⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⡖⢉⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⠰⠎⢀⣣⣈⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠍⠟⠉⣩⠖⠉⠁⠀⠈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢸⣏⠀⠀⠀⢠⣤⣤⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠘⠂⣸⠇⠀⢀⡿⣀⠤⢀⠖⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣤⣤⡶⠋⠀⣠⣾⣿⡵⠦⢡⡬⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣤⣶⡲⡲⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣴⣿⠋⡟⢧⠈⢂⡐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⠖⠉⠀⠀⠀⠈⠉⠪⢦⡙⢷⡄⠀⠀⢠⠜⠃⡠⠀⠀⣠⣾⠟⠁⠀⠈⠂⡆⠂⣀⣀⠀⠀⠀⠀⠀⠀
⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡐⢍⢆⠀⠀⠇⠢⠆⢀⣴⡿⠋⡠⠔⠒⠦⡄⠀⠀⠜⠻⠁⠀⠀⠀⠀⠀
⡜⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠘⢮⢑⢆⠀⠀⠀⣴⡿⠋⠀⢰⠀⠠⢄⢀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⢀⣾⡿⠛⠛⠷⣄⠀⠀⠀⠈⢮⡘⡄⠀⣼⢿⡇⠅⠀⠈⠳⠦⠊⡀⢰⠤⠶⢶⣦⡄⠀⠀⠀⠀⠀
⢧⠀⠀⠀⠸⣿⠁⢀⠀⠀⠘⡆⠀⠀⢀⠈⢎⢇⣸⠃⠂⠹⣄⡁⠂⠠⠀⢂⠔⠁⢀⠤⠀⣿⣿⠀⠀⠀⠀⠀
⠘⣆⠀⠀⠀⠈⠒⠚⠀⠀⠀⡇⠀⠘⠻⠀⠘⣿⡏⠈⣠⠤⢬⣝⠛⠛⠉⢁⡀⠀⠘⢶⣶⡿⠃⠀⠀⠀⠀⠀
⠀⠘⣆⠀⠀⠀⠀⠀⠀⢀⡴⠁⢀⠀⠀⢀⠀⣿⣡⠎⢀⠔⣤⠈⡇⠀⢄⠈⠑⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠷⣄⣀⢀⣀⣠⠏⠀⠀⣄⠀⢌⠸⠀⣿⣿⠀⠈⠄⠡⠌⠀⠀⡈⣀⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠄⡃⠩⡆⡁⠠⣿⣏⠀⠀⣠⠶⠶⡄⠀⠁⢀⣈⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠉⠉⠄⢸⡿⢻⡀⠀⢿⣄⠇⡹⢠⣶⡿⠛⠛⠻⢿⣦⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠆⡈⣄⢴⠂⠃⠀⠀⠀⠠⣿⠰⠙⣦⠤⠤⠊⢰⣿⠃⠀⠀⣀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢙⣻⡾⡛⠩⠉⠍⠙⡳⢦⡀⢻⡨⠁⠈⠳⡀⠀⢸⣿⡀⠀⢸⣋⠻⡄⠀⠘⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡴⢁⠁⠀⠀⠀⠀⠀⠀⠂⠙⢾⣇⠂⡎⣙⡟⡄⠀⢻⣧⠀⠀⠀⡰⠁⠀⢠⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡸⠡⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠹⣦⡱⢬⡤⠇⠀⠀⠉⠛⠒⠉⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣏⡇⠀⠀⢀⡜⠉⠀⠀⠙⢆⠀⠀⠀⠹⣟⠢⣀⡀⠀⠀⠀⠀⢀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠣⡹⡄⠀⠘⣄⠀⠈⡁⠀⢸⡆⠀⠀⠀⠙⣎⢃⠊⠋⢍⣸⣉⡉⠁⢤⣴⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⡂⢝⢦⣀⠈⠛⠈⠀⠀⡜⠀⣘⠂⢚⠀⠈⢧⡡⠠⠏⠱⣲⠙⡄⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠑⡡⡪⡫⡓⡦⠤⡄⠊⠀⠈⠁⢂⠊⠁⠀⠀⠹⣄⢇⡘⢶⣞⣁⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠳⣌⠉⠁⢠⢒⣦⠀⢡⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⣤⣸⠇⠀⠀⠈⠣⡀⢹⣌⣁⣠⠎⡴⠚⠉⠑⢦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣀⣀⣀⣠⡴⢶⡶⠾⣦⡈⠉⠀⠸⣅⢠⡄⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⢀⠊⣀⡂⡀⠈⠢⢄⡀⠈⠉⠀⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣃⡼⠀⠀⠈⠀⠉⠛⠲⠟⠋⠁