⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⣰⠋⠀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⠖⡗⡞⠢⣀⣴⣷⡢⢄⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣾⢺⣀⢸⠁⠀⣹⠤⣆⠈⡆⠛⠺⢥⣼⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠉⠑⢤⡀⠀⢀⣠⠤⠖⠒⠚⠋⠉⠉⢏⠀⡸⢳⣲⣁⣤⢸⡗⠛⢻⠲⣼⢿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢲⠀⠀⠀⠀⠹⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣤⠀⠁⠛⠫⢿⠀⠘⠚⠋⣼⢸⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⢶⡄⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢯⡇⠀⠀⠀⠈⠳⢤⣤⢴⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⣳⠟⠒⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢇⢠⣾⡗⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠉⠚⠚⣼⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠶⠞⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡀⠀⠀⡀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⢀⠇⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢃⠢⡀⠈⠤⡀⠡⡀⠀⠀⠀⣠⣀⡀⣸⠀⠀⠀⠘⣦⠀⠀⠀⠀⠇⠀⡌⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣥⣳⡈⠢⢄⡈⠐⠬⣒⣄⡘⡇⠀⠉⢻⠦⣄⡀⣠⠞⠂⠀⠀⡘⠀⡜⢡⣾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⣟⠳⠦⢌⣁⠒⠒⠽⠿⠿⡀⠀⠀⢱⢻⠫⡍⠙⢆⠀⡴⢡⠊⣠⠟⢧⣥⢻⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣉⠲⣄⡘⠾⣿⣶⣄⠀⠈⡉⠒⡾⢡⠂⠰⠀⢸⣪⣒⣵⠾⣕⣋⡹⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢹⠆⠈⠙⠃⠀⠀⠹⠿⠶⠩⣴⣁⠴⢋⣉⠤⠤⠿⢦⡤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣹⡓⠤⣄⡀⠀⠀⠀⠀⢀⣤⠛⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣏⣤⡤⢄⡀⢤⠿⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠈⠑⠠⣙⠓⢤⡤⠔⠛⠛⠓⠒⠠⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⣀⣤⢴⣿⣟⣫⠧⢤⡀⠀⠉⢻⡀⠀⠀⣠⠴⠚⠉⠀⠀⠉⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠈⠰⡄⠘⣦⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⢴⣩⣽⡏⠁⠀⠀⠈⣢⠀⠀⢁⢀⡞⠁⠀⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠈⢃⠀⠁⠠⣀⣴⣾⣢⡀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢹⡆⠀⠀⠀⠀⠘⣆⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⡤⠇⠀⠀⠀⠻⠿⠳⠀⠀⠀⠀⠙⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣠⠟⠀⠀⠀⠀⠀⠀⢹⣛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣏⠠⣚⣆⣠⠶⣄⠀⠀⠀⣀⣤⣀⣿⡶⠋⠀⠀⠀⠀⠀⠀⠀⠘⡟⡏⠳⣄⠀⠀⠀⠀⠀⠀⠀⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠑⠦⣄⡀⠀⢀⣀⣀⣀⣀⣤⣤⠶⡾⢵⣲⣿⣿⡿⠀⠈⣱⢻⡟⠉⠀⡘⢛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡄⠙⣗⠶⢤⣤⣤⡴⠞⠁⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣩⠟⠉⠀⠀⠁⠀⠈⠁⣰⣿⣏⡁⠉⠀⠀⠀⡼⣦⠏⠀⠀⠰⠁⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⠀⠘⡆⠀⢀⡇⠀⠀⠀⠀
⠀⠀⠀⢀⠟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣞⡏⣿⣛⡿⢅⣀⠀⢀⠗⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢿⠀⠀⢹⣤⡞⠀⠀⠀⠀⠀
⠀⠀⠀⡼⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠙⠣⠤⣟⣺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠁⠀⢸⠀⠀⠈⣯⡀⠀⠀⠀⠀⠀
⠀⠀⠀⣇⠀⠀⢷⡀⠀⣀⣶⠶⡶⠉⠉⢿⠰⢶⣰⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠉⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢿⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢰⠀⢸⡇⠀⠀⠏⢷⡀⠀⠀⠀⠀
⠀⠀⠀⡇⠀⠀⣠⡝⠋⡽⠃⡜⣄⠀⠀⢈⠆⢣⣴⠇⡏⠉⠉⢛⠒⢒⠲⢲⣶⡶⡶⠞⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠑⢦⣄⡀⠀⠀⢀⣀⣀⡤⠖⣋⡀⠀⠀⠘⠀⢸⡇⠀⠀⣴⠈⣣⠀⠀⠀⠀
⠀⠀⠈⣇⢀⣼⠁⠉⠉⠁⢻⣉⡏⠁⠂⠉⢸⠉⠉⢳⠈⣰⣶⡁⠐⢯⡗⢈⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⡞⠀⠉⠉⠉⣩⠉⠁⠀⢀⡇⠙⡄⠀⢘⠀⠰⡇⠀⠀⢻⢀⡾⠀⠀⠀⠀
⠀⠀⠀⠈⢿⠃⠀⠀⠀⠀⠀⡴⠋⠉⠑⡄⢈⢗⡋⠁⢭⡀⠀⢀⡇⠙⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠸⠀⠀⠀⠀⡞⠁⠳⡄⠀⠈⢳⣈⡕⠀⢈⠀⢰⡇⠀⠀⢸⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠳⢀⣀⠴⠃⠐⠴⠃⣞⡇⢩⢭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠇⠀⠀⢸⡉⢧⡴⠺⡤⠒⣤⣟⣿⠂⠀⡸⠀⢸⠇⢀⡴⠋⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣸⠀⠀⠀⢸⠃⠘⢦⡔⢧⡴⠻⠼⣭⠇⠀⣃⠠⠿⡞⠋⠀⠀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⡇⠀⠀⠀⠘⠀⠀⠘⠶⠎⠙⠳⠲⣼⠆⠀⡇⠀⠀⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⣠⠾⢤⣀⠀⠀⠀⠀⠀⠐⣤⡆⠀⠀⠀⠀⢀⣴⠀⣀⠼⠋⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢰⡅⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⢀⡇⠀⢐⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⢠⡽⠉⠓⠒⠖⠶⢿⡄⠀⠀⠀⠀⢸⠛⠉⠘⣦⠀⠀⠐⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⢸⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⢀⡴⠋⠀⠀⠀⠀⣀⠴⠚⡟⠀⠀⠀⢠⡮⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⢸⠀⠀⠀⠈⢧⠀⠀⠏⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⣠⠟⠀⢸⠀⠀⠙⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠸⡄⠀⠀⠀⢠⠞⠁⠀⠀⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠸⡷⣄⡀⠀⠘⢍⡲⠤⡄⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠛⠉⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⣧⠀⠀⢀⡏⠀⠀⠀⠀⠈⠲⣄⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⢷⠀⠙⢦⡀⠀⢹⢖⢁⣔⠱⠮⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠸⡆⠀⢸⡀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠹⡄⠀⠀⠀⠀⠀⡖⡦⠀⠀⠀⠹⡄⠘⣆⡠⣄⠘⢳⡏⢨⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀
⠀⠀⠇⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠙⢆⠀⠀⢀⣀⢳⠃⠀⠀⠀⠀⠹⡄⢹⣄⣰⡣⡤⠷⡆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀
⠀⠀⢸⠀⠈⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠱⡄⠈⠳⡀⠘⢆⡟⢪⠇⠀⠀⢰⠢⣿⡄⠻⡄⢝⡷⡞⠛⢿⠑⣢⠀⠀⠀⠀⢰⣦⠀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡉⢦⣠⢤⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀
⠀⠀⢸⠀⠀⡇⠀⠀⠀⠠⣶⣻⣿⠄⠀⠀⠹⡄⠈⠙⢦⣰⠉⠉⠀⢀⡰⣗⣷⠷⣷⣤⠙⡞⠀⣸⣶⢛⡟⢣⡰⠲⡆⠀⠀⡇⠀⡳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⢻⠐⠂⠁⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠀⢀⡴⣆⠀⠀⠀
⠀⠀⢸⠆⠀⣇⠀⠀⠀⠀⢀⠏⠉⠀⠀⢠⠤⣹⡄⠀⠀⠻⡄⢀⡤⣾⣿⡬⢼⠉⠉⣹⡄⠻⣶⠃⠈⣉⠷⣤⣇⡴⠃⣄⡴⣼⡴⠁⢰⢦⡟⡆⣠⠶⣞⢳⠀⠀⠀⠀⠉⠘⣏⣱⣤⠲⡤⢤⣠⠶⠛⠉⠓⢲⠶⠶⡶⠒⠛⠋⢫⠉⠹⣄⠤⡄⢘⣦⣠⡗⠀⠀
⠀⠀⢸⡅⠀⡏⠀⠀⠀⠀⠘⠀⠀⢀⠀⠈⢳⣐⣷⠀⠀⠀⠹⡦⠷⣜⣻⢳⣬⠔⣄⡿⠉⡂⠹⡤⠄⠧⠴⠋⡅⢀⢰⡿⠏⠉⣷⢤⡦⣿⢇⠰⣹⣟⡻⠛⢣⡴⢤⠀⠰⣫⡽⣋⣹⣟⠳⢞⠀⡔⣦⠀⠀⠀⠇⠪⠼⠀⠀⠀⠀⠱⡀⣻⠤⡸⣧⠼⣟⡇⠀⠀
⠀⠀⢸⡆⠀⢹⠀⢠⠴⡄⢸⠀⢰⠁⡇⠀⡀⠀⠀⣆⠀⠀⠀⡽⣖⠉⢇⠈⡏⢳⠼⣧⡔⠣⡼⢀⡼⡠⣄⡚⠑⣦⡤⠇⠀⠀⠏⢏⡩⡸⣺⢞⣹⢯⠈⢲⠛⣿⠋⠱⣤⠋⢱⠈⠁⠪⡀⢠⢇⠗⠉⣄⡀⠀⠘⣄⠀⠀⡴⢤⠀⠀⡱⣽⠖⢥⠼⠀⠈⠁⠀⠀
⠀⢠⢼⣆⡄⣬⢧⣘⠀⡇⠈⣦⢼⣘⣆⣻⢼⠖⡄⣽⠒⢢⠎⣳⢞⣲⠈⡴⡃⠙⠔⢣⣱⣶⢋⢹⢻⠠⣘⡜⣿⣹⠆⠀⡠⠐⢦⠤⣜⡑⠁⢫⡿⡜⠃⠈⠙⠉⡳⠒⢳⣞⠙⠀⣖⣚⡿⢏⠉⢆⢀⡅⣁⠀⣻⢴⡓⡆⡼⢒⣏⣙⡟⣯⡙⠃⢀⣄⣠⣤⠀⠀
⠀⠈⠲⡿⡖⠊⡼⠛⡾⠢⣄⠼⡔⢳⠘⠲⠊⠉⠀⠈⠁⡞⠘⣾⡽⣢⣽⢏⣡⣠⡚⠓⣷⡸⢎⡉⣸⠗⠓⡄⡠⢄⠀⠀⠓⡦⠿⣤⡿⠤⡀⠈⠑⠁⠀⢀⡀⠀⠘⠒⠚⠓⠿⠿⠋⠀⣏⣸⣽⢽⣉⡽⢏⣹⠧⠞⠉⠀⠉⠹⣚⡧⣽⣁⠿⡄⠈⠻⡽⠉⠀⠀
⠀⠀⠀⠉⠁⠀⢦⣀⠚⡴⠋⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢻⣹⠋⠧⠎⠈⠉⢇⣀⡆⢺⣼⣧⠟⡲⢾⡷⠞⠁⠀⠀⢣⣶⣏⣀⠶⠃⠀⠀⠀⠀⣹⣾⣙⡖⠘⢾⡔⠑⡆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠝⠑⢺⡙⢽⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⡄⠀⠸⢄⠴⠊⠙⢣⠎⠘⢦⠖⠒⠤⠚⢻⢃⡵⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⢹⠋⣫⠟⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡠⡀⠈⠋⠁⠀⠀⠀⢀⡠⡄⡤⢍⠖⢺⠠⠤⣴⣁⢮⠈⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡝⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡃⣧⣰⡀⠀⠀⠀⠀⠀⠺⠤⣰⣧⡜⠀⠸⠀⠰⣻⠇⠘⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⡦⠜⠀⠀⠀⠀⠀⠀⢀⡷⡟⢳⡴⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣼⠖⡄⠀⠀⠀⣤⡔⠿⠂⡜⢐⣗⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠈⠳⡞⣇⠁⠀⠀⠀⢹⣷⠄⠀⠉⠉⢹⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⢾⣼⡁⠀⠱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
oops, looks like you're lost..
go home?