Black and white dog Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠂⠀⠀⠒⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠴⠄⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⣤⡴⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⡘⡹⠁⠀⠀⠶⠶⢀⠁⠀⠀⠀⠀⠀⠀⠀⢦⠔⠀⠀⠀⠀⠹⣦⡀⠄⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⢐⣿⠇⠀⠀⢠⣶⣷⡆⠀⡄⠀⠀⠀⠀⠠⠀⠀⣴⣖⢲⣤⠁⠀⣿⣷⣄⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢰⣾⠀⢠⠀⠙⠿⠟⠋⠐⠀⠀⠀⠀⠀⠀⢰⡏⠛⠿⠿⠋⠁⠠⠸⣿⣟⠀⢰⡇⠀⠀⠈⠂
⠀⠀⠀⠀⢀⠟⣀⡆⠀⠀⢸⣿⠄⠀⢠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⠀⠃⠀⢻⣿⡀⠘⠇⠀⠀⠀⠀⠲⡀
⠀⠀⠀⠀⣼⡞⠋⠁⠀⠀⠘⣿⠀⠠⡍⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⢾⣿⣷⢀⠀⠀⠀⠀⠀⠲⠳⢄
⠀⠀⠀⠀⣿⣿⣶⣠⠀⠀⠀⢻⡆⡦⢀⡀⠀⠀⠈⢀⣦⣴⣦⣴⣾⣿⣦⡀⢠⠀⠀⠀⡀⠈⢱⣴⢻⣿⡤⣷⣦⡀⠠⣶⢆⣰⣮
⠀⠀⠀⠀⣯⣿⣿⣿⠾⡼⣶⢸⣇⡇⠈⣾⡁⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⠇⠀⠡⠀⣀⣿⡿⢸⣿⢸⣿⡇⣿⣻⣷⡾⠿⣠⡟⠃
⠀⠀⠀⠀⢹⣿⣻⣇⣾⣿⣿⢸⣶⠙⢄⠸⣏⠊⠀⠀⠉⠛⢿⣿⠿⠟⠉⠀⠀⠀⢰⠟⠁⠴⢿⡿⠻⣿⡇⢻⣿⣿⠆⣴⢻
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡄⣸⠧⠀⠀⠀⢰⡄⠀⠀⠀⠀⣤⣁⠆⠀⠀⠀⠀⢠⡞⠀⠀⣀⣌⠀⢤⣿⣷⠸⣿⣫⣤⢋⡎
⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⢰⢏⣴⡗⠀⠀⠘⢿⣶⣤⣶⡴⠿⢿⣿⣶⣶⣤⡴⢏⡽⠋⠀⠀⠀⠀⠸⡛⢿⡆⣿⣻⣷⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠵⢿⠉⠁⠀⠀⠘⠓⠀⠻⢿⣯⠀⠀⠈⠀⠀⣸⣿⡽⠁⠀⠀⠀⠀⠢⠀⠀⠈⣊⣿⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠈⢿⣦⣄⣀⣀⣴⣿⠟⠀⠀⠀⠀⠀⠀⡄⠀⠀⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣼⣦⠀⢰⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⢰⡦⠀⠘⣂⣀⣼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠇⠹⡇⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠰⠿⠟⠟⠛⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠈⠀⠸⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢌⡂⠀⡄⠀⠀⠀⢀⡀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠈⠻⣷⣦⠘⣖⢠⣀⠀⣤⣰⣤⠀⠘⠛⠀⠀⠀⠀⠀⠀⠉⠐⢈⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠉⠑⠛⠊⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠷⣿⠛⠛⠿⣛⠛⠛⠛⠛⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⠴⠶⠖⠛⠛⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡀⠀⠀⠀⠀⢀⡴⢟⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡴⠋⣰⠟⠁
⢠⡶⠀⠖⠲⠶⠶⠚⠉⣀⣠⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠈⣻⠛⠦⣄⣀⣠⣼⠷⠀⢀⡾⠁⢰⡟
⠛⠲⢦⣤⣀⠐⠛⠓⠿⠛⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠛⣿⡇⠀⣿⠀⠀⠀⠉⠁⠀⠀⢠⠟⠀⢀⣿⠁
⠀⠀⠀⠈⠉⠛⢦⣄⡀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣟⣁⣀⡙⣷⠀⢻⡏⠛⠒⠲⠶⠤⠴⠋⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣿⠃⠀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⠿⣿⣿⣆⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠚⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣾⣿⠿⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢰⡄⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢸⡇⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠙⢿⣿⣿⣿⣿⠇⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢹⣿⠁⣀⣠⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠖⠒⠻⣆⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⢀⣈⠉⠙⠛⠛⠛⠋⢁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⡖⠁⠀⠀⠀⠙⣆⡀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⢀⣴⠟⠉⢹⡟⠒⠲⠖⠋⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⢇⠀⠀⠀⠀⠀⠀⠉⠛⢦⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⢠⣟⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠁⠀⠀⠨⠟⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢸⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⣿⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠹⣤
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣠⡟

⠀⠀⠀⠀⠀⠀⠀⢀⡠⣠⣤⣄⡀
⠀⠀⠀⠀⡶⠒⠂⣿⣽⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢄
⠀⠀⠀⠀⠡⢀⡀⠉⣿⣿⣿⣿⣿⡿⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡆
⠀⠀⠀⠀⠀⠀⠁⣾⣿⣿⣿⡿⠋⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡿⠁⠀⠀⠀⠈⢲⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⢤⣤⣤⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠁⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣹⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣫⣿⣿⡟⠣⣤⠉⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⡇⠀⠠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠚⠃⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣉⣭⣥⣤⡀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣡⠀⢸⠛⠛⠿⠿⠖⠒⠒⠋⠉⠁⠀⠀⠹⣷⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⢦⣀⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⢠⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠍⡎⠹⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣤⠞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠔⠁⠠⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠦⠎

⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⡔⠓⣦⢀
⠀⠀⠀⠀⠀⠀⠁⢰⡆⠀⠀⠀⡇⠀⠃⠀⣄⠂⡀
⠀⠀⣀⡠⠂⠀⠀⠈⠓⠀⠀⠀⡇⠀⢀⣼⢏⠀⠈⠢
⠀⠀⠲⣖⠀⠀⠀⠀⣀⡤⣄⠀⠹⡶⠋⠁⣾⠀⠀⠀⠘⣦⣤⣀
⠀⠀⠀⠈⠀⠔⠒⢈⠽⠶⢋⠀⠀⠀⠀⠀⣟⠀⠀⠀⣴⡟⠁⣿⣧⡈⢲⣶⣶⣶⣶⣤⣴⣶⠶⠶⡶⠶⠶⡤⢤⣄⣀
⠀⠀⠀⠀⠀⠚⠞⠃⠀⠀⠀⢠⡀⠄⠀⢲⡏⠀⠀⡼⠁⠀⣠⣿⣿⡆⠀⢹⣿⣿⠳⢦⣤⣤⣤⢶⣶⠶⠤⠄⠀⠀⠀⠈⠀⠲⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠈⡇⠀⠀⠀⠀⠀⡈⢻⣿⠀⠀⠸⡏⠁⠀⢰⡿⠇⠈⠂⠉⠀⠀⠀⠀⢀⡴⠀⠀⠳⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⣸⠁⢸⠏⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠓⠃⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⢦⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⢻⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⡄⡑⠂⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠱⡀⡌⢳⠀⠀⠀⢰⣏⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⣾⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠶⠶⠿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠚⠦⡀⠀⠀⠉⣼⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢹⡆⠙⢿⣿⣦⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣼⠟⠀⠀⢸⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⢹⣿⣧⣀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⡈⢿⣿⣿⣧⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⡿⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠻⣿⡟⢳⡀⠘⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠁⠀⢱⠀⢘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣸⠀⢰⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡟⠀⠀⠈⠂⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠈⢰⠇⢀⠌⡀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠧⣤⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠛⠁⣴⣉⣏⣃⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠳⠛⠀⢰⡄⣌⣁⠂

⠀⠀⠀⠀⠀⠀⡀⠼⠋⠉⠀⠐⠤⠀⠀⡀
⠀⠀⠀⠀⢀⠜⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀
⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠌⣠⠆⠊⠀⠀⠀⠀⠀⠀⠁⠈⠲⠄⠀⠀⠀⠀⠑⠠⡀
⠀⣰⠀⢀⣄⡢⡀⠀⠀⠀⢀⣠⣔⢀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠢
⠀⠀⡀⢸⣽⣷⢠⠀⠀⠀⢸⣷⣿⠆⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠑⡀
⠀⠀⠠⠈⠻⢥⠆⠀⠀⡄⠀⠛⠉⠊⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐
⡇⠀⠀⠃⠀⠈⠠⣀⠔⠁⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⢁
⡇⠀⠀⢄⠀⠀⠀⠰⢄⡀⠀⠀⠀⣠⠔⠁⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⠈
⠃⠀⠀⠀⠁⠀⡏⠀⠄⠀⠉⠍⠔⠁⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠠⠀⠀⠀⠀⠀⡟⡀⠀⠀⢠⠌⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠑⠄⠀⠠⠈⠈⠢⢤⡠⢂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠐⡉⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⡀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⡆⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠒⢤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠡⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉
⠀⠀⠀⠀⢔⠂⠀⠒⢂⣀⠀⢀⠀⠀⠀⠀⠀⢠⡀⠄⠐⠛⠉⠓⡀⠀⠀⠀⠀⠀⠀⠀⢠⠌
⠀⠀⠀⢁⠃⠠⠊⠐⢀⠄⠀⠉⠀⠀⠀⠀⠀⡈⠔⢁⠠⠀⠀⢀⠈⠦⢀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠐⠬⢀⡁⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠰⢧⠀⡆⠀⠀⠨⠁⡠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠠⢀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠁⠁⠈⡀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣤⠔⠒⠈⠉⠉⠉⠉⠉⠉⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⣤⡀⠀⠀⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠆⠀⢀⣄⡀⠀⠀⠀⠀⠀⣀⠉⠀⠀⠀⠆⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢰⠀⠀⠳⠟⠉⠀⠀⠀⠀⠀⣙⣃⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⡎⠀⠀⠀⠀⠞⠁⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠰⠀⡇⠀⡀⠀⠈⠳⡀⢀⡤⠂⠀⠀⠀⢠⠀⠀⢰⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣸⢿⡀⢣⡂⡀⠀⣨⣅⣀⣀⣀⣠⢴⠏⠀⣠⡿⢦⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⠳⣄⠹⣌⡏⠀⠀⠀⢹⣉⡴⠃⡠⠊⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠈⢧⣸⠀⠀⠀⠀⢸⡁⣠⠎⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠸⡄⠀⠀⠀⡇⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⠀⠀⢳⡀⠀⠀⠘⠲⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢸⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢀⡇⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⣾⠃⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⣆⠇⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡜⢳⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⡆⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢀⡼⠀⠈⢧⠀⠀⠀⠀⠈⣇
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠉⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣴⠋⠀⠀⠀⠈⢧⡀⠀⠀⠀⢻⡀
⢠⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠈⡇⠀⠀⠀⡼⢻⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠘⡇
⡎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠸⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢿⠀⢀⡜⠁⢸⡆⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢳
⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⢀⠃⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠸⡆⠈⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠘⣇
⢳⡀⠘⢆⡀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠸⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢻⣤⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢻⡀
⠀⠳⣄⠈⠙⠲⠤⣤⣤⡤⠶⠚⣆⠀⠀⠀⢀⠀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⣷⠖⠛⠓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠈⢷⣀
⠀⠀⠈⠳⢦⣄⣀⠀⠀⠀⠀⢀⣘⣶⠀⠀⡀⠀⠉⠻⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡇⠀⠀⠀⠸⣦⣀⡀⠑⣎⡧⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁⠳⣤⣤⣧⣀⣸⣄⡼⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⣧⠀⠀⢰⠀⠠⡍⢻⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⡦⠀⠙
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣳⣶⣛⣤⣤⣷⣚⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣛⣛⣊⣉
⣿⣿⡟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡌⠊⠒⠹⠅⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣍⠉⢲⡭⢀⡐⠀⠀⠀⠀⠻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⣿⣿⣿⣶⠇⠈⠀⠀⠀⣀⠀⢖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠠⠁⠀⠀⠀⠀⠀⠀⢸⡅⠸⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡧⣅⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⣀⣠⣄⣀⠴⠲⠊⠀⡇⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⠀⢠⠀⠀⠑⠢⣀⡀⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣼⡉⠒⠒⠒⢒⡿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠃⠛⠉⠉⠉⠁⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠈⠑⠦⡀⠀⠁⢱⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠘⡆⠀⠀⠋⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⣆⠀⢹⠀⠀⡇⠀⣀⣀⣀⣀⠀⠙⠶⣄⠀⠀⠀⠸⡀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠬⡇⠀⣧⠞⠁⠀⠀⠈⠙⠦⠀⠈⠳⣄⠀⢠⠇⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢹⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡎⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠙⣲⣷⢸⡆⠈⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢴⣋⡤⠈⠉⠁⣼⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣸⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠔⠊⠙⠳⠛⠶⠚⠉⠉⠛⠛⠛⠋⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣶⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠀⠀⠻⣿⣿⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠟⠙⠉⠀⠀⢀⣀⠈⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠸⣿⣿⡿⢸⣿⠟⠋⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⣬⣯⣴⡿⠋⣀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠈⢷⣤⡾⠀⢸⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢠⡿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠛⠀⡀⠀⠀⢀⣿⡇⠻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣄⣴⣿⣿⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣷⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⢰⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠁⠸⡇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠻⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⠛⣤⣤⣠⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⢀⣀⣨⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠈⣆⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⢀⣠⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⡄
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⢀⣤⣴⡶⠶⢦⣤⣄⣀⢀⣀⣤⣶⠿⠿⢷⣮⡙⢿⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿
⠀⢰⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⢳⣦⣀⣴⠟⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠈⢿⣦⠐⠛⠛⠿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢿⠝⠁⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣿⣧⠀⠀⠀⠈⠻⣿⣿⣿⡿
⣸⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠋⠙⠻⣿⣷⠀⠀⠀⠀⠀⠀⠉⠉⠛⢷⣶⣿⣿⡆⠀⠀⠀⠀⠹⣿⡿⠁
⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⢿⣦⢸⡟⠀⠀⠀⠀⠀⣰⣿⢿⡷⣄⠹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠿⠛⠉⠈⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠉⠀⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠀⠀⠀⠀⢀⣠⣤⣶⣦⣤⣄⠈⠉⠛⠲⠶⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠸⣿⢻⣿⣿⡛⣿⠃⠀⠀⠀⠀⠀⠉⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⡿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠀⠀⣀⣴⣿⣿⣦⣄⣀⠀⢀⣀⣠⣾⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠻⠿⠿⠿⠟⢋⣟⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⣠⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣶⣾⠟⠋⠁
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠀⠂⠘⠂⠀⠂⠒⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⠀⡎⣠⣄⠀⠀⢀⣴⡈⡆⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⡀⢀⠁⠉⠁⣴⢶⡄⠉⠀⡃⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣼⠀⡀⠀⣿⣿⡇⠀⡀⢸⣄⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠚⡘⠻⢶⡉⠉⣱⠾⠁⠘⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠁⡂⠒⠟⠛⠕⠂⠊⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠲⢯⣿⣿⣷⣾⣷⣶⣶⣶⣶⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⢋⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⣧⠈⢿⣿⣿⣿⡿⠁⢹⠂⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠰⠟⠀⠀⠋⠻⡏⠀⠀⠙⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣤⢾⠀⠐⠀⠐⠀⠀⠀⡄⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠛⢦⠚⠈⠈⠁⠖⠁⠀⡐⠓⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢱⠀⡀⠀⣎⢁⠀⢸⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡠⣞⠀⠁⠀⠈⣯⠄⠘⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠊⠀⡏⠓⠠⠔⠚⠁⠀⢸⠐⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠚⠁⠀⠀⠀⢐⡄⠀⠘⡓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣿⣟⣛⣟⣛⣻⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣤⡶⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⡄⠰⡀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⣠⣤⣿⠁⠀⠀⠁⠀⠁⠀⢰⡌⠳⣄
⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⢀⣾⣿⣯⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⢧⣹⡇
⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠊⠁⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⡀
⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣽⣷⣦⡄
⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⢿⣆⠠⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠻⣷⣴⡄⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡏⠁⣿
⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⣿⣿⣿⣿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣠⣤⣤⣤⣴⣿⣿⣿⣿⣿⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⡿⠛⣻⣿⣿⠿⢿⣿⣿⠃⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠞⠀⠀⡞⠟⡿⠀⠀⠘⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⢳⠀⠀⠀⠐⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢳⡀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠜⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠈⡘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⣀⡀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⣾⣿⣿⣿⣷⣄⠀⠐⣮⠣⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⡠⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⡸
⠀⠀⠀⡇⠀⠈⠳⡤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣶⣾⣿⣦⠀⠻⣿⣿⣿⣿⣿⡿⢅⣠⣀⣈⡦⠤⠊
⠀⠀⠀⠘⢄⡀⠀⠂⠀⠈⣽⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠃⠀⠈⠉⡿⠋⠉
⠀⠀⠀⠀⠀⠈⠙⠒⢦⠰⣿⡿⠋⠙⠛⠿⠿⠟⠀⠀⠉⠉⠁⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋
⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢀⠴⢤⣄⣀⡀⠀⠀⠀⣀⡀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⠔⢉⡴⠋⠀⠀⠉⠉⠉⠉⠁⡇⠀⠀⡎⡇
⠀⠀⠀⠀⠀⠀⢷⠀⠀⡏⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⣷⡃
⠀⠀⠀⠀⠀⠀⠘⢦⣤⣙⡦⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣤⣽⠿

⠀⠀⠀⠀⠀⠀⢀⠤⠒⠋⠉⠙⠲⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠑⠢⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠲⡄
⠀⠀⠀⢠⠀⠀⣠⠏⠀⠀⠀⢀⣁⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸
⠀⠀⠀⠘⣄⡰⠃⣠⠔⠚⠉⠉⠁⠀⠉⠉⠑⠢⢀⣤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸
⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢹⡄⠀⢀⡠⠤⠖⠒⠲⠤⠄⠀⠰⠁⡏
⠀⠀⠠⡤⠐⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠈⣗⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⢸⠅⠀⠈⠁⠀⠀⠀⠀⣰⣶⠀⢰⠃⠀⠀⠀⠀⢀⡀⠀⠀⢿⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⡆⢰⣶⣦⡀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠠⠒⠊⠉⠉⠉⣳⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠣⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢃⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢀⡙⠓⠶⢶⢖⠻⠁⠀⠀⠀⠀⠀⠀⢀⣀⡴⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⡼
⡔⢉⠄⢀⡎⠀⢀⡴⣁⣀⡤⠴⠀⠤⣄⣀⣀⠴⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠱⡃⠀⠈⠧⠴⠊⠀⢀⢀⣀⣀⣀⣀⡀⠀⢀⠂⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠑⠄⢧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠃⠀⠀⠀⠀⠀⠀⠀⡾⠤⠒⠂⢷⡀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠈⠑⠒⠁⠀⠀⠀⠀⢀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠈⠙⠦⢤⣄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡄⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠘⢄⣀⡴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠚⠋⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠲⢄⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⡄
⠀⠀⠀⠀⢰⠀⠀⠀⡴⠁⠀⠀⠀⠈⢃⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⡀
⠀⠀⠀⠀⢠⠀⢀⡞⠀⠁⣀⡤⠤⠶⠖⠒⠺⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⡇
⠀⠀⠀⠀⠈⠦⠊⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⠞⠛⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢸⡇
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⡠⠴⠒⠒⠒⠒⠒⠤⠄⠀⠘⠀⡟
⠀⠀⠀⣀⠄⠈⡼⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠐⣌⠀⠀⠉⠁⠀⠀⠀⠀⠀⣠⣦⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⢰⠁⣠⣤⡀⠀⠀⠀⠀⠀⠀⠧⠞⠀⠐⠀⠀⢀⡠⠴⠒⠒⠓⠲⡄⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⢃⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠇⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠈⠀⠘⡟⠛⠃⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠥⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⢀⣀⠀⠀⢢⠜⠙⠛⢛⠟⠫⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⡜⢁⡄⠀⢰⠃⠀⠀⡴⢃⣀⣀⡤⠖⠀⠤⢄⣀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠡⡎⠀⠀⠸⣤⡤⠞⠁⠀⠈⣀⣀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠑⠄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⡤⠤⠼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠳⢄⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠹⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠆⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠳⣄⣠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡠⠔⠒⠉⠉⠷⠿⣶⣦⣭⠭⠉⠉⠉⠙⠳⣆⠠⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣴⠶⠆⠀⠐⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢺⡏⣠⠀⢠⠂⠀⠀⠀⠀⠀⠀⠈⠀⠢⡀⠀⠀⠘⡇⠀⠄⠀⠀⠀⠀⠈⣏⢧⠸⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣾⠁⠀⣨⣴⡇⠀⡇⠀⠀⠀⢀⡀⠀⠀⣀⡆⣠⠇⠀⠀⠀⠁⢦⣠⣶⣀⠤⠀⠀⢸⣾⠀⠃⠉⠻⣄
⠀⠀⠀⠀⠀⠀⣼⢸⣿⡇⠸⣿⣿⡇⢰⡇⠀⠀⣀⡾⣿⣻⣿⣿⣆⢿⠀⠀⠀⠀⠀⠀⠻⣿⣽⣷⠄⡀⠈⣟⡇⠀⠀⠀⠿⢷
⠀⠀⠀⠀⠀⠀⢹⣆⢻⡇⠀⢻⣿⡇⢸⡇⠀⠉⠉⠁⢼⡿⠉⣿⡏⠀⠀⠀⠀⣷⠀⠀⠰⡙⠧⠀⢀⡄⠀⣯⡇⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⠀⠀⢿⣷⠀⡿⡄⠀⢤⣀⠀⠀⢈⣿⠆⠀⠀⣀⣸⡟⠃⠀⠀⢀⣰⠿⠋⠀⠀⣿⣇⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⢸⣿⡀⡇⠀⠀⠀⠙⢻⡇⠀⡏⢀⡴⠛⠉⣠⣤⣄⠐⢶⣦⠙⣦⠀⠀⠀⣿⣏⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⢸⣿⢣⣇⠀⠀⠀⠀⠊⠀⠀⠀⡜⠁⠀⠀⣭⣷⠄⣀⠸⣯⡅⠸⠀⠀⢠⣿⣿⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠾⣃⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⣿⡷⠞⠀⠀⠠⢇⠀⡿⢿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⢿⣿⡇⠀⠋⠘⣵⣆⠀⠀⠀⠀⡀⡀⢸⣿⣿⢈⣶⡆⠄⠀⢾⠃⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠈⣿⣷⡀⠀⠀⠻⣿⣆⠀⠀⡄⡄⢤⠴⣿⢻⣾⣿⣷⣍⣀⠌⡄⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⢹⠈⢳⣄⠀⠀⠘⡿⢿⣶⣤⣤⡴⣚⠛⠯⠋⠀⢹⡛⣉⠞⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡼⡆⠀⢇⠀⠉⠑⣦⡀⠈⠙⠛⠻⣏⣴⡙⠦⣀⠀⠀⠘⣿⠃⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠈⣆⠀⠀⠈⠛⠂⠰⢤⣀⠙⠻⠿⠶⠶⠖⢚⡶⠋⠀⠀⠀⣼⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⠈⠀⠀⢠⢠⠀⠀⠀⠈⠑⢶⣶⣶⠃⠈⠁⠀⠀⠀⠀⡀⢸⡟⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣻⣿⠃⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢀⡾⣿⣿⡀⠀⠀⠀⠀⠀⢠⠀⢸⠃⠀⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢸⣿⡀⠀⠀⠀⠀⠀⠘⢱⠃⡀⠀⠀⠀⠀⠙⢿⣟⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠁⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢿⣇⣤⠀⠀⠀⠀⠀⢸⣿⡇⢀⡄⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡇⠀⠀⠀⠻⡿⣆⠀⠀⠀⠀⠈⠈⢿⣿⣧⣆⠀⣠⣶⣄⠀⣀⠀⠀⠀⠠⣹⡆⠀⠀⠀⡏⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⡀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠁⠙⠻⢶⡏⠀⠉⠻⠇⠈⠁⠀⠀⢹⠃⠀⠀⡼⠃⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠻⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠳⣄⢀⡀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠈⠛⢷⣾⣷⣄⢲⣄⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣷⠖⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢀⡴⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠰⠤⣀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠀⠀⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠐⠊⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠘⣄⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⠄⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠉⠓⢦⡶⠒⠓⠒⠂⠀⠁⠀⠋⣀⢤⠀⠀⠀⠘⣤⣤⣤⣤⡤⠤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢀⡀⠀⢈⠠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠁⠀⠀⡴⠛⠂⠘⠀⠀⣤⣬⡁
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠙
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢠⠏⢸⠀⠀⠀⠀⠀⢀⢠⠀⢀⣄⠀⠀⣀⡀
⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⠰⠋⠀⣴⠀⠀⠐⡻⠛⠊⠀⠀⠈⠁⠀⠔⠻⢁⡀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⣲⣾⣿⡿⠿⠿⢿⣷⡄
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣷⣤⣤⣾⣿⣿
⠹⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢲⠞⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠘⠿⣿⣿⣿⣿⣷⣄⡀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠈⠀⠀⢢⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠛⠋
⠀⠀⠀⠈⠙⠻⠿⢿⣿⠿⠋⠁⠀⢹⣿⣿⣶⣶⣶⣶⣶⡿⢻⣧⠀⠀⠀⠡⡀⠀⠀⠀⠈⠑⠒⢀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠙⢷⡀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠈⠰⡆⠦⠀⣀⡄⠀⠀⠀⠀⣀⠔⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢀⡞⠀⢀⣴⣿⣿⣿⣶⣄⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠑⠠⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⢸⠁⠀⢾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣶⣿⣿⣿⣶⡄⠀⠀⠉⠢⢄⠀⠀⠀⠀⠈⠐⠂⠼⠷⢦⡀
⠀⠀⠀⠀⠀⢸⡆⠀⠈⠿⣿⣿⣿⡿⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠒⠄⣀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⠖⠢⡀
⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠐⣆⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠼⠿⡶⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠾⠿⠁⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡘⠀⠀⢄⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠘⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠈⠆⠐⠀⠀⠀⠀⠁⠀⠀⠂⠠⢀⠀⠀⢀⠀⠤⣀
⠀⠀⠀⠀⠈⠓⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠑⠀⠑⠄⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⡈⢢⡀⠐⣀⢸⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠛⠛⠀⠙⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠴⠛⠹⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⢀⡤⠞⠃⠀⠀⠀⣠⠤⠤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠢⢤⣄⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉
⠈⢳⣤⣀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡿
⠀⠀⠉⠉⠡⣴⠶⠊⢹⡇⠀⠀⠀⠀⠀⠀⣰⡯⢶⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⡤⣰⠟⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣀⣤⣾⠋⠀⠀⢠⠟⠀⠀⠙⠓⠆⠒⠷⠒⠋⠀⠀⠀⠀⣸⢱⡇
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡴⠋⠉⠀⠾⢦⡀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⢠⡏⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⢷⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣿⠈⠓⢤⣀
⠀⠀⠀⠀⠀⠈⡇⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣤⣭⠆⠀⠀⠀⠀⠀⠈⠓⣦⠀⠀⠘⠦⣤⡴⠞
⠀⠀⠀⠀⠀⠀⠱⣦⣄⣀⣨⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⢰⣬⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢉⠉⣀⠀⠉⠐⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⢠⡙⣿⠁⣼⠟⣀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⠉⠁⠃⠄⠹⠀⠋⢈⣷⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢈⣿⣷⠀⠰⢲⢳⠢⠀⢠⣿⢽⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠃⣿⡀⣤⢠⣇⢠⠀⢸⣿⢸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢧⣥⢟⡹⢦⣀⣸⣏⣷⡍⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣽⠃⢲⣿⠿⠊⠑⣫⣾⣿⠇⠘⡆⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⢘⡇⠀⠀⢠⣿⣿⣿⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣾⣷⣆⣴⣿⣿⣿⠁⠀⠀⠀⣾⠁⢠⠀⢸⣄⣤⣤⠀⠀⠀⠻⠦⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⣰⣿⠀⣾⠀⢸⣿⣿⣿⣤⡀⠀⠀⠀⠀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠄⠀⠀⠙⠻⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⣿⣿⣾⡟⢀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⣸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⣀⡀⠸⣧⣤⣀⠀⢀⣠⣤⣀⣠⣶⠃⠀⢰⣿⣿⣿⡿⠛⠛⠻⢟⡁⠙⠻⡷⣷⡀⠰⠁⢻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⣠⡝⠁⠀⠀⠈⠛⠿⣿⣿⡿⠿⠟⠋⠁⢀⠀⠀⠛⠉⠀⠀⠀⠀⠀⣼⣿⡤⠔⣃⡼⠃⠀⠁⠀⠹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⡰⠋⠁⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⣠⣤⠞⠋⠁⠀⠀⠀⠀⠀⠈⢌⡉⠟⠋⠀⢸⡋⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿
⠀⠀⠄⠒⠉⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⢠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒
⡤⢀⢀⡄⣠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠁⠀⠀⠁
⠓⠛⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢠⠀⡧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠤⣤⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣽⠀⠀⢠⠄⠀⠘⠇⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⡝⠀⠀⠈⠛⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠀⠀⠀⠀⠀⠠⣇⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠓⠀⠀⠄⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡗⠲⠛⠦⡀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠙⡄⠀⠘⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣠⠤⠶⢤⡀⠀⢢⠀⠀⠀⡔⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠉⠀⠀⠀⠀⠹⡆⠈⡄⠀⠀⡇⠀⣠⠀⠸⡇
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢧⠀⠀⣧⠞⠹⡄⠀⡇
⠀⠀⠀⠀⢸⡷⡄⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸⠀⠀⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠰⣧⠙⢦⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⡠⠚⡇⠀⡇⠀⠀⢇⠀⠇
⠀⠀⠀⠀⠀⠈⣷⣄⠈⠓⠦⢄⣸⣄⣀⠀⠀⠀⢀⡤⠚⢁⣠⣖⠉⠉⠙⡇⠀⢧⠀⠀⠈⢣⠘⠂
⠀⠀⠀⠀⠀⠀⠈⠛⠢⠤⠄⠠⠤⠾⣅⣀⣀⣀⣈⣉⣉⡀⣠⡠⠏⠉⠀⠙⢄⠀⡁⣠⠀⠀⠁⠠⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣤⠖⠊⠉⠁⠀⠈⠉⠉⠒⠶⣤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢇⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⠇⠀⠀⠀⣿⣙⠄⢀⡠⢤⡀⠠⣋⣿⠀⠀⠀⢸⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⠤⠤⢤⣀⣉⡩⠔⣉⠤⠄⣈⠳⠭⣩⠤⠤⠤⠬⡇⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⡇⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢸⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠢⡴⠞⠙⡶⠖⠂⠀⠀⠀⠀⠀⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠙⠦⠔⠃⠀⠀⠀⠀⠀⢀⡴⢻⠁⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠑⠒⠤⠤⠤⠄⠤⠤⠤⠤⠔⠒⠉⡇⠀⣎⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢹⡎⠀⢉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢹⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⡇⠙⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢇⠀⠀⠀⠉⠒⢦⠔⠒⠉⠀⠀⠀⣸⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠦⠤⢘⣆⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⡃⠠⠴⠥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⢀⠀⡎⡀⠉⠉⠉⠀⢸⠀⠀⠈⢑⠋⢁⢹⠀⡀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠼⠤⠟⠧⢄⣧⠤⠴⠚⠑⠢⠤⠼⡤⠼⠞⠤⠧⠜⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⠿⠿⠿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⢀⣤⣴⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠻⢷⡶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣙⣷⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠉⠁⠀⠀⠀⠀⠀⠀⠘⠻⣷⣄
⠀⠀⠀⣀⣴⣿⠟⠁⣀⣤⣶⣾⣿⡷⠀⠀⠀⢀⣼⠏⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠙⢷⡄⠀⠀⢰⣿⣷⣤⣀⡀⠈⠻⣷⣦⡀
⢀⣴⣾⣿⣿⣷⡿⠿⠛⠋⠉⠀⣿⡇⠀⠀⠀⣼⣇⣀⡀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⣀⠈⣿⠀⠀⢸⣿⡍⠉⠛⠿⣷⣶⣬⣽⣿⣷⣤⡀
⣿⣿⣟⡋⠉⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⣿⣿⣏⣽⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣩⡇⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿
⠀⠙⠛⠿⣿⣶⣶⣤⣤⣤⣤⣾⣿⠁⠀⠀⠀⠙⠿⢿⣿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⡷⠟⠀⠀⠀⣿⣧⣀⣀⡀⢀⣀⣠⣤⣶⣾⣿⠿
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣯⣍⣙⢲⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠈⠛⢿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⣀⣀⣀⣤⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡀⠀⠀⠀⠀⠈⣽⡿⠛⠻⠿⠿⠿⠿⠿⢿⣿⣥⣬⣿⠿⠿⠿⠟⠛⠛⢿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⢿⣧⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠈⢿⣷⣤⣀⣀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠈⠛⠻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⡀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⡀⠀⢀⣤⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣶⣶⣶⣶⣶⣶⣾⠿⠟⠁⠛⠿⣷⣶⣶⣶⣶⣶⣶⣿⠿⠿⠛⠋
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠙⠛⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡏⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⢤⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣴⠞⠋⠁⠸⠇⠀⠀⠀⠀⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⢀⣤⠶⠦⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⢀⣀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠙⠛⠛⠛⠉⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄
⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠙⣳⣤⣄⠀⠀⠀⠀⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣾⠃
⠀⠀⠈⠉⠉⠡⣤⣶⠞⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⢀⠄⣼⠟⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⣤⡾⠁⠀⠀⢀⣾⠃⠀⠈⠻⠶⡤⠠⠴⣶⠤⠞⠁⠀⠀⠀⠀⢠⡏⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⠶⠛⠋⢹⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿
⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⢀⣴⡟⠁⠀⠀⠀⠈⠙⢷⡀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢹⡇⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣤⣦⡼⠇⠀⠀⠀⠀⠀⠀⠀⠉⠹⣄⠀⠀⠀⠛⢦⣤⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⣀⠀⢀⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣦⣹⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⠀⠀⠀⠀⠀⣰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⠈⡇⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢁⣾⠀⢱⣤⣤⣿⣿⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣾⡇⠀⣿⣿⣿⣿⡻⢷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡇⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣆⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠉⣭⣽⣆⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠉⢹⡿⠃⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⢻⣿⣧⡀⠠⣄⡀⠀⠀⠀⠀⢹⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠙⢿⣿⣶⣤⣭⣷⣶⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠙⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣯⣍⠉⠛⠉⠉⠁⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣷⡄⠀⠀⠀⢠⣤⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦⠀⠀⠀⠉⠛⠿⠿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠈⠀⠀⠀⠑⣠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⡠⡪⠉⠀⠀⠀⠀⠀⠑⠔⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⡀⠔⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⡀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⣦⣄⠀⠀⢀⠌⠀⠀⠀⠡⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢿⣿⠄⠁⠂⢠⣾⡮⢰⠄⠃⢀⠀⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⢠⡒⠒⠲⢄⠈⠻⠿⠀⠀⡀⠈⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠿⣿⡶⠟⠣⠀⣀⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠉⠁⠀⠀⠠⢐⠹⣄⠀⠀⠀⠀⠀⠀⠀⠸⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡀⡀⠠⠀⠂⡁⠔⠁⠀⠈⠐⠠⢄⠀⠀⠀⠀⠡⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢼⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⡼⡄⠀⠀⢡⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⢸⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠠⠂⠀⠀⠨⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣄⣀⣈⠀⠀⠀⢠⠊⠈⠁⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠀⠂⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣛⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠸⡇⠀⠀⣠⣒⠲⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣇⠀⠀⠀⠁⠀⠀⢿⣿⣿⣿⠃⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⣿⠈⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⣿⣟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⢦⣄⠈⠄⢰⡏⠀⠈⠛⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠛⠁⠀⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣶⣶⣶⣾⣿⡇⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⡟⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡁⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣯⡆⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⢀⣤⠴⠚⠛⠉⠉⠓⣦⣤⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠈⢽⢷⣶⣎⣩⣤⣤⣤⣶⣶⠾⠋⠉⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢣⣄⠀⠀⠀⠀⠀⠀⠈⠙⠻⡿⢿⡿⠛⠛⠁⠀⢠⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⢴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣾⠟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠼⠶⣤⣴⣶⣤⣤⣶⡶⣿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⢀⣤⣴⣶⣿⣿⣧⣼⣿⣿⣿⣿⣿⣻⣇
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢟⣽⣿⣿⡄
⠀⠀⠀⠈⠻⠿⠿⠿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡼⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⣿⣿⣿⣿⡟⣿⣿⢟⣫⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢋⣴⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢣⣿⡟⠹⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢊⣿⣇⠀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⠾⠿⠟⠸⣫⣯⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠟⠃⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠟⠛⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⡍⢻⣿⣿⣿⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠁⠙⠁⣼⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠳⡀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡆⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣸⣿⢹⣿⣿⣿⠋⠀⠀⠀⢀⡀⢀⠀⠈⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⡏⠁⠀⠈⠁⠀⠀⠀⢀⣼⣿⣿⣷⠀⠸⢿⣿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⠆⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⠟⠀⠀⠀⠀⣻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⣄⠀⠀⠈⠐⠐⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠠⣍⣀⣠⡴⠇⠀⠀⠀⢠⣽⣿⣄
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⡄⠀⠀⠉⠉⠀⠀⠀⠀⣤⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣽⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡤⠄⠀⣀⡀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠁⠀⠀⠐⠉⠉⠀⠀⠈⠁⠀⠀⠐⠀⠒⠒⠂⠶⡶⢄⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢀⣿⡏⠠⠂⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢀
⠀⠀⠀⠀⡀⢀⠀⠀⠀⢰⡆⠀⠀⣤⠏⡤⠀⠀⠀⠐⠂⡰⠦⠀⠀⠀⠄⠂⠀⠀⣤⠂⠀⠀⠀⠀⠀⠀⠀⢹⣷⠈⠛⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡄⢀⣴⣏⣜⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢳⢦⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⣡⡄⠀⠀⣀⣤⣔⢄⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡆⢿⠘⢠⠁⠀⠀⠀⣿⠀⡄
⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⣼⣟⣵⠶⠓⢠⣿⣿⣧⣿⡌⠹⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣿⢷⣶⡀⠀⠈⠛⢾⡇⠀⡇⠀⠀⠀⢉⠀⡿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠉⣿⣿⡿⣀⠀⠀⠑⠘⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠺⠻⣟⡽⠳⠀⣸⠸⣿⠁⠀⠀⠀⠀⠀⠈⢸⠃
⠀⠀⠀⠀⠰⡟⡀⠀⠀⠀⡟⢰⣿⣿⠀⠈⠹⣿⣶⠀⠀⠀⠀⢀⣤⡄⠠⠀⡀⣀⠀⠀⠀⠣⡀⠀⢀⣤⠀⠘⡓⢿⠀⠀⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠈⠻⣆⠀⢀⠁⣾⠏⡿⠀⠀⣀⢹⣿⡀⠀⠀⣰⡿⣋⡀⠀⠌⠁⠈⠻⣄⠀⠀⠐⣶⣿⡏⠀⠀⣿⣿⢸⣇⠀⠀⠀⢰⢧⠇
⠀⠀⠀⠀⠀⠀⠀⠘⢇⡜⢴⣿⢸⡇⠀⠀⠛⡿⡭⠁⠀⢠⣿⣶⣿⣿⠁⡀⢺⣿⣷⣼⡄⠀⠀⠻⣿⠀⠀⠀⣽⣿⡘⢿⡀⠀⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⣼⡇⣸⠗⠋⠁⠈⠀⠃⠀⠀⠀⠑⣧⡈⢡⣼⣗⣠⠉⣻⠿⠇⠀⠀⠀⠉⠲⣀⢀⡿⣹⣇⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⢃⣿⢀⡴⣶⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⢠⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⣀⠀⢸⡇⡿⣿⠐⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣻⡯⠸⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⢄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠈⣧⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣩⣿⠚⣧⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣤⣿⣦⣡⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⡼⢏⣼⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠸⡇⢻⣿⣿⣤⣄⣀⣠⣴⡿⣿⣟⣙⣧⣀⠀⠀⠀⠀⢠⠎⠁⠔⠃⠛⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⣇⣿⣿⣿⣿⠗⠒⠂⢺⣿⡋⠀⠿⣷⣶⣶⣶⡿⠐⠀⠀⠛⠰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡷⠞⣨⠛⠁⠀⠀⠀⠙⠋⠁⠀⠀⠸⣯⣽⣟⠓⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠹⠿⣿⡿⠿⠛⣷⡶⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠃



⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠁⠀⠀⠀⠁⠈⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁

⠀⠀⣄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠉⠊⠉⠁⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣶⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⣿⣿⣶⣶
⠀⠀⠀⠀⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠂⠀⠀⠀⠀⢰⣿⡿⠿⠛⢿⣿⡀⠀⠀⠀⠂⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⠍⠀⠀⠈⠛⠋⠋
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠟⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣀⣀⣂⣆⠀⠀⠀⠀⠀⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠐⠀⠘⠿⠧⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠈⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣧⠀⢀⣾⣿⣆⠀⠀⠀⠀⡞⠃⠌⢁⠀⠀⠀⠰⠟⡿⠃⠀⢰⡏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⡄⠀⠀⠰⢦⣖⣰⠞⠀⠀⠀⠀⠀⠀⣘⣃⡈⠃⠀⠀⠀⣆⠀⠀⠀⢠⠀⠀⠈
⠀⠰⠀⠐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠇⠀⠂⠀⠀⠘⠟⠛⠛⠃⠀⠀⠀⠀⠙⠙⠀⠀⠀⠀⠀⠀⠘⠽⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡀⠤⡤⠀⢀⠄⠀⠀⡀⠀⣺⣦⣄⡖⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠰⠆⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠁⠈⠋⠀⠀⠀⠳⠂⠀⠀⠀⠀⠲⠞⠁⠀⠀⢠⣶⣿⠛⣧⣹⣎⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣤⡄⠀⠐⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠹⣋⠠⡆⢀⡈⠀⠀⠀⠀⡸⢧⡏⣤⠀⣧⡛⠀⠀⠀⠀⠀⠀⠀⠄⢠⡄⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠳⢶⠖⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⢀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢤⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣤⣦⡦⣣⠔⣶⣄⠀⠀⠈⣷⣿⡿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠰⣇⣽⠛⢫⣻⡃⠀⠀⠀⠀⣀⠀⠀⢀⠉⢡⡟
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⠿⣿⡿⠄⢠⡾⠯⠙⠂⠀⠀⠟⠋⣤⠝⠛⠃⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠰⣿⣿⠲⢾⣟⣿⠀⠀⠀⠘⠿⠀⣄⢙⣁⠄⠡
⠀⠀⠀⠀⣓⠈⠀⠀⠀⠀⠀⠀⠀⠞⠻⠏⢻⡟⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠐⠀⠉⠁⠀⠀⠀⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠢⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢶⣶⣤⠀⠀⠀⠀⠀⠀⠀⢩⠁⠀⠈⠋⠀⢹⠿⠃⠀⠀⠀⠀⠈⠈⣡⣴⠀⠁⠀⠀⠀⠘⠀⠀⠂⠀⠀⠀⠰⣶⡆⣶
⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠂⣥⣄⢀⡹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⢀⠀⠀⠀⠀⠀⠀⡖⠁⠈⡏⠀⢀⠀⠀⠀⠂⠀⠀⠘⠀⠀⠀⠀⠿⣁⠙
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢿⠟⠘⠁⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠲⣴⣼⠬⡵⡃⠀⠀⠀⠀⠀⠀⡇⠀⡂⠈⠀⠠⠀⠀⠀⠐⠐⠗⠈⠀⠀⠀⠀⠀⠉
⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠙⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠟
⠀⠀⠘⠙⠁⢸⡿⣶⣶⡆⠀⠀⢠⢀⠐⣦⡴⡆⠀⠀⠀⣟⣿⡄⣤⣾⡿⠂⠀⠀⢀⣠⣸⣶⣿⣧⡤⠀⠀⠀⠀⠀⠀⠀⣤⠞⠚⢷⣦⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⣿⣿⣿⠘⠃⠀⢐⣿⡿⠀⠸⢦⡟⠀⠀⠀⣼⣻⠇⣟⣿⠀⠀⠀⠀⠀⢩⠿⠛⠛⠛⠄⠀⠀⠀⠀⠀⢀⠀⠿⠛⠓⠚⠂⠀⠀⠀⠀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣙⢿⡿⠀⠀⠀⠸⣿⠴⣿⢷⣴⡿⠀⠀⠀⠙⠁⣀⠈⠃⠀⠀⠀⠂⠀⠃⠀⣶⡆⠀⠀⠄⠀⠀⠀⠠⠆⢀⣶⢀⣀⢰⣤⢀⡄⠀⠀⠛⢿⠿⠿⡟
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠛⠒⠿⠾⠟⠁⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠘⠀⠀⠼⢄⣀⡠⠀⠀⠀⠀⠀⠓⢺⣿⣬⣋⣼⡷⠜⠁⠀⠀⠀⠘⠦⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡠⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⢶⣶⢶⢶⡶⠿⣯⣍⠻⢿⣦⠙⣿⣟⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣦⡴⠾⠻⠉⠁⠠⠀⠈⡜⠉⠈⠁⠀⠠⠙⣷⣄⠻⣦⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣶⠟⠿⢻⣽⣿⠏⠀⠀⠀⠀⠀⣧⡀⠀⢠⣥⢀⣄⠀⢀⠀⠹⣿⣦⠀⢲⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡋⢸⠁⠀⠀⣾⣿⠏⠀⠀⠀⠤⢴⣾⣾⣧⠀⢠⣿⣿⡿⣧⣾⣿⣤⣤⣿⣷⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⣤⠾⠿⢿⣿⣆⢸⣿⠁⠀⠀⣿⡿⢬⠉⠻⣿⠟⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⢠⣿⣿⠀⠀⠐⣼⣧⡀⠀⠀⣿⣿⠈⢿⣷⣦⣾⣿⣷⢶⣼⣿⣿⡆⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⣸⣿⣿⠀⠀⠈⢡⢴⣾⡓⢸⡿⠛⡆⢀⡛⢯⣼⣧⣵⠞⣼⠋⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣶⠏⢸⣷⣠⣶⡞⠻⢌⡙⠷⣾⡁⠠⠐⠀⠉⠘⠙⢷⣶⣾⣿⡄⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢚⡟⠁⠀⢐⣦⣀⣀⣠⠏⠀⢰⣶⣦⠀⠀⠀⠀⠈⠉⠹⠇⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠐⠛⠿⠛⠃⠀⠀⣈⡉⠀⠐⣲⣶⣤⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠁⣴⣾⣿⣿⠗⠀⠀⠀⣼⣿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡷⢿⣿⣶⣦⡀⠀⠀⠀⠀⠐⣼⣿⢻⠿⣖⣆⠀⠀⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣴⣽⣿⣿⣷⡄⡀⠀⠀⢸⣵⣧⡼⠦⠀⢉⣴⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠼⢿⣿⣿⣿⣿⣿⣉⠐⠛⢀⣠⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⢈⡋⠈⣩⣾⣿⣿⣿⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⣀⣉⠽⣿⣿⣿⣿⢿⡇⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣍⠋⠀⠘⠲⠿⠞⢻⣏⣾⣸⠃⠹⣿⢳⣿⡿⣏⠻⠿⠛⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠁⠀⡄⢀⣤⠀⠀⠀⠈⠙⠁⠀⠀⠀⠊⠋⠉⠀⠀⠀⢀⣀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠛⢿⣿⣷⣶⣖⣫⣴⣸⡀⠀⠀⠀⠀⠀⢀⣾⣶⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⠄⠚⠛⠻⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠘⣿⠏⢙⡿⢿⣿⣿⣟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠈⢻⣿⣿⡿⠛⠿⠷⠿⠳⠖⠚⢿⡀⠛⠀⠀⠀⠀⠉⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⢰⡆⠀⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⠀⠀⠆⠀⡌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣤⠀⠀⠰⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠃⠀⢸⠀⠁⡀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢧⡰⣿⢶⣄⣸⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣄⠀⣿⣄⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠁
⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠿⠿⠿⢿⣶⣤⡀⠀⠀⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⠀⣠⡞⠉⠉⠛⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣶⣄⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠀⢰⡄⠀⠀⠈⠙⢦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠋⠉⢉⠉⠛⢷⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣾⠿⠛⠉⠁⠀⠀⠀⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⡙⠻⣿⣆⠀⣿⣷⡄⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣰⡿⣧⡉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠹⡆⠘⣿⡀⢹⣿⣿⣄⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⣿⠁⠈⣿⡄⠘⡆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣸⣷⠀⣿⡇⠀⠙⣿⠿⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⢸⠇⠀⠘⣿⣷⣤⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇⢀⣿⠁⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⣿⡀⠀⠀⢿⣿⣿⡿⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣤⠾⢃⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⡾⠿⣷⣤⡀⠈⠻⣿⣤⡾⠃⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠙⢧⣴⠶⠒⠲⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠙⢿⣷⣤⣠⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⠿⠿⢿⣷⠀⠀⠀⠀⢘⡏⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠉⠑⠛⠻⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡀⠀⢀⣰⣿⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠙⢿⣿⠿⠿⠿⠟⠛⠁⠀⣠⣴⣿⠏⠀⠀⠀⠀⠠⠾⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠛⠿⣶⣤⣤⣄⣠⣤⣤⣴⠾⠿⠗⠶⠾⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⠀⠀⠀⠀⠹⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣾⠿⠿⠿⠿⣷⣄⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠿⢿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣶⣶⠞
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⣤⣤⣶⣿⣿⡇⠀⠀⢀⡇⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⢠⡇⣆⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠏⢸⠀⠀⠀⢸⣧⠀⠘⣿
⠀⠀⠀⠀⠈⣇⠘⢦⡀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠀⠀⡿⠀⠀⠀⢸⣿⠀⠀⠻⣧⣤⡀
⠀⠀⠀⠀⠀⠹⣄⠀⠙⠶⣤⣤⣿⣿⣧⠀⠀⠀⠀⠀⣸⣿⠿⠟⠛⠛⢦⡇⠀⠀⠀⠘⠿⠛⢦⡀⣄⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣀⣀⣉⣉⣁⣀⢀⠀⠀⢀⣉⣄⡀⠀⣾⣇⠘⣧⡀⠀⠀⣤⠀⢰⠘⣧⣼⣦⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⢿⣿⡿⠿⠛⠙⠛⠿⠿⠟⠻⠿⠛⠿⠿⠿⠿⠷⠟⠻⠟⠀⠈⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢄⡀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⠴⡊⠉⠓⠢⢤⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠞⠉⠀⠀⡠⠀⡩⠶⠶⠞⠁⠀⠘⠓⠒⠶⢥⡊⠈⡀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⣧⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡇⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⠶⠅⠤⢄⠀⠀⠀⢀⣠⠱⣄⣷⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡴⠁⢠⣴⡆⠀⠱⡄⠀⡜⢠⠀⠈⣿⢧⡀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⣇⠀⢻⣿⣷⡆⢠⡇⠀⢹⣿⣦⡆⣿⡈⠳⣄⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⣰⡿⠀⠀⣈⡦⠤⣌⣁⣤⠿⢒⠖⠚⠛⠻⡒⠃⠉⢢⡈⠳⢦⣀⣀⡷
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢀⡾⢻⡅⠀⠀⠁⢠⢖⠀⠀⠀⠀⠀⠓⠦⡤⠋⠀⢀⣄⢸⡇⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢧⣀⣤⠞⠋⠀⠀⢷⠀⠀⠀⠀⠀⠑⢦⣀⣀⣀⣀⣠⣄⣀⠴⠃⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠤⣀⣀⢀⠀⠈⠫⡉⠉⠛⣿⠟⢀⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠈⢏⠙⠳⠤⣄⣀⣈⣉⣠⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠌⠀⡙⡄
⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠰⡖⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢙⢧
⠀⠀⡇⣇⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢸⠁⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠉⢸⡆
⠀⠀⡇⠹⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⣾⠃
⠀⠀⢻⡀⠙⢦⣀⣀⡴⠶⠾⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⡏⠀⠀⠀⢠⠖⠀⣇
⠀⠀⠀⠻⣦⣀⢀⡏⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⠀⡐⠁⠀⢸⠈⣧
⠀⠀⠀⠀⠀⠉⠹⡇⠀⠀⠀⠀⠙⡄⠀⢺⠀⠀⠀⠀⢸⠖⡟⠉⠀⠀⠀⡞⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢹⠀⡿⠀⠀⠀⠀⢸⣰⡇⠀⠀⠀⢠⠃⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠸⢤⡇⠀⣀⣀⢀⣀⣏⡇⠀⠀⠀⢸⣰⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⠀⠀⢱⠀⠀⠀⠀⣆⠙⡌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣰⣄⣠⣦⣤⣇⡀⠀⢀⡆⠀⣠⣸⣧⣤⣀⣀⣨⣀⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠓⠀⠀⠰⣶⣆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⡀⠀⢀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠶⠐⠗⠀⢀⣀⠀⢹⠟⠀⠀⠀⠀⠀⢀⢸⡿⠃⠄⢀⣿⣄⠲⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠄⠿⠀⢺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠂⠀⠀⠉⠀⣼⠀⠀⠀⠀⠀⣴⣿⠛⠳⣆⠀⠀⠉⠃⠀⣴⣆⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⣶⣦⠉⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠰⣆⠀⠀⣀⣄⡝⠀⠀⠀⠀⠀⠸⣿⢄⠣⢄⡀⠀⢶⣀⣀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⢥⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⠀⢩⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⢻⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⢒⡤⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠲⢀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣂⠘⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠁⣤⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⣴⢰⡆⠛⠀⠈⠓⣿⢺
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢀⡙⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣀⡀⣀⡰⠿⠁⠀⠀⠀⠀⠀⢻⠀⣷⣄⣀⢀⢸⣏⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡏⠐⢿⣏⢈⣿⣿⡇⠀⠀⠀⠀⠀⠐⢄⠀⠈⣿⡇⢉⣛⣛⡛⠟⠀⠀⠀⠀⠀⠀⢀⡀⢋⠀⢼⣧⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠁⠐⠛⠙⠉⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠑⠊⢛⡀⢸⠏⢹⠁⠀⠀⠀⠀⠀⠀⠀⢘⠳⣄⠲⠸⠷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠰⠄⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡼⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠂⢄⠐⡆⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡄⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠀⠀⢠⣄⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠶⠀⠐⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢸⡇⠛⠀⠀⠛⢸⠁⠡⠀⠀⠀⠀⠀⠀⣠⡶⣿⣅⠈⠁⠚⠻⠀⠐⣄⠀⠀⠀⠀⠀⠀⠈⠠⡆⠀⠀⠂⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣅⠈⢻⠟⠀⣨⠷⠂⠀⠀⠀⠀⠀⠘⣿⣇⠳⠈⠂⠀⢂⡀⠀⢸⣿⠂⠀⠀⠀⠀⢠⡇⠀⢿⣄⠲⠶⡦⣭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⢿⣾⣷⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠁⠈⠳⠀⠀⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠲⠺⣇⠘⡟⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣲⣥⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡖⠛⠛⠲⢄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠃⠀⠀⠀⠈⠣⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠛⠉⢀⠴⠒⠒⠢⢄⠀⠁⠀⠺⡀⠀⠀⠀⠉⢢⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡤⠋⠀⠀⠀⠀⠀⠁⠀⣰⠶⢸⠀⠰⢶⡄⠀⠙⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠠⡦⠀⠀⡶⠰⠄⡀⠀⠀⣰⣿⣿⣟⠛⠛⠛⢿⣷
⠀⠀⢀⠀⠀⠀⢀⡔⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠐⠀⠀⠒⠀⠐⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠀⠀⡴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⣼⠁⡇⠀⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋⠃
⠀⢀⠀⠠⡇⠀⢷⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡄
⠀⠀⣄⠀⢧⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⠇⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠓⢤⣀⠙⢦⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠻⠀⠀⢠⣔⡉⠉⠑⠒⠢⠤⠄⢀⣀⣀⣀⡠⠔⠂⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣲⠏⠁⠀⠀⢻⣿⣿⣿⣿⣶⣾⡿⠀⠘⢄⠀⠀⠀⠐⠺⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠿⠏⠓⠒⠶⠤⠤⠤⢦⠀⠀⡼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⠀⠀⠀⠄⣀⠂⠄⣸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡝⠂⠉⠀⠀⠀⠀⠈⠀⠐⠠⣄⠒⣌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠘⠚⢄⣀⠀⠀⠀⠀⠀⠀⠀⠢⡐⢂⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠂⠐⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠖⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⣀⣀⣀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⣿⣿⣿⣿⣷⡄⠀⢱⡜⠒⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡞⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠜⠸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡀⠀⢀⠜
⠀⠀⠀⣇⠀⠀⠙⠒⠦⠤⣤⣀⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣷⠀⠙⠿⣿⣿⣿⠿⠓⠒⠒⠔⠚⠚⠁
⠀⠀⠀⠈⠓⠦⣀⣀⠀⢰⣿⣿⣿⣿⣿⣿⣯⠙⠻⠿⠿⠿⠋⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠙⠛⠁⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠔⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⡎⠀⠀⢀⡠⠊⡨⠋⠒⠒⠂⠤⠒⠒⡆⠀⠀⡔⡇
⠀⠀⠀⠀⠀⠀⡇⠀⢠⠊⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣷⠁
⠀⠀⠀⠀⠀⠀⢣⠀⠘⢤⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢘⢾⣦
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠏⠀⡀⠀⠀⠀⠀⢱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠮⠁⠶⣿⠆⢘⢋⡀⠒⠦⠀⠬⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢿⣆⡈⢥⡤⣯⠍⠁⣤⠐⢠⠐⢨⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣯⡿⢿⠷⡒⠗⠀⣤⣴⣷⠶⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣯⣿⡷⣞⣼⡏⠀⣆⠀⠉⠁⠀⠀⠀⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣤⢾⣿⣿⣿⣶⡜⣆⠀⠀⠀⠀⠰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⢼⣄⠂⠀⠀⠠⠸⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⣍⠘⡟⠓⢻⣿⡿⢿⣓⣻⣏⢸⠛⢛⡱⠞⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢡⠀⢁⠈⡷⠄⠀⠀⠉⠻⢿⠉⠁⠚⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠄⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠠⠾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⣦⠀⠛⠻⣿⣤⡀⠈⣁⣄⠀⠀⠀⠀⢀⠦⢤⣴⡟⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡇⡀⠂⠐⠄⠹⣝⣳⣮⠵⠀⠁⠀⠰⠋⠀⠈⢻⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠁⠆⠀⠀⠁⢻⣿⡆⢐⠀⠀⠀⠗⠀⠀⠀⠀⠓⠤⠤⢀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣷⣀⠄⠀⠀⠰⣿⢿⣤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢶⡌⠀⠀⠈⠉⠓⢮⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⠀⡘⣀⠂⡽⠤⠴⠬⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉


⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣿⣟⣛⣻⣿⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⣀⣀⡀⠀⠀⣀⣤⣤⣤⣤⣴⠶⠶⠶⠶⠶⢶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠶⢦⣤⣤⣾⠟⠁⠘⠋⠹⠿⢿⣿⣿⡾⠋⢉⣤⠴⠒⠒⠒⠛⠋⠉⠉⠉⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠟⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠶⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⢻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣤⡀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣋⡵⠒⠋⢹⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢽⣶⡄⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⣴⢿⡿⠋⠁⠀⢀⣴⣯⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⣙⣦⣀⣴⠿⠃
⠀⠀⠀⠀⠀⣸⡏⣼⣀⣀⠀⠀⣨⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠻⣿⠋⠁
⠀⠀⠀⠀⠀⣿⣵⠟⠉⠙⠷⣦⣹⠟⠀⠀⢀⡴⣫⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⢨⡿⠃⠀⠀⢸⢸⣿⣿⢛⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⣿⡏⣧⠀⠀⠀⠀⠀⠀⠘⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠈⠿⣿⣿⣿⠟⢁⣄⡀⠀⠀⠀⠀⠸⣿⣿⣿⡿⣣⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃
⠀⠀⠀⠀⣠⣤⣴⣤⣄⣀⣸⣿⠀⠀⠀⠀⠀⢠⣤⠴⠿⠉⠳⠿⠱⡄⢀⡴⣾⣦⠬⠭⢍⡉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡸⢿⣦⡀
⠀⠀⣠⡾⠛⢛⠁⣬⣿⡿⠟⠻⣄⠀⠀⠀⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠰⢿⣇⠀⠀⠀⠀⠀⢀⡴⠋⢠⣤⣌⠻⣶⣄
⠀⣸⡟⠀⢰⣿⣷⡸⣿⢇⣶⣆⠘⡆⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠛⠛⢶⣦⠰⠆⠀⠀⠈⠉⠛⠢⣄⠀⠀⠀⡏⣰⣦⡸⣿⡏⣠⣾⣿⣆
⠀⣿⣧⡀⣶⣮⡍⣴⣶⣮⣛⠋⠀⣿⠀⠀⠀⠀⠀⠈⠅⠸⣿⣶⣶⣶⣿⠟⠀⠒⠀⠀⠀⠀⠀⠀⠈⠁⠀⣸⡇⢙⣫⣥⣶⣜⠿⡿⢸⣿⡀
⠀⠹⣿⣅⠈⠋⣴⣿⣿⣿⠿⠃⠀⠿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠃⠛⠿⢿⣿⣿⣴⣶⡦⣿⡇
⠀⠀⠈⠻⣿⣀⠉⠉⠀⠀⠀⠀⠀⠀⠋⣧⠀⠀⠀⠀⠀⠀⠠⠚⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠿⠏⢋⣼⡟
⠀⠀⠀⠀⠈⠙⢿⡶⢤⡄⠀⠀⠀⠀⠀⣿⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⣠⡤⢖⡿⣹⣆⠀⠀⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠈⣿⡄⣤⣀⠀⠀⠀⠀⢻⡈⠉⠉⠛⠻⠶⠦⠖⠳⣤⠦⠤⢀⣈⣻⠶⠛⠃⠉⠉⠀⡼⠁⢻⠀⠀⠀⠀⠀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣸⡷⠀⠉⠉⠉⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠘⠂⠀⠀⠀⣸⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠸⠟



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠐⠀⠰⠀⠀⢠⣄⣀⠀⠀⠠⠴⠠⠀⠴⠀⠀⠀⠀⠀⠐⠀⠤⠀⠀⠌⠀⠘⠐⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⠀⠀⠐⡀⠀⠻⠟⠋⠀⠀⠀⣈⣤⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠘⠟⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠰⠂⠰⡆⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠰⠮⠖⠁⠐⡄⠀⣿⠒⠧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⠛⠃⠀⠀⠈⠉⠀⠐⠊⠰⠃⠑⠂⠠⢠⡀⠀⠀⠀⠀⠀⢠⠠⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠀⡀⠀⠈⠀⠁⠀⠀⠠⠀⠀⠀⠰⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⡷⣦⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠛⠙⠿⠀⠄⠀⠀⠁⠀⠁⡀⠀⠁⠀⠀⠀⡀⠉⡀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⠰⠦⠈⠓⠒⠀⢈⢉⢉⠻⠀⢈⡄⠀⢤⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣣⡔⠢⠤⢤⠀⠀⠀⣠⠠⠀⡄⠀⠀⠀⠀⠈⠛⠛⠗⠠⠀⠀⠀⣠⠄⣈⣀⣀⠀⠀⠀⠀⢀⢃⠰⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⢀⣀⡀⡀⠀⠀⠀⡀⣠⣤⣤⣤⣄⠁⡀⠀⠁⠀⠀⠀⠀⢆⠀⠀⠈⠁⠘⠷⠲⠖⠒⠐⠏⠃⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠈⠁⠀⠀⠚⠇⡙⠛⠛⠻⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠢⠦⠀⠀⠀⠀⠈⢠⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣹⣷⠄⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠐⠀⠀⠉⠏⠀⠀⠘⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠦⠄⠀⢐⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠂⠀⠀⠀⠀⠀⠀⢀⣤⡀⠒⠒⠂⠀⠂⠤⠄⠀⠴⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠒⢦⡀⠀⠀⠀⠀⠀⠀⢘⣿⣧⠀⠀⢄⠀⠀⢀⠀⠀⢀⠒⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⡿⢿⣀⣀⠐⠂⠀⠀⠀⠄⡀⠀⠰⠀⠀⠘⣿⣿⣷⣶⠄⠈⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠠⠀⠀⠀⠐⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⠀⠀⡀⠀⡟⡏⠀⠀⠛⠀⣀⠀⠈⠀⠀⠃⠀⡀⠀⠀⠀⠐⠉⠀⠀⠀⢰⡾⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⡆⡄⠈⠁⠈⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢀⠀⡆⠀⠀⠀⠐⠀⠀⠀⢈⠁⠁⠀⠀⢠⠙⠁⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠒⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠀⠀⠀⠀⠀⢀⡈⠆⠐⠒⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⢀⠔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠑⡆⠁⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⡠⠔⠁⡐⠁⠀⠀⠀⠀⢀⠀⢀⠀⠀⠘⡒⡀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⣠⢎⡀⠀⠀⠀⢀⠔⠁⠀⠀⠑⡄⠀⠀⠰⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢱⣿⣟⡀⠃⢀⠊⠀⣠⣄⢤⡀⠐⠀⠀⠀⠡⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠛⠻⠃⠀⠀⠀⢸⣿⣯⡄⡏⠀⡇⠀⠀⠀⠀⠑⠠⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢾⣍⣉⠉⠙⣦⠀⠉⠛⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠻⣿⡿⠿⠛⠀⠤⠀⠤⠔⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⡀⠔⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡂⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡶⠀⠂⠒⠂⠀⡈⠅⠂⡩⠂⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠐⠀⠈⡔⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢛⡖⠂⠀⠀⢁⠠⠐⠁⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠁⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠻⢶⡒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⢰⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⡇⠀⠀⠠⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⡴⢇⠀⠀⠀⢣⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠁⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⠀⠀⠀⢸⡄⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠸⠀⠀⠀⠘⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠄⠀⠀⢀⠔⠁⠀⠀⠀⣘⠤⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠣⠰⣥⠂⡄⠀⢀⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠂⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⣿⠿⠿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠁⠒⠆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡚⠲⡄
⢠⠐⠒⠀⠉⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠠⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠇⠈⠁
⡇⠀⠀⠀⢀⡀⠀⠈⠁⢀⡈⠀⠠⠀⠿⠀⠱⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⠀⠀⠀⢦⠈⢆
⢱⡀⠀⠀⠁⠀⠀⠀⠎⢉⣿⣿⣦⠀⠀⠀⡀⠀⠀⠀⠈⠀⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⢀⣀⡀⠀⡼
⠀⢱⡀⠀⠀⠀⠀⠀⠁⢈⣻⡿⠟⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢹⠀⠀⢰⠀⠈⠀⠀⠊⠀⡀⠠⣿⠏
⠀⢀⠃⠀⠀⠀⠠⣀⡠⠴⠢⡀⠀⢀⠀⠀⣸⠇⠀⠀⣀⡤⠖⠋⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢋⠉⠘⠁
⠀⠸⡀⡄⠀⠀⠀⡀⠀⠀⠀⠈⠉⠁⠀⠀⢱⠁⢀⠎⠁⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠢
⠀⠀⠈⠀⣸⠀⠀⠇⠀⠀⠀⣰⠀⠀⠀⠀⢏
⠀⠀⠀⢠⠇⠀⠀⠘⠦⣤⠴⠃⠀⠀⠀⠐⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⠀⠀⢀⠄
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⠀⠂⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠈⠉⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠠⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⣶⡈⢦⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠈⢧⠀⠀⣀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⣀⠄⠈⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢣⠀⠀⠑⢄⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠠⠴⠶⣤⡀⢘⢀⠀⠀⠑⠄⠀⠀⠳⣄
⠀⠀⠀⠀⢠⠔⠐⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⣶⣾⣻⡇⠀⠲⡄⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠁⢠⡀⠀⠀⠀⠛⡟⠋⠀⠀⡠⠓⠀⠀⠤⠤⠤⠶⠶⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠄⠤⠂⠀⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠐⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣾⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠈⡆⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢧⣿⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣳⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣤⡀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣴⣾⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⢿⣿⡆⠀⠀⠀⠀⠀⢀⡞
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡞⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣟⠔⠀⢿⡀⠀⠀⠀⠀⡞
⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⡸⠀⠐⠉⠿⠿⠟⠀⠀⢀⡤⠔⠒⠲⣤⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢸
⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣄⠀⠘
⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀⡞⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠉⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠣⡠⠊⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡠⢴⠉⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠑⠒⠒⠒⢄⡀⠀⠀⠀⡀⠄⠊⠉⠁⠀⠀⠱⡀⠀⠀⠀⠀⠀⡄⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⢀⠎⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢅⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠘⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠈⠇⠀⠀⠀⠀⠀⢀⠁⠈⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠁⠀⠀⠀⠀⠀⠀⣘⣀⡔⠂⠀⠀⠀⠀⠀⠀⡸⠀⠔⠁⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⣀⠀⢰⠀⠀⠀⣀⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⡗⠚⡀⠀⠀⠀⠀⡀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠈⠁⠀⠈⠢⠀⢄⣀⣀⠤⠠⠞⠀⠀⠀⠁⠈⠁⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠖⠚⠉⠉⠉⠉⠒⠲⢤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢸⠀⠀⠀⢀⣶⢦⠀⠀⠀⠀⠀⠀⡴⣶⡀⠀⠀⠸⡄⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⣞⣀⡀⠀⠈⠿⠞⣠⠖⠉⠉⠳⢄⡳⠿⠁⢀⣀⡀⢧⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⢠⠏⠉⠉⠙⠛⠛⠉⢰⣾⣭⣭⣷⡆⠉⠉⠉⠉⠉⠉⠙⡄⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠀⠀⠀⠀⠀⠀⢀⡀⢉⣹⢿⣉⣀⡀⠀⠀⠀⠀⠀⠀⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠉⢏⡁⢀⡟⠁⠀⠀⠀⠀⠀⠀⣰⡷⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⠤⣀⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣀⣠⣤⠚⢹⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠉⠉⠓⠒⠒⠒⠒⠚⠉⠉⠁⠀⢸⢀⡼⠦⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⢸⢯⡀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢳⠀⠀⠘⠦⣄⡀⠀⠀⢀⣠⠔⠁⠀⠀⡼⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⣇⠀⠀⠀⠀⠉⢳⠏⠉⠀⠀⠀⠀⢰⠃⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠓⠆⡸⢦⣀⣀⣀⠀⢸⠀⠀⢀⡀⢀⡠⢇⠰⠞⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠀⡠⢸⣡⡄⠀⡀⠀⠀⢸⡀⠀⠀⢩⠉⠠⡌⡇⣀⠀⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠓⠖⠛⠧⠤⠷⠴⠒⠋⠉⠓⠶⠼⠤⠴⠛⠓⠻⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠶⣶⠶⠞⠿⠶⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⡀⣠⠶⠌⠀⠐⠤⡀⠀⠀⠀⢀⠠⠔⠒⢲⣤⣄⡀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⣼⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣷⡀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢰⣿⠅⠀⠀⢀⣤⢶⣶⣤⡀⠀⠀⢠⣴⠶⣶⣦⣄⠀⠀⣹⣷⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠘⣿⣤⣀⡔⢿⣿⣾⣿⣿⠧⠤⠠⠼⠿⠿⣿⣿⡟⢳⣠⣿⠿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⡟⠉⠀⢸⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠹⢖⠀⠀⢠⠆⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⢰⡇⠀⠀⠁⠀⠀⢀⣴⣶⠾⠛⣷⣦⡀⠀⠀⠀⠁⢠⡏⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠈⢻⡗⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠹⡆⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠈⠻⢿⡿⠛⠁⠀⠀⠀⠀⠀⠠⡇⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣦⣤⣤⣾⣿⣄⠀⠀⠀⠀⠀⠀⢀⡔⢣⡀⠀⠀⠀⠀⠀⠀⢀⣇⡀⢀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠹⢄⣘⣦⡤⠔⠓⠁⠀⠀⠙⠑⠶⣄⣀⣜⣠⠞⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠲⠦⠦⣄⣤⠤⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⢻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⣁⣤⣤⣤⣄⣀⡀⠀⣀⣤⣶⢶⣬⡻⣿⠀⠈⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠋⠀⠙⣶⣀⡞⠋⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠈⢻⣦⠚⠛⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠁⠀⠀⠀⠹⠉⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠠⣤⣀⠀⣿⣆⠀⠀⠀⢻⣿⣿⠇
⠀⠀⠀⠀⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⣤⣦⡈⣿⠀⠀⠀⠀⢀⣴⣤⡈⢻⣿⣿⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠞⠃⠉⠀⠀⠀⠀⠘⠳⠿⠛⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠂⠀⠀⠀⣠⣴⣶⣦⣤⡀⠉⠓⠲⠾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠛⣩⣿⣿⡹⠃⠀⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠋⠀⠀⠀⠀⠀⠀⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⢀⣠⣿⣷⣄⡀⠀⢀⣀⣼⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⢋⣽⣻⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⣀⣠⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉