⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠈⠉⠓⠲⠦⢤⣄⣀⣀⣀⣛⣳⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠒⠚⣛⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⢩⠉⠉⠉⠉⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣀⣤⡾⠟⠷⠾⣿⣿⣶⣦⣤⣀⡀⠀⠈⣀⣀⣠⣤⣤⣬⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠴⠚⠉⠀⣀⠀⠀⠀⠀⠉⣙⠻⢾⣿⣟⡓⠶⣿⣯⠉⠁⠈⠹⣿⠃⠈⠙⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⣠⠴⠒⠛⠉⢡⠔⠛⠉⠉⠉⠁⠀⠀⠈⠙⠻⣶⣾⣿⣷⣄⠀⠀⢹⣧⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⢁⣠⠖⠋⠁⠀⠀⠀⠀⠀⣠⣀⣤⠴⣶⡖⠋⠉⠉⠀⠀⠀⠀⠉⢿⣿⡀⠀⣬⣿⣇⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣦⣤⣄⡀⢀⣀⣤⡶⠚⠋⠀⣠⡴⠋⠁⠀⠀⣠⠄⢀⣤⢴⣿⣻⢈⡿⣤⣿⣿⣷⡀⠀⢰⡆⠀⠀⠀⠀⢻⣿⣴⣾⣿⣿⡄⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡟⠛⠉⠉⠀⠀⠀⣠⠞⠉⠀⢀⣤⠖⠛⣡⡞⠉⢀⡾⠃⣿⣾⡥⠛⠛⢿⣌⢳⣄⠈⢷⡀⠀⠀⠀⠀⢻⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣆⡀⠀⠀⣠⠞⠁⠀⣠⣶⡏⠁⢀⣼⡏⠀⣰⠟⢁⡼⠟⠉⠀⠀⠀⠀⠀⡀⠉⢷⣼⣇⠀⠀⠀⠀⠈⢻⣿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣦⣘⡋⢀⣴⠞⠁⢸⡇⢀⡾⢹⢃⣴⠋⣠⠎⠀⠀⠀⠀⠀⢀⣀⣼⣇⣠⣾⡿⣿⠀⠀⠀⠀⠀⠀⢻⣧⣨⣽⣷⣄⡀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀
⢿⡟⠉⠻⣿⣿⣿⡿⢻⠟⠁⠀⠀⣿⡇⣼⠃⣼⠟⠁⡼⠃⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⢀⡌⠻⣆⠀⠀⠀⠀⠘⣧⠀⠀⢀⣤⣾⠀
⠸⠁⠀⠀⠀⢽⡿⠁⠀⠀⠀⠀⠀⣿⢿⡇⠀⠁⠀⠐⠃⠀⢀⣾⠟⠋⡼⠻⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⢸⠏⠀⢠⠞⠉⠀⠀⠹⡄⠀⠀⠀⠀⠛⠒⠚⠋⢁⡿⠀⠀
⠀⠀⠀⠀⠰⣾⡇⠀⠀⢠⠀⠀⠀⢿⠳⡅⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⢸⠀⢠⠿⢦⡀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠃⠀⣠⣾⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣾⡀⠁⠀⠈⢻⡀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣠⡾⠻⣿⠀⠀⠀⣿⣷⣴⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⣿⡟⣿⠀⠀⠀⠀⠀⠿⣇⠀⠀⢠⡞⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠻⢤⣤⣀⣀⠀
⠀⠀⠀⠀⠀⠸⠟⠁⠘⣿⠀⠀⣰⣿⢿⣿⣿⡻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠟⠛⣧⠀⠀⠀⠀⠀⠀⢹⡀⡴⠋⠀⠀⠀⢀⡾⠃⠀⠀⣀⣀⣀⣀⣀⣀⠀⣼⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣴⠟⠙⢷⣽⣿⣹⣿⡀⠀⠀⠀⠀⠀⠀⠓⠒⠶⠒⠋⠁⠀⠀⠀⠘⣧⣄⠀⠀⠀⠀⠈⣷⡄⠀⣀⣴⠶⠋⠡⣤⡔⠋⠉⠁⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⣈⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⣸⢿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣷⠀⠀⢠⠇⢘⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠘⣧⢠⠏⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣃⣴⠟⠁⠀⠀⠀⠀⠀⠠⣤⣤⣤⠤⠴⠖⠚⠻⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠃⠀⣠⠟⢧⣄⠀⠀⠀⠰⣶⣤⣀⣈⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⢿⠀⣰⠏⠀⠀⠹⣿⣶⣤⣀⣈⣻⡍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠳⠤⢤⣀⣀⣀⣀⣤⡴⢾⣿⡿⠃⠀⠀⠈⢷⣏⣀⣠⡤⠶⠛⠛⠉⠙⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡾⠋⠀⠀⠀⠀⠀⠈⣿⠁⢀⣤⣴⣾⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣞⡿⠞⠋⠀⢀⣀⣀⣤⡴⠞⠛⠛⠷⣤⡀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡀⠀⠀⠀⠀⠀⣀⡴⠟⠋⣀⣤⠶⠛⢋⣵⠟⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⣋⣤⣶⠞⠋⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣽⡿⠛⣩⠞⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠉⠙⠚⠋⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠉⠓⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀