ᵀᵉʳᵐᶤᶰᵒˡᵒᵍʸ
ᴹᵒᶰᵒᶻʸᵍᵒᵗᶤᶜ – ᵐᵘˡᵗᶤᵖˡᵉ ⁽ᵗʸᵖᶤᶜᵃˡˡʸ ᵗʷᵒ⁾ ᶠᵉᵗᵘˢᵉˢ ᵖʳᵒᵈᵘᶜᵉᵈ ᵇʸ ᵗʰᵉ ˢᵖˡᶤᵗᵗᶤᶰᵍ ᵒᶠ ᵃ ˢᶤᶰᵍˡᵉ ᶻʸᵍᵒᵗᵉ
ᴰᶤᶻʸᵍᵒᵗᶤᶜ – ᵐᵘˡᵗᶤᵖˡᵉ ⁽ᵗʸᵖᶤᶜᵃˡˡʸ ᵗʷᵒ⁾ ᶠᵉᵗᵘˢᵉˢ ᵖʳᵒᵈᵘᶜᵉᵈ ᵇʸ ᵗʷᵒ ᶻʸᵍᵒᵗᵉˢ
ᴾᵒˡʸᶻʸᵍᵒᵗᶤᶜ – ᵐᵘˡᵗᶤᵖˡᵉ ᶠᵒᵉᵗᵘˢᵉˢ ᵖʳᵒᵈᵘᶜᵉᵈ ᵇʸ ᵗʷᵒ ᵒʳ ᵐᵒʳᵉ ᶻʸᵍᵒᵗᵉˢ
ᵀᵉʳᵐˢ ᵘˢᵉᵈ ᶠᵒʳ ᵗʰᵉ ᵒʳᵈᵉʳ ᵒᶠ ᵐᵘˡᵗᶤᵖˡᵉ ᵇᶤʳᵗʰˢ ᶤᶰ ʰᵘᵐᵃᶰ ᵇᵉᶤᶰᵍˢ ᵃʳᵉ ˡᵃʳᵍᵉˡʸ ᵈᵉʳᶤᵛᵉᵈ ᶠʳᵒᵐ ᵗʰᵉ ᴸᵃᵗᶤᶰ ᶰᵃᵐᵉˢ ᶠᵒʳ ᶰᵘᵐᵇᵉʳˢˑ ᵀʷᵒ ᵒᶠᶠˢᵖʳᶤᶰᵍ ⁽ᵗʷᶤᶰˢ⁾ ᶤˢ ᵗʰᵉ ᵐᵒˢᵗ ᶜᵒᵐᵐᵒᶰ ᶠᵒʳᵐ˒ ⁹ ⁽ᶰᵒᶰᵘᵖˡᵉᵗˢ⁾ ᶤˢ ᵗʰᵉ ˡᵃʳᵍᵉˢᵗ ᶰᵘᵐᵇᵉʳ ᵉᵛᵉʳ ˢᵘᶜᶜᵉˢˢᶠᵘˡˡʸ ᶜᵃʳʳᶤᵉᵈ ᵗᵒ ᶠᵘˡˡ ᵗᵉʳᵐ ᵃᵗ ᵒᶰᶜᵉ ʷᶤᵗʰ ᵃˡˡ ᶜʰᶤˡᵈʳᵉᶰ ˢᵘʳᵛᶤᵛᶤᶰᵍ ᵗᵒ ᵃᵗ ˡᵉᵃˢᵗ ᵒᶰᵉ ʸᵉᵃʳ ᵒˡᵈˑ
ᵀʷᵒ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ᵗʷᶤᶰˢ
ᵀʰʳᵉᵉ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ᵗʳᶤᵖˡᵉᵗˢ
ᶠᵒᵘʳ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ᵠᵘᵃᵈʳᵘᵖˡᵉᵗˢ
ᶠᶤᵛᵉ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ᵠᵘᶤᶰᵗᵘᵖˡᵉᵗˢ
ˢᶤˣ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ˢᵉˣᵗᵘᵖˡᵉᵗˢ
ˢᵉᵛᵉᶰ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ˢᵉᵖᵗᵘᵖˡᵉᵗˢ
ᴱᶤᵍʰᵗ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ᵒᶜᵗᵘᵖˡᵉᵗˢ
ᴺᶤᶰᵉ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ᶰᵒᶰᵘᵖˡᵉᵗˢ
ᵀᵉᶰ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ᵈᵉᶜᵃᵖˡᵉᵗˢ
ᴱˡᵉᵛᵉᶰ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ᵘᶰᵈᵉᶜᵃᵖˡᵉᵗˢ
ᵀʷᵉˡᵛᵉ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ᵈᵘᵒᵈᵉᶜᵃᵖˡᵉᵗˢ
ᵀʰᶤʳᵗᵉᵉᶰ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ᵗʳᶤᵈᵉᶜᵃᵖˡᵉᵗˢ
ᶠᵒᵘʳᵗᵉᵉᶰ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ᵠᵘᵃᵈᵉᶜᵃᵖˡᵉᵗˢ
ᶠᶤᶠᵗᵉᵉᶰ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ᵠᵘᶤᶰᵈᵉᶜᵃᵖˡᵉᵗˢ
ˢᶤˣᵗᵉᵉᶰ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ˢᵉˣᵈᵉᶜᵘᵖˡᵉᵗˢ
ˢᵉᵛᵉᶰᵗᵉᵉᶰ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ˢᵉᵖᵈᵉᶜᵘᵖˡᵉᵗˢ
ᴱᶤᵍʰᵗᵉᵉᶰ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ᵒᶜᵗᵈᵉᶜᵘᵖˡᵉᵗˢ
ᴺᶤᶰᵉᵗᵉᵉᶰ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ᶰᵒᶰᵈᵉᶜᵘᵖˡᵉᵗˢ
ᵀʷᵉᶰᵗʸ ᵒᶠᶠˢᵖʳᶤᶰᵍ – ᶤᶜᵒˢᵘᵖˡᵉᵗˢ
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⣠⣀⠾⠿⣿⣿⣿⣿⣿⣹⢯⢏⠵⣋⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⣻⣿⣿⠿⠋⠀⠀⢀⣀⠔⠁⢠⡞⡹⠁⠀⡴⡡⠋⣰⢎⢉⠊⠀⠀⠀⠀⢀⡮⢰⣿⡿⢢⠪⠁⣠⠂⡴⠋⢀⠈⠀⠀⠀⠀⠀⢀⠆⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⣀⢀⣞⠻⢛⢷⡃⠀⠀⠀⠀⣩⢿⣿⣿⢷⠻⡞⠯⡘⢧⢯⡽⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢮⠞⡵⣛⠿⡅⢠⠀⠀⣠⡶⠋⠀⣰⡿⠜⠀⢀⠞⡞⢁⣶⢃⡠⠃⠀⠀⡰⢁⣤⠟⢰⡿⢁⣾⠇⠀⡴⢃⡾⠁⠀⠄⠠⠠⠀⠀⠀⢠⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢽⡿⣻⣿⣿
⠀⠀⠀⠀⠊⠷⠉⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⢽⠃⠈⠀⠀⠀⠀⣰⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡟⠎⠱⢉⣓⡀⠀⢀⡾⠋⠀⢀⣼⡿⠁⠀⢀⠎⡔⢠⢣⠋⠩⠀⠀⠀⡔⢀⣾⠟⢀⡞⢁⢎⠃⠀⠀⢠⠟⠀⢀⠄⢀⡄⠀⠀⢀⡀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢤⠶⠇⠀⠀⠀⠀⠘⣳⣶⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⡿⡄⠀⠈⠀⢤⡟⡁⠀⢠⣾⡿⠀⠀⢀⢆⠜⡔⢃⠇⣴⠃⠀⠀⡘⢠⣾⡏⢠⡟⢁⡞⡎⠀⡀⢠⠟⠀⢀⣺⠣⠋⠀⠀⣠⠊⠁⡠⠀⢀⡞⡡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡹⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⣤⣳⣿⡿⣟⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣉⠀⠉⠀⢠⢾⠟⠈⠀⣰⡿⡻⠁⠀⢀⣮⠋⡸⠀⣮⣾⠁⠀⠀⡔⢀⣿⡟⣠⣿⢣⡟⡌⠀⠀⣰⠟⠀⡀⢺⣡⠃⠠⠀⠙⠁⢀⡴⠏⢠⣾⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣯⣿⣿⣿⣞⣯⣿⣾⣳⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⣽⣿⣿⣿⣿⢿⠿⡞⠀⠀⢀⢿⣃⠊⠀⣸⡼⡹⠁⠀⣠⠋⠃⣼⠅⡼⣿⠆⠀⢀⠎⡴⡟⡜⢠⣯⡟⡼⠜⠀⠀⢠⡟⢀⠎⢠⡿⠁⠀⠀⣀⠀⢠⠎⠞⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠱⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢷⣞⡷⢫⠙⢓⡛⢾⡽⢾⣙⠮⣹⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣿⣿⣿⣿⣛⠎⢃⡠⢂⣀⠏⣎⠄⢀⣼⡟⡔⠁⠀⢠⡏⡼⣾⡟⠰⢡⠇⠀⢀⠎⢠⡾⡿⢡⣿⡟⣼⡕⠀⠀⢠⠏⣰⠃⢀⠞⢠⠁⠀⣰⡟⢠⠾⠊⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⡹⣎⢿⡞⢤⢃⣜⣮⣽⣲⣼⣻⣬⣳⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡝⣠⠎⢀⢊⡜⡸⠁⠀⣨⣿⡝⠀⠀⣴⡿⠉⣰⣏⡾⢡⠏⠀⠀⡞⣰⡻⡼⢁⣾⣿⣽⠋⠀⠀⢠⠏⣼⠏⢀⠜⠠⠁⢀⣴⠏⡴⣃⡶⡸⢣⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣿⣽⡻⠜⠃⠺⢽⡞⠃⠉⢘⡷⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡘⠡⣼⠃⡰⢁⡟⣸⠁⢀⣠⡿⡿⠀⡀⣠⡾⠀⣰⢿⡾⠀⡐⠀⠀⡜⣠⡟⡴⢃⣿⣹⣿⣏⠀⠀⣰⠏⡰⠁⢀⡾⠰⠁⢠⡿⠃⡾⢞⠝⠔⡡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠄⠀⢀⡾⡑⠈⠀⠀⠋⢳⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⡷⠂⡼⠁⢠⢣⠊⢀⠇⠀⣾⡿⡰⠀⢄⠖⡟⠁⣴⢿⡞⡿⡴⠁⠀⠸⢠⣿⢻⢃⣾⢿⢿⣿⠃⠀⣰⡏⡰⢁⠀⡼⠑⠀⣠⢟⣴⡞⡵⢣⣪⠞⠁⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣟⡳⢡⡼⠀⢠⢃⡆⠀⠎⠀⣰⡿⡑⠁⢠⠎⣸⢁⣼⣯⣿⢸⣧⠁⠀⢠⠃⣾⣧⠏⣼⣟⡿⣻⠃⠀⢠⣿⢡⢣⢁⠎⡀⠀⣰⣷⡟⣴⡿⣡⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢲⢦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⣅⡟⠀⠀⠈⡼⠀⠜⢀⣼⣿⠟⠁⣠⣿⡟⢃⣾⣿⣹⣯⢸⠇⠀⠀⡎⢀⢹⠇⣴⣿⢿⣵⠃⠀⠀⢠⢃⡾⢃⠎⠈⠀⣼⣿⡿⣸⢋⣼⢯⡱⣎⠴⣉⠟⡻⠿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠡⢈⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⢞⡿⣿⣿⣿⣿⣿⣿⣿⣿⠯⣡⠎⠀⠀⠀⠘⠁⡌⠀⣿⣿⠏⠀⣰⣿⡿⢁⡾⣽⢿⣞⣏⡎⠀⠀⢰⠀⣼⡏⢰⡧⣻⣟⡟⠀⠀⢀⣏⡾⠁⡌⠀⢠⢞⣿⢟⡜⣡⣿⣟⣦⢳⣌⣣⣈⠍⢣⠻⣴⢹⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡐⡌⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠍⠊⠹⢻⣿⣿⣿⠛⠿⠟⡯⡵⠁⠀⡰⠰⢁⡧⡜⢀⣼⡿⠁⠀⣸⣿⢯⡏⣾⢰⡟⣾⣹⣿⠁⠀⠀⡆⣼⡟⠀⡾⣵⣿⣿⠃⠀⠀⡾⣹⠃⡸⠁⡰⢣⡟⣡⠏⣼⣿⣿⣿⣿⣿⣾⣷⣭⡛⣧⣫⠴⣟⣞⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠐⡠⡙⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣀⠀⢀⣼⣿⡿⠃⠁⠈⢀⡽⠁⠀⡜⠀⢀⠞⡀⢀⣾⡿⠀⣰⣿⡿⣫⣏⣇⣷⣿⣳⣿⣰⠇⠀⠀⢸⢀⣧⢷⢣⢛⣿⣿⡏⠀⢀⢴⣷⡏⢰⠃⢰⣡⣟⡾⡟⣽⣿⣿⣿⣿⣿⣿⣿⣧⣣⠽⢧⣛⣿⣹⢾⣽⢿⣿⡿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠁⢦⠱⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢩⣟⣿⣿⡻⠉⢀⠀⣠⠶⠛⠀⣠⡞⠀⢀⣮⠄⢀⣾⡻⠀⣼⣼⢏⣵⣿⣿⢸⣻⣼⡟⣿⣿⠀⠀⠀⡞⢸⡜⣿⢯⣿⡿⣽⠃⠀⣈⣾⣾⢁⠏⢰⣻⣿⡟⣱⢿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣮⣽⣳⢯⣿⣾⣟⣯⣿⢿⣽⡾⣿⣻⣧⣇⠠⠄⠠⠁⢂⠁⠠⠈⡐⢀⠦⡙⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢯⣟⡾⣯⣿⣷⣿⣬⡟⡥⠃⠀⢰⡡⠁⢠⢊⠎⣰⡟⡝⠀⢈⣿⢏⣾⣿⣟⡇⡟⣼⣿⣹⣿⡏⢸⠀⢰⠃⡾⣰⠇⣾⣿⢿⡇⢀⢀⣿⣯⡇⡸⠀⣾⣿⡟⡼⣳⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⡌⡙⢿⣿⣿⣯⣿⣾⢯⣷⢿⣯⣷⣟⣧⢷⣛⣬⣁⠆⢂⠡⠠⢈⠄⡡⢀⢣⢒⡽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣤⣀⣄⣤⣻⣽⣷⡿⣾⣿⣿⣿⣿⣿⠣⠍⠠⡊⣰⢧⠃⡼⢁⢊⣼⢋⠞⠀⢀⡾⣡⣿⣿⣿⣿⢹⢇⡿⣿⣽⣿⢁⡼⠀⣼⣰⢃⡟⢸⣿⣿⣿⡇⠈⢸⣽⢟⣧⠇⣰⣿⣿⢫⢵⢻⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣛⣿⣿⣿⣿⣟⣾⡿⣾⣳⣟⡞⣯⡳⡜⢣⡘⠢⡄⠣⠄⣊⠰⣉⠦⣙⡾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣽⢯⡛⠟⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⠎⠰⢡⠆⣠⡷⢁⡾⣢⠊⠀⣠⣻⡷⣿⣿⣿⣿⡟⢸⠿⣿⣯⣇⣿⣰⠇⠀⡧⢣⣼⢣⢺⣿⣿⢹⠇⠀⣑⣿⣿⡜⢠⣿⣿⣳⢋⡞⣸⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣷⣿⣽⡿⣝⡞⣳⡱⠍⣆⠹⡄⡣⠵⢎⡱⣋⣖⣫⣞⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠫⢿⣽⣷⣮⣼⣼⣯⣿⣿⣿⣿⣿⣿⡿⡛⠔⠀⠰⠁⣠⣟⠇⣰⠟⢀⡞⡴⠁⢀⣴⣟⣿⣛⣿⣿⣿⣿⢡⡟⣿⣿⡏⣿⡟⡼⠀⠠⣷⠘⣏⡎⣿⣿⡿⡿⠀⠐⣶⣿⣿⠀⣸⢾⣿⡿⡜⠇⠌⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠺⡼⠡⠧⠍⠆⡱⢠⡑⣣⣭⢳⣭⣶⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡠⡴⣩⠓⠫⡙⢟⡿⣿⢿⣟⡿⣟⠯⠛⠥⠃⠁⠐⠉⢀⡴⡻⢃⡴⠋⠠⢋⠜⠀⡴⣶⣿⡟⣲⣿⣿⣿⣿⡟⣸⢿⣿⣿⢼⣿⣹⡇⠀⠀⢾⢀⣿⢁⣾⣿⣹⡇⠀⣾⣧⣿⠇⠀⣷⣹⣿⡃⢜⠐⠊⢤⠹⣿⣿⣿⣿⣷⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣟⣿⠷⠍⣂⠒⢈⡐⢢⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⠤⠲⠜⠁⠃⠱⠌⠵⡘⠎⡼⢯⣿⣾⡑⠂⠀⠀⠀⠀⠀⢀⣴⢯⠞⠁⡸⠁⢀⣾⠋⠀⡼⢿⡾⢯⣼⣿⣿⣿⡟⣽⢣⢟⣿⣿⣿⣼⡟⣿⣇⠀⢠⡞⢸⢸⣹⣿⣻⣿⣆⠀⣿⣯⡿⢸⢈⣿⠜⡃⣐⡂⡈⠑⢀⠀⢉⠻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣽⡿⣿⣜⢷⡧⡙⠿⠿⠡⠀⠀⠉⢂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠁⠀⠀⠀⠀⠀⣰⠞⣉⠉⠀⡰⠁⣰⠟⠁⣠⠞⢱⠯⣝⣭⣿⣿⣛⡿⣸⡏⣿⣿⣯⣿⡿⣽⣻⣿⡌⠀⢸⢃⣿⠈⡟⣿⣿⣿⠁⢸⢹⣿⡇⡁⢨⢿⡌⠁⡄⠆⠀⠄⠀⠐⠠⠀⠠⣋⠛⠿⠿⣿⠿⡛⠍⡉⢉⠠⠉⡉⢀⠐⠱⠒⠀⠀⠀⠄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡷⡋⠀⣠⡎⠀⣴⠋⢠⡾⠁⣲⣏⣷⣾⣿⣿⣿⡿⣷⡟⣰⣿⢭⣿⣳⣷⣿⣿⢣⠇⠀⡜⣸⢸⢰⠹⣿⣿⣗⠀⢸⢸⢿⡇⠀⢸⡭⠣⠐⠤⠁⠀⡀⠀⠀⠀⠈⠐⢠⠉⠜⠰⢂⡡⠁⠦⠐⠠⠄⠁⠀⢀⠂⠁⠊⠀⠀⠀⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⢊⠜⡴⢊⠏⣀⡜⠁⢰⡋⢤⢃⡟⣴⣿⣿⢿⣿⣿⣽⡿⢁⣿⣿⡾⣽⣿⣟⡾⣏⣾⠀⠀⢇⠇⣿⢸⡇⣿⣿⡽⠀⢸⢸⢼⢣⠀⠘⣧⡨⠱⠀⣀⢂⠀⠀⡀⠀⠀⡁⢂⠈⠆⡐⣀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⢁⡴⠉⣈⡰⠃⠐⠝⣠⡾⢱⣗⠺⣥⣿⣿⣿⣿⣿⡿⣣⡾⢁⣞⢿⣿⣿⡿⣿⣿⣹⣇⡟⠀⠀⡎⠀⣷⠘⣅⣾⣿⡗⠀⢨⢸⣼⢸⠀⠁⠸⢿⠀⡅⠠⠄⡀⠢⠐⡠⠁⡐⡠⢌⠐⡐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣶⠿⠉⢠⡴⠋⣠⡾⠛⠀⡠⢃⣴⡯⢠⡿⣍⣷⣿⣿⣿⡿⣿⡿⢡⣞⢠⣞⡿⣼⣿⣿⣿⣿⢧⣿⣿⠇⠀⣸⠝⣜⠟⡶⢳⣿⣿⡃⠀⡎⢤⣇⠸⠀⡧⠐⡸⡇⠆⡰⢤⣁⠒⡡⢂⠵⡐⢡⡦⣌⢤⣓⣮⣤⣔⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣲⣟⣽⠿⠛⣡⣴⡿⢉⣴⢞⠟⢀⠔⢈⡴⣛⣪⣴⠿⣳⣽⣾⣿⣿⡿⣿⡟⢁⣺⠃⡾⣾⢩⣿⣻⣿⣿⣏⣾⣿⣿⡄⢀⢻⠀⢻⢇⢸⢸⣿⣿⠁⠀⡇⢈⣏⢨⠀⢹⡀⠃⣿⢲⢲⢒⣬⣫⣕⣏⣖⡿⣟⣿⣿⣿⣿⣿⡟⠿⣿⠿⠿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⠟⠛⠙⠉⢀⣠⣼⠟⣋⣴⡿⠟⠁⠀⢁⣴⣋⡶⢩⣛⣼⣿⣿⣿⣿⣿⣿⢡⡟⠤⣱⢃⣺⠩⢣⣿⣿⣿⣿⣿⣽⣻⣿⡿⠀⠎⢸⡄⣸⢺⡜⠎⣿⣿⠀⡆⠱⡞⣸⢸⠀⠀⠹⣦⢿⣏⣿⣟⣻⣼⣯⠿⢗⡛⠫⠙⠿⣿⣿⠁⠘⠃⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹
⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⠀⠠⠞⠚⣉⣠⣴⢾⣿⠏⠀⠀⢀⣴⠿⢞⡥⢞⣻⣽⣿⣿⣟⣿⣿⡟⣵⠟⢀⡿⢡⡷⠠⣼⣿⣿⣿⣷⣿⣿⣿⣽⣿⡇⠀⠀⢡⠇⣿⠂⣿⠀⣿⡟⠀⠇⡄⢷⢣⡇⠀⢄⠁⢹⣿⣿⣍⡛⡟⠷⠾⠫⠄⣐⠐⠀⠀⣿⣧⡀⠆⢀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣼⢃
⠠⠦⣴⣤⣄⠦⣄⡤⣄⣠⣴⣴⣶⣿⠟⠋⡠⠔⠀⢀⡄⣠⠞⢥⣰⣯⣧⣿⣿⣿⣿⣷⣿⣿⣻⡾⠃⢠⡞⣴⡿⢁⡵⣹⣿⣿⣟⣿⣿⣿⠯⣾⣿⠄⠀⠀⡼⢸⢸⣀⣿⠨⣿⣷⢠⠀⡇⢿⣜⡇⠀⠸⡀⢸⣿⣿⣶⢱⠈⢁⠂⢁⠀⠀⠁⠀⢴⣿⣿⣿⣿⣧⣊⢟⣿⣆⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⢇⡎
⠀⠀⠀⠀⠀⠠⠁⢉⣉⣉⣁⣩⡼⠢⠔⠊⢀⣠⠔⠙⣪⢔⣭⣿⣿⣽⣿⣿⣿⣿⡟⣶⣿⣽⡧⠃⣰⢋⣾⡿⢣⡿⣸⣿⣿⣿⣽⣿⣿⣿⢹⣿⣿⠀⠀⢀⡇⣾⠸⣸⢿⠐⣿⡧⢸⠠⡃⢾⠸⣇⠀⠀⠇⣌⣿⣿⣿⣿⣦⡄⠠⠄⠀⠀⠀⢀⣹⣿⣿⣾⣹⣿⣿⣷⢮⣿⣆⡀⣉⣁⠀⢢⡥⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣎⠳⢮⣜
⠀⠘⠲⠦⠤⣤⣀⣀⠀⠀⠀⠀⢀⣤⠾⢛⡁⠀⢀⣬⡞⣭⣾⣿⡿⡿⣿⣿⣿⠗⣼⣯⡾⢉⠀⠞⣡⣾⠟⣱⡟⡌⣿⣾⣿⣿⣿⣿⣿⡟⣿⣷⡇⡀⠂⡼⢠⣏⢠⡿⣿⢸⣿⡷⣀⠀⡃⣻⠸⡗⠀⢰⠐⣌⢿⣿⣿⣿⣿⣿⣯⣤⣀⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣗⠮⢿⣽⣯⡯⢳⣇⢳⣽⣿⢯⣿⣿⣿⣿⣿⣿⣿⢏⣿⣳⡏⣩⡗⢮
⣤⠤⢤⢤⣀⡤⣤⣤⣤⡶⢖⣻⣽⠦⠛⠁⣠⢖⡿⣩⣾⣿⣿⣻⣿⣽⣿⣿⢋⣾⡿⣟⣡⠎⢠⢞⠡⣿⣿⣿⣳⣩⢿⣿⣿⣿⣿⣿⣿⢿⣿⣼⡗⠀⡛⣱⣸⠃⢸⡆⣿⢸⣿⡃⣸⠀⡇⣻⢹⣳⠘⡄⠃⣬⢂⢻⣿⡿⣿⢿⣿⣿⣿⣿⣷⣦⠀⠙⢿⣿⣿⣳⣿⣾⣿⣾⣷⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡟⡡⢧⣛⡵
⠰⠉⠎⠲⢛⣛⣛⣋⠭⠒⠁⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠏⣡⣛⣻⠟⠉⣀⠴⠁⣰⣾⣿⣿⡻⣡⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠁⢂⣧⠃⡇⡁⣾⡅⣿⢆⢿⡇⢽⠀⠡⢹⣸⣼⠀⢱⢸⠘⣿⡌⣟⣿⡵⣫⢏⣿⣿⣿⣿⣿⣿⣯⣌⣫⠽⣿⣿⣯⣿⣿⣿⢫⡝⣹⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⢿⣿⣿⡐⣭⣳⢏⡖
⠉⠋⠉⠉⠉⠀⠀⠀⢀⣀⣤⣴⣾⣿⠿⣛⣵⣿⣿⣿⣟⣾⣿⠿⣋⠃⢌⣡⡿⠁⠀⠀⢈⣤⣾⣿⣿⠟⡽⣳⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢨⡜⡁⢰⢿⠁⣿⡄⣻⠸⣯⠛⣼⠀⡇⠰⣿⡜⢰⢸⠈⠀⢸⢳⠘⣿⣼⡳⣏⡶⣭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣧⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣹⢰⡷⣯⢿⡀
⠀⠀⠀⠀⢖⣲⣿⣾⣿⣿⣻⣿⢏⣵⣾⣿⣿⣿⣿⣿⡾⠛⡡⣸⠏⣴⡿⢋⣔⠄⢀⣴⣿⣿⣿⢟⣿⣞⣽⢻⣱⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠣⢡⠂⠇⣼⢸⢹⢿⡸⣏⡘⣿⡇⢹⣀⡇⠄⣿⡁⣸⠀⢃⢸⢸⡎⢧⢠⢿⣽⣳⢻⣾⢽⣧⣛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣿⣿⡷⢣⡿⣽⡽⣗⡘
⣶⡾⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢅⠠⢡⠞⣡⠞⢋⣴⡜⠉⣰⣯⣿⡿⣫⣵⣏⣽⡟⣣⣯⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣏⠀⡾⠀⠀⡟⡜⢸⡘⣅⣿⢸⣿⡄⣸⠈⡇⠀⣿⡅⠸⡄⠸⢘⡀⣿⣸⡇⢮⣿⡝⣷⣫⢟⡿⣽⣻⣿⣿⣿⣿⣿⣿⡿⢇⠛⢡⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣿⠃⣼⡟⣷⢻⢇⡜
⣷⠌⢄⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⣀⡤⠟⠀⣨⣤⡖⢡⣴⠗⣡⢔⣼⣟⣛⣵⡞⣿⣷⣿⠿⣰⣽⣾⣿⢿⣿⣿⣿⣿⣿⣯⣾⣿⣇⡈⡅⠀⢢⣽⠃⣸⢴⢸⡏⢺⣿⡇⢻⡀⣷⣲⣿⡇⠀⣆⠀⠀⡇⠹⡉⢿⠜⠾⣿⣧⣛⠾⡽⣿⢿⣿⣿⡿⣿⣾⡟⠁⣠⢘⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣿⣼⣿⡟⢀⣿⡹⣞⢯⣎⡓
⠃⠎⠉⠶⠺⠯⠍⠋⠛⠛⠋⢈⡁⢐⠒⡉⠥⢠⣧⡾⠋⣩⠔⣋⣤⣮⣿⢞⣯⠾⣛⣽⣾⣿⣿⡿⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⡟⣄⡇⢀⠀⡏⡄⣿⢘⢸⡇⣾⣿⠇⢺⡁⡇⠀⣿⡇⠀⡎⠀⢰⡁⢇⠡⠸⡁⠀⠙⠙⠛⣿⣿⣿⣿⠟⠛⠘⠻⣟⣉⡴⣿⣿⢟⣿⣿⣿⣿⣿⣿⡿⡿⣳⣿⣯⣿⣿⣟⠰⢠⢳⡿⣱⢏⡾⡼⡱
⠀⢀⣀⣐⠰⠬⣟⣹⣍⣛⣳⣶⣶⣿⡾⢋⣴⠟⢉⡠⠞⢁⣨⢟⣻⣡⣿⣛⣿⣿⣿⣿⣿⣿⣿⡑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣃⡸⠀⢀⡷⠃⡇⢸⠞⣼⡇⣿⡿⣤⢸⠁⢇⢄⢿⡇⠀⡇⠀⡇⢳⢀⠀⠀⢳⠀⠀⠡⣸⣼⠿⠉⠀⠀⠀⠀⠀⠹⢿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣳⡿⣿⣿⡏⢈⣮⣽⢗⠣⡟⡼⣃⠗
⠀⠠⢭⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⢗⡋⠤⠊⢡⣤⣽⢟⣻⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠁⠀⡸⠘⣼⠃⡏⠒⡟⡄⣿⡅⡇⣇⠀⠀⢼⣎⠇⢀⡇⠀⠇⢸⡺⠖⢶⡌⣦⢀⣵⠟⠉⠀⠀⢤⡀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⢱⣿⣷⡿⣽⣿⣿⡄⠀⢿⣵⡞⢣⡝⡼⣩⠎
⢨⢳⠠⣏⣿⣿⣿⣟⣯⡿⠟⣋⠥⠒⠁⣀⣴⣶⣻⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⡿⢁⠀⡟⢰⡿⢠⡇⠈⣷⢃⣿⣻⠇⡆⣸⡀⣼⣽⠂⣸⡇⠀⠸⢾⣿⡱⢎⣹⣼⣿⣯⡀⠀⠀⠀⠀⠈⣒⢦⣄⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢷⢯⣷⡿⣱⣿⣿⣝⡀⡧⣾⣹⢻⡆⣟⢜⡣⢚
⢰⢊⣗⣼⠿⠿⠛⠉⠁⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⢁⠃⢀⢄⣾⡇⢸⡘⢠⡏⣸⣏⣧⢳⠃⠁⠇⢻⡏⠀⣿⠀⠀⠀⢸⣿⣿⣿⠿⠛⢿⣽⣟⠦⣄⠀⠀⠙⠦⢤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⡾⣿⣹⣿⣿⣟⡾⠘⣿⡇⣿⣽⡧⠘⢆⡣⠝
⠋⠉⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣏⠎⠀⡌⣸⣿⠂⡟⡔⡾⢡⣿⣻⡏⣸⠀⠀⡄⢸⡃⡄⠁⢀⠀⡀⣼⣿⠟⠁⠀⠀⠀⠙⢿⣷⣿⣷⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢽⡿⣷⣿⣿⣟⣾⢱⢢⣿⠃⣽⣿⡇⢍⠚⡴⣉
⣠⢄⡴⢶⣺⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣽⣿⣻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡞⠀⠐⢡⠟⡏⡸⢸⢹⡕⣼⢻⣿⡇⣿⠄⠰⠀⢸⢁⡀⠇⡆⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣶⠿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠂⣿⢳⣿⣿⢏⣿⡇⣰⣾⣿⢁⢺⣿⠁⢮⠰⠱⣌
⢮⢙⣵⣿⡿⣟⣵⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢿⣿⣿⠁⠀⢸⠏⡴⢁⣷⠃⡼⢸⣯⣼⣿⠀⡏⠀⠀⠀⢸⠨⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⣋⡝⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣼⢧⣿⣿⢿⣾⡏⢠⣿⡙⣿⢸⡇⣿⠘⣜⠀⡝⡦
⣠⣿⡯⢃⣷⣿⠟⣫⣾⣿⣿⣿⣿⢻⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡏⠀⠀⢸⡶⢃⣾⠃⣸⠅⢾⣷⣿⣿⢢⢇⠀⢀⠀⠈⠀⠀⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⡒⣱⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣟⣾⡟⣥⣾⣿⡐⢇⠞⣼⠛⡜⡜⢢⠜⣩
⣿⠉⢰⡟⣿⣣⣾⣿⣿⣿⣿⣿⣿⣝⣻⣿⣇⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣠⠛⠁⢼⡧⢊⠎⣸⣽⣯⣿⣏⠏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⢘⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢠⣿⣿⢏⣾⠿⣁⣾⣿⡛⢼⠡⣾⡟⢹⢨⠝⣣⠸⡅
⠂⢤⠋⣼⣵⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⢿⣷⢺⣿⣿⣿⣟⣿⠿⠞⠛⠛⠛⠛⠋⠹⠿⠿⣿⣿⣿⠿⠿⣿⣿⣿⢿⣿⣟⣿⣽⡿⠁⠀⢀⠃⠀⣰⠪⠴⠏⡰⣿⣳⣿⣿⣽⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠄⣾⣿⣿⢟⣽⣿⣿⣿⢿⣿⣿⣿⣿⣿⠃⢸⣿⡯⣾⢏⢆⣿⣿⢸⢁⡧⢺⣿⠇⣃⡯⣜⢣⡱⢌
⢌⡧⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣭⣿⣿⣎⣿⢿⣿⣏⣷⣿⣝⡚⡛⠿⠿⣿⣷⣶⣶⣤⣬⣁⣘⢗⣃⡴⠾⠿⠿⣛⣛⡵⠁⠀⡐⠃⢀⠞⡁⠠⢊⣼⡟⣡⣾⣿⣿⡏⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠀⣼⣿⣯⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⢣⢇⡇⢸⣿⣽⡏⣮⣿⣿⡏⣲⢸⡗⣧⣿⢣⣽⡇⡼⡂⡵⢸
⠏⣲⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣽⡿⣿⡽⣿⣿⣺⣗⡿⣿⠽⢶⢿⣯⣍⣁⠙⢊⢋⣛⠛⠛⠿⢿⣿⣿⣿⣧⣬⣷⣽⣾⠿⡑⠀⠀⣠⣴⠋⠀⢠⢣⠞⣨⣾⣿⣿⣿⡏⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡐⠀⣁⣴⣿⢟⣼⣿⣿⣿⣿⣿⣿⣿⣿⡯⣟⣇⣾⡇⠸⣿⣟⣰⣿⣿⣿⣱⠇⣿⣟⣯⡇⢦⡟⡔⣣⢡⢇⡻
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣗⣟⣹⣿⣻⣽⣿⡶⣿⢿⣻⣿⣭⣿⣿⡾⠿⠶⣖⡊⠙⠿⣮⣑⣊⣖⠚⣯⣉⣭⣭⣾⠁⠔⠁⢀⣼⡟⠁⢀⡴⠃⣡⣾⣿⣯⣿⣿⡟⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡐⠀⡰⣬⡟⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⠾⣼⣻⣆⠀⣿⢳⣿⣿⣿⢣⣿⠰⣿⣛⣷⠐⣿⣿⢈⡑⢢⢎⡵
⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣳⣫⢿⣟⡷⣯⢿⣿⣧⢹⣿⢿⠿⣿⡿⣠⣀⣤⢶⣤⣉⡃⠤⠤⢬⣥⣀⣐⣠⠤⠛⣋⠡⠀⡠⢎⡿⠁⠀⣠⠞⢀⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠐⠡⣘⠱⣘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠯⣕⢣⣷⣿⠀⣿⣿⣿⣿⣇⢺⡇⢸⣿⣏⡇⢽⣯⡿⡌⠀⡉⢪⡴
⣿⣿⣿⣿⢿⣽⣾⣿⣛⣶⣟⠧⣾⣽⢻⣏⣟⣛⣿⠛⠉⢉⣙⠓⠒⠒⠻⢜⠚⠛⠛⠋⠂⢀⠀⠉⣉⣥⣤⢶⡟⠒⠀⢘⡔⠋⠀⣀⣼⣛⣼⣿⣿⣿⣿⣿⣿⣿⣥⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠡⢀⢉⠐⡈⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠎⣿⣏⢦⣿⢛⡆⣿⣿⣿⣿⣳⡿⠁⣿⣿⡜⠃⡿⣟⢧⣘⠇⡌⣵⢊
⣿⣿⣿⣽⣿⣯⣿⠿⣭⣾⢯⡗⣿⣛⡭⡩⣿⣟⣉⣀⡀⠀⠠⠉⣁⣤⣤⣴⣶⣴⣶⣶⣶⣶⣿⣻⣛⣏⣽⡟⠀⠔⠡⣋⡠⢂⣶⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠀⠤⠈⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣙⠼⣿⢨⣾⡿⣎⡇⣺⣿⣿⣿⡟⠃⢴⣿⣿⢋⠤⣟⡷⢠⢏⡎⢴⣋⠞
⣿⣿⣿⡿⣿⣿⢟⣵⣿⠿⣛⢾⡵⣳⢎⣽⡟⣩⣽⣶⣶⣦⣤⠸⣿⣿⣿⣏⠿⣿⣿⣷⣝⣿⡿⢿⣶⡿⠊⠠⣊⡴⣋⢷⡵⢿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡑⣎⣽⡷⠬⣽⣷⢻⡆⢸⣿⣹⣿⠇⠰⣸⣿⣿⡰⢂⢏⠅⢋⡏⡔⢮⣱⢋
⣿⣿⣿⣿⣛⣧⣾⣿⣿⢛⣽⠯⡿⣭⣾⣿⣞⣿⣿⣯⣬⣷⣶⣄⠀⠉⢛⠛⠿⢿⣛⣛⣩⠄⠀⡔⠉⠀⣴⣷⠟⣃⣼⣫⣷⣿⣽⣿⢿⣿⣿⣿⣿⣿⣻⣿⣿⠏⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⡵⡺⣏⢱⣿⡾⡽⣿⣿⠀⣿⣿⡿⡀⢰⡻⢿⢏⠉⣎⠸⢠⣛⡏⢬⠳⢆⡏
⣿⣿⠿⣣⣿⣿⣿⣻⣞⣳⠒⠶⣷⣋⡒⠀⠿⠿⠿⠿⠇⠻⣿⣛⣛⣂⣀⡠⠤⠉⠁⢀⣀⡾⠋⠀⢤⣼⢟⣿⢎⣠⡘⢿⣷⣮⣿⣯⣟⣼⠿⢛⣷⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣤⣷⡿⣾⣡⡿⢿⣹⡏⣿⠀⢿⣿⣧⠇⣴⣧⣾⢺⠀⣿⠠⣿⡜⢂⡏⠞⣜⡂
⢏⣵⣾⣿⣿⣿⣽⡟⣞⣞⢛⣒⣣⣤⣭⣭⡭⣤⣤⡖⠒⠶⠤⠴⢀⣁⣤⣴⣶⣴⡝⣫⡧⢊⣤⣾⣿⠞⣋⣴⣿⣿⣿⣵⠹⣿⣿⣿⣭⣷⣟⣥⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⡿⢰⡇⣿⡿⣽⣿⢡⣿⡆⣽⣿⢁⠀⢻⣾⠂⠣⠆⡝⢼⡿⠘⡘⣸⠱⣌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣯⣟⡷⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠉⠛⢿⣿⣮⡻⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣵⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠙⢿⣿⣞⢷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⣴⡄⠀⠀⠹⣿⣎⢿⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⣿⣄⠀⠀⠹⣿⣏⣿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣽⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣧⣤⣾⠟⠃⠀⠀⢹⣿⣼⣷⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠛⠀⠀⠀⠀⠀⣿⣷⣿⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣴⣿⣿⣿⣶⣶⠀⠀⠀⣿⣿⢾⣏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣧⣻⣼⣿⠋⠀⠀⢠⣿⣿⣾⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣾⣿⣿⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡿⠿⣿⡧⠀⢀⣾⣿⢧⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣠⣾⣿⢯⣿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠈⠁⠉⠉⠉⠻⠧⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣾⣿⣿⣿⣿⡽⡞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⣿⣟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣹⣟⣿⣶⡀⠀⠀⠀⣀⡀⢀⠀⠄⡀⠹⣿⣿⡹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡟⣾⣿⡇⠀⠠⠜⠁⠀⠄⡈⢀⠐⠀⣻⣿⣧⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⠏⠀⣰⠃⠠⠈⠐⡀⠄⢢⡔⠀⢸⣿⡷⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢀⠁⣂⣤⠾⠋⠀⠀⣾⣿⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠋⠁⢀⣤⣤⣾⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣽⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠛⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⢉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⢹⣿⣞⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⢻⣿⣹⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣠⣴⡿⠋⠀⡀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣯⣀⠄⠁⠠⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⡇⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⣁⡀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⣟⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠠⣿⣿⣟⡿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠟⠁⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢷⢹⣿⡾⣝⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣯⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⢶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⠀⠻⣿⣯⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣻⣷⡄⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣽⣟⡿⢶⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣍⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣿⠶⣿⣿⣿⣿⣿⠿⡛⢏⡍⠳⣌⠲⡐⠦⡑⢎⡙⢻⢿⣿⣶⣻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡉⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣿⣿⡟⣍⠳⣈⢇⡙⢢⡜⡱⢄⢣⡙⠴⣉⠦⡙⢦⡉⣿⣿⣿⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⣰⠎⠀⠂⢁⠠⠐⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⣿⣿⣧⢂⠳⡌⢦⡙⢆⡜⡰⣉⠖⠬⡑⢆⢣⡙⢤⣽⣿⢏⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠈⡀⠄⠁⠠⠀⢢⡿⠛⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⢸⣿⣿⡌⡱⡘⠴⣘⠢⡜⣡⠒⣌⠣⢍⠎⣆⣙⣾⣿⢋⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣦⣄⡀⠐⠀⡈⠠⠁⠈⠁⠀⠀⠀⠀⣀⣤⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⢸⣿⣿⡖⣡⠙⢦⢡⢓⡸⢄⢫⠰⣉⠦⣉⣶⣿⡟⣥⣾⡿⣿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣧⣄⣤⣤⣤⣶⣶⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠦⣙⠢⣑⠪⡔⢪⢅⠳⣈⢶⣽⡿⢣⣾⣿⢟⣾⠋⠀⠀
⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⡟⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣸⣿⣿⢃⠳⡄⢳⢨⠱⡌⢣⢌⢳⣼⣿⢯⣱⣿⡟⣳⡟⠁⠀⠀⠀
⠀⠀⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⠃⠀⠀⠀⠀⠀⠙⠹⠙⠫⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣦⣶⣿⣿⡟⡌⢣⠜⡡⢎⡱⢌⢣⣮⣿⠿⣱⣾⣿⣫⡾⠋⠀⠀⠀⠀⠀
⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏⠀⠂⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⢋⡝⡛⠿⠿⠿⡟⢫⠔⡩⢆⡹⣐⢣⢲⣼⣿⠿⣙⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀
⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⣿⣧⠀⠀⠀⠀⣀⣠⣤⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡿⢋⡔⢣⠜⣌⢣⡙⠦⡙⠦⣙⠰⣃⠴⣨⣶⣿⡟⣽⣾⡿⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠻⣿⣿⣶⣿⣿⡿⠿⠛⠉⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⢟⠣⡜⡡⢎⡑⠎⡔⢢⡑⢎⡡⢓⠬⡑⢦⣷⣿⠟⣧⣽⣿⣏⠀⢠⣟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⣠⣴⡶⢶⡤⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⢛⠬⡌⢳⠰⡑⢎⡜⡱⡘⢥⠚⡤⠣⢍⣲⣽⣿⢟⣱⣾⣿⣿⠿⣿⣿⣫⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⢠⣿⠋⠁⠈⠁⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⢯⡽⣫⠾⡽⢮⢧⡻⣎⢷⣣⢻⢮⡻⣵⣻⣾⣿⢿⣯⣾⣿⣿⣿⣿⡿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⣿⣆⡀⠀⠀⢀⣠⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣿⣿⣿⡿⢿⡻⣧⢫⡷⡽⣭⢟⡵⢯⣎⣳⢞⡷⢯⡟⣮⣿⣿⣿⢟⣯⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣷⣴⣶⣾⣿⡿⠋⠙⢿⣷⡀⠀⠀⠀⠠⣶⣶⣾⣿⣿⣿⠿⠿⡛⡍⢦⠑⣎⡱⢌⢆⢣⡱⢌⢎⡱⢊⡜⡡⢎⡱⢪⣴⣿⡿⣛⣼⣾⣿⢿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠹⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⢀⣼⣿⣿⠫⣌⢣⢣⠱⡘⢦⡩⢔⡡⢎⡜⢢⡑⢎⢢⡑⢣⠜⣑⣮⣽⣿⠟⣏⣶⣿⡿⣿⣵⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣻⣵⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣯⣽⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣤⣀⣀⣴⣿⣿⡛⠥⣃⢆⢣⠎⡱⣉⢒⡌⢦⡑⣊⠌⢧⡘⡌⠦⣙⣢⣽⣿⡿⢫⢥⣿⣾⣿⣫⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⢿⡿⢿⡿⢿⣿⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⡿⢛⡍⢳⡐⢆⡛⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⠿⡛⢤⡙⢢⡑⣊⠦⡙⠴⡡⢎⡘⠦⢱⡘⡜⢢⢱⣸⣵⣿⡿⢟⢣⣾⣿⣿⣿⣽⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⢫⠱⡌⢣⡘⢥⡘⠦⠱⣌⠹⢻⢿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⡿⡛⢥⠒⡔⢢⠜⣢⢙⠴⣈⠇⡜⠤⢣⡙⠦⡱⢎⠬⣑⢣⠒⣍⣶⣿⣿⢟⢫⣼⣾⣿⣿⣯⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣿⣿⡿⢡⠎⡱⢌⠣⢍⠦⢱⠩⡱⢌⢣⢃⠎⡜⣩⠛⡟⣛⠻⡛⢭⡙⡔⢢⡙⢆⡹⢌⢣⠚⣄⢋⠦⡑⢎⡌⢣⠣⢜⡡⢓⡌⢲⣡⣾⣿⣿⠿⣋⣶⣾⣿⡿⣻⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣇⠣⢎⡑⢎⡱⢊⡜⡡⢎⠱⡌⢦⡉⠞⡰⢡⢋⠴⢡⢣⢙⠢⡜⢌⠣⡜⣡⠚⡌⢦⡙⠤⢋⠴⣉⠖⣌⢣⡙⢦⡘⣥⣾⣿⡿⢟⢫⣔⣿⣾⡿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡙⢆⡍⠲⢌⠣⡜⡰⡉⢖⠱⣂⠭⡘⣅⠣⠎⡜⡡⢎⡌⡓⡌⢎⡱⡘⢤⡙⠜⡢⢅⠫⠜⣢⠑⡎⡔⣢⣵⣶⣿⡿⠟⡭⣮⣽⣾⢿⣯⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣷⣌⠜⡱⢊⠵⣨⠑⡍⢎⠲⡡⢎⡱⢢⡙⡜⡰⡑⢎⠴⢱⡘⠦⣡⠙⡆⡜⣡⠓⣌⢣⡙⣤⣫⣴⣿⣿⠿⣛⣥⣽⣾⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧⣛⣿⣿⣯⣖⡩⢒⡡⢍⡜⠬⣑⠱⣊⠔⡣⢜⡰⠱⣉⠎⡜⡡⢜⠢⣅⠳⣘⢰⣡⣯⣴⣷⣿⣿⠿⣟⣹⣦⣿⣿⠿⠋⠁⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣬⢛⣿⣿⣿⣷⣮⣶⣘⣦⢡⠓⡬⡘⢥⢢⡑⢣⠜⡘⠴⣑⣮⣵⣦⣷⣾⣿⣿⡿⢟⡻⣍⣶⣷⣿⣿⣿⣏⠀⠀⠀⠀⣼⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣍⣛⠻⠿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⢿⠛⣏⣹⣔⣮⣷⣿⣿⣿⣿⣧⣳⣞⣿⣷⣦⣶⡾⣫⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣷⣭⣖⣦⣩⡍⢯⣙⣛⡛⣛⠻⡹⣍⣫⣕⣲⣬⣽⣶⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣯⣽⣽⣭⣽⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⡿⢻⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⡿⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀