⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⡄⠀⠀⠠⣤⠀⠀⠀⠠⠄⠀⠀⠀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡎⣡⣄⠸⠀⠀⠀⢰⠂⢿⡿⡆⢻⠠⢿⡿⠀⡅⠀⠀⠀⡇⢠⣤⣤⠉⡆⠀⠀⠀⡠⢄⣀⠀⠀⠀⠀⠀
⠀⠀⡔⠂⣉⣤⡈⢢⠀⠀⠀⢸⢠⡟⢽⡀⡆⠀⠀⠈⢳⠀⣿⣽⠘⡆⢸⡇⡖⠁⠀⠀⠀⠣⡄⢹⡍⢀⡇⠀⠀⢀⠃⣴⣤⠘⠀⠀⠀⠀
⠀⠞⣰⠟⢋⠉⣿⠰⠀⠀⠀⡇⢸⠇⢸⡇⢸⠀⠀⠀⢸⠀⣷⢹⣧⠑⢸⡇⡃⠀⠀⠀⠀⠀⡇⢸⡄⠇⠀⠀⠀⡸⢠⡿⢹⡄⡆⠀⠀⠀
⠀⠀⣿⠀⢹⣀⡁⢼⠀⠀⠰⢀⡟⠸⠆⣿⠀⠇⠀⠀⢘⠀⣯⠀⢿⡆⢸⡇⡅⡖⢒⠒⠒⠂⡇⢸⡄⠃⠀⠀⢀⠃⣼⠇⠸⣇⢱⠀⠀⠀
⠀⠀⣿⠀⠖⢀⣉⢩⠀⠀⡄⣸⣧⣶⡶⢾⣇⢰⠀⠀⢸⠀⣷⢸⠘⣷⣸⡇⡇⡆⠘⣿⠿⠀⡇⢸⡄⡃⠀⠀⡘⢠⡟⠐⠇⢿⠈⡆⠀⠀
⠀⠀⣿⠀⡀⠟⣿⢠⠀⢰⠃⣿⢡⡤⢴⠄⣿⡀⠧⢦⠞⠠⣿⠘⢃⢹⣿⠆⡇⠈⡇⣿⡃⠶⠇⣹⠆⡅⠀⢀⠇⣾⠿⠷⢶⣾⡆⢁⠀⠀
⠀⠀⣿⠀⢳⠀⣿⠰⡔⢊⣸⣇⡀⠩⠆⢰⣿⢳⠆⢹⡀⠿⠯⠇⣼⡌⠿⠃⣇⠀⢣⠙⠷⣶⣶⡾⠃⡆⣈⢉⣰⡿⠰⢒⢤⡄⣿⠘⡀⠀
⠀⠀⣿⣀⣁⣤⠟⡘⡇⠹⠛⢋⣁⡔⠃⠤⠤⠤⠒⠋⠒⠒⠒⠒⠃⠙⠒⠒⠋⠀⠀⠑⠢⠤⠤⠤⠊⠀⢜⠘⠛⠟⠇⢸⠂⢠⣹⡆⠣⢄
⠀⢆⠙⠛⣉⡉⠴⠁⠓⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠜⠣⣈⠛⠛⠇⢼
⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠚
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢿⣿⢋⣭⡉⣿⠟⣩⣋⣙⠿⡿⢋⣩⣙⡻⣿⡶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢤⡀⠀⢸⠆⠀⢠⠀⠀⢀⣴⣿⢿⡽⣷⣻⡿⢡⠏⣟⢰⣯⣘⣁⡆⣿⠸⡇⣟⢰⠈⡇⣿⣽⢯⣷⢿⣻⣦⡄⠀⢠⡀⠀⢀⡇⠀⢀⠀
⠀⠀⢳⡄⣸⡇⣴⠇⠀⠀⣿⣻⢾⣻⡿⣽⡟⣰⠋⠂⣯⠘⣿⢩⠶⠶⠟⣸⡇⣏⢸⠀⡇⣿⢾⣯⣟⣯⣟⡷⣿⠀⠀⢹⣆⢸⡇⣠⠟⠀
⠈⠲⢦⣹⣼⣵⣣⡴⠚⠀⠙⢿⣻⣽⣻⡽⣷⣌⣉⠉⡿⢁⣿⢸⠀⡯⣩⢩⡇⡷⠸⠄⡇⣾⣿⣳⣯⢿⡾⡿⠋⠈⠓⢦⣝⣮⣵⣫⡤⠖
⠀⠀⠴⠶⠻⠗⠦⠄⠀⠀⠀⠀⠉⠓⠯⢿⣷⣻⢿⣐⣛⣂⣷⣘⣛⣓⣛⣰⣧⣙⣚⣛⣡⣿⣳⡿⠞⠛⠉⠀⠀⠀⠀⠤⠖⠿⠞⠦⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠛⠚⠙⠚⠋⠛⠚⠓⠛⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢔⡵⠲⡰⡇⣶⡁⡰⣴⠎⢆⡵⠲⡴⡇⡶⠉⣰⠎⡇⢶⠲⢶⢡⠀⠀⣥⠖⢶⠲⡦⢉⢶⠶⢺⢸⠀⢠⠱⣌⡀⠀⡅⣶⡡⡰⣱⠎⠀
⠀⡸⣖⣓⢒⠀⣧⢋⢱⢹⠈⢸⡇⠇⣽⠀⣇⣼⢑⠀⢈⢿⣘⢒⠂⠀⠀⠪⠤⢸⠰⠭⠸⢸⣘⡓⠈⠀⡆⡇⢼⢰⠀⢸⢆⢣⣱⢹⢸⠀
⠀⢚⡒⠆⣃⡠⣏⠞⠣⢺⢠⣹⡆⠇⣻⡀⡏⢈⣆⠄⡨⢾⠰⢚⢢⠀⠀⠀⣀⢸⠠⠀⠰⢸⠰⢒⢲⠐⣸⢩⠝⣇⢀⡸⢎⠌⢃⢾⠸⠀
⠀⠁⠝⠩⠘⠣⠙⠴⠪⠙⠣⠁⠝⠩⠌⠃⠏⠝⠨⠡⠣⠙⠍⠏⠜⠀⠀⠀⠣⠙⠣⠀⠠⠋⠝⠫⠼⠌⠫⠜⠠⠋⠥⠃⠏⠼⠺⠉⠇