⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⣄⠀⠀⠀⠀⠀⠀⠀⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡡⠤⠒⠓⠒⠒⠒⠒⠢⠤⣇⠈⠢⡀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠔⠒⠒⠂⢇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⢉⡚⠯⠴⠦⠄⠀⠀⠀⠀⠀⠁⠀⠬⠖⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢒⠉⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⢀⠃⠸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠊⠀⠈⢢⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡮⠁⢀⠃⠀⡘⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣀⣤⠖⠊⠁⠈⢷⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣛⡅⠀⣠⠦⡄⢠⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⠟⠁⠀⠀⠀⢀⣀⣀⣀⢠⡴⣞⢕⣡⠤⠤⠤⠤⠤⢄⡀⠀⠀⢠⠀⠀⢀⠜⡠⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢠⣈⣡⣴⣽⣯⠑⠉⠀⢀⢤⣰⣶⣤⣤⣤⣤⣀⣀⣠⠘⠠⠤⣒⠟⠁⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠨⣿⡏⠉⢹⣿⠂⠀⠀⢰⡛⠉⠸⣿⣿⡇⠍⣿⣿⠅⠀⢗⠊⢀⣰⠾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⡘⡘⡇⠀⠰⣿⠀⠀⠀⢸⠀⠀⠈⣿⡿⠃⢰⠇⠀⠀⠀⠠⡿⠅⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⡇⡷⠿⠀⣴⣯⣤⠤⠒⠈⠀⠀⠀⠀⢠⠠⡸⠲⡀⠀⠀⠀⠃⠀⢄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⢻⠐⡀⠀⠁⠉⠁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⣠⠁⠀⡆⢀⠆⠀⠈⢆⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣫⠆⠙⢣⠈⡒⢤⣈⠉⠉⠁⠉⠁⠀⢀⡀⡤⠒⢍⢸⢀⡜⠹⠊⠀⠀⠀⠘⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡙⠀⠀⠀⡗⠧⠎⠀⠉⠐⠒⢲⡶⠟⠋⠀⢀⠀⠀⠙⠋⠀⣀⠴⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣁⡀⠀⠀⠀⠀⠀⣸⠀⠀⢀⣀⠨⠭⠙⠛⠉⠀⠀⠈⠹⠶⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡠⠟⢛⣐⡲⠟⠛⠉⠉⠉⠉⠉⠉⠓⠤⡀⠀⠀⠀⠀⠀⠀⡇⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠋⠉⠉⠉⠉⢀⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡿⡀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⣠⢳⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠇⡰⡿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠊⠀⠀⢜⠁⠛⠃⠤⠤⣀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⢶⣤⡄⠀⠀⢀⣀⢀⣀⡠⠤⠊⠙⢶⣄⡤⠄⡐⠚⠈⠁⢀⣀⡀⠀⠀⠑⠢⢄⡀⠀⠈⠳⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⡏⠙⠓⢶⠥⢴⡝⠊⠀⠀⠀⠀⠀⠈⠑⠓⠂⠈⡏⠁⠀⠀⡝⠢⡀⠀⠀⠀⠈⠐⢄⡀⠡⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⡆⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⢠⡁⠀⠈⣷⢄⠀⠀⠀⠀⠈⠐⢾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢰⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣄⢸⡵⣄⣘⡏⠀⠉⠒⠒⠒⠒⢲⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠘⠀⠀⢸⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠰⡀⠈⠪⢷⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠤⢧⣠⢾⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠑⠫⡒⠤⣤⠤⠤⠒⠒⠒⠢⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠢⡈⠷⡆⠀⠀⠐⠒⢶⣶⣒⠻⠦⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⢢⠈⢦⡀⠀⠀⠀⠈⠙⠵⡢⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠱⡀⠙⣄⠀⠀⠀⠀⠀⠈⠪⡳⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⢦⡀⠀⠀⠀⠀⠀⠈⢪⢦⠀
⠀⠀⠀⠀⠀⠀⢀⡠⡴⡆⠀⠈⣽⡀⠀⢣⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠉⠀⢜⡀⠀⠀⠀⠀⠹⢧
⠀⠀⠀⠀⣠⠞⠉⢠⠁⠁⠀⠀⠘⢇⠀⠀⠑⢄⠀⠙⡁⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢢⡬⣦⠀⠀⠀⠀⠸
⠀⠀⢀⠞⠁⠀⠀⡈⠀⡆⠀⠀⠀⠸⡀⠀⠀⠀⠷⡄⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢳⡀⠀⠀⠀⠀⠀
⠀⢠⠋⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠑⢖⠤⢀⣀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢣⠀⠀⠀⠀⠀
⢠⠃⠀⠀⠀⠀⠀⠃⠀⢣⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠸⠀⠀⠀⠀⠀
⡞⠀⠀⠀⠀⠀⠀⢸⠀⠸⡛⣄⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⢇⠀⢣⠈⢢⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠈⢶⣆⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠑⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⠀⠀⠀⠀⠀
⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡌⠀⠀⠀⠀⠀