⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⣰⠃⠀⠀⠀⠀⠤⣄⣀⡤⠤⢬⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⢀⣴⠛⠛⢒⠚⠦⡴⠋⠀⠀⠉⠙⠲⠦⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠊⠀⢠⠞⣷⡶⠚⠀⠀⠠⠶⠶⢶⡦⠤⣄⠉⣿⠒⢦⣀⠀⠠⢖⣺⣷⠖⠛⠓⠿⣖⡉⠓⠦⢤⣀⡀⢀⣸⣇⣤⠖⠋⠛⠖⠛⠋⠉⢿⠿⣍⠳⢤⡀⠙⢦⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠴⠋⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⠛⠳⠤⣴⣯⣤⡶⢋⠉⠀⣠⡤⠤⣤⡄⠉⠓⢤⣄⡀⠉⠛⠲⢬⡉⠓⢦⣀⠀⠀⠀⠀⠸⡇⠘⡇⠀⣷⠀⠈⡇⠀ ⠀⠀⠀⠀⢠⡞⠀⠀⠚⡇⣀⣴⣶⡀⠀⢀⡤⢤⣤⠴⢗⡀⠀⠀⣀⡇⢀⡏⠀⢀⣰⣾⣁⠤⣀⠈⠳⣀⠀⠀⠉⠉⠲⢤⡀⠀⠉⣓⠦⣜⣷⣦⣤⣤⠀⣧⠀⠇⠀⠻⡄⠀⢇⠀ ⠀⠀⠀⠀⣟⠀⠀⣰⠟⠁⠻⣄⠀⢳⣶⣻⠚⢋⡴⠚⠳⣭⢷⣌⠉⠁⣸⠇⠀⢸⣀⣛⠹⢦⣈⡷⡄⠈⠳⢤⡀⡀⠀⠀⠉⠲⢤⣠⠟⠋⠁⣀⣽⢯⡀⢸⠀⠀⠀⠀⢹⡄⠸⠀ ⠀⠀⠀⢰⡏⠀⢠⠏⣸⠀⠀⢈⡷⣄⠈⠛⢦⡀⣤⠤⣤⡘⠋⠛⠁⡾⢁⣠⠶⠛⠻⡭⠔⠚⠋⣄⠙⢄⠀⠀⠙⢧⣀⠀⠀⣠⠞⠁⠀⣠⡾⠋⢈⠳⡆⠈⠃⢰⠀⠀⠀⠳⠀⠆ ⠀⠀⠀⣸⠁⠀⡟⢠⡇⠀⠀⡾⠁⣙⢦⠀⢈⣿⠇⠀⠀⠀⣠⢀⡾⠁⣏⡀⠀⠀⠀⠖⢲⠄⠳⡘⢦⣈⠳⡄⠀⠀⡼⠷⠶⠃⢀⣠⠞⠉⠻⣆⡀⢳⣹⣧⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⠀⢸⢣⣾⣀⣠⡴⠁⣰⠃⢈⡿⠋⠁⠀⢀⡴⠚⠁⠉⣄⢸⣄⡙⢿⣷⣤⣄⠸⣤⡀⠙⢦⠈⠳⣽⣤⡀⠙⢦⡀⣰⠯⠀⠀⠀⠀⢿⠓⡆⢳⣹⣇⣾⣄⠀⠀⠀⠀⠀ ⠀⠀⠸⠃⠀⠀⡇⠏⢙⡟⠁⣰⠃⢠⠏⠀⠀⠀⠀⣿⠀⢠⡄⢀⣾⠞⠉⠉⠉⠹⠶⠛⠉⠻⣽⣦⣀⠙⠀⠈⠙⠿⣦⢤⠙⠳⢤⢀⣀⡀⢠⠜⠀⣇⠀⠙⡟⢿⠈⠓⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⣸⠀⣰⠃⢠⡏⠀⠀⣠⠒⡋⠉⠀⣸⣧⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣄⡀⠀⠀⠈⢧⠀⠘⠈⠀⣩⠟⢦⡀⠙⠳⣄⡀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠇⢠⠏⢰⠃⢀⡞⠀⢀⡼⠁⣰⠃⢀⣾⡿⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⣀⠀⠀⠲⣄⡚⠁⠈⠀⠱⣄⠀⠀⢙⣆⢹⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡄⢿⠀⠺⡄⣸⠁⢠⣾⣧⠞⠁⠀⣸⣿⠀⠘⢦⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣷⣦⠤⠽⠶⢤⣀⠀⠈⠳⡄⠀⠻⡄⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⣸⠿⡇⣹⠇⢀⡟⡼⣿⡀⣠⣾⣥⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣦⣤⡉⠈⠁⠘⢿⡀⠀⢧⠸⡄⢀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⣿⢠⡇⢿⠛⠉⢸⣿⣿⡃⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠞⠛⢿⣷⣄⠀⠈⢧⠀⠘⡆⢀⣼⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⢻⡀⢳⡀⣀⣤⢿⣿⣿⡇⠈⠋⠉⠉⠙⠛⠳⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠁⠀⠀⠀⠈⠛⢿⣇⡀⣾⠀⠀⣻⠞⢸⡀⠀ ⠀⠀⠀⠀⠀⣿⡆⠈⡇⣴⣷⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣨⢿⣇⢈⣧⣾⠟⣢⣼⣷⡆ ⠀⠀⠀⠀⠀⣸⠿⣦⡘⣿⣿⣻⣶⣤⣹⣿⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⡀⠀⣀⣾⣁⣼⣿⣿⣿⣿⣿⡿⡿⡏⠀ ⠀⠀⠀⠀⠀⣻⡀⠈⠻⣿⣿⣿⣿⣷⣧⣼⣇⣠⣽⣶⣤⣀⣠⣄⠀⠀⣤⡤⠶⢲⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⣴⣷⣿⣿⣿⣿⣿⠛⠛⣿⠉⠀⠀⡇⠀⠀ ⠀⠀⠀⢀⡞⢻⠀⠀⠀⠸⡏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣶⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣋⣿⣿⠿⣿⡿⠟⣻⣿⣿⣶⣾⡟⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠘⠀⢸⠀⠀⠀⢰⠃⠀⠀⢀⡟⢹⣿⡋⠈⣻⣷⣄⡘⢿⣿⠿⠯⣟⣻⡿⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣻⡿⠛⢁⣴⣋⣴⠟⢹⣿⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀⠀⢀⣘⣇⣈⣻⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣛⣉⣉⣛⡟⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠙⣿⣿⠉⠙⣷⣿⣿⠃⠈⠿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⡇⠀⣸⢸⠉⠁⣿⣿⡁⠀⠀⠀⢀⡽⠋⠈⢹⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢻⡄⠀⣸⡿⢸⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⠸⡆⢸⢻⣿⣧⠀⠀⠀⠿⠁⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡰⣀⠀⠀⠀⠀⠀⠁⠀⠈⠳⠄⣿⠁⢸⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀ ⢠⠖⠀⠀⠀⣤⠀⠀⠀⠀⢸⡆⠈⣧⣧⢸⡇⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠀⡞⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⡇⢠⠏⡇⢸⡇⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣲⣾⠀⢿⠀⡇⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣿⡿⠁⠀⠀⠀⠀⠀⠀⢠⣾⡿⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢹⠀⣸⠀⡇⠀⣦⠀⠸⡟⢷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⣤⣶⠿⢷⣄⠀⠀⠀⠀⢀⣴⡟⢹⣿⠀⢨⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⢸⠀⢿⠀⠀⣸⠟⠀⢰⠁⠀⢹⡿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⣿⡤⢾⡿⠗⠀⢀⣴⠟⠋⢀⡿⢸⠀⢸⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⡸⠀⢠⡏⠀⣰⢺⠀⠀⠀⠹⣿⣿⣟⠶⣤⣄⡀⠀⠀⠀⢤⣄⣀⣀⣴⠞⠁⢀⣴⠟⠁⠀⠀⡼⢻⢸⠀⢸⠀⠀⢰⡇⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⡅⠀⢹⡸⣆⠀⠀⠀⣸⣿⣿⢿⣮⡽⣿⣷⣦⣄⣀⠙⢿⣿⣉⣠⠞⠋⢰⠀⢀⣼⡟⠁⢸⠈⡆⠸⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⢳⠀⠀⢸⣷⡀⠈⣇⣼⠀⢰⡏⠁⣿⣿⠈⠙⠿⣿⣿⣯⣿⣿⠏⠉⢻⠁⠀⠀⠀⢸⣠⡞⢸⡇⠀⠈⠀⡇⠀⠀⠀⢸⠇⢷⠀⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠘⡆⠀⠀⠀⡄⠀⠸⠈⡇⠀⠀⣿⠃⠀⢿⡇⠀⠀⡇⠀⣿⣿⠀⠀⠀⠀⠉⠻⣍⢿⡀⠀⢸⣦⣀⣀⡠⣿⠁⠀⢸⡄⠀⠀⠀⣇⠀⠀⠀⢸⠃⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢡⠀⠀⠀⡇⠀⠀⢿⠀⠀⢸⡇⣰⠀⣇⣤⡿⠋⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠸⡇⠀⠀⠀⡏⠀⠀⠘⠃⠀⠀⡇⡏⠀⠀⠀⢸⡀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⡀⠀⠀⣷⠀⠀⢸⡄⠀⢻⣷⠃⢀⡇⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣳⢤⡀⠀⠀⠀⣳⠀⠀⠀⢀⣀⣀⣷⡇⢀⠀⠀⢸⡀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡇⠀⠀⢸⡄⠀⢸⢿⠀⠈⣧⠀⢸⣷⣿⣳⣄⣀⠀⠀⠀⠀⠀⠀⢀⣼⣻⠿⢿⡿⣶⣶⣿⡶⣶⡚⠛⠉⠙⠛⠿⣾⣦⣠⡾⠃⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡳⠀⠀⠀⠃⠀⠀⠀⡇⠀⢸⣿⠀⢠⣿⡴⠻⠟⣾⣏⣻⣬⣷⣲⣦⡤⢶⣾⡯⠞⠋⠀⢈⡇⣿⢀⣈⣷⣼⣧⣤⠴⠖⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢷⠀⠈⢿⡀⠀⢻⠀⠀⠀⠘⢬⣿⣁⣠⣭⠙⠛⠋⠀⠀⠀⠀⣠⠞⢻⣯⠉⠉⠀⠙⣆⠙⣧⡀⠀⠀⠀⠀⠀⢿⡗⠀⢸⠀⠀⠀⠀⠀ ⠀⡼⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣧⣀⣸⢧⣤⠴⠞⠛⢻⡥⣄⠀⠀⠀⠲⣄⠀⡀⣠⠏⠀⠈⣿⣇⠀⠀⠀⠈⠳⣌⠳⣄⠀⠀⠀⠀⠘⡇⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢸⡇⠉⢹⡄⠀⠀⠀⠀⢀⡳⡞⠀⠀⠀⢀⠈⢉⡵⠋⠀⠀⠀⠸⡿⣆⠀⠀⠀⠀⠘⢦⠙⢦⡀⠀⠀⠈⣇⠀⢸⠀⠀⠀⠀⠀