Boys planet Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⢀⠇⠀⠀⠀⢰⠁⠀⠀⢀⠤⠀⠀⢀⠀⣤⡀⠀⠀⠀⠀⣠⠤⣀⠤⢀⡀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡸⠁⠀⠀⠀⠑⠚⠣⡀⡰⠁⠀⠀⠀⠈⠢⠴⠚⡠⢀⡀⠾⠠⠤⠤⣀⡀⠀⠀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣣⠤⠔⠒⠉⢆⠀⠀⠐⢄⠠⡄⠈⠳⡄⠀⢀⡰⠀⠀⠀⡰⠧⢄⡼⠀⠀⠀⠀⠀⠈⠢⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢅⠤⠃⠀⢠⠀⠀⠀⠀⠘⢦⠀⠀⠀⠈⠉⠀⠒⣶⠖⠋⠀⠀⠀⡰⠁⠀⢀⠇⠀⡄⠀⡆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⢀⠀⠀⠀⢸⠄⡀⠀⠀⠀⠈⠳⡀⠀⢠⠶⣟⣆⠾⠊⠉⢄⢀⡴⠁⣀⠀⡜⠀⣜⠀⠀⡧⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⢸⠀⠀⠀⢸⠁⠀⠀⠀⠀⣀⡠⠜⠲⡧⡀⣹⢮⡭⠒⠙⠊⠁⠙⠤⡃⢰⠁⠐⢏⣠⠚⠁⠑⠶⠒⠂
⠀⠀⠀⠀⡀⠀⠀⠐⠒⠉⠀⠉⢉⡛⢧⡀⣸⠤⠤⠒⠂⠉⣀⠤⠔⠒⠁⣈⣀⡸⠤⠤⣀⠀⠀⠀⠀⠘⡎⠀⢠⠞⠉⠙⠖⠒⠆⠄
⠀⠀⠰⣉⡨⠇⡠⠔⠒⢦⠀⠒⠁⠀⠀⢳⡼⠤⢔⣒⡺⢧⡀⠀⠀⠪⣁⠀⠀⠀⠀⠀⡨⠁⠒⠒⠂⠔⠛⠲⡁⠀⣀⠀⠀⠀⡤⠒⠐⠒⠉⠉⠲
⠀⠀⠀⠀⠀⠈⠒⠤⠔⢊⡴⡚⠑⠖⣪⣝⡇⠀⢇⠀⠀⣀⠅⠀⠀⠀⠀⠉⢦⠀⠀⡜⠀⠀⠀⠀⠀⠠⠶⡖⠟⠋⢑⡤⠀⠀⢗⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢱⠀⠁⠀⣧⡼⠇⠀⠀⠓⠔⠁⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡼⠒⡲⠯⢦⠀⠀⠈⠉⠑⠒⠒⠒⠋
⠀⠀⠀⢀⠤⠔⠉⠲⡸⡂⡠⠶⣤⠊⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⠞⠀⠈⠳⠤⠔⠋⠉⠑⠂⠁⠀⢸⠀⠀⠀⠱⡀
⠀⠀⠀⢘⠄⠀⡸⠱⠧⠾⢳⠖⠃⠀⠀⠀⢀⠔⠉⠀⠀⢀⠉⠁⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠱⡀
⠀⠀⠀⠘⠤⠏⠀⠀⠀⠀⡎⠀⠀⢀⠠⠄⠜⠀⢄⠴⠓⠊⠐⠛⢴⡀⠀⠀⠀⠀⠀⢠⠴⠓⠊⠓⠒⢤⠀⠀⠔⠁⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠋⠀⠀⠀⢠⠋⢀⣴⣶⣶⣦⡀⠑⡀⠀⠀⠀⢰⠁⢠⣶⣶⣶⣦⠀⢱⠀⠢⢄⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡀⠘⢄⠀⠀⠀⢸⠀⢸⣿⣿⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⢈⣀⠀⠀⠈⠲⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠙⢦⠀⠉⠁⠈⠉⢆⠀⠛⠿⠿⠛⠁⡰⠁⠖⠉⢢⠘⣄⠈⠻⠿⠿⠋⢀⡜⠀⠉⠲⣄⣠⠇⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠢⡀⡇⠀⢀⡠⡆⠀⠑⠢⢤⠤⠔⠊⠀⠀⠀⠀⠀⠀⢈⠗⠦⠄⠄⠀⠉⠀⠠⣶⢤⣀⢀⣠⠞⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⠑⠒⠉⠀⢓⣠⠕⠀⠀⠑⠢⠤⣀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠰⠦⣤⠌⠀⠀⠈⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠒⠒⢦⡀⢀⡰⢦⡙⠂⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠊⡴⢆⡀⢠⠊⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠙⡮⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠈⠉⠑⠗⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⠑⠒⠊⠉⡆⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⢱⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⠖⠁⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠘⠂⠠⠤⠤⠤⠠⠔⠓⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺⣼⠋⠱⠤⢀⠛⢄⠀⠀⢠⠔⠢⠒⠒⢦⠀⡇⢎⢉⢌⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡤⠒⠲⣞⠀⠀⣿⠀⠀⢀⠎⠀⠀⠑⢄⡤⠀⠀⠀⠀⠈⠒⢌⠓⠒⢋⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢇⠀⠀⠀⠀⠘⠒⢄⢻⡄⠠⢋⡄⠀⠀⠀⢦⠃⠀⠀⠀⠀⠀⠀⢮⠐⣎⠁⠀⠀⠀⡇⠰⡉⠐⠠⡀
⠀⠀⠀⠀⠀⠀⡊⠉⠀⢓⢠⠋⠀⠀⠀⠀⠀⠀⢰⢸⡇⢀⠜⠀⠀⠀⠀⠀⢉⡲⠀⠀⠀⠀⢰⣒⡉⠁⠀⠀⠀⣤⣰⠀⡑⠠⠤⠇⠀⢀⡀
⠀⠀⠀⠀⠀⠋⠀⠀⡰⠁⠀⠓⡄⠀⠀⠀⠀⠀⣠⠚⢘⠙⣢⡶⠤⠤⠄⠈⠳⠤⣤⢤⣀⡤⠚⠠⡙⠒⡄⠀⠀⠸⡖⠉⡧⣄⢀⣀⣨⠌
⠀⠀⠀⠀⠀⠐⠊⠉⢠⠤⢀⡀⠑⢄⣀⡠⢶⢪⡡⠔⠋⠉⠀⠀⠀⢀⣀⡀⠤⠔⠁⠀⡄⠑⡄⢐⠁⣸⠀⠀⠇⠲⢿⣠⠁⠈⣠⠟⠳⡀
⠀⠀⠀⢠⠒⠂⢦⠀⠈⡆⠀⠈⡹⠒⠂⣤⠜⠉⠀⠀⠀⠀⠀⠀⠘⠧⢀⠀⠀⠀⠀⢀⠃⠀⠈⠁⠉⠀⢑⣶⠛⠦⢄⣩⣴⠿⠥⢲⠆⣇
⠀⠀⠰⠁⣀⠔⢱⠦⠤⢼⣖⠉⣁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⢠⠃⠀⠀⠀⠀⠀⠀⠸⡄⠫⠃⡎⠉⢣⠀⠀⠎⠘⡄⠉⠱⡀
⠀⠀⠀⠀⠀⢀⠀⢣⠀⣠⢋⠜⡡⡉⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⢀⠀⠀⠀⡠⠋⢉⠝⠹⢆⠈⠑⡞⠀⠀⠈⡁⠒⠁
⠀⠀⠀⣀⣗⠏⠦⢄⢻⠁⢀⠷⠬⠤⠇⠀⠀⠀⣀⠀⢀⣀⠀⠀⠀⠀⣀⠔⠁⠀⠈⠂⠔⠊⠀⠈⠉⠉⠀⠀⡇⠀⠀⠀⢣⡰⠁⠀⡤⠴⠱⣻⣀
⠀⠀⠀⠙⢯⠀⢸⢽⠈⢧⡌⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢇⠀⠀⡯⡇⠀⠵⠋
⠀⠀⠀⠀⠀⡄⢹⠁⠀⡸⠀⠀⠀⡠⠤⠤⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠈⡄⠀⠈⡍⣸
⠀⠀⠀⠀⠀⠘⡄⠑⢄⡇⠀⠀⡘⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡜⠢⢄⠀⠀⠀⠀⢡⡠⠊⢠⠃
⠀⠀⠀⠀⠀⠀⠘⢦⢠⠙⢄⠀⠱⣀⠀⠀⠀⠘⢄⠀⠀⠀⠀⡠⠧⠀⠀⠀⠀⠀⠀⠠⢧⡀⠀⠀⠀⢀⠞⠀⠀⠀⠉⠢⡀⠀⠨⢀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠑⣄⠀⠉⠒⢄⠀⠉⠹⠒⠲⠊⠙⠀⠀⠀⠀⠀⡄⠀⠀⠈⠉⠲⠒⠺⠉⡱⠉⠉⠢⡀⠀⢱⠀⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢨⠀⠀⠀⠈⢆⣀⣀⠀⡀⠀⠀⠀⠀⠀⠣⠤⠃⠀⡠⠄⠒⠀⠠⠔⠚⠁⠀⠀⠀⠑⠤⠜⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⡀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠈⠁⠈⠉⢹⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡈⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠔⠉⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠛⠴⠄⠀⠀⠠⠆⠚⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠋⠉⠁⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣶⣄⠀⢀⣀⡤⠤⠴⢒⣒⣒⡒⠲⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⡀⠀⠀⠘⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣭⣒⠪⢍⣁⣒⡒⠢⠈⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⣸⣇⣤⡀⢰⠋⣍⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡭⠔⠒⠒⡌
⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠰⢿⡁⣮⢿⡞⠷⠭⡿⠃⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⢠⠇⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠈⠳⠶⠏⠀⠀⠀⠀⠀⠉⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠈⣿⣷⣠⠋⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⢀⣠⠶⠂⠀⠀⠀⠀⠀⣠⢶⣦⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⢠⣿⠁⠀⠀⡤⢤⣀⣠⣴⠿⠋⠁⢠⠤⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠛⠷⠶⠶⠟⠛⠋⠁⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⡂⠀⠀⠀⠒⢂⣠⠔⠋⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢒⠚⠉⣉⣠⠞⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⢀⣴⣾⠃
⠀⠀⠀⡴⣡⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⣠⡴⣿⣿⠏
⠀⢀⡞⠑⡵⡻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⠀⠀⣀⡴⠞⢁⣼⣿⠏
⢀⡞⠀⡜⡸⢱⠙⢿⣷⡄⠀⠀⠀⠀⣀⡠⠴⠚⠉⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⢀⣴⣿⠟⠁
⣼⠁⠀⠃⠃⠈⠳⠤⠿⠿⠶⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⢉⣀⣤⣾⡿⠟⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣯⣵⣶⣾⡿⠿⠛⠉
⠹⣧⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠶⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠄⣒⡒⠢⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠪⠥⠤⠤⠤⠀⠀⠀⠀⠙⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠏⠐⠒⠀⠀⠀⣀⢀⣀⣀⣀⡐⠂⠠⠀⣀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠐⠒⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠀⢀⠀⠹⣄
⠀⣀⠤⠤⠒⠒⣒⣒⣒⡂⠤⠤⠤⠤⡴⠁⠀⢀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠄⠀⠐⠒⠂⠀⠀⠈⠁⠀⢀⡀⠸⣆
⠀⢧⠀⠀⠸⡁⠀⠀⠀⠀⠉⠉⠉⢺⠃⠠⠊⠤⠀⠀⠀⠀⡞⢭⣵⠤⠤⠤⠤⠤⣾⡭⢱⠂⠀⠀⠉⠀⠀⠀⣸⡄
⠀⠀⠑⢤⡀⠈⠒⢤⡀⠀⠀⠀⠀⡼⠀⠒⠠⠄⠀⠀⢀⣀⠈⠒⠋⠀⢀⠀⠀⠀⠉⠒⠁⣀⡀⠠⠄⠂⣈⡁⠀⡇
⠀⠀⠀⠀⠈⠑⠤⣀⠈⠑⠢⢤⣀⡟⠀⠀⠀⠒⠒⠀⠀⠀⠒⠈⠀⠀⠀⠉⠀⠐⠊⠁⠐⠒⠀⠀⠉⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠉⠒⠢⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠤⠄⠒⠂⠀⠀⠀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⡦⢤⣀⠀⠉⠓⠢⠤⣔⡂⠀⠉⠀⠀⠀⠀⠶⠥⠀⠒⠀⠀⣀⡀⠀⡉⣩⠓⠬⣑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⣀⣉⠑⠒⠤⣄⣀⠈⠉⠓⠒⠤⢤⣄⣤⠄⠀⠐⠊⠥⠤⠤⠄⢠⠏⠀⠀⠀⠉⠒⠬⣑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⡀⣀⣀⡀⠀⠉⠳⠖⠤⢤⣀⡀⠈⠉⠒⠒⠤⠤⣤⣄⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠠⠆⠀⠰⠆⠀⠀⣀⣈⣉⣉⣑⡒⠢⢤⣤⣀⣀⠈⠉⠙⠒⠒⠒⠤⠤⠤⠤⠤⠤⠋⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣒⠒⠒⠒⠒⠒⠀⠠⣄⠀⠀⠀⣀⠴⠊⠁⠀⠈⠉⠉⠓⠒⠒⠒⠂⠠⠤⠤⠄⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠂⠤⠤⠄⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠡⡀⠀⠀⠀⠀⠀⣀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠃⠀⠀⠈⢆⠀⡀⠀⠊⠀⠀⠀⢠⠄⠀⠠⣀⡠⠔⠂⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠁⠒⢾⠀⠀⠀⢠⠊⠁⠀⠉⠀⠀⠄⢄⠀⠀⠀⠀⢈⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠠⠊⠀⠈⠂⡄⠀⠀⠀⠀⣀⠀⠀⠘⠒⡄⠀⠐⠣⡤⠖⢍⠁⠀⢈⠇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠔⠉⠀⠉⠃⠀⠀⠀⠀⠚⠢⡀⠀⠘⠀⠀⠀⠀⢰⠁⠀⠀⠀⡀⠀⠀⢡⠠⣇⠀⠀⠐⢯⠝
⠀⠀⠀⠀⠀⠀⢴⡃⢩⡃⢀⡀⠀⠸⠀⠀⠀⠀⢠⠊⠉⢢⠀⠀⠀⠃⠀⠀⠀⠆⢀⠒⠊⠀⢀⡤⠔⡁⠒⡄⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠀⠀⠀⠙⠆⠀⠀⠈⠢⠄⠊⠀⠀⡤⢆⠀⠀⠀⢀⣤⠀⠀⠀⢀⠀⠀⠈⠈⠁⠀⠰⠊⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣹⠂⠀⠀⡸⡀⠀⠀⠀⢀⠀⠀⠀⢀⠇⠀⠑⠀⠐⡇⠀⡘⠀⠂⠙⠤⠀⠤⠢⢀⡀⠜⠢⡀⢠⡜⠑⡞
⠀⠀⠀⠀⠀⣀⢀⡄⠀⠀⠀⠀⢀⠌⠀⠉⠒⠀⠒⠉⠑⠀⠐⠈⠀⠀⠀⠀⠀⠆⠀⢇⠀⠀⣀⠤⢀⣀⠠⠊⠀⠔⠂⠛⢆⠘⠊⠉⠀⠀⣄⠀⡄
⠀⠀⠀⠰⠢⡄⠦⢸⣠⡀⠀⢀⠊⠀⠀⠀⠀⠀⣀⠤⠄⠠⠄⠀⠀⠀⠀⠤⠊⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠈⢂⠀⠀⣠⣰⠠⠆⡤⠒
⠀⠀⠀⠲⡓⠀⠀⠀⡔⠀⠀⠆⠀⠀⠀⠀⠀⡘⠁⠀⢀⡀⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⡄⣀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠆⠀⠐⠀⠀⠀⠐⣓⠂
⠀⠀⠀⠀⠈⠰⡀⠀⢆⠀⢈⠀⠀⢀⠔⠀⠒⠁⢈⠖⠁⣀⣀⣀⠈⠣⡀⠀⠀⠀⠀⡠⠋⢀⣀⣀⡈⠑⢎⠀⡎⠀⠀⠀⠀⠀⢠⠀⢀⠇⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠑⣶⠀⠀⠄⠀⠀⠀⠀⠆⠀⣾⣿⣿⣿⣷⠀⢱⠀⠀⠀⠰⠀⢰⣿⣿⣿⣿⡆⠈⡆⠈⠑⠠⢀⠀⠀⠀⡖⠁⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡇⠱⣀⠈⠢⠄⠀⠤⡄⠀⢻⣿⣿⣿⡿⠀⡸⠀⠀⠀⠰⠀⠸⣿⣿⣿⣿⠇⠀⠖⠠⢄⠀⠀⠱⠀⠀⡇⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠇⠀⠈⢣⠀⠀⠀⠀⠈⠢⣀⠈⠉⠉⣀⠔⠁⢀⠀⠀⠀⠑⢄⡈⠉⠉⢁⡠⠊⠀⠀⠀⠣⡀⠀⡁⠀⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠫⣉⠀⠀⠀⠀⢄⡠⠂⢀⠂⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠒⠤⠀⠠⠤⠄⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠰⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁⢀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⡀⣄⠀⠀⠀⠀⠀⠀⣴⡁⠤⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠖⠒⠒⠒⠒⡦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⡀⠤⠤⠄⠒⠁⠀⡰⠁⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠑⠤⢄⠀⠀⠀⢜⠀⠀⢀⠖⠉⠁⠉⠲⣄
⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢀⡈⠷⡀
⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠘⢆
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠈⢧
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⡠⠄⠒⢒⡒⣈⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠈⡆
⠀⠀⠀⡇⠀⠀⢀⠔⠢⢄⠴⠁⠀⠀⡃⣶⡆⡃⠀⠀⠀⠀⠀⠀⢘⢴⣦⢘⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⢇⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠑⠢⠒⠁⠀⠀⠀⠀⠀⠀⠈⠂⠔⠊⠀⠀⠀⠈⠉⠉⠑⠢⡀⠀⠈⡇
⠀⠀⢸⠀⠳⣄⠈⠒⠤⠤⠐⠒⠠⢄⡀⠀⠀⠀⠀⠀⠲⠖⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠒⠤⡀⠀⠈⢢⠀⡇
⠀⠀⢸⡀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠊⢀⡇
⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⢄⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠸⡀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⢳⡀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠱⡄⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠂⡂⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠸⡀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⢣⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⢁⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠦⠤⠤⠤⠤⠴⠚⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠐⠒⠂⠉⠉⠩⠁⠀⠀⡀⠀⠀⡀⠉⠉⠁⠒⠂⠤⣄⡀⠀⠀⠀⠀⠀⠒⠀⠀⣀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⢃⠀⠀⠀⢀⠠⠠⠄⠂⢀⣀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠐⠒⠊⠁⠀⠀⠀⢊⠀⠀⠁⠂⠀⠊⠀⠀⢀⠀⠀⠀⡀⠠⡄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⢀⠀⣀⣀⡠⠂⠀⠂⠤⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣂⣀⠀⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠢⡀⠀⠁⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⣠⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⠤⣄⡈⠃⠀⠀⠀⠀⠀⠀⠑⠠⣀⠈⠀⠁⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⣠⠒⢉⣻⠦⡀⠀⠀⠀⡞⢱⡆⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠠⠄⢚⡄
⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠁⠀⡇⠀⠀⠀⢷⡐⠀⠂⣸⠇⠀⠀⠀⠀⠀⢀⣀⠤⠄⠂⠁⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠠⠠⠄⠀⣀⣀⡀⠁⠒⢠⢀⣀⡈⠲⠦⠔⠚⠒⠂⠀⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠆⠉
⠀⣠⠔⠒⢶⡀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠈⠳⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠐⠂⠉⠀⠀⠈⢡⠀⠀⠇⠀⠂⠀⠐
⠀⢸⡄⠀⣠⠆⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⠒⠂⠁⠀⢰
⠀⠀⠁⠈⠁⠀⠀⠀⢣⠀⠀⠀⠀⠀⠂⠈⠀⡠⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⡀⠀⠐⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⢀⡤⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⢄⠀⢀⠂⠀⠧⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⣠⠞⠀⢸⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠑⢌⠂⡀⡠⠒⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠠⠤⠐⠂⠉⠀⠀⠀⠀⡠⠞⠁⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠉⠣⢄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⣀⣄⡀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⢀⣀⠨⠆⠒⠉⠁
⠀⠀⣻⠀⠀⠸⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⢲⡦⠀⠀⠀⠐⠒⠒⠂⠉⢹⡇
⠀⠀⠉⠆⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠉⠉⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈
⣶⣶⣶⣾⣶⡷⢾⣾⣿⣿⣿⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣷⣶⣾⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⢷⡾⢷⢶⠶⠿⣶⡶⠶⢶⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠄⢐⠒⠢⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠈⠀⠠⠤⠄⠀⠀⠀⠀⠙⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠐⠂⠀⠀⠀⡀⠀⠀⠀⢀⠀⠂⠀⠀⢀⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⢀⠀⠹⣄
⠀⢀⠤⠄⠒⠒⣒⣒⣒⠀⠤⠤⠤⠄⡴⠁⠀⢀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⡀⠈⣆
⠀⢣⠀⠀⠸⡁⠀⠀⠀⠀⠉⠉⠁⢰⠃⠠⠊⠤⠀⠀⠀⠀⡞⢩⣵⠄⠀⠤⠤⠤⡮⡭⢱⠂⠀⠀⠉⠀⠀⠀⣸⡄
⠀⠀⠑⢤⡀⠈⠒⢄⡀⠀⠀⠀⠀⡼⠀⠂⠀⠄⠀⠀⢀⣀⠈⠒⠉⠀⠀⠀⠀⠀⠈⠒⠁⢀⠀⠀⠄⠂⣈⠁⠀⣇
⠀⠀⠀⠀⠈⠑⠤⣀⠈⠑⠢⢄⣀⡙⠀⠀⠀⠐⠒⠀⠀⠀⠒⠈⠀⠀⠀⠉⠀⠐⠊⠁⠐⠒⠀⠀⠈⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠉⠒⠢⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠐⠀⠀⠀⠀⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡦⠤⣀⠀⠉⠓⠂⠤⢔⡀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠒⠀⠀⣀⠀⠀⠈⣩⠓⠬⣑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢀⡉⠑⠒⠤⣄⣀⠀⠉⠓⠒⠤⢤⣄⡤⠄⠀⠀⠂⠠⠀⠄⠀⢠⠏⠀⠀⠀⠉⠒⠬⣑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⢀⡀⠀⠀⠉⠑⠒⠤⠤⣀⡀⠈⠉⠓⠒⠤⠤⣤⣀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣀⠀⠠⠆⠀⠰⠆⠀⠀⠀⣈⢉⢉⢑⡒⠢⠤⣤⣀⣀⠈⠉⠙⠒⠒⠂⠤⠤⠤⠤⠤⠤⠊⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣐⠀⠒⠒⠀⠒⠀⠠⣀⠀⠀⠀⣀⠤⠊⠁⠀⠈⠉⠁⠓⠒⠒⠒⠂⠠⠤⠤⠄⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠂⠠⠤⠄⠐⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠚⠉⠉⠉⠉⠉⠉⠉⠉⠓⠲⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⢠⠃⠀⠀⠀⢀⠞⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣀⡴⠋⠀⠀⠀⠀⠈⠢⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢀⡾⠀⠢⢄⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⢄⡀⢀⣼⠀⠀⡿⠀⠀⠀⠀⣷⣄⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⡇⠀⠀⠀⢠⠃⠀⠀⠀⠀⢧⠀⠀⠀⠙⠛⠛⠀⢠⠃⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⣇⢀⣀⣔⡥⠄⠒⠤⡀⠀⠀⠓⢤⣀⣀⣀⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠸⡇⢠⠞⠁⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠂⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⠤⣄⠀⠀⠀⢸⠇
⠀⠀⠀⠀⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡔⠊⠉⠉⠉⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⣀⠎⠀⠀⠀⡏
⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠓⠤⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⡤⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡸⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡠⠤⠒⠁⠀⠀⠀⠀⢠⠎⠁⠀⠉⢦⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠈⠦⣀⡀⣀⡼⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢈⠆⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠤⢤⣀⣀⣀⣀⣉⣒⣁⣀⡤⠤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⢀⠀⠀⠱⢀⠀⠇⠀⠀⠀⠀⢠⠀⠘⠀⠀⠀⠀⠂⠀⡐⠁⢀⠀⠀⠁⠀⠀⠈⢢⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⡀⢔⡧⠊⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠰⠄⢀⠀⠀⠀⠆⠀⠀⠃⠀⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡠⢔⠨⠒⠡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢆⠀⢀⠐⠠⠀⠀⠀⠄⡰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠪⠓⡀
⣂⠅⠊⢁⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⡄⠀⠀⠑⠢⠄⡀⠐⠀⡉⠞⠁⠀⠈⠀⠀⠀⠀⠀⢠⠐⡄⠀⠀⠈⢌⡠⠴
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠈⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠁⠐⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠄⠐⠒⠂⣤⣔⣈⠨⡂
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⢴⠁⠀⠂⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⣠⠶⠻⠋⠈⠣⣼⡥⠀⠀⠀⠈⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢌⠈⠀⠀⠁⠀⠁⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡴⠊⠕⠁⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡂⠀⠀⠀⡀⠀⠀⠀⣠⠀⠅⠀⠀⠀⠀⠀⠀⠀⢀⣾⡩⠊⠀⠀⠀⠀⠀⠀⠀⠰
⣄⣦⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⢈⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣱⣀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⢔⠌
⠀⠐⢄⢄⠑⢄⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡑⠀⠀⠀⠈⠂⠙⠉⠑⠂⠀⠐⠈⠀⢀⠀⠀⠀⠀⠈⢜⠄
⠀⠀⠀⠢⡡⡀⢡⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠠⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠑⠜⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠁⠀⠀⠀⠀⢈⠞⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⢄⡀⡀⣠⡔⢁⠜⡘⠀⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⡠⠄⠒⠂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠒⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡂⠀⢠⠋⠀⠖⠀⠀⠀⠄⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡇⠒⠀⠀⠠⠄⠀⠀⠀⠀⡆
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠖⠁⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⢀⠠⠀⠀⠀⠇⠁⡂⠠⢀⠀⠀⠈⠀⢀⠋
⠠⠀⠀⠠⠀⠀⠀⠀⠀⣬⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢀⠀⠀⠐⠂⠁⠀⠀⠈⠢⢄⠀⠀⠄⠈⠐⡠⠎⠀⠔
⡀⠀⠂⠀⠀⠀⠀⠀⠀⠑⠮⣇⣀⠀⠠⠀⠀⠀⠀⠀⢰⢉⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠉⠉⠚⠒⠒⠚⢻⠿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠰⡉⠇⠀⠀⠀⠀⠑⠂⠤⠤⠄⠊⠁⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠂⠉⠀⠀⠑⠢⡖⢒⢤⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠂⠉⡀⠒⠤⡀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠐⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢸⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⠜⠀⠀⠀⠀⣎⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢀⠞⠣⠤⠤⠒⠉⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢠⣏⣀⣀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⡞⠀⠀⠈⠃⠀⠀⠀⢸⠀⠀⢀⡀⠀⢠⡇⠀⠁⠀⠀⠀⢸⣆⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⢰⠃⠀⠀⢀⠆⠀⠀⠀⠘⡄⠀⠀⠙⠛⠟⠁⢀⠇⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⢸⡀⢀⣠⡪⠤⠀⠤⡀⠀⠈⠢⢄⣀⣀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⢀⠔⠁⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠃⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠢⡀⠀⠀⠀⡇
⠀⠀⠀⠸⡞⠀⠀⠀⠀⠀⠀⠀⠈⡆⢠⠊⠁⠀⠈⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⢠⠇
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢁⢂⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⡀⣀⠔⠁⠀⠀⡼
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢸⠘⢄⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡌⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡔⠉⠈⠡⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⣠⠜⠁⠀⠀⠀⢀⠤⠒⠤⡀⠀⠀⠀⠀⠀⠐⠤⠤⠞⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡉⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠉⠐⠒⠁⠞⠉⢱⠀⠀⠀⠀⠀⢀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⣀⡀⠀⠀⠑⠐⢋⣀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⡿⠿⢿⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⡿⠈⠉⠉⠛⠻⠿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠛⠋⠁⠀⠀⠘⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠛⠶⠶⠤⢤⡀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣼⠃⢀⣠⣤⣄⡀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠙⢿⣿⣧⡀
⠀⠀⠀⠀⠀⣰⣿⣿⠋⠀⠀⠀⠀⢠⡴⠖⢦⡀⠀⠘⡆⠀⠀⠀⠀⢻⠀⠀⠀⢀⡼⠃⠀⢾⣿⣿⣿⣿⣦⡀⠀⠏⠀⠀⡴⠳⠀⠀⠀⠙⢿⣿⣆
⠀⠀⠀⢀⣼⣿⡟⠁⠀⠀⠀⠀⠀⡟⠀⠀⠀⢧⠀⠀⣹⣴⣶⣿⣿⣿⣿⣷⠶⠋⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⡄⣄⠀⠸⠀⠘⢇⠀⠀⠀⠈⢻⣿⣦
⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠘⢦⣾⡿⢿⣿⡿⠿⢿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡈⠑⡂⠀⠀⣸⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠈⢻⣧⠀⠀⣀⣤⣶⣾⣶⣧⣤⠀⢹⣿⡧⠌⠙⠒⠚⠁⠀⠀⠀⠀⠀⠀⢻⣿⣧
⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠁⣿⡇⠀⠀⣾⣿⣳⢸⣿⠀⣼⡿⠉⠀⠀⠀⠈⠻⣿⡄⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇
⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠹⣷⣄⡀⠙⢛⣫⣾⠏⢸⣿⠁⠀⢠⣾⡟⣢⠀⣿⣧⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣧⡄⠘⣿⣧⠀⠘⢿⣿⠟⣰⣿⣧⠐⠀⠈⣆⠘⡍⢆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣾⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠛⠉⠁⠁⠀⠀⠀⠀⠈⠻⣿⣶⣶⣶⣾⣿⢋⡀⠀⠀⠀⢸⠀⣹⠘⣆⠀⣀⣀⣀⠀⠀⠀⢸⣿
⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠿⠿⠿⠿⠦⠤⠤⠄⢤⠀⠘⠋⠁⠀⠈⠉⠉⠁⢹⠀⠀⠀⢸⣿
⣿⣿⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣦⣤⣄⡀⠀⠈⠢⢤⣀⣀⣀⣀⡤⠤⠖⠛⠀⠀⠀⢸⣿
⣿⣿⡇⢸⡄⠀⠀⢠⠞⠑⠢⡀⠀⡀⠀⠀⠀⢻⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠚⠉⠉⠙⣿⣿⠛⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⢹⣿⣧⠀⣧⠀⠀⡏⠀⠀⠀⠘⢤⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⡿⠀⢀⠀⠀⠀⣿⣿⠀⠀⠈⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠸⣿⣿⡄⠘⣆⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⢿⣿⣷⠀⠘⣆⠀⠳⡀⠀⠀⣀⡀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏
⠀⠘⣿⣿⣇⠀⠈⠳⡀⠈⠒⠋⠁⡇⠀⢀⣀⣀⡀⠙⠷⣦⣤⣀⡀⠀⠀⠀⣀⣠⣴⣾⣿⡿⠋⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟
⠀⠀⠸⣿⣿⣇⠀⠀⠈⠛⠛⠉⠙⡎⠉⠀⠀⠀⠀⠈⠁⠚⠻⡿⢿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠙⣿⣿⣧⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠁
⠀⠀⠀⠀⠘⢿⣿⣷⡄⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⢿⣶⣶⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣰⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣌⠙⠓⠲⠶⢦⣄⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣤⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣄⣀⠀⠹⣦⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣶⣿⣦⣀⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣈⣁⣄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠒⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠙⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡀⠀⠀⠀⡿⠀⡁⠀⠀⠀⠀⢸⠿⢈⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⠉⡳⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠁⠀⢑⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⠔⠊⠀⠀⠀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠉⠀⢀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⣸⠀⡂⠀⠂⠀⠀⠰⠀⡂⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠉⠁⠀⣀⠤⠔⡎⠁
⠀⠀⠀⠀⠀⠀⡠⠔⠋⠀⢀⠔⠊⠀⣇⠑⠒⠁⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠊⠉⠀⣀⡠⠤⠒⠊⠉⠀⠀⣸
⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠧⣀⣀⣀⢸⡤⠤⠤⠐⠒⠚⠉⠉⠀⢀⣀⡤⠤⠲⠊⠉⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡤⠤⠔⠒⠊⢉⠁⠀⠑⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠁⠀⠑⢤⡀⠀⠀⠀⠀⡁⠀⠀⢅⠁⠀⠀⠀⠂⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⡈⠀⠀⠀⠀⠀⠀⢀⣨⠤⠒⠁
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠁⠀⢀⠉⠉⠁⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠠⠱⡄
⠀⠔⠂⢀⠭⠭⠥⠤⠄⠐⢒⡲⠁⡀⠄⠀⠂⠀⣀⢄⡀⠀⠀⠀⢀⡀⠁⢀⠀⠀⠀⠀⠘⡄
⠀⠑⢄⠈⠢⢄⠀⠀⠀⠀⠀⠇⠈⡁⠀⠀⠀⠀⠣⠿⠃⠀⠀⠀⠙⠯⠜⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠁⠢⢄⡉⠒⠤⣀⢐⠂⠀⠀⠀⠠⠥⠄⠀⠂⠀⠀⠒⠀⠰⠤⠀⠀⠀⠐⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡈⠑⠂⠤⣄⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠒⠠⢄⡈⠁⠒⠢⠅⣀⡀⠀⠀⠘⠀⠀⠈⠁⠀⠀⠀⢠⠏⠐⠨⢕⡢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠙⠒⠒⠤⣀⣈⠉⠙⠚⠡⠄⣈⡀⠀⠀⢀⠎⠀⠀⠀⠀⠈⠑⠨⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⠀⠠⠅⠀⠤⠄⠀⠈⠙⠒⠒⠠⣤⣀⣉⠉⠙⠒⠂⠤⠤⠄⠀⠀⠀⠨⠂⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⣐⡒⠀⠀⠀⠤⠄⠀⣀⡠⠔⠉⠀⠉⠁⠀⠐⠒⠂⠀⠀⠀⠀⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠂⠈⠉

⣶⣶⣶⣶⢶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⠶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠢⡀⠀⢀⡜⠁⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡠⠓⠌⣲⠿⠀⢀⠄⠀⠀⠀⠈⠣⡀⠰⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣆⠞⢀⡼⠁⢠⣾⠃⠀⠀⠀⠀⠀⠀⣀⡄⣀⣸⠿⠀⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠙⡶⠋⠀⣠⣟⣡⣀⣀⠀⠀⠀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⢈⣳⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠉⠉⠃⢀⣀⣀⠀⠀⠀⠀⠀⡀⠀⣠⡄⡄⠀⢄⡄⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⢀⣴⠟⠁⣼⡇⠀⠀⠀⣼⠇⠀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣠⣾⢀⣠⠄⠀⢀⣀⣌⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⣾⠃⠀⣰⣿⢁⣤⣤⣼⣿⣤⠀⡩⣀⣀⠀⣠⡀⢀⣤⡄⣸⡿⠁⣤⠀⣘⢻⡉⣰⡏⣠⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡇⣀⣤⣿⢳⡿⢃⣼⣿⣿⡏⡰⣿⡟⡹⢣⣿⡴⢫⡿⢁⡿⠁⣼⠏⣰⡏⣸⣿⠏⣾⢋⡼⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⢸⡏⠁⣼⣿⢾⣣⠏⢸⡏⢿⣣⠁⢿⣉⡔⠹⡿⠁⢿⣁⡼⣇⡴⣯⠜⢿⡼⣿⠏⡸⡏⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠘⠇⠀⢿⡟⠀⠁⠀⠀⠀⠀⣁⠀⣀⠀⣀⢀⣀⠀⢀⣉⠀⠀⠀⠀⠀⠀⠀⡯⠊⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠂⣿⢢⣿⠸⣧⣼⣿⡇⠈⣧⠐⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠃⠀⣠⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣰⣿⣫⣶⠿⠛⠂⠀⠀⠀⠀⠐⠂⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⠟⠛⠀⠀⠒⠂⠀⠶⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⠟⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡶⠀⠀⣠⡤⡀⠀⠀⠀⠀⠀⠒⠫⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠐⢿⡿⢋⣵⠄⣦⣄⠀⠈⣧⠀⠀⠀⠀⠀⠀⣀⣀⡠⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠈⣇⠀⡀⠀⠀⠳⣈⢀⡴⠛⠉⠱⡄⠘⡑⠒⣒⣛⣋⡩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣽⠋⢀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⡆⢹⣿⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠁⠘⠃⠁⢐⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠿⠓⡿⠀⠁⠀⠀⠀⠀⠀⢠⠊⠉⠳⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠄⠀⠀⡉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠚⠁⠀⡄⠀⠀⠀⠀⠀⣸⠄⠲⠖⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠑⢄⡠⠒⠀⠀⠀⡀⠀⡇⠀⢀⠔⠊⣀⠀⠀⠠⠂⢀⠴⠒⢀⡠⠆⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣌⠁⠢⣀⣰⠉⡒⠀⣜⣡⣀⠈⠀⢃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢰⠎⠀⠀⠉⠙⠀⣡⣬⣌⢣⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⣗⢷⡙⠲⠦⠀⠀⠀⠖⢹⣻⠇⠀⠁⣴⠅⢀⡅⠀⠀⠀⣀⠤⠒⣶⠀⠀⠀⠀⠀⡠⠚⠉⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣻⣆⣹⣟⠳⣤⠤⢤⡔⣊⢟⡀⠀⠀⠀⠑⠦⣄⣀⡠⠊⠁⠀⠀⣿⠀⠀⠀⡠⠊⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠹⣉⡙⡿⠿⠛⠉⠛⠃⠀⣀⡤⠖⠚⠛⠁⢀⣠⡄⠀⠀⠘⡦⢚⠾⠁⡨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡭⠍⢉⡀⠀⠀⣀⠠⠐⠚⠁⠀⠀⠀⠀⠔⠁⠘⠀⢀⡴⣊⠔⣁⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠖⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⠞⠁⠀⠀⠁⢀⡥⠚⢗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡠⠀⠀⠤⠀⠘⠈⠀⠀⠀⠀⠒⢦⡁⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠎⢸⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⢸⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣠⠇⣼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡛⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⢀⣀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⣀⡀⠀⠀⣀⠀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠉⠓⠶⠿⠟⠾⠿⠛⠲⠮⠛⠛⠻⠛⠛⠳⠂⠈⠛⠒⠲⠦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⢰⠄⠰⣓⠂⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣛⡆⠘⣯⠅⠀⠀⠘⠁⠙⠚⠁⠀⠀⢯⣀⡿⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢳⡈⠋⠈⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠉⠀⠸⣤⠞⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢇⡀⠙⠋⠀⢀⡴⣾⠟⠒⠀⠀⠀⠀⠀⠀⢠⠀⠈⠁⠀⠠⠀⠀⠀⠴⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⡀⠁⢀⡀⠀⣾⠸⡇⠀⠀⢀⠀⠀⠀⠀⠐⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠉⠀⠀⠀⠁⠀⠘⢦⣉⣒⡶⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠁⢀⣦⡀⠁⠀⠀⠋⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⣆⡆⠀⠀⣼⡤⠀⠁⠀⠀⠀⠀⠀⠤⠀⣰⢿⣦⠀⠀⣀⡀⠀⠀⠀⠈⠟⠁⠀⠰⠂⠀⠉⣻⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⡈⠀⢀⠀⠘⠀⣠⣿⣄⠀⠂⠀⠀⠀⢰⠇⢹⡘⣇⠘⠃⢹⠀⠀⠉⠀⢠⣄⠀⠀⠀⠀⠈⣡⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⡀⠀⢀⡼⠃⣼⠸⡆⠰⠆⠀⣰⠋⢀⡞⠀⠈⢁⡴⠋⠀⠆⠀⡴⠻⡏⢷⠀⠀⠀⠀⠓⠘⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⢹⡆⠀⢁⡴⠋⠀⢰⡇⠀⢹⣄⣠⠞⠁⠀⣾⣁⡠⢀⡞⣠⠶⡄⢠⠾⣇⢀⡟⠈⠳⣄⠛⠀⢘⣿⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⠄⠀⠈⢀⡄⠀⠈⢳⣴⠋⠈⠻⡄⠀⠈⠋⠉⠀⠸⡇⢻⡀⠡⡀⠀⠙⣾⠁⠀⣤⠈⠃⠀⢨⣄⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠄⠀⢀⠾⡿⣆⠀⠀⠉⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠹⣄⢳⡀⠙⠀⠀⠀⠀⡴⣿⢧⠀⠀⠛⠚⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⢦⠀⠀⢠⣷⡀⠀⠀⢀⣤⣀⣀⣀⣀⡀⠹⢸⠇⢀⣿⡀⠀⢀⡴⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠆⣠⢞⣟⢦⡀⠐⢫⣯⡓⠀⢀⡾⡴⠀⠀⢠⢠⣿⣆⠋⠀⢋⣿⡙⠀⢀⡾⣿⠳⡄⠰⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⠀⡴⢛⣟⠢⡀⠐⣫⣯⡛⢀⣞⡁⠙⠓⠒⠋⡼⣻⣘⣦⠐⢫⣿⣝⠂⢠⠞⣿⡳⡄⠘⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡴⢛⣟⠳⡄⠜⣩⣯⡙⠆⢉⣉⣙⠛⠒⠞⠛⢋⣉⡀⠰⣫⣿⣝⠆⡠⢞⣿⡛⢦⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣫⣏⠳⢦⢚⣵⣷⣍⠂⠰⠆⣄⠰⠶⠶⠀⣀⠰⠆⠘⣡⣿⣌⠃⡴⢋⣿⡙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠏⠑⠀⢋⣴⣷⣌⠓⠈⣼⣿⣄⢉⡉⣴⣿⣆⠁⢚⣡⣿⣮⡓⠀⠋⠻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡴⡷⣌⠓⢈⡴⡿⣆⠐⢀⡴⣿⢦⠀⠋⡴⣿⢦⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠾⡿⢮⠀⠈⡼⡿⠦⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⣶
⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠸⣿⣶⣤⡉⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠈⠿⠿⠃⠀⠀⠀⠀⠀⢿⣿⡿⠀⣠⣤⡄⣠⡄⠉⣻⣿⠘⣿⡄⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⠿⠿⠁
⠀⠀⠀⣰⣿⣮⣧⣿⣦⠀⠀⠀⢀⣴⣶⣶⣿⣿⣥⣤⠙⠻⣿⡟⠋⠀⠹⠿⢷⣆⣆⣦⣤⣄⡀⠀⠀⣴⣿⣼⣵⣿⣆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⣼⣿⣿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⢻⣧⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣹⣿⣿⣿⢿⡇⠀⢠⣿⣿⣯⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣧⠈⠛⠀⢸⡿⣿⣿⣿⡇⣿⡆
⠀⠀⠀⠁⣿⣿⣿⣿⠈⠁⠀⢸⣿⡟⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠟⠛⣿⣿⠀⠀⠀⠈⠁⣿⣿⣿⣿⠈
⠀⠀⠀⠀⣿⡿⢹⣿⠀⠀⠀⣸⣿⠇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⢿⣿⡀⠀⠀⠀⠀⣿⡇⣿⣿
⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠈⠻⣿⡄⠀⠀⢀⣿⡇⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠁⠀⠀⠑⠢⣄⠀⠀⠀⠀⠀⠤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣰⣴⣬⣧⠀⠀⣠⣤⣀⡀⣀⣀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠐⠒⠲⣾⠫⣴⣶⣿⡏⠐⠲⣞⢠⡫⠁⠙⢷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣏⡀⠀⠀⠀⠌⢸⡿⠋⠉⠉⠀⠱⣸⣆⡁⠀⢈⠋⢳⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠃⠀⣼⠿⠶⢀⢞⠁⡀⠀⠀⠀⢠⣿⣿⡇⠤⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠔⣨⢴⡞⠉⠁⠀⢋⠂⡸⠃⠀⠙⣦⠀⠀⠸⡏⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠂⠜⠀⣿⠇⡀⠀⠀⣸⣴⣥⠄⡠⢶⡻⡧⠀⢠⣴⠎
⠀⠀⠀⠀⠀⠀⣇⡘⠀⢰⣿⢋⣀⠀⣤⡿⣿⠁⠊⠀⠈⠉⠀⢦⡀⠷⠸⡀
⠀⠀⠀⠀⠀⠘⠿⠇⠀⣼⠟⠋⡀⠀⠈⠻⣾⣆⠀⠀⢰⡷⠁⠀⢷⣀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡠⣤⣾⡄⠠⠀⡠⠂⠁⠀⢀⢸⣥⡀⠀⠈⠻⣄⠀⠀⠙⠳⣤⣀⡀⢄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⠿⣿⣣⣾⡁⠀⠀⠀⣼⡿⠉⠻⢗⢦⣄⣀⠉⠒⠠⠤⢄⣉⠳⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⠉⠉⠉⢹⣷⣭⡴⠊⠀⠀⢰⠋⠀⠈⣿⡄⠀⠀⠀⠈⠉⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠽⣿⡸⣿⣄⣠⢶⣯⣤⡴⠤⢉⡇⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢘⢡⠉⠻⢿⠘⠁⢉⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⢸⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⡶⣞⠁⠀⠀⠀⠀⠀⠈⢧⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡼⢇⡟⠀⠀⠀⠀⠀⠀⠀⣾⠃⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠣⡾⢇⡼⠁⠀⠀⠀⠀⠀⠀⠀⢹⡁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸⣷⡤⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃⠀⠀⣀⣠⣴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣶⡏⡏⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠁⡁⠀⣀⣀⡄⣓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠛⠛⠛⠋⠉⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⠛⠛⠛⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠤⠶⠖⠋

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢴⠔⢜⣫⠝⣠⠀⠀⠀⠀⠀⠀⠀⠰⣄⠸⠟⣀⡖⠀⠀⠀⠀⠀⠀⠀⣀⣄⢰⡶⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⡀
⠀⢰⣿⣷⢸⣿⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⢦⣯⠜⢳⣶⠻⣼⡵⠋⠀⠀⠀⠀⠐⠿⠿⠏⠺⡾⢒⣕⡏
⠀⠀⣿⣇⡼⠿⡌⣿⠃⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⠂⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⢠⣶⣶⡆⢴⢶⠀⠨⡪⣇
⠀⢸⠉⠉⡆⠀⡗⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠸⠿⠀⠿⠇⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠈⠙⠁
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⣶⡶⠖⢶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣄⠶⡠⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⢰⣶⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀
⠀⠀⣠⣿⡇⢙⠸⣿⣤⠈⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣭⣤⣤⢧⣤⣬⣥⣄⠀⠀⠀⠀⠀⣠⣼⣧⣤⣿⣄⣀
⠀⠀⣾⡚⠷⣿⡾⠗⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⢾⣿⡿⣿⣿⠟⠀⠀⠀⠀⠘⠁⣿⣯⣀⣿⣌
⠀⠀⠘⢷⣤⣿⣦⣾⠏⠀⠀⠀⠀⠀⠀⡞⠛⡇⠀⢸⠀⢠⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⣿⠀⠀⠀⠀⢀⣈⣛⣁⣉⣛⣁⣈⣓⡀
⠀⠀⠀⠈⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠐⠓⠒⠓⠒⠛⠒⠚⠂⠀⠀⠀⠀⠈⠉⠁⠘⠙⠁⠉⠉

⠀⢀⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢤⣤⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⢀⡀
⠀⠘⣿⣿⡉⣩⣿⡿⠁⠀⠀⠀⠀⠀⣄⢰⣶⢀⡟⠑⠚⠛⠀⠀⠀⠀⠀⠤⠀⢁⣠⣀⡀⠁⠤⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢈⣽⣷⣾⣍⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠘⣧⣼⠃⠀⢠⠄⠀⠀⠀⢰⣶⣾⢷⡆⢠⡾⣷⣶⡆
⠀⠀⣿⣿⠉⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣼⣧⠀⠀⡄⠀⠀⠀⠀⠈⠉⠙⠛⠁⠈⠙⠋⠉⠁
⠀⠀⠘⠿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⠐⠂

⠀⠀⣀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣿⢋⢁⣉⢻⠇⢀⠀⠀⠀⠀⠀⠰⡄⢸⡿⠘⡿⠂⠀⠀⠀⠀⠀⠀⡀⠀⠠⡆⠐⢼⣧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠂⢸⣌⣛⣫⣾⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣲⠟⠁⠀⠀⠀⠀⠀⠀⣠⣧⡄⢾⣿⠂⢸⡇⠀⠀⠀⠀⠀⠠⠖⢛⣿⣶⣜⠿⠟
⠀⠀⠀⠈⠙⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⣸⣿⠀⠞⠓⠀⠀⠀⠀⠀⠀⡉⠉⣉⢉⡉⠁
⠀⠀⠀⠀⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⡀⡇⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢛⣫⣭⣭⣿⣿⣿⣿⡿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠿⠃⢐⣛⣛⣛⣛⣭⣭⠵⢚⣴⣯⡻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠛⠛⠉⠉⠉⠉⣀⣠⣴⣿⠟⠘⡿⣎⢿⣿⡀
⠀⠀⠀⠀⠀⠀⣴⡿⠋⢀⣀⣤⣤⣴⣶⣶⣿⣿⣿⠿⠛⠁⠀⠀⢻⢻⣆⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢸⡟⢀⣴⣿⣿⠿⣿⣟⣛⠋⠉⠁⠀⢠⡴⠒⠒⠆⠘⡏⣿⣎⠃⠀⠀⠀⠀⠀⢀⠀⠀⣷
⠀⠀⠀⠀⠀⢸⡇⣼⣿⠏⣴⡎⢉⣈⣉⠃⠀⠀⠀⠉⢠⣶⡶⣦⠆⢳⡘⣿⣆⠀⠀⠀⠀⠀⢸⠀⢠⣿
⠀⠀⠀⠀⠀⠀⢻⣿⡏⢸⣿⡟⢏⡹⡿⠃⠀⠀⠀⠀⠁⠉⠝⠃⠀⠈⢷⡈⠻⢷⣤⣀⣀⠴⠃⣠⢞⡏
⠀⠀⠀⠀⠀⠀⠀⢹⣷⢸⣿⣷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠛⢶⣤⣄⣀⣤⡴⠞⣡⠟
⠀⠀⠀⠀⢀⠄⠀⠀⢿⠘⣿⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⢿⣶⣤⣤⣤⣤⡶⠟⠁⠀⣀
⠀⡄⠀⠀⢢⠀⠀⢀⡟⠀⣿⣿⡇⣷⣄⠀⠻⣍⣩⡽⠃⠀⣀⣾⡇⢻⣇⠀⠀⠀⠉⠀⠀⠀⣰⣾⣿⠃
⠀⢱⡀⠀⠀⠙⠛⠉⠀⢠⣟⣾⡇⢸⣿⣷⣦⣄⣀⣠⡤⠚⠹⣿⣧⠈⢿⡄⠀⠀⠀⢳⡄⠀⠉⠉
⠀⠀⠙⢦⣀⡀⠀⢀⣤⣯⠞⢹⠃⢸⡇⣿⣿⣧⠀⠀⠀⠀⠀⠙⢿⣷⡈⠻⣆⠀⠀⠈⡇⠀⠀⡀⠀⢀⡄
⠀⢀⠀⠀⠈⠉⠉⠉⠉⠀⣠⠏⠀⣾⠃⣿⣿⡟⠀⠀⣀⡤⠶⠛⠉⠉⠛⢦⡈⢧⡀⢰⠁⢠⠞⣠⣶⣿⠁
⠀⢸⡀⠀⢀⡀⠀⢀⣠⡾⠃⠀⣼⠏⣸⣿⡿⠁⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠻⡄⠳⣘⢠⡏⣸⣿⡿⠃⡴
⠀⠀⢳⣄⠀⠙⠛⠋⠁⢀⣠⣾⠏⣰⣿⠟⠁⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢻⠘⣇⣛⣁⡤⠞⠁
⢦⣄⡀⠙⠷⣶⣶⣶⣾⣟⣫⣵⡾⠟⠁⠀⣀⣠⠤⠤⠀⠉⠛⢶⣄⣇⠀⠀⠀⠀⠀⢀⡔⣡⡭⠤⠤⡀
⠈⠻⣷⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⢠⡶⠋⠁⠀⣀⣀⡀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⣸⠋⠀⢧⠻⣿⣦⡀
⠀⠀⠀⠁⢄⠰⡠⠚⠙⢲⡀⠀⣰⠏⠀⣤⠾⠋⠉⠉⠉⠛⢦⡄⠈⣿⠀⠀⠀⠀⡰⠃⠀⠀⠀⠑⠪⠝⠛
⠀⠰⠶⠶⠦⠑⢷⠀⠀⠀⠇⠀⣿⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠹⡄⡟⠀⣀⣴⣋⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠻⣄⠻⣦⣀⣀⡄⠀⠀⠀⠀⠀⢇⡤⠞⠋⠉⣀⣀⣀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠉⠛⠻⠛⠋⠀⠀⠀⠀⢀⠔⠉⠀⠀⣠⣾⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣤⣀⣀⣀⣤⠔⠚⠁⠀⠒⠊⠉
⣿⣿⠛⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⢾⣿⣷⠀⠀⠀⣠⣤⣄⡀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⢠⣴⣶⣶⣄
⠀⠀⠀⠀⠀⠙⣿⣷⡀⣼⣿⣿⣿⣷⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠘⣿⣷⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣯⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢸⣿⣿⣿⣿⣿⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⠀⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣇⢀⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⡧⣀⢳⡜⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣉⣙⣿⣿⣿⣿⣌⡲⣯⡳⣄⠙⠛⠿⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⠟⠟⡁⠀⠑⠑⠄⠙⢿⣿⣕⣿⣿⣌⠑⠴⠿⠦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣭⣉⣉⣠⣴⣿⣧⣷⠶⠛⢶⣤⣀⡈⡙⠛⠿⠿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣷⣤⣭⣻⣿⣿⣷⣶⣷⣶⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⣖⣤⣶⢿⡿⣫⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡿⢋⣷⢟⣽⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⡿⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡦⡽⠛⠁⠀⠀⢀⣴⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢼⣿⡠⡀⠙⠋⣿⣿⣥⣤⣀⠀⠀⠀⠀⣠⣶⣶⣿⡿⢋⡟⢀⡄⠀⠀⠀⢨⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣧⡀⠀⠀⠹⣿⡅⠀⠃⠀⠀⠀⣞⢩⣿⣿⢗⣰⣿⣿⡏⣀⣀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠁⣾⣀⣴⣿⣿⣿⣷⣦⡀⠘⠃⠾⣋⣴⣿⣿⣿⣿⣟⣽⣇⣺⡵⠖⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠘⠛⢿⣿⣿⣿⣿⣿⣞⡁⢀⠀⠀⠀⣀⠀⠀⣰⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠉⠉⠛⢿⣿⣿⣷⡾⣿⣿⣿⣿⣿⣿⣿⣊⣅⣀⠄⠘⠉⢴⡿⠋
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣿⣿⣿⣿⣿⠁⠀⣠⣴⣿⡿⠟⠁⠀⠈⢈⠽⣿⣿⣿⣿⣿⣯⡷⠀⢀⣈⣍
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⡉⢈⣿⣿⣿⣿⠉⠀⠀⠛⠋⠁⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⠉⠀⠴⠖⠀⠀⠀⠠⠒
⠀⠀⠀⠀⠈⠳⢤⣀⣙⣷⣤⣀⠀⠀⠉⢸⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠐⠿⢻⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠐⢌⣹⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣩⣿⡿⢋⣤⣤⠄⠀⠀⢀⠄⠀⠀⠀⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠽⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣤⣴⣦⠀⠀⠀⠀⠀⠀⢛⣿⣾⠋⠁⣠⣤⡴⠊⠁⠀⠀⢀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⠛⠁⠀⠀⠀⠀⠀⣴⣿⡿⣷⠞⢉⡡⠈⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠿⠛⠋⠁⠏⠈⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⣾⣟⣽⠁⠀⠀⠀⠀⠀⢠⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢼⣿⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢋⣠⣤⣄⡀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠪⠤⢍⡉⣻⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠈⠈⢉⠉⠉⠐⠒⠥⢄⣀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠃⠀⠀⠀⡠⠀⠈⠙⠢⣄⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⡆⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⣿⣦⠸⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠃⠀⠈⠁⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠈⠫⠌⡿⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠠⡼⠣⠀⠀⠀⠈⢋⠉⠉⠉⠉⠉⢳⠀⠀⣰⣻⠿⠴⠲⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠕⠭⡁⢸⣦⣄⣀⠀⠀⠑⠤⢀⡠⢔⣁⠔⠺⣅⠀⠀⠀⣀⣀⠀⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⣒⣁⡀⠉⠉⠉⠉⠙⠋⢷⡉⠉⢁⠄⠀⠀⠈⠓⣤⠚⠉⠩⣇⡀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣼⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠉⠹⡁⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣴⣿⣶⣄⡠⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⣿⣿⣦⡤⠤⠔⠾⣿⣿⣿⣿⠃⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠔⠘⡏
⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⢹⠿⠛⠛⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⡩⠉⠉⠁⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠹⡍⠁⠀⠀⠀⢀⡊⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠙⢦⡀⢰⣾⣿⣿⡤⠤⠀⢒⡿⠃⠀⠀⠀⠀⠀⢀⣤⠤⣄⠀⠀⠈⢷⣅⣀⠀⠀⠀⠀⠀⣠⠊⠉⣛⠻⡉⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠤⠶⠚⠉⠀⣘⠲⠦⠀⠀⡴⠉⠑⣷⣄⠱⢤⣀⡜⠁⠀⢉⡶⢦⣀⠔⠛⠓⣾⣉⣹⣇⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⢳⣂⡉⠤⢿⣦⣀⢩⡙⠢⡴⠋⠀⠀⠀⠀⠀⠀⢾⣀⠤⣬⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡒⣉⠵⣽⡁⠈⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⢉⡝⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣊⣩⣷⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⡾⠉⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠙⣧⠀⠀⠀⠀⢻⡄⣴⠏⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⣴⠋⠀⠀⠀⡶⠛⢷⡞⠛⣦⠀⠀⢰⡏⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠘⣷⠀⠀⢸⣇⡀⠘⠁⢀⣿⠀⠀⠀⣹⠆⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⢸⠁⠀⠀⠸⣏⠀⢈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡿⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣷⠀⠀⠀⢸⡇⢀⡀⢸⠀⠀⠀⢠⡇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣾⣇⣿⠀⠀⠀⢸⣗⣏⣿⣸⠀⠀⠀⢸⣇⣞⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠹⠏⣿⠀⠀⠀⢸⡿⠿⠿⢹⠀⠀⠀⢸⡯⣭⡿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⣤⣤⣿⣄⠀⢀⣼⣧⣤⣤⣼⣄⠀⢀⣼⣧⣤⣤⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣼⠀⢸⣇⣀⣀⣀⣀⣸⠇⢸⣄⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠚⠛⠛⠛⠒⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡂⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠉⠰⠄⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠐⠂⠢⠤⢀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠱⣀⣀⠀⠀⠠⠤⠤⠤⠄⠈⠒⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⠀⠀⣀⡀⢰⣶⡆⢠⣄⣀⣤⠀⠀⣼⠓⠒⠒⡞⣷⡀⠰⢤⣴⡄⢰⣦⠀⢀⢀⣀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⠆⢠⠏⠲⠟⠀⢥⣾⡁⣸⣟⠧⢸⣇⣼⣀⡀⠿⠙⣷⡿⢋⡉⢿⣾⣍⣧⣜⡏⣹⣧⠀⣠⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡴⣆⣤⣄⣤⡄⢤⣤⢼⣿⣸⣿⠈⠳⡏⠻⡟⢩⡌⢠⣸⡷⠻⣇⠘⠛⠀⠈⠙⠿⢿⣽⣿⣿⣏⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣉⣛⠿⠉⢿⣯⣿⣿⡏⠀⠻⠿⠟⢓⠋⢠⣦⡏⢻⡇⠹⠟⠀⠄⠀⠀⠀⣐⡀⠀⠀⡤⣄⣈⢙⣫⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣸⣿⣧⣽⣧⢿⡏⢘⠿⣿⣟⡙⢾⣷⢯⣽⣧⠈⣧⠁⢲⡇⢤⣖⠈⣽⢛⣿⣯⣿⠀⢹⣿⢛⢿⣦⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣧⣿⣧⣬⣇⣸⣯⣿⣤⣤⣿⣿⣷⣿⣷⣖⠛⠛⢻⣿⣿⣿⣴⣇⣿⣾⣿⣾⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⠛⠲⠿⠿⢿⣿⣿⣿⡿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⠟⠛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠉⠁⠀⠀⠉⠙⠻⣿⣿⣟⣩⣤⣠⣴⠲⢲⣄⢀⠀⣀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠶⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⡶⠿⠖⠛⠋⠉⠁⠀⠀⠀⠈⠉⣽⠒⣾⡿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⡇⠈⠝⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⣰⠆⠀⠀⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⢀⣠⡤⠶⠚⠋⡋⠹⠉⠻⠃⣤⡐⠿⠛⠷⢤⣄⣀⡀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⠖⠉⠀⠀⠀⠀⢰⠇⣼⠀⠀⢸⠀⣇⠀⠀⠀⠀⠈⠉⠻⢷⣶⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⣠⡟⠀⣿⠀⠀⠈⣧⠈⢣⡄⠀⠀⠀⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠺⠿⣤⣴⣿⣀⣀⡀⣻⣧⣀⣿⠶⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣀⡀⢠⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⢉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠉⠁⠀⠀⠁⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠇⢳⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡐⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⡆⢻⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠠⠃⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡜⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣧⠼⢦⡼⠃⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⡐⠁⠀⠀⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠎⠀⠀⠀⢧⣀⣀⣀⣀⣀⣤⣤⣀⢼⠠⠤⠴⠶⠶⠶⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠮⠍⠤⠛⠀⠀⡂⢽⠩⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠳⠀⠀⣠⡆⠀⠁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⣀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⣧⠇⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣶⡞⠀⠀⣿⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⢣⣀⠀⣀⣀⣠⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⢀⡄⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⡸⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠌⠁⡅⠀⠀⠀⠀⡠⠂⢰⠀⢠⣷⠃⠀⠑⠌⣢⡀⠀⠀⠀⠀⢠⡾⠛⠉⢦⠀⢸⠀⠀⠀⠀⢀⡞⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⢠⠊⡠⠊⠀⠀⡇⠀⠀⣠⠊⠀⠀⠀⡇⠀⣿⣶⣄⡀⠀⠈⠳⢄⠀⠀⠀⣼⠃⢠⠔⠊⠛⢾⣤⡀⠀⠀⡼⣧⠀⠀⠀⣼
⠀⠀⠀⠀⡐⠁⠊⠀⠀⠀⠀⢻⠀⢸⠃⠀⠀⠀⠀⡇⠀⠉⢻⠁⠉⠂⢀⠤⠊⠀⠀⣸⡇⠀⡇⠀⠀⠀⢈⡉⠁⠀⣿⠁⣿⡶⠶⢶⠋
⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠒⠒⠊⠁⠀⠀⢀⢜⡜⡇⢰⠃⠀⠀⠀⣈⡁⠀⠀⣯⠀⢉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣤⡤⠖⠊⠉⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡟⠀⠀⠼⣦⣀⣀⣴⠋⢧⠀⠀⠘⡇⢨⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣄⣀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠹⣄⠄⠀⠀⠉⢉⡰⠀⠸⡆⠀⢠⠃⡏⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠙⢻⡄⠈⡁⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠉⠱⠖⠊⠉⠁⠀⠀⠀⢻⡀⣼⠀⡇⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡇⢀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢹⡀⣧⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⡇⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢤⣇⡟⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡺⣿⠧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⡴⠚⣇⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⡛⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⣷⣤⣾⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠟⠛⠛⠿⠟⠁⠈⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⣤⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠃⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣄⠀⠀⠀⠐⠒⠄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⠀⠀⠡⠁⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⡄⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⠀⠀⠀⠀⠐⠀⣄⣀⣀⣤⠊⠀⠀⡇⠀⠀⠀⣴⠃⠁⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⡿⠿⡿⢿⠀⠀⢰⡇⠀⠀⠀⢈⡆⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠲⣄⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣞⣀⣀⠀⠀⡼⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠁⢾⠀⠀⠀⠀⠘⠢⠄⣀⠀⠀⢀⣀⡠⠔⠛⢆⠀⢸⣉⣉⣁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠱⡈⠑⢄⣀⠤⠎⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠈⣇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠤⠐⠊⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢶⠶⠦⠴⠶⠶⠒⠚⠛⠉⠉⡗⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇⠀⠀⠀⠀⠀⠀⣀⣠⣞⠁⢠⡟⠐⠢⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠦⣀⣠⠏⠙⠋⠉⠉⠀⠉⠑⣯⠝⢃⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣰⠋⠉⠀⠀⠀⠀⠀⢀⣴⣯⣵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⢤⣉⠓⠶⢤⣀⠀⠀⠀⠈⠉⠛⠿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠶⣶⣤⣄⡀
⠀⠀⠀⠀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⣦⡄⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⣶⡄
⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣇⣤⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣇⣤⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⣿⠏⠉⣿⡝⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠛⣽⡏⠉⢿⡝⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⣰⡟⠀⠀⠘⣷⡀⠀⠈⢿⣆⠀⠀⠀⢀⣾⠏⠁⠀⣰⡟⠀⠀⠘⣷⡀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⢀⣿⠃⠀⣠⡾⠋⠀⠀⠀⠀⠈⢿⣦⡀⠀⢻⣇⠀⢀⣿⠃⠀⣠⣾⠏⠀⠀⠀⠀⠈⠻⣦⡀⠀⢻⣇⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠈⠛⠷⢶⣤⣤⣼⡿⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢶⣿⣤⣼⡿⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢶⣿⣤⣤⣴⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⣀⣀⣀⣀⣀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⣀⣀⣀⣀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠁




⣄⣀⣀⣀⣀⣄⣠⣀⣀⣠⣤⣠⣀⣀⣀⣤⣤⣤⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣠⣤⣀⣠⣤⣤⣤⣤⣤⣤⣀⣠⣀⣀⣀⣠⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠔⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠑⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣠⣶⣾⣶⣦⡀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠉⠀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠈⠁⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣠⢿⠴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⢼⢇⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆⢻⣿⣿⣿⣿⣿⡿⣿⣿⢃⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⢿⣿⣿⣿⣿⣿⣿⢿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⣫⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⣡⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⢉⣡⡴⢛⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣠⣾⣿⣿⣿⠿⢛⣋⣩⣥⣤⣶⣶⣶⠶⠿⠛⠛⢉⣴⡟⢻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⣾⣿⣿⣿⣽⣶⣿⠿⠟⠛⠋⠉⠉⢀⣀⣠⣤⣶⡾⠟⠉⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⣿⣿⣿⡿⠟⠋⠁⢀⣠⣤⣴⣶⡿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⠟⠉⢀⣠⡄⠈⣩⡥⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠶⢤⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⢀⣴⣿⣿⠀⠀⣀⣀⢀⠀⠉⠙⠃⠀⠀⠀⠀⠘⠋⠉⣀⣀⣀⠀⣿⣿⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⣴⣿⡟⠈⢿⡄⠰⣿⠛⣿⣿⡟⠦⠀⠀⠀⠀⠀⠠⢾⣿⣿⠛⡿⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⣾⣿⣿⣷⡀⠀⠁⠀⠈⠓⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠊⠁⣸⣧⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⢻⣿⣿⣿⡟⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡏⣿⣿⣿⣿⣿⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠤⠴⠀⠀⠀⠀⠀⣸⣿⠟⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⢷⢸⣿⣿⡹⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⣀⣠⣄⣀⣤⣀⡀⠀⠀⣰⡟⠁⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠈⢧⡙⢿⣿⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠹⢯⣍⣉⡴⠋⠀⢀⣾⠋⢀⣴⡿⠟⠁⠀⠀⠀⢠⡞⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⠈⢻⣷⣶⣾⣷⣿⣿⣿⣇⠙⢷⣤⣀⠀⠀⠈⠁⠀⣠⣶⣿⠃⢠⣿⠋⠀⡠⢤⣄⠀⢀⣿⢡⣿⡟⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⢻⣷⡹⣿⣿⣿⣿⣿⠀⠀⠉⠻⢷⣶⣶⣶⣾⣿⣿⣿⠀⢸⣯⠀⠀⠀⠀⢹⡇⠸⣿⣼⡟⠀⢀⠀⠀⢸⣿
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⢻⣷⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠉⠉⠸⣿⣿⣿⣧⠀⠻⣷⣤⣀⣤⣿⠃⠀⢿⣿⠁⣠⣏⠀⠀⣿⣿
⠀⠰⣌⠙⠻⣦⡀⠀⠀⠀⠀⠀⠘⢿⣿⣧⠀⢿⡇⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⣌⡉⠛⠉⠀⠀⠀⠀⠻⢠⣟⡿⠀⠀⣿⡿
⠀⠀⠘⣷⡀⢙⢿⡆⠀⢰⡄⢀⠀⠘⣿⣿⣧⢸⣧⠸⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣯⣙⠛⠿⣿⣶⣌⡓⠶⣄⠀⣼⣻⡇⠀⢰⣿⠁
⠀⠀⠀⠙⢿⣌⠪⡻⣆⠸⡷⠋⠀⠀⠘⣿⣿⡌⡏⠀⠀⠀⢀⠶⠋⠉⠉⠛⢶⣄⠀⠀⠀⠙⢦⣙⢿⣿⣿⣦⣄⠉⠻⣿⣆⠀⠀⢿⡿⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠙⠳⠮⠳⢄⠁⠀⠀⠀⠀⢻⣿⢻⡇⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠈⠓⢌⡻⣿⣿⣷⡄⠈⢿⣇⠀⠘⢁⠴⠋⣠⣴⡶⠿⠿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⢸⣿⢸⡇⠀⠀⠀⠁⠀⣠⠂⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠙⠮⡻⣿⣿⡄⠀⣿⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⢠⠖⠈⠀⠀⠀⠀⠀⠀⢀⣿⣿⡸⣿⡀⠀⠀⠀⣼⠃⠀⣠⣴⡟⠀⠀⠀⠻⣆⠀⠀⠀⠠⢄⣀⠙⡌⢿⣿⡀⢹⠆⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠹⣷⡀⠀⢰⡏⠀⣴⣿⡟⠁⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠉⠳⣬⡘⣿⡇⣿⠀⠀⢀⣀⣀⣀⣀⠐⢤⣤⣤⠾⠋
⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⠀⠀⠈⠻⣄⠈⠇⢰⠿⠋⣀⣤⠤⠤⠄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠈⢷⡜⠃⠃⢀⣦⠭⠭⠭⠉⠻⢷⣦
⠀⠀⠀⠀⠀⠀⠙⠻⠶⠾⠟⠛⠉⠀⠀⠀⠘⠻⠿⠿⠶⠦⠁⣶⣦⢀⣈⣀⣀⣀⠀⠀⠀⠀⠈⣣⡴⠖⠒⠄⠀⠀⠀⢿⡀⠀⠀⠙⠛⠿⠿⠶⠶⠆⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠓⢀⣤⠉⡅⢲⣬⣙⠛⠛⠛⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⣠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⢸⣿⡄⠻⣿⣷⣄⠀⠀⠀⠀⢹⣿⣄⡀⠀⣀⣠⣾⠃⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⢸⣿⣧⠀⠈⠻⢿⣷⡀⠀⠀⠀⠙⠿⠿⠿⠟⠋⠁⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠁⠀⠀⠸⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠋⠈⠉⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣁⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⡀⠀⠀⠓⠀⠱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⠁⠢⠀⠀⡀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠴⢊⠉⡑⠂⠌⠳⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢇⠈⡀⢀⠁⠠⢤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠉⠈⠓⠲⠂⠀⠃⢛⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠤⠀⠈⠂⢀⡞⡠⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡤⠆⠀⠀⢠⠁⠐⢄⣎⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠺⡤⠀⠀⠀⠀⡈⡺⠐⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢥⣤⣀⠔⠁⢀⠐⢁⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠀⠉⠈⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⢆⠉⠂⠦⢀⠀⠀⠀⠀⠢⠄⣁⠠⠐⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣀⡁⠈⠀⣖⠀⠀⠘⡎⠳⠀⠀⠀⠀⠀⢀⠠⠄⣀⢣⡀⠀⠀⠱⡀⠀⠀⠀⠀⡆⢑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⠀⢀⢄⣐⠁⠀⢀⣀⠂⢼⠄⠀⠀⢃⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠃⣸⣧⠑⠘⠢⠄⡬⠁⢨⠈⠁⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⡠⠏⡀⠀⢢⡢⠀⠀⠀⠁⠘⣁⡤⡠⠋⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠑⠢⢄⡈⣙⠁⠭⠀⠡⠲⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡉⠂⠀⣠⠊⠐⢈⢲⠀⠈⠀⠈⠀⡔⠂⡆⡀⠀⠀⠜⠃⠀⠪⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡨⠗⢒⠀⠈⠉⠀⠀⠀⠀⣔⠀⣀⠌⣂⢬⢀⡚⠠⡐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠤⠖⠋⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠠⠂⡀⠀⠀⠈⢆⠀⢰⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠲⠉⠠⡴⠁⢀⡀⠀⡈⠀⠠⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠐⠂⠀⢀⠜⠈⡴⢏⢁⠸⠍⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡆⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⣀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡄⠀⠀⣤⣀⣠⣿⣿⣿⣆⠀⣠⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣦⣾⣧⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⡿⢟⣯⣷⣶⣿⣻⡷⣞⠏⢙⣛⠿⠿⢿⣿⣿⡿⢿⣟⣯⣿⢟⣿⣿⢏⣫⣝⢮⠛⠻⠿⣛⡿⠇
⠀⠀⠀⠀⠀⠀⠈⣓⣊⣉⣭⢅⢂⣱⢿⠟⣫⢽⣥⣞⣭⡈⢐⣥⣽⣿⣷⣦⣶⣶⣾⣿⣿⣛⡵⠾⢽⣾⣿⣯⣧⣲⡭⠷⣒⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠯⠛⠋⣉⣭⣭⣏⣛⠻⢿⣓⣯⠴⣭⡷⠿⡿⠿⣶⡿⢿⡿⣯⣷⣶⣯⠭⠿⠟⠛⣒⣙⣻⡵⠾⢛⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢝⣛⣒⣒⣋⣝⣻⠶⣬⡯⠭⡁⠶⣛⣿⣯⢿⣿⣿⣷⣶⣯⢭⣩⣍⣄⣐⣙⣹⢷⡗⠶⣛⡭⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢴⢶⣶⡿⠻⢽⣛⡫⠽⠶⢾⣛⣭⠽⣖⡿⢷⣾⣒⣿⣿⣿⣲⡶⠦⡠⠤⠶⢷⣾⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⣿⠧⣔⡦⢬⣍⡉⠀⠤⢖⣋⣶⣿⣯⢵⣶⣶⠶⣖⣺⣷⣈⡲⢶⣄⣈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠦⢊⡅⢒⣶⣶⠦⠭⡿⣶⣙⣠⡑⠶⣾⡿⢿⣿⣧⣒⡫⠟⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠪⠭⣠⢽⠟⣛⠫⣉⣹⣿⣿⡿⠿⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁



⡿⢿⠿⠿⠿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣛⣻⣿⣿⡿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠄⠀⣀⡀⠀⢀⣤⡤⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢩⣤⡰⠿⣃⡀⠚⠛⣧⣤⣤⠛⠛⢟⡀⠀⣼⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⡿⠈⠛⣁⢰⡿⣣⣤⠌⠉⠉⢡⣤⣀⢼⣿⡏⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠄⠰⠿⡷⠘⠿⠃⠸⠛⠉⢶⣶⣦⠺⢿⡏⠀⢨⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣧⡄⢴⣾⠟⠓⢀⣿⣰⣾⡿⠋⢿⠏⠀⣰⣶⠄⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⠐⠿⠏⠀⣠⣷⣤⣾⡿⠏⣿⠁⢤⣴⡿⠗⠘⢻⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠻⡃⠀⣸⣷⡦⠻⠿⠷⣀⣤⡆⢠⣶⡄⢾⣶⠆⠚⠿⠟⠁
⠀⠀⠀⠀⠀⠀⣤⣀⢸⣿⡗⠉⠛⢃⣀⣀⡐⠛⢫⣾⠇⢉⣤⡀⣾⣶⠄
⠀⠀⠀⠀⠀⠸⠿⡟⠀⠈⣵⣤⣤⠛⠛⢻⣤⡴⠈⢩⣶⠎⠛⣃⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠚⠛⠁⠀⠈⠉⠀⠐⠿⠏

⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣽⣾⣿⠟⣛⠫⡿⣆⠀⠀⠈
⠈⠙⠻⠿⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⠀⠀⠀⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠄⡵⠉⠁⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣶⣦⣀⣀⣄⣤⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⠛⢾⣿⣿⣷⣶⡖⠚⠛⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃
⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⣶⣦⣀⢀⣀⣀⣀⣠⣴⣶⣶⣶⣶⣦⣤⣶⣦⣶⣦⣤⣀⠀⢀⣠⣤⣀⣀⣀⣀⣿⣟⠀⠀⠀⣀⣤⣄⣀⣀⣀⣀⣤⣴⣶⣾⣿⣄⣀⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠶⠖⣶⣶⣶⣾⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⠿⣿⠿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿⠛⠁⠉⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⣤⠤⠦⠠⠦⠀⠀⣤⣤⣤⣠⣤⣤⡀⣠⣤⣤⣄⣠⣀⣤⣤⣠⣙⣷⢆⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣠⣤⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠘⠛⠋⠉⠉⠙⠿⠟⠛⠿⠟⠹⠛⠛⠉⢻⣿⣿⠿⣿⣿⣿⣿⣿⠿⠛⣿⡿⠻⢿⣯⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠖⠛⠀⠀⠀⠀⠀⠩⠇⠤⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠤⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠩⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⣠⣶⣶⡄⠀⠀⠀⣰⣿⠋⢹⡆⠀⣸⣿⡇⣀⠀⠀⢀⡄⢀⡠⢊⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢰⣿⡿⠀⢸⡇⠀⣿⣿⣿⣿⡇⠀⠊⠀⠀⠀⢁⠄⠂⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⠀⠀⣿⣿⡇⠀⡾⠀⠨⢿⣿⣿⣿⠇⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣿⣿⡇⡼⠃⠀⠰⠾⠷⢾⣶⠶⣶⠶⠶⠷⠿⠶⠶⠶⠶⠶⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⢀⣀⡴⠒⢦⡀⠀⢠⣤⣤⠀⣠⣦⡀⠀⠀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣾⣿⣿⠀⠀⣷⠀⣿⣿⣿⠀⣿⢸⡇⠀⣾⣿⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⡀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣧⠀⠀⣿⠀⣿⣿⣿⠀⠸⣾⠁⣸⣿⣿⡵⠟⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢰⠇⠀⠈⢿⣿⡇⠀⢀⡾⣿⣿⡈⢷⣤⣏⡴⢻⣿⣿⠀⢠⡟⠛⠻⣿⣿⡀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡤⠏⠀⠀⠀⠈⠻⠿⠶⠞⠁⠈⠻⠷⠶⠋⠉⠀⠀⠙⠿⠶⠋⠀⠀⠀⠙⠻⠷⠶⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⢶⡒⢿⡛⠻⡟⠛⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⣿⣤⢿⡦⢿⡶⠶⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⣼⣯⠙⠓⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡾⠀⣾⢁⣼⢁⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⢠⣤⡀⠀⢀⣄⠀⠀⣤⠀⠀⣠⣤⡄⠀⣠⣤⠀⠀⣤⢀⣄⣤⣤⣠⠀⣤⠀⢠⡄⢠⣤⣄⡀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡇⠀⢸⡏⠻⣦⠈⣿⠀⢀⣿⠀⣾⠋⠀⠀⢠⡿⢹⡇⠀⣿⠀⠉⢹⡏⠉⠀⣿⠀⢸⡇⢸⡇⠉⣿⡄⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣨⣿⠀⢸⡇⠀⣿⠀⣿⡄⣸⡇⢸⣧⣤⣤⠀⢸⡇⠘⣿⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⢸⡇⢸⣧⣶⠟⠀⣿⣧⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⢻⡆⣹⡇⣠⡿⠀⢸⣧⣿⠀⠸⣧⠀⢀⣤⢸⡇⠀⣿⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⢸⡇⣼⡟⢷⣄⠀⢻⡄⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠸⠇⠻⠿⠛⠀⠀⠈⠿⠃⠀⠀⠙⠷⠟⠁⠸⠇⠀⠙⠿⠋⠀⠀⠸⠇⠀⠀⠙⠷⠟⠀⠻⠃⠀⠹⠃⠈⠻⠾⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠐⢿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣩⣽⣿⣧⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⣤⣤⣤⣄⣀⣿⡇
⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⠶⠿⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⣴⣾⣿⣿⣿⣿⣿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡴⠀⠀⠀⠀⠀⣆⠀⠀⠹⣿⣦⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⣷⣤⣴⣶⣶⣄⢹⠀⣠⣀⠀⠉⠉⠀⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣶⡀⠀⠼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠶⣾⣿⠀⢹⣿⣿⣿⣿⣧⠀⠀⣻⣿⣿⣿⠃⣶⣿⣿⣿⣯⠉⠀⠀⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣼⣿⣿⠘⣿⣿⠀⠀⣿⣿⣿⣿⠰⠉⣿⣿⣿⡌⠳⡄⢸⣿⠋⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠀⠻⠿⢣⣾⣿⣿⣿⣿⣆⢠⣿⣿⢿⡇⠀⠀⣿⡟⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣍⣿⡿⣿⣟⠉⠀⣿⠋⣾⡀⠀⠀⣿⣿⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⠻⢇⣿⡟⠀⠀⢿⡀⣿⠀⠄⠀⣽⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣼⡟⠁⠀⠀⢸⡇⠀⠀⠀⠺⠟⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠐⠁⠀⠀⠀⠀⠀⠀⠹⠇⡘⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⡄⠀⣀⣀⣀⣀⣠⣤⡤⠤⠤⠴⠖⠒⠒⠒⠊⠉⠉⠒⠢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⡤⠤⠾⠖⠒⢚⡙⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠙⠻⠶⣤⣀
⢀⠤⠤⠴⠶⠒⠒⠙⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⠐⡖⠒⠒⢤⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤
⡆⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⢠⠀⣴⠴⠶⠶⠆⢶⣄⠀⢸⡀⠀⠘⡇⠀⢸⡄⠀⠸⡄⢻⣠⠴⠚⠀⢸⡤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠
⢹⢾⡀⠀⠀⢰⣆⠀⠀⠀⣏⠙⢦⠘⣆⠀⡌⠀⢻⣀⣀⣀⠀⢸⡍⢷⡈⣇⠀⠀⢧⠀⠈⢧⡀⢸⠃⢸⡟⢦⡀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁
⠘⣿⣇⠀⠀⢸⠘⣆⠀⠀⢹⡀⢘⡇⠹⡄⡇⠀⢸⡇⠀⠀⠀⠈⡇⠀⠙⢿⠀⠀⠸⠄⠀⠈⠙⠃⠀⠀⠃⠀⠙⠂⠀⠉⠉⠉⠁⠀⠀⠀⡠⠖⠁
⠀⢿⣿⠀⠀⡷⠖⠘⣆⠀⠈⣇⠜⠁⠀⢻⠁⠀⠀⠷⠶⠶⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠊
⠀⢸⣿⡀⠀⠃⠀⠀⠙⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢀⠀⠠⢤⣤⣤⣤⣶⣶⣦⣤⣤⣴⠶⠶⠶⠶⠟⠛⠋
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⡤⠤⣤⣴⣖⣲⠶⣶⠶⠶⠖⠻⠟⠛⠛⠛⠉⠉⠉⠉⠉
⠀⠀⢙⣳⣾⣤⣐⠶⠶⠮⠿⠛⠓⠛⠊⠉⠉⠁⠀⠀⠀⠀⢸⡆⠀⠀⠀⡇
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠳⠀⠀⠀⠸⣤⡆⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠐⡄⢠⠀⠀⠀⢀⡿⠀⠋⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠙⢆⠘⢆⢇⠀⠀⣼⣷⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠣⠘⡞⠀⡈⣿⢿⣀⠞⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡉⠪⠐⠄⢹⠷⣗⣨⠁⣁⠀⠀⠲⠊⠁⠀⠀⢴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠈⠁⠠⠤⠭⠤⠄⠀⠐⠟⠛⠒⠚⠛⠒⠒⠒⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠠⣦⣄⠀⠀⢀⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠈⠻⣷⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⣴⣿⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣼⠟⠁⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠿⠿⠿⢿⣿⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣥⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣀⣄⠀⠀⢀⣿⣿⠀⠀⠈⢈⣭⣭⣭⣍⡉⠉⠉⣿⣿⠉⠉⢉⣩⣿⣯⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣾⠟⠁⠀⠀⢸⣿⣿⠀⢀⣾⡟⠋⠉⠉⠻⣿⡄⢸⣿⣿⠀⣰⣿⠋⠁⠀⠈⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣄⠀⠀⠀⢸⣿⣿⠀⣾⣿⠀⠀⠀⠀⠀⣿⣷⢸⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠈⠙⠷⡄⠀⢸⣿⡿⠀⠸⣿⣦⣀⠀⢀⣠⣿⠇⣸⣿⡇⠀⠘⢿⣦⣤⣀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⢠⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣧⣀⣀⣈⣙⣿⣿⣿⣟⣁⣀⣿⣿⣇⣤⣤⣤⣭⣭⣽⣭⣭⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⣉⣉⣛⠛⠛⢻⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⡟⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠛⠛⢿⣦⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠘⣿⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⣰⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣤⣤⣴⣾⠟⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃