Surgical instrument Emojis & Symbols

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢀⠄⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⡇⠀⢸⠀⠀⠃⠀⠘⣀⠁⠀⢰⠀⠀⢰⡀
⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣧⠀⣿⠀⠀⠀⠀⡇⠀⢸⠀⠀⠣⡀⢠⣾⡀⢀⠆⠀⠀⠘⣷
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠇⠀⢸⠀⠀⠀⠀⢸⣿⠁⠁⠀⠀⠀⠀⣟⡇
⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢐⡗⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⢸⠀⡌⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣟⡅
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⢨⢩⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠘⡀⡇⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⣇⠃⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢘⣻⠀⠀⠀⢀⠔⠲⣇⡇⠂⢄
⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠂⠀⠀⡽⡀⠀⠈⠄
⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠰⠄⠔⠀⠑⠄⠔


⠀⠀⠀⡠⠤⡀⠀⡠⠤⡀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⡰⠁⠀⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⢆⠀⠱⡀⠀⠀⠀⠠⣿⡆⠀⠀⠀⠀⠧⢧⠤⠄⠀⠀⠀⠀⢿⠆
⠀⠀⠀⠣⡀⣠⣷⣀⣠⠆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⡅⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⣽⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⢫⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣠⠞⠢⡀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡾⠸⡆⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⣯⡆⠀⠀⠀⠀⢇⡀⢀⠇⠀⠀⠀⠀⣯⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢰⠀⢠⠁⠀⠀⠀⢀⡇⠀⣇⠀⠀⠀⠀⠀⢡⢠⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⠍⢹⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⠀⠈⡆⡎⠀⢀⠔⠀⢺⣄⣀⣼⠆⠒⠄⠀⠀⠸⣼⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⠀⠈⡆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⢸⠀⠀⡌⠀⠀⡘⠁⠀⠘⡀⠀⠈⡄⠀⠀⡇⠀⠀⠀⠀⢸⣯⡇⠀⠀⠀⠀⡆⠀⠀⡇⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠸⠀⠀⠐⠤⠚⠀⠀⠀⠀⠐⠢⠔⠀⠀⠀⠇⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⠀⠑⠤⠔⠁⠀⠀⠀⠀⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⡔⠉⠙⢢⡀⠀⣀⣑⣤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⠀⠀⣼⠁⢸⡆
⠀⠀⠀⠀⠀⠣⣀⣀⠜⠉⠉⠛⢿⣿⡿⠿⠿⠷⠶⢶⣆⣰⣶⣶⣤⠀⠀⠀⠀⠀⣸⢹⡄⠀⢠⡇⢸⡇⠀⣿⡆⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⣀⡀⠀⠀⠀⠀⣠⣤⠶⠚⠃⠀⠀⠀⠀⣿⣾⡇⠀⢸⣧⣼⡇⠀⢸⣷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠙⠻⠶⣦⣄⣈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢠⣿⣿⡅⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⣀⠀⣿⢿⡇⠀⢸⡿⣿⡇⠀⢸⡟⣿
⠀⠀⢀⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠤⠴⣿⡆⣿⢸⣿⠀⣼⠇⢸⡇⠀⣾⠇⢻⡇
⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠙⢰⣿⠈⣿⠀⣿⠀⠘⣷⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣿⢀⡏⠀⠀⣿⠀⡿⠀⠈⣇
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠉⠉⠉⠃⠀⢸⡇⠀⣿⢸⡇⠀⠀⣿⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠛⠿⠿⠟⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⢸⡇⠀⠀⣿⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⣀⣤⣤⠶⠶⠛⠛⠛⠉⠛⠳⣦⡀⢸⡇⠀⣿⠈⡇⠀⠀⡟⠀⡇⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡇⠀⣿⠀⣧⠀⢰⡇⠀⣿⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣀⠀⠀⠀⠀⠀⢀⠀⠈⡇⠀⡿⠀⢻⠀⢸⠁⠀⢹⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠶⠛⠋⠀⠀⠁⠀⠁⠀⠈⠀⠈⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠀⠒⠂⠉⠉⠉⠉⠉⠉⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠂
⠀⠀⠀⠀⠀⠄⠞⠉⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⠴⠤⠤⠤⢀⡀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀
⠀⠀⠀⡀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⣿⠈⡇
⠀⠀⡈⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣿⠀⡇
⠀⠀⢫⡀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢀⠀⠀⣀⠤⢄⡀⠀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢽⠀⡇
⠀⠀⠀⢟⠦⣀⠀⠀⠀⠀⢀⡠⢔⠉⠀⠁⠀⠀⢀⠀⠈⠁⠊⠐⠀⠐⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢸⠀⡇
⠀⠀⠀⠀⠈⠊⠉⠒⠒⠊⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢹⢳⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠀⠈⡏⡆⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⠀⠀⠀⠀⠀⡅⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⣧⡇⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⡬⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣥⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠃⢸⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡇
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⡇⠀⣇⣀⣀⡀
⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⢸⠀⠀⢨⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠙⠚⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡰⡆⠀⠀⠀⠀⠀⠀⠸⣅⡽⠀⠀⠀⠀⠀⠀⠴⠀⠆⠀⠀⠀⢀⡋⢩⢱⠀⠀⠀⠒⢎⣰⡆⠀⠀⠀⢶⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠧⠘⠀⠀⠀⠀⠀⠀⢀⠚⢂⠀⠀⠀⠀⠀⠀⡖⠋⢀⠀⠀⠀⠀⠈⡊⡹⡀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠸⠀⠀⠀⢠⣯⣦
⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⢠⠟⠁⠙⢧⠀⠀⠀⠀⠀⣇⠤⢞⠀⠀⠀⠀⠀⠐⠡⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠿⠄⠀⠀⠀⡆⠐
⠀⠀⠀⠀⢄⠆⠀⠠⠀⠀⠀⠀⡏⠀⠀⠀⠈⡇⠀⠀⠀⣐⠈⠀⠠⣀⠀⠀⠀⠄⠁⠀⠁⡄⠀⠀⡇⠀⠀⠀⠀⢸⠃⡇⠀⠀⠀⠇
⠀⠀⠀⠀⡴⠀⠀⢦⠀⠀⠀⠘⡁⠀⠀⠀⠀⣸⠀⠀⢀⡈⠀⠀⠀⢁⠀⠀⠀⠃⠀⠀⠀⠂⠀⠀⠁⠈⡆⠀⠀⢸⠀⣧⠀⠀⠰⣤⠤
⠀⠀⠀⢀⠃⠀⠀⠈⡀⠀⠀⠀⡇⠀⠀⠀⠀⡉⠀⠀⠀⡃⠀⠀⠀⢀⠀⠀⠀⢀⡁⠀⣆⠀⠀⠀⢠⣀⠄⠀⠀⢸⣀⡼⠀⠀⢀⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢠⣀⣠⣤⣤⣤⠀⠀⠀⣠⣤⣤⣤⣠⢤⠀⠀⠀⡌⠘⢤⡄⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠤⠀⠀⢼⣦⣀⣀⠄⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠠⡀⠀⠀⠀⠀⠉⠉⠁⠊⠘⠛⠛⠛⠛⠘⠀⠃
⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡉⢍⠉⠉⠉⠉⠉⠉⠁⠀⠑⠤⠄⠀⠀⠀⠒⠛⠋⠛⠉⠉⠉⠒⠒⠦⢤⣀⣄
⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠀⠀⠤⠛⠒⠛⠛⠛⠛⠃⠀⠁⠋⠃⠀⠀⠀⠶⠤⠤⠤⠤⠤⠤⠔⠒⠚⠁⠉⠁
⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⡾⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⠋⠀⠀⠀⠀⠀⢶⠒⠲⠆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⢰⡼⠀⠀⠀⠀⠀⠀⠨⠀⠈
⠀⠀⠀⠀⠠⢫⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠐⡖⠃⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠠⣔⠶
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠈⠈
⠀⠀⢀⣠⠀⣤⡔⢀⡀⠀⠀⢀⡀⠀⠠⣀⡀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⣀⠑⣤⡄⢀⡀⠀⠀⢀⡀⢀⣤⡀⣀⠀⠀⠀⣀⠀⣤⡔⢀⡀
⠀⠀⢞⠁⢸⠁⡏⠀⣹⠀⠰⡁⠈⣠⡎⠀⣹⠀⢰⡁⢈⣤⡎⠀⡱⠀⢸⡁⢈⡇⢼⠁⢸⠆⠀⣏⠀⣹⠠⡉⠀⠱⠀⢸⡁⢈⡷⣏⠀⣹
⠀⠀⠈⠉⠉⠀⠈⠉⠁⠀⠀⠉⠉⠁⠈⠉⠁⠀⠀⠉⠉⠀⠉⠉⠁⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠈⠉⠁⠀⠈⠉⠁⠀⠀⠉⠉⠀⠈⠉⠁

⠀⠀⠀⢀⡠⣀⡀
⠀⠀⠀⡆⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡤⠄⠀⠀⠀⠀⠣⡀⠀⠀⠀⠈⠓⡄
⠀⠀⠀⠀⠑⢢⠄⠀⠀⠀⠀⠸⡇⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⣿⠆⠀⠀⠀⠀⣿⡄⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠘⡗⠀⠀⠀⠸⣆⠀⠀⠀⠀⢹⡆⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⠀⠀⠀⠸⡄⠀⠀⠀⠹⡄⠀⠀⠀⠀⣷⡀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠘⡄⠀⠀⠀⢻⡀⡀⠀⠀⠸⣧⡀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠘⣾⣆⠀⠀⠻⣿⡀⠀⠀⢹⣷⠀⠀⠈⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠘⣿⣆⠀⠀⢻⣷⡀⠀⠀⢿⣇⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⠘⢿⣧⠀⠀⢿⣧⠀⠀⠸⣿⡄⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠈⣿⠧⠀⠈⡟⢣⠀⠀⢻⠓⠀⠀⢹⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠘⣦⠀⠀⠹⡄⢆⠀⠈⣇⠀⠀⠘⣟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠘⣧⠀⠀⢹⡈⠆⠀⢸⣆⡀⠀⢹⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠘⢧⣤⠀⢳⣾⡀⠀⢻⣣⠀⠘⣟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠈⢫⠣⠀⢻⣧⠀⠀⢯⠄⠀⢻⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠳⡀⠀⢻⣇⠀⠈⢇⠀⠘⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠙⡄⠀⠙⢦⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢳⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡿⢷⣦⣤⣀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠢⠄⠀⠘⢦⠀⠀⠀⠀⡆⠀⠀⡇⠀⠀⡇⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠀⣿
⠀⠀⢀⣴⣦⡄⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠀⣿
⠀⠀⢸⣿⢿⡇⠀⠠⠄⠤⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡄⠀⠀⠀⡏⠀⠀⡿⠀⠀⣿⠀⠀⣿⠀⠀⣿
⠀⠀⢸⣏⢸⡇⠀⠀⠀⠀⠈⠀⠀⢀⣀⠤⠖⠛⠉⠉⠉⠁⠀⠀⢠⣷⠀⢀⣿⠀⠀⣿⠀⠀⣿⠀⠀⣿
⠀⠀⢸⡿⢻⣇⠀⠀⠀⣀⣼⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠁⠀⠀⠁⠀⢀⣁⡀
⠀⠀⢸⠁⠀⣿⠀⠀⠁⠀⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣅⠀⡨
⠀⠀⣿⠀⠀⣿⠀⠀⠈⠉⠀⢀⣀⣀⣀⣀⣤⣤⣤⣶⣿⠿⠿⠿⠦⠀⠒⠚⠛⠛⠛⠻⠯⢭⣍⣉⡀
⠀⠀⣿⠀⠀⣿⠀⠀⠶⠞⠛⠉⠉⠉⠙⣤⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠈⠂
⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢱⠀⠀⠉⠉
⠀⠀⡏⠀⠀⢸⡇⠀⠐⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⡄⠀⠀⠀⠀⠀⢘⡶⠒⠁
⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢀⡤⠶⠒⠺⠷⣦⣤⣶⣿⣿⣿⣿⠟⠁⠀⠀⣀⡤⠒⢉⣹⣤⡤⠄⠠⡀
⠀⢸⡇⠀⠀⢸⡇⠀⠀⢰⠏⠀⡴⠛⠛⠻⢿⣿⣿⣿⡿⠛⠁⢀⣠⡴⠾⠗⠒⠉⠁⠀⠈⠠⠀⠔⠃
⠀⢸⡇⠀⠀⢸⣇⠀⠀⡟⠀⠀⣇⠀⠀⠀⠀⠈⠙⠉⠠⠴⠚⠋⠁
⠀⣿⡇⠀⠀⢸⣿⡀⠸⡇⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣩⠽⠿⠟⠛⠛⠻⢶⣶⠤⣄⣠⡉⠉⢱
⠀⠛⠃⠀⠀⠈⠛⠀⠀⠛⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠈⠙⢲⣤⣉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠒⢤⣤⡤⠴⠶⠒⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⢠⡀⠀⡱
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠉⠉⣉⣩⠥⠞⠓⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⣀⣈⡇⠀⠀⠀⠤⠊⠉⢁⣆⣀⣐⡀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣽⣿⣇⠀⠀⠉⠀⠒⠂⠀⠠⠠⠤⠄⢀⣴⣾⠁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣾⣿⣿⣿⣧⠀⠀⠀⠀⣠⣼⣇⣀⠀⠀⠀⣿⣿⡇⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⣦⠀⠀⢸⡇⢹⣿⣿⣿⢻⠀⠸⡀⠀⠀⠹⠏⠉⠀⠀⠀⣿⣿⠇⠀⢰⢿⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⡏⣀⠀⠀⠀⠀⠀⣹⡄⠀⢸⡇⢸⣿⣿⣿⣸⠀⠀⠀⠀⠈⠉⠉⠒⠂⠠⠠⠟⠁⠀⠀⡎⠈⡆
⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⢻⣿⡇⠀⢸⡇⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠁⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠈⢹⡇⠀⠈⠛⠛⠛⠛⠛⠁⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠸⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠧⣸⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⣤⣧⡄⠀⠀⣧⠀⠀⠀⠀⠀⠸
⠀⠀⠀⢠⠀⣿⠇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠸⠀⠀⠠
⠀⠀⠀⢀⠀⣿⡀⠀⠀⠀⠂⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠰⠔⠋⠀⠀⠀⠀⠀⠐⠐⠃⠀⠐⠐
⠀⠀⠀⠉⠘⣯⠉⠀⠀⠈⢳⣿⠉⠀⠀⠐⣋⣹⣷⠒⠒⠛⠟⠛⠙⠓⠒⠲⢤⣎⡀
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢉⣏⠁⠈⠀⠐⠸⠛⠋⠀⠀⠀⠸⣆⠀⠀⠀⠀⡾⠀⠉⠳⣄⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣤⣤⣴⠃⠀⠀⠀⠈⢣⠀⠀⢲⡆⣐⣒⣒⣒⣒⣒⠖⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⡴⠃⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⠉⠉⠉⠉⠛⢻⡄⡿
⠀⠀⠿⠿⠖⠒⠒⠶⠶⠶⠶⠶⠶⠶⠤⠀⠀⠷⠦⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢸⠃⢱
⠀⠀⣐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⡇⠀⣄⣀⣀⣤⠏⠀⢸
⠀⠀⠈⠑⠢⠶⠾⠿⠿⢿⣿⣭⣭⣭⡭⠭⠭⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠓⢦⣤⣤⡴⠞⠁⠀⠀⠀⡇⠀⠈⣉⣭⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠉⢣⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠠⢀⡤⣠⣾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⡀⠀⢳⡀⢸
⠀⠀⠁⠘⠻⠿⠷⠶⠿⠿⢳⡇⠀⡀⣀⣀⣀⣀⠀⣀⡄⠀⠠⠀⣿⡀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⢸⠀⣴⣿⣿⣿⣿⣾⡇⣌
⠀⠀⠀⠀⠀⠀⠐⠒⠒⢺⡿⠀⠀⠀⠉⠉⢉⠉⠉⠉⠀⢒⠙⠀⠿⢁⡀⠀⠈⠉⠉⡉⠉⠉⠀⠀⢸⡆⠻⠿⠿⠟⠿⠟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠐⣲⡿⠀⠀⠀⠀⠀⠚⢓⣒⠒⠀⠀⠰⠲⠒⠒⠲⠇⠀⠐⠒⣂⡘⠒⠀⠀⠀⠠⠤⠤⠤⠉⠉⠠⠤⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢠⡟⠀⠀⠀⣾⠃⠀⠀⠈⣧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡠⠀⠄
⠀⠀⠀⠀⠊⠈⠂⠀⠀⠂⠈⢢⠀⠀⠀⣿⠀⠀⢸⠃⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢧⣠⠔
⠀⠀⠀⠀⠀⠀⠺⡤⣴⠇⠀⠂⠀⠀⠀⣿⠀⠀⢸⡄⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⣽⡀⠀⣸⡀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⢀⡴⢋⣀⣠⢤⡔⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡄⠀⠀⣿⡇⠀⠰⡿⠛⠉⠁⠀⠈⠂⠠⠊
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⢻⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⠁⠀⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡆⠀⣿⡇⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡀⠀⠀⣼⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⡇⠀⠉⠁⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⢀⡿⣇⣀⠀⠀⠀⠀⢀⣀⡀⣸⡄⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠃⡟⠀⢈⠀⠀⠀⡏⠀⢹⠁⢹⠁⠀⡄⠀⠀⢠⠀⠀⠋⠁⠉⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠂⠐⠁⠐⠀⠊⠀⠀⠀⠘⠒⠋⠀⠈⠓⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡆⠀⠀⠀⠀⠀⢀⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⠀⠀⠀⠀⠀⢸⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⠀⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢀⠃⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢷⠀⠀⠀⣸⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠸⡀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡇⠀⢠⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡣⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡴⠚⠋⠁⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡆⠠⡊⣱⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣮⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢰⠊⢏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡞⠀⢸⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡈⠙⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠃⠀⠀⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡈⠑⠢⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣸⠀⠀⠀⢳⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠑⠢⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡏⠀⠀⠀⠸⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠃⠀⠀⠀⠀⡇⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡸⠀⠀⠀⠀⠀⢻⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡇⠀⠀⠀⠀⠀⠸⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢰⠁⠀⠀⠀⠀⠀⠀⣇⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡜⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣠⠔⠊⠉⠉⠉⠒⠼⠀⢀⠗⠒⢢⠀⠀⠀⣴⠒⠚⡆⠀⠧⠒⠉⠉⠉⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡰⠁⢀⠔⠊⠉⠒⢄⠀⠀⢸⠋⠉⠉⠀⠀⠀⠈⠉⠉⢇⠀⠀⢠⠖⠈⠑⠢⡀⠈⢣⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⢘⠀⠀⠀⠀⠈⠄⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢸⠀⠈⠆⠀⠀⠀⠀⠀⠀⡇
⢣⠀⠘⢦⡀⢀⣠⠞⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠱⢄⡀⢀⡠⠊⠀⡸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠑⢄⡀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⡀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⢩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡴⠋⠀⠀⣠⠴⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⡴⠋⠀⠀⠀⣼⢡⠎⠉⠙⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢀⡴⠋⠀⠀⠀⠀⠀⢹⡘⢦⣀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⢲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢀⠞⠁⠀⠀⢀⡠⢖⣒⡒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡴⠋⠀⢀⡠⠖⢻⢱⠏⠀⠈⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣡⠞⢁⡤⠞⢉⡤⠖⠻⣌⠣⠤⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢀⡷⣞⣉⡤⠞⠉⠀⠀⠀⠈⠑⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣠⢏⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠁⢀⡼⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢷⡎⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢊⣡⣶⠋⡽⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢊⡡⠖⢉⡜⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠁⠀⣠⢋⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⢾⡽⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠾⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⠀⠀⣀⠀⣀⠀⣀⠀⠀⠀⡀⠀⠀⡀⠀⣀⠀⣀⡀⢀⣀⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠂⣇⢈⠕⠀⢸⢰⠽⡄⡓⡧⣃⠀⡗⠂⠈⢓⡄⢸⠀⠖⡗⣅⢈⢺⠿⡀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠉⠁⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⠿⡿⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠈⢉⣉⣭⡛⠃⠀⠀⠛⣫⣍⣉⠉⠀⢸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠻⣆⠀⠈⠸⠿⠙⢂⣀⣀⠛⠽⠿⠈⠀⢀⡞⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⡏⡷⠶⠶⠚⠋⠁⠀⠈⠉⠛⠲⠶⠶⡏⣏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⠀⠀⠀⠀⢀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠙⠒⠤⠔⠚⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⣶⠞⠉⠩⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠻⡝⠒⠲⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠋⠉⠀⠀⠀⠀⣇⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢹⡀⠀⠀⠀⠀⠈⠉⠓⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠷⢶⣄⠈⢆⣀⠀⠀⠀⠀⠀⢀⣠⠎⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡄⠘⣇⠉⠉⠉⠉⠉⢁⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠘⡇⠀⠘⡄⠀⠀⠀⢀⡞⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢿⠀⠀⠸⡄⠀⠀⡼⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢸⡄⠀⠀⠹⡄⡼⠁⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⡇⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⡇⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⠞⠓⠒⠚⠁⠀⠀⠀⠀⠀⣠⡤⠛⢵⡄⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹
⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣄⠀⡠⡃⠀⠀⠀⠀⠀⠀⠀⡇
⠉⠓⠲⠤⣤⣀⡀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣀⣠⡤⠴⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠈⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡉⠀⠀⠁⢠⣤⡄⠀⠀⠀⠀⡤⣤⡄⠀⠀⠀⢛⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠻⠿⠃⠀⠀⠀⠀⠻⠿⠃⠐⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⣀⠀⠀⠁⠀⣠⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠳⣶⣶⡾⠋⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⠂⠠⢀⡀⠀⡀⠠⠔⢻⠆
⠀⠈⠁⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠟⠀⠀⠀⠀⠀⠀⠀⠂⠸⡅⠀⠀⣤
⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠀⠀⠀⠀⠀⢂⣀⠙⠁⠀⠀⠀⠈⠀⢀
⠷⠀⠆⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢉⠐⠂⠰⠖⠉⠆⠀⠃
⠘⢧⠒⠀⢊⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠀⠀⠉⠲⡀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠛⠁
⠀⠀⠀⠀⠀⠀⠻⢤⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⠰⠍⠀⠀⠀⠀⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠔⠠⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡻⠗⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢀⠂⡀⣀⠀⡀⣀⡀⣀⡤⠖⠉⢡⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⣀⣀⠀⠄⣀⣀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣠⠀⠐⠄⢀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⠠⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠺⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⢈⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠻⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄

⠀⠀⠀⠀⢠⡟⠿⢻
⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⠀⢸⡇⠀⢸⡀
⠀⠀⠀⠀⢸⡇⣶⠿⠯⠭⠭⠽⠿⣆
⠀⠀⠀⠀⢸⡇⢻⣤⣤⣤⣤⣤⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⣠⣿⣿⠟⠻⠛⠛⠻⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⡴⠒⢺⢛⣡⢄⠀⠈⠀⠀⠀⠈⠁⠀⣠⠈⡛⣗⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠉⠙⠻⣿⣿⠟⠿⢿⣿⣿⡄
⢧⡀⢻⠀⠉⠉⠀⠀⠢⠄⠠⠔⠁⠀⠈⠉⠁⣽⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣇⠀⠰⠀⠀⠀⠰⠆⠀⠘⠷⢀⣀⣿⠿⣿⠃
⠀⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻⡁⠀⠐⠤⠔⠀⠀⠘⠑⠀⠀⠁⠀⠀⢸⠆
⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣤⣾⣄
⠀⠀⠀⠀⠐⡿⢻⠛⡖⠒⠒⣲⠛⡟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣛⡖⠒⠒⠒⢛⡏⠛⣿⣿⡿⠟⠛
⠀⠀⠀⠀⢰⠃⡞⠀⠘⠒⠒⠁⠀⢻⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠈⢳⡙⣟⠿⢿⠋⠙⠦⡀⢸⡿⠿⠄
⠀⠀⠀⠀⡏⢸⠁⠀⠀⠀⠀⠀⠀⠀⡇⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⠀⢘⡇⢸⠀⠀⠀⠀⠀⠸⡆⢧
⠀⠀⠀⣸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢀⡼⢁⠞⠀⠀⠀⠀⠀⠀⣇⠘⡄
⠀⠀⣠⠃⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢶⠿⡖⠉⠀⠀⠀⠀⠀⠀⠀⢹⠀⠳⡀
⠀⠀⠙⠒⢺⡗⡶⢶⡦⠤⠴⢶⡶⢶⡞⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢺⠀⣷⡶⣶⠤⠤⠴⢶⡶⢶⠛⠒⠚⠁
⠀⠀⠀⠀⢸⡇⢧⠀⠈⡗⢺⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡇⠀⢹⡒⢺⡅⠀⢸
⠀⠀⠀⠀⢸⡇⢸⡄⠀⡇⢸⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢻⠀⢸⡇⠀⡇⠀⢸
⠀⠀⠀⠀⢸⡇⢈⣇⠀⣇⣸⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠘⡆⠀⡇⠀⣧⠀⣸
⠀⠀⠀⣴⠚⠉⠉⣽⣀⡿⢹⣀⣺⠉⠉⠛⣢⠀⠀⠀⠀⠐⠒⠀⠒⠘⠛⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⡗⠛⣇⣀⡏⠉⣿⣀⡸⠓⠒⠢⣄
⠀⠀⠀⡏⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠋⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡗⠒⠒⠲⠶⠶⠶⠒⠒⠒⠚⠉⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⠤⠤⠶⠶⠶⠶⠶⠦⢤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⣚⣻⡍⠉⠁⠀⠲⠖⠒⠛⠓⠀⠀⠀⠀⠀⠲⠶⠦⣭⡉⠙⠓⠦⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠐⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠺⠛⠻⢯⣍⠉⠉⠉⠛⠛⠶⠶⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣤⣤⣤⡤⠴⠶⠶⠖⠛⠛⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣧⡆⠀⠰⠖⠛⠛⢻⡆⠀⠀⠀⠀⠀⢀⡏⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣻⣏⣀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⣀⣸⡇⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⠉⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⠀⠀⠀⣸⠃⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠐⣶⠀⢀⣄⣀⣤⣤⣼⡇⠀⠀⠀⠀⢀⡟⢠⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣌⣽⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠐⠛⣻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣼⠁⠀⠀⠀⠀⣼⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡟⠀⠘⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠐⣿⠄⢠⣤⣤⣤⡤⣿⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠰⠶⣿⠒⠀⠀⠀⠀⠀⠾⠧⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢘⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⣿⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣿⣁⡀⠀⠀⠀⠀⠀⣼⡇⠀⠴⠶⠶⠚⠋⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣀⣤⣴⡶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠒⠒⠲⠶⠶⠶⠶⠶⠖⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⣀⡉⢛⣤⡽⠭⣍⠛⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣳⠘⢋⢶⣶⣶⡆⠀⠹⢯⠁⢹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⠛⣻⠀⠘⠘⠛⠋⠀⠀⠀⢣⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢠⣉⣒⣀⣤⣴⡆⠀⠀⣰⣇⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡙⢦⣤⠶⠋⠀⣠⢾⣿⣿⣿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⢴⡞⠁⢸⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⣀⣤⠤⠔⠆⠳⠶⠍⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠐⣶⣾⠇⠀⢈⣷⠦⣄⡀
⠀⠀⠀⠀⠀⠘⠯⣁⡀⠊⠀⠀⠀⣀⣀⡽⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⠄⣠⠞⣿⠏⠀⣠⡟⢹⡄⠀⠉⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠸⡋⠀⡠⠋⠢⣀⠀⠀⠀⠀⠀⣠⠊⠀⣠⢊⢴⠏⣸⣿⣤⣾⠟⠀⡿⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⠀⠀⠈⠑⢄⡀⡠⠞⠁⠀⡔⠁⢀⣿⠀⣿⣿⣿⠏⣤⠾⣟⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠙⠆⠀⠀⠀⡆⠀⢸⡇⢰⣿⣿⠏⡼⠡⠀⢸⡦⠀⠳⡄⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⢀⡠⠖⢃⢰⣟⡇⢸⣿⠏⣸⠇⠀⠀⣸⠁⠀⣰⠻⡄⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠤⠒⠉⠀⠀⠘⡛⠿⠃⢸⡟⠠⡿⡄⢀⣰⠏⠀⡴⠃⠀⠘⣄⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢸⡁⠀⠈⠁⠙⠋⢀⡜⠁⠀⠀⠀⡨⠒⠛⠁⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢸⢀⠀⠀⠀⠀⢠⠎⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠉⠀⠀⠀⡰⡇⢀⡴⠛⡁⠀⠀⠀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠦⠁⠀⠀⠀⠀⡘⠉⠣⣀⣑⠶⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⢃⢰⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡼⢇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠈⢢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣦⣄⣀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⢷⡶⢶⣶⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠛⠛⠻⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⢿⣟⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠙⠳⠆⠀⠈⠀⠀⢉⣻⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠷⠄⠀⠀⠀⣀⣴⠿⠛⣋⣉⣉⠛⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⠀⠀⠀⢀⣼⠟⣡⡾⠟⢛⣙⠛⠿⣶⡌⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠙⠀⠀⢀⣾⠃⣾⠏⣴⡾⠛⠛⢿⣦⠘⣿⡀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠲⠀⠀⢸⡏⢸⡏⢸⡏⠀⠀⠀⠀⢻⡇⣹⡇⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⡶⠶⢶⣶⠶⠶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠙⢷⣦⡀⢸⡇⢸⣇⠸⣷⣄⠀⠀⢀⣾⢃⣿⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠛⢿⡄⠀⠉⠳⠀⠀⠙⠃⠀⠈⠙⠂⠈⠻⠟⠛⢿⠶⣶⣤⣤⣭⣿⣿⣿⡄⠻⣷⣬⣉⣠⣴⠟⣡⡾⢃⡾⠃
⠀⠀⠀⠀⠀⣀⣤⣶⡟⠋⠉⠙⠷⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣤⣤⣤⣄⣀⡙⠊⠉⠻⠍⠙⠿⣶⣬⣉⣉⣩⣥⡾⢋⣴⠟⠁
⠀⠀⠀⠀⠺⣿⡁⠘⠿⠆⠀⠀⠀⠀⣀⣤⣴⡶⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⢷⣶⣤⣤⣄⣀⣉⣉⣉⣩⣥⡶⠟⠁
⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⢀⣠⣶⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣷⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣌⣛⣿⣷⣾⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⢻⣿⣿⣿⣿⡿⠛⢉⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠋⣠⠾⠋⣁⣠⣄⣀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣿⣿⣿⡟⢀⡾⠃⣰⠞⢋⣉⡉⠙⢻⣄⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⣿⣿⠁⣼⠃⣼⠃⣰⣿⣿⣿⣷⠀⢻⡄⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⣿⠀⣿⠀⢻⣿⣿⣿⣿⠃⣼⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⠐⢶⣶⣦⡐⣶⣶⣄⠠⣤⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢻⡄⠘⢷⣄⣸⣿⡿⠋⣰⠏⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠲⣿⣿⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣷⣾⣿⣦⣶⣦⣀⢤⣀⠀⣀⣀⠈⠻⣦⣄⣉⣉⣁⣤⠞⢁⡴⠋
⠀⠀⠀⠀⢀⣠⡀⠘⢿⣿⣿⣶⣿⣿⣿⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⢿⣾⣿⣷⣦⣀⣉⣉⣉⣉⣤⡶⠛⠁
⠀⠀⠀⠀⠈⢻⣿⣶⣾⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠙⣿⡿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠻⠿⢿⡿⠋⠁⠈⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⠀⠔⣛⢻⣶⡄⢰⣿⣛⣳⠀⢸⠗⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠉⠙⠉⠹⠃⠈⠉⠉⠀⠀⣸⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠂⠰⠋⡈⠙⢊⠁⠈⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠤⠤⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⡀⠀⠀⠀⣠⠋⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⣧⡽⠿⠶⠒⠂⠁⡀⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠻⢀⡿⠈⢇⠀⠀⢠⣿⣿⣷⡄⠀⠀⠀⢸⠀⠀⠀⠐⠤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠃⠸⡇⠀⠈⢆⡠⠛⣿⣿⡏⠻⣀⠆⢀⡿⠤⠼⠀⠀⠀⠀⠈⠐⠒⠒⢄
⠀⠀⠀⠀⢀⠐⠉⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⢣⡀⣿⣿⣷⠀⡜⢀⣼⢥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⡞⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠹⣿⣿⣿⡞⢁⡟⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢘⣇⡠⡀⠀⠹⣿⡟⠀⠸⡇⠀⠀⠀⠘⠇⠀⢠⡇
⠀⠀⠀⣼⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⢴⠿⠋⠀⠘⠄⠠⡏⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⢦⣤⣤⠆⠀⠀⣷⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⢻⣲
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸
⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⡀⠀⣠⡦⣼⢧⡇
⠀⠀⠀⢢⠹⡆⠀⠀⠀⠀⠀⠈⣵⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⡶⡣⠊⡰⡀⠀⠀⠀⢀
⠀⠀⠀⠈⣇⠘⠀⠀⠀⠀⠀⠀⢹⠛⠒⠦⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⢀⠈⡰⠁⠀⠀⠀⠈
⠀⠀⠀⠀⢸⡄⠀⠀⠀⣀⣀⣀⣸⣀⠀⠀⠀⠀⢸⠋⠁⠀⠀⠀⠁⠀⠒⠒⠶⠏⠀⠀⠈⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⣈⣭⣿⡶⢶⣤⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠂⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⠻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⢻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣤⡄⠀⠀⠀⣤⣄⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⣠⣦⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠙⠛⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣤⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⢀⣴⡆⢠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠹⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠻⢷⣤⣀⣀⠀⠀⢀⣀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠈⠙⠛⢻⣶⠊⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡼⠛⠁⢸⣿⣧⣤⣤⣀⠀⠀⠀⠀⠀⣸⡿⣧⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⣿⣿⡟⠀⠀⠀⢸⣿⠋⠈⠉⠉⠀⠠⣶⣶⣾⣿⠄⠈⠻⣿⣿⡷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⣴⡆⠀⠀⠀⣿⣿⡇⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣿⣿⡇⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠋⠀⠀⠀⠈⢃⣄⠀⠀⣿⣿⡇⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⣿⣿⠀⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠟⠀⠀⠀⠀⠀⠸⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣿⣿⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⣿⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣠⣴⣿⣿⣷⣦⡀⠀⠹⠃
⠀⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠟⢿⣿⠙⠻⣿⣦⡀
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠀⠀⠹⣿⣿⣄⣀⡀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣤⣾⣿⣦⣤⣾⣿⡇⢸
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⣼⣟⠛⠛⠉⢱⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠉⠛⠛⠉⠙⠻⣿⣿⣿
⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⣄⠈⠻⠿⠀⠘⠃⣨⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠘⣿⣀⣴⡄⠀⠀⠀⠻⣿⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠇⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠿⣏⣀⣴⣦⣄⣼⣿⡇⠀⠀⠀⠀⠀⣰⣿⡿⠇⠀⠀⣾⡀⠀⠀⠀⠀⢠⣿⣿
⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⣿⡟⠈⢻⡇⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⢸⣿⡇⠀⠀⠀⠀⢿⣿⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢩⣿
⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⣶⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣿⡇⠀⠀⠀⠀⠀⢿⣿⣦⣀⡀⣿⣿⡄⠀⠀⢸⣆⣠⣿⣿
⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠀⠀⣴⣾⣿⡿⠛⠃
⣿⡃⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡇⠀⠀⠙⣿⡿
⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⡇
⠿⠁⠀⠀⠀⠀⠀⠀⠀⠙⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⢸⠃
⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠿⣇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸
⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡄
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠙⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⣼⣇
⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⢤⣾⣿⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣆⣀⣴⣶⡎⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⣴⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣶⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢠⣤⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠶⠂⠀⠒⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⠓⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠸⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⡸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⣸⣿⠀⠈⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢠⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣸⡆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣄⠀⠀⠀⠀⢻⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠈⠃⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢻⣄⠀⠀⠀⢸⣷⣤⡀⠀⠀⠈⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠙⢷⣄⠀⠸⠟⠉⠀⣶⣶⡄⠀⠀⢙⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠂⣀⣀⠀⠀⠈⢻⣷⣶⡾⠟⠁⢀⣴⣶⣶⡾⠟⠋⠘⠿⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣤⣴⠛⠛⢀⣤⣤⣴⣿⠟⠁⣤⡄⠈⠉⠉⠉⠁⠀⣤⣤⣤⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⠿⠟⠛⠛⠀⠀⠀⠈⣱⡄⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣀⣀⣀⣀⣀⣀⣠⣴⣤⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣧⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠦⠾⣽⣷⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠃⠠⠄⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠶⣤⠁⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⣺⣿⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠖⠒⠋⢋⠉⠄⠰⠿⣻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⣉⢠⡤⠀⠆⣒⣂⣩⡤⠴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡫⣶⢀⣃⡴⠴⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣾⣟⣷⣶⣶⣶⣶⡶⡶⡖⣖⣒⣚⣛⣟⣋⣭⡩⡴⠦⠶⠒⡛⢋⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠿⠟⠛⢛⡛⢉⡉⢉⡉⢩⡅⢡⡅⠠⣄⠀⡆⠰⠇⠘⣃⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢩⡄⠰⠆⠘⣁⣘⣃⣀⣥⣬⣥⣤⠥⠬⠥⠶⠶⠖⠒⠚⠋⠉⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⣶⣾⣿⣿⣿⣯⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠤⠖⡒⠋⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⡿⠿⠿⠛⠛⢛⡋⠉⡭⠉⢩⠉⠁⠄⠀⢰⠀⠀⠇⠀⣓⣀⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢩⠄⠀⡆⠀⠩⢀⢀⡃⣀⣁⣀⣨⣡⣤⣤⠤⠴⠴⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠻⣂⣠⠤⠶⠒⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣷⣤⣤⣤⣤⣤⣤⡤⡤⢤⠤⠤⠤⠴⢶⢶⣶⣶⡶⢶⣶⣶⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⣷⡿⣶⣺⢹⣦⣞⣼⣣⣷⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠓⠛⠛⠛⠚⠓⠓⠚⠛⠛⠛⣛⣛⣉⣩⡭⠿⠿⣛⠻⢴⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠶⢖⠒⢋⢉⣩⠉⠤⡀⡶⠀⠿⢀⣚⡤⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢐⠹⢂⣚⣡⣭⠴⠴⠴⠒⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⢻⡛⡟⣻⠟⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠛⠛⠛⠁⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⢠⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡏⠙⠶⠶⠆⠀⠈⠉⠙⢷⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⠶⠀⠀⠠⢦⠀⠀⠀⠀⠷⣀⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠁⣤⡀⠀⠀⣀⡀⠀⠀⠀⠀⠙⠀⠀⣀⠋
⠀⠀⠀⠀⠀⠀⠀⠐⣯⠀⠈⢻⠁⠀⠀⠛⠁⠀⠀⠀⠀⢀⣤⣼⢿⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠂⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⣽⠖⠘⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢤⣤⣤⡤⣤⣤⣤⡤⠀⠛⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼⡄⠀⠀⠀⠀⢀⣾⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢶⣿⡏⢻⡷⠴⠶⠀⠉⠙⣿⠀⠀⠙⣷⢴⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢠⣿⠇⢸⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⣿⡟⠉⠲⢦⡀
⠀⠀⠀⠀⠀⠀⢀⣜⠁⠀⠀⢸⣿⠀⠈⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⣿⡇⠀⠀⢈⡿⢦⡀
⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⡇⠀⣿⡇⠀⢠⡞⠁⠀⠻⡆
⠀⠀⠀⠀⠀⡄⠻⠇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠇⠀⠘⠃⠀⠀⠀⠸⠆
⠀⠀⠀⠀⡀⠋⠀⠀⢀⣴⣿⠿⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⠀⢰⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⠇⠀⠀⠀⢸⣿⣵⣶⡦⣼⣿⣇⠀⠀⠀⠀⣴⠀⠀⠀⡟⠀⣸⡿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⡿⠀⠀⡇⠀⣿⡏⠀⢸⡁⢸⡟⣿⡆⠀⠀⠀⣿⠀⢀⣾⠿⠿⢿⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠃⠀⠀⡇⢸⣿⠁⠀⢸⡇⢸⠀⢻⣇⠀⠀⠀⣿⠀⣾⠄⠁⠀⠀⢼⡇⠀⢰⡆⠀⠀⠀⠀⠀⠀⢻
⠀⠀⣷⠀⠀⠰⣇⢸⡿⠀⠀⠘⠁⢸⠃⠘⣿⡀⠀⠀⣿⠀⣸⡶⠟⠈⢻⡆⠁⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⣶
⠀⣠⠀⠀⠀⢠⡟⢻⣇⠀⠀⠀⠀⣸⠀⠀⣿⡇⠀⠀⣿⠀⣿⠀⠀⠁⠀⠀⠀⠀⠀⠈⢡⡀⠀⠀⠀⠀⠀⠙
⠀⡿⠀⠀⠀⠀⡇⠈⠻⣶⣤⡀⢰⣿⣶⣾⠏⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⣷
⣄⠀⠀⠀⠀⠀⡇⠀⠀⠈⠛⠁⣼⡟⠉⠁⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠙
⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡆
⠟⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠇
⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⣤⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢀⠟
⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢀⠛
⠀⠀⠀⠀⢷⡀⠀⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢠⡜
⠀⠀⠀⠀⠀⠳⣴⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⡀⠀⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⢃⡈⠓⣦⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⣴⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠓⠀⠼⠀⠀⠀⠀⠀⣸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠛⠛⠛⠛⠛⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠑⠲⠒⠒⠶⠒⢿⠀⠀⠀⠀⣨⠿⠖⠆⣀⣀⣀⡀⢴⡞⠁
⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⣴⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⡴⠂⠁⠀⠀⠀⠀⠀⠀⣠⡖⠛⠋
⠀⠀⠀⠀⠉⠦⠤⠀⠀⢤⡤⠞⠋⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⣤⠞⠁
⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⡿⠟⠻⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣠⠈⢧⣀⣴⣊⡀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣠⠏⠉⠯⣉⠉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⢤⡤⠀⠹⢄⡉⡇
⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠙⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠶⠌⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠓⣖⠁⠀⢀⣶⢏⠷⡄
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠠⡰⠖⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣿⠔⠦⢤⣶⡿⠛⠁⡰⠉⠐⠦⣀
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠐⢇⠀⠀⠘⡆⠀⠀⠀⠀⠀⣠⢶⠋⡇⠀⠸⡇⢀⣾⠛⠒⠒⠉⡠⠀⢀⠤⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢀⡀⠀⡾⣀⣀⣠⠶⠤⠚⠹⡼⢸⠇⠀⠀⣿⣼⠃⠀⠀⠀⡔⠠⣞⣡⡴⡶⡶⣿⡆
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢹⠁⠈⠉⠀⠘⢉⣁⣀⣀⣀⣀⣙⡏⠀⠀⢰⢿⡿⠂⠀⠀⡐⡴⢰⠋⢀⠀⠀⢀⢀⡿
⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢸⠛⠲⢦⣀⣀⣤⠴⠶⠬⣭⣉⢻⡇⢀⣰⢏⡾⠃⠀⠀⠌⡜⢠⡏⠔⢁⡠⠔⠉⣼⡇
⠀⠀⢠⡏⠀⠀⠀⢷⠀⠀⢸⣦⣤⢾⡍⣉⡉⠑⣞⠛⠉⠉⢻⠛⠿⠟⡻⠁⠀⠀⢀⠞⡴⠉⠁⠉⠀⠀⢀⣼⢻⡇
⠀⠀⣼⠀⠀⠀⠀⢸⠀⠀⢸⡏⠀⠈⠻⣶⣄⡀⠈⠒⠲⢤⣿⣀⣀⣰⠁⣀⣀⣰⠧⣼⣅⡀⠀⠀⢀⡴⣿⡧⣾⣀⡀
⠀⢠⠇⠀⠀⠀⠀⢸⡄⠀⠈⡇⠀⠀⠀⠀⠀⠙⠦⠤⢼⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠀⠰⢋⣾⠃⣠⠇⠈⠉⠛⣦
⠀⠸⡧⠄⠀⠭⣤⠰⢇⠐⠂⠙⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⠤⠤⢤⣤⣀⣀⠀⠀⠀⠀⠀⠉⣠⡾⠁⡼⠁⠀⠀⠀⢰⠇
⠀⢸⠃⠀⢒⠒⠛⣏⠈⠳⣄⠀⠈⢦⡀⠀⠀⣀⣀⡤⠾⣁⠀⢀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⡛⠋⢠⣦⣧⣄⣀⠀⢀⡞
⠀⢸⠈⠉⠉⠀⣀⠈⣆⢀⣨⠷⢦⣀⠙⠶⢋⡉⠁⠀⠠⢌⣑⡪⣭⠽⢒⣒⣒⠲⠄⠐⠊⠁⠀⣠⠎⠈⡇⠀⣹⠛⠛⠁
⠀⠀⠀⠀⠀⠉⣉⣀⣉⣐⡁⠀⠀⠈⠑⠲⠤⣼⡷⢤⠀⠀⠀⠀⣀⣀⡀⠀⠠⠤⠤⠄⢀⣀⡘⠁⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢦⣤⣄⣀⣀⢀⠀⠀⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠈⠀⠀⢀⡷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡶⠚⠁⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⡀⠀⢀⣾⡁⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠾⠉⠙⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⠀⠀⠓⠈⠅⠀⠀⢰⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠍⣾⠈⠙⠒⠒⠒⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠠⡀⠀⠀⠈⠁⠀⠀⡀⠀⢀⡄⠀⡥⠀⠀⠀⣰⠊⠁⠈⠻⣆
⠀⠀⠀⠀⠤⠤⠤⣤⡤⠴⣦⣤⡤⠤⢆⠄⡀⠀⠰⣄⣀⣀⡈⡟⠉⣍⠂⡺⢀⡀⠀⠀⢠⣴⠇⠀⠀⠀⠀⠈⠉⠳⢦
⠀⠀⠀⣀⣀⢀⣌⠁⠀⠘⢻⣿⡿⠆⠈⠃⣄⣀⡤⠻⣿⣿⡐⡟⠀⡈⣠⠇⠀⢉⡆⠀⠈⢿⣆⠀⠀⡀
⠀⠀⠀⠀⠀⢺⣤⡀⣶⣿⣿⠆⠠⢀⠀⠀⠸⠀⠀⠇⢸⢸⣽⣷⣰⡷⢺⠀⠀⢸⢁⠀⠀⠀⠉⠳⠮⠤⠖⢂⣢⡀
⠀⠀⠀⠀⠀⠘⢿⣿⠟⠸⠉⠀⠀⡀⠀⠀⠘⠢⣂⡀⠀⢘⢻⣇⣻⡷⠞⠅⠀⠈⠈⠑⠠⡀⢀⣀⣣⣼⡿⠿⣯⣙⠓
⠀⠀⠀⠀⠀⠀⠘⢯⠀⠀⢀⡀⠀⡠⠀⠀⠀⠀⠀⠉⠓⠺⠞⠋⠘⣏⠔⠁⠀⢂⡀⠀⠀⠀⢸⡄⠁⠀⠀⠀⠈⠛⠕
⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠚⣮⡉⠉⠁⠀⠀⢸⠁
⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠘⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡹⣧⠀⠀⠶⠀⢺⣦⠤⢤⠤⠶⠶⠛⠛
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡄⠀⠉⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣝⢧⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢰⠀⠀⢀⠀⡅⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣆⢡⠀⠀⠀⠀⠀⠠⣠⡴⠞
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡙⠳⣥⣀⣀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⢷⡙⢏⠛⠛⠯⣉⠁
⠀⠀⠀⠀⠀⠀⢁⠀⡀⠀⠀⠁⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣽⣌⣳⣄⢀⠄⠉
⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⢤⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠟⣯⠁⠠
⠀⠀⠀⠀⠀⠀⢀⡯⡁⠀⠈⠈⠉⠉⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡻⡇⣿⡀⠁
⠀⠀⠀⠀⠀⠀⣟⠁⠚⡇⠀⠀⠆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡕⢄⠨⠫⢸⠄
⠀⠀⠀⠀⠀⠰⣧⠀⠨⠇⠀⠀⢈⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠳⡄⠈
⣶⣶⠶⠶⠶⣶⣿⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣾⣶⣷⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⣩⣍⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣠⣤⣬⣥⣤⣄⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⠉⣉⣉⠀⠀⣘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⡘⠃⡨⢁⠘⢃⡈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠛⠋⠉⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠄⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢡⡧⠀⠀⣬⠄⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠐⠲⠔⠂⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠈⠀⠀⠀⠈⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣪⠕⢯⠑⢂⡔⠒⣹⠲⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡀⠀⣤⣤⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⡿⢧⡸⣤⠘⡏⢻⡟⢛⠇⢠⡼⠨⡏⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⡦⢄⡡⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢸⠀⠀⡇⠳⡄⢹⣼⣿⡜⢀⡜⢀⣴⣣⡄⠀⠸⡄⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣀⠀⠀⣨⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠘⠀⣰⠁⠀⠘⢦⣻⣿⡡⠋⠀⠈⠻⠿⠃⠀⠀⡇⠀⠀⠀⠀⠀⣴⣿⣹⣿⣿⣿⣷⣾⡿⠿⠿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠭⠭⠤⠭⠤⠤⠤⠿⠿⠥⠤⠤⠤⠤⠤⠤⠤⠤⠿⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡶⠞⠛⠛⠛⠛⠛⠛⠷⠶⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣶⣄⡀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠈⣯⠉⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⡀
⠀⠀⠀⠀⣶⢦⣤⣨⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠘⣦⡈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⣠⡶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠳⢶⣄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⡟⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠻⣇⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⡿⠀⠀⠘⠋⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠛⠉⠉⠙⠃⠀⠀⠀⠀⣿⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⣿⠀⡷⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣠⣦⡄⠀⠀⠀⠀⠀⣿⠀⣸⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣿⣸⡇⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠸⣧⣸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠛⠋⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⠶⠾⣋⣼⣿⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠹⣿⣭⣭⣭⣭⣤⣶⣾⣋⣸⡇⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠉⠷⣤⣤⡟⠉⣁⣠⡿⠋⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣄⠀⠀⠀⠀⠀⢠⡔⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣭⣽⣟⠀⠀⠀⠀⠀⢈⣿⣭⣭⠛⢿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⣶⣿⡿⠋⢼⣿⡉⠈⠻⣦⡀⠀⠀⣠⡾⠋⠈⣹⣿⠀⠈⠻⣿⣶⣤⣠⣄⣀⡀
⠀⠀⠀⠀⠀⢀⣤⠞⠛⠛⣿⠋⠉⠉⠉⠁⢀⣼⣿⠁⠀⠘⣿⢷⡀⠀⠈⠻⣤⡼⠋⠀⠀⣰⣿⡟⠀⠀⢠⡟⢿⣯⡈⠉⠉⠉⢻⠟⠛⠛⠳⣤⡀
⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⣿⣿⡀⠀⠀⢿⡘⢷⡀⣠⡾⠛⠳⣦⡀⣼⠏⣸⠇⠀⠀⣾⠇⢸⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡇⢸⣧⠀⠀⢸⡇⢨⡿⠋⠀⠀⠀⠈⠻⣏⢰⡏⠀⠀⢰⡏⠀⣸⣿⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣧
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠇⠈⢿⡀⠀⠀⢻⡏⠻⣤⣀⣀⣀⣠⡾⠋⣿⠁⠀⠀⣸⠇⠀⣿⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⣿⣆⠀⢸⡇⠀⠀⠘⣧⠀⣼⠋⠉⠙⢻⡄⢸⠟⠀⠀⢰⡿⠀⢰⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡿⠉⢿⣦⣼⣿⠷⡶⣦⣿⣴⡿⠀⠀⠀⠸⣧⣿⠀⢶⣶⠾⠃⠀⠈⣿⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣿⣶⣿⣛⡿⠷⠶⠶⠛⠛⠛⢿⣛⢯⣿⣿⠁⠀⠀⠀⠀⣿⡇⠀⠀⣿⠇⠀⠀⠀⠙⢿⣷⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣇
⠀⢀⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣏⣿⡆⠀⠀⠀⢠⡿⠀⢠⡾⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⠀⠀⣸⠇⣠⡾⠁⢀⣤⡶⠶⠶⣤⣾⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⢰⡏⣠⡟⠀⣰⡟⠁⠀⠀⠀⠀⠙⣧⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠸⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⣾⣿⠏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⠃⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⡏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠈⠳⣦⣄⣀⣠⣤⠾⠃⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣾⠛⠛⣷⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢸⢻⣇⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⣤⣴⠟⠉⣳⡄⠀⠀⠀⠀⠀⠸⠷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⢻⡄
⣿⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿⠉⠛⠛⠛⠲⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣇
⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⣿⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡆
⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇
⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⡇
⣿⣀⣀⣀⣀⣀⣀⣸⡟⠀⣿⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣸⡇⠀⢸⣇⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠛⠋⠙⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣪⣵⡾⠷⢶⡭⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣹⡟⠁⠀⠀⠀⠙⡌⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣏⣓⢦⡀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣪⡷⠿⣻⣿⣸⠛⣇⠀⢀⣟⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣽⠞⠉⠀⠀⢈⠝⣡⣾⣿⡤⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣪⠖⠋⠀⠀⢀⡤⣚⡵⠞⣽⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⣭⠞⠁⠀⢀⡠⢖⣽⠞⠉⢀⢾⠏⢸⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠵⠋⠀⠀⣠⣖⣭⠞⣻⠏⠀⢀⣾⡟⠀⣸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⣠⣔⡿⠞⠉⠀⣸⠏⠀⢀⣮⡟⡇⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠀⣠⣴⡿⠞⠉⠀⠀⠀⣴⠏⠀⢀⢮⠟⠘⡇⠀⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣾⠟⠁⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⣸⠏⠀⢠⢫⠏⠀⡆⡇⠀⡇⡇
⠀⠀⠀⠀⠀⠀⣀⣴⣾⡯⠵⠒⠲⣼⡿⣅⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⣰⢣⠏⠀⠀⢱⡇⠀⣧⡇
⠀⠀⠀⠀⣠⣞⡵⠛⠁⠀⠀⠀⠀⡸⢠⢟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣰⣣⠏⠀⠀⠀⢸⡇⢠⢻⠃
⠀⠀⢀⢞⡵⠋⠀⠀⠀⠀⠀⠀⢰⠃⡞⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣰⣳⠏⠀⠀⠀⠀⢸⡇⢸⢸
⠀⢀⣏⡞⠀⠀⠀⠀⠀⠀⠀⣰⢃⡜⢁⣿⡟⠀⠀⠀⠀⠀⠀⢀⣠⠷⢷⣴⣿⠏⠀⠀⠀⠀⠀⢸⡇⢸⢸
⠀⢰⡿⠀⠀⠀⠀⠀⠀⢀⠔⡡⠋⡠⣿⡟⠀⠀⠀⠀⠀⢀⡴⣫⠴⠚⢯⢹⣿⣆⠀⠀⠀⠀⠀⢸⡇⢸⣿
⠀⠈⢿⣄⠀⠀⣀⡠⢖⣵⣪⠴⣫⡾⠋⠀⠀⠀⠀⠀⢀⣞⡼⠁⠀⠀⢸⢀⡇⢻⡆⠀⠀⠀⠀⢸⡇⠸⣿
⠀⠀⠀⠙⠛⠿⠿⠿⠭⠥⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⡼⣸⠁⠘⡇⠀⠀⠀⢠⣾⠽⢿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⣰⣷⠇⠀⣸⠃⠀⠀⢠⣿⠃⠀⠈⣿⡜⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡆⠀⢀⡴⡿⠋⢀⣴⠃⠀⠀⠀⢸⣿⠀⠀⠀⢹⡇⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣽⠮⢴⣺⠟⠁⠀⠀⠀⠀⢸⣿⡀⠀⠀⣸⠃⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢧⣣⣀⣴⣟⣴⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣛⣉⣁⣀⣀⣀⣀⣀
⣿⣿⠋⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⣏⡌⠀⠀⣠⠂⠀⠀⠀⠉⢛⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢿⠇⠈⠚⠁⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡞⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠋⠁⢿⡇⠀⠙⢦⡀⠀⢤⡀⠀⠀⣰⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠙⠓⠶⣬⣿⡀⠀⠀⠙⢦⡈⠙⠶⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠲⢄⠀⠀⠀⠀⢠⡇⠘⣷⣀⣠⡤⠔⠓⣾⢻⣷⡷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠈⢳⡀⠀⠀⠈⠳⣄⣹⡏⠈⢦⠀⢸⠃⢸⡿⠉⠛⣧⠓⢄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⠙⢿⡀⠈⢧⢸⡇⣿⣧⠀⠀⠈⢧⠀⣇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⣟⣦⡈⢿⣧⡟⢸⠀⠀⠀⠈⢇⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⡏⢌⢿⡝⣎⣿⡇⠘⣧⣀⡀⠀⠘⣾
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠙⠒⠋⠀⠈⢿⠁⠀⠀⠉⠁⠘⠓⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢠⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠈⡜⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠘⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⣧⢯⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠲⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⢧⣀⠀⠀⢀⣠⠖⠋⠀⠀⠀⣠⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⢤⣼⡀⢀⡠⠤⠶⠶⠖⣛⠲⢦⣨⣻⠟⣋⣠⣄⢀⠶⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡿⠁⠀⠀⠀⠰⠶⣦⣬⠿⠋⢰⡛⡇⢧⠈⡿⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠛⠳⢦⣤⣀⠀⠀⠀⢀⡞⢰⣇⣀⡤⠖⠋⣩⠿⠋⠁⣠⠴⢮⣁⣨⠤⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⣸⠉⢻⠃⠀⢠⡴⣋⣁⡤⠖⢻⠯⣦⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠠⠖⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⠴⠚⠤⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠙⠋⠲⠶⣦⣄⣀
⠀⡠⠠⣭⡀⠀⠀⠀⠀⠄⠠⣀⠀⠈⠀⠛⠁⠠⠠⣦⣤⡀⠀⠉⣡⣶⡀
⠀⢀⣤⣴⣶⣶⣶⣤⣤⣤⣀⣲⡤⢌⣉⡐⠒⠢⢄⠀⡌⣫⡔⠛⠋⠹⣿⡄
⠀⢸⣿⣿⠟⠛⠻⠿⠿⠿⢿⡿⠿⣿⣷⣾⣭⣓⢶⣴⡜⠇⠀⠀⠆⠀⠹⣿
⠂⣾⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠿⠿⣿⣧⡹⣿⣎⠀⠀⠀⢀⣀⠀⠠
⡀⡇⠀⠀⠀⢀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⢹⡟⠀⠀⣴⢻⡿⠀⠀⠄
⡀⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢿⣦⡀⢹⣆⣧⢀⢠⡄
⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⡿⠇⢀⡿⠈⠰⡌⡇
⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢁⢻⠀⢸⡗⡀⠀⢹⡟
⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠘⠛⡄⡜⡇⠇⠀⣼⠁
⠁⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⣠⠙⢱⡇⣆⠔⠁
⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠁⠀⠀⠀⠀⠀⠀⡅⠈⣸⣿⣿⣆
⠀⠠⢌⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣠⡶⠟⢝⡯
⠀⠀⠀⠀⠉⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣦⠔⠁⠀⠈⠁⠒⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⢙⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢄⣀⠀⠀⠸⣿⣿⠗⠲⠤⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠋⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⣀⠶⠀⠀⠀⢁⣒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⣀⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢒⣛⣉⣉⣙⠛⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⣀⠴⠊⡀⠀⠀⠀⢳⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⡀⢀⣠⡤⠶⠒⠋⠉⠀⠀⠀⠘⣆⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢔⣡⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢁⠖⡠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢠⢃⡼⢱⡇⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⣠⣤⠄⠀⣿⡇⠇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠇⡼⠁⢸⠇⠈⠘⠿⠎⠁⠀⡀⠀⠀⠀⠙⠛⠀⠀⡇⡇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⠃⡆⠘⡆⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠸⠀⡇⠀⢣⠀⠀⠀⠀⠀⠀⢄⣠⠀⠀⠀⠀⠀⣸⢰⠃⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⣆⠀⠀⠀⠀⡀⠀⡀⠀⢄⡀⠀⠀⡏⣼⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢃⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠄⢠⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⠈⢆⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⢠⠇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡈⢦⠸⡇⠈⠓⠦⠤⠤⠤⠀⠀⢠⡿⢠⣎⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠷⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡯⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢻⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡎⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢋⡄⠀⡏⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠸⣆⠈⠓⠦⣄⡀
⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠸⡇⠀⠁⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠤⠤⠴⢾⠁⠀⠀⢀⠓⠈⠀⠀⠀⠉⠳⢦⣀
⠀⠀⠀⡠⠂⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⢀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢄⠁⠀⠀⠀⠈⡆⠀⠀⠀⠈⠃⢀
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠤⠐⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠈⢧
⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣇
⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠑⢄⠀⠀⠀⠀⠈⢧⠀⠀⠀⢠⠃⠀⠀⢀⡴⠊⢄⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠙⣦⠀⠀⠐⠤⡀⠀⠀⠈⡆⠀⠀⡎⠀⢀⠴⠋⠀⠀⠀⠣⡀⠀⡏⠀⠀⠀⡇⠀⠀⠀⢸⡆
⢀⡇⠀⠀⠀⢰⡄⠀⠀⠀⠈⢧⡀⢀⡿⠀⠀⠀⠀⠈⠀⠀⡀⠘⡄⢰⢀⠔⠁⠀⠀⠀⠀⠀⠀⠁⣾⡁⠀⠀⠀⡇⣀⠀⠀⠈⣧
⢸⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢰⡌⠀⠀⠀⠀⠀⠀⠀⠀⡀⡬⠁⠈⠀⠠⠆⣷⠃⠀⠀⠀⠻
⡎⠀⠀⠀⠘⡌⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⠏⠄
⣧⣤⣤⣤⣤⣷⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣶⣦⣤⣤⣤⣤
⣿⣭⣭⣭⣽⣧⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣶⣾⣿⣿⣾⣿⣷⣾⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⢒⡛⠭⠉⢂⣀⠒⠠⠤⠶⣤⡖⣂⡀⠉⠭⠝⣒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢋⠩⢔⡂⠭⣐⣂⣭⣑⣦⣶⣶⣗⣚⣛⣛⣓⣚⡾⢿⣷⣥⣶⢬⣕⣪⢙⠲⣄
⠀⠀⠀⠀⠀⠀⢀⡴⢋⠕⡪⢔⡨⣐⡬⣟⣿⠿⠛⡋⠋⠙⠉⠙⡏⠛⠻⠛⠿⣯⣭⣛⠲⢭⣛⠦⣍⠳⣝⠢⡙⢦
⠀⠀⠀⠀⠀⡴⢋⠚⡡⡪⢊⢵⠟⣡⠞⡏⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠃⠀⠋⡹⢶⠈⠳⣌⢧⡈⢷⡌⢎⢧
⠀⠀⠀⠀⣼⢡⠃⡔⡱⠱⢱⠁⣼⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⣟⠀⠀⠸⣾⠡⠈⠘⠀⡊⡇
⠀⠀⠀⠀⣿⢀⠘⠀⡇⠀⢸⢠⡏⠀⠀⠀⠀⣀⣠⠤⠤⠴⠶⠶⠦⠤⣤⣀⡀⠀⠀⠇⣼⠉⠳⡄⣰⢃⠎⡜⢠⢀⣵⡇
⠀⠀⠀⠀⣿⡜⡀⢄⢇⠰⢰⠈⣧⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣤⠇⠀⣠⣿⠗⡡⢊⠔⡡⣫⠏⡇
⠀⠀⠀⠀⡇⣿⡐⡌⢎⢢⠑⡕⢌⠳⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡖⢟⡫⢔⡨⢒⡥⣪⠞⠁⠀⡇
⠀⠀⠀⠀⣧⠉⠻⣌⠢⡱⢕⢬⡑⠬⢚⣽⣓⣶⢤⣤⣤⣤⣤⣤⣴⠶⠶⠞⢛⡋⠭⢐⠪⠅⡒⠥⣢⣵⣯⡥⠴⢶⠖⠟⠒⠶⠒⠖⠲⠶⠒⠲⢦⢤
⠀⠀⠀⠀⣿⠀⠸⠋⢻⢮⣑⠩⣙⠲⠦⣤⣉⣉⣀⣀⣈⣉⣉⠀⠀⠴⠆⠑⣂⠠⣉⣂⣬⣵⠞⢻⠉⠉⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠇⣼
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢹⠛⠶⢬⣍⣙⡛⠒⠖⠒⠒⠒⠀⢒⣈⣃⣽⣾⠿⠻⠋⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⠇
⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠈⠀⠀⠀⠁⢹⠉⠙⠛⠛⠛⡏⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⡞
⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠖⠒⠛⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠴⠖⠚⠋⠉
⠀⠁
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠤⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠜⠉⠀⠀⠈⠀⠀⠈⠀⠐⢠⡀⠑⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡜⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠹⣆⢱⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡦⠀⢠⢡⠀⠀⢻⣰⠀⡇
⣤⣄⡪⠎⠉⠑⢒⠒⠒⠠⠤⠄⢀⣀⡀⠀⠂⠀⠀⠀⠀⠀⠛⠁⠀⠁⡼⠀⠀⣽⢸⢀⡇
⠘⠋⠉⠋⠙⠓⠒⠶⠦⠤⢬⣄⣐⠀⠀⠉⠡⡀⡀⠀⠀⠙⠒⠒⠒⠊⢠⠔⠾⠗⠯⠴⠦⠀⠀⡀⠀⠀⢀⢄⣤⢄⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⠒⠆⠈⡢⣄⣀⡀⠀⢀⣀⣬⡴⠒⣀⣞⣛⢳⡶⠴⡖⠀⠠⠮⠾⣫⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠓⠀⠀⠀⠰⠃⠘⠛⡏⣟⠐⠛⠖⣺⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢞⣡⠗⠖⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠉⠉⠉⠉⠛⠛⠻⠭⣛⡳⢶⣤⡀
⠀⠀⠀⠀⠀⣠⠾⠛⠓⠉⠉⠉⠉⠉⠒⠲⠤⣄⡀⠀⠀⠉⠳⣌⠛⢶⣄
⠀⠀⠀⢠⡞⠁⠀⠀⣀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠉⠲⣄⡀⠀⣸⠇⠀⠹⣧⡀
⠀⠀⢠⠏⠀⣠⡶⠛⠉⠉⠀⠈⠉⠉⠛⠷⣦⣄⠀⠀⠀⠉⠛⠁⠀⠀⢀⡼⣷⡀
⠀⢀⡟⢀⡼⠋⢀⣤⠶⠖⠒⠶⠦⣤⣀⠀⠀⠙⢷⣄⠀⠀⠀⢀⣠⠞⣡⠴⠜⣷
⠀⢸⠇⢸⠁⢰⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⠙⢷⡀⠠⡏⢠⠊⠀⠀⠘⣼⡇
⠀⢸⡀⢿⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠈⢿⡀⠹⡌⡄⠀⠀⠀⣐⣷
⠀⠘⡇⠸⣀⡈⠉⠓⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⣷⠀⢹⡐⣀⡴⠚⠉⢿
⠀⠀⡵⠦⢤⣉⠙⠲⢤⣀⠉⠓⢤⡀⠀⠀⠀⠀⠀⢱⠀⠀⢸⡀⠀⣇⡅⠀⠀⠀⠘⡄
⠀⢀⡇⠀⠀⠈⠙⠓⠤⣈⠛⢦⣀⠈⠲⣄⠀⠀⠀⢸⠀⠀⢸⡇⠀⣿⡀⠑⠲⠴⡾⠁
⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠑⠢⡈⠳⢤⡀⠑⢄⣠⠏⠀⠀⡾⠀⢠⡟⣁⣀⢤⣾⡁
⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⢦⡀⠁⠀⢀⠞⠁⠀⢼⣠⠤⠚⠉⠀⢹
⠀⠀⠀⠈⠛⠷⠶⠶⠶⣶⣤⣤⣀⡀⠀⠀⠀⠙⠶⠚⠁⠀⠀⠀⠀⠀⠀⣀⠴⠛⠻⢤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠲⠶⠤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠸⠿⠶⣲⡴⢤⣄⣀⣀⠀⠀⠀⢀⡖⠒⡶⠤⢤⣤⣈⣉⡭⠿⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠦⠶⠚⠁⠀⠀⠀⠀⠉⠉⠛⠓⠾⠿⣿⣶⣤⣤⣂⡀⠠⡠⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠄⢀⣂⣰⣶⠶⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠄⠒⣂⣉⣭⡤⠤⠶⠦⠘⠂⠐⠒⠐⠒⠐⠒⣦⣴⡿
⠀⠀⠀⠀⠀⠀⠀⢠⠶⣲⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠒⠒⠒⠒⠒⢒⣒⣒⡒⢒⠲⣽⡿⠋
⠀⠀⠀⠀⡀⠤⠤⢼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣿
⠀⢀⠔⡡⠐⠂⠀⠺⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠒⡺⡇
⠀⡎⠎⢀⢔⣮⠿⣶⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣒⣂⣀⣀⢠⣷⠇
⢠⢸⠀⢸⡎⠇⠀⠙⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⠀⠘⢸
⠈⡎⡄⢸⢧⠇⠀⠀⢹⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⡞⡇
⠀⢱⢣⠈⡾⡸⡀⠀⢸⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠤⠤⢤⣧⡇
⠀⠀⢫⢆⠸⣷⣣⠀⠀⡇⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹
⠀⠀⠀⢫⢦⠘⢷⣷⡴⣿⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⡾⡞
⠀⠀⠀⠀⠳⣕⢄⠈⠉⠁⣦⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢠⣥⠇
⠀⠀⠀⠀⠀⠈⠑⠯⣒⣦⡇⡎⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠺⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠐⠚⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠠⠴⠤⢼⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⢧⡿⢭⣀⣒⣒⣒⣒⣒⡒⢒⠒⠒⢒⣊⣉⣽⣴⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣒⣊⣒⣒⣒⣂⣀⣀⣨⣍⣭⣉⣉⣙⣐⣒⣚⣁⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⢀⠰⣧⡄⢂⣀⣀⠂⣤⡷⢘⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢋⡀⠈⢀⡈⢀⠌⠠⠐⢄⠉⡀⠌⠀⡌⢛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⣰⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠇⠀⠀⠀⠀⠀⠘⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⣾⠏⢘⠀⠀⠀⠀⠀⠀⠀⢐⠋⣿⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⣁⣤⣶⣿⣷⣼⣆⠀⠀⠀⠀⠀⢀⡾⠀⣿⠀⠀⠙⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢠⣿⠋⠀⠀⠈⢻⣿⣦⠀⠀⠀⣠⣾⠇⠀⣿⠇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⣿⠀⠀⡀⠀⠀⣿⣿⣿⣶⣾⣿⡟⠀⢰⡏⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠂⠀⣴⣿⢹⣿⣿⣿⡿⠁⠀⣾⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⠁⠀⠀⠠⡏⠉⠀⢻⣿⡿⠁⡔⠌⢉⠀⠀⠀⡀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⡇⢂⠀⠀⠐⠀⠀⠀⠻⡁⠀⢄⠄⢀⠀⠀⠀⡇⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠈⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠠⠃⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠣⠀⠀⠀⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿