⣛⣋⡭⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢻⣛⣩⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠛⢿⣄⠄⠀⢤⡤⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⡶⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠸⣽⣷⣦⣀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢂⣶⣿⣷⣾⣿⣷⣦⠠⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠁⢀⢤⣽⣿⣿⣷⡄⠀⠀⠀⡇⠀⢸⠀⠀⢹⣿⣿⣿⣿⣿⡟⠻⣷⣒⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⡿⣏⠋⢹⡇⠀⠀⠀⡇⠀⢸⠀⠀⢸⠋⣿⣪⡟⢸⡇⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⠀⣃⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠉⠁⠉⠉⠐⠟⠉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣓⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⡃⠀⢘⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣚⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣴⣆⣴⣤⣄⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠄⢀⡀⠴⠂⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⣿⢿⡏⢛⡻⣿⣗⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⣠⣯⣥⣬⠆⠀⠀⠀⠀⡇
⠀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣿⣿⣍⣃⡈⢠⣿⣿⣦⠄⠀⡇⠀⢸⠀⠀⢀⣀⢂⣩⣟⣻⣝⡁⠁⠀⠀⠀⡇
⠀⢀⣻⠁⠀⠛⢿⡇⠀⠀⠀⠀⢸⡇⠀⠀⢹⣿⣿⣶⣾⣿⣿⡟⠀⠀⠀⡇⠀⢸⠀⠀⠀⠈⠁⢿⢹⡯⡟⠐⠓⠁⠀⠀⡇
⣾⡿⠋⠤⠠⠀⢤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⢿⢺⡿⠿⠋⠁⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢀⣷⣶⠄⠀⠀⠀⠀⠀⡇
⠉⠃⠈⣶⣿⣤⡷⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⡇
⣧⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⣶⠤⠄⠀⠠⠀⠀⠀⠀⠀⠀⠸⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠲⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣧⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⣠⣷⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣦⣆⣾⡄⠀⠀⠀⠀⠀⠀⠀⢠⡀⢶⣿⣷⣠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣟⠛⠛⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣓⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠉⣻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠠⠄⠀⠀⠀⢤⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⣠⠾⠛⠃⠄⣀
⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡴⠟⠉⠀⢀⣾⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣿⣴⣷⣧⢀⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠰⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠉⠃
⣿⣿⣿⣿⣿⣿⣷⣿⣠⡀⣦⣷⢠⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣼⣧⣧⣼⣰⣇⢠⡀⣿⡆⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⣠⢸⣷⣿⣦
⣿⣿⣿⣿⢿⢿⡿⠿⠛⠛⠟⠿⠛⠋⠛⠉⠉⠋⠉⠉⠋⠈⠉⠛⠁⠀⠋⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⣸⣧⡆⢠⢀⣿⣾⣷⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⣾⡧⢀⡀⣸⡇⣰⣠⣧⣴⣰⣿⣰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⢸⣿⣿⣾⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣸⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⠻⣿⣿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠀⠀⠈⠁⠈⠀⠁⠈⠈⠉⠈⠉⠙⠛⠋⠉⠉⠛⠻⠟⠿⢻⡿⣿⠿
⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⢠
⣿⠃⢹⣿⣿⣿⣿⣿⡃⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣸⡇
⡟⠀⢐⣻⣿⣿⣿⣿⣷⣼⣿⣧⡀⢀⣦⠀⠀⠀⢰⣿⠄⠀⠀⠀⠀⠀⢸⣿⣯
⠉⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣸⣿⡄⠀⢰⣾⣿⡇⠀⢰⡆⠀⠀⣿⣿⣿⡁⠀⠀⣾⠄⠀⠀⠀⢰⡧
⠂⠀⠴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢺⣿⣿⣶⣤⣾⣿⠀⣘⣿⣿⣿⣶⠆⢸⣿⡇⠀⠀⠀⣿⣟
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣘⣿⣿⣿⡟⢻⣿⣿⣦⣽⣿⣿⣿⣿⡥⣿⡿⠿⠀⠀⣽⣿⣿⠇
⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣶⣤⣿⣿⣿⣷⡤⠀⠀⢰⡇
⠀⠀⠀⣤⣽⣿⣿⣿⡧⠀⠀⢽⣿⣿⣿⡿⢻⣿⣿⠦⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠠⢽⣿⣿⣿⣿⣿⣧⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠤⠼⣿⡟⠓⠀⠀⠙⢿⣿⣿⡃⠀⣿⡟⠃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠙⢿⣿⣿⣿⣿⣷⡖⣸⣿⣿⡅⠀⢀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠒⠚⣉⠁⠀⠀⢤⣿⣿⡟⠀⠀⠹⡏⠁⠀⠀⣤⣿⣿⡿⠁⢿⣿⣿⣏⠁⠀⠀⢤⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢁⣾⣇⠀⣸⣿⣟
⠀⠀⠀⠀⠠⠴⠒⠀⠀⠀⠀⠐⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠃⠀⠘⣿⣟⠀⠀⠀⠀⠐⢺⠻⣿⣿⠁⢻⣿⣿⡟⢻⣿⣽⣿⣧⣠⣿⣿⣿⣃⣾⠀⠀⣴
⠀⠀⠀⠀⠤⠦⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⢒⣿⠁⠀⢈⣿⣿⠀⠈⣿⠙⣿⣿⣿⠇⢸⣿⣿⣿⡆⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠉⣉⠅⠀⠀⠀⠙⠀⠀⠀⠋⠀⣿⣿⡿⠀⠈⣿⣿⣿⣷⣾⣿⣿

⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⣿⣿⣿⡷⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⢾⣿⣿⣿⣯⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⣿⣿⣿⡀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣉⡀⠀⠀⣿⠿⠿⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⣀⣠⣾⣿⣿⣿⢷⣤⡀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣦⣀⠀⠀⠀⣹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡇⣀⣰⣿⣿⡿⣋⠹⡏⣼⢹⣿⡄⠀⠀⠀⠀⣰⡿⣿⣮⡿⠩⣿⣿⣿⣧⣀⣀⣹⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣻⣿⣿⣟⠁⡁⢙⡀⠄⠠⠎⠞⠛⢦⣾⣆⣼⢋⣇⡱⠀⠀⢰⡋⢈⠙⣿⣿⣿⣯⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣯⣿⣿⠄⠓⠸⠧⠀⠀⠂⣆⡄⠈⣿⣿⣰⣄⡏⡃⡀⠀⠞⠁⠄⠰⠿⣿⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣶⣶⠲⣶⣾⣶⡷⡖⠒⢦⣿⣟⡻⢿⣶⣶⣶⣻⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣟⠻⢿⣷⣿⢿⡇⢑⠍⣉⠀⣿⡏⠐⣻⣿⠉⣹⠿⣷⣾⣿⢿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡉⢶⣊⠁⠉⠒⠀⡍⠀⠀⠀⢽⡇⠀⠀⢷⣧⠐⠊⠉⠙⣻⣾⣸⣳⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢷⣟⠲⠍⣀⠖⠀⣤⢀⠀⠀⠀⠸⠃⠀⠀⢀⡆⣤⠑⢟⣈⡹⢟⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⢿⣿⣶⢾⣥⢴⣆⠤⠀⠀⠀⠀⠀⠀⠀⠈⢧⣾⢿⣬⣶⣶⣯⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⠏⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡀⠈⡂⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠂⠀⠀⠂⠖⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠄⠛⠈⠐⢂⣀⣼⠯⣼⡀⠀⠌⠁⠀⣸⠆⠐⠴⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢧⠄⣤⠀⠐⠎⠀⠀⠳⠀⠈⡁⠀⢀⡴⠔⠀⠈⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣍⠀⠀⠛⠀⠀⢰⠂⢂⠩⡀⠀⠠⠀⠀⠰⠉⠂⢀⢓⠀⠀⠀⠀⠀⡁⠀⠀⠐⠘⠳⠦⠄⢀⠔⡀⠀⣠⠀⠀⢀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠰⠄⢊⠀⠂⠀⡇⠂⠁⣶⣀⠀⠠⠀⠀⠀⢠⠀⡀⠀⠐⠒⢦⣀⠀⠀⢀⡀⠀⢀⣀⡀⠼⢇⣀⡀⣈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⣠⣄⠈⠀⠀⣰⣾⠉⠀⠐⠠⡄⠦⠀⠀⠀⡠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢸⡆⠈⡁⠁⠈⡠⠊⠁⠈⠑⠀⠀⢀⢁⡀⠋⠈⠩⠁⠀⠀⠥⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⠂⠀⠀⠀⠅⡆⠀⠀⠀⠥⠀⠀⠄⠄⠀⠀⢤⡀⠠⠀⠀⠀⠀⠁⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠒⠶⠦⣠⢀⠀⣡⡈⠀⠀⠀⢀⠀⣀⠀⠃⢀⠀⠀⣰⣀⠀⢀⡀⠙⠆⠀⠀⠀⠀⠧⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆⠆⠈⠋⣃⠉⠀⡀⢰⡟⠀⠁⠀⢀⠍⡀⠊⠁⠀⠀⠚⠄⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠠⣗⠀⠀⠀⠀⠀⢭⡀⠰⠛⠸⠇⠀⠀⠀⠉⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⢠⢠⡖⠡⣄⠠⠀⠙⡠⠀⠀⠈⠪⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⡄⠐⢶⠀⠱⠆⢸⠂⠀⠀⠉⢈⡁⠂⣴⠆⠀⠀⠐⠲⡈⠀⠐⡊⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠤⣁⣀⣀⣀⠀⠀⠀⠀⢧⡀⠈⠫⠁⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠉⠙⠛⡦⠴⠖⠒⠋⠀⠀⠀⢠⠀⠀⠠⠐⠀⠀⠂⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⡀⢉⠴⠡⠄⠀⡠⠀⠑⠄⠀⡀⠀⠈⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠄⠀⠀⠀⡤⠀⢀⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠿⠀⠄⠀⡁⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠈⡄⠁⠀⠄⢦⡰⠀⠙⠂⠉⠀⠴⢠⡀⣀⠀⠚⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣈⠀⢢⡀⠀⠀⡀⣘⡄⠀⠀⠀⠀⠀⢆⡇⠀⡀⠀⡀⠸⠋⠶⠆⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⡐⠋⡉⠉⠐⠉⠑⢳⣦⣴⣤⣚⡉⠀⠀⢈⡁⢆⠀⠀⠀⡅⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠋⠔⡲⠦⠄⢸⣇⢧⠙⡇⠐⠀⠉⠀⡈⡗⢀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢠⣄⠴⣶⢲⡆⢤⣴⣤⠄⣰⢲⡶⢂⣤⠄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠻⣧⣄⠀⠹⠀⣽⡇⠰⠉⠀⣠⣾⠋⠀⠀⠀⠀⢠⣾⠏⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⢻⣿⡄⠁⠏⢀⠁⣰⡿⠉⠀⠀⠀⠀⠀⠀⢊⣽⣿⣯⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠈⡿⠞⠀⠈⠻⣏⠀⠀⠀⠀⠀⣴⣶⣶⡽⢻⡿⡿⢻⣹⣾⣶⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⣤⣄⡘⢿⣿⠇⠀⢇⠃⠀⣿⣿⠋⣀⣴⡄⠀⠀⠀⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⡠⠀⠀⢠⠤⠾⠟⠋⠁⠀⠀⠀⠀⠀⠈⠙⠻⠿⢧⣤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡶⢶⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢶⣦⠆⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡾⣏⡙⣃⢈⡄⠀⠀⠤⠄⢀⠀⠀⡀⢠⣶⡄⢀⡀⠀⠀⡠⠤⠀⠀⠀⢈⣠⣼⣧⣄⡃
⠀⠀⠀⠀⠀⠀⣨⣭⣿⣿⣟⣯⡭⡄⠀⠀⠀⠀⠀⠈⣓⢉⣿⣿⣿⡉⢉⠀⠀⠀⠀⠀⠀⠀⣈⣉⣿⣿⣋⣀⡀
⠀⠀⠀⠀⠀⢀⠃⣾⣿⣿⣿⡇⢇⠰⠀⠀⠈⠙⠱⠋⠁⠞⠈⣿⠉⠣⠀⠙⠟⠛⠁⠀⠀⠎⠀⣿⣿⣿⣿⠁⠰⡄
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣇⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣿⣿⣿⣿⡷⠦
⠀⠀⠀⠀⠀⢸⠁⣿⣿⣿⣿⡟⢸⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢀⠇⠹⣷⣿⣍⣠⠊⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠈⠉⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⢠⡇⢸⠀⠀⠀⠐⠣⠬⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠑⠟⠀⠀⠀⣿⣦⡀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⣿⠙⢿⣶⣄⣈⣀⣀⣴⣇⠀⠀⢀⣠⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠈⠙⠛⠛⠋⠉⠛⠿⠟⠛⣿⣏⣀⣠⡤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⣶⡿⠛⠁⠀⠀⠀⢀⣠⠤⠤⢤⣶⡛⠹⣿⡏⠉⠹⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢀⣸⣧⣾⡟⠉⠉⣷⠋⠀⣠⣤⡀⠈⢳⡀⣿⠇⢀⠀⢹⡇⠀⡇
⠀⠀⠀⠀⠀⢠⣴⠾⠛⣿⡏⠁⠀⠻⣿⠀⠀⣿⢀⡞⠉⠛⣿⡆⠀⣷⠹⠀⣼⣧⠀⠃⠀⡗⠂
⠀⠀⡖⠒⡀⠘⣿⣧⠀⠸⡇⠀⠀⠀⠹⡄⠀⢿⢸⡇⠀⠀⢸⣿⠀⣿⠀⢠⡏⢿⣧⠀⢀⣷⡶⠤⠤
⠀⠀⠉⠚⠀⠀⠸⣿⣆⠀⠃⠀⢸⣆⠀⠀⠀⢸⡈⢧⡀⠀⣸⠇⣰⣿⣦⣼⠀⢈⣿⣧⡾⠃
⠀⠀⠀⢀⣠⣴⣾⢿⣿⡆⠀⠀⣿⢿⣧⡀⠀⢸⣷⣤⣉⣉⣡⡾⠁⠉⣉⢅⣀⣀⣧⡀⠀⠀⢠⣂⣆
⠀⠀⠀⠀⠀⠀⢀⡠⢻⣿⡄⠀⣿⣴⢿⣷⣤⣞⠉⠛⠛⠛⠁⠀⡀⠀⡒⢒⡙⢆⡈⠉⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠋⢠⠞⠻⠿⠟⠉⠀⠀⠉⠀⠙⣆⠀⢀⡴⠋⢉⡉⠓⠇⠀⠙⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⢹⢠⠏⢠⠞⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣕⣀⣠⠁⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠘

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⣀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⠂⢄⠀⠘⠒⠶⠀⠸⠇⠀⠀⠀⠈⠁⠀⢸⡀⠀⠐⢀⡀⠀⠙⠃⣤⡄⠁⠌⠁⠠⠀⠀⠀⠙⠂⠀⠒⠊⠀⠈⠠⠀⢀⠐⠂⣀⡀⠀⠉
⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠰⠆⠀⠀⠄⢀⣀⠀⠉⠁⠉⠀⣀⡄⠘⠦⡷⢛⣀⠀⠀⠀⠙⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⠋⠁⠀⠀⠠
⠀⠀⠀⠀⠀⣶⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠯⠀⠘⠗⠀⠺⠿⠀⠀⠀⠀⠀⠀⣠⠈⠈⠀⠀⠛⠀⡐⠀⠀⠀⢀⡀⠀⠠⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠄⠬⡙⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⢐⠣⠀⡆⠀⣀⡰⢶⣶⡀⠀⠀⠑⠀⢀⠠⠀⠦⡀⠀⣠⡦⠀⠀⠀⠀⠀⠀⣠⠄⠀⡉
⠀⠀⠀⠀⠉⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢛⣁⠼⠏⠀⠀⠤⠄⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⠄⠀⠈⠉⠀⠈⠉⠁⢀⣂⠒⣤⠀⠀⠀⠠⠀⠀⠀⠤⠾⠀⠸⠀⠀⠀⠀⣀⠀⠐⠂⠴⠆⠀⠠
⠀⠀⠀⠂⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠀⠀⡺⣿⡿⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠈
⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠒⠀⠈⠀⠀⠠⠆⠀⠀⠀⠀⠀⠦⠀⠀⠛⣾⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠂
⠀⠀⠀⢀⠄⡀⢀⡀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠀⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣀⠀⠀⡆
⠀⠀⠀⠀⣀⡀⠀⠀⠤⠤⠦⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⣠⣿⣿⡿⢿⠿⠿⠿⢿⢿⣿⣧⡀⠀⠀⠀⢰⡲⡀
⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠙⠋
⠀⠀⠀⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠉⠀⠀⠀⠀⢠⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠀⠂⠻⠀⣀⠈⠀⠀⢀
⠀⠀⠀⠀⠤⠀⢁⡀⠀⠀⠀⠀⠀⠀⠰⠀⣤⣴⡇⠀⠀⠀⠻⣿⣤⣬⣧⣬⣥⣤⣧⣤⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⣠⡈⡀
⠀⠀⠀⠘⡀⠀⠀⠠⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠆⠀⠘⠓⠓⠀⠀⠀⠀⠁⣈⡁
⠀⠀⠀⠀⠴⡀⠀⠀⢘⣻⣿⠩⣬⠀⠀⠉⠀⠀⠀⠉⣸⠏⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠰⠆⠀⠛⠈⠶⠆⢐⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠌⡇⠀⠠⠠⠀⠀⠀⠰⠒⠚⠀⠐⠁⠀⠛⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠈⠀⠄⢠⡄⠀⠀⠶⠐⠀⡴⡆⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠠⠤⠴⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠆⠀⢸⠀⢨⡀⠛⠀⠀⢰⠛⣆
⠀⠀⠀⡀⠀⠀⠀⡀⠄⠀⠀⠀⠔⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠐⠀⠘⠐⠂⠀⠀⠑⠉⠀⠀⠉⠉⠂⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠲⢷⣤⣶⠟⠀⣀⢀⠀⠈⠠⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⡀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⣀⠈⠉⠀⠈⠀⠸⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠄⠀⠀⢤⢰⠀⠀⠀⠀⠀⢀⠀⠀⢀⢀⠀⠀⡀⡀⠀⠈⠁
⠀⠀⠀⠠⠀⠐⠂⠀⠀⠀⠀⠈⠈⠉⠀⣠⠈⠉⠀⢤⣰⠔⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡠⠀⠀⠀⠀⠉⠁⠀⠉⠈⣀⠈⠉⠁⠀⠈
⠀⠀⠀⠀⠀⢀⣀⣀⠆⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠥⠠⠀⠀⠀⠄⢈⠀⠀⠀⠐⠀⠀⢀⠌⡉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠢⠀⠁⠉⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠄⠲⣄⠀⣨⠀⠀⡠⠀⠀⠀⠈⠂⠁⠂⠀⠀⠀⠀⠁⠀⢀⠀⠀⠠⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠐⠀⠀⠈⠃⠃⠀⠴⠆⠀⠶⠀⠀⠀⠂⠉⠀⠰⠆⠈⠛⠀⠀⠀⠘⠐

⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⡿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣠⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⡀
⣼⠟⢤⠀⠀⠀⠀⠀⣀⣀⣠⣴⣽⣿⣿⣿⠟⠻⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⡟⢠⣯⡄⠀⠀⠘⠛⠻⠿⠿⣧⣀⣿⣿⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢿⢿⣄
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣟⡉⢛⣉⡏⡀⣀⣸⣿⣿⡶⠿⠒
⠀⣾⡻⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣄⡄⠀⠀⠀⠀⠀⢸⡏⣿⣿⠟⢿⣿⠿⢿⣿⣿⣿⡀⢀⣠⣶⡀⣠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣄
⡟⠀⠙⠃⠀⠀⠀⠀⠀⢸⡿⢯⣿⣤⣀⣻⣆⣠⠿⣿⠟⣿⣯⣨⣿⣹⡟⣹⣿⣿⢿⣋⡀⣄⣽⢳⣻⡿⠁⠀⠀⠀⠀⣼⣇
⠅⠀⢰⡀⠀⠀⠀⠀⠀⠈⢄⣈⣭⣿⣿⣿⣣⡿⠷⣯⣟⣯⣅⠉⣻⣿⣾⣿⡿⠿⣫⡻⣿⠿⢻⣿⣼⣧⠀⠀⠀⠀⠀⠈⢿⣧⡀
⡟⠀⢺⡇⠀⠀⠀⠀⠀⠀⢘⣿⡿⡿⡼⡟⢶⣅⣄⣀⣿⣾⣿⣷⣿⣿⣿⣍⣴⣶⡿⠏⣥⣤⢿⣷⠖⢯⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠁⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢗⡋⢱⣐⣯⣶⣽⣿⠿⠿⣻⣿⣿⣭⣔⡻⠿⢿⣾⣷⣚⣺⣛⣸⣗⡋⣻⡖⠀⠀⠀⠀⠀⠀⠘⢿
⠀⣿⣿⡇⢠⡄⠀⠀⠀⠾⣷⡿⠷⠛⢫⣽⠋⠡⡶⡖⠀⠛⠿⣿⣿⣿⣥⣤⡀⠈⠉⢻⣿⣿⣿⣿⣵⣾⣷⠄⠀⠀⠀⠀⠀⠀⠈
⢸⣿⡿⣰⣿⡇⠀⠀⠀⠈⠛⠿⣿⠿⣿⣯⣤⣤⡍⢵⣶⣿⣿⣿⣿⣿⣿⡿⠟⠙⣛⠋⠛⠋⢻⣾⡿⠟⠛
⣿⣿⣧⣿⣿⠃⠀⠀⠀⠀⢀⠀⠈⠙⢿⣿⣿⣻⣶⣿⣿⣿⣿⡿⠋⠁⠀⣠⣤⣤⣤⡼⣿⣿⡫⢋⣤⣀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠐⢿⠇⡀⠀⢸⣿⢿⣽⣿⣿⣿⣿⢿⣿⣶⡶⣾⠟⡓⣿⣫⣿⣿⠋⢀⣈⠛⠃⠀⠀⠀⠀⠀⠀⢰⣾⡇
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⡀⠉⠀⠈⣿⠐⠙⣿⣥⣿⣇⣦⢻⠻⠐⡿⣾⣿⣧⣼⢿⣿⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⣈⠀⢿⣰⣿⣿⣿⣿⣿⣷⣼⠀⣰⣿⣿⣿⣿⠀⢘⣿⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣴⣦⡉⠙⣿⣿⣿⢿⣿⣿⠀⣿⣿⡿⠛⠃⠀⢘⣿⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡏⢀⣶⣦⠀⠀⠀⠀⠈⠀⠀⠻⠟⠁⠀⣿⣿⣿⠀⢻⣿⣶⣿⠏⠀⠀⡀⠀⢸⣿⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝
⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣿⣿⣿⠀⢸⡟⠟⠡⣿⣿⡟⠀⠀⠘⠁⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠛⠿⠿⠀⠘⠇⠀⠀⠉⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠢⠀⢀⣄⣤
⠀⠀⠀⠀⠀⡖⠀⠒⠠⠀⠀⠀⠀⠀⠇⠀⢠⠀⠀⠈⠻⠟⠀⠀⠀⣀⠠⠄⠐⡄⠀⢀⢠⠤⠀⠀⢀⠀⠀⠀⠀⠑⡄⢑⠀⠀⢀⢀⢴
⠀⠀⠀⠀⠀⠡⠀⠀⢂⢣⠀⠀⠀⢠⠀⠀⢸⠰⠀⠀⠀⠀⠀⠀⡊⢸⠀⠀⠀⡇⠀⡇⢠⠀⠀⠀⢸⠀⠀⠀⢠⠞⠒⠊⠀⠀⢈⣁⠷
⠀⠀⠀⠀⠀⠀⢂⠀⠀⠆⢳⠱⡑⡼⠀⠀⢸⠀⡤⠀⠈⠁⠀⠢⢇⢸⠀⠀⠀⡇⠀⠀⡄⠀⠀⠀⡌⠀⠀⠠⣢
⠀⠀⠀⠀⠀⠀⠈⠄⠀⠈⠆⠀⠐⠆⠀⠀⢠⠀⡆⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠅⡜⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⢀⠄⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢨⠀⡇⢠⡏⠀⠈⠳⠀⠀⢠⠀⢸⡌⢡⡄⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢀⡔⠁⠘
⠀⠀⠀⢈⠀⢸⡄⠀⠑⡀⠀⠀⢸⡄⠀⠀⢸⠀⠃⠰⡘⢄⣀⡔⠀⠀⢸⠀⠘⠁⠸⠇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⣀⠤
⠀⠀⠀⠈⡄⢸⡇⠀⠀⠀⠀⠀⡠⠉⣠⢄⡀⢤⠂⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠱⠎⠤⠊⠀⠀⠣⣀⠑⠄⠀⠀⢀⣀⡄⠸⠀⠀⠀⢰⠀⠀⠀⠀⠀⠁⠀⢠⠠⢲⠀⠀⠀⢁⠔⠁⠀⠀⢀
⠀⠀⠀⠀⠀⢨⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠁⠀⠁⠀⠀⠀⠀⡀⠱⠀⠀⠀⠀⡀⠀⠈⠒⠊⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠄⠐⡄⠀⠀⠀⡇⠀⠂⢀⠞⢡⣀⣉⣀⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⢡⠇⠀⠀⠀⡃⠈⠀⠀⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⡡⠃⠸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⠐⠉⠳⠄⠀⠀⠈⠀⠐⠊⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⢀⣠⡾⠃⠀⠀⠀⠀⠀⣠⠞⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠰⠠⠴⠁⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠈⣻⢯⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣀⠤⠊⠀⠀⢀⡜⢠
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⢀⠈⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠀⠀⡠⠊⢀⠂
⠀⠀⠀⡜⠀⡀⠀⠀⠀⠀⠈⠀⠀⡠⡊⡀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠠⠂⠀⠀⠀⡰⡆
⠀⠀⠀⠀⠾⠊⠀⠀⠀⠀⠀⢁⡔⠴⠊⠀⠀⠀⠀⠀⡰⢻⠇⠀⠀⠀⠀⠑⠀⠀⣀⠀⠀⠀⠀⠀⠠⠔⠊⠁⠀⢀⠔⠀⠀⠀⣀⠜⡱
⠀⠀⠀⠀⣡⣀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢀⡀⢀⠊⡦⢁⡾⠊⢉⠽⠀⠀⠀⠀⠀⠐⠠⠔⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠊⠑⠊
⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⡠⢄⢀⠎⠸⠞⣸⣷⠿⠒⠋⢁⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⢸⠘⢀⢇⣡⣿⠷⠶⠶⠖⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠐⠀⡇⡘⣃⣮⣾⡏⠀⠀⠀⡀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠐⣦⠀⠀⠀⠀⠱⠀⡇⣷⣿⡿⠛⠡⡀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠠⠔⠂⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⣱⡿⠿⢁⠀⠀⠀⠈⠆⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠐⠒⠚⠛⠛⠚⠙⠊⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠐⠀⠀⢂⠁⠀⠠⠃⠀⠀⠀⠀⠀⠐⢢⢠⡄⠀⣔⠀⣰⡆⢀⣖⠀⣰⠀⢀⡂⠀⣐⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠈⠉⠉⠉⠀⠀⠉⠁⠀⠀⠀⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⠒⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⣠⠀⡆⣨⡍⠀⢀⠠⠉⠋⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡔⠒⠌⠀⠉⠀⠈⠉⠁⢾⠰⠒⠄⣥⠴⡒⢶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⣶⢾⢤⠉⡄⠡⡀⢠⠄⠀⢠⡄⢀⡀⡀⢀⡄⡤⠤⢉⡀⠀⣀⢀⡈⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠥⠙⠏⠷⠚⠁⢲⠴⠛⣀⢔⡂⡘⠷⠞⠷⠐⢼⠂⡯⠥⠸⡟⠚⢿⠸⢻⣧⣬⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⡈⠀⠀⠈⠉⠚⠆⠀⠋⡛⠉⠚⢁⠛⠠⠙⠂⠐⠀⠀⣓⡐⠖⠀⢀⠐⠀⠒⢄⠐⠶⠿⡀
⠀⠀⠀⠀⠀⠀⢀⣜⠂⣀⡀⠀⢠⣤⣀⢀⣠⡤⢀⡄⠀⢀⡀⢀⠀⡀⣀⠄⠀⠉⠀⠀⠀⠀⠀⣄⡀⢀⣠⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠈⠉⠉⠈⠉⠳⠈⠁⠈⠉⠉⠉⢁⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠇⠍⠘⠀⠎⠰⠃⠘⠷⢿⠼⠾⠅⡲⡾⠷⡿⢿⡟⡇⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⣄⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⡦⠠⡀⠀⠄⠀⠀⠀⡅⠀⢠⠆⠀⠀⠈⠳⠸⣗⠀⠀⠀⠀⠀⠀⠀⠌⠀⠠⠀⠀⠠⠀⠠⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠄⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠄⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠆⠠⠸⡇⠀⠀⠀⠠⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⣀⣠⢌⡃
⠀⠀⠀⠀⠀⠀⣘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⡀⡀⠀⢠⣤⣤⣄⡗⠈⠹⡋⣰⠃
⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡄⠜⠻⣽⡷⣟⣷⢿⣋⠀⠀⠨⠇⠈⡀⠀⣪⠴⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠈⣷⣲⡶⠆⢠⠙⢣⡔⣿⡏⠄⡄⠀⠀⠀⠀⠌⣷⣶⢶⡶⡣⢠⡎⣆⢉⠣⡥⠀⠈⠋⠡⠴⠙⠶⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣶⣤⡞⢢⡌⣀⡭⠔⠀⠓⠀⠀⠀⠀⠘⠋⠉⠀⠀⠋⠈⠴⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠿⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡻⠛⠙⠸⣇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠂⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡗⠀⣠⢾⡳⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠭⣱⣦⣺⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣅⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⡄⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠘⠁⠈⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⣀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠙⠂⠀⠀⢠⣀⣠⠖⣿⠄⢸⢇⡋⠶⠒⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠠⠟⣊⠒⠒⢯⡀⢀⣨⣽⣟⣧⡀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠉⠉⠙⠛⠚⠃⠁⠀⠀⠀⠀⠀⣳⠦⠴⠣⠕⠎⠱⡏⢱⣴⠏⣬⣥⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡠⠁⠀⠀⠀⠨⠄⠒⠁⠆⠀⠠⠄⠄⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠤⡀⠀⠀⠀⠀⠀⠠⡮⠷⠂⠀⠁⠈⠈⠁⠀⠀⠀⠀⠈⠓⠀⠃⠈⠈⠜⠃
⠀⠀⠀⠀⠀⢀⣀⣀⡀⣠⣄⠀⡐⠂⠀⠀⠀⠉⠀⠁⠁⢀⠈⠉⠉⠋⠀⠅⠇⠀⠐⠐⠆⠀⠒⠇⠦⠲⠂⠀⠸⠤⠤⠦⠳⠀⠾
⠀⠀⠀⢀⣴⡞⠋⣼⠓⢀⡉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠊⠈⠻⡓⣲⠀⣤⡤⠀⢀⠠⠀⢠⠀⠀⠀⢀⠀⠀⢠⢤⡀⢀⢠⡀⢀
⠀⠀⢀⣈⣉⡆⣠⣄⣆⡂⠤⡄⠌⣷⠼⠴⠆⠄⠲⣦⣶⡀⣂⢘⡇⠠⠾⣦⢰⣴⣦⣀⡄⣠⣓⣦⢿⣄⣰⡆⣈⣀⣰⡄⣮⣐⣢⡄
⠀⠀⠈⠉⠈⠉⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠢⡤⠤⡤⠤⣠⣀⣀⡀⣸⣴⣿⢹⣷⣼⠄⣀⡀⣠⡠⠤⡠⢦⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠈⠀⠘⣦⣽⣿⣿⣻⣭⡍⡏⠈⡏⢩⢙⡹⠻⠙⣣⠔⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢄⠀⠀⢀⣠⠄⠀⠰⠁
⠀⢂⡛⣯⠛⠘⠫⠝⣿⡛⠅⠣⠀⠓⠘⣛⣚⠠⠛⠈⠋⡏⣻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⢠⠀⢀⠀⠁
⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠉⠈⠂⠀⠈⠁⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⣀⠠⣤⠀⠀⠀⣤⢄⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢰⠁⠀⠀⠀⠉⡀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠴⠀⠂⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⠢⠀⠀⠠⠊⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠄⢀⠀⠀⠀⠐⠂⠀⠉⠀⠁⠂⠺⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢀⡤⠀⢄⡀⠸
⠀⠀⠂⢬⠓⠉⠀⠄⠐⢒⡏⠈⠈⠀⢟⠒⠀⠀⠀⠑⢫⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠻⠈⠀⠠⠟⢃⡀
⠀⠀⠀⠀⢣⡖⠢⡍⠙⡻⢃⠀⠀⠀⠚⢛⠁⡥⠒⣦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠠⠃⣀⠘⠄⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠈⣰⡇⠀⠀⠀⢳⡈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡀⠀⠀⠀⣸⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⢣⡀⠀⢀⠃⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠠⠀⠀⠀⠀⠀⢄⡄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠁⠇⠀⠀⠀⠀⠀⠰⠈⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⢠⢠⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠤⠀⠀⠘⠠
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠈⠆⠉⡞⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣀⠓⠀⢃⣠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠄⠀⠣⡀⠀⣠⠀⠀⠀⡀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⢈⠀⠀⠀⠉⠀⠉⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠁⠀⠎⠁⢱⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠒⠀⠐⢤⠊⠁⠀⠉⠓⠴⡀⠀⠒⣁⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁⢴⡃⠀⠀⠀⢘⡆⠌⢀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⡸⠃⠆⠀⠀⠀⠀⠀⢆⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⢈⠁⠐⡀
⠀⠀⠀⠀⠀⠀⠜⠁⢂⠘⡀⠀⠀⠀⠘⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⠀⠀⠀⠀⠀⢲⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⡤⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠼⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⢀⠠⠁⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⢰⣦⠀⡟⢦⣠⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠑⣤⡭⠧⣧⡚⠁⠀⢹⠁⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠲⣦⣄⡀⢇⠀⢰⠍⠀⠀⠀⠙⢆⠀⠀⠀⠀⢨⡦⡴⢤⣀⣀⢀⣀⠤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠓⠦⣀⠀⠈⢇⠈⢻⣄⣸⣆⠀⠀⠀⠀⠈⠀⣄⣆⣠⠋⠀⠀⠀⠋⠘⢿⣇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⣾⣧⡴⠚⠿⣿⣿⡿⠿⣄⣖⠙⠢⣄⠀⠉⠛⢿⣦⡀⣠⠖⠛⠛⠻⣿⠓⠒⠲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⡿⠁⠀⣠⠿⣯⠄⠀⠘⠫⠿⢶⢤⣿⢿⣇⠀⣠⣄⣠⣾⣥⠴⠚⠋⠉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠛⢷⡀⠀⠀⠇⠀⠞⠁⠀⡼⠷⢖⣰⣋⠙⢻⡀⠁⠀⠈⣾⠃⠀⠈⠛⠖⣤⣴⡊⠉⣻⠟⠉
⠀⠀⠀⠀⠀⢀⣠⣤⠒⣾⠀⠀⠀⠀⠀⠁⠐⢓⡀⠀⣀⡤⠾⢧⠀⣜⠉⠉⠉⢢⠱⣄⠀⢀⡎⠀⠠⠄⠀⠈⠉⠛⣇⠴⠁
⠀⠀⠀⠀⠀⠈⠉⢉⣲⣿⣄⣀⡠⠲⡤⣥⣚⣛⣉⠵⠿⠀⠀⣰⠋⣹⣤⠶⣦⣸⣶⠿⣶⣿⣦⠀⠀⣀⣠⣤⣤⣴⣧⠤⣀⡀
⠀⠀⠀⢀⣤⣴⣞⣁⠬⠿⠛⠛⢣⡄⡠⠋⠁⠀⢀⠀⠀⢀⡾⠁⠀⠙⢦⣴⠄⠌⠃⠲⣶⣾⠻⡏⠉⠁⠀⠀⠹⣿⣏⣀⣀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠔⠋⠉⠓⠋⠀⠀⠀⠀⠀⠙⠶⢦⣖⡆⠄⣅⣸⡧⠀⢀⣀⠀⠀⠀⣽⣿⣿⣋⠉⠉⠉⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠾⠿⢤⡀⠀⢘⡇⠀⠀⣿⣿⣯⠛⠻⣕⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠧⠴⣾⣿⣿⣷⡀⠀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠌⢿⡌⠙⠒⠒⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢟⣭⣭⡉⢙⣛⣉⠉⠻⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣟⠻⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠛⠛⣿⣿⣷⣿⣾⡄⠈⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⡀⣀⢼⣿⣿⣭⣴⣾⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣷⣄⢈⣿⣿⣿⣿⣷⠈⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠍⠡⣨⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣇⢸⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⠃⣹⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣶⣾⣶⣾⡀⠙⣿⣼⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣾⣧⡀⢪⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⠦⢹⣏⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⢾⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⢹⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠙⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠏⠀⠉⠠⠈
⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢴⣶⠄
⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⢠⡄⠀⢀⠘⡀⠀⠠⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠫⠄⠀⠀⠀⠀⠈⠀⡐⢄⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⢠⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⢀⠂⠀⠢⡠⠃⠀⠀⠀⠘⡀⠴⠀⢀⠄⠊⡐⠀⢀⠶⠉⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠰⡐⠂⠠⠴⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⢀⠁⠀⠁⠀⠀⠀⠀⠠⠗⠊
⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠐⡄⠀⠀⢀⠀⠀⠀⠀⡀⢀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠤
⠀⠀⠀⠀⠀⠀⠤⡐⠀⠈⠁⠀⠀⠀⢸⡇⣰⣆⢸⡇⣾⠋⢻⡄⣿⣠⡄⢰⡟⠀⠀⠀⠁⠀⠂⠤⢀
⠀⠀⠀⠀⠀⠀⣀⠀⠁⠢⢄⠀⠀⠀⠸⣷⡟⢻⣿⠛⣿⣀⣿⢱⣿⠟⣿⣾⠁⠀⠀⡀⠀⠠⠄⠒⠀⠉
⠀⢀⢀⡀⣀⣀⡈⠀⠠⠂⠁⠀⡀⠀⠀⠿⠁⠀⠛⠀⠉⠋⠁⠘⠋⠀⠹⠃⠀⠀⠀⣐⡀⠀⠀⠀⡀
⠀⠀⠉⠈⠀⠀⢀⠀⠀⠀⠀⠴⠁⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠅⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠝⠂⠈⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⠤⠀⠀⡠⠀⠀⡠⢀⡔⢄⠀⠀⠀⠆⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⡐⢀⠤⠊⠀⠀⠄⠊⠀⡅⠠⠁⠈⠀⠀⠑⢄⠀⢀⠀⠀⠀⠉⠒⠤
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⢀⠀⠀⠢⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⣔⠀⠀⠀⠀⡄⠀⠀⠀⠈⡄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢰⠏⠁⠀⠀⠀⠀⠀⢀⣀⠀⠠⠀⠀⠀⠀⠐⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⠀⠀⢀⠀⡀⠀⣠⣿⣄⠀⢀⠀⠀⠀⠀⣠⡔⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠻⣄⠈⢲⣷⣶⠿⠿⠿⣿⣿⡶⠁⣠⠶⠁⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠂⠉⠉⠁⠉⢉⣛⣿⣿⣶⣤⣄⣀⡈⢓⣿⣿⣿⣧⣰⣤⣿⣿⣿⣛⣁⣤⡴⠶⠟⠻⠿⠍⣉⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠁⣀⣤⣎⣁⣈⣹⣿⠟⠙⢻⣿⣿⡿⣿⣿⡿⠋⠻⠍⠲⣤⣤⣤⠷⠦⢄⡀
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠔⠉⠀⠀⡤⢻⠛⠀⠀⠀⠀⢸⣿⣟⣛⣿⣿⣷⡀⠀⠀⠀⠈⢦⠉⠲⣄⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⣟⠀⠀⠀⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠢⣀⠀⠀⢆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡤⠖⠊⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⡄⠈⠛⠶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⠻⣿⣿⣿⡿⠛⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣶⣶⣶⡄⠘⠛⠀⣠⣶⣶⣿⣷⣾⣷⢦⣶⠆⠈⠙⠛⠷⠶⠄
⠀⠀⠀⠀⢸⡿⠊⠉⠉⠙⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⣦⠾⠿⠛⠃⠀⠀⠀⠀⠐⠓
⠀⠀⠀⠀⣶⡿⠀⠀⠀⢀⣾⠛⠋⠻⣿⣿⣤⣄⣀⣀⡰⠖⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣤⣶⣤⣴⣿⠋⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⠀⠀⠈⠻⣿⣶⣷⡆
⠀⠀⠀⠀⣻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀⠀⠀⠀⠀⠻⡿⠁⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⣠⣤
⠀⠀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿
⠀⠀⠀⠀⠸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠤⢀⡀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠲⣦⠀⠀⠀⠀⠸⠆⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠋⠀⠀⠀⠋

⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠧⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⠛⠛⠀⠂⠙⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⠀⠾⠐⠀⠆⠀⠀⠀⡠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠁

⠀⠀⠀⠀⠀⢘⡔⢁⠀⠀⡠⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣶⣾⣛⠀⠈⠢
⠀⠀⠀⠀⢀⡈⠀⡜⢀⠴⠡⣚⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠂⠄⠐⠖⠋⠀⠘⣿⠋
⠀⠀⠀⢠⣼⣧⡄⠀⠀⠀⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠰⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠏⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⡗
⣶⣤⣾⠂⠀⠒⡄
⠉⢻⡿⠃
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⠦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⣉⠊⡆
⣀⣴⣄⣠⠔⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣁
⠀⣽⣿⡏⠁⠐⠄⠀⠀⡠⠊⠠⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣷⣶⡾⠆
⠴⠋⠀⠀⠀⢀⡁⢀⣌⠀⢐⠀⠀⠠⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣿⠟
⠀⠀⠀⠀⡠⠜⢻⣿⡇⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⣀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠸⢲⠞⢧⣼⡉⡿⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢢⠃⠀⠀⣀⠀⢠⡀⢀⠀⠐
⠀⠐⠊⢀⡀⠀⠈⠙⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⡀⠁⠀⠀⠀⠃⠰⠄
⠀⠠⠀⠈⠀⠀⠈⡀⠀⢄⠂⠐⠀⠀⠰⠀⠀⠀⠀⡀⠀⠀⡆⠀⢀⡼⢷⣾⣁⡄⠀⠀⢀⣠⠤⢄⠀⠉⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠁⠀⠀⠀⠛⠇⢸⣁⢀⠀⠃⠀⠀⢰⡆⠀⢸⠀⠀⣠⢂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠀⠀⠀⢀⡜⠀⠀⠸⠊⣶⢃⠾⡆⣠⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⢸⡁⠀⠀⠀⠀⠀⠈⠰⠘⠤⠉⠋⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⣃⡀⠀⠀⠠⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣶⡀⢷⣄⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠻⠃⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⢰⡆
⠀⠐⠂⠀⠀⠀⠀⠀⠀⢰⣦⢸⣇⣀⣸⣧⠈⠙⠻⣇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⣤⠀⠀⠀⠀⠈⢦⡏
⠀⠀⠀⠀⣤⡄⠀⢀⡀⠘⣿⠀⣿⡟⠉⢻⡆⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⡄⠸⣇⣠⡄⣿⠀⣇⢠⣇⠀⠸⡇
⠀⠀⠀⠀⠈⠹⣆⢸⠿⣶⣿⠀⠸⠇⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⠀⢿⡏⠙⣿⠀⠈⠀⠻⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠈⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢄
⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⡀
⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠂⠆
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⣀⠄⠄⠀⠐⠂⠒⠒⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠈⡀⠀⢀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡅
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠂⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⡁⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠒⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⢆⢤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢀⡄⠆⠀⠀⠰⣶⡀⢠⡀⢰⣿⣀⡿⣯⠀⣿
⠀⠀⠐⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠖⡖⠡⠃⠰⠼⠄⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠘⣿⡿⢿⡿⠈⠏⠻⠙⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠐⠆⠀⠀⠂⠀⠀⠂⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠐

⠀⠀⠀⠀⠀⡤⢤⡀⢀⡠⢤⠀⠀⠀⢀⡤⠤⡄⠀⠀⢠⠴⠒⠲⠤⣄⠀⢠⠖⠒⠒⠒⢤⡀⢀⠤⣄⠀⠀⠀⡠⢤⡀
⠀⠀⠀⠀⠀⡇⢸⡇⢸⠀⠀⡇⠀⠀⡜⢀⡀⢸⡀⠀⢸⠀⢠⠐⡄⠀⢳⢸⠀⠀⠔⢀⠀⠹⠈⢆⠘⢆⠀⡜⠁⣠⠃
⠀⠀⠀⠀⠀⡇⠈⠓⠞⠀⠀⡇⠀⢰⠁⠬⠰⠀⢇⠀⢸⠀⠀⣉⣀⡴⠃⢸⠀⠀⠉⠁⣀⠜⠀⠈⢢⡈⠊⢀⠞⠁
⠀⠀⠀⠀⠀⡇⠀⡞⠙⡆⠀⡇⠀⡎⠀⡠⠤⡀⠸⡄⢸⠀⢰⡇⠀⠀⠀⢸⡀⢸⠉⠉⠀⠀⠀⠀⠀⢣⠀⡁
⠀⠀⠀⠀⠀⡇⠀⡇⠸⣇⣀⡇⣸⠀⣸⠁⠀⢱⡀⢱⠸⡇⢀⡇⠀⠀⠀⠸⠇⢸⠀⠀⠀⠀⠀⠀⠀⡸⠀⡇
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠁⠀⠈⠉⠁⠀⠀⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠳⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠘⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡈⠓⠦⠤⣄⣀⣀⠤⠤⠒⢉⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠤⠤⠤⠒⠊⠉

⠒⣒⡶⠴⠶⠒⠒⠒⠒⠒⠲⠶⠶⣶⣒⠒⢲⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⣿⣿⣿⣿⣿⣿
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠾⣭⠩⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣤⢉⠭⠭⠭⠭⠭⠭⠭⢭⣍⣭⣭⣭⣭⣍⣩⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⢭⣭⢽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⣀⣀⣤⣬⢷⣒⣒⣒⣒⣶⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣒⢒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣿⣿⣿⣿
⢰⣿⡇⣿⡇⣾⡿⣰⣾⣿⣷⣸⣿⣴⣿⣇⣿⡏⣿⡏⠘⣗⣒⣒⣾⣿⣿⡟⢰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣶⣒⣒⣒⣒⣒⣒⣒⣒⣒⣺⣿⣿⣿
⠈⣿⣷⣿⣷⣿⡇⣿⡇⣸⣿⠛⣿⣿⢿⣿⣿⠁⣛⠁⢀⣧⡾⠋⠙⢿⣿⡇⢻⢡⡏⣸⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠤⠦⠶⠶⠦⢿⣿⣿
⠀⣿⣿⡏⣿⣿⠃⠻⠿⠿⠋⠀⠟⠛⠘⠛⠋⠈⠛⠀⣼⣿⣷⣫⣤⡴⠞⠿⣆⠀⠀⠠⠶⠶⣷⣶⣤⡙⢿⣿⣿⣿⣟⢿⣿⣿⡭⠭⠭⠭⢽⣿⣿
⠀⠙⠋⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠻⠋⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⢻⣷⣌⠙⣧⢻⣿⣿⣹⣽⣫⣩⣿⣿
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣚⣹⡇⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣿⡆⠘⠆⢿⣿⣗⣒⣒⣒⣿⣿
⣛⣛⣒⡦⠤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⢳⣒⣒⣿⠃⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣒⣒⣂⣿⣿
⠭⠤⠤⠵⠤⠤⠤⠤⠤⠤⠤⠭⠷⠦⣤⢀⠹⡤⢼⣾⣾⣿⠁⠀⠀⠀⠐⠦⣤⡀⠀⠀⠀⢀⣀⣤⠖⠒⢾⣿⣿⣿⣿⡆⠀⢸⣿⣿⠤⠤⠤⣿⣿
⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠿⣽⣿⣿⠇⠀⢀⣴⣞⣓⣀⠀⠁⠀⠀⠀⠉⠉⢀⣐⣲⣾⣿⣿⣿⠉⠁⠀⢸⣿⣿⠬⠭⠭⣿⣿
⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣉⣿⣿⣿⣿⠀⠀⠀⠻⠍⠻⠟⠁⠀⠀⠀⠀⠀⠘⠉⢽⣟⣽⣿⡿⢁⠀⠀⠀⣼⣿⣇⣙⣉⣁⣿⣿
⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣲⣿⣿⣿⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠁⣼⠀⠀⢠⣿⣿⣖⣒⣒⣺⣿⣿
⠶⠶⠶⠶⠶⠶⠒⠶⠶⠖⠖⠶⠲⠲⠖⣿⣿⣿⣿⣇⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣾⣿⠀⣰⡿⠀⠀⣼⠏⣿⣿⣷⡖⣾⣿⣿
⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⣿⣿⣿⢳⠹⣆⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⣿⣷⣼⣿⡇⠀⢠⡟⠸⡇⠙⢿⣿⣿⣿⣿
⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠽⣿⣎⢧⡁⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⣿⣿⣿⢿⠃⠀⢸⠃⠀⠁⠀⠘⣿⣿⣿⣿
⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣚⣿⣦⡁⠀⢻⡆⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡀⠀⠀⣿⣿⠏⠈⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣛⣷⡄⠈⣿⣆⠀⠀⠀⠀⢀⡈⠛⠛⠛⢉⠄⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿
⠤⠤⠤⠶⠶⠶⠤⠤⠤⠴⠶⠶⠦⠤⠤⠤⠤⠤⠼⠽⣿⠀⢹⡟⣧⡀⠀⠀⠀⠈⠑⠒⠚⠁⠀⠀⣰⣿⠁⠀⠀⠀⠀⣸⡄⠀⣴⣿⣿⣿⣿⣿⣿
⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⢭⡿⠀⢸⡇⢿⣿⣦⣄⡀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠀⠀⠀⠀⣠⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿
⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠍⠋⠀⠀⢸⡇⢸⣿⠿⣿⣿⣶⣦⣴⣾⣿⣿⣿⣿⣿⣦⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⡒⠂⠀⠀⠀⠀⠈⠀⠘⡟⠀⠈⠻⣿⣿⣿⣿⣿⣿⡟⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣒⣒⣒⣒⠒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⢿⣿⣿⣿⣿⠃⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡭⠭⠭⠤⠤⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣉⣻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣮⣧⣤⣥⣭⣭⣭⣭⡭⠭⠭⠭⠭⠅⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀
⠀⡀⡇⠀⠀⡀⣼⡀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐
⢰⡇⣿⣿⠀⣧⣿⡇⢰⢾⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠛⠿⣿⣀⣿⣿⡇⣼⣾⡆⣷⢀⡇⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢿⡧⠇⢄⡀
⠀⠀⠀⠀⠓⠉⠛⠓⠿⠿⢯⣿⣤⣧⣾⣠⡆⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠇⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠇⠀⠀⢳⠀⢸⠄⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠑⠄⠀⡬⡆⢀⠂⢠⠈
⠀⠀⠆⠠⠒⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⢀⠀⠀⠒⠣⣀⡤⡀⣸⣭⠆⠠
⠐⡆⢰⣛⣒⡀⣤⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢘⠌⢨⠅⣀⠹⣷⣥⣕⠂⢓

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠙⢏⠛⠃⢤⠀⠀⠉⠉⠳⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠳⠀⢄⣠⣄⡈⢦⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⢺⠝⣧
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢦⣀⣃⠀⠉⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⠞⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⣨⠟⠒⢀⣀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠘⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠗⠒⠛⠉⠀⠈⠲⢝⢢⡀⠀⡀⠀⠀⣀⠀⡼⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠳⡑⡾⠁⠀⠀⠈⢏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠂⠛⠐⠒⠢⢄⣀⠀⠀⠙⣜⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠘⣞⡄⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡏
⠀⠀⢀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠤⠤⣄⡀⠀⢀⠀⠀⠀⢳⡀⠘⢂⡔⠓⠂⠀⠀⠀⠀⠠⠶⠊⠁⠀⣷
⠀⠀⠈⠑⠤⣄⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀⢳⠀⣄⢹⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡇⢰⠸⠀⠀⣠⠚⠁⠀⡀⡠⠊⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⢲⣄⣀⠠⣄⡰⠖⠛⠁⠈⠛⢦⡀⡆⢰⠃⠀⢀⢀⠟⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡤⠧⢤⣿⠀⠀⠈⠿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠑⠚⠛⠒⠦⣄⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡦⣾⠤⠖⠛⠛⠛⠲⣄⠀⣀⣀⣀⡈⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⠉⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠃⠀⠀⢀⡀⠀⠀⠀⣼⢰⡖⣪⡅⠪⣽⢃⠀⢀⡤⠀⠀⠀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣆⠀⣀⡇⠉⠓⣤⡾⢻⣌⠳⢭⣠⠞⠉⢧⠞⠁⠀⠀⠀⠀⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣨⠟⠋⠀⠀⣼⠋⠀⠀⠉⠳⣄⠟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠤⠐⠒⠠⡏⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⡏⠀⠀⣠⠞⠒⣒⢦⡄⠀⣠⡶⠶⠋
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠹⣦⡀⠀⠀⣀⣉⠤⠞⠁⣠⠎⠹⣄⠀⢠⠏⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⡠⠞⢋⠟⠉⠀⠀⠀⣀⡾⠁⠀⠀⠀⠉⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⢤⣄⠀⠀⠀⠀⠰⢟⣁⢀⣠⢞⠟⠒⠒⠉⢩⠑⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣤⣀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⣉⡩⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠶⠚⠉⠂⠈⠙⠓⠛⠛⠲⠶⠴⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠢⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⠀⢸⠀⡏⠀⠀⡰⣡⠔⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢌⢇⠘⠀⠀⢀⣾⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡈⠓⠄⢀⠼⠚⠓⠒⠲⡟⠁⠠⠊⢀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡏⠀⢛⢀⠘⠃⢸⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢒⣒⠭⠛⠧⡀⠘⠚⠀⢀⡼⢍⠑⠒⠤⣄⣀⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠁⢀⠤⠀⠀⢨⣷⠒⠒⠁⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠴⠁⡰⠁⢀⣿⣿⠀⢰⠀⠳⡀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠻⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡿⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡸⢰⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⠤⠒⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠳⢄⡀⢀⡰⠁⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡠⠊⢁⡠⠖⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⠣⡀⠀⢀⡠⠴⠊⠁⠀⣠⠊⢀⠴⠋⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⢀⠜⢁⡔⠁⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠣⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡠⠃⠴⠋⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠢⣄⠀⠳⡄⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⠜⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡈⠁⠀⠈⠢⡀⠀⠀⠀⠘⡌⡄⠀⠀⠀⢠⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠈⢦⡀⠀⠀⢃⢱⠀⠀⢠⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠈⠢⣀⠸⡈⡆⢠⠇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡓⢧⠱⣎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⢉⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠿⠒⣴⠞⣴⠛⣱⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢹⣿⡏⣀⠁⡐⢃⡴⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣫⠔⠚⠘⣿⠿⢆⣿⣴⢳⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣈⣴⣿⣦⠀⣘⠙⠿⣟⠻⠈⣾⣿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣤⣤⢾⣴⣫⣍⡻⡎⣶⡕⢸⡿⢼⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠋⣾⣏⠙⢓⣣⣿⣷⢈⣽⠀⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⢿⣦⣭⣭⣿⣧⣤⡰⣾⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣷⣮⣽⣿⡟⠁⠘⣷⠘⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⠛⣋⡾⣮⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠉⠉⠙⣿⣿⣿⣿⠟⠳⣬⢳⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⡀⠀⠸⣿⣿⡇⠀⡄⠘⣷⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣇⠀⣠⣿⣿⣿⣶⣿⣆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⢻⡟⠛⠉⣿⠏⠉⠙⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⢻⣦⡀⣿⡆⠀⠀⡿⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠙⢿⣾⣷⡀⠐⠁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒
⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣟⣿⣟

⠀⠀⠀⠀⠀⠀⣴⠀⠝⠓⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣯⡤⠀⠴⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⣠⠀⠀⠈⠃⣴⠃⣴⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢿⡿⣿⠏⠀⠀⠀⣄
⠀⠀⠀⠀⠈⣷⠀⠀⣤⠃⣰⡇⠀⠀⢠⠀⠀⠀⣀⣀⠀⠀⠀⠈⠁⣿⣄⡀⢀⡴⠊⠀⠀⠀⠀⠀⠀⣀⠀⣠⠆⠃
⠀⠀⠀⠀⠀⠸⣆⠀⢁⣠⢿⠁⠀⠀⠀⠀⠀⠀⠙⠙⠗⠀⠀⠠⠆⠹⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢻
⠀⠀⠀⠀⡄⣰⠹⣶⡈⣧⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠂
⠀⠀⠀⠀⢱⡏⠐⠋⣇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠈⠁⠁⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣆⣠⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⠤⠄⠀⠀⠀⢀⠤⢴⠲⠶⠶⠛⠉⠃⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⢿⡟⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⡿⢦⠄⠤⠼⠛⢻⠀⠇⣠⠀⠀⠀⡈⣠⢆⠀⠈⠇⠀⠤⠆⢠⡖⠀⠀⠀⢸⡇⣠⠛⠢⠀⠐⠁⢀
⠀⠀⢠⠃⣰⡇⠀⠀⠀⠀⠀⠀⣇⣼⠇⠀⢀⣴⠿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢰⠃⠀⠀⠀⠀⠀⣸
⠀⠀⢸⣾⡁⠧⠶⠄⠀⠀⠀⠀⠸⠿⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢀⣿⡇⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⣿⣿⣆⠀⣼⣿⣿⠀⢀⣾⣿⡇⠀⠀⠀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⡀⣿⣿⣿⣶⣿⣿⣿⣧⣿⣿⣿⠇⣀⣴⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠘⢷⣶⣤⣀⡀⢻⣿⣿⣿⣿⣿⠹⣿⣿⠈⣿⣿⠏⣿⣿⣾⣿⣿⡿⠁⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⠈⠛⢿⠀⠘⠃⠀⠹⠁⢀⣿⠟⣉⠿⢿⣥⣶⣾⣿⡿⠋
⠀⠀⠀⠠⣤⣄⡀⢀⣀⣈⣻⣿⣮⡉⢸⣷⣶⢀⠀⣦⣀⣇⣠⡆⢀⡀⢠⣿⣿⡇⣻⣿⡿⠋
⠀⠀⠀⠀⠠⣶⣾⣎⢿⣿⠿⢛⠻⠷⢸⣿⣿⠘⢛⣭⣴⣶⣭⣕⠛⣀⢸⣿⣿⢱⣿⠿⢷⣶⣶⣶⢆⡐⠖
⣤⣾⣿⡄⠀⠹⣿⣿⣎⢿⢸⣿⣿⡄⢸⣿⣿⣰⣿⡿⠟⠻⣿⣿⣧⠁⣾⣿⣿⠀⣠⣿⣶⠙⠟⣱⣿⣿⡆
⠈⠻⣿⣿⣆⢶⡹⣿⣿⣆⢸⣿⡿⣿⣼⣿⣿⢿⣿⡅⠀⢀⣼⣿⣿⢠⣿⣿⣧⣾⣿⣿⣿⢀⣾⣿⡿⢋⣾⣶⣤
⠀⠀⠘⢿⣿⣦⠀⠹⣿⣿⣿⣿⠁⠹⣿⣿⣿⢈⠻⣿⣿⣿⣿⡿⡃⣼⣿⣿⣿⢟⡁⣿⣷⣿⣿⠟⣠⣿⣿⣿⠟
⠀⠀⠀⠀⠉⣥⣶⡀⢻⣿⡿⢏⣴⣶⠙⠉⠉⢀⡷⢠⡍⣭⠱⣦⠁⠀⠀⢮⣤⣬⢱⣿⣿⡿⢃⠐⢿⣿⠟⠁
⠀⠀⠀⠀⠐⠙⣿⡿⠀⠉⣸⣿⣿⣡⣴⣾⠃⠀⡀⠘⠀⠘⠀⡈⠀⢲⣤⡈⢻⣿⣷⠮⠛⢰⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢿⣿⣏⣴⣾⡇⢀⣾⡄⢀⣿⣦⠸⣿⣿⣿⣿⣿⣆⠀⠀⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠛⠉⠀⣾⣿⣿⡿⣿⣧⣾⣿⣿⣼⣿⣿⣷⣿⣿⠉⠛⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⡿⠋⠀⣿⣿⣿⠋⣿⣿⣿⠃⠻⣿⣿⡇⠀⠀⠈⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⠀⣿⣿⠃⠀⠘⣿⣿⠀⠀⠈⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠹⡏⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣷⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣮⣩⡄⠀⣥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⢳⠀⠀⠠⠀⡀⠀⠀⣤⣀⠈⢸⠘⢻⠛⠟⠛
⠀⠠⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠐⠀⠀⠱⡄⢸⣿⡿⠟⢻⡆⠖
⢲⣾⣻⠯⢀⣀⡀⢀⣄⠀⠀⢀⠄⠂⠀⢠⠀⠀⠀⠐⡄⢠⡈⠑⠄⣀⠀⢹⢨⣤⣤⡈⢻⠐⣿⣷⣦
⠘⡇⢨⠀⠫⠀⠀⢹⣿⠀⠀⣠⠀⠀⠴⠋⠀⣾⠀⠀⡅⠀⠁⠀⠀⠻⣤⡀⢢⠀⠙⠑⢾⣠⠐⠈⠁
⠠⠶⠾⠶⠴⣤⡄⠉⡉⠀⠘⣿⠗⠀⠈⠀⣤⣤⣤⣦⡥⣤⣤⣤⣥⣴⣴⣶⣶⣷⣶⣶⣼⡷⠶⠛⢻⣯
⢰⣦⢞⣀⣠⡀⡀⣀⣀⣒⣸⣿⣧⣤⣤⡤⠬⣿⠭⢭⠽⠟⢻⣿⣿⣿⣻⣿⣿⣿⡟⡙⣹⡄⢠⡀⣾⣿
⣀⡶⢚⣻⢲⣿⠌⣱⣿⠟⣿⡿⠿⠿⠃⠀⠀⠠⠴⠫⣷⣖⠶⢿⢿⣿⣽⠟⠉⠈⢰⡟⣿⡥⣿⣄⣿⣿⠄
⠡⠺⠯⠖⠁⠀⠀⠿⠷⠏⠁⠀⠐⠂⢚⡁⢀⣉⡉⠉⡉⠙⠛⠿⠓⡬⣁⠉⠃⠀⣷⡀⣿⣗⠥⣸⣿⣿⣦
⠀⠀⢐⣒⣀⠀⠀⠀⠀⠀⠒⠀⠠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠸⠦⠉⠀⠀⢠⣿⠀⣼⠁⠀⣿⣿⣿⣧
⢴⣾⠏⣽⡿⢿⡶⣴⣏⣿⠦⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⢟⡃⢹⠅⠈⣻⡿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡀⡰⠃
⠀⠀⠹⣿⣿⣦⣀⠀⠀⡰⢆⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠙⠻⣁⡐⠙⠆⠓⠈⣇⣀⣀⣼⣇⣀⣈⠧⠀⠠⠐⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⢀⠀⠤⠀⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠙⢛⢠⣴⠖⠋⠉⠙⠄⠈⠀⡄⠀⠁⠒⠂⠀⠀⠀⠀⠀⢸⠄⠀⠀⠈⠉⠁⠀⠀⠀⡀⣠⣀⠈⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⠀⠀⠀⣀⢤⡆⠀⠅⠂⠘⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠽⠍⠙⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠒⠂⠀⠀⠐⠂⢄⡀
⠀⠀⠀⣠⣴⣶⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠉⠉⢓⡐⠒⠂⠀⠀⠈⠉⠻⣦
⠀⡴⣾⠿⠿⡶⡤⣄⠈⠀⣖⢲⡖⢲⣴⣤⣄⠀⠀⠀⢀⠀⠴⢶⠋⢻⡀⠀⠀⢨⣿⠁⠀⠀⠀⠀⠀⢀⣻⠄
⠀⠀⣙⠻⡱⣓⡗⠀⠘⢼⠃⣜⠣⡞⠥⠗⢽⣳⠄⠀⠀⠀⠀⠘⢷⠮⢶⣦⣤⣸⣷⣤⣶⣷⣶⣶⡶⠿⠛
⠀⠀⠈⠋⠀⠈⠈⠱⠤⢥⠔⢤⠞⣥⠖⠀⠲⠟⠁⠀⠀⠀⠀⠀⠘⠀⣀⡿⠙⢇⠈⠉⠉⠉⠉⠙⠶⠶⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣴⠠⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠡⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⢀⠀⣰⡓⣐⣄⣶⣷⣰⣄⠀⠙⠻⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠘⠳⣄⡀⠀⠀⠀⠀⠈
⠀⢀⡏⣴⣆⡀⣿⣿⣍⣽⣿⠏⡷⢧⣀⡄⢋⠁⠦⠀⠀⠀⠀⠀⣀⣤⣠⣴⣤⠴⠊⢉⣿⢟⡶⣺⢿⣷⣾⠉⠈
⠀⠘⢦⡟⠁⠀⠉⡿⠛⠁⠉⠙⠃⠀⠺⢣⣄⠱⠀⡁⠀⠀⣠⣾⣿⣿⡇⣼⡿⢿⢸⢧⡿⣻⠟⢯⡞⠙⡾
⠀⠀⠀⠑⢰⣶⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⢠⠄⠀⠈⠙⠛⠉⠉⠁⠁⠀⠀⠉⠉⠉⠑⡄⠀⠀⠠⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂

⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀
⠀⠀⠀⠀⢹⣿⡟⢻⣿⣶⡄⠀⠀⣀⣀⡀⠀⠘⣿⣿⡇⢸⣿⣿⠁⠀⣀⣀⢀⣀⠀⢀⣀⠀⣀⡀
⠀⠀⠀⠀⠘⣿⡇⣨⣿⣿⣿⢠⣟⣉⣿⣿⣆⠀⣿⣿⠁⢸⣿⣿⠀⣾⣿⠛⢷⣿⠀⢸⣿⣾⣿⣿⠇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠃⠸⣿⣿⣿⣿⡟⠀⣿⣿⠀⢸⣿⡟⠀⣿⣿⣷⣾⣿⠀⢸⣿⠁⠀⠈
⠀⠀⠀⠀⠚⠛⠉⠉⠁⠀⠀⠀⠉⠛⠛⠉⠀⠐⠛⠛⠀⠚⠛⠓⠀⠈⠛⠋⠀⠋⠁⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢈⡙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠛⠛⠉⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣴⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠻⠿⠿⠒




⣶⣶⡶⡶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⡦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣄⡈⠙⠲⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣴⣶⣶⣶⣒⣴⣧⡀⠀⠙⣿⣷⡄⢹⡎⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣮⣿⣿⣿⢷⣄⠀⠈⣿⣧⡀⠁⠂⠹⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣋⣾⠁⣿⣷⣶⣦⣾⣿⠍⠀⠠⠄⠛⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣤⡛⠿⣿⣿⡟⠛⠀⠀⠀⢀⣴⠀⠵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡧⢀⠀⣀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠻⢻⣿⠛⠻⣤⠉⠛⢠⠈⠁⠈⠉⠁⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢠⣿⣿⣿⣷⣾⣦⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣼⣿⡿⠋⢉⣿⡿⣷⣀⣀⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣄⣾⡿⠃⠸⠛⠛⠋⢻⣿⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠛⠁⠉⠛⠛⠛⠉⠉⠀⡀⠀⠀⠀⠘⢿⠀⠀⠘⣦⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⡤⠄⠀⠀⢀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⠀⢰⡇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻⣿⡔⠃⠀⠀⠈⠉⣉⣱⡦⠶⠆⠀⢀⣴⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢀⡀⢁⡠⢔⣰⣿⣿⣏⣴⣶⣶⡾⠟⠛⠁⠀⠀⠀⠀⠃⠀⠀⠀⡄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⣬⣶⣼⣿⣿⣿⣿⠟⠛⠁⠀⠰⣤⣄⠂⠀⠀⠀⠄⠀⠀⠀⠀⢀⣷⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣶⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠘⠋⠀⢠⣰⠂⠀⠀⠀⢂⣤⣿⣿⣿⣧⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣶⣾⣯⣧⣿⣿⢻⠛⣿⠁⡉

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⣀⣀⣀⣀⡀⣀⡀⢀⣀⣀⣀⣀⣀⣀⡀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⢀⡀⡀⣀⣀⡀⢀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠠⣤⣼⣢⠞⠀⠀⠘⢦⣸⠃⠀⠀⠀⠹⡄⠀⡄⠀⣠⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣇⣀⣀⣻⡀⠈⢿⡀⠀⢀⣠⡖⢷⡄⢻⠞⠃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢦⣀⠈⡏⠉⣩⠍⠻⣄⠀⣷⠞⠋⠳⢤⠀⢳⣈⡆⠀⠀⢸⣀⣠⠀⠀⠠⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠓⣷⠚⠁⠀⠀⠙⢾⡇⠀⡀⠀⣄⠀⠈⣿⣀⣤⠶⠛⠙⠀⠁⠀⠀⢀⡤⠚⠻⣝⢩⠻⡏⣏⡙⠟⢦⣀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢼⠄⠀⠀⠀⠀⣿⡤⠞⠁⠀⠘⣇⣸⠋⠁⠖⡄⠀⡃⠀⠀⠀⡴⢋⣀⣀⠀⠈⢻⣴⣬⣤⣧⣷⣧⣽⣦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣸⣇⣤⣦⣶⣠⣏⣀⣀⣠⣶⠀⣸⠏⠀⡄⠡⣧⣤⢶⡤⣄⣼⡇⣯⢉⢹⡇⠀⠀⡇⣶⢶⠲⣆⠀⠀⣷⣤⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣡⣬⣤⣤⣤⣤⣤⣥⣄⣉⣉⠉⠉⠛⠛⠛⠛⠛⢳⠲⠶⠷⠦⠼⣯⣍⣇⣹⡈⠀⡇⠀⠀⡇⠿⠾⠴⠟⠀⠀⣿⣉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠛⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠙⢓⠲⠷⠦⣤⣤⣀⡀⠀⣻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡶⠶⠶⠶⠴⠦⠶⠤⠤⣤⣤⣄⣤⣀⣀⡀⠠⢀⠀⠀⠈⠉⠙⠻⢦⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠶⠤⣤⣄⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡤⠤⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⡿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠳⣌⠠⠀⠀⠀⢀⠀⠈⠉⠉⠉⠙⠛⡓⠲⠦⠤⢤⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⢀⡞⠳⣬⡛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢶⣶⣶⠓⠚⡛⠓⠓⠺⠶⡶⢴⣤⣄⡀⠀⢂⠌⡃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⡀⠃⠀⢸⡳⣄⡞⣉⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡌⠁⣀⡀⠁⡀⢀⠈⡀⣵⠟⢳⡄⢍⡓⠦⣄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣞⣯⣹⢦⡀⠈⢇⣸⢉⡽⠋⠀⠀⢀⣀⣠⣤⣤⣤⡄⠀⠠⠀⠙⠲⢤⣄⠠⠀⣀⠀⣀⠙⢳⡟⠂⠠⡸⠁⢨⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⡈⢹⡃⡴⠛⣿⣾⡟⣭⡄⢀⡤⢾⡏⠸⣇⡼⠿⡿⠁⠀⠀⠁⠀⢰⡟⠻⡟⢦⣠⣄⢀⡀⣹⡏⣈⡴⢦⣴⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠉⠛⣟⠁⡴⢻⠍⣿⡿⣠⢾⡇⢸⣧⣞⡉⣩⠟⠁⠀⠀⠀⠀⠀⠈⡿⠛⠁⠈⣧⡶⣄⣤⣼⣏⣉⠷⣴⠛⠖⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡙⠲⢿⠞⠁⡼⠀⢸⣠⢿⣠⠿⢯⣤⡤⠛⠁⠀⠄⠀⠀⡀⠀⠀⢰⣇⣤⡀⠀⢸⣿⠉⡄⢼⡇⢉⣨⣏⢉⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠙⠲⢬⣇⠼⡁⠘⢿⡿⠿⠛⠛⠉⠁⠀⠀⢐⠀⠀⣻⡟⠛⢦⠀⣸⢿⣬⡿⠀⢸⣿⠤⠴⢾⡇⣤⠼⣯⢠⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢴⣤⣿⣾⠷⣦⣄⣻⣠⣤⢀⣄⡀⠂⠈⡆⠈⠳⢹⣷⣊⡼⠀⢻⠀⣿⠀⠀⢸⢿⠄⠰⢸⡧⠄⠄⡧⠤⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠈⠹⡇⠀⠀⠉⠻⣏⣿⠟⠋⢠⠀⢀⡗⠀⢠⠏⠠⢻⠀⠀⢸⠀⢸⠀⠀⢸⢸⠖⠒⢺⡗⠶⠒⡷⠲⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠉⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠴⠧⣄⣀⣠⠾⠤⠤⠖⢉⡏⠉⠉⠉⠹⣟⣃⣀⣀⡠⠖⠀⠀⠀⠸⠥⠤⠔⠋⠷⠚⠙⣦⠄
⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⢠⣼⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡤⣄⠀⠀⠀⠀⠀⢠⡄⣤
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣤⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠉⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⢸⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣀⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣿⢺⡇⠀⠀⠀⠀⠀⡇⣠⠀⠀⠀⠀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⣈⣉⠁⠀⣀⣀⠀⠀⣈⣉⡁⢀⣀⡀⠀⣉⣈⠁⣀⣀⠀⢀⣀⣉⣉⣀⣀⠀⢀⣀⣈⣁⣉
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢀⣿⣿⡇⠀⣿⣿⡇⣼⣿⡇⠀⣿⣿⠀⣿⣿⡇⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⢸⣿⣿⣇⢠⣿⣿⠀⣿⣿⡇⠀⣿⣿⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⣿⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⢸⣿⡟⠀⣿⣿⣧⣤⣿⣿⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⣿⣿⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢿⣿⣾⣿⡇⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢸⣿⣿⣿⠀⠀⣿⣿⡇⠀⣿⣿⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⡟⠀⠀⢿⣿⡇⠀⣿⣿⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⣿⣿⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⣿⣿⠇⠀⠀⢸⣿⡇⠀⣿⣿⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣤⣥⣾⣧⣬⣤⡄⠠⣤⠀⡀⠀⢰⠀⠀⠀⡡⠤⠁⠀⠀⠐
⠀⠀⠳⡀⠀⠀⠀⢀⣴⠋⢳⣆⠀⠀⠀⠀⡠⠊⠀⠀⠀⠊⢱⡄⠀⠀⠀⠀⠀⠀⣀⠘⢺⠿⢣⡜⠿⡖⠃⣀⠀⠀⠀⠀⠀⠢⡠⣆⠀⠀⢀⣠
⠀⠀⠀⠀⡘⠂⠂⣈⢻⡄⣼⢋⡀⠀⠐⡂⠀⠀⠀⠀⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠛⡿⠋⠉⡄⡀
⠀⠀⠀⠀⠀⠈⠁⠉⢁⠸⢀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠑⣄⡳⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡈⠀⠀⠀⠀⢀⢁⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠑⢄⣀⠴⢊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠠⠆⡀⠑⢦⢠⠖⠁⠰⠄⠀⠀⠀⠀⠀⡀⢡⠌⠉⠁⡎⠀⠀⠀⠀⠂⠉⠉⠀⠀⠀⠙⣗⢸⡏⠁⠀⠀⠀⠉⠐⠂⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⢀⡡⢬⡇⠀⣿⠤⣅⠀⠀⠀⠀⠀⠀⠈⠴⠈⠹⠁⠶⠒⠁⠀⠀⠈⠂⠀⠀⠀⡀⠀⣯⢸⡃⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⢇⠈⠳⢤⠛⠈⢃⠴⠋⣀⠆⠀⠀⠀⠀⢠⠀⠛⠂⠛⠀⢤⠀⠀⠀⠀⠀⠀⢹⣏⢇⣀⡘⣏⣀⣠⢯⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠙⠂⠂⠀⡉⠀⠒⠒⠁⠀⠀⠀⠀⠀⠄⠈⠓⠐⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠋⢹⡛⢟⠻⠌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡠⠉⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠂⠒⠲⠤⠐⣄⣧⣥⡔⠡⠤⠒⠂⠀⠀⠀⠀⠀⡆⠀⠀⡥⠀⢀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⠀⠀⠀⠀⣶⡐⠙⡆
⠀⠀⠀⠀⠀⠀⠐⢻⠂⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⠔⠛⠢⣈⠆⠀⠀⠀⠀⢀⠘⣇⠀⠀⢰⡤⣴⠀⠀⢀⡟⢀⠀⠀⠀⠀⠀⣹⣇⢀⡇
⠀⠀⠀⠀⠀⠀⡠⡖⠋⠙⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠦⠤⠏⠀⠀⠀⠀⠀⠀⠀⢼⡄⢀⣻⣿⣿⢒⡀⣼⠁⠀⠀⠀⠀⠀⠀⣿⣷⣾
⠀⠀⠀⠀⠀⠌⠐⢇⠀⢀⠟⠀⠣⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠸⠐⣄⠀⠀⠀⠀⡌⠸⣇⠀⠙⢿⠿⠋⢀⣿⠞⡄⠀⠀⠀⠀⠀⢸⠳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⢀⢴⡄⠈⠀⠀⠀⠀⠐⢀⠘⡦⠀⠈⠀⠠⡞⢀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠀⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠑⠂⡀⠀⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠰⠆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡽⠤⡧⠬⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠗⢏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠤⠐⠂⢆⡇⠀⠀⠀⠀⢤⡀⠀⠒⠒⠀⢀⡤
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠹⣦⡾⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠴⠖⠢⠔⢣⠤⠀⠀⠀⢰⠒⠇⢹⠋⠉⠉⠸⠐⡆
⠀⠀⠀⢀⠄⠁⠀⠀⠁⠀⠀⠊⢃⠀⠀⠀⠀⠀⠀⡆⡠⠊⠤⠆⠤⠄⠢⡀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠆⠀⠀⠀⠀⣄⠀⢠⡕⠀⣠
⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⢰⠂⠀⠀⠀⢠⠀⡀⠀⠹⠁⠨⠖⠀⠐⠲⠀⠹⠅⠀⣀⢠⠀⠀⠀⠀⠃⡀⠀⢈⠀⠀⠀⠀⠀⠢⡀⢦⠂⠐⡄⢀⠔
⠀⠀⠀⠀⠀⠀⢙⠒⠶⠚⡘⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠐⠔
⠀⠀⠀⠀⠀⠀⠀⠑

⠈⠀⠀⠀⣹⡀⠀⠀⠀⣷⠀⠀⣴⣀⣿⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣄⣠⠶⠛⠉⠁⠀⡀⠀⣿⣷⢠⡿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠸⣇⠀⣿⣿⡾⢡⡏⡿⠈⠙⢄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠞⡄⠀⢀⠔⠀⠐⠂⠐
⡄⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⢁⣿⣿⠃⠀⠁⠈⢈⡀⢠⣤⣤⣤⣧⡔⠁⢸⠋⡴⠁⡀⢸⡇
⠂⠀⠀⠀⠀⠄⠀⠀⠈⣿⢾⣼⣻⡏⣠⣴⡆⣪⣶⣗⠉⣉⠛⣯⣝⠳⢄⣾⢉⣁⣠⢀⠏⠈⠐⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⣹⣿⣿⣿⣿⣿⡟⠟⠛⠛⠒⠛⠛⢯⡛⠓⣾⢿⣍⣀⣠⠟⠀⡀⠀⠀⠀⠉⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⡟⠁⢸⡀⠀⠀⠀⠀⠀⠹⢾⣃⠘⠓⡾⠉⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠋⠀⠁⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⢈⡄⠀⠀⠀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣄⡀⠀⠀⠀⠀⡀⣼⣿⣿⣿⠀⠀⠀⢸⠁
⠛⠒⠀⠘⠀⠼⢹⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢤⠤⠤⠴⠤⠤⠤⠤⠤⠤⠄
⡀⠀⢠⠀⢀⡀⣾⣿⣿⣿⠀⡀⢠⠈⠀⠀⠀⠋⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂
⠙⣶⠞⢣⠸⡇⡸⠋⠉⠙⣨⣡⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣆⠀⠀⢠⠶⠆⡒⣂⠀⢀⠀⣔⢉⠰
⡷⠛⣿⡾⢻⣶⣧⡄⣠⠃⡟⢁⡶⠂⠀⢠⡐⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢉⠚⠀⠌⠘⠛⠉⠀⠀⠀⠀⠈⠉⠀⠉⠀⡐⠋⠀⠀⠉⠘⠻⡟⠛⠂
⣁⣤⣯⣧⣾⣿⣾⡖⣹⣰⢴⠋⠀⠀⠀⠀⢙⣆⠙⣄⣀⣀⣀⣀⢀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣈⣡⣄⣈⢀⣀⣀⣄⣀⡀⢀⣄⣀⠀⣀
⠉⡁⣿⢹⠗⣿⣷⣧⣽⣿⡏⣉⡔⠁⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠂⠀⠤⢭⣝⣯⡙⠛⣛⠛⠛⠛⠧⠷
⠀⢰⢻⢸⡄⣿⠂⣿⢟⣸⠔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠘⡇⠸⣿⠃⠈⣯⣌⠃⠖⡾
⠲⣶⣼⣆⢻⢠⣾⡟⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⣼⣾⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⡠⠆
⣽⠿⠿⢿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠔⠁⠈
⠀⠀⠀⠘⣋⢩⣿⡛⣯⠈⠙⢢⣴⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⡂⢠⠮⠂⣴⠤⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⡀⠀⠐⢒⠉⢤⣼⣿⣾⣷⣽⣿⡯⠭⢭⠹⣿⣿⡂⢀⣴⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡜⡩⠋⠀⠀⠿⠤⠄⠠⠀⠘⠀⠀⠀⢸⣻⡅⢀⣀⠺⠄
⡄⠔⠀⠀⠀⡀⢭⣥⣥⣨⣿⣷⣤⡶⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣄⣠⢆⣀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢡
⣄⣸⢀⣶⣭⣀⡨⠙⣻⣿⣯⣿⣇⣠⣼⣶⣾⠋⢻⠿⠿⢟⣿⣻⣿⡿⢿⣿⣿⣿⠋⣩⡿⠉⠀⠀⡀⢀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠁
⣯⢿⣿⣿⣿⣿⣿⣿⣾⠿⠻⠛⠙⣿⣾⣿⡿⣿⣿⠤⣴⢿⣭⣭⣿⣿⣿⣿⣿⣿⠀⠟⢿⣧⣤⠛⠉⠙⠺⠇⠀⠀⢈⣤⣄⡀⠀⠀⠀⠀⠀⢀⡀
⣟⣿⣿⣿⢿⣿⠋⡭⣄⠀⣀⣀⣼⣿⣿⣍⣟⠉⣃⡾⢣⣴⣶⠶⣶⡿⣿⣿⡏⠉⠉⠀⠀⠻⡇⠀⠠⣤⣤⢆⠀⠀⣸⠄⠈⠁⠀⠀⠀⠀⠀⠀⠈⠲⣤⣄⣀⣀
⣿⣿⣿⣷⠿⠁⢀⣀⣙⣿⡟⠋⠉⠙⣿⣿⣿⣿⣿⣾⡿⠛⠛⠛⠻⣿⣿⣿⣠⣤⣤⣤⣀⣀⣼⣶⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠙⠛⠿⠿
⣻⣿⣟⣱⣟⠻⣧⡄⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡶⠒⠒⢛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡀⣠⣤⣤⣤⣤⣴⣶⣟⠋⠉⠀⢄⣤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢠⣿⣼⣾⣇⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠆⢠⣷⢠⣾⡇⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡠⢿⠟⠉⣿⣿⣧⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⢸⣻⣾⣿⡏⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣶⣦⣴⣶⡶⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣁⣤⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⡞⠙⣿⣶⡄⣿⡀⢰⢸⡏⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣿⣿⡿⢄
⠀⠀⠀⠀⢀⠴⠛⢀⣴⣿⣿⣿⣿⣧⣼⣦⣷⡄⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⠀⣿⣿⡇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠹⣿⣿⣿⣿⣿⡟⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠰⢷⣤⣿⣿⡿⡆⠁
⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠈⠛⠋⠉⠁⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢰⡈⠻⠿⠟⢠⠇
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡆⢰⠀⡄⠀⣿⠀⠀⠀⢣⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠸⣦⣷⣶⣿⣶⣷⣴⠇⣸⠆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⢤⣤⣄⣀⣀⠀⠈⠦⠠⣄⡀⠙⢦⡟⣋⣙⣿⣿⣿⣿⠶⠃⣀⡴⠰⠀⠉⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⡠⠐⠋⠁⠁⠀⠈⠉⠛⠛⠲⠤⠌⣹⣶⢤⣀⣀⣉⣗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣀⣠⣤⣖⣋⡩⠭⠛⠛⠒⠀⠐⠀⠂⠈⠑⠢⣄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠀⠐⠲⠖⠚⠛⢲⠟⠽⠿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠿⠶⠤⣤⠄⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⣠⢴⠏⠀⠄⠀⣼⡇⢠⣿⣿⣿⡌⢿⠁⣙⢿⡉⢹⣦⣀⠀⠀⠀⠀⠀⠈⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⡠⠚⠉⠁⡼⢀⡄⠀⠘⠁⣭⣿⣿⣿⣿⣿⣦⡀⠘⠆⢁⢹⡇⠈⠑⠦⡀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠊⠀⠀⠀⣀⣿⡀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⢜⣶⣇⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠘⣿⡾⢻⡏⢿⣿⣷⣿⣿⣿⣿⣿⠟⢹⣦⣿⣿⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⠙⢿⣿⣿⣿⠟⠋⠀⢸⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠀⠀⠀⠈⠉⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⢸⠇⣻⠿⢿⡁⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠿⢛⠿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠎⠀⠘⠶⣿⣡⣚⡷⠊⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⠿⠗⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⣤⡶⣾⣿⣿⠶⣦⣄⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠎⠹⠃⣤⡄⠀⢀⣤⡀⠟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⣘⠀⡀⠀⢼⠆⠀⡀⢸⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡿⣴⢿⣦⢸⢠⣾⠷⡜⣆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡊⠺⣦⠀⠀⠀⢾⡷⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠀⣆⠘⡟⢰⢈⡿⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠈⠀⠐⠀⠁⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢹⠀⠹⠾⠞⠁⢸⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⢀⣴⢦⠈⠁⣿⡍⠿⣅⢺⡿⠡⢀⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠴⠴⣄⡤⠤⠶⣾⡋⠀⢨⣠⣄⣿⠃⠀⢸⣿⠇⠀⣼⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⣼⠛⢏⢀⣘⣿⡀⠀⣿⡇⣤⣴⡙⢿⡄⠀⣛⠁⢙⡁⣸⠇⢿⣦⣮⠇⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⢼⣏⡀⡀⣻⡟⠛⣃⠀⣿⣄⢪⣿⡃⣼⣿⡄⠉⢠⡈⠀⡜⣰⡞⠒⣦⠀⣠⠏
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢷⣄⠀⠓⢐⣄⠀⠝⢿⡄⠉⢁⡏⠘⢷⡶⠞⠷⠶⠃⠘⢷⡶⠏⢻⠁
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⢷⣆⣰⣿⣿⠟⠀⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⠙⠛⠁⢉⠙⠓⠲⠶⠦⠤⠴⠶⠶⠖⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠿⠈⠓⠶⠶⠞
⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣶⡞
⠀⠀⣾⣿⣿⣿⣿⣿⡿⠞⠉⠉⠛⠳⠶⠄⠀⠀⠀⠀⡴⠶⠛⠋⠉⠻⣿⣿⣿⣿⣿⣿⠇
⠀⠀⣿⣿⣿⣿⣿⣿⡇⣀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣏⠙⠃⠈⠻⣍⣼⡧⠀⠀⠀⠀⠀⠀⠀⢰⣾⣌⠝⠋⢸⣿⣿⣿⣿⡟
⠀⠀⢻⣿⣿⣿⣿⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇
⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟
⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠘⠛⠿⠟⠋⠀⠀⠀⠀⣠⣿⣿⣿⡿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠈⠢⢄⠀⠀⠀⠀⠀⣀⠔⠋⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣀⠠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⣿⣿⡄⡀
⣀⡤⠔⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⢿⣧⠸⣿⣧⡀⢉⠒⠠⠄⣀
⠀⠂⠄⠀⡀⠀⠉⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡜⣿⣆⢙⠻⣿⣦⣀⡀⠀⠀⠁⠀⠑⠂⠄
⠀⡁⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠑⡄
⠀⠃⠀⡀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠙⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⣠⡄⠂⠀⢀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⣰⣿⢀⡆⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣼⠋⠀⠘⠄⠙⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢿⣿⣿⠀⠀⠀⡼⠛⠿⠟⠋⠉⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡄⠀⠀⣀⣠⣤⣾⣿⣯⣷⣞⡿⣿⠀⠀⠐⣡⠀⠀⠀⠀⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⠀⣴⣏⠀⣴⣾⣷⣾⡿⣿⠛⠻⣿⡿⣁⣿⣆⠀⣎⠀⠀⠀⠀⠘⠀⠀⣼⣻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣷⣿⢿⣼⣿⣿⣿⣿⠋⠋⠒⠶⠿⠟⠛⠋⢹⠀⠹⡄⠐⣄⢳⢁⣼⠏⠙⢿⣜⡇
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⢿⠟⣾⣿⣿⣿⡟⣿⠘⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠸⡆⢸⡎⢈⠃⠀⠀⠀⣿⠁
⠀⠀⠀⠀⣴⠟⠻⣿⣉⣿⣿⣿⣿⣷⣿⡿⢻⡟⢻⣿⣭⠿⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠗⠉⠀⡀⢀⡀⣿
⠀⠀⠀⢸⣿⠀⠀⢹⣿⣿⡿⠿⠟⡛⣋⣀⠟⢁⣸⣿⣿⠀⠘⣦⢻⡿⠓⠿⢳⡶⠆⠀⠀⡆⠀⠘⢆⡀⢠⠁⠀⠀⣿
⠀⠀⠀⠸⣿⣦⣶⣿⣿⣿⣷⣤⣤⡿⠯⡉⣀⣾⠈⠻⣿⣔⣛⡁⠈⠐⢦⣆⣈⣧⠀⠀⢤⣷⠐⠂⢨⣿⣿⠂⠆⢰⣿
⠀⠀⠀⠀⣸⣹⣹⣿⠿⠥⠾⠷⠦⠶⣾⣿⣌⡙⠛⠚⠚⠛⠛⠓⠒⠂⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠉⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡴⠄
⠀⣀⠀⠀⣁⣀⠀⠀⠀⠉⠉⠛⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣝⣿⣶⣟⣹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⢀⠀⠀⠘⢿⡷⣤⣀⠀⠀⣀⣴⣿⣿⣿⣟⢻⣽⣿⣿⣷⣄⡀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⡰
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠈⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠄⠀⠈⠀⠀⠀⣀⣠⡾⠃⠀⠀⠀⠀⣠
⠀⠀⠙⠲⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⢁⣷⣶⣶⣶⣶⣾⣿⡿⠛⠉⢀⣠⣤⣴⣶⠎⠁
⠀⠀⠀⠀⠘⢿⣿⣿⠿⣤⡄⢀⡀⠀⠀⠀⢘⡿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠙⢿⣿⣶⣿⣿⣿⣿⣿⣿⠟⠁⣀⢰⣶⠟⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠛⣳⣾⣿⣿⡟⠀⠀⠀⠙⢲⣦⣝⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⡿⣿⡿⠃⠀⠘⣿⣿⣿⣞⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣠⣼⣾⣿⡟⠛⢦⣤⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣾⢅⣤⠞⠋⠹⣯⣯⣅⡀
⠀⠀⠀⠀⠀⠀⠐⠩⠋⢸⣿⣿⡀⢈⠿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠿⠿⠟⠁⢀⣾⣷⣿⣿⣿⣿⣋⣁⠀⢠⡴⣿⡗⣯⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡼⠾⣿⣿⣿⣷⣿⣿⣿⣷⣦⣤⣤⣤⣶⣿⣿⢿⣿⣿⣿⣿⣿⠙⠂⠀⠰⣿⣿⠻⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⡏⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣴⠂⠀⢀⣽⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠁⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠻⣿⣿⣿⣿⣷⣿⡿⢿⠃⠀⣸⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠐⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣌⡃⠀⠀⠀⠃⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣼⠀⣠⣤⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⠿⣿⣿⣻⣾⣷⣤⣀⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡄⠘⢿⣿⣿⣯⡿⢿⡿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⡋⢘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣷⢣⣸⡜⠋⠿⠛⠁⠀⢻⣷⣿⣿⣿⣿⣿⡟⠀⠀⣸⣿⣿⣿⣿⣧⠻⠀⠀⠉⠻⠀⠁⣿⡟⢠⡹
⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⢹⣿⣿⣿⡏⠛⠀⠀⠀⠀⠀⠀⠀⢼⣧⢾⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣧⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠿⠃⢀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡧⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣤⡀⠘⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠒
⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠙⠛⡷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⡤
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣴⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠙⢿⣧⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⣠⣿⠏⠀⠀⠀⠀⣤⠛⠙⣿⣄⠀⠐⣄⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⣶⣤⡤⠀⡀⣠⣿⣿⣿⠋⠀⡀⠀⣠⣴⣞⠁⡀⠀⠀⠙⣳⣶⣿⣿⣿⠷⠦⠀⠸⠇⣷⣤⡄
⠀⠀⠀⠤⠈⣋⣾⣿⣯⣿⣿⣿⣿⡟⣿⣿⣶⠿⢛⡿⠟⠁⢤⣾⣿⣿⣿⣿⣯⠱⠶⢶⣄⠀⢀⠈⠁⠀⠄
⠀⠀⠀⠰⣾⣯⣿⣿⣾⣾⣿⣿⣿⣷⣿⣿⣿⣷⣾⣷⣾⣾⡆⠉⢻⣽⣿⣿⠿⠁⠀⢀⣨⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣟⠙⠿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠋
⠀⠀⠀⠀⠀⠀⠻⠿⡿⣿⣿⣿⣿⣿⣏⠙⠻⣿⣿⣿⣿⡛⠀⠂⢀⣀⣠⣬⣯⣭⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣶⣶⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠿⠿⠟⠙⠋⠉⠉

⠀⠀⠀⠀⢀⣀⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣩⠶⡀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠆⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⡴⠀⠈⠐⣀⣧⢞⠁⢠⠀⠀⢀⠠⠀⠀⠄⠚⢢⡄⠊⠉⠹⡄
⠀⡲⠐⠄⡀⠀⢀⣼⣗⠇⠈⠀⠀⠈⠀⠀⢧⠀⢀⢸⠏⠜⢈⣶⡋⠈⠓⠀⠀⣠⠞⠀⠀⠀⡁⠀⠀⢠⢃⠄
⠀⠸⡂⠬⣟⣴⡯⠦⠯⠋⠀⠀⠀⠀⠀⠂⠈⠿⣿⣴⣮⠜⠉⠜⢁⠠⠀⠀⠀⠘⢄⡢⣀⠢⠁⣀⣀⡜⠁
⠀⠀⠄⠀⡐⡿⠗⠀⠀⠤⠀⠀⠀⠀⠀⢀⡴⠚⢹⠋⠟⣛⣿⢣⡀⠀⠀⠀⠀⠀⠀⣉⡻⠛⢻⠛⠓⡀
⠀⠀⠀⠈⠁⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠜⠀⠀⠀⠈⡆⠀⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⣾⣿⣿⣿⣷⣤⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⠀⢀⣴⣶⣿⣷⣶⡄⠀⣿⣿⠀⠀⣰⣿⡟⠁
⠀⢻⣿⠀⠀⣿⣿⡆⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⡄⠀⢸⣿⡇⠀⠀⠛⠁⠀⣿⣿⠀⣴⣿⠏
⠀⣸⣿⣷⣾⣿⣟⠀⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⠀⣿⣧⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⣾⣿⣇
⠀⣿⣿⡇⠈⢻⣿⡆⣿⣿⡀⠀⠀⠀⠀⢰⣿⣿⣶⣿⣿⡄⢸⣿⡅⠀⠀⣀⠀⠀⣿⣿⡿⠻⣿⣆
⠀⢸⣿⣷⣶⣿⡿⠁⣿⣿⣷⣶⣶⣶⠀⣾⣿⠃⠀⢸⣿⣧⠘⢿⣷⣶⣾⡿⠇⠀⣿⣿⠀⠀⠹⣿⣦⠀⠀⠀⡀⣀
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠁⠈⠈⠀⠀⠁⠀⠀⠀⠁⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠂





⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⣄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⣏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢦⡘⢶⡿⢈⣷⣫⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣾⣆⠃⠋
⠀⠀⠀⢠⣴⣶⣶⣶⣾⣶⣦⣸⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠀⠀⠀⠀⠀⠀⠀⣀⠛⠶⠟⠀⠀⠀⠀⠀⠀⢲⣤⡀⠀⣥⣭⣿⡆⠺⠟⠁
⠀⠀⠀⢼⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⠘⠻⢋⢻⣷⣶⠆
⠀⠀⠀⢾⣿⣸⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⢰⣿⣿⣿⠟
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠙⢿⡿⡾⠿⠛⠁
⠀⠀⢰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⣿⣿⣆⠀⠘⢀⣐⣒⢢⣄⡀
⠀⠀⠀⠙⠺⣬⣿⣿⣿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⡟⢿⣿⣠⣴⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣭⣿⡟⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⣏⡿⣿⣿⣿⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⠃⣴⠀⠀⠀⢀⣴⣤⣄⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⡜⢿⣿⠟
⠀⠀⠀⠀⠠⣤⡀⠀⢀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠓⠀⢸⡿⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⢿⣿⣷⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⠁⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠻⠿⢧⠄⠀⠀⠀⣾⣤⠀⠁⠀⠀⠀⠀⢀⣿⣿⠿⠃⢸⣿⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⢤⣤⣶⡚⣠⣶⠀⣠⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣾⣿⣿⣿
⠀⠀⠀⢴⣦⡈⢻⣿⣿⡟⠁⠈⠁⢠⡜⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣿⣿⣿⡿⠀⠀⠀⢠⣼
⠀⠀⠀⠸⣿⣿⡄⠈⠛⢿⠟⠃⢤⣜⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡟⣿⣿⣿⣿⠇⢠⢀⣴⠿⡟
⠀⠀⠀⠈⢻⣿⣿⡏⢀⣰⣾⣆⡰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠈⣿⣿⣿⣿⠟⢀⣼⣿⡿⠞
⠀⠀⠀⣀⣼⣿⣿⣷⡀⠈⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢄⠹⣌⠛⢃⣴⣤⣤⣤
⠀⠀⠀⠉⠻⢿⣿⣿⣇⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠉⠁⠈⢉⣥⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠠⠼⠿⠂⢸⣿⣿⣿⣿⡿⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠻⠛⠀⠠⠀⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠿⠿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⣠⡶⠆⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡉⠉⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈⠀⠘⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠰⣄⠀⠀⢃⠀⠀⠀⠈⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠲⣶⣾⣿⣿⣿⣿⣧⠀⠀⠀⠉⠀⠀⠐⠲⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡦⠀⠀⠙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣴⣄⡀
⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠐⠋⠀⢸⡖⡄⣸⣿⣿⣿⣿⣿⠃⠀⠀⠀⣀⣴⣦⡀⠀⠀⠀⠘⣿⣷⣦⡄
⠴⠖⠀⠀⠀⠀⠘⠛⢠⠀⢀⣠⣤⣄⡀⣱⣿⣯⣶⣾⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣶⣔⡄⠀⠈⠉⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣁⡉⠉⠙⠛⠛⠻⢿⣿⠿⠿⠿⠷⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣿⣿⣿⡛⠂⠀⠀⠀⠀⠀⢀⣶⡀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣷⣶⣦⣤⣶⣾⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆
⠀⠀⠀⠀⠀⠲⢶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠏⠉⠉⠉⠉⠁⠈⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠛⢿⣿⣄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠉⠻⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠽⠞⠋⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣮⣉⠋⠓⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⢿⣿⣿⣿⣿⡿⢻⣿⣷⣶⣦⣍⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢟⠿⢿⣿⡿⠟⠹⠋⡤⠰⠁⠸⡟⠋⠛⠛⠿⠻⢶⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠐⠁⠐⠟⡩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣴⣷⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢀⣴⣷⢇⣶⣾⢰⡄⠀⢱⣠⡆⢠⢰⢿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠀⡄⢰⣿⣿⣿⣿⣿⣿⣠⣿⣇⣾⣿⠃⢠⣾⠘⣿⡇⠙⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⢧⠆⡾⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣸⡏⣾⢸⡟⢀⢿⣇⡄⠀⢹⡏⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⡟⣸⠃⢸⡏⣼⣿⣿⣿⣿⣿⣿⡿⣷⠟⣸⠃⡾⠁⡟⢻⡿⠛⠓⠈⠇⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣸⢃⡟⠀⣿⢱⣿⢟⣿⠿⠛⠁⠋⠀⠁⠀⠁⠈⠁⠀⠀⠀⠀⣀⣀⠀⠀⠐⢿⣿⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠇⣟⢸⠃⢰⡟⢸⠇⠛⠀⠀⠠⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠟⠘⠂⠀⢸⣿⡇⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢰⡏⠀⠐⠙⢃⠎⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠈⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠞⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡸⢸⠁⠀⣾⣄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⠃⡟⠀⠀⣿⢁⡗⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⢿⠀⠀⠀⠄⠀⠀⠀⠀⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠌⣸⠇⠀⠀⣿⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡾⠀⠀⠈⠀⠀⠀⠀⠀⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢰⡾⢁⡆⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣿
⠀⠀⠀⠀⠀⠀⣾⠃⣸⢣⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢀⡖⠢⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⠀⠀⠀⠀⠀⠀⠈⠢⡍
⠀⠀⠀⠀⠀⢠⡟⢰⣿⣿⣿⣿⣿⠿⠟⠋⠉⡟⠀⠀⠀⠀⠀⠀⠀⠞⠑⠤⣀⠀⠉⠒⠤⠤⠤⠤⠴⠞⠁⠈⠇⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⢸⠇⣾⣿⠿⠛⠉⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⣀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠢⣄⡀
⠀⠀⠀⠀⠀⢸⣸⣏⠁⠐⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠖⠃⠈⠛⠓⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣁⡟
⠀⠀⠀⠀⠀⢸⠏⠀⠑⠀⠀⠀⠄⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠑⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢤⠁⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄

⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢂⢐⠞⠂⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⡀⢈⡄⡀⠀⢀⠀⠀⠀⠀⠀⣊⣀⢀⠀⠠
⠀⠘⠓⠀⠀⠈⢐⣁⠀⠀⠀⠀⠀⠀⣲⣏⣷⡄⠀⠀⠀⠀⠀⠀⠀⣀⣦⡾⡉⡹⡓⠒⠁⠀⠀⢠⠆⠈⣹⠟⠷⡄⠊
⠀⠰⢹⡄⠀⠀⠀⠉⡧⠀⠀⠀⠐⠀⢣⢺⠃⡏⠀⠀⠀⠀⠀⠀⠚⠁⢠⣾⢋⡔⠘⠐⠊⠀⢠⡀⡘⠁⣠⡀⣠⠡
⠀⠀⠹⢄⠀⣀⠀⠄⠁⠀⠀⠀⠀⠠⠊⢹⠡⠁⠀⠀⠀⠀⠀⠊⠁⠀⠚⠕⠂⣸⠀⠀⠀⠠⠚⠀⠁⢀⡈⠀⡤
⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠠⠀⡤⡼⠀⠈⠈⠄⠀⠒⠁⠀⠀⠀⠐⠀⠀⠐⠀⠁⠀⠁
⠀⠀⠀⢈⣉⠑⢨⡚⠠⠄⢐⠀⠀⠀⠀⢸⠀⠠⡀⠀⠀⣡⢜⠞⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⡀⢀⣈
⠀⠀⡔⠉⠇⠀⡡⠝⡠⡍⠁⠑⠀⠀⠀⢸⠀⠀⠁⠀⠀⢦⠈⠆⠑⠌⠀⠀⠀⠀⠠⠀⠀⠀⠤⡚⠈⢀⣤⡀⢀⢠⠄
⠀⠘⠀⠀⠀⠤⠔⣾⠸⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠀⠠⠶⡦⠤⠀⠀⡀⠀⠉⠰⢸⠀⣈⣭⣀⢀
⠀⠀⠀⠀⠀⠠⠔⠁⢀⠀⠀⠀⣰⠀⢰⡴⢻⡆⠪⡁⢠⣞⡹⢠⡎⠀⢸⠇⠰⣉⠂⠀⠁⠄⢰⣾⣛⣭⠾⠯⡲⡀
⠀⠀⠀⠀⠀⠂⠀⠰⠁⠀⠀⡄⢿⡠⢺⠀⢸⡠⢄⣸⠾⢧⡤⠚⢧⡤⠾⠤⢄⣨⡇⠀⠀⠀⠁⡇⠡⢶⣺⠁⠇
⠀⠀⠀⠀⠀⠀⢀⠰⣀⠀⠰⠀⠀⠀⢀⠀⡇⡀⢀⢀⢀⠀⡀⡇⢸⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡉⠁
⠀⠀⠈⠂⢀⡲⠊⠌⢶⠈⠀⠈⠀⠀⠸⠄⠇⠃⠘⠹⠰⠛⠆⠧⠸⠘⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⢶⣀⠊
⠀⠁⠀⠉⠀⠁⠂⠀⠼⡁⠂⠒⠀⠈⢠⢤⠤⡤⢀⠀⢀⠀⠀⠀⢀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠐⠀⢽⣿⡅
⠀⡀⠄⠂⠁⠀⠀⢠⠀⠈⠄⠀⠀⠀⠀⠀⠒⢩⣥⣄⣩⠇⠀⠁⠞⢦⠼⠧⣄⣤⠤⢄⡀⠀⠀⠀⢀⢚⣘⡶⡀
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⡀⠠⣎⣠⠀⠑⡌⠉⠆⠀⠀⠀⠁⠀⠀⠀⠀⠐⠄⠀⠀⠁⡠⠃⢰⣶⡺⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⢁⣆⠀⠀⠀⠀⠀⠀⠀⠠⡄⢠⣴⣆⣠⠂⠀⠀⠀⠀⢠⢼⡖⣄⣈⠳⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠠⡤⠀⡏⠊⠀⠀⠀⣠⡄⠀⠀⠀⠈⣋⠉⠉⡇⢀⡀⠀⠄⣀⣀⣧⠙⢦⣌⣀⡐⣁⠀⠠
⠀⠸⠁⠀⠀⠀⠀⠀⠀⠠⠜⠁⠀⠁⠀⠘⢢⣀⡯⠂⠀⠀⠈⠰⢼⠀⠠⡎⠁⠀⠀⠀⠀⠀⠸⠇⠴⠉⠁⠙⠈⠂
⠀⠀⠐⠦⠄⡀⠀⡀⠑⢢⡀⠀⠀⠀⠀⡐⡻⣿⡅⠐⠀⠀⠀⠂⢂⠀⠀⠙⡤⠀⡀⠀⠀⠀⠠⠤⠤⢠⣧
⠀⠀⠀⠀⠀⠈⠁⠈⠉⠢⣉⠄⠀⠤⠀⠸⡴⠋⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠂⡀⠸⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠈

⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠎⠀⠴⣾⣿⣿⡇⠈⠃⠉⠛⠂⠀⠀⠂⠀⠀⠀⠰⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠤⠒⠚⣸⣿⣿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠈⡇⠀⠀⢀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡿⠋⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼
⠀⣀⠔⠂⠀⠦⢄⠀⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠠⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡄⢀⣾⡟
⠴⠁⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠈⠙⢂⣀⣀⣀⡀⢀⡠⠐⠒⠦⢄⠀⠀⠀⠑⠇⡀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⣾⡿⠋
⠆⠤⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢡⠀⠀⡀⠀⠐⢄⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⢤⣶⣶⣼⣷⣷⣤⣾⣿⣿⣿⠖⠈
⠀⠀⠀⠀⠠⠀⠀⠐⠠⠀⠄⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⢳⡎⠀⠁⠈⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠛⢛⣟⣿⣿⣿⣷⣶⣖
⣦⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠎⢳⠀⠀⠀⠀⣠⠤⠀⠠⠤⢺⣿⣿⠘⠻⠟⠿
⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠊⠁⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣆⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣻⣷⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⡄
⠀⠀⠀⠈⠀⣦⢄⡀⣀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠐
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠤⠱⠶⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⡇⠀⣾⡇⠀⢀⠔⠀⡠⠊⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠢⣀⣀⣀⠀⠉⠙⢿⣿⣿⣇⢰⣿⣷⣾⣿⡵⠄⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠘⠛⠛⠛⢻⣿⣾⣿⡿⢿⡅⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠂⠸⡄⠀⠀⡼⠀⠀⣠⡄
⠀⣠⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁⠈⠁
⠀⠠⢀⣸⣆⠀⠀⠀⠀⠀⢉⡂⠀⡀⠀⠀⠀⠀⠀⠀⠠⠶⠒⣈⡽⠟⠉⠉⠻⣧⠀⠉⠀⠀⠀⠶⠤⢄⠀⢀⠌⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣠⠂
⠀⠀⠀⠀⠹⠞⠀⢀⠂⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠴⢒⢀⠝⠉⠡⠚⠐⠆⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢠⠀⠀⠀⠀⠀⠀⣠⣄⡀⢸⠀⠀⠀⠀⠀⢀
⠀⣀⠀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠋⠉⠉⠻⢟⢿⣇⣠⡀⡀⠀⠀⠀⠀⠐
⠊⠁⠀⠀⠀⢀⠀⠀⢀⠈⠈⠲⠤⢶⡀⠀⣀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡄⠀⠀⢀⠀⢠⠀⠀⢀⣴
⠀⠀⠀⠀⡤⣈⣀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢳⣇⠀⢸⣧⣤⣤⣶⡿⠛
⣀⠀⠀⠀⡎⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠿⠿⠛⠂
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡄⠀⡌⠀⠀⠀⢀⣴⣾⡥⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣍⠀⠀⠀⠐⠊
⠀⠀⠀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠀⠀⠀⠤⣄⡀⠀⠀⠀⣹⣿⣿⣄⣄⡆⠀⣴⣾⣿⠯⢀⡄⠀⠂⠐⠀⠀⠲⠀⠠⠁⠈⠀⠈⠳⣍⡀⠒⠒
⠒⠠⢀⠀⠀⠀⠁⠀⠀⠢⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠙⢿⣿⡏⠃⢠⣿⣿⣯⠖⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣷⣶⡅⣤⠛⠲⣹⣿⣣⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠆⠀⠀⠀⠐⠚⠋⠉⠁⠘⠞⠛⠙⠋⢻⡿⢿⠅⣀⣶⠋⣵⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠉⠉⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⠀⠀⣿⣷⠀⢠⠀⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⡀⠀⢾⣿⡿⠠⠤⢿⢿⠧⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣿⡿⠁⠀⠐⠁⠇⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠿⠟⠛⠿⠿⣷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡴⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⣴⣾⠟⢹⣿⡆⠀⣠⣾⡗⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⣿⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⢀⣾⣿⢁⣴⣿⡿⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣷⣀⢀⡀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⢠⣾⣿⣣⣿⣿⡿⣡⡾⣫⣄⠀⠀⠀⠀⠀⢀⡀⠀⠘⢿⣿⣷⣤⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⣿⣿⣿⢟⣿⣿⣷⠟⣡⡍⢉⣄⢀⣤⠀⢴⣿⠧⢀⣠⣄⢈⣯⣭⡉⠀⠀⠀⠴⣤
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣼⣿⣿⠟⠁⣾⣿⣿⠋⣰⡟⢁⣾⡿⣿⠏⣠⡿⠁⣴⣿⠵⢋⠞⣽⠟⣡⠞⠛⠲⣶⠛⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡈⣄⠺⡿⠛⠁⠀⢸⣿⡿⠁⠀⣿⡵⣿⠋⢸⣿⠴⣿⣧⠞⢿⣤⡴⠋⢸⣿⠔⢁⣠⣄⠀⣹⣷⠈⠁
⠀⠀⠀⢐⣶⣶⣶⣿⣛⣨⣷⣶⣿⣿⣤⣤⣄⣀⣀⣤⣤⣤⣴⣄⣀⣤⣤⣀⡀⠀⠀⠀⣀⣀⣀⠀⠀⣿⣇⡀⠀⣹⡿
⠀⠀⠈⠁⠀⠀⠀⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠟⠻⠛⠛⠛⠳⢯⣽⣷⣶⣾⣟⣉⠉⠙⠲⠿⠿⠷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣤⣤⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⡾⠿⠻⠛⠻⠉⠉⠉⠁⠁⠉⠙⠋⠋⢻⡿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠐⠛⣻⣠⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⡴⠁⡿⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢀⣀⢀⣀⣒⣶⣶⡦⢀⢀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣠⣴⣦⣦⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⡦⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢈⣿⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣄⣀⠀⠐⠟⠻⠀⠀⠀⣼⣶⣦⡄⠀⠀⠀⠀⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⢿⢿⣿⣷⣾⢿⣿⣻⡻⠈⠁⠘⠛⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣟⢿⣽⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣧⣸⠁⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣳⣿⡡⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠏⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣿⢤⡄⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡘⠁⠀⢀⣠⣴⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⠷⠶⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⢸⡏⠳⣄⠀⠀⠀⠀⡾⠙⣆⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⣏⠙⠦⣄⠀⠀⢸⠃⠀⠘⢦⡀⠀⡼⠁⠀⠘⣆⠀⢀⡤⠞⠁⢸⡄
⠀⠀⢀⣀⠀⠀⠀⢸⠀⠀⠈⠳⢤⣼⠀⠀⠀⠀⠙⡾⠁⠀⠀⠀⠘⣶⠏⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠈⢯⠓⠶⢤⣘⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣀⡤⠖⠋⢩⡇⢀⣠⣄
⠀⠀⠀⠈⢇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠸⠟⠋⢁⡏
⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⠎⠀⠀⠀⠀⠀⠙⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼⠁
⠀⠀⠀⠀⠀⢈⣧⠴⢆⠀⣰⢦⡀⠸⠉⠉⠉⡇⠀⠀⣠⢄⠀⠀⠈⡇⠈⢹⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠛⠲⣤
⠀⠀⠀⠀⣾⠉⠀⠀⠈⢦⠃⠀⠱⠇⠀⠀⢀⡇⠀⠀⠉⠋⠀⠀⠀⡇⠀⠸⠚⠁⢻⡤⠚⠉⠓⢦⡀⢠⠃⠀⠀⡴⠋
⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⡏⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⡀⠀⠀⠀⢸⠀⠈⠓⠒⠒⠒⠋⡅⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠳⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢀⡸⠑⣤⠤⠴⠾⠀⠀⠀⠀⠀⠀⠀⠳⢤⡴⠛⡀⠀⠀⣠⠎⠀⠀⠀⡞⠙⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢧⠀⠀⠀⣀⣄⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠙⠓⠞⠁⠀⠀⠀⠀⡽⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠞⠉⠈⠳⠴⠋⠙⠳⣤⠴⠋⠙⢦⡴⠞⠙⢦⣠⡴⠛⠳⣄⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿