⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠈⠉⠀⠀⠀⠠⠀⣀⠀⠐⠲⠌⡑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢴⠮⠵⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⡶⠌⣉⡉⠲⣄⡀⢈⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠊⢀⡀⠐⠒⠒⠒⠒⠒⡠⠟⠛⠉⠉⠉⠁⠒⠿⣶⣿⣟⠮⠁⠢⢄⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⡤⡤⣄⡨⠁⠀⠀⠀⠠⠋⠀⠀⣴⣶⡿⠟⠿⢷⣮⣷⠗⢷⡧⠄⠀⠀⠑⢤⢀⡠⠤⠃⠠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⠁⣹⢼⣾⡿⢿⡭⣝⣻⣆⢀⡠⢤⣀⣒⣲⣛⡿⣗⢊⣩⣭⣉⡛⢻⣿⣾⣧⠤⠄⠒⣋⣩⣤⡤⢒⠒⢪⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡝⣼⡯⣿⣿⣟⣻⣟⢿⣿⣿⣿⠛⠙⠁⠀⣼⣿⡞⢳⢹⡿⠿⠓⠋⣹⡩⠤⢴⣶⣿⢿⣋⠁⠀⣀⠉⠙⠺⢄⠀⠀⠀⠀⠀
⠀⠀⠀⣠⢾⣿⣿⣿⢛⣿⣻⢻⣈⡉⣹⣫⣷⣲⣶⣻⣿⣿⠟⠛⡏⣥⠒⠦⠙⠋⢐⡺⠿⠋⠉⠁⠀⠀⠀⠈⠉⠑⠲⢤⡑⢄⠀⠀⠀
⠀⢀⣎⠗⠁⠘⣌⣿⣓⣗⣺⣾⠏⠀⠀⠻⣿⣿⣂⣿⣻⣿⣷⣴⣵⣀⡀⢀⡰⠒⠉⠀⠀⠀⠀⠀⠠⡤⢀⣀⠢⢤⣀⠙⢿⣦⡑⡄⠀
⢀⡞⠁⠀⣀⣀⣼⣷⡾⢿⡟⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⡿⠿⠿⠟⠛⠓⠒⠒⠒⠛⠛⣛⡿⠻⢿⣶⣬⠻⢄⠺⣷⢤⠐⠿⡘⡀
⢿⣀⢠⣤⣾⡟⢱⡀⢠⡎⡇⠀⠀⠀⣀⡀⠀⠀⠈⢻⣿⣮⠑⠂⠀⠀⠀⠀⠀⣐⣒⣺⣭⣭⠐⡲⣀⣼⣿⡿⠇⠀⣴⡿⡇⠳⠀⢻⡇
⠘⢟⣀⡻⡿⠻⠿⢷⣾⣿⣿⣦⠀⠀⠀⢴⣾⣧⣄⣠⣿⡿⠀⠀⠐⢲⡶⠿⡟⠿⠟⣛⡭⠔⣫⣾⣿⣿⣿⣾⠂⣾⠵⠞⠀⠀⠀⠘⠇
⠀⠀⢻⠗⢷⡀⣠⣀⡰⠿⠿⢿⣿⣿⣿⠿⡿⠿⢟⣉⠤⠤⠤⢖⣈⡁⠤⣴⣶⣮⣭⣴⣾⣿⠛⢻⣿⣿⣿⣷⡔⠀⠀⠀⠀⠀⠀⣸⠀
⠀⠀⣾⡇⣾⣿⣾⣦⣱⡈⢀⣴⣯⣡⣆⣀⣲⣠⣧⣤⣶⣾⣿⣥⣴⣶⡿⣿⣿⣿⢛⣿⣽⣎⣧⣼⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⣼⠇⠀
⠀⠀⣿⡃⣿⡿⣧⠟⠛⠿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠿⠿⠛⠛⢿⠁⠿⠿⠋⡟⢰⣿⣿⣿⣿⣿⠟⣱⠇⠀⡴⠀⣦⠀⢀⣴⠟⠀⠀
⠀⠀⣿⠁⣽⣠⠻⣦⣀⠀⡏⠀⠘⢸⠁⠀⠀⠀⠘⡇⠀⠀⠀⠀⣸⣀⣠⣤⣾⣿⢿⣿⣿⡿⠃⠀⠈⠁⠀⡼⠀⠀⠘⢶⡿⠋⠀⠀⠀
⠀⠀⡹⣧⠙⢿⣄⠟⣿⣿⣷⣶⣶⣼⣤⣤⣤⣦⣴⣧⣶⣾⣿⣿⣿⣿⠟⢛⣩⠷⣿⢿⠍⠀⠀⠀⠀⠀⣸⠁⢀⢇⡔⠁⠀⠀⠀⠀⠀
⠀⠀⢿⡻⡓⠘⠻⣦⣀⢹⠙⠛⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠛⠛⣙⡤⠖⢋⠤⠊⠐⠁⠀⠀⠀⠀⠀⢠⠇⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⣷⠁⠀⠀⢈⡉⠙⠷⠶⠦⠾⠦⠤⠤⠤⠤⠾⠒⠒⠒⣉⠡⠔⠊⠁⠊⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠎⠘⣜⠀⠀⠰⠤⣯⣄⠀⠀⠀⠀⠀⠠⠤⠒⠒⠒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⠀⠐⠚⠛⣻⣦⠤⣼⡍⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣀⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⡠⠀⠀⠀⠀⠉⠙⠿⢵⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⣼⢿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡣⢶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⡄⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢷⣄⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠮⣡⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠳⣀⢀⡀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⢊⡡⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠑⠪⢄⣀⠀⠈⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⡭⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠂⠠⠤⠤⠤⠤⠄⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀hehehehar