⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⢇⠀⡴⢄⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠹⡄⢠⠞⡆⣀⡵⣌⠣⢿⠘⣍⡩⢤⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠳⣙⠞⠂⠳⢫⢘⣤⠭⠶⠖⣤⡀⢸⠉⠉⠉⠉⠒⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⠤⣸⠟⠒⠀⠀⠒⠲⢧⣼⠢⡀⠀⠀⠀⠀⠀⠀⠈⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⢠⡄⠀⡀⠀⠀⠙⢆⢱⠴⡀⠀⠀⠀⡀⢠⠜⠁⠀⠀⢀⣠⠤⢤⠲⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⡲⠀⠀⠀⠈⠉⣉⣴⣶⣶⣦⠈⢞⢠⠷⢺⡿⠋⠁⠀⢇⠀⠀⠀⡎⠀⠀⠘⣾⠟⢆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⢶⢵⣀⣐⡋⠘⠛⠹⠃⠟⣃⣈⣀⣸⡁⠀⢸⠊⠉⢀⡤⣊⡇⠀⠀⠀⢸⣧⡀⢧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡮⢤⡟⠒⠢⣽⡦⠖⣒⡩⠭⠤⣰⠒⠿⡯⣿⣷⣶⡲⠽⠛⠉⢗⡆⠠⣀⣹⢸⣧⡘⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣞⡉⠋⢹⢯⢗⣒⣒⡶⠿⡿⠻⢿⡿⠏⡁⠀⠀⠀⠀⠀⠀⣽⡞⢃⡞⡼⣷⡇⢣⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣚⣽⣯⠽⠿⣩⣧⣶⣶⡛⡿⠫⠗⠋⣸⠠⠤⠤⠤⠤⣴⠞⠳⠼⣇⠗⡏⢇⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡫⣁⠀⣉⣟⣶⣃⡟⠃⡞⠉⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢰⢻⠀⠙⣼⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⢛⣿⠉⠫⡿⠥⣺⣿⠯⢰⠁⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⠠⡄⠀⢸⢈⠠⡔⢺⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢯⡘⠂⠀⠀⠀⠀⢸⣀⣾⠀⡔⡱⠒⠊⠉⠉⠀⠀⠀⠀⠀⡇⣀⡌⠘⢄⣇⣼⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢏⣿⠍⠉⢽⡖⠒⣼⠛⣿⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢣⣧⠔⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⠚⢍⣉⡇⠈⠉⠉⠉⠐⠒⠭⢧⡏⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⡀⣉⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢦⢀⢿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠘⠁⠈⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡼⢞⢹⣕⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢰⠊⠁⠀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡜⠀⠀⢙⣥⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡒⠉⠁⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠸⡀⠈⡆⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⢐⡻⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡁⢀⠀⡄⣳⠖⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢌⣉⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠓⣚⣒⡞⠁⠀⠀⠘⠦⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠇⠈⠳⠀⠀⠀⠀⠀⠢⣀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠥⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢖⠂⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣃⠀⠤⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣁⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⣮⠃⠀⠀⢨⠗⠢⡀⠀⠀⠀⣀⠤⣤⠞⠁⠀⠈⢆⠀⠀⠀⠀⠀⠀
⠀⢠⣾⣷⡏⠀⠀⢀⣀⢤⠤⠤⠖⢒⡎⠀⠀⠀⠀⠁⠀⠀⠀⠏⠀⠀⣸⣦⠀⠈⠀⣰⠃⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀
⠀⢸⡉⢿⠉⠉⠉⠁⠈⣾⣀⠤⠔⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠈⢇⠀⠐⡅⠀⢰⠀⡴⠀⢠⡇⠀⠀⠀⠀⠀
⢠⠃⠁⡚⠓⠒⢒⡩⠽⠊⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠑⠒⠅⠀⣸⡜⠀⠀⠀⡇⠀⠀⠀⠀⠀
⠘⢲⠂⠊⠉⠉⠁⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⣰⠧⠒⠊⣹⠀⣇⠀⠀⠀⠀⠀
⢰⡫⠤⠀⠀⠀⠀⠀⠀⢀⡴⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⣀⡼⠥⢧⣄⡠⢯⠞⢹⠀⠀⠀⠀⠀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢹⠀⠀⢀⣴⡋⣜⡀⢸⠀⠀⢈⡆⡠⠃⠀⠀⠀⠀
⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢠⠏⠀⢀⡼⠁⠛⠉⠧⠆⠦⠏⠉⠉⠀⠀⠀⠀⠀⠀
⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠳⠶⣤⡤⠤⠤⠒⠋⠁⠙⠦⣀⠀⠀⠀⠀⠀⢀⣀⠤⠶⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀