⠀⠀⠀⠀⠀⢸⡀⠀⠀
⠀⠀⠀⠀⠀⠸⣣
⠀⠀⠀⠀⠀⠻⢿⣃⠀⠀
⠀⠀⡀⠀⠀⢰⢿⡟⠄
⠀⠠⣴⣿⣦⣀⢸⠛⢿⣤⣤⣤⣤⠀⠀
⠀⠀⠙⠿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣷⠀
⠀⠀⠀⠀⠉⢻⢿⡿⡟⢛⣻⣿⣿⡇
⠀⠀⠀⢀⣾⣭⡝⣭⣷⣭⣼⣿⣿⡇
⠀⠀⠀⠣⡬⠊⡠⡿⣽⣿⣿⣿⣿
⠀⠀⠀⠽⠿⣿⠄⠈⣻⣿⣿⣿⡿⠗⠒⠒⢄
⠀⠀⠎⠀⢀⠄⠂⠁⠊⠙⠻⠋⢁⠀⠀⠀⠀⢡
⠀⠊⠀⠀⡈⠀⡀⠌⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄
⡌⠀⠀⠰⠁⢠⡏⠀⠀⠀⠀⠀⠀⡆⠁⠀⠀⠀⡇
⠀⠀⠐⢁⢠⣿⣇⠀⠀⠀⡆⠀⢀⣿⡄⠀⠀⠀⠁
⠂⠀⠊⠀⠀⢿⣿⣦⠄⠀⠡⣴⣿⣿⡇⠀⠀⢰
⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡆⠀
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠎⠀⢀⠰
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠂⠀⠀⠌⠀⠀⢠⠂⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣖⣚⣉⠉⠉⠓⢶⡲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠉⠀⠀⠐⣆⠈⠳⣦⡀⠀⢳⡉⠛⣷⣄⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣴⢫⡟⡼⠀⠀⢀⠀⠀⠘⣦⡀⠈⢻⣤⠀⢹⣦⣈⢻⣦⠀⠀⣴⠋⢈⡗⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⡇⡿⢀⡇⡆⣀⠘⢦⣀⣄⣜⡷⣄⠀⢙⣷⣄⠹⣟⢄⢿⣆⡾⠁⠀⡼⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⢻⢰⢷⣻⣧⣿⡙⠻⣿⣭⠯⣉⠉⠉⠳⢤⡈⢿⣦⣙⣾⣬⠟⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣾⢨⣿⡿⠉⠈⠙⢰⣷⣿⣿⡿⣿⣶⡶⠀⠉⢹⡿⢋⢩⡏⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣤⣄⣀⠀⢿⡟⣾⣿⣷⣧⠀⠀⢸⣿⣩⣥⣶⠞⠁⠀⠀⠀⢸⡷⢣⠞⢧⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀
⠀⡠⠂⠘⢯⣷⣈⢗⠋⣿⣞⡽⠇⠀⠘⣿⣿⡿⢺⡁⢀⡀⠀⠀⠈⣷⠋⠀⠘⣧⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⠀⢀⡙⠻⣗⠓⠲⠶⢦⣀⠀⠀⠀⠀⣄⡀⠙⢦⠈⡃⣿⣧⣸⣼⠇⢻⡆⠀⠀⠀⠀⠀⠀⠀
⣆⠀⠀⠀⠀⠈⠙⣄⠉⣲⣄⡙⠀⠀⠀⢹⡇⠀⠀⠀⠹⡍⣲⠄⠓⣥⡟⠹⣟⢻⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀
⠙⢶⣄⡀⠀⠀⠀⠈⠓⠀⠉⠛⠂⠀⠀⣨⡿⠀⠀⠀⠀⠈⠁⣠⣶⠟⢠⡎⢿⣶⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀
⢀⡈⢿⠛⠿⣶⣤⣤⣄⣤⣤⣤⣤⣤⣾⡟⠁⠀⠀⠀⢠⣤⣾⣿⠋⠀⡞⠀⠀⢻⣇⠀⠘⣟⣧⠀⠀⠀⠀⠀
⠀⠐⠛⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠈⠹⣤⣀⣀⣤⣾⣿⣿⡿⠃⠀⢰⠇⠀⠀⠈⠛⠦⣤⣘⣮⠳⣄⣀⡀⠀
⠀⠀⠀⠀⠀⢰⣧⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣽⣻⡿⠉⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣩⠭⠉⠉⠉⠉⠉⠙
⣤⣴⡾⠶⠖⠛⠁⠀⠀⠀⣠⡤⠶⠖⢒⡓⠛⠋⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀
⠭⠀⠀⠀⠀⠀⠀⠀⠀⣾⢣⡇⠀⠀⠀⠉⠳⠤⡤⠏⡄⢀⡀⠀⠼⢶⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⡴⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⢤⣀⡀⠀⠀
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣷⡀⠀
⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⡄⡐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⣿⡂
⠀⣴⢛⢡⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠄⡓⡴⣉⠑⡂⠄⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠘⣷
⠀⠘⣧⠊⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠐⢨⠱⢔⡣⠘⡠⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢀⣿
⠀⠀⠹⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢹⡄⠀⠀⠈⠠⠙⠂⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⣠⡟⠃
⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⢿⣆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢀⣰⠿⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠉⠿⢿⡏⠀⢀⣠⠤⠤⠀⠀⠀⠀⠙⠲⠦⣤⣤⣤⡤⠴⠶⠛⠉⠀⠀⣀⣿⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⠋⠀⠀⠀⠀⠀⢀⡀⠸
⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠈⠓⠲⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⠀⠀⠀⠀⠀⢸⣷⡀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⣧⣀⣀⡀⠀⠀⣼⠀⢳
⠀⠀⠀⣠⡟⠂⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠹⡍⠛⠯⣗⣾⡟⠢⡼
⢠⠔⠋⡟⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⠉⠳⡄⠀

⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡞⠁⠀⠀⠸
⠀⠀⠀⠀⠀⣴⣧⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀
⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⢤⡀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡾⣷
⠀⠀⠀⠀⠀⠀⠀⢻⡆⢰⣤⣀⣉⣛⠶⠶⠛⠁⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌
⠀⠀⠀⠀⠀⢶⠀⠘⣿⣄⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡀⠤⠐⢂⣠⣼⣷⡟⠉⠻⣿⣦⣴⠆⠀⠀⠀⠀⠀⠀⢀⣰⠞⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠶⠖⠚⠋⠉⠁⠀⠁⠀⠀⠀⠈⠙⢷⣀⣀⣀⣤⣤⣶⣿⠃⠀⠀⠀⠀⠈⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡈⠉⠉⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀