Mongrel Emojis & Text

Copy & Paste Mongrel Emojis & Symbols 👅👩🏿‍🦱 | star, rock, cute, music, kawaii,👀♡‧₊˚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⢀⣀⣤⣤⣤⣤⣤⣴⣦⣼⣀⣐⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⢿⡫⠉⠋⠘⠻⠝⠈⠛⠋⠹⠿⡿⣾⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⢋⠛⢮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢿⣷⣾⡢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣻⣯⡹⣄⡀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣽⣮⣿⣮⡒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣙⣾⣽⣷⠿⠷⠶⠶⢶⣶⣦⣰⢦⣤⣶⣶⠶⠶⠶⠶⢶⣿⣽⡞⠙⠿⢿⣶⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠷⣼⣿⡟⠋⠁⠀⢀⠀⠀⠀⠈⠙⣿⣿⣿⡟⠀⢠⡀⡀⠀⠀⠈⠙⣿⣦⠀⢹⡽⣿⣮⠢⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⣼⣿⠏⠀⢠⣶⣿⣿⣿⣿⣷⡀⠀⠙⡏⠏⢠⣼⣿⣿⣿⣿⣦⣄⠀⡉⠻⣷⡈⠉⢻⡻⣯⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⠅⢸⣿⡏⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⣿⡿⣿⣿⣿⣿⣾⣿⣧⠀⠀⣻⡷⠀⠀⢀⣙⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⣼⣿⣇⡇⠘⣿⡟⡿⢿⣿⣹⣿⠋⠀⢀⡀⠀⠹⣿⡜⣿⡛⠟⢡⣿⠏⠀⢀⣿⣷⠀⠀⠓⣿⣿⣧⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣟⡣⠀⣿⣿⣿⣆⠀⠈⠛⠛⠛⠿⠛⠃⠀⣠⣿⣷⣄⠀⠈⠛⠛⠻⠛⠛⠛⠠⣀⣾⣿⡏⠀⠀⠀⠐⠓⣾⣷⠓⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⡗⠁⠀⢻⣿⣿⣿⣦⣤⣀⣀⣀⣀⣀⣤⣾⣿⡿⢿⣿⣷⣤⣀⣀⣀⣀⣒⣭⣵⣿⣿⡿⠁⠀⠀⠀⠀⠀⠁⣿⡇⢀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⡀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡜⠀⠀ ⠀⠀⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀ ⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠹⣿⣥⠄ ⢀⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠖⠒⠂⠂⠙⣿⢀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣶⣷⣶⣶⣶⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⣿⡞ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⡛⠛⠛⠻⢿⡿⣿⡿⢿⡟⣀⡀⢀⣰⣿⡇ ⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣆⣴⣀⣴⣾⣿⠛⠀ ⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣄⣀⣤⣤⣤⣤⣤⣶⣦⣤⣤⣼⣶⣾⣿⣷⣿⣿⠿⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠐⠁⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⢀⣀⣽⣤⣴⣷⣾⣯⣙⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣿⠛⣿⣿⣷⣶⣦⣤⣤⣀⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠟⠛⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡈⣣⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣴⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠻⠿⠻⠟⠛⠛⠛⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠉⠙⠛⠛⠻⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠀⠀
👅👩🏿‍🦱
star, rock, cute, music, kawaii,👀♡‧₊˚🖇️✩ ₊˚🎧⊹♡

Related Text & Emojis

⭑ ✰ ✮༄
✩°。⋆✺ ☽⋆。°✩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠲⢤⡀⢀⠤⢶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠶⣄⢠⠞⠁⠀⠀⠀⠀⠀⠀⠙⠋⢰⠀⠈⠢⢤⡀⠀ ⠀⠠⡶⠚⠉⠀⣖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠈⢆ ⠀⠀⡆⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⣧⠀⠀⠀⠀⡾ ⠀⠀⣧⠀⠀⠀⠈⣷⠀⣠⣖⢦⠀⠀⠀⠀⢰⠓⡍⢧⢻⣧⠀⣠⠚⠀ ⠀⠀⠸⣆⠀⠀⠀⢹⠀⣧⣨⡆⡇⠀⠀⠀⠸⣷⡇⡸⠀⡏⠉⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⢀⣧⡀⢻⣿⡡⠁⠀⠀⠀⠀⠙⠒⠣⣜⣀⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⡀⠙⣶⡬⠀⠀⢠⣾⡟⠛⢻⠀⠀⢸⠁⠀⠙⠄⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢳⣄⠀⠈⠿⢿⣒⣋⣀⣴⠇⠀⠀⠼⡀⠀ ⠀⠀⠀⠀⢀⠤⠴⣧⣀⠀⠀⠉⠉⠉⠉⠉⠁⠈⠉⣁⣀⠀⠀⠀⢸⠀ ⠀⠀⠀⢠⠃⠀⠀⠈⣇⠀⠀⢀⣤⡶⡶⢶⠛⠋⠉⠉⠉⠷⣤⡤⠂⠀ ⠸⡄⠀⢸⡆⠀⠀⠀⠹⣷⣾⠟⠃⠀⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⡘⢤⣀⣿⡄⠀⠀⢠⡿⠧⣴⠀⠀⣷⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠲⠤⠭⣥⣤⣤⢽⣤⣶⣸⣤⣰⣌⣼⠾⠼⠀⠀⠀⠀⠀⠀⠀⠀
┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ┊ ˚★⋆。˚ ⋆ ┊ ┊ ┊ ⋆ ┊ ┊ ★⋆ ┊ ◦ ★⋆ ┊ . ˚ ˚★
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⣶⣶⣶⡒⠶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠘⡿⠛⠻⣆⠹⡏⢱⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣿⣷⣤⠀⠀⠀⠀⢠⡶⣮⠀⡇⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⣄⢻⡏⠁⣀⣄⠀⠀⠘⠉⠙⢧⡇⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⢻⣄⠱⡈⣿⠟⠀⢠⣶⣶⠀⠀⢹⣾⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⠉⠙⠻⡇⡆⠀⠀⠙⢿⠴⣲⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣶⣤⡗⠒⠀⠚⠓⠊⠹⣷⠀⠀⠀⠀ ⠀⢀⣀⠀⠀⠀⠀⣠⡞⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀ ⣴⡷⢋⣴⠆⢀⣾⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⠈⢀⣾⠁⢠⠟⠁⠈⢿⣆⠀⠀⠀⢀⣀⠀⠀⠀⠀⢈⢻⠀⠀⠀ ⠀⢸⣿⢀⡟⠀⠀⠀⢸⣿⣦⠀⠀⠈⡟⠀⠀⠀⣠⡿⠀⢇⠀⠀ ⠀⠘⣿⣼⡇⠀⠀⠀⣼⣿⣿⠀⠀⠀⣧⣀⣤⣾⣿⠀⠀⢸⡀⠀ ⠀⠀⠹⣿⣧⣠⣶⣶⣿⣿⣿⠆⠀⢀⣼⡿⠟⠉⡼⠀⠠⠾⢧⡀ ⠀⠀⠀⠈⠻⡉⢀⠀⣄⢈⡇⠀⠛⠋⢁⢣⠀⠀⠱⣤⡀⣳⢱⣹ ⠀⠀⠀⠀⠀⠉⠉⠁⠉⠁⠙⠲⠤⠼⠼⠟⠀⠀⠀⠀⠉⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠴⠒⠒⠒⠶⠶⠶⠤⠤⠴⠶⠶⠤⠤⠤⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠱⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⠋⣺⣽⡿⠀⠀⠀⠀⣀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢠⣴⣦⣀⠀⠀⠀⠘⣿⣦⡀⠙⢷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⠟⠁⡠⣴⡇⡸⠁⠀⢠⣾⣿⣿⣿⣷⣠⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣦⠀⠀⢸⠹⣷⣄⠀⠙⣿⡀⠀⠀⠀⠀ ⠀⠀⢰⡞⠉⠁⠀⠤⠊⢠⡿⢱⠇⠀⠐⢛⡿⠿⠿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⠛⣿⣿⠛⠁⠀⠹⡷⣿⡇⠳⢄⡈⠳⢶⣦⡀⠀ ⠀⠠⣾⠃⠀⡀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⢄⢈⠢⣀⣿⡷⠦ ⠀⣼⡷⠀⢀⠔⠂⡰⠁⢈⡇⡇⠀⠀⠀⠀⢀⡴⠁⠀⠀⣠⣶⣶⣿⣿⣿⣶⣦⡀⠀⠀⠳⡀⠀⠀⠀⠀⠀⣿⣧⡀⠀⡙⠱⣌⢻⣿⡂ ⠰⢿⣧⠞⢁⡤⠊⠀⠀⣼⣇⡇⠀⡠⠔⠊⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠑⠢⢄⠀⢠⣿⡟⡇⠠⡘⢦⠈⢺⣯⠁ ⠀⠸⣿⠶⠋⣠⠎⢀⡞⠙⣿⡇⠀⡇⣸⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣀⠈⡆⣸⣿⡻⠀⠀⠻⣄⡳⣼⣿⡀ ⠀⠀⢿⣶⠏⢁⣶⠟⠀⠀⣿⣧⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠈⠉⢻⣿⣛⠉⠀⠀⠀⠀⠀⢠⣾⣿⡆⠁⣿⡟⡇⠀⣦⡑⠂⣱⣿⣿⠇ ⠀⠀⠈⢻⣷⡊⠀⢀⣀⢤⢿⡟⢴⠄⠘⣻⣿⣄⡀⠀⠀⠀⣀⣠⢿⡿⣄⣀⡀⠀⠀⠠⣴⢿⣿⡿⠁⢰⣿⡇⢣⠀⢌⣣⣷⠟⠁⠀⠀ ⠀⠀⠀⠀⠙⣿⣿⣋⡿⢫⣿⣧⣰⠀⠀⢇⢻⣏⠉⡛⡟⠋⠉⠀⢸⡇⠀⠉⠉⣻⣿⠟⠁⢰⡟⠀⠀⣼⣿⣇⢠⡇⣸⠟⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠿⠿⠶⣿⢿⣿⡏⡄⠀⠈⣶⢿⡀⢸⣷⠀⠀⠀⠸⠀⠀⠀⢀⣿⡟⠀⢠⡿⠀⠀⣄⠹⠻⣿⣄⣹⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⢸⡏⠀⢼⡟⢡⡀⠀⠸⣈⢷⡈⢻⡄⠀⠀⠀⠀⠀⠀⢸⡟⠁⢠⣿⠃⢸⣾⣿⠀⠀⢻⡙⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢉⢸⠁⠀⠘⢇⣾⠁⠀⠀⠙⡆⠳⡌⢷⡀⠀⠀⠀⠀⣠⡟⣠⣶⡿⠃⠈⡈⠛⣇⠀⠀⢸⠧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣸⡆⠀⠀⢸⣡⣶⣇⠀⠀⠈⢦⡙⢦⡛⠶⠦⠤⠖⣫⣾⣿⡿⠀⣤⢠⣇⠀⠁⠀⢠⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣏⢿⡄⠀⠘⢻⣿⠿⡇⠀⠀⠀⠉⠪⣿⣿⣶⣶⣾⣟⡩⠀⠀⠀⣿⣼⡟⠀⠀⠀⡞⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣷⡀⠀⠈⢻⣴⣷⣶⠀⠀⠀⡀⠀⠉⠚⠓⠚⠁⠀⠀⠀⠐⣿⠿⠀⠀⠀⡸⢁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠃⠀⠀⠀⠋⢃⣸⡺⠂⠀⣧⡼⢷⡄⢠⣄⡄⢀⣼⡟⣰⠻⠀⠀⠀⡰⢡⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠛⠙⠁⠀⠘⠛⠁⢻⣿⠋⣿⡧⠈⢈⡴⠁⠀⠀⠀⠀⢁⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠙⠁⠰⠋⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠲⠀⠀⡀⠰⠐⠁⠐⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠟⡡⢫⣿⣟⣿⠏⠈⢏⠙⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⣿⣿⠏⣰⢡⣿⣿⢟⣸⠀⡀⠈⡆⠈⢿⣿⣾⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣏⣽⣟⣾⣿⡏⢀⣧⣿⣿⠏⡜⡇⠀⠘⢆⠈⡄⠈⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⡟⣾⣿⣿⠀⢸⢿⣿⣿⡄⢰⠁⠀⠀⠀⢧⠘⡄⢸⣿⣿⣿⣿⣿⣴⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡿⠁⠋⣸⢿⠔⢻⡿⣿⠋⠀⡞⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⠇⠀⣀⣿⣠⣔⠉⠠⠃⠀⢰⠃⠀⢀⣀⣤⣤⣆⠀⣼⢿⣿⣿⣿⣿⣾⡀⠀ ⠀⠀⠀⠀⢾⣿⠏⣴⣿⠟⠛⠿⣿⣿⣆⠀⠀⠈⠀⣶⣿⠿⠛⠛⠻⣷⣴⠀⢹⣿⣿⣿⡿⠵⠀ ⠀⠀⠀⠀⢸⣿⠀⣿⣇⢸⣿⣿⠎⣿⣿⠀⠀⠀⢸⣿⡏⣠⣶⣶⡀⢸⣿⠀⠀⣿⣿⣿⣿⠀⠀ ⠠⠤⠤⠤⢼⣿⡄⠘⣿⣦⣭⣽⣿⡿⠟⠀⠀⠀⠸⣿⣿⣼⣿⣟⣽⣿⠏⠀⢰⣿⣿⣿⣿⡘⠀ ⠀⠀⠀⠀⢸⣿⣧⠀⠈⠻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⢀⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⢸⣿⣿⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣰⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⣰⡶⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣷⢦⡀⠀⠀⠀⠻⠟⠛⠿⠙⠂⠀⣠⠞⣉⡴⣫⣿⣿⣿⣿⣿⣿⣿⡇⡆ ⠀⠀⠀⢠⣸⣿⣿⣿⣿⣄⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣡⡾⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠇ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⡈⠻⣦⣄⣠⣄⣀⣠⣿⠟⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⡈⠙⠛⠛⢛⣉⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⣛⣋⣠⡶⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣧⡅⠀⠀ ⠀⠀⠀⢠⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡄⠀ ⠀⠀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⡿⠛⠾⣿⣧⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡄ ⠰⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠹⢷⣤⣤⠴⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⡇ ⠀⠑⡄⠀⣿⡇⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢷⢃⢙⡇ ⠀⠀⠀⠀⠘⠧⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠘⢿⡾⠻
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣾⣾⣿⣷⣄⠀⠀⠀ ⠀⢀⣠⣴⣶⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣷⣦⣄⣀⣀⣀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⣀⣴⣶⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣷⣄⠀ ⠐⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢀⣾⡋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⡉⠛⠆⠀⠀⠀⠀ ⠀⠀⠘⠛⠛⠻⣏⡉⠉⣿⣿⣿⣿⣿⣿⣟⣿⡏⠉⢉⡟⠻⡷⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠻⣏⠉⠉⣿⣿⣿⣿⣿⣿⣛⣿⡟⠉⢉⡿⠛⠛⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠲⠾⣿⣿⣿⣿⣿⣿⣯⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⣼⣿⣿⣿⣿⣿⣿⡿⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⣶⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠈⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⠀⠸⣿⡟⠉⠙⢿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠃⠀⠈⠉⠛⠛⠿⠷⠶⢤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⠴⠶⢶⣿⠿⠿⣿⡿⠁⠁⠀⠀⠀⠀⠀ ⠀⣰⡄⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠃⠀⣀⣾⠃⠃⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⣴⡿⠃⠀⠀⠀⢀⣶⠀⠀⠀ ⠀⠁⡻⣷⠀⠀⠀⠀⠀⠀⠀⠈⢿⣉⠉⠙⠛⠲⠶⠆⠀⠴⠦⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢴⠶⠾⠋⢛⣿⠟⠀⠀⠀⠀⢠⣾⡏⠀⠀⠀ ⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⠀⠀⠀⠀⣰⣾⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠹⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠾⠛⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠛⠷⣶⣼⣿⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠛⠉⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠉⠙⠛⢶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣧⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢿⡇⠀⠀⠀ ⠀⠀⠹⣿⡎⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⡆⠀⠀⣆⣿⡇⠀⠀⠀ ⠀⠀⠀⣿⡀⠀⡀⠀⣿⠁⠀⢠⣾⣿⡿⠆⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠆⠀⠀⠀⢈⣿⠀⣄⣾⡿⠁⠀⠀⠀ ⠀⠀⠀⠘⣿⣧⣇⢀⣇⠀⠀⠘⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠖⠀⠀⠀⢸⣿⣷⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠻⣿⣆⡀⠀⠀⠉⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣿⠁⣀⣀⣀⠀⠀⠀⠀ ⠀⢀⣠⡶⠾⠛⠓⠶⣿⡟⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠋⠉⠛⠻⣦⡀⠀ ⢀⣾⠋⠀⠀⠀⠀⠀⠘⣿⣠⣄⡀⠀⠀⠀⠀⠛⠿⠟⠁⠀⠀⠀⠀⠀⡀⡀⠀⣴⣾⡏⠀⠀⠀⠀⠀⠈⣿⡄ ⢸⣯⠀⢠⠀⠀⢀⣄⣠⣿⠿⢿⣷⣤⣦⣀⣤⣤⣤⣤⣀⣀⣀⣼⣆⣼⣷⣿⡾⠿⢿⣧⣀⣦⠀⠀⣤⠀⣸⡧ ⠘⠿⣷⣾⣷⣤⠾⠿⠛⠁⠀⠀⠀⠁⠀⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠛⠻⠷⠾⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠾⠿⠟⠛⠉⠉⠉⠛⠛⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⣠⣶⣿⠟⠛⠿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⢀⣴⡾⠟⠉⠉⠉⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠜⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⢠⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣿⡟⠀⠀⠀⠀⠀⡀⠀⠀⣼⣿⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⣸⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢸⣿⡇⠀⠀⠀⠀⠀⣷⡄⠀⢿⣿⠀⠀⣾⡿⠀⢀⣼⣇⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠘⣿⠁⠀⠀⠀⠀⠰⣿⡇⠀⢸⡿⠀⢠⣿⠇⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢠⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢿⣧⠀⠀⠀⠀⠀⠋⠀⠀⣹⡇⠀⢸⣿⣇⠀⠘⢿⠃⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⣼⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡈⣻⣷⣄⣀⠀⠀⠀⢀⣸⣿⠀⠀⠘⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⢀⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⢿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠻⣿⣧⣄⣀⣀⣀⣀⣠⣴⠟⠋⠀⠀⢠⣾⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣍⠙⠻⠿⠛⠃⠀⠀⠀⠀⠀⠀⠠⢤⣝⡻⠿⣿⣯⣿⢟⡥⠀⠀⣠⡼⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠾⡶⠒⢂⣠⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⢠⣾⣏⣠⣾⣿⣟⣛⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⢿⣿⢿⡟⠉⠀⡿⠉⣡⣿⠁⠠⠉⢛⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⠈⠷⠀⠀⠷⠀⠈⠁⠀⠀⠀⠘⣷⡿⢷⣶⠦⠤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧⣸⡏⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠒⠶⢶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⡀⠀⠈⢉⡉⠉⠛⠲⠶⢦⣤⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⡴⠟⣰⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠠⠴⠦⢤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⢀⣠⡴⠞⢋⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⢀⡄⠀⠀⣿⡟⠛⠿⠶⠶⣦⣤⣭⣭⣍⣉⣙⣛⣛⣓⣛⣛⣩⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢷⣤⣀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣾⣿⣿⡿⠋⡴⢫⣾⡿⣻⣿⠋⠉⢹⡉⢻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⣿⣿⢿⣿⢿⡿⠁⡜⢠⣟⣿⣽⠟⡼⠀⡀⠀⢣⠀⠙⣿⣿⣷⡻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⣿⢫⣿⣿⡟⠁⡼⢡⣿⣿⣿⠏⣟⡇⠀⢰⡀⠈⢧⠀⠘⣿⣿⣿⡽⣿⣿⣧⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⣸⣿⢣⣿⣿⣿⠁⢠⣧⣾⣿⣿⠏⡼⣸⠁⠀⠀⠙⣄⠈⣦⠀⠘⣿⣿⣷⣿⣿⣿⢧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⢳⣿⢧⣿⣿⣿⠇⠀⣼⣿⣿⣿⣏⡤⠀⡿⠀⠀⠀⠀⠸⣆⠈⣆⠀⢻⣿⣿⣿⣿⣿⣞⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⢠⡏⣽⣿⢀⣠⣿⣹⣿⣿⠟⠁⢰⠃⠀⠀⠀⠀⠀⠘⠀⠘⢦⣸⣿⣿⣿⣿⣿⣿⢵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⠀⡀⣿⠘⠋⢁⣿⠋⢱⠃⠀⠀⡼⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⣿⠁⠀⣀⣼⣿⣴⣶⡉⠀⠠⠏⠀⠀⢠⡇⠀⠀⣀⣤⣴⣶⣾⣍⡀⠀⡟⠿⣟⣿⣿⣿⣿⣯⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢾⣿⣿⠁⣄⣾⡿⠿⠿⢿⣿⣿⣿⣆⠀⠀⠀⠈⠁⢲⣾⣿⣿⠟⠛⠛⠿⣿⣆⣇⠀⠙⣿⣿⣿⣿⣿⠣⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡏⠀⣿⣿⠁⣴⣶⣶⣌⠻⣿⣿⡆⠀⠀⠀⠀⣿⣿⡟⠁⣠⣤⣄⠀⠘⣿⢻⠀⠀⢹⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⡇⠀⢻⣿⣄⠻⣿⣿⢯⣴⣿⣿⠀⠀⠀⠀⢸⣿⣿⣇⢸⣿⣿⣿⠦⣰⣿⡼⠀⠀⣸⣿⣿⣿⣿⡏⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠒⠾⣿⣿⠀⠀⠻⣿⡷⣶⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠻⣿⣿⣷⣿⣻⣥⣶⣿⡟⠁⠀⢰⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⣿⣇⠀⠀⠘⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠀⣴⣷⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣾⠟⢩⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⣿⣿⣿⣿⣿⡼⣆⠀⠀⠀⠀⠀⢻⡿⠙⠹⢿⠏⠛⠀⠀⢀⣴⠟⣁⡴⢏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠃⣿⣿⣿⣿⣿⣆⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣡⣾⠟⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣸⣿⣿⣿⣿⣿⣿⣧⡀⠙⣷⣄⠀⡀⠀⠀⠀⠀⢀⢠⣴⣴⡿⠛⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠻⣿⣦⣴⣲⢖⣠⣴⣿⠟⠉⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠉⠙⠛⠛⠋⢉⣠⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡛⠷⠶⠟⠉⣠⣴⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠶⠶⠟⠋⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣧⠀⠀⠀⠀⠀⢘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⠶⢿⣿⣦⡀⠀⠀⠀⠒⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡄⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢿⣧⣤⣄⣀⣠⣾⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣏⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠳⡀⠀⠀⣧⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠿⡏⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢹⠛⢦⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⠀⠀⢻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⡸⣞⣆⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠹⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠻⣻⡿⠋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⠖⠒⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⣠⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠙⠲⢤⣀⠀⠀⠀⢀⠀⠀⠀ ⠀⠘⣿⣉⣿⣿⣿⣷⣤⣀⡴⠃⠀⠀⠀⠀⢀⣠⠶⠛⠛⠛⠶⣤⣀⣀⣠⣶⣾⢿⣦⣠⣾⣿⣷⡆ ⠀⠀⠙⠛⠛⠛⠛⠋⢹⡟⡁⠀⠀⠀⠀⠀⣸⣷⣿⣿⣿⣿⣷⣶⡎⠉⠙⣿⣿⣿⣿⡿⠿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡧⠇⠀⠀⠀⠀⣸⣿⠏⠉⢀⣤⣤⡄⠙⢿⡀⢠⣿⢋⣥⡽⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡖⡄⠀⠀⠀⠀⣿⠇⠀⢰⣿⣿⣿⣿⡄⢸⣧⢸⡇⢸⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡁⠀⠀⠀⠀⢻⣧⠀⠈⠻⠿⠿⠋⢀⣿⡇⢸⣇⠸⠟⣁⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣆⡀⠀⠀⠀⠛⣿⣶⣶⣶⣶⣾⣿⠿⠃⠈⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣄⠀⠀⢈⣿⣿⣦⣀⠀⠀⠀⡉⠉⠉⠉⠉⠁⣴⣾⣿⡏⠀⣼⣁⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⠿⠿⠿⠾⠛⠛⠛⠛⠛⠳⠶⣾⠁⠀⠀⠀⠀⠀⠛⠿⠋⠀⡾⠷⠛⠉⠛⠃⠀⠀ ⠒⠒⠿⣿⣯⣤⣤⣤⣄⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⡤⠤⠔⠒⠲⣾⣿⣽⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠙⠻⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣷⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠒⠒⠋⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠙⠒⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⣼⣿⣶⡦⣿⣿⢫⠑⠂⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀ ⡟⢰⡿⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⣰⠃⠀⣶⢸⡇ ⠁⣼⣀⣂⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⢄⠀⠀⠀⢄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢰⡃⠆⣀⣠⣿⣤⣤⢿⠘⠃ ⠀⣿⠉⣿⠀⠀⠀⠀⣠⠞⠁⠀⢠⠀⣰⠇⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⠀⢿⠳⡄⠀⠀⢄⠘⣦⠀⠀⠀⢳⡀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠘⠿⠛⠋⣹⡇⣼⣟⠀⡆⠀ ⠀⣾⠀⠏⠀⠀⢀⣼⠃⠀⠀⣠⠇⡰⠃⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢆⠘⣇⠘⣆⠀⠈⢦⠘⣷⡀⠀⠀⠙⡄⠀⢆⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠹⢼⠟⣀⠀⠁⠀ ⠀⢿⠀⠀⠀⠀⡾⡡⠀⠀⢀⠏⠀⠃⠀⠀⠀⢀⣾⡇⠀⠀⡆⠀⠀⠀⠀⠀⠀⢹⡄⠈⣄⢿⣧⠘⣆⠀⠈⢧⢻⢳⡄⠀⠀⠘⡄⠀⠣⢠⠘⢿⣆⠀⠀⠀⠀⠀⠀⢀⣾⠿⣿⠇⠀ ⠀⠘⠀⠀⠀⡼⡽⠁⠀⠀⡾⠀⢠⡇⠀⠀⠀⠸⣿⡇⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⢿⡀⠘⣼⠈⢷⡘⢦⠀⠈⢿⡄⢻⡀⠀⡆⠘⠆⡀⠀⠱⡌⣿⣦⠀⠀⠀⠀⠀⠸⠁⣼⠏⠀⠀ ⠀⠀⠀⠀⣰⣧⠃⠀⠀⣼⠁⠀⢸⡇⠀⠀⢠⠇⣿⡇⠀⢀⣶⠀⠀⠀⠀⢸⡆⠀⢸⣧⠀⢻⡇⠀⢳⣿⡆⠀⠘⣿⡄⢷⡀⠸⡄⠀⠐⠀⠀⠙⣎⢿⣧⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀ ⠀⠀⠀⢀⡿⠈⢀⡞⢰⡏⠀⠀⢸⣇⠀⠀⣼⢰⢻⣸⠀⢸⣿⡇⠀⠀⠀⢸⣧⠀⠀⣿⡄⣈⣇⠀⢺⣿⣿⡄⠀⢸⣿⡈⣇⠀⠻⠄⠀⠀⠀⣄⠘⣮⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠇⠀⣸⢻⣾⠁⠀⠀⣾⣿⡀⠀⣿⡜⠈⣿⡇⠀⣿⣿⠀⠀⠀⠘⣿⠀⠀⢸⣿⠉⢻⠑⠒⢭⣿⣿⡄⠀⣯⣧⡘⠀⠀⠀⠀⠀⠀⢸⡀⠈⣯⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⣰⡿⢸⣿⠀⠀⠀⣏⣿⡇⠀⣿⠇⡀⢻⣷⡀⣿⢿⣇⠀⠀⠀⣿⡇⠀⢸⡽⡆⢸⡇⠀⠀⠘⢻⣿⡄⢸⣸⣷⡀⠀⡇⠀⣇⠀⠀⣇⠀⢹⣿⡹⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⢀⢿⡇⢸⡏⠀⢀⠀⢹⢻⣇⢰⣿⠀⠹⡜⣿⣏⢸⣷⣿⡄⠀⠀⢸⣷⠀⠀⣷⢻⡘⡇⠀⠀⠀⠀⢻⣷⢸⠀⢻⡇⢈⡇⠀⢸⠀⠀⣿⠀⢸⣿⡇⢹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣾⢸⡇⣿⣧⠀⢸⠀⢸⠘⣿⠘⡏⢀⡤⠛⠹⣿⡌⢿⢻⣿⡄⠀⠀⣿⣇⠘⣽⡈⣷⡧⠄⠀⢀⣀⣀⣻⣿⠀⠘⡇⣼⣷⠀⢸⠀⢠⣟⡇⢸⣾⣿⢠⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣇⢸⡇⠏⣿⠀⢸⣇⠸⡄⢹⣷⡗⠋⠀⠀⠐⠚⣿⣞⡆⠙⣿⣄⠀⢸⣿⡄⡏⡇⣿⡶⢿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣯⣿⠀⣸⡄⢸⡯⣧⠘⣿⣿⠀⡏⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⢿⣿⡄⢻⡆⠘⣿⡀⡇⠈⢿⡇⠀⠀⠀⣀⣬⣿⣿⣷⡤⠈⣿⣦⣩⣿⣷⡇⠀⠉⠀⠘⠛⠛⠛⠻⠷⢶⠿⠉⠿⠿⣿⢒⣿⡇⣸⠀⣿⢸⣿⣿⢦⠁⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣸⣿⣇⠸⣿⠀⠙⣷⣹⡄⠘⣷⣠⣶⣿⣿⣿⣯⡽⠝⠳⠄⠈⠹⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⡇⡿⣰⣿⢸⣿⣿⣼⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣏⣿⣿⡐⣿⣇⠀⢹⣿⣧⣠⣿⣿⣟⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣡⣾⢿⣿⣸⣿⣿⠇⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣯⢿⣼⣇⣽⣿⣦⠈⣿⣿⣿⠧⠬⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢈⣿⡟⢸⣿⣿⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢻⣿⣿⣿⣿⣏⠻⣧⢹⣮⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢻⣇⣾⠟⢡⣿⣿⡟⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡜⣿⣿⣿⣿⣿⡀⠛⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⢁⣴⡿⢻⡟⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠈⢿⣿⣿⣿⣷⡀⣀⡙⠿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣵⣶⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣮⣍⣉⠙⣧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢻⠓⠷⠶⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠙⣮⢿⡙⢿⢿⣿⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡯⠉⠁⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⢀⣼⡿⢡⣧⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠁⠈⠇⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⣸⠃⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀ ⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⢿⣶⣄⡀⠀⠀⠀⠀⠀⠈⠳⣴⡖⢒⡾⠁⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣏⠓⠶⢤⣤⣀⠀⠀⠀⠙⠉⠁⢀⣠⠶⢋⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀ ⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠉⠉⠙⠲⣖⠶⢖⣿⢹⣴⢟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠹⣗⠶⣤⣀⠀⠀⠉⢧⡌⠿⠛⣡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠈⠣⣀⡉⠙⠒⠒⠋⢑⣀⠐⢁⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀
⠀⠀⠀⠀⠀⢀⡴⠋⠉⠛⠒⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠏⠀⠀⣶⡄⠀⠀⣛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⡤⠋⠠⠉⠡⢤⢀⠀ ⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢉⣝⠲⠤⣄⣀⣀⠌ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⢀⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡉⠉⠧⠍⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠓⠛⠛⠛⠒⠻⠿⠛⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣟⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣠⣴⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⣄⠀⠈⢻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢰⣿⣿⣶⣶⣾⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣮⣽⣿⠷⣄⠈⢿⣽⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⣿⢹⣿ ⠐⠂⠠⠴⠀⢤⣭⣭⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿ ⣄⣽⣿⠿⢿⣿⡿⣧⣼⠃⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⡿⠟⣁⣰⡿⠋⢉⣿⣿⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣶⠶⢴⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣶⣿⣿⣿⣧⣾⣿⣿⠟⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢠⣶⣿⣿⠆⠤⠀⠆⣛⠛⣧⣤⡈⡉⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡤⠊⠁⠀⠀⠀⠀⣰⣿⣿⣿⣶⣷⣤⣦⣴⣶⣦⣤⣤⣴⣶⣶⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣗⣶⡾⠁⠀⠀⠀⢠⠆⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡔⠤⠀⠀⠀⠀⠀⢦⣀⣀⣼⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿ ⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠃⠀⠀⠀⠀⠀⠘⠻⣶⣬⡙⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢛⣿⡿⠃⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿ ⢠⣾⠃⣻⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠋⠀⠀⠀⠀⢀⣤⣀⣴⣿⣽⣜⣿⣿ ⣿⢃⠅⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣀⣴⠛⢻⣿⣿⣿⣷⣿⣿⣿ ⡿⠀⠀⠛⣾⣿⣿⣿⠿⠟⣿⣿⢿⡿⠃⡟⠻⣷⣦⢀⣴⡆⠹⡏⣹⣿⣿⣿⣿⣿⣿⡛⡿⠁⠀⠀⠀⠀⣿⢟⡄⠀⠀⠻⣿⣿⣿⣿⣿⣿ ⡇⠈⠀⣰⣿⠛⠁⠀⠀⠀⠀⠁⣾⠃⠀⠇⠀⣹⣿⣼⣿⡗⢠⣿⣿⠿⢛⣿⠛⡉⣦⣴⠀⠲⣦⣀⣰⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿ ⠶⢀⣼⠿⠁⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠈⢹⣿⣿⣷⣿⣿⣿⣦⡾⣿⠗⣶⣉⣷⣤⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⠿⢿ ⠿⠛⠁⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠘⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠳⢤⣛⣹⠋⠛⠛⠿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣤⡏⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠃⠀⠀⣾⡟⣽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠜⠁⢀⣰⣿⣷⣿⣿⣿⠛⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⠋⠀⠀⢬⣿⣿⠟⠃⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⡤⠊⠀⠀⣠⣽⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣾⣿⣿⣿⣿⣿⣿⡒⠀⠀⠀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡴⠋⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠤⠖⠒⠒⠛⣉⡙⢦⠀⠘⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡤⠆⠀⣾⠟⢁⠀⠀⠀⠀⢠⠀⠉⠳⡷⡀⠈⠳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⢸⡏⣴⠃⠐⠲⣄⠀⢸⡤⢦⡀⢻⠙⣦⣀⠘⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⠸⠁⣏⠀⠴⣤⠈⢳⠀⢻⡾⣣⠾⢿⣿⣿⡟⠳⣥⠀ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⢸⡀⠀⢹⡀⠶⣿⠃⢸⢁⠴⣟⠁⣠⣾⣿⡿⠁⠀⣹⢲ ⠀⠀⠀⠀⡤⠁⠀⠀⠀⠀⣧⠀⠠⠿⠒⠒⠀⡜⠁⠀⠛⠛⠛⣿⡟⠁⠀⣰⠋⢸ ⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⡀⠈⠀⢀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡾ ⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢸⡐⠋⠹⣦⣀⠀⠀⠀⠀⠉⠁⣀⠤⣪⠃⠀⠀⢰⠇ ⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣸⠷⣤⣀⠀⠉⠉⠓⠒⠒⠊⠉⣁⠶⢳⠀⠀⢠⡏⠀ ⢰⡆⠀⠀⠀⢻⣆⠀⠀⠀⣿⠀⠀⠈⠉⣿⡓⠒⠒⠒⠚⣏⡇⠀⠈⠷⠶⠋⠀⠀ ⡇⢱⣠⡀⠀⠀⠹⣷⣄⣸⠏⠀⠀⣠⠖⠣⣟⣷⢲⡖⣿⣻⣅⠀⠀⠀⠀⠀⠀⠀ ⢧⠀⠏⢳⠀⠀⠀⠀⠉⠉⠀⢀⡞⠁⠀⠀⠀⠉⠉⠉⡟⠉⠺⢇⠀⠀⠀⠀⠀⠀ ⠸⣆⠀⠀⢇⣦⡀⠀⠀⣀⣤⠏⠀⠀⡄⠀⠀⠀⡀⠀⠣⢄⡴⢸⡆⠀⠀⠀⠀⠀ ⠀⠙⣆⠀⠀⠁⢳⣠⠞⠁⠈⡀⠀⢸⠁⠀⠀⢸⠁⠀⠀⡶⠇⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⣄⡀⣸⠃⠀⠀⠀⠈⠳⣼⡀⠀⠀⢸⡀⠀⠜⢁⠞⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠹⡇⠀⠀⠀⣀⣀⣀⣿⡇⠀⡀⠤⠿⠶⢶⡃⠀⠙⠛⠛⢗⠦⡀⠀ ⠀⠀⠀⠀⠀⠀⢷⡀⢠⠊⠀⢄⠀⢍⢳⡆⠀⠠⡀⠘⢆⣿⠀⠀⠈⢱⢀⣧⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢻⣄⣀⣸⣀⣸⡼⠷⣄⣀⣵⣤⠾⠛⠛⠒⠒⠛⡋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⠿⠶⢶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⣠⣤⣶⣷⢀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠘⠛⠁⠀⣀⣼⣿⣦⠀⠀⠀⠀⠀⠙⣦⣮⣹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠰⢿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠈⠙⠛⠳⠶⣤⣄⡀⠀⠀ ⠀⠀⠀⠀⢀⣾⡿⠛⢀⡀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⣉⣉⣉⣙⣧⠀ ⠀⠀⠀⠀⣼⠏⠀⠀⠀⣷⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠀⠀⠀⣿⠀⢿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⢀⡿⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣯⣤⡾⠃⠀⠀⠀⠈⠻⠶⣾⣿⣿⣿⣿⠄ ⠀⠀⠀⣸⡇⠀⠀⠀⢰⣿⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠀ ⠀⠀⣰⡿⠀⠀⠀⠀⠈⢹⣿⡼⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠟⠁⠀ ⠀⣰⡿⢡⠂⠀⠀⠀⠀⠀⣿⣇⣰⣂⣠⠀⠀⠀⣟⣀⣀⠀⠀⠀⠀⠀⣠⣤⠶⠿⠿⠿⠛⠿⣧⠀⠀⠀ ⣰⡿⢠⣏⡔⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⢠⡀⠀⢿⣿⣿⣿⣍⣙⠛⢻⣏⣤⠾⣦⡀⠀⠀⠀⢹⡇⠀⠀ ⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡿⣶⣾⣿⣶⣦⣴⡟⠁⠀⠀ ⠹⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠉⠉⠉⠙⠿⠟⠁⠈⠙⠛⢻⡿⠀⠀⠀⠀ ⠀⠀⠙⠻⣧⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⠀⠀⡴⣾⣿⣷⣶⣤⣤⣤⣤⣤⣶⠤⠶⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣶⣤⣤⣤⣴⣿⣿⣿⣿⠃⠀⠀⠀⢰⡟⢿⣿⣿⡿⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁⠙⢿⣿⠀⢠⠄⠀⡼⠀⢸⣿⢹⡇⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⡟⣸⠁⠃⠀⣿⣿⡀⠧⠀⣸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣴⣿⠀⠀⠀⣿⠹⡇⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣻⡿⢿⣆⢠⣿⠀⠁⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠋⠁⢈⣿⣿⣿⡇⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠉⢿⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠓⠛⠓⠚⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠋⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠙⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢀⣾⣿⣭⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠽⠿⠦⢸⣿⣿ ⠻⢛⠛⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿ ⣬⠟⣻⠿⣧⡇⠐⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⣵⣾⣧⣴⣿⠃⠀⢘⡄⠀⠀⢀⣴⣿⠩⠩⠛⠫⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⣿⣦⡰⠁⠀⢀⢤⣿⣿⣿⣷⣶⣿⣶⣶⣿⣿⣿⣆⢀⠀⠀⠀⣀⢀⣼ ⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿ ⢠⠟⣿⣿⣿⣿⣧⡀⠀⠀⠀⠹⣷⣶⣾⣿⣿⣿⣿⣯⣵⡾⠉⠀⠀⣀⣠⣿⣽⣿ ⡏⠀⣿⣿⣿⣿⣿⣿⡿⣦⣄⠀⣙⢿⢿⣿⣿⣿⣿⣿⠛⠀⢀⣤⠊⠹⣿⣿⣿⣿ ⠇⢀⣾⠋⠁⠀⠉⡸⠀⠁⢹⣷⣿⢠⣾⠟⣿⠋⣭⠀⢦⣀⠈⠉⠁⠀⠸⣿⣿⣿ ⡥⠞⠁⠀⠀⢀⠔⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣽⣾⣷⣿⡿⠀⠀⠀⠀⠀⢻⠛⠙ ⠀⠀⠀⠀⠠⠂⠀⣰⠀⠀⠀⠀⢙⠻⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⢰⠁⠀⣰⣻⡄⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠊⢀⣼⣷⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠔⠁⢀⣽⠟⠉⠁⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠀⠀⠀⠀⠀ ⠁⣀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⠧⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠿⠛⠉⠉⠉⠉⠉⠙⠻⢿⣦⡀⠀⠀⢀⣴⡾⠿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⣾⠑⣄⠀⠀⠈⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠀⢹⣇⠀⠀⠀⠀⠙⠷⣶⣶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣠⣶⠿⠋⠀⢀⣄⠈⠙⢿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⠀⠀ ⠀⠀⠀⣴⣿⠟⠛⠉⠁⠀⠀⠀⢸⣿⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⣿⣶⡀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⣴⣟⠿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠻⣆⠈⢿⣷⠀⢿⣿⣿⡄⠀⠀⠀⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣼⡟⠛⣷⡄⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢹⡇⠀⣿⡇⠈⣿⣿⣿⣦⣀⣤⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⣿⡇⠀⢘⣷⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣾⡟⠀⣿⡇⠀⠈⣿⡍⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠘⣿⣿⣦⣼⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠃⢠⣿⠁⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⢠⣿⠀⠀⠀⢿⣿⣿⣿⠏⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣅⣴⡿⣁⡀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⣠⣾⣿⣷⣄⠀⠈⢿⣿⣯⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠻⣯⣀⣤⠶⠦⢤⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠙⠻⣷⣦⣄⠉⠉⠉⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠈⠻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠬⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠉⠁⠀⠉⢻⡇⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⣤⣤⣴⣿⠇⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⣿⣦⣀⠀⠀⠀⠀⠈⠻⠟⠛⠛⣩⣉⠉⠀⣀⣠⣴⣿⣿⠋⠀⠀⠀⠀⠀⠞⠻⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣶⣤⣤⣤⡤⠶⠾⠿⠛⠛⠛⠛⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⣿⣿⣷⣄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣶⣶⣿⣿⡿⠿⣷⣦⡀⠀⠀⠀⠀⢀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠈⢿⣿⣶⣤⣤⣤⡞⠁⠀⠀⠀ ⢀⣄⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣀⣀⣀⣀⣴⣾⣿⡟⠉⠉⠉⣟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀ ⢸⢷⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡟⡿⠀⠀⠀⢰⣿⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠈⣧⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⡿⠋⠀⡇⠀⠀⠀⢸⣿⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡄⠈⢷⣄⡀⠀⠸⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣟⣀⡀⢰⠇⠀⠀⠀⢸⣿⣆⠀⠘⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣆⠀⠙⠳⢶⣤⣿⣿⣿⡆⠀⠀⠀⠀⠀⣾⣿⠿⠛⠉⠉⠻⣾⠀⠀⠀⠀⠘⠛⡟⢷⣄⢰⡄⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⢶⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣽⣄⣀⠀⢸⣿⡀⢻⣇⠀⠀⢐⣦⠀⢹⡀⢿⣤⣿⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⡿⠿⣿⠿⠻⣿⣿⣿⢿⣷⣾⠿⣿⠋⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢹⡆⠀⠀⢀⣼⠃ ⠀⠀⠀⠀⠀⠀⢀⡠⠄⣒⣀⣭⣥⣤⣤⣤⣤⣭⣅⣐⠂⠤⣈⣢⠹⠶⠞⢋⡡⠊ ⠀⣀⠤⠤⠤⢂⣥⠶⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠶⣤⣭⣈⡉⠄⡀⠀ ⣥⡶⠞⢻⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⢷⣬⡁ ⠁⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⢠⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⢳⡄⠀ ⠀⡆⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⢙⠫⠄⠢⡄⢿⡀ ⢰⠇⠀⢀⡀⣀⣉⡛⠁⠀⠀⠀⠀⠸⣇⣀⡴⠶⠤⡼⠀⠀⠀⢇⣀⣀⠤⠃⣸⣇ ⣿⠀⠰⡅⠀⠀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠙ ⠻⢦⣀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠾⠿⢧⣄⠀ ⠀⠀⠉⠛⠷⣶⡦⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠶⠾⠟⠛⠻⣯⡁⠀⠀⡄⠀⠹⣧ ⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⣠⣷⠀⠀⣿ ⢡⡾⠛⢳⣾⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠉⣷⢠⡿ ⢸⣇⠀⠀⢻⠄⠀⠀⠀⠀⠀⢷⡀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⣾⠟⠁
⠀⠀⠀⠀⠀⢀⣀⣤⣄⠀⢀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣾⣿⣿⡿⠟⠋⠁⠀⠀⠀⠈⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⠀⠀⠀ ⠀⠀⢿⣿⣿⠇⠀⠀⢼⣏⡥⠀⠀⠀⠀⢀⣀⡀⠀⠘⣿⣿⣷⡄⠀ ⠀⠀⢸⣿⠏⠀⠀⠀⠀⠉⢀⣤⣄⣀⠀⢺⣼⡗⠀⠀⣿⣿⣿⣿⡄ ⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢹⣽⣿⣟⠇⠀⠀⠀⠀⠀⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣽⡏⠁⠀⠀⡰⠀⠀⠀⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠉⠀⠻⣶⣤⡶⠁⠀⠀⠀⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⡄⣿⡇⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢙⣣⣴⣦⠛⣥⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⡆⠋⠁⠀⠀⠀⠀⣴⡆⢿⠇⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⢉⣥⣶⣶⠉⣵⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣇⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⠴⠤⠤⠤⠴⠠⠤⠤⠀⠖⠶⠖⠶⠐⠖⠤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣥⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⠀⢲⡷⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣾⡿⣿⣿⣿⣯⣽⣴⣞⣙⡘⣦⡉⣦⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣾⣝⣿⡟⠉⠀⠀⠈⠙⠳⣄⠀⠀⠙⣮⡙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢈⣷⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠒⠒⠒⡒⢒⣶⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⢀⣀⣤⣾⣷⣤⡾⠿⣾⢷⣆⠀⠀⠀⠀⠀⠀⣰⣶⠒⠒⡒⡖⣦⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣝⢿⣿⣻⣿⣿⣿⣿⡿⢿⣿⣿⠯⣿⣿⣿⣿⣟⣻⢿⡿⠁⠀⠀⠈⢯⣿⡀⠀⠀⠀⠀⢀⢯⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⣾⠿⠿⠿⠿⠿⣿⣿⣿⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠙⡿⠛⠁⣼⣧⠀⠀⠀⡤⠜⣻⡷⡀⠀⠀⠀⢸⣸⣿⡿⠿⠿⠿⠿⢿⡇⠀ ⠀⢀⠉⠀⠀⠀⠀⢠⣿⠿⢿⡆⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⡿⣿⣿⣿⣷⣶⣾⣿⡏⠀⠀⠉⠁⢹⢀⣴⡿⠛⣷⡤⢴⠛⢏⠉⢳⣧⡀⠀⠀⢸⡿⢿⣷⠀⠀⠀⠀⠀⠁⠀ ⣿⣽⣀⣀⣀⣀⣀⣘⣿⣿⣾⡷⣶⡽⠛⣿⣿⣿⣿⣿⣿⣿⣟⢠⣤⣽⣿⣿⣿⣿⣿⣿⣿⡷⠶⠶⢶⣶⣾⣟⣥⣤⣼⠁⠇⠈⠄⠘⠀⠀⡟⠻⢿⣶⣿⣾⣿⣿⣀⣀⣀⣀⣀⣠⣿ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣯⣿⠂⠀⠀⠀⠛⠛⠿⢿⢿⣿⡿⠋⠉⠉⠀⠘⣿⣿⣿⣿⣿⣿⡧⣄⠤⣤⢀⣟⠀⠀⠉⠙⢣⣀⣀⣀⣤⠴⠶⠃⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⣿⣿⣧⣤⣤⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠙⠇⢠⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡏⠀⡆⠙⠢⡀⠘⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣿⣿⣿⣿⣿⣷⣿⡿⠁⠹⣿⣷⡄⡇⠀⠀⠉⢦⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠻⣿⣿⣀⡀⢀⣼⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠿⣿⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⢷⣌⠣⠀⢿⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠙⣷⠀⠀⢧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣿⡏⣿⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⣿⣼⠀⢸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣾⡟⢿⡄⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⡔⠉⠈⠿⠷⡙⡖⠄⠀ ⠀⠀⠀⢠⢾⡷⠀⠀⠀⠖⢧⠓⡇⠀ ⠀⠀⠀⢸⢣⣣⡾⠃⢠⣶⠀⢱⠧⠀ ⠀⠀⠀⠘⠢⢬⣁⡇⠀⡝⠽⣇⠀⠀ ⢀⡀⠀⠀⣠⠙⠋⠀⠀⠀⠀⠺⡄⠀ ⠛⡔⢁⠞⢹⡄⠀⠀⠀⠀⠀⠠⡄⠀ ⠀⡇⡎⠀⠀⣿⡄⠀⠙⠀⣀⡞⠀⠀ ⠀⢿⣇⣠⣴⣿⡇⠀⣸⡾⢛⠃⠸⡄ ⠀⠀⠹⠀⠀⠼⣀⠉⡉⡀⠈⠂⠤⠾ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⢸⡇⠀⠀⠀⠀⢀⣠⠟⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠁⠀⠈⡇⠀⠀⢀⣴⣟⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⢰⣇⣠⠾⠋⡰⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⠀⡼⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠴⠖⠚⠛⠒⠒⠦⢄⣀⣤⠞⠋⠁⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡖⠒⠒⠒⠒⠲⠤⢤⡤⠤⣏⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⡆⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣇⠀⣀⣀⠀⡄⠀⠀⠐⠊⠉⠉⠓⣤⡀⣀⣤⡴⣤⡀⠀⠀⠀⠀⠀⠀⠢⢤⣀⣀⣀⣼⣧⣶⠇⠀⠀⠰⢡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢯⣹⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⠈⠉⠈⠛⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⡤⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣏⣳⣄⣀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠐⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠞⠛⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⡯⣽⡿⢉⣿⣿⢷⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠛⠧⡀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⢀⡀⠀ ⣷⠁⠀⢧⡈⠙⠋⠛⠶⢧⣿⣯⣹⣿⠿⣦⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡑⠀⢹⠀⠀⠀⠀⠀⠹⣧⣀⣀⡴⡿⢀⡀ ⠈⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠻⡄⠈⣹⠿⡇⠰⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠹⡟⠁⢀⠏⠀⠀⠀⠀⠀⠀⣸⠏⠹⣦⠗⣻⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠞⢁⣤⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠘⡄⠀⠠⣤⣽⠶⠗⢰⠁⠀⠀⠀⠀⠀⢀⡼⠋⠀⡜⠁⢠⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⣰⣿⠟⠀⣰⠊⠀⠀⠀⠀⠀⠀⢀⡜⢠⠚⠉⠉⠀⠀⠀⣸⠆⠀⠀⠀⢀⣴⠟⠁⣀⠴⡷⠴⠛⡷⠤ ⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⠋⢀⣸⡻⠋⠀⠈⠀⠀⠀⠀⠀⠀⡠⠖⢉⡴⠃⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣠⠞⠁⠀⣞⠁⢰⠃⢀⡾⠃⠀ ⠀⠀⠀⣿⣄⣦⡀⢠⢾⢧⣸⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠞⠁⠀⠀⠀⠀⠀⢠⠋⠀⢀⣴⠟⠁⠀⢰⠉⡿⠉⢁⣴⣏⣤⡴⠀ ⠀⠀⠀⠸⣿⣇⠻⣏⡻⠖⠋⠀⢀⡠⠖⠊⠛⠦⣄⣀⣀⠀⡸⠀⠊⠀⠀⠀⠀⠀⠀⣴⢁⣠⣴⠿⠋⣀⡀⠀⠘⠒⢁⣴⠞⠉⠋⠉⠉⠙ ⠀⠀⠀⠀⢻⣍⠉⠁⢀⣠⠴⠚⠉⠀⠀⠀⠀⠐⣯⠀⠀⢺⠁⠀⠀⠀⠀⠀⣠⣶⡴⠟⠋⠁⠀⠀⢸⠁⢸⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣸⣦⡀⠀⢀⣠⠾⣿⣷⣤⡀⢰⠉⡷⠀⠈⣉⣵⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡍⠀⢈⠉⠉⠠⠤⡄⠀⠉⣷⠈⢒⣡⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡽⠛⣿⡄⠸⠇⠀⠀⠑⠃⣠⣴⣷⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠒⠉⠉⠳⢤⣤⡤⠶⠞⠛⣩⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠟⠛⠛⠛⠛⠿⣦⣄⠀⠀⢀⣤⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣴⡟⢢⡀⠈⠙⠿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⠟⠛⠻⢿⣦⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣷⠀⠀⠀⠈⠛⠻⣶⣄⠀⠀ ⠀⠀⣠⣶⠶⠛⠋⠁⠀⢰⡗⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠈⣷⡀⠀⠀⠀⠀⠀⢀⣾⠇ ⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⢀⡴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡍⠻⣧⠀⣿⣷⡀⠀⠀⠀⢀⡾⠃⠀ ⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢿⡇⠀⢠⡟⠻⣆⠙⣆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡄⢹⡇⠸⣿⣿⣄⣀⡴⠋⠀⠀⠀ ⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⢸⡇⠀⣼⣧⠀⣽⡆⢹⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⠇⢸⡇⠀⢸⡏⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠻⣦⡀⠀⠀⠀⣸⠁⠀⢹⣿⣿⣿⠃⡼⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⣠⡿⠁⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⣠⣿⣧⡀⠈⢿⣿⣧⡴⠃⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⠉⠈⠳⣏⣠⡤⠤⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠉⠻⣷⣄⣉⡉⠀⠀⠀⠀⣴⣾⣿⣿⡿⢿⣿⡆⠀⠀⠀⢸⡏⠀⠀⠀⠙⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠊⠑⠚⠻⣿⠁⠀⠀⠀⠀⢿⣿⣿⣀⡀⢀⣼⡇⠀⠀⢀⣾⠀⠀⠀⠀⢀⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠘⠿⠿⠿⣛⡛⠉⢀⣠⣴⣿⠇⠀⠀⠀⠠⠾⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣇⠀⠀⠀⠀⠀⠙⠻⠷⠶⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠛⢿⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⡀⠀⠀⠀⠀⠀⡟⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠈⢻⡁⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣿⠿⠟⠛⠛⠉⠉⠉⠉⢿⣷⣤⣀⣀⡼⠁⠀⠀ ⢠⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⣷⣤⣀⣀⣠⣶⣿⠛⠋⠉⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀ ⡟⣆⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⡏⠀⠀⢰⡇⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠘⣦⡀⠀⠘⣿⣆⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁⢀⡇⠀⠀⢸⣧⠀⠸⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣦⡈⠛⠶⢤⣿⣿⡇⠀⠀⠀⠀⣾⡿⠛⠋⠙⣾⠀⠀⠀⠘⢛⡳⣄⢠⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠶⠦⣤⣤⣤⣤⣤⣀⣀⣀⣷⣤⣀⣾⣧⣸⣧⣀⣀⣶⡀⣧⣹⡾⢷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠈⠉⠛⠉⠙⠉⠉⠛⠛⠉⠛⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠀⠀⠀⠀⠘⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡤⠴⠶⠶⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⢤⣀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡇⠀⠀⠀⢸⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀ ⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠷⠶⠶⠶⠾⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀ ⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣠⣤⠤⣤⡄⠀⠀⠀⠀⣤⠤⠤⣄⣀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇ ⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⡮⠷⠋⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠙⠺⢯⡀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠇ ⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⣠⠴⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠶⣽⡀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢠⡿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃⢀⡜⠁⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⣰⠋⠀⢀⠀⠀⠈⢳⡀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣄⠀ ⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⡞⠀⠀⠀⠀⣿⠀⠀⠘⣇⠀⠀⠀⢸⠃⠀⠀⢸⡀⠀⠀⠀⢻⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣆ ⣿⠀⠀⠀⠀⠀⠀⢠⡴⠒⠲⣾⡇⢸⠁⠀⠀⣠⣼⣿⣤⡀⠀⢹⡀⠀⠀⡏⠀⢀⣴⣿⣷⣄⠀⠀⠀⣇⢸⣷⠖⠒⠲⣄⠀⠀⠀⠀⠀⠈⣿ ⢿⡀⠀⠀⠀⠀⢰⠏⠀⡄⠀⠙⢷⣿⠀⠀⢸⣿⣿⣿⣟⣿⠀⢸⡇⠀⢸⡇⠀⣿⣟⣿⣿⣿⣧⠀⠀⣿⡾⠁⠀⢀⠀⠘⣆⠀⠀⠀⠀⢰⡿ ⠀⢷⣄⠀⠀⠀⢸⡀⠀⠻⡄⠀⢸⢿⡄⠀⠈⠻⢿⣿⡿⠏⣀⣼⣷⣶⣦⣥⣀⠘⢿⣿⡿⠿⠃⠀⢀⡿⡇⠀⢀⠟⠀⢀⡿⠀⠀⠀⣠⡾⠁ ⠀⠀⠙⠳⣤⣄⣀⣷⡀⠀⣿⢠⡞⠀⠙⠲⢤⣤⠩⡿⢀⣼⠟⡽⢿⣿⢻⢿⣿⣦⡀⢹⠉⢤⠤⠶⠛⡁⠹⡄⢿⠀⠀⣼⣁⣠⣤⠞⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠁⠨⣾⠶⠊⠉⠓⢦⡀⠁⢸⣟⣠⣀⣼⠏⠀⠈⣿⣿⡇⠈⢀⣴⠞⠉⠙⠲⡵⠆⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡟⠐⠤⣤⠼⠁⢃⠀⢸⣿⣿⣋⠁⠀⢀⣠⣿⣿⡇⠀⢸⠈⠳⢤⡤⠖⢻⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⢷⠀⠀⢰⠀⠀⠸⡄⠀⠙⣿⣿⣶⣴⣾⣿⣿⠏⠀⠀⡇⠀⠀⡎⠀⠀⣸⠀⠀⢠⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠘⡆⠀⠈⢦⠀⠀⠙⢄⡀⠀⠉⠙⠛⠋⠉⠀⠀⣠⠞⠀⠀⣰⠃⠀⢠⠇⠀⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠹⣄⠀⠈⠳⡄⠀⠀⠙⠓⠤⠤⠀⠤⠤⠒⠋⠀⠀⢀⡴⠁⠀⢠⠟⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢢⡀⠀⠈⠳⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠉⠀⢀⡴⠋⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣾⣷⣄⠈⠳⢄⡀⠈⠙⠿⠿⣿⣿⣿⡿⠿⠛⠁⠀⣀⠴⠋⣠⣾⣷⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣋⠈⡛⢷⣄⠀⠉⠑⠂⠀⠤⢤⣤⣤⠄⠄⠀⠀⠈⠀⢠⣾⠻⠛⠉⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣶⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣷⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣭⣿⣿⣛⣻⣟⣿⣿⣿⣶⢶⣶⣶⣶⣿⣿⣿⣛⣟⣛⣋⣉⣩⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠙⠿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣰⣄⣀⣠⣤⣀⣀⣀⣀⣀⣀⣀⣀⣄⠀⢀⣀⣀⣀⣀⠀⠀⠀⡄⠤⣤⢤⣠⡄⢤⣤⢦⣤⢤⢀⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠓⠛⠃⠚⠒⠑⠘⠛⠚⠛⠓⠛⠂⠛⠚⠚⠃⠓⠃⠀⠀⠓⠒⠃⠋⠓⠓⠓⠒⠛⠚⠘⠚⠛⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣾⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⣀⠔ ⠀⢸⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠛⠉⠉⠉⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢰⠁⠀ ⠀⢸⠀⠀⠀⠀⠀⢀⣿⣿⡏⠠⢴⣦⡄⠀⣠⣿⣽⣿⡿⢷⡀⠀⠀⠀⠀⢸⠆⠀ ⠀⢸⠀⠀⠀⠀⢀⢾⡿⣿⡇⢚⣿⡿⡇⠀⢿⣟⣿⣿⣿⣿⡇⠀⠀⠀⡠⠁⠀⠀ ⠀⢸⣀⣹⣽⣙⣿⣷⣟⣿⡇⠙⠛⢵⠏⠀⠈⠛⠟⣿⣿⣿⣁⣀⣠⠞⠀⠀⠀⢀ ⠀⢸⣴⣾⣖⣒⠳⣚⣾⣾⡅⠀⠀⢀⣀⣀⠀⠀⠠⢻⣿⣿⠒⣾⠏⠀⠀⡰⡒⠠ ⠀⢸⠉⠈⠁⠀⠀⠀⠁⢿⣷⡀⠀⠉⠉⠉⠁⠀⢀⣼⢿⡃⠉⡹⠀⢀⡀⠳⠒⣅ ⣐⣧⣬⣿⣤⣭⣭⣬⣭⣭⣼⣿⣦⣀⠀⠀⣠⡴⣿⡏⠈⠉⠉⣁⠀⠄⣀⢼⣶⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢖⡳⠾⠛⠛⢛⣻⣟⣷⣶⠤⠤⠼⢆⠀⠀⠙⠻⡋ ⣿⣿⣿⣿⣿⣿⣿⣿⢟⠂⠩⠤⠄⠀⢒⡒⠺⠻⠇⣿⡛⠀⠀⠀⠀⠑⠢⡀⠀⠸ ⣻⣟⣻⣟⡹⠿⠛⠀⠐⠦⣠⡤⣈⠉⠀⢀⣀⡀⢀⡯⠉⠒⠂⠀⠠⠤⠀⣀⠀⠜ ⣷⡦⠒⠉⠀⢀⡀⣀⣀⡀⠀⠈⠐⠈⠙⠊⠁⠀⠁⠈⠲⢦⣀⡀⠄⡀⠀⢀⡜⣢ ⠁⠀⡀⠀⠒⠸⠟⠷⠤⠤⠀⠀⠀⠀⣀⠠⠄⠒⠈⡀⢤⡤⣌⢻⠎⠀⢀⢪⠁⣿ ⠀⠸⣿⡶⢤⠀⡀⠀⠀⠀⠀⠀⠈⢁⡀⠄⠐⠈⠁⠀⠈⠻⢋⡞⠀⢠⠇⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠦⢄⡀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠶⠿⢷⣶⠒⠙⠛⠿⢦⡀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠈⠑⣶⣖⠉⠀⠀⣠⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⡻⣝⣆⡾⠯⠀⠉⢳⣤⡔⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣴⠶⢶⢸⠁⡼⡀⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣯⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⠀⠀⠀ ⠀⢠⣿⢹⡿⣇⣸⡏⢠⠧⡿⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⢤⡀⠈⠙⠻⠶⢦⣄⡀ ⠀⢸⡻⠿⠃⠙⡟⢀⣾⣠⠃⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⠳⡀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠴⡶⠦⠤⠤⣴⣿⠀⠀⠀⠀⠀⠈⠛ ⡾⠋⢿⢀⡀⠀⠀⠞⣩⠏⢰⢳⡿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠟⣸⣥⡤⠼⣶⠶⢦⡀⠀⠀⠀⠳⣄⣱⣷⡀⠀⢀⡼⢿⢦⡄⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⣬⣥⣔⣾⠗⣡⠟⢸⠇⠀⠀⣰⡧⠔⠒⡶⣄⣀⡾⠋⠀⢀⣀⣨⣷⣄⠙⡦⠀⠀⠀⣞⣮⡢⣌⣉⣡⣴⠾⠊⠘⢷⣤⡀⠀⠀ ⠀⠀⠀⠨⠛⢻⡟⠛⠚⢇⢀⣼⠀⠀⠊⣽⡁⣠⢾⡇⣸⠇⠀⠀⣾⣿⣿⣿⣷⣾⠿⣿⣶⣄⠀⢸⣽⡙⢯⡉⠉⠁⠀⠀⠀⠀⠈⠻⣄⠀ ⠀⠀⠀⠀⠀⠈⠧⠄⢀⡴⡏⡞⠀⠀⢀⣿⠋⣿⢿⢧⠋⠀⠀⠀⠑⠚⠛⠿⠟⠀⠀⣿⢹⢈⡇⠀⣣⣷⢄⠹⢦⡀⠀⠀⠀⠀⠀⠀⠈⠱ ⠀⠀⠀⣀⠤⠴⠚⣯⠉⠀⡇⡇⠀⠉⠹⣟⢇⣹⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠮⣼⡇⠀⠙⡆⠈⢦⠀⠙⢦⣄⠀⠀⠀⠀⣠⠚ ⠀⢠⠞⠁⡴⠁⣼⠁⣰⠀⢱⣧⠀⡀⢀⠸⣆⠉⠓⠀⠀⠰⠶⠶⠀⠀⠀⠀⠀⠀⡾⠁⠀⢘⡇⠀⢰⠃⡄⠘⡆⢦⠀⢹⡇⠀⡠⠊⠀⠀ ⣰⠋⠀⡼⠁⢸⢿⢠⠃⠀⡸⢻⠀⢹⣾⣗⣪⢝⣶⠄⠀⠀⠀⣀⠀⡀⠀⠀⠀⣰⠃⠀⠀⠀⠇⣦⠇⠀⠀⠀⠸⣼⠀⢸⣧⠞⠀⠀⠀⠀ ⠁⠀⣸⢡⡀⢸⣈⣾⠠⠞⠀⠀⠓⣼⡏⢟⢎⠉⠁⠀⠀⠒⠛⡉⠉⠀⠀⠀⣼⡟⠀⠀⠀⣰⢺⠇⠀⠀⠀⣠⣦⠃⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠹⣼⠳⣼⡏⠉⣷⡀⠠⠤⠞⠻⢷⡘⣎⠑⣤⡀⠀⠀⠀⠀⠀⠀⢀⡞⢱⡇⠀⠀⣠⢣⠞⠀⢀⣠⠔⢁⣣⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣨⠏⠀⢁⡴⠃⠉⠀⠀⠀⠞⠁⠙⠪⢗⣎⡟⠶⢤⣀⣀⡠⠴⠋⠀⢸⠃⠀⣴⡿⠁⠀⣸⠷⠚⠉⢁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣴⣾⣥⣤⣖⣉⣀⣀⣀⣀⣀⣤⣤⣀⣀⣀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢘⡏⠀⡠⠚⠙⢦⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼ ⠁⠘⠉⢹⡍⢆⠉⠉⠛⠛⡯⣄⡞⢺⡟⡛⠻⣶⡾⢥⣀⣀⠀⠀⠀⠀⠀⠀⣐⡿⠾⠗⠋⢽⣦⠤⠤⠿⠒⠒⠶⣤⣤⣀⠀⠀⠀⣴⠏⠀ ⠀⠀⠀⢸⡇⢸⡀⠀⡠⠊⣠⠎⢈⣿⣿⠗⠒⠻⢿⡛⠷⠿⣿⡙⠧⠐⠀⠚⠁⠀⠀⢀⠔⠉⣟⣷⠀⠀⠀⠀⠀⠀⠉⠙⠷⣄⡐⡏⠀⠀ ⠀⠀⠀⢸⠇⠀⣇⡜⢁⠔⣡⡴⠋⠁⠀⠀⠀⠀⠰⡽⣦⡀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⢀⣼⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢺⣅⠀⠀ ⠀⠀⠀⡜⠀⠀⡟⡰⠃⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⢄⡀⠀⠀⠹⠟⠀⠀⠀⣠⣴⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀ ⠦⢤⣤⡇⠀⢸⣷⠁⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀ ⠀⣾⡾⠀⣼⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀ ⠀⣿⠀⡸⡇⡏⠀⠻⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡹⠃⠀ ⠀⣇⠘⣿⢱⠈⠂⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀ ⠀⣿⣾⠹⣧⡱⢄⡀⠸⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⡄⣀⢀⡼⣿⠁⠀⠀⠀ ⠀⢹⣻⡗⠬⣟⣬⠥⠄⠳⣯⠣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣽⢶⣾⠿⣋⠘⡇⠀⠀⠀ ⠀⠀⢯⢞⢆⠀⠀⠀⠀⠀⢨⡿⢽⣦⣀⣤⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⠀⣻⠀⠈⠑⠿⣶⣀⠄ ⠀⠀⠘⢯⣓⡯⠶⠦⣴⡞⣣⣷⣾⡿⡋⠉⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡄⠘⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⠯⠭⣥⣾⣿⠁⠀⢳⣧⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡧⡀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⢿⣧⡗⠀⠀⠘⣿⡀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⡇⠸⣼⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢟⠉⣯⢣⠀⠀⠀⢻⢧⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⣸⠃⣰⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⣫⣋⠇⣀⠀⠈⡟⡆⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⡇⣼⡯⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢻⢿⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⡞⠀⡷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠆⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⣞⠀⠀⠑⠉⠚⠁⠀⠀⠀
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⡴⡇⢀⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⢠⠋⠀⠙⢆⠀⠀⣀⣀⣼⠁⠛⠉⣵⣋⡀⠀⠀⣠⠖⠋⠙⡄ ⠀⡞⠀⠀⠀⠈⠓⠋⠁⠀⠃⠀⠤⠴⠚⠃⠉⠙⠚⠁⠀⠀⠀⡇ ⠀⡇⠀⡶⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⢹ ⢰⠁⠀⡇⠀⠀⢸⣵⣿⡇⠀⠀⠀⠀⠀⢰⣹⣿⠀⠀⠀⡇⠀⢸ ⢸⠀⠀⡇⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⡇⠀⢸ ⢸⠀⠀⡇⠀⠀⠀⠻⠟⠃⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⡇⠀⡾ ⠈⠒⠖⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡤⠃ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⢿⣿⠆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⢳⡀⠀⠀⠀⠰⠶⠶⠛⠙⠷⠦⠄⠀⠀⠀⠀⣸⠁⠀⠀ ⠀⠀⠀⠀⠱⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠖⠋⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠤⡴⡯⢉⠻⡕⡋⠎⠻⣽⡖⣆⠀⠀⠀⠀ ⠀⠀⠀⣠⣺⣯⢁⢁⠹⣥⣧⢎⡀⠛⢄⠠⡙⢋⣷⢀⣀⣀ ⠀⣠⣾⣯⣿⣿⠿⢿⣯⠞⡉⠙⢿⣧⢍⡘⢆⣡⣿⣡⠔⠃ ⠞⣿⢾⣵⣤⣈⣙⣦⣿⢳⡾⠿⠆⡀⠩⡉⠉⢻⡏⠀⠀⠀ ⠀⠓⠿⣽⣖⣴⠻⡽⣟⠊⣿⣣⡀⠱⠀⠁⠀⠀⢿⣲⠀⠀ ⠀⠀⢫⣼⠋⢘⡄⡃⡇⡧⢈⢠⣣⠀⠀⠀⠀⠀⠈⢯⡇⠀ ⠀⠀⠘⠝⢳⣌⣾⠱⣴⢻⠸⠢⣾⡔⠮⡄⠀⠓⠠⡞⡇⠀ ⠀⠀⠀⠀⠀⠿⣨⠀⣈⡓⠱⠀⢯⢻⣆⠈⠲⣴⣷⢳⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠘⠐⢰⢤⠉⠕⡒⡚⡑⣹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠘⠄⠿⠵⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⣴⣦⣤⣶⣶⣶⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠋⠀⠀⠀⠀⠀⠀⠃⢻⣿⣿⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⣾⣶⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠛⠛⠛⠛⠻⢿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠘⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠘⢷⡀⠀⠀⠀⠀ ⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠈⣧⡀⠀⠀⠀ ⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠛⠉⠉⢁⣴⣿⣿⣿⣿⣶⡀⠈⢉⣿⣧⡖⠋⠉⠉⢉⣿⣿⣿⣟⠾⣾⣿⠀⠀⢸⣧⠀⠀⠀ ⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⢿⡄⠀⠀⣴⣿⣿⣿⣿⣿⠀⣿⣿⡀⠀⠈⢻⡀⠀⠀ ⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣤⣘⣿⣿⣿⣿⣿⡿⠃⠴⠿⣋⡜⠓⠦⣤⣿⣿⣿⣿⣿⣿⣸⡏⣿⠇⠀⠀⢸⣧⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⡁⠠⠒⠊⠁⠀⠀⠀⠀⠈⢙⠛⠛⢻⣱⣯⣿⡿⠀⠀⠀⢸⣿⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⢀⣿⠃⠀⠀⠀⢸⣿⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⢴⣿⠀⠀ ⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀ ⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀ ⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣀⣀⣀⣀⣤⣤⣦⡶⠶⠶⠶⠶⣾⠿⢿⣶⣿⣤⣤⠴⠾⣿⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⡴⠛⠉⠳⣾⠟⠁⠈⢹⠛⠲⣶⣴⣆⠀⢀⣼⠀⠀⠀ ⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣾⠁⠀⠀⣰⠏⠀⠀⢠⡇⣀⠄⠉⠙⢿⣧⣾⡏⠀⠀⠀ ⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⡇⠀⠀⣸⡟⠀⠀⠀⢰⡿⠋⠀⠀⣰⡏⠁⠈⢳⡀⠀⠀ ⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⣿⠃⠀⠀⢀⣾⠇⠀⠀⢰⣿⣧⣀⡀⢀⣿⠀⠀ ⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠸⣸⠂⠀⢰⣿⡇⠀⠀⠀⣿⣿⣟⠻⠿⠛⣿⡆⠀ ⠀⠀⠀⠀⠀⠈⢿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⢀⠏⠀⠀⠸⠿⠷⢄⣤⢸⣿⠁⢿⣶⣶⣶⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠋⢸⣿⣴⠀⠀⠉⢩⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⢸⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣶⣤⣄⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⣧⠀⠀⠀⠀⠻⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣿⠀⠀⠀⠀⠀⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣀⣼⡿⢿⣆⠹⣷⣄⠀⣠⣴⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠆⠀⠀⠐⠒⠿⢿⣏⠀⠀⠈⣷⠿⠿⠿⠟⠛⣉⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠤⠤⠤⠤⠴⠿⠋⠀⠀⠀⠙⠻⠶⠶⠖⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⡖⠒⠒⠒⠒⠚⠿⣧⡀⠈⠑⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠬⠗⡤⠄⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⠁⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣴⣫⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠽⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠀⣤⣤⣄⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⡇⠀⣿⣇⡍⠉⠁⠈⠛⣶⡖⢻⠓⠀⢿⣿⠀⠀⠀⠀⠀⠀⠙⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡿⠉⣹⠃⠀⣿⣿⠇⠀⠀⠀⠀⣿⣿⡾⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣜⠀⢰⣷⡀⠀⠈⠉⠰⣶⡶⠄⠀⠙⠛⠁⠀⠀⠸⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢇⠀⠈⠙⣧⣄⣀⡀⠴⠛⠢⣄⠀⠀⠀⠀⢀⡔⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠘⢧⣀⣠⡼⠛⢿⣅⣀⡀⠀⠀⠀⠀⠀⠈⠁⣀⣀⣠⣼⠿⣄⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠙⡟⠢⡀⠀⠀⠀ ⠀⠈⠉⠀⠀⠀⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡈⠑⠦⣄⣀⣀⣠⠟⠁⠀⠀⠀⠀⠀⡇⠀⠙⡄⠀⠀ ⠀⠀⠀⠀⢀⡾⡯⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠹⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢹⡴⡆ ⠀⠀⠀⠀⠀⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠞⣿⣿ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢀⣾⣿⠇ ⠀⠀⠀⢀⣤⣼⡅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⡒⠒⠀⠀⠈⠢⢤⡀⠤⠔⠒⠁⠀⠀⢀⣴⣿⡽⠃⠀ ⠀⠀⠀⢀⡾⣽⡇⠀⠀⠀⡁⠀⢸⠃⠀⠀⠀⠀⡆⢠⣿⠿⠂⠀⠀⠀⠀⠀⠀⢷⣦⡀⠀⠐⠶⠾⠿⢿⣿⠟⠃⠀ ⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠇⠀⢸⡇⠀⠀⠀⠠⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠉⠉⠓⠒⠒⠊⠉⠀⠀⠀⠀ ⠀⠀⢠⠞⡉⢸⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⣿⠘⣿⣶⣤⠄⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣤⣷⡇⢰⠄⠀⠀⣿⣠⣾⢫⠀⠀⡀⢰⣿⣠⣿⣿⣇⢀⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠙⠓⠼⠧⠜⠛⠃⠈⠳⣼⣷⣦⣼⣬⠋⠹⣿⣍⣉⣽⡤⠽⠭⠤⠶⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⣿⣿⣤⣋⣔⡄⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠑⡄⢱⢱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣶⣶⣷⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠷⢶⡾⡟⠉⠙⣇⠀⠀⣸⣷⣶⣷⡀ ⣠⠁⠀⢸⣟⣄⡤⣿⣿⣿⡟⢿⣿⣿⣿⣏⣉⣘⣴⢻⠆⡗⠙⣦⣀⣿⡇⠀⠀⢁ ⠉⣿⣿⣿⣿⠀⠀⠙⠛⠛⠉⠉⣹⣿⣿⣗⣒⣼⠈⠉⠂⠐⠒⠁⠀⣿⣿⣿⣿⡏ ⠀⠹⠿⠿⠿⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠹⠿⠿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⡋⢅⠆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠋⠈⠳⣇⣀⡧⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡇⠀⠀⠀⠀⢀⠫⣃⢨⢂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠸⣄⣸⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢱⣷⣷⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠒⠒⠶⣤⣾⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣴⣿⣿⠃⢀⡤⠾⢶⣌⠙⠻⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⣷⠉⢿⣿⣿⠀⣾⢧⣄⡀⠈⠓⣦⠀⠉⣙⢛⣛⣿⣷⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠿⡄⣸⣿⠏⠠⠿⠦⢤⣉⣛⣶⠏⠀⣰⣯⠉⠁⠀⠹⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠁⠀⠈⠙⠲⠦⣄⣀⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠖⠋⠁⠀⣀⣀⣀⣀⣀⠀⠉⠏⢽⡛⢙⣮⣉⡓⠲⣴⠟⠲⣄⠀⠀⠀⠀⠀⠀⠀ ⠳⣄⠀⠀⠀⠀⠀⠀⠉⠉⠻⠿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣯⠆⣠⠖⠋⠉⡿⡄⠈⠉⠙⢦⡀⠀⢹⡏⠙⠻⠉⠛⠷⣟⠃⢸⡆⠀⠀⠀⠀⠀⠀ ⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢡⢾⢹⡀⠀⢠⠇⢹⡄⠀⠀⣼⣿⠓⠒⣿⠉⠙⢳⣦⠀⠈⣧⡼⠁⠀⢀⣤⣤⣄⡀ ⠀⠀⢀⡏⠀⡏⠙⠒⠲⠤⢤⡀⠀⠘⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⢸⡃⣏⡼⠀⢧⠀⡞⠀⠀⢧⢀⡴⠁⢸⠀⣼⠋⡇⢀⡞⡏⢳⡀⡿⠀⣠⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⣧⠀⢷⠀⠀⠀⠰⣄⢁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⢧⡈⠻⠦⠼⣿⠥⠤⠤⠼⠿⠤⢤⣸⣟⡁⠀⣇⠞⠀⣇⢈⡇⢧⣸⣿⣿⡿⠛⠛⠛⠿ ⠀⠀⠀⠘⢦⣈⣳⣄⡤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢤⣄⣿⢟⡇⣸⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⣽⠁⠀⠀⠀⢀⣀⠀⠀⠀⢰⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣮⣝⣻⡵⠋⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣤⣠⠔⠋⠉⠉⠉⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠉⠀⠀⠀⠰⣤⣤⣤⣤⣶⠋⠁⠀⠀⠀⠀⠹⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⣿⣿⡃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣷⣶⣤⣀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⣠⣾⣿⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠿⠟⢿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉⠉⠿⠛⣿⠿⣿⠛⠿⠟⠁⢹⡄⠀⠀⠀⠈⠉⢸⠟⠙⡿⠛⠛⠛⠛⠛⠉⠁⠈⠙⢓⡦⣤⣏⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣡⠶⠚⣀⣤⠀⠀⠀⠀⢀⣀⣁⡤⠤⠴⠚⠋⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠤⣄⣀⠀⠀⠀⠐⠦⢤⣈⠙⢳⣈⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣏⣁⣠⠤⠴⠒⠋⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣤⣀⣀⣹⠦⠴⠏⠁⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠿⠟⠛⠋⠉⠉⢹⢗⣬⡞⢀⠏⠭⢟⣿⢹⣯⣯⣿⠞⠁⠁⠀⠀⠀⠀⠀ ⣟⠉⢀⣀⣀⣠⣴⣶⣶⣭⠆⡏⠇⢸⡀⠀⠈⠇⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣉⠁⠒⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣇⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣯⣿⣿⢟⣲⣿⣿⡿⣻⣿⢟⡿⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⠿⠻⠓⢳⡿⠉⠓⠵⡉⠚⠮⠿⣟⢿⣿⣿⣿⣦⣄⠀⢀⣀⡀⡀ ⠀⠀⠀⠀⠀⢿⠀⢣⠀⠘⡇⠀⠀⠀⠈⠑⢤⠀⠈⠙⠯⢿⣿⣿⣿⣿⣶⣖⣽⣶ ⠀⠀⠀⠀⠀⢸⡐⢀⣄⠀⢸⡤⠶⠲⣶⡄⠀⠀⠀⠀⠐⣿⠧⢼⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⠗⠋⣹⠒⠉⠀⠀⠀⠈⠁⠀⠀⠀⢠⢉⣏⡠⠊⠀⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡞⠀⠀⢡⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡉⡇⠀⣀⡶⢹⠿⠻⠛ ⠀⠀⠀⠀⢀⡧⠄⣀⣈⡿⠉⡓⠤⢄⡀⠀⠀⠀⠔⠊⢺⣗⡥⡀⡫⠒⠁⠀⠀⠀ ⠀⠀⠀⠀⣜⠀⠀⠀⠀⠉⠳⣷⠤⢀⣈⡉⠒⠂⠤⡤⢸⡵⠟⠱⡇⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⣶⣿⣿⣿⣶⡤⠰⡧⣀⠀⠀⠈⠙⢲⡞⠁⡼⠀⠀⠀⠀⠀⠆⡣⠼⢀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠃⠠⢉⣁⣒⠂⠁⣠⠞⠀⠀⠀⠀⠀⠀⣀⠠⢁⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣧⢸⢸⣤⣀⡀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡁⡠⠐⡩⠪⠀
⣿⣿⣿⣷⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⡏⠈⠉⠉⠀⠈⠻⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⡀⠘⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣧⡀⠘⣿⣿⣿⣿⣿⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢹⣿⡿⠇⢾⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣧⡀⠸⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠻⠿⢧⣤⣀⡀⠀⠀⠀⠀⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣧⠀⠹⣿⣟⡿⠇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣀⢠⣿⣿⡇⠻⠿⠏⠿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠙⢷⠀⠘⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣧⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⢀⣴⡅⠀⢀⣼⣿⣿⣿ ⣿⣿⠿⠋⠁⠉⠿⣿⣿⣿⠀⠀⣴⣦⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⠋⠀⠀⠀⠀⠀⠈⣿⣿⣶⣼⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢿⣿⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢆⣾⡟⠀⠀⠁⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠺⠿⢟⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣧⣼⣯⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣿⣄⣴⣶⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠹⣿⣉⠈⠻⢿⣿⣿⣿⣿⡿⢿⠾⠵⠖⠛⢹⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣴⡍⠀⠀⠀⠀⠈⠻⣧⡀⠀⢻⣿⣿⡟⠁⠟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠒⣙⣿⣦⣤⣤⣀⣀⠀⠀⠈⣠⣶⡾⠛⠉⠀⣴⣿⣿⠷⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣹⣿⣿⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠿⠍⠉⠀⠄⠀⠀⠘⣧⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠋⣿⠇⣸⣿⣿⣿⣿⣿ ⣦⣤⣀⣬⣿⣿⣿⣿⡿⡟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⣿⣷⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠟⠋⢁⣴⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠐⣟⠁⠀⠒⠛⠛⠉⠁⣀⣀⣀⣠⠤⣶⣒⣹⣿⣷⣾⣿⣿⣿⣿⠟⠋⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣷⣶⣶⣾⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⡀⠄⢢⣾⣃⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢻⣿⠟⠋⠁⠀⠀⢀⣡⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⢀⠶⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢀⣿⣧⣿⡿⠛⠻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣻⡟⠉⠀⢀⠤⠚⠉⠀⠀⠀⣠⣴⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠠⠶⡲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⣿⣿⡿⠀⠀⠂⢸⣿⣿⣿ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢠⠞⢋⠀⠀⠁⠀⠀⠀⣀⣢⣶⣿⣿⣿⣿⣿⣿⣯⣉⣛⠷⢧⣤⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠟⠁⢠⡾⢱⣿⡁⠀⠀⠀⠘⢿⣿⣿ ⠀⠈⠻⣿⣿⣿⣿⡿⠋⡀⠁⣀⡴⠞⠁⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣾⣿⣇⠀⠀⠀⠀⠀⠈⠛ ⠀⠀⠀⠈⢻⣿⣿⡇⠀⠑⣚⣉⣠⣴⡶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠛⠻⠿⠶⠞⡿⠿⠛⠃⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⣛⢻⣿⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣰⣿⣿⣿⣿⣿⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⢿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣍⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠈⢻⣆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣤⠖⠛⠉⠉⠉⠉⠉⠙⠒⠦⣿⣏⣀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⡄⠀⠀ ⠀⢰⣯⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⠀⠀ ⠀⠈⣇⢀⢠⠇⠀⣶⡶⠄⠀⠀⠀⢠⣶⡶⠀⠀⣸⣀⣼⠟⠀⠀ ⠀⠀⠙⠛⠾⡆⠀⠙⠛⠃⠀⠀⠀⠀⠙⠋⠀⠀⣹⠟⠁⠀⠀⠀ ⢀⡴⠚⠉⠛⢿⠀⠀⠀⠀⢿⣿⠆⠀⠀⠀⠀⢀⣿⠋⠉⠉⢳⡄ ⢾⡀⡄⠀⣄⡼⠻⢧⠤⣤⠤⠤⣤⣠⣦⣾⠶⠞⢿⣤⡄⣠⣀⡷ ⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⢤⣄⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⣾⣿⣿⣿⣿⣭⢻⣻⣿⣿⣿⣇⣤⡷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⠋⠁⠑⡄⠀⠉⠙⠻⣿⣵⡀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠐⠀⠀⠀⠀⠈⢿⣿⡀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧ ⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⣠⣤⡘⣿ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠽⠿⣿⠿⢷⡄⠀⠀⠀⠾⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠊⢁⣶⣿⣿⣦⠀⢠⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣿⣿⣿⣿⠂⠸⡟⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡀⢀⣸⣿⣿⣿⣗⡧⡘⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣈⠉⠉⠉⠉⢁⠌⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡟⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡼⠁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⣂⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡾⠚⠁⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢷⡀⠱⣄⠙⢦⡀⣾⠋⠀⠀⠀ ⢀⡀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣼⣿⣦⡈⠻⢶⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⢯⣉⠁⠀⠘⢷⡄⠀⠀⠀ ⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⡠⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢡⠀⢹⡍⢿⡇⠀⢹⡀⠀⠀ ⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣼⡗⠀⠀⠀⡏⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⢣⠘⣇⠀⠀⢧⠀⠀ ⠀⠀⠀⡜⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠸⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠘⡆⢹⡆⢡⡈⢆⠀ ⠀⠀⢰⠁⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⢠⠇⠀⠀⠀⡇⠀⠀⠀⠀⡾⡇⠀⠀⢣⠘⣿⣄⢱⠀⠳ ⡀⢀⠇⠀⠀⢀⠜⠁⢀⠔⠁⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⣠⠖⠁⢀⡴⠀⠀⢀⡾⠀⠀⢀⣼⠀⠀⠀⠀⢸⡇⡇⢳⢄⠀⠀⢯⣿⠛⣷⣤ ⠁⣾⠀⠀⣴⡯⠤⠴⢧⣤⡄⣀⣀⣰⣯⠎⠀⠀⢀⣤⠊⠀⠀⣠⠏⠀⠀⢀⣾⠃⠀⢀⣾⡏⠀⠀⠀⠀⣿⣧⡇⢻⣦⡉⠑⠉⠁⠀⢸⣿ ⢀⡏⠀⠀⠀⠀⠀⠀⢸⣯⠇⠀⠈⠀⠬⠤⠤⠤⣤⡃⢉⡽⠚⠥⠤⣀⣀⣾⣃⣀⣠⣞⣏⣀⠀⠀⠀⣸⣿⣿⣿⠀⠙⢿⣆⣀⠀⣠⣺⣿ ⡞⡇⠀⠀⢀⣠⠔⠂⠉⠀⣀⡀⠤⠤⠀⠠⠤⠤⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⡿⡟⠋⠑⠲⢿⣼⠃⡟⠀⠀⣼⠉⠛⣯⣴⡌⠇ ⢃⡇⣠⣶⢻⠇⠀⠀⠀⠈⠀⢀⣀⡀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢛⣹⣼⣧⡷⠴⠶⠖⠛⠋⠀⡇⠀⢠⠃⠀⠀⣿⠁⢳⢠ ⡿⣿⢿⢯⢸⣆⣰⣶⣶⣶⣶⣿⣿⣶⣶⣦⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠁⢠⠃⠀⡆⢀⡏⠀⠀⢸ ⢇⡟⡾⢀⣸⣻⠉⢻⡄⠀⠀⠀⠀⠀⣻⣈⣧⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣠⠃⠀⢰⠃⣸⣷⠀⠀⡸ ⣼⣧⠃⡸⣿⡟⢇⠈⠻⣦⣤⡶⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠁⠀⢀⠏⢠⡟⢯⠀⢀⠀ ⣿⠹⠀⡿⣿⣷⣼⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠁⠀⢀⡎⢠⡟⠀⡠⠚⠁⠀ ⡏⠀⢰⢱⠛⡋⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡴⠃⠀⠀⢠⠎⢠⣿⣧⠎⠀⠀⠀⠀ ⠀⠀⡈⡎⠀⢡⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⢀⡴⠋⠀⠀⢀⣰⣿⣴⣿⣟⣛⠲⣄⠀⠀⠀ ⠀⠀⢱⠃⠀⠀⠳⡀⢳⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣉⣤⣤⠖⠉⠀⠀⣠⣴⣿⣟⣡⣾⣾⠘⣿⣤⣹⠀⠀⠀ ⠀⠀⡎⠀⠀⠀⠀⠈⢶⢳⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⣤⣤⣴⣿⣿⡿⠟⠋⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⡟⣿⣿⣭⠿⣿⣦⣄⡀ ⠀⡸⠀⠀⠀⠀⠀⠀⠀⣳⣱⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣾⣿⡶⢀⣤⣾⣿⣿⡿⠁⠈⠏⠻⣿⣿⣇⠘⣿⣿⠦⣈⠻⢿⣿ ⢰⠃⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣦⡀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠟⠀⠀⠀⠸⡄⠈⢿⣿⠀⠸⣿⠀⠈⠻⢽⣋ ⠃⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢱⠀⠀⢻⠀⠀⢣⢣⠀⠀⠀⠀ ⣤⣾⣿⣿⣿⣿⣿⣿⣿⢟⣯⣾⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇⠀⠈⡄⢧⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡟⢀⣠⠟⠙⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢱⠀⠀⢣⣸⠃⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠙⡟⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢀⣼⠿⣇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⡟⣆⠀⠀⠀⠀⠀⠀⢈⠀⢰⠀⢘⢿⣇⡈⡀⠀ ⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠉⠑⠉⠛⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡇⠘⣦⠀⠀⠀⠀⠀⠈⠀⢸⠀⠘⠦⡾⢿⣿⣶
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠒⠂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠤⣐⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⢠⣖⡥⣤⠤⠤⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀ ⢀⢴⢋⡾⠊⠀⠒⠠⢀⡀⠀⠈⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀ ⣣⡃⠜⣿⠶⣦⣄⡤⢀⠈⠒⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠡⠀ ⢡⠸⠀⠏⣀⠤⣍⠻⣦⡕⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⡇ ⡼⡇⢀⣈⡃⢿⠿⡅⡈⠃⠀⠀⠀⠀⠀⠀⢄⠀⠀⠑⡀⠀⠀⠀⠀⡘⠀ ⡄⢇⠀⠀⠀⠁⠊⢄⡀⠀⠀⠀⠀⠀⣤⠠⡀⠑⢄⠀⣷⠀⠀⠀⡔⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⢀⠄⣋⣙⢿⣦⠠⠈⢢⠃⡇⢀⠎⠀⠀⠀ ⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠪⣱⣮⣷⠙⣷⡄⡈⠀⢰⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠐⢂⠀⠀⠀⠀⠀⠀⠘⢔⠋⠤⠚⢻⠁⠀⣿⡘⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠐⢌⠤⡀⣠⡟⠠⢠⢻⡟⠀⠀⠀⠀ ⠀⠠⡀⠀⠀⠀⠀⠀⠀⢿⣆⡀⠀⠀⢀⣠⡾⣹⣴⠃⡾⠞⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡋⠁⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⠞⠀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡷⣄⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡽⣣⢖⣋⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠙⣞⣦⡀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⣰⡟⢞⡟⠀⠀⠀⢀⣤⣶⡶⣶⣤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣶⡦⣀⠀⠀⠀⠘⣞⣾⣆⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⡼⠟⠁⢀⡴⢣⣿⠇⡼⠁⠀⠀⣰⣿⣿⣯⣿⣿⣻⣧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣽⣷⣯⢦⡀⠀⠀⢻⠘⣿⣷⣄⠀⠀⢽⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⢙⣶⠋⠉⠀⠀⣀⠴⠋⠀⣿⡏⣼⠇⠀⠀⠈⢻⡿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡿⠿⣿⣿⣛⠉⠁⠀⠈⢿⢷⣾⣿⠈⠳⢄⠀⠙⠾⣿⣿⣀⠀⠀ ⠀⢀⣼⡟⠀⠀⢀⠀⠀⠀⠀⢸⣿⢠⣿⠀⠀⠀⠀⠀⠈⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠀⢠⡀⠈⠢⣀⠈⢿⣷⣦⣀ ⠀⣠⣟⠀⢀⠴⠋⡠⠀⢠⠆⠀⣿⢸⡏⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠙⢢⡳⡌⠳⣼⣿⣬⡉ ⡰⣿⡟⠀⢀⠔⠋⢀⡴⠋⠀⠀⣿⢸⡇⠀⠀⠀⠀⢀⣀⠴⠃⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠘⠧⣀⠀⠀⠀⠀⠀⢀⣿⣿⢸⠀⠀⢢⠀⠙⢦⡈⣿⢷⡀ ⠾⢿⣷⡔⠁⢀⡴⠋⠁⠀⢀⣤⣿⣸⡇⠀⢠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠓⠲⢤⡀⠀⢸⣿⣿⢸⠀⠐⣆⠳⣄⠀⠓⣿⡄⠀ ⠀⢹⣿⣧⠖⠁⢀⡴⠃⢀⡾⠙⣷⣿⡇⠀⣏⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⢣⠀⣾⣿⠏⡏⠀⠀⠮⣆⠘⢧⢀⣿⣷⠀ ⠀⠈⣿⣇⣤⠶⢋⡴⡠⣾⠁⠀⣿⣿⡇⠀⠘⠀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⢆⢸⠀⣿⣿⣼⠀⠠⣄⠢⣌⠟⣎⣹⣿⣿⠀ ⠀⠀⢻⣿⡟⠀⣫⢞⠝⠁⠀⠀⣼⣹⣧⢀⡀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠦⠄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⡟⠀⢰⣿⡏⣿⠀⠀⢿⡳⣄⢠⣾⠿⡿⠟⠀ ⠀⠀⠈⠙⣿⣟⣁⡀⠀⣀⣠⢤⡟⣿⡏⠜⡤⠀⢃⢻⣿⣷⣄⡀⠀⠀⠀⠠⣀⣠⡼⢿⡿⣦⣐⣄⡀⠀⠀⠠⠤⣴⡟⣿⡿⡸⠀⠀⣾⣿⡇⡙⣆⠈⢦⣘⣮⣿⠻⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⢻⣿⢿⠞⣙⣿⢟⣾⣿⣇⢠⡇⠀⠸⡇⢻⣷⡉⠛⠛⣿⠛⠛⠉⠉⠀⢸⡇⠀⠉⠉⠛⢻⣿⣿⠟⠉⠀⣾⡇⠀⠀⢠⣿⣿⣧⢠⡝⡇⢸⡟⢿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣞⢿⣿⣠⣾⣿⣿⣿⣿⢁⠀⠀⠹⣌⣻⡟⠀⢹⣿⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣿⢻⡏⠀⠀⣻⡿⠀⠀⡐⠸⣿⣿⣿⡀⠹⣧⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⣩⣿⠹⠻⢿⢇⡼⠀⠀⠀⠹⡏⢿⡄⠈⣿⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⣯⡿⠀⠀⣰⣿⠁⣄⡀⣿⡄⠙⠈⢿⣿⣦⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⡇⠀⠰⡾⡞⢁⣦⠀⠀⠀⢧⣈⢷⡄⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⣴⣿⠃⠀⣱⣷⡿⡇⠀⡇⢸⣆⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⡇⠀⠀⠇⡇⣸⡯⠀⠀⠀⠈⢻⡀⠻⣄⠸⣷⡀⠀⠀⠀⠀⠀⠀⣴⡟⢀⣤⣾⡿⠃⠀⠁⠹⠋⣧⠀⠀⠁⢀⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡇⠀⠀⠀⢣⡟⣠⣰⡃⠀⠀⠀⠱⡄⠙⣦⡘⢿⣦⣄⣀⣀⣠⡾⢋⣴⣿⣿⠟⠀⣀⠀⢸⠀⠀⠛⠁⠀⢀⣾⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⡷⡀⠀⠀⢸⣷⢛⣿⣇⡆⠀⠀⠀⠘⠦⣌⠻⣶⣬⣉⠉⠉⣀⣴⣿⠿⠟⠕⠁⢠⢻⡟⣿⡖⠀⠀⠀⠀⡼⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢱⣷⠀⠀⠀⠁⣿⢹⠋⣿⠃⠀⠀⠀⠀⠈⠓⢼⡻⣯⣭⣭⣿⢟⡡⠔⠂⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⢠⡇⡈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢿⣇⠀⠀⠀⠛⢿⣰⣿⣾⡆⠀⠀⠀⢀⠀⠀⠈⠁⠒⠒⠒⠉⠀⠀⠀⠠⠀⠚⣿⠻⣦⠀⠀⠀⢀⡟⢠⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣬⠻⡆⠀⠀⠀⠸⠟⠾⠀⣷⢼⣆⠀⠈⡇⣰⢿⣤⠀⠀⣀⢀⠀⠀⣰⣿⠅⢠⢿⡆⠁⠀⠀⢀⡞⢀⢯⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡐⠀⠀⠀⠀⠀⣼⣴⢿⠃⠀⠀⣦⣷⠏⢪⣿⣄⡾⣿⣿⠀⡼⠫⠏⣰⠏⠀⠀⠀⠀⠀⡞⠀⣯⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠁⠀⠁⣿⣏⠀⣿⣞⠇⠀⢀⠾⠁⠀⠀⠂⠀⠀⠈⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠘⠀⠘⠉⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠈⢀⠀⠀⡀⡇⠉⠐⢈⠀⡐⡉⣙⠚⠛⠇⠐⠀⡁⠸⠆⠋⠀⠘⡃⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣞⡩⠽⢷⣆⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⡤⢿⠀⢹⠖⠒⡛⠧⠐⠉⣧⠀⠀⠀⠀ ⠀⢀⡠⠴⣲⣭⡁⠲⠇⢈⡑⢚⠪⠭⠤⠤⢄⣀⣿⠀⠀⠀⠀ ⢠⠃⠤⠄⠉⠉⠀⠐⠉⣡⠞⠁⢀⡴⠞⠉⢉⣩⠿⠶⠤⣄⠀ ⢸⠀⠀⠀⠀⡄⠀⠀⣰⠃⠀⢠⡞⠀⠀⡴⢋⣴⣿⣿⣷⡘⣆ ⢸⠀⠀⠀⠀⡇⠀⠀⡏⠀⠀⣾⠀⠀⡜⢀⣾⣿⣤⣾⣿⡇⣿ ⢨⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⡏⠀⠀⡇⢸⣿⣿⣿⣿⣿⢁⡏ ⠈⠀⣀⠀⠀⣷⠀⠀⠘⢄⠀⢳⠀⠀⡇⠸⣿⣿⣹⡿⢃⡼⠁ ⢰⡀⠛⠓⠀⢻⠀⠀⠀⠀⢙⣻⡷⠦⣼⣦⣈⣉⣡⡴⠚⠀⠀ ⠀⢷⣄⡀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠉⠛⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⢶⣿⡿⢢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣷⣷⣮⣥⡳⢂⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢽⣿⣿⢿⣿⠿⡿⢱⣦⢂⠀⠀⠀ ⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⡿⣷⢽⣎⢆⣿⣶⣷⣶⣿⣾⡧⡀⠀ ⠀⡔⡝⣿⣿⣿⠻⣿⣻⣿⣿⢨⣷⣽⣶⣼⣼⣤⣿⣭⣿⢻⣿⣿⣯⣧⣿⡜⢄ ⠸⡇⢹⣿⡿⣿⣾⣯⣻⣿⣿⡘⣿⡘⣿⣿⣿⣿⣿⣿⣯⣿⣧⣽⣶⣿⣿⢻⣮ ⠀⠁⠌⢿⡷⣹⣿⢿⣿⢻⣿⣧⠽⣿⣭⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠏ ⠀⠀⠀⠈⠳⣻⣿⣿⣝⠿⢿⣿⣪⠩⠑⠊⠙⢻⣿⣿⣟⣿⣿⣿⣿⣿⠻⠃⠀ ⠀⠀⠀⠀⠀⠀⢈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠸⢫⣿⣿⣿⣿⢿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣸⣿⣷⡐⠄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣦⣀⠀⠀⠀⣀⠜⢿⣫⣿⣿⣿⣿⡦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠿⠋⠞⢧⣻⣿⡗⢠⢾⣷⣾⣿⣿⡿⣿⣿⣿⣿⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠚⠛⢿⣿⣿⡶⢒⣿⣿⣿⠟⣋⣦⣿⠟⠻⣿⣿⣤⣀⠀ ⠀⠀⠀⠀⠀⣰⡫⣏⠂⠀⠀⢹⠋⢀⡞⠛⠛⠓⢓⡻⠋⠁⢀⣴⢞⣙⣭⠿⠛ ⠀⠀⠀⠀⣰⣿⣿⣯⠀⠀⡠⠃⠀⢸⣒⣀⢁⠠⠁⠀⢠⢖⡕⠛⡋⢑⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣠⣤⣄⣠⣄⠀⠀⠀⠀⠀ ⠀⣀⡤⠔⡾⠟⠁⠀⢠⠏⠀⠀⠉⠪⢻⡟⠲⢤⡀⠀ ⢸⠁⣀⣸⣥⣤⣄⣀⣸⣀⣀⣤⣤⣄⣈⣳⡀⠀⠙⡆ ⠘⡆⠘⣧⣿⣿⣿⣿⠏⣏⣼⣿⣿⣿⡟⢹⡇⠀⢰⠇ ⠀⠙⣦⣿⣿⣿⣿⠟⠀⠘⢿⣿⣿⡿⠃⢸⣇⡴⠋⠀ ⠀⠀⠘⠋⣇⢠⢣⡶⣲⣶⣦⠈⢦⠀⠀⡾⠙⠀⠀⠀ ⠀⠀⠀⠀⠘⢾⠀⠳⢿⠶⠃⠀⣸⣶⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡗⡶⢾⠷⢶⠒⣷⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡇⠈⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣒⣖⣺⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠤⠴⠤⠤⠠⠴⠠⠤⠄⠀⠂⠶⠦⠴⠤⠂⠴⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠉⠀⠈⠙⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡷⠶⢤⣀⣶⡷⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣗⣠⠴⠞⠁⢀⣴⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡀⢀⣠⡤⢶⡟⠋⠲⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠻⣤⠞⠁⠀⠐⢮⡙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠙⣧⠀⣟⠀⢸⠀⠀⠀⠹⠎⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠘⣦⠹⠀⣾⠀⠀⠀⡀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢀⡴⠋⠀⠀⢠⡞⠈⢧⠀⡇⠀⠀⢸⠁⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠉⠛⡇⠀⢀⡴⠋⠀⠀⢀⣷⠷⠒⠀⣿⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⢀⣤⢴⣺⣷⣶⣋⣤⡤⣤⡶⠋⠁⠀⠀⣰⠃⠀⠀⠀⠀⠀⣠⠾⣆⣀⣠⣤⠤⠶⠒⠒⠉⠛⣿⠉⠛⠓⢲ ⠀⠀⠀⠀⠀⠀⡞⠋⠀⠀⠀⠀⢠⢾⡟⣷⡾⣿⣺⣿⣯⢰⡞⠉⠀⣠⡴⠚⣉⠙⠲⢶⡶⠒⠒⠒⠀⠀⢹⡻⣄⠀⠀⣠⣤⣄⡈⠉⠉⣀⣴⠞⠋ ⠀⠀⠀⠀⢀⣿⠀⢀⡴⠞⠉⡆⠸⢯⣟⢀⡝⣿⣇⣀⣀⣀⣹⣶⣟⣁⣐⣋⢁⣠⠞⠉⠀⠀⠀⠀⠀⣠⡾⠋⢉⣿⣹⣿⣶⠄⣈⣴⣞⣯⣄⣀⠀ ⠀⠀⠀⠀⠘⢿⣶⣋⣀⣀⣤⡇⠀⠀⠙⢛⣤⠜⠟⠹⣭⣳⠀⠈⠙⢦⣀⡌⠋⠁⢀⡀⠀⠀⣀⡤⣞⣫⠤⠶⠛⣛⣿⣷⠷⠿⠉⠀⠀⠀⠉⠙⠁ ⠀⠀⠀⠀⠀⢀⣛⣿⣿⣻⣻⣯⣍⡉⠉⠉⠉⠁⠈⠉⢛⣟⣶⡦⠤⠀⠘⢧⠀⠀⠀⠘⢿⡉⠹⡏⠁⠀⣀⣤⣾⣿⣿⣿⡿⢿⡙⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⢯⣿⣯⡉⣹⡛⠲⣭⣷⣤⣤⣀⡤⠺⡟⠓⠒⣦⠀⠀⠀⠈⢳⣄⠀⠀⠈⢳⣤⣿⣶⣾⣟⣾⠿⢿⣿⣿⠗⠈⠳⣄⡀⠀⠀⠀⠀ ⠀⠀⣠⡖⠁⠀⢀⡄⢸⡏⠉⢹⣿⠳⣶⣄⠀⠀⠀⠀⠹⣆⠀⠘⣦⣴⡶⠒⣿⠈⢳⢦⣤⠾⠛⢿⡷⢯⣭⣀⡾⠉⢉⣿⣤⣤⣀⠈⠻⣦⠀⠀⠀ ⠀⣴⠃⠀⣠⣞⣿⡇⣾⠀⢠⢿⠏⢀⠸⣟⢷⡀⠀⠀⠀⠘⣆⣪⠟⢉⠀⣼⠃⢀⣸⠙⠳⣄⠀⠀⠙⢻⡶⢯⣻⡾⣅⣀⣈⠙⣮⠻⣦⠈⢷⠀⠀ ⣸⠃⠀⣰⡿⣷⠋⠀⣯⣠⣟⡇⢀⠸⡆⢻⠈⢷⠀⠀⠀⠀⠹⠇⢰⡏⠀⢻⠋⠉⡻⠐⢾⡿⣇⠀⠀⢀⣿⣒⣚⡛⠳⣝⢿⣿⣟⣇⠈⣇⠘⡇⠀ ⡟⠀⠀⣿⢰⡇⠀⠀⢸⣧⡞⠀⢸⠀⣳⢸⠀⢘⡆⠀⠀⠀⠀⡠⠿⢧⣠⠟⠀⠀⠃⠾⠷⠶⡟⠀⢀⡾⣧⣬⣍⣍⡛⠛⠒⠃⠘⣿⠀⢸⠀⡇⠀ ⣧⠀⠀⣿⡘⣧⠀⠀⠀⠉⠀⢠⡏⢰⡇⣾⢠⡟⠀⠀⢀⣴⠞⠁⠀⠘⢧⡀⠀⠒⡲⡂⠀⠠⠃⣠⠞⠛⢻⡿⣬⣍⣹⡝⠒⠚⣡⡟⠀⣼⠀⡇⠀ ⠸⣆⠀⠸⣽⠎⠳⢤⣀⡠⠖⠋⣠⠏⣾⢻⠋⢀⣠⡾⠿⠊⠀⠀⠀⠀⠀⠙⠶⠞⠛⠉⠳⣦⡘⢳⡀⠀⠀⠳⡄⠀⠉⠉⠙⣿⠟⠁⣰⠇⣸⠃⠀ ⠀⠙⢦⡀⠈⠳⠦⢤⣀⡤⠴⢛⣡⠞⠙⠚⠋⠛⠚⠙⠛⠒⠒⠒⠒⠒⠛⠛⠛⠛⠓⠒⠒⠚⠟⠀⢳⣄⠀⠀⠙⠷⣴⣖⣋⣁⡴⠞⢁⡼⠃⠀⠀ ⠀⠀⠀⠙⠲⠤⣄⣀⣠⡤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⣀⠀⠀⠀⠀⢀⣠⡶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠘⢉⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢀⡇⣇⡰⠲⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢰⣾⡦⣾⠁⠀⢸⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⠞⠁⠀⠀⠀⠘⡆⣀⣿⠀⠀⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡱⣶⡾⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⢰⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢸⡧⠏⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡴⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⢸⣿⣾⠀⠀⠀⠀⠀⠀⣜⣀⣾⠿⣷⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡿⠀⢠⣄⠸⢹⣷⠀⠀⢆⠀⠀⣏⡿⠉⠀⠈⢹⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠟⠀⣤⠀⣿⠃⠞⢹⣶⣰⣼⠀⠀⠉⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀ ⠀⠀⠀⣀⡾⠧⢴⣾⣿⢠⠏⠀⠀⠘⢹⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀ ⠐⠺⢿⣿⣧⣠⣴⣿⣥⣿⡄⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⣽⣿⡍⠙⠛⢻⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⣀⢰⣿⡀⠀ ⠀⠀⠀⣸⠟⣿⣰⠃⠀⠈⣿⢷⠀⣀⠀⠀⠀⠀⠐⣦⡀⢸⣧⠀⢸⣿⣼⡟⡇⠀ ⠀⠀⠀⠋⣼⣿⣿⢀⡄⠀⠈⠈⢧⣼⣦⡸⣄⠀⠀⣼⢷⡞⠙⢷⣾⣿⠹⣿⡁⠀ ⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠛⠌⠳⣿⢷⣤⡇⠈⠀⠀⠀⠙⢿⣆⠈⠻⡄ ⠀⠀⠀⠀⢹⢁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢧⡀⠀⠀⠀⠀⠀⢹⠙⣷⣧ ⠀⠀⠀⠀⠘⠸⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⠛
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⠀⠀⠀⠀⠀⠈⠁⠙⣧⣻⣧⡛⣜⢣⢏⡳⣍⢧⠫⡵⣩⠎⡝⡬⡍⢯⠹⡍⢯⡹⡹⣍⢯⡙⢯⣍⠻⣜⢣⡝⣎⢳⢭⣛⡼⢭⣏⢯⡽⢭⣏⡽⢭⢯⠽⣭⢯⡽⣭⢯⢽⣩⠯⡽⡭⢯⡽⣹⢯⡝⣯⠽⣭⠯⡽⣭⢯⡝⣯⡝⣯⡝⣯⢯⡝⣯⡝⣯⢟⣯⢿⣹⢯⢿⣹⢯⣟⣯⣛ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡹⣷⣪⡝⢮⡱⢎⣎⢳⡱⢥⡛⡼⣑⠞⣥⡛⣬⢣⣕⠳⣜⢢⡝⡲⣌⣗⢎⢳⣜⣮⣹⣚⠼⣎⠷⣎⢷⣚⡗⡮⣝⠾⣹⢞⣱⢮⡳⣝⢮⡳⣭⣳⢽⣙⣧⡝⣧⡻⣼⢣⣟⡼⣫⢷⡹⢮⡽⣖⣻⡼⣽⢣⡿⣹⡖⣯⡽⣾⣹⢾⣭⡟⣯⡽⡾⣽⡾⣭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⣿⣿⣣⠝⡮⣜⢣⡝⢦⡝⡲⣍⠞⡴⣙⢦⢫⡌⠷⣌⢧⡚⡵⣫⣿⣿⠟⠛⠛⠿⠿⣷⣾⡳⣜⢣⡟⣼⣱⢫⡞⣵⢫⡞⣧⢻⡜⣧⢻⡵⣫⢞⡵⣾⡹⣧⢻⣵⡻⣼⡝⣧⢯⣽⢳⡽⣝⣶⣛⣮⢟⣵⡳⣽⢳⣽⣳⢯⣟⣶⢻⣳⡽⣏⣿⣽⣳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣮⡕⣎⡱⢎⠳⡜⡵⣪⢝⡲⣙⢎⡳⣜⡳⡜⣦⠝⣼⣿⣯⡀⠠⠀⠀⠀⢠⡀⠘⢿⣎⢷⡸⣓⢮⡳⣹⢎⡷⣹⢎⡷⣹⢎⡷⣹⣣⢯⣟⢶⣻⣭⡟⣶⣛⣧⢿⡽⣞⣞⡯⣟⡽⣶⣛⣮⢟⣮⢷⣯⢟⡾⣝⣻⢾⣹⢯⣷⣫⣽⣞⡷⣽ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢤⠓⡮⡱⣍⠶⡱⢎⡵⣩⢎⡵⢪⠵⣙⢦⡛⡼⣿⣀⠙⠷⢶⣤⣀⠀⠙⠀⠈⣿⢪⢵⢫⢶⣹⡱⣎⢷⡹⣞⡼⣣⢟⡼⣣⢏⡟⣮⢻⡵⣛⡞⣷⢫⢾⡹⣟⢾⣣⢿⡽⡽⣶⣛⡾⢯⣞⡷⣞⣯⢿⡽⣏⡿⣽⣻⢶⣻⢶⣯⣟⣾ ⠀⠀⢀⣤⣶⣾⣿⣿⠓⠀⠀⠀⠀⠀⠀⠉⢹⣿⣥⢣⡕⡎⢞⣱⢋⠶⡱⠮⣜⢣⡛⡬⢞⡱⢣⠟⣿⣷⣤⣄⡈⠉⠁⠀⠀⠘⣿⣿⣎⡗⣫⢶⣙⢮⡳⣝⣎⢷⡹⣎⢷⡹⢮⡝⣮⢳⣝⣣⣟⣼⢫⡷⣻⠽⡾⣭⣟⡾⣽⢳⣯⣽⡻⣾⢽⣻⡼⣯⡽⣏⣿⣳⢯⡿⣽⣻⢾⣽⡾ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣜⡜⣡⢎⡣⢝⠲⡹⢤⢣⢇⡹⢎⡵⢋⡼⣘⠻⣿⡽⠟⠻⣶⣄⡀⠀⢸⣿⣷⣸⢓⡮⢎⡷⣹⣺⣼⣮⣷⡿⠿⠻⠗⠛⠛⠛⠻⢿⣿⣾⣯⣗⢯⡻⣵⣻⣼⣛⣾⣛⣶⡳⣿⣭⣟⡷⣻⣵⣻⡽⣾⡽⣯⣟⣷⣻⣟⡾⣿ ⠀⠀⣿⣿⣿⠁⠉⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣜⢢⠑⣎⠱⢣⠞⡰⢊⡴⢣⠜⣣⠝⣥⠛⡼⣷⣭⣒⣤⣿⣧⡀⢾⣿⣿⢻⣧⣿⣿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠙⠛⠿⣷⣿⣟⣧⣳⣛⣶⣻⡼⣷⣧⣻⣼⣻⣵⣿⣿⠿⠷⣿⣷⣟⣞⡿⣾⡽⣿ ⠀⠀⠘⣿⣿⣦⡄⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣼⢀⡛⠤⣋⠵⣉⠖⣡⡛⡴⣋⠶⣙⢖⣩⢛⡿⣯⣍⣹⣧⣀⠹⢿⡟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣟⣶⣏⣷⡻⣼⣷⡿⠟⠋⠀⠀⢀⠀⠈⠻⣿⣯⣿⣳⣟⣷ ⠀⠀⠀⠘⣿⣿⣇⠩⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠼⡱⢌⢖⡩⠞⣥⢛⡴⣩⠞⡱⢎⡖⣭⢒⡏⣿⣿⡿⣿⡦⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⠿⠋⠀⠀⠐⠒⠰⠿⠃⠀⠀⢹⣿⣾⣳⣟⣾ ⠀⠀⠀⠀⠈⠿⣿⣿⣤⣈⣡⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣿⣿⣧⣷⡜⢮⡱⣋⠶⣩⠖⣥⢫⡕⣫⠜⡥⣏⣾⡿⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠟⠁⠀⠀⠀⣤⠀⠈⠿⢶⡶⠆⢀⣿⣿⣿⣳⣟⣾ ⠀⠀⠀⠀⠀⠀⠛⠻⣿⡿⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠿⣿⣿⣿⣆⢳⣭⢚⡥⣛⢤⠳⡜⣥⢋⣷⣿⠏⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⣓⣂⣀⣀⣀⣠⣾⣿⣿⣻⣿⡾⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣏⢿⡏⡾⣰⢉⡎⣷⠹⣆⢏⣿⠇⡀⠀⡏⠀⢀⠀⠀⠀⠀⠰⢶⢶⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣸⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣿⣿⣏⡵⣙⠮⣜⣥⢛⣬⣿⠏⣳⢀⠌⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠙⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠊⢸⣿⣿⣿⣿⣻⣽⣳⣿⣿⣿⣟⣯⣿⣽⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣽⣿⣷⣽⡞⣴⣿⢌⣿⡟⣰⣧⣿⠀⠀⡀⣶⣴⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣹⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⡷⣿⣿⣿⣿⣟⣯⣿⣿⣻⣿⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣖⣿⣾⣿⢁⣴⣿⠇⠀⣠⣿⣿⠿⠛⠋⠉⠁⠈⠙⠿⣿⣿⣿⣿⣿⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠁⠀⠀⠀⢽⣿⣿⣿⣽⣾⢿⣾⢿⣻⣽⣿⣻⣷⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⣿⣿⣿⣿⠇⢸⣿⠏⡀⢤⣿⡥⢈⡄⠀⠀⠀⠀⢀⠀⠀⠈⠙⢿⣷⣽⣛⣹⡿⢷⠆⣀⣀⣀⣤⣠⣼⡟⣩⣭⣾⣷⣶⣶⣦⣄⣶⣀⢄⣻⣿⣿⡾⣽⣿⣻⣿⣿⣿⣽⣿⣳⣿⣿⣿ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣖⣿⡿⢀⠐⣂⠟⠲⣀⡆⠀⠀⠀⢈⡛⠓⠶⢤⣄⠀⠉⣿⡿⣿⣿⣾⡆⠉⠉⠉⢉⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡽⣿⣿⣽⣿⣟⣿⣿⣾⢿⣻⣾⢿⣯⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢹⣿⣿⣾⡿⡁⠆⡘⠆⠀⠁⠛⢷⣿⣶⣿⣿⣭⣤⣤⣀⣿⢿⣦⣘⠛⠿⠿⠟⠇⠀⠀⣙⢾⣿⣿⣿⠿⠛⠛⠉⠉⠁⠀⠁⡉⢛⣿⣿⣿⣿⣿⣿⣻⣯⣷⣿⣿⡿⣿⣿⡿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣽⣿⢡⡃⠄⢃⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣏⣉⣠⣄⣠⣤⣤⣀⣀⣀⠠⢤⢻⣿⣿⣿⣿⣽⣿⣻⣽⣯⣷⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⡣⠌⡀⠈⠄⠀⠀⣀⠀⠠⣌⡙⠛⠿⠾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠛⢿⣿⣿⣿⣦⣤⣭⣙⠛⣿⣷⣾⣿⣿⣿⣿⣻⣾⡿⣟⣿⣿⣿⡿⣿⣟⣿⣿ ⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣏⣷⠄⠀⠈⠄⠀⠀⠙⠛⠶⣮⣥⣦⣤⣤⡴⠶⠀⠀⢀⠴⣇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿ ⣄⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⣿⣿⡷⢁⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠈⠉⠁⠀⠀⢀⣠⡶⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⢀⣍⡛⠿⣿⣿⣿⠟⠋⠋⡐⣹⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣆⣠⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠙⠻⢶⣤⣤⣤⣀⣀⠀⡐⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠿⣶⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣴⡦⠉⠀⠠⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⢀⣠⣼⠟⠋⢿⣷⣶⣾⣿⣿⡟⠷⠆⣀⣀⠀⠀⢶⣀⣡⣀⠀⠀⠀⠀⠉⠉⠉⠛⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣭⣃⣤⡀⠈⠹⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡿⠋⢀⠳⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢀⣶⣿⠟⠁⠀⠀⠘⠻⠿⠿⣿⣿⣿⣿⣷⣤⣭⣴⣾⣿⣿⡿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣮⡻⣷⣄⡀⠛⠻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⡿⠁⡐⢬⠃⠀⠀⠀⠀⠀⣼⡟⠀⠀⣠⡿⠛⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠉⢻⠿⢿⡿⣿⢿⠿⠿⠃⠈⠹⣿⡆⠀⠀⠀⠀⠀⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣄⠛⢿⣿⣿⣿⣿⣮⡹⢿⣦⡀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢂⡔⢃⠠⠀⠀⠀⠀⠀⠉⠛⢷⡾⠋⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⠀⠀⠀⠀⣿⣀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣤⠙⢻⣿⣿⣿⣿⣷⣿⢿⣶⡀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⠇⡘⢌⠢⠄⠀⡀⠈⠀⠀⠀⠀⠀⠁⠤⠀⢀⡀⣀⣠⡄⢀⢀⣀⣀⣤⣀⣘⡛⢓⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⢸⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⣄⠈⠻⣿⣿⣿⣿⣿⣿⡿⣷⣄⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡜⣄⠣⣍⠂⠀⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣾⣿⣿⡿⣟⠻⣟⠻⠿⠿⣶⣶⣶⣶⣶⣦⣤⣄⡀⣀⠀⢀⡹⣿⡧⠀⢰⡄⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣶⡙⠛⣿⣿⣿⣿⣿⣯⣙⢿⣆⡀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠰⣾⣿⠤⣓⢬⡁⢂⠀⠰⠀⠀⣤⠀⠀⠀⢰⠟⠉⠉⠉⠉⠹⠛⠛⠛⠛⠛⠛⠷⠾⠶⠶⣖⣨⣍⣻⣻⣿⣿⣿⣿⣿⡟⢡⣿⠇⠀⢸⠂⡁⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠉⠻⣿⣿⣿⣿⣷⣯⣻⣦⣌⠹⢷⣦⡀⠀⠀⠀⠠⢀⣾⠇⠀⠀⣿⣿⢢⡑⢦⡱⠂⠀⢀⠀⠀⢸⣆⡀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠠⠄⠄⠶⠤⢦⣤⣤⣈⡉⠉⠙⡛⢫⣿⠿⡛⠏⣁⣾⠉⠀⠀⠄⡣⢌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠛⠿⣿⣿⣿⣿⣿⣿⣷⣼⣟⢿⡗⠀⠀⠀⢿⣿⠀⠀⠀⣿⣿⢧⡙⢦⠱⡉⠄⠂⠐⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠀⢈⠣⢄⠩⣉⠙⡙⢢⠐⡠⢀⠂⠥⠐⣼⠇⠀⠀⡀⣄⣿⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠘⠛⠟⠛⠋⠛⠛⠁⠀⢸⣿⠀⠀⠀⣾⡟⠀⠀⠀⣿⣏⠦⡙⢆⠫⡕⠠⢀⡘⢀⠒⣴⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈⠃⠈⠱⢄⠫⡔⣡⢃⡜⢨⠁⢂⣼⡟⠀⠀⢰⢧⣿⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠃⠀⠀⠀⣿⣿⣮⢷⠚⡱⢀⢣⠀⠐⠠⠖⣹⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠄⡉⢮⠡⢎⣤⡟⠁⠀⣀⣾⣷⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⣰⣿⠀⠀⡀⠀⣿⣿⣏⠞⣿⡠⢃⢦⣁⠂⠡⢌⣐⡛⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⢀⡄⢋⠻⠛⠁⠀⢐⣿⣿⠿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⣿⡿⠀⠀⠀⠀⣽⣿⣿⡜⡌⠿⣧⣆⠻⣧⠂⠌⠻⢿⣷⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠠⢄⢃⠠⢁⠏⠀⠀⢤⣿⣿⢏⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣇⣾⠈⠀⠀⠈⢹⣿⣿⠸⢰⠉⣿⣷⡀⠉⢰⠁⡎⣹⠿⣿⣆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⢀⠀⡆⠀⠆⠈⢰⡀⠀⣾⣿⢁⠆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣄⣿⣾⢹⣧⠀⠀⠀⠈⢻⣿⣇⢣⡙⡴⣙⢿⣦⡁⠐⠠⡙⢦⣹⠿⣄⠀⠠⢁⠀⠉⠂⠀⠀⠈⠀⠁⠀⠀⠀⠠⠘⣠⠉⠖⡈⠠⢰⣿⣿⠏⡸⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡏⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⣀⣠⣿⣿⣿⣿⣿⡆⡀⠀⠀⠀⠉⢿⣷⣍⠲⡥⢎⡽⣷⡉⠰⣀⠹⢿⣷⣎⣴⡁⢆⢂⠰⠠⣀⢂⢄⡀⠊⢀⠂⡍⢄⡃⠦⡉⢄⣀⣳⣿⡿⢏⢰⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⡟⠋⠉⠙⣿⣿⣿⣿⢹⡄⠀⠀⠀⠀⠻⣿⣗⠩⡖⡼⣹⣿⣥⣀⡐⢨⡙⣿⣿⣿⣦⣮⢖⡱⣆⢣⢎⡬⡱⢎⢶⣈⣦⢝⣢⣔⣮⣿⡿⠿⢆⢠⣿⣿⣿⡣⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠹⣦⣹⠉⠀⠱⡆⠀⠀⠀⠀⠘⢻⣷⣝⡲⢧⣿⣿⣿⣇⡆⡰⠠⠌⡙⠻⠿⣿⣷⣯⣿⣮⣳⣝⣞⣮⣽⣎⣷⣾⣿⡿⢏⠴⣉⣾⣿⣿⣿⣿⣍⢢⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠉⠀⠈⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣭⣞⠿⣿⣿⣿⣷⣦⣱⡈⢄⠠⠀⠈⠁⠉⠙⠛⠻⠟⡿⢻⠟⡿⣙⢦⣙⡎⣶⣿⣯⣿⣿⣿⣿⠌⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢨⡙⠛⠿⣷⣄⡀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣽⣿⣿⣿⣿⣿⣿⣦⣦⡐⣄⡀⢆⡐⠆⡰⢌⡰⣡⢚⣴⣯⣶⣽⣾⣿⣿⣿⣿⣿⣿⡟⠀⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⡈⠛⠶⢦⣀⡀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⠿⣿⣿⣿⣶⣿⣶⣾⣷⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⣉⣿⠁⠀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢦⣤⣍⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠻⠟⠿⠿⠿⠿⠿⣿⣿⠶⠟⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠸⣏⣀⠀⡀⠀⠀⢠⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢄⡀⠈⠉⠉⠉⠛⠛⠒⠶⠶⢦⣤⣄⣀⣀⣀⣀⣀⣀⣈⣀⣁⣀⣀⣀⣀⣀⣀⣈⣙⡙⠋⠋⠀⠐⠂⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⣀⠀⠀⠀⠒⠠⣄⣀⣈⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⢶⣄⣠⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣗⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣴⣦⣸⢸⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⢻⣿⣿⣾⠴⠌⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣧⣤⣤⣤⡦⣾⡛⣿⣅⣽⡆⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣯⡏⡿⠀⠀⣿⡇⠉⢿⣿⣇⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⡿⠛⠉⠀⠈⠓⠮⣿⣽⣿⠿⠃⠀⠀⢸⡟⠀⠈⣿⡿⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢰⡄⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣷⣒⢢⡄⠀⣀⠤⣴⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣶⣛⠷⢃⣞⣿⣿⣯⣿⣾⣿⠜⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠃⣿⡄⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⢶⡮⠥⠬⠽⠛⠁⠀⠉⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣰⡿⣿⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⣔⠙⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡏⠀⠀⠀⠀⣴⣿⡿⠁⠀⠀⠀⠀⣄⣰⣿⡄⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⣿⡿⢿⡁⠀⠀⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⣀⣴⣿⠋⠀⢀⣷⠀⠀⠀⠙⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠁⠀⠀⢠⣼⣭⣿⠿⠋⠀⢠⢸⡟⠀⢰⣴⠀⠹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⣼⣆⣄⡀⠀⠀⠀⠀⠀⠀⡀⢈⣤⣴⢶⣿⠟⠛⢁⣀⠀⠀⣾⠟⠀⠀⢈⣿⠀⠀⢳⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣤⣙⢮⣿⣷⣦⣀⠀⠀⠐⠶⣽⣟⠛⠋⠉⠉⠀⠀⣿⣏⠂⣸⡏⠀⠀⠀⢸⡟⠀⠀⠈⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠙⠛⠉⠉⠙⠉⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣼⡿⠉⢀⣿⡁⠀⠀⢀⡞⠁⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠃⠀⣾⠟⠁⠀⠀⣾⠇⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⣴⡿⠀⠀⠀⣾⠋⠀⠀⠀⣰⠞⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣇⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠏⠀⠀⢠⣿⠀⠀⠀⠸⠃⠀⠀⢀⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣿⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡿⠃⠀⠀⠀⣺⡟⠀⠀⠀⠀⠀⠀⢐⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⡟⠀⠀⠀⠀⣷⡄⠀⠀⠀⢀⠀⠀⠘⠛⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⣤⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⡇⠀⠀⠀⠀⢹⣿⡀⠀⠀⠘⣶⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣴⣷⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠉⣿⠀⠀⠀⠀⣾⠋⢿⣳⡀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⢹⠁⠀⠀⠀⠀ ⠀⠀⢀⣠⡴⠞⠉⠀⠀⠀⢠⠇⠀⠀⠀⣼⠇⠀⣀⣿⡿⠦⠀⠀⣿⠂⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣸⡞⠀⠀⠀⠀⠀ ⠀⢰⣿⡉⢠⡀⠀⢀⡠⠶⢻⠀⠀⠀⠀⣿⠛⠿⠛⠉⠁⠀⠀⠀⡇⠀⠀⠀⠀⢀⣼⡧⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀ ⠀⠈⠙⠓⠿⠒⠛⠁⠀⠀⢀⡇⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠟⠁⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⢀⣿⢧⣀⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡴⠻⠝⠛⢁⣽⠇⠀⠀⠀⣼⣡⡤⠤⣄⡀⠀⠀⠀⢀⣸⡏⠀⠀⠀⠀⢨⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⡿⠃⠀⢀⣴⠟⠁⠀⠀⡀⣿⠃⠀⠀⠀⠀⠈⠉⠉⠉⠁⣺⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡿⠁⢀⡴⠋⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⢛⣯⢀⣀⣴⣀⣠⡾⡟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠒⠉⢀⣠⣤⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣦⣤⣄⡀⠀⠀⠀⣴⣦⣾⣬⣵⡆⠀⢀⣤⣶⡿⣳⣵⣾⠿⠛⠁⠀⠀⠀⠀⠀⢰⣶ ⠀⠀⠀⠀⠀⣠⣾⣿⢚⡆⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡻⣿⣿⣿⣾⢿⣿⣭⢽⣿⣿⣿⣾⣽⡿⣷⣤⣪⣽⣿⣷⣿⣿⣿⠈⣻⣿⣷⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿ ⠀⠀⠀⠀⣰⣿⣷⣾⣽⣿⣶⠄⣀⣴⣶⢿⣿⣿⣿⣿⣿⣞⣿⣿⣻⣿⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣦⡉⠉⠛⢿⣿⠀⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿ ⠀⡄⠀⠀⣿⣿⣟⣿⣿⡵⣭⢗⢧⣼⣿⣿⣿⡼⣿⣿⣿⣿⣻⣿⣏⣿⣿⣿⣭⣷⣶⣿⣿⣿⣿⣶⣾⣿⣿⡿⣿⣿⣿⣷⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⢿ ⣼⣿⣦⣀⠟⠉⢴⣦⣬⣥⡄⢠⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⡿⣿⣿⣿⠟⠉⠛⠉⠉⠉⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⢿⣻⣿⣿⣿ ⢟⣽⣫⡜⣽⣤⣜⡛⠛⢉⣴⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣧⡿⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣟⣿⣷⡿⣿⣿⣿⣦⡀⠀⠀⣠⣴⡾⢿⣿⡿⣿⣯⣷⣿⣿⣿⣿⣿ ⢸⣿⣿⣯⣾⠒⠓⢈⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡈⠻⣿⣿⣿⣿⣽⣿⣿⣿⣿⣦⡈⠉⠑⠚⠋⠁⢪⣿⣛⢿⣿⣿⣿⠿⠛ ⣼⠟⠉⠀⠉⢀⣴⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠉⠘⠛⠛⠉⠀⠀⠀ ⠋⠀⠀⢀⣴⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⡀⢀⣤⣒⡒⠀⢿⣿⣿⡿⣯⣿⣯⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣨⣿⣿⣿⣿⡿⣅⣸⣿⣿⢻⣿⣿⣿⣯⣟⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡼⠁⢴⣭⣗⣻⣟⠛⢳⠖⠉⡿⠛⢿⣿⣿⣟⢿⣿⣿⣾⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣴⣿⡿⣾⣿⢿⣤⡷⢻⣿⡿⣿⣿⣿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡁⠚⡿⢱⢛⣿⣮⡧⠖⠂⠀⢣⣶⣄⢻⣿⣿⣯⣻⣿⣿⣿⣿⣷⣦⡀⠀⠉⠉⠉⠉⠉⠉⠉ ⣸⣿⣿⣱⣿⢯⣿⡷⢁⣼⣿⣷⣿⣿⡏⣿⣏⢀⠐⠒⠲⠶⠶⠶⠶⣶⣶⣒⠛⠀⠀⠀⠀⠁⠚⠉⠉⠀⠀⣶⣿⢿⣿⣿⡘⢸⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡟⣿⡿⡿⡟⠁⣼⢿⣿⣿⣿⣿⢸⣿⣿⡀⠀⠀⠀⠀⢴⣮⢾⣿⡿⢿⠤⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣾⣷⣾⣿⡅⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣀ ⣿⣿⣧⣿⠇⠈⠁⣼⣿⣿⢿⣿⣝⣿⣿⣿⣿⣷⡄⢀⣀⣺⠏⣟⣿⣦⣼⠟⠀⠀⠀⠀⠀⢀⠀⠉⠉⠛⠋⣿⣿⣽⣿⣧⣼⡿⢿⣟⢻⣿⢿⣿⣿⣿⣷⣮⣭⣭⣭⣷⣶⣶⣿⣿⣿ ⣿⣿⢻⣿⠀⢀⣼⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣄⣉⣿⣤⣘⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢾⣿⣿⠁⣟⢛⠡⣤⡙⣧⣙⣷⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢸⣿⣀⣾⣿⣿⣿⣳⣿⣿⣿⣿⣿⡏⣿⢿⣿⡿⢧⡀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣉⠄⡴⠃⢾⣿⠿⢠⣿⣿⣧⣍⣧⣾⢷⢿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⡁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡽⡞⣿⡅⠲⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣰⢯⣵⣾⠄⠀⠀⠏⢀⣾⣝⣻⠋⢉⡉⠻⣏⣷⢿⣿⣮⣿⣷⣶⣿⣾⣿⣿⣿⣿⣾⣿ ⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢁⢿⣿⣿⣿⣿⣻⡞⣷⣆⠿⢾⡏⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠈⣿⣷⡘⣿⡷⢣⡛⣻⣴⡿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣟⣻⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡍⠘⣿⣿⣿⣿⣧⢻⣹⣿⣷⣾⣷⣤⡬⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠈⢻⣿⣶⣾⣻⣿⣿⣿⣿⣽⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣽⣿⣿⣿⡿⠃⣾⡀⠀⣿⣿⣿⣿⣿⡟⣯⢿⣿⡏⣯⣿⣧⣿⣸⣿⣯⣿⣷⡒⠒⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣽⣿⣿⣿⣿⣷⣿⡿⣿⣿⣿⣾⡿⠿⢿⣿ ⣿⣿⣯⣿⣿⣿⣿⠟⢀⣾⣿⡷⠀⣟⣿⣿⣿⣿⣿⢻⣾⣿⣿⣿⡀⢀⢹⣿⡟⣉⡈⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠀⠀⠀⠀⠀⠈ ⣿⢿⣿⣿⣿⣿⢋⣤⡿⠟⠁⠀⢀⣿⣿⣿⣿⣿⣿⡾⣷⣿⣿⣇⣿⣁⣼⡟⣧⡻⠷⢂⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣷⡦⣄⡀⠀⠀⠀⠀ ⣟⣿⣿⣿⢿⡵⠞⠉⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⣯⣉⣿⣿⢿⣷⣿⠛⣻⣿⣿⡇⠀⢀⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⣍⣓⣦⣀⣀ ⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⣿⣿⣿⣿⣿⢳⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢯⣹⣿ ⣿⡿⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢸⡿⠟⠛⠉⠉⠉⠙⣯⠻⣿⣿⣿⣯⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻ ⣿⢻⣿⣧⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⣿⣿⣿⣿⡿⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⡀⣠⣾⣿⣿⣿⣿⡿⣾⣿⣿⡿⢋⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⣴⣾⣿⣿⣷⣦⣄⡒⠒⠲⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠟⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⣿⢿⣿⣿⣿⣿⣿⣿⣏⣽⡿⣿⣦⣄⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣾⣿⣿⣿⣯⢿⣿⣿⣿⣿⠟⠋⠁⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣹⣿⣷⣄⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⣠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣶⢛⣿⣿⣿⣿⣿⣿⣿⣿⣟⠷⠅⣮⣷⣦⣄⡀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣠⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣃⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⠋⠻⣄⡉⠑⠶⢼⣄⠀⠀⠀⠀⠀⠀⠀ ⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠈⢻⡿⢷⣮⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣿⣿⣎⠛⠦⢄⣈⠙⠲⠤⣀⣴⠂⠤ ⣿⣿⣿⠋⠙⠛⠻⠟⠛⠛⠛⠛⠿⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⡀⠈⣧⣿⣛⡿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢄⣀⣨⠭⠒⠛⠋⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠞⠉⠀⠀⠀⠀⠉⠳⡶⠚⠛⠉⠉⠉⠉⠉⠉⠙⠛⠶⠤⣄⣀⡤⠴⠶⠶⠶⠶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢀⡠⠶⠒⠒⠲⢦⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢀⣀⣀⣤⣤⣤⣀⡀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣠⠊⠀⠀⣀⡀⠀⠈⣇⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣭⡀⠀⠀⠀⠀⠀⠉⢣⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢰⠃⠀⠀⠀⣹⠏⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⠛⠂⠀⠀⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠘⣇⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⡤⠖⠒⠒⠒⠒⠺⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡟⠇⠀⠀⢀⣀⣀⣀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⣿⣩⣿⣿⡆⠀⠀⠀⢿⠄⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢠⣄⠈⢭⡉⠃⣤⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠸⣧⡀⣀⣤⣈⡛⢒⣾⣿⡁⠀⣀⡾⠁⠀⠀⠀⠀⣠⠾⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠙⠶⢤⣀⣀⡀⣰⠞⣉⢭⡿⠛⠉⠁⠀⠀⠉⠻⣿⣫⣽⣿⡏⠀⢀⣀⡤⠖⠋⠁⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⠉⢹⡏⢻⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣼⠇⠀⠀⠀⣠⡀⠀⠀⣠⣶⡆⠀⠀⢻⣦⡤⢤⡄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣻⡟⢹⣿⣟⣛⣧⠀⠀⢨⣗⣀⡰⣛⣧⡾⠃⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣧⠀⠀⠀⠀⢿⠀⣼⣿⣽⣷⠼⠗⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠙⢷⡀⠀⠀⠈⠓⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣴⣋⣉⣙⡓⢒⡞⢑⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⢧⣿⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⣀⣠⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣀⡀⠀⠀⢀⢀⣀⣴⢿⣯⠉⠉⣉⣤⠼⠗⠒⠛⠒⠲⠤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣿⠉⡿⠚⠿⠋⢉⡵⢶⣽⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⢦⣄⡀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⣼⣿⣿⡆⠀⠀⣾⠃⡼⣿⠃⠀⠀⠀⠀⠀⣠⣤⢤⣄⡀⠀⠀⢹⡆ ⠀⠀⠀⣀⡤⠴⠒⠒⠳⠤⢤⣀⠉⠛⠛⠒⠒⠒⠚⠛⠲⠤⢤⣀⣀⣀⣀⣴⣿⡾⠷⣿⠀⠙⢦⣀⣙⣿⡽⠃⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⢿⠀⠀⠈⡇ ⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣁⣀⡀⢘⡇⠀⠀⠈⠉⠉⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⡇ ⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⣾⠁⢠⡇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⡾⠀⢀⡾⠀ ⣿⠀⠀⢠⡞⠛⠉⠉⠉⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠻⢶⣻⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡾⠁⠀ ⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡶⠖⠋⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠿⣀⣀⣀⣀⡤⠞⠁⠀⣴⠏⠀⠀⠀ ⢻⣄⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⣀⡴⠚⠁⠀⠀⠀⠀ ⠀⠙⣦⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⣀⣀⣠⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⢄⡀⠀⠉⠑⠶⠤⣄⣠⠤⠞⠁⠀⠀⠀⠀⣀⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⡇⠀⠀⠀⠀⣼⠃⢠⡟⣰⣿⠟⣿⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡙⢷⡀⠈⠉⠙⣧⡘⣧⠈⣿⡎⣿⣿⣿⣿⣿⣿⡼⣿⣧⣿⣽⣿⣿⣧⠉⢳⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⡏⢀⡿⣰⢿⡏⡼⠃⠀⠘⠀⠀⠀⠀⠀⣀⣀⣠⠤⠀⠈⠻⢮⣷⡀⠀⠀⠘⣧⢹⡇⢹⣷⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣄⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⠁⢸⡇⡏⠸⣼⠃⠀⠀⠀⠀⣀⣤⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠸⡎⣷⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣿⢻⠃⣧⣿⡇⠀⠀⠀⡾⣫⡾⠋⠀⠀⠀⢀⣠⡴⣶⡆⠀⠀⠾⣇⠀⠀⠀⠻⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣧⣿⡿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢰⠀⠀⠀⢠⣿⠈⠀⣾⣿⢷⠀⣠⣾⠟⠉⠀⠀⣠⡴⠚⠉⣠⣴⣿⠀⠀⠀⠀⢿⡆⣰⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠿⢹⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⡆⠀⠀⢸⡉⠀⢀⣿⣷⡾⡾⠿⠟⠛⠀⢀⡾⠋⢀⣠⣾⠟⠁⡿⡆⠀⠀⠀⢸⣇⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⠇⠀⠘⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡇⠀⠀⠸⣧⠀⢸⣿⣿⢿⣷⡀⠀⠀⠀⠜⠇⢠⣿⠟⠁⠀⢸⠁⣇⠀⠀⠀⢸⣿⣿⡇⡄⠀⣿⠿⢿⣿⡿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣶⣶⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣧⠀⢠⠀⣿⡆⢸⠋⣿⠀⣷⠷⣄⠀⠀⠀⠸⠿⢿⣷⡀⢀⡞⢀⡿⠀⠀⠀⠀⣿⣿⣹⠃⣸⡟⢀⣿⡟⣻⣿⣿⢁⣿⣿⣿⣿⠏⠈⢿⣿⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢻⣆⠘⡆⢹⡧⣼⠀⠟⠀⢹⣧⣬⢶⣄⠀⠀⠀⠀⢻⣣⠞⠀⠘⠃⠀⠀⠀⢰⣿⣿⠏⠰⠟⠁⣾⠟⢠⣿⣿⠇⣸⡿⣿⣿⠏⠀⣀⣰⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠸⢿⡀⢻⡌⣿⣿⠀⠁⠀⠈⢻⣿⡀⣬⡗⢦⡀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⣠⡿⣿⠈⠸⣹⡟⢠⣿⢻⡿⠁⠀⠀⣿⢻⣿⣿⣷⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢻⡈⢷⡜⣿⠀⠀⠀⠀⠀⡏⢹⣟⣁⡀⠉⢢⡀⠓⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⣀⡴⠏⢰⡏⠀⣰⡟⢀⣿⢣⡟⠁⠀⠀⠸⣿⢸⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢳⡌⢻⣿⣇⠀⠀⠀⢰⠁⣸⠀⠈⠉⠙⠲⣽⣄⠀⠀⠀⠀⢀⣾⢟⣡⡴⠞⠋⠀⠄⣼⠀⣴⠟⢀⣞⣡⡟⠀⠀⠀⠀⠀⣻⠀⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠙⢦⡻⣿⣆⠀⢠⡏⠀⡇⠀⠀⢦⠀⠀⠀⠉⠀⠀⠀⠐⠛⠛⠉⠁⠀⠀⠀⠀⢰⣿⠰⠏⢀⡾⢹⡟⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⠀⠀⠘⣿⡿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣷⡞⠀⢠⠇⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢀⣾⢡⣟⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⣿⣿⣤⣶⣿⡿⢡⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠁⠀⢸⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢸⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠸⢦⣀⣠⡼⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⣿⡇⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⣀⠀⠈⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣿⡇⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⣀⣤⣤⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠶⣿⠟⢉⡵⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠿⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⢀⡤⠊⠁⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣎⠤⠒⡒⢁⣐⡒⠂⠵⣄⠀⠈⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠊⡕⡪⠐⢉⠭⠋⠁⠀⠀⠉⠒⢄⠑⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠒⠉⣠⠎⠮⡶⠛⣭⣄⣀⣀⣀⡀⠀⠀⠀⢣⠘⡀⠀⠀⠀⠀⠀⠀ ⠀⡠⠔⠋⢀⡼⠊⢹⢸⡴⠛⠀⠀⠀⡠⠒⠐⠲⢄⠀⠀⠀⡆⣧⠀⠀⠀⠀⠀⠀ ⠈⢀⡤⠚⠁⠀⠀⢸⢉⠗⠒⢄⠀⠀⢇⠰⣹⣷⢸⠀⠀⡡⢻⡫⢂⠀⠀⠀⠀⠀ ⠖⠉⠀⠀⠀⠀⠀⠀⢿⡀⣿⣿⠀⠀⠀⠒⠘⠒⠁⠀⠀⠀⣻⡽⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⡖⠸⣀⠶⠀⠀⠀⠀⠀⠀⢀⠠⠕⠒⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢡⠀⠀⠀⠀⠀⠀⡠⠔⠈⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡣⡀⠚⠛⣫⠪⢤⠰⠖⠠⠤⣀⣀⣀⣀⢂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡰⠐⣩⠔⠉⠀⠀⠀⠀⠀⠀⠈⠒⢄⠈⠙⠦⡀ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠂⠁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠐⠒⠒⠀⢒⡨⢔⠞⠁⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣦⡤⠴⠶⠟⠛⠛⠛⠿⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣿⣿⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣆⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠙⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⢰⡏⠙⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀ ⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣦⣄⡀⠀⠘⢿⣿⡿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢻⣹⣿⣿⣿⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠻⣿⣿⣿⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⣀⣀⣴⣿⣧⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠟⠋⠈⢿⣷⣤⣀⣀⣠⡶⠃⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣏⠀⠀⠀⠀⠀⠉⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⣀⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣤⡀⣾⣿⣿⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⡇⠘⠛⠁⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣉⣤⣾⣿⣿⡆⠉⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⡀⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⢰⣿⣿⠇⣠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠛⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠛⡋⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣴⣿⣿⣷⠀⢠⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⣀⡀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠛⠞⠛⠻⠟⠛⠛⠟⠻⠛⠐⠛⠛⠛⠃⠀⠘⠾⠳⠆⠊⠙⠚⠐⠈⠋⠀⠓⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡏⢿⣿⣿⠙⠿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿ ⣸⣿⣿⣿⣿⠘⣇⠹⣿⣿⡿⡧⠀⢻⣿⠀⠀⠈⠻⢧⠙⢿⣿⣿⣿⣿⣿⡟⡀⠀ ⣿⢿⣿⣿⡇⠑⢌⠁⠘⢿⠇⠁⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠑⠙⣿⣿⣿⠁⠈⠂ ⠃⢸⣿⣿⡍⠐⠄⡑⠀⠈⠠⠐⠑⠅⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⠈⢿⣿⠀⠀⠀ ⠀⢸⠏⢿⣏⠍⡐⠘⠢⢤⢉⠮⠆⠀⠀⢀⡤⢞⣷⠄⠅⣤⠀⠀⠀⠀⠇⠈⠀⠁ ⠰⣶⣷⣿⡟⡄⢆⢻⣶⠶⡀⠀⠁⠴⡞⣕⣵⡷⠽⠻⠕⠃⠀⠀⠀⠀⠀⢀⡠⢰ ⢀⣿⣿⡟⠁⠐⡤⡑⠒⢒⢿⡆⠀⢈⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⣡⣿ ⢨⣿⣿⠃⠀⠀⠘⡀⠉⡡⠊⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⣿ ⢿⣿⣿⠀⠀⠀⠀⠘⠍⢀⠌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿ ⠈⠁⠀⠉⠂⠀⠀⠀⡜⢇⢰⠡⢄⣠⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⠀⠀⠀⢡⡼⡣⠀⡆⠬⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢈⣀⠀⠀⢸⠁⠁⠑⢇⠀⠚⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠄⠀⠀⠊⠀⠀⠀⠁⠀⠀⠸⣷⢜⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡄⠀⢿⠀⠘⣁⣢⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣠⣶⠚⠛⠿⠷⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⢠⡄⠀⠀⠀⠀⠀⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠘⣷⣴⠏⠀⠀⣠⡄⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠺⣇⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠘⣻⣻⡆⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⢰⡟⢷⡄⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠶⢤⡀ ⠀⠀⠀⣾⣇⠀⠻⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣴⣿ ⠀⠀⢸⡟⠻⣆⠀⠈⠳⢄⡀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⢤⣬⡿⠁ ⠀⢀⣿⠃⠀⠹⣆⠀⠀⠀⠙⠓⠿⢧⡀⠀⢠⡴⣶⣶⣒⣋⣀⣀⣤⣶⣶⠟⠁⠀ ⠀⣼⡏⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⠵⣶⠒⠚⠻⠿⠋⠁⠀⠀⠀⠀ ⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠈⠿⠂⠀⠀⠈⠀⠀⠀⠀⠈⠀⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠈⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠑⡠⢰⠀⠀⠉⠭⢁⡠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣯⣯⣿⣷⠀⣠⠃⠏⡄⠀⢢⡀⠉⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠛⠛⠁⠀⢄⠀⢡⠀⢀⠁⠸⡋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⢄⠻⢿⠇⠀⠑⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⣴⣨⣵⣮⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⣿⣿⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣡⣾⣦⣽⣛⡿⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣸⣿⡿⣿⣿⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⡄⣼⠊⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠬⣼⠃⣰⣿⡟⠁⠀⠀⡠⠂⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⢓⢘⠉⢳⣿⠏⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠦⡀⠀⠀⠀⠀⠀⢀⠘⢿⣿⣮⡤⡜⠋⣠⣾⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡄⠀⠀⠁⠀⠀⠐⢌⠻⡿⣿⣽⣿⣿⡿⠁⠈⠑⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⡟⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠫⠸⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⣆⡀⣶⠿⠷⢶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠙⠦⠓⢀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣴⡶⠿⠿⠿⠿⠿⠿⠿⣿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⣴⠟⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀ ⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀ ⢰⡟⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀ ⣼⠃⠀⠀⠀⠀⠀⠀⠀⠺⠿⠇⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠂ ⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠛⠛⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀ ⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀ ⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀ ⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⣶⡶⠶⠶⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢸⡇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣾⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡀⢀⣿⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠏⠁⠀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⣠⣾⡿⠋⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⠛⠀⠀⣠⣾⡿⠋⠀⢀⣴⣿⠟⠁⠀⢀⣤⡄⠀⠀⠀ ⠀⣠⣾⣿⣿⣿⣷⣤⣾⡿⠋⠀⢀⣴⣿⠟⠁⠀⢀⣴⣿⠟⠁⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣴⣿⠟⠁⠀⢀⣴⣿⠟⠁⠀⣠⣾⡿⠂ ⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⢀⣴⣿⠟⠁⠀⣠⣾⡿⠋⠀⠀ ⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⠟⠁⠀⣠⣾⡿⠋⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣷⣴⣿⣿⠟⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠛⠋⠁⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠴⠶⠶⠶⠾⠷⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠒⠒⠒⠶⠒⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⣟⣹⠛⠓⠲⠀⠀⠠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⠉⠋⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠀⠀⣿⡟⢀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣠⡞⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀ ⠀⠀⣾⡟⢃⡞⠀⠀⠀⠀⠐⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀ ⠀⢠⣿⡅⣿⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄ ⠀⣼⢹⠇⢿⣷⣦⠤⠤⠤⣀⠀⡇⠀⢀⡀⣀⣠⣤⣤⣤⣤⣶⣶⣶⡞⠛⠋⠁⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⢻⣿⣆⣈⣻⣿⣄⣸⡇⣾⣿⣏⠉⠉⣿⣿⣿⣿⣿⡿⢋⣍⡉⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧ ⠀⢸⣿⣿⡇⠘⢿⣿⣯⣿⣿⡏⠣⡀⣸⣿⣿⣿⣿⢋⠀⠸⣯⠇⣼⢀⣤⡶⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀ ⠀⠐⣿⣿⣿⣦⡀⠉⠙⢿⣿⣇⠀⠀⠉⣿⣤⣍⡟⣿⣷⣶⠶⢶⣿⠿⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀ ⠀⠀⠘⣿⣿⣿⣿⣆⢠⣾⣿⣿⠀⠀⢰⠇⢸⡿⡿⠶⣄⡈⠉⠉⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣾⣯⡤⣿⠀⢠⡿⠞⡛⠉⠉⠳⣄⠙⣆⠀⠀⠀⠀⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀ ⠀⠀⠀⠀⠻⣿⢻⣹⣿⡻⡀⠸⢷⣿⡀⠀⠉⢳⡀⠀⠘⡆⠘⡆⢠⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⢻⡄⠀⠻⡇⠀⠀⠀⣇⠀⠀⢳⠀⠙⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣄⠙⣆⠀⢹⠀⠀⠀⠘⣆⡀⠈⡇⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣾⠀⣾⠃⠀⠀⠀⠘⠻⢦⣁⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⣭⣄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣀⡴⠖⠋⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠶⠦⠤⠤⠤⠤⠤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠨⣿⠄⠀⠀⠀⠀ ⢀⣀⣀⠀⠀⢀⣀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀ ⢸⣿⣿⣆⠀⢸⣿⠀⢀⣾⡿⠛⠛⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠸⣿⣆⢸⣿⠀⢸⣿⠁⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠹⣿⣾⣿⠀⢸⣿⡄⠀⠀⢀⣿⡏⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠸⣿⣿⠀⠀⠻⢿⣶⣶⡿⠟⠁⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠋⠉⠉⢀⡴⠉⠉⣩⡶⠋⠀⠀⢀⠀⢻⡏⠁⢰⡄⠉⠀⠀⠉⠉⠙⠛⢤⣌⣻⣿ ⠀⠀⣠⣾⣱⣇⣸⠯⠋⠀⢀⣴⠿⣿⡬⣿⣀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡈⣿⣿⣿ ⡄⢔⣿⣿⣿⣷⢏⠂⠠⡲⣏⡻⠴⢛⣟⣿⡆⣼⡇⠀⠀⠀⠀⠀⢰⡸⣿⣎⢿⣿ ⡯⣿⣿⣿⢿⠏⠂⠀⣼⣹⢑⡪⢽⣴⠗⠀⣿⣿⣇⣠⠄⠀⠀⠀⢸⣧⣿⣿⣾⣿ ⣷⣿⡿⠁⠃⠀⠀⠀⠈⢁⡼⢯⣽⣋⠀⠀⢸⣿⣧⡯⠰⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠡⠒⠉⠈⠙⠛⠉⠙⣿⣿⢇⡄⠀⠀⠀⣸⣿⣿⣿⣿⣿ ⣿⠁⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⢣⣿⣾⠃⠀⢠⡄⡟⣿⣿⣿⣿⣿ ⠹⠀⠀⠀⠕⡒⠂⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⢻⣿⣟⡀⢰⣻⣇⡇⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠊⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡼⣿⣳⣏⣿⣸⣹⢸⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠄⣛⠻⠿⠿⠿⠿⠿⠿⠟⠻⠁⠀⢡⣿⣿⣿⣿⠇⠞⣸⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡜⢱⣿⡿⡟⡘⢠⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠧⠋⣠⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣥⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠈⠙⠲⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⢀⠀⠀⣠⠊⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣤⠎⠀⡀⠀⡔⠁⠀⢰⠁⠀⠀⢀⢀⠏⠀⠀⠀⢐⢹⡀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡜⠁⡜⠀⠀⢠⠃⠀⠀⠀⡜⠸⠀⠀⠀⠀⡸⢸⣇⠀⠀⠀⠀⠀⠀⠈⡄⢣⠀⠀⠀⢀⠀⠘⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⡸⠁⣼⠃⠀⢀⡎⠀⠀⠀⢀⠃⡇⠀⠀⠀⠀⡇⡇⢸⢠⠀⢸⠀⠀⠀⠀⠘⡄⢆⠀⠀⠘⡄⠀⠀⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⠃⡜⡏⠀⢀⣾⢁⠔⠀⠀⡼⠀⠁⠀⠀⠀⢀⡿⡁⢀⡆⡆⠸⡄⠀⠀⠀⠀⢱⠈⣆⠀⠀⢧⠀⠀⠈⣆⣀ ⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⡎⢰⡹⠀⣀⡼⡟⠁⠀⠀⠀⡇⢐⠀⠀⠑⢄⣸⠳⠁⠘⣇⡇⠀⡇⠀⠀⢀⠀⠀⠆⠸⣄⠀⢸⡄⠀⠀⠈⠁ ⢐⠛⠛⠀⠈⢨⠃⠀⠀⡸⠃⡞⠋⠉⢠⠟⠃⠀⠀⠀⠀⡇⢸⠀⠀⢠⠀⡟⠲⢄⡀⠃⢰⠀⣧⣴⡆⣸⠀⢠⠀⠀⢻⡆⠀⣧⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⢸⠀⠀⠀⣧⣄⣀⣀⣤⣾⣶⣶⡶⠒⠒⠀⢧⣈⠀⢀⠇⡸⠁⠀⠀⠈⠙⠟⠒⠃⠀⠀⢼⠀⠘⡀⠀⠸⡗⠀⢹⡄⠀⠀⢀ ⠀⠀⠀⠀⠀⣼⠀⢀⢸⣿⣀⣼⡿⠿⠿⣿⣿⣿⠀⠀⠀⠀⠁⠉⠻⢿⣭⣰⣶⣤⣄⠀⠧⣄⢸⠀⠀⢘⡆⠀⢣⠀⠀⣿⠀⠘⡇⠀⠀⠈ ⠀⠀⠀⠀⠀⡇⠀⣿⡟⣿⡽⣿⠀⢰⠺⣿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⣿⣿⣿⣿⡂⠈⢻⠀⠀⢸⣧⠀⠘⡆⠀⠛⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⢰⠇⢸⣿⢠⣿⠀⠛⡀⠘⣆⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⣿⠻⢿⠛⢿⣆⢸⠀⢀⣿⠟⡆⠀⣽⡀⠀⠀⠀⡃⠀⠀⠀ ⠀⠀⠀⠀⡸⢀⣿⣇⠸⣿⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣀⣠⠎⠀⣸⣿⣿⣄⣈⣿⡧⢷⠀⠘⣷⡄⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⢠⣇⡞⣼⢹⡀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠒⠉⢩⡧⠀⢹⣿⡷⢏⢳⡀⠈⢷⣀⠀⡇⠀⠀⠀ ⠀⠀⢀⣾⠟⢰⡟⡾⣿⣶⠻⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⡸⢸⠀⣸⡠⣷⡀⠈⢿⡇⣇⠀⠀⠀ ⠀⣠⠞⠁⢠⡿⣿⣿⣻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢁⡤⢀⠇⢸⠞⠋⣡⣾⠹⣦⡀⠹⢽⡀⡄⠀ ⠒⢁⣠⠞⢹⣿⡏⢽⡿⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣡⠞⠁⡜⠀⣾⣴⠚⣿⣿⣇⣿⣿⣷⣶⣷⣦⡀ ⠡⠀⠁⣠⣿⣿⡇⢸⣶⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣌⠉⠐⡄⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⣰⠇⢠⡿⢹⠀⣿⡀⠻⣿⣿⡙⡿⢷⣼⡀ ⠤⠴⠊⣡⠋⣿⢳⠘⣄⣾⣿⡿⣿⣿⣷⣤⡀⠀⠀⠀⠉⠉⠁⠀⠀⢀⣠⣶⣿⠟⢻⡟⠀⣠⡿⠀⣼⣷⣼⠀⢹⣷⣄⢘⠻⢿⣿⣄⠫⠋ ⣀⣠⠖⣡⠞⣿⣈⣆⠹⣭⣥⡴⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⡤⠴⢟⣻⡟⠋⠀⠀⡸⠁⣰⣿⠇⢰⣿⣹⠿⣧⠀⢇⠻⣿⣶⢤⣀⣈⠳⡄ ⠉⠉⢙⡿⠛⢿⣤⣬⣷⠬⠿⠿⢻⣿⣿⣿⣿⡟⠀⣺⡏⠓⠒⠊⣩⠊⠁⠀⢀⡼⣡⠞⢻⡏⣠⣿⣿⣿⣿⣿⣷⠈⢗⢻⣿⣧⣹⠉⠓⠺ ⠀⠀⣸⡅⠀⠀⣿⣟⣁⣀⠀⢀⣾⣿⣿⡟⢹⠁⠀⡏⠣⡀⠀⡴⠻⢤⣤⣴⢿⡿⠁⠀⣼⣴⣿⣿⣿⣿⣿⣟⣹⢯⡺⣷⡭⠛⠿⣧⡀⠀ ⠀⠀⣿⣿⣄⣾⣿⠉⠉⣿⠉⣹⡿⠋⡿⢀⡇⠀⢀⣧⡤⠤⠾⣷⠚⠉⣀⡴⢋⣠⣴⣿⣿⣿⡿⠟⠛⠉⣿⡿⠋⠉⡇⠀⠉⠑⠒⠨⠙⠢ ⠀⠀⣿⣿⣿⣿⠟⠀⠀⣿⣤⣿⠇⠠⠃⡸⢀⡴⢋⣿⢳⡀⠀⠈⠉⠉⠀⣰⣻⣿⣿⣿⠟⠉⠀⠀⠀⣸⡟⠁⣠⣼⡽⠤⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣞⣉⣭⠤⠶⠶⠶⠶⠶⠤⣤⣉⣱⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣏⣸⠁⠀⢀⠤⠤⠤⡄⠀⣀⣀⣈⢷⡘⢦⣀⡀⠀⠀⠀ ⣠⣶⣽⣶⣿⣷⣗⡄⠀⣷⣿⡿⣿⡾⡀⣇⣿⣯⡆⠙⢲⢈⣷⣢⣀⠀ ⢯⢿⣿⣽⣿⣽⣿⢾⡸⣿⣽⠓⢫⣼⢣⢸⢿⣿⢡⣪⣿⢸⣿⣿⣿⠇ ⠈⢎⢿⣷⠿⣿⣿⢏⣿⣿⣷⣶⡾⣿⣏⡜⣼⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⠀⠘⣞⣿⡾⣏⠀⣜⣿⣛⣳⠋⢻⣛⣿⣰⢏⣿⠟⢹⣿⣿⣿⠏⠀⠀ ⠀⠀⠘⠶⣶⣿⣄⣉⣉⣉⣁⣀⣀⣉⣉⣉⣈⡉⣠⣿⣷⠷⠃⠀⠀⠀ ⠀⠀⠀⢸⠃⠀⣬⣭⢹⣿⠰⣶⠦⣶⡶⣿⣯⢩⡅⠀⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠈⡗⠀⠹⢉⣛⣛⣦⣿⣤⣿⣿⣛⣛⡸⠿⠀⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣤⡤⠟⢧⡙⠦⣄⠀⣀⡴⠛⡩⠻⢤⣤⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⣽⣡⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⣆⠤⠤⠤⣄⣀⠤⣖⠞⢋⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⡾⢗⡪⠯⣭⣹⣨⡁⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢀⠀⠀⡴⠚⢡⡞⠁⠀⠀⡠⢖⢟⠉⠀⠀⢀⡀⠀⠀⠈⢑⣄⢀⠀⠀⠀⠀⠀ ⠐⠄⠑⡀⣳⣴⠏⠀⠀⡠⠊⠀⠂⢸⠠⡀⠢⡀⡈⠲⣄⡠⡀⠹⣟⢒⡀⠀⠀⠀ ⠉⣚⠠⣸⣽⢍⡀⢀⠔⡠⠂⡠⢣⠇⢰⡹⠀⠸⢖⠀⠈⢷⣹⡌⣺⡷⠖⠀⠀⠀ ⠤⣸⢧⡼⢛⠢⣗⠵⠊⢀⣠⣿⢿⣜⣸⢵⠷⡑⠈⢆⠀⠀⢹⣿⣾⢧⠀⠀⠀⠀ ⢰⠓⢾⣢⡰⠻⠳⡾⢻⡿⡟⢸⡊⠀⠀⢸⠀⠙⢦⣸⡀⠀⢾⡎⢻⡄⠀⠀⠀⠀ ⢬⠀⠈⣷⣿⡆⠈⣾⣎⣞⣀⣀⣇⠀⢀⣾⠒⣉⣥⢽⣷⢀⢷⣿⣧⠃⠀⠀⠀⠀ ⠋⠐⠀⣼⢿⡤⣾⡗⡿⡖⠶⠆⡼⣠⢻⠃⠈⠈⠙⢁⠟⣿⣿⣿⣑⡠⣄⣒⣠⠀ ⣀⣀⠜⢹⣾⣧⠹⣷⣧⠀⠀⣰⠟⠁⠁⠀⠀⠀⠀⠀⢠⠻⣿⣟⡗⢻⠿⡏⡙⣆ ⠊⠟⠆⡞⣾⡷⡀⡟⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⣿⣋⢱⣤⣧⡇⡇⠸ ⠀⠀⣸⣇⣿⡈⠀⡠⣺⡿⡑⣄⠀⠀⠀⠀⠀⠀⠀⡠⠁⣸⢹⢻⠘⣿⣿⡇⡇⠀ ⠀⣠⣱⡻⠉⠁⠀⠀⣹⣿⠳⣹⣿⡦⡀⠀⠀⡠⠊⣀⡼⠁⡞⠆⡄⣿⣿⡇⡇⠀ ⢈⣽⠟⠑⡰⣄⢀⣾⣟⡇⣇⠹⣿⣇⠈⢙⣽⠿⣾⣯⡀⣸⠀⠏⠱⣿⣿⣇⡆⠀ ⠅⠂⠉⠉⠁⠲⣿⣿⣾⡇⢹⣿⡷⠻⠴⡛⠰⢷⡷⠣⡵⡇⠀⠀⠀⣿⠿⣿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠋⠉⠀⠈⢳⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⢀⣠⠴⠚⠉⠁⢉⣷⣀⡀⠀⠀⠀ ⠀⠀⣀⣤⣤⠤⠤⢤⣄⣀⢀⣧⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⣹⠀⠀⠀ ⣴⣿⡿⠋⠀⠀⠀⠑⢄⠉⠻⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡿⠀⠀⠀ ⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀ ⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠘⡗⠉⠀⠀⠉⠐⠢⡀⠀⠀⠀⢳⠀⠀ ⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢈⢴⠇⠀⠀⢀⡀⠀⠀⠈⢄⠀⠀⢸⠆⠀ ⠀⠀⠙⢦⣄⠀⠠⠤⠤⠀⠊⣡⠏⠀⢀⠎⣀⡀⠈⠢⠀⠀⠄⠀⠘⣿⣷ ⠀⠀⠀⠀⠈⠙⠒⠶⢶⠒⠋⠀⢃⠀⠸⡎⣴⣶⡧⠀⡇⠀⣸⠔⠉⢸⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠑⢄⡑⠛⣛⡓⠨⠐⠈⠋⢢⡴⠋⠀ ⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠈⠳⢤⣀⣀⠀⠀⢀⣀⣀⣠⠼⠞⠉⠀⠀⠀ ⠀⠀⠀⠀⣸⠃⠇⠻⡄⣀⣀⣀⣀⣤⡽⡹⠉⠉⠉⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⡀⠈⢢⣝⡡⠤⡤⢠⠀⢪⢀⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢶⡄⠑⠴⠴⠃⠘⠒⠊⠁⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⡇⢀⣸⠀⠀⠀⡏⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠴⢻⠟⠋⢹⡀⠀⢸⢇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⢸⣧⠀⠸⡆⠀⠈⡇⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣀⣸⡟⢦⣀⣹⡀⠀⢻⣠⣼⣾⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⡷⠈⠛⠿⠇⠀⠈⠻⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀