⠀⣴⣿⡟⣸⣿⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⢧⡀⢸⡷⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⡱⡜⣇⣿⣿⣿⣿⣿⣿⣿⡳⣄⠀ ⠀⠀⠸⣿⠻⣷⣿⣿⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣼⡷⡈⣿⡵⡀⠀⠀⠀⠀⠀⠸⣷⣄⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢷⣄⠀⠘⠾⣼⣿⣿⣿⠻⠛⠉⠈⣿⣎⠳ ⠀⠀⠀⣿⣇⠙⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣼⠃⠸⣷⣸⡵⡙⡀⡀⠀⠀⠀⠀⢿⢿⣧⡹⡕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡳⣄⠈⢾⣿⡿⡿⠀⠀⠀⠀⢹⡈⠃ ⠀⠀⢠⣿⣿⣷⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⣿⠀⠀⠹⣧⣷⠹⡜⡷⡄⠀⢣⠀⠸⡄⠙⢾⣾⢆⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⢣⡈⢎⣧⣿⠀⠀⢀⣀⠤⡇⠐ ⠀⠀⣾⣻⢻⣿⣿⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠹⡟⣧⠘⣌⢿⣆⠀⢧⠀⢷⡀⠀⠙⢿⣷⡳⡕⢄⡀⠀⢠⠀⠀⠀⠐⢄⠀⠀⠱⡀⠙⢌⠈⣿⣟⡿⠿⠿⠿⢇⠀ ⠀⢰⡟⠛⠼⠿⢻⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠘⣜⣆⠈⢮⣻⣷⡈⢦⠈⢧⠀⠀⠀⠙⢭⠘⣶⣝⠢⡀⠱⡀⠀⠀⠈⢢⡀⠀⣷⡀⠈⠺⣞⢿⠇⠀⠀⠀⠘⠀ ⠀⠎⡇⠀⠀⠀⢸⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠱⣿⣮⢦⣧⠘⣇⠀⠀⣴⠋⢱⢮⣻⡷⣌⠑⠷⠄⠀⠀⠀⣱⢄⣿⣵⣈⢢⠉⢻⡧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠈⢿⣷⡑⠧⠸⣇⠠⠁⠀⠂⠀⣙⢷⣞⣳⣤⡀⠀⠀⠀⡁⠀⠀⠀⣻⠀⢷⡀⠻⡄⠀⠀⠀⠀ ⠀⠀⡦⣒⣶⡄⢸⢰⡀⠀⠀⠀⠀⠀⠀⠀⠸⡜⣾⠚⠋⠉⠙⠛⠓⠲⢤⣀⠈⠃⠀⠀⠻⣿⢦⡀⠹⣧⠀⢠⢞⣥⣾⣿⣿⣿⣿⣿⣶⣶⣦⡌⠳⡴⣿⢳⣇⢯⢷⣄⠹⡄⠀⠀⠀ ⠂⠀⡇⠈⠉⠁⠸⣾⣷⠀⠀⠀⡆⠀⠀⠀⠀⢇⢻⡄⠀⠀⣀⠠⠤⢀⡀⠈⠳⠄⠀⠀⠀⠈⢧⡑⢤⣹⡷⢞⣿⢿⠉⡀⢠⡔⠻⣻⡟⠹⣙⣿⠘⡆⠹⣇⡿⡌⠟⡍⠳⣼⣄⠀⠀ ⠀⠀⣵⠀⠀⠀⠀⢿⡸⢧⠀⡇⢰⠀⠀⠀⢇⢸⣜⣧⣴⠯⠖⠒⠛⠛⠛⠛⠛⠻⢷⣦⠀⠀⠈⣣⣀⣷⠥⡻⡏⠘⣾⡧⡜⠃⢠⣻⠇⣸⠋⣇⣽⣞⣄⢻⣹⣿⣾⣥⠀⠈⠻⡆⠀ ⠀⠀⢻⡄⠀⠀⠀⠸⣧⢿⢧⣴⡘⣧⠀⠀⠘⣾⠯⡉⡀⢀⣠⣤⣍⣁⣒⡤⠀⠀⠀⢻⣿⡿⠛⠛⠿⣟⡀⠈⠻⣆⠈⢴⣀⣀⡵⠏⣠⠀⢀⣿⣿⣭⢿⡌⠧⡿⡿⣿⡆⠀⠀⠀⠀ ⠀⠀⣿⣳⠀⠀⢀⣀⣻⣎⣧⣜⠇⢻⣄⠀⢢⡿⣼⣽⣵⡿⠟⠋⠉⠙⠛⠻⠿⣆⠀⣸⡏⠀⠀⠀⠀⠘⢷⣄⡀⠈⠁⢀⣀⣤⣔⣺⣧⣶⠿⡏⣰⣿⣼⣻⠀⢱⠇⢸⡇⢀⣀⡀⠀ ⠀⠀⠸⠿⣗⠊⠁⠀⠀⠈⣯⣿⢆⠈⣿⣄⢻⣴⣧⡻⡍⢧⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠉⣿⡀⣸⢆⠀⡇⣿⣿⣿⣯⣇⠘⣾⠁⣿⠁⢀⠃⠀ ⠀⠀⠀⠀⠈⢳⡒⠀⠀⠀⠈⠉⠉⠓⢬⣿⣦⠳⡙⢿⣿⣬⣧⣤⣤⣤⠴⠖⠚⠋⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠁⠈⣆⣷⢈⡏⢀⣹⣿⠀⣿⠀⠀⠀⣸⡀⠀ ⠀⣠⣄⠀⠀⠀⢹⠉⠁⠀⠀⠉⠉⠙⠒⠪⠭⣳⢌⢦⡈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⣎⢸⣵⠊⠉⡇⡇⢸⠄⠀⡤⠋⠀⠀ ⠜⠁⠈⢷⡀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢭⡦⣙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠈⢎⣿⣆⠀⠃⢳⢸⡵⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⡄⡇⣿⠀⠀⠀⠀⢠⣤⠤⠤⠔⠒⠒⠚⠛⠙⢷⣤⣕⣦⡀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⣀⣤⠞⠁⠀⠀⠀⠀⠀⣠⠋⢳⠀⠀⠈⢻⡿⣦⠀⡸⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣾⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠙⣷⣄⠉⠃⠀⠀⠀⠀⠀⠉⢩⠉⠹⠀⠀⠇⠀⠀⠀⠀⡠⣂⣼⣿⣧⠀⢧⠀⠀⠀⢻⡬⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢇⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠀⠙⣿⠀⠈⢿⢗⣦⡀⠀⠀⠀⠀⠀⠘⢆⠀⠀⣼⠀⠀⠀⠀⣪⠖⣿⣿⠘⢿⠳⣌⣆⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠄⠀⠀⠘⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣾⠟⠀⠀⠈⢆⢹⢿⣷⣦⣄⠀⠀⠀⠀⠉⠉⠀⢀⢀⡤⠊⠀⠀⣟⡘⡆⠈⡇⢀⡿⢟⠄⠀⠀⠘⢄⠀⠀⠀⣠⢾⠁⠀ ⠀⡴⠃⠀⠀⠀⠀⠸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⣀⣤⡈⣚⢻⠻⣿⣆⠉⠒⠢⢖⣤⣄⡖⠗⠉⠀⠀⠀⣴⡿⠒⠓⠢⠶⢟⣗⢺⡎⢢⡀⠀⠈⢣⡀⣸⡏⠘⠺⠀ ⡜⠁⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢸⡏⠀⠀⣽⡎⡆⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⡼⠜⣗⢒⠠⣄⠀⠀⠀⠉⠓⠀⠽⣦⠀⠀⠻⣿⡇⠂⠀⠀ ⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢆⠀⠙⠒⠊⠈⡇⠁⠀⢿⣷⣄⠀⠀⠀⠀⠀⠈⠁⣰⢫⡾⠉⠉⠑⠻⠶⢭⣖⡦⣄⠀⠀⠀⠈⠣⡀⠀⠀⠙⢄⠀⠀ ⠀⣾⠏⠁⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠻⣎⠷⠀⠀⠀⠈⠊⢸⢰⢸⣧⡙⢧⡀⠀⠀⠀⣠⠞⣱⠟⠻⡱⣆⢤⡀⠀⠀⠀⠈⠛⢄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀ ⠀⠻⣷⣄⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⢸⢎⡂⠈⣟⡄⠈⠓⢤⢾⡡⠊⠁⠀⠀⣳⣀⣙⣺⡵⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠁⠀⠀⠀⠀⣀⠀⠀⠠⣶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠸⠈⣦⡧⠝⢟⡄⢠⡾⣏⠉⠲⣄⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⣠⡶⠛⠁⢷⡄⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⡆⠀⢼⡇⢀⡨⠟⠁⠀⠀⠑⢄⠈⢢⣱⠹⠶⢶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢆⠀⠀⠀⠀⢸⣄⠀⡽⠀⠻⡆⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⠇⢀⡼⠋⠁⠀⠀⠀⠀⠀⠀⠈⢂⠀⢿⣤⡔⠋⠱⣦⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢳⣄⠺⣄⠀⠉⠉⠀⢀⠐⠃⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠽⠷⣯⡠⠄⠀⠀⠀⠀⠀⠀⡤⠴⡛⡆⠈⡄⠙⠒⣤⣬⣾⣦⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⢀⠈⠈⠑⢌⡻⠦⠤⠂⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⡠⠊⠁⣠⣴⠒⠮⡉⠁⣀⠠⢀⣀⡀⠀⠤⠄⢡⠖⢁⡴⣶⠳⣍⠭⠒⢠⣻⢻⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢦⡑⢦⣤⠤⣬⣲⣤⡄⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢀⠔⠁⣠⡾⠋⠁⠀⠀⠘⠫⣤⡶⣛⡶⠿⠒⠀⠀⠀⠓⢻⠂⠿⣦⠉⠳⣄⣮⣿⡟⠀⠈⠳⢄⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⣄⠻⡕⢴⣢⠭⠭⠉⠉⣀⡠⠭⠋⠀⠸⣇⣠⣋⡴⠛⠛⢦⣄⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⣀⣀⣘⡲⢾⣿⡄⠀⠈⠻⣭⠁⠀⠀⠀⠀⠉⠶⢄⣐⠀⢀⠀⠀⠀⠀