Asteroid Emojis & Symbols

⠹⡖⠢⠄⣀⣀⠀⠀⣀
⠀⠈⣦⠀⠀⠀⠉⠑⠻⠗⢦⡀
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣄⡀⠀⣀
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢹⡓⠦⣀⠀⠀⠉⠓⠛⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢣⠀⠀⠙⠢⡴⠤⣀⡀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠈⠓⠦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣦⡀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣸⠄⠀⠀⠘⡗⠦⡀⠀⠀⠀⠀⠀⠈⠓⢤⡤⣀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠙⢄⠀⠀⠀⠈⢆⠈⠑⠦⣀⡀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡈⠑⠢⠏⠑⠲⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⠳⣄⠀⠀⠈⢦⠀⠀⠀⠉⠓⠟⠉⠒⠤⣤⢀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠈⠙⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⣞⠗⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⢀⣀⠬⠶⠤⠤⢤⣀⡀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠈⢦⡀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠀⠐⠒⠀⠒⠂⠄⠈⠑⠦⣀⡀⠈⠓⢴⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠱⡄⠀⠀⣠⡧⠀⠀⠀⠀⢀⠴⠋⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⡒⠀⡀⠈⠳⣄⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠘⣟⠂⠀⠑⣄⠀⠀⠀⡠⠀⠀⡠⠂⠀⡠⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⢦⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⢣⡀⠀⠈⢢⣀⠞⠁⠴⠊⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣉⣀⠄⠀⠀⢣⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠱⣄⠀⢀⡏⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠈⡆⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠓⣼⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⢱⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡎⠠⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⠉⠑⠀⠀⠈⠒⠴⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡬⠄⠀⡇⠀⠈⠁⠘⠦⠆⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡄⠀⡠⢄⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⠀⠐⠉⠉⠒⠄⠀⠈⠐⠋⣀⢀⠀⠀⠀⠀⡆⠀⣀⠀⠀⡰⠁⡰⠁⠀⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢸⡇⠘⡀⠀⢀⠀⡤⠀⡀⠀⠀⠀⠱⡀⠀⡠⠈⠉⠀⠉⠉⠀⠐⢄⡀⠀⡀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⣇⠀⣇⣰⠋⠉⣀⣄⣙⠦⠤⢄⣀⡜⠸⡀⠀⣈⠆⢀⠎⠑⠀⠀⠙⠚⠀⠀⡜⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢰⡀⠈⠁⠀⡎⠀⠀⠀⠉⠲⣄⠀⠀⠀⣈⣉⡁⠀⢪⣀⠴⡠⠒⢄⡀⠀⡜⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠑⢦⡀⠀⠑⣄⠀⠀⠀⠀⠈⠀⡰⠋⠀⠀⠈⠲⢄⠀⣐⠁⠀⠀⠁⡠⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠉⠢⡀⠈⢧⡀⠀⠀⢸⠀⢣⡀⠀⠀⠀⠀⡸⠀⠀⠉⠊⡠⠞⠁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡈⠳⢄⡁⠀⢀⡸⠀⠀⠹⣄⣀⣠⠀⠁⣀⠠⠔⠋⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠈⠓⠤⢄⣀⣀⣀⣀⣀⡤⠔⠊⠀⠀⠀⣀⠴⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣒⣒⣢⣤⣤⣤⣤⣤⣤⣤⣀⣀⣋⣉⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣤⣤⠴⢶⣿⣿⣿⠛⠿⠿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠋⠹⠛⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠻⠟⠿⢧⣄⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣛⣿⡿⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡴⠛⠀⠀⠰⣶⣾⣿⣿⣿⣿⠖⣀⠀⡀⢀⠀⠀⢀⣀⣀⣀⣠⣀⠀⠉⠛⠷⢄⡀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠷⠃⠀⠀⠀⣰⡌⠿⠿⠿⠟⠿⠫⠼⠿⠁⠀⠈⣠⣴⡟⣵⣿⣿⣿⣿⣷⡀⠀⠀⠈⠑⣄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠠⠈⠬⠛⡷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⠸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠹⢷⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠹⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠙⠿⠛⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣛⣛⣩⢾⠄⠀⠀⠀⠀⠀⠀⢱⡿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢉⠠⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣴⣿⡏⠀⠀⢀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣰⣿⣶⣾⣭⣝⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠐⠀⠀⣠⣿⣿⣠⠄⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣯⣳⣤⡄⠀⠀⠀⠀⠀⠀⣠⣾⣶⣶⠇⠀⠀⠀⠀⢀⡼⣎⣿⠇
⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣹⠿⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⠀⠀⠀⠀⠀⣸⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠘⠳⣏⠀⠀⠀⠀⠀⢿⣿⣿⣇⡤⠀⠀⠠⣿⣿⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⡰⣾⣿⣿⣿⡟⠀⠀⠀⠀⢀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣄⠀⠀⠀⠈⢿⣿⣿⣿⠶⠀⠀⠈⠁⢶⡶⠶⠾⠏⠀⠀⠀⠀⠀⠀⣻⣿⣿⡿⠋⠁⠀⠀⠀⠀⣤⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣝⡗⠀⠀⠃⠀⠉⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⢠⢞⡿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣞⣃⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣾⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣦⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠉⣸⢿⣿⣿⣿⣿⡆⣿⠁⠀⠀⠀⠀⠀⠀⠈⣀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⣀⣀⠐⢿⡄⠀⠁⠀⠀⠀⠀⠀⠈⢾⣿⣭⠉⠀⠁⠀⠀⠀⠀⠀⢠⣬⣟⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣾⣷⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⣭⣭⣤⣀⣀⡤⠴⣶⣂⢐⣲⡞⠂⠀⠐⢂⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢿⣭⣟⣻⣻⣿⣾⣵⠋⠙⠿⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣤⣴⣶⣿⢿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⠀⠀⠀⠀⠀⠀⡀⣤⣴⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⣀⣠⣴⣿⣵⣾⣿⠟⣻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣭⠄⠀⠀⠀⠀⠀⠀⠀⠂⣤⢻⣿⣿⢿⣷⡄
⠀⠀⠀⠀⠀⢀⣴⠖⠛⠛⣯⣭⡉⢉⣽⣿⣿⣶⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⡴⢠⣾⣿⢟⡟⠀⠀⠀⠀⠀⠀⠀⡠⠞⢁⠿⣽⣿⣿⣾⣿⣿
⠀⠀⠀⠀⣰⠿⠋⠐⢻⣿⣹⣿⣿⡈⢹⣟⡿⣿⠟⠁⠀⠀⠀⠀⠀⣀⡤⢾⢿⡿⢫⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠟⠀⠈⠀⠘⣿⣿⣿⣟⣿⣇⡀
⠀⠀⠀⠸⡇⢘⠻⣷⠈⣿⣿⣿⣿⣿⠉⣡⠞⠁⠀⠀⠀⠀⠀⠀⢼⣿⣷⡀⠈⢡⣿⡵⠊⠀⠀⠀⠀⠀⠀⠀⡐⢠⡦⣀⣴⣶⣿⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⢳⣨⣷⣤⣾⣿⣿⣻⣿⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠿⠂⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢜⡃⣿⣿⣿⣻⣿⣿⣯⣿⠟⠁
⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⢄⠀⠀⠀⠀⠀⠑⢸⣿⣾⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣾⣾⣿⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢈⣻⣿⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⣡⣄⠀⢾⣿⠁⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠐⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⢀⡀⠀⠲⠈⣿⣷⣄
⠀⠀⠀⠀⢀⢀⣴⠖⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⢀⡀⢴⡿⣻⣟⣻⡆
⠀⠀⠀⡾⠃⠈⠁⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠛⢷⡜⠆⠀⡠⠨⠄⠀⢤⣿⣟⣐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⠀⠐⠛⣡⣾⣿⣿⣿⡟
⠀⠀⠀⢶⡄⠀⣿⠐⣭⣿⣿⣿⡛⠋⠀⠀⠀⠀⠀⠀⣨⠾⡿⠿⠧⠤⢀⣤⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣼⣿⣿⠁
⠀⠀⠀⠈⢿⠀⣾⠿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢺⣶⣾⣿⡿⣿⣿⣖⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠭⠝⠛⠛⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠒⠣⠶⠒⠋⠉⠉⠉⠉⠛⠛⠛⠓⠛⠓⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠙⠛⠒⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠛⠛⠋⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⡀
⠀⠀⠀⠀⢀⡶⠦⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠉⠙⠳⢤⣀⣀⣀
⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠷⠴⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢳⡀
⢠⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⠿⠟⠛⠛⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣷
⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠘⡿⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠘⣯⣀⣴⠆⠀⠀⠀⠀⠀⠀⢹
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁
⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇
⠀⠈⠻⣿⣶⣦⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠷⡿⠀⠀⠀⠀⠈⠉⠀⢹⣦⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⢹⡇⠀⠀⠀⢸⣿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠻⣷⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡴⠿⠋⠀⠀⠀⠀⢀⡿⠃
⠀⠀⠀⠠⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣤⣤⡶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⠿⠿⠛⠛⠋⠁
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⠟⢿⣿⢾⣟⡭⢀⣥⠼⣿⣦⡒⠈⢻⣿⠟⣠⢹⣿⣿
⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡿⣷⣾⣿⣶⣿⣿⣿⡄⢀⣼⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠈⠙⠛⠀⢀⡈⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠙⣿⠿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣰⣿⢹⡖⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡟⠛⠻⢿⣿⣿⣿⣿⣧⣈⣃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣟⡛⠄⠐⠂⠸⠿⠿⢿⣿⣿⣿⣿⣏⣭⡀⠙⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⢀⣀⣀⠀⠉⢻⣿⣯⣵⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⡀⠚⠓⠛⢉⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢶⡆⠀⢠⡎⠀⠀⠀⢠⣄⡀⠀⠤⣈⠛⠻⣿⣷⣶⣶⣾⡟⠉⠻⣏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠈⣻⣿⣿⡏⠀⣄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⡆⠀⡾⠁⠀⣀⡀⠀⠀⣴⣿⠿⣿⣿⣷⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠒⢶⣴⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢀⣻⣻⣷⣾⣿⣿⣷⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠁⠀⠀⢈⣿⣶⠦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣕⣈⣥⣴⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣥⣤⣽⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠖⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠚⠀⡀⠘⠀⠀⣤⠀⠁⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⠀⠀⠀⠀⠀⠀⢀⠀⡄⡀⠀⢰⠆⠸⢀⣠⡀⢀⣉⠾⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⣦⣄⡀⠢⡀⠀⠀⠀⠞⢤⡄⣁⠤⢤⢄⣀⠌⠉⣶⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠂⠀⠀⠀⠀⠁⠙⢧⠸⢇⣹⢶⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⢀⡀⢤⠄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⢀⠔⠉⠁⣀⠀⠀⠀⠉⣙⡢⠀⠀⠀⠀⠀⢀⠀⡀⠄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⣂⠀⠀⠘⠛⠀⠙⢢⠘⠛⠙⢢⣤⠀⠀⠚⡄⠕⠀⠀⠀⠀⠀⡀⠀⠁⢀⠄
⠀⠀⢸⠉⢠⡄⠀⣀⣀⠀⠈⠃⠀⡀⡴⢿⠀⠀⠀⠁⠀⠀⠀⠀⠠⠂
⠀⠀⠸⠀⢠⠀⠠⣿⠿⢀⠠⢟⣠⣮⣿⠟⠀⠀⠀⠀⠀⠀⣴⠓⢿⢶⣨
⠀⠀⠀⢤⡌⢁⣠⠀⠰⠈⣥⣼⣿⣿⣾⠂⠀⠀⠀⠀⠀⠘⠀⠐⢈⡉⣷⡯⡠⠊⠀⠀⠀⠀⠀⣀⠠⣶⣴⣦⡀
⠀⠀⠀⠀⠙⠞⣻⣡⣾⣦⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⣈⣾⠾⠋⠀⠀⠀⠀⠀⠀⠺⣤⣰⣷⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⠶⠶⣶⣶⣶⠶⠾⠿⠛⠻⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⡀⠀⠀⠀⡎⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠀⠈⠉⠉⠙⠻⣷⠀⠀⠀⢣⣀⣨⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢈⣽⠿⠿⣄⠀⠀⣠⠶⠒⠲⣄⠀⠀⠀⠀⠀⠁⠀⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠞⢹⣿⠀⠀⠀⠀⠀⣾⠁⣴⣷⡌⣷⢸⡃⢰⣿⣳⠘⡇⠀⠀⠀⠀⠈⠑⠹⣶⠶⢦⣤⡀
⠀⠀⠀⣠⠖⠛⠉⠉⠁⠀⠀⢸⡿⠀⠀⠀⠀⠀⢽⣆⣈⣉⣴⠏⠈⢧⣀⡙⣉⡼⠃⠀⠀⠀⠀⠀⠐⠁⠙⢆⠀⠸⣇
⠀⢠⠞⠁⠀⡠⠒⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠘⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⢠⡏⠀⠀⡞⠀⠀⣯⣀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⢿
⣾⠀⠀⠸⣀⣀⢾⡀⠀⠀⠀⠀⠀⠀⢹⠋⠉⠁⠀⠸⢦⣤⣤⣤⣠⣤⣼⠟⠀⠴⠞⢿⠋⠁⠀⠀⢀⣀⡞⠀⠀⢘⠀⠀⢸
⣿⠀⠀⠀⢹⡁⠀⠃⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡈⠀⢹⡅⠀⠀⠀⠀⠀⠈⣧⠀⠀⣰⠋⠈⢱⡶⠒⠁⠀⠀⣼
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⣤⣀⣀⣀⣑⠒⢚⣀⣀⣀⣀⣀⣠⡴⠟⠀⠠⡇⠀⠀⢠⠇⠀⠀⢀⣼⠏
⠸⣧⠀⠀⠀⢠⠖⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠓⠤⠔⠋⠀⣠⣶⠟⠁
⠀⠙⢷⣄⠀⢸⡀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠹⣷⡀⢧⡀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠢⡀⣠⣿⠋
⠀⠀⠀⠀⠘⣷⠀⠙⠒⠚⠁⡤⠠⣀⠀⠀⣰⠧⠴⠷⠶⠧⣤⠖⠂⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣾⡿⠁
⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠁⠠⠨⠀⠀⠈⠓⠲⠦⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣠⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⠷⣶⣶⣶⣶⣶⣶⡾⠿⠛⠁
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣄⡀⢀⣀⣀⡀⠐⠛⠉⠉⠒⠐⠒⠒⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠚⠉⠀⠀⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠗⠒⢳⣄
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⠳⣄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⣀⣼⡆⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠹⣿⣇⢹
⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⡀⠙⠃
⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠗⠀⣸
⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣿
⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⡷⠀⠀⠀⢸⡿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⢸⣧
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠉⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁
⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣧⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠈⠿⣿⠿⠿⠿⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣠⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⠿⠿⠻⢶⣶⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠉
⣿⣿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠐⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠂⢀⠀⠃⠀⢠⡄⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡄⠀⠶⠀⠏⢀⣀⠀⣈⣑⠟⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⣤⣄⡀⠂⡀⠀⠀⠀⠞⣤⢀⣁⠤⣤⣀⣠⠈⢠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠴⠂⠀⠀⠀⠀⠈⠻⢇⠸⣊⡷⡾⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊
⠀⠀⠀⢀⠖⠉⢁⣀⠀⠀⠀⠉⣙⢢⠀⠀⠀⠀⢀⢀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⣃⠀⠀⠘⠋⠀⠙⣀⠘⠋⠙⣢⣄⠀⠀⠪⡤⠗⠀⠀⠀⠀⢀⠀⠀⠀⡠
⠀⠀⢸⠁⢠⡄⠀⣀⣁⠀⠈⠃⢠⡁⡶⢿⠀⠀⠀⠁⠀⠀⠀⠀⠔⠁
⠀⠀⠸⠂⢠⠀⠰⣿⠟⢀⠠⢟⣦⣬⡿⠛⠀⠀⠀⠀⠀⢀⡔⠹⡷⣗⡄
⠀⠀⠀⢠⡌⢀⣠⠀⠰⠈⣤⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⠀⠀⢈⢨⢾⠅⠐⠀⠀⠀⠀⠀⢀⡄⢴⣧⣵⣄
⠀⠀⠀⠀⠙⢞⣻⣰⣾⣦⣿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣡⡾⠞⠁⠀⠀⠀⠀⠀⠐⢿⣬⣺⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣶⣶⣶⣶⢶⣶⣶⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠀⣀⡴⠞⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢩⣟⡴⠞⠉⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠰⠟⠉⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣿⠁⢀⡴⠋⠀⠀⠀⠀⢀⡴⠂⠀⠀⣼⠿⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣸⢃⡴⠋⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢰⣿⠋⠀⠀⣠⠗⢀⣴⣿⠋⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠀⠀⠀⣠⠞⠁⠀⠀⠛⠁⢀⣤⡾⠁⣴⢋⡼⠁⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢰⡇⢀⣴⠟⠁⠀⠀⠀⠀⢀⣔⡽⠋⢀⡾⣡⠞⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣠⠟⠁⠀⣸⣵⠟⠀⠀⢀⡀⠀⢀⡴⢫⠞⠁⣠⠞⡴⠃⢀⣴⠆⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⣿⠏⠀⠀⠀⠛⠁⠀⣠⣴⢟⡡⠞⠉⠀⠏⢀⠔⢁⡾⢁⣴⡟⠁⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣠⡴⠞⠃⠀⠀⠀⣀⡾⢣⠿⠋⠀⠀⠀⠀⠐⠁⠀⢀⡴⠻⠋⠀⠀⢀⡴⣋⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⠶⢛⣁⣀⣀⣠⣄⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⢴⠿⢋⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢫⣾⡵⠚⠋⠉⠉⠉⠀⠀⠉⠛⠲⠶⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡴⢣⡏⠀⠒⢳⡆⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⣀⠀⢠⡏⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⡼⢡⠊⣠⠞⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢸⡅⠀⠀⠘⠋⢀⡼⠁⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⢸⢇⡇⣾⠁⠀⣠⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢰⠏⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⢠⡟⡼⢡⡟⠀⠀⠛⠀⠀⠀⢠⡀⠈⡇⠀⠀⠀⠀⢠⡞⠁⢀⡾⠁⠀⢠⠟⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⣠⠟⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⢠⡟⠀⠀⠀⠁⠀⠀⠀⢀⡼⠃
⠀⠀⠀⢰⠏⢀⡟⠘⣧⠀⠀⣾⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢀⣼⠁⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⣿⠀⠀⣧⠀⠈⢷⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠆⠁⣴⠚⠋⠁⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⢿⡀⠀⠘⠀⠀⢸⡄⠀⠀⠀⠀⠀⠠⢤⣴⠖⠋⢀⡴⠃⠀⣠⠎⠀⠀⠀⣠⡴⠋⠁
⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠻⢦⣤⣤⣤⡤⠶⠋⠉⠉⠉⠉⣀⡴⠋⠁⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠲⠦⣤⣀⡀⠀⢀⣠⠶⠶⠚⠛⠉⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⣀⠀⠉⠉⠛⠉⠀⠀⣀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⢀⣠⣤⣤⣤⣶⡿⠿⠿⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠿⠋⠙⠻⠟⠋⠉⠉⠹⠟⠀⢀⠀⠀⠛⠝⢿⣇⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣾⡿⠟⠇⠀⠀⠀⠀⢀⡤⠖⣲⠆⠀⠘⠉⣉⡁⠓⠺⠖⢸⣿⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⡏⢃⣠⣠⣠⡶⣶⣤⡌⠙⠉⠁⣀⣴⡿⣿⣭⣙⠳⢦⣄⠈⠛⠻⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⣠⡶⣻⢽⣠⡟⠂⠀⢀⡀⠀⠀⡀⠀⢉⡿⢿⣷⣀⡽⢷⡄⠐⠩⢿⣷⣄
⠀⠀⠀⠀⠀⣰⡾⠟⠋⠁⣼⣋⣫⣽⡞⠋⢁⡀⠀⠈⠐⠃⠀⠳⡄⠈⠀⠠⠏⠉⠟⠛⣇⠀⠀⠉⠚⢿⣦
⠀⠀⠀⠀⣰⣿⡷⠂⡔⠀⣿⠋⡇⠀⠁⠀⠋⠀⠰⣒⣚⣀⠀⣀⠀⠀⠀⠀⠲⠂⠀⠀⠉⠘⠿⠀⠀⢞⣿⠇⠀⣀
⠀⠀⠀⠀⣿⡧⠀⠈⢁⣤⡀⡄⠀⠀⣠⠄⣠⣶⣛⡯⣭⠝⡧⠸⠀⠀⡠⢖⣺⣷⣛⣿⣤⣤⣄⠀⡟⢸⣿⠀⠀⠸⡄
⠀⠀⠀⠰⣿⣍⠀⠀⣿⡈⣧⢳⡀⠘⣡⡞⢹⣺⠿⠇⣃⡼⠃⠀⠀⠈⣴⢋⢱⢶⡁⣨⢁⣅⡝⣷⠁⠸⣿⡄
⠀⠀⠀⠀⢈⣿⠃⠸⣟⢗⠹⣆⡁⠸⢯⣼⣽⣯⡴⠟⣉⡄⠀⡠⠀⠀⢿⣷⣫⢞⣼⣁⣎⣬⠾⡃⠀⢰⢸⣿
⠀⠀⠀⠀⣾⡟⡀⢠⡙⣧⢀⡿⠃⠀⠒⠖⠀⠀⠀⠀⢡⠴⠊⠀⠀⠙⠦⠭⣭⠟⠉⠉⠭⠖⠋⠀⣀⢨⣾⡇
⠀⠀⠀⠀⠹⣿⡧⠀⠳⠍⣛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣚⡶⠀⠀⠀⡄⠀⠀⣤⢰⠇⣸⣿⠇
⠀⠀⠀⢀⠀⢻⣧⠀⠀⢀⡀⠀⣤⠬⠿⢥⣤⡤⣴⡳⡄⠘⠛⠛⠉⠉⠀⢀⣀⣤⠶⣿⠀⣼⠁⠈⣾⡟⠉⠀⢀⡴
⠀⠀⠀⠈⢧⠈⢿⣦⣴⣦⠉⠀⢷⣤⣄⢻⣿⣚⣼⠃⠀⠀⠀⢤⣠⣦⢶⢾⢫⣧⠾⢃⡴⠃⡀⣰⡿⠃⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣷⣾⡓⠈⠉⠉⡭⠽⠂⢀⠀⠀⠳⣾⣛⣭⣾⠾⠛⠁⠐⠋⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⡀⢀⡀⣀⠑⠻⠂⠖⠀⢠⠄⠀⣶⣠⣶⠶⠾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣾⣥⣤⣼⣆⣀⣠⣤⣴⣶⡿⠋⠁⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡄⠀⠀⠉⠉⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⣤⡶⠛
⠀⠀⠀⠀⣯⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣠⠶⣻⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣡⠴⠞⣫⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⠞⢋⡄⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⣊⡤⠞⠻⠟⠉⠀⣈⡵⠞⠋
⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⣀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠈⠧⠛⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡴⠿⠴⠋⡡⠂⠀⠈⠁⣀⡽⠃⠠⠖⠁⠀⠀⢀⡜⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣫⣆⣠⡴⠋⠀⠀⠀⠀⠀⣀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠠
⠀⠀⠄⠀⠀⠀⠀⠀⠀⣴⠶⠞⠉⠀⠉⠡⠔⠀⠀⠠⠂⠀⣨⡴⠋⠁⠀⣠
⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⡾⠛⢛⠛⣛⢶⣤⡀⠀⠀⠀⢈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⡟⢡⣟⢈⡴⢶⡌⠿⡃⢹⡇⠀⣘⡵⠋⠀⣀⠄⠀⠀⠀⠀⢀⡴⢦⡄
⠀⠀⠀⠀⠀⠀⠀⣇⠰⣿⢀⠙⣋⡀⠸⠟⣼⡏⢈⡿⠀⠠⠊⠁⠀⠀⠀⠀⠀⠹⠔⠚⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡙⣷⣌⣛⣣⣼⣶⣿⡶⠋
⠀⠀⠀⠀⣠⠀⠀⠀⠘⠷⢦⣍⣉⣩⡖⠛⠁
⠀⠀⠠⡖⠉⢳⠂⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡦
⠀⠀⠀⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠲⠦⢤⣀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣞⣉⠀⠀⢀⣄⠀⠀⠈⠙⠲⠤⣄⡀⠀⠀⢳⠀⠃
⠀⠀⠀⠀⡇⠀⠀⣞⠉⠉⠓⣒⠋⠁⢸⣿⣍⣳⠀⠀⡉⠀⠘⠀⠀⠀⢀⠀⠉⢧⠀⠈
⠀⠀⠀⠀⣧⠀⠀⠘⢿⠄⠀⠉⢠⡄⢤⡙⠛⠋⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢲⡜⠦⣄⡀
⠀⠀⢸⡀⠘⣆⠀⠀⠈⠳⡄⢠⠀⠀⠀⠉⠑⡒⠀⣀⠀⠀⠀⠀⠀⠘⣿⣿⣤⡿⠀⠀⠙⠢⣄
⠀⠀⠀⠙⢄⠘⢦⠀⠀⠀⠘⢿⡈⣇⡀⠂⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣙⠿⣷⠈⠓⢤⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠈⠓⠷⠼⣦⣴⠀⣄⢳⡀⠐⠂⢀⠀⠀⠀⠠⡦⠀⠈⢉⡁⠀⠀⣤⠈⠉⠙⣒⣒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢧⠀⠠⣿⣯⣢⡀⠀⢠⠀⠀⠸⣷⣾⣦⢀⠀⠋⠀⠹⣾⣷⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣐⣮⣟⣛⠁⡀⠀⢀⠑⠦⠄⠉⠋⠀⠐⠂⠀⠈⠀⣁⡴⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠿⠽⠦⠬⢥⣥⣼⣮⠷⠦⠶⠶⠷⠒⠚⠉⠁⠀⡠⠋⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠴⣶⣾⠿⢷⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠁⠀⠀⠀⠁⠁⠀⠀⠚⠻⠟⠉⠉⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⣴⣶⣦⡀⠀⠀⠀⠀⠀⢄⠀⣶⣶⣤⣦⢌⠻⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠄⢀⡀⠀⠀⠀⢯⣭⠿⠃⠀⠀⠀⠀⠀⠀⠁⠀⠉⠻⢿⣿⣿⡌⢻⢮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣋⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠻⠂⡘⠋⠨⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢸⢹⡿⣦
⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⢀⣤⣤⠀⠀⠀⢰⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠨⠘⢿⡸⡇
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⣾⣿⣿⣿⣧⠀⠀⠀⠀⣤⣤⣌⣀⣄⠀⠀⠀⠀⠀⠄⠀⠀⢠⣟⣿⡇
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠙⠁⠀⠀⠀⢳⣷⣿⣿⣷⣽⠀⠀⡀⠀⠀⠀⠀⢠⣿⣿⡟⢿
⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⣸⣦⡀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠉⠯⠻⣿⣟⣅⠀⠄⠀⠀⠀⠀⠈⢰⣿⣿⣧⢸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡇⡏
⠀⠀⠀⠀⠀⠀⢻⡃⠂⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⣿⣿⡿⢸⠇
⠀⠀⠀⠀⠀⠀⠘⣿⠣⠀⠈⣿⣿⣿⣿⣧⠀⠀⠀⠀⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠈⠻⢿⣿⣿⣇⠀⠀⠀⢉⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⣒⣶⡆⠀⠘⠀⢨⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠸⠀⡀⠀⣈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣻⣿⠃⠀⠈⢰⣺⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠅⠘⠿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⢀⣾⣷⣄⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⡀⠀⠘⠻⢿⣿⣿⠿⠂⠀⠀⠀⢀⣀⣴⣷⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⣤⣤⣤⣷⣾⣶⣷⠶⠶⠟⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢞⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠈⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⡠⠞⠁⡀⢠⠄⠀⣠⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣿⠴⠛⠋⣀⢴⣿⢗⡟⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠁⣀⠴⠊⠁⠀⡠⠊⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢁⡄⠀⡀⠠⠊⠁⠀⠀⢀⠞⠁⠀⣠⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⢿⣇⠴⢋⣧⢾⠃⠀⠀⠀⠀⣴⠷⡿⠀⠘⢋⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠁⠉⠁⠀⠀⢀⡏⠀⠀⠀⠀⠈⠁⡴⠁⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⢀⠞⠀⢀⡴⠀⠀⢀⠞⠁⠀⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⠎⣠⠔⣹⠃⠀⠐⡿⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⠷⠋⠀⠴⢷⠇⣀⡾⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⢀⡾⢚⣝⣡⠞⠁
⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⡟⠁
⠀⠀⠀⠀⣠⣴⡷⠖⠒⠋⠛⠒⠚⠒⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⢀⠞⣿⠉⡀⠀⠈⠏⠀⠰⢦⡀⠀⢿⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠘⡇⣸⠧⣇⠀⠀⠀⠀⣀⠀⢸⠀⣏⠀⠀⠀⢀⡴⠋
⠀⠀⡜⠁⣧⠀⠘⣲⠀⠀⠈⡉⠳⡄⠀⢸⠆⣀⠴⠋
⠀⠈⣟⠀⣿⠀⠀⠓⠶⠦⠀⢁⣀⡵⢀⡾⢸⠃
⠀⠀⠈⣻⠈⠙⠓⢦⣀⣀⣀⡈⣡⠴⢋⠔⠋
⠀⠀⢠⡷⠚⣆⠴⡄⣉⡅⢉⣉⡡⠚⠋
⠀⠀⠀⠀⠀⠁⠀⠉⠀⠘⠋⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣀⠀⠀⢀⣤⣶⣿⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠃⠀⣠⣶⠟⠁⣰⣿⠀⢀⣠⣶⠟⠁⣠⣶⣿⣿⣿⠿⠋⠁⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠞⠁⣰⢾⠟⠁⣠⣾⡿⢃⣴⣿⣿⣇⣠⣾⣿⣿⡿⠋⠁⠀⡀⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡾⡁⠿⡴⣞⡵⢋⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣼⠇⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣺⠏⠀⣰⠏⠀⣡⡴⠛⠉⣠⢿⣽⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣴⣿⠏⠀⠈⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⡞⠁⢀⡼⠃⠀⣴⠋⠀⣠⠞⠡⠝⣻⢟⠼⠿⣿⣿⣿⣷⣶⣾⣿⠟⠁⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢾⣀⣠⠞⠁⠀⠀⠙⠲⠛⠁⠐⠀⠁⠠⠈⣤⠀⣩⢾⣿⣿⠿⢋⣡⣶⠟⠁⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡏⠀⠀⣰⠋⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣾⡷⠛⠉⢀⣴⣿⣿⣥⣴⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⠇⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢀⣠⢞⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠁⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡛⡫⢕⣚⣭⠷⠟⠉
⠀⠀⠀⠀⠀⠀⠀⣴⠏⠉⠉⠛⠛⠓⠶⠶⢦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⠋⠉
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⣶⣿⠆⣀⡀⠀⠀⠙⠛⠒⠒⠶⢶⣶⣄⡀⠀⠀⠀⠀⠀⣠⡶⠛⠉
⠀⠀⢀⣴⠟⠁⢈⣉⡀⠸⠿⠟⠁⠀⠉⠀⠀⠀⢀⣠⡀⠀⢀⣾⣿⣿⣿⣷⠀⠀⠀⢰⡏
⠀⠀⣿⠁⠀⣴⣿⣿⡿⠀⠀⢀⣤⣶⣶⡀⠀⢰⣿⡿⠁⣴⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⡇
⠀⠀⢹⡀⢸⣿⣿⠟⠁⠀⣴⣿⣿⣿⣿⠀⠀⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⢀⣴⠟
⠀⠀⡼⠀⠈⠉⠁⠀⠀⢰⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⣤⠞⠋
⢠⡞⠁⠀⢀⣴⣾⣿⠀⠈⠛⠛⠋⢀⣠⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⡟⠉
⠘⣧⠀⠀⣿⣿⣿⠏⢠⠄⠀⠀⠀⠛⠛⠁⠀⢀⣴⣿⣿⣿⣿⣿⠟⠁
⠀⠘⢷⡀⠛⠛⠁⠀⠀⢀⣀⣤⣴⣶⣶⣤⣴⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠈⢻⣦⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠈⠉⠁⠀⠤⠤⢄⣀⣉⠉⠑⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡩⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠤⢄⡀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⡠⢚⣥⣶⣿⣿⣿⣷⡄⠀⠀⠀⠈⠉⠀⠀⠀⠀⣴⣶⣦⣌⠓⢤⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⡼⢡⡾⢋⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡝⢆⠀⠀⠀⠀⢿⣄
⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⡇⣿⠃⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠈⠻⣿⣿⡌⣇⠀⠀⠀⢸⣿⣆
⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠃⣿⣼⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣯⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡀⠀⣽⣷
⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⣿⡆
⠀⠀⠀⠀⣿⡇⢠⣶⡀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡀⠀⠀⠀⢀⡄⢿⡀⣿⡇
⠀⠀⠀⠀⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠋⠀⠀⢀⠃⠀⠀⠀⠀⠀⢸⡇⣿⡇
⠀⠀⠀⠀⢿⡇⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡼⠀⠀⠀⠀⡾⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠸⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⠁⠀⠀⠀⠀⠁⠀⣿⣿⡿
⠀⠀⠀⠀⠀⢻⣆⣿⣿⣆⠀⠀⠀⠀⠀⠀⢆⠱⣝⠿⣿⣿⠟⠀⠀⠀⠀⣀⡀⣀⣼⣧⡾⠃⠀⠀⠀⠀⠀⡀⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢿⣿⣞⣿⣇⠀⠀⠀⠀⠀⠀⠑⠮⢉⡂⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⠓⠒⠒⠀⠀⠀⠜⣱⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣄⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠁⠀⠏⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢿⣷⣦⣀⠀⠀⣄⡀⠀⠀⠀⠀⣶⣶⣶⣄⠀⢀⡄⠀⠀⠀⣸⣿⠟⣡⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣍⡻⢿⣿⣿⣟⡻⣦⣄⡀⠀⠈⠉⠉⠉⠀⠈⠀⠀⢀⣠⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣶⣶⣶⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣟⣛⣛⣛⣛⣻⡯⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⡠⠀⠀⠀⣴⢀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠆⠆⠀⠛⠀⠃⡴⠆⢠⠶⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠀⠁⠀⠀⠀⠉⠚⠢⣶⡍⢿⠶⣆⣀⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠑⠨⠶⠉⠉
⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠔⠒⠀⠁⠀⠘⠓⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡆⠀⠀⠺⠂⠰⢀⠐⠟⠚⣀⡄⠀⠠⢂⡠⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡞⠁⢠⠀⠀⢈⠀⠈⠃⢀⡀⡼⣗⠀⠀⠈
⠀⠀⠑⠀⡄⠀⢾⠿⢀⡀⢛⣤⣽⡿⠃⠀⠀⠀⠀⠀⡴⠲⠷⢆⡄
⠀⠀⠀⢦⠉⣠⡄⠐⠀⣴⣼⣿⣿⡟⠀⠀⠀⠀⠀⠘⡀⠀⢈⠠⣮⠀⠀⠀⠀⠀⠀⢀⡄⠴⣧⣴⣄
⠀⠀⠀⠀⠑⠙⠧⣾⣷⡿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⠋⠀⠀⠀⠀⠀⠀⠻⣤⣽⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣠⣴⡮⠁⢀⣠⠤⠤⠀⠀⠀⠀⣰⠎⠀⠀⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣌⠰⢣⠎⠁⣀⣀⣴⡿⣡⠖⠛⣒⣒⣒⣪⠟⠀⠀⣠⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⢁⡖⠂⣱⠋⢉⡽⠛⢋⣠⠃⣰⠋⣉⣁⠀⠀⠀⣀⢴⢳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⣩⠥⢞⡭⠶⠖⠃⠀⢿⠷⠛⢉⠁⣰⢏⣮⠞⡠⠀⣀⡼⠓⢋⡼⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠪⡎⢀⢠⠏⠀⠀⠀⠒⠒⠀⡀⠀⣀⡴⠃⡠⣲⠞⣡⠛⣩⣖⣫⠍⣀⠤⡟
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⣀⣠⣯⣧⠏⣠⠴⠀⠘⠀⠀⢰⣾⣯⠴⠶⠚⢡⠇⠠⣇⣤⠉⠉⡼⢋⠔⠊
⠀⠀⠀⠀⠀⠀⠸⠁⠀⣾⡿⢛⠽⠋⣴⣡⠇⠀⢀⡤⠴⠛⡿⠃⢠⣖⣮⣵⣣⢀⣤⠎⡠⠔⢡⠏⡎
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠛⠋⠉⠀⠘⠛⠁⠀⢀⣧⣔⠀⣸⠀⠀⡞⢿⣿⠋⠉⠉⣠⠤⠴⡖⣵⡾⠃
⠀⠀⠀⠀⠀⢸⣤⢤⡄⠀⢀⠀⠀⠀⢀⠇⠀⠈⠛⠋⠙⠃⢀⠔⢡⠆⡇⠀⠀⣟⢁⡴⠾⢞⡽⣵⠁
⠀⠀⠀⠀⠀⣼⡇⡎⠀⠆⡁⠀⠀⠐⠁⠀⠀⠀⡠⠂⠀⠀⠲⠒⡹⢀⡇⠀⣠⣿⣿⠀⣴⢉⣴⠟
⠀⠀⠀⠀⢸⢹⡗⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠇⠀⠀⢀⡔⢋⡤⠿⠠⣎⣽⣿⡇⢸⢿⡟⡟
⠀⠀⠀⠀⣿⠀⠀⠆⠀⣀⣤⠶⠶⠦⠤⣀⠀⠀⠀⠀⡀⢸⣷⡏⠀⢀⡠⠴⢺⣿⠃⠃⡠⠚⠁
⠀⠀⠀⠀⠳⣄⠀⠁⣼⠃⢀⣀⡀⢀⠀⠈⠓⠀⠀⠀⠀⡠⠟⠁⠀⣻⠄⣰⠞⠁⢠⣎⡄
⠀⠀⠀⠀⢀⡟⠀⠀⣧⣾⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠈⢀⣠⠀⠾⢳⣴⠇⠀⢀⡼⠋
⠀⠀⠀⠀⠀⢻⡀⠀⢻⡏⠉⠙⢿⣿⣿⣷⣀⠀⠀⠀⠀⠈⠀⠀⠀⠊⢁⡤⢖⠋
⠀⠀⠀⠀⠀⠀⠻⣷⠀⠑⠀⠀⢀⣿⣿⡿⠀⠀⣰⠀⠀⡐⢀⡔⣤⡤⣘⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⢀⠉⠛⠛⠛⠀⠀⠀⠁⢀⣴⠿⠞⠀⢈⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠴⢶⣤⣄⡠⠀⢀⣀⣡⣤⠴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠁

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢞⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠚⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⠀⠀⣠⣯⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⢃⡴⠷⠊⢀⣤⣞⣴⠏⠀⠈⢋⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠛⠉⢀⡠⠖⠉⠚⣡⠎⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⡠⠖⠉⠀⠀⢀⠜⠁⠀⢀⢜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡅⢀⠴⡇⣠⡆⠈⠀⠀⠀⠀⣰⣫⡄⠀⣴⢷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⡽⠖⠁⠐⠛⡹⠀⠀⠀⠀⠀⠼⠋⡼⠁⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⠀⠀⠀⢀⡼⠁⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⡤⡿⠀⠀⣠⠎⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⣡⠔⢋⡼⡁⠀⢀⡿⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠊⠀⠀⠚⢫⢇⡤⡾⢁⡤⠊
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠟⢋⣞⣥⠋
⠀⠀⠀⠀⠀⠀⢠⠋⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠟⠁
⠀⠀⠀⠀⡠⣴⡿⠚⠛⢋⡉⠙⠛⠉⠛⢲⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⡞⢾⡉⣀⠀⠀⠙⠁⠀⠞⢦⡀⠀⡷⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠘⡇⣨⠇⢧⠀⠀⠀⠀⢀⡀⠀⡷⢰⡇⠀⠀⠀⢀⠔⠋
⠀⠀⡴⠁⢿⠀⠈⢳⠂⠀⠀⢉⠙⢦⠀⠀⣽⠀⣠⠖⠁
⠀⠈⢻⠀⢸⠀⠀⠘⠶⠦⠀⠈⡀⣈⠇⢀⡇⣼⠁
⠀⠀⠈⢻⠈⠛⠒⢦⡀⢀⣀⡀⠉⣡⠴⢫⠖⠋
⠀⠀⢀⣮⠔⣆⡠⡄⠙⣉⠉⣛⠛⡡⠒⠃
⠀⠀⠀⠀⠀⠉⠀⠛⠊⠈⠖⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢊⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⢀⡠⠔⠉⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡽⢁⡠⠒⠉⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢊⡥⠞⠊⠁⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡡⠔⠊⠁⠀⠀⠀⠀⠀⠀⢀⡠⢊⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢈⠕⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣁⠤⣒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠯⠒⠉⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⡁
⠀⠀⠀⠀⠀⡠⠒⠁⣠⠤⠒⠂⠉⠉⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠞
⠀⠀⠀⢀⠜⠁⢀⠞⡠⠔⠂⠉⠉⠉⠒⠒⢄⡈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠎⠀⢠⠁⢘⠀⠀⣀⠠⠤⠤⣀⣀⠔⠃⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠸⠀⠀⠇⢠⣈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠈⠆⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⢠⠀⠀⠀⢸⠈⠢⡀⠀⠀⠀⠀⠀⣀⠜⠀⠀⢸⠀⠸⠀⠀⠀⠀⡠⠊
⠀⠀⠈⠆⠀⢣⠈⢄⠀⠈⡆⠀⠀⠀⠊⠀⠀⠀⢀⠆⢠⠇⠀⠀⡠⠊
⠀⠀⠀⠘⢄⠀⠑⢌⡢⠤⠃⠀⠀⠀⠣⣀⣀⡤⠊⡰⠃⢀⡔⠋
⠀⠀⠀⠀⠈⠢⡀⠀⠙⠦⡀⠀⠀⠀⠀⢀⡠⠔⠉⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠉⠁⠈⠉⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠐⠒⠀⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠐⢿⡒⠶⠦⠤⣤⣀⣀⠀⠀⠰⢶⡶⠤⢤⣄⣀
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠉⠉⠓⠒⠾⠷⠶⣤⣈⠉⠙⠒⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠙⢦⡀⠈⢯⡙⠓⠲⠶⠤⢤⣄⣀⡻⣿⣒⠶⠤⢤⣀⣀⠉⠙⠒⠶⠤⣄⣘⣷⡦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠉⠦⡀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠲⠆⠀⠈⠉⠛⠲⠦⢤⣄⣀⠉⠙⣳⣌⡙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠢⡀⠀⠘⢯⡓⠒⠶⠤⠤⣔⣿⣗⡲⠦⠤⣄⣀⡀⠈⠉⠓⠺⠿⢯⣓⠦⣍⡓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠢⡄⠀⠙⢦⡀⠀⠀⠀⠀⠈⠉⠑⠂⠀⠀⠉⠙⠒⠶⠤⣄⣰⣦⣄⣀⠙⠲⣬⡓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣦⡀⠈⠳⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠞⠛⠛⠻⠷⢾⣹⣍⡳⢭⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⡙⢦⡀⢾⣷⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡉⣱⠞⠁⠀⠀⠀⡀⠀⠀⠀⠈⠉⠟⢛⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠉⠂⠳⣍⠳⣄⠐⣿⢦⡀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⢀⠴⠋⠙⢦⠀⠀⠀⠀⠀⠀⠙⢟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣄⠀⠈⠳⡈⠁⠈⠳⣝⠢⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⣧⡀⠠⣾⣦⡀⠀⢈⣧⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⠙⢦⡘⢮⡻⣄⠈⠳⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠙⠂⠱⣌⠑⢄⠈⣇⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠈⠳⡄⠀⢹⠐⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣸⠄⠀⠈⠁⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⢢⡼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⢰⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠋⠀⠸⡄⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡇⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⣏⠉⠹⣄⠀⠀⣸⣠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡈⠙⢲⠮⢤⣀⡀⠀⠀⠀⠀⡔⣀⡴⢶⠋⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢾⣠⠞⠙⠻⠿⣿⡀⣰⣛⣁⣹⣾⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠤⠬⡷⠯⠵⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⣔⡢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢊⣥⣶⢶⣯⡅⢨⠯⣑⠢⢄⠀⠀⠀⠀⠀⠀⠀⣴⢻⡟⠀⡿⡇⢸⣟⡿⣿⣿⠉⢷⣦⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⣆⡘⠀⣄⡤⠫⠃⢤⣏⠉⠳⢨⡷⡄⠀⠀⠀⠀⣸⠟⠘⡿⣄⠙⠁⠸⣾⡵⣷⠘⣷⣄⢉⣼⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣛⡻⠸⣙⡰⣤⡄⠚⢿⠟⠀⡶⣶⣝⣿⣧⠀⠀⠀⣸⣧⣹⣠⡜⠉⠀⠀⠀⠋⠒⢡⣿⣿⡿⡿⡅⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣟⢻⣾⢿⣿⣶⣦⣶⣾⣿⣟⣷⢜⣋⠴⣀⠇⠀⠀⣼⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣟⣼⣷⡀
⠀⠀⠀⠀⠀⠀⢿⢮⠻⣿⣿⣷⢾⣿⣋⣹⢿⣿⡽⠃⣾⣋⣠⠁⠀⠀⠀⠘⣿⣿⢂⣠⣠⡀⣤⣤⠄⠀⣰⡶⣦⠌⠁⡌⡇
⠀⠀⠀⠀⠀⠀⠈⢻⣑⣧⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡜⠀⠀⠀⠀⠀⠀⠀⠙⢿⡞⢮⣄⠿⢤⡁⠀⣀⣬⠟⢛⠲⣦⢜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣽⡿⣶⣿⣿⣟⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅⡀⠀⠀⠀⢴⣲⡦⣦⣰⣽⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠶⠳⠭⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠾⠿⣿⡱⠿⣧⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠶⠒⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⢯⣤⢶⠖⠒⠒⠫⡿⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠒⠂⠀⠀⠒⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⣈⣾⣷⣿⣴⡶⢦⡘⢟⠿⠌⡅⠀⠀⠀⠀⣀⡠⢤⡔⠾⣿⣿⣷⣶⣤⣤⢴⣨⣾⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠋⠁⣴⣿⣿⡇⢸⣿⡿⢿⣿⠀⣿⢰⣶⠀⠀⢠⣾⣿⡧⠏⠛⢦⣀⣼⢿⣧⣶⣼⣿⣽⣹⣷⣧
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣅⠀⣠⣾⡿⠃⣼⡁⡿⣷⢭⡿⢻⢃⣟⡾⣸⠀⠀⠈⣧⣉⣿⣿⣿⣮⣝⣱⣾⣿⣿⣿⣾⣻⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣩⣤⣬⣉⠠⡾⠃⣿⡆⠆⡄⣰⡿⠾⣿⣿⠏⠀⠀⠀⣿⢿⣷⣉⢙⣛⡿⠋⣻⡿⣿⣿⣿⡇⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠻⣽⡿⣷⣄⠁⠈⠛⠺⣥⣴⡄⢸⡿⠁⠀⠀⠀⠰⣿⣾⣿⣿⣿⣿⣁⣀⡰⠙⢃⣊⣡⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣉⣐⡝⢻⠷⣿⡿⢷⣼⣿⡿⠞⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣴⣿⣶⣄⣡⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠾⠛⠿⣮⣧⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⢀⡀⠀⢀⠀⡀⠀⠀⠀⠀⡀
⣿⣏⢽⣟⡛⣛⣛⡛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⢂⠔⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣡⠖⠁⠀⡴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⠔⠁⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⠔⠁⠀⡠⡢⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡠⢊⠔⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡠⠊⠀⠀⠀⢀⠔⠈⡠⠃⢀⠔⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠂⠈⠀⠀⠀⠠⠈⠁⠀⠊⠀⠀⠊⢈⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⡅⠀⠠⠊⠀⡠⠊⠨⠀⠁⠀⢀⠔⠁⠀⠀⠀⣀⡁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠐⠀⠘⠐⣁⠠⠒⠁⠀⣀⡀⠀⠀⠠⠆⢒⠄⠀⠀⠀⡡⠊
⠀⠀⠀⠀⠀⠀⣀⠀⢀⠎⡠⠒⠆⠄⠂⢉⡀⠤⠐⠊⠁⠀⡩⠃⠀⠀⡠⠃⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠰⠈⠔⡡⠊⢀⠠⠀⠒⠈⠉⠐⠒⢄⠀⠀⢐⠆⠀⡠⠊⠀⡠⠒⠁
⠀⠀⠀⠀⠠⠁⢠⠊⡠⢊⡡⠀⠠⠀⠀⠀⠀⠢⡀⠡⡠⠂⡠⠊⠀⠔⠉
⠀⠀⢸⠑⠁⡰⢁⠎⡔⠁⠀⢀⠌⡠⠀⠀⠌⠀⢡⠀⡇⢌⠀⠰⠥⢤
⠀⠀⢘⠀⢠⠁⠆⠈⠀⢀⠔⠡⠊⢀⠀⠈⠀⠀⠠⢀⠃⠌⡀⠀⢠⠂
⠀⠀⠘⡀⠀⠀⡄⠐⠔⠁⠀⠑⠒⠊⠀⠈⠢⠐⠁⠌⠀⡔⠁⡠⠁
⠀⠀⠀⠡⠰⡀⠰⡀⠀⠔⠈⠉⠁⠈⠑⢂⠀⢀⠜⡠⠊⠀⠊
⠀⠀⠀⠀⠡⡈⠢⡈⠢⡑⠠⠄⠀⠤⠐⢁⠠⡢⠊⡠⠒⠁
⠀⠀⠀⠀⠀⠈⠂⢄⡑⠂⠅⢀⣀⣂⠨⠕⣊⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠈⠉

⠉⠰⣤⡀
⠀⠀⢌⠻⠳⠆
⠀⠀⠘⡆⠒⠄⡇⠄⡀⠀⠀⠀⠀⠒⠊⠝⠢⠀⣒⠤⣀
⠀⠀⠀⠐⠁⠰⠛⡄⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢕⢤⠑⠔⢄
⠀⠀⠀⠀⠘⠐⠡⠀⠁⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⠂⢂⡰⡑⠣⠀⠀⠀⠀⡀⡀⠀⢄⢀
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠂⠘⡁⢡⡀⠀⠀⠀⠀⠀⠀⡘⠆⢀⠁⡈⠢⡣⢆⠀⠀⠀⠓⣎⠁⢘⠩⡂
⠀⠀⠀⢀⡀⠀⢈⠆⢂⠀⠈⢄⠀⡙⢷⡆⠲⠴⠦⠞⢋⠀⠀⠀⠀⠁⢄⠢⠑⣀⠀⠠⡬⠀⢀⠢⡀⠁⢀
⠀⠀⠀⠀⢷⡐⠀⣶⡂⠀⠀⠀⠢⣑⠄⠈⠀⠐⠀⠣⠈⠀⠀⠠⡀⢢⠒⠳⢤⣤⣀⢔⡨⢀⠐⠀⠀⠀⠀⠙⠢
⠀⠀⠀⠀⠐⢍⠩⡃⢄⣀⠠⡀⡠⠠⣀⠀⠠⣀⠔⠂⠀⠠⠘⡀⠀⠀⢁⠌⣷⠈⡀⡀⠑⠢⠄⣼⡦⡀⢄⡢⠀⠐⡉⠒⣠⢄⡀
⠀⠀⠀⠀⠀⢀⠹⣊⡐⠂⠥⠀⠘⠚⠒⠄⠂⢄⣠⠀⣇⡀⠂⠙⠅⠊⡀⡛⡀⠀⡨⠈⠸⠦⣔⠌⠉⢊⡐⡤⠄⠀⢀⠀⠤⡬⣇⢡⡂⠄
⠀⠀⠀⠀⠀⠀⠱⣈⠒⢵⣶⠐⠁⠀⠁⠀⠐⠀⠐⠶⡂⠑⠀⣄⠀⢀⠨⠈⢀⢠⣿⣀⠢⣀⣌⢀⣈⣉⣡⠭⠤⠒⡓⠚⠒⠶⠤⡀⠋⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠑⠈⠤⠬⣤⡀⠑⠦⠀⠂⢄⠅⣦⡑⢆⠷⠥⣘⠟⢉⠀⣀⡈⢚⡩⠟⠫⣠⠰⠵⣌⡀⠀⠉⠀⠀⠀⠈⠒⠄⡊⢆⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠩⡒⢍⠂⠈⠊⠹⢦⡄⠠⣹⡆⢈⠃⠀⣢⠞⠁⣀⠞⢁⢀⠀⠟⠀⠰⠀⠀⠀⢀⣥⣦⠔⡈⠂⠘⣕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡅⠈⠞⢄⠂⠁⡐⡍⠠⠈⠂⣼⠉⠀⠁⠇⠀⠉⠉⠀⠀⠀⢀⠀⠀⠀⢸⡄⠈⠁⠘⣄⠑⡈⡌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢅⠀⢲⡠⡈⠂⠁⡌⡼⠁⠀⡁⠠⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠁⠐⢿⡆⠰⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢢⡈⡂⣻⣬⣤⡻⢰⢂⣰⡆⢁⠐⠘⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠸⠖⢊⠄⠀⡅⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⡀⠀⢝⣌⠘⢏⢻⡎⢻⠁⠌⢀⢰⣆⡌⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡀⠊⠀⢸⣇⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠈⠻⡕⢝⠶⡇⠊⠀⠓⠀⡌⠀⠁⠀⠀⠀⠀⠀⠀⠲⠁⠃⠀⢈⡑⠔⠀⠀⢸⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢕⠋⣐⠅⠁⠢⠀⠜⠑⠈⠘⠄⠂⠀⠀⠀⡀⠀⠀⢹⠂⠐⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⠳⡀⠆⢡⠈⠎⠀⣀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠳⠆⠁⡊⠀⠀⣰⠃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⢝⡓⠾⡤⠐⠄⢸⡾⠟⠝⠒⠦⢀⡀⠀⠀⠀⠀⠈⠀⠀⡸⢁⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣅⠘⠄⠘⠢⢄⣔⠙⢶⡄⠀⠀⠠⠞⠀⠀⠠⢈⢀⠤⡪⠜⡡⠊⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢖⠢⠄⡐⠙⠳⠶⠬⠤⣀⣉⠀⠫⠔⢊⣩⠕⠀⠔⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢢⣄⢄⠉⠤⠤⠄⠀⠀⠠⠄⢚⠁⠠⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢉⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⢀⡤⠚⠁⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡟⠀⠀⣀⠴⠚⠁⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⡡⢋⡠⠔⠋⠁⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢋⣠⠾⠛⠉⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣀⡤⠖⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠯⠖⢚⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡾⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⣁⡤⠖⢉⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⠥⠖⠋⠁⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉
⠀⠀⠀⠀⠀⢀⡠⠔⠋⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣚⢥⡖
⠀⠀⠀⢀⠴⠋⠀⢀⡤⠖⠒⠉⠉⠀⠀⠉⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡠⠋
⠀⠀⡰⠋⠀⢀⠔⠁⡠⠴⠒⠋⠉⠑⠒⠲⠤⣄⡀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⡜⠁⠀⣠⠋⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠆⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⣸⠁⠀⢠⠃⠀⢹⣀⣀⡤⠖⠚⠉⠉⠑⠒⠒⠚⠁⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⡇⠀⠀⡍⠀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⡀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⡇⠀⠀⡇⠀⡇⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢀⡴⠋
⢳⠀⠀⢳⠀⢱⡀⠀⠈⢳⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⢠⠃⠀⡞⠀⠀⠀⢀⡴⠋
⠈⢧⠀⠀⠳⡀⠳⡀⠀⠀⡇⠀⠀⠀⠸⡄⠀⠀⠀⠀⣠⠏⢀⠞⠀⠀⢀⠴⠋
⠀⠈⢣⡀⠀⠈⠲⣌⠒⠚⠁⠀⠀⠀⠀⠑⠤⡠⠤⠚⢁⡴⠋⠀⣠⠖⠁
⠀⠀⠀⠙⢄⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠉⠑⠒⠒⠒⠊⠉⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⣀⣠⡤⠖⠋⠁
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠾⢟⡿⠋⢁⣀⣤⣤⣤⣤⣴⡶⣶⣶⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠁⣠⣶⣫⣴⡾⠟⠋⠉⢉⣉⣥⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⡀⠀⣠⡾⠟⠋⡉⠀⠀⣀⡴⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⣠⠞⠀⢀⣡⣤⣶⠏⢀⣠⣾⣫⣤⣤⣤⣤⣤⣴⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢿⠟⣋⣴⡿⠋⣠⠞⢋⡵⠋⣠⠴⠟⠛⠛⣉⣭⣭⠿⠟⠋
⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⣡⠞⢋⣼⡡⠚⢁⡴⠋⠀⠀⠀⠀⣠⡶⠟⠋⠁
⠀⠀⠀⠀⠀⢀⣾⣧⣾⠟⠁⢠⠟⠋⢀⣴⣫⣴⣶⠶⢃⣴⠟⠋
⠀⠀⠀⠀⠀⣾⢋⣠⠥⠤⠤⣅⠀⠰⠛⣩⠽⣋⣥⡶⠟⠁
⠀⠀⠀⠀⢸⡿⣩⠘⠁⠀⠀⠈⣧⢠⣞⣵⠟⠉⠁
⠀⠀⠀⠀⠈⣷⠉⣙⠀⠀⢀⠀⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠷⣭⣀⣀⣭⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡠⣀⡴⣂⡴⣠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣖⣠⣶⣿⣶⣿⣶⢿⣾⡿⠂⠂⠀⠀⠀⠀⠀⠀⠀⢀⡤⢂⣴⠊⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⣛⡽⢟⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⠀⡀⢀⣴⠟⣠⡿⢡⠀⡡⠂⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠋⠊⠺⢿⣤⣛⡄⡵⣿⣿⣝⠛⠛⠁⠀⠀⠀⢠⢞⣵⠞⣵⣿⠏⣴⣿⣣⡏⠈⠀⠀⠀⡀⠀⣠⡞⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⣦⠐⣃⡀⠀⠙⠥⠰⣾⣿⠟⠃⠀⠀⠀⢀⣠⠂⡴⡿⣫⡴⣼⠿⢾⣿⣿⠟⠀⠀⠀⠀⠚⣠⣾⣿⣿⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⡃⠸⠿⠃⠀⠀⢢⣾⠟⠁⠀⢀⡠⢀⣴⡏⣿⣞⣵⣿⣟⣵⣾⣿⣿⣿⠏⠀⠀⠀⠀⢄⣼⡏⣿⣿⣇⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠱⣿⡆⠀⠀⣠⠟⠁⠀⣀⡴⠋⣰⣿⣿⣿⣿⢟⣿⣿⣟⡟⣿⣿⡿⢣⡞⠀⠀⢀⣦⢏⣿⡿⣿⣿⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠀⠀⠊⠁⠀⠀⠰⣫⣴⣫⡿⢟⣻⠟⣡⣾⣿⣏⣼⢣⣿⢟⣵⠏⠀⡴⣱⡿⣵⢫⣿⢇⣭⢺⡏⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣿⠟⢁⣴⠟⢁⠜⢋⣾⣿⣿⣣⣫⠋⠈⠁⠀⢈⡼⣩⣿⣷⣿⣿⡿⣽⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠘⡁⠀⢊⡵⠀⡉⢀⠾⣿⣿⢟⣽⡵⠁⠀⠀⢀⣾⣿⣿⣿⠁⣿⣿⣣⡿⢾⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠈⢀⣴⡟⣁⣴⢏⣠⠞⠁⢀⣾⣿⢫⣾⠟⠁⠀⠀⣠⢾⠟⣡⡾⠃⠀⠋⣹⣿⣱⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡅⢀⣴⣴⣿⣿⣿⣿⣿⡿⢋⡤⠀⠋⣼⣳⣿⠃⠀⠀⢀⣴⠋⠀⡴⠟⢁⡆⡀⣼⠟⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣵⣿⡷⠿⠿⠿⢿⣿⣿⣿⣿⣶⠏⠀⠀⣼⣷⡿⠃⠀⠀⢀⡞⣡⣴⠿⠇⠠⢿⣿⠀⠋⠸⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡼⣻⠛⢉⠀⠀⣀⠀⠀⣀⣀⠙⢻⣿⣣⡴⢂⣾⣿⡿⠁⠀⠀⠀⠎⡴⠛⠁⠀⣾⣿⡄⠹⣾⠗⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠜⡼⠃⣼⣿⡗⠀⣉⣀⡘⢿⣿⡧⠀⢹⠟⡀⣸⣿⠟⠀⠀⠀⠀⠀⠸⢠⣶⡆⠃⣘⠛⠀⠀⠋⣴⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠛⠋⠀⣾⣿⣿⡷⢠⣄⠀⠀⢠⡾⣱⣿⠋⠀⠀⠀⠀⠀⠀⢰⠈⣛⢡⣾⣿⠇⠀⠀⠀⢇⡏
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⣦⠀⠙⠛⠛⠁⠈⠁⠀⠀⣸⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⣛⠁⢹⡥⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠈⠋⠀⠠⠦⠀⠁⠀⠀⢠⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠖⠂⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣄⡀⠀⠀⠀⢀⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣤⡾⠋
⠀⠀⠀⠈⠧⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⡤⠀⢀⣤⢖⣫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⠖⠚⣩⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣀⡤⠞⣉⠴⣀⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢊⡵⠞⠉⠛⠁⢀⣠⠴⠛⠁
⠀⠀⠀⠀⢀⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠞⠉⠀⢀⠔⠀⣴⡋⠁⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣀⠄⠀⠀⣠⠞⠙⠋⠁⠚⠁⠀⠀⣠⡴⠋⠀⠈⠁⠀⠀⠀⢾⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠻⠴⠋⡁⠀⠀⣀⠀⠠⢖⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠃⠀⠀⠀⠀⢀⡴⢋⣭⣤⣤⣤⣄⡉⠀⠀⠈⠁⠠⣶⡋⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⢠⣼⢱⡟⠅⣀⡂⢴⡏⢻⡆⠀⢠⢄⡴⠋⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢸⡅⣹⡇⠺⠥⠟⠨⣶⢈⣿⠠⣶⡋⢀⡠⠚⠁⠀⠀⠀⠀⢞⣁⣽⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠈⢧⡙⣷⡆⠲⠷⣀⣄⣼⣇⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣨⡛⠛⠛⣫⡽⠟⠁
⠀⠀⢀⡤⠻⢤⠀⠀⠀⠀⠉⠛⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠗⠒⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡥⠽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣔⢌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡻⢷⡕⢜⠦⣄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢽⣮⡓⢌⢦⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠠⡝⣿⣧⠳⣮⣊⡳⣔⣄⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢻⡌⣿⡇⢤⠳⡙⠚⠞⢦⡈⢆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢳⡘⠻⣮⣈⣉⠢⣝⢶⡝⢌⡑⢿⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣭⣓⡂⠹⣿⡳⣌⢡⣌⢢⡙⠧⢻⣄⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠹⣿⣆⢪⡉⡻⢄⢉⠳⠙⢿⡈⢿⣦⡝⣦⡀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣿⣯⡳⡌⡄⠀⠠⠈⡀⠓⢆⠉⡳⠌⢿⣶⣦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠙⢷⣤⣝⢦⣄⠧⠠⠀⢂⠀⢁⠀⠐⠉⠂⠲⠫⢿⣏⢿⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣙⢿⣷⣮⢱⡌⠀⠌⠘⠂⣄⠁⡀⠈⠁⠉⠄⢐⡘⢧⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠹⣿⣿⡿⢷⣦⢀⡂⠀⠠⣀⠀⠆⠐⠀⠐⢈⡌⠀⢀⠁⢸⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣌⣙⣻⣑⡲⢀⠈⠀⡄⡀⠀⠠⠄⢠⢈⠀⡀⠈⠈⡀⠈⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣝⢢⠀⢀⢀⠐⠀⠀⠀⢀⠈⠀⠀⠉⠐⢠⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣃⣝⠑⢀⠀⠀⡀⠀⠀⠀⠀⡀⠆⣀⠠⠤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⣷⠶⠀⡀⠁⢀⠀⠀⠆⠀⠤⠀⢦⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⣠⣤⣈⣎⡼⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⠿⠿⠿⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣊⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠠⠂⠀⠂⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠜⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣦⡄⠀⠀⠀⠀⡇⠀⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠆⠀⠈⠁⠀⠈⠉⠻⣿⠀⠀⠀⠀⠻⣄⣀⣨⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣯⣀⠀⠀⠀⢀⣤⠴⠶⣤⡈⠀⠀⠀⠀⠀⠈⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⣿⡆⠀⠀⠀⠀⠀⠀⣰⠏⠁⣠⣤⡉⢷⡀⢰⡏⠀⣠⣤⣄⠙⣆⠀⠀⠀⠀⠀⠀⠄⢄⠸⣇⣀⣀⣀
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠟⠋⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢿⡀⠘⢿⣷⠇⣸⠇⢺⡄⠀⢿⣷⡾⠀⡿⠀⠀⠀⠀⠀⠀⢃⠀⡃⠹⣏⠉⠙⠻⣷
⠀⠀⠀⢀⡴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠾⣷⣤⣀⣠⡴⠏⠀⠈⠻⣤⣀⣀⣤⣾⣁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⠧⠀⠀⢻⣇
⠀⠀⣰⠏⠀⠀⢀⡴⠒⢶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠐⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀
⠀⣼⠃⠀⠀⣰⠋⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿
⢸⡇⠀⠀⢰⡇⠀⠀⣰⠋⠛⠀⠀⠀⠀⠀⠀⠐⢚⡿⠿⢦⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⣠⣴⣶⡶⠄⠀⠀⠀⠀⠀⠀⡤⠂⠉⠐⡄⠀⠀⠘
⣿⠃⠀⠀⠘⢦⡤⠞⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠙⠛⠶⢶⠶⠶⣶⠿⠿⠛⠁⠀⠛⠉⠈⢧⡀⠀⠀⠀⠀⣠⠤⢼⡀⠀⠀⣠⠃⠀⠀⢀
⣿⡀⠀⠀⠀⠈⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢀⡾⠁⠀⠀⢻⠒⠋⠁⠀⠀⠀⣼
⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⢦⣤⣀⣀⣀⠀⠀⠐⠲⠶⠛⠀⠀⠀⠀⠀⣀⣀⣠⣴⠟⠀⠀⢸⠃⠀⠀⠀⢸⠁⠀⠀⠀⢀⣼⡟
⢸⣿⡀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠘⢆⣀⣀⡴⠃⠀⠀⣠⣴⡿⠋
⠀⠻⣷⡀⠀⠀⠀⡿⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣶⣦⣤⣤⣤⣤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣠⣾⡿⠋
⠀⠀⠙⢿⣦⡀⠀⢻⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋
⠀⠀⠀⠀⠙⢿⣆⠈⢧⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠲⡄⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠈⣿⣆⠈⠛⠶⠶⠛⠀⣠⠄⣀⠀⠀⠀⠀⣼⣤⣤⣯⣤⣴⣇⣀⡤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⣷⣿⠟
⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠣⡀⠀⢱⠀⠀⠘⠷⢤⣀⣀⣀⣀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣶⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⣿⣶⣶⣶⣶⣶⣾⣿⠿⠟⠋⠁
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢒⣒⢢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣤⠤⢤⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠞⣡⠶⠷⢿⣷⠠⣟⣥⡐⠢⡀⠀⠀⠀⠀⠀⢀⣾⢹⡇⢸⢟⠀⡾⢽⢻⡿⣏⠹⢷⡦⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣤⡁⠰⡴⠊⣋⣰⡯⠁⠙⣠⣿⣆⠀⠀⠀⢀⠼⣃⠘⣿⡆⠉⠀⢓⡿⢻⢇⣹⣷⣀⡴⢧
⠀⠀⠀⠀⠀⠀⢸⣯⣭⡋⣸⣄⡳⠦⠈⠹⣟⣀⣽⢿⣾⡿⠿⡀⠀⠀⢼⣦⣽⠴⠋⠀⠀⠀⠈⠈⠁⠾⣿⡟⡛⣣⠈
⠀⠀⠀⠀⠀⠀⡾⢿⣭⣿⣿⠻⣿⣿⣾⣿⣿⣿⡻⢏⣭⠘⡡⠃⠀⠀⢾⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⢿⡇
⠀⠀⠀⠀⠀⠀⢯⣷⢻⢿⣿⣿⣿⣯⣤⣾⣿⣿⠃⠻⡮⠴⠀⠀⠀⠀⠘⣿⣏⢰⠶⢶⣴⠮⠖⠀⠠⢿⣻⣗⠀⠸⡸
⠀⠀⠀⠀⠀⠀⠀⠻⠼⢿⣿⠿⣿⡟⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⠛⠎⠛⠢⠄⠀⠖⠛⠉⠍⣿⣗⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⣻⠿⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⢀⣠⣭⡿⢻⣧⠛⠻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠳⠭⠽⠗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢋⣀⣈⣀⡨⣽⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⢯⣿⣻⣃⣠⣀⠀⣿⣿⠛⡆⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣥⣀⡀⠀⠀⡠⢊⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠁⣸⣿⣿⢛⣿⣿⣿⣶⡑⢬⢁⣀⠀⠀⢀⣰⣶⣋⡿⣦⡉⠛⣿⣿⣋⡙⣯⡾⢿⣯⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⢀⣼⡿⢛⡟⢼⣿⣻⣽⣿⡇⣿⣼⢹⠀⠀⠸⡛⠿⣭⣴⣌⡻⠾⣋⣿⣿⣿⣟⣿⣷⣻⣿⠁
⠀⠀⠀⠀⠀⠀⠠⣿⡟⠇⣈⠻⠟⢡⡾⢣⡎⢉⣉⣉⣼⣱⣿⣿⡾⠀⠀⢀⣿⣶⡏⠻⢿⣿⡿⠿⣿⣿⣿⣿⣷⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠙⣝⣿⣶⡝⠑⠙⠣⠦⠖⣚⡋⢀⣿⠏⠀⠀⠀⢸⡿⣿⣿⣶⣶⣾⠁⠐⡙⠮⠩⠟⣫⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠘⠋⢼⢿⣶⣴⣶⣦⣹⣿⣿⡼⠃⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣧⣤⡶⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣟⣴⣧⣍⠛⣈⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣻⣻⣿⣿⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠴⠒⠚⠛⠛⠓⠒⣒⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠚⠉⠉⠀⠚⠉⡀⣀⣤⠤⠤⠴⠒⠋⢁⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⡡⠊⠁⠀⠀⠀⠀⠀⢀⡴⠒⠉⠀⠀⠀⠀⣠⠖⢁⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⠞⠁⠐⠉⠀⠀⣀⠀⠀⢀⡠⠞⠁⠀⠀⠀⢀⣀⡤⠞⠁⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠚⠁⠀⠀⠀⠀⡠⠊⢀⣠⣔⣩⠤⠤⠔⠒⠚⠉⠛⠉⠀⠀⢂⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠀⢀⠞⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⣀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⣐⣁⡠⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⡴⠊⠁⠒⠲⠀⠐⠢⣕⢢⡀⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠖⠋⠉
⣼⠁⠁⢴⣦⢾⠆⢺⠅⠈⠆⠃⠀⠀⠀⠀⣀⣠⠤⣤⠶⠒⠛⠉⠉
⡇⠀⢀⠐⠃⢀⣠⣈⣼⠀⡜⠀⢀⣀⣤⠤⠤⠖⠋⠁
⠹⡄⠀⡲⠤⡀⠀⠑⠮⠔⣁⡴⠋⠁
⠀⠈⠢⣌⣑⡒⢂⣀⡤⠞⠁
⣶⡶⠲⠖⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠠⡀⠐⢄⠚⠨⠄⠄⢀⠤⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣠⠎⠀⢠⢞⠀⣀⠉⣀⠦⡈⢁⡁⠌⠀⠠⠤⠂⡤⠀⡁⠁⠉⠁⠀⠢⠀⠔
⠀⠀⠀⠀⠄⠀⢀⢀⡄⠀⠨⠚⢰⠴⠛⡳⢈⡀⣀⣘⣠⠟⢉⡥⢞⣤⣥⡃⠠⠖⣶⣶⣴⠿⠶⠐⣊⡼⣲⡬⢀⠀⠀⠤⠀⠄
⠀⠀⠀⠀⠀⡆⠈⠀⠄⡨⢣⣴⠇⠴⠟⠐⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠉⠁⠉⠥⠌⠀⠊⠻⠔⠐⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⢠⠈⣠⠴⠊⠉⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⡀⠀⢀⠀⠂⢠⡄⠀⠀⠀⠀⢐⠀⡉⠀⠘
⠀⠀⠀⢀⠴⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢂⠀⢐⢨⣴⢪⡔⠢⠕⠛⠉⠉⠐⠡⠶⠀⠀⠁⠃
⠀⠀⠰⠃⠀⠀⠁⠀⡀⠀⡀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡤⢎⣉⡫⡈⠉⠁⠘⠐⠂⠰⣀⣄
⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠴⢺⠅⡀⠉⡠⠀⠠⠐
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠔⠒⡘⠃⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠫⡥⠄⠑⠂⠁
⠃⢐⡈⠸⠃⠀⠀⠘⠀⠒⠠⢣⡞⠢⠈⣴⡋⡀⠀⠀⠀⣀⠔⢁⡀⢩⠂⡀⢀⡤
⠀⡀⢤⠀⠀⢰⡶⣀⠀⠀⠜⠀⠉⣤⣠⡔⡴⠃⠀⠀⠀⣁⠔⣁⣰⠦⠤⠍⠉
⠀⠡⡈⢿⣠⢮⣖⡵⠿⢉⣵⡷⢮⡀⡼⣷⢏⠀⣠⡡⠈⣼⡷⠋⠃
⠀⠀⠐⠀⠁⢌⣽⢦⠀⢥⡻⣄⣬⣰⡻⠋⢀⠔⠁⡀⠟⡉
⠀⠀⠀⠀⠐⠀⠈⠉⠉⠉⠓⠋⠉⣁⠨⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⢤⡀
⠀⠀⢈⢙⠃⠄⠀⠀⠀⠀⢀⠀⣄⠀⢀
⠀⠀⠈⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⣐⠀⢄
⠀⠀⠀⠀⠀⠈⠀⠈⢆⠀⠀⠀⠀⠀⠀⠘⣄⠀⡀⠑⠆⠀⠀⠀⠀⠀⢄⢀
⠀⠀⠀⠀⠀⢌⠀⠀⢈⠀⢠⡀⠀⠀⠀⢀⣜⠀⠀⠀⡢⠐⠀⠀⠈⠲⠀⠈⠑
⠀⠀⠀⢠⠀⠀⣈⠂⠀⠀⡀⠘⠃⠙⠈⠉⠀⠀⠀⠀⠀⣢⡀⠒⠀⠚⠀⠀⠐⠀⠐⠄
⠀⠀⠀⠀⢕⠒⠏⠀⠀⠀⠈⡀⠀⢀⠀⠤⠀⠀⠀⠁⠀⢀⢮⠉⢀⠐⠄⡀⣤⠀⢀⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠒⠄⠀⠤⠄⠃⡀⠈⠂⠂⣘⡀⠀⡀⠁⠢⠄⠉⣀⡠⠠⠄⠀⠀⠤⠭⠀⡀
⠀⠀⠀⠀⠀⠘⠀⠐⠿⠀⠀⠀⠀⠀⡀⠙⠂⠀⠐⢄⢠⡀⠠⣤⠷⠄⠢⢦⢤⣬⠴⢒⠂⠍⠉⠙⠓⠀⠁⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠈⠁⠀⠀⠜⢢⣁⠁⠀⡄⠀⠐⢆⡴⠊⢠⠞⠉⢱⠂⠀⠀⠀⠀⣤⣈⠈⠔⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠲⢄⠌⠀⢜⠁⠠⢠⠎⠀⠀⠁⠘⠊⠀⠀⠀⠀⠀⢸⡉⠉⠑⣄⠂⢩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠀⢢⡀⡀⢀⢀⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⣻⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⠀⡟⠳⡄⣬⣲⠇⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⣴⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⡆⡱⣼⠠⠃⡀⢀⠉⠃⠀⠀⠀⠀⠀⠄⠀⠀⢀⠐⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡋⢈⠈⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠐⡈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡑⡔⣠⠀⠀⠠⣀⣀⣀⡀⠀⠀⠀⠈⠃⠠⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠣⠈⠀⠯⣀⠀⠉⢐⡄⠀⠀⠀⠀⠠⡠⠂⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠄⠀⠛⠢⠬⠥⡄⠈⠐⠀⢒⣋⠅⠠⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠄⠁⠀⠀⠀⠀⠀⠈⠀⠂
⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣤⠴⠖⠚⠛⠉⠿⠿⠛⠀⠉⠉⠹⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⢻⠦⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⠉⠀⢄⣤⣶⣶⣾⣶⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⡈⡉⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠋⠀⠀⢀⡄⠿⣿⡿⠿⠿⣫⡾⡏⠀⠀⢁⣤⡾⣯⣾⣿⣿⣶⡄⠀⠀⠈⠣⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠈⠛⡶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠠⣿⠸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠻⢾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⠻⠿⣳⣶⣦
⠀⠀⠀⠀⠀⠀⢀⡾⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⣛⣭⡾⠇⠀⠀⠀⠠⠀⠐⢾⢹⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢰⢻⣇⠀⠀⠰⠀⠀⣼⡄⠀⠁⠀⠀⠀⠺⣿⣿⣷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⡘⣿⡷
⠀⠀⠀⠀⠀⢹⡿⠁⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡞⣿⠂⠀⠀⠀⠀⠀⣰⣿⣿⣿⠁⠀⠀⠀⠀⣾⣷⠾⠃
⠀⠀⠀⠀⠀⠘⢿⡦⠀⠀⠀⠀⢸⣿⣿⣧⢀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⢠⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢹⣆⡀⠈⠀⠀⢻⣿⣿⣿⣤⡀⠈⠛⠋⣭⣻⡯⣿⠋⠀⠀⠀⠀⠰⣿⣿⣿⡿⠃⠀⠀⠀⠀⣁⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⡆⡀⠐⠀⠙⠻⡟⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⢠⢞⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡗⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣴⣃⡿⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣣⣟⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⢤⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠁⣿⣿⣿⣿⣿⡆⣿⠀⠀⠀⠀⠀⠐⢈⣡⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣤⣀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠸⠿⠯⠍⠀⠁⠀⠀⠀⠀⢠⣽⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣚⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣶⡶⣶⣶⣤⣿⣻⣧⣠⣽⣯⣥⣀⣠⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠿⣭⡽⠟⠁⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠉⢿⣲⣦⣌⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠠⣈⡳⢿⣿⣷⣦⣐⠂⢔⡀⣀
⠀⠀⠀⠀⠀⠠⡀⠈⣿⣶⣿⣿⣿⣿⣿⣦⣌⠪⣕⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡈⡙⢿⣿⣿⣿⣿⣿⣿⢷⣌⡳⠄⠙⡲⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠻⢿⢿⣿⣿⣿⣲⣭⡻⣷⣦⣝⡢⠁⢬⡀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡉⠻⣿⣿⣿⡝⢿⣯⣿⣿⣷⣦⣙⠶⣤⣄⠈⠳⠄⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠹⣄⠀⠙⢶⡌⢿⣿⣿⣬⡙⠿⣿⣟⢿⣿⠷⣦⣌⠓⠐⣄⠈⠳⣄⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡘⢷⡄⠀⠙⢧⠹⣿⣿⣿⣦⡙⢿⣿⣿⣷⣄⡙⢿⣦⡘⠷⢦⡈⢳⡄⡑⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠻⣤⡄⢦⡀⠈⠻⣿⣿⢷⣀⡙⠻⢿⣿⣿⣦⠙⠿⣷⣶⣌⠂⣑⠘⢦⠠⣌⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠹⢮⠳⣌⠻⣿⣿⢿⡷⣤⡙⠿⣿⣿⣶⣦⡈⠻⣧⡙⠳⣌⠓⢦⡳⣌⢧⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⢀⠀⠁⠘⢷⣄⡙⠻⢿⣦⡝⢷⡄⠙⢷⣿⣿⠠⣝⠿⣷⣬⡙⣦⠹⣦⣈⠳⠄⢢⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠱⣄⠀⠀⠰⠙⣷⣮⠻⢿⣦⡹⣦⠀⠙⢿⣧⣙⣇⠈⢻⣿⡌⠳⣬⣙⡛⠦⣌⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠱⣄⠀⠘⢿⣷⣦⣬⡛⣿⠀⠀⣀⣈⠉⠻⣦⡀⠹⣷⣄⠙⠻⠿⣷⣜⣧⠉⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠈⣂⠘⣦⣍⣉⡙⠻⣼⣇⠀⠉⠉⠀⠀⠈⣧⡀⠙⠛⠻⢿⣦⡈⠙⢿⣧⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠈⠓⠙⠧⠈⠻⣿⣿⣇⠈⠙⠿⣷⣚⠀⠀⠀⠈⠙⠳⠆⠀⠀⠹⣧⡀⠀⢻⡎⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⢤⣬⣙⣿⣆⠀⢠⠌⠉⠀⠀⠴⠷⠀⠀⠀⠛⠀⣤⠙⠻⣦⠛⢿⣦⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠈⠳⢦⡙⢿⣇⠉⠛⢃⡀⠐⠾⠀⠴⠂⠀⠀⠀⢀⡄⠀⠀⠀⠘⣧⠀⣿⡇⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⢦⡀⠈⠈⠻⣷⣄⢈⡁⢴⠄⠀⠀⠀⠀⠀⠀⠨⠄⠀⠀⠀⠛⠋⠀⣼⡇⠸⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠳⠀⢦⣄⣈⠻⣦⢥⠀⠀⠶⠀⠀⡁⠀⠀⡄⠀⠀⣤⠆⠀⣀⠀⠀⠁⠘⢺⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠙⢿⣿⡛⠀⠀⠀⠴⠆⠀⠉⠀⠀⠀⠴⠂⠀⠀⠀⠉⠀⠠⡄⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠶⢀⣀⠀⢠⡖⠀⢠⡄⠀⢀⡀⠀⡤⠀⠀⠀⠁⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠶⣮⡍⠀⢠⣤⢠⠀⠤⠀⠀⠀⣀⠀⠀⠁⠀⠠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣀⠀⠀⠀⠘⠃⠘⠀⡬⠀⠀⡠⣷⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣀⣀⣠⣀⣀⣶⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢢⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣻⠟⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡀⠀⠀⣰⣧⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⣰⢿⠖⠋⢀⣤⣞⣡⡿⠀⠀⠘⢋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠡⠷⠋⠁⢀⣠⠖⠋⠾⢋⡼⠁⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⣠⠋⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⢀⣄⠀⢀⠀⡴⠋⠀⠀⠀⠀⢠⠞⠁⠀⠀⣠⣯⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⡿⢀⡴⠋⣇⡴⡿⠀⠀⠀⠀⠀⠀⣴⡧⢾⠀⠀⠚⢋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠸⠟⠉⠀⠈⠉⣸⠃⠀⠀⠀⠀⠀⠾⠋⢠⠏⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⠀⠀⠀⠀⣰⠋⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⣴⡏⠀⠀⢀⡜⠁⠀⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⣠⠖⢉⡞⠀⠀⠀⣻⠇⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠵⠋⠀⢠⡿⢾⠇⢀⣼⠏⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⢠⣯⠔⣻⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣼⣵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠋⢀⡀⣠⣄⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⠋
⠀⠀⠀⠀⢀⡤⣶⡿⠟⠉⠙⣉⡈⠉⠉⠉⠉⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⢠⠯⣾⠋⢀⠀⠀⠈⠯⠁⠀⡴⢧⡀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⢻⡄⢸⡇⣞⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣰⠇⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⡼⠡⡏⠀⠈⣧⣄⠀⠀⠀⠒⠳⣄⠚⠁⠘⣧⠀⠀⢀⡴⠋
⠀⠀⢼⡅⠀⣿⠀⠀⢀⡇⠀⠀⠀⠰⠄⠘⣇⠀⠀⡟⢠⡶⠋
⠀⠀⠸⣇⡀⣿⣀⡀⠀⠉⠛⠛⠀⠀⢠⡤⠞⢁⡼⠃⣺
⠀⠀⠀⠀⡷⠈⠉⠉⠳⣦⣀⣀⣀⣀⢀⣠⠴⠋⡴⠋⠁
⠀⠀⠀⣰⡧⠞⣆⣠⣤⠈⢉⡁⠈⢛⠛⣡⠖⠛⠁
⠀⠀⠀⠈⠀⠀⠛⠁⠘⠒⠉⢹⡴⠋⠟⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿