⠀⠀⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⣿⡂⢹⡇⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⢸⣇⢸⣇⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⣯⡀⡆⠀⠀
⢸⣷⢸⣇⣸⣇⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣂⠀⣿⡄⢸⡀⣤
⢠⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣊⡝⠛⠙⠂⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣼⣷⣼⣁⠼
⢸⣿⣿⣿⣿⣿⣿⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡻⣥⢋⡔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣂⣜⣿⡟⢿⣿⣿⣄
⠈⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⢯⣿⣾⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢪⣷⣿⢿⣿⣿
⠀⣿⣿⣟⢿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠛⠉⡉⢸⡉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣽⣗⣿⠇
⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡇⣤⡤⢔⡿⣇⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣯⠀
⠘⡟⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⣿⠗⡲⠏⠟⠿⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠍⠁⠁⠀
⠃⡜⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⣿⡟⢡⡿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠒⠂⠂
⠐⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠸⣡⢶⣿⣟⡃⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⡀⠀
⢠⡏⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢨⠣⠉⠉⠋⠉⠀⠀⠀⠀⢈⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⠀⠀
⢺⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⢛⢭⠏⣢⠍⠈⠖⠀⠀⠒⣶⢦⡁⠂⠀⠀⠀⠀⠀⠯⠤⣤⣴⢶⣍⠝⣯⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⠱⠀⠀⠀⠀⠀
⣯⣯⠸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠍⠶⠤⠈⣆⠀⠀⠀⠀⠀⠀⠀⣷⡻⠀⣼⠀⠀⠀
⣯⣨⡀⢀⡠⠤⣐⠤⣀⣰⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠐⠐⠢⠺⠥⡾⠉⡠⠀⠀⠀
⠋⠙⠈⠉⠉⠁⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠇⣣⡁⢶⣠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⠀⡶⣲⠀⣆⡒⣰⠒⢦⢰⠀⢰⡆⣴⠐⣶⠒⣐⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣺⣿⣿⣿⠛
⠀⠀⠑⢌⠻⣗⣔⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠚⠃⠻⠴⠃⠦⠝⠘⠤⠎⠸⠤⠘⠧⠞⠀⠛⠀⠰⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣾⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠉⠢⠁⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⢠⣤⠀⠀⣤⣄⠀⠀⠀⣤⣤⠀⢠⣤⣤⣤⣤⣤⡄⢠⣤⣄⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⢠⣤⡄⠀⠀⠀⢘⡮⡝⣿⣿⡿⢆⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠉⠉⢿⣷⠀⢸⣿⠀⠠⣿⣿⣧⡀⠀⣿⣿⠀⢸⣿⡏⠉⠉⠉⠁⢼⣿⣿⡄⠀⠀⢸⡿⣿⡇⠀⠀⢀⣿⢻⣷⠀⠀⠀⠞⡜⣹⣿⣿⡙⢆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠐⣿⡯⢻⣷⡀⣿⣿⠀⢸⣿⣷⣶⣶⡆⠀⢺⣿⠹⣿⡀⢠⣿⠃⣿⡇⠀⠀⣾⡟⠀⢿⣧⠀⠀⠀⠠⢽⣿⣯⡙⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⣠⣤⠀⢸⣿⠀⢈⣿⡧⠀⠹⣿⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡄⢻⣧⣾⡏⢠⣿⡇⠀⣼⣿⣷⣶⣾⣿⣇⠀⠀⠀⠘⣿⢣⠜⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣾⣿⠏⠀⢸⣿⠀⠀⣿⡷⠀⠀⠹⣿⣿⠀⢸⣿⣿⣿⣿⣿⡆⢸⣿⡆⠀⢿⡿⠀⢰⣿⡇⢀⣿⡏⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠈⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠉⠀⠀⠉⠁⠀⠀⠀⠉⠉⠀⠈⠉⠉⠈⠉⠉⠁⠈⠉⠀⠀⠈⠁⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠈⠉⠁⠐⡀⠀⠀⠀⠀⠀⠀⠀