⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⡶⠲⠲⠖⠖⠖⠶⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣀⣤⣤⣶⣿⡟⢉⠉⡁⢐⣠⣤⣤⣄⡀⠠⠀⠀⠀⠉⠙⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣿⣿⣿⣿⣿⠍⡐⠠⢁⠂⢰⣿⠿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠑⠊⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠿⣙⠢⠉⡄⠱⠀⢆⠀⡀⠀⠀⠀⠀⠈⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢌⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣭⣳⠢⠡⠁⠈⡁⢎⡐⣂⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢿⠋⡀⠀⠀⠀⠀⠰⣬⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣊⣔⣀⡀⠀⠀⠀⣿⣟⠡⡉⢀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢛⠛⢛⣿⣧⣄⣸⣿⣿⡿⠿⠿⠿⢿⣤⣤⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡡⠀⢾⣿⣿⣾⣿⣿⢧⡐⡀⠀⠀⣾⣧⣿⣿⡏⠛⢦⡄⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⢿⣷⣄⠈⠻⠿⠟⣻⠻⣷⣲⢡⠀⠀⠻⢿⣿⠿⠃⢀⣼⠇⢐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣯⠻⢿⣿⣤⣴⡶⣟⢣⡽⢿⣧⣟⣤⡒⡤⢤⣤⣶⠿⠃⡐⢌⠠⠀⢂⠒⠠⠀⢂⠀⠀⠀⠌⣀⢻⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⢯⡄⠀⠀⠀⠀⠀⠀⣿⣿⣯⢿⣿⣮⣝⢯⡹⡱⢎⢣⠛⡷⣭⣛⠿⠿⠿⠿⢛⢁⠢⡑⢨⠀⠆⡉⠤⡘⠄⠡⠀⢀⠐⢀⡘⢠⣿⡿⣤⡀⠀⠀⠀ ⠀⠀⣀⣀⣀⣀⣀⣤⣬⣿⣂⠀⠀⠙⣆⠀⠀⠀⠀⠀⢸⣿⣟⣯⡿⣽⣿⣎⠵⡱⢈⠂⢍⠰⡁⠙⠛⠶⢶⠌⠂⠄⡃⠄⠃⠘⡐⠌⠂⠐⠀⠂⠀⡀⢈⠠⣐⣷⠏⠀⠈⣷⠀⠀⠀ ⡶⠋⢣⡠⠀⣠⠀⠀⠀⠀⠉⠂⠀⠀⢸⡄⡀⠀⠀⠀⠀⣿⣿⣯⣟⣯⣟⣯⡳⣅⠣⠌⢀⠣⠀⠀⠀⠀⠀⠀⠀⢀⠁⠠⠁⠂⢀⠠⠀⠈⢀⠀⡁⠠⢀⣶⠟⠁⠀⢰⣿⠛⠀⠀⠀ ⣧⣤⡼⠥⠤⠓⠶⠒⠈⠉⠉⠒⠢⢄⡈⠛⣇⠀⠀⠀⠀⠘⣿⣾⣽⢯⡿⣽⣳⢮⣱⣎⣴⣨⣡⡄⡀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠠⡐⢄⠒⠠⣵⡿⠇⢒⠲⣾⠛⠁⠀⠀⠀⠀ ⠹⢯⣤⣀⣤⣤⣤⣴⣦⣴⣤⣤⣀⣴⠄⣸⡿⠀⠀⠀⠀⠀⠹⣿⣿⣻⣽⣻⣟⣛⠛⡛⢛⠛⡛⠛⠛⠋⣉⣩⣥⡴⣖⠳⣎⠥⣍⢢⠱⣈⢦⣩⣿⢋⣤⡶⠖⡀⠉⣲⡦⢤⣀⣀⠀ ⠀⠈⠉⠉⠉⠉⠉⠀⠈⠉⠙⠛⠻⠿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣯⣷⣿⣿⣷⣯⣦⣳⣴⣳⣮⣿⣿⢷⣧⣟⣼⡻⣬⢳⣎⢧⣻⣴⡿⠟⠛⣿⡏⣠⡼⣫⡾⠋⠰⣦⠀⠈⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⡾⣽⢯⣟⣾⣻⣿⣿⣣⣶⣣⠍⠛⠿⣾⣏⠀⠀⠀⣼⣆⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣿⣿⣯⡀⠀⢀⣿⠻⠿⠛⠛⠉⠁⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⢤⡀⠉⢛⠿⠿⠿⢿⣿⣿⡿⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⡇⠀⠀⠀⠀⣀⣀⣤⣴⣒⣀⣠⣀⣀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⡟⢣⡏⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣯⣽⣼⣯⢭⡝⠛⡟⠡⢌⠣⠜⣿⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⡤⠉⡌⠓⠺⢦⡼⠖⣋⠔⣈⠢⢁⣿⠟⣧⣠⢤⣶⣿⣿⣿⣿⣿⡟⢣⠝⣷⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠿⣶⣥⣤⣀⣄⠠⢌⣳⣬⡾⢾⢛⣩⣿⡿⡿⢿⠿⡿⣗⠺⡏⢙⡿⣄⠂⡜⠠⢮⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣉⠉⠉⠙⠛⣉⣥⣶⣾⣿⣿⡿⣵⢫⣃⢎⡐⡉⠛⠿⣉⠳⡌⢷⣄⠓⣼⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠟⠛⠋⠀⢾⣿⣟⠻⠿⢷⣼⣦⣴⣠⣍⣲⣥⣳⣼⡾⠟⠛⣉⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣶⣢⣄⣀⣈⠉⢉⡙⢉⣡⣤⣶⡶⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠓⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀