⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣄⣤⡴⠶⠶⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⢠⢴⣵⣿⣿⣿⣿⣿⣿⠟⠛⠛⠋⠩⣄⣀⡀⠂⠀⠄⠀⠉⠛⠳⢦⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠟⠻⢤⡀⠂⠠⠀⠄⠀⠙⠻⣟⠲⠶⠦⣤⣀⢰⡏⢩⡽⢳⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠟⣁⠂⠦⡀⠙⢦⡀⠡⢈⠐⢂⠀⠘⣦⠀⠀⣀⣬⣽⠷⣌⡳⠦⠯⢻⣧⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣄⣠⣾⣿⣿⣿⣿⣿⢏⡈⠄⠖⡀⠙⢦⡀⠙⢦⡈⠀⠄⠆⠀⠈⣧⠺⠛⠉⠀⠀⠈⠙⢶⡶⠞⢳⡈⣩⣽⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢫⣽⡿⣽⣿⣿⣿⣿⠇⡈⢳⡌⢦⠣⠑⠄⡙⢦⠈⢳⡄⠂⠈⠶⣄⣹⡄⠀⠀⠀⣠⣠⣶⣿⣿⣦⣄⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣜⣿⣼⣿⣿⣿⣿⡏⠐⡠⠄⠹⣄⢳⡀⠚⡄⠈⠙⣦⠟⠀⠡⠀⠈⠙⠳⣦⠀⠻⣿⡟⡱⢢⣝⡆⠈⠙⣮⢿⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣿⣾⣿⣿⣿⣿⠁⡊⠄⠂⠄⠙⣆⢳⡀⠁⣠⠞⠉⠓⠶⣤⣴⠶⠞⠋⠁⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⢸⣏⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣽⣿⣿⣿⣿⣿⠀⡡⠌⣌⠠⢁⠘⣆⢃⡴⣏⡀⠁⠂⠄⠀⣈⡭⢇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⡜⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣳⣿⣿⣿⣿⣿⡄⡐⠌⢆⠑⠒⢊⠞⠋⡀⠌⠛⢿⣛⡛⢛⣵⣿⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢯⡗⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣻⣿⣿⣿⣿⣽⡄⠊⡜⢀⡀⠸⡆⠐⠠⢌⠀⠂⠄⢉⣹⡟⡤⢓⣼⠇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣿⣿⣾⣧⣤⣤⣀⠀⠀⠀⠀⠀ ⢿⡻⣟⣿⣿⣿⣿⣎⡿⣄⠑⠢⠌⡑⠹⠄⢡⠈⠻⣶⡚⣿⡿⠛⢾⠛⠁⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠋⢉⡿⣿⣽⡻⣛⣿⡿⢿⣶⠀⠀ ⢧⣛⣬⢻⣿⣿⣿⣿⣹⢻⣬⠑⡌⠰⡁⠎⢄⠩⡐⠄⣉⠛⠓⡛⣲⠂⠀⠀⠂⢀⣠⣴⢾⡟⠻⣏⢘⣦⣾⣹⡙⠿⣧⣿⣷⢻⢬⠴⣧⡄ ⠀⢺⡴⣋⡞⣿⣿⣿⣿⡝⣾⣳⡌⠱⡈⢧⠬⣆⠱⡈⢔⣨⣥⠾⠧⣤⣤⠴⢾⣻⣿⣿⣶⣿⢿⣿⣟⡿⣿⢟⣻⣷⣏⠉⠉⣾⢌⣶⣟⣷ ⠀⠀⠳⡝⣞⡵⣚⢶⡹⣿⣧⢏⡿⣦⡑⢚⣧⡘⠳⢮⣔⣢⠄⡓⠜⡠⣐⣾⣿⣿⣿⣿⣻⣯⡞⡩⣾⣟⡿⣿⣿⢿⣩⡴⣾⣧⣻⠎⠈⠻ ⠀⠀⠀⠙⠪⣖⠽⣎⠷⣭⢻⣿⣵⣫⣷⠈⣿⢷⣭⣢⣉⡻⢿⣽⣿⣯⣽⣟⡙⣿⣿⣳⢫⣞⣿⣽⣿⢩⣝⢶⡞⣩⢑⡾⣯⣴⡁⠀⠀⢄ ⠀⠀⠀⠀⠀⠀⠓⢬⣛⢼⡣⣏⢿⣶⣿⣼⣯⣻⡜⣯⣟⣿⣿⣯⣿⣿⣿⣯⣐⢿⣿⣯⣿⣶⣷⣿⡿⣿⣽⠦⢿⣤⢟⡴⠉⠙⠿⣶⣬⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⡔⣻⡜⣏⠿⣿⣶⣹⣛⣿⣿⣿⡽⣾⣽⣿⣿⣿⣧⡎⣼⣿⣿⣿⡻⢟⡡⣾⣿⢯⣟⣿⣿⣎⣀⡀⠂⣴⢾⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣝⣮⣙⣶⣽⢛⣯⢛⢜⡻⣿⢻⣙⡞⢿⣻⣿⣜⣾⣻⣿⣽⣻⠟⠉⠁⣸⣿⣿⣿⡿⣾⣧⣿⣽⣾⣿⡿⢃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠓⠋⠉⠉⠓⢿⡡⣏⠞⣧⡹⣛⢿⡾⢿⠿⡾⢿⣦⣤⣾⣿⣿⡿⢿⣷⡜⣭⣙⠻⣉⠿⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠿⠖⠳⠛⠦⣏⡳⢫⡝⢾⣘⢧⠳⣿⣿⢐⡣⣼⡾⠤⠷⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡚⢧⡙⠮⣩⠾⠿⠷⠞⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⡉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡉⠛⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⠷⠿⠾⣩⠮⡙⢧⡚⢷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠚⠷⠤⡾⣼⡣⢐⣿⣿⠳⢧⣘⢾⡝⢫⡳⣏⠦⠛⠳⠖⠿⠒⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠚⠿⣉⠻⣙⣭⡜⣷⢿⡿⣿⣿⣾⣤⣦⢿⡾⠿⢿⡾⢿⣛⡹⣧⠞⣏⡡⢿⠓⠉⠉⠋⠓⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢃⡿⣿⣾⣽⣿⣧⣾⡿⣿⣿⣿⣸⠁⠉⠟⣻⣽⣿⣻⣾⣜⣿⣻⢿⡞⣙⢻⣿⡻⢜⢛⣯⢛⣽⣶⣙⣮⣝⠦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣿⢾⣴⠂⡀⣀⣎⣿⣿⣟⢯⣿⣾⡡⢟⡻⣿⣿⣿⣼⡎⣧⣿⣿⣿⣽⣾⡽⣿⣿⣿⣛⣹⣶⣿⠿⣏⡜⣻⡔⠻⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣬⣶⠿⠙⠉⡴⢟⣤⢿⠦⣽⣿⡿⣿⣷⣶⣿⣯⣿⢿⣐⣯⣿⣿⣿⣯⣿⣿⣟⣯⡜⣻⣯⣼⣿⣶⢿⣏⡣⢼⣛⢬⠓⠀⠀⠀⠀⠀⠀ ⢄⠀⠀⡁⣴⣯⡾⢑⣩⡞⢶⣝⢩⣿⣽⣿⣞⢫⣳⣿⣿⡙⣟⣽⣯⣿⣽⢿⡻⣉⣢⣭⢷⣿⠈⣷⣫⣵⣿⢻⣭⠷⣎⠽⣖⠪⠙⠀⠀⠀ ⠻⠈⠎⣻⣧⣾⡴⣩⢿⣿⣿⡿⣟⣾⡩⡞⣯⣻⣿⣿⣿⣿⣾⣐⡠⠜⡓⠄⣢⣔⢮⠳⡘⣧⢚⡑⣦⡿⢏⣧⣿⡹⢶⣚⡵⣞⡝⠳⠀⠀ ⣷⣟⣶⢌⣾⠉⠉⣏⣷⣻⢟⣿⡿⣟⣿⢿⣿⣶⣿⣿⣻⢾⠴⣤⣤⠧⠾⣥⣨⢔⡈⠱⣆⠬⢧⡈⠱⡌⣳⣾⡝⣿⣿⣿⣿⡞⣋⡴⢺⠀ ⡄⣧⠴⢬⢻⣷⣿⣧⠿⡙⣹⣾⣦⢘⣏⠻⡟⢾⣴⣠⢀⠂⠀⠀⠂⣲⡛⠓⠛⣉⠄⡐⠩⢄⠎⡁⠰⡌⠑⣬⢻⣹⣿⣿⣿⣿⢻⣬⣛⢧ ⠀⠀⣶⢿⡿⣿⣛⡻⣽⣿⡿⢉⠋⣿⣿⣴⣀⠀⠀⠀⠀⠀⠀⠁⠛⢾⠛⡿⣿⡚⣶⠻⠈⢡⠄⠹⡑⠌⠢⠑⣄⡿⣎⣿⣿⣿⣿⣟⡻⢿ ⠀⠀⠀⠀⠀⣀⣤⣤⣧⣾⣿⣿⣟⣾⢠⠀⠀⠀⠀⠀⠀⠀⠇⣼⢓⡤⡟⣹⢉⠄⠂⠀⢌⠠⠐⡆⠸⡀⢀⡜⠊⡄⣽⣿⣿⣿⣿⣻⣷⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡗⢯⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠿⣿⣵⢛⡛⣛⢿⠛⠌⡀⠋⠞⢊⠒⠑⢆⠌⡐⡄⣿⣿⣿⣿⣿⣳⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡜⣿⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⢇⡭⣈⠀⠄⠂⠁⡀⣏⡴⢃⣆⠘⢁⠠⣌⠌⡡⠀⣿⣿⣿⣿⣿⣽⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⣷⣏⢸⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠁⠋⠞⠶⣴⣤⠶⠓⠉⠞⣠⠁⡀⢳⣆⠙⠄⠂⠄⡊⠁⣿⣿⣿⣿⣾⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣽⢿⣮⠙⠈⡆⣝⢢⡱⡟⣿⠻⠀⣦⠳⠙⠈⠀⠡⠀⠟⣦⠙⠈⡄⠚⡀⢳⣄⠹⠄⡠⠐⡏⣿⣿⣿⣿⣼⣿⣜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⠙⣄⣦⣿⣿⣶⣠⣠⠀⠀⠀⡄⣹⣄⠶⠈⠂⡄⢳⠈⢦⡙⠄⠑⠣⢦⡌⢳⡈⠇⣿⣿⣿⣿⣽⡿⣽⢫ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣽⣩⡈⢳⠞⡶⢶⠙⠈⠀⠀⠉⠛⠺⣧⠈⠀⠆⠄⠀⡈⢦⠙⡀⢦⠙⡀⠖⠄⡈⢏⣿⣿⣿⣿⣿⣾⣠⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣧⢻⠯⠦⡳⣌⠷⣽⣬⣀⠀⠀⣦⠘⠀⢂⠐⢈⠡⡀⢦⠙⡀⠦⠂⣁⠟⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢿⢳⡽⢩⡏⢰⣀⣤⠦⠶⠲⣟⠻⠙⠀⠄⠀⠠⠂⡀⢤⠻⠟⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣦⣴⢦⠳⠛⠉⠀⠄⠀⠂⡀⣀⣄⠩⠋⠛⠛⠟⣿⣿⣿⣿⣿⣿⣵⢴⢠⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⡴⣤⣄⣿⣿⣿⣿⣿⣿⣾⣴⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀