⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢥⢪⣵⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠳⣿⣿⣿⣾⣄⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡑⠀⠀⠀
⠀⠀⠀⢙⢿⣿⣿⣿⣦⣼⣔⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢀⣀⣲⢼⡟⠗⠀⠀
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣯⡀⠢⣄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⠒⢊⣤⣔⣿⡿⡋⠈⣤⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠙⢿⣿⣿⣽⣣⠁⢪⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣆⠀⡐⡈⢔⣽⣿⣿⣯⡟⡡⠌⠀⠀⠀⠀
⠀⣀⣶⠾⠟⢻⠿⢷⣶⣌⠙⠷⡟⢅⠆⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠃⠀⠀⡎⠀⠞⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⡉⢄⣦⣾⣿⣿⣿⣿⣷⡄⠀⠈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⡌⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀
⢌⢦⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠃⠀⠀⠀⠀⠀⣠⣶⣿⣏⣉⣉⡟⠲⣄⠀⠀⠀
⠺⣿⣿⠇⡀⠘⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣄⡈⠙⣆⠀
⠐⠋⡿⡴⠀⠀⣿⠙⣿⣿⣿⡟⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⣿⣿⣿⣿⣿⣿⣿⡏⠻⣿⣆⠈⠀
⠀⢋⠀⠘⣄⠀⠘⢶⣴⣿⠟⢀⣘⣿⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣿⠁⢻⡿⣿⣿⣿⣻⠀⠀⠛⣿⣷⠀
⠀⠈⠀⡘⣈⢲⢤⣀⢀⣀⡴⠦⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢅⠀⠸⣿⣿⢈⣠⡏⠀⠀⡤⢫⣿⠠
⠀⠀⠞⠁⠐⡷⣹⣦⣤⣴⡶⣯⠢⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠚⠓⠲⣄⠈⠙⠋⠋⠀⢀⠔⢠⣸⡶⠀
⠀⠀⠀⠀⡖⠁⠌⢸⢨⠁⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠌⠁⠙⠐⠀⠄⢁⠲⢍⢺⠓⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⡿⡾⣿⠛⡀⠹⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡅⠐⠁⠘⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢥⢪⣵⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠳⣿⣿⣿⣾⣄⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡑⠀⠀⠀
⠀⠀⠀⢙⢿⣿⣿⣿⣦⣼⣔⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢀⣀⣲⢼⡟⠗⠀⠀
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣯⡀⠢⣄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⠒⢊⣤⣔⣿⡿⡋⠈⣤⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠙⢿⣿⣿⣽⣣⠁⢪⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣆⠀⡐⡈⢔⣽⣿⣿⣯⡟⡡⠌⠀⠀⠀⠀
⠀⣀⣶⠾⠟⢻⠿⢷⣶⣌⠙⠷⡟⢅⠆⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠃⠀⠀⡎⠀⠞⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⡉⢄⣦⣾⣿⣿⣿⣿⣷⡄⠀⠈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⡌⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀
⢌⢦⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠃⠀⠀⠀⠀⠀⣠⣶⣿⣏⣉⣉⡟⠲⣄⠀⠀⠀
⠺⣿⣿⠇⡀⠘⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣄⡈⠙⣆⠀
⠐⠋⡿⡴⠀⠀⣿⠙⣿⣿⣿⡟⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⣿⣿⣿⣿⣿⣿⣿⡏⠻⣿⣆⠈⠀
⠀⢋⠀⠘⣄⠀⠘⢶⣴⣿⠟⢀⣘⣿⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣿⠁⢻⡿⣿⣿⣿⣻⠀⠀⠛⣿⣷⠀
⠀⠈⠀⡘⣈⢲⢤⣀⢀⣀⡴⠦⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢅⠀⠸⣿⣿⢈⣠⡏⠀⠀⡤⢫⣿⠠
⠀⠀⠞⠁⠐⡷⣹⣦⣤⣴⡶⣯⠢⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠚⠓⠲⣄⠈⠙⠋⠋⠀⢀⠔⢠⣸⡶⠀
⠀⠀⠀⠀⡖⠁⠌⢸⢨⠁⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠌⠁⠙⠐⠀⠄⢁⠲⢍⢺⠓⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⡿⡾⣿⠛⡀⠹⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡅⠐⠁⠘⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀
