Hand pointing Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⠤⠀⠀⠠⠤⠤⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⢖⣏⣡⣤⣤⣄⣀⣤⣠⣄⣀⣀⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠈⠁⣢
⠀⠀⠀⢰⠟⠆⠠⠼⣈⠦⣌⠉⡹⠑⠲⣶⣦⣀⡴⠾⢛⣁⣤⡿⠿⠋⠉⠉⠀⠀⠀⠀⠉⠉⢉⠉⠙⢛⠿⠿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⣾⠈⠓⣖⢮⣛⣰⡇⢄⡠⠞⣾⢹⡏⢋⠁⠀⠉⠈⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣤⣴⣿⣯⣤⣙⣤⣤⡿
⠀⠀⠐⢸⢠⣻⣽⢵⣾⣿⣿⡐⢌⣠⣿⢸⣇⣼⠀⠀⠀⠀⠀⠀⠀⢀⢀⣶⣾⣿⣿⣿⣻⡿⡟⠉⠉⢩⠏⠉
⠀⠀⡀⢸⢀⣿⣿⣿⣿⣷⣿⣿⣤⣿⢹⠸⣯⣥⣤⣀⢀⣀⣠⣤⣾⣿⣿⣯⣿⣿⣥⣼⣿⣇⣁⣤⠶⣇
⠀⠀⡄⢸⣺⣿⣿⣿⣿⣿⣯⣿⣿⣽⡏⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⣿⣯⣽⠋⠁⢀⣠⠏
⠀⠀⢸⡘⣿⣿⣿⣿⢽⣿⣿⣿⡟⢷⣷⣼⣿⣿⡿⠛⢛⡻⠟⠛⠛⠻⠛⢿⣿⡿⢿⣿⡿⠶⠞⢻⡉
⠀⠀⠸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣗⣾⣽⣿⣯⣽⣿⣾⣃⣠⣀⣀⣊⣄⣌⠜⠿⣷⣞⣛⣇⣀⣤⡿⠁
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋
⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠋

⠴⠶⠶⢶⡶⠶⡶⠒⣶⠚⡶⠒⢶⡄⠀⢀⣀⣀⣤⣤⠴⠶⠶⠖⠒⠒⠛⠛⠛⠛⠛⠉⠙⠛⠛⠛⠒⠶⢤⣄⣀
⠀⠀⠀⢸⠇⢸⠇⢠⠇⣸⠷⠖⠚⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⡀
⠀⠀⠀⠸⠀⢼⠀⡟⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣤⣀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣟⠛⠛⠳⢦⣤⣀⣀⣀⣀⡀⠀⠀⠀⠈⠳⠤⠙
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠉⠉⠉⠈⠙⠶⣤⣤⣀⣠⣤⠞
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⢀⠀⣿⣀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⣦⣀⡤⠞⠁
⠀⠀⣤⢰⡇⢸⡀⣿⠉⠉⠛⠛⣿⡶⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⢀⡼⠁
⠀⠀⣿⠈⣧⢸⡇⢸⡄⠀⠀⠀⣸⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠹⣟⠓⢦⣀⠀⠀⠹⣦⠤⠶⠛⠁
⣤⣤⣿⣤⣿⣤⣧⣈⣧⣀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠙⠃⢀⡼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⠿⡿⣿⣿⣿⣿⠿⠿⠟⠿⠛⠛⠛⠉⠙⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣿⣿⣿⣿⣿⣿⡿⠋⠁
⣿⣿⣿⣿⠟⠉
⣿⠿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠒⠒⠲⠤⢤⣀⣀⡤⣖⣮⠍⠉⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣿⣦⡤⠄⠀⠀⠀⠀⢰⣆⠀⠺⣿⣿⣥⡄⠀⠀⠀⠑⢠⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣯⡭⠥⠀⢀⡀⠀⠀⠀⠀⠀⣿⡷⠈⠉⠋⠭⠇⠀⠀⠀⠀⣠⡙⠖⠠⠄⣀
⠀⠀⠀⠀⠀⢠⢿⣿⡿⠟⣛⣧⣤⣄⡉⠀⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠁⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⢎⣾⡏⢰⠟⠿⠃⠀⠀⠈⠳⣌⠢⣸⣿⣿⣿⣄⡀⠀⠀⠀⠀⣾⣠⣾⡿⠀⠀⠀⠄⡤⠠⠑⢄
⠀⠀⠀⠀⢠⣿⡿⠀⠼⠛⠛⠒⠂⠄⢀⠀⢹⡆⢹⣿⣿⣿⡗⠀⠀⠀⠀⣾⣿⡏⠀⢒⠂⠀⠀⠀⠃⢠⡄⣀⠁⠀⢄⡀
⠀⠀⠀⠀⠀⣿⣧⠘⠀⠀⠀⠀⠀⠀⠠⡀⠠⡇⠘⣿⣿⣿⠗⠀⠀⠀⢰⣿⣿⣴⠞⠃⠀⠄⠀⠀⢰⣿⣷⣹⣷⣶⣄⠙⣄
⠀⠀⠀⠀⠀⠙⡝⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣼⣿⡻⠕⠋⠀⠀⠀⠀⠀⣼⣿⣿⣷⠳⡉⠉⠀⢹⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣷⣆⣀⣀⢀⣀⣀⣠⣼⡼⣰⣿⣿⣟⠀⠀⠀⢠⣿⡏⣀⡤⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣟⣻⣿⣽⣾⣿⣿⣿⠛⠀⠀⠀⣾⣿⠭⢔⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⢀⣴⣻⡻⡐⣿⣿⣿⣿⣿⡿⣿⡿⡋⠉⠑⠀⠀⠀⣶⣿⣟⠁⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠆⠀⠀⠀⠀⡸
⠀⠀⠀⢀⡴⠛⠋⠉⢩⣿⣿⣿⣿⣿⣟⠷⣦⡄⠑⠀⠀⠀⠀⢰⣿⡿⠃⠂⠀⠁⠀⠀⠀⠀⢠⣿⣿⡟⠈⠀⠀⠀⠀⠀⡇
⠀⠀⢠⣫⠎⠀⠀⠀⠚⣻⣯⣿⣿⣿⣝⣳⣤⡽⣷⣴⣤⣶⣶⣿⣿⣛⠡⠤⠄⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⡸
⠀⠀⣸⡇⢠⠂⠀⡠⠚⣻⢿⡋⠀⠀⠀⠉⠿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣥⣄⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⢹⡃⣷⣿⠏⢠⠏⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡻⣿⣓⠀⠀⠀⢀⣼⣿⠻⠆⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠘⣷⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠒⠒⠂⢀⠈⢻⣿⣿⣿⣿⣿⣿⣏⠁⠀⣤⣤⡶⠟⠁
⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠤⠤⠄⠈⠀⡆⠀⢿⣿⣿⠿⠿⣛⣿⠿⠛⠉
⠀⠀⠀⠀⠘⢿⣇⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⢀⡀⠀⠀⣷⢀⣾⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠙⢆⠀⢀⣾⡧⣦⢲⢠⣶⣰⣧⢷⠀⣀⣶⣶⠖⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠧⡭⣤⣬⣬⣭⣝⣋⣛⡛⠿⠶⠖⢂⣐⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠒⠊⠉⠁⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠈⠙⠛⠛⠦⣼⠀⣀⣀⣀⣀⣀⣀⣤⣤⠤⠎
⠀⠀⠀⠀⠀⠛⠻⠿⠿⣿⠋⠀⡰⠒⠁⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣠⡄⠀⠈⠻⠍⠁
⠀⠀⠀⠀⢀⢀⣀⡀⣀⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⡋⠉⡍⠙⠦⣄⣠⣴⠖⣀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⡠⣶⣿⣿⠋⢙⠓⠲⠖⠚⠛⢛⢛⠁
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢿⡝⠒⠒⠛⠉⠥⢾⣿⣿⣏⢻⠺⣤⣀⣀⣤⣤⣬⠼
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠰⣾⠞⣿⠲⣄⣀⡀⠀⣀⣾⣿⠿⠿⢤⣀⣀⣀⣀⣠⠆
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣾⠂⠀⠁⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠖⠒⠊⠉⠉⠀⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠉⠉⠉⠉⠉⠉⠉⠫⣅⠀⠀⠀⠀⣀⡤⠴⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⣠⠖⠲⣄⣈⣳⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠀⢀⡠⡾⠁⠀⠀⠀⠀⠀⠀⣠⢊⣡⠦⠒⠀⠉⠉⡆
⠀⠀⠀⠀⢠⠔⠒⠚⠉⠉⢠⣾⠿⠛⠉⢰⠁⠀⠀⠀⠀⠀⠀⠁⡼⣏⡀⣀⣀⠀⠀⠸⡅
⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⢀⠎⢢⡴⠋⠁⠀⠀⠀⢠⡇
⠀⠀⠀⢀⡇⠀⠀⠀⠀⢿⡀⠠⠤⢐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠳⠴⠒⠊⠁⠀⢀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣧⠀⠀⠁⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⣤⡤⠔⠋
⠀⠀⠀⢯⡀⠀⠀⠀⠀⠀⠸⣆⠀⢀⣤⣴⠾⠦⠤⢤⣄⣀⣀⣀⣀⠤⠗⠋⠁
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠙⠻⠿⠟⡟
⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⢀⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠒⠊⠉

⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣀⣀⣀⣀⣀⢀⡠⠄⠄⠀⠰⠦⠗⠰⢶⣦⣄⡀
⠀⠀⠀⠐⠉⠀⠈⢤⠔⠀⠂⣦⠈⠉⢹⡞⠀⠀⠀⠄⠄⡀⢀⡀⠔⠁⢙⣿⢶⣄⡀⠀⠀⢠⠀⠀⠠⣶⣤⣤⣤⣤
⠀⠀⠀⠐⠤⠀⠠⠤⠤⠤⠤⠤⠀⣀⠜⡴⠀⠀⢠⢿⣾⣿⡓⠀⠀⠀⠀⠁⠚⠿⡿⣷⡶⡾⡟⠍⠁⠹⣽⣿⡋⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠤⠀⠄⠀⠁⠀⣠⠾⣷⡄⠀⠀⠀⠀⠀⠀⠁⠁⠁⠃⢹⠀⠀⠀⢣⠃⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⡠⠔⠋⠁⠀⠈⢹⣷⠂⠂⠀⠀⣶⡀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⡇⠀⠀⠀⠀⡠⠖⠟⠘⡇⠀⠂⠂⣟⡐⠘⠀⠀⠸⠀⠀⠀⠀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡠⠔⠊⠀⠀⢀⡜⠁⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⢰⡇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣀⠀⠠⠟⠀⠀⠀⠀⢀⡠⠄⠀⠀⢻⠃⠀⠀⠀⣸⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡤⠤⠚⠁⠀⠀⠀⠀⠙⠦⠤⠄⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⢰⡅⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠄⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⡿⣡⢀⣴⡖⠒⠢⢄⢸⣿⠀⠀⠀⣄⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⠃⠀⡄⢻⣿⠘⠛⠛⠉⠑⠒⢷⣻⠀⠀⠀⠀⠀⠀⢃⠑⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⢈⣽⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢸⠀⠀⠠⣷⣄⠀⠀⠀⣄⡼⠋⠀⠀⠀⠠⡆⠀⠀⠀⢠⡀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢀⠈⡀⠀⣳⣿⣸⡿⠿⠛⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡟⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣑⢷⣴⡟⣛⣹⡃⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡜⠁⠀⠀⣣
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠐⠩⠝⡟⠋⣿⢇⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢠⠇⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡠⠒⠒⠒⣧⣦⡈⠈⠑⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡞⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠎⠀⠀⠀⠀⠈⠛⢷⣀⡷⡄⠀⡀⠀⢀⡼⠁⠀⠀⡼⠁⣰⠋
⠀⠀⠀⠀⠀⠀⠀⢹⠢⢀⡄⢠⠆⡄⠀⠀⠀⠀⠀⠹⣧⣤⢤⡞⠛⠉⠀⠀⠀⡼⢁⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠬⣔⡻⣶⣣⡞⠛⠒⢤⣀⠀⠸⡄⠀⠱⢦⣤⣄⡠⠊⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢄⡀⠀⢱⢠⠇⠀⠀⠀⠉⠒⠶⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢹⣿⠀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣾⠿⠛⠛⠛⢿⣷⣄⣴⡿⠟⠛⠛⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠹⣿⡿⠁⠀⠀⠀⠀⢹⣿⣤⣶⡿⠿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢀⣶⡿⠿⠿⣷⣦⡀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⣾⣿⠀⠀⠀⠈⠙⢿⣦⣀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠸⣿⣆⠀⠀⠀⠀⠀⠙⢿⣶⡀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠙⢿⣦⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣿⠿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠙⠛⢻⣶⣶⡤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣵⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⢚⡟⣸⡏⡠⠀⠀⠀⠀⠀⠀⠀⠲⢿⣿⡄⠀⠀⠀⡙⣦⡀
⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠈⠀⣽⣿⠁⠀⡠⢊⡥⠴⢶⠀⠀⢄⡙⢿⡀⢈⡄⢱⠈⠛⠳⣄
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢀⡴⢁⡴⠚⠛⠁⠀⢀⣹⣾⡇⠈⡇⠘⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣾⡵⠁⠀⠀⠀⠀⠀⠈⢻⣿⡧⠀⡑⡎⠀⠀⠀⠀⠈⠺⣄
⠀⠀⠀⠀⢸⡆⠙⣆⠀⠀⠀⠀⠀⠀⠹⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠃⢸⠀⣧⠀⠀⠀⠀⠀⠑⢦
⠀⠀⠀⡴⠋⠋⢀⡈⠆⠀⠀⠀⠀⠀⠀⢻⣷⣿⣇⡀⠀⠀⠀⠀⠀⣠⣿⣯⠀⠀⠘⣧⣿⠁⠀⠀⠀⠀⠀⠈⡇
⠀⠀⣼⠁⠀⠀⠀⠙⠆⠀⡀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣶⣦⣤⣴⣾⣿⣿⣯⣄⡀⣸⣿⡯⠀⠀⠀⠀⠀⠘⡄⣧
⠀⠀⣿⡀⠀⠀⠀⠀⠀⢀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢻⣿⣿⣏⠉⠻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘⣾⡄
⠀⠀⢸⡿⠶⣦⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣥⣀⠸⣿⣿⣂⡀⠀⠀⠀⠀⠀⠐⢬⡳⡀
⠀⠀⢀⣇⣄⠀⠀⠀⠀⠀⠀⠺⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠋⠉⠀⢹⣿⠥⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷
⠀⠀⢸⠁⠁⠀⢀⣀⠀⠀⠀⠀⠉⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠃⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠸⣄⠀⠀⠈⠙⣷⣆⠀⠀⠀⠈⢻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠐⢄⠀⡀⢀⣿
⠀⠀⠀⠹⣄⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠋⢿⣷⣄⣀⡀⠀⠀⠀⢀⠄⢊⣠⣿⡟⠀⠀⠀⠀⠀⠀⠐⠀⠉⠈⠂⢨⣠⠏
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠈⢿⣦⠀⠀⠀⠉⢛⢿⣿⣯⣤⣦⣦⣤⣴⣿⣿⠋⠀⠀⠀⢀⣠⣄⠀⠀⠀⣀⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠙⢷⣄⠀⠀⠀⠪⣻⡿⢻⢿⢿⣿⠋⣸⡇⠀⠀⢀⣴⠟⠁⡈⣳⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠹⣷⣦⣀⠀⠀⢀⢁⣡⣾⠏⠀⣿⣷⡇⠀⠟⠁⠀⠀⡜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠙⠻⠿⣿⣵⣿⡿⠋⠀⠀⠘⢿⣿⣄⣶⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣮⡴⠾⠋⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋

⣿⣿⠛⢛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠖⠒⠈⠀⠀⠀⠀⠀⠐⠒⠤⠤⣤⣀⢀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⢻⠻⣳⡶⠾⣿⣃⠊⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠑⢾⣠⣀⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣸⣟⣧⣗⣟⡌⢼⡅⠁⠀⠀⠀⠀⠀⠀⠀⠠⢀⣄⣀⣀⣀⣀⠀⡀⠀⠀⠀⠼⡺⣴⣵⣹⣾⣠⣰⣆⣤⣀⣀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢹⡯⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠉⠁⢙⠳⢦⣄⡀⠀⠀⢒⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⡀⠀⠀⠐⠒⠠⢤⣕⣠⣾⣿⣿⠻⣿⠿⠷⢘⠂⠈⠀⠂⠀⠀⠀⠉⠉
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣮⠆⠀⠠⠲⠶⠶⠛⠉⠛⠋⢁⣀⡏⠀⠈⠂⢳⣦⣄⡆⠀⠀⠀⠄⢆⡠⠃
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠉⢢⣉⠀⠁⠈⠈⠉⠉⠉⠉⠛⡏
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⢣⣇⢿⣿⠉⠀⢀⠀⠀⠀⠀⠀⠠⠈⢧⡐⠀⠁⠘⠳⠦⣤⣄⣀⣀⢀⢀⡢⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣾⣸⣸⡎⢂⠈⢰⡷⣷⣧⣄⠀⠈⠐⠜⢷⣦⣀⠀⠀⠀⠀⠉⡟⠉⠉⠁
⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠁⠀⠀⠀⠀⠉⠙⠛⠛⠛⠓⠛⠛⠛⠉⠉⠉⠉⠙⠒⠒⠈



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⢶⡶⣶⣶⣶⡶⣶⣶⢶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⠚⠉⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠛⠉⠉⠉⠉⠁⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠋
⠀⠀⠀⠀⢠⡟⠙⠋⠁⠸⠿⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠓⠚⠋⠉⠉⠁⠒⠒⠲⠶⠦⠤⠤⠤⠤⢤⣀⣀⡀
⠀⠀⠀⠀⡟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⢸⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡁⠀⠈⠛⠶⠶⠶⠾⢷⡒⠒⠒⠚⠓⠒⠒⠒⠒⠒⠒⠒⠊
⠀⠀⠀⠸⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠖⠚⡻⠿⠷⣦⡀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⢷⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⡀⠀⠄⠉⠓⠲⠦⣤⣀⣠⠞
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠸⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠙⠲⣤⣀⡀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠑⠀⠒⠒⠒⠛⠁⠈⠉⠙⠒⠶⢦⣤⣤⣀⣙⣦⣀⠀⠀⢈⡽⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠉⠓⠦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠓⠲⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠤⠤⠴⠶⠖⠒⠒⠉⠉⠉⠙⠓⠒⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠶⠿⡇⠈⠙⠋⢻⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠁⠒⠒⠊⠀⠒⠒⠒⠚⠒⠒⠒⢒⡾⠷⠶⠶⠲⠛⠁⠀⢈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⣤⠾⠿⢟⠓⠲⠚⠚⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⡠⠶⠖⠚⠉⠠⠀⢀⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢀⣠⣤⠶⠋⠀⣠⠆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠇⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢯⡀⠀⠀⣀⣴⣋⣀⣤⣴⡶⠶⠒⠋⠉⠀⠈⠛⠒⠓⠂⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠁⠈



⣿⣿⡿⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⠀⠀⠠⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠶⢤⠤⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠋⠁⠀⠀⠀⢶⣦⣤⣤⣤⣴⡄⠀⠀⡀⢿⡄⢀⣰⣆⣄⣀⣠⣄⣤⣸⣦⣤⣶⣾⡦⠴⠖⠋
⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣄⠀⢧⡘⣿⣾⡿⠿⠿⠚⢿⡛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⢛⡛⠉⢉⡄⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣵⣿⣿⣿⣏⡀⠀⠷⣀⣼⣧⣤⣤⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⠁⠈⣻⣻⣿⠉⠉⠉⠉⠙⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⣶⡶⠶⣻⣿⣿⣿⡿⠛⠛⠛⠻⠿⠿⠶⠶⣴⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⢠⠇⠟⠇⢠⣄⠂⠉⠀⠈⠀⠛⣷⣦⣶⣗⣰⠇⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠐⢄⣘⣚⣠⣥⣥⣤⣴⡶⠶⣾⣿⠿⣦⣷⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡷⠄⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠾⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⣀⡤⠤⠔⠒⠚⠉⠉⠙⠫⢭⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⢳
⠀⠀⠀⠀⣼⠉⠀⠀⢠⡿⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣤⡤⠤⠤⠤⠤⠤⠶⠶⠶⠖⠒⠋
⠀⠀⠀⢀⡇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣼⠦⢤⣤⠀⠀⢾⣉⣉⣶⡄
⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⢿⢦⡜⠀⠉⠓⠒⠶⠖⢋⡏
⠀⠀⠀⢸⡇⠀⠀⠀⡏⠀⠀⠀⠀⠒⠒⠚⠻⢿⠛⢷⡞⠀⠙⠒⠒⠒⠒⢲⠒⠋
⠀⠀⠀⢸⡇⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠉⠉⠒⠶⢤⣄⣀⡠⠞
⠀⠀⠀⠸⡇⠀⠙⠀⣿⣧⣄⡀⠀⠀⠀⠀⠀⢀⣀⣹⣶⣤⣀⣀⡼⠃
⠀⠀⠀⠀⠻⠶⠶⠶⠾⠁⠀⠉⠉⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠂⣀⠀⠠⠠⠤⠤⠤⠤⠤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠁⠀⠀⠀⠀⠉⡄⠑⠀⠀⣀⣠⣤⡀⢀⣀⣀⣀⣀⣽
⠀⠀⠀⠀⠀⠶⠶⠶⠋⠀⠀⠀⠠⣰⣤⣀⣀⣀⠀⠀⠔⠈⢹⡟⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⡀⠀⠈⠙⠂⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢲⣿⣿⣿⠀⠀⠈⠉⢉⣻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢀⣼⠇
⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠈⠁⠀⢘⠁⠀⠠⣤⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣄⣀⣀⣀⣼⣤⣀⣠⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠸⣃
⠀⠀⠀⠀⢀⣴⡶⠿⠛⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢈⡄⠡⠀⠉⠉⠁⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⢺⣼⣄⢀⠀⠀⢤⣾
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡏⠸⠋⠉⠉⢻⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⡐⢁⡀⠃⠘⠀⣰⣾⣧⣀⠀⠠⢀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⡏⠀⠀⠀⠚⢒⣿⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠉⠉⠛⠙⠷⠀⢀⣤⡄⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢱⠀⠠⠄⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠂⠄⡀⠀⢀⣆⣇⠀⠈⡽⠁⠀⠀⣿⣿⣿⣿⡀⢰⣄⣀⣠⣿⣄⠀⠀⠀⠀⠀⢸⣄⣀⢀⣶⣿⠂
⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⣉⠙⠛⠼⠄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣚⠿⠉⠉⠙⠛⠻⠶⠶⠶⠶⠿⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⢢⡀⠀⠈⠓⠒⠒⠰⣿⣶⠖⠁⠀⠀⠀⠀⠀⠈⣿⡿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠉⠢⢤⣿⣶⣶⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢸⣿⢀⣾⠟⠋⠉⠙⢻⣦⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⠿⠿⠋⠀⠀⠀⠀⠀⢿⣿⠿⠛⠛⠻⢷⣄⣀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢸⣿⠀⢠⣤⣤⣀⣻⣏⠁⢈⣉⡙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⢸⣾⡇⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠈⠹⣿⠀⠉⠉⠉⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠳⡄⠀⢿⡇⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢱⣦⣙⣦⣸⣇⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⡾⠋⠉⠻⡏⠛⠛⠛⠛⠛⠛⠻⣿⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⢠⡿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⢤⣀⠀⠀⠀⢀⣠⡾⣿⣀⠀⣀⣴⡿⠻⣷⣀⣀⣠⡟⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠙⣿⡟⠙⠛⠣⣄⡈⠻⠟⠛⠿⣄⠀⠀⠉⠉⠁⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⣦⠀⠀⠀⠙⢦⡀⠀⠀⠈⠛⠢⠄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣠⠿⡿⠀⠈⠱⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠊⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡿⢋⣿⣿⠷⣶⣶⣶⣶⠶⠶⠚⠋⠡⣤⡤⠶⠶⠿⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠙⠻⠶⣤⣄⣀⡀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠐⣿⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠻⠿⣶⣦⣄⣀⠀⠈⠉⠛⠻⠶⢶⣿⣤⣀⣀⣀⣀⣀⣀⣿⣛⠛⠿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠙⠛⠿⢶⣦⣤⣄⣀⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⣠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠶⢶⣶⣶⣶⣶⣶⡾⠿⠟⠋⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣩⣿⣹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡖⠒⢢⣀⣠⣤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡖⠉⠛⠲⣾⣿⣿⡇⠀⠀⢻⣿⡁⢀⢀⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡏⠉⢻⣿⣿⣿⡀⠀⠀⠿⣿⣿⡇⠀⠀⢀⣿⠟⠃⢨⣵⣌⣷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠘⣻⣿⣻⡗⠀⣔⢄⣽⣿⣯⣠⣶⣿⣿⣴⣰⡎⠙⣉⣁⣠⡑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⣿⣿⣿⢿⡄⠁⢸⣿⣿⣿⣾⠿⣿⢿⣿⣇⢁⣾⡿⢟⠛⠿⠏⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⡏⣊⢠⠂⢺⣿⣽⡟⠉⠘⠏⢹⣿⣛⢿⡿⣳⡿⠃⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡗⠀⠀⢸⣿⡆⠐⠠⠀⣼⠟⣀⠇⠀⠀⠈⠀⣿⡅⠀⠳⣹⡇⢀⣀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⢾⣟⠁⠀⠠⠘⢿⡆⣁⣤⣀⢀⠀⠀⠿⠁⠀⠀⡈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠈⠻⣇⠀⠀⠀⢨⣿⣿⠖⠐⠒⢤⣀⠲⠄⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣰⣷⣄⣀⣀⣬⣦⡀⠀⢸⣿⡏⠀⠀⠀⠀⣼⣔⠂⠀⡁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡿⠶⠤⣄⣀⣉⢻⣿⣧⡱⠤⢤⣤⠼⠋⠀⠀⣠⠋⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⢿⣿⣿⡏⠀⠀⠀⠀⠌⠉⠀⠙⢿⠿⣶⣤⣤⣤⣄⣀⠀⠁⠀⢠⠋
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⢩⣾⡿⠋⠛⠠⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣭⡈⠁⠁⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣇⣤⣿⠛⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⣴⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⣤⣀⡀⠀⠀⠀⠀⠀⣠⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣛⣿⣿⣷⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠒⠒⠒⠒⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⡤⣤⣤⡄⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⡠⠤⠔⠶⠦⠤⡀⠀⢸⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢻⠀⡜⠁⠀⠀⠀⠀⠀⠀⠈⡆⢸⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⡇⠀⠀⠀⣀⣀⣀⣀⢀⡌⢸⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠁⠉⠉⠁⠀⠀⠈⠉⠀⣸⠀⠀⠀⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡛⠒⠒⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣠⠶⠛⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡾⠁⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠙⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠀⡇
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⡀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⡠⢄⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⢠⠴⠞⠁⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⡰⠋⠀⠀⢳⡀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⡀⠀⠀⠀⢀⡴⠋⠉⠛⠒⠒⠚⢻⠃⠀⠀⢀⡞⠀⠀⠀⠀⠀⢳⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠠⠴⠊⠀⠀⠀⣠⠟⠓⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢸⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⢇⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⢈⡦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠶⠿⢿⣿⣭⣭⡀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠉⠁⠁⠀⠐⠂
⢹⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⢀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠳⣶⣤⣄⣀⣀⣀⣀⡀⣀⣤⢀⣀⢀⣀⣶⣀⣀⣀⣀⣤
⢹⣿⣿⣿⣿⣿⠟⢋⣿⣿⣤⣾⠿⠋⠁⠀⠀⠀⠀⢀⣀⣠⣄⣤⣠⣤⣤⣀⠀⠀⢙⠿⠿⢿⠿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉
⣾⣿⡿⣿⡿⠁⣠⣿⡿⠉⠁⠀⠀⢀⠀⠀⢀⢄⣤⣤⣿⣿⣿⣿⣿⡿⢿⣿⣷⣤⣼⣲⣶⣶⣂⠀⠀⢀
⢈⣥⣟⣿⠁⢠⣿⣿⣇⢴⡤⡀⣤⣀⣱⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣅⣦⣻⣍⠛⠛⠋⠉⠁⠀⠉⠀⠀⡇
⢸⣿⣿⡿⠀⢸⣿⣿⣿⣯⣮⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⡿⣿⣷⣶⣤⣤⣀⣀⡀⣠⣴⠟
⣸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⢫⡅
⢲⣿⣿⣧⠀⠸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣨⠙⢿⣿⣷⣦⣄⣀⣀⣀⡼⠃
⣸⣿⣿⡏⠀⠀⣿⣿⣿⣿⣿⣷⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠉⠛⠛⢛⡏⠉
⢿⣿⣿⡇⠁⠀⢹⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣠⡼⠁
⣼⣿⣿⣷⠀⣴⣌⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠿⠛⠉⠉⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁
⢸⣿⣿⣿⣆⡻⠿⢟⣰⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡟⠉⠉⠉⠛⠳⣶⠶⣖⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠀⠁⠀⠀⠀⠀⠀⣡⠞⢉⣀⣘⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠛⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠈⠀⠁⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⡖⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣠⣶⣶⣶⣦⡀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⣿⠀⠀⠀⢸⡿⠀⠀⠀⠀⢀⣿⠉⢡⣶⣶⣯⣧⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡟⠀⠀⠀⣸⡇⠀⠀⠀⠀⣾⣿⣶⣤⣬⣭⣷⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿⡇⠀⠀⠀⣽⡇⠀⠀⠀⠀⠙⢻⣿⡿⣿⠟⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢹⣇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢸⣿⠴⠋⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠈⢿⡄⠀⠀⠘⢿⣄⠤⣤⡤⠄⣸⣿⠊⠀⠀⠀⢨⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣎⣿⣶⣶⣿⠿⠛⢛⡛⠛⠛⠋⠉⠉⠀⠀⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠹⣏⣰⠟⠉⠹⢳⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠶⠿⣿⣤⣀⢀⡶⣧⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠉⠉⠛⠲⢶⡶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠋⠉⠀⠁⠀⠀⠀⠀⠀⣠⡞⢉⣀⡘⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣿⠀⠋⠉⠉⠁⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⡀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⣧⢠⣤⣤⣤⣤⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠉⠁⠀⠢⣭⠅⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⣿⣦⣄⣀⣠⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⣿⠠⠋⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⢿⡀⠀⠀⠘⢷⡀⠀⣀⠠⠀⢸⣿⠀⠀⠀⠀⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣈⣻⣶⡖⢢⡾⠛⠓⠶⠶⠛⠛⠉⠁⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⢹⡏⢠⠞⠉⠉⢢⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠶⣶⣶⣯⣀⠀⠀⡄⣂⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠾⠷⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡊⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡃⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⢉⠄⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣼⣗⠀⠀⠀⠀⠀⠱⣄
⣠⠴⠒⠒⠋⠉⢉⠉⠉⠉⠀⣨⢀⠀⠀⠉⢉⡇⠀⠀⢠⡄⠼⢛⡇⢸⠀⠀⠀⠀⠀⠀⠈⢧⡀
⢿⣿⣾⣾⣴⣴⣿⣿⣷⣾⣶⣿⣿⣦⣴⣦⣾⣄⣀⡰⣬⣿⣀⢸⡏⠝⢀⣦⠂⠀⠀⠀⠀⠀⠻⣄
⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⠀⠉⠛⠛⠛⠛⠛⠋⠉⠽⢿⣖⢻⣾⠇⢂⠆⠀⠀⠀⠀⠈⠷⠶⢴⣶⣶⣤⣤⣄⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣤⣀⠀⣤⣶⠀⠀⠀⣶⣿⣿⣞⣽⣾⣿⢡⡄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠿⠿⣿⣿⠿⠟⠋⠉⠀⣈⣹⣿⣆⠙⣿⣿⡕⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣀⠀⠀⣠⣦⣤⣬⣿⣿⣮⠛⠶⢬⡉⠛⠃⠠⠤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠿⠟⠛⠋⠉⣠⣼⣿⡟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⢶⣷⣤⣀⣿⣿⣯⡦⡪⣀⣀⣀⡀⠀⠀⠀⠀⡀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣿⣦⡥⢾⣼⣿⣸⣿⣿⣿⣿⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⣟⣿⣿⣿⣿⣿⣷⡀
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⣶⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⢀⣠⣶⣿⠿⠛⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠙⣿⣦⡀
⠀⠀⠀⣰⣿⣿⠟⠁⠀⠰⠛⠁⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠈⠻⣿⣦⣀
⠀⠀⢰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⣠⣴⠶⠶⢶⣄⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣾⠟⠁⠀⣀⣤⣿⠧⠀⠀⢹⡇⠀⠀⠀⢰⣆⠀⠀⠀⠉⠻⣷⣄
⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⢀⣴⡿⠛⠉⠀⠀⠀⠀⣸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠙⢿⣷
⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠘⣿⡇
⣼⡿⠀⠀⠀⠀⠀⣄⣀⣼⠂⠀⠀⠀⠀⠘⢷⣤⣀⣀⣀⣠⣴⣾⣿⠟⠛⢷⣤⣀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⣿⡇⠀⠀⠀⠀⠀⠈⠉⠻⣷⣄⠀⠀⠀⠀⠀⠉⠙⠋⠉⠉⠉⢿⣧⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧
⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⣼⣿⠀⠀⣤⡆⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡿⠛⠛⠛⠃⠀⠀⠀⠀⠀⢻⣿
⣿⡇⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣿⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠘⣿⣧⡀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠈⠻⣿⣶⣄⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠈⠛⠿⠷⠶⢶⣾⣿⣿⡟⠀⠀⠀⠀⢀⣀⣀⡀⣀⣴⣾⡿⠟⠉
⠀⠀⠀⠈⠛⢿⣷⣤⡀⠀⠀⠙⠻⣶⣄⡀⠀⠀⠀⠀⠀⢀⣾⣿⢻⣿⡇⠀⢀⣤⡾⠛⠉⠙⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⣀⠀⠀⠙⠻⢷⣶⣤⡶⢾⣿⡿⠃⠘⣿⣇⠀⢿⣏⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⣤⣀⡀⠀⢀⣴⣿⠟⠁⠀⠀⠘⢿⣷⣬⣿⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠉⠀⠀⠐⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⢠
⠀⠀⠀⣒⣒⢒⠚⡛⠛⠛⠛⠛⠛⣻⠲⢤⣄⡤⠊⠁⠀⠀⠀⠀⠀⠀⢀⣐⣾⡿⠿⣿⣤⠀⠀⣏⡁⠉⠀⣀⢈⡀⠐⠀⠀⠀⠀⢀
⠀⠀⠠⣠⣄⢀⣠⣄⡈⠋⢩⠋⢡⡏⠀⠰⢸⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⢧⡤⠼⠿⠿⣧⣬⣱⢲⣶⣿⣟⣛⣇⣾⢶⣴⣴⡼
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣴⣦⣠⣾⡇⠀⡆⢀⠇⠀⠀⠁⠀⠀⠀⢠⣶⣏⣝⣦⠀⣀⠀⠀⠀⠀⠀⠉⠱
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣁⠈⠁⠀⠀⠑⢃⣤⣎⣽⣛⣟⠛⠓⠾⢿⣥⣴⣶⣷⣦⣤⠜
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢠⡏⠀⠠⠶⠀⠒⠚⠋⠉⠿⠿⠯⣿⣳⣦⣄⣀⠀⠈⠉⡃
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⢨⡧⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣀⡀⠉⠛⠻⠿⠿⠗⠁
⠀⣿⣿⣿⡿⠉⠉⣿⠫⡩⢹⣿⣯⣥⠊⠙⠂⠌⣉⠑⢄⠀⠀⣈⠉⠿⠿⢿⢿⣾⢷⣶⠆
⠀⢹⣿⣿⡿⣶⠾⠿⡶⠶⠾⢿⢟⡇⠀⠀⠀⠀⠀⠈⠉⠀⠀⠒⠊⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⡒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⣿⣿⣶⣶⣶⣶⣤⣀⠀⠀⠀⢀⣠⣤⠶⠛⠉⠀⠀⠀⠀⠉⠉⠛⠳⢦⣤⣀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⡀⣀⡀
⠀⣿⣿⣿⣿⣿⠟⢻⣿⣧⣴⡾⠏⠉⠀⠀⠀⠀⡀⣀⣀⣀⣀⣠⣄⡀⠀⠉⡻⠿⠷⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉
⠀⣯⠽⣛⡿⠁⣰⣿⠏⠀⠀⠀⠀⡀⠀⡀⣀⣤⣜⣿⣿⣿⣿⡿⢿⣿⣦⣤⣓⣶⡶⣄
⠀⢰⣺⣽⠃⢠⣿⣿⣄⠠⡀⠰⣤⢸⣺⣿⣽⣽⡻⣯⣿⣿⣿⣤⣤⣷⠉⠉⠉⠁⠀⠀⠀⢀⡰
⠀⢾⣿⣿⠀⢸⣿⣿⣾⣴⣴⣷⣧⣯⣿⣿⣿⣯⣿⣿⣿⣿⣯⣰⣿⣿⣿⣶⣦⣤⣤⣄⡶⠞⠁
⠀⣺⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣠⣿⠻⢿⣿⣷⣀⠀⠀⠀⠀⢰
⠀⣿⣿⡇⠂⠀⣿⣿⣿⣿⣯⣋⢻⣮⣿⣿⣾⣿⣿⣿⣿⣯⡻⣤⠀⠙⠛⠿⢷⣶⠶⠖⠁
⠨⣿⣿⣇⠀⠀⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⣰⠂
⠀⣿⣿⣿⠀⣠⡈⡿⢧⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠙⠛⠿⠿⠟⠃
⠀⣿⣿⣿⣆⡺⠿⢇⡴⠃⠀⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⣠⣾⣿⣧⠀⠈⢳⣤⣾⡟⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣾⡿⡀⠀⠉⠑⣿⣿⣿⣿⠀⠀⠀⢻⣷⣆⡀⠲⡄⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠉⠀⠹⣿⣯⣿⣷⠀⠀⠘⡛⣿⣿⣿⠀⠀⠀⣸⣿⠋⠄⢨⣽⣶⣬⠷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠈⣻⣿⣿⣽⡇⢠⢮⢠⣾⣿⣿⣤⣶⣿⣿⣿⣴⣲⡇⠈⣉⣩⣠⣤⡑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠀⠀⢿⣿⣿⣿⣃⡌⠀⢸⣿⣿⢿⣷⡿⢿⣿⣿⣿⡧⢁⣬⣿⠿⡛⠻⢷⠟⠷⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢸⣿⣿⡵⢋⡀⠀⢾⣿⣩⣿⠟⠃⠹⠓⣹⡿⠛⢿⣿⢟⣿⠿⠂⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡧⠀⠀⢸⣿⣯⠑⠇⡁⢀⣻⡿⢋⣿⠀⠀⠀⠂⠈⣿⡋⠈⢫⡸⣿⠀⠀⠀⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⢸⣿⠯⠀⠂⢀⠴⣿⡅⠿⠉⠁⠀⠀⠀⠀⣿⠗⠀⠀⠉⠛⠺⠺⠖⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡗⠀⠆⠹⢿⣦⠀⠀⠡⠀⣿⣷⣶⣿⣿⣗⣒⠦⢄⣿⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠙⢆⠀⠀⠀⢹⣿⣿⠋⠀⠀⠈⠙⣦⠈⡑⠲⠮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣿⣿⣷⡴⠶⠶⠞⢷⣄⣀⣸⡿⣏⠀⠀⠀⠀⢠⡟⡤⠁⠀⣠⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⠿⠛⠓⠶⢤⣤⣌⢹⣿⣷⣌⠓⠒⠶⠶⠛⠁⠀⠀⡰⠋⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⣿⣿⣿⣏⠀⠀⠀⠀⠠⡙⠂⠀⠙⢿⡛⠿⣶⣦⣤⣤⣤⣄⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠟⠉⣰⣿⡿⠋⡝⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣁⠈⠁⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⣀⣼⣟⠋⠀⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⣀⢄⠀⣠⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠧⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠻⢟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣤⣤⣄⣤⣀⣤⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣾⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠟⣿⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⠶⠾⠿⠛⠋⠉⠀⠀⠀⠉⠙⠛⠻⠿⣶⣦⣤⣀
⠀⠀⠀⠀⣀⣀⣀⣀⣤⣴⣾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⣄
⠀⠀⣴⣿⠟⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠘⣿⡆
⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠉⢀⣠⣤⣄⣿⣷
⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠈⠻⣿
⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣠⠤⠶⠶⠶⠤⣤⡀⢻
⠹⣷⡀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣸⣧⠤⠴⠶⠤⠤⣤⡇⢸
⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣷⣦⣄⣀⣀⣀⣀⣠⣴⡿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠉⠛⠛⠛⢻⣿⠋
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣸⣷⠾⠀⠀⠀⠀⣿⣿
⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⢀⣠⡿⠿⠿⠿⠿⠷⣶⣦⣴⣿⠛⠳⠄⠀⠀⠀⣿⣿
⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠻⣧⡀⠀⠀⣴⠟⠁⣀⠤⠤⣤⣀⠀⠀⠀⠉⠻⣧⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠈⠙⠻⠶⠶⠶⠿⠛⠻⠶⠾⣏⡰⠋⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⢿⠀⠀⠀⠀⣰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣀⡀⢀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣯⡁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣤⣤⣶⣶⣾⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠿⠛⠛⠋⠙⠻⡿⡿⠷⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠁⠀⠀⣀⣤⣤⣤⣤⡄⢻⣶⣧⣄⠀⠀⠉⠉⠒
⡛⠂⠈⠁⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠉⠙⠛⠿⣷⣦⣄⠀⠀⠀⠀⢦⣤⣤⣤⣀⡀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠗⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠳⣤⣀⡀⠀⠀⠁⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣄⠀⠀⠀⣴⣿⡿⠀⢀⣴⣿⣆⠀⠀⠀⠀⠈⡀⠀⠀⠈⠻⣿⣷⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠛⣿⣿⣿⣷⣶⣾⣿⣷⣤⣴⣿⣿⡏⠁⠁⡀⠀⠀⡹⠛⠿⠒⠂⠀⠙⢿⣿⣷⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠠⣧⠠⠤⠐⢦⠲⠤⠰⠿⠿⣿⠙⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠙⠳⡖⠒⢸⣿⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣼⣦⣀⠀⢸⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠻⠿⠿⠟⠛⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠐⠂⠐⠒⠲⢶⣶⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣡⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣿⣿⠉⠛⠓⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣷⡀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⢛⡟⢰⣿⢁⡤⠀⠀⠀⠀⠀⠀⠀⠉⠉⠱⣾⣿⣿⡄⢂⠀⠀⠀⡈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠰⠋⠀⢻⣿⡾⠁⠀⠀⡠⠔⢊⣁⣀⡀⠀⠀⡀⠉⢻⣿⠈⡀⢱⠀⢱⡀⠻⢟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠊⣠⠞⠋⣉⣭⣷⠄⠀⠈⠳⣦⣹⡶⠀⢸⠀⠀⡇⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⡀⠀⢀⡾⢁⡴⠚⠉⠁⠀⠀⠀⠀⣤⣾⣿⣧⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⣙⢦
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣄⣿⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⠁⠀⠸⢦⠀⠀⠄⠀⠀⠀⠈⠻⢧⡀
⠀⠀⠀⠀⠀⠈⣷⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠀⠀⡇⠘⡄⢸⣇⠀⠀⠀⠀⠀⠀⠙⠲⡄
⠀⠀⠀⠀⠀⡰⣏⡄⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣼⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣥⠄⠀⠁⠀⣧⢸⣷⡦⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⢠⠞⠁⠁⠁⠸⣦⡘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣶⣦⢀⠀⠀⠀⠀⠀⣠⣾⣿⣷⡆⠀⠀⠀⣿⣿⣷⣂⠀⠀⠀⠀⠀⠀⡄⠀⣿
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠈⠻⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣦⣴⣶⣿⣿⣿⣿⣯⣦⣤⡀⢀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠘⡄⢽⡀
⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢹⢹⢻⣿⣿⣿⡍⠉⠛⢿⣿⣿⣿⣯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣧
⠀⠀⠀⢿⣷⣤⣄⠀⠀⠀⠀⠀⠈⢻⣿⣧⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡧⠀⠀⢹⣿⣿⣇⠅⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⢿⡆
⠀⠀⠀⠸⡆⠉⠛⠓⠀⠀⠀⠀⠀⠐⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠷⠦⠄⢻⣿⣿⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣽⡄
⠀⠀⠀⢰⣧⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡻⠀⠀⠀⢸⣿⡿⢒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⡀
⠀⠀⠀⣼⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠭⢿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⡇⠀⠀⠀⣼⣿⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢛⣷⡀
⠀⠀⠀⢻⠀⠀⠀⠀⠘⠻⣷⣦⡀⠀⠀⠀⠀⠈⢻⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡐⠀⠀⢰⣿⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠌⣻⠇
⠀⠀⠀⠘⣷⠂⠀⠀⠀⠈⠙⣿⣿⡄⠀⠀⠀⠀⠐⢚⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⢀⣷⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡠⡙⡄⠳⢄⠓⣾
⠀⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⠛⢿⣦⡀⠀⠀⠀⠁⠐⢻⣿⣷⣦⣄⣀⡤⠀⠀⠀⣀⠔⠊⣠⣢⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⢀⣶⣴⠏
⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⢛⣿⣦⠀⠀⠀⠀⠡⠞⣻⣿⣿⣶⣪⣴⣢⣪⣴⣤⣾⣿⣿⡿⠉⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⢀⣀⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⠀⠀⠀⠈⠿⣷⣄⠀⠀⠀⠈⡠⢺⢿⣿⡿⢿⣿⣿⣿⣿⠋⢱⣿⠁⠀⠀⠀⠀⣠⠞⠋⠉⠙⣤⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⠀⠀⠘⢿⣷⣄⡀⠀⠀⠑⠛⠉⠠⢋⠟⣸⣿⠇⠀⣿⣧⣠⠀⠀⢰⡿⠋⠀⠀⠈⣦⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⠀⠩⢻⣿⣶⣤⣀⠀⣠⢔⣥⣶⣿⠟⠀⠀⢿⣿⣿⡄⠀⡏⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠈⠙⠿⢿⣿⣶⣿⣿⠟⠋⠀⠀⠀⠈⠻⣿⣷⡄⣿⣠⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣦⣴⣩⣤⣼⠿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠐⠛⢛⢻⠷⢶⣦⡤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠔⣁⠀⠀⠉⠁⠀⠀⢩⣺⣷⡰⡄⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⣀⡠⠴⢚⡟⣏⡞⢁⠄⢠⠔⣊⡩⠉⠉⠛⢿⣿⣿⡔⡀⢂⠘⣦⣀
⠀⠀⠀⢀⡴⠋⠀⠀⠈⠋⠐⣿⡰⡃⢀⡔⢉⡤⠤⢄⠐⠦⣭⣻⣿⣧⣀⠀⠂⠈⠻⡷⣄
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢥⣾⣷⠁⢋⠞⢁⡴⠞⠉⠁⠀⠤⣜⣿⣇⢹⡰⣶⠀⠀⠉⢸⣷⡄
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣨⣺⣯⢳⢏⣴⣫⠆⠀⠀⠀⠀⢐⣿⢸⣗⠘⡿⡏⢠⡔⠀⠀⠈⠻⣄
⠀⠀⢹⣦⠑⢄⠀⠀⠀⠀⠚⢴⢿⡼⣿⠋⠀⠀⠀⠀⠀⠀⣶⣿⣸⣷⢸⡇⢳⠈⣇⠄⠀⠀⠀⡘⠑⢄
⢀⡴⠻⢧⢷⡈⠆⠀⠀⠀⠀⠐⢽⣿⣷⡀⠀⠀⢀⠀⡀⣿⣿⣣⣿⣟⡈⠁⢺⡄⣿⡩⠀⠀⠀⠑⠄⢘⡇
⡾⠀⠀⠀⠘⠻⡌⠂⡀⠀⠀⠀⠀⠋⠿⣝⣳⣶⣷⣞⣚⣭⣿⣿⣿⣽⡃⠀⢸⣿⡷⡖⠀⠀⠀⠀⠘⣆⣧
⣷⡔⠀⠀⠀⠀⠁⢀⡇⠀⠀⠀⠀⠀⠀⠘⡜⡽⡽⡹⠹⠻⡻⣿⣛⠋⠙⣷⣾⣿⣷⡀⠀⠀⠀⠀⠀⠐⢿⡄
⢹⣿⣿⣦⠀⠀⠈⠭⢙⣾⢀⠀⠀⠀⠀⠀⠈⠝⡱⢣⣷⢰⣷⣼⡯⠤⢤⡘⣿⣿⢥⣒⡀⠀⠀⠀⠀⢙⣷⣷⡀
⢨⣇⠈⠻⣇⠀⠀⠀⠙⠿⢿⡆⠀⠀⠀⠀⠀⠈⢡⣿⢃⣿⠻⠋⡿⡎⠁⠈⠊⣿⣿⣤⠠⠤⡀⠀⠀⠀⠛⠿⣧
⢸⠾⠟⢄⣺⣇⡀⠀⠀⠈⢉⢳⣴⢂⠀⠀⠀⠀⠐⣣⠋⠃⠁⠐⠃⠀⠀⢀⣳⣿⣗⣂⠀⠀⠀⠀⠈⠉⠉⢛⣚
⠸⡄⠀⠀⠉⠻⣿⣄⠀⠀⠀⠠⢹⣾⡔⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡀⣠⣿⠯⠷⠦⠀⠀⠀⠀⢀⠀⡄⠀⡀⢀
⠀⠹⣗⡄⠀⠀⠙⣿⣧⠀⠀⠀⠑⠽⣷⣶⠇⠀⢀⠀⠀⢀⢀⣶⣿⣧⣿⣫⠥⠀⠀⠀⠀⠀⠰⠪⠓⠊⠆⢨⡠
⠀⠀⠈⠻⣵⣂⠄⠘⢝⣿⣄⠀⠀⠈⣪⢿⣿⣦⡮⠶⠴⣧⣿⣿⣾⡿⣓⡚⠃⠀⡄⣠⣤⠴⠀⠠⣵⡾⠖⠊⠁
⠀⠀⠀⠀⠈⠑⢿⣢⣀⠪⢿⣧⣄⠀⠐⢵⣿⣿⣿⣿⣿⢿⡿⠉⢰⣏⡖⠀⢠⡴⠋⠁⠈⣲⡽⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠳⢶⣀⠈⢿⣾⣀⢀⡉⢀⡽⠟⣡⢞⠃⠀⠘⣗⠏⠀⠋⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣬⡋⢿⣿⣿⣿⣶⠟⡡⠀⠀⠀⠀⠹⣭⡆⠀⠀⠀⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣲⣾⣿⣽⣟⣋⣀⣀⣀⣀⣀⣀⣈⣙⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣀⠤⠤⠤⣄⢀⣠⠤⠒⠒⠊⠉⠉⠀⠈⠑⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⢰⠇⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⡲⠶⣒⠚⠒⠚⠚⠋⠉⠉⠉⠁
⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢘⣶⣾⡉⢻⠳⢤⣈⣓⣒⣺⢷
⠀⠀⠀⣼⠀⠀⠀⣼⠀⠀⠀⠀⣀⣠⣤⣤⡾⣇⣸⠙⢧⣀⣀⣀⣈⣉⡤⠋
⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⢣⠼⠳⢤⣀⡀⠀⠀⣀⠃
⠀⠀⠀⢻⠀⠰⠆⢸⣦⡀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠉⣹⠉⠁
⠀⠀⠀⠘⢧⣤⠤⠼⠏⠉⠓⠒⠒⠒⠒⠒⠉⠉⠁⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢠⣶⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀⣠⣤⢶⢒⠞⠉⠁⠀⠀⠀⠀⠀⠈⠉⠘⠒⠐⠢⢀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⠹⣷⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣂⢆⢄⡤⠀⣠⢀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠉⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣷⡞⠃⠒⢦⣄⡀⠀⠀⠩⣏⠉⠉⠉⠉⠉⠉⠉
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠦⠄⢴⣶⣦⣶⣿⢿⣿⠿⠆⠢⠘⠀⠊⠉⠀⠀⠈⠁⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠀⠠⠗⠶⠛⠋⠉⠉⠈⣐⡇⠀⠁⢘⣶⣤⣆⣀⣀⣀⣲⡴⠃
⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⣔⠁⠈⠲⢄⡀⠀⠀⠀⠉⠉⠩⠛
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⢻⢧⠀⠐⣴⣄⡄⠀⠀⢄⢸⣎⠀⠀⠈⠙⠻⠶⣶⠦⠥⠔⠁
⠀⠀⠹⠿⢿⣿⡿⠿⠿⠿⠟⠛⠛⠊⠁⠁⠀⠿⠿⢿⢶⣤⠥⠬⠿⠓⠒⠦⠤⠤⠠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢠⢤
⠀⠀⠀⠀⠀⢠⢤⡀⠀⢸⡃⠸⡀⠀⢰⠃⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠸⡆⠀⢀⠇⢘⡇⠀⢀⡤⡄
⠀⠀⠀⠀⠀⢻⠀⢳⠀⠘⡇⠀⣇⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⣸⠀⢸⠃⠀⡞⠀⡟
⠀⠀⠀⠀⠀⢸⡀⠈⣇⠀⡇⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⢸⠀⢸⠁⢀⡇
⠀⣏⠙⢦⠀⠀⡇⠀⢸⡀⢹⠀⠘⡄⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢰⠃⠀⡏⢀⡇⠀⢸⠀⠀⡴⠋⣹
⠀⠘⣆⠀⢳⡀⢸⠀⠀⢇⢸⠀⠀⣇⡎⠀⢸⠀⠀⠀⠀⠀⡠⠒⡆⢰⠒⢄⠀⠀⠀⠀⠀⡇⠀⢻⡸⠀⠀⡇⡼⠀⠀⡇⢀⡞⠀⣰⠃
⠀⠀⠘⢆⠀⠱⡀⡇⠀⠈⠾⠃⠀⠈⠁⠁⠈⡆⠀⠀⢀⠞⠀⡰⠁⠈⢆⠀⠳⡀⠀⠀⢰⠁⠀⠈⠁⠀⠈⠷⠃⠀⢸⢀⠞⠀⡰⠃
⠀⠀⠀⠈⢦⠀⠙⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⣠⠎⠀⣰⠁⠀⠀⠈⣆⠀⠱⣄⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠋⠀⡴⠁
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠉⠁⠀⢀⠃⠀⠀⠀⠀⠘⡀⠀⠈⠉⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠲⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠋⠀⠀⠀⣤⣽⣿⣿⣿⣿⣶⣶⡦⠀⠠⠤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠚⠻⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠙⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢡⣾⠴⠿⠿⠿⠧⢅⡐⠦⣝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠂⠛⠉⠁⠀⠀⠀⠀⠀⢰⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⡇
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣇⡠⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣸⠁⠀⠐⠶⠖⠒⠒⠢⠤⣄⠀⠈⠻
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠄⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⢀⢀⡟
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢀⣨⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠐⠛⠋⠀⠀⠀⠀⠀⠀⠈⣿⠃
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢼⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⠀⡐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢉⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣦⣀⡀⠀⠀⠀⣀⣠⣶⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠼⣿⣿⠁⠀⠀⠀⠠⠤⣤⠄⣁⠂⠀⢻⣿⣿⣿⣿⠟⢿⡿⠟⠉⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⢠⣿⡇⠀⠀⢀⠀⠀⠀⣼⠟⣿⠀⠀⠀⠈⠉⠉⠉⠙⠒⠂⠀⢈⣿⣿⣿⠃⠀⠀⣰⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠐⠈⣨⣿⣇⠀⠈⠀⠀⠀⢰⠟⠘⣿⠀⠀⠀⠀⣀⣀⠀⠉⠉⠙⠒⢾⣿⣿⠇⠀⣠⡾⠃⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⣠⣶⣿⣿⠀⠀⠀⠤⢤⣲⣦⣤⣿⡄⢀⣤⣴⣿⣿⣿⡄⠀⢀⣠⣾⣿⣿⣶⣾⠟⣻⡦⠄⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣿⣿⣿⣿⣧⠀⢀⣴⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣤⣴⣿⣿⡿⠿⠿⠿⣏⠁⠉⠁⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠃⠺⠿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠿⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠙⠈⢦⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡼⠋⠀⠀⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀⡴⠋⠀⠈⠉⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡿⠁⠀⠀⠀⠀⠀⣾⠀⠀⠀⡔⠀⠀⠀⠀⢶⣿⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣿⡃⠀⠀⠀⠀⠀⣼⠿⠆⠀⡼⠀⠀⠀⠀⡀⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠒⠋⠥⢤⣀⣰⠃⠀⠀⠀⣼⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠞⠛⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣉⡤⠴⢤⣠⣠⣤⠄⣠⣤⣤⣀⣤⣠⣄⣄⣀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠒⠚⠉⠀⠀⢀⡄⠙⣿⡿⠛⠻⣍⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⢤⡄⣠⠄⠀⠀⠀⠀⠀⣰⣦⣶⣾⣿⣷⣀⡈⢓⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⠁⠀⢰⠃⠀⠀⠀⢀⣤⠿⠉⣽⡿⠤⣼⣭⣭⣭⡯⠠⠐⠏
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⣼⣆⠀⠀⠾⠛⠉⣠⣾⣿⣿⢶⣄⣦⣤⣠⣄⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠸⣿⣿⡧⠀⠀⢿⣿⣿⣤⣤⣶⣾⢟⣽⣿⣿⣶⣶⠠⣀⣄⠀⡱
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⡿⠁⠈⠈⠉⡩⠽⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⠤⣼⣿⠛⠛⠛⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡧⠐
⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿