⠀⠀⠀⠀⠀⣷⣭⣭⣖⣚⣯⠶⢈⣥⣖⣓⠦⢴⣶⡤⣀⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⢀⣠⣤⠞⠉⢉⠽⠖
⠀⠀⠀⠀⠀⡏⠩⠿⢗⣚⣛⣩⡥⠾⠏⣩⣛⠛⠿⠭⢌⡙⠦⠀⣰⣿⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠠⠔⠚⠋⡝⠁⢀⡄⠀⠀⠀
⠀⠀⠀⠀⠀⣗⣒⣖⣀⣀⣀⣀⣈⠭⠭⠤⠠⠤⠤⠀⠀⠀⠀⣼⠿⠁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⣀⢴⠃⠀⡸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡿⠿⠿⠿⠛⠛⠳⣶⣦⣤⣄⠀⠀⠀⠀⠀⢀⣾⣿⠋⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠈⠛⡿⠀⣰⠃⠀⠀⡄⠀
⠀⠀⠀⠀⠀⣗⡺⠦⠉⠩⠄⠀⢒⣂⠢⡀⢀⠀⠀⠀⢠⣿⠿⡋⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣿⡄⢠⠃⢠⠃⠀⠀⠀⡇⠀
⠀⠀⠀⠀⠀⣷⣶⣶⠤⠭⠗⢒⠨⠭⠅⠀⢀⣀⠤⣴⣿⣿⣿⣤⣾⡟⢉⣙⡓⠶⠦⢄⣀⡀⠀⠀⢸⣿⠈⣿⣧⢸⢀⠏⠀⠀⠀⢸⠀⠀
⠀⠀⠀⠀⠀⡯⢾⣒⣊⠭⢕⡀⠌⣀⡤⠚⣉⠴⡾⠿⠛⠉⠉⠀⠀⠀⠉⠿⠶⠭⠷⣦⡀⠸⡉⠓⢾⣿⣤⣿⣿⠈⣿⡀⠀⠀⢠⠇⠀⠀
⠀⠀⠀⠀⠀⣯⢽⢖⣋⡩⣖⣨⠟⠁⠀⠀⠀⠀⠀⢀⣠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⡰⠈⠙⣻⢿⣿⡆⠹⡍⠉⠉⠹⣄⠀⠀
⠀⠀⠀⠀⠀⣗⣿⣟⣲⢍⣠⠋⠀⠀⠀⠀⣠⣶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⡻⢦⣜⢮⡀⠀⣀⡩⣅
⠀⠀⠀⠀⠀⣿⣿⣟⣮⡟⠁⠀⠀⠀⢠⡞⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠪⡪⡻⣷⡹⣿⣝⢮⣂
⠀⠀⠀⠀⠀⣿⠾⣿⠏⠀⠀⠀⠊⢠⣮⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⢸⠀⠀⢠⡀⠀⠙⢞⡜⢿⡄⡙⢷⣮
⠀⠀⠀⠀⠀⣗⣿⡟⠀⠀⠀⠎⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⡰⠔⢀⡼⢸⠘⣇⠀⠀⢇⠠⠀⠈⢢⡈⢿⣦⡱⠙
⠀⠀⠀⠀⠀⣏⣺⠀⠀⠀⡜⣠⠯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠜⢹⠡⠀⢠⠃⣠⢾⢁⡏⠀⣿⡰⠀⠸⡀⢷⠀⠀⠱⠈⣷⣥⣴
⠀⠀⠀⠀⠀⣿⡏⠀⠀⡸⢡⠋⠀⠀⠀⠀⢀⣴⠇⠀⠀⢀⡤⠋⣠⠏⠀⡏⠀⠰⢃⡔⢁⠇⣸⠃⠀⠸⣱⢇⠀⠇⠈⡆⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⢸⣡⢠⠀⣷⢏⠀⠀⠀⠀⡠⡺⠃⠀⠀⡠⠊⠀⡴⣅⠀⣸⠀⢀⡴⠋⢜⡎⢠⡏⠀⠀⠀⢏⡾⡄⠘⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⡿⢻⢮⢀⠇⠂⠀⠀⡠⡪⡾⠃⠀⣠⠞⡡⢪⣞⠻⣽⣻⡇⡠⠋⠀⢀⡞⢀⡾⠁⠀⠀⠀⠸⣱⣣⠀⠀⢀⣠⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⣇⡆⡜⡀⠀⠠⢚⣼⠟⠁⠀⠜⡡⢘⣵⡿⣾⡇⢀⣿⠞⠀⠀⣠⠎⢠⣾⠁⠀⢀⣠⡤⠒⢣⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡷⡽⠶⡷⣄⡀⢠⠞⠁⠀⢀⢤⡺⡾⠛⠿⣟⠽⢡⢟⠁⠀⣀⡴⠋⣰⡟⢁⣠⠾⢋⣫⣽⣧⣌⣻⡆⠀⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡽⠀⠀⢱⠸⣟⢶⣶⠶⢖⡊⢡⠞⠁⠀⠀⢀⡴⠁⢀⡠⠞⢉⣠⠞⠉⠀⠁⢠⢴⣿⣿⣿⢷⠉⢷⡇⠀⣶⣿⡿⣿⣧⣌⢿
⠀⠀⠀⠀⣸⠁⡀⠀⣁⠀⢻⣌⣑⠂⣠⠔⠁⠀⠀⠀⣴⣿⣾⣚⣩⠶⠛⠉⠀⠀⠀⠀⠘⢆⠈⢯⣿⢿⡟⠀⠀⡇⠀⢹⣟⣿⠧⢤⣽⠿
⠀⠀⠀⠀⢻⢸⡇⠀⢏⠀⠀⠙⠛⠉⠁⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠙⠒⠶⠋⠉⣷⠀⠈⢿⡛⠋⢉⣾⣾
⠀⠀⠀⠀⠈⢧⠹⣄⠈⣦⡀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄⠘⣿⡄⠉⢉⣱
⠀⠀⠀⠀⠀⢸⣆⠀⠉⠛⠓⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⡄⠸⣿⣦⣝⣿
⠀⠀⠀⠀⠀⢸⢸⣦⡀⣀⣤⣦⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣧⣯⣍⣑⠦⡀⠀⠀⠀⠀⠀⠀⠀⡟⡀⠃⠁⢄⠙⣭⣽⣿
⠀⠀⠀⠀⠀⢸⢸⡆⠉⢺⣏⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣟⣼⡇⠀⠀⠀⠀⠀⠀⢠⠇⡇⢰⠀⢸⡆⠈⣿⣿
⠀⠀⠀⠀⠀⣿⢈⡇⠈⢸⣿⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣼⢰⠁⡌⠀⢸⡇⠀⣿⣿
⠀⠀⠀⠀⢠⣿⢸⣧⠀⢸⣿⠀⠀⠳⡀⠀⠀⠀⢠⠒⠛⠢⡨⡇⠀⠈⠻⣿⠿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣼⣿⠘⢀⠇⡄⣿⠃⢰⣿⣿
⠀⠀⠀⠀⢸⣿⢸⣿⢸⢸⣿⠀⠀⠀⡝⠓⠲⣤⠇⠀⠀⠀⡇⣧⠀⠀⠀⠀⠀⢹⣿⡁⠀⠀⠀⠀⠀⣠⣿⡿⣿⢠⢸⠀⣿⣿⠀⣾⣿⣿
⠀⠀⠀⠀⢸⣿⢸⣾⠈⣼⣿⠀⠀⣸⠁⠀⠀⣹⠀⠀⠀⢠⠇⠘⢆⡀⠀⠀⢀⣼⣯⡇⠀⠀⠀⢀⣼⣿⣞⢳⡇⢸⠁⠀⣿⣏⠀⣿⣿⣿
⣀⡉⠘⠛⠻⣿⢸⣿⡄⢻⣿⠀⢀⠇⠀⠀⠀⡿⠀⠀⠀⣸⠀⠀⠀⠉⠛⠛⠓⠛⠁⠀⠀⢀⣴⡯⣟⢿⡟⣾⡇⡏⡀⢀⣿⣿⣦⣌⠙⢿
⠓⢜⢄⢠⠖⠋⢻⣻⣇⣦⢸⡀⡾⠀⠀⠀⣠⠃⠀⠀⠀⡟⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠁⠀⢸⣿⡹⣽⣿⠝⢧⣼⣿⡿⠋⢿⠀⣿
⠀⠀⠀⢻⠀⠀⠀⣷⢹⢹⣿⣸⠁⢀⡠⠖⢹⠀⠀⠀⠀⡇⠀⠉⠲⢤⣀⣀⣀⠴⣚⡽⠋⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⢸⠀⠀⠀⢹⡟⣄⠛⡇⠀⠀⠀⠀⡎⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡦⠀⠀⢸⠀⠀⠀⣸⣽⢙⣿⠀⠀⠀⠀⢰⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⣀⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⢸⠀⠀⣰⢻⡇⣿⡇⠀⠀⠀⠀⡜⠠⣀⣀⠀⡏⠈⠙⡄⠀⢠⣖⡿⠁⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⡾⠀⠈⠀⣾⡇⡸⠀⠀⠒⠲⢠⠇⠀⠀⠀⢠⡇⢠⡋⣹⣠⣮⠋⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡇⠀⠀⠀⣿⣧⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⡸⢀⣾⣿⣿⡿⠃⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠇⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣧⣾⣿⣿⠏⠀⠀⠀⠀⢒⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⡀⠀⡿⡃⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⢀⡀⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣶⣶⣶⣿⣷⣶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⢸⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⣿⣿⣿⣸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣿⣿⣿⣿⡏⠿⢺⣿⣿⣿⣿⣿⣿⠟⠃⠠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠥⠙⠉⠉⠉⠉⠉⠀⠀⠀⠀⣿⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⢿⣿⠁⠀⢀⠠⠭⠭⣙⠛⣂⠄⠀⣰⢿⣿⢿⠷⣪⠟⣹⡯⣿⢟⣿⣿⣿⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⢱⠻⡺⣿⣄⣶⠬⣶⣶⢶⣾⡄⠀⠀⠈⠁⠁⠀⣠⢷⡟⣿⣹⠙⣓⢺⣿⡿⣏⠔⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⢇⣇⣿⡏⢶⣀⣷⣾⣿⢁⡹⠀⠀⠀⠀⠀⠀⠀⠹⠹⠿⡿⠿⠏⣿⣿⣶⠹⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡣⡹⠈⢿⡀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⢇⡘⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣬⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠊⣡⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠚⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣆⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⣿⣿⣿⣿⣷⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⢄⠀⠀⠀⠈⢉⠁⠀⣉⣉⡁⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⣿⣿⣿⣿⣿⠀⠑⢄⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⡠⠊⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣿⣿⣿⣿⣿⡇⠀⠀⠑⠢⢀⠀⠀⠀⠀⣀⠴⠊⠀⠀⢸⣿⣟⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠻⣿⡇⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⡜⣛⠺⢟⣻⡟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⣿⡟⢰⣍⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⡙⢧⠺⣑⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡤⢞⠻⣋⡝⠀⠀⠉⠉⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠞⠀⠈⡎⠿⡣⡅⡋⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⢖⡭⠍⡱⢡⢊⡝⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⣄⡀⣀⡠⠔⠊⠁⠀⠀⠀⠀⢯⢧⡹⡬⣱⢘⠤⣉⢶⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣾⢃⣖⢒⡩⢌⡓⢌⡾⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠑⢫⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⢔⠖⢧⠱⣈⢶⡒⢌⢫⢿⢆⠀⠀⠀⠀
⠀⢀⣀⢤⣒⣞⢭⣳⢌⣴⠼⡌⢖⣌⢶⡁⠸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⢀⠤⢰⢣⠀⠀⠀⠀⠀⠀⠀⣸⠈⢞⡈⣧⢮⡖⡬⢃⡱⢫⢯⡷⣢⣄⣀
⡊⠵⡨⣱⢋⣯⢋⡟⡡⡊⡕⢋⢎⢱⠋⠇⡇⡈⢆⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⠈⠚⢸⠈⢧⠀⠀⠀⠀⠀⢀⠇⢣⡈⠁⢘⡦⣜⡵⠩⡑⠎⡜⣧⢛⢦⠱
⢌⣲⢝⣱⣹⣣⢎⣰⣃⢖⡩⢖⢬⠇⢸⠀⡱⠁⠈⢧⠀⠀⠀⠀⠀⡼⢍⡂⢼⠀⠀⢸⠈⠈⢇⠀⠀⠀⠀⡞⠀⢠⠇⠀⡌⠱⣢⣎⠥⡣⡩⢜⢻⢧⢊⠧