Weightlifting Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣝⢷⣄
⠀⠀⠀⣴⢿⣿⣿⣿⣿⣿⣧⠹⣷
⢀⠀⣰⣿⣿⣿⢿⣿⣿⣿⣿⡄⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡳⣦⡀
⠙⠒⢤⣬⣭⡅⢀⢈⣿⣿⣿⡇⢸⡿⠉⢢⢤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣯⣿⣿⣿⣿⣷⡘⣷
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⡇⠀⠇⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠿⠷⢾⠇⠙⡿⠛⢻⣿⣿⡇⣿⣆⡀
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⢏⣼⡟⠑⠀⠰⡀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠈⢷⠀⢹⣶⣾⣿⣿⣇⣿⠛⠛
⠀⠀⠀⠈⠻⢿⣿⣿⣛⣵⡿⠋⠀⠀⡆⠀⠱⡄⠀⠀⠀⣼⣿⡿⢋⡙⢇⠀⠀⠀⢸⠆⠀⣿⣿⣿⢟⣾⠏
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢹⡄⠀⠹⣄⠀⠀⣿⠛⠀⠈⠀⢸⠀⠀⠀⣎⡀⠀⡿⠿⠷⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠱⣄⡙⠂⢀⣀⠀⢸⣄⡤⠋⠀⠁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣠⣀⠉⠑⠢⣌⠙⠻⢦⡀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠙⠉⠂⠀⠀⢹⣧⡀⠀⢳⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠠⢄⣸⣿⣿⣷⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⣼⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣠⣼⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠛⠋⠷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠉⠁⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⡤⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣰⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⣠⣿⡇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡆⢢⡄⣀⣀⠀⢠⠋⠙⠊⠉⠁⠐⡇⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣦⣻⡀⠀⠈⠓⠁⠀⠀⠀⢀⡠⠚⢏⣁⣩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⣾⣁⣀⣉⣳⣤⣀⠀⠀⣠⣴⣋⣀⣀⣼⣿⣿⣷⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢦⣶⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣰⡯⠙⠛⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣸⣿⣿⣿⣏⣤⣿⣆⠀⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣏⢷⡿⠏⠲⣤⠙⣆⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢺⠿⠛⣿⣿⣿⣿⣿⡷⠀⠀⠀⠈⠃⢹⠂⠄⢠⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣄⠀⠀⣀⣴⠶⠋⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠸⢿⢸⠀⣼⣿⡟⠁⠙⠿⢆⣄
⠀⠀⠀⠀⠀⢰⣿⣿⠛⢿⣿⠻⣿⠋⠀⠀⠀⠀⠠⠿⠿⢿⣟⣛⣂⣠⣤⡤⠤⠴⣾⢸⡆⢻⣿⡇⠘⠟⣿⡟⠋
⠀⠀⠀⡄⠀⢸⣿⡇⢰⣂⢥⣼⠷⠶⠒⠒⠚⢛⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⣧⣷⡜⣿⣿⣦⣴⣿⠇
⠀⠀⠀⢣⢠⠸⣿⣿⣄⣴⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠣⣧⣙⢿⣿⣿⡿⠃⠀⠀⠀⠀⠐⢿⣿⣿⡿⣟⠛⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢠⠘⠁⣿⠇⢻⡄⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣸⡏⠀⠀⣇⡰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢹⣷⠀⠀⠈⠃⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣇⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⣾⣿⣇⠀⢛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠉⠉⠁⠀⠓⠛⠃

⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠷⠾⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠆
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀⠀⣴⣿⣿⣦⠀⠀⠀⠀⢀⣠⣿⣿⡿⠏⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣀⡀⢸⣿⣿⣿⣿⠀⠀⢀⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠁⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠈⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠘⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠉⠉⠉⠉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠒⢤⡀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⢀⣿⠀⠈⣷⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⡄⠘⠿⠋⠀⢠⡿⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢦⣄⣠⣴⠟⠁⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠋⢿⡄⠈⠻⣿⣦⡀⠀⠀⢀⣠⣤⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣿⣿⣿⠿⠛⠉⢿⣿⠀⠈⠛⠀⠀⠀⠙⢿⣶⣜⠉⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣆⠀⠀⢠⠀⢀⣴⣶⣿⡟⠉⠛⠳⡄⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠀⠀⠀⢱⣾⣿⣿⣿⣿⠀⢀⣄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢹⣿⣿⣿⠈⠉⠀⠀⠁⢀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⠉⣯⣈⡅⡀⠀⠀⠠⠆⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡍⠉⣀⣤⠀⠀⠉⢤⣷⣶⡶⠶⠀⢀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠸⣿⠀⠀⢸⡆⢹⣿⡿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣿⠀⠀⠀⠃⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⢀⠁⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⢀⠔⠀⠀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠿⣷⣦⣤⠴⠖⠁⠀⠀⠀⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣀⣀⣀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣶⣿⠟⠋⠉⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠐⠢⣄⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠂⠀⠀⠀⠀⢈⣷⣄⠀⠀⠀⠀⣸⣿⠋⠁⠀⠀⠀⢀⣠⣴⡿⠁⠀⠀⡠⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⣠⣿⣷⣦⣤⣶⣶⣿⣿⣿⣿⡇⠀⠀⢰⢣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⠀⠀⠀⢀⣼⣿⣿⠃⣀⣠⣴⡿⠿⠿⠟⠛⠛⠋⠉⠀⢸⣿⡇⠀⠀⠉⠆
⣠⣴⣦⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠊⠀⢠⣿⣾⣿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠸
⣿⣿⣿⠀⣤⣀⣀⠀⠈⠑⣦⣤⡤⢾⡇⢀⡅⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠇
⢹⣿⣿⣷⠟⠛⠿⣷⣤⣤⡇⠀⠀⠈⢻⣏⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠃⠀⠺⠇
⢻⣿⣿⡇⠀⠀⠀⠀⠙⢿⡇⣀⠀⠀⠀⠙⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣠⡄
⠘⠿⢿⣷⠄⠀⠀⠀⠀⠀⠻⠼⠗⠢⠴⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⣄⣀⣀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⢠⣤⣾⠛⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣶⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢛⣷⣤⡄
⠀⠀⠀⠀⠀⢸⡇⢸⠀⣿⢸⡇⠀⠀⢠⣤⣤⣤⣤⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠻⣮⠙⠷⣤⠀⠀⠀⠀⢀⣤⣤⣤⣤⡄⠀⠀⢸⡇⣿⢸⡇⢸⡇
⠀⠀⠀⠀⢸⣿⡇⢸⠀⣿⢸⣷⣶⣶⣾⣇⡀⢀⣼⣷⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣿⣶⣶⣶⣶⣾⣧⡀⢀⣸⣷⣶⣶⣾⡇⣿⢸⡇⢸⣿⡇
⠀⠀⠀⠀⠀⢹⡇⢸⠀⣿⢸⡇⠀⠀⠀⠉⢻⣏⠙⢧⡀⠀⠀⠀⢹⣣⡟⠳⠶⣤⣤⣤⣤⣤⠀⣿⠀⠀⠀⢠⡾⠉⣹⡟⠁⠀⠀⠀⢸⡇⣿⢸⡇⢸⡏
⠀⠀⠀⠀⠀⠸⠷⣾⣀⣿⢸⡇⠀⠀⠀⠀⠀⢹⣄⠈⢻⣄⠀⠀⢹⣿⡃⠲⠶⠀⠀⠾⠆⢸⡆⣿⠀⠀⣰⠟⠀⣰⠏⠀⠀⠀⠀⠀⢸⡇⣿⣨⡷⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠾⠇⠀⠀⠀⠀⠀⠀⠻⣆⠀⠹⣦⣄⠘⢿⣇⠀⢀⣀⣀⠀⢀⣾⣿⠃⣠⡼⠋⠀⣰⠏⠀⠀⠀⠀⠀⠀⠸⠷⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠙⠳⣌⠙⢦⣀⣉⣉⣠⠾⢋⣵⠞⠉⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠘⢷⣴⣟⠉⠉⣿⣤⡾⠁⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣠⡟⠁⠙⠛⠛⠋⠈⢷⣄⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢀⣤⡄⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢹⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠉⠉⠉⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⣤⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⡇⢹⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢦⣾⠀⠈⣷⠴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢰⡏⠀⠀⢻⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⢸⡇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣤⣼⠁⠀⠀⠘⣧⣤⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠁

⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⡟⣉⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⣤⣶⣚⣋⣭⣬⠹⣆⡀
⠀⠀⠀⠀⠀⣿⠏⠉⠡⠤⠬⣿⡏⣿
⠀⠀⠀⠀⢸⡇⢋⣀⠠⠤⠤⣼⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠖⠒⠒⠒⠀⢀⣠⠄
⠀⠀⠀⠀⢸⠀⠈⠀⣐⣶⠤⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠒⠶⠶⠶⠞⠋⠁
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⡶⢋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢿⠀⣯⣀⣀⣠⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⣀⣀⣀⡠⣄
⠀⠀⠀⠀⠘⣆⠀⠉⠭⡵⡞⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⠀⠰⣡⠚⠷⠚
⠀⠀⠀⠀⠀⢻⡀⢄⠀⠈⠙⣆⠹⣆⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠉⠉⠙⠛⢿⣿⢶⡄⠠⣤⡀
⠀⠀⠀⠀⠀⢸⡇⠘⣆⠀⠀⠈⠃⠙⣦⡀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠹⣆⠈⠻⣆
⠀⠀⠀⠀⠀⢸⡇⠀⠘⣆⠀⠀⠀⠀⠈⠛⢦⣼⢇⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠙⢷⣤⣀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠻⣮⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⢀⠉⠙⢦⡈⠙⠛⠳⠶⠶⠶
⠀⠀⠀⠀⠀⠸⡇⢄⠀⢸⡳⣄⠀⠀⠀⠀⠀⠀⠘⣟⢻⡄⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢸⠀⡆⠀⠇
⠀⠀⠀⠀⠀⠀⢿⡨⣂⠸⡟⢾⣶⣲⠤⠀⠀⠀⠀⣻⣤⡇⣀⣀⡀⢀⣀⣴⠟⠁⣠⠄⠀⢸⣤⡇
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣷⡀⠀⠀⠀⠀⢀⣀⣠⠟⢿⠑⠀⠉⠉⠉⠉⡁⠀⣞⠟⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⠻⠶⢤⣤⣤⣤⠅⠀⠀⠸⠀⣤⠀⠀⠀⠐⢬⣊⣸⠄⠀⠀⣾⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠘⢦⡀⠀⠀⠀⠀⠀⣠⠤⠖⠃⠀⠀⠀⠀⠀⠀⠀⠁⣠⡾⠃⠈⠻⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⡙⠲⠤⠴⠀⠈⢀⣀⣠⣤⣀⣀⣤⣤⣤⡴⠾⠛⠉⠀⠀⠀⠀⠀⠉⠛⠛⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣤⡴⠞⠛⠉⠉⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣦⢱⡀
⠀⠀⠀⠀⢀⣤⣸⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⢢
⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⢸⡏⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⣿⣿⣿⡎⡇
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢹⣿⣿⣿⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠈⠻⣿⣆⡀⠀⠀⠀⢠⣿⣿⣷⡄⠰⠃⡤⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣜⠦⢀⣀⣸⣿⣿⣿⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣾⣯⣿⣿⣿⣧⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢿⣿⣿⣿⣿⣇⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣡⣿⣿⣿⣿⣿⣿⡿⣻⣽⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠋⠉⠉⠉⢉⣼⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⢰⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣤
⠀⢀⣸⣿⣿⣿⣷⣀⣄⣀⣀⣀⣀⣠⣤⣤⣤⣤⣀⣠⣄⣰⣿⣿⣿⣿⣀⡀⢀⣰⣿⣿⣿⣿⣠⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⢤⣿⣿⣿⣿⣄⡀
⠀⠈⠹⣿⣿⣿⣿⠈⢿⣤⡀⠀⠀⣀⣀⠀⠀⢀⣤⡾⠃⠸⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⠀⠻⣦⣄⠀⠀⣠⣄⠀⠀⢀⣴⡾⠃⠀⣿⣿⣿⣿
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠙⣿⣦⣄⣿⣿⣀⣴⣿⠋⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠈⢿⣷⣤⣿⣿⣤⣴⣿⠏⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠁⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠅⠀⠀⠀⠀⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣿⣿⣯⣽⡏⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⡿⢀⣄
⠀⠀⠀⠀⠀⠀⣠⡿⠋⠉⠳⡀⠀⠀⠀⣻⣿⣿⡆⠀⢸⡀⠀⠀⢀⡀⣀⣤⠛⠙⠛⢶⣿⣿⢸⣧⣸⣿⣿⠆
⠀⠀⠀⠀⠀⣰⣿⡇⢀⣤⣠⣷⣶⣶⣭⣽⢀⠀⢠⣄⣸⠛⠛⠛⠛⠋⠉⠉⠛⣿⡆⢠⠈⢿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠘⠛⣿⣿⣾⠏⢨⡇⢀⣴⠋⠁⠀⠀⠀⠹⠧⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⡇⠀⠈⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠛⣴⡿⠃⢀⡖⠀⠀⠀⣀⠀⠀⠀⠀⢦⣀⡀⢀⣼⣷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢠⡁⠀⠀⠀⠉⠉⠃⠀⠀⠈⠣⠄⠙⠃⠈⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⢤⠀⠀⠀⠀⠰⣶⣶⣄⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠰⣿⠋⣸⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⡄⠀⠀⠀⢀⡼⠋⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⣀⠀⠉⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣤⣌⣁⣠⣤⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠛⢿⣿⡿⠟⠛⠛⠛⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠹⡇⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⠀⢠⡇⠀⠀⠀⠀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣠⠋⢹⣄⡀⠀⢀⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣀⠁⠀⠀⣿⡧⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠏⠀⠀⠀⠇⠀⠀⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣀⠀⠀⠀⡘⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢰⠇⠀⠀⠀⢷⡔⠆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡾⠀⠀⠀⠀⠈⢿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣵⣄⡀⠀⠀⠀⠸⡇⠀⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠟⠛⠁⠀⠀⠀⠀⣿⣤⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠶⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠀⠀⠉⢯⢢
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠙⡜⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣘⠀⢀⡴⣦⡀⠈⡆⢃
⠀⠀⠀⠀⠀⢀⣆⣀⢔⠺⡆⠀⠀⢁⠸⣖⣾⡋⢶⠤⠭⠭⠭⠭⠭⠑⠺⣯⢽⡥⠤⠨⣗⣼⠇⠀⡇⢸⠗
⠀⠀⠀⠀⠀⠙⡖⠂⠻⠶⠃⠀⠀⡈⢠⠀⠀⢣⠈⢆⠀⢀⣠⢤⡴⣤⡠⠋⠻⠘⣄⠀⠀⠀⠀⣰⢁⠆
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣠⢃⠎⠀⠀⠘⡄⠈⣴⠋⢁⣀⣀⣸⠃⢠⠃⠀⠈⠢⠤⠤⠴⠥⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠴⠞⠓⠉⠀⠀⠀⠀⠘⡄⠹⣦⡏⢙⢷⣿⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢹⢿⡻⠿⣇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠁⠀⠙⢒⡃⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⣀⢀⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡤⢺⡎⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⠺⢣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⢭⡥⢒⡚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠀⠀⡨⡓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣘⣤⣸⠈⡒⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢻⠑⢺⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣅⣀⠔⠛⢩⠄⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠟⠢⡄⠸⠄⠉⢉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡽⡥⢤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⣀⣾⡑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠻⠀⡔⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠗⠟⡠⠐⠉⢁⣀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠱⢆⡅⠀⠀⢐⡁⢊⣉⡴⠒⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣁⢺⡏⠀⠀⠘⠁⠀⡨⣧⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠑⠊⠀⠁⠀⠐⠐⠉⠀⠀⠈⠑⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠉⢀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⠠⡀⠤⠤⠚⠟⠉⠉⠀⠈⠀⡄⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠈⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢎⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⣠⡀⠀⠀⠀⢀⠳⣄⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⣿⢠⡅⣠⠈⠲⠄⠄⢸⠀⠈⠉⠐⠒⠈⠀⢀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠘⠿⠘⠂⠀⠀⠀⠀⠀⠀⠉⢂⡀⠀⢀⠀⠠⠒⠲⡦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⡆⠀⠀⠀⠈⢌⢆⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠈⠁⠀⡷⠷⠘⠲⠉⠢⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠈⠸⢢⡀⠀⠀⠀⠙⠃⠀⢀⠱⠀⠀⣀⡀⠀⠤⠀⠖⠈⠉⠒⠄⡀⠠⢴⣷⠦⣀⠰⠂⢀
⠀⣠⠔⠀⠒⡒⠒⠒⠄⢄⣺⣂⡗⠂⠧⢄⡀⠑⠄⠀⠀⠠⠀⠀⠰⡀⣳⡜⣣⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠁
⠀⢏⠀⠀⠀⠑⢘⣿⣹⠁⣿⠃⠻⡀⠀⠀⠀⠑⢦⢢⠀⠃⠀⠀⠀⣇⣰⡍⢠⣀⣀⣤⣄⣀⣀⡀
⠀⠀⠂⣀⣤⣥⣜⣻⣷⣷⣿⣧⣀⠈⠀⠀⠀⠀⢘⣮⣼⣄⠀⣀⣀⣬⡷⠶⠒⠻⢍⠋⠳⠶⠿⢪
⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⡟⠛⠚⠚⠋⡀⠉⡆⢈⣾⣶⣶⣤⣤⣤⣤⣤⣤⣼⣿⣶⠄
⠀⠈⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⠾⠿⠿⠿⠿⠿⠿⢷⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄
⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠉⣼⣷⡀⠀⣀⠙⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⠛⠋⠁⠀⠀⠀⢿⡿⠃⣸⣿⡇⠀⠈⠛⢿⣶⣄⡀⠀⠀⠀⠀⠀⠸⣿⡀
⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣀⣀⡀⣻⣇
⢸⣿⣀⣀⣠⣤⣤⣤⣶⣶⡶⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⣿
⣿⡟⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡾⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠶⣶⡆⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⣿
⣿⡇⠀⠀⢀⣿⣷⠀⠀⠀⠀⠈⠁⣀⣠⣤⣶⡾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⣿
⣿⡇⠀⠀⣸⡟⣿⡇⠀⠀⠀⠀⣾⡟⠋⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠉⠙⣿⠆⠀⠀⠀⠀⠀⢿⣷⣿⠀⠀⣿
⢸⣷⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠘⢿⣦⣀⣀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⣀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢰⣿
⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⢠⣶⠀⠀⠀⢰⡆⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣼⡏
⠀⢻⣷⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⢰⣿⠁
⠀⠈⢿⣆⠀⠀⠀⠀⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠃⠀⢀⣿⠇
⠀⠀⠈⢿⣆⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣷⣦⣾⠿⣷⣦⣴⡿⣷⣤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠷⣶⣶⣶⣶⣶⣶⣶⡶⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠻⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠦⠀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⣠⠁⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡏⠀⠠⣤⣜⡓⠘⠰⣶⣂⣀⣀⠀⢠⠋⡄⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣰⠃⠀⠈⠉⠉⠀⠀⠀⠉⠉⠛⠋⠁⢸⠀⣇⣠⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⣀⠀⠀⢀⠀⢀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠒⠋⠉⠒⠶⠮⠜⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠢⠤⠚⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡦⡠⠖⠋⠙⠶⠊⡇⠀⠀⠀⠀⠀⠀⠀⡶⢄⠜⠲⢄⡉⠙⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠒⠂⠤⠤⠤⠤⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡼⠉⠉⠉⢹⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⢤⡇⠀⠀⠀⠀⣇⡸⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠀⠓⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠠⣀⠀⢀⡄⢠⡀⢠⣤⡀⠀⢠⡄⡤⣠⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⣿⡇⠀⣿⠀⠹⣷⡀⠀⠀⠁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠟⠁⠻⠇⠰⠟⠠⠀⠹⠿⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡄⢀⡄⠠⣄⢠⣤⠀⠀⠀⣤⣄⠀⢠⡄⣤⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⣿⠸⣿⠀⠀⠀⠈⢿⣆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠆⠙⠇⠰⠛⠈⠻⠄⠀⠀⠀⠈⠻⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠴⢰⣦⢰⢠⣶⠀⣴⡆⢴⡆⠰⠄⠀⣶⡆⢠⣄⠀⣰⡄⠰⣶⡀⠀⣤⠀⠦
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠂⣿⡇⢸⡇⠆⠀⠀⣿⡇⢸⣿⠀⠸⣿⡀⢹⣷⠀⠻⠿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠘⠛⠀⠛⠃⠚⠃⠐⠃⠀⠛⠃⠘⠁⠀⠀⠛⠃⠘⠛⠀⠓⠀⠘⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣆⠀⣶⡆⠀⣴⡄⠀⣶⡆⡀⠀⢰⣶⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⣿⡇⠀⠸⣿⡀⣿⡿⣷⡀⢸⣿⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠛⠃⠀⠀⠛⠃⠛⠃⠙⠓⠘⠛⠐⠃
⠀⠀⠀⠀⠀⠀⠚⢸⣷⠘⢰⣿⠀⣾⡇⢸⡇⠘⠂⠀⣿⡇⠸⣦⠀⢼⣆⠘⣿⡄⠀⣶⣀⠛
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⢸⡇⠃⡀⠀⣿⡇⢰⡿⠀⠘⣿⡄⢸⣿⠀⡈⠛⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠀⠉⠁⠈⠁⠈⠁⠀⠉⠁⠈⠀⠀⠀⠈⠁⠈⠉⠀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠈⢃⣾⠀⢸⣦⢸⡇⠀⠀⠈⢿⣆⠀⠘⢸⣿⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢀⡜⣿⠀⢸⡟⢸⣇⠀⠀⠀⠀⢻⣦⠀⢸⣿⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠈⠁⠁⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⠿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠃⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠘⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⢀⣠⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣄⡀⠀⠈⢿⣿⣷
⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⣰⣿⣿⡿⠋⠀⠀⠈⠻⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⠟⠁⠀⠀⠙⢿⣿⣿⣤⠀⠈⣿⣿⣧
⠀⠀⠀⠀⠀⢰⣿⣿⠃⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⠘⣿⣿⡆
⠀⠀⠀⠀⠀⣿⣿⡟⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⢻⣿⣿
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⢁⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧
⠀⠀⠀⠀⣸⣿⣿⢁⣾⣿⡟⠁⠈⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷
⠀⠀⠀⣠⣿⣿⡇⣾⣿⡿⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣄
⠀⢀⣾⣿⡿⠋⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡀
⢀⣿⣿⡟⠀⠀⠀⢹⣿⣿⣄⣀⣀⣠⣿⣿⠏⠀⠰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⣼⣿⡿⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠻⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠟
⠀⠀⠀⠈⠛⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⣠⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣷⣶⣤⣤⣤⣤⣶⣾⣿⣿⡿⠟⠉
⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠛⠿⢿⣿⣿⡿⠿⠛⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣶⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⣀⡀⢀⠀⠀⠀⠀⢀⠀⠀⢀⣀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⣸⣿⡏⠀⣿⣿⣿⣿⣿⣇⠘⣿⣷⠀⠀⣸⣿⡏⠀⣻⣿⣿⣿⣿⣷⠀⢸⣿⠿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⣿⣿⠃⠀⣿⣧⣤⣠⠆⠀⠀⢹⣿⡇⢰⣿⡿⠀⠀⣿⣿⣬⣤⠤⠀⠀⢸⣿⣤⣾⣿⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⡿⠀⠀⣿⡿⠿⠿⠀⢀⠀⠀⢿⣷⣾⣿⠃⠁⠀⢹⣿⠿⠿⠂⠀⡀⢸⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣶⣶⣶⣆⠁⠀⠸⣿⣿⡇⠀⠀⠀⢸⣿⣷⣶⣶⣶⠁⢸⣿⡟⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠈⠉⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡆⠀⠀⠀⢀⠀⠰⡄⠀⠀⠀⣶⠀⠀⠀⠀⣠⡦⠀⣠⠒⠉⡂⠀⠀⠀⣶⢴⢠⣄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⠁⠀⠀⢠⠃⢀⠜⠀⠀⠀⡴⠇⠀⠀⠀⣰⠃⠀⡴⠁⠄⠊⠀⠀⢀⡜⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡎⠀⠀⠀⣏⠔⠁⠀⠀⢠⠎⠸⠀⠀⠀⡠⠇⠀⢸⠁⠀⠀⠀⠀⡠⠊⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⠇⠀⣀⠔⠇⠀⠀⠀⠀⠁⠀⢀⠀⢀⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠶⠀⠀⠲⠀⠀⠂⠀⠀⠀⠒⡒⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⢀⠀⠀⠉⠀⠀⠡⠀⠀⠀⠤⠀⠁⠐⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠰⠆⠀⠀⢠⡄⠀⠀⠀⠀⣄⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠙⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⢀⣀⣀⣀⠀⢀⣀⠀⠀⣀⣀⢀⣀⣀⣀⣀⡀⠀⠀⢀⣀⡀⠀⢀⣀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠛⠛⠁⠀⠸⢿⣿⠿⠀⢹⣿⡀⢠⣿⠇⠀⣿⠿⠿⠿⠂⠀⠀⢸⣿⠀⠀⢸⣿⠀⣿⡟⠛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⣀⣀⣀⣄⠀⢸⣿⠀⠀⠀⣿⣇⣿⡟⠀⠀⣿⣷⣾⠁⠀⠀⠀⢸⣿⡄⠀⣼⣿⠀⣸⣷⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣿⣿⣿⠀⣤⣾⣿⣶⡖⠀⠸⣿⣿⠁⠀⠀⣿⣦⣤⣴⡀⠀⠀⠈⢿⣷⣴⣿⠇⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠀⠉⠉⠉⠉⠁⠀⠀⠉⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡖⠛⠉⢿⣦⣶⣿⣿⣿⣿⣿⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⢀⣖⣾⣧⠀⢸⣿⣟⡿⠟⠻⣿⣿⢿⣿⣿⣿⣿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⢀⠀⡀⢾⣿⣿⠄⣠⣾⠏⠻⣷⣷⣶⣂⠙⠲⠄⠘⠻⣗⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠁⢀⣠⡴⠋⠀⣘⠲⢀⣴⣾⡋⢽⠂⠀⢰⣿⣿⡇⠑⠂⠀⠀⠁⡻⣆⠀⠀⣄⢄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢉⣁⣤⣤⠴⠾⠛⠁⠀⠀⢰⡏⠀⢸⢉⣉⣵⣿⠀⠀⠈⢿⣉⡝⠀⠀⢇⢲⠀⠀⢘⣶⣦⡙⠾⠇
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢻⡏⠁⠀⢰⣧⣤⣤⠾⠛⢿⡏⠓⠻⣿⢿⣿⠇⠀⠀⠀⢸⡟⣍⠁⠀⠈⠉⠀⠀⠿⣧⣻⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣗⠛⠉⢷⡀⠀⠈⢳⣭⠅⠀⢀⡀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⣧⠈⠑⠀⠀⠀⠀⠀⠀⣄⣙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣀⣠⣷⠄⠀⣸⡇⠀⢰⣯⠗⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠉⠈⢷⣬⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠙⢿⣟⠳⣤⡀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⣠⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠈⠻⣆⠀⠉⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠞⠋⠁⣠⡞⠁⠀⠈⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠉⢙⡷⢄⠀⣼⢿⡛⠋⠉⠁⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⣴⣏⣦⡘⣾⡁⢈⣿⣄⠀⠀⢀⣴⠞⠉⠀⠀⠀⢠⣆⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⠃⠈⠛⡿⢺⣿⡭⠔⠻⣧⣰⠟⠁⠀⠀⠀⠀⠀⠀⢹⡄⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣾⡏⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠶⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠴⡾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡞⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⠞⢿⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⡇⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠶⠻⡏⠁⠐⣦⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⣿⣇⡏⠀⠀⠀⠀⠀⠀⢠⣾⣿⣅⣀⣤⣴⡇⠀⠀⢹⡀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣶⣦⣄⣀⠀⠀⠀⠀⢸⣇⡿⠙⠛⠃⠀⠀⠀⠀⠀⠀⠘⠛⠛⣿⠟⡏⠀⣿⠀⠀⢸⡅⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⣶⣤⣬⣭⣁⣠⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣾⠿⢻⠇⠀⢿⠀⠀⠘⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠘⣦⠀⣾⠀⠀⠀⡇⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠘⠛⠓⠏⠀⠀⠀⡿⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠈⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠒⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢸⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⡒⠩⠅⠒⠛⠁⠘⠛⠛⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣷⣶⣄⠀⠀⢠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣿⣿⠀⠀⢸⡇⠉⠉⠀⠀⠀⠀⣠⣤⠀⠀⠠⡡⠚⠳⠀⠀⠀⣓⠀⠐⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠋⠀⠀⠸⡿⠿⠛⠀⠀⠀⢸⡏⢹⡄⠀⣦⠀⠀⠀⠀⠀⢠⣿⡄⣸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⢸⣧⣤⣤⡀⠀⠀⣿⣧⣼⡇⠀⢡⠐⡀⠀⠤⠀⢸⣿⠁⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⠹⣿⣷⡆⠀⠈⠉⠉⠉⠁⠀⢸⣿⠁⠈⣿⠀⠀⠁⠈⠁⠀⠀⠸⠿⠀⠠⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣷⣾⣥⡤⠄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⠀⠀⠀⠀⠀⠀⠉⢉⣿⣿⡿⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠁⠈⢇⠀⠀⠀⠀⠀⠀⢰⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠚⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⢸⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⣸⣿⣽⣆⠀⠰⣆⠀⠀⠀⠀⣿⣶⣿⣿⣿⠏⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣄⢻⡆⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠃
⠀⠀⠀⠀⠀⢀⡿⢲⢦⡀
⠀⠀⠀⠀⠀⢸⡏⠳⣞⣻⡆⠀⢀⣀⡀⠀⠀⢰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⢰⣷⠀⠀⠀⣠⣶⣶⣧
⠀⠀⠀⠀⠀⢸⡿⠀⡿⣭⣿⠀⢸⡏⣻⡆⠀⢸⣦⣤⠄⠀⠀⢠⡿⢿⠀⠀⠀⣸⡿⢿⣤⣿⢿⣇⠀⠀⢿⣅⡀
⠀⠀⠀⠀⠀⢸⡗⢾⣱⣾⠏⠀⣿⣿⡛⠁⠀⢸⣁⡀⠀⠀⠀⣼⣧⣼⡄⠀⠀⣿⡇⠈⠿⠃⠸⣿⡄⠀⠀⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠘⠛⠛⠉⠁⠀⠀⣿⡟⢿⣆⠀⠘⠻⠛⠛⠀⢀⣿⠋⠹⣇⠀⠘⠛⠀⠀⠀⠀⠀⠛⠃⠀⣤⣤⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉


⣶⣶⣶⠶⡶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠛⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⠀⢻⡇⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⣼⡟⣁⣀⣠⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠛⠻⢿⣿⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠘⠿⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⣾⠟⠛⠻⣷⣄⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣀⣤⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠻⣧⣤⣤⣤⣿⠿⠂⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠐⢿⣿⣍⡀⠀⣈⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⣀⡀⠀⠀⠀⣀⣠⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉


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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢘⣘⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣠⣾⣿⣷⠠⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣰⠟⢳⣿⠗⠶⣾⠟⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣼⡇⠐⢛⡟⠀⢀⠀⠀⢸⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣿⢫⡘⣿⡇⠀⠈⠇⠀⠸⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⣱⡆⢟⡇⢀⣤⠶⡿⠟⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢀⠙⢀⣾⣷⣿⣿⣶⠆⣿⣧⣿⣟⣧⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣧⣾⢲⣾⣷⣀⣹⣿⣏⣀⣉⣽⣿⣿⣿⣿⣯⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⡍⣽⣿⢿⣿⠟⣿⢋⣽⡏⣽⣟⢩⣗⣿⡋⣽⡇⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡜⣿⠟⠻⣷⢋⢾⣿⡇⣸⣿⠘⣿⣿⡇⣿⣷⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣤⣾⣧⣤⣾⣿⣿⣃⣘⣿⣄⣉⣥⣧⣉⣩⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⠴⠶⠶⠿⠿⠿⠛⠻⠿⠴⠷⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠕⣄⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠉⠁⠉⠉⠉⠉⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⣀⡄⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡀⢀⡀⡄⠰⠇⠸⡀⠰⣠⡀⢠⣤⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘⠀⠀⣝⢤⠑⡌⠹⠘⠃⢴⠃⠱⠀⠋⠓⠁⢡⠘⢃
⠀⠀⠀⠀⠈⠄⠊⠉⠀⠀⠀⠀⡆⠀⠰⠀⠀⢫⠀⠀⢀⣀⣀⡴⠀⡤⠀⠠⣄⠀⠀⢸⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠓⢤⡀⠀⡌⠰⣠⡎⠥⠒⠉⠱⡄⠧⠀⡠⠊⠻⢍⣮⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠔⠒⠵⣤⡃⠀⡇⠀⠀⠀⠀⣷⡁⠀⠸⠁⠀⠀⣾⠈⣿⡓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠐⢊⡇⠀⠀⢠⠀⠐⢄⡀⠀⢀⠵⠁⠀⠈⡣⢄⣀⡠⠚⡝⢫⡃⠀⠀⠛⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣐⡃⠀⠀⠉⠀⠀⠀⠈⠉⢡⠀⠀⠈⠉⠃⠀⠀⠀⢀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⢀⠀⠔⠀⠀⠀⠀⠈⡄⠀⠀⠋⠀⠀⡄⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⡇
⠀⠀⠀⠀⠐⠕⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢠⠃⠀⠀⠛⢀⠔⠊⠉⢢⠀⠀⠀⠐⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠼⠦⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡀⠀⠀⠠⡏⠒⠢⠤⠤⣄⣀⣀⣀⣀⣀⡤⢤⡒⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⡴⠀⢀⠀⠀⠙⢄⠀⡠⠒⠲⣥⠟⢦⠀⢀⠇⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⡀⠈⠁⢀⠃⠀⠀⠂⠀⠉⠀⠀⠀⠁⠀⢀⠖⢱⠀⠀⠀⢸⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠈⠉⠒⠖⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣧⠠⠤⠚⡇⠀⠀⠨⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢡⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠐⢲
⠀⠀⠀⠀⠀⠀⢀⡏⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⢩⡀
⠀⠀⠀⠀⡖⢒⣊⠁⠀⠀⠀⡨⢮⠁⠿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢋⠉⡷⢇⠀⠀⠀⠀⢙⠒⢒⠄
⠀⠀⠀⠀⠀⠀⠈⣇⡇⠀⠀⡇⠀⠡⠈⠢⢄⠀⠀⠀⠀⠀⢀⠠⠄⡀⠀⠀⠀⠀⠀⡀⠔⠁⡜⠀⢸⠀⠀⢸⣘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠠⠇⠀⠀⠑⢄⡀⠑⠒⠠⠀⠀⡀⠀⠀⢸⠀⠀⡠⠐⠊⠀⡀⠜⠀⠀⠸⠄⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠑⠂⠐⠀⠀⠒⠒⠈⠁⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢤⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠚



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢰⠋⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢱
⠀⢠⠒⢺⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡗⠒
⠀⢼⠀⠸⡇⠀⢸⠀⠀⠀⠀⠀⢀⣠⢤⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡤⢤⢄⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⡶
⣤⢸⡀⠀⡇⠀⠸⣒⡒⢒⣒⣒⣇⢠⡠⠀⢗⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⠂⡤⢠⡁⠀⠀⠀⢈⡇⠀⢸⡇⠀⡇
⠛⠀⡇⠀⡇⠀⠀⠁⠀⠀⠀⠀⠙⣆⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⣴⠋⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⡇
⠀⠒⡇⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⣀⡤⢤⣤⡄⠀⢀⢤⡖⠲⠤⣀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠘⡇⠀⠉
⠀⠀⠣⠤⡇⠀⠀⡇⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠘⠉⠀⠈⢑⠈⠉⠀⠀⠈⠳⣼⠃⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⠒
⠀⠀⠀⠀⠣⠄⠤⠃⠀⠀⠀⠀⠀⡸⣇⠀⠀⠀⠀⠀⣀⠀⠎⣤⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠓⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠈⠀⠀⠀⡄⠘⠛⠀⡆⠉⠁⢀⠃⠀⠀⠈⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠂⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⠀⡠⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡀⠀⠀⠀⠑⠠⣀⡀⠀⠀⠀⡀⡀⠐⠀⠀⠀⠀⠀⡀⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠂⠀⠀⠀⠀⠀⠀⠖⠂⠀⠃⠠⠃⠀⠔⠀⠀⠀⠀⠀⠀⠼⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⣀⡉⠦⠀⠀⠀⠐⠤⠀⠀⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⣀⢀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⡤⡀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠑⠒⠒⠒⠉⣿⠀⢹⡏⠉⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⠀⢸⣇⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⢂⠀⢀⡹⠂⢎⡀⠈⡐⠉⠈⠲⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄
⠀⠀⠀⠀⢀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡀
⠀⠀⠀⢠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄
⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷
⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟
⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇
⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿
⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃
⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⡅⠀⠀⠀⠀⠀⠀⢨⠟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠃
⠀⠀⠀⠀⠈⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣤⣽⡄⠀⠀⠀⠀⢠⣯⣤⣬⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⢸⠀⠀⠀⢨⠃⠀⠀⠀⠀⠘⡅⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣄⠀⠀⠀⠣⣀⡤⠋⠀⠀⠀⠀⠀⠀⠙⢤⣀⠜⠀⠀⠀⣠⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣀⣤⣴⡶⠶⠿⠟⠛⠛⠻⠿⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⠾⠛⠉⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣈⠙⠻⣶⣄
⠀⠀⠀⠀⠀⢀⣴⣾⡏⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠋⣽⣿⠁⠀⠀⠀⠀⠀⠀⠘⢁⡴⠀⣠⠂⠀⠈⢳⣄⠀⠘⠋⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡾⢠⣾⠙⡆⠀⠀⡏⢹⣧⡘⡀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⢀⡆⠀⠀⠸⣷⣿⣿⠀⡇⠀⠀⡇⢸⣿⣿⣷⠀⠀⠀⠀⠘⡇⢀⣠⡀
⠀⠀⠀⠀⠀⢸⣿⣇⠉⠀⠀⣼⡇⠀⢠⣾⠛⠟⠃⢀⡇⠀⠀⢇⠀⠛⠟⢻⠷⠀⠀⢀⠀⣿⡏⣠⢼⡆
⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⢸⢻⡇⠀⠀⠘⣧⠀⠀⣼⠃⠀⢸⡜⣦⡀⢀⡜⠀⠀⠀⣾⠀⢿⣷⣏⢸⠃
⠀⠀⠀⠀⣾⠋⢀⠙⢧⡀⠙⠛⠀⠀⠀⠳⣌⣙⠋⠁⠀⠀⠀⠹⣮⠙⢩⡴⠃⠀⠀⢻⠇⠸⣧⠉⡟⠀⠀⠀⢀⡤⠴
⠀⠀⠀⠀⢿⣠⡎⢳⡄⠀⠀⠀⢸⡇⠀⠰⠬⠉⠀⠐⠋⠀⠀⠀⠈⠳⣤⡘⠁⠀⠀⢸⡆⠀⢻⣷⠇⠀⠀⠀⠉⠠⠒⠋⣉⣉⡁
⠀⠀⠀⠀⠈⢿⡁⠸⣿⡄⠀⠀⣼⣿⠀⠀⠀⠀⡤⠀⠛⠛⠷⠶⣤⣀⠈⠙⢦⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⡴⠚⠉⠉⠉⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠙⢦⡈⠁⡀⠀⡆⡟⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈⠉⠐⢋⠀⠀⠀⠀⠀⢸⣿⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠸⣴⠇⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⣾⡏⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⢾⠃⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠸⡇⠀⠀⣼⡿⢁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣷⡀⠀⠀⠀⢸⣤⠞⠋⠉⠁⣤⣤⣤⠀⠉⠙⢶⣄⡇⢀⣾⡿⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠙⢿⣄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣵⡿⠋⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠙⠷⣦⣄⣘⣦⣄⡀⠀⠀⠀⠀⠀⣀⣠⡾⠋⠁⠀⠀⠀⠀⠈⠳⢤⡤⡀⠀⠀⠀⠀⣠⠾⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠰⣿⠓⣄⠀⣉⠽⠛⢿⠿⢷⣶⣾⣿⣿⠋⠀⠀⠀⠀⠀⣠⠤⣄⣠⣎⡼⣿⠦⠤⠖⠋⠁⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡴⠛⠉⣀⡤⣶⢿⣦⣠⣴⣮⠀⡾⠛⣦⡀⠀⠀⣰⢧⡀⠈⠻⣏⢰⡏⠀⠀⠠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣾⣧⠀⠀⠀⠀⢫⡴⢾⠟⣿⠶⣌⠡⠞⠁⠘⡎⢷⡀⠀⣷⣄⢙⡏⠁⠈⠹⣷⡀⠀⠐⠚⠉
⠀⠀⠀⠀⠀⠀⢀⣴⣯⡤⠴⠾⠃⠀⠀⠀⠀⠈⢀⡿⠀⣷⠀⠀⠀⠀⠀⣠⣿⡇⣹⠶⢿⠆⢺⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⣠⣤⣤⣤⣶⡏⠀⣼⣿⡆⠀⠀⠀⠀⠈⢷⡾⠁⣠⠼⢷⡀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⢀⣠⠞⠁⠀⠀⠀⢺⣤⣴⣿⣿⣿⣀⣀⣀⣀⣀⣸⣇⠀⡏⠀⠀⠉⢠⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⣀⣄⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣻⣤⣤⣴⣾⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣏⣀⣠⣤⣤⣤⣤⣤⣄⠻⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⢿⣿⣿⡇⢹⣿⠁⠀⠀⠈⣿⡇⠀⢿⡿⣿⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠖⠚⠯⠤⠝⢻⡄⠸⡿⠀⠀⠀⠀⣿⡇⣠⠾⠤⠼⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄⣉⣀⡤⠖⠲⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⣤⣀⠈⠿⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡿⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⢷⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠈⠛⠲⠦⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠴⠖⠛⠁⠀⠀⢸⠆
⠀⠀⠀⠀⡀⠀⠀⠷⠶⠦⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⢀⣠⡀⢠⣤⡄⠀⣠⣤⢠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠴⠶⠾⠀⠀⢀
⠀⠀⠀⠀⢿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⡇⠘⣯⣧⢀⣷⡇⢸⢿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡿
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡇⠀⠀⣟⣿⢻⣿⠇⠀⢻⣾⣾⣾⠁⢸⢿⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠠⣄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠸⣿⣿⡟⠀⠀⠘⣷⣷⠇⠀⣸⢿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣠⠄
⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣷⡶⡆⠀⢻⣿⠁⠀⠀⠀⢻⡾⠀⠀⣼⣻⣲⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⠃⠀⠀⠀⠀⠈⠃⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠲⣦⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣴⠖
⠀⠀⠀⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢼⠀⡛⡄⣄⢠⡀⣠⡀⠀⢀⠀⠀⠀⠀⣤⠀⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉
⠀⠀⢠⣤⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠁⠘⠾⠃⢻⢇⡀⢻⡅⢰⡷⠀⢿⣀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣤⡄
⠀⠀⠀⠀⠀⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⠇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣠⠎⠉
⠀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣥⡀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠄⣿⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⠠⠚⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠠⢈⣇⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⣸⡁⠀⠀⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠁⠀⢁⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡈⠀⠈⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⡖⠁⡎⠉⡞⠉⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠑⡎⠉⡎⠉⡆
⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡇
⣀⣀⣀⣀⢀⡎⡇⠀⡇⠀⡇⠀⠉⢡⣤⣤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⣤⣤⡎⠃⠀⡇⠀⡇⠀⡏⣃⢀⢀⣀⣀
⠓⠒⠒⠒⠒⣇⡇⠀⡇⠀⡇⠀⣀⡿⠞⠓⢚⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⠈⢛⣇⡀⠀⡇⠀⡇⠀⣇⡓⠐⠒⠒⠂
⠀⠀⠀⠀⠀⠈⡇⠀⡇⠀⡇⠀⠀⠀⠣⡤⠚⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣩⣀⣀⣉⢂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⢠⠂⠈⠁⠀⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⢇⢀⣇⣀⢇⣀⠄⠀⠀⠐⡄⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⡟⠷⠆⢴⡾⢿⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⡰⠁⠀⠀⢄⢀⣇⣀⢇⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⡀⠉⠁⠂⣄⣀⡀⠀⠣⢠⢐⡀⠀⠎⠀⠀⠀⡠⠒⠉⠀⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠈⠂⠇⡀⠀⠁⡞⠂⠅⠡⠘⡖⠂⠉⠉⢡⠊⠁⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⡄⢰⠀⠀⠈⠂⠤⠤⠚⠀⠀⠀⠀⣀⠦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢆⠀⡠⠂⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠸⠉⢃⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠉⠢⠀⡰⠁⠀⠀⠢⡀⢀⠔⠊⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠁⢢⠟⠀⠀⠀⠀⠀⠘⢦⠔⠂⠉⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢢⣀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⢵⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣠⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠙⢲⡋⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣘⡻⠚⠓⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠠


⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⣹⠳⡀
⠀⠀⠀⠀⠀⢀⡞⠁⡟⠀⢠⠃⠀⡇
⠀⠀⠀⠀⠀⡼⠀⢸⠃⠀⡎⠀⠀⠃
⠀⠀⠀⠀⢰⠇⠀⡟⠀⢰⠃⢀⢰
⠀⠀⠀⠀⣸⠀⢰⡇⠀⡾⠀⣾⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢦⠤⣀
⠀⠘⠀⠠⡿⠀⣸⠀⢀⡇⢠⡿⠧⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡸⠀⢸
⠀⠀⠀⠀⡇⠀⡿⠀⢸⠁⢸⣿⠃⠐⠂⠀⠨⢍⠋⣰⠀⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢠⡇⠀⣸⠑⣆
⠀⠀⠀⠀⡇⠀⡟⠀⢸⠀⢸⢋⠀⠀⠀⠀⠀⢐⠀⠀⠀⠉⠐⠚⠀⠬⢐⡂⠀⠄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠜⡤⠀⡼⠀⢠⡇⠀⡏
⠀⠀⠀⠀⡇⠀⡇⠀⣾⠀⠀⠆⠀⠀⠀⠀⠀⠸⡄⠀⠀⠤⣤⡉⣿⠆⠀⠀⠀⠁⠒⠇⡀⡐⠀⠄⠀⠀⡜⣼⠇⢰⠃⠀⡾⠀⢰⠃
⠀⠀⠀⠀⢃⠀⡇⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⢄⡉⠈⠛⠑⠀⠈⠑⡄⠀⠀⢀⡴⠀⠀⠈⠑⠂⠨⣙⡟⢀⠏⠀⣸⠃⢀⡟
⠀⠀⠀⠀⠈⠉⢧⠀⢧⢠⠃⠀⠀⠀⠀⠀⠠⡀⠀⠀⠙⢄⠀⠀⠀⠀⠠⣼⡤⠔⠋⠀⠀⠀⠀⠀⢀⢱⡿⢀⡞⠀⢰⠏⠀⡼⢀
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠙⢶⠢⢲⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠞⠁⡜⠀⢠⠏⠀⡼⠁⠂⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖⠉⠉⣽⣦⣄⣀⣠⣴⣄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡼⠁⢠⠏⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠻⠿⣿⣿⠿⡇⠑⣄⠀⠀⡀⠈⠀⡎⠀⡜⠀⣠⠋⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡿⣿⣦⣤⣀⣀⣴⡇⠀⠈⡠⠊⠀⠀⠀⣇⠎⢀⡴⢇⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡈⠙⠻⠿⢻⠏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠙⠷⠶⠞⠁⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠁⠀⠀⠀⠀⠀⠁⠀⠐⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⣦⣄⡀⢰⡟⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣭⡶⢷⣦⠉⠻⣾⡷⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⣦⣄⡀⢠⡿⠛⢻⡄⠀⠀⣴⠟⣁⣀⣀⡈⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣦⣉⠻⣾⡷⣦⠾⢃⡘⠷⠶⠾⠋⣉⣉⠻⠶⠶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⡈⢻⡆⠀⠈⠻⠶⠶⠾⠛⠋⠙⠷⢶⣶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⣠⡾⢿⣄⠛⣛⣿⡇⠀⠀⠀⠀⣴⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⡇⠀⣿⠀⠀⠙⠛⢋⣉⣤⣤⣶⠶⣶⣿⣄⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣿⠆⠀⠀⢰⡟⠉⠁⣀⣀⣤⡙⣷⣭⣥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⣾⠋⠀⠀⠀⠀⠈⠻⣦⣀⠙⢿⡝⢷⣮⣵⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⢠⡶⠟⠛⠛⠷⣮⠙⣷⠈⣿⢀⣴⠾⠛⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠹⡇⢿⠀⠿⢼⠇⠀⠀⠀⠀⠈⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠸⠐⢠⢆⡠
⠀⠀⠀⠀⠀⠀⠀⡈⠂⠀⡠⠤⠦⢄⡀⠉⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⡜⠀⠀⠀⠀⢱⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠈⢁⠀⠱⡀⠀⠀⢀⡜⠀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⢡⠔⢂⡈⠉⠉⠉⠀⢄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢠⠃⠸⠄⠈⠀⠀⠀⠀⢠⠞⠉⠉⢢⠀⠀⠀⠠⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢦⠀⠀⠀⢃⡜⠛⠲⣄⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣲⡿⣗⡇⠀⢀⠞⠍⠳⢤⠈⢹⡆⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠣⡀⠉⠉⣏⢰⠄⠩⣈⡇⣸⠃⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠤⠬⣉⠁⠈⠓⠒⠒⢟⠲⠋⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⡁⠈⡆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢅⠈⠉⠉⠉⠉⠉⢉⣉⡏⠉⠙⢄⡀⠐⢀⡜⢱⠄⡇⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠲⠤⠝⠒⠒⠊⠉⠉⡁⠀⠈⢢⠀⠀⠉⢲⠎⠀⠀⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠬⠤⢄⣀⣀⣀⣁⣀⣀⣀⣀⠤⠧⠤⠔⠋⠀⠀⠀⠱⢌⣻⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠎⠀⠀⠉⠁⠈⠓⠒⠓⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⢲⡀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣵⡾⣿⣶⣄⢷⠀⣰⠇⣠⠞⠙⢦⡲⣄⠀⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠫⢎⡥⠖⢺⡽⡏⠁⢧⠀⠀⠀⠀⠀⢩⡄⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠈⢠⣞⣉⡤⣇⠀⠀⣶⠀⢤⣀⡀⠈⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢀⡟⠉⠈⢉⡁⠀⠀⠀⠀⣀⠈⠀⠀⠛⠻⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⡴⢿⠉⠀⠀⠀⠘⠋⠀⢀⡀⠈⠙⠀⠀⠀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⡞⠁⠈⠙⢲⡀⣦⠀⢀⡤⣤⡤⢤⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸⠁⠀⠀⠀⠈⢳⡀⠀⠈⠓⠚⠓⠚⠁⠸⢆⡞⠀⠀⠀⡐⡆
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠙⢲⡤⣤⡄⠀⠀⠤⢶⠋⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠙⡾⠲⢤⣀⡤⢼⡁⠀⠀⠀⠀⠀⢈⡧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⡼⠁⠀⠀⢻⣀⣠⡽⣆⠀⠀⢀⡴⣫⣀⣀⡟⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡞⠁⠀⠀⠀⠈⠁⠀⠓⠮⣷⣤⡮⠴⠏⠀⠉⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⠉⠁⠀⣇⣀⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡏⠉⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⣠⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢦⡀⠀⠀⠀⠀⠀⠀⠈⡋⠀⠀⠀⠀⠀⠀⣴⣴⠀⠀⠀⠀⢠⣤⣄
⠀⠀⣠⣿⣿⣄⣄⣼⣿⣧⡄⠀⠀⠀⣰⠛⢻⣷⣶⣾⡇⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⡏⠁
⠀⠀⠀⠿⣿⠁⠀⢸⡿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠚⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣶⣄⣀⣀⣰⣶⠀⠀⠀⠀⡷⠶⠶⠶⠶⠶⡇⠀⠀⠀⠀⠀⠀⢠⣥⡄⠀⠀⠀⠀⠀⢰⣿⣿⡆
⠀⠀⣤⡄⠿⠏⢉⣯⡹⠿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⢀⣹⣏⣀⣀⣀⣀⣀⣀
⠀⠀⣿⡟⠛⠛⠻⣿⠅⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠈⢹⡏⠉⠉⠉⠉⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠘⢷⠂⠀⠀⢠⡾⠏⠀⠀⠀⠀⣀⠀⣴⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⣀⠄⢀⠤⣀⢰⣄
⠀⠀⣤⣾⣶⣶⣶⠾⢧⡀⠀⠀⠀⠈⣿⠀⠉⠉⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⣈⡀⠀⠀⠀⠀⠀⢈⡁
⠀⠀⢿⣯⣼⣿⣿⣄⣠⠇⠀⠀⠀⠸⠿⠸⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⡇⠀⠀⠙⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠙⠋
⠀⠀⠀⠉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⢠⣄⢀⣤⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣠⣤⣤⣤⣤⣿⣇⠀⠀⠀⠀⣿⣿⣤⣄⣾⣿⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄⠀⠀⠀⠀⠙⢻⠉⢹⣿⡍⠉⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣄⣅⣸⣿⠀⠀⠀⠀⠀⢸⠀⢸⣿⡇⠀⡇
⠀⠀⢶⣶⣶⡶⡶⣶⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣍⠀⠀⠀⠀⠀⠼⠄⠨⠿⠄⠤⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⡇⣸⣀⡀⠀⢀⠀⡄⢀⣀⡀⢀⠀⡄⠀⠀⣀⢀⡀⣀⠀⣠⠄⣀⣠⡔⣿⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⢸⣆⠀⠀⣾⢀⡇⣾⢸⣿⣼⢀⡇⣠⠀⣿⢸⡇⡿⣾⢰⡇⣿⠀⡇⣿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⢸⡄⠀⠈⢩⡟⠉⠉⠁⠈⠉⠉⠁⠀⠈⠉⠉⠁⠈⠉⠉⠉⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⠀⠀⠀⢯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡆⢀⡤⣄⠀⠐⣶⠀⠀⣶⠀⣠⣤⣤⢠⡤⣤⢤⡄⢶⠂⠠⣤⠀⣤⠀⢴⡆⠀⢴⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⣇⠘⡆⠀⣿⡄⢰⣿⠀⣿⠀⠈⠀⠀⣿⠀⠀⢸⠀⠀⡇⠀⣿⠀⢸⢧⠀⣼⠀⡞⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⣿⠈⠛⡷⠚⡇⢧⡾⢸⡀⣿⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⡇⠀⣿⠀⢸⠘⡆⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠀⣧⢸⡀⢠⠇⠀⡇⠘⠃⢸⡇⣿⠉⣀⠀⠀⣿⠀⠀⢸⠋⠉⣇⠀⢹⠀⢸⠀⢹⡇⠈⢧⠘⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠖⠁⠀⠉⠉⠀⠈⠋⠀⠀⠀⠀⠘⠛⠉⠀⠀⠛⠀⠀⠘⠃⠀⠉⠀⠛⠂⠛⠀⠀⠁⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⢹⡏⣿⢺⡄⡔⡧⣰⠞⡆⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠟⠸⠷⠿⠥⠿⠀⠧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⣀⣀⠀⠀⣀⣀⠀⠀⢠⣤⣴⠦⣤⣀⠀⠠⢤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⢸⣿⠀⢹⡏⠀⣼⠋⠙⢷⠀⠀⢸⡇⠀⠀⠙⡇⠀⢸⡇⠀⣸⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣿⢹⡇⣼⠀⠀⣿⣆⠀⢸⡇⠀⢸⡇⠀⢀⣼⠇⠀⢸⣇⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢠⡟⠸⣇⣿⠀⢰⡇⠈⠛⠶⣷⠶⠾⣧⡴⣟⠁⠀⠀⢸⡟⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⣿⣿⠀⠘⣇⠀⠀⢠⡇⠀⠘⡇⠀⢻⡄⠀⠀⢸⡇⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⢿⡇⠀⠀⢿⡀⠀⣼⠃⠀⠀⡇⠀⠀⠻⣄⣀⢸⡇⠀⠀⠻⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠘⠃⠀⠀⠈⠙⠛⠁⠀⠀⢴⣷⠄⠀⠀⠈⠁⠾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢆⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⢸⡗⢢⡶⣶⢸⢗⡆⠀⢰⡆⣿⠀⢠⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡞⠧⠟⠚⠸⠷⠃⠘⠧⠿⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠈⠻⠿⠏⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡏⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⢀⣠⣴⣶⣶⣶⣦⡘⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣛⠿⢿⣿⣿⣿⠿⢿⡇⣿⡿⣋⣭⣬⣭⡻⠟⣩⣥⣭⣝⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⡇⣿⢱⣿⣿⣿⣿⣷⡞⢿⣿⣿⣿⣇⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠛⠛⠉⣴⣿⢸⣿⣿⣿⣿⣿⢣⣎⠿⠿⢿⡏⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⣤⡀⣿⣿⣆⢳⣶⣶⡙⡟⣸⣿⣿⣿⡿⣱⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⣭⡝⣿⣷⣌⠻⣿⣤⣿⣿⠟⣫⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⢸⣿⢠⣤⣤⣤⣤⣤⡄⣿⡇⣿⡇⣛⢻⣿⣿⣮⡙⢟⣵⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⢸⣿⠈⠛⠛⠛⠛⠛⠁⣿⡇⣿⡇⣭⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⣛⣡⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠛⠁⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⣀⣠⢀⣆⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⠀⠀⠀⠀⠀⠀⣰⣀⣀⣀⣀⣀⣶⡀
⠀⠀⠀⠀⠀⠙⠶⣾⣷⡶⠞⠁⠀⠀⠀⠀⠀⢰⣿⠻⠦⠄⣴⠂⠀⠀⠀⠀⠀⠠⠞⣿⢦⣠⢀⡿⠀⠀⠀⠀⠘⠐⣆⡶⣠⠆⠛
⠀⠀⠀⠀⠀⠀⣀⣼⣿⣄⡀⠀⠀⠀⠀⠀⠀⢶⣭⣷⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣸⠟⢶⡀⣸⠇⠀⠀⠀⠀⠀⠀⢘⣿⡏
⠀⠀⠀⠀⠀⠀⢻⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢹⠶⠿⠻⣗⠀⠀⠀⠀⠀⠀⢠⣭⣥⣴⣾⣶⡿⠀⠀⠀⠀⠀⠀⠀⣼⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢉⡳⢄⠀⠀⠀⠀⠀⠀⠀⠐⢲⡂⢶⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣸⣃⣀⡽⠂⠀⠀⠀⠀⠀⠀⠀⠹⣶⣦⡄⠀⠀⠀⠀⠀⠀⢈⣭⣀⣠⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣥⡀
⠀⠀⠀⠀⠀⠀⢹⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠟⠂⠀⠀⠀⠀⠀⠀⠻⣿⣥⣄⠈⣻⡇⠀⠀⠀⠀⠀⣠⠿⣿⣿⢷⣄
⠀⠀⠀⠀⠀⣤⣬⣿⣏⣿⣤⣄⠀⠀⠀⠀⠀⠀⣾⠁⢻⡀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣷⡟⣷⣿⡇⠀⠀⠀⠀⠀⠘⣿⠿⢿⣿⠃
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⡀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⢠⡴⣿⣿⠦⡄⠀⠀⠀⠀⠀⠀⠀⢠⢾⣷⣆⠀⠀⠀⠀⠀⠀⠠⡾⣿⢧⡀⢀⡾⠃⠀⠀⠀⠀⢶⠎⣷⣦⣤⣄
⠀⠀⠀⠀⠀⢰⠀⣿⣿⠀⡰⠀⠀⠀⠀⠀⠀⠀⠘⣼⣿⣮⡅⠀⠀⠀⠀⠀⠀⢹⡟⢳⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣮⡙⣷
⠀⠀⠀⠀⠀⠈⠢⡌⣿⠴⠁⠀⠀⠀⠀⠀⠠⠴⠚⠉⠀⠸⠁⠀⠀⠀⠀⠀⠀⢸⠃⠼⢤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠹⣄⡀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⣰⠛⣿⡇⠀⠀⠀⠀⠀⠀⠰⡶⣻⠄⢀⣄⡀⠀⠀⠀⠀⠀⠀⠈⢉⣹⣷⡘⠟
⠀⠀⠀⠀⠀⠀⠸⢿⣟⢻⠆⠀⠀⠀⠀⠀⠀⠀⠸⡶⢛⡇⠀⠀⠀⠀⠀⠀⠀⠐⠿⣷⣾⡿⢻⡄⠀⠀⠀⠀⠠⣔⣛⡯⠽⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠒⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠭⡓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠈⠈⢳⡀
⠀⣀⡤⠤⣤⣀⠀⠀⠀⠉⠓⠦⣄⠈⣇
⡞⠁⠒⠒⠂⠉⠓⢦⡀⠀⠀⠀⠈⢧⣿
⢧⡀⠀⠀⠀⣀⡀⠀⠙⣆⠀⠀⠀⠸⡏⠀⠀⠀⢀⣠⣀⣠⣤⣤⣀⡀
⠀⠉⠙⠋⠉⠉⠉⠙⠲⣌⣧⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⢠⡏⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠙⣆
⠀⠀⣠⢚⣛⠛⠒⠶⢤⡀⠀⠀⠀⠀⠀⢸⡇⣠⠴⠛⠉⠀⠈⠳⣤⣀⠀⠀⣹
⠀⠘⣇⠁⠀⢀⣤⠴⠦⢭⣷⡄⠀⠀⠀⣼⠛⠃⠀⠈⠓⠚⡁⠀⠀⢉⠛⢶⠏
⠀⠀⠈⠓⠛⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠹⣦⠀⠀⠀⠉⠉⠀⠀⠘⠬⢶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠶⠦⣄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣟⠻⢦⣀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠉⠁⠀⠉⠙⠛⠛⠛⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⡛⠶⠦⢤⣤⣀⡀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣾⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠉⣻⠋⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠘⣧⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⡀⣠⡏⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⢸⠿⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⡿⣋⡴⠳⠦⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⣀⠀⠀⠀⠈⢷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⢀⣤⣄⣉⣙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢲⡏⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠓⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠉⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⣊⣤⣶⣾⣿⣿⣿⣿⣥⠈⠉⠒⠚⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⣫⣴⣿⣿⠿⣻⡿⠛⠋⠉⠉⠉⠛⠢⠀⠀⠀⠈⠐⣶⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢥⣾⣿⡶⠛⠁⠞⠁⠄⣒⠒⠒⠂⣀⣀⢀⠀⠀⠀⠀⠀⠈⠃⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢠⣾⣿⣟⠁⠀⠀⣠⡴⠟⣛⣻⣶⣜⢿⣿⢎⠳⡷⠀⠰⠶⣷⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡀⢸⣿⣿⠃⠀⣠⣿⠋⣰⠟⠉⠉⠉⠉⠐⠀⠀⠀⠀⠀⠀⠀⠈⣿⣣⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣇⠈⠐⣶⣆⣰⠃⢡⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⢷⣿⣿⣿⠋⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠈⠻⠻⠷⣾⡷⠀⠀⠀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣷⣄⣷⣦⣾⣟⠁⠀⠀⠈⣀⣀⣀⣉⠙⠛⠃⠀⠀⠀⠴⣛⣉⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣮⣿⣿⡇⣙⢿⣷⣪⠂⠀⠀⠙⠻⣟⣿⠏⠳⠄⠀⠀⠀⡴⠻⡟⠉⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⡿⡟⠱⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣅⢻⣄⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠙⣿⣿⣷⣦⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⡠⠞⠙⣿⣿⣿⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠿⠶⠾⡦⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⠀⠀⣿⢸⣿⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠩⠷⠶⠖⠀⡰⠁
⠀⠀⠀⠀⠀⠀⣸⣿⡄⢀⡴⠞⠀⢰⣯⣾⣿⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠘⣿⣏⡀⣨⣿⠁⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢄⣻⣿⠃⢀⣨⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡿⢷⢾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⠟⡀⠤⠤⠄⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢠⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠛⠋⡀⠀⠀⠁⠘⠢⠤⣀⠀⠈⠂⠀⠈⠻⠮⡳⣌⠐⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠘⠻⠧⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠑⠀⠀⠈⠪⡓⡙⠛⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠉⠉⠉⠉⠉⠉⠁⠛⠁⠀⠘⠛⠛⠛⠛⠛⠓⠒⠒⠒⠂⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢠⣤⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠻⣧⠀⢸⡿⠀⠀⣠⣤⣀⠀⣿⡿⠀⠀⢸⣿⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠹⣷⣿⠃⢀⣾⠟⠙⣿⡆⣿⣿⠀⠀⢸⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡏⠀⢸⡏⠀⠀⣿⡇⣿⣿⠀⠀⢸⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⣇⠀⢸⡇⠀⠀⣿⠁⣿⡟⠀⠀⢸⡟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠙⠛⠀⠀⠻⠶⠾⠋⠀⠻⣿⣦⡴⠟⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⣦⠀⠀⢠⣴⣦⠀⠀⣠⣄⠀⢠⣶⡀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣾⠁⠀⠀⠉⠀⠀⣿⠃⠸⡇⠀⣿⡟⣆⢸⣿⡇⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⣿⡀⠀⠀⢀⡀⢠⣿⣤⣤⡇⠀⣿⡇⠹⣎⣿⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣧⡀⢀⣿⡇⣼⡿⠀⠨⣿⠀⣿⡇⠀⢻⣿⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠛⠛⠋⠀⠿⠃⠀⠀⠿⠀⠿⠇⠀⠈⠿⠃⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣶⡶⢦⣄⠀⠀⠀⣀⡀⠀⢠⣤⣤⡄⢠⣤⣤⣤⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠹⣆⢠⣾⠛⢻⡆⠀⢸⣧⠀⠀⠀⣿⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢸⡇⠀⠀⣿⣾⠃⠀⢸⡇⠀⠐⡿⠀⠀⠀⣿⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⣠⠏⢻⡄⠀⣸⠃⠀⠈⣷⠀⠀⠀⢻⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠘⠛⠛⠁⠀⠈⠛⠚⠋⠀⠘⠛⠛⠟⠀⠀⠸⠇⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉






⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣀⣀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡄⠀⠀⠀⠀⢨⣯⣿⣿⣿⠀⠀⠀⠀⠀⢠⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣝⢿⣿⣷⡀⣠⡖⢲⣾⣿⣿⣿⣿⣷⡖⢲⣄⣰⡟⣼⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠹⣎⢿⣿⡷⢻⠛⠛⠉⠱⠎⠀⠱⡉⠛⠛⠟⢉⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠛⢿⡟⢺⡷⢠⡥⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⡛⣽⡷⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠻⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡌⣁⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⣀⣀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⣆⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣽⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⢰⣰⣤⡖⢦⣤⣢⠀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠰⣏⣩⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠶⢶⣶⣶⣾⣻⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠰⣄⣰⠈⢃⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⢤⡾⠟⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡁⠁⠀⠀⠀⠀⠀⠀⠀⢾⡁⢀⣺⡇⣿⣿⢘⢘⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⠈⢘⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢫⣿⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣄⠡⠉⠩⠈⡭⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣪⣿⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣍⣽⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠩⠛⠷⠞⠛⠉⠀⡄⠀⠀⠀⠀⠀⠀⢀⣀⢐⣏⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠸⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠊⠉⠉⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢠⡌⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠲⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⢿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⠶⠿⡟⢘⡓⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣀⣥⡻⠷⢴⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⣾⣿⡷⣼⡴⢦⣤⡰⢂⣀⡐⣥⡴⢴⣦⣈⢿⣿⣿⡄⠈⠛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⣾⣿⡿⠁⠙⠷⠾⢻⣿⣿⣿⣿⠟⠷⠾⠃⠙⣧⢻⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⠂⠀⠀⠀⠀⢘⣛⣿⣿⣿⠀⠀⠀⠀⠀⠘⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠉⠉⠡

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⡀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡀
⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣧⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣼⣿⣿⣿⣿⣿⣶⣤⡄
⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⡇⠈⢿⣦⡀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⢀⣴⡿⠃⢸⣿⣿⣿⡿⠻
⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⠈⠻⣿⣦⣄⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣠⣴⣿⠟⠁⠀⠘⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⣶⣤⣼⣿⣿⣧⣤⣶⣾⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⠘⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄⠀⠀⢠⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠁

⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣿⣿⣿⣛⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣴⣾⠛⠃⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢪⣾⣿⣿⡁⠀⡄⢉⠸⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣿⣿⣧⠀⠁⡠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢿⣿⣿⡟⢀⣴⡅⠰⢐⠖⠁⣹⣖⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠑⢾⣻⣧⠀⡚⠚⠉⡽⢌⣁⣁⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠛⠟⠀⠈⠲⠊⠀⠀⠀⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠋⠁⠀⠀⡄⠀⠀⠀⠀⠀⠘⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢩⠀⠀⠀⠀⠄⠀⢢⣄⠀⠀⠀⠈⠀⢰⠀⠀⠀⠀⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡄⠀⠀⠀⠀⠠⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠁⠠⠄⠀⠃⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⠀⠀⡀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡰⠁⠔⠚⠈⠈⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠧⣀⠀⢆⣀⡠⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠉⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠖⠒⠚⢱⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠹⠉⡗⠒⠂⠀⠀⠀⠀⠀⠀⠀⠤⣴⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⠃⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⡀⡌⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠚⠁⠘⠧⢔⡒⠠⠤⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⢠⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣁⠉⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⡚⣃⡭⠳⡤⠋⡆⢹⠀⠀⠒⡖⠆⠀⢀⡠⠊⠓⢄⡠⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⢐⡇⠑⢄⠀⠀⡇⠀⢣⠀⢀⠀⠀⢠⠁⠀⢥⠂⡄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⠁⠹⣯⡧⢠⠇⠀⢸⡆⠉⣀⠀⣸⡀⣀⠈⠘⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢒⠞⠀⠀⢀⣙⣞⣡⣴⠲⣻⠙⣯⣽⣼⢛⠋⣫⢀⣉⢠⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠹⠀⠀⠙⠛⠿⠿⠿⣯⠴⣷⣾⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⠿⠿⠿⠿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠍⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠁⠀⠀⠀⠉⠉⠉⠀⠄⠀⠈⠁⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢡⣶⠞⢺⣿⠛⢀⣼⠀⠀⠀⠀⠀⠙⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡿⠁⢢⠀⢠⡂⠈⢻⡆⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠂⡇⠀⠉⠀⠈⠁⠀⠸⡂⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠲⡔⡇⠂⠁⠀⢤⡀⠁⠓⣧⠔⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡆⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢡⠀⠀⠀⠀⠀⠀⠃⠢⠀⣀⣀⣀⠔⠉⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⢰⠡⣀⣀⣀⣀⠀⡀⠀⣃⠀⠀⠀⣠⠊
⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⣄⠀⠀⠀⢡⡀⠀⠀⠇⠀⠈⠀⠀⠐⠅⠀⠘⠁⠀⠌⠸⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⠤⣄
⠀⢠⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⡺⠊⠑⠂⢁⣀⠀⠊⠀⢳⠠⢀⡔⢣⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡅⡄
⢀⣸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⡸⢁⡆⠀⢀⠔⠋⠈⠉⠉⢒⣞⢀⠋⠀⡀⢀⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠
⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⢤⠃⠀⠀⠈⡎⠱⠄⠀⠀⠨⢀⠃⠀⠀⠡⡤⠏⠅⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⡇⣏
⠈⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠺⠢⠤⢄⢤⠗⢰⠀⠀⠀⠀⢸⠄⠄⠤⠤⠃⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉
⠀⠘⠸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠀⠀⠀⢑⡌⠢⣀⠀⠠⢄⠀⡦⣀⠀⠐⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡧⠆
⠀⠀⠀⢇⣀⣀⣀⣀⣀⣀⣀⡼⠀⠀⠀⠠⣂⣀⣀⣄⠍⠉⠡⠀⠧⢀⣉⣄⣀⣍⣐⣠⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠀⠀⠀⠠⢤⡤⣖⠂⠀⠀⠠⠄⠴⠶⠦⠤⠀⠀⣠⠀⠀⠀⠠⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⣀⣤⠄⠀⠑⠀⠃⢀⠁⢬⠀⠀⠉⠀⠀⣿⣿⣿⣿⡆⠀⠀⢀⣴⣶⣾⣃⡌⠀⠀⣤⣄⣾⣾⣷⡖⠐⢀⣀⢀⠀⠀⡀
⠀⠀⠀⠄⠀⠀⠈⠀⢠⡽⣷⣿⣷⡄⣄⠀⠀⠀⡄⡀⠀⠀⠐⢣⣐⣒⢛⡁⠈⠛⠫⡄⢀⣩⢿⡭⣿⣷⣄⡘⢷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠿⠛⠁
⠀⠀⡀⣀⡀⣂⡀⠀⠈⠉⠙⢻⣿⣷⣿⡑⠄⠀⠈⠐⣀⢒⡊⠳⢦⣬⣽⣲⣦⠀⠀⠀⠀⠙⠷⣾⠛⣿⣿⢥⣿⣿⣿⣿⣽⣿⣿⡿⡟⠛⠋⠁⠀⡀
⠀⠀⠁⠈⠙⢿⡗⢀⣀⠠⠺⣿⣿⡿⣿⣆⣐⡀⠚⣤⣞⢎⣻⠟⠋⠉⠉⠁⠀⠀⠀⣀⣀⠀⢈⠊⢻⣿⣿⣟⣛⣿⡿⢿⣏⢿⣿⢾⣿⣿⣵⣾⣶⡀⠀⠂
⠀⠀⠀⡀⣀⣠⢷⣈⣵⣾⣷⣿⣻⣿⣿⣿⣿⣽⡿⠿⣆⣠⣼⣶⣤⣤⣤⣤⣶⣶⣿⣿⣿⡆⠀⠀⡀⣿⣿⣾⣿⣿⣿⣿⣷⣿⣧⣿⣿⣿⣯⣿⣿⣷⣶⣶⣦⣄
⠀⠀⢁⠈⠵⡄⢘⣛⢘⣿⣿⡿⠯⢿⣿⡍⢉⢽⣆⣐⣋⣽⣮⢻⣮⣭⣶⡈⠉⠉⠉⠉⢿⣿⣶⡷⠛⠙⢿⣿⣿⣿⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⢀⣀⣁⠉⠾⢿⣯⣭⣭⣯⣭⣍⢿⣆⣔⣀⣉⣁⣚⣳⣾⣷⡙⢿⡟⠳⠎⠉⠉⠀⠈⠛⢿⡷⣄⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⡻⣿⣛⣾⠿⢿⠟⠉
⠀⠐⠛⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠙⠛⠛⠛⠋⠉⢡⡿⢆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓
⠀⢀⣀⣀⣀⣘⣻⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⣀⢑⠒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠉⠓⠟⠛⠓⠐⠛⠾⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣭⠹⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠒⠂⠂⠐⠂⠐⠀⠂⠀⠀⠀⠀⠐⠒⠀⠀⠂⠀⠒⠀⠀⠀⡂⡀⠓⢂⡐⠂⣀⣀⣂⡀⠂⠒⠐⠀⠂⠐⠒⠐⠒⠂⠐⠒⠀⠀⠒⠀⠒⠒⠒⠒⠒⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣉⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡟
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⣿⡇
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠉⠁
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⣀⣀⣤⣴⣶⣶⣿⡿⠋⢻⡇⠀⢀⣤
⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣿⡇⠀⢾⣿
⠉⠛⠿⠿⣿⣿⣿⣿⣿⣷⣽⣟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⢸⣟⣀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠓⠒⠒⠒⠒⠒⠒⠻⠿⠿⢿⣿⣏⡁⠀⠈⢻⣷⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣦⣾⣃⣔⣀⣼⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠉⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣀⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⠏⠀⠀⠀⠀⠈⣿⠇⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡄⢠⣿⣿⣿⣿⣿⡀⢸⣿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢋⣤⠀⡟⠀⠀⠀⠀⠀⠀⢻⠆⣤⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠞⣿⠁⣿⣿⣿⣿⣿⣿⣧⢸⡟⢶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢳⡄⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣆⢹⣿⣿⣿⣿⣿⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⣀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠿⠿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠛⠀⠀⠉⠉⠀⠀⠛⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⢛⠉⢡⣿⣿⣿⣶⣿⣿⣧⡍⠙⡛⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡞⠉⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠉⢳⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢋⣴⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣷⣎⢻⣿⣿⣿⣿
⠀⠀⠀⠀⢸⠁⠀⠀⢸⣿⣿⣦⣀⣀⣀⣀⣤⣿⣿⡇⠀⠀⠀⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⢸⣿⣿⣿⠀⠀⠙⠿⠿⠿⠿⠟⠁⠀⢸⣿⣿⣿⡆⣿⣿⣿⣿
⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿
⠀⠀⠀⠀⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢚⣀⣓⡛⣀⠀⠀⠀⠀⠀⠂⠈⠅⠛⠁⠀⠀⠀⠀⠀⡠⡀⢲⢣⠆⠀⠀⠀⠀⣖⡄⠂⣆⣓
⠀⠀⠀⠀⠀⣿⣿⡿⠿⠾⠿⠄⠀⠀⠀⣻⣽⣟⢴⣿⣽⣿⡁⠀⠀⢲⢆⣶⢲⢶⣾⠟⠀⠀⡀⠉⢉⠉⡉⠁⡀
⠀⠀⠀⠀⢴⡶⢂⢰⠏⣦⣄⠀⠀⠀⠘⠉⠉⠉⠉⢉⠉⠉⠁⠀⠀⣼⣫⣽⣬⣼⡽⠷⠀⠀⠳⢩⠊⠈⠘⠚⠥⠂
⠀⠀⠀⠀⠈⠀⠀⠋⠒⠉⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠂⢉⣰⢀⢐
⠀⠀⠀⠀⢀⡤⣌⣤⣴⣶⣶⡆⠀⠀⠀⡄⠀⣀⢀⣀⠀⣠⠀⠀⠀⠘⠷⢶⡄⢳⢷⡇⠀⠀⠀⠆⠂⠐⠈⡂⡄
⠀⠀⠀⠀⡸⠠⡯⠭⠁⢀⣒⡂⠀⠀⠀⠳⢂⣿⣾⡟⢺⠏⠀⠀⠀⠀⢨⡭⡄⠂⣄⡄⠀⠀⠀⢻⡿⣿⣛⢿⡟
⠀⠀⠀⠀⠀⠀⣇⡀⠃⠀⠈⠁⠀⠀⠀⠰⠟⠉⠀⠃⠉⠀⠀⠀⠀⠀⠸⠷⠃⠀⠛⠀⠀⠀⠀⠛⠿⠟⠛⠊⠛⠂
⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⡄⠀⠀⠀⢠⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⡀⡀⣀⣐⣐⣒⣀⣀⣀⠀⠀⣸⣿⣿⣛⣿⣞⣵⣇⠀⠀⣠⢏⣚⠘⠆⡿⣩⠅⠀⠀⠀⠀⠚⠃⠛⠃
⠀⠀⠀⠀⢻⢽⠿⠙⢯⢽⣋⣏⡏⠀⠀⠉⠉⠩⠉⠉⠉⠉⠉⠀⠈⢁⣐⣀⣉⣼⣿⣷⡟⠀⠀⢰⢶⢶⣶⣶⢲⣶
⠀⠀⠀⠀⠿⠾⠿⠷⠿⠾⠿⠾⠷⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⢠⣧⣇⣿⣽⣿⣷⠄⠀⠀⠸⠿⠿⠷⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣰⣶⢾⣿⠟⠿⠟⡀⠀⠀⠀⠀⠀⣀⠤⡴⠖⠒⡶⠖⢢⠀⠀⠀⠀⡘⠿⠻⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⣴⣦⣶⣶⣾⣿⣿⡇⠀⠀⢀⡔⢲⡉⢀⡆⡀⠼⠳⠖⠾⡀⠀⠀⠐⣿⣿⣷⣶⣶⣴⣦
⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣗⣶⣶⣾⣤⡄⣧⣌⣧⣫⣀⣀⡀⠀⠸⣶⣶⡒⣿⣿⣿⣿⣿⣿⣿⣥⣄
⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢿⠛⠟⢻⣿⠟⠿⠛⢻⡆⠀⠀⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⠂⠀⢸⠁⠀⠀⠀⠘⠀⣀⠜⠁⠀⠐⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⠁⠀⠀⠸⡄⠀⣀⣀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⣹⣿⣿⣿⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣻⣷⠀⠀⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⠀⠈⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠰⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⣟⣶⣶⣶⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡿⣿⣿⣄⠀⣠⢤⣠⣿⣿⣿⣿⣠⡤⣄⠀⣼⢫⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡈⢻⡝⣿⣿⡞⡿⠶⠛⢫⡝⠉⢩⠛⠶⢿⠟⣣⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⢾⣧⢨⡅⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠲⠉⠻⢻⡶⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡦⢥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢤⣶⣤⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠥⠶⠏⠳⢦⡄⢀⠁⠀⠀⠀⠀⠀⠀⠀⠘⣧⣞⠙⠉
⠀⠀⠀⠀⠀⠉⣽⣯⣭⣥⡍⠞⠀⠀⠀⠀⠀⠀⢀⡠⠀⢄⡄⣷⣾⠀⡥⠀⢠⠀⠀⠀⡄⠀⠀⢠⠶⢩⣭⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠿⠿⠿⣿⣇⣄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠃⠿⠿⠀⠆⠀⠘⠀⠀⠀⠃⠀⠀⠘⣠⣸⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⡾⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⡚⢦⣤⣼⠴⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢧
⠀⠀⠀⠀⠀⠀⠸⠿⠟⠛⠿⠗⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠘⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠿⡟⢘⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⣬⡿⠷⢴⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⣿⣿⢧⣷⠶⣤⣜⣃⣀⣘⣤⠶⣶⣦⡹⣿⣿⣆⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣵⣿⣿⠏⠀⠙⠚⠋⣿⣿⣿⣿⠙⠓⠋⠀⢻⡜⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⣯⢿⠿⠿⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈

⠀⠀⠀⠀⠀⠄⠀⠀⡠⠀⠠⡔⠀⠀⣾⠃⠁⡀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⢐⣷⣦⠀⠏⠀⠀⡧⠃⠀⠃
⠀⠀⠀⠀⠀⠞⠁⠀⠀⠒⣺⣿⡿⠀⠀⠀⠸⠁⠞⢀⡅
⠀⠀⠀⠀⡔⠀⠀⠀⣤⣾⠋⣡⣦⣤⡶⠴⠛⠀⣐⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡄
⠀⠀⠀⡀⠀⠀⠀⠼⠛⠻⣿⣿⣷⠶⠤⡤⡦⠀⡤⣀⠈⠂⢠⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠇⠘⡠⠶
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠰⢡⣿⠻⠓⠀⠀⠀⠀⠀⣚⠗⣼⠆⠈⣠⣴⡶⠶⠶⠛⠛⢩⣍⣤⣴⡶⢸⡟⢻⡇
⠀⠀⠀⠀⠉⠲⡖⠚⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡉⠈⣁⡄⢨⡆⢰⡶⠟⠛⣿⠀⣿⡇⣿⣄⡄⢸⣇⣼⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣸⢿⣋⣀⣀⣀⣀⡠⠔⠚⠃⠀⣿⣷⣸⡇⢸⣧⣤⠀⢿⣧⣿⠀⣿⣋⣁⢸⡏⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠋⠉⠉⠉⠀⠀⠀⢀⡄⠀⣿⠸⣿⡇⢸⣧⣤⡄⠸⣿⣇⠀⢻⡟⢩⣌⣷⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠤⠤⠀⠐⠒⠂⠉⢽⡇⠀⢿⣀⡙⣣⣼⣏⢁⣶⢺⡟⠋⠀⢸⡇⢸⣿⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡟⢉⣋⣿⠙⣿⣸⡇⢸⡿⠇⠀⢸⣇⣸⡟⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣀⣀⣀⣀⣀⣴⠶⣟⢸⣧⢈⣿⣿⡆⢻⣿⠁⠸⠟⠛⠀⣀⠩⠭⠔⠒⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠛⢛⣋⣉⣥⠤⠶⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠒⠒⠒⠒⠒⠋⠉⠘⡟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡤⠀⡀⠐⡈⡉⠤⠄⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠭⢑⡑⠧⠘⢀⠞⠁⠀⢀⣤⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣁⣀⡀⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⢡⠔⠂⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠔⠊⢉⡀⠀⢀⠠⠐⢈⡁⠄⠤⠤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢔⢞⡉⢠⠖⢁⠤⠊⠁⠠⠐⢀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠁⠀⢀⠷⢅⡐⠀⢸⡇⠴⠊⠙⠒⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠨⠑⠀⠀⠀⠁⠤⡴⠙⠂⠉⠉⠀⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠘⠀⡇⠀⠀⠀⡀⣈⠀⢀⣀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠠⡀⡃⠀⢀⡾⠉⠉⢀⠎⠀⠈⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡤⣾⡿⡀⠨⠃⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠰⠉⣴⠋⠀⠙⠢⠄⠊⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠈⠉⠈⠉⢀⡄⢀⠄⠀⠐⠒⠃⠀⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⢀⠄⠂⠉⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡘⢷⣤⣀⠌⠀⠀⠒⠂⢤⠆
⠀⠀⠀⠀⠀⠀⢠⠤⣀⡱⡆⠹⣉⠒⠠⠤⠄⣤⠜
⠀⠀⠀⠀⠀⠀⠎⢠⠏⢩⢧⡀⠘⠝⠁⣎⠉⢽⠋
⠀⠀⠀⠀⠀⣸⢦⣴⣀⠔⠋⠳⠄⢈⠀⠈⠁⠁
⠀⠀⠀⠀⣴⠉⢈⡾⠍⡲⡶⢶⣤⢷⣄
⠀⠀⢀⣤⣴⣿⣷⣷⣶⣿⣶⣚⣋⣅⡀⢙⣿⣿⣷⣶⣶⣤⣤
⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄
⠀⠀⠀⠀⠀⠐⡇⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡆
⠀⠀⢠⣀⢐⠁⠁⠀⠀⡱⢆⠘⡷⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠰⠶⠶⢆⠀⡶⡁⠀⠀⠁⠉⣂⣀⡄
⠀⠀⠀⠀⠀⢁⡇⠀⠀⠁⠈⢂⠑⠤⡀⠀⠀⠀⠀⢀⠠⢀⠀⠀⠀⠀⠀⢀⠔⠀⡜⠀⠀⠀⠀⣇⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠢⢄⠈⠀⠂⡀⠀⠀⠀⠀⡁⠀⢀⠔⠊⠁⡠⠈⠀⠀⠐⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠈⠑⠂⠀⠀⠓⠈⠁⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠀⠀⠀⠀⠀⠀⠀⢰⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢀⠖⠄⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠊⠀⠈⢄⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠐⠁⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⠁⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠆⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠊⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠂⡄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠒⠛⠢⣄
⠀⠀⠀⠀⢀⣠⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⢀⡞⠉⢀⢰⣶⣠⡀⠀⠀⡰⢅⠀⠀⢀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⣼⠀⠀⠀⠀⠀⢙⣿⣀⣤⣶⣀⠲⡠⠁⣠⣢⠤⠀⠀⠀⠀⠘⠳⢦⣄
⠀⠀⠘⣄⠀⠀⠐⠋⠋⠉⠉⣙⣻⣿⡷⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⠶⣄
⠀⠀⢀⡞⠱⠦⠤⠒⠊⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠝⠳⡄
⠀⡰⡯⠐⠲⣆⠀⠀⠀⠾⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢰⡄⠀⢀⡃⠒⠀⠀⠀⣈⣴⡶⠶⠶⠾⢤⡄⣠⡤⣴⢂⠠⠲⠆⢀⠀⠀⠀⠀⠀⠀⠃⠠⡌⢳⡶⠾⠟⠒⠦⠴⢿⡓⣦⣄⣀
⠀⠙⣺⠛⠳⠶⢒⣋⣉⣉⣀⣀⢀⣤⣴⠿⣿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠘⣷⣆⢸⠀⠀⠀⠬⢷⠁⠍⠏⠉⠓⠲⠦⢤⣤⣤
⠀⢀⣇⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⡔⠀⠘⣉⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣋⢸⠀⠀⠀⢀⣸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈
⠀⠀⠻⣧⣸⣠⣄⣀⢀⣐⠀⡉⠠⣩⣴⡼⠟⢫⣤⡙⢿⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡧
⠀⠀⠀⠈⢹⡋⠛⠛⠛⠛⠒⠛⠛⠛⢩⠀⠀⣼⡯⠔⠉⠉⠓⠆⣤⣶⣤⣀⡀⠀⠄⢄⡀⢀⠀⠀⠀⡞⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠘⢷⣦⣀⡀⡀⠀⠀⣄⣀⣷⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠰⠀⠀⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠉⠉⠁⠈⠙⠿⢼⣐⡜⣁⢀⠀⠀⠀⠀⠀⠀⠉⠀⠁⣠⣀⠀⠀⢠⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠚⠿⢧⣤⣥⣶⠾⠶⠛⠛⢶⣙⡀⡏⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⠀⠀⠀⠀⠀⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠃⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢢⣄⣀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⣿⡟⡇⡀⡄⠀⠂⠀⠂⠀⡐⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣱⣹⡡⡐⣐⡀⡀⢀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣵⣿⣿⣿⣟⡙⠐⢡⢃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠾⠮⢼⣔⣐⣃⣩⡄

⠀⠀⠀⠀⢀⢰⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣆⣀⡆⠃⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠐⢻⡟⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⣦⡀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⢾⡷⡴⠂
⠀⠀⠀⠀⠀⣞⡷⠀⠀⠀⠀⠀⢀⣯⣍⠁⠀⣻⣇⠀⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⠀⢀⣀⡿⣇⢣
⠀⠀⠀⠀⡀⠘⠃⢀⠀⠀⠀⠀⠘⢿⡿⠃⠀⢏⠉⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⢠⡄⢠⣼⣼⣦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⣻⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡟⠀⠀⠀⠀⠀⠀⡞⣿⡦⠓⠀⠀⠀⠀⠀⠀⣠⡾⣷⡄
⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⣰⠿⣬⠁⠀⠀⠀⠀⠀⠀⠓⣿⡄⠀⠀⠀⠀⠀⢀⡼⢻⡄⠸⣿⡀
⠀⠀⠀⠀⠰⠁⢸⠀⠀⠀⠀⠀⠀⠞⠁⠀⠈⠳⡄⠀⠀⠀⠀⠀⠰⠁⡇⠀⠀⠀⠀⠀⠏⠀⠞⠀⠀⠻⠇

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣶⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢈⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⠐⣿⠂⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⣤⣾⣿⡇⠀⠀⠀⠀⠀⣀⣤⠟⠻⢿⠀⠀⠀⠀⠀⠀⠼⣿⠄⠀⠀⠀⠀⠀⣶⣾⣷⣶⣶⣦
⠀⠀⠀⠀⠘⠿⠿⠁⠀⠀⠀⠀⠾⠉⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢶⠠⢠⡄⡄⡦⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠙⢾⡗⠋⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠀⠀⠁
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡄⠀⠀⠀⠀⠀⠀⠀⡎⠋⡇
⠀⠀⠀⠀⠀⡃⠃⠀⠀⠀⠀⠀⠀⣸⠀⠀⠓⠂⡄⠀⠀⠀⠀⠀⡞⠀⣇⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠀⠙⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡄⠀⠙⢿⣷⣦⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠙⠻⣾⠟⠻⡿⢿⣷⡈⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣄⡀⢸⠗⠂⠀⣜⠛⢇⣀⠘⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢶⠀⣠⢟⣴⣿⠟⠁⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣵⣿⠋⠁⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠉⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠀⠀⠈⢿⠀⢠⡄⠀⠀⠀⠐⣆⠀⠀⠀⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡃⠀⠀⠀⢀⠁⣿⣿⡄⠀⠀⠀⣿⣇⠀⠀⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇⠀⠀⠀⠘⣷⡜⢿⣿⡀⠀⠀⣿⣿⠀⠀⠙⠉⠉⠉⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⣭⣝⣈⢿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⣿⣿⣿⡜⠇⠀⢰⣿⣿⠐⣿⣿⡇⣶⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠛⠛⠛⠛⢸⣿⣿⣿⡇⣦⠀⠈⠁⠀⡄⣿⣿⣇⣿⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢇⣿⡇⠀⠀⢸⡇⣿⣿⢸⡇⠀⠀⠈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠀⢀⣀⠀⠀⢸⣿⣿⣿⢸⡟⠀⠀⢀⣿⡇⣿⣿⣸⡇⠀⠀⠀⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇⠀⠀⠀⢸⣿⣷⡦⢸⣿⣿⡇⡾⠁⠀⢀⣾⣿⢧⣿⡇⣿⢁⣠⣴⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⠃⣾⣿⣿⡇⠁⠀⣠⣾⣿⡏⣾⣿⣧⣿⠈⢻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏⠀⠀⠀⢀⣼⣿⣿⠃⠀⢿⣿⣿⣴⣶⠆⣨⣭⣭⣼⣿⣿⢸⡟⠀⠀⠹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⡿⠁⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠸⣿⣿⡈⠛⠛⠿⠿⣿⣿⠼⠇⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠻⢿⣷⣶⣤⣝⡋⠀⠀⣀⣴⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⡄⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⣀⣤⣦⣤⣤⡀
⢰⣶⣶⣶⣶⣶⣶⣶⣿⣋⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠚⠿⠿⣿⣿⣿⣿⣆
⣾⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠋⠛⠙⠛⠛⠀⠀⠀⠀⠀⢻⣿⣷⣄⠀⠀⠀⠀⠀⠈⠙⠿⣿⣧⡀
⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠙⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠀⠀⠙⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠙⠄
⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⣠⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠀⠙⢿⣿⣿⣿⣷⣦⡀⠹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⠻⣿⣿⣿⡿⠃⢹⣿⣿⣿
⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠛⠁⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣶⣾⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣶⣿⣿⣿⣿⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠁⠈⠙⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠿⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣤⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⢿⣿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣄⣀⣀⣀⣁⣄⣀⣠⣀⣤⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠸⠿⠿⠿⠿⠿⠿⠿⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⢀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣽⣿⣷⣤⡎⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣏⢹⣼⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣴⣿⣿⣿⣿⠟⠛⣸⡿⠛⠙⠻⢿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠶⠶⢤⣀⠀⠀⠀⢠⣾⣷⣿⣿⣿⣿⡿⠛⠁⣤⣶⡉⣶⣄⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⡡⠀⠀⡰⠋⠀⠀⠀⣈⣭⠓⢒⣾⠏⢉⡿⠛⡋⠁⠀⢠⣾⣿⡇⠉⣦⣀⣱⣀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⡈⠀⠀⣰⡔⠀⠀⠀⠀⠀⠁⠐⠋⠁⠀⠜⠀⡞⠀⠀⠔⢋⡀⢸⣇⣴⣯⡿⣏⠃⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⢸⡄⢀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣴⡟⠀⣿⡟⠛⢦⣏⠈⢀
⠀⠀⠀⠀⠀⠒⠶⣾⣿⣿⣿⣿⠀⣇⢸⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⠀⠁⠀⣼⡟⢀⣼⠏⠀⠀⠀⠙⣦⣛⣷⡞
⠀⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⣧⡈⠀⣿⣧⠈⠻⢦⡐⢤⣄⣠⣾⠃⠀⣧⠀⠀⠀⣼⡿⢡⡟⢁⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠙⠛⠋⠉⠀⠁⠁⠘⣧⢠⠾⠿⢷⣄⠀⠈⠑⠈⠉⣿⠀⣠⡞⠳⣤⡀⠹⠵⠋⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣱⣶⠇⠈⢳⣶⣶⣤⣤⣿⣾⢿⡇⣰⡿⠧⢀⣐⡺⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢰⣿⠋⠀⠀⡼⡿⢻⠋⠙⢻⠁⠀⠹⡿⠷⠻⢿⣟⠓⢤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣻⡇⠀⠀⠀⠹⣼⢿⡀⠀⠘⣧⡄⠐⡇⠀⠀⠀⠉⠻⣆⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠈⠻⡹⣄⡀⠘⣿⡄⢃⠀⠀⠀⠀⠀⠘⢿⡦⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡽⣆⠀⠀⠀⠀⠀⠙⣿⣷⡀⢸⡅⠈⡆⠀⠀⠀⠀⠀⠀⠹⡜⣦
⠀⠀⠀⠀⠀⠀⠉⠁⢀⡀⠀⠀⠀⠀⠀⢷⣿⣇⠀⠀⠀⠀⠀⢹⣿⠛⣸⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⢻⡈⣷
⠀⠀⠀⠀⠈⠙⠓⠀⣈⣛⠛⠛⣓⠒⠒⣾⡟⠛⡆⠀⠀⠀⠀⢠⡾⣏⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠙⠊⠉⠛⠁⠀⠀⠀⠀⢸⣿⠟⠉⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠘⠶⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠙⠛⠛⠓⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣤⣤⣀⠛⠿⢿⣷⣤⡀⠀⠀⣿⡏⠀⣰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⣉⣉⣉⠉⠉⠛⠛⠿⢿⣶⣤⡈⠻⣷⡄⠀⣿⣧⣼⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⠿⠿⠿⠿⠿⠿⠿⣷⣶⣦⣄⡉⠻⣿⣦⣼⣿⣿⡿⠟⠛⠛⠿⢿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠉⠙⣿⣷⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣤⡀
⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠿⣿⡿⠛⠛⠻⢿⣷⣾⡿⠟⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣦⡀
⠀⠀⢰⣿⣋⣩⣽⣿⡿⠿⠃⠀⣠⣴⡿⠛⠉⢀⣴⣿⠟⠁⠀⠀⢀⣿⡿⠉⠀⠀⠀⠀⠀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⢀⣾⠟⠁⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⣤⡀⣤⣄⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⣶⠶⠾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⢹⣿⠃⠀⠀⠲⣮⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡿⠛⠛⠋⠀⠀⠀⢀⣴⣾⣷⠘⣿⣆⠀⠀⠀⠀⠈⠀⠀⣶⣶⣌⠻⣯⡙⢿⣿⣷⣄⠀⠀⠀⠙⠿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⢰⣟⣡⣾⠇⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠙⢷⣄⠻⣿⣿⣷⣄⠀⠀⠀⠀⠉⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠀⣼⣿⠃⢀⣠⣄⡀⠀⠀⠘⠻⠿⠋⠀⠀⠀⠀⠻⣿⣦⣄⣀⠀⠀⠀⠹⣿⣿⣦⠈⠻⣧⠈⠋⢹⣿⡆⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⣠⣤⡶⢾⣿⣿⡿⠁⢠⣿⡿⠀⠉⠉⠙⠿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣶⣄⠘⣿⣿⠃⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣾⣿⠃
⠀⠀⣾⣿⣁⣤⣾⡿⠋⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⡶⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣶⡀⠈⢹⣿⠀⠘⣿⡀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣸⣿⡏
⠀⠀⠻⠿⠿⠟⠋⠀⠀⠀⠀⣼⣿⠁⣀⣀⡀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⠀⠀⢹⣷⠀⠀⠀⠀⢸⣿⣧⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠻⣿⡿⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⡀⠀⠈⣿⡄⠀⠀⠀⢸⣿⣿⣀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢸⣿⣇⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠀⠀⠀⠀⠀⠉⢫⣥⣄⡀⣹⣯⡀⠀⠀⢸⣿⣿⣿⠟⠋
⠀⠀⠀⠀⣠⣴⣾⣿⡿⠀⠀⠀⣿⣿⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣇⠀⠀⠈⣿⣿⠁
⠀⠀⣰⣿⣋⣰⣿⠟⠀⠀⠀⠀⠘⣿⣧⠀⣰⣿⠏⠀⠀⣀⣤⣶⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡹⣿⡄⠀⠀⢻⣿⡀
⠀⠀⠙⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣏⣠⣶⡿⠟⠛⠉⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣿⣿⣆⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠟⠋⠁⠀⢴⣤⣤⣀⡀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡿⠛⣿⣦⠀⠀⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣄⠀⠀⠉⠙⠻⢷⣶⡄⠘⢿⠄⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠋⠀⠀⠈⢿⣧⠀⠀⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣤⣀⣀⠀⠈⠁⠀⠀⠀⠀⢀⣠⣤⣶⣿⠿⠛⠁⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣶⣶⣶⣿⣿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣒⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠛⠻⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡏⠀⠀⠀⠀⠉⠛⣳⣦⣤⣄⠀⠀⠀⣀⣤⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠇⠀⠀⠐⠿⠿⣿⣿⣿⣿⠿⠟⣰⣾⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣟⠿⢿⣷⡄⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⢿⠉⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⣌⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣄⣠⣿⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣬⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠻⣷⣤⡀⠀⠀⠀⠀⠀⠱⢶⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⠀⠀⠈⢿⣿⣶⣤⣀⡀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⣿⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢻⡄⠀⠀⣰⠟⠈⠻⢿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠃⠀⢠⡟⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⠛⠶⣤⣀
⠀⠀⠀⢀⣿⣿⠿⠿⠛⠻⠿⠁⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠤⠄⠀⠀⠐⠒⠒⠛⠛⠛⠂⠉⠉
⠀⠀⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠚⠓⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣥⢲⠴⠶⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠾⢻⢾⣾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⠦⠤⠴⠤⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠲⠾⢶⠲⠆⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠶⠾⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣦⢰⢢⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠠⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣒⠆⠀⠀⠀⢑⢒⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠄⠀⠀⠀⠀⠀⠢⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢈⢡⢸⠖⣓⣶⡈⢁⡀⡀⢀⡤⡞⠻⡦⠲⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠠⠸⡿⢿⠹⢿⠻⠹⠿⠿⠿⠿⡟⢿⠇⠠⢒⡔⠀⡰⠹⠷⡿⠿⠾⠾⢾⡷⠇⠠⠤⠄
⠀⠀⠀⠀⠀⠀⢠⣶⣺⣶⣶⢲⢶⣶⣷⣶⣶⣿⢸⢼⡷⣇⡇⣟⢻⢼⠼⢿⡿⢧⢤⠤⣦⢤⣦⡄⣬⡥⠐⠒⠒⠂
⠀⠀⠀⠀⠒⠒⠒⠶⠀⠂⠶⠆⠲⠒⠶⠶⠶⠠⠶⠖⠶⠶⠦⠆⠶⠶⠲⠶⠒⠈⠰⠶⠖⠰⠶⠠⠶⠖⠶⠆

⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⢠⠶⠾⠉⠉⠉⠷⢶⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⣴⠆⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠿⣿⠖⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢻⡿⠀⠀⠀⣠⠴⠿⢤⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠏⠀⠀⢘⣇⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠘⠁⠀⠀⡞⠁⠀⣷⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣴⠞⢋⡍⠛⢦⡀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠺⣇⠀⠀⠛⠒⠂⣸
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣸⠃⠀⢨⣇⣀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣧⡀⠀⠉⠉⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣶⣶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢛⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠘⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠛⣿⣿⡿⠟⣛⣉⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⣼⣿⡟⣴⣿⣿⠛⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡿⢋⣥⣶⣶⣦⣄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⡀⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢱⣿⣿⣿⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⢸⣿⣿⣿⣬⣭⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠟⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⠻⠛⡟⣻⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠔⠐⠄⡠⠤⠤⣠⠈⠀⠀⣾⠇⠈⢀⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⣼⣆⠀⠀⡿⠀⠀⢰⡰⠁⢰
⠀⠀⠀⠀⠀⠀⢀⣤⠴⠛⠁⢀⣾⣿⣧⠀⠀⠀⠀⡿⠁⡀⠈⡀
⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠚⢋⣿⣿⡟⠀⣀⠀⠐⠁⡜⠃⣠
⠀⠀⠀⠀⠀⡈⠀⠀⠀⢀⣴⡿⠋⣁⡀⢀⣇⣠⡾⠃⠠⠜⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠀⠀⠀⢠⣟⣿⣦⣶⣿⠛⠻⠭⠭⠀⣀⠒⠛⠄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⢀⡟⢀
⠀⠀⠀⢠⡁⠀⠀⢰⠟⠉⠉⣿⣿⣿⣿⠿⢷⢶⡶⠒⣢⢤⣄⠈⢀⠰⣦⣤⣤⣤⣤⣤⣤⡤⠤⠄⣀⣀⡀⠀⠀⠀⠘⠃⠈⡴⠟⠃
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠏⣸⡟⣿⠆⠐⠀⠀⠊⠀⠠⠟⢷⢸⠄⠈⠀⣠⣤⣶⣶⡶⠾⠟⢛⣉⣁⣤⣤⡦⣾⡿⢿⣷
⠀⠀⠀⠀⠱⢤⣀⣀⣠⣄⠤⠖⠛⠉⠀⠤⠐⠀⠀⠀⠠⠐⡇⠴⠟⠀⠀⠚⠋⣉⣥⣤⢴⣶⠀⣼⡿⣿⡟⠉⠁⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠻⣋⣉⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣶⡆⢸⣿⢸⣿⠋⠉⠸⣿⠀⣿⡇⣿⣷⣶⡆⣿⣷⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⣾⣿⠄⠀⠀⠀⢀⣀⡤⠖⠟⠀⢸⣿⣷⢸⣿⢸⣿⣤⣄⠀⣿⣧⣿⠃⣿⡏⢉⡁⣿⡏⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣴⣿⠛⠛⠛⠛⠉⠁⠀⠀⠤⠀⢸⣿⢻⣿⣿⢸⣿⠉⠁⠀⢹⣿⡿⠀⣿⣿⠿⢏⡛⣣⣼⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⠀⢸⣿⠈⣿⣿⢰⣿⣿⠿⡀⣘⣯⣥⡄⢰⣿⠀⢸⣇⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠲⠶⠖⠒⠒⠉⠉⠉⠱⣿⠀⠸⢿⣀⡈⢻⣤⣶⡀⢸⡿⢿⡏⠉⠀⢸⣿⠀⢸⣿⣿⣇⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠀⢰⡿⠛⠿⢻⡇⣿⡇⣼⡇⣿⣷⣷⠀⢸⣿⠀⣸⡟⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡄⢸⡇⢴⣶⣾⡇⢸⣿⣿⠀⣿⣇⣤⡄⠀⠿⣷⠟⠁⣛⣃⣤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⣤⣄⣀⣀⣈⣤⣾⠟⢿⡇⢸⣇⢀⣿⢻⡇⠘⣿⡿⠀⠛⠛⠋⠁⣀⠤⠶⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢻⡇⠘⠿⠿⠋⠈⣁⣠⣤⡴⠖⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣤⣄⣀⣀⣀⣠⣤⠴⠞⢧⣴⣶⠶⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⠠⠉⠉⠉⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠾⠶⢘⣿⣀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⡠⣦⢀⣸⣿⣧⡀⠀⠀⢀⡴⠾⠗⠒⢳⣦
⠀⠀⠀⠐⢶⡄⠀⢸⣿⣿⣧⡀⠀⢠⣤⣤⣿⣿⣿⠶⣤⠀⠀⢠⡞⢋⣿⠉⢷⡄⠀⠀⢸⣿⣿⣾⣿⠛⢿⡶⠄⠀⢈⡿⣰⣺⡆⢸⡇
⠀⠀⠀⠀⣾⣵⠃⣿⢯⣅⡀⠀⠀⠀⠀⢘⢿⣿⣿⣀⡀⠀⠀⠈⣷⠟⠁⢀⣾⠇⠀⠀⣼⠿⠿⢸⣿⣿⣿⣧⠀⠀⢸⡇⠻⠿⠇⢸⣿
⠀⠀⠀⠀⠻⠛⠛⠁⠀⠙⠿⠆⠀⠀⠀⠿⢷⣭⣽⡯⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠛⠁⠀⣿⠀⠀⠀⠸⠇⠀⠀⠰⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⠒⠒⠒⠛⠃⠈⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠈⠙⡇⢀⣠⣤⣤⣤⣤⣴⡶⠶⢶⣦⠄⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣶⣿⣶⣶⠾⠿⡇⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠋⠁⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠘⢆⣶⡄⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⠴⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠀⠀⠀⠀⠀⠀⠘⠃⢸⡆⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢠⡏⠀⣤⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠛⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠘⣧⣀⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡶⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⣃
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⣇⣼⠏⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠘⠛⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠓⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡷⢦⣄⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣧⡀⢀⣀⣀⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠙⠻⣷⣶⣤⣤⣀⣀⡀⠀⠀⠀⣀⣀⣀⣤⣴⣾⣿⣿⡿⠋⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⣀⣠⣀⠀⢿⡛⢿⣿⣿⡿⣿⣿⣿⢿⣿⣿⠿⠿⠛⠛⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⡞⠉⠀⠼⡇⠀⠙⠿⣧⣴⣟⡩⠴⠶⠚⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀⠀⠀⣈⣷⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠈⠳⣤⣤⣤⣿⡇⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡄⠀⠀⢸⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⢹⣿⠟⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣆⠰⠚⢧⡍⠁⢙⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣀⠀⠀⣙⡋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣩⣆⣤⣾⡡⠖⣩⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠙⠛⠿⣿⣿⣶⣶⣶⣶⣶⠶⠿⠛⢻⣿⣿⣿⡿⠃⠈⠋⣠⠴⠋⢀⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠧⣤⣾⣿⣿⠿⠿⠿⣿⣿⣷⣄⡤⠿⣿⣿⣿⣧⣀⡴⠚⠁⠀⢀⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠴⠿⠛⠁⠀⠀⠀⠀⠈⠙⠿⣿⣷⣦⣿⡿⠟⠁⠙⢦⣄⣀⣠⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⠐⠒⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠠⠐⠂⠀⠀⡂⠀⠐⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠾⠦⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡢⢦⠦⠄⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⠀⠀⠀⠀⠀⣀⣾
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⣀⠀⢀⣀⣀⣀⣠⣁⣻⣀⠀⣘⣿⣦⣄⡤⠂⠶⣔⣰⡶⠿⣿⢿⠿⠥⠤⠄⠀⢠⠀⢽
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⡅⡀⠐⣲⣴⠿⠟⠿⢿⣻⣟⣿⠏⠉⠷⠙⠙⠆⣰⠞⠛⠐⠂⠈⠋⠀⠠⠔⢻⣽⠋⠑⡄⠈⠀⠀⠀⠀⠀⠈⠀⢿
⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⡷⠘⠀⢠⠖⠁⠀⠠⣮⡖⠋⠁⠀⠁⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⣿⠀⠀⢿⠀⠀⠀⠀⡙⠀⠀⠀⢀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣵⠦⣀⠈⢇⠀⠀⡀⢀⠂⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠀⠑⠒⠶⠦⠿⠿⠉⠙⠻⠿⢏⣡⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⠀⢈⠉⠚⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠠⠐⠂⠀⠸⠆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡤⠇⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⣁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠶⠶⠦⣄⠀⠀⠀⠀⠀⣽⡄⡆⠀⠀⠀⠀⢀⣾⡟⣬⣾⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⠳⣄⡀⠈⠐⠀⡑⠦⣘⡧⠀⠀⠀⠀⣀⣸⡿⠀⣼⡇⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡀⠀⠀⠻⣦⡀⠀⢄⠁⠀⠙⢦⡄⠀⠀⠀⡏⠁⠀⣸⡇⠘⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⠠⢅⠀⠀⠀⢩⡴⡀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠇⠀⠀⢸⣇⠀⠀⡇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡓⣄⠣⡀⠀⠀⢷⣶⡀⠀⠀⠀⠈⠀⣆⠀⠀⠀⠀⠀⠀⠣⡀⠀⢧⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣌⠢⣀⠀⠙⢿⣦⣄⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⣦⠘⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣮⣇⠀⠀⠻⣟⢿⡗⡢⠤⣄⡠⣔⢠⣤⣀⡀⠄⢸⠀⠀⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢨⠀⠀⠐⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠈⠀⠀⠀⠣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠐⠀⠊⠀⠈⠀⠀⢀⣀⡀⣠⢀⢀⠀⠀⠀⠀⠀⠀⡀⠨⠀⠀⠀⠀⠘⡀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠛⠛⠳⢦⡄
⠀⠀⠀⢀⣠⡶⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣿⡆
⣼⠃⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠛⠛⠋⠉⠉⠀⠸⣇
⣿⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢿⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣤⠀⠀⠀⢸⡆⢸⡆
⢸⡇⠀⠀⠀⣀⣤⣤⠿⠀⠀⠀⠀⠹⠂⠀⠀⠈⠁⠘⣧
⠀⢷⡀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢿⡀⠀⠀⠀⢀⣠⡴⠶⠞⠛⠶⠶⣤⡀
⠀⠘⢷⡀⠈⠷⣤⣄⠀⠀⠀⠀⢀⣤⡴⠞⠛⢉⣿⠀⢸⡇⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀
⠀⠀⠀⠙⠢⣤⣤⣿⡀⠀⠀⠀⠀⠹⢦⣤⣤⠞⠃⠀⣿⠀⠀⣼⠃⠀⠀⢀⣤⠶⠶⢦⣄⠀⠀⠈⢿⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⢀⡟⠀⠀⠀⣾⠁⠀⠀⠀⢻⡆⠀⠀⢸⡇
⠀⠀⣠⠀⠀⠀⠀⠀⣠⠿⠳⢦⣤⣤⣤⣤⡴⠾⢯⡀⠀⠀⠀⣿⠀⠀⠀⢻⣄⠀⠀⣀⡾⠁⠀⠀⢸⡇
⠀⣼⠋⠀⠀⠀⢠⡾⠁⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠙⣦⡀⠀⠹⣆⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⣠⡟⠀⠀⠀⣸
⢰⡏⠀⠀⠀⢠⡟⠀⠀⠀⣠⡾⠛⠉⠉⠉⠙⠷⣤⡀⠘⣧⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠉
⣼⠁⠀⠀⠀⢸⡇⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣿⡀⠀⠀⠀⠈⢹⡟⠛⠛⠛⢻⡍
⣿⠀⠀⠀⠀⢸⡇⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⣨⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠸⣇
⠉⠀⠀⠀⠀⢸⡇⠀⠀⠘⣧⡀⠀⠀⠀⢀⣴⠏⠀⠀⣴⠏⠁⠈⠉⠙⢷⣼⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠻⢦⣄⣠⡾⠁⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⣰⠿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠈⠙⢷⣶⣤⣀⠀⠀⠀⢰⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⡇⠈⠉⠛⠳⠶⣼⣧⣀⣤⠾⠃
⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠶⠶⠶⢾⡃
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣤⣤⣤⣤⣤⣼⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⢠⣴⣮⣿⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣾⣯⣶⣤
⠀⠀⠀⡿⡟⠟⠙⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠘⠙⠟⡿⡆
⠀⠀⠀⡇⠀⠀⠀⢸⣿⣯⣭⠭⠭⠭⠿⠿⠿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠺⠿⠿⠯⠭⠭⢭⣭⣿⣿⠀⠀⠀⠀⡇
⠀⠀⠀⢱⢠⢀⡀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⣀⢀⢰⠁
⠀⠀⠀⠈⢿⠿⣿⣿⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⡿⢿⠏
⠀⠀⠀⠀⠀⠉⠁⠑⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠁⠉⠁

⠀⠀⠀⠀⠶⢶⡶⠶⠀⣶⠶⢶⣦⠀⢰⣶⠀⠀⢠⣶⣆⠀⠰⠶⣶⡶⠆⢰⡆⠀⠀⢰⡆⠀⣶⡆⠀⠀⣠⣶⠾⠷⣶⣄⠀⢰⣶⣄⠀⠀⣶⡆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣤⣼⠟⠀⢸⣿⠀⢀⣾⠏⢿⡆⠀⠀⣿⡆⠀⢸⣿⣶⣶⣾⡇⠀⣿⡇⠀⢠⣿⠁⠀⠀⠈⣿⡆⢸⣿⠻⣧⡀⣿⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠉⢿⣆⠀⢸⣿⠀⣼⡿⠓⠻⣿⡄⠀⣿⡇⠀⢸⡇⠀⠀⣸⡇⠀⣿⣇⣀⡀⢻⣧⣄⣠⣴⡿⠀⢸⣿⠀⠈⢿⣿⡇
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠉⠁⠈⠉⠈⠉⠀⠀⠀⠈⠁⠀⠉⠀⠀⠈⠁⠀⠀⠈⠁⠀⠉⠉⠉⠁⠀⠈⠉⠉⠁⠀⠀⠈⠉⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⠉⠉⠙⠳⢦⣀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠉⠉⠉⠉⠛⠲⣤⡀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠉⠉⠉⠙⠛⠦⣄
⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⢀⣀⠀⠈⠻⣆⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⢳⡄
⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠈⣷⠀⢰⠇⠀⠀⠀⠀⠀⣀⣤⣜⠛⠀⠀⠀⠸⡆⠀⣾⠁⠀⠀⠀⣠⡤⢤⣄⡛⠁⠀⡀⠀⢻⡀
⠀⠀⠀⢸⡇⠀⠈⠀⠁⠀⣁⣈⣤⣿⠀⠿⠂⠁⢸⡄⣿⠀⠀⠀⠀⠀⢾⡟⣥⠉⠓⠀⠀⠀⠀⣿⠠⡇⠀⠀⠀⠀⠃⣠⣿⠟⠙⠒⠋⠀⠀⢸⡇
⠀⠀⠀⠸⣇⠀⠀⠀⠈⠉⠁⠈⠉⠉⠀⠀⠀⠀⣼⠀⢻⡀⠀⡰⣿⣾⡂⢻⠉⢴⣿⣮⡂⠀⢀⡟⠀⣧⠀⠀⠀⢀⡴⠛⣻⠆⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠈⢷⡀⠀⠙⠟⠃⠀⠀⠐⠙⠟⠁⢀⡾⠁⠀⠸⣆⠀⣀⠊⠀⣈⣁⣀⣀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠻⢦⣀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠶⠖⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⡿⠋⢙⣻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣛⣻⠭⠡⢔⣭⡿⢉⣼⡧⣲⡀
⠀⠀⠀⠀⠀⠀⠀⣎⣴⣯⠉⠁⡀⣶⣶⠴⠀⢿⣿⣋⣻⣧⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣤⠙⠀⠀⣀⠀⠠⠐⣖⣺⣿⡄⠀⠐
⠀⠀⠀⠀⠀⢲⣮⣿⣿⣿⣿⠟⣀⡐⠮⢀⣤⣤⠀⠉⣿⣿⠕⡀⠀⠀⠀⠄
⠀⠀⠂⢠⡖⢩⠒⠚⡿⣿⣯⣤⣿⠱⣟⢿⡵⠖⠀⠐⠉⠸⠆⡃⠀⠁
⠀⠀⠀⢀⠉⡇⢀⠤⡆⠹⣷⠺⢿⣧⠀⠘⠓⠀⠀⣰⠂⢱⣖
⠀⠀⠀⠀⠘⢲⡧⢶⠃⠰⣿⡀⠀⣿⠁⢀⡖⢤⡀⠈⠀⡀⠹⢷⡄
⠀⠀⠀⠀⢀⡸⢧⡉⠲⡀⠈⢻⣦⣿⣿⣃⣤⡤⠍⠀⡰⠁⢸⠀⢷⠈⠲⠤⣀⡀
⠀⠀⠀⠀⠈⢑⡮⣻⣆⠘⢆⣀⡙⣧⡉⢠⠿⠂⠀⡠⠁⢠⡆⠀⢸⣇⡘⠀⠀⠉⠲⣄⡀
⠀⠀⠀⠀⠀⣾⡇⠈⢿⡄⠀⢰⢹⣿⠻⣦⣤⠤⠚⠁⠀⡾⡀⠀⢨⡥⡍⠂⠤⡄⠀⢈⣹⣦⡀
⠀⠀⠀⠀⢰⣿⡇⢀⡿⠀⠀⢠⠋⣇⠀⠹⣿⣦⡄⠀⣜⣡⡁⠀⢸⠛⠀⢀⠆⢠⠞⣉⢁⠀⠙⣆
⠀⠀⠀⢀⡿⡏⢧⣾⠁⠀⠀⡜⢀⠹⣧⡀⠘⣿⣿⣼⢀⢹⣷⡄⢸⠀⢀⠏⣰⣣⠊⢁⠎⠀⠀⣌⣆
⠀⠀⢀⡾⠁⢡⣾⠃⠀⠀⢠⢃⠘⡆⠈⢷⣇⣿⣿⡇⢸⣿⣿⡿⡞⢀⡞⢠⠓⠁⢠⠎⠀⠀⠀⣼⠸⡄
⠀⠀⣼⣤⣤⣿⠇⠀⠀⠀⡞⠈⣇⠸⡄⠈⠻⣿⣿⢡⠟⢿⡿⠀⠀⣼⠀⡞⢀⡴⢃⠀⠀⠀⢠⡏⠀⢷
⠀⢸⣇⣰⣿⡏⠀⠀⠀⢰⠁⣆⠹⡄⠹⣄⠀⢻⡏⣼⡇⣸⠃⠀⡇⡟⢀⡵⢋⡴⠁⠀⠀⠀⠉⠀⡾⠸⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⢤⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⣄
⠀⠀⠀⣴⣮⣿⠿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⢿⣯⣶⡄
⠀⠀⢸⠉⡇⢸⠀⣿⣿⣿⣿⣷⡀⠤⠤⠤⠐⠒⠒⠒⠒⠒⠒⠠⠤⠤⠄⣰⣿⣿⣿⣿⠇⢸⠀⡏⢹
⠀⠀⣸⠀⡇⢸⠀⢸⣿⡟⣧⣴⣶⠶⠿⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⠷⢶⣶⣤⡟⣿⣿⠀⢸⠀⡇⢸⡀
⠀⠀⢳⡆⢡⠀⡆⠈⣿⣿⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⡏⠀⡆⢠⠁⣾⠃
⠀⠀⠀⠱⡈⣆⣰⣠⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣰⣀⡎⡰⠁
⠀⠀⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣟⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠋⠐⢢⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⠘⠀⠉⢽⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠈⠀⠀⠊⠁⠀⠈⠁⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠒⠲⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠂⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⣄⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠠⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⡶⠄⠲⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠢⡀⠀⠀⠈⠃⠀⠀⢁⠀⣀⡀⠀⠀⠀⠆⠈⠙⠂⠀⠠⢼⡶⢄⡠⠂
⠀⢠⠖⠀⠀⠀⣀⣀⡠⢰⡬⡂⠘⠰⠀⠙⠀⠀⠀⠁⠀⠐⠀⢶⡋⠤
⠀⠘⡀⠀⠀⠌⣭⣿⣃⢸⡀⠁⠀⠀⠀⠀⢓⠀⡌⠀⠀⠀⢠⣼⠀⣦⡤⣶⠂⢄⣤
⢀⣠⣤⣤⣶⣷⣶⣾⣿⣿⣿⣦⣀⡀⢀⣀⣼⣿⣿⡄⠐⣢⠞⠻⠁⠀⣁⣀⣀⠉⠁⠃⠀⠀⢀⣄⣀
⠈⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣶⣶⣆⣼⣶⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁