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

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