찐 으갸갸갹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣴⣿⣿⣿⣿⣿⣿⣿⣾⣶⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠿⣟⡟⠿⢿⣿⠟⢿⠙⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠈⠁⠈⢂⢂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⡫⡱⢂⡢⠤⠑⢂⠀⢀⣀⣀⡀⣀⠓⣆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣦⠵⣹⣦⠥⣘⢈⢡⣾⣿⣿⣿⣿⡟⢫⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⢙⣛⣷⡟⠃⠀⠀⡰⢟⢏⠓⠿⠛⠋⢇⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣣⠿⣿⣏⠅⣰⢾⣇⢲⡝⣁⣀⣀⣤⣒⣒⡁⢺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⢰⠟⢯⣥⣖⣿⣚⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠃⠀⢀⣿⢇⠇⠀⣼⣿⣿⣿⣻⣿⣿⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣠⣤⣤⣀⣸⣵⣟⢢⠐⠫⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠻⠷⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⢀⣀⣴⠶⢛⣋⣝⣳⣟⣛⣩⣭⣭⣭⣭⣿⡏⢦⡀⣉⣣⣶⣿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣠⡴⢚⣋⣭⣴⠾⢛⣉⣭⣭⣭⣭⣥⣾⣭⣭⣥⣿⣿⢁⡔⣫⢵⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢡⠶⢛⣩⣤⡶⠾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⣏⠲⣥⢻⡾⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣍⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⣛⣷⢃⠀⠀⠀⠺⢛⣩⣥⣤⣶⣶⣶⣿⣿⣿⣷⣶⣦⣤⣄⣤⠸⠿⢿⡷⣞⣿⣿⣿⣿⣿⣿⣿⡿⠉⡝⣡⠰⠶⠮⣅⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡵⣻⣡⣺⣶⣿⣿⣆⣠⢶⣿⣿⣿⣿⢿⣻⠉⠁⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠘⡿⣩⣑⣢⢄⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣆⠀⠀⠀⢻⣿⣻⣿⣿⡿⣿⢟⣻⣾⣿⣟⣿⣻⣓⠎⠁⡰⣋⣹⠟⣛⣿⢿⡿⢿⡏⠉⠉⠉⠓⠪⠻⣿⣿⣿⣿⡿⠥⠐⠀⡞⣱⠛⡙⣩⢆⡞⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⢻⠟⣫⢳⣙⢎⠯⣘⣿⢱⣾⣿⣯⣷⢞⡴⣋⣥⡾⢟⣛⣩⣼⣶⣿⡟⠻⠿⠿⣿⣿⣷⣷⣿⣿⣿⣥⡄⠀⢀⣹⣽⣵⣵⣶⣿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠤⠐⢺⣿⣿⡀⢂⡂⠬⢵⣃⠛⠷⢬⢥⣼⣣⣿⣻⣟⣾⣣⣾⡝⠓⣸⣵⡾⣛⣭⣶⣿⡟⣿⡀⠀⠀⠀⢠⣿⣿⣿⣿⣯⡟⠛⢉⣻⣾⣿⣿⣿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⡿⡓⢮⢀⣠⣾⣿⣿⣧⣄⢹⡜⡈⣹⣲⣞⣿⣾⣟⣷⣿⣿⣿⣿⣟⣯⠖⣹⣭⣥⣽⣽⣾⣛⣟⡇⠀⠁⠀⠀⣠⣾⡿⠛⢿⣿⣟⣀⠀⡼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⠚⣿⢡⡔⣡⣽⣾⣿⣯⣿⣿⣿⣿⣿⣷⡅⣿⡷⠟⠊⠉⡿⢿⣿⣿⣿⣿⣿⣿⣾⠿⠟⣿⡿⡻⠭⠭⠭⠟⡅⠀⠀⠀⣀⣹⣿⣿⣷⣾⣿⣦⣺⡏⠀⠉⣽⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⢹⠇⣿⣸⣾⣿⣷⣿⣿⣿⣿⣿⢟⣿⣿⡿⢿⠿⠋⠉⠀⠀⠀⢸⢰⡼⢿⣿⠷⣭⣍⡒⠬⠩⠽⢷⣶⣶⣶⣶⣞⣿⠯⠗⠛⠉⠉⣼⣿⣉⣿⣿⢻⢿⣿⣧⡉⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣟⡽⣳⣟⣿⣻⢿⣿⣿⣿⣯⣥⣵⣟⣷⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⠟⢈⣿⣌⠻⣦⣄⠉⠛⠷⢶⣺⣿⣛⡿⢿⣯⣥⡽⠠⠀⠀⠀⠀⣿⠷⣹⣿⢧⡻⣾⢃⠙⢷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⣴⣾⣽⣎⡿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣸⡌⠛⣽⡟⠉⠓⠆⠀⠁⡿⣿⣟⣛⣿⣖⣦⣧⣀⣀⠀⠀⢿⣿⣿⢸⣿⣾⣷⡟⠈⣧⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⠤⠄⠠⠤⠤⠤⠄⠐⠒⠘⢻⣳⣶⣯⣯⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣤⢼⢧⣸⣿⣀⠀⠙⠂⠀⢀⠇⡈⠛⠿⢿⣿⣿⣉⡙⠛⠿⣿⣶⣾⣬⣤⣉⣻⠋⢀⣀⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡰⠡⣁⣰⣄⠀⠀⠀⢀⠀⠐⣡⣷⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡻⠉⠿⢳⢽⣯⡈⠛⠄⠀⠀⣸⢹⡐⡛⢿⣷⣶⣭⣉⡉⠁⢀⣀⣿⣿⣿⣿⣿⠿⠷⣦⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⠁⣰⣿⣿⡿⠟⢂⠔⣩⣤⡾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⣾⡧⠭⠄⠀⠀⠀⣏⢷⣱⡉⢞⣷⡏⡉⠛⠛⠓⠀⠞⢉⠉⡙⢻⡏⠈⠙⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣿⠽⢛⡋⢀⣦⣧⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢠⣿⠁⠀⠀⠀⡀⢸⡙⠾⣳⢿⣄⣸⠑⠚⠽⠿⠞⢷⣿⣿⣿⣿⣷⣧⣒⣈⣿⣿⡟⣌⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⡿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣀⣢⠟⣾⡓⣶⡒⣶⣧⣄⣾⠽⣿⡿⣿⣿⣷⣧⣀⠀⠀⠀⡏⢦⡉⠍⢻⠀⠉⢃⣹⣿⣿⣛⠈⡁⠀⣦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⡶⠁⣼⣿⠅⠘⠚⠛⠛⠻⣿⣷⣦⣄⠀⠀⢸⠀⠀⠉⠒⠀⢣⡀⠙⠛⢟⠓⠈⢠⣿⣿⣿⣿⣇⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣠⠏⠀⢠⣿⣿⠀⠀⠀⠀⠀⣔⣀⣤⣭⣽⣿⣿⣿⡾⠿⠟⠛⢻⡿⣿⢿⣿⡞⠒⠒⠂⠉⠙⠿⢿⣿⣟⠿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠘⠁⠀⠀⣼⣿⢻⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⣼⠒⢡⡎⢸⠀⢠⡌⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠠⠊⠀⠀⢰⣿⠿⠁⠀⢀⠊⣼⣿⣿⣿⣿⣿⣿⡟⡤⢁⠈⠁⠀⢠⣷⣿⣶⣶⡾⠔⢁⠂⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢠⠟⣽⣫⡟⢿⠻⡟⠉⠉⠓⠒⠄⠀⠞⣡⣈⣄⣡⠧⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⠃⠀⠀⢠⣾⡟⠁⠀⠀⣀⣀⣀⣾⣹⣒⣥⣼⣤⣷⣧⣤⣤⠤⠶⠶⣶⠿⢿⣿⡽⠯⢒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣⠃⠀⠀⢀⣺⡿⠁⣀⢆⡱⣎⣶⣿⣿⣿⣿⣿⣿⣿⠛⠋⠙⠒⠒⠲⣤⣷⣴⣶⣭⣵⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⢤⣄⡠⠷⣿⢁⠔⠂⠀⠀⠈⣿⣏⠛⠹⠻⢟⡿⡧⠶⣤⣤⣤⠒⠉⣟⣹⣯⣿⡟⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠇⠀⠀⢀⣼⡇⢡⣾⣆⠀⠀⠀⡇⣚⡹⢣⣄⣀⢸⠀⠀⠀⠈⠙⠋⢓⣷⣋⢞⡜⡁⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡸⣿⡇⠛⠿⠿⠇⠀⠀⠇⠁⠙⠛⠿⢿⡿⢲⠤⣄⠀⠚⢸⣿⢿⣿⣿⠇⠓⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢠⣽⡿⡇⠀⠀⠀⠀⠀⠀⢰⠀⠆⠠⠀⠀⢇⠀⠑⠮⣑⢄⢺⠻⠯⡍⡏⠀⠀⠀⢘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣴⣿⣿⣋⡏⠉⣉⣀⣀⣀⣀⣸⣿⣿⣿⣿⠶⢺⠤⠀⠀⡀⠉⢻⢧⣀⡐⢘⠀⡀⣞⡡⠚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣶⣶⣿⣿⣿⢿⡏⠉⠉⠁⠀⠀⠈⠉⠛⢿⣮⡱⢛⢿⣶⠦⠤⢄⣈⣾⣿⣷⣿⢟⡈⠄⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠍⠉⠉⣹⡏⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠤⠽⠃⠀⣮⣛⣭⢾⡿⠋⠉⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀