⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣾⣾⣴⣦⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠿⠿⠿⠟⡟⠟⡻⢛⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⠁⠌⡐⠀⠈⠀⠡⠀⠠⢀⠀⠆⡑⢢⠜⣌⠻⢿⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠐⠡⢈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠘⠴⢡⠫⡰⣈⣷⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠳⣿⡇⠀⠬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢰⢉⢗⡤⣷⡟⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠱⣿⢂⠁⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⢄⡎⠷⣿⢿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣘⡐⣽⡗⠢⠁⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⠬⠲⣌⢳⣻⡽⣿⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⠘⣿⠠⡘⢌⠊⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢌⠱⡸⢏⡷⡿⣽⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⢧⡊⢺⢫⠐⣾⡿⠯⠲⠴⣶⣤⡀⠀⠀⠠⠀⢄⣰⣶⣼⣦⠷⣼⣯⣿⡽⣽⣿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠟⢪⣝⠸⡜⢩⠯⠳⣯⢷⣿⣷⢯⡹⠲⡈⠀⢳⣿⢟⡿⣷⣶⣾⣷⢿⣿⣽⣻⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠼⠟⣾⡎⡊⡀⠈⠡⠈⠏⠉⠄⠡⢀⠄⢀⣼⡟⣍⡠⢍⡩⣃⡟⡟⡼⡷⣿⢿⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⢑⢸⣝⠤⠁⠂⠀⠀⠁⠀⠀⠀⣈⠊⠡⣎⡧⠇⡁⠈⠁⠠⠜⡬⡝⣾⣽⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣆⡌⣏⠌⠀⠀⠀⠀⠀⠂⢠⠐⡄⠀⢨⢹⡞⣴⡀⢀⢈⠀⡘⠴⣹⣿⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢹⡄⣂⠀⢤⠴⠊⠀⠲⠶⢤⠀⣀⣷⡾⣼⠇⡆⢔⡂⢎⣱⣳⢯⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢅⡌⢯⢀⡸⢀⠃⠄⠀⠙⠛⠋⢅⡦⠻⡾⡥⣽⢸⣿⣹⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡊⡄⠀⠐⠙⢦⡇⣖⣔⣀⣖⣂⣖⣼⣿⢿⢇⠙⣼⠇⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡕⣀⠀⠀⠁⠄⡁⢐⠁⠑⠬⠒⣎⣳⠂⠀⣼⠟⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⣍⠂⡄⠀⠀⠀⠠⠑⢁⠚⡙⠨⢃⢤⣿⢯⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⢿⣯⡜⠄⡀⢀⠀⠈⠨⢘⠠⣥⣳⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡧⣎⢻⡿⣷⣦⣥⣇⣾⣼⣮⣷⣿⣿⣿⣿⡿⣿⣽⣻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⢃⣿⢂⠧⣘⠡⡙⠻⢻⣿⢿⡿⣿⣿⢿⡿⢿⣽⢳⣯⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢨⣯⢏⡌⡌⡍⠔⡈⠀⢂⠣⢙⠢⢙⠢⡙⣟⠖⡿⣜⢻⣾⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⢊⠼⠋⡐⠝⡰⠤⣁⠢⠁⠀⢰⠀⠌⢰⠭⠪⢡⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣶⣥⣼⣼⣴⣭⣭⣷⣴⣴⣤⣮⣬⣥⣮⣼⣦⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶