⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⣀⣀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢞⡯⢽⣟⣿⣽⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⢛⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⣻⣜⣮⡜⣿⣻⡞⣧⣻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠦⣏⡼⡹⢷⡀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠉⠉⠉⠉⠙⠻⣧⣿⣱⣳⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠉⠉⠉⠙⠺⣯⣓⠮⣕⣫⢳⢻⣤⢶⠶⣶⢲⣿⠏⠀⢀⡴⠖⠒⠒⠲⣤⡀⠠⠹⣶⣻⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣷⣭⠶⠿⠟⠛⠚⠓⠚⠳⡏⠀⣰⠏⠀⠀⠀⠀⠀⠀⢳⡇⠀⢹⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠘⢧⡀⠀⠀⠀⠀⠀⣸⠇⢀⣾⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣠⣞⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⣀⡴⠿⠿⢿⣦⡙⠲⣤⣤⣤⡴⠋⠀⣼⡟⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣾⢋⡵⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⠜⠡⠀⠀⠀⠀⠉⢿⣦⠀⠈⠁⢀⣠⣾⡿⣼⣻⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢃⠊⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⢀⠂⠀⠄⠀⠀⠀⠀⠀⠀⢹⣧⠀⠉⠉⠀⢿⣳⢧⡿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⡀⠁⡘⡿⣎⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡝⢠⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡀⠀⠄⣿⣽⢾⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⢸⡄⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠂⠂⡏⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⣷⣆⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠁⠆⠁⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢇⠸⣿⣿⣿⣤⣿⠁⢠⠒⠒⢢⠀⠀⠀⣆⠀⠸⣿⣷⣄⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠂⠀⢱⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠒⠚⢎⢦⣻⣿⣿⠿⠁⠀⠀⠉⡖⠁⠀⡀⠀⠘⢆⠀⢿⣿⣿⣷⣶⣤⣴⣶⠿⣿⠟⡠⠔⠒⠒⠲⣟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⠼⣧⠀⠁⠀⠀⠀⠀⠂⠙⣭⢫⡽⢃⠀⠀⠈⠳⢌⣿⣿⣿⣿⣿⣿⡿⠖⠁⠀⠳⣄⣀⣁⡠⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⡁⠂⠀⢀⠀⠀⠱⡟⠀⢸⠀⠀⠀⠀⠠⠈⠉⠙⠛⠉⠉⠀⠀⠀⠐⠀⣠⢜⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠁⠐⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣤⠶⠛⠁⠂⠀⠀⠈⠀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣙⡷⢶⠶⢤⣤⣤⣤⣠⣤⣬⣤⣤⣶⢶⡾⠛⠙⠛⠦⣄⡀⠠⠀⠀⠀⠀⠄⠅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠐⢠⠇⠀⠀⡀⠀⠀⡆⠁⣎⠀⠀⠀⢸⡀⠀⠀⠀⠀⠐⠉⡛⢲⠮⠤⣄⠩⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⡏⢀⠂⠉⠀⠈⠑⢌⠉⠁⠐⠈⠀⠄⢳⡀⠀⠀⠀⠀⠀⠄⠀⠀⣀⡼⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⠀⠀⠀⠀⢸⠃⢸⠀⠀⠀⠀⠀⢸⠀⢈⠀⠂⠁⠠⠀⠙⠦⣄⡀⠀⠐⠀⠀⣾⠉⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⠋⠙⢿⣦⣀⣀⣀⣼⡀⠀⠑⠢⠤⠤⠐⠁⠀⠂⠀⠄⢁⣠⣀⣁⣀⣀⣉⡿⠲⠶⠶⠃⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠚⠁⠠⡀⠀⠂⠠⢳⣌⠉⠁⠀⢳⣤⣁⣀⣠⣀⣠⣈⣠⣤⠗⠚⠉⠀⠀⠀⠈⠉⠻⣄⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⣠⠖⠉⢀⠄⠀⢄⠀⢐⣠⣾⠟⠃⠀⠀⠀⢸⠁⠀⠉⠀⠉⠉⡉⡇⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢀⠀⠀⠀⠂⠀⠀⠀ ⢀⡴⡋⠀⠀⠐⠔⢀⣰⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢀⠀⠀⡇⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢌⡆⠀⠀⠀⠀⠠⠀⠀⠀ ⠙⠲⠤⠤⠤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠤⠤⠤⠴⠒⠋⠀⠀⠀⠘⠳⠦⠤⠤⠤⠤⠴⢖⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⢖⠴⠤⠤⠤⠤⠦⠳⠘⠀⠀⠀⠋⠒⠴⠤⠤⠤⠦⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠞⠶⠤⠤⠤⠲⠙ ⠀⠀⠀⠠⠀⠀⠀⠀⡆⢌⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⡇⠀⠀⢀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠉⠛⠾⣴⣰⢀⠔⠐⠀⠀⡋⡴⢀ ⠀⠀⠀⠂⠀⠀⠀⢀⠀⢆⠘⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⡇⡉⠉⠉⠀⠉⠀⠁⢸⠀⠀⠀⠃⠟⣾⣠⢐⠀⢄⠀⠄⢀⠉⠖⣠⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⣄⠻⠉⠈⠀⠀⠀⠉⠚⠗⣤⣠⣈⣠⣀⣠⣀⣁⣤⢳⠀⠁⠉⣌⢳⠠⠂⠀⡀⠠⠁⠚⡤⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠃⠶⠶⠲⡿⣉⣀⣀⣁⣀⣠⢁⠄⠀⠂⠀⠁⠐⠤⠤⠢⠑⠀⡀⣼⣀⣀⣀⣦⢿⠙⠋⢖⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠂⠀⠉⣾⠀⠀⠐⠀⡀⣄⠦⠙⠀⠠⠁⠂⠀⢈⠀⢸⠀⠀⠀⠀⠀⢸⠃⢸⠀⠀⠀⠀⣯⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⡼⣀⠀⠀⠄⠀⠀⠀⠀⠀⡀⢳⠄⠀⠈⠐⠁⠉⢌⠑⠈⠀⠉⠂⢀⡏⠀⠀⠀⠀⠎⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠩⣄⠤⠮⢲⡛⠉⠐⠀⠀⠀⠀⡀⢸⠀⠀⠀⣎⠁⡆⠀⠀⡀⠀⠀⠇⢠⠐⠉⠞⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠅⠄⠀⠀⠀⠀⠠⡀⣄⠦⠛⠙⠛⡾⢶⣶⣤⣤⣬⣤⣠⣤⣤⣤⢤⠶⢶⡷⣙⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⠀⠈⠀⠀⠂⠁⠛⠶⣤⣀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠐⠁⠀⣀⣤⠶⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⢜⣠⠀⠐⠀⠀⠀⠉⠉⠛⠙⠉⠈⠠⠀⠀⠀⠀⢸⠀⡟⠱⠀⠀⢀⠀⠂⡁⣄⠷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠞⡠⣁⣀⣄⠳⠀⠁⠖⡿⣿⣿⣿⣿⣿⣿⢌⠳⠈⠀⠀⢃⡽⢫⣭⠙⠂⠀⠀⠀⠀⠁⠀⣧⠼⣀⣄⠰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣟⠲⠒⠒⠔⡠⠟⣿⠿⣶⣴⣤⣶⣷⣿⣿⢿⠀⢆⠘⠀⡀⠀⠁⡖⠉⠀⠀⠁⠿⣿⣿⣻⢦⢎⠚⠒⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⢱⠀⠂⠀⠀⡟⣿⣴⢀⠀⠀⠀⠀⠀⣄⣷⣿⠸⠀⣆⠀⠀⠀⢢⠒⠒⢠⠁⣿⣤⣿⣿⣿⠸⢇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠁⠆⠁⠀⠇⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⣿⣿⣶⣆⣷⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠉⠉⡏⠂⠂⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⡿⣿⢠⠀⠀⡄⢸⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣽⢾⣽⣿⠄⠀⡀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⢠⡝⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⣿⣎⡿⡘⠁⡀⠀⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡆⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡆⠃⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⡿⢧⣳⢿⠀⠉⠉⠀⣧⢹⠀⠀⠀⠀⠀⠀⠄⠀⠂⢀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⣷⢹⠀⠀⠊⢃⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣻⣼⡿⣾⣠⢀⠁⠈⠀⣦⢿⠉⠀⠀⠀⠀⠡⠜⢀⠀⠃⡰⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠿⡵⢋⣾⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⡟⣼⠀⠋⡴⣤⣤⣤⠲⡙⣦⢿⠿⠿⡴⣀⠁⠊⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⣞⣠⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣾⢀⠇⣸⠀⠀⠀⠀⠀⡀⢧⠘⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠴⣠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠾⡴⣠⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⢹⠀⡇⢳⠀⠀⠀⠀⠀⠀⠏⣰⠀⡏⠳⠚⠓⠚⠛⠟⠿⠶⣭⣷⣏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⣻⣶⠹⠠⡀⣤⠲⠒⠒⠖⡴⢀⠀⠏⣿⢲⣶⠶⢶⣤⢻⢳⣫⣕⠮⣓⣯⠺⠙⠉⠉⠉⠚⠖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣳⣱⣿⣧⠻⠙⠉⠉⠉⠉⠋⠟⡾⣤⢀⠀⠀⠀⠀⠀⡀⢷⡹⡼⣏⠦⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣻⣧⡞⣻⣿⡜⣮⣜⣻⣞⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡷⢛⣭⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣦⣽⣿⣟⢽⡯⢞⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⣀⣀⣀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀