⠀⠀⠀⠀⣀⣠⡤⠤⢤⣀⡀⠀⢀⡴⢶⡀⠀⠀⣀⡤⡶⢒⠛⡩⢙⠓⣒⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣴⡿⠿⠛⠛⠛⠓⠾⢽⣶⢋⡿⣟⣿⡶⢛⣹⠖⡰⢡⠎⡑⢎⡑⢢⡉⠦⢠⠙⡓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣹⣿⣾⡿⢉⠜⡩⠔⡘⠤⢃⠬⡱⢌⠬⡡⠜⣐⠣⡑⢌⠢⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣳⣢⣿⢋⠱⡈⢆⠱⡨⢑⠊⣅⠲⣁⠎⢢⠱⡑⠌⣆⠱⡈⢆⠱⡈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⢇⣾⣦⣱⣌⣂⠱⠨⠜⡠⢃⢆⡙⢢⠱⣈⠱⣀⠣⡑⢌⣢⠑⡘⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⢂⠛⠟⠿⢿⣿⣷⣷⣌⠱⡈⠆⡜⠡⢆⣡⣶⣴⣷⣼⣶⣿⡗⢠⠙⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠓⡌⢦⣿⣴⣧⣾⣮⣿⣿⡿⢆⠡⢋⠌⣱⣿⣿⣿⣿⣿⠛⢩⠡⡘⠄⢣⢹⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣶⢺⣼⡿⢉⢍⠩⡉⡍⢩⢁⠎⡡⢃⠎⡄⢛⠛⡻⠿⢿⣿⣶⣧⣷⡌⢢⠘⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⠋⡄⢧⣿⡿⢑⠪⣄⢣⠱⢨⡁⢎⡰⢑⠪⡐⢌⢃⠣⢆⠱⢂⠤⡉⣿⢳⣜⣦⠑⡸⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡞⢡⠃⡜⢠⠒⡌⢢⠱⢄⠪⢌⠥⡘⢢⢘⠂⣇⠩⢒⠬⡑⣌⢪⠘⠆⡥⢙⣮⣛⣿⢈⠔⡹⣇⠀⠀⠀⠀
⠀⠀⠀⢀⡴⢋⠴⠁⢎⠰⡁⢎⠰⣡⢊⢌⠱⡊⡔⣡⢃⠎⡱⢠⡙⣐⢊⡔⠢⡌⢍⠎⡰⢡⢂⢍⡰⢈⠒⠤⡙⢦⡀⠀⠀
⠀⠀⣰⠟⡅⢎⠰⢉⠢⢱⣼⢀⠣⡔⢌⠪⠔⡱⠌⡴⢈⠎⣅⠣⠔⡡⢎⡐⢣⠜⢢⡉⠖⣡⢊⠴⣀⠣⡘⠤⡑⠌⢷⣄⠀
⠀⢸⣿⡑⠌⡜⢠⠃⡜⣸⡿⣀⠣⠜⢢⠑⠎⡔⢣⠰⣉⠒⡤⢋⠜⡡⠆⣍⠒⡸⢠⠜⣡⠒⣌⠒⠤⠱⣇⠢⢩⠘⡄⠺⣧
⠀⠈⢿⣷⣈⢦⢡⠞⣴⣿⢷⠀⠧⡉⢆⡉⠖⡘⠤⢃⠴⡁⢆⠣⣊⠱⡘⠤⡉⢆⢣⡘⢄⠣⡘⢌⠢⡑⢻⣷⣌⢲⢨⣅⣿
⠀⠀⠀⠈⠛⠺⠷⠛⠛⣿⡈⠜⡰⢑⢢⡘⣴⣱⠾⢶⣢⠍⡢⡑⢤⢃⠥⠓⣈⣦⠿⣶⣌⡡⢉⠆⢣⠘⡌⣿⠾⠯⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣱⣚⣶⡿⠋⠁⠀⠀⠈⣿⡐⡑⠆⣌⠢⡑⣾⠏⠀⠈⠙⢿⣧⣚⣤⢣⣾⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⣴⣉⡤⢣⣽⡟⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀