⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⢁⣢⣤⣄⣁⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⢿⣿⣦⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢸⣿⣏⢑⢻⣿⣾⣿⣷⣦⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⢸⣯⣻⢦⠐⣉⣦⣷⣾⣿⣷⣄⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢨⡍⠋⠁⠈⣬⡽⠽⠈⣻⢿⡿⣖⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⣡⣤⣠⣤⡈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣔⠀⠐⠁⡈⡡⠈⣿⣿⣿⣿⣟⡞⠂⠉⠀⠀⠀⠀⠀⡠⠄⠐⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣠⣾⣿⣿⣿⣿⣽⣿⣷⡀⠸⠀ ⠀⠀⠀⠀⠀⢐⠀⣾⠰⡆⠀⠠⣤⣾⣶⡟⠫⣑⣤⣤⣤⠀⠙⠢⢈⣐⢂⣡⣴⣮⡏⠈⠲⠢⢅⠐⠤⠀⠀⠀⠀⠀⠠⠞⢀⣴⣿⣿⡿⣿⡿⠛⢹⡝⡿⣿⣇⠀⡇ ⠀⠀⠀⠀⠀⠀⡆⢻⡇⠁⠀⠀⠀⠯⣁⣤⣾⣿⣿⣿⡿⣾⣓⢢⢧⣸⣟⣯⣿⢡⣿⣧⢄⣴⣄⠨⢑⠤⣁⡒⣐⣊⣠⣴⣿⣿⡟⣿⠟⢁⡠⡄⢸⣏⠱⣝⣿⠀⠁ ⠀⠀⠀⠀⠀⡰⢀⣾⡋⠁⠀⠀⣐⣾⣿⣷⣯⣻⣗⣏⣜⣯⣿⣿⣿⣿⡿⣿⣟⣿⣯⢿⣷⣿⣿⢿⣎⠟⢓⣽⣿⣿⣿⣿⣟⡻⠋⠀⠀⠈⠀⠇⢸⠙⠈⣻⡟⠀⡁ ⠀⠀⠀⢀⠞⣠⢺⡿⠿⡇⠀⢀⣾⣟⣿⣿⣟⣿⡿⣷⣳⣾⣟⡞⢱⣭⢷⢹⣿⣯⣿⣷⣿⣻⣿⣿⣻⣲⣾⣽⣻⣿⣿⡿⠋⠀⠐⠁⠀⢀⠆⢠⢏⡄⣤⣽⡇⠀⡇ ⠀⠀⠀⡘⢰⠡⢿⣿⣀⠉⡀⠸⢾⡯⣳⣽⣿⣿⣽⣻⣷⣿⣿⡇⢸⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⡿⠿⣻⣿⠀⢠⠀⠀⠀⠠⠊⣰⠟⢋⣼⣽⡿⠀⡰⠁ ⠀⠀⠀⡇⢸⡰⠿⠊⢻⠀⢌⣀⠈⣡⣟⣾⣿⣿⣻⣿⣽⣿⣿⡇⢸⣿⢻⣿⣿⣟⣿⣿⣿⣙⣿⣿⣿⢽⡿⠵⣵⣈⢩⣷⡀⢀⠀⡀⠀⡰⢁⡄⢹⣽⣟⠁⢠⠀⠀ ⠀⠀⡰⠀⠇⠁⠀⣈⠤⣜⣘⣿⠯⠕⠛⠚⠻⣟⣽⣿⣿⣟⣉⡁⣘⣛⣷⣿⡷⣟⣿⣿⣿⣟⣟⣯⣾⣊⣤⣸⢏⣿⣷⡾⡇⠘⢀⠇⢰⣷⣯⣊⢸⠏⡟⠀⠅⠀⠀ ⠀⢠⠁⡜⠀⠸⣯⣳⣞⡷⠚⠁⠀⠂⠈⠐⡀⢹⣿⣿⣿⣿⣻⢡⣿⣿⣿⣿⡿⣷⣿⣿⠿⣷⣟⢾⣵⡼⣾⣔⠕⠂⠽⢿⣿⠀⠉⢠⡿⣣⡿⢷⢽⣾⠁⡘⠀⠀⠀ ⠀⡌⢠⠡⡆⠘⢾⣿⡿⠁⡀⠀⠀⠀⠀⠀⠇⢸⣵⣿⣷⣿⣿⣼⣾⣿⣿⣶⣿⣿⠿⠋⠉⠑⠻⣾⣯⣷⣿⣢⡄⣴⣼⣽⣿⡇⠀⣼⢿⣿⣟⠧⣌⡃⢀⠃⠀⠀⠀ ⠰⠁⡎⡀⠁⢰⣿⣾⣇⠀⡇⠀⠀⠀⢀⠀⣠⣟⣹⣿⣿⡧⡽⡟⣿⣿⣿⢿⡟⠁⡠⠈⠀⠁⠀⠈⢿⠽⡦⣽⣼⣯⣿⣿⣿⣽⠀⠿⣿⡛⢊⠇⡘⠀⠌⠀⠀⠀⠀ ⠀⡆⠳⠛⠄⢽⣿⣿⣿⣄⠘⠂⠀⠐⣡⣴⣿⣏⡿⢻⡿⠗⠙⠙⡽⡿⠁⡈⠀⡌⠀⠀⠀⠀⠀⠱⠈⣷⣿⣻⠟⠿⣏⡉⠉⠀⠚⠁⠀⠹⠌⠘⠀⠘⠀⠀⠀⠀⠀ ⠀⡇⠠⢺⡄⠇⣻⣿⣿⣿⣷⣶⣶⣾⣿⢯⣿⡿⣬⠉⠀⠀⠀⠀⠁⢀⣰⢧⠀⠦⠀⠀⠤⠤⠐⠊⡠⠃⠻⢿⣷⣶⣀⠙⢒⢻⣄⠠⠀⠐⢣⠁⡸⠀⠀⠀⠀⠀⠀ ⠀⡇⢸⢃⢀⠲⣕⣫⣱⣿⣺⣿⣿⣿⡟⣿⣟⣿⣏⡀⠀⠀⠈⠀⢄⣾⡻⣿⣷⣦⣄⣤⣦⣶⣶⣾⣷⣖⡵⣻⣝⣻⣿⡨⣀⣥⢘⡤⠰⣰⠃⢰⠁⠀⠀⠀⠀⠀⠀ ⠀⢱⠀⣏⠀⠓⢭⣾⣏⣬⠽⡟⢾⢟⡻⢷⣿⣿⣿⣿⣀⠀⢠⣠⣼⠧⣾⡉⣾⡻⣿⣯⣿⣿⣿⣿⣟⠿⢻⣿⡿⢊⣙⣯⣻⡻⣷⣌⠶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⢩⠈⠢⣸⣿⠻⡿⠻⠟⢙⣫⣿⣾⢿⣿⣿⣿⣿⣧⣸⡏⠛⠑⠳⡻⣿⢿⣿⣿⣿⣿⣿⣯⣯⣯⡽⢿⠻⡮⣳⣿⣗⠿⢿⡵⡞⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢇⠸⡄⢰⣄⣉⣿⠗⣲⣖⡋⣻⣿⣟⣵⣿⣿⣿⢿⣿⡟⠀⠀⣀⢀⣤⣼⣾⣿⣿⣿⣿⣿⣿⣿⣮⣼⣷⣟⠵⢶⣾⣳⣿⣳⡿⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡄⠹⡟⡿⠟⢻⣿⣟⣟⣯⣿⣿⣿⣿⣿⢿⣽⡿⣾⣍⢲⣤⣤⣵⣴⣽⣮⣿⣿⣿⣟⢻⣿⣿⣿⣿⣷⣬⣯⣉⢖⣻⡙⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡄⠙⣄⡀⣀⠵⠛⢿⠟⠉⠻⠋⠁⣿⠿⡿⣿⣿⣿⣯⣦⣿⣿⣿⣭⣿⣽⣟⣷⢼⣝⣝⣾⢽⠻⣏⣿⣿⣿⣿⡯⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢆⠘⣏⠀⠀⠀⠀⠦⠀⠀⠀⠖⡤⡀⢰⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢷⣿⣿⢿⣽⡿⣽⣿⡷⠞⣿⠎⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢢⠈⢧⡀⠀⢀⡿⢅⢠⡐⡳⡬⡸⠴⢯⡇⢨⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢾⡿⣪⠞⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠣⠈⠳⠤⠵⢆⣠⢭⣠⣟⣁⡶⠃⠼⣵⢿⣴⡿⣯⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣯⠕⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⠀⠀⠄⠀⠀⡈⠉⠲⢄⡍⠩⠟⡻⠂⠭⣿⣿⣿⣿⡿⠟⠛⠛⠷⠿⠝⠉⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠉⠚⠥⣀⣀⣏⠧⠟⠋⢀⠤⠒⠂⠒⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠤⠤⠤⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀