⠀⠀⠀⠀⠀⢠⠇⢸⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢠⠸⡄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢷⡘⡄⠀⠀⠈⣦⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣯⢻⠀⠀⠀⢋⢣⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡍⠀⢼⠀⠀⠀⡈⡆⠀⠀⠀⠀⠀⠀⡇⠘⡄⠀⠀⠀⠀⡀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢸⡭⢧⣃⠀⠀⠘⡄⢳⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⡰⠁⡇⠀⠀⠀⠀⠀⠀⠸⡀⢳⡀⠀⠀⠀⢹⠀⠀⠸⡀⠀⠀⠀⠀⠀⢸⡆⢿⠙⣆⠀⠀⢱⠀⠹⡦⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⠀⡇⠀⣿⠀⢠⠇⢵⢷⠀⢸⡀⠀⠀⠀⠀⢧⠈⣧⠀⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⠀⢠⠀⡇⠀⠱⣼⣆⠀⡀⢇⠀⠙⣝⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⡇⠀⣿⠀⡞⠀⡿⣸⡀⠀⣇⠀⠀⠀⠀⠘⡆⠸⣆⠀⠀⠀⢹⠀⠀⡇⠀⠀⠉⠉⣹⠉⡏⠒⠂⠐⢽⣦⠐⢈⢆⠀⠈⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⡇⢈⣿⣾⠃⡼⠀⣿⣇⡀⣸⡆⠀⠀⠀⠀⠘⡆⠘⣄⠀⠀⠈⡇⠀⡇⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠈⠻⣦⠀⠘⣦⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⡇⢠⣿⡇⢸⣃⠜⢣⣿⠀⠘⣿⡀⠀⠀⠀⠀⠸⡄⠸⡄⠘⡀⢻⠀⠇⠀⠀⠀⢸⡿⢠⠇⠀⠀⠀⠀⠀⠣⣇⠀⠸⣤⣜⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⢹⣇⣸⣿⣺⠃⠀⠀⠈⣿⡆⠀⢧⢷⡀⠀⠀⠀⠈⠹⣄⠹⡄⢣⠘⡆⢸⠀⠀⠀⣾⠃⢻⠂⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡇⠠⣿⣏⠐⡿⠁⠀⠀⠀⠀⠘⣷⠀⢸⡆⢳⡀⠀⠀⠀⠀⠘⢗⡼⣎⡆⢱⠸⡀⠀⡼⠃⢘⡘⠀⢀⣀⣀⣀⣀⣀⣀⣀⠙⢦⡈⢻⡀⠀⠀⠀⠀⢠⠄⠀
⠀⠀⡇⠀⠿⢃⠘⡇⠀⠀⠀⠀⠀⠀⠘⣆⠀⣷⠙⢷⣄⠀⠐⢄⠀⠀⠱⣼⣿⡀⢇⡇⡼⠟⣻⣿⣧⣥⣴⣿⣶⣾⣿⣿⣿⣿⣿⣶⣽⣦⣙⣮⣤⡴⠞⠉⠀⠀
⠀⠀⡇⠀⣰⠻⡄⣇⠀⠀⠀⢀⣚⣉⣉⡘⢆⠘⣇⠀⠘⢦⣄⠈⠐⢇⡀⠀⠉⢿⡾⣟⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣶⡀⠉⠉⢻⣿⠛⠷⣄⠀⠀⠀⠀
⠀⠀⢱⠀⢸⠀⡇⣇⣒⣞⣯⣥⣦⣾⣭⡉⠈⠢⡹⡄⠀⠀⠉⠳⢤⣀⢙⠦⣀⠈⢿⣜⢏⠀⠐⣿⡿⣽⡟⠿⣿⠞⡙⣯⣟⣿⡇⠀⠀⣸⡏⠀⠀⠈⢙⠫⠗⠲
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠻⣄⠀⠀⠀⠀⠈⠉⠑⠚⠓⠬⣫⡙⢦⡀⠹⣿⡽⣆⠡⠌⡒⢤⣟⠾⣼⡇⠀⢠⢿⠀⡠⠀⠀⢸⠀⠀⠀
⣄⣤⣴⣾⣿⡟⠻⡿⣿⣿⢿⡿⢯⣿⠞⢳⡿⣧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠹⣿⢭⠳⣜⣰⡟⡜⣫⣼⣡⠴⠫⢼⠀⣿⠀⠀⢸⠀⠀⠀
⠀⠀⠀⢿⢿⣷⠀⠘⣟⢿⣻⣄⠢⢉⡐⣸⠻⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠾⠽⢶⠾⠛⠻⣋⣁⠔⠁⡞⢸⢸⠀⠀⡜⠀⠀⠀
⠀⠀⠀⠸⣆⠙⡷⡄⠙⣌⢿⣯⢳⣆⣴⣃⣟⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⠃⣾⢸⠀⠀⡇⠀⠀⠀
⠀⠀⠀⠀⢻⣆⢱⡈⠲⢤⣭⣽⣽⡟⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⣻⢸⠀⢀⡇⠀⠀⠀
⢦⠀⠀⡀⠀⠻⣦⢳⠈⠲⠯⠤⠘⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⠏⢽⡎⠀⡼⢀⢠⠀⠀
⢄⠳⡄⠂⠀⠀⠙⣧⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣡⠋⠀⣾⠇⣰⠇⡎⠨⠀⢠
⠀⠑⢬⡲⣌⠓⢤⣈⠻⣕⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⠊⠀⠀⠀⢸⢰⡟⣰⠁⠀⢠⠎
⠀⠀⠰⢹⡙⠓⠦⣙⣷⣬⠷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⡴⠃⠀⣠⠋⣰
⠀⠀⠸⡀⡇⢣⠀⠀⠩⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⣀⠠⠔⣪⣵⠞⢁⣠⠞⣁⡼⠋
⠀⠀⠀⡇⢹⢸⠀⠀⠀⢣⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢉⣩⠍⡾⢉⡴⡏⢀⠀⠀⠀⠀
⠀⠀⠀⡇⠘⡆⡇⠀⠈⡿⣼⡈⠗⣦⣄⡀⠀⠀⠀⠀⡠⠖⢉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣟⣍⣠⢞⡵⠋⠀⡇⠘⠀⠀⠀⠀
⠀⠀⠀⡇⢸⣷⠇⠀⠀⡇⡧⡁⠀⠈⠙⡩⡷⣴⠴⠊⠀⠒⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⠙⠛⣛⡟⠀⠀⠀⡗⠀⠀⠀⠀⠀
⠀⠀⢀⡇⣼⢸⡌⠀⠀⢱⢹⠄⠀⢀⠔⢣⠞⠁⠀⠀⢀⡴⣅⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡖⠊⠁⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⣀⡇⠀⠀⠀⠀⢀
⠀⠀⢸⠀⡇⠈⡇⠀⠀⢸⢸⠂⢢⢪⡞⠁⠀⠀⣤⠚⣽⡖⠈⣭⠛⢲⣤⣤⣤⣤⡖⠚⢩⢡⠊⣿⠀⠀⠀⠀⠀⠀⠀⣴⣾⠋⠀⢠⣤⠒⠋⢡⡇⢠⠀⠀⠀⢰
⢠⠂⡸⢀⡇⠈⡇⠀⠀⢸⢸⢂⡴⠋⠀⠀⢀⣾⠡⠀⢸⡇⠈⠀⢂⡁⢻⠩⢋⡟⠐⡈⡾⢈⠄⣿⣀⣀⣀⣀⣀⣐⡶⢯⠤⠒⠛⡉⠄⠣⠘⡀⡇⢸⠀⠀⠀⢸
⡎⠀⣿⢸⠁⢰⡏⠀⠀⣼⣸⠋⠀⠀⢀⡴⢃⢸⠀⠀⢘⡇⠀⠀⠠⠁⢸⠀⡾⠐⢂⣐⡇⣆⢸⢻⡭⢯⡝⢯⡟⢣⠑⠌⣀⠃⡡⠘⣈⣴⣱⠴⡗⠸⠀⠀⠀⣞
⠇⢸⢳⡞⠀⡞⢸⠀⢀⡿⠁⠀⠀⣠⠏⠃⠑⢸⠀⠀⢸⠁⠀⠀⠀⢆⣺⢰⠇⣉⣤⣾⣼⣶⣿⣿⡧⢳⡜⠯⡘⢄⣊⣴⣤⠦⠵⠚⠋⠉⠀⠀⠄⡏⠀⠀⠀⢸