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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣴⡟⣲⡙⢮⣱⢣⡝⣜⢣⢞⡹⢎⡝⢮⡹⣜⢣⢎⡗⢮⣙⢦⠻⣔⡣⣝⡹⢎⡳⣜⠲⣍⠮⣝⢲⢣⢏⡵⢪⠵⡳⢬⣛⡜⣣⠳⣍⡳⡹⣌⢏⢮⡱⡝⢮⡙⢮⣱⢫⡜⣱⢎⡳⣜⢣⣎⢳⡹⡜⢦⡝⣜⡣⡝⣦⡙⢧⡚⡼⣘⡎⢶⡹⣻⣯⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡷⡟⢦⡝⢦⡝⣣⢎⡳⡜⣎⠳⣎⠵⣫⡜⣣⠳⣬⢓⠮⣜⢣⠞⣬⡓⢮⠵⣪⢕⡫⢖⡭⣓⢮⡹⣌⢧⣋⡞⣜⢣⢏⡵⢳⡜⡼⣡⢟⡲⣱⢣⢏⡞⢦⢳⡙⢮⣙⠶⣡⣓⠮⣕⢮⡱⢎⡳⢬⣣⢳⡙⡮⣜⢲⡹⡜⢦⣙⢧⡙⢶⡩⢞⡥⢳⡱⣚⢷⣜⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣷⢟⣱⢹⣆⡛⢦⡝⢦⣋⠶⡹⣌⠷⣬⢳⡱⢎⡵⣋⢶⣩⢛⡬⢣⠟⣦⢹⢣⣛⠴⣫⣜⢣⢞⡱⣎⠵⣚⢦⠳⣜⢎⡳⢮⡜⣣⢞⡱⢣⢮⡱⢣⢏⡞⣜⢣⢇⣏⠳⣬⢛⡴⣩⠞⣜⡲⢭⠳⣍⡳⣌⢧⡹⣱⢎⢧⠳⣍⡳⢎⠶⣩⢧⣙⠮⣜⢣⡳⣍⢮⡹⢳⣞⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⡾⢏⡞⣬⠳⣬⡙⢮⡜⣣⢎⠷⡹⣌⢳⡬⢣⡝⣎⠶⣩⠶⣡⢏⡼⣍⠞⣦⢋⡶⣍⢞⡱⢬⡓⢮⡕⣎⡳⣍⢮⡓⣎⠮⣕⡣⢞⡱⣎⠵⣋⠶⣩⣓⠮⡼⣌⡳⢎⣜⠳⣬⢓⢮⣱⢫⡜⣱⢋⠷⣌⡳⣜⢲⢣⡓⠾⣌⠷⣡⢟⡬⣛⡴⢣⣎⠳⣎⢧⠳⡜⢦⡝⣣⢞⣷⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣿⢯⣙⠮⣜⠶⣙⠦⣝⡣⢞⡱⢮⡹⡱⢎⠷⣘⠷⡜⣎⠳⣥⢛⡴⣋⠶⣩⠞⣦⢛⡴⣍⢎⡳⢣⡝⣣⠞⣬⠳⣜⢲⡹⢬⡓⢮⣙⠮⡵⢎⡝⣎⠳⡕⣎⢳⡱⢎⡵⢫⡜⣣⢇⢯⠲⣥⠳⡜⣥⡛⡞⣬⠳⡬⢏⠶⣹⠹⣌⡳⢣⢞⡲⢵⣊⠷⣬⢓⣎⢎⣳⡙⣮⢜⡱⣎⢳⣻⣍⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⢯⣾⢏⠶⣩⠞⣬⠳⣍⡞⣲⡙⢮⣱⢣⠳⣍⢏⡞⣭⢚⡵⢪⡝⢦⣋⢶⡩⢞⡥⣛⠴⣋⢶⡩⢮⡕⣫⠼⣡⡛⢶⡹⣌⢧⣹⣖⣹⣇⣮⣳⣽⣮⣼⣜⣧⣝⣬⣣⠝⡮⣜⡣⢞⡱⣚⢎⡳⣬⢳⡙⡦⡝⣜⠲⣍⡳⢭⠳⣥⢛⢦⣙⠧⢮⡱⢇⣎⢳⡬⢳⡜⢮⡱⣙⢦⢫⡕⣎⢳⠬⣝⣧⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⣳⡿⣓⢎⡻⣔⢫⠖⡝⣦⣙⠦⣝⡣⢎⢧⡛⣜⠮⣜⡲⣍⡞⡱⣎⡳⡜⢦⡝⣎⠶⣍⡞⣱⢎⡵⣣⢞⣥⣻⣶⣽⣶⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠻⢿⣿⢿⣿⣿⣿⣿⣿⣶⣿⣧⣷⣍⡮⡕⣎⢧⣙⠶⣹⢬⡛⣴⡙⣎⡳⢥⣋⡞⣬⢋⡧⣝⠺⣌⠷⣘⢧⡹⢲⡹⡜⣎⠳⡜⡬⣇⠻⡔⢯⣷⡙⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⣵⣏⠳⣍⠮⣕⢮⡙⣞⡹⢴⡩⢞⡴⣍⢏⠶⡹⣌⡳⢥⠳⡜⡼⡱⢎⡵⣙⠮⣜⢬⠳⡜⣼⣱⣾⣶⣿⣿⣿⣿⣿⣻⢿⣻⣿⣷⡿⠟⠉⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⡿⣾⡿⣿⡽⣿⣻⣿⣿⣿⣾⣶⣭⣞⡱⢎⡵⢲⣙⠦⣝⢲⢣⠞⣬⠳⣜⡬⢳⣍⠞⣭⠲⣍⡳⣱⠹⣌⣳⡙⢶⣩⢳⡙⡮⡜⣷⡘⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⣿⠟⣬⢛⡬⣓⠮⣖⡹⢦⣙⠶⣙⡎⢶⡩⢮⣹⢱⢣⡝⢮⡹⣱⢣⡝⣭⠲⣍⠾⣘⣮⣿⣿⡿⣿⣟⡿⣽⡾⣿⣾⣳⣿⣟⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡷⣿⢷⣟⣷⣿⣞⣿⡽⣿⢿⣿⣷⣾⣳⡜⣹⢬⢣⢏⡞⣥⢛⡴⣩⠳⣌⡟⡴⣛⠴⣹⢌⡗⣣⠖⣭⠳⣌⢧⡝⣲⠹⣜⣻⡜⣦⠀⠀⠀ ⠀⠀⠀⢀⡾⣱⣏⠻⣔⡫⢖⡭⢞⡲⣙⠶⣩⠞⣥⢋⡧⣝⠲⣥⢋⡶⣙⠶⣙⠦⣏⢼⢲⣹⣾⣿⣿⡿⣿⢯⣟⡷⣯⣿⡿⣽⢷⣻⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣾⣻⢷⣟⣯⣿⡽⣾⣽⣻⣟⣿⡿⣷⣮⣙⠮⣜⢦⣋⠶⣣⢛⡴⣙⠶⣙⢮⡱⣚⠼⣡⠟⣦⢛⡜⡦⣝⢲⡙⡦⣍⢿⡜⣇⠀⠀ ⠀⠀⠀⡾⣱⡟⣬⢛⠦⣝⢣⠞⣥⠳⣍⡞⣱⢫⡜⡳⡜⣥⢛⠦⣏⠶⣩⠞⣥⢛⣜⣮⣿⣿⢿⣻⣯⡿⣯⣿⢯⣿⣳⣯⢿⣯⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣽⣻⣾⣻⣷⣻⢷⣯⡿⣽⣾⢿⣿⢿⣿⣿⣜⢦⡭⢳⣥⢋⡶⣍⢞⡱⣎⠵⣩⠳⣍⠾⣰⢫⡜⣱⢎⢧⣙⠶⣩⢖⣻⡜⡄⠀ ⠀⠀⣼⣱⡿⣙⠦⣏⠽⣘⢧⡛⣬⠳⣎⡼⢥⣓⠮⡵⣙⠦⣏⢳⢬⡓⢧⡛⣬⣷⣿⡿⣿⣽⣿⣻⣿⣽⡷⣯⣿⣻⢷⣯⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣯⣷⣻⢯⣟⣯⢿⣽⣻⣿⡾⣯⣿⣻⣿⣷⣞⣣⢎⡝⣲⢍⡞⣱⢎⡽⣡⠟⣬⠳⣥⢓⠮⡕⣎⡳⢬⢳⡱⢎⡞⣷⠹⡄ ⠀⠀⣷⣿⢱⠏⣷⡈⡏⢷⡎⣱⡎⢷⣸⠸⣇⡎⢷⢱⣉⡾⣈⢷⡎⡹⢶⣹⣿⣿⣹⣿⣹⡿⣾⣷⣏⣿⡿⣿⣾⣹⣿⣿⣇⣀⣰⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢹⣿⣏⣿⣏⡿⣿⣏⣿⣾⣹⣿⣹⣷⣏⣿⣿⣿⡾⣸⢱⠾⣸⢱⡎⡶⢇⢿⡰⢏⡶⣉⢷⠹⣆⡹⡎⣇⠹⣎⡸⢹⡇⠇ ⠀⣸⣿⣏⠮⡝⢦⡹⣙⠦⣝⡱⢎⡳⣬⢳⡱⢎⡏⣖⢣⠞⣭⠲⣭⣙⣾⣿⣿⣻⣽⣾⣳⢿⣟⣾⣽⣳⣿⣳⢯⣿⠟⠁⠀⠀⠀⠀⠀⠉⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠋⠉⠉⠈⠁⠈⠙⢻⣿⡾⣽⣻⢿⡾⣽⢯⣷⣟⣷⢿⣿⣿⣟⢿⣷⡭⡞⣥⠳⣎⡝⣎⢧⣙⢎⠶⣍⢮⠳⣥⢳⡹⣌⠻⡴⣍⠳⢿⡀ ⢸⣟⣿⢬⠳⣭⢓⢧⡹⢎⡵⣩⢏⡵⣊⢧⡝⢮⡜⣎⢧⡛⡴⣛⣶⣿⣿⣿⣞⣯⣷⣿⣽⣻⢾⣯⡿⣽⡾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣽⣟⣯⡿⣿⢿⣳⢿⡾⣿⢾⣽⣿⣮⢟⣿⣷⢎⡷⣱⢚⡼⢢⢏⡎⡗⣎⢎⠷⣌⢧⡓⢮⡝⡲⣍⠻⡜⡇ ⣿⣿⣏⡎⢷⣡⢏⠮⣕⡫⢖⣣⠞⡴⢫⡖⣹⢆⡻⡜⢦⢫⣵⣿⢿⣿⣿⣷⣻⡽⣾⣻⣽⡿⣯⣟⣿⣷⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢾⣽⡿⣯⣿⢿⡿⣽⢿⣞⡿⣿⣷⣊⠿⣷⣧⢣⢏⡼⣣⢏⡼⡱⢎⣝⠺⣜⡲⢭⠳⡜⡵⢪⡝⣭⣽ ⢹⡿⢦⡝⣲⢵⢪⡛⡴⣍⡳⢎⣝⢺⡱⣚⠵⣪⢵⣩⡓⣧⣿⢯⣿⣿⢯⡿⣽⡿⣷⣟⣯⣿⣳⣟⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣯⣟⣷⣻⣿⣻⣽⣯⡿⣟⣿⣿⡮⡝⣽⣿⣞⡜⡖⢧⢮⡱⡝⢮⡜⣫⢖⡹⢎⣳⠹⣜⠳⣜⠲⡝ ⢸⡿⡱⢎⡵⢎⢧⡝⣲⢥⡛⡼⢬⢣⠳⣍⡞⣱⢎⡶⣹⣿⢏⣾⣿⣿⢯⣟⣯⣿⢿⣯⣷⣻⢿⣯⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣽⣾⣟⡷⣿⣯⡿⣽⣻⣞⣿⣿⡱⣎⠽⣿⣮⢝⡚⣦⢳⡙⡶⣙⢦⢫⣜⢣⢧⡛⣬⢛⡬⢏⡝ ⣿⠷⣩⠗⣮⠹⣎⢼⡱⢎⡵⣋⡞⣭⢳⡱⣚⠵⣪⢷⣿⢏⡞⣿⡿⣯⣿⢿⣻⣞⡿⣷⣻⣽⣟⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣟⣾⣟⣷⢿⣻⣟⣿⣽⣻⣿⣗⣎⠻⣼⣿⣎⠷⣌⢧⡝⣲⠭⣎⢳⢬⡓⣮⢱⢣⢏⡼⢣⢞ ⣿⢫⡕⣫⢖⣫⢜⠶⣩⢛⡴⡹⡜⢦⢳⡱⣋⡞⣧⣿⡟⣎⢾⣿⣿⢯⣿⢿⡽⣯⢿⣽⣟⡿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣟⣿⣽⣯⢷⡿⣯⣿⣳⣿⣿⢬⡛⣖⣻⣿⢮⡱⡞⣼⡡⡟⣬⠳⣎⠵⣎⢧⣋⠾⣜⢣⢏ ⣯⢳⠼⡱⡞⣜⢮⢫⣕⢫⢖⡳⡝⢮⡣⢗⣣⣽⣿⡿⡜⣎⣿⣿⣿⢯⣟⣯⡿⣟⣿⣾⣻⣟⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⢿⣾⣳⣯⡿⣿⣽⣳⣿⣻⣿⡮⢵⢎⡳⢿⣷⢣⡝⢦⢳⣙⢦⣛⡬⢳⡚⣦⠝⡞⣜⣣⢞ ⡻⢬⡳⢳⡹⢬⡓⢧⡎⣏⢮⢵⣹⠲⣍⡳⢖⣿⣿⠷⣙⠶⣿⣿⡽⣿⣻⣾⣽⢿⣟⣾⢷⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⣿⡀⠘⠀⠀⠀⠀⢀⣶⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⣾⡽⣿⢿⣳⣯⣷⡿⣯⣿⣏⡗⢮⡝⡿⣿⣗⡺⣙⠮⡵⣚⡴⣋⠷⣙⢦⡛⣝⡲⢵⢪ ⣙⢧⣙⢧⣙⢧⢫⣓⠮⣵⡚⢦⢇⡟⡼⣩⢻⣿⡿⡭⣍⣻⣿⡿⣽⣻⣿⣽⡾⣟⣾⣯⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⣿⡽⣯⣿⣻⣽⣻⢷⣿⣧⡛⢦⢏⠷⣿⣷⢣⢏⡳⣝⠲⡵⣙⢮⣙⠶⣹⢬⡓⣏⢳ ⢞⡼⡸⡖⡭⣎⠷⣬⢛⡴⡹⣭⢚⡼⣱⢣⣿⣿⡟⡵⢎⣳⣿⣿⢿⣷⣻⣽⣿⣿⢾⣷⢿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢋⠁⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠋⢏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣯⣿⣷⣿⣻⢷⣿⡿⣾⣷⡹⣍⢮⢻⣽⣿⢣⡞⣱⢎⡟⡼⣡⠗⣮⣙⠦⢧⡝⣬⠳ ⢺⠴⣛⠼⣱⢎⡳⣬⢓⢮⠵⢮⣙⠶⣙⣎⣿⣿⣟⡹⢎⣽⣿⣿⣯⣟⡷⣟⣾⣽⣯⢿⣻⡽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣰⠏⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢯⣿⣳⣿⣳⢿⣻⣯⣿⢿⡷⣓⢎⢧⣻⣾⣿⠳⣜⢳⣚⠼⣱⣙⠮⣕⢮⡹⢲⡙⢦⣛ ⣻⡜⡭⣞⡱⣎⡳⢥⣛⢮⡹⢎⢧⣫⠵⣪⣿⣿⡯⣕⡫⢞⣿⣷⣯⣿⢿⣿⣟⣾⣻⡿⣿⣽⣟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣾⣟⡷⣿⣿⣻⡷⣯⣿⡷⣍⡞⢮⣹⢾⣿⣛⢬⡓⢮⣙⠦⡝⣮⢱⢎⡵⢫⣝⡲⣍ ⣿⡼⡱⢎⡵⢣⡝⡳⢎⢧⠽⣙⢦⡓⢯⡱⣿⣻⡿⡴⣙⢏⣿⣿⣳⣯⢿⣾⣯⢷⣻⣽⣟⣿⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⣯⣿⢾⣽⣻⣷⢿⣯⣿⣽⣿⣗⠺⣜⡣⢿⣻⣿⢬⢧⡹⢣⡞⣹⢜⡲⢭⣚⡜⣣⠮⡕⢮ ⢻⡷⣩⢛⣜⣣⡛⡵⢫⣎⠯⡝⢦⡛⢧⠳⣽⣿⣿⡱⢭⡺⣼⣿⣿⢿⣯⡷⣿⢿⣻⢷⣻⢾⣻⣽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣽⣾⣻⣟⡿⣽⣟⡾⣿⣽⣿⠼⣙⢦⡝⡿⣿⡟⣎⠶⣙⡳⡜⢧⡚⣝⡲⢣⠞⣥⡛⡼⢣ ⡾⣿⢥⣋⠶⣱⣙⢞⡱⢎⡻⡜⢧⡝⢮⡝⡼⣷⣿⡝⡶⡱⢎⣿⣿⡿⣾⣽⣯⢿⡿⣿⣻⡿⣿⡽⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣽⣷⡿⣷⢿⣻⣽⣾⢿⡷⣿⣏⠞⡭⢶⣹⢷⣿⢟⡼⣩⢇⣳⢹⢎⡝⢦⠽⣩⠞⣥⢛⡼⣣ ⣿⢻⡗⣮⣙⠳⣎⡝⡺⣍⠳⣝⡣⢞⣣⢞⡱⢯⣿⣿⡵⡹⢭⢾⣿⣟⣿⣽⡾⣯⣿⡽⣷⣿⣳⣟⡿⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣽⣻⣾⡿⣽⣯⣟⣷⡿⣿⣽⣿⢎⡝⣎⡳⣜⣾⡿⢎⠶⣱⡚⣬⢓⢮⡚⣭⢚⣥⠻⣬⠳⣜⡳ ⢻⡞⣿⢦⡍⠷⣎⢞⡵⣪⡝⡲⣍⡳⢎⢮⡕⣫⢿⣿⣷⣩⢓⠮⢿⣿⣽⢾⣻⣷⡿⣿⣽⣳⣿⣟⣿⡽⣯⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠄⠀⠀⠀⠀⣠⣾⣿⢿⣟⡿⣟⣷⣻⣟⣷⡿⣽⣻⢷⣿⢳⢎⡞⡴⣻⣼⣿⢽⡩⢞⡥⣛⠴⣫⢖⡹⢆⡏⣖⠻⣔⠻⡔⡟ ⠈⣷⣿⣳⡜⡻⡜⣎⠶⣥⢫⠵⣎⠵⣋⠶⣙⢦⣛⢾⣿⣜⡏⣞⢣⢿⣿⣯⣟⣷⣿⣳⣯⣟⣾⣟⣾⢿⣷⣻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣯⣟⡿⣟⣾⣟⣾⡿⣽⣯⢿⣿⢏⡳⢎⡞⣱⢷⣿⢧⣛⣜⡣⢞⡥⣛⡴⢫⣜⠳⣜⢮⡹⣜⢣⢱⠁ ⠀⠸⡟⣷⡭⢳⡹⣌⠷⣌⢏⠾⣌⠷⣩⠳⣍⠶⣩⢞⣻⣿⣞⡬⢇⡏⣿⣿⣾⣳⣯⢿⣟⣯⣷⣯⡿⣟⣾⣟⣾⡿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣻⣽⣻⢿⣽⣯⣟⣯⢿⣽⡷⣿⣿⢏⡮⣕⡫⣼⣣⣿⣟⢮⡱⢎⡵⣋⠶⡱⢎⡳⢬⡛⡜⢦⠳⣬⢃⡆⠐ ⠀⠀⢷⡹⣯⢣⢳⢭⢞⣬⢋⡾⣌⡳⢥⠻⣌⡳⢇⡮⢳⡼⣿⣾⡍⣞⠴⣛⣿⣿⣽⣟⣾⣻⡽⣷⡿⣽⣯⢿⣽⣻⡷⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣟⣿⡽⣷⣯⣟⣿⣳⢯⣟⣿⢾⣿⣿⡙⣎⠶⣡⣟⣳⣿⡟⣮⢣⡝⡺⢴⡙⡮⡝⢮⣱⢣⣛⠼⣩⢳⣌⡿⢠⠉ ⠀⠀⠈⢷⡹⣏⡳⢎⡞⣴⢋⡶⣡⣛⣜⡣⢧⣙⠮⣜⢣⠞⡽⢿⣾⣌⢳⢣⢞⡹⣿⣾⣷⣿⣽⣻⣽⣟⣾⣯⣟⣿⣽⣷⣿⣻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣯⣟⣯⣿⣽⡾⣟⡾⣽⣻⢿⣾⣿⠟⣦⢹⣌⡳⣝⣾⡿⣳⣛⡴⢣⢞⡱⣣⢝⡲⣍⡳⣬⠳⣌⡻⢴⢣⣾⢇⠇⠀ ⠀⠀⠀⠘⢷⡹⣟⡼⣘⢦⣋⢶⡱⢎⠶⣙⠦⣝⠺⣌⢧⡛⣜⢯⡻⣿⣎⡳⢎⡵⣩⠟⣿⣾⣷⣻⢾⡽⣯⢿⣽⣞⣿⣞⣷⣯⣟⣾⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣳⡿⣾⣽⡾⣷⢯⣟⣯⣿⣳⣿⣿⠟⡵⢫⡜⣣⢮⣵⣿⢯⡝⣧⠳⣜⢫⢎⡵⢣⢞⡱⢎⡵⣊⠷⣩⠞⣭⣾⢏⡞⠀⠀ ⠀⠀⠀⠀⠈⢷⢿⣞⡱⡺⡜⣦⠹⣍⡞⣥⡛⣬⠳⣍⠶⡹⡜⣎⠷⣽⢻⣿⣎⠶⣡⡛⢶⡩⣟⢿⣿⣿⣽⣻⢾⣻⣾⣽⣾⢷⣿⢯⣿⣻⡿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⣿⢷⡿⣽⣿⣳⣯⣿⣟⡿⣞⣯⣷⡿⣛⢬⡛⣜⣣⠽⣜⣿⡿⣍⢯⣙⢦⡛⣬⢓⡮⣜⠳⣎⡝⣎⠶⣙⢮⡱⣋⣾⢫⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢯⣻⣭⢳⡹⣌⢻⠴⣙⠦⣝⠲⣝⡬⢳⣍⢳⢬⡳⣍⠷⣽⣻⣯⣧⣙⢦⠳⣬⠳⣜⡹⡻⢿⣿⣿⣟⣾⣽⣻⣯⣿⣞⣷⡿⣯⣟⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⣽⣻⣽⣻⣿⣻⣞⣷⣿⣳⣯⣿⢿⢫⢇⡳⣍⠶⣙⣦⣭⣿⣿⢣⡽⡜⢮⡱⢎⡵⣊⠷⣸⢌⠷⡸⣜⢬⡳⣍⡖⣳⣿⢡⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⡙⣧⡗⣎⣳⢫⡕⣫⡜⣫⠖⣭⠳⣬⢓⢮⡱⢎⡝⣎⡳⣽⢻⣿⣬⣛⡴⣋⠶⡱⢭⠳⣌⢏⡟⣻⠿⣷⣿⣷⣿⣯⣿⣻⣽⣿⡾⣽⡿⣿⣷⣦⣄⡀⢀⣠⣶⣿⣿⣿⣟⡷⣿⣟⣯⣿⣯⣷⣿⢿⠿⣛⢏⡳⡜⣎⠳⣎⢵⢪⣝⣮⣾⢿⡛⣜⢣⡳⣙⠶⣩⠳⡜⣥⡛⡴⣋⣞⡱⢎⠶⡳⡜⣜⡿⢣⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣜⣿⡶⣡⠗⣮⢱⢎⡵⣋⠶⣙⠶⣩⠶⣙⢮⡱⢎⡵⣩⣓⢮⣛⣷⣯⣝⣺⣙⢎⡳⣍⡞⡼⣡⣛⠴⡲⣍⢞⡹⣙⢟⡻⣛⢿⢻⠿⡟⢿⡻⢿⣿⣿⣿⢻⠟⡿⣛⡟⣟⡻⢻⡝⣭⢫⡕⣎⢎⡳⣍⢮⣱⠹⣌⡗⢾⣩⣷⡿⣯⣝⢲⡹⢬⢣⠳⣍⠞⡥⢏⡵⢲⣍⢳⡱⢎⡵⣋⠷⣱⢫⡾⣳⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⢿⣥⠻⣔⢫⠞⣴⣩⠳⣍⠾⣡⠟⡜⡦⣝⠺⣜⡱⢎⡶⡱⢎⡽⣛⢿⣾⣮⣕⠮⣜⡱⢇⣎⡳⢵⡚⣬⠳⣍⢮⠵⣩⢎⢧⡛⣜⡣⣝⣾⡟⡽⣷⣫⢞⡱⢣⢞⡲⣍⢳⡜⣲⢣⠞⣬⢫⡕⣚⣦⢇⣟⣧⣿⡿⣻⢭⢳⡱⢎⢧⣙⢮⡙⢧⡙⣞⡹⢎⡼⢳⢬⢣⡝⣎⠶⣩⢞⣵⢟⡴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡙⣯⣜⣣⠻⡴⢣⣛⣬⠳⣍⢞⡹⢲⣍⠳⣎⠵⣋⠶⣙⢮⡱⢭⡚⣬⢛⡻⢿⣶⣽⣎⢶⡙⢶⡙⢶⡹⡜⣎⠳⣍⠞⣬⠳⣌⡳⣽⣿⠹⣜⢻⣷⢎⡵⣋⠮⡕⣎⠳⡼⣡⢏⣞⢲⣣⣞⣵⣾⢿⡻⣏⠳⣜⡱⢎⢧⡙⡞⡼⣘⠶⣩⢇⡻⢴⡙⢮⡜⡳⢎⡳⠼⣌⡳⢣⣾⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⢿⣶⡹⣜⠳⡜⢦⣛⡜⢮⣱⢫⡜⣳⢬⡛⣬⠳⣍⠶⣩⢧⣙⢦⢫⡕⣫⠜⣭⡛⡿⢿⣷⣿⣦⣷⣹⣌⠻⣌⠻⣔⠻⣌⢳⣿⢧⡛⣬⢻⣿⢺⠴⣍⡳⣹⣌⣻⣴⣧⣿⡾⢿⢟⡻⡹⢎⢧⠳⡼⣙⢦⢫⡝⢮⣱⡙⢶⡩⢞⡱⢎⡵⢣⢏⡳⣜⢣⡛⣜⣣⢧⣽⣟⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣙⣷⡮⣝⠺⣥⢓⣎⢳⡬⢳⡜⡱⣎⢵⣊⠷⣩⢞⡱⢎⡜⣎⡳⣜⢣⠟⡴⡹⣜⢣⡖⢮⡹⣙⡛⡟⡿⢿⢿⡾⣷⣾⣿⣿⣶⣿⣶⣿⣿⣷⡿⣾⠿⣛⡟⣻⢹⡙⢶⣩⢓⠮⡵⣙⢮⢣⣛⢴⢫⢎⡳⣜⢣⠶⣩⢧⣙⢮⣱⢫⡜⣣⢏⠶⣩⢎⡵⣣⣽⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⢻⢿⣷⣌⡳⢬⠳⣜⢣⢞⡱⣎⠶⣩⢞⡱⢮⡱⢫⡜⢶⡱⢎⢧⢫⡕⡳⣜⢣⠞⣥⠳⣍⢞⣱⡙⣎⠶⡱⢎⡶⣿⡿⣌⡳⢼⡹⣿⣲⢱⢣⢏⡵⢪⡕⣣⢛⠶⣡⢏⣳⡱⢭⢎⡳⡜⣎⠳⣎⢵⣊⢧⡛⡴⢣⠞⣦⡙⡦⡝⢦⣋⡞⣱⢎⣷⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣼⡿⢷⣝⠮⣝⠬⣏⠮⣕⢎⡳⢵⣊⢗⡣⣝⢣⠞⣥⢛⡼⣊⠷⡸⡕⣎⢧⣛⡴⢫⡜⣎⠶⡹⣌⡳⡝⢮⣽⣿⡳⢥⡛⢦⣟⣿⡧⣋⡞⡼⣚⠵⣚⣥⢛⠮⣕⡺⢴⡙⣎⠮⡵⡹⣌⡗⣎⠶⣩⢖⡭⡳⣍⠻⡴⣩⠳⣍⡳⡜⣼⣵⡿⣋⢿⣎⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⣼⢏⡳⢭⢻⢿⣮⡳⢬⣓⠮⣎⠵⣫⠜⣮⢱⠮⣍⡻⣔⢫⠖⣭⢚⡵⡹⡜⢦⠳⣜⢣⡝⣬⠳⡵⣩⠖⣭⡷⣾⡿⣱⢣⡛⣜⣾⣿⣗⡱⢮⢵⡩⢞⡱⢎⡝⢮⡱⣙⢦⣛⡬⢳⡕⣣⠳⡼⣌⡳⢣⢞⡲⡝⣬⢳⡱⢣⣛⡴⣹⣾⢟⡹⢲⡍⢶⢻⣦⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⡿⣍⠮⡵⣋⢮⢣⡛⡿⣷⣎⡳⢼⡙⣦⠻⡴⣋⢞⡴⢳⡜⡭⢞⡥⣋⠶⣱⡹⢎⡳⢎⡳⣜⠲⣝⢲⢥⠻⣼⣿⣿⢯⡱⣣⢝⡲⢿⣽⣿⡜⣣⢮⡱⢫⠼⣍⢞⡱⡳⢭⢲⢥⣋⠷⣘⢧⡛⣴⢣⡝⡳⢎⡵⣙⢦⠳⣍⢧⣳⡾⡟⣥⢫⣜⠳⣜⡣⢏⠾⣧⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣷⡿⡱⢎⣳⡱⣙⡎⣧⡙⢶⣩⢛⣿⣧⣝⢦⡛⣴⢋⡞⣜⢣⢞⡱⣋⢶⣩⢓⢧⣙⠮⣕⡫⢖⡭⢳⣍⠞⣬⠳⡽⣟⢯⣇⣳⠱⢮⡱⢻⣞⣿⣿⡕⢮⠵⣫⠝⡜⣮⢱⢭⣋⠗⣮⢜⡣⢏⠶⣙⢦⠳⣎⠵⣫⠜⣵⣪⣿⡾⣟⢭⢳⡙⢦⡓⢮⡹⣌⡳⣍⠻⣝⢷⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣽⢏⠶⡹⣍⠶⡱⣍⠞⡴⣙⢦⢣⢏⠶⣩⠟⣿⣷⣮⣓⡞⣬⢋⡮⢵⡩⢶⡡⢟⡼⣌⡳⢎⡵⢫⡜⢧⢎⣝⡲⣍⡳⣜⢲⡜⣬⢋⣧⡙⢧⡻⣿⣿⣿⢎⡳⢥⡛⡝⢦⣋⢶⡩⢞⢦⣫⢜⡫⢞⡭⣚⢧⣙⢮⣵⣿⢾⡛⣥⠳⡜⣎⠧⣝⡲⢭⢣⡳⣜⡱⣎⠽⣌⠿⣷⡹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣼⢏⡞⣭⢓⣎⢳⡹⣌⠻⣜⡱⢎⡳⢎⡳⢥⡛⡴⢪⡝⡻⢿⣶⣯⣜⣧⢹⢲⡙⣎⠶⣡⠟⣼⡘⢧⡚⢧⣚⢦⠳⣜⡱⢎⡳⣜⠲⣭⢲⡙⢧⡓⢿⣹⣿⢎⡵⢫⣜⡹⢎⡵⢎⡵⣋⠶⡱⢮⣱⢋⣶⣭⣶⡿⣟⢫⡜⢶⡙⢦⡛⡼⣌⡳⢎⡵⣋⠶⣱⢎⡵⢪⡝⣬⢫⡽⣧⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣼⢏⡞⡼⣡⠯⣜⢣⠗⡼⣙⠦⣝⢣⡝⣣⡝⢶⡹⣜⢣⣞⣱⢋⠶⣙⢟⡻⢿⣷⣽⣬⣳⣍⠞⡦⣝⡣⣝⢣⠞⣬⢛⡴⢭⢣⣓⠮⡝⢦⡣⢏⢧⡹⢎⠶⣙⠮⣜⠳⣜⢣⢏⡼⣍⠶⣍⣳⣭⣷⡾⢿⡛⡝⢦⡳⢬⠳⣜⢣⡝⣣⢝⡲⣍⢞⡱⢎⡵⣋⠶⣩⢞⡱⢞⠦⣇⠻⣽⣧⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣱⡟⢮⡼⣱⢣⡛⡬⢇⡯⣱⠭⡞⣬⠳⡼⡱⢎⢧⠳⣬⠳⡜⢦⡫⡝⣜⢮⡱⣋⠶⣩⠟⡽⡻⢿⣷⣾⣵⣮⣭⣻⣔⣫⣜⡣⢏⣜⡣⣝⢣⡝⣮⣧⣙⢮⡝⣎⣳⣍⣟⣬⣯⣾⣶⢿⢿⣛⠯⣝⡲⣙⠶⡹⣜⢣⡝⣎⠳⣍⠞⡼⡱⢎⡵⢾⣌⢳⣋⠶⣙⢮⡱⢎⡝⢮⠳⣜⡹⢲⡽⣧⢻⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⢱⡿⡸⢇⡾⣁⢇⣹⠸⣇⠾⣁⠿⡸⢶⣏⣷⡿⣉⡎⢷⣁⠿⡸⢇⢷⢹⡸⣆⢷⡉⡾⣁⠿⣶⢉⠷⣆⢇⡏⡹⢏⡿⠿⡿⢿⡿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⡿⢿⠏⣿⢉⡏⣱⢎⡹⣆⠹⡾⣰⢇⡹⡎⣷⣈⢷⡸⣸⢹⡈⢿⡰⢏⡾⡸⣿⣏⡶⣉⠾⣉⢶⠹⡎⡾⣉⠷⣎⢱⡏⣸⢿⡆⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⢧⣿⢣⡝⢮⠵⣩⠞⣬⢓⣎⢳⡍⣞⡹⢎⣾⣿⢱⢣⢞⡣⢮⡹⣱⢋⣎⢧⠳⡜⡦⣝⠲⣍⡳⢬⣋⠾⣜⠺⡼⣱⢋⡶⡹⣜⡣⢞⡱⢆⡳⢆⡳⢼⣼⣿⢆⡳⢦⣙⢮⣙⢦⡫⣜⡱⢮⡱⢎⣳⢱⢣⡞⣱⡙⣦⡙⣦⠳⡥⣇⡛⢶⡹⢎⡖⡳⡽⣿⡳⣍⢞⡱⣎⠻⣜⡱⣍⡞⣬⠳⣜⢣⢯⣷⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣟⣾⢏⡳⣜⢣⣛⡴⣋⣖⢫⡜⣣⠞⣴⣩⣿⡿⡞⣥⢫⢎⡵⢣⠳⡥⢯⡜⢮⡹⣱⠳⣜⡹⢦⡹⢣⢎⠷⣘⢧⠳⣥⢋⡶⣙⢦⡝⢮⣱⢫⡕⣫⢜⡳⣾⣿⢎⡵⢫⡜⢶⡩⢶⡱⢣⡝⡲⣍⡳⢬⣇⡳⠼⣥⢛⡴⣙⢦⡛⡴⢣⣝⢲⡙⢮⡜⡵⢻⣿⣷⢩⡎⣵⢪⡝⢦⡛⡴⣙⢦⡛⡬⢇⣏⢾⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣼⡟⢮⡱⣎⢳⡱⢎⡵⣊⠷⡸⢥⡛⡴⣿⣿⣟⡱⢎⡳⢎⡼⣍⢳⣙⠦⣝⡲⡝⢦⡛⡴⣹⠲⣍⡳⣋⡞⡭⢎⡳⡜⣭⠲⣭⢲⡙⢶⣡⠳⣎⠵⣊⢷⣹⣿⢪⡜⢧⡚⢧⡹⢲⣍⡳⣜⢣⢧⡹⠶⣌⣳⣙⠦⣏⢶⡩⢖⡭⢳⡍⣎⢧⡹⢣⢞⡱⢫⣾⣿⡳⡜⢦⡓⢮⣣⡝⢶⡩⠶⣍⡳⣍⢎⠷⣿⢿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⣿⣙⡖⣣⡝⣲⣙⣮⣖⣹⢎⡝⢶⡹⢼⣿⣿⠲⣍⠧⡝⢮⡱⢎⡳⢎⣝⢲⡱⡹⢎⡵⣙⢦⡛⣴⡙⡦⡝⣜⣣⢳⡙⣦⢛⡖⣣⢛⢦⢣⣛⢬⠳⣍⢾⣹⡿⢆⡏⢧⡝⢮⡱⢳⣌⢳⢬⡓⣮⢱⣋⠶⡱⢎⡳⣜⡲⡹⣍⢞⡱⢞⡜⢦⡝⡳⢎⡝⣣⢞⣿⣟⡝⡲⢭⣓⠦⣝⡲⣍⠗⣮⢱⡚⢮⡹⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⢿⣗⢣⣞⣵⣿⣿⣿⢿⡿⣿⣿⣾⣧⣝⠺⣽⣿⡹⣌⡻⣜⢣⡝⢮⡕⣫⢜⣣⠳⣍⡳⣜⢣⠮⣕⡣⣝⢲⡹⣜⢲⢣⣛⠴⣫⢜⡥⢏⣎⢳⢬⢣⠟⡜⣮⢽⣟⡺⣜⢣⠞⣥⢋⠷⣬⢓⢮⡱⢎⡳⢬⠳⣍⡳⣱⢣⢳⣱⢚⠮⣕⡫⣜⢣⢞⡱⣫⠼⣱⢺⣼⣿⡽⣱⢫⣜⢳⣎⣵⣾⣿⣶⣿⣼⣣⣝⣽⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⣿⣾⣷⣿⣿⣻⡽⣾⣿⣿⣳⡿⣿⣿⣿⣿⣿⣧⡳⣜⡱⢎⡳⣜⢣⢞⡱⣚⡴⣛⢬⠳⡬⢇⡻⣔⡳⢎⢧⠳⣬⢣⢏⣜⢣⣓⢮⡜⡳⢬⡓⢮⢣⢏⡳⣜⣻⣯⠕⣮⡙⡞⣬⢋⡾⣰⢋⡮⣕⢫⡕⣫⠳⣥⠳⣥⢛⢦⢣⢏⣞⠲⡕⣮⡙⢮⡱⢣⣛⠴⣋⡞⣿⡼⣡⣷⣾⣿⡿⣿⣿⣻⣽⢯⣿⢿⣿⣿⣿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⢸⣷⣿⣿⣻⢯⣟⡿⣽⣟⡾⣽⣿⣿⣿⢯⣟⡾⣽⣿⣿⡖⣭⢳⡱⢎⡝⢮⣱⢣⡞⣱⢎⡻⡜⣭⠳⣌⡳⢭⣎⠳⣥⣋⢞⡬⢳⣍⠶⣩⡓⢧⡹⢣⢏⢮⡱⣭⢻⣯⠞⡴⡹⣜⠲⣭⢲⡱⣋⢶⡩⢶⡩⢇⡻⣔⢫⢖⡭⢎⡳⢮⡜⣹⡜⢦⡝⣣⢝⣣⠮⣝⠲⣭⣿⣿⣿⣿⣻⣿⣿⣽⣳⡿⣿⣯⣿⣻⣽⣯⣷⡿⢧⠀⠀⠀ ⠀⠀⠀⢰⣻⣿⣿⣻⣽⣿⢾⣟⣿⣾⣟⣷⣻⣿⣽⢿⣻⡿⣟⡿⣿⡟⡴⣣⢝⡺⣜⢣⢎⡳⣜⢣⡞⣱⡙⢦⣛⡴⣹⠲⣜⡹⢦⡙⢮⡜⢧⢎⡳⢥⣋⠧⣝⢣⡞⣥⢓⡮⢿⣟⡼⣱⠳⣜⡹⢆⢧⠳⣍⠶⣙⢦⡝⢮⡱⢎⡳⢎⡼⢣⣝⢲⣙⢦⡹⢦⡹⡜⣎⠶⡹⢬⣻⣿⡿⣯⣷⣯⣷⢿⣿⣿⣽⣻⢷⣻⢾⣟⡷⣯⢷⣿⣿⣧⠀⠀ ⠀⠀⠀⢈⣿⣿⣳⣯⣿⣾⣟⣾⣳⣟⣾⣻⣽⡿⣿⣿⣽⢿⣟⣿⡿⣙⠶⣡⢏⠶⣩⢎⢧⠳⣜⣣⠞⣥⢛⡵⣊⡖⢧⡛⣴⢋⡶⣙⢧⢺⡱⢎⡳⢳⢬⡛⣬⠳⣜⡲⣍⢾⣻⡯⢖⣥⠻⡴⣙⢮⢣⣛⢬⠳⣭⢲⡹⢲⡍⢧⢫⡝⡜⢧⢎⡳⣜⡲⣝⢲⢣⣛⢬⠳⣍⡳⣹⣿⣿⡽⣯⣷⡿⣯⣿⣿⢯⣿⣯⣿⣻⢾⣟⡿⣿⣞⡷⣿⠀⡀ ⠀⠀⠀⠘⣹⣿⣽⣻⢷⣻⢾⣟⣷⡿⣽⣳⣯⣿⣻⢿⡿⣿⣿⣟⡱⢭⢞⡱⢮⣙⠶⣩⢞⣣⠳⣌⡻⢴⣋⠶⣱⡹⢲⣙⢦⡛⡴⣋⢎⠧⡝⢮⡱⢏⠶⣙⠶⣙⢦⣓⢎⡳⣽⣟⢣⢎⣳⠱⡭⢎⡳⢬⣋⠷⣌⢧⡙⢧⣚⠭⣖⡹⣜⠳⡮⡕⢮⡱⢎⢧⢧⡙⣮⠹⣌⡳⢥⡛⣿⣿⣿⣽⣿⣿⡿⣯⣟⣾⡷⣯⣟⡿⣞⣿⣽⢾⣟⣿⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣯⣿⣽⣿⢾⡿⣽⣻⡷⣯⣿⡽⣯⣟⣷⡿⣌⠷⣩⢎⡳⢣⡝⢮⡕⡺⢴⡛⣬⢓⢧⢺⣙⠦⣝⡣⢞⢦⠽⡱⢭⡚⡽⣘⢧⡹⢎⡝⢮⡝⣎⠳⣬⢫⢵⣻⣯⢓⡮⣱⢫⣜⢣⡝⣣⢎⣳⢚⡬⣝⡲⣍⢞⡲⣱⢎⠷⡱⣭⢣⠽⣩⢞⡲⣙⢦⣛⢬⡓⢧⡹⡜⣿⣿⣻⣯⣷⢿⣻⣟⣷⢿⣳⡿⣿⣻⡾⣽⣻⣾⡟⠀⠀ ⠀⠀⠀⠀⠀⠹⢿⣿⣷⣿⢾⣯⢿⣻⣟⣿⣻⢾⣽⣿⣽⢿⡸⣜⢣⢧⢫⡜⢧⡝⢶⣩⢓⢧⡹⢆⡻⢬⣓⢎⡻⢴⣙⡞⣎⡳⣍⣳⡙⢶⡙⡶⣙⠮⡝⡦⡝⣬⢛⡴⣋⢾⣹⡷⣋⡖⢧⠳⣬⠳⡼⣱⢚⡴⣋⠶⣡⠗⣎⠮⣕⢣⡞⣭⠳⡜⣭⢛⢦⣋⠶⣙⢦⢏⠶⣙⢧⢳⡹⡜⣿⣿⣷⣯⣿⢿⣾⢯⣿⣽⣻⡷⣿⡽⣯⢗⡿⠑⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣾⣿⣽⣿⣽⣯⣿⣾⣿⣟⠓⡷⢾⣧⣾⣱⣚⢧⡚⢧⢎⡝⣦⢫⣍⡳⣍⠞⡼⣱⣋⠶⣙⢦⠳⣍⠶⣩⢇⡻⡜⣥⢻⡱⣣⢛⡴⣋⢶⡙⣮⢽⣷⠳⣜⢫⢳⢬⢳⡱⢣⢏⢶⡙⢮⡱⢫⡜⡳⢎⡳⣜⠲⣍⡻⣔⢫⠶⣩⠞⣭⢚⠮⡝⣎⠞⣥⢳⡹⣜⣻⣿⣷⣿⣻⢾⡿⣯⣟⣷⡿⣽⢟⡇⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⣭⣿⣭⣭⠷⠾⠉⠉⠉⠛⢿⢸⡟⡽⣛⠿⡿⢷⣮⣽⣦⣋⣶⡹⣌⢯⢳⡱⢎⣝⡣⣞⡹⢬⡛⣵⣊⠷⣙⡖⣣⠷⣱⢋⡶⡹⢆⡟⣼⣻⣧⡛⣬⢏⡞⡬⢧⣙⠳⣎⢮⡙⣧⡙⢧⡹⣱⢋⡶⣍⠿⣌⠷⣜⢣⣛⠶⣹⡒⣏⡳⣝⣬⣻⣬⣧⣷⠶⠿⣿⣿⢷⣿⣯⡟⢿⣛⣾⡭⢞⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣏⠷⣩⢞⡱⣋⠶⣙⢮⢻⡙⣟⡻⢟⡷⢽⣚⢦⡳⣎⡵⣫⢼⡱⢎⡽⢪⠵⣍⡞⣥⡛⣴⢋⡯⣜⠶⣿⣷⡹⢆⡯⡜⢧⡳⣍⡳⢎⡶⣙⢦⡝⣣⠳⣕⢫⠖⣭⣚⣬⣳⣮⣷⣮⡷⣷⠿⡾⢟⣻⢛⡽⢻⡇⣿⠛⠉⠀⠀⠘⠈⠛⠭⠽⠟⠛⠓⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣏⠷⡱⢎⡳⣍⡳⢭⢎⢧⡝⢦⡝⢮⣜⢣⢎⢧⠳⣍⠞⣥⢫⡝⣫⠞⣭⠳⡞⣼⠲⣝⠶⣫⠶⣭⢾⡹⢦⡽⣺⢴⣫⢧⡳⡼⣱⢏⡶⡝⢶⡹⢞⡝⣎⢏⡻⢥⣋⠶⣥⢋⠶⡱⢮⡱⢫⣜⢫⠖⣭⢚⣽⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣏⡞⣭⢳⡱⢎⡵⣋⠞⣦⠹⣎⡼⢣⢎⡳⢎⢧⡛⣬⢛⡴⢳⡜⣥⠻⣔⡫⠵⣎⡝⣎⢳⢥⡛⡴⢣⡝⢶⡱⢣⡞⡴⢣⢳⡱⣣⢞⡲⣙⠶⣙⠮⣜⢎⢧⡹⢖⡭⣚⠦⣏⡳⢭⡳⣍⠷⣬⢣⡛⢦⢏⢾⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣧⢛⡴⢣⡝⡺⣔⢫⡝⣲⣙⢦⡙⢧⡚⡵⣋⠮⣕⢎⡳⣜⠳⣜⡲⣋⠶⣩⠗⡮⡜⣎⠳⣎⠵⣭⢣⡛⢦⡝⣣⢞⡱⣋⢧⢳⡱⢎⡵⣍⠞⣥⢛⡜⣎⢮⡱⣋⢶⣩⢓⢮⡱⢇⡳⢎⡳⢬⣣⢝⡣⣞⣹⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣼⣧⣫⣜⣳⣜⣳⣬⣳⣜⣱⣎⣮⣙⣶⣙⣶⣩⣞⣜⣮⣱⣎⣝⣦⣳⣍⣳⣥⣛⣴⣹⣌⣟⣬⣳⣌⣧⣝⣮⣜⣱⣎⣵⣍⣎⣧⣙⣎⣶⣩⣞⣥⣫⣼⣜⣲⣍⣳⣎⣖⣫⣖⣹⣎⣵⣫⣜⣣⣞⣬⣳⣌⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀