⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠖⠚⡇⠀⠹⣄⣠⠴⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⢀⣇⡴⠚⠉⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠦⣄⡀⠀⠀⠀⢀⡞⢦⣠⠞⠁⠀⠀⠀⠀⠀⠀⠰⠚⠁⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣄⣉⠳⢤⡀⢸⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⡤⠴⣲⠆⠀⠀⢠⣾⣄⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠀⠈⢙⢦⡙⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠈⠉⠳⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠡⣹⡄⠀⠀⠀⠀⠀⠀⠰⠤⢤⣢⠀⣦⣤⣀⣘⡆⠀⠀⠀⠀⠀⠀⠀⣈⡧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠰⣳⠀⠀⠀⢀⡤⠤⣄⡀⠀⠈⠙⠚⠀⠀⡴⠓⠲⣄⠀⠀⠀⠐⠯⡁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠃⠃⠀⢰⠃⠀⢀⠀⠱⡄⠀⠀⠀⠀⢸⣥⡀⠀⠈⡇⠀⠀⠀⠀⠘⢆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣼⠀⠀⣿⣿⡄⠁⠀⠀⠀⠀⢸⣿⡇⠀⠀⠟⠴⠯⢭⣭⡙⠺⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢀⠰⢼⡀⠀⠹⠿⠃⠀⠀⠀⠐⣈⠀⠉⠁⠀⠀⠂⠀⠀⢀⡴⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡶⠋⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⢀⠛⠁⠀⠀⠀⠀⢠⡴⠖⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⣩⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠓⠃⢀⣠⣞⠲⢤⣹⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⡀⣇⢠⣶⣛⣢⣤⣀⣀⣀⣀⡤⡴⠺⣍⠉⠉⠉⠳⣌⢁⣄⡀⢀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⠛⠁⠀⠀⠙⣇⠀⠀⠀⢀⠴⠁⢀⡼⠀⠀⠀⠀⠸⡏⠀⣧⠋⠈⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⢸⠛⠇⠀⠉⠀⠸⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⡿⢤⣀⡀⠀⠀⢀⣀⣠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⡧⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢸⣧⣤⣀⡀⢠⣿⣤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣹⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡅⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡿⠶⣾⣯⣭⡻⠿⠿⢟⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢀⡿⣿⣟⣛⣛⣙⣛⣻⡿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡊⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⢀⣀⣀⡤⢖⣿⣿⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡇⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣩⣭⣴⡾⢟⣻⣿⣿⡶⣭⣿⣿⢻⣿⣆⡗⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣓⡾⢿⣿⣿⣿⣿⣿⣿⣿⢏⣿⣷⢲⣿⣿⣿⣿⣿⢱⣿⣿⡇⣾⣿⢡⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠉⡱⢀⣿⣿⣿⣿⣿⣿⠟⣫⣾⣿⡿⣼⣿⣿⣿⣿⡏⣾⣿⣿⡇⣿⠧⠎⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠚⠉⠉⠀⠀⠀⠠⢔⣡⣾⣿⣿⣛⣛⣭⣶⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⡟⠀⠀⠀⠀
⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⢏⣾⣿⡿⠟⠋⠀⠀⠀⠀⠀
⠀⠀⣰⠋⠀⠀⠀⠀⢠⣐⡬⠤⠖⠚⠉⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⣰⠃⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⢀⡇⠀⠀⠀⢠⠏⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⢸⠀⠀⠸⡿⠃⠀⢀⡴⠒⠦⣄⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⠛⠹⡀⠀⠀⠀⠀⠀⠀⠀
⠐⡗⡀⠀⠀⠈⢦⠀⠀⠀⢀⡰⠋⠀⠀⠀⠈⢧⠸⡗⠛⠛⠻⠛⠛⠛⠿⠿⠿⠛⢻⡛⠛⢉⠂⠀⠀⠀⣳⠛⠀⠀⠀⠀⠀⠀⠀
⠀⢳⡘⢄⠀⠀⠀⠙⠒⠒⠋⠀⠀⠀⠀⠀⠀⡼⢀⣟⣀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣷⣶⣶⠶⢿⣻⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠳⣄⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣃⠀⠀⣿⣦⣄⣀⣀⣀⣀⣀⣀⣤⣾⣿⣓⣒⣚⣛⣻⣯⣽⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠲⣄⡁⠢⠀⠀⠀⠀⠀⢐⣢⣾⣿⣿⣿⣷⣿⡷⢯⣽⣟⣛⣛⣻⣯⡽⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀