⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣛⣛⠻⡄⠀⠀⠀⠀⠀⠀⢘⣛⠻⣥⡀⠀⠀⠀⠀⠀⡜⣛⡛⡟⠀⠀⠀⠀⠀⠀⡜⣛⣛⠻⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡱⣎⡿⢂⣠⣤⢛⣛⡛⣆⡀⠋⢧⣎⠁⠀⠀⠀⠀⢧⣎⠌⠉⢠⣘⣛⡛⢧⣤⡀⢹⢧⣎⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⣠⣟⡳⢎⡳⣬⠷⠼⢵⣛⣦⡀⠀⠀⠀⠀⠀⠀⢠⠼⢵⠷⠼⢦⣙⢎⡳⢽⣣⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⢮⡕⣫⠶⣉⡀⠀⢈⢳⣾⡇⠀⠀⠀⠀⠀⠀⣹⣷⣉⠀⠀⣂⡙⢮⣱⢣⣗⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⣞⡵⠿⠀⣯⠁⠀⢸⡏⢹⡇⠀⠀⠀⠀⠀⠀⢼⡋⣽⠀⠀⠁⣿⠨⢗⣣⡞⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣏⣿⠀⠀⠉⠀⠀⠌⠱⡎⠁⠀⠀⠀⠀⠀⠀⠈⢱⠈⠄⠀⠀⠉⠀⢸⣿⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠶⠶⢶⠿⠉⠶⠷⣀⣣⣄⡰⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⣀⣔⣀⣀⠾⠆⠹⢷⡶⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⣁⠣⡘⢌⣾⠅⠀⠄⣿⠹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠹⣿⠀⠠⢘⣎⢡⢂⠱⢬⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠲⢒⢾⣷⡥⢆⣹⡞⣿⠂⠀⣤⠛⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣜⠛⡄⠀⢨⡟⢳⡎⡴⣪⣿⢖⠲⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠡⣬⣵⣯⡞⠋⠙⣻⡇⠀⠛⢣⣤⠛⣬⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⠛⣤⡔⠃⠈⢹⡗⠃⠙⣮⣷⣦⢬⠑⢢⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⠃⢀⢨⡇⠀⢸⡇⢠⠀⠀⢠⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠄⠀⠠⡀⢿⠆⠀⣿⡄⠀⠛⠛⢳⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⣤⠀⡜⢈⠦⡞⠃⢠⡜⠛⢻⡟⠛⣻⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⣟⠛⢻⡟⠛⣥⡀⠛⢦⡁⠣⢌⢠⣴⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢧⢻⣴⡧⣘⠧⢠⣴⢣⡟⠃⢠⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⢣⡆⠘⢳⡼⣥⠀⢺⢄⣷⣮⢛⡴⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⠶⣦⢹⡇⢠⡜⣳⡟⢀⡠⠝⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠉⠛⢦⣀⡴⠋⠁⠀⠘⡆⠀⠀⠀⠀⠀⠀⠘⠡⢄⠛⢳⡟⣤⠀⣿⡰⣎⢷⣮⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⣀⠋⡏⠓⢤⡻⠜⡣⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⣰⠛⢧⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠡⢜⠳⣛⠤⠛⣶⠋⡰⠷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⣀⢏⡀⠰⢇⡈⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠴⠶⡾⠛⠛⠛⠛⣿⠳⢻⠷⢤⠀⠀⠀⠀⠀⠀⠀⢰⠎⢁⠿⠀⣀⠿⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠷⣀⡸⢷⡾⠂⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁⠘⣇⡾⠁⣠⣶⣶⡄⠈⢷⡏⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠸⢷⠾⣀⣀⠿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠎⠹⡷⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⣼⣇⠀⠀⠹⣿⡿⠇⢀⡾⢷⠀⠀⢀⡹⠀⠀⠀⠀⠀⠀⢸⠷⣿⠉⠶⠶⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣀⠀⢸⡇⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣴⣇⣈⣧⣀⣀⣀⣀⣾⡥⡼⣷⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⡃⣿⡁⠀⣂⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠸⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠈⠈⠹⣇⣠⠟⠁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⣿⠄⣜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣀⡼⠻⢦⡀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣿⣦⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝⢾⣯⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠚⠉⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⣿⡹⣮⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣾⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣷⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀