⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠒⠷⣄⣄⠀⠀⠀⠀⠀⠀⣠⣄⠟⠓⡒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢁⢰⣘⢦⣴⣿⣿⠿⠤⣒⣶⢦⠾⢿⣿⣿⣖⠴⡀⠌⡑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠄⠒⠠⡘⡤⠺⣿⢯⢤⢶⠶⣴⠶⡦⣷⢦⣬⢿⡿⢿⠞⣤⠐⡀⠌⠢⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠋⠠⢈⠐⣈⡐⡜⣁⣠⠃⠀⠸⢿⠟⢆⠀⠐⠿⠿⠀⠀⠣⢀⠻⡵⣳⠀⠌⡐⠈⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠁⠠⢁⠂⣐⢊⠞⠀⢳⠀⠰⢤⣀⠀⢀⡌⠀⢢⠀⠀⠀⠀⠀⣼⠀⠹⣕⠻⣆⠠⢁⠠⢳⡀⠀⠀⠀ ⠀⠀⠀⡾⠁⠌⡐⢀⠂⢋⡎⠀⠀⠈⢧⠀⠀⢈⡵⢊⣙⠓⣎⡙⢷⡂⠀⢀⠏⠀⠀⠸⡗⡜⢦⠀⠂⠄⢳⡀⠀⠀ ⠀⠀⣸⠇⡘⠠⠀⠄⡘⡼⠀⠀⠀⠀⠸⣤⠀⢻⣼⣿⣿⣿⣿⣿⡄⡇⢀⡼⠀⠀⠀⠀⢻⡻⡜⡄⢃⠘⡘⣇⠀⠀ ⠀⢠⡟⡠⠄⠡⢈⢐⠠⡇⠀⠀⠀⠀⠀⠈⠺⢜⡜⠿⣿⣿⣿⠿⣧⠿⠋⠀⠀⠀⠀⠀⠘⣷⠹⡔⡀⠂⠄⢹⡄⠀ ⠀⣼⢃⠂⠄⡁⢂⢸⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠒⣲⠓⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⡳⠠⠁⠌⡐⣧⠀ ⠀⣿⢊⠐⠠⠐⠠⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣤⣥⣤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢬⡱⢁⠌⡐⠀⣿⠀ ⢀⣿⡈⠄⠡⢈⠐⡈⢺⠀⠀⠀⠀⢀⣀⠔⢋⣶⡿⢗⣻⢿⡹⣻⣕⣎⠓⢤⡀⠀⠀⠀⠀⣿⢆⡳⢈⠄⠠⠁⣾⡆ ⠀⣷⡜⣠⠁⢂⠐⠘⡞⠀⠀⣀⣴⣾⣴⡴⡛⢥⢚⣰⡟⠈⣷⡐⢪⡙⢾⡦⣾⣶⣄⡀⠀⢹⣮⢱⡃⡌⠠⢁⡿⠀ ⠀⠘⢿⡤⡓⠤⢈⣶⣡⣴⣾⡿⠛⢹⣿⣅⠳⣈⠖⡸⢷⡴⢿⡈⢧⡘⢆⣻⣽⠙⠻⣿⣶⣤⣿⣢⢝⡰⣃⡾⠃⠀ ⠀⠀⠈⠓⢿⣦⢹⣁⣹⡿⠋⠀⠀⣼⣾⣿⣿⣷⣾⣷⣶⣿⣶⣿⣶⣾⣷⣿⣿⡄⠀⠈⠻⢿⣀⣿⣊⡶⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠳⣷⠁⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⢤⣉⡉⠉⠉⠉⠋⠉⠉⠉⣉⣡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡾⣛⡻⠯⠿⠿⣟⡻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⡇⠈⡏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣾⡇⠀⣿⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠏⠈⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠛⠋⠉⠉⠉⠙⠛⠓⠦⣤⡀⢰⡶⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡉⠛⠒⠶⠶⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⡾⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⣄⠀⠙⢿⣿⣻⣷⠶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣾⠗⠋⠀⢀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⢻⢦⠀⠀⠀⠀⢀⡌⢦⡀⢈⣳⣹⣻⡄⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⣀⡤⢀⡇⠠⣀⠀⣰⠸⠀⠀⠀⠀⠀⢸⡆⢣⡀⡠⠚⠁⠀⢸⣳⢼⠈⣧⣿⢳⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢃⡔⡎⡿⢁⣼⠀⠀⠈⣹⠯⣄⣇⠀⠀⠀⠀⠸⢧⠔⢻⡀⠀⠀⠀⠈⡏⣇⠘⡟⣿⡇⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣻⢰⢻⠻⡾⣤⢀⣀⢰⡛⠀⠀⠹⡀⠀⠀⠀⠀⡇⠀⠀⠹⡆⠀⠀⢀⡗⡿⡟⣿⣿⡇⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡎⡈⡸⠀⡟⡎⠉⣿⣇⠀⠀⠀⠹⡀⢠⠀⢰⣷⠀⢀⣠⠾⣏⠀⢸⠁⣿⣇⣿⢸⠁⣀⠤⡾⡷⢶⣶⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⣿⡺⣅⣧⢇⡆⠃⢡⠸⢸⠉⠓⠶⣤⡀⠹⡌⣦⠀⢸⣴⣋⠁⠀⠸⣆⠸⠀⡟⣿⠿⠛⠉⠁⠀⣇⢻⠚⣿⣻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡽⣇⠱⡞⡟⣼⣾⣸⡘⠂⡈⠀⢀⡴⠞⠉⠀⠈⠻⢵⠆⡄⠉⠙⡓⣶⣿⡃⢀⣿⠃⠀⠀⠀⠀⠀⢹⠈⡤⣷⡾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡝⠛⢲⢣⡿⠏⠈⢻⣧⠀⡇⢚⢉⡄⠀⠀⢠⠤⣤⡀⠿⠯⣑⡜⠛⠋⣧⢃⢸⡇⠀⠀⠀⠀⠀⠀⠸⠀⢷⢫⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⠎⠀⠀⡘⢸⠃⠀⠀⠀⠈⢧⣷⠈⠋⠀⠀⠀⣟⠁⠀⠀⠀⠀⠀⠸⣄⡠⣏⣾⡟⠀⠀⠀⠀⠀⣀⣀⣠⡧⠼⠈⡎⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⣠⠃⠀⠀⠀⣇⣜⣀⣀⡀⠀⠀⠸⣽⣵⣶⣤⣄⣀⣹⣀⣀⣀⢤⠤⣶⠪⠽⣧⣿⣿⣡⠤⠶⠖⠛⠉⠉⢷⠀⠀⠀⠀⠸⡈⢷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠟⠀⢠⠃⠀⠀⠀⠀⠀⣰⠋⠉⠉⠉⠉⠙⠻⠟⠚⠻⠿⠿⠶⣦⢻⣼⡿⣤⢻⡷⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢳⠈⣧⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠁⠀⢀⠃⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⠷⣲⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠈⡄⠘⣇⠀⠀ ⠀⠀⠀⢠⡞⠀⠀⠀⡏⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡴⠟⣠⠋⠀⢸⠠⠄⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢱⠀⠹⡆⠀ ⠀⠀⢠⡟⢀⡴⠀⢰⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢻⢹⡇⠀⠀⠹⣄⡠⠞⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠀⠀⢻⡀ ⠀⢀⡞⢀⣾⠃⠀⡌⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣜⣿⣿⠀⣀⣀⠁⠀⠀⠀⠀⢠⣾⣿⡾⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇ ⠀⣸⠁⡾⣽⠀⠀⠃⠀⠀⠀⡄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡟⢿⣿⢟⠉⠉⢳⣄⠀⣠⣴⣿⣝⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⡿⡀⠀⠀⠀⠀⠀⡄⢠⠀⢻ ⠀⡏⣸⠁⢿⠀⠀⠀⠀⠀⢰⡇⡿⠀⠀⠀⢀⣀⣠⠴⠖⠚⠉⠁⠀⣹⡵⠞⠿⠿⢿⣿⣈⣽⣿⡟⠻⠷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⡇⠀⠀⠀⠀⠀⡇⣾⠀⢸ ⢠⣷⡇⠀⢸⡀⠀⡆⠀⠀⣸⣿⡇⠀⠀⠀⢸⣇⢣⡀⠀⢀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠙⡯⠭⢔⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣿⠃⠀⠀⠀⠀⠀⣣⣿⡄⢸ ⠀⣿⠁⠀⠀⣷⠀⢇⠀⠀⣿⠘⡿⠀⠀⠀⠀⠙⠻⠷⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢸⠀⠀⠀⠀⠀⣸⠟⢸⡇⡞ ⠀⠈⠀⠀⠀⠈⢧⡸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⣼⠀⠀⠀⠀⣴⠋⠀⢸⣽⠇ ⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⣿⠀⠀⣠⠞⠁⠀⠀⣿⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣿⢀⡴⠋⠀⠀⠀⢰⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠮⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣦⡀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣿⢯⣿⣉⠡⣌⢹⣿⣏⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡽⠇⣽⣿⣿⡾⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣿⡿⠻⡢⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠁⠀⠉⢙⣿⣧⠏⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠚⠡⣒⠬⣑⠂⠤⠤⠠⣤⠤⠾⣿⣷⣲⠒⣾⣏⣀⡀⢻⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠛⠩⢴⣾⠀⢰⠀⡈⡣⣪⣔⠃⠀⢡⢸⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣶⣴⡵⠋⠈⣳⣴⢻⢸⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣟⠬⠋⠀⡠⢊⢁⠗⠚⢸⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣾⡿⠛⢁⡠⢴⣿⠀⠁⢸⠀⠀⢸⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣍⣀⣤⡞⢇⠄⢀⠿⡇⠀⠸⡄⠀⣸⣿⣿⢿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢯⣷⣿⣿⡸⠆⠠⠃⠀⠉⠀⠀⠱⠀⣿⣿⡿⢸⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⣷⣶⣷⣦⣤⣤⣶⣶⣶⣦⣿⣿⠃⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢸⣿⠿⡿⠿⢿⣿⣿⣿⣿⡿⠿⠿⢻⣿⢉⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡟⠀⠃⠀⠀⠸⠁⠀⠀⠇⠀⢀⠨⡇⡜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⣿⠃⢀⠀⠀⢀⠃⠀⠀⠀⠸⠠⠊⠀⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡟⠀⢸⠀⠀⡜⠀⠀⠀⠀⠀⠇⠆⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢸⠀⣤⠃⠀⠀⠀⠀⠀⣸⠒⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢀⢯⠦⢸⠀⠀⠀⠀⠀⠀⢻⠇⡀⢚⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⠂⡜⠀⠀⠀⠀⠀⠀⠞⠸⠘⡀⠸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣧⣥⣴⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀ ⠀⠀⢀⠤⡒⠐⣂⣈⣒⡂⠤⢄⣀⣀⣀⣀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀ ⠉⠁⠀⠀⠁⠉⠦⣄⠐⠨⠽⠤⣀⣀⢀⣼⣿⣿⡖⢩⢮⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⡿⣿⠀ ⠀⠀⠐⠒⠊⠉⠉⠀⠉⠉⠐⠒⠂⢤⣾⣿⣿⣿⠗⠚⠓⠿⠶⠶⠶⠶⠦⠤⢤⣤⣀⣿⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠯⠭⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣭⣭⠭⠃