Cute face Emojis & Symbols

⣟⠉⣻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⢰⢂⠀⠐⠂⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠘⠋⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠐⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠠⠉⠈⠀⠈⠉⢐⠂⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠏⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⢠⠀⠈⠀⠈⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁

⣿⣿⣿⣿⣿⣿⣥⣬⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣥⣽⣿⣿⣿⣿
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠀⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣭⣻⣟⣸⣿⠓⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠈⢿⣦⣍⡒⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠉⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠗⠀⠀⢠⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢣⣀⡼⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣦⣄⣀⣀⠀⠀⠀⠀⠀⣀⣀⣠⣴⡾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠶⠂⠀⠀⠀⢄⠳⣄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢆⣸⠀⢾⣿⣿⣿⣶⣢⡴⡪⣾⢡⢠⠳⣾⣷⣄⢹⡄
⠀⠀⠀⠀⠀⠀⣼⣄⣧⡀⠌⣻⣿⠿⠿⢿⣟⣻⣭⠷⣫⡾⠱⣸⡆⠣⡘⣿⣿⢿⣿⡄⢸⣠
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣿⣿⣿⡿⠟⣉⣤⡾⠋⣠⢣⣿⣧⠀⣷⠸⣿⡣⠙⣿⡌⡇⡇
⠀⠀⠀⠀⠀⠀⠈⣩⣿⣿⢟⣫⣿⠟⣉⣴⠾⠛⡡⣠⡾⣣⣿⣿⣿⠀⣽⠀⣿⢳⡀⢸⠇⣱⠃
⠀⠀⠀⠠⠤⣶⣿⣿⠟⣱⡿⢋⡵⠞⠉⠠⢐⣩⡾⣫⣾⣿⡟⣼⡇⠀⣿⠀⣿⠸⡇⠈⠀⠫⠀⢠⡀⣷⣦⠆
⠀⠀⠀⠀⠀⡾⣱⠃⠊⠀⠀⠁⢀⣀⣤⡶⢛⣥⣾⣿⣿⠏⣰⡿⠀⢸⣿⢀⠇⢰⡿⠀⢱⣝⡶⣤⣷⣿⣿⠃
⠀⠀⠀⠀⡼⠡⠃⠀⠀⡀⣀⣈⣉⣭⣴⣾⠟⣫⣾⠟⢁⣼⡟⠁⢠⣿⠃⠊⠀⡼⠗⠀⠀⠉⢻⣿⣿⡯⠅
⠀⠀⠀⠀⠇⡀⠀⠀⠀⡟⠒⠛⣛⣉⣥⡶⠟⠋⣡⣴⠿⠋⢀⣴⡟⠁⠀⣠⠞⢁⡜⠀⢸⠀⡆⣧
⠀⠀⠀⠀⠀⡇⢸⡇⠀⠳⠤⣭⣭⣭⣤⣶⣶⡿⠛⢁⣠⣴⠟⠋⠀⠀⠉⣀⡴⠋⠀⠀⢸⡆⣿⣼
⠀⠀⠀⠀⠀⢷⣾⠀⠀⠀⠈⠛⠛⠛⠉⠁⠈⠐⠛⠉⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢸⢱⡿⠟
⠀⠀⠀⢠⣾⣷⣼⡄⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠏⡼⣷⣾⣦
⠀⠀⠀⢸⣿⢀⣀⡁⠀⠀⠀⠀⠉⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠉⠀⠀⠀⠀⠈⣀⡀⣾⣿
⠀⠀⠀⠈⢿⣿⠋⢻⡄⠀⠠⣾⣿⣯⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣷⣿⡄⠀⠀⡾⠉⣷⣿⠃
⠀⠀⠀⠀⠈⢻⣷⣌⣣⠀⠀⠠⠿⠨⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠉⢿⡿⠿⠷⠀⠀⢠⣃⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠛⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣸⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠈⠉⠁⠉⠀⠀⠀⠀⢀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣄⣀⣀⠀⠀⠀⠀⠀⣰⣶⣽⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡤⢴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣇⡞⠉⠀⣯⡤⠖⠚⠋⢉⡽⠃⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣾⠀⠟⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠉⠛⢛⣉⣵⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⢖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⡄⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⢶⣭⣤⠔⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢠⣇⡠⢺⢃⡴⠋⠙⠒⠤⣀⠀⠀⡀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡎⢀⣠⠞⠁⢳⣠⠔⠋⠁⠐⠋⠁⠀⠀⠀⠀⠀⠀⠑⢦⠘⡄⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠞⠒⠉⠠⠔⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⠒⠄⠀⠱⡅⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣾⠀⠀⡇⠀⠀⠀⣠⠤⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⣒⠤⡀⠀⠀⠇⢀⣴⣇⡀
⠀⠀⠀⠀⠀⠀⢀⡞⣉⡙⢦⡇⠀⢀⡟⢡⣟⢉⣿⡆⠀⠀⠀⠀⠀⠀⠀⣾⣏⣹⣷⡜⣧⠀⣼⠋⠤⢄⢱
⠀⠀⠀⠀⠀⠀⠸⡀⠁⡈⠀⠃⠀⠀⠇⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⢇⠇⠀⠀⠀⡰⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⣀⠀⠀⠈⠐⠓⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠁⠀⠀⣠⢤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⢄⣀⣀⡠⠔⠂⠀⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣓⡶⠒⠶⠶⠒⣶⢏⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⠀⠻⢅⣀⡀⠀⠀⣈⠗⢨⠗⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠑⠢⣄⡀⠉⠉⠉⣀⠔⠁⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣤⣶⣿⣿⣿⣷⣦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⠿⠛⠉⠹⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣤⣶⣶⠆⠀⠀⠀⠀⠘⠻⠿⠛⠀⠀⢻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⢈⣁⣀⡀⠀⠀⠀⠀⢀⢴⣶⣦⡀⠀⢼⣛⠓⢄
⠀⠀⠀⠀⠀⠀⠀⢼⠀⢲⡇⠀⠐⠛⣿⠏⠁⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⣘⢁⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣶⣶⣶⡇⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠙⠧⠴⠃⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⢤⣀⣀⡀⠤⠤⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢣⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠊⠉⢧⠑⢄⠀⠀⠀⠀⡴⠋⣸⠉⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠈⢇⠀⠑⢄⣠⠎⠀⢰⠃⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⡼⢷⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⢰⠀⠳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗
⠀⠀⠀⠀⠀⠸⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠒⠲⠦⠤⠤⠤⠼⠦⠤⠤⠤⠤⠤⠒⠒⠚⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠉⠉⠉⠉⠉⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣀⣀⣀⡤⠤⣤⣀⣀⡀⠀⣠⠤⢤⣀⡀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠁⢀⣀⣀⣀⣀⣀⣀⣉⢻⠀⠀⠀⠀⠉⢦⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠷⠾⠭⢍⣉⣉⠓⠒⠦⠤⣀⠉⠉⠒⠦⢄⡀⠈⡆⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⢄⡀⠉⠒⠦⣀⠀⠈⠑⠿⣀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠉⡿⡗⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⣈⠑⠢⣄⠀⠀⠙⠢⣄⠀⠘⡄
⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢸⠃⠹⣄⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢝⣲⢤⡀⠀⠑⢦⡸⡄
⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⡜⠀⠀⠈⢳⣄⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣤⣽⣷⡀
⠀⠀⠀⠀⣰⠁⠀⠀⢀⡼⠁⠀⠀⡰⠃⠈⠛⢶⣤⣀⡀⠀⠉⠑⠒⠤⢄⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣅⣠⢧⠳⡀
⠀⠀⢀⡴⠁⠀⠀⡠⠊⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠙⠺⠭⣒⣒⠤⠤⠤⠤⠤⠭⠭⠟⢛⣋⣩⣤⣒⣚⣋⣉⠤⢎⡀⠈⠲⠔⠒
⢀⡴⠋⠀⣠⠔⠋⠀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢌⡉⠉⠉⠉⠉⠉⠉⠉⠉⠓⠲⠤⠬⠭⢤⠤⡤⠚⠁
⠀⠉⠛⡿⢲⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢸⣤⣀⣀⣀⠴⠊
⠀⠀⡰⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠤⢤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢧
⠀⠀⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢨⠇
⠀⠀⠘⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢾⡁⠀⠀⠀⠀⠀⠀⣠⠟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣄⣀⡀⠀⠤⠤⠠⠤⠄⠀⣀⣀⡤⠴⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠃⠹⠙⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡏
⠀⠀⠀⠀⠘⣿⣿⣿⡏⠀⠐⠋⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠙⠂⠀⠀⢻⣿⣿⠁
⠀⠀⠀⠀⣠⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⢄
⠀⠀⠀⠠⡇⠀⠙⠟⠀⠀⠀⠀⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠄⠀⠀⠀⠸⠏⠀⠈⡇
⠀⠀⠀⠀⠳⣄⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠠⣄⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣖⠒⠒⠒⣒⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣄⣀⣀⣀⣀⣀⣀⣀⣠⠤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡴⢞⠻⢏⡑⠄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣅⡶⠋⠑⢆⠀⠀⠀⠀⠀⠀⠀⢀⢞⡫⠿⠂⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠧⣀⢀
⠀⠀⠀⢘⢁⠀⠀⠀⡈⣅⡀⠀⠀⠀⠀⠀⠀⢸⡆⡀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠸⠢⢀⠀⠀⠀⠀⢿
⠀⠀⠰⠟⠈⠀⠀⠀⠁⠛⠟⠁⠀⠀⠀⠀⠀⠈⢆⠁⠀⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⢺⣉⡌⠀⠀⠈⣬⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⣠⠤⢤⣄⣠⢤
⠀⠀⠀⢰⠀⠀⠀⠠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠈⡟⠐⢁⠧⢀⠻⠏
⠀⠀⠀⠂⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⠁⡀⠀⢀⠐⣤⠀⠀⠀⠀⠀⠀⠀⠀⢰⢈⠀⠀⢀⠀⢳⠂⠀⠀⠀⠀⠀⠀⠀⠇⣀⠀⠀⢀⡌⠁
⠀⠀⠀⠀⠈⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠁⠀⠈⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⣺
⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠉⠀⡇
⠀⠀⠀⠀⠁⠆⠀⠠⠄⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇⠂⠀⠀⠒⡸⡆⠀⠀⠀⠀⠀⠀⠀⢣⡘⠀⠀⠀⠘⣸⡇⠀⠀⠀⠀⠀⠀⠀⠸⠹⠗⠐⠽⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠃⠧⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠄⠀⠀⠀⠳⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢒⣒⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠉⠉⢇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠢⡀
⠀⠀⠀⡇⠂⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⣀⡬⠐⠁⠈⠐⢱⣄⠀⠀⠀⠀⠀⠀⠀⢸⢩⠀⠀⢀⡀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠔⡉⠀⠀⢀⠐⠆
⠀⠀⠀⠐⢆⠃⠀⠀⠋⡸⠁⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⢀⠒⠒⢒⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠒⠒⠒⠉⠉⠉⠉⠐⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⡁⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⡑⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠂⠀⣀⠀⠀⠀⠀⠈⠒⠢⠤⣀⣀⠀⠀⠀⠀⠠⡀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠌⠀⡐⢀⠤⠊⢁⢀⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⠎⠀⠙⠢⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⠈⠑⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠈⢉⣲⣦⣤⡄⢤⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⣄⠀⢰⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⡇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⡏⡸⣞⣀⡞⠁⠀⡀⢀⡈⡄⠀⠀⠀⠀⢠⠁⡀⠀⠀⠈⢳⣳⠠⡅⢹
⠀⠀⠀⠀⠀⠀⠀⠁⠽⡏⠙⠁⠀⠀⠀⠿⠇⠘⠀⠀⠀⠀⠃⠸⠿⢀⠀⠀⠈⠟⠳⠅⠈⠄
⠀⠀⠀⠀⠀⢀⠆⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⠀⠀⠲⡀
⠀⠀⢀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⡀
⠀⠀⠘⢆⠀⠒⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡰⠃
⠀⠀⠀⠀⠑⠤⣀⡀⠀⠀⠀⠈⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢿⣿⣿⣿⣿⣿⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⡱⡑⢁⣿⣿⣿⣿⣿⣿⣦⡝⢟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠂⢡⠀⡟⣿⠟⠉⠉⠛⢏⢻⣿⠌⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡜⡄⣦⠱⢸⠇⠀⠀⠀⠀⠈⠈⡼⠀⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⡱⡱⠐⡟⡀⡾⠀⠀⠀⠀⠀⠀⠀⠁⠄⢸⢹⣨
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡜⠑⠁⠐⠁⢰⢓⠲⠦⠀⠀⠤⠖⢚⡆⠀⠀⢸⡟⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣠⢪⢊⠄⡠⠋⠉⠁⠀⠀⠀⠀⠈⠉⠉⢆⠀⢈⢟⠜⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡇⡼⡱⡵⢃⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣌⠲⣄⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣱⢱⣟⣴⣿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⠏⣿⣿⡇⢳⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣼⣹⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⢆⢿⡜⣷⡀⣻⡀⠀⠀⠀⠀⠀⠀⢠⣾⢣⢳⢻⢿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡘⠌⢷⡜⣞⠌⢷⡀⠀⠀⠀⠀⣠⣿⠃⣰⢇⠏⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣷⡀⠀⢊⠈⡎⠈⢳⠀⠀⠀⠰⢱⠃⡴⡏⡌⢠⢹⡿⣄
⠀⠀⠀⠀⠀⠀⡀⠄⡾⡇⢹⣷⡐⡀⡆⢸⡄⢠⠇⠀⠀⠀⡏⣾⢡⢸⡱⢸⢸⣿⡪⡲⢄⣀
⠀⠀⠀⠀⠀⠀⡠⢊⠔⡠⢿⡟⣿⣸⡆⢸⡇⠈⠀⠀⠀⠀⣟⡾⠀⡟⢻⣌⠘⣟⢿⡢⣄⠀⠁
⠀⠀⠀⠀⠀⠀⣷⡣⠊⣰⡿⠃⣹⢿⠃⡾⡇⠀⠀⠀⠀⠀⢸⡗⠀⢹⠀⠻⣷⢌⢣⠙⠌⢣⠁
⠀⠀⠀⠀⠀⠀⠛⠀⣼⠟⢁⠴⠳⣫⠞⣑⠐⠑⠂⠀⠀⠂⠁⠙⠜⣆⠢⡀⠈⠂⢡⠇⠀⠸
⠀⠀⠀⠀⠀⠀⠤⠞⠁⠀⠀⠀⠊⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢶⠦⢄⠀⠀⠀⡖⠦⣄⣏⢢⢀⠷⡴⠆⠀⠀⠀⡠⠒⠉⢉⠒⢤⡀
⠀⠀⠀⠀⢀⡀⠀⠀⡞⡱⢪⠵⠯⡀⠃⢀⣀⣬⠶⠶⠿⠮⠯⠚⠒⠲⠦⢤⣸⡁⡌⡔⡒⡌⠀⢳
⠀⠀⠀⠀⠙⠃⠀⠸⡇⣅⠳⠬⣣⡧⠟⠉⠀⢀⠠⠀⠀⠀⠀⠐⠠⢄⡀⠀⠈⠙⠳⣌⣈⡠⢀⠏
⠀⠀⠀⠀⠀⠀⡀⠀⠓⠬⢍⡽⠋⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠈⠳⣖⠁⠀⠀⠀⢰⠊⣲
⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⠞⠀⠀⡠⠊⠀⠀⡄⠀⠀⠀⣠⠀⠀⠀⠀⡀⠀⠈⠣⡀⠀⠀⠹⡆⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⡐⠁⠀⢠⣾⠀⠀⠀⢠⢿⠀⠀⠀⠀⢻⢄⠀⠀⠑⡄⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡈⠀⢀⡴⠁⡇⠀⠀⣠⠏⠘⡇⠀⠀⠀⢸⡈⢣⡀⠀⠰⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⠀⡠⠊⠀⢸⠃⢀⡴⠁⠀⠀⣷⠀⠀⠀⢸⡇⠀⠹⡄⠀⢣⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢠⠞⣧⢀⣰⠊⠀⠀⠀⠘⠖⠋⠀⠀⠀⠀⠸⣄⢀⣀⡸⠀⠀⠀⠈⠓⢺⣤⣰⠋⠢⡀
⠀⠀⠀⠀⠀⢰⠃⠰⢸⠏⢹⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣄⣠⠀⠀⠀⢸⠀⢻⡄⠀⠹⡄
⠀⠀⠀⠀⠀⡏⠀⡇⠹⣄⠘⡄⠀⠀⠰⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⢿⠁⠀⠀⣸⣀⡼⠣⡀⠀⢷
⠀⠀⠀⠀⠀⢧⠀⡇⠀⠘⡗⢳⠀⠀⠀⠻⢾⠿⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⢀⠏⠁⠀⠀⢳⠀⢸
⠀⠀⠀⠀⠀⠘⢆⡱⡀⠀⠙⡆⠳⡀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⡀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⣸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠉⣛⠲⠞⠀⠀⠈⠳⢤⣀⠀⠀⠀⠘⠢⠤⠚⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀⡴⠃⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠘⠤⠕⠭⠇⠀⠀⠀⠀⢈⡩⠷⣶⡶⠶⠶⠖⣶⡾⠯⢤⡀⠀⠀⠀⠀⠀⠀⠉⣲⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⣰⠁⠳⢤⣤⠴⠋⠸⡄⠀⣨⠆⠀⠀⠀⠀⠀⠀⢰⢓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠇⠀⠀⠀⠀⠀⠀⠀⠳⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣒⣚⠲⣦⣤⠔⣒⣒⣒⣒⡢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⠋⠡⠤⠭⠭⣿⣿⣿⣛⡭⠥⠤⠤⠄⠀⠈⠛⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣀⣀⠀⠛⠛⢿⣿⣿⣿⣿⣷⣛⡛⠛⠳⠶⢦⣄⡈⠻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⣴⡿⠛⢉⣤⠶⠛⢛⣛⣻⣿⠋⣠⣤⣦⣄⠉⠉⠐⠂⠀⠙⠳⢦⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣣⣾⠟⠁⠀⡴⠋⢀⣤⣾⣿⣿⣿⣿⣿⣫⣿⡿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢪⣿⠟⠁⠀⠀⠀⢀⣴⣿⣿⡿⠿⠛⠛⠛⢿⠟⠛⠿⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⣿⠋⠀⠀⠀⠀⣴⣿⠿⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡿⠁⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⠁⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠰⡇⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠿⠿⠶⠌⠳⣄⡀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣿⣿⡟⠀⠰⠞⠛⠛⠛⠛⠻⠿⠷⠀⠀⠀⠀⠀⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⠙⣿⣷⢦⣄⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⢲⣤⠀⠀⠀⢹⠁⠟⢿⡟⠳⣬⣇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠛⠀⠹⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠀⠀⠀⢸⡇⠀⢸⡇⠀⢸⡏
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢸⡄⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣄⣾⠃⠀⠈⡇
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠘⣧⡈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢁⣾⡏⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣿⣌⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣾⣿⠇⠀⠀⠀⣣
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⣿⣦⣬⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠁⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣠⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⢠⡇⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⢸⡇⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡈⢻⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⣿⣿⠱⡆⠛⠀⠀⣴⢀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⢸⡇⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⣿⣟⣾⢇⠇⠰⡄⠀⣿⡞⣄⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⢸⡇⠀⠀⠀⠀⠈⠙⠒⠂⠖⠒⠒⠉⠀⠀⠀⠀⢿⣾⡏⣿⢠⢀⡇⢀⣿⣿⣿⡄⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⣹⡇⠸⠇⣸⣿⣿⣿⡇⠀⠀⠀⣿⣰
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⣿⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⠀⣰⣿⣿⣿⣿⡇⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧⣸⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⠇⠀⠀⡼⠛⠃
⠀⠀⠀⠀⠀⠀⣇⢀⣀⣤⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⣁⠴⠋⣠⡖⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣰⡯⠒⠋⣹⠃⠀⣼⢧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⣿⠁⣠⠞⠁⣀⢼⣿⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠘⠙⠛⠐⠛⠡⠞⠋⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠢⠤⠤⠖⠚⠛⠉⠁


⣿⣿⣿⡿⠿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣦⣤⣤⣶⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣯⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠈⢘⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠻⢿⣿⣿⣦⠹⡎⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣼⡟⢋⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⡈⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠞⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢧⠀⠐⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠃⠀⠀⢸⠃⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⡈⣿⡀⠁⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢀⠀⠀⣿⣈⣵⣿⣿⣟⠋⠀⠀⠘⢋⣿⣿⣶⣅⣻⣷⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣱⣿⣾⣼⠇⠈⠛⠖⠒⠉⠀⠀⠀⠀⠉⠑⠒⠛⠋⠈⣿⣧⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠼⢿⣷⣽⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠛⢛⣿⣿⣿⣿⣿⣿⣶⣧⠀⠀⠀⠀⠀⠒⠀⠀⠒⠀⠀⠀⠀⠀⣼⣶⣾⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⣿⣿⡄⠀⠀⠠⣴⡾⠷⠾⣷⣦⠄⠀⠀⢠⣿⣿⡟⣿⠻⣯⡙⢿⣟⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠿⡿⢹⡟⣿⡇⢸⣿⣿⣄⠀⠀⠈⠛⠿⠿⠛⠁⠀⠀⣠⣿⣿⣿⡁⠘⢷⡈⢻⣆⠙⣧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣇⠀⠃⢸⠁⠙⠀⠀⣿⠙⠙⣷⣄⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⢻⣿⣷⡀⠀⠻⡄⠹⣆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠈⠀⠀⠀⠀⢹⣧⠀⠸⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣧⡙⢿⣿⣶⡀⣀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡆⠀⠀⠀⠀⠀⠀⢻⣷⣥⣿⠀⠉⠛⠛⠉⢰⣿⣿⢿⣿⡿⣅⠀⠙⢿⣿⣸⣧⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⢰⠀⣷⠀⢀⠀⢿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣟⠘⣯⠳⠌⢧⠀⡘⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣼⡇⣿⡄⣾⣷⣾⡟⠁⠀⠀⠀⠀⠀⠀⢻⣿⣆⠹⣷⡀⠀⠃⣷⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣽⣷⠀⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠟⠡⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣷⣶⣤⡀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡉⠉⠉⠛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠟⠛⠛⢁⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⡟⢻⣿⣿⣿⣦⠀⠘⠻⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠋⣿⣿⡿⠋⠀⢸⣿⣷⠀⠙⣿⣿⣿⣧⠀⠀⠀⠈⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⣿⡿⠀⠀⠀⠘⣿⣿⠀⠀⠈⢽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⢀⣿⣥⣄⣀⠀⠀⣿⣿⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣤⣤⣠⣾⣿⣿⣿⣿⡿⠿⣤⣿⣿⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠏⠈⢿⣆⠙⠻⣿⣷⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⣿⡏⠀⠀⠘⣿⡆⠀⠈⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠻⠀⠀⠀⠀⢹⣿⡀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⠱⣆⠀⠀⠀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠻⠄⢠⠀⡀⠈⡼⣋⠄⠀⠂⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⣉⣉⣉⡛⠷⢦⡈⣵⠲⣮⢢⣞⡼⠋⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡒⢼⣋⣬⢿⣾⣲⠅⠒⣝⢾⣷⢳⣿⣋⣴⣆⣽⣥⣤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⡴⠄⣶⣤⣠⠆⡀⠀⠀⠉⠒⠾⣾⣷⢿⣭⣭⣍⡤⢀⣀⣈⠁⢀⠙⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠛⠓⠒⡯⠔⢊⢹⡇⠡⠀⡀⠈⠉⠒⠶⣤⡛⠘⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠆⣠⡾⣫⣿⠁⠀⠏⠙⠑⠴⠄⣀⠀⠉⠢⡀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢁⡼⢋⡴⣇⡟⡧⠀⢸⠈⡓⠀⠀⠁⠘⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠰⢋⣴⡟⢰⢸⠇⣶⠀⠘⢀⡋⠀⠀⠀⠀⠀⠘⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⣠⡟⠉⠀⠆⣿⠀⢹⡀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣤⠋⠀⠀⠀⠘⡿⠀⠋⠷⢀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢰⢰⣷⠀⠀⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠻⣷⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣄⠻⣿⡆⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⡇⢰⡿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠉⠉⠁

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠉⠈⠉⠙⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢓⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢟⣩⣾⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣍⣛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠋⣱⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢂⣦⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠤⣤⣀⣤⣦⣜⡆⢠⠀⠀⠀⠀⠀⢀⣀⣾⣣⣶⣤⣤⣤⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⣷⣼⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠻⡋⣿⢿⣿⣿⣏⡀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⣠⣻⣿⣿⡿⣏⠻⠿⠿⣿⣿⣿
⣿⣿⡿⠀⢀⠎⠀⢀⣿⣿⣿⠋⠀⠀⢠⣿⣿⣿⣿⣿⢻⣿⣿⣿⠿⠿⠿⠇⠃⠈⠿⠿⠿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣷⠀⠀⠈⠻⣿⣿⣿⡈⠀⢲⠀⠘⢿⣿
⣿⣿⠃⠀⡆⠀⢀⣾⣿⣿⡷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢿⣿⣿⣷⣦⠀⢣⠀⠹⣿
⣿⠇⠀⠰⠃⣸⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⣀⣠⣤⣤⣄⣀⡀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠈⠃⠀⠸
⠁⢀⡄⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢀
⠀⢸⡠⠀⠰⣿⣿⣿⣿⣿⡄⠀⠀⣸⣿⣿⡿⠋⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡆⠀⠀⠀⠀⠈⠻⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠈⣧
⣶⡿⠁⠀⢰⣿⣿⣿⣿⣿⡟⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⡞⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⢇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⢾⣿⣿⣿⣿⣿⡇⠀⠀⢻
⡿⠀⠀⠈⢸⣿⣿⣿⣿⣿⠇⠀⣸⣿⠟⠁⠀⠀⠀⠀⢀⡔⠉⠀⠀⠈⣻⣿⣿⣿⣿⣟⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆⠀⢹⣿⣿⣿⣿⣿⡇
⣷⡗⠀⠀⣾⣿⣿⣿⣿⣿⠀⢠⣿⣷⣄⡄⠀⠠⠀⠀⠈⠀⢤⡀⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⡄⢀⣿⣿⣿⣿⣿⡇⠀⠀⢺
⣿⣿⡀⢰⣿⣿⣿⣿⣿⡇⢰⣿⢿⠿⠋⠀⠄⠀⠀⠀⡠⣸⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⡔⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡄⢺⣿⣿⣿⣿⣿⡀⠀⣾
⣿⣿⣧⣸⣿⣿⣿⣿⣿⣷⣿⡏⠀⠀⠀⠀⠀⠀⣄⣼⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣆⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⣿⣿⣿⣿⣿⣇⢸⣿
⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣴⣦⣾⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣶⣴⣤⣠⣘⣶⣿⣿⣧⣿⣿⣿⣿⣿⢻⣿⣿
⣿⣿⣿⣿⣝⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠛⠻⢿⡿⠟⠛⠁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢋⣿⣿⣿
⣿⣿⣿⣿⣿⣦⡀⠻⣿⣿⣿⣿⣿⡀⢻⠻⠿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠋⠛⠏⢀⣿⣿⣿⣿⣿⡟⢀⣠⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⢢⣽⡿⣿⣿⣿⣷⣦⣂⠀⣽⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡟⠀⢀⣠⣾⣿⣿⣿⡿⣫⡔⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠁⠀⢽⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣷⣿⣿⣿⣿⣿⣿⣇⣱⣯⠀⠀⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⣴⣦⣤⡀⠀⠀⠀⠀⢀⣴⣤⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠉⠉⠉⠙⠈⠋⠈⠛⠿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠁⠘⠁⠛⠉⠉⠋⠁⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡆⢀⡄⠀⣀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢸⣿⣿⡀⣼⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⣠⡀⣢⡀⢠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⢹⠀⣆⠸⡇⢻⣷⡄⠀⠀⢠⢀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⣠⠆⡜⠀⢠⣺⣿⢸⣇⢰⢣⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡀⠀⢀⠀⠀⢀⣴⣿⣿⣿⣇⡀⠀⣴⠇⠀⠀⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠒⠀⠒⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣾⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⡿⠋⠉⠙⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⢛⠋⠉
⠀⢀⣴⣶⣶⣦⠀⠆⠀⠄⠀⡸⠋⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⢠⠚⠛⢖⠻⢇⡀
⠀⠸⡿⠋⠉⠙⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⡆
⠀⠀⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣦⣄⠀⠀⡠⠶⠆⠀⢠⣄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠛⢿⣿⣿⣷⠀⠀⠀⠀⠄⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⢀⠀⠀⠸⣿⣿⣧⠀⠀⢠⣿⣿⣟⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠙⠿⠿⠇⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⢰⣶⣶⣶⣶⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⠛⠋⠉⠹⡇⠀⠀⢀⡀⠀⡀⠀⠀⢸⣷⡄⠀⠀⠸⣿⡆
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠿⠿⠀⢀⠉⠀⠀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⢸⣷⣦⢤⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠁
⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⠛⠛⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣽⣦⠀⣿⣡⣴⣿⡿⠿⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣟⣥⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⢿⣿⣿⣿⣿⣟⠛⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣴⠏⠀⣀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠁⣼⣿⠿⡿⠙⣿⡆⠀⠈⠋
⠀⠀⢀⣤⣶⣾⣿⣿⣶⣿⣾⣿⣾⣟⠿⢿⣆⠀⠀⠀⠀⣿⠁⠀⣰⣿⠇⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⢀⣴⠶⠿⣿⣿⣿⡉⠛⢷⡀⠈⠀⠀⠀⠀⠃⢀⡼⢹⠏⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⢰⡟⠁⠀⣼⠛⢿⣿⣷⠀⠀⡇⠀⠀⠀⠀⠀⢀⡾⠁⠈
⠀⠀⠀⠀⠈⠁⠀⠀⢿⡆⠈⢷⡙⡇⠀⠁⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣾⣷⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣼⣿⣿⣿⣼⣿⣷⣯⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠿⠿⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⣴⡶⠶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⠿⣮⣵⠱⠿⢿⡚⠻⣅⢉⢳⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠽⢟⠻⣉⢒⣖⣀⣌⣃⡸⡿⢾⠟⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣧⡶⢆⣙⣦⠉⠉⠙⠉⠉⠁⣸⣠⣄⣴⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⢭⣏⢻⡍⢵⠆⣀⡀⠀⠀⢠⣿⣿⣟⡿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡗⣦⡈⣐⡺⣙⠫⠝⢧⡔⡈⠉⠉⠉⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣟⡵⣏⡳⢿⡻⠬⢷⠴⣖⣷⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡳⣭⣛⣶⠥⣮⡉⣖⣒⣶⡢⢦⣾⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣱⢽⣵⣪⣟⣛⣿⢟⡽⣯⢴⡯⣸⣿⠈⠏⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠨⢙⡒⠯⣶⢶⣚⣫⢗⠛⣺⠧⢋⣿⡆⣺⢊⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠈⣯⠙⢒⡙⠉⡠⢗⣐⠏⡴⢟⣞⠛⣿⠦⠖⡎⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡢⠝⠲⣂⣸⣏⣭⠔⣋⡴⣚⠝⣽⢿⣟⢻⡕⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢟⣉⣠⢒⣸⠦⠶⠋⣁⡸⢵⡎⡼⡾⣿⣿⡻⣷⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡬⠴⠣⠤⡥⠒⠣⡭⢖⣫⡞⡴⣣⢼⣿⣿⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣔⡗⣓⠿⢟⣩⣖⡾⠃⢞⣩⡦⠋⠻⡿⣷⡻⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣶⣬⣔⣛⠲⣦⠬⠭⠭⢖⣞⡽⢛⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠏⠈⠳⠷⢹⣆⠸⣭⣭⠵⣶⣪⡴⣻⣿⣿⣿⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣤⣤⣱⣏⠐⠚⡉⠛⠻⠬⡠⢼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⡂⣠⣶⣫⡞⠁⠀⠀⣽⡶⠢⣯⠂⠤⢤⡀⢲⡹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣰⢭⣙⢀⣤⡴⢻⠁⠀⠘⢷⣤⣤⡈⢄⡼⣝⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣙⠂⠈⣿⣿⣯⣛⠢⢄⡀⠘⣿⠀⠙⠀⠁⢸⡸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠳⡌⠙⠲⠇⠀⢿⡄⢀⡴⠀⠗⢧⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⢸⣷⠀⢿⡂⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⠀⠀⠀⠀⠀⠀⠈⣿⡄⠈⠥⡀⡲⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⡆⠀⠀⠀⠀⠀⠀⠛⠉⢒⢀⣇⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠳⠃

⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠂⠉⠉⠉⠉⠐⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⣀⢀⡠⠤⠤⠤⢄⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⢠⠁⢠⣶⢿⡆⠀⠀⢰⡿⣦⡀⠈⡄⠀⠀⠀⠀⠈⡟⠀⣀⣤⡄⠀⢀⣤⣄⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠘⡀⢺⣿⡿⠃⢠⡄⠸⣿⣿⠇⢀⠃⠀⠀⠀⠀⠀⡇⢸⣿⣷⡟⠀⠸⣷⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠀⠀⠈⠁⠀⠀⢁⡠⠊⠀⠀⠀⠀⠀⠀⠣⡀⠉⠉⠀⠟⠄⠈⠉⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠶⠒⠒⢶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠒⠊⠁


⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⣀⠠⠤⢀⣀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⢰⣿⠛⣻⠟⠉⠀⠀⠀⠀⠀⠀⠉⠻⡟⠛⣿⡆⠀⢀⣴⠛⡿⠋⠁⠀⠀⠀⠀⠙⠻⡛⢷⡄
⠀⠀⠀⠀⠈⠻⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠟⠁⠀⠘⢷⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⠇
⠀⠀⠀⠀⠀⡘⠀⣠⣶⣶⣶⡀⠀⠀⢠⣶⣶⣶⣄⠀⢇⠀⠀⠀⢨⠁⢀⣴⣶⡄⠀⢀⣴⣦⣄⠀⡇
⠀⠀⠀⠀⠀⡇⢸⣿⣿⣯⣿⡇⠀⠀⢸⣿⣽⣿⣿⡇⢸⠀⠀⠀⢸⠀⣿⣿⣾⡟⠀⠸⣷⣿⣿⡆⡀
⠀⠀⠀⠀⠀⠰⡘⢿⣿⣿⠟⠁⣤⣤⠈⢿⣿⣿⡿⢣⠃⠀⠀⠀⠈⢆⠈⠛⠉⠀⠿⠄⠈⠛⠋⢀⠃
⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⣀⡀⠚⠓⣀⣀⡀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠑⠠⠄⢀⣀⣀⠠⠤⠒⠁

⣟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠦⡄
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠘⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠚⡀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⢀⢆⠀⠀⠐⠀⠀⢀⠀⠀⣸
⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢀⡠⠃⠁⠀⠀⠀⠀⠀⠀⠀⠣⣄⠀⠀⠀⠁⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣄⣀⣄⣠⠄⡀
⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢼⡵⡻⠛⠛⠛⠻⢝⣾⡀
⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠰⠀⠈⠉⠉⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠄⠀⠀⠠⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠂⠀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢔⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠠⠐⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⠀⠀⠈⢢⠀⠀⠀⠀⠀⢠⠔⠉⠁⠈⠁⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⢀⠀⠀⠀⠀⠈⡗⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠐⠠⢄⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠂⠀⠀⢰⠀⠀⠀⠠⠁⠀⠀⠀⠀⠐⠀⠀⠐⠄⢱⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⣀⠔⠁⠀⠀⠠⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⣠⠆⠀⠀⠀⢈⠱
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠊⠉⠑⠒⠉⠀⠀⠉⠉⠁
⣀⢀⡀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢴⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠠⢶⣾⠿⢿⠉⠁
⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠖⠶⠦⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠑⠾⢟⠛⠛⠃
⠀⠀⠀⢀⣴⣞⡭⢴⣟⣠⠤⢤⡶⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⡜⠰⠿⡛⠛⠃
⠀⠀⠐⠋⠿⠋⠀⠛⠁⠀⡴⠟⠒⠒⣲⠶⠂⠀⠑⣄⠀⠀⢰⠳⢾⣟⠋⠀⢀⣠⠤⠐⠒⠒⠒⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⣉⣷⠶⠌⢣⡀⡆⢠⠞⢁⠴⠊⠁⠠⣤⣄⣀⠘⣶⠦⣄⣰⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣉⣉⡓⠦⡳⣵⢃⠞⠁⣐⣶⣖⠒⠺⢷⡀⠉⠺⠇⠀⠙⣧⠙⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢉⠀⢀⣤⠎⢉⣷⣼⡏⣹⢾⡿⠷⠮⠭⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⣶⣰⢻⡴⢩⠗⠊⢹⠋⠻⣩⠩⡷⣅⢰⣧⢠⡆⢉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣤⡜⠸⠇⠘⠁⠀⠀⠀⠈⣻⠁⡟⠒⠁⠈⠻⢹⡼⢻⢸⡇⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡋⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠈⠀⢸⡎⣧⣿⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣇⠀⠀⠀⠀⠀⠀⠈⠀⢸⢿⣾⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠒⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠈⠁⢀⣸⣆⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⢻⠀⠈⠉⠀⠘⣆⠀⡾⡔⣇⠔⠡⢝⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢆⣣⠈⡧⠴⠖⠚⠁⠈⢣⣧⠃⠻⢰⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠙⠀⣸⠄⠀⠀⠀⠀⣠⠭⠷⠆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣯⣀⣽⣭⣭⣭⣭⣿⣽⣭⣭⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣿⣯⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⡄⢠⡶⢀⡄
⠀⠀⠀⠀⠀⠀⣤⠅⠀⠀⢀⠛⠃⠀⠀⠀⢸⠧⣿⣇⡞⢀
⠀⠀⠀⠀⠀⠘⢁⡀⠘⢶⡾⢦⠀⠀⠀⠀⣼⢀⡇⢹⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢀⡀⠀⠈⠀⢀⣹⣿⡄⠀⠀⠀⠀⠻⠏⠓⢾⢆⣴⡁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⢠⠀⠀⢠⠆⠀⠉⢟⠀⠀⠀⠀⠀⠘⠃⠀⠀⠙⢻⣿⠇⠀⠀⠀⠀⢀⡤⠊⠀⢀⡤
⠀⠀⠀⢀⠀⠀⣼⠃⡀⠀⡍⠀⠀⠀⠀⠀⠀⠠⠀⠈⠈⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⣾⠃
⠀⠀⠀⠈⠀⠱⢼⣀⡜⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⢀⠜⠀⢀⢰⡟⠃
⠀⠀⠀⢠⡿⢀⣮⡼⠁⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠾⣿⣿⠃⠀⠐⠄⠛⠁⠀⠀⠀⣀⠄⠀⢀⠄
⠀⠀⠀⢸⢃⣾⣿⣧⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝⠁⢥⡀⠀⠀⠀⢀⠀⠈⣛⣷⣾⣯⡄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⣼⣿⣴⡏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⠋⠀⠀⠀⠀⢈⡿⠿⢿⣿⣿⡛⠓⠂
⠀⠀⠀⢸⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠐⢉⠻⠶⠇⠉⠋⠉⠉⠀⠀⠀⠒⠈
⠀⠀⠀⠸⢻⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⢐⠁⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢸⡆⠀⡇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠑⢦
⠀⠀⠀⠀⢀⢿⡏⠀⠀⠀⠀⠀⠀⠐⢄⡀⠠⡠⣄⢠⡄⡟⠀⠀⠀⠀⠀⠀⢀⠠⢤⢀⣀⠀⣀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⢀⠀⠀⠙⢷⣴⣿⡛⠓⠃⠀⠀⠀⠀⠀⠀⠹⠷⢮⡁⠠⠙⠿⠟⢢⣄
⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⡁⣦⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⢀⡇⠀⠈⡁⠄
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⢠⣾⣷⡇⠀⠀⠀⠀⠀⠀⢢⡜⢿⣿⣾⡉⠐⢛⡐⠛
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠈⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠠⣈⠀⠄⠀⠗⢁⠄⡀
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠶⢄⠀⠀⠀⠀⠀⢀⣴⠰⢦
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⣀⣤⡴⠖⠀⠀⣀⡙⠛⠻⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣴⣾⣿⠋⣠⢂⣴⣿⣏⣠⠶⠶⠶⣮⣝⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⢰⢃⣿⣿⣿⠟⠛⢛⠂⠀⠢⣍⠛⢦⣙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣌⢿⣿⣿⣿⣇⢸⣼⣿⣿⣿⣿⣿⣟⠻⢿⣷⡌⠳⣦⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⠸⣿⣦⣙⢿⣿⣿⡀⠻⣿⣿⡏⠙⠻⣿⣿⣦⡉⠛⠀⠈⢷⣄⠹⣷⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢋⡍⠀⣈⣿⣿⡷⠌⠉⠓⠀⠈⣙⡛⠂⠀⠀⠙⠿⣿⣆⠀⢀⠀⢻⣧⡘⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢁⣩⠶⠛⣉⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠈⠻⣧⠘⣧⠀⢻⣷⡌⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠠⠋⣠⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠈⠀⢹⣇⠀⢿⣿⡌⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣡⣤⠞⣫⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠀⠘⣿⣿⡌⢿⣇
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⢉⡿⢠⣯⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣄⣻⣿⣷⡘⣿⡆
⠀⠀⠀⠀⠀⠀⢀⣿⡏⢰⣿⢡⣿⣿⠁⠀⠀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣰⣇⣹⡆⢿⣿⣿⣿⣧⠸⣿⡀
⠀⠀⠀⠀⠀⠀⣸⣿⡇⣿⣿⣾⡿⠃⠀⠀⠊⠉⠉⠉⠛⠿⢿⣶⣦⠀⠀⠀⣧⠀⠀⣴⣿⠿⠛⢻⡟⢻⣷⠸⣿⣿⣿⣿⣇⢻⣧
⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⠛⣵⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠈⠙⠀⠀⠀⢸⠀⠀⠉⠀⢀⣀⣿⠃⢀⣿⠀⢹⣿⣿⣿⣿⡈⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⡇⠀⡿⠀⠀⠀⠰⣶⡶⠲⣶⣶⠤⣀⠀⠀⠀⠀⠀⡇⠀⠠⣭⣶⣼⣯⣀⣸⣿⠀⠀⢻⣿⣿⣿⣇⢹⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣷⠘⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⢱⠀⠀⠈⢻⡟⠀⠉⢸⣿⠀⣴⠀⢻⣿⣿⣿⡈⣿
⠀⠀⠀⠀⠀⠀⢿⣿⡌⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢠⡟⠀⠀⠀⣿⡿⠀⣿⡇⠀⠹⣿⣿⡇⢻
⠀⠀⠀⠀⠀⠀⠸⣿⡗⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠸⠁⠀⠀⠀⣿⠃⣸⣿⣷⠀⡄⠙⣿⣷⠈
⠀⠀⠀⠀⠀⠀⣄⠹⣿⡈⠻⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠂⠀⠀⠀⠀⢰⡟⠀⣿⣿⣿⠀⣿⣆⠘⣿
⠀⠀⠀⠀⠀⠀⣿⣆⠹⣧⠐⢮⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣿⣿⣿⡆⣿⣿⡄⠘
⠀⠀⠀⠀⠀⠀⢿⣿⡇⠈⠧⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⠁⢿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣄⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠛⠛⢛⣿⣷⡄⠀⠀⠀⠀⠀⠁⢸⣿⣿⠏⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⡇⡄⠀⣿⡀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠿⣿⣿⡿⠀⠀⠀⠀⢀⡶⠀⣿⡿⠋⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⡇⢿⡀⣿⣧⢀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⣠⣾⠃⠼⠋⡀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣷⣿⣿⡜⣷⣄⠙⢧⡀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠇⣀⣴⣾⠃⢀⠀⡄⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡹⣿⠃⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⢀⣠⡾⣿⣿⡟⢰⣿⣿⡟⠀⡜⢀⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⡙⣧⡀⠀⠀⠀⠀⢀⠉⠛⠶⢶⣾⣿⠟⠁⠀⣸⡿⢁⣿⣿⣿⠁⣰⣇⣼⡇⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣌⡙⢛⣣⠆⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢠⣾⣿⣿⠃⢠⣿⣿⣿⡇⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠁⣰⣿⣿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣍⣛⣋⣩⣤⣴⣶⣶⣤⠄⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⣠⣾⣿⣿⠏⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠶⣶⣿⡿⠿⢋⡥⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠈⠉⠉⠉⠉⠲⢠⣄⡀
⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣀⢀⠤⣀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⢸⣦⣀⡀⠀⠀⡆⢻⡿⢂⡙⠃⠀⠀⢀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⡏⠉⠈⠻⢆⡀⠈⠁⠈⠋⠉⠀⠀⢠⡞⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⡇⢀⣀⠠⢾⡃⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⢨⡿⠦⢀
⠀⠀⠀⠀⠀⢃⣘⡏⠂⠴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠈⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢻⣄⣄⡴⠀⠀⠀⢀⡠⠶⠦⠶⢾⣟⠁⠀⠀⠀⠀⠀⠙⢿⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⢀⡴⠟⠡⡄⠀⠀⠀⠀⠘⠷⢦⡀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⢰⠃⠀⠀⠀⠈⠑⢦⣀⣤⠆⠀⠀⠈⠐⠠⣀⠀⠀⠀⠀⠀⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡊⠀⠀⡀⠀⣠⠀⠀⢹⡄⠀⠀⢀⡀⠀⠀⠈⠓⣦⣀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢿⠄⠀⠋⠀⠀⠰⣶⡏⠀⠀⢤⠋⠁⠀⢀⣀⣠⠄⠉⠛⢦⣀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣸⠀⢸⡀⠀⠀⠀⠀⠑⢀⠀⠀⣦⡀⠀⣠⠀⠁⠀⠀⠀⠀⠈⠳⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠉⠁⠀⠀⠀⠀⠈⢷⠸⡁⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⣹⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠱⣄⠀⠀⠷⠴⣦⣄⡀⠀⠀⣀⠛⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣀⡷⠠⡀⠀⠀⠈⠉⠛⠛⢧⣄⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⠀⠈⠀⠀⠀⠀⠀⠀⠈⣧⠉⠀⠀⠀⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠈⠐⣿⠀⠀⠀⠙⣦⡀⠀⠀⠀⣤⠀⠀⠠⠿⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠙⠁⢄⣀⡠⠦⡈⠳⣤⠄⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠂⣀⠁⠀⠀⡀⠀⠀⠀⡀⠈⠀⢄⠈⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣄⠐⣄⡀⠀⠄⠀⠀⠀⠈⠙⠲⠢⣬⠒⣤⠀⠀⠁⠒⠀⠈⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⠒⢴⣶⡖⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣤⣤⣤⣀⣀⣀⣀⣀⣤⣶⣿⣿⣟⣛⣿⣷⣦⣤⣤⡀⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⡜⠄⠈⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠈⠁⠀⠙⣿⣯⠀⠀⠀⠀⠀⠀⠈⠳⣬⣙⠓⠀⠀⠀⠀⠀⠀⠀⢱⠈⠐⢿⠁⠀⠉⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⠙⠲⢤⣄⡒⠢⣤⣤⠼⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣛⣡⣤⣤⣄⠀⠶⠶⠶⠛⠀⠸⣆⠀⠀⠈⠙⠳⣤⣀⣄⡀⠀⠀⣤⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠸⡅⠉⡟⠛⠲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢿⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠘⢇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠘⡀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢃⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠩⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿
⣿⣿⣿⠏⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠉⠉⠉⠉⠙⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠉⠁⠀⢀⣀⣀⣀⣀⡉⠑⢯⠀⠀⠀⠈⠙⢆⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣴⣒⣛⣛⠛⠒⠲⠤⢤⣉⡉⠉⠒⠦⢤⣀⠀⠘⡆⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠀⠀⠀⠀⠈⠉⠙⠒⠦⢄⡀⠉⠓⠦⣄⠀⠈⠙⠲⢵⡀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⡿⣶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⠉⠲⢄⡀⠀⠉⠒⢤⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⡇⠙⣆⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣍⡒⢤⣀⠀⠉⠲⢄⠘⡄
⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢠⠇⠀⠈⢧⣄⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠿⢶⣤⣀⣱⣿⡀
⠀⠀⠀⠀⢀⠎⠀⠀⠀⢀⠎⠀⠀⠀⡼⠉⠳⣦⣀⡀⠀⠈⠙⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠟⠋⣝⠳⡀
⠀⠀⠀⢀⠎⠀⠀⠀⡰⠋⠀⠀⣠⠞⠀⠀⠀⠀⠙⠻⢷⣒⡤⠤⣄⣀⣈⣉⠙⢒⣒⣒⣲⡶⠶⠒⢚⣩⡭⠿⠓⢋⡹⠃⠙⢤⣀⣠⢤
⠀⢀⡴⠃⠀⢀⡴⠊⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠤⠬⠭⠭⠤⠤⠔⠲⢾⣉⡙⠒⠒⠒⠋⢉⣩⠗
⠘⠓⢤⣴⣊⣁⡤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢏⠹⡀⠀⠀⠀⠀⣠⠞
⠀⠀⢀⡏⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢏⠓⠒⠒⠉
⠀⠀⡎⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⡆
⠀⠀⠣⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠐⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠃
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⠤⣄⣀⣒⣒⣒⣒⣃⣠⠤⠤⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⠒⠒⠒⠒⠀⠗⠦⢴⣀⠀⠠⠒⠈⠐⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⡀⠰⠒⠄⠙⡄
⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠱⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢌⣁⠒⠁⢀⠇⢀
⠀⠀⠀⠀⠀⠀⢣⡀⠁⠂⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢏⠠⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠉⢒⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢀⠜⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠐⠀⠄⠀⠀⠀⠀⠆⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠉⠒⠠⠠⠤⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠶
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡜⠀⠀⠀⠐⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠙⠂⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⢀⢀⡤⠔⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⡀⢀⠀⠀⠀⠀⣘
⠀⠀⠀⠀⠀⢀⠞⠁⢣⢸⠀⠀⠀⢲⠋⢠⣴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡶⣄⠈⢧⠂⠀⠀⢠⠃⠉⢢
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣧⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣀⣨⡆⠸⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠚⠀⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠁⠐⠆⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠉⡆⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⡜⠒⠠⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⣀⠤⠚⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⠄⣀⣀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠉⠙⠋⠛⠛⠉⠈⠑⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣾⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣶⣾⣿⣆⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣇⠀⠀⠀⣰⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠙⢿⣿⣿⣿⣦⠀⣰⣿⣿⣿⠿⢁⣠⣤⣶⣶⣶⣶⣶⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⡿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⠋⠛⠛⠛⠻⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠀⠀⣡⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠈⠻⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⣿⣿⣿⠋⢸⣿⣿⣿⣿⡇⠀⠙⣿⣿⣿⣟⠻⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠃⢀⣿⣿⣿⠉⠀⢸⣿⣿⣏⣿⣷⠀⠀⠙⢿⣿⣿⡄⠀⠉⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⢸⣿⣿⠃⣿⣿⠀⠀⠀⠀⠙⠟⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠋⠁⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠰⢄⠀⠀⢀⠄⠂⠀⠉⠉⠀⠂⢄⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠙⠉⠉⠀⠉⠉⠋⢗⣄
⠀⠀⠀⠀⠀⢘⠨⣆⠐⣁⠀⠀⠀⠀⠀⠀⠀⠀⡐⢄⡎⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⢀⠀⠀⡀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⢨⢅⡎⠘⠁⡌⠘⠀⢠⠀⠈⠈⠄⠟⠘⢂⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⣠⠜⢇⠸⣆⠘⢧⣀⣀⡆⢽
⠀⠀⠀⠀⠀⠸⣃⡄⢀⠀⣃⣠⠠⠚⢆⠠⣀⡀⣀⠀⣅⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⣇⢨⣇⣀⠀⠙⠋⠉⠋⣁⣹⡇⣼⠘⡇
⠀⠀⠀⠀⠀⠀⢩⢅⢶⠉⢀⣀⠀⠀⠀⢀⣀⠉⢹⢆⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣋⢻⡈⠛⠃⠀⠀⠀⠘⠛⠁⡟⣹⠈⡯
⠀⠀⠀⠀⠀⠀⠐⢄⠀⠰⠛⠿⠀⠀⠀⠸⠿⠻⠀⢁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠈⠚⠓⢤⣄⣀⣀⣀⣠⡤⠚⠓⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠚⠧⢄⡀⠀⠀⠀⠀⣀⡤⠟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠭⠤⠔⢫⠊⠈⠉⠁⠑⡌⠢⠤⠭⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠁⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠤⠤⠤⠀⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣴⠢⡀⡠⠂⠁⠀⠀⠈⠈⠁⠢⡀⡠⢒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣤⣤⣶⣦⣤⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⡶⠢⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⢣⠚⠉⠁⠀⠀⠀⠀⠙⠑⡶⢁⣖
⠀⠀⠀⠀⠀⠀⣢⢠⠁⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠃⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⡧⢀⡤⠄⡸⣌⠢⠄⠤⡄⢺⣄⡇
⠀⠀⠀⠀⠀⠀⢱⡌⣤⠜⠱⠤⠈⠈⠁⠉⠈⠰⢤⡏⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⡌⢀⣀⠀⠀⠁⢀⡀⢱⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢾⠀⠴⣶⠄⠀⠀⢰⣶⠆⢸⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢁⠙⠿⠀⠀⠀⠿⠟⡙⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡳⣄⠀⠀⠀⠀⠀⢀⡠⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠳⣤⣤⣤⣤⣤⡞⠛⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣩⠟⠀⠀⠫⣥⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠉⠀⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⠉⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣴⣦⣄⡀⠀⠸⡁⠤⡤⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠐⠸⠿⠿⠉⠀⢀⠜⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠠⠀⠀⠀⠀⠀⠀⢸⠦⡀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⠀⠈⡄⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠉⠈⠓⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⢈⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⡀⢰⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠈⠁⠐⡁⢀⣀⣄⣀⠀⠀⠀⠀⠔⠠⠊⠀⠈⠴⠁⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⠁⠀⡀⠄⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⡁⡀⠀⠁⠀⠁⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠴⠀⠀⠀⢠⠄⢴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠒⠈⠁⠂⠁⠀⠜⠁⠀⠀⠈⠂⣴⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢸⣣⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠉⠉⠁⠘⠂⠲⣄⠂⠠⠀⠀⠀⠀⠀⠤⢠⣔⣈⠠⠐⠁⠀⠀⠀⠀⢀⠀⡩
⠀⠀⠀⠀⠀⣀⠤⠔⡊⠀⣖⠋⠀⠐⠀⠀⠐⠒⠁⠙⠚⠧⢠⡴⠄⠚⠑⠈⠀⠀⠀⠀⠀⠀⡀⠀⠰⡶⣡⠔⠁
⠀⠀⡠⠆⠉⣀⠐⡏⠑⠀⠀⠀⠀⠈⠀⢐⡒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣠⠾⠊⠁
⠀⠀⠁⠀⠀⠉⠀⠀⠐⠒⠀⠈⠁⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢎⣴⠏⠀⠰⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠔⢀⡀⣀⢴⢾⣠⣤⡔⠀⠀⠀⠀⠀⣀⡀⢀⠄⢀⡠⠒⠚⠋⡏⠚⣫⡤⠀⡜⠉⠉⠺⢆
⠀⠀⠀⠀⠀⣀⡴⢒⠅⠊⠀⠈⠀⠀⠀⠀⠉⠘⠀⠀⠚⠿⠛⠁⠈⠁⠰⣄⣀⠴⠔⠋⠀⡄⠘⢤⠿⣱⠢⡀⢱⡦⡆
⠀⠀⠀⡠⢚⠥⠊⡡⠀⠀⣀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠁⠀⠈⠙⠛⠃
⢀⢔⡠⢒⣡⠔⠁⢀⠴⠊
⠳⠈⣴⠋⣀⠤⠊⠁

⠀⠀⣴⡿⠛⠻⣶⣄
⠀⣸⡏⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⣦⣤⡀
⢀⣿⠀⠀⠀⠀⠀⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠙⣷
⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢩⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⢹
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⠀⠀⠀⠀⠀⠀⠀⠘
⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠰
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⣿⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡇⠀⠀⠀⣿⡟⠁⠉⠻⣧⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⢸
⠀⣿⣇⠀⠀⠀⣿⡇⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢠⡾⠋⠀⢹⣿⠀⠀⠀⠀⣾
⠀⢸⣯⠀⠀⠀⣿⡄⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠈⣿⡇⠀⠀⢰⣿
⠀⠘⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⣸⡿
⠀⠀⢻⣇⠀⠀⢹⣧⠀⠀⠀⠀⠀⢽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⢰⣿⡇⠀⢀⣿⠇
⠀⠀⠘⣿⡀⠀⢸⣿⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡆⠀⠀⠀⠀⢸⣿⠀⠀⣼⡿
⠀⠀⠀⢸⣇⠀⠈⣿⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣀⣠⡄⠰⣾⡿⠿⠿⠿⠿⠷⠖⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⠏⠀⢀⣿⠃
⠀⠀⠀⠀⣿⡆⠀⢸⣧⠀⠀⠀⠀⠀⠁⢀⣠⣤⠚⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠠⠀⠀⠀⡇⠀⠀⠀⠀⢰⣿⠀⠀⣼⡇
⠀⠀⠀⠀⠘⣷⡀⠈⢿⣇⠀⠀⠀⠀⢠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣼⠃⠀⢠⡿
⠀⠀⠀⠀⠀⢻⣷⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⢻⣧⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠀⣼⡟
⠀⠀⠀⠀⠀⠀⢠⣾⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣼⡿
⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟
⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⢶⣦
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠈⠃
⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦
⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⠿⠿⠛⠛⠛⠛⠿⠿⢿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠘⠟⠀⠀⠀⠋⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋
⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⠀⠀⠀⠀⠀⠈⠑⠶⢶⠶⠶⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁
⠀⣾⠟⠋⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⣹⡿⢷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣤⣄
⠀⣿⡄⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⢠⣾⠋⠀⠀⠈⠉⠉⠛⠛⢻⣿⣿⣶⣾⣷⣶⣾⠟⠛⠛⠋⠁⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠉⠀⠙⣿
⠀⠸⣷⡀⠀⠀⠀⠀⠈⠙⠷⣶⣤⣴⣿⡁⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⠉⠉⠉⠛⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⣀⣠⡾⠟⠁⠀⠀⠀⠀⢰⣿
⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠐⠿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⢠⠟⠁
⠀⠀⠀⠀⠛⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠟⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠐⠺⠿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣠⣶⣴⣾⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠈⠁⠘⠛⠀⢺⡟⠛⠻⠛⠛⠛⠛⠛⠉⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠛⠉⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⣀⣤⣀⣠⣤⣤⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⡴⢂⠐⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣧⠐⢀⣀⠀⠀⠙⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⢐⣭⠉⠸⠗⣈⣿⣶⠠⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⣿⣷⣆⠙⠖⠀⣹⠃⠰⢁⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠉⠻⠿⣿⠦⠄⣀⡉⢠⡂⣤⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢗⣫⢹⠢⡬⣷⡍⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠗⣿⣿⡼⣿⡄⡺⢭⢭⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⢿⣿⢯⡽⣿⣿⡛⡯⣳⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠁⢬⣿⣿⣿⢗⠷⣿⠻⠖⣿⠽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣮⢁⣿⣼⣿⡝⣻⣯⣼⠿⡷⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣌⠛⠿⣮⡟⣕⠌⢹⡿⣤⣤⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣜⣆⠻⣿⣝⣷⣾⣯⢿⢷⢋⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡸⡤⠌⣿⡌⠉⢻⣬⣼⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡝⣲⣎⡻⣄⠀⢹⠙⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡰⠮⣆⠑⣛⣧⣀⡅⠈⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢿⡴⢭⢥⣖⢺⡓⠟⢿⣿⣧⣀⠙⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⣄⢀⠀⠀⠀⢓⣸⠂⠀⢻⣿⣮⡳⣤⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠆⠀⠀⠀⠘⠁⠀⠀⠀⢿⡿⣟⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠒⠐⠉⠈⠛⠀⠀⠀⠀⠈⢻⡙⣯⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡄⠀⠀⠀⠀⠀⠁⠘⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⣀⢰⣤⡀⣠⣴⠀⡀⠀⠀⠀⠀⠀⠀⢐⣳⣶⡄⢀⣤⡤⠀⠀⠀⠐⠲⣶⣠⣶⣖⠀⠀⢀⣀⣀⣻⣆⠀⣀⣄⣀
⠀⠀⠀⠀⠘⢻⣿⣷⣿⣿⣿⣥⡀⠀⢀⠀⠀⣰⣯⡿⠛⣿⠿⣿⡻⣆⠀⠠⠾⢿⣿⣿⣿⡿⠷⠄⢴⣿⣿⠟⣯⢼⡿⠿⣿⠂
⠀⠀⠀⠀⠒⠛⡿⠁⠙⣿⣍⠁⠀⢠⣾⡿⢶⠿⣟⠣⣼⠃⠀⣸⠇⠋⠀⠀⠐⠛⠁⣿⠙⠀⠀⠀⠘⠹⡏⠀⡇⠈⢿⡆⠈
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠉⠀⠀⠈⠸⡇⠀⢧⠈⢰⡟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠃
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣄⠀⠀⠀⠀⠀⢠⣤⣤⡀⣠⣶⣖⣀⠀⠀⢀⣤⣶⣦⣀⣠⣴⡦⠀⠀⠀⠀⠀⡀⢠⣶⣦⠄
⠀⠀⠀⠀⣀⠀⣴⢠⣬⣿⣿⣶⣞⣀⡀⠐⣻⣿⣿⣿⡿⠿⣯⡅⠀⠀⣴⢿⣿⣿⣿⣿⣿⣷⡄⠀⢠⢶⣿⣿⣿⣿⣿⠯
⠀⠀⠀⠤⣿⣷⣿⠛⠛⡠⢻⣏⠛⠿⡄⠀⣟⠰⡏⠀⢆⠀⠀⠙⠀⠀⠀⢸⡟⣸⠃⢻⡿⠛⠀⠀⠰⠛⣿⠀⠱⡀⠈⠃
⠀⠀⠀⠸⠋⣿⠀⢳⡾⠁⢰⠟⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⡟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠈⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⠿⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

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

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⣾⠁⢈⡵⢊⠁⠀⠈⠀⠀⠉⡓⢎⡁⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠢⣀⠴⣾⣟⣛⣛⣛⣻⣷⠦⣀⠔⢙
⠀⠀⠀⠀⠀⠀⠇⢩⡏⠔⠁⠀⠀⠀⠀⠀⠀⠈⢆⢳⡉⢼⠀⠀⠀⠀⠀⠀⠀⠀⠐⡃⢠⠋⠀⠀⠉⠉⠉⠉⠉⠈⠑⢜⡄⢸
⠀⠀⠀⠀⠀⢸⡁⡎⡜⠄⠀⠀⡄⣸⣄⡀⠀⠀⢂⠃⢇⢘⠆⠀⠀⠀⠀⠀⠀⠀⢈⡏⡫⠀⡀⡀⠀⠀⡀⢀⠷⡀⠀⠀⣟⢹
⠀⠀⠀⠀⠀⠸⣀⡇⢰⡛⠛⢛⠛⠁⠈⠙⡓⠛⢻⠄⣼⡨⠂⠀⠀⠀⠀⠀⠀⠀⠀⣗⠿⠿⠷⣶⠷⠮⠔⠊⠀⣘⠣⡷⠷⣺
⠀⠀⠀⠀⠀⠀⢱⠺⢀⡇⠈⠛⠃⠀⠀⠘⠛⠁⣼⠰⠷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡝⣷⣤⣶⡄⠀⠀⠀⢠⣶⣄⡟⢯⣽
⠀⠀⠀⠀⠀⠀⢸⠉⠩⠛⣄⠀⠀⠠⠄⠀⠀⣰⠛⠍⢩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡧⢸⡉⠻⠟⠀⠀⠀⠻⠛⢉⡇⣾⣋
⠀⠀⠀⠀⠀⠀⠈⠙⠣⠴⠋⢑⡶⡶⢶⢶⠋⠙⠦⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡎⠟⠶⣤⣀⣀⣀⣤⢴⠛⣰⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡼⢼⡴⡦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠥⣶⡻⠃⠀⠀⠀⠘⢟⡦⠬⠝



⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠂⠀⠀⠀⠀⢄⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⢀⣤⣶⠶⠶⠖⣢⢄⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⢧⡸⠋⠀⠀⠀⠀⠀⠀⠀⠀⢋⢫⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠁⣶⠟⠉⢀⡀⠀⠀⠀⠙⠳⣶⠈⢐⡇
⠀⠀⠀⠀⠀⠀⠀⢳⠁⡆⠀⡀⢒⠀⠜⠀⣀⠀⢰⡀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⡞⠃⢐⣤⣜⣀⠜⠢⠤⣤⠀⠋⢦⢰⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡀⣧⠁⣁⡀⠀⠀⢀⣀⡀⣼⢇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡏⣎⠉⠀⠀⠀⠀⠀⠀⠈⠉⡣⣻⣼
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡼⡈⠙⠃⠀⠀⠘⠋⢁⣵⡬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠳⡙⠲⣿⠄⠀⠀⠀⢰⣷⠒⣋⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠘⠾⠀⠈⠀⠀⠀⠀⠀⢠⠁⠈⡼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡅⠑⢄⠀⠀⠀⠄⠀⠀⢀⡴⠋⢩⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡦⠃⠀⠀⠀⠀⠈⢧⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠚⠉⢐⡖⠒⢲⡊⠉⠛⠑⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢄⠔⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠤⢄⠀⠀⠔⠀⠀⠀⠀⠠⠄⠀⠀⢠⠤⠀⠀⠠⡄⠀⠀⢀⡀⠀⠀⠀⠀⢀⢀
⠀⠀⠾⠀⠀⠀⠀⠾⠇⠀⠀⠀⢰⠆⠰⡷⡀⠀⠀⠀⠐⠀⡀⠀⠀⠾⠂⠀⠀⠐⠓⠂⠀⠐⠚⠀⠀⠀⠘⠟⢀⢀⠘⠟⠀⠀⢡⣵⠀⠀⡀⠀⢠⡧
⠀⠀⠀⠀⠘⠚⠀⠀⠀⠀⠀⠀⠑⠤⠤⠔⠁⠀⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⠀⠈⠢⠤⠔⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁


⠀⠀⠰⣂⠀⠀⠀⡒⠀⠀⠠⠂⠀⠀⠀⠀⠀⠂⠀⠀⠐⣦⠀⠀⢀⣼⠀⠀⠀⠀⢰⣆⠀⣿⠀⠀⠀⠀⠊⣉⠀⠀⢊⡁⠀⠀⠀⠄⡀⠀⠀⠠⠊⡀
⠀⠀⠈⠛⠠⠤⠘⠋⠀⠀⠈⠛⠀⠦⠤⠄⠐⠛⠀⠀⠀⠉⠀⠄⠀⠁⠀⠀⠀⠀⠪⣁⠀⣩⠆⠀⠀⠀⠈⠋⠄⡤⠌⠉⠀⠀⠀⠻⠃⠤⠄⠀⠸⠃


⠀⠀⠀⠀⠀⠀⠠⢂⠀⠀⠀⠀⡠⠀⡔⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⢀⠄⠀⠀⠀⠂⠂⠀⠀⠠⠊⠀⠀⠀⢤⡄⠀⠀⢀⣒
⠀⠀⠢⠔⠀⢠⠀⠾⠃⠀⠀⠀⢸⠇⠰⠿⢠⠀⠀⠀⢴⠆⣀⠀⣀⠠⣶⠀⠀⠤⠂⠄⠀⠀⠰⠇⠀⠰⡿⠀⠀⠀⢀⠰⡇⠀⠀⠺⠃⡀⠀⡠⠉
⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠐⠤⠔⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠁⠀⠀⠀⠀⠈⠈⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⢀⡀
⠀⠀⣤⡀⠀⠀⠀⣠⡄⠀⠀⣭⠁⠀⠀⢀⢠⣦⠀⢠⡶⠁⠀⠀⠑⠒⠂⠀⠀⢠⡦⠀⠀⠈⠤⠆⠀⠀⠰⡶⠀⠀⠰⡗⠀⠀⢀⣬⠂⠀⠀⠰⢁⡄
⠀⠀⠉⠀⠑⠒⠀⠉⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠀⠀⠀⠈⠑⠂⠉⠀⠀⠀⠀⠀⠀⠑⠀⠐⠁⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠈⠁⠐⠉⠉⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣈⠂⠀⠀⠐⠁⡀⠀⠠⠄⠀⠀⠀⢀⠄⠀⠀⠀⠀⠢⠀⠀⠂⣤⠀⠀⠀⢀⣦⠀⠀⠀⠀⣦⠀⢀⡤⢄⠀⠀⢀⠤⡀⠀⢀⣦⠁⠀⠀⠩⠤
⠀⠸⠏⡀⠀⠀⡠⠘⠇⠀⢰⡇⢀⡀⣀⠀⢼⠆⠀⠀⠑⡀⠀⠀⠀⡋⠀⠀⠀⠈⠁⠀⠔⠄⠀⠉⠀⠀⠀⠦⡀⢀⡰⠂⠀⠀⠀⠉⢄⠀⠀⡰
⠀⠀⠀⠀⠉⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⠘⠃⠊⠁⠀⠀⠈⠀⠐⠂⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣔⠀⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠓⠢⢤⡀⠀⠀⢠⡐⢧⡀⢠⠐⠀⢠⢦⠀⠀⡀⠀⢀⣤⣀⣀⣀⣘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠲⠀⠒⠶⣂⣀⡉⣶⡉⢨⡓⠄⠢⣤⣙⠚⠛⡉⠛⡦⡟⢋⡙⢻⠻⠛⢩⠍⠙⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⢀⠘⠿⠷⠶⠄⠹⣧⣌⣻⣦⡍⠁⢒⣻⡃⠈⢱⡆⣀⠐⠀⢀⠁⢈⠂⠀⠉⣠⠾⣍⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣁⣘⡋⠀⠀⠠⢤⣀⠀⠕⠂⠛⠻⠯⠂⠰⠿⠈⢐⠒⠞⠁⠀⠈⠁⠂⢀⠀⢠⣾⠙⢦⠈⠻⣦⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣛⠉⠉⠛⢡⣤⣀⣀⣰⣍⠓⠠⠀⠀⠀⠀⢀⠉⠀⠉⡁⠀⠀⠈⠠⠔⠀⡁⠀⢿⣍⠁⠀⠀⠀⠀⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣶⣦⣤⣤⡌⣙⠀⠀⣤⣄⠀⠀⠀⠀⢤⡾⠿⠏⠋⠉⠀⠀⠀⣠⠾⠾⢦⣽⣷⣄⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⡶⠞⠉⡙⠋⠉⢐⣠⠤⠈⠁⠦⠀⠉⠁⠀⠀⡸⠿⢷⣦⣄⡀⠀⣀⠀⠀⢡⣶⣶⣦⣽⡿⢿⣿⣦⣄⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣽⣿⡶⠛⣻⠛⠑⡾⠟⠓⢶⡀⠀⠀⠹⣿⣆⡙⢷⡈⠿⢶⣍⡻⣿⣿⣄⠀⠀⣿⣿⣿⣿⣿⣿⣦⣽⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣽⣟⢉⡩⠛⠲⠿⠷⠀⠴⣄⠙⠒⠠⠀⠙⢷⣄⠀⠀⢚⣲⣿⣗⡛⠻⣿⣷⣴⣿⣿⣿⣿⣿⣿⡿⢻⠕⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠱⠿⠷⠦⠶⡆⠘⠒⢂⠀⠀⠰⠂⠀⠀⠀⠀⠈⠀⠸⠿⢷⣮⣽⣦⡸⠏⢻⣿⣿⣿⠿⣿⠽⠊⠁⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠬⠶⠛⠓⠲⢶⣶⣦⣦⣤⣵⣷⠎⠁⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠀⠛⠿⣽⣷⣤⣹⣷⣾⣷⠄⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⢀⢀⣠⣶⣶⣶⡦⢤⣤⣌⡛⠏⣛⢛⠛⢿⡏⠘⡁⠀⣠⡀⠁⠀⠐⡦⠀⠀⠀⠀⠁⠙⠢⠄⠀⣾⣯⡉⣛⣿⣿⣧⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣈⣉⣉⣭⣿⣿⣿⣿⡽⠻⢷⡤⣤⡁⠑⠢⣈⢿⡁⠈⠉⠑⠒⠒⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠻⣿⡿⠇
⠀⠀⠀⠀⠀⠁⢉⣿⣿⠿⢿⣿⣿⡏⠻⠀⡙⡞⣾⡻⣶⡓⠈⣰⠏⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⡀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠠⠖⣶⣿⡿⢿⢓⠝⠋⠴⠁⠀⠀⠀⠀⠈⣋⠡⠽⣿⣦⠟⠂⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⢦⣀⡁
⠀⠀⢰⣿⣿⠋⠋⠐⠛⠠⠈⠀⠒⠀⠀⠀⠀⠀⠘⠃⠀⠁⢻⡆⠆⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠃
⠀⠀⠸⠟⡋⢠⠊⠀⠊⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠐⠤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠒⠆⠈⠀⠀⠈⢿⣦⡐
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠞⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⢭⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⡁⠙⠗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⡷⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⢦⣤⣤⡾⠷⣀⣈⣿⠂⠔⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠟⣔⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⣤⡄⠀⠀⠀⠀⠀⠈⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢸⡿⣾⢿⡝⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠈⠉⡴⠤⣤⠚⠀⠊⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿⣍⣉⢺⡍⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠾⠁⠀⢹⡤⠀⠀⠈⠂⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⢉⢙⣷⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠻⣏⣩⣩⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣙⠗
⣀⣀⣀⢀⣀⡀⡀⣀⠀⣀⣀⢀⢀⣀⢀⣀⡀⢀⣀⠀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⠀⠀⢀⠀⣀⣀⡀⡀⢀⠀⣀⡀⢀⡀⠀⣀⡀⠀⠀⡀
⣿⠉⠉⣿⢛⠛⢛⢛⡛⢻⡛⣻⡛⠛⢻⠟⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣻⣿⣿⣛⣛⣛⣛⣛⣻

⠀⠀⢀⠠⠄⠂⠀⠀⠀⠐⠂⠀⠄⡀
⠀⣾⣿⣷⣠⣀⣠⢤⡀⠀⠀⠀⠀⠈⡑⣄
⠀⢻⣿⣿⣿⣧⣀⣤⣼⠁⠀⠀⠀⠀⠈⠺⠴⣄
⠀⢸⡿⣿⣿⣿⡟⢻⡿⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠒⠄⢀⡀
⠀⠈⠛⠇⠈⠉⢹⣿⡿⠂⠀⠀⢀⠂⠀⢀⠀⠀⠀⣄⡀⢦⡉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢋⠁⢠⡌⠁⠈⠠⠪⣦⠂⠀⠈⠙⠉⠉⠉⣴⠦⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢮⡙⡋⠃⣆⢀⣥⣿⣇⠀⠀⠀⠀⠀⣀⡄⡈⡄⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣶⣿⣿⣿⣿⣿⣿⠌⡁⠀⠀⢠⣦⢀⡀⠐⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣯⣿⡑⠅⡀⠀⠃⠀⠀⠔⠈⠀⠀⠀⠀⠱⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣽⣿⣿⣷⣄⠀⠦⠠⠄⢠⠠⠀⠀⠀⠀⢀⠀⠘⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠉⣿⠋⠳⢷⣶⣤⡀⠀⢠⠀⠀⣦⣬⠈⠀⠀⠘⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠱⠔⢊⣤⠤⢾⣿⣿⠿⠟⢲⣶⣿⣿⠲⣿⣶⣤⠁⣙⡀⢹⡙⠳⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠅⠊⠀⠀⠀⠀⠉⠑⠻⣿⣿⠀⠀⠉⠀⠀⠀⠙⢅⠳⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡑⠂⠐⠀⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⡛⠹⣦⡀⠈⠀⠀⣀⣠⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⢿⣿⠿⠲⠇⡆⠀⠀⠙⠓⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠠⣞⡿⠟⠛⢩⠟⠉⠀⠀⢼⡇⢸⡌⠻⣿⡶⣠⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠙⠀⡑⢼⣿⡄⠈⠰⢽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢸⡇⠈⣿⣇⠀⠀⠈⠙⠉
⣀⣀⣀⣀⣀⣀⣀⣀⡼⠀⢀⣀⡀⣀⠘⣀⣈⢇⣀⣿⣷⠀⢀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀
⠉⠉⠉⠉⠉⠉⠙⠉⠇⠀⠺⠛⢋⠦⠉⠙⠷⠶⠇⠸⡿⠀⠈⠉⠉⠉⠛⠛⠛⠛⠟⠋⠉⠉⠙⠛⠛⠋⠉⠉⠉⠉⠉⠉⠓
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⣀⣀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠐
⠒⠠⠤⠤⠤⠤⠀⠀⠀⠀⡔⠈⠈⠉⠀⠀⠘⠓⠒⠀⠀⠀⠀⠀⣀⣀⣉⣘⡋⠢⠤⠤⠄⠀⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠓⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⣦⠈
⠀⠀⠀⠠⡀
⠀⠀⠉⠀⠴⠦⠤⠲⠒⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠷⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠛⢿⣿⣿⣷⣶⣦⣤⠋⠀⠀⠹⡄
⠀⠀⠀⠀⢠⠀⠀⠀⠀⣠⢔⡭⠂⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⡟⠀⠈⠳⣄⣧⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣞⢕⡵⠎⣀⠄⠀⠀⠀⠀⠀⢤⣾⣿⣿⡿⠿⣶⣶⣾⡁⠀⠱⠀⠒⠒⠲⢦⣄
⠀⠀⠀⠀⠀⢀⢠⡟⣠⣿⣴⣯⠷⠭⠶⠤⠤⠦⠬⠿⠟⣻⠏⠀⠀⠀⠙⢿⣿⡖⠓⣖⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⢸⡟⣰⡿⣛⣵⣶⠾⠖⠒⢶⣶⣤⣶⡶⠿⠋⠀⠀⠀⠀⠀⠀⢻⣧⠀⠈⠷⠰⣦⠃
⠀⠀⠀⠀⠀⢸⣇⢟⣾⣟⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⢀⡞
⠀⠀⠀⠀⠀⠘⡏⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⡟⠋
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠊⠉⠉⠙⠂⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⢿⣿⣇⡂
⠀⠀⠀⠀⠀⠰⢿⣿⣿⠀⠀⣠⣶⣶⢶⣄⠀⠀⠀⠀⠀⠀⢠⡶⣿⣷⣦⡀⠀⢸⡿⢟⠣⡀
⠀⠀⠀⠀⢠⣦⡶⢮⣻⠀⠀⠿⠉⢿⣿⡿⠃⠀⠀⠀⠀⠀⠛⢿⡿⠃⠛⠁⠀⢩⣎⢹⣷⣰
⠀⠀⠀⠀⠘⢻⡓⠸⢻⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⢈⡿⠇⠐
⠀⠀⠀⠀⠀⠀⠙⠢⣤⡆⠀⠀⠀⠀⠀⠀⠀⠂⠂⠐⠀⠂⠀⠀⠀⠀⠀⠀⢰⡧⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⡀⢤⡤⠄⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠂⠐⠂⠀⠀⠀⢀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠤⣄⣠⠤⠒⠈⠉⠉

⠀⠀⠀⠀⣰⣾⡖⣀⠀⠀⠀⠀⠀⠀⣴⣾⠖⡀⠀⠀⠀⠀⠀⠠⢶⣷⣦⠀⠀⠀⠀⠀⢠⠶⣿⣦⡀⠀⠀⠀⠀⠀⣰⣾⡶⢀⠀⠀⠀⠀⠀⠀⣠⣶⡷⢆
⠀⠀⠀⠀⠱⢿⡿⠏⢀⣠⣤⣤⣀⠈⠻⣿⠿⠃⠀⠀⠀⠀⠀⠹⣾⣿⡽⢀⣤⣶⣶⣤⠸⣾⣿⡽⠃⠀⠀⠀⠀⠀⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠹⣿⣿⠟
⠀⠀⠀⠐⠿⠂⠀⠀⣿⠿⠿⣿⣿⡇⠀⠀⠺⠗⠀⠀⠀⠀⠀⢰⡶⠁⠀⠈⣿⡟⠁⡿⠀⠀⠁⢶⡆⠀⠀⠀⠀⠰⠿⠀⠀⠀⠸⢦⡼⢧⡴⠇⠀⠀⠀⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⣬⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠚⠁


⠀⠀⠀⠀⠀⢷⣦⣀⠀⠀⠀⠀⠀⢀⣠⡾⠇⠀⠀⠀⠀⠀⢀⣶⣿⣷⡄⠀⠀⠀⠀⠀⠀⣰⣾⣿⣦⠀⠀⠀⠀⠀⣰⡾⠛⢷⣄⠀⠀⠀⠀⢠⡾⠟⢷⣆
⠀⠀⠀⠀⠀⣀⣼⡿⠃⡀⠀⠀⡀⠻⢿⣤⡀⠀⠀⠀⠀⠀⠈⠿⣿⡶⠃⠀⠀⠀⠀⠀⠀⠹⢿⣷⠞⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⣶⡆
⠀⠀⠀⢠⣤⠋⠁⠀⠀⠻⠶⠾⠋⠀⠀⠉⢻⣤⠀⠀⠀⠀⠺⡷⠀⠀⠀⠸⣦⡼⢧⡴⠃⠀⠰⠆⢿⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠠⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⣼⣿⣟⣻⠀⠀⠀⠀⠀⢘⣿⣿⣛⡄⠀⠀⠀⠀⠀⣨⡃⠀⠈⠃⢀⣀⣀⡀⠙⠁⠀⢙⣅⠀⠀⠀⠀⠀⣰⡟⠉⢿⡄⠀⠀⠀⠀⢠⡾⠋⠻⣦
⠀⠀⠀⠀⣘⠻⠟⠃⠀⠀⠀⠀⠀⡀⠙⠿⠛⠁⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⡿⠻⢿⣿⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⣴⡆⠀⠀⢠⣶⣿⣿⣶⡄⠀⠀⢰⣶
⠀⠀⠀⠀⠛⠃⠀⢼⣿⣿⣶⣶⣿⣿⡆⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⣯⡈⢙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⣴⣈⣷⢦⠀⠀⠀⠀⠀⠀⢶⣹⡷⡄⠀⠀⠀⠀⠀⣰⣾⡗⢢⠀⠀⠀⠀⠀⠀⡴⣿⡗⡄⠀⠀⠀⠀⠀⠰⣎⣿⢦⠀⠀⠀⠀⠀⠀⢴⣩⡷⢆
⠀⠀⠀⠀⠻⢟⡡⠎⠀⠀⠀⠀⠀⠈⠻⡏⠴⠃⠀⠀⠀⠀⠀⠙⠌⡹⠟⢀⣠⣤⣤⣄⡀⠣⢍⠿⠃⠀⠀⠀⠀⠀⠘⠟⠡⠜⠀⣀⠀⠀⣀⠀⠻⢏⠥⠊
⠀⠀⠀⠐⠿⠂⠀⠀⠘⠶⠞⠶⠞⠁⠀⠀⠸⠗⠀⠀⠀⠀⠀⠿⠆⠀⠀⢸⠿⠿⢿⣿⡇⠀⠀⠸⠿⠀⠀⠀⠀⠀⠾⠆⠀⠀⠀⠙⠻⠟⠋⠀⠀⠀⠰⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⠟

⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠘⢿⣿⣯⣵⠀⢀⣀⣀⠀⠰⣿⣿⣭⠟⠁⠀⠀⠀⠙⢿⣿⣯⡵⠀⠀⠀⠀⠀⠀⣿⣿⣭⡟⠃⠀⠀⠀⠙⢿⣿⣯⣵⠀⠀⠀⠀⠀⠀⣿⣿⣯⡝⠋
⠀⠀⠀⢠⣦⠙⠋⠁⢸⡿⠿⣿⣿⠀⠉⠛⢡⣦⠀⠀⠀⠀⠀⣤⡝⠋⠁⠀⣠⡀⢀⡄⠀⠈⠛⢫⣤⠀⠀⠀⠀⠀⣤⡝⠛⠁⠀⢶⣤⣤⣶⠀⠈⠙⢫⣤
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠳⠤⠼⠋⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠙⠟⠀⠀⠀⠈⠉


⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⡔⠀⠸⡄⠀⠀⠀⠀⠀⠀⣀⢀⠄⠊⠁⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠮⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠨⠃⠀⢀⡤⣀⠀⠀⡜⢇
⠀⠀⠀⠀⠀⠀⢐⠀⢸⡀⡀⢀⠀⠀⠀⡀⢀⣀⡇⢀⠇⠀⠀⠀⠀⠀⠀⠀⡇⢰⠊⠉⠀⠈⠑⠒⡇⢸
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠲⠀⠉⠁⠀⠈⠁⠀⠆⢁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡐⠃⠀⠀⠐⢲⣧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢖⢂⢈⡆⠀⠀⠀⢶⢀⡐⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡧⠀⠀⠀⠀⢼⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⠉⠀⠀⠀⠀⠀⢉⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡧⠁⠀⠀⠀⠀⠈⣶⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢔⡈⠉⠉⠉⠉⢁⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡰⠣⠏⠀⠀⠀⠀⠀⠈⠿⠹⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠁⠐⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⠔⡀⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠚⠅⢢⣤⡀⠀⠀⣥⢼⠈⠑⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣡⣤⡀⠈⠒⢋⣤⣌⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⢘⠀⠈⠤⣀⠀⠀⠀⣀⡤⠂⠀⡂⠀⠀⠀⠀⠀⠀⠘⣿⢲⠉⠛⠀⠀⠀⠘⠛⢩⠶⣽
⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⡤⠊⠈⠛⠁⠑⣤⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⢿⣇⣈⣶⢤⠄⢠⠴⣖⣁⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠤⠄⠤⠵⠜⠉

⣏⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉
⠀⠀⢀⣤⣶⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠢⠄⡀
⠀⢀⣾⣿⣿⠿⡿⠿⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⠁⠀⡠⢄⠄⠀⠤⠓
⠀⠘⣿⠃⠀⠀⠀⠀⠠⡈⡃⠀⠀⠀⠀⠀⠐⠖⠸⣷⠄⢤⣤⠤⠴⠶⠛⠀⠀⠀⠀⠈⣀⠀⢀⠀⠄⠀⠤⠐
⠀⠀⠐⠀⠆⠶⠀⠱⠶⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠉
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠂⠀⠀⠠⠀⠒⠠
⠀⠐⠀⠀⠀⠀⠀⢄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠈⠀⠀⠀⣶⡆⠠⣽⡂⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠄
⠀⠠⠀⠀⡌⠀⠀⠀⠀⠅⠀⠀⠀⠀⠄⠀⠀⠀⠀⣤⣀⡤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⠀⠀⢀
⠠⠀⠀⠀⠈⠑⠀⠀⠁⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠄⠤⠔⠋⠀⠀⠘
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⢀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⣠⡖⠁⠀⠀⠈⠳⡄
⠀⠀⠈⢁⣤⢠⡤⠀⠀⢠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⢀⠄⠀⠀⠀⠠⠀⠀⠀⠁⡇⠀⠀⢢⠀⠰⠀⠁
⠀⠀⠀⠀⠁⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠊⠀⢈⡠⠃⠀⠆
⠀⠀⠈⠢⠀⣈⡀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠁⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠴⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⢀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠉⢁⡠⠂⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⣨⠏⠀⠈⠁⢀⡄⠊⣀⠴⠋⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠄⠐⠀⡈⠀⠀⠐⡋⠁⠀⠀⠀⠂⣁⡤⠚⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠤⠠⣤⠖⠉⠉⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡀⠄⠀⠀⠀⠀⡀⠄⢀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉

⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⠀⠀⢠⡄⠀⢀⣄⠀⠀⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⢠⡄⠈⠀⠀⠀⠀⢶⡆⠀⠀⠀⠈⠃⠀⠀⠋⠀⠀⠈⠀⠀⠀⠉⠀⠀⠈⠀⣤⠌⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢶⠂⠀⠲⠀⠀⠀⠏⠀⠀⠻⠀⠀⠘⠓⠀⠘⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠆⠀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢠⡤⠀⠀⢤⡀⠀⠀⠀⠀⠰⢶⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⠈⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⢰⣴⠀⠠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠘⠁⠀⠀⠀⢤⡄⠀⠀⠀⠘⠋⢀⡈⠛⠀⠀⠘⠀⠀⠀⠋⠀⠀⠀⠀⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣄⢾⣿⣿⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣷⣦⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣄⣿⣷⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣿⣿⣿⣿⣿⣿⠖⢿⡟⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠈⠻⠿⡛⠋⣿⣿⣿⢀⡀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⠓⠀⠛⣿⡿⠙⢹⣿⠏⢹⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠆⠀⠀⠀⣿⡇⠀⠻⠋⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣼⣿⣿⣿⣿⣿⡧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢹⣿⡿⠻⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠘⣿⠀⠀⢸⡏⠁
⠀⠀⠀⠀⠀⢀⣤⣴⣷⣶⣶⣤⡀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢾⣯⡿⣿⣯⡿⠿⠃⠀⠀⠀⠰⡿⠛⢰⡟⠻⣿⠖⠀⢸⡇
⠀⠀⠀⠀⠀⠘⠿⠃⢸⡟⠀⠈⠛⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣿⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠿⠄⠀⠸⠧

⠀⠀⠀⠀⠀⠀⢀⡤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢂⠠⠤⠄⢀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢱⠴⢒⣈⠭⠭⢉⣒⠦⣞⠁⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠀⠀⣀⠠⠤⠄⣀⠈⠀⢌⠑⡄
⠀⠀⠀⠀⠀⠀⡇⢀⢠⣜⠕⠊⠀⠀⠀⠀⠀⠀⠉⠢⣵⡔⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢁⡔⠉⠀⠀⣴⡀⠀⠈⠲⡀⠁⠘
⠀⠀⠀⠀⠀⠀⡇⢀⠏⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠙⡆⠀⠇⠀⠀⠀⠀⠀⠀⢰⡒⠷⡆⠈⠀⠀⣠⠞⠁⠻⣄⡀⠀⠀⠐⢶⠖⡲
⠀⠀⠀⠀⠀⠀⢡⡾⠀⠀⠀⠀⠀⠀⢀⡼⡀⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⣯⡈⣇⠒⠂⠉⠁⠀⠀⠀⠈⠉⠐⠒⣦⡏⣨⡇
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢰⡏⠉⠉⠁⠀⠈⠉⠉⡇⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡸⡇⠰⣶⡄⠀⠀⠀⠀⣴⡶⠀⡟⣀⠜
⠀⠀⠀⠀⠀⠀⢀⡼⡆⢴⠊⠀⠒⠀⠀⠀⠀⠐⠂⠈⢲⢀⡾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠦⣀⡀⠀⠀⠀⠀⣀⡤⠚⠉⢹
⠀⠀⠀⠀⠀⠀⠘⠮⣥⠋⣱⠈⠻⠃⠀⠀⠐⠛⠁⣸⡙⢦⡥⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠈⠉⠉⠀⠀⡆⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠴⠓⠢⠤⠄⠀⠤⠔⠚⠧⠽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡄⣸⡇⠀⠀⠀⠀⠀⠀⣿⡀⣦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠃⠠⢘⠶⣄⣀⣀⡤⣄⣀⡀⡠⢞⠡⠀⢛⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠉⢲⡤⣾⣍⣉⠉⠉⢉⣙⣿⠦⡔⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠰⠀⣤⠗⣉⡠⠤⣀⡠⠄⣈⠑⢯⡰⠲⢈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢶⡏⠈⠁⠉⠉⠉⠉⠉⠉⠁⠁⠘⣦⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠨⡾⢱⣺⠆⠂⠀⠈⠀⠐⠂⢿⣲⢻⡍⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡾⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠁⠈⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢳⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣄⢠⢀⡎⠣⣘⣌⣆⢣⡶⠛⣄⢀⢠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⠀⣴⣞⡤⠊⠈⠣⣘⣄⢢⡀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⢨⢿⣸⠈⣴⣶⡀⠀⠀⠀⣰⣶⠍⢢⡼⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣸⢰⡇⠀⠄⠀⠀⠀⠀⠉⠙⣷⢸⣸
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡛⣆⠈⠛⠁⠀⠀⠀⠙⠁⣠⡟⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢻⢻⡄⣷⢿⣿⠀⠀⠀⢰⣿⢷⠇⡞⣹⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⢽⠶⠒⠶⠶⠖⠲⢮⠥⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠤⢇⣴⣄⡀⠀⠀⠀⠀⣀⣼⡜⠧⢼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠋⠓⠂⠈⠉⠒⠉⠉⠀⠒⠋⠻⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢋⠁⡇⠦⢄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠯⣙⠶⠯⠝⠛⠋⠩⠥⠟⡦⢄⡀⠀⠀⠀⠀⠀⣠⡾
⠀⢀⡀⠀⢤⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⢔⠭⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⠓⢄⠀⢀⣴⡟⣡⠇
⠀⠀⠹⣦⣀⠹⣦⡀⠘⣷⡀⠰⡆⠀⣀⠔⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣏⣴⡟⠀⢀⡀
⠀⠀⠀⠀⠻⣷⡌⢻⣦⠸⣿⡄⣿⣀⢿⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣟⣿⣿⠏⠀⣠⡞
⠀⠀⠀⠀⠀⠘⣿⣦⡹⣷⣾⣿⣾⣧⢿⡇⢸⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠻⣿⣿⣿⣿⣟⣱⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠈⢿⣿⡝⣯⢿⣿⣿⣸⣷⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣝⢻⣿⣿⣿⣿⣿⣫⣦⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⢼⣿⣿⣿⣿⣿⣯⣽⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡹⣷⢻⣿⣿⣿⣿⢿⣿⣤⣴⣶⣄⡀⠀⠀⠀⡐⠀⣾⣿⡿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⡿⢿⠹⠞⠞⣿⣿⣻⣿⣿⡿⣦⡀⠐⠃⠀⣿⣿⡛⢿⣿⣿⣻⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣀⠤⠤⠖⠢⣀⠙⠉⢋⣟⢿⣿⣧⠅⠀⣰⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣩⣥⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠉⠲⢄⠈⢦⢿⣿⠂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣩⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠢⡀⠀⠀⠀⠀⠀⠀⠘⢆⢨⢉⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠆⠈⠲⢤⡀⠀⠀⠁⠀⢸⣷⣺⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⠀⠀⠀⠈⠢⠀⠀⣸⠟⠛⠉⠀⠀⣿⣿⣿⣿⣻⣿⣿⣿⡟⠁⠀⠀⠀⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡄⠀⠀⢀⡠⠔⠈⠀⠀⠀⠀⠀⢸⣿⣿⣯⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠈⠈⠀⠈⢀⠀⠀⠀⠀⠀⢀⢤⣜⠿⣿⣿⣿⣿⣿⣯⡁⠈⠀⠀⠀⢆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⢶⠏⠱⢆⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣛⣃⣼⠻⣿⣦⡐⣦⢉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⣦⡘⠙⠃⡀⢀⣈⣠⣤⢀⣤⡤⠤⡀⠈⠋⠉⢨⣍⡀⢹⣿⡟⣰⣏⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡄⢴⣾⡿⠆⠲⣟⠉⡉⠉⠛⠻⣿⣳⢰⣦⣴⣦⣚⣿⣿⣿⠄⣩⣾⣿⣿⣇⠡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠑⢮⣄⢠⣴⣾⣿⣿⣾⣿⣷⣽⠹⣩⣵⣿⣿⣿⣿⣿⡻⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣯⣟⣸⠦⠤⠶⠚⠿⠎⢻⣿⣿⣿⣿⣿⣁⠱⠀⡄⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⠏⢻⣿⣷⠏⡀⢢⢠⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⢹⣇⠘⠀⠈⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⠏⠀⠁⠀⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠇⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⣤⣄⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠠⣤⣄⠀⠀⠀⠠⣤⣄⠀⠀⠀⢀⣤⡤⠀⠀⠀⠀⢠⣤⠄
⠀⠀⢀⡛⠛⢠⣴⣶⣄⠙⢛⣁⠀⠀⠀⢘⡿⠏⣴⣶⢶⠘⠿⣏⠀⠀⠀⢈⡻⠟⢀⠀⡀⢀⠘⠿⣋
⠀⠀⠈⠁⠀⠘⢅⣹⠏⠀⠀⠁⠀⠀⠀⠈⠁⠀⠘⠧⠎⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠉⠉⠁⠀⠀⠉

⠀⠀⠀⢤⣄⠀⠀⠀⠀⣠⡴⠀⠀⠀⠀⣰⣦⡄⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⡴⠶⡄⠀⠀⠀⡴⠶⡄
⠀⠀⠀⢠⠞⠃⣄⣠⡌⠻⢦⠀⠀⠀⢀⣛⠗⠀⡀⢀⢀⡀⢻⣗⣀⠀⠀⠰⠆⠀⠀⢰⣷⠀⠀⠀⠶
⠀⠀⠘⠃⠀⠀⠈⠉⠀⠀⠀⠛⠀⠀⠈⠁⠀⠀⠉⠉⠉⠀⠈⠉⠁

⠀⠀⢀⣿⣗⠂⠀⠀⠀⣶⣟⡀⠀⠀⠀⣘⠋⠙⢂⣀⣀⠚⠉⢓⡀⠀⠀⢀⡼⠻⡄⠀⠀⠀⡴⠻⣆
⠀⠀⢠⡝⠋⣤⣀⣀⣤⡈⢋⡅⠀⠀⠀⠉⠀⠀⢹⡛⡿⠀⠀⠈⠁⠀⠀⠐⠆⠀⢰⡿⢿⡷⠀⠀⠖
⠀⠀⠀⠀⠀⠛⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁
⠀⠀⠀⡀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠐⠿⠫⠀⠀⠀⠀⠿⡋⠇⠀⠀⠀⠪⠛⠖⣀⣤⣄⡀⠝⠷⠀⠀⠀⠀⠿⠫⠃⣀⢀⡀⠺⠟⠅
⠀⠀⠘⠃⠀⠈⠛⠓⠃⠀⠈⠋⠀⠀⠀⠛⠀⠀⢟⠛⢿⠇⠀⠘⠁⠀⠀⠘⠃⠀⠀⠉⠋⠁⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⢠⣴⡦⠀⠀⠀⠀⣤⡦⣤⠀⠀⠠⣤⣶⠄⠀⠀⠀⢀⣴⣦⡄⠀⠀⢴⣴⡦⡀⠀⠀⠀⢠⣶⢤
⠀⠀⢠⡟⠛⢰⠾⢷⡆⠙⠛⣥⠀⠀⠀⣼⠛⠃⢀⣀⣀⠀⠛⢫⡀⠀⠀⢀⡝⠛⠀⢤⣠⡄⠘⠛⣇
⠀⠀⠀⠀⠀⠀⠑⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠤⠤⠤⠤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠶⢤⣄⡀⠀⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠉⠓⢦⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⣰⢻⡀⠀⠀⠀⠀⢰⡀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢀⡼⠁⠈⣧⠀⠀⠀⠀⠸⡷⣄⠀⠘⢷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠈⢧⡀⠀⠀⠀⠹⣮⣑⠒⠲⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢿
⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠉⠛⠒⢒⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠸⡇
⠀⠀⠀⠀⠀⠀⡜⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⢁⣤⣶⣷⣶⠦⠀⠀⠀⠀⠀⠀⠠⢶⣶⣶⣦⡌⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⡏
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠙⢦⠀⠀⠀⠀⠀⠀⠈⠀⣰⡇
⠀⠀⠀⠀⢰⣫⣭⡱⡄⠀⠀⠀⠀⠀⠘⠋⠀⠘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠘⠓⠀⠀⠀⠀⠀⢀⡞⣩⢭⣷
⠀⠀⠀⠀⢸⠀⠃⡏⢿⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠛⠉⠉⠀⢀⠀⠀⣀⠀⠈⠉⠛⠛⠓⠋⠁⠀⠀⠀⠀⠀⠀⢸⠹⡅⠁⣿
⠀⠀⠀⠀⠘⣆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢀⠏
⠀⠀⠀⠀⠀⠈⠢⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣦⣤⣤⣴⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠻⣿⡛⠛⠛⠛⠛⠛⣻⠟⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠤⠤⠤⠤⠖⠋⠁
⠀⠀⢀
⠀⡁⣈

⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠈⣩⠗⠊⠉⠉⠉⠉⠉⠲⢏⠁⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠈⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠃
⠀⠀⠀⠀⠀⠀⢻⣄⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡾⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢶⣤⠀⠀⠀⠀⣠⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⣼⢀⣴⣿⣿⣿⣷⡄⠀⣾⣿⣿⣿⣷⣄⢹⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⢾⣿⣬⡇⢀⡀⢸⣧⣿⣷⢹⣿⣷⡄
⠀⠀⠀⠀⠀⢀⡇⣾⣿⣿⢿⣯⣿⡇⠘⣿⣭⣿⢿⣿⣿⢈⣇⠀⠀⠀⠀⠀⠀⠀⠛⠈⠙⠛⠛⠋⠀⠘⠃⠀⠙⠛⠛⠋⠁⠛⠁
⠀⠀⠀⠀⠀⠈⠷⣌⠛⠻⠷⠛⠋⢰⡦⠙⠛⠷⠿⠛⣋⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⠤⢀⣈⣁⣀⠤⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠀⠀⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠁



⠀⠀⠀⠀⠀⠀⢠⡖⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⣀⠤⡀⠀⣀⡀⠀⣀⠀⢀⠠⢀⡀⢀
⠀⠀⠀⠀⠀⠀⣸⠀⢰⣤⣝⣦⣤⣴⣶⣤⣤⣞⣥⣤⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠊⠁⠀⠀⠀⠀⠈⠑⠾⣽⣿⠈
⠀⠀⠀⠀⠀⠀⢻⠀⡼⠟⠉⠙⠙⢿⡿⠋⠁⠉⠙⢿⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⣃⠀⠄⠄⣀⠀⠀⢀⠀⠀⠄⢘⢣
⠀⠀⠀⠀⠀⠀⠈⣿⢃⣀⣀⣀⠀⢸⡇⠀⢀⣀⣀⣀⢿⡋⠀⠀⠀⠀⠀⠀⠀⣀⢜⠩⠐⠂⢀⠒⢤⠱⡔⡡⠒⠀⠐⠒⠌⡳⣄
⠀⠀⠀⠀⠀⠀⡰⠋⣡⣴⡶⢦⡝⢾⣧⢊⣴⠶⣶⣤⠙⢧⡀⠀⠀⠀⠀⠀⠀⠛⢅⣤⣶⢿⣯⣿⣆⡆⡇⣱⣮⣿⡿⣷⣤⣈⠟
⠀⠀⠀⠀⠀⢻⡡⣴⣿⣯⡻⢿⣿⠈⠃⢸⡿⠟⣹⣿⣷⡄⣽⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣽⠿⠛⢴⡥⠙⠿⣯⣵⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⠁⠰⡷⠀⠙⢿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠤⣀⠀⠀⠐⠓⠀⠀⣀⠠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠦⠄⣀⣁⡤⠤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢏⣟⣟⣯⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣷⣄⣀⠀⠀⠀⡀⢀⠀⠀⢴⣿⣿⡃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⡿⢿⣿⣿⠟⢡⣴⠦⣵⣤⡰⣿⣰⣿⣿⣿⠀⠀⠱⡀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠈⠉⠉⠰⢾⣿⣿⣷⣺⣿⣿⡿⣿⡿⠃⠀⠀⠀⠎⠀⢈⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣤⣀⢀⡙⣿⣿⣿⣿⣿⣫⠿⢡⣾⣤⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠟⠻⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣃⣾⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣰⣶⣾⣿⣿⣿⣿⣿⣿⣵⣶⣠⣤⣶⣾⡉⠀⠒⠖⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟⣿⣟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⠻⠛⢁⡜⠙⣠⣿⣿⣿⣿⣿⣿⡟⠻⣿⡿⢿⣿⣿⢿⣿⠄⠀⢄⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠀⢀⣴⡯⢀⣾⢿⣿⠿⠛⣿⡿⣿⣿⣮⣽⣻⠈⠹⣿⣿⣿⣿⡢⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢰⡿⠇⠀⠀⢠⣾⠟⣠⣯⢿⣟⠏⠀⢰⣿⡇⠙⣿⣿⣿⢿⣿⡆⠸⠛⣿⡾⣿⣆
⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⡾⠃⠀⢿⡸⠈⠀⠀⠀⢸⣿⠀⠀⠈⠇⢻⣿⣳⢯⠀⠀⠁⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠸⠁⠀⠀⠀⠀⢸⣻⠀⠀⠀⠀⠈⠛⣾⣗⠄⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⢈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠰⣆⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⢻⣦⢰⣿⣿⠏⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⣼⣿⡿⠀⣀
⠀⠰⠟⣻⣿⣷⣌⢻⣿⣿⣵⣾⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢛⣿⣿⣦⡘⣷⣿⣯⣴⣿⡃
⠀⠀⠀⣀⣤⣭⣿⣿⣿⣿⣿⣯⣭⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣽⣿⣟⣿⣿⣯⣥⣤⣤⣤⣄⡀
⠀⢠⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡻⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⢿⣟⡿⣿⣯⡟⠛⠉⠙
⠀⣼⣿⡿⠋⣿⣿⡿⠀⢿⣿⣷⡝⢿⣷⠀⠀⠀⢰⣄⠀⣠⠄⢀⣀⠀⠀⠀⢠⣿⡿⠟⢹⣿⣿⠇⠘⡿⣿⣦⠛⢿⡄⠀⠀⠀⣤⡀⢀⡄⠀⣀
⠸⠋⠁⠀⠀⣽⣿⠇⠀⠘⡆⢿⣿⣀⣨⣶⣶⣤⣄⣿⣾⣿⣿⡟⠁⠀⠀⠀⠟⠉⠀⠀⢨⣿⡻⠀⠀⢳⠘⣿⣆⣀⣵⣶⣤⣤⣸⣧⡟⣴⡟⠉
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⣷⢀⣻⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⢸⡄⢈⣿⣿⣿⣿⣿⣿⣿⠋⣼⣳⣿⠿⡿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠉⠉⠉⠉⣉⣿⣿⣿⣿⠻⣿⣿⣦⡝⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⠉⠉⣩⣿⣿⣿⡟⠻⣿⣶⣌⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⢴⣿⣿⠏⣿⣿⡇⠈⠉⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠⣾⣿⡟⢸⣿⣿⠀⠁⠙⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡴⠃⣾⣿⠋⠀⠸⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠞⢠⣿⡏⠁⠀⢿⣿⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡞⠁⠀⠹⠃⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⠃⠀⠀⠛⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣯⣞⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣵⣃⡀

⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⡞⠛⠋⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠀⠀⠘⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠒⠂⠐⠒⢀⣀
⠀⠃⠒⠀⠰⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠀⠈⠛⠛⠛⠛⠛⠛⠋
⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⢀⡿⠋⠈⠙⠳⢄⠀⠃⠀⠀⠀⠉⠀⠰⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠯⠉⠑⠒⠦
⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⣠⣤⣄⡀⠈
⠀⠀⣀⡄⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣻⣿⣿⣿⣶⡀⠀⣼⡿⠿⠿⣿
⠀⠠⠉⠁⠀⠀⠀⠡⠀⠀⠀⠀⢠⡀⠀⠀⠀⠐⣿⣿⣿⠉⠀⠈⣿⣿⣿⡇⠀⠋⠀⠀⠀⠈
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠐⣠⠀⠀⢻⣿⣿⡆⢀⢀⣿⣿⠿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠉⠁⠀⠈⠉⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠄⠀⠤⠀⠀⠀⣿⣷⠀⠀⠀⢺⣿⠀⠀⠀⢀⠀⠀⢠
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⢼⡿⠀⠀⢠⡀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣲⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠇
⠀⠀⣿⠿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣦⡀⠀⢀⣄⠀⠀⣠⠄⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠇⠀⠈⠉⠁⠈⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠟⠻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣤⣤⣄⡉⠉⠙⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣶⣄⠀⣿⣧⠀⠀⠀⢀⣤⣶⡶⣶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠂⠀⠀⣀⣀⣠⣤⣖⡢⢿⣿⣦⠈⣿⠀⢀⣴⡿⠿⠍⠉⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠉⢁⣴⣾⣿⣯⠛⠟⡻⡫⢿⣷⡝⢿⣇⣽⢠⣿⣟⠃⠀⣠⢄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣰⣿⡿⠛⠀⠀⣀⣀⣀⡀⠉⢴⣿⣆⢿⣿⣿⡟⢡⣴⣾⣿⣿⣿⣟⢿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢸⣏⢠⣿⡿⢋⣴⣾⣿⣿⣿⣿⣿⢿⣶⣍⡻⣼⣻⠟⣡⣾⠿⠿⠿⡟⠛⠻⠃⠁⠀⠉⠳⡄
⠀⠀⠀⢠⡶⠛⠉⠛⠻⠿⣿⣦⣄⢿⣼⡟⣰⣿⣼⢻⣿⣿⣿⣶⣬⣦⣅⣭⣿⣶⡦⣬⣕⠿⣿⠿⢿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣰⣦⣬⣝⠻⣿⣿⣇⡿⢋⡯⢾⣟⣛⣻⡿⠏⢩⣿⣿⣿⡟⢿⡎⠻⣿⣮⡳⡀⠉⠙⣿⣿⣦⡀
⠀⠀⠀⢀⣴⣿⣿⡿⣿⣿⠿⣿⣷⡮⣛⣭⣴⣿⣏⡛⣻⠿⣿⣿⣋⣿⡟⢹⡿⠀⠘⣿⡀⠉⢿⣻⣿⣦⡀⠘⠁⡿⣿⡄
⠀⠀⢠⡟⠁⠈⠈⢀⣥⣾⠿⡻⣩⡾⢻⣾⠿⣿⣿⣿⣦⡀⠁⠊⢹⣿⢹⠈⠇⠀⠀⢻⡇⠀⠰⣿⣿⣿⣇⠀⠀⠀⢹⣷
⠀⠀⠈⠀⠀⠀⣰⣿⠏⠁⣠⣴⡿⠁⢸⡇⠀⠉⣷⠀⢻⢿⣆⠀⢸⣿⠆⠁⠀⠀⠀⢸⣷⠀⠀⠸⢹⣿⣯⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⢰⣿⠙⠀⢰⣿⣿⣇⠀⠘⣿⠀⠀⠉⠀⠈⢸⣿⡆⠈⣧⣃⠀⠀⠀⠀⣸⣿⠀⠀⠀⢱⣿⣿⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢿⡏⠀⠀⢸⣿⣿⡃⠀⠀⢿⣇⠀⠀⠀⠀⠈⠋⣿⠀⠹⡾⠀⠀⠀⠀⡿⣿⠀⠀⠀⢉⣿⡟
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣿⣷⡁⠀⠀⠘⣿⡆⠀⠀⠀⠀⠸⢿⠀⠀⠱⠀⠀⠀⠀⡏⣿⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠹⣼⣄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢰⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⣜⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣎⢧⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠳⣄⠀⠀⠀⠀⠀⠀⡾⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣄⡄⠀⡀⠙⣶⡈⢶⣧⢴⢇⣎⣼⢃⣾⣿⡄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠦⣝⢾⣿⣄⠈⣻⣿⣷⣀⡙⢿⣿⣿⠃⢸⣿⣿⣿⣿⠷⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢙⠛⣿⣿⣿⣶⣾⣬⣻⣿⣧⣄⣽⠃⣀⣿⡿⣿⣿⣟⣉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣧⣽⣿⣿⣝⣯⣅⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡴⣤⡀⣀⠠⠤⠤⠤⣀⠀⡠⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠉⠛⠉⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⢟⢰⢡⠋⠁⠀⠀⠀⠀⠀⠙⢆⠃⠛⡄⠀⠀⠀⠀⠀⠀⠀⡞⡝⠁⠀⡄⡀⠀⠀⠀⠀⠀⠈⢏⢢
⠀⠀⠀⠀⠀⠀⢸⠘⣼⣧⣦⣦⣠⣠⣤⣄⣔⣴⣤⣷⠀⢡⠀⠀⠀⠀⠀⠀⡼⢹⠀⣌⠜⠡⠑⣌⢪⢎⠣⣠⡆⠘⠋⡆
⠀⠀⠀⠀⠀⠀⢸⠀⣿⠟⢉⠉⠙⠉⠁⠉⠉⣉⠹⣿⠀⢸⠀⠀⠀⠀⠀⠀⡇⠋⠀⠃⠤⠄⠀⠀⠀⠈⠨⠅⢠⠀⢇⡇
⠀⠀⠀⠀⠀⠀⢸⠀⡹⣄⠉⠶⠀⠀⠀⠀⠶⠏⢠⢿⠀⡌⠀⠀⠀⠀⠀⠀⠘⡽⢄⣤⠶⣶⡀⠀⠀⢠⣶⢶⣬⡾⡟
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣉⠳⠤⣀⣐⣂⣀⠤⠶⣉⡾⠋⠁⠀⠀⠀⠀⠀⠀⣰⠳⣸⡁⠈⠻⠁⠀⠀⠙⠋⠀⢸⡠⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠥⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣈⣳⢄⣀⣀⣀⣀⣀⣀⣴⣏⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠴⠒⣊⣉⡒⠢⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟
⠀⠀⠀⠀⠀⠀⠀⢸⢨⡟⣡⠚⠉⠉⠉⠉⠓⢮⠳⡅⣽⠀⠀⠀⠀⠀⠀⠀⢸⠜⢄⠀⡀⠔⠐⠤⠐⠐⢄⡀⢀⠌⢼
⠀⠀⠀⠀⠀⠀⠀⢸⣾⢸⠃⠔⢀⠔⣠⢾⡄⠌⠇⢻⣾⠀⠀⠀⠀⠀⠀⠀⢸⡪⣢⠟⢠⠀⠀⠀⠀⠀⢠⠘⢧⡪⣻
⠀⠀⠀⠀⠀⠀⠀⢸⡿⡆⠠⣶⡒⠊⠁⢀⣙⠲⢠⢾⡗⠀⠀⠀⠀⠀⠀⠀⠸⣗⡸⠀⣄⢡⢆⣀⡼⣄⣁⡄⢸⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢾⣻⡈⠻⠇⠀⠀⠸⠟⠃⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⢘⡖⢀⣀⡀⠀⠀⣀⣀⠐⡎⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⠛⣦⣤⣤⣤⣤⡴⠚⡕⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡖⡌⠉⠀⠀⠀⠈⠉⠔⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡿⢥⡠⢄⡠⢽⡦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠦⣀⠀⢀⡠⠊⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⢄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⢤⡀
⠀⠀⠀⠀⠀⠀⢠⠏⠐⠀⠀⠂⠘⡆⠀⠀⠀⠀⠀⣸⠁⡀⠀⢀⠀⢳⠀⠀⠀⠀⠀⠀⡞⢐⠂⠀⠘⠈⣇⠀⠀⠀⠀⠀⢠⠋⢨⠀⠀⡄⠹⡄
⠀⠀⠀⠀⠀⠀⠘⣄⠈⠓⠚⠁⢠⠇⠀⠀⠀⠀⠀⢹⡀⢁⠤⡌⠁⡼⠀⠀⠀⠀⠀⠀⢧⠘⠶⠶⠞⢀⡏⠀⠀⠀⠀⠀⠸⣄⠀⠰⠆⠰⣦⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠒⠁


⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠂⠐⠈⢳⡀⠀⠀⠀⠀⠀⢠⠋⠐⠀⠐⠙⢧⠀⠀⠀⠀⠀⠀⡴⠻⠆⠀⠾⠙⡄⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠻⢿⡃
⠀⠀⠀⠀⠀⠀⢸⡀⠡⢀⠀⠜⢀⡇⠀⠀⠀⠀⠀⢺⡈⠀⢀⠀⠈⢸⠀⠀⠀⠀⠀⠀⡇⠂⠀⠂⢀⠂⡗⠀⠀⠀⠀⠀⢸⡀⠐⠂⠐⠂⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠱⢤⣀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠘⡿⣇⣀⣀⡵⠋⠀⠀⠀⠀⠀⠀⠙⢦⣀⣉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠳⢤⣐⣂⡤⠎



⠀⠀⠀⠀⠀⠀⠀⡰⠚⠉⠉⠓⢦⠀⠀⠀⠀⠀⠀⢰⣶⣋⣉⣉⣳⡦⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⢙⢦⡀⠀⠀⠀⠀⠀⣘⡴⠺⠉⠉⠗⢆⣃
⠀⠀⠀⠀⠀⠀⢸⠁⣀⡀⢀⣀⠈⡇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠠⠀⢸⠀⠀⠀⠀⠀⠀⡏⢐⣀⢁⣀⡀⡇⠀⠀⠀⠀⠀⢹⠁⣆⣀⣀⣰⠈⡏
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠠⠀⢀⡼⠁⠀⠀⠀⠀⠀⠘⣄⠐⠤⠐⣠⠞⠀⠀⠀⠀⠀⠀⠳⡌⢙⡿⠿⠳⠃⠀⠀⠀⠀⠀⠘⢧⣘⠛⠉⣁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉


⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⢠⠋⠈⠀⠀⠁⠘⡆⠀⠀⠀⠀⠀⣸⢁⠁⠀⠈⠀⢳⠀⠀⠀⠀⠀⠀⡞⠐⠂⠀⠘⠈⡇⠀⠀⠀⠀⠀⢰⠋⡈⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠘⣄⣄⠈⠉⠀⢠⠇⠀⠀⠀⠀⠀⢹⡀⢠⡤⡤⠀⡼⠀⠀⠀⠀⠀⠀⢧⠈⠒⠒⠊⢁⡏⠀⠀⠀⠀⠀⠘⡄⠙⠒⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠘⠿⠟⠦⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠈⠑⠦⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠢⢄⡀⠀⠀⠀⠀⠀⢀⠴⠚⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠉⠢⣀⣀⡠⠞⠁⠀⠀⠀⡧⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠉⢹⠀⠀⠀⠀⠀⡎⠈⢣⠀⠀⠀⠀⢰⠁⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⣇⠀⡼⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⡾⠵⠳⣄⣀⡤⠖⠉⠉⠉⠲⢤⣀⡤⠓⠬⣧⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠟⠀⠀⢠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢠⠋⢦⡀⠀⠀⠀⣀⢤⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⠜⢣⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⢀⡨⠆⠀⣠⠤⡇⠀⠀⠉⢉⢻⣉⣅⡀⠑⠦⢄⣀⣀⠤⠺⣁⣏⣹⠛⠋⠉⠁⠀⠀⢧⠤⡀⠀⠀⠀⠫⡀
⠀⠀⠀⢀⠔⠁⠀⠀⠀⢇⢸⠁⠀⠀⣠⢫⠊⢀⣤⣝⡄⠀⣀⣀⣀⠀⡞⢡⣤⡌⢻⢦⠀⠀⠀⠀⢸⠀⡸⠀⠀⠀⠀⠈⣆
⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠘⢆⡈⠛⣫⢷⠋⠀⠀⠈⢱⢧⡈⠛⡃⠚⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣀⣀⡤⡉⠉⠀⢸⡀⠀⠀⠀⣰⠀⠈⢩⢅⣀⣀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠈⠣⣄⡀⠀⠀⠀⠀⠈⢧⠀⣇⠙⠀⡇⠀⠀⠀⠉⡒⠒⡊⠁⠀⠀⢸⠀⠋⡸⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠉⣹⠀⠀⠀⠀⠀⠳⣌⠢⠴⠁⠀⠀⠀⠀⠘⠚⠁⠀⠀⠀⠘⠦⠞⠁⠀⣠⠞⠀⠀⠀⠀⠀⠰⡍
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⡎⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⠀⠀⠀⣀⡤⠊⠀⠉⠓⠒⠢⠤⠤⠤⠤⠒⠒⠊⠉⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠤⠖⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠲⢤⣀⠀⠀⡤⠖⠋⠉⠉⠓⢦⡀⠀⠀⢀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠈⠳⠞⠀⠀⠀⠀⠀⠀⠀⠙⣆⡴⠋⠀⠀⠀⠈⠙⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢧⢀⣀⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⢀⣠⠤⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⣄⣀
⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠶⠒⠒⠒⠒⠶⠦⠤⣄⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⡴⠋⢁⣠⡤⢈⡑⣄⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡴⣋⡄⢤⣄⠈⠳⡄⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢸⠁⢰⠋⠀⠀⢀⡽⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⡀⠀⠈⢳⠀⢹⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⣠⠽⠀⠀⠀⠀⠀⠀⠸⡄⠸⡄⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡼⠀⡼⠀⠀⠀⠀⠀⠀⣾⡁
⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠈⠧⡀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⡰⠋
⠀⡴⠋⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠻⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠟⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠙⠲⣄
⢸⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈
⢸⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠳⡄⠀⠀⠀⠀⠀⢹⡉⠉⠉⠙⠒⠂⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠰⠒⠒⠉⠉⢉⡇⠀⠀⠀⠀⠀⠀⣠
⠀⠀⡞⠀⠀⠀⠀⠀⠈⣇⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠒⠒⠒⣺⠃⠀⠀⠠⣤⠤⠚⠁
⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣄⠤⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠤⣤⡇⠀⠀⠀⠀⠈⢦
⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠈⠳⠤⣤⡀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠤⠤⢤⣤⣄⣀⣀⣀⣀⣤⣤⠤⠤⠤⠶⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠓⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⡤⠤⣄⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⣠⠞⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣒⣒⣒⣋⣁⣈⣓⣶⣤⣶⣖⣉⣀⣈⣉⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⡟⠁⠀⠀⠀⠀⠀⢠⣄⡄⠀⠀⠸⢿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠋⠀⠀⠀⠀⠀⠀⢻⡿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠄⠀⠀⠀⣿⠋⠛⢿⣦⣀⣤⠤⠼⣿⣿⠤⠤⣄⣠⣾⡿⠋⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢿⣄⡒⠒⠈⠙⢿⠀⠀⣿⡇⠀⢰⠟⠉⠐⠒⢚⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠛⠛⢡⠶⠻⠃⠀⠀⠘⠁⠀⠀⠛⠿⢦⠙⠛⠫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡦⠄⠀⢀⢴⣦⡀⠀⠀⠀⠀⢀⣴⢦⠀⠀⠤⣴⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡀⠀⠀⠀⠀⠘⣌⣁⠇⠀⡀⡀⠀⢃⣉⡘⠀⠀⠀⠀⠀⢈⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠛⠛⠛⣛⣃⣀⠀⠀⣰⠀⠀⠀⠀⠀⠀⡄⠀⢀⣀⣙⣛⠛⠛⠛⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣅⡀⢠⠖⠁⠀⠀⠀⣉⠒⣧⣄⣀⣀⣀⣀⣤⡷⠊⠁⠀⠀⠀⠉⠢⡀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⡇⠀⠀⠐⢦⡀⠀⠀⠘⠿⣿⣿⣿⡿⠟⠁⠁⠀⢤⠔⠂⠀⠀⡇⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠰⡀⠀⠀⠀⢣⠁⠀⠀⠀⠀⢸⡅⠀⠂⠀⠠⣠⠃⠀⠀⠀⡰⠁⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢌⣦⡀⠀⠀⠑⢤⠤⠤⠔⠁⠈⠒⠒⠒⡊⠁⠀⠀⣀⣜⠥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀⣸⠀⠀⠀⠀⠀⠀⠀⢀⣇⡠⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⣀⣀⣀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⡀⣀⣴⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠋⠀⠀⠀⠈⠙⠻⠇

⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣦⣤⣄⡀
⠀⠀⢀⣴⣾⣿⢿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⣴⠟⠛⣿⣾⣜⢿⣿⣿⣿⣿⣿⣟⢫⣿⣿⣿⣿⣿⣆
⠀⣀⣻⡏⢟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣾⣿⠗⠙⢻⣿⣅
⠀⣿⣿⣿⣿⣿⣿⣿⠛⣝⠏⣣⡗⢡⣿⣿⣿⠀⠀⠈⠋⢻⣷⡆
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⣿⣿⣿⡟⠁⠀⠀⣐⣾⣿⡆
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠫⠉⡜⢋⠹⣿⣿⣿⣷⡄
⠀⠈⢻⣿⣏⠉⠙⠛⠛⣿⣿⣿⠟⢁⣈⡥⢈⡄⠚⢲⣿⣞⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠙⠻⢦⡀⠀⠀⠉⠿⠏⠀⠃⣸⡄⣬⣷⣎⡲⣿⣿⢿⣿⣿⣿⣿⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⣴⡾⠋⣧⢀⣧⡈⢿⡻⢿⣶⣿⣿⡝⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⢈⡈⠋⡹⡝⠷⡶⣽⣿⣿⣿⣄⠈⢙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠈⣿⣿⣿⣿⠳⠟⢣⡄⠖⢻⠖⠽⠏⣹⣷⣾⡿⠿⡏⢠⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⢀⡔⢿⣿⣼⠶⣶⠁⢃⣦⡶⠛⢶⡻⠛⢀⡙⠶⣞⢿⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⣿⣾⣿⢯⣴⡏⠓⢨⣿⣧⣤⠚⢡⣦⣈⠉⣶⢉⣼⣧⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢰⣿⣷⣴⡞⠁⠁⣾⣗⣈⣼⣿⡄⠛⠀⠷⢻⡄⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣧⣠⠠⣿⡟⠉⠈⢸⣿⣶⣀⣰⣦⣹⣶⡆⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡽⣿⡽⣿⣿⣿⣤⣾⠙⣧⡀⠀⣼⡇⠁⢿⡎⠈⠉⠺⣷⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⣿⣻⣿⢻⡿⣿⣦⡿⢧⣴⣿⣇⠀⠀⣤⠀⠀⢀⣿⣧⠀⠀⢘⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠿⣿⣿⣼⣇⣿⣯⠀⣰⡎⠈⣿⣄⣠⣿⣷⣤⣾⣿⣿⣷⡀⣸⡆⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢿⣾⣿⣿⣿⢿⣿⡏⠀⠀⣿⡟⠉⣿⠏⠹⠋⢻⣿⣿⡍⢿⣧⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡈⠛⢻⣿⡄⣿⠃⠀⠘⣿⣿⠀⢸⡄⠀⡅⢸⣿⣿⣿⡌⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠙⠇⣿⡄⠀⢠⣿⡟⠀⠀⣧⡀⠀⢸⣿⡿⣿⣿⣮⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠙⠃⢠⣿⣿⠻⡀⠀⠳⠧⠀⢸⣿⣿⠘⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡌⠾⠿⡤⣼⢧⣌⣻⢿⡽⡦⠌⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣂⣀⣤⣾⣿⡌⢻⣆⢺⣐⡈⠤⢻⣧⠈⣷⡹⣮⠌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⣴⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡄⢻⣧⣻⣷⡐⡸⣿⣇⠈⣿⣿⣿⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣭⢽⣧⡿⠃⠀⠉⢻⡽⣋⣣⣼⣛⣯⣿⣿⡦⣹⣿⠀⠘⣿⣿⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⡴⠖⢡⣀⢭⣼⣿⣿⣿⠟⢹⡟⢿⣷⣿⣿⣧⣂⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⣻⣢⣿⠎⠥⣈⢉⡐⠋⠀⠘⣴⣿⣦⣿⠿⣧⡀⠈⢻⡶⣿⣿⣿⣿⣿⣆⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣈⠋⢙⠻⣥⣬⣟⣋⣠⣾⣿⣾⣷⣿⢿⣿⣿⣿⣿⣿⣄⠸⣁⣿⣟⣿⣿⣿⣿⡌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣿⣿⣿⣿⣿⣿⡇⣹⣿⣿⣹⣿⣿⣿⣿⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡟⣿⣿⣷⣍⣻⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣄⠀⣴⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠛⢛⣻⣷⣿⣿⣿⣿⣋⣁⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢉⣩⣿⣿⣿⣿⣿⣿⣯⣭⣍⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣟⣿⣿⣿⡿⢹⣿⣿⣿⠿⣿⣍⠻⢷⣄⣀⣀⡀⠀⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⣟⣽⠧⢼⡿⠃⢸⣿⢿⣿⣧⠈⠙⠧⢀⣹⣧⣬⣹⣶⣾⣿⣿⣛⡛⠒
⠀⠀⠀⠀⠀⠀⣀⣤⣽⣿⣿⣿⣷⣶⣾⣿⠶⢾⡿⠀⠻⢿⡇⠀⠞⠉⠁⠀⣈⣿⣿⣿⣿⣿⣭⡉⠃
⠀⠀⠀⠀⠀⠈⢡⡴⣿⣿⣿⣿⣿⡿⣿⣏⠃⠈⠇⠀⠀⠈⠟⠀⠀⣠⣴⢟⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢰⠏⡼⢻⣿⣿⣿⣿⣿⣦⠉⠃⠀⠀⠀⠀⡀⠀⠀⠼⠋⢠⠟⢛⣿⡿⣿⡇⢻⡏⠙⠀⠉
⠀⠀⠀⠀⠀⠘⠀⠀⣿⢹⡟⢸⣿⠈⠛⣧⡀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⣿⠟⠀⢻⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠻⡄⠀⠀⠑⡀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⡆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⡇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢠⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢷⣿⣶⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⣋⣀⣀⣀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⢀⡀⢀⠀⣀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⢤⡴⢢⣤⡄⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⢄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠹⡏⢀⡇⠀⠀⠀⠀⠀⠀⢸⠁⠆⠀⠠⠄⢳⠀⠀⠀⠀⠀⠀⡏⣁⡹⠻⢁⡉⣄⠀⠀⠀⠀⠀⢰⠋⠤⠀⠀⠤⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣭⣛⣟⡭⡄⠀⠀⠀⠀⠀⠀⢹⡀⠒⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢧⠐⠦⠤⠀⢀⡇⠀⠀⠀⠀⠀⠸⡆⠀⡀⢀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠢⠼⠧⠖⠃⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⠒⠁


⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡞⢡⠀⠀⡌⢳⡀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠉⢦⠀⠀⠀⠀⠀⠀⡴⢋⠀⠀⢀⠹⡄⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⢸⡀⠀⣠⣄⠀⢀⡇⠀⠀⠀⠀⠀⢺⠀⠲⠤⠴⠂⢸⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠈⠀⡷⠀⠀⠀⠀⠀⢸⡀⠐⢀⠀⠂⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠱⢤⣙⣛⡤⠞⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠱⢬⣉⣉⡥⠎



⠀⠀⠀⠀⠀⠀⠀⡰⠚⠉⠁⡆⣽⡁⠀⠀⠀⠀⠀⢀⡴⠋⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⣴⣞⡉⢉⣳⣦
⠀⠀⠀⠀⠀⠀⢸⠁⠠⠄⠀⠤⠀⡆⠀⠀⠀⠀⠀⢼⠀⠐⠀⠐⠀⢸⠀⠀⠀⠀⠀⠀⡏⠐⠦⠀⠶⠂⡧⠀⠀⠀⠀⠀⢸⠁⢈⠵⠮⡁⠈⡇
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠰⠆⢀⡼⠁⠀⠀⠀⠀⠀⠘⣄⠀⠻⠢⣦⣾⠀⠀⠀⠀⠀⠀⠳⣀⠒⠀⠂⡠⠃⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉


⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⢲⣶⣄⡀⠀⠀⠀⠀⠀⠀⣠⡴⠒⢶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠒⠮⣄⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⢠⠋⢐⠀⠈⡱⠿⡇⠀⠀⠀⠀⠀⢸⠁⠆⠀⠠⠄⢳⠀⠀⠀⠀⠀⠀⡞⡈⠁⠀⠈⡌⣇⠀⠀⠀⠀⠀⢰⠻⣾⠇⠸⣷⠛⡄
⠀⠀⠀⠀⠀⠀⠘⣆⢀⠤⠤⡀⢰⠇⠀⠀⠀⠀⠀⢹⡀⢦⣤⣤⠆⡼⠀⠀⠀⠀⠀⠀⢧⠀⠠⠤⠐⢀⡏⠀⠀⠀⠀⠀⠘⡆⠀⠠⠄⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⡀⠀⣠⠞⠙⣆⣠⠤⣶⣦⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⡀⠟⠿⢇⡀⠀⣭⠄⠀⠻⠟⠀⣿⡿⢦⡀⠀⠠⣶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠘⠣⣤⣤⠘⠃⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⢳⣄⣀⣽⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠯⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠋⠉⠛⠶⠛⠛⠛⠶⠛⠛⠓⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⡙⠻⣶⣌⣷⣶⣿⣶⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣀⠀⠻⣿⣷⣄⠻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣶⣽⣿⣿⣦⢻⣿⣿⣿⣿⣿⣿⠛⠟⠋⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣴⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣿⡿⡿⠿⢸⣿⣽⣿⣿⠇⣻⣿⡛⠹⢾⣿⣿⣿⣶⣶⣤⣴⣤
⠀⠀⠀⠀⠀⠠⣄⠻⣷⣼⡇⣠⡄⠀⠀⠀⣠⣶⣿⠿⠟⠋⢁⣾⣿⣿⣧⡀⠀⢾⣿⢻⣿⣿⣿⣿⣇⢀⣀⣀
⠀⠀⠀⣰⣿⡿⣿⣷⣿⣿⣿⡿⢀⣀⡀⣸⠿⠋⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⡿⢿⣿⣬⢻⣿⣿⣿⡿⣟⣻⣿⠟
⠀⠀⠘⠛⠛⡛⣿⣍⠻⣿⣿⣿⣋⡉⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣿⢻⡿⡷⢀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⡀
⠀⠀⠀⠀⣿⣯⣭⣭⣿⡟⠛⠛⣯⠙⠲⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⣿⠀⠀⠀⠿⠛⢿⣿⣯⡿⢻⣿⣿⣯⣝⣛⣿
⠀⠀⠀⣸⡟⠉⠁⠿⠿⠁⠹⣶⣝⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⢞⣵⣿⣿⣇⢨⣿⣭⡉⠛⢿⣿⡄
⠀⠀⠀⠉⠀⠀⠀⠀⢀⣶⠀⠀⠙⣷⣄⠀⢹⣇⣽⣿⣰⡏⠀⠀⠀⣿⠀⠀⢰⣿⠈⣿⣿⡇⢿⣾⣿⣿⢿⣷⣶⣯⣃
⠀⠀⢸⣷⣶⣦⣴⢟⣿⣷⣄⠀⣀⣈⡙⢿⣄⢿⣿⣿⡿⣢⣤⣤⠀⣿⠀⠀⠸⣏⠀⠛⢹⡇⠈⠘⣿⣿⠀⢹⣇⠉⠉
⠀⢐⣶⣾⣿⣿⣿⣾⣿⣿⣿⡶⠦⣬⣙⢿⣿⣾⡿⢿⣿⣿⣙⣛⠇⣿⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠘⠿⠀⠀⠃
⠀⣿⣛⣉⡙⠛⣿⠁⠴⣿⣷⣦⣴⣾⣿⣿⠿⣿⣧⠸⣏⣉⡉⠛⠓⣿⠀⠀⠀⠀⠀⠀⣿
⠀⣼⠿⠛⣿⣿⢻⣧⡶⢾⡇⠹⠇⠉⠁⢠⣾⣿⠛⢻⣿⡙⠻⢿⠆⣿⠀⠀⠀⠀⠀⢀⣿
⠈⠁⠀⠀⣿⣿⢾⠙⢧⢸⣷⡀⠀⠀⠞⠋⢀⡏⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠛⠁⢸⡄⠈⢹⡈⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⠁⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠂⠘⠛⠛⢻⠷⠶⠶⠶⠶⣶⣶⣾⣿⣶⣦⣤⣤⣤⣿⣿⣤⣤⣤⣤⣤⣤⣼⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄
⣀⣀⣠⣀⣀⣀⣀⣀⣀⣉⣉⣻⣿⣿⣉⣉⣉⣉⣈⣉⣉⣙⣻⣿⣿⣿⣿⣋⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⡍⢽⡟⠛⠛⠛⠛⠛⢛⠻⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿