Worm Emojis & Symbols

⠀⠀⠀⠀⢀⣀⣠⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡤⣤⣀⣄⣄⡄⠀⣀
⠀⢀⣤⡾⣟⣻⣿⣭⣿⣿⣻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣾⣼⣿⣷⣦⣤⣤⣤⣤⣶⣿⣵⡾⡿⣻⢛⣛⢛⡛⠿⢿⣿⣤⣥⣔⡄
⠀⣼⣯⣿⣿⠟⠋⠉⠛⠛⠿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡿⠿⠯⠦⠂⠬⠽⣛⡻⠿⣿⢿⣛⠽⠝⠓⠉⠉⠀⠀⠀⠉⠉⠐⠲⠬⠭⠿⠿⠂
⠀⣿⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⢯⣩⣸⡿⣿⣦⣀⣀⣀⣤⣶⣽⣿⢇⡄⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠹⣿⣻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠦⣞⡿⣿⣿⣿⣿⣟⣫⠗⠉
⠀⠀⠈⠛⠿⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠛⠋⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠉⠉⠉⠙⠢⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣁⢸⠉⠁⠀⠀⠈⢂⡔⠋⠩⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡴⠊⠀⠘⡄⠀⠀⠀⢀⡎⠀⠑⠀⠐⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡌⠀⠀⠀⠀⠱⡀⠀⠀⡼⠀⠀⠀⠐⣀⡥⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠢⣄⣀⠀⠀⠀⠀⡹⠶⠖⣇⠀⣠⠖⠉⠀⠀⠄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠔⠁⠀⠈⠉⠓⢲⠋⠀⠀⠀⢘⡟⠁⠀⠀⠀⠆⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠸⡇⣀⡠⠔⠊⠉⢩⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡙⠢⢄⣀⣀⣀⡴⠛⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⣠⢤⡇⠀⠀⣀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⢀⡠⢤⢒⠣⡁⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢸⡇⠀⠀⡠⠖⠋⠀⠈⠊⣦⠸⠥⠖⠧⠄
⠀⠀⢀⣤⡔⢠⠣⠂⢸⠁⠀⠙⠦⡀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠈⣧⣠⠎⠀⠀⠀⠀⣠⠊⠀⠀⢠⢄⢰⡞⡆
⠀⢰⠁⠀⠀⡎⠀⠀⢸⠀⠀⠀⠀⠈⢑⠞⠁⠀⠀⠀⠀⠀⠀⠰⢯⢿⡀⠀⠀⠀⢰⣇⠀⠀⣠⠀⠘⠀⠁⢑⡄
⠒⠚⠲⣤⡤⢧⣀⣀⣨⣧⣄⣀⣠⣴⢿⠒⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⣿⢲⣤⣀⡠⡟⠢⣀⣻⠤⣀⡠⠔⢚⣒⣒⢂
⢀⣀⣠⣤⣽⣋⣀⣙⣷⣇⣐⣒⣓⣒⣿⣤⣤⠤⠮⠭⢍⣛⣛⣫⣤⡭⠬⠭⣤⣬⣷⣿⣴⣲⠾⠯⠟⠿⠿⠿⠿⠿⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢻⡟⠛⠛⠛⢳⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠉⠀⠀⢸⡇⠀⠀⠀⢸⠇⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢿⡀⠀⣀⣤⠷⠶⠶⠦⣿⡀⠀⠀⣼⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠈⢷⡾⠋⠀⠀⠀⠀⠀⠈⠻⣦⣰⠏⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⣠⡞⠁⢻⣄⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⢀⣼⠛⢧⡀
⠀⣀⣤⣤⡴⢾⡏⠀⠀⠀⢙⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⡟⠁⠀⢠⡟⠷⣤⣤⣤⣄⣀⡀
⣾⠉⢿⣼⠇⠀⢷⡀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣴⠟⠀⠀⠀⡿⠀⠀⠉⢹
⠻⣄⣀⣀⣀⣠⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣾⣃⣀⣀⣤⠾

⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠒⠒⠦⢄⡀
⠀⠀⠀⠀⠀⡰⠊⠐⠀⠂⠀⠀⠒⠒⠉⠢⡀
⠀⠀⠀⠀⡼⢁⠖⣭⣵⡄⠀⠀⣴⣭⡕⠄⠹⡀
⠀⠀⠀⢰⡇⠈⢎⣿⣿⠃⠀⠀⢿⣿⣧⠆⠀⣧⠀⠀⣀⣠⠤⢤⡤⢤⣀⡀
⠀⠀⠀⠸⡆⠀⠀⠀⠀⢾⠖⣶⠂⠀⠀⠀⠀⣿⠖⠉⠀⠀⠀⠀⠱⡄⠀⠉⠑⠦⣀⠀⠀⠀⢀⣠⠤⣤⣤⣀⡀
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⢷⣤⠚⠁⡰⠊⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠳⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠈⠳⣼⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⡇⠈⠓⠤⢄⣀⣠⠤⠖⠋⢸⠀⠀⠈⢧⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡆⠀⠀⠈⠙⠒⢶⠆⠀⠀⠀⠀⢹⠤⠤⠦⢤⡀
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⠀⢸⠀⠀⢀⣀⣠⣏⣀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⡾⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⢁⣼⠔⠊⠉⠀⠀⠀⠀⠉⠓⠧⣄⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⣼⣁⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⢀⣀⣤⣪⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢄⣀⣠⣃⣀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠒⠓⠓⠚⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠤⢄⠀⢀⣀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⣶⣦⣤⣤⡤⠂⡜⠀⠀⠀⠀⠀⠀⡰⠋⠉⠉⠉⣻⠀⠀⠀⣀⠔⢢
⠀⠀⠀⠀⠀⠀⠀⢸⠁⢹⠿⣿⠿⠿⡗⠐⡇⠀⠀⠀⠀⠀⠀⠙⢶⠒⠚⠋⡙⠀⢠⠞⠁⡔⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠹⣀⠁⠀⡼⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⡇⡴⠃⣠⠞⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠈⠉⠉⠀⠀⣀⡇⠀⠀⣀⣀⣀⠀⠀⠀⠈⡆⠀⣗⣱⠟⠁⠀⣠⣯⣤⠶⠶⠛⠛⠛⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠒⠒⠂⠉⠀⡷⠚⠉⠉⠉⠉⠛⠳⢦⣄⣱⠀⣏⢛⣠⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠠⠂⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣿⣩⣟⡁⠀⠀⠀⠀⠀⢄⠀⠀⢀⣀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠂⠈⠀⠀⡠⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢀⠵⢞⢡⡀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⡀⠔⠊⠀⢀⠝⢦⡐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠁⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢀⠔⠁⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⠢⡄⠁⠀⠀⢀⡰⢃⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣈⠒⠒⠚⡉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣤⣀⣀⣀⣀⣀⣠⣤⣤⣤⡀⠀⠀⠄⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⠽⠯⠟⠛⡙⠓⠶⠶⠴⠶⠞⠋⠁

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

⠀⠀⡔⠛⠲⡴⠒⠲⡖⠛⠛⠛⠲⢤⡀
⠀⢘⢰⣿⢰⠁⣶⡄⢸⠀⠀⠀⠀⠀⠙⢆
⠀⢹⠘⠟⢸⡀⠿⠃⡸⠀⠀⠀⠀⠀⠀⠈⢧
⠀⡠⠓⠶⠊⠱⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠈⡆
⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢻
⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠸
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠛⠛⠒⢆
⠀⠙⢆⡀⠀⠀⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⡞⠙⢦⡀
⠀⠀⠀⠙⠲⠤⠤⡤⠖⠋⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡱⡄
⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⡸⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡘⠀⠹⡀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⠓⠤⣄⣀⣀⣀⠤⠀⡎⠀⠀⠀⠀⢰⠁⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⠀⠀⣧⠀⠀⢠⠞⠁⢀⡤⠛⠲⡀
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⣈⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⣼⠀⢠⠧⠤⣀⣌⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡏⠉⠲⣄⠀⢹⣀⣀⡤⠖⠊⢳⠀⠀⠀⠀⡘⢸⠀⢸⠀⠀⢸⡈⡦⠒⠲⠄⠃
⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⢰⠀⠀⠀⠈⠆⣘⠉⠀⠀⠀⠀⠘⡄⠀⠀⢠⠁⠈⡄⢸⡠⠚⠉⢻⠇⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⢹⠈⠉⠛⠋⠉⠀⠀⠹⡀⠀⠀⣠⠛⠢⡀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢧⠀⠀⠈⠀⠀⣇⠈⣆⠀⠀⡼⢤⡀⠀⠀⣇⣀⣀⣠⢤
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠁⠀⠀⠘⡄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⡈⠳⠼⣶⠊⠀⠀⠱⡀⢰⠋⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠘⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠⠁⠀⠀⠈⠆⠀⠀⠀⢠⠏⠀⠀⠀⠰⡠
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣀⡴⠋⠀⠀⠀⠀⢰⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡰⠳⢤⣤⣤⣴⣾⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡉⠁⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⣼⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⣀⣠⣴⣿⣷⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⢠⣃⣠⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡏⢀⠤⣄⠀⣿⠀⠀⠀⠀⣠⠖⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⣸⢰⡃⢀⠈⢳⢸⡀⠀⠀⣼⠁⣴⠛⢷⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢾⠸⡀⠀⠆⠘⡏⢧⠀⠀⡇⠀⡇⠀⡜⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⣇⠑⢤⣠⠼⠁⠈⢣⣀⠳⡀⠑⠊⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠄⠉⠫⣷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⠠⠊⠀⠀⠀⠀⢙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⢀⠞⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⡤⠚⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡇⢻⡄⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢺⠁⣸⠃⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢸⠀⣿⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⣸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣯⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠁⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⣿⠀⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣿⠀⣿⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣿⠀⣿⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡿⠒⠀⠤⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠸⡆⠀⠀⣀⣠⣤⣀⣀⠀⠀⠀⠀⣟⡴⠁⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠙⢦⣎⠁⠀⠀⣰⠋⠙⠛⠲⠲⠟⠲⢤⡀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⡉⠛⠲⢤⣧⣀⠀⠀⠀⠀⠀⠀⣀⣹⡦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢙⠛⣲⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠖⠛⠛⠛⠛⠛⠳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠙⠆⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠶⠶⠛⠚⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣠⡾⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠖⠒⢶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠙⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⠛⠁⠀⠀⠀⠈⢙⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⢰⠏⠀⠈⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⡀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢉⡀⠀⠀⠈⢿⡈⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡴⠶⠦⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣁⠀⠈⢛⣦⣤⣀⣈⠁⠀⠀⣤⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠃⣰⠏⠁⠀⠈⠉⠛⠶⣤⣿⠀⠀⠀⠀⣽⠉⠛⠲⢦⣄⣀⡀⠀⠀⣀⣴⠏⠀⠙⠛⢦⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⢀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣐⠋⠀⠀⠀⢠⡄⠉⠉⠛⠛⣿⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠛⠁⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣤⣀⣸⡇⠀⠀⠀⠀⠙⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠤⠤⠶⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠖⠂⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠸⠃⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠦⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⣴⠛⠻⣶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠙⣶⡏
⠻⢦⣌⡁⠀⠀⠉⣉⠛⠛⠓⠒⠒⠛⡿⠁⠀⢀⣴⠏
⠀⠀⠈⠉⠛⠶⠾⢯⣤⣄⣀⣀⣀⣈⣣⣤⠶⠛⠁
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⡀
⠀⠀⡔⢉⠙⣿⠋⠉⢻⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢉⠉⣯⠏⠉⢳⡉⠑⣄
⠀⠐⡇⢶⠀⣇⢨⣇⢠⡇⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠷⠄⣼⢨⡏⢀⠇⠀⠈⡆
⠀⢸⠙⠒⠋⠙⣲⡶⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠓⠋⠈⠒⠒⠋⠀⠀⠀⣻
⠀⠸⣄⠀⠀⣀⣿⣿⣤⣤⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⡸⢃⣀⠀⠀⢀⡏
⠀⠀⠈⠛⠛⣿⠛⢉⣿⣠⣶⣭⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⢻⠚⢉⣧⣠⢖⡢⣱⡀
⠀⠀⠀⢠⣾⡏⢼⣿⡿⢻⣿⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⡇⢰⡡⡔⠙⠬⠵⢻⡃
⠀⠀⠀⠈⠉⡇⠀⠀⣷⣀⠐⣚⣋⢻⣦⡴⢤⣴⡶⠶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠈⠉⡇⠀⠀⣧⡀⠀⢀⣀⠉⠦⠴⠤⡴⠒⠒⠦⠤⣄
⠀⠀⠀⢀⣴⣧⢰⣿⢿⡏⢼⣿⣽⡇⢃⣤⣄⠛⢠⣶⡌⢿⣿⠀⠀⠀⠀⠀⠀⠀⡔⣧⠠⣊⢤⡎⠠⡁⠖⡁⠀⣠⣄⠀⢀⠴⡄⠺⣾
⠀⠀⠀⠀⠉⠙⣆⠀⠀⣷⣶⡝⠋⠀⠘⠿⠟⢠⡈⢉⣵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⣆⠀⠀⡳⢲⠉⠈⠀⠀⠣⠔⠁⠀⠉⣠⠋⠁
⠀⠀⠀⠀⠀⢰⣿⠦⣸⠟⠛⠻⣶⣷⣤⣤⣴⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⠦⣸⠔⠊⠳⡴⢲⣀⣀⣤⠖⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠖⠒⠿⠗⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠖⠒⠷⠗⠒⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣿⣽⣯⣭⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠉⠙⠓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⠆⢁⠈⠢⡀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡄⠸⣿⡷⠀⡃⠀⡔⢀⡁⠲⡀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠤⠀⠠⠞⠀⠘⠀⣿⣿⠀⠅⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢰⠢⣄⠀⠑⠤⠤⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⠈⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠁⠀⠀⠀⠠⢴⠃⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠴⠊⠉⠉⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⢻⠃⢀⣀⠀⠠⠄⠀⠈⠢⡴⠃⠀⠀⠀⡠⠁⠀⢹⠀⣠⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡞⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀⠔⠁⠀⠀⢸⠋⠀⠀⠀⢨⠳⡄
⠀⠀⠀⠀⠀⠀⢠⡟⠁⠉⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣤⡁⠀⠀⣀⣀⡀⠀⠀⠀⠠⠁⠀⢹
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠠⠎⠳⢄⡀⠀⠀⠀⠀⣰⡤⣾⠄⣸⠊⠁⠀⠀⠑⡄⣠⠂⠀⠀⠀⢸
⠀⠀⠀⠀⢀⡤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⡸⠋⢱⣀⣀⠠⣆⠀⢀
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢀⠀⢤⠀⠀⠈⠓⠲⠶⠖⠊⠀⠀⢠⠀⠀⠀⠈⠉⠉
⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠧⣀⣀⣁⣀⡠
⢀⡴⠋⠉⠱⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠽⡁⢙
⣾⡀⣀⣀⣀⣸⣄⣀⠴⠦⣀⡀⣠⠋⠀⠀⠈⡆⢀⡤⠒⠒⠒⢤⡀⠀⠀⢀⠔⠚⠲⣀⠖⠉⠑⣆⣴⣁⣀⣀⡼⠋
⠀⠉⠉⠉⠉⠁⠈⠙⠶⠶⣥⡤⠿⠤⠤⠤⠤⢾⣧⡀⠀⠀⠀⠀⠈⠉⢳⣯⣤⣤⢴⣧⣤⡤⠴⠾⠋⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⢶⡶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⢿⡀⠀⠈⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢧⣄⠀⠀⣀⡀⠈⣷⠀⢀⣀⠀⠀⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡆⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠙⢷⣌⠧⠜⠀⢸⡇⠻⡬⠃⢰⡏⠈⢻⡄
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⣸⠃⣰⠇⠀⠀⠀⠀⠀⠀⣼⡁⠀⢀⡤⣄⠹⣦⠀⠀⠀⣷⠀⠀⢀⡿⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⣰⠟⢧⣾⣁⣠⠟⠻⢶⡟⠻⡟⠳⣦⠀⠀⢰⡏⠙⠷⣌⠲⠋⠀⠘⣧⡴⠞⠛⠲⣤⡾⠃⣞⣙⠄⣼⣷
⠀⠀⠀⠀⠀⣿⢓⡿⣄⣨⡏⠙⠛⢺⠗⠒⢻⠉⢹⡇⢀⣾⠀⢀⡤⡘⢷⡄⢀⡼⠋⠀⠀⠀⠀⠈⢻⡄⠀⢁⣴⠏⢸⡆
⠀⠀⠀⠀⠀⠘⢿⣥⣀⣿⣉⣛⡒⡾⠒⠶⢾⠒⣿⣧⠞⠙⢷⡜⠶⠃⠀⢻⡾⠁⠀⠀⠀⠀⠀⠀⢸⣇⣴⢟⡥⡄⠈⣷⡀
⠀⠀⠀⠀⠀⢰⠋⢁⣉⢻⣉⡭⠿⠿⣶⠶⣿⣞⠙⣧⠀⠀⡀⠹⣆⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠘⠲⣫⡾⠉⠙⣷⢦⣄
⠀⠀⠀⠀⠀⠸⣄⡈⣛⡼⢻⠰⡷⠀⢸⠟⠁⠸⠇⠘⣧⢯⣹⠂⢹⡆⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⡴⠟⡵⢦⠀⣰⠏⠀⢹⡆
⠀⠀⠀⠀⠀⠀⢸⡏⠱⣄⡼⠳⠤⠴⠋⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠁⠀⠀⠙⢊⣴⠟⣎⣳⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣴⠟⢁⡀⣈⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⠀⠀⢠⡄⠀⠀⠀⢸⣇⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠙⠛⠒⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠙⠛⣿⠒⠒⠒⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠻

⠀⠀⣠⡴⠶⠛⠛⠛⠛⠛⠷⠶⣤⡀
⠀⣰⠏⠀⠒⠒⠒⠒⠂⠠⠤⢀⠈⢻⡄
⢀⡿⢀⣤⡄⠀⠀⠀⠀⠀⠀⣀⠈⢸⡇
⢸⡇⠉⣁⡀⠀⠀⠀⠀⠀⠀⡙⠃⢸⡇
⢸⡇⠐⣶⡿⠀⠀⠀⠀⠀⢢⣼⠂⣾⠃
⢸⡇⠀⠀⠀⠢⠀⣀⣀⠀⠀⠀⠀⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⢸⡇⠑⠂⠠⠤⠤⠤⠤⠄⠀⠊⣿⠁
⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣿⠈⠙⠓⠒⠲⠶⠶⠒⠒⠚⠋⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠈⣿⠓⠲⠤⠤⠤⠤⠤⠴⢶⡟⠁⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⢀⣴⡟⠉⠀⠀⠀⠙⣷⣄⠀⠀⠀⣴⠞⠛⠛⠛⢶⡄⠀⠀⠀⣾⠋⠛⠳⣆
⠀⢸⣇⠀⠀⠀⠀⠀⣀⠤⠊⠘⠳⡶⠶⠟⠁⠐⡀⠀⠀⠀⢠⠁⠙⢷⣤⡾⠋⠂⠀⠀⠀⠀⢻⡄⠀⠀⠙⣧⡀⠀⢻
⠀⠀⢻⣅⠈⠉⠀⠁⠀⠀⠀⢀⠌⠀⠀⢸⠀⠀⠁⠀⠀⢀⠂⠀⠀⠀⠃⠀⠀⠘⠀⠀⠀⠀⢀⠻⣦⣤⣴⡟⠀⠁⢺
⠀⠀⠀⠙⢷⣄⣀⠀⠀⢀⠄⠀⠀⠀⠀⣠⣤⠾⠛⠛⠳⣮⠀⠀⠀⠀⢠⠀⣠⣴⣦⣄⠀⠀⠘⠀⠀⠀⠀⢠⠀⢀⣾
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠷⠶⠶⠶⠶⠛⠋⠀⠀⠀⠀⠀⠘⢧⣤⣀⣀⣼⡴⠋⠀⠀⠙⢷⣤⣃⣀⣀⣀⣀⣤⡶⠟⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠒⢤⣸⣼⣀⣀⣀⡀
⠀⢀⡴⠋⠁⠀⠀⢀⡀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄⣀⣀
⢀⢸⠀⠀⠀⢀⣠⣤⣉⠳⠀⠀⠙⣆⠀⠀⠀⣠⠴⡚⠉⠁⠘⡆⠀⠈⡇⠉⢙⡦⡀
⢸⠀⡤⠤⢤⡏⠀⠀⠈⢳⠀⠀⠀⠈⠳⠂⠁⠀⠀⠘⢆⠀⠀⢹⠀⠀⡇⠀⢸⠁⢹⣆
⠀⠸⡇⣤⠀⢰⡷⠀⢀⡞⠀⠀⣀⣤⣶⣿⣿⡄⠀⠀⠈⡆⢀⣸⣤⠴⢧⣠⠏⢀⡜⠙⢦⡀⠀⠀⠠⢶⣿⡲⠄
⠀⠀⠳⣄⣠⠦⠤⠖⣋⡤⠖⠛⠻⣿⢿⠉⣰⠃⢀⡧⠴⠛⠉⠀⠀⠀⠀⠈⣦⠞⠀⢠⠏⢹⠒⠶⡖⢏⢸⣷
⠀⠀⠀⠀⠀⠙⠚⠋⠁⠀⠀⢀⣀⣧⡤⠔⢁⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢠⠋⠀⡞⠀⠀⢳⠈⣿⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠤⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣄⣀⣳⣀⣠⠴⢿⣿⠟⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠛⠛⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⢀⡤⣤⣉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⣠⣤⠤⠀⠀⠀⠀⠀⠀⠀⢀⡤⠬⣅⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣠⠞⠉⢀⣀⣀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠑⢄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠉⠀⡰⠋⠀⠀⠙⢢⡀⠀⠀⠀⠘⣰⢾⣷⡄⠀⢣⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠰⠀⠀⣠⣤⡀⠀⠙⡄⠀⠀⠀⢳⣴⣿⡿⠀⠈⡆⠘⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢠⠀⠀⣨⣿⣿⡆⠀⢱⠀⠀⠀⠈⢏⠉⠁⢀⠔⠁⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠸⡄⠀⠻⣿⣿⠇⠀⢸⠀⠀⠀⠀⠈⠑⠒⠃⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠛⠚⠛⠒⠦⣀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⡀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠞⢿⡇⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣟⠛⠛⠛⠛⠛⠋⠉⢉⠀⠔⠊⡾⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⠤⠤⠶⠚⠉⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡄⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢤⠄⣀⣀⡀⠀⠈⣷⣄⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠒⠛⠉⢁⡼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠒⣿⠈⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠤⠞⠉⠀⡏
⠀⠀⠀⠀⠀⠀⢀⣴⡯⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⣇⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢈⠉⢆
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢻⡀⠀⣿⠀⢀⡾⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢀⡴⠀⢠⡄
⠀⠀⢀⡟⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡌⡇⢰⠇⣠⣾⠁⠀⠀⠀⠀⠀⠄⣀⣀⠀⠀⠀⢀⣀⣀⡤⠞⡿⠶⠒⠛⠀⠀⠀⣷
⠀⠀⣸⢃⡞⠁⠀⠀⠀⠀⠀⠀⠒⠒⠒⠲⢤⣿⣷⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⢰⠇⠀⠀⠀⠀⠀⢀⡿
⠀⠀⣿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢸⠀⠀⠀⣾⠃
⠀⠀⢹⡇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢸⠃⣠⠞⠁
⠀⠀⠘⣿⠀⠀⡟⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⠀⠀⠀⠀⠀⣀⣤⡾⠁⠀⢀⣴⠷⠛⠁
⠀⠀⠀⠹⣆⠀⢿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⣩⣿⡤⠶⠚⠋
⠀⠀⠀⠀⠙⣆⠸⣆⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉
⠀⠀⠀⠀⠀⠈⠳⣼⣦⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣙⣦⣀⠀⠀⠀⠀⠀⣈⣉⣳⣶⡶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⠒⠂⠀⢀⡼⠤⠀⠀⠀⢀⡨⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⣠⠴⠟⠒⠒⡂⠋⠈⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣿⣀⣴⠞⠋⠀⠀⠀⠀⠀⠑⠒⠃⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠅⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⣠⣄⣰⠏⠀⠀⠀⠀⠘⣧⣰⠻⡶⣄⠀⠀⠀⠀⠀⠀⠀⣠⠟⢦⡤⢶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣧⢀⣴⣿⠋⠳⡀⠀⠀⠀⢠⡞⢉⣯⠻⡄⠀⠀⣠⠶⠦⠞⠃⠸⣟⠎⠳⢄⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠙⣦⣤⡴⠋⢰⡿⣌⣢⠈⠳⢮⣁⣀⣀⠀⠀⠀⠹⡗⢀⣀⣵⢶⣷⡾⠁⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣠⠴⣿⠁⠀⠀⠀⠘⢧⣀⡈⠑⠀⠀⠀⠀⠈⠑⠄⠀⠀⠉⠉⠁⠀⠸⣅⠙⠲⠦⢤⡴⢺⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⢀⣿⡄⠀⠀⠀⠀⣤⣻⡍⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣹⠇⢸⡄⠀⠀⡞⣰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⢸⣿⣇⠀⠀⠀⠀⠸⣟⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⢠⠘⣆⣿⣇⠀⡼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠀⢹⠀⠈⠙⠢⠀⣤⠀⠀⠀⢀⣿⣷⠀⠀⠀⣿⡆⢸⣿⣿⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⢄⠀⠀⣾⡇⠸⡀⠀⠀⠀⢠⣿⡆⠀⠀⢸⣿⣿⡂⠀⢠⣿⡇⢸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⣿⣦⣿⣷⠀⠙⢂⠀⠀⢸⣿⣇⠀⠀⣼⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡷⢦⡴⢄⣀⣿⣿⣿⣀⣀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣾⣧⣴⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠟⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⢉⣩⠽⠤⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠈⠉⠐⠁⠀⠀⠀⠀⠀⠀⠒⠒⠮⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠊⠀⠀⠀⠀⠀⠀⣀⡤⠀⣤⠀⡄⢸⠢⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠂⢠⠀⠀⠀⠌⠁⠈⠁⢉⡹⠒⠙⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠒⠉⡴⠀⠀⡰⠋⠉⢡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣒⢴⠇⠀⠀⢇⡀⢴⡁⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠄⠀⠀⠀⠀⠀⠀⠙⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⠀⠀⠀⠀⡠⠦⢄⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠀⠀⡠⠊⠀⠀⠀⠈⠐⠂⠠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⢽⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠳⣍⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠒⠀⠠⣠⡥⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡧⠒⠉⠁⠁⠀⠀⠇⠀⠘⠧⡀⠀⢀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠌⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠱⠙⠘⠦⣎⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠴⠴⠁⠈⡑⠀⠀⠀⣸⠁⠀⠀⢣⡀⢀⠐⠀⠧⠌⠍⠠⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⢒⠚⡀⢠⠉⠐⡤⢰⣀⣀⣀⡀⠀⢼⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠥⠄⡈⠉⠃⠁⠀⢰⠃⣆⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣤⣄⣿⣄⢢⡀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡏⠀⠹⠿⠏⠉⣶⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠜⠀⠀⠀⢀⠠⢪⢋⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠥⠄⠀⠵

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡀⠘⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠁⠀⠀⠀⠀⢠⠀⠀⠘⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠸⠈⠃⠀⠀⠀⠀⢀⠰⠀⠀⠀⠠⡀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⠀⠀⠀⠀⢀⠐⠒⠀⠀⠀⠀⠀⠔⡀⠀⡠⠀⠁⠀⠀⠲⠀⠀⠀⠀⣀⠀⠉⠀⠀⠀⠀⠐⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠠⠈⠀⠈⠢⠔⠊⠁⠀⠀⡀⠄⠂⠀⠀⢎⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⠀⠀⢀⠇⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠤⠀⠀⣀⡠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠠⠀⠉⠐⠢⢀⠀⢧
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠐⠂⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣎⠠⠂⠁⠀⡀⠀⠀⠀⠀⠈⠁⠀⠡⢄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⣀⣤⣄⣠⣬⣭⣷
⠀⠀⠀⠀⠀⡏⠡⠀⣀⣀⣀⣤⣄⣀⠀⠀⣠⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣇⠐⠋⠉⠉⠉⠀⠀⠀⣀⣀⠀⠀⠀⣀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡟⠛⠳⢦⣠⣄⡀⠴⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⠀⠀⠀⠀⣤⣾⣦⡐⠛⠉⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢷⣦⡀⠀⠈⠁⠀⣀⣤⣾⣷⣦⣤⣄⣀⣀⣤⣦⣴⣶⣾⣷⣷⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢿⠀⠄⠺⠦⠴⠶⠴⠶⣤⣤⡤⣤⣤⣤⣤⣠⣤⣄⣀⣀⣀⣈⣉⣉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣿⠛⢻⠖⠊⠈⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣭⣬⣭⣭⢽⠶⠶⠶⠦⢤⠄⢀⣀⠀⠀⠀⠈⠉⠛⠛⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⡤⣿⠶⠶⣦⣄⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠅⠀⠀⠀⠀⠀⠀⠉⠙⢩⣙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⢋⣉⡤⠤⠤⠐⠒⠂⠠⢤⣄⣀⡄⠈⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢛⡡⠔⠊⢉⡤⠴⢒⣉⣉⠉⠀⢀⣉⡄⣿⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠔⠉⢀⣤⠾⠕⠒⠉⠁⠀⢀⣀⡤⢶⡏⣸⢿⡀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⢼⣅⣀⣔⠉⠀⠤⢤⣤⣴⡖⠚⠋⠉⠀⣾⢠⢛⢨⠳⣄⠀⠀⢀⡾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠉⠙⠛⡛⠓⠒⠛⠛⠛⠛⠃⢠⣇⢨⠘⡈⢦⡀⠉⠛⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠐⠋⠛⠀⠐⠛⠳⠀⠀⠀⢸⡟⣎⠣⣜⠢⣍⣲⣶⡶⢟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢠⣦⢰⠀⣠⡄⠀⠀⠀⠈⢷⣌⠓⢦⣭⢷⣆⠐⠒⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢘⡷⠃⠘⠟⠁⠀⠀⠀⠀⠀⠙⠻⢋⡴⠂⢸⣆⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢣⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡈⠛⠂⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣎⢿⣉⣉⣉⣉⡓⠦⡄⠘⣧⠀⠀⠀⠹⢤⣄⣤⠶⢻⠃⠀⠀⠀⠀⠀⠐⣦⣀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣴⣿⣮⣿⣿⣿⣿⣿⣷⣿⠀⠈⠳⣄⠀⠀⠀⢸⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠿⠿⣿⣿⣿⡿⠿⠋⡇⠀⠀⠀⠈⠳⢦⡀⠈⠉⠁⠀⠀⠀⢀⣀⣤⠄⠀⢹⡓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠙⠳⣤⣤⡴⠶⢚⣻⣿⠀⠀⠀⣸⠇⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⢋⡁⢸⡆⣴⠚⠁⠀⢠⠏⠉⠛⠛⠛⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⠤⣄⡴⢤⣀⣤⡀⣰⠏⠁⢹⡀⣹⣼⣧⡆⠱⡄⢀⡏⠀⠀⢀⡄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢼⣄⡀⠀⠀⠀⠀⠀⢸⡯⣭⠗⠚⣉⣭⡿⢊⣽⣿⠠⡀⠘⠿⠓⠺⠿⠒⠚⣹⡾⠀⠀⣄⢸⠇
⠀⠀⠀⠀⠀⠀⡾⡏⠀⠀⠀⠈⠙⢦⡀⠀⢀⣠⠼⠿⣥⣶⠏⠩⠿⣏⠷⢶⡶⠾⢿⣖⢦⡈⠉⠒⠊⠉⠀⠀⠀⠀⠹⣾⡀
⠀⠀⠀⠀⠀⠀⣧⢳⡀⠀⠀⠀⠀⠀⠙⢦⣯⣾⣿⣿⣿⣮⣿⣗⡶⠦⣍⣻⡖⢮⡝⣻⣿⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⡞⢿⢧⡙⣆⠀⠀⠀⠀⠀⠈⢻⡍⠉⠉⠉⣹⣋⣧⣴⣿⡭⠷⠛⠋⠉⠉⠉⢳⡀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠠⡇⠈⢳⡳⣌⠳⣄⠀⠀⠀⠀⠀⡷⣤⠞⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢛⡆⢸⡇⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢳⡀⠀⠹⣌⠳⣌⠳⢤⣤⣤⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⢚⡩⢔⣿⠔⠛⢛⡉⠓⣄⡀⢀⣀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠈⠳⢬⣳⣄⡀⢆⡽⢩⠷⢤⣤⣤⣤⡤⠶⣚⣫⡭⠶⢒⣫⡥⠾⠧⢴⡾⠛⠉⠀⠀⠈⢿⠛⢤⠙⠛⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠈⠉⠉⠉⠀⠈⠲⣤⡤⠖⣒⣚⣩⡭⠴⠒⠛⠉⠁⢀⣠⠶⢋⣠⠀⠀⠀⠀⠀⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⡀⠀⠀⠈⠉⠉⠉⠉⠀⠀⣀⣀⣤⠴⠾⣟⣛⣒⡯⠯⣁⣠⣤⠴⣶⣟⣁⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠒⠚⠋⠉⠉⠉⠁⠀⠀⠰⣏⣭⣭⣤⠞⠉⠀⠀⠀⠀⠻⢬⣥⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢴⣶⡒⠶⣿⡙⠻⣿⣍⠉⠻⣿⡙⢿⡖⢶⡶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠺⢿⣭⣉⡛⠷⢮⣝⡲⢬⣙⠳⢤⡉⠳⢤⡈⠳⣄⠹⡌⢧⢹⢸⢇⡟⣹⠖⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⢯⣛⡿⠷⠶⢤⠤⠭⡙⠳⠦⣬⣙⠳⢮⣝⡲⠬⡓⠤⣙⠢⠈⠃⠈⠀⠈⠈⠈⠐⠡⢞⡡⠞⣋⣷⢤⡀
⠀⠀⠀⠀⢀⣴⣿⠿⠀⠀⠈⢲⡀⠀⣰⠃⠀⣨⠉⠓⣤⣌⣙⣒⠦⢍⡓⠤⢁⠀⠁⠀⠀⢠⠞⠉⠉⠉⠳⡄⠀⠐⠈⠥⠴⠶⢛⣳⣄
⠀⠀⢀⣴⣫⠔⠢⣅⣠⡞⠉⠳⢄⡀⠉⠀⠠⠉⠁⢀⣼⠷⢻⣿⣷⢶⡌⠉⠂⠀⢀⡴⢲⡇⠀⠀⠀⠀⠀⢸⣀⣠⠞⠛⣯⡩⠭⠭⠭⣷⣄
⠀⢠⣾⣿⣶⣾⣿⣿⣿⣷⣄⠰⠞⣉⡦⠴⠞⣳⠖⠋⠁⠀⠘⣿⡏⠀⠈⠓⣲⡯⣍⡀⣨⢷⠴⠚⠓⢦⣤⣾⣾⡃⠀⣼⡿⠻⢏⣹⢷⠚⠙⢦
⢠⣿⣿⣿⣿⣿⣇⣤⡤⣉⡛⠳⢿⡀⣀⣴⣞⠁⢀⠀⠀⠀⣩⣿⡿⠀⢀⡟⠙⠲⡀⠉⠳⢤⣴⡶⠾⡿⠟⡻⠉⠀⠀⣘⣷⠀⠀⢙⣷⣯⣴⣾⣇
⣼⣿⣿⣿⣿⣷⠟⣽⣻⣯⣿⣷⣶⡉⠛⢿⣿⣿⣶⡄⠀⣴⣿⠓⠀⣠⣿⣤⣤⣠⠞⢀⣀⢤⣬⣻⣮⣄⠈⠀⠀⢀⣠⣿⣿⣤⣾⣿⡿⣿⣟⣿⣿
⣿⣿⡟⣷⡿⣿⢻⡼⣧⣷⣿⣶⣿⣿⣶⣄⣌⡙⠻⢿⣼⣧⣤⣤⣾⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⢬⣿⣿⢿⡟⣿⣾⣿⣿⣻⣯⣿⣿
⣿⣿⢿⣿⣷⣞⣚⣿⣿⣭⣿⣿⣿⢻⣿⣶⡬⠝⠳⣤⣈⣙⠻⢿⣿⣿⣿⣟⡷⠾⠿⠛⢛⣋⣭⣭⣷⣶⣾⣷⣿⣿⠿⣾⣝⣗⣯⣷⣿⣿⢾⣿⣿
⢹⣿⣾⣿⣷⣮⣿⣧⣿⣭⣻⣏⡽⣻⣿⣿⣿⣷⣄⡙⠻⣿⡷⢯⣤⡿⠉⣿⣀⡀⠝⠻⠿⠷⠶⠯⢿⣧⢾⣛⣿⣶⡿⣿⣿⣿⣷⣿⣿⣹⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡟⣿⣆⣤⣍⣳⣯⡳⣄⣈⠙⠛⠻⠶⣬⣵⣾⣿⠿⠷⠿⠯⠿⢶⣿⣟⣿⣞⢻⡿⣽⣿⣿⣿⠃
⠀⠀⠹⣿⡽⢿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣗⣺⠭⣿⡷⣷⣿⣾⣳⣾⣿⣦⣽⡷⠀⠀⠀⠈⠹⣿⣿⣿⣯⠭⠽⢿⣟⣒⣶⣭⣝⣛⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠻⣷⣾⣷⣺⣭⣿⣿⣿⣿⣭⢟⡻⢿⡲⢭⣓⢪⣽⣿⡿⠟⠋⠁⠀⠀⠀⡀⠀⠀⢸⣿⣛⣛⣯⣭⡿⢾⣛⣛⣿⣭⣭⣭⡽⠋
⠀⠀⠀⠀⠀⠈⠛⢿⣞⣛⡻⣍⣯⣭⣝⣿⣮⡓⣭⣷⡾⠟⠋⠁⠀⠀⠤⠀⠀⠀⡀⠀⠀⢀⣼⡿⣟⣻⠽⢗⣛⣭⠭⠴⣶⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣿⣽⣹⣯⣷⡿⣿⣭⠁⠄⠀⠀⠀⠒⡤⠀⠁⠀⠴⠀⣠⡶⣛⠽⣛⣭⠶⣚⡭⢵⣲⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣯⣶⣶⣖⢐⣠⣶⠖⠔⠐⠀⢢⣾⣷⣻⣵⣟⣯⣶⠿⠗⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠉⢆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⠐⠀⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠋⠀⠀⠀⠀⡾⢈⡄⠔⠊⠙⠒⠺⠒⠐⠲⢤⡊⠀⣿⠀⠀⠀⠀⠙⠒⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠗⠁⠀⠀⡊⠀⠀⠀⠀⣈⡂⠀⠉⠲⠃⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠱⠀⢀⠊⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠀⢄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⣸⡷⡄
⠀⠀⠐⣆⠈⠇⠀⢀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠴⠿⣾⡇⢻⠷⠛⠀⠄⠀⡀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆
⠀⠀⠀⠃⠀⡀⢠⠈⠆⡄⠀⠑⢢⣄⣀⣀⢀⡠⢊⣀⠠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠄⣑⣄⡀⠀⢀⠔⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠋⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠆⠀⠀⠀⠀⢠⠃⠀⠀⠀⠠⣿⣿⡆⠀⢀⣾⣿⣦⠀⠀⠀⢸⠀⢆⠀⠀⠀⢠⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠠⠀⠀⠀⠀⡐⠀⢦⠀⠀⠀⠀⠙⠋⠁⠀⠀⠛⠛⠃⠀⠀⢀⠜⠀⡨⠓⠊⠀⠀⠇⢀⠃⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⠀⠈⠒⠈⠳⣄⠀⠉⠒⠀⠀⠂⠀⠀⠐⠀⠀⠤⠤⠐⠒⠁⡠⠊⠀⠀⠀⠀⠀⣧⣾⣾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⡀⠇⠩⣅⡠⠚⠉⢁⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠊⠀⠀⠀⠀⠀⠀⣐⡘⠛⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠙⢂⠀⠑⠄⡉⠁⠔⠊⣷⣤⡀⠀⠀⠀⣀⡀⢀⣴⠟⠀⠀⠀⠀⠀⠀⡖⠉⠉⠉⠀⠂
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠺⠿⠛⠀⢀⣦⠀⠀⠘⣷⣦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡴⠒⢩⠛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⡜
⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠄⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠀⠑⡄
⠀⠀⠀⠀⠀⠀⡿⢍⡐⠢⡀⠀⠈⠂⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠂⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠘⠀⠉⠢⡍⠐⡒⠂⠀⠀⠀⠈⠢⠄⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠄⠀⠀⠤⠄⠀⠉⠉⠁⠀⠀⢀⣤⠀⠊
⠀⠀⠀⠀⠀⠀⠀⡆⠆⠀⠀⠀⠈⠢⣄⣲⡀⠐⢄⡀⠀⠀⢀⣀⡀⠈⠑⠈⠁⠀⠀⠈⠀⠀⠀⣀⠤⠤⢀⣀⡠⢒⡬⢽⠋⡖
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⣀⠀⠀⠀⠈⠂⠈⠑⠊⠉⠿⠒⡶⠨⢇⣀⣒⠭⠉⠩⠅⣂⣒⠮⠀⣶⠒⠦⠶⠂⠁⠀⢘⣠⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣶⣤⣀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣂⣨⣠⣤⣾⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠷⠶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⡿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠲⠀⠆⠀⠀⠀⠀⠀⠂⠐⠐⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⠖⡩⡁⠀⠀⢀⣉⡓⢤⡀
⠀⠀⠀⠀⢀⡞⢁⠤⢤⡀⠀⠀⠀⡠⠤⣀⠱⡄
⠀⠀⠀⠀⡞⠀⡇⣾⣿⣷⠀⠀⢸⣿⣿⠌⠀⢹⡀
⠀⠀⠀⠀⡇⠀⠙⠸⠟⢃⣀⣀⡈⠛⠯⠊⠀⠀⡇⣀⡤⠖⠒⠛⠻⣟⠒⠒⠤⣄⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠏⠹⠃⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠙⠢⣄⠀⢀⡠⠔⢒⡻⠷⠶⠦⣄
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⠳⡉⠀⡰⠁⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⢹⢦⡀⠀⠀⠀⠀⠀⠀⢀⡠⡾⠀⠙⢦⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⠀⠈⠲⣅⡀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⣸⠀⠈⠓⠲⠤⠤⠖⠚⠉⠀⢧⠀⠀⠈⣇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠉⠙⠟⠀⠀⠀⠀⠀⡗⠒⠒⠛⢲
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣄⠀⣽⠀⢀⣀⡤⠴⠧⣤⣀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠇⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⣠⠷⠚⠉⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣠⣯⣤⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⣀⣀⣀⣤⣮⠥⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⢤⣠⣎⣀⡤⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣻⣿⠿⠿⢿⣶⣶⣤⣀⠀⠀⠀⠀⠀⢠⢤⣄⡀
⠀⠀⠀⢰⣷⣄⠀⠀⠀⢠⣴⣶⣶⣿⣟⡿⢾⣝⠻⣷⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣷⣄⠀⠀⠀⡏⡞⡞⡟
⠀⠀⠀⠀⢿⠘⣧⠀⢠⣿⢫⣿⣿⠉⠙⠻⣶⣝⡻⣶⣭⣝⣛⣛⣟⣛⣛⣿⡿⣟⣽⣿⣿⡀⠀⢸⠃⠛⢳⠃
⠀⠀⠀⠀⠘⣧⠘⣇⢸⣿⣾⢹⣿⠀⠀⠀⠀⠙⠿⣶⣮⣭⣽⣛⣻⣯⣭⣵⣾⠿⠛⠉⢿⣿⡄⢸⠀⣠⠏
⠀⠀⠀⠀⢀⣿⡄⢸⣿⣧⣿⣿⠏⢠⣤⣤⣄⠀⠀⠀⠉⠉⠛⠛⠛⢉⣉⣉⡀⠀⠀⠀⠸⣿⡷⣾⣼⡁
⠀⠀⠀⠀⢸⠀⣷⠀⢿⡟⠛⠁⠀⢀⡞⣉⡉⠻⡟⠛⠀⠀⠈⠛⣿⣋⡉⠙⣏⠁⠀⠀⠀⢿⢠⣧⡏⡷
⠀⠀⠀⠀⠸⣇⢸⡇⢸⡇⠀⠀⠀⢸⡟⣻⣿⡆⣿⠀⠀⠀⠀⢰⡟⣻⣿⡆⢹⠀⠀⠀⠀⠸⣿⣼⣰⠇
⠀⠀⠀⠀⠀⠘⢷⣿⠀⣧⠀⠀⠀⠘⣧⣽⣿⣇⣿⠀⢀⣀⡀⢈⣧⣼⣿⣃⣾⠀⠀⠀⠀⢠⣇⡿⠋
⠀⠀⠀⠀⠀⠀⢨⡿⡆⢿⠀⣠⠶⣀⣭⣉⡁⠀⠀⠀⠋⠐⠙⣀⣭⣍⣉⣩⣭⣘⢷⡄⠀⣸⣹⡄
⠀⠀⠀⠀⠀⠀⢸⡄⣷⢸⠀⠃⠈⠁⠙⢧⣹⠽⢿⢷⣶⣲⠞⠁⡠⢈⡧⠋⠀⠀⠀⠃⢀⣯⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣷⣿⠿⠶⠶⢾⣹⡆⠀⠈⠛⠶⠶⠾⠥⠴⠾⠛⠉⣦⣀⠀⣾⣹⠶⠾⠿⢿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣯⢠⠤⠶⠖⢻⣯⣄⣀⣀⣀⡀⠉⠛⠛⠋⠀⠀⣀⡙⠟⠀⡬⣿⠓⠶⠦⢤⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠒⠚⢋⣉⡷⠀⠈⠉⠻⢥⣀⣀⣀⣀⣠⡼⠟⠁⠀⠀⢘⣏⣙⡓⠲⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠛⢋⣉⣩⠟⠀⠀⠀⠀⢀⡈⠉⠉⢉⣁⡤⠖⢁⠀⠀⠸⢯⣉⣉⠛⠃⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢧⣉⣽⢿⣄⠀⠀⠀⠀⠀⠀⠉⠉⢭⠭⠤⠖⠚⠁⠀⠀⠀⢀⣸⣿⣍⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢤⣄⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠲⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣧⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⣠⣷⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣦⣆⣾⡄⠀⠀⠀⠀⠀⠀⠀⢠⡀⢶⣿⣷⣠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣟⠛⠛⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣓⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠉⣻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⡤⢤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⣤⣄⡀⠀⠀⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢠⣾⡿⠿⠻⢦⣄⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡁⠀⠀⢠⣶⣴⠋⠃⠁⣶⣾⣄⠙⣷⠁⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⣄⣳⡿⠏⠀⣀⣢⣼⣿⠯⠀⠘⣷⠔⠀⢐⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣰⣼⠿⠉⢀⣶⡬⠟⢡⠋⠁⠀⠀⣺⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠠⠤⠖⠒⠖⠶⣤⣄⡀⠀⠀⠀⢸⠀⠀⠰⣿⣥⣤⣨⣿⠿⠴⠚⠉⠀⠀⠀⢀⣿⡄⠀⠀⠀⡇
⠀⠀⠀⠀⢀⠴⠋⠀⢀⠀⠀⠀⠀⠀⠀⠈⢿⡓⠶⢤⣘⣆⠀⠀⠈⠊⠈⠙⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠐⣸⠁
⠀⠀⠀⢰⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⠶⣤⣬⣤⣄⣀⣀⠀⠄⠀⢀⣰⠞⠋⠂⠀⠀⠠⣹⠋
⠀⠀⠀⡏⠀⠀⠀⣺⠷⠿⠿⠷⣷⣣⢀⡄⡀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠉⠉⣿⠟⠛⠉⠀⠀⠀⠀⠀⢠⡴⠃
⠀⠀⠀⡇⠀⠀⢸⠇⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀⡠⢀⡀⢀⡴⠀⠀⠀⠀⠀⡛⠀⠀⠀⢠⠀⠀⠀⡰⠊
⠀⠀⠀⢸⡀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠾⢧⡀⠀⠀⠀⠀⣿⣠⠀⣀⢀⡬⠖⠉
⠀⠀⠀⠀⠹⣄⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠙⠊⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠓⢆⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣟⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣭⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡓⠂⠀⠀⠀⠚⡉⠂⠀⠀⠉⠉⢉⢩⡅⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠿⠆⠀⠀⠸⠿⠃⠀⠀⠀⠀⢱⡆⠃⣀⠔⢸⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣈⢴⠊⠀⠐⠋⠉⢉⠍⣠⠞
⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⠀⢧⠀⢤⠤⠤⢀⡠⠄⠀⠀⠀⡀⠡⡼⢶⠶⠿⠭⠄⠒⠈⠁
⠀⠇⠀⠄⠋⠓⣦⢤⡀⠀⣠⣤⣷⡄⠻⠉⠹⠁⠀⠀⢀⡔⣀⣴⣿⣷⣤⣤⣀⡀
⠀⡄⠀⠀⠓⠀⡌⠀⢰⣾⣿⣿⡏⢹⡄⠒⠃⠀⣠⣴⡫⢕⡫⡾⠃⣿⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠈⢦⡀⠈⠠⢁⣴⣿⣿⣿⣿⣿⣿⣿⣶⢖⣋⠉⡀⠀⠁⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠄⠊⠙⠻⣿⣿⣿⣿⣿⣿⣿⣍⠽⠳⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣷⡄
⡀⠀⠀⠀⠀⡇⠀⠀⣠⠶⠟⠋⠨⠟⠛⠛⠛⠛⠛⠛⠛⠳⣬⣙⠿⠿⢿⡿⠟⠛⢷⣽⣿⣿⠟⠋⠉⠙⢄
⡇⠀⠀⠀⢠⢂⠴⠋⠀⢀⠤⠤⣀⣈⣀⣤⡀⡠⣤⣠⣤⣾⣿⣿⣷⣿⠛⠀⠀⠀⠀⠈⠉⠉⠀⠂⠀⠀⠀⠙⠢⢄
⠱⠤⠤⠄⠊⠁⠀⠀⠀⢸⣿⣿⣿⠿⣿⠿⡿⢿⣿⣟⣿⣟⡁⠉⠉⠙⢼⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣿⢿⣿⣽⣿⣿⣿⣿⣟⣳⣆⠀⠀⢀⠊⠐⠤⠐⠀⠂⠉⠀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⢄⠀⠀⢼⠛⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⠿⠁⢈⡡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠉⠐⠒⠦⠤⠭⠭⠉⠭⠭⠽⠯⠥⠜⠂⠲⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠠⠄⠀⠀⠀⢤⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⣠⠾⠛⠃⠄⣀
⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡴⠟⠉⠀⢀⣾⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣿⣴⣷⣧⢀⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠰⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠉⠃
⣿⣿⣿⣿⣿⣿⣷⣿⣠⡀⣦⣷⢠⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣼⣧⣧⣼⣰⣇⢠⡀⣿⡆⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⣠⢸⣷⣿⣦
⣿⣿⣿⣿⢿⢿⡿⠿⠛⠛⠟⠿⠛⠋⠛⠉⠉⠋⠉⠉⠋⠈⠉⠛⠁⠀⠋⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⣸⣧⡆⢠⢀⣿⣾⣷⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⣾⡧⢀⡀⣸⡇⣰⣠⣧⣴⣰⣿⣰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⢸⣿⣿⣾⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣸⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⠻⣿⣿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠀⠀⠈⠁⠈⠀⠁⠈⠈⠉⠈⠉⠙⠛⠋⠉⠉⠛⠻⠟⠿⢻⡿⣿⠿
⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⢠
⣿⠃⢹⣿⣿⣿⣿⣿⡃⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣸⡇
⡟⠀⢐⣻⣿⣿⣿⣿⣷⣼⣿⣧⡀⢀⣦⠀⠀⠀⢰⣿⠄⠀⠀⠀⠀⠀⢸⣿⣯
⠉⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣸⣿⡄⠀⢰⣾⣿⡇⠀⢰⡆⠀⠀⣿⣿⣿⡁⠀⠀⣾⠄⠀⠀⠀⢰⡧
⠂⠀⠴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢺⣿⣿⣶⣤⣾⣿⠀⣘⣿⣿⣿⣶⠆⢸⣿⡇⠀⠀⠀⣿⣟
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣘⣿⣿⣿⡟⢻⣿⣿⣦⣽⣿⣿⣿⣿⡥⣿⡿⠿⠀⠀⣽⣿⣿⠇
⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣶⣤⣿⣿⣿⣷⡤⠀⠀⢰⡇
⠀⠀⠀⣤⣽⣿⣿⣿⡧⠀⠀⢽⣿⣿⣿⡿⢻⣿⣿⠦⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠠⢽⣿⣿⣿⣿⣿⣧⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠤⠼⣿⡟⠓⠀⠀⠙⢿⣿⣿⡃⠀⣿⡟⠃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠙⢿⣿⣿⣿⣿⣷⡖⣸⣿⣿⡅⠀⢀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠒⠚⣉⠁⠀⠀⢤⣿⣿⡟⠀⠀⠹⡏⠁⠀⠀⣤⣿⣿⡿⠁⢿⣿⣿⣏⠁⠀⠀⢤⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢁⣾⣇⠀⣸⣿⣟
⠀⠀⠀⠀⠠⠴⠒⠀⠀⠀⠀⠐⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠃⠀⠘⣿⣟⠀⠀⠀⠀⠐⢺⠻⣿⣿⠁⢻⣿⣿⡟⢻⣿⣽⣿⣧⣠⣿⣿⣿⣃⣾⠀⠀⣴
⠀⠀⠀⠀⠤⠦⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⢒⣿⠁⠀⢈⣿⣿⠀⠈⣿⠙⣿⣿⣿⠇⢸⣿⣿⣿⡆⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠉⣉⠅⠀⠀⠀⠙⠀⠀⠀⠋⠀⣿⣿⡿⠀⠈⣿⣿⣿⣷⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠈⣦⣀⣀⣤⣄⣀⣀⣠⠞⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣤⠶⠛⠉⠉⠀⠀⠀⠈⠉⠙⠳⢦⣄⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⣸⠏⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠢⠀⠀⠀⠀⠀⢺⡗⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢿⡒⠀⠀⠀⠀⠀⣀⣀⣐⡷⠤⠿⠤⣤⡀⠀⢀⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠸⣅⡀⠀⠁⠀⠀⠀⢀⡿⣠⡿⣅⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣽⠦⣄⠐⠒⠈⠉⠛⠒⠶⢖⣛⡿⠟⠉⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢀⠀⠉⠀⠀⠀⠒⠒⠛⠉⣁⠤⠤⢄⣀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢜⠁⢠⠀⠀⡈⠳⡄⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⡠⠷⠖⠶⢤⡀⠀⠀⠀⠀⠈⠉⠣⣀⣠⣇⣀⡟⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠉⠀⠀⠀⣀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⢈⡇
⣴⠚⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣤⠼⠦⡤⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⠈⢢⠱⡀
⣧⠀⠀⠘⢇⠀⠀⣀⡤⠶⢄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇⢠⠞⡠⠃
⠸⣦⡀⠀⢀⠏⡋⠀⣀⣠⠀⢧⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⠜⡆
⠀⠈⠻⠶⢥⡤⠷⠞⠋⠹⣆⠈⠳⠼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠰⠉⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣤⠼⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠓⢤⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⠀⠀⠉⠻⢶⣤⣄⣀⣀⣀⣀⣀⣀⣤⣴⠞⠉⠀⠀⢀⢹⡀⠀⠊⢈⡀⢀⠀⠀⠀⢀⡱⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠀⡀⠀⢠⡞⠁⠈⠉⠉⠉⠉⠉⠉⠀⠈⢷⡀⠀⢀⠈⡟⠀⢠⡀⠀⠉⠐⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠶⠟⠚⠁⠀⠀⠙⠢⢤⣀⣀⣀⣀⠤⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠞⠩⠖⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠓⠒⠒⠒⠒⠧⢄⡀
⠀⠀⠔⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢠⡶⠆⠀⠀⠀⢠⣦⡀⠈⠳⣄
⠀⢘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡞⢰
⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡈⠀⠀⡀⠀⠰⠀⡀⠀⠀⠂⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡄⡄
⠀⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢃⠀⠠⡷⠀⢀⠀⡿⠀⠀⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⢠⠁
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⠀⠀⠢⠀⠀⠠⠈⠀⠀⠀⠊⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠈
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠙⠤⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢠
⡴⠒⠶⡏⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠈⡿⠖⠲
⢹⠤⣠⡇⠀⢀⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⡄⠀⠀⣧⡠⢼
⠈⢦⣀⣑⣶⠋⢀⡤⢈⣉⠛⠒⠢⠤⢄⣀⣀⡀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣀⣀⠤⠤⠒⠚⢋⣉⠠⣄⠈⢲⣖⢁⣠⠊
⠀⠸⢄⣀⣨⡟⠉⠀⠀⠀⠉⠉⠒⠒⠒⠤⠤⠤⠭⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠥⠤⠤⠔⠒⠒⠊⠉⠁⠀⠀⠈⠙⣧⣀⣁⠼
⠀⠀⠀⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⡇
⠀⠀⠀⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⡀⠀⠀⠀⣀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢹⢹⡏⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⣤⣀⣀⡇⢸⢸⡇⣇⣀⣠⡤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠉⠁⢸⢸⡃⠋⠁⠀⠀⠀⠀⠀⠀⠉⠲⣄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣯⣿⣵⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣾⣿⣷⣶⣶⣷⣶

⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⡿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣠⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⡀
⣼⠟⢤⠀⠀⠀⠀⠀⣀⣀⣠⣴⣽⣿⣿⣿⠟⠻⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⡟⢠⣯⡄⠀⠀⠘⠛⠻⠿⠿⣧⣀⣿⣿⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢿⢿⣄
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣟⡉⢛⣉⡏⡀⣀⣸⣿⣿⡶⠿⠒
⠀⣾⡻⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣄⡄⠀⠀⠀⠀⠀⢸⡏⣿⣿⠟⢿⣿⠿⢿⣿⣿⣿⡀⢀⣠⣶⡀⣠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣄
⡟⠀⠙⠃⠀⠀⠀⠀⠀⢸⡿⢯⣿⣤⣀⣻⣆⣠⠿⣿⠟⣿⣯⣨⣿⣹⡟⣹⣿⣿⢿⣋⡀⣄⣽⢳⣻⡿⠁⠀⠀⠀⠀⣼⣇
⠅⠀⢰⡀⠀⠀⠀⠀⠀⠈⢄⣈⣭⣿⣿⣿⣣⡿⠷⣯⣟⣯⣅⠉⣻⣿⣾⣿⡿⠿⣫⡻⣿⠿⢻⣿⣼⣧⠀⠀⠀⠀⠀⠈⢿⣧⡀
⡟⠀⢺⡇⠀⠀⠀⠀⠀⠀⢘⣿⡿⡿⡼⡟⢶⣅⣄⣀⣿⣾⣿⣷⣿⣿⣿⣍⣴⣶⡿⠏⣥⣤⢿⣷⠖⢯⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠁⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢗⡋⢱⣐⣯⣶⣽⣿⠿⠿⣻⣿⣿⣭⣔⡻⠿⢿⣾⣷⣚⣺⣛⣸⣗⡋⣻⡖⠀⠀⠀⠀⠀⠀⠘⢿
⠀⣿⣿⡇⢠⡄⠀⠀⠀⠾⣷⡿⠷⠛⢫⣽⠋⠡⡶⡖⠀⠛⠿⣿⣿⣿⣥⣤⡀⠈⠉⢻⣿⣿⣿⣿⣵⣾⣷⠄⠀⠀⠀⠀⠀⠀⠈
⢸⣿⡿⣰⣿⡇⠀⠀⠀⠈⠛⠿⣿⠿⣿⣯⣤⣤⡍⢵⣶⣿⣿⣿⣿⣿⣿⡿⠟⠙⣛⠋⠛⠋⢻⣾⡿⠟⠛
⣿⣿⣧⣿⣿⠃⠀⠀⠀⠀⢀⠀⠈⠙⢿⣿⣿⣻⣶⣿⣿⣿⣿⡿⠋⠁⠀⣠⣤⣤⣤⡼⣿⣿⡫⢋⣤⣀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠐⢿⠇⡀⠀⢸⣿⢿⣽⣿⣿⣿⣿⢿⣿⣶⡶⣾⠟⡓⣿⣫⣿⣿⠋⢀⣈⠛⠃⠀⠀⠀⠀⠀⠀⢰⣾⡇
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⡀⠉⠀⠈⣿⠐⠙⣿⣥⣿⣇⣦⢻⠻⠐⡿⣾⣿⣧⣼⢿⣿⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⣈⠀⢿⣰⣿⣿⣿⣿⣿⣷⣼⠀⣰⣿⣿⣿⣿⠀⢘⣿⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣴⣦⡉⠙⣿⣿⣿⢿⣿⣿⠀⣿⣿⡿⠛⠃⠀⢘⣿⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡏⢀⣶⣦⠀⠀⠀⠀⠈⠀⠀⠻⠟⠁⠀⣿⣿⣿⠀⢻⣿⣶⣿⠏⠀⠀⡀⠀⢸⣿⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝
⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣿⣿⣿⠀⢸⡟⠟⠡⣿⣿⡟⠀⠀⠘⠁⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠛⠿⠿⠀⠘⠇⠀⠀⠉⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠢⢤⣈⠙⠫⢍⡉⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠫⠤⣀⡀⠀⠀⠀⠀⠙⠻⢔⠛⠲⠄⠀⠑⢌⣛⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠚⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠒⠒⢒⡒⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⣀⣀⣤⣤⣤⠄⠀⠀⡄⠀⠉⠉⠑⠲⠒⠀⠒⠄⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠉⠁⠐⢲⡆⠙⣄⠀⠠⡀⠀⢀⠀⣠⢃⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡣⠼⠀⠤⣀⢀⡀⢴⢅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⠐⣿⡳⠒⠒⠒⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠉⠉⠀⠨⡋⢻⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⠃⠀⠀⢇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠓⠢⡌⠘⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠚⠉⢀⡀⡇⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠉⡇⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢤⠄⠈⠲⠤⢀⡀⠀⠠⠔⠁⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠘⡤⠊⠉⢢⠀⡁⠀⠀⠀⠀⡠⢴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢹⠀⠀⠀⠀⠘⠀⠀⠹⣀⠔⠃⠀⢇⠀⢀⠔⣻⣶⡞⠛⣶⠞⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⡌⠀⠀⣀⣀⣨⡇⠀⠀⠙⠢⠀⠀⢹⣤⣿⣯⣮⠡⠟⠋⢁⢺⡟⡽⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢸⠃⠀⠀⠙⢢⣿⣧⣤⣤⠄⣀⣠⣤⣼⣋⡽⠁⠀⠀⠀⠀⣆⠀⠘⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⠀⠀⠀⠀⡸⠢⣀⠿⠿⣀⡸⠿⣇⣀⣿⠛⠒⢄⠀⠀⠀⠀⠑⢆⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣧⣀⠀⢀⠞⠀⠀⠈⢢⣘⠿⢇⣀⡽⡿⠃⠀⠀⠀⠑⣄⠀⢀⠄⢤⡠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⢳⠃⠀⠡⠉⣲⣦⠃⠀⠀⠙⢤⡜⠛⡷⠁⠀⠰⣀⣤⠚⠁⠀⠈⢀⠀⢧⠠⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠓⠒⠺⣤⠇⠑⠒⠉⡏⠀⠀⠀⠀⠈⢳⡜⠀⠀⠀⠀⢻⡛⠒⠒⠒⠂⠀⢤⠎⡀⠠⠧⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠈⢓⠒⢂⣷⣰⠉⣉⠉⣁⠉⠀⠁⠀⢀⢀⡁⣈⣀⣀⣀⣈⣉⣉⣉⣉⠉⣇⡼⢰⠗⠂⠤⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠈⠙⠧⠏⡠⠊⣀⠤⠤⠀⢐⡀⠐⠒⠒⠒⠒⠂⠠⠤⠤⠄⣀⠀⠀⠑⡄⠉⠉⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠸⣦⣄⣛⣓⠒⠒⠒⠒⠒⠐⠂⠀⠀⣈⣉⣠⣼⠂⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠘⠂⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡞⠛⢻⡟⠛⣿⠾⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡟⠁⠸⡇⠀⢸⡇⠀⡿⠀⠀⡼⠛⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣟⠈⢿⡄⠀⣷⠀⢸⡇⢀⡇⠀⣼⠁⠀⢀⡿⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⢶⣟⠀⢻⣆⠈⣷⠀⢻⡀⢸⣇⢸⡇⢠⡟⠀⢠⡞⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠟⠉⠀⠀⢻⣆⠀⠻⣦⣹⡷⠾⠛⠟⠙⠛⠻⠾⢷⣤⣿⠀⣠⡾⠁⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣶⠶⣿⠀⠀⠀⠀⠀⠀⠹⢷⣤⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢿⣄⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠛⣿⠉⢹⡇⠀⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠁
⠀⠀⠀⠀⠀⠀⣠⣼⡏⠀⢿⠀⢸⡀⢸⡇⠀⢹⠀⠀⣷⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⢀⣾⠃⠈⢷⡀⠘⣇⠈⣇⠀⣧⠀⣸⡇⢠⣿⣆⣀⣤⣾⠟⠁
⠀⠀⠀⢰⡟⠙⢳⡄⠈⢷⡀⢹⣄⣿⡶⠟⠿⠛⠛⠛⠉⠙⠛⠉
⠀⠀⢀⡾⢷⣄⠀⠙⢦⣈⣿⠛⠉
⠀⠀⣸⣧⡀⠙⠳⣤⣌⡿⠁
⠀⠀⣿⠁⠙⠓⠶⢤⡿
⠀⢠⡿⠛⠛⠲⠶⠤⣟
⠀⠸⣷⣤⣤⡤⠤⠤⣿⡀
⠀⠀⣿⠁⠀⣀⣤⠴⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠻⣷⡀
⠀⠀⠻⣿⠟⠉⢀⣠⠶⠻⣦⡀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠻⣇⠀⢸⣷
⠀⠀⠈⣿⣀⣰⠟⠁⢀⡴⠛⣿⠿⣷⠿⠷⡾⠋⢹⡟⠉⠻⡏⠉⠙⡷⠟⠷⣶⠶⣶⣤⣶⣦⣴⠶⣶⠟⠛⣧⠀⠙⣆⠠⣿
⠀⠀⠀⠈⢻⣿⠀⣴⠏⠀⣰⠇⠀⡟⠀⢰⡇⠀⠸⡇⠀⠀⣧⠀⢰⡇⠀⠀⡿⠀⠀⡏⠀⢸⡇⠀⠘⡆⠀⠈⣇⠀⠈⣿⡟
⠀⠀⠀⠀⠀⠻⣷⣟⠠⢠⡟⠀⠀⡇⠀⠈⣇⠀⠀⣷⠀⠀⣿⠀⣸⠀⠀⢀⡇⠀⠀⡇⠀⠸⡇⠀⠀⣷⠀⠀⢸⣄⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣾⣇⠀⢀⣧⠀⠀⣻⣦⣤⣿⣷⣶⣿⣤⣿⣅⣀⣾⠃⠀⢰⡇⠀⠀⣇⠀⠀⣼⠀⠀⣸⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠟⠿⠟⠋⠉⠉⠁⠀⠀⠀⠈⠁⠉⠙⠙⠻⠶⠾⠷⣦⣶⠿⢶⡶⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⡻⣿⣿⣿⣿⣿⣿⣿⣿⢟⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⣠⣭⣛⣛⡛⢛⣯⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⡍⣽⣾⣿⣿⣿⣿⣿⣷⣭⢩⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⠃⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⠿⣿⠿⣿⣿⣿⠀⠀⣷⠀⣹⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣵⣶⣭⣿⡿⠃⠀⣴⠋⣾⠁⢰⠋⠀⣾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣛⣛⣛⠋⠀⠀⠀⣘⣁⠘⠃⠘⢃⣴⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⢤⣾⣿⣿⣿⠷⣀⣀⣾⡿⣫⣶⣿⣟⣮⢁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣝⡻⡿⢟⣺⣿⣿⣟⣱⣿⣾⣿⣿⣟⣸⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣶⣶⣶⡄⠘⠛⠀⣠⣶⣶⣿⣷⣾⣷⢦⣶⠆⠈⠙⠛⠷⠶⠄
⠀⠀⠀⠀⢸⡿⠊⠉⠉⠙⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⣦⠾⠿⠛⠃⠀⠀⠀⠀⠐⠓
⠀⠀⠀⠀⣶⡿⠀⠀⠀⢀⣾⠛⠋⠻⣿⣿⣤⣄⣀⣀⡰⠖⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣤⣶⣤⣴⣿⠋⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⠀⠀⠈⠻⣿⣶⣷⡆
⠀⠀⠀⠀⣻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀⠀⠀⠀⠀⠻⡿⠁⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⣠⣤
⠀⠀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿
⠀⠀⠀⠀⠸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠤⢀⡀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠲⣦⠀⠀⠀⠀⠸⠆⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠋⠀⠀⠀⠋

⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠧⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⠛⠛⠀⠂⠙⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⠀⠾⠐⠀⠆⠀⠀⠀⡠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠓⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⢸⣁⡤⠴⢦⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠫⢠⣶⢨⣴⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⡈⠁⠙⠉⠀⠀⠀⢸⠃
⠀⠀⠀⠀⢀⡴⠋⣠⠇⠀⠀⣠⠀⠀⣸
⠀⣀⡤⠞⢉⣠⠞⠁⣀⣠⠞⣽⠀⠀⡿
⣿⣁⣤⡶⠛⣿⠀⠈⣍⣠⣴⡏⠀⢠⡇
⠈⠉⠁⠀⠀⡏⠀⢀⠸⠛⣿⠁⠀⢸⠃
⠀⠀⠀⠀⠀⡇⠀⢣⡉⠋⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠟⠛⠛⠳⢦⣤⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⢸⠃⠉⠂⠉⠑⠒⠋⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣧
⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠐⢄⠀⠈⣧⠀⠀⣰⠂⡇⠀⠀⠀⡼⠁⣿⡆
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢳⣀⡿⠟⠛⠛⢾⣅⠀⠀⠊⠠⠊⠀⢿⡀
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠛⠶⣄
⠀⠀⠀⠀⣿⠉⠒⠤⠤⠤⠤⠴⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠹⣷⠐⠂⠁⠀⠀⣨⠿⢦⣄⣀⣀⣤⠾⠫⣄⠀⠀⠀⠀⠘
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢠⡾⠋⠲⣄⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠚⠁⠀⢀⠈⠉⠉⠀⠀⠀⠘⣆⠀⠀⠀⢠
⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⣀⡠⠛⣷⣤⣀⣠⣤⡾⠿⡁⠀⠀⠈⢷⡀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⡏⠀⠀⠀⢠⠀⠀⠀⢸⡆⠀⣠⣾
⠀⠀⠀⠀⠀⢿⡍⠙⠛⠉⠁⠀⠀⠀⠉⠉⠉⠉⠑⠀⠀⠀⠀⠀⠈⣷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⣀⡼⠁⠀⠀⠀⢸⡄⠀⠀⢸⣧⣾⠟⠁
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣤⣄⣀⣀⣀⣼⣥⣴⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⢀⡼⢀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢶⣾⣥⣾⣴⠶⠶⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣶⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⢛⡻⢿⣿⠇⠀⠀⠀⠘⣿⣿⠿⠿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣷⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠛⠀⠀⣄⣠⡄⠀⠈⠻⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣉⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠉⠉⠐⠢⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⣄⡠⠊⠁


⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⠶⠶⠶⠶⢶⣶⠶⠶⣶⠶⠶⠶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠉⠙⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⠤⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⡁⠀⠀⠀⣷⣄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣟⡛⠷⣤⣴⠏⠉⠛⠛⠁⣀⣀⡠⠤⢤⠤⠤⠤⡤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣿⢏⡋⠀⢴⠆⠀⢰⣺⡆⠀⡠⢒⡩⠷⣒⠰⠟⣹⣿⣉⣝⣽⣶⣖⠮⢽⡓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡿⠋⠀⠀⠀⠀⢒⡎⢼⠃⠀⠹⢬⣓⡊⠭⠉⣿⣧⣍⣹⣿⣦⡤⠿⠟⣚⡧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠓⠶⠦⠦⢸⡇⠀⠀⠀⠈⠉⠙⠛⣿⠒⠒⣒⣲⣶⠿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡷⠶⣒⡀⠀⢒⢒⠿⢥⣀⣀⠀⠀⣀⣠⠖⠋⢉⡟⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡴⠛⠁⠀⠈⠓⢛⢄⡙⠊⣥⣄⠈⠻⣏⠉⠉⠀⠀⣠⠞
⠀⠀⠀⠀⠀⢠⡟⠲⣄⣴⠋⠀⠀⣠⠆⣀⣀⣬⠭⠥⠴⠾⠷⠶⠦⢼⣷⣀⣠⠞⠁
⠀⠀⠀⠀⠀⢸⣧⣤⣼⡇⠀⠀⣸⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁
⠀⠀⠀⠀⢶⡛⠉⣠⣿⠀⠀⢠⡟⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⠳⠞⠁⢸⡄⠀⢸⡇⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⡇⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠹⣦⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣼⡏⠀⠀⠸⡷⠶⣤⣤⣤⣤⠶⣶⠶⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⣰⡏⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣰⣿⣇⣠⣴⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠛⠂

⠀⠀⡀
⠀⡀⡇⠀⠀⡀⣼⡀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐
⢰⡇⣿⣿⠀⣧⣿⡇⢰⢾⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠛⠿⣿⣀⣿⣿⡇⣼⣾⡆⣷⢀⡇⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢿⡧⠇⢄⡀
⠀⠀⠀⠀⠓⠉⠛⠓⠿⠿⢯⣿⣤⣧⣾⣠⡆⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠇⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠇⠀⠀⢳⠀⢸⠄⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠑⠄⠀⡬⡆⢀⠂⢠⠈
⠀⠀⠆⠠⠒⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⢀⠀⠀⠒⠣⣀⡤⡀⣸⣭⠆⠠
⠐⡆⢰⣛⣒⡀⣤⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢘⠌⢨⠅⣀⠹⣷⣥⣕⠂⢓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁⣂⠠⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠵⢻⠆⠁⣸⠇⠀⠀⠀⠀⠀⠀⡀⡀⢀⣀⣬⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡫⠉⢁⡭⡝⡆⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢈⣿⠟⠉⠋⠙⠻⣾⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⡀⠀⠀⠀⣨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠒⠲⢤⣾⠃⠀⠀⠀⠀⠀⠀⠀⣾⡅⠀⠰⡀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣩⡄⣀⠲⢠⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠭⠖⠁⠀⠀⠀⠀⠰⡞⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣦⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠰⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⣠⣾⣿⣴⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⡁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠄⠐⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠾⠛⣻⣿⣿⡿⠿⠋⠋⠀⠀⠀⠀⢻⡉⠀⠀⠀⠀⠀⢿⣹⣇⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠱⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⠀⡀⠀⠢⡈⠁⠀⢢⠂⠀⠀⠀⠀⠀⢿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡰⣱⡀⠀⠀⠀⠀⠀⢸⠟⢻⠷⡀⠀⠑⠀⠀⠀⠈⠄⠊⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡅⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠤⠂⠀⠠⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠈⠒⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠜⠃⢶⠦⢄⠀⠁
⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠈⠉⠉⠉⠁⢹⣿⣿⠄⠀⠀⠀⠀⠸⣴⡢⢀⣼⡇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⢀⡀⠀⠀⠀⢸⣿⣿⠀⠀⠘⣅⠁⠃⠘⡆⠀⠀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣛⣿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠀⣿⠎⠈⡀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠘⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠨⠀⠀⠀⠀⠀⠒⠐⠀⠀⠐⠒⠒⠒⠒⠒⠒⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⡠⠐⢄⠀⠀⠸⣧
⢀⣶⠟⠛⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⠊⠀⠀⠀⠆⠀⠀⣿
⣾⠃⠀⠀⡀⢀⠈⠻⢷⡄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠶⠶⢶⠶⠶⠿⢤⣤⣁⠀⠀⠀⠀⢠⠀⠀⣿
⣿⠀⠀⢰⠀⠀⠑⢄⠈⠻⣦⡀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠘⠀⠀⣿
⣿⡀⠀⢸⠀⠀⠀⠀⠑⢀⣸⠟⠋⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⢰⡟
⢸⡇⠀⠈⡀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠻⠿⠦⠀⠀⠘⣦⣾⠃
⠈⣿⡀⠀⢡⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠀⡀⠀⡀⠀⠀⠈⢿⡀
⠀⠸⣧⠀⢀⡾⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠔⠁⠀⠀⠀⣠⣖⡊⠙⠓⢴⠁⠀⠀⠀⠘⣷⡀
⠀⠀⢻⡆⢸⠁⠀⢠⡿⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣠⡆⠀⢇⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢿⣾⠀⠀⠈⠀⠀⢀⣱⢄⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⢿⣿⠿⠃⢀⡎⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠈⣿⠀⠀⠀⠐⠢⡞⣿⣿⣄⣠⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠠⠴⠊⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⡇⢿⣿⣿⡿⠃⢀⠇⠀⠀⠀⣀⡠⣤⣄⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠘⢦⣈⣁⣀⡠⠊⠀⠀⣀⠾⣷⣶⣿⠏⠀⠀⢠⠀⠀⠉⠑⠢⡀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠈⣧⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠘⢤⡀⢀⡴⠃⠈⠉⠉⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠠⠂⠀⠀⣀⡤⠞⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣤⣄⣀⣁⡀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠶⠚⠋⠙⡄⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⡏⡙⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠸⣧⣀⡀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⡏⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⠟⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣇⣴⠟⠁⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡟⠋⠁⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠛⠒⠒⣾⣤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢰⣃⣀⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⡀⠀⠀⣰⢋⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣠⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⣿⣦⣤⣅⣀⣠⣤⣇⠀⠀⡄⠀⠠⠀⢀⣇⣀⣀⣤⣴⠾⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣛⣿⣶⣷⣶⣿⣾⣟⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠒⠚⠲⠶⡶⠦⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡾⠟⠁⠐⢀⠲⣄⠀⣀⠀⢢⠀⠦⣀⠈⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠡⣀⣀⣤⠶⠿⠋⠉⠉⠁⠀⠉⡉⣧⣀⡈⠀⢀⠀⢤⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⣟⣿⢻⠊⠀⠀⠀⠀⣀⡀⠀⠀⠀⢋⣯⣷⣄⣼⣆⣠⣏⣶⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠰⢿⡇⠈⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⢹⢯⣿⢿⣿⣿⣿⡿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢻⣿⡄⠢⡘⠷⠄⠂⡀⠀⠀⠙⠛⠛⠁⠀⠀⢀⡜⢣⣿⣾⣿⣿⣏⡀⠙⢘⠟⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡘⡏⣷⣄⠐⠟⢪⣟⡺⠷⠦⠀⠀⢀⣀⠠⣰⡬⠂⣉⣭⣿⡿⠋⣁⠉⢢⡅⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣹⢼⡉⠃⢠⠠⣙⠻⠳⠨⠄⠑⠙⡲⠃⠀⣾⢿⣿⣽⡟⠁⣾⣾⣿⡆⢷⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⡞⣦⢻⡦⣤⡄⣲⠶⠒⠂⠀⡂⣀⣀⣐⣀⠀⠀⣿⡿⠁⢸⣿⣿⣿⡇⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠻⣧⢸⡇⢻⣶⠦⠦⠘⠃⢈⠠⣋⠥⠤⠦⠠⢝⣢⡈⣟⠀⡼⠉⣿⠃⡧⣿⣻⠜⢿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣿⡆⢁⢸⣿⢷⡶⣴⢶⣸⡄⡇⠀⣴⣶⣤⡄⠈⠉⠺⢂⣘⡀⠋⠓⡿⠉⢋⡡⡞
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣿⣿⡇⠸⠈⣿⡓⠐⠁⠈⠁⡄⠁⢰⠏⠀⣙⠛⢱⢦⣄⠈⠁⠋⠓⠲⠒⠉⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⣿⣟⠚⠂⢴⣂⡰⢠⣿⢠⣿⣿⣿⣮⣰⣮⡵⢖⣦⣖⢴⣤⣜⣩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⣿⡉⢎⠙⢰⢧⠣⠈⢿⣿⠉⠉⠁⢹⣿⠟⢷⣾⢿⠿⣮⡷⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⢀⣼⣷⣮⣄⢻⡜⢮⢡⠈⣿⠀⠀⠀⢸⡏⠀⢸⣿⠀⠀⢹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣼⠻⣦⠻⠀⠺⠀⢽⣶⣴⣶⣿⣧⣤⣾⣿⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⠀⢿⠀⠀⠻⠀⣿⡟⠉⠀⣸⣿⣡⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠶⠴⢤⡽⠿⠾⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠄⠀⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⢻⡋⠛⣛⣛⣒⡢⢤⣀
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⡀
⠀⠀⠀⠀⣜⣀⠊⢗⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢌⡱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢈⣾⣹⣿⣶⣤⣁⢋⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠇⠈⠑⠢⡤⠤⠀⢀
⠀⠀⣤⠒⠨⡙⠻⢾⣿⢏⠂⡀⢀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠈⠑⢂⠀⠀⣀⢀⠀⢸⡾⠀⠀⠀⠠⠀⠀⠀⣸⡆
⠀⠜⡈⠀⠴⣠⢮⠕⢀⠀⠉⣸⠩⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⣑⠈⢸⡇⠀⠀⠀⡄⠀⠀⢠⣿⠁
⠀⠑⠚⠵⣢⠄⡉⢀⠂⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠛⠉⠙⠛⠓⠳⠶⣾⡇
⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⠀⠀⠀⠀⠴⠶⡈⢦⠀⠀⠠⠀⢀⡠⠊⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣒⣒⡠⡞⠊⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠸⠈⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡴⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣆⣾⣀⣸⣆⣆⣀⣀⣀⣀⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣍⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣟⣿⣿⣿⣿⡟⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣯⣿⣿⣧⣿⡯⢿⣿⣿⢿⣿⣿⣻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢿⣷⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣾⣿⣿⣻⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣍⠿⢧⣿⣿⣟⣻⣿⣿⣿⣿⣿⡾⣿⣽⡷⣿⣿⣟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣽⣿⣿⣿⣿⣿⣿⣻⡗⣾⣟⣽⣿⡿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⠁⢿⣻⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⠅⣼⣿⣹⣿⣿⣿⣿⣟⣽⣟⣷⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢒⠳⣿⣬⡿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠿⣯⣿⣟⣽⣿⣿⣿⣿⣿⣿⠿⣿⣿⣻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣄⡝⠺⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣴⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣧⡭⠙⠛⠻⠿⣿⣿⣿⣿⣷⣿⣟⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⡀⣐⠠⠖⣄⢮⣝⡉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣿⣿⣶⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⡖⣂⠾⣿⣟⣹⣷⣿⣿⣿⣿⣿⣽⣿⣿⣿⣝⣻⣿⣟⣿⣿⡿⣿⣿⡿⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢖⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣤⣦⣦⣾⣿⣥⣭⣤⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠉⠙⠋⠙⠈⠋⠋⠉⠉⠉⠉⠉⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⣿⢻⡟⡿⢿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⢻⣇⣼⣿⣷⣷⣾⣿⣷⣾⣀⡞⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⡶⠟⣿⣁⣿⣤⣾⣿⣿⠟⠟⠛⠉⠉⠛⢿⣿⣴⢋⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣹⡷⢦⣤⣤⡤⣤⣤⣶⡾⣿⣁⣼⣷⣾⣿⡿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣟⡡⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣧⣿⣧⣼⣅⣿⣀⣿⣤⣿⣫⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣤⣖⣫⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠧⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⠿⠴⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⠁⠀⠀⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡖⢒⣶⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢽⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⢿⡳⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⣿⢿⣷⣽⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⢿⣿⣶⣶⢶⡶⣿⣿⣿⢿⡿⡿⡟⢻⢹⡜⣯⣷⣷⣼⣷⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⣿⣏⢻⢹⣿⢸⣀⣿⣿⣾⣷⣿⣷⣿⣼⣶⣷⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⢿⣿⣶⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢻⣿⣿⣷⣟⣽⣿⣦
⠀⠀⠀⠀⠀⣰⣿⢿⣛⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⣼⣿⣟⣲⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣧⣿⣷⣼⠿⠋⠉⠉⠻⣿⣿⣿⣿⣷
⠀⠀⠀⢰⣿⣥⣭⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠻⣧⣼⣿⡟⠁⠀⠀⠀⠀⠀⠨⣿⣷⣤⣿⡀
⠀⠀⠀⣾⣿⡷⣺⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣙⣶⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢶⣿⡇
⠀⠀⠀⣿⣿⣭⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⣌⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣛⢻⣿⡇
⠀⠀⠀⣿⣿⠖⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡻⣿⣿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠻⣿⣿⡿
⠀⠀⠀⣿⣷⢟⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢻⣿⣿⣙⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣉⣿⣿⡟
⠀⠀⠀⢻⣿⢋⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⢹⣿⡿⣯⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢮⣽⣿⠟
⠀⠀⠀⠘⣿⣟⣠⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢁⣿⣿⣟⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣛⣾⣿⠏
⠀⠀⠀⠀⠘⣿⣯⡼⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡞⣻⣼⣿⣿⣿⣹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠻⣷⣿⣭⡿⢿⣿⣶⣤⣀⣀⣀⣀⣀⣀⡤⢶⣟⣹⣧⣼⣿⡿⢿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣯⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣿⣯⣹⣟⣻⣿⠻⣿⡿⢿⣿⣿⣿⠿⣿⣯⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠷⠾⠿⠾⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣷⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣮⣩⡄⠀⣥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⢳⠀⠀⠠⠀⡀⠀⠀⣤⣀⠈⢸⠘⢻⠛⠟⠛
⠀⠠⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠐⠀⠀⠱⡄⢸⣿⡿⠟⢻⡆⠖
⢲⣾⣻⠯⢀⣀⡀⢀⣄⠀⠀⢀⠄⠂⠀⢠⠀⠀⠀⠐⡄⢠⡈⠑⠄⣀⠀⢹⢨⣤⣤⡈⢻⠐⣿⣷⣦
⠘⡇⢨⠀⠫⠀⠀⢹⣿⠀⠀⣠⠀⠀⠴⠋⠀⣾⠀⠀⡅⠀⠁⠀⠀⠻⣤⡀⢢⠀⠙⠑⢾⣠⠐⠈⠁
⠠⠶⠾⠶⠴⣤⡄⠉⡉⠀⠘⣿⠗⠀⠈⠀⣤⣤⣤⣦⡥⣤⣤⣤⣥⣴⣴⣶⣶⣷⣶⣶⣼⡷⠶⠛⢻⣯
⢰⣦⢞⣀⣠⡀⡀⣀⣀⣒⣸⣿⣧⣤⣤⡤⠬⣿⠭⢭⠽⠟⢻⣿⣿⣿⣻⣿⣿⣿⡟⡙⣹⡄⢠⡀⣾⣿
⣀⡶⢚⣻⢲⣿⠌⣱⣿⠟⣿⡿⠿⠿⠃⠀⠀⠠⠴⠫⣷⣖⠶⢿⢿⣿⣽⠟⠉⠈⢰⡟⣿⡥⣿⣄⣿⣿⠄
⠡⠺⠯⠖⠁⠀⠀⠿⠷⠏⠁⠀⠐⠂⢚⡁⢀⣉⡉⠉⡉⠙⠛⠿⠓⡬⣁⠉⠃⠀⣷⡀⣿⣗⠥⣸⣿⣿⣦
⠀⠀⢐⣒⣀⠀⠀⠀⠀⠀⠒⠀⠠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠸⠦⠉⠀⠀⢠⣿⠀⣼⠁⠀⣿⣿⣿⣧
⢴⣾⠏⣽⡿⢿⡶⣴⣏⣿⠦⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⢟⡃⢹⠅⠈⣻⡿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⠄⢀⣠⠎⠉⢷⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡰⡞⠈⠀⠀⠀⢀⠈⠵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢧⢱⠀⠒⠂⡀⠈⠀⢀⠉⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡀⠈⠓⠂⠀⠀⠀⡀⠀⠉⠀⠙⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠐⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⣀⣹⠀⠀⠀⠀⠀⡀⠤⠀⡂⠱⠌⡰
⠀⠀⠀⠀⢀⠔⠊⠒⠒⠀⢄⡀⠀⠰⠈⠈⠉⠀⠀⠀⠁⠀⠈⠈⠀⠉⠁⠠⠀⠀⠀⠀⠘⠰⠈
⠀⠀⠀⠔⠃⠈⠀⠀⠀⢀⠀⠀⠁⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡄⣆
⠀⠀⡎⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠡⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡔⠈⠠⠀⠀⠀⠑⢢
⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠨⠀⢀⡴⠒⠒⠒⠲⢄⡀⢠⠀⢸⠀⠀⠈⠀⠀⠀⠂⠀⡇
⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢸⡧⠀⠀⣿⠆⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⡀⠀⣤⠀⠀⠀⠀⠹⠃⠀⡇⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠙⡒⠒⠠⠤⠤⠤⠴⢤⠂
⠀⠀⠀⢱⠀⠉⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠈⠲⠤⠤⠤⠴⠚⢡⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠤⠄⠒⠒⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣴⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣾⣷⣤⣤⣤
⣠⡄⠈⠃⠉⠘⠁⣦⡄⠀⠀⠀⠀⠀⠀⠀⡸⠏⠀⠻⠙⠉⢧⠀⠀⠀⠀⠀⠀⠀⠸⢉⣤⡀⢀⣤⡙⠃⠀⠀⠀⠀⠀⠀⢻⡿⠋⠁⠀⠀⠈⠻⢿⣤
⢸⣏⠁⢐⣀⡀⢈⣹⠁⠀⠀⠀⠀⠀⠀⠠⣯⣁⣤⣤⣤⣄⣽⡆⠀⠀⠀⠀⠀⠀⠇⣾⠟⠃⠈⠻⣿⠸⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⣀⣀⠀⠀⢸⡟
⡀⠲⠂⠀⠉⠁⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣿⣿⣾⠟⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠙⠛⠀⡠⠃⠀⠀⠀⠀⠀⠰⣿⣷⣀⠀⠈⠉⠀⣠⣾⠿
⢛⠀⣘⠀⠐⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⡿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣷⣶⣶⣿⠛⠃
⠘⣴⡇⢠⠄⡤⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⠭⢭⢭⠽⡄⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⣶⢰⡆⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⠠⠃
⠈⠛⠆⣸⡀⣇⠰⠛⠃⠀⠀⠀⠀⠀⠀⠀⣾⢉⣻⣛⣼⡉⠷⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⢿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⢿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢶⣆⢀⣶⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠈⠁⠀⠉⠙⢿⠟⠀⠀⠀⠀⠀⢀⣠⣄⠀⣀⡀
⠀⢀⠀⠐⠒⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣠⣤⣤⣤⣀⣈⠀⠀⠀⠀⠀⢠⠋⣸⣾⠿⠿⠿⣷⣄
⠣⠁⠀⠀⠀⠀⠀⠡⠇⠀⠀⠀⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢰⣿⢻⡟⠁⠠⠀⠀⠀⢻⡛⣷
⠠⠀⠀⢿⣿⠿⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⢩⠉⠀⠀⠀⠀⠀⠀⠀⠹⣏⠳⢄⠀⠀⠀⡀⠈⢛⡯
⠀⠑⠤⠀⣀⠠⡔⠁⠀⠀⠀⠀⠀⠸⢿⣿⣷⣄⠀⠀⠀⣠⣾⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠐⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡏⠉⠹⣷⣄⢿⣞
⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠈⣬⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⢀⣿⣜⡞
⢠⠂⠀⠀⠀⠀⠀⡓⡄⠀⠀⠀⠀⠀⠀⠀⢸⡿⢃⣴⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢘⠀⡄⣤⢚⠎⠀⠀⠀⠀⠀⠀⠐⢿⣿⣷⣤⣾⣿⣿⣿
⠈⠉⠺⠭⠶⠭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠖⠲⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠓⠻⠆⠀⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⣀⣀⣀⣀⡀⣀⡀⢀⣀⣀⣀⣀⣀⣀⡀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⢀⡀⡀⣀⣀⡀⢀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠠⣤⣼⣢⠞⠀⠀⠘⢦⣸⠃⠀⠀⠀⠹⡄⠀⡄⠀⣠⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣇⣀⣀⣻⡀⠈⢿⡀⠀⢀⣠⡖⢷⡄⢻⠞⠃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢦⣀⠈⡏⠉⣩⠍⠻⣄⠀⣷⠞⠋⠳⢤⠀⢳⣈⡆⠀⠀⢸⣀⣠⠀⠀⠠⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠓⣷⠚⠁⠀⠀⠙⢾⡇⠀⡀⠀⣄⠀⠈⣿⣀⣤⠶⠛⠙⠀⠁⠀⠀⢀⡤⠚⠻⣝⢩⠻⡏⣏⡙⠟⢦⣀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢼⠄⠀⠀⠀⠀⣿⡤⠞⠁⠀⠘⣇⣸⠋⠁⠖⡄⠀⡃⠀⠀⠀⡴⢋⣀⣀⠀⠈⢻⣴⣬⣤⣧⣷⣧⣽⣦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣸⣇⣤⣦⣶⣠⣏⣀⣀⣠⣶⠀⣸⠏⠀⡄⠡⣧⣤⢶⡤⣄⣼⡇⣯⢉⢹⡇⠀⠀⡇⣶⢶⠲⣆⠀⠀⣷⣤⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣡⣬⣤⣤⣤⣤⣤⣥⣄⣉⣉⠉⠉⠛⠛⠛⠛⠛⢳⠲⠶⠷⠦⠼⣯⣍⣇⣹⡈⠀⡇⠀⠀⡇⠿⠾⠴⠟⠀⠀⣿⣉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠛⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠙⢓⠲⠷⠦⣤⣤⣀⡀⠀⣻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡶⠶⠶⠶⠴⠦⠶⠤⠤⣤⣤⣄⣤⣀⣀⡀⠠⢀⠀⠀⠈⠉⠙⠻⢦⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠶⠤⣤⣄⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡤⠤⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⡿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠳⣌⠠⠀⠀⠀⢀⠀⠈⠉⠉⠉⠙⠛⡓⠲⠦⠤⢤⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⢀⡞⠳⣬⡛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢶⣶⣶⠓⠚⡛⠓⠓⠺⠶⡶⢴⣤⣄⡀⠀⢂⠌⡃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⡀⠃⠀⢸⡳⣄⡞⣉⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡌⠁⣀⡀⠁⡀⢀⠈⡀⣵⠟⢳⡄⢍⡓⠦⣄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣞⣯⣹⢦⡀⠈⢇⣸⢉⡽⠋⠀⠀⢀⣀⣠⣤⣤⣤⡄⠀⠠⠀⠙⠲⢤⣄⠠⠀⣀⠀⣀⠙⢳⡟⠂⠠⡸⠁⢨⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⡈⢹⡃⡴⠛⣿⣾⡟⣭⡄⢀⡤⢾⡏⠸⣇⡼⠿⡿⠁⠀⠀⠁⠀⢰⡟⠻⡟⢦⣠⣄⢀⡀⣹⡏⣈⡴⢦⣴⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠉⠛⣟⠁⡴⢻⠍⣿⡿⣠⢾⡇⢸⣧⣞⡉⣩⠟⠁⠀⠀⠀⠀⠀⠈⡿⠛⠁⠈⣧⡶⣄⣤⣼⣏⣉⠷⣴⠛⠖⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡙⠲⢿⠞⠁⡼⠀⢸⣠⢿⣠⠿⢯⣤⡤⠛⠁⠀⠄⠀⠀⡀⠀⠀⢰⣇⣤⡀⠀⢸⣿⠉⡄⢼⡇⢉⣨⣏⢉⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠙⠲⢬⣇⠼⡁⠘⢿⡿⠿⠛⠛⠉⠁⠀⠀⢐⠀⠀⣻⡟⠛⢦⠀⣸⢿⣬⡿⠀⢸⣿⠤⠴⢾⡇⣤⠼⣯⢠⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢴⣤⣿⣾⠷⣦⣄⣻⣠⣤⢀⣄⡀⠂⠈⡆⠈⠳⢹⣷⣊⡼⠀⢻⠀⣿⠀⠀⢸⢿⠄⠰⢸⡧⠄⠄⡧⠤⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠈⠹⡇⠀⠀⠉⠻⣏⣿⠟⠋⢠⠀⢀⡗⠀⢠⠏⠠⢻⠀⠀⢸⠀⢸⠀⠀⢸⢸⠖⠒⢺⡗⠶⠒⡷⠲⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢀⠲⡄⠀⠀⡠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⠢⡜⢱⠀⠣⠤⠧⣤⠎⠙⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⣧⠈⢧⠀⠀⡴⠙⢄⣀⡎⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢫⢣⡀⠑⢌⡲⢤⣀⡼⠀⠀⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠳⣝⠢⢄⣉⠑⠚⢒⣚⡩⠥⢺⡤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣀⣠⣀⠀⠀⠀⠀⠉⠒⠂⠬⠝⠓⠚⠉⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⢤⣀⠀⠀⠀⠀⡇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠼⠶⠠⠤⡀⠀⠀⠀⠑⠐⠷⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⡇⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠈⠳⠀⠀⣀⠄⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⡼⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡠⢾⠀⡰⠃
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡷⡖⡏⠀⢸⠀⡧⣂⠢⣄
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⣇⠀⢸⠀⠳⠽⠃⠈⡆
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠉⠒⠚⠀⠀⠘⡆⠈⢧⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠵⢖⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠲⠤⠄⠀⠀⠀⢸⠤⢄⣀⣋⣻⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⣠⡃⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡦⠤⠤⠖⠚⡗⠒⢶⠒⠋⠀⠐⢲⡏⠣⣌⡉⠓⠚⠉⢉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⡸⠁⠀⢸⡀⠀⠀⢀⡜⠙⢦⣀⠈⠉⠉⣉⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠙⠲⠖⠋⠀⠀⠀⠈⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⢶⡏⠉⠙⢿⠛⠒⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠙⢦⠀⠀⢻⠀⠀⢸⠀⠀⠈⡏⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠉⠳⣄⠀⢈⠇⠀⠘⠀⠀⠘⠀⠀⡼⠁⢀⡟⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⢦⡀⠀⢸⣤⠴⠚⠋⠉⠉⠉⠉⠛⠲⣄⠠⠊⠀⠀⣸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⣄⡀⠙⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⡠⠖⠁⠈⣧
⠀⠀⠀⠀⠀⠀⠀⣠⠾⣅⠀⠀⢹⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⣀⠞⠙⣧
⠀⠀⠀⢀⣀⡤⠾⢧⣄⠀⠑⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⠁⠀⢀⡞⢧⡀
⣴⠚⠉⠉⠙⢳⡀⠀⠘⣆⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠖⠋⠀⢰⠟⠳⣤⣤⡀
⢻⡀⠉⠀⠀⠀⡷⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠴⠋⠀⢠⠏⠀⠙
⠀⠉⠓⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣔⣁⣠⡤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠖⠚⢛⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⡠⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣾⡿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⠒⠉⣀⣀⣀⣀⣀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢀⣴⣿⣿⡿⠋⢀⣈⣭⣿⣿⠟⠁⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠻⣶⣿⣿⡿⠿⠟⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠴⣾⣿⠿⣁⣀⣼⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣉⣻⣿⡟⠁⣬⣂⡀⣩⣿⣿⣿⠟⠁⠀⠀⠀⠈⣩⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⠛⣉⠉⠛⠻⠃⠀⢈⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠂⠀⠀⠀⠀⣠⣿⣿⣿⣿⣆⠀⠀⠀⠀⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⢹⣿⣿⡇⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣀⠀⠀⠀⠀⠀⠘⠛⠛⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⣿⣿⠇⢸⣆⠋⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣌⠁⠀⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣈⠙⠦⠀⠿⠿⠏⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⣿⣷⡆⠀⠀⠀⠀⠀⣹⡆⢠⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀⢻⣿⣷⠆⠀⠂⠀⠰⡿⠇⠈⠹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠻⡿⠟⠀⠀⠀⣉⣡⡴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠋⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣰⣿⣿⠁⠀⢀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⢉⣠⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⣰⠿⠚⠿⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡄⠂

⠈⠀⠀⠀⣹⡀⠀⠀⠀⣷⠀⠀⣴⣀⣿⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣄⣠⠶⠛⠉⠁⠀⡀⠀⣿⣷⢠⡿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠸⣇⠀⣿⣿⡾⢡⡏⡿⠈⠙⢄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠞⡄⠀⢀⠔⠀⠐⠂⠐
⡄⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⢁⣿⣿⠃⠀⠁⠈⢈⡀⢠⣤⣤⣤⣧⡔⠁⢸⠋⡴⠁⡀⢸⡇
⠂⠀⠀⠀⠀⠄⠀⠀⠈⣿⢾⣼⣻⡏⣠⣴⡆⣪⣶⣗⠉⣉⠛⣯⣝⠳⢄⣾⢉⣁⣠⢀⠏⠈⠐⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⣹⣿⣿⣿⣿⣿⡟⠟⠛⠛⠒⠛⠛⢯⡛⠓⣾⢿⣍⣀⣠⠟⠀⡀⠀⠀⠀⠉⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⡟⠁⢸⡀⠀⠀⠀⠀⠀⠹⢾⣃⠘⠓⡾⠉⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠋⠀⠁⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⢈⡄⠀⠀⠀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣄⡀⠀⠀⠀⠀⡀⣼⣿⣿⣿⠀⠀⠀⢸⠁
⠛⠒⠀⠘⠀⠼⢹⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢤⠤⠤⠴⠤⠤⠤⠤⠤⠤⠄
⡀⠀⢠⠀⢀⡀⣾⣿⣿⣿⠀⡀⢠⠈⠀⠀⠀⠋⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂
⠙⣶⠞⢣⠸⡇⡸⠋⠉⠙⣨⣡⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣆⠀⠀⢠⠶⠆⡒⣂⠀⢀⠀⣔⢉⠰
⡷⠛⣿⡾⢻⣶⣧⡄⣠⠃⡟⢁⡶⠂⠀⢠⡐⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢉⠚⠀⠌⠘⠛⠉⠀⠀⠀⠀⠈⠉⠀⠉⠀⡐⠋⠀⠀⠉⠘⠻⡟⠛⠂
⣁⣤⣯⣧⣾⣿⣾⡖⣹⣰⢴⠋⠀⠀⠀⠀⢙⣆⠙⣄⣀⣀⣀⣀⢀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣈⣡⣄⣈⢀⣀⣀⣄⣀⡀⢀⣄⣀⠀⣀
⠉⡁⣿⢹⠗⣿⣷⣧⣽⣿⡏⣉⡔⠁⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠂⠀⠤⢭⣝⣯⡙⠛⣛⠛⠛⠛⠧⠷
⠀⢰⢻⢸⡄⣿⠂⣿⢟⣸⠔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠘⡇⠸⣿⠃⠈⣯⣌⠃⠖⡾
⠲⣶⣼⣆⢻⢠⣾⡟⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⣼⣾⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⡠⠆
⣽⠿⠿⢿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠔⠁⠈
⠀⠀⠀⠘⣋⢩⣿⡛⣯⠈⠙⢢⣴⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⡂⢠⠮⠂⣴⠤⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⡀⠀⠐⢒⠉⢤⣼⣿⣾⣷⣽⣿⡯⠭⢭⠹⣿⣿⡂⢀⣴⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡜⡩⠋⠀⠀⠿⠤⠄⠠⠀⠘⠀⠀⠀⢸⣻⡅⢀⣀⠺⠄
⡄⠔⠀⠀⠀⡀⢭⣥⣥⣨⣿⣷⣤⡶⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣄⣠⢆⣀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢡
⣄⣸⢀⣶⣭⣀⡨⠙⣻⣿⣯⣿⣇⣠⣼⣶⣾⠋⢻⠿⠿⢟⣿⣻⣿⡿⢿⣿⣿⣿⠋⣩⡿⠉⠀⠀⡀⢀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠁
⣯⢿⣿⣿⣿⣿⣿⣿⣾⠿⠻⠛⠙⣿⣾⣿⡿⣿⣿⠤⣴⢿⣭⣭⣿⣿⣿⣿⣿⣿⠀⠟⢿⣧⣤⠛⠉⠙⠺⠇⠀⠀⢈⣤⣄⡀⠀⠀⠀⠀⠀⢀⡀
⣟⣿⣿⣿⢿⣿⠋⡭⣄⠀⣀⣀⣼⣿⣿⣍⣟⠉⣃⡾⢣⣴⣶⠶⣶⡿⣿⣿⡏⠉⠉⠀⠀⠻⡇⠀⠠⣤⣤⢆⠀⠀⣸⠄⠈⠁⠀⠀⠀⠀⠀⠀⠈⠲⣤⣄⣀⣀
⣿⣿⣿⣷⠿⠁⢀⣀⣙⣿⡟⠋⠉⠙⣿⣿⣿⣿⣿⣾⡿⠛⠛⠛⠻⣿⣿⣿⣠⣤⣤⣤⣀⣀⣼⣶⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠙⠛⠿⠿
⣻⣿⣟⣱⣟⠻⣧⡄⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡶⠒⠒⢛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡀⣠⣤⣤⣤⣤⣴⣶⣟⠋⠉⠀⢄⣤⣄⣀

⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠳⠦
⠀⠀⠀⡴⠉⠀⢴⠄⠀⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠈⠀⠀⠀⠸⡄⠛⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠒⠂⢒⠚⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⣒⣒⣒⣦⣀
⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢀⠀⣀⠈⡇
⠀⠀⠀⠑⢤⡀⠀⠀⠀⡠⠋⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠠⠤⠤⠤⠤⠤⠤⠀⠒⠒⠒⠒⠒⠒⠂⠀⠤⠤⠤⣄⠀⠀⠀⡇⠀⠂⠀⠀⠠⠅⠀⠂
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡠⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠇⢀⣁⣈⠀⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⢦⠀⠀⠸⠀⢀⠀⠐⠀⠀⠀⠀⠀⢠
⠀⠀⣀⡀⣀⣀⣠⣄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠀⠀⠀⢀⢤⡀⡰⣤⠀⣤⢶⢀⣴⠀⠏⢡⠜⡷⠋⠀⠀⢠⠀⠀⡄⠈⠀⠉⠀⠀⠀⡀
⠀⡧⠈⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠠⢈⠀⠀⠀⣦⠌⠀⡾⢁⣎⣰⠇⠰⠤⠊⠃⠘⠉⠀⠀⠀⠀⢀⠖⠁⠀⠀⢸⠀⠀⠑⠠⠤⠶⠤⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢰⡂⠀⠈⠀⠳⠠⠊⠑⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠴⠮⠀⠀⠀⠀⢸
⠀⠈⠀⠒⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠡⠀⠀⠀⢸⣀⡀⠤⠀⣄
⠀⠀⠀⠀⠀⠀⢰⢧⢀⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠔⠀⠀⠀⢸⠋⡠⠀⡆⠡⡱⠄
⠀⠀⠀⠀⠀⠀⠀⢸⠈⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠶⠆⠠⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠂⠄⠀⢀⠓⠏
⠀⠀⠀⠀⠀⢠⠞⠋⠉⢳⠹⠄⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣈⣀⣀⣈⣴⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⡔⠈⠂⠤⠄⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠠⠤⠤⠤⠰⠒⠒⠠⡀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢆⣀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⡀⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠒⠀⠈⠙⢢⣀⠄⢀⣀⠀⠀⠘⠢⠤⠤⠤⠚⢀⣀⣀
⠀⠀⣠⠞⠉⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⣈⣉⡉⡩⠭⠛⠋⠢⠀⠀⢀⠜⠁⠀⠀⠀⢠⠊⡤⢀⠀⠀⠈⣲⡀⠀⠀⠀⢰⠁⠀⠀⠀⡿⢝
⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⡔⢘⠈⡡⠫⡃⠈⡀⠄⠀⣐⠀⡂⠀⣆⠀⠀⠀⢀⠔⠁⠮⠀⠀⠑⢀⠔⠡⠋⠀⠀⠀⢸⠀⠀⠀⠀⡧⠘
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡄⠀⡇⣂⠊⢀⠄⠀⢁⡁⠐⠠⠅⠲⠁⢄⠛⠒⠒⠒⢻⢇⡒⠤⢀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠰⠁⠁
⠀⠹⡄⠀⠀⢀⣀⠀⠀⡏⠉⠈⠇⠀⠐⠀⠁⠀⠈⠁⠀⠀⢀⠔⠁⡠⠔⢂⠑⡀⠀⠀⠀⡐⠉⠁⢀⠐⠚⢳⠀⠀⡠⢆⣠⡏⠀⠙⠒⠚⠃
⠀⠀⠈⢦⣰⠉⡀⠱⡀⠘⡈⣀⡄⠀⠀⠀⠀⢀⠤⠒⠀⠀⠙⠄⠈⠔⡨⠐⢀⠐⡄⠀⠀⡑⠠⠀⢀⠕⢀⠎⠀⠌⠀⠀⠉⠁⠊
⠀⠀⠀⠀⠙⢄⠈⢄⢠⠀⠑⠉⠈⠂⠢⡀⠀⢃⠀⠀⠀⠀⠀⠈⢀⠈⠔⠈⢀⡤⠊⠀⠎⠁⠀⠀⠁⡔⠁⠀⠀⢆⡀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⢢⠀⠀⠀⠀⠀⠈⢆⡀⠂⠁⠀⠀⡜⣫⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠡⠀⢀⠠⠐⠀⠉⠀⠀⠀⠀⢀⣡⠏⠐⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⢀⠴⡿⠿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠆⠀⠀⠀⠀⠐⠶⠶⣾⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠈⣿⣤⣴⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⡿⢿⣶⠶⠒
⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇
⠀⢀⣀⣺⣿⣿⣿⣿⣿⣿⣿⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡀
⣐⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠈⢿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷
⠉⠉⠛⠻⠟⠋⠋⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠙⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀⠘⢿⣄
⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⣀⣤⣴⣶⠞⠃
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⡀
⠀⠀⢠⣿⠋⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⣠⣦⣤
⠀⠀⠐⠛⢁⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣶⣶⣾⡏⠀⡀
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⣴⣾⣶⣿⣿⣿⣿⣿⣿⣴⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿
⠀⠀⠀⠉⠋⣿⣿⠏⠙⣿⣿⠉⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⡍⠀⠀⠀⠀⠀⠀⣿⡏⠛⢿⣿⡿⠿⣿⣿⠻⠿⠁
⠀⠀⠀⠀⢰⣿⡏⠀⠀⢸⣿⠀⠀⠀⠀⠠⡾⠟⣿⣟⣿⣿⣿⣿⡏⠀⠀⠛⠓⠂⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⣸⣿⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠶⠟⠛⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⢠⡄⠀⠀⠀⡠⠄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠁⠀⠀⠀⠀⢠⣿⠀⠀⣙⠒⠖⠀⠐⠤⢖⡌⠀⢠⣧
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠉⠈⠐⠀⠀⠀⠈⠁⠀⠘⠛⣀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠈⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠈⠀⢈⠀⠀⠀⠀⠀⣐⠦⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⣀⠤⢒⡀⣴⠖⠷⠤⠖⠒⠛⠺⣾⠀⠘⢦⡀⠀⠀⠀⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⣷⠘⠳⠖⠖⠲⠲⠆⠚⠁⠀⣾⡀⠙⣦⢴⢪⣡⣾⣷⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢸⡝⣆⠀⠀⠀⠀⠀⠀⠀⢀⡼⣹⠁⣴⣧⢾⡹⣟⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠰⣆⠀⢸⡇⢻⡷⠄⡀⠀⢀⣤⠐⡿⢁⡏⣸⣯⢧⢃⡵⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢹⠀⠀⡇⠀⣧⠞⠻⣤⣼⠉⣻⠅⢸⢃⣿⣧⣿⡞⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⠀⠀⢻⡀⢹⡄⠀⣿⣟⣷⣃⢀⣾⣾⣿⣷⠿⢸⠇⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⣌⡇⠀⡾⣿⣻⣼⢋⢀⣽⣯⢀⢠⣏⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⢸⡧⠖⠦⢤⡀⡄⢸⠀⠀⠀⢸⠏⣷⠀⡿⢸⣿⠻⡟⠚⠉⠀⣼⢹⣸⣒⠉⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⣰⠋⢧⡞⣦⠀⠀⢸⡀⣿⠀⡇⢸⡇⢰⠇⠀⢀⡖⣏⣸⠈⢦⢱⡄⠀⢸⡇
⠀⠀⠀⢀⣀⣀⣸⣇⠀⠀⣿⠀⠒⢧⣼⠀⠀⣘⣧⣿⣀⣇⣈⣧⣿⠤⢤⣼⣼⠉⠀⠀⢸⣇⡇⠀⣼⣀⣀⣀⣀⣀
⠀⠀⠀⣶⡯⠩⠷⠭⣿⣖⣿⣦⡉⢀⣼⣛⡟⣡⠖⠂⠀⠉⠁⠀⠀⠸⡆⠙⣿⣄⣀⣀⣼⣯⣴⣾⢏⡁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢤⡉⣠⠎⠀⠉⠛⠛⢩⡟⢠⡏⠀⠀⠀⠀⠀⠀⠀⢀⠿⠀⣹⠏⠉⠉⠉⠉⠉⠙⣦⠐⠀⠀⡀
⠀⠀⠀⠀⠐⠩⢭⡞⠑⠃⠀⠀⠀⠰⠾⠿⢿⡶⣤⠭⢍⣉⣀⠀⠠⠖⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠼⣧⡀⠐⠂
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢠⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠁⠠⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢇
⠀⠀⠀⠐⠀⠀⠀⠀⠐⡀⠈⡀⠀⠂⠀⠀⠀⠃⢄⠀⠤⣶⠃⢾⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⡁⠀⠀⠀⠀⠀⠀⢠⠗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠘⠸⡄
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠅⠀⠄⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠋⠀⠒⠄⡀⠀⠐⣾⠇⡃
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢚⠁⠀⠀⠀⠀⠀⠐⠋⠈
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡎⡏
⠀⠀⠈⠀⠀⠔⠀⠀⠁⠀⠀⠀⠀⢠⣮⠍⠕⠡⣏⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⢤
⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⣾⠇⠀⠀⠀⡇⡧⠀⠀⠀⠀⠀⠀⣀⡴⡊⠐⢇⠀⠀⠀⠀⠀⠀⢨⢛⠋⢱⢸
⢀⠀⠀⠀⠀⠀⠈⠉⠒⠤⠀⠀⡾⠉⠀⠀⠀⢠⠏⠁⠀⠀⠀⠀⠀⠈⠵⠁⠁⢀⠀⠀⠀⠀⣀⡠⠠⠃⠀⢀⡾
⠈⠄⠀⠀⠀⠀⠀⢀⠄⠒⢲⠿⢹⠂⠀⢠⠤⠞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠠⣜⠁⠀⠀⢠⡸⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠏⠒⠁⠀⠐⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠘⠀⠀⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢦⡀⠀⠀⢀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡄⠀⠀⠀⢙⣦⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡣⡋⡄⠀⠀⠊⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠅⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠢⠰⠆⠀⠀⠀⠀⠐⠠⠿⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠒⠀⠀⢀⡀⢀⣀⣒⠀⠀⠀⠤⠀⠐⣀⢤⣤⠷⠟⠍⠂
⠀⠀⠀⠀⠀⠀⠀⡄⠉⠓⠓⠶⢤⣠⠀⢀⠀⠀⠤⣝⡈⠛⠛⠠⣀⣀⣤⡶⠿⠛⠉⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠀⠀⠈⠑⠓⠒⠲⡘⠀⡼⠟⠛⠋⠁⠀⢂⠨⠄⠁⠢⠀⡠⠞⠰
⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⠄⠒⣀⠄⠀⠀⠀⠀⠀⠃⠀⠐⠀⠀⠀⠀⢈⠁⠁⠶⢤⡄⠜⢸⣏⡀
⠀⠀⠀⠀⠀⡬⠐⢧⡀⢠⢊⠰⣢⠀⠀⢠⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⣆⡀⢀⢄⠀⠸⡧⠆
⠀⠀⠀⠀⠀⠡⡈⣰⣿⠀⠀⠀⢂⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠁⠓⠂⠀⠀⠳⡆
⠀⠀⠀⠀⠀⠀⠈⠚⠛⠀⠀⡤⠀⠀⠈⠫⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠄⠛⣙⢰⡆⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⢿⠂⠀⠀⠀⠀⠀⠀⠀⠘⠉⢉⣠⠖⠦⠉⠁⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠈⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠠⠘⠀⠁⠀⠀⢀⠠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⣀⠀⠀⠀⠀⠀⠀⡎⢰⠄⡆⠀⠀⠀⠀⡠⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠒⠢⠤⠄⡹⢍⠄⠠⠖⠀⠉⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠂
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢉⣉⣇⣠
⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠠⠐⡄⣄⢤⠤⠴⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⡀⠀⠄⠠⠀⢰⡇⠺⠠⠦⠀⠂⠀⠀⠀⠀⠆⠀⠄⠠⠘⠉⠉⠙⢻⠓⠀⠀⠀⠀⠐⢻
⠀⠀⠀⠀⠀⠀⣄⠀⣠⠀⣀⣤⣶⣿⠗⠈⠃⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⠤⢄⣼⣀⣀⠀⠀⠀⠀⢸
⠀⠠⠀⠀⠀⠀⠘⣆⠈⠻⣿⣿⣿⣿⣧⠠⠀⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡞⠉⠉⠰⣄⡀⢁⠉⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⢹⣿⣿⣿⣿⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⡁⠀⡆⠀⡣⠀⠀⠀⡍⠈⠉⠋⠠⠠⡔⠃⠈
⠀⠀⠀⠀⢃⠀⠀⠦⢿⡀⣿⣿⣿⣿⡟⠁⣶⠀⠀⠀⠀⠀⠀⢶⠀⠀⢀⢷⡎⠀⠈⠉⠀⠀⠀⠠⠀⣀⠀⠀⠀⠄
⠀⣠⣶⡄⠀⠀⠤⡄⠀⠃⢻⣿⣿⣿⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡏⠀⠠⠀⠄⠀⠀⠀⠐⠀⠄⢀⡀⠀⠘
⢸⣿⣿⣿⣆⡀⢀⠀⠀⢰⣿⣿⣿⣿⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄⠀⠀⠀⠀⠀⠀⢙⠻⡶⡆
⢸⣿⣿⣿⣿⢁⡜⢤⣦⠾⠿⢿⣿⣿⣿⣁⣀⣄⣤⣤⣀⣀⡀⣀⠀⠀⡀⡄⠀⢠⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⣸⡌⡔
⠀⢀⠄⠀⢱⠶⠻⠇⠀⠀⠀⠀⠈⠘⠿⠿⣿⣿⡿⠿⣿⣿⣿⣿⠃⠁⠘⣧⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡜
⠀⠘⠒⣤⣤⣠⣦⠴⠛⠠⠶⠳⠿⣿⣶⡤⠚⢃⠀⠀⠀⠀⠀⠛⠁⠀⠰⠇⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⢸⠷⠁
⠀⠀⠘⠙⡿⢿⡟⠃⠀⠠⠴⠄⠒⠂⠀⠉⣁⠀⠀⠀⠲⠀⠐⣒⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣾⠓⣒
⠀⡤⠘⣂⠐⠋⠈⡈⠙⠀⠒⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠻⠈⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠾⠁⠉⣐⡀
⠀⠀⠀⠻⠒⠲⠤⠀⢰⣶⣤⣀⣀⣀⣤⡝⠙⠛⠚⠛⠃⠄⠄⠀⠀⠀⠉⠛⠺⣿⣦⣄⣀⣴⠾⠯⠤⠔⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡛⠋⠁⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡟⠧⣤⣀⣀⡀⠀⠐⠂⠉⠁
⠀⠀⠀⠀⠉⠓⠂⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⢁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠜⠁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠔⠢⡀⠀⢀⠔⠉⠀⠀⠀⠉⠢⠤⠊⠉⠒⠨⠕⠢⡀
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠇⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠉⠘⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢠⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⡆⡇
⠀⠀⠀⠀⠀⠀⠸⡸⡀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠑⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢎⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠔⠊⠁⠀⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠋⠑⠒⡄⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡒⠤⠤⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⠜⠀⠀⣆⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠂⠉⠀⠈⠑⠂⠤⠐⠂⠁⠀⠀⠀⠈




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠒⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠉⠓⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⠀⠀⠀⠀⠀⠀⢒⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⢀⣐⠀⠀⠀⠀⠀⣪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣀⡑⠸⡑⠦⠀⠀⠀⠀⢙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠵⠠⢌⡉⠁⠠⣤⢖⡁⢀⣀⣀⣀⡀⠀⠤⠔⠰⠽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢲⠤⣄⠴⠋⠀⠀⠀⠀⠙⠀⠀⢡⠐⡅⠀⠀⠀⠀⠀⢀⣀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢖⡶⠊⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣀⡠⠤⠶⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⠀⠀⠀⠀⣆⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣄⡀⠈⠑⠲⢳⡀⠀⠀⣸⣿⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡖⠂⠉⠉⠀⠠⣄⠙⢶⡾⢿⡏⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⣈⣣⠀⠀⠀⠀⠀⡿⠇⠀⢉⣻⣯⠁⠀⠈⡆
⠀⠀⠀⡠⠴⠚⠁⠀⠉⠀⠀⠀⢸⠁⠀⠀⠀⢰⢧⠒⠒⠋⠉⠀⢠⠀⠀⠳⡀
⠀⠀⠚⠀⠀⢀⣀⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠎⠀⡀⠀⢀⣀⡤⠏⢣⡀⠀⠴⠒⠢⡄⡀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠙⠛⠊⠁⠀⠀⠉⠉⠉⠁⠀⠀⠀⠉⠐⠒⠲⠓⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠒
⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠙⠛⡷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⡤
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣴⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠙⢿⣧⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⣠⣿⠏⠀⠀⠀⠀⣤⠛⠙⣿⣄⠀⠐⣄⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⣶⣤⡤⠀⡀⣠⣿⣿⣿⠋⠀⡀⠀⣠⣴⣞⠁⡀⠀⠀⠙⣳⣶⣿⣿⣿⠷⠦⠀⠸⠇⣷⣤⡄
⠀⠀⠀⠤⠈⣋⣾⣿⣯⣿⣿⣿⣿⡟⣿⣿⣶⠿⢛⡿⠟⠁⢤⣾⣿⣿⣿⣿⣯⠱⠶⢶⣄⠀⢀⠈⠁⠀⠄
⠀⠀⠀⠰⣾⣯⣿⣿⣾⣾⣿⣿⣿⣷⣿⣿⣿⣷⣾⣷⣾⣾⡆⠉⢻⣽⣿⣿⠿⠁⠀⢀⣨⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣟⠙⠿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠋
⠀⠀⠀⠀⠀⠀⠻⠿⡿⣿⣿⣿⣿⣿⣏⠙⠻⣿⣿⣿⣿⡛⠀⠂⢀⣀⣠⣬⣯⣭⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣶⣶⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠿⠿⠟⠙⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠓⡀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠔⠈⠑⠂⠁⠀⠈⠂⠀⢀
⠀⠀⠀⣄⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠐⠈⠂⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠦⠀⠀⠈⣐⠁
⠀⠀⠀⣏⠀⠟⠀⢠⢨⡁⠀⠀⠀⠈⠒⠁⠀⠀⠈⡈⠀⠀⠘⡐⢂⠀⠀⠐⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢎
⠀⠀⠀⠀⠓⠀⠀⠀⠓⠉⠢⡀⠀⠀⠈⠀⠀⠀⠠⠦⠄⢀⣨⠠⠴⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⡆⠀⠀⠀⠀⠸⠆⣄⠀⠀⡀⠀⢀⠀⠀⠤⠀⠉⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠠⣶⡄⢀⣒⣼⡓
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢙⡁⠀⠀⠰⠿⠀⢈⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣠⡁⠄⠀⠀⠀⠀⢅⠁⠢⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⣄⠉⠡⠋⠘⠌
⠀⠀⠀⠀⠉⠂⠂⠚⠀⠀⠀⠀⠊⠀⠰⠈⡄⠀⠀⠀⠀⠉⠃⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠔⠀⠂⠈⠀⠀⠀⠀⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠠⢀⠁⠀⠀⠀⠀⠀⡅⠀⠠⣶⠆⠀⠢⠤⠀⠀⠀⠀⡐⠁⠀⠀⠐⠂⠠⠀⢀⠁⠀⢀⡀⠀⠀⠐⠄⠐⠀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂⢀⠂⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠂⠀⠀⠠⠚⡔⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠀⠊⠁⠀⠀⡀⠀⠀⠀⠀⠇⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⢆⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡐⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⠐⠢⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠢⡈⠢⡡⠀⠀⠀⠠⣹⠓⠂⠀⠃⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠱⠄⠀⠀⠀⠀⡅⠁⠁⠐⠀⠀⠀⠀⠀⢀⠀⢠⠀⠠⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⢖⣈⠶⢌⠀⠀⠀⠈⠂
⠀⠀⠀⣂⡠⠐⠀⠃⢀⠚⠀⠀⠀⠀⠀⢈⠂⠒⠁⠀⠀⠀⢈⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⣀
⠀⠀⠈⠚⠢⢀⣀⠠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠄⠤

⠀⠀⠀⠀⢀⡤⠤⣀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⢀
⠀⠀⠐⢦⠏⠀⠀⢸⠀⠀⡀⠀⢸⣇⠀⠀⠀⠀⢸⡇⠀⠀⣆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈
⠈⢀⠀⠶⠁⠀⠀⠟⠓⢸⡇⠀⣿⠿⣆⠀⠀⣴⣿⣷⠀⠀⢹⡄⠀⠘⡄⠀⡆⠳⠀⠀⠀⠀⠀⡄
⠀⠘⣇⠀⠀⠀⠀⢄⠀⢸⣷⡀⣿⠀⢹⣆⢸⣯⢻⣿⡜⢿⠀⢳⡀⠀⢹⡀⢷⠀⠀⠀⢱⡀⠀⠧⠄⠀⣀
⠀⢰⡏⠀⠀⠀⠀⠈⣦⠈⠻⣿⣿⢰⡆⢿⡆⢿⣿⣿⣿⣦⠀⢸⣷⡄⢸⣧⠸⣆⠐⡀⠈⣷⡀⠀⠀⠀⢸
⠀⠘⠧⣤⡀⠀⠀⠀⠘⢧⡀⣼⣿⣦⡁⢸⣿⣀⣩⣿⣿⣿⣷⣼⣿⣿⣾⡏⢣⢹⣧⣿⡄⠹⣿⡄⠀⡾⠁⠀⠀⣴⠂
⡀⠀⠀⠀⣿⡆⠀⠀⠀⠈⣷⣿⣇⡜⢿⣿⣿⣿⣿⠛⣻⣿⣿⣿⣿⣿⣿⣇⠤⢿⣿⣿⣿⡄⢹⣿⡄⠻⠀⠀⠀⢻⡄
⠘⠄⠀⠀⠈⠷⡤⠀⠀⢠⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣾⠸⣿⣿⣿⣆⢻⣷⠀⠀⠀⠀⢠⡇
⠀⣿⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣿⣿⡇⣸⢳⣿⣿⡏⢿⣾⣿⡆⢠⡔⠒⠉
⠀⠈⠙⠓⢦⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣍⡭⣭⠧⠰⢃⡜⠿⣿⣬⣼⣿⣿⣶⣾⣿⣿⡇⠈⡇
⠀⠀⠀⠀⣼⠀⠀⠸⣿⡹⣿⣿⣿⣿⢟⡿⡟⣫⡖⣤⡄⢠⣄⡐⠆⡴⢀⠀⣁⣻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠁⠀⠀⠀⡜⠉
⠀⠀⠀⠀⠘⠦⠖⠀⢻⣷⣾⣿⣿⣿⠈⣡⣥⣍⣁⣛⣁⠘⣿⠃⠸⣚⣯⡄⠙⢹⣿⣿⣿⣿⣿⣿⣿⠀⢀⡀⠀⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡀⠙⢿⣿⣿⣿⡗⣿⠻⣟⣛⣛⡛⡁⠀⠘⠛⢛⣿⡛⠛⠋⢻⣿⣿⣿⣿⣿⡇⠀⠟⠛⠓⠛⠉
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠙⢻⣿⠓⣛⡃⠈⠉⢉⡾⢡⡇⠀⠶⣏⠛⠁⠀⠀⢸⣿⣿⣿⣿⡟⠀⡘⠀⠀⠀⠄
⠀⠀⣠⣶⣉⠙⠋⠁⠀⠀⠀⠀⡘⢿⣧⢙⣌⠀⠀⠀⢀⡞⠰⣿⠆⣨⢉⣁⢠⣶⠈⢙⣿⣿⣿⡇⠈⠀⠀⠢⡄⠀⠳⠶⡄
⠀⠀⠈⠁⣿⠀⢠⡞⠳⠶⠶⠋⠀⠀⠸⣇⢹⡔⢿⢀⣾⣅⠀⣭⡀⠛⡉⢟⠶⠁⣾⣿⡿⠟⠉⠀⣀⠀⠀⢠⠇⠀⠀⠀⠳
⠀⠀⠠⠤⢤⣤⡿⠁⠀⠀⠀⠀⠀⢀⡀⢻⣤⣷⣾⣿⣿⣿⣿⣿⣷⣤⡉⠛⠘⣻⡿⠃⠀⠀⣠⠞⠁⠀⢀⣯
⠀⠀⠀⠀⠀⠀⠀⣰⠶⠦⡀⠀⠀⠊⠀⢸⣿⡏⣠⡌⢙⡛⠛⠛⢻⣿⣿⠀⢸⡟⣠⠞⠁⠀⢧⣀⣀⠀⠈⠙⠓⠒⣄
⠀⠀⠀⢀⠀⠀⢀⡿⠀⠀⠈⠂⠚⠀⠀⠸⣧⣭⡈⡁⠘⠟⠀⠀⢸⠟⣁⣴⣟⣇⠈⠙⣦⠀⠀⠀⠉⣷⠀⠀⠀⠀⣼
⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣷⣞⣀⢐⣀⣀⣱⣿⡏⣇⠹⣝⢦⡀⡠⠀⣠⠤⠔⠃⠀⠀⠀⠀⢿⣀⡀
⠀⠀⠀⠀⢀⣠⣤⠴⠶⣶⣛⣛⣿⣯⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢻⡌⢷⡘⣆⢹⡶⣟⡀⠀⠁
⠀⠀⢠⣾⣿⡥⠖⣚⣫⡭⠖⠁⢀⣴⣿⣿⡷⣋⣿⣿⢿⠀⣿⡿⣆⢳⣌⠻⣮⡟⠀⠀⠉⠑⠒⠲⠬⠅⣀⡀⠀⡄
⠀⠀⢾⣿⣷⡶⠥⣛⣩⣤⠶⠚⡋⠉⣩⠿⠾⢋⣾⣏⡞⢸⡇⢧⠙⢦⣙⡷⠏⠀⢠⠀⢠⠀⠀⡀⢦⡀⠀⠀⠙⣾⣷⡀
⠀⡀⣾⣿⣿⣟⠋⠉⣥⣶⠞⣫⠔⣪⡅⣠⠖⢋⠉⠛⠳⣾⣇⣸⡷⡞⠉⢠⡆⠀⡿⡆⢸⣆⠀⡧⠈⣿⡄⠀⣠⣿⡿⠃
⠀⡗⡏⣿⢿⣿⣿⣾⣿⣥⣀⣀⣾⣿⣞⠁⣴⠟⠀⡾⠀⠈⠛⠁⢰⠇⠀⢾⠇⠰⣽⠃⠘⣿⠀⣓⣀⣼⣷⣾⣿⣿⡇
⠀⣷⡇⢹⡄⠀⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⠋⣼⠁
⠀⢻⣿⠀⠀⠀⣼⠀⠀⢠⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠉⡉⠉⡉⠁⠉⠁⠈⠉⠁⡀⠀⠀⠀⠀⢠⡄⠀⠀⡌⢠⡏
⠀⠘⣿⣆⠀⢸⣿⠀⠀⣸⡇⠀⠀⣰⡇⠀⣾⠀⣷⠀⢸⡇⢀⣷⠀⣰⡇⠀⡇⢠⡗⢠⡆⢰⡆⢸⡿⠰⣲⣀⣾⠁
⠀⠀⢿⣿⣿⣿⣧⣤⣤⣿⣀⣀⣀⣛⣁⣀⣋⣠⣭⣤⣬⣥⣬⣯⣤⣼⣥⣬⣁⣬⣥⣬⣥⣤⣤⣶⣶⣿⣿⡿⠁
⠀⠀⠈⠙⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⡁⠀⢸⢸⡇
⠀⠀⠀⠸⣿⡄⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⠀⠀⢀⡆⠀⠀⣰⠆⠀⠀⢰⡆⠀⠠⡇⠀⠰⠇⠀⣼⡞⠁
⠀⠀⠀⠀⠀⠙⢷⣄⣸⠆⠀⢸⡆⠀⢸⡆⠀⢸⣀⣀⣘⣯⣤⣤⣭⣤⣤⣤⣤⣴⣶⣶⣶⣾⣾⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠿⠿⠿⠿⠿⡿⠋⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡄⠀⠘⠋⠁⠀⠀⢀⠀⠉⠁⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠁⠀⠀⢀⣠⡄⠀⠈⡔⢤⡄⠀⠀⢷⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⡙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣻⡌⠋⠁⠀⠀⢰⠀⠈⠓⠶⠇⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⡀⠀⠀⠚⠛⢦⡀⠀⠀⠀⣠⠔⠀⠀⡟⠀⠀⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠯⣉⠉⠙⢺⣷⡄⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⣼⠃⠀⠀⠀⢘⣿⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠉⠙⣶⡞⢹⡛⢶⣄⠀⠀⠀⠄⠴⠰⠀⣠⣾⠃⠀⠀⠀⠰⢹⣿⢷⣇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⣹⠟⠇⡀⢸⠇⠀⠈⢹⡗⠶⠶⢶⠛⠻⡍⣿⢷⡄⠀⠀⠠⡞⢷⣂⠨⢞⡥⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣻⠴⠷⣶⣬⠀⠀⢰⡟⠀⡟⠀⠈⡇⠀⠀⠈⣧⠙⣦⡀⠀⠹⡎⢁⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡾⡗⢹⢰⠀⡇⠘⠧⣴⠟⠀⠀⢀⡀⠀⢰⢹⡆⢳⡈⢦⣧⡿⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⢀⢾⡇⡇⢸⢸⠀⣿⢸⠀⣿⠀⠀⠀⠹⡜⣤⠆⠘⠑⣺⢃⡈⠻⡀⠀⣸⠃⠸⡆
⠀⠀⠀⠀⠀⠀⣸⢸⡇⣷⣸⠸⠀⣿⢘⣀⣷⠇⠀⢠⡄⣷⠀⠀⠀⣀⡭⠞⠀⠀⣟⢠⡏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⢸⡇⢻⣿⠀⣀⣿⠞⠋⢡⠀⠀⣸⣇⡝⢀⡴⠋⢁⣴⣦⣤⡼⠙⢾⠁⠀⢀⡇
⠀⠀⠀⠀⠀⢸⣿⢸⡇⡆⢸⠿⣿⣅⠀⠀⠘⡟⡟⢫⡽⠁⡞⡟⡾⢫⡿⠈⠳⣄⠀⢀⣤⠠⠞⠦⣄⡀
⠀⠀⠀⠀⠀⢸⣿⠀⡇⣼⢸⠀⡇⢹⣆⠀⠀⠸⣷⠋⠀⣴⠁⡇⡟⣼⠇⠀⠀⢈⠟⠡⠤⠤⠄⠀⢄⣀⠝⣢⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠈⣿⣦⣧⣜⣸⢀⠃⢠⠹⣦⠀⠀⠀⠀⢠⠟⠀⣇⣵⣿⢀⣀⣤⣼⡏⠒⠒⠖⠈⠉⠉⠀⠀⡟⢿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⣿⠀⠉⠙⠛⠛⠛⠿⠾⠿⢷⡄⠀⢠⡿⢾⣿⣿⣿⣿⣿⣿⣿⠀⠹⢦⣀⠀⠀⣀⣀⡴⠚⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣈⣉⣉⣁⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣽⡇
⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠐⠚⠛⠛⠛⠶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠛⢿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠻⣦⠈⠙⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣤⣤⣤⣤⣤⣼⣿⣄⡀⠀⠀⠀⠈⢷⡀⢸⡇⣈⣽⣿⡟⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠙⢷⣄⠀⠀⠈⢳⣾⣿⣿⣿⣿⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠙⣷⡀⣠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠛⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣿⣫⣾⣿⣶⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣛⢿⡾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⡃⡼⠃⠀⠀⠀⠀⣴⣶⣶⣼⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢤⠀⠀⠀⠀⠈⢃⣀⣀⡸⢱⣀⠤⠙⠛⠛⠛⠿⣿⣿⡿⠃⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⢠⣄⣀⣠⠊⠁⠀⠐⢁⠜⢣⠀⢸⣏⣶⣤⡀⠘⣿⣿⣷⡄⠐⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠈⠒⢤⠤⠀⠠⠀⠘⠀⢀⠀⠆⢠⣉⡙⠻⠛⢹⡏⠉⠉⠁⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣰⢏⠤⠒⠚⢄⠀⠢⠴⢶⡊⠁⠀⢰⠀⡏⢙⡀⠀⠠⡀⠀⠀⣴⠟⣻⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠱⣁⣀⢶⣾⠂⢣⡀⠀⠸⣨⠗⠈⠙⠚⠀⠛⠳⡦⡁⠇⠀⠠⠵⣾⣿⣝⢿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⠀⠐⡇⠛⠿⣤⣽⣿⣿⣇⣀⣰⠁⠀⣀⣀⠀⠠⢆⡀⠀⠙⣄⠀⠀⠀⠈⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⢠⣀⡇⠀⠒⢃⠜⠋⢡⣂⡄⠀⣉⠲⠄⠋⢀⣠⣴⠀⣀⠤⡀⠉⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡡⠨⢳⡀⠀⡏⠀⠀⢨⡽⢗⠻⠀⠀⡎⠁⡪⠽⠋⠰⠥⡀⡨⢰⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠰⡅⡀⡇⠙⠂⠖⠂⠘⠁⢀⣎⠀⣀⠔⠋⠉⠑⠢⣾⠼⣀⣈⢣⠸⣌⠆⡀⢀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠂⠳⢌⣘⡦⡄⣠⡀⠀⣤⠈⠈⢶⠁⠠⡄⣠⣶⣴⠈⡞⠀⡏⡆⣠⠃⠊⠐⠂⠐⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠕⠠⢊⠼⢿⠀⠉⣀⣀⣄⠀⠀⠸⠀⠀⢀⠁⢀⡀⠀⢰⠊⠀⠀⢹⠍⠉⡓⣎⠔⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⠡⡐⠆⠆⠀⠻⠽⠟⠀⠀⠀⡆⠧⡸⠀⠿⠃⠀⠸⠀⠀⠇⢸⠈⢑⠈⢘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⣿⠖⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⣶⣶⣶⣿⡖⠒⠒⠚⠧⠁⣂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠀⠀⠀⠀⠀⣴⣾⣷⣦⡀⠀⠀⠈⠛⠟⠛⠁⠀⠀⣠⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣶⣤⣀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢀⣀⡀⠀⠀⠀⣰⣶⣶⣦⡀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠰⢶⢀⣠⣤⣴⣶⢖⣶⣶⣶⣄⡀
⠀⢰⣕⣀⡒⢻⡷⠞⠀⠞⡵⣿⣿⠋⡘⣷⡄
⠰⠦⠟⠋⢉⢠⣾⡧⠂⠀⠠⠌⠀⠀⡙⠦⠹⠀⠃
⠐⠒⢣⠀⠛⡆⠐⠃⠰⠻⠂⠀⠙⠂⠉⠀⣴⣷⠂
⠀⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟
⠐⣌⣦⢀⡤⠀⠀⠀⠀⠀⣁⣤⡀⠀⠀⠀⢩⡌
⠀⠙⢁⠠⡴⣶⡄⠀⠀⠐⠛⠛⠉⠀⠀⠀⠈⠡
⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⡰⠁⠀⠐⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣥⠞⠀⠀⣀⣰⠗⠀⠀⠀⠀⠀⠀⠢⡶⢌⠋⢹⡆⠀⠀⠒⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠚⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡌⠃⣷⠀⠀⠀⠀⠱⣄⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢛⣧⠈⠀⠀⠀⣀⠀⠘⠁⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⣀⠀⠀⠈⣄⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠆⠀⠀⠀⣃⠃⠊⠀⠀⠀⠀⠀⠲⠁⢰⡆⠀⢴⡏⠀⢸⣶⡶
⠀⠀⠐⠀⠀⠀⠙⠀⡰⠁⠑⠦⣄⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⡈⢰⠇⠈⠳⠄⠀⠀⠈⡀⠘⠀⠀⠸⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢘⣠⣤⣶⣤⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⣤⠞⣱⠂⠀⠀⠀⠐⢦⠀⠀⢃⡴⠀⡞⠀⢱⣶⣶⣄
⠀⠀⣀⠀⠀⠀⠠⡌⣿⡿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣯⣯⣁⠂⠇⠀⠀⠀⠀⠀⠀⢣⠀⠏⠀⣼⣍⠥⠛⠛⠋⠁
⠀⠐⠁⢈⠀⠢⢠⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⢡⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⡀⢹⠖⣀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⣠⣵⣿⣿⣿⣿⣿⣿⠿⢆⡀⠀⠀⠀⣰⢃⣠⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⢱⣾⠟⠛⠛⠛⠛⠛⠛⠁⠀⠀⠙⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠔⠀⠴⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠐⡆⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⢠⢀⡀⠘⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠊⢀⢒⡥⠒⠀⡆⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠌⠾⠠⠈⠀⠉⢶
⠀⠀⠀⠀⠀⠄⠢⠄⣐⣀⣘⡣⠄⠐⢬⣁⠀⢃⢻⡈⠠⣀⡤⠛⡀⠀⠀⢸⢳⠀⢰⣻⠀⠀⢀⢅⡀⢀
⠀⠀⠀⠀⠀⠀⡀⠈⠹⣄⠀⠉⠀⡀⠾⣁⢒⡌⢀⡀⠐⠒⠒⠻⠧⡀⠀⠈⢻⠒⡟⠁⠀⠀⠞⠘⠃⠀⡟⠠⡄
⠀⠀⠀⠀⠀⢰⢣⡆⠀⣬⠄⣤⠀⢠⠎⠀⢸⡴⠉⠉⢣⠐⠑⠲⣠⡆⠀⠀⠰⠀⠃⠀⠀⢰⠒⠐⢦⣀⠀⠺⠄⣤
⠀⠀⠀⠀⠀⠘⡎⠓⢈⡤⠤⠤⠀⣏⠀⠀⠈⣁⡤⠤⢄⠔⠋⠉⠉⠀⡀⠀⠀⠀⠀⠀⢀⠀⢠⠤⠀⠘⠧⠀⠿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢠⠀⠀⣀⣀⣠⡾⢁⡀⢾⠁⠀⠀⠀⠄⣀⡄⠨⠀⠀⠈⠉⠨⠁⠈⠃⠀⣠⡟⠀⣶⠈⠁
⠀⠀⠀⠀⠀⠉⣀⠀⡆⠀⠈⢦⠎⠁⠀⢸⠁⢸⠀⠈⢀⠀⠀⠀⢤⠈⠻⡌⣭⣤⣭⠁⠁⢀⡷⠰⠎⠉⠀⢴⡂⠛
⠀⠀⠀⠀⠐⠉⠉⣁⣇⢰⣃⣀⣀⡀⠀⠸⠀⢀⠔⢉⠀⠀⠀⠀⢈⡇⠀⢇⠈⠙⡅⠀⠀⡼⠁⢠⡔⠀⣯⠐⠋
⠀⠀⠀⠀⠀⠀⡞⠁⢠⠞⠉⡀⠀⠀⠀⠀⠀⡏⠀⢯⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡇⡠⠞⣁⠀⠊⠁
⠀⠀⠀⠀⠀⣈⠤⠀⡟⠀⣼⠁⠒⠉⢉⠃⠀⣇⠀⠘⣆⠈⠲⠤⠄⠀⠀⠀⢀⡼⠁⢠⠞⠁
⠀⠀⠀⠀⠀⡇⠀⠀⢻⠀⠈⠒⢠⠊⠉⠉⠙⠚⠆⠀⠘⡆⠀⢰⡀⠀⠀⡂⠉⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠙⠄⠓⠶⠔⠂⠀⠘⡀⠀⢠⠀⢠⡄⠄⠄⠧⠀⠼⠷⠊⠉⠀⠀⠀⠴⠀⠄⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠃⠀⡀⠀⢼⡅⠀⠀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣀⡀⠀⢈⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠘⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢤
⠀⢨⣿⣿⢟⢿⣿⣧⠀⠀⠀⣰⣞⡛⣳⣦⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠶⢤⠁⠆⠰⠆
⠀⠸⣿⣯⠈⠠⣿⡗⠀⠀⢠⡟⠛⠁⠙⠛⡇⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢿⣤⣬⣇⠁⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⢶⢆⣶⣶⣇⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄
⠀⠀⠀⠤⠤⠤⠆⠀⠀⠂⠀⠉⠉⠈⠉⠈⠀⠀⠀⠠⠄⠀⠤⠀⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠻⡿⠿⠃
⠀⠀⠀⠀⢀⢀⠀⠀⣈⠥⠀⠀⠰⣠⡆⣴⢰⣴⢰⠀⣤⣤⢀⡆⣦⢰⠀⣆⣤⡄⠀⠀⠀⠀⠀⠀⠀⠓⠂
⠀⠀⠀⠐⠻⠳⠀⠀⠉⠁⠀⠀⠈⠁⠀⠈⠈⠈⡈⡀⣁⡈⡀⡅⠀⠈⠀⠉⠁⠁⠀⠀⠀⠀⠀⢠⡀⠀⠀⣠⡄
⠀⠀⢠⡀⣀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣿⡶⣾⣏
⠀⠀⠀⠁⠈⠁⠁⠀⠀⣶⡄⠀⠀⢠⣶⠀⠀⣀⣻⠟⢉⠙⢿⣃⡀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⣿⠙⢹⣿
⠀⠀⠀⠏⠀⢒⣛⠀⠀⠘⡇⠀⠀⢸⠇⠀⠀⣭⣿⠀⠀⠀⢈⣯⡅⠀⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⣿⠀⢸⡟
⠀⠀⠀⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⢹⡷⣶⣶⣿⡍⠁⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⢸⣶⣾
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣍⠀⠀⠀⠀⠶⠖⠀⣬⣿⡄⠘⠿⠗⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡾⠛⣻⣭⠽⢟⣳⢮⡻⣟⣿⡿⠿⡶⣶⣶⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡿⠉⠁⣰⠟⡡⠂⣀⡀⢌⣣⣿⣇⢈⣶⣂⢴⠎⣿⣷⢶⣬⣄⣔⠀⢽⡁
⠀⠀⠀⠀⢠⣄⡐⠐⢾⣿⣧⣼⣿⣧⣼⠀⣾⣿⡷⢸⠟⣃⣿⣾⣿⣿⣿⣷⠙⣯⣾⣿⠞⠉⠙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠙⢿⣿⡿⢿⠈⢿⣿⣾⣿⠋⠉⠉⣿⣿⢷⣽⣿⣶⣮⢼⣏⠀⣄⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣯⣿⣿⣧⠘⣆⠀⠹⣿⣿⣶⣶⣾⣿⣶⣿⣿⣹⣿⢏⣾⣿⣍⡊⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡈⢧⡈⠳⣄⡙⠛⢿⣋⣡⣿⢻⣷⡿⠿⠋⠸⣿⠝⠿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣈⠛⢦⣤⣉⣛⣛⣉⣽⣿⣿⣿⡗⢂⢒⣐⣻⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣵⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠈⠆⠀⠀⠃⢀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠈⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣦⣤⣤⣴⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⡀⣢⣉⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢹⣿⣿⣿⣿⢿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⢠⣆⢢⣲⣶⣠⣀⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠘⠋⠀⠉
⠀⠀⠀⠀⠀⠀⣜⣶⣿⢿⠎⠑⡛⢽⣿⣟⡀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⡔⠃
⡀⠀⠀⠀⠀⢠⣟⡫⠇⠈⡀⠀⡇⠈⠈⡿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠳⡀
⢿⠆⠀⠀⠀⣞⣛⣒⠀⠂⡆⠀⡇⠀⢈⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠄⠈⠂⠀⠀⠀⠀⠀⠀⠀⢰⣿⠷⠤⠤⠤
⣾⡆⠀⠀⠀⠴⣖⣚⠀⠀⠹⡿⠇⠀⠈⣙⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠈⢂⢀⡀⠀⠀⠀⠀⠀⠀⣾⣤⣦⣄⠀⢠
⣿⡇⠀⠀⠀⠈⠟⣶⣧⠀⡀⣐⣀⣀⢠⣻⡦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠒⠻
⡻⠃⠀⠀⠀⠀⠘⠻⣻⣿⣿⣿⣴⣷⣿⠏⠛⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢻⠀⠒⠒⠐⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣤⣤⣶⣦⠠⣶⣶⣶⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣄⣄⡀⡀⡄
⠀⠀⠰⠖⠂⠀⠀⠀⠒⠚⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣀⣀⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠼⠍⠉⢼⢗⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⣀⡿⣿⣿⡂
⠀⠀⠀⠀⠈⠡⠻⠓⡈⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠀⠀⠀⠤⣯⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣤⣤⣤⣼⣿⢚⣛⡁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⢤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⢲⡞⠂
⠀⠀⠀⠘⡀⢸⠀⠐⠀⡰⠁⠈⠀⠀⠀⠀⠀⡴⢧⡖⠀⠀⠐⠊⠀⠈⠹⣮⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢦⠠⠀⢠⣥⡀⠄⢰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣿⣿⡷⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣦⣿⣿⣤⣾⣆
⠀⠀⠀⢀⣀⡀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⡿⢿⠿⡿⢿⣿⣧⣶⣦
⠀⠀⠀⠈⠁⠙⣿⣿⡅⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⡇⠀⡆⠀⢸⣿⣿⡿⠃
⠀⠀⠀⢀⠠⠀⠛⣿⠃⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢻⣀⣿⠀⠀⡀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⡇⠀⠃⠆⠸⣿⣿⣿⠗
⠀⠀⠀⢸⠛⠰⣶⣶⡆⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠂⠈⠟⠛⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⢷⠇⠀⣿⣿⣿⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣾⣾⣗⡿⣟⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⣿⢿⣷⣿⣿⣷⡄⠀⢀⣴⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣴⣿⣿⣿⣿⣿⣷⢠⣿⣿⠃⠀⣠⣶⣾⡿⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⡻⠋⣀⠉⠛⠿⠿⠿⢟⢻⡿⠓⣾⡿⢋⣭⡴⠶⠶⢶⣮⡽⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⠂⠔⠁⠀⣶⠀⠀⢰⣾⣿⣿⣶⡏⣼⠛⠉⣠⣶⠚⢟⣢⢹⡟⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣄⣄⢠⠉⠀⠀⢀⠁⠛⢁⡿⣸⣧⢂⠰⡟⣇⡛⢿⠿⡄⣿⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⢐⣷⣶⠔⣀⠸⠇⣿⣿⠐⠀⢫⡇⠀⣽⠄⠞⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣏⣿⣿⣿⠿⢸⢟⡿⡆⠡⡿⢸⠙⠀⠀⠸⣿⣤⠴⠺⣁⠀⠏⠀⠀⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣾⣿⣿⣢⠸⢹⡇⠇⠀⠃⠀⠀⠀⣴⣶⡛⠈⠀⠠⣠⠟⠀⠀⣼⠇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⣿⣿⣿⣿⡈⢀⣴⡀⠀⠀⠀⠀⡄⠀⠈⣿⣿⣢⢞⡻⠃⠀⠀⢠⡟⠀⣾⡏⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣌⢻⣟⣿⡇⠈⠻⠁⢼⠘⡀⣧⠀⠀⠀⢸⣿⢣⡏⠀⠀⠀⢠⡾⠁⣰⡿⢙⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣞⣿⣿⣿⠀⠻⠶⠠⠀⠁⠙⠀⠀⠀⢸⠁⢸⠁⠀⠄⢠⡟⠀⢠⡿⠁⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⡄⢠⣀⠀⠀⠀⠀⠀⠀⠘⢶⡿⠀⠁⢀⡞⠀⢠⣿⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⣾⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠁⠀⣾⡏⠐⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣷⡗⣦⣠⣤⡀⣿⣄⠸⠘⠀⠀⠀⠀⢨⣿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠿⡧⠷⠈⠃⠉⠁⠘⣿⣆⠀⠄⠀⠀⢠⣾⠃⢤⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣦⣤⣴⣾⣿⣿⣿⣿⣿⣷⣦⣤⣶⡿⠇⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⡿⠿⠿⠿⢿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⠉⠀⠀⢀⡀⠀⠀⠀⠀⠈⠙⢻⣷⣄
⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⢺⣹⠆⣔⢄⠀⠀⠀⠀⢹⣿⡄
⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⣀⣀⣔⢻⣅⢤⡥⠦⠃⠀⠀⠀⠀⣿⡇
⢠⣿⠟⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠑⣰⠇⠀⠀⠀⠀⠀⢰⣿⠁
⣾⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⢀⣿⠃
⣿⣇⠀⠀⠀⠀⠀⠀⠙⢤⣤⣤⣤⠶⠋⠀⠀⠀⠀⠀⢠⡾⠃
⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠈⠻⢿⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⡶⠟⠋
⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠋⢉⡴⢒⡶⠀⠀⠀⠀⠀⢠⡤⠖⠒⠒⠢⢄⠀⣀⣤⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢩⠒⡄⠀⠀⠀⢀⡴⠛⠓⠀⠀⠀⠀⠉⠁⠐⠛⠳⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⢀⣴⣣⠀⣀⣤⣤⣞⠳⢤⣀⣤⣀⠀⠀⠀⢨⣽⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣁⢃⣾⣿⠫⢹⠙⣧⣰⣟⢻⡛⣷⣦⡀⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠛⡟⠘⢦⡾⠀⣿⠻⣄⣼⠀⢸⡎⣧⡜⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡇⢻⣄⠀⢀⣰⣿⣄⠀⠀⢀⣼⠁⢸⡇⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠈⠉⠙⠁⠙⠙⠳⠶⠛⠁⠀⢀⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⣄⣀⣀⣠⣤⠴⣶⢦⣄⠀⠀⣼⢃⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠈⠉⠉⠁⠈⠳⢬⡼⠉⢀⣼⠟⢁⣴⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⡀⠀⠀⠀⠀⠀⢀⣤⢿⣿⣟⣛⣦⠀⠀⠀⠀⢀⡼⢁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢹⣦⡀⠀⠀⠀⠀⠀⣴⢻⡇⠘⠟⠛⠛⣲⡿⠟⢻⠁⢸⡏⠉⢻⡅⠀⠀⠀⠀⣞⠳⠞⣯⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠣⡙⣆⠀⠀⠀⢠⡇⠀⢷⠀⠀⠈⠉⠀⢀⡴⠃⠀⢸⡇⠀⠀⢿⠀⠀⠀⠀⠈⡟⣠⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢨⢸⡄⠀⠀⣼⠁⠀⢸⡇⠀⠀⠀⠐⠉⠀⠀⠀⠀⡇⣤⠀⠘⣇⠀⠀⠀⡼⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⢦⣧⠀⢀⣿⠀⠀⣼⡧⠶⠶⠤⢤⣄⡀⠀⠀⠀⣷⣿⡆⠀⣹⣦⣤⢶⡛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠾⣿⢤⡟⠁⠀⢠⡇⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠉⢸⣿⡄⠀⠀⣏⣾⣟⡛⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠴⣿⣷⣿⣠⡶⠋⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠷⣄⣸⣿⡏⠈⢉⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠉⣹⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣟⣿⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣤⣤⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⡾⠿⠻⠛⠻⠉⠉⠉⠁⠁⠉⠙⠋⠋⢻⡿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠐⠛⣻⣠⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⡴⠁⡿⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢀⣀⢀⣀⣒⣶⣶⡦⢀⢀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣠⣴⣦⣦⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⡦⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢈⣿⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣄⣀⠀⠐⠟⠻⠀⠀⠀⣼⣶⣦⡄⠀⠀⠀⠀⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⢿⢿⣿⣷⣾⢿⣿⣻⡻⠈⠁⠘⠛⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣟⢿⣽⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣧⣸⠁⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣳⣿⡡⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠏⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣿⢤⡄⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡘⠁⠀⢀⣠⣴⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⠷⠶⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡜⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠔⠁⠀⠒⠒⠒⠢⡀⢰⠁⠀⠀⠈⡆⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠒⡒⢒⡂⢰⠀⠀⠀⡆⢣⡀⠈⠀⠑⣠⠆⠈⢆⣀⣀⠢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣶⠀⠘⠀⠈⠀⠀⠀⠀⠀⢈⣉⠉⠉⠀⠀⡀⠤⢄⡀⠀⠀⠀⣄⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⡁⣠⣃⠀⠀⠂⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠉⠉⠉⠂⠀⠀⠊⣉⢠⠸⡉⢉⢇⠀⡁⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠄⠁⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠩⠉⠉⠉⠉⡀⠀⢢⢠⠊⠀⠀⢁⣀⣉⣀⣀⣀⠀⠈⠉⠉⠉⠉⠉⡅⠐⠐⠓⠒⠗⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠁⠀⠘⠜⠀⠀⠀⠁⡀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠢⠀⠎⠔⡆⠀⡼⠄⢠⢀⡄⠠⢇⠈⠉⠉⠉⠁⠀⠁⠀⠀⢐⣁⣈⡆
⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠁⠀⡀⠘⠀⠂⠀⠃⣠⠈⠉⠁⠭⠀⠉⠁⢀⠀⠐⠒⠒⠒⠒⠒⠀⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠠⢵⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⡠⠠⡀⠘⠀⠰⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠛⠛⠛⠋⠳⠀⡠⠘⠢⡄⢹⠀⠀⠄⠂⠠⠀⠀⠀⠀⢀⠀⠢⡤⠂⢀⠀⠈⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠀⠀⠀⣀⠀⣬⠁⠁⠀⢸⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⢀⢄⠀⠀⠘⠀⡁⡠⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠶⠦⠀⠈⠠⠀⡀⠀⢠⢾⠀⢴⠊⡀⡈⠢⠀⠀⠀⠀⡂⠈⡄⠐⠒⡄⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠁⢤⢁⣸⠀⠸⠤⢤⠃⠤⠀⠄⠄⠀⢈⠯⠀⠈⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠈⠂⠀⠀⠀⠢⡈⠲⡉⠫⠙⢇⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠄⠤⠀⠈⢂⠘⠀⠑⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⡄⠀⢠⠐⠀⠐⠁⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢉⠜⠉⠀⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠒⠒⠲⣄⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠩⡷⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢀⣀⠤⢶⣒⣖⣲⣖⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⡀⢀⣄⣤⣴⣂⡀⢐⡏⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⣠⠞⣁⠤⢍⠺⢷⡿⢶⣑⣴⠇⠀⠀⠀⣀⣤⣶⣒⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠔⠋⢉⣹⣿⡏⢈⣻⡛⢦⡗⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⣧⣬⠷⠾⡻⢯⣜⣫⣶⠟⠉⣀⣤⣤⣴⠗⠋⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠂⠀⠘⠳⠞⣱⣏⡿⠃⡾⠀⠲⠆⢀⡀⠀⠀⠀⠸⣇⠀⠀⠀⢀⣀⣈⣳⣿⡛⠈⠀⠀⠰⣿⡏⠁⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡠⠶⠒⢮⣶⣄⡾⠁⠀⠀⠀⠘⠛⠀⠯⠆⢠⡟⠁⠘⡖⠝⢃⡜⢋⣤⡇⠀⠀⠀⣀⡠⠽⠶⡚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢳⣅⡀⢀⣨⠽⠫⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠈⠚⠳⠋⠁⠘⡇⠀⠀⡞⠁⠚⢂⡠⢾⡀
⠀⠀⠀⠀⠀⣠⠶⠋⠉⠉⠙⢳⣾⠁⢿⣿⡶⠒⠒⠶⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠿⠟⢚⡧⢃⡠⢤⠔
⠀⠀⠀⠀⣴⠿⣶⣤⡀⠀⠀⠈⢿⣶⡾⠟⠁⠀⠀⢀⣠⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠈⢓⡉⢉⡁⣼⢿⣇⡬⠃
⠀⠀⢀⡾⠁⢀⡾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⢻⡟⠛⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⣤⠀⠀⠀⠀⠀⠀⠸⡍⢻⡟⢡⡗⠛
⠀⠀⢸⠃⠀⣾⢸⠃⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⢠⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⣤⠀⠀⠀⢠⡗⠤⣈⣹⡄
⠀⠀⠘⣇⠀⠘⢾⡀⠀⣀⡀⠀⠀⠀⣀⣿⡤⣄⣴⠋⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⢧⣈⣁⣀⣀
⠀⠀⠀⠈⠳⣄⠀⠙⠛⠑⢧⣄⠀⠰⣿⠈⠀⢈⣀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠒⠛⠦⠤⠶⠤
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⣀⣺⠃⠀⢻⣃⣤⠟⠉⡶⠳⠞⠛⢃⡀⡀
⠀⠀⠀⠀⠀⠀⠀⢧⠙⠚⠋⠁⠀⠀⠀⠉⢧⡀⠉⠙⠛⠛⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣀⡠⠤⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢤⡱
⠀⠀⠀⢀⡴⠊⢀⢤⡀⠥⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠠⠞⠁
⠀⠀⢠⠚⢠⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠘⡄
⠀⠀⠏⠀⠴⠁⠀⠀⠀⠀⠀⣀⠤⢖⠊⢉⠀⢨⠉⠢⡄⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⡲⢄⡀
⠀⠀⡆⠀⢢⣀⣀⣀⡠⠴⡊⠁⢀⡠⠖⠚⠉⠙⢖⡁⢘⡄⠀⠀⠀⠀⠀⠀⠀⠙⠻⢄⡠⠈⠑⡦⢄⡀
⠀⠀⠑⢤⡆⢀⡅⠀⣰⡀⠔⠊⠁⠀⠀⠀⠀⠀⡸⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠦⣀⡀⠉⢢⡀
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⡀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠂⠂⠉⣃⠀⢠⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⢉⠃
⠀⠀⠀⠀⠀⠀⡠⠊⠁⣀⡸⠆⠘⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠔⠉⠣⡠⠋
⠀⠀⠀⠀⢀⠜⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢈⠉⠩⠉⠈⠁⠐⣀⡈⠖⠊
⠀⠀⠀⢠⠊⢠⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠀⠈⠁⠉
⠀⠀⠀⠈⠲⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢠⠠⢠⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⡒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠈⠉⠀⢘⡀⢠⣀⣢⠀⡄⠉⡱⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣀⣰⠶⠷⣤⠂⠑⣄⠀⠀⠀⢀⠔⠊⠀⢄⡠⠖⠚⠉⠁⠀⠀⠀⠀⠀⠉⠺⣠⠄⠓⡄
⠀⠀⠀⠀⠀⠀⠀⡜⠁⢠⠜⠁⠀⠀⠈⢲⠁⠈⡄⠀⠀⠈⠢⠼⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢱
⠀⠀⠀⠀⠀⠀⣜⠁⢠⠎⠀⠀⠀⠀⠀⠈⡇⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠂⠼
⠀⢘⠁⠓⠒⠋⠀⣡⠊⠀⠀⠀⠀⠀⠀⠀⠹⣀⠘⢢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠖⠐⠒⠲⠒⢠⠀⠴⠲⠏⠁⡴⠁
⠀⠈⠓⠆⠷⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣆⢠⠅⢹⠀⠀⠀⠀⠀⠀⠑⠚⠶⠶⠀⠤⠀⠤⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠈⡦⠀⠀⠌⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⡀⢠⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⢀⡀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⢂⠀⠀⠁⠀⠂⠀⠀⣀⠌⠀⢀
⡡⠊⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⡈⢀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⡈⠀⠀⠁⠤⠈⠀⠀⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡤⢊⠽⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠄
⠀⠠⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠐⠃⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠓⢄⡀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣠⣴⠆⠀⠠
⠀⠀⠀⣀⠤⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠠⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉
⡤⠴⠋⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢄⠘⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⡐⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡂⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠊
⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠈⠓⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠂⠀⠂⠀⠀⠈⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡴⠻⣄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣟⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢀⠁⠀⠀⠀⠀⠀⠀⠈⣶⠀⡀⠈⠐⠋⠀⠀⠈⢷⡄⠀⠠⠀⡀⠀⠀⠀⠈⠁⢀
⠀⠀⠀⠘⢶⣤⣄⡀⠀⡜⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⣀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⡀⠀⠀⠀⠉⠙⠛⠾⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠙⠒⠒⠋⠙⠃
⡀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠂⠀⠀⡄⠀⠃⠀⠀⢀⠀⠀⠀⢀⠀⡄⠀⠠⠐⠂⠄
⠀⠀⠀⠀⠐⠄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠠⠀⠈⠂⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⢀⠀⠄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠠⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠔⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠔⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣈⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣔⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⡾⢛⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⠋⠀⠘⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⢲⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⢹⣾⣿⣿⣷⡄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⡾⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⣼⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⢰⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣽⣿⣿⡀
⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡀
⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣧⣀⠉⣨⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣦⣀⣠⡄⠀⠀⡀⢀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢹⣇⣠⡄⠊⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⣉⣉⢛⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠿⣿⡿⠿⠿⠟⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⡿⠛⠋⢛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠄⠀⠀⠀⠐⢻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢻⡇⠀⠀⠀⡀⣀⣤⣴⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⡇⣸⣤⣤⣶⣾⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣶⣤⣴⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⠶⠿⠟⠛⠛⠛⠛⠛⠛⠷⢶⣶⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧
⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣇⣀⣀
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠿⠋⠉⠉⠉⠙⠛⠷⢶⣤⡀
⠀⠀⠚⠋⠁⠴⠦⢤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣴⣶⣶⠶⠾⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⣸⠷⢦⣤⣄⡀⠈⠉⠉⠉⠉⠉⠉⠛⠛⠛⠓⠚⠻⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⣿⠀⠀⣸⠏⠙⠛⠛⠓⠶⠶⠶⠶⠦⠤⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣠⣤⣶⠿⠋
⠀⠀⣿⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⡿⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⢿⣿⣿⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠿⣿⠟⠋⠉⠉
⢀⣴⡿⢦⣌⠁⠀⠀⠀⠀⠀⠀⠀⠈⢉⣀⣠⡤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣙⣛⠛⠷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿
⣾⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠉⠀⣀⣀⡈⠙⢷⡄⠀⠀⠀⠀⠀⣠⡾⠋⠉⠉⠉⠉⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣶⣇
⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣰⣿⣿⡟⠛⢧⡀⢹⡆⠀⠀⠀⣰⠟⠀⢠⣶⣿⡿⠛⢦⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣿
⠘⢿⣦⣤⣴⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣥⣤⣾⠇⢸⡇⠀⠀⠀⣿⠀⠀⣿⣿⣿⣇⣀⣴⡷⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣾⣇⣀⣤⡿
⠀⠀⠈⠉⢿⡄⠀⠀⠀⠀⠀⠀⢻⣄⠀⠘⠿⡿⢿⡿⠛⢀⣼⠃⠀⠀⠀⢻⣄⠀⠹⣿⣿⣿⣿⡿⠃⢀⣿⠇⠀⠀⠀⠀⠀⠀⣴⡟⠛⠛⠋
⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣀⣀⣠⣴⠟⢁⡴⠀⠀⠀⠀⠻⣦⡀⠈⠉⠉⠉⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⢰⣟⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⠶⠶⠟⠋⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠈⠑⠾⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣀⣀⡀⠀⠀⠀⠀⠤⠤⠀⠀⢀⣀⣀⣤⡴⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⠿⠿⠿⢶⡾⠿⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⠶⠆⠀⠉⠁⠀⠀⠈⠉⠑⠲⡶⠖⠒⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⢀⣀⣴⠞⠃⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠖⠒⠒⠒⢲⠒⠒⠒⠒⢆
⠀⠀⠀⠀⠀⠀⢀⡤⠋⠙⢳⡄⢀⡴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⢸⣷⠀⠀⠀⢸⠃⠀⠀⠀⠛⠃⠀⠀⠀⣸
⠀⠀⠀⠀⠀⡴⠋⠀⠀⣠⠞⠛⠋⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⣤⠟⠉⠒⣤⡀⢸⠇⠀⠀⠀⣤⡄⠀⠀⠀⣿
⠀⠀⠀⠀⣤⠁⠀⠰⠶⣄⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠁⠑⢦⡀⠀⠙⢻⡄⠀⠀⠀⠈⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠙⢦⣀⠀⠀⠈⠙⠲⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠙⠷⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠛⠲⣄⡀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⢀⠉⠁⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⣰⠂⣄⢈⡽⠆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⡈⠛⠂⠀⠀⠈⢰⠄
⠀⠀⠀⠀⠀⠀⢁⠀⠈⠏⠀⠀⣠⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣉⠶⠦⠀⠀⠙⠣
⠀⠀⠀⠀⠀⠀⠀⠐⠷⢠⡤⠞⠉⢸⡟⠛⠛⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠖⠶⠲⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢢⠄⠂⠲⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⡉⡀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⢛⠉⠉⠉⠉⠉⢻⡇⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣶⠒⠒⠒⢶⠞⠃⠀⠀⠀⠀⢸⡆⢀⣠⣤⡀⠶⠇⣤⣄
⠀⠀⠀⢀⡀⠀⠀⣀⡀⠠⠤⠤⠈⠋⠀⠉⠉⠁⠀⢠⠗⠀⠀⠀⢀⡤⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦
⠀⢀⠶⠋⠁⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠇⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⣀⣀⣀⣎⠀⠤⠤⢈⡙⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⢀⡼⠃
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⣁⣤⣤⡤⠶⠶⠋⠁⠀⠀⠧⣤⣄⠀⠀⠀⠀⠀⠀⠁⠈⠁⣨⡇
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⠟⠛⠻⠟⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣁⣀⣈⣀⣀⣠⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡌⢻⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠘⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣿⣶⣿⣴⣤⡤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠉⢹⣿⠟⠿⠇⠀⠈⢻⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠁⠀⠀⠀⠀⢀⣠⣿⣿⣿⣷⣦⣀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⡶⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠿⠶⠖⠂⠀⠠⣈⠛⠓⠀⠀⠀⠉⠛⠿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⠀⠀⠐⢦⡤⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣄⣀⠀⣰⣄⠀⡀⠀⣼⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣯⣴⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠋⠘⠋⠈⢋⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⣄⣤⣝⠈⠁⠀⠀⠀⠤⣴⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⡄⠀⠀⣀⡀⠀⠐⠀⠀⠀⠀⢠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⣿⣿⣿⣪⣠⡏⠀⠀⠀⠀⠀⢀⡄⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⢀⣄⢀⣿⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⡀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠀⠙⢿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⢿⣿⣿⡇⢀⠀⢀⠸⠿⠿⠿⠦⠤⠄⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣽⡛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣽⣿⣿⣿⠀⣴⡿⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠎⠉⠉⠻⠿⠿⣿⡿⣤⠾⣛⣋⣉⡛⣦⡀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣅⠀⠀⠃⠀⠾⡿⣷⣯⠞⢉⡤⠂⣹⢿⣷⠀⠀⠀⢰⣿⣿
⠉⠉⠉⠙⠛⠒⣲⣶⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⠠⣤⠀⢠⡟⣿⠀⠘⡇⢨⠛⣼⢿⡆⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣿⡟⠀⡟⠆⠙⠐⠀⠀⢿⣤⠼⠁⠘⠈⡏⢸⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⡇⢀⠁⠀⠀⠀⠀⣾⣏⠀⣠⠜⠀⢠⠇⣾⠀⠀⠀⣾⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⣧⢻⣽⡇⠘⠁⠄⢠⠀⠀⢸⡿⡽⠋⠀⢀⡎⢰⡏⡀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠃⠀⠈⠀⠀⣘⢁⠁⡀⢠⠟⢠⠟⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⣿⠀⠀⠀⠀⠘⠛⠀⢠⠋⢠⡟⠀⠀⠀⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⢦⣤⡄⣶⡀⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢴⣿⣯⣉⣁⣀⣄⣸⣧⡀⠀⢀⣼⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠻⠿⠿⠶⠟⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⠿⠷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣵⣶⣾⣿⣋
⠛⠋⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠔⠉⠉⠑⣄⣀⡀⢀⠔⠊⠑⠢⠤⠤⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠈⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣀⠗⠚⠉⠉⠀⠀⠉⠉⠐⠢⢒⠄⠀⠀⠘
⠀⠀⠀⠀⠀⡰⠃⣀⣀⣠⡔⠉⠹⡖⣈⣈⣉⣐⣓⣄⠀⠀⠀⠀⠀⢠⠽⠞⠁⠀⠀⠀⠀⠀⠀⡔⠐⢄⠀⠑⠐⡄⠀⠘⢢
⠀⠀⠀⠀⢰⠁⠸⡀⠀⢠⠔⢤⣠⠏⠀⠀⠀⠀⠈⠫⣣⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀⣌⠑⠂⠠⡘⡄⠀⢀
⠀⠀⠀⠀⡼⠀⠀⠑⠤⠃⡶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡆⠀⠀⠘⢤⣀⣀⣀⠀⠀⢀⣀⣀⠤⠒⡏⠃⠀⠴⠁⢱⠒⠉
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡇⠈⠁⠋⠒⠤⣀⣠⣀⣀⣀⡶⠁⠀⠀⠀⠀⠀⠈⠈⠉⠉⠀⠒⠀⠀⠀⠃⠈⠁⠀⠀⡌
⠀⠀⠀⠀⠇⠀⠀⠀⠀⢠⠃⠀⠈⠁⠀⠀⠀⢠⠀⡌⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠐⠀⠀⠀⢆⣀⡠⣄⡴⠁
⠀⠀⢀⡼⠀⠀⠀⠀⢀⠎⠀⠀⠈⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠲⡤⠒⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠈⠑⡄⢀⠀⢠⠪⣶⡄⢀⠀⠉⠂⢂⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠤⣤⠀⢒⠦⠅⡀
⠀⠀⠀⠀⠈⠁⣷⠃⠀⠁⠉⠈⢻⠋⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⠃⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠇⡀⠀⢀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡰⠀⢀⠀⠘⣄⠀⢰⡀⠁⠦⢄⡀⠀⠀⡀⠠⠂⠀⠀⠀⠀⠀⠄⢀⠈⢰⠀⠀⠀⠀⢀
⠀⠀⠠⠀⠀⠉⢠⠈⠢⣀⠀⠉⠚⠭⠶⣄⢀⠈⠐⡦⢄⡀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠝⣀⠀⠀⠀⠀⠀⡠⡄
⠀⠀⢰⠀⠀⠀⠘⠀⠀⠀⠉⠒⠒⢄⣀⣨⠖⠑⠒⠁⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠠⢄
⠀⠀⢸⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠀⠀⠀⠀⠀⡀⠴⠆⠀⠀⠀⠘⠀⠁⠉⠄⠂⠉
⠀⠀⠸⠄⠀⠀⡇⠀⠁⠠⡀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇⠤⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠊⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⢐⡊⠍⠒⠀⠀⠀⠀⠐⢀⡀⢀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠥⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐

⠀⠀⠐⠿⡆⢀⢠⣤⣴⣶⡾⣛⣿⣶⣶⣤⣀
⠀⢀⣀⠀⠨⠤⢿⣫⠽⠃⠠⢋⣶⣿⣿⠿⡙⢿⣦
⢀⡀⣻⠟⠻⠂⢈⣵⣞⡠⠀⠈⣁⠙⠈⠀⠙⢦⡉⣳⠀⡆
⢀⣈⡥⠀⢠⣆⡘⠛⡡⠀⢴⣄⠀⠀⢤⡀⠳⡌⠁⣌⣄⡀
⠀⣄⢰⠃⠀⠁⠥⠄⠂⠈⠁⠉⠀⠀⠀⠀⠀⠀⢘⢿⣿
⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠨⣽⢋
⠐⣤⡱⡀⣠⠆⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⢡⡄
⠀⠛⠁⠁⣠⢶⣦⡄⠀⠀⠀⠜⠻⠛⠉⠀⠀⠀⠀⠘⠡
⠀⠀⠈⢳⠈⠈⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⣠⠃⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡾⠒⡶⠀⠀⠀⠀⡰⣁⠀⠀⠀⠈⠑⠢⢀⠀⣀⠠⣤⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠑⠃⠀⢀⡠⢢⡟⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⠳⡌⠀⢹⡄⡀⠀⠀⠉⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢘⡀⣿⠀⠀⠀⠀⠀⠙⢆⣀⠤⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣹⠧⠈⠀⠀⠀⢀⠀⠀⠈⠇⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡜⠐⠁⠀⠀⠀⠀⠀⠠⣌⠁⢀⣆⠀⠀⣴⠏⠀⠀⣧⣤⡤
⠀⠀⢀⠀⠀⠀⠙⠢⡀⠀⡜⠱⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠙⠀⣰⠂⡰⢄⠀⠀⠀⠀⠲⠄⢸⠇⠀⠀⢿⣶⡶⠞⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠉⡕⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⣠⠆⡀⠋⠀⠀⠀⠁⠀⠀⠀⠀⠄⢀⠀⢠⡄⠐⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢢⣶⣾⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⣾⣄⡠⣄⣠⡿⠁⢼⠁⠀⠀⠀⠀⠀⠘⢆⠀⠀⣤⠊⠀⣬⣥⠀⣼⣿⣿⣿⠄
⠀⠀⣠⠀⠀⠀⠀⠰⡆⢹⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⡸⢿⣿⣿⣾⣦⣤⡉⠎⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠃⠀⣴⣦⣐⠊⠉⠉⠁
⠀⠐⠉⠀⡀⠀⠆⢀⠃⠙⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⢊⡷⠂⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⡎⠀⣠⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃⣤⣾⣿⣿⠿⠿⠿⠿⠿⠟⠋⠀⠀⠓⠦⠀⠀⠀⠍⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠠⠀⠂⡤⠀⡀⠂⢀⣀⣴⠿⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣬⣤⣶⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰
⠀⠀⠀⢀⠔⢛⠓⠲⢄⠠⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠁⠘⠉⠂⠁⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠐⠀⠀⠀⢀⠂⠒⠀⠀⢰⠐⡀⠂⠀⠠⠀⠄⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠀⠐
⠀⡀⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⢀⡐⠀⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠤⠐⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢈⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⠀⢀⠔⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⡔⠒⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠤⠀⠀⠃⠀⠀⠇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣬⣥⣤⣤⣤⣥⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠄⡀⠀⠐⡀⠀⠀⠀⠀⠈⠁⢰⠀⠀⡀⠀⠐⠼⠁⠀⠀⠀⠀⢀⠂
⠀⠈⠄⠀⠰⡄⠀⠀⠁⢀⡤⠀⠀⠀⠀⠀⠀⢸⡄⡞⠀⠀⠀⠀⢆⢤⠀⠐⠀⠆⠐
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢀⣦⠘⢄⠒⠲⠆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⡇⡄⠀⠀⠀⠊⠁⠔⠂⠀⠀⠀⠀⠀⠄⠐⠂⠀⠀⠀⠐⠀⡀⠀⠀⠈
⠀⠀⠀⡀⠸⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣷⠁⠀⠀⠥⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⡀⠠⠀⠀⡀⠀⢀⠖⠀⠊⢀⠁
⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠄⠀⠀⠀⠀⡦⠃⠀⢠⠀⡇⢀⠀⢰⡁⠀⢸⠀⡰⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠱⠠⠀⠀⠘⠁
⠀⠀⠤⠀⡤⠤⠒⡠⠔⠀⠀⠀⠀⠂⠀⡀⢀⡒⢦⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠒⠀⠤⠠⠠⣄
⠐⢀⣠⡀⠄⠀⠀⡀⠀⠀⣀⠐⠁⢀⠔⠁⠠⠉⠋⠁⠀⠀⠀⠀⠀⢀⣻⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠐⠰⠲
⠀⠘⠛⠉⠀⠈⠀⠀⠉⠁⠙⠶⠛⠛⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠈⠢⣄
⠀⠀⠀⠀⠀⠤⢠⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠈⠀⠀⠀⠁
⠀⡄⢠⠀⠀⠀⢐⡀⣠⠀⠀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡾⠋
⠀⠻⠶⠘⡆⠀⠀⡼⠘⠛⠾⠧⠢⠀⠠⠄⠀⠀⠀⠀⠀⠀⡸⠟⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠄⠀⠘⠂⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿