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