⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡅⠀⠐⠀⠄⠠⠀⠄⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠑⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠈⡂⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠂⠄⢀⠀⡀⢀⠀⡀⡀⠀⡀⡀⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠅⠀⠀⠈⡧⡀⠀⠀⡈⡰⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⢁⠄⠊⠀⠀⠁⠄⡀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢐⠀⠀⡀⠆⠁⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠡⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢆⠀⡀⡀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠁⠀⠀⠀⠀⠈⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠝⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⡠⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⡠⠜⠀⠀⠁⠁⠁⠁⠁⠁⠀⠀⠑⢄⣀⡠⠤⠄⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠁⠀⠀⠀⠀⠔⠋⠠⠽⠿⠿⠏⢉⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡯⡅⠈⠛⠃⠁⠀⠀⠀
⣷⣴⡆⠀⠀⣰⠁⠀⠊⣠⡛⠀⠀⣀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣌⠀⠠⡀⠀⠀⠀⠀⠀
⣿⣿⣧⡀⢸⡿⣶⠟⣡⡬⣀⡰⠟⢫⣴⣶⣦⣈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⢻⣧⣻⡀⠀⠀⠀⠀⠀
⣿⣿⡿⢸⡏⠁⣡⢄⣥⣶⣿⣿⣿⣿⣮⣿⣿⣿⣇⡈⠿⠻⠿⣿⣿⣿⣿⣿⣿⡿⠟⣭⠿⠿⣿⡛⢿⣦⡹⠆⢠⡆⣣⢻⡇⠀⠀⠀⠀⠀
⣿⡿⠋⠀⠃⠘⣡⣿⣿⣿⠿⠛⠉⠉⠙⢿⣿⣟⢿⣷⣤⣾⡂⠸⣿⣿⡿⠻⠋⠀⠀⠀⠀⠀⠠⠌⢼⠇⢽⣦⠈⣁⠹⢱⡧⠀⠀⠀⠀⠀
⠉⠁⠀⡀⢶⢠⣿⣿⣏⠀⠀⡀⠄⠀⠀⠀⠈⠛⢦⣿⣿⣿⣧⠈⣿⣿⡇⠀⠀⠀⠀⣀⣤⣀⠀⠀⠈⠣⠸⣿⡰⣿⠸⣎⠇⠀⠀⠀⠀⠀
⠷⣤⠀⠸⡘⢸⣿⣿⠁⡴⠉⢀⡤⠶⢶⣤⡀⠀⠀⣼⣿⣿⣿⠀⠨⢿⡧⡀⠀⠀⠊⠀⠀⠙⣿⡂⠀⠀⠀⢻⡇⡾⠀⣧⠀⡀⠀⠀⠀⠀
⠀⠹⡆⠀⠃⢸⣿⡇⠘⠁⣼⣟⠀⠀⢠⡽⠃⠀⢰⣿⣿⣿⣿⡆⠀⣦⣜⣮⡂⠀⠀⠀⠀⠨⢉⡡⠄⠀⠐⡈⢿⡄⠸⢿⠀⠀⠀⠀⠀⠀
⠀⠀⠑⣀⠀⣿⣿⡇⠀⠰⣬⣍⣢⢄⠀⠂⡀⣴⣿⣿⣿⣿⣿⣷⢀⣹⡜⣿⣿⣦⣀⠀⠀⠀⣀⣀⣀⣀⣀⣲⣜⢷⡀⣼⡧⠀⠀⠀⠀⠀
⠀⠀⠀⠛⢀⣿⣿⣿⣿⣧⣴⣿⣧⣶⢞⣡⣾⣿⣿⣿⣿⣿⣿⣿⠀⠈⢿⣌⢻⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⡾⣼⣿⣷⡜⠇⠃⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢂⢧⢜⢿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⣿⣿⣷⡃⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⡁⠃⣾⠛⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡐⡜⣿⣿⡇⢀⠀⠀⠀⠀
⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⢿⡏⠘⡀⠼⠁⠰⡇⢹⣿⣿⣿⣿⣿⣿⣿⠻⢱⢁⡯⣿⣿⡟⡌⡀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣸⣆⢻⡀⠀⢳⡇⣾⣿⣿⣿⣿⣿⣿⠿⠜⠘⠠⠛⣾⢿⣱⢦⠙⡀⠄⠀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣼⡟⠛⢈⣭⣶⡾⢠⣿⣿⣿⣿⣿⣿⡿⣸⣸⠎⢻⡨⡼⣿⣮⠛⡀⠨⠀⠀
⠀⠀⢀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠹⡏⠈⠑⠻⣿⣿⣿⣿⣿⣿⡟⠟⠀⠑⡀⠡⣛⣢⠁⣷⡰⢰⠈⠂
⠀⠀⠀⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⡠⠊⠀⠀⠁⠀⠀⠀⠀⠻⡙⢿⣿⣿⣶⡄⠀⠀⠇⣮⠢⢻⢶⠰⢀⠚⠘⠀
⠀⢠⡂⠀⣈⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠕⡄⠸⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠙⠻⠿⠿⠁⠀⠀⠈⠈⠆⢂⠁⣾⠆⠉⡘
⠀⣠⣾⣬⡟⠑⣘⢻⣿⠟⣿⡿⣿⣿⣿⣿⣿⢟⣟⠘⡃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⡂⡡⡜⢾⡇
⠈⣿⠉⠉⠠⠈⢷⡄⠙⢨⣟⣯⠛⢛⡛⡾⡻⠘⠏⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢇⠇⠀
⠀⢮⠀⠂⠈⠁⠈⠀⠄⢿⡏⡕⡣⠟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠠⠀⠊⠇⠇⠁⠌⣆⠀
⠀⠸⡆⢠⠀⠀⠀⠀⠀⠈⡇⠻⢛⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠸⣄⣳⡹⡂
⠀⠐⡝⡇⠢⡀⠀⠀⠀⠀⠸⢉⡝⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡄⠀⠀⠍⠀⡇⠂
⠀⠀⠀⠠⡦⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⢈⠃⠀
⠀⠀⡐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠑⢎⠀⡀⠀
⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⢑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠋⠜⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀