⡁⠢⠐⠀⠀⠀⠀⠀⡞⢀⠏⠀⠀⠀⠀⠀⠀⢰⠎⠀⡜⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣰⡿⠁⢇⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀ ⡁⠆⠡⠈⠐⠀⠀⢸⢀⡾⢠⠇⠀⠀⠀⠀⢀⡿⠀⣈⣼⣥⡧⠔⣒⢒⠦⠄⠀⠀⠀⠀⠀⠀⠀⢰⡇⢰⣿⣧⠖⢾⡖⢧⢤⣀⠀⠀⢻⠀⠀⠀⠀⠸⡆⠀⠀⣌⠳⡄⠀⠀⠀⠀⠀ ⠢⠌⢂⠐⡀⠀⢀⡇⡜⡇⡼⠀⠀⠀⠀⠀⢸⣃⡴⢻⢯⠀⢻⠀⢸⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣧⠇⠀⠘⣿⡌⢦⠀⠉⠲⣜⡆⠀⠀⠀⠀⣷⠀⠀⠈⠢⣌⡣⠀⠀⠀⠀ ⠰⠐⡀⢂⠀⠀⣼⣷⢹⢀⡇⠀⠀⠀⠀⠀⣿⠉⠀⣞⠏⠀⠈⣧⠈⡆⢹⠀⠀⠀⠀⠀⠀⢠⠀⢸⢠⣿⠏⠀⠀⠀⠘⠿⣌⢷⡀⠀⠈⡷⡄⠀⠀⠀⢸⣇⠀⠰⡀⠈⢮⡈⠀⠀⠀ ⠀⠡⠀⠂⠀⠀⣿⣿⢸⢸⡇⠀⠀⠀⠀⠀⣿⠀⣸⠙⠀⣀⣤⣼⣦⡿⡌⣇⠀⠀⠀⠀⠀⢸⡆⢸⡿⠏⢠⡤⢶⣒⡤⠤⢼⣮⡳⡄⠀⣿⠀⠀⠀⠀⣼⠹⣄⠀⠙⣦⢄⣙⠦⡀⠀ ⠈⠄⡁⠠⠀⠀⣿⡇⠘⣾⡇⠀⠀⠀⠀⠀⣿⢠⣇⡴⣪⡷⠛⠉⠉⠻⢷⡘⡄⠀⠀⠀⠀⠀⢣⢸⠃⠀⢠⡟⠋⠋⠉⠙⠛⢿⣽⣿⢆⣿⠀⠀⠀⠀⡏⠀⠙⢦⡀⠈⠣⡀⠉⠉⠀ ⠀⠂⠄⠀⠀⠀⢿⣇⠀⢿⣿⠀⠀⠀⠀⠀⢻⣾⣿⡞⠁⢀⣴⣾⣿⣷⣦⠉⢻⣄⠀⠀⠀⠀⠘⡾⣤⠀⠈⢀⣴⣾⣿⣶⣤⠀⠛⣿⣻⡷⠀⠀⠀⣰⠷⣄⠀⠀⠙⠲⠤⣙⢦⠀⠀ ⠀⡁⠀⠀⠀⠀⠸⠼⢀⠞⣿⡆⠀⠀⠀⠀⢸⣿⢿⠁⠀⣾⣿⣿⣿⣿⣿⣧⠀⠫⡳⣄⠀⠀⠀⠘⢷⠀⠀⣾⣿⣿⣿⣿⣿⣧⠀⠙⣧⡇⠀⠀⢰⡟⠀⠈⡙⠂⠈⠀⣠⠼⠋⠀⠀ ⠀⡐⠀⡀⠀⠀⠀⢀⠎⠀⠈⢿⡀⠀⠀⠀⢻⣻⡆⠀⠠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠚⠽⣦⣤⣀⠈⢦⡀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠀⠀⢀⡿⠁⠈⠀⢽⡷⣖⣿⡅⠀⠀⠀⠀ ⠀⠄⣁⣠⣴⠶⠷⢿⡀⠀⠀⠀⠑⣄⠀⠀⠈⢧⣯⠀⠀⠁⣹⡿⠿⢟⣯⠇⠀⠀⠀⠀⠀⠀⠁⠈⠉⠙⠃⢻⣿⡻⢿⣿⣇⠀⠀⢠⣯⠂⢀⣾⠙⡆⢠⣠⡤⠞⢋⣁⠀⠀⠀⠀⠀ ⠭⠙⠛⠉⠀⠀⠀⠀⠈⠉⠒⠤⣀⡇⢱⠦⣄⣈⣫⡆⠀⣀⡙⠛⠛⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡛⠛⠛⠉⠀⠀⡾⢃⡠⠊⠀⠀⣿⡰⠽⠋⠉⠉⠈⠉⠑⠢⢄⣀ ⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠙⠺⣄⠀⠻⡉⠉⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠾⠓⡿⠑⠀⣣⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⡰⠋⠘⣦⢝⠀⢠⣄⠀⠀⠙⢦⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣡⠴⠊⠁⠀⠀⠀⣀⠴⠚⣆⢞⢦⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠊⠀⡠⠎⣸⣿⠋⠉⠙⠒⣢⠤⣀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⣀⠤⣒⠮⠉⠁⠀⠀⠂⣮⠈⠳⡦⡀⠀ ⠀⡠⠖⠉⢀⡴⠋⡼⠋⠁⠉⣦⠀⠀⠀⠀⠙⠪⢕⣦⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⢀⡤⡪⠗⠋⠀⠀⠰⣄⠀⠀⠀⠸⡆⠀⠘⢢⣀ ⠉⠀⣠⠞⠁⢀⡞⠁⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠁⠻⣄⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⡠⠊⠀⠀⣠⠖⡡⠚⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠹⡄⠀⠀⠈ ⠀⠊⠀⠀⢠⡞⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⡲⠽⠓⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠚⢤⣤⡔⠚⣡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣢⢄⣘⣆⠀⠀ ⠀⠀⠀⢠⡟⠺⢭⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢕⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠚⠉⠉⠉⠙⠚⠣⡀ ⠀⠀⣠⠋⠀⠀⠀⠀⠈⢩⢫⣿⠛⠛⠛⠿⢧⡀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣶⠶⠒⠛⡉⢹⣯⣧⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⡔⠁⠀⠀⠀⠀⠀⠀⢸⢸⢹⡀⠌⠂⠄⢣⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣵⠠⢈⠰⢀⢸⡧⣽⠀⠀⠀⠀⠀⠀⠀⠀ ⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡌⢧⡐⢈⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠐⢨⠀⢄⡿⢱⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠻⣄⡺⠃⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠈⣇⠂⢌⡾⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⡁⢺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⠋⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡆⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀