⠀⠀⡴⣖⢶⣿⣍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⠱⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⡻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠘⣧⢸⣿⣷⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣬⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢺⣩⡾⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣴⢽⣧⣝⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢹⣴⣼⣛⣻⣿⣿⠀⠀⠀⠀⠀⣀⣀⣀⣠⡰⢖⡲⣾⣿⠟⠛⠛⠛⠛⠛⠻⢿⣭⠙⢿⣶⣶⠤⠤⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣧⡴⡏⢽⣿⣿⡇⡀⠀⠀⢠⠟⣫⢙⡩⠤⣼⡋⠐⠀⠀⢠⢶⠀⠀⠀⠀⠈⢻⡆⢆⠙⢝⠛⣷⣷⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡶⢯⢀⣻⣿⣿⠀⠀⠀⢸⠸⣿⣴⢠⡇⣿⣇⠀⠀⢰⠃⣎⠀⠀⠀⠀⠀⣼⠨⣸⣴⠁⠈⢸⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣿⣿⣾⢿⣿⣯⣽⣿⣿⡟⢳⣹⡟⢺⣳⣥⣟⠳⡆⢸⢠⢡⠗⠛⣑⠿⢆⣹⡀⣿⠃⢠⡄⣾⣿⡏⠀⠀⠀⠀⠀
⢠⢤⡤⠴⠾⢿⡊⣱⣿⣦⢿⣻⣟⠟⣿⣿⡀⢽⣗⣷⣿⡟⠛⢫⠗⡞⡌⠱⠠⠾⠿⠗⢘⣾⣷⠙⢀⣸⣿⣿⠻⠄⠀⠀⠀⠀⠀
⠐⠂⡏⠉⡭⢽⣯⣯⣯⣿⡞⣭⣿⡸⢹⣿⣇⠈⠉⣿⣿⣿⣦⢋⣼⠇⡶⠀⠇⠀⢤⣶⣇⣿⣿⣧⣾⢿⡯⠀⠁⠀⠀⠀⠀⠀⠀
⠠⡧⣧⣤⣽⣿⣿⣷⣿⣽⣽⣨⣛⣏⡆⢿⣿⣇⠀⢸⢿⣿⠟⠽⠛⠀⣮⢳⠀⣠⢠⢈⡏⣟⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠀⣴⣞⠒⢽⢢⣹⠻⢹⢃⠟⣾⡏⣸⣿⣿⣵⢸⠸⠏⣶⣯⣵⣦⠁⠒⣿⢋⣸⣼⣿⣻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⢽⣯⡿⣽⣷⣷⠆⢀⢈⣼⣟⢿⣿⣿⣿⡿⢼⣀⡆⠙⢿⡿⠿⡄⡐⢸⣿⣫⡿⡻⣻⠿⢧⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢹⣎⣽⡇⣉⣤⣾⣡⣤⣯⣿⣿⠟⠃⠉⢩⠯⠭⢶⡌⠓⠚⢥⡤⣮⡚⠵⣼⠯⣁⢲⠭⠆⣚⠿⠿⣶⣶⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣯⠙⣉⡽⠉⠙⣿⡇⢃⣿⠃⠀⠀⢠⢾⣁⣿⣾⣿⡶⠼⣿⡿⢛⣟⣂⠓⣾⠟⠓⠤⢄⠀⣹⣦⣼⣿⣟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣭⣧⣤⡗⢚⣻⣗⢚⡹⠩⡁⠀⢈⣟⢹⢿⡥⠘⠳⠽⠫⠵⣾⣧⣼⣿⠊⠀⢠⠊⣽⣿⠋⢄⣿⣿⣏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣭⣿⣗⣿⣿⣿⡇⢠⣀⡀⠱⣤⣞⡗⢻⣋⣉⣉⣉⣉⣉⣙⣏⣠⣻⣧⣼⡒⢁⣼⠃⣠⢄⡤⠾⢿⣿⣦⡀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⢿⡧⢾⣯⢭⣷⠘⣧⠘⣄⣎⢾⡇⠛⠿⠿⠿⠿⠿⣿⢿⢸⠀⣯⣟⢿⣿⡿⠁⠈⠙⠋⠀⣀⠀⢻⣿⣧⡆⠀
⠀⠀⠀⠀⠀⠀⣿⣾⣿⣷⣾⣶⣿⢤⣿⣇⣫⠋⢸⠀⠈⠁⠀⠀⣀⣤⢶⡂⣉⣉⣂⣁⡑⣿⣇⠀⠠⡘⢶⠊⠀⠀⢀⣿⣿⣇⠀
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⢸⣿⣟⢃⠀⠸⡀⢰⠀⡠⢪⢾⣵⣿⣿⣧⡥⠬⠤⢤⣉⠻⢿⣟⠉⠙⠂⠀⠀⠊⣼⣿⣟⡀
⠀⠀⠀⠀⠀⠀⢈⣛⣿⣿⣿⣿⢷⢯⣾⣿⠧⣽⣿⡏⠉⡝⣰⣃⡿⣍⡿⡫⠀⢈⣀⠄⠀⠈⠢⣨⢿⣧⢴⣂⣀⠀⠀⡸⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠓⣿⣿⣿⣟⠀⣾⢡⡽⢁⣿⣴⡄⣸⢠⠏⣸⣝⣾⠊⣤⣶⣟⣽⣿⣿⣧⣤⢟⠁⠈⠉⠳⡀⠀⢰⢡⣼⣿⡟