⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⣩⢴⣶⢶⣽⣿⣷⣼⡘⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡽⢏⣠⣶⣿⣿⣧⣿⣾⣿⣿⣿⣿⡈⢋⡳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣞⢉⣴⣾⣿⣟⣿⡿⣿⡿⠿⣿⣿⣿⣰⠇⣆⣧⠘⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢻⣿⠋⣡⣾⣿⣿⣽⠿⠟⠀⢻⣿⣯⣯⣿⣿⠏⢠⣷⢻⡃⠜⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣰⣿⠋⡼⣫⣞⠟⠛⠩⠆⠄⠀⠈⠻⢿⣷⣿⣿⣢⡿⡿⣼⡄⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣏⣼⣽⣿⡿⠀⢰⡾⣶⣄⠀⠀⢀⣠⣿⣿⠿⢻⣠⢣⣿⡇⠀⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢟⡟⣹⡿⡇⠀⠘⠻⠒⢫⡀⠀⠉⠈⢩⣯⢦⡿⠁⢸⣿⡄⣰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠏⡆⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣫⡿⠋⡰⣠⠿⡿⢠⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⢹⣷⡇⡿⣦⣀⣀⡀⠀⠀⢀⣾⠿⠛⢀⡔⡱⣷⢪⠁⡎⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡤⠶⠶⠶⠶⠶⠶⠤⢷⣵⣝⢢⣀⢀⣠⠴⠒⠒⠦⣄⡀⢀⣀⡴⣒⡭⢺⢙⡾⣘⣟⡽⡼⣟⣿⣿⣏⣩⠟⡿⢁⣤⡶⣫⣾⡿⢡⠇⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠉⠀⠀⠀⠈⠉⠉⠛⠒⠶⠄⠀⠀⠀⠀⠀⠀⠉⠙⠿⣷⠤⠄⣀⣀⣀⣈⣙⣦⣍⠀⢬⣼⣿⡷⢋⣼⢌⣾⡿⡿⡽⣷⣭⢏⣴⣿⣿⣭⢣⡿⢁⡞⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠦⢄⣀⣀⣤⠴⠖⠛⡡⢋⡤⣺⣫⢾⡇⣖⣵⣷⣿⣷⣿⣟⡟⣞⠃⣾⡇⢘⠃⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⢩⣿⣿⣿⣿⣿⠉⠉⠛⠻⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⠙⣷⣶⣤⣤⣀⣀⡠⢤⣴⣶⣾⣿⢿⣯⣿⠿⢯⣽⣻⣛⣿⢹⢠⣿⠀⣿⡇⢸⢸⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠋⠀⢨⣿⣿⣟⣧⠤⠤⠤⠤⠀⠐⠒⠒⠒⠒⠒⠶⠦⠤⠤⠤⢤⣤⣥⣭⣭⣟⣿⣭⣿⣾⣈⡟⢛⣿⣿⣾⠷⠿⠿⣤⣄⡀⠀⠉⠛⣿⢶⢸⢹⡄⡿⣇⠰⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠷⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⠿⣿⣽⣿⣿⢷⣶⠿⢭⣽⣿⡿⠿⠷⠶⠶⠶⣿⡸⡹⡸⡉⢷⠿⢦⣇⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠻⣿⣷⣌⠡⡄⠈⠉⠁⠀⠀⠀⠀⠀⠀⠳⣝⠳⣧⡘⣆⠀⠈⠙⢧⣄⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡑⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢿⣷⣎⣦⣀⠀⠀⠙⣆⠀⠀ ⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠉⠳⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢻⡙⠻⠿⣿⣖⣂⣸⣤⣤ ⠀⣀⣤⣔⠾⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣾⠲⢤⣤⣤⠉⠳⣄⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⣇⠀ ⠛⠉⠁⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⢼⣿⣿⡀⠘⡆⠀⠀⠀⠀⢸⡽⣴⣒⣒⣒⣦⣿⠀ ⣀⣠⣤⣴⠶⠚⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠙⣿⣿⣆⢸⡀⠀⠀⠀⢸⣧⢿⠀⠀⠀⠙⣿⡄ ⠟⠋⢁⣀⠤⠖⢋⡼⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠛⢿⣇⠃⠀⠀⠀⠀⣿⠸⡖⠛⠙⣦⠘⡇ ⠀⠀⠀⢀⣠⣴⠛⠰⡄⠈⢾⣿⡗⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠈⢿⡀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠈⢧⡇ ⣖⢲⣿⣟⡿⠃⠀⠀⠸⡆⠈⣯⡇⣿⣿⣿⣿⣿⣿⢻⣶⣶⣶⣶⣶⠿⠿⢿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠈⠃⠀⠀⠀⢰⡿⣸⠃⠀⠀⠠⣎⢱ ⠛⠉⣡⡿⡇⠀⠀⠀⠀⠁⠀⠙⣃⣟⡎⢩⢟⣿⢿⣿⣟⣯⢉⣋⣉⡀⣰⣾⣏⣿⢹⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢆⠀⠀⠀⠀⠀⠀⢸⢧⠟⠀⠀⠀⠀⠙⢾ ⠀⣰⡿⣻⡇⠀⠀⠀⠀⠆⠀⢀⣿⣹⢠⣿⠛⢻⠸⢧⢟⡾⢿⣿⡿⢻⢿⢸⡟⣿⢹⣷⡟⣷⡗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢸⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠸ ⡼⡽⡼⣿⡄⠀⠀⠐⠊⢀⣴⢻⠃⡇⢸⡼⠀⢸⢸⡏⠉⠰⡏⣾⣿⢸⢸⡼⣧⣿⢸⠀⡇⣿⣆⢿⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢏⣿⣷⠓⠀⢀⡴⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠱⡇⡇⣟⣤⠶⠶⣶⣴⡿⠁⡼⢸⢳⣶⡇⠀⠈⠉⠁⠄⠀⠉⠛⠙⠋⠈⠉⠉⠉⠉⠀⠉⠉⠉⠻⣟⣹⢟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠸⢋⣡⡴⠞⠉⠀⣾⣿⡆⠀⢀⢴⡆⠀⢠⠇ ⠀⢸⢿⠋⠀⣠⣾⣿⡿⠁⠀⡇⢸⠘⣿⡃⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠚⠻⠿⠿⠿⠿⣿⣷⣶⣶⣶⣾⣿⡾⠟⠛⣿⠇⠀⠀⠀⠘⢹⡿⣅⣴⡷⠘⠀⢠⠏⡠

⡠⠏⢠⠀⠘⡷⣴⣅⡿⢹⠘⠀⠀⠀⠇⣿⠛⠟⡾⣿⣾⣶⣶⣶⣷⣿⠿⠿⠿⠿⠻⠚⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⡃⣿⠘⢸⡇⠀⠁⡿⣿⣾⣠⠀⠋⢿⢸⠀ ⠇⢠⠀⡆⢴⢀⠀⡆⣿⣾⠀⠉⠞⡴⣡⢋⠸⠀⠏⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢟⣹⣟⠻⠉⠉⠉⠀⠉⠉⠉⠉⠈⠋⠙⠛⠉⠀⠄⠁⠉⠈⠀⡇⣶⢳⢸⡼⠁⡿⣴⣶⠶⠶⣤⣟⡇⡇⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⢿⡴⢀⠀⠓⣷⣿⢏⠏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣷⢿⣆⣿⡇⠀⢸⣿⣧⡼⢸⢸⣿⣾⡏⠰⠉⡏⢸⢸⠀⡼⢸⡇⠃⢻⣴⢀⠊⠐⠀⠀⡄⣿⡼⡽⡼ ⠸⠀⠀⠀⠀⠀⠀⠋⡾⢀⠀⠀⠀⠀⠀⢸⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡗⣷⡟⣷⢹⣿⡟⢸⢿⢻⡿⣿⢿⡾⢟⢧⠸⢻⠛⣿⢠⣹⣿⢀⠀⠆⠀⠀⠀⠀⡇⣻⡿⣰⠀ ⢾⠙⠀⠀⠀⠀⠟⢧⢸⠀⠀⠀⠀⠀⠀⢆⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢹⣿⣏⣾⣰⡀⣉⣋⢉⣯⣟⣿⢿⣿⢟⢩⡎⣟⣃⠙⠀⠁⠀⠀⠀⠀⡇⡿⣡⠉⠛ ⢱⣎⠠⠀⠀⠃⣸⡿⢰⠀⠀⠀⠃⠈⠀⠀⣇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣿⢿⠿⠿⣶⣶⣶⣶⣶⢻⣿⣿⣿⣿⣿⣿⡇⣯⠈⡆⠸⠀⠀⠃⡿⣟⣿⢲⣖ ⡇⢧⠈⠀⠀⡇⠀⣿⠀⠀⠀⠀⡀⢿⠈⠀⠀⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣹⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣦⡗⣿⢾⠈⡄⠰⠛⣴⣠⢀⠀⠀⠀ ⡇⠘⣦⠙⠛⡖⠸⣿⠀⠀⠀⠀⠃⣇⢿⠛⠀⡄⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢦⠛⡼⢋⠖⠤⣀⢁⠋⠟ ⡄⣿⠙⠀⠀⠀⢿⣧⢸⠀⠀⠀⡀⢸⣆⣿⣿⠙⡄⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠛⠚⠶⣴⣤⣠⣀ ⠀⣿⣦⣒⣒⣒⣴⡽⢸⠀⠀⠀⠀⡆⠘⡀⣿⣿⢼⡀⣧⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠁⠉⠛ ⠀⣇⠉⠈⠀⠀⠀⡄⢻⠀⠀⠀⠀⠀⣄⠳⠉⣤⣤⢤⠲⣾⣷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠾⣔⣤⣀⠀ ⣤⣤⣸⣂⣖⣿⠿⠻⡙⢻⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠳⠉⣄⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀ ⠀⠀⣆⠙⠀⠀⣀⣦⣎⣷⢿⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⡑⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀ ⠀⠀⠀⣄⢧⠙⠈⠀⣆⡘⣧⠳⣝⠳⠀⠀⠀⠀⠀⠀⠁⠉⠈⡄⠡⣌⣷⣿⠻⠀⠀⠀⠀⠁⠚⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣇⢦⠿⢷⡉⡸⡹⡸⣿⠶⠶⠶⠷⠿⡿⣿⣽⢭⠿⣶⢷⣿⣿⣽⣿⠿⣿⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⠛⠷⣿⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢸⠰⣇⡿⡄⢹⢸⢶⣿⠛⠉⠀⡀⣄⣤⠿⠿⠷⣾⣿⣿⢛⡟⣈⣾⣿⣭⣿⣟⣭⣭⣥⣤⢤⠤⠤⠤⠦⠶⠒⠒⠒⠒⠒⠐⠀⠤⠤⠤⠤⣧⣟⣿⣿⢨⠀⠋⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⢸⢸⡇⣿⠀⣿⢠⢹⣿⣛⣻⣽⢯⠿⣿⣯⢿⣿⣾⣶⣴⢤⡠⣀⣀⣤⣤⣶⣷⠙⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⢿⠻⠛⠉⠉⣿⣿⣿⣿⣿⢩⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⣿⠃⢘⡇⣾⠃⣞⡟⣟⣿⣷⣿⣷⣵⣖⡇⢾⣫⣺⡤⢋⡡⠛⠖⠴⣤⣀⣀⢄⠦⣈⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣼⡞⢁⡿⢣⣭⣿⣿⣴⢏⣭⣷⡽⡿⡿⣾⢌⣼⢋⡷⣿⣼⢬⠀⣍⣦⣙⣈⣀⣀⣀⠄⠤⣷⠿⠙⠉⠀⠀⠀⠀⠀⠀⠄⠶⠒⠛⠉⠉⠈⠀⠀⠀⠉⠋⡞⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠇⢡⡿⣾⣫⡶⣤⢁⡿⠟⣩⣏⣿⣿⣟⡼⡽⣟⣘⡾⢙⢺⡭⣒⡴⣀⢀⡀⣄⠦⠒⠒⠴⣠⢀⣀⢢⣝⣵⢷⠤⠶⠶⠶⠶⠶⠶⡤⣠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡎⠁⢪⣷⡱⡔⢀⠛⠿⣾⢀⠀⠀⡀⣀⣀⣦⡿⡇⣷⢹⢿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⢠⡿⠿⣠⡰⠋⡿⣫⣠⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⡆⠏⣿⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⡄⣿⢸⠁⡿⢦⣯⢩⠈⠉⠀⡀⢫⠒⠻⠘⠀⡇⡿⣹⡟⢟⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠇⠀⡇⣿⢣⣠⢻⠿⣿⣿⣠⢀⠀⠀⣄⣶⡾⢰⠀⡿⣿⣽⣼⣏⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⡄⣼⡿⡿⣢⣿⣿⣷⢿⠻⠈⠀⠄⠆⠩⠛⠟⣞⣫⡼⠋⣿⣰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠜⡃⢻⣷⢠⠏⣿⣿⣯⣯⣿⢻⠀⠟⠿⣽⣿⣿⣾⣡⠋⣿⢻⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣆⠘⣧⣆⠇⣰⣿⣿⣿⠿⡿⣿⡿⣿⣟⣿⣾⣴⢉⣞⣾⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⡳⢋⡈⣿⣿⣿⣿⣾⣿⣧⣿⣿⣶⣠⢏⡽⣞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⡘⣼⣷⣿⣽⢶⣶⢴⣩⠉⠛⠾⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀