⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⣍⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡉⠉⠉⠉⠉⠉⠉⡉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠻⣿⣿⣿⣶⣔⡄⠀⠀⠀⠄⠐⠄⠀⣾⠇⠀⠀⠀⠀⠀⠠⠂⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢾⣽⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⢺⡎⢀⣠⣆⣆⣠⣄⠤⣲⣞⣭⡕⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣽⣿⣿⣿⣿⣿⣷⠄⠐⠀⡠⣿⣵⣿⣿⣿⠿⠋⠁⠀⢗⣿⡿⠟⣛⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⣺⣿⣿⡿⣿⣿⣿⣷⣥⢤⣼⣿⠟⠋⠛⠁⠀⠀⠀⠀⠀⠙⢠⢖⡂⠭⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠈⠉⠉⠙⠚⠛⠁⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠘⢟⠗⠫⠥⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠈⡜⢉⡩⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡴⠃⠀⣀⡤⣶⣢⡤⠀⠀⠸⠺⢜⢾⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠛⠷⠶⣦⣄⣐⣮⠃⡤⢂⡵⡎⢿⣿⣠⢽⠇⠀⠀⠀⠀⢿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⢿⣿⡯⡽⢟⢳⠀⠣⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢡⠀⠐⠶⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠁⠀⢨⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠋⣸⠒⠢⠤⣄⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠀⣀⣼⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⠒⠚⠁⠀⠀⠀⠀⠈⠓⡆⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡪⠙⠋⠀⠈⣽⡄⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⡐⡄⠀⠀⠀⠀⠀⠀⡿⠀⢀⡇⠀⠀⠀⠀⢀⡴⠋⠁⣠⠞⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⣤⠴⠀⢀⣠⣶⣿⣿⠿⠳⡀⠀⠀⠀⠀⠷⣤⠤⠞⠙⠓⠁⠀⠀⠀⠀⠀⣸⠀⠀⢸⡇⠀⢀⠞⠁⠀⣠⠎⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⢄⣵⡟⠋⠁⣠⣴⣾⣿⣿⠟⠋⠁⠀⠀⠈⡶⣤⡀⠀⠀⠀⣄⡂⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡎⢣⢸⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡸⢶⡻⠚⠉⣠⣶⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⡠⠒⠖⠊⠉⣉⣉⠝⠺⠀⠀⠀⠀⠀⣘⠀⠸⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⣾⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⢵⡐⠒⠊⢉⣠⠴⠋⠀⠀⠀⠀⠀⢰⠏⠀⠀⡇⠀⢸⠉⠹⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠹⢿⣤⠀⢻⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢸⠀⠀⡇⠀⢡⠀⠀⠀⠀⠀⣿⠒⠧⡤⣤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢪⢉⢶⡀⢤⣄⠉⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣡⠳⡀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⢰⠀⠀⠀⢸⠀⠀⡇⠀⡇⠀⠀⡠⠊⠀⠀⠀⡇⡇⠅⠏⠂⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠑⡄⣙⢦⣍⠳⣄⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢰⠁⠀⠙⠦⣀⣀⡀⠤⠞⠁⠀⡠⠁⠀⠀⠀⠀⡇⠀⢸⡞⠀⡠⠃⠀⠀⢀⠔⡡⠊⡨⡨⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣌⢻⣷⣄⣀⣀⣀⣀⣀⣰⣟⣀⣀⣀⣌⣀⣀⣀⣀⣀⣈⣙⣒⣘⣁⣠⣎⣀