Neutering Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⡾⣿⢿⣿⣿⡷⠶⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠉⠁⠈⣱⠶⠛⠉⠉⠀⠀⠀⠀⢀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⠲⠶⠶⠖⠚⠓⠒⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⣀⣠⡾⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣭⣤⡾⠃⠀⠀⠀⠀⠘⠛⠿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠙⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣤⣤⣤⠞⠋⠁⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉⠛⠶⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⣦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠹⣏⢣⡀
⠀⠀⠛⣿⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠘⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⢹⣀⠄⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠛⢀⣤⣤⣤⡶⠶⠖⠒
⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⢀⣠⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⣠⣶⣿⠿⠟⠋⠉
⠀⠀⢀⣾⣿⠃⠀⠀⠀⣴⡿⠟⠁⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣠⣾⠟⠋⠁
⠀⣰⣿⡿⠃⠀⠀⢀⣾⠋⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⡛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢰⣿⡿⠃⠀⠀⢠⡿⠁⠀⠀⠀⠀⣨⠾⠛⠉⠉⠉⠉⠛⢿⣎⢳⠀⠀⠀⠀⠀⠀⠀⣰⠋⣠⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⣾⠟⠁⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠃⠀⠀⠀⠀⢀⡼⠃⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⣿⡄⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢀⡾⢁⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⣿⢿⣄⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⡼⢁⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⢀⣀
⠈⠳⣽⣷⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⢰⠃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⣀⡙⠛⠿⣷⣄
⠀⠀⠈⠻⢯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢟⡟⠁⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⣿⣿⣿⣷⣆⠈⠹
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣉⣏⡀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢸⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠻⢷⣄⠀⠀⠸⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣤⡾⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢿⢹⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⢶⣶⣶⣶⣶⣶⣶⣿⣿⡿⢟⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠚⠛⠛⠛⠛⠛⠻⠿⠿⠿⠛⠁⠀⠀⠘⣷⣭⣿⣇⣤⣤⠶⠶⠖⠛⠛⠛⠛⠿⠶⢶⣶⣶⣾⣿⣿⣯⣭⣤⣶⣾⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠰⠋⣀⢀⡄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠂⠀⠀⢨⠉⠉⣱⠊⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡚⠠⠃⠒⢄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⣀⠤⡘⠁⠀⠀⠲⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣀⡄⠀⠙⠠⠄⣠⠄⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⠀⣀⠒⠪⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠞⠁⠀⠘⢂⠀⠀⣐⠁⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠈⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠑⠀⠁⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡤⠀⣠⠀⠀⠠⢀⣀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⠀⠀⠀⠈⢛⣀⠀⠀⢀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠈⠈⠀⠀⠀⠑⠠⣄⠜⠉⠳⢄⠀⠠⠂⠀⢀
⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡜⠀⠀⠀⠀⣩⣧⡀⠀⠀⢂⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠐⠢⣀⢀⡠⠅⠀⠀⠀⠀⠳⠀⠀⠛⠈⠐⠁
⠀⠀⠀⠀⠀⢠⡃⠀⠀⠀⢠⠁⠀⠀⠀⣾⣿⣿⣿⡆⢀⢜⣀⡇⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢠⠀⠀⠀⠨⢭⡤⠀⠀⠀⢆⠐⠖⠀⠀⠀⠀⡀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠲⠀⠀⠐⠒⠂⠈⠉⠷⠀⠀⠀⡍⠈⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⡘⠀⠀⠀⠀⣤⠦⠄⠀⠀⠀⠲⠁⠘⠀⠰⢂⡠⠂⣈
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠇⠀⠀⠀⠀⠀⠚⠙⣐⠲⠀⠀⢰⠀⠇⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢠⠃⠀⠀⠀⢠⣶⣦⣶⣿⣆⠀⠉⢃⠀⠀⠀⠠⠀⠀⠀⡰⢀
⠀⠀⠀⠀⠀⠀⠈⠂⠀⢰⡀⠀⠀⠀⠀⠀⠀⡈⠁⠖⠒⣘⡀⠸⠤⡀⠀⠀⠀⢳⠤⣀⡀⠀⡎⠀⠀⠀⠀⠹⢿⣿⣿⡿⠃⠀⠀⢰⠂⠀⣄⠰⠚⣩⠈⠁⠃
⠀⠀⠀⠀⠀⠀⠀⣘⠋⠀⣇⠀⠀⠀⠸⠋⠀⠀⡐⢄⣠⠋⣇⠀⠀⢎⠀⠀⠀⠁⠀⠀⠈⡛⠀⠀⠀⠀⠀⠀⢀⡙⡋⢀⡀⠀⠀⠈⠁⢀⡸⠁⠙⢷⡂⠈
⠀⠀⠀⠀⠀⠀⠸⣾⣶⡶⠋⠀⠀⢀⡀⠐⠂⠛⣴⡞⠁⠀⠻⠀⠰⠋⠀⠀⠀⠸⠄⠀⠀⡅⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠀⠀⠀⠀⠸⠈⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⣠⠟⠁⠔⠂⠁⠙⠀⢀⡀⠁⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⡀⣦⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⣤⡀⠀⢠⠚⠀⢈⠀⠐⡀
⠀⣀⣀⡄⠂⢺⣿⠀⠀⢀⠀⡀⠀⢠⢀⣾⡀⢸⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠐⢩⠀⠀⠀⠀⠀⠤⡌⠀⠰⠱⠀⡀⠉⡔⠀⢈⡄⠱⠖⠁⠈
⠀⠀⠀⠀⠀⢸⡿⣀⢀⡏⠀⠉⠒⠁⠸⣷⡾⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢐⢠⡦⣄⡼⠓⠶⢄⣀⢀⣀⡒⠀⠲⠂⠚⠓⣀⠀⠐⠋⢠⡀
⠀⠀⠀⠀⠀⢸⡇⠉⠉⠑⠋⠶⢳⠀⠀⠀⠀⡆⢠⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠉⠉⠀⠈⠀⠉⡀⠀⠀⠀⢀⠼⠃⢠⠂
⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠐⠚⢉⠁⢠⡄⠐⠁⠀⡄⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡀⠀⡁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⡏⠉⠉⠁⠈⢀⠝⠉⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢱⠀⠑⠊
⠀⠀⠀⠄⠀⠀⠘⠀⠀⠀⢀⠔⠁⠀⠀⢸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢂⠀⠀⠀⠀⠀⠀⠀⠀⠰⡃⡸
⠀⠒⠒⠘⡄⠀⠇⠀⠀⠀⠣⢁⠂⠤⠀⠀⡇⠀⠀⠀⠠⠔⠒⠈⣩⠆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠐⠳⠀⠸⡤⠖⠒⢀⠄⠁⠲⠀⠀⡁⠀⠈⠀⠀⢀⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠐⢋⠀⠀⠤⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠂⠄⠀⠠⢀⣀⢀⡀⠤⠊⠀⠀⠀⠀⠀⡰⠶⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠐⠒⠠⠴⠀⠀⠐⠂⠀⠐⣂⡤⠖⠒⠂⠂⢐⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠟⠒⠀⠀⠁⠚⡏⠉⠉⠉⣉⣉⡀⣀⣠⠤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣀⣈⣉⣠⡧⢀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠖⠛⠛⠀⠀⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠈⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠈⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⣸⠇⠀⢀⡀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⢠⡏⠀⠀⠀⣧⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⡆⣀⠀⠀⠀⠀⠀⠰⣿⠁⠀⠀⠀⢻⡀⠀⠀⠀⡟⠀⠀⠀⢀⣼
⠀⢸⣿⠷⣦⣄⡀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠘⣿⠿⡀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⢸⡇⠀⠀⠸⡇⠀⢀⡴⢿⣿
⠀⣾⡟⠀⠈⠉⠛⠿⢷⣤⣄⡀⠙⣆⠀⠀⠀⠘⣷⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⢸⣇⣴⠟⠀⣾⠏
⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠛⢾⣿⡄⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣾⠟⠁⠀⣸⡿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⢻⡇⠘⢷⣄⢠⡀⣦⠀⠀⠀⠘⣿⢠⡟⠁⠀⠀⢰⣿⠇
⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠛⠆⠀⠈⣿⣄⠈⠛⠘⠁⢩⡀⢠⠆⠀⢹⡿⠀⠀⠀⠀⣾⠏
⠀⠀⢿⣇⠀⠀⠀⠀⠀⡀⠹⣆⠀⠀⠀⠀⠀⢠⢠⡆⠈⣿⠀⠀⠀⠀⠰⡇⣼⢰⡆⠰⡇⠀⠀⠀⣰⣿⡀
⠀⠀⠈⣿⡀⠀⠀⠀⠀⢻⣆⠹⣇⠠⣄⠀⢀⡈⣾⠙⠂⢸⡆⠀⠀⠀⠀⠀⠛⢸⡇⠀⣧⡴⠛⠛⠛⠋⠛⣿⣿
⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠻⣄⠙⣄⠙⠃⠘⠗⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢸⡇⢀⡿⠁⠀⠀⢀⣴⠾⠛⠁
⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠹⣦⠙⠂⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⠃⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠱⣯⠁⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⣰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠙⢷⡀⠀⢾⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢁⣼⣿⣹⡏
⣶⣷⣶⣦⣤⣤⣤⣤⣹⣦⡀⠀⠀⣬⠑⠀⣾⡇⠉⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⢸⣧⣾⠻⣿⣿⡇
⠈⣿⣧⡀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠙⠃⠀⣿⠀⠀⠀⠀⠈⠙⠷⣦⣄⠀⠀⠀⣸⡿⠁⢸⣿⣿⠁
⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⠀⣿⠁⠀⣸⣿⣿
⠀⠀⠀⠻⣿⡛⢷⣄⡀⠀⠀⠀⠀⠠⣦⡀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⠀⠀⣿⣿⠏
⠀⠀⠀⠀⠈⢿⣦⡈⠛⠷⣤⣄⠘⢦⣌⣁⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢰⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠉⠙⠶⣮⣉⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⠀⠀⠉⠛⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⢱⡀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⣀⡈⠛⠀⠀⢀⣀⠀⠀⠸⣷⡀⢹⡆⣤⢸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢶⣤⣀⠙⢦⡀⠀⠘⣷⡀⠸⣫⡎⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣽⣦⡀⠈⢷⡀⢿⣷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⠀⠈⠁⠈⣿⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣼⠗⠀⠀⠀⠀⢠⡿⠁⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⢀⣼⠋⠀⠀⣠⡿⢠⡿⠁⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⡿⠁⠀⢀⣼⠋⣰⠟⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣰⡿⠃⠀⣠⡟⢁⡾⠉⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⣰⡿⠁⠀⣴⣏⣴⠋⠀⢀⣴⠏⠀⢀⣴⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⣸⡿⠁⢀⣾⣿⡟⠁⢀⣴⠟⠁⢀⣴⠟⠁⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢀⡾⡉⠁⣠⠟⢡⠛⢀⣴⠟⢁⣠⡾⠋⢀⣠⣤⣶⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠈⣶⣥⠞⢁⠔⢁⡴⠟⣁⣴⣿⠋⣠⣴⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⡼⠟⣡⠶⣁⣴⣯⣴⣾⣿⣿⣷⡾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⣠⡾⢁⣴⣿⣿⣿⣿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣿⣾⣿⡿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⢉⣉⠙⢿⣿⣿⣿⣿⠿⠿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⢿⣿⠇⢸⣿⡿⠿⠿⠂⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⠈⠉⣠⣤⣤⣴⣿⠃⣠⣶⡄⢸⣿⣾⣿⣿⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⣦⣼⣿⣿⣿⣿⣄⠙⠛⠁⣸⣿⣿⣿⡇⠀⠀⠀⣰⣿⣷⡄⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣄⠙⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⢁⣴⣦⠈⢿⣿⣿⣿⣿⣆⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣷⡀⠹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⢠⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠾⠟⠋⠀⣼⣿⣿⣿⠏⠀⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⡇⢸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠉⡉⠉⠉⠉⠉⠉⣉⡉⠉⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣬⣙⠳⣿⡃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣄⣠⣶⣶⣶⣿⣿⠟⠁⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⠉⠻⣏⠉⠙⢷⣌⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⡿⠛⠛⢻⡇⣀⣀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⠾⢿⣷⡶⠿⣿⣧⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣘⢃⣀⣀⣈⣃⣀⣀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⣹⣧⣀⢈⣿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢀⡴⠞⠒⠶⣄⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⠲⣄⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣈⣃⠀⠀⠀⢠⣶⣶⣶⣦⣤⡀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣀⣶⣿⣿⣿⠀⠀⠀⠀⢿⡿⠟⠉⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢾⣿⡈⠙⠻⡟⠀⠀⠀⣾⣷⣵⣂⣐⣯⣾⣿⣆
⠀⠀⠀⠀⠀⠀⢠⣶⡿⣿⣷⣦⡙⠓⠒⠉⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣰⣿⣿⢾⣿⣯⢿⣿⣶⣄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣶⠀⠀⡀
⠀⠀⠀⠀⣰⣿⣿⣿⣯⢿⣿⣎⡙⢿⣿⣷⣤⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⡿⠏⠀⣴⣇⣴⡆
⠀⠀⠀⢠⣿⣿⣿⣿⣿⡞⢿⣿⣿⣿⣷⣶⣿⡍⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣾⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠉⠉⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡟
⠀⣀⣀⢹⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣷⡝⠻⣿⣿⣿⣿⣦⣄⢶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠸⣮⣿⢿⣿⣿⣿⣷⡌⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣝⢿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣼⣿⣿⣿⢏⡜⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣼⣿⣿⣿⢃⣾⣧⢹⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣾⣿⣿⣿⢣⣾⣿⣿⡎⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠻⣿⡿⠃⠉⠉⠉⠉⠁⠸⣿⣿⠟⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠈⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠉⢻⣆⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⢸⡇⠀⢀⡀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⣿⠀⠀⢸⡷⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⡏⠀⠀⠀⣷⠀⠀⠀⠀⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⡆⣄⠀⠀⠀⠀⠀⠰⣾⡁⠀⠀⠀⢹⡄⠀⠀⠀⣿⠀⠀⠀⢀⣼
⠀⢸⣿⠷⣦⣄⡀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠘⣿⠿⡀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⢀⡴⢿⣿
⠀⣾⡟⠀⠀⠉⠛⠻⢷⣤⣄⡀⠘⣇⠀⠀⠀⠘⣶⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸⡇⠀⠀⢸⣇⣴⠟⠀⣾⠏
⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡄⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣾⠟⠁⠀⢰⡿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⢻⡇⠘⢷⣄⢠⡄⣦⠀⠀⠀⠈⣿⢠⡟⠁⠀⠀⢠⣿⠇
⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠙⠂⠀⠈⢿⣄⠈⠛⠘⢁⠀⡀⢠⠄⠀⢹⡿⠀⠀⠀⠀⣾⠏
⠀⠀⢿⣇⠀⠀⠀⠀⠀⡀⠹⣆⠀⠀⠀⠀⠀⢠⢠⡆⠘⣿⠀⠀⠀⠀⠰⡇⣼⢰⡆⠸⡧⠀⠀⠀⣰⣿⡀
⠀⠀⠈⣿⡀⠀⠀⠀⠀⠻⣆⠹⣇⠠⣄⠀⢀⡈⣿⠙⠂⢸⡆⠀⠀⠀⠀⠀⠛⢀⡇⠀⣧⡴⠛⠛⠛⠉⠛⣻⣿
⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠻⣄⠘⣄⠙⠃⠘⠗⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⡇⢀⣿⠃⠀⠀⢀⣤⠾⠛⠁
⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠹⣦⠙⠂⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⠃⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠹⣏⠁⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠙⢷⡀⠀⢸⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢁⣼⣿⢸⡏
⣶⣷⣶⣦⣤⣤⣤⣤⣹⣦⡀⠀⠀⣤⠑⠀⣼⡇⠉⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⢸⣧⣾⠻⣿⣿⡇
⠈⣿⣧⡀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠘⠇⠀⣿⠀⠀⠀⠀⠈⠙⠿⣶⣄⡀⠀⠀⣸⡿⠁⢸⣿⣿⠃
⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⣿⠁⠀⢸⣿⣿
⠀⠀⠀⠻⣿⡛⠷⣄⡀⠀⠀⠀⠀⠰⢦⡀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⠀⠀⣿⣿⠏
⠀⠀⠀⠀⠘⢻⣦⡈⠛⠷⣤⣄⡘⢦⣄⣁⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢰⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠉⠙⠶⣮⣉⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⠀⠀⠈⠛⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣄⢱⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣶⣄⣀⡈⠛⠀⠀⠀⣀⠀⠀⠘⣧⡀⠹⠆⣧⢸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢷⣤⣀⡙⢦⡀⠀⠈⢷⡀⠸⣣⡎⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣽⣦⡀⠈⢿⡀⢿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⠀⠈⠁⠈⣿⣄⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣼⡗⠀⠀⠀⠀⢀⣿⠁⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⢀⣼⠋⠀⠀⣠⡾⢡⡿⠁⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⢀⡾⠁⠀⢀⣼⠋⣰⠟⠁⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣰⡿⠃⠀⢠⡞⢁⠴⠉⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⣰⣿⠁⠀⣰⣏⣴⠋⠀⠀⣴⠟⠀⢀⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⣸⡿⠁⢀⣾⣿⡿⠃⢀⣴⠟⠁⢀⡴⠟⠉⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢀⡾⡉⠁⣠⠞⢡⠋⢀⣴⠟⠁⣠⡾⠋⠀⣀⣤⣶⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠈⣴⣥⠖⢁⠔⢁⡴⠛⣁⣴⣿⠋⣠⣴⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡴⠟⢡⠶⢋⣴⣯⣴⣾⣿⣿⣷⡾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⣠⡾⢁⣴⣿⣿⣿⣿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣿⣾⣿⡿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⣛⠁⠘⠂⠀⠈⠱⡀⢄⠀⠌⣽⡄⠐⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⢀⡀⠙⢦⡘⣿⠏⠻⣇⡀⠀⠰⣷⠈⣦⠚⠀⠓⠲⢦⣆⠀⠀⠘⠉⠙⠶⣦⡤⠀⣀⣠⣀⡀
⠀⡤⠀⠀⠀⡉⡙⠳⢦⣤⣴⠌⠳⣜⢎⣄⠡⡛⡭⡿⣿⣴⣵⣿⣮⠘⣦⡀⠀⠈⠉⠀⠀⠀⠁⡀⠀⡹⠃⣸⣿⣿⡟
⠘⠀⠅⠀⠘⠷⠃⠀⠀⠈⠙⠻⢦⣀⣀⣹⣷⣽⣍⣷⣹⣿⣿⠟⠋⠠⠥⣽⣶⣆⣀⢀⠀⠀⢠⡇⠀⡁⢀⣿⣿⢿⠃⠀⣂⠀⠊⠀⢀
⠀⠄⠲⠆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣤⡀⠀⠀⠈⠙⠻⢷⡄⢀⣸⣉⠀⠈⠺⠿⠟⠁⠂⠴
⠀⠀⠀⠀⠀⠂⠀⠕⠀⠀⠀⢀⣠⢷⣲⣽⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡄⠀⢰⣶⣶⣶⣿⣿⣿⣷⣶⣶⡄⠀⠀⠘⠀⠞⠈⢀⠁⠀⡤
⠀⠀⠀⠀⠀⣈⣀⣐⠀⠀⠀⠿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡣⡻⠀⢈⡛⢻⠟⢻⢿⣿⣿⣏⠁⠀⠀⣀⠀⣰⠀⠀⠐⠠⠎⠁
⢀⡀⠀⠀⠐⣶⣿⣿⣿⣦⣴⣤⣶⣿⡟⠛⠛⠋⢉⠻⢿⣿⣿⢿⣿⣿⣷⣷⣤⣴⣷⣦⢄⠱⠨⡉⠋⣀⣄⡀⠀⠀⠀⠒⢀⠉
⠈⠁⣴⢿⠀⠉⠛⢻⣻⣿⣿⣿⡿⠋⠀⡀⢰⣆⣀⣠⣄⡌⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣸⣄⣤⠀⠀⠀⠈⠂⠀⠠
⠀⡘⠿⠼⠀⣤⣰⣼⣿⣿⣿⡟⠀⠀⢀⣼⣿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠽⢭⣽⣿⣿⣿⣿⣯⣷⡁⠀⠞⠀⠢⢄⠐
⠀⢉⠀⠀⣿⣾⣿⣿⣿⠿⣿⡇⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⡇⠈⠈⠀⡀
⠀⠈⠁⣿⣿⣿⣿⡯⠀⠑⢿⡇⠀⠀⣹⣿⣿⣼⣿⣿⣿⣿⣏⣼⣿⣿⣿⣿⡿⠀⢠⣤⡄⣀⠀⠀⢈⡿⠟⠛⠛⠉⠁⠀⠀⠀⠈⢢⡀
⠀⠀⠠⡿⠛⠿⠿⠏⠀⢸⣿⣧⠢⠀⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣿⣽⣯⣒⠦⠋⠀⠂⣀⠀⠀⠀⠀⡁⡶⠤⣀⠡
⠀⠀⠀⠀⠄⠀⠇⠢⠀⣾⢻⣿⣿⣴⣢⡾⠋⠉⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠏⣿⣿⣿⡷⣦⡀⠀⠈⢂⠀⠀⠀⡸⣁
⠀⠀⠀⠀⠠⠀⠀⠀⠻⠵⣦⣉⣿⢻⣿⢹⢂⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⢀⣠⣿⠿⣿⣿⡦⢿⠂⠀⠀⠀⠀⠚⠁⠀⠉⠓
⠀⠀⠀⠀⠂⠐⡁⠀⢀⡜⠽⣿⣿⣷⣌⣄⠀⠁⠀⠩⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣟⣀⡟⠛⠃⠀⢉⠀⢀⡴⢫⣄⠒⠀⠠
⠀⠀⠀⠀⠈⠀⠀⠀⣈⠀⠃⣿⣿⣿⣿⣿⠅⠏⠒⠄⠰⣠⣿⠙⡁⣿⣏⠭⠈⠀⠀⠈⠛⠋⠁⠆⠀⠀⠀⣠⠊⠀⡄⠈⢂
⠀⠀⠀⠂⠠⢤⠈⠀⠁⠀⣴⣿⠋⠻⢿⡏⠀⠑⢍⠀⠀⠘⢿⡄⢠⣿⣟⣠⣤⣔⣠⡌⠀⠀⢁⢀⠀⠀⠈⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠺⠠⢁⠉⠀⡠⠀⠀⢫⠀⠀⠐⠉⠀⠀⠹⠃⢸⣿⠛⡉⠿⠀⡀⢸⠃⠂⠌⢻⠀⢀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠠⠀⠈⡆⠀⢹⡀⠀⠀⠀⠀⡈⠀⠀⠐⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣅⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠠⣛⣣
⠀⠀⠀⠀⠀⠀⢫⣮⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡵⠂⠀⠀⠀⠀⠉⠁
⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣒⡄
⠀⠀⢪⣭⠂⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠹⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣛⡧⠀⠀⢀⣀⠀⠀⢴⣛⡧⠀⠀⠀⠀⠈⠿⠟
⠀⠀⠀⠀⠀⠀⢫⣮⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣓⣣⠀⠀⠀⠀⠈⠉⠁⠀⠀⢻⣮⠂⠀⠈⠉⠁⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⡽⠂
⠀⠀⠀⣠⠦⣆⢀⣾⣿⣷⣦⠀⠀⠀⣤⣶⣷⣦⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⣴⣿⣿⣦⠀⠀⠀⣠⣶⣷⣦
⠀⠀⠀⠘⠛⠃⢸⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⣄⡄⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⣼⣿⣿⣿⣿⡇⠀⣄⣄
⠀⠀⠀⣀⡀⠀⠘⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡿⠀⠀⠀⠈⠶⠞⢀⡀⠀⠈⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⠁⠈⠷⠞
⠀⠀⣾⣿⣿⣷⡄⠘⠿⠿⠟⠁⠀⠻⣿⡿⠟⠁⣀⣤⣤⡀⠀⣼⣿⣿⣷⣄⠈⠻⠿⠿⠁⠀⠹⢿⣿⠟⠁⢀⣤⣤⣄
⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡄
⠀⠀⠘⢿⣿⣿⡿⠀⢀⣴⣾⣿⣿⣶⣄⠀⢸⣿⣿⣿⣿⡟⠀⠘⢿⣿⣿⣿⠃⢀⣴⣾⣿⣿⣷⣤⡀⠠⣿⣿⣿⣿⡿
⠀⠀⢀⢀⠉⠉⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⢿⠿⠋⠀⢀⣀⡀⠈⠉⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣄⠻⢿⠿⠟⠁
⠀⠀⣪⣭⠆⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢺⣭⡗⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠠⣓⣣
⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠛⠉⠉⠛⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠛⠛⠋⠉⠙⠛⠿⠟⠋⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠀⠀⠀⠁⣐⠒⠒⠒⠒⠂⠒⠀⠀⡀⢰⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠴⠂⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⣄⢠⡆⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣠⠶⠀⠚⠛⠛⠒⠂⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠈⢷⣄⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⢀⡴⠋⠀⠀⠰⡦⠄⠠⠄⠂⡠⠂⠀⢰⠀⠀⠀⢀⠀⡀⡘⠀⠀⠀⠀⠀⠀⠸⢰⠀⡆⢠⡟⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣄⠀⠀⠀⣑⠦⠀⠼⠀⠔⢀⣸⡇⢠⠀⠀⡄⠁⠀⡆⠀⠀⠀⠀⠀⠀⢸⠆⠻⡓⠀⡶⠃⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠹⣄⣴⠋⠀⢀⡀⣜⣉⠤⠈⣰⡟⠸⡏⠀⢧⣴⣾⠇⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⡘⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠁⠈⡁⢡⠠⠆⠁⠈⠁⣧⢰⠛⠡⠈⡟⠀⢈⣸⠃⠐⠄⠀⠀⠀⠠⡤⠠⠀⠀⠀⠀⠠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠹⡀⠛⠀⣤⠀⠀⠀⠀⣠⠀⠚⢀⡴⠏⢉⣡⡷⣀⠀⢀⠀⣴⣆⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠄⠀⢀⠀⠀⢩⠀⠰⣊⣈⠾⠏⠠⠏⠋⠓⣩⠛⠆⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⣾⣿⣿⣷⣎⠘⡦⠆⢞⣊⣉⣈⠓⠄⠀⠰⢀⢾⠉⠳⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠱⣿⣿⣿⡋⢹⣿⠀⢙⣶⡿⣿⣿⣿⣿⣅⠀⠆⣠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠋⠀⡾⣿⣆⣼⣿⣿⣿⣿⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⠁⡀⠁⠀⠈⠁⠛⢿⣿⣿⣿⠿⠉⠀⠈⠁⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⣤⣤⡒⢄⠆⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⡀⢀⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⠨⠀⠒⠐⠞⠳⡄⠀⠀⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣦⣤⣶⣶⣶⣾⣷⣦⡈⠓⡜⠺⣶⠦⠴⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠻⢿⣿⣿⣿⡇⠀⠀⠔⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡀⢁⠀⠈⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠈⠂⣤⣤⠭⠙⢛⡷⣤⣄⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠐⠈⠁⠀⠀⠀⠈⠳⠋⠛⠐⢬⡙⠻⢿⣿⣿⣿⣿⣿⣿⠟⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡄⠀⢀⣄⠀⠀⢀⢃⢧⠀⠑⢄⠈⠑⠢⢄⣈⡉⠉⢉⡁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣿⣿⡿⣿⣿⣿⣿⣄⠈⠁⠀⠀⠈⡄⢨⡇⠀⠀⠉⠒⠠⠌⠻⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⣤⣴⣶⣿⣿⣿⣿⣿⡇⠀⠀⡀⠣⢀⡀⠘⠂⠀⠀⠀⠠⢴⠃⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⠁⠀⠘⠁⠀⠁⠀⠀⠀⠀⠆⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣤⣾⣷⡄⢰⡆⣀⠸⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣷⣿⡆⠀⡆⠀⠀⠀⠂⠀⠀⠀⣠⣾⣿⣿⣿⣿⣄⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠛⡿⠛⠛⠉⠀⣠⣿⣯⢿⠀⢰⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣷⣄
⠀⠀⠀⢀⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠏⠁⠄⠀⠀⠄⠀⢀⠟⣨⠁⠸⡄⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⡛⠉
⠀⠀⠀⠈⠀⠆⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠃⠀⠀⠀⠀⢠⠀⠒⠀⠸⠄⠱⠈⠦⡇⡌⠀⠈⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⡿⠿⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠰⠀⠐⠘⢛⠿⢿⢿⣿⣿⣿⣿⣿⠿⠿⠋⠀⠀⣤⠀⡄⠀⠀⣰⡿⠃⠀⠀⢀⠋⠀⡿⠁⡇⠀⠀⠘⣿⣿⣿⣿⠇⠀⢸⣿⡿⢃⣴⣾⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⡇⠀⡇⠀⢻⣯⠈⠀⢀⠀⢸⠀⠀⠃⠈⠁⠀⠀⠀⠘⢿⣿⡟⠀⠀⠀⠈⠀⠸⣿⢿⣿⣿⠀⠉⠉
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠟⠀⠀⡇⠀⠈⠁⠀⠀⠛⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠇⠀⠀⠁⡀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠣⠴⠂⠀⠈⠀⠀⠀⠀⡀⠀⢴⣶⣶⡿⢄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠻⣎⠁⠠⠄⢤
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠁⠀⠀⠈⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⣠⣴⣶⣾⡇⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⠤⠐⠛⠛⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣴⡄⠀⠀⠀⣀⣤⢴⣾⣿⠷⠶⠒⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠇
⠀⠀⢰⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⠄⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠋⢿⣏⠳⢠⡄⢀⡀⢀⣀⣄⠀⠀⡀⣾⣿⣏⣻⣷⡄
⠀⠀⠀⣹⠿⣿⣿⡿⠗⠀⠀⠀⣿⠻⣏⠀⠀⠀⠀⣀⣿⠉⢻⣆⠀⠀⠀⣹⣶⡿⣿⣿⣿⣄⡀⠀⠀⢀⣿⢻⡇⠀⢹⡿⢿⣿⣿⠛⠁⠀⠈⣹⣿⢿⡿⡿⠁
⠀⠀⠀⠛⠂⠀⠘⠂⠀⠒⠂⠘⠃⠀⠙⠓⠀⠀⠚⠋⠁⠀⠀⠛⠀⠀⠈⠑⠃⠀⠀⠀⠑⠀⠁⠀⠀⠚⠃⠈⠛⠀⠛⠓⠀⠀⠛⠀⠀⠀⠘⠛⠃⠘⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⢠⣴⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣠⣭⣥⡀⡀⢀⣠⣤⡀⠀⠀⠀⠀⠀⣀⣾⠗⢀⠀⠉⠀⠀⢾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚
⠀⠀⠀⢠⣿⣿⡻⠶⠒⠃⠀⣀⣤⡀⠀⠀⠀⠙⢻⣿⣿⣿⢿⣿⣿⠋⠁⠀⠀⠀⠀⣾⣿⣓⣒⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠋⠁
⠀⠀⠀⠀⣿⠟⣷⢠⣾⡿⣿⣿⠋⠁⠀⠀⠀⢀⣸⣿⣿⣇⣀⣀⣽⣀⣤⡄⠀⠀⠀⢻⣷⡟⠁⠀⣠⣾⡟⠃⠀⠀⠀⠀⠐⠋⠉⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠾⠋⠀⠹⠆⠏⠀⠀⠸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⠇⢿⣀⣸⣿⠛⡇⠀⠀⠀⠀⠀⠀⠀⣠⠴⣿⡿⠿⣿⣭
⠀⠀⠀⠈⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠈⠀⠈⠉⡀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⠉⡉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢠⣤⣴
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢀⣠⠶⢀⣟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣾⣯⣾⠇⢀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⣰⣿⠿⣦⠞⠛⠛⠳⣦⡦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠚⢿⣄⠀⠀⠀⠀⢸⣿⠀⠀⢀⣼⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢩⣿⣷⣄
⠀⠀⠰⠛⣷⣦⣶⣦⣤⣤⣴⣿⣷⣶⠶⠂⠀⠀⠀⣠⣾⡿⠉⣉⣷⣿⣿⡆⠀⠀⠀⣠⣿⣶⣾⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⢠⣾⣿⠿⠆⠀⠀⠾⢫⡾⠋
⠀⠀⠀⣴⠿⢿⡿⡿⣿⣿⣿⣿⡿⡿⠀⠀⠀⢄⣰⣿⡏⡇⠀⢹⣿⣿⣿⡅⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⣠⣿⡟⢹⠀⠀⣀⣀⠀⠈⣷

⠀⠀⠀⠀⠀⠉⠉⠀⠁⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⣴⣾⡟⠟⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠠⣿⣿⣧⠀⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠄⠂⠀⠀⠀⠀⠀⣄⠠⢤⠆
⠀⠀⠀⠙⢿⡟⠺⣧⡬⠃⠀⠆⠤⠠⠰⠀⠀⠀⠀⠣⠀⠂⠀⠐⠀⠀⠀⠀⠀⠼⠀⠀⢁
⠀⠀⠀⠀⢸⣿⡟⠟⣷⣤⣄⡂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠂⠀⠀⣀⠈
⠀⠀⠀⠀⣸⠛⢿⣿⣿⣿⣿⣿⣄⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⢠⡀⠀⠀⠀⠰⠎⢉⠄
⠀⠀⣶⣿⡗⠀⠈⢿⣿⣿⣿⣿⣿⡄⡩⠀⠁⠀⢀⡀⡀⠠⠟⢀⡞⠁⠀⠀⠀⢠⣶⡈⣳⣶⣦⠄
⠀⠀⠀⣮⡟⣤⢀⡩⣿⣹⣿⣆⣹⢣⣴⣀⣀⣠⢞⣷⣄⣙⣈⣩⣧⡠⠂⣀⠀⢹⣿⣿⣿⣿⡿⠀⠀⠀⣴⣶⡖
⠀⠀⠀⠸⣧⣹⣇⡸⡟⢉⣿⣿⣟⠼⣿⣿⣿⡉⠀⠁⠀⠈⠉⠀⠀⠀⠀⠻⡴⣤⣻⣷⣿⣆⠆⠀⠀⠀⣿⣿
⠀⠀⠀⠀⢻⡏⣿⣿⣿⣿⠋⠀⠜⡿⢿⣿⣿⡷⠆⠀⠀⠀⠀⠈⠐⠈⠀⠂⠀⠉⠈⣿⣟⡟⠛⢧⡀⠀⡇⠸⠁
⠀⠀⠀⠀⠸⣷⡿⢻⠄⠁⠀⠀⣰⠁⢀⣿⣿⣿⣧⡔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣥⣤⠀⠙⢶⡗
⠀⠀⠀⠀⠀⣿⣟⣤⣃⡈⠀⣰⠃⠄⣸⠛⠛⠻⢿⣧⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⡁⠈⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅⢀⡾⠀⠀⠀⢃⡀⠀⠀⠉⣦⠀⠀⠀⠀⠀⢀⣴⣾⣿⣧⠊⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⣿⣿⢿⡏⠀⣼⣡⣄⠀⠀⠈⣿⣶⠀⠀⢸⣂⣀⡀⠀⢀⣿⣿⣿⡿⠏⠀⠀⠠⣴⣆⣀⣶⣶
⠀⠀⠀⠀⢸⡟⠻⠿⠟⢿⣿⣿⠻⣷⠀⠀⢻⣿⡄⠀⠈⣛⣋⠀⠀⢸⣿⡿⠋⠀⠀⠁⠀⠀⠀⠚⠉⠆⠦
⠀⠀⠀⠀⣼⠇⠀⠀⢀⣤⣻⣿⢳⣿⣧⠀⠈⢿⣿⠀⠀⠟⠀⠀⠀⣸⡟⠀⠀⠀⠀⠤⠄⢊⣤⡄⠀⠐⢸
⠀⠀⠀⢠⡟⠀⠰⠶⣧⣄⡈⠛⠞⣤⣿⣆⠀⠀⣄⡆⠀⣠⣴⣷⣦⣿⡇⡀⣀⠄⢠⠄⡚⣧⣾⠏
⠀⠀⠒⠾⠁⠀⠀⠀⠉⠛⠿⠿⣿⣦⣧⠈⢂⠀⠉⡙⠃⠛⠛⠻⠿⣿⣿⣶⣿⣷⣿⡿⠿⢛⣡⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡙⠻⠷⢿⣿⣶⡄⠐⠀⠀⡌⠙⠻⠶⢿⠟⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠲⠦⠦⢄⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠐⣶⣶⣶⣛⣛⣃⣀⣀⡐⣶⡛⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠉⢙⡓⠿⠀⠁
⣶⣶⡶⠶⠶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⠁⠀⢹⠀⠀⠀⠀⢐⢶⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣤⠞⠑⠚⠁⢀⡞⠉⠳⡅⠀⠀⠀⢸⠀⠀⣠⠛⣦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⠉⠁⠀⠀⠀⠀⠣⣤⠴⠁⠀⠀⢀⠏⢀⡼⠁⠀⠈⢆⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣀⢮⡀⠀⠀⠀⠈⢧⠀⠀⢉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣲⣄⣀⣀⣀⣀⣀⣀⣀⡤⠤⠖⠊⠁⠀⠱⡄⠀⠀⠀⠀⢳⡒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⣀⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⡟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠃⢠⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠘⢯⣉⣀⣀⢴⡟⠀⠀⠀⢀⣏⠤⠤⢤⣀⣀⡀⠀⠀⠀⡟⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠞⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⡇⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣻⣟⣟⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠳⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣱⡀⠀⢀⡆
⠀⠀⠀⢠⣄⣘⠀⠀⣾⣿⣿⣷⡄⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢄⡀
⣤⣽⢘⡿⣿⣿⣦⣀⡛⢻⣯⢥⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⡄⠇⠀⠈⠑⣀⣴⣤
⠘⢿⣃⣴⠿⠟⠻⠿⣿⣿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⣀⢦⣉⢂⠀⠀⠚⣿⣿⣟⠋⠁
⠀⠀⠀⠈⠀⠀⠀⠀⢻⣿⣸⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢉⣳⣿⣾⣼⡷⠞⠉⠀⣤⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣿⣿⣿⣿⣿⣶⣧⣴⣾⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣉⣹⠟⣿⢻⡿⣿⡀⠀⠉⠻⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠈⠹⠻⢋⣤⠟⢨⠇⠘⣯⠒⠒
⠀⠀⢰⡖⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠰⠏⠀⠀⣦⣀⢠⣟⢲⢤⠀⠀⠀⠀⢀⣀
⠀⠀⠈⢷⣀⠈⠃⠀⠀⠀⠀⠀⠀⠇⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠁⠆⠘⠈⠃⠃⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢐⢀⠁⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⣸⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⣿⣤⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⣿⡟⣯⡀⠀⠀⠀⠀⠀⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢰⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠸⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠇⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢴⠀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠈⣿⡟⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⡄⠀⠀⠀⢀⣡⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣂⠀⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠃⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠙⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⣠⠤⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠉⡆
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠁⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠾⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠙
⠀⠀⠀⠀⠀⡀⠈⠙⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃
⠀⠀⠀⠈⠀⠀⠀⠀⠩⠽⠇⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠠⠄⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠒⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠀⠒⠆⠀⠶⠆⠄⠀⠀⠀⠀⠀⠀⠰⠤⠆⠰⠤⠂⠄
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠉⣄⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⢄⠐⠇
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢠⣀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠛⡀⠀⠀⠀⠀⢀⡀⠤⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⡏⡘⠃⠉
⠀⠀⠀⠐⠀⠀⢠⣤⠄⠀⠐⠈⠁⠀⠀⠀⠀⣀⢊⡁⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡟⢛⣻⠀⠀⠀⠐⠃⠋⠉⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠈⠁⠀⠈⣽⣦⣀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠁⠀⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢀⡀⢠⣠⢈⣤⣉⢡⡀⠀⠀⠀⠀⢀⣀⣠⡀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠉⠀⠀⠀⢫⡀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⡄⢠⠀⠀⠀⠀⠀⠀⠀⠻⠶⠉⠉⠧⠄⢤⡃⠀⠀⠀⠀⠀⠀⢰⡏⠀⠈⢻
⠀⠀⠰⠀⠀⠀⠠⠶⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣀⡀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘
⣀⠐⠀⠀⠀⠀⠀⣀⠋⠀⣀⣠⠄⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠐⢄
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠂⠀⠙⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐
⠀⠀⠁⠀⠁⠀⠀⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⡶⠶⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠠⠴⠾⡿⠛
⠀⠀⠀⠀⠸⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠂⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣯⣿⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠂⠒⠆⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠰⠀⠶⠴⠖⠀⠀⠀⠀⠀⠀⠀⠶⠶⠀⠲⠖⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠋⠉⠉⠙⠓⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠉⠉⠉⠙⠓⠶⢤⣀⡞⠁⠀⢀⣀⠀⠀⠹⡄⠀⠈⠙⠲⣄⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⢀⣠⠴⠒⠒⠒⠒⠦⢤⡀⠀⡾⠀⠀⢀⡞⠙⣆⠀⠀⠙⣆⠀⠀⠀⠈⢧⠀⠀⠈
⠀⠀⠀⠀⡠⠞⠁⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡇⠀⠀⣾⠓⢦⡘⢦⠀⠀⠘⢦⠀⠀⠀⠈⡇
⠀⠀⡠⠊⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⣀⡤⢤⣄⠀⠀⠀⠸⡇⠀⠀⢿⠀⠀⠙⢮⣧⡀⠀⠈⢧⠀⠀⢀⡇
⣠⠞⠁⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡾⠁⠀⠀⠈⢳⠀⠀⠀⢷⠀⠀⠘⢆⠀⠀⠀⠙⣷⡀⠀⠈⢳⣀⡞⠀⠀⢀
⠙⣄⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢧⠀⠀⠀⠀⣸⠁⠀⣠⢬⣧⡀⠀⠈⠳⢤⣀⣠⠞⢳⡄⠀⠀⠉⠀⠀⢀⠞
⠀⠈⠳⣄⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠙⠲⠖⠚⠁⢀⣄⣷⠀⢻⣷⣤⡀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠈⠳⣄⡀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠻⣧⠀⢿⣧⠙⢶⣦⣤⣀⣀⣀⣠⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠈⠓⠦⢤⣤⣤⡤⠴⠚⢧⠀⢿⣇⠈⢿⣆⠈⣿⡄⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣀⣀⣀⢀⣀⣀⣠⠼⢧⠈⢿⣆⠘⣿⡆⠘⠿⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣀⣀⡀⠘⣆⠘⠿⠀⠈⠁⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠙⢦⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢀⣠⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡴⠞⠉⠁
⣿⣿⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡀⠀⠀⠀⠀⠀⣰⣶
⠀⠀⢀⣴⣿⡏⣄⣿⣷⣦⠀⠀⠀⠀⢻⣿⣿⣶⣴⣦⣾⣿⣿⠟⠀⠀⠀⢀⣀⣤⣶⣿⣷⣺⣸⣿⣷⣦⣀⣀⠀⠀⠀⠈⣿⣷⣄⡀⡆⣀⣼⣿⠇
⠀⣴⠿⠟⠉⠤⡗⠨⡉⠿⢷⡦⠀⠀⠀⠈⠙⣛⣿⣿⡛⠉⠁⠀⠀⠀⠀⠘⠻⠿⠋⡥⠝⢻⠛⢳⡉⠻⠿⠛⠀⠀⠀⠀⠈⠿⢋⣉⡿⢝⠻⠋
⠀⠀⠀⠀⡖⠀⠗⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⢿⠆⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡧⠘
⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⢀⣀⠀⠀⣀⣀⡄⣀⡀⠀⢀⣀⠀⢠⡀⠀⠀⠀⢀⡀⠀⠀⠀⢠⠄⠀⠀⠀⠀⣀⣤⣄⡀⢴⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⡄⡀⣤⣀
⠈⠻⢿⡿⣿⡿⡿⢿⡿⣿⠿⠋⠀⠈⠿⣷⣶⣿⢾⠿⣿⣶⡾⠿⠀⠀⠀⠉⠛⠛⠻⠿⠿⢿⠿⠿⠿⠛⠛⠋⠁⠀⠀⠹⢿⣿⡿⠿⡿⢿⣿⡿⠟
⠀⠀⠀⠀⠠⠖⠟⣳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⢺⠉⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢺⠒⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⡏⠙⣦
⠀⠀⠀⠀⢠⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠀⡏⢈⡁
⠀⠀⠀⠀⠀⢀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠈⠁


⠠⣤⣤⣄⡀⠀⡀⠀⣀⣤⣤⡤⠀⠀⢀⡐⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣆⢀⡄⢠⣶⣶⡄
⠀⠈⠻⣿⣿⣶⣷⣾⣿⡿⠋⠀⠀⢠⣿⣿⣶⣶⣾⣷⣶⣶⣿⣿⠄⠀⠲⣦⣤⣶⣾⣿⠿⢿⡿⢿⣿⣷⣶⣴⡶⠃⠀⠚⠛⠛⠿⢿⣿⠿⠟⠛⠛
⠀⠀⠀⠀⠡⠖⡗⢢⡍⠀⠀⠀⠀⠀⠙⠿⠿⣋⣹⣍⡙⠿⠿⠋⠀⠀⠀⠀⠈⠉⠉⠀⠚⢻⠉⢳⠈⠉⠉⠀⠀⠀⠀⠀⠀⠐⠶⣚⡟⢷
⠀⠀⠀⠀⠲⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢹⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠈⠏⣠
⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣄⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣸⡆⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⢐⣷⣤⢄⠀⣘⢧⡘⣷⣡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠷⢼⣆⠘⢋⠙⠧⡑⠌⠓⢷⣞⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢐⡲⠿⣦⠨⢠⠀⠙⡌⡐⢮⡟⠔⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡠⡂⢌⡓⢜⢧⠀⠀⠁⢘⣿⠱⣿⣪⣵⠖⢚⡒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢄⠐⢌⣢⣘⣿⡶⢋⡭⠗⠒⣚⡻⢧⣎⡥⠒⣀⢙⡳⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣍⣒⣾⡿⡿⠀⡏⠀⣴⠟⣉⣉⣁⣻⣿⢧⣤⠀⠀⠀⠂⠁⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡚⠉⠻⢍⡉⠉⢱⡇⢸⠁⣸⢣⠞⡉⠁⠀⠁⠉⠙⠛⠻⠷⠶⠶⢦⡤⠬⢽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠁⠂⠄⠀⠑⢨⡇⡘⢀⡇⡞⠀⠈⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠸⣏⢉⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠦⠤⠤⠤⢄⣙⡞⡴⠁⡼⣸⠁⠀⠀⠀⠃⢀⡄⡀⠁⠀⠀⠐⠁⠀⡗⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠢⠤⠤⠀⣲⢎⠞⢠⢞⡴⠃⠀⠀⠀⣰⢗⡚⣿⠃⠀⠀⠀⠀⠀⠀⣹⡬⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡒⠒⡈⢡⡿⢃⢜⡵⠋⠀⠀⠀⠀⠀⣿⣝⣫⣾⣦⣄⢀⠀⠀⠀⠀⠀⠹⣎⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠠⢰⣿⡇⣎⠞⠀⠀⠀⠀⢀⠀⠸⠁⠁⠉⠈⠋⠒⠄⠀⠀⠀⠠⠀⢀⡿⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⠂⡏⡞⢧⣿⠀⠀⠀⠠⠐⢁⠀⡐⠀⠂⠸⠀⠀⠀⢀⠀⢀⠀⠀⢀⡾⡓⣼⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠂⠈⣇⢷⠈⣿⣦⠀⠀⡠⠞⠁⠄⠀⠐⠀⠘⠀⠀⠀⠀⠱⡄⢀⣶⠿⣱⣾⢻⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢀⠘⣦⡑⠹⣮⣑⢺⢤⣤⣦⠤⠶⠒⠒⣓⣲⠶⠶⢶⡖⣛⠛⢛⠭⣑⡡⢎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⢠⠁⠙⠓⠶⣬⡙⠣⢍⡚⠯⢭⣭⡭⠥⠒⠊⣉⠤⠔⣒⣬⡭⠴⣞⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣆⣠⣃⣆⣙⣳⣤⣈⠓⠲⠶⠶⠖⢚⣉⣤⡶⠉⣇⠀⠨⣄⠀⢹⣍⣛⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⣉⠉⠉⠙⠹⠐⠙⠋⢁⣱⣿⢱⡀⢳⡈⠑⢿⠀⡟⢸⣄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠬⠤⠤⠖⣫⣼⡟⠈⣇⠚⣎⠑⡟⠘⠧⢸⡙⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⣧⢠⡜⢦⠹⠌⡁⠀⠀⢿⡇⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠉⢁⡀⠈⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣄⠉⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣙⣰⠃⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⠉⠉⠀⠀⠀⠀⣀⣄⠀⠈⠙⠁⠀⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣇⣿⣿⢄⣀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣾⣿⡎⠛⣃⡈⠉⢾⣿⡇⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠘⠛⣡⣼⣿⣿⣦⡀⠉⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣄⠀⠀⠈⠁⠀⠀⠉⠀⠀⢀⣤⣶⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣦⣀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠰⣿⡷⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣤⣤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣤⣤⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⢀⠔⠒⣒⡒⠒⠒⠒⠒⠒⠒⠒⠒⢤⠀⡠⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⣒⠢⡀⢠⠔⠒⠒⠒⡲⠶⢶⠒⠒⠒⠒⠒⣄
⢸⠀⢈⠿⡉⠉⠉⠳⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⢀⢤⣤⡲⣶⠭⠛⠒⡦⠀⡇⢸⠀⣀⠔⡫⠖⠉⠉⠀⠀⠀⠀⠀⢸
⢸⡠⠊⠉⠑⡄⠀⠀⠀⠀⠂⠀⠀⢸⠀⡇⠀⠀⢸⢇⣠⡄⣿⠀⠀⠀⡇⠀⡇⢸⢊⡠⠊⠀⠠⠀⠀⠁⠀⠀⠀⠀⢸
⢸⡟⠀⠀⠀⠃⠀⠠⡲⠤⠄⢒⡒⢽⠀⡇⠀⠤⢚⡇⠀⠀⣿⠆⠀⠀⡇⠀⡇⢸⠉⠀⠀⠀⠀⣀⠤⡦⠄⢐⣒⡒⢿
⢸⡇⠀⠀⠀⠇⣠⣒⠭⠓⠀⠀⠀⢸⠀⡇⠀⠀⢘⡕⠒⠀⣿⠀⠀⠀⡇⠀⡇⢸⠀⠘⠃⠀⡎⡠⣒⠭⠂⠀⠀⠀⢸
⢸⡟⠒⠒⠒⣣⣟⡲⢭⡂⢀⡠⠒⢹⠀⡇⠛⠉⢱⣣⡤⠤⠿⠄⢀⣀⡗⠀⡇⢸⠀⢐⡰⠀⢀⣏⡲⢭⡂⢀⡠⠒⢹
⠘⢌⣉⣉⣉⣁⣈⣙⣗⣊⣁⣀⣀⡼⠀⠣⣀⣀⣀⣀⣀⣈⣉⣉⣐⣒⣒⡠⠃⠸⣄⣀⣀⣀⣀⣉⣺⣕⣊⣁⣀⣀⠜
⠀⡠⠤⠤⠤⠤⢤⣤⣤⡤⠤⠤⠤⣀⠀⢀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄⠀⢀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡀
⢸⠀⠀⡴⠊⠉⠁⠀⠀⠉⠲⡀⠀⢸⠀⡇⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢀⠔⠦⡀⠀⠀⠀⠀⠀⡤⠲⢄⢸
⢸⠀⢸⠀⡠⢄⡴⢄⡶⣄⠀⠸⠀⢸⠀⡇⡼⠠⠤⠧⣀⠀⠀⠀⠀⣀⣀⠀⡇⢸⠘⢤⡤⠃⠠⡦⣠⣤⠀⠧⣠⠜⢸
⢸⠀⢸⣰⠁⣬⠁⡀⢀⡌⠑⣦⠀⢸⠀⣷⠇⠀⠀⠀⠀⠉⠉⠐⢾⠁⠀⢳⡇⢸⢠⠊⠓⡄⣈⣁⣁⣉⡀⡖⠙⢦⢸
⢸⠀⠣⡉⡏⠉⠀⠀⠉⠉⡏⣡⠇⢸⠀⡏⡇⠀⠀⠀⠀⠀⠀⠀⣽⠀⡠⠃⡇⢸⢸⠀⠀⡇⠉⠉⠉⠉⠁⡇⠀⢸⢸
⢸⠀⠀⠘⠧⣀⠀⠀⢀⡠⠟⠀⠀⢸⠀⡇⠘⢄⡀⠀⠀⠀⣀⡠⠟⠊⠀⠀⡇⢸⢸⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⡾⢸
⠸⡀⠀⣠⠤⢼⡉⠉⢙⠤⢤⡀⠀⣸⠀⢇⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⠇⢸⡈⠛⠛⠁⠀⠀⠀⠀⠀⠙⠛⠃⡼

⠀⠀⠀⠀⠀⢶⡲⣄⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠉⠟⡳⢦⣄⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⡴⢛⡙⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠑⢮⠱⡀⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⠀⠀⠀⠐⢦⡀⠱⣎⣻⢧⡀⠀⣀⣀⠑⠀⠀⠀⠀⡃⠏⠀⠀⡀⠀⡀⠶⣚⡡⠏⠁
⠀⠀⠠⣄⡀⠀⠀⠈⢳⠱⡄⠀⢤⠀⠀⠀⢸⡿⠓⠁⠂⠀⠄⡐⠈⠀⣷⠀⣭⣽⠌⢷⡸⡁⠀⠂⢰⠀⠀⢠⡹⠀⡄⠀⢀⠞⡰⠋⠁⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠘⣞⡷⣤⣀⠀⠱⡇⠦⢀⠀⢀⣀⠀⢧⠠⠑⢀⠈⠀⠈⢲⡀⣍⠔⢶⠇⠀⠈⣇⠈⠂⠀⠈⠀⢠⠏⠃⡰⠡⢀⠎⡾⠀⠀⣈⠀⠀⢀⣴⢻⠇
⠀⠀⠀⠀⢸⡦⠺⡍⠳⢤⡈⠛⢌⡁⠦⣝⣦⡘⣆⠱⡀⠠⠀⠀⡀⣷⣟⣳⠯⠀⠠⠬⣿⠀⢠⠟⣠⡔⡧⠂⣴⠅⠀⣿⠸⠀⣠⠜⣡⠐⣆⣹⡼⡛
⠀⠀⠀⠀⠀⣷⠞⠗⠀⠘⠹⢶⣀⠉⠒⢨⣝⠟⢾⣧⡈⠀⠁⠀⠐⡽⢤⡃⠀⠀⠀⠀⣻⣰⡿⡾⡡⠊⠁⣊⡥⢚⢰⡇⠇⣴⡕⢣⡼⠛⡉⠁⣰⠃⠀⡀⠀⠀⡂
⠀⠠⠂⠀⠀⠸⡗⢛⠠⠂⢀⠌⢉⠷⡀⠳⣞⠻⠦⠌⣟⢦⡀⠐⠄⢿⣹⠤⠐⠒⠒⢲⣿⣫⣗⣫⠴⠛⠉⣠⡀⠸⣼⢸⣾⠋⢳⠎⠀⠀⠀⣀⡎⠀⣀⠤⠒⠊
⠀⠀⠀⠢⢤⡀⠻⡉⣳⣄⠀⠀⠀⠠⠛⣆⠘⡎⠶⠶⢦⠀⠙⡛⠦⣾⡟⣗⠉⠉⢍⣽⠟⠋⠁⣀⠤⠒⠩⠁⠃⠀⡿⣸⡏⣹⠫⢌⠒⠠⡀⢬⠁⣞⠡⠐⠒⠢
⠀⠀⢰⡂⠀⢍⡢⡙⢇⣈⠛⢤⣄⣀⠔⠩⢦⢹⠐⢈⠂⣁⠒⠮⠲⣌⠻⡽⣆⢀⡾⠃⣠⠖⣩⢤⠆⡰⠁⠀⠀⠀⣅⡯⢈⡏⢁⠢⣌⠢⣬⢃⡾⠥
⠀⠠⣖⠲⢄⡀⠘⠛⠶⢭⣖⢾⣀⣽⠓⣦⣼⣼⠀⡏⠀⢸⡆⢨⠳⣌⠂⠙⡝⣾⠁⣜⠕⠀⠠⢃⡴⠁⡸⡐⡄⠀⣿⢦⡾⠁⠢⡑⢤⣿⡥⠮⠤⢄⣀
⠀⠀⠈⠙⠲⣝⡳⠶⠲⠖⣒⣚⣻⣿⣿⣷⣼⣛⡀⡇⠇⠈⠈⡄⢳⠌⢷⡀⢹⡇⣸⠃⣀⠤⠖⠋⡠⢀⡷⣰⠇⡼⣯⡟⠁⢆⣢⣼⠫⠕⠀⢈⣋⣀⣀⣭⣷⠖
⠀⠀⠀⠀⠀⠀⠈⢉⡩⠛⡉⠀⡴⠒⠒⠶⣤⡙⢧⠹⣄⠐⡰⠴⠘⡎⢂⠁⠀⡇⠟⢉⡠⠔⡒⢩⢃⡾⠐⢁⣼⣽⠾⠾⠾⠿⣿⣇⠈⠉⠉⠉⠁⠀⠈⠛⠁
⠀⠀⠀⠀⠀⣠⡴⢋⡤⠊⠤⠛⠓⣉⣉⣉⡉⠙⠊⢧⠘⠂⢁⡐⣧⠙⣄⢣⠀⡇⢠⠟⠀⢈⡴⠁⢈⡠⣖⣫⡥⠒⠒⠒⠒⠤⢄⡀⠛⢦⡂⠀⠀⠀⠀⣀⡀⠠⡀
⠀⠀⢀⠤⠟⡑⢶⡓⠂⡀⠈⢉⠤⡀⠤⡀⢠⡈⠷⢦⣑⠠⡀⠑⢮⣣⣈⠳⡇⢃⣏⠴⣞⠭⠔⣚⠉⠚⠡⠤⣤⡀⠀⠀⠒⠂⠀⠈⠁⠆⠉⣠⣤⢒⡪⠥⠒⠚⠁
⠀⠀⠈⠀⠀⢈⠀⠙⢦⡈⠮⣃⠳⣌⠒⠠⠤⠲⠞⠛⡋⠡⠄⠑⠒⠈⠙⠳⠦⢶⢄⣐⡚⠭⠭⣭⡉⢉⣒⢤⡐⠤⣩⡍⠉⠡⡤⢀⡴⢂⡾⣫⠖⠉⡔⠁⠈⠂
⠀⠀⠀⠄⠀⣠⣌⡳⣀⠙⢦⣈⠓⠪⠽⠶⠖⡀⠀⢁⠴⢾⠟⠁⣀⠴⠒⢲⠿⢹⠐⡻⣭⣍⡒⠲⠤⣅⡈⠄⣉⠢⣈⠒⠒⠓⠊⢁⣴⣩⠞⠁⣠⣬⣀
⠀⠀⠑⠒⠊⠁⢀⣈⣉⣙⣒⣾⡿⢶⣲⡾⠋⠀⡴⠃⠠⠋⢠⠊⡰⠫⣂⠌⡔⠸⡆⢻⡀⣍⢻⠳⣄⠀⠈⠙⠶⣤⣄⣀⣠⡤⢾⠛⣏⣻⣉⣟⢰⠆⢀⡀⠀⠁
⠀⠀⠀⡀⠺⣏⣹⢧⡼⢤⠿⠴⡗⣊⡟⢀⠆⡬⢀⡔⠁⡠⠃⠴⠗⣊⡤⠞⠀⠇⢰⠀⢳⡄⠁⠑⢌⠳⡈⠻⡒⢬⡙⢾⡦⠗⠛⠉⡇⠁⢀⠈⠈⠑⡷⡜⢢⡀
⠀⢀⡞⢡⡖⠡⠀⠀⠱⠀⠂⢀⣴⡟⠀⡞⢀⠔⢋⠤⠎⠀⠒⠀⢉⣡⣴⢂⠀⡰⠆⢆⠀⠙⠲⢤⣈⠃⠙⢆⠘⣦⠙⢦⡹⣶⣠⢀⡇⠀⠈⠀⠀⠀⠇⣻⣿⣩⠶

⠀⣚⠼⠿⠤⠤⢦⡴⡤⠦⠖⣾⣗⠃⣸⠔⡡⠔⣂⠂⠀⠐⣈⣩⠵⢛⡁⠊⢸⠃⡆⠘⢆⠀⢶⣤⣈⡉⠙⠚⠳⠘⢧⠢⠱⡜⢿⢿⢷⣿⣚⡚⠚⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⢾⠰⣫⠊⡀⠈⠀⢀⣒⣉⢡⣠⢶⡟⢸⠀⠘⠄⡸⠰⡎⢧⡀⠑⢬⣉⡉⠥⠖⠒⠮⠷⣦⣙⣌⢧⠱⣝⠯⡛⠿⢿⣍⢁
⠀⠀⠀⠐⠠⠀⠤⠐⣢⠞⣽⢁⣾⠰⢃⠤⠰⣞⢙⣧⣠⠷⢊⡟⢸⡀⢿⡄⠠⣠⢣⠇⣼⠘⣿⣶⣤⣈⠉⠉⠉⠉⠉⠉⠉⠙⠙⠊⢷⠈⠢⡈⠒⠄⠈⢦⠁
⠀⠀⣖⠀⠒⠒⣢⡾⠋⡰⠁⡜⢹⡜⢛⡶⠞⢏⡉⠁⠀⡉⣾⣇⠘⡔⢼⡱⠐⣣⠃⠀⡇⢸⣧⢛⠷⢾⣽⠛⡾⣿⣿⣟⣋⣛⡩⠧⣌⡃⢄⡀⠅⣀⡑⢼⡄
⠀⠀⠈⠉⠉⣹⠋⢀⡼⢁⠞⠀⣬⣽⡋⠉⠑⠲⢌⠑⢦⣼⠟⡟⣆⠘⢄⠁⢇⠇⠆⡰⢁⡟⢻⡤⠂⠀⠙⠻⠷⣾⡹⢆⠦⣄⠉⢙⠫⢝⢦⡈⠉⠘⠛⠶⣷
⠀⠀⠀⠀⢐⠀⣠⠞⡰⠊⠀⣴⣹⢇⡀⠀⠀⠀⠀⢳⡴⡻⠀⠹⡝⣧⡀⢲⠻⣀⠞⣠⡟⠀⠈⣿⣥⠈⡀⢁⡜⠉⠳⣮⠧⡈⢅⢀⠙⠀⠱⢟⣦⡀⠀⠀⠈⠁
⠀⠀⠀⢀⣤⠾⢩⠘⠀⣀⠾⢧⡯⡀⠈⢢⡀⢈⡶⢊⡔⠁⠐⢄⠱⣸⡁⠄⢘⡥⠊⢹⡇⢀⡀⢹⠫⣝⠓⠮⣄⡀⢡⠈⢿⣽⠟⣥⣀⠀⠀⠀⠙⢟⠢⢄⡀
⠀⠀⢔⣀⡠⠖⢁⣤⡞⠉⣷⠞⣄⣈⣤⡤⠛⠉⠀⠀⠇⠠⠀⡸⢘⡇⡇⠸⠊⠀⠀⠀⢳⡂⢒⡟⠀⠈⠅⠂⠄⠈⠑⠓⠢⠮⣿⢧⡼⠳⣄⠀⠀⠀⠙⢦⣌⣳⡄
⠀⠀⠀⠀⠀⠐⠛⠘⠛⠛⠉⠈⠉⠁⠀⠀⠀⠀⠀⠤⠜⠀⠀⠀⢼⠩⠁⠀⠀⠀⠀⠀⠀⠡⠌⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠑⠲⠭⠦⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠬⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣮⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣼⣿⡿⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠠⣶⣶⣬⢻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⣠⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⣿⣿⡇⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠄⣿⣿⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡅⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠰⢴⣦⣴⣤⣤⣤⣤⣴⠶⠆⠀⠻⣿⣿⣷⣮⣝⠃⠀⠀⠀⠐⠶⣦⣤⣤⣤⣤⣴⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣷⣄⠀⠀⠀⠀⢿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣶⡝⣿⣿⡇⠀⠀⢀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣦⣿⣇⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⠿⠁⠀⢀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿⣿⡆⠀⠀⢸⡿⡟⠙⣿⡋⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣿⣆⡀⠀⠈⠻⣿⣶⣝⡁⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣷⡄⠀⠀⠀⢙⠛⢿⣆⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣿⣿⣷⡀⠀⠀⢸⣷⣸⣯⢀⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣷⡀⠀⠀⣿⠟⢡⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡃⠘⠃⡏⢀⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⠀⢀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⣿⣦⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⠁⠀⢻⡄
⠀⠀⠀⠀⠀⠀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⢿⠳⡝⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠘⡆⠙⢦⡉⠙⠻⢷⣤⡀⠀⠀⠀⠀⣸⡇⢰⠇⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⣫⢟⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠑⠀⠀⠀⠙⢿⡳⣄⠀⠀⣿⡇⢸⠀⣤⡆⠀⠸⢠⠀⠀⠀⠀⠀⣀⡤⠖⠀⣠⡿⢋⣵⠏⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢦⠀⠀⠀⠀⠻⣌⢳⡄⢿⣇⢸⠀⠈⠃⠀⡇⣸⠀⠀⢀⣴⣞⣡⣦⠴⠋⠁⡴⢣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠸⣷⡄⠹⣆⠹⣾⣿⠸⡀⠀⠀⢸⢃⡟⢀⣴⡿⣫⡾⣋⣁⠀⠀⢈⡵⢣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡀⠻⣦⡈⠙⢦⠘⣧⣜⠿⡆⠁⠀⢀⣿⡿⢣⣾⣿⡿⠋⠸⣿⠟⣠⡶⠋⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠉⢦⡀⠀⠘⣿⢧⢻⡖⠀⠘⠙⠀⣿⣿⠟⠁⠀⢀⣴⠟⣱⣀⡴⠃
⠀⠀⠀⣀⣠⣤⠤⠶⠶⠶⢶⣀⡀⠀⠙⠳⣤⡙⢦⣄⠘⣞⡏⠃⢀⡄⠆⣼⡿⠋⣀⣴⣾⣿⣫⡴⠟⠋⠁
⣠⠶⠛⠉⢀⣀⡀⠈⠙⠓⠒⠿⠯⢿⣉⣳⣶⣭⣓⡮⠷⢼⣄⣆⣨⣶⣮⣟⡵⠚⠛⢩⣿⣯⡥⠴⠶⠶⣶⠶⢤⣀
⣿⡶⠶⠒⠀⡀⠀⠀⠀⠀⢶⣟⣒⡶⠆⠉⠙⠒⠯⣿⣦⣧⠙⠋⣀⠀⠻⡇⢀⠂⠀⣶⣾⡿⠷⠴⠤⠤⠤⠤⠤⠬⠙⠦⣄⡀
⠈⠳⣄⠀⠀⠙⠶⢤⣀⣀⣀⣉⣈⣉⣀⠀⢠⣤⣶⡞⠿⠟⠀⠀⠉⠀⢘⣁⠉⢠⣤⣄⣀⡀⠀⠀⠐⢿⣿⣳⡆⠀⠀⠀⠀⠈⠙⠻⣶⣤⣄
⠀⠀⠀⠉⠀⠀⠀⠀⠀⣉⣉⣉⣁⣤⣤⠴⢖⣻⡭⣀⢤⡆⡄⢤⣟⠆⠉⡯⣝⡲⣽⡳⠯⣭⣛⣒⠒⠶⠶⠦⠤⠀⠐⠁⠀⠐⠚⠛⠓⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣯⠟⠋⢁⣞⡼⣴⡞⣯⢠⠐⣝⢦⠙⠳⢿⣷⢦⡿⢿⡿⠿⠶⠶⠦⠤⠦⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⠾⢋⣄⡄⢠⢏⡞⡾⣿⠁⢸⠸⣆⢜⣯⢳⡄⠀⠈⠓⢦⣀⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢡⡞⠁⠀⠙⠋⣠⣿⠏⣼⣻⢧⠆⢸⡇⢹⡏⢿⣦⠙⢦⠀⠛⢦⡝⠳⣄⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⣠⠞⡽⠃⢰⣿⡟⠈⠁⢸⡇⢸⡇⠀⠻⣷⡈⠳⣄⠙⠿⠀⠈⢳⣌⠳
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣀⠤⠒⠉⠀⠈⠀⠀⡾⢈⠇⠀⠄⢸⠀⠈⡇⠀⠀⠈⠣⡀⠈⠓⢦⣀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⡾⠁⠒⠀⠘⠁⢀⡠⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⣼⠀⣼⠁⠀⠀⠀⠀⠈⠢⣀⠀⠈⠛⢦⣄⠈⢷⡄
⠀⠀⠀⠀⠀⣸⢃⣀⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡏⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠄⣀⠉⠳⣜⣿⡄
⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠂⠈⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⠆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡶⣿⣿⣿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣻⣿⣿⣿⠋⣀⣬⣥⣀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢟⣽⣿⣟⣿⡿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣽⡏⢰⣿⣿⣿⣿⡆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⣿⣿⣿⣿⡿⢿⣿⣿⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠈⠻⣿⣿⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠃⣸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠈⠻⣿⣿⣿⣷⣄⡐⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣾⣿⣦⣠⣉⡈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⡁⣉⠉⢁⡈⠻⣽⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠿⢷⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣾⣿⡿⣿⣿⣿⣿⠁⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠿⣿⢟⢾⣻⡁⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⡈⣀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢻⣿⣿⣿⣿⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣯⣀⣤⣷⣤⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⠈⢛⣿⡟⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢷⣿⣿⣻⣿⣟⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣿⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡽⣿⣿⣷⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃⠈⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢀⡃⠘⠀⠸⠱⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠁⠀⣰⠶⠆⠏⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠷⣄⠀⠐⠶⡦⡘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢲⠈⣧⠀⠀⠇⡟⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠞⠀⢻⢀⣤⣝⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠈⠹⡀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣸⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⣀⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠴⠊⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⡆⠀⠀⠸⣄⠀⠀⠁⠀⣀⣤⣤⣄⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢦⣼⡀⣗⢀⠀⠀⠙⠷⠶⢿⡿⠋⠁⠀⠈⠙⣦⡀⢹⡆⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⣹⠇⣛⠉⣻⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠈⣷⠘⣷⡀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢡⣆⠹⣏⠉⠀⣶⠄⠀⢿⠀⠀⠀⡄⠀⠀⠀⢹⡇⠹⣷⣤⣀⣀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⠟⠹⣆⣸⠀⠀⠀⠀⠀⠸⣇⠀⢀⡇⠀⠀⠀⢸⡇⠀⠈⠻⢿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⣿⣿⣷⣶⣦⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠟⠋
⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋
⠄⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⢀⡶⠒⢲⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠛⢿⣷⠀⠀⠀⠀⠀⠀⠀⢠⠞⢦
⠀⠀⠀⠀⠀⢺⡷⠆⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⣀⡀⠀⣻⠀⠀⠀⠀⠀⠀⢠⠏⡤⡈⣦⢀⡤⢤⡀
⠀⠀⠀⡀⠀⠸⣷⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣼⣿⣿⣰⠟⠀⠀⠀⠀⠀⠀⠸⠤⢽⡥⠼⡿⠀⠀⠁
⠀⠀⠀⢇⠀⠀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠁
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁

⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦
⠀⠀⠀⠀⠀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⣿⡏
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⠾⣿⡿⢿⣿⠶⡆⠀⠀⠀⠀⠀⠀⠀⢨⢀⣀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⡇
⠀⠀⠀⠀⠀⢿⡿⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⢿⡇⢸⡏⠀⢹⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣡⠇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⣿⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠃⠘⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⢠⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠉⠉⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣗⠂⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠈⢷⣶⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⢤⡄⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁
⠀⠀⠀⢠⣴⣾⣍⣩⣷⣶⣄⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⠁⠉⠻⠃⠀⠀⠀⠀⠀⣠⣾⣿⣿⣧⣭⣭⣭⣤⡀⠀⠀⠀⠀⢀⣀⡼⠿⠋
⠀⠀⠀⢸⣿⣿⣿⣿⣏⣉⣿⠀⠀⠀⠀⠀⠀⠸⣄⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠓⠛⠛⠂⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠉⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣴⡄
⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⣿⣿⣿⣿⠾⠛
⠀⠀⠀⢸⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠜⠙⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣀⡠⠤⣀⡀⠀⠀⠀⠀⠀⢀⡠⠤⢄⣀⠀⠀⠀⠀⠀⢀⣀⠤⠄⣀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣀⡀
⠀⠀⡠⠊⠀⠀⠀⠀⠈⠢⡀⠀⢀⠞⢡⣤⢀⠀⠈⠑⡄⠀⠀⡔⠉⠀⠀⠀⠀⠙⢆⠀⠀⡠⠊⠀⢀⣠⣠⠈⠢⡀
⠀⠀⠃⢸⠁⠈⡅⠀⢸⠄⢃⠀⡎⠀⠯⠽⠄⢀⣄⠀⢸⠀⢸⠐⢒⠀⠀⠀⠐⠒⡎⡆⢀⠃⠀⠀⠀⠻⠟⠒⠀⠃
⠀⠀⢇⠸⠤⠠⠇⠈⠸⢀⡆⠀⢣⠀⣒⣒⠂⠸⠉⠉⡸⠀⠸⡈⠲⠤⠤⠤⠤⠒⢡⠃⠀⣆⠀⠀⠀⠀⢱⡂⢧⡆
⠀⠀⠈⠢⢄⣀⣀⣀⠤⠊⠀⠀⠀⠑⢤⣀⣀⣀⡠⠞⠁⠀⠀⠙⠦⣀⣀⣀⣀⠔⠁⠀⠀⠈⠢⢄⣀⣀⣀⠤⠊

⠀⠀⢀⠔⠊⠉⢉⠉⠒⢄⠀⠀⠀⡠⠊⠉⠉⠉⠑⢦⡀⠀⠀⣠⠖⠉⠉⠉⠉⠢⣀⠀⠀⢀⡔⡊⢉⠉⠉⠲⣄
⠀⠀⠏⢀⡠⠒⠒⠐⠄⠈⠇⠀⡜⠀⢶⠆⠀⠀⣶⠀⢱⠀⢰⠁⠀⠀⢀⣠⣄⣡⠸⡆⢠⡏⢶⣿⣿⡶⠀⠀⠈⣧
⠀⠀⡄⠀⢘⢠⣦⡞⠐⠄⡌⠀⢇⢰⣿⡇⠀⢰⣿⡇⢸⠀⢸⠀⢀⡰⠥⠔⠀⠀⢀⠆⠰⡆⠈⠟⠿⠰⣶⣶⠀⡿
⠀⠀⠑⢌⠀⠀⠙⠒⢒⠔⠁⠀⠈⢮⡉⠁⠀⠈⢉⡡⠃⠀⠀⠣⣉⠀⠀⠀⠀⣠⠎⠀⠀⠑⢄⠀⠀⠀⠉⢁⠔⠁
⠀⠀⠀⠀⠉⠑⠒⠉⠁⠀⠀⠀⠀⠀⠈⠁⠒⠊⠉⠀⠀⠀⠀⠀⠈⠉⠒⠂⠉⠀⠀⠀⠀⠀⠀⠉⠑⠒⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠚⠋⠉⠁⠀⠀⠀⠉⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣧⣤⡴⡄⠀⢠⣤⣤⣴⡄⡆⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠙⠂⡅⠛⠀⡈⠳⣾⢉⡅⠀⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠁⡈⡁⠈⠁⢰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⢹⣶⣶⣰⣦⣤⢆⣙⢶⠀⢰⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠻⣯⠉⠉⢹⡿⠛⠚⠀⢸⡿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠈⠉⠙⠟⠀⠀⣠⡰⠋⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣯⡻⣔⠀⠂⠀⣲⣶⠋⣠⡾⠂⢸⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡙⠶⣌⡉⠙⠉⣡⡾⠛⠁⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡄⠈⠙⣃⣤⡉⠀⠀⠀⠀⣾⣷⠀⠠⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠗⠂⠺⠿⠿⠿⠷⠄⠀⠰⠾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡆⠀⣶⣆⢰⡆⢰⡶⠶⢠⣶⠶⠆⠲⣶⠶⠂⣦⠀⣶⠀⣶⠶⠆⢠⡶⠶⠄⢶⡶⠀⢰⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⢿⡄⣿⠙⣿⡇⢸⣏⣉⢀⣙⣻⡧⠀⣿⠀⠀⣿⠉⣿⠀⣿⣉⡁⢈⣛⣻⠆⣸⣇⢠⡿⠼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠈⠀⠈⠉⠉⠀⠉⠉⠀⠀⠈⠀⠀⠁⠀⠈⠀⠈⠉⠁⠀⠉⠁⠀⠉⠉⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠀⠀⠀⠀⠄⢄⠤⠠⠤⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⡀⣀⢀⠛⡀⠀⠀⠹⠛⠒⡉⠗⠛⠁⠀⠀⠀⠰⠂⣺⡇⠀⠀⠀⠀⠀⠅⢸⣅⡁⢁⡃⠘⠀⠀⠀⠛⡁⠒⠀⠈⡉
⠀⠀⠀⠀⠀⠛⠈⠀⣍⡍⢐⠋⠀⠀⠀⠁⠠⢠⡄⡦⠤⠈⠀⠀⠀⠐⣤⡔⢳⠀⠀⠀⠀⠀⠂⠸⠦⠄⠤⠃⠤⠀⠀⠈⠀⠀⢒⣁⠒
⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⡤⡄⠀⠀⠀⠁⠡⢰⡇⡦⡬⢈⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠀⣥⣤⡄⠃⠆⠇⢠⠀⠀⠀⠠⠆⠁⠀⠹⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡔⣤⠀⠀⠀⠀⠀⠀⠀⠔⡀⠀⡀⠀⠀⠀⠀⠀⢠⡄⢀⡄⠀⠀⠀⢀⣤⣤⣤⡄⢀
⠀⠀⠀⠀⠀⠀⢰⠀⣿⡏⠠⠀⠀⠀⠀⠀⢀⣀⠃⠁⠀⠀⠀⠀⠀⠀⢀⡄⠔⠈⠁⠀⠀⠀⠀⢠⢀⣀⢈⠀⠀⠀⠀⠈⠡⠭⢥⠁⣉⠴⡶
⠀⠀⠀⠀⠀⠀⠀⠞⠒⠂⠄⠀⠀⠀⠀⢯⠿⠥⠭⢬⠥⡽⠀⠀⠀⠀⠒⣷⠴⠦⠀⠀⠀⠀⣞⣂⣆⣀⣸⣀⣠⠀⠀⠀⢠⣀⡤⠀⢈⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠻⣒⡂⠁⠀⠀⠀⠀⡼⠋⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠶⣤⡤⠀⠀⠀⠀⢈⠍⠉⠉⠉⠩⡉⠀⠀⠀⠒⠒⠒⠂⠉

⠀⠀⠀⠀⠀⠰⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⢀⠴⢍⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖
⠀⠀⠀⠀⠀⠀⠁⡆⠀⠀⠑⣤⠀⠀⠀⠀⠸⠒⠲⡇⠆⠀⠀⠀⠀⢰⣖⡆⠀⠙⠀⠀⠀⠀⡄⠰⣴⣠⡈⣄⠀⠀⠀⠀⠀⣄⢉⣤⣅
⠀⠀⠀⠀⠀⠀⠀⣇⠑⣈⢁⡿⠀⠀⠀⠀⢰⠄⢀⡇⠀⠀⠀⠀⠀⠢⠄⠁⢠⣄⡄⠀⠀⠀⠀⠀⡄⠈⣤⠳⢦⡀⠀⠀⠀⢿⢀⡟⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠇⠋⠀⠀⠀⠀⠀⠘⠀⠸⠀⠀⠀⠀⠀⠀⠻⠁⠄⠀⠽⠀⠀⠀⠀⠀⠠⠴⠲⠀⠶⠶⠄⠀⠀⠀⠸⠿⠃⠟⠇

⠀⠀⠀⠀⠀⠀⣤⣷⠄⠼⠂⠄⠀⠀⠀⢶⢺⠡⢘⢲⡆⠀⠀⠀⠀⠀⡃⠀⠀⠠⡀⠀⠀⠀⠀⠭⢼⣇⣩⡏⠀⠀⠀⠀⠀⠀⠂⡈⠀⣠
⠀⠀⠀⠀⠀⠀⡃⠀⣄⠀⠀⠀⠀⠀⠀⣿⢰⣖⣖⢸⡇⡇⠀⠀⠀⢰⠇⣠⡆⠊⠀⠀⠀⠀⠀⠠⡀⠶⠶⢇⡀⠀⠀⠀⢘⠁⠐⠦
⠀⠀⠀⠀⠀⠀⡏⠉⠇⠁⠀⠀⠀⠀⠀⣿⢨⡤⠅⢸⡇⡇⠀⠀⠀⠸⡆⠁⠦⠤⠄⠀⠀⠀⠀⢈⢁⠁⠀⢨⡅⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠚⠒⠒⠒⠚⠃⠃⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠘⠂⠀⠛⠀⠀⠀⠀⠈⠀⠀⠀⠈

⠀⠀⠀⠀⣴⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠿⠇⠉⠄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣊⣉⣀⠀⠀⠀⠘⣿⡗⠀⠀⠚⠃⠄⠀⠀⠀⣶⣶⣶⣎⡀⠀⠄
⠀⠀⠀⠀⡀⠀⢀⣥⣬⣷⣶⣄⠀⠀⠀⣾⣿⣷⣶⣦⠀⣿⣿⣿⠀⠀⠀⢠⣥⣤⡄⢸⣶⣶⡆⠀⠀⠀⢹⠿⢿⣿⠇⠀⠀⣀
⠀⠀⠀⠀⠢⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠛⠛⠻⠿⠋⠀⠄⠀⠔⠀⠀⠀⠘⠉⠉⠃⠈⠉⠉⠁⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠃⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠔⠂⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⢸⠉⠒⠲⠠⢤⠀⠀⠀⠀⠀⠀⢆⠀⣾⣿⣷
⠀⠀⠀⠀⠁⠴⠃⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠔⢾⠋⠈⠀⠀⢠⣶⣾⠀⠀⢀⢀⣸⣤⠿⠆⠀⠀⢸⡟⢈⣻⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡱⠀⠀⣠⠂⠀⠊⠁⠀⠀⠀⠀⠀⠀⢹⠘⠒⢀⢀⣰⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛

⠀⠀⠀⠀⠀⠀⣐⣚⣛⣓⡀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⡀⠀⠀⠀⠀⣴⠶⣶⠶⢶⠶⣶⠶⢶⡀
⠀⠀⠀⠀⠀⠀⡿⠉⠉⠹⡇⠀⠀⠀⠀⠀⠀⠿⠉⠈⠹⠇⠀⠀⠀⠀⠐⢛⣛⡛⠛⡛⠛⠓⠂⠀⠀⣿⢠⣿⡄⣨⢀⣽⡅⢸⠃
⠀⠀⠀⠀⠀⢀⣠⣿⣿⣷⣜⠀⠀⠀⠀⠀⢀⣴⣯⣯⣷⣄⠀⠀⠀⠀⠀⠘⠟⠇⢘⣟⠀⠀⠀⠀⠀⣿⢀⣿⡀⢸⠀⣻⡂⢸⡁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡄⡀⠐⠒⠿⠃⢠⠀⠀⠀⠉⠉⠩⠽⠿⠯⠭⠉⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢒⡒⠦⣄⠀⠀⠀⠀⠀⢀⡤⠖⠒⠦⣄
⠀⠀⠀⠀⣴⣿⣿⣦⠀⣠⣤⡀⠀⠀⠀⣀⡀⠀⡦⣀⡀⢀⣀⠀⠀⢀⡞⣷⣆⣻⣇⣴⡎⢧⠀⠀⠀⡴⢻⣶⡄⠀⣴⣦⠱⡄
⠀⠀⠀⠀⠷⣾⣷⠏⠸⣿⣿⠇⠀⠀⢀⣹⡃⣬⣥⣤⣤⢘⣝⡀⠀⢸⠀⣾⣷⡿⢿⣾⣷⢸⠀⠀⠀⡇⢨⣿⡝⢦⣽⣯⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢾⡷⠀⠀⠀⠀⠀⠘⠛⠓⠀⠀⠀⠀⠘⠛⠃⠀⠈⢧⡀⣾⣷⣾⣿⣦⠞⠀⠀⠀⠱⣾⠿⠇⠀⠿⢿⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠚⠁⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣯⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢰⣿⣿⣷⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣴⣦⡸⣿⣿⡿⠸⣿⣿⡿⣠⣶⣄⠀⢀⣴⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠸⣿⣿⡇⢀⣡⣶⣶⣦⣅⡀⣿⣿⣿⠀⢸⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠉⢠⣿⣿⣿⣿⣿⣿⣷⡌⠉⠁⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡇⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⣷⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⣿⣌⠛⠛⢻⣿⡿⠃⠀⠀⠀⢸⣿⡇⢸⡇⠀⠀⠀⣾⣧⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠋⠀⠀⠀⠀⠀⢸⣿⡇⢸⡇⠀⠺⢿⣿⣿⡿⠇⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢸⣿⡇⢸⡇⠀⠀⠀⠻⠏⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢸⣿⡇⠸⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣾⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⡶⢶⡿⣌⣙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⡏
⠀⠀⠀⠀⠀⢒⠀⠈⣿⣦⡼⣯⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⡿⢿⢿⣤⠆
⠀⠀⠀⠀⢰⠉⢿⡀⢷⠛⢿⡧⢘⡟⠁⠀⠀⠀⠀⠀⢐⠂⠀⣠⡆⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⠇⠀⠀⠀⠀⠀⠀⠀⢐⡂⠄⠀⡆⢴⡀⠆
⠀⠀⠀⠀⠸⢠⢾⣿⡌⣳⠶⠆⣿⠀⠀⠀⠀⠀⠀⠀⠈⠄⠐⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⡌⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠁⠀⠐⠃
⠀⠀⠀⠀⠀⢻⠛⣧⠞⢻⣄⢀⡿⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠉⠉⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠘⢄⠈⡀⠀⠈⠉⠀⢘⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⡇⣽⡄
⠀⠀⠀⠀⢰⣇⣀⣺⣤⣭⣯⣿⣿⣷⣼⣇⠀⠀⡤⡀⠀⢠⠀⣀⠀⠀⠠⠤⡤⠀⠀⠀⠀⢀⡀⢠⡄⠀⣤⠄⢤⡄⠀⣲⠀⠀⢀⡠⠄⡀⣀⢀⠠⡤⠀⡄⣠
⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠆⠘⠐⠛⠆⠈⠠⠾⠀⠀⢟⠀⠀⠸⠿⣉⣐⠁⠀⠀⠤⣾⣈⠛⠻⠧⡄⠀⠨⠰⠆⠱⠹⡎⠀⡆⠸⠳⠏
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠟⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣉⣉⣤⣆⠁⠀⠀⠐⠓⠘⠁
⠀⠀⠀⠀⠀⢼⠏⢿⠟⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠈⢁⡀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠸⣿⣿⠃⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠠⠀⠩⠱⠄⠀⠀⢈⡠⢂⠀⠀⠀⠀⠈⢀⠠⣥⠃⢹⠀⠛⢀⡇⣶⡃⠀⠀⡀⠀⠈⠛⣀⡟⢛⣀⢿⣿⠇⠀⠀⠀⠀⠀⢡⠀⡉⢘⠃⣄⡖⠬⡄
⠀⠀⠀⠀⠀⠀⢶⡀⡀⢤⡔⠋⢳⡀⠃⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠈⠁⠈⠁⠀⠈⢷⣿⣷⡿⠻⠷⣿⣿⣿⣷⣿⣆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠤⠐⠏⠁⣤⣷⠖⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠠⣿⣿⣿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠐⠚⠙⠛⠛⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠚⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣴⠲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠠⣄⠀⠀⠀⠀⢠⠚⢦⠀⣖⡂⠀⣴⡀⡦⡀⠀⠀⠀⠘⢿⣿⡏⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠒⠐⠒⠀⢖⠀⣆⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣾⠟⠃⢉⡤⠈⠀⠃⠀⠛⠀⠉⠄⠘⠉⠀⠁⠈⠃⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠠⠈⠃⠈⠁
⠀⠀⠀⠀⠀⠐⡔⠀⢠⡖⠀⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣿⣦⣴⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠘⠁⠀⠈⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠋⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⠤⣀⠀⠤⠀⡀⠀⠀⠀⠀⣠⣤⠀⠙⠩⢿⡾⠒⠀⠀⢠⡀⠀⠀⠀⢀⡀⡀⠀⡀⠀⣠⠄⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⢇⠀⠠⡠⠘⠣⠠⠄⠟⠄⠀⠀⠀⠉⠋⠀⠀⣀⠈⠓⠀⠐⠀⠶⠆⠀⠀⠸⠟⠷⠀⠞⠻⠀⢀⠆⠟⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⢴⣶⡖⢃⣴⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⡙⡳⣦⣀⣀⢀⣀⣀⣀⣈⡵⠴⣒⠢⢀⠀⣨⡏⡀⣾⢀⣠⠖⠛⠷⣦⢄⡕⢋⣤⣯⣁⣀⣁⣀⣠⡤⠶⠶⠶⣞⡊⠓⣂⣩⡽⣿⠃
⠙⢏⠫⡀⠀⠰⠒⠀⠈⠁⠀⠀⠀⠙⢦⡟⣝⣩⣴⣥⠞⣧⠆⠀⠀⠘⣾⠗⠉⠀⠀⠈⠉⠉⠁⠀⢀⠀⠀⠀⠀⢙⢎⡵⢋⠄⠁
⠀⠘⢆⠈⠐⡆⠀⠀⠀⠀⠀⠀⠀⣀⣼⡷⣿⣴⡰⠀⠀⣿⡇⡀⠀⢸⡇⡀⢀⠰⢠⣀⣴⣿⣟⣛⠁⠀⠀⠀⢀⢏⠎⣰⠥⠄⠀⠐⠒
⠒⠂⠉⣙⠢⠵⣄⠀⠀⠀⠀⢀⣠⠟⠁⠂⠀⠀⠙⢦⡀⠘⠇⠁⡀⣾⣠⡾⠟⠛⠛⠛⢻⣿⠿⣭⠁⠀⠀⢀⡾⠃⣐⣡⣔⣈⡁⠤
⠉⠉⠳⣌⣓⠒⣘⡓⣲⣤⣤⣬⠏⠀⠹⣆⠄⠀⠀⠀⠙⢤⣀⣼⠵⠛⠉⠀⠀⠀⠀⣰⣿⠸⣧⠤⠾⣳⠶⠗⠒⠋⠁⠀⠀⠀⢹⡤
⢀⣀⠪⠥⠀⠠⠐⡞⠁⠀⠈⣿⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⣰⣿⠏⣼⣿⢂⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠛⠐⠀⠈⣁⠂⡄⠀⠀⠀⠀⢹⡀⠀⠀⠒⢾⣿⣦⣀⠀⠀⠀⣠⣤⠞⣵⠏⣰⡷⠋⠀⠐⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠓⢦⡀
⣀⠀⠀⢂⡬⠒⠁⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢉⠙⢿⣷⡚⣿⠛⢿⠿⣿⣸⠟⠉⠀⠀⠀⠈⠻⣦⡡⠀⠀⠀⠀⠀⠀⠀⣏⣤⠤⠤⣕
⠲⠄⣌⢰⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠈⣧⣸⣯⣭⠟⠀⠘⠐⢿⣿⣦⣀⣀⡤⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⢰⠏⢀⠔⡂⠿
⠀⠀⠀⠁⢧⠀⠀⠀⠀⠀⠀⢰⠞⠀⠀⠀⠀⠀⣀⣤⣯⠈⢤⡀⠀⡤⠔⣹⣾⡏⣁⣀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⢀⡞⡠⠂⠞⠀⠘
⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⢹⣿⠒⠋⠛⠛⠫⣽⡿⣿⣐⣳⡛⠼⣯⣜⣰⣤⣿⣿⣟⣳⠒⠂⠒⠉⣰⢿⠏⠳⣤⠖⠛⠈⠴⠊
⣀⣤⡀⠀⠈⣡⠊⣈⣵⣶⣤⣏⠀⠀⠀⠀⠀⠁⠀⠁⠹⣳⣿⡪⠁⢸⣿⡿⢙⠻⡉⢛⣻⣿⣶⠶⠛⠀⠀⠀⠈⠃⣌⡉⠐⢤⡀
⠁⠀⠀⠀⡑⢡⠞⠉⠡⢾⣿⣿⣆⠀⠀⠀⠀⠀⣀⣀⡀⠀⠙⣧⠀⠀⠃⠱⣀⡖⠋⠋⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⢦⣁⠂⣬⠅⠶
⠀⠀⠀⠐⣰⠇⠀⡠⠚⠹⢲⢿⡿⠿⠶⡶⢞⡿⢟⡿⠛⣦⣀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠑⡈⠆
⢠⣠⠤⠂⢹⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋⢰⠏⠀⠀⠙⢹⣿⣄⣀⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠼⠔⠒⢚⠾⠦
⠎⠁⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠰⣰⠛⠸⠍⠏⠹⢷⣄⠀⠀⠀⠀⠀⠀⠀⣠⡖⠩⣉⠢⣈⠂⠴⠎⢄⣠⡤
⡛⠁⢀⠉⠀⢈⣷⠦⢶⡶⢤⣀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⣸⣀⣄⡀⠀⠀⠀⠙⣗⠠⢄⣄⣄⠀⠛⠂⡈⠑⡈⡄⠐⠀⠀⠉
⠒⠒⠒⠒⠊⠁⠁⠀⠉⠀⢠⠉⠓⠶⠖⣫⠏⠙⠒⠒⠚⠉⠉⠁⡈⣝⣷⠦⣤⣤⠟⢁⠀⠀⠀⠩⢶⣄⠐⢆⠀⠺⢦⡀⠀⠀⠉⠳⡀
⣿⣿⠟⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⡄⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠙⠛⠿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡋⠉⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠈⢿⣿⣦⣄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣿⣿⠿⠛⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣤⣄⣀⣀⣀⣠⣤⣴⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⢻⣿⣧⠀⣀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣹⣿⣿⠿⠿⠿⠿⠿⢿⣿⣏⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⠇⠀⠀⣸⣿⡿
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⡿⣿⣿⣯⣀⠀⠀⠀⢀⣸⣿⣿⡿⣿⣿⣿⣿⣷⣶⣶⣦⣤⡀⠀⠘⠿⠛⠋⠁⠀⠀⢀⣼⣿⡟
⠀⠀⠀⢀⣠⣾⣿⡿⠟⠛⠉⠉⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠉⠉⠉⠛⠻⢿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣎⠉⢡⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠿⠿⠋
⢀⣾⣿⠟⠁⠀⠀⠀⣠⣶⣶⣶⣶⣄⣀⠀⠀⠀⠈⢿⣿⣦⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡄
⣼⣿⡏⠀⠀⠀⠀⣸⣿⡟⠉⠉⠻⠿⣿⣿⣦⡄⠀⠈⢻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆
⣿⣿⠀⠀⠀⠀⢠⣿⣿⠃⠀⢀⣀⠀⠀⠙⢿⣿⣆⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧
⣿⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⢻⣿⣧⣤⣤⣾⣿⣿⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡀
⣿⣿⠀⠀⠀⠀⢸⣿⣇⠀⠀⣰⣿⣿⠿⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀
⣿⣿⠀⠀⠀⠀⠈⢿⣿⣷⣶⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣶⣦⣤⣄⣀⡀⠀⠀⠀⠙⣿⣿⡄
⣿⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠹⣿⣷⣤⣀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⠆⠀⠀⠘⣿⣿⡄
⣿⣿⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇
⣿⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⠉⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣿⣿⣿⣿⣶⣦⠀⠀⢀⡀⠀⠀⣴⣿⣿⠃
⣿⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠉⠉⠁⠀⠀⢿⠿⠀⠀⠛⠛⠁
⢿⣿⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢸⡟⢹⡛⣧⣯⣾⠀⢰⣿⠷⠀⢻⡇⢹⢩⣴⣷⡄⢸⢾⣿⠿⢷⣎⢴⡇⢸⡇⣝⣻⣻⠀⢸⣙⠀⣿⣗⣈⣞⣯⣨⡷⣽⣿⡇
⠀⠀⠀⢸⣇⡺⢛⢟⣈⣿⠀⢸⣿⡆⢀⣾⡃⢸⣛⣠⣿⡇⢸⢈⣿⢋⣼⡻⣿⠃⢨⡉⠉⠉⢉⠀⢸⣯⡁⣟⣿⣯⣽⢋⢻⣄⣿⣽⠇
⠀⠀⠀⢸⣯⣿⣽⣞⡙⢛⣀⡈⢣⣶⣿⣭⡁⡸⣯⡿⠟⣠⣿⣸⣿⣿⠿⢷⣿⢂⣘⣟⣫⣿⢻⣀⠘⠟⠁⢿⣿⣿⣽⣾⢈⡟⣿⢹⡇
⠀⠀⠀⢸⡿⣛⣷⣾⣍⣳⣴⢖⣚⣦⣽⢻⡐⠶⡖⣴⢿⡇⠛⢶⣰⡶⣖⢒⣆⣦⣶⢘⣿⣉⣷⠖⠲⣶⢖⣶⣶⡶⢛⣇⣴⡟⣤⣼⡇
⠀⠀⠀⢸⣿⡃⢘⢿⣬⣏⣟⡉⣿⣣⡞⡛⠷⡛⢯⠁⣸⠿⠛⢛⣀⣀⣙⡛⠳⠿⢉⡌⢫⡟⢛⢿⣮⣻⣚⢣⡷⣾⢇⢹⣿⣼⣷⣿⡇
⠀⠀⠀⢸⣿⣶⣼⡿⣧⣿⣾⠽⣧⢾⡭⠋⡘⢻⠓⢈⡤⠖⠋⠉⠁⠀⠉⠉⠛⠶⣄⠘⢧⢺⣙⣀⣸⢢⡿⣐⣲⣡⡿⣯⣿⣿⠕⣻⡇
⠀⠀⠀⢸⣿⢻⡵⣭⡿⢃⣿⣶⣿⢀⣇⣺⠳⢂⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡈⠙⡯⣽⣎⣟⣭⡯⢩⡶⣟⢒⣟⣿⢹⡇
⠀⠀⠀⢸⡿⣾⡿⢿⡾⣧⣼⣟⣿⣏⢁⡝⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠰⣿⢟⡵⣦⠤⣼⣿⣿⣷⣯⡲⢻⡇
⠀⠀⠀⢸⡇⣿⡥⠰⠛⡿⠼⡟⣿⣽⠋⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠑⠋⡋⣟⣡⡿⢻⡍⣹⣭⢇⣾⡇
⠀⠀⠀⢸⡷⣿⠿⣷⡖⢷⣶⡿⢃⠿⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢈⣥⡿⠮⢝⣿⣞⣧⡤⣿⢿⣿⠃
⠀⠀⠀⢸⣷⡿⢿⠻⣧⡞⢳⣶⢹⣳⠸⣿⣿⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠷⣄⠀⢸⣿⣿⠘⡛⢮⡇⣴⡄⣻⣯⣎⣹⡴⢿⡇
⠀⠀⠀⢸⡿⢁⡶⣤⣼⠗⣰⡿⢫⡻⠀⢿⣿⠀⡿⠛⣿⣿⠿⡄⠀⠘⡿⣻⣯⣤⣄⠉⠀⢸⣿⣿⠀⣳⡼⣿⡀⣹⡧⣸⠛⢸⣤⢹⡇
⠀⠀⠀⠘⣣⣾⣶⢿⣯⢈⡿⡿⣧⣿⣡⢸⣿⡇⠀⠾⠿⠿⡐⠈⠀⠠⠁⠉⠉⠉⠃⠄⠀⠸⣿⠉⡆⢰⣲⣜⣏⢻⡗⡩⣴⡏⣯⢼⡇
⠀⠀⠀⢸⣿⡍⣷⢾⡿⣾⣷⡶⠷⣌⣵⠀⣟⡇⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢄⡇⣟⠙⣙⣻⢟⡷⣹⣽⠻⣶⢿⡇
⠀⠀⠀⢸⣟⣥⠟⣻⠏⣷⣌⣥⣥⡿⢿⡇⢸⡇⠀⠀⠀⢠⠊⠁⠀⠀⠘⣈⠢⡀⠀⠀⠀⠀⢀⡘⢐⣣⡾⠟⠯⣿⣧⠺⠿⡲⣾⢿⡇
⠀⠀⠀⢸⣿⠻⢳⣝⣶⡏⣣⣅⢘⣗⣸⣶⢸⣧⠀⡀⡐⢁⣈⣿⣶⣴⣾⣥⣄⣈⣦⢀⠀⠀⡾⠁⣞⣧⢿⣲⣶⡟⢻⣿⢧⡟⠻⢿⡇
⠀⠀⠀⢸⣿⣿⡶⢿⠛⡷⡾⣞⣋⣯⠿⡋⡀⢿⡄⢷⠻⣿⢿⣿⠿⠿⣿⡿⠟⠛⡇⡾⠀⣰⠇⣈⣿⣿⣿⣉⢸⣏⣽⣟⠇⣧⠠⢺⡇
⠀⠀⠀⢸⣿⠿⣁⣬⠛⣟⢫⡠⣾⣃⣾⠛⡱⡈⢳⡌⠁⡄⠀⠠⠤⠴⠖⠂⠀⠀⡅⠀⣰⠏⢼⡽⡸⠦⢴⣛⣭⣽⣽⠛⡞⢻⣶⣻⡇
⠀⠀⠀⢸⡟⣾⡿⠟⣛⠢⣻⣶⣏⢈⡳⠤⣼⣡⡄⢻⣆⢣⠀⠀⠀⠀⠀⠀⠀⢀⣇⣾⠏⣤⢴⣛⣧⣶⡞⡟⣯⡴⣼⡷⢣⣾⠻⣬⡇
⠀⠀⠀⢸⣇⣿⠟⣻⣿⣿⣴⡻⣿⡞⢿⣗⡐⠞⠛⡄⢻⣿⣦⡀⠀⠀⠀⢀⣠⠞⣩⡏⣨⣽⣶⣧⡈⠏⠾⠿⡟⢇⣺⣓⣿⣽⡞⢻⡇
⠀⠀⠀⢸⣶⢈⠛⣉⣇⢛⣆⡶⠯⣻⢧⣍⢈⡷⠌⠃⠈⠻⢿⡏⠙⠶⢟⣩⠵⠋⢀⡀⠍⣵⢶⠘⣻⢽⣼⣑⢭⢫⣯⣍⡿⡿⣟⣿⡇
⠀⠀⠀⢸⣷⣈⣶⢟⡹⣿⡝⢣⣀⣿⣛⠿⣆⣶⣿⣶⡶⢀⣼⣿⡄⠀⢼⣿⡆⠀⣸⣿⣦⡈⠻⣭⢿⣾⠑⣻⠿⢃⣻⡝⡷⣾⣿⣾⡇
⠀⠀⠀⢸⣟⢻⣿⣿⣻⣀⣟⢀⣿⣾⢟⠶⣏⣙⡟⠉⣠⣾⣿⣿⣧⠀⣸⣿⡀⢠⣿⣿⣿⣿⣦⡀⢾⡏⡶⣽⡏⢿⡿⢹⡫⣯⢽⢾⡇
⠀⠀⠀⢸⡯⣛⢩⣛⣹⢋⡨⣟⣩⢉⡶⢷⣿⡟⢁⣼⣿⣿⣿⣿⣿⣦⣿⣿⣇⣿⣿⣿⣿⣿⣿⣷⣄⠉⣹⡭⣥⣼⣴⣿⡁⡓⣂⣼⡇
⠀⠀⠀⢸⣿⢿⡿⢿⡿⠺⡄⣹⢻⣟⢰⣎⡴⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⡶⠛⣽⣧⣼⡛⣿⡟⢹⡇
⠀⠀⠀⢸⣯⣿⣷⣉⣴⣎⣧⡞⣿⣤⣏⠙⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣦⣿⠿⢷⠶⣿⣍⣽⡇

⠀⠄⠃⣀⠀⠐⠐⠀⠐⢂⠐⠲⣄⠀⢀⠈⠀⡀⠀⠀⠀⢀⠐⠀⠀⠀⡀⠀⡀⠀⠀⠀⢀⡀⠂⡀⠂⢀⠐⢀⠀⢀⠀⠀⠀⠀⢀⠐⢀⠀⠂⡀⠀⡀⠐
⠒⡴⠊⠁⠄⠀⠀⢘⢁⣈⣠⡀⡸⣄⣀⣀⠀⡄⠀⠀⠀⢀⡀⠀⠀⡀⣀⠀⠀⠀⠀⣠⢀⡄⠂⠀⢂⡄⠐⠀⠀⠀⣀⣄⣀⡀⠀⠐⠀⢀⠀⠀⢀⡀⠐⠀⠐
⠀⢇⠀⣦⠖⠒⠚⠋⠉⣁⠤⠋⠀⣿⣥⣿⣿⣿⣿⠀⢠⡿⣷⣟⣻⡟⣷⣿⣿⣿⡄⠸⣿⢳⣿⣿⠻⣟⣷⣿⡅⢸⣯⣽⣿⣿⣿⠀⣰⠿⣷⡟⢻⡏⠰
⠀⠀⡬⣵⡾⠿⠿⠿⣷⣦⣁⣤⠀⠁⣈⡀⠈⣀⠁⣀⠀⡀⢀⡈⢀⠁⠀⢈⠉⣈⢈⣀⣀⠀⣉⡉⣀⣉⢀⠉⠀⠀⣉⢀⠀⣻⠁⣀⠈⠀⠀⠁⠀⠀⠠⠈
⠀⠀⣸⣿⡥⢘⣿⣢⣼⣷⡯⠀⠀⢀⠺⢛⠛⠛⠻⠛⠿⠛⠘⠛⠛⠻⠟⠿⠛⠛⠛⠛⠛⠛⠟⠃⡙⠛⠻⠚⠟⠛⠛⡘⠛⠛⠛⣋⣀⣀⠀⠀⡀
⣤⣤⣭⣭⡴⠋⠉⠉⠉⠳⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⠁⠀⠉⠛⠦⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠿⠛⠛⠛⢿⣦⣤⣤⣤⣤⣤
⠉⠉⠉⣉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠉⠉⠉⢹⡀⠀⠀⠀⠀⠀⠀⢺⠉⠉⢩⣿⣿⣿⣿⢿⣿⣿⣍⠉⠉⠉⠉⠉⠙⠇⠀⠀⠀⠀⠀⠙⠋⠉⠉⠉⠉
⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢇⠀⠐⠦⠄⠀⠀⠈⠋⠀⢺⣿⠋⠀⠀⠀⠈⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⡼⡆⠀⠀⠀⠀⠀⠿⠀⠀⠈⠋⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠉⠋⠉⠓
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠘⠋⠛⠙⠋⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⡀⠀⠛⠀⠁⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢀⣴⣾⡶⢶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣾⠟⠋⠁⠀⠉⠻⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⡦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠂
⠀⢸⣆⠀⠀⠀⠀⠀⠀⢠⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠏⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐
⠀⢸⣿⣦⣀⠀⡀⣀⣴⣿⣄⠄⠀⢠⠤⠄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠁⠀⣀⡤⣤⣄⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠉⠉⠀⠄⠘⠋⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠂⠓⠦⢄⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡀⠀⢠⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠠
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠛⠓⠓⠚⠊⠓⠆⢀⣠⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⣾⣿⣿⠿⠷⠄⠀⠀⠀⠀⠈⢀⣤⡤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠻⢷⣶⣿⣦⣤⠶⠲⠷⠖⠢⡀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠸⢿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠤⠤⠤⠤⢤⣄⣤⡸⠋⠉⠉⠁⠙⢴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠑⢀⠀⠸⡿⠀⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠀⠀⠀⠀⠀⠛⠊⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠀⢀⣀⡀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠌⠀⢈⣴⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠛⠃⠈⠛⠏⠀⠈⠉⠁⢀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠃

⠀⠿⠿⢿⣦⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⡸⠧⡀⠀⠀⠀⣀⣀⣀⠀⠄⣴⡄⠀⠀⠀⠀⣀⣀⣀⡠⠠⡐
⠀⢒⠀⠨⠙⣁⣈⠃⠀⠀⠀⢀⣠⣤⣆⣀⡀⢸⣤⣤⡄⠀⠀⠀⠸⠿⠏⠀⢀⣉⣁⡀⠀⠀⠀⣿⣿⣿⣧⡄⠀⠠
⠠⠀⠀⣴⣶⣾⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⡇⢸⠛⠛⠃⠀⠀⠀⣼⣿⣿⡆⢿⣿⢿⠇⠀⠀⠀⢸⠙⠻⠟⢃⠔⠁
⠀⠑⢀⠹⠿⠿⠿⠿⠇⠀⠀⠀⠉⠉⠉⠉⠠⠈⠀⠀⠀⠀⠀⠀⠅⠀⠀⠄⠠⠀⠠⠀⠀⠀⠀⠀⠉⠂⠄⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⢐⠁⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣬⡣⠀⠀⠀⠀⠀⠀⠈⡏⠉⢲⢀⣀⠀⠀⠀⣀⣥⢀⣿⣿⣿
⠀⠱⠋⠀⠀⠀⠀⠀⡴⠄⠀⠀⠀⠀⠀⠐⣙⠏⠁⠀⠀⠀⠸⠿⣥⣀⠀⡕⠲⠶⠞⠛⠀⠀⠀⢹⣇⣠⣽⣿⣏
⠀⠀⠀⠈⠀⠀⠀⣸⢅⡠⠃⠀⠠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡧⠤⠞⠀⠀⠀⠀⠀⠈⠛⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢠⣭⣭⣭⣥⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣶⣄⡀⠀⠀⠀⡟⠛⣿⠛⢻⠛⣿⠛
⠀⠀⠸⢇⣀⣀⡸⡄⠀⠀⠀⠀⠀⠘⢇⣂⣀⠸⠁⠀⠀⠀⠀⢹⢩⣭⡍⢉⣍⠉⢹⠁⠀⠀⡧⠰⣿⠆⢼⠠⣿⠦
⠀⠀⣢⣾⣾⣿⣷⡜⠀⠀⠀⠀⠀⣰⣾⣿⣿⣷⡄⠀⠀⠀⠀⢸⠘⠙⠁⢸⣯⠀⢸⠀⠀⠀⣇⣠⣿⣄⣸⣀⣿⣄
⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠤⠬⠝⠟⠛⠤⠼⠀⠀⠀⠀⠀⠒⠚⠛⠓⠒

⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣭⡓⠲⢄⠀⠀⠀⠀⢀⣤⠖⠋⠙⠓⢦⡀
⣰⠿⣿⢿⡆⣠⣶⣦⡀⠀⠀⢠⣤⠀⢸⣦⢤⠀⣠⣄⠀⠀⢰⠋⣿⢦⣿⡅⢿⠏⢧⠀⠀⠀⡞⢽⣷⣄⠀⣾⣷⠹
⠘⠿⠿⠿⣁⠻⢿⠿⠃⠀⠀⣨⣮⡰⠶⠶⠶⠶⣸⣮⠀⠀⢸⠸⠿⣿⠟⢿⡿⠷⣸⠀⠀⠘⡇⣼⣿⡌⠳⣾⣷⢀
⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠛⠛⠀⠀⠈⠣⣰⠿⠷⠿⢿⡶⠃⠀⠀⠀⠙⣟⠛⠃⠀⠛⣻⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠶⠾⠶⠒⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠤⣼⣧⣤⣏⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⣉⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⢠⡏⠀⣀⣀⣀⡀⠀⠀⠀⢀⣉⡉⠉⠛⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠿⢋⣉⡉⠉⠙⢛⣛⣛⠛⢻⡶⠋⠀⠀⠀⠀⠀⣼⠀⡀⠒⠀⠀⠀⠀⡠⠖⠒⢦⠰⢏⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣉⠁⠀⠈⠁⠀⠀⣄⠀⠀⠀⠀⠈⠟⢻⡆⠀⠀⠀⢀⡇⢰⠀⠀⣠⣖⣻⠜⣁⣄⠀⢀⠇⡘⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⣶⠚⠁⠀⠀⠀⢸⠃⡆⠀⠀⣷⡼⠯⠜⣀⡘⠒⢫⢺⠁⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠲⢤⣀⣀⣀⣀⣠⡾⠃⢠⡏⠀⠀⠀⠀⠀⣾⠀⡇⠀⣼⡟⠀⣀⠼⠀⠧⢤⡈⡎⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⠳⢤⣌⣉⣉⣉⣀⣤⠶⢯⡀⠀⠀⠀⠀⠀⣿⣀⣧⢼⡟⡤⠞⠆⠀⠀⠀⣎⢀⡇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠉⠛⠓⠒⠛⠛⠉⣹⣦⡞⠁⠘⠶⠊⣩⠃⠀⠀⢹⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⠙⣏⠀⣀⣀⣠⣞⣁⣀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⣄⡤⠶⠚⠋⣉⣉⡉⠙⠳⢦⡀⢰⠖⠚⠋⣉⣸⣧⣀⣈⣈⣉⣉⣀⣀⠀⠀⠁⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣿⢉⡴⠶⡄⠘⢯⡬⠇⠀⣀⡈⣷⢸⡇⠀⠀⠓⠒⠒⠲⠶⡶⢾⡿⠿⠭⣭⣽⣿⣟⣒⣶⠾⠧⣤
⠀⠀⠀⠀⠀⢀⣼⡄⠀⠀⢹⡄⠓⠞⠃⠀⠀⠀⠀⢾⣉⡷⢸⢸⡇⠀⠀⠀⠀⠀⢀⡼⢁⡾⠀⠀⠀⢿⠈⣇⠀⡏⠉⠉⠛⠛
⠀⠀⠀⠀⠀⣞⠉⢳⣄⠀⠀⠙⠲⠶⡶⢦⡀⠀⢀⡀⠉⢀⡿⢸⡇⠀⠀⠀⠀⢠⠞⢠⡞⠁⠀⠀⠀⠸⣇⠸⡆⡇
⠀⠀⠀⠀⠀⠙⢶⣄⠈⠛⠶⢤⣤⣤⠷⠞⠁⠰⣏⣽⢂⡞⠁⢸⡇⠀⠀⠀⣰⢏⡴⠋⠀⠀⠀⠀⠀⠀⠹⡆⢻⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⡀⢰⣟⣳⠀⣈⡴⠋⠀⠀⢸⡇⠀⠀⢰⢏⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⡇
⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⣯⣨⠇⠀⣉⣥⣾⠛⠒⠛⠛⡟⠛⠁⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠷⢤⣤⣤⡵⠶⠛⢹⡇⢻⡀⠀⠀⠀⣿⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢰⡇⠈⢧⠀⠀⠀⠸⡆⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⢛⣻⠛⠁⠀⠈⢻⣛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⣼⣉⡉⠉⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⣗⣂⡀⢀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⣗⠒⠊⠁⠀⠀⢹⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢫⡉⠁⠀⠀⢀⡜⠀⠀⠉⠑⠲⠤⣀⣀⠤⠒⠋⠉⠀⠀⠈⠉⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣉⣸⠁⠀⠀⠀⠀⠀⢀⠤⣀⣀⢤⡔⠉⠉⠉⠉⠳⡤⣄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡇⠀⠀⠀⠀⠀⠀⢸⣤⠟⠺⠼⣇⠀⠀⠀⠀⢀⡧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣀⣴⣊⣉⣳⡀⠀⠈⠑⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⣀⠴⠒⠓⠒⠒⠒⠒⡇⠀⢀⣀⠤⠤⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢰⠃⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠀⠀⠀⠀⠀⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠈⢦⡀⠀⠀⠀⢀⡠⠤⠒⠢⢄⡀⠀⠀⠤⠤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢀⠤⠿⠖⠒⠻⠷⠶⠶⠶⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣤⡀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⣾⡿⠟⠛⠛⠉⠉⠉⠁⠀⠀⡄⣸⣯⣽⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⢿⠷⣾⡇⡙⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠘⡦⠈⣧⠀⣆⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠸⡿⠀⢹⣦⠉⡄⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣿⠀⠀⢿⣦⡜⢣⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡸⣿⣵⣿⣿⣧⣼⣧⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣏⢹⣇⣽⣇⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠀⣿⡏⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣆⠹⣿⣿⣿⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣆⠉⣿⣿⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣶⣄⣸⡟⠙⢹⡏⢳⡄⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⣴⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢼⣿⡿⠿⠛⠛⠛⠛⠛⠻⢿⣧⠀⠀⠀⠀⠀⠀⠙⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠀⠀⠀⢀⣀⣀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⠉⢁⣤⣤⣶⣶⣤⡀⠉⠁⠀⠀⠀⠀⣴⡾⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣟⠋⠛⠿⠏⣹⣷⡄⡿⠀⠀⠀⠀⠙⠷⣶⣿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠉⠛⠓⠒⠛⠉⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⣤⣀⣴⠷⣤⣀⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⣤⣾⣻⣷⣤⣬⣍⣹⣧⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⣿⡿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣻⣶⣿⣟⣛⣿⣻⡿⠛⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢀⣼⠟⠃⠀⠉⣿⣿⡉⠁⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣠⡟⠁⠀⠀⠀⣼⠿⠿⠿⢦⡀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⠀⠀⣰⡏⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⢷⣄⠀⢀⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⢀⣠⡶⠛⠁
⠀⠀⠠⣦⣰⠞⠛⢶⡄⠀⠀⠀⠀⠘⣧⠀⠙⢷⣾⣷⡖⠒⢶⡀⢠⡤⣿⠀⢀⣀⣴⣿⣾⠛⠁
⠀⠀⠐⣿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⣆⠀⢸⣿⢿⠛⠓⠛⣿⢾⣿⡿⠛⣻⡿⠟⠀⣿
⠀⠀⠈⡏⠀⠀⠀⠀⣿⠄⣴⡖⢶⡄⠀⠈⠳⣾⡇⠘⣦⠀⠀⣿⢸⣿⣷⣾⡋⠀⣶⠀⣿⠀⠀⠀⠀⢀⣴⠶⢦⡀⠀⣴⠟⠲⡄⠀⠀⠀⠀⢀⡴⠶⢦⡀
⠀⠀⠠⡇⠀⠀⠀⠀⣿⠀⣿⠁⠀⠀⠀⠀⠀⢸⣿⡷⠿⣧⣴⠋⢻⡟⠁⠈⣷⠀⣇⠀⣿⠀⠀⠀⠀⠘⠁⣀⣈⡟⠀⣿⡀⠀⠿⠀⠀⠀⠀⠙⠁⡀⣨⡇
⠀⠀⠀⣇⠀⠀⢀⡼⠃⠀⣸⠀⠀⠀⠀⠀⠀⢿⡍⠙⠛⠛⠁⠀⢸⡇⠀⠀⣿⠀⡇⠀⣿⠀⠀⠀⠀⣴⠋⠀⣸⡟⢠⣈⠛⢦⣄⠀⠀⠀⠀⣴⠋⠀⣹⡇
⠀⠀⠀⠛⠷⠶⠋⠁⠀⠀⠙⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠈⠃⠀⠀⠛⠀⠁⠀⠙⠀⠀⠀⠀⠉⠓⠒⠙⠟⠀⠉⠳⠖⠋⠀⠀⠀⠀⠉⠓⠊⠙⠃




⠀⠀⢠⣷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⣷⠀⠀⣾⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣿⠀⠀⣿⡇⠀⢠⡇⠀⡴⠋⠹⣦⠀⣿⠀⣿⠏⠱⠀⣿⠀⠀⣶⠆⣴⠟⠉⣶
⠀⠀⠀⣿⠀⣀⠹⡇⠀⢸⡇⠀⣁⡀⢠⣿⠀⣿⠀⡟⠀⠀⠀⣿⠀⠀⣿⠀⠻⣦⡀⠻
⠀⠀⠀⢻⣤⡟⠀⢳⣤⡟⠀⢸⣏⣀⢠⣿⠀⣿⠀⣧⠀⠀⠀⣿⣀⣠⣿⠀⢤⣈⡙⣶⡄
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⣼⡟⡶⠒⢲⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣄⡀⠀⠀⠀⠀⠀⣀⠀⠴⠉⠷⠄⢀⠀⠀⠀⠀⠀⠀⠀⣴⡄⣾⡇⣠⡀
⠀⠀⠀⠀⠀⠀⠛⢻⠀⣀⡁⢛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠛⠁⠀⠀⠀⠀⠀⡇⠀⣀⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣥⣮⡘⢛⣥
⠀⠀⠀⠀⠀⠀⠀⢀⠻⠾⠟⡸⠀⠀⠀⠀⠀⠀⠐⣏⣠⣾⣿⠿⣷⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠷⠆⠛⠇⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋


⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠤⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠
⠀⠀⠀⠀⠀⠀⣾⣷⣤⣤⣤⣾⣷⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡈⠀⣁⠃⠀⠀⠀⠀⠀⡰⢾⣿⣿⣿⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠙⣇
⠀⠀⠀⠀⠀⠀⢿⣭⣟⣿⣻⣭⡿⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⢿⣆⡴⣤⢶⣶⣿⠀⠀⠀⠀⠀⠀⣀⠘⣍⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠢⡀⠂⠤⠤⠐⡩⠂⠀⠀⠀⠀⠀⠈⠁⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠻⣏⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠆⣰⣖⣦⠀⠀⠀⠀⠀⠀⠀⢞⠉⣿⣿⡇⡏⢹⠆
⠀⠀⠀⠀⠀⠀⠀⡀⡠⠊⡠⠒⠘⠀⠀⠀⠀⠀⠀⣴⢞⣿⠿⣯⣿⣦⠀⠀⠀⠀⠀⠀⣇⣀⢸⠸⡿⠇⢇⠀⠀⠀⠀⠀⠀⠈⠓⠿⣿⡷⠗⠁
⠀⠀⠀⠀⠀⠀⢆⡈⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡿⡨⠀⠳⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣄
⠀⠀⠀⠀⠀⠀⠀⠑⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠤⠼⠃


⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⡖⡀⡍⢠⢩⢡⢲⠀⠀⠀⠀⠀⠀⢀⡶⢅⠩⡌⠱⡆⠀⠀⠀⠀⠀⠀⠑⠜⣲⠾⣯⠤⠆⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⠉⢦⡀
⠀⠀⠀⠀⠀⠀⣷⣦⣤⣤⣤⣤⣶⠄⠀⠀⠀⠀⢀⠇⠈⠉⠉⠉⠉⠈⡆⠀⠀⠀⠀⠀⠀⠯⠝⠀⣶⣾⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠿⠼⠿⠿⠧⢧⠿⠀⠀⠀⠀⠀⠘⠤⠤⠤⠤⠤⠤⠤⠟⠀⠀⠀⠀⠀⠰⠶⠞⠋⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣍⣩⣥⣤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠸⡆⠀⠙⠳⠢⡀⢻⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡱⣌⠐⠠⢀⠀⠀⠹⡄⠀⠀⠘⣄⠸⡇⠀⠐⠄⠀⠀⠀⡔⠉⠉⠢
⠀⠀⠀⠀⠀⠀⣠⠔⠂⠤⠄⡈⢷⠙⠳⣆⡀⠑⢆⠀⠹⡄⠀⠀⠘⢶⡇⠀⠀⠈⢆⠀⣸⠁⡄⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠙⠣⢄⡈⠉⠀⠀⠳⣄⠻⡀⠀⠀⠈⣇⠀⠀⠀⠀⢀⡏⢀⠁⠀⠀⡄⢀⡠⠊⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣁⠀⠀⠀⠀⠈⠒⢄⡀⠀⠈⠢⠙⡄⠀⠀⠸⡄⠀⠄⠀⢸⠁⠸⠀⠀⢀⠗⠋⠀⠀⢠⠁
⠀⠀⠀⠀⡀⠰⠦⠄⠀⠠⠈⢶⣄⠀⠀⠀⠀⠀⠉⠀⡀⠀⢳⡌⢦⣠⡀⢳⡄⠐⡄⢸⠀⠆⠀⢀⠆⠀⠀⠀⠀⠈⣀⣀⣀⡀⠤⣄
⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠠⣷⣄⠹⣿⡄⠻⣿⣿⣿⣄⣇⣿⣄⠆⡠⠊⠀⡀⠀⡠⠘⠃⠉⠿⠉⠀⢀⠜
⠀⠀⠀⢠⠄⠀⠀⠙⠶⠦⠀⠀⠀⠀⠀⠉⠙⠲⠦⣀⣝⣻⣦⣼⣿⣦⣽⣿⣿⣿⣿⣿⡿⣾⣤⣤⣻⡤⠊⠀⣀⠔⠂⠀⠀⠔⠁
⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⠠⠠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⣤⣶⣋⣥⡴⠶⠊⠐⠚⢀⣀⣤⠌⠁
⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⡀⣀⣀⡀⠀⠀⠀⠀⠑⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣾⣿⣿⣿⣿⣯⡾⠿⠖⡲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠉⠁⠈⠉⠀⠐⡶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠷⡉⠅⣉⣿⠷⣴⣿⣥⠾⢶⡿⠛⠒⠒⠒⣒⠒⠒⠒⠒⠒⠘⠃
⠀⠀⠀⠀⠀⠀⢠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⢸⣥⠁⡌⢺⣅⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠤⡀
⠀⠀⠀⠀⠀⠀⢎⢀⣀⣤⠤⠤⠶⣶⣶⡾⠟⠋⠁⠀⢉⡿⠁⣸⣿⣿⣿⣿⣿⣿⣷⣝⠈⠠⡡⠆⢄⡩⣺⡿⣿⣏⠝⠛⠉⠙⠒⠶⣤⣀⡉⠒⠤⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣠⠶⠟⠋⡁⠤⠒⣠⡤⠚⢉⡀⢔⣿⣿⣿⡿⣿⣿⣿⣿⣿⣗⣐⣣⣾⣯⣼⢧⡀⠂⠉⠓⠢⢤⣀⡀⠀⠀⠈⠉⠙⠲⠤⢄⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⡤⢒⣭⡴⡶⠋⠁⢀⡴⠋⣰⣿⣿⠞⠉⣠⣿⣿⣿⣿⣿⣿⡿⠟⠻⣿⣿⣦⡙⢦⡀⠀⠀⢀⡀⠉⠲⣄⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⡡⠂⠀⣠⠔⠁⢀⣾⠃⠠⠁⠀⣰⠏⠙⠁⢻⣿⡈⢿⡣⠈⢆⠀⠉⠿⣳⡄⠙⢦⡀⠀⠈⠂⡀⠀⠉⠒⠤⢄⣀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⡴⣟⠁⢀⣴⡟⠃⣴⠃⠀⣴⠏⠀⠀⠀⢸⡏⠁⠸⣯⠀⠀⠑⡄⠀⠀⠙⠢⡀⠳⣄⠀⠀⠈⢀⠀⠀⠀⠀⠈⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢉⡼⠋⠀⣠⣾⠇⢠⡞⠉⠀⠈⠀⠀⣿⠀⠀⠀⢿⡄⠀⠀⠈⢢⡀⠀⠀⠙⣄⠈⠢⣄⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣠⠴⠋⠀⠀⠀⡿⠃⣠⠏⠄⠀⠠⡁⠀⢠⡏⠀⠀⠀⠘⡿⣆⠀⠀⠈⢷⡀⠀⠀⠰⠆⠀⠈⢳⡄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣠⡴⠋⢸⠀⠀⢂⠁⠀⡾⠁⠀⠀⠀⠀⡇⠈⠇⠀⠀⠸⡇⢄⠀⠀⠑⠀⠀⠀⠙⠢⢄⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⠞⠉⠀⠀⠸⠀⠀⠄⠀⡼⠁⢰⠀⠀⠀⢰⡇⠀⠈⠆⠀⠀⢷⠈⠢⡀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢆⠀⣠⠞⠁⠀⠘⡄⠀⢠⠞⠀⠀⠀⠘⡀⠀⢸⠀⠀⠈⢦⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡟⠁⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⠀⠀⠢⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧
⠀⠀⠀⢀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠛⠛⠛⢻⣿
⠀⠀⠠⡀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⣤⣤⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⡀
⠀⠀⠀⠱⠈⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣼⣿⣿⣧⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠛⠛⠢⡈⢀⢂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠂⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣠⣴⣾⣶⣦⣤⠋
⠀⡤⠊⠉⠉⠉⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠤⡀
⠀⢃⠀⠀⢀⠛⡄⠀⠀⡸⠀⠀⠀⠀⠀⠀⠉⠀⢻⣿⣿⣿⣿⣿⣿⡏⠈⠉⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠐⡄
⠀⠀⠉⠉⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⠿⣿⣿⠿⠛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⡀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠉⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠘⠀⠀⠔⠀⠀⠀⠑⠀⠀⠀⠀⠰⠌⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡂
⠀⠊⠈⠂⠐⠁⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈
⠀⠐⠐⠁⠀⠀⠁⠀⠀⠀⡀⠀⠄⠀⠀⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠤⠐⠀⠀⢀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠆⠀⠀⡾⢷⠀⠀⣠⣭⣤⣥⣤⣤⣤⣤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠄⠀⠀⠀⠧
⠀⠐⠈⠂⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣨⣷⣗⣔⣼⣧⣿⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠁⠀⠀⠊⠈⠀⠀⠀⠰⠆⠀⠀⢨⡉⡥⣬⢠⡤⣄⣤⢠⣤⡶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⡀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣷⡇⣿⢸⣷⡟⣿⢸⣏⡟⢶⠀⠀⠈⠀⠀⠁⠀⡂⠀⠀⠀⠠⠄⠀⢀
⠀⠛⠉⠛⠚⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠛⠘⠃⠛⠙⠛⠉⠛⠛⠠⢀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠃⠈⠡⠀⠸⠿⢿⠸⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠆⠀⠠
⠀⠀⣀⠀⠀⠒⠄⠃⠀⠀⠀⠀⢠⡇⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⡠⠒⠂⠂⠀⠀⠀⠀⠀⠀⢡⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠠
⠀⡀⠀⢠⠀⠀⠀⢠⠒⠌⠁⠢⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠤
⠀⠀⠀⠐⠀⠀⠀⠸⡄⠀⢄⠰⠀⠀⠀⠀⠀⠀⠦⠠⠦⠃⠀⢀⠀⠀⠀⠀⠠⠐⠀⠈⠀⠀⠀⠐⠀⠀⠘⠉⣩⡉⠙
⠀⢀⠀⣠⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⢈⠀⠐
⠀⡤⡄⢠⡤⠀⣠⡀⣠⣤⡀⣠⡄⢠⣄⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠰⡦⠀⠀⠀⠀⠀⡠⠔⠈⡆⠀⠀⠱⡒⢒⠒⠲
⠀⣧⡇⢸⠒⠀⠿⡅⣿⢼⠁⣿⠂⣽⠒⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠂⠄⠂⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠂⠐
⠀⠓⠃⠘⠓⠀⠛⠋⠋⠘⠀⠛⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠄⠠
⡟⠉⣻⣛⣛⣛⣻⣟⣻⣛⣻⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣟⣻⣿⣟⣟

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠒⠒⠒⠂⠉⠉⠉⠉⠉⠉⠉⠉⠐⠒⠒⠒⠠⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⢖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⠂
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⣀⣠⢤⠤⠖⠒⠒⠒⠋⠉⠉⠉⠉⠙⠓⠒⠒⠒⠦⢤⢄⣀⡀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢻⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠼⠄⠀⠀⠼⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⠀⠀⠀⠤⣀
⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠧⠤⠤⠤⠤⠤⠼⠤⠤⠤⠤⠤⠤
⡇
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠚⠉⠉⠉⠉⠓⠲⢄⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⢀⣤⣄⠀⠀⣠⢤⡀⠀⠈⢢⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠸⣄⣸⠃⠘⣇⣠⠇⠀⠀⠀⠹⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢀⣀⡀⠈⠁⣀⣀⠈⠁⢀⣀⡀⠀⠀⢱
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠷⠃⣴⠋⠉⠉⠙⣦⠘⠾⠃⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡴⠖⠋⠀⠀⠀⠀⠙⠲⢦⠀⠀⠀⣸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⡇⠀⠀⣀⣀⣀⣀⠀⣾⣾⣶⠀⣠⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠛⠚⠋⠉⠁⠉⣭⣿⣿⣿⣿⣴⣧⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣄⣀⣀⣀⣿⣿⣿⣿⣿⠿⠿⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣻⣿⣿
⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⠔⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠤⠤⠤⢀⠔⢁⠀⠉⠒⠊⠁⢠⠀⠀⠑⠒⠚⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠎⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠈⠁⢢⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠒⠉⠀⠀⠀⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇⠀⠀⠴⠀⢙⠊⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠃⠀⡘⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣄⠀⠀⣀⠤⢄⡀⠀⠀⠀⣀⢄⡀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡠⠚⠋⠀⠒⠒⠒⠀⠤⠃⠀⠀⠙⠉⠀⠀⠀⠉⠒⠊⠁⠀⠀⠈⠙⠢⣄⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠇⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⢇⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣸⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢼⡄⢇
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⣠⣄⣀⣀⣀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣀⣀⣀⣠⡀
⠀⠀⠀⡶⠛⠛⠿⠿⠿⠿⠿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣿⣿⡿⠿⠿⠯⠭⠍⠙⡆
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⢻⠿⠟⣦⣨⠻⢿⡟⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣀⡆⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣧⣀
⡴⠋⠀⠛⠉⢁⣠⣇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣺⣀⡈⠙⠓⠈⠑
⡅⠀⠀⠀⠀⠉⢁⣀⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣤⣀⠈⠁
⠡⡀⠀⠀⠀⠀⠉⣁⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡉⠁⠀⠀⠀⠀⢀
⠀⠑⠤⣀⠀⠤⠤⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠤⠄⢀⡀⠴⠋
⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡉⠉⠉⠉⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠄⠀⠀⠤⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅
⠀⠀⠀⠀⠈⠉⠉⠀⠒⠒⠒⠠⠤⠤⠤⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡦⢀⣀⢀⠀⢼⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠤⠤⠄⠒⠒⠒⠂⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢀⣤⡶⢦⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⣴⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⣂⣀⣀⣠⣈⣀⠀⠀⠀⢀⣼⠿⠿⠛⠿⢿⣦⣀⠀⠀⠀⢢⠛⢀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠘⠈⠀⠀⠨⣿⠷⠊⢿⠿⠒⢿⡉⠛⠀⠀⠀⣿⡆⢊⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣟⢠⣤⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⣸⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⢨⡄⠀⠀⠀⠀⠀⠀⢀⠔⡶⣧⣩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠶⠟⠯⠻⢏⣄⠀⠀⠀⠀⠀⠀⠈⠒⡿⣯⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣠⣔⡠⢄⠀⢀⣠⠀⢀⠀⠁⠀⠀⠀⠂⠠⠀⠀⢩⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠂⠂⠘⠻⠛⠛⠛⠆⠀⠀⠀⠀⠀⠨⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠘⠀⠀⠀⠀⠀⠀⠀⢠⠂⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡠⣦⣴⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣟⡼⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⢶⣯⡟⣱⡟⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣶⣿⠿⢻⣿⣿⡇⢳⡘⢦⡀⠦⣄⣀⣀⣀⣀⣀⣤⣦⣤⣶⣿⣿⡧⠆⣴⣿⠭⢻⣿⣿⣶⣛⠿⣿⣶⣦⣤⣀⡀
⠀⠀⢀⣀⣤⣶⣿⠟⠯⠊⠁⡄⠨⠭⣲⢿⡇⠸⠣⠀⠙⢦⡈⠙⠻⡿⢿⣿⣿⣟⣿⡯⠻⠍⢁⣾⣿⣿⡍⢸⡏⣿⣿⣿⣹⢽⣭⣻⢿⣿⣽⣿⣶⣤⣀⡀
⣴⡾⠿⠿⣛⣻⣬⡭⠡⠌⠄⠀⣤⢾⡯⢸⡗⠐⠁⠀⠀⠀⠙⢢⣀⠀⠀⠀⠁⠀⠀⠀⣠⣶⣿⣿⢿⣷⣤⣼⡧⣯⣿⠿⣿⣿⢿⣾⠯⢛⣿⣿⣿⣿⣿⣿⣿⣶⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠠⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠉⠉⠛⠿⣷⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣴⣾⠟⠋⠉⠉⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣄⠘⢿⡿⠃⠻⣿⠿⢁⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⣴⣿⣷⡄⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠙⢋⣤⣾⣿⣿⣿⣿⣦⡈⠋⠁⠀⠀⠀⠀⠀⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣄⠀⠀⠙⠻⠿⠿⠟⠻⠿⠿⠟⠁⠀⢀⣤⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣀⠀⠀⣠⣴⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢠⣶⣶⡆⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⠻⠿⠃⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣶⣤⣤⣤⣤⣤⣴⣾⣿⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣛⣛⣛⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡀⠀⣀⠤⠀⠐⠀⠐⢂⠒⠲⣄⠐⢠⣀⣀⠀⡂⠀⠀⢀⡀⠀⢀⢀⡀⠀⠀⢂⣀⠐⠀⠀⠀⠀⠂⢀⡀⠀⠐⢀⡀⡂⠀⠁⣀⠈⢂⠀⣀⡀⠂⡀⠀⢀
⠐⡴⠊⠁⠤⠐⠀⢘⢁⣈⣤⡀⡸⠀⠀⡿⣽⣿⣿⣿⠀⡾⢷⣿⢻⢿⣾⣿⣷⢠⣿⡟⢿⢳⣷⣾⣷⣾⢿⣿⡟⠀⣿⠿⣿⡟⢿⡿⣿⠀⣾⡇⠂⠀⠐
⠈⢇⠀⣦⠴⠒⠟⠋⠉⣁⠄⠊⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡤⣤⣤⣀⠀⢠⣍⣀⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠
⠀⠀⡤⣵⡾⠿⠿⠿⣷⣦⣀⣤⠀⠀⠈⠠⠀⠁⠀⠀⠠⠈⠤⠈⠀⠄⠀⠀⠙⠖⠛⢿⠛⠐⠋⠛⠉⠛⠠⠀⠠⠀⠀⠄⠀⠠⠀⠠⠀⠠⠄⠁
⠀⠀⣰⣿⡧⠸⣿⡈⣼⣿⡭⠀⠀⢸⣿⢶⡾⢶⣾⣶⣶⠰⢶⡶⣶⣶⣶⡆⠶⢦⢿⢾⣶⣶⡷⢰⡶⢶⡇⢶⣾⡶⠷⣶⢰⡶⢶⡷⠴⢶⡷⡶⢆⣠⣤⣌
⣤⣤⣤⣭⣴⣿⡯⠄⢽⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠤⢧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡾⠿⣿⣶⣤⣤⣤⣾⡋⡈⢹⣧
⠉⠉⠉⠉⠉⡹⡱⣶⠌⠹⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠄⠤⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⢠⢿⡉⠉⠉⠉⠉⠉⠔⠛⣉
⠀⠀⠀⠀⡴⠐⠀⠉⠀⣁⠘⠆⠰⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠐⠇⠰⢠⠀⣰⡄⢀⠀⠀⠀⠀⡋⠘⠃⠀⠀⠐⠒⠉⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠤⡟⠛⡯⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣾⣤⣤⣾⣿⣧⢀⠒⠠⡄⠀⠸⠀⠀⠀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠤⠤⠶⠿⠾⠏⠤⠤⠴⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠇⠛⢻⠲⡄⠀⢐⠃⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠖⣄⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈
⠀⠀⣤⡀⣤⣠⣄⠀⠘⠈⢋⡀⠈⠉⠉⠉⠙⠁⠁⠀⡙⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⢠⠦⢤⡤⡤⠀⠀⠀⠀⣀⡀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠘⠰⠶⠶⠰⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠻⠿⠿⠐⠀⠀⠀⢠⠀⠀⠀⠀⣾⠋⠛⣦⡄⠐
⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠈⣹⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⢿⣤⡀⠙⠁⠀⣐⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠘⠀⠀⡖⠀⠀⠀⠀⢀⣤⣾⠗⠐⢋⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢀⣀⣀⣀⡀⠈⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⡀⠈⠀⠀⠀⠀⠀⠈⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⡴⢶⣦⠀⠀⢠⣞⢦⡀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠘⢦⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠓⠀⠀⢸⠁⢰⡀⠀⠀⠀⠀⠐⠉⠟⢛⠀⢀⠀⠀⠐⠟⢠⡟⣸⠀⠀⠀⠀⠁⠹⠆⠀⠀⠈⢢⡶⠂
⠀⠀⢀⡄⡀⠀⠐⠶⠒⠒⠃⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⢰⡋⡀⠀⢀⣀⡀⠀⡠⠤⠈⠀⢧⠉⠀⠀⠠⠤⠗⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢁⡂
⠀⠀⢈⠀⠡⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠉⠉⠋⠉⠀⠀⠀⠈⠓⠱⠈⢠⣤⠄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠀⠤⠉⠀⠠⢄
⠀⠀⠘⠢⢀⣅⠀⠐⠸⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠁⠀⠤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⠒⡒⣦⠀⠀⠀⠀⠀⠀⠀⠁⢠⡄⣤⡜⠑⠁⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠀⠿⠀⠀⠀⠀⠈⠈⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠈⠀⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠲⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣰⠄⠀⡀⠀⠀⠠⣖⠉⢻⣤⠶⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠋⣹⡆⠠⠦⠀⠀⠀⢀⣴⣶⣦⠀⠄⠀⠠⢀⠀⠀⠀⠀⠈⠘⠃⠀⡰⠀⡜⢢⠀⠀⠀⠆⠀⠀⠀⠈⠁⠈⢷⠀⢾⠃⠊⠘⠁
⠀⠀⠀⠀⠀⠀⢸⣷⡟⢃⠀⠀⠀⠀⠀⠀⢸⡿⣻⣷⡄⠀⠀⠈⠐⠡⠀⠀⠀⠀⠀⠀⠈⣷⣾⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⡅⠀⢸⣤⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠒⠀⢸⣷⠹⣯⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⢀⡀⣿⣧⣬⡆⠀⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠰⠉⠇⠀⠀⠠⠀⠁⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠎⠰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢻⡄⠀⠀⡠⠊⠀⠠⠀⡀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⡤⠘⡇⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠄⠀⠀⠀⠀⣴⠃⢰⡟⢣⠎⠀⡠⣄⠀⠀⠀⠀⠴⠀⠀⠀⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠐⠁⣴⣏⠓⢠⠀⢰⡇⠘⢣⡀⠀⠀⠀⡇⠀⠀⠀⡦⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠏⢱⠆⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠈⢀⠀⣹⡶⠊⣀⢠⡄⢸⠇⠀⠀⠀⠀⠀⢠
⠀⠀⣠⡀⠐⠀⠀⠤⠴⠶⠦⢀⡀⠀⠀⠀⢠⣞⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠘⠋⠁⠀⠁⠘⡇⡀⠀⠀⠀⠀⠀⠀⢸
⠀⢰⣍⣁⣀⣀⠀⣀⡀⢀⣀⣼⠇⠀⠀⢠⠿⠋⢠⡄⠀⢀⡴⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⢺⣇⠀⢠⠀⠀⠀⡀⠈
⠀⠀⠈⠉⠉⠛⠛⠛⢿⡋⠉⠀⠀⠀⢀⣸⠆⠀⣬⠁⢀⣾⠃⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠈⣦⠈⠀⢀⠀⣠⡀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣄⠀⠀⢸⡏⣶⠀⠸⢿⡿⠁⠀⠀⠀⠀⠆⠀⠳⡀⠀⠀⠀⠀⠙⢰⡆⢸⡂⢹⡇⠸⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠷⢦⣴⣏⡹⣶⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄⠀⠀⠀⢸⡇⢸⡇⢹⣁⣀⣅⠀⠀⢠⠈⠁⠀⢸⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠞⠁⠀⡀⠀⠀⠀⠠⣌⡙⢿⣩⡟⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠆⡀⠀⣾⡆⣸⢇⣸⠋⠻⠏⠀⠀⠀⠀⠀⠀⠈⠀⢠⡞⢛⣿
⠀⣠⠴⠞⠛⠉⠁⣀⣈⡙⣳⠄⠀⠀⠙⠻⢦⡹⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⣶⠈⣇⠋⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣾⠃⣼⣿
⢄⡁⠀⠄⠰⠾⠛⣻⣯⡙⠋⠀⠳⣤⠆⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⣾⠋⢻⣿⠀⣾⠀⠀⠀⠀⠀⠀⢀⣴⣄⣿⠃⢰⣿⡟
⠘⠿⠖⠀⠀⠀⢾⣉⢀⠐⢠⠒⠑⢉⣠⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⢸⡇⢸⣧⣄⢸⠆⠀⠀⠀⣀⣶⡿⠛⠉⣿⢀⣿⣿⠁
⠀⠀⠀⠀⠀⢠⡄⠉⠙⢶⠄⡉⠐⢈⢰⣿⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⡇⠀⢿⠙⠀⠀⢀⢀⣿⠟⡡⠀⠀⠀⠙⠾⠟⠁
⠀⠀⠀⠀⠀⣨⣇⠀⠀⠀⠙⠻⣦⣄⣘⢿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠴⠂⠀⣿⡆⣼⠂⣰⠞⣠⠞⠁⡴⠁
⠀⠀⠀⠀⢀⡟⠈⢷⠀⠀⠀⠀⠈⢻⣿⣣⡘⠿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢿⣀⡟⠶⢡⡾⠃⢠⠜
⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⢻⣿⣿⣤⣿⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠆⠸⠇⠀⠀⠀⠀⣿⡧⡌⣴⠏⢀⣴⠁
⠀⠀⠀⠀⢸⠇⠀⠈⠉⣆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠰⠄⠀⠈⠀⠀⣸⠇⡼⢃⣤⣿⡇
⠀⠀⠀⠀⠀⣶⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠈⠙⠻⣧⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠊⣻⣿
⠀⠀⠀⠀⠀⠈⡀⢀⡀⣆⡀⢵⣆⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⡀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈⣱⠔⢫⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣉⢠⡄⠺⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⢦⣽⣉⣿⣿⣷⣆⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣆⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⡄⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⣘⣻⡇⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⡀⠉⡄⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⢹⡆⠀⠀⢹⣆⠸⠃⠀⠀⠰⣧⣿⡿⠀⠀⠀⢰⣿⠀⠀⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⢹⣆⠀⠀⢿⡀⣱⠂⠀⠀⠛⣿⡏⠀⠀⠀⣾⠇⠀⠀⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⢻⡆⠀⠘⣧⠿⡀⠰⢞⠃⣿⡧⠀⠀⢸⣿⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠈⢻⡄⠀⢻⣦⠿⢀⠚⢿⣿⣧⠀⢠⣾⠇⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠘⢿⣄⠀⣿⣰⡏⠀⢾⣿⣿⠀⣸⡿⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠘⢹⡄⢹⣿⡁⠀⠺⣿⣿⣶⣿⠇⠀⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⢈⣵⡦⣿⣇⠀⠄⢹⣿⣿⣿⠀⣸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡟⣧⡀⣀⢷⣾⣿⠀⠚⣿⣿⣿⠃⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⢿⡔⢯⣽⡇⠸⠿⢿⡿⠀⣇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣿⡘⢯⠃⣼⡷⢺⣇⢣⣜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡼⠷⠾⠆⠈⠉⠋⠙⣾⣃⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⢠⠄⠀⢤⠤⣄⣀⣈⡹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠐⠒⠀⠀⡄⠘⣯⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢆⠘⠿⠈⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣀⣠⡀⣠⣿⠟

⠀⠀⠀⣀⠤⠒⠉⠉⠉⠉⠑⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢠⠞⠁⠀⠀⢀⣀⣀⣀⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡈⠲⡀
⢠⠃⠀⠀⡠⠊⠁⠀⠀⠀⠈⠲⡀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⠀⠀⠀⢀⡽⠀⠈⠢⡀
⡆⠀⠀⢰⠁⠀⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠑⢄⡴⠋⠀⡠⠒⢦⡈
⡇⠀⠀⢸⠀⠀⠀⠀⠉⠉⠉⠀⢀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠑⢤⠊⠀⠀⠀⠉
⢱⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠳⡀⠀⠀⠈⠒⠀⠄⠐⠊⠁⠀⠀⡠⠂⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢄⠀⠀⠀⠀⣠⠦⡠⠃
⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⠀⣀⠠⠊⠁⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠑⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠈⠢⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠐⢄⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠈⢢⣀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⠔⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⢀⠔⠁
⠀⢀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠿⢧⣠⠀⡠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡰⠀⠁⠀⠀⠀⠄⠀⠀⠀⡠⠂⠁⣀⠴⠋⠁
⠂⠄⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠑⡀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣄⡀⠰⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⢀⡠⠚⠁⠀⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠙⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠿⢿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀⣠⡴⠞⠋
⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠛⠀⠉⠘⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁
⠛⠿⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⡀⠴⠊⠁
⠀⠀⠀⠀⠉⠉⠓⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣶⣶⣦⣤⣠⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⢀⠄⠤⠒
⢤⡀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠘⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠒⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣶⣿⣿⣿⣿⣷⣾⣿⣿⣿⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒
⠠⠶⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⣤⠴⢲⡬⠥⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡐⠠⠤⢤⣄⣀⣀⡀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠠⠀⢈⣠⣴⣶⣿⣿⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡁⠈⠙⠛⠻⠾⢳
⠀⠀⠀⠀⣀⡤⠄⠒⠊⠀⠀⢂⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠙⡿⠋⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⡤⠲⠚⣉⠥⠀⠈⠀⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣰⣿⣿⡷⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠤⠒⡉⠄⠂⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣹⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢄
⠂⡁⠀⠀⠀⠀⢠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣿⣦⣄⠊⠀⢿⣧⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣅⣿⣿⣿⣿⡗
⠄⠛⣿⣿⡷⣤⠀⠁⠣⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⢿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⡇








⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⡖⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠰⣷⡄⠀⠀⠀⠀⠀⢠⣦⠐⢰⠀⠀⠀⠀⠀⣠⡤⠄⡀⡀⢄
⠀⠀⠀⠌⠠⠒⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡘⣿⠒⠀⠀⠀⠀⠈⠊⢀⠐⢣⡴⠊⠀⠀⠀⠀⠀⠄⠚⠀⠒⢈⠀⠀⠀⠀⡌⠠⠀⡡⡌⢠⠤⠁
⠀⠀⠀⠀⢀⠢⠚⠷⠵⠀⠀⠀⠀⠀⠘⠁⠔⠛⠢⠀⠀⠀⠀⠀⢀⡬⠑⠊⢀⡀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠡⡐⠜⣈⠀⡀
⠀⠀⠀⠁⠀⡉⡀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢙⠈⢻⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠊⠀⠀⠀⠀⠈⠐⢄⣀⡠⠞⠀⠀⠀⠀⠀⠑⠀⠁⠐⠁

⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⣠⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⡤⠔⠠⢄⠀⠀⠀⠀⠀⠀⢠⢴⢄
⠀⠀⠀⣠⠀⠰⡃⠈⠊⡀⠀⠀⠀⠈⠀⠀⠀⣴⠃⢀⠀⠀⠀⢰⠁⡠⠂⠰⣄⠐⡀⠀⠀⠀⠐⠸⠈⠈⡄⢰⠀⠀⠀⠀⢀⠀⠈⡀⡦⠤⠷⠦
⠀⠀⢰⡤⠦⠶⠷⠃⢀⣣⠀⠀⠀⠸⡉⠀⠀⢉⠃⠉⠀⠀⠀⢃⠀⣄⠀⢀⡠⠄⣇⠀⠀⠀⠀⢠⠀⠀⠣⡜⠀⠀⠀⠀⢀⡀⠚⠃⡀⠠⣀⠄
⠀⠀⠀⣉⡛⠘⠉⢛⣈⠁⠀⠀⠀⠀⠈⢲⡖⠁⡆⠄⠀⠀⠀⠘⢦⡀⠁⠈⣀⡴⠃⠀⠀⠀⠀⢠⠰⠴⠄⡤⠀⠀⠀⠀⠋⠉⠉⠉⠉⠂⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠈⠉⠉⡩⡉⡆⠀⠀⠀⠀⠀⠀⡇⢀⠐⠀⠀⠀⠀⠀⠀⠀⠌⢀⡀⠡⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⡀⠀⠀⠀⠀⡠⢤⡀⠀⠺⠃
⠀⠀⠀⠀⠈⠀⠑⠁⡇⠀⠀⠀⠀⠀⠀⡇⠀⣄⠀⠀⠀⠀⠀⠀⣈⣀⢡⡌⣄⡁⠀⠀⠀⠀⠂⠀⠀⠀⡌⠹⠄⠀⠀⠀⢤⡴⠦⢧⠤⢭⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠠⣠⠇⢀⠴⠦⠀⠀⠀⠀⠈⡈⡕⠂⠐⢺⠁⠁⠀⠀⠀⠀⠀⠀⣀⢸⡆⠍⠀⠀⠀⠀⡽⠃⠀⠘⢯
⠀⠀⠀⠈⠃⠐⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠓⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⢀⠀⣀⠐⢀⣀⣀⠀⠀⠀⠀⠀⡄⠀⠚⡆⠀⠀⠀⠀⠈⠀⠠⢀⠀⠅⡀⠀⠀⠀⢀⠄⠀⡰⢠⠠⠻⣅⠀⠀⠀⠀⢠⠎⠀⠈⢣
⠀⠀⠀⢀⡀⣛⢉⠙⠛⠘⠀⠀⠀⠀⠀⠠⢐⠸⡇⠀⠀⠀⠀⠀⠐⢀⡠⠀⠄⠃⠀⠀⠀⡀⠀⡠⠤⠥⠥⠡⢉⠀⠀⠀⠀⡆⠀⡇⡁⠀⡆
⠀⠀⠀⠁⠑⠀⠉⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠐⢄⡀⠔⡀⢈⡆⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠦⣸⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠬⠆⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠈⠀⠀⠀⠀⠀⠀⠞⠃

⠀⠀⠀⣠⠞⠁⠑⢦⠀⠀⠀⠀⠀⠀⡀⠀⠐⡠⢁⡄⠀⠀⠀⠀⢸⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠌⠣⠀⠀⠀⠀⠀⢘⠉⠉⢉⡙⠀⢀
⠀⠀⠀⠀⢠⠈⡂⠀⡇⠀⠀⠀⠀⠢⠩⡀⠄⢤⡈⠀⠀⠀⠀⠀⢘⠀⠜⢋⡄⠀⠀⠀⠀⠀⠀⠫⠂⡄⠀⠄⠀⠀⠀⠀⠨⠀⠀⢸⠀⠀⠉
⠀⠀⠀⠲⣄⢲⢀⠴⠁⠀⠀⠀⠀⠀⠑⠒⡆⡖⠊⠀⠀⠀⠀⠀⠈⠁⢰⠠⠌⠂⠀⠀⠀⠀⠀⢸⠉⡖⢄⡄⠀⠀⠀⠀⠀⢄⡀⡈⠀⠀⠈
⠀⠀⠀⠀⠀⠸⠀⠈⠚⠀⠀⠀⠀⠀⠀⢠⠶⢦⠈⠠⠀⠀⠀⠀⠀⠀⠸⠤⠛⠇⠀⠀⠀⠀⠀⢰⠉⡆⠀⠁⠀⠀⠀⠀⠀⠀⠱⠁⠉

⠀⣠⠴⠤⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡀⠀⢀⡤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠶⠤⠤⠤⠦⣄⠀⠀⡤⠤⠤⠶⠤⠤⣴⣤⣤⠦⠦⠦⠤⠤⠶⢤⡀
⠀⡇⠀⠸⣭⠗⠒⠒⠒⣦⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⠀⠀⠀⠀⠀⢀⣀⣀⠤⢄⣒⣒⡪⡍⣿⢸⡆⢸⡇⠀⠀⣀⠴⢋⠤⠤⠼⠃⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⣸⣉⣇⠀⠀⠀⠈⠔⠠⠀⠀⠀⠀⠀⣿⠀⢻⠀⠀⠀⢰⣫⠗⠒⠊⣿⠁⠀⠀⠀⠃⠗⢸⡁⢸⣇⡤⠚⣡⠞⠁⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⡇
⠀⣧⠋⠀⠀⠀⢹⡄⠀⢐⠈⠀⠀⠁⠀⠀⠀⣿⠀⣿⠀⠀⠀⠸⢛⡤⠴⠆⣿⠂⠀⠀⠀⠀⣷⢸⠂⢸⣇⡤⠊⠀⠀⠀⠂⠀⠂⠐⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠋⠉⠉⠉⢹⡆⠀⠨⣸⠭⠭⢭⣉⣉⡭⣿⠀⣿⠀⠠⠤⢚⣱⠀⠀⠀⣿⡿⠀⠀⠀⠃⣯⢸⠂⢸⡏⠀⠀⠀⠀⠠⠀⢠⠤⣺⠭⣍⣉⣉⣒⡩⡇
⠀⣿⠀⠀⠀⠀⢸⡇⣀⠤⢊⡵⠆⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠸⣚⠤⠄⠀⣿⠁⠀⠀⠀⠃⣿⢸⡆⢸⡇⠀⠰⠆⠀⢰⠉⣁⠤⢛⡶⠆⠀⠀⠀⠀⡇
⠀⣿⣤⣤⣤⣤⣼⢃⣗⣫⠥⣂⠀⠀⠀⢀⡤⣿⠀⣿⢠⡦⠤⢚⣱⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⢸⠇⢸⡇⠀⡠⢄⠀⡎⢨⢗⣫⠥⣂⠀⠀⠀⢀⡤⡇
⠀⡿⣄⣀⣀⣀⣸⠿⢥⣒⡫⠵⣂⡤⠖⠁⠀⣿⠀⣿⠀⠀⠀⠘⠮⠭⠭⢍⣛⣓⣒⡒⠒⠖⡿⢸⠇⢸⡇⠀⠓⠚⠀⠈⠺⣥⢒⡫⠵⣂⡤⠞⠁⠀⡇
⠀⠳⢤⣤⣤⣤⣤⣤⣤⣬⣴⣭⣤⣤⣤⣤⡤⠏⠀⠘⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⡥⠞⠀⠈⠧⣤⣤⣤⣤⣤⣤⣤⣭⣶⣭⣤⣤⣤⣤⠴⠃
⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⡏⠀⠀⢀⠔⠒⠒⠋⠉⠉⠙⠲⢄⠀⠀⠀⣷⠀⣼⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢰⡇⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⡇
⠀⡇⠀⢰⠁⠀⠀⠀⣀⠀⢠⠀⠀⠀⢳⠀⠀⣿⠀⣿⠀⡰⠋⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⡏⠀⠈⣷⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⡆⡇
⠀⡇⠀⡇⠀⡸⠳⣤⡏⠢⠼⠑⢄⡀⠀⡇⠀⣿⠀⣿⢸⠉⠉⠉⠛⠢⢤⣀⣀⠀⠀⢀⡤⠤⣄⢸⡃⢸⡇⠙⠲⠖⠁⠀⣩⡃⡖⡶⡆⠈⠓⠶⠚⠁⡇
⠀⡇⠀⣇⣰⠁⢠⡄⢀⣀⠀⣴⠀⠉⣆⡇⠀⣿⠀⢻⡎⠀⠐⠠⠄⠀⠀⠀⠈⠉⠉⡇⠀⠀⠈⣾⡁⢸⠇⡞⠉⠙⣦⢀⣉⣁⣀⣀⣄⢠⠋⠉⠙⡄⡇
⠀⡇⠐⣅⠉⡟⠉⠉⠉⠉⠉⠉⠙⡏⠉⡽⠀⣿⠀⣻⢰⠐⠠⢀⠀⠀⠀⠀⢀⠀⠀⡇⠀⢀⡼⢸⠀⢸⡇⡇⠀⠀⡿⠘⠋⠉⠉⠉⠋⢸⡀⠀⠀⡇⡇
⠀⡇⠀⠈⠳⣇⠀⠀⠀⠀⠀⠀⠀⣷⠊⠀⠀⣿⠀⣿⠈⣆⠄⣀⠀⠀⠀⠀⡀⠀⠀⣇⠴⠊⠀⢸⡇⢸⡇⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⡇
⠀⡇⠀⠀⠀⠈⠓⢦⠤⠤⠤⡖⠋⠀⠀⠀⠀⣿⠀⣻⠀⠈⠓⠦⠤⠤⠤⠤⠔⠒⠉⠀⠀⠀⠀⢸⡇⢸⡇⣧⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⣇⣀⣸⠃⡇
⠀⢧⡀⣀⣤⣒⣒⣇⣀⣀⣀⣝⣒⣒⣄⣀⣀⠟⠀⠹⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼⠁⠘⢇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣭⣽⣿⣿⣿⣿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠛⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢿⠀⠀⢸⠀⠀⢸⠿⢿⣿⡿⣋⣥⣬⣭⣭⣭⣭⣭⣭⣭⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣷⠖⠛⠓⠶⣏⠀⠈⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⠁⠀⠀⠀⠀⠘⣷⣾⣿⢸⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣄⣀⡀⠀⢀⣿⣿⣿⢸⣿⣿⢸⣿⣿⡟⢻⣿⣿⣷⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣬⣉⣁⣤⣾⣿⣿⣿⢸⣿⣿⢸⣿⣉⠁⠀⣉⣿⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⢸⣿⣿⢸⣿⣿⣧⣼⣿⣿⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃


⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣛⣻⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠒⠛⠉⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣼⣢⠀⠀⠀⠀⠀⣀⣤⠶⠶⠦⠀⠀⠀⠀⠀⣠⡶⣶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⣿⡇⣴⠟⠀⢀⣁⣴⣤⣤⡀⠀⣀⠀⠀⢠⠀⣴⣭⡄⠤⢬⡄⠀⠀⠘⠦⠄⠀⠀⢰⡃⢌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣿⣿⠃⠀⠀⠀⠋⠀⠀⠀⠉⠅⢿⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣧⣼⠁
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠈⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡿⠟⠛⠀⡀
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠐⠄⠙⣿⠀⠀⠀⣀⣤⠶⠶⠃⠀⣄⠀⠀⠀⠀⢁⡀⡙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣰⠏⠀⠀⠋⢀⣄⡀⣤⣤⡄⣀⠑⠄⡤⠞⠁⠙⠁⢀⣀⣀⡐⠂⢤⠀⠀⠀⠀⠀⢃⠀⡄⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡟⠀⢀⣌⡠⠉⢌⡢⠜⠹⠇⢩⡇⢰⡀⢀⡀⢈⣧⠀⢹⡄⠀⢈⠚⠣⠀⠀⠀⠀⠈⡄⠁⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⠈⠙⠁⠀⠺⣿⡶⠶⠶⡿⠟⠛⠋⠉⠩⠥⠥⠤⢶⣢⣤⡾⠂⠀⠀⠀⠀⠀⠀⢸⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠈⢹⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠰⡟⠿⢟⣶⠷⠶⠶⠶⢶⣿⣿⠿⢣⡎⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠁⠀⡀⠀⠀⠀⠀⠙⢀⠀⠈⠉⠛⠛⠋⠉⠉⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠀⠲⠶⠶⠖⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⣠⠞⠁⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠔⠆⠀⢰⣯⠅⣰⣄⢀⡆⡀⠀⣀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠁⠀⠀⠀⠙⠀⠚⠑⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠘⠛⢉⡝⢿⡷⡷⠀⠀⠂⠀⡀⠐⠠⠄⣀⡀⠀⠀⣀⣤⡞⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠸⢷⠀⠚⢀⡠⠤
⠀⠀⠀⠠⠖⠒⠚⢿⢂⡶⢀⠔⢩⠃⡘⠋⠀⠆⠀⠠⠉⠀⢒⡖⠂⠁⠀⡈⠁⠀⠁⠀⠀⠀⢸⠒⠒⡀⢢⠈⣕⡀⣜⠱⠂⠂⠘⠀⠑
⠀⠀⠀⠀⢀⣀⣀⣟⢶⠖⠉⠀⢾⣤⠀⢀⠀⠀⠀⠋⠄⠀⠙⠓⢠⢄⣶⡃⡠⠀⣶⡒⠉⠀⣶⢀⡜⠀⢸⠀⠄⢁⠿⢈⢁⠃⡋⠀⠀⢠
⠀⠀⠀⠀⠀⡇⢤⠤⠬⠇⢒⡁⠉⣁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⠀⠀⠀⣤⠛⠗⠶⠶⠂⢾⠀⠀⢸⠀⡃⠀⢸⢸⢠⠁⡆⠀⠄⢠
⠀⠀⠀⠀⠀⣇⠉⠁⠀⢀⡿⠁⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠘⠙⠂⠀⠘⠀⠆⠀⠀⡜⠀⢧⠀⡼⠘⣴⠠⣇⢀⡆⠘⡀
⠀⠀⠀⠀⠀⡏⣽⠉⠁⠹⡦⣴⣿⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⢒⠒⠀⢣⣀⡀⡖⠐⠐⠶⠂⢸⠇⠀⠠⠤⠤⠄⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠉⠨⠰⠯⠀⠀⠀⠐⠚⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢤⠞⢃⠀⡠⠀⠀⠈⠘⠛⠚⠀⠀⠀⠀⠀⠀⠀⠶⠂⠂⢀⠀⠀⠉⠉⠁⠐⠒⠠⠄
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢨⡁⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠰⠀⠄⠎⠈⠈

⠀⣠⣤⢀⡀⣤⣤⠀⠀⢀⠀⢠⢀⠀⠀⡀⡄⠀⢀⠀⠀⢀⠀⣀⢀⢀⠀⠀⣀⠀⠀⢠
⠀⢛⠋⢊⡄⣛⡛⠀⠘⠈⠀⠈⠘⠀⠁⠀⠀⠃⠉⠈⠁⠀⠀⠈⠀⠐⠀⠀⠉⠑⠀⠀⠘
⠀⣔⣈⠉⢤⡄⣠⠀⠐⠀⠈⠚⠑⠠
⠀⠛⠛⠐⠀⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢤⡈⠀⠒⢀⠄⠀⠀⠀⢠⡶⠆
⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⠀⠀⠀⠀⠐⠚⠃⠀⠐
⠀⠀⠀⠀⠉⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⢄⠀⠋⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠦⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⣄⠀⠀⠀⠀⠀⠀⠠⠐⠢⡀
⠀⠀⠀⠈⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡁⡀⠀⠀⠀⠀⠀⠰⣀⢠⠁
⠀⠀⠀⠀⡐⠉⠀⠈⢁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢠⠐⠒
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠉⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⣀⢠
⠀⠀⠀⢀⡅⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠄⠀⠀⠄⠀⠀⠁⠉⠀⠀⠉⠈

⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠤⢀⡀⠀⠀⠀⠁⠈⠉⠛⠲⣦⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠄⠀⠀⠀⠀⠀⠈⠐⣄⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢸
⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⣼⣿⣠⣤⣤⣄⠀⢠⣶⣶⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⢸
⠀⢸⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⢻⣿⠁⠋⠉⠈⠀⠀⠈⠉⠀⠠⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢸
⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⡀⣤⣀⣤⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠰⢶⠿⠛⠛⡻⠒⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠙⣷⡀⠈⠳⠿⠟⠃⠀⢀⣼⠏⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣦⣀⣀⣀⣠⣴⠟⠁⣼⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⡀⠀⠀⠁⠀⠀⠀⢀⣠⣤⣶⣿⣿⠏⠹⡏⢭⠉⠉⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠐⣠⣾⣿⣿⣿⣿⡿⠃⠀⢠⣶⣆⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⢸
⠀⢸⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠁⠀⠀⣸⣿⡟⠀⠠⠾⠿⠟⠛⠛⠛⠛⢉⣉⡉⠉⠭⠅⠀⠀⣿⣷⢸
⠀⢸⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠃⠀⢰⠀⢀⡀⠠⠤⠀⠀⠒⠒⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢸
⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠁⡇⢸
⠀⢸⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⡆⠀⡇⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⣉⡉⠁⠢⠀⢀⣾⢀⣾⢸⠇⢸
⠀⢸⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⡇⠀⡇⠀⠀⠀⢹⣵⠂⠄⠀⠀⡅⠀⠀⠀⠘⠃⢸⣿⣼⢟⢸⠀⢸
⠀⢸⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⢣⡶⣄⠀⡀⠾⡺⣄⠀⠀⠀⢸⣿⡟⠀⢸⠀⢸
⠀⢸⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⡇⢠⠀⣀⣤⣤⢄⡀⠙⢆⡐⠋⠉⣡⣾⣆⠀⠀⢼⣿⣷⠰⠼⠀⢸
⠀⢸⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⢠⠀⢸⢸⣿⢿⣿⣾⡻⣵⣦⡈⠙⠷⢿⣿⣿⣿⡖⣾⣿⡏⢸⣿⠀⢸
⠀⢸⣀⣠⣸⣿⣿⣿⡟⠀⠀⠀⠀⢸⠀⢸⠘⠿⢾⣿⣼⡗⡿⢾⣿⣤⠀⠀⠻⢿⣾⣳⣿⣿⡇⢸⣿⠀⢸

⠀⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⣴⣶⡀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆
⠀⠀⠀⠀⢴⣿⣭⣿⡦⠀⠀⠀⠀⠀⣼⣿⣽⣷⡄⠀⠀⠀⠀⢀⣼⣯⣿⣄⠀⠀⠀⠀⠀⠺⣿⣿⣿⠇
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠉


⠀⠀⠀⠀⢠⣼⣿⣧⣄⠀⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⠀⠀⣠⡾⣦⣀⠀⠀⠀⠀⠀⠀⣠⣿⣄⡀
⠀⠀⠀⠀⠙⢿⣶⡿⠋⠀⠀⠀⠀⠀⠙⢿⣾⠛⠁⠀⠀⠀⠀⠈⠙⣷⡟⠋⠀⠀⠀⠀⠀⠈⠙⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢴⣾⠿⣷⣦⠀⠀⠀⠀⠀⣶⣿⢿⣶⡄⠀⠀⠀⠀⢠⣤⡿⣧⣤⠀⠀⠀⠀⠀⢰⣾⠿⣷⡆
⠀⠀⠀⠀⠈⣿⣿⣿⠇⠀⠀⠀⠀⠀⠸⣿⢿⡿⠀⠀⠀⠀⠀⠀⢼⠿⢿⠅⠀⠀⠀⠀⠀⠐⢿⠿⡿⠂


⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⢺⣿⣛⣿⡗⠀⠀⠀⠀⠀⣻⣿⣻⣿⠀⠀⠀⠀⠀⠀⣿⣟⣿⡇⠀⠀⠀⠀⠀⢸⣿⣛⣿⡇
⠀⠀⠀⠀⠙⠻⣿⠟⠋⠀⠀⠀⠀⠀⠙⠻⠿⠛⠁⠀⠀⠀⠀⠈⠉⠻⠋⠉⠀⠀⠀⠀⠀⠘⠻⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣿⣶⣤⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⣿⡟⠻⠟⠻⠟⣿⣿⡿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⢁⡤⠅⠀⠀⠀⠀⠘⠛⠀⣸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⢠⣶⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡏
⠀⠀⠀⠀⠀⢀⡤⠶⠒⠚⠛⠛⠛⠓⣦⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢿⠶⣄
⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣤⣤⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⢷⣄⣀⡰⠀⣀⣤⣤⡀⣠⡾⡋⠁⠀⠈⢳⣄
⠀⠀⠀⢀⣞⡿⣧⣭⣥⣤⣼⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⣸⣟⠯⠊⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⢸⢸⡅⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣰⠆⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠈⢧⡽⠏⠉⠉⠙⢳⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠶⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⠀⠀⢀⡴⠛⢳⠀⠀⠀⠀⠀⣠⣴⡋⢠⡾⠁⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠘⣷
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⣾⠤⠖⠋⠀⠀⠀⣴⠞⠁⣈⣿⠏⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢻⡄
⣏⡉⠳⣄⠀⢠⠖⢦⡀⠀⢀⡇⠀⢸⣤⣤⣤⣄⣠⣤⣤⣤⠴⠿⣤⡾⠋⠉⠻⣦⡀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠉⠓⠺⠇⠈⠲⢤⣳⡀⣸⠇⢀⣼⣶⣄⣀⠈⠁⠀⠀⠀⢀⣀⣿⣄⠀⠀⠀⠈⠛⢦⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠈⢳⣦⣄⠉⠙⠛⠛⠛⠛⠉⠉⠁⠙⢦⡀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢀⣀⣀⠀⠀⢻⣿⣞⣛⣋⡉⠉⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣬⡿⢦⣄⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢯⣡⠭⠟⠃⠈⣿⣟⣛⣩⡅⠀⠀⠀⢀⣴⠟⠉⠉⠉⠉⠉⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⢀⣠⢤⡄⠀⠀⠀⠀⣀⢹⣿⣭⣵⠞⣃⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣞⠉⣠⠎⠀⠀⠀⣠⠚⡿⠀⠀⠀⠙⠛⠉⠀⠀⣶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⣤⣤⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⠾
⠈⠋⠁⠀⠀⠀⠸⣅⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣈⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢲⠂⡘⡌⡀⠀⠀⢀⡠⠴⠦⣄⣀⠤⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠠⢨⣾⡇⡁⠐⠀⣰⡋⠀⠀⠀⠄⡴⠀⣸⠿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⡈⢇⣤⠀⡰⠋⠀⢎⢃⠀⣸⠋⠠⣀⠴⣒⣯⢰⣿⠓⠃
⠀⠀⠀⠀⠀⠀⢤⠤⠀⠺⠶⣄⢨⡇⠐⠀⢠⣀⠈⣄⣼⡋⠀⠀⠀⠈⡹⣿⠟⢰⣯⡍⠙⣆⡤⠒⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⣀⡨⢽⣧⣇⣰⠃⢈⡟⠁⢸⠀⠀⡄⢀⠔⠐⣙⣀⠀⣀⡠⠞⠉⣀⠘⠒⠁
⠀⠀⠀⠀⠀⢦⢀⣠⣴⠟⠉⠀⠂⠀⠀⠹⢖⡸⠠⢸⡡⣀⣠⠞⠁⡀⣰⣣⠔⠛⡉⠲⠄⠀⠂
⠀⠀⠀⠀⠀⡄⢠⣴⠋⠁⠀⢀⠤⢶⠂⡜⣑⢶⠹⣷⠙⡆⢠⣀⣀⠖⠻⠁⠀⠀⢀⣠⠆⠀⣠⠄
⠀⠀⠀⢀⠨⣄⠢⣉⠻⠒⠀⢈⠦⢶⠅⣆⠚⠿⠜⠚⡰⢁⡄⠈⠁⡀⠀⠀⠱⢶⣤⣴⡦⠾⠶⢤⡀
⠀⠀⠀⢬⠭⠀⡒⠂⠀⠤⢶⠚⠮⠴⠢⣤⢉⠀⠒⡀⡰⡄⠙⡖⠂⠀⠀⠀⠠⣧⡙⠙⠷⠶⠧
⠀⠀⠀⠠⢄⡭⠒⢰⠡⠢⠁⠀⠀⠂⠚⠀⡬⢀⢰⡇⢂⠏⠺⠡⣌⣁⣀⠀⠝⠛⠛⠂⠀⠄
⠀⠀⢀⣠⠄⣠⠎⡜⢠⣤⠁⠀⠀⠤⣪⣧⠹⡄⠂⠈⠃⠸⠀⠀⢘⣷⡄⠀⠛⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠊⠃⠜⠛⠛⡁⠀⠀⢹⣿⠂⠐⠄⠀⠀⠀⠀⢇⡴⠀⠛⣇⠈⡁⠀⡤⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡠⠐⠁⠃⠐⡄⠀⠌⣀⣱⣴⢾⣇⠀⠴⠘⣗⠀⠀⠉⠀⠀⠢⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⢠⠇⠀⢦⠀⡆⠀⠀⠈⢩⠛⠘⡷⠄⠐⠀⢹⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠑⠀⠂⠀⠇⢡⡀⠜⣟⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠸⡄⠘⠐⢻⢷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢤⣤⣤⣶⣶⣤⡐⠿⢂⣤⣶⣶⣤⣤⣤
⠈⠻⠿⠿⣿⣿⡿⣿⢾⣿⣿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠶⣶⣶
⠀⠀⠀⠀⠀⠽⠶⣿⠦⡍⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠿⠿⠿⣿⠿⠿⢿⣿⠿⠿⢿⣿⣿⣿⡿⢥⣿⠋⣻⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠏⠱⣿⠎⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠀⠀⢰⣇⠀⠀⢸⣿⣿⣿⡇⠀⡟⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋
⠀⠀⠀⠀⠀⠸⡄⠙⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⣷⣤⣾⠄⠀⠀⠀⠀⠀⢀⣴⣷⡻⣿⢿⣿⣶
⠀⠀⠀⠀⠀⠀⢈⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣵⢟⣻⠻
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠙⠛⠚⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣷⡀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠛⠿⠷⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⣛⣻⣿⣿⣿⡃⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿
⠀⠀⢰⣿⣿⣿⣿⣯⣽⣧⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⣿⣦⠀⠀⠀⠐⠒⠛⠛⠛⠶⠶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿
⠀⠀⠈⠿⣦⣤⣤⣤⣄⠈⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⢰⣶⡆⠀⠶⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⡖⠂⠀⠀⠐⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⣳⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣦⡀
⠀⠀⢀⡼⠁⢧⡀⣴⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡦⠞⠱⠒⢦⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣆
⠀⠀⢸⣷⣶⣶⡇⣿⠍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡽⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⠴⠲⡘⢆⣠⣿⣄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡉
⠀⠀⢸⡿⠿⠿⡇⣿⣃⣿⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⢠⠏⠉⠻⠇⠀⠀⠀⠀⠀⠀⢠⣶⣧⣀⠴⠁⠀⠙⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠘⠧⠤⠴⠇⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠠⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣶⣝⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠿⠿⠿⠟
⣀⡠⠖⡤⡀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣿⣿⣿⣿⠀⠀⠀⢴⠖
⣷⣶⣶⣾⣩⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢯⣄⡀⢶⣶⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠉⠻⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⡀⣀⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣧⢒⣣⣿⣷⡂⡀⡀
⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣾⣿⣿⣿⣿⡆⢓⠺⠏⣿⠿⠓⠶⣄
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣾⡟⣐⡲⣾⣕⣒⣒⡢⢤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠚⣿⡍⣿⢿⣿⣿⣷
⣿⣿⣧⡀⢠⣌⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣾⡿⢿⣮⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⡋⠙⠶⢞⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⡟⠉⠀⠀⢀⡟⠀⠀⠀⠀⢀⣼⡿⡿⣿⠛⢿⣿
⣿⣿⣿⠿⢿⣿⣤⣿⣿⣿⣿⣿⣿⣿⠿⢿⡍⠙⡇⠀⠀⡄⠀⠀⠀⢹⣿⣤⣤⣤⣴⡿⠿⣦⡀⠈⠉
⡙⣯⣈⠀⠘⠛⢻⣿⣿⠝⠿⠻⠋⢁⠴⠖⠛⡆⡃⠀⠀⢸⣦⣠⣜⠈⣿⣿⣿⣯⠀⠀⠀⠀⠈
⣿⣿⣿⣷⡂⠀⠀⣤⣤⣤⣤⣤⣤⣾⣶⣶⣿⡇⣁⢤⣴⣿⣿⡿⢯⣄⣀⣨⣿⠇
⣿⣿⣿⣿⡃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠞⠋⠹⠀⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⢤⣀
⠟⡹⣿⣿⡅⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⡷⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠛⠷⣆⡀
⠀⠙⠺⢭⣇⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣟⢠⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛⠿⢵
⠀⠀⢀⣴⣤⣬⡉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⣀⠀⠌⣳⣄
⠂⠀⠀⠨⠍⠑⣲⡖⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⡿⠉⠁⠈⠀⠉⠀⠉⠙⠛⠛⠛⠓⠦⣤⣤⣤⣀
⣿⣿⠿⠶⠶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿

⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⡇⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣀
⠀⡇⠀⣠⡾⠛⠉⠉⠓⠶⠶⠾⠛⠶⠶⠖⠛⠉⠉⠻⣷⡄⠀⢸⠀⠀⡇⠀⢠⣾⠟⠉⠉⠙⠲⠶⠶⠛⠳⠶⠶⠚⠉⠉⠛⢿⣦
⠀⡇⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⣿⡄⢸⠀⠀⡇⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡆⠀⠀⠀⠀⢻⡇
⠀⡇⢸⡇⠀⠀⠀⠀⣟⢻⣾⡀⡇⠺⣍⢸⠏⣇⠀⠀⠀⢸⡇⢸⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⢸⡛⡷⡇⢸⢸⡇⡇⠀⠀⠀⠀⠈⡗
⠀⡇⠸⡇⠀⠀⠀⠀⡟⠉⠈⠉⠉⠉⠉⠈⠀⠉⠀⠀⠀⢸⠃⢸⠀⠀⡇⠈⣇⠀⠀⠀⠀⠀⢸⠋⠁⠉⠉⠈⠀⠁⠀⠀⠀⠀⢰⡇
⠀⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⠀⠀⡇⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⢸⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⡇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⠀⠀⡇⠠⡿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⠀⠀⡇⠀⢹⡄⠀⠀⠀⠀⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠠
⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⠀⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⠀⠀⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⠀⠀⡇⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠈⢿⣆⠀⠀⠀⠀⣀⣀⡀⠀⣀⣤⡀⠀⠀⠀⢀⣴⡟⠀⢸⠀⠀⡇⠀⢻⣧⡀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⠀⠀⣠⡿⠁
⠀⡇⠀⠀⠙⠻⠶⠖⠋⠁⠀⠉⠛⠉⠀⠉⠙⠲⠶⠟⠋⠀⠀⢸⠀⠀⡇⠀⠀⠙⠻⠷⠖⠋⠉⠀⠈⠓⠉⠀⠈⠙⠒⠶⠟⠋
⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢄⡀⠀⠀⠀⠘⢏⡿⣦⠀⠀⠈⠀⠈⣷⠀⠀⠀⠑⠀⠀⠀⠀⣿⠀⠀⠘⠠⢋⡟⠀⠀⣸⡏⡚⠁⠀⠀⠀⡴⠟⠁⠀⠀⡀
⠈⠳⡠⡀⠀⠀⠀⠙⡿⣧⡀⠀⠀⠀⠸⣇⠀⠀⠘⠀⠀⠀⠀⡇⠀⠀⠀⡜⣽⠁⠀⣰⢋⡔⠀⠀⠀⢠⠖⠀⠀⠀⠀⣴⠟
⢄⠀⠈⠑⢤⡀⠀⠀⠈⠊⣳⡄⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠇⠀⠠⢃⠊⠀⠀⠀⡰⠁⠀⠀⢀⡤⠊⢀⣤
⣥⠓⢤⠀⠀⠈⠄⡀⠀⠀⠀⠙⢆⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡎⠀⠠⠃⠀⠀⠀⠀⠈⠀⠀⢀⠔⠋⢀⠦⠋⠁
⢉⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⢆⠀⠀⠀⠀⠀⣀⣀⣀⡈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠔⠁⡠⠎⠁⠀⠀⢀
⠀⠁⠀⠈⠙⠠⢀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠈⠄⠀⣠⣴⣿⣿⣿⣿⣿⣶⣌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠿⠓⠀⠹⢿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉
⠛⠳⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⢀⠠⠐⠉⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠉⠓⠒⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⣦⣴⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⠀⣚⠉
⠒⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣏⢙⣋⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠
⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣭⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠤⣒⡤⠔⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠄⣀⣀⣀⡀⠉⠉⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣈⣡⣴⣶⣿⣿⣿⡇⠘⠻⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣌⡉⠉⠛⠛⠷⡲
⠀⢀⣀⠤⠄⠒⠈⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣨⣏⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⣋⣉⠤⠒⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢺⣿⡿⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠍⠐⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠲
⠀⣷⣤⡀⠀⢰⣧⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣿⣿⣿⡷⣤
⠤⢛⣿⣿⣦⡄⠓⠣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⢀
⠀⠀⣿⣿⣿⣿⣟⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢦
⣠⠎⢈⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⢀⡶⡫⠎⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠋⠊⠈⠀⠰⠟⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠿⠿⠻⠿⠿⠿⠿⠗

⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣤⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣭⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⡏⣿⡟⣴⣿⣿⣿⣿⡜⣿⡿⢋⡿⢹⣿⣿⣷⣌⣙⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⢳⡿⣱⣿⣿⣿⣿⣿⣧⣈⣵⠟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣷⠘⢃⣿⣿⣿⣿⣿⣿⣿⢏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣲⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣻⣿⣿⣛⣿⣿⣿⣿⣿⣿⣟⣛⣋⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣬⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠛⠛⠛⠛⠛⠛⠛⢳⡄⠀⠀⠀⠀⣴⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⢚⣓⣚⣛⣛⣛⣛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠚⢦⠀⣤⠤⠴⠛⠦⢼⡇⠀⠀⠀⣠⣿⢠⡤⠤⠤⠤⠤⠤⠤⢤⠀⡏⢩⣭⡉⢩⣭⡉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠈⢿⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⣿⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⡇⣿⠚⡇⣿⠚⡃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⣀⣀⣀⣀⣀⣸⠃⠀⠀⠀⡇⣿⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⡧⠀⠀⡇⣿⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠼⠧⡤⣤⣤⣤⣤⢤⣤⡇⣿⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⡇⢺⠀⡇⣿⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢿⣈⣉⣉⣉⣉⣉⣉⣉⠉⠀⣧⣈⣛⣁⣈⣛⣁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⢦⠀⠈⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡁⡈⢁⠉⡈⡈⢁⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠈⠁⠀⠀⠀⢸⡇⠀⠀⣀⣀⠀⠀⠀⠀⣻⣄⣄⣀⣠⣀⣀⣤⣤⣄⣀⣄⣀⣀⣀⣀⣀⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡆⠀⣠⠤⠼⠧⠤⠴⠧⠼⠦⣤⠤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠈⣣⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢠⡇⠀⠳⠤⣤⠤⠤⠤⠤⣤⣤⡼⠤⢵⡀⠁⠈⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠞⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⡇⠀⠀⣹⠘⠃⠛⠛⠃⠀⠀⠈⠘⠛⠃⠛⠘⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢤⢤⣤⠤⣼⠀⡇⢰⠋⣻⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⣀⣀⣠⠞⠀⡇⢸⠀⢼⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠬⠥⠤⠤⠞⠁⢸⠀⢸⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣸⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠲⡏⣹⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣰⠋⠉⠉⠀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠄⢀⡉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⡏⠉⠳⣄⣩⣭⣭⣍⣭⣍⠉⢉⣍⣭⣭⣭⣡⡞⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣿⡆⠀⠀⣾⣿⣿⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠋⠉⠙⠿⠟⠁⠀⠀⠙⠿⠟⠉⠉⠛⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣤⣤⠀⣠⣤⡄⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⢼⣿⣿⡷⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣴⣿⣎⠻⢟⣁⣙⠿⠋⣾⣷⡄⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠻⠿⢣⣾⣿⣿⣿⣿⣆⠻⠿⠁⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⠆⠀⠀⢀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⠀⠀⠈⠉⠁⠀⠀⠉⠉⠀⠀⢀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠿⣷⣦⠀⠙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠃⠀⠀⠘⣿⣇⠀⠈⠻⣿⣿⣶⣤⣤⣤⣤⣤⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⣴⠟⢋⣉⠛⢷⡄⠀⠀⢻⣿⠀⠀⠀⠈⠙⠻⠿⠿⣿⡿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⢸⡏⢰⣿⣿⣷⠈⣿⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠈⢿⣄⡙⠛⣁⣼⠏⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠈⢿⣷⣤⣀⣀⣀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠰⢾⣿⣿⠶⠀⠀⠀⢰⠞⠛⠛⠛⢲⡄⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⡀⣤⡾⠀⠀⠀⢰⡄⠀⠈⠂
⠀⠀⠀⠄⠀⠠⠄⠀⠀⠀⠈⢻⡷⠷⠛⠛⠀⠀⠀⠀⠁⣂⠀⠀⠀⠀⣨⠠⠌⠀⠀⠀⠀⠡⢌⡲⠞⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠶⠁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠰⡅⠀⠀⠀⠀⠀⠀⠀⣦⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢻⢿⣿⣀⠀⠀⠀⠀⠀⡄
⠀⠀⠙⠲⢤⣤⣶⣿⣿⣾⡭⠙⠃⠀⠀⢘⠀⠀⠈⠉⠉⠁⠀⠀⡇⠀⠀⠀⡿⠿⠙⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⣿⣿⡿⢿⣿⣅⠀⠀⠀⠀⢸⠀⠀⠠⢾⡷⠄⠀⠀⡇⠀⠀⠀⢣⡄⢠⠍⠋⢹⣿⢿⡄
⠀⠀⠀⠀⢾⡋⢿⡁⢸⣿⠃⠀⠀⠀⠀⠨⣀⣀⣀⣈⣁⣀⣀⣀⠇⠀⠀⠀⠈⠇⡆⠀⠀⠀⠙⠚⠹⠆
⠀⠀⠀⠀⠀⠓⠀⠉⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄
⠀⠀⢠⣌⣤⣍⣤⠀⠀⠀⢀⡴⠒⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠴⠋⠑⠒⠊⠱⠆
⠀⠰⡖⢾⠟⢳⠖⡖⠀⠀⠈⠀⠀⢠⡟⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⠁⢩⠆⠀⠀⠁⠀⠀⠀⡾⠿⢷
⠀⠀⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠈⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⢀⣀⡤⠖⠒⠛⠋⠉⠉⠙⠛⠒⠲⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⢀⡀⠀⢠⠀⠀⠀⢀⠀⠀⠉⢹⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠂⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⡀⠀⠀⠁⡀⠀⡄⠈⠙⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣠⣶⡟⠁⠤⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠟⢿⣿⣿⣿⡀
⠀⠀⠀⠀⣠⣾⣿⠋⠀⠐⠀⠀⠂⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡀⠈⢻⣿⣿⣇
⠀⠀⠀⣰⣿⣿⠋⠀⠤⠀⠠⡀⠠⠄⠀⠡⠀⠀⠠⠀⠉⠀⠀⠠⠀⠈⠀⠀⠀⠀⠈⠁⠀⠌⠀⠀⠉⠀⠀⣿⣿⣿⡄
⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⠆⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⣿⣿⣷
⠀⠀⢸⣿⣿⠁⠀⠀⠁⠀⠀⡄⠀⠁⠀⠀⢁⠀⠉⠀⠀⠀⠀⠨⠀⠈⠁⢀⠀⠁⠀⠀⠀⡅⠀⠈⠀⠀⠀⣿⣿⣿⣿⣇⡀
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⣿⣿⡟⠁⣷
⠀⠀⢸⣿⣿⡆⠐⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⡀⠀⠐⠀⠀⢀⠀⠀⣀⣤⣶⣶⣿⣿⣷⣶⣆⠀⠀⠀⠀⣿⣿⣿⡇⢠⡇
⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⠀⠸⢿⠿⠏⠉⠡⠤⠌⠉⠋⠀⠂⠀⠀⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠘⣿⣿⣆⠀⠐⠀⢀⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢰⣾⣿⠀⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠘⡇
⠀⠀⠀⠀⠘⣿⣿⡀⠀⠰⣿⡿⣟⠑⠀⣠⣤⡄⢀⠀⢀⡀⠀⢀⠀⠁⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠁⠀⠀⣿⣿⣿⡇⣼⠃
⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠅⠛⠙⠁⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋⠉⠁⢠⡇
⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠉⠀⢈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⠀⠠⠀⠀⠀⠀⠀⠄⠀⠶⠦⠤⠀⠀⠄⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠂⠀⠀⡀⠁⠀⠀⡗⠀⠀⠇⠀⠈⠀⠀⢀⣠⣤⣤⣧⣤⣄⣀⣁⠀⠀⠀⠀⠀⠈⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣀⠀⠊⣠⣴⣼⣶⣤⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠠⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠇⠀⠀⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣀⠀⠁⣿⣿⣿⡿⢟⠛⢋⡉⢉⢉⡁⠈⠁⣀⠰⢒⡽⠏⠀⡀⠄⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠂⠈⠉⠁⠰⢎⠒⠂⠄⠀⠖⠲⠐⠊⣁⠴⠋⠄⠀⠐⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠁⢆⠀⠀⠀⠀⠀⠑⡐⠒⠒⠒⢒⠚⠉⠁⠀⣀⠀⢀⠀⠀⡀⠀⢀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠄⠆⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠐⢦⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠃⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠉⠳⣄⠨⠀⠀⠀⠈⠀⠀⠀⠀⠁⣠⠎⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣌⠳⠦⣤⡤⠴⠶⠶⠶⠒⢋⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠲⠒⠚⠛⠛⠉⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⠀⠀⠀⠈⠉⠛⠻⠶⣦⣴⠶⠾⠛⠉⠉⠀⠀⠀⠀⠈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣀⣤⣤⣤⡶⣶⠀⠀⠀⠀⣶⢦⣤⣤⣤⣤⣤⣤⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣿⠀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠞⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⣠⣴⠶⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⠛⠟⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⣣⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡁⠀⡏⢹⣇⣴⠟⠛⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣈⡁⠀⠀⠀⠁⠀⠸⣇⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⣠⡶⠶⣤⣀⡀⣾⡁⠀⠀⠉⠛⠷⢦⣤⣀⠀⠀⠙⣧⡀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⢰⣯⠀⠀⠀⠉⠙⠿⢷⣦⣄⣀⠀⠀⠀⠈⠉⠛⠶⣦⣌⣻⣦⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠙⠷⢶⣄⣀⠀⠀⠀⠈⢉⣛⣿⣶⣦⣄⡀⠀⠀⠀⠈⠙⠛⢷⣄⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⢠⡾⠋⠙⠻⢶⣦⣾⠋⠉⠉⠉⠙⠛⠛⠛⠷⠶⠶⠶⣶⣦⣤⣤⣤⣄⣀⣀⡈⢻⣄
⠀⠀⠀⠀⠀⠸⣧⣀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠛⢷⣦⣄⡈⠛⠶⠶⠶⢶⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠉⠙⠛⣿⣶⣤⠶⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⡴⠶⠛⠋⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⢻⣄⠀⣀⣠⣤⡶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⢀⣠⣤⡿⠿⠛⠉⠁⠀⠀⠀⢀⣀⣤⣶⡾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⢠⡾⠛⠉⠀⠀⠀⠀⣀⣠⣤⡶⠾⠛⠋⠉⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠟⠉
⠀⠘⣷⣀⣀⣤⣴⣾⠿⠛⠋⠀⠀⠀⠀⢀⣀⣤⣶⡾⠟⠛⠃⠀⠀⠀⠀⢀⣠⣤⡶⠾⠛⠉⠁
⠀⠀⠀⠉⠉⠁⢸⣇⠀⠀⣀⣠⣴⣶⠿⠛⠋⠉⠀⠀⠀⠀⣀⣠⣴⠶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⢸⡇⠀⠀⢀⣀⣤⡴⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠟⠛⠉


⠀⠀⠀⠄⡗⢠⡀⣰⠒⠂⡤⢤⡀⠄⠐⠂⠀⣠⠀⣧⠀⠀⠀⡄⢠⠀⡄⠀⠠⠀⠰⠀⠴⡄⠈⠀⡘⠀⡀⢪⠦⢐⠀⠰⠂⣀⡴⡄
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣯⠳⡀⠛⠘⡂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⡃⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠰⡊⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠘⠀⠈⠁⠀⠁⠐
⠀⠀⠀⠀⢀⡀⠀⠀⠈⠀⠀⠀⢃⠀⠀⠀⠀⠀⢀⠀⡀⡁⠂⡀⠄⠀⠀⠀⢄⠀⠀⢀⠀⢁⡄
⠀⠀⠀⠀⢸⣷⠦⠀⡂⣄⣀⢠⠀⡄⠀⠀⠈⠀⢉⡄⢘⣶⢠⡁⡆⠊⠀⠨⠀⠀⡠⠃⠰
⠀⠀⠀⠀⠘⣿⣲⠀⠀⡀⢀⣑⠷⣌⠢⡀⢠⡉⠜⠑⠀⠀⠁⢱⠕⡊⠀⠘⠀⣼⠃
⠀⠀⠀⠀⠀⠈⠁⠐⠀⣀⠀⠌⠁⣘⡳⠮⠤⠇⠀⠀⠀⠀⠀⠟⠈⠁⢰⠆⡰⠁⡀⢀⣴⣃⣀⣤
⠀⠀⠒⠐⠀⠀⢈⡓⠀⠙⠓⢤⣶⣙⠁⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⣀⠜⢁⣼⣞⠉⠐⠄⠀⠁⠀⠈
⠀⠀⠠⠀⠀⠀⠠⣄⣀⣈⣀⣨⠝⠉⠠⡀⠀⠀⠀⢀⢹⣀⠀⠀⢀⡴⠃⠀⠉⢉⡀⠀⠈
⠀⠀⠀⠠⠒⠀⠀⡀⠀⠈⣴⡇⠀⠀⠀⢀⡀⠒⠲⠾⡭⠎⠉⠙⠡⣄⠀⠀⠀⣹⠋⠠⠚⢠⠀⢴⣶⡀
⠀⠀⠀⠁⡀⠈⠀⠀⠀⢄⠀⣀⠀⢀⣠⠂⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠻⢶⠞⠁⢠⠄⠀⢀⡠⠧⠸⠃
⠀⠀⠀⠢⠀⠀⠀⠜⢲⠶⠼⠛⠛⠉⠿⢲⣤⢄⡀⠀⠀⠙⠒⢤⣤⣄⣤⠑⠮⣒⠂⠐⡲⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠔⢀⡴⢊⠍⢠⠂⢢⠀⠀⠀⠀⠜⢀⠱⡙⣦⢽⣄⢉⠁⠊⠉⠠
⠀⠀⠀⠀⠀⠀⠠⠢⠗⠁⠀⠀⠈⠀⠰⡂⠱⡘⠀⠀⢤⡤⠀⠀⠋⡀⢱⠈⢀⢣⠳⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠄⢀⠀⠀⠀⢐⠂⠜⠀⢁⠃⠀⠀⠂⠁⠂⠀⠀⠙⠀⢧⡈⢈⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠰⠆⠀⠈⠀⠀⠐⠀⠀⠘⠀⠘⠀⠅⠰⠀⡰⠠⠆⠀⢀⠀⠈⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡏⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢠⡇⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠴⠛⢳⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠰
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠐⠀⢠⢠⠠⠠⠂⠀⠀⠀⠀⣀⡄⠗⡦⡤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠸⠉⠃⠀⠀⠀⠀⠀⠀⠉⢈⠁⠠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠆⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⢀⣘⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠂⠀⠀⠀⠀⠀⠀⠟⠀⠠⠀⢰⣷⡄
⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠐⠈⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠰⠤⠤⠀⠀⠀⠀⠀⠀⠀⠠⠤⠰⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⢄⣴⣠⣀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠁
⠀⠀⠀⠀⠘⠹⠁⠀⢻⡆⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⢹⡀⠀⠀⠀⠀⢰⣆⠠⠈⠂⠂⠀⠀⠀⠀⠀⠀⠀⢠⣤⣻⣿⣤⡀
⠀⢀⡀⡇⠀⠀⠀⠀⠈⡹⡆⠀⠀⠀⠈⠇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠉⢣⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠿⣶⣧⣀
⠀⠀⠄⠡⠀⠰⠶⠂⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⠿⠟⠟⠿⠟⠹⡿⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠐⠒⠂⠐⠀⠒⠒⠂⠀⠀⠀⠀⠀⠘⠓⠐⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠾⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡴⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠰⠆⠀⠀⠀⠀⠀⠁⠀⠉⠡⣀⠀⠀⠌⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠁⠀⠀⡀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⢤⠤⠿⠯⠬⠤⠤⠤⠤⠽⠤⠤⠤⠤⠼⠧⠤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀
⠀⠀⢀⣶⣿⣿⣿⣷⣆⠀⢸⣿⣿⣿⣿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣦
⠀⠀⢻⡟⠉⠛⠉⠉⠿⠀⠈⢿⠁⠀⠁⠀⠈⠁⠀⠀⠆⠀⠀⠀⡆⠀⠛⠁⠀⠀⠀⠘⠏⠀⠀⠀⠀⠈⠁⠀⠈⠉⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣴⣦⠀⠀⠀⠀⠀⠀⠈⢱⣦⡖⠐
⠀⢶⣀⣀⣹⣥⣤⣤⣤⣤⡄⠀⠀⠀⠄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧
⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡆⠀⠀⠲⡀⠀⠀⠀⠀⣿⢻⡇⠀⠀⠀⠀⠀⠀⣸⠟⠙⢿⡀
⠀⠀⠀⠀⢘⠃⠀⣃⠀⠀⠀⠀⠀⠀⠘⡉⣃⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⢀⡃⠘⡃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢁⠄

⠀⠀⠀⢯⠭⠭⠭⠭⠿⠀⠀⠀⠀⠀⠺⡭⠭⡭⠭⠿⠇⠀⠀⠀⠀⠸⠯⠭⠍⣭⠽⠇⠀⠀⠀⠀⠀⠿⠭⢭⡭⠽⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣼⣿⠀⠀⠀⠀⣠⡀
⠀⠀⠀⢶⣶⣶⣶⣶⣿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣶⣶⣶⣶⣿⡇⠀⠀⠀⠀⠀⠀⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⢠⣿⠃⠉⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⢿⣦⠈⣿⡆
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⠀⠀⠀⠀⠀⢠⣶⠿⠿⠿⠿⠿⠿⢷⣦⡀⠀⠀⠀⢠⣿⠃⠀⠈⣿⠀⢿⣇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⢻⣇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣿⡇⠀⠀⣸⡿⠀⠘⢿⣄
⠀⠀⢀⡀⠀⠀⢸⣷⡶⠿⣿⠀⠀⠀⢀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣼⣿⠀⠀⠀⢻⣧⣀⠀⠈⠁⠀⠀⠈⣿
⠀⣾⠟⠻⣷⡀⠀⣿⡄⠀⣿⡇⠀⠀⢠⣿⠉⠉⢉⣉⣉⣉⠉⠉⢹⣿⠀⠀⠀⠀⣿⡟⢻⣿⣦⣀⣀⣴⠿
⢸⣿⣄⣰⣿⠀⠀⠘⠻⠟⠋⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⠀⠀⠀⠀⣿⣇⢸⣿⠉⠻⠛⠁
⣾⡏⠉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠈⢻⡿⠃
⠻⣧⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⢾⣿⠆
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣼⣿⡿⠿⠿⠿⣿⣿⣤⣤⣄⣀⣀⣀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠛⠋⠉⠉⠁⠙⢿⣦⣀⣴⠟⠁⠈⠉⠉⠙⠛⠛⠿⢷⣤⡀
⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⣿⡇⠀⢸⣇
⠀⠀⠀⠀⠀⠀⣿⣦⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⢻⣿⠀⣿⣷⣤⣼⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⣸⣿⠀⣿⡇⠀⠸⣿
⠀⠀⡀⠀⠀⣸⣿⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⣿⣇⠀⢀⣿⡀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠂⠀⠘⠁⠀⠀⠂⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢀⣩⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣍⡀⢿⣷
⠀⠀⠀⠀⠀⠀⣼⣇⠈⠁⢛⡛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢛⡛⠈⠁⣸⣧
⠀⠀⠀⠀⠀⡀⠻⡿⢰⣿⠟⠁⠀⠀⠀⠀⠀⣼⣿⣿⡄⢠⣿⣿⣧⠀⠀⠀⠀⠀⠈⠻⣿⡆⢿⠟⢀
⠀⠀⠀⠀⠀⣿⣆⠀⣤⡶⠀⠀⠀⠀⢠⣤⣄⠘⢿⣿⠇⠸⣿⡿⠃⣠⣤⡄⠀⠀⠀⠀⣶⣤⠀⣰⣿
⠀⠀⠀⠀⢀⠙⠟⠸⢟⡁⠀⠀⠀⠀⢻⣿⣿⡇⢀⣴⣾⣷⣦⡀⢸⣿⣿⡟⠀⠀⠀⠀⢈⡻⠇⠻⠋⡀
⠀⠀⠀⠀⠸⣷⣄⢠⣿⠇⠀⠀⠀⠀⠀⠉⠉⣠⣾⣿⣿⣿⣿⣷⣄⠉⠉⠀⠀⠀⠀⠀⠸⣿⡄⣠⣾⠇
⠀⠀⠀⠀⢀⡙⠛⠈⢉⣶⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣶⡉⠁⠛⢋⡀
⠀⠀⠀⠀⠀⢻⣷⣄⢸⡿⣀⠀⠀⠀⠀⠀⠻⢿⣿⠿⠿⠿⠿⣿⡿⠟⠀⠀⠀⠀⠀⣀⢿⡇⣠⣾⡟
⠀⠀⠀⠀⠀⠀⣍⡉⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⢉⣉
⠀⠀⠀⠀⠀⠀⠙⠿⣷⣈⣛⣐⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣂⣛⣁⣾⠿⠋
⠀⠀⠀⠀⣀⣀⣀⡀⣿⣿⣿⡿⣿⢻⢛⣿⡛⣻⣿⢟⣻⡿⣿⣿⣿⢻⣿⡿⣿⣛⣿⣿⣿⣿⢀⣀⣀⣀
⠀⠀⠀⠀⠹⣿⣿⡇⣿⣿⣿⣷⣡⣿⣰⣿⣇⣿⣿⣜⣿⣧⣻⣿⣿⣿⣍⣇⣧⣻⣿⣿⣿⣿⢸⣿⣿⠏
⠀⠀⠀⠀⢠⣿⣿⣇⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣸⣿⣿⡄
⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠀⠐⠆⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⢀⢄⢄⠀⠀⠀⠀⠀⠤⡨⠒⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢠⣾⣎⣾⣦⡈⠀⠀⠀⠀⢨⣈⣡⠃⠀⠀⠀⠀⠈⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣿⣿⠇⢹⣿⣇⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢰⠉⠀⠑⠄⠀⠀⢰⣦⣴⣤⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠸⡩⠊⠢⡤⠎⠀⠀⠀⠘⣿⣀⣸⡟⠀⠀⠀⢀⣼⣿⣶
⠀⠀⠀⠀⠀⠢⡀⣀⠇⠀⠀⠀⠀⠀⠈⠛⠏⠀⠀⠀⠀⠘⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣠⠿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⣶⣾⣿⣿⣷⡀⠀⠀⠀⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⢰⠖⠒⠒⠒⠲⡆⠀⠀⠀⠻⡿⠿⡿⠃⠀⠀⢠⡞⠡⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⣸⠸⡆⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⢀⡤⢦⣄⠀⠀⠀⠸⣇⠀⠁⣄⣸⠃
⠀⠀⠀⠀⠀⠀⢧⣀⡼⠀⠀⠀⠀⠈⠴⠿⠷⠉⠀⠀⠀⠀⠛⠛⠛⠛⠃⠀⠀⠀⠈⠓⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣦⡀⠀⠀⠀⢸⣿⣧⣽⣿⠂⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡴⣏⣩⠙⢢⡀
⠀⠀⠀⠀⠀⠀⣿⢔⢼⡇⠀⠀⠀⠘⣿⠃⢹⣿⠀⠀⠀⠀⠀⠈⠣⡀⠀⠂⠀⠸⡇⠚⠻⣗⢠⡇
⠀⠀⠀⠀⠀⠀⠻⠶⠾⠃⠀⠀⠀⠀⠿⠇⠼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠬⠼⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠄⠀⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣷⣄⠸⣿⣿⣿⣿⣿⣛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⣿⡇⢰⣿⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡻⣿⣮⡻⣷
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⠙⠟⢃⣈⠻⠛⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣝⢿⣿⣮⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣠⣾⡟⠛⣷⣄⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡲⣌⢳⣼⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠉⠀⠀⠉⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡻⣿⣮⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣆⣀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⢿⡎⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋

⠀⠿⠿⢿⣦⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡸⠧⡀⠀⠀⠀⣀⣀⣀⠀⠀⣤⡄⠀⠀⠀⠀⣀⣀⣀⡠⠠⡐
⠀⢒⠠⠬⠛⣁⡈⠁⠀⠀⠀⠀⣀⣤⣆⣀⠀⢠⣤⣤⡄⠀⠀⠀⠘⠿⢏⠀⢀⣉⣁⡄⠀⠀⠀⣿⣿⣿⣧⡄⠀⠠
⠀⠀⠀⣴⣶⣾⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⡗⠸⠛⠛⠃⠀⠀⠀⣸⣷⣾⡆⢾⣿⣿⡇⠀⠀⠀⢸⡙⠻⠟⠁⠔⠁⠶
⠀⠀⢀⠹⠿⠿⠿⠿⠃⠀⠀⠈⠉⠉⠉⠉⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠁⠄⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⢐⠉⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣢⠀⠀⠀⠀⢘⠀⠈⡟⠑⠢⢀⣀⠀⠀⠀⣀⣇⢀⣿⣿⣿
⠀⠱⠊⠀⠀⠀⠀⠄⡴⢄⠀⠀⠀⠀⠀⠐⢙⠋⠃⠀⠀⠀⠸⢿⣝⡀⠀⠅⠠⠴⠾⠻⠀⠀⠀⢹⣇⣠⣽⣻⣏
⠀⠀⠀⠀⠀⠀⠈⣰⣁⡠⠃⠀⢀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢉⣧⠤⠜⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢠⣨⣭⣭⣥⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⣀⣤⣶⣷⣦⣄⡀⠀⠀⠀⡖⠒⣶⠒⢒⠒⣶⡒⢲
⠀⠀⠸⢇⣀⣀⠸⡄⠀⠀⠀⠀⠀⠘⢇⣀⣀⠸⠁⠀⠀⠀⠀⠘⢩⣩⡉⢉⣉⠉⢹⠁⠀⠀⡧⠴⣿⠦⢼⠤⣿⠦⢼
⠀⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠸⠘⢛⢃⢸⣿⠀⢸⠀⠀⠀⣇⣠⣿⣄⣸⣀⣿⣅⣸
⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠤⠬⠼⠾⠿⠤⠼⠀⠀⠀⠀⠀⠤⠼⠿⠧⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣒⡒⠢⣄⠀⠀⠀⠀⠀⣠⠔⠒⠒⠲⢤⡀
⣰⢿⣿⢷⡄⢠⣴⣤⠀⠀⠀⢀⣀⠀⢐⢆⣤⠀⢀⣀⠀⠀⢠⠋⣷⣆⣿⡅⣶⠎⢧⠀⠀⠀⡜⢹⣶⡄⠀⣶⣶⠹⡄
⠘⢿⣿⡾⠃⠻⣿⡿⠃⠀⠀⢨⣏⠠⣤⣤⣤⡦⣩⣏⠀⠀⢸⠰⡿⣾⠟⢷⡾⡷⢸⠀⠀⠀⡇⣼⣿⡝⠢⣽⣿⠀⡇
⠀⠀⠀⠸⣿⠆⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠛⠛⠀⠀⠈⢦⣰⣿⡷⣾⣷⡦⠋⠀⠀⠀⠱⣟⠛⠃⠀⠛⢻⡞
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣷⣶⣶⣯⣤⣤⣤⣤⣤⣤⣬⣽⣶⣶⣾⣥⣤⣤
⣿⣯⣼⣭⣬⣭⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢻⡀⠀⣀⡄⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⠷⢿⡉⠀⠀⠁⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⣏⠀⠀⠈⢷⠀⠀⢠⡾⠋⠉⠉⠉⠛⢦⣤⠞⠋⠁⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡶⠂⠀⠘⣧⠀⣾⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡤⠀⠸⡆⠸⣆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢀⡀⢻⡄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡋⠁⠀⣿⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⣿⠁⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣼⣦⠤⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⢻⡀⠀⣿⠀⠀⠀⢀⡶⠛⢳⡄⠀⠀⠀⢿⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⠇⠀⣿⠀⠀⠀⣾⠀⠀⠀⢹⡄⠀⠀⢸⡇⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣰⠇⠀⠀⠀⠀⢻⡄⢀⣼⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡤⠤⠶⠶⠶⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠭⣆⢸⢙⠠⡏⠇⠸⡅⢻⠀⡏⢱⢸⠹⠂⢯⡀⡇⡭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠁⠈⠁⠈⠀⠁⠈⠀⠉⠀⠉⠀⠀⠉⠁

⠆⢨⣅⣀⠁⣠⣃⡐⠲⣶⣐⠗⠈⠾⠶⠀⢀⣠⣶⡿⣷⣿⣿⡿⢿⣿⣿⣿⣿⣶⣄⡀⠠⠥⠰⢀⣶⡶⢃⣠⣀⣈⢃⣬⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣿⠟⠉⠀⠀⠀⠀⠉⠻⢿⣯⣭⣥⣄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣵⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡀⢀⡤⣤⡄⠀⠠⣶⣚⡃⠀⢠⣽⣿⣿⣿⣿⠀⠀⢸
⡀⠀⣀⢀⡀⣀⢀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⡆⠀⠘⠙⠉⠀⠈⠉⠁⠁⠀⡎⣿⣿⣿⣿⣿⠀⠀⢸
⠉⢪⠈⣉⠙⠈⠊⠼⣽⠁⠁⠀⠀⠿⣿⣿⣿⣿⣷⠀⠀⠀⢆⠀⠀⣀⣀⠀⠀⣱⣿⣿⣿⣿⡏⠀⠀⢸⠿⠙⢙⠛⠊⠀⢉
⠀⡛⡠⢍⢈⠃⠆⠀⢨⡺⠷⡀⠦⠘⣷⣝⢿⣿⣿⣇⠀⠿⢿⣿⣿⠟⠛⠀⠠⣿⣿⣿⣿⡟⠀⠀⠀⢸⠓⠙⡆⠁⡄⠆⣉
⠀⣠⠈⢩⠔⡢⠼⠓⠀⢰⠂⢱⡗⠀⠈⠻⣿⣶⣿⣿⣷⡀⠀⠀⠀⠀⢸⡖⣰⣿⣿⡿⠋⠀⠀⠀⠀⢸⢀⡁⠠⠐⠢⣐⠉
⠉⠐⠆⠀⡐⣁⡷⠄⡀⠝⠀⠼⠀⠀⠀⠀⠈⠻⢿⣿⣿⣏⠀⠀⠀⢒⣋⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠸⢌⡢⠀⠀⠀⡥⠩
⠀⡘⡄⠀⡉⡏⠈⠉⠁⠈⠃⠰⡆⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠚⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⣄⣦⣠⠶⡧⡏
⠃⡀⠀⠀⠄⠚⠀⠠⠐⣁⠆⢤⡜⡠⡠⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⣀⠀⣀⠀⢀⡀⢁⠐⠚⢘⡅⠁⠈⡶
⡇⣓⠀⠄⠀⠊⡅⡀⠁⠘⠇⠐⡃⢣⡇⠇⢀⡂⡘⠇⣂⢒⣐⢆⠔⢂⠦⠀⠀⠵⣷⠀⡡⡆⠒⠂⢀⠈⠐⠰⡖⢘⢈⣸⡇
⢡⣏⡁⢄⡀⠑⠀⠚⠢⢄⡁⠂⠆⠺⢘⡶⢣⠋⢹⡇⡏⡿⠘⣜⢄⡟⠘⡿⠎⣮⠠⢤⣷⠂⠸⠑⠀⠇⠀⡀⠁⡨⠤⡴⢹
⠈⠹⠤⠴⢢⠑⠎⣤⠃⡈⠃⡈⡀⠰⣼⣿⣸⣸⢩⡀⠐⡑⢴⡄⣢⡇⠜⣣⠘⢹⢸⠙⠉⠀⡀⢠⠀⠐⠠⠀⠈⣱⣤⡁⠈
⠐⠅⡀⠀⠂⣘⠖⠀⠋⠹⠀⠰⠁⠑⠀⠀⢯⡽⠀⠀⠀⠈⠊⠀⢈⢱⡏⢁⠘⠶⠋⠃⠀⠀⠍⠘⠙⢂⠀⣶⣞⡟⠁⢰⠟
⠁⣁⠑⠁⡀⠉⠐⠢⠐⣤⢴⠟⡩⠰⣦⢠⣴⠆⣀⡰⣄⠺⠵⡖⣦⣼⡅⣬⢰⠁⣤⠀⠀⠀⠀⠀⠐⠩⠐⣄⡟⠠⢈⡇⠙
⠎⠰⠆⠀⠀⠀⣄⠀⠀⢿⠀⠻⢷⡶⠟⣰⠃⠶⣼⠇⣇⣣⠀⡇⣮⣭⢥⡇⡏⠀⠅⡆⠎⢏⠈⠀⣀⠁⢀⠈⡆⠀⠊⠟⡶
⣚⠮⠎⣀⢠⠀⠋⠈⠂⠐⢀⠸⠵⢾⣿⢁⠺⡷⢻⣼⢰⣦⠑⣇⣤⣶⠆⡇⢇⣀⣠⢩⡗⠸⠠⣞⠀⠆⠬⠌⠠⡟⠃⢨
⢓⣤⠴⠀⠀⠀⡄⢀⠋⠐⠛⠂⣠⠈⢻⣽⢟⡥⢇⣩⠥⠻⠶⢻⢹⡯⠠⠷⠵⣿⡭⢼⣦⡆⠀⠶⠘⠁⠀⡀⢩⠇⡄⢡⠒
⢇⢘⠀⠀⠀⢀⠠⠜⠰⢑⠋⣌⠙⣂⢓⡢⡀⢀⡂⠀⠀⠀⠀⠸⡆⢀⠈⠈⠠⢤⡄⠀⠀⠠⠄⡐⡄⠀⡠⠀⠠⠀⠰⣤⢀
⠀⡈⠡⠄⠊⠈⠄⠀⠀⠀⠞⠓⠀⢡⣶⠟⣸⣠⢹⠀⠤⢈⠀⠁⡧⠔⡀⠀⠧⢲⡝⡒⣂⣴⢫⡅⡃⠈⠀⠃⠀⠆⡀⠀⢰
⠙⣗⠾⣁⢐⢃⠔⠀⢡⡄⠱⡄⠀⠸⡋⠲⠉⣹⢸⠃⣻⠂⡷⡂⣤⣈⠁⠞⡄⣈⢷⡑⡸⣿⣸⡀⠰⠦⠘⠀⠒⠀⠀⠀⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠰⣦⣀⠀⠀⠰⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠀⠀⣀⣴
⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠉⠳⠆⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢴⠞⠉⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠂⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⠉⠀⠀⠀⠀⠘⠉⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢸⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣴⠶⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠞⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡄⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠉⠲⠿⢦⡄⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣙⣒⠚⠒⢛⠇⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠘⢻⣤⣀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠡⠀⠀⠀⢈⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠲⠚⠛⠋⠉⢵⣶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡛⠁⠀⠁⠀⠈⠀⠀⠖⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢀⠢⠮⣙⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠄⣄⣐⣦⣤⣳⡾⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠿⠿⠟⠿⣛⣻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⣄⣙⣲⢮⣿⣿⠟⠋
⣤⣶⣶⣶⣿⣿⡿⢿⣭⡀⣀⢺⣶⣽⣥⣌⣭⣿⣷⣿⣦⣤⣤⣤⣤⣶⣶⣶⣾⠿⠛⠉⠀⠈⠉⠙⠋⠉⠁
⠙⠉⠉⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣶⣿⣯⣿⡿⠋⠉⠉⠉⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⡇⣤⣤⣦⣠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣸⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣌⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣷⣦⠼⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀
⠐⠶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⠻⣿⣿⠟⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣶⠶
⠀⠰⢤⣴⣶⣶⣶⣿⡿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⣿⣿⢀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠿⣿⣷⣶⣶⣶⡶⠆
⠀⠀⠀⠀⢬⣥⣴⣶⣾⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣶⣦⣤⡤
⠀⠀⠀⠀⠀⠈⠉⣭⣤⣶⡿⠿⣛⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠇⣿⣿⠸⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣮⣙⠿⢿⣶⣦⡬⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠋⠱⠿⠋⠼⠟⠹⠟⠙⠛⠁⠉⠁⠀⠀⠀⣿⣿⠀⠀⠀⠈⠉⠈⠛⠃⠻⠏⠻⠧⠙⠿⠎⠙⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣦⣤⣤⣤⣤⣤⣭⣭⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⣾⣷⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⠒⢶⠀⠀⠀⣿⣿⠀⣀⣀⡖⠒⠛⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠘⣿⣿⡗⣿⣿⣼⣿⣿⠁⠀⢰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⢻⡛⠃⣿⣿⠉⢩⡇⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣇⠀⠈⣧⠀⣿⣿⠀⡾⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣾⡄⠀⢸⣦⣤⣤⣼⠃⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢧⠀⠀⢿⠛⠛⡟⠀⠀⣼⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠸⡆⢸⠃⠀⢰⠃⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠀⠀⢻⡏⠀⠀⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡁⣇⠀⠈⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢸⡇⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇