⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣴⣶⣿⣿⣿⣿⣾⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢆⢳⣹⣏⣯⣽⣾⡽⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⢛⢿⣿⡿⢏⠳⣿⣿⣿⣼⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠇⣫⣆⡄⠀⣌⠯⣽⣿⣯⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣯⣤⣽⣌⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⣿⢿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣾⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡟⣿⣿⣿⣿⣿⣿⡛⡛⢧⠜⣿⣿⠟⣼⣟⣿⣿⣷⣖⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⡿⣿⣽⣿⣿⣷⣿⣿⡿⣿⣿⣿⣏⠛⠒⠛⠉⠁⣰⣿⣿⣿⣿⣿⣻⣷⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣟⣾⣯⣿⣽⣿⣿⣿⣿⣿⣟⣆⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣶⢶⣾⢿⣻⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣽⢹⣿⣷⣿⣿⣿⠿⢿⠿⣿⢻⣻⣻⣿⣛⣇⠀⢀⣿⣿⣿⣛⣻⣻⣿⣿⠿⣿⣾⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣟⣻⡴⣿⣿⣯⣿⣿⣽⣷⣿⣿⣽⣿⣆⣼⣿⣿⣿⣿⣿⣿⣿⣛⣯⣿⣽⣿⡿⣷⠀⠀⠀⠀⠀ ⠀⠀⣿⣾⣿⢿⣻⡿⣿⣿⣿⡿⠿⡻⣛⣛⣟⣛⣛⣛⣟⣟⣿⢛⣻⣿⣯⢹⣿⡛⣿⣿⣿⠿⣻⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⢷⣿⣿⣾⣿⣿⣿⣽⣿⣿⣾⣷⣿⣯⣧⣿⣿⣇⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⡇⠀⠀⠀⠀ ⠀⠀⡼⣶⣧⣯⣿⣟⣿⣿⣿⣿⣿⣿⣟⣟⣿⣻⣻⡇⣟⣻⣿⢹⣿⣿⣟⣟⣿⣿⣿⣿⣻⣿⣭⣿⣿⣿⡄⠀⠀⠀ ⠀⡰⣿⣿⣷⣿⣿⣿⣿⣿⣧⣿⣿⣷⣿⣿⣷⣷⣿⣇⣿⣼⣿⣼⣿⣽⣷⣿⣿⣷⣿⣿⣿⣿⣸⡿⣿⣿⡇⠀⠀⠀ ⠀⢻⣶⣷⣏⣭⣽⣿⣿⣯⣟⣿⣟⣛⣛⣛⣙⣹⣽⣯⢩⣻⣭⢹⣭⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀ ⠀⣾⣭⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣶⣿⣷⣼⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⡷⢽⣯⣽⣿⣿⡆⠀⠀ ⣸⣿⢻⣷⣮⣽⣿⣾⣿⢿⣯⣽⣿⣟⡛⣿⣹⡻⣭⣽⢩⠭⣿⡏⣭⣽⣯⢭⣽⣿⣾⣷⣷⣿⣿⣽⣿⣿⣿⠁⠀⠀ ⢿⣿⣿⣏⠿⣾⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡾⣿⣿⠀⠀⠀ ⠈⣿⣿⢎⡻⢽⣿⣿⣷⣿⣷⣟⣿⢭⣽⣿⣭⠭⣿⣿⢩⡽⣿⡭⣭⣽⣯⣏⣿⣲⣟⢿⣿⣿⣏⢾⣹⣿⣿⠀⠀⠀ ⠀⢿⣿⣧⡝⢮⣿⣿⣛⣿⣿⣿⣿⣾⣿⣿⢼⣷⣿⣿⣼⣷⣿⣿⣷⣿⣿⣿⣿⣿⢿⣻⣿⣿⢮⡷⣯⣿⣿⠀⠀⠀ ⠀⠸⣿⣿⡼⢩⢿⣿⣽⣿⣷⣿⣿⢯⣭⣭⣹⣉⣿⣭⢩⣭⣿⣿⣭⣽⣿⡿⣿⣶⣿⣿⣿⣿⣧⢿⣿⣿⡇⠀⠀⠀ ⠀⠀⢹⣿⣿⡱⣿⣿⣿⡟⡿⣿⣿⣾⣿⣿⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⢿⣿⣻⣽⣿⣿⣟⣾⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⢻⣯⡿⣜⣿⣿⣷⣯⣿⣿⢹⣛⣿⣼⣍⣿⣿⣹⣯⣿⣿⣼⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⣖⣻⣿⣏⣭⣿⣛⢻⡿⣿⠿⠿⡿⣿⡿⣿⣿⣿⠿⠿⣟⣛⣯⣿⣯⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣞⢿⣿⢿⣿⣯⣿⣿⣿⣧⣯⣽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⠿⣿⣿⣿⢿⣾⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⢊⣿⣿⣿⢼⣽⣿⣿⢺⣛⣿⡿⠽⠉⡿⢿⡿⣟⢿⣿⣾⣷⣿⢿⡿⣽⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣻⡽⢣⡞⢿⣿⣿⣿⣯⣾⣿⣿⣇⣏⣰⠃⢈⣿⣿⣧⣿⣿⣿⡷⠛⢀⣹⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣟⣵⡟⠀⠀⠉⠛⠻⢭⣝⣛⣛⣹⣿⣿⢰⢿⣎⣿⣻⣭⠾⠋⠀⠄⣠⠘⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⢛⣻⣿⣸⣿⠄⣌⠻⡁⢀⠠⢌⠰⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⢌⠣⣿⡿⠿⢞⣛⣩⢱⡠⢌⣒⡀⣶⣦⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣦⠀⠰⠖⠀⠀⠀⠀⠀⠌⡘⢄⠣⡿⣧⠹⢏⠞⠴⡩⡽⡜⢠⡐⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⡀⠀⠉⠀⠀⠀⠀⠀⣰⣿⠈⡾⠁⠙⡞⢾⣈⢓⡱⠐⠌⡥⣘⢢⡞⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢯⣇⠠⠄⣠⠀⠀⣀⣼⣿⣿⣾⠃⠀⠀⠸⣆⠙⣛⠁⠺⠶⢤⢃⠾⣞⣻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⢻⡀⠀⠀⠀⠀⡁⠠⠀⣿⡇⠀⠀⠀⠀⢿⠰⡉⢻⣦⣤⣴⣾⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⡹⢦⣄⣠⣤⣴⣶⣿⢏⣽⠀⠀⠀⠀⠀⠸⣇⠤⠑⠊⠙⠿⢿⠿⠇⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠧⢷⢿⣿⣿⣿⣿⡟⡀⣾⡏⠀⠀⠀⠀⠀⠀⡷⢆⠌⠐⡀⠂⠆⡑⠨⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⢆⠈⠛⠟⠛⠉⡐⠰⢘⡇⠀⠀⠀⠀⠀⠀⣿⣩⠄⡡⠠⢡⠈⡄⢃⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣏⠤⣉⠰⡈⠰⡁⢬⣽⣻⠂⠀⠀⠀⠀⠀⠀⢹⡖⠤⡁⢂⠁⣂⠘⡄⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⠆⠀⢢⢁⣃⢉⣾⢧⡇⠀⠀⠀⠀⠀⠀⠀⠘⣏⢶⣥⣦⣁⣤⣈⣰⣻⡽⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡰⠎⣙⣏⡻⣿⢩⣇⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠎⣿⡋⡭⢉⢭⣭⣽⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⡷⢶⣙⣩⡭⠭⠟⣫⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣹⠷⣄⣃⠶⢦⣭⣯⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣋⠶⠾⠯⣷⣿⢿⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠻⣬⣉⠙⣒⣦⣽⣳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⡉⠄⠶⢋⠡⣤⢞⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢥⡋⡙⠦⠍⠠⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣧⡑⢊⢘⡥⢞⣡⢞⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠢⣉⠕⡰⣌⠁⠎⣳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠨⢅⠚⢋⠔⡊⠔⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⡄⢫⢐⠠⠉⡔⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡯⠄⡉⢆⠸⡐⢩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠚⡥⢊⠔⡡⢂⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠣⠆⠱⡈⢆⠱⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠌⡐⢣⠘⢄⠣⢾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣐⠊⠥⠘⡄⢃⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣎⠡⢃⠎⡰⢉⣻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣬⡍⢢⠑⡠⢎⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠧⣈⠒⠡⢧⣹⡃⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠳⢌⠣⡘⡐⢂⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢰⠡⢎⡑⣶⢫⡅⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡛⢢⠑⡡⠘⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢋⠞⣡⢃⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⢡⠚⡠⢙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⡬⢂⠧⣉⢾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⣦⣃⢇⠱⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠼⣏⠶⣡⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⣾⣥⣮⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⡠⢞⣛⣉⣍⡻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢟⣩⣭⣛⡻⣄⡀⠀⠀ ⠀⠀⡞⠖⣋⣹⣿⣽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⣿⣽⣿⣽⣳⣾⡄⠀ ⠀⢸⣿⣿⣿⣿⣷⣯⣭⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣩⣶⣷⣾⣿⣿⣿⣿⡄ ⠀⠘⢿⣛⡿⢿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣿⣿⣿⣿⣿⣿⣽⣿⠇ ⠀⠀⠀⠈⠉⠉⠙⠛⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀