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