⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠠⢄⣠⠔⠋⠁⠀⠀⣠⣽⡀⠙⢠⣚⣓⠒⠒⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⠤⣴⠾⠛⠋⠉⠁⣠⡿⠋⠀⠀⠀⢀⠔⢋⠀⠀⠀⠀⠀⠈⠉⠛⢦⡀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣞⠥⢒⠖⠂⠀⠐⠊⠉⠀⠀⣀⠠⢤⣼⠏⠀⠀⠀⠀⡰⠃⢠⠊⠀⠀⠀⠀⠀⣠⠀⠀⠀⠙⡄⠀⠀⡀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠊⠀⢠⠁⠀⠀⠀⠀⠀⢀⡴⢋⣠⣶⡿⠃⠀⠀⠀⠀⡜⠀⡰⠁⠀⠀⠀⠀⠀⡰⠁⠀⢀⡀⠀⠘⡆⠀⡇⠀⠸⣵⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢀⠔⣊⣽⣷⡿⠟⢛⢇⠀⠀⠀⢀⡞⠀⡰⠁⠀⠀⠀⠀⠀⡰⠁⣀⠴⠋⠀⠀⡄⠸⡄⠱⠄⠀⢹⣷⠀⢬⡐⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣠⣼⡿⢿⣿⡽⠊⠀⢀⣿⣆⠉⠒⠠⢼⣀⣰⣅⠀⠀⠀⢀⣀⠴⠗⠊⠁⠀⠀⠀⠀⠁⠀⢡⠀⠀⠀⠈⣿⡇⠀⠙⡸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⠟⠓⠋⢁⠜⠁⠀⠀⡜⠈⢫⡁⠀⠀⠀⠀⣿⡿⣧⣠⣾⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢸⡇⠀⠀⢹⢧⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⣿⢟⡧⠊⠀⠀⣠⠊⠀⠀⠀⡾⠃⠀⠀⠉⠢⠤⣀⡀⣿⣥⡿⣿⡀⣼⠁⠀⠀⠀⠀⠀⠀⣠⡴⡇⢀⠀⠃⠀⠀⠀⠨⣷⠀⠀⠘⠀⠳⡄⠀⠀
⠀⠀⠀⣰⣿⣿⡟⠋⠀⠀⢀⠴⠁⠀⠀⠀⡰⠃⠀⠀⠀⣰⣥⢀⠴⠛⡯⢟⠳⢿⡿⣿⠶⢚⣀⠠⠴⠒⠛⠁⢰⡵⠋⡆⠀⠀⠀⠀⠀⡿⣇⠀⠀⡄⠀⠈⢆⠀
⠀⠀⣼⣿⣿⣿⡇⠀⢀⡴⠋⠀⢀⡀⣠⠞⡀⠀⠀⠀⢰⢿⣰⢁⣀⣰⣁⡈⣆⠀⠈⠉⠉⠁⠀⠀⠀⠶⠶⠶⠓⢲⠒⠂⠀⠀⠀⠀⠀⡇⣿⠢⡀⠱⡀⠀⠈⡆
⠀⠀⠃⠈⠁⢀⣠⣔⣉⡤⣴⠊⠁⠘⠉⠀⡇⠀⠀⡠⠃⠸⡟⠛⠛⠛⠛⠿⠾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⡏⢰⢦⣀⡇⠀⠀⠀⠀⡇⣿⡀⢹⡀⠑⠄⠀⢸
⠀⠀⠀⠉⠉⠁⠀⠀⠀⡰⠁⠀⠀⠀⠀⡸⠁⡠⠞⠁⠀⢀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣴⣾⣤⣌⠀⡛⠀⠀⢀⣾⣰⢀⣿⢳⠸⢳⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠞⠚⠁⠀⠀⠀⠀⠸⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣿⣷⢄⡠⠋⡸⢃⣾⡟⠀⢧⢨⠂⠀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⣀⡴⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⡳⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⠤⠶⣥⠞⠒⠉⠀⠀⣡⣾⣿⠁⠀⠘⡞⢀⠜⣧⠃
⠀⠀⠀⠀⠀⢀⢴⡥⣴⣖⢈⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⣞⠁⠀⠀⠈⢱⣲⡄⠀⢀⡠⠔⡊⠁⠀⠀⠀⢴⣾⣿⡿⠁⠀⠀⠀⡧⠋⠼⠃⠀
⠀⠀⠀⠐⠚⠁⡔⠀⣿⡯⠊⢀⡤⡞⣠⠆⠀⠀⠀⠀⠀⠀⠀⢸⣅⠀⠀⠀⠘⢄⠀⠀⠀⠀⣹⠃⣴⡯⡶⠋⠀⠀⡠⠒⠀⠈⠛⠉⣠⠀⠀⢀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⡰⠋⠑⠲⣗⠒⠉⠁⠘⠋⡜⣠⢤⡄⠀⠀⢀⡼⡡⠋⠈⠳⣄⠀⠀⠀⠉⠒⠒⠉⠀⡼⠋⣸⠀⠀⢀⣴⠃⠀⠀⠀⢀⡴⠃⠀⠀⡼⢀⠃⠀⠀⠀⠀
⠀⠀⠀⠀⣇⣀⢲⣄⣬⣆⠀⠀⠀⣼⠏⠀⡸⢁⡠⢔⡽⠻⡄⠀⠀⠀⢸⠙⠢⣄⠀⠀⢀⣠⠤⡖⢪⢇⡠⠔⠋⡈⠀⢀⡤⠖⢁⣀⡤⠔⠋⢠⠞⠀⠀⠀⠀⠀
⠀⠀⡠⠞⠁⠀⠙⢌⠻⣿⠀⠀⡽⠁⠀⡔⠋⠁⠀⠀⠀⠀⠈⢻⡷⢄⡏⠀⠀⠀⠉⠉⠁⠀⠀⡵⠋⠁⣀⣤⡶⠗⠋⣝⡵⠊⠁⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀
⢠⠖⠋⢍⠉⠲⢄⠀⠱⡈⡠⠉⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣧⡀⠀⠀⠀⠀⠀⠀⢀⡇⣉⣉⣁⡀⠀⠤⠤⠯⠤⡖⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⠠⠤⠊⠙⢦⣾⣦⣶⣯⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⣿⣷⣶⣦⣤⣶⣶⡿⢿⠀⠀⠀⠀⠀⢀⡠⠖⠈⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀
⠘⡆⠀⠀⠀⠀⠙⢻⠉⠿⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠘⠿⣿⣿⣿⣿⣿⣿⣿⣠⠟⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀
⠀⢰⠀⠀⠀⠉⠑⠃⠀⠀⢀⡜⠀⠀⠀⠀⠀⣀⡤⢔⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠇⣀⣤⣤⣄⣤⣾⣿⡟⠀⠀⠀⣠⠔⠋⠁⠀⠀⠈⠉⠒⠒⠀⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡀⢠⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣼⡀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡿⠿⢿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⣀⡀⠠⠤⠤⠄⠀⠀⡆⠀⠀⠀⢷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⡠⠔⠊⠉⠰⡄⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠒⠂⠀⠉⠉⡏⠉⠉⠉⠀⠐⠒⠦⠤⠥⠊⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⡀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢰⢰⠀⠀⠀⢷⣤⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠘⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡀⠆⠀⣀⣼⣿⡇⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠘⡄⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠘⢆⠀⠀⠈⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⣇