Orang Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠿⣿⠛⠛⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣷⡀⠀⠀⠀⠀⡴⡿⠈⡷⠂⡀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠈⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏⢺⡇⠀⠀⠀⠀⢻⠉⠀⣀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠤⠽⢿⡄
⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠉⠀⣾⠁⠀⠀⠀⠀⠈⠳⠴⢁⠀⠀⠸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⠀⡀
⠀⠀⠸⢿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⣿⣧⠃⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⡜⠃⡠⠆⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠘⢆
⠀⠀⠀⢠⣛⠿⣿⣿⣿⣿⣿⣷⡀⠀⠈⣿⣿⡀⠀⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⣀⠀⠀⡀⠀⠈⡀
⠀⠀⠀⠀⠙⢀⣀⣛⣻⣿⣿⣿⣇⠀⠀⠘⣿⣧⡼⠃⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢠⣈⠃⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⢀⣿⣿⡿⠇⣀⠀⠀⠀⡀⢣
⠀⠀⠀⢀⣴⠟⠛⠿⠫⢿⣿⡿⠿⣀⡀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⣀⣤⠁⠠⢠⣬⣿⣿⣷⣀⣆⠀⠀⠀⠅⡘
⠀⠀⠠⣯⣠⠶⢶⣴⡶⠚⣁⡀⠀⠉⠁⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣿⣿⣿⡿⠟⠻⠋⠛⠀⠀⠂⢀⡇
⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠞⢳⡿⣿⣏⢹⣿⢟⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠊⠀⠋⠈⠀⠙⢀⠀⠀⠀⠄⠀⢀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⢄⡙⠂⠘⠀⣀⣀⠀⣀⡀⠔⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣁⣐⠀⠠⠅⠤⠤⢀⣀⣤⠴⠊⠁
⠀⠀⢀⣀⡀⠴⠶⠶⠿⠿⢷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠛⠋⠉⠁
⠀⠀⠈⠙⠿⣾⣄⡀⠀⠒⠒⠦⣼⣿⢦⣲⣤⣠⠻⠷⠶⠀⠀⣀
⠀⠀⠀⠀⠀⠈⠛⠿⣶⣶⣿⣷⣶⣾⣶⡽⣾⣿⣶⣏⣀⡀⠀⠈⠑⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠋⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠈⠀⠉⠛⢿⣿⣿⡷⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⡇⠀⠀⠀⠀⠀⣼⠁⠀⡀⠀⠀⠀⠀⣠⣀⣰⣷⣶⡃⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢶⣶⣿⡿⠟⠛⢻⣿⣿⣅⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢙⣿⣧⣄⢀⣸⣿⣿⡷⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢻⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⠁⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠈⠉⠙⢟⣿⡿⢿⣿⠟⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠈⠙⠉⠀⠈⠂⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣧⣄⣀⡀⠀⠀⠀⢀⣤⣀⣐⣶⣭⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣶⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣤⣀⣀⡀⠀⣀⣠⡤⠖⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡀⡆⠀⠀⣴⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣠⣄⣀⠢⢑⣯⢽⣿⡶⡻⠏⢁⠐⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠿⣿⡿⠷⠦⠀⠊⠉⢐⡁⠔⣲⣞⢛⣻⢷⠴⡆
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣶⠶⠆⠀⠀⠀⠚⠋⠙⠁⠌⠤⠼⠀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⣿⠿⠟⠛⣿⣽⣶⣾⢏⣾⡞⠎⠑⢒⢷⣾⣤⣿⢗⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢰⢂⣴⢻⣿⣿⢿⢿⣿⣾⣷⡄⣀⢀⠑⠻⠿⣫⠏⠀⠀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣬⡄⠀⢬⣴⣋⡩⣷⣷⣾⢻⣿⡟⠻⢏⣘⠆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠁⠿⠟⠟⠛⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣤⣤⣀⣄⣀⣀⣠⣤⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⢠⣀⣶⣿⣾⣾⣷⣯⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⢀⣄⢾⣹⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠄⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⢿⣿⣷⡿⣷⣾⡿⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡁⢀⣿⣻⣿⠿⣿⣿⡏⠀⠀⠀⠀⠀⠚⠓⠂⠤⡀⠀⢸⠀⢀⠰⠂⠀⠀⠀⠀⠀⠀⣠⣾⣿⡀⢢
⠀⠀⠀⠀⢿⢿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠣⣛⣿⢾⣿⣿⣿⣿⣿⣿⣝⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⢀⣠⣄⠀⠀⢻⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠘⠾⢿⡿⣛⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠐⠀⠒⠒⠈⠀⠀⢀⡀⠠⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠀⠈⠙⠿⠟⢹⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢰⠀⢁⠘⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠈⠀⠹⠶⠦⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠀⠘⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⠘⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⢀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢈⣠⣤⡶⣶⣤⣶⣦⣌⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠘⢃⠂⣽⡁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠻⣿⣿⣯⣾⣿⡿⣿⣿⣿⣧⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⢀⣩⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢀⣠⢼⣴⠆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⢁⣠⣤⣿⣿⣿⣿⣿⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣞⡙⣺⣷⣼⠿⠆⠀⠀⠀⠀⠀⠀⠀⣶⠖⠒⠛⣻⣿⣿⣿⣿⡟⢿⣿⣏⡿⠋⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⣵⣟⡿⣶⠓⣩⠂⠀⠀⠀⠀⠀⠀⢀⠙⠴⠶⣾⣻⣛⣛⣛⣿⡤⠜⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⡏⠏⠊⠀⠀⠂⠀⠀⠀⠀⠀⠀⠱⣦⣀⠈⡉⠉⠉⠉⢀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡯⡉⠉⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠧⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣦⣶⢄⣦⣰⣴⣔⣦⡶⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠉⠉⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡴⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣬⣂⡀
⠀⠀⠀⠀⣘⠁⠠⠀⣮⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠐⠘⠟⠁⠀⠀⠀⠘⠆
⠀⠠⠤⠌⠉⢀⡀⠀⠡⠶⠞⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠤
⠈⠀⠀⠀⠑⠺⠂⠀⠐⠄⣠⣝⡀⣤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠉⠀⠐⠁⠀⠀⠀⠀⠘⣄⣌⢀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠐⠁⠈⠀⠀⠁⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡰⡷⠀⠁⠀⢤⡀
⠀⡀⣀⣄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠠⡈⠙⠛⠀⢀⠠⡀⢀⠐⠒⠂
⢠⡏⣿⡣⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⠶⠂⠴⠶⣐⠊⠀⠀⠙⠋⡀⠀⠀⣀
⠸⡅⠈⢡⡄⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠠⠸⣤⠎⠀⠀⠀⠀⠀⠈⠂⠀⠈
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠁⠀⠀⠀⠀⠑⠀⠀⠄
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⡄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠸⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠙⣿⣟⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠹⣿⣿⣻⣇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠐⠶⣤⣤⣀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠉⠉⠻⣿⠀⠀⢸⣧⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⠿⠿⠿⠿⣷⢶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣄⠀⠀⢀⣀⡀⠀⠀⠸⠀⠀⠈⠈⠇⠀⠀⡠⣾⠿⠋⠘⠉⣈⠀⣀⣀⣀⣤⣤⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⡄⠀⠈⠙⠻⣶⣶⣤⡀⢀⣴⣶⣤⡊⣁⣀⣤⣰⣿⣿⣾⡿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⢿⣿⣿⣿⡄⠀⠀⠠⣿⠉⢻⢷⣿⣿⣿⣿⣧⡽⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣇⠀⠀⠀⠉⢀⠼⣾⣿⣿⣿⣿⣿⠷⣤⠴⠂
⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⢀⣀⣀⠀⠀⠀⠙⠙⠟⠀⠀⢀⡾⡠⢀⣿⠟⠛⠉⠉
⠀⣠⣶⣿⣿⣿⣿⣿⡷⠦⠔⠻⠿⡇⠀⠀⠀⠀⢠⣠⠞⠋⠉⠒⢅⠀⠀⠐⠠⠄⡀⠀⠈⠰
⠠⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡉⠉⠑⢦⣀⠀⠀⢱⠤⣤⣤⣤⣴⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⡂⡀⠀⣀⣾⠙⠉⢄⠀⣀⣿⣷⣶⣾⡿⠙⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠴⠶⠞⠋⠉⠉⠀⠀⠀⠀⢈⣏⣴⠋⠀⠀⢀⣼⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⢿⣟⠉⠁⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠋⠀⣀⡤⢾⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠰⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣆⣢⡄⡀⠀⠀⠐⠸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⢲⣤⣄⣀⡀⠀⠀⠀⢀⣀⣠⠴⠞⠋⣉⣐⣦⣬⣭⣵⣦⣀
⠀⠀⠀⠀⠉⠻⣯⣍⡉⠉⠉⠉⡁⢀⣰⡶⡶⠋⡹⠃⠀⣠⠴⠶⠿⢷⣄⣰⠏⠉⣲⡀
⠀⠀⠀⠀⠀⠀⠈⠛⢮⣍⡉⠉⠉⠋⠀⠐⠁⢀⣡⠴⠋⠁⠀⠀⠀⠀⣸⠇⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠶⢖⣿⣿⣷⣾⡿⠿⠿⠿⠿⣿⡟⢀⣾⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠉⠁⠀⠀⠀⠀⠠⠴⠾⢧⣾⡙⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣷⣶⣦⣤⣤⣤⣴⣶⣶⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⡾⢿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⢠⣴⣶⣤⣤⠤⣬⣉⢉⣉⠉⠁⠈⠉⠉⠙⠛⠿⢿⣿⣶⣄⠀⠀⠀⢀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠉⠻⢿⣿⣷⣤⡈⢍⢉⠉⢙⠛⠲⠶⢶⣶⣶⣮⣍⡿⢯⡙⢶⣦⣄⠂⢠⡓⠿⣿⢿⣿⡿⠐⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣥⣀⣀⡨⢀⣄⣢⣄⠩⠃⣩⣍⡓⠻⠾⣝⠻⣷⣸⡇⣀⣠⣄⣤⠤⠖⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣷⣞⣭⣿⣶⣿⣾⣯⣿⣿⣿⡶⠿⢟⣻⡯⣿⣯⣅⣤⣀⣀⡀⠀⠀⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠉⠉⠉⠉⠍⠙⠟⠿⣿⣿⠟⢫⠴⠛⠉⠛⠫⣾⡚⡻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⢯⣿⣿⣿⠿⠌⠃⠀⠀⠀⢀⠂⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⣌⠁⠀⠀⠀⠀⠀⠀⠀⢹⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡄⢖⣸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣾⡗⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⡝⢿⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢣⣹⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⢼⡳⡷⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠄⣷⢞⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⠆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣤⢚⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡷⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢋⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣵⣿⣆⡢⠙⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⣽⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣷⣿⣿⣤⣄⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣍⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⡷⣦⣙⠟⣽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣦⣴⣾⣤⣀⣤⣄⣠⡀⠠⠀⣴⣿⣡⣶⣤⣴⣴⢿⢫⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠒⠒⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠂⠀⠀⢀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⡰⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠉⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡔⠋⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠈⠀⣠⠀⠠⠀⠀⣄⠀⠂⠀⠀⠀⠀⠂⠂⠀⠀⠤⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠸⡆⢩⠀⢰⠉⠀⣠⠁⠀⠂⠀⡀⠐⠀⠈⡀⠀⠄⠁⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠋⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠑⠝⠊⠈⠑⠗⠈⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢲⡀
⠀⠀⠀⠀⡗⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠈⢄⣀⢀⢀⠠⡐⠊⠁⠀⠈⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣻⠀⠓⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡼⡇
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢠⠃
⠀⠀⠀⠀⠘⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣐⠖⠁⠀⡞
⠀⠀⠀⠀⠀⢹⡽⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠖⠊⠁⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠳⣿⣿⣿⣷⣦⣤⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣠⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⠖⢚⡓⡊⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣍⡻⡀⠀⡄⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣕⠙⠀⠀⠀⠈⠐⡀⠀⢀⠀⣠⣴⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣦⣤⣾⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢀⡀
⠀⠀⠀⠀⠀⠀⡀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢛⣄⡸
⠀⠀⠀⠀⠀⠘⠾⠷⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⢁⠀⡄
⠀⠀⠀⠀⠀⢀⡄⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢿⣵⣴⢶⣤⡈⠁⠀⢆⠀⢠⢾⠄⠀⠀⠀⠀⠀⠀⣀⣴⠶⠃
⠀⠀⠀⠀⠀⠀⢠⡀⣤⠎⠀⠀⠀⠀⠀⠀⢠⣤⡋⠁⠀⠈⢻⣆⠀⠙⠇⡠⠈⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠆⠂
⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠘⢋⠁⣠⡴⠒⠀⠉⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠁⠈⠉⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠛⠁⢈⣤⣀⣀⣠⣤⣤⣄⠙⠁⠀⠀⠀⠀⠀⠀⠠⡐⠒⡟⠈
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡽⠟⠉⠃⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⣤⣄⠔⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⡿⡻⡛⡟⠟⢟⢿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠫⡡⡑⡑⡔⠜⢌⢌⢎⢊⢢⠢⡫⡻⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⠻⡡⡱⡑⡔⡔⣜⣌⣮⣮⣦⣦⣧⣥⣵⣕⣐⡜⠟⢦⣀⠀⠀⠀⣴⣶⣶⡄
⠀⠀⠀⠀⢀⣴⠿⡱⡑⣑⣴⠾⠾⠛⠙⠉⠉⢀⣀⣀⣄⣤⣤⣤⣤⣮⣴⣼⣯⣿⣦⣼⠓⢚⣿⠃
⠀⠀⠀⢠⡾⡓⠐⠌⠊⠉⠀⢀⣠⣴⣴⣾⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣄⠀⡿⠤⠠⣿⣛⠦⣄⡀
⠀⠀⣰⡟⠑⠀⢀⣠⣤⡴⠿⢛⣽⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣃⠀⣉⣹⣿⠷⠾⠧⢶⣤⡀
⠀⣼⣯⣦⠶⠛⠛⠉⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡀⢰⣿⣇⢐⣾⡟⠉⠀⠀⠀⠀⠀⠀⠙⢦⡄
⡼⠛⠁⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠋⠁⠀⠀⠀⠀⢈⡻⠿⣿⢿⠣⣤⣤⣀⡀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠘⣦⠀⠀⠀⠉⠻⢦⡀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⢸⣿⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⡀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢨⣤⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣄⣀⠂⠀⠀⠀⠀⠄⠠⠂⠈⠀⠀⠠⡀⣀⣠⣵⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣶⣶⣶⣶⣤⣶⣶⣶⣾⣿⣿⣿⡿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⠀⠀⠀⠀⠙⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣴⣄⠀⠀⠈⠋⣽⣿⡆⠀⠀⠀⠀⠀⠀⣠⠴⠋⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣰⡖⢐⣦⣆⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣷⠄⠀⢀⠈⠛⣧⠀⠀⠀⠀⣠⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⢈⠀⠉⠃
⠀⠀⠐⠀⠠⠤⠤⢠⢤⡤⡤⣤⣄⡀⠀⠀⠀⠈⠙⠃⠀⠀⢼⠀⠀⡠⠀⡎⢰⡿⠃⢉⡁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣿⡇⡾⣸⣿⣴
⠀⠀⠀⠈⠛⠒⠀⡀⠀⢃⠘⡟⣿⢿⣷⣤⡀⠀⢠⣤⡀⡄⠸⠀⣤⣤⣾⣾⣏⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣧⣃⡇⣯⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣽⠹⣿⣿⣿⣿⣄⢸⡿⣿⣧⡎⠂⢹⣇⡿⢡⣿⣩⣶⣶⣶⣤⣀⠀⠀⠀⠀⣰⡶⢄⣤⠄⠀⠀⢿⣿⠁⠀⣿⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠲⢶⣤⣙⣿⣶⣿⣿⣿⡏⠘⢧⠘⡿⠁⠀⢹⣿⠷⠞⣿⣿⣿⠟⢻⡿⠋⣀⣄⠔⠊⢀⡠⡿⠋⠀⠀⠀⠈⠏⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣆⡠⢽⡀⠘⣻⡁⠀⠀⠀⣽⣳⡹⡀⢠⣤⡤⢠⠀⠀⣹⣷⠴⠯⠡⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠀⠱⠾⡿⠿⣶⠄⠀⣼⡧⠢⢿⠿⣿⢡⠿⣴⠞⡙⠉⠛⣅⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣀⣠⣶⣿⣿⣶⢤⣀⣤⡄⠊⢉⢟⣵⡿⠂⢤⣿⣿⠋⡇⠀⣸⠈⣡⣆⣠⣿⣷⣂⠴⣠⣤⣽⠅⣀⡄⠠⠤
⠀⠀⠀⠀⠀⠠⢤⡤⠐⠚⣋⢉⡡⣘⣿⠏⠀⠀⠋⡿⠁⠀⠺⣿⢫⡇⠀⠀⠙⢇⠀⢩⢿⢿⠅⠀⣨⣿⣛⣟⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠰⣄⠀⠀⣄⡀⠀⠀⠈⢺⣧⣴⡖⣲⣿⢿⠂⢾⠿⠁⠲⣭⣍⠋⠐⠒⠛⠓⠂⠀⠀⠀⠀⣀⣀⣀⣀⡤
⠀⠀⠀⠀⢀⣄⣴⣐⡲⣦⣠⣄⠀⠀⠀⠀⠸⢷⣄⠹⣿⣆⠀⢠⣾⣷⠛⢠⣿⠃⣿⣄⣸⣷⣶⣤⡼⠇⠀⢀⣀⣀⢒⣲⣶⣿⣿⣿⣿⣿⣭
⠀⠀⠀⣴⡝⢿⣍⠞⢳⠹⢽⡧⠱⢀⠠⡀⠀⣐⣿⣞⣿⠋⣦⣻⡟⠙⣧⡗⡟⢐⣿⣿⣿⡿⠿⠋⣁⣔⣶⣿⣿⣿⣿⣿⡿⠿⠿⣿⡟⡿⠁
⠀⠀⣼⠌⠈⠃⠈⠀⠁⠘⠏⠈⡀⢈⠀⢁⠀⠀⢬⣻⣿⠀⣿⡿⠁⣠⢻⣤⣠⠋⢉⣉⠀⠀⠀⡄⢠⡽⠛⣿⣿⡿⢿⣿⣯⣽⣿⣿⠏
⠀⡄⠰⢕⡠⢂⡀⡆⠄⣴⡊⢉⣒⠂⡂⢸⠀⠀⠀⠋⠩⣿⣼⡇⢘⣿⡟⣿⠇⠀⠈⠙⠀⠀⠀⠀⠀⢰⣾⠟⠋⠛⠓⠂⠠⣴
⠀⢻⡄⠠⢦⡠⠀⠀⢨⠛⡅⢂⠉⠀⣠⡟⠀⠀⠀⠀⢠⡈⢛⣵⢞⠐⠃⡏⠀⠀⠀⠀⠀⠀⠀⢀⠾⠊⠀⠀⠀⠀⠀⢀⠁⠁
⠀⠀⠻⣶⣄⡁⠒⠓⠠⠚⠒⣊⣤⣾⠟⠀⠀⠀⠀⠀⠂⠀⠉⠻⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⡤⠤⢿⣼⣷⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⡿⣟⣿⡏⠀⠀⠀⠙⣿⡀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⠟⡙⠀⣷⡻⠁⠀⠀⠀⠀⠈⣧⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡿⠋⢠⠀⠁⣼⡟⠁⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠛⠁⠀⣠⠋⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠴⠟⠋⠁⠀⠆⠴⣊⠥⠿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠀⠐⠂⠀⠀⢀⠀⠀⢀⡿⡄⠀⠀⢀⣤⡴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⡾⠀⠆⠀⢰⡏⠁⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢀⠔⠀⠀⠀⠘⣆⠀⠀⠀⢰⠀⢀⡟⣸⠉⢸⢀⡔⠍⡙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⢿⡀⠀⠀⠀⠀⠉⠉⠑⠲⠋⠀⠈⢷⡏⢀⡧⠋⢈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⠙⢦⡴⠃⠀⠀⠀⠀⠠⠀⠀⠀⣸⠀⡘⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠠⣡⠾⣝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣧⣀⠀⢰⠃⢀⠀⡀⠀⠀⠀⠁⢀⠀⠘⠟⢀⠾⣁⣐⠵⠋⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠉⠉⠛⠋⠀⠋⠀⠈⠁⠀⠀⡀⠀⠁⠀⠠⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠈⠀⠀⠦⡤⣄⡀⠀⠀⠙⠆⠀⢀⣠⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⠿⡿⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣯⠝⠁⢠⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁




⣏⠉⣻⣛⣛⣛⣛⣻⣛⣛⣛⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⣛⣻⣟⣛⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢠⠀⠀⣀⣤⠴⠶⠖⠒⠲⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⠁⠀⢸⡴⠞⠉⠀⠀⠀⡀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠃⠀⠀⡘⠀⠀⠀⢀⠄⠈⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡰⠁⠀⣠⠐⠁⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠉⠉⠓⠢⢤⣀⣠⠔⠁
⠀⠀⠀⠀⢀⡠⠞⠋⠁⠀⠀⠀⠈⠉⠑⠤⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⡠⠋⠀⠀⣀⣀⠤⠤⠖⠒⠒⠖⠂⠀⠀⠀⠠⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠠⣤⡤⠤⢤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠰⠀⠀⠀⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⢀⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠶⠶⠶⠖⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠟⠉⠂⠻⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⠏⠀⠀⠀⠀⠀⢹⣿⣿⣿⡆⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣿⣾⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⢀⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣇⠀⠀⠀⡀⠀⠀⢰⣿⣿⠏⠀⢠⠈⣠⠾⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⡈⡀⠐⠞⡀⠢⠛⠋⠁⢀⣤⠾⠿⠿⠿⠦⣄⣀⢀
⠀⠀⢠⣤⣀⣀⣀⠀⠀⣀⣀⣤⣤⣤⢠⡿⢿⣻⣷⢿⣧⠦⠴⠓⠓⠒⠒⠈⠁⠀⢲⣆⠀⠀⠀⠈⠛⠿⢦
⠀⠀⠀⠀⠀⠈⠉⠛⠉⣿⣿⣿⢫⡽⠋⠉⠋⠀⠀⠐⢲⠀⠀⠈⠛⠳⣶⣦⡄⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣦⣘⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣧⣩⣿⣷⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠁⠀⠀⣆⡀⣀⣀⣠⣴⣷⣼⣿⣾⣿⣿⣿⣿⣿⠋⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠐⠀⠂⠀⠀⠀⠳⡄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⣂⠀⠀⣸⡆
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠃
⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⢃⣨
⠀⠀⠀⠀⣮⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠄⠐⠀⠀⠀⠀⠀⡢⠊⠀⢠⡏
⠀⠀⠀⠀⠘⣾⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠒⠿⠀⠀⠀⡽
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣛⣄⣐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣓⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣷⣶⣾⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⡝⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠘⠁⠀⠀⠩
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⣀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠐⢠⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡈⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⡀⠄⠀⠀⠀⡀⠀⢠⡀⢀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⣄⡀⠀⡀⠀⠋⠉⡁
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⢰⡠⢁⠀⠱⡉⠂⠀⠀⡀⢤⠀⢀⡏⠉⠀⠄⠐⠃
⠀⠀⠀⠄⠠⣀⠀⠠⠀⠀⡄⠂⡐⠁⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⢀⠈⠓⡘⠀⠤⠀⠀⠀⣠⡀⣀⠈⠁⠀⠀⣠⣀⢀⣠
⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠻⢣⣏⣀⣠⣤⣴⣿⣿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⢿⢛⠋⡽⡟⠋⠉⠙⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡄⠠⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠸⠈⠁⡧⠈⠀⠓⠂⠈⠗⠀⢀⠛⠀⠀⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠐⠂⠀⠒⠒⠒⠠⢄⡀
⠀⠀⠀⠠⠀⠀⡠⠀⠀⡀⠀⠀⠀⠀⠀⡎⠀⠀⠌⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠓⠀⠰⠄⠀⠨⡃⠀⡼⠀⠀⣠⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠘⠄⠔⠰⡀⣠⢧⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠆⠀⠀⣐⡘⠀⠘⠆⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣛⣿⣶⣾⡟⣟⣩⣒⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⢻⣳⣶⠟⠉⡉⢩⣿⣾⣿⣟⣻⣿⣟⠛⠿⢷⣾⣷⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡴⣻⣿⣿⡿⠋⠀⣴⢊⣼⡿⠏⠐⠂⠀⠉⠉⠙⢳⣦⣀⠈⠙⢿⣿⣦
⠀⠀⠀⠀⠀⣰⡯⢞⣽⡿⠋⠠⠠⡾⣡⣾⡟⠁⠀⠰⣶⣿⣿⡶⠶⠂⠹⣿⣌⠳⣌⠻⣿⣷⡀
⠀⠀⠀⢀⣼⣽⣷⣿⡿⠁⠄⠰⣼⣿⣿⠟⠉⠀⠁⠛⣿⣿⣿⣿⣷⣦⡀⠹⣿⣥⠌⠄⠙⣿⣿⡀
⠀⠀⠀⡼⣿⣿⡿⠉⠀⠜⣼⡴⣿⣿⠏⢀⠀⠀⠀⣙⣻⣿⣿⣿⣿⡿⢷⣤⣿⣷⣶⡌⠀⠙⣿⣷⡀
⠀⠀⢸⢷⣿⡿⠃⠀⡘⣠⡟⢻⣿⠇⠘⠁⠀⠀⠐⣒⣿⣿⣿⣿⣿⣟⣛⡻⣿⣿⣿⡃⠆⠀⢻⡿⣇
⠀⠀⣿⣾⣿⣇⠀⡁⢈⠻⡧⣼⡏⠙⠃⠈⠡⣤⣤⣤⣽⣿⣿⣿⣿⣟⣽⣿⣿⣧⣾⣧⡄⠀⢀⣿⢹⡀
⠀⠀⣿⣿⣿⠁⠀⠸⣷⣀⣰⡿⠓⠖⠀⠀⠀⠀⠀⠩⠭⣽⣿⢯⣍⣉⣼⣾⣿⣿⣿⠿⠁⠀⠸⣿⣿⡇
⠀⠘⣿⣿⣧⡗⠰⣶⣾⣿⣿⡏⠰⠆⠀⠁⠀⠀⠉⠐⣒⣶⣾⠿⠍⠉⠉⣉⣨⣿⣿⣾⠖⠀⠀⣿⣿⡇
⠀⠀⣿⣿⣟⣤⣸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠅⠒⠾⡿⢿⣿⣿⣿⣷⣾⠄⢰⣿⣿⡇
⠀⠀⢻⣿⣿⣷⣿⣿⣿⣿⣷⠀⠘⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⡦⢶⣿⣿⣿⣿⣿⡫⠀⣿⢹⣿⡇
⠀⠀⠘⣷⣿⣿⣿⣿⣹⣿⣟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⡴⢿⣿⣿⣿⣿⣯⠀⣼⢻⣾⣿
⠀⠀⠀⠹⣿⣿⣿⣿⢿⣿⣿⣷⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣒⣫⣽⣿⣿⣿⣿⣿⣴⣫⡀⣴⠃
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠹⡷⢅⡀⠀⠀⠀⠀⠀⣀⣀⣿⣿⠿⢿⣿⣿⣿⣿⣿⡿⢫⣿⣷⠋
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣮⠊⣒⣔⣢⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣯⡿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣹⣶⣭⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣟⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⣔⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⡀⠀⠀⠐
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣧
⠀⠀⠀⠀⠈⡌⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡸⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡿⠻⢿⡇⠆⠀⠰
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⢀⠔⢄⣀⡀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣰⢊⠇⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣀⣾⣇⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠘⣷⣄⣠⡀⠔⢀⣤⣧⣯⣾⣿⣿⣿⣾⣷⣿⠇⠀⠀⢀⠀⢼⠡⠀⠀⢤⠈⠘⠛⠰⠿⠶⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣾⣿⣷⣾⣿⣿⣿⣽⣿⣿⣿⠋⠀⠀⠸⡀⠠⡀⠀⠀⠀⣴⣦⣠⣠⡀⠀⠀⠀⢀⣠⠀⡆⠀⠀⠀⠀⠀⠀⠻⣿⣿⠇⣸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠐⢄⣁⡀⠀⠀⠈⠋⣌⣻⣏⣀⠄⠀⡈⠟⢀⠀⠀⠀⠀⠀⠀⠀⠠⣈⠁⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠢⣶⣷⣤⡈⠙⠂⠶⠖⠈⢋⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣶⠶⠶⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢂⠀⣠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠸⠋⣾⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡀⢦⣋⣴⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋⠀⡴⣦⣹⡴⢃⣤⡒⣣⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢬⠅⠀⠈⠁⠚⠫⠤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡠⡈⢶⣮⠻⡿⠙⠋⢟⣛⣁⣢⠀⠀⡄⠀⠀⠀⠀⠈⢿⣿⣦⣤⣀⣀⣠⡀⠐⢦⡴⠶⣄⠀⠀⠀⢀⡦⣷⡖⡃
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣠⡶⠀⠀⠐⠺⠼⢓⠀⠀⠀⠀⢨⣩⣍⣥⠀⠀⣇⠀⠀⠀⠀⠐⠘⠛⠛⠛⠛⠛⠉⠉⠉⠀⣀⡄⢹⡿⣿⣆⣆⠔⠾⠂⠀⠃
⠀⠀⠀⠀⠢⣄⠀⠀⢀⠀⢰⣾⣷⠀⠀⠡⠴⣿⠛⢤⠰⡆⠸⡣⠒⠿⠋⠀⠀⠌⠀⠀⠀⡄⠄⠀⠉⣁⣀⣠⣤⡀⡀⠀⢀⡙⠇⢸⣅⣩⣩⡁⠀⠀⡤⠂
⠀⠀⠀⠀⠀⠘⠿⣶⣿⣿⣿⣿⣿⣧⡀⠀⠈⣅⠼⢁⡦⡶⢧⠝⠆⠀⡠⢁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠛⠫⢊⣻⣷⠴⣡⡄⠛⢀⡾⠿⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⢐⣉⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣐⣤⣀⣀⠈⣉⣉⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢤⣦⣴⣶⠾⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣶⢎⣺⠯⣏⡼⣶⡀⡔⣄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠐⠀⠄⣀⣤⣴⣦⣭⣭⣬⣶⠖
⠀⠀⠀⠀⠀⣀⣤⠤⣽⡽⢻⣾⢥⣥⢟⣏⢹⣾⣶⣥⡮⣄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⡛⢻⣏⠉
⠀⠀⠀⠀⠀⠶⣿⣤⣷⣲⠻⣯⣳⣼⣧⣭⣿⣿⣽⣻⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣂⠈⠢
⠀⠀⠀⠴⣦⢾⣿⡿⢻⣯⢗⣛⣻⡜⢹⣿⣶⡿⣿⡥⡷⢴⣴⡄⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠓⢿⣷⣤⣁⣄
⠀⠀⠀⠀⢘⡾⢧⠞⣏⣡⣼⡋⢿⣾⡟⣋⣾⠽⢿⣽⣷⢾⡾⠇⠀⠀⠘⢶⡄⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠉⠙⠛⠉
⠀⠀⠀⣰⣭⣴⢾⣏⣽⣏⣿⡿⣯⢼⢻⣿⡿⢷⣿⡞⢻⣶⡗⠂⠀⠀⠀⠀⠉⠻⠦⠤⠠⠄⠈
⠀⠀⠀⠉⠈⠈⠻⠛⠋⠻⠤⣣⠘⡌⢀⡨⠁⠙⠻⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⠰⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠳⢦⣠⠀⣠⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠛⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⣋⣥⡀⠹⡆⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⣛⣭⡴⠞⠛⠉⠘⣧⠀⣿⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣞⣯⡵⠞⠛⠉⠀⠀⠀⠀⠀⠀⣿⠀⡿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣞⡋⠻⠿⠿⠯⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠋⣸⠇⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣛⡛⠒⠶⠶⠶⢦⣤⣤⣤⣀⣀⡀⠀⣰⠏⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠞⣋⣭⠶⢻⣿⣿⣿⡟⣿⢷⡄⠀⠈⠉⠛⠶⠶⣤⣤⣤⣄⠀⠈⠉⠉⣿⠏⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠛⣋⣡⡴⠶⠛⠉⠀⣰⢟⣿⣿⠁⣷⠸⣆⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⣹⠇⠀⣠⡾⠁⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠾⠛⢉⣡⡴⠖⠛⠉⠁⠀⠀⠀⠀⣴⠋⣼⢳⡏⠀⢹⡄⢻⡄⠈⢷⡀⠀⠀⠀⠀⣠⡾⠃⢀⡴⠋⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠰⣿⡉⠉⠻⣤⡀⠸⣏⡁⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢰⡏⣼⠁⠀⠈⣧⠀⢿⡀⠀⠻⣆⡀⢀⡴⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⢷⣌⠙⠶⣤⣀⡀⠀⠀⣴⠟⠀⠀⡿⢠⡟⠀⠀⠀⢹⡄⠈⢻⡄⠀⠈⠙⠋⣠⡾⠋⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠛⢶⣄⡉⠉⠛⠛⠁⠀⠀⣸⠃⢼⡃⠀⣀⣀⣼⠇⠀⠀⢻⣄⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠈⠙⠳⠶⣤⣤⣀⣰⣟⣀⣈⣛⣛⣉⣁⣀⣤⡤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉






⣷⣶⣶⣶⣶⣷⢿⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⡿⣶⠿⠶⠶⠶⣶⣾⠶⠾⢶⡶⠾⠶⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣆⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣶⠲⠂⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⠀⠀⠀⠀⠘⠀⠀⠈⠑⠲⢤⣀⠀⠀⠀⠀⠀⣸⡏⠀⠈⠻⣧⠄⠂⠀⠀⠀⠀⠰⠀⠺⡶⣶⣿⡿⣽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣦⣠⣦⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣉⡓⣦⠀⠀⠀⣿⡃⠀⢤⡀⠹⣦⡚⣾⡆⠀⠀⠀⠂⣁⣶⣿⡿⠷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠿⣣⠟⠀⠀⠀⢌⠛⢣⣜⡻⣄⠘⠶⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⣽⣿⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣁⣨⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⣶⡎⠈⢹⣿⣿⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠈⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠄⠀⠀⠀⠀⠀⠀⠻⡶⢹⠷⠚⢿⣶⣿⠃
⠀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⢺⣿⣧⠀⠀⢀⣼⣏⠀⠀⠀⠀⠀⢀⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠞⠛⠘⠀⣤⡠⡅⣠⠀⠀⠀⠙⠾⠶⠶⠼⠟⠉
⠀⠀⠀⣿⣿⣿⣷⣦⣤⣤⣤⣤⣽⣿⣿⠀⠀⢸⣿⣿⣦⣤⣀⣤⣶⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⠀⠀⢰⡒⢝⠶⣰⣿
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢙⣭⣉⣇⣤⣾⣿⠇
⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠉⠛⠿⠻⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋

⠀⠀⠀⢀⠀⠀⠀⢠⡄⠀⢀⣠⠄⠀⠀⠀⠀⠠⠄⠀⢀⣄⡀⠀⠀⠠⠀⢀⣤⠖⠂
⠀⠀⢀⠈⠀⠀⠀⠀⠀⠈⠋⠀⢀⣴⣶⣿⣶⣦⡀⠀⢻⣿⠇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣆⠀⡄⠀⠁⣰⣴⠀⠙⠷⣤⣀⠀⠀⢀⠀⠀⡦⠀⠀⢄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⡙⠉⠀⠀⠀⠀⠀⠀⠄⠈⢀⣀⣀⣀⡁⠀⢺⡆⣠
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠐⠀⠀⠀⠀⠐⠃⢀⣶⣿⣿⣿⣿⣿⣶⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣀⡄⢀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡀⠀⠀⠀⠐⠃⠀⣼⣶⣇⠀⠀⠉⢹⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠻⠋⠁⠒⠘⡐⠀⠀⠚⠟⠣⠀⠃⠀⢸⡇⠀⠘⠃⠘⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⡀
⠀⠀⠀⠠⠒⢄⠀⠀⠀⠈⠀⠀⠀⢀⠀⡠⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⣾⡗⠀⠀⠂⠀⠀⠈⠉⠉⡉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⢀⡠⠀⠀⠜⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠤⠉⠀⠀⠀⠀⠂⢠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣈⡀⠀⠀⠢⡠⠂⠀⡰⠉⠹⡄
⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⡿⢡⣾⣿⠟⠀⣄⠀⠀⠈⢡⣧⣤⣤⣧
⠀⠀⢀⣠⡴⠞⠀⠘⠃⠀⢠⣶⣶⣦⣄⠙⠃⠀⠀⠀⠀⠀⣠⣤⡀⢀⣴⣄⠀⠀⢸⠋⠁⣀⡀⠀⠀⣶⠀⢸⣿⣇⣿⣿
⠀⠀⢺⣏⣀⣤⠾⠿⣿⣦⠈⠻⠿⠿⠟⠃⠠⠀⠀⠀⠀⠀⠙⠛⠁⠆⠉⠁⠀⢀⠀⢴⣿⣿⣿⠇⠀⠀⠀⠈⠛⠛⠛⠋
⠀⢀⣶⠟⠛⠛⣶⣶⣟⠋⠀⡀⡀⠀⣶⣶⡦⠀⠄⠀⠀⠀⣤⠐⠂⠂⠇⠀⠀⠋⠐⠀⠈⠉⠁⠄⠀⠈⠉⠉⠃⡄⢰⡇
⠀⠘⣿⣤⡴⠟⠉⠉⢹⣷⠀⠻⠃⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⡆⠀⠻⣿⠛⠀⠀⣿⡇
⠀⠀⢠⣿⠟⠶⠶⠶⠿⠃⡄⠀⠂⡤⠒⢦⠀⠀⠀⠀⠀⠀⣀⢀⡂⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢠⣤⣿⣤⡄⠃⢸⡇
⠀⠀⠀⢻⣷⡀⠀⠀⡀⠀⣴⠀⠘⠃⠀⠈⠁⠀⠀⠀⠐⠀⣿⣿⠇⠒⠀⠀⢸⣿⣿⣻⣝⣿⣿⡇⠀⣀⠀⠀⠀⡀⠀⡇
⠀⠀⠠⠄⢈⠁⠀⠘⡳⠀⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠈⠠⠄⢸⣿⣿⣛⣟⣿⣿⡇⠐⡿⠀⠀⠀⢳⡀⠁
⠀⠀⠀⠀⠙⠀⠀⠈⡽⠀⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠃⠀⠀⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠓⢸⣧
⠀⠀⠀⠛⠀⠀⠀⠈⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠉⠉⠉⠀⠐⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢤⣀⡀
⠀⠀⠀⠀⠀⢀⡴⣋⣷⣷⣲⣿⣶⣿⡦⡀⠀⠀⢀⢀⣤⣠⣶⣦⠤⡀⠀⠀⠀⠀⣠⢊⣷⣿⣾⣿⣷⣮⡳⣄
⠀⠀⠀⠀⠀⡞⣿⣿⣿⣿⣿⣷⣿⡿⣇⢳⠀⠀⣆⢼⣿⣿⡿⢿⣿⣿⢕⣄⠀⢰⣷⣿⣿⣿⣿⣿⣿⣿⣧⣸⡄
⠀⠀⠀⠀⠀⡷⣿⣿⣿⣯⣬⣿⣿⣿⡟⣽⠀⠀⣿⣦⡙⣿⣿⣶⣿⣿⣿⡟⠀⢸⣽⣿⣿⣿⣭⣿⣿⣿⣿⢸⠇
⠀⠀⠀⠀⠀⢧⢻⣿⣿⡿⣿⣿⣿⠿⢣⠏⠀⠀⢻⣿⣿⣾⣭⣛⣛⣻⣟⣵⠀⠘⣗⣿⣿⣯⣿⣿⣿⡿⢿⡾
⠀⠀⠀⠀⠀⠀⠳⢌⡻⠿⠻⠿⣏⡴⠋⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠈⠳⢽⣛⣻⣿⣛⡥⠚
⠀⠀⢔⢠⣴⢰⣿⢦⣍⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣀⠤⠖⢒⠠⢄⠀⠈⠉⠉⠁⠀⠀⢀⣌⡳⡄
⠀⢐⣿⣾⣻⣾⣹⣗⢹⣧⠀⠀⠀⣼⢡⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⢞⣵⢾⣿⣟⣿⣶⡝⡄⠀⠀⠀⠀⢰⣿⣿⣿⡹
⠀⣲⡶⣿⣩⣿⣿⣷⢸⣿⡇⠀⠀⣿⡇⢿⣿⣿⣆⣀⡀⠀⠀⠀⣸⢸⡿⡮⣟⢻⣿⣿⢏⠀⠀⠀⢀⣶⣾⣿⣿⣿⡂
⠀⢫⣾⣿⣿⣿⣾⡏⣼⣿⠇⠀⠀⢿⣿⡜⣿⣿⣿⣿⣿⣷⡆⠀⢸⡿⢿⣷⣿⣟⣶⣛⡟⡍⠀⣴⣿⣿⡿⣿⣿⠟⣼
⠀⠘⢝⠸⠿⠯⢋⣼⡿⠋⠀⠀⠀⠈⠻⣿⣮⣟⡛⠿⠛⣉⠔⠁⠀⠑⢬⣓⡻⠿⣟⣫⠎⠀⠘⠦⣽⣻⣟⣋⡭⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠚⠙⠒⠶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠱⣶⡆⠀⠀⠀⠀⠀⢙⡹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⢀⠀⠀⣀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⣿⣿⣆
⠀⠀⠀⠀⠀⢠⢤⣄⣀⠀⠌⠀⠉⠀⠀⠀⡀⠀⠀⢦⠀⠉⠒⠄⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣮⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠑⢬⡙⠟⠀⢅⠂⠀⠀⠠⣀⢀⡠⠰⡦⡖⣦⢁⡊⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣿⣿⠇
⠀⠀⠀⠲⣦⣬⣙⣾⣿⡀⠀⠀⠀⠀⠀⠁⠘⠂⢈⢛⠸⣻⣿⡆⠀⠆⠐⠑⠢⣂⠀⠀⠀⡔⠀⢀⢈⢴⣿⣿⣿⠁
⠀⠀⠀⠀⠘⠿⣿⣟⣽⠀⠀⠀⠀⠑⠐⢷⢶⣒⠶⣅⣄⠐⠱⢄⣉⡈⢶⠄⠀⠙⣷⣀⢴⣦⣂⣠⣻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⡴⠛⡩⣿⢤⠀⠀⠀⠀⠀⠀⠑⠻⡿⣽⠿⢗⡨⠒⣿⢥⣿⢐⣀⢈⣉⣿⣷⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⣠⣴⡿⠿⠟⠃⠄⠀⠀⠀⠀⠀⠀⠠⠈⠑⠈⢙⠙⣿⣙⣿⣽⣎⣹⡏⠙⢸⣿⡟⠘⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢀⠰⡏⢹⣫⣿⠿⠿⠶⣿⢫⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⢀⠘⣉⣓⢯⣉⡟⢙⣛⣁⣠⣾⡿⢹⣶⢶⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢙⣼⣿⣿⢿⣿⣾⣿⣿⣿⣻⢣⣿⣿⡛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢒⣽⢿⣁⣰⢿⣿⡿⣿⣿⣿⣿⣿⣟⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠻⠆⠀⠀⠈⠉⠛⠿⠿⠿⣿⣿⠦




⠀⠀⡀

⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠋⠂⠀⠵⠤⡐⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⢠⠄⠏⣃⢈⠘⠀⠀⠀⠀⠀⣠⠞⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠉⠑⠊⠁⣡⠄⠒⠀⠀⠀⣼⡏⣲⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠂⡤⠀⠻⡁⠸⣟⡆⠀⠀⢠⢼⣏⡿⠋⠀⠀⠐⣆⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠆⢰⣞⣤⣈⠳⡈⢣⠀⢠⠞⠋⠁⠀⠀⠀⢀⣠⢿⠀⠀⠀⣼⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠁⠀⠚⠀⠀⠀⠙⠷⣾⣠⠋⠀⠀⠀⠀⣠⢞⡉⣠⡿⠀⠀⡜⢡⣿⣧
⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠿⡻⠟⠉⠑⠦⣄⠀⠀⠀⠀⢹⣏⠀⠀⠀⠀⣼⣷⣟⡤⣿⡇⠀⢸⡄⢸⡃⣼
⠀⠀⠀⠀⢀⣴⢿⡟⠋⠁⠈⠁⠀⠀⠀⠀⠈⢳⣄⣀⣴⠾⢿⡆⠀⠀⢸⣿⣿⣛⣼⡿⠀⠀⠸⣦⣜⣿⠏⣀
⠀⠀⠀⠀⣾⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣾⠁⠀⢼⢷⡀⢀⣼⣿⣿⡿⠛⠁⠀⠀⠀⣹⠿⠓⠈
⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿⣿⡆⠀⠀⢿⣧⣾⠟⠉⠁⠀⠀⡀⠠⢶⣿⣷⡶⢤⡀
⠀⠀⠀⠀⠹⣽⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⠀⢸⣿⠁⣀⠔⢉⠁⠀⠀⠀⠈⢿⣻⡻⣄⣹⡀
⠀⠀⠀⠀⠀⢻⣿⣵⣶⣄⡀⢀⠀⣬⣶⣿⣻⣿⣿⡿⠀⠀⠀⣾⡥⠊⣴⣯⣥⣿⣟⣭⣶⡄⠀⠙⠳⢬⡿⡤⠄
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣷⣶⣾⣿⣿⣿⣿⣿⠟⠀⠀⢠⣾⣿⢻⣿⢿⣿⣟⡴⠟⠉⠉⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⣴⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠃⠲⣟⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠂⠀⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣽⣾⣿⣿⣿⣿⣿⡇
⠀⠀⢰⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢹⣿⣄⠃⠦⣸⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣟⣿⣿⣿⣛⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣻⣿⣟⢿⣿⣿⣯⠀⠀⠀⠠⠀⠀⠀⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠛⠻⠋⠙⢛⣾⣿⡇
⠀⠀⣿⣿⣿⠈⢹⣿⠉⢹⣿⣿⣿⠀⠀⠀⠘⣿⣿⣷⣄⢹⣿⣿⣎⠿⠛⠀⠀⠀⠀⠀⠀⢸⣿⣿⡂⠀⠀⢀⠀⣼⣿⣿⡇
⠀⢠⣿⣿⣯⣤⣈⣉⣠⣼⣿⣿⣿⠀⠀⠀⠀⠈⠻⣿⣿⣄⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣰⣿⡄⣿⣿⣿⡇
⠀⢸⣿⠁⣻⠟⡻⣟⣿⠿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣾⣿⣥⣿⣿⣿⡇
⠀⢸⣿⡶⠿⣫⢮⣟⣯⣬⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣌⣛⣛⣛⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡙⣿⣦⣤⣤⣴⣦⣄⠈⠉⠉⠉⠉
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⡿⢿⡿⣿⣿⣇
⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡈⠈⢻⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠃⠀⠘⠈⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣆⠀⠀⠀⢶⣦⠄⠀⠀⢠⡄
⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠹⣿⠳⣿⣿⣧⣀
⠸⣿⣿⣿⣿⡿⡵⢊⠈⣿⣿⣿⡀⠀⠀⠀⠈⠃⢿⣿⣿⣿⡿⣦⣄
⠀⢻⣿⣿⣿⡇⢇⠀⢳⣿⣿⣿⣷⠀⠀⠀⠀⠲⠶⠛⠠⢭⣕⣿⡿⠀⠀⠀⠀⠀⠀⡰⠦⢤
⠀⠀⢿⣿⣿⣿⠦⣀⠀⠙⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⣴⣁⠳⢢⣤⡀⠀⠀⢠⣤⣤⣀
⠀⠀⠈⣿⣿⣯⣠⠈⠛⠴⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣍⡅⠀⠈⠁⠀⠀⠀⣿⡟⢹
⠀⠀⠀⠘⣿⣿⣿⣤⡄⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⡴⠀⢀⠀⠂⠀⠊
⠀⠀⠀⠀⠹⣿⣿⣿⣷⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⠀⢀⣀
⠀⠀⠀⠀⠀⢻⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠀⡔⠀⢡⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⣠⠞⠁⠀⢰⠛⢉⠍⠉⠀⠀⠠⠀⠀⠀⡀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⡜⢁⡀⠄⢀⠎⣠⠦⠤⠶⠲⠶⠷⠾⠉⠉⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⠊⠁⢀⣰⠕⠛⠓⠒⠲⠤⣄⡀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢠⠀⡀⣻⠏⠄⢀⠀⢀⠀⢀⣀⣀⣉⡥⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡞⢦⣽⠷⡶⠶⠦⠌⣉⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠱⡒⡀⢹⠠⡀⠀⠀⠀⠀⠈⠉⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠤⠤⡠⠄⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣤⣀⣀⣀⣀⣀⣠⠤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡿⣿⣿⠿⢿⠛⠿⢿⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠛⠃⠀⠘⠀⠈⠀⠀⠈⠻⠈⠁⠀⠀⠉⠀⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠛⠿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⡀⠈⠀⣀⣠⣶⡄⠀⠀⢀⡴⠊⠀⠀⠂⡀⢀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠛⣾⢿⣤⡄⠙⠐⠤⣿⣿⣿⣷⣄⡀⢠⠀⠀⠀⠀⠀⢹⡦⢑⢦⣶⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠢⠀⠀⠀⠈⣷⣾⣿⡇⠀⠀⠀⡄⠀⢹⠏⠈⠀⢸⢀⠀⠀⠀⠀⠀⠙⠚⠀⠙⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠈⡈⠹⡅⠀⣠⠤⡿⠀⠀⠀⣠⡟⣸⣿⠽⠟⠛⢷⣦⣄⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢉⡷⢞⡻⠁⠀⠀⠀⢀⣼⡟⠁⠘⠋⠀⠀⠀⠀⠙⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⣀⣔⣁⠀⠈⢹⣷⣶⣤⣀⣾⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣿⡄
⠀⠀⠀⢀⡔⢎⠩⡯⠥⣴⣀⠀⠀⠀⠀⠒⠛⠛⠛⠉⠉⠁⡈⢻⡙⢾⣿⠑⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣯⠿⡇
⠀⠀⣄⡠⠶⠶⠛⠛⠛⠋⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢁⣸⡿⢦⠈⢳⣿⣾⡿⠷⠄⠀⠀⠀⠀⢀⣿⣿⣶⠇
⠠⠞⠁⠀⠀⠀⠀⠀⠠⡿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠁⢰⢏⣠⠏⢸⣾⣧⠈⠻⣿⠀⠀⠀⠀⠀⣀⢾⣾⣿⣽⠋
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣰⡄⠀⠀⠀⠀⠀⠀⢠⢰⣫⡞⠁⠀⠀⢹⣼⠀⠀⠉⠠⢤⣈⣁⣉⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⢀⡫⠿⣾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣞⠨⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣤⣤⣾⣿⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⣤⣶⣶⣿⣿⡿⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣛⣛⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣩⣛⣭⣛⣿⣩⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣴⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⣀⡀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣀⣶⣦⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠋⠻⠿⠃⠀⠀⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣷⣾⣿⠅
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣠⣤⣤⣶⣶⣾⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠁⠀⠀⠀⢻⣿⣿⣷⣮⣭⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠐⠺⠿⠿⠿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⢄⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡈⢧⣀⠀⢀⣠⠊⠀⢀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣷⡈⢿⡄⢼⣏⣴⣶⣯⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠙⡛⠀⠢⣰⣦⣄⡀⠀⠀⠀⠀⠀⠈⠈⢿⣿⠸⡇⢈⡕⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⡉⠛⠿⢶⡀⠀⠀⠀⠀⠀⠘⣿⠀⣷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⢀⠀⠉⠀⠉⢲⣦⣀⡀⢹⠞⠁⣠⣴⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣄⠀⠀⠀⢠⣄⣀⣤⡖⠉⠁⠉⢡⠃⣀⣾⣿⠿⠿⠿⠿⠿⠿⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃⠐⠖⠂⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢦⣤⣵⡄⠐⠛⠉⠀⠀⢻⠀⠀⣴⡡⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⣄⠀⠀⢀⣀⠀⠀⠈⢶⣴⣤⣌⠛⢿⣆⠀⠀⢀⡀⠀⠀⠈⠀⠰⠆⠂⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢳⠀⠀⡀⠁⡀⠀⠀⠛⢿⣿⠇⠀⠙⢆⠀⠀⡃⠀⠀⢠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠇⠀⠄⠀⠇⠀⠀⠀⠀⢀⡄⢀⡀⢸⡀⣼⣥⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠀⠀⣀⣤⣦⡶⠀⠀⠀⠈⣁⡤⠗⠀⠙⢮⢹⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠺⠶⠶⠶⢤⣤⣄⡀⠀⠀⠀⠠⠴⠉⡃⠈⠟⢁⣠⠤⠐⠈⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⡀⠀⣰⣤⣷⡾⡿⡁⢰⣾⣦⠀⢀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⣯⠝⠉⠀⠀⠀⠀⠀⣾⣿⠒⣢⣬⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠡⣴⣎⠀⢀⣀⣀⣀⡀⠀⠀⢸⣿⡾⠁⠀⠉⠛⢦⣈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠉⠉⠀⢀⣠⣤⣾⣿⣿⣿⣿⠿⢿⠶⣷⡞⠁⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⣿⢃⣿⣧⣴⠶⠛⠛⠓⠶⢦⣀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⠋⢠⣿⣿⣿⡇⠙⣆⠀⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣄⣤⣴⣿⣿⣿⣿⣶⠀⢹⡀⠀⠀⠀⠀⢀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣂⢀⡄⠀⠀⠀⠀⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣶⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⡿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠙⢋⣴⣟⢫⢻⠀⡏⣸⠋⣽⣦⣀⡁⠁⠙⠋⢉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠋⠁⠀⠀⣿⣷⢰⡿⣿⣸⢧⠏⣸⠏⢘⣿⡄⠀⠀⠀⠉⠀⠉⠛⢿⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣋⡁⣠⡶⠿⠛⠁⠀⠀⠀⠄⠀⣿⣿⣾⢳⣷⣿⠟⣴⠋⣴⠟⣽⣿⠂⠀⠀⠀⢄⡀⠀⠀⠚⠛⠷⣦⠐⣉⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⠟⠄⠀⠀⢄⠁⠀⠀⢀⣿⣿⣿⣿⡿⣫⡞⣱⢞⣥⣼⡿⢿⣄⠀⠀⠀⠀⠀⠲⠄⠀⠀⠞⢯⡟⠛⠻⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠏⠀⣀⣈⢈⣀⣀⣀⣀⣀⡑⠲⣶⣾⣟⠿⣽⣿⣿⣿⣿⣡⠾⣛⣽⣶⣾⡟⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢸⣦⢀⠘⠿⣿⣿⣿⣿
⣿⣿⣿⣍⢀⣴⡟⠀⠀⠀⡀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣾⣷⠀⣶⣿⣦⣄⠀⠀⠀⠑⠀⠀⠀⠀⠈⣷⡄⢈⣽⣿⣿
⣿⣿⠏⠊⡍⠋⠉⠀⠠⠂⠀⠀⠀⠀⠀⠀⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡏⠀⣠⡿⠸⣿⣿⣶⣄⡀⠀⠀⠀⠢⠀⠈⠉⠫⡈⠋⢿⣿
⠿⢿⣤⣾⡀⣀⡀⠊⠀⠰⣤⣴⣄⠴⣵⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡿⠉⠀⠀⣿⡇⢰⣿⣯⣙⡿⣿⣦⡀⠀⠀⠈⢂⣀⡀⣸⣦⣼⠿
⠐⠉⠉⠉⠚⠛⠑⠀⠀⠀⢸⠿⠏⠀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⡇⢀⣤⣿⣿⢁⣾⣿⣛⣿⣷⣶⣽⣿⣶⣄⠀⠀⠉⠛⠋⠉⠉⠰
⡀⠄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠆⢀⣠⣶⣾⣿⣇⢿⡿⠿⢿⣿⣿⣿⣷⣿⣿⣟⠀⠀⣿⣿⠟⣾⣿⣿⡿⠛⠁⠀⠈⠉⣿⣼⣷⣤⡀
⠀⠉⠒⠠⠀⠀⣀⣴⣟⣯⣶⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣾⣿⣿⣿⣿⣻⣿⣤⣀⣿⠇⣠⣾⣿⣇⣀⣀⡦⣶⣶⣧⣿⣿⢛⣙⢻⣄⠀⠐⠚⠁
⠀⠀⠀⢀⣴⣾⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⢟⣉⣨⣿⡄
⠀⠰⢾⣻⣉⣁⣀⡀⡀⠀⠀⠀⣿⣁⣀⡀⠉⠙⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣧⣼⡿⠋⣙⡇⠀⠐
⠀⢰⠌⣉⣥⣤⣤⠼⣤⠤⠀⢀⠹⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢿⣻⣿⡟⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⠟⣿⣿⣿⣧
⠀⠘⣷⣬⣼⣶⠿⢿⣿⣿⣯⣠⣴⡖⠉⠉⢸⣷⡀⠀⠀⢀⣠⣾⣿⣿⡃⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣥⡾⣯⣶⣿⣿⣿⣿⣬⣦⣀
⠀⣨⡿⣽⣿⣁⣀⣀⣾⣟⣃⣼⣿⡇⠀⠀⠀⢿⢷⡀⠰⣟⣿⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣡⣶⣾⣿⣿⣿⣿⡿⣿⣿⣿⠿⠟
⠀⠹⣿⣓⣛⣚⣛⣛⣛⣚⣓⣳⣷⣶⠀⠀⠀⠈⠃⠁⠀⠀⠉⠉⣡⡿⣯⣯⣝⣿⣿⠀⠀⠀⠈⠹⣿⣿⣿⣿⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⠿⠿⠋⠀⠀⠀⠀⠀⠈⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⡀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣀⢰⣀⠀⠠⣿⡦⣾⣾⣿⣿⣷⣶⣾⢾⣗⣻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣉⡻⣦⡟⢻⠀⡿⠿⣧⡼⣿⣉⢿⣾⣿⣷⡞⢽⡿⣛⣿⢶⣧⣠⠦⢤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠙⣆⠊⠙⡿⣷⡂⣤⣟⡮⣏⣽⡊⣿⣯⣽⣟⢠⢿⣿⣿⣿⡿⢿⠛⠺⠁
⠀⠀⠀⠀⠀⠠⣴⣧⣬⡜⠙⢉⡾⢲⡿⠿⢉⣷⢻⡥⣟⢻⡟⣯⡝⣿⣛⣿⣿⣿⣿⣧⣽⣹⡄
⠀⠀⠀⠀⠋⠛⢨⣷⢾⡲⢿⣿⡿⢿⠆⣀⣘⣮⡿⣷⣟⣜⣿⣿⣗⡁⠈⠉⠳⢘⢿⣟⣻⣧⣼⠤⠂
⠀⠀⠀⠀⠴⠈⣢⣼⣾⡶⠶⠿⣏⣻⣖⠛⠩⢪⢇⢚⠷⡿⢿⣷⠚⣿⣶⡐⡿⢓⣿⡿⠛⠋⡉
⠀⠀⠀⢠⠒⣀⡹⠤⢦⢃⣀⠀⣉⢽⣷⣤⡗⠾⣁⣦⣤⣳⠚⡟⢸⣿⣭⡋⣡⣾⡛⣿⣆⡀
⠀⠀⠀⠀⠐⠋⠀⠀⢆⣀⠉⠘⢠⣾⠿⠯⡀⠴⣟⣥⣽⡿⠃⠹⡟⠾⣤⣿⡟⠛⠿⠛⡿⡿⣵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⢈⠆⠀⠀⠀⠉⡄⠀⠉⠀⠊⠂⠆⠈⢢⠏⠀⠀⠢⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠀⠀⠈⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠁⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣛⡇⡼⠤⢄
⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠙⢥⡀⠸⠴⠁⢠⡼⠋⠲⢄
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠈⢧⣀⣠⠶⠴⠃⠀⠀⠀⠱⣄
⠀⢠⣿⡿⠋⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⣼⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⣿⣿⣇⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⢀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⢀⣠⡤⠶⠶⠶⠶⣶⣶⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣦⣀⠀⠀⠙⠳⢤⣌⣉⣙⣻⢆⠀⠀⣠⠊
⠀⠀⠈⠉⠉⠉⢉⣉⣭⣭⠷⢿⡶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⣿⢤⣤⣤⣤⡀⠉⠁⠀⣀⣌⠀⠘⢦⡀
⠀⠀⠀⠀⢀⣴⣿⡟⠉⠀⠀⠋⠀⠀⠙⣷⡀⠀⠀⠀⠀⢀⣀⡀⠛⠛⠲⠦⣤⣴⡶⢟⣻⡽⢷⡶⢂⣰⠃⠘⢿⣕⢦⡉⠃
⠀⠀⠀⠀⢸⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠐⠚⠯⠭⠭⣭⣝⣓⣦⣄⠀⣤⢶⣫⣥⢶⣿⡞⠛⠛⠛⣿⡄⠹⣦⡙⣆
⠀⠀⠀⠀⢸⣿⣿⣅⡀⢀⣀⣀⣀⣴⣾⣿⠇⠀⠀⢀⣤⣤⣤⣤⣄⣉⣙⣿⠷⠤⡒⠠⢴⣿⡷⠀⠀⠀⠀⠈⠙⣦⣈⠳⣼⡆
⠀⠀⠀⠀⠀⠻⣿⡿⠿⣿⣿⡿⣿⢛⣿⠟⠀⣠⠴⢛⣿⣿⠟⠁⠀⠀⠉⠉⣷⣶⣧⠀⢸⣿⣧⠀⠀⠀⠀⠀⢀⣿⣿⣿⠛⠇
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠶⠶⠶⠛⠋⠁⠠⠾⠷⠚⠋⣿⡇⠀⠀⠀⠀⠀⢠⡟⢸⡇⣇⢘⣿⣿⣷⣦⣀⣤⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠠⢠⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣀⠀⠀⢀⣾⡇⣿⡇⣿⢸⣿⣿⣿⣿⢿⣿⠟⣛⣿⠟
⠀⠀⠀⠰⣤⣀⡻⣯⡿⣯⣆⠀⠀⠀⠀⢀⡤⣤⠀⠀⠹⣿⡿⣿⣿⣿⣾⣿⣷⢸⣇⡇⠀⢹⣿⡿⠛⠛⠛⠛⠉
⠀⠀⠐⠈⣊⣽⣟⣙⣿⣟⣋⡇⠀⠀⠀⣪⠞⠁⠀⠀⠀⠈⠻⢯⣍⣟⣻⣿⡿⠓⣿⠁⠀⢸⠞⠀⠀⣠⠠⣷⣀⣾⠋⠓⠄
⠀⠀⠀⢻⢋⡽⠋⢿⠈⠉⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣿⣦⣽⠿⣧⣤⠴⠷⢸⡆
⠀⠀⠀⠈⠋⠡⠄⠹⠟⠀⠁⠀⠀⠀⠠⠐⠒⢀⡴⣠⣿⠷⡿⡆⠀⠀⠀⠀⠀⢀⣀⡤⠔⡪⠋⠀⠙⠶⢾⣷⢦⣿⠿⢷⡞⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠞⠏⢻⣿⡽⣷⠌⠁⠀⠀⠀⣠⠶⣋⣡⡴⠟⠁⠀⠀⢄⠀⢸⠇⠀⢹⡧⠔⣰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠳⣦⣤⣤⣬⠴⢛⣽⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣚⣛⣛⣉⣀⣀⣀
⣿⣿⠋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠆⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠒
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠘⠀⠀⠀⢂⣴⣟
⣿⣿⣿⣿⡟⠛⠃⠙⢿⣿⣿⣿⣿⣿⠛⠿⣿⣿⡟⠛⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠄⠀⠀⢀⣠⣤⠄⠀⢃⣤⣤⠀⠀⠀⠀⢂⣴⣿⣿⣿⠀⠀⠐
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠙⢿⣿⣿⣿⠀⡀⠀⢻⡇⠀⡀⠈⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⢂⣼⣿⣿⣿⠀⠀⢉⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠙⢿⣿⣴⣿⣦⡀⢳⣾⣿⣦⡈⣿⣿⣿⣿⣿⠀⠀⡀⠈⢸⡿⢿⣿⣿⣿⡿⣿⣿⣿⠀⣱⣿⣿⣿⣿⣿⠟⠉⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠈⠙⠛⠛⠋⠻⣿⣿⣿⣟⠀⠀⠀⢀⣼⣶⣶⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⡀⠀⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⠔⡀⢦⣄⠀⠀⠀⢸⣿⣿⣿⠀⠀⣠⣿⣿⣿⣿⠿⢛⡛⠿⢿⣿⣿⣿⣿⣿⠟⠁⠀⡀⠀⠀⢀
⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣦⡀⠀⠀⠸⣿⡘⠿⢂⡿⠀⠀⣠⠸⣿⣿⣿⠀⠀⢻⣿⣿⣿⣧⣇⠻⠟⢀⣸⣿⣿⣿⠟⠁⠀⠀⠀⣀⠀⢀
⣿⣿⣿⣿⡷⠚⠓⠾⠛⠛⠿⢿⣿⣦⡀⠀⠙⠻⠟⠁⠀⠀⠀⣿⣼⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣤⣤⣶⣤⣤⣯⣤⣿⠁
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠉⠙⢿⣿⣦⡀⠀⠀⠀⠀⢀⣴⡿⣹⣿⣿⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣷⣦⡐⠿⠿⠟⠛⢠⣿⣿⣿⣿⠒⠀⠀⠹⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠉⠉⠀⠈⠉⠀⠀⣤⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⣿⣿⣿⣿⣆⠀⠀⣠⣿⣿⣿⣷⢿⡍⢡⣄⠀⠘⢿⣿⣿⠋⠀⠀⢠⠀⠀⠐⠀⠀⠀⠂⠀⣴⠛⢦⠀⠀⠐
⣿⣿⣿⡟⢿⣿⣿⡿⢻⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣠⣾⣿⣿⣿⣿⣉⣿⠲⠖⠐⠂⠀⠀⠻⠇⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⣦⠙⠒⠋⣵⡀
⣿⣿⣿⣇⠀⢹⣛⡇⠘⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⢻⣿⣿⣿⣿⣶⠿⣾⣭⣬⢋⣀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢰⣿⣷⣶⣿⣿⠃
⣿⣿⣿⣿⣷⣼⣫⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⣿⣻⣿⣻⠆⠰⠶⠀⠀⠀⣸⣿⣄⠊⠁⠀⠈⠀⠀⠀⠘⢀⣾⣿⣿⡟⠋⠉
⣿⣿⣿⣿⣿⣼⣭⣇⠀⠀⠨⠛⠿⣿⣿⣿⠿⠛⠁⠀⠀⣸⣿⣿⣿⠿⣤⢿⡙⢋⣀⠀⠀⠀⣿⣿⣿⣷⣶⣀⣀⢀⣈⣴⣶⣿⣿⣿⠟⠈⠀⢀
⣿⣿⣿⣿⣿⣵⣯⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⢿⣿⣿⣿⣛⣿⠴⠶⠁⠀⠀⣴⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠀⢀
⣿⣿⣿⣿⣿⢾⣶⣿⡿⠙⢿⣶⣦⣄⠀⣠⣴⣶⣿⣿⡏⠀⠘⣿⣿⣿⠿⣽⣃⣘⠓⠀⢠⣿⣿⡇⠀⢸⣿⠛⢿⣿⠟⣻⡏⠀⣀⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣾⣾⣿⡃⣀⢸⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣻⠌⠡⠄⠀⣾⣿⣿⡇⠀⠰⣿⠀⠈⠁⢀⣾⡇⠀⠀⠀⠀⠀⠀⠁⠀⢠
⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⣭⢿⣚⠓⠀⢰⣿⣿⣿⡇⠀⠀⠻⣧⣤⣤⣴⡟⠀⠀⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣟⣾⢥⡄⠀⣿⣿⣿⣿⡇⠀⠀⠀⠈⠉⠉⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠
⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⣿⣿⣽⢒⠀⢸⣿⣿⣿⣿⣧⣴⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠰⠄
⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠸⣷⣻⡭⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀
⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣾⢃⡀⠀⠀⢿⣿⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⣠⣌⣉⣉⣉⣉⣉⣩⣥⣾⡇⠀⠀⠸⣿⢹⣿⣿⣿⡇⠙⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⡿⠋⠓⠀⠀⠀⠀⠀⠐⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢹⣾⣿⣿⣿⣿⠏⠀⠀⠀⠁⠀⠀⣠⣾⡿⠋⠙⠀⠀⠀⠁⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠻⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⢺⣏⠉⠉⠉⠁⠀⠀⠀⠀⠀⣠⣾⡿⠋
⣿⣿⣿⣿⣿⡿⠟⠛⠻⠛⠛⠛⠛⠛⠛⠿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣆⠁⢀⠀⠉⠀⠀⢠⣿⣿⣯⣤⣤⣤⣦⣤⣤⣤⣤⣥⣄⡀⠈⠁⢀
⣿⣿⣿⣿⡏⠀⠀⠀⢰⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⡆⠈⠀⢀⠀⠈⠛⡛⠛⠛⢛⠛⠛⠛⠉⠉⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣇⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⠀⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠭⠯⠽⠭⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⠀⠀⢠⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⢠⠀⠀⠀⡄⠀⠀⢠⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⢽⡞⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠐⠐⢾⣽⣿⣿⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠
⣿⣿⣿⣿⡇⠻⠘⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢙⣹⣿⣿⠇⠰⠀⠀⠀⠄⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⣠⣾⣶⣿⣾⡂⠀⠰
⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠘⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠏⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠂⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡏⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣉⠏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡆⠀⠀⠀⠀⢀⣴⣿⣿⣿⣾⠏⠐⠁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⣆⠀⢀⡴⠲⠿⣿⣿⣿⣿⠃⣠⠆⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣶⠀⠉⠐⠀⢀⠀⠀⠀⠀⠀⡀⠀⢸⡏⠀⠂⠀⠀⢠⣿⣿⣿⡟⠛⠓⣟⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⡀⠀⠀⠀⠢⡀⠀⠀⠙⣀⣿⡇⢀⠀⢀⣞⣼⣿⡿⣿⠀⠀⢠⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣆⣀⠀⠀⠈⢂⠀⠀⢉⣋⠀⠘⡆⢰⣿⣿⡻⠇⠸⣧⣰⡿⠋⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⢦⠀⠘⣧⡀⠈⠙⢶⣿⡇⢿⣀⣼⡿⠟⠐⠂⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣿⡐⣂⣸⣇⠀⣼⢷⠆⣀⣀⣹⠈⣗⣾⣿⣀⣀⣀⠠⢚⣁⣀⣤⡄⠤⡀⠀⠀⠀⡀
⠰⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⣋⠛⣿⡀⢸⡌⢷⡿⠉⠉⢻⣿⠏⠉⠛⠰⣶⣿⣿⣿⣿⣿⠖⠂⠀⣀⣈⣤⡜⢛⡿⠂
⠀⠀⡑⢍⡾⣻⠙⠿⠷⠂⠀⡀⠀⠀⠀⠀⠀⠀⠃⢸⡇⠈⠈⣷⠙⢡⡄⢤⡾⢁⡄⢀⣼⢿⣷⣄⣀⣀⣸⣿⣿⠙⢆⣠⠤⠄⠒⠊⢁⠀⠀⠁
⠀⠀⠀⠈⠳⣷⠀⠀⠀⠀⠂⠈⠐⢄⠀⠀⠀⠀⠀⠸⣇⠀⣠⠇⣠⠀⠲⣾⠑⣶⣶⠚⣡⣿⣿⣿⣿⣿⣿⡿⠗⠚⢉⡁⠀⢠⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⠂⠘⠀⣱⣼⣿⠀⠀⢸⢠⡿⠁⣴⣿⣿⣿⣿⡟⠛⠉⠒⣤⡀⢤⡌⠁⢒⣂⠠⠊
⠀⠀⠀⠀⡄⠀⠈⢷⡆⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⠈⣨⡟⣿⠀⠀⣿⣿⣷⣾⠿⠿⠭⣥⣩⣼⣧⣴⣦⣴⡖⠋⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠈⠲⠌⢣⣌⠀⢲⠀⠑⠀⠁⣶⠐⠂⠠⡀⠀⠘⡇⢸⣧⣄⣿⡿⠟⠉⢀⠀⣴⠎⠀⠈⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠙⣄⡟⠀⠀⠀⠠⣸⣧⠀⠀⢰⠀⢠⡇⢸⣿⡟⠉⠀⢠⠿⢀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠈⢣⣄⠈⢷⡀⡾⠃⠃⣵⣿⣿⣦⡼⠀⠘⡇⢾⡏⠀⠀⠀⣠⠖⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⣿⣿⡀⢼⣿⠼⠿⣿⠁⠀⠀⣿⡼⠀⠀⡰⠊⠀⠀⠀⡀⠄⠐⠂⠀⠀⠈⠀⠈⠁⠀⠒⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣿⠀⣻⡀⠀⣀⡿⢀⡤⠊⠀⡀⠐⠒⠀⠀⠀⢀⠔⠀⠀⠀⡀⠀⠀⠀⠀⠠⠄⠒⠀⠀⠉⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠀⡼⢀⠾⠱⠐⠁⢀⠐⢀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠇⠀⠃⡀⡦⢀⠤⠒⠋⠁⠀⠀⠀⠀⠀⠈⠉⠒⠢⢀⠀⠀⠀⠀⣀⢀⣀⡠⠤⠤⠀⠐⠒⠀⠉⠁⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠄⡲⠀⢸⣿⡀⢀⠞⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⡚⠉⠉⠉⠁⠀⠤⠀⣀⡀⠀⠐⠂⡔⠁
⠀⠀⠀⠀⠐⣿⣶⣿⣾⣟⠻⠁⠉⠁⠀⠀⣹⣇⣴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠐⠢⠄⢀⡀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⢒⠂⠀⠀⠀⡝⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⣀⠔⠉
⠀⠀⠀⠀⠀⠀⢹⣿⠿⣿⣳⠀⠀⠀⠀⠰⠞⠣⠄⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣌⡁⠤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠃⠂⠀⣩⢝⠓⠐⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⣠⣿⣸⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠐⣡⠏⠁⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⢀⠌⡴⠃⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡠⣣⠞⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⢰⡿⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⢠⡜⠁
⠀⠀⠀⠀⠀⠀⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣀⣀⣀⣀⣀⣀⣠⠤⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠐⠹⠀⠀⠀⠠⠔⢑⠄⢀⠂⠀⠀⠀⠺⠇⢀⡄⠀⠀⠀⠀⠀⠀⣀⡆⠀⠀⠀⠀⠃
⠀⠀⠀⣄⠀⠦⠀⠀⠀⠀⠰⡁⢈⠖⠊⠂⠀⠀⠀⠀⠀⠘⠋⠀⠀⢀⠠⠄⢁⠐⠀⠀⠀⢀⡀⠆
⠀⠀⠀⢄⡄⢀⠔⢲⠂⠀⠀⠐⠀⠊⠈⠀⠀⠿⠃⢀⠀⠀⠀⠀⠀⠋⠈⠉⢀⠀⡀⠀⠀⠀⠹⡇⢀
⠀⠀⠀⠀⠓⠉⠁⠀⠀⠀⣰⠆⠀⠀⠦⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠈⡠⡄⢃⠄⠂⠀⠀⠀⣶⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠊⠜⠀⠀⠦⠰⠀⠀⠀⠀⠇⠸⠟⠀⠀⠀⢂⣓⠀⣦⣆⠊⠄⠁
⠀⠀⠀⠀⠀⠀⠊⠋⠈⠀⠀⠀⠀⠀⢿⠀⠴⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⡀⡙⡝⠄⢐
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠙⠀⢀⠀⠀⢸⠀⠀⠀⠀⠆⠀⠀⢼⡄⠀⠀⠀⠀⠡⠀⠈⠀⠀⠀⢀⡀
⠀⠀⢙⡧⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠃
⠀⠀⠐⢞⡀⠀⠀⠀⠘⠿⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡇⠀⠀⠀⠆⠀⠀⢀
⠀⠀⢀⣋⡄⠀⢀⣀⠀⠀⠀⠉⠀⠀⠐⠂⢀⠀⠀⠀⠀⠀⣘⡧⠀⠰⠢⠰⡁⠈⢂⠀⠀⠀⢀⣤
⠀⠀⠀⠉⠀⠀⠈⠋⠀⢠⠀⠀⠀⠀⠈⠀⢂⠃⡀⠀⠀⠀⠈⠁⠀⠀⠠⡀⠈⡄⠈⠀⠀⠀⠈⠋⢴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠆⠀⠀⠠⠈⢀⢡⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⡀⠚⠁⡀⠀⠀⠀⣢⠀⠀⠀⠀⠸⠀⠁⠀⠀⡀⠀⢀⡈⠋⠀⢠
⠀⠀⠐⠂⣈⠶⠸⠂⠀⠀⡄⠀⠀⢼⣏⠀⠀⠀⠈⠀⠀⠀⢤⠤⠑⢤⠀⡌⠡⠀⠀⠉⠀⡀⠀⠀⢀
⠀⠀⠀⢗⠉⣀⣂⠁⠀⠀⠀⠀⠠⢺⡇⠀⠀⣐⢀⠤⢢⠀⠈⠃⢤⡄⠀⡷⠃⠀⠀⠀⠀⠀⡄⠀⠿⠃
⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠐⣬⢔⠀⠬⠪⣸⣰⡠⢂⠐⠀⠀⠀⠘⠀⠀⠀⠰⡆
⠀⠀⠈⠁⠀⠀⠀⢀⡠⠀⠀⠀⠈⠚⠁⠠⢀⡡⢺⠟⢯⣑⡄⠀⠀⠀⠀⠀⠀⠀⢰⡸⠀⠠⠂⠀⠀⠚
⠀⠀⠀⠘⠁⠀⠠⠎⠒⠀⠀⠀⠀⠀⠀⠀⠐⠈⢆⠂⠑⠁⠀⠀⠀⠀⠀⠀⠀⢠⠿⠁⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢈⡩⠀⠀⠲⡖⠀⠉⠑⢒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⡔⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠗⠂⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠉⠉⠢⡀⠀⠀⠀⠀⡄⠀⠀⠈⠀⠀⠀⠴⠤⡀⢄
⠀⠀⠀⠀⠀⠀⠀⢀⢿⠀⡄⠀⠀⠀⠀⠀⠢⣀⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⠈⠊⢧
⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⢧⣤⣀⣀⡀⠀⠀⠈⠱⠄⠃⠈⠲⠋⠀⠀⠀⠀⠀⣀⡆⢣
⠀⠀⠀⠀⠀⠀⠐⡇⠀⢣⠘⠀⠀⠀⠀⠀⠀⠉⠙⡆⠘⠗⠀⡉⠉⠀⠀⠀⠀⠀⠙⡄⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢆⠀⡀⠀⠀⠀⠀⠀⠈⠉⠂⠰⡅⠈⠳⠄⠀⠀⠀⠀⠀⡇⢰
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⢣⡈⠢⢴⠊⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⡀⠀⠀⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠙⢦⡈⠢⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡖⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠈⠳⢄⡉⠳⢄⡀⠀⠀⢘⡄⠀⠀⣀⡤⠚⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠈⠑⠲⠤⣉⣙⠉⠈⢉⣉⡥⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠉⢉⣡⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠊⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢺⣿⠻⠿⠿⢟⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣷⠀⠀⠀⠀⢰⣻⠃⠹⢃⡄⠀⠀⠀⠀⠀⠙⠳⢦⣀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⣿⠀⠀⠀⠀⠘⣇⠀⣴⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠉⠛⠐⠚⠛⠧⡀
⠀⠀⣀⣤⣴⣶⣤⣤⣄⡀⠀⠀⠀⠀⣾⡿⡏⠀⢘⡟⠀⠀⠀⠀⠀⠘⣉⡱⠂⢀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⢄
⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣿⡟⠁⢀⣸⡇⠀⠀⠀⠀⠀⠀⠛⠀⠆⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠁⠀⠀⠀⠈⢆
⠀⠀⠀⠑⢮⠙⢻⣿⣿⣿⣿⣇⠀⠀⢻⣿⡆⢠⠞⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢾⣿⣿⠶⠄⠀⠀⠀⠈⡄
⠀⠀⠀⠀⣀⡴⣶⣶⠿⣿⣿⣿⠀⠀⠀⢻⡟⠉⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠙⡖⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⣀⣿⣿⣯⠓⡂⠀⠀⠈⠀⡇
⠀⠀⢀⣞⣋⣀⣀⣈⣩⠟⠋⠁⠷⠂⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠊⠀⠀⠀⠀⠀⢀⣴⣿⣇⣤⣽⣿⣿⣿⢿⡷⠷⠈⠀⠀⠀⠃
⠀⠀⠈⠙⠛⠲⠟⠉⠀⠂⠁⠀⠀⠀⠀⠈⠳⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⠿⣿⣿⣿⢿⣿⢿⠋⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠠⠋⠸⠛⠊⠙⠎⠀⠀⢀⡠⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⡀⠲⠄⠂⠀⠀⠀⠀⣀⣠⠀⠀⠀⢀⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⣍⡀⠀⠀⠉⢉⠉⠁⢀⣠⡤⠖⠉
⠀⠀⢀⣀⠠⠴⠶⠶⠶⢶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠂⠉⠉
⠀⠀⠈⠙⢿⣧⣄⠐⠒⠒⠶⣽⣿⣦⣲⣤⣢⠻⠷⠖⠀⢄⡀
⠀⠀⠀⠀⠀⠉⠛⠷⢶⣽⣿⣶⣿⣷⣾⣿⣿⣾⣭⣄⡀⠀⠈⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠚⠋⠉⠉⠉⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁⠀⠈⠑⠿⣿⣿⠗⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⡀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⣿⠀⠄⠀⠀⠀⣀⣸⣶⣶⣿⣿⣕⡀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢽⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠿⣿⣿⠛⠉⠸⣿⣿⡇⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡟⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢠⠿⣿⣶⣤⣴⣿⣿⠟⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢻⣿⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⠁⠀⠀⠀⠀⠀⠀⢷⡀⠁⠀⠀⠈⠋⠿⠿⡉⠛⡉⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣾⣶⣶⣤⣠⣴⣷⣶⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⡀⠁⠀⠀⠀⠀⠀⣀⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠓⠒⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡀⠀⡀⠀⢀⠫⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠂⢛⡯⠂⠀⠀⠀⢻⡜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠄⠈⠀⢾⡏⠄⠡⣔⢳⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣠⠖⠀⠼⠏⠻⡀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢠⡠⢤⣄⠶⠛⠚⠓⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠚⠛⠚⠉⠉⠠⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⢸
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣠⣄⣠⣄⠤⠤⠄⠈⠳⣄⣷⡄⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠃⠀⡇⢣⡠⡀
⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠉⠳⠤⠦⣀⣠⡤⠒⠋⠁⠀⢠⠀⠀⣇⠀⢳⠘⡄
⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣛⠉⠀⠀⠀⠀⠀⠀⢀⣩⣿⠃⠀⠀⠀⠀⠀⠚⠀⠀⢿⣆⠀⡇⣿
⠀⠀⠀⠀⠄⠀⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⠐⡠⠔⠈⢁⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡧⡄⣁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣨⣤⠶⠞⠋⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠣⡏⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡽⢠⣄⠀⠀⠀⠀⠀⠀⣼⡏⡹⣰⠅⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠁⠛⣶⡤⣠⡶⠛⠿⠓⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⢬⣗⠲⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠂⣀⠀⠀⠀⠀⠀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⢠⣤⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⢀⣀⠀⣤⡀⠀⠀⢸⡅⠀⠘⠻⣧⡄⠀⠀⠰⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠁⠀⠀⠈⠻⣿⣤⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⣶⠀⢿⣷
⠀⠀⢀⣤⠀⠀⠀⠀⢰⣦⠀⠀⠀⣠⠂⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⢠⡤⠒⠀⢀⠀⠀⠀⢾⠿⣴⣾⠇
⠀⠀⢾⣿⣤⣤⣀⣄⣸⣿⡇⠀⢸⣿⣄⡀⣠⣴⣾⣿⡇⠀⠀⠀⠀⠀⣀⡐⠂⣿⡇
⠀⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠈⠿⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠛⢿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠉





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⣶⣶⣶⣶⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠉⠀⠈⠛⠟⠉⠻⠇⠀⣾⣿⣶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠛⢿⣿⣿⠿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣤⠟⠛⠋⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢀⣾⣟⣡⣤⣼⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣧⣴⣿⠁⠀⢀⡀⠀⢠⣀⣤⣀⣿⣇⣠⣿⣾⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠿⣏⣀⣀⣶⣦⡀⣵⣦⡀⠘⢿⠟⠀⠘⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢴⣶⣾⡟⠛⠿⠿⠿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠿⣿⣿⠿⠿⣿⣿⣯⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣸⣿⣿⣷⠿⠶⢶⣾⣿⣿⣿⣷⣶⡄⠀⠠⠄⠀⠀⢀⠿⣿⣶⣦⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠻⣿⣟⣷⣄⡀⠀⢨⣿⣿⣿⡿⢻⣷⡄⢀⡀⢠⣤⠉⣦⣄⠉⠙⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠁⢀⣀⡹⠿⣿⣥⣾⡿⠈⣿⣿⠉⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠻⣿⡿⠟⢧⡼⠛⠿⣿⣍⠿⣷⡌⠙⠿⠁⠀⠉⣿⣷⡀⠻⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣎⢁⠄⠀⣿⣿⡄⠿⠇⠀⠀⠀⠀⠀⢻⣿⣿⣶⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⢠⣤⣿⣿⣷⣄⣼⡆⢀⡀⢀⡀⠀⣿⣿⣟⣻⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⢀⣸⣿⠁⣼⣿⣼⣇⠀⣿⣿⣿⣿⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠉⠉⠙⠻⠿⠿⠿⢿⣿⡿⠿⠚⠻⠟⠛⠉⠀⠀⠐






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⢀⣤⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇
⠀⠀⠀⠀⢰⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷
⠀⠀⠀⢰⣿⣿⣿⣿⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢠⣿⣿⣿⣿⣿⣧⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣄⣀⣠⣤⡼⠟⠛⣦⣤⣴⡤⢠⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣤⣴⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠉⠉⠉⠉⠁




⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣠⡄⠀⠘⢿⣿⡟⠁⠙⢿⣷
⠀⠀⠀⠘⣿⡇⠀⠀⠈⠻⣿⣦⣄⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣤⣤⣶⣾⣿⣿⣿⣶⣾⡇
⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠈⢻⣿⣆⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⣿⣿⣏⣀⣸⣿⡿
⠀⠀⠀⢸⣿⠀⠀⠀⢦⡀⠀⠈⢿⣿⠀⢠⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣾⣿⣿⣿⣿⡟⠛⠁
⠀⠀⠀⠸⢿⣶⣦⡀⠀⢿⣤⡀⠈⠋⣠⣌⠙⣛⠁⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⠋⠉⠉⠉⠉
⠀⠀⠀⢠⣄⠀⠈⠻⣷⣄⠛⠃⡀⠀⠉⢛⣿⡿
⠀⠀⠀⠀⠈⠻⢤⣄⡈⢻⣷⣾⣿⣶⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⣻⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⣠⡄⠀⠻⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡗⠛⢿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣼⡿⣿⠖⢶⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣁⣴⠿⠀⠀⠉⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⡾⠛⠋⠀⠉⠁⠀⡀⠀⣤⡄⠀⣤⠀⠀⠀⠀⠀⠀⠘⢿⣷⣴⣶⣶⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⡸⢿⣆⠀⡀⢀⣿⡇
⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣈⡉⠻⢷⡝⠋⣠⣿⣿⠁
⠀⠀⠀⠀⠀⠘⢿⣷⣄⠸⠿⢇⡀⢀⣡⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⣤⣾⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣪⣛⠾⠛⠛⠙⠾⡿⣓⠄⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢛⠁⠀⠀⠀⠀⠀⢹⠀⡟⠀⠀⠀⠀⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢆⠀⢀⣀⠠⢀⠴⠚⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠄⠐⠤⠄⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠒⠀⠀⠈⢀⠀⠀⠀⢀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠀⠄⠀⠀⢀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢨⠐⣀⢀⠁
⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢩⠖⠀⠐
⠀⠀⠀⠀⡀⢀⣀⠄⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠴⡀⠀⠀⠀⠀⠔⠲⠂⠒⠒⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠊⠁⠀⠀⠀⢀⣉⡉⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠀⠀⠀⠓⠒⠒⠀⠐⠀⠄⠀⠐⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠛⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠖⠒⠂⠀⠀⠀⢠⠂⠀⠀⠠⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⡀⠀⢀⠀⣬⠀⠀⠍⠰⠀⠠⠆⠀⠀⠯⠆⠀⠀⠀⢃⠀⠀⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠈⠀⠈⠢⠤⠀⠈⠀⠀⠈⠓⠲⠂⠀⠀⠀⠀⠀⠁⣄⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⡀⢀⠀⠀⢺⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠯⠍⠙⠛⠂⠉⠥⠂⣧
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠑⠳⠚⠀⠀⠁⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠠⠤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⡀⠀⣇⠀⠀⠂⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠀⠀⠐⠈⡀⠀⠀⠓⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠁⠈
⠀⠀⠉⠆⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⣿⣿⣿⣾⡀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣭⣿⣷⣾⣻⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣬⣿⣿⣿⡁⠀⠀⢀⣤⣶⣿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣾⣿⣿⣇⣴⣾⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣽⢻⠏
⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠐⠤⡀⠑⠄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡉⢻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⠲⢽⣿⣦⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⡆⠙⠛⠉⠙⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠀⠀⠀⢱⠙⠳⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠈⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢾⡆
⠀⠀⠀⠀⠀⠘⡀⠁⠀⠀⠀⠀⠈⠐⠀⠀⣈⡄⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⢥⢈⡐⢀⠀⠀⠀⠀⢀⠀⠁⡀⠁⠀⠀⠀⠀⢼⣿⣛
⠀⠀⠀⠀⠀⢄⣀⢂⠀⠀⠀⠀⠀⠐⢂⣀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⣸⣀⡠⠀⠀⠀⠀⢀⣀⣿⣟⣣⠀⠀⠀⠀⠀⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠉⠘⠉⠉⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⣐⣶⣷⢤⡀⠀⠀⠀⢠⣾⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀
⠀⠀⠀⠀⢸⡿⣧⣽⣿⡿⠀⠀⠀⠘⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣢⢻⣥⠆⠀⠀⠀⢤⣶⣶⣾⣦⠆
⠀⠀⠀⠀⠀⠙⠉⠋⠉⠀⠀⠀⠀⠀⠙⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠛⠛⠋

⠀⠀⠀⠀⠀⣤⡆⣦⠀⠀⠀⠀⠀⢀⡴⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣆⣀⠀⠀⠀⠀⠀⣤⢀⣲⠤⡀⠀⠀⠀⠀⠀⣤⣄⣤⣄⠀⠀⠀⠀⣸⢗⡄
⠀⠀⠀⠀⠸⣯⣿⣍⡛⠀⠀⠀⠀⣨⣭⣿⣿⡆⠀⠀⠀⠀⠀⠲⣶⣿⡿⡇⠀⠀⠀⠀⠀⡿⢽⡿⠿⣶⠀⠀⠀⠀⠘⢿⣿⣿⠼⠂⠀⠀⠸⣍⠊⡇
⠀⠀⠀⠀⠀⠻⣿⠟⠁⠀⠀⠀⠀⠓⠎⠙⠙⠉⠀⠀⠀⠀⠀⠀⠋⠛⠛⠁⠀⠀⠀⠀⠀⠉⠉⠁⠁⠁⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣀⡀⣀
⠀⠀⠀⠀⢀⣂⣀⣰⣄⠀⠀⠀⣄⣿⣬⣿⣷⣦⠀⠀⠀⠀⣾⣿⣿⣿⣧⡄⠀⠀⠠⣾⠟⢀⠸⣪⣷⠀⠀⠀⠠⣰⣟⡖⠀⠀⠀⠀⢻⣾⣟⣻⡓⠇
⠀⠀⠀⠀⠈⠛⠛⠋⠉⠀⠀⠀⠐⠻⠟⠙⠛⠛⠀⠀⠀⠀⠈⠛⠛⠛⠛⠃⠀⠀⠀⠉⠀⠀⠀⠙⠋⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠈⠈⠁

⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⣠⠤⣤⢄⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠠⡄⠀⡀⠀⠀⠀⠀⢀⠄⣄⢀⣤⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣼⡄⠱⠦⢄⡀⠀⠀⠀⢸⡟⢿⡿⢺⡇⠀⠀⠀⠘⣟⡑⠀⠀⠀⠀⠀⠀⠠⠁⣬⠀⠀⠀⠀⢀⣛⣷⢮⠻⡞⠀⠀⠀⣴⣿⡿⡿⢶⡄
⠀⠀⠀⠀⠀⠰⠛⠃⠀⠈⠁⠀⠀⠀⠀⠑⠛⠛⠉⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠁⠉⠚⠛⠛⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢠⢽⣿⣿⣿⡦⠀⠀⠀⠀⣿⣴⡗⠀⠀⠀⠀⢀⠀⢠⠠⠄⠀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⣿⠄
⠀⠀⠀⠀⠈⠛⠛⠋⠛⠋⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠐⠶⠖⠀⠀⠀⠀⠀⠈⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⢻⠀⠀⠀⢀⣠⠄⠤⠀⠀⠤⣀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡠⠆⡆⠐⡀⠀⠀⡆
⠀⠀⠀⠀⢀⡠⠂⠁⢀⠀⠀⠀⠐⠀⠀⣈⠒⢄⠀⠀⠀⠁⠀⠀⠄⡠⠁⠀⠀⢀⠞⢑⣨⠄⠀⢇⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠠⠊⠠⠃⢐⠠⣧⠁⠀⢰⡆⠠⠋⠡⠀⠱⠀⠀⠀⠀⢀⠆⠂⠀⠀⣴⣷⣚⣕⣂⡸⠀⢸⠀⠀⠀⠀⠀⡤⠈
⠀⠀⢠⠃⠀⠒⠦⣌⡱⢌⣦⢁⡞⠁⠐⣀⡀⠀⠀⠁⠀⢠⠘⠉⠀⠀⣰⠆⡎⢿⠳⣝⠏⡡⠀⡘⠀⠀⠀⠀⢠⠅
⠀⠀⠀⠀⡀⠈⠑⠂⠙⠲⣽⢾⡴⠞⠋⢉⡙⠂⠆⢸⠀⠀⠀⠀⠀⠚⠙⣸⠃⡜⡏⠎⠃⠀⢀⠅⠀⠀⠀⠠
⠀⠀⠰⠀⠒⢒⠦⠴⢚⢋⡿⢻⡙⡳⢮⣀⠤⡠⠁⡌⠀⠀⠀⠐⠻⠀⠁⠏⠄⠐⠹⠰⠀⢀⠌⠀⠀⠀⠰⢆⠒
⠀⢀⠀⠡⡀⠀⡐⠂⠄⡼⠡⠈⣧⠨⠷⢌⡀⠀⡔⠀⠀⢴⠛⠂⡀⠀⠀⠀⠉⠁⠀⣀⡴⠃⠀⡀⠀⠀⠚⠁⠀⠀⣴
⠀⠘⡀⠀⠈⠢⡀⠊⠒⠧⢁⠂⠘⠀⠔⠈⠠⠊⠀⠀⠀⠀⠁⠀⢉⡒⡀⠤⠀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠘⡤⠀⠀⠀⠀⠑⠠⠤⠠⠠⠠⠄⠂⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⡨⠀⠠⢀⠈⠐⢦⡀
⠀⠀⠱⡀⡂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠲⢰⠀⢀⡞⢡⠞⠀⠈⡕⡄
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⢤⢤⡀⢾⠀⠀⠀⠀⢰⠀⠀⢡⡇⣤⠀⠀⠀⠐⠁⣎⣆⢷⣻⣠⠏⣠⣶⠞⠁⠀⡇
⠀⠀⠀⠀⠀⠀⣀⠔⠒⠈⠉⠀⠴⠶⠀⡼⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠜⠠⠣⣬⣩⣳⣿⣗⣛⣝⠉⠀⠀⠰⠁⠀⢰
⠀⠀⠀⢀⡀⠖⠁⠀⠀⠈⠀⠀⠀⠀⠛⠀⠈⠢⡀⠀⠀⡀⠀⠀⠀⠁⠀⢰⠀⠚⣉⣡⢖⣹⢋⠧⣀⠈⡲⠀⢀
⠀⠀⢀⠈⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⠘⢀⡍⠝⠅⠆⠀⣃⠉⠁⠀⠠⠁
⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠔⠁⢀⠀⠀⠆⠈⠁⠀⠀⠀⠁⠀⣀⠄⠊
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠁⠐⠀⠀⠑⠦⡦⠴⠒⠒⠁
⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢰⠀⠀⠤⠖⠦⢌⣁⣀⠀⠀⠀⠀⠐⠀⠄⠀⠐⠊⠀⠀⠀⡤⠁
⠀⠀⠠⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⡀⠀⠲⠂⣍⡩⠬⠟⣷⣄⠀⠀⠐⠀⢀⡄⠀⠀⡀⠀⠖
⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠱⡀⠀⢈⠀⠔⢀⠞⡿⡹⡷⣀⡀⠀⠈⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠑⡀⠈⠂⠐⠁⢁⡇⠅⠘⠦⠙⠖⠀⠀⠀⠀⣈⠑
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠐⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠠⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠐⠀⠀⠀⠀⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢣⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⡀⠀⠀⠀⠀⠠⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣟⠁⠀⠀⠀⠐⠀⣤⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡗⠈⠀⠁⠠⠀⠀⣜⠁⠀⠠⠂
⠀⠀⠀⠀⠀⢠⣆⡄⡀⢠⣴⠋⠀⠀⠀⡀⠂⡐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠂⠀⠀⠈⡄⣻⡻⠃⠀⠀⢐⣀⣴⡄⠀⠰⠞
⠀⠀⠀⠀⠀⠀⠆⠄⢀⣄⠋⠀⠀⣠⡀⣠⠌⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡟⢠⠀⠀⠃⠀⠀⠀⠀⣞⠀⠛⣋⡀⠤⣶⠊⠻⢍⠑⢯⠂⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢼⣧⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⡰⠀⠀⠀⠀⢁⠀⡄⠀⢀⡀⠀⠀⠀⠙⠂⢠⡀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡤⠂⠀⠐⠀⠁⠄⠁⠀⠀⠀⠀⣴⠀⡀⠞⠀⣀⣠⣄⣀⠁⠀⠀⠘⣠⠞⠁⠀⢀⡌⠁⠀⠀⠀⠀⢁⠐⡷
⠀⠀⠀⠀⠀⠀⠀⡀⠖⠊⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣟⠁⠈⣀⠀⠀⠀⠙⠛⠁⠀⢀⣄⣼⣅⠀⠀⠀⠛⠁⢀⣤⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠐⠟⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠛⠻⠿⣿⣿⣟⠛⠃⠀⠛⠀⠁⣀⠿⠿⠁⠀⠀⠣⢴⠎⠠⠐⠒⠘⠁⠈⠙⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡴⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣨⣿⣥⣄⠿⣦⣀⣙⠂⢉⡓⡀⠀⠀⢲⡀⠠⠄⢠⡄⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⢀⠘⢩⡏⠺⢿⣦⣌⡋⠻⢯⡜⢳⡈⠀⠁⢸⣷⣔⠀⠉⢌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠉⠉⠀⠀⠀⡿⠋⠀⠀⠀⠀⠉⢿⣿⣶⠁⠀⠳⠀⠀⠀⣿⣧⠀⠀⢤⣈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢠⡴⠛⣡⠀⠀⠀⠀⠀⠀⠀⢠⠆⡄⠀⠀⠀⠀⠐⠘⣿⣟⠀⠀⠀⠀⠀⠈⠉⠏⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠉⣤⠀⢠⠀⠀⠀⢀⣼⣿⠃⣄
⠀⠀⠀⠀⢀⠔⠈⣥⡀⠀⠀⠀⠀⠀⠈⣷⣶⡄⢠⡄⠤⠀⣄⠢⠀⠀⠀⠀⠀⠸⡇⠉⠀⠀⠠⠐⠛⠁⠀⠀⠙
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⢤⠀⠙⠙⠉⠛⠛⠃⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣤⣀⣠⣤⣤⡴⡶⠃⠀⠀⣠⠖⡀⢴⠄⣀⣀⡀⠒⠒⠀⠉⠀⠉⠉⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠏
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠠⠴⠆⢲⣾⣇⠊⠀⣀⣠⣿⣿⣧⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠘⠀⠀⠀⢀⡤⢀⠀⢀⣀⡤⡤
⠀⠀⠠⠶⠒⠛⠷⠀⣠⣶⡶⢶⠋⢡⣾⣇⠺⣿⠁⠉⢁⠁⠉⠉⠁⠐⠒⠀⠤⠄⠀⠀⠁⠀⠀⠀⠀⠀⠙⠃⢀⡄⠀⠃⠀⠀⠀⠘⠱⠆⠐⢉⣀⢀⣴⣿⠄
⠀⠀⠀⠀⠀⠀⣠⠜⠉⠁⠀⠀⠀⠈⢻⣷⠀⡿⣡⡄⢻⣷⣦⣴⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣤⣄⠀⢠⣦⣴⡏⠀⠀⠀⠀⠈⠉⡅
⠀⠀⠀⠀⠀⣠⡄⠈⠁⠀⠀⠀⠀⠀⠀⢹⣷⡀⢹⡟⣸⠉⠀⠠⠉⠘⢿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣼⡛⠛⠀⡸⠿⣿⡎⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡸⠋⠱⠀⠤⠀⠀⠀⠀⠀⠀⣸⣿⣿⣬⣿⠃⠀⠀⠀⠀⠀⠈⠿⠙⠳⠄⠀⠀⠀⠀⣀⠄⠀⠀⠀⠋⠉⠚⠋⠀⠀⣈⠀⣀⣀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠏⢹⣿⡆⠀⠀⠀⢀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠺⣿⣤⡤⠀⣀⠀⠰⠈⠉⡀⠄⠀⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠿⠛⠛⠟⠛⠁⠄⠸⠻⡿⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠦⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠲⡞⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣴⢿⣇⢹⡇⣀⡿⢤
⠀⠀⠀⠀⢀⣀⡴⠇⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⢸⡿⠶⢽⣾⣻⣿⠤⣶⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡐⠋⠁⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⡈⢷⣤⠾⢻⡟⢣⣄⡼⠀⠀⠀⠀⠀⠀⣁
⠒⢶⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⣠⣤⡀⠖⢲⣶⣿⠛⠃⣿⣻⠀⠀⠀⠀⠀⠀⠙⠾⠾⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⢖⣄⠋⢹⣌⣲⠶⠓⡿⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣲⡄
⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠘⠛⠉⠉⢠⠔⠁⠀⠀⠀⠀⠀⠈⠃⢄⡀⠀⠀⠀⠀⠀⢘⣧⠛⠛⡁
⠀⠀⠀⢀⠄⢀⣠⣶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⣶⣁⢺⣤⡇
⠀⠀⠀⠁⣴⡋⠙⣇⡿⠋⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⣃⠀⠀⠀⠀⣿⣫⠽⢿⡇
⠀⠀⠀⢸⣏⢙⣿⣟⣿⣟⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠀⠸⣄⠈⣿⣀⣘⡃
⠀⠀⠀⠈⢿⣯⢫⠟⢻⡉⢙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠮⡿⠇
⠀⠀⠀⠀⠈⠛⠻⠦⠴⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣞⠉⣿⠉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣈⣿⢿⣶⣋⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣍⣩⣽⡿⣿⡉⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣼⣇⣸⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣀
⠀⠀⠀⠀⠀⠀⢰⡛⠉⠉⠐⠲⣄⠀⠀⣴⡄⠀⠀⠀⠀⠈⠉⠉⠡⠄⠂⠀⠀⠀⠀⠀⠀⠴⡀⠦⠀⠀⠀⠀⠀⠉⠉
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡙⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡖⠀⠀⠀⠀⠀⠀⢀⣾⣶
⣻⣷⣤⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠁⠙⠇⠀⠀⠀⠀⠀⠀⣸⠋⢅
⣥⠏⠿⠈⢣⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢹⠀⢹
⠛⠆⢶⣞⣻⡷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠉⠓⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠑⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀
⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣛⣿⣟⣿⣟⣻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⢀⡘⢓⡀⠀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢧⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⣸⣿⡿⣯⡓⠉⠂⠀⠀⠠⠀⠀⠀⠀⢔⡀⠀⠀⠈⠕⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢂⡥⠤⠠⠀⠒⠀⠄⠉⠻⣿⡧⡙⠆⠀⠀⠀⠀⠀⠀⠀⠐⣒⠥⣂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠤⢈⡁⠀⡤⢋⣀⠦⠀⠀⠚⠸⣿⣧⣻⢷⠀⠀⠀⠀⠀⠀⠀⠀⠤⢒⡫⢕⡋⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣀⣀⠠⠀⠨⣧⣾⣵⣛⡃⠀⠁⠰⠁⠰⣿⣿⣷⣵⣀⠀⠀⠀⠀⠀⠀⠀⣭⢵⣾⣵⠅⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⢀⣴⠃⠐⢈⣁⣀⡿⣿⣁⣰⣯⠯⠉⡍⠑⢀⡀⢰⣿⣿⣿⣿⣿⣿⣿⠶⠲⡙⠀⡀⠸⢭⡻⢎⠀⢀⣴⣿⠇
⠀⠀⠀⠀⠀⢀⠎⠃⣠⠶⠂⠉⣴⢚⠁⣿⠝⠳⣄⢠⢍⣴⠏⢀⣿⣿⣿⣿⣿⣿⡋⣁⠘⠤⣈⡀⠹⣮⡉⠋⣀⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠈⠀⠠⠀⢀⡤⠆⠉⠔⣘⠁⡠⠔⢀⠴⠋⠁⢁⣾⣿⣿⠿⣋⢀⡸⢤⡈⠁⠀⠀⢠⠀⢹⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⢀⡠⠑⠉⠃⠄⠄⠂⠀⠀⠔⠊⠀⠀⢀⣠⣿⡿⠛⠁⣰⠁⠀⠳⡀⠁⠃⡊⠌⠂⡄⢸⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡯⣘⠢⣀⠀⡅⠢⠀⠀⠀⠀⠀⠁⠚⡎⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢶⣷⣶⣾⣿⣿⣿⣯⣿⣷⣌⠓⡤⡈⠢⡁⠆⣀⠄⠀⣀⠠⠐⣁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠙⠻⣿⣦⡀⠀⠉⠐⠢⠌⡁⠤⢴⡶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠤⠄⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⣠⣼⢿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⠀⠀⡾
⠀⠀⠀⠀⢽⣧⣴⣿⠀⠀⠀⠀⢠⠁⠀⠆⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡗
⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⣰⠊⠀⠸⠀⠀⢠⡷⠄⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣀⠀⠀⠀⠀⠀⡤⠎⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣾⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠈⠉⠀⠀⠀⠀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢀⠋⠀⠀⠀⠊⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠐⡠⡀⠀⠀⠰⣿⠆⠀⠀⢘⡆⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⣀
⠀⠀⢠⠾⡄⠀⠈⠁⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠀⠀⠀⠆⠀⠀⢀⠇⠀⠀⠀⠁
⠀⠀⠈⠙⠀⠀⠀⠀⠀⠈⢈⠀⠠⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠲⠘⢁⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠈⠁
⠀⣤⠋⠶⣤⠁⣨⠀⣠⠈⠁⠀⢀⠀⡄⠀⠀⠀⢠⠿⡿⠒⠀⠀⠘⠛⠀⠀⠀⠀⠀⢠⠄⠈⠢⠅⠀⠛
⠀⠀⣄⠀⡀⠀⠈⡛⠈⠤⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⢨⠋⢀⡀
⠀⠀⢀⠀⠲⠀⠀⠁⠠⠆⠀⠀⠀⢈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣤⣤⠋⠀⠀⠰⠀⠀⢠⡁⠔⠈⠁
⠀⠀⡝⠉⠁⠛⠀⡄⠲⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠚⠁⠀⠀⠀⠀⠀⠀⠐⢬⠀⠀⠀⢸
⠀⠀⠀⠐⠂⠀⠀⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠰⠀⠀⠀⣠⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⡼⠄⠀⠀⠀⠀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⢢⣢⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣤⡿⠢⠀⠀⠛⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢄⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠞⠉⣰⣶⢿⡟
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣴⠞⠃⣼⢴⣷⢿⣷⠞
⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⡀⠄⠄⠂⢤⠤⠂⠀⠀⠀⠀⢹⠀⠀⣠⠟⣠⣼⣸⣿⣿⣡⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⣿⣾⣿⣿⣿⣶⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣬⣿⡿⠟⢻⡿⠉⠉⣩⠿⠛⣲⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠒⠚⠙⠛⠛⠙⠛⠧⢼⣿⣷⣽⣧⣰⠗⢈⣀⡴⠀⠀⠤⠀⠉⡣⠤⡤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣶⣾⣯⣤⣾⣁⣤⠖⢀⣀⡄⣁⣀⣋⣹⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣽⣏⣩⣻⣿⣿⣿⣿⢻⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠲⠛⠒⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢉⠀⠤⠀⠀⠒⠈⠐⢦⠀⡈⠳⣦
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡀⠈⠐⠀⢈⠀⠐⠈⠀⠄⠊⢎⠤⡈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠂⠀⢀⡀⠐⠈⠀⠀⠀⡐⠈⠄⠀⠀⠡⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠨⠁⠀⢀⠈⠈⠂⡤⠲⢘⡀⠀⠠⠅⠀⠁⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣨⡀⠀⢀⠢⠀⠀⠀⠀⢘⠀⠀⠀⠤⠖⠈⠀⠴⠀⣀⢬⠁⠠⠄⠠⠀⠀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣽⣿⢿⣿⣦⢤⣤⣞⣹⡆⠸⡀⠀⢀⠀⠄⠤⠠⠁⠀⠁⠀⠀⠅⠀⢀⠁⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢔⠁⠤⠀⠀⠀⠀⠂⠤⠂⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡈⠀⠘⠂⠀⢈⣁⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢠⠀⣤⠀⢀⣤⢀⣄⣀⣠⣠⣴⣭⣿⣭⣿⣀⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣠⣤⣤⣽⠤⣤⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣿⢿⡭⠉⢀⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣯⡻⣿⣿⣿⣿⣿⣿⣷⣾⣿⣹⣿⣿⣯⠀⠀⣠⣴⣿⣿⡿⢻⣿⣿⣷⡈⡙⢾⣿⣿⣿
⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠁⠠⢃⢿⣿⣿⣧⢿⡀⡹⣿⡟⣰
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣟⣫⣉⡘⢣⠖⠂⠀⠀⠀⢀⡠⣾⣿⢿⣿⣼⣷⢡⣻⣿⣿⣆
⠀⠀⠀⠀⠈⣿⣿⣿⢟⣽⣿⣿⣿⣿⣏⣯⠕⣿⣿⣿⢏⢛⣋⠈⠤⠀⠀⠀⢀⣡⣴⣿⡿⢟⡏⣿⣿⡾⢋⣿⣿⣿
⠀⠀⠀⠀⠘⣹⣷⣷⣿⣿⢟⡁⣻⡿⣼⡿⣾⣏⡾⠃⣿⣿⣶⣚⠀⠥⢐⣪⣿⣿⣯⣷⠾⠟⣼⣿⠛⢰⣿⣿⣿⡇
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣉⣁⣼⣿⣿⣿⣷⣤⣴⣿⡟⠛⠉⠀⣸⢟⡼⠃⠀⢰⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣶⣶⠦⢤⠴⢿⡭⠿⢉⡀⣀⠀⣐⡵⠞⠁⢀⡴⠟⠁⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣭⣷⣆⡈⠩⠖⢀⡶⢶⣤⣤⣶⠏⠁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⣿⣻⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣷⣿⣿⢿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠉⠉⠉⠀⠿⠋⠉⠁⠀⠀⠘⠃⠀⠀⠀⠀⠈⠁⠀⠈⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣰⠋⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⣀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣄⠀⠙⠂⠨⣷⡀⣴⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⡀⠀⠈⠁⢿⠀⢰⢇⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣷⣜⣾⣦⣴⣿⣏⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣝⣧⣔⣖⡤⢠⠀⣤⢤⣤⡤⢤⣤⣤⠀⠀⠀⠀⠫⣍⠘⠉⠀⠀⠈⠁⠉⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⣹⠀⢰⠃⠀⠀⣠⡶⠋⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠏⠀⠀⣠⡾⠃⢀⣇⠤⠴⠚⠉⠀⠀⡀⣀⣼⢀⡄⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⣄⣠⢏⠎⢀⣠⡞⣋⣠⣔⣸⣁⣀⣀⠀⠀⠀⠠⠿⢿⣟⣽⡏⡀⢠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠀⠀⠀⠀⠀⠀⠀⡀⣉⣯⡐⢻⣯⡽⠛⠉⠉⠉⣙⣷⣄⠀⠀⠀⠀⠀⠀⣈⢻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⣸⠏⠹⢶⣦⠩⣄⣉⠀⠈⠉⠋⠁⠙⣷⠀⠀⠀⠰⢆⣿⣹⣷⣀⣀⠀⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠳⠿⢿⡀⠀⠀⠹⣧⡈⠻⡗⠶⢤⠠⠤⠀⠀⠀⠀⠄⠀⠈⢿⡛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⣷⣶⣤⣄⡀⠀⠦⠀⠀⠀⢤⡴⠂⠀⠀⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠻⣇⡀⠉⠛⠶⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣧⠀⠈⠙⢧⣉⠀⠀⠀⢀⡀⠀⠈⠀⠀⠂⠤⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠙⣇⠨⠭⣁⡀
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡿⠳⣄⠀⠀⠘⣆⠀⠈⣅⠀⠠⣀⣀⠒⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠈⠲⢄⡀⠈⠁⠀⠈⢷⣄⡀⠈⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠉⠒⠒⠤⠤⣤⠄⠡⠤⠤⠄⠰⠂⠐⠒⠛⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠐⠂⠠⠤⠀⠐⠂⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⠊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠓⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠂⠀⠂⠀⣀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣤⣶⣷⣯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠙⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⡧⢢⣠⣾⣿⡿⠛⠁⡀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣶⣤⣄⡈⠀⠲⠙⠼⠀⠘⠟⠛⢡⡀⢀⣀⠠⠄⢀⣤⡶⣾⣿⠟⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡌⠉⠓⠙⠀⠀⠀⢀⣠⡤⠖⠳⡸⡌⡇⢸⣿⣾⠟⠋
⠀⠀⠀⠘⢤⣄⣀⣀⠀⠀⠀⠀⠀⠁⢢⠘⠀⠀⠀⣀⣤⣴⢚⢛⡤⢢⠂⡀⠿⣀⢻⠖⠉
⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⠶⣤⡀⠀⠀⠰⣶⢰⣿⡟⠃⢸⡗⠊⠀⠀⣤⣤⠃⠘⠒⠄⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠂⠘⠁⡄⠙⠀⡅⠀⠀⠁⠙⠁⣰⠋⠀⡀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠁⣠⣴⣶⣦⣤⣀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠲⠇⠀⠀⠀⠀⣀⣤⣤⣷⣿⣶⣤⣨⡀⣧⣄⠀⠀⡄⢀⣾⠿⠿⠛⠋⠁⠀⠀⠀⠀⡉
⠀⠀⠀⠀⠀⠤⣤⣤⣤⣤⣶⣾⢿⠿⠟⠛⠉⠉⠉⠉⠁⢳⡿⠻⣮⡻⠋⠀⠀⠀⠀⣀⠀⠖⠀⠁⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣆⢰⠋⠠⠁⠀⡀⠰⠀⠁⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠐⢀⣿⡇⠀⠀⠠⠀⠁⠀⠀⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠢⠀⠈⢻⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣠⠴⠾⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠀⠀⠈⠀⡀⠀⠀⠀⠈⣇⣀⠈⠀⠀⣠⠦⢼⣤⣶⠁⢲⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⠟⠁⠀⢰⢰⡋⣓⣷⣟⢉⣾⣥⣧⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⡾⠀⠀⠀⠸⣄⢯⣩⡽⠻⣿⢿⠦⠐⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⢸⠃⠀⠀⠀⠀⠙⣅⠠⠬⠨⠩⠬⠐⢊⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠀⠤⠚⠁

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