Sousaphone Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⢀⣀⡀⠀⠀⠴⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠠⡀
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠁⢙⠋⠉⢍⣿⣿⣏⣽⡉⢉⠉⠛⠙⠛⠻⡇⠀⠀⢰⢁⡞⠁⢀⣀⡘⢱⢠
⠀⣀⣤⣄⡀⢀⣀⡀⠀⠀⢀⣼⣇⠀⠀⠀⠉⠛⠙⠻⠿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⣦⣸⣇⢸⢹
⠀⣿⣿⣿⣿⣄⣠⣤⣘⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡀⠰⡟⢹⣿⣿⣿⣿⢸
⠀⢻⡉⠀⠈⠻⣿⣿⡿⠛⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣤⢤⣤⢽⠀⠀⠀⠀⠀⡇⠀⣿⣮⣿⣳⣟⢻⢻
⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠋⣔⣺⣟⣦⡈⢡⡁⠀⠀⡀⢀⠃⠀⣿⣿⣻⣿⣧⣾⢸
⠀⠀⢀⠴⠦⣤⣤⣤⡀⠀⠈⠀⠀⠀⠀⠀⡂⠀⠀⠀⠘⢛⣿⣿⣿⣿⢿⣇⠣⡀⠈⠋⢹⠏⠛⣿⡿⠙⠛⠋⠈⡘
⠀⠀⠀⡰⡊⠍⠀⢙⣯⢤⡶⢦⣄⠀⠀⠀⢧⡀⠀⢸⡖⣒⣿⣛⣿⣿⠻⠃⢟⡇⠀⠀⢸⠀⠀⢹⡗⠦⢤⠤⠔⠁
⠀⠀⡎⠈⠀⠀⠀⠀⠁⠀⣹⣾⣿⣧⠀⠀⠀⠈⠒⠤⣽⣧⣤⣀⣀⣼⢀⡠⠊⠀⠀⢀⡞⠀⠀⡘⣷⡀
⡄⠸⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣷⡏⠀⠀⣦⣤⣶⠷⠶⠶⠛⠒⠚⠋⠉⠀⠀⠐⠂⠛⠃⠀⠐⠛⠚⠛⠒
⢳⠀⢇⠀⠀⠀⠀⢸⡻⣏⠽⢿⢫⠇⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚
⠀⠳⣌⠳⣄⠀⠀⠘⠿⣻⡴⢃⠎⠀⠀⠀⡇⠀⠀⠈⠙⡏⠙⠋⠉⠉⠉⢻⢯⠭⣯⠿⠻⠷⣿⠄⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠈⠳⠮⣍⣓⣚⣩⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀⠑⠒⠓⠚⠒⠒⠐⠒⠲⠾⠶⠶⠤⠤⠤⠬⠤⠄⠤⠀⠠⠤⠤⠄⢠⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⣚⣵⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠤⠤⠤⠒⣒⣉⡥⠶⠞⠛⠋⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠖⠒⠒⠒⠉⠉⠉⠙⠛⠉⠒⠒⠒⣀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣤⣭⡭⠭⠭⠭⠭⠭⠭⣭⣉⣉⣉⣛⠛⠛⠿⠿⣿⣿⣷⣮⣿
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣾⣿⡕⡘⡏⢩⢾⡟⣿⣽⣭⣩⣍⠋⠉⠍⣛⡋⠒⠒⠤⡉⠙⠛⠿⣶⣶⣶⣟⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠘⠏⠑⢒⠁⣼⣸⡇⣏⡿⣾⣾⡶⠤⠀⠠⠾⠄⠀⠁⢢⡈⢢⠀⠀⠈⢻⣝⠻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠑⠤⣼⡖⣉⣉⣉⣑⣚⠛⣋⣛⢛⡛⣓⣲⡂⢤⠀⠀⢳⠀⣶⠀⠀⠀⠙⠗⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡠⠎⠹⣟⡷⠿⠤⠭⠽⠍⠨⠯⠮⡭⢿⣅⠁⠌⡌⢀⡜⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢽⣟⣷⣤⣀⣹⣏⣉⣉⣉⣉⣉⣙⣛⣷⡒⠒⣒⣉⣽⣿⣟⠋⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣷⣭⣗⡂⠭⣭⣽⣿⠿⠟⠛⠛⠛⣛⣙⡿⠿⠿⣿⠟⠁⠁⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠉⠙⠂⠁⠀⠀⠀⠈⠉⠉⠉⠁⠓⠀⠀⠈⠀⠀⠀⠀⠀⠼

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣆⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣁⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣯⣴⠿⠛⠉⢩⣿⠟⢻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠁⠀⠰⠞⠙⢦⡰⡧⣌⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢳⢟⣿⡿⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡾⣸⢠⠇⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢰⢃⡇⡼⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠸⠜⢰⠃⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣦⣤⣀⣀⣀⣠⣾⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⠛⠛⠛⠛⠛⠛⠛⠓⠶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠋⠉⠀⠀⠀⠀⠉⠛⢻⣿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢻⡿⠟⠀⠀⠀⠠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣀⡀⠀⠈⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⢸⠟⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⣀⠀⠀⠀⠀⠀⢠⡟⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡌⠃⠀⠀⠀⠀⣾⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⠉⠉⠙⠓⠖⠒⠂⠀⠐⠒⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⣴⣿⣿⣿⣽⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⣾⣏⠁⠀⠉⠉⢋⡉⠀⠀⠠⠊⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢺⣿⡿⠛⠀⠐⠀⠈⠰⠂⠁⠀⠀⠀⠀⡠⠔⠚⠂⠀⠀⠀⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⢀⠉⠂⠀⠴⠂⠀⠀⡄⠀⢀⣤⣥⠄⠈⠀⢄⠐⢲⢆⣄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠑⡖⠀⠀⠀⠀⣀⣙⣚⠋⣻⣇⣦⠦⠼⣭⠦⢪⡾⣈⡭⠭⠉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⣠⠔⠈⡉⢗⡶⣟⣯⣤⣤⡀⢀⡻⠋⠀⠀⢪⣤⣶⡿⢘⣉⡀⠒⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⡐⣻⢟⣖⣸⣤⣷⣿⣿⣿⡟⡷⢸⣷⠤⡾⢟⠾⡋⠾⢘⣋⠐⡶⠁⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣘⣿⠶⠖⣋⠥⢶⡞⢿⡶⢺⣧⠄⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⢉⠤⣒⣭⠶⢛⣡⠴⡏⢀⠈⠁⠀⠀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠈⠻⣿⣿⡿⠿⠟⠛⠿⣇⡀⠀⢚⣥⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢀⡤⠐⠀⠀⠀⣀⠀⠀⠀⠉⠁⠀⠅⠀⠀⠐⠊⠁⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠙⢻⣿⠷⣶⣶⣶⣦⣴⣶⣶⠶⢿⠟⠛⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣀⣙⣧⣤⣾⣀⣀⡎⠀⠀⣿⠀⣼⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠁⠈⠉⠁⠀⠀⠀⠉⠻⠟⠛⠻⠷⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠖⠛⠛⠛⠛⠛⠓⠲⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣠⠔⠋⠁⠀⠀⠀⢀⣀⣤⣤⣶⣴⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠈⠡⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣰⡟⠁⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢠⡾⠉⠀⠀⠀⠀⣴⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⡀⠘
⠀⠀⠀⠀⠀⠀⠀⣾⠇⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣽⣿⣿⣿⣿⣿⣿⣿⣬⣿⢻⣿⣷⠀⠀⠀⠀⠀⢡⠀⠆
⠀⠀⠀⠀⠀⠀⢸⣏⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⡇⠀⠀⠀⠀⢸⠀⠠
⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⢃⡄⠀⠀⠀⢸⠀⡶
⠀⠀⠀⠀⠀⠀⢸⡁⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⢀⣿⡼⠁⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠈⣤⠀⠈⢷⡀⠀⠀⠀⠀⠀⠸⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⡿⠻⠁⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠢⡈⢷⡀⠀⠀⠀⠀⠀⠻⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢫⣾⣿⠗⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢄⠙⢦⡀⠀⠀⠀⠀⠀⠐⠹⠛⠻⠿⠟⠟⠙⠉⢁⣴⠿⠋⠁⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⠦⡙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢌⣉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⡷⢾⣿⣿⠛⢉⠛⣡⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⢀⣾⠃⢹⣠⡾⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣣⣾⣡⣶⡿⢋⣴⣿⣿⣿⣶⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢨⡗⣹⣿⣿⣿⣿⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⣎⣠⣾⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢹⡿⣿⣿⣷⣽⣯⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡇⣸⢟⣽⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣨⢿⣷⣭⢿⣿⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⣿⢏⣽⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠠⣤⢀⣾⣿⣿⠿⣶⣿⡿⢾⣿⡀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⡎⢀⡜⢁⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡿⠋⢥⣠⡼⣻⡅⣼⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠋⢀⠎⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣯⣿⣷⣬⣷⣴⣿⣿⣿⢋⣴⡿⣹⡇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡿⣼⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣻⣾⣿⣿⣿⣿⣟⣿⢣⣿⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣹⣿⣿⡿⠋⢉⣽⣿⡿⢛⣹⣿⣿⢏⣼⣷⣿⢣⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣟⣿⠟⠁⣠⣴⣿⣿⣯⡶⣻⢻⡿⢣⣾⣿⣿⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣿⣇⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠋⢃⣤⣾⣿⠟⠛⠟⠉⢷⣵⠋⣴⣿⣿⣟⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⣜⣿⡄⠀⠀⠀⣠⡞⣻⠟⠁⣠⣿⣿⠿⡋⠀⢀⡤⣺⡵⢛⣵⣾⣿⣿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠱⡤⢘⣧⡻⢦⡀⠀⣻⣇⠻⢶⣿⠿⣟⣁⡠⠵⡎⠱⢟⣭⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠙⢷⣝⣻⣦⡉⠁⢙⣛⣿⣿⣭⣭⠥⠖⢀⣠⣴⣾⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⡜⠛⢶⣤⣍⣉⣩⣭⣤⣴⣶⣶⣿⣿⣿⣿⣿⣟⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣤⣙⢿⣿⣿⣿⣿⣿⣿⣽⣶⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠋⠙⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡍⠻⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡶⢶⣽⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⢷⣦⣙⢿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⡟⠛⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⣠⡾⣻⣿⡏⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣸⡿⠋⢉⣴⢿⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣫⣿⣶⣿⣵⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⠛⣿⣿⣿⣯⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⣫⡾⠻⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣴⡿⠋⠛⠋⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣻⣿⣷⣦⣄⣴⡿⠋⠱⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣽⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣞⣫⣭⣭⣭⣙⣓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⣸⣿⣿⣿⠟⠛⢾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⣠⢖⣿⣿⣿⣽⣟⣦⠀⠈⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⢻⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢿⣿⣅⠀⠈⠁⠀⣀⣼⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡈⠻⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣍⣙⣛⣹⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣟⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣾⣿⣿⣿⣿⣿⣯⣥⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣼⣿⣿⣿⣿⠿⠛⠋⠉⠙⠛⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠁⢠⡐⠾⣿⡿⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⢨⡾⣫⢆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⣫⠠⠄⣺⠕⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⡠⠪⣖⢈⠥⠷⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⠻⣿⣿⣿⣦⡀⠀⠸⣌⢊⠔⢋⡶⢊⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢯⣿⣿⣿⣿⣷⣶⠞⣡⡾⢋⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⢡⡾⠋⠴⠛⠉

⢀⣀⡀⠀⣀⡀⢀⣀⣀⠀⡀⡀⣀⢀⡀⡀⣀⢀⣀⡀⣀⡀⠀⠀⠀⡀⡀⣀⡀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⢀⢀⣀⡀⡀⣀⣀⣀⣀⣀
⣿⡏⠏⢋⠩⢿⣿⣿⣿⡏⣹⠉⠉⠉⣿⣿⣿⣿⠉⡍⠍⢹⣿⣿⣿⣿⠉⠍⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⢛⠉⠉⡉⠙⠛⠛⠉⡛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠶⠶⠶⠶⠶⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠛⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠁⠀⠀⠀⠀⠉⠙⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠲⣤⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀⠙⡿⠟⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡿⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⢠⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣌⠓⠀⠀⠀⠀⣼⠁⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠈⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠈⠉⠂⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠟⠂⠀⠀⠀⠀⣰⡟⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠉⠓⠲⠖⠶⠶⠶⠖⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⣰⡿⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⣼⣟⣉⠉⠉⠉⢋⠁⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⢸⣿⡿⠛⠀⠐⡀⠀⠀⠈⠙⣄⠀⠀⣀⠄⠐⠒⠀⠀⠀⠀⠀⠀⠀⢈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠉⠃⠀⠐⠀⠀⠀⡂⢈⣲⣿⡶⠈⠁⠀⠀⠀⠢⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⣀⣀⢉⡻⢙⣿⣥⡴⠒⠦⡕⠀⡴⢀⠨⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⣠⡖⠀⠀⢻⡟⣿⣧⣶⣦⡀⢨⡟⠁⢀⡀⣤⡾⡿⢃⡭⠄⠐⠂⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢰⣩⣋⣿⣸⣶⣿⣿⣿⣿⣻⡇⣿⡗⠲⢟⡻⠯⠝⢃⡩⠄⢹⠁⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢳⡸⠿⠚⣋⠁⣒⠛⢙⡷⠀⡵⠦⠄⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⠤⢂⡽⠖⢉⣡⠖⣺⢀⡄⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠙⠿⢿⡿⠟⠉⠛⠛⠧⣈⣊⠥⠶⢋⠈⠴⣊⠕⠉⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⢠⠀⠈⠀⠀⠢⠤⣀⣀⣀⣀⣑⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠛⣿⠛⠛⡿⠟⢻⡟⠛⡿⠉⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠀⠀⢴⣬⣿⠶⢷⡶⠴⠃⠀⠸⢧⣤⣧⣤⣞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠂⠒⠂⠐⠀⠀⠆⠂⠂⠀⠀⠂⠀⠀⠐⠐⠀⠂⠀⠀⠀⠀⠈⠀⠀⠁⠈⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⡰⠛⠉⠫⠭⠉⠀⠈⢡⣄⡀⠀⠀⣀⣤⣾⣿⣿⣿⣿⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢇⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣀⣤⣴⣶⣶⣶⣤⣤⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠿⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠉⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠉⠻⣿⣿⣿⣿⠟⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣜⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠘⠋⠀⠀⠀⠀⠀⠘⣿⣿⠏⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠛⠛⠛⠷⠶⣤⣤⣤⣐⣂⣀⣀⣀⡤⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⣀⣤⣤⡿⠿⠿⠿⢿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣀⣴⡾⠛⠉⠁⣀⣤⣤⡤⠤⢭⣍⣉⣁⠈⠉⢒⣀⣤⣤⣤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⢀⡴⠋⠁⢀⡴⠚⠉⠁⠀⠀⠀⠀⢰⡖⢛⣿⠶⠿⣤⡟⠉⠹⢬⡳⣾⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⣰⡟⠁⣀⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠈⢻⣄⡀⠀⡙⣯⣿⣿⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰⠏⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢟⣤⠛⡿⢻⣷⢛⣇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⡴⣛⣛⣡⡴⢿⡵⢋⡵⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣾⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⡶⣫⡶⢭⣿⣾⡵⣋⢔⣡⣞⡽
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⣴⠞⣩⣾⡿⢟⣟⡷⣾⢟⡵⢋⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣂⣨⠼⣻⠿⣯⢶⣬⣥⢸⡿⣋⣵⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠸⣧⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠾⢋⣴⠟⠁⣈⠔⠩⣈⡽⢋⣴⣿⠋⢠⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢪⣿⡀⠀⠀⢿⣆⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢋⠁⣠⣞⠁⢀⠔⣩⠶⠋⣿⠋⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⢻⣷⡌⠳⡀⠀⠀⠀⠀⠀⠀⠀⠐⣈⠖⣵⠊⢀⣿⠞⡡⠊⡴⠂⣼⠏⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠙⢿⣦⡙⠢⠀⠀⠀⠀⠀⠀⠀⠸⠘⢿⠺⣟⡥⢾⡤⠊⣠⡾⠋⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠻⣦⡀⠀⠈⠻⣿⣦⡀⠀⠀⢀⡀⠀⠀⠀⠘⠲⣿⡧⠖⢉⣵⡾⠋⠀⢀⣴⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡻⣦⣄⠀⠀⠉⠻⢷⣦⣤⣀⣀⣀⣀⣀⣀⣠⣴⠾⠟⠋⠁⢀⣴⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠭⣷⣶⣤⣀⡀⠀⠉⠉⠉⠋⠉⠉⠉⠁⠀⢀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠶⠶⠶⣶⡶⠶⠶⠾⠟⠛⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⢰⠚⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠒⠒⠒⠒⠲⠶⠦⣤⡀
⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣠⠴⠖⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣸⣥⡖⠉⠹⣄⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡟⢸⠁⠀⠀⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣠⣇⣸⣀⣄⣸⣃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡏⢻⠀⠀⢸⣩⡟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡴⠋⢹⡸⣟⡷⡿⢸⢇⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⣷⣹⡞⡇⣸⡏⣷⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⢤⡴⣒⣛⣉⣭⠭⠭⠭⠭⠭⢭⣍⣉⣓⡚⠧⣄⡀⣸⡽⣇⣧⡇⣿⠁⡏⠙⡆⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣾⣆⡠⠏⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⢛⡦⣝⠣⡶⠛⣼⣧⣄⣼⣿⡄⡇⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠎⣰⠋⠙⣷⡤⣫⣇⣼⣏⡀⣇⡇⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⠃⠀⠀⣿⢿⣅⣨⢿⢿⡷⡏⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡞⢀⣠⣤⠿⣷⢿⡾⠻⣿⠧⡇⣇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠸⠤⠖⣿⠧⣼⣷⣲⣟⡠⢟⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠸⡥⡞⣁⣘⣏⣈⡗⣻⣿⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⣿⣩⠵⠋⣻⡖⠻⣷⣻⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⢀⡷⢷⣞⣩⠿⡗⣾⣼⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢠⢎⡴⠯⣽⣛⣻⡇⢱⣸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⠀⣏⣼⠀⠀⠀⠀⠀⣧⣼⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⣄⠃⡇⠀⠀⠀⠀⠀⡗⡼⡿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢹⡆⡇⠀⠀⠀⠀⢠⣇⣷⠇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡷⣇⠀⠀⠀⣀⡼⣹⠋⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⠭⠭⠭⠥⠒⠁⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⡀⠀⠀⠀⠀⢀⣀⣀⡤⠖⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣆
⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⢸⣆⠀⠀⠀⠀⠀⠀⠀⢀⣾⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦
⠀⠀⠀⠀⢸⣮⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣤⡀⠀⠀⠀⠀⣠⣼⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⢫⣾
⠀⠀⠀⠀⢿⣛⣦⣾⣤⣤⣀⠀⠀⠀⢠⡾⡡⡸⠓⠒⠢⣝⣦⣄⣤⢞⡥⡒⡲⡻⠤⠿⣦⠀⠀⠀⢀⣠⣤⣽⣦⣟⣻⠄
⠀⠀⠀⠀⣴⢛⡿⠷⠒⠦⢭⣛⣦⣴⠋⣪⡶⠞⠛⠻⢶⣄⢙⢿⢟⢕⣴⠾⠛⠛⠶⣦⠈⢷⣤⣾⣫⠥⠒⠢⡿⣟⣳⡄
⠀⠀⠀⣼⡡⣢⣴⠶⠷⠶⣥⡉⠛⠁⢠⣿⠀⠀⠀⠀⠀⢻⣔⠕⠁⣾⠃⠀⠀⠀⠀⢸⣷⢐⢝⠉⣁⡴⠾⠾⢶⣮⡈⢹⡄
⠀⠀⣼⡡⣠⣿⡃⠀⠀⠀⠈⢿⠠⠪⠺⣿⢦⣀⠀⢀⣠⣾⢇⠀⡠⢻⣦⣀⠀⢀⣠⢾⠟⢕⠁⣴⠏⠀⠀⠀⠀⣿⣷⢄⢻⡄
⠀⠀⢷⡈⠸⡘⢧⡀⠀⠀⣀⣾⡷⠤⠪⠮⠦⢍⣉⣩⢟⠕⠌⣅⡀⡠⡻⠭⣙⣯⢅⠞⢔⠕⠕⢹⣆⡀⠀⠀⣠⠟⣙⠐⣰⠇
⠀⠀⠈⣧⠀⠙⢦⣉⣛⣫⠽⠃⠊⢂⣂⣠⣤⣤⣶⣶⣶⡄⠴⠊⠉⡛⣾⣶⣾⣧⣥⣤⣁⣀⠄⠪⠻⢍⣛⣋⡥⣞⡑⢡⡏
⠀⠀⠀⠈⠛⠶⣅⣑⣑⣠⣴⣶⠿⢛⣫⠍⢕⢖⠜⢝⣉⣁⣀⣀⣊⣊⣉⠉⠙⢒⢖⠽⠏⣛⠻⢷⣦⣬⣊⣀⣠⡦⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢰⠏⠲⠫⡊⢢⣤⠶⠖⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠶⣵⣇⠠⡪⡀⠈⣷⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⠨⢪⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡯⡨⢸⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠿⣠⢀⠛⢭⣛⠶⠦⣤⣤⣀⣀⣀⣀⣀⣠⣤⡤⠶⠞⣫⡽⠫⡪⠸⠟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣤⣀⡐⠕⠝⠝⠓⠒⡲⡲⡠⠼⡷⢔⠖⢖⢖⠝⠉⠀⠠⣢⣪⣮⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠲⠶⠦⠬⣬⣤⣼⣤⣤⡥⠴⠷⠶⠒⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣊⣉⡉⣉⣉⣓⠦⣄⠀⢀⡤⢖⣋⣉⡉⣉⣉⡒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⢟⡫⠿⠟⠳⢯⣝⢿⣮⣳⣫⣾⢟⡭⠿⠛⠻⢯⣛⢷⣜⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣠⢏⣾⣣⣿⠖⠛⠉⠉⠙⠻⣷⡽⣿⡿⣵⡿⠛⠋⠉⠉⠛⢿⣷⢹⣦⢷⣀⣀⣄⣠⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡠⢞⣩⣥⠤⠶⠶⣾⣭⣾⡇⣿⠃⠀⠀⠀⠀⠀⠀⠘⣧⣿⣧⡟⠀⠀⠀⠀⠀⠀⠀⢻⡇⣿⣮⣭⡶⠶⠦⢤⣬⣙⠢⣄
⠀⠀⠀⠀⠀⢠⠞⣴⢟⡽⢚⣉⣭⣽⣶⣝⢻⣷⢻⡀⠀⠀⠀⠀⠀⠀⢠⢏⣿⣇⢧⠀⠀⠀⠀⠀⠀⠀⣸⢣⣿⢟⣵⣚⣩⣍⣙⣶⣝⢷⣌⢦
⠀⠀⠀⠀⠀⡟⣼⢯⣟⡷⠋⠁⠀⠀⠉⠻⣷⢻⣷⣙⢦⣀⣀⣀⣠⠴⣫⣾⠿⢿⣮⡳⢤⣀⣀⣀⣠⢖⣱⣿⢳⡿⠋⠁⠀⠀⠉⠙⣿⣧⢿⡞⣇
⠀⠀⠀⠀⢸⡇⣿⢸⡟⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣷⣶⣯⣽⣶⠿⣛⢵⣿⣷⣽⡻⢷⣾⣿⣿⣶⣿⣿⣿⢾⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⡇⣿
⠀⠀⠀⠀⠀⣷⢻⣟⢧⡀⠀⠀⠀⠀⠀⢀⣌⣼⣿⣿⢛⣽⠶⡖⢚⣋⡵⠞⠁⠙⠻⣿⣻⠒⠒⣿⣽⡻⣿⣿⣞⣆⠀⠀⠀⠀⠀⠀⢠⢏⣿⢳⡇
⠀⠀⠀⠀⠀⠸⣷⡻⣷⣝⡶⠤⢤⠤⢖⣫⣾⣿⣿⢣⣿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢿⣷⢻⣿⣿⣮⣗⡦⠤⠤⠴⣞⣵⡿⣣⡟
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣽⣟⣿⣿⣿⣛⣿⣛⡿⣿⣇⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⣾⡿⣟⣻⣟⣻⣿⣿⣿⣿⣽⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠾⢿⣿⣿⠿⣿⠿⣿⡎⣿⣷⣝⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⣡⣿⡟⣼⡿⠿⡿⢿⣿⣿⡿⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣩⣍⣋⣴⣿⣿⣿⣷⣬⣙⡲⠦⠤⠤⠤⠤⠶⢚⣩⣴⣿⣿⣿⣷⣌⣛⣭⢙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣮⣝⡻⢿⣿⣿⣿⣿⣿⠟⣠⣶⠟⠀⣠⣾⣿⣿⣿⣿⣿⣿⠿⣟⣭⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣟⡚⢯⠽⢏⣅⣘⣛⣁⣀⣾⣛⣛⣛⣛⣯⣭⣵⣒⣩⠼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠤⠤⢬⣭⣭⣭⣽⡿⠿⠿⠟⠛⠋⠉






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠷⠷⠄⡀⠀⠀⡀⠴⠷⢇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⠤⠠⠀⠠⢀⣄⠲⠆⣬⠁⣩⡄⠲⢂⣄⠡⠀⠀⠠⢴⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠌⡡⠀⠜⠳⢆⠟⠀⠀⠀⠈⡏⡏⠀⠀⠀⠘⣧⠶⠛⠄⠠⡉⠄
⠀⠀⠀⠀⠀⠀⠀⢰⠘⣿⠀⠀⠀⠀⢗⣄⡀⠀⢀⣿⣇⠀⠀⣀⣄⠇⠀⠀⠀⢸⡗⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠄⣀⣀⢄⣾⡻⠋⠛⠏⠁⠉⠟⠋⠻⣻⣆⢄⣀⡀⢜⣁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠟⠫⢭⡻⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣫⠭⠛⠿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣽⣿⣦⣄⣀⣀⣀⣠⣴⣿⣿⣅⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠉⠉⠛⣻⣷⣿⡛⠋⠉⠉⠙⠛⠉

⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⡄⠀⠀⠀⠀⠠⠀⠀⠙⠋⠀⠐⡄⠀⠀⡈⠀⠀⠀⠀⠀⣠⠊⠉⣝⠻⠶⡟⠢⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠠⠀⠀⠈⠉⠀⠠⠄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠃⢀⢠⣿⣟⡔⡾⠘⠉⠳⣄⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⡀⠀⠀⠀⠀⣛⠉⡛⡟⠽⡻⠢⡄⠀⠀⠘⣷⣤⡄⠀⠀⠁
⠀⠀⠿⣦⣤⣤⣴⣾⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⢱⡀⠀⠀⠛⠈⠓⠴⠀⠐⠳⠤⠉⠀⠀⠀⠘⢿⠕
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠒⠂⠁
⠀⠀⠀⣀⡀⠀⢀⡴⠀⠀⢀⡄⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠨⠀⠀⠀⠰⠀⠀⠀⠀⠂⠈⠀⠀⡠⠴⠲⡆
⠀⠀⠀⢹⡯⢽⡿⠀⠀⠀⠘⠛⠙⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⡲⢉⣀⡤⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠁⡜⠀⠀⠀⠀⡤⠒⠀⢀
⠀⠀⠀⡀⠀⠀⢀⡂⠀⠀⠀⢀⠀⡆⢀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⢈⠇
⠀⠀⠀⠉⠙⠋⠉⠁⠀⠀⠀⠘⠒⠐⠊⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠙⠒⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠠⣤⣤⣀⣀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡆
⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠈⢠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⠋⢉⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣬⣿⢩⣬⡇⣬⣽⢪⣤⣍⣍⣡⣤⣤⣴⣦⣴⣶⣶⣶⣶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡤⠠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠸⡿⠛⢿⠟⠹⣿⠛⠙⠇⠉⠉⠉⠉⠉⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⡶⠿⠖⠛⠒⢲⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢳⣶⠖⣶⡖⢂⡖⠒⠀⠐⠒⠒⠒⠒⠤⡀⠀⠀⠀⠀⠀⠈⠙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠱⣿⠉⢺⡏⡁⠀⠀⠀⠀⠀⣠⣤⠈⣇⠀⠀⠀⠀⠀⠀⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⣴⠩⠶⠥⣤⡤⢤⡔⣠⣬⣥⡤⣬⣤⠬⣤⡬⢤⣤⣬⠭⡭⣽⠦⣥⣿⠹⠶⣶⡶⠦⡀
⠀⠀⠀⠀⣠⠖⠂⠐⠢⡀⠀⠈⠳⣄⣀⣀⣘⣶⣶⠶⠶⠶⣿⠰⠶⣾⠃⠐⣏⡈⠲⡄⠘⠛⠻⠟⠛⠛⢛⡛⢿⡿⠘⠛⠛⠛⠋⠁
⠀⠀⠀⠀⣛⡄⠀⠂⣰⡇⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⢸⡀⣀⣿⠀⠀⡇⠈⣷⣛⡛⣻⡟⠛⠛⠛⠛⠛⢛⡅
⠀⠀⠀⠀⣿⠆⠀⡷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠥⠤⠤⠤⠤⠤⠤⠿⠥⠼⠦⠤⠶⠖⠚⠉
⠀⠀⠀⠀⡿⢶⡤⠟⣿⣗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠲⡀
⠀⠀⠀⠀⠇⠈⠁⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣆⣆⢀
⠀⠀⠀⠀⠈⠀⠈⣠⣿⡀⢢⡀⢀⣀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠉⠁⠉⠭⠟⠙⡟⠈⠁⠛⢏⠉⠉⠛⠛⠛⠒⠶⣤⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠁⠈⠇⠀⢏⢀⣇⠀⢀⡀⣀⣀⣀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠃⠇⡀⠐⠃⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⢻⠀⢿⡀⠛⠉⠉⠉⠙⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠗⠋⠀⠁⠀⣈⠠⠀⠀⠸⠀⢸⠀⠸⠄⠄⠀⠀⠀⠀⠀⢀⡠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠰⢲⠒⣼⠂⣸⣀⣴⠀⣀⠀⢆⠀⠀⢰⠁⠀⠀⠀⢹⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⣰⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠆⠀⢸⠀⢿⠀⢹⣿⢸⠀⡇⢩⣾⡇⠀⢸⡀⠀⠀⠀⡠⠈⠳⣦⡄⠀⣀⡤⣄⣀⣀⣀⣀⣀⣐⣗⣀⣀⣉⣠⣼
⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠰⠀⢸⠀⠀⣿⣼⠀⣇⢎⡏⡇⠀⠀⠈⠐⠐⠊⠀⠀⠚⠁⠀⣼⠫⠊⢙⣽⣿⣿⣛⣛⣙⣛⠛⠛⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠈⣎⠆⠈⠲⣄⣀⢸⡀⠀⣿⠀⢀⡡⢊⢨⠃⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⡅⢐⠛⠀⢠⣾⣿⣦⠀⠈⡆⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢯⡢⡀⠀⠀⢹⡃⠁⠿⠉⠈⢁⡼⠃⠀⠀⠀⠈⠉⠉⠀⠀⠛⠀⠄⠀⠘⢿⣥⣼⣿⣿⣶⣾⣿⣟⣉⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠇⢀⣰⡇⢐⣣⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⡀⠀⢀⣀⠀⣠⣤⣤⡤⠖⠚⠉⠀⣿
⠀⠀⠀⠀⣼⠋⢹⡏⠉⣿⠉⠉⠉⠉⠉⠉⠉⢹⡿⣿⠿⢿⡿⠿⢿⡿⠿⠿⠿⠿⠿⢿⣟⣿⣿⢤⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⢿⡀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢸⠃⠀⢸⠃⠀⠀⠀⠀⠀⠀⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠠⠤⠀⠄⠀⢠⠠⠠⠀⠀⠠⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠆⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠈⠀⠀⣀⣤⠄⢀⠀⠀⠀⣶⠚⠒⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢠⣿⣇⣴⡏⠀⠀⠀⠨⠀⠀⣼⣿⡷⢤⡀⠀⠀⠀⠀⠀⠀⠈⠚⢤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣧⢘⣿⣿⣿⡇⠀⢠⠀⠈⠀⢀⣿⠏⠁⠀⠑⣄⠀⠀⠑⢦⡀⠀⠀⡈⢀⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢭⠿⠿⠖⠀⠉⠻⣿⠃⠀⠀⠀⠀⡠⠋⠀⠀⢀⣤⣾⣿⣧⠀⠀⠀⠈⢶⡀⢛⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠛⣄⠀⠙⣧⢂⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠢⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣦⣤⣬⡳⡀⠘⠧⢠⠀⣠⣴⣿⣿⣿⠛⠋⠙⢻⣿⠇⠀⠀⠀⢀⠀⠰⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠃⠤⠀⠀⠀⠀⠀⠃⠀⠤⣅⠀⣀⣼⣿⡿⠟⣉⢔⣲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡌⠀⠄⢠⣿⣷⢆⣸⣾⡀⠀⠀⠀⣠⣶⠟⢷⣮⡻⣿⡀⠻⢛⣭⣿⣿⣿⠻⠿⠀⠄⠀⠀⠀⠀⠀⠀⠃⢁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠺⠇⠀⠙⢷⣄⣴⠀⣟⠁⣠⣾⡿⣳⢌⣵⠞⠛⣿⡉⠉⠙⠷⠀⠀⡀⠀⠀⡀⢀⠀⠀⠈⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⣀⠹⣿⡿⢿⡙⣏⠸⣏⡳⠀⠀⢾⡠⣀⠈⠀⡼⠃⠀⠀⠀⠀⠱⢠⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠑⠀⠀⠀⠀⢀⣠⠞⠋⢀⣴⡿⢟⣦⠹⣟⠈⣷⣴⡷⡝⠿⠌⢆⠈⢷⡷⡶⠋⠀⠀⠀⠀⠀⠀⣀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠷⡄⠀⠀⢀⡔⠛⠁⣠⣶⢟⣩⡴⠛⢟⠷⡙⠈⡿⢮⢿⠊⢄⡲⡼⣅⠀⠻⣦⠀⠀⠀⠀⠀⠁⠘⠡⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣴⡿⢉⣴⠟⠁⠀⠀⠋⠙⢷⣤⣄⣴⡱⣾⣦⠳⢶⡊⣦⠀⠹⣧⢸⡄⣆⢶⠀⠔⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⣿⢠⣿⠁⠀⣀⠀⣶⠀⠻⣀⣈⣉⡑⢶⠋⢅⠀⠀⠀⠘⣧⡠⡘⢿⣹⣿⡻⣓⡶⠲⠦⢤⣤⣌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠸⣿⠀⠿⠂⣂⣭⣴⣶⢾⠿⠙⠻⠟⠙⣺⣷⡈⠧⠀⣀⡴⢿⡝⡇⠈⣿⣧⣿⣉⣻⣛⡿⠂⠈⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢤⡆⠀⠀⠘⣁⣠⡴⢶⡾⠿⢛⣋⢈⡲⠠⣏⡖⢛⡴⠀⢈⣩⣴⡶⢏⠁⠀⠀⣻⢸⡆⢸⣟⠿⣿⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣶⡾⠛⠉⠈⡃⢒⣶⢭⣵⠤⠃⠭⠶⠚⢉⣩⠴⠚⣉⡤⠓⣿⡇⣗⣤⣞⠥⠚⢀⣼⠋⣾⢎⡓⢦⣀⠀⠀⢂⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠐⣿⠙⠀⠀⠀⣖⣈⡡⠴⠾⣿⣦⢀⣤⡶⣟⢉⣤⠔⠋⠁⣀⡠⠖⠚⠿⠀⠤⠤⠖⢿⠻⠛⠾⠟⢿⡤⠙⢿⣶⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣟⣿⠁⠘⠾⣧⡤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡄⣄⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣴⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠛⣿⢻⡟⣿⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⠛⠉⠛⣿⠛⠛⠛⠛⣿⢻⡟⣿⠛⠛⠛⠛⠛⠳⣆⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣴⣶⣶⣿⣼⣧⣿⣤⣥⣥⣴⣧⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠘⠃⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆
⠀⠀⠀⠀⠀⠀⣠⣤⡤⢤⠤⠤⠤⠤⣤⠤⠤⢴⣶⣶⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠰⡏⢸⠇⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠙⠻⡇
⠀⠀⠀⠀⠀⠀⠙⠛⠓⠚⠒⠒⠒⠒⠓⠲⠖⠲⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⢀⣀⣤⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡿⢡⡾⠛⠉⠉⠉⠙⠿⣭⠭⠽⠯⠭⠭⢭⡙⡉⠙⠻⣿⣿⡛⢿⡿
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣸⡇⠀⠀⠀⠣⠤⠧⠤⡬⠤⢬⣿⡯⣿⣯⠅⠀⠀⣿⠘⣧⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣶⣤⣤⣴⣶⣶⣶⣷⣶⣾⣿⣿⣿⣿⣥⣤⡾⠟⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⢀⡀
⠀⠀⠻⣍⢃
⠀⠀⠀⢹⣎⠄⠀⠀⠀⣠⠴⣒⡫⠍⠉⠉⠉⠛⠒⠦⣄⡀
⠀⠀⠀⠀⢻⡖⠀⠠⢊⠕⠋⠀⣀⣀⠀⠀⠀⠀⠀⠉⠒⣍⡲⣄
⠀⠀⠀⠀⠈⢿⡁⢰⠛⢴⣤⡾⢧⣉⣷⣤⡀⠀⠀⣰⠛⠉⢻⣮⡳⡄⠀⠀⠀⢠⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠘⠁⣏⠀⢠⡿⣡⢀⣽⢋⡿⠃⠀⢀⡿⢀⣠⡼⠃⠱⡹⡄⠀⠀⠀⣿⡟⠛⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣦⠹⠁⢀⡿⣡⣾⣥⡄⢠⡾⣡⡟⠉⠀⠀⠀⢷⢳⠀⠀⠀⣜⠀⡴⢷⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠰⡘⣿⡆⠀⠘⡤⢴⡫⠹⠿⠟⠀⣘⣳⣤⣀⠀⠀⣼⣾⠀⢀⣜⣛⢆⠀⠀⠹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠳⡙⣿⣤⡟⢡⡼⠛⣳⣞⣡⡬⠶⢮⣇⣯⢑⣶⠣⢃⣴⡿⢟⡿⢳⡄⠀⠀⣸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡻⣷⣿⣠⣜⣏⠉⠁⠀⠀⣀⣿⡽⢟⣡⡴⠟⢋⣴⣋⣤⣾⠷⠿⠟⢟⠿⠟⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣭⣛⠁⠠⣭⣭⣭⣭⡽⠶⠞⠛⠉⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠙⠒⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⠶⠶⠶⠴⠶⠶⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⣀⣴⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⣟⣭⠿⠿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣟⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⡿⣻⡗⠉⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⠀⠀⠈⠙⢿⣿⣿⣶⣶⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢸⣿⣿⣿⠟⠁⠀⠀⠀⠈⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠙⢾⣿⣿⡆
⠀⠀⠀⠀⢾⣿⣛⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⣀⠀⠀⢀⣠⢾⣽⣿⣿⣧⣀⠀⠀⠀⢀⣤⢿⣿⡏⠀⠀⠀⠀⠀⠀⠈⣿⡿⣷
⠀⠀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣠⣿⢷⡇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣶⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⡏⠛⡏⣷⣺⣶⣖⣿⢹⡛⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣾⣿⣿⡞
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠙⠋⠉⠀⠈⠉⠙⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣼⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠿⠿⠟⠛⠉⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⠶⠶⠶⠶⣶⠶⠶⠶⢶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣿⣿⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣄
⢀⠤⠤⠤⠶⡤⡴⠶⠦⠤⡤⠤⠤⠤⠤⠤⠤⠤⣤⠤⠴⠶⠶⣿⠶⠶⢶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢿⣄⣀⣀⣀⣇⣇⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣼⣠⣄⣀⣀⣿⣀⣀⣀⣸⣀⣀⣀⣈⣉⣉⣛⣻⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⡟⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⢀⣁⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⣾⣿⣿⣷
⢰⣶⣦⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣾⣿⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢸⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡏⠙⠛⠛⠿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣸⣿⢺⣿⢺⣿⣇⣀⣠⣤⣤⣤⣤⣦⣄⣀⣀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠉⠻⡿
⠀⠀⠀⠀⠀⠈⠿⣦⣄⣀⣀⣰⣟⣛⣛⣛⣛⣛⣻⣿⣾⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⣸⣿⣻⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠀⠈⢁⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠸⠿⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠶⠶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⣀⣠⠤⠤⠴⠒⠒⢋⡿⠛⠉⠀⢀⣰⣆⣶⣰⣎⣻⡙⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠛⠛⠛⠻⣷⣆⢻⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠁⠀⠀⠀⠀⠀⣸⢿⡶⠾⢿⣷⣋⣉⣉⣉⣙⣉⠉⢹⡝⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢰⣿⡞⢡⣴⡞⢿⢿⣿⠻⣿⠟⣿⡗⢺⡗⠲⣾⣿⣷⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⡄⠀⡄⠀⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣾⣹⢻⡟⢻⡗⢾⣿⣼⣾⣾⣿⡷⣷⢾⣤⠶⠿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⡇⢰⣶⣰⣷⣰⣶⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣶⡆
⠀⠀⠀⠀⠀⠀⢹⣿⡞⣇⠘⠷⠟⣿⢼⢼⣿⣿⡷⡏⢸⡏⣇⢀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣷⢿⣿⢹⣿⣽⣿⣷⣼⡿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⣿⣷⡈⠓⠶⠦⢿⢾⢾⣾⣿⣷⡇⢈⣷⣇⣼⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⡗⣾⣿⢺⣿⢻⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣷⣄⣤⡴⣿⢸⠈⠉⠸⡿⣧⣼⢻⡿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⠟⠘⠛⠈⡟⣿⣿⡇⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣝⡓⢿⣾⠓⠒⠚⢿⣿⡶⠋⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣟⢻⠋⠉⠉⢹⡏⣿⣿⣷⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠿⠟⠻⠶⠶⠛⠛⠉⢉⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⡄⠀⠀⠘⣧⣿⣿⡏⢸⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠛⠛⠛⣩⡟⢸⡇⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⣟⡛⠛⢛⣉⣴⠟⠁⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⡏⠉⠛⠋⠉⠁⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡼⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣄⡀⠀⠀⠀⣀⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣻⣿⣿⣿⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⢻⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣷⣦⣽⣿⣿⣧⠘⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢏⣽⠞⠛⠻⢿⣿⡽⣿⣿⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⠁⠀⠀⠀⠈⣿⡷⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⠀⠀⠀⠀⠀⣻⣧⣿⣿⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣿⡿⠀⠶⠴⢦⢆⣼⣿⢹⣿⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⠛⠃⠗⣸⢨⣿⣿⣿⣿⠀⢸⣿⣷⠤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⠀⣀⢇⡾⡀⣺⠀⣿⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣏⣰⣿⣈⡴⢧⢸⠀⢻⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⠸⣿⡇⢸⣾⠀⢸⣿⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⡿⣟⣿⢸⣿⡷⢾⣿⠀⢸⣿⡄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⡿⡿⢿⠸⣿⡇⢸⣿⡍⢹⣿⡅⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⡇⡿⣿⠺⡿⣇⣼⣿⡄⣸⣿⠃⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣧⣗⣽⠀⡇⠈⠁⣾⠃⢹⣿⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⢻⡜⠿⠃⠀⢀⡿⠀⢸⡿⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⡙⠶⠶⠶⠟⠁⣠⣿⠃⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣾⣿⣿⣯⣵⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠞⣿⡟⠉⠉⠉⠉⠁⠹⣿⣿⠿⠛⠿⢛⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃⠀⡉⣃⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⣈⢛⣯⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠜⣭⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠛⣿⣿⣿⠏⢀⡠⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣰⣿⣿⣯⡔⠋⠀⠠⠐⠲⠦⣤⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠟⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣈⢻⡶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⣿⣻⠇⠀⠀⠀⠀⠀⠀⠸⣠⢉⡇⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣭⠤⣽⣿⣿⢠⠂⠀⠀⠀⠐⢻⠐⡏⠸⡇⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⢸⡏⡿⠉⠀⠀⠀⠀⠀⣸⠀⡇⠘⠃⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⣜⠁⣧⠘⠀⠀⠀⢰⡄⣹⣄⣧⣀⡄⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⣿⢸⠻⣄⡄⠌⠀⣤⠀⣼⡏⡀⠈⡀⠉⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⡏⡿⢀⠙⡿⠉⡏⣏⡴⣹⠄⢳⢼⠇⢴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣛⡹⠿⣷⡖⡗⣿⣠⢻⠃⢰⣦⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃⠍⢷⣤⣤⣥⣥⣽⠹⢸⡏⢸⣿⡆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⠉⠏⢿⣀⣎⣃⣁⣳⠮⢸⡛⠛⣇⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠀⠃⠂⢹⡏⠉⠉⣯⡀⢸⡥⣤⠼⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢻⡇⠠⠸⣸⡇⠀⠀⠘⠻⣿⠁⡇⠀⡇⢤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⣿⡀⢂⠹⡆⠀⢂⣀⠀⠹⡦⣹⢣⢤⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣷⡄⠳⣼⣦⣌⣛⣒⣊⡔⠑⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢿⣦⣄⣉⠍⣫⣍⣩⣥⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣀⣀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣉⣈⣁⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣷⣶⣶⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⢻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⢹⣿⡀⠹⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⣀⠀⠉⠻⢶⣤⡀⠀⠀⢻⡇⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣦⡄⠀⠙⢿⣦⠀⠀⣿⠀⠀⠀⠀⣛⣿⣿⣿⣿⣿⣿⢰⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆⠀⠀⢻⣷⡀⢸⡄⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣾⣿⡏
⠀⠀⠀⠀⠀⢠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣿⣷⠘⠇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠐⠀⠀⠀⠀⢈⣿⣿⢻⣿⡿⣿⣿⠁
⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢰⠀⠀⠀⠀⠸⣿⣿⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠲⠀⠀⠰⠆⠀⠀⠖⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣀⣀⡄⠀⢀⣤⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⣀⣀⣀⣉⡉⠘⠛⠿⠿⠗
⠀⠀⠀⠀⠀⣿⣿⣤⡆⠀⠀⠀⠘⣧⠀⠀⣿⢀⠀⢹⡇⠐⠉⠀⢀⠀⠀⣿⢃⡠⠚⢁⣠⣾⣿⣿⣿⣷⣶⣶⣶⣄⠤⠴⣤⣀⣀⣤⠠⠄⠐⠒⠁
⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠃⠀⣿⠆⠀⣹⣿⠀⠘⠿⠗⠀⠀⢈⡇⠈⠁⣬⠁⣴⡿⠋⠉⠈⣿⣿⢸⣿⣿⣿⠟⠀⠀⠀⠈⠉⠉⠙⢳⣶⣦⣼
⠀⠀⠀⠀⠀⣿⣿⡆⢀⣤⠞⢻⣾⡇⠀⠀⠀⢷⠀⢘⡿⠓⢄⠀⢾⣁⠀⠀⣾⡘⠛⠀⠀⠀⠀⢹⣿⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⣿⡟⠀⢻⣴⣶⡎⢹⣷⡄⢿⣧⠈⣇⢘⡟⠶⢠⣇⠈⢿⣆⢈⣿⢷⣦⡀⠐⣤⠀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡿⠀⢸⣼⡿⢹⡗⢨⡟⠀⢸⣿⠀⡟⢸⡧⠀⠘⠋⠀⢾⡏⢸⣿⠈⣿⠁⠀⣿⣧⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⢀⡇⠀⠘⢻⡇⢸⡇⠈⣿⠀⢸⣿⠀⣷⠀⣷⠀⠀⠀⢠⢼⣿⢰⣿⠀⣿⠀⠀⣿⣿⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⡇⠀⠈⢘⡇⢸⣇⠘⠋⠀⠊⠛⠀⠃⠐⠋⠀⠀⢻⠀⢸⡇⢸⣿⡀⢿⠀⠀⣿⣿⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⡇⠀⢀⢘⡇⢸⣿⠀⠀⠀⠃⠀⢀⠃⢠⠀⠀⢀⡴⠀⢹⡇⢸⣿⠀⢸⠀⠀⣿⣿⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⡇⠀⠐⢸⡇⢸⣿⠀⠀⠀⠀⠒⠀⠀⢰⡆⠀⠀⠀⠀⢸⣟⢸⣿⠀⢸⠀⠀⣿⣿⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⡇⠀⠀⣠⡇⢸⣯⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁⠈⠀⠀⢸⣿⢸⣿⠀⢸⡄⠀⣿⣿⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⡇⠀⢸⡟⡇⢘⣿⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠸⣿⠀⢸⡇⠀⣿⣿⢼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⠀⢸⠺⡟⢹⣿⢰⣆⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸⡇⠘⣿⠀⢸⡇⠀⣿⣿⢘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣷⡆⢸⠀⡇⢸⣿⢈⡙⠓⠆⠐⠒⠐⠲⠀⠀⠀⣠⠁⢰⣿⣆⠈⠀⠀⣁⢴⣿⡿⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⡏⠸⠀⡇⢸⣿⠀⠃⠀⠀⠀⠀⠀⢠⡆⠀⢀⣿⢀⣸⣿⣿⣿⠀⠀⣤⣾⠟⠁⢸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣹⣿⢀⣶⣷⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠓⠻⠿⠃⡸⣿⡟⢻⣿⠃⠈⣿⠁⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⣿⡛⠂⠀⡀⢰⣦⣀⣀⣀⣤⡴⠖⠀⠈⠉⠀⢹⠁⢸⣿⠀⠀⢸⠀⠀⠀⢻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⣿⣿⠀⢹⣿⣶⣿⠁⠘⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⢸⠀⠀⠀⢸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢿⣿⠀⡸⣿⡌⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⣀⠀⠀⠀⠸⣿⢿⣿⠁
⠀⠀⠀⠀⠀⣄⡁⠀⡇⠈⢻⣦⠀⢠⣶⣤⠀⠀⠀⠀⠀⠀⠤⠈⠀⣴⡿⠃⠀⠀⠀⣹⡃⠀⠀⢰⣿⣿⣿⡄
⠀⠀⠀⠂⠐⢿⣧⠀⣃⠀⠀⠁⠀⢸⣿⣄⣀⠀⠁⢀⣀⣀⣤⣾⡿⠋⠀⠀⠀⠀⠀⠙⠁⠈⠛⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣿⠀⢹⡇⠀⠀⠀⡘⠛⠛⠛⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠃⠀⢸⣿⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⣈⢻⣷⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣦⠐⢻⣿⡿⠿⠐⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠹⣧⣄⣀⣀⣀⣮⣼⡿⠿⠿⠶⠶⠦⠤⠖⠐⠒⠊⠉⠀⠀⠀⢠⣴⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣧⣄⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣶⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⠿⠿⡿⠿⠟⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣰⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⡴⢫⠕⣲⣒⣒⣒⣲⣶⡶⡶⣶⣒⣟⠛⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠈⠙⠷⣦⣄⡀
⠀⠀⢸⠀⡇⢸⠔⠒⠒⠚⢃⣀⣿⣷⢿⣿⣷⡂⠀⢨⠀⡰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠩⢗⡭⡻⢶⣄
⠀⠀⠸⡄⢧⣹⡓⠒⠒⣒⣳⣶⣦⣼⢿⣻⠷⠶⠶⠗⠊⣠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣉⠤⠼⠀⠙⢷⠄
⠀⠀⠀⠘⠢⠤⢌⣉⣀⣀⣀⣀⣀⣀⣀⣙⣄⡀⠀⢴⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣠⢞⠕⠊⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠙⠢⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡰⣵⡧⣠⠤⢤⣖⡉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠧⠀⠀⠀⠀⠀⠃⠀⠀⢀⢦⠀⠀⠀⠀⣜⡜⣸⡳⢿⢸⢠⢸⢦⡿⢟⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⣀⣀⡠⠴⠋⢺⡆⠀⠀⢠⢿⢰⠁⢱⣸⢸⡇⣿⢸⠤⣄⠑⡜⡄
⠀⠀⠀⠀⠀⡠⠴⠒⣒⣒⣒⣂⣉⣉⠉⠩⢽⠩⠭⠭⠭⠤⠤⠤⡴⣚⣿⡇⠀⠀⠸⣼⠣⠭⣟⢸⣸⣇⡿⣸⣏⣁⣃⣱⣧
⠀⠀⠀⢀⢎⡔⢋⡡⢤⣤⣤⣤⣤⣤⣤⡤⠼⣦⠤⢤⡀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⢯⢿⣸⣝⡸⣻⣞⣷⣛⣷⡔⢣⢿⡇
⠀⠀⠀⢸⡜⢰⢻⣶⠾⢿⣋⡇⣖⣿⠿⣿⣿⣛⣻⡟⡍⠉⠉⠉⠒⢌⣿⡇⠀⠀⠀⠈⠫⡻⣻⡶⠺⠰⠸⠒⠛⢻⢟⠟⠀⣀⣀⡠⡄
⠀⠀⠀⠸⣧⠸⣟⣿⣀⣞⣿⣿⢻⣿⣎⣀⣀⠇⠀⡸⡇⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠈⠛⠿⢾⣮⣼⡶⠾⠓⠉⠉⠉
⠀⠀⠀⠀⠹⢷⣌⡺⠷⠶⠶⠶⠶⠶⠶⠶⠯⢽⣋⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡂⣂⣠⣤⣤⣤⣤⣤⠤⡒⠒⢯⣾⡇
⠀⠀⠀⢀⣀⣀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⠤⠤⠒⠒⣵⣿⠀⠀⠀⠉⠁⢹⠉⢉⣉⣉⢋⡏⢇⣀⣀⣀⣀⠀⠀⣹⠀⠉⠢⣽⠁
⠀⠀⠠⡋⠀⢸⠁⡇⠀⡆⠀⠀⢸⢸⠀⠀⠉⠉⠉⠉⠉⠻⡟⠀⠀⠀⠀⠀⠈⠉⠈⠒⠂⠙⠂⠐⠒⠒⠒⠚⠉⠉⠁
⠀⠀⠀⠑⠒⠚⠒⠓⠒⠓⠚⠛⠛⠿⠶⡤⠤⡤⠤⠤⠤⢤⣁⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠛⠒⠛⠒⠒⠒⠒⠦⠤⠤⠤⠤⠬⠉⣉⣉⣉⣉⣉⣑⣦
⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣼⣷⣭⣿⣥⣵⣯⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⠈⠟⠁⢹⠋⠈⠿⠀⠀⡴⠶⠄
⣿⣶⡶⠶⠾⠿⠛⠻⠿⢿⣟⠛⠛⠀⢐⣠⣤⣶⠾⠞⣛⣿⢛⣷⠟⢷⡾⢻⣄⡀⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⢀⣴⠟⠉⢀⣠⠴⠛⠉⠑⠚⠛⠖⣾⡶⠚⠉⠛⠷⢦⣄⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⣿⠃⡀⠔⠉⠀⠀⠀⠀⣴⣤⢠⣆⡿⣧⣤⡀⠀⠀⠀⢹⡷⣦⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢣⡿⢁⠈⠀⠀⠀⠀⠀⠀⠀⡟⠀⣼⠏⢡⡿⠈⣇⠀⠀⠀⠈⡷⠈⢿⣧⡈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⡀⠁⠀⠀⠀⠀⠀⠀⢀⠠⠀⣀⢠⣅⠄⣀⡸⠿⠀⠀⠀⢀⠃⠀⠈⢿⣷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡖⣀⣤⣦⠤⣴⠤⢤⠀⣤⣶⣿⢴⣾⢍⡦⡿⢹⡾⣶⠐⣦⣤⣰⣦⣀⠈⣿⣷⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣰⣏⠀⠈⢳⡀⠀⢸⠶⠀⠀⡿⢲⡗⢨⠃⡇⠜⠁⠀⣤⠄⠀⠀⠀⠉⠹⣌⢯⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠻⣿⢧⡀⠸⡇⠀⢸⠀⠀⠀⣿⢰⠁⣘⢘⡧⠀⠀⠀⠆⡏⣦⡄⠀⠀⠀⢸⡎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠳⣝⣲⣧⣀⡈⢀⠀⣀⡧⢸⣸⢯⣀⠁⠀⠀⠀⠆⡃⠁⠀⠀⠀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠄⠀⠀⠈⣹⠛⠿⣇⠸⠿⠿⡇⠘⣥⣌⠀⠀⠀⠀⢀⠀⡅⠀⠀⠀⠀⠀⣿⢱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣌⡀⢠⡴⠋⣀⠀⣧⢀⠀⢀⡇⢠⠀⣀⢀⠀⠀⠀⢸⠂⠀⠀⠀⠀⣀⣼⡿⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠙⠚⠓⠒⠛⠒⡧⠘⠛⠚⡇⣿⠙⢻⢹⠁⠿⠟⢿⠀⢷⡶⠿⠤⠍⠘⢁⠇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⡆⠀⠀⠀⠀⣿⡆⠀⠀⡗⣿⠘⠋⢸⣤⠀⠀⢸⣤⠀⣷⠀⠀⠴⢁⠎⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠹⣄⠂⢊⠀⠛⠂⢰⡚⠃⠀⠀⣸⠓⠀⡟⠀⢊⡴⠋⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠈⠀⠀⠘⢦⡀⠉⠁⠀⢀⣡⠠⠞⣡⠔⠋⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⡀⠀⠀⠀⠉⠐⠚⢛⣉⣴⠶⠋⠁⠀⠀⠀⠜⠁
⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠉⠉⠉⢉⡉⠥⠞⠉⠀⠀⠀⠀⡀⠄
⠀⠀⠀⣻⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢏⣠⠔⠚⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢘⣯⣻⢍⡙⠛⠻⠶⠶⠦⠦⠶⠤⠖⠲⠚⠐⠊⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠘⣷⡌⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠈⡹⣿⡿⠿⠿⠟⠳⠒⠒⠘
⠀⠀⠀⠀⠀⠘⣩⠁⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠑⡆⣀⡀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄⡤⠄⠙⠄⠀⡀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣀⠀⠈⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⣴⡏⠠⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⠅⡀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠇
⣶⣶⣶⠶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡾⠛⠀⠀⠀⠀⡜⡔⠙⡄⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠿⠋⢀⠃⠀⠀⠀⠀⡇⡇⢀⡿⣾⡀⠀⠀⠀⠀⠀⠀⣴⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⣴⡇⣼⠀⠀⠀⠀⠀⣿⣫⠜⣿⠉⡇⠀⠀⠀⠀⠀⣴⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣤⢹⣿⡇⣿⠀⠀⠀⠀⠀⢹⣇⠀⣰⠒⣇⠀⠀⠀⠀⣼⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⡲⠈⢧⢻⣧⠹⡄⠀⢀⠀⢄⢸⣋⡥⢻⣾⢹⠀⠀⢀⡾⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠁⠙⢷⣜⢦⡈⣧⢟⠘⣇⣀⠸⢻⡸⡆⢀⡞⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⣻⠏⡘⣇⡴⠚⣿⡇⣧⠊⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⣶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣿⡻⣼⠀⢻⣷⠛⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⣴⣶⠿⠛⢉⣉⣀⣈⠒⠦⣄⡀⠀⠀⠀⢉⠙⠲⣅⡺⢷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠠⠟⣩⠴⠒⠉⠁⠀⠀⠈⠉⠒⠦⣙⠲⢤⡄⢸⠀⠀⠀⠙⠲⣝⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢁⡴⠋⠁⠀⠀⢀⠄⠂⢉⣀⠀⠉⠒⠤⣍⡒⠆⢸⣦⣄⡀⠀⠀⠀⠙⠪⣑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⢠⠁⣠⠊⠁⠀⠀⠈⠐⠠⢄⣉⠃⣬⢿⣷⣯⣗⣤⣀⠀⠀⠀⠁⠈⡳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⠀⠀⢀⡛⣏⡛⢤⡠⢉⠒⠌⡙⠀⠽⣿⣿⣦⢄⠀⠀⠀⠀⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠱⣄⠀⠀⠠⡬⠁⣤⣛⡌⠃⢄⡈⠐⢢⣑⢤⣈⠈⠋⢝⠿⣶⡀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣈⠹⣲⠤⣀⠀⠠⡶⢅⡀⠀⠨⠕⡢⢁⡀⣿⡟⣶⠤⡈⠢⡙⢦⡀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢍⡓⠵⣖⡿⣶⠬⣑⡢⠀⠀⣹⠀⡿⣧⠸⡆⠈⢢⠈⡆⠹⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣟⣦⣭⣓⠺⢾⡿⢗⣦⣍⣂⠿⢿⣀⣇⠀⣸⠃⡇⢀⠇⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡾⣿⠃⠈⠉⠒⣤⣄⡉⠉⠂⠿⣶⡤⠭⡍⠥⠊⣠⠎⠀⠀⢘⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣻⣿⣷⡆⠀⠀⠀⠀⡍⠃⢹⠷⣦⣤⣀⠈⠉⠛⠛⠋⠁⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡾⢋⣴⣿⣿⣹⠃⠀⠀⠀⠀⠁⢸⠘⢃⡟⣴⠌⠛⠓⠶⠶⣶⣞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠿⣿⣿⡏⣿⠀⠀⠀⠀⠀⢸⠸⡠⣟⣀⠥⣤⡶⠶⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢿⡄⠀⠀⠀⠀⠈⡀⡇⢹⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣇⢦⡘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡀⠀⢀⡤⠀⡀⠀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠠⢽⣂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣼⠋⣀⣘⣷⢾⣃⡀⢣⣬⠟⣀⣀⣀⣠⣤⡶⡊⠀⠼⠀⠀⢿⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⢚⡩⡵⣤⣀⣀⢽⢾⢄⣉⣭⡿⣍⣉⣉⡁⢀⣀⣀⣀⣠⠄⠀⢀⣾⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣏⣴⣞⣿⣛⣿⡗⢛⡟⠛⣿⡛⢻⣿⣾⡟⠋⣿⡿⠿⠿⠛⠿⠿⣟⣀⣤⣤⣼⣻⠄
⠀⠀⠀⢈⣄⣷⣠⡀⠀⠀⢀⣠⣾⡾⠿⡭⠿⠅⠀⠀⠿⠷⠾⠴⠠⠿⠷⠹⠤⠿⣧⣾⣯⣴⣖⡀⠠⢀⠀⠀⠩⢉⣛⣿⠹
⠀⠀⠀⠈⠙⣋⢙⡯⠉⠉⠉⣭⣭⣭⣭⣯⣭⣩⣭⣿⣿⡟⢻⣿⢿⡿⠿⣷⢖⡒⠚⠛⠳⠲⠟⢿⣳⣦⣄⡀⠀⠀⠉⠛
⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⡇⢸⣇⣇⡔⠉⢀⣀⠀⡼⠧⠾⠷⠸⠷⠶⠿⠸⠷⠼⢿⡗⠶⠦⣄⠈⠻⣧⠉⠳⣤⠲⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣿⡿⠊⠀⠉⣀⠀⣤⣾⣤⣟⣛⣂⣂⣒⣂⣀⣀⣀⠀⠐⠖⠿⢳⡀⢺⡆⠀⠘⡆⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⢿⠃⠀⣰⣧⣀⠀⠸⠿⠿⠥⠿⣾⣟⣸⡽⡏⠀⢹⠀⠱⠀⠰⣾⡇⠀⣇⠀⠀⢹⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠀⢀⡇⠉⠙⣦⠀⠉⠩⢁⠈⢉⣉⣉⡍⠊⠀⢸⠀⠀⢀⢠⢹⡇⠀⠉⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡜⡇⠁⠘⠀⠰⠨⠬⠤⠭⠬⠭⠤⢀⣠⠀⠙⣗⣚⣥⣫⡞⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣝⠦⢄⡀⠀⠲⣶⣶⣦⣿⣚⣛⣛⣛⣿⣃⣈⣭⠭⠁⢂⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠏⠙⠛⢛⣛⠉⣉⢉⣉⣩⣭⢡⣀⣀⡤⠀⠀⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠉⠉⠁⠀⠈⠁



⡖⠒⢲⠖⠶⠶⠶⠶⡖⠶⠶⠶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⡶⡶⢶⣶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠉⠙⠛⢉⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣾⣿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠛⠛⢉⣉⡉⠙⠛⠳⢦⣄⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⢀⣴⣶⣿⣿⣿⣿⣿⣿⣦⣀⠉⠳⣄⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⢀⣾⣿⡟⢀⣴⠟⠋⠉⠀⠀⠀⠀⠈⠉⠻⢿⣧⡀⠙⣆⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⣾⣿⡟⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠈⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⣹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⡇⠀⠀⠠⣶⠄⠰⣶⠄⢴⡦⠀⠀⠀⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⣿⣧⠀⡇⠀⠀⣤⣿⣤⣤⣷⣄⣴⣧⡄⠀⠀⣿⣿⠀⢸⣿⣿⠿⠿⠿⠿⠷⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⣿⣇⠀⡇⠀⠀⣿⡿⢰⣿⡇⣼⣿⡃⡇⠀⠀⣿⣿⠀⠜⢡⣴⣾⣿⣿⣿⡿⠷⢶⣶⣤⣴⣦⣤⣤⣄⣀⡤⢶⣦
⠀⠀⠀⠀⢀⣿⣿⣿⠀⣧⡤⢒⣛⣷⠸⣿⣇⠛⣿⣧⣙⣒⠀⣿⣿⡜⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⡟⠀⠀⠉⠉⠛⠻⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣧⣴⠏⣴⣿⣿⡏⣴⠏⣿⡆⣿⡏⣍⣿⣷⡌⣿⡇⢨⣭⣍⡙⢿⣿⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⣿⡏⢸⡇⣿⠚⣿⠓⣿⡇⡏⢹⣿⣷⢿⣿⢻⢞⣿⣿⡆⣿⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣿⡇⢸⡇⣿⠠⣿⡏⢹⡇⡇⢸⣿⠏⣿⣿⢼⢸⣿⣿⡇⣿⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣿⡇⢸⡇⣿⡆⢩⡇⢸⡇⠁⢸⣿⡷⢻⣿⢸⢸⣿⣿⣇⣿⣿⡃⠀⠀⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣿⡇⢸⡇⠘⢧⣮⠴⢸⡇⡀⢸⣿⣇⣼⣿⢸⠀⣿⣿⡇⣾⣿⡇⠀⢰⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣿⣷⢸⡇⠀⠀⠀⠀⢸⡧⠀⢸⣿⡗⣽⣿⢸⠀⣿⣿⣏⣿⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣿⣿⢸⡇⠀⠀⠀⠀⢸⡇⠀⠸⣿⣧⢹⣿⢸⠀⣿⣿⣿⣿⣿⡇⠀⢸⡿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣿⣿⢸⡇⠀⠀⠀⠀⢸⣷⠀⢰⣿⣿⢼⣿⡙⠀⣿⣿⠏⣿⣿⠃⠀⢸⡇
⠀⠀⠀⠀⠀⣿⣿⣿⢿⡇⣿⣏⢸⡇⠀⠀⠀⠀⢸⡿⠁⡼⣿⡿⢸⣿⢿⡶⣾⣶⣾⣿⣿⠀⠀⣼⡇
⠀⠀⠀⠀⠀⣽⣿⡇⢸⡇⣝⠿⣸⡇⠀⠀⠀⠀⠘⣷⡚⢤⡾⢏⣾⡇⠀⠆⢾⣿⣿⣿⡇⠀⠀⣿⠇
⠀⠀⠀⠀⠀⣿⣿⡧⢸⡇⣿⣷⣿⣧⣄⣀⣀⣠⣽⠿⠛⠳⠛⠉⣿⡇⢸⡆⢸⣿⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⣾⣿⣷⢺⡇⣿⣿⣿⣿⠌⠉⠉⠁⠀⠀⠀⠀⠀⢠⣿⡁⣸⠃⢸⣿⣿⣿⡇⠀⢠⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣼⡇⡆⢻⣿⣿⢤⣄⠀⠀⠀⠀⠀⣀⣴⠿⣽⣷⠃⠀⢸⣿⣿⣿⣇⠀⣸⡯
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⡇⠀⢹⡿⣴⣍⣛⣻⣚⣻⣿⣉⣿⣿⠟⠁⠀⠀⢸⣿⣿⡟⠛⠀⣾⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢷⠀⢸⣿⠉⠙⠛⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⣸⣿⠃
⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠈⢧⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⡅⣧⣬⣿⡇⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁⠀⣠⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣮⣭⣵⣆⠉⠙⠳⠶⠶⠶⠶⠶⠖⠚⠉⠁⠀⢀⣀⣤⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣶⣤⣤⣤⣀⣀⣀⣀⠀⢀⣤⣶⣾⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣫⣾⣿⣿⠿⠿⠿⠿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⣡⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⣡⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⣡⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣡⡾⠟⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣡⡾⣫⣴⣿⡿⠿⢿⣷⣄⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣾⠟⣡⡾⣫⣾⡿⠋⠁⢀⣠⣀⢹⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⣄⠀⠀⣰⢁⡴⠋⣡⡾⣫⣾⡿⠋⠀⣠⡾⠋⢁⣿⣸⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⣶⣜⣿⡛⠦⣿⠋⣠⠞⣡⣾⡿⠋⠀⣠⠞⠁⢀⣴⣟⣵⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⣽⣯⠉⠳⣄⠀⠺⣡⣾⡿⠋⠀⣠⠞⠁⢀⣴⢟⣵⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠈⠳⣄⠈⠳⣄⠈⠉⢀⣤⠞⠁⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣡⣄⠈⠳⣄⠈⠳⣄⠈⠁⢀⡴⣻⣽⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣵⣿⣿⣿⡗⠀⠈⠳⣄⠈⠳⣄⠈⠺⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡵⢋⣼⡿⣿⣝⢿⣦⣱⣄⠈⠳⣄⠈⠳⣤⣘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣵⡿⠋⠀⠈⠻⣷⣿⣿⣿⣷⣄⠈⠳⣦⣽⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠟⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⡄⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠋
⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠹⢿⣦⣤⣤⣤⣴⣾⡿⠋
⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠁
⠀⠰⢾⣿⡏
⠀⠀⠀⠙⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣇⣃⢰⠀⡀⠀⠶⠐⠊⠉⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠈⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡌⠁⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⡇⠆⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⡀⠅⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡇⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⣀⣠⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⠁⢸⠀⠀⠐⠀⡀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠇⢸⠀⠀⢀⠀⠈⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡆⢸⠀⠀⣀⠀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣸⠁⣀⢸⠀⢰⡋⠀⠈⠂⢀⣈⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠃⢸⠀⠺⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⠀⡄⢸⡆⠁⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⣿⠀⠁⢸⠀⡃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡀⠀⡄⡀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢹⠀⡀⢸⠀⣆⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣉⠀⣁⡚⢀⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡉⢉⡁⠈⠃⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⠀⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠼⠞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠐⠊⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠀⠁⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠤⠄⠂⠈⠁⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⣀⡧⠤⠀⠀⢀⠀⠀⠀⢆⣀⠤⠄⠒⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢉⠆⠀⠘⡤⠀⠀⠒⠉⠉⠀⠀⠀⠀⠀⠤⠚⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣽⣯⣽⣽⣿⣦⣭⣿⣥⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣶⣶⣿⣷⣾⣿⣷⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⡴⠻⣦
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⠀⠀⠀⢀⢋⠶⠋
⠀⠀⢸⠃⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠔⡉⠃
⠀⠀⢸⣀⡴⠂⠀⠀⠀⢀⠠⠐⠈⠉⠁⠀⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠉⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⡀⢀⡤⠀⠀⠀⠀⠁⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢂⠊⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⡐⠈⡠⠀⡠⠂⠉⠈⠛⠦⣄⡁⠢⢉⠲⢄⡀⠀⡠⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⡐⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣁⠂⢍⡛⢠⣅⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠄⠀⠄⠀⠀⠀⠀⠀⢀⡜⢳⡶⠾⢉⠓⡈⣑⠳⣬⡈⣹⡿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⡀
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠐⡀⠰⡀⠠⡀⠀⠀⠀⢀⡞⢳⡾⠓⢦⣬⣰⡶⣍⠙⠦⣍⡛⢦⣐⠈⡐⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠈⠀⠰⣄⡈⠂⠄⡀⠈⠹⡟⠙⠲⣾⣤⢉⠳⢬⣙⠢⢀⠙⠲⣬⡛⠦⣅⣠⠟⠛⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠙⠲⢷⡈⠀⠄⡀⠱⢶⣤⢧⣜⠛⢦⣌⠓⢦⣅⠲⢏⠉⠓⢦⣙⠲⣥⡂⣀⣵⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⠀⠀⠀⠀⠈⠓⠦⣀⡇⠠⣬⣙⠌⠙⠲⣌⡙⠂⣨⠬⢦⣌⡐⠄⡈⠙⢦⢙⡙⢻⡀⢴⣻⠖⠠⣀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠀⠀⠈⠙⠲⢬⡙⠷⣦⣴⣤⢉⠻⢥⡊⠁⠠⡙⠲⢬⣁⠈⠌⡽⠳⡄⢢⠝⠐⠄⡀⠑⢄⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⠀⠀⠀⠀⢠⡹⠷⠤⣙⠳⢾⣁⠂⢌⠐⠄⡀⠑⠠⢉⠢⡞⠁⠀⠀⢀⠒⠄⡀⠈⢂⠀⠂⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⡀⠀⠈⠀⠀⠈⠑⠢⣌⠓⢦⣼⡒⠌⡑⠠⠄⢀⠂⠀⡠⠂⠌⠀⠀⠐⡄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡀⠀⠀⠀⠀⢮⢟⠒⠌⡙⠶⣬⠓⡲⢉⣀⣈⣤⡶⠊⠀⠀⠀⡀⠀⢰⠆⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠈⠑⠦⢀⠁⠠⣀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠏⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠁⠂⠤⠤⠄⠊⡀⠔⠁⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⢄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⢀⡀⠀⠀⠀⠀⠀⡀⠠⠒⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣆⠀⠀⠀⠀⠀⣰⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⣄⡀⠀⠀⣠⠟⢛⣉⡛⢦⣤⡴⢛⣉⡙⠻⣄⠀⠀⠀⣠⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠟⣋⣩⣙⢋⣾⣿⣿⣿⣷⣤⣾⣿⣿⣿⣷⡙⣋⣍⣙⠻⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⣮⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣵⡌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⡛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡷⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠚⠓⠒⠛⠛⠛⠒⠒⠛⠋⠉⠁


⠀⠀⠀⢸⠀⠀⠀⡴⠋⠉⢳⡀⣿⠉⠙⣧⢐⡏⠉⠉⠀⣿⡆⠀⣸⡇⢸⣿⢸⣿⢻⣷⢼⣿⡻⠇⣿⡇⢸⣷⢸⣿⣧⢸⣿⣿
⠀⠀⠀⢸⠀⠀⠀⣇⠀⠀⢸⠇⣿⠛⢻⡁⢀⡟⠛⠛⠀⡇⢻⣰⠃⡇⢸⣿⢸⣿⠛⠋⣠⡝⢿⣦⣿⡇⢸⣿⢸⡏⣿⣿⢿⣿
⠀⠀⠀⠘⠒⠒⠂⠈⠓⠒⠋⠀⠛⠀⠀⠛⠀⠓⠒⠒⠂⠃⠈⠋⠀⠃⠘⠛⠘⠛⠀⠀⠘⠛⠛⠃⠘⠛⠛⠃⠘⠃⠘⠛⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⢁⣆⠀⢎⢈⠶⡁⡅⡰⢧⢸⢢⡆⢰⠆⠆⡆⠀⠸⢸⢰⡇

⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⢰⣄⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣦⣌⠂⠄⠀⢀⡀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠛⠓⠶⠶⠦⠬⠭⣥⣐⣶⣺⣟⣒⣀⣤⡤⠤⠤⠄⠀⣀⢀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠄⠀⠀⠉⠉⠉⠉⠉⠘⠛⠒⠒⠒⠋⠉⠉⠉⠠⠬⠒⢲⣦⣄⡀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⣄⡀⣀⠀⠈⠑⠙⠢⡀
⠀⠀⠀⠀⠀⢸⣷⣦⣤⠤⠤⠤⠄⢐⣒⣒⣒⣻⣯⣭⣽⣿⣿⣬⡻⣿⣭⣭⣿⣿⣿⡿⡿⢿⣿⡶⣿⣿⡿⠿⠿⠾⢿⣷⣦⡄⠀⠈⢆
⠀⠀⠀⠀⠀⣼⡋⣁⣤⣶⣿⡿⢿⡿⠛⢛⣟⣹⡿⠿⠿⠿⠿⣟⣿⣎⠷⠶⠾⠿⠧⠤⠄⠀⠚⠧⠜⠾⠧⣀⠀⠀⠀⠈⠻⣿⣆⠀⠀⢧
⠀⠀⠀⠀⠀⣿⣿⣿⠟⠫⠀⠈⠀⢀⣴⠖⢁⡤⠖⠒⠛⢻⢟⡩⢲⡟⣋⣯⣉⣉⣍⣍⣍⣩⣻⣟⢻⡯⣷⡈⡙⠄⠀⠀⠀⠘⣿⡄⠀⠈
⠀⠀⠀⠀⠀⢹⡿⡡⠁⠀⠀⠀⠀⣸⡏⠠⠃⠀⠀⠾⢾⣯⣭⣭⢻⣇⣿⡻⠛⠋⠟⠿⠺⠭⠙⠿⣠⡏⢉⠁⡗⢸⠀⠀⠀⠀⢻⡇⠀⠀⡄
⠀⠀⠀⠀⠀⢘⠏⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠾⢾⣯⡭⠿⠾⢯⡭⠭⠭⣭⠍⢻⣿⣭⣭⣉⣍⣭⣥⢖⣠⣾⠃⠀⠀⠀⣾⠇⠀⠀⠃
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣾⡀⢀⠀⠀⠀⠿⠺⣯⣥⣼⢩⠈⣬⣏⣛⣛⣛⣛⣛⣛⣛⢙⣙⣙⣛⣛⣛⣛⣒⣒⡢⣾⡿⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠑⠤⠀⣀⣀⣈⣻⣿⣜⣆⠲⣄⠐⠚⠁⠚⠛⠿⠟⠛⠀⠀⠀⠠⠤⠤⣄⣴⣃⡞⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣄⣀⣀⣀⣉⣈⣉⣉⣉⣉⣉⡛⠛⠋⠉⢉⡉⠉⠉⠙⠛⠛⠛⠉⠉⢉⢁⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠙⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⣀⠤⡄
⠀⠀⠀⠀⠀⠀⠘⣷⡿⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⣔⠂⣀⡡⠄⠒⠁
⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠣⠄⠀⠀⠀⠀⠀⢁⠏⠁
⠀⠀⠀⠀⢀⣜⠀⠀⢀⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢩⢉⠵⢤⣼⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠚⠁⠢⢦⡄
⠀⠀⠀⠀⣌⣹⠤⣽⣿⣯⢄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⡀⠈⠆⠀⠀⠑⢅⢢⣀⠀⠀⠐⢶⠎⠉⢲⣄⠀⠄
⠀⠀⠀⠀⠈⣯⡘⠉⠉⠻⣄⡜⡁⠀⠀⠠⠄⠀⠀⠀⠀⢤⠀⠰⢹⠃⠀⠀⠀⠀⠀⠈⠈⠓⢤⡀⠀⠀⠀⠀⠀⣉⡴
⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠒⠒⠒⠂⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⠒⠒⠒⠠⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⢀⣠⠴⠒⠒⠉⠉⠉⠉⠒⠒⠤⣄⡀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⢰⠋⠀⠀⠀⢀⡠⠔⠒⠈⠉⠉⠐⠒⠤⡀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⢀⠇⠀⠀⠀⢠⠋⠀⣀⣤⠶⠒⠋⠑⠒⠦⢼⣆⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⢸⠀⠀⠀⠀⡇⢀⡞⠉⣠⠔⠚⠛⠉⠛⠒⢤⡈⠳⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⢸⠀⠀⠀⠀⣧⠏⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠙⡆⢹⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⣿⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠘⠀⠀⠀⠀⣿⠀⣿⠀⢠⣤⡄⣤⣤⡤⣤⣤⠀⢸⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⣿⠀⣠⣿⣧⣼⣿⣤⣿⣧⠀⢸⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡀⠀⠀⠀⠀⣿⠀⣿⠀⢸⠉⣏⡿⢹⣯⠉⢩⠀⣸⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⣿⠴⠛⠒⢚⡆⡟⣧⠸⣿⣖⣛⠒⠻⣬⣧⣿⣤⣤⣤⣤⣤⣤⣤⠤⠤⠀⣬⠀⣀⣀⡀⢀⣴⣢⡀
⡇⠀⠀⠀⠀⣿⢠⣿⠉⡟⢳⠟⣻⠆⣿⠯⣝⢻⡄⢻⡖⡖⡒⠚⠓⠚⠛⠛⠛⠛⠛⠛⡟⠛⠛⠛⠹⢯⣉⣏⡗
⡇⠀⠀⠀⠀⣿⢸⣿⠀⡇⢸⠀⣿⠀⣿⠀⣿⢸⠁⢸⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠉⠁
⡇⠀⠀⠀⠀⣿⢸⣿⠀⡇⢸⠀⣿⠆⣿⠀⡿⢸⠀⢸⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⣿⢸⣿⠀⡇⢸⠂⣿⠀⣿⠀⡇⢸⠀⢸⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⣿⢸⣿⠀⡇⢸⡄⠻⢀⣿⠀⡇⢸⠀⢸⡇⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⡇⠀⠀⠀⠀⣿⢸⣿⠀⡇⢸⠟⠻⢏⣹⠀⡇⢸⠀⢸⡇⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⣿⢸⣿⠀⡇⢸⠉⢹⠂⣿⠀⡇⢸⠀⢸⡇⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⣿⢸⣿⠀⡇⢸⠀⢸⠀⣿⠀⡇⢸⠀⢸⡇⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⣿⢸⣿⠀⡇⢸⠀⢸⠀⣿⠀⡇⢸⠀⢸⡇⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡎
⡇⠀⠀⠀⠀⣿⢸⣿⠀⡇⢸⠀⢸⠀⣿⡀⢧⡼⠀⣸⡇⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⣿⠸⣿⢠⡇⢸⡀⣸⢃⡇⠙⠶⠶⢾⠠⡇⠃⠀⡇⠀⠀⠀⠀⠀⠀⢰⡇
⡇⠀⠀⠀⠀⣿⠢⣬⢭⡟⢦⠬⠵⠚⠀⠀⠀⠀⢹⢘⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⢈⡇
⡇⠀⠀⠀⠀⣿⠀⣿⠀⢱⡈⢦⣀⡀⠀⢀⣀⡴⢋⡴⠁⠀⠀⣿⠈⠉⠉⠉⠉⠉⠙⡇
⡇⠀⠀⠀⠀⣿⠀⣿⠀⠀⠙⠲⢌⣉⣉⣉⣡⠴⢾⠁⢸⠀⠀⣿⠐⠂⠒⠒⠒⠒⠺⡇
⡇⠀⠀⠀⠀⣿⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⣿⡄⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣸⠀⠀⡏⠀⠀⠀⠀⠀⠀⢀⠃
⢣⠀⠀⠀⠀⠸⡵⣄⠈⠲⢄⣀⣀⣀⣀⣠⠴⠊⠀⡰⠃⠀⣰⠁⠀⠀⠀⠀⠀⠀⣾
⠘⣆⠀⠀⠀⠀⠙⢎⡳⢤⣀⡀⠀⠀⠀⢀⣀⡴⠚⠁⢀⡴⠃⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠘⣆⠀⠀⠀⠀⠀⠙⠒⠬⢍⣉⣉⣉⣉⣁⣀⠤⠖⠉⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠞⠉