Friction Emojis & Text

Copy & Paste Friction Emojis & Symbols I often get paired with a player named Mort, I wil

I often get paired with a player named Mort, I will admit, I have paid for my collection, I have been here since March I think and now I very very rarely find a card in packs I don't have in multiple (But I digress) the point I am making is this, in the months I have been playing, Mort has beaten me exactly ONE time, and I'm sure his record against other players is about the same, but he is there Every day, has never conceded a single match against me.My point is the kid has heart and determination, and one day with what little CUE gives you every day he will have enough great cards to win on the regular like the rest of us. That's the kind of players this game needs supporting it.✨

Related Text & Emojis

⠄⠄⠄⠄⠄⠄⣀⣀⣀⣤⣶⣿⣿⣶⣶⣶⣤⣄⣠⣴⣶⣿⣿⣿⣿⣶⣦⣄⠄⠄ ⠄⠄⣠⣴⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦ ⢠⠾⣋⣭⣄⡀⠄⠄⠈⠙⠻⣿⣿⡿⠛⠋⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⡎⣾⡟⢻⣿⣷⠄⠄⠄⠄⠄⡼⣡⣾⣿⣿⣦⠄⠄⠄⠄⠄⠈⠛⢿⣿⣿⣿⣿⣿ ⡇⢿⣷⣾⣿⠟⠄⠄⠄⠄⢰⠁⣿⣇⣸⣿⣿⠄⠄⠄⠄⠄⠄⠄⣠⣼⣿⣿⣿⣿ ⢸⣦⣭⣭⣄⣤⣤⣤⣴⣶⣿⣧⡘⠻⠛⠛⠁⠄⠄⠄⠄⣀⣴⣿⣿⣿⣿⣿⣿⣿ ⠄⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢰⡿⠛⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠸⡇⠄⠄⢀⣀⣀⠄⠄⠄⠄⠄⠉⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⠈⣆⠄⠄⢿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⡀⠄⠄⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⠄⣿⡀⠄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⠄⣿⡇⠄⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⠄⣿⡇⠄⠠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠄⠄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⠄⣿⠁⠄⠐⠛⠛⠛⠛⠉⠉⠉⠉⠄⠄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠄⠄⠻⣦⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠲⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡖⠒⠒⠶⢿⣤⣀⠀⠀⠀⠀⠀⠉⠙⠒⢦⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡴⠖⠛⠉⢉⣉⣉⠉⠓⠶⢤⣀⠉⠁⠀⠀⣀⣀⣤⣤⡤⠤⠤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣄⠀⠀⠀⠀ ⠀⠀⢠⣾⡵⠶⠛⠉⠉⠉⠉⠉⠉⠙⠳⢦⡈⠙⢶⣴⢋⣉⣠⠴⠶⠖⠚⠛⠓⠶⠦⣍⡙⠲⣦⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀ ⠀⣠⠟⢁⣤⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⣟⣋⣡⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠙⠳⣄⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀ ⣼⠋⢰⣿⡿⠿⣿⠟⣿⡆⠀⠀⠀⠀⠀⠀⢀⡾⢹⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣈⣀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀ ⣧⠀⠸⣿⣧⣠⣾⢿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⡋⠉⢹⣧⣨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⣿⣿⣿⡇ ⠘⢷⡀⠙⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⣠⣾⡄⠘⣿⣷⣶⣾⣛⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠚⠋⠁⠀⠀⠀⠀⠀⢹⣿⣿⣷ ⠀⠀⣽⠶⠦⣄⣀⣀⣀⣀⣀⣀⡴⠶⠛⠁⠀⠻⣆⡈⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⣠⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠈⠓⠦⢤⡤⣤⡤⠤⠤⠤⠶⠞⠀⠀⠀⠀⢻⣝⠶⢤⣄⣀⣀⣀⣀⣀⣀⣠⠤⠖⢋⣁⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿ ⠀⠀⢠⡴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣄⣉⣉⣉⣉⣭⣥⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⡇⣠⣤⡤⠤⠤⠦⠦⠴⠶⠶⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿ ⠀⢰⡟⠉⠀⠀⣀⣀⣤⣤⣤⣀⣀⣀⠀⠀⠀⠈⠉⠉⠛⠲⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠙⢧⡀⠸⣏⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⠀⠈⠙⠳⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿ ⠀⠀⠀⠀⢻⡄⠙⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠈⠙⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡇⠀⣧⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⡇⠀⣧⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏ ⠀⠀⠀⠀⢸⡇⠀⡏⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢁⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⢸⠀⢰⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⢸⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⣿⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠟⠋⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠹⡆⠀⠈⠙⠶⠶⢤⣄⣀⣀⣀⣤⡽⠿⠛⠉⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣷⢦⣤⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⡤⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠲⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠒⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠸⣶⣦⣤⡤⣾⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣠⣴⣿⡟⠁⠀⠙⣯⣠⣼⣿⣿⣄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣠⣶⣤⣄⣠⣶⣿⣿⣿⣷⣾⣿⣿⣏⣁⣀⣿⣴⣿⣿⣿⣿⣿⣿⣷⣿⣄⣀⣶⣄⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣤⣾⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣟⢂⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠊⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡜⣿⣦⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⡀⠀⠀⣂⣤⠴ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⣿⣿⠉⠀ ⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢙⡇⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡾⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠉⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⡇⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⢻⣿⣿⣷⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣧⠈⢿⣆⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢿⣿⣿⡄⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣿⣿⣄⠈⢿⣆⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠑⠶⠿⠶⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣧⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠇⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠀⠀⠀⠀⠀⢸⣿⡟⢻⣿⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⣾⡟⠀⠀⣹⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⡭⠿⢿⣷⣦⣀⡀⠀⣴⡏⠀⠀⣠⣿⡿⠋⣀⣀⣠⣿⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⠟⢉⣦⣤⣌⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠛⠋⠀⣤⣴⣿⣿⣿⣃⡾⠛⠁⠀⠀⢿⠏⣠⡾⠛⠛⣿⣿⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⠸⣿⡿⠋⢻⣿⣦⡹⣿⣿⣿⣿⣿⣿⣿⠟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣀⠈⠁⠲⠟⢛⣱⣦⠞⠁⠀⠀⠀⠀⠘⣇⠋⠠⡠⢾⣿⣿⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⠀⠉⠀⠀⠀⠉⣹⣷⢨⣟⠛⢿⣿⣿⣿⢠⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢶⡾⢿⡻⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣶⣦⣼⡿⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⣿⣧⠀⠀⠀⣾⣿⣿⣿⣿⡿⠀⠀⢻⣿⣿⣿⣿⡘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣬⣿⢿⣧⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⡀⠀⠀⢹⣿⠿⢉⡟⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠉⢠⣿⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠛⠀⠘⣷⡀⠀⠀⢀⣿⣷⢸⣿⣏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠃⡄⠀⠈⣿⣿⣿⡟⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡿⡇⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣡⠀⠀⣿⣿⣿⣿⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⣤⣤⣤⣤⣤⣤⢠⡞⠀⠀⣱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠿⣦⣤⣴⡿⠀⠀⠛⠛⠻⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠻⠿⣿⣿⣿⣛⣿⣷⣌⡉⠁⢀⣾⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠉⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⡀⢀⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⢷⣼⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⡟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣴⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠓⢀⣤⠞⠃⢀⣤⣴⣾⣟⣿⣿⣿⣿⣽⣿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⣍⡉⠻⢿⣿⣿⣿⣿⣿⣿⡿⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠙⣿⣿⣿⡟⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣆⠀⠈⠉⠻⠷⣿⠟⢉⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⣀⣀⣀⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⣶⣶⣤⣤⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢿⣄⢀⣺⣿⠈⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠈⢻⠸⠋⠁⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠘⢰⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢦⣄⡰⠶⠛⠗⣀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠉⣩⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠐⠒⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠈⠉⠛⠶⠶⢆⣀⠀⠀⠀⠀⠤⢄⡀⠀⠀⠀⠀⢀⣀⣤⡶⠛⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿ ⠀⠀⢀⣤⠔⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣼⡛ ⢀⣼⣿⣿⡶⠶⠶⠶⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟ ⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡿⠟⠀⠀⠀⠉⠛⢻⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣠⢤⡆⠀⠀⠀⠀⠀⠀⠙⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠀⣤⣴⣶⣾⣯⡷⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⢀⣀⣠⣶⣞⣩⣽⣿⡿⠷⠿⠿⠿⠿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⢰⣾⣀⡀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⢿⠟⠃⠀⠀⢀⣀⣠⣤⣤⣤⣦⣶⣤⡇ ⣠⣶⣿⠿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡶⢴⢊⣿⣷⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⠃⢀⣀⣴⣾⡿⠟⠛⠛⠛⢻⣿⣿⣿⡏⠀ ⠙⠿⠃⠀⠀⠀⠀⠛⠛⠛⠻⠾⠂⠀⠈⠻⠿⢿⢿⡟⠛⠿⠛⠃⠈⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢺⣿⢿⢰⣾⣿⠋⣁⠀⠠⠀⠀⣰⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⢠⣀⣀⠳⣄⡀⠀⣀⡀⠀⣀⣀⣀⣠⣤⣴⣴⣲⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⣦⣬⣉⣉⣉⣙⠒⠒⠒⠛⠿⠛⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠙⠛⠛⠿⢿⡿⠿⠿⢿⣿⠿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣏⠉⠙⢻⣿⣿⣷⣶⣦⣤⣤⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠶⠤⠤⠴⠤⠤⠤⠤⠖⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠇⢰⡎⠁⠉⠉⠟⢻⣿⡿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠐⠿⠶⠶⠶⠚⠊⠇⠓⠎⢻⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠁⠐⠁⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⠀⠀⢀⣵⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⣀⡀⢀⣠⣴⣶⣶⣶⣤⣤⣤⣤⣶⡾⠿⠿⠿⠮⠽⢶⣶⡿⠟⠀⠀⠀⠀⠀⡸⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣀⣀⣴⣶⡶⠟⠋⠀⠀⠀⠀⠀⡐⣦⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⢀⡀⣡⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⠈⠉⠛⠿⠿⣿⣿⣄⠀⠀⠀⢀⣾⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠻⢷⣦⣼⡟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣝⣙⣿⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠂⠀⠀⠀⠀⠀⣀⣤⡶⠢⠤⠴⠒⠄⠀⠀⠀⣀⣀⣠⣤⣴⣶⣷⣾⣿⣿⣭⣭⣽⣙⣿⠿⠿⣛⣛⣿⣿⣿⣻⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣤⠤⠶⠛⠋⠁⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡟⡛⢩⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⣏⢉⡙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⡀⠈⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠙⠆⠀⠀⠀⠈⠙⢿⣭⢉⣭⣿⣿⡛⠛⢻⣿⣿⣿⣿⣿⣯⣭⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢰⡄⠠⠀⠀⠀⠀⠀⠹⠛⠛⠉⠉⠀⠀⠀⠈⣿⠿⠿⠟⠛⢛⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠁⠈⢰⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣠⡾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠇⠀⣦⡀⡛⠛⠶⣤⣠⣤⣤⣤⣤⣴⢶⣟⡷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢤⢀⠠⡄⢀⠀⠀⠙⠛⡿⠿⢷⣶⠶⢶⠶⠶⢧⡾⠛⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠤⣀⡰⠭⡉⠉⠐⠂⠄⠂⠉⠀⠉⠁⠂⢄⠀⠀⠀ ⠀⢠⢞⣒⡀⠉⠀⠒⢅⢲⠬⠙⠒⠚⠛⠵⡢⢄⠀⠀⠈⣷⡀⠀ ⢠⠁⣿⣻⣿⠀⠀⠀⡔⣽⠿⣟⣦⠀⠀⠀⠈⠒⢠⠀⠀⢹⣷⠀ ⠀⢑⠌⣉⣁⣀⡠⠔⠳⡘⠷⠿⠋⠀⠀⠀⡠⣊⠁⠀⠀⠘⣿⡆ ⠀⢀⠭⠃⠀⠀⠉⠀⠀⠙⠥⠒⠒⠲⠬⠕⠊⠁⠀⠀⠀⠀⣿⡇ ⠀⢸⡊⠩⠭⢭⣉⣉⣁⡐⠒⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇ ⠀⠀⠘⠘⡀⠀⢿⣿⣿⣿⣿⣷⣶⣤⡉⢲⠀⠀⠀⠀⠀⢸⣿⡇ ⠀⠀⠀⠀⠇⠀⠈⢿⣿⣿⣿⣿⣿⣿⠟⡜⠀⠀⠀⠀⢀⣿⣿⠀ ⠀⠀⢀⢸⠀⠀⠀⠘⣿⣿⣿⣿⠟⢡⠊⠀⠀⠀⠀⢀⣼⣿⠃⠀ ⠀⠀⠘⡈⠒⠤⠄⠀⠸⠟⢋⡡⠒⠁⠀⠀⠀⢀⣤⣿⠟⠁⠀⠀ ⠀⠀⠀⠘⠩⢀⣒⠒⠀⠉⠁⠀⠀⣀⣀⠤⠶⠛⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣦⠘⢲⣺⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⢶⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣷⣶⣰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢒⡇⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⠄ ⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣧⡙⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠋⠉⠁⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣇⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣇⣳⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇ ⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠓⠀⠀⢀⡴⠿⠛⠛⠛⠲⠀⠀⠀⣴⣾⠇ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠐⠈⠀⣀⣤⣀⠀⢀⠇⢀⣤⠏⢨⠀ ⠀⢻⣿⡟⣽⠮⣝⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠎⠩⠰⠿⣿⠊⠀⠸⠑⣉⣿⠀ ⠀⠸⣿⣷⠀⢠⣼⣾⠏⢻⣷⡾⠄⠀⠀⠀⠀⠀⠀⠭⠽⠟⠁⠀⠀⠀⢉⣻⣾⠀ ⠀⠀⠸⣿⣇⠀⠋⢫⠀⢸⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡀ ⠀⠀⠀⢻⣿⣷⣄⠀⣠⢘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣤⣤⠄⠄⢸⠁ ⠀⠀⠀⠘⣿⣿⡟⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠛⢧⣰⠏⠀ ⠀⠀⠀⠀⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⡠⠀⣀⣤⣤⣴⡿⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢓⠶⣿⣿⣿⢿⠏⠀⠀⠀ ⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡘⠻⠽⢿⠆⠀⠀⠀ ⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⢴⡶⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠓⢊⡴⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠴⢒⡤⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠀⠀⠀⠀⠀⠀⠐⢀⡀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣠⣔⣦⣾⡟⣩⣿⣿⠢⡄⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣬⢧⡀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣍⣱⢦⡀ ⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣏⣹⠃⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠀⠀⠀⠀⠀⠈⠙⠻⣿⣹⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣴⠶⠶⠶⠦⠀⠀⣤⣿⡇⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣀⡤⢶⣾⡶⠀⣴⣃⣸⠁⠀ ⠈⣿⣿⡏⠙⣻⣿⣿⣿⡇⠀⠀⠀⠀⠙⢶⣿⠟⠀⠀⢻⣼⣿⠀⠀ ⠀⠹⣿⣧⠈⠛⣇⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠀⠀ ⠀⠀⢹⣿⣷⣄⣈⠸⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠆⢸⡀⠀ ⠀⠀⠸⣿⣿⠏⠟⠀⠁⠀⠀⢸⣷⠐⠿⡇⠀⠀⠀⠈⣙⣳⡟⠀⠀ ⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠐⠀⠀⠀⠀⢿⣭⣶⣾⣿⣟⡽⠀⠀⠀ ⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢳⣌⠻⠿⣿⠀⠀⠀⠀ ⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠈⢷⣿⣷⣾⡇⠀⠀⠀⠀ ⠀⠀⠀⠘⢆⠀⠀⠀⡀⠸⣄⠀⠀⠀⢿⡿⢆⣼⡿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠦⣀⡀⠀⠉⢙⣶⡆⠀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
─── ・ 。゚☆: *.☽ .* :☆゚.・ 。゚☆: *.☽ .* :☆゚.・ ───
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠉⠉⠉⠙⠛⠛⠙⠛⠓⠶⠶⣦⣤⡀⠀⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣾⣧⠈⠻⣆⠀⠀⠀⢀⣀⣤⡄ ⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣾⠞⠋⠉⣾⠁ ⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⣧⠀ ⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⠈⢻⣆⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠀⢸⡇ ⢸⡟⠶⣬⣿⠀⢀⣰⣧⠀⠀⣠⡴⠛⠹⣆⠀⠀⠀⠀⢀⣠⠞⠋⠙⢧⡀⠀⢀⣤⠾⠛⣿⡄⠀⠀⣸⡇ ⠘⣇⠀⠈⢱⣦⠟⠁⢸⡶⠟⠁⠀⠀⠀⠻⣆⠀⣠⠶⠋⠁⠀⠀⠀⠀⠙⠚⠋⠀⠀⠀⠨⡇⠀⢀⡿⠁ ⠀⢻⣄⣀⢸⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⣼⠃⠀ ⠀⠀⠉⠋⢻⡦⠀⠀⠀⠀⢾⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣄⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣼⠃⠀⠀ ⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠈⠛⠀⠀⢠⣤⡶⠖⠚⠛⠛⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⢸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⢀⡤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⣤⠶⠒⠒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢼⠀ ⠀⠀⠀⠀⣧⠀⠀⠀⣠⡿⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⢻⠚⠛⠋⠁⠀⠀⠀⣴⠋⠁⠀⠀⠙⣧⠀⠀⠀⠀⠙⢷⣀⣀⣤⠾⠃⢸⡀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢷⣀⡀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⡄⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠛⠋⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠛⠀ ⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⠄⠀⢀⣠⣤⣴⣶⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿ ⠐⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⠛⢻⡏ ⠀⠀⢀⡀⢠⣤⣤⣤⣄⣠⠀⠀⠀⢀⠀⠀⠀⠀⢄⣤⣴⠮⠁⠀⠀⠀⢡ ⢴⠞⠛⠋⠩⣀⠀⣼⣿⣿⣷⢲⠶⠊⠁⠀⠀⠀⣿⣏⣠⠶⠚⠛⣻⣿⠃ ⠀⠀⠢⠴⣤⣤⣤⣤⠴⠶⠂⠀⠀⠀⠀⠀⠀⠀⠈⠓⡯⢬⣥⣌⣛⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠤⠭⠟⠿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣀⡀⠀⢀⣀⡠⣀⣀⠄⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠿⢿⣿⣿⣿⣤⣴⡗⠁⠀⠀⡾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠌⠙⠛⢧⣀⡴⠋⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⢀⡠⠄⠤⠀⢀⣀⣠⣤⣤⣄⣀⡴⢦⣶⣾⡿⠀⠀⠀ ⠀⠀⠀⣴⣶⣶⣬⣥⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢦⡈⡍⠛⠻⣿⠿⣿⣿⣿⣿⣭⢿⣯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠠⢀⠀⠈⠛⠉⠀⠈⠟⢛⣻⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⡀⡈⠀⢬⢵⣖⣒⢲⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣠⡴⠛⢀⡴⠛⠀⠀⠀⣀⠀⢀⡜⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⢦⣷⡀⠀⠀⠀⠀⠀⠀⠄⠐ ⠀⠀⠀⠀⠀⡘⠀⠀⣠⡞⠁⢀⡴⠋⠀⠀⠀⠀⣴⠃⢀⡞⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢀⠀⠀⠀⠀⠀⠀⡉⠁⢱⣤⡀⠀⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠀⡇⣄⡼⠃⡀⣠⡞⠁⡀⠀⠀⠀⡼⠃⢀⡞⠀⢠⠟⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⢸⠀⠀⠀⠀⠀⠀⠻⡄⠀⠫⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⢋⣴⠋⣠⠏⠀⡴⠃⠀⠀⣼⠃⠀⡞⠁⢠⠟⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⣟⠀⢸⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠘⢂⠀⠀⠀⠀ ⠈⠋⢀⣴⠟⢡⡞⢡⣴⠋⠀⡼⠁⠀⠀⢠⡟⠀⠀⠁⢠⠏⢠⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠁⠀⢸⠸⡿⡄⠀⠀⠀⡄⠀⢸⡘⣧⠀⠀⠀⠀⢢⡀⠀⡄ ⠀⣠⠞⠁⣠⣟⣼⣿⠃⠀⣼⠇⠀⠀⣠⣿⡇⠀⠀⢀⡞⢀⡆⠀⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⢸⠀⣷⣧⠀⠀⠀⢿⠀⠀⢧⣹⡄⠀⠀⠀⠀⠀⠀⠀ ⠼⠁⠀⣰⣿⠟⢡⡏⠀⢰⠏⠀⠀⢰⠏⢸⡇⠀⡄⡞⠀⠈⠁⠀⣹⣤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⠿⣤⣤⣀⠀⢸⡇⢿⣿⡄⠀⠀⠘⡆⠀⠘⣏⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡟⠁⠀⡾⠀⠀⡾⠀⠀⢠⠏⡀⢸⡇⢸⣿⢁⣀⣤⣶⠿⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡾⠋⠀⠀⠈⠙⢷⣤⡇⢸⢻⣇⠀⠀⠀⢷⠀⠀⣸⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⣼⡟⠀⠀⢰⠇⠀⣸⠇⠀⢠⠏⠘⢃⣨⣧⣼⡟⠛⠋⠁⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡼⠀⠀⠀⠀⠀⠀⠀⠈⢿⣜⡎⣿⡀⠀⠀⢸⡆⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀ ⠘⠋⠀⠀⠀⣿⠀⢠⣿⠀⠀⡾⣠⠖⠉⠁⠹⢧⣷⡀⠀⢀⣠⠤⣄⡘⣷⡀⠀⠀⠀⠀⠀⠀⢰⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣷⠾⣧⣀⠀⠀⡇⠀⠈⣿⢿⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⠀⠀⣿⢠⡟⢿⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠹⣷⡄⠀⠀⠀⠀⢀⡿⣇⡟⠀⠀⢠⡔⠛⠉⠒⠒⠂⠀⢷⢹⠀⢻⡏⠉⠀⢷⠀⠀⢻⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡞⠁⣸⡀⡏⠀⠀⠀⠀⠀⠀⠀⠴⠖⠒⠒⠊⠉⠓⠲⠀⠘⢿⢦⡀⠀⠀⣸⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⢷⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⢿⡇⠀⡟⢷⣧⠀⠀⣀⣸⣷⣶⣶⣶⣶⣶⣶⣶⣒⣲⣦⠤⠀⠀⠀⠙⠶⢤⡇⢸⡏⠀⠀⠈⠉⠉⠙⢳⡲⠦⢄⣀⡀⠘⢿⡀⠈⣧⠀⢸⠃⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢰⠃⣀⣈⣻⣿⣿⣛⣋⠁⠀⠀⠀⠀⠀⢉⣻⠛⠃⠁⠀⢀⣀⠀⣀⡠⢀⣀⠤⢄⡀⠤⣬⡿⠷⠯⠿⣶⣶⣼⣯⣓⠚⢷⡀⢹⡀⣾⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠠⣽⣿⠋⠙⢋⠉⠉⠙⠶⠶⠒⡀⠠⣴⣯⠄⠀⠀⠒⠉⢀⡭⠝⠀⠉⠀⠀⠉⠀⠀⢬⡔⠲⣤⡀⠀⠈⠉⠙⠻⣷⣶⣽⣤⣿⠏⡇⠀⠘⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡏⠀⠈⠛⠓⢠⣬⠇⠄⠒⠒⠂⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠓⠲⢬⣿⣒⠒⠊⠉⠙⢶⣽⣿⣿⣿⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⡶⠲⠞⠋⠀⣀⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠮⠷⠯⠉⠁⠀⠀⡞⠀⠀⠀⡤⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠀⣾⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣰⠁⠀⠀⠀⠀⠀ ⠀⠀⢀⡇⣸⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⣼⠃⠀⠀⠀⠀⠀⢰ ⠀⠀⢸⢠⣿⣆⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠶⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⣸⠃⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⢸⣿⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⣁⣀⣀⣀⣀⣀⡈⠉⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⣿⣿⣷⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠓⠀⠹⣿⣿⣿⣿⣿⣿⣿⣶⣄⣙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⢰⣿⡟⡟⠷⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⣠⠏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⢸⣽⠁⣧⡇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢀⡼⠁⣨⡯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢈⠗⢀⣿⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣠⡤⣤⡀⠀⠀⢻⣿⣿⣿⣿⡿⠿⢿⣿⡿⠿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⡰⠏⣆⣼⢋⣶⠷⠀⠀⠀⠀⠠⠄⠀⣠⠞ ⠀⢹⣋⡿⢻⠁⠀⠀⠸⣧⠀⠀⠀⡤⠟⠉⠀⠀⠉⡇⠀⠘⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡀⠀⠀⠀⠓⠒⠉⠉⠿⣿⠀⠀⠀⠀⢀⠜⠁⠀ ⠀⢸⣽⠀⢸⡄⠀⠀⠀⣿⣧⡀⠀⠳⣄⠀⠀⠀⢰⡇⠀⠀⠹⣿⣀⠀⠀⠀⠀⢀⣀⣄⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⣠⠞⠁⠀⠀⠀⠀⢠⢠⡼⡿⠓⢰⣾⣦⡞⠋⠀⠀⠀ ⠐⢸⣇⠀⠀⣿⠀⠀⣼⣿⣿⣿⣄⠀⠈⠢⠤⠤⠚⠀⠀⠀⢠⡰⠯⣭⣭⣭⣭⣭⡷⠋⠙⠃⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣴⠏⠀⠀⠀⢀⠀⠀⢸⡰⢌⠁⢠⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⢿⠀⠀⣿⠀⠢⠟⠁⠙⠙⠻⣷⣄⠀⠀⠀⣠⠤⣄⠀⡜⠀⠀⠀⠀⠈⢧⠀⠇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣴⣿⡟⡀⢀⣠⣤⣼⠷⡄⣸⠚⠋⢀⣾⠟⠀⣴⠁⠀⠀⠀⠀ ⣤⠀⢸⡀⢀⡿⣀⠄⠀⠀⠀⠀⠀⠈⠙⣷⣄⠘⠷⠴⠇⢰⠇⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⠀⢀⣤⠞⠁⢀⡴⠟⢱⠟⠀⠁⠉⢱⡾⢋⠜⡴⠃⠀⠀⣾⡟⢠⡾⠁⠀⠀⠀⠀⡰ ⣜⣆⠀⣷⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣄⡀⠀⠘⠛⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣀⡴⠋⢁⣠⠾⠋⠀⢀⡞⡀⠀⠀⢠⡼⠆⠁⠀⠀⠀⢀⣼⡿⢡⡞⠁⠀⠀⠀⠀⡴⡇ ⠹⡌⢧⠸⡍⠛⠢⣤⣠⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣠⠴⢛⣥⡴⠚⢉⣀⣤⠤⠶⣿⡹⠀⠀⠀⡚⠗⣄⠀⠀⠀⣀⣼⣿⣣⡞⠁⠀⠀⠠⠀⠘⠁⠃
⠀⠀⠀⠀⣀⢠⢄⣴⣖⣼⣦⢄⢀⠀⠀⠀ ⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣏⡇⠤⡀ ⠀⣴⣿⣿⣿⣿⣿⣿⠿⠿⠛⠻⢿⣿⡍⠀ ⢠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠹⣷⠀ ⠈⣿⣿⣿⣿⣿⡿⠁⠀⠊⣉⣭⠀⡔⡛⠀ ⠀⢹⣯⢹⡿⢿⡇⠀⠀⠙⠾⠋⠀⠯⠇⠀ ⠀⠀⢿⣦⣐⢺⠷⠀⠀⠀⠀⠠⣤⡄⡀⠀ ⠀⠀⠘⢿⠈⠀⠀⠈⠃⠙⣤⣀⣤⢭⠁⠀ ⠀⠀⢠⠋⠀⠀⠀⠀⠠⠀⣙⣝⣛⠇⠀⠀ ⠀⠀⠘⢄⠀⢀⠠⡀⠀⢴⠌⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠑⠂⠤⠌⠷⠶⠛⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿ ⠀⢠⣶⣯⣀⣀⣤⣴⠶⠿⠿⠿⠿⠿⠿⠟⠻⠿⠿⠿⠿⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣶⣶⣾⣧ ⠐⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠉⠉⠛⠻⢿⣿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣤⠴⢶⠀⠀⠀⠀⠀⢻⡆ ⠀⠀⠀⠀⢀⣠⠤⣶⣶⣶⣶⣶⣶⣶⣤⣴⣆⡀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠠⣎⣤⣶⣿⣿⠿⠃⠈⠀⠀⠀⠀⠀⡀⡷ ⢀⣤⣶⠿⠿⠟⠛⠉⠉⠉⠉⠀⣨⣿⣿⣿⣿⣿⣤⡤⣲⣦⠟⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⠉⣁⣠⣶⠶⠿⠿⢿⣿⣿⡿⠁ ⠈⠛⠀⠀⠀⢀⠀⠉⠓⠶⠀⠈⠻⠿⠿⠟⠛⠛⠃⠹⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡗⢾⣿⣋⣀⠀⠀⢀⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠦⣤⣷⣤⣤⣤⣤⣤⣤⣴⣶⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢷⠶⢶⣦⣭⣍⣉⡉⠉⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠠⣉⣉⣉⣉⣉⣉⠅⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢠⠛⠛⠛⠿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠓⠒⠒⠂⠛⠙⠉⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠄⠈⡧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡀⠀⢀⣤⠀⠀⠀⠀⢠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣀⣤⣤⣤⣾⣿⣿⣶⣶⣶⣾⣟⠛⠛⣓⣛⣿⠟⠃⠀⠀⠀⣠⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠿⢿⣿⣾⣿⣿⣿⣶⣾⣿⡏⠀⠀⠀⠀⠀⢐⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡉⠙⠛⠿⢿⣧⡀⠀⠀⣰⡷⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠛⢷⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣄⢉⡀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣴⠶⣶⣶⣶⣶⣶⣷⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣁⡀⢠⡤⠴⠚⠋⠁⠀⣀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣶⣿⣛⣿⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣶⡀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠘⠆⠀⠀⠈⠻⢿⣛⣻⣿⡿⠟⢿⣿⣿⣿⣿⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠆⠀⡀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠸⡟⠛⠛⣩⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⢧⠀⡀⠠⣤⣄⡀⠀⣀⣀⣀⣀⣤⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⣀⡀⡀⠀⠙⢻⠶⣶⣯⣭⡭⠭⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
➖➖➖🟩🟩➖🟩🟩 ➖🟩🟩🟩🟩🟩🟩🟩🟩 🔲⬛⬜🟩🔲⬛⬜🟩🟩 ⬛🔲⬜🟩⬛🔲⬜🟩🟩 ➖🟩🟩🟩🟩🟩🟩🟩🟩 🟧🟧🟧🟧🟧🟧🟩🟩🟩 ➖🟥🟥🟥🟥🟧🟧🟩🟩 ➖🟥🟥🟥🟥🟧🟩🟩🟩 ➖🟥🟥🟥🟧🟧🟩🟩🟩 ➖🟧🟧🟧🟩🟩🟩🟩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠏⠛⠿⣖⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⡤⣤⣶⠿⠛⠁⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢀⣠⠴⠚⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠙⠲⠶⠄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠴⠒⠒⠚⠒⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣐⣲⣶⣤⣄⣸⣗⣦⣴⣖⣶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠲⣶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣿⣿⡿⢻⡋⠋⠉⠉⠉⣙⡛⠻⡟⢿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣶⣶⣤⣿⣷⣦⣬⣽⡖⠦⣄⠀⠀⠀⠀⠀⠀⠀ ⢀⣻⣷⣾⠟⣿⠈⠓⠒⢶⣀⣘⣾⠟⢉⣈⡿⠁⠀⠀⠀⣠⠄⣀⡀⠀⢀⡀⠔⠀⠀⠀⠀⣴⢛⣿⣶⣀⡉⣩⣝⡻⠿⣿⣶⣍⡂⠀⠀⠀⠀⠀ ⠀⠙⠿⠷⠄⠈⡻⢶⣶⡾⣠⠆⠀⠿⠿⣄⣽⢀⡠⣖⡯⠐⢺⣿⠗⠚⠁⠀⠀⣀⡤⠖⣀⡼⢯⣠⡀⠻⣿⣿⣿⡻⠶⢦⣉⠻⣿⣶⣤⣄⠀⠀ ⠀⣠⣖⠥⠺⣏⣣⠼⢋⡠⣔⡯⠖⠀⠀⢀⡠⠔⠊⠁⠀⠀⣸⣶⣀⡀⢄⡒⠍⠀⠀⢀⡾⡔⠈⢛⠛⠛⠛⠷⢤⣥⣀⢀⣽⠿⠋⠙⣿⣧⣿⣀ ⣠⡾⢝⣮⣴⢿⡯⠂⠌⠊⠋⠀⠀⠠⠚⠉⠀⠀⠀⠀⠀⠀⠻⠉⠉⠀⠈⠀⠀⠀⠀⢸⡿⣖⠬⠉⠀⡀⠀⠀⠀⠙⢫⡈⣡⠀⠠⠶⠟⠛⠉⠉ ⢨⡾⠛⡁⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠩⠋⢒⡬⠔⠒⠋⠁⠀ ⠉⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠛⠛⠒⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠉⢠⣤⣤⣤⣤⣤⣤⣀⡈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣌⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠯⠁⠀⠀⠀⠀⠀⡀⠅⢨⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⠐⠢⠀⠀⠀⠀⣈⣁⡾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⣭⣛⡒⣒⣒⣚⣭⡿⠋⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⢫⡀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⠀⠀⠀⠀⠀⠀⢱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣶⣶⠒⠒⠶⡦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠽⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠶⣄⠀⠈⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠈⢳⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣖⠒⠶⢤⣀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠈⠳⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠶⠶⢤⣻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⢀⣤⠖⠛⠉⠀⠀⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣀⣀⣠⣀⣀⠀⠀⠈⠙⠓⠒⠚⠁⣀⣴⣿⣿⣿⣿⡆⠀⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣸⡏⠁⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⡤⣴⣾⣿⣿⣿⣿⣿⣿⣿⠀⢸⠃⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⢠⣿⠀⠀⣠⣿⣿⣿⡿⠟⠛⠛⠛⠋⠙⠻⢿⣿⠞⠋⠉⠀⠀⠀⠉⠙⠻⣇⠀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⢨⡇⠀⠀⠀⠀⠈⡏⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡖⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣿⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠻⣻⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡴⠚⠉⠑⣦⣀⠀⠸⣇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⠃⠀⠀⠀⣀⣀⣀⣶⣿⣿⣀⡀⠀⠀⠀⠀⠀ ⢀⡞⣹⡷⠒⢶⠏⠁⠉⠁⠀⠻⣦⠀⠈⠳⣤⣀⣀⣀⣠⣤⣤⡤⠴⠚⠛⢳⢻⣽⣟⠿⠋⠉⠛⠘⠀⠉⠙⠲⣄⡀⠀⠀ ⣸⡇⠋⠀⠀⠈⠦⣤⡀⠀⠀⠀⠈⣻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠉⠙⢦ ⣿⡇⠀⠀⠀⠀⣠⠏⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋⣀⣠⣦⣄⠀⢸ ⢸⣳⠀⠀⠀⢀⣻⣤⡄⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⡾ ⠀⠙⢧⡀⠀⠿⢄⡝⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠙⠒⠢⠀⢹⡶⠂⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⢿⠖⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⡛⠿⢿⡟⢋⣹⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⣤⣤⣀⣀⣀⠀⢀⣀⣀⣠⡤⢤⣀⣩⠷⠒⠛⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⡿⠟⢁⣴⣿⡿⠋⠀⠀⣼⣿⣿⣿⡟⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣦⣤⣤⣾⣿⣿⣿⣿⣧⣀⣀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣿⣿⣿⠟⢁⠀⠉⠉⠉⣻⡿⣛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⣟⣿⠀⠀⠀⢸⣟⢻⢛⣷⠀⠀⠀⠀⠈⣿⠈⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣮⡁⠀⠀⠀⢈⣿⣮⡉⠉⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠉⠙⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⣿⣿⣿⣿⠿⠿⠿⠟⠋⣿⡿⢷⣶⣶⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⣭⣭⣭⣄⡀⠀⠘⠻⣦⣌⣀⣤⡴⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠉⠉⠉⠛⠛⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⢀⣠⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣄⡀⠀⠀⡀⠈⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣾⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣦⠀⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡇⠸⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢰⣿⣾⠃⢠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠈⢳⣌⠻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣠⣿⣿⢃⣴⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⠀⠀⠀⠈⠐⠲⢿⣿⣿⡟⠀⠀⠀⠀⠀⢰⣷⣿⣿⣵⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⡀⠀⠀⠀⣀⣠⣿⣿⡟⠀⠀⠀⣀⣴⣿⣿⣿⠟⠛⠉⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣠⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣽⣅⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣤⣤⣤⣤⣶⡆⠀⠀ ⢸⣿⣿⠿⠟⠛⠻⠿⢿⣿⣷⣶⣶⣶⣶⣾⣧⣾⣿⡿⠋⠁⠀⠀⠀⠀⢈⣽⡿⠋⠀⠀⠀⠀⠀⠀⣹⣿⣿⠿⠿⠿⠟⢿⠉⠀⢀⣠⠀⠈⣿⣿⡿⠿⠟⠛⠛⣿⣿⡇⠀⠀ ⢸⣿⣿⠀⠀⠀⣶⣄⠀⠙⣿⡿⠟⠛⠛⠻⢿⣿⡟⠀⠀⠀⢠⣴⣦⣄⣾⡏⢀⣀⣀⣠⣶⣶⣤⣾⣿⣿⣿⣠⡄⣤⣤⣾⠀⠀⢹⡟⠀⢠⣿⣏⠀⠀⠐⠲⠶⢿⣿⣷⡄⠀ ⠀⣿⣿⠀⠀⠀⡿⠋⠀⠀⠛⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣿⣿⠟⠛⠛⠋⠉⠉⠉⣿⣿⠛⠋⠉⠉⠉⠁⠈⡇⠛⠛⣿⡇⠀⢀⣧⠀⠈⠙⢿⣷⣦⣤⡀⠀⠀⠹⣿⣿⡆ ⠀⣿⣿⡆⠀⠀⣤⣀⣢⣾⠀⠀⢠⣾⣶⡦⠀⢸⡆⠀⠀⠀⢻⣿⣤⡄⠀⢠⡄⢰⠞⢻⣿⣶⠆⠀⠀⠐⣾⠛⠉⠀⠛⠛⠃⠀⢸⣿⣆⠀⣠⡄⠈⠙⠛⠃⠀⠀⢀⣿⣿⡇ ⠀⣿⣿⣧⠀⣀⣸⣿⡿⣿⣄⠀⠈⠿⡿⠇⠀⢈⣷⡄⠀⠀⠈⠉⠉⠱⠶⠈⢠⡿⠀⠀⠉⠁⠀⠀⠀⣠⣿⣆⣀⣀⣠⣤⣤⣶⣾⣿⣿⣾⣿⣄⡀⠀⠀⠀⢀⣠⣾⣿⡟⠀ ⠀⢹⣿⣿⣿⣿⣿⠿⠷⢿⣿⣷⣤⣄⣀⣤⣶⣿⣿⣿⣦⣀⠀⠀⠀⠀⣀⣴⣿⣷⣄⡀⠀⠀⣀⣠⣾⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠋⠉⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠛⠛⠓⠒⠓⠒⠒⠒⠂⠈⠉⠙⠛⠛⠒⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⣳⡖⠛⠋⠉⠉⠉⠉⣉⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡥⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠶⠖⠒⠶⠶⠾⠭⣆⣀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⣀⣤⡤⠶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⡀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠒⠛⠉⠀⠀⠀⠀⠀⠀⠙⢳⣴⡶⠶⠖⠲⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠖⢛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠶⠶⣦⣤⡀⠀⠀⠀⠀⠈⣿⠳⣄⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⠀⣴⠋⠀⢀⡞⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⣾⣴⡿⠃⠀⣴⣟⠀⠀⠀⠀⣠⠾⠛⠁⠀⠀⠀⣠⣤⣤⡙⠿⣦⣀⠀⠀⢹⠀⠻⣷⠀⠀⠀⠹⣄⠀⠀ ⠀⣠⣾⠁⠀⠀⣾⠀⣠⣶⠾⢟⣿⣿⣿⣯⡙⠿⣷⣴⣿⠏⠁⠀⠀⣿⣿⠀⠀⠀⡿⠋⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣷⣄⠙⣧⠀⢸⠀⠀⠹⣧⠀⠀⠀⠻⡄⠀ ⢸⣿⡇⠀⠀⢀⡏⠀⡏⠀⢀⣿⣿⣿⣿⣿⣿⡆⣸⡿⠃⠀⠀⠀⠀⢿⣿⠀⠀⠰⣷⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⡀⢸⠀⠀⠀⢻⣦⠀⠀⠀⣷⠀ ⠈⢿⣷⠀⠀⢸⠁⠘⡇⠀⣼⣿⣿⣿⣿⣿⣿⣷⣿⠁⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠻⣷⣄⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡇⡿⠀⠀⠀⠀⢻⡆⠀⠀⢸⡇ ⠀⠸⣿⠀⠀⣾⠀⠀⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣀⠀⠀⢷⡀⠀⠀⠘⠻⢿⣦⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢻⡀⠀⠈⡇ ⠀⠀⠹⣷⣄⣿⣀⠀⠀⠈⠉⠛⠉⠉⠙⠛⢹⣿⠀⠀⠀⠀⠀⠀⠻⠻⣦⣈⠳⣦⣤⣀⡀⠀⠈⠛⠛⠛⠛⢛⣭⣤⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⡇ ⠀⠀⠀⢳⡈⢩⡟⠛⠿⠷⠶⠦⣄⣀⠀⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣏⠉⠛⠛⠿⠿⠿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⡇ ⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⢀⣀⡼⠿⠛⠋⠁⠀⠀⠀⠀⠀⢀⣶⣶⣦⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⡇ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠈⠻⣷⡀⢰⣶⣶⣶⣶⡦⠀⠀⠀⠛⢿⣿⣿⣧⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁ ⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣍⣛⣛⡁⠀⠀⠀⠀⠀⠀⠈⠩⡭⠤⠼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀ ⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀ ⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀ ⠀⠀⠀⠈⣧⡀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣇⠀⠀ ⠀⠀⠀⠀⢿⣿⠄⠀⢸⠃⠳⣄⣀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠀⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠷⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⠀⢸⡆⠀⠀⠙⢿⣿⠷⣶⣶⣶⣶⣾⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⣿⣿⠷⢿⣿⡿⠟⠉⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣷⠀⠈⣇⠀⠀⠀⠀⠉⠳⣾⣇⣀⣸⡇⠀⠀⠈⢻⣿⣿⣿⡇⠀⢀⣠⣿⡷⠟⠉⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠚⣿⡖⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣷⣦⣤⣄⣹⣿⣿⣶⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣿⣭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠦⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⢀⣶⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀⢀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⣠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣆⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⢀⣼⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠃⠀⠀⠀⣰⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⡆⠈⠙⠻⣷⣶⣦⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣠⣴⣾⠿⠋⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠈⠈⠙⠛⠻⠿⠿⢿⡿⠿⠿⠿⠛⠟⠉⠁⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣤⣤⣄⣀⣀⣀⢀⣀⣠⣄⣴⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠒⠢⢀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠤⠄⠀⠡⠀⠀⠀⠀⢀⠠⠐⠂⢐⣒⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣼⣷⣂⡄⣀⠀⢃⠀⠀⠀⠀⡠⣲⠬⣿⣛⠛⢿⠷⣶⣤⡴⠃ ⠲⢾⡟⠉⡝⠷⠼⢹⡓⠀⢸⠀⠀⠀⠀⠉⠀⠸⠤⢭⠥⠤⡳⠾⠟⠁⠀ ⠀⠀⢹⠟⡙⣉⠡⢐⣀⡄⠁⠀⠀⠀⠀⠄⠁⠀⠀⠁⠀⠀⠐⠛⠛⠀⠀ ⠀⠈⠠⠕⠈⠔⠘⠉⠀⠀⣠⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⢊⣡⣤⣭⣍⣐⡂⢤⣄⠀⠀⢀⣺⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡾⡿⣿⣿⡿⢿⡿⢿⡏⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠓⠁⢈⠇⢠⡑⢁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠠⡴⢋⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣶⣿⣦⣠⣾⣿⣿⣿⣿⣷⣄⠀⡀⠀⣴⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣠⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⣀⡹⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠉⠙⣿⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠉⢉⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⠆⠈⠇⣾⢀⣾⣿⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢹⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⠀⠁⠀⣤⠤⠀⠀⢠⠄⠀⡼⠘⠛⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⢰⠿⡍⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⣏⣽⣿⣦⠀⠋⠀⣼⢃⣤⢼⣏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⢸⣠⡟⠋⡙⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⡀⢨⡉⠙⣻⡟⠀⠀⢸⡏⢹⣄⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡞⠿⣄⢸⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠑⠀⠉⠉⠉⢀⠀⢸⡀⢷⡀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣷⢾⡝⠟⣦⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⠀⠦⡀⠀⠈⠀⠈⠇⠈⢳⠀⠸⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣝⡿⠟⠁⣿⣿⣿⠃⣤⠀⠢⡄⠀⠈⣇⠀⢹⣀⡞⠀⣀⠒⠛⢛⡇⢀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠈⢉⠉⠀⠙⠛⠁⠀⠻⠤⣤⡈⠀⠀⠈⢀⡼⡇⠙⠛⢻⡇⣠⠞⢀⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⠃⢠⡎⠀⠀⠀⢷⡄⡀⠠⡀⡀⠹⠆⠀⠀⠞⠁⠳⠀⠀⠀⢈⣻⣶⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠁⠀⡜⠁⠀⠀⠀⠈⡟⡼⣄⠱⠌⠲⡄⠠⣄⣀⣀⣀⡠⠶⠚⠉⡉⢹⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⢠⠀⠀⠀⢠⠃⢸⠈⠓⠀⠀⢸⠀⠘⣿⢥⣤⣤⣶⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⣠⠀⠀⠀⠀⠸⠀⠀⠀⠈⠀⢈⠀⢳⠀⣠⠋⠀⠀⠘⡆⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡤⠖⠋⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠘⠀⠸⠀⢳⠀⠀⡐⠀⢧⡀⠛⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⠉⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⠀⠀⠀⣠⠀⠀⠹⣦⠀⠀⠀⠀⣄⠈⠎⢷⡀⢹⡀⠈⠻⠶⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣧⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠛⢇⠀⠈⢦⡈⠣⡀⢠⡑⠦⠙⠳⣶⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠁⠀⠀⠀⠀⠘⣦⠀⠀⠙⠦⣀⠀⠙⢓⣠⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⢸⠈⠳⣄⣀⣀⣈⣽⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠉⡉⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢠⠞⠁⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠤⣀⡀⠀⠀⠀⠀⢀⡏⠀⣠⣏⡤⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠉⠉⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠏⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡏⠀⠀⠀⠀⠀⠀⣀⣨⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⢀⡴⢿⠏⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢀⣠⠴⠚⠉⣹⢿⡟⠛⠿⢶⣶⡿⣕⡶⣤⣴⣏⣴⡿⢶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⢀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢰⡘⠉⠀⠀⢀⡼⠃⢸⡇⠀⠈⠁⠐⠙⢳⣶⣟⣀⣀⣼⡧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢸⠀⠀⠀⠀⠀⠀⠈⡘ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⠐⠲⠿⠵⣾⣿⣿⣷⣤⣼⣁⡀⠀⠀⠀⢠⡾⠋⠈⠉⠩⣿⢃⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢰⠀⠀⠀⠀⠀⠐⠠⠁ ⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣟⣷⣦⣰⡞⠁⠀⠀⠀⢀⡧⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⣰⠋⠀⠀⠈⡆⠀⠀⠀⠀⡑⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⣾⣿⣿⠿⠋⠉⠁⠈⡟⠉⣿⢿⣿⣷⣄⠀⠀⢳⣼⢡⢿⠘⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡇⠈⣠⣾⣁⠀⠀⠀⠀⡇⠀⠀⣰⡔⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣠⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⣷⣰⣿⡞⠉⢻⣿⣶⡀⠀⢹⣿⢸⠀⠓⢿⠀⣀⠀⠀⠀⠀⠀⣀⣴⡤⣤⣾⡷⢶⢾⣿⡁⠀⠉⠉⠑⠲⣧⣀⡷⠋⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⢀⣿⡽⠟⣿⣯⠁⠀⠀⠀⠀⠀⠀⣿⠇⡿⠁⠀⠀⠙⢿⣿⣄⢸⡟⣿⠀⠀⠀⠁⠈⠻⠾⠃⣴⠻⠋⠀⢀⣼⠟⠀⣰⢏⠀⠉⠉⠉⠉⠉⠉⢻⠻⣿⡢⣄⠀⠀⠀ ⠀⠀⢰⠀⣧⠀⠘⣿⠀⠀⢿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣠⠥⠤⢤⣄⠈⢻⣿⣿⣿⠀⢸⠀⢠⠆⠀⠀⠐⢡⠞⠋⠀⠀⢀⣾⡟⠀⣰⡯⠊⠀⠀⠀⠀⠀⠀⠀⢾⠀⣿⠫⡛⠽⣶⣤ ⠀⠀⢸⠀⣾⡄⠀⣿⣠⠀⣼⣿⠀⠀⠀⢤⣤⠶⠶⢟⣡⣤⣀⣀⡈⠓⠲⣮⣻⣿⠀⢸⠀⡜⠀⠀⠀⠀⡜⠀⠀⠀⢠⡟⡽⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⣿⠀⠀⠀⠈⠉ ⠀⠀⢸⢠⢿⣷⠀⣿⣿⣄⡏⠹⡄⠀⠀⠀⠈⢳⣤⡀⢹⠀⢯⢉⡗⢦⡀⠀⠁⢸⠀⢸⠀⡇⠀⠀⠀⠀⣹⠀⠀⢠⠎⡼⣡⠞⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⡇⢸⣿⡆⠀⠀⠀⠠ ⠀⠀⢰⣼⢸⣿⡄⣿⣿⣿⠀⠀⠻⡄⠀⠀⠀⠠⣅⠀⠀⢧⣠⠟⠠⠜⣧⡀⠀⠀⠀⠈⡆⡇⠀⠀⠀⢰⠏⠀⢀⠏⣸⡿⠁⠀⣈⣁⣀⣀⣦⡈⠉⠛⠓⠲⢶⣥⣏⣿⡇⠀⠀⠀⠈ ⠀⠀⢸⡏⠘⣿⣿⡟⣿⣿⡄⢠⡤⠵⣤⠀⠀⠀⠘⢦⡀⠀⠀⠀⣀⡶⠛⠯⠄⠀⠀⠀⣿⣻⠀⠀⠀⡏⢀⠀⡜⠶⠋⠠⠴⠒⣺⠿⠿⢿⣿⣿⣿⣷⣶⣤⣼⡾⠙⣿⡇⠀⠀⠀⢰ ⠀⠀⠈⠀⠀⠛⣿⣧⢹⣿⣷⠘⠒⠒⢾⣤⣀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣟⡆⠀⢸⠁⢸⣸⠃⠀⠀⠀⠀⠀⠀⣀⣀⣀⡁⠀⠙⠛⠻⢿⣿⣷⣾⣿⠁⠀⠀⠀⡌ ⠀⠀⠀⠀⠀⠀⣿⣿⣆⢫⣿⣧⣄⢧⠘⡆⡈⣝⠓⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢻⡀⡜⠀⢸⡇⠀⠀⠀⠀⢀⡴⠋⢉⠀⠈⠉⠳⣄⠀⠀⡼⠛⢿⣿⣿⣷⣄⡀⢠⠀ ⠀⠀⠀⠀⠀⣼⡿⠈⣿⣾⡏⢿⣿⡎⣧⢹⣷⠸⣿⡄⡄⣧⠘⣆⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢧⡇⠀⢸⠀⠈⠓⢶⡶⠋⠀⠀⡟⣇⣠⠖⣶⠘⠦⠾⠁⠀⠀⣹⣿⣿⡌⢻⣧⠀ ⠀⠀⠀⠀⢀⣿⡇⠀⣸⣿⣿⡸⣿⣿⡘⣆⢻⢧⢹⣿⡼⡌⣇⠹⡜⣆⣃⡤⠃⡄⠸⣄⠀⠀⠀⠈⠃⠀⠈⠀⠀⠀⠀⢹⡄⠀⠀⡇⠋⢀⠼⠹⣦⡀⠀⠀⠀⢰⣿⠻⣿⣿⡟⠀⠀ ⠀⠀⠀⢰⣾⣿⠇⠀⠁⣿⢿⠹⠙⢷⠳⠘⠊⠟⠇⢻⢷⣻⡼⣷⣻⣿⣿⣇⠀⣼⡀⢯⠆⠀⢶⠀⠀⠀⠀⠀⠀⠀⠢⢄⣁⡀⠀⠹⠔⠋⠀⠠⣈⢻⡦⣀⢰⡼⠁⠀⢻⣿⡇⠀⠀ ⠀⠀⠀⢸⣿⢸⡇⠀⢸⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣳⠻⢧⢷⣹⣿⡴⡜⢷⡘⣴⠀⠈⡆⠀⠀⢠⠀⠢⣄⡀⠀⠀⠙⠢⢤⣤⣤⠴⠚⠉⠙⠲⣌⡼⠁⠀⠀⢈⣿⣿⠀⠀ ⠀⠀⠀⢸⡏⠈⡇⠀⢸⣬⡇⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⢻⣷⡁⠐⢧⠹⡄⣄⢱⡸⣤⠘⠀⡄⢈⡙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⣶⣿⣿⣿⡆⠀ ⡄⠀⠀⢸⡇⠀⢷⡀⠀⠉⠀⠀⠀⠀⠀⣸⣿⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠁⠘⣆⢻⡽⣸⣇⣟⣇⣦⢧⡈⡇⠀⢀⠙⠳⣄⡀⣀⠀⠀⠀⠀⠠⠶⠚⠛⠋⢉⡿⣿⡏⠃⠀ ⠃⠀⠀⣼⡇⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠏⠘⠀⠀⠈⠂⠻⢧⣻⣼⣾⣿⣸⢣⢿⠀⢸⣧⠀⠈⣿⠛⠛⠲⢤⡀⠀⠀⠀⣰⢁⡾⠁⠈⡇⠀⢠ ⢸⠀⠀⢿⣿⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣿⡟⣆⣤⡀⠈⠓⠢⣄⡀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠈⠙⠁⢳⢿⣇⠈⣼⡆⠈⡿⡄⡄⠈⢳⣤⣀⣠⡇⠀⢀⡼⢁⡾⠁⠀⠀⠀⠀⣾ ⠀⣇⠀⠈⣷⢻⣄⣧⠻⣆⠀⠀⠀⠀⠀⢹⠖⠚⣇⠙⢦⡀⠀⠀⠉⠒⣆⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣿⡘⢣⢿⢰⣿⢧⢹⣇⢸⡀⠩⠉⠁⢠⠏⣠⡟⠁⠀⠀⠀⠀⣰⠏ ⠀⠹⡆⠀⡿⣆⢻⡏⡆⠸⣆⠀⠀⠀⠀⠘⠀⣀⡼⣆⠀⠈⠳⠦⣀⡀⠘⠞⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣷⠆⠘⡇⢻⣾⡏⣿⡸⣧⠀⠸⡆⣠⡾⣋⠀⠀⠀⠀⠀⣰⠏⠀ ⠀⠀⠹⡀⡇⠹⡷⣝⢹⣄⣘⣧⠀⠀⠀⣆⡞⠁⠀⠈⠙⡦⣄⡀⠀⠉⠙⠲⠦⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠀⠀⠹⠜⣷⡇⣿⡟⠿⡾⠶⣿⣿⣿⠟⠀⢀⡀⣠⠾⠁⠀⠀ ⠀⠀⠀⠹⣿⠀⠀⠈⠓⠦⣄⡉⠳⡄⢰⡿⠀⠀⠀⠠⣄⡿⡴⠈⠛⠲⠤⣀⡀⠀⣀⡀⠙⠦⠖⠛⠉⢹⡭⣉⡿⠁⠀⠀⠀⠀⠘⠛⢇⢻⣘⣃⣤⣶⣿⣵⣽⣽⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠓⠻⣟⡇⠀⠀⠀⠀⢸⣿⠧⠀⠀⠀⠀⠈⠉⢻⢉⠟⠢⠄⠙⢶⠖⠚⢤⠏⠀⠀⡀⠀⠀⠀⠀⠀⠈⠋⣩⣿⠟⠛⠻⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⢰⢯⠇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢏⠔⢺⣿⠀⠀⠀⠣⠴⠃⠀⣤⣴⡴⠚⠉⠀⠀⠀⣰⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠳⡀⠀⠺⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡴⠉⠀⣾⡿⠀⠀⠀⣀⣠⠴⠞⠋⠁⠀⠀⠀⠀⣠⡾⣃⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⠿⢦⠀⢸⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣽⣁⣀⠤⠤⠴⠒⣿⠏⠁⣤⡄⠀⠀⠀⠀⠀⣀⣴⣿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠋⠀⠀⠀⠘⠖⠋⠀⠀⠉⠉⠉⠉⠉⠉⢹⣋⣀⡜⠃⠀⠀⠀⠀⠀⣰⢻⠀⠀⣟⡿⠆⠀⣀⡤⠾⣛⣋⣥⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠔⠒⠊⠉⠙⠒⠒⠒⠦⠤⣀⢲⢤⡀⠀⠀⠀⠀ ⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⣆⡤⠔⡲ ⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢧ ⡈⢱⡄⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣀⣄⠀⠀⠀⣀⡤⠂⢸ ⡏⠙⣣⡴⢻⡠⠚⠁⠸⡄⢀⡤⠊⠁⠈⠲⠔⠋⠈⢣⠀⡼ ⠘⠤⣌⠀⠀⢀⣤⠀⠀⠈⠁⠀⠀⢿⠀⠀⠀⠀⠀⢸⢰⠁ ⠀⠀⠸⡀⠀⠀⠛⠀⠠⡴⠒⠒⡟⠂⠀⠀⠀⠀⠀⡼⠃⠀ ⠀⠀⠀⠱⣄⠀⠀⠀⠀⠙⠢⠴⠃⠀⠀⠀⠀⠀⡔⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⡩⠥⢤⡀⠀⠀⠀⢸ ⠀⠀⡏⠁⢉⡇⠀⠀⣀⣀⠀⠀⠀⢸⠁⠀⠀⣧⠀⠀⠀⢸ ⠀⠀⢏⠉⠁⠀⢠⠏⠀⠀⢱⡀⠀⠈⠣⠤⠚⠁⡆⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠘⢆⡀⣀⡼⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⡄ ⠀⠀⠸⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠑⠤⠤⠖⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠥⡶⠋⠉⠉⠉⠒⠂⠀⡌⡝⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠏⡏⢰⠃⠀⠀⠀⠀⠀⠀⠀⠆⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⠴⢾⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠃⠀⠀⠀⠀⢠⠏⢰⢁⠏⠀⠀⠀⠀⠀⠀⠀⢸⢠⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⢀⠎⠀⣼⡞⠀⠀⠀⠀⡀⠀⠀⠀⡟⠈⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡇⠀⠀⢰⡄⠀⠀⠀⠀⠀ ⠀⠸⣿⠀⠀⠀⣠⠋⠀⢠⣟⣠⠔⢚⣉⣉⠛⠁⠀⡼⢱⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⡌⡀⠃⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⡇⠇⢀⡼⠁⠀⣴⣿⣿⣿⣿⠿⣿⣿⣶⣤⠆⠁⡼⠀⠀⣀⣷⠀⠀⠀⠀⠀⢀⣴⠟⣠⣴⣖⣦⣶⠃⠀⢀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⢡⣴⠊⠀⣠⣾⣿⣿⣿⣿⣿⣧⡀⣈⣙⣯⡓⢠⣇⠴⠋⠉⡟⠀⠀⠀⠀⢒⠞⠁⣴⣿⣿⣿⠛⢿⣦⡴⠋⣽⡇⠀⠀⠀⠀⠀ ⠀⠀⠘⡇⠀⢨⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠈⢻⡷⠋⠁⠀⠀⠀⠃⠀⠀⠀⠀⣎⡠⢞⣿⣿⣿⣿⠠⣄⣿⡏⢉⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠖⠿⣿⣿⣿⣿⣼⡿⠿⣶⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣾⡿⣿⣿⠛⠀⠈⣿⠁⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣇⠀⠘⢿⣿⠇⠈⠀⢤⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠙⢿⡟⠀⢰⠃⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡄⠀⠀⠙⠷⣄⣀⣀⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡟⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠠⠤⠤⠤⠤⣤⠗⠤⠤⠄⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠤⠤⠤⠤⢤⣤⠤⠤⠤⣤⠤⠤⠤⣤⣤⣤⣿⡤⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⣤⣄⣴⣾⣿⣿⣿⣿⣷⣶⡄⢀⠀⠈⠉⠉⠋⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠻⠿⠿⢿⣿⣿⣿⣾⡗⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠾⣦⡀⠀⠀⣀⣴⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢾⣿⡟⢻⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡤⠶⠂⠀⠐⠒⠒⠂⣀⣀⠲⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣴⠛⢉⣭⣶⣿⣿⣿⣿⣿⣧⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⡿⠿⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣤⣾⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⠉⠀⢾⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠙⠿⡅⠀⠽⠿⠟⠻⠿⠿⠭⠁⠀⡄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣡⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢊⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⠶⠶⠶⠶⠶⣾⣿⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠦⠤⠀⠀⠀⠀⠀⠀⠉⠉⠒⠢⢤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠐⠒⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⠀⠀⠀⠉⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⣀⡠⢴⣾⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⣠⡖ ⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣕⣲⠤⣀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠠⢖⣩⡶⠾⣿⣿⣉⣉⡉⠙⢿⡟⠿⢿⣿⣶⡿⠋⠀ ⠐⠶⣶⣶⣿⠿⠛⠋⢩⢿⣥⣄⣩⠻⡟⠦⢅⡀⠘⡿⠀⠀⠀⠀⠀⠀⠖⠉⠀⢀⣸⣁⣀⣉⣛⣋⣀⣀⣵⣤⣾⣿⡿⠂⠀⠀ ⠀⠀⠀⠙⠻⢷⣤⣠⣧⣤⠬⣭⠭⠴⠓⣆⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠉⠉⣉⠋⠉⣙⠉⠏⢹⢈⣭⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⠋⣀⠁⢀⡁⠤⠒⠉⣁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⠓⠈⠁⠀⠀ ⠀⠀⠀⠀⠖⡩⠔⣩⠔⠊⢁⡠⣴⠾⠛⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠔⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⣀⣉⡉⠉⠒⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣴⣾⣀⡠⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⣼⣿⡗⠀⠀⠀⠀⠸⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⣏⡴⠃⠀⠘⡿⠉⠀⡰⣩⠟⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢰⠃⠀⣴⡵⠃⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⢤⡤⡾⠋⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⣉⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠘ ⠁⣾⠿⣦⠀⢠⡞⢻⣆⠀⢠⡶⠲⠆⠀⣴⠖⠶⠀⢰⠶⠶⠀⣾⠛⣶⣴⠟⠷⢀ ⠀⣿⠀⣿⠁⣿⠀⠀⣿⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⣿⣦⡿⠹⣧⠀⢸ ⠀⣿⡴⠋⠀⣿⠀⠀⣿⠀⣿⠈⠛⣷⢼⡇⠙⢻⡆⢸⣷⠶⠀⣿⠿⣧⠀⠘⣷⢸ ⡇⣿⠁⠀⠀⢻⡄⢀⣿⠀⢻⡄⢠⡏⠸⣧⠀⣼⠃⢸⡇⠀⠀⣿⠀⣿⢀⡀⢹⢿ ⡇⠻⠀⠀⠀⠀⠛⠚⠃⠀⠈⠛⠛⠁⠀⠙⠛⠋⠀⠘⠳⠖⠀⠿⠀⠉⠘⠳⠋⢸ ⣧⣤⣤⣤⢤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⣠⣤⡤⠤⢤⣤⠤⣤⣤⣤⣼ ⠀⠀⠀⠀⡼⢰⡞⠁⣈⠤⠭⢭⣉⣉⡡⠖⠚⠛⠓⢦⣘⡒⠒⢦⡉⢦⠀⠀⠀⠁ ⠀⠀⠀⠀⠃⢸⡴⠋⠤⠒⠂⠀⣙⡯⠠⠒⡯⠟⣋⣉⣀⠩⠷⡄⢳⠘⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⢀⣠⣶⠟⣿⣶⣦⠈⢲⠊⢱⣿⣿⣿⣀⣸⣿⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠻⢅⣈⣿⣿⡿⠗⠛⠒⠒⠛⢉⣩⠿⣷⡇⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⢰⡚⠉⣍⣙⣛⡒⣒⣒⣒⣒⣊⣩⡭⠴⣾⣿⠃⢀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣄⠉⠛⠒⠲⠮⠭⠭⠭⠽⠿⠿⠒⠒⣚⣟⠁⣠⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⡄⠈⢻⡟⠶⣤⣤⣀⣤⣤⣤⡤⣤⠴⠞⠋⠉⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠿⢦⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠹⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠁⠀⠀⠀⠀⢈⢙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⠶⣄⠀⠀⠀⠀⣼⠷⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣼⡦⣿⢠⣴⣄⠀⣇⣴⣦⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⣀⣻⣿⠏⢈⣭⣽⡁⢳⣿⡟⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢻⠏⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣷⣦⡙⠿⠿⠿⠟⣱⣿⣿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠙⢿⣿⣷⣶⣶⣿⣿⣿⣿⠉⠉⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⣠⡾⠀⠀⠀⠙⢻⣿⣿⣿⣿⠋⠀⠀⢰⡀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢠⣾⠏⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⢻⣆⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⢠⣿⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣰⡿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⣿⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡝⣷⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⣴⣿⠃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣷⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣸⣿⠃⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠹⣿⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣠⣿⠃⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⢻⣷⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⣿⠏⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠻⣧⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⣿⠏⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣧⡘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣰⣿⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠻⣷⡞⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣴⣿⠃⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠹⣷⡌⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⡿⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠙⣿⡆⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣯⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣞⠻⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣝⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⢷⣄⠀⠀⠀⠀ ⠀⠀⣠⡾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣝⣷⡀⠀⠀ ⢠⣾⣵⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣯⣷⡄ ⠈⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣒⡫⠭⠭⠭⠭⠭⠭⠭⠤⠄⠀⠈⠉⠙⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡩⠔⠋⠀⠀⠀⠀⠀⠛⠛⠓⠢⠤⢄⡀⠀⠀⠀⠀⠀⠈⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠋⠉⠛⠛⠒⠧⢄⣀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠥⠔⠒⠋⠉⠉⠓⠦⣄⣠⣤⠤⣤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠳⡀⠀⠀⠀ ⠀⠀⢀⡠⠶⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡖⠀⢸⠀⠀⠀⠀⠀⣀⣤⠶⠶⢤⣄⡀⠀⠀⠀⢻⠷⣄⠀⠀⠱⡄⠀⠀ ⠀⡰⠋⠀⢰⠃⠀⣀⣤⣶⣶⣶⣤⡀⢰⣧⡿⠁⢰⣾⠀⠀⢀⣴⠛⠉⠀⠀⣠⣶⣤⣝⠳⣤⠀⠈⡇⠹⣆⠀⠀⠹⡄⠀ ⣾⠃⠀⠀⡇⢰⠛⢉⣿⣿⣿⣷⡌⢻⣿⠋⠀⠀⢸⢸⠀⠀⣼⠁⠀⠀⠀⣾⣿⣿⣿⣿⣷⡈⣧⠀⡇⠀⢹⣆⠀⠀⢳⠀ ⢿⡄⠀⢸⠁⢾⠀⣼⣿⣿⣿⣿⣷⣿⠁⠀⠀⠀⠀⣿⡀⠀⠹⣧⣀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⢰⠃⠀⠀⢻⡄⠀⠘⡆ ⠸⣇⠀⣾⠀⠸⣤⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣄⠀⢣⡀⠀⠈⠻⢷⣤⣿⣿⣿⣿⡿⠿⣿⡿⠋⠀⠀⠀⠀⢻⡀⠀⡇ ⠀⢻⠲⠿⣤⣀⣀⣀⠁⠀⠈⠁⣿⠀⠀⠀⠀⠀⠋⠳⠬⣟⣲⠦⣤⣄⣉⣉⣉⣭⡶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⢳⠀⡇ ⠀⠀⢳⡼⠁⠀⠈⠉⢉⣷⠶⠟⠁⠀⠀⠀⠀⣤⣤⣀⠀⠈⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡇ ⠀⠀⢸⠃⠀⠀⠀⠘⠿⣄⢰⣦⣶⣦⡄⠀⠀⠻⣿⣿⣧⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃ ⠀⠀⡞⠀⠀⠀⠀⠀⠀⠈⠳⠬⠭⠅⠀⠀⠀⠀⠀⠐⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⢸⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠈⣇⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀ ⠀⠀⢹⣷⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⢀⣿⡁⠀ ⠀⠀⢸⣿⠀⠀⡇⠳⣤⣀⣀⡀⠀⠀⠀⣀⣠⣤⣤⣦⣤⣤⣀⣀⣀⢀⣀⣀⣀⡴⠚⠉⢹⠃⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀ ⠀⠀⠈⣿⡄⠀⡇⠀⠀⠙⢿⡙⡿⠿⢿⠛⠛⢻⣿⣿⣿⠛⠛⠻⣿⣻⡿⠛⠁⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠹⣷⠄⢻⠀⠀⠀⠀⠉⠛⠶⢾⣤⣄⣀⠹⣿⣿⣤⣴⠾⠛⠉⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀ ⠀⠀⠀⠀⢻⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣷⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⣰⡟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠉⠻⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⡀⠀⠉⠛⠛⠿⠳⠶⠶⠺⠿⠻⠛⠉⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠾⡶⣶⣶⣦⣶⣶⣾⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠳⢶⣶⣶⣶⣤⣤⣤⣀⣀⠉⠓⢷⣤⡀⠀⠀⢀⡠⠤⠀⠀⠐⠀⠈⠉⡛⢤⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣹⣿⣿⣿⣿⣿⠿⣿⡟⠒⠦⣿⡿⠦⠚⠋⠁⠀⠀⠀⠀⠀⠑⠢⣌⠢⡉⠪⠢⣈⣙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⡿⠋⠉⠉⠙⢿⡄⢹⠀⣀⣼⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠱⡄⠀⠈⠫⠑⢤⡉⠪⣳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠛⠀⠀⠀⠀⠀⢸⣇⣸⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠘⠢⣀⠀⠘⣆⠀⠀⠀⠀⠙⢆⡈⠣⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⣿⣇⠀⠀⠀⠀⠀⢈⣑⠦⣄⡀⠈⠿⣶⢤⣤⣀⣈⢿⣦⣼⣦⠠⠀⠀⠀⠘⣷⣄⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⢟⣻⣿⡟⢀⡏⠞⡄⠀⠈⢦⢣⠀⠙⢯⡛⠻⢗⣲⢼⡻⡍⠉⠓⢤⡘⣿⠻⣷⣇⠀⠀⠀⠘⣿⢦⠀⢘⣿⣿⣿⡀⠀⠀⠀ ⢿⡿⠛⢉⣴⡿⢿⠏⡇⠈⡇⠀⢘⡄⠀⠀⠻⣧⡀⠀⠙⢾⡉⠈⢠⠞⠻⣦⢤⣢⣽⣿⡷⠿⣿⡄⡇⠀⠀⠈⢇⢣⠀⢻⠿⠿⠿⠦⠀⠠ ⠉⣠⣶⠟⠁⠀⡼⠀⡇⠀⢇⠨⠈⠻⡀⠀⢀⠙⢻⡗⢤⣀⠸⢶⣄⡀⠜⣽⡿⠿⠋⡸⠁⢠⣼⣧⣗⠀⠀⠀⠸⠀⢧⠈⢇⠀⠀⠀⠀⠀ ⢸⠟⠁⠀⠀⠀⡇⠀⠀⠀⠘⠀⡇⠀⢹⡦⣾⣄⡀⠉⠂⠈⠑⠒⠽⠿⣖⠻⠓⠚⢋⣥⢚⡿⠛⣿⣿⠀⠀⠀⠀⠀⡘⣧⠈⡆⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢀⣹⡏⠙⡿⢷⣟⡛⠶⠶⢶⣤⣌⠳⡀⡶⣽⡱⠎⠀⠀⢹⣿⠀⠀⠀⠀⠀⡇⡟⣧⠘⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣇⠀⠘⣿⡽⣜⠀⣤⣽⡿⠦⡀⠀⠀⣈⣿⣿⠀⢀⠀⠀⠀⠀⢸⢹⡄⠀⠀⠀⠀⡇⢸⢸⢧⠈⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⡃⠀⠀⠘⣆⠀⢿⠀⣼⢻⠙⠺⣾⣿⡿⠛⠀⡨⢦⣴⢋⡿⠃⠀⢀⣀⣤⣀⡀⠈⡆⣿⠀⠀⡄⢠⡇⢸⣇⠀⠀⠀⠳⡀ ⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠘⢆⠸⡆⢹⠀⡇⠀⣿⠿⠷⠋⢸⢏⣾⡟⠘⠀⢀⣴⣿⣿⣿⠿⢿⡄⢃⢹⠀⠀⢣⣸⡇⢸⣿⡄⠠⡀⠀⢳ ⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⠈⢧⣻⡎⢳⣿⡸⣇⠀⣠⠶⣧⡞⡏⠀⠀⠀⣾⣿⠛⠛⠁⠀⠀⠱⡈⣼⡆⠀⠀⢻⡇⢸⣸⠷⣤⣿⡌⣆ ⠀⠀⠀⠀⠀⢀⣾⡏⣼⠀⠀⠀⢈⢻⣿⣆⠹⣷⡛⠉⠙⠊⠛⠁⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⡇⠹⣝⣧⣤⣤⣿⣾⢏⡔⠈⣿⣷⠘ ⠀⠀⠐⠒⠚⠛⠉⣧⣿⡆⠀⠀⠘⣆⠙⠮⠙⠺⣷⣦⣀⣀⡀⠠⠀⢀⣀⠄⠀⠀⠉⠛⠑⠒⢤⡷⠃⠀⢹⣿⣟⠉⡽⠛⣾⣶⣶⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡿⣽⡇⠀⠀⣧⢿⠃⠀⠀⠠⠭⠟⢛⡿⠯⢍⣉⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⡇⣇⡠⢿⣧⡜⠑⣶⠊⠈⢿⣿⡝⣿⣌ ⠀⠀⠀⠀⠀⣀⡞⢻⢻⣇⠀⠀⢸⣸⣷⣄⠀⣒⠒⠶⢤⣭⣿⣿⣷⣯⣟⣛⠛⠷⣦⡴⠿⠂⢙⠋⠀⠀⢠⣿⡧⠤⣿⣿⣷⣮⣻⣿⣿⠈ ⠀⠀⠀⠀⣸⣿⡀⠈⢸⣿⣄⠀⠸⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠉⠙⢿⡏⠛⠶⣮⣿⣆⣀⠈⠀⠀⣰⡼⠛⢿⣿⣿⣿⣯⡀⠉⢿⣿⠀ ⣄⣠⣤⣾⡿⠿⠇⠀⠘⣿⢹⡄⠀⢹⡿⣍⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⣄⠀⢨⣻⢉⣉⣑⢶⡟⢉⡉⠒⠛⢿⣿⣿⣿⣯⣞⠻⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠛⠛⠿⣦⣄⠀⠀⠀⢀⣾⠟⠁⢠⣿⠁⠀⣠⣶⠾⠛⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠈⠙⣳⣦⣰⠟⠁⠀⠀⠸⣿⣦⣼⢫⣥⣤⣄⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⡁⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠉⢿⣿⠷⠿⢿⣦⣤⣾⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⡟⠉⠻⢷⣦⣄⣀⣤⣶⣿⡿⠉⠁⠀⠛⠛⢷⣦⣀⣀⣀⣴⣿⠟⠛⠿⣶⣿⡉⠛⢿⣿⣷⣤⣤⣤⣶⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⢀⣽⠟⠉⢠⠟⢀⣠⣶⠶⠶⣶⣦⡀⠉⠉⢿⣿⣶⣆⠀⠀⠈⠻⣷⣤⣾⡟⠀⠀⠀⠀⢉⣼⡿⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⢀⣠⣤⡶⢞⣿⠃⠀⠀⠀⣰⡿⠋⠀⢠⣾⣿⣿⣿⡀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠹⣿⣿⠀⣀⣠⣴⣾⠿⠋⠁⠀⠀⠀⠀ ⣠⣤⣶⡿⠿⠛⠉⠁⠀⣼⡏⠀⠀⠀⣼⡿⠁⠀⠀⢼⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⠇⠀⠀⠀⢀⣿⠿⣿⣟⣻⡿⣷⡄⠀⠀⠀⠀⣀⡀ ⡟⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠁⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠹⣿⣄⣀⣀⣀⣤⣾⠏⠀⠹⣿⣇⠀⠈⠻⣷⣶⣶⠿⢿⡇ ⠿⣶⣤⣀⣀⣀⣀⣀⣸⣿⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠈⣽⡿⠃⠀⠀⠀⠀⣀⣉⠛⠛⠛⠉⠀⠀⠀⠀⠈⣿⣧⠀⣰⡇⠀⠀⠀⢸⡟ ⠀⠀⠉⣿⡟⠛⠛⠋⢹⣿⡀⠀⠀⠀⠈⠻⣷⣦⣤⣴⡾⠟⠁⠀⠀⣠⣾⠟⠛⠛⠻⣶⡀⠀⠀⠀⠀⠀⠀⢘⣿⣰⡿⠁⠀⠀⠀⣾⡇ ⠀⠀⠀⢻⣿⣤⣤⣶⠾⠻⣷⣄⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⢀⣾⡿⠟⠁⠀⠀⠀⣴⡿⠀ ⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⣹⣿⡷⢾⠟⠛⠛⣿⣶⠀⠀⠀⠀⠀⠘⣿⣄⡀⢀⣠⣾⠏⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⣠⣾⠟⠁⠀ ⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⣸⡇⣠⣴⣿⣥⣀⣀⡀⠀⠀⠀⠈⠙⠛⠛⠋⢁⢀⣀⣤⣾⣿⣿⣭⣤⣤⣤⣤⣶⠾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⣰⣿⣿⡟⠁⠀⠈⠉⠙⠛⠿⠿⠿⠶⠶⠾⠿⠟⠛⠛⠉⠉⠀⠓⢦⣌⡉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣧⣄⣀⣴⡾⠟⠉⡽⠻⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⣼⣧⡾⠿⠋⠀⠀⠀⠀⠀⡀⢀⣀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⣠⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠞⠋⠁⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠉⠻⣿⣦⣤⣤⣀⠀⠀⠀⣀⣀⣀⣠⣤⣴⢾⡟⠛⠉⠁⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠟⠉⠀⠀⠀⠀⢀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠁⠀⠀⣀⣀⣤⣴⣾⣷⠶⠿⠛⠛⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠻⣿⣿⡛⠿⣿⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⢀⣠⣴⣿⣿⡿⠛⠋⠁⢀⣀⣀⣀⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠿⠿⢿⣿⣷⣤⣙⠻⠿⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⡿⠃⠀⣠⣶⣿⣿⣿⠟⠁⠀⣠⣶⡿⠿⠛⠛⠛⠛⠿⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠁⠀⠀⠀⣠⣴⣿⣿⠿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⠟⠀⣠⣾⣿⣿⡿⠏⠁⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⢹⣷⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠏⠀⠚⠉⠉⠉⠉⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⠀⠀⠀⠀ ⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣿⡇⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⢹⣿⠀⠀⠀⠀ ⠀⣾⡟⠀⠀⠀⠀⠀⠀⢀⣤⣼⣷⠿⣿⣷⡀⠸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣤⣤⣤⣠⣤⣤⣤⣤⣴⣶⣿⣟⠀⢸⣿⡇⠀⠀⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣼⡧⠻⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⠿⠋⠉⠀⠈⠉⠙⠛⢿⣿⣿⡇⠀⠀⠀ ⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠉⠛⠿⢿⣷⣶⣶⣶⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⢀⣀⣠⣄⣀⣀⠀⠀⠉⠻⣿⣄⠀⠀ ⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⡾⣿⣿⠏⠀⢀⣴⣿⠟⠛⠛⠛⠿⣷⣆⠀⠀⠘⣿⣦⠀ ⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠋⢉⡉⠁⠀⣴⣿⠏⠀⢀⣾⣿⣿⣤⣤⣄⣀⠀⠈⣿⣇⠀⠀⢹⣿⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⢀⣾⣿⡏⠀⠀⣾⡿⠋⣿⡿⠁⣿⡏⣿⣿⢻⣿⡄⠀⠘⣿⡆ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢸⣿⡿⠀⠀⢸⣿⣧⣤⣿⣤⣤⣽⣤⣽⣯⣤⣿⡇⠀⢠⣿⠁ ⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⣼⣿⠀ ⢻⣿⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢀⣿⡏⠀ ⠈⣿⡇⠀⠘⣧⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⣼⣿⠀⠀ ⠀⢻⣷⡀⠀⢻⣇⠀⠀⣿⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⢠⣿⠃⠀⠀ ⠀⠘⣿⡇⠀⠀⢻⡆⠀⢻⡆⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⢸⣿⠀⠀⠀ ⠀⠀⢹⣿⡄⠀⠀⢻⣆⠈⣿⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠈⢿⣷⠀⠀⠀⠹⡆⠈⣧⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠈⣿⣇⠀⠀ ⠀⠀⠀⠸⣿⣆⠀⠀⠀⠹⡀⠘⡆⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠤⢬⣛⠶⣄⠀⠀⠀⠀⠀⠀⣾⡟⠀⢸⣿⣁⡀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⢹⣿⠀⠀ ⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⢻⠀⠹⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢶⣤⣀⠉⠳⢯⣶⡀⠀⠀⠀⣰⣿⠃⠀⣿⣿⠛⠛⠛⠳⠶⣦⡀⠀⠀⢻⣿⡀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠈⣧⠀⢹⡄⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⠈⠉⠀⠀⠀⣿⡏⠀⠀⣿⠇⠀⠀⠀⠀⠀⠈⠻⣧⡀⠘⣿⡇⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠸⣇⠈⢿⡀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠲⠶⠶⣤⣤⣀⠀⠀⠙⠿⣦⡀⠀⢸⣿⠀⠀⢠⣿⠀⣀⣀⠀⣀⣀⣀⣀⣘⣿⣄⣿⡇⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠙⣦⠈⢷⡀⠀⠀⠀⠉⠷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣶⣄⠀⠈⠙⠆⣿⣿⠀⠀⢸⣿⠛⠛⢿⡟⠻⣿⠛⣿⡏⠉⢻⣿⠁⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠈⢳⡀⠙⣦⣀⠀⠀⠀⠘⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡄⠀⣿⣿⠀⠀⢸⣿⣧⡀⣼⣧⣠⣿⠀⣸⡇⢠⣿⡏⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠙⢦⡀⠉⠛⠶⣄⡀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣿⣿⠀⠀⠀⢿⣿⡟⠉⠉⠙⠛⠷⣿⣿⣿⡟⠀⠀⠀⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠙⠷⣄⣀⠀⠙⠳⣤⣀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡀⠀⠀⠀⠻⣿⣦⣄⣀⣀⣠⣴⣾⠟⠀⠀⠀⣸⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠉⠓⠶⣤⣀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⢀⣾⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠉⠛⠒⠤⣤⣈⠙⠛⠛⠛⠻⠶⢤⡤⠀⠀⢈⡻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠶⠦⢤⣀⣀⠀⠀⠈⠉⠛⠿⠿⣷⣶⣶⣶⣶⣶⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⠻⠿⣷⣶⣶⣶⣶⡿⠿⡛⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⣠⠞⠁⠀⢀⠀⢠⠎⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠳⡼⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡔⠁⢠⠞⠁⠀⠀⢠⠋⢠⠋⢀⡾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⢀⠀⠀⠀⠀⠰⡄⠘⡷⡀⠀⠀⠀⠈ ⠀⠀⠀⢠⡿⢋⠔⣰⠃⣠⠂⠀⢠⠏⢀⠏⢀⠞⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠃⢸⠀⠀⠀⠀⠀⢱⡀⠀⠙⠆⠀⠀⠀ ⠈⠀⣴⠋⡴⣣⡾⠁⣰⠃⠀⢀⡞⠀⠀⢠⠎⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠁⠀⡇⣾⡀⠀⠀⡀⠀⢆⢇⠀⠀⠀⠠⠀⠀ ⣠⠞⢁⣼⡷⢻⠁⢠⠏⠀⢀⠞⡇⠀⢀⡎⠰⠇⢸⡀⠰⠀⠀⠀⠀⠀⠀⠀⠠⣀⣴⡟⠀⠀⠀⡇⣿⣇⠀⠀⢳⠀⠘⣿⡄⠀⠀⠀⠀⠀ ⠀⢀⡾⠋⢀⠇⠀⡏⠀⢀⠎⠀⡇⢰⡿⢀⣠⣤⠾⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠏⠉⠙⠳⣦⣥⢹⢿⡀⠀⠈⡆⠀⢹⣧⠀⠀⠀⠀⠀ ⢀⡾⠁⠀⡼⠀⣸⠁⢀⡎⠉⣀⣷⣾⡟⠉⠉⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⡏⣰⠁⠀⠀⠀⠀⠀⢹⣼⡞⣇⠀⠀⢣⠀⢸⣿⡀⠀⠀⠀⠀ ⠈⠀⠀⠀⡇⢠⣿⠀⡸⠐⠉⠀⠈⠛⠳⠀⠐⠒⠒⠮⢷⡀⠀⠀⠀⠀⣸⣧⠇⠀⠀⣠⠤⢀⣀⠈⣇⡏⢻⡦⠄⢸⠀⠈⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⠏⢸⢀⠇⠀⠀⠀⠀⠀⠠⠤⠤⠄⠠⠤⠈⢿⣆⠀⠀⢠⠟⡿⠀⠀⠈⠀⠀⠀⠀⠀⠸⣵⠀⢧⠀⢸⡄⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡀⡿⢾⣄⣀⣠⣶⣶⡶⠶⠶⣶⣶⣶⣦⡄⠀⠀⠑⠦⠼⠸⡇⠀⠀⢉⡁⢲⡖⠤⢄⣀⠙⣇⠈⡆⢀⡇⠀⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⣤⣼⢿⡯⠭⢤⣀⣀⠀⠀⢠⠏⠉⠀⡠⠄⠠⠄⠢⠔⠂⠄⠒⠾⣛⠛⠛⠻⠿⢷⣬⣙⣦⢸⣸⡇⠀⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠈⠻⠧⢀⣴⠀⠠⠭⠁⠀⠀⠹⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠥⣙⣦⡤⠄⠐⠬⣿⣿⣿⡇⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⡖⢒⡛⢁⣨⣿⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⡼⠀⠀⡰⠀⠀⠀⠀ ⠀⠀⡄⢰⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡰⠁⠀⠀⠀⢀ ⠀⠀⣷⡿⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡗⠀⡸⠁⠀⠀⠀⠀⠈ ⠀⢀⣿⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⢡⣤⣤⣤⣤⣤⣉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡿⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⣀⣻⣿⣿⣿⣿⣿⣿⣶⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⢿⠿⣷⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⡴⢃⣴⢥⠀⠀⠀⠀⠀⠀⠀ ⠀⣌⣤⣿⠀⠀⢧⠀⠀⠀⠀⣠⠖⠢⣄⠀⢸⣿⣿⡿⠛⠛⠿⠟⠛⠻⣿⠃⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠚⠱⢞⣵⣞⣀⠀⠀⠀⠀⡠⠚ ⠀⣾⠏⢹⠀⠀⠈⣧⡀⠀⣏⠀⠀⠀⢸⠀⠈⣿⡏⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⣰⠏⣠⠆⠀⠀⠀⠀⡀⣼⠏⢠⣄⣠⠖⠀⠀ ⠀⢿⠀⠈⡇⠀⢸⣿⣿⣄⠈⠳⠤⠤⠊⠀⠀⣈⠽⢒⣒⣒⣲⡿⠋⠇⠀⠀⠀⠀⠀⣠⠞⢁⡴⠃⠀⠀⠀⠀⢠⡌⡃⢠⣿⠟⠁⠀⠀⠀ ⠀⠘⡄⠀⡇⠐⠋⠈⠉⠛⢷⣄⠀⢀⡖⣢⢀⠏⠀⠀⠀⠙⡄⠃⠀⠀⠀⠀⢀⡠⠞⢁⡴⣿⠃⣠⡤⢶⡿⡆⡜⠉⢁⣾⠃⡰⠁⠀⠀⠀ ⣷⡀⢇⣰⡧⠂⠀⠀⠀⠀⠀⠘⣷⣄⠉⠉⠸⠆⠀⠀⠀⠀⢿⠀⠀⠀⢀⠴⠋⣠⠴⠋⢰⠃⠀⠀⢸⠋⠚⠋⠀⢀⣾⢇⡼⠁⠀⠀⠀⡜ ⢻⠳⠸⡟⠢⢄⣀⠀⠀⠀⢀⣰⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣙⣠⠴⣊⡥⠖⢋⣁⡤⢴⣻⠂⠀⠐⠇⡀⠀⠀⢀⣾⣟⡞⠁⠀⠀⠀⠀⠀
⡟⠈⠁⠀⠀⢠⠃⢸⠀⠀⢀⡇⠀⢃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡴⠀⠀⠀⠉⠘ ⠃⠀⠀⢀⣴⠎⠀⠸⠄⠀⠾⠀⠄⠸⣄⣀⡴⢀⠀⠤⠄⠚⠀⠀⢣⠣⠤⠀⡠⠀ ⢉⠉⠉⠀⠂⠀⠒⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠤⠀⠀⠀⠀ ⣬⣶⣶⡶⠶⠶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠁⣀⣤⣴⣶⢶⣶⣶⣶⣅ ⡟⠉⠠⠀⣠⣶⡿⣷⣯⡛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣫⣿⣿⣷⣤⠀⠀⠉⠻ ⡇⠀⠀⢰⠁⠻⠑⢺⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⢏⠓⢹⡗⡇⠀⠀⠀ ⠳⠀⠀⠀⠣⣑⠈⢁⡡⠃⠀⠀⢀⡤⣄⠤⠀⠀⠀⠀⠀⠣⣑⠉⢐⠱⠃⠀⠀⠸ ⠀⠀⠀⠀⢀⡀⣀⡠⢀⢄⠪⣂⡵⢋⠱⢒⢀⠀⠀⣠⠔⡂⠤⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⢈⣅⢞⠌⠊⠐⡡⠜⡡⠒⡡⢒⢥⢢⢗⡫⠐⠉⠀⠀⣂⠅⡢⠕⠀⠀⠀ ⠄⠠⣪⠾⠋⠀⢀⠄⡊⠔⣁⢔⡭⢞⢯⠪⠂⠁⠀⢀⠠⠐⠩⢐⠥⠂⠀⠀⠀⠀ ⡇⠋⠁⠀⠀⠀⠀⠈⠀⠈⠀⠀⢂⠔⠉⠉⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡍⠉⣉⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢠⠉⠉⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋ ⢡⠈⢳⣅⡀⠀⠀⠀⠀⠀⠀⢸⡄⠈⠂⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀ ⢸⠀⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠎⠐⢤⡤⠔⠁⠆⠀⠀⢀⣀⣤⣶⡿⠁⠀⠀⠀
⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣾⣛⢿⣛⡟⡿⣶⣦⣄⣀⣤⣾⡟⣯⢻⡽⣛⢯⡟⡿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⣿⢿⣯⣿⣝⣳⠿⣞⡵⣫⣗⣧⣯⣿⣿⣽⣶⣹⡞⣭⢗⣯⡳⣽⢳⣭⣛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⠿⠛⠛⠛⠛⠛⠷⣯⣿⢿⣮⣿⣿⣯⠿⠷⠟⠟⠿⠾⢿⣿⣿⣾⣶⡹⢧⡟⣶⡹⣎⢿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⡿⢯⣥⣶⣦⣄⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠙⢷⣟⣿⢧⣻⡜⣷⡹⣞⣳⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡟⢰⣿⡿⢻⣿⣻⣷⠀⠀⠀⠀⠀⢸⡿⣿⣿⠿⣿⡿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣶⡻⣜⣳⡭⣟⣯⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣧⠈⢿⣷⣶⣿⣿⠏⠀⠀⠀⠀⠀⣿⠖⣿⣧⣄⣸⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⠿⣏⢷⣣⢟⡽⣞⡿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⢷⣄⣉⠙⠉⠀⠀⠀⢀⣠⣴⢿⡻⣷⡈⠻⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⣠⣶⢿⣿⢎⡿⣼⢳⣝⣮⢻⡽⣞⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣮⢷⡹⣿⣷⣦⣤⣀⣀⣀⣀⣠⣤⣶⣾⣻⣽⢿⡹⣞⣵⢫⣗⠾⣜⡧⣿⠽⣯⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⢶⡻⣝⢮⡳⣝⢶⡹⣞⡼⣣⢟⡭⣟⢷⣿⣯⣿⢿⡿⢿⣟⡻⣝⢯⡞⣧⡻⣼⢎⡷⣚⣯⢳⡝⣾⣻⣽⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣯⣷⡿⣿⢿⡿⣿⢿⢿⡿⣾⢷⣿⣾⣽⣞⣶⣳⢎⡷⣹⢳⡞⣵⣛⣮⢽⣲⡝⣧⢯⡳⣏⡞⣧⣛⣷⣛⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢺⣻⣯⣷⣻⡿⣿⢿⡿⣿⣾⣷⣿⣯⣾⣧⣿⣝⣯⡟⣿⢿⣷⣯⣾⣱⢏⡞⣧⣳⢻⡜⣧⢟⡼⣝⡶⣝⡾⣽⢾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢸⣷⣟⣿⡽⣯⣟⣷⣻⣞⣷⣻⣽⢿⣽⡿⣿⣿⣿⣾⣷⣽⣹⣟⣿⣾⢵⣫⢗⣻⢼⣫⢞⡵⣻⢼⣻⣭⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⡾⣿⣳⣟⣾⣳⣟⡾⣽⢯⣿⣳⣿⣟⣾⣯⣿⣟⣿⣿⣾⣳⣿⣣⢟⡮⣝⣮⢳⢯⡝⣧⣟⣳⢯⣟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣽⣯⢟⣿⣳⣞⣷⣻⢾⡽⣯⢿⣳⣿⣳⡿⣯⣷⣿⣻⣯⣿⡿⣿⢷⡹⣞⡽⣺⡜⣯⢞⣽⢲⣯⢟⣽⠇⠀⠀⠀⠀ ⠀⠀⣠⣶⠶⠶⠿⡯⠾⠿⠿⠿⠷⣿⣮⣟⣯⢿⣽⣻⣟⣾⣽⣟⣿⣳⣿⣿⠿⣽⣽⡟⣮⢳⡝⣾⣱⣻⣜⢯⣞⣻⢮⣿⠋⠓⠚⠒⠓⣦ ⠀⠀⢼⡁⠀⠒⢀⠀⠀⣳⣅⠀⠀⠀⠉⢻⣞⡿⣞⣷⠟⠉⠉⣩⠙⠙⠛⣿⣻⣿⢫⣞⣵⠟⠛⠉⠉⠉⢉⠛⢻⣯⣟⣿⠀⠀⠄⠠⢰⡇ ⠀⠀⢺⠄⡈⠔⠠⢀⣡⣿⣿⠀⡈⠐⡀⠂⣿⣿⡟⠀⡀⠄⣁⣿⡍⠠⠐⡉⢻⣧⣟⡞⠁⢠⠀⢂⣐⣬⣤⣜⣾⣿⣟⣿⠠⠈⠤⢁⢸⡅ ⠀⠀⢺⡅⠐⡨⠐⡀⢲⣿⡿⠐⠠⠑⠠⢡⣿⣿⢀⠒⡐⠠⢸⣿⡇⠠⢑⠀⢢⣿⣿⡁⠌⡄⡈⠤⣿⣿⡿⠿⠟⠻⣿⣯⡇⢈⡐⠄⡾⠄ ⠀⠀⢼⡆⠑⡄⠣⢐⠠⢩⡑⢨⢐⣡⣣⣿⣿⣿⠀⢆⡘⢠⢻⣿⡇⠰⢨⠘⣠⣿⢻⡆⡘⢄⠰⡈⣿⣿⡇⠠⠌⢒⣿⣿⣟⣒⣚⣍⣁⠀ ⠀⠀⢸⡇⡘⢄⠣⢌⠒⣿⢿⠿⠿⢿⣭⣳⣭⣻⣧⠂⡜⢠⠺⣿⠃⡜⢠⢃⣼⣯⠿⢷⣌⠢⣁⠒⡌⢡⣂⠱⡈⡜⣿⢿⡇⢄⠢⡐⢼⡆ ⠀⠀⠘⣧⣼⣦⣵⣮⡶⡿⠏⠀⠀⠀⠀⠉⠙⠋⠙⠷⢼⣦⣥⣧⣼⣴⡧⠿⠃⠀⠀⠀⠻⠷⢦⠷⡼⢾⡿⠶⠷⠾⠏⠈⠷⠾⠶⠵⠾⠃ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⣀⣴⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⣤⣠⣿⡷⠿⠙⠻⠟⠋⠠⠿⠶⣶⡴⣦⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠺⢿⣧⣴⣤⠀ ⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡗⠀⠀⠀⠀⠀⢀⡼⠛⠀ ⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⣄⣀⣀⢀⣀⣠⣴⠿⠛⠳⠶⠦⢤⣤⣀⡼⡧⠀⠀ ⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⢻⣄⢧⠀⠀ ⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⢀⣠⣦⣤⣀⠀⠀⠀⠀⠀⠘⡇⠀ ⠙⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡏⠀⠀⠀⢠⣿⠟⡛⣏⠉⠉⠙⠓⠀⢰⡾⠻⡿⠇ ⠀⣿⡇⠀⣠⣤⣤⡀⠀⠀⠀⢠⣾⠟⠂⠀⠀⠀⠀⠀⢀⡼⠿⣯⡀⠀⠀⢀⡼⢇⡰⡇⠀ ⠀⠹⣿⢰⣿⣿⣷⣯⡳⢦⡀⠘⣿⡀⠀⠀⠀⠀⠀⠰⠉⠀⢸⣿⡟⠀⠀⢸⡷⠻⢿⣟⠂ ⠀⠀⢹⡌⢫⣳⢰⣿⣿⠸⣿⡌⢛⣏⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⠀⠀⠀⠀⠃⠀⢾⡇⠀ ⠀⠀⠀⢳⡜⣏⠘⠟⢹⣄⣿⡁⢙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⠀ ⠀⠀⠀⠈⣧⠘⢣⡄⠀⢹⠿⣷⣾⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠀⣤⡄⢀⣰⣤⡿⠀ ⠀⠀⠀⠀⢸⡇⠀⣼⡓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠙⢾⣁⡾⠃⠀ ⠀⠀⠀⠀⠸⢧⢼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⣤⣤⣶⣶⠊⣽⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣟⢰⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡞⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
︶︶︶ ⊹ ︶︶︶⠀୨♡୧⠀︶︶︶ ⊹ ︶︶︶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠊⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡧⣄⠀⠀⠀⣸⠾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⣶⣸⢠⣤⡄⣧⣶⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⠟⢃⣴⣾⣧⣼⣿⣵⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⢶⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢽⣶⣌⠻⠿⢛⣽⣿⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠀⠙⠻⣿⣿⣿⣿⠿⠃⢀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢠⣾⠁⠀⠀⠀⠈⠛⠛⠋⠀⠀⠘⢧⡀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡄⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣰⡟⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢻⣄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣸⡟⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢻⡆⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣰⡿⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⢿⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣰⡿⠁⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢿⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⣰⡟⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢻⣦⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣼⡟⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⢻⣆⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠹⣧⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠘⢷⣽⣄⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣄⠀⠀⠀⠀⠀⣀⣀⣀⣤⣶⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀ ⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣢⣄ ⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠿⠿⢿⣷⣦⣀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⢠⣿⠋⠀⠀⢀⣴⣶⡿⠿⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠟⠁⠀⠀⠀⠀⠀⠈⠛⠻⣷⣄⡀⢀⣰⡿⠋⠀⠀⠀⣿⣿⣀⠀⣴⡿⢟⣁⡀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣾⠋⠀⠀⠀⠀⠀⠙⠻⢿⣿⣧⣼⣟⠻⣿⣦⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡿⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣟⠻⠿⠿⣿⣷⣤⣼⣿⡟⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡿⠙⠻⢿⣷⣤⣀⠀⠀⣠⣴⣾⣿⣿⠋⠁⠀⠀⠻⠟⢿⣷⣤⡀⠀⠀⣀⣠⣾⣿⠿⠛⠿⣿⣮⣿⠉⠙⠻⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠉⢛⣿⣿⠟⠉⢰⡟⠁⠀⣀⣤⣤⣤⣤⣄⡈⠉⠛⠿⠿⣿⣿⣏⣥⡀⠀⠀⠀⠙⣿⣷⡀⠀⣼⣿⠋⠉⠉⠉⠉⠙⠛⢛⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⢀⣠⣤⣾⠋⠀⠀⠀⠛⠀⣴⣾⡿⠛⠉⣁⣽⣿⣿⣤⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⢻⣿⣿⣿⠏⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣇⣠⣤⣶⠾⠟⢩⣿⠏⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⣴⣿⣿⣿⣻⣿⡄⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣿⣄⣠⣤⣴⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣴⣾⣿⠿⠟⠛⠉⠀⠀⢠⣿⡟⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣽⣿⢿⣿⣿⣛⣫⣽⣿⣦⡀⠀⠀⠀⠀⠀⠀⣀⠀ ⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠻⣿⣿⡋⠀⠘⠻⣷⣤⣄⣀⣠⣾⣿⣿⠀ ⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⢼⣿⡇⠀⠀⠀⠀⠀⠈⠻⠿⣿⣷⡟⠀⠀⠀⠀⠀⠙⠻⢿⣶⣶⣶⣾⡿⠟⠋⠀⠀⠀⠙⢿⣧⡄⠀⠀⢨⣟⠻⠛⠛⠉⢸⣿⡀ ⠛⠿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣿⡇⠀⠀⠀⠀⠈⢿⣷⣀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⣀⣠⣤⣔⣈⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡄⢀⣾⡇⠀⠀⠀⠀⢸⣿⡁ ⠀⠀⠀⠉⣿⣿⠛⠛⠛⠉⠉⣿⣿⡀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣄⣤⣶⣿⠿⠋⠀⠀⠀⠀⣠⣾⡿⠛⠋⠛⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⣾⡿⠁⠀⠀⠀⠀⣼⣿⠀ ⠀⠀⠀⠀⢿⣿⣆⣀⣀⣠⣤⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⣿⠛⠁⠀⠀⠀⠀⠀⢻⣿⠆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⠀⣰⣿⠏⠀ ⠀⠀⠀⠀⠸⣿⣏⠙⠛⠋⠉⠀⠘⢿⣿⣦⣀⣠⣤⣤⣤⣤⣦⣄⡀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⣤⣿⡿⠟⢻⡏⠉⠉⠉⣹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣤⣠⣤⣾⡿⠋⠀⠀⠀⠀⠀⣠⣴⣾⡿⠋⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢀⣠⣾⣿⣯⣤⣀⡀⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⣀⣴⣾⣿⣿⣿⣥⣤⣤⣤⣤⣤⣴⣶⠿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣿⠟⠋⠉⠉⠙⠛⠛⠿⠿⣿⣶⣶⣶⣴⣶⣦⣾⣶⡶⠿⠿⠟⠛⠋⠁⠙⢦⣍⡉⠙⠋⠙⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⢀⣴⣿⠟⠻⣿⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣦⣶⣿⡿⠛⠁⢀⣼⠋⠛⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⣼⣯⣴⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⢀⢀⢀⣀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠟⠛⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⡿⠟⠛⠉⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈⢻⣿⢿⣶⣦⣤⣄⣀⣀⠀⠀⣀⣀⣀⣀⣤⣶⣶⣿⢿⣛⡋⣉⣀⡀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣇⠄⠚⠉⠁⠀⠀⠀⠀⠀⢀⠐⣾⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠘⠀⠀⢸⡇⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡀⣄⠀⠀⠀⠀⡀⠉⠈⠛⠦⢀⣧ ⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠈⣧⠀⠰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣷⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢱⠏⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⣿⠇⠀⡆⠀⠀⢻⡄⠀⠀⠀⠀⢼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡄⣿⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⡟⠀⠀⠀⠀⠹⢤⣀⣀⣀⣰⡷⢿⡀⠀⢧⠇⠀⠸⣿⠀⠀⠀⠀⡾⣷⣀⣀⣀⣠⡤⠤⢴⡞⠛⠉⠁⠀⠀⠀⠀⠸⢶⠇⠷⠤⢤⣄⣀⣀⣀⡇⠀⠀ ⠤⣤⠤⠤⠤⠤⠶⠒⢻⠅⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠈⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠤⠔⠒⠒⠒⠲⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠖⠒⠒⠒⠒⠒⠒⠢⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣴⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⣀⣠⢽⣷⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣠⡆⠀⠘⠁⠀⠀⠀⠀⢀⣀⣠⣴⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣟⡁⠀ ⣤⣾⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⢻⣿⡿⢿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⢀⣠⣤⣴⣾⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿ ⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣬⡉⠛⠿⣿⣗⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣫⣿⡿⠛⣫⣵⣾⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿ ⣏⠀⠀⠀⠀⠈⠁⠀⢀⣴⣿⣿⣿⣿⠿⠿⣿⣿⣿⣶⡠⠈⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠒⠀⠀⠀⠀⠘ ⡿⠀⠀⠀⠀⠀⠀⠀⣿⠋⢹⡿⣿⠧⣄⡤⠼⡿⡇⢈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠿⣿⣽⠿⣿⢻⣧⣼⡆⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⢻⡀⠈⠀⣰⠇⣹⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠈⣇⢷⡀⠀⠁⠀⡸⢻⡇⢸⡇⠀⠀⠀⠀⠀⠀⢐ ⣿⡆⠀⠀⠀⠀⠀⠀⠻⣆⠘⢧⡀⠙⠲⠔⠁⡴⠃⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠙⣆⡙⠶⠴⠋⢁⡼⠀⣸⠃⠀⠀⠀⠀⠀⠀⣸ ⠘⠿⠄⠀⠀⠀⠀⠀⠀⠙⢦⡈⠉⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⣂⣄⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠈⠉⠀⠀⠀⠉⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠛⠋⠁⠀⠀⠀⢀⡤⠂⣠⠴⠏⢊⣵⡾⠛⣁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⡴⠚⢁⠴⠋⣁⣥⣾⠟⠋⠀⣻⠿⠋⠁⠀⠀⣀⠀⠀⣀⠀⣀⣴⡾⠗⠁⣀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠿⠛⣩⠿⣟⠿⢋⡠⠞⢉⡠⠚⢁⡠⣾⡿⠋⠁⣠⠴⠋⠀⣀⡦⡊⠐⢋⡠⠔⣫⢴⡺⠟⢉⣠⠴⠛⠁⠈⠉⠙⢛⣳⠶⠃⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠊⠀⣀⠴⣛⡵⢋⡥⠞⠉⡠⠒⠙⠀⢀⡤⠚⠁⣀⡴⠟⠁⢀⣤⠾⠛⣋⡤⢒⣡⢔⡫⠟⣋⣤⠖⠋⠀⠀⠀⠀⠀⠠⠚⠉⢀⣠⠴⠛⣡⡤⠊⠀⢀⠠⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⢀⡴⢞⣽⢞⣩⠶⠋⠀⠀⠀⠀⠀⣠⠖⠋⢀⣤⠞⠉⠀⣠⡶⠛⢁⡴⢚⡭⠖⣩⠖⣉⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⢉⣠⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⡀ ⢈⠄⠀⠀⣠⠖⣫⠴⣫⠖⠋⠁⠀⠀⠀⠀⣀⡴⠚⠁⣠⠶⠋⠀⢀⣴⠟⢉⡴⣾⠿⢊⣡⠖⣩⡴⠚⠁⠀⡀⠒⠉⠀⠀⠀⣀⡤⠖⠋⠁⣠⠶⠋⢁⣤⠔⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⡇⠀⠐⢉⣴⣿⠷⠋⠀⠀⠀⠀⠀⠀⡠⠞⠉⣠⡴⠋⠁⣀⣴⠞⢋⣤⣾⠟⠋⡡⠖⣉⡴⠛⠉⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠐⠋⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⠀⢾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠠⠞⠋⠁⠀⠈⢉⡤⠔⠀⣠⠾⠟⠛⠛⠳⢤⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⡗⣶⠒⠲⠖⠶⠶⠶⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣸⡇⣿⢨⣅⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠛⠙⡇⠻⠷⣤⠷⠞⠛⠛⠛⠷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿ ⣿⡟⠻⣦⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀ ⢻⡁⠀⢹⣷⡀⢣⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀ ⠘⡇⠀⠀⠙⢿⣦⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀ ⠀⣧⠀⠀⠀⠈⢿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⣆⠀⠀⠀⠱⠀⠀⠀⠀⠀⢀⣴⠋⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠈⢿⣿⣿⢿⡿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⠑⢦⣀⡀⢀⠀⠀⣀⡴⠟⠁⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣟⠿⣶⣄⣀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⣹⠛⡟⠛⠉⠀⠀⠀⢙⠃⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣲⣦⣤⣴⣂⡠⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢔⣵⡿⣛⣻⣿⣛⡻⣿⣿⣷⣕⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣰⡮⠿⢷⡮⢖⠒⣪⣝⣛⣒⡹⡿⣿⣎⠄⠀⠀⠀⠀ ⠀⢀⢮⡿⡡⣤⡀⠀⢈⢶⣉⠉⠁⠲⡙⢯⠹⡞⢿⡞⢄⡀⠀⠀ ⠀⠘⣿⣇⠳⠾⠇⠀⣎⢯⣽⡇⠀⠀⢸⢸⣠⣿⠿⠉⠑⢪⢆⠀ ⢀⢜⣟⣙⣫⡖⠒⠈⠉⠢⠄⠀⠤⢒⠕⠁⣿⣿⣧⡞⠙⡽⡇⡆ ⢸⢏⠴⣶⣦⣤⣭⣉⡒⠢⠬⣉⡉⠁⠀⠀⢻⣿⣽⡓⠶⢁⣇⡇ ⠀⠳⢕⡦⣙⠻⣿⣿⣿⣿⣶⣦⣍⡓⠤⡀⠀⣿⣿⣷⢖⣫⠾⠁ ⠀⠀⠀⢨⡸⢰⡿⠛⢋⠽⠛⠻⢿⣿⡦⢸⣰⣟⣟⡾⠉⠁⠀⠀ ⠀⠀⠀⡌⡇⣾⠁⠀⠀⠀⠀⠀⢀⡽⢡⠏⣨⢎⡾⠁⠀⠀⠀⠀ ⠀⢀⣀⡁⡇⣿⠀⢀⣤⣤⡄⢴⣯⢴⡧⣞⡵⠋⡀⠀⠀⠀⠀⠀ ⠀⢊⠉⡍⠻⠛⠛⡿⠁⣤⡜⢁⣠⣉⡞⣓⠉⡍⣹⠟⣛⣷⠀⠀ ⠀⢸⡀⢠⣆⠸⢃⣇⡈⠻⠀⡸⠯⠀⡘⢚⣃⣧⣈⠓⠂⢱⡃⠀ ⠀⠘⠿⠿⠛⠛⠓⠛⠷⠶⠮⠵⣶⡮⠗⠚⠛⠛⠛⠫⠭⠿⠃⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣦⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡋⠄⡌⠀⢤⣴⠾⠿⠛⠛⠛⠛⠛⣛⠻⢷⣦⣀⣀⣀⡴⣾⢿⣿⣇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠀⠁⠈⠀⠀⠀⣀⣤⣤⡶⢶⣿⣾⣿⡿⠿⠛⠋⠉⠻⣿⣿⡔⣩⣷⣽⡆⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠁⠚⠛⢩⣭⣴⣴⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⢧⡂⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣟⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣀⣄⢢⡀⢃⣻⡄⠀ ⣻⣿⣿⣿⣿⣿⣿⡏⡐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠰⣴⣶⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣦⣵⣂⣿⡇⠀ ⡹⣾⡙⣿⣿⣿⡟⢡⠐⣁⠂⡔⠀⡀⠀⢀⠀⢠⡰⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣀⣆⣰⣤⣤⣡⣙⣛⢿⣄ ⡿⠡⣘⣿⣿⣿⠍⡆⣍⢐⠢⢄⢃⡐⠌⣄⣚⡾⠃⠀⢀⠠⠀⠃⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣯⡃⣿ ⠁⠣⢼⣿⣿⣿⡚⢴⡨⢎⡱⣩⠲⣌⣷⡾⠋⠀⠠⠈⢁⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣳⠿ ⠀⢡⢿⣿⣿⣯⡝⣦⣓⢧⠳⣵⣿⡿⠃⡀⢄⢂⣡⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠞⠉⠀ ⣤⢮⡻⣏⢷⣚⡼⣳⢯⣞⣽⢟⢫⡐⣡⠜⣠⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⣿⢣⡟⡭⣖⢧⡹⣏⡷⢪⡑⢎⠦⡱⣁⢞⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⡟⢦⡻⣵⢫⡎⡵⢫⡜⠥⡘⣬⡗⣡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⣝⢺⡽⣞⡽⣮⡑⠣⡜⣡⢰⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⢎⡳⣽⢯⣟⢶⡡⢃⠼⡐⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⣍⠞⣭⣟⡾⣣⢗⡩⢺⣱⢈⡱⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⡌⣏⠷⣭⢳⢏⢮⣑⢻⣿⡀⢲⣏⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡜⢬⡛⣜⢣⠞⡜⡬⢿⣿⠀⠢⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡜⢢⠝⡌⢧⡛⣬⠱⣻⣿⠀⡑⢼⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢡⢋⠼⣡⠝⡼⣇⡣⣿⡆⡘⢬⣿⣽⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢡⠎⡜⢢⢇⡻⣜⢻⣧⡹⣷⡌⢳⢞⣿⣧⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⠜⣌⢣⢚⡴⣩⢞⡽⣷⡽⣿⢨⢻⣿⣿⣽⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠡⢍⢢⢃⡞⣰⢣⣏⠾⣽⣷⣻⣧⢣⢿⣾⢿⣷⢭⡻⣿⣿⣿⣿⣿⣿⣿⢿⣳⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠱⣈⠦⡓⡼⣡⢗⡮⣟⢶⣫⣟⣿⣧⢊⣿⣿⣿⣷⡹⢎⡿⢿⣿⣿⡿⣯⣟⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠡⢎⢲⡹⣔⣣⠞⣵⢫⡾⣱⢞⡿⣿⣿⡌⣿⣿⣿⣿⣯⣼⣫⡝⣎⣳⣭⡿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠒⠚⠓⠒⠒⠢⣄⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⡉⠓⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢖⠊⠉⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢴⠶⢖⣪⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⠦⡀⠀⠙⢆⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⣰⠋⠀⢀⡠⠔⠚⠛⠓⠦⢄⡀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠛⠲⢤⡀⠀⠘⣆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⣤⣤⣭⣶⣤⣧⣤⣴⣯⣤⣤⣤⣤⣤⣤⣤⣽⣦⣤⣤⣴⣯⣤⣤⣤⣤⣤⣤⣤⣽⣦⣤⣼⣦⣤⣼⣤⣤⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⠛⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⠟⢿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⢹⣿⣿⣿⣉⡿⢿⣩⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣷⣏⡽⢿⣏⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⡽⠃⠀⡀⠙⢿⣿⣿⣷⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡟⠸⣿⠟⠛⠛⠛⠛⠿⠿⠿⠿⠟⠉⠀⠀⠀⠙⢦⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⢘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣧⠀⠀⠀⠀⠀⠀⡴⣶⣶⣦⣤⣤⣄⣄⣤⣤⣴⣶⣶⣿⡆⠀⠀⠀⠀⠀⣼⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⢹⡏⠒⠒⣦⡤⠤⠤⢤⣤⣔⠒⠚⣿⠁⠀⠈⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢀⡏⢧⡴⢺⡽⡼⠤⣤⣾⣏⡏⠳⢤⠏⣇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⢀⠀⣾⠀⠀⠀⠀⣧⠹⣆⣠⠟⢸⠃⠀⠀⠀⢸⣄⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⠀⠈⠳⢤⣀⡀⠘⡆⡗⠛⣇⡏⠀⢀⡠⠖⠋⠈⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⢠⡴⠋⠀⠀⢳⡧⠔⣿⠃⠀⠈⠳⣤⠀⠀⣧⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠁⠑⣆⠀⠀⠸⡆⠐⡟⠀⠀⢀⠜⠁⠀⢠⢹⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠴⢶⣦⡀⣶⣰⣷⣀⠀⠀⣸⠀⠀⣿⠀⠀⠀⠀⠈⢳⡀⠀⣷⢻⣷⢶⣶⣿⡶⣴⡶⠚⢸⠀⢤⣼⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣟⣿⠀⠙⣿⣷⣆⡏⢀⣄⠃⠀⠀⠀⣀⣀⠀⠹⡄⠘⡟⢀⡞⢠⣿⢰⣿⠀⠀⢸⠀⣏⡹⣦⣸⣿⣇⣉⠀⠀⢀⡀⠀⠀ ⠠⣶⣏⣿⣿⣿⠢⠴⢾⣿⠑⣿⡟⠻⣿⡦⠄⣿⡟⠛⣿⡿⠿⡄⢃⡞⠤⣼⣿⠉⣿⠀⠀⠀⠘⣿⡟⠛⢹⣿⡏⠉⠠⣾⡟⢿⣦⠄ ⠀⠈⢻⣿⣿⣿⠒⠒⢾⣿⠀⣿⡇⠀⣿⡇⠠⣿⡇⠀⣹⡇⠀⠛⠚⠀⠐⢾⡿⢰⡿⠀⠀⠀⠀⣿⡇⠀⢸⣿⡇⠀⠀⣿⡷⠚⠁⠀ ⠀⣠⣴⣿⡟⣿⣶⣤⣼⡿⠀⣿⣧⣄⣿⡇⠀⣿⣧⡤⢿⣧⠀⠀⠀⠀⠀⣸⣷⣯⣤⣶⣤⣀⠀⣿⣇⡀⢸⣿⣧⣠⢀⣿⣧⣤⡤⠀ ⠈⠉⠀⣿⡇⣿⠉⠛⠃⠀⠀⠀⠉⠉⠁⠀⠀⣨⣟⣀⣈⣿⡧⠀⠀⠀⠚⠉⠁⠀⠈⠉⠛⠁⠀⠙⠋⠀⠀⠈⠉⠀⠀⠉⠉⠉⠀⠀ ⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣦⣦⣦⣶⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠉⠀⠀⠀⠀⠀⠀⠙⠉⠁⠈⠉⠛⠛⠻⠿⠿⢶⣦⣀⡀⠈⢿⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣼⣇⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀ ⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠀⠀⠀⢻⣆⢠⣦⣤⡶⠛⠋⣿⠇ ⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠁⠀⠀⢸⡇⠀ ⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀ ⠀⢰⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆ ⠀⠈⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠄⠀⢹⡇ ⣠⣤⣀⠀⠿⣿⡀⠀⠀⢐⡆⠀⠀⠀⠀⠀⢀⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⣄⠀⠀⠀⠀⠀⠀⣀⣴⣶⡟⠋⠁⠀⠀⢸⡇ ⣿⣯⠙⠻⣷⣿⠃⠀⣠⣾⢿⡆⠀⢀⣤⡾⠟⠁⠘⢿⡀⠀⠀⠀⠀⠀⣀⣴⠿⠉⠀⠀⠹⣷⣄⠀⣀⣴⠾⠋⠉⢹⣿⡀⠀⠀⠀⣿⡇ ⠙⣿⠀⠀⠀⢠⢞⣼⠟⠁⠀⣧⣴⠟⠁⠀⠀⠀⠀⠘⣷⡀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋⠁⠀⠀⠀⠀⣹⡇⠀⠀⢰⡿⠁ ⠀⢹⣆⠀⠀⢸⡿⠃⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⡴⠟⠁⠀⠀⠀⢀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⣿⠁⠀ ⠀⠈⠻⢷⣶⣼⣇⠀⠀⠀⠀⠀⠀⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⠁⠀⠀⠀⠀⠀⢻⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⢠⣶⣶⠶⠾⠟⠛⠉⠙⣿⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠻⠶⠶⠶⠶⠶⠾⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠳⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⣤⡶⠛⠛⠛⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⣿⢀⣤⣤⡶⠾⠛⠁⠀⠀⠀⣠⡶⠟⠛⠛⠻⢷⣄⠀⠀⠀⠀⠀⠘⢿⣄⡀⠀⠀⠀⢀⣾⠋⢻⠀⠀⠀⠀⠀⠀⠀⠟⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠹⢧⣤⡴⠾⠛⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠠⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢄⣤⣴⠾⠏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠸⣧⠀ ⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣄⡀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡙⠛⠛⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠻⣴⣶⣶⣦⣤⣙⣶⣄⡀⠄⠒⠀⠀⢉⢅⠒⣆⠬⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣰⠟⠉⠙⡏⢏⣠⠋⠁⠀⠀⠀⠀⠀⠀⠁⠑⡀⠙⠕⢍⠣⣠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡽⣦⠀⠀⠀⠀⣄⡀⠂⣤⣀⣑⣦⣘⣄⠀⠀⠱⣌⠁⢀⠀⠀⠀⠀ ⣿⣿⢟⣻⡿⠡⠀⠂⠀⢚⡄⠙⢌⡳⠚⢯⡉⢢⣽⣻⣶⢠⠀⠹⠆⠈⣿⣧⡀⠀ ⢋⠴⠋⠀⠂⠀⠀⠘⢆⠀⡙⢆⠄⠱⣤⡀⣿⡿⢋⢁⣸⣷⠀⠀⠘⢀⢊⠉⠁⠀ ⠋⠀⠀⢰⠀⠀⠀⠀⢈⣿⠗⣤⣤⢤⢤⣈⢁⡁⡔⡝⠉⢷⡄⠀⠀⢸⣆⢦⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⡇⣈⡯⢦⣰⡿⠂⣀⠠⣿⠁⠂⠀⠀⢸⣧⠀⠀⠀⣼⠃⠡⡀ ⠀⠀⠀⠀⠀⠀⠡⣸⢸⣰⢀⡟⠂⢠⣿⠓⠀⣠⣶⡿⠻⡈⣸⠀⢠⠀⢻⡀⡄⡱ ⠀⠀⠀⢠⡇⠀⠀⠙⣵⡙⢯⠇⠊⠛⠁⠀⠰⣿⣄⠀⠀⢘⠱⣦⣨⣷⣞⠍⣿⡜ ⠀⠀⠈⠉⣰⡇⠀⡼⣌⠈⠹⠷⣦⡤⠤⠀⠀⠀⠉⠈⠰⡏⢀⣿⠫⣈⠽⣿⣿⡻ ⠀⠀⢀⣠⠻⣇⠀⢠⣷⣄⣒⣒⡬⠵⢾⣯⣟⡲⢬⠒⠊⠉⠁⣹⣇⣿⣶⡝⣿⡏ ⣄⣠⡼⠟⠀⣟⣇⠈⣿⡻⡿⠉⠀⠀⠀⠈⠃⡉⠱⣳⠂⠤⡼⢋⠹⢿⣿⣶⡸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣴⣶⢶⣒⡂⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡔⠍⠋⠀⠀⠀⠒⠂⠠⠄⡀⠀⠀⠁⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠉⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠀⠷⠀⣀⠀⠈⠢⡀⠀⠀ ⠀⠀⠀⣀⡴⠃⠉⠁⠈⠑⠒⡖⢲⠁⠀⠀⢀⣀⣀⠀⠀⠑⣄⠀⠐⡄⠀ ⠀⡠⠉⡐⢀⣤⣶⣶⢤⣰⠞⠀⡎⠀⡠⠊⠁⣠⣶⣭⡲⡄⠁⢳⡀⠘⡀ ⠘⡇⠀⠇⡇⣼⣿⣿⣷⠋⠀⠀⢿⠀⢳⣀⠀⣿⣿⣿⣿⢰⡄⠀⢳⠀⢱ ⠀⢹⢴⣀⡑⠛⠛⠛⡏⠀⠀⠰⢦⣣⣄⣉⣓⣛⣛⣿⠽⠋⠀⠀⠀⢣⢸ ⠀⠀⢳⠁⠈⢩⠗⣊⣁⠀⠀⣤⣤⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾ ⠀⠀⡆⠀⠀⠀⠑⠩⠏⠁⠀⠈⠉⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄ ⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃ ⠀⠈⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⠀⢷⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣣⠀⠀⠀⠀⣸⠀ ⠀⠀⢸⡅⢠⠉⠲⣶⡤⢶⠖⢿⣿⡟⠲⣶⡶⠖⠉⠀⡄⠀⠀⠀⠀⡏⠀ ⠀⠀⠀⢷⠸⠀⠀⠈⠉⠛⠲⠬⠿⠗⠚⠉⠀⠀⠀⠰⠁⠀⠀⠀⣸⠇⠀ ⠀⠀⠀⠘⣧⠀⠀⠀⠀⠠⠀⣀⡀⠀⠀⠀⠀⠀⠠⠃⢀⡀⠀⢠⡟⠀⠀ ⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢠⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣎⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡙⠳⢦⣀⣀⣀⣀⣠⠴⠟⠁⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠁⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬜⬜⬜⬛⬜⬜⬜⬛⬛⬛ ⬛⬜⬛⬜⬛⬜⬛⬜⬛⬛⬛ ⬛⬜⬛⬜⬛⬜⬛⬜⬛⬛⬛ ⬛⬜⬛⬜⬛⬜⬛⬜⬛⬛⬛ ⬛⬜⬛⬜⬛⬜⬜⬜⬛⬜⬛ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛
⠀⠀⠈⠟⢛⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⢄⡴⢦⡀⠀⠀⠀⠉⠛⠒⠛⠉⠉⠀⠀⠀⠀⠀⢠⡴⠚⣟⠛⠓⢦⣄⣀⣠⣤⣼⡆⠀⢀⣩⣀⣤⣆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡞⠀⠀⠻⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⠚⠉⠀⠀⠠⠤⠀⠀⠀⠙⠁⠀⠛⠿⢿⣬⣍⡉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⢩⡟⠁⠀⠘⢿⡻⢿⡲⣌⡛⠆⠀⠀⠀⠀⠀⢀⡞⣡⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠀⠀⢀⡤⣾⡤⠾⢧⡀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠏⠀⠀⢀⣀⣈⣿⣄⠙⣮⠙⢦⡲⣄⠀⠀⡴⠋⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠚⠛⠓⠚⠚⢓⣠⡴⠞⠋⠀⠀⠀⢳⡀⠀⠀ ⢀⣀⠊⠁⠲⢄⡀⠀⠀⠀⠀⠀⢡⡏⠠⠾⠭⣭⡀⠀⠀⠈⠀⠈⢣⡀⠙⢦⣴⣏⠤⠤⠴⠿⠿⠧⠤⠤⣄⣉⣙⣲⠀⠾⠷⢄⡀⠀⠤⢄⡤⣶⡾⢿⣿⠤⡶⠆⠀⠀⠀⠀⢣⠀⠀ ⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⢠⡿⠀⠀⢠⡾⠋⠀⠀⠀⣀⣤⠤⠲⠇⠀⠀⠁⣠⡆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢤⣈⣠⡴⠞⣩⠞⠋⠐⠋⢁⣞⣁⡀⠀⠀⠀⠀⠘⡆⠀ ⠀⠠⠂⠀⠀⠉⠓⠶⢤⣤⠴⣾⡇⠀⣔⣁⣀⠤⣠⠴⠋⠁⠀⠀⠀⢀⡄⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢉⡹⠇⠀⠀⠀⢿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣿⠇⠈⠁⣸⠇⢞⡥⠀⠀⠀⠀⢀⡴⠋⣠⡟⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠀⠀⠀⠈⢳⡄⡄⠀⠀⠀⠀⠀⣾⣯⠀⠀⠀⠀⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⡘⠀⣠⠞⢁⡴⠋⠀⠀⢀⡆⢀⡞⠀⣰⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⢰⠏⠀⠀⠀⠀⠀⠉⠙⣄⠀⠀⠀⠀⠈⢿⡁⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠞⠁⣠⠏⠀⠀⠀⢀⠟⠀⡞⠀⡼⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⡇⠀⠀⠀⠀⢰⡀⠘⠳⣄⠀⠀⠀⣆⡇⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⡟⠡⠈⣠⠋⣠⠇⠀⢀⡞⠀⠀⠀⡼⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡇⠀⡇⠀⠀⠀⠀⢀⢧⠀⠀⠈⢧⡘⢦⢿⠃⠀⠀⠀⠀⠀⢧ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⣠⡾⠁⢰⠇⠀⢀⣾⡇⠀⠀⡼⠁⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⣇⢸⣧⠀⠀⢤⠀⠘⣞⣆⠀⠀⠈⠓⠈⠻⣆⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⢀⣰⠋⢀⣼⡾⢻⠇⢀⡟⠀⢀⡞⢹⡇⠀⣸⠁⠈⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⢿⣀⡀⠀⢹⢸⣿⠀⠀⠈⣧⠀⠸⣻⡀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠁⠁ ⠀⠀⠀⠄⢀⡞⣡⢀⡾⠋⠀⡏⠀⣾⠀⢀⡞⠀⢸⡇⢼⢃⣠⣴⠾⢻⡄⠀⠀⠀⠀⠀⠀⠀⢠⠀⡼⠋⠀⠈⠙⠳⣼⡖⡝⣆⠀⠀⢹⡀⠀⣿⡇⠀⠀⠀⠀⠀⠘⠏⠀⠀⠐⠠⠠ ⠀⠀⠀⣰⣯⡞⢡⡿⠁⠀⣸⠁⢰⠇⠀⣼⢁⡡⠼⣷⢿⠉⠁⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⣾⣴⠁⠀⠀⠀⠀⠀⠈⣷⣧⢻⡀⠀⠘⡇⠀⢹⢻⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠁⠀ ⠀⠀⠜⣳⠏⢠⣾⠃⠀⠀⣿⢠⣿⠀⢰⠃⠉⠀⠀⠈⠙⠂⠀⠀⠛⠛⠾⢷⡄⠀⠀⠀⠀⣼⣯⠏⠀⢀⣠⠤⠤⠄⠀⢸⣻⠈⢷⠂⠀⣇⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀ ⠀⣞⣾⡟⠀⢸⢸⠀⠀⠀⣿⡏⢸⡄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⢿⣦⡀⠀⢠⢿⣿⠀⠀⠈⠀⠀⠀⠀⠀⠈⢿⡆⠘⡆⠀⢹⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀ ⢌⠟⡞⠀⠀⠈⣿⠀⠀⠀⢻⡅⢸⠻⢧⣀⣀⣴⣶⡶⠶⠶⠶⣶⣦⣔⡶⠀⠀⠀⠙⠶⠿⢸⡇⠀⠀⢉⡉⢹⣖⠲⠤⢀⠈⢷⡀⠹⡀⣸⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿ ⠆⡔⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⡇⣤⣤⡿⣿⠿⠄⠀⣀⡀⠀⠀⢸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠻⢛⣛⠛⠛⠻⠿⣦⣬⡳⣤⣷⣿⡆⠀⠇⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⢠⠀⠀⠀⠀⡾⠀⠀⠀⠀⡶⢸⡇⠙⠿⠄⣘⡆⠀⠤⠍⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠠⣌⣳⣤⣶⠒⠲⣽⣿⣷⣿⠉⡇⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⡄⠀⠀⠀⢀⡇⠀⠀⠀⢸⠃⣾⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢶⠰⠞⠋⢁⣹⡿⣷⠀⠀⢀⡟⠀⠀⠀⢠⠂⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⣼⠀⠀⠀⢠⡏⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡾⠀⠀⠀⠀⡼⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⡇⠀⠀⠀⣼⢃⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⡼⠁⠀⠀⠀⢠⡇⠀⠀⠀⠀⣺⣿ ⠀⠀⠀⢰⠃⠀⠀⠀⣏⣼⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠅⢀⡼⠁⠀⠀⠀⠀⣟⡛⢀⠀⠀⠀⣿⣿ ⠀⠀⢠⣾⠀⠀⠀⠀⣿⡟⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⢻⣀⣠⣄⣀⣉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⡞⠁⠀⠀⠀⠀⠸⠁⢀⢸⠀⠀⠀⣿⣿ ⠀⠀⡼⣼⠀⠀⠀⣿⣿⣿⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠁⠘⣿⣿⣿⣿⣿⣿⣶⣌⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⣠⠟⠀⠀⠀⠀⠀⢀⡀⠀⠀⣸⠀⠀⠘⣿⣿ ⠀⢠⣿⢧⢠⠀⣴⣿⡟⣷⠟⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⡼⠃⠀⠀⠀⠀⠀⠀⠊⠀⣠⣰⠏⠀⢀⠄⠘⠟ ⠀⣸⠃⢈⢸⠘⣿⣽⣅⢿⡆⠈⢧⡀⠀⠀⠀⠀⣀⣤⣀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠊⣠⠞⠁⠇⠀⠀⠀⣠⠴⢚⡿⠃⠀⠀⡞⠄⠀⠀ ⠀⣿⠀⢸⣿⠀⠉⡍⡽⢿⢣⠀⠘⣷⡀⠀⢠⠚⠉⠀⠈⢳⠀⠹⣿⠏⠀⠀⠀⠀⠀⠀⣀⡟⠀⠀⠀⠀⠀⠀⠀⣴⢟⡁⠀⠀⠀⠀⠀⠀⠛⠇⢀⡜⢀⡴⠋⠀⠀⠀⣼⠁⠀⠀⡀ ⠀⡿⠀⢸⣿⡇⠀⢿⠃⠘⣿⠀⣄⣿⣷⣄⠈⠷⣄⣀⣀⠏⠀⠀⠛⣦⡤⠤⠤⠤⣴⡶⠟⠀⠀⠀⠀⠀⠀⣠⠞⢁⡾⠁⠀⠀⠀⠀⠐⠒⠂⢠⣿⡿⠋⠀⠀⢀⢀⣸⡟⠀⠀⠀⠈ ⠀⡇⠀⠀⢻⣯⡄⠚⡆⠀⣿⣴⣼⠏⠿⢿⣧⡀⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⢯⠉⠁⠀⠀⠀⠀⠀⠀⣠⠞⢁⣴⡿⠀⠀⢀⣠⣀⠀⠠⠁⢀⣾⠏⣰⠃⠀⠀⠞⣸⢿⡗⠀⠀⠀⠀ ⠀⣧⠀⠀⠀⢻⣇⠀⣇⢀⣿⣧⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠀⠀⠀⠀⢀⡴⠞⢁⡴⠛⣿⡿⠛⠛⣽⠏⠀⠀⠀⢀⣾⠋⣵⠃⠀⢀⠆⣴⡿⡞⣷⠀⠠⠶⣦ ⡀⢰⠄⠐⠒⠺⣿⣆⢸⣿⣛⠁⠀⠀⠀⠀⠀⠀⣸⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⠖⣋⡤⠖⠋⢀⣸⡿⠁⢀⣶⠃⠃⠀⠀⢀⣾⡟⣾⠃⠀⢀⡎⡼⣿⡧⠘⣎⢇⡀⠀⠀ ⠀⠈⢄⠀⠀⠀⠘⣮⣿⣧⠈⠑⠶⣄⡀⢠⣠⣶⣿⣿⣿⣏⢀⣄⡀⠀⠀⠀⠀⠺⠶⠿⣗⣉⡡⠴⠖⠚⠉⠿⠁⠀⠸⣽⣀⠀⠀⢀⣾⡟⣽⡿⠀⢠⢿⣾⠁⣿⠥⠤⣌⣿⣇⣀⣀ ⠒⠒⠀⠀⠀⠀⠀⠈⠛⠚⠛⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⡈⠙⠛⠒⠒⠒⡃⠉⢉⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡉⡃⣠⣿⣿⣿⡟⠀⠰⢫⣿⣧⠤⠟⠛⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠤⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠂⠁⡠⡀⠀⠀⡀⢀⡀⡀⡭⠖⠠⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠺⠊⠛⠙⠵⠃⠘⠀⢩⠄⠀⠑⡑⡀⡀⢖⢬⢢⡀⠀⠀⠀⠀ ⠀⠀⠰⠁⣆⢄⠀⠠⠀⡄⣄⢀⢂⣳⡀⠀⠈⣸⡸⡀⠹⡣⡙⢄⠀⠀⠀ ⠀⠀⣧⢄⠕⡞⡄⡀⣇⢳⣽⢻⣀⡙⠿⣃⣄⣽⡉⣿⢎⢾⣶⡈⠀⠀⠀ ⢀⡔⠑⠅⠐⠠⠑⡠⢉⠪⣞⣀⡵⢾⡦⠀⢈⡿⢶⣿⢸⢸⡇⠇⠀⠀⠀ ⠀⠣⡀⢀⠐⡁⠀⢛⠛⡢⡛⠡⢤⡼⠇⠀⢽⡆⠿⢟⡿⣧⣄⡀⠀⠀⠀ ⠀⠀⡈⢓⢡⠸⡌⠢⡢⣘⠢⣀⠀⠀⠀⠀⠀⢜⠠⣿⣇⣀⠠⠃⠀⠀⠀ ⢠⠐⠐⠙⠈⠐⠽⣄⠈⢓⢇⠲⠁⠒⠀⡀⢄⣢⣽⡏⢯⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡨⠹⡟⡄⠢⣎⢧⡀⡇⡀⠩⢝⠛⡫⣆⠀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠇⡇⡇⠈⢣⡀⠑⡱⡁⢁⠀⠀⢺⢇⠈⢧⡀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡄⡇⠁⠀⠀⠙⢄⠈⢴⣉⢶⡎⠱⣄⠉⠀⠿⢄⠷⣄⠀⠀ ⠀⠀⠀⢀⢆⠃⡿⠀⠀⠀⠀⠀⠑⠄⠙⢿⣿⣀⠙⢟⠤⡀⠀⠑⠨⣳⡀ ⠀⠀⢀⢪⠎⢠⡯⠩⠁⠂⠌⡢⠀⠈⢢⡌⠳⣌⠓⠠⠍⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠋⠀⠈⠀⠀⠀⠀⠀⠈⠁⠒⠶⢿⠚⢦⠱⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠣⠜⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡠⠖⠋⠁⠀⠀⠉⠁⠒⠤⡀⢀⡀⠤⠐⠒⠒⠒⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠋⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠒⠉⠁⠀⠀⠀⠈⠉⠒⢬⣆⠤⠤⠤⠀⠀⠠⠤⠤⢼⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢄⣒⣒⣀⡼⠦⡀⠀⠀⠀⠠⠤⠤⠤⠤⠭⢒⡄⠀⠀ ⠀⠀⠀⢀⠤⠐⣈⠤⠒⠉⠀⠀⠀⠀⠀⠉⠚⣶⠒⠂⠉⠉⢁⣀⣀⣈⣉⡚⣧⡀ ⠀⠀⠰⠍⣈⣉⣀⡀⠤⠔⣲⡞⣿⣧⣄⠀⠀⠹⠒⠀⠉⢁⣴⣛⣿⣷⣆⠀⠈⠃ ⠀⠀⠀⠀⠀⣑⠢⣄⠀⠸⣿⣟⣿⣤⣿⠧⠔⡧⠤⠀⢀⣸⣿⣽⣷⠼⠿⢦⡶⠁ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙⢴⠖⢒⣉⠁⢐⣒⢤⡠⠐⠊⠉⠐⠲⢇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠒⠒⠒⢠⠋⠀⠀⠀⠀⠀⠀⠀⠑⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⣼⣿⣁⣵⡖⠛⠉⠉⠉⠙⠒⢦⠀⠀⣍⢙⠂⣯⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠈⠈⠈⢩⡇⠄⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢰⡟⡿⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⢠⡟⢀⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡇⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠏⠉⢿⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⢠⠟⠀⠀⠀⠀⠀⠀⢠⡿⠀⣼⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⣏⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⠀⠀⠀⠀⡷⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡄⠀⠀⠀⠀⢠⠟⠀⠀⢸⡿⠁⣀⣤⠴⠲⠒⠺⡾⠀⠀⠀⡞⢰⠈⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⡇⠀⠀⠀⠀⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⣧⠀⠀⠀⣰⠋⠀⠀⢠⣿⢶⣞⣭⣤⣶⣶⣖⣋⡀⠀⢀⢸⠁⣸⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡼⠀⠁⠀⡀⠀⢀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠘⠆⢀⡾⠃⠀⢀⣼⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣦⠆⠀⢠⡏⠀⠀⣀⣀⡟⡄⠀⠀⠀⠀⠀⠀⢀⣼⠞⢁⣴⣾⣏⣭⣶⣟⠁⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣄⣴⠟⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢉⡻⣯⠛⠢⡼⢁⡴⠞⠁⠘⡇⠇⠀⠀⠀⠀⠐⢢⠟⠀⣰⣿⣿⣿⣿⠿⠿⣿⣷⣠⠞⠉⣽⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠁⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠉⠹⣟⢷⡴⠛⠋⠀⠀⠀⠀⡧⠀⠀⢀⡀⠀⢠⠏⠀⣴⣿⣿⣿⣿⣿⣆⡀⠈⣿⣟⠓⢲⡏⠿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡆⢀⣰⣿⣿⣿⣿⣿⡿⢿⣿⣿⡟⠉⣻⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⣏⡴⠋⢱⣿⣿⣿⣿⣿⡇⠉⢳⣸⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⠋⠹⠻⣿⣿⣿⣿⣿⣾⡏⠛⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⣿⡏⣻⣿⣿⣉⠀⠀⠀⣿⠃⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡆⠀⠀⠻⣿⡿⣿⠀⠀⠀⣠⣀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡙⠋⠙⣿⣿⠁⠀⢰⠏⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⠻⣷⣄⠀⠀⠀⠛⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⢀⣾⠃⠀⢀⠏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠙⠓⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⡃⠀⠄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠓⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠤⠶⠤⠤⠤⣤⡼⠷⠤⠤⠤⠤⠴⠦⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⢤⡤⡤⠤⣤⡤⠤⢤⣤⡤⠤⢤⣤⡤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠬⠤⢤⣤⢷⡤⠀⠀⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⢀⣉⣁⡀⢀⣠⣶⣾⣿⣿⣿⣿⣶⣤⣌⠀⠀⠉⠉⠛⠛⠛⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣷⣀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⣿⣿⣿⣿⣿⠁⢱⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢾⣷⣀⠀⠀⠀⢀⣠⣾⣿⣿⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⣦⣴⣿⣿⠿⢾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣀⡀⠀⠀⣀⣠⣽⣿⣿⣤⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⡾⠿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⣠⣤⣦⡶⢉⣽⣿⣿⣿⣿⣿⡿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⡾⠋⠁⣨⣶⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣠⣶⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⡀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠁⣰⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⠳⢧⠀⠀⠰⡿⠛⠛⠻⠿⡿⠿⠶⠀⠀⢠⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⣿⡟⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⣡⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠒⠒⠒⠀⠚⢉⣠⣴⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⠿⠿⠿⠿⠟⠛⠿⣿⣿⠋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠒⠒⠒⠒⠒⠒⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠞⠉⣀⣠⠦⠴⠆⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⡻⣿⡶⣦⡀⠀⠀ ⠀⠀⣴⠋⣠⣶⠟⢋⡤⠶⠶⠶⢶⡀⠀⠀⠀⠀⠀⢀⡴⠛⠉⢉⣿⡶⡍⠀⠀ ⠀⣼⠁⠚⠛⠁⢠⠏⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢠⡏⠀⠀⠀⠙⠛⠁⣇⠀⠀ ⢰⡇⠀⠀⠀⣠⣼⠀⣾⣿⡆⠀⠀⢸⡇⠀⠀⠀⠸⣆⠀⠀⠀⠀⣀⡼⢻⡀⠀ ⣸⠀⠀⠀⠈⠉⠎⠳⢭⣉⣀⣀⣠⠞⠁⠀⠀⠀⠀⠈⢙⡿⠛⠉⠉⠛⢾⡇⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠤⠤⠤⠤⠤⢲⡟⢁⣴⠋⠛⢳⡄⠹⡆ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡿⠀⣾⣹⣋⣏⣟⣷⠀⡇ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡏⠀⠀⠀⠀⣹⢠⠇ ⢹⡄⢣⠀⡆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⢠⠇⡾⠀ ⠈⣧⠈⢃⢹⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⣿⠀⡇⠀ ⠀⠸⡆⠀⢇⢃⠀⠈⡆⠀⠀⠀⠀⠨⢕⣄⠀⠀⠀⡟⢸⣃⡀⠀⠀⢿⠀⢹⠀ ⠀⠀⢻⡄⠈⡌⣆⠀⢡⠀⠀⠀⠈⠉⠓⢬⡑⠀⣸⠁⣾⠀⠈⠙⢦⢸⡇⢸⠀ ⠀⠀⠀⢳⡀⠘⠌⢄⠀⠑⢄⠀⠈⠉⠓⠦⡉⠂⣿⠀⣿⠒⡖⡖⡖⢻⠃⢸⠀ ⠀⠀⠀⠀⠻⣄⠈⠢⣑⠢⢄⠑⠤⡀⠀⠀⠈⠳⣿⠀⠹⣏⠙⠓⣷⠟⠀⣼⠀ ⠀⠀⠀⠀⠀⠙⠳⣄⡀⠑⠂⠍⣂⠤⠀⢀⣀⠀⠹⣄⠀⠈⠛⠛⠉⣀⡼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠈⠁⠐⠒⠀⠀⠉⠙⠒⣶⠶⠚⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢤⣤⣠⣤⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠘⣿⡿⠟⠛⠛⠛⠷⢦⣤⣈⠉⠙⠻⠿⡟⠋⠀⢻⣿⡿⣿⣿⣿⣿⠟⠋⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣠⣴⣋⡥⠴⠒⠒⠒⠒⠢⠤⣈⡙⠻⢶⣤⡀⢀⣤⠞⠛⠋⢉⣉⣉⣉⣉⠛⠒⠶⢤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⢀⣾⠟⢉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡈⠛⣫⠤⠒⠋⠉⠉⠀⠀⠀⠉⠉⠙⠒⠦⣄⠉⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⢀⡾ ⠀⡼⢁⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢙⠞⢁⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡈⢿⣿⣿⣿⣿⠟⠀⠀⣠⡼⠋⠀ ⢰⠃⣿⣿⠋⠉⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⣿⣿⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢯⣽⠇⠀⢠⡾⠋⠀⠀⠀ ⢸⠀⢿⣿⣷⣤⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⣿⡅⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡏⠀⢰⠏⠀⠀⠀⠀⠀ ⠈⢧⡈⠛⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣰⣇⠀⠘⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣾⠀⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⣟⠲⠤⠤⠤⠤⠤⠤⣤⣤⢤⡴⠒⠋⠁⠘⢦⣄⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⡴⠂⡇⠀⣸⠇⠀⠀⠀⠀⠀⢠ ⠀⠀⠈⠙⢒⣶⠖⠒⠒⠒⠚⠋⠉⠉⠀⣀⢀⠀⠀⢻⡉⠓⠲⠤⢤⣄⣀⣀⣀⣠⠤⠴⠒⠉⢀⣠⡴⠊⠀⢰⡇⠀⣿⠀⠀⠀⠀⠀⢠⣿ ⠀⠀⡠⠖⠋⠤⠤⠤⠤⣤⣤⣤⣤⣴⡾⠋⠘⢷⣄⡀⠙⠳⢤⣄⣀⣀⣀⣀⣠⣤⠤⠴⠖⠚⠉⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⢸⡿ ⠀⢸⣁⣀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣉⣛⡛⠒⠲⠶⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⠀⠀⠀⠀⠀⣾⡇ ⠀⢸⣏⠀⠀⣠⣤⠶⠶⠶⠶⠶⠶⠶⢶⣦⣤⣤⣀⣈⠉⠙⠓⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡀⠀⠀⠀⠀⢸⡇ ⠀⠀⠹⣦⠀⠻⣄⠀⢘⣘⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠉⠙⠒⠦⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢸⡇⠀⠀⠀⠀⣸⡇ ⠀⠀⠀⠈⢳⠀⠙⣦⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠸⡇⠀⢻⡷⠶⠾⠿⠿⠇ ⠀⠀⠀⠀⢸⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⡇⠀⠀⠀⠀⠀⠀⣷⠀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠐⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢷⠀⢿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢿⡀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣀⠀⠀ ⠀⠀⠀⠀⢸⠀⠈⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣛⣯⡽⠾⠛⣉⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⠙⠲ ⠀⠀⠀⠀⠘⢷⣄⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⢉⣁⣀⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢹⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣠⣜⠫⠭⠭⠍⣓⠲⢤⡉⢃⠤⠟⠙⣛⡛⠥⠤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠞⣩⣤⣤⣄⠀⠀⠀⠉⠢⣍⠕⣈⣁⠀⠀⠀⠈⠁⠢⣉⠻⣿⣿⣿⠟⠉⣀⠜ ⠘⣼⡏⠙⣿⣿⠀⠀⠀⠀⠰⢁⣾⠿⣿⣷⠀⠀⠀⠀⠀⠀⠑⠋⢭⠏⢠⠞⠁⠀ ⠠⡘⢿⣿⡿⠋⠀⠀⠀⢀⡇⠘⣷⣤⣿⡿⠀⠀⠀⠀⠀⠀⡠⠒⡟⢠⠏⠀⠀⠀ ⠀⠫⠖⣒⣒⡒⠲⠶⠆⠁⠈⢢⠌⣉⠉⠀⠀⠀⢀⡀⠔⠊⡠⠂⡇⣸⠀⠀⠀⢰ ⠀⡤⠒⠥⠤⠤⠤⠤⠴⠃⢦⣄⡓⠤⠄⠉⠉⠭⠤⠒⠊⠉⠀⠀⡇⡇⠀⠀⠀⡿ ⠀⡖⠂⣉⡩⠭⠭⠭⢭⣍⣐⣒⠂⠭⢍⣁⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⡇ ⠀⠙⢆⠳⡄⣭⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣉⠑⠒⠤⡀⠀⠀⠀⢣⠸⣄⣀⣠⡇ ⠀⠀⢸⠀⢿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢱⠀⠀⠀⢸⡀⢻⠀⠀⠀ ⠀⠀⢸⠀⡆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠎⠀⠀⠀⠀⢇⢸⠀⠀⠀ ⠀⠀⢸⠀⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡡⠋⠀⠀⠀⠀⠀⠘⡌⡆⠀⠀ ⠀⠀⢸⠀⡇⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⠟⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⢄⡀ ⠀⠀⠸⣄⠉⠒⠂⠤⠤⠤⠒⢒⣚⠭⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣾⣿⣿⣾⣧⣴⣾⣿⣿⣶⣿⣿⣶⣿⣷⣶⣾⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢯⠁⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⡯⠆⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⢸⣿⣤⣄⡀⠀⠀⠀⠀⠀⣀⣚⣛⠛⠛⠋⠀⠀⠈⠑⠷⠶⠖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⡟⠛⠛⠿⢧⠀⠀⠘⠟⠛⠛⠻⠿⢿⣶⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠖⠲⢶⡀⠀⠀⠀⢀⣤⣤⣤⣤⣄⡉⠙⠓⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⢿⣄⣀⣠⡾⠋⠉⠀⠈⠙⣷⡄⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⣠⡿⠙⣯⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣤⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢉⡙⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠒⣴⡿⠁⠀⢸⣧⠀⠀⠀⠀⠀⣠⡞⠓⠛⠛⢿⣫⣽⣿⣿⣿⣿⣿⣿⠟⢋⣴⡾⠛⢿⡤⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⣾⠋⠀⠀⠀⠀⠉⠻⠶⠶⠶⠟⠋⠁⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⢃⣴⣿⣿⣆⠀⠸⠃⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⢠⣾⠇⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠁⠈⢹⣿⡯⠃⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠃⣠⠞⣻⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠏⠁⠀⠀⢠⡿⠋⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣾⣿⡿⠀⠀⠀⠀⠙⠧⠄⠀⠀⣼⣿⠏⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢳⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠙⢿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣽⡿⠋⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⣿⣿⣿⣿⣿⣿⠟⣶⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠁⣼⡟⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠰⡿⠿⠿⠿⠛⠁⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣿⠿⠟⠋⠁⠀⣠⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⣶⣶⣶⣶⠟⠋⠁⠀⠀⠀⠀⢀⣤⣤⣤⣶⠶⠾⠿⠿⠟⠋⠉⠀⠀⠀⠀⣠⠞⣱⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⣼⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡖⠛⠛⠛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠈⠻⢷⣦⣄⣀⣀⣀⣀⣴⡿⠟⠀⠀⠀⢀⣀⣴⣶⡿⢟⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣄⣤⢶⣾⣿⣿⠿⣿⣭⣟⣀⣀⣤⡴⢞⣫⣿⢟⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢼⣿⣿⣿⠈⢿⡿⠛⠒⣒⣚⣋⣭⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣝⣒⠂⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢧⣿⣿⣿⣿⠀⠀⣿⣿⣿⡿⣟⣿⣿⣿⣯⣵⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿ ⠀⠀⠀⠀⣀⣤⣤⣠⣴⣿⣿⣿⡟⣾⣿⣿⣿⡟⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⢋⡡⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿ ⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⡟⣽⡿⣿⣯⣿⣯⠀⣠⡶⠋⣼⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣿⣿⣿⣿ ⢠⣼⣿⣿⢟⣿⣿⣿⣟⣿⣿⢯⡿⣿⣿⢳⣿⣟⣾⣿⠃⣿⣿⡟⣿⣿⠋⢀⣼⣿⣟⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⡿⢻⣵⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿ ⢸⣿⡿⢫⣿⣿⣿⠇⣼⣿⣿⣾⣥⣿⡇⣾⣿⣿⣿⠏⠸⣿⣿⣿⣿⣿⢀⣾⣿⣫⣾⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⡇⢧⣿⣿⣿⣿⣿⣿ ⢸⡿⣱⣿⣿⣿⡏⣸⣿⣿⣿⣿⣾⣿⢰⣿⣿⣿⠁⠀⢠⡿⢿⣿⣿⣯⣿⢟⣿⣿⣿⣿⣿⣮⢿⣿⣮⡻⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣾⣿⣿⣿⣿⣿⣿ ⢸⢃⣿⣿⣿⡿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⢯⡴⠚⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⣻⣾⣿⣿⣿⣮⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿ ⢈⣼⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢻⣯⣽⣿⣿⣿⠘⡵⠋⠀⠀⣽⣿⣿⣿⣿⣿⣿⣟⣭⣾⣿⣿⣿⣿⣿⣿⣿⢛⣵⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣈⣀⡀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢟⣴⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣿⣿⡇⠾⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⡿⢋⣾⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠚⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠲⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠲⠦⣄⡀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠚⠉⠀⠀⠀⠀⣀⣉⠉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⢀⣤⠴⢶⣟⣻⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⣤⣞ ⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣽⣿⣽⣓⠲⢤⣄⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⣩⣶⡶⢿⡿⡛⠉⠙⢻⠛⢿⣿⠿⣿⣿⣿⣷⣶⣶⣿⠟⠁ ⣤⣤⣤⣤⣤⣴⣿⣿⡿⠟⠛⣻⢿⠛⠛⠛⠿⣶⣦⣍⠓⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡵⠖⠋⠉⠁⣰⠋⠈⠛⠿⣿⢾⠆⠀⠈⢧⡀⢈⣽⣿⣿⢟⠅⠀⠀ ⠀⠉⠛⢿⣿⣿⡍⠁⠀⠀⡼⠛⠻⢭⣵⣶⠇⠹⡆⠉⠙⠲⠄⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⢒⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣞⣭⡽⢿⣻⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢿⣷⣤⣴⣧⣶⡶⠶⣶⠖⠒⠚⠉⣹⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⠀⠀⢀⡠⠅⠀⢀⠨⠤⠃⠀⣧⢤⣖⣶⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⡟⣽⠋⢀⣉⠀⠂⣁⡠⠶⠊⠉⢀⣀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠀⠀⠀⠀⠀⡀⠤⠂⠀⠀⠀⠠⠐⠒⠋⠭⠿⠒⠈⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⠞⣉⡤⠚⣉⡤⠖⠉⠀⣀⡠⣶⡪⠟⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⢊⣁⠴⠊⠁⢀⡠⠖⠋⠑⠉⠁⠀⠀⠀⠀⠀⢠⣆⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠤⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⠀⣀⣀⣀⣀⣀⡀⠈⠙⠛⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣤⣾⣏⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣤⢀⣽⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣿⠟⢻⡟⠛⠿⣿⣿⠿⠟⠛⢻⠿⢧⠀⠙⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠸⣧⠴⠋⠀⠀⠀⢹⡇⠀⠀⢠⢇⡴⠋⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⢀⡾⠀⠀⣰⣫⠞⠁⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⡀⠀⠀⢀⣀⣠⣾⡟⠁⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠘⠻⠕⠋⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠶⠶⠖⠒⠒⠒⠒⠶⠶⠶⠶⢶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣛⣿⣷⣦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⣀⣠⣴⣶⡶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⠉⠛⠿⣿⣿⢿⣷⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠛⠁⣀⣴⣾⡿⠟⠋⢁⣀⣤⣤⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠿⠿⠿⣷⣮⣝⠻⠷⠀⠀⠀ ⠀⠀⠀⢠⣾⠏⢀⣴⣾⣿⡿⠋⢀⣴⡾⠟⠉⠉⠉⠉⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⢠⣾⣿⣿⠻⣷⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠴⠛⠛⠛⠁⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⣿⠀⠀⠀⠀ ⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀ ⠀⢰⣿⠀⠀⠀⠀⠀⠀⢤⣶⣿⡇⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠙⣿⠀⠀⠀ ⠀⣸⡇⠀⠀⠀⠀⠐⠚⠋⢉⡟⢿⣦⡙⠛⠋⠁⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⠿⠛⠛⠛⠿⢷⣤⣿⠀⠀⠀ ⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠉⠛⠿⢶⣶⣦⣴⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠁⢀⣀⣀⣀⣀⠀⠉⠻⣧⡀⠀ ⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⠶⠾⢿⣿⠋⠀⣴⣿⠋⠉⠉⠛⢷⡄⠀⠘⣿⡀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⣰⣿⠃⠀⣼⡿⢿⡿⢳⡶⣦⣼⣿⡀⠀⣿⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⢰⣿⣀⣼⣥⣼⣇⣼⣇⣽⡇⠀⣼⡇ ⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡁⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢹⡇⢀⣿⠁ ⠀⣿⡆⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣿⠃⣸⡏⠀ ⠀⢸⣧⠀⠸⣆⠀⢸⡀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⡏⢠⣿⠁⠀ ⠀⠀⣿⡆⠀⠹⡄⠘⣇⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡿⠀⢸⣿⠀⠀ ⠀⠀⠸⣷⡀⠀⠹⡄⠹⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠸⣿⠀⠀ ⠀⠀⠀⢻⣇⠀⠀⠹⡄⢳⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠎⢍⡲⣄⠀⠀⠀⠀⠀⣼⡏⢀⣿⠁⠀⠀⠀⠀⠀⢸⣧⠀⠀⢿⡆⠀ ⠀⠀⠀⠈⢿⡆⠀⠀⢱⠀⢣⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠒⠶⣤⣉⠛⠷⣄⠀⠀⢰⡿⠀⢸⡿⠛⠛⠓⠶⣤⡀⠀⣿⡆⠀⢸⡇⠀ ⠀⠀⠀⠀⠘⣿⡄⠀⠀⢧⠈⣧⠀⠀⠘⣇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠉⠳⣤⡀⠀⠀⣿⠇⠀⣸⡇⠀⠀⠀⠀⠈⠻⣆⢸⡷⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠘⣿⡄⠀⠈⢧⠘⢆⠀⠀⠈⠳⣄⠀⠀⠀⠈⠉⠛⠳⢦⣄⡈⠙⠦⢠⣿⠀⠀⣿⡷⠶⣶⠶⣶⢶⡶⠿⣿⡇⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠈⠳⡌⠳⣄⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⢸⣿⠀⠀⣿⣧⣠⣿⣄⣿⢈⣧⣠⣿⠁⠀⣸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠈⠦⣀⠉⠓⢤⣀⠈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠙⣾⣿⠀⠀⠘⣿⣏⠀⠈⠉⠛⣿⣿⠃⠀⢠⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠈⠑⠦⣤⣈⠓⠦⣀⡈⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠈⠛⠿⠶⠶⠾⠟⠁⠀⢠⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣀⠀⠀⠈⠑⠒⠠⢍⣑⡒⠒⠒⠶⠤⠄⠀⠈⣻⣧⣄⡀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣄⡀⠀⠀⠀⠈⠉⠛⠒⠲⠄⠀⠀⠀⠈⠙⠛⠿⢿⣶⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣤⣤⣶⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠹⢶⣤⠴⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⣀⣶⣤⣄⣠⣶⣿⠏⢠⡄⣿⣾⣿⣿⣧⣠⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡶⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢉⣿⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣣⣿⣿⡀⠀⠠⢀⣀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣿⡏⠀ ⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣹⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠁⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣧⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣿⣿⣿⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡄⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⣿⣿⡇⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣻⣷⠈⢿⡄⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠉⠉⠀⠀⠀⠀⣠⣾⠿⠟⠛⠉⠉⠉⠉⠙⠷⠄⠀⠀⠀⠀⣾⣿⣿⡟⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⡤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠀⠀⠀⢀⣿⠁⠙⡇⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣴⡶⠶⣶⣤⣀⠀⣤⠏⠀⢠⣶⠟⢉⣀⣠⡇⠀ ⠀⠸⢿⣿⣿⣿⢏⣰⣶⣤⣙⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠛⢁⡠⢴⣿⡿⠿⡼⠋⠀⠀⢸⣣⡴⠛⢹⣿⡇⠀ ⠀⠀⢸⣿⣿⣿⡘⠿⠁⠘⠻⢷⠻⣿⣿⣿⣿⡏⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣤⣉⣴⣾⠟⠀⠀⠀⠀⠀⠳⣤⣑⣙⣿⡇⠀ ⠀⠀⠘⣿⣿⣿⣧⠀⠀⣴⣶⣿⣷⡿⠀⠹⣿⣷⣿⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠿⠒⠁⠀⠀⠀⠀⠀⠀⠀⢤⣉⣿⣿⡅⠀ ⠀⠀⠀⠈⢿⣿⣿⡄⠀⠘⡿⠋⣿⠀⠀⠀⣿⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡈⠉⢸⡇⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠹⡄⠀⠀⣿⣧⣿⣷⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⣇⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⡀⠀⠀⠀⡇⠀⢾⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⣀⣀⣀⣀⡀⣸⠀⢸⡍⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢶⣤⣴⡇⠀⠙⠛⠛⠻⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠻⢿⣿⣿⣛⣯⡍⠁⢀⣾⠃⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠁⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠈⡙⠻⣧⡀⣿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠦⣀⡴⠂⣀⣠⣶⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⡌⠙⢿⣿⣿⣿⣿⣽⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠈⠛⠻⢦⡿⢟⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⣀⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⡄⠀⣹⡟⢖⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢻⠰⠞⢃⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⡆⠸⢰⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣜⣛⣛⣣⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢐⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠑⠒⠤⠤⡀⠀⠀⠀⠤⢀⠀⠀⠉⠀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⠅⠚⠉⠁⠀⠀⠀⠀⣀⡞⠀⢸⠀⠀⠀⠀⠀⢸⠏⠀⠀⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡀⡄⠀⠀⠀⠈⠈⠛⠂⢷ ⡄⠀⠀⠀⠀⠀⠀⠀⠠⡽⠀⠀⢸⠀⠀⠀⠀⣰⡿⠀⠀⠀⢸⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⣴⣼⠁⠀⠀⠸⣄⣀⣀⣠⡿⡇⠀⣤⠀⠘⣧⠀⠀⠀⣿⣄⣀⣀⣀⣠⢤⡴⠚⠃⠀⠀⠀⠻⣼⢳⣄⣀⣀⣀⣰⠀⠀ ⠶⠤⠴⠖⠒⠒⢻⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡔⠉⠉⠉⠉⠉⠉⠁⠒⠀⠀⠀⠀⠀⠀⠀ ⢀⣱⣦⣤⣶⣶⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠐⠋⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣤⣤⣤⣤⡞⠀ ⣵⣾⣿⡿⠟⠛⠉⠉⠉⠙⣻⣿⡿⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⣀⣤⣴⣾⣿⣿⣿⡟⠛⠛⠛⠛⠻⠿⣿⣿⣷ ⡿⠋⠁⠀⠤⠀⠀⣠⣶⣿⣿⣿⣿⣶⣌⡙⠻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⢋⣵⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠉⢻ ⡇⠀⠀⠀⠀⠀⣸⠛⣿⣿⣏⣈⣹⣿⡛⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⡿⣯⣱⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⣿⠀⡇⠸⡀⠁⣠⠏⡇⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣏⢧⡀⠁⣀⠗⡏⢸⡇⠀⠀⠀⠀⢀ ⢿⡆⠀⠀⠀⠀⠘⣇⠙⠦⠈⠙⠁⠚⢠⡟⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠦⠝⠋⠁⠔⢁⡾⠀⠀⠀⠀⠀⢸ ⠀⠁⠀⠀⠀⠀⠀⠈⠑⠦⠤⠤⠤⠞⠋⠀⠀⢀⡀⢀⡠⠾⣛⣵⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠤⠔⠋⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⡀⢀⡠⠚⡡⠖⣉⣵⡾⠋⢑⡿⠛⠁⠀⢀⠀⢀⡀⣀⣴⠺⠋⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠴⠛⣋⣽⡻⢟⡩⠔⣉⠔⠋⢀⡾⠟⢁⡠⠚⠁⣠⡶⠃⡈⢀⣀⣵⠞⢋⡡⠖⠋⠀⠀⢈⡩⠟⠋⣠⠴⢂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⣪⠕⣫⠖⠉⠀⠈⠀⣠⠖⠋⣠⠖⠉⢀⡴⠋⣡⢔⡫⢖⠝⣊⡤⠚⠁⠀⠀⠀⠀⠀⢀⡤⠒⢉⡤⠚⠁⠀⠀⠀⠀⠀ ⡀⠀⠀⠠⢖⣭⡾⠗⠉⠀⠀⠀⣀⠴⠊⣡⠴⠋⢀⡤⢞⣡⣶⠿⣋⠅⣊⠴⠊⠁⠀⠀⠀⠀⢀⡠⠔⠊⣁⠴⠚⣡⠄⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠚⢁⡴⠊⢁⣤⠞⠋⡴⠟⠉⠄⣊⣴⣏⡀⠀⠀⠀⠀⠀⠴⠊⠁⠀⠀⠈⠁⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠐⠊⢠⠞⠉⠀⠀⠉⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⡶⠶⠶⠶⠶⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⣿⣿⡩⢀⣀⣀⣠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⠀⢸⠈⠙⠋⠉⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋ ⢿⠀⠹⣦⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀ ⢸⡄⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠱⡀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀ ⠀⡇⠀⠀⠈⢻⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⠢⣀⠀⠁⠀⠀⠀⣠⠞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⡶⣤⣀⡀⠀⠀⠀⠀⢣⠀⠀⠙⣶⢲⠒⠋⠀⠀⠙⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠔⢊⠔⠁⠠⢠⠂⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠒⣄⠀⠀⠀ ⠀⠀⡴⡫⡰⠡⠂⢠⠁⠂⠌⡄⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢡⠈⠁⠀⠀ ⡠⢊⡬⡞⢠⠃⠠⡇⠀⠌⠆⡇⠀⠀⠀⠀⠀⣀⣰⠋⠀⣼⡇⠀⠆⢡⡆⠀⠀⠀ ⢀⡞⢠⠁⡆⢠⠅⢇⡶⠤⠖⢫⠀⠀⠀⠀⠀⡘⠁⠉⠳⣇⣿⠀⢰⠀⣿⠀⠀⠀ ⠈⠀⠈⡼⠀⠇⠈⠙⠓⠀⠐⠨⢧⠀⠀⢀⣧⠁⡀⠤⠀⠸⡟⢧⠄⡀⢹⠀⠀⠀ ⠀⠀⢸⢠⢾⠀⣠⣤⣤⣭⣥⣍⠈⠓⠄⡌⡏⠀⠀⢤⠄⣀⠻⡘⡄⡇⢸⠀⠀⠀ ⠀⠀⠀⡈⢶⡛⣛⠂⠤⠀⢼⠉⠀⠂⠖⠐⠐⠀⣯⢭⡉⢛⡺⣵⣥⠇⠈⠀⠀⠀ ⠀⠀⢀⡇⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⣘⡋⠹⢶⠀⠀⠀⠀ ⠀⠀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢠⠂⠀⠀ ⠀⣷⠳⠀⠀⠀⠀⠀⠀⠀⡠⠐⢒⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠃⠀⠀⠀ ⢀⣿⠦⡀⠀⠀⠀⠀⠀⢸⣅⣹⣿⣿⣿⣶⣗⠀⠀⠀⠀⠀⢀⠌⡰⡁⠀⠀⠀⠀ ⢉⣹⡇⠡⡀⠀⢀⡤⢀⠈⣿⡿⠿⠿⠿⢿⡏⠀⠀⠀⠀⡰⠁⠮⢔⣥⠀⠀⠀⡠ ⢰⠏⠇⠀⣷⡀⠧⡀⠠⠀⠻⡄⠀⢀⡤⡎⠀⠀⠀⡠⢊⠔⠀⠀⢠⠞⢡⡦⠊⠀ ⠀⡇⠀⠐⠉⠙⠦⡀⢄⡄⡊⠈⠉⣭⠀⠀⠀⡠⢊⢴⠏⠠⡴⣂⠞⢡⢏⡔⠀⢀ ⠷⣰⠯⣀⠀⠀⢀⣿⣦⠀⠁⠀⠀⢹⡀⣔⠭⢒⣁⣬⠀⠰⡊⠀⢠⣟⠎⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣿⣿⣿⣿⠿⠿⠿⠿⢶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠈⠉⠀⠀⠉⠛⠒⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡆⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⢿⣿⠏⢁⠋⠉⠉⠉⠙⠃⠀⠀⠀⠠⠖⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⡷⠟⠻⠟⠚⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀ ⠀⣠⣿⣿⡇⠀⡤⠀⠀⠀⠀⠀⠀⠠⣀⡀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀ ⠀⣿⣿⠉⢡⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀ ⣰⣿⡿⣠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠂⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦ ⣿⣿⣇⡇⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣴⣾⡿⠟⠁⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⡟⠁⢹⣿⣿⣿⡟⠙⢛⡛⠳⠦⣄⡀⠀⣇⠀⠀⢀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣧⠀⠀⠹⣿⣿⢧⠀⢸⣿⣽⣦⣾⣿⣿⡛⠙⠚⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠛⢯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢿⣿⣿⣶⡶⠶⣿⣿⣾⠳⣌⣝⣻⣿⣿⣿⡟⠳⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠟⠁⢰⣿⡝⢶⠀⢸⣏⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟ ⢸⣿⣿⣿⡇⠀⠙⢿⣟⣿⣿⣿⣿⣿⣿⣇⠐⠻⣆⠀⣠⣿⣿⣯⢿⣻⣿⣿⠇⠀⠀⠈⠿⢯⠞⠀⡼⡟⢠⣤⣶⡿⠋⠁⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢑ ⢸⣿⣿⣿⣷⣤⡀⠀⠙⠙⠛⢧⣾⣿⣿⣧⠀⠀⠈⠐⠛⠛⡓⠀⠀⠛⢻⣿⣿⡳⢤⣄⣀⣀⣠⣼⣷⣷⣿⠟⠁⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀ ⠀⢻⣿⣿⢻⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⣿⡶⠀⠐⠀⠀⠀⠛⠺⣿⣶⣮⣌⠛⢿⠶⢿⣥⣄⣈⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀ ⠀⠀⢿⣿⣼⣿⣿⣿⣿⣄⠀⠀⣾⣿⣿⡇⣷⠀⠀⠀⢠⣾⠇⠀⣿⡿⠿⠿⢿⣦⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⠇⠈⢿⣷⠀⠀⢀⣼⣏⣠⡿⠿⠴⠶⠶⣦⡌⠙⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀ ⠀⠀⠀⠻⣿⡇⣿⣿⣿⣿⣿⣿⣿⡟⠓⢲⣿⠀⠀⣾⠟⠛⠁⢠⣀⠀⠀⠀⠈⠻⣦⡀⠙⣧⡀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⢙⣿⢹⣿⣿⠿⣧⠀⠸⣿⣶⣾⣿⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⢸⣧⠀⠘⣧⠀⠀⣴⡾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣾⡏⣿⣿⣿⡇⠹⣧⡀⠀⠉⢻⣿⡂⠀⠀⠀⠀⠨⢧⠀⠀⠀⠀⢿⡀⠀⠻⣧⣽⣿⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡆⠙⣧⡀⠀⠈⠻⡅⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠘⣧⠀⠀⠀⢰⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣧⢹⣧⠀⠘⢿⡄⠀⠀⢹⡄⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⢹⡀⠀⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⠀⢹⡄⠀⢸⣷⠀⠀⠀⠀⠀⡀⢻⣶⣄⡀⠀⣇⠀⠀⠘⣆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⡇⠀⣾⡟⣿⠙⡏⢻⠋⡍⢻⣍⢉⣽⣾⠋⢋⢻⡏⣍⠹⡟⢩⡙⣧⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣾⡿⠷⣿⢀⠀⢸⠀⡇⢸⣿⢸⡇⢸⡀⢨⢾⡁⣿⠀⡇⢸⠉⣿⠀⠀⠀⣀⣤⡶⠟⠉⠁⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣏⣸⣄⣼⠤⢡⠼⠿⠼⠇⠸⠧⠾⠘⠧⠭⠴⠷⠬⠤⣯⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙⠛⠿⠶⠶⡶⢦⣤⣤⣤⣦⣤⣤⣤⠶⢿⣟⠋⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠛⠛⠛⠛⠛⠛⣲⣶⣶⠾⠿⠿⢿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⣠⣤⣦⡀⠐⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⡟⠀⢀⣾⠟⠛⠛⠓⠚⠋⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⡟⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀ ⠀⠀⣰⣿⠏⠀⠀⢸⣁⠀⠀⠀⠀⠀⠀⠠⠔⠒⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀ ⠀⣰⣿⠏⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀ ⢰⣿⠏⡼⠀⠀⢰⣧⠾⠷⣦⡀⠀⠀⠀⣠⠾⡛⠛⠦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀ ⣾⡟⣰⡇⠀⠀⠸⣧⡶⠦⣤⡄⠀⠀⠀⢀⣴⠾⢦⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄ ⢹⣃⣿⠃⠀⠀⣰⣿⡟⠒⠀⠁⠀⠀⠀⢘⡿⡷⠀⣱⡜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠸⣿⣿⡀⢠⣸⣧⠴⠿⠿⠛⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇ ⠀⠸⢿⡇⢸⡇⠘⣆⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷ ⠀⠀⠘⣧⣸⣿⡄⠘⠷⡄⠈⠉⠁⠘⡄⠀⠀⠀⠀⠀⢠⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠘⣿⣿⣧⡤⠞⠁⠀⠀⠀⠀⠹⡀⠀⠀⠀⢠⠟⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠈⠋⠳⣦⣀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡿⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⠗⠀⠀⠹⡄⠀⡇⠀⠀⠀⣿⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠃⠀⠀⠀⠚⠁⢰⠁⠀⠀⠀⣿⣿⢷⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣼⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣛⡿⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⣿⣾⣇⡀⠀⠀⠀⠀⠀⣼⢀⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⣿⣿⣿⠀⣤⣂⠀⣠⣿⣾⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⢸⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢨⣿⣿⠟⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⣸⡿⠁⢀⡿⠛⠋⢰⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⢀⣴⠾⢿⡇⠀⠀⠀⠀⠀⠋⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡛⠁⠀⠀⠀⢀⡤⢤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢈⣟⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠉⢀⡀⠀⠀⠀⠀⣀⣤⡄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠘⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠛⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠓⠒⠋⠀⠀⠀⠀⠀⠀⠙⠰⣤⣄⣉⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣴⠓⠐⢀⣀⣀⣐⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡏⠀⠀⠀⠀⠀⠀⠹⣿⣤⣐⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣧⣀⣀⣀⣀⣀⣀⣀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣰⢏⣴⣿⡟⠛⠛⠛⠛⠛⠛⠛⢿⡏⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣷⣶⣶⣶⣿⣿⣿⣿⡆⢀⡴⠋⣿⣿⣿⡇⠀⠀⣤⡄⢠⣤⠀⢸⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⠏⠀⠀⣿⣿⣿⡇⠀⠀⣿⡇⢸⣿⠀⢸⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⠈⠁⠀⠉⢠⣾⡧⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⣴⡇⣿⠀⠀⠀⣿⣿⣿⣷⣶⡆⢀⣴⣶⣶⡿⠋⠀⠀⠀⠀⣷⠸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⡿⠿⢿⣿⣿⣿⣿⡇⡄⠰⣿⠁⣿⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⠀⢻⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⢷⠀⠀⠀⠀⠀⠀⠚⢿⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡟⠀⢸⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⢦⣀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡾⠁⠀⠘⣿⠀⠀⣿⣿⣿⣿⣿⡿⢫⠟⢀⡾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠉⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠁⠀⠀⠀⠀⢸⡞⢷⢿⣿⠟⠛⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠈⠁⠀⢠⠞⠀⢠⡞⢀⠀⢠⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠈⠐⠈⣀⣠⣶⣏⡴⢋⡴⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠈⢷⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡎⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠈⠳⣄⠀⢀⡼⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⡏⠀⠀⠀⠀⠀⠀⣀⣀⠨⠷⠮⠤⢬⣇⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀ ⠀⠀⠀⠐⠂⠀⠈⠂⠀⠀⠀⠀⠀⣈⣁⠀⡸⠀⠀⢀⣠⠴⠚⢉⣠⡤⠔⠒⢲⣦⣤⣌⡑⠦⣀⣀⠤⠖⣿⠁⠀⠀⠀⠀ ⠠⠄⣀⡀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠁⠀⠈⠁⣠⠖⠉⣠⠴⠚⣋⠤⠖⠒⠉⠉⠉⠉⠉⢿⣶⡈⢧⠀⢀⠇⠀⠀⠀⠀⠀ ⠀⠀⢀⡽⠚⠁⠀⠀⣠⠎⠀⠀⠀⠀⢀⡤⠊⣠⠴⢋⡡⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣸⡤⠊⠀⠀⠀⠀⠀⠀ ⠀⢠⠎⠀⠀⢀⡤⠚⡏⠀⠀⠀⢀⡴⠋⣠⣾⣡⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⠀⠀⢀⠎⠀⠀⡇⠀⢀⡴⢋⣴⣿⣿⠟⠉⠀⠨⠕⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠃⠀⣠⡄⠀⠀⠀⠀ ⠀⡇⠀⠀⠘⠀⠀⠀⣁⡴⢋⣴⣿⣿⡟⠁⠀⠉⠀⣀⠠⢤⣚⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣂⡂⠛⡅⠀⠀⠀⠀⠀ ⠀⢃⠀⠀⠀⠀⠀⠀⣿⣴⣿⣿⣯⠀⢇⠀⠀⣤⠶⠒⠋⠉⠀⢀⣤⣬⡍⠑⠲⡖⠒⠒⠒⢠⣶⡟⠛⡄⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⢿⡈⣿⡇⢸⠀⠀⠈⠓⢄⡀⠀⠀⠘⠿⠷⠏⠀⠀⣧⠀⠀⠀⠙⠷⠟⠀⣷⠀⢣⠀⠀⠀⠀ ⠀⠀⡆⠀⠀⠀⠀⠀⡜⢀⡾⠁⢿⣇⠸⡀⠀⢀⠀⠙⠮⣑⠲⠤⠤⠀⠠⢤⠞⢧⡉⠶⣒⣤⠖⢒⣺⠿⡄⠈⡆⠀⠀⠀ ⠀⠀⢠⠀⡆⠀⠀⢠⡇⢸⡇⠀⠀⠙⢷⣽⡀⠀⠑⠒⠤⠤⠬⢥⠴⠶⠒⠉⠀⠀⠙⢶⠤⠚⠂⢸⡅⠀⠱⡄⠘⢄⠀⠀ ⠀⠀⢸⢀⠇⠀⣠⢄⣱⣼⡇⠀⠀⠰⢫⡞⠉⠉⠒⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣀⠽⡗⠤⣘⣦⡈⠓⠀ ⠀⠀⠇⠀⢀⡴⠁⠀⠀⢹⡇⠀⠀⠀⠈⢳⡀⢿⡶⠤⣄⣀⡀⠈⠉⠓⠒⠒⠒⠒⠒⠒⠈⠉⠁⣠⣞⣹⠀⠀⠈⠉⠉⠂ ⠀⠀⠤⠒⠉⠀⠀⠀⠀⠸⣷⡀⢀⠀⠀⠀⠙⠢⡉⠓⠶⣟⡛⠛⠿⣅⡒⠒⠒⣶⠋⠉⠉⠓⡄⠑⡄⠹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠉⠲⠤⣀⠉⠙⠒⠊⠻⠶⠾⠯⠤⠤⠔⠚⢁⡤⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣄⡀⠀⠀⠀⠀⠉⠓⠢⠤⠤⠤⠒⠒⠒⠂⠀⣩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠦⠤⠤⠤⠤⠤⠐⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⡯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣏⠉⢻⡙⠛⠛⠛⠓⠒⠶⡤⠤⣄⡀⠀⣀⣀⣤⣴⠟⣡⣄⡠⡃⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠻⡄⠀⠀⠀⢀⣀⠘⠳⣮⣽⣿⠭⠽⠷⠨⠟⠛⠚⠓⠷⠾⠿⠧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠻⡄⠀⠀⠙⣿⡷⠞⠋⠁⠀⠀⠀⠀⣀⡤⠔⠂⠀⠀⠀⠀⠀⠀⠉⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠦⠀⢹⠀⣠⠞⠉⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡟⠃⠀⢸⡞⠁⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⢀⡤⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⣝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⣾⡿⠋⠁⠙⢿⣷⣴⠏⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⡞⠀⣰⠃⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈⢧⡈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣰⣿⠇⣰⠏⠀⢠⣿⣇⠀⠀⠟⢇⠀⠀⠀⢹⡀⠈⢳⡀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⢸⠁⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠃⠀⠀⢀⣾⣯⣦⣤⡆⠘⡇⠀⠀⢸⣧⡀⢶⡧⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣻⡀⠀⠀⠀⠀⢸⠇⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⡟⢻⣿⡆⣼⢻⡀⢹⠀⠀⣾⣿⣳⡌⠇⠻⣦⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠁⠀⠀⠀⠀⢸⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣞⢏⣷⠏⢸⡇⢸⠂⣴⣿⣿⠻⣿⠀⠀⠸⣷⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣠⠞⠋⠙⢷⡀⢰⡧⠀⣾⠟⠀⣿⡆⠙⡇⠀⠐⣿⡽⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢠⡾⠋⣉⠻⣦⠀⠀⠀⢀⣰⠞⢡⠞⠁⠀⠀⠀⢀⣟⢿⣧⠾⢋⠴⠋⠹⣷⢠⡇⠀⠀⣻⠃⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⡁⠈⠉⠓⡿⠀⣠⡴⡟⠁⠀⠐⠒⠒⠒⠒⠢⠭⣭⠛⠁⠀⠉⠀⠀⣤⣿⣿⠀⠀⣰⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠘⣧⡀⠇⣼⡷⠛⣅⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠛⠳⢴⣿⡇⢀⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠙⣶⡏⢷⠀⠸⣦⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣩⣍⣓⣲⠀⠸⡏⡿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠘⣷⠘⣧⡀⠘⠻⣮⣷⣤⡀⠀⠀⠀⠀⢶⡞⠛⢿⣿⡟⠋⠀⢀⡷⣧⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣧⡈⠳⣤⣀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠻⣄⡀⢹⠇⠀⠀⣸⠇⢸⢿⣿⡄⠀⠀⠀⠀⠀⣀⣠⡤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠃⠀⠀⠀⣠⠖⠲⢦⡀⠈⠛⢶⣬⣉⣙⣲⢾⠟⠁⠀⠀⠀⠳⣄⠈⠓⢛⣄⣠⠾⠃⢀⣿⠀⠿⠇⠀⠀⠀⠀⡾⠉⢷⠶⠙⢳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠀⠀⠀⣠⠞⠁⠀⢠⡄⠙⣶⣾⣾⠏⣿⠀⠀⠈⠛⣶⣤⣤⣀⡀⣈⣻⣿⡟⢻⡁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣧⡀⠸⠀⣀⡿⠀⠀⠀⠀⠀ ⠰⣀⣀⡀⠀⢀⣀⣤⠾⠋⠀⠀⠀⢀⡼⠋⠀⠀⢠⣾⠃⣰⣿⣿⣧⡤⣿⣤⠶⠖⠋⢙⣷⣤⠭⠿⢿⡀⠀⢃⠘⠻⡏⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠻⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠘⠻⣭⡋⠉⠉⠀⠀⢀⣠⣴⠒⠋⠁⠀⠀⢀⡾⠃⢠⣿⡿⠋⠁⢙⣿⣝⣆⠀⣠⣾⣿⡝⠀⠀⠈⣧⠀⠸⡇⠀⣿⠀⣠⠴⠚⡿⠀⠀⠀⣻⣦⣶⣶⣶⣷⣶⣤⡀⠀⣀⣀⠀ ⠀⠀⠀⠀⠉⠛⠛⢶⡟⠋⠁⠘⣆⠀⠙⠦⠀⢿⠇⠀⣾⣿⠃⠀⠀⣼⠀⠈⠻⣾⣿⣟⡞⠀⠀⠀⠀⢹⡄⠀⣁⡤⠞⠋⢁⣤⠟⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⠊⠁ ⠀⠀⠀⠀⠀⠀⣰⡟⢰⠇⠀⠀⠈⠳⣤⣤⣀⣿⠀⣸⣿⠏⠀⠀⢰⠃⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⢀⡿⠊⢁⣠⣴⠞⡹⣧⠀⣠⡴⢾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⢀⡎⠀⠀⢀⣤⣾⠃⠀⠙⡟⢠⣿⣿⠀⠀⢠⡏⠀⠀⠀⣼⣿⣧⠀⠀⠀⣬⣥⣤⠎⠀⣴⣟⣁⣨⣽⡿⠟⠀⠈⠛⣿⣿⣿⠋⠃⠛⠛⠛⠛⢿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⢸⡃⢸⠇⢀⡼⠋⣰⠇⠀⠀⣼⠁⣸⣿⡇⠀⠀⡜⠀⠀⠀⢸⣿⡟⠘⢶⡖⠋⠁⣴⠋⢠⡾⢧⡟⠉⣿⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠘⡇⢸⣥⣾⣴⣾⠃⠀⠀⣰⠏⢀⣿⣿⣀⠀⠠⠗⠂⠀⠀⣿⣿⠇⠀⢰⠃⢀⡾⠁⡴⠋⢠⡟⠀⠀⡟⠀⠀⠀⠀⠀⠙⢻⣿⣿⣶⡦⣤⣀⣤⣤⣾⣿⣿⡿⠂⠀ ⠀⠀⣶⣿⡛⠛⢻⡼⢟⠁⣸⠋⠀⠀⣰⠏⠀⢸⣿⡇⠈⠛⡶⣄⡀⠀⢲⣿⡿⠀⠀⣾⣴⠏⢀⡞⠁⢠⡿⣇⠀⢰⠇⠀⠀⠀⠀⠀⢀⣼⣿⣿⢿⠄⣾⢥⣹⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠻⠯⠳⠓⠲⠗⠺⠶⠿⠶⠶⠶⠏⠀⠀⠿⡿⠷⠀⠈⠇⠒⠋⠳⠾⡿⠷⠶⠶⠿⠁⡠⠾⠶⠶⠿⠶⠿⠶⠿⠶⠶⢶⡄⠀⠀⠾⠿⠿⠷⠿⠓⠛⠒⠻⠺⠿⠿⠿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠒⣶⠀⣶⠒⢶⡀⣰⡞⠻⣆⠀⣶⠒⢶⡀⣶⠖⠓⠒⣶⠒⢶⡀⣴⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⠿⢰⡇⠀⢸⡇⣿⠀⣤⣭⢸⣇⢠⣬⡄⣿⠦⠤⠀⣿⣤⣾⠋⠻⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⣿⣀⣼⠃⠻⣆⣠⣿⠈⣿⣀⣼⡇⣿⣄⣀⡀⣿⠀⢿⡆⢶⣐⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠒⠛⠛⠋⠋⠓⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠋⠀⠀⠒⠒⠀⠐⠒⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀ ⠀⠀⢀⣴⡿⡄⢀⡀⠀⠀⡠⠔⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀ ⠀⢠⡿⠛⠓⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀ ⠀⣼⠃⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡰⠁⠀⠀⠀⠀⠀⢹⠀ ⣸⣏⡎⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⢆⠀⠀⠀⠀⠀⠀⠀⣇ ⣿⠏⣷⣤⠤⠤⢀⢸⠀⠀⢀⣀⣤⣤⣤⣤⣤⡶⠚⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸ ⣿⣦⠼⣿⣄⣿⣾⡿⠍⠉⣿⣿⣿⡿⢫⡥⠙⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢹⣿⣄⠙⠻⢿⣿⡆⠁⠸⡟⡻⢿⣤⣈⣉⣸⣧⠞⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠈⣿⣿⣷⡄⣠⣿⡣⠀⢠⠆⡿⠷⢭⡉⠓⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⠀⠹⣿⣿⢿⣿⡖⣿⢀⠟⠊⣉⠉⠱⡌⢆⠀⢀⣠⠤⠂⠀⠀⠀⠀⠀⠀⢠⠇⠀ ⠀⠀⠙⣾⣿⣯⢣⠈⠻⡆⠀⠀⡇⠀⢡⠘⠶⡿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀ ⠀⠀⠀⠀⠙⢿⣆⠱⡀⢰⠀⠀⠘⣄⠀⡆⠀⡃⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠧⣅⣼⡏⢹⠉⣯⡕⡎⡰⡍⣮⠥⠀⢀⣠⠔⠉⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠾⠶⣛⣃⣓⣘⣓⣷⠶⠒⠉⠀⠀⠀⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣰⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣾⣿⣿⣷⣦⣾⡀⠀⠀ ⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠄ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠻⣿⣿⣿⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⢻⡿⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⣤⠶⠦⠄⢤⢠⡇⠀ ⠀⠀⠀⠀⣿⣿⠩⣻⣿⣿⡇⠀⠐⠀⣲⡄⠀⣘⢠⡇⠀ ⠀⠀⠀⠀⣿⣿⣾⣥⢸⣿⡀⠀⠀⠊⠒⠁⢀⢣⠹⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⠵⠙⠿⠃⡐⠄⠡⢰⠐⣤⢐⢆⠀⠀ ⠀⠀⠀⠀⠈⢻⠋⡌⠀⢰⢄⠄⠁⠀⠁⣀⠠⠷⡃⠀⠀ ⠀⠀⢀⠠⠒⡁⠀⠠⠀⠘⠘⠅⡘⠈⠗⣶⣾⠟⠁⠀⠀ ⠔⠊⠁⢀⠎⠀⠀⡀⠢⡀⠀⠀⠡⡰⡘⢬⠝⠀⠀⠀⠀ ⠘⠄⠀⠁⠀⠀⢜⠁⠀⠐⡀⠀⢌⣂⠄⠃⠀⠀⠀⠀⠀ ⠀⠈⠢⢀⠀⠀⠀⠀⠀⢰⠈⡩⠹⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠐⠂⠀⠤⠮⠔⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠶⠶⠶⠿⠿⠿⠛⠻⠛⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⠤⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣇⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣋⣙⠉⠉⠑⠂⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀ ⠀⠀⢠⣿⡿⠉⠙⠉⠉⠑⠤⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀ ⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀ ⠀⣼⣿⡇⢠⠀⠀⠀⠀⠀⠠⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀ ⢰⣿⡏⣴⠋⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀ ⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠏⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⣿⣿⠇⢻⣿⣷⡶⠒⠒⠦⢤⡀⠀⣇⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⡄⠀⢻⣿⣧⡀⢿⣿⣤⣿⣿⡏⠛⠉⢹⣿⣿⣿⣿⣿⣿⡿⢛⣁⠉⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢹⣿⣿⡏⠙⣿⣿⣿⣾⣿⣿⣿⠋⣭⠀⠀⣼⣿⣿⣿⣿⡿⠋⠀⢸⣿⣹⠀⣿⠀⣀⣠⡴⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏ ⢸⣿⣿⣧⡀⠈⠙⠿⢿⣽⣿⣿⡀⠈⠁⠺⠿⠏⠉⠿⢿⣷⡦⣄⣀⣉⣁⣼⣿⣶⠟⠋⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⠈⢿⣿⣿⣿⣷⡄⠀⠀⢸⣿⣿⡷⠀⠀⠀⢀⠛⢻⣶⣮⣙⠻⠿⠯⣬⣩⢿⠟⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀ ⠀⠈⣿⣿⣿⣿⣿⣆⢠⣾⡿⢿⣿⠀⠀⢀⡿⢁⣼⣟⣛⣛⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀ ⠀⠀⠹⣿⣹⣿⣿⣿⣿⣿⡧⢤⣿⠀⢀⡾⠿⠋⠉⠉⠉⠉⢻⣄⠙⢦⠀⠀⠀⠀⠀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀ ⠀⠀⠀⠻⣿⠟⣿⣿⣿⡿⣇⠀⢿⣦⣾⡃⠀⠀⠈⢳⡄⠀⠀⢹⡆⠈⣧⠀⣠⡶⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⠙⣧⠀⠈⢻⡧⠀⠀⠀⠀⣇⠀⠀⠀⢷⠀⠘⠛⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡆⠘⢧⡀⠀⢹⡀⠀⠀⠀⠈⣆⠀⠀⠘⡆⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⠈⢣⠀⢸⣧⠀⠀⠀⢀⣘⣷⣄⠀⢳⡀⠀⣣⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣬⠇⣸⣯⡏⠉⢹⠉⠈⣯⢨⠿⡏⢩⣹⢡⠙⡏⣭⣱⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣭⡇⣄⢸⣀⢀⣿⣸⠀⣇⣰⢣⣘⣀⣇⣃⣈⣀⣠⡴⠞⠋⠁⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡸⠗⠎⠁⠉⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠆⣱⣀⠀⠀⠀⠀⠀ ⠀⣠⠃⠀⠀⡰⢰⡜⠀⠀⠀⠀⠸⡄⢸⠀⠀⠀⠀⠀⠀⠋⠈⡀⠁⠀⠀⠀⠀ ⠀⢧⠀⠀⡐⠁⣞⡠⢄⣒⠆⢀⢣⠀⢨⠀⠀⠀⠀⠰⡸⠀⠀⡇⠀⡇⠀⠀⠀ ⠀⢀⢂⠎⣠⣾⣿⣿⡛⠻⣷⡊⡌⡠⢼⡆⠀⠀⡠⢎⣴⣮⣶⡁⡰⡇⠀⠀⠀ ⠀⠀⡅⣨⣿⣿⢿⣿⠿⠉⠙⠒⠉⠀⠘⠀⠀⢰⡡⣺⣿⣷⠤⣿⢰⠑⠀⠀⠀ ⠀⠀⢩⠉⢿⢿⠛⢉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡯⢻⡆⢀⠇⡎⠀⠀⠀⠀ ⠀⠀⠀⢃⠀⠙⠢⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠜⡁⠈⠀⡇⠀⠀⠀⠀ ⠠⠠⠤⠬⠢⠄⠀⠀⠠⠤⠤⠤⢤⠤⠤⠤⢤⣤⣄⡤⠤⠤⢤⣤⣥⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠿⠿⢿⣿⣷⣴⠄⠀⠀⠀⠀⣠⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⣤⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠂⠐⠒⢒⣀⢖⣿⣶⣿⠿ ⠀⠀⠀⠀⠀⠀⠶⡦⢤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⢟⣡⡴⢿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠉⠻⣿⠟⢿⣿⣿⣿⠭⠁⢸⣿⣿⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢌⣿⣹⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠤⠤⣭⡖⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠔⠛⠉⠉⠉⠛⠳⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠏⢀⣴⠶⢀⠤⢤⡀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀ ⠀⢀⣼⠏⢠⠏⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀ ⢀⣾⠃⠀⡸⠂⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀ ⣼⢣⠃⠀⡗⣛⢆⠀⠀⢔⣉⡑⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀ ⢟⣾⠀⢀⠿⣒⡙⠀⠀⢸⣖⡱⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀ ⠘⢿⢸⡟⡏⠉⡁⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⠀⠘⣾⣷⢈⡳⠈⠁⠡⠀⠀⠀⡔⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠈⠙⡥⣀⣀⣀⠀⢡⠀⠸⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⣸⡇ ⠀⠀⠀⠀⢡⣿⣿⠟⠁⠠⠃⡄⠀⠀⣧⡆⠀⠀⠀⠀⡀⣀⣿⠀ ⠀⠀⠀⠀⢾⠯⠋⠀⠀⠀⠀⠀⠀⢀⣿⣿⣄⠀⠀⢀⣇⣿⠇⠀ ⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⠔⠉⣿⣿⣿⣾⣧⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡴⠁⠀⠀⡾⠋⡹⠟⢻⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠦⠠⠔⠛⡇⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⣳⣦⣶⣶⣿⣿⠿⢿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⣠⣶⠾⢿⣶⠀⢈⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⣼⡿⠛⠋⠙⠛⠓⠛⠉⠉⠉⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⠃⠀⠀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⡿⠃⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⣾⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀ ⠀⠀⣼⣿⡿⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀ ⠀⣸⣿⡿⢀⡟⠀⠀⠀⣾⢃⡾⢷⣦⣀⠀⠀⠀⠀⠀⠀⣴⠿⠿⠿⣶⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀ ⢀⣿⡿⠀⣾⠀⠀⠀⠀⣿⠉⣠⣄⠉⢛⡃⠀⠀⠀⠀⠚⢁⣬⣤⣄⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀ ⠸⣿⡇⣼⣿⠀⠀⠀⠀⢸⣿⣯⠈⠛⠟⡇⠀⠀⠀⠀⠰⣯⣥⡈⠻⣦⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀ ⠀⣿⢡⣿⡏⠀⠀⠀⢠⠿⢿⡛⠉⠀⠀⠁⠀⠀⠀⠀⠀⣝⣻⠟⠀⣠⡿⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀ ⠀⢸⣿⣿⡇⠀⡄⣰⣏⣤⠴⠭⠭⠴⠛⠁⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀ ⠀⠈⢻⣿⣿⠀⣧⡏⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⠀⠈⢸⣿⠀⣯⣧⡀⠘⣷⣄⠀⠐⠶⢶⡄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀ ⠀⠀⠀⠈⢻⣧⣿⣿⢧⠀⠈⠙⣳⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣼⠏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣼⣦⣴⠟⠁⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⣾⠃⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀ ⠀⠀⠀⠀⠀⠀⠘⠍⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⣾⠃⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣿⣦⣤⣤⣤⣤⣤⡀⠀⠀⠹⡄⠀⠀⣿⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣹⡆⠀⡏⠀⠀⠀⠀⢸⣿⡄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣾⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠉⠀⢸⠁⠀⠀⠀⠀⢸⣿⣷⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢰⢰⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⣿⣿⢸⣷⠀⢀⠀⠀⠀⠀⠀⠀⢀⣾⠀⣼⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠳⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣰⢸⠀⠀⣤⢀⠀⠀⢸⣏⣸⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠋⢿⣿⣿⣿⣿⣿⠀⣼⡇⣾⢀⢴⣿⣿⣿⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⢸⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⡾⣿⠋⠀⢸⣿⠯⠿⠋⣹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡁⠀⠀⠀⠀⠀⠀⢸⠿⠁⠀⢀⡾⠃⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⣀⣴⠾⠛⠹⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢄⠀⢠⠾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡼⢏⣿⣞⣿⣽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⡻⣿⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⠈⠻⣶⣿⠟⢉⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡾⠁⠀⠀⠀⠀⠀⠀⢱⡌⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢂⣞⠇⠀⠀⠀⠀⠀⠀⠀⠈⡟⡌⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢎⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡌⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢎⡞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠹⡌⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣬⡞⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠙⣟⠄⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠏⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠘⢾⣆⠀⠀⠀ ⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠻⢄⣀⣀⣀⣀⣀⣤⠾⠁⠀⠀⠀⠀⠀⠻⣧⡀⠀ ⠐⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣯⣾⣯⣤⣾⣿⣇⣈⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⣿⣿⡏⠉⢹⣿⡛⠛⢿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⣀⡼⣯⣀⣀⡜⠀⠀⠸⣿⠏⠙⣻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡿⠿⠿⣦⣤⣑⠊⠐⠂⠀⠀⢀⡟⢀⣰⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣦⡄⡀⣿⣿⣿⣶⡄⠀⠀⠘⣿⠟⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠘⢟⢿⣿⣿⠃⠀⠀⣰⢏⣼⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⣿⡇⠀⢀⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀ ⣀⣤⣤⣤⣀⠀⣀⡀⣻⡿⠶⠶⢾⡿⠶⠶⢿⣯⣠⣤⡶⠶⠶⣦⣤⣤⣤⡄ ⢿⡇⢠⡌⢹⠟⠛⠻⡏⠀⣠⣤⡎⠠⣤⣦⠾⠿⠭⣤⡇⠺⠀⣿⡉⠒⠼⣧ ⢸⡇⠀⣤⡆⠠⣶⠀⡇⠀⠻⠄⡠⡰⠻⠖⠀⢰⠃⠘⢃⣸⣆⡌⠙⠃⢀⣿ ⠸⠿⠛⠛⠻⣶⣤⣶⠿⣦⣄⣠⣴⣷⣤⣤⣴⠟⠛⠛⠛⠉⠛⠛⠿⠿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⣠⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠁⠀⠀⠠⠤⠶⠦⠦⠤⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⢀⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⡤⠂⠀⠀⠀⠶⣖⠀⠠⠄⠀⠀⠀⠀⠈⢿⣿ ⠀⠀⠀⠀⣸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⣀⣀⣀⡀⠀⠀⠈⠉⠑⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠤⠤⠤⠤⠤⣴⡋⢈⣠⣤⣬⣀⣀⡀⣤⣀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⠀⠀⠀⠀⠀⠙⠳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⢏⣽⡷⠶⠶⠶⠶⠶⢾⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣿⣿⣷⢀⡴⢳⣿⣿⡇⠀⢠⡄⢠⡄⢸⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀ ⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡎⠀⢸⣿⣿⡇⠀⠸⠇⠸⠇⢸⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢫⡟⡇⠀⢸⣿⣿⣇⣀⠀⣀⣀⣴⡿⠃⠀⠀⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠈⠙⢿⣿⠿⣿⣿⣿⣿⢁⠀⣾⠁⡇⠀⢸⣿⣿⣿⣿⣴⣿⡿⠋⠀⠀⠀⠀⡇⠘⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⢁⡄⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⠄⠀⠀⠀⠀⠻⠇⢸⠀⡇⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⡀⡇⠀⣧⠀⢹⣿⣿⣿⣿⣿⣿⠃⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠀⠙⠦⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⡠⠞⠁⠀⢹⣀⣠⣿⣿⡿⠟⠱⠋⣸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠟⠿⠁⢀⠄⠀⡼⠁⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢖⠂⠔⣀⣠⣞⡱⢃⣼⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡟⠛⡟⠒⠒⠒⠒⠦⢤⣄⠀⢀⣀⣤⡶⢫⣄⣸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⡄⠘⣆⠀⠀⢠⣄⣉⣺⠿⠟⠛⠃⠙⠉⠉⠙⠚⠛⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣄⠘⡄⠀⣨⠟⠉⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⣿⠇⠀⣧⠎⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡿⠋⠉⠛⢷⣶⠃⠀⠀⠀⢰⠋⠀⠀⠀⠀⢀⡼⠀⡼⠀⢀⠀⠀⢠⠀⠀⠀⠀⠙⡌⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣦⠀⠀⢠⠇⠀⠀⠀⢀⠇⠀⠀⠀⠀⣠⠞⠃⠜⠁⠀⢿⣧⠀⡈⢣⠀⠀⢰⡀⢘⡆⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣷⣦⣼⠀⠀⠀⠀⣸⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⢰⢿⣿⢙⣷⠈⡆⠀⣸⣷⡘⡗⢦⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⢿⠀⠀⠀⠀⣇⣀⡴⠋⠀⠀⠀⠀⠀⠀⣰⠋⣸⣿⡾⠉⡇⠃⣰⣿⡿⣿⡄⠀⢳⣌⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⣁⣀⡀⠀⠀⠀⠀⢀⠜⣡⠞⠉⠙⢧⣠⡇⣰⠟⣠⣷⠈⡇⠀⢸⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⣼⠁⠠⣜⡆⠀⢀⡴⠃⢐⣁⣀⣀⡀⣾⠿⠟⠁⠊⠀⢹⣷⡇⠀⣸⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢻⡀⠀⣼⡵⠚⢹⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠤⢬⣿⡟⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠙⢲⡟⡆⠸⣦⢧⡀⠀⠀⠀⠀⠀⠀⢐⣩⣕⣲⠀⢸⡿⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠈⢧⠹⣄⠈⠻⡿⠦⠄⠀⠀⠀⢿⠉⠻⡟⠁⠀⢸⠳⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢀⣄⡀⠈⠳⣌⡳⠦⣬⣲⡤⠀⠀⠠⡄⠑⠤⢇⠀⣠⠏⢰⠛⣿⠀⠀⠀⢀⡴⣾⡛⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡴⠁⠀⡈⠲⣴⣾⠟⡏⠉⠙⢢⣤⣀⡀⠈⣲⣶⠾⡏⠁⣠⠟⠀⠀⠀⠀⠀⢸⡀⠸⠀⣸⠁⠀⠀ ⢦⣄⣀⣀⣀⡤⠞⠁⠀⠀⣠⠋⠀⠀⣼⠃⣸⣿⣧⣴⣷⡴⠒⠋⣻⣤⠽⠻⡅⠀⡀⠻⡏⠁⠀⢀⡀⠀⠀⡀⠀⠉⠛⠉⠀⠀⠀⠀ ⠀⠙⠻⢥⣀⣀⣠⠴⢾⡉⠀⡀⠀⣼⠃⢰⣿⠋⠀⠸⠿⢷⣀⣾⣿⠎⠀⠀⢰⠀⠐⠀⣷⡤⠞⣩⠇⠀⢀⣽⣿⣿⣿⣿⣶⣤⣤⡤ ⠀⠀⠀⠀⠀⡽⢡⠀⠀⠳⣄⣈⠀⡏⢀⣿⡏⠀⢀⠃⠀⠀⣿⣿⠋⠀⠀⠀⠈⣧⠔⢊⣁⠴⣾⠁⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⣼⠁⠇⠀⢀⣤⡟⠉⢹⠇⣼⣿⠀⠀⡆⠀⠀⣸⣿⡇⠀⢀⣐⣠⡞⢁⣴⣋⣉⣿⠟⠀⠙⢻⣿⣿⠋⠛⠛⠛⢻⣿⣿⠀ ⠀⠀⠀⠀⡏⠈⠀⡴⢋⡜⠀⠀⡼⢠⣿⠇⠀⢰⡀⠀⢀⣿⡇⠙⡾⠉⢠⠎⣠⠞⡟⠉⡏⠀⠀⠀⠀⣾⣿⣇⠀⠀⠀⠀⢀⣿⣿⡀ ⠀⢀⣤⣤⣽⣰⡿⠛⡿⠀⠀⡰⠁⢸⡿⠲⢄⡈⠀⠀⣼⣿⠁⠀⣇⡴⠃⡔⠁⣼⠁⢀⡇⠀⠀⠀⠀⢀⣿⣿⡟⢳⡖⢾⣿⣿⡟⠁ ⠀⠹⠿⠦⠠⠯⠧⠼⠤⠤⠴⠃⠀⢾⠧⠀⠸⠉⠓⠤⢿⠿⠤⠼⠟⠠⠼⠤⠼⠭⠧⠼⠤⠤⡄⠀⠠⠾⠿⠿⠷⠾⠿⠿⠿⠿⠧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⢦⣠⡖⢶⠀⡴⠛⡆⢠⠖⢲⠀⡶⠒⠲⡖⢲⣀⣶⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠚⢹⡀⢸⠿⣇⠰⣶⢾⡀⢶⠀⡟⠂⠀⡷⢾⠁⡙⣳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠓⠛⠀⠙⠚⠛⠈⠓⠛⠂⠛⠒⠒⠃⠘⠃⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⣄⡀⣠⣼⣿⣷⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣀⠀⠒⠂⠀⠀⠸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⠿⠛⠻⠿⠆⠈⠢⡆⣼⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⣻⢿⣿⣿⣿⣿⡿⠀⠀⠀⠠⠀⢀⢤⣆⠀⠠⠂⣰⠃⢩⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⣉⡧⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⡘⠻⢿⡇⠀⢰⡟⣞⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠿⣄⡎⠸⣿⣿⡄⠀⠀⠀⠀⠁⠈⠑⠉⠀⠀⡀⢧⠈⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣍⣹⡾⣿⣿⣇⠀⠀⠀⠀⢠⠀⢦⠀⡀⠀⠁⢈⣧⠘⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⠋⠀⠻⠟⠁⢸⣀⠑⠀⠀⠃⣨⡏⠣⢶⡆⢀⠞⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⠃⢠⠃⠀⠀⣦⢀⠀⠀⠙⠆⠀⠰⠃⠀⠀⠀⢙⣧⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠋⠀⠀⠀⢸⢱⡧⡁⠈⢢⠰⣤⡤⠤⠒⢉⣩⣄⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠆⠀⠀⠘⠀⠃⡄⠀⡜⠀⠘⡟⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⢀⣀⠤⠚⠁⠀⣀⠴⠃⠀⠀⠀⠠⡀⠀⠀⠀⠀⠁⠸⡀⠀⡀⢡⡈⠻⠿⡿⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⠀⠀⠀⡸⠋⠀⠀⠀⠀⡄⠀⠈⣧⠀⠀⠀⢄⠁⠹⡄⢧⣀⠙⢛⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⡀⠀⠀⠘⠀⠀⠀⠀⠀⣼⠃⠀⠀⠈⢧⠀⠘⢆⡁⠈⠪⠀⣀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠳⣄⣀⣉⣷⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣠⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠠⠀⢀⠀⠀⠀⠀⠀⢀⠏⠀⣰⠁⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒⠚⠓⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣄⡤⢷⣶⠿⢹⣄⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⠛⠉⠙⠁⠀⠀⠀⠀⠀⠉⠉⠹⢿⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠿⢴⣶⠀ ⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣴⣋⣀⠀⠀⠀⣰⠋⠀ ⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⠑⠒⠒⠚⠉⠀⠀⠈⠉⠻⢿⢹⡁⠀ ⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣷⠀ ⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠇⠀⠀⢀⣤⣶⣶⢤⣀⠀⠀⣠⣹⡀ ⠀⢸⡇⠀⡀⡀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠛⠉⣼⣤⠀⠀⠀⣸⡋⣝⠁ ⠀⠘⣷⢸⣿⣿⣗⢦⡀⢘⣇⠀⠀⠀⠀⠰⠊⠀⣿⠗⠀⠸⡷⠺⣞⠂ ⠀⠀⠹⡘⡽⢰⣿⡏⢻⣌⣻⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠃⠐⣏⠀ ⠀⠀⠀⢳⠹⣌⠁⠳⣾⣆⣿⢲⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣄⣸⠀ ⠀⠀⠀⠈⡇⠈⡷⠴⠃⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠳⣴⢫⠏⠀ ⠀⠀⠀⠀⠷⢼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣈⡽⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠶⣶⣿⡇⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣢⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⠞⠋⠉⠓⢦⡀⢠⠞⠁⣼⡁⣠⢞⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣞⠁⠀⠀⠀⢀⣴⣿⣧⡀⠀⠈⠙⣷⡿⢷⣄⣼⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡾⠉⠙⢲⡶⠞⡿⢁⣠⣍⡛⠲⠶⣾⣋⠉⠻⣇⣉⡿⠓⠒⠒⣶⠀⠀ ⠀⠀⣼⣡⡤⢖⡟⠀⠀⣴⠛⢡⣾⣿⡆⠰⣿⣿⡆⠀⠘⣿⣁⣤⣴⠞⠃⠀⠀ ⡞⠛⠉⠀⠀⣾⠁⠀⣼⠃⠀⠸⣿⣿⡏⠀⠻⣏⠁⢀⣰⠏⢻⣖⠙⢷⣤⣤⣶ ⠳⢦⣤⣤⣤⣿⠀⠀⠻⣄⠀⠀⣨⠟⠀⠀⣠⣬⣉⠉⠁⠀⠀⠹⡇⣰⠃⠀⢸ ⠀⠀⣿⣤⣤⠿⣆⠀⠀⠈⠙⠋⠁⠀⢠⡚⠁⠀⢸⡆⠀⠀⠀⣰⡿⠋⠀⢀⡟ ⠀⠀⢸⡆⠀⠀⠹⠛⡏⢉⣽⠇⠀⠀⠀⠳⣤⡴⠟⠀⣀⣤⡾⠋⢀⣀⣴⠟⠀ ⠀⠀⠀⢿⡀⠀⠀⣰⣷⡛⠉⠙⠛⠒⠶⠴⠶⠖⠒⠛⠉⠺⣍⡉⠉⠉⠀⠀⠀ ⠀⠀⠀⠈⠳⠶⠟⠉⣔⣩⠿⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁⠀⠀⠀⠀⠉⠙⠛⠉⠉⠀⠀⢀⣠⢾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⠙⢶⣄⣀⡀⠀⠀⣀⣀⣠⠴⠖⠛⠉⠀⠘⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⠔⠀⠀⠀⠀⣀⠤⠀⠒⠒⠀⢄⠀⠰⡀⠀⠀⠀ ⠀⠀⠢⡀⠀⡐⠒⣚⢉⡁⠀⠀⠈⡁⠐⡀⠐⡀⠘⠀⠀⠀ ⠀⠀⣶⣾⢶⢶⣶⣶⣶⣶⣶⢶⡿⣶⢶⣶⣷⣶⣶⣶⡆⠀ ⠀⠀⠙⢻⣷⣵⣿⣿⣿⣿⠇⠈⢿⣿⣷⣿⣿⣿⣿⠛⠁⠀ ⠀⠀⠀⠣⣩⠉⠉⠉⠉⠁⠐⠈⠀⠉⡉⠉⠉⢹⡠⠃⠀⠀ ⠀⠀⠀⠀⠈⢢⠀⠀⠻⣿⣿⣿⣿⡿⠓⠀⠠⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠥⠦⠄⢀⣀⣀⣀⡀⡤⠦⠅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠀⢠⠓⠚⢳⣲⠻⠐⠱⡀⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢠⠀⠱⠂⢿⠹⠇⠰⡉⢠⠸⠀⠀⠀⠀⠀ ⠠⢤⣠⢤⡀⡀⢸⠀⠈⠢⠘⣼⠤⡮⡤⢺⢀⠀⣠⡄⠀⠀ ⠠⣾⣿⢀⣿⣷⢳⡆⡖⢲⠣⡡⢡⡟⡇⠈⢲⠛⣿⠀⣖⡦ ⠠⢼⣿⠦⠟⠻⠼⠃⢧⠸⡄⠀⠠⠿⠴⠤⠸⠄⠿⠄⠧⠄ ⠀⠈⠉⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠉⠉⠉⠒⠒⠦⠤⣀⣀⠀⠀⢀⡇⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠾⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣏⠉⠑⠒⠲⠤⢄⣀⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠔⠊⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⡼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠉⠁⠀⠈⠓⢤⣀⡀⠀⠀⢿⠢⢄⡀⠀⠀⠀⢿⠢⣄⡀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⢸⠀⠉⠉⠒⠺⠄⠀⠈⠉⠒⠢⠼⠆⠀⠈⠙⢲⠦⢼⡄⠀⣠⣶⢦⠀⠀⠀⠀⢸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⢀⡼⠊⠉⠑⢦⠀⠀⣠⣖⠋⠉⠙⠒⠦⣄⠀⠀⠘⡄⠀⠀⡼⢹⣟⠃⣇⠀⠀⢾⠾⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠳⡀⢾⠀⢰⡄⠀⠈⡇⠀⢏⠻⠆⠀⠀⠀⠀⢸⠄⠀⠀⢳⠀⢰⠃⣾⡿⡆⣿⠀⠀⢸⡆⠀⠀ ⢰⠤⣤⡞⠳⣤⠿⡋⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⢀⡼⠁⠀⠈⠓⠤⠤⠤⠄⠒⠋⠀⠀⠀⠘⣆⡎⢠⣿⢀⣷⠏⠀⠀⡼⠁⠀⠀ ⠘⡟⠉⣇⠀⣿⢆⣻⡿⠁⠀⠀⠀⠀⠀⣹⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠀⠀⠘⢃⡞⠈⠉⠀⠀⠀⣼⣁⠀⠀⠀ ⠀⢹⡦⠘⠛⠁⠀⠁⠀⠀⠀⠀⠀⠀⠘⠓⠒⠤⡤⣤⣤⣤⣤⠤⠤⠴⠒⠊⠉⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢀⡠⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠘⠓⣤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠋⠀⠀⠀⣀⣀⣀⡠⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⠤⠤⠤⠤⠤⠄⠒⠚⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠒⠲⠶⠤⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠶⠤⣄⣀⡀⠀⠀⢀⡿⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⣼⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠦⠤⣤⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠉⠙⠓⠲⠤⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣠⡴⠶⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⡁⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⣼⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠚⠋⠁⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠈⡟⢦⣄⠀⠀⠀⠀⠀⠈⣟⢦⣀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⢸⠍⠛⠒⠦⢤⣀⣻⠀⠈⠙⠒⠦⣤⣀⡀⢹⡄⠉⠙⠒⠦⣤⣀⠀⢻⡀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣶⡶⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⠀⠈⠉⠁⠀⠀⢀⣀⣀⣈⣉⠙⠃⠀⠀⠀⠀⠀⣏⠙⠚⠗⠀⢠⢞⡿⣏⢷⠀⠀⠀⠀⣀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⢀⡾⠋⠁⠀⠈⠳⣄⠀⠀⣠⢞⣋⠁⠀⠀⠉⠉⠳⢦⡀⠀⠀⠀⢹⠀⠀⠀⢠⡏⣼⣧⡉⠸⡇⠀⠀⠸⣿⠻⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣾⠀⢀⣤⡄⠀⠀⢹⡄⠀⢻⠘⣿⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣇⠀⢀⡾⢠⣿⣻⣧⠀⣧⠀⠀⠀⢸⠀⠀⠀⠀ ⣀⣀⠀⢠⡴⣦⡀⣠⡶⡷⠂⠀⠀⠀⠀⠀⠈⠳⣿⠀⠀⠙⠁⠀⢀⣾⠃⠀⠈⢷⣉⠀⠀⠀⠀⣀⣠⡴⠏⠀⠀⠀⠀⢹⡀⣸⠃⢘⣿⠋⣸⣠⡇⠀⠀⠀⣼⠀⠀⠀⠀ ⣿⡉⣻⢿⠀⠈⣷⡏⢸⣆⣀⡀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⢀⣠⠟⠁⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⣀⡀⠀⠀⢧⡟⠀⡿⣽⣤⡿⠟⠁⠀⠀⣰⠇⠀⠀⠀⠀ ⢹⣏⠀⢸⣆⠀⢹⠻⣄⣩⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁⠀⠀⠘⠃⣼⠁⠀⠀⠀⠀⠀⠀⣴⣏⣠⠀⠀⠀⠀ ⠀⢹⣦⡀⠛⠓⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠦⠤⢤⣤⣄⣀⣀⣀⣀⣠⣠⡤⠤⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀ ⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠲⠯⠿⣶⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠶⣯⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠀⢀⣀⣀⣤⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⣤⣀⣀⣀⣀⣀⣠⠤⠤⠖⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣤⡀⠀⠀⠀⠀⠀⢀⠯⡀⠀⠒⡒⠒⡀⠀⠀⠸⣿ ⠀⠀⠀⢸⣷⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢠⠊⠁⣀⣀⡀⠈⠐⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡜⢀⣀⣀⡀⢀⡀⠀⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⣀⣀⣙⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣶⣶⣶⣾⣷⡠⢳⣿⠀⣤⢠⢸⡇⢻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠐⠶⣾⣿⣿⣿⣿⣿⠿⡝⠀⢸⣿⣀⠉⣈⡼⠃⠀⣻⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠈⠻⡟⠻⠿⢧⠰⠃⠀⠸⠿⣿⠾⠟⠀⠀⠀⠀⡟⢿⣿⣿⣿⡿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠢⠀⠈⠁⠀⠀⠀⠠⠞⠀⢃⣬⡿⠟⠓⠡⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠁⢀⣔⠁⡔⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⢣⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠆⠁⠀⠀⠀⡀⠀⠎⠀⠀⠀⣀⡑⠤⠊⣧⠀⠀⠀⠀⡀⠀⠀⠀ ⡀⠀⠉⠈⠀⠀⡠⠤⠀⠼⢀⠄⢂⡭⢒⡢⠭⠶⠶⣥⠢⡒⢹⠁⠀⠀⠀ ⠀⡩⠂⠀⣀⠊⠀⠀⡠⢂⠥⡪⠕⠈⠀⠀⠀⠀⠀⢘⣷⡧⠃⠀⠀⠀⠀ ⢰⠁⢠⠊⢸⠀⡠⢊⣴⠿⢘⠒⠠⡀⠀⠀⠀⠀⠀⠈⠛⠇⢀⠄⠀⠀⠀ ⢸⠀⠀⠀⢸⣪⣾⡟⠏⠀⣀⡰⠆⠛⢓⡠⠤⡤⠀⠀⣀⠫⡑⡀⠀⠀⠀ ⠈⠀⠀⠀⠀⠝⡇⣿⢸⠀⠉⢢⢀⡀⠛⠚⢀⡧⣀⡘⢿⣃⡇⢡⠀⠀⠀ ⠀⡇⡄⠀⢸⢸⠁⠙⢮⣆⡐⠠⠭⠜⠿⠟⠋⠈⢪⠥⠂⢎⠘⠄⢂⠀⠀ ⠀⠇⠃⠔⠐⢺⠀⠀⠹⡀⣬⢉⡐⠂⠤⠤⠤⠤⠤⠤⢐⣪⡎⠚⠲⠥⠄ ⠀⠒⠁⠀⠀⠘⢦⡀⠀⠈⠪⣑⠪⠭⣛⣭⣉⡽⠉⣉⠆⠢⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣀⠀⠉⠒⠢⠤⠌⠒⢒⡒⠎⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠉⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⢀⣼⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⠋⠀⢐⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠃⠀⣸⠇⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠋⠋⠉⠉⠉⠙⠻⢤⡀⠀⠀⠀⠀⠀⢀⣠⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⣀⡟⠀⠀⠀⣀⡤⠖⠋⠁⣀⣤⠶⠞⠛⠛⣛⣻⣿⣶⣦⣄⡙⠳⢄⡠⠤⠖⠛⢸⡏⠀⠀⠀⠀⠀⠀ ⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠈⠁⢀⡴⠛⠁⢀⡤⠶⠛⢃⣠⡤⠶⠛⠉⠉⠀⠀⠀⠉⠙⣿⣷⠀⠻⡄⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⢳⡦⠖⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⣠⠞⠋⢀⣤⠞⠋⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⣷⡄⢳⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡼⠋⠀⠀⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⣠⠞⠁⣤⠶⠋⣈⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⣿⣷⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠁⠀⠀⠀⣠⠞⠉⢸⠀⠀⠀⠀⠀⣠⠞⢁⣠⣾⢏⡤⠞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠁⠀⠀⠀⣸⠁⠀⠀⡏⠀⠀⠀⣠⠞⢁⣴⡿⣿⡷⠟⠈⠉⢉⠉⠙⡲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠃⠀⢠⣤⠄⠀⠀⠀⠀⠀ ⢾⠀⠀⠀⢸⠃⠀⠀⠀⢹⠀⣠⠞⢁⣴⣿⣿⣿⠟⠀⠰⠚⠉⠁⠀⠀⢀⣀⣙⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⣶⡟⠁⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠸⠀⠀⠀⠀⣸⡞⢁⣴⣿⣿⡟⠙⡏⠀⠀⠀⠀⠀⢰⣒⣩⠵⠶⠖⠋⠙⠳⠦⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⡲⢾⣧⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣿⣿⡿⣿⣧⠀⢹⡄⠀⠀⢸⡏⠉⠉⠀⠀⠀⠀⢀⣶⣿⢿⡆⠀⠀⢻⡀⠉⠉⠉⠉⣰⣿⣿⡍⠈⣧⠀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢻⡄⢹⣿⡇⢀⡇⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠈⠿⠿⠾⠇⠀⠀⢸⣇⠀⠀⠀⠀⠙⠿⠾⠃⠀⣿⠀⠈⣇⠀⠀⠀⠀⠀ ⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣼⠇⢸⣿⡇⢰⡇⠀⠀⠀⠀⠐⠮⣙⠲⠤⣄⣀⣀⠀⠀⠀⣀⣠⢾⣉⠓⡦⠤⣄⣀⣨⡥⠤⢜⣿⡄⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⡇⠀⡀⠀⠀⠀⠀⣾⠀⣼⡟⠀⠈⠻⣿⣄⠹⣄⠀⠐⠦⣄⡀⠈⠙⠒⠦⠭⢉⡉⣉⣩⠽⠋⠀⠙⢦⣌⡉⠓⢲⣒⢐⣶⠛⠁⢹⡀⠀⢳⡀⠀⠀⠀ ⠀⠀⡇⠀⣿⠀⠀⠀⠰⢻⠀⣿⡇⠀⠀⠀⠈⢛⡷⣿⣀⣀⠀⠀⠉⠙⠛⠒⠒⠲⠖⠚⠋⠁⠀⠀⠀⠀⠀⠹⣟⠋⠉⠀⠈⢻⡆⡀⠀⠹⣄⠀⠱⣄⠀⠀ ⠀⠀⡇⠀⡟⠀⠀⣰⢦⣘⣆⣿⡇⠀⠀⠀⢰⠋⡾⠉⠀⠉⠉⠓⠲⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣠⠿⣝⠲⣤⣙⢷⡀⠈⠣⡀ ⠀⢰⠃⡌⠀⢀⡴⠃⠀⠈⠉⣿⡇⠀⠀⠀⠀⠀⢻⡄⠀⣿⣧⣤⣀⠀⠀⠈⠉⠉⠒⠒⠒⠲⠤⠤⠤⠤⠔⠒⠒⠒⠒⠋⠉⣠⡶⢻⡄⠀⠈⠉⠙⠓⠒⠒ ⠀⠋⠀⣠⡴⠋⠀⠀⠀⠀⠀⣿⡇⡀⠀⠀⠀⠀⠀⠙⢦⡈⠻⢦⣈⣉⣻⣶⣶⣦⣤⠤⢤⣤⣤⣤⣤⣤⡤⠤⠤⠦⣄⡀⠹⣍⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣮⣀⠄⠀⠀⠀⠀⠀⠙⢦⡀⠉⠛⠷⢤⣄⣉⠙⠳⢦⣄⡀⠀⣔⣿⠀⠀⠀⠀⢈⣷⠀⢸⡄⠘⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀⠀⠀⠀⠀⠀⠉⠳⠤⣄⡀⠀⠈⠉⠛⠒⠺⠭⠿⠯⠥⠤⠤⠖⠚⠋⠁⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣄⣀⣀⣀⡤⠴⠶⠶⠒⠒⠒⢚⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡤⠤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⠹⡉⠉⣉⢰⣢⠶⠾⠵⠾⠼⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢘⡧⢱⢀⠟⠉⢀⡠⠒⠈⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡴⠛⢧⡜⠁⠀⡰⠁⠀⠀⡐⠰⠀⠀⢀⠀⠀⠙⡓⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⣄⢀⠁⠀⢠⠁⠀⣠⠞⠁⠁⢨⡧⢤⢂⠀⣧⢰⡀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⠀⠀⢸⡠⠊⠁⠀⠀⡠⢃⣷⠏⡜⣰⢿⢯⠈⣮⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡀⠀⢠⠒⣢⠀⢀⠔⠕⠁⢈⣶⠵⡃⠺⣼⠀⡇⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠀⠘⢄⣼⢪⢁⠀⠀⠀⠈⠁⢀⡒⢼⣇⡔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⢏⢆⠛⡷⠄⠀⠀⡖⢻⠋⢈⢯⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠋⠀⡐⠂⢌⣳⢯⠶⢗⡀⠐⢌⣚⡤⠊⡌⠛⠀⠀⠚⡏⠢⠀⠀ ⢤⡀⠤⠒⠁⡠⠊⠀⡞⣸⡿⢼⡔⢚⣯⠙⢋⠁⠱⡉⢀⡄⠀⣀⣁⣃⠁⠀⠀ ⠀⠁⢒⢆⠉⢄⠀⠸⢠⡏⠀⠎⠙⣾⠏⠀⠘⡄⠄⡋⡕⢁⣰⣿⣿⣿⣿⣞⠁ ⠀⠀⡎⡆⡠⡼⠉⡇⣾⠁⡘⠀⣸⠧⡀⠄⠔⣰⠭⠝⠃⠘⣿⡏⠉⠉⢻⣿⠀ ⢀⡀⢇⡿⡶⠁⡰⢰⡯⢄⡃⢀⣿⠀⣇⢊⠎⣜⢠⠀⠀⠈⣹⣷⢢⢴⣾⡟⠀ ⠘⠓⠘⠒⠓⠒⠁⢘⣃⢈⢈⢚⣳⢚⣁⢒⡺⢚⢚⢒⣆⠐⠛⠛⠈⠙⠛⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠒⢹⣀⢺⣐⡾⣐⣼⣒⢸⢺⢙⣶⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠋⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⢀⠟⠀⠀⠀⠀⠀⠀⢠⣆⢸⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⣾⠤⡄⠀⡤⢶⣜⡀⠈⠓⢺⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠟⠐⢆⠀⡰⠒⠢⡍⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡷⠄⡴⠘⡄⠀⠀⡹⠶⢶⣿⣿⣿⡿⣫⠽⡹⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⡎⣀⠀⠈⠉⠉⠀⠀⠨⣿⡿⠟⢺⡿⠀⣵⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣋⠈⠛⠁⠀⠀⠀⠀⠀⣸⣿⠀⠀⠫⠀⣼⠏⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡜⣿⣶⣤⣀⠀⠀⠀⠐⠿⠋⠀⠀⣠⣾⢣⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⢟⣛⡩⠎⠀⠀⣀⣀⣠⣤⠴⠚⠋⡡⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠼⣏⠀⠀⠀⢸⡁⠀⠀⠀⢀⣠⣪⣾⣿⣿⡇⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⣄⣉⣷⡶⣖⣟⣁⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⢀⠀⠀ ⠀⠀⠀⠀⣀⣴⣾⣿⠈⣿⣿⣷⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴ ⢀⣴⣾⣾⣿⣯⣿⣿⣾⣿⣿⣏⡭⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿ ⣿⣿⣿⢯⣿⣯⡟⣿⡿⢹⣿⣿⣴⣿⣿⣿⣝⣿⣿⣫⣿⣿⣿⣷⣿⣿⡟⣿⣿⣿ ⢫⣿⣟⣿⣿⣿⣿⣿⡤⡾⢺⣿⣿⣿⣿⣷⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⡇⢤⣾⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⡿⠿⠿⠟⠿⠻⠿⠷⣶⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⠟⢫⡉⠔⠢⡅⠓⡌⢣⠙⡌⠱⡠⢉⠛⠿⣷⣄⠀⠀⠀ ⠀⠀⢀⣼⡿⢋⠴⣈⣥⣌⣩⡑⠬⡑⡘⢢⠱⣈⠓⡰⢉⣼⣴⣭⣿⣦⠀⠀ ⠀⢀⣾⠏⢴⣽⡾⠛⣻⣿⣿⣿⣶⠡⡑⣦⣷⣶⣍⡔⣿⡟⠀⢠⣿⣿⣧⠀ ⠀⣼⡟⢬⣾⠋⠀⢸⣿⣿⣿⣿⣿⡇⣽⣿⣿⣿⣿⣶⢿⡇⢠⣿⣿⣿⣿⡆ ⠠⣿⣇⢾⡇⠀⠀⢸⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⡾⣷⡈⣿⣿⣿⣿⣿ ⠘⣿⡌⢻⣧⠀⠀⠀⠙⠿⣿⣿⠃⢾⣿⣿⠻⣭⡙⣿⡇⣻⣷⣝⢿⣿⡿⣿ ⠈⣿⡇⢎⡹⣷⣦⣀⣤⣾⠟⡡⢚⢸⣿⣇⠻⡴⣙⢾⣷⠱⣎⢻⠿⣶⣾⡿ ⠀⠸⣿⣎⠳⣥⢯⡽⣩⢇⢯⠳⣌⢂⣿⣏⣳⠱⡭⢾⣏⠳⣿⢻⢳⣧⡿⠁ ⠀⠀⠙⣿⣵⢛⡞⣳⢛⡭⢎⣝⠺⣆⠜⣿⣶⢫⢵⡿⠻⡱⢎⠧⣿⡟⠁⠀ ⠀⠀⠀⠈⠻⣿⣼⣡⢏⡜⣣⢎⡳⣹⠰⡈⡝⠻⠟⡡⢃⠽⣭⡿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⣷⣾⣱⡎⡵⡝⠰⠡⠜⣡⢚⣤⣿⡿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠷⠿⠾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠋⠉⠉⠉⠉⠛⠛⠶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⡀⠀⠀⠀⢀⣀⣤⠴⠾⠛⠉⠉⠁⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠶⠖⠒⠶⠶⠶⢦⣤⣀⡀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣄⡀⣿⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣄⣀⣀⣙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠚⠋⠉⣉⣠⣤⣤⣤⣤⣤⣭⣍⣉⠛⠛⢶⣄⡀⠀⠀⠀⠀⠠⠴⠒⠒⠛⠛⠋⠉⠉⠉⠉⠉⠙⠛⠒⠒⠶⢿⣆⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⣀⣤⠶⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣮⣿⡀⣀⣀⣠⡤⠶⠶⠖⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠳⠶⣬⣛⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠟⠉⠁⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠉⡻⣧⡀⠀ ⠀⠀⠀⠀⠀⣀⣤⣾⢤⣤⠤⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡴⡶⡞⣛⠛⠛⠋⠉⠉⠉⠉⠉⠻⣿⣃⣀⣠⠤⠴⠖⠚⠛⠋⢉⣭⣶⣶⣶⣶⣦⣤⡀⠀⠉⠉⠙⠛⠻⣿⠂ ⠀⠀⠀⠀⠀⢿⣿⣄⣀⡀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⠚⠋⣹⣿⡟⠛⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢀⡟⠋⠉⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁⠈⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢯⡉⠉⠉⠉⠁⠀⠀⠀⠀⣼⣿⣿⣷⣤⣿⣿⠟⠛⢻⣿⣷⡄⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣾⣿⡏⠉⢹⣿⣿⣧⠀⠀⠀⣠⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠳⠦⣄⣀⠀⠀⠀⢰⣿⣿⣿⡿⠛⣿⣿⣄⣀⣰⣿⣿⣷⣤⡴⠞⣿⣤⣄⣀⣀⡀⠀⠀⠀⣼⣿⣿⣧⣠⣿⣿⣷⣶⣾⣿⣿⣿⠶⣶⣾⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⠤⠞⠛⠋⠉⠉⠉⠉⠛⠛⠿⣶⣿⡿⠿⠿⠛⠛⠋⠉⢀⣀⣴⠿⠁⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⣛⣛⣛⣛⣉⠉⠁⠀⢀⡴⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣤⡶⠶⠛⠛⠛⠉⠉⠙⠛⠛⠲⠦⣤⣀⠀⢀⣠⡴⠞⠛⠛⠋⠙⠛⠛⠳⢦⣞⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⣀⣤⠴⠖⠚⠒⠒⠒⠲⠶⣤⣄⣩⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠁⣀⣤⡤⠶⠶⠶⠶⢦⣄⣀⣼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠀⠀⠀⠂⠒⠀⠀⠀⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣶⠞⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀⣀⣤⣷⣦⣤⣤⣀⡀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣿⣧⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠁⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⠀⠀⠀⢀⣴⣤⡙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢁⣽⠆⠀⠀⠀⢀⣴⡾⠿⠿⠿⢿⣿⣿⠇⠀⠀⢸⣿⡿⢿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⣼⠁⠀⠀⠀⢠⠟⠉⠀⢀⣀⡀⠀⢻⡇⠀⠀⠀⢸⣟⣁⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣼⣿⣿⡿⠟⠋⠠⠀⠀⠀⢀⣾⠃⠀⠀⠀⢰⠏⠀⣼⡗⠋⢉⣍⣷⣼⣷⣀⠀⠀⢸⠋⢉⢻⣿⣇⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣼⠋⠀⠈⠉⠛⠛⠓⢶⡄⢤⠶⠶⢾⡷⣦⣤⣤⣤⣄⡀⠀⠉⠙⠲⢼⣿⠟⠹⠋⣹⣧⣠⣬⣆⣸⡿⢻⣧⣉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⡟⠙⢶⡄⠀⠈⣧⠀⠀⠀⡟⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⢻⠃⠀⠀⠀⢛⣿⠁⠀⠀⢹⠁⠈⡏⠙⢻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡿⠀⢀⣾⣿⠀⠀⢸⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⣀⣾⠇⠀⠀⠀⢹⣆⠀⣇⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠲⠦⢼⣌⣧⠀⣾⣿⣿⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⡛⠀⠀⠀⠀⠀⠀⢉⢻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢢⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣿⠀⠈⠻⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣤⣶⣶⣶⢤⡀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⢦⣄⠈⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁⠴⡿⢋⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣶⠟⠉⠃⢈⡛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣤⡾⠀⠀⣿⠃⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢿⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⡟⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣾⣾⣿⣤⠶⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣁⠀⠂⠒⠶⢦⣤⣤⣤⣤⣤⣤⣶⣿⡇⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣀⣀⣀⣀⡈⠉⠛⠛⠛⣉⣉⣉⣀⣴⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠛⠛⠻⠿⠿⢿⣿⠿⠿⢿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣶⣶⣶⠶⠖⠛⣹⣧⣴⠟⠁⢀⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠈⠿⣿⣿⣿⢷⣠⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠋⠉⠀⠀⠀⢰⣿⡏⠀⠀⠀⣸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠈⢉⢀⣼⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣄⡀⠀ ⠀⠀⠀⠀⠀⢠⣿⡟⠠⠀⠀⠀⣿⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⡟⣿⣿⣄⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣯ ⠀⠀⠀⠀⠀⣼⣿⠱⠃⠀⠀⠀⢸⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢰⣿⠇⡄⠀⠀⠀⠀⠀⣇⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣉⠻⠿ ⠀⠀⠀⢀⣾⡟⠰⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣮⣙⠄⠀⠀⠀⣀⣀⢤⣷⣿⠇⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠉⠒ ⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣷⢿⡿⠛⠛⣿⣿⠁⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀ ⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢁⡼⠁⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀ ⠀⡀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠈⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠴⠞⠁⠀⠀⣰⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀
⠀⠈⠁⠀⠀⠀⠀⡰⠒⣄⠀⠉⠁⠀⠀⡠⠮⠏⠑⠒⠒⠇⠴⣖⡂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⡴⠁⣈⣋⢳⢅⣀⠀⠔⠑⠀⠀⠀⠀⠀⠀⠤⠮⠤⡰⠖⠈⢆⠀ ⠀⠀⡰⠀⠀⢰⠁⡡⠂⢀⡀⠡⠑⢒⠀⠉⠁⠀⠚⠣⢅⣂⢔⠞⠛⣳⣁⠀⠈⡀ ⠀⠀⠀⠉⢈⡟⢘⡖⡆⠁⠀⡐⡰⠁⠀⠀⠀⠀⢀⠄⡀⠀⢇⡀⠀⠀⣔⠁⠀⢃ ⠀⠀⠀⠀⢸⡥⢪⠊⠀⡌⠌⡜⠁⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡐⢄⢀⢰⠀⠀⢸ ⠀⠀⠀⢠⠊⣠⢣⠁⣸⠀⡜⢸⠀⠀⠀⠀⠀⢠⠎⢀⡆⠀⡀⣧⠀⠃⠺⡀⠀⠈ ⠀⠀⣔⢡⠋⠆⡆⡐⢸⣰⡠⠼⡀⠀⠀⠀⢠⠋⠐⢼⡹⠀⢃⢸⡄⠀⠀⠃⠀⠀ ⠀⣺⢣⡇⢰⡰⢠⠃⠉⠓⠀⠒⠳⡀⠀⣸⠇⠠⠠⠀⣯⢃⠸⠘⡇⠀⠀⠀⠀⠀ ⠘⠃⢘⠃⠘⢥⠪⣠⡶⠴⠶⢦⠄⠉⠲⠹⠀⣀⣲⣠⡘⡌⣄⠀⡇⢀⠀⠀⠀⢰ ⠀⠀⡘⠀⢠⡈⠛⠹⡀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠵⢴⢹⡿⣏⡆⠀⡌⠀⠀⠀⢸ ⠀⠀⠁⠀⢆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠃⡐⠀⢀⠀⠀⣸ ⠀⢰⠀⢸⡾⡇⠀⠀⠀⠀⠀⣠⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⡎⡰⠀⠀⡼⢂⠀⣿ ⠀⡟⠀⣸⣧⡇⠀⠀⠀⠀⢸⣌⣿⣿⣷⣧⡆⠀⠀⠀⢀⢌⠔⠀⠀⠠⠀⡌⠀⢿ ⢸⢡⡞⢿⣷⠘⡀⢀⠤⠠⠸⡿⠛⠛⠛⡿⠀⠀⠀⡠⠂⠀⠂⠂⠠⢒⠝⠀⠔⠀ ⠘⠘⣇⢸⢸⣠⢷⣌⠢⠜⠀⠱⠶⡶⠒⠁⠀⢀⢎⡜⠀⡀⠀⢠⢟⠅⠀⣼⠀⠀ ⢐⠀⢸⡜⣼⠃⠀⠈⢱⣄⠀⠀⠀⢹⠀⡠⡂⠔⣹⠋⠝⠀⢀⣮⠃⠠⢼⢻⡄⠒ ⠄⠀⠀⠹⠧⠑⠢⣶⣿⣿⣔⠤⠄⠌⠙⠑⠂⠉⠃⠘⡣⢠⣾⡟⢰⣟⠸⠄⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠛⠉⠉⠀⠈⠉⠉⠲⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⣠⠖⠒⢦⡀⠘⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢹⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⣀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠘⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠑⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢄⣹⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠋⠀⠀⠀⢀⡤⠒⠈⠉⠉⠉⠑⠒⠤⣀⠀⠀⢀⠴⠋⣀⣀⣀⠈⢿⠀⠀⠀⠀ ⠀⠀⠀⢰⠃⠀⠀⠀⢠⠏⠀⠀⣀⣤⣤⣶⣤⣄⣀⠀⠉⠉⢁⣴⣾⣿⣿⣿⡇⢸⡄⠀⠀⠀ ⠀⠀⠀⡎⠀⠀⠀⢀⡟⠀⢠⣾⣿⣿⡿⠿⠿⠟⠿⣿⣿⡿⠛⠛⠛⠛⠻⢿⡇⢸⠀⠀⠀⠀ ⠀⠀⠀⣇⠀⠀⠀⠈⡇⠀⢻⣿⠋⠀⠀⠀⠀⠀⠀⣠⣽⡆⠀⠀⠀⠀⢠⣾⣿⡟⠀⠀⠀⠀ ⠀⠀⢀⣸⠦⣀⠀⠀⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠿⢿⡇⠀⠀⠀⠀⢀⣹⡿⠁⠀⠀⠀⠀ ⠀⡔⣯⣤⣤⠞⠓⠀⠸⣆⠀⠳⣄⠀⠀⠀⢀⣀⣀⡤⠾⢤⣤⣤⡶⠖⠿⠹⠙⠲⢄⡀⠀⠀ ⢸⠙⠃⠀⠘⢤⡄⠀⠀⠈⣳⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⡠⠖⠋⠙⢦ ⢻⡆⠀⠀⠀⡎⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣤⣴⣶⣄⣸ ⠈⢷⡀⠀⣞⢻⠃⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡟ ⠀⠀⠉⠲⠄⠈⣦⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠘⢆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡻⠿⡿⢛⣳⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠤⣤⣀⣤⣤⣤⣤⠤⠜⠛⠉⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠄⠀⠀⠀⠐⠖⠢⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡂⠄⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⣀⣀⣉⡀⠀⠀⠀⠀⠀⠠⠖⠐⠂⠀⠀⠁⠀⠀⠀ ⠀⠀⣤⣴⡶⠴⠶⡶⣶⠄⠀⠀⠀⠀⠀⣬⣀⣲⣂⣤⢀⠀⠀⠀⠀ ⠐⠿⠙⣬⡽⡚⠯⣺⢀⡤⢢⡆⠐⢀⠠⣰⣟⢢⣾⡭⢛⢦⣄⡀⠀ ⠠⣧⢽⠎⠖⠋⠠⠂⠁⠀⠘⠓⠐⠀⢰⡯⠐⠁⠉⠲⣘⢡⠽⡛⠂ ⠈⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⡄⠀⠀⠀⠀⡠⠐⣂⡒⠂⢄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀ ⠀⠰⠃⠀⠀⠀⢸⣅⣸⣿⣿⣿⣷⣾⡢⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢿⣿⣿⣿⠃⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣋⠀⢀⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠆⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⣠⣤⣾⣶⣶⣄⣀⠀⠀⠑⢢⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡇⠀⠀⠀⢀⣤⣶⣾⣿⣷⡆⠀⠀⣾⣷⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣿⣿⣿⣿⠿⠋⠁⢀⡞⠁⠀⠀⡴⠋⠁⠀⠀⠘⣿⠁⠀⠀⣿⡋⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢷⣿⣿⣿⠋⠀⠀⠀⢀⡞⠀⠀⠀⠘⠁⢰⡟⠉⣭⣷⣿⣄⡀⠀⡏⢉⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣀⣄⡉⠈⠙⡆⠒⠛⢻⠛⠒⠲⠶⠤⠤⢄⣉⣻⡿⠁⠉⢸⣷⠶⠒⢼⠏⢿⢦⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡟⠀⣹⡆⠀⢹⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣠⡏⠀⠀⢸⡄⢸⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠒⠒⠦⢼⣸⡄⢰⡿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠋⠀⠀⠀⠀⢙⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠐⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠿⠛⠛⣶⡴⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⠋⠑⢶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠠⣴⠂⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢧⠀⠀⢀⣀⣠⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠷⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠙⠻⠿⠿⠛⠛⠛⣿⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠻⠿⠷⣶⡶⠾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡇⠀⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⠶⠖⠚⢹⣷⠾⠁⢠⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⠻⢿⡿⢷⢼⣿⣿⣿⣿⣧⣀⣀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⢀⣿⢃⠀⠀⣼⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣤⣿⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣷⣦⡄ ⠀⠀⠀⠀⣼⣯⠀⠀⠀⢹⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡜⢿⣷⣄⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿ ⠀⠀⠀⢸⡿⠀⠀⠀⠀⠈⣆⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⢀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠻⣿⣆⠀⠀⠀⠀⠀⡈⠛⠭⠙⠻ ⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠘⠆⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣥⣀⣀⣠⣤⣶⣿⠟⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⢦⡀⠀⠉ ⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⢻⠏⠀⢸⡇⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⢳⠀⠀ ⠀⣀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠃⠀⢀⡞⠂⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠿⠿⠿⠿⠶⣦⣤⣄⣀⠈⠉⠛⠿⢿⣿⡿⠛⠉⠀⢻⣿⣻⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣴⠞⠋⣁⣀⣤⣤⣤⣤⣀⣀⠉⠙⠛⢿⣶⣤⡀⠀⠈⠉⠀⣠⣴⡾⠿⠿⠾⠿⠿⠿⠿⠿⢶⣤⣤⣄⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣠⣾⣿⠷⠞⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠓⠶⣄⡀⠉⠻⣷⣦⣰⠾⠋⢁⣀⣤⠤⠶⠶⠶⠶⠶⠦⢤⣤⣀⠉⠙⠻⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⢙ ⠀⠀⣼⡿⠋⠀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠉⣡⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⢀⣴⡟ ⠀⢸⠟⢀⣴⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠞⠁⣀⣤⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⢹⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣴⠟⠋⠀ ⢀⡏⢠⣿⣿⡿⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⣼⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣭⣛⣛⠛⣿⠋⠀⠀⢀⣼⠟⠁⠀⠀⠀ ⢸⠀⢸⣿⣿⡄⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣼⣿⡿⠋⠉⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡏⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀ ⠸⡄⠈⣿⣿⣿⣷⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣿⣿⣧⡀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⡟⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⡄⠈⠻⠿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣼⠇⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠟⠋⠙⢦⡀⠀⠈⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⢀⣤⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠘⠦⣤⣍⣉⣉⣉⣉⣉⣉⣉⣩⣭⣭⣽⡧⠄⠀⠀⠀⠀⠀⠹⣷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⣠⡞⠁⢠⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⢀⣬⠟⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣤⢠⡀⠀⠀⠻⣆⠈⠉⠙⠒⠒⠶⠤⠤⠤⠤⠤⠶⠒⠚⠋⠁⠀⣀⣤⡴⠞⠁⠀⠀⢸⣿⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣸⣿ ⠀⠀⢀⣴⠞⠋⢡⣤⣤⣤⣤⣤⣤⣤⣤⣀⣠⣴⣾⠿⠃⠘⢿⣦⣀⠀⠉⠻⠶⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠶⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣟ ⠀⢠⡟⠁⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣀⣀⣀⣀⠀⠙⠻⠿⠶⠦⢤⣤⣤⣍⣉⣉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢸⣇⠀⠀⠀⠀⠀⠀⢠⣿⡇ ⠀⢸⣷⡾⠛⠛⠋⠉⠉⠉⠀⣀⣀⣀⣀⣀⣀⣀⣉⠉⠉⠉⠛⠛⠛⠳⠶⢤⣤⣀⣀⠈⠉⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠸⣿⡇ ⠀⠘⢿⣤⠀⠀⢠⣶⠟⠛⠛⡛⣛⣛⠛⢛⠛⠛⡛⢻⣿⣷⣶⣶⣦⣤⣄⡀⠀⠉⠙⠛⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⡄⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠈⠻⣧⡀⠘⢿⡄⠀⢠⣁⡙⣏⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠉⠙⠳⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢻⡇⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⠈⢷⡄⠀⢻⣦⠀⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⡀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠘⢿⣶⣶⣶⣶⣶⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡇⣸⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⣿⠀⠉⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⡇⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⢀⣼⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠈⣿⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⢰⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡘⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⡿⠋⣠⡴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣟⠟⣛⣿⣷⠿⠛⢁⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠛⠶⣤⣀ ⠀⠀⠀⠀⠀⠀⣇⡀⠀⠙⠻⠷⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡴⠶⠿⠛⠉⣀⣤⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠻⣧⣤⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⣀⣀⣠⣤⠶⠛⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁⠀⠀⠀⢀⠀⢀⠀
⠀⠀⠀⠀⢴⠁⠀⢀⣸⣅⣀⠀⠀⢀⢴⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠎⡐⢈⡰⢹⠈⠛⠻⣕⣁⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀ ⠀⠀⠀⣸⠀⣩⣿⡿⢿⣶⣤⡎⠀⣰⣽⠃⠀⠀⠀⠀⠀⢀⠀⢀⠜⠀⡇⠀⠠⠀ ⠀⠀⠀⣧⣾⡿⠁⠀⠘⣼⠎⠻⣆⢸⡝⠐⠀⢀⢀⡤⠂⡾⢲⠯⠥⠤⢦⣞⠁⠀ ⠀⡆⡆⣯⢘⡇⠀⣀⣀⣜⡒⠠⢙⣿⠘⠀⠀⢠⠋⢀⠾⡠⠋⠀⠀⠀⠘⡏⠙⠲ ⠀⣿⣇⣿⡞⠱⠀⠀⠂⠰⡡⠃⣆⠈⢰⡇⠀⣰⢀⢮⠗⢐⣒⣖⠂⠤⣆⣻⠀⠀ ⠀⠃⢹⣟⣿⠨⢵⢄⡈⠒⠒⠊⠉⠀⠀⠷⢀⢹⠌⠁⠈⣉⠉⣛⠛⢷⣯⣞⠀⠘ ⠀⠀⣸⠹⣾⢿⣥⢧⢲⠙⡠⣀⠀⠈⡀⠀⢻⠈⠀⠢⡎⢰⡦⢰⠣⠊⢈⣿⣕⠆ ⠀⢰⣿⠀⡿⠛⠗⠋⠋⠻⡷⣿⣯⠰⣱⠀⡀⢀⢀⠀⠥⢈⠂⡀⠵⡠⡞⠈⣿⠀ ⠀⢸⠸⠀⠟⠀⠀⣴⡀⠀⠁⠀⠙⡆⠡⢦⣡⣄⣀⠍⠂⢄⠀⠀⠀⡀⠤⢾⣿⠀ ⠀⢸⡄⢣⠀⠀⠀⡿⣈⠂⠄⡀⠀⠁⠀⠈⠙⢻⣷⢹⢸⣄⠫⣁⡢⢀⢔⠎⠘⢰ ⠘⡸⢟⣷⠣⠀⠀⢉⠱⡑⠠⢈⠢⠒⠒⠀⠀⠀⠸⡌⢟⣯⣷⡆⢀⣡⠃⠀⢀⠎ ⠀⠑⠎⠑⠡⢑⣤⠃⠀⢼⡅⠂⠤⢉⣀⠂⣒⡲⡾⠁⠈⠙⠛⢬⣭⣯⡶⠒⠁⠀ ⠀⠀⠀⠀⠀⠀⠸⣄⠀⡞⠀⠀⠀⠀⠀⢀⠓⣺⠀⠐⣂⠤⠒⠉⢀⢾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠃⠢⠄⠀⠤⠤⢤⣔⠝⠐⠒⣸⠉⣦⠀⣀⡴⡻⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠁⠀⠒⠂⠠⠄⣀⠀⡘⠉⠢⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡤⠤⠀⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢱⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢲⠀ ⠀⠀⠀⠀⠀⠀⠤⠀⠦⡀⠀⠀⢤⡀⠀⠀⢠⡀⠀⠀⢠⠀⠀⠀⠀⠀⠁⠮⡀ ⠀⠀⠀⠀⠀⠘⠄⠀⠀⢘⠁⠒⠘⠈⠁⠒⠨⠀⠁⢲⠬⠆⠠⣶⡄⠀⠀⡎⠁ ⠀⠀⠀⠀⠀⠀⠈⠢⢠⠊⡀⠈⡆⢸⢧⠀⠈⠑⡄⠀⡆⢠⢹⣧⢡⠀⢩⠁⠀ ⢰⡲⡊⣶⢋⡀⠀⠀⠈⢄⣀⠔⠁⠀⠒⠀⠒⠊⠀⡀⠰⡆⡾⠼⠂⢀⠎⠀⠀ ⠈⡦⠓⠂⠉⠁⠀⠀⠀⠊⠤⣤⣤⣤⠤⠤⠐⠂⠁⠀⠀⡜⠀⠀⠀⡈⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠉⠁⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⢀⡩⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠒⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠒⠒⠒⠒⠒⠒⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣤⣀⣀⠔⠁⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠉⠉⠀⠉⠉⠑⠢⣀⠀⠀⠳⡀⠀⠀⠀⠀⠀ ⠀⠀⠈⢣⠀⠀⠀⠀⢠⡤⢤⡶⠖⠛⠛⠀⠀⠀⠀⠀⠀⠑⠒⠢⠤⡀⠈⢢⡀⠀⠙⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠱⢄⠀⢀⠎⠀⣀⠔⠒⠒⠒⠤⡀⠀⠀⠀⣠⠔⠒⠐⠒⠢⣀⠀⢣⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⣶⣶⣾⣿⣾⣶⣾⣷⣶⣶⣶⣶⣶⣾⣶⣶⣾⣷⣶⣶⣶⣶⣶⣾⣷⣾⣷⣶⣿⣶⡆⠀⠀ ⠀⠀⠀⠛⣿⣿⣴⣻⣶⣛⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣜⣻⣶⣻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀ ⠀⠀⠀⠀⠈⢹⢿⣿⣾⣿⣶⣿⣿⣿⣿⣿⠟⠁⢀⠘⢿⣿⣷⣾⣿⣾⣿⣿⣿⣿⠿⡏⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣏⠘⡏⠉⠉⠉⠉⠉⠉⠉⠁⠀⢠⣀⣱⠀⠈⠉⠉⠉⠉⠉⠉⠉⡿⠀⡽⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠒⢾⡀⠀⠀⠀⠀⣠⣤⣄⣀⣀⢀⣀⣀⣤⣤⣤⠀⠀⠀⠀⢠⠗⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠁⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠛⢲⠤⢤⣀⣀⣀⣀⣀⡠⠤⡖⠛⠛⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢠⠟⡦⠶⣿⡧⠤⣼⣿⠓⢤⠟⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡀⢾⡀⠀⠀⢣⢱⢴⡏⡞⠀⠀⢀⡵⡄⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⡇⠀⢈⡱⠂⠘⣾⡀⣿⠃⠀⠾⡁⠀⣸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡇⠀⠈⠢⡀⠀⢹⠀⡞⠀⢀⡴⠃⠀⣻⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠐⠚⣷⣤⡶⢷⣤⡀⢸⠀⢰⠇⠀⠀⠀⠑⡄⠈⣯⠗⡾⢿⡖⣶⠋⢹⠀⣶⡇⢀⣴⣶⠀⠀⠀⠀ ⢀⡤⣿⣿⣇⣀⣽⡿⣯⡴⣶⣤⣀⣴⠶⣦⣼⣆⠛⣰⢁⣿⠾⣿⠀⠘⢲⣷⠿⢾⣿⠖⢀⣤⢶⣄ ⠈⠻⣿⣿⡇⠀⢼⡇⢸⡇⠀⣿⠀⣿⠀⢸⡇⠘⠒⠁⠨⣿⢠⡟⠀⠀⠀⣿⠀⢸⣿⠀⠀⣿⠴⠋ ⣠⡴⣿⣿⣿⣶⡾⠃⠸⢷⣤⠿⠀⢿⡦⢺⣇⠀⠀⠀⣠⡿⠿⢶⣶⡤⠀⣿⠄⠸⢿⡤⠠⢿⣦⠴ ⠀⠀⢿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠶⠿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠉⠉⠉⠀⠀⠀⠀⠉⠉⠐⠂⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠭⠙⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣋⠔⣤⠴⣦⠞⣠⡇⠀⢰⡀⠀⣶⠀⠑⠁⠙⢆⠹⡄⠀⠀⠀⢄⡉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠋⡽⠁⠀⠁⠀⠀⠺⠟⠁⠀⡞⠀⢀⠸⡗⠀⠀⠀⠀⢣⠘⣆⠐⡄⠰⣝⢷⡢⢝⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠁⢰⠀⡀⠀⠀⠀⢠⡀⠀⠂⢀⣁⠀⠰⡀⢻⣄⠀⠀⠀⠀⢣⠘⣆⠘⡀⠈⠻⡻⣆⠙⢷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⢣⠀⣼⠞⠹⣦⠀⠀⠸⡇⢸⡇⢸⣽⣆⣤⠵⣦⣿⣧⡄⠀⠀⠀⢇⣯⣦⣷⡀⠀⠙⣌⢳⡄⠙⡄⠀⠀⠀⠀ ⠀⠀⠀⡿⣬⠔⢁⠼⡆⢻⡀⠀⠀⣷⠀⣷⢀⡿⢻⡇⠀⠈⠛⢿⣟⠣⢄⠀⣸⡏⢹⢸⣷⢆⠹⣾⣷⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⢠⠟⣁⠔⠁⣠⠃⢸⢇⠸⡀⢻⣧⠘⡏⢇⠀⠻⣎⠙⠲⡀⠈⠉⠛⢻⣿⣗⣛⣸⣷⠘⣧⢹⣷⠘⣧⠀⠀⠀⠀⠀ ⠀⣶⠁⠀⠻⠦⠤⠏⢀⡎⠈⣧⡱⡘⡄⠳⢽⣞⡄⣰⡾⠟⢿⣧⠦⠀⠀⢈⡿⠿⣿⣿⣿⠀⣟⣸⢿⡇⢹⠀⠀⠀⠀⠀ ⠀⢻⡆⠀⠀⠀⠀⢠⠎⠀⠀⢿⣿⢷⣿⡄⢰⣿⡟⠁⠀⠀⣿⡿⠀⠀⢰⣿⣄⡀⣿⣿⡿⠂⣿⣏⠈⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠤⣀⡠⢔⡡⣦⡀⢢⠈⢣⡀⠨⣌⠒⠀⠉⠛⠛⠛⠛⠁⠀⠀⠈⠻⠯⡉⠉⢙⣷⣷⠻⠻⠷⠶⢤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⠖⠋⣀⡸⣷⡀⠑⢄⠑⣄⠘⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡾⣿⡏⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀ ⠀⠀⢠⠞⣡⢴⠋⢣⣀⠘⣷⡀⠀⠑⣬⣓⢦⣈⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠈⣲⠤⣼⣿⣷⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⢠⡖⠁⠊⠁⠈⠁⠀⠠⠅⠼⣷⡀⠀⠈⢌⠻⣗⠛⠋⠒⠛⠉⠀⠀⠀⠠⢖⣫⣴⣶⣿⠁⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠛⠒⠒⢲⣶⠒⠒⢲⣾⣿⡀⠠⠈⢆⢹⣦⡀⠀⢰⠀⠀⠘⢻⠲⢿⣿⣿⠿⢏⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡆⢣⠘⣿⡇⢳⡀⠀⠨⠦⡙⢷⡀⠸⢀⣄⠀⠈⠑⢄⣀⣠⡔⠻⣆⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⡆⣿⠀⠀⠹⣆⠀⠀⠙⣄⠱⡚⠁⢸⠀⠀⠀⠠⢴⣿⣅⠀⠙⣧⡀⠀⠹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢱⠀⡇⣿⠀⠀⠀⠘⢷⣄⠀⠈⢆⠱⡀⣀⣇⠀⠀⣀⢴⠋⠙⢧⡀⠈⢿⣄⠀⠙⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⠠⠀⡇⡇⠀⠀⠀⠀⠀⠙⢦⡀⠀⠣⡹⡄⣨⢿⣿⠀⠘⣧⣀⠀⠀⠀⠘⢿⢧⡀⠺⢷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⡆⠀⣷⠃⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⢿⣥⣾⣿⣷⠀⠈⢿⣷⢤⠀⠀⠀⠀⠈⠳⣄⠻⢷⠄⠀ ⠀⠀⠀⠀⠀⠀⡎⡸⠀⢸⡿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠹⡕⠀⠈⢿⣿⠿⣶⣄⠀⠙⢦⡙⠣⢄⣀⡀⠀⠀⠑⠦⣷⡄ ⠀⠀⠀⠀⢀⠞⣰⠇⠀⢨⠟⣉⠉⠒⠢⢤⣀⠈⢢⠀⠀⠀⠈⢦⢀⢀⠹⣷⣈⠓⢷⣄⣀⠉⠓⠒⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢋⣴⠏⠀⢠⡿⠋⠀⠈⠁⠀⠀⠀⠙⠢⢵⣄⠀⠀⠀⢳⣧⡐⢼⢮⡳⣄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠾⣿⡟⠻⢷⡅⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠻⡆⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡛⠁⠀⠀⠀⠈⠶⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠶⠒⠚⠛⠛⠛⠛⠛⠓⠒⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⢠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⠀⢙⠲⠤⠄⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⡤⢢⣦⣴⣶⡴⠏⢠⢟⠀⠈⢱⡀⠀⢰⢷⠀⠘⠪⠃⠙⢧⠘⢷⡀⠀⠀⠀⠀⣄⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠛⣡⠊⠀⠘⠋⠀⠉⢱⣼⡇⠇⠀⢀⡞⠁⢀⠀⣷⣧⠀⠀⠀⠀⠀⢳⡀⠹⡄⠀⣄⠀⢬⣙⢶⡦⣌⡱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢸⠃⠀⠸⡆⠸⣵⡀⠀⠀⠀⠀⠀⠹⡄⢹⡄⠈⣆⠀⠙⢦⡹⣮⡙⠪⣳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠀⠀⡇⢀⣠⠀⠀⠀⠀⠀⣶⠀⢀⡇⠀⢸⠀⠀⡆⠹⡀⠹⡿⣀⠀⠀⠀⠀⠀⠹⡀⢿⡄⢸⡄⠀⠀⠹⣌⢻⣄⠈⠻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⢡⠀⢰⡡⠋⠈⣷⡇⠀⠀⠀⢿⠀⢸⣧⠀⢸⢸⣇⣧⣤⣿⣶⣬⣝⠢⡀⠀⠀⠀⠀⢧⢸⣻⣤⣷⡄⠀⠀⠙⣦⠙⣷⠀⠘⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡏⡄⣠⠋⢀⡼⡆⢸⡇⠀⡆⠀⢸⣆⠀⡿⡀⢸⣾⢿⢱⠀⠀⠈⠻⣝⣿⡺⢷⡀⠀⠀⢸⣿⠋⡏⢸⣿⣶⡄⠻⡜⣷⣜⣧⠀⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣥⠟⢁⡴⡋⠀⡇⠈⣿⡄⢳⠀⢸⣹⡄⠘⣷⢿⡇⠈⢯⣇⡤⠤⣄⠈⠙⠓⠦⣭⣗⣤⣞⣿⣠⡇⢸⣿⠁⢹⡄⢹⣾⡎⢯⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⣴⡋⠀⠸⣸⠁⢰⡏⢷⠈⢇⠀⣧⠻⣄⢻⡆⢳⠀⠈⠛⣦⣀⣈⣳⠄⠀⠀⠀⠀⢹⣿⣿⣴⣶⣼⣿⡇⠸⣿⠀⣿⣷⠀⢿⡄⠀⠀⠀⠀⠀ ⢀⣿⡁⠀⠈⠙⠧⠤⠴⠃⠀⡼⡅⠀⣳⡜⢦⠸⡄⠈⠳⣽⣞⣆⢠⣽⠿⠛⠛⣿⣶⠗⠀⠀⠀⣠⡿⠟⢛⣿⣿⣿⣇⢀⣧⣄⡿⣿⡀⠸⡇⠀⠀⠀⠀⠀ ⠀⡿⡇⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠈⣿⣟⠿⣳⣽⡄⠀⣾⣿⡟⠋⠀⠀⠀⢺⣿⠇⠀⠀⠀⠸⣿⣀⠀⠰⣿⣿⢻⢹⠘⣿⣿⠀⠁⠇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠻⣆⠀⠀⠀⢀⡴⠋⣤⡀⢠⡀⠘⢎⠉⠀⡹⡙⢦⣀⠉⠛⣷⣖⣒⣒⣿⠿⠉⠀⠀⠀⢸⣿⣝⠛⠛⠿⢫⣟⣸⣤⣯⣿⡲⢤⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⢶⠊⣉⡴⠊⠹⣹⡀⠙⣄⠈⠳⡀⠈⢫⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢳⠀⠀⣰⣵⢿⡏⠈⠀⠉⠉⠁⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣨⠟⠁⣀⣤⠔⢻⣵⡀⠈⠣⣄⠙⢦⡀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢰⠏⠀⣴⠟⣿⢿⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡰⠋⣀⢴⠏⠁⢧⣀⠀⢳⣷⡀⠀⠈⠳⣦⣙⠶⣄⣈⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣶⢤⣼⣿⣿⣗⡮⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡤⠚⢡⠞⠁⠈⠓⠀⠀⠈⠉⣀⣻⣳⡀⠀⠀⠘⣎⠻⣖⠮⢽⣷⡒⠮⠽⠟⠓⠀⠀⠀⠀⣠⡤⠞⣋⣥⣼⣿⠇⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠧⠤⢤⣤⣀⣀⣉⣉⣉⣉⣉⣀⣈⣹⣷⡀⠀⠀⠈⢦⠸⣳⡄⠀⠀⠀⣀⡄⠀⠀⢰⣶⣀⣀⣶⣾⣿⣾⢧⡿⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⢄⠀⣷⣿⡟⢧⠀⠓⢆⠈⡆⢼⣟⣤⠄⠈⢸⡇⠀⠀⠀⠸⣌⠉⠻⡿⡯⡟⠉⣳⡀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡇⠸⡆⠘⣿⡇⠈⢷⡀⠀⠑⢜⠦⡈⠻⢆⠀⢸⠀⣠⡄⠀⠀⠈⠳⣄⣀⣀⣴⠞⠹⣷⡀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠀⢹⡀⣿⡇⠀⠈⢻⣇⠀⠀⠀⠙⣄⠈⢧⠺⠚⠁⢧⠀⠀⠀⠀⢀⣤⣿⣿⡀⠀⠘⢟⣆⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⡀⢸⡇⣿⡇⠀⠀⠀⠹⣷⡀⠀⠀⠈⢧⠈⢧⡀⠀⢸⡆⠀⠀⠀⠀⢈⡿⠻⡱⣄⠀⠈⢫⡷⡀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠂⢸⡇⣿⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠳⡈⢳⠐⠺⠧⢤⣤⡤⠞⢻⣆⠀⠈⠛⠷⠄⠀⣙⢼⣆⠀⠈⢻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⠀⢸⡇⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠙⢆⢳⣀⣴⠻⣿⣣⠀⠀⢻⣧⢆⠀⠀⠀⠀⠈⠻⡝⢧⣀⢳⡹⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⡾⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠻⣿⣄⣿⣿⣿⣦⡀⠀⠹⣿⡳⣄⡀⠀⠀⡀⠀⠀⠘⠳⣄⠈⠫⡓⢤⡀ ⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⠃⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡢⡀⠈⠹⣯⢿⣿⣿⡵⡄⠀⠘⢿⣌⠙⢶⣦⠀⠀⠀⠀⠀⠈⠓⢦⣈⢦⡁ ⠀⠀⠀⠀⠀⠀⢀⡞⢠⡏⠀⠰⣿⣇⡤⠤⣀⣀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠹⣄⠀⠀⠘⢿⣧⡉⠻⣟⢦⡀⠀⠙⠳⣤⣀⣉⡓⠒⠤⠄⠀⠀⠀⠈⠙⠛ ⠀⠀⠀⠀⠀⣠⠎⣠⡿⠃⠀⢠⡞⣡⠤⣄⣀⠉⠙⠲⠦⣄⡀⠹⣄⠀⠀⠀⠀⠈⢦⢠⡠⠄⠱⣝⢦⡈⠙⠻⠶⢤⣀⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢃⣴⡿⠁⠀⢀⣿⠞⠁⠀⠀⠈⠃⠀⠀⠀⠀⠉⠳⢬⣣⡀⠀⠀⠀⠈⢳⡻⣌⠑⣬⢳⡙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⡿⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢶⣤⣶⣶⣷⣿⠷⢮⡳⡙⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢹⣿⠀⠀⠉⢿⣆⠀⠱⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠹⣆⠀⠹⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣋⠁⠀⠀⠀⠀⠀⠘⠟⠆⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠦⠤⢄⡀⠀⠀⣀⡤⠔⠒⠒⠒⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠤⠴⠿⠭⣍⣙⠓⠦⠄⠀⠀⠀⠀⠈⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀ ⠀⠀⣠⣾⠥⠖⠒⠒⠒⠒⠒⠬⣙⠲⢤⡴⢒⣉⡭⠭⠭⠿⠿⢭⣒⠦⣄⡀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀ ⢀⡼⢋⣴⣶⣶⣄⠀⠀⠀⠀⠀⠈⢣⣴⣿⣭⣤⣄⡀⠀⠀⠀⠀⠈⠙⢦⡙⠢⡀⠀⠀⠀⠀⢿⣿⡆⠀ ⣜⠀⣾⡟⠙⣿⣽⡇⠀⠀⠀⠀⢀⠎⢸⣿⠿⢿⠟⣿⡆⠀⠀⠀⠀⠀⠀⠙⠒⠢⣄⠀⠀⠀⢸⣿⣿⡄ ⠹⣄⠘⠿⣿⣿⠿⠁⠀⠀⠀⠀⣸⡄⢸⣷⣤⣼⢿⣿⠇⠀⠀⠀⠀⠀⠀⢀⡤⠴⠋⠀⠀⠀⠀⣿⣿⣇ ⠀⠈⡗⠦⠤⢄⣀⣀⡠⠤⠖⠋⠁⠙⣄⡙⠛⠛⠛⠉⠀⠀⠀⠀⠀⣠⠔⢁⡤⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⠀⠀⠈⣙⡶⠒⠒⠒⠒⠛⠋⠀⠀⠀⠹⣍⠓⠢⠤⠤⠤⠤⠔⢒⣉⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⢰⠋⣁⣀⣀⣀⣀⣠⣤⣀⣀⣀⠀⠀⠀⠉⠓⠒⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⢸⡋⠁⢀⣀⡤⢤⣤⣀⣀⣀⠈⠉⠉⠓⠒⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿ ⠀⠀⠙⢦⠘⣄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣈⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠈⡆⢸⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠀⢀⡇⢸⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇ ⠀⠀⠀⢸⠃⣸⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠀ ⠀⠀⠀⢸⠀⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠏⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠁⠀ ⠀⠀⠀⢸⠀⢷⣀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⠋⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠘⣆⠀⠉⠓⠒⠦⠤⠤⠤⠞⠛⠉⣀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢯⡛⠒⠒⠲⠤⠤⠖⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠀⠀⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢞⣩⣥⣶⣶⣶⣶⣶⣶⣶⣶⣦⣭⣙⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣋⣴⣾⣿⣿⣿⣿⣿⣿⣭⣟⣿⢿⣿⣿⣿⣿⣿⣦⣍⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⣾⣿⣿⡿⠟⢛⣉⣩⣤⣤⣭⣉⡛⠻⢦⣝⡻⣿⣿⣿⣿⣷⡌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣼⣿⡿⠟⠡⠶⠟⠛⣛⣛⠛⠻⢿⣿⣿⣿⣦⣈⠻⣮⡻⣿⣿⣿⣿⣦⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠖⣚⣽⣧⣾⣿⣿⠷⠶⢶⣶⣾⡛⠛⠛⠛⢷⣦⣍⠛⠛⠛⠿⠷⠈⢻⣮⢻⣿⣿⣿⣧⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⢏⣴⣿⡿⠟⠋⠉⠉⠉⠉⠳⢶⣄⠙⢿⣦⣠⣶⣿⣟⡛⠛⠻⠿⣶⣶⣶⣦⣿⣧⡹⣿⣿⣿⣇⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡞⣰⣿⣿⠏⣀⣀⣀⡀⠀⠀⠀⠀⠀⠙⣷⡶⠛⠉⠁⠀⠀⠉⠙⢷⣄⠈⠻⣷⡄⠙⢿⣷⡘⣿⣿⣿⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⢱⣿⣿⠏⡼⠛⠻⣿⣿⣆⠀⠀⠀⢀⣾⢫⣼⣶⣦⣤⡀⠀⠀⠀⠀⠙⢷⡀⠈⢿⠀⠀⣿⣧⡈⣛⣻⣷⣘⣓⠲⢤⡀⠀⠀⠀⠀ ⠀⠀⢠⠇⣾⣿⣿⡀⢻⣦⣤⡟⣿⡿⠀⠀⠀⢸⠃⣿⡁⠈⣻⣿⣷⠀⠀⠀⠀⠀⠘⢷⠀⢸⡧⢠⣾⣿⣿⣿⢟⡫⠭⣟⡳⣦⡙⢦⡀⠀⠀ ⠀⠀⢸⡀⣿⣿⣿⣷⡄⠙⠛⠛⠋⠁⠀⠀⠀⣸⡆⠹⣿⣾⣯⣽⡟⠀⠀⠀⠀⠀⢀⣼⢀⡾⢀⣿⣿⣿⣿⣱⠏⠀⠀⠀⠉⠈⢷⡎⢳⡀⠀ ⠀⠀⢠⠇⣹⣿⠟⢷⣝⠷⢦⣄⣀⣠⣤⠶⠟⠋⢻⣄⠀⠉⠉⠀⠀⠀⠀⢀⣠⡶⠋⢁⡾⠁⣼⣿⣿⣿⡇⡇⢀⣠⡿⠻⢶⠟⣿⣿⡈⢷⠀ ⠀⣠⠏⣼⣟⣁⣀⣀⣉⣛⣒⠒⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⠤⣤⠤⠶⠞⠋⢁⣠⡴⠋⠀⠀⣿⣿⣿⣿⡇⣥⣿⣿⠁⠀⠘⣷⡼⢹⡇⢸⡆ ⢰⢇⣾⠟⠁⠀⠀⠀⠈⠉⠉⠛⠛⠻⠶⠦⣤⣄⣀⡀⠀⠀⠤⠤⠤⠤⠶⠛⠋⠁⠀⠀⠀⠀⢹⣿⣿⣿⣇⣿⣿⣿⠀⣀⣠⣽⠇⢸⡇⢸⡇ ⢸⡘⣿⡀⣶⢿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⣀⠉⠉⠛⠳⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣼⣯⠛⠛⠿⠟⠀⢀⣾⠇⣼⡇ ⠀⢳⡈⠻⣮⡀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⠀⠉⠙⠛⢶⣤⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣮⣅⣀⠀⢀⣠⣾⠏⣼⣿⠃ ⠀⠀⠙⢶⣌⠙⢷⣦⣀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠙⠻⢶⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⢋⣡⣾⡿⠃⠀ ⠀⠀⠀⠀⠈⠛⠶⣬⡛⢻⡦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠙⢿⣦⠀⠀⣼⣯⣿⢿⡿⢹⣥⣤⣾⣿⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⠇⣾⠇⢀⣿⣿⣿⡿⠟⠛⠉⣫⣿⠿⠛⠿⣿⣽⣯⣿⡿⣿⣿⡆⠀⢹⡆⣰⣟⣾⢿⣿⢃⣾⡿⠋⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⢰⡟⠀⣸⣿⡿⠋⠀⠀⠀⠾⠋⠁⠀⠀⠀⠈⠉⠹⣿⣼⣿⣿⠇⢀⣾⢱⣯⡿⢣⣿⢃⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡏⣼⠃⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠃⠀⣾⠇⠀⠉⣴⡿⢁⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣴⠟⠁⢠⣾⠋⠀⣠⣾⠋⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⢀⣰⡿⠃⣠⣾⠟⣡⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣀⣼⡀⣿⡀⢸⣿⡇⠀⠀⢀⣠⠴⣖⣛⣓⣲⠦⠶⠟⣓⣒⡲⠿⣏⣴⠾⢋⣠⣾⡿⠫⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⢻⠿⠿⠶⠶⣭⡳⣶⣿⣿⣟⠶⡞⣵⠚⠉⠉⠉⠉⣳⠖⠋⠉⠉⠉⠳⣮⡡⠶⢛⣋⡷⠒⠒⠒⠶⣝⢦⢤⢔⣒⣒⡲⣄⠀⠀⠀⠀ ⠀⠀⢻⢸⠀⠀⣤⡄⠈⠻⠋⠁⠀⠈⠻⡾⣵⠁⢀⣠⣤⣼⠋⠀⠀⣀⣤⣄⢀⣨⡟⠉⠉⠉⡇⠀⣿⡆⠀⣸⣷⠋⠉⣉⣉⣿⢺⡇⠀⠀⠀ ⠀⠀⢸⢸⡇⠀⠙⠁⠀⠀⠀⣀⣤⡀⠀⡇⠁⠀⣾⣿⡿⠟⠒⠒⠚⣿⡿⠿⠿⠟⠛⣶⠛⢿⣧⠀⢈⡀⠐⢿⣷⣄⡀⠉⠙⠻⣌⢳⡀⠀⠀ ⠀⠀⢸⢸⡇⠀⢀⣴⣿⡄⠀⠿⠿⠇⠀⣧⠀⡀⠘⠿⠷⠆⠀⠀⣴⠿⣷⡤⠀⠀⢠⡟⠘⠛⠋⠀⠘⣷⡀⣠⠌⠛⠿⠗⠀⠀⢸⠏⡇⠀⠀ ⠀⠀⠘⡌⣇⣀⣤⣷⣳⣙⠦⣤⣤⡤⢞⣫⢷⣗⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⢀⣠⣯⠤⠤⠶⣶⢒⣚⣿⣿⡳⢦⣀⣀⣀⣀⣴⢏⣼⡇⠀⠀ ⠀⠀⠀⠳⣿⣯⣿⣿⣿⠏⠳⢶⣶⣶⣿⠟⠳⣭⣝⣒⣒⣋⣭⣬⣑⡒⠖⣚⣫⣵⣶⡶⠿⠿⠟⠛⠛⠛⠉⠛⠲⣮⣭⣭⣽⣶⣿⠿⠁⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉⠉⠛⠻⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀
If you'd like to report a bug or suggest a feature, you can provide feedback here. Here's our privacy policy. Thanks!
AI Story Generator - AI Chat