Ugandan Knuckles Emojis & Text

⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⢻⡫⡌⠀⠀⡠⣼⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣿⣿⣿⡟⠿⠣⠃⠀⢠⠂⠛⣿⣷⡀⠀⠀⠀ ⢀⣔⣈⣾⡿⡜⢿⡟⢧⠤⠐⠈⠑⠢⢰⣿⠿⢃⡏⣢⣄⠀ ⢛⣿⠏⣉⠃⠁⠫⠀⢊⠳⣤⢀⣤⡔⠁⡈⡠⣭⡏⠙⣿⡵ ⠀⠀⠀⡿⣦⡀⠄⢄⠀⠣⡙⡲⣟⠈⠊⢌⣾⡺⡁⠀⠀⠁ ⠀⠀⠀⠈⡷⣦⣍⣁⣓⢠⠀⡍⠃⠑⣏⣩⣵⣶⡅⠀⠀⠀ ⠀⠀⠀⠰⡈⣵⢏⣽⣿⣿⣟⠋⢩⣿⣿⣿⣯⡎⢃⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⡿⡏⠉⠙⠢⠞⠋⠉⣻⡌⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠎⠉⠽⠀⠀⠀⠀⠀⠐⠅⠁⠰⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡴⠋⠉⢉⠍⣉⡉⠉⠉⠉⠓⠲⠶⠤⣄⠀⠀⠀ ⠀⠀⢀⠎⠀⠪⠾⢊⣁⣀⡀⠄⠀⠀⡌⠉⠁⠄⠀⢳⠀⠀ ⠀⣰⠟⣢⣤⣐⠘⠛⣻⠻⠭⠇⠀⢤⡶⠟⠛⠂⠀⢌⢷⡀ ⢸⢈⢸⠠⡶⠬⣉⡉⠁⠀⣠⢄⡀⠀⠳⣄⠑⠚⣏⠁⣪⠇ ⠀⢯⡊⠀⠹⡦⣼⣍⠛⢲⠯⢭⣁⣲⣚⣁⣬⢾⢿⠈⡜⠀ ⠀⠀⠙⡄⠀⠘⢾⡉⠙⡟⠶⢶⣿⣶⣿⣶⣿⣾⣿⠀⡇⠀ ⠀⠀⠀⠙⢦⣤⡠⡙⠲⠧⠀⣠⣇⣨⣏⣽⡹⠽⠏⠀⡇⠀ ⠀⠀⠀⠀⠀⠈⠙⠦⢕⡋⠶⠄⣤⠤⠤⠤⠤⠂⡠⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠤⣄⣀⣀⣀⣠⠔⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠉⠀⠀⠀⠀⠉⠙⠓⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢟⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣿⠀⠀⢀⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⣿⠀⢀⡏⠀⠀⣠⣤⣿⣿⣶⣄⠀⠀⣠⣾⣿⣦⡀⠀⢹⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⢹⠀⢸⡅⢀⣾⣿⣿⣿⣿⣿⣿⡆⢠⣿⣿⣿⣿⣷⡄⢛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣌⣇⠀⠳⢸⣿⣿⣿⣿⣿⣿⡿⠀⠨⣿⣿⣿⣿⣿⡇⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣽⠖⠀⠈⠻⣿⣿⣿⡿⣯⣴⣶⣦⣻⢿⣿⣿⠏⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⢀⣤⠿⠅⠿⠿⣿⣿⠋⢬⣄⡀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⣾⢛⣷⠀⠀⠀⠀⠀⠀⠀⣸⣮⣥⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢸⣿⣏⡷⢦⠤⣤⢤⡶⣎⣿⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠶⣯⣹⡒⣿⣛⣯⠿⠚⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⠀⠀⠿⠥⠕⠂⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣦⣄⣀⣀⣀⣀⣀⣀⣴⣶⣋⣁⣀⣴⣷⣦⡀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣽⣽⣷⣶⣤⣀⡟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡛⢿⡟⢻⣿⡿⢿⡟⢻⣯⣷⣯⣿⣿⣿⣿⣷⠏⠀⡿⠀⠀⠀⠀⠀⢸⣽⡆⢀⣴⣶⣿⣿⢿⡷ ⢀⣤⣼⣶⣷⣾⡿⣿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⡟⠳⣯⣿⣿⣿⣯⡍⠻⣴⣚⡛⢋⣉⣤⢞⣻⣦⠀⢻⡀⠀⠀⠀⠀⠀⣟⣽⣿⣿⣟⣟⣿⣿⡄ ⠈⠛⠚⣻⣿⣿⣿⢿⣭⣷⣤⡤⣤⣀⡀⠀⠀⠀⠀⠀⣠⠟⢀⣴⡿⢦⣬⣭⣭⣴⠶⡇⠸⢶⣬⣭⣭⣧⣶⠿⢁⣿⠧⡀⠻⣄⡀⠀⠀⣀⣿⣿⣿⣿⣿⣛⢻⣿⠁ ⠀⣠⣾⣿⣿⡿⠛⠶⣿⡀⠉⠙⠳⠾⠭⣶⣦⡶⠶⠞⢁⣴⠋⠁⢷⣤⣉⣉⣉⣵⡴⣇⢈⡳⢬⣉⣉⣉⣠⣴⣾⠋⠀⠻⣄⢈⣹⠷⠚⢉⣿⣿⠟⠋⠉⢿⡏⠀⠀ ⠀⠛⢿⡿⠏⠀⠀⠀⠀⠉⠓⠒⠦⢤⣤⣀⣉⡧⠀⢰⠞⠁⠀⠀⠘⠧⣭⣭⣯⣴⠞⢹⣶⣛⣦⡬⠭⠽⢶⣿⠏⠀⠀⠀⣯⣾⣁⣠⠖⣫⡿⠃⠀⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠗⠛⠀⠀⠀⠀⠀⠀⠀⣩⣟⣁⡀⠈⣯⠭⠿⣇⢀⣤⡼⠶⢦⣄⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠉⠙⢓⣿⣿⡿⠟⠋⠀⣀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠶⣲⡾⠉⠀⠀⠀⡾⠟⢁⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⠀⠁⠀⠀⠀⠀⠀⠴⢺⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠛⣿⠀⠀⠀⠀⣠⡤⠆⠀⠀⠀⣼⠇⠈⠉⠛⠛⠛⠳⠋⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣙⣷⣤⡤⠞⠁⠉⠓⠶⠶⠚⠻⠶⠟⠉⠉⠙⡷⠲⣤⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢁⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⣾⠇⢀⣸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣡⢞⣥⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⣶⣴⡿⢟⡵⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⢿⣇⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣼⠋⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⠈⢳⡙⣦⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡀⠙⠾⢷⣤⡄⠀⠀⠀⠀⠀⢸⣿⣯⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⢶⣦⣼⣧⡀⠀⠀⠀⠀⠘⣟⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⠾⠿⣅⣸⡇⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡟⣳⡟⣡⢗⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⠤⣚⠋⣡⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠤⢾⠮⠕⠒⠚⣩⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢀⡀⢀⠞⠁⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⡴⠃⢀⡴⠃⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢠⠏⢠⠏⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡟⠁⣤⡞⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣰⠃⠀⢀⡞⢀⠏⠀⠀⣰⠃⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠞⢠⠞⡟⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢰⡇⠀⠀⣾⠁⡾⠀⠀⢰⡟⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⣷⡀⠀⠀⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡎⣠⠏⣼⠁⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡾⠀⠀⢸⡟⢸⠃⠀⢀⣿⣧⢔⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⡟⣇⠀⠀⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⢠⠏⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⡇⠀⢀⣏⢇⣟⣀⡤⣾⣿⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣳⣄⡇⢸⠀⠀⢸⡆⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢀⣾⠀⢸⠀⠀⠀⠀⡘⠀⠀⠀⢸⡇⢀⡏⡇⠐⢺⢿⣻⡏⠀⢀⠇⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⡧⣼⡆⠀⢸⢧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⡸⢹⠀⡼⠀⠀⠀⢠⡇⠀⠀⠀⡼⡇⢸⠁⡇⠀⡼⢸⡟⢣⠀⢸⠀⡇⢸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⠀⠈⡏⠒⣾⢾⡀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠁⡌⠀⡇⠀⢠⡄⢸⡇⠀⠀⠀⡇⡇⡌⠀⡇⠀⡇⢸⡇⢸⠀⢸⠀⣧⢸⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⡏⠀⠀⡇⠀⡇⠈⡇⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠃⠀⡇⠀⠀⡇⠈⡇⠀⠀⠀⡇⣧⡇⠀⢸⡀⡇⠀⠇⠈⣧⣼⠀⢸⡼⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣠⠇⠀⠀⡇⢸⠀⠀⣿⠀⣾⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⡇⠀⠀⣧⠀⢻⠀⠀⡇⡇⢹⣧⣀⣼⣷⣷⣶⣤⣀⠻⣿⠢⢜⣿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⢻⠀⠀⠀⣇⡏⠀⠀⢸⠀⣿⢀⣿⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⡃⠀⠀⣧⠀⠀⢸⡀⠘⡄⠀⢿⣿⣾⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣄⠀⢹⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡧⣼⡯⠀⠀⢰⡟⠀⠀⠀⢸⢀⣿⣸⢹⠄⠀⠉⠓⠤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⣿⡀⠀⠀⣧⠀⢳⡀⠘⡏⢿⠻⠀⠘⠋⢹⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⡀⠀⠀⡀⠀⠀⠀⢀⣼⡟⠀⣿⣀⣤⣴⣾⣦⣤⣄⠀⢸⣸⣷⠃⢸⠃⠀⠀⠀⠀⣾⡿⣿⢲⠒ ⠈⠀⠀⠀⠛⠻⡄⠀⠘⣇⠀⢳⡀⢹⡀⠀⠁⠀⢹⣏⠘⠯⣭⡋⢽⡟⠹⠄⠀⠀⡇⠀⢀⡇⠀⠀⠠⣾⡟⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⠃⠀⢸⠀⠀⠀⠀⣾⡝⠀⡏⢸⠀ ⠀⠀⠀⠀⠀⠀⠱⣄⠀⢸⣆⠀⢻⣄⢳⡀⠀⠀⠰⠿⠦⣄⣀⣰⣞⠁⠀⠀⠀⠀⡇⢠⠞⡇⠀⢀⣴⠟⠒⠋⢰⡏⠈⣿⣿⣿⡿⢿⣿⡟⣿⣷⣔⢀⡏⠀⠀⠀⡼⠁⡇⠀⡇⠘⠀ ⠀⠀⠀⠀⠀⣰⠃⠈⡇⣸⢸⣦⡈⡎⠛⠿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠵⠋⣠⢃⡴⠞⠁⠀⠀⠀⠘⣿⠿⠁⠉⠉⠀⠈⣿⠇⠈⣿⡿⢿⠧⠀⢀⡼⠁⣀⠇⣰⠃⠀⠀ ⢀⠀⠀⠀⣠⠋⠀⠀⣷⠇⢸⡇⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠠⠔⠛⠋⠀⠀⠀⠀⠀⠀⠠⠼⢇⣀⣀⣀⣀⡸⠃⠀⠀⠁⢀⠏⠀⣠⢾⠗⠒⢁⡴⠃⠀⠀⠀ ⣶⠃⠀⡴⠃⠀⣠⠴⠋⠀⢸⡇⠀⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣠⣿⣮⡞⢁⡞⢀⣴⠋⠀⠀⠀⠀⠀ ⠁⣠⠎⠀⡴⣷⠋⠀⠀⠀⠈⡇⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢫⣿⡟⠀⣸⠟⢹⣿⠀⠀⠀⠀⠀⠆ ⠟⠁⢀⣼⡿⠁⠀⠀⠀⠀⢀⣷⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⢠⠇⠀⢸⣿⠀⠀⠀⠀⠀⠈ ⠀⣠⢾⠟⠀⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⠀⠀⠀⣰⡿⠃⠀⢠⣿⠀⠀⠈⡿⡆⠀⠀⠀⠀⠀ ⢼⡝⠁⠀⠀⠀⠀⠀⠀⠀⡜⢨⡇⠀⠀⢸⡈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣶⡀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠉⠙⠛⠻⠦⣾⣏⠀⠀⣠⠻⣿⠀⠀⠀⢹⢷⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡼⢿⠀⠀⠸⡇⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢾⠏⠁⠈⢻⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣥⣀⣻⡆⠀⠀⠈⣯⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣸⠃⠘⡆⠀⠀⣷⠀⠀⢸⣟⢲⣄⠀⠀⠀⠀⠀⠸⣇⠀⠀⢈⡇⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢄⡀⠀⠈⢿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⢃⡴⠁⠀⠀⢳⠀⠀⠸⡄⠀⢸⡙⢸⠈⠛⢦⣀⠀⠀⠀⠘⠲⠖⠋⠁⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠻⡄⠀⠀ ⠀⠀⠀⠀⠀⣠⢞⡤⠋⠀⠀⠀⠀⣼⣇⠀⠀⢧⠀⣾⡇⣘⣤⡾⠃⠈⠳⣤⣀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄⡀ ⠀⠀⠀⢠⣾⡵⠋⠀⠀⠀⠀⠀⠀⡿⡝⡆⠀⢸⣦⡿⠛⠉⠉⠀⠀⠀⢀⣽⠉⠑⠚⠋⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⣼⢳⠁⣹⡄⠈⢧⠀⠀⠀⠀⠀⠀⠀⣼⡿⡄⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠞⠋⠁⣷⠀⢸⠀⠀⠀⠀⠀⠀⣰⡿⠁⡇⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⣿⡇⠘⡄⠀⠀⠀⠀⣰⣿⡁⠀⢷⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠔⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⡤⠀⠀⠀⠀⢀⡟⠈⠃⠀⠚⠳⠤⢤⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢴⣤⣤⣴⣶⠖⣰⣶⡲⠲⠤⣾⠀⢺⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠿⣼⡌⢿⡞⡐⠱⠁⠀⢰⡋⠀⢸⡈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡏⡸⢹⠉⢻⣅⡧⢴⣤⣤⢤⣽⠦⠈⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢁⢃⣴⣾⡉⠁⠀⢸⢨⢿⣾⣿⣆⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣼⠋⠘⠻⣯⣢⡀⠘⡞⢿⣟⠻⠇⢠⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⠤⢄⡀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⠀⠙⣿⠇⠀⠙⠊⢡⣶⣶⣿⢷⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⢉⠀⠒⢌⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠣⠄⣎⡀⣤⣾⣛⣩⡆⢼⣆⠀⣀⡀⢠⠏⣀⣀⡀⣀⠠⠄⡀⠁⢂⠣⠈⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢉⡵⠋⠀⡼⢸⠋⡅⡈⣻⣿⠋⠉⠙⠳⣍⠢⡈⢢⠈⡄⡇⢸⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠸⣄⢀⡔⡜⡸⣀⢢⠃⠈⢹⡄⠀⠀⠀⠈⢷⠹⡀⠁⠀⠀⠸⠹⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⠻⣎⣠⠃⠈⣩⡇⠱⢾⠁⠀⠀⠀⠀⠈⣇⢃⠀⠀⠀⢸⠀⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠢⡄⠀⣀⣀⣀⣦⡀⠀⠀⣞⠀⠀⠀⠀⠀⠀⢹⢸⡆⠀⠀⢸⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⠁⠀⡏⠉⠈⠣⡑⢄⠈⠉⠱⡄⠀⠀⠀⠀⢸⣸⡹⠀⠀⣄⣴⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢸⠻⡄⠀⠀⠘⡌⢣⠀⠀⠙⡄⠀⠀⠀⢸⣿⠇⢀⣰⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⣸⠀⢳⠀⠀⠀⢸⠀⡇⠀⠀⠹⡄⠀⠀⣿⢇⡶⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⡇⠀⠘⡀⠀⠀⣸⠀⡁⠀⠀⠀⢱⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢀⡸⠀⠀⠤⠃⠀⠀⠳⠤⡇⠀⠀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠁⢿⡿⢶⣤⣀⣴⣾⣿⡿⠟⠁⠀⠀ ⠀⡀⠐⠉⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⢤⣮⣾⣿⣿⡿⠋⠀⡀⠀⠀⠀ ⠛⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣮⣝⠛⠛⠓⠓⠛⠓⠓⠒⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⡿⠛⠉⠈⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠒⠒⠒⠛⠒⠒ ⠀⠀⠀⣠⠴⢋⣵⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀ ⠀⣠⠞⣡⣾⣿⣿⣿⣿⣿⣿⡿⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠠⠂⠁ ⠞⠁⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠄ ⠀⣸⡿⢹⣿⣿⣿⣿⣿⣿⡟⢉⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇⢀⠀ ⠀⡿⠁⢸⣿⣿⣿⣿⡿⢏⣠⠋⠀⡟⠀⠀⠀⠀⠀⠀⣀⣀⢄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠋⠀ ⠀⠁⠀⢸⣿⣿⣿⡟⠀⠀⠙⠤⠚⠁⠀⠀⠀⠐⠛⠛⠿⢿⣷⣷⣄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀ ⠀⠀⢀⣈⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢿⣷⣷⠄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀ ⣠⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡇⠀⠀⠀⠻⣿⡖⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠃⠀⠀⠀ ⣿⣿⣯⠿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀ ⣿⡿⠁⢰⠋⠏⡇⠀⠀⢈⢳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣛⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⠿⣾⣿⣦⣄⠀ ⠻⣿⠀⢻⡀⠀⠸⡀⠀⠈⠟⠒⠙⠢⠤⠀⠀⠀⠀⠀⠀⠀⠋⠉⣡⡾⣿⣿⡿⣿⣿⣿⣿⡿⠟⠀⢸⣿⣿⣿⣿⣿⣿⡻⡀⢹⣷⣟⣆⡀ ⠀⠜⢳⠎⠳⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⢴⣾⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⠀⢳⢭⡙⢦⠉⠁ ⠁⠐⣻⡀⠀⠱⡀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⣲⣷⣾⣿⣿⣿⣿⡿⠋⠀⠀⣀⣠⣴⣾⣿⣿⣿⡿⠋⣿⣷⠈⠘⡆⣽⡶⠁⠀ ⠀⣠⡧⠞⢉⠖⡾⠀⠈⠉⠓⠒⠒⠒⠦⡤⠤⢤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠓⣶⣶⣿⣿⣿⡿⠿⠿⡛⠁⠀⢸⠀⣿⡄⣀⠟⠉⠀⠀⠀ ⠞⠁⣀⣤⣊⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣿⣿⣿⣿⣿⣿⢿⡿⠋⠀⠀⠀⠈⢻⣏⣈⣛⣛⣐⣶⢼⣦⣀⠀⢳⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⡜⠁⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⡿⠋⢀⣼⠗⠒⠒⠀⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠃⠓⠒⠤⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⣿⠋⣾⠁⡠⠊⢸⠀⠀⢀⣀⠤⠤⠐⠒⠒⠒⠒⠂⠤⠤⣄⣀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠏⠀⠀⠀⢸⡆⠀⠀⠀⣰⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀ ⡆⠀⠀⠀⢸⣇⡀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⣶⣄⣀⣠⣿⣟⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀ ⠉⠉⠉⠉⠉⠋⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⢿⠀⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠶⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⣿⣿⣿⡿⢿⠚⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⣼⣷⡶⡶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣧⣤⣿⣿⣿⡗⢺⡄⢸⢹⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠿⣿⡟⠀⢐⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⡟⠻⣿⣿⣿⣿⣷⡎⠁⠈⣎⣿⣿⣿⡿⣿⡦⠈⣟⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣤ ⣨⣿⣿⣍⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠁⠐⠛⠻⠿⣿⠉⣷⠀⠀⠈⠈⠿⠿⣿⢿⣷⣤⣼⣼⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠻⢿⣿⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⣿⣿⣿⣿⡿⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠚⠋⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠠⠼⡷⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠲⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⠸⡌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠂⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣠⡀⠀⠀⠐⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡰⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢸⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠏⠁⢃⠀⠀⠀⠀⠋⢿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠈⢁⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⠀⠀⣸⠀⠀⠘⣿⣿⣿⣿⣿⡿⠁⠀⠀⣮⡀⠀⠀⠀⠀⢀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⣰⣿⣇⠀⠀⠈⢿⣿⣿⠟⠁⠀⠀⣰⣯⠻⣦⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⢠⣿⣿⣿⣦⠀⠀⠈⢻⠁⠀⠀⢀⣼⡿⢿⠀⠈⠻⣦⣀⠀⠀⠀⠀⢀⣠⣤⣶⠟⠋⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣧⡀⠀⠀⠑⢄⣰⣿⣿⠃⠈⠳⣄⠀⠈⠻⣿⣶⣶⡿⠿⠛⠉⠀⠀⠀⡸⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠟⠁⠙⣆⠀⠀⠀⠹⣿⣿⡀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠊⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⡹⠋⠀⠀⠀⢀⣨⠿⣆⠀⠀⠈⠻⢇⡀⠀⠀⢀⣴⡛⠓⠶⢶⣖⡉⠁⠀⠀⠀⠀⠀⠀⠘⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠀⠀⠀⣀⣴⠟⠁⡠⢻⣷⡄⠀⠀⢀⠼⠉⠉⠙⢶⠀⣴⡆⠀⡇⠸⡄⠀⠀⠀⠀⠀⠀⣰⠁⣸⣿⣿⣿⣿⡏⠉⠉⠉⠉⠛⠛⠻⠿⣿ ⢄⡀⢠⡾⠛⠛⠒⢤⡀⢀⡟⢯⣇⠔⠁⠀⠀⠀⠀⠈⢦⠀⠀⢸⠀⣠⣇⠀⠀⠀⠀⠀⣰⡏⢀⣿⣿⣿⡟⡻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢄⡷⣤⣀⡀⠀⠙⢯⣠⠟⠁⠀⠀⠀⢠⣤⠔⠀⠀⠑⠢⣼⣿⣿⣿⡄⠀⠀⠀⡠⢃⣄⣼⣿⡿⠟⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⢶⣛⣿⣿⣿⠿⠿⠶⠶⠾⠿⢿⣿⣯⣛⡷⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣷⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⢶⣝⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠁⠀⣀⣤⡴⠶⠶⣦⣤⡀⠀⠀⠀⣠⣴⡶⠶⢶⣤⣄⠀⠈⢻⡄⠀⠀⠀ ⠀⠀⠀⣾⠁⢠⡾⢋⣵⠶⠖⠲⢶⣬⡻⣷⣴⡟⣩⡶⠶⠒⠶⣦⣝⢿⣆⠈⣿⠀⠀⠀ ⠀⠀⢰⡟⢰⡟⣰⡟⠁⠀⣠⣤⣤⡈⢻⡌⢿⡾⢃⣤⣤⣄⠀⠀⠹⣦⠹⣇⢸⠀⠀⠀ ⠀⠀⠀⡇⢸⡇⣿⠀⠀⢰⣿⠀⠈⣿⠈⣿⢸⡇⣿⠁⠀⣹⡇⠀⠀⣻⠀⣿⣾⠀⠀⠀ ⠀⠀⠀⡇⠸⣇⢹⣆⠀⠀⠛⠷⠾⠋⣼⠏⡞⣧⡙⠿⠶⠛⠁⠀⣠⡿⢠⡟⢸⠀⠀⠀ ⠀⠀⠀⡇⠀⠙⣧⣙⠷⣦⣤⣤⣴⠞⣫⡾⢿⣌⡻⢦⣤⣤⣤⠶⢋⣴⠟⠁⢸⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠈⠙⠳⠶⠤⠴⠶⠟⠋⠀⠀⠈⠛⠶⠶⣤⠶⠾⠛⠁⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⣤⡟⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⠀⠀⣀⣀⣠⣤⠄⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀ ⠀⢰⡿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣤⡾⢿⡇⠀ ⠀⠈⣿⣦⡈⠻⣦⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⠟⢉⣴⣿⡁⠀ ⠀⣼⠟⡟⠻⣦⣈⠻⣿⣍⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⢉⣽⠟⢁⣴⠟⢻⠙⣧⠀ ⢠⡟⠀⡇⠀⠈⣿⡷⣾⠋⠀⢀⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠈⢷⣶⣿⠁⠀⢸⠀⢻⡆ ⢸⡇⠀⡇⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠸⡇ ⣸⠀⠀⣷⣄⣀⣿⡇⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⣿⣀⣀⣼⠀⠀⣷ ⢹⡄⠀⣿⠉⢉⣿⠇⠀⠀⠀⠀⠙⠷⢦⣤⣤⠶⠟⠁⠀⠀⠀⠀⠀⣿⡉⠉⣹⠀⠀⡇ ⣼⣧⣤⣿⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣿⣤⣼⣧ ⣻⡇⠀⢹⣿⣷⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣶⣿⡏⠁⢨⣟ ⣿⠀⠀⠀⠈⠹⣯⠉⠻⣯⡉⠉⠁⠉⢉⣭⣭⡅⠉⠉⠀⠉⣽⠟⠉⣽⠟⠉⠀⠀⠀⣿ ⠻⢶⣦⡈⣻⡿⠋⠀⠀⠸⣧⣤⣤⣤⣼⡇⢸⣧⣤⣤⣤⣼⡏⠀⠀⠙⢿⣟⢁⣤⡴⠟ ⠀⠀⠈⠛⠋⠁⠀⠀⠀⢸⣏⣀⣀⣀⣹⡇⢸⣏⣀⣀⣀⣹⡇⠀⠀⠀⠀⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠡⠤⠤⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⡬⠭⣭⡅⣠⢿⡿⣭⣿⣿⣿⣿⣿⣿⣿⠀⠀⣶⣻⣦⡞⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠆⠒⠀⠉⠒⠊⠀⡏⠓⠛⠁⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠋⠃⠈⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⡆⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣤⠀⠀⠀⠀⠀⠠⠤⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣙⣛⠂⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠦⢐⣀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇⠀⠀⠀⠀⢠⡏⢻⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣟⣥⣿⣸⠦⣀⣀⣀⣀⠟⢆⢻⣿⡦⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠦⢜⣻⣿⡿⢇⡀⢸⠿⢳⡠⠜⠙⠛⠓⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡟⠉⠐⠀⢱⣞⡙⠃⠀⢹⢬⡴⢣⠀⠀⠀⢠⡧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡏⠀⠀⠀⣸⡇⢤⠄⠀⢸⢸⡇⡘⠀⠀⠀⢸⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣷⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣍⠻⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣢⣾ ⣿⡗⣌⠹⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠟⡁⢀ ⢹⣿⡜⣢⠙⣿⣶⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⡾⠿⠋⠀⡄⣶⠿ ⠀⢿⣧⢣⢧⡐⠛⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⡶⠿⠉⢡⠀⣷⣼⡿⠟⠀ ⠀⠀⢻⡧⢎⡕⣋⠠⠙⠿⣤⣤⣤⡶⠶⠿⠛⠛⠛⠛⠻⠿⠟⠛⠿⠷⠶⣶⣤⣄⣀⣀⣀⣠⣤⣤⣴⠶⠟⠉⠀⠄⢂⣤⣽⡿⡃⠀⠀⠀ ⠀⠀⣹⣿⠿⠞⠩⠑⡌⢠⠀⡍⢠⠀⡄⠠⠀⢌⠢⠐⡀⢠⠠⢀⠄⡠⢐⠠⢠⣉⡟⣟⣉⠉⢠⠀⡄⣴⣤⢊⡵⣊⢦⣿⣿⠁⠀⠀⠀⠀ ⠐⣤⣿⠇⠢⡍⠂⠥⡐⢂⡡⢐⢂⠡⡐⣠⠁⣆⠢⢅⢢⣁⠲⢌⢢⡑⢢⣌⢢⠄⡰⢀⠌⡱⢒⢯⢾⡰⣎⡳⢼⣧⣿⠿⠀⠀⠀⠀⠀⠀ ⣽⣿⠏⢠⠑⡄⠩⡐⢌⡣⡜⡥⣎⢷⡩⢖⡭⢂⡕⣪⠱⣌⡳⢮⣗⡻⢯⣝⣧⣿⣶⣙⢦⢣⡍⢆⠊⣿⣯⢽⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⡘⠄⡒⢠⢑⣌⣦⣳⣱⢳⣎⢷⡹⢧⢎⡱⡜⡴⣓⠮⣝⣳⢮⣽⣿⣿⣿⣿⣿⣿⣿⣷⣾⣭⠒⡄⢻⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠠⡁⠎⡐⣿⣿⣿⣿⣿⣿⣿⣾⡮⠱⣉⢆⠳⡜⡱⣭⠛⡼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠿⣿⡌⢡⢛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⡔⢡⠘⡜⢿⡿⣿⣿⡿⠿⢛⣷⠡⠈⢆⡙⠰⡱⢌⠓⣼⡟⣻⢛⡿⣻⢿⣿⣿⢿⡻⣝⢮⣛⡜⣿⣦⠩⢾⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⣿⡃⡌⡡⢊⠜⡩⣱⣉⠴⣀⢃⢆⠩⢂⠍⠢⢌⠓⡤⢃⣞⣿⡱⡡⢏⠲⣙⠎⡖⡍⢾⡱⣏⢾⡱⣏⡼⣷⣍⠺⡽⣿⣦⠀⠀⠀⠀⠀⠀ ⡧⡗⡬⣑⠮⡶⣵⢫⠍⢦⡑⣺⡎⢆⠣⣌⠱⣈⢒⢬⣱⣾⢏⡴⡑⢎⡔⡡⢊⡴⢌⢆⡱⢩⠖⣽⢲⡝⣮⢿⡥⢳⢭⣿⣧⡄⠀⠀⠀⠀ ⡱⣛⣶⣵⣾⠷⣧⢏⡞⡱⣎⣽⣹⢮⣷⣾⢿⣿⣿⣿⣿⣋⢎⢶⡙⢮⡔⣣⢏⠶⣙⢮⡱⢫⣞⢲⣏⣾⢳⡞⣽⢣⢮⣝⡻⣿⡀⠀⠀⠀ ⣷⣹⣿⣿⣎⢿⡘⢧⠚⡽⢋⠿⣷⣻⡼⣞⣯⣞⣷⣻⣿⣾⣚⠮⣝⢶⣙⠦⣏⣾⡹⣎⡷⢯⣞⣿⣽⢮⣟⡞⣧⢟⡧⣞⡽⣻⣿⠀⠀⠀ ⣿⡲⡽⣿⡿⣷⣿⣶⣿⣶⣯⣾⣹⣷⣻⡼⣳⢿⣾⣿⣿⡶⢭⣓⢮⢣⣯⣿⣼⢷⣫⡷⠿⣏⣿⣿⢿⡻⣞⡽⣎⠿⣜⢧⡻⣵⢺⣷⣦⣀ ⣿⢧⡹⣳⢛⠴⣻⣿⣿⣿⢼⡹⣷⣿⣷⣻⣭⠿⡽⣾⣝⣟⣶⡽⡻⢟⡏⢹⣬⡷⢋⣱⣿⡿⣟⢯⠳⣝⢮⡳⣭⣛⢮⡳⣝⢮⢷⡺⣼⣯ ⣿⣇⡗⣣⢏⡷⢢⡝⣿⣿⢢⠳⠌⡹⣿⣿⠻⣿⣻⣿⠛⢋⠯⣿⡟⠠⡀⢸⡏⢰⣶⣿⡳⣝⢮⠞⣝⢮⡳⣝⠶⣭⢳⡝⣮⣛⣮⢗⡧⣿ ⠙⠿⣷⡱⢎⡗⡯⣜⡹⣿⣇⡙⠆⠠⠙⣿⡀⠉⢿⡂⠠⠄⡀⠹⣧⠀⡁⢀⣾⣿⣛⢶⡹⡜⣎⡻⣜⢧⡻⣜⡻⣜⢧⣛⡶⣏⡾⣝⢾⣱ ⠀⠀⠹⣷⣿⡼⡱⢎⡽⢯⣿⣿⡆⠡⡈⠽⠹⠀⠌⣿⠁⠑⢢⣤⢀⣠⣷⣿⣟⡳⣝⢮⢵⣋⢶⣓⢮⡳⣝⢮⣵⢫⡾⣝⢾⣱⢟⡮⣟⡼ ⠀⠀⠀⠈⠻⣿⣽⢎⡽⣫⡿⣿⣿⣶⣷⣬⣡⣌⣠⣍⣄⣠⣸⣿⣾⣿⣛⠶⣭⢳⡭⣞⢮⡝⣮⠽⣎⢷⡹⣞⡼⣏⣷⢫⣟⢮⣻⡜⣧⣛ ⠀⠀⠀⠀⠀⠘⣿⡘⢶⡹⣝⡷⣻⣟⣿⣿⣿⣿⣿⣿⣿⡿⣟⡯⣗⡧⣏⡟⣼⢣⡗⣮⢳⣛⣞⣯⢽⡾⣝⣧⢿⣹⢮⣟⣼⣛⢶⣹⢳⡜ ⠀⠀⠀⠀⠀⠀⢹⣿⢦⣝⠎⡷⣹⢞⡷⣻⣞⣯⣟⡿⢯⡽⣺⢵⣫⠞⣵⢫⡞⣵⢻⣜⢯⣳⢯⡞⣯⢾⣝⣮⠷⣏⡷⣞⢮⡽⣎⢷⣫⢞ ⠀⠀⠀⠀⠀⠀⠀⣿⠿⡀⠫⣔⣯⢞⣵⣫⢞⣭⢻⡜⢧⡛⡵⣎⢧⡻⣜⢧⣝⢮⣳⢞⣯⣳⢯⣟⡾⣝⡾⣞⣻⢽⡳⣏⠿⣼⡹⢞⣣⢯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡖⠁⠐⠒⠂⠀⠐⠒⠂⠁⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀ ⠀⠀⠀⣴⣿⠣⠠⠄⠀⠠⠐⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀ ⠀⠀⣼⡏⠉⠉⠂⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⠆⠀ ⠀⣼⠟⡐⠀⠀⠀⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡎⠀⠀⠀⠀⠀⠘⡀ ⠰⣿⡜⣆⣀⣀⡀⢸⠀⠀⠀⢀⣀⣀⣀⣀⡤⠞⠁⠑⢄⠀⠀⠀⠀⠀⡇ ⠈⣿⣂⢹⡧⣐⣸⡿⡀⢰⣾⣿⡿⢋⣍⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄ ⠀⢻⣿⣄⠙⠻⣿⡇⠁⠻⣋⡻⣗⣌⣩⣾⠔⠉⢈⠀⠀⠀⠀⠀⠀⢀⠃ ⠀⠘⢿⣿⢣⠤⠿⣏⠀⡔⡸⠛⠺⢌⣉⡡⢐⠢⠸⠀⠀⠀⠀⠀⠀⡈⠀ ⠀⠀⠘⣿⣷⣳⣄⢸⡴⢡⠀⠀⠀⢀⣠⠖⠁⣠⣶⠀⠀⠀⠀⠀⡴⠃⠀ ⠀⠀⠀⠈⢻⣷⡜⢿⡛⠛⣛⡶⠎⠉⠁⠀⣰⠟⠁⠀⠀⠀⢀⡜⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣦⢄⠀⠑⡄⠀⠀⠀⢠⠋⠀⠀⠀⢀⠴⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⢅⣀⣀⣀⣀⣀⣠⠔⠊⠁⠀⠸⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠊⠉⠉⠉⠉⠉⠉⠉⠒⡒⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⢀⣄⠀⠀⡐⠟⠀⠀⠀⣀⠀⠘⡄⠹⣶⢤⡌⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⣾⡿⢄⠸⠀⠀⠀⠀⠀⠀⠙⢦⡙⢦⠘⠁⣠⢤⡀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⣰⠿⠅⠘⠂⠀⠐⢲⣿⣶⣦⣄⠀⠙⢿⡵⠊⠀⠀⣀⣀⠀⢢⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⣀⣴⡞⠛⢿⣿⣦⡀⠀⣧⠀⢠⣾⠿⣤⡀⠈⠳⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⢠⠋⣿⣿⠄⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⡀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢶⡈⠁⢀⣾⣿⣿⣿⣻⠀⠈⢿⣿⠦⢤⣾⢿⠀⢢⡀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⣀⣉⣉⣩⢿⣿⣿⡏⣿⡆⠀⠘⣿⣍⡛⡿⠃⠀⠀⠁⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢻⡿⠋⠀⠉⠀⠀⠀⠈⢫⣿⡄⠀⠀⠀⡀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠘⡟⠷⣆⠀⡀⠀⠀⢀⡿⣿⠃⠀⠀⠀⠛⠀⠀⢰⡄⢷⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣿⡀⣏⣧⣵⣄⣠⣾⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⠀ ⠀⠀⢸⡆⠀⠀⠀⠀⠀⠈⢧⠀⠀⠠⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⣈⣉⣉⢛⣤⣌⣧⠀⠀⠀⢀⡤⠂⠀⢀⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠘⢯⡐⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⣠⣾⡿⠻⡿⢻⣿⣿⡿⠀⠀⣰⡿⠁⠀⠀⣾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣧⠀⠰⡀⠀⠀⠀⠀⠉⠂⠛⣷⡄⠀⠀⠀⠀⠀⠀⣾⣧⣼⣧⣤⣧⣤⣧⣼⣿⣿⣇⠀⢀⡿⠁⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢧⡀⠑⣄⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⢠⡏⣽⠻⢿⣿⣿⣿⣿⠿⠟⢻⡗⠀⠀⠃⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠙⠳⣄⡀⢀⣀⡤⠤⣴⣯⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣽⣷⣄⡙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⢉⠉⠀⠀⠀⣼⡏⠀⠠⢴⠿⠋⠀⠀⠀⠀⠀⠀⣄⠀⣀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠳⡈⠻⣷⣦⣤⣀⣀⣀⣀⣀⣤⣶⣧⣀⠀⠀⠀⠁⠀⠀⢀⣼⠟⠒⠒⠊⠁⠀⠀⣠⣤⣤⣞⡗⠀⢻⠁⠀⠀ ⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠈⠓⠦⣍⡙⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⠻⣀⡠⠎⠰⢰⡆ ⠀⠀⣠⠞⠒⠊⠉⠁⠈⠉⠑⢄⠀⠈⠙⢲⣄⣀⣤⡾⢿⣻⣿⣿⣿⣿⣿⣿⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⣄⠏⠇⠀⣖⣩⠷ ⠀⡴⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠙⠿⠋⠀⠀⠉⠛⠿⣷⡿⢫⣯⡆⠀⠀⢙⣦⣦⣴⣶⣶⡌⣿⡷⢀⠴⣋⡤⠒⠋⠉⠀⠀ ⢰⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡙⡄⠀⠀⠀⠀⠀⠀⠀⢠⣶⡞⠀⣼⠏⠀⢈⣻⠏⢸⣯⣤⣼⣯⣿⣽⠗⢁⡾⠋⠀⠀⠀⠀⠀⠀ ⡼⠀⣿⣇⠰⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣣⡤⠔⠚⠗⣒⡦⢤⣬⢿⡿⠛⣡⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠈⣿⡆⠈⢆⠀⠀⠀⠀⠀⠀⠀⣠⡎⠉⠒⠤⣤⣴⡾⠭⠓⠚⠉⢀⣤⣶⡿⠟⠁⠀⠀⠙⣧⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠐⢼⣿⣄⠘⢳⡀⠀⠀⠀⢀⣾⣿⠧⣄⡀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠉⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠻⢷⣄⣃⡄⠀⢠⣿⠟⠁⠀⠀⠉⠑⠲⢇⡰⠿⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠰⢟⡁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⢀⣾⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠻⢿⣿⣿⣿⣿⣇⠀ ⢀⣿⣿⣿⣿⣿⠏⠀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣙⣿⣿⣿⣿⣆ ⣼⣿⣿⣿⣿⡟⣰⡿⠛⠉⠛⢷⡄⢀⣾⠛⠋⠙⢻⣿⣿⣿⡿ ⠸⣿⣿⣿⣿⡇⣿⡀⠰⠆⠀⢸⡿⢸⣿⠀⠶⠄⠈⣿⣿⠟⠁ ⠀⢻⣿⣿⣿⡇⠙⢷⣦⣤⣴⡿⢃⣤⠻⣶⣤⣤⡾⣿⣿⠀⠀ ⠀⣴⣿⣿⣿⠇⠀⠀⠀⠉⠀⠀⠀⢻⣆⠀⠈⠁⠀⣿⣿⣦⡀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⠀⠀⠀⠀⣿⣿⢸⣿ ⠘⢿⣷⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠃ ⠀⠀⠉⠙⣿⣧⠀⠀⠀⣠⣀⣀⣀⣀⣠⣾⠃⠀⢸⣿⠇⠀⠀ ⠀⠀⠀⠀⠸⣿⣦⡀⠀⠈⠙⠛⠛⠛⠋⠀⠀⢠⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠻⣿⣶⣤⣄⣀⣀⣀⣠⣤⣶⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠉⠛⠒⢦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⢀⣠⠤⠤⣄⣀⠈⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠒⠲⢤⣄⡀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⠟⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⢧⠈⡇⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⢀⣀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠏⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⣼⢀⡇⠀⠀ ⠀⠀⢀⡞⠀⣠⠚⠁⠀⠉⠓⠦⣀⠀⠀⠀⠙⢦⡀⠀⠸⡦⡀⠀⠀⠀⠠⢺⠁⠀⢠⡟⠀⠀⢀⡞⠀⠀⠀⢠⠴⣖⢀⣠⠜⢁⠞⠀⠀⠀ ⠀⠀⢸⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠈⠳⣄⠀⠹⣄⠀⠀⠀⢀⡏⠀⢀⡞⠀⠀⠀⡾⠀⠀⠀⠀⠈⠓⠮⠭⠔⠚⠁⠀⠀⠀⠀ ⠀⠀⢸⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠙⢦⡀⢸⢦⡀⢀⢾⠀⢠⠟⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠳⣄⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢴⣄⠀⠀⠙⢾⠀⠉⠁⢸⡴⠋⠀⢀⣀⠼⡏⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⣄⡀⠀ ⠀⠀⠀⠀⠈⠓⢤⣙⢦⡀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠒⡺⢻⠀⠀⠀⡸⠛⣖⠒⠉⠀⢰⠃⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠈⠻⡄ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢦⠀⠀⠀⠀⠀⢸⠀⢆⠀⠸⡀⠈⡆⢠⠎⠀⡰⠃⠀⠀⠀⣼⣀⣠⠴⠚⠉⠀⠀⠀⠀⣀⡤⠤⣁⢢⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⣀⡀⠀⢈⣿⠇⠀⠀⠀⣀⡎⠀⢸⠀⠀⢳⢶⡋⢱⠔⡞⠁⢹⣀⣀⣠⡯⣀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⡿⠀⠀⡇ ⠀⠀⣠⠞⠋⠉⠉⠉⠉⠉⠉⠙⠛⠛⠉⣹⠁⠀⢸⠀⠀⠀⢷⠓⢻⠎⡤⣴⠾⢛⣚⢛⣿⣝⣛⣀⠴⠚⠁⠀⠀⠀⠀⠀⣠⠞⠁⢀⡼⠀ ⠀⣰⠃⠀⣠⠤⠶⠦⠤⢄⣀⡰⡶⠖⣶⣏⣀⠠⢾⣤⣀⠀⠸⣠⣣⢞⣠⣴⣩⠵⡮⠽⣻⣟⠋⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⣀⡴⠋⠀⠀ ⠀⡏⠀⢰⠁⠀⠀⠀⢀⣠⣞⠭⠭⢭⣍⡀⠙⣛⡭⢘⠙⠓⢴⣏⠁⠀⢁⠔⠚⣿⣷⡄⠈⠻⡄⠀⠀⠀⢀⡴⠋⣀⡤⠖⠋⠁⠀⠀⠀⠀ ⠀⢷⠀⠸⣄⠀⠀⠀⠉⠉⠀⣰⣯⡭⢽⢊⣥⣠⣅⣼⢸⠀⠀⠙⠲⢎⡁⠀⡴⣅⡈⢧⠀⠀⢻⡀⠀⢠⠋⡴⠚⠁⠀⠀⠀⠀⠀⢀⣀⡀ ⠀⠘⢧⡀⠈⠳⢤⡀⠀⣠⡾⢫⠏⡰⢣⢾⡟⠁⠀⣈⣿⣵⣦⣄⡀⠀⠈⠙⠢⢄⣉⣺⣆⠀⠀⢧⠀⢸⠘⣅⠀⣀⡄⠀⠀⠀⠀⢊⠔⢮ ⢋⡭⡳⣍⠓⠦⢄⡈⠑⢄⢠⠟⠉⢱⡇⢸⣧⣴⠟⠛⡇⠀⠈⡟⠻⢽⣦⣄⡀⠀⠀⠀⠉⠃⠀⠘⣇⠀⠓⠤⠽⠛⠁⠀⠀⠀⠀⠀⠉⠀ ⢸⠀⠠⠜⠀⠀⠀⠈⢳⣸⠏⠀⠀⣸⣷⢿⠟⠁⠀⠀⢳⠀⢀⣇⠀⠀⢸⠙⠛⠷⣦⣄⡀⠀⠀⠀⠸⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⣿⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⡿⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⣏⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢷⣾⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⡾⠋⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⢀⡿⠿⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣷⠀⠀⠀⠀⣾⠿⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⡄⠀⣴⡄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣇⠀⠀⠀⣿⠀⠀⢠⡀⠀⠈⣷⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⣿⣧⣤⣴⡇⠀⠀⠀⣿⠃⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⠀⠀⠀⣿⠀⠀⠈⢻⣦⠶⠿⣷⣤⡀⠀⠀⠈⠁⠀⢠⡾⠋⣀⣤⣀⠀⠉⠙⣿⡟⠀⣿⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡆⠀⠀⣿⠀⠰⣶⠟⠁⢀⡶⠒⣦⠙⢧⠀⠀⠀⠀⣿⠀⢰⣏⢀⡿⠀⠀⠀⢸⡇⠀⣿⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⠀⠀⣿⠀⠀⢾⡀⠀⠀⠛⠖⠛⠀⣼⠀⠀⠀⠀⣿⡀⠀⠉⠉⠀⠀⠀⠀⣿⠃⠀⣿⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡄⠀⣿⠀⠀⠘⣷⡀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠘⠷⣤⣀⠀⠀⠀⣀⣼⠃⠀⠀⣿⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⡀⣿⠂⠀⠀⠈⠙⠒⠶⠶⠚⠋⠀⢠⡟⠛⢷⡄⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⢠⡿⢀⡟⠀⠀⠀⣶⠀⠀⢰⡀⠀⢠⣦⣤⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣇⣿⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⣀⣨⣷⣶⣿⣥⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⠃⠀⠀⢰⣿⣇⢀⣾⣷⠀⢸⣇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠉⠀⠀⣤⣶⣿⠛⢻⣿⣿⣿⡏⠉⠻⣷⣦⡀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⢸⡟⢻⣾⡇⢹⣇⠈⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⢠⣾⣿⣿⣯⣤⣼⣿⣿⣿⣷⣶⣾⣿⣿⣻⡄⠀⢀⡀⠀⢸⣿⠀⠀⠀⠀⣼⡇⠀⠻⠇⠘⣿⡄⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠉⠀⢸⣇⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠈⠃⠙⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣄⠀⠀⣠⡄⠀⠀⠀⠀⢠⣄⡀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣿⠀⠀⢸⣧⣴⠟⠛⢿⣆⠙⢷⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠶⡶⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⣿⠿⠿⢿⣿⡿⠷⠶⠶⠶⠶⠶⢿⣷⠀⠀⠀⠀⣿⡶⠶⢿⣿⣿⠀⠀⠀⢹⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠻⣦⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⣿⣄⠀⠈⣿⠸⣷⣄⣀⣴⠟⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⣴⠋⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣄⠀⠀⣠⠀⠀⢀⡀⠀⣀⠀⠀⣰⠀⠀⣀⣀⠀⣀⡀⠀⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⢸⣿⣆⣸⠿⣧⠀⠘⣧⠀⣿⣧⡀⢹⡇⣸⠏⠙⢷⠘⢷⣾⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠻⣿⠿⠶⠶⠶⢶⣶⣶⣤⣤⣤⣤⣴⣶⣶⠶⠟⠛⠁⠀⠀⠀⠀⠀⢸⡇⠻⠟⠀⢻⣄⠀⣿⠀⣿⠙⢿⣼⡏⣿⠀⠀⢸⠃⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠘⢿⠄⢿⠀⢺⠀⠀⠙⠁⠙⠻⠷⠋⠀⠀⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡤⣤⣿⠃⠀⠀⠀⠀⢀⣤⣤⣤⡶⠾⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⢀⣀⣀⣤⣀⣀⣾⣿⣟⣉⣛⣛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠤⠤⡀⠀⠀⠀⠀⠀⠻⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠋⠀⠀⠀⠘⡀⣄⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⡇⢳⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⣀⡀⡾⢛⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠉⢛⣋⡛⠁⢳⣾⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⣿⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣄⣀⠀ ⠇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠁⠴⠒⠉⠀⠘⣿⣿⣿⣿⡎⢷⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⠃⠀ ⠘⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⠈⢧⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀ ⠀⠳⢄⣀⣀⣾⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⣤⣀⠀⠀⠀⠻⣿⣿⠀⣴⣢⡤⠀⠘⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢻⣿⣿⣿⣿⡎⢀⣼⡿⠟⠋⠁⠀⠀⠀⠀⠈⠱⠀⠀⠉⠙⠛⢶⣼⣿⣹⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡇⢸⣿⣿⣿⣿⠓⢻⡽⠀⠀⠀⠀⠀⢀⡠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠸⠸⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠀⠳⣿⣷⣿⡇⠀⠀⠀⢀⡀⠀⡇⢀⡀⠀⠀⠀⢈⠀⠀⠀⠀⢀⣠⣾⡇⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⡄⠀⠸⣏⠹⣷⡀⠀⢠⠋⡈⢠⠋⡱⠁⣀⡀⠀⡼⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠘⡆⢠⠟⣷⢦⣿⠢⣬⠀⣧⠃⢸⡡⢊⡴⠃⠈⠀⠀⢀⣠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣡⠎⠀⢩⣸⣿⡄⠹⠐⠀⠀⠀⡀⠺⠚⣡⣾⠶⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠐⠁⣻⣿⣄⠀⠀⠀⠀⠀⢠⡏⠉⠁⢰⢻⣿⣟⣻⣿⣿⣿⣿⣿⡄⠀⢰⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠓⡏⢹⠀⠀⠀⠀⠀⢸⠁⠀⠀⠘⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣦⡏⢇⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣆⣸⡃⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⢻⣶⠾⠛⠛⠛⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⡴⠋⢠⣤⡴⢦⣄⠀⠀⢿⣤⡤⠶⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣾⠁⣼⠟⠁⠀⠀⣼⠀⢀⡿⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⡀⠀⠀⢀⣠⣴⡞⠉⠀⠇⠘⠇⠀⠀⣠⠞⢃⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀ ⢿⣿⠟⠛⠛⠋⠉⣬⣄⡀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠻⣆⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀ ⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠉⠙⠳⠶⣄⠀ ⠀⠀⠀⠀⠈⠙⣿⡶⠶⣶⣶⠟⠀⠀⢀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠘⣧ ⠀⠀⠀⠀⠀⠀⠿⠶⣶⡏⠀⣀⣤⠶⠿⠤⣴⣶⠾⠃⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⢿⣥⣀⣀⣀⣠⡤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⢀⠀⢀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠚⡟⠚⡛⣻⠟⣻⢻⣿⢻⣓⠐⠒⠒⠛⠀⠀⠘⠀⡈⠗⡛⠊⠙⠛⠲⠛⠘⠋⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠙⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢰⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⢻⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢘⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⡄⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠸⣇⠀⠀⣾⠁⠀⠀⠀⣸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣸⣧⠀⠀⠀⠀⣿⡀⢠⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠉⠉⠉⣿⠀⠀⠀⠀⢸⣇⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀ ⢀⣴⠾⠛⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⣾⠁⠀⠀⢿⡄⠀⠀⢀⣼⠟⠛⠛⠻⠶⢦⣤⣀⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⢸⣇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⣦⣼⡇⠀⠀⠀⠀⠀ ⢸⣇⠀⠀⠀⢻⡄⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⢸⣿⡄⠀⠀⠀⢻⣄⠀⠀⠙⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠸⣟⠻⣦⣀⠀⠀⣹⣷⣦⡴⠾⠋⠉⠙⠛⢻⡏⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀ ⠀⣿⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀ ⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⣸⡇⠀⠀⠀⠀ ⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀ ⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣄⣀⣀⣀⣀⣠⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡐⠈⠛⠛⠙⠀⠃⠛⠛⠓⠀⠒⠒⠛⠀⠀⠀⠈⠛⠐⠓⠀⠙⠛⠒⠂⠒⠓

⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⣴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠶⣶⠚⢉⣽⣿⠀⠀⠈⣷⠀⠀⠀⠀⠀⠉⠉⠙⠓⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠇⠀⠀⢀⣴⠟⠁⠀⠀⠀⢀⣴⠾⠟⠛⠓⠲⣄⠀⠈⢳⣼⢷⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⢀⣾⠃⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠹⣵⠆⢠⢿⣿⠃⠀⠀⠀⣿⣆⣤⣤⣤⡤⣰⡄⢠⣄⣶⣆⠀⠀⠀⠈⠙⢶⣄⠀⠀⡸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⠀⢀⣾⠇⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡟⣸⠇⠀⠀⠀⠀⣿⣿⣷⣿⣿⢿⣿⣿⣏⣿⣝⣏⡼⣦⣄⣰⠀⠀⠈⠻⣦⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⡿⠀⠀⢸⣿⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢰⠇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣿⣷⣷⣶⣾⣿⣦⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⢼⢹⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⣀⡤⠞⢁⡴⠋⠀⠀⠀⠀⠀⣼⠋⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣼⢳⡀⠀⠀⠀ ⠀⠀⠀⢿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⢋⣉⡤⠞⠉⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⠀⠹⡆⠀⠀ ⠀⠀⠀⠘⡇⠀⢸⣿⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠘⡆⠀⠹⣆⠀ ⠀⠀⠀⠀⢹⣠⢫⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣳⡀⠀⠹⡆ ⠀⠀⠀⠀⢸⣡⣟⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⡆⢹⣷⡀⠀⢹ ⠀⠀⠀⠀⡼⡵⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢳⢣⡀⠀ ⠀⠀⠀⣰⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⣶⣶⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡼⢹⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣷⠀ ⠀⠀⢀⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣠⣾⣻⣿⣫⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠟⠃⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⢳ ⠀⠀⣼⣽⣿⣿⣿⣿⣿⣿⢿⣿⡿⣡⣾⣿⣿⡿⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣿⢻⣿⣿⣿⡻⢷⣼⣿⣿⣧⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠ ⠀⠀⠙⠻⣿⣿⣳⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢀⣀⠀⠀⠀⢠⡟⠀⣼⠏⢸⣿⣿⣯⠇⠀⢹⣿⣿⡏⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⡤⠊⠁ ⠀⢸⣿⣶⠟⣻⣿⣿⣿⠏⠉⠛⠻⣿⣾⣿⣿⣿⣦⠀⠀⣠⣴⣾⡿⣿⣿⣿⣿⣿⣷⣾⣍⠳⣆⡞⠀⣠⠏⠀⢸⣿⣏⡟⠀⠀⣼⣿⢸⡇⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀ ⠀⢸⣯⠏⣰⣿⣿⣏⡿⠤⡶⠶⢦⣀⠉⠻⢿⡟⠁⣠⢞⣾⠟⠁⢸⠿⢷⣄⣈⣉⡉⢿⣿⢷⣮⢳⡖⠁⠀⠀⠈⣿⡞⠀⢀⣴⣿⣃⣼⢁⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⣸⠇⣰⣿⣿⣿⣿⡇⠀⢹⠀⣰⠋⠳⣄⠀⠙⠒⠃⠈⠏⠀⠀⠠⣤⠚⠁⠛⠿⠃⠄⣿⠈⠃⠀⢀⣀⠀⠀⠀⠚⠀⣴⢿⣿⣴⠾⠿⣾⣶⣼⡿⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⣠⠋⢠⣿⣿⣿⣿⣿⣷⣤⠼⢇⡁⠀⢰⣿⣦⣀⣀⡠⠄⣀⣀⡀⠤⠚⠛⠛⠛⠛⠛⠚⠧⠀⠀⠀⠀⠈⠙⠛⠲⠦⣄⣾⠟⠉⠀⠀⠀⠀⠈⠻⡷⣼⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀ ⠋⣤⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠹⣄⢺⡀⣯⡈⠙⡋⠓⡲⣬⡙⠲⢤⣀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠺⢷⣢⣌⡑⢪⣍⡀⠀⠀⣀⠀⠀⠀⠀⢥⣾⣿⣿⣿⣿⡿⣿⣇⠀⠀⠀⠀ ⣼⣾⣿⣿⣿⣿⣿⣿⡿⠙⣿⣦⠀⠀⠈⠻⠿⠏⠙⠪⣕⠪⢕⡻⣓⠦⣌⠙⣶⣄⡀⠈⠓⠀⠒⠀⠀⠀⠀⠀⠀⠉⠟⠀⠉⠳⣔⢮⣁⠁⠦⠐⣼⣿⣿⣿⣿⣿⠇⣿⣿⡄⠀⠀⠀ ⣽⣿⣿⣿⣿⣿⣿⣏⣀⣴⣿⣿⣿⣦⣀⠀⢺⣽⠆⠀⠀⠀⠀⠉⠈⠙⠠⣹⣿⣿⣿⣤⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠁⠈⢣⡀⠀⣿⣿⣿⢻⣿⣿⠸⢻⣿⣿⡀⠀⠀ ⣿⣿⣿⣿⠿⠛⠉⠁⠀⠈⠙⠻⢿⣿⣿⣷⣦⣤⣶⡆⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⠀⠈⠷⠋⠁⠀⠀⠉⠙⠻⣿⣿⣖⣠⣿⡇⠀⠀⠀⠀⠈⢻⣿⣿⣿⡄⢻⣿⡇⠘⡿⣿⣷⡀⠀ ⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣾⣿⣦⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠘⣿⣿⠀⢳⠻⣿⣷⡀ ⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡉⠻⣿⠛⠘⣿⣄⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠁⠀⠀⠀⢠⣿⣿⣿⡇⢻⡇⠀⣿⣿⣧⠸⣆⠹⣿⣷ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠈⣧⡀⠻⣿⣷⣄⡀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⣠⣿⣿⣿⣿⠁⢸⠁⠀⡇⠹⣿⣧⢻⡄⠹⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣷⡀⢻⣿⣿⣿⣦⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣀⣴⣾⣿⣿⣿⣿⣿⠀⠘⡆⠀⣇⠸⡿⣿⣦⣿⣆⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢻⣿⣧⣹⣿⣿⣿⣿⣷⣄⠈⠛⠦⢤⣀⠀⣀⣀⡠⠴⠛⢁⣤⠶⠛⠉⠉⠙⠿⣿⣿⣿⣽⠀⠀⢣⠀⣿⡀⣿⣻⣿⣿⣿⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠸⣿⣿⡿⠘⠻⡿⢿⣿⣿⣿⣶⣄⡀⠈⠉⠉⣁⣤⡶⢾⠉⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⠀⢸⣦⣿⡇⢹⣯⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣿⠻⣧⠒⠲⠆⣸⣿⣿⡿⢿⣿⣿⣷⣾⣿⡉⠀⠻⣌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⣸⣽⢸⣇⠈⣿⣯⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠸⡆⠀⠐⠀⠚⠛⢹⡟⠁⠀⣿⣏⠉⠉⠉⢳⡀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢠⣿⢻⢸⣿⠀⣿⣿⣿⣿⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⢀⣰⠏⠀⠀⠀⣿⢹⡄⠀⠀⠈⢧⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢸⣿⣼⣼⣿⠀⣿⣿⣿⢸⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠸⣏⢧⣄⡀⣋⡈⠁⢀⡼⠃⠀⣷⡀⠀⠀⢸⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⠀⣿⣿⠇⣈⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀ ⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀ ⠀⢀⡟⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⡀⠀⠀⠘⡄⠀ ⠀⣸⠁⠀⠀⠀⠀⠀⣄⣀⣈⣁⣀⢴⣶⠒⠒⠒⣶⢢⣀⣀⡀⠀⠀⠀⢳⠀ ⢠⡏⠀⠀⠀⠀⠉⣉⣿⣟⡛⠛⠟⣿⡏⠀⣰⠀⢹⣿⠛⠛⢛⢻⠀⠀⠀⡇ ⢸⠃⠀⠀⠀⠀⠤⢼⣿⣏⡁⣀⣈⣿⠀⠀⢿⠀⠘⣿⣄⢀⣩⡼⡄⠀⢀⠁ ⢸⠀⠀⠀⠀⠀⠀⠘⠻⣯⣿⣿⠟⢈⡤⣀⣿⣷⣄⣸⡿⠯⠿⠃⣀⠀⢸⠀ ⠸⡄⢠⠊⠉⠈⠁⣀⣀⣬⣭⣤⣾⣿⣿⡿⢟⣉⠿⠿⣵⣤⣀⣀⠀⢱⡙⠀ ⠀⠳⡼⠀⢰⡿⠛⠉⠉⠉⠉⠛⠻⢯⡴⣶⣿⣿⡭⡵⠞⠛⠉⢙⣛⢇⠇⠀ ⠀⠀⠙⢤⡀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠎⠽⢿⡉⠂⠀⠀⠀⠠⠊⢡⠊⠀⠀ ⠀⠀⠀⠈⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠢⢤⣀⣀⠀⠀⠀⠀⠈⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠒⠒⣲⡒⠒⢦⢀⢸⠋⠉⠑⠒⠢⢤⣼⠓⠒⢲⡒⠒⢦⣴⡗⠒⣶⠀⠀⢰⠒⠒⠒⠒⠒⠺⡞⢶⠓⠒⢦⡖⠒⣶⠆ ⠀⠀⠀⠘⠀⠀⢿⠇⠀⣼⠏⡏⠀⢰⣶⡄⠀⢸⢽⠀⠀⢸⡏⠀⣼⣿⠇⠀⢸⠀⠀⢸⠀⠀⡴⢤⠀⠀⡇⠈⠳⡄⠀⠐⡴⠁⠀ ⠀⠀⠀⢸⠀⠀⣟⣆⠀⠸⣼⡁⠀⠈⠉⠀⢀⡇⢸⠀⠀⢸⡟⠀⢸⡿⡅⠀⠸⢤⠤⣼⠄⠀⠉⠉⠀⠀⡇⢠⠞⠁⣀⠀⠘⢦⡀ ⠀⠀⠀⠘⠓⠒⠃⠘⠒⠒⠃⠉⠉⠒⠒⠤⠼⠁⠘⠒⠒⠒⠓⠒⠋⠀⠓⠒⠒⠛⠒⠛⠒⠒⠒⠒⠒⠒⠓⠓⠒⠚⠃⠓⠒⠚⠗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠶⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣖⣒⣂⣉⣭⣭⣍⣕⣻⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠀⠀⣀⣠⣀⣀⣀⣀⣀⣀⡀⠀⢀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠻⣄⢠⠖⠉⠉⣹⣉⡛⣿⣿⣶⣍⣿⣀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⡻⣿⠗⢦⡀⠀⠀⠈⢹⡆⠀⠀⠘⠟⠁⠙⠿⣿⠿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠙⢭⡛⠚⠁⠀⠀⠈⠲⢄⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠁⠀⠀⠉⠲⢄⠀⠀⠀⠀⡼⡿⢹⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⣀⡠⠤⠔⠒⠊⠉⠙⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠙⠢⣤⣼⠟⠀⢸⡷⣤⣀⡀⠀⡀⠀⠀⣀⣀⣼⠋⢣⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠇⠀⠀⠈⢷⡈⠉⣒⣚⠚⠛⠓⠒⣷⡇⠀⢀⣳⡄⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⢀⣴⣅⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⢻⠀⠀⠀⠀⠸⡟⠚⢯⡽⣄⣀⣤⡾⢿⠒⢮⠙⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀ ⠀⣼⣏⠓⢝⡲⣀⠀⠀⠀⠀⡼⠁⢸⡎⠀⠀⠀⠀⠀⣧⡴⢻⠀⡠⢛⡿⡵⡈⢣⠀⢣⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀ ⠀⠈⠙⢵⣤⣉⠺⢕⠦⣤⠞⠁⠀⣇⠇⠀⣀⠀⠀⠀⠙⠁⠸⠊⠀⡼⠀⠘⣵⡄⠳⡀⠱⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀ ⠀⠀⠀⠀⠈⠻⢷⣄⣽⠋⠀⢀⣤⣿⡀⠈⠛⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⢿⢄⠱⡀⠘⢆⠱⡀⠀⠀⠀⢀⣠⢤⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⡏⠁⠀⠀⠉⠑⠶⢄⡀⠀⣻⠛⠀⠀⠸⣿⡀⠀⠀⠈⢫⢆⠙⣄⠈⢦⢸⣤⢴⣞⠭⣶⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⡴⠚⠉⠈⠙⠛⠓⠶⡒⠒⠢⠷⡀⠀⠀⠀⠫⣦⣼⣶⣾⡿⠛⠉⡠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⣰⠁⠀⠀⠀⢀⣶⠀⠀⠱⡀⠀⠀⠳⡀⠀⣠⢞⡝⢉⣼⣟⠥⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣞⠘⢇⠀⠀⠘⢆⠀⠀⠳⣜⣵⣫⠴⢻⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠸⡄⠀⠀⠀⠀⣾⠀⠈⢣⠀⠀⠈⢣⡀⠀⠈⠁⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⠀⢳⠀⠀⢀⡠⣼⠀⠀⠈⢧⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠯⣲⣷⣺⠽⠊⠀⠀⠀⠀⠈⢧⠀⠀⠀⠙⢄⠀⠀⢀⣀⣀⠤⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢸⠋⠉⢁⣀⠤⠲⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⣰⡧⠔⠚⠉⠀⠀⠀⠈⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠔⠒⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣤⣄⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⢶⣤⣄⠙⣏⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣳⢮⣽⣿⣾⣷⣌⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠷⢮⣿⣿⣿⣿⡄⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠉⠉⠉⠙⠓⠦⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡿⣟⡛⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠀⠀⢸⣿⣷⣾⠿⠋⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⣆⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡇⣠⣶⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠮⡳⣄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠀⠛⠛⠉⠙⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢀⠈⠛⠀⡜⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠳⣄⠀⢇⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡴⠞⣛⣋⡉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠢⠸⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⣿⣿⣶⣶⣾⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠠⡀⠀⡏⠲⣄⠀⠀⠀⠀⠀⢰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡳⡀⢳⠀⠈⠑⣤⡀⠀⠀⠈⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡢⠀⢰⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⢠⠀⢄⢱⠉⠲⢤⣄⣈⡚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⢀⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣎⢦⠸⡄⠀⡀⡜⠁⢀⢿⡗⠋⢻⣛⣿⡿⠿⣿⠟⠋⠁⠀⠀⠀⠀⠈⠉⠒⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣤⡇⠇⠀⣼⡟⠀⠀⢀⡇⠀⠀⢠⠇⠀⠀⠀⢰⠀⠀⠀⠀⣸⢄⠀⠘⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡇⠀⡀⢻⣇⠀⠀⡞⠀⠀⡠⠋⠀⠀⠀⠀⡏⡇⠀⠀⢰⠃⣸⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⡇⠀⠸⡄⣼⠀⡠⠚⠁⠀⠀⢀⡀⠀⡇⣷⡞⡰⠃⢠⢿⡇⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡄⡇⠀⢠⡁⡾⣏⠀⠀⠀⠀⠀⠀⠻⣶⣷⣻⣷⠁⠀⠎⠈⡇⢇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠂⢸⠀⠀⡟⢆⡈⢳⡄⢣⡀⢣⡀⠀⠱⡽⣷⠇⠀⠀⠀⠀⡇⢸⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⠘⠀⣸⠀⠀⠙⢦⣗⢦⣿⣦⣽⣦⡀⠑⢾⡄⠀⠀⠀⠀⢱⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡄⠀⡇⠀⠀⠀⢀⣈⣙⣿⣯⣽⣟⣿⠿⠾⡇⠀⠀⠀⠀⠸⡐⣵⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⡇⢹⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡼⠁⠲⣄⡀⠀⠀⠀⠀⠐⠒⠐⠒⠒⢂⣿⠀⣀⣠⣀⡀⢸⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡴⣷⡀⠀⠀⠉⠓⠲⠤⠤⠤⠤⠤⢒⡾⠋⣿⡗⠒⠓⠒⠤⣄⡇⠣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣸⠁⠘⡝⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠺⣿⠃⠀⣖⣢⢤⣄⡸⡌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣳⠃⢣⠀⠘⠆⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣀⣽⣿⣶⣬⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠻⣆⠈⢇⠀⠀⠀⡄⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣭⣿⣿⣦⠙⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠰⢿⣆⠘⣧⠀⠀⠙⢦⡈⠻⣦⣄⠀⢀⣀⣀⣸⡏⢠⣀⣀⠤⠤⠀⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠸⢠⠘⣿⣆⠘⣷⣄⠀⠢⡙⠲⣬⣻⣿⣷⣶⣽⣿⠧⠀⠀⠀⠀⠀⢠⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠈⣇⠘⡄⠸⣿⣦⠈⢿⣷⣄⠈⠳⢦⣭⣟⣿⣿⣿⣿⠛⣃⠀⠀⠀⠀⡸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡸⢸⠀⣧⠀⢹⣿⣷⡈⢻⣿⣷⠦⣄⡀⠉⠉⠉⠛⠃⠀⠀⠈⠙⣧⣀⠇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠒⠒⠒⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⢀⡠⠺⢿⣈⣷⣤⣀⠀⠀⠈⠉⠛⢙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠉⣡⡤⠒⠋⠁⣸⡀⠀⠉⠁⠒⠒⢂⣩⡏⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⣧⢴⡶⠋⣬⣀⣀⢀⡀⢻⢿⣄⠀⠀⢀⣴⠿⢴⣷⣚⡭⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢯⡽⣟⡋⠀⠀⣿⣿⡿⢿⡟⢛⣦⣿⣷⠶⠀⠉⠉⣹⣏⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢸⣿⡑⢤⣜⣠⠿⠖⡞⣋⠭⢔⡞⠁⠀⠀⢠⣶⠃⡇⠠⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠏⢀⠞⡇⢳⡽⠡⠒⠂⣹⠁⠀⠀⡎⢇⠀⣠⣖⣁⡧⠤⠿⠚⣺⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⣸⠀⡜⠀⡇⢀⢷⡀⠀⢠⠃⠀⠀⠀⠀⠘⡄⠀⠇⠀⠀⠀⠀⢰⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⢫⡰⢠⠃⡇⢸⠀⢳⣀⡎⠀⠀⠀⠀⡇⠀⢱⡀⠀⢄⠀⠀⠀⢸⡜⡜⡄⠀⠀⠀⠀⠀⠀⠀ ⢠⣤⣴⡾⠿⠶⣶⣶⣴⣘⣄⣆⣈⠇⡎⠀⡇⠘⡄⣜⣿⣀⠸⣠⡀⠀⠘⡄⠀⢳⠃⡟⠶⡄⠀⠀⢷⠰⠹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠓⠶⣤⣈⡉⠙⠛⡿⢿⣿⣦⡀⡇⠀⢻⡿⣍⣿⣿⡿⣿⠢⣀⣘⣄⠀⢞⢿⣦⣹⣷⣦⣄⣳⣀⠱⡀⠀⠀⣶⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣾⣥⣴⣁⣉⣻⣿⣠⠎⠙⠾⣿⠟⢟⣿⠙⠛⠛⠻⢦⡈⣆⢯⡽⣷⠛⠛⠚⢻⣦⣼⣤⣾⣿⣴⠆ ⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣶⣶⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠉⠉⠉⢹⣮⡉⠉⠻⠉⠛⠛⠛⠛⢛⠙⠻⠿⠿⣿⡟⠛⠛⠛⢿⣿⡿⠟⠛⠛⣿⣿⠛⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⠛⡋⠉⠀⠀⠒⠂⠀⠀⠀⠛⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠃⠀⠀⠚⠛⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⢠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⠀⠀⡾⠋⡀⠹⣆⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⡰⠋⠀⠀⢷⡀⢿⡄⠹⡇⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⣴⠟⢁⡴⠟⢡⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⢠⣿⢃⡾⠁⠀⠀⠀⠈⢳⡈⠿⣤⠿⠯⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⣁⡴⠏⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⣀⣤⣽⠾⠟⠒⠒⠒⠒⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡽⢿⣥⣚⣯⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⢰⣿⠟⠀⠀⠀⠀⢀⣼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠉⠒⠶⠦⠤⢀⣈⢻⠄⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀ ⢰⠀⠀⠀⠀⠀⣰⡿⢿⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⣠⠤⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀ ⢺⡁⠀⢀⣤⠾⠋⠀⣿⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⣀⣤⣶⣿⡿⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡯⠶⠶⠬⣝⡂⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣷⠚⠋⠀⠀⠀⠀⢿⠀⠀⠀⣾⣿⠏⠀⠀⣠⣴⣿⠟⠉⠁⠀⠀⠀⠹⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⠟⠛⠿⢾⣿⣶⣄⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⡜⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⣿⡏⠀⠀⣼⣿⠟⠁⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣀⡿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⡇⢿⠀⠀⠀⠀⠀⢀⣴⠟⠀⢸⣿⡇⠀⢀⡟⡏⠀⠀⠀⢠⣾⠁⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⠿⣦⡀⠀⠀⠀⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⢸⣀⣠⢴⣶⠞⠉⠀⠀⠀⣸⣿⡇⠀⠸⢻⡇⠀⠀⠀⠛⢷⣶⣦⣴⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠷⣄⡀⠀⠀⣇⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀ ⡾⠛⠉⣠⠞⠁⠀⠀⠀⠀⢀⡟⠻⡇⠀⠀⠈⠁⠀⠀⢠⣴⡚⠿⡿⢇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣽⣿⣷⠂⢸⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⡇⠀⢰⠏⠀⠀⠀⠀⠀⠀⣼⣧⣿⣿⠀⠀⠀⠰⠗⠦⠬⠿⠷⠦⠴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠉⠉⠁⢀⣼⠇⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀ ⠻⣄⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⠚⠛⠡⠤⠀⣼⠃⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀ ⠀⠈⠃⠀⡀⠀⠀⠀⢰⣿⣿⡏⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡾⠃⠀⠀⢠⣾⡿⠁⡇⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡿⠁⠀⠀⢀⣾⣿⡇⠀⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣦⣠⣾⣦⠀⠀⠀⢀⣼⠋⠀⠀⠀⣰⠞⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣾⠁⠀⠀⢀⣾⣿⣿⣷⣤⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⢻⡇⠀⣠⠟⠁⠀⠀⠀⢸⠃⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁ ⢸⠇⠀⠀⠀⣿⣿⣿⣿⠋⣿⣿⣶⣦⣙⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣼⠋⠀⠀⠀⠀⠀⠘⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⢸⠀⠀⠀⢸⣿⣿⣿⠃⠀⣿⣿⣿⣿⡻⣿⣦⡀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀ ⣼⡄⠀⠀⠀⢿⣿⠿⠶⠶⣼⣿⣿⣿⣷⢿⣿⣷⣄⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀ ⠙⢿⣄⠀⠀⠀⢿⣄⠀⠀⠀⠙⢿⣿⣿⣸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠘⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠈⣳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣧⠀⠀⠀ ⢀⢰⠙⠷⣤⣀⣀⣉⣳⣆⣶⠀⠀⠹⣿⣿⣿⡿⢿⣿⣎⣻⢦⣄⠀⠀⠀⠉⠳⠦⣄⣀⣀⣀⣀⣀⣀⣠⠴⠟⠁⢀⣀⣤⡶⠞⣿⣿⣿⣦⠀⠀⣰⠂⠀⠀⠀⣸⠀⠀⠀⢸⡀⠀⠀ ⢸⢸⠀⠀⠀⠈⠉⠉⠉⢹⡇⠀⠀⠀⠘⣿⣿⠃⠈⢻⡿⠋⢸⣟⠛⢦⣄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣀⣠⣤⡖⡟⣿⡟⠁⠀⠹⣿⣿⣿⣠⡜⠃⠀⠀⢠⣴⠏⠀⠀⠀⠈⣿⠀⢀ ⠈⢸⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠿⠃⠀⢠⡿⠀⠀⣾⣿⣦⣸⢹⠙⠶⣄⣀⣀⣀⣀⡴⠶⣾⣏⢩⡆⡿⣇⡏⠀⠀⢀⣀⣹⣿⡿⢉⣀⣼⣭⠶⠋⠁⠀⠀⠀⠀⣸⠃⠰⠋ ⠀⠸⡄⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⢰⡿⣿⠙⢷⡄⢸⠀⠀⠈⠉⠁⢰⢂⡄⣿⡏⢸⢿⢻⢹⡇⠀⠀⠀⠙⢻⢿⣞⡛⢩⡞⠁⠀⠀⠀⣀⣠⡤⠞⠻⣄⢰⡀ ⠀⠀⣷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⣸⣇⢿⠀⠀⠹⣾⠀⠀⢸⠀⠆⡼⢸⣾⣇⣇⣈⣸⢸⣾⡇⠀⠀⠀⠀⠀⢸⡏⠛⢿⣧⡴⠶⠾⠿⠿⠭⠤⣤⣀⣙⠿⠧ ⠀⠀⠘⣇⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⢠⡿⡼⣾⠀⠀⠀⠈⠳⣤⣸⣒⣓⣒⠚⠚⠳⠧⠭⢭⡿⠀⡇⠀⠀⠀⠀⠀⢸⣧⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲ ⠀⠀⠀⢻⡄⠀⠀⠀⡏⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⣿⠃⢹⣽⡀⠀⠀⠀⠀⠈⠉⠒⠚⠛⠂⠀⠁⠀⢀⡾⠁⠀⠇⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⢧⠀⠀⢸⡇⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⣰⠇⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⣾⢿⣟⣶⠀⠀⢸⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁ ⠀⠀⠀⠀⠘⣆⠀⣼⠁⠀⠀⢀⡼⠁⠀⠀⣀⣠⡾⠉⠀⠀⠀⣿⣷⠳⡆⠀⠀⠀⠀⠀⠀⠀⣀⡴⢾⣿⠃⠀⠀⠀⣿⣿⣷⡿⠀⠀⢸⣿⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠔⠂ ⡀⠀⠀⠀⠀⠸⡄⡟⠀⠀⢀⡿⢁⣤⣶⣿⣿⣿⠁⠀⠀⠀⠀⣿⢹⡄⠙⣦⡀⠀⠀⢀⡴⠋⠁⣰⣿⠁⠀⠀⠀⢠⣿⣷⣼⠃⠀⠀⢸⡇⣷⡇⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⣿⠁⠀⢠⣾⣶⠿⠿⠟⠛⢻⡇⠀⠀⠀⠀⢠⡟⠘⡇⠀⠈⠉⠀⠐⠋⠀⠀⡼⢻⠃⠀⠀⢀⣠⡾⢷⣿⣿⠀⠀⠀⢸⡗⡟⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀ ⠀⢃⠀⠀⢀⣾⠃⠀⠀⠛⠋⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⢸⠇⠀⡇⠀⠀⠀⠀⠀⠀⢠⠞⣥⣮⠴⠖⠛⠋⠁⠀⠀⠙⢿⣧⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢶⣾⠀⠀⢳⠀⠀⠀⠀⠀⣰⡿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣼⣧⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⢀⠀⠀⠀⠀ ⢄⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⢸⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣼⠃⣠⠴⠊⠁⠀⠀⠀⠀ ⠀⢱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⡄⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⣇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛ ⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠚⠉⠀⢠⣄⣤⠶⠶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠛⠉⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣀⣤⡴⠶⠞⠉⠀⠀⠀⠀⠀⠀⣠⡤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⢰⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣉⣤⠼⠋⠁⠀⠀⠀⠀⣀⣀⣠⣤⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠹⣞⣦⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣤⡶⣋⡥⠞⠉⠀⠀⢀⣀⡴⠖⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠈⢮⣷⡀⠀⠀⠀⢣⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣼⡿⠟⠁⠀⣀⣠⠶⠞⠋⠀⠀⣀⣀⣀⣤⡤⠤⠶⠶⠾⣿⣿⠟⠋⠀⠀⠀⣀⣀⣀⣀⣠⠤⠤ ⢹⡀⠀⠀⠀⠀⠈⠉⢧⠀⠀⠀⠈⠺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠷⠶⠶⢾⣍⣀⣠⣤⡴⠖⠋⠉⠁⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⣀⣠⠶⢾⡟⠉⠀⠀⠀⠀⠀ ⠘⣷⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⢀⡤⠞⠋⠁⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡆⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⢀⡶⠋⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣄⣤⠞⡋⠀⠀⠀⠀⢀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠊⠉⠉⠁⣽⣿⣿⡿⠋⠀⠀⠀⠀⣠⠖⠁⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠇⢀⣀⣀⣀⣀⣀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣀⠴⠋⠉⠁⠀⠀⠀⠀⠀⠉⠙⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀ ⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⣾⢙⣶⡄⠀⠀⠰⢤⣠⡤⠤⠔⠒⠂⠉⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀ ⠀⠀⠀⠀⠀⠀⣮⣞⣹⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠃ ⠀⠀⠀⠀⠀⢰⠛⠿⠁⣈⣀⣀⣀⣤⠀⠀⠀⢠⠖⠒⠲⡄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢰⠧⠤⠔⠂⠐⠈⠈⠀⠀⠀⣠⠔⠊⠁⠀⠀ ⠀⠀⠀⠀⢠⡟⣇⠀⠉⢿⣿⣿⣿⣿⠀⠀⠀⢯⡐⠲⣠⡇⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣦⡟⠀⠀⠈⢿⠟⠛⢻⠀⠀⠀⠀⠙⠚⠋⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠳⣄⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⠬⠷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠃⠢⢄⠀⠈⢣⡀⠀⠀⠀⠀⠀⢀⡽⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⠔⠊⠁⠀⠀⠀⠈⠳⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠈⠀⠀⠘⡿⢆⠀⠀⣠⠔⠉⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⡏⠸⠀⠀⠀⠀⠀⠀⠀⢢⠀⠈⠳⢄⣀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣀⡀⠀⠀⠀⠱⡈⠣⡀⠀⢠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⠦⢤⣀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠤⠼⠛⠁⠀⠀⠀⠀⠘⣆⠙⢶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠒⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠳⣾⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⣀⡤⠔⠲⣶⣆⣀⡀⠀⠐⠤⠤⠔⠒⠉⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣥⠤⢴⠚⠉⠀⠀⠀⠈⠉⠒⠂⠤⠤⢤⡤⠞⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠒⢆⠀⠀⠀⠀⠀⢀⠂⠀⢇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠀⠈⠐⠠⣀⢀⠂⠀⠀⢸⣿⡇⠀⢀⠠⢐⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠉⠀⣀⡀⠀⠿⠛⠈⠀⠀⣾⣤⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣡⠀⢀⠔⠉⠀⠀⠀⠀⠁⠢⡀⠀⢠⣿⣿⣿⠀⠀⠀⠀ ⠈⠂⢄⠀⠀⠀⠀⢠⠁⠀⠠⠢⢑⠩⢀⡂⠠⠎⠄⠘⠿⠿⢯⠤⣄⠀⠀ ⠀⠀⠀⠑⣄⠀⠀⠀⠖⠤⠬⠅⡒⠈⠄⠀⠀⣁⡌⡄⠀⡠⣣⣶⣧⣤⣤ ⠀⠀⠀⠀⣀⠕⠀⢀⡆⢀⣀⠤⠼⡘⡀⠉⠉⠀⠸⢁⠀⠙⢿⣿⡟⠋⠀ ⠀⠀⠊⠅⣀⠀⠀⢸⠫⡀⠀⢀⠐⡀⢠⠂⠀⢂⡵⢸⠤⣠⣆⣽⣿⣦⣀ ⠀⠀⠀⠀⠉⠳⢦⠀⡄⠠⠀⠤⠂⢠⢈⠈⠉⠉⠀⢸⣧⡌⣿⣿⡿⠟⠁ ⠀⠀⠀⠀⡠⠐⠁⢈⠠⠀⠀⠀⠀⠀⣉⣀⠀⠀⠀⡼⣿⣤⣤⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠈⢭⡇⠉⢃⢀⠄⠊⠑⢄⠈⡀⠀⢠⢿⣤⣿⣿⠛⠛⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠒⢹⣢⡀⠀⠈⠁⠁⠉⣠⣯⣿⣿⡿⠛⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣈⣶⡄⠀⠐⢺⣿⣿⣿⣟⣁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⢈⢳⠉⠀⠀⠈⢛⢫⠗⠤⣀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠈⠳⡀⡇⢨⠀⢸⠟⢸⢸⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⠔⠁⠀⢠⢸⠀⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⣸⣄⡌⡤⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⡠⠐⠈⠀⠀⠀⠈⠑⢄⠀⠀⠀⣰⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠌⠀⠀⠀⠀⠀⠀⢀⠄⡂⢵⠀⡔⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⠸⠀⢐⠭⢐⣂⠤⢐⡵⠁⠀⠢⡆⠈⠓⢄⡀ ⣀⣀⣀⣀⣀⣒⣥⣀⠀⠀⠀⠀⠀⠇⠤⠤⢤⠬⣾⠤⠀⠠⠐⠂⢀⡴⠉⠀ ⣀⡀⣤⣀⠀⠀⠀⠀⢨⠖⠀⢀⠀⠢⡀⠀⢀⡠⠉⠦⠄⠠⠔⡇⠘⣆⠀⠀ ⡟⠱⡔⢬⡳⢤⣠⠂⠁⠀⢀⢼⠀⠁⠠⠤⠂⠈⢆⢰⠈⠀⠁⡖⡄⢬⠒⠀ ⡙⢏⣈⢆⠹⣦⡙⢿⣓⡂⠰⣈⡀⠀⣠⢄⡀⣀⡀⣁⣀⡠⡀⡗⢇⣸⠀⠀ ⠋⠂⠛⠛⠓⡘⢟⠂⠙⠡⣤⣠⢡⠀⢏⡛⠟⠙⠛⠛⠙⡉⢇⣛⡍⢹⠀⠀ ⠀⠀⣶⠒⢲⠹⣌⠂⠀⠀⠈⠃⢶⡧⡀⠀⠀⠀⠀⠀⠀⣀⣾⢸⠀⢸⠀⠀ ⠒⠒⠓⠒⠚⠘⠘⠀⠀⠀⡠⠒⠒⠣⣿⡗⠂⠠⠤⡔⢺⣉⣿⢸⠀⢸⠀⠀ ⠠⢠⠤⠤⠠⠤⠤⠀⡠⠊⠀⠀⠀⠀⠄⡗⠠⠤⠔⣯⠀⠀⠀⠹⡆⢸⠀⠀ ⠀⠸⠀⠀⠠⢤⠄⠀⠀⠀⣠⠂⠀⣜⠀⡇⠀⠀⠀⠁⢂⠀⠀⡆⠱⣾⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠃⣀⠀ ⠀⢀⣀⣤⣶⣿⠛⢁⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀⠙⠿⣿⣤⣄ ⠀⠈⠉⠁⠀⠼⢻⣿⣿⣿⣿⣿⡟⢦⣤⠀⠀⠀⠠⠴⢿⣿⣿⣿⣿⣿⡟⢦⣤⠉⠋ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠃⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣴⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⠿⠿⠿⠟⠛⠿⠿⠿⢿⣿⣿⣶⣶⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⣤⣍⠛⠿⣿⣿⣷⣦ ⠀⠀⠀⣀⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛ ⡀⢀⣴⠟⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠉⠉⢩⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⡟⢀⣶⣦⠀⣠⣶⣶⣶⣶⣶⡆⠀⠀⠀⣠⣀⠀⣠⣶⣿⣶⡄ ⠀⠀⠀⠀⣾⣿⡟⠀⢈⣻⡛⢰⣿⡟⠉⠉⠉⠉⠁⠀⠀⠀⣿⣿⠀⣿⣿⣉⣿⡿ ⠀⠀⠀⣼⣿⡿⠁⢰⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⠀⠘⠿⠿⠟⠁ ⠀⠀⣸⣿⣿⣁⣀⣘⣋⣀⣼⣿⡇⠀⠀⢀⣿⡿⢹⣿⡇⠀⣿⣿⣀⣀⣀⣀⡀⠀ ⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⡟⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣉⠁⠘⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢹⡄⠀⠀⠉⢢⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠈⡷⠀⠀⠀⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢱⢃⣀⣜⠀⠀⠀⠀⠀ ⠀⠀⠀⡤⢤⣃⠉⠁⠒⢭⠉⠛⢓⣚⡞⡖⠒⠒⣋⣭⢲⠀ ⢀⣤⡶⣧⣀⡀⠈⠑⠒⠧⢝⡚⠬⠟⠐⠒⠀⠹⠀⠀⢨⠄ ⠀⠙⠛⠷⣾⣭⣟⣶⠤⡤⠔⠁⠀⠀⠀⢀⣀⡰⢪⣽⠃⠀ ⠀⠀⠀⠀⣿⡏⠉⡟⠿⡧⠴⣖⢂⠝⠉⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⡇⠀⣇⠀⢸⢸⠀⠀⠀⠀⠀⣼⡇⠀⠀ ⠀⠀⠀⠀⠙⠃⣰⣫⣂⣿⠀⢸⢸⠀⠀⠀⠀⠀⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠋⠋⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠉⠀⠉⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠯⠤⠤⠤⠿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⡬⠥⢥⣀⠀⠀⠀⠀⠀⢀⡠⠾⠷⢤⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣾⡇⠀⠀⠀⠀⢀⡾⣋⣄⠀⠈⠉⢶⠀⠀⠀⣴⡟⣁⣀⠀⠀⠙⣆⠀⠀⠀⠀⠀⢸⣅⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⢹⡇⠀⠀⠀⠀⢼⣿⣿⣿⣿⣦⡀⢈⡇⠀⠀⣿⣿⣿⣿⣿⡄⠀⣿⠀⠀⠀⠀⠀⢸⡏⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⠿⢀⡾⠁⠀⠀⠘⣿⣿⣿⡿⠁⣠⠏⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣴⠾⠷⠾⢶⡄⠀⠀⠀⠉⠛⠷⠒⠋⠀⠀⠀⠀⠀⠈⠙⠛⠒⠊⠁⠀⠀⠀⣠⡶⠶⠾⠷⣦⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣾⣿⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢠⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠛⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠞⠋⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⢻⣿⣿⡛⠛⠛⠛⠛⢻⣿⣿⣽⣭⣭⣭⣭⣭⣭⣿⣟⠋⠟⠛⢛⣿⣿⡟⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣤⣭⣿⣤⣤⣤⣼⣯⣤⣴⣤⣤⣦⣤⣤⣤⣤⣿⣦⣤⣾⣯⣥⣆⠉⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⣿⣠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢿⡷⢶⡄⣿⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣿⣼⠀⠀⠀⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⢬⡇⢸⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢳⣄⠀⢀⣿⣿⠀⠀⢠⡾⡇⠀⡀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣿⣿⣼⠀⢀⡼⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠉⢻⣿⣿⣿⠀⠀⣼⠇⢿⣴⣷⠀⠀⠀⠀⣠⣾⣿⣄⣿⡄⠀⠀⢹⣿⣿⣟⠋⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⢰⡟⠉⣿⢻⠷⠶⠿⠀⠸⠏⠘⣦⠀⡿⠒⠛⠃⢸⣿⡟⠿⠿⠷⠿⡟⣿⠹⣆⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠉⠓⢶⣴⠟⠁⠀⣿⣼⠀⠀⠀⠀⠀⠀⠀⠹⣾⠁⠀⠀⠀⠈⢿⠀⠀⠀⠀⢀⡇⣿⠀⠘⣷⣴⠖⠉⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣤⡀⢠⡾⠃⠀⠀⠀⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣿⠀⠀⠈⢻⣄⠀⣠⣼⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠈⠻⣿⠁⠀⠀⠀⢀⣿⠘⢿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⠟⠫⣽⠀⠀⠀⠀⣹⡟⠁⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡾⠿⠟⢻⡄⠀⠀⠀⢰⡿⠀⠀⠀⠀⠘⣿⣶⡾⠉⢻⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣠⡞⠉⠳⣶⣿⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⣸⡟⠲⠶⣦⡀⠀⠀⠀ ⠀⢀⡾⠋⠀⠀⠀⠈⠳⣦⣤⡴⠟⠀⠀⠀⠀⠀⢈⣿⠈⢷⣤⡾⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢿⣷⡾⠛⣿⠀⠀⠀⠀⠀⠙⢦⣤⣤⠴⠋⠁⠀⠀⠀⠻⣄⠀⠀ ⣤⡟⠀⠀⣤⢦⣀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣤⣷⣤⣤⣤⣴⣼⣧⣶⣴⣦⣦⣤⣤⣤⣤⣤⣤⣦⣤⣠⣿⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢀⣴⢦⡀⠀⠹⣦⠀ ⣿⡀⢠⠞⠁⢀⣽⠇⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣻⡄⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⢿⡀⠀⠻⣄⠀⣿⡃ ⠈⣷⠏⠀⣠⡿⠁⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠤⠤⠤⠤⠤⠤⢾⣟⠁⠀⢈⡷⠦⠦⠤⠤⠤⠤⠶⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠹⣆⠀⠈⣷⠏⠀ ⠀⠀⠀⢴⣯⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⣽⠶⠚⢿⡅⠀⠀⠀⠀⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣬⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠛⠛⠛⠛⠛⠻⢯⣄⠀⣤⠟⠛⠛⠛⠛⠛⠛⠻⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⣀⣠⣤⣤⣤⣿⠟⠈⠻⣦⣀⣀⣀⣀⣀⣀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠯⠿⠿⠭⢯⣉⣉⣉⣿⡀⠠⣾⣏⣀⣀⡠⠶⠶⠿⠿⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠀⠀⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡷⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⣄⡀⢀⣴⣿⡿⠟⠛⠻⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠉⠛⠻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣶⣶⣶⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⢿⡁⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⡿⠟⠛⠛⠛⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀ ⣿⣿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⠿⠿⣿⣿⣿⣷⣦⡀ ⣿⣿⠀⢀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠻⣿⣷⡄⠀⠀⠀⠀⢀⣤⣾⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿ ⣿⣿⡇⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠉⢻⣿⣦⣀⢀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⢻⣿⡇⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣸⠛⠶⠤⠴⠶⠚⠋⠁⣀⣤⣤⣤⠴⠶⠶⠶⠶⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⢸⣿⡇⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⢀⣠⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿ ⠘⣿⣿⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣀⡞⠉⠛⠒⠒⠚⠋⠁⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣿⣿⡿⠟ ⠀⣿⣿⠀⠀⠀⠀⠀⠻⠦⠤⠤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠿⠿⠛⠛⠛⠉⠉⠀⠀ ⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⣨⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠑⠦⣀⡀⠀⠀⠀⠀⣀⡤⠚⡁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠓⠢⢄⣀⡈⠉⠉⠉⠉⢀⡠⠊⠀⢹⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⡼⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⡦⢀⣾⣿⣶⣶⣶⣶⣶⡂⠤⠤⠤⠤⠤⠄ ⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣾⣿⣷⣤⣀⣴⠋⠙⣆⠀⠀⠀⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⢧⡀⠉⠉⠉⠛⠛⠻⠿⠿⠿⣿⣦⣄⡀⠀⣀⣤⣾⣤⣞⣁⣠⠟⠉⣉⣭⠿⣿⣿⡏⠉⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⡈⠉⠉⠉⠙⠛⠛⠿⠿⠿⣿⣿⣿⣷⣶⣿⣿⣁⣠⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣿⣿⣿⣿⡿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣷⣷⡶⢶⣶⣶⣤⣤⣤⣬⣭⣭⣭⣍⣉⣉⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢀⣾⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⢸⡇⠈⣿⣿⣿⣿⣿⣿⣿⠟⢿⡛⡟⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⢣⣿⣿⣿⣼⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⠿⡇⠀⣿⡟⣿⣿⣿⣿⣿⠀⠘⣇⢫⢃⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡸⠃⣸⣿⣿⣿⣿⢱⣿⣇⡀⠀⣿⣿⣿⣿⣿⣿⠀⡇⠀⣸⡇⣿⡏⣿⣿⣿⡇⠀⢻⡀⢸⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⡏⢸⡟⠀⠈⠁⣿⣿⣿⣿⣿⣿⡇⠛⠋⢹⡏⢻⡇⢸⣿⣿⡇⡀⢸⣿⡎⣶⣿⣿⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⣿⣿⣿⠁⢸⠃⠀⠀⠀⢹⠛⣿⣿⣿⣿⡇⠀⠀⠀⠃⢸⡇⢸⣿⣿⡇⣇⢸⣿⣷⣿⡿⣿⠀⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠛⢾⢤⣌⣑⠒⢾⠀⣿⣿⣿⣿⠃⢀⡀⠤⠀⠘⡇⠘⣿⢿⣷⣿⢸⣿⣿⣿⠇⢸⠀⠘⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⣠⠤⠤⠤⠿⠟⠻⠄⢹⠉⠙⠸⢤⣤⣤⡶⠶⠞⠓⠚⣿⢻⣿⣿⣿⣭⡉⠻⡄⠀⠀⡜⠀⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣇⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠶⠃⠸⠟⢿⠋⠈⢻⠀⢸⠀⢰⠃⠀⠈⡆⠀⠀ ⠀⠀⠀⠀⢿⠳⡄⠀⢏⠸⡌⢲⡇⠀⠀⠀⠀⠀⠀⣶⠖⠒⠒⠒⠒⢆⠀⠀⡿⣽⣏⣉⣯⣉⡳⠰⠃⠀⢀⡜⢠⠏⢀⡏⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠈⢧⠘⡄⠘⡄⢣⠀⠑⠦⣀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⡸⠀⢠⠯⣿⣏⣾⡏⣰⣧⣔⣒⣈⡩⠔⠋⠀⡼⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⢣⠘⢆⣧⠘⡆⠀⠀⠈⠑⠲⠤⣄⣀⠃⠀⠀⠠⡚⠁⢀⣚⣛⣭⣴⣿⡏⢹⠘⠁⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣷⡄⢹⠀ ⠀⠀⠀⠀⠀⢠⠖⢷⠀⡀⠀⠙⣶⣤⣤⣀⣀⣀⣠⡴⢿⣿⣿⣛⡡⠴⠚⣉⣿⣯⣈⡟⠀⣘⠀⠀⢀⠔⢉⠇⠀⠀⢱⠸⣷⣤⣿⠇⣸⠀ ⠀⠀⠀⠀⢠⡞⠣⣄⢹⣇⠉⠒⠚⠻⣿⣿⣿⣿⣿⣏⢂⡸⢧⠔⢒⣩⣴⣾⣿⣿⡿⠁⢀⣿⣿⠞⠁⡰⠋⠀⠀⠀⠀⠳⠤⠀⠠⠔⠁⠀ ⠀⠀⠀⠀⠀⣟⠒⠼⢉⡝⠓⠢⠀⢀⣿⣿⣿⣿⣿⣿⣇⢣⡎⣼⣿⣿⣿⣿⣿⣿⠃⠀⠈⡛⠁⣠⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⣦⠀⠋⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣆⣱⣿⣿⣿⣿⣿⡿⠯⠐⠊⠉⣱⣠⠚⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡜⢿⡟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⢻⣿⣿⣿⣿⣿⣇⠀⠀⡔⠊⠟⢁⡤⠺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⣷⣌⣓⠦⠄⠛⣡⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⠀⠀⠈⣇⠀⠻⠤⠔⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡶⠛⠉⠉⠙⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⠉⠙⢷⣦⡀⠀⠀⠀⠀ ⠀⢀⣼⣷⣦⣄⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠴⠶⠶⠶⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠈⣻⡆⠀⠀⠀ ⣰⠟⠙⠃⠛⠙⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣫⣏⡄⣠⡄⠀⠀⠀⠀⠀⢀⡉⠛⠲⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠁⠀⠀⠀⠀⣿⣷⣿⣇⠀⠀⠀ ⢿⣼⡇⣤⠀⢰⣦⠀⡦⣤⣀⢀⠀⠀⠈⠻⢦⡀⠀⠀⢠⡾⠋⠀⠀⠉⠛⠚⠡⠾⠄⠀⠀⠀⠀⠉⢤⣖⠤⠀⠙⢷⣄⠀⠀⠀⠀⣀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⢷⡄⠀ ⠀⠙⠻⠿⠷⠾⠿⠾⣧⣇⡌⢹⣷⢤⣀⠀⠀⠘⠳⣴⠏⠀⠴⠋⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⠔⢋⡄⠀⠹⣦⣀⣴⠾⠋⠁⠀⠀⡀⠀⣀⢀⢠⠀⠀⠀⠀⠀⠘⣿⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣿⣼⢹⠃⡶⡄⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠞⢉⡴⠂⠀⠘⣯⠁⠀⢀⡠⡆⡆⡇⣗⣹⣸⣸⡋⡲⣦⣤⣀⡀⣿⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣾⣴⢷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠜⣡⠴⣫⠤⣀⣿⣷⣶⢸⣀⣇⠷⠗⠋⠉⠉⠻⣶⣿⣿⣸⣸⣾⠟⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⠇⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠃⠚⣡⢞⡵⣿⣿⡿⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢠⢶⣯⣇⣠⣤⣤⣤⣄⣀⠀⢀⢀⣤⣄⡀⣠⣤⣤⣤⣤⣀⣳⡿⢊⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡴⣫⣿⣿⣿⣿⣿⣿⣿⣽⣷⠟⠿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣫⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣞⣽⢻⣯⣿⣿⣿⣿⣿⣿⡟⠀⠀⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠁⠘⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣱⣯⣿⣿⣿⣿⣿⣿⣷⡿⠈⠳⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣟⠀⠀⠀⠙⠛⠓⠛⠋⠁⠀⣰⣿⣷⣿⣧⣯⢿⣏⠙⠛⠛⠛⠁⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠁⠀⠘⢶⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⣿⣿⣿⡟⢯⠀⠀⠀⠀⠀⠀⠀⣾⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⡀⠀⣀⣤⠶⠟⠉⠀⠀⣀⡄⢸⣾⣸⣿⡶⣾⣟⣿⣷⡆⠀⠈⠉⠉⠀⣸⣏⣉⡀⠀⠀⣠⣶⣲⣶⠄⣿⠃⠀⠈⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠟⠁⠀⠉⠉⠙⠉⠀⠀⠀⢀⡀⡄⣯⣷⡾⠟⠉⠈⣿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠿⠆⠀⢀⣿⣿⢯⡫⣗⣿⣴⣦⣀⡀⠀⠈⠛⠲⠦⢤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀ ⣰⢧⣄⣀⠀⠀⠀⠀⠀⠀⠀⢤⣯⣧⠿⠋⠁⠀⠀⠀⠀⠘⣿⠀⢸⣿⡟⣷⢲⢶⣶⠶⣶⡶⡶⡶⣾⣿⣿⣿⠀⣿⠟⠙⠻⣿⣬⢿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣆⠀⠀ ⠙⠿⣧⡏⠇⠀⠀⠀⠀⢀⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠈⢿⣏⣻⣻⡟⡗⡷⣾⣿⣿⣟⣿⣿⡿⠇⢠⣇⠀⠀⠀⠀⠙⠿⣾⣧⡟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀ ⠀⢰⡟⠀⠀⠀⠀⢀⣴⣸⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⣫⡿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢣⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀ ⠀⠸⣷⣆⢖⢠⣶⢸⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠰⣿⣳⢿⢦⣀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⡷⡆⣀⠀⢰⣶⣴⠾⠋⠀⠀ ⠀⠀⠙⠻⠿⠾⠿⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣤⣤⣤⣠⣼⣵⣧⣧⣾⠼⢧⡤⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣇⣃⣟⣇⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡾⢿⡿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠁⢠⡟⠀⠀⠉⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣽⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢟⣿⠁⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢰⡟⢨⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣸⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡿⠁⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⡟⢀⣀⠀⠀⢸⠇⠀⠀⢀⠀⠀⣸⠇⠀⠀⠀⠰⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢀⣿⣿⣿⣷⣄⠹⢀⣤⣾⣿⣷⣦⣿⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢀⣿⣿⡿⠋⠙⢿⣿⣿⣿⣿⣿⣿⠋⠉⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡇⠀⣼⣿⣿⣷⣄⣠⡿⠿⣿⣿⣿⠟⣿⣤⣀⣼⣿⣿⣿⣧⡀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣿⣿⣿⣿⣿⣿⣿⣦⣹⣮⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣮⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⢀⡼⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠈⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⣠⠀⠋⣠⣾⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠐⠶⣄⠀⠈⠳⠦⠜⢿⣿⣿⡿⠀⢀⣀⣤⡾⠛⢁⣴⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡄⠀⠈⠛⠷⠦⣤⣤⣄⣙⣿⡄⠀⠉⠁⢀⣤⠾⣿⢿⣿⣿⡿⠿⠿⠿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣝⣿⣆⠀⠀⠀⠀⠀⠈⢉⣽⠟⠀⣠⣤⣾⣿⣿⣾⣧⡞⢹⣿⣆⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠛⡿⢷⣄⡀⠀⠀⣶⣿⣵⠶⠟⠉⢀⣿⣿⣿⣿⣿⠇⢸⣿⣿⣆⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⠀⢸⣷⣄⠙⠿⠾⠟⠛⣁⣀⣀⣀⣘⠻⠟⠛⠿⢋⣡⣾⡿⢿⣿⠘⣧⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⢀⣼⡉⠻⣷⣶⣶⣶⣿⠟⠿⠻⠟⠿⣿⣶⣶⣾⡿⠟⠁⠀⠈⣷⠀⠘⣆⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣰⡿⣿⣿⣦⡀⠉⠉⠙⢷⡀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⣀⣤⣶⣿⠀⠀⠘⣇⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣦⣤⡾⣿⣄⠀⣠⢾⡏⢀⣿⣿⣿⣿⣦⡤⠶⠚⠛⠶⡤⠶⠛⠳⢤⣀⠀⣠⣾⣿⣿⣿⣿⡇⠀⠀⠸⡆⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠿⠛⢻⣧⡘⣿⠟⠁⣼⠁⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⣿⣿⣿⡿⠿⠛⡛⣷⠀⠀⢀⣿⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⣤⡤⠤⠤⠤⠤⢤⣤⣄⡙⠧⣤⡬⠿⠿⠿⠄⡰⠿⠶⠿⠿⠿⠿⠿⠿⠧⠤⠤⠤⠤⡧⠤⠾⢯⣹⠿⠿⠿⠶⠶⠶⠶⠶⠿⢀⣀⠸⠯⠭⠥⠿⠷⠤⠤⠤⠤⠤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣤⣶⣶⣦⣤⣶⣶⣶⣶⣶⣄⠀⣠⣴⣶⣶⣴⣶⣶⣤⣤⣤⣴⣶⣶⣶⣤⡤⠀⣠⣴⣶⣶⣶⣤⣤⣴⣶⣶⣶⣶⣶⣤⣴⣶⣶⣶⣶⣤⣄⠀⢤⣴⣶⣶⣶⣶⣤⣤⣤⣶⣶⣶⣄ ⠉⣿⠏⠁⠁⠀⣿⣯⠉⠉⣿⣿⠇⠀⠈⠈⣿⡏⠀⠉⠀⣼⣿⠻⠋⠉⠉⠙⢠⣾⡿⠏⠉⠉⠉⠉⠀⣻⣯⠁⠉⠀⠀⠀⢸⣿⡍⠉⢹⣿⡏⠀⢀⣿⡏⠁⠁⠀⠀⠈⣿⠉⠀⠉⠉ ⠀⣿⠀⠀⠀⠀⣿⣿⣤⣼⣿⠏⠀⠀⠀⠀⣿⡇⠀⠀⢠⣿⣧⠠⠾⣿⣿⡿⣿⣿⡏⠰⠿⣾⣾⡷⠲⣿⣿⡿⢿⠶⠶⠀⢸⣿⣧⣤⣿⣿⠃⠀⢠⣿⣿⢷⣾⠿⠀⠀⢻⠀⠀⠀⠀ ⠀⠏⠀⠀⠀⠀⣿⣿⠙⢻⣷⡄⠀⠀⠀⠘⣿⡇⠀⠀⠀⣿⣿⡀⠀⠀⢹⣷⢹⣿⣧⡀⠀⢀⣿⠆⠀⣿⣧⠀⠀⠀⠀⠀⢈⣿⡛⠛⣿⣧⠀⠀⠰⣿⠇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⣿⣿⣀⣀⣿⣿⣄⣴⣶⣾⣿⣷⣶⣦⡀⠈⣿⣿⣶⣶⣾⣿⠜⠻⣿⣿⣶⣾⣿⣦⣤⣿⣿⣶⣶⣶⣶⣤⣼⣿⡧⠀⠹⣿⣦⣀⣼⣿⣷⣶⣶⣶⣄⣀⣴⣶⣶⣶⠟ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠈⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠉⠉⠁⠉⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠋⠀⠙⣿⡾⠿⢶⣦⣤⣶⠿⢷⣾⡏⠁⠉⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣦⣴⠾⠋⠀⠀⠀⠙⠋⠀⠀⠀⠙⠿⣦⣴⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡿⠁⣸⣿⠀⠀⠀⢀⣤⣤⣠⣤⣀⠀⠀⠀⣸⣏⠈⢻⣦⠀⠀⠀⠀ ⠀⠀⣰⡿⢁⣾⠟⠙⢿⣄⣠⣿⡉⠙⠋⠉⣿⣆⣠⣾⠋⠹⣷⡄⢻⣧⠀⠀⠀ ⠀⢰⡿⢡⣿⠋⠀⠀⢸⣿⢙⣿⣟⠀⠀⣺⣿⣏⣻⡇⠀⠀⠘⢿⣄⢻⣇⠀⠀ ⢀⣿⢣⣿⠃⠀⠀⠀⠘⣿⠈⣧⡼⠁⠀⢿⣸⠅⣿⡇⠀⠀⠀⠈⢿⡌⣿⡄⠀ ⣸⣏⣾⠃⢀⣠⣤⣶⠿⢿⣧⣀⠀⢲⡶⠀⢀⣴⡿⠿⣶⣤⣄⡀⠘⣿⣼⣷⠀ ⣿⣿⡏⠀⠙⠿⣧⣄⠀⠀⢻⣿⣷⣤⣤⣾⣿⡿⠁⠀⣀⣼⡿⠛⠀⠸⣿⣿⠀ ⣿⡿⢠⡾⠿⣶⡌⠛⣷⣦⣀⢻⣧⠉⠉⣰⡟⢀⣴⣾⡛⢁⣶⠿⢷⣆⢻⣿⠁ ⢻⣧⠈⠁⠀⣸⡇⠈⣿⡛⠛⠿⣿⡟⠻⣿⡿⠟⠛⣿⠇⢸⣿⡀⠈⠁⣸⡿⠀ ⠀⠙⠿⠶⠿⠋⠀⠀⣿⣇⣀⣤⣿⣦⣴⣿⣤⣄⣠⣿⠀⠀⠙⠿⠶⠿⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠋⠉⠀⠀⠀⠀⠈⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣇⣀⡀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⢀⣤⡀⠉⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣄⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠿⠿⠛⠛⠋⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠘⠿⢿⣿⠇⡄⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠉⠛⠱⢦⣄⢀⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⣿⡟⠘⣇⠀⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣤⣤⡒⣾⣿⡿⠿⠀⠀⠀⠀⠀⠀⠁⢳⣆⠀⠀⠀⠀⠀⠀⠀⠘⠹⣿⣿⣶⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠀⠉⠁⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣇⠀⠀⠀⠀⣀⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢠⣤⣿⠓⠀⢠⣀⠈⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠐⠀⠀⢿⣿⠿⠁⠀⠀⠀⢠⣴⣶⣤⠀⠀⠀⠀⢠⣶⣶⣤⠐⠀⠀⠀⠸⣿⣿⠇⠀⠈⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⠿⠿⠛⠀⠀⠀⠀⠈⠿⠿⠟⠈⠀⡀⠀⠀⠌⠁⠀⠀⠀⠀⢠⣼⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⣀⣀⣀⡀⠀⠀⠀⠀⠘⠀⠀⠂⢀⣀⣀⣭⣴⠦⠐⣶⣦⠺⡆⠀⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠀⠀⠈⠀⠀⣄⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣶⣶⣿⣾⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⠈⠀⠉⠀⠘⢻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⢸⣄⣼⣧⣤⣤⣄⡀⠀⠀⠀⠀⠉⠙⠿⣿⠟⠋⠁⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣀⣀⣀⡀⠀⠠⠤⢤⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣴⡏⠀⠀⠀⠀⣴⠟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠻⣆⠀⠀⠂⠀⠀⠀⢿⢶⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠘⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣾⠇⠠⠘⢿⣿⣿⣿⣿⣿⣿⠃⠀⢴⠇⠀⢈⣗⣄⢀⡀⣤⣾⡇⠈⠻⣿⣿⣿⣿⣿⡿⠏⠀⠠⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣧⣀⣤⣤⣉⣛⠛⠛⠋⣀⣀⡂⢺⠀⠀⠈⢻⠁⠘⠟⣿⢿⣿⡳⣂⣈⣛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠋⠉⠳⡌⠉⠁⠀⠤⠀⣸⣏⣿⣟⠂⠀⠀⠘⠃⠀⠀⣉⣹⣿⡇⠈⠉⠉⣳⠿⠶⢦⣀⡀⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⠂⠀⠠⡄⠰⣤⡄⠀⠀⢿⣿⣾⡿⠦⠀⠀⠀⠀⠀⠀⢀⣿⣯⡁⠀⢀⣰⡏⠀⠀⢠⣏⢉⡀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⡷⣄⡀⠀⠀⠀⠃⠉⡅⠀⠶⢿⣿⣿⣦⡀⠀⠀⠀⠀⡀⣀⣿⣏⡙⢶⣴⠃⠀⣶⠀⠀⠀⠀⠙⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣏⣿⣄⠀⠀⣤⠞⠃⠀⠀⣾⣿⣿⣿⣿⣶⣶⣴⣶⣿⣿⣿⣿⣿⣶⡏⠀⠀⣭⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡃⢀⣼⠇⠀⢰⣄⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠉⢿⣄⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣴⣾⠏⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⣿⣷⣴⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⡀⠛⠀⠀⠀⠀⠀⠀⠈⠩⠿⣿⠿⣿⠟⠉⠀⠀⠀⢤⠄⢀⣀⡰⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣶⣤⣤⣀⠈⠉⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠚⣣⣤⡁⠁⠸⠋⣻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡾⡀⠀⠸⣿⣿⠟⠀⢀⡀⠀⠘⣿⣿⠟⠓⠌⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡏⠀⠀⠀⠀⢀⣀⡀⠃⠀⣀⠘⣔⢀⠐⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⡘⠛⠠⠀⠀⠀⠋⠀⢙⡟⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠸⣿⣿⡷⠀⣀⣁⠈⢠⣿⣿⡟⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣝⣧⣤⣾⣿⢂⢸⣯⣄⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡈⢆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⡋⢹⠀⢀⢤⡴⡨⡉⡥⣐⠤⠭⠈⠉⢐⣧⠀⠒⠀⠤⠄⣄⡄ ⠀⠀⠀⠀⠀⣸⠀⠀⡾⣰⣿⡻⣫⠪⣔⣵⠞⡉⣡⣢⡀⠀⠉⠀⢀⡠⢔⣈⠏⠀ ⠀⠀⠀⠀⢠⡇⣜⠀⣧⠉⠠⠈⢃⠠⣾⣿⣄⠣⣵⢟⠳⡂⠀⣠⠞⠁⢩⣯⠀⠀ ⠀⠀⠀⢀⠉⠀⠋⢠⠏⠀⢀⣀⠀⡇⠀⠛⠫⢟⣯⠷⠿⢅⠠⠉⠋⠒⣻⠂⠀⠀ ⠀⠀⠀⠘⠦⢶⣄⠼⠤⠤⡤⣢⣤⠳⡄⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢀⠈⢑⣢⠄ ⠀⠀⠀⠆⡄⠀⢃⠀⠀⠀⠈⠛⠻⡀⡿⠀⠀⠀⠀⠀⢐⠀⡌⢂⠀⠀⡠⢭⡶⢀ ⠀⠀⠈⠀⡇⠀⣸⡂⠇⠀⢀⠀⠀⠣⣅⠉⠢⣣⣀⢦⡀⠀⡇⠈⢳⣲⢤⣥⡽⠅ ⢠⠤⢸⠀⠁⢾⣼⣄⠈⠀⠀⠃⠀⠀⠈⠦⡀⠈⡟⢽⠿⢺⠀⠸⠻⣾⡿⣿⣍⡀ ⡌⠀⠀⠀⠇⠸⠘⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⢧⢨⠎⠀⠨⠀⠇⠀⠟⣼⢯⡃⠀

⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠊⢁⡤⠤⣄⡉⠓⠦⣄⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠊⢉⣀⡈⠙⢦⡀⠀⠀⠀⠀ ⠀⢀⣀⣠⠞⢀⡴⠋⠀⠀⠀⠉⠳⢦⣈⠙⠲⣄⡀⣠⠞⠉⠀⠀⠀⠀⠀⠉⠳⣄⠀⢀⡤⠞⠉⣠⠴⠊⠁⠀⠈⠳⣄⠙⢦⡀⠀⠀ ⠀⠸⣇⣀⡴⠋⠀⣀⣀⣀⠀⠀⠀⠀⠈⠓⢦⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡁⣠⠔⠋⠁⠀⠀⢀⣀⣀⡀⠈⢳⣄⠈⢙⡆ ⠀⠀⠀⠀⢀⠴⠋⢁⣀⣈⠉⠒⠦⣀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⢀⡠⠖⠊⢉⣀⣀⡉⠳⣤⠈⠉⠁⠀ ⠀⠀⢀⡴⠋⣠⠞⠁⠀⠀⠉⠲⢤⣀⠉⠲⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠊⢁⣠⠴⠊⠉⠀⠀⠙⢦⡀⠳⣄⠀⠀ ⢸⣏⠁⣠⠞⠁⢀⣠⢤⣀⡀⠀⠀⠈⠙⢲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠚⠉⠀⠀⢀⣀⣠⢤⣀⠀⠙⢦⡀⢉⣹ ⠀⠀⠉⠁⢠⠞⢁⣠⠤⣀⡉⠑⠶⢄⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⡤⠖⠊⢉⣀⡤⢤⡈⠳⣄⠀⠉⠉⠀ ⠀⠀⢀⣰⠋⣰⠋⠀⠀⠀⠈⠙⠦⢤⣈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣁⡤⠴⠚⠉⠀⠀⠀⠈⢧⡘⢧⡀⠀⠀ ⠀⢰⠋⢀⡼⠁⢀⡤⠚⠋⠙⠒⠦⢄⣈⠙⢻⡄⠀⢀⣠⠤⠒⠒⠒⠦⢄⡀⠀⠀⢠⠟⠋⢁⣀⠤⠖⠒⠦⣄⡀⠀⠀⢳⣀⠉⣳⠀ ⠀⠈⠉⠉⢀⡴⠋⣠⠖⠋⠙⠲⠤⣀⡈⠙⠒⢷⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⠯⠖⠋⢁⣀⠤⠖⠒⠦⣄⠙⢦⡀⠀⠈⠉⠉⠀ ⠀⠀⢀⣠⠏⢀⡞⠁⠀⠀⠀⠀⠀⠀⠙⠲⠤⣰⡃⠀⠀⣤⣄⠀⢀⣄⠀⠀⠘⣇⣠⠴⠚⠉⠀⠀⠀⠀⠀⠘⢳⡀⠹⣄⠀⠀⠀⠀ ⠀⢰⣋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠸⣿⣿⠀⣩⣏⡇⠀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⠛⣆⠀⠀ ⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡦⣍⣁⣀⣈⣯⢴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣸⠀⠀⢈⣇⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡾⠿⠿⠿⠟⠻⠿⠿⠿⢶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠛⣉⠡⠠⢀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⣁⠄⢊⡡⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢉⠔⢊⠤⠂⠁⣠⡶⠟⠛⠓⠦⠀⠀⠀⠀⠀⠀⠀⠴⠞⠛⠛⢶⣤⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⠟⢁⠔⡡⠊⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡿⠃⣠⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀ ⠀⠀⢀⣾⡟⠁⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⣿⣶⣤⡀⠀⠀⣠⣶⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀ ⠀⠀⣾⡟⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠀⠈⠻⣷⣤⣾⡿⠋⠁⠀⠀⠉⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀ ⠀⣸⣿⠁⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⠏⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀ ⢠⣿⡇⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄ ⣸⣿⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡆⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠙⠋⠁⠀⠀⠀⢠⠀⠀⠀⠀⠈⠛⠁⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⠀⠀⣀⣴⡿⠙⣿⣦⣀⠀⠀⠀⢀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⡿⠟⠋⠀⠀⠘⣿⠿⠿⣷⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏ ⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣼⣿⠃ ⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣰⣿⡟⠀ ⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣠⣿⡿⠀⠀ ⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣰⣿⡿⠁⠀⠀ ⠀⠀⠀⠈⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⣾⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢁⣴⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⣠⣴⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣍⡀⠒⠤⠤⢀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⠠⠄⠒⠈⢁⣠⣴⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣶⣦⣤⣀⣀⣈⣉⠈⠀⣀⣀⣀⣀⣤⣤⣶⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣟⣛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⢿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⢛⣛⣿⣿⣿ ⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠙⠻⠟⠈⠙⠿⠛⠁⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠶⠶⠖⠛⠛⠛⠻⠿⠶⠶⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠢⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀ ⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀ ⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀ ⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠙⠛⠿⠛⠛⢋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⣉⡉⣉⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠈⣷⡀ ⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣠⣤⣤⣤⣄⡀⣲⣿⣿⣍⠙⠋⠁⠀⠉⣿⣟⢈⣁⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠘⣷ ⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⢀⠀⠐⠻⣿⣿⣿⣿⣿⠿⢿⣿⣿⡿⠦⠄⠀⠀⠀⢸ ⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣸⣿⣿⣅⡀⠀⠀⠀⠀⢩⣿⡿⠀⠀⠀⢠⣾⠀⠀⠀⣿⡿⡏⠉⠀⠀⠀⣀⣘⣷⠀⠀⠀⠀⠀⢸ ⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣷⣿⣄⣠⣀⣀⣶⣿⣇⠀⠀⠀⢸⣿⡀⠀⠀⢿⣷⣷⣄⣀⣤⣸⣿⣏⣿⡀⠀⠀⠀⠀⢸ ⣿⡇⠀⠀⠀⠀⣠⣤⣄⣀⠉⠙⠛⠛⢻⣿⣿⣿⡿⠋⠉⠙⠛⠛⠻⢿⡅⠀⠀⢈⣿⡇⠀⠀⠈⢿⣿⣿⣿⡋⠉⠉⠙⠻⣄⣤⢦⡀⠀⣼ ⣿⠃⠀⠀⠀⢰⡏⠀⢦⡈⠻⠄⠀⠀⠀⠙⠿⣿⣷⣤⣄⣀⣠⡤⠀⢀⣁⠄⠀⣸⣿⣷⣄⠀⠀⠀⣿⡿⠿⠿⠟⠚⠉⣠⡿⠃⠀⠃⢀⣿ ⣿⡀⠀⠀⠀⢹⡄⠀⠀⠻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⣰⣿⣛⣴⣶⣾⣿⣿⣿⣿⣶⣶⣾⠇⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⢸⡗ ⢹⣇⠀⠀⠀⠀⠁⠀⠀⠀⠈⠛⢿⣦⣤⣀⣀⣀⠀⠀⠀⢀⣀⣀⣭⣻⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣍⣠⣤⣶⣾⣿⠏⠀⠀⠀⠀⠀⢸⠇ ⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣭⣭⣭⣍⣭⣹⣳⣾⣯⣿⣽⣿⣿⣿⢻⡿⠃⠀⠀⠀⠀⠀⢀⣾⠀ ⠀⠉⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣻⣿⣿⣿⢭⣽⠾⢧⣀⡼⣷⢶⣾⣿⣟⣿⣾⡿⠁⠀⠀⠀⠀⠀⠀⢸⡏⠀ ⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢯⣙⣻⡟⠓⠛⢳⣤⣿⣿⣿⣿⣯⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀ ⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣿⡿⠿⠿⣿⡏⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⢶⣶⣦⣤⣤⣤⣤⠴⠶⠚⠋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠶⠶⠶⢿⡟⠛⠛⠻⢷⣦⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣒⣋⡉⠉⠁⠀⠀⠀⠀⠀⣿⡇⠀⢀⡴⢋⡹⠟⢿⣦⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠓⠒⠶⠶⠶⢿⣷⣤⣾⣿⣋⣀⡀⠀⠈⠛⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⢰⣶⣤⣾⣯⡅⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣽⡶⠟⠉⠙⢶⣄⠀⠀⠀⡿⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⢩⣿⡿⠟⠉⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠘⣆⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠳⣦⡀⠘⣧⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢀⣾⠟⠁⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⣰⡞⣿⡄⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⡿⠁⠀⠀⠀⣀⣤⡾⠟⣫⣤⡤⠤⠤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠀⠈⢿⡄⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡿⠀⠀⠀⣠⣾⠛⣩⡴⠟⠉⠁⠀⠀⠀⠀⠈⠉⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⡇⠀⢀⣼⡿⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡛⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⢿⠿⡄⠀⠀⠀⠀ ⢠⠀⠿⣹⠇⠀⠈⠁⠀⣼⠑⠲⠶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣆⢹⣆⠀⠀⠀ ⢸⠀⢠⡏⠀⠀⠀⠀⢀⡟⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⢿⡄⢻⡀⠀⠀ ⢸⠀⣿⠀⠀⠀⠀⠀⠀⢿⡶⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠤⠤⣄⣀⣀⣀⣠⣤⡶⠟⠁⠀⠀⠀⠀⠘⣷⡀⣷⠀⠀ ⢸⣾⡟⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀ ⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠻⢷⣄⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣶⣶⣶⡶⠾⣿⣿⠷⠶⠿⠟⣻⣶⣶⣶⣦⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠟⡛⣩⣍⡀⠀⢸⣧⣀⣀⣀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣾⠿⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀ ⢸⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠿⠛⠉⠉⠻⠿⠿⠟⠛⠋⠛⢛⣋⣉⣉⣭⣽⣿⣿⣿⣯⣭⣉⣁⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠈⣿⠀ ⢸⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠋⠀⠀⠀⠀⣀⣤⣤⣶⣾⣷⠿⠟⠛⠛⠛⠉⢩⣿⠀⠀⠀⠉⠉⠉⢻⣷⣦⡀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⢸⡀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⢀⣠⣤⡾⠿⠿⣻⣿⣯⣤⣤⡴⠶⠾⠿⠿⠻⠿⣿⣦⣤⣀⡀⠀⣶⡿⠋⠙⢿⣆⠀⣿⡆⠀⠀⠀⠀⠀⢰⡿⠀ ⠀⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⣴⣿⠋⣁⣤⠶⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣷⣄⠀⠀⢹⣷⣿⠇⠀⠀⠀⠀⠀⢸⣷⠀ ⠀⣿⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⣿⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⢻⣿⠀⠀⠀⠀⠀⠀⠈⣿⠀ ⠀⢿⡄⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⠏⠀⠀⠀⠀⠀⠀⠀⠉⡇ ⠀⠈⠻⡄⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⣶⡇ ⠀⠀⠀⢻⣞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇ ⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀ ⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⢹⡿⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠉⠛⠳⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣷⠀⠀⠀⠀⠀⢀⣙⠻⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⡿⢻⣏⠉⠉⠉⠉⣉⠙⠋⢁⣾⡉⠳⢭⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⣿⠟⠀⣸⣿⣿⣭⣭⣽⡇⠀⠀⠀⠀⣨⠡⣀⡈⠉⢳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡿⢿⣿⣭⣰⣿⠋⢉⠉⠛⠁⡟⠀⠀⠀⠀⢀⣓⠂⠤⢟⣀⡛⢡⠬⠭⣑⠶⢶⡀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⣿⡇⠀⢽⡏⠀⣀⡇⠀⢀⣧⡞⢉⡽⠀⠁⢀⡁⠀⠀⠈⠑⠬⠗⡖⠚⠣⣀⠙⣆⠀⠀⠀⠀⠀ ⠀⠸⣇⣿⡇⠀⡸⣧⠀⠉⠐⢠⡟⠀⠉⠉⠀⠀⢀⡤⠥⠤⡀⠀⠀⠀⠀⠀⠀⠀⢠⡈⢹⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣧⠀⡇⣿⡀⠀⠀⣸⠃⣎⡽⠀⡰⢠⡃⠀⠀⠀⠘⣦⠖⠒⠒⠢⡀⠐⢒⡸⠃⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⠘⠄⢳⠸⣇⠀⢠⣟⣀⣤⢠⡞⠀⠈⠿⣿⣶⣶⡶⣧⣄⣀⡀⢀⡇⢀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⠄⣇⠘⣇⢹⣶⠋⠁⠀⣹⠿⠃⠠⠧⣀⠘⠋⠉⢄⠑⣾⣛⠫⠝⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣧⡟⢀⣿⣿⣿⣷⣖⠛⠃⠀⠀⠀⠀⠀⣹⡒⣲⣬⢷⣄⣉⣳⣦⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣬⠿⢷⣯⣿⠿⣿⣿⣄⠑⢦⠤⢌⣁⠀⠀⠈⠛⠓⠘⠋⠁⠀⢀⡏⢀⣱⡄⠀⢀⣄⣀⠴⣶⣦ ⠀⢠⠏⠡⢤⡞⣿⡅⠀⢿⣿⣿⣿⣷⣤⣄⣈⣿⣶⣶⣖⡦⠤⠤⢄⣀⣸⣿⢿⡝⣿⢠⣾⡾⠁⠀⢸⣿ ⠀⡾⢠⠀⢸⠁⢠⣿⡀⠀⢙⢿⣿⠉⠛⠋⠿⣿⣿⣿⣿⣷⣤⣤⣤⣾⣿⠇⠀⠈⣾⢿⠁⠀⢀⣠⣾⣿ ⠐⣿⣿⣄⢸⣿⣿⡟⠀⠀⠀⢰⣿⣿⣷⣷⣶⣾⡿⣿⣭⣈⣻⣿⡿⣿⣿⣠⣀⣠⠇⠸⣦⠒⣋⡤⠟⠉ ⠀⠈⠻⣿⣿⣿⣿⣿⣧⡴⠃⣼⣤⣼⢉⠿⠿⠛⠋⠸⣿⡿⡿⢧⡀⠈⠻⡿⣿⠟⠀⠀⠈⠉⠁⠀⠀⠀ ⠀⠀⠀⡜⠙⠻⠿⣿⣤⣤⠾⢻⠏⢸⢸⠀⠀⠀⠀⠀⠹⡇⡇⠀⠹⣄⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡀⠀⠀⢀⡟⠀⠤⠄⢸⠀⢸⢺⠀⠀⠀⠀⠀⠀⡷⣧⠀⣤⣼⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⢄⡀⢸⣇⣠⣤⣀⡈⢧⣸⢸⠀⠀⠀⠀⠀⠀⡇⣿⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠲⢿⣿⣿⣿⣿⣼⣿⣼⣤⣤⡀⠀⠀⢀⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠛⠛⠛⠃⠀⠀⠘⠛⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠱⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠠⠤⠒⠒⠒⠒⠒⠒⠢⠤⢧⣀⡀⡇⠀⢀⠤⠒⢢⠀⠀ ⠀⡠⠒⠛⢄⠀⠀⠀⠀⣠⣾⣯⣷⠀⠀⠈⡀⠘⠑⢢⠊⠀⢠⠃⠀⠀ ⢰⡁⠶⠰⠀⠆⠀⠀⠀⠘⠬⠩⠊⠀⠎⣽⣿⣳⠀⠈⠢⢖⠁⠀⠀⠀ ⠀⠑⠄⣠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠬⠟⠁⠀⠀⠀⠈⢆⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⢁⠖⠒⠂⡴⠀⠀⠀⠀⢀⢆⠀⠀⠀⢀⠀⠘⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⡎⠀⣇⠀⠑⠒⢠⠤⠤⠜⢚⠃⠀⠈⡌⡀⠀⢱⠀⠀ ⠀⠀⠀⠀⠀⠘⠤⢺⠉⠐⢸⡁⠈⢀⠀⠀⡘⠀⠀⡀⠁⢀⢦⣸⠀⠀ ⠀⠀⠀⠀⢤⡠⠄⢺⠦⠒⠉⠣⠴⠊⠦⡠⠳⠤⠞⠙⠒⢳⢄⡀⠀⠀ ⠀⠀⠀⠀⠞⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⡆⠈⡶⡀ ⠀⠀⠀⠀⠀⡦⢜⡀⢤⣀⢰⢄⠀⠀⡄⠀⡠⡴⠀⣀⡤⣀⢧⡖⡇⠀ ⠀⠀⠀⠀⠲⣚⠀⠀⠉⠀⠙⠇⠱⠾⠛⠁⠀⠉⠁⠈⠁⠀⢈⠕⠁⠀ ⠀⠀⠀⠀⡔⠩⢤⡄⢀⠀⢀⣀⠀⡰⡀⣠⠾⢄⣸⡦⢴⠒⠒⠳⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠈⠋⠀⠉⠀⠀⠸⣿⡃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠀⠛⠃⠀⠀⠀⠀⠀⠀⠈⠓⠒⠛⠁⠀⠀⠀⠀

⠀⠀⠀⠀⢀⡠⠤⠤⠐⠒⠒⠂⠘⠋⡿⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢞⣿⣷⡈⣴⣶⣶⣦⠀⠀⡼⠃⠀⡼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣷⣝⣻⡿⠤⡤⡖⠓⢒⡮⢶⠑⠒⠒⣶⠒⢶⡖⢄⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⠋⠉⠀⠀⢠⠃⠈⣑⢠⣈⠑⠖⡀⠄⡀⠻⠍⠷⠤⠵⡆⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⡟⢀⡮⢜⢗⡽⠐⠂⢄⡀⠄⠤⡀⠀⠟⡞⠁⠀⠀⠀ ⠀⢸⣿⣿⠇⢹⠀⠀⠀⢠⠟⡩⡀⡴⢿⣀⣀⣀⣸⣀⡀⠀⣸⢀⠎⠀⠀⠀⠀⠀ ⠀⠸⣿⡿⠇⢸⠀⠀⢀⠿⠤⡗⢹⢐⠔⡑⠿⠕⠫⡑⠽⡑⢁⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠃⠀⢘⣄⣴⣿⠔⠚⠁⣅⡟⠀⠈⡯⢕⠦⠝⠲⣼⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣤⣤⠞⣿⢯⣸⣝⡂⢜⠷⣁⣀⡀⠀⡀⠀⣀⠸⣏⣨⡋⢦⣄⣤⠞⣷⣆ ⢰⢟⠠⢲⣟⣦⡿⠊⢿⡻⢿⣗⣶⣶⢺⣾⣿⣶⣽⣶⣾⠩⠻⣷⣾⠳⡏⠀⡽⢿ ⢸⣼⣇⣿⠀⠉⠁⠠⡾⠉⢻⡤⠤⣤⡤⠛⢻⠷⠖⡶⣿⣀⣀⣸⣿⣥⠴⢋⠴⠋ ⠀⠉⡞⠻⢦⣀⣀⣼⡥⠄⠀⣹⡿⠿⠥⠄⠚⠻⣿⠳⢦⡈⢧⠀⠀⠉⠒⠁⠀⠀ ⠀⠀⡄⠀⠀⢰⣿⣿⠁⠀⠀⠸⡇⠀⠀⠀⠀⠀⢹⢣⠈⢳⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⢄⠀⣾⣿⣧⠀⠀⠀⠈⡇⠀⠀⠀⠀⢰⣘⢸⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠙⠛⠿⠧⠀⠀⣿⣷⣶⣆⠀⠤⠼⠿⠷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠟⢿⣯⠉⠻⢦⣄⠀⠀⠀⢀⣴⠾⠋⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡏⠀⠀⢿⡆⠀⠀⠙⢷⣤⣴⡞⠁⢀⣀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⣼⠃⠀⠀⠀⠘⠃⠙⠿⠿⠿⠶⠿⠿⣧⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡇⡀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣒⡬⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠇⠃⠀⠀⠠⢔⣾⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠹⠿⢷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⠀⠀⠀⠀⣠⡟⢩⣄⠉⣿⡀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⢀⣼⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡟⠀⠀⠀⠐⠛⢿⣤⣈⣃⣨⡿⠁⠀⠀⠠⣶⣶⠀⣀⣉⣛⣛⠋⠁⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⣀⣀⣀⣀⣤⡶⠟⣛⣉⣉⡉⠛⢷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠤⣴⡏⢀⣾⡟⠉⠉⡿⣆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⢸⡇⠃⠀⠀⢀⡟⢸⠃⠀⠀⠀⢠⡄⠀⠀⢀⣤⣤⣤⡀⢠⣤⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⢸⠃⣿⠀⠀⠀⠀⢸⡇⠀⠀⣾⡏⠁⢹⣷⠸⣿⠀⠀ ⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣸⠃⠀⠀⠀⢸⠀⢻⠀⠀⠀⠀⢸⣇⣀⡀⢻⣧⣂⣼⡟⠀⣿⣀⣀ ⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⢰⡏⣰⡏⠀⠀⠀⠀⢸⡆⣼⠀⠀⠀⠀⠘⠛⠛⠛⠀⠙⠛⠉⠀⠀⠛⠛⠛ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣍⣿⡀⢸⡆⠀⠀⠀⢀⡾⢁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡈⠻⠶⠴⠾⣛⣥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⢶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⡤⠶⠶⠶⠶⠶⠶⠶⠶⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠀⣀⣤⣤⣀⣀⣀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⣴⡶⣿⣿⣿⣿⠟⠙⠛⠿⢿⣿⣿⣿⡟⠿⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢀⣴⡾⠛⠉⠀⠟⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⠛⠃⠀⠀⠈⠙⠳⢶⣀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠃⠀⢀⣴⠟⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⣠⡟⠁⠀⠀⡞⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⢢⠀⠀⠈⢷⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢱⡆⠀⠀⠀⠀ ⠀⠀⢀⣼⠃⠀⡞⢁⠇⠀⠀⣼⠀⠀⠀⢀⠏⠀⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠘⡇⠀⠀⠈⣧⠀⠀⠀⠈⣧⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀ ⠀⠀⣰⡇⠀⡞⠁⡞⠀⠀⢠⠇⠀⠀⠀⣾⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢱⠀⠀⠀⠘⡄⠀⠀⠀⠘⡆⠀⠀⠀⠀⢸⡄⠀⠀⠀ ⠀⠀⣿⠇⣸⠁⢰⠃⠀⠀⣾⠀⠀⠀⢰⡿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⡇⠀⠀⠀⢿⠀⠀⠀⠀⢻⠀⠀⠀⠀⠸⡇⠀⠀⠀ ⠀⠀⣿⢠⡇⠀⣿⢀⠀⠀⡇⠀⠀⠀⣼⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⣠⠀⢷⠀⠀⠀⠘⡆⠀⠀⠀⠀⣧⠀⠀⠀⠀⣷⠀⠀⠀ ⠀⠀⣽⠸⠁⠀⣿⣼⠀⠀⠇⠀⠀⠀⣿⡏⠚⡧⠀⠀⠀⠀⠀⠀⢈⡇⢺⡏⠁⠀⠀⢸⣆⠀⠀⠀⣷⠀⠀⠀⠀⢻⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠇⠀⠀⠀⡿⣿⠀⢸⠀⠀⠀⠀⣿⡇⠀⣧⠀⠀⠀⠀⠀⠀⢸⡇⢸⣷⠀⠀⠀⠈⡿⡀⢠⠀⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⣿⠀⣿⠀⠀⠀⠀⣿⡇⠀⣿⡀⢠⠀⠀⠀⠀⢘⡇⢸⣿⡇⠀⠀⠀⣷⣧⠘⡄⠘⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢿⠀⣿⡀⠀⠀⠀⣿⢽⠀⢿⡄⢸⡄⠀⠀⠀⢸⡏⢸⢿⢧⠀⠀⠀⢹⢹⡀⣷⠀⣧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡄⠀⠀⠀⣿⠸⣆⣏⡷⠶⠦⠤⠟⠀⢆⡸⢻⣲⢧⣀⣀⣀⣠⠷⠼⠜⠿⠤⠤⠤⠞⢛⣗⠿⣀⠟⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣆⡐ ⠀⢸⠀⢠⠀⠀⠸⡄⣿⢿⣷⣄⣀⠀⢀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣴⣶⡿⠿⠀⣿⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⢸⡄ ⠀⠘⠀⢸⡆⠀⠀⠳⣾⠄⠉⠉⠛⠿⣶⣯⣕⡲⠄⠀⠀⠀⠀⠀⠀⠀⢸⣭⣶⠿⠟⠋⠉⠀⠀⠀⣿⠀⠀⠀⠀⣿⣯⡆⠀⠀⠠⠀⠈⡇ ⢠⡆⠀⠀⡇⠀⠀⠀⢹⠀⣤⣀⣀⣀⣀⣩⣽⣿⠟⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⢶⣶⣶⣦⣤⣄⠀⡿⠀⠀⠀⢠⠃⣽⡇⠀⠀⢰⡆⠀⡏ ⣿⡇⠀⡆⢸⡀⣀⡀⣈⡇⠘⠟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⡇⠀⠀⡖⣸⣠⠿⡇⠀⠀⣸⠃⣸⠗ ⣿⢧⠀⢣⠘⡇⡄⠀⠨⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡇⣿⠃⢠⠃⢀⡴⠃⡰⠃⠠ ⠛⢸⢦⡘⢧⣹⡟⡆⠐⢽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠂⠀⣸⣷⠇⠀⢈⣠⢞⣡⠞⠁⠀⠀ ⠀⠀⠀⠑⢦⣿⣿⣿⡀⠀⢷⣿⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⣼⡁⠀⣿⣿⡀⣀⣼⣷⡍⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⣿⢻⣧⣀⣸⣿⠁⠀⠉⡷⢦⣤⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⣯⣤⣄⠀⣿⣀⣼⣿⢿⣿⣿⣴⣿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⢸⣿⣧⣿⡿⠀⠉⠉⠉⡓⠻⣄⠀⠠⠭⣍⠉⠩⠉⠀⠾⠧⣄⠈⠙⢦⡀⠙⣿⣿⣿⠃⢸⣿⣿⣿⣿⣅⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣧⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣤⣀⣀⣀⣠⡔⡇⠀⠈⠳⡀⠀⠙⠐⣿⠛⠛⠲⣶⢿⣿⣿⡿⢻⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⣿⣿⣿⠟⠛⠃⢧⠀⠀⠀⠀⠀⠀⠀⠀⣨⣈⠑⢤⠀⠳⢇⠈⠂⠀⠀⠀⠀⠀⢀⣟⣀⡠⠴⣥⡟⣿⣿⣷⣾⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⡷⠶⢄⣈⣳⣤⣀⠀⠀⠀⣀⡴⣽⣮⠃⠀⠙⠂⢈⡳⣄⣀⣀⣀⣀⡴⠋⠈⠳⣄⠀⠘⣷⣿⣿⣿⣿⣿⢿⣦⡀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⣇⠀⠀⢠⠛⡏⠈⠙⠉⣍⠁⠀⠈⣽⠢⣄⡄⠳⣎⣀⣀⣍⠉⠉⢹⠿⢄⣀⣀⡼⠀⠀⢹⠉⠻⣿⣿⣷⣾⣿⡇⣾ ⠀⠀⠀⢹⣿⣿⡏⠀⠳⠀⠀⠁⠀⣻⣅⣠⠞⠀⠛⠶⢦⣞⡀⠈⠱⢄⢰⣼⣷⢨⠀⢀⡿⠁⠀⠀⢈⢺⠀⠀⣟⠀⠀⢈⡛⣿⣿⡟⡃⢹

⠀⠀⠀⠀⠀⠀⣠⠊⡦⠒⠀⠀⠀⠁⠐⠢⢶⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢺⠘⡀⢱⡀⠀⠀⡀⢀⠠⠄⢘⠆⠷⡀⠀⠀⠀ ⠀⠀⢀⣾⠿⢿⣦⡰⠖⡉⠩⡄⠉⠷⢒⠒⠯⣐⢠⣭⡀⠀⠀ ⠀⠀⢾⣾⣷⠌⠀⠀⠁⢀⠪⠀⠀⠀⠀⠡⡀⠀⠙⢿⢳⠀⠀ ⠀⠸⠈⡿⠃⣀⠊⠀⢀⠂⠆⡄⠀⠆⠀⠀⠐⠈⠄⠈⢢⠀⠀ ⠀⢸⢐⠃⡰⠃⠀⠀⠀⠜⢰⢣⠀⠰⠀⠀⠀⠃⠈⠀⠀⢃⠀ ⠀⠨⠋⡰⠁⢀⠔⠑⠀⢀⣎⣡⠡⡀⢃⢀⣾⡜⡀⠠⠀⢈⢆ ⠀⡐⠨⠁⢐⡡⠊⠀⡘⠁⠀⠀⠑⠔⢌⠖⠉⠀⢣⠀⢣⠀⡀ ⠈⠀⠉⢀⢺⠀⠀⢀⢡⠐⠚⠛⠀⢠⣰⡯⠖⠢⢴⡄⢸⠁⢇ ⠀⠀⡴⠃⡨⣆⡀⢘⢌⣧⣀⣀⡠⠏⠀⠱⣄⣀⣸⡷⠈⣆⠈ ⠀⠐⠡⠊⠀⠐⣇⢸⡤⡀⠀⠀⠀⠀⠀⠀⠀⡡⠣⢃⠦⠃⠉ ⠀⠀⠀⠀⠀⣰⣿⣦⡙⢦⠑⠠⢀⡀⢀⠠⠊⠰⠓⠁⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⡬⠹⣧⡀⢠⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⣀⣀⣤⠲⢿⣿⣟⣀⡜⠲⠚⡟⠽⢧⣸⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⢻⠋⠸⠀⠉⠙⠳⠦⠬⣿⠧⠀⠀⢷⣿⡿⠑⡄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠚⠉⠙⠓⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠙⢾⣭⡞⠀⠀⠀⠀⠀⣨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠛⢦⣀⣼⠁⠀⠀⠀⠈⢻⡇⠀⠀⣠⠶⠞⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⡇⢀⠞⠁⠀⠀⢠⣾⠖⡻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣧⠏⠀⠀⠀⠀⠀⢀⡴⢶⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣠⡶⠋⣩⡿⠛⢢⡀⠀⠀⡾⠉⠙⠒⢦⣄⠀⢰⡟⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⠹⣤⡾⠁⠀⠀⠀⠀⠈⠳⡏⠀⠀⢸⠀⢧⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢠⣧⣾⣯⠶⢦⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢥⠀⠀⢸⠀⣸⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠸⣿⡿⠁⠠⢾⣿⠀⠀⠀⠀⠀⠀⣠⣖⣛⠛⠳⣤⠏⢀⣤⠏⢀⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢧⡀⢹⡀⠀⠀⣼⣿⣧⠀⠀⠀⢀⡾⠉⠉⣿⣷⡀⠘⣿⡭⠏⢀⡾⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣮⣳⡀⣇⢸⣾⣿⣿⠏⠀⠀⠀⣸⣅⣠⠖⢿⡿⡇⠀⠀⢀⣴⣯⡤⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣍⣉⣽⣿⣿⡿⠋⢀⣀⣀⠀⢹⣿⣿⣿⣿⡇⠀⢀⣀⡀⡿⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡁⢡⣄⡙⠢⠀⠀⠠⠀⠠⠿⠛⠛⠛⠒⠲⠞⠓⣾⠃⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⢯⣿⠢⠤⠤⢤⡤⠤⠤⢞⡷⠆⠀⠀⠀⣰⠏⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡾⠉⠀⠀⠀⣏⠛⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣈⠻⣝⠒⠄⠀⠀⠀⣴⠞⠁⠀⠀⢠⡼⠃⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⠀⠀⠀⠀⠀⠈⣧⠀⠀⠉⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣬⡙⠒⠒⠒⠊⠁⠀⣀⣤⠖⠋⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣀⡀⠀⠀⠀⣠⡏⠉⠙⠓⠒⠒⠛⢻⡍⠀⠀⠀⠀⠀⣶⡶⠶⣺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢷⡀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⠋⠀⠀⠀⠀⠀⠀⣀⡠⠽⠷⣤⠤⠤⢔⣃⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠲⠦⠤⠤⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⣸⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠒⠒⠒⠲⠤⠤⣼⠁⠀⠀⠀⠀⠀⠀⠸⢧⣄⣀⣤⣞⠁⠀⠀⣠⡞⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢿⠞⢁⣤⣶⡮⢷⣯⠞⠋⠉⠀⠀⠉⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢸⣦⣀⣀⡠⠶⢡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣄⣀⣀⣀⠈⢇⠀⠀⠀⢀⡤⠔⠒⠤⠤⣀⠈⠷⠞⠁⠀⠀⠈⠙⢦⡀⠀⠀⢦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠒⠚⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⠙⠗⠋⠉⠛⠻⢦⣀⠀⡎⠀⠀⠀⠀⠀⠈⠑⢤⠀⠀⠀⠀⠀⢀⡼⢻⠒⠦⡀⢻⡱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠙⢷⡇⠀⠀⠀⣀⣀⠀⠀⠀⢳⡀⠀⠀⢰⡏⠀⣸⠀⠀⠙⢼⠃⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⠁⠀⢻⡄⠀⠀⢷⠀⠀⠘⠧⠴⠃⠀⢀⠀⠁⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠘⡄⠀⠀⡇⠀⠀⠸⡴⠚⠉⠒⢦⣀⠀⡟⠢⠄⠴⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠿⠶⠤⣄⣀⠀⠀⠹⢦⡀⢠⡇⠀⠀⠀⠀⠀⢀⣇⡤⠀⠀⠀⢀⣤⡞⠋⠀⠀⠀⠀⠻⣄⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠤⢾⡟⣿⠁⠀⠀⠀⠀⠀⣼⡏⢠⠴⠒⠊⠉⠈⠙⠓⠦⣄⡀⠀⢀⡼⢧⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠋⢡⠏⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡋⠀⠀⠉⠓⠦⢤⣤⣤⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⣈⠙⠶⣀⠀⠀⠀⣀⡴⠖⠋⠉⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠬⠥⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢀⣰⠇⠀⠀⠀⠀⠙⢦⡀⠀⣀⠤⠚⠋⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠳⣮⣁⣀⣠⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡳⡶⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢠⡄⠀⠀⠀⠀⠀⠈⢹⣅⣽⡿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠷⢯⡄⢀⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣓⠶⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠏⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣋⣆⢀⣩⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡙⠋⠛⢒⡶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⠶⢦⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠰⢷⣤⣀⣰⠃⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠁⠀⠀⢻⠀⠀⠀⠀⠀⠀⠻⣶⠿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⠀⠉⣉⣳⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠰⠿⢶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣀⡀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠴⠗⠋⠁⠙⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⣼⣧⠀⠀⠀ ⢰⠇⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣄⣩⡷⠦⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⢿⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⢈⣿⣩⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀ ⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⠇⠀ ⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⡸⠀⠀ ⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠋⠁⠀⠀⢰⠃⠀⠀ ⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⠤⠤⢄⣀⣀⣀⣠⠤⠤⠤⠒⠚⠉⠁⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀ ⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠐⣶⠤⡼⠙⣆⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠀⠀⠈⣳⠀⠀⣠⠼⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠷⠚⠙⢾⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠉⠉⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠒⠒⠒⢶⣶⠶⠒⠛⠓⠒⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣤⣀⣀⠀⠀⠀⠀ ⠀⠀⠠⠶⢿⣭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣰⡿⣴⣿⣾⣧⢿⣄⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡼⠛⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⡾⣻⢡⡏⣿⡏⠘⣯⢿⣧⢻⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀ ⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣿⣿⠁⡏⣾⠀⢿⣧⠀⠸⣿⡏⣮⢷⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀ ⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠘⣿⡏⢀⡇⣿⠀⠘⣿⡆⠀⢿⣷⠙⣿⣦⡀⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡇⠀⠀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣤⣴⣿⣿⣽⣿⡏⠀⠀⠈⠻⣆⣸⣟⣤⣼⢾⣷⣖⠚⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀ ⣸⡇⠀⠀⠀⠀⠀⠀⢀⣴⣟⣍⣹⣶⣷⣬⣍⠌⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⣴⣿⣿⣷⣦⣼⡟⣹⣶⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⢿⡇⠀⠀⠀⠀⢀⣼⡿⣿⣿⡿⠛⢻⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⢻⣿⣿⣿⣿⣿⣹⡟⣧⡀⠀⠀⠀⢿⡠⢠⡄ ⠈⡇⠀⠀⠀⠀⣼⢹⡇⢸⣿⣷⣤⣾⣿⡋⢹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣾⣿⣋⣹⣿⣿⣿⠁⠘⢷⠀⠀⠀⠀⢙⣿⡇ ⠀⢻⠀⠀⠀⣼⡇⠈⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⣻⠛⣼⠀⠀⠘⠃⢠⣤⣤⣽⠟⠃ ⠀⢸⣦⠀⠀⠿⠀⠀⣷⠀⠈⠻⠧⠽⠷⠼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠧⠼⠿⠷⠟⠁⢀⡏⠀⠀⠀⠀⠘⢿⣿⣩⣥⡆ ⠀⣼⣿⡆⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⣥⣿⠿⠏⠁ ⠀⠉⠈⢷⡀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⣤⣼⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⠀⢀⣄⠀⣸⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠙⠓⠢⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠋⠁⠀⠀⠀⣠⣾⣫⠞⠛⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⠟⠛⠛⣿⡛⣯⣁⠀⠀⠀⣀⣤⣶⠞⠹⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓⠚⠻⣾⣷⣄⠀⣀⣤⣶⡟⣱⡏⠀⠀⠀⠈⢹⡎⠻⣗⡶⣿⣭⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⣿⣫⡿⠿⣿⠀⢿⣷⣒⣶⣖⣾⣽⠇⠀⢻⡏⠑⠺⢯⡓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡿⠛⠁⠀⢰⡇⠀⠘⢧⡀⠀⠀⢠⡿⠀⠀⣈⣷⠀⠀⠀⢻⡎⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣼⠃⠀⠀⣠⡞⠛⠓⠶⢮⣻⣦⣴⣯⡴⠞⠋⠉⠻⣄⠠⣄⠀⢹⡜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡟⢠⣽⡾⠋⠀⠀⠀⠀⠀⠀⢹⡟⠁⣀⣀⣀⣀⣀⣸⣷⣿⠋⠸⣧⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠁⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣷⠀⠀⠀⠀⣿⣿⡿⠀⠀⣿⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡞⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠿⠶⠦⠴⠾⠿⠇⣿⠀⠀⠸⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡇⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠨⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⣸⠀⣴⣶⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⣟⣷⠀⣿⡀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢰⣿⣦⡟⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢻⣹⡆⢸⡇⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣾⠃⠀⠀⠀⢸⣿⢿⣿⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⢳⡿⢿⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⢀⣀⣸⡇⠀⣀⣀⡀⠀⠀⢀⣀⣀⣼⠇⠀⠀⠀⠀⢈⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣇⣀⠀⠀⠀⢀⣿⣭⣽⣿⡿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⡿⢿⣿⢾⡿⣦⡀⠀⠀⢀⣸⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣛⣛⣿⡏⢸⡇⣷⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣿⣼⠀⠘⣿⣿⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⣎⣿⢿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠙⣃⡀⠀⠀⠀⠀⠀⣿⢿⠀⠀⣿⣷⣶⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣼⣿⠇⢸⡇⡏⠀⠀⠀⠀⠀⠀⠴⣿⠋⠁⠀⠀⠀⠀⠀⣿⢸⠀⠀⠹⣿⣯⠞⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⣇⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡟⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠃⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡗⡇⠀⠀⠀⠀⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣧⠀⠀⠀⠀⠀⠀⠀⣸⠿⢿⡀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣾⠷⡶⠾⢿⡾⠋⠀⠈⠛⢶⣤⠾⣶⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣩⣭⣍⣹⠃⠀⠀⠀⠀⠀⢻⣉⣡⣬⣍⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠁⠀⠀⢹⡀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⢿⣀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣶⡶⠚⠒⠒⠒⠒⠒⠒⠲⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠠⠤⢶⣚⠛⠛⠛⠓⠦⢜⣿⠲⢄⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⣠⣖⡛⠉⠉⠉⠉⠃⠀⠀⠀⠀⠀⠙⠀⠀⠓⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣤⣴⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣵⡀⠀⠀⠀⠀⢀⣤⠶⠋⠉⠁⠀⠀⠀⠈⠁⠀⠉⠀⠀⠈⠙⠳⣦⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠁⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡗⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⠀⠀⠀⣇⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣧⣀⡤⢴⢶⡶⠦⣀⠀⠀⠀⠀⢰⣞⣩⣷⣴⣶⡮⠤⠽⡆⠀⢻⠀⢰⡟⡉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⣿⠴⠖⣺⣿⣿⣿⡟⢃⡀⠀⠀⠈⠁⣸⣟⣿⣿⡻⠇⠀⠀⠀⠸⣦⡟⡽⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡜⣿⡏⠀⠀⠿⠽⢿⠟⠛⠳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢱⡗⣆⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣧⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢻⡆⠀⠀⠀⠀⠀⣧⣀⣀⠀⢀⡠⠶⠞⠁⠀⠀⠲⣄⠀⠀⠀⢠⣿⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⠀⠀⠀⢀⡠⣄⣠⡽⠁⢀⣀⠾⠯⢤⣀⡀⠈⠀⣀⠶⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣣⡀⠀⢸⡿⠵⠶⠬⠭⠗⠚⠋⢉⣩⣿⠃⠀⢀⡏⠀⢣⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣻⡀⠀⢻⣶⣶⠖⠒⠒⠒⢊⣹⣻⠃⠀⠀⠘⡽⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢷⡀⠀⠑⢯⣓⠲⠶⠒⣩⠖⠁⠀⠀⠸⠀⠆⣾⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⢿⡓⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⢠⣌⢈⡾⠃⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣸⢷⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢈⡾⠁⠀⢸⡅⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⢀⡏⠀⠻⣮⡑⢓⠀⠜⠜⠲⡦⠠⢜⣰⠟⠁⠀⠀⠘⣷⡄⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⢻⡏⠁⠀⠀⣾⠁⠀⠀⠈⠛⠶⣥⣤⣠⣤⣤⡼⠛⠁⠀⠀⠀⠀⠀⠈⡧⠀⠀⠘⣿⠓⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⢠⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢹⡆⠀⠀⠀⠉⠓⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⠁⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⠀⠀⠀ ⠀⠀⣀⣤⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢸⠛⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀ ⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢸⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⢻⡇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢀⣠⣤⡼⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠒⠒⠛⠉⠉⠀⠀⠿⣦⣄⣀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡧⠶⠖⠋⠉⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠉⠉⠙⠛⠒⠒⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠳⣤⣀⠀⠀⠀⣿⣝⣏⣿⣯⣇⣛⣉⣛⣁⣹⣋⣉⣻

⠀⢀⣠⣤⡶⠶⠶⠶⠶⠦⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠶⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠶⠶⢤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣯⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣢⠤⠤⠀⠤⠭⠭⣉⣙⣛⣛⣛⣷⣶⣶⠤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠈⠻⣦⣉⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠓⠒⠒⠦⣤⣀⠀⠀⢀⣈⠉⠉⠒⠒⠋⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⠳⣦⡄ ⠀⠀⠀⠀⠉⠛⠲⠦⢬⣍⣙⣓⠒⠦⢤⣄⣀⡀⠀⠀⠀⠀⣤⡤⢤⣀⡀⠀⠀⠀⠛⠻⢝⡒⠒⠤⠤⢭⣉⣉⠉⠉⠑⠒⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢫⡇ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣯⣙⠒⣶⣶⣽⣿⣟⣒⣶⡶⠿⢶⣶⣾⣿⣖⠒⠲⢤⣀⣙⣲⣶⠶⠶⢶⣿⣭⣉⠑⠒⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣠⡴⣯⣿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠋⣫⡿⡌⠹⡝⢿⡋⠈⠓⠶⠾⠿⠋⠉⠛⠛⠓⠶⠶⠯⣭⣭⣛⡓⠚⠻⠿⠯⠭⣭⣁⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⢤⣶⣾⣯⣽⠟⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠀⠻⣥⠟⠀⣿⣼⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠶⠦⣤⣤⣤⣤⣀⣀⣤⣤⣤⣼⣷⡮⣿⠟⠛⢉⣽⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⣅⣀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠛⢿⣶⣤⣀⣤⠖⠻⠷⣦⡵⠟⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢱⡶⢦⠀⢹⣽⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠈⢳⠞⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⠲⠞⠑⠆⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠃⠈⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢇⠀⠀⡀⢀⣀⠠⠴⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣨⣦⢈⠐⠀⢹⣀⡀⡅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣿⠇⢁⠤⠥⠀⠮⡂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⡏⠀⣰⠀⠀⠀⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⡑⠍⡉⢤⣴⣿⠻⠾⣴⠷⡄⠀ ⠀⠀⠀⠀⢐⠄⡀⠉⢸⠣⣰⢯⡶⣷⠧⡈⡇⠀ ⠀⠀⡠⠊⠁⠁⢂⠉⠉⢀⡀⠈⢿⠉⠂⠀⡇⠀ ⠀⢰⢀⠀⠀⠀⢸⡆⠀⠈⠁⠀⠘⢎⡆⠀⠈⡄ ⠀⡎⠀⠈⠁⡰⠁⠀⠀⠀⠚⠃⠶⠆⠱⡀⠀⡇ ⢠⡇⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠊⠀ ⠈⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠃⠀ ⠀⠂⠀⠀⢀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠢⠦⠠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠉⠉⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡤⠤⠤⠤⠤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠻⠇⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⠻⣆⠀⠀⠀⠀⠀⠀⠀⠛⠛⠶⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢠⠀⠀⠀⢀⣴⠟⠛⠛⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠙⢷⡜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣦⠀⠠⣾⠁⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣠⡄⠀⠈⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠹⣄⠀⠀⠀⢰⣿⡦⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢠⣿⣷⢀⣴⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠈⠳⢦⣄⣸⣿⣇⣂⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣶⠼⣿⣟⠛⠁⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠂⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣶⣶⠶⠶⠒⠚⢿⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣶⣶⣤⣀⠀⠀⠀⢀⣠⣶⣶⣶⣦⡀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⠞⠉⠀⢀⡴⠞⠋⠁⠀⠀⠈⠉⠉⠷⢦⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⣄⣤⠖⠀⠀⠠⠶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣠⡴⠚⠛⠛⠛⠛⠛⠿⢦⣀⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠛⠋⠉⠉⠛⠶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠓⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⢀⡿⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⠁⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣏⠁⠀⠀⠈⠉⠉⠉⠀⣀⣀⣀⣀⣀⣀⣉⣉⡿⠿⢯⣍⣁⣀⡀⠙⠶⠴⠾⠋⠁⣼⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠹⣧⠀⠀⠀⠀⢀⡾⠋⢉⣁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣦⠀⠀⠀⣼⠇⠀⠀⠙⡇⠀⠀⠀⠀ ⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣘⣷⠴⠶⠶⣾⣷⣤⣼⣿⣦⣤⣤⣴⣿⣧⣤⣤⣤⣿⣦⣀⣀⣤⣾⣀⣀⣾⠋⠀⠀⠀⢀⣻⠀⠀⠀⠀ ⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠀⠀⠀⠀⣹⡎⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠉⠉⠙⠲⠦⢤⣤⡾⠟⠀⠀⠀⠀ ⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠒⠶⠦⣤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠶⠛⠛⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢷⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠷⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⠀⠀⠀⠀ ⠀⠀⢠⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀ ⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀ ⠀⣿⠀⢠⣶⡄⠀⠀⢾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄ ⢰⡇⠀⢠⠉⢠⡀⢀⣶⠀⠀⠀⠀⠀⠀⠀⡄⢀⡀⠀⢸⣧ ⠘⣇⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⡇⠀⢸⠏ ⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⡟⠀ ⠀⠀⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⠟⠀⠀ ⠀⠠⣦⣸⡟⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢾⡇⠀⠀⠀ ⠀⠀⣼⣿⣇⠀⠀⠉⠙⠛⣿⣶⠚⠛⠉⠁⢀⣾⠀⠀⠀⠀ ⠀⠀⠙⢿⡋⠀⠀⠀⠀⢀⣿⡿⢷⣦⣄⣤⡾⠃⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣦⣀⠀⣀⣾⣿⡇⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⠒⠒⠋⠀⠈⢙⣻⣉⣳⣧⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠉⠀⢀⡤⠖⠒⠶⠛⢁⣈⠙⢿⡄⠀⠀⠀⢸⣿⠗⠚⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠂⢀⡴⠋⠀⣀⣀⡀⢰⠋⠉⣧⠀⢻⠀⠀⠀⠈⢿⣟⡉⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠋⢣⠹⣌⠳⣄⠀⠀⠀⠀⠀⠀⠘⣷⠆⢸⡇⠀⣼⠁⠀⠈⣿⣦⣠⠟⠀⠸⣆⠀⢀⣠⣾⣍⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣆⠀⢳⣌⠑⣾⣣⣀⠀⠀⠀⠀⢰⡿⠓⢾⡇⠀⠙⠳⠦⠶⢯⣉⢀⣆⠀⠀⢹⣆⠘⠛⠛⣧⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⢋⠿⠛⣿⣟⢯⣗⡦⣄⡀⠘⣇⣻⡀⠀⠀⠀⠀⠀⠀⠀⣹⣍⣙⠛⠻⣿⡿⠛⢦⠀⠘⣧⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠉⠀⠞⠛⣻⣷⣬⣉⡙⠛⢦⠈⠛⠶⣷⣄⠀⠀⠀⠀⣠⡇⠀⠈⠉⠉⠉⠙⢦⣾⠟⠛⡿⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⢸⣆⠀⠀⠀⠈⢩⣿⣟⣠⡿⢛⣿⠤⠶⢾⡉⠉⠛⢶⣶⡿⠥⠼⢷⣦⣤⣀⣀⣀⣠⠟⠀⢠⡇⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠷⣦⡀⠀⠠⢿⣍⣩⠞⠋⠀⠀⠀⠀⢳⠀⠀⠀⠙⠛⠷⠖⠛⠁⠀⠀⠀⠀⠀⠀⣧⢸⣇⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⢿⣦⣤⣀⣠⣾⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢨⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣠⣭⣿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣧⡀⠀⢀⣀⡄⢠⡾⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⠷⢶⡷⠶⠿⠖⠛⢉⡿⠃⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡶⠶⠶⠶⣶⣶⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢀⣀⣤⠴⠶⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⡴⠾⠋⠉⠿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⢠⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⢀⣠⣤⠶⠲⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⠶⠾⠿⢿⣧⣀⣀⣴⣞⠉⠁⠀⠀⣸⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠁⠀⠀⠀⠀⠀⠀⠙⣷⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣦⣀⣀⣠⣴⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡿⠁⠙⢦⣄⣀⢀⣠⣴⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠉⠁⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡴⠟⠁⠀⢀⣀⣬⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡉⠛⠓⠶⠶⠛⠻⢶⣤⡀⠀⠀⠀ ⠀⣰⠶⠻⢿⣤⣀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⢤⣤⣤⡤⠾⠃⠀⠀⠀ ⠈⠛⠶⢦⣤⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⡤⠤⠤⠤⠤⢤⡤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡋⣳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠤⢀⣴⠝⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⡾⠛⡏⣮⠔⠂⠀⢘⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡟⣈⠃⣿⣋⣃⠡⠀⣴⣺⣽⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⡔⣿⣿⣻⣿⣯⣄⣹⣯⣴⠢⡙⠻⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠈⠻⢿⡿⠟⡭⡽⠋⡆⢹⡟⡟⣿⡿⢿⣮⣿⠳⣶⣏⣰⡲⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢟⡞⡅⡄⠙⡀⢃⠡⠣⣻⣷⡾⡸⠀⢀⣭⡽⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣷⡸⢈⣀⠘⢄⢑⣄⠚⠙⠊⠀⣰⣟⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⣷⣷⣿⡿⠛⠁⠀⠑⠫⢯⣢⣤⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣲⢉⣡⣾⠿⢿⢵⠉⠀⠀⠀⠀⠀⣀⣤⣽⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⣩⠄⠋⠁⠂⣴⣕⣕⡥⣒⠤⣴⣶⣿⡿⠛⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠚⠃⡰⠂⣀⠈⠉⠁⠿⠋⠑⠺⠙⠋⠈⡄⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠚⠃⢁⡫⢚⣁⢴⡠⡆⡐⠁⠀⠀⠀⢰⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠘⠁⠘⠀⠘⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿⠿⢿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⠉⠛⠛⠿⠿⢷⣽⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣾⣿⣿⠿⠿⠟⠛⠋⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⢷⣦⣤⣀⣀⡀⠀⠀⠀⠀⢸⣿⡟⠁⠉⠉⠙⣿⣿⣿⣿⣭⠉⢹⣿⣷⠀⠀⠀⠀⠀⣀⣀⣤⣴⡾⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠈⠉⠛⠛⣿⣿⠷⠶⣿⣿⣧⣤⣤⣄⣤⣿⣿⣯⣿⣤⣤⣤⣿⣿⡶⠶⣾⡟⠛⠛⠉⠉⠀⠀⢹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⢻⡿⠭⡭⠭⢽⣿⣿⡟⠀⠀⠈⠙⠀⠀⠀⠈⠉⢹⡏⠉⢹⡯⠀⠀⠙⠉⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡏⢸⡇⠀⠀⣀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣶⣾⣷⣶⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⢶⣦⣴⣿⡇⠀⠀⠀ ⠀⠀⠀⣿⠋⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⣷⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣼⠟⠀⢀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀ ⠀⠀⣸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀ ⠀⢀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣴⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣿⠀⠀ ⠀⣾⡇⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⡗⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀ ⢠⣿⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡏⢸⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣷⣾ ⣿⣿⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⢀⣿⣿ ⣿⣿⠻⢷⡒⠤⠤⢤⣉⣓⣢⣤⣄⣀⡀⠀⠀⠀⠀⠀⣀⣠⠾⠛⣿⣿⠛⠷⣄⡀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣔⣚⣉⡤⠤⢴⣶⡾⠟⣻⣿ ⢻⡁⠀⠀⠈⠙⠒⠀⠀⠀⠀⠀⠉⢉⠩⠿⠟⠛⠛⠉⠉⠀⠀⢀⣟⢻⡀⠀⠀⠈⠉⠛⠛⠻⠿⠍⡉⠉⠀⠀⠀⠀⠀⠒⠋⠁⠀⠀⢉⣿ ⠘⠷⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠻ ⠀⠀⠀⠀⠉⠙⠛⠛⠲⠶⠤⢤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⢛⠋⡁⠈⠙⠛⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠾⠛⠛⠋⢉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣷⣦⣀⣴⣿⣿⠵⠖⠛⠛⠛⠛⠛⠛⠓⠶⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⠿⠟⠻⠁⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣷⡝⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⣷⠀⢸⣷⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⢩⣿⠁⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡇⠀⠀⠀⠀⣦⡄⢰⣾⣿⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣿⡄⢾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⣾⣿⠀⠀⣷⣄⠀⠀⠀⠀⠀⣿⣦⣿⡇⠀⠀⠀⢠⣿⡇⣸⣿⣿⡀⠀⠀⠀⠀⠀⢀⣿⣷⣀⣿⣷⣾⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⣀⠀⣿⣿⡀⢠⣿⣿⡀⠀⠀⣀⢸⣿⣿⣿⣿⡄⠀⠀⢸⣿⣷⣿⢿⣿⣷⣶⣦⣀⠀⣠⣾⣏⣿⣿⡿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣱⣿⡇⠏⠀⣿⡟⣿⣿⣿⠿⢿⣶⣶⣿⣿⠟⠛⠿⠹⣿⣶⣶⠿⠟⠻⠿⠈⠛⠿⠟⠛⠛⢛⠟⢻⣭⣙⠙⠻⣿⡋⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣿⣿⣧⠀⣸⣿⡀⢠⡟⠁⠀⣰⣿⣷⡜⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢰⠏⠀⢺⣿⡿⠀⠀⢹⣧⣸⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⣿⣿⣿⡼⣿⣿⡇⢸⡄⠀⠀⠘⠿⠟⠁⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠹⣆⠀⠀⠁⠀⠀⢀⣾⣿⣿⣤⣤⣭⣷⣦⣤⣤⣤⣄⡀ ⠀⠀⠀⠀⠀⢀⣤⠞⠁⣸⢀⣠⣿⣿⣿⣿⣿⣿⣷⠈⠳⣄⠀⠀⠀⠀⢠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠤⠔⠒⠋⠙⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⢀⣠⣴⡿⠶⠖⠛⣿⡍⠙⠋⠁⡀⣴⣿⠃⠈⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁ ⢠⣾⡿⢧⠄⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀ ⣠⠻⢿⣪⣅⡀⠀⠀⠀⠸⠇⠀⠀⠀⠁⣿⡇⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀ ⠁⠀⠀⠙⠳⢯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡥⣠⡼⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⢳⣶⣤⣀⡀⠀⠀⠀⠈⢳⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣿⣿⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠈⠉⠙⠳⣦⡀⠀⠀⠈⠷⣄⠀⠉⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢉⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⣤⡈⢻⣄⠀⠀⠀⠈⠛⢦⣄⡀⠀⠉⠛⠲⠤⠤⢤⣀⣀⣀⣀⣀⣀⣠⡤⠤⠤⠒⠛⠉⣀⣤⡾⠿⠛⠁⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⡿⠁⠈⢿⡄⠀⠀⠀⠀⠀⠈⠙⠓⢶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣿⣭⣁⣀⡀⠀⢠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠈⢿⡆⠀⣠⣤⡴⠖⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠻⣶⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⡀⠀⠀⠀⠈⠻⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣿⠏⠁⠀⠐⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢦⣤⣤⣤⣴⣦⣴⣮⣿⡗⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠴⣾⣿⣯⣀⣉⣐⣠⣤⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣅⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⣴⡟⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣄⣀⣐⣤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠤⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠴⠞⢉⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠶⠶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠛⠉⠉⠀⠀⠀⠈⠉⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⠀⢹⡄⠀⠀⠀⠀⠀⢠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡄⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣆⠀⠀⠀⣿⠃⠀⠀⠀⠙⢦⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣀⡄⠀ ⠀⣿⠉⠳⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣠⡴⠞⠛⠑⣿⠀ ⠀⣿⠀⠀⠘⢧⣿⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⡴⠞⠋⠁⠀⠀⠀⢰⡿⠀ ⠀⢸⡆⠀⢷⡈⣿⡏⠙⠳⣤⡏⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⡤⠀⠀⠀⢸⡇⠀ ⠀⠈⣿⡄⠀⢹⣿⡟⠳⣤⣽⡄⠀⠀⠀⠀⠘⣦⣠⠤⠶⠖⣛⣛⣋⣽⣽⣯⣍⣛⣳⣄⠘⣷⡄⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⣿⠁⠀ ⠀⠀⠘⣧⣸⡟⢻⡇⢸⡏⣿⣇⣀⠀⠀⠀⠀⠹⣦⣤⠖⠿⣏⠉⠀⣻⣀⣹⡇⠀⠉⠉⠓⠋⢷⡄⠀⠀⣴⠛⠁⠀⠀⢀⣴⡋⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀ ⠀⠀⠀⠙⣿⡳⢹⣷⠸⣧⡻⣽⠟⠀⠀⠀⠀⠀⠈⠉⠀⠀⠘⠶⣄⣀⣉⡿⠃⠀⠀⠀⠀⠀⠘⣷⣠⡞⠁⠀⠀⠀⡴⠋⠉⡇⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀ ⠀⠀⠀⠀⠙⣧⡀⢿⡇⢈⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⢀⠞⠁⠀⣸⠇⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣼⣧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⣦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣰⣏⣠⠎⠀⢀⣴⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢨⡟⠁⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⠋⠉⠁⢀⣰⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⢳⡆⠀⠀⠀⠀⢀⣠⢶⠋⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⣀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢀⣀⡤⠶⠖⢋⣁⣀⡤⠴⠒⢋⣡⠬⣷⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⢶⣚⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⣴⠶⠛⣿⠒⡶⢯⡉⠉⠁⠀⢀⡴⠋⠀⢀⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠉⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠇⠀⢀⣤⠶⠋⢿⣆⠀⠸⣄⡇⠀⠹⣆⠀⢀⡞⠁⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣠⠖⠋⠀⠀⠀⣨⣿⣆⠀⠈⠃⠀⠀⠘⣧⡼⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠁⢻⣧⠀⠀⠀⠀⠀⢸⣇⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠙⠉⠁⠀⠀⣀⣤⠟⠀⠀⠀⠀⢀⣴⡿⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀ ⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠒⠒⠖⠛⠋⠀⠀⠀⠀⠀⣰⡿⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀ ⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇ ⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡄⠀⠀⠀⠀⢀⣠⡾⠛⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠤⠤⠤⠿ ⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣤⣶⠟⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⣤⡶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⣀⣤⡤⠴⠖⠚⠛⠛⠓⠶⢦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⣠⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡧⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣤⣀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢸⡇⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠘⣧⠀⠀⠀⠀⠀⠀⡾⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⣿⡆⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡳⣄⠀⠀⢣⡀⠀⠀⠀⠑⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡳⣄⣀⣙⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄ ⠀⠀⠀⠀⠀⠀⠀⡞⣼⣿⣿⣿⡿⣿⠟⣫⣿⣿⣶⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠛⠻⢿⣿⠿⠛⠛⠛⠿ ⠀⠀⠀⠀⡀⡠⢖⣵⣿⣟⣩⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢀⣀⣀⣀⣀⠈⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀ ⠀⠠⣒⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠉⢻⣿⠿⠛⠊⠉⠉⠉⠉⠉⠓⠲⢿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣄⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡁⠀⠀⠀⣀⣤⣼⡇⠀⠀⠀⣠⡴⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⣼⡿⠀⡄⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠟⠉⠀⠀⠹⣿⣿⣿⣿⣷⣦⡾⠟⠋⠉⠉⢇⠀⠀⣰⡟⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠇⠀⠀⠀⠀⠀⠀⠀ ⣿⠋⠀⠀⠀⠀⠀⠈⠛⢿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠃⠀⣿⣠⠴⠖⠒⠒⠚⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⣠⠔⠛⠒⠛⠁⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀ ⣿⣦⣀⡀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡾⠁⠀⠀⢠⡴⠋⠀⣸⠇⠀⠀⣤⢖⠀⢸⠀⢀⠄⠀⣄⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀ ⠈⠙⠛⠛⠿⠿⠿⣿⣿⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠻⣤⠴⠋⠁⠀⠀⢸⡙⢿⣤⣯⠔⠋⠀⣠⣿⡄⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣤⣴⣿⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⣤⣤⣶⠾⠋⠀⢳⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀ ⣶⣿⣼⣿⣿⣿⣿⠏⠀⠀⡀⢱⠀⠀⢸⣄⡀⠀⢀⣠⠴⠒⠒⠒⠲⣄⠀⠀⠀⣠⠟⠛⠓⠒⠢⢤⣸⡇⠀⠀⣰⣤⣿⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⢇⠈⢧⠀⠀⢿⠯⣍⡋⠀⣀⣀⠤⠤⠤⣼⡆⠀⠠⢧⡤⠤⢤⣀⣀⠀⢉⣥⠀⢰⡟⣿⢹⡧⠴⠾⣔⢦⠀⠀ ⠀⠉⠉⡟⢧⡀⠀⠀⠀⠀⠈⢆⠈⠣⡀⠈⢳⣄⠉⠉⠁⠀⠀⠀⠀⣿⠛⠛⢻⡿⠀⠀⣦⢀⣀⣹⠟⢹⡀⢸⣇⢡⡋⢿⣷⡀⠘⣿⢇⠀ ⠀⠀⠀⠘⠪⣛⠶⠤⠤⠶⢧⠈⢣⡀⠙⠢⢄⣉⠻⠧⠤⣄⠀⠀⠀⢹⡆⢐⣾⠃⠀⠀⠸⣆⠀⠀⠀⠀⢣⠘⣌⢦⣽⣉⣿⠇⢠⡟⣞⣀ ⠀⠀⠀⠀⠀⠈⠙⠓⠒⣿⣻⠀⠀⠙⣶⢄⣀⡀⠀⣀⣴⣿⣦⣤⣄⣘⣷⠟⠙⣶⣶⣾⣿⡛⠲⠤⠴⠻⡄⠑⢄⣉⠉⠉⢀⣠⡾⣱⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡳⣇⣀⣀⣴⠃⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⡋⡏⠀⠀⣿⣿⣿⡿⠟⠁⠀⠀⠀⠙⠢⣀⣀⣉⣩⡽⣫⣾⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠪⢭⣿⡸⡄⠀⠀⠀⠀⢀⣹⣿⣿⠛⠋⢹⠁⠀⢰⠟⠿⣿⣤⣄⣀⡀⠀⠀⠀⠀⠙⢺⠏⣿⡹⡏⠻⠋⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡇⡇⠀⢠⣤⣶⣿⣿⣿⣿⣷⠖⠲⠬⣔⣋⣤⣴⣿⣿⣿⣿⠿⣤⣀⠀⠀⠀⢸⣠⣷⢡⡇⢠⣄⠀⠀ ⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠇⠀⠀⠙⠿⣿⣿⣿⠟⣿⣷⣤⣠⣾⣯⡻⣿⣿⣿⢿⣁⣀⡼⠡⠉⠓⢲⠋⠁⢹⣻⠀⠀⠀⠀⠀ ⠀⠀⢀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⣿⣿⣿⣿⣿⡏⠈⠉⠀⠀⠀⠉⠁⢳⡦⢤⣸⣄⢀⣇⡏⢀⣠⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⢿⣛⣫⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⠛⠻⢿⣿⣿⣿⠿⢿⣿⣷⣦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣯⣥⣶⣾⣿⣿⣿⣿⣿⣿⠟⠉⣀⣀⣀⠈⠙⣿⣿⣿⣿⣿⠇⠀⠀⠀⢠⡿⠋⣉⠆⠀⢻⣟⢿⣿⣷⣄ ⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⢙⡿⠗⠋⠉⠉⠉⠉⠉⠓⠿⣿⣿⣿⡟⠀⠀⠀⣰⠏⣀⡼⢥⣀⣀⡀⢻⡄⢻⣿⣿ ⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢰⠏⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀⠀⣼⡏⡰⢁⡤⠀⢁⣄⠙⡞⣿⠘⣿⣿ ⣠⣾⣿⣿⣿⣿⡿⠟⠉⢿⣿⣿⣿⣆⣀⣤⡤⠶⢿⠀⠀⢠⠞⠋⠙⠻⣦⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⠀⡇⢸⠀⠀⠉⢹⠀⡑⣿⣼⣿⣿ ⣿⣿⣿⣿⣿⠟⠀⠀⠀⠈⠻⣿⣿⡿⠛⠁⠀⠀⠀⠃⠀⣾⣀⣠⠤⠤⠽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣷⡀⠳⣤⠔⠋⣠⠃⣿⣿⡿⠃ ⠋⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⢐⡿⠁⠀⠀⠀⠀⣠⠴⠦⡿⠉⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠙⡄⢁⡴⠚⢁⣼⣿⠟⠁⠀ ⠀⠹⣿⣿⣿⣦⣀⡀⠀⠀⣀⣿⠁⠀⠀⠀⢀⡞⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⣟⣨⡤⠶⠛⠛⣿⠀⠀⠀ ⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡞⠀⠀⢀⡞⠁⣀⠟⠀⢠⣖⡶⣾⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸⡇⠙⠁⠀⠀⢀⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⠉⠛⠛⣿⣿⠃⠀⠀⠀⢠⡇⠀⠀⠈⠓⠊⠁⠀⠀⠸⣌⠛⠛⠊⠀⣠⠟⣇⠀⠀⠀⠀⢸⣷⠀⣤⣀⣹⡟⠁⠀⠀⠀⠀ ⣷⣤⣀⣤⣤⠴⠶⣾⣿⣿⡟⠀⠀⢠⠀⠘⡇⠀⠀⠀⢀⣀⡤⣄⡀⠀⠈⠛⣲⡷⢾⣁⡀⢸⠀⠀⠀⡀⣾⡏⢠⣿⡏⠁⠀⠀⠀⠀⠀⠀ ⠛⠿⣿⣿⣿⣷⣾⡿⠿⠋⠀⠀⢆⠘⡄⠀⢷⣶⠤⠚⠉⠀⣀⣀⣹⡄⠀⢼⣁⣀⣀⠀⠉⠚⡓⠀⣸⠟⢹⣧⣼⡋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠙⠛⢧⠀⠀⠀⠀⠘⡄⠱⡄⠈⢧⡉⠒⠋⠉⠀⠀⢽⠛⠒⣾⠁⠀⢠⣍⣱⡾⢃⠀⣿⠠⠚⣷⡄⠹⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⢶⠘⢆⠈⠢⠤⠙⠦⠤⣄⠀⠀⢸⡄⢀⡟⠀⠀⢹⡈⠁⠀⠘⣄⢻⣧⣿⣿⡟⢠⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣱⠢⢤⣀⣠⣴⣿⣶⣦⣬⣿⠋⢹⣶⣶⣿⣙⠒⠒⠻⡈⠢⢌⣉⣀⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠶⡇⠀⠀⠙⠻⢿⣿⣿⣿⣧⠇⠀⢸⣿⣿⠛⠉⠀⠀⠀⠈⠲⣤⣤⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢀⣠⣾⣿⣧⣀⣘⠠⢠⠏⠉⣿⣿⣶⣦⡄⠀⠀⠀⢸⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢿⣿⣿⣿⣿⣿⣉⢉⣿⣿⣿⣿⣿⣿⡉⣹⠓⠤⢄⡾⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⠉⠋⠁⠉⠙⠓⠦⣄⣘⡇⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⠇⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡎⠀⠀⣰⣿⣿⣿⣿⠟⠛⢷⡄⠀⠀⠀⢠⡟⠀⡼⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣤⡤⣄⡀⠀⠀⠀⢰⠃⠀⡼⠀⠀⣰⣿⡏⣯⣿⣿⣆⡀⠀⠉⠂⠀⢠⡟⠀⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠀⢈⡠⣤⢄⠈⣿⡆⢀⣠⡏⣠⠞⠀⠀⣠⡿⡻⠁⠹⣿⣿⣟⠿⢶⣦⣼⣴⠋⠀⠀⣸⠡⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠞⠋⠻⠿⠶⠖⣚⣻⣁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⡈⠉⠉⠙⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢋⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣷⡤⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡧⠀⠀⠀⠀⠈⢿⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠈⢷⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⠟⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠸⡄⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣴⠋⠀⠀⢀⣤⣤⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡼⠋⠁⠀⠀⠙⠳⣤⠀⠀⠀⢳⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣾⣿⣿⣿⡆⠀⣼⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠘⡇⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⢸⣿⣿⣿⣿⡇⢀⡟⠀⠀⠀⠀⠀⠀⡇⢠⣴⣶⣦⡀⠀⠀⠀⢻⡄⠀⠀⢳⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠸⣿⣿⣿⠟⠁⣾⠁⠀⠀⠀⠀⠀⢰⣇⣾⣿⣿⣿⡇⠀⠀⠀⠀⣧⠀⠀⠸⡇⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠾⢥⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣄⣀⠉⠁⠀⣸⠇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⣿⠀⠀⠀⢹⡄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠁⠀⣤⠤⣤⣤⣀⠀⠀⢻⡻⢿⠿⠋⠀⠀⠀⢀⣾⠋⠀⠀⠀⠈⣧⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡞⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣇⠀⠀⠀⠀⠛⢦⣀⡠⠬⠗⠀⠈⠻⠶⣤⣀⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠸⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣠⡾⠓⠲⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢄⣀⣀⡤⣆⡀⠀⠀⠀⠀⣠⣄⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣆⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣼⣻⣃⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣽⣿⡏⠉⠳⡾⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠁⣤⡌⣹⡟⠀⢀⡇⠀⠈⠻⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢦⣰⡏⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡶⡿⣿⣿⡍⠲⢾⣇⠀⠀⢸⠇⡿⠙⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠈⢻⡁⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣷⣥⣾⡿⠃⠀⡎⠉⠓⠲⠿⠶⠷⠶⠖⠚⠋⠙⠓⠲⠶⠦⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠴⠶⠻⡏⣇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⠁⠀⠙⢦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠶⠶⠶⠶⠶⠶⢤⣀⠀⠀⠀⠉⠙⠶⣄⡀⠀⠀⣇⣿⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡟⣿⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠈⠻⣦⠀⣿⠸⡆⠀⠀⠀⠘⣇⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀ ⠀⠀⢀⣾⠀⠈⣿⢹⡀⢀⡼⠉⠙⠳⣶⢤⣄⣀⣀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢠⡀⠀⠀⠀⠘⡇⢸⡄⣷⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⣼⠧⢶⣾⡅⣼⣷⡏⠁⠀⠀⢀⡟⣼⠁⢨⡟⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢹⣆⠀⠀⣰⠇⠀⣷⢹⡄⠀⠀⠀⠈⣧⠀⠀⠀⠀⠘⣇⠀⠀⠀ ⠀⠀⣿⠟⠉⣿⣄⢿⣾⣧⠀⠀⠀⢸⢇⡟⠀⣾⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠹⣦⡴⠟⠀⠀⢹⡾⣇⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢿⠀⠀⠀ ⠀⣸⠇⠀⠀⣿⢻⠈⣿⣧⡀⠀⢠⣯⣾⠁⣼⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⣦⠀⠀⠀⠈⣷⢹⡆⠀⠀⠀⠀⣷⠀⠀⠀⠀⠘⣇⠀⠀ ⠀⣿⠀⠀⠀⠻⣿⣷⣜⢻⡿⢦⣼⣫⣿⠟⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢷⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢿⠀⠀ ⢰⡇⠀⠀⠀⠀⣿⠋⠉⠳⠛⢸⠗⣿⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⣧⠀⠀⠀⢻⡜⣧⠀⠀⠀⠀⢹⡄⠀⠀⠀⢸⡇⠀ ⢸⠇⠀⠀⠀⣼⠃⠀⠀⠀⢰⡏⣸⢿⡇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⡼⣇⠀⠀⠀⠀⢻⡀⠀⠀⠀⢧⠀ ⣿⠀⠀⠀⢀⡏⠀⠀⠀⢠⡟⢰⠇⢸⡄⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⢳⡼⣇⠀⠀⠀⠀⣿⠀⠀⠀⢸⡄ ⢿⡀⠀⠀⢸⡄⠀⢀⣴⠟⣰⠏⠀⠈⣧⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⢳⡼⣆⠀⠀⠀⣸⠀⠀⠀⢸⠇ ⠘⣧⡄⠀⠀⠛⠛⢋⣤⠞⠃⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠈⠳⢤⣄⠀⠀⠀⠀⠀⠀⢀⣤⠜⠃⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⡝⢦⣤⡤⠟⠀⠀⣰⠏⠀ ⠀⠈⠛⠛⠒⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⣦⣄⠀⠀⠀⠀⣀⡬⢿⣗⠒⠒⢒⡿⢯⣄⡀⠀⢀⣀⣠⡴⢿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⣤⡴⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⡤⠴⠒⠛⠋⠉⠀⠉⠉⠉⠉⠁⠀⠀⣹⠀⠀⣾⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠙⠛⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡴⠖⠋⠉⠉⡉⠁⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠉⠓⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⢠⡼⠋⠀⠀⢰⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠎⠁⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⢸⡄⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣦⣀⣀⣸⡅⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣀⣠⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⣇⣀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠙⠶⠶⠤⠼⠷⠶⠶⠶⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⡤⠴⠿⠶⠶⠞⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣠⣤⣤⣶⣚⣋⡉⠉⠉⠉⠙⠓⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⢧⡖⢀⡤⢀⣬⡉⠁⢒⠒⠤⡀⣀⡀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠴⠖⠒⠒⠒⠲⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠻⠶⣤⠏⣷⡔⠀⡠⠊⢀⠄⢈⠝⠒⠢⣄⡙⠳⣄⡀⣠⠴⠚⢋⣁⠤⠔⠒⠊⠉⠉⢫⠉⠳⡉⠑⢖⠚⠭⣷⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠶⠾⣇⡀⠠⢒⣑⣁⣉⣿⠷⢶⣟⣇⣴⣚⣽⣠⢧⢘⡌⢢⠐⡄⠀⢣⠀⠘⡄⠈⣆⠀⢦⠈⣟⠻⢶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠼⠛⠋⠉⠁⣀⡠⠤⠐⡒⡿⠱⢴⡿⠿⠿⣯⣯⠟⡄⢇⠘⠄⠀⢇⠀⠸⡀⠘⣄⣄⡆⠘⠀⣠⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⣀⡠⣴⠒⢏⠀⢇⠀⢦⣽⣇⠀⠀⠈⠐⠤⣀⠉⠛⠿⣼⡄⠘⠀⢸⡿⣄⣁⣤⠿⠹⠦⠖⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢀⡠⡔⠋⢁⠀⠘⡄⠘⡄⠘⣄⣾⣿⣿⣷⣀⠀⠁⡐⠋⠑⢄⠀⠀⠙⢿⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠞⠁⢀⡤⠒⢩⠀⠸⡄⠈⢶⡶⢷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⡔⠉⢀⠑⢄⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠟⣁⡤⠊⢇⠘⣤⣤⢣⠀⢱⣠⣼⣧⣾⣿⣿⣿⣿⣿⣿⣙⣻⣿⣿⢿⣦⣀⣰⣁⡀⠀⠱⡀⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⠵⠞⡅⠸⡀⠈⢆⢀⣻⠻⠚⠉⠀⣰⣿⣿⣿⠿⠛⢻⡟⠀⢹⣿⡿⠻⠛⣿⡏⠻⣿⣀⠞⢁⠈⢆⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠷⠦⠦⣼⠤⠵⠖⠚⠉⠀⠀⠀⠀⢰⡿⠛⠁⠀⠀⠀⡼⠥⠖⠋⣽⡃⠀⢾⣿⠀⠀⠀⠉⠻⣥⡄⡈⢣⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢥⣀⣀⣠⡟⢷⣀⣽⠇⠀⠀⠀⠀⠀⢾⣛⡟⢟⢧⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢀⣠⠟⣻⠁⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠉⠓⠿⢬⣃⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡿⠒⠚⢉⠈⣰⠇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠳⢤⣠⣆⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢀⣠⠴⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠷⠒⠋⠉⡗⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣏⡀⠀⠀⠠⠕⠂⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠉⠉⠒⣷⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⣠⠴⠚⣿⠍⠉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡴⠋⠀⠀⠐⠒⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢠⢬⣉⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣠⡏⠉⠉⠛⠒⠚⠟⠛⠉⠁⣿⠠⠤⣀⣀⠤⠤⢄⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠒⠂⠁⠁⠀⠸⠇⠀⠀⠀⢹⣿⣷⣤⡀⠀⠘⣧⠀⠐⡇⠀⠀⢀⠳⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡒⠋⠉⠉⠑⠀⠀⠀⠀⠉⠁⠀⠀⠀⠘⠆⠀⢱⣶⣫⣥⢺⣿⣿⣧⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠉⠻⣿⠃⠀⠀⠀⠀⢄⠀⠀⠰⠞⠉⠙⠳⣾⡗⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⡇⠀⠄⢿⡄⢀⣀⡠⠤⢄⠀⠀⢀⣀⡀⠤⣤⣿⣇⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣿⠃⣸⣄⣤⣺⣿⣥⣴⣤⣄⡀⠙⡞⠁⠀⢀⣠⠿⢠⠃⢒⠷⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣶⣿⣿⣟⣾⠿⠛⠉⠁⢀⣉⣹⣟⣳⣧⣴⢊⣉⣉⠉⠛⠶⣿⣤⣯⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠤⠊⠁⠀⣠⡴⠋⢩⠋⠉⠷⣤⡉⠑⠀⠈⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣭⣍⣁⠀⠀⠀⢀⠄⠀⠀⠀⡔⣱⠁⠀⢸⠀⠀⠀⠈⢳⠀⢀⠀⠈⢣⡹⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠁⠀⢀⡴⠋⠀⠀⠀⡜⠀⡏⠀⠀⠘⠀⠀⠀⠀⠀⢣⠈⢃⠀⠀⠀⠈⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠋⠂⠀⢠⡿⠁⠀⠀⠀⠜⠀⢰⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⡆⠈⠆⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣄⣿⠿⠟⠡⠃⠀⣠⡏⠀⠀⢀⡤⠀⠀⡠⠃⣠⠇⠀⠀⡆⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⣀⠤⠴⡟⠀⠀⢐⡿⢁⠶⠚⠑⢸⢿⡄⠀⠀⠃⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣨⠋⠀⢀⡼⠀⣠⠴⠋⡰⠃⠀⠀⣰⣃⠼⣷⠂⠀⠸⡀⠀⠀⢠⡤⣼⡆⠀⢸⠀⠀⠈⣿⢦⣤⠤⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠇⠠⠴⠯⠤⠬⢥⣴⠞⠁⠀⢰⠞⠁⠀⣀⣹⣷⡀⠀⢧⠀⢠⣾⣷⠃⠹⡀⢸⠀⢠⡀⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠾⠃⣀⠄⠀⢀⡴⠁⢸⠁⠀⠀⠀⣯⣴⣾⣿⣿⣯⡹⡟⢄⠘⣷⣾⢻⣿⣶⣦⣷⡈⣆⠀⢹⠒⢾⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡴⠊⠁⠀⠀⠀⢀⣠⡼⠁⢀⣿⡄⠀⠀⢀⣿⣻⣿⠿⣿⠏⠁⠘⣦⡳⣼⣽⣿⣿⡿⢙⣿⣧⠈⢢⣼⡳⡄⠳⡀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠛⠒⠒⠒⠲⠿⣭⠝⢁⣴⠋⠘⣷⡀⠀⠸⣧⣿⠋⠀⠉⠀⠀⠀⣿⡿⢿⡏⠉⠘⠑⢺⣿⣿⣆⠀⠱⡿⡜⣦⣬⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⢉⡏⠀⠀⣹⣷⠀⢰⡟⠛⢯⣀⠀⠀⣠⡾⠋⠀⠀⠻⣄⡀⢀⣿⣿⡟⠘⣆⠀⣷⠘⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠶⣶⣿⣿⣿⠀⢸⣷⣄⠀⠉⠉⠉⠁⠀⢀⣀⠀⠀⠀⢉⣽⣿⡄⢡⣀⣿⡄⢻⠄⠨⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⡆⢾⠘⣿⣗⠦⣄⡀⠀⠀⠉⠁⠀⣀⣴⣯⣰⠋⢱⠀⠙⠛⠀⡼⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣸⣦⡙⣿⣷⣤⣭⣵⣦⣤⣴⣿⣿⣏⡀⠙⠂⠀⢣⣀⠀⠀⡇⠀⠀⡇⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡿⢻⡽⠿⢶⡄⠙⠿⣷⣷⣤⣀⡇⠻⣧⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣾⠀⢀⡈⠉⠻⣿⣿⣯⣽⣿⣿⣿⡃⠀⠀⠀⢹⣿⣿⠿⡆⠁⠉⣙⣶⣿⡀⠀⢸⣿⣿⣿⣷⣄⡈⠙⢦⡀⠀ ⠀⠀⠀⠀⢸⣅⡸⢿⡟⠋⢸⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⡿⣧⣀⠀⢀⣼⣿⣿⣿⠀⠀⠀⡨⣏⠿⣧⣀⢸⣿⣼⡇⠹⣿⣿⣶⢤⣱⡄ ⠀⠀⢀⣤⣎⣼⣧⣸⣧⢀⡏⠀⠀⠀⠀⠀⠀⠀⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⡇⠉⠳⣼⠿⢿⡇⣇⣷⠀⠙⣎⢻⣄⠙⢿ ⠠⠐⠛⠁⣧⡟⠉⢻⣿⣾⠀⠈⠁⠒⠒⠂⢀⠜⠁⠀⣿⣿⣿⢿⣿⠀⣽⡍⠛⡛⠛⡟⠙⢆⢣⠀⠀⠀⠙⢿⣟⣻⣹⡄⠂⣸⣟⠿⣧⡀ ⠀⠀⠀⢰⣃⡠⠴⣾⣿⢟⡧⠀⠀⠀⣠⡶⠃⠀⣀⠀⠈⣧⡀⠀⠀⢠⠁⢿⣦⡠⣴⠧⠄⢈⣿⠉⠐⠀⠀⢻⣿⣿⡟⠿⠿⠷⠋⠀⢹⣿

⢀⠊⠀⢀⡇⣸⠃⠀⡦⡈⠀⢀⡆⢠⣿⣿⣿⡄⠀⣿⢿⡉⠻⣷⢡⠀⠀⠁⠀⠀ ⠀⠄⠀⣼⠀⠏⠀⢰⠳⠁⠀⡼⠃⣺⣿⡟⠛⣧⠀⡏⠣⡑⡀⠡⣯⠱⡶⡄⢀⡀ ⠌⠀⣨⠞⠎⠀⠠⣣⡁⠀⡐⡼⢰⠇⣼⠁⣶⠙⢠⠀⠀⣸⢴⠠⡇⢱⣿⠃⠸⡉ ⠀⠈⠀⡀⠌⠃⣰⡟⡠⠊⠔⢸⣴⣸⠇⢠⣿⠇⣆⡤⠊⢠⣼⡄⠳⡀⢿⡄⠀⠡ ⣀⣈⣁⢠⣤⢞⢏⠔⠁⠈⣠⢾⣟⡜⢀⡞⡜⡘⢁⣦⣶⠛⣟⣧⣤⢕⢌⢛⠶⠖ ⡉⠓⠐⠚⠒⠋⠀⠀⡠⢞⣗⣽⡱⢁⠞⠰⡑⠹⠛⣾⡿⠄⠁⣿⡏⡄⣷⣄⡈⠐ ⠘⠓⡶⡒⣒⣶⣱⡜⢾⣿⣇⡩⢻⡊⣰⠏⠀⠀⠀⠀⠀⠀⠔⢹⠃⡡⣿⠯⠍⠀ ⡆⠰⠀⡙⣼⢊⠀⣁⢠⠀⣔⠕⢁⠜⠁⠀⠀⠀⠀⠀⠀⠢⠶⢵⣶⠛⣯⠙⢧⣊ ⣠⡇⠀⣟⣹⠁⢀⠤⠼⠚⠁⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣎⢂⠘⣫⠲⠌ ⡸⡇⠀⠑⢽⠀⠈⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣄⠑⠁⢈⢷⡀ ⣴⡻⣦⡀⠀⠄⠀⠈⠐⠀⠠⢀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠈⢾⡷⡙⢧⠪⢢⡁⢪ ⢳⡇⣿⣿⢂⠈⠁⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⢀⡴⡇⠀⠸⠟⢖⡌⢷⣵⡙⡆ ⢸⡇⢿⡇⢂⠹⣦⣄⡀⠀⠀⠀⠀⠈⣷⣶⣤⡴⠟⢁⠇⠀⢸⠀⠀⢻⢸⠟⠳⡈ ⢸⠇⠈⣷⠀⠗⡾⠻⠉⠂⠀⠀⠀⠀⢄⠈⠁⠀⠀⠌⠀⠀⢸⠀⠀⣸⡌⠀⠀⠱ ⡆⣟⡀⢻⣻⠀⠈⢢⡁⠠⠀⠀⠀⡬⣀⠁⢒⣤⣸⣤⡀⠀⢸⠀⠈⢩⡗⠁⠂⠀

⠀⠀⠀⠀⢀⣴⣶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠏⠀⣠⡾⠿⠿⠟⠛⠛⠛⠛⠛⠛⠷⣶⣌⢻⣦⡀⠀⠀ ⠀⠀⢀⣾⠏⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠹⣿⣄⠀ ⠀⢠⣾⠋⢠⣾⠋⣠⣤⠄⣤⣤⣄⠀⣀⣀⡀⠀⣤⣤⡀⢻⣇⠘⢿⣧ ⣰⡿⠁⢰⡿⠁⠀⢿⣄⠀⢸⡏⠁⢸⡏⠙⣿⢠⣿⣉⣿⠆⣿⡆⢸⣿ ⣿⡇⠀⢻⣧⠀⠀⢠⣿⠇⢸⡇⠀⠸⣧⣼⠟⢸⡏⠉⠉⢠⡿⠀⣸⡿ ⠈⠻⣦⡀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣠⡿⠁⣰⣿⠃ ⠀⠀⠈⢻⣦⡈⠛⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⣴⡿⠁⠀ ⠀⠀⠀⠀⠙⠿⣦⣀⠈⠉⠙⠛⠛⠶⠶⠶⠶⠾⠿⠋⣠⣾⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⣿⢿⡿⣿⣿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣲⢭⣒⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠮⣝⡮⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢍⡒⢭⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠶⡭⣗⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⣠⠔⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠢⢄⡇⢠ ⠀⡼⠇⠀⠀⠀⢀⠨⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠐⢧⣸ ⠰⣅⠀⠀⢀⡠⢧⡀⠀⠈⠂⠀⢀⣀⠠⠤⠤⠄⣀⡀⠀⠐⠋⠀⣸⣀⠀⢠⡟⠁ ⠀⠙⢷⣀⠡⠄⠀⠀⢀⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠤⠔⠋⠀⠀ ⠀⠀⠀⢣⡀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀ ⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⢰⠖⠒⠒⠶⠒⠒⢒⡆⠀⠀⣶⠒⠒⠶⠒⠂⠠⡤⢸⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠁⠒⠀⠀⠀⠒⠁⠀⠀⠀⠀⠑⠂⠤⠤⠄⠊⠁⣸⠀⠀⠀ ⠀⠀⠀⠼⠓⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠙⣆⠀⠀ ⠀⠀⠀⠀⠤⠚⠢⡄⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⡄⠀⠀⢳⡀ ⠀⠀⠀⠀⠀⢀⡠⢄⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠒⢄⠀⠀⠀⠀⣠⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⡇⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠋⠁⠀⠀⠀⠀⠈⢉⡉⠁⠀⠀⠀⠀⠸

⠀⢀⣀⣀⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡘⠀⡃⠀⠀⢠⣶⣿⣿⣿⣷⣶⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⢣⠀⠀⠀⡅⠀⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⢦⡇⠀⠤⡇⢠⠀⣠⣾⣿⡿⠛⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⢹⡄⠀⠀⢸⠀⣿⣿⡏⣤⣄⣀⢀⣤⣤⡦⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⢱⠰⠀⠘⠀⠙⢿⢀⣈⣉⡉⠀⢉⢍⣀⣀⠀⣸⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠘⣼⠀⡄⠀⠀⡨⠀⠀⠉⣛⣁⠋⠁⠀⠀⢼⣿⠋⠙⣿⣿⠀⠀⠀⠀ ⡏⠉⠁⢣⠀⡇⠀⡜⠀⠀⠀⠀⠐⠛⣀⠤⠀⢤⠀⠁⠀⢠⣿⣿⠀⠀⠀⠀ ⠈⠢⠀⠸⠀⡇⠀⠱⡀⠀⢍⢋⠉⢹⠀⠀⣆⠜⠀⣀⣶⣿⠿⠃⠀⠀⠀⠀ ⠀⠀⠀⠈⠆⠀⡤⠖⠓⢤⢀⣉⠐⠒⠃⢉⣀⠀⠀⡁⡼⡂⠒⢒⠖⢄⠀⠀ ⠀⠀⠀⣸⢠⡜⠀⡄⠀⠘⡸⣼⠢⡀⠀⠀⠀⣀⢔⡿⡱⠁⢠⠃⠀⠘⡆⠀ ⠀⢀⣰⠁⢸⠁⠀⢁⠀⠀⠡⡇⠀⠀⠈⠉⠁⠀⢸⠔⠁⢀⠇⠀⠀⠀⢇⠀ ⣏⣹⢸⠀⢸⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⠀⠀⠀⠀⢸⠀ ⠀⢹⠘⠀⠈⠀⠀⢠⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠈⡀ ⠀⠘⠀⠀⠇⠀⠀⡸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡃

⠾⣿⠁⠒⣊⡉⠉⠀⠤⠐⠒⠁⢀⣴⣾⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⣀⠠⠔⣺⣿⣿⣿⠿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⢠⠀⠀⠀⠀⠀⢿⣿⠏⡀⠄⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠫⠂⠀⠀⠀⠀⠈⡏⣾⠀⠀⢰⠀⡔⠁⠈⢢⠀⠈⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀ ⠉⢀⠀⠀⠀⠀⢀⠔⠃⢄⠀⣤⠛⢸⠃⠀⠀⡘⠀⣠⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠉⠒⢄⠰⠁⠀⠀⠀⠉⠿⠇⠈⠂⠤⠐⠁⢸⣿⡟⠋⠛⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⣿⣿⣿⠇⠐⠀ ⠀⠄⠂⠉⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣤⣾⣿⣿⣛⣁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠁⠈⠉⠂⠀⢀⡀⡄⠀⡿⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠤⠘⢇⢲⠒⠒⠒⠛⢁⠔⠁⢀⠏⡸⠹⢭⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⢁⠊⡘⡌⡜⢄⣐⣒⣈⣁⠠⡔⢁⡔⡡⠃⠀⢀⠝⠲⢄⠀⠀⠀ ⠀⠀⠀⢀⠎⠀⠆⠀⡇⡟⢀⠤⢆⡄⠀⠀⣜⠴⡫⠞⠀⠀⡔⠁⠀⠀⠀⠑⡄⠀ ⠀⠀⠀⡞⠀⡸⠀⠀⢡⡡⠃⠀⠀⠙⣆⣰⡡⠊⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡀ ⠀⠀⢠⠁⢀⡇⠀⠀⢸⠀⠀⠀⠀⠁⠒⠊⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⣶⣶⣶⣶⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡴⠛⢉⣾⣾⣿⣿⣿⣿⣿⣿⣷⣦⣉⠛⢶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⠻⣦⡀⠀⠀⠀ ⠀⠀⢀⡾⠁⠀⠀⢰⣿⣿⣿⣭⣙⠙⠿⣿⡿⢿⣿⣿⣿⣿⣿⡚⣤⣈⢳⡄⠀⠀ ⠀⢠⡟⠀⠀⠀⠀⣾⣿⣾⣿⣿⣿⣿⣷⣱⣴⣤⣣⣿⣿⣿⣿⠄⢹⡟⣆⠹⡄⠀ ⠀⡾⠀⠀⠀⠀⢸⣿⢿⣽⡿⠙⠻⢿⣻⣿⣿⣿⣿⣿⣿⣿⠟⠒⣾⣷⣿⡆⢻⠀ ⢰⡇⠀⠀⠀⠀⢸⣿⡠⠆⠀⠀⠐⢎⠛⢻⣿⣿⣿⣿⣿⡟⠀⣰⢿⠿⣿⡇⠸⡇ ⢸⡇⠀⠀⠀⠀⣾⣿⡆⠈⠁⠀⠀⢤⢿⣿⣿⣿⣦⣈⡙⢣⣼⣿⣷⣷⣼⡇⠀⡇ ⠸⡇⠀⠀⠀⢀⣿⣿⣷⣻⠓⡤⢀⣼⡌⡞⣿⣟⠉⢳⣮⣍⡙⢿⡿⢿⣿⣷⢠⡇ ⠀⢷⠀⠀⠀⢼⣿⣿⣿⣯⣭⣤⣾⣜⢮⡇⡎⢿⣷⣿⣿⣿⣿⣷⣴⠊⣿⣿⣼⠁ ⠀⠘⣧⠀⢀⣸⣿⣿⣿⣿⣿⡟⡔⢹⣿⣿⡽⡄⠈⠻⣿⣿⣿⣿⣷⣅⣻⣿⠇⠀ ⠀⠀⠘⢧⣿⣿⣿⣿⣿⣿⣿⣴⠁⣿⣿⣿⡇⠈⠦⠀⠀⢉⠻⢿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠻⣿⣿⣿⢿⣿⣿⣿⣼⢳⣿⣿⣿⣆⠀⠀⠀⠀⢂⢀⣵⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣾⡜⣿⡿⣻⣿⣿⣿⣿⡿⡱⡀⢀⣠⠼⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠿⠿⠿⠧⠿⠷⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣴⣾⣿⡿⢿⣿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣷⡀ ⠀⡠⣵⠏⠃⠉⠉⠀⠌⠉⢡⣥⣈⡙⠛⣿⣿⣿⣿⣇⢸⠒⢈⠠⡙⢿⣿⣿⣿⣷ ⢠⡿⣕⡒⠚⠉⠁⣀⣀⠀⠀⣈⠙⠿⣷⢾⣿⣿⡿⠟⡀⠢⣃⣡⣈⠈⢿⣿⣿⣿ ⡜⠣⡐⡖⢖⣓⣤⣯⠭⠭⢭⣶⡿⠦⣌⠻⣿⣿⣿⣵⣉⡄⠀⠙⢿⠀⢸⣿⣿⣿ ⠀⠀⢜⣓⣂⣬⣵⣛⡿⣭⠟⠳⣦⣬⣴⠟⠻⢦⠉⠙⢷⣄⡑⢄⠀⠀⠞⢿⣿⣿ ⠀⢀⠐⣻⠤⢀⠀⠀⢠⠇⢀⣾⣏⡥⠁⠀⠀⠀⠱⠀⠘⠟⠳⣍⠐⠒⠚⠫⠙⢿ ⡄⢂⡄⠣⡀⠀⠃⣀⣾⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠻⢦⣤⣀⣱⡃ ⣟⢄⢏⢦⣌⣢⣘⠉⢻⠐⠙⠅⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢍⠉⣿ ⣿⣗⡤⡀⠛⢕⠠⢈⠘⣦⣶⣢⡾⠃⠀⠀⠀⠀⠀⢀⣀⣤⡴⠤⣄⠀⠀⠀⠁⢹ ⣿⣟⣦⡈⢷⣶⡷⠦⢤⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣾⣿⡧⠄⣥⠃⠀⠀⠀⢸ ⢷⠹⣿⣷⣤⣿⣿⣵⣼⣻⣿⡯⡖⠦⠀⠀⠀⠀⠘⠇⡟⣿⠇⠀⢿⣀⠀⠀⠀⢸ ⠚⠶⠾⢿⣟⡿⣾⣿⣿⣧⣿⣙⠈⠄⠀⠀⠀⠀⠀⢠⣴⠿⢷⣼⠣⠚⠀⠀⠀⢸ ⢀⣀⣀⣨⡿⢴⡽⣿⣿⣿⣿⣿⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⡀⠀⣠⣴⡏ ⠀⠀⠀⠀⠀⠉⠻⣮⣿⣿⣿⣿⡿⣿⣿⣿⣥⣀⣀⣀⣀⣀⣀⣠⣤⡾⣟⠿⣻⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠖⢻⣿⡇⠺⣿⣷⣿⡻⢿⣿⣟⡿⠿⠟⠛⠛⠛⠛⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠒⠚⠛⠛⠛⠛⠛⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⣀⣀⠀⠀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣻⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀ ⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠀⠀⠀⠀⠀⠀⡀⠀⠉⠙⠳⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠈⠙⢷⡄ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⡟⠲⢤⡴⠋⠛⡖⠲⢤⣤⡼⠋⠉⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⡿⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠜⠉⠛⠊⠉⠸⠏⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣾⡁⠀⣀⠴⢚⡇⠀⠀⠀⠀⠀⣸⠏ ⠈⣿⡀⠀⠀⠀⣀⣀⣀⣀⠀⡾⠁⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠀⠀⠀⢀⣼⠋⠉⠉⠀⢀⣾⣁⡠⠖⠛⡇⢠⡟⠀ ⠀⠘⣷⣀⡴⠋⠁⠀⠀⠈⠙⠳⠦⠒⠋⣼⡧⠶⠲⣦⠀⠀⠀⠀⠀⠀⣻⠍⢀⡟⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢳⡿⠀⠀ ⠀⠀⠈⣿⠁⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠙⣧⡀⢀⡿⠀⠀⢀⣠⡴⠚⠁⣠⠋⠀⠀⠀⠀⠀⠈⠙⠓⠶⣤⣀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀ ⠀⠀⠀⢿⡆⠀⠀⠙⢿⡀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠛⢳⡶⣤⣄⣰⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⠦⣄⣀⣀⣉⣉⡴⠾⠷⠶⡤⠤⠶⠶⠶⠖⠒⠿⢭⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠒⠶⣾⡁⢀⣠⡯⢤⣄⡈⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢀⠈⠙⠳⠤⣄⣀⠀⠀⣾⠁⢺⠀⠀⠀⠙⣿⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣄⠀⠀⠀⠈⢳⡄⠀⠀⠀⠉⠙⢻⠇⠀⢸⣧⣄⣀⣴⡋⠉⠉⠙⠻⣯⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠙⣦⣀⠀⠀⠀⠀⠀⠀⣼⢡⣟⠁⠉⠙⢷⣀⣀⡴⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠹⡏⠙⠒⠶⢿⡄⣸⠃⠈⢻⡦⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣶⠻⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢹⣇⠀⣰⡟⠑⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡋⠋⠛⢷⣞⣿⠾⠃⠀⠀⠀⣿⡷⢤⣀⡀⠀⠀⠀⢀⣀⣼⡗⡀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣻⣦⣄⡀⠉⠀⠀⠀⠀⠀⠀⠙⢳⣤⡌⠉⠉⠉⠉⠉⢁⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣾⠉⠉⠉⠉⠑⠀⠀⠀⠀⠀⠀⢠⣾⡉⡻⡄⠀⠀⠀⢀⣾⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⠤⠤⢤⣴⠖⠂⠀⠀⣠⣾⡇⠀⠀⢉⣽⢻⣤⣴⣾⡿⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⠀⠀⣠⠞⠁⣈⡿⡖⠒⠋⠁⠀⣿⣿⣗⠾⠂⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣈⡷⠤⠔⠚⠛⠻⠞⠁⠀⠀⠀⠀⢀⣤⠟⠉⠒⢁⣴⣋⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠚⠋⠛⠒⠦⣎⡉⠉⠉⠉⠉⠉⠉⠉⠓⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠤⣄⣀⣀⣀⠀⠀⣀⣀⣀⣀⠤⠾⣏⣀⣀⣀⣀⣀⣠⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢈⠉⠉⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀ ⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⣀⣀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀ ⠈⡍⠳⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣘⡲⣀⣦⡒⠂⠀⠀⠐⡀⠀⠀⠀⠀ ⠀⢹⡢⢝⡏⠢⡀⠀⠀⠀⠀⢠⠿⠯⠝⡿⠓⢲⢹⡄⠀⠀⠀⡇⠀⢀⣀⠀ ⠀⠘⡝⠳⡸⡄⡗⡀⠀⠀⠀⡇⠀⠀⠹⣅⢰⣋⠾⢾⠤⢀⣀⠇⡀⠁⡨⠀ ⠀⠀⠡⡀⠀⠙⡅⣷⣂⠀⠀⠘⡒⠤⠄⠉⢉⠱⠀⠀⢤⢤⡝⠰⠨⠟⠹⣠ ⠀⠀⠀⠘⠷⠒⢿⡏⠀⠥⢤⠀⠘⠢⢉⣛⣵⣀⣄⣒⣥⣚⣀⣰⠀⠲⣤⡿ ⠀⠀⠀⠀⠀⠣⣶⣿⣏⢀⠘⠒⠀⠀⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣡⠃ ⠀⠀⠀⠀⢰⠁⡀⡣⣟⣦⡤⠤⠤⠀⠒⡂⠀⠀⠀⠓⢒⡤⡈⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠸⠠⠃⠙⠄⠀⠀⠀⠀⣇⣀⣀⡀⠄⠂⠈⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠶⢶⣤⠀⠀⠀⠀⠀⠀⢀⣥⣀⠀⢰⠄⠀⣠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣶⣭⢧⡿⠀⠀⠀⠀⡀⠤⠲⣀⡉⢿⠁⠀⠰⡥⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣯⣿⣻⣾⡑⠀⢠⠋⠀⠀⢀⠔⠃⠉⠑⠂⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⣠⣜⣿⣿⣅⣀⣈⡇⢾⢧⡄⣀⣰⡀⠀⠀⠀⠀⢀⣀⠤⠞⠀⠀⠀⠀ ⠀⠀⠉⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠉⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⢤⣤⣤⣤⣤⠤⠤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⠈⠻⡖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠿⣖⡒⠒⢲⡒⠒⠦⡄⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣄⠀⠱⣜⣿⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣉⡿⠛⡛⠻⣷⡄⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡙⠦⢜⣿⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠛⢧⡞⢻⡿⠚⠉⠈⡇⢸⣷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⡀⠀⠀ ⠀⠀⢸⡟⢿⣦⣌⢣⡀⠀⣷⡀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⢻⣿⠁⠀⣴⡶⠃⣼⣏⣧⠀⠀⠀⠀⠀⣿⠀⢀⡴⠁⠀⣹⠀⠀ ⠀⠀⠈⢇⠀⠉⠻⢝⣳⣄⠇⢳⠠⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠻⣖⣒⣫⣴⠾⠋⠉⠿⠓⠛⠒⢦⣼⠇⢠⠎⣀⣠⣔⠋⠀⠀ ⠀⠀⠀⠘⡄⠀⠀⠀⠉⢿⡀⢸⣸⠇⠀⠀⠀⠀⠀⢿⠶⢤⠤⠄⠀⠀⠉⠀⢀⠦⠀⠀⠀⣀⣀⣀⣨⡏⢀⠏⢠⡿⠟⠦⣷⢤⠀ ⠀⠀⠀⠀⠈⢒⢠⣤⣀⣈⣷⣾⠟⠚⢳⠀⠀⠀⠀⠈⢧⡈⠓⠠⣤⣤⡴⣞⠁⠀⠀⢀⣀⡼⠋⣠⠟⠀⢸⡄⠀⢀⡄⠀⢈⣤⠇ ⠀⠀⠀⠀⠀⠀⠙⠛⢉⠟⠻⣿⡀⠀⢘⠒⠒⣦⠀⠀⠀⠉⠓⠦⣄⣉⣓⣚⣀⣀⣦⣤⣤⣶⣚⣁⣀⣀⣘⣇⠀⠀⠛⣶⡿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢯⣀⣤⣿⣿⣽⠁⠀⠀⠿⠠⠤⠂⠒⠂⠉⠉⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠇⢠⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⠛⢻⠙⣿⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠴⠷⠶⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⡴⢊⡷⣿⣻⣦⣠⡤⠤⠤⠤⠖⠒⠒⠛⡇⠀⠀⠀⠀⠀⠈⠉⠉⢫⣭⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠓⠊⢠⠊⠀⡞⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡴⠃⠙⣌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠚⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡷⠄⣀⣀⡠⠤⠒⠉⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⢠⣤⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡟⢉⡼⢦⡌⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠻⠿⣶⣤⣤⠞⠁⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣮⣷⡾⢥⣾⡝⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠚⢧⣀⠀⠀⢳⡇⠀⠀⠀⠀⢿⡤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠛⣿⠿⠾⣿⣿⣳⠄⠀⠀⢀⡼⠉⠀⠀⠀⠀⠀⣈⠽⠒⠚⠛⠦⢄⣀⠀⠀⠈⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣬⣿⣿⣶⣿⠿⠯⠣⣀⠀⠀⢸⡁⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠀⣤⣾⣿⣿⣿⣿⡀⠀⠀⠀⠈⡏⣿⣾⣷⣤⣀⣀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠺⠿⠿⣭⣿⣿⢿⣿⣿⣿⡿⠟⠁⠈⠉⠉⠉⠉⠉⠉⠙⠛⠳⠤⠤⠤⠤⠤⠤⠤⠖⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠒⠒⠠⡀⠀ ⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⢠⠀⠀⠈⢢ ⠀⠀⠀⠀⢀⠂⠀⠀⠀⠉⠐⠊⠕⡢⠄⠸ ⠀⠀⠀⠀⡾⠄⠤⡤⠄⢲⡒⢲⠶⣤⣕⡄ ⠀⢠⣴⠶⢞⢱⣢⡌⠀⠘⠧⠘⠒⠁⢲⠁ ⠸⣿⣿⣟⣀⠱⠶⢠⣀⠠⢠⠤⠶⣒⠎⠀ ⢀⠄⠏⡹⡈⠒⠚⡲⡀⣌⡿⠊⠐⡱⠀⠀ ⠸⡳⣂⢘⢷⣆⣧⡣⠃⠳⡸⢀⠏⠀⠀⠀ ⠀⢈⡑⢺⠀⡉⠐⢒⣼⣄⠀⠁⠀⠀⠀⠀ ⡌⠀⠐⠛⠀⡉⠉⠙⡏⠀⢱⠀⣀⠀⠀⠀ ⠰⡀⠀⠉⠉⠡⣰⠁⠁⠀⠉⠀⠀⠈⢢⠀ ⠀⠈⠢⠄⠀⠴⠃⠉⠒⠒⠀⠤⠤⠤⠊⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠞⠕⢩⠀⠿⠷⣄⣀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠤⡔⠁⢐⠘⠀⠇⠧⡈⢗⡾⢃⠃⠙⡀⠀⠀⠀⠀⠀⢠⠤⡀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠉⠸⠄⣀⣧⣚⠋⠀⡀⢰⣀⠁⠀⠀⠀⠀⠀⡸⠀⠀⡄⠀⠀⠀ ⠀⣰⠆⠖⠰⠄⠀⡆⠀⠀⠠⢈⣀⣨⠋⠀⠻⠀⠀⠀⠀⢀⣰⠄⠀⠀⠀⠀⠀⠀ ⠀⢇⡁⠀⠀⠀⠁⣤⠈⠠⠄⠀⠁⠀⠀⠀⠀⠁⠎⠀⠀⠀⠘⠟⠆⠀⠎⠀⠀⠀ ⠀⠈⠃⠀⠀⠀⠀⠀⠢⡄⡀⠀⠀⣀⠀⠀⣀⡜⠀⠀⠀⢸⠂⠈⠂⠌⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⡜⢡⠠⠀⠀⠀⠀⡞⠀⠀⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠠⣰⠀⠈⠀⢂⠀⠀⠀⠇⠄⠈⠤⢠⡀⣀⠠⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣈⣿⠀⠀⠀⠀⠀⢀⠌⢄⠀⠀⠀⠀⠀⠀⡠⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⠀⠠⠉⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠿⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⡿⠂⠀⣠⣶⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣷⣤⡀⠀⢸⣆⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠘⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢀⡀⡀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⠟⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠀⠀⠀⠉⠛⠋⠉⠁⠀⠀⠀⢠⣾⠁⣿⣆⠀⠀⠀⠀⠉⠉⠛⠉⠁⠀⠀⢰⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣀⣀⡀⣿⡼⣄⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⣿⣿⡀⣿⣿⡇⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⣜⣽⠃⣀⣀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⠛⠛⠛⣿⣌⠻⢿⣽⣟⣻⣭⣿⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣮⣽⣟⣿⣥⠿⢫⣾⠟⠛⠙⢿⣿⡄⠀⠀⠀ ⠀⣀⣼⣿⠏⠀⠀⠀⠈⢻⣷⣄⠉⠉⠉⠉⣿⠀⢸⠇⠐⣿⠀⠀⣴⡄⠀⢰⠆⠈⢿⠀⣼⠉⠉⠉⠉⢀⣴⣿⠋⠀⠀⠀⠈⣿⣿⣄⠀⠀ ⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⢸⣷⣸⠀⠀⡼⠀⠀⣿⠁⠀⢸⡄⠀⢸⣠⡿⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠈⠙⢻⣿⡆ ⢿⣷⡐⢤⣀⣀⣀⣀⣀⡀⠀⠀⠉⠻⣷⣦⣈⠻⣿⣧⣀⣇⠀⠀⣿⠀⠀⢸⣇⣠⣾⡿⢁⣠⣶⠿⠋⠁⠀⠀⣀⣀⣀⣀⣀⣀⢤⣸⣿⠃ ⠈⠙⠿⠿⠶⠶⢿⣷⣶⣬⣝⡲⢤⣀⠀⠉⠻⢿⣦⣝⡛⠻⠿⠿⠿⠿⠿⠿⠛⣋⣥⡾⠟⠋⠀⢀⣠⠴⣚⣭⣴⣾⣿⠷⠶⠿⠿⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣬⣗⡦⣄⡀⠈⠙⠻⣶⣤⣀⠀⠀⣠⣴⠾⠛⠉⠀⣀⡤⣖⣽⣵⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣾⣭⣒⢤⣀⠀⢉⣿⡷⠟⠋⠁⠀⣠⣴⣾⣽⣾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣷⣾⡿⠛⠉⠀⢀⡠⣶⣿⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⣀⣴⣾⣷⡿⠟⠋⠉⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠶⠟⠛⠉⠀⠀⠀⣠⣼⣿⠿⠛⠻⣿⣦⣄⡀⠀⠀⠈⠙⠻⠷⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠋⠉⠀⠀⠀⠀⢀⣠⣴⡿⠟⠋⠁⠀⠀⠀⠀⠙⠛⢿⣷⣤⣀⠀⠀⠀⠀⠈⠉⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⡄⠀⠀⠀⢀⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⡀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⣸⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⠀⠀⣄⡀⠀⣀⣀⠀⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠢⢵⠐⡄⢰⠀⣤⠈⠆⠔⢸⡄⢘⠀⡧⢤⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣼⣦⣤⣾⣤⣷⣬⣦⣿⣴⣧⣼⣤⣇⠈⠀⠓⠸⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣾⣿⣿⣿⣿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⡛⠳⣿⠉⣿⠉⡍⢻⡍⢻⡏⣯⠙⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣍⣛⣃⣼⣀⣿⣠⣇⣸⣇⣸⡇⣛⣁⣿⣿⡿⠀⠀⢀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷⣿⣿⣿⢿⡥⠖⠋⠉⠉⠀⠀⠀⠀⠉⠉⠓⠢⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠞⠛⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⣉⣟⠓⢶⣦⣤⣤⣄⠀⠀⠈⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡿⠿⠛⠋⠀⣉⣉⡉⠙⠻⣦⣀⣀⣈⠈⠙⠛⠛⠒⠲⣦⠤⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣋⣉⣭⠿⢿⣾⣯⡤⠼⠿⣿⡷⢀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⠶⠦⣤⣄⣀⣀⡀⠀⠠⡄⢸⣿⣞⣉⣀⣀⣤⣼⣿⡷⢤⣤⣴⣿⡷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡤⠐⠋⠁⠈⠉⠙⠋⠀⠘⠋⠉⠀⠈⠙⠉⢉⣀⣙⣶⣤⣤⣤⣤⠀⠀⠀⠀⣠⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠛⠋⠉⠁⠀⠀⢀⡼⠋⠀⢀⣠⡾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀�