⠀⠀⠀⠀⠀⠀⣷⠀⢀⡂⠀⢸⠀⠀⠘⡆⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⢾⣷⣘⣇⠀⠀⠀⣿⣀⠀⠐⠈⠓⠀⠀⠀⢀⠾⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢽⠀⠈⢿⠀⢸⡆⠀⣠⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠻⢿⣄⣦⡠⡟⠁⠀⠀⠀⠀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⡄⠘⣷⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⡀⠀⠀⠀⠀⠙⠻⣟⡳⣄⣀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀
⢤⣤⣀⣀⣀⡀⠀⠘⣷⠀⢹⣦⠟⠁⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠈⠙⠾⢭⣛⢿⣶⣤⡀⠀⠀⠀
⠀⢦⡈⠉⠉⠉⠛⠛⣿⣷⡼⠋⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠉⠛⢾⣍⠛⢶⣤⣀⠀
⣦⡈⠛⠦⠀⠀⠀⠀⣈⡿⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⠀⠀⠀⢀⣹⠷⡄⠺⣽⣳⢦⣄⠀⠀⠀⠀
⠈⠙⢦⣤⣀⠀⠀⠀⣼⢁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢠⡀⠀⠀⠀⢀⣈⣭⢭⣩⡟⠃⠀⠈⠂⠀⠉⠻⢮⣟
⠀⠀⠀⠀⠉⠉⠉⣽⢃⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠙⣿⠿⣽⣿⠒⠛⠋⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⢀⣟⡟⠀⠀⠀⠀⡀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢤⣀⠀⠙⣶⠀⠉⠛⠓⠶⢤⣤⡤⡶⣾⡟⠁⠀
⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⡀⠀⠀⡄⠀⠀⠘⡀⠀⠠⠀⠀⠀⠀⠀⢸⠇⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠘⠻⠶⢖⣒⣿⣟⣯⡵⠞⢩⡤⠀⠀⠀
⠀⠀⠀⢀⣤⠟⠁⠀⢀⣼⠃⠀⠀⠈⠀⠀⠀⣇⠀⠀⢳⠀⠀⠀⠀⠸⣇⠀⠀⠘⡛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⠿⢿⣿⣧⣬⠤⠶⠚⣿⢧⠀
⠀⠀⠤⣀⣀⣠⡴⠞⠋⣿⢀⠀⠀⠀⠀⡖⠀⣻⠀⠀⠀⢿⠀⠀⠀⠀⢹⡄⠀⠀⡇⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣧⣸⠦⠤⠶⠶⠦
⠀⠀⠀⠀⢀⣿⠀⠀⠀⡇⡎⠀⠀⠀⢰⡇⠀⣿⢧⡀⠀⠀⢳⡀⠀⠀⠈⣇⠀⢰⠃⠀⢀⣈⡷⢤⡰⠆⠈⠛⠳⢦⣤⣄⣀⣀⣀⣀⣠⠤⠶⣚⣿⠋⠀⠀⠘⡗⣶⡆
⠀⠀⠀⠀⢸⡏⠀⠀⢰⢿⠇⠀⠀⣰⡻⠁⠀⡿⠈⢿⡀⠀⠀⠱⢄⠀⠀⢸⡄⣸⡶⠚⠉⠁⠀⠀⢙⣶⣄⣀⣠⡄⠉⠷⣿⣯⣭⣭⠥⠶⣞⠛⠎⢳⣤⣄⣀⡇⠙⣿
⠀⠀⠀⠀⣾⠁⠀⠀⣾⠘⠀⠀⣠⢷⡇⠀⢰⠃⠀⢈⣷⡀⠀⠀⠈⠳⣄⠀⠁⣿⠀⠀⣀⣴⣶⣾⣿⡿⣿⡿⠻⣶⠤⣄⣀⣉⣓⣶⣤⣤⣽⡆⠀⠈⢻⣿⡈⣷⠀⣿
⠀⠀⠀⢀⡟⠀⠀⣰⠏⠀⠀⠀⠉⣸⠁⠀⣾⠛⠉⠉⠉⠙⢦⡀⠀⠀⠈⠳⣄⢿⠀⡼⠛⠿⣿⠿⣿⣗⡼⠁⠀⢸⠀⠀⠉⠉⡏⠉⢿⡇⠈⣇⠀⠀⢳⡿⣷⣹⠀⠘
⠀⠀⢀⡿⠀⠀⣰⠋⠀⠀⠀⠀⣸⢷⡄⢰⣟⣀⣰⣭⣯⣥⣼⣻⣷⢆⣀⡀⠈⠸⣇⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠘⣧⠀⢹⠀⠀⠀⢷⠹⣿⠀⣠⣆
⠀⣠⡾⠁⣠⣞⣁⣀⡤⠖⢀⣼⣷⢾⡷⣿⣿⡿⠻⠿⡿⢿⣿⡇⠈⠻⢯⡙⠲⠦⣌⣓⣶⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢹⠀⠀⢹⠀⠸⣇⠀⠀⠈⣷⣿⡾⠁
⡾⠋⠒⠉⠉⠉⣹⣫⣄⣴⡿⠏⠁⡼⣷⣿⡏⠹⠶⠼⠿⠟⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡄⡀⠀⠀⣼⠀⠀⢸⡄⢀⡿⣇⠀⠀⠘⣯⢻⡀⠀
⠋⠀⠀⠀⣠⣾⣿⣿⣿⣿⠀⠀⣸⡿⠁⢹⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⠃⠀⠀⣿⠀⢠⡘⡇⢠⣧⠈⢣⠀⠀⠘⣇⢷⡀⠀
⠀⠀⠀⣾⣿⣿⢡⣿⠹⢿⠀⠐⠋⠀⠀⠸⣇⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣏⡟⠀⡴⣼⡗⠀⠈⡇⠁⡾⣿⣧⠀⠁⠀⠀⠻⣎⣷⢄⠀⠀
⣤⣤⡾⣿⣿⢷⣿⡟⠀⣿⠀⠀⢀⠀⠀⠀⢻⣌⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣽⡟⠁⠀⣼⣿⠁⠀⠀⢃⢀⣧⡿⣿⠂⠀⠀⠀⠀⠻⠘⣿
⠋⠀⣠⣿⢟⣿⠟⠘⠀⣿⣇⠀⠘⣧⡀⠀⠀⠛⣦⣈⠻⣦⣀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⡟⠀⣠⠞⠉⣿⠀⠀⠀⢸⣸⢻⡇⠘⢧⡀⠀⠀⠀⠀⠀
⠀⢰⣿⣿⣾⠟⠀⠀⠀⣿⠛⢧⡀⠘⢷⣄⠀⠀⠀⠉⠛⠛⠋⣹⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣴⣣⡴⢺⡇⠀⠀⠸⡄⠀⠀⢸⣯⣾⡹⠀⠈⢻⡄⠀⠀⠀⠀
⢠⣼⣿⣿⢋⡞⠀⠀⠀⣿⠀⢸⣷⣤⡀⠙⠓⠦⠤⣈⣛⠛⠛⠷⣤⣀⠙⠛⢦⣤⣀⠀⣠⣾⣯⣤⣴⣾⣶⣶⣶⣾⣇⠀⠀⠀⢻⡀⢀⡾⠋⣼⠀⡆⠀⠀⠹⣤⠀⠀⠀
⣿⡟⢻⣿⢸⠀⠀⠀⢠⣿⣷⣿⣇⠀⠉⢙⣿⠟⠛⠛⠛⠻⢷⣤⣦⣬⣍⣙⣘⣷⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⠉⠀⢸⡇⢸⡇⠀⠀⠀⠈⣿⡄⠀
⣿⣷⣿⣿⢸⠀⠀⣠⠙⣿⣧⢻⣽⣄⣰⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣦⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠀⢰⡏⠀⢰⡇⠀⠀⠀⠀⠀⠀⠠⣀⠀
⢸⣟⣿⣿⠀⠀⠀⣿⠀⣿⠘⢿⣷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡎⢿⣿⣿⡛⠲⣶⡴⡞⠫⠛⣿⣷⣤⠄⢈⣹⣿⣯⡤⢴⠄⣼⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀
⠸⢻⣿⡇⠀⢰⢸⠸⠀⢿⡄⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⣿⣿⣿⣄⠹⣷⣄⡀⠀⣉⣙⢿⣿⣛⣉⡀⠉⠛⢿⢾⣯⣛⠓⢚⠓⠓⠲⠦⣤⡀⠀⠀
⣆⠘⢿⣇⡀⠈⣿⠀⡄⠸⣇⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣻⣦⡈⠙⠿⣷⣤⣈⠳⠶⣍⣍⢷⣀⣀⣾⡷⣆⠩⣿⣾⣝⢶⡲⣄⠀⠙⢳⣄⠀
⡿⣦⣄⠻⣷⠀⠘⡄⣷⠀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠉⠈⠻⣦⡀⠘⢿⡛⠷⢶⣤⠍⠛⢾⣏⡙⢁⣈⣩⣻⣟⠉⢁⣿⣾⠳⣀⠀⠙⣆