⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⣀⣤⣀⠀⠑⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢀⣤⠞⢫⢅⢣⢹⡷⣄⠀⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡴⢋⠦⡙⢢⢎⡶⠛⠉⠉⢆⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⡴⢋⠴⣉⠒⣍⡶⠋⠀⠀⠀⠀⠈⡆⠀⢁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⡴⣋⠴⣉⣶⣷⣭⡞⠁⢀⡴⢲⣒⣶⣲⣾⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣠⡿⢃⡄⢇⡸⣿⣿⣿⠃⣠⡇⣿⣿⢧⢿⣇⡿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⡴⣋⠔⣣⠘⢦⢡⢋⣵⠃⢠⡿⡿⣿⣋⣯⢟⣛⠻⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⡱⢌⠚⡤⢙⡂⢎⣲⠇⠀⢎⡹⠓⠉⠀⠀⠀⠈⠓⡏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠀⢀⣠⢖⢫⠰⣑⠊⡵⢈⠣⡜⢢⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢚⡍⠲⢌⠆⡓⠬⡱⢌⢃⠳⣨⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢠⣾⢋⠴⣈⠇⣌⠳⢌⡊⠵⡑⢢⢍⡊⠵⡠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠙⠚⢦⣑⠪⣄⠳⠌⡜⡡⠎⢥⠒⣌⠓⡔⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠰⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠀⠀⣼⢂⠳⣠⠋⡜⡰⢡⢋⠆⣍⢢⡙⢤⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣞⢣⢊⠵⡠⢋⠴⢡⢃⠎⣜⠰⣂⠍⡆⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢠⡾⢡⠆⡍⠦⣑⢩⠒⡥⢊⣜⡾⡗⣌⢚⣰⠇⠀⠀⠀⠀⠀⠀⢀⣴⠟⣧⠀⠠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⡟⡰⢃⡜⠬⡑⡌⠦⡙⢤⢣⡞⠁⠹⣔⣦⡞⠀⠀⠀⠀⠀⢀⣴⠟⣡⠚⣸⡇⠀⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢠⡟⢄⢣⠱⢌⠲⡑⢬⡑⡱⣺⠃⠀⠀⠀⠉⠉⠀⠀⠀⠀⣠⠖⠿⣥⡚⢤⡙⠤⣧⠀⢰⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣈⠎⢆⡍⣊⠵⡘⢢⠜⣵⠃⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⡠⣀⠀⠙⢷⡬⣑⢻⠀⠈⠀⠀
⡐⠁⢀⣠⡤⠶⠶⠶⢦⠤⡤⢤⠤⡞⠥⣋⠴⣉⠲⢌⠒⣆⡙⠆⡾⠃⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠄⠊⠀⠈⠱⡄⠀⢳⡌⣾⠀⢠⠀⠀
⡇⠀⠻⣭⡒⢍⢎⡱⢊⠖⣑⢊⠖⣉⠖⣡⠒⡬⢑⢪⠱⡰⢌⢳⡃⠀⠀⢀⡠⠔⠊⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠙⠃⠀⡘⠀⠀
⠘⠄⡀⠈⠙⠾⣴⡨⡑⢎⠴⡉⡜⡰⢊⠴⣉⠴⡉⢆⡓⣴⣩⡮⠽⠖⠊⠁⠀⠀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠊⠀⠀⠀
⠀⠀⠈⠓⣤⠀⠈⣧⠑⡎⢢⢱⡌⣥⠉⣶⣬⣶⠛⠋⠉⠁⠀⠀⠀⣤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⢠⣏⠲⢡⠎⢢⢱⡾⠛⠉⠀⡀⠀⠀⠠⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠇⠀⣸⠣⢜⡡⢎⣱⠏⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠀⢠⣏⠱⣊⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⠀⠸⣧⠷⠞⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀