Be mine Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤
⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠴⣲⣾⣶⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣤⣶⣼
⠀⠀⢀⣴⣿⣏⠀⠙⣿⣷⡄⠀⠀⢤⣿⣿⣿⣽⣿⣭⣿⡥⠀⠀⠀⠀⣠⣰⣶⡆⣄⠀⠀⠀⠀⠀⣿⣽⣿⣻⣿⡀
⠀⠀⠈⠋⠀⠙⢦⡞⠋⠙⠃⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣾⣿⠿⣿⡇⣿⣷⡀⠀⠀⠀⣿⣼⡇⠀⢸⢳⡀
⠀⠀⠀⠀⣠⡾⠃⠙⢦⣀⠀⠀⠀⠀⢨⢿⡿⡿⢟⡽⡅⠀⠀⠀⢨⣭⣭⣺⣀⡿⣭⣭⣅⠀⠀⠀⣿⣼⡇⠀⠀⡇⢣
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠁⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉⠉⠉⠀⠀⠀⠉⠈⠁⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⢀⣴⣾⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷
⠀⠀⠀⣘⣛⡱⣉⢎⣛⣃⡀⠀⠀⠀⠀⠰⣿⣿⣿⠆⠀⠀⠀⠀⠀⠈⠉⠙⡋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠿⢿⡿⡿⠻⠇
⠀⠀⢘⡏⠉⣭⠉⣭⠉⢹⡇⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣾⣆
⠀⠀⠈⢇⢀⡴⠶⢦⡀⡼⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⢱⣝⣽⢸⣿
⠀⠀⠀⠈⠓⠦⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠤⠿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠿⠷⠯⠷⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣟⡛⣻⣆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⣤⣶⣄⢀⣠⣤⡄⠀⠀⠀⠀⠀⢉⠙⠁⠋⠹⠀⠀⠀⠀⠀⣤⠛⣉⡀⣉⠙⢤⠀⠀⠀⠀⣴⣿⠟⣿⡟⠿⣷⡀
⠀⠀⠀⣛⣛⣋⠘⠛⣛⡃⠀⠀⠀⠀⠀⠈⢓⣲⣒⠁⠀⠀⠀⠀⢘⡇⠸⠛⣤⡼⠳⠘⡇⠀⠀⢸⣿⣥⣤⡻⢋⣤⣹⣷
⠀⠀⠸⠿⢋⣭⣤⡘⢿⣿⠂⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠈⣧⡀⠴⠋⠑⠄⣼⠁⠀⠀⠘⣿⣿⢋⣴⣮⣻⣿⠇
⠀⠀⠀⠀⠈⠻⠟⠃⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠛⠲⠖⠖⠛⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⠁⢸⣿⣿⠀⢠⠴⣤⡀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣾⣿⡇⠀⠀⠀⠀⣠⣾⠟⢢
⠀⠀⠀⠀⠀⠀⢀⠔⣿⣿⡄⡌⠀⣸⣿⡇⡰⠁⢸⣿⡇⠀⠀⠀⠀⠴⣄⠀⠀⠀⠀⢨⣧⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⢰⣿⣏⡠⠊
⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⣧⠁⠀⣿⣿⣷⠁⠀⣼⣿⡇⠀⠀⠀⢀⣬⣿⠀⠀⠀⢀⢄⣿⡀⠀⠀⢸⣿⡿⠀⠀⠀⢀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠹⣿⡇⠀⠀⣿⣿⠁⠀⠀⢠⠊⣿⣿⠀⠀⡠⠃⢸⣿⣦⠀⠀⣿⣿⡇⠀⠀⢀⠎⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠉⠁⠀⠀⣿⣿⠀⠀⡰⠁⠀⠘⢿⣄⠜⠁⠀⠀⠙⠃⠀⠀⣿⣿⠀⠀⣠⠋⠀⠀⠹⢷⣀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠉⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⡞⢀⣶⡟⠃⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠉⣾⡏⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣿⡇⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⣠⡶⠒⢦⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣠⠖⣷⡄⠀⣰⡿⠁⢀⠆⠀⠀⣾⡋⡇⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⢹⣷⠰⣿⡇⠄⠁⠀⠀⠀⠘⡿⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⡠⢾⡿⠀⣿⡅⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡜⢀⡿⠃⠀⠘⢧⡀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠁⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡄
⠀⢀⡤⠒⠦⣄⠀⠀⠀⠀⠀⠀⢀⠎⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣾⡇
⢰⠃⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⡞⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣿⡇⠀⠀⠀⠀⠀⢀⣠⣀
⡎⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⠃⢸⣿⡇⠀⠀⢀⠀⠀⠀⡀⠀⡎⠀⢸⣿⡇⠀⠀⠀⠀⣴⡿⠁⢨⠇⠀⢀⡀
⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡘⠀⢸⣿⡇⠀⠀⣬⠅⠀⡞⢻⣶⠁⠀⢸⣿⡇⠀⠀⠀⣼⣿⠃⣠⠎⠀⠀⣿⡟⠀⡼
⢣⠀⠀⠀⠀⠀⢸⣿⡴⠻⣦⡇⠀⢸⣿⡇⠀⢸⣿⠀⢰⠇⢸⣿⠀⠀⢸⣿⡇⠀⠀⢰⣿⡯⠚⠁⠀⠀⠀⣸⠃⠉
⠘⣆⠀⠀⠀⠀⢸⣿⡇⠀⣿⠁⠀⢸⣿⡇⠀⢹⡇⠀⣸⠀⢸⣿⠀⠀⣸⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⡰⠁
⠀⠈⠀⠀⠀⠀⠸⣿⠇⠀⠛⠀⠀⢸⣿⡇⠀⡘⢷⣠⠏⠀⠘⠟⠀⠀⣿⣿⠀⠀⠀⢠⠿⣧⣀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⡸⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠿⠛⠛⠛⣻⣿⣄
⠀⠀⠀⠀⢀⣴⣿⣿⠟⣋⣤⣦⠀⠀⢠⣿⣿⣿
⠀⠀⠀⢀⣾⣿⠟⠁⢰⣿⣿⣿⠀⣰⣿⣿⣿⣧⣤⣄⡀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣷⣶⣄
⠀⠀⢀⣾⣿⠋⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⡿⠿⢿⣿⣦⡀⠀⠀⣰⣿⣿⣿⠟⠉⠀⢹⣧
⠀⠀⢸⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⢨⣿⣿⡄⢰⣿⣿⣿⠏⠀⢀⣠⣾⠏
⠀⠀⠈⠛⠀⠀⠀⠀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡷⢸⣿⣿⣿⠶⠿⠟⠋⣁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠸⣿⣿⡇⠀⠀⠀⢰⣿⣧⢀⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠏⠀⠀⠹⣿⣇⠀⢀⣠⣿⣿⠇⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣠⣾⣿⣿⣿⠋⠀⠀⠀⠀⠈⠻⠿⠿⠟⠛⠁⢸⣿⣿⣿⡟⠀⣀⣄⠀⠀⣀⡀
⠀⠀⣠⣤⠀⠀⠀⠀⢿⣿⣿⡏⠀⠀⣠⣼⣿⣿⣿⠟⠁⠀⣴⣶⣄⠀⠀⠀⠀⠀⠀⣤⣄⣾⣿⣿⠏⠀⢰⣿⣿⣧⣾⣿⣿⠂
⠀⠀⢻⣿⠀⠀⠀⠀⠀⠉⢛⣡⣴⣾⣿⣿⡿⠛⠁⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠁⠀⠀⢾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠙⠳⣶⣶⣶⣶⣿⣿⡿⠿⠟⠋⣡⣤⣤⣀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡀⠀⠀⠈⠙⠁⣀⡀⠀⠀⠸⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢀⣾⠟⢩⣿⣿⣿⡆⠀⢰⣦⣄⠀⠀⢘⣿⣷⣆⠀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⣦⣄⣾⡏⠀⣼⣿⣿⣿⡿⠀⣾⣿⣿⡆⠀⢸⣿⣿⣿⣾⡿⠁⣾⣿⣿⣿⠀⠀⣠⣾⣿⣿⡿⠿⣦
⢀⣶⣿⣿⣶⣄⠀⢰⣿⢟⣿⣿⣿⡿⠀⢀⣿⣿⣿⣿⡇⢠⣿⣿⣿⡇⠀⢸⣿⣿⣿⡿⠁⣰⣿⣿⣿⡏⢀⣾⣿⣿⡿⠋⠀⠀⣼
⣼⣿⡏⠀⣿⣿⣇⣿⡟⢸⣿⣿⣿⡇⠀⣼⣿⣿⣿⡿⠀⣸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠁⢠⣿⣿⣿⣿⠁⣼⣿⣿⣿⠁⢀⣠⣾⡿
⢻⣿⡇⠀⣿⣿⣿⣿⠇⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⠇⠀⣿⣿⣿⡇⠀⠀⣾⣿⣿⡇⢀⣾⣿⣿⣿⠃⢰⣿⣿⣿⡷⠾⠟⠛⠁
⠈⠻⣷⡀⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⡏⠀⣸⣿⣿⣿⠁⠀⣰⣿⣿⣿⠀⣸⣿⣿⣿⡏⠀⢸⣿⣿⣿⠀⠀⠀⢸⣷⣄
⠀⠀⠈⠉⢸⣿⣿⣿⠀⢸⣿⣿⣿⠃⠀⣿⣿⣿⠁⣰⡿⢻⣿⣿⡀⣴⡿⣿⣿⡟⢠⣿⣿⣿⡿⠀⠀⠈⣿⣿⣿⠀⠀⣠⣿⣿⡿
⠀⠀⠀⠀⠸⣿⣿⣿⠀⠸⣿⣿⣿⠀⠀⠻⢿⣿⣶⡿⠁⠀⠉⠛⠿⠋⠀⠈⠉⠁⣾⣿⣿⣿⠃⠀⠀⣰⡿⢿⣿⣤⣾⣿⡿⠟⠁
⠀⠀⠀⠀⣦⣄⣉⣉⣀⠀⠈⠛⢃⣀⣀⣀⣤⣬⣥⣴⣶⣶⣶⣾⣷⣶⣄⠀⠀⢰⣿⣿⣿⡟⠀⠀⣰⡟⠁⠀⠈⠛⠛⠉
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠻⢿⡆⠀⢸⣿⣿⣿⠃⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣾⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⠠⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣥⢀⣀⠨⠝⠚⢕⣪⢕⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠒⡀⠀⠒⠢⠭⣅⡈⣵⡮⣗⠮⣐⠄⠀⠀⠀⠀⢀⡠⠬⣝⣓⡒⠦⣈⠭⢐⡲⢀
⠀⠀⠀⠀⠀⠀⢐⠡⠀⠀⠈⠅⢦⠅⣒⠮⣝⣲⢷⣽⣀⠅⣤⣀⣀⣒⡂⠩⡅⢒⣢⠄⢙⣊⢉⡠⠝⠂⠊⠄
⠀⠀⠀⠀⠀⢀⡄⠥⢔⣈⠉⠉⠉⠓⢲⣿⣔⣮⣕⡨⢛⢯⣳⣟⢓⣰⠄⠌⣀⢂⠉⠍⣀⠬⠑⠌⠠⡐⠀⠐⢄
⠀⠀⠀⠀⠀⠈⠂⠀⠋⠖⡩⣥⡬⠉⣓⡯⢟⡫⣷⢽⣺⣗⣾⣳⣿⡯⠍⢄⡁⢒⠲⢯⠁⢛⠄⠉⠀⠀⠂⠀⠄⠁
⠀⠀⠀⠀⠀⠀⡀⡀⠀⠘⣢⢽⣉⠉⣐⠯⣗⢯⣻⣝⣿⣛⡗⢾⣷⡾⣛⠁⢨⠗⠠⢀⠤⡈⠃⢀⠁⠈⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠸⢷⠄⠸⢡⣈⡴⣛⣲⣙⡻⢽⡺⣿⣿⡿⣿⣿⣿⣟⣯⣅⡨⠓⠉⠀⠀⠢⡀⠊⡀⡠⡃⡠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣬⠙⢘⢻⡶⠤⣉⣓⣿⣻⣿⣿⣿⣿⣿⡺⣿⡿⣄⠁⡀⡐⠄⢑⢄⡄⢴⠕⠑⠀⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣠⣸⣿⣾⣼⣡⣤⣼⣳⣽⣿⣿⣿⣿⣿⢗⡿⢩⡂⠘⠈⠈⠀⠣⠈⠁⠆⠀⡰⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣰⠃⢷⢿⣶⣻⣷⣽⣿⣿⣿⣷⣽⣿⣗⣿⣿⣽⡐⠂⠀⠀⠄⢀⠀⠂⠊⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠲⢧⠼⣿⡶⣶⡦⡀⣹⣿⡻⣽⣿⣿⣿⣿⣟⠿⡟⣫⣿⣳⠠⡀⠀⠀⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡟⠀⢌⠈⠉⠨⣿⣛⣿⣽⡿⡿⢿⡿⣿⣧⣧⣺⡇⡥⢠⠀⠈⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠱⣀⣟⣬⣿⣽⣿⣿⣾⣿⣿⣶⣿⣞⣏⣍⡔⢠⠄⠏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡋⠾⢛⣽⣿⣿⠂⠩⠿⠿⣉⠱⣄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⡛⣿⢶⢼⣟⣾⣙⡠⠂⠏⠴⠈⠂⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢊⢰⠛⡷⠻⣪⡝⢃⠀⠊⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣠⠀⢠⠀⣤⠀⢠⢠⡖⠒⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡖⠋⢳⠀⢸⠉⠉⠀⠀⠀⠀⢸⢷⠀⡿⡇⢸⠀⢻⢇⢸⠸⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⠯⡀⢸⠤⠤⠀⠀⠀⠀⢸⡀⢿⠁⡇⢸⡆⢸⠘⣶⡀⡆⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡿⢸⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡇⠈⡇⢸⠀⠹⠇⠧⠤⠄⠀⠠
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠰⠷⠶⠞⠁⠘⠒⠒⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠠

⢀⠂⠀⠠
⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⣀⡤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⣷⡀⠀⢠⣿⣿⢃⡾⣫⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⠲⢤⣰⡇⢀⣿⠃⠀⣾⣿⣿⠏⠘⠿⣿⠁⠀⣠⣴⣶⣄⠀⢠⡶⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠙⠀⣼⠏⠀⢸⣿⡿⠃⠀⣀⣤⣾⡇⣰⣿⣿⣫⠞⠀⢸⡇⣸⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⢰⡟⠀⣀⣀⠉⠁⣴⠟⢁⣾⣿⠇⣿⣿⠁⢀⡴⠀⢸⡇⢉⣠⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠈⠻⠁⣸⢿⣿⣧⠀⠻⢶⠿⠟⠁⠀⠈⠛⠚⠉⠀⠀⠘⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⢠⣤⡀⢠⡏⢸⣿⡿⠀⢀⡲⠀⠀⠀⠀⠀⣴⣿⣶⡄⠀⢠⣶⣶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⣿⣼⠀⣾⣿⡇⢠⣿⣿⠀⢸⣿⣷⣸⠃⣿⣿⡇⠀⣿⣿⡧⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⣿⣿⡇⠀⣿⣿⠃⢸⣿⣿⢀⡾⣿⣿⡏⠀⣿⣿⡇⢸⣿⣿⡀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠉⠋⠀⠀⣿⣿⠀⣼⠿⣿⠞⠁⠀⠉⠀⠀⢿⣿⢀⡟⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡷⠃⣾⣦⣠⣾⣷⠀⠀⠀⠈⠙⠋⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡜⣮⣧⣀⣀⣤⣤⣤⣤⣤⡄⠻⣿⣿⣿⠇⠠⠤⠤⠤⠤⠤⠤⠤⠤⠬⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠐⠫⠞⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠉⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢀⡤⢄⠀⠀⠘⠷⠶⠶⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡾⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⡇⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢸⡴⠃⣠⣤⡀⠀⠀⢠⠴⠒⣆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⢿⠀⡾⠁⠀⣿⠀⣰⠏⢀⣠⠏⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢠⠃⢸⣼⠃⢀⡤⣿⠒⡟⠋⠉⠀⠀⢀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠘⠀⠘⣿⠀⢾⣠⠟⠀⣷⡀⠀⣀⡴⠋⠀⠀⠀⠀⠻⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠁⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠒⠲⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⣼⡇⠀⠐⠒⡖⠛⠂⠀⢀⣇⠀⠀⠀⠀⢀⡇⠀⠀⢸⡏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⢰⢿⠃⠀⠀⢰⡇⠀⠀⠀⢸⠻⡄⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣿⢹⡄⢀⡟⢸⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⢷⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢿⣼⠁⢸⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠘⣇⠀⠀⢸⠇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠈⠃⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⢹⡄⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢳⡀⢸⠀⠀⠀⢸⣧⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠈⣧⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠃⠀⠘⠛⠛⠃⠀⠀⠘⠀⠀⠀⠀⠀⠘⠁⠀⠀⠘⠓⠒⠒⠒⠒⠒⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠦⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠴⠶⠶⠶⠶⠖⠒⠛⠛⠋⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠂⠒⠂⠐⠒⠀⠐⠀⠐⠀⠀⠒⠒⠒⠂⠂⡰⠁⠀⠀⠀⠀⠀⠀⢀⡦⢀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡀⠀⠀⠌⠀⠏⠁⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠀⠀⠀⢠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⣷⡀⠀⡄⠀⠰⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠙⠃⣅⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠸⢀⡄⠀⠀⠀⠀⡄⠀⡆⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠂⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠐⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⢸⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠁
⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠂⠀⢠⣶
⠀⡄⠈⠀⠙⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀
⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣌⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣈⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣛⣛⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⡤⡤⠤⡤⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⡀⠀⠠⠀⠀⠁⠀⠠⢠⢀⠀⠀⠀⢀⣀⡀⠠⢤⢤⠐⢶⢶⣀⡀⢐⠂⡆⠀⠀⠒⠆⠴⠀⠂⠃⢸⣤⢀⡿⠊
⠁⠀⡀⠰⣀⣤⠀⠬⠈⠉⠭⠩⠧⠤⠀⣂⣐⠐⢀⠐⠂⠆⠀⠀⠤⠀⠁⡅⢈⠀⢀⢐⠰⣆⠀⠸⠁⣼⠃⠀⢀
⠀⡅⡩⠀⢠⠬⢤⠩⠅⠬⠁⠧⠀⡐⣂⠐⢂⢀⢀⠌⠈⠉⢉⡐⠀⠖⠖⠀⠬⠄⠄⢈⢨⡜⠂⠀⢠⣿⠀⢠⠇
⠠⠁⠶⠀⠆⠆⠠⠰⠒⠲⠀⠰⠂⠆⠠⠴⠠⡤⢨⠠⢛⣈⡉⠂⠘⠀⠀⠆⠛⠓⢶⡉⠼⠀⢀⠄⣼⠃⠀⣾
⡀⠶⠲⠀⠆⠘⡀⠂⠀⠿⠂⠀⡆⠶⠰⠀⠰⠰⠀⠖⠠⠈⢠⢘⢘⢑⠂⠂⠬⠘⠋⠁⠀⣰⠃⢠⡇⠀⠀⡇
⡀⠰⡆⠄⢰⠐⠶⢠⡀⠆⠀⠶⠀⡆⠀⡆⢰⢂⠀⠀⡄⡄⢠⠌⠁⠈⠁⠀⠀⠠⠀⢰⣾⣷⣄⣼⠀⠠⢠⠇⠁
⠁⠀⢀⠀⠀⠀⠄⢀⡀⢠⠀⢠⣄⣀⠠⣠⢀⠀⢀⠀⠀⢁⢨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠢⠤
⠆⠀⠴⠆⠠⠈⠇⠈⢃⠈⠀⠘⠀⠀⠘⠃⠈⠀⠈⠀⠁⠏⣸⠀⢠⠂⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠈⢉⠀⠀⠀⠉⠀⠀⠉⠋⠀⠀⢀⠀⠋⢠⡇⠀⠀⢰⠞⠀⠰⠂⠀⠀⠀⠤⠄
⠰⠀⠀⠘⠂⣙⣀⠈⠡⡌⠁⠀⠈⢀⣀⡀⠐⢦⡀⠀⠀⠀⣠⠞⢀⠄⠀⣦⠄⡀⠀⠀⠀⠠⠄
⡀⠚⠻⠃⠀⢀⠈⠀⠀⠀⠀⠀⠠⠀⠉⠁⢀⣠⠐⠷⠆⠀⠉⣤⠞⠀⢀⠀⠀⠀⠈
⠉⠀⠀⠘⠛⠛⠓⠀⠀⠀⠀⠠⡶⡀⠀⠀⣄⢠⡉⠍⡀⠄⠀⠈⢃⡐⠆⠀⠀⠀⠈⠂
⠁⠶⠌⢀⡀⠀⠷⠀⠐⠩⠀⠂⠀⠁⢀⡀⠈⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢰⡆⣠⠔⣿⠷⣤⡀⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣼⣷⠃⣰⡟⠀⢹⣿⡄⣰⣿⡥⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠛⣗⢦⣿⡇⠉⠉⣀⣤⠶⣿⡟⢻⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠈⠁⢿⡇⣠⠞⠉⠀⠀⣿⡇⠸⣷⡀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠘⢳⡏⠀⠀⠀⣼⡿⠁⠀⠈⣉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣀⠀⠀⠘⢧⣀⣠⡾⠟⠁⠀⢠⠎⠈⣿⡆
⠀⠀⠀⠀⠀⢀⡰⠒⣦⠀⠀⠉⠉⢁⣠⡀⠀⠀⣀⠀⠀⣄⠀⢠⠇⠀⢰⣿⠀⠀⣠⡞⠙⡆
⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⢀⣀⢀⡎⢸⣷⠀⢘⡉⠀⠀⣿⡇⡟⠀⠀⣼⡟⠀⢰⣿⣠⠜⢀⣄
⠀⠀⠀⠀⠀⢧⠇⠀⣿⣷⠋⣿⡞⠀⣼⡏⠀⢸⣿⠀⢠⣿⣿⠁⠀⢀⣿⠃⠀⣸⣿⡀⠀⢸⡞
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠻⠃⠀⣿⡇⠀⣸⣿⡀⡼⠹⠇⠀⠀⢸⣿⠀⢰⠃⠙⠳⠴⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⢹⣧⡰⠃⠈⠉⠁⠀⠀⠀⠀⢸⣷⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⢤⣄⣀⣠⠴⠖⠛⠛⠉⠉⠙⠛⠒⠲⠤⣀⢀⡤⠖⠛⠛⠓⢦⣀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⠙⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⢀⣀⣀⣀⡀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⡟⠀⠀⣠⠖⠒⠒⠦⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡉⠁⠀⠈⢹⡄⠀⠀⣇
⠀⠀⠀⠀⠀⠸⡇⠀⠀⢿⡀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣠⡟⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⢳⣄⠀⠈⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⢡⣬⣧⠀⠀⠀⠀⠀⣴⢫⣍⢳⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠀⠀⠀⠀⠀⠘⠿⠿⠋⠀⠀⠀⠀⢀⣾⣀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠹⣦⡀⠀⠀⠀⠀⣀⡠⠤⠒⠚⠋⠉⠛⠲⢤⣄⡀⠀⠀⠀⢀⡾⠁⠈⠙⠲⣤⡀
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠈⠻⢦⣀⠀⠀⣧⠀⠀⠀⢰⣾⣿⣶⡆⠀⢈⡿⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣰⠋⠛⠳⢾⣄⠀⠀⠀⠙⡿⠛⠀⢀⡾⠤⠶⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠙⠓⠶⠤⠴⠷⠤⠖⠋⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢰⠇⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣾⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣏⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣸⣧⡤⣤⣀⣀⣀⣀⣀⣴
⢻⣦⡀⠀⢀⣀⣤⠶⣿⠟⠉⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀⠀⠀⠀⠀⣠⠖⠛⠉⠁⠀⠀⠀⠈⠙⠻⣦⠀⠀⠉⠉⠉⠁
⠀⠈⠙⠛⠋⠉⠀⢰⠇⠀⠀⠀⠀⡴⠢⡄⢠⠶⢦⡀⠹⣄⠀⠀⣼⠁⢀⡤⢦⠀⣠⠖⢲⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⡟⠀⡾⠛⠢⡄⢧⠀⢹⠘⣆⠀⣷⠀⢹⣤⣼⡇⠀⣾⠀⢸⠀⣏⠀⡼⣠⠔⠛⢳⢸⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢧⣄⣀⡿⠈⢓⣛⣀⣈⠛⠁⠀⠀⣇⢸⡇⠀⠙⠒⠋⠀⠈⠉⠁⢿⣀⣠⡼⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠉⡴⠚⠉⠀⠀⠈⠙⠲⢤⡀⢹⠸⡇⠀⢠⠖⠚⠉⠉⠉⠲⢄⠉⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀⣸⠃⢸⠀⢻⡄⠸⣆⠀⠀⠀⠀⠀⢀⡇⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠈⠙⠓⠲⠶⠶⠚⠁⢀⡞⠀⠀⢻⣄⠈⠙⠒⠒⠒⠒⠋⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣤⡤⠴⠚⠉⠀⠀⠀⠀⠙⠳⠶⣤⣤⣤⣤⠶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠁⠁⠁⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⡀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠂⡢⠁⠦⠒⠀⠒⠢⡀
⠀⠀⠀⠀⠀⠀⡔⢡⣶⢤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠈⣢⠀⢰⡲⣄⣽
⠀⠀⠀⠀⠀⠀⠑⢬⣉⡈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠔⡡⢠⣿⢧⣀⣐⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⢼⣼⣿⠇⠀⠀⠀⡫⡈⣾⣽⣶⣡⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡭⠛⠈⣉⣁⣈⡉⠉⠉⠻⣍⢋⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⠀⠀⡎⠀⠀⢸⣥⣾⣿⣿⠆⢰⣶⢻⣵⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⡀⡇⠀⠀⠀⠉⢻⠛⠉⣠⠗⣟⣹⠊⡢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣵⢄⡀⠠⣀⣸⣀⡠⢏⣮⣼⣧⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⠫⡫⢛⠾⡽⣽⣻⣫⣫⢿⣟⢫⡺⠦⡄
⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⢀⠴⣷⠃⠋⠔⠕⡁⠙⠁⠠⡺⢧⠪⠊⠨⡳⢤⡀
⠀⠀⠀⠀⠀⢀⠎⠀⠀⡰⢢⡿⠁⠀⠀⠀⠀⠈⠲⡡⠊⢔⢽⣇⠀⠀⠀⢲⢝⡄
⠀⠀⠀⠀⡔⠊⠀⠀⡐⠡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠨⢐⢕⠠⢩⡇⡀⠀⠐⢕⡱⡀
⠀⠀⠀⣰⣦⢤⡄⢈⡠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡡⡪⠊⣻⡄⠀⠀⡀⢉⠾⢆
⢀⠖⠉⠁⠀⠀⠈⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⡪⠈⢜⢷⡵⠉⠀⠀⠀⠐⠹⣦⡀
⡌⢀⠔⠒⠒⠒⠤⣀⢀⠝⣦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⢔⢕⢕⢵⠃⠀⠀⢀⠤⠤⢌⡂⢝⣄
⡁⡌⠀⠀⠀⠀⠀⠈⠳⡡⣻⡂⣀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢕⢁⣥⡏⠀⢀⠔⠁⠀⠀⠀⠘⢖⠹⡄
⡇⠃⠀⠀⠀⠀⠅⠈⠂⢹⣺⡏⠀⠄⠀⠀⠀⠀⠀⠀⠀⢕⠕⡅⣻⠀⠀⠎⠀⠀⠀⢠⠉⠀⢸⢸⡇
⢀⠸⡀⠀⠀⠀⢑⡠⠂⠌⣅⡿⠠⠂⠀⡀⠀⢀⢀⢀⠔⢡⣡⣾⡇⠀⠜⠀⠀⠀⣐⠀⠀⠁⡾⣾⣀
⠀⢲⣵⡀⠀⠀⢐⠂⡀⢸⣃⣯⣄⣀⣀⣠⡤⣰⣱⣡⣪⣊⢕⣵⣿⠀⠂⠀⠀⠐⠂⡀⠄⣼⣿⠉⢩⡝⠳⠦⠄
⠀⠀⠙⢿⣦⣀⣀⠭⣢⠾⣾⡧⠭⠭⠭⠟⠻⠟⠉⠙⠛⣉⣛⣛⣿⣸⠀⠀⡠⠀⠤⣠⣾⠿⠓⢀⣐⣒⢙⣉⡛⠟⠂
⠀⠀⠀⠀⠙⠛⠻⠟⢟⠛⣁⡂⠀⡤⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠭⢫⣧⣤⣬⣝⡾⠴⠛⢓⣐⠛⠷⠐⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⣀⣤⣄⠀⠀⣙⣧⣴⠶⠛⠛⠓⠒⠶⠶⠶⠤⣤⣠⡞⠉⢀⣀⣀⣈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢨⣿⣿⣟⠵⠋⠁⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠈⠙⠾⣿⣿⣦⠍⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⠃⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠹⣄⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⢀⣈⠁⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠠⠴⠟⠛⠓⣤⣾⣿⣿⣻⣆⠿⠿⢥⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⢠⡾⠁⠀⠀⠉⠓⠶⣤⣙⣧⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢀⡇⠀⠀⢀⡄⠀⠀⠀⠀⢀⡼⢁⣠⡤⠶⠖⠒⠒⠲⡄
⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠰⠄⠉⠛⢷⣤⣀⠀⠀⠀⠀⠀⠈⠙⠲⠚⠳⠶⠒⠋⠀⠀⠀⣀⣴⡿⠞⠋⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⢠⠟⠛⠿⣷⡶⢦⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⡾⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠉⠙⠒⣶⡿⣿⢻⣏⣽⣏⠻⡻⡅⠀⠀⠈⢷⡀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⡜⣽⣱⢃⣾⢻⡜⡿⣄⡇⢹⠀⠀⠀⠈⣷⡀⠩⢷⣢⠄⠀⣀⣤⠟
⠀⠀⠀⠈⠙⠻⠶⢤⣤⣀⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠳⠬⠗⢫⠏⣸⠂⣷⠤⠴⠋⠀⠀⠀⠀⠸⣧⣤⣬⡶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣿⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣸⣄⣤⠴⠦⢤⣄⠀⠀⠀⠀⠀⣾⣀⣸⠑⠶⠚⠂⠀⠀⠀⠀⠀⢀⣠⣿⣇⡀
⠀⠀⠀⠀⠀⣰⠋⠁⠈⠉⠲⣌⠛⢦⡀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⡴⠋⣠⠋⠀⠙⢷⡄
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠈⢧⠈⢿⡄⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣼⠁⡼⠁⠀⠀⠀⠀⢹⡆
⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⣷⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⣸⠃⡸⠁⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢹⡇⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢀⡏⢀⠇⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⢸⣿⡄⡆⠠⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⢀⡼⠳⠤⣄⣀⡀⢀⣀⣸⣿⠀⠀⣼⠃⢸⠀⠀⠀⠀⠀⡀⠀⠀⣼
⠀⠀⠀⠈⣿⣧⡇⠀⢨⢰⢠⠀⠀⣸⢠⡿⢀⡴⠋⠀⠀⠀⠀⠀⠉⠉⠉⠀⠙⣷⡀⣿⠀⢸⠀⣸⠸⣸⢰⠟⠀⢠⡟
⠀⠀⠀⠀⠈⠻⣷⣾⣼⣸⣚⣀⣴⣧⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⣧⠸⡀⠉⠃⠉⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢤⣤⡴⠖⠋⠁

⠀⣀⣤⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠉⠈⠀⠈⠡⡀⠈⠈⠨⠈⠉⠩⠡⠀⠀⠀⠀⠂⠀⠀⡠⠀⣠⣀⠀⡀⠀⢠⠄⡍⠉⢉⠩⢤⠀⣠⢠⢠⠄⢠⣆⡀⢠⡇⠆
⠅⠀⠀⠀⡀⡀⠀⠀⠀⠈⠶⠃⠄⠤⠄⠀⠉⡯⢀⠉⡋⡉⢀⡙⡐⠚⠚⢀⠂⠐⠆⠆⠠⠄⠄⡈⡥⣄⡀⠀⢸⠟⠀⣿⠁
⠁⠠⢠⡤⠱⠘⠯⠠⠭⠤⠠⢈⢃⠈⠙⣙⡂⠒⠖⠂⠀⠄⠤⠠⢡⢀⠁⡈⢁⡀⠘⠃⠢⠂⠰⠂⡤⡈⢣⠀⠈⠀⢸⡏⠀⠀⡔
⠀⠶⠰⠂⠐⠔⠃⠒⠀⠒⠐⠂⠒⠒⠀⠆⠤⠁⠍⠬⠅⡍⠀⣀⢀⣀⠤⠡⠌⠁⠃⡊⢛⡇⠘⢀⡄⢰⠊⠀⠀⠀⣿⠃⠀⣼⠁
⠐⠄⠾⠃⠘⠈⠀⠀⠀⠉⠙⠃⠀⠛⠈⠃⠐⠚⠀⠲⠂⠆⠠⠩⢤⡄⢙⠀⠃⠐⠐⠇⠍⠛⣛⣏⠁⠏⠀⡀⠀⢸⠃⠀⢠⡇
⡀⢰⠚⠆⠘⠀⠛⡀⠃⠀⠻⠓⠈⠰⠤⠿⠰⠃⠀⠇⠗⠰⠖⠠⡠⢀⡄⡃⡃⡓⠐⠠⠾⠄⠉⠁⠀⠀⣼⠁⠀⡟⠀⠀⢸⠁
⠀⠀⣦⢠⠀⡆⠲⣦⢀⡆⠴⠀⠠⡶⠀⡆⠀⣆⢀⡄⡀⠀⠀⠄⡀⠀⣨⠉⠁⠉⠀⠀⠠⠀⡀⣀⣲⣿⣧⣄⣼⠃⠀⠀⣸
⠋⠀⠉⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⢀⠀⠁⠀⡉⡈⠀⠁⠀⠀⠀⠃⠘⣅⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠉⠉⠑⠒⠲⠾⣀⣀
⡄⠀⠀⣅⠀⠠⠰⠄⠀⡧⠀⠇⠀⠞⠉⠋⠀⡏⠃⠇⠀⠛⠀⠂⡼⢠⡇⠀⣠⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠
⠁⠀⠀⠈⠀⠀⠀⠀⠀⠒⠲⠀⠀⠀⠀⠤⠀⠀⠠⢤⠄⠀⠀⠀⠁⡼⠃⢠⠃⠀⠀⢀⣹⠀⠀⣠⠀⠀⠀⠀⠠
⠀⠀⢀⠀⡄⠄⡄⠀⠀⠤⠀⢤⠀⠀⠠⠀⡀⡀⠀⡀⠀⠀⠀⠐⠀⠀⠀⡟⠀⠀⠀⡘⠉⠀⠀⠁⠀⠀⠀⠀⠉⠃
⠈⠀⣀⠀⠈⠀⠼⢤⠀⠐⠶⠀⠀⠀⠀⠤⢤⡄⠀⠉⠳⢀⡀⠀⠐⣠⠟⠀⡰⠁⠀⠖⠂⠀⢀⠀⠀⠀⠐⠂
⡅⠈⠙⠛⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢤⢄⢙⣛⠃⠀⠀⢰⡾⠁⠀⠠⠀⠈
⠉⠀⠀⠀⠙⠋⠛⠃⠀⠀⠀⠀⠀⢴⠶⡀⠀⠀⢠⡀⣌⠉⢄⡀⠄⠠⠀⠙⣀⠐⠆⠀⠀⠀⠀⠉
⠉⠴⠄⠁⢀⠀⠐⣆⠀⠐⢘⡂⠰⠄⠀⠁⠀⡀⠌⠛⠀⠀⠈⠉⠀⠀⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣐⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠋⠉⠀⠀⠈⠉⠻⢿⣿⣦⣤⣤⣤⣤⣤⣤⣄⣠⣾⣿⠟⠋⠉⠉⠉⠉⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⠛⠛⠛⠛⠿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠁⠀⠀⠀⠀⠈⠙⠋⣡⣴⡶⠶⠶⠶⣶⣤⡈⠛⠛⠁⠀⠀⠀⠀⢸⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⢠⣶⣶⣦⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢻⣿⣿⣿⠇⠀⠀⠹⣷⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⢿⡇⠀⢶⣄⣀⣴⢿⣄⣀⣠⡦⢀⣿⠃⠀⠀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠈⢿⣄⠀⠉⠉⠁⠀⠉⠉⠉⢀⣾⠏⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⣄⣀⣹⣿⣷⣦⡀⠀⠙⢷⣦⣄⣀⣀⣠⣤⣶⠟⠁⠀⣠⣶⣿⣿⣃⢀⣤⣶⣶⣿⣿⣿⣶⣦⣄⡀
⠀⢀⣴⣿⣿⠟⠛⠋⠉⠛⠻⢿⣿⡿⠛⠁⠉⠻⢷⣦⣤⣀⣉⣉⣉⣉⣁⣠⣤⣶⠿⠋⠁⠙⠻⣿⣿⡿⠛⠉⠉⠁⠉⠉⠛⢿⣿⣦
⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿
⠀⠻⣿⣧⣄⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⡀⠀⠀⠀⢀⣠⣴⣿⡿⠁
⠀⠀⠈⠻⣿⣿⣶⣶⣶⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠉⢹⣿⣇⣤⣤⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⣿⣿⠁
⠀⠀⠀⠀⠀⢀⣾⣿⠟⠋⠁⠀⠀⠉⠙⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⠉⠁⠈⠉⠛⢿⣿⣿⡀
⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⣤⣤⣤⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⡀⠀⠀⠀⢀⣠⣾⣿⡟⠛⠛⠛⠛⢿⣿⣦⣀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣾⣿⣿⣿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠦⣤⣀⠀⠀⣀⣤⡤⠴⠶⠶⠦⢤⣄⣀⠀⠀⢀⣠⠴⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⠐⠂⠒⠂⣹⠷⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣟⣁⠰⠂⠲⢀⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡌⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠈⡥⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠰⠄⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣀⠴⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⡟⠀⠀⠀⠀⢀⣤⠀⠀⠀⣀⣀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣷⣥⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢛⡵⠚⠉⢉⠉⠉⠓⢾⡛⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⡞⠀⠀⠸⣿⣿⠆⠀⠀⢷⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠈⠓⠶⠶⠶⠶⠚⠁⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⡷⣤⡤⢤⣄⣀⣀⣀⢀⣠⡤⢤⡴⢾⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣻⠏⢀⡏⠀⠀⠈⡟⠀⠈⣿⠁⠀⠀⢹⠈⠻⡝⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣼⠃⠀⠈⣧⡀⠀⣀⡿⠤⠴⢿⣀⠀⢀⡼⠀⠀⠹⣆⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣼⠃⠀⠀⠀⠈⠉⠉⠁⠀⡤⠀⠀⠈⠉⠉⠀⠀⠀⠀⠹⡆⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢻
⠀⠀⠀⠀⣠⡴⠶⠶⢤⡀⢠⡾⠃⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢳⡄⢀⡴⠒⠒⠶⣄
⠀⠀⠀⣼⠷⠀⣤⠀⠀⠻⡏⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣹⠏⠀⠀⠴⠐⠞⣧
⠀⠀⢰⡇⠀⠀⠀⠳⠀⠀⢹⣤⠶⠖⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠓⠶⢴⠏⠀⢀⡛⠀⠀⠀⢸⡆
⠀⠀⢸⡇⠀⠀⠀⠈⣃⠀⠀⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⢩⡀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⢸⠃
⠀⠀⠀⣷⠀⠀⠀⠀⢨⡄⠀⠀⠀⠀⠀⠀⠀⢀⣩⠿⠶⢤⣄⣀⣀⣀⣀⣀⣀⣤⠤⠖⠿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⡿
⠀⠀⠀⠸⣆⠀⠀⠀⠰⠆⠀⠀⢀⣀⣤⠶⠚⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣤⣀⡀⠀⠰⠆⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠈⠙⠒⠶⠶⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡸⣍⣇⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠸⠆⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡠⠀⠀⢠⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡴⡦⠤⠴⠖⡶⠛⠀⠘⠛⠛⠉⠈⠂⠃
⠀⠀⠀⠀⠀⠀⣀⠠⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⢰⠁⠀⠀⠀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠄⠊⢹⡄⡠⠄⡨⠀⠀⠐⠀⠈⣳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠁⣸⡂⠀⠀⠀⠀⠀⡄⠀⠃
⠀⠀⠀⠀⢀⡤⠛⠿⡄⠈⠀⠀⠀⠀⠀⣄⡀⣠⡼⠁⠂⢄⠀⠀⠀⠀⠄⢹⡇⠀⠀⠀⢰⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢠⠀⠺⣷⡀⣿⠃⠢⠄⣀⠀⠀⠀⠀⠀⠘⠘⠻⠛⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡼⣆⠡⠛⠉⠉⠈⠁⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⣿⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⢿⣿⣿⣧⠀⠈⡀⠅⠈⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⣄⣀⠀⢀⣤⣄⠀⠀⠉⠛⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠋⠉⠀⢠⣿⣿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⠀⠀⠀⣩⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠴⠾⠟⠋⠀⠀⠀⠘⣧⠀⠀⠀⢨⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠘⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢻⣿⣿⣿⣿⣸⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⠏⠹⡇⢸⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡜⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⡉⢄⠀⢷⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠻⣿
⠀⣶⠀⠀⠀⠀⠀⠻⣼⢦⠘⡇⠀⠒⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣠⣿⣿⣿⣿⣿⣿⣿⡁⠁⠀⠀⢸⣿⣇⠈⠉⢛⣫⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿
⠀⠘⣧⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⠀⠘⣿⣿⣆⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿
⠀⠀⠹⣷⣦⣀⠀⠀⠀⠀⠈⢻⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠋⠉⠀⠉⢻⣿⣿⣿⣿⡆⠀⢿⣿⣿⡆⠀⠈⢿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿
⠀⠀⠀⠹⣿⣿⠁⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠱⢦⣀⣠⣤⠀⠀⠈⠛⠿⣿⣿⣇⡜⡘⣿⣿⣿⡄⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿
⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⣄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠀⠀⠩⠿⢿⣶⣶⡇⠀⠀⠀⠙⢿⡼⣷⢿⣿⣿⡷⠀⠀⠘⣿⣿⣿⣿⡿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣧⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠈⣿⣹⣤⣿⠿⡥⠃⠀⠀⠸⣿⣿⣿⡇⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣤⣤⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣈⠻⣷⣦⣤⣴⣿⣿⠟⠁⡆⠀⠀⠀⠀⣰⣿⣿⣿⡇⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⠀⠀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣧⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣼⣷⣼⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⡇⠀⢰⣾⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣼⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣰⣦⡀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⡴⠛⠿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⣿⣦⠀⠀⠀⠀⠀⠲⣌⠻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⢻⣿⣿
⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠹⢶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠀⠀⢲⡄⠀⠀⠀⠀⠀⣤⠄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢸⡟⠛⠛⠛⠋⢰⡏⢰⠇⣰⢂⠀⣠⡄
⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⢹⠀⠀⠀⢰⠇⡼⢣⡾⢱⡆⢀⣿⢀⡿⢸⢳⡟⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⠈⠀⠸⡷⠊⠀⢸⡇⣼⢁⡟⠘⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠿⠀⠈⣷⣀⡀⠀⠀⠀⠁⠘⠇⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠀⠀⠠⠟⣸⡤⠖⠚⠛⠛⠛⠶⢼⢃⡶⢰⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣯⠁⡀⡆⢸⡆⢰⡆⢀⡿⠃⠛⠛⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⣴⠃⢸⡆⣿⠸⣇⠇⣿⠀⣾⠁⣾⠃⣼⢠⡆⢀⣤⢀⣀
⠀⠀⠀⠀⠀⠀⢠⡆⠁⠲⣄⠀⠘⣇⣿⠀⣼⠀⢿⠘⣇⠰⠏⢸⡇⣾⡃⣼⠃⣼⠋⣹⢻⡏⢰⡇
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⢷⡄⡏⢿⡄⠙⠂⠘⠇⠉⠀⠀⠀⠀⠈⠁⠙⠺⠃⣼⠃⣼⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠘⠓
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⢿⣦⡀⠀⠀⠉⠒⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⠀⠈⠉⠻⣶⣄⠀⠀⠀⠀⠁⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢸⣦⣶⣤⠞⠉⠙⠃⠀⠀⠐⠀⠺⢿⣷⣄⠤⠒⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⣿⢻⣷⣤⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢐⣦⣄⠀⠀⠀⠀⠀⠀⢶⣶⣤⣿⣮⣿⣿⣿⣦⡀⠀⠀⡆⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠀⠀⠀⢀⡀⣀⠀⢉⠤⠈⠁⠈⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠘⠀⡀⠀⠀⠄⠨⣿⣨⠶⠆⠂⠀⠀⠀⠀⢸⣿⣦⣅⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠘⢿⠀⡄⠀⢀⡄⠁⠰⣞⣏⡻⠀⠀⠀⡾⠻⠝⢿⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠘⣷⠀⣤⠁⣀⠀⠀⢺⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠐⠆⠀⠀⠰⠏⠀⠀⠄⣸⣆⠀⠘⠏⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠰⣿⣏⠈⠙⠲⣦⢄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠷⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⢀⣀⡀⡿
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠐⢠⣤⡴⠂⠀⠀⣿⠁⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠃⠀⠋⠀⠀⠰⡾⠏
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⡗⢚⠉⢋⡡⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠰⠞⠂
⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣀⣠⣴⣶⣾⣿⣶⣶⡶⠄⠀⠀⠀⣠⠀⠀⠀⡠⠉
⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⠀⠀⠀⠀⣀⣤⣤⣴⣤⣤⣶⣶⣶⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣨⣤⣙⣶⣴⣾⣿⣿⣿⣿⣯⣿⣯⠙⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⡇⢿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣅⢸⣿⠀⠀⠀⣠⣾⣿⢟⡿⠟⣿⣿⣿⣿⡿⠿⢿⣿⣿⣼⣿⢏⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⣠⣿⣿⣷⣿⡵⠿⠟⠉⠻⣅⣉⣴⢸⣿⣿⢹⠏⣾⣿⣿⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡀⢇⠀⢠⣧⠉⠉⠻⣄⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⢎⣼⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⢀⣠⡴⣿⣿⣼⣄⣾⣿⣷⣄⠀⠘⢷⣦⣄⡀⠀⠀⠀⣀⣀⣤⢻⣿⣿⠿⠛⠿⢟⣽⣿⣿⣿⡿
⠀⠀⠀⠸⡀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣆⡀⠘⢻⣿⣿⣶⣾⣿⡿⣱⡿⠋⠁⠀⠀⢀⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠈⠙⠿⠿⠿⣿⣿⣦⣀⠙⡻⢿⣿⣿⡟⠁⠀⢀⣀⣤⣶⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢿⣿⣶⣤⣄⣀⣀⣀⠀⣀⠀⠈⣉⣫⡽⠟⠛⠛⠛⠿⠷⣶⣾⠿⠿⠿⣿⣿⣿⣿⣿⣁⣀
⠀⠀⠀⢀⣤⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⡏⠀⠀⠀⣀⣠⣴⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣿⣿⣿⡿⠿⡿⠦⣀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⡟⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂
⠀⠀⠀⠉⠁⠀⣠⣶⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡷⣄⢀⣠⣴⣾⣿⢿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⢠⠿⠛⠛⠻⠿⠿⡿⠿⠿⠛⠁⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿⡿⠋⠁⠛⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠉⠉

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡠⡄
⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⡠⡜⢄⠉⣇⣀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⡠⠚⠢⢠⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢍⠳⢘⡌⠢⡨⠊⠀⠀⠰⠝⠊⢀⠀⠀⠀⠊⠈⢃⡀⠤⠆⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⡏⡭⡢⡀⠙⠢⠅⢀⡴⢊⠁⠀⠰⠇⠀⠈⠀⠀⠀⠀⣠⡄⠀⠀⢀⠀⠀⠀⠰⡹⠁⠹⠂
⠀⠀⠀⡖⠢⡀⠘⢄⡚⡀⠀⢀⠔⠉⠀⠣⠐⠀⠀⠀⠀⠀⠐⠂⠀⠄⠻⢀⡠⠐⠁⠀⠀⠀⠛⠃⢀
⠀⠀⠀⠘⢄⠑⠄⡄⠀⠀⠘⠀⠀⠀⠀⠀⣠⡾⢑⢄⠀⠈⠐⠁⠀⠐⠂⠁⠀⠎⠐⠀⠀⠀⠀⠀⠃⠁
⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⣰⢯⣲⠃⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠞⢛⣼⠃⡐⠀⢀⠀⡰⡡⢀⠀⠀⠀⠀⠛⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠂⠀⠀⠀⠀⠠⡒⠁⠀⠀⠀⠉⢤⡾⠋⢉⠔⠀⠀⠈⢄⣔⢲⠇⠀⠂⠂⠢⡀⢀⠾⠆⠀⠞⢂⠄
⠀⠀⠀⠀⡀⢄⡀⠀⠈⠈⠁⠀⠀⢀⠀⠀⠀⠁⠀⢀⢤⡀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠁⠀⠀⢀
⠀⠀⡄⠊⡤⠊⠑⡀⠀⠀⠀⠀⠒⠀⠆⠀⠀⠀⠰⡟⠋⡰⠀⠀⠈⢇⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠈⢎⠀⠀⠅⠅⠀⠀⠀⠀⠀⠆⠐⠄⠀⠀⠀⣵⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡁
⠀⠀⠀⣊⡇⠀⠀⠀⠀⢀⠊⠀⠉⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠊⠉⠉⠀⠀⢠⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⠀⠀⣈⠀⠀⠀⠀⠂⠀⠀⠠⠒⢀⠀⠀⠒⠀⠀⠠⡀⠀⠀⠀⡞⠂⠂
⠀⠀⠀⠀⠀⢶⣀⠀⢀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠐⠀⠀⠐⢄⣀⣶⣠⡔⠁⠀⠀⠀⠁⠀⠘
⠀⠀⠀⠀⠄⠄⠌⠍⡒⠀⠀⠀⠀⢀⠴⣗⢄⠀⠀⠀⠀⠀⠀⠀⠌⠍⢿⡇⠀⡃⠀⠀⠀⣀⣀⡀
⠀⠀⢠⢆⠀⢊⠈⠌⠀⠀⠀⠀⣰⡁⠀⠈⡪⠇⠀⠀⠄⠀⠀⠀⡂⠀⢺⣇⣀⡁⠀⠸⠛⠃⠉⢁
⠠⠀⠀⠀⠁⠆⠆⠀⠀⠀⠀⠀⠀⠀⢠⢊⠀⠀⠀⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢆⠄⠀⠘⠃⠀⠀⠂
⠀⠀⠄⠆⠶⠲⠀⠀⠀⢀⠀⠀⠀⠀⠈⠈⠀⠀⠘⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣵⣾⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⢿⣻⣿⣿⣿⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⣀⡼⣿⣹⣿⣿⡆⠀⠈⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣧⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡝⣯⡇⠈⢻⣿⣿⣿⣿⣿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣼⣷⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣱⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠉⠒⢄⣀⠤⠔⠒⠒⠒⠒⠒⠒⠤⠄⣀⠤⠒⠉⠉⠉⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣠⠒⠒⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⣄⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡁⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⠃⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠘⠤⠃⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⢰⣶⠄⠀⠀⠀⠀⠀⢠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⠡⠴⠒⠐⠐⠲⠤⢅⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢠⠊⠁⠀⠀⡊⠉⠉⠂⠀⠀⠉⢢⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⡇⠀⠀⠀⠀⠈⢹⠋⠀⠀⡀⠀⠀⡂⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠢⢄⠣⡀⠀⠀⠀⠀⠘⠀⠀⢀⠄⠀⢠⣁⠔⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠉⠛⠦⠄⣀⣁⣀⣀⣀⡠⠤⠞⠋⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡸⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⠈⠐⠠⡀⠀⠀⢇⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠈⡆⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⠰⢧⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡷⠔⠒⠒⠠⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠈⠺⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠗⠁⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠤⠠⠄⡀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⠄⠂⠒⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠐⠀⠀⠀⠀⠈⢂⠀⡗⠢⣀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢺⠀⡔⠀⠀⠀⠀⠀⢁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢠⠀⠀⠀⠀⠀⠈⢠⠓⠤⢀⣈⠀⠒⠒⠒⠂⢉⡀⠴⠚⡄⠀⠀⠀⠀⠀⠀⡄⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢥⣄⡀⠀⣠⠞⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠳⣄⠀⢀⣠⡬⠔⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢀⢀⠀⡀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠴⠶⠦⠤⠤⣀⡀
⠀⠀⠀⠀⠀⢀⡄⢀⡤⠖⠋⠉⠀⢀⡠⠴⠒⠚⠛⠛⠛⠒⠀⠉⠛⢦⣄
⠀⠀⣀⢶⡒⠈⡷⠉⠀⢀⠀⠀⠈⠁⠀⠀⣀⣠⠤⠴⠒⠒⠀⢀⣀⣠⠽⢚⡥⣰⠃
⠀⠀⠉⢢⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⡤⠶⠊⠉⠠⠒⣩⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣤⣤⡤⢤⣤⣀
⠀⠀⣰⠃⠄⠀⠀⠀⠀⠐⠂⠤⠤⠤⠤⠤⠤⠐⠒⠉⠀⠀⠀⠀⣠⡴⠞⠁⡌⣇⠀⠀⠀⠀⢀⣀⡠⠔⣉⠤⠒⠉⠀⠀⠀⠀⠀⠀⢉⣲⣄⣀⡴⠋⡙⠛⢶⡄
⠀⢰⠃⡜⠀⢠⠂⠀⠀⠀⠀⡀⢀⣀⣀⣀⣀⣀⣤⣤⠤⠶⠚⠋⠁⠀⠀⠀⢱⣹⠀⠀⣠⠞⠩⠎⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⢿⣀⡠⠀⠹⡄
⠀⡟⢠⡆⠀⡇⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣼⠃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣆⢷⡠⠔⠀⡇
⠀⡇⢸⡇⠀⢀⠄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⠆⠀⡇⢰⢻⠸⡀⠀⠀⠀⠀⠀⢈⣉⣉⠉⠑⠒⠤⣄⡀⠀⠀⠀⠀⣠⠟⡾⠇⠀⣸⠃
⠀⣧⠀⠇⣠⠋⣠⣤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⡇⢸⠸⢀⠓⢦⣄⣦⠤⣄⣀⠀⠈⠙⠲⢤⡀⠀⠉⠓⠶⠶⠾⣫⠀⡷⠴⠚⠁
⠀⢻⡀⠀⡏⣾⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⠀⠀⣸⠁⠘⣇⣸⠰⠀⠀⣤⠀⠀⠉⠙⢦⡀⠀⢀⠙⣆⠐⠀⠀⠀⠊⠁⡔⡇
⠀⠘⣷⠀⠀⠙⢮⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡼⣰⠃⠀⠀⠈⢿⠀⡄⠀⠈⠀⠀⠀⠀⠀⠃⢸⡍⢱⡈⠀⠀⠀⢀⠄⡼⢡⡇
⠀⠀⠸⣧⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⢞⡵⠃⠀⠀⠀⠀⢸⡘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢬⠼⠁⠀⠀⠂⣡⠞⢁⣾⠁
⠀⠀⠀⠈⠳⣄⡙⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⢉⡴⠋⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⡤⠎⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠒⠉⠀⣠⣿⠋
⠀⠀⠀⠀⠀⠈⠙⠓⠺⠷⠦⢄⣀⡀⠀⠀⠀⠀⢀⣀⣀⡤⠖⠋⠀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠂⠤⠤⠖⣋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⡄⠈⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠙⠒⠤⣄⡀⠀⠀⣀⣠⣷⣤⠤⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠓⠤⠍⠓⢤⡀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣦⣀⣀⠀⠀⠀⠀⠀⢀⡨⢆⣀⢎⡀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠰⡄⠀⠀⠀⠀⢡⠈⠧⠀⠀⠀⠀⠹⣿⣿⣿⡿⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⠀⡆⠣⢄⡀⠀⠀⠀⠀⠙⠛⠁⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠛⠃⠀⠀⠀⠀⠀⠀⢡⠀⠀⠉⠙⠒⠶⡶⠜⣦⠤⠴⠚⠉⢈⠀⠀⠀⠀⠀⠀⠸⣄⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠊⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠳⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡞⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⠲⡄⠀⠀⢀⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢠⠇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠦⠤⠿⠗⢒⠋⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢑⣠⠀⡀⠀⣀⣠⣼⢰⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⠞⠉⢂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠾⢦⢰⣴⡉⡿⠾⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠃⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⠤⣤⣄⣀⣤⡤⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣄⡤⡀⠀⣏⠋⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢮⠀⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠜⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠈⠰⠩⠽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠐⠂⠈⠉⠀⠉⠉⠉⠀⠐⠒⠒⠂⠠⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⢀⠴⠒⠒⢤⡀⠀⡠⠖⠒⠒⠲⢄⠀⠀⠀⠀⠀⠀⢀⠔⠒⠒⢄⡀⠀⡠⠖⠒⠒⠦⡀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⡌⠀⢐⠄⠀⠈⠎⠀⠤⡊⠔⢀⠈⡆⠀⠀⠀⠀⠠⠁⠀⡂⠄⡀⠑⣜⠀⢔⠡⢊⠀⢹⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠰⡀⠀⠄⢊⠔⡀⠔⣊⠔⡊⠅⢠⠁⠀⠀⠀⠀⢸⠀⠨⢔⠩⢂⠀⡠⢐⠡⢂⠕⠀⠐⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠄⢊⠔⡪⢔⠨⠐⡠⠁⠀⠀⠀⠀⠀⠀⢆⠀⠠⢊⠄⡨⢐⠡⢊⠅⠊⡠⠁⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠩⢂⠥⣢⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠁⡨⢂⠥⢊⠕⢊⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠡⠊⢔⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠃⠌
⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⡀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠀⠀⠀⠀⡀⠆⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⠒⠒⠒⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡠⠀⠠⠁⢀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⣁⣈⠀⠂⠐⠂⠀⠁⠀⠊⠐⠁⠊⠀⢁⣠⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠒⠐⠊⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⡀⠄⠀⡀⠄⠂⢀⠠⠀⣀⠤⠀⡀⠄⢀⠠⠀⣀⠄⠀⢀⠄⠀⡀⠄⢂⠠⠒⡀⠄⢂⠀⠀⡀⠄⢈⠡⠀⡁⠀⡠⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠡⠔⠊⢁⠄⠒⢈⠤⠒⣁⠠⠒⡁⠄⠊⡁⠔⢊⡠⠔⢈⠠⠐⡉⠔⢈⠠⠐⢉⠤⠂⡡⠐⠉⠠⠂⠁⠔⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠉⠀⠂⠁⠀⠈⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⢤⣄⡀⠀⢀⣠⡴⠶⠚⠛⠛⠛⠛⠛⠓⠲⠶⢤⣄⡀⠀⣀⡴⠖⠚⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠈⠙⠿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣀⣠⣄⣀⡀⠀⠈⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢀⡴⠖⠛⠛⠓⢦⡀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠉⠀⠀⠉⠙⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢸⡗⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⡄⠀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⡟⠁⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠈⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢶⡄⠀⠀⠀⠀⠀⠀⠀⣤⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⢸⣄⣿⣷⡿⠀⠀⠀⠀⠀⠀⢸⣇⣶⣦⣿⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⡄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠃⠀⠀⠀⠀⠀⢀⣾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠛⠛⠛⠛⠶⣦⣄⡀⠀⠀⠀⠀⠀⢀⣾⠃⠈⠉⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⢸⡉⠀⠀⠀⠀⣤⣶⣶⣤⣤⠀⠈⠙⣷⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠈⢹⡷⣦⣤⣈⣇⠀⠀⠀⠀⠙⢿⣿⣿⠏⠀⠀⣼⠁⢀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢰⠉⠉⠛⠻⢦⣀⠀⠀⠀⠈⡏⠀⠀⣠⡾⠋⠉⠉⠙⡞⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢈⡄⠀⠀⠀⠀⠈⠉⠓⢲⠚⠛⢲⠚⠉⠀⠀⠀⠀⢸⠃⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢼⡀⠀⠀⠀⠀⠀⠀⣀⠼⣄⣀⣸⣀⣀⣀⡀⠀⠀⣘⡆⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠉⠙⠛⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣟⣠⡤⠴⠶⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠶⢶⣿⣿⡓⠶⠶⠤⣤⣤⣤⣤⣾⠟
⠹⣷⣄⣀⣀⣀⣠⣴⡾⠟⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠈⠉⠛⠛⠛⠉⠁⠀⣼⠃⠀⠀⠀⠀⢠⡤⠤⣄⠀⣴⢶⣤⡀⠙⣷⡀⠀⠀⣰⡏⠀⢀⣤⣦⡀⠀⣴⠒⢳⡆⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣴⠶⢦⣀⠈⣇⠀⠸⡆⢻⠀⠈⢷⠀⠘⣧⣀⣠⣿⠀⠀⡞⠁⢸⡇⢸⠃⠀⣼⠂⣠⠴⠶⣦⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠸⣏⠀⠀⠘⡇⠹⣄⣤⠇⠈⠳⣤⡾⠀⠀⢸⡏⢹⡟⠀⠈⣧⣀⡼⠁⠘⠷⠶⠋⢼⠁⠀⠀⣸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⠳⠶⠾⠃⣀⡤⠴⠖⠲⠦⣄⡀⠀⠀⠀⣧⢸⡇⠀⠀⠈⠁⣀⣀⣀⣄⣀⡀⠘⠷⠶⠞⠋⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠉⠳⣦⠀⣿⠘⣿⠀⠀⣼⠋⠉⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣾⠀⢹⣆⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠉⠛⠲⠶⢤⣤⠴⠾⠋⠀⢀⡟⠀⠀⠹⣧⡀⠈⠛⠲⠶⠶⠶⠶⠛⠋⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣀⣀⠀⠀⢀⣀⣤⠶⠋⠀⠀⠀⠀⠘⢿⣦⣄⣀⣀⠀⢀⣀⣠⣴⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡼⠛⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣀⢳⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡇⣿⢸⠇⠔⣽⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡓⢄⠀⢹⣿⠋⣀⢸⣿⠏⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠸⢟⣫⠴⠶⠶⢷⣍⠈⢷⣀⢡⣶⣶⡿⠃
⠀⠀⠀⠀⠀⠀⢀⡾⢁⣤⡤⡒⡠⣟⢦⡀⠈⡎⠹⣏⡀
⠀⠀⠀⠀⢠⣤⢞⡵⢇⣧⡘⢩⣿⠀⡇⣁⠀⡇⠀⠈⣷
⠀⠀⠀⠀⠘⢿⠁⠀⠀⣌⠃⢺⠏⡸⢁⠿⢺⠁⠀⢠⠏
⠀⠀⠀⠀⠀⠈⣵⢤⣊⡉⠉⣀⡴⢃⡎⢠⡟⢀⠊⡣⠀⡀
⠀⠀⠀⠀⠀⠐⡇⠀⠀⣹⡟⠛⠉⣉⣤⠟⠉⢉⡼⣡⢾⣿⡄
⠀⠀⠀⢀⣴⣣⡱⣄⠀⠈⠉⢉⠟⠀⠀⢀⣀⡿⢰⢃⣿⣿⣧
⠀⠀⠀⠘⠛⠿⠿⠾⠵⠒⣂⠓⣒⣦⠥⠤⠤⠅⠇⢠⣿⣿⡏⡠⢤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣧⠙⠿⣻⣾⠿⠿⠶⢌⣻⡟⠀⢴⣿⡿⠁
⠀⢀⣠⣤⠴⠶⠤⠤⣄⠁⢿⣯⠤⡼⠯⣤⣀⠀⠀⠀⠈⠉⢹⠚⠋
⠀⠀⠙⣿⣿⣿⣷⣦⣠⢠⡟⠁⠀⣠⠦⠤⢌⣙⣶⡖⠦⣄⠀⠙⢦⡀⠀⢀⠴⣲⣿⡇
⠀⠀⠀⠀⠙⠿⢿⣿⣿⣽⣧⠖⡿⢁⡴⣾⡛⣝⢯⣿⣄⠈⢳⡤⢤⡷⠐⢃⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⡠⠋⣸⡇⢸⡇⣯⡾⣿⢿⣿⣾⠏⡟⠀⠀⣿⠈⢿⠀⢼⡿⠟⠁⠀⠀⠀⠀⢀⡴⢦⢤⢄⡀
⠀⠀⠀⠀⠀⠀⢰⠃⠀⢿⢳⣴⡗⣸⡿⠵⢋⣼⢋⡴⣧⣀⡴⡿⠀⢸⡄⣀⡀⢤⣀⡀⣀⣀⠤⠾⢦⣖⣚⣪⠅
⠀⠀⠀⠀⠀⠀⢸⣆⠀⢸⡀⠈⢷⣀⣈⠿⠉⣰⠟⢀⡿⠀⣰⠃⠀⣼⢁⣴⣶⣿⡿⣱⠯⣧⠤⠴⢶⣤⣬⢯⠶⠆⠠⢄⣠⣤
⠀⠀⢀⣤⣖⣈⣜⣧⠀⠀⠙⢦⣤⠬⠤⠶⠛⢁⣠⠞⣡⠞⠁⣠⣾⡟⠾⠿⣟⡋⢰⣿⡶⢯⡼⣀⡾⢕⣢⠌⣷⢠⣶⣿⠟⠃
⠀⠀⠀⠙⠻⢿⣿⣮⠳⡀⠀⠘⠳⣶⣶⣶⡾⠿⠗⠋⠁⠀⢀⣿⣿⣤⡤⣄⠈⠙⢦⡉⠑⠺⡛⠓⠺⡉⢀⣛⣁⡉⠛⠲⢄⡀
⠀⠀⠀⠀⠀⣠⠞⣀⣤⣴⡀⠒⣏⠀⠀⠙⢻⡷⠶⠴⠶⢒⣽⡜⣿⣿⣿⣿⣿⣦⣄⠹⣆⠈⢿⣿⣶⣜⢎⢿⣿⣿⣿⣷⣦⣽⣄
⠀⠀⠀⠀⣴⣡⣾⣿⣿⠟⡇⣾⣾⠲⢤⣤⡿⠀⠀⢠⢱⣿⡿⠁⠈⠻⢿⣿⣿⣿⣿⣷⣼⣇⠀⠙⠻⠿⠿⠄⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠐⠛⠛⠛⠉⠀⠀⠱⡿⠋⠀⠀⠀⠀⠀⠀⠘⡿⠋⠁⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⣄⠀⠀⠀⢀⣠⣶⠀⠀⢠⣄⣀⣀⣤⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡁⠀⠈⠛⠛⠛⠋⠉⡈⢛⣶⠟⠉⠉⠉⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠈⠹⢦⣄⡀⠀⠀⠰⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠈⢳⣤⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⡾⠛⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢦⣽⠿⢧⣄⠀⠀⠀⠀⠀⠀⠀⢐⠆⣠⡾⠋⠀⠀⠀⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠙⠿⣦⣣⠀⠀⢤⠀⣠⣿⠋⠁⠀⠀⠀⠀⠀⠠⡈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣤⣀⣤⠞⠓⠿⠟⠛⠛⠳⣧⡀⠀⢀⣴⠛⠃⠀⠀⠀⠀⠀⠀⠘⠿⣷⣦⣤⣿⠛⠀⠐⠀⠀⠀⠀⠀⠀⣠⣾⢿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣈⣁⣀⠀⠠⠤⣤⠀⠰⡉⠙⢿⣿⠋⠁⠀⠀⠀⠀⢀⠀⠀⠀⠈⣪⣿⠿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣿⡋⣮⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠛⠋⠉⠉⢛⢶⣠⠴⠦⢀⡽⠀⠘⣿⡿⢾⣆⠀⠀⠀⠀⠀⠰⣤⣾⡿⠀⠀⠈⠙⢷⣱⡄⠀⢀⣴⣿⡱⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣰⠀⠀⠀⠀⢀⠀⢻⢳⣀⣀⣴⠾⢿⢧⣸⡀⠀⠹⣷⣶⣦⣀⣀⣶⡻⠆⠀⠀⢆⠀⠀⠀⠹⠿⣦⡾⣿⣥⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⡟⠀⠀⠀⠀⠀⠀⢻⠁⠙⠉⠀⠢⡀⢳⡿⣿⣗⠀⠀⠐⢦⡀⠉⡉⠻⣤⣤⣬⣄⠀⠀⠀⢀⣾⡻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡸⠀⠀⠙⠿⠷⣶⡎⠠⠶⠀⣠⡀⠀⠙⢿⣄⢆⣰⣿⣯⡷⠏
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣼⠏⢀⣀⠘⠁⠉⠀⠀⠈⢻⣿⣿⣿⣿⠁
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢸⠇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢼⣏⣰⠏⢹⣆⠀⡞⠻⠄⠀⠀⠉⠳⠛⠹⣧⡀
⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡋⠁⠀⣀⣉⡗⣀⠀⣠⢤⡀⠠⣤⡄⠀⠈⣷
⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢛⣿⠿⣿⣿⠀⢃⢁⣀⡀⢸⣿⣶⡾⠃
⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⡁⢀⣿⡏⢀⠀⢻⣏⠁⣽⡿⠟
⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡡⠀⣡⡾⠋⣿⣄⣴⠿⠿⡷⠿
⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⣴⢋⠀⠀⣀⣾⠋⠀⠀⠈⠛⠛
⠀⠀⠀⠀⠉⢷⣄⡀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠸⡆⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⣠⠟⠡⠀⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡹⠄⠀⠀⠀⠀⠀⠀⠈⢂⠀⢠⡾⡃⠂⢀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⢀⡶⠋⠁⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣴⠟⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠴⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⢦⣼⢳⡀⠀⠀⠀⢀⡴⠋⠁⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡙⣸⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⡴⠲⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⡇⣈⠵⠃
⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠈⢧⣡⠃⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠉⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣯⠤⠤⠤⠤⠤⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣺⣿
⠀⠀⠀⠀⠀⠀⢸⠛⢦⣄⠠⠤⠤⠤⠤⠄⠀⠀⠀⠀⢀⡀⢀⡀⢒⡒⣒⠂⠀⣀⡴⠚⠁⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠳⢦⡀⠀⠀⣤⣀⡄⠀⠀⠈⠯⠟⠀⠘⢭⢟⡤⠞⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠶⣄⠈⠳⠁⠀⠢⠄⠀⠀⢄⡠⠖⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⣠⠴⠶⢤⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡟⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣙⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣟⣛⣟⣛⣻⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⣳⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣄⣀⣤⣶⠟⠃⠀⢿⣿⣿⣿⢻⠻⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⣿⣿⣿⣇⣷⢹⣿⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⢹⣿⣦⢠⣤⢀⡀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⢠⠦⣠⣶⣦⣤⣤⣤⣵⣦⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣏⣾⣿⣿⣶⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⢠⣀⣴⣿⣿⣿⡿⢉⠀⠀⠀⠰⣦⣤⣄⣀⠀⠀⠉⢩⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣧⣶⣴⣸⣿⣿⣿⣿⣶⣶⣿⣿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⠇⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠
⡄⠀⠀⠀⠀⠀⠀⠀⠉⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣼⣿⣿⣿⣿⣿⣿⡇⣹⡁⢀⣴⡀
⣿⣶⣄⣠⣾⣿⣿⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⠉⠿⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣯⣷⣿⣷⣿⣿⣦⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠐⠒⢦⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⢼⠁⠀⡀⠀⠀⢀⡠⠂⠀⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⢰⠀⢷⠀⠀⢀⡎⠀⠒⢋⡡⠔⠂⠓⠀⠀⢠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡅⠀⠀⡆⡼⣠⡏⠀⠀⠈⠀⢀⡀⠁⡀⣀⡀⠀⠀⠀⠢⠳⢄⠈⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠛⣿⡦⠀⢰⠂⢸⡀⠀⠊⣳⡀⠈⠴⢆⠤⣀⠀⠈⠉⠀⡣⠠⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠀⢹⠀⢳⡷⡡⠈⢆⡸⢷⡀⢣⣿⢣⡀⠐⠒⠲⡄⢡⠀⠀⡆⠘⣀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣠⣿⣿⠻⡀⠀⢿⠹⣆⠈⢷⣤⣥⡈⣿⣶⡙⣶⣗⠀⠈⠉⠀⠀⠁⠀⠈⠙⢢⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠈⢙⣿⣶⠀⠀⠈⠓⠿⣦⡈⢯⡛⠭⠛⠻⢿⣾⠾⢷⣼⣠⣇⡀⣀⣀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⡴⣻⠁⢻⣦⣄⠀⠀⠀⠀⠙⠮⣧⣶⣤⣦⢀⣉⣁⣂⢀⠈⣭⣽⣿⡏⠀⠀⠸⠀⠀⢸⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣽⣿⣾⠀⠀⣿⣯⣿⢦⣕⣒⣄⠀⠉⠻⢷⣄⡀⠢⢤⣄⠈⢈⠈⢉⣁⣠⣴⣿⠄⠀⢀⡿⠁⠉⠉⢩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣾⢿⣿⡀⠀⠘⣿⣿⡇⠈⣁⣽⢷⣤⣤⣤⣈⠉⠛⠦⣄⣀⠀⢏⣿⣿⣿⣻⠋⠀⠀⠊⠁⠀⠀⠉⠀⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢈⣿⠏⢸⡿⣇⠀⠀⠈⠻⣗⣀⣿⣿⣤⡀⠈⠙⡟⠛⠒⠲⡾⣯⣟⣿⡿⠿⠛⠁⠀⠀⡀⠀⠀⠀⣸⡦⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⡟⣏⡔⠀⣾⣿⣷⣄⣀⠀⠈⠻⣟⣋⣹⣛⠻⠶⠾⠿⠤⠧⠿⠽⠿⠞⠛⠛⠁⠀⠀⠈⣥⠀⠀⢰⣧⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡏⠙⢻⣷⣔⡝⠹⣻⠛⡿⣿⣿⣶⣄⡉⠻⢯⣍⠒⠤⣤⣤⣀⣀⠀⠀⠀⣀⣀⣀⢴⣶⣶⠏⣱⠚⠚⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠡⡇⠀⠈⢻⣿⣿⣦⣻⣔⣏⡿⣿⣿⣿⣿⣿⣷⠎⡇⠀⢹⣶⣤⢏⣿⣿⣿⣿⣿⡷⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣿⣶⣶⡀⠻⡏⠉⠍⣹⢿⣏⣿⣿⣿⣿⣿⢿⠀⣷⠀⠠⣸⣏⣾⡿⠿⠛⠋⡉⠈⠁⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣾⡄⠀⠴⠊⣿⣿⣿⡟⣵⣷⣿⣆⠸⣤⡶⠛⣩⡶⠶⠖⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣿⣿⣿⣿⣷⠙⡆⠀⢠⣿⣿⣟⢟⣻⣧⡿⠿⠤⢟⣒⡉⠁⠀⢀⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡟⣼⣶⣤⣘⣿⣿⡶⠚⠉⠀⠀⢠⣶⣟⣿⣿⣶⣾⣿⠯⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⠈⢏⠀⢀⡀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠠⠶⢶⣶⡶⠶⠿⣿⣿⡿⡿⠿⠟⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣀⣸⡷⣶⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠀⠀⣀⣀⣠⣾⣿⠿⠋⣽⠏⠙⣿⠟⠻⠿⣿⣿⣿⣧⣽⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⣼⠏⠁⡸⠃⠀⠀⠀⠀⠀⠀⠈⢻⡍⢿⠸⣧⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⣧⢻⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣿⣝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠾⠛⠹⣇
⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠾⠛⠉⠁⢀⣀⣴⠾⠛
⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠋⠁⠀⣀⣤⡴⠞⠛⠉
⠀⠀⠀⠀⠀⠈⣷⢻⣆⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠛⠉⢀⣀⣤⡴⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢻⡆⢿⣆⣀⣀⣤⡶⠟⠋⢁⣀⣼⡴⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢈⣿⣾⠛⠹⣯⣡⣴⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠘⣿⣽⣇⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣜⣧⣠⡴⠞⡿⠛⠻⣦⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⣿⣿⣿⣤⣾⣁⣈⣴⠾⠛⢛⣉⡟⠻⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣻⠛⢧⠀⣆⠻⣝⠛⠃⢀⣴⡋⢻⠀⠘⠙⣷
⠀⠀⠀⠀⢠⣾⢻⡟⣿⠃⡿⠆⠈⠃⠘⠦⢨⡿⠛⠛⠉⠛⠻⣧⣦⣤⣿⣄
⠀⠀⠀⠀⢿⣿⣺⡷⣾⡿⣷⠳⢆⡄⣰⣿⠛⢻⣶⣦⣀⢀⡀⠈⢿⢤⡈⢹⣟⣷⠀⣀
⠀⠀⠀⠀⠐⠭⡙⠷⣾⣿⣉⣛⣿⢿⡿⠿⢶⣋⡴⠛⢹⣧⣷⠶⢿⣶⣤⣾⢋⣥⣤⡙⠂
⠀⠀⠀⠀⠀⣤⡶⢦⡈⠙⣩⣍⣿⣾⣇⡐⠦⣟⣠⣴⣼⠇⠿⢶⡶⠟⡀⠀⠸⢧⣬⡿
⠀⠀⠀⠀⠀⠙⠛⠛⠃⢄⠻⣯⣿⠋⢍⣿⡛⠛⠉⠍⡄⠈⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠉⠉⠙⠳⢦⡀⠀⠀⣀⡤⠶⠒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠹⣦⠞⠁⠀⠀⠀⢀⣀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣰⡟⢻⣿⣶⣿⣿⣿⣷⠀⢸⣤⡞⣹⣿⣾⣿⣿⣷⡀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣇⣿⣿⣿⣿⣿⣿⣿⠇⢀⡿⣿⣾⣿⣿⣿⣿⣿⠁⠀⢸⠇⠀⠀⠀⢀⡀
⠀⢀⣤⣤⣤⡀⠀⠀⢳⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠋⠀⣸⠃⠈⠻⢿⣿⡿⠛⠁⠀⢀⡾⠀⠀⠀⠛⠉⡟⠷⡄
⠀⠋⠉⣧⠀⠀⠀⠀⠈⢳⡀⠀⠀⠈⠙⠻⠛⠉⠀⢀⣴⠋⠳⣄⡀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⢰⠃
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠉⠳⢤⣄⣀⣀⣀⣤⠶⠋⠁⠀⠀⠈⠙⠓⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠤⣤⣤⣤⣤⣤⠤⠶⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣤⡤⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣄⣼⡿⣷⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣶⡏⢟⡇⠻⢿⠿⣇⠊⢳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠋⡿⡿⠿⢶⢷⡌⢀⣼⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠶⠿⡏⠂⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠙⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⡿⠂⠁⠀⠀⢠⡀⣀⢂⠀⠀⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣬⡙⢋⠇
⠀⠀⠀⠀⠀⣠⣶⡿⠿⢫⠙⠿⠶⠒⢂⠐⠛⣄⠻⠿⠻⠁⠀⠀⠠⣆⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⢦⢢⣦⣼⡇
⠀⠀⠀⢀⣾⣷⣮⡀⣠⣀⡄⣀⠀⣰⣺⣠⣀⢿⠋⠀⠀⠡⠀⠀⠀⠈⠝⠀⠀⣿⡛⠶⣤⠀⠀⠀⣼⣿⣶⣿⣿⡿
⠀⠀⢀⣾⣿⣿⡟⠁⠈⣛⣾⡿⠒⠺⣿⣿⣉⠀⠀⠀⢀⡴⡆⠇⢠⠀⠀⠀⠀⠈⠛⠂⠈⠁⠀⢸⡿⢿⠿⢿⡿⠁
⠀⠀⢸⣿⣿⣟⠂⠀⣼⢿⡿⠁⠀⢠⣿⣿⡇⠀⠀⢀⠊⢠⠇⠀⠠⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⢹
⠀⠀⢸⣾⣿⡏⠀⠀⢻⣸⣄⣼⠯⠛⢱⣶⣬⠀⠀⠈⠀⠁⠀⠀⠄⠈⠒⠦⠄⠀⡀⠀⠀⠀⠀⠀⠒⠃⡠⠂
⠀⠀⠘⣿⡜⡿⠁⠀⠸⣷⡜⣿⡷⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠁
⠀⠀⠀⢿⡷⣘⣴⣦⢀⠀⣤⣿⠃⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠘⠬⢀⡀⣀⢀⡀⠤⠄⠐⠊
⠀⠀⠀⠘⣿⡹⣿⣷⢀⢸⣿⣇⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⢀⠈⢀⠘⣿⣷⡍⢻⣶⣿⡉⠑⠚⠁⠀⠀⢀⣠⠤⠖⠊⠁
⠀⠀⠈⣾⣶⣿⡇⣾⣿⣽⣿⣿⡿⠇
⠀⠀⠀⠙⠝⠟⠿⣿⣦⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣀⡈⠤⠴⠒⠒⠒⠒⠂⠂⠤⢅⣀⣤⣶⣶⣤⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⣈⣉⣉⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠦⡀⠀⠀⢀⠙⠦⣀⠀⡀⠀⣀⠴⠊⠀⠀⠀⢀⣔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠻⣷⣤⣀⡑⣤⡤⠉⠉⡉⢄⣤⣊⣤⣴⣾⠟⠀⠈⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠻⠿⣿⣿⣶⣶⣾⣿⡟⠛⠉⠁⠀⠁⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠉⠉⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠀⠦⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣠⣬⣉⡑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣁⣤⣤⣤⣌⠲⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣌⠢⠀⠀⠀⠀⠀⠊⣠⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢿⣿⣿⣿⣿⣿⡿⠀⠤⠤⠤⠀⢿⣿⣿⣿⣿⣿⠟⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣈⡙⠛⠛⣉⠠⠀⠀⠀⠀⠀⠀⣉⠛⢛⣉⠡⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⠿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄⡤⢠⢠⢤⣀⡤⣄⡴⣄⣤⠀⢠⡄⢤⡤⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⡿⢾⢸⢸⣿⡇⡀⡇⣿⣿⠀⣾⣿⢸⡇⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠃⠘⠈⠛⠉⠛⠁⠛⠋⠙⠛⠋⠙⠘⠁⠙⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠤⠤⠄⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠈⢨⠿⡤⠄⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡀⠀⠀⠀⠀⠀⠈⠉⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠐⠀⠀⠂⠀⢀⠂⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠠⢀⠤⢤⢀⠂⢠⡾⠀⠀⣀⠀⠀⠀⠇⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠅⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⢀⠎⠑⠂⠠⠀⠜⠉⠐⢗⡩⢇
⠀⠀⠀⠀⠀⠀⢀⠾⠁⠀⠀⠀⡄⠀⠐⠠⠤⠤⢇⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄
⠀⠀⠀⠀⠀⠀⡮⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠲⢄⡀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢰⠓⠒⠢⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠡⡸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠤⣀⣀⣀⡀⠀⠀⠀⠀⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠑⠲⠋⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠦⡀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠚⠙⡆
⠀⢀⡤⢄⣾⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣤⠴⠊⠁
⠀⣏⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠖⠒⠒⠒⠛⠳⢤⡀
⠀⠘⠦⠤⠤⣴⠇⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⠖⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⢀⣠⡤⠤⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠛⡷
⠀⠀⠀⠀⠀⣀⣉⣳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠃
⠻⣏⠉⠉⠉⠉⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢸
⠀⠈⢳⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⢦⣀⣀⡀
⠀⠀⠀⢳⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡠⠚⠉⢧
⠀⠀⠀⢸⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡤⠊⠀⠀⠀⢸⡀
⠀⢀⣠⠋⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠸⡇
⢰⠋⠁⠈⠁⠓⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠸⣆⠁⠀⠀⠀⠀⠀⠉⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢻
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⣄⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠙⠢⣀
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠤⠤⠶⠶⠛⠓⠋
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠶⠒⠒⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⣰⡥⠤⠖⠒⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣄⣀⣠⣤⣤⣤⣤⣤⣤⣤⣠⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⡛⠛⠿⠟⠛⠛⡉⠩⠍⣛⡻⠯⢝⣫⢿⣿⣿⣟⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠪⠓⠢⢍⠉⠉⠩⠤⠔⠂⠀⠥⢒⠈⠁⠈⠁⠊⠙⠙⢚⢗⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⡬⠷⡶⠖⡷⠿⢷⠥⠀⠈⠰⠀⠄⠠⠄⠀⠀⠀⠀⠀⠀⠒⠀⠉⠛⠻⠿⣿⡿⢿⣿⡟⠛
⠀⠀⠀⠀⠈⢿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣫⣤⣦⣶⣶⣼⣿⣧⣦⣶⣡⡂⠘⠙⠰⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠐⠁⢀
⠀⠀⠀⠀⠀⡩⠳⠚⠐⠻⢻⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣶⣤⣈⠙⠻⢶⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⣤⣶⣖⢠⣠⡖⢶⣦⡀⠉⠛⠻⢿⣿⣿⣷⣀⣉⠛⢿⣴⣤⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⠿⠿⣿⣿⣿⣿⠅⠀⠀⠀⠀⢸⣿⢯⢙⣼⣤⣀⣽⣿⡇⠀⠀⠀⠀⠉⠻⢿⣿⣿⣶⣦⡉⠻⢿⣮⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⠋⢀⣾⠟⠛⡩⣷⠀⠀⠀⠀⠀⠀⠻⠉⠛⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠐⢹⣿⣿⣿⣿⡆⠄⠙⠻⣯⣢⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠈⠻⠒⠒⠚⠻⠧⣀⠀⠀⠀⠀⠀⠑⢿⣶⣶⣾⠟⠀⠀⠀⠀⠀⠀⠁⠡⠈⠀⠁⠞⠉⠻⠿⡷⠂⠀⠀⠉⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⣲⠦⣄⣈⠃⠶⡠⠄⢀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣦⣤⣀⣁⣀⣀⢀⡀⣀⣀⣀⣠⣤⡴⡾⢯⠣⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠜⠉⢉⡛⠛⠛⠛⠿⠛⠋⠙⠙⠩⠁

⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣦⣄⡀
⠀⠀⢀⣴⣾⣿⠿⠛⠋⠉⠉⠛⠻⢿⣿⣦⣀⣴⣶⣿⡿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣿⣷⣶⣄⣠⣾⣿⠿⠛⠛⠉⠙⠛⠛⢿⣿⣶⣄
⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧
⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⢰⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⢸⣿
⠈⣿⣿⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⢸⣿
⠀⢻⣿⣧⡀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⣠⣿⡿
⠀⠀⠙⢿⣷⣤⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠉⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠟⠀⠀⠀⣠⣶⣿⣿⣿⣿⣶⡄⠀⠀⠸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣼⣿⣿⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣽⡟⠁⠉⠉⠙⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠁⠘⣿⣏⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿
⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⣿⣿⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⢸
⠙⢿⣿⣶⣶⣶⣿⣿⠿⠟⠛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠛⠻⠿⣿⣿⣶⣶⣾⣿
⠀⠀⠀⠈⠉⠀⠀⠀⢀⣀⣴⣿⣧⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣿⣷⣄⣀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⠉⣉⣉⡉⠉⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠉⠉⣉⣉⡉⠙⠻⢷⣦⡀
⠀⠀⠀⠀⢀⣾⠟⣡⡴⠟⠛⢉⠉⠛⠳⣦⡀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠉⢀⣤⠾⠛⠋⠉⠙⠛⠷⣤⡙⢿⣆
⠀⠀⠀⠀⣾⠏⣼⠋⣠⠂⠁⠀⠉⠙⠦⡀⠻⣦⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⣰⡟⠁⡤⠞⠁⠀⠉⠑⢦⡈⢻⡌⢿⡆
⠀⠀⠀⢸⣿⢸⡇⡸⠁⠀⠀⡀⠀⠀⠀⠹⡀⢹⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⡟⠀⡜⠁⠀⠀⠀⠀⠀⠀⠹⡀⣿⣸⡇
⠀⠀⠀⢸⣿⢿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⣾⡇
⠀⠀⠀⠀⢿⣿⡁⢷⡀⠀⠀⠀⠀⠀⠀⣰⠃⣼⣇⣼⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣧⡸⣷⠀⣧⠀⠀⠀⠀⠀⠀⢀⣼⢃⣿⣿⠇
⠀⠀⠀⠀⠈⠻⣷⣤⡙⠶⣤⣤⣤⡴⠞⣁⣼⣿⡿⠟⠛⠻⠿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⠿⠛⠛⢿⣿⣷⣌⡻⢦⣤⣤⣤⡴⠟⣡⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣶⣶⡾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣶⣿⣷⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢉⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡋⠀⠀⠀⣀⡤⠤⠤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠈⠑⢦⡀⠀⠀⢀⡤⠚⠁⠀⠙⢦⠔⠋⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠉⠳⠔⠋⠀⠀⠀⠀⣰⠃⢠⠴⠒⠲⢄⡤⠖⠒⢦⡀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠳⡄⠀⠀⠀⠀⠀⠀⣠⠞⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⣴⢋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣣⠀⠀⠈⠢⣀⠀⠀⣠⠞⠁⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠳⣄⠀⠀⠈⠳⠚⠁⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⠤⠤⠴⠖⠋




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠛⠒⠲⠤⢤⣀⣀⠀⠀⠀⢀⡤⠏⠹⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠷⠶⠚⠀⠀⠀⠈⠙⠦⣀⠀⠀⠀⣀
⠀⠀⠀⠀⣠⣶⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⠒⠚⠁⠀⠀⠀⠀⠀⠀⢤⣀⡤⠚⠅⡉⡡⠋
⠀⠀⠀⣸⠃⠈⠉⠛⠒⠤⢤⣀⡀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡀⢀⣔⡼⢋⠉⠁⠠⠠⠆⡀⠠⠀⢁⠀⠂⢀⣄
⠀⠀⠀⠻⠬⣂⡀⠀⠀⠀⠀⠀⠉⠙⠶⢏⠉⠓⠁⠀⠀⠀⢐⡠⣾⠟⠁⠈⠘⠒⠪⣤⠒⠀⠀⡜⠀⠁⠠⠐⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⣄⣀⠀⠀⠓⠤⢢⡀⠀⠀⢸⣵⠞⢉⠀⠀⠀⠠⠐⠂⡠⢄⡁⠁⡀⠎⠁⠀⠀⢀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠤⢄⣉⠇⠰⠸⣄⠀⠈⠉⠒⠀⠠⠄⠁⠈⣀⠔⠈⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠐⠘⢦⣀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠑⢦⡀⢀⣀⠀⠀⠉⢿⠒⠦⠤⣀⣺⡉⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠒⠒⠚⠁⠀⠀⠀⠈



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

⠤⠴⠞⠿⠻⠗⠾⠀⠀⠤⠠⠀⠄⠶⠶⠶⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠾⠷⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⣴
⡐⠀⠈⠠⡄⢠⠉⢩⠀⠁⠀⡌⣁⠈⡈⢐⢀⢂⠀⠒⠂⢀⣐⢢⣀⣠⣠⡀⠐⡴⠶⠖⣠⠀⠂⠰⠖⠰⠂⠖⠠⠐⠒⠶⢠⣴⢀⠖⠜⠃⠀⣯⣤⠄⣴⡏⠘
⠖⠀⣀⢀⠀⣀⢀⠀⠀⠀⠀⠂⠱⠞⠓⠖⠐⠤⠀⠭⠁⢭⠌⢠⠀⡅⠨⠁⣥⠍⣀⠋⢉⡋⢀⡙⠀⠻⠀⠂⠀⠆⠠⠀⡤⣤⢤⣀⡄⠀⢀⡿⠃⢠⣿⠃
⠁⢠⡄⣤⣤⢡⠬⢼⣩⠀⣍⣁⡀⢀⣈⢓⡈⠉⠛⠚⠂⠰⠠⠴⠂⠀⠤⢄⡄⢀⣁⣁⣈⠀⠉⠉⠀⠀⠚⠃⠂⡔⠀⢰⠆⣥⢈⠙⣇⠁⠀⠃⠀⢸⡏⠀⠀⢠⡖
⠀⢠⡀⣨⠄⢠⢄⢤⠤⣤⠀⠤⠄⠤⡌⢠⠧⡄⢀⡉⣉⡘⢐⢂⡐⠒⠒⠂⠤⠠⠨⢀⣉⡀⠃⠈⠟⢸⠃⠔⡶⠶⠀⠖⠀⠀⠉⣤⠙⠀⠀⠀⢰⣾⠇⠀⠀⡾
⠁⡈⢁⣥⡄⢨⡄⣤⠀⢀⠀⣴⡤⣤⡄⠀⢠⡄⢠⡄⢈⣁⣈⠀⣈⡃⢘⠐⠰⠷⠐⠒⠲⢅⠈⡍⠁⡐⢰⡆⠰⢿⣤⣤⠔⠏⣠⠇⠀⠀⢀⠀⣼⡏⠀⠀⣸⠃
⠀⠃⠈⣁⠁⢈⠀⠈⣀⢈⡀⠀⢀⣨⡁⢀⡈⡁⠀⡁⠈⡉⠉⠀⡙⣁⠘⠀⠋⠘⠒⡶⠀⢠⡀⣀⣀⢁⠈⠃⠘⡄⢠⣼⣷⠀⠙⠀⢀⡖⠁⢰⡏⠀⠀⠀⣿
⡀⠘⠗⠙⠦⠈⠃⠀⠁⡀⠙⠀⠈⠟⠋⠀⠀⠻⠰⠿⠐⠋⠂⠸⠇⠟⠀⠻⠃⠔⡰⠂⣰⢌⡅⡁⢈⣋⠈⠁⠶⠂⠈⠀⠀⠀⠀⢠⡾⠀⠀⣸⠁⠀⠀⠰⡇
⠀⠀⢤⡄⢄⠀⢴⠀⠶⣤⠀⡴⠠⣶⠀⠰⣤⠄⢠⡆⠀⢰⡀⠀⡤⠀⠀⠀⢠⡄⡀⠀⢁⣈⠙⠁⠉⠉⠀⠀⢀⡀⢀⠀⠀⢲⣾⣿⣧⡀⢠⡟⠀⠀⡀⢠⡇⠘
⠶⠀⠘⠃⠀⠀⠈⠂⠀⠁⠀⠙⠀⠈⠀⠀⠘⠀⠈⠃⠀⠘⠃⠘⠀⠛⠀⠀⠈⠁⠇⠀⡟⠁⢀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠉⠛⠛⠳⠦⠤⢤⣼
⠀⠀⠀⠠⠔⠀⠀⠀⣀⠉⠀⣶⠀⢱⡆⠀⢰⡶⡤⣄⠐⢲⢶⠀⡆⠐⢠⡄⠀⠀⢠⡄⢸⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠂⠀⣀⡀⠈⠉⠛⠓
⠿⢠⢁⠀⢶⠀⢠⠃⠸⠀⠀⠻⠀⠀⠁⠀⠘⠀⠀⠀⠀⠟⠀⠀⠁⠀⠈⠀⠈⠀⡞⠀⣿⠀⠀⣴⠃⠀⠀⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠛⠓⠀⠀⠀⠀⠒⠒⠀⠀⠀⠶⠶⠦⠀⠀⠀⠀⠀⢰⠏⠀⣰⠣⠀⠀⠀⢀⣸⡄⠀⠀⣤⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⣀⠀⡄⠀⢠⡀⠀⠀⡤⡄⠀⣄⠀⠀⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠀⢀⡿⠀⠀⠀⢀⠸⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠛
⠘⠇⠀⠀⠀⠙⠈⢈⣃⡀⠀⠀⢤⣄⠈⠀⠀⠀⠀⢀⣁⣉⠀⠈⠛⢦⠀⠀⠀⠁⠠⠀⣰⡞⠁⢠⠆⠀⠈⣤⠴⢀⠐⡀⠠⠀⠀⠀⢤⠄
⠆⠠⠶⣿⣷⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠠⣶⣤⡀⠀⠘⠋⢀⣤⠏⠀⠀⠀⠀⠠⠀⠁⠙
⣧⠀⠀⠀⠀⣠⣤⣤⣦⣀⠀⠀⠀⠀⠂⠀⠀⠉⠉⠀⠀⠀⠀⠀⠛⢳⣤⡤⠴⠀⠈⠀⠀⠛⣍⠀⠀⠀⠘⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠶⠿⢛⡀⠀⣀⠀⢶⡀⢶⡀⠒⢀⡄⠒⠀⠤⠀⠉⠡⠄⠛⠂⠀⠀⠀⠀⠀⠈
⠉⠠⣦⡈⠉⠀⠀⠀⠘⡇⠀⠐⠂⢙⡀⠰⠦⠀⠀⠁⠀⠀⠠⠈⠛⠂⠀⠠⠈⠉⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠈⠀⠴⠀⠀⠴⠶⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠿⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⢿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠉⠀⠀⠀⠀⠀⠈⠻⣿⣶⣿⣿⣿⣿⣷⣶⣿⡿⠋⠁⠀⠀⠀⠀⠙⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⡀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠈⠉⣩⣴⠶⠾⠿⠷⢶⣤⡉⠋⠁⠀⠀⠀⠀⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢀⣾⠏⠁⢠⣾⣿⣶⠀⠈⠻⣦⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⣾⠇⠀⠀⠘⠿⠿⠟⠀⠀⠀⢻⡇⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⣿⠀⢀⡀⠀⢀⣤⠀⠀⢀⡀⢸⡇⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠹⣧⠈⠛⠶⠛⠉⠳⠶⠋⢁⡿⠁⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⢹⣿⣷⣄⠀⠙⠷⣦⣀⣀⣀⣀⣠⣴⠟⠁⢀⣤⣾⣿⡃⢀⣠⣴⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠛⠛⠛⠿⣿⣿⠟⠋⠙⠻⢶⣤⣌⣉⣙⣛⣋⣉⣠⣴⠾⠛⠉⠙⠿⣿⣿⠟⠋⠉⠉⠉⠛⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠉⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣶⣤⣀⣀⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣦⣤⣴⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣏⣁⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣼⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠋⠉⠉⠉⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠉⠉⠛⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⢠⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣃⢀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⢀⣼⣿⠿⠿⠿⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣶⣶⣶⣿⠿⠃⠀⠀⠀⠀⠘⢿⣿⣶⣶⣴⣶⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠞⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠚⢶⣤⢀⠀⠘⠇
⠀⠀⠀⠐⠐⢄⠀⠀⣄⠀⢉⣀⠀⠀⢀⣏⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠲⠦⣤⡌⡀⠀⠀⠀⠀⠀⠘⠤⡉⠁⠀⡠
⠀⠀⠀⠛⠲⡀⠁⠒⠀⠘⣤⡁⢭⣍⢉⡄⠉⠒⠒⠛⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⡞⠀⠀⠀⠀⡾⡔
⠀⠀⠀⠀⠠⣄⠙⠢⠀⠀⠀⠀⠀⠈⠻⠃⠀⢄⠀⣢⡀⠀⠀⠀⠀⡆⠀⣀⡀⢠⡞⠀⠀⠀⠀⡰⡝⠀⠀⢀⡒⠉⠠⡁⢄⠀⠀⠀⠀⠂⠀⠀⠀⢠⡀
⠀⠀⠀⠀⢸⠄⠉⠒⠲⠠⠄⡐⠀⠀⠘⠂⠀⠄⠀⠉⠃⠀⠀⢀⠂⠀⠉⠙⠻⠃⠷⣤⣤⣀⡜⠸⠁⠀⠀⡀⠈⢂⡀⢱⢸⡀⠀⠀⠀⠀⠀⠈⠉⠀⠁
⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠨⠀⠀⠁⠀⠀⠀⢠⡁⠀⠀⠀⠈⢙⡧⠁⠀⠀⠀⠙⠦⠬⠧⠰⠈⠀⠀⠀⠐⠴⠤⡄⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⣄⡀⠀⠀⣠⡟⠀⠀⠀⠀⠀⡾⠁⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠷⢶⡿⣀⡀⠀⠀⠠⡰⠁⠀⠰⣪⢟⣭⣿⣿⣢⠀⠀⠀⠀⠀⡄⠙⠐⠃⠃
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣾⠃⠀⢀⡄⠁⠏⡀⠁⠾⠋⣣⡀⠀⠀⠀⣇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠓⠖⠖⠆⠒⠂⠖⠉⠁⠀⠀⡀⠈⠙⠛⠒⠂⠁
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⡀⠈⠀⢀⣠⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢴⡿⠏⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠰⢅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⠀⠀⠹⣧⣾⡷⢾⣯⡿⢳⡀⠀⠀⠀⠀⢀⣴⣏⠁⠀⢿⣿⠜⡶⣄⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠀⠀⠀⣧⢠⣆⣥⢴⢋⣵⡿⢛⣭⠶⢿⣷⣦⣄⠠⠂⠈⠻⣿⣷⣤⢄⠌⠛⢦⣄⡙⠳⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣵⣰⢿⣋⣵⣾⡛⣟⣿⠶⡶⢞⠉⠀⠀⠀⠀⠈⠢⡝⢃⠀⠀⠀⠀⠈⠑⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠈⠁⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠠⠀⡿⠀⠀⠀⠸⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠤⠤⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⡍⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡤⣤⣄⠀⠰⣈⣉⢀⣠⠞
⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⡀⢠⠆⠀⠀⠀⠸⠄⠀⡈⠙⠡⠄⠠⠤⠄⠀⠀⠴⠕⣀
⠀⠀⠀⠀⠀⣉⠆⠀⠀⠀⠀⣢⡀⠀⠀⠒⠄⠾⠀⠀⠀⠀⠀⢸⡣⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠉⠁⠀⠐⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢷⣄⠈⢢⣤⣶⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠙⢷⣌⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⢢⠀⠒⠀⠀⠀⠀⠂
⠀⠀⠀⠠⠄⠀⠀⠴⠀⠀⠀⠀⠠⠀⠀⠀⢰⠁⠀⠀⣾⣶⡠⠤⣀⢀⡴⣛⠲⡀⠀⢠⠀⡀⠄⢀⡴⠃⠀⢀⡄⠠⠀⠄⠀⢺⠀⠀⢀⠆⠀⠄⢀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡁⠐⢂⣀⣈⠶⠀⠀⠀⠉⠂⠄⠀⢡⠔⠁⠀⠈⠳⣄⣽⣴⠖⠀⠀⠀⠀⠸⡀⠀⠂⠀⠲⢂⣀⠴⠚⠖⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠠⠈⠙⢣⠀⠀⠀⠌⠙⠃⡄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠚⢒⠀⠀⡀⠀⠐⠉⢃
⠀⠀⠀⢠⣀⡀⠀⡄⠓⠂⠋⠈⠈⠈⠈⠒⠒⠄⡀⠀⢀⡤⡀⠀⠀⢀⠱⠆⠊⠁⠁⠁⠉⠑⠐⠢⢀⠀⢀⡀⡀
⠀⠀⠀⡄⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣀⢀⠂⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢀⢀
⠀⠀⠀⣐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣
⡀⠠⢤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠠⠦
⠱⣀⢴⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠠
⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠰⠁⢀⣠⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⣄⠀⠱⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠔⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠛⢻⡆⠀⠀⠀⠀⠀⠀⢰⠟⠛⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⡜⠒⡀
⠀⠡⠠⠼⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⠀⡀⠃⠀⠀⠀⠀⠀⠀⠸⣄⠀⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣸⠄⠄⠆
⠀⠀⠀⠠⢥⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⡀
⠀⠀⠠⠁⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡋⠀⡐
⠀⠀⠀⠈⠈⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠁
⠀⠀⠀⠀⠀⠠⠈⠙⢢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⠉⢃
⠀⠀⠀⠀⠀⠀⠁⠂⠃⠈⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠑⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠈⠑⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠋⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠨⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖⠓⡀⠈⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠄⠁⡱⠦⢤⠀⣀⠤⠶⠌⠐⠠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠌⠉⠐⢀⠠⠂
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠒⠒⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⢀⡀⠒⠂⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⢀⣴⡆⢀⣴⠋⠁⣤⣬⣹⣿⣄⡄⢠⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢇⠀⠍⢱⣬⡵⢾⠟⠛⢿⣿⣿⣇⢻⣾⠟⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠆⢈⠈⢭⠓⠂⠀⠴⣿⣿⣴⣿⢛⣥⢾⣿⡆⠀⠒⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣦⣄⡀⢠⣿⡆⠀⠀⠀⠀⣂⡈⣓⠺⣧⣀⣠⣦⣬⣭⣍⣽⣿⣷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣷⣤⣄⡀⠀⠈⢳⣽⣿⣤⣤⣬⣉⣛⠻⢿⣿⣿⣿⠟⠁⠀⠀⣠⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⢉⡙⠻⣿⣧⡀⠀⣀⣙⡛⢿⣿⣿⣿⣋⣿⣿⣿⣿⣵⣶⣿⠛⣿⣟⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢿⣿⠿⣿⢿⣿⡿⠋⢉⣿⣿⢿⣿⣿⣿⣿⣿⡏⠉⠻⣼⡁⠉⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣈⣀⡡⠉⠉⠀⠀⠀⠀⠛⠋⠁⠈⠿⣿⣷⣷⡀⠀⠘⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣉⠀⠄⠀⠀⠀⠀⠀⢀⣠⣾⢿⣦⣾⡿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡻⣿⣦⠀⠀⠀⠀⢐⢋⣶⣿⣺⣿⣿⠶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠹⡟⠛⠉⡻⣧⣀⣀⠈⢨⣿⡍⣿⡿⢿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣶⣬⣛⣶⣬⣿⣿⣿⣦⠈⣿⡏⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠿⢁⠋⠀⢱⣤⠇⠀⠀⣀⣴⡆⠀⠀⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣼⠃⠀⢀⣾⣿⡿⠿⢤⣾⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡔⠀⣴⣿⣿⣿⠋⢸⣠⡿⠟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣾⣿⣿⣿⢀⣁⣸⣿⣧⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⡹⠿⣿⠿⣿⣿⣿⣿⡦⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⠠⣴⣿⡷⢶⣮⠭⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠿⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢹⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⢸⡆⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢉⠙⠋⠉⠱⣦⣆⠀⠀⠀⣀⠀⠀⣰⣿⠃⣤⡀⠀⠈⢿⣶
⠀⠀⠀⢸⡷⠀⠆⠰⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⡞⠀⠀⢧⠀⣿⢿⢃⠀⠀⠙⠛⠚⠋⠁⣀⣈⠙⠛⠛⢋⠁⠤⣄
⠀⠀⠀⠘⣿⣀⠐⠠⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⡀⣸⠃⠀⠀⢸⠀⣽⣿⠸⠀⠀⠀⣠⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⣴⣿
⠀⠀⠀⠀⠈⢿⣷⢀⢠⣠⠀⠁⡰⠀⠀⠀⠀⠀⠆⡏⠀⠀⠀⠘⠀⢹⣿⡇⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⢶⣤⣾⠿⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠔⡀⠐⢃⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠐⢃⠈⠞⡄⠀⠀⢂⢸⡄⠀⠀⢀⡇⣼⣿⡇⠀⠀⠀⠀⠀⠀⣤⣄⣠⣽⡟⠂⢑⣦⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣑⠂⢀⠀⠀⢸⡞⣿⣆⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⢤⣤⡾⠋⣹⣿⡛⡛⢿⣧⡐⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠒⠂⠀⠈⢿⣿⣿⣇⣼⣿⡟⠁⣀⠀⠚⣻⣦⡴⢻⣁⣩⣿⣿⢻⣿⣿⣿⣵⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣀⠤⠤⠤⠤⡠⠤⠤⠤⣍⠛⠻⠟⠋⠀⠀⠈⠙⠲⢿⣿⡽⣯⣭⣻⣿⣿⣾⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⡷⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⢀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⠄⣿⠠⠤⠶⠤⣧⠠⠶⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡄⠀⠀⠀⠁⠀⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣿⠀⠀⠀⢸⡿⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⠈⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⣷⠶⠦⠒⢲⡗⠶⠦⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡀⠀⠀⢻⣇⠀⣀⡘⢟⣆⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠛⠖⠋⠁⠈⠉⠁⠈⠉⠉⠉⢉⢷⡅⠘⠶⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⢀⡘⠁⠀⠀⠀⠀⠀⣀⡀⠀⣒⣒⣒⣂⣰⡇
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣄⠀⡰⠃⠠⣤⠋⠀⠀⣤⣄⡀⠀⣉⣙⡛⠛⠂⠉⠛⠃⠠⠄⣴⣾⡆
⠀⠀⢀⡀⠀⠀⠀⢀⣀⠀⣦⣿⣬⣿⣿⣿⣿⣾⣿⣿⣿⠀⠢⣄⣠⣀⣙⠓⠈⠻⢭⠉⢛⠛⣲⣶⠶⠶⠿⠻⠿⣥⣠⣶⣾⡇
⠀⠀⠼⢻⣦⣲⣤⣤⣿⣿⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠪⡉⠻⣬⡛⣶⣤⣤⣄⣈⠁⠈⠀⠀⠀⢀⣴⣾⣿⣿⣿⣯⡀
⠀⢀⡤⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠂⢀⠙⢧⣄⠀⣀⣩⣽⢷⣶⣤⡀⣸⣿⣿⣿⣿⣿⣿⡿
⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠢⢨⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡰⠁⠀⠀⠈⡇⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠃⠀⠀⠀⠀⠸⠃⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡰⡄⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡰⠁⠹⡄⠀⠀⠀⠀⠈⡇⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠚⠀⠀⡰⠁⠀⠀⠱⡀⠀⠀⠀⠀⠋⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢠⠃⢰⠛⢄⠀⠱⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⡇⠀⠀⠳⡀⢳⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⡆⢇⠀⠀⠀⢳⠀⡇⣀⣀⣀⣸⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣦⡤⠒⠉⠉⠙⠒⢤⡀⢈⡷⠋⠉⠀⠈⠉⠓⣌⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡜⠀⡴⢦⠀⠀⠀⠀⠙⠞⠀⠀⠀⠠⣎⣳⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠉⠁⠀⡀⢠⣀⣇⣰⣁⡆⡄⠀⠈⠀⠀⡜⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⢄⠀⠀⠀⢸⡊⠉⣞⣳⠀⢉⡽⠀⠀⢀⠞⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⠳⣄⠀⠀⠏⡲⢪⠥⡖⠻⠈⢀⡴⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮⡑⢦⡀⠀⠈⠀⠀⠀⡠⣪⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢬⡓⢄⡀⣠⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣀⡴⢚⣉⣁⡀⠁⠉⠉⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠦⠴⠃⣠⠞⢁⡞⠋⠀⢀⡔⢋⠉⠀⠠⡀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠈⢣⠀⢸⡆⠀⠀⡸⢠⡎⠉⠢⠀⠈⢣⡄⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠁⠀⠀⠀⠀⣠⠏⢀⣾⡇⢆⡇⢡⠘⢌⢂⣰⢱⢀⠀⡥⢆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣼⡏⢀⡞⠁⠘⢦⠱⣀⠀⣠⣤⣥⡖⣚⣐⣡⠇⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⡎⠀⠀⠀⠈⢆⣀⣉⠢⡀⠤⠒⠋⠉⠁⢀⡞⠁⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠒⠢⢄⠀⠀⠀⣀⣀⣸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠳⣌⠢⢄⡉⠐⢲⠞⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠀⠀⠙⠄⠀⠀⠉⢻⡇⠀⠀⠀⠀⠛⣀⡠⠤⠶⠶⠤⢄⡠⢀⣨⠷⠖⠒⠛⠉⠀⢰⠖⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠠⡀⠀⠈⡄⠀⢀⡼⢷⡀⠀⢠⡖⠛⠓⠤⣀⢀⣠⣤⡀⠈⠋⢁⣀⡀⠀⣿⠛⠒⠋⠀⢨
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠙⠢⣰⠀⣸⠁⡜⠁⠀⠀⣙⡷⣾⠁⠀⠀⠀⠈⠉⠁⠀⠀⠑⠢⠞⣹⠟⠊⠁⠀⢀⡶⢤⠎
⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⢂⡇⣸⢁⡠⠖⠋⢁⡞⢉⣷⣤⣄⣀⣀⡀⠀⠀⣀⣀⡤⢞⣁⡀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠉⠉⠁⠒⠠⠈⠟⣁⣁⣀⣀⡼⠉⡴⠋⠁⢡⠉⠉⠉⠉⠛⠿⣟⡶⠾⠛⠉⠉⠑⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⣀⣤⢸⠀⠀⣠⠟⣠⠊⠀⣀⠤⢼⡴⠂⠤⠤⢤⣀⠀⠙⢄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠈⣇⢀⠔⢡⠼⠁⠀⡼⠁⠀⠈⠀⠀⠀⠀⢠⠟⠀⠀⠈⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⡴⠃⠀⢀⡼⢁⣠⠔⠋⠀⠀⠀⣠⠏⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠈⣓⣒⣀⡛⠻⢭⡐⠢⢄⣀⣠⠔⠛⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠖⠉⠀⠀⠈⠙⢦⠀⠈⠢⡀⠈⠳⡒⠤⠄⠀⠀⠈⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠘⡄⠀⢳⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣸⠷⠦⠤⠤⠤⠶⠒⠒⠂⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠉⠉⠙⠛⠿⢿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄
⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦
⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀
⠀⣼⣿⡏⠀⠀⠀⣀⣤⣤⣤⣿⣿⠿⠿⣿⣷⡀⠀⠀⠀⠀⢀⣾⣿⡿⠿⣿⣿⣤⣤⣤⣀⠀⠀⠀⢹⣿⣧
⢰⣿⡿⠀⠀⠀⣼⣿⠿⠛⢿⣿⠇⠀⠀⠹⣿⣷⠀⠀⠀⠀⣾⣿⡏⠀⠀⠸⣿⡿⠛⠿⣿⣷⠀⠀⠀⢿⣿
⣾⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠂⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠻⣿⣷⣄⡀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣶⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣶⣾⣿⡿⠟⠋⠀⠀⠀⠀⠀⣿
⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⢻⣿⣇⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⡟
⠀⠈⢿⣿⣆⠀⠀⠀⠀⢻⣿⣯⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⢩⣿⣿⠁⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠻⣿⣷⡀⠀⠀⠀⠹⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠁⠀⠀⠀⢀⣾⣿⠟
⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠈⠻⢿⣿⣶⣦⣤⣀⣀⣀⣠⣤⣶⣾⣿⠿⠋⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⡀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⢀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣶⣤⣄⣀⣀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣠⠀⠀⠀⠠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⠤⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣂⠴⠄⢙⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠄⠀⠀⣠⠞⠃⠀⠈⠻⡄⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠙⣆⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠈⡀⠀⡀⠀⣀⠀⠤⠀⠀⠀⠀⠈⢆⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣴⢦⣈⡃⢠⡀⢀⠂⠀⠒⠀⠀⠀⠀⠈⢆⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠚⢠⡀⢩⡇⠸⡸⢎⠀⢳⠀⡆⠄⠀⠀⠀⠀⠀⠀⠈⢧⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⢰⠋⠁⢁⠘⠀⡠⠇⠀⠂⣼⠖⠁⢀⢑⡄⠀⠀⠀⠀⠀⠈⢇⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⢁⣀⠔⠀⡰⠂⠈⠀⠈⡠⠀⠀⡁⠀⢀⠀⣸⡍⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠴⠊⠁⠀⠀⠀⠍⠉⠂⡆⠀⠁⠂⣶⣁⣱⡈⠈⠢⡀⠀⠀⠀⠀⠀⠹⣤⣀⠁
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⢀⠀⠄⠈⢆⠀⠀⡀⠀⠀⠀⠀⠈⣧⠓⠈⢆⠙⢂⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠊⠀⠀⡰⠂⠀⡀⠀⠀⠀⠁⠀⠀⢸⡀⢰⠁⠠⠀⠀⢀⡄⠈⠀⠀⠘⡀⠀⠃⠢⢀
⠀⠀⠀⠐⢀⠀⠐⢘⠈⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⣇⢈⠀⠀⠀⠈⡇⢱⠀⠀⠀⠀⢦⡠⠂⠁⠀⠈⢀
⠀⠀⠀⠀⠈⠓⢦⡘⡀⠀⢠⠀⠀⠀⠀⠡⢀⡀⠀⠀⠈⠀⠀⠀⠀⡃⠀⡇⠀⠀⠀⠘⣍⢫⠀⠀⠀⠀⡧⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠳⢤⡀⠀⠀⠀⠀⣅⠀⣀⠀⡠⢌⣁⡀⠀⣦⣠⣅⣰⣀⠀⢀⣸⠗⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠁⠈⠉⠁⠈⡤⠀⠁⠈⠭⠀⠨⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⠉⢉⠱⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⣆⢴⣏⣀⣀⣠⣨⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡾⢿⠻⠿⠃⠁⠝⠉⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠛⠻⠟⠁⠀⠀⠀⠀⠑⢐⠀⠀⠀⢀⡈⠳⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⣆⠦⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡗⣤⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣾⢿⣿⡁⠬⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⠲⣶⡀⠀⠀⠀⠀⠀⠀⢺⣤⠋⠀⠀⢀⢻⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣦⡝⠁⠀⠀⠀⠸⠘⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠀⠀⠀⠀⠀⠢⢹⡄⠀⠀⢀⡤⠃⠀⠀⠀⠀⠀⢀⣾⡄⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠁⠀⠀⠀⠀⠀⠀⠻⢷⡀⠀⠉⠀⠀⢀⠀⠀⠀⠀⣠⠟⠛⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⠖⠛⣳⠀⡤⠀⠀⠀⡀⡤⠔⣻⠟⠰⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⣤⠶⠉⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⣀⠀⠀⠀⠀⢀⣀⣤⣾⠃⠀⠠⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠛⠛⠛⠋⢻⣿⣏⠀⠀⠗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣿⣾⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⡄⠀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠿⠉⠛⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠏⠁⠀⠀⠀⢸⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⣼⣧⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⡀⢸⣿⠘⣇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢻⣿⡀⣿⠀⠀⠀⠀⠀⠀⢸⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢩⠂⠀⠀⠀⠀⠘⢻⡇⣿⠀⠀⠀⠀⠀⠀⢸⠃⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⡇⠿⠀⠀⠀⠀⠃⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⢿⠟⢻⠿⡿⠟⣿⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣒⣦⠀⠀⠀⠴⢦⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠉⠀⣲⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠉⠉⠒⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⣀⠀⢀⣸⣶⣇⣀⣠⣤⠄⠸⣄⢀⠄⠀⠀⠀⡞⡃⢠⠅⠀⠀⢀⡀⠍⡉⠙
⠀⠀⠀⠀⠀⠀⢀⣀⡠⠄⠀⠀⠀⠀⠀⠘⠱⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⢄⣤⡤⠦⢤⣀⣀⣀⣁⣠⣤⠀⠸⠁⠀⠀⠀⠀⠉⠑⠛⠓⠶⠷⠤⠈⠷⠿⠦
⠀⠀⠀⠀⠚⢀⡀⠀⠀⢀⣀⣤⡶⠓
⠀⠀⠀⠀⠑⠠⢬⣙⠻⣾⡏⢁⡐⠠⡀⢄⠀⠴⢒⠀⠀⠀⠀⠀⢀⡠⠐⠚⠦⠀⠀⠀⠀⢀⣦⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠺⠷⠾⠳⠶⠏⠂⢀⠀⠀⠀⠀⠀⠀⡁⠀⠠⢐⡂⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠰⠆⠀⠀⢀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠣⠀⠡⣤⡀⠀⠀⠿⢙⡒⠶⠆⠀⠀⠀⠀⠀⠹⣅⢂⡵⠖⠊⠁⠀⠀⠀⢀⠠⠤⠤⠤⠀⢀⠀⡀⡤⠀⠀⠀⠀⠀⠳⡄⢢⣩⣤⠴⠚⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⣀⠰⠎⠠⢐⢂⣒⣁⣐⣋⠄⠀⠀⠀⠀⠙⡌⢍⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣧⡀⠀⠖⢂⣰
⠀⠀⠀⢀⣀⣀⣀⣁⠀⢀⡴⠐⠋⠐⠀⠠⣌⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠡⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣡⣴⢺⡿⠂
⠀⠀⠀⡶⢠⠤⠤⠭⠾⠇⠀⠀⢠⣓⣤⣄⢉⡽⣤⠇⠀⠀⠀⠀⣀⣀⠤⠢⠄⢀⡤⠖⣋⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠠⢀⣀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠰⢧⣤⣶⣿⡀⠀⠀⣐⡄⣠⣌⠟⣋⡕⠂⠀⠀⠀⠀⠀⠀⠉⡄⠐⠓⢈⣀⡼⠖⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠓⠀⠶⢦⡀⡈⣀
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠉⠉⠀⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⣻⠟⠭⠂⠶⠊⠉⢛⠉⠛⡆⠀⠀⠀⠀⠀⢸⣠⠀⠀⠀⠀⠈⠉⢹⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢢⠀⢈⣒⣇⣣⣤⠷⠞⠃⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠛⠛⠓⠀⠓⠁
⠀⠀⠀⠀⢀⣀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠰⠊⠁⠘⠀⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⢩⠟⡷⠄⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠐⠢⡀
⠀⠀⠀⢦⡀⠒⠉⠀⠋⠆⠀⠀⠀⠀⠀⠀⡠⠤⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⣜⡵⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⡀⠠
⠀⠀⠀⠈⡏⡀⠀⠠⠀⠘⡄⠀⠀⠀⠀⠈⠉⠠⠀⠁⠴⢊⠁⠀⠀⢀⢀⠘⠒⠇⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠱⠂⠈⠐⠢⠩⠍⠉⠥⠞
⠀⠀⠀⠀⢹⣠⠀⠀⡬⠰⠳⠀⠀⠀⠀⠀⣖⢶⢤⣅⡠⠐⢉⠀⣄⡤⠀⣤⡾⠂⠀⠀⠀⠀⠀⠰⣁⣒⣤⠔⡓⡴⠁
⠀⠀⠀⠀⠀⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡠⠀⢀⣉⡁⠶⠶⠶⢄⠛⠘⠚⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢹⡆⠀⠀⠀⠈⡇⠀⢀⢀⠁⣀⣀⣠⡤⠀⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠙⠦⠔⠛⠉⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠤⠶⠒⠚⠙⢿⡀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⡤⠖⠂⠲⡃⠈⠁⠀⠀⠉⢣⠀⠀⣀⣲⣤⣷⡴⠮⠟⠛⠛⢆
⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠈⠀⠀⠀⠻⡆⠑⠀⠀⣀⣙⣆⣤⣴⡾⠶⠛⣾⠛⠉⠉⠀⠀⠹⣦⠀⠂⠀⣠⣳
⠠⠋⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢠⠞⠀⠄⠲⡤⢄⡠⢡⠐⠀⠀⠀⠀⠉⠹⡆⣁⣤⣤⡤⠽⡷⠛⠛⠋⠉⠙⠇⠀⠠⡆⠀⠈⣆⠀⣠⡤⠴⠖⠚⠚⠉⠉⠉⠁
⡦⡉⠒⠒⠂⣀⠉⠁⠳⠀⠀⠀⠀⠁⠈⠠⠀⡄⠀⢀⠀⠀⠂⢀⠀⠀⠀⠀⢢⡻⡭⠉⠀⠀⠀⢰⡄⠀⢀⣀⣀⣰⣄⠠⠖⠚⠛⢉⠁⠀⣠⠆⠀⣀⡴⠆⠐⠒⠂
⠘⠂⠘⠐⠒⠙⠀⠉⠀⠀⠀⠀⠀⠈⢺⠷⠂⠶⢤⣵⣤⠐⠒⠁⠀⠀⠀⠀⠀⢷⠉⣂⣠⠤⠶⠶⠓⠊⠉⢩⢀⣀⠀⣀⣀⠠⠴⠟⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠡⠄⠁⠉⢙⡀⢠⠀⠀⠀⠀⠀⠀⠀⠈⢾⡇⠀⢀⣀⣀⠶⠗⠒⠚⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⣴⣌⡄⣈⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁
⣶⣶⡶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣟⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⠟⠁⠀⠀⣠⣿⢃⣾⠃⠀⣾⠇⠀⣠⡿⣧⣼⡿⠛⠁⠀⠀⠀⠀⠀⠀⢠⡾⠃⢀⡜⠁⠀⠀⢠⣿⣧⣃⣤⢾⡟⠀⢀⡆
⠛⠁⠀⢀⡴⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⣠⡾⠛⠻⠟⠁⠀⠀⢿⣤⡾⠋⠀⠀⢻⣀⣀⣴⠖⠀⠀⠀⠀⢀⡿⢁⡴⠋⠀⠀⢀⡴⣿⣏⡟⠉⠀⣾⠁⢠⠚⠷⣴
⣀⣀⡴⠞⠀⠀⠀⠀⠀⠀⠸⣿⡀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣾⡷⠋⠀⠀⢀⡴⠋⠀⠻⠛⠀⠀⠀⠿⠖⠁⠀⠀⠸
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄
⠀⠀⠀⢠⡾⠛⣦⠀⢀⣠⣾⠆⠀⠀⠀⠀⠀⣴⡶⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⢀⣿⣿⣰⣿⡶⠿⣿⡏⠀⢀⡄⠀⢠⣾⠋⢠⣾⠇⠀⠀⠀⠀⠀⠀⣠⡟⠁⢀⡼⠁⢀⠄⠀⠀⠀⢴⡆⠀⠀⢀⡀⠀⢀⣴⢿⡆⢠⡀⠀⠀⠀⣠⣿⣿⠁
⠀⣴⣿⣿⢋⣿⠋⠀⣸⣿⠀⢀⣾⡇⢠⣿⣃⣴⠿⠃⠀⠀⠀⠀⠀⢀⣾⡿⠁⣰⠟⠀⣠⢷⣠⡤⠊⣠⠏⠀⠀⠀⣼⠃⣠⣞⡡⠋⠀⢸⠃⠀⠀⣰⣿⡿⠁
⡾⠋⢿⣇⡼⠃⠀⠀⣿⡇⢠⣾⠉⠓⢾⡿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣡⡞⠁⢠⢾⣏⡠⠀⠀⢠⠏⠀⠀⣠⠎⠻⣴⣿⠋⠀⠀⣠⡟⠀⠀⢠⣿⡿⠁
⠁⠀⠀⠉⠀⠀⠀⠀⠻⢷⠿⠁⠀⠀⠸⣇⣀⣀⣤⡴⠂⠀⠀⢀⣿⣿⠟⠃⢀⡴⠋⠈⠉⠀⠀⠀⣏⠀⢀⡼⠁⠀⠀⢾⣿⣀⣠⣾⠏⠀⠀⢠⣿⡿⠁⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⣿⣟⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠿⠶⠋⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⣼⡿⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⣠⠟⠀⠀⡠⣄⠀⠀⡀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀
⡆⠀⢸⡆⠀⠀⠀⠀⠀⢀⣾⣿⢃⡾⠋⠀⣠⣶⡇⠏⣠⣾⠏⠀⣴⠂⢠⣾⣿⣿⠋⠀⠀⡀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⢠⣿⢻⡆⠀⣠⣿⠃⢀⡀⠀⣠⡿⠋
⠀⠀⣸⠇⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⢀⣴⣿⣏⡟⠋⣹⡟⠀⡴⣿⣤⣿⡿⠋⠁⠀⣠⠎⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣼⡿⣿⣧⣾⣿⠃⠀⣸⡇⢰⣿⣡⣾
⠀⣴⠏⠀⠀⠀⠀⠶⣾⣿⡏⠀⢀⣴⠏⠸⠿⠟⠀⠀⢿⣧⠞⠁⠀⠹⣿⣄⣀⣤⡾⠃⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠛⢹⡏⠀⣰⡟⠙⣿⠟⠋⠁
⡾⠋⠀⠀⠀⠀⠀⠀⣿⣿⣥⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⣠⣿⠛⢿⠟⠀⠀⣿⡇⣴⡿⠁⠀⢿⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠙⠻⠛
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⣠⡖⢶⡄⠀⢀⣴⡷⠀⠀⠀⠀⠀⣠⣾⠟⣶⡀⢠⡏⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⢠⣿⡇⣼⣧⣶⢿⣿⠃⠀⣀⠀⠀⣴⡟⠁⣴⡿⠀⢸⡇⠀⠀⣠⣾⠟⠀⠀⠀⣠⠖⠀⣸⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀
⠁⣶⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⣰⣿⡿⢻⣿⠉⠀⣾⡏⠀⢠⣿⠀⢰⣿⣠⡾⠛⠀⠀⠀⠳⠶⠿⠋⠁⠀⠀⢠⣾⠏⢀⡼⠁⣠⠈⠀⡠⢀⡟⠁⠀⢀⡖⠀⣰⢏
⢠⠇⠀⢠⣿⡿⠃⠀⠀⠀⢠⣾⠟⣿⢃⣾⠃⠀⢰⣿⠃⢠⡿⠉⠳⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢏⣴⠋⢀⣴⠋⡙⠋⢀⡞⠀⠀⣠⢾⣇⣼⡿⠋
⠏⠀⢀⣾⣿⠃⠀⠀⢀⣴⡟⠁⠀⠉⠛⠁⠀⠀⠈⢿⣴⠟⠁⠀⠀⠹⣇⣀⣠⣴⠖⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠁⣴⠋⠘⠛⠀⠀⡼⠀⢀⡴⠁⠀⢸⣿⠀⣀
⠀⠀⣸⣿⠃⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢁⣠⠟⠁⠀⠀⠀⠀⠀⠿⡶⠋⠀⠀⠀⠈⠛⠛⠋
⠀⠀⣿⡏⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠁
⠀⠀⠻⢧⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⣠⣾⠟⠁⢠⣤⣄⠀⠀⣠⣶⠄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢷⠀⠀⠀⢀⡀
⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣠⣾⡟⠁⠀⢠⣿⣧⣿⠶⢻⣿⠃⠀⢠⡄⢀⣔⢋⣼⠃⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣠⠏⠀⠀⢠⡏⡃⠀⠀⣠⡟

⠀⠀⠀⠀⠀⡠⠄⠂⢉⡐⠤⢀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠁⠂⡝⠁⠒⠄⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠠⢄⠀⠀⠀⠀⠀⠁⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠍⠐⡄⡀⢀⡌⠀⠀⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠌⡐⠀⠁⠈⠐⠂⢄⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡐⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠐⠄⢠⡤⢤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⡅⠠⠀⠀⠀⢀⣴⠏⢋⠉⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠡⢀⣴⣿⣿⠀⠀⢂⠀⠐⠠⡊⠁
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠂⢉⣛⡛⠋⢀⣀⠀⢢⠀⠀⠀⠺⡀⠑⢄
⠀⠀⠀⠀⠀⢀⠂⠀⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢷⣄⠡⠈⣿⣿⠃⠠⠉⢉⢽⠀⠀⠀⠀⠈⠀⠀⠱⢄
⠀⠀⠀⠀⢀⠂⠀⠌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠩⠷⣡⠸⡿⠠⢁⠔⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⢄
⠀⠀⠀⢀⠂⠀⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠠⠄⠙⠷⠷⠦⠠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⡆⠀⠑⢄
⠀⠀⢀⠂⠀⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠁⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⢀⠱
⠀⢀⠀⠀⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠈⢀
⢀⠂⠀⠎⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠡⠀⠈⢄
⡆⠀⠎⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠤⠄⠤⠤⠤⠤⠥⠄⠬
⣤⣶⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠛⠛⠛⠛⠻⠷⣶⣤⡀⠀⠀⠀⢀⣤⣶⡾⠿⠟⠛⠻⠿⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⠀⠀⠀⠀⡘⣄⠳⣀⣀⠀⠀⠐⠘⣟⣿⣿⠋⠐⠲⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣌⠑⢦⣤⣤⡼⢾⣿⣽⣷⣭⣶⣾⣿⣿⣿⣿⣷⣶⣤⣧⣀⠈⠙⣷⣆⡀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⢤⣬⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡀⠙⢦⡀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢒⣲⣿⣿⣻⣿⣿⠋⢯⣹⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⠀⠙⠦⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠹⣿⣿⡇⠀⠘⢻⣿⣿⠟⠺⢷⣿⣿⣿⣿⣿⡟⣿⣿⡿⠻⣿⣮⣳⡀⠈⠂⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠁⢻⣻⣿⠀⠀⠈⣿⣂⠖⠈⠙⢿⣿⣿⣿⡿⠫⢿⡟⠀⠀⢿⢻⣷⡝⠄⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⢰⢿⢿⣧⣄⠀⠘⢿⡀⠀⠀⠀⠏⠉⣉⣋⢠⠟⠀⠀⠀⠈⠀⢙⣿⡄⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠁⠀⠹⣿⣿⣷⣄⠀⠙⠦⣴⡊⡈⠸⡁⢘⠁⠀⠀⠀⠀⠀⢀⣄⢉⡿⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⢹⡗⣿⣿⣿⣷⣶⣤⡀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠊⠉⣿⠛⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢸⣿⠇⠙⣿⢶⡟⠉⠙⣏⡉⠉⠉⠉⠀⠠⠤⠐⠀⠀⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⣿⠀⠀⠘⣿⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⢀⣤⡾⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢿⣦⣿⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⢻⢷⣦⣀⣀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢂⢠⢊⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⡇⢸⠃⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⢢⣼⡡⠞⡰⠖⢂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⢹⡀⡜⠁⠀⠘⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡤⠤⢤⣀⠀⡁⠀⠈⠁⡇⠀⠀⠀⢳⠀⣀⠔⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⢒⡶⠋⠀⠀⠀⠀⠈⠉⠢⡀⠈⠳⣇⠀⢰⠂⠀⠀⠀⢀⡮⠞⢋⠨⠵⠆
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠄⠀⠤⠤⣄⡀⠀⣠⠊⠁⠀⡤⠒⠋⢐⣲⡤⠤⠤⠄⡀⠀⠀⠘⡆⠀⠘⡧⣌⡙⠓⠒⠚⠉⠀⠚⢥
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⠁⠀⠀⠸⠀⢠⠊⠀⢀⠤⠠⢤⠀⠘⠦⡀⠀⠸⠀⠀⠘⣄⣜⠉⠉⠉⠉⠓⢦⡀⠇
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠉⠒⠦⣄⣨⢧⠀⠀⠀⠰⠀⣼⢆⠠⣡⠖⠀⠒⣿⠀⠀⣸⠀⠀⡇⠀⠀⢁⠈⠉⠲⣄⠀⠀⠀⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣀⠀⠀⣠⠖⠋⠁⠘⡆⠀⠀⠀⠱⠝⣄⠙⠢⠤⠖⠊⣛⡤⠊⡌⢀⡴⠁⠀⠀⢸⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠈⢑⠞⠀⠀⠀⠀⠀⢳⠀⠀⠀⢠⠆⠈⠢⡀⠀⠠⠀⠉⠀⠀⣧⠊⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠊⠹⡀⢀⡴⠊⠉⠉⠙⢆⠀⠀⡎⠀⠀⠀⠑⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⣸⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠲⢄⣀⡀⠀⠀⣳⠋⠀⠀⠀⠀⠀⠀⠑⢦⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠴⢊⠝⠋⠁⠀⠀⠀⠀⠀⢠⡏⠁⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⠭⣧⠤⢤⡀⠀⠀⠀⡴⠿⠶⣤⡈⠉⠀⠒⠠⠶⠶⠒⠒⠉⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⣠⡞⢀⡤⠂⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠙⢖⠤⢀⣀⣀⣀⠠⣤⡴⠋⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠉⠙⠳⢦⡀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠒⠒⠒⠒⠚⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠒⠚⢻⠤⠤⣤⡤⠤⠴⠶⠒⠈⠿⠄⠀⠀⠀⠀⠀⠹⣟⠁
⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⣀⣀⣘⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠐⠢⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⠶⠋⠉⠀⡴⠛⡏⠉⠓⠲⡖⠒⠒⣶⣏⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢀⠞⠁⠀⢰⡄⠀⠀⠁⠀⠀⣿⠀⠉⠛⠲⠦⠤⣤⣤⠤⠴⠚⠁⠀⠀⠀⠙⠲⢤⣤⣀⣀⣀⠤⠤⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠊⠀⠀⠀⢸⠛⠦⣄⡀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠉⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⡠⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠚⠉⠉⠉⠉⠓⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠉⠉⠉⠉⠑⠒⠤⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠘⢆⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠉⠓⢴⡁⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠈⠙⠢⣄⠈⡆⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡼⠁⠀⠀⠀⠠⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘
⢠⠏⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⢣⡜⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢀⣌⡉⠛⠻⠂
⡞⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⣴⡟⠻⣿
⡇⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣴⣿⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⣿⣧⣴⣿
⣇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢸⡀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠻⢷⣄⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠘⣷⡀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⣞⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠘⢷⣄⠀⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠙⠻⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠶⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠒⠉⠀⠙⠻⢶⣤⡀⠀⠀⠀⠀⠀⢀⢔⣿⠇
⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣤⣾⣵⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢗⣦⣀⠀⠀⠀⠀⠀⠀⣀⠤⢺⣧⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢸⣿⠀⠉⠲⢤⣤⠒⠉⠀⠀⠀⢿⡄⠀⠀⢸⡟⠢⠤⠖⠊⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠁⢸⡿⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⢸⣷⣄⠀⢸⡇⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠼⣿⡿⠷⢸⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠰⠿⣿⡿⠄⢸⡇⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠾⠷⡄⠀⠈⠻⣦⡖⠤⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠸⣀⠀⠈⠲⢄⠀⠀⠀⡠⠼⠧⡄⠀⠀⠀⢀⡤⠿⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢠⠃⠀⠀⠀⠀⠀⠉⠢⡄⠀⢱⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢠⠖⠉⠉⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠁⢠⠃⠀⠀⢣⠀⠀⠇⠀⠀⠀⠀⠸⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠰⡤⢃⡤⠒⠒⠋⠀⢸⠀⠀⠀⡠⠔⠒⠁⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠊⠉⠁⠀⠉⠁⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠮⣀⠀⠉⠐⠀⠀⠀⡠⠤⠒⠊⠁⠀⠀⣀⠠⠄⣛⠤⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠈⠑⠲⠭⣐⡠⠀⠀⢸⠀⣀⡠⠄⠀⢀⠤⠶⠺⠫⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⢄⣜⠀⠀⠉⠀⡤⢈⣩⠥⠶⠚⡿⠁⢠⡄⣀⣠⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡿⣦⣀⠀⠃⢸⠁⠀⣀⣷⠡⠒⠛⠋⠁⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡄⣷⡈⠫⠙⡷⠼⠞⠋⠁⠀⠀⠀⠀⠀⢀⣒⡚⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢰⠂⠀⠳⡼⠉⢦⣀⣁⣤⠤⣤⡤⠔⢶⣺⠋⡩⢁⠞⠀⠚⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⢶⡤⠦⡄⠑⡄⠀⠙⠁⠀⠀⠁⠀⢀⡾⣡⡞⣀⣌⡠⠤⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠠⣲⣄⠉⠉⡟⠀⢴⡃⢱⢌⠲⠠⠧⠬⠤⠀⠚⢛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠀⠰⡀⠀⠀⠙⣆⡏⠀⠀⠀⢀⢀⣀⣭⣽⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⣀⠀⠀⢠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⡀⣸⠀⣆⠀⡇⠀⢰⡇⡒⢰⡧⣴⡇⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⣇⢠⡘⡦⣇⣻⣇⣿⣄⣷⣷⣿⠃⣇⣾⢣⣿⣼⣿⡿⣄⡴⣴⡆⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⢌⣿⣧⣿⣿⣼⣽⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⢟⣿⣿⣾⢋⣿⣯⣾⣣⡞⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠦⣀⣻⣖⣻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣡⡾⣃⡴⠋⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⣨⣿⣿⣿⣿⣿⣿⡿⠿⠛⢋⠉⠉⣍⣉⡟⢩⢋⠻⡿⣿⣿⠿⣿⣿⣿⣿⣿⣻⣵⣿⣿⣾⣯⡴⢟⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠉⢹⣿⠁⠀⠀⠀⣶⡿⠻⠟⠛⣷⠎⠀⠘⣿⣿⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣫⣴⡯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣿⣿⡿⠋⠀⠀⠀⠀⠸⣿⡛⠀⠀⢘⣿⣧⡀⠀⣠⣿⣖⡁⠀⢿⡿⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣭⣥⣤⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⢿⣧⡠⢔⡩⣻⠿⠷⠾⠿⡃⠀⠀⢀⣾⠁⢀⣠⣤⢤⣶⣴⣾⣿⠿⡿⣍⡛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢚⣋⡙⠻⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⠻⣿⣧⠞⡅⠀⠀⠀⠀⢳⡌⣠⠞⠁⣀⣢⣤⣶⣿⣿⣯⠛⢫⢔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢩⠟⢿⣶⣶⣿⣯⣭⣤⣌⣙⣿⣶⣦⣤⣤⣤⣶⣿⣷⣾⣿⣿⡿⢿⠛⠓⠀⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⡀⠈⠈⠁⠋⠉⠋⠙⠛⢛⠛⠟⠛⢿⠛⣿⠛⠏⠙⡟⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠁









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

⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⢠⠄⡀⣀⠁⠀⠀⠀⠉⡑⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣤⣄⣶⣾⣿⣤⡄
⠀⠀⡟⢀⠀⠀⠀⠇⠈⠀⠀⠀⠀⢀⡴⠗⠁⠀⠙⠀⠀⠀⠀⠘⠃⠀⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠓⠂
⠀⠀⡇⢀⠴⠊⡠⠢⡄⣰⣀⣤⢚⡁⠸⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⣀⠀⣸⣿⡿⢿⠂⠸⠿⣶⣶⣶⣆⣶⣀⡀⣀⣀⣠⣠⣤⡄
⠀⡄⡇⢸⣤⣰⠥⡾⢿⣿⣿⣿⣗⡒⢦⣀⣠⣭⡝⢺⠴⠾⠙⠛⠋⠻⣄⡸⠿⠛⠛⠀⠀⠀⠛⠛⠛⠟⠛⠛⠓⠚⠛⠛⠛⠛⠃
⠘⠑⠂⠚⠋⠉⢉⢉⢉⡀⠤⠌⣉⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣷⣶⢾⡿⠿⠿⢿⣿⣿⣀⣀⠸⠿⠿⠿⠷⠾⠿⠁
⠀⢲⠿⢿⠿⡿⡟⢿⢻⣧⣤⡤⠛⠉⠉⠉⠉⡉⠁⢀⠀⠀⣶⡄⣤⣰⠂⠀⢋⣄⡀⠀⠀⠀⣿⣿⠀⠀⣠⠤
⠀⠀⣆⢸⡾⠁⠘⣾⢀⡇⠀⠀⠀⣀⢀⣀⡠⠒⢂⣠⡄⣠⣿⡿⠋⣈⣈⠐⢧⣌⣱⣾⣿⠃⣿⣿⠀⠐⣿⡀⠠⠀⣀⠀⠀⠂⠁
⠀⠀⠘⢟⠁⠠⠀⢘⣸⡇⠀⣤⣀⡡⣬⣥⣤⣄⠙⣛⢋⣿⣿⡷⣸⣯⣿⣿⣿⢻⣿⣿⣿⡧⣿⣿⠀⠀⣿⡷⢲⠾⠃
⠀⠀⠀⠀⣱⣰⣏⠸⢿⡇⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣯⣿⣿⣿⣿⣛⣿⣿⠀⠀⣿⢃⠏
⠀⠀⠀⠀⠈⠹⣿⣷⣾⡇⠀⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⠿⣿⣿⣿⢋⣿⣿⠻⣿⡧⠀⠀⣿⣦⠁⠀⠐
⠀⠀⢀⠈⠡⠀⠘⣇⢸⡇⠀⢐⠀⠀⠀⡞⢁⠈⠀⠀⠶⠂⠬⠁⠠⢼⡊⣸⣿⣷⣟⠀⠄⣴⣿⡇⠀⠀⣿⣽⣇⠀⢀⣀⣷⠆
⠀⠀⠠⠀⠂⣀⠂⣻⣽⡇⠀⠠⠔⠣⣿⢠⣝⠇⠿⣀⠠⠆⣀⡓⠲⠶⢦⣼⣿⣿⣟⣡⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡶⢍⢀⡀
⠀⠀⠀⢠⣜⣉⣻⢨⣿⡇⠀⢀⣦⡴⠶⡖⠈⣒⢀⣞⠀⡂⠘⡅⠡⣄⣨⣩⣿⣿⣿⣿⣿⣭⣿⡇⢀⠀⣷⣿⣿⣿⣷⠼⠛⠷⠖
⠀⠠⠔⠋⠏⣀⠤⠴⢿⡇⠀⢠⡞⣣⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣸⠁⢹⣿⣿⣿⣿⣿⡇⡇⠀⠀⣿⠋⣽⣟⣷⡀⠀⢴⡀
⠀⠀⠀⢀⣭⣧⢴⢶⣷⡇⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣾⣿⣿⡟⠛⠉⠁⡃⠈⢠⠃⠘⣡⣶⡏⠉⠉⠉⠁
⠀⠀⠀⢸⠿⡔⠛⣸⣛⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠂⢀⣼⠀⠀⢸⣦⢾⣿⣩⣧⣤⡄
⠀⠀⠀⣻⣅⠜⢻⡷⣿⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣷⢜⠀⠂⠀⣿⢸⣿⣿
⠀⠀⠀⢿⣿⡶⠿⠣⣥⣛⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⢹⣆⣿⢨⠀⠀⠀⣸⣟⣿⣿⠓⠂
⠀⠀⠀⠀⠉⠻⣶⣴⣉⣭⣖⢚⣿⡿⣿⣿⢻⣿⡏⠛⠋⠉⠉⣿⠉⠉⠉⠉⡟⠉⠉⠉⠉⡟⠛⠃⠈⣏⠈⠉⠁⠍⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣛⠻⠾⠿⣯⣽⡿⣺⣟⡲⣿⣿⣶⣷⣞⠻⣿⣇⣸⣭⣭⠿⠟⠛⠛⠉⠙⢛⠿⠟⠃⠈⠛⠉⠁
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠙⡙⠿⠀⠀⠈⢿⣾⣿⡏⢩⡟⣿⡏⠩⠿⢦⡈⠙⢰⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢈⡓⠀⠀⢀⠈⠿⠿⣿⣟⣻⣿⢆⠀⢄⣰⣹⣆⣦⠀⠠⠀⠈⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⣠⠀⠀⠢⠀⠀⠈⠉⠹⣯⠼⠀⠀⢹⠎⣻⣧⣆⣀⡀⠤⠀⢀⠀⠀⢸⡟⣿⡶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠤⠀⠀⠸⠿⣿⣻⡇⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡶⠶⠿⠿⠿⠿⠿⠿⠿⠷⠶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣄⣴⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠈⠛⠃⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠈⠛⠋⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣤⣀⣀⣀⣀⣀⣠⣤⣴⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠷⢶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠿⠟⠛⠋⠉
⣿⣿⣿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣤⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡶⠶⠶⠶⠶⢶⣶⡄⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣰⢚⡆⠀⠈⠙⢶⣤⡄
⠀⠀⢀⣤⣠⣿⣿⣷⣀⣤⠀⠀⠀⠀⠀⠀⢸⣯⢱⡶⠶⠶⢶⠊⣿⡇⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠈⠉⠳⣄⠀⣠⠞⠙⢷⡀
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢸⣿⢸⡇⠃⠀⣸⠀⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⢇⣠⣄⠀⠁
⠘⠛⠛⠛⣻⠿⢼⡛⠛⠛⠛⠛⠀⠀⠀⠀⢸⣿⡴⠃⠀⠀⠘⢦⣿⡇⠀⠀⠀⠀⠀⠻⣟⡻⣿⣿⣻⡿⠃⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢾⣿⣿⡇
⠀⠀⠀⠀⣘⠍⠀⠉⠛⠰⠦⢄⡀⠀⠀⠀⠈⠋⠁⠀⠀⠁⠁⠈⠙⠁⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠋⠁


⠀⠀⠀⠰⡛⢳⠂⢰⣾⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡦
⠀⠀⠶⠶⣿⣿⠶⠦⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⠀⡀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢀⣀
⠀⠀⠀⠀⣿⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣯⣉⣉⡁⠀⠀⠀⠀⣠⣤⣤⣄⣿⣭⣭⣴⣿⢿⡏
⠀⠀⠀⠀⢻⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣏⣻⣙⣥⣤⣿⣧⣄⠀⠀⠀⠀⠀⠀⣨⡶⣮⡽⣿⢿⣽⢿⣽⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠋⠁⢸⣧⡄
⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠠⢿⣿⣭⣿⣛⣛⣻⠿⠀⠀⠀⠀⠀⠀⢿⣿⣿⠏⠉⠻⣿⣷⡿⠀⠀⠀⠀⠀⠈⢻⣯⣽⣽⣭⡯⣷⠀⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣽⡍⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣀⠠⠐⠚⠲⣯⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⢰⡿⢦⡀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠺⣽⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣯⡀
⠉⠀⠀⠀⠀⣿⣇⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣧⠀⠉⠁⢀⣨⣄⡀⠀⠀⠀⠀⠀⠀⣸⠟⣧⠉⠃⠠⣤⣤⣄⠀⠀⠀⠀⠀⠘⣻⣿⠈⠉⠀⣭⣥⣾⣿⣦⠄
⠀⠀⠀⠀⣴⢃⣟⠀⣸⣿⡇⠀⠀⠀⠀⢴⠏⠸⠇⠀⠰⠿⢿⡿⠿⠖⠀⠀⠀⠀⠸⠋⠀⠿⠀⠀⠺⠿⡿⠿⠿⠆⠀⠀⠀⣴⠏⢸⡇⠀⠀⠹⣿⠿⣿⠟
⠀⠈⠉⠉⠉⠁⠈⠉⠁⠀⠁

⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀
⠀⠀⠀⠀⢸⣇⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀
⠀⡀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⢨⣽⣭⡍⠻⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⡆⠀⠀⣿⣿⣿⣿⣿⠐⠘⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣾⡟
⠀⠀⠀⠀⢿⣿⣿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⣯⣽⣯⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣶⡶⠤⠤⠤⢤⣄⣀⡀⠀⠀⣠⣤⡀⠀⠀⠀⣿⣿⣿⠛⠛⣛⣛⣛⣻⣿⠿⠿⣿⣿⡿⠛⠻⣿⣿
⠀⠀⠘⠻⢿⠀⠀⠀⠀⠀⠀⠈⡆⠀⣿⣿⣷⠀⠀⠀⣿⣿⣿⣤⣀⣿⣿⣿⣿⣿⣿⣿⡜⣿⡇⠀⠀⢿⣿
⠀⠀⠀⠀⡾⠀⢴⣶⣦⣶⣦⠀⡇⠀⢹⣿⣿⠀⠀⠀⣿⣿⣿⣿⡏⣿⡟⠉⠙⠋⠉⣿⡇⣿⣷⠀⠀⢸⣿
⠀⠀⠀⢠⡇⠀⠈⠻⣿⠿⠃⢰⠃⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⢳⣿⣿⣦⡀⢀⣴⣿⢸⣿⣿⠀⠀⣾⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⣠⣿⣿
⠀⠀⠀⠸⡄⠀⢠⣤⣤⣤⣶⣾⣷⡆⠸⠃⠀⠀⠀⠀⣿⣿⣿⣿⡬⣷⣿⠿⠛⠛⠛⠋⠈⢙⣿⣴⣿⣿⣿
⠀⠀⠀⠀⠙⠤⠴⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣝⣛⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣠⣶⠾⠿⠿⠿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠿⠿⠿⢶⣦⣀
⠀⣠⡿⠋⠁⠀⢀⡀⠀⠀⠈⢿⣆⠀⢀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⣾⡟⠀⠀⠀⡀⠀⠀⠈⠻⣷⡀
⣰⡿⠁⠀⣴⣾⣿⣿⣿⣾⣦⣼⡿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣄⣾⣿⣿⣿⣿⣷⡄⠀⠘⣿
⣿⠃⠀⣼⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⡀⠀⢹
⢿⣇⠀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠁⢀⣿
⠈⠻⣦⣌⣻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣋⣤⡾⠋
⠀⠀⠈⠙⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠉
⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡩⠔⠒⠉⣉⡉⠑⠒⠬⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⣾⣿⣿⡇⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣄⣨⣿⣏⢀⡄⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⣧⠀⠀⠀⠙⠋⠁⠉⠋⠀⠀⠀⢰⠇⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣄⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣀⣤⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⢙⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣟⠉⠻⢷⣦⡀
⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠋⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⢰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⡀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⠀⣿⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⢹⡧
⠀⠀⠀⠻⣧⣀⠀⠀⢀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⢀⣠⡿⠃
⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣶⣤⣀⣀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠉⠉⠉⢹⠉⠉⠉⠉⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣄⠀⠀⠀⠀⣀⣴⣿⣦⣄⠀⠀⠀⠀⣀⣴⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠉⠉⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⡔⠋⠉⠓⣄⢹⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣸⣀⣀⡤⠴⠚⠚⠒⠦⠤⣄⡀⡴⣉⣤⣄⡀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡅⠀⠀⠙⡆⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢀⡟⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠭⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣀⡤⠬⣿⣀⣀⡀⢠⣶⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡞⠁⠀⠸⣿⣿⣿⣿⡝⠫⣄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡇⠀⠀⠀⠈⠙⠋⠉⠀⠀⠈⣇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢒⡞⠙⠢⣝⠲⠤⢤⣀⣀⣀⠤⠚⠀⠀⠀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⢀⡞⢀⣀⣀⣀⣉⡓⠲⠤⠤⠤⠤⠤⢤⣶⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⢀⡴⠟⠋⠁⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⢀⡎⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢸⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡴⠒⢶⡲⠤⣼⣦⡀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⣸⠟⢠⣦⣇⠀⠀⠀⢙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⣷⣿⣷⠀⡏⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢹⡿⠋⡼⠁⠀⠀⠀⠀⠘⢷⠦⣀⠀⠀⢀⠔⠊⢉⠉⠛⢶⡦⡀⠀⢸⢻⡀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠒⠒⠛⠋⠉⠙⠮⣝⢲⢿⣶⠄⠻⠟⣠⣄⢱⠹⣄⡟⠀⠉⠙⡷⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⣴⣾⣷⣶⣌⠋⣸⠀⡏⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣿⣿⣿⠷⠃⡰⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⠭⠭⠤⠴⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋⠀⠀⠀⢀⣴⣶⣄⠀⣀⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⣄⠀⠀⠙⠛⠋⠁⣠⣴⣾⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣤⣄⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣠⣤⣴⣦⣤⣄
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⡿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣿⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣀⣀⣹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡟⠋⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠙⢻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠐
⠀⠀⠀⠀⢀⣀⣀⠌⠀⠀⣀⣀⡀⠉⠙⠛⠿⣿⣿⣿⣟⡁⢄⠀⣾⣷⠀⠀⠀⠀⠀⠀⣾⣷⠀⡠⢊⣻⣿⣿⣿⠿⠟⠋⠉⢀⣀⣀⠀⠀⠡⣀⣀⡀
⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠂⢸⣿⡷⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⢸⣿⡇⠔⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⡛⢷⣤⡶⠒⠶⣄⠀⠀⠀⠀⣀⠀⣴⠋⣡⢹⡆⢠⡞⢉⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⡴⠛⡿⢸⠏⠰⠟⠃⠿⠤⣤⡤⠾⠛⣿⠃⢰⢃⣞⠛⠛⠀⢈⣩⣉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢰⡀⠼⢁⠆⢰⣐⣋⡴⣷⣦⠤⣤⡤⠶⡏⠀⣠⠿⠿⢿⠂⣸⠿⠛⢯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⣿⣿⠟⠀⠋⠙⠁⣲⠘⠁⡆⠈⠐⠇⠁⠘⠁⡼⠀⡾⢀⡏⠰⢃⠺⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠘⠛⣡⣆⢠⣇⣈⣀⣂⣶⣐⣋⣄⣘⣼⡇⠠⠤⠶⠀⠚⠢⣥⣤⣭⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠉⠉⠉⠉⢿⡉⠛⠛⠛⠋⠉⣁⣀⠰⣶⣾⡿⠆⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠚⠋⠉⠙⠳⠶⠶⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢸⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⣧⠀⠀⠀⠀⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⠛⠛⠛⢻⠲⠟⠛⠛⠒⣿⠓⠚⠋⠁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢻⣿⡕⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣘⣲⣖⢒⡒⠿⠛⠿⣿⣛⠛⢟⡛⠛⠛⠓⡿⣻⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢦⠈⠛⠃⠀⠀⠀⠀⠀⠀⠈⠲⣤⣄⣀⡠⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠠⠋⠉⠀⠈⠅⠒⠒⠀⠀⣤⡤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠦⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⠤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠙⢦⡀⠀⠀⢀⣴⣋⢀⡴⠚⠛⠲⣄⠀⣠⠖⠛⠛⢶⡄⣈⣷⡀
⠀⠀⠀⢠⡏⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠛⠻⢿⣷⡄⠈⢷⠀⡼⠋⠁⠉⠛⠀⠀⠀⠀⢸⠆⡏⠀⠀⠀⠀⠛⠉⠉⠉⢳⡀
⠀⠀⠀⡿⠀⢰⣿⠟⣋⣉⣀⠀⠀⠀⠀⢠⣾⣷⡆⠙⠟⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⡇⠀⠈⠁⣾⠿⠿⠿⣷⠀⠀⠀⠸⣿⣿⡷⠤⢤⡀⢀⣿⠿⢶⣤⣀⠀⠀⠀⢀⡞⠀⠀⠀⢻⡄⠀⠀⠀⢀⣠⠶⢿
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠹⠏⠀⠀⠀⠘⡏⠓⢦⣤⡞⠀⠀⠀⠀⠀⠻⣄⡴⠞⠉⠀⠀⣿
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠚⢙⠆⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠠⣦⣄⣀⡀⠀⠀⣀⣠⣴⡄⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠤⠬⠃⠀⠈⠳⣄⠀⠀⠀⠀⣠⠞⢧⡀⠀⠀⠙⢦⣉⠉⠉⠉⣉⡴⠏⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠷⣄⣠⠞⠁⠀⠀⠛⢦⣀⠀⠀⠈⠉⠛⠋⠉⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⠤⡤⠤⠴⠖⠛⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⠤⣤⠤⠴⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠐⠀⢀⡴⢠⡀⠀⠰⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢠⠀⠀⠀⠏⠀⠀⠉⢠⠀⡀⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⠀⠀⠀⡃⢿⡀⠀⠀⠀⡄⠀⠀⠀⡄⢡⠀⠀⠀⠀⠀⠀⢠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠐⠤⢄⣀⠁⠌⠁⠀⠀⠀⠓⠂⠀⠁⠙⠚⠟⠒⠀⣀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⡀⢸⡀⠂⠀⠀⠀⢀⣀⠀⠀⠀⠔⠀⠀⢀⡠⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠙⠛⠀⢀⡜⠊⠀⠀⠀⠀⠀⠠⠴⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⠠⠐⠈⢱⠄⠀⠀⠀⠈⠀⠀⢀⣀⣈⣲⡒⠀⠶⠓⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⢀⠟⠢⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣤⠄⠀⠀⠀⠀⠐⠉⠁⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠐⠂⠛⠁⠀⠀⠀⠀⠀⠓⠒⠛⠓⠲⠶⡒⡟⠀⠈⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠛⠒⠒⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠻⡀⠎⠀⠀⠀⠀⠀⠉⠉⠓⠐⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⡀⠀⠐⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿