Frozen Text Art

⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠒⠒⠒⠒⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠖⣋⣤⣶⣾⠿⠟⡻⠻⡍⢲⣦⣌⡛⢦⡀⠀⠀⠀⠀ ⠀⠀⣠⠞⣡⣾⣿⡿⠓⠁⡀⡌⠀⠁⠒⠚⠿⢻⣿⣦⡙⢦⡀⠀⠀ ⠀⣴⢃⣼⣿⢿⡏⢇⠱⢄⣣⢕⣤⣄⠁⠀⠈⠈⣿⢿⣿⣆⠻⡄⠀ ⢰⠃⡾⠻⢫⣾⡟⠖⠟⠋⡀⠈⠁⢀⣡⢄⠈⢰⣿⣾⠸⢻⡆⢻⡀ ⡟⢰⣏⡎⡤⣳⣿⣰⠗⢺⡦⠀⠀⠰⣿⣣⠷⢸⣿⣡⡅⣞⣿⠘⡇ ⡇⢸⠫⡄⡔⡏⣿⣧⡤⠀⠀⠀⠀⠀⠀⡘⢵⣿⡟⡗⡇⡬⢽⠀⡇ ⢷⠘⣷⣷⣹⠾⡻⣻⣧⡀⢢⡉⠛⣠⠊⠀⢺⡫⠿⢿⣧⣿⡿⢰⡇ ⠘⣆⠹⣩⣬⡝⣟⢿⣿⣿⡞⠉⠈⢹⣦⠄⠘⣟⡿⣭⣍⣹⢃⡾⠀ ⠀⠙⣆⠹⣿⣿⣶⣉⠉⠀⠀⠠⠤⡞⠙⠀⣠⣷⣾⣿⡿⢁⡾⠁⠀ ⠀⠀⠈⠳⣌⠃⠈⠙⠳⣄⣀⠀⢞⠁⠀⣠⠟⠉⠀⢈⣴⠏⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠉⠉⠹⣄⡠⢿⣄⣤⠶⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠛⢆⠁⠈⠧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⣤⣶⣿⣿⣷⣤⣶⣶⣆⡀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀ ⠘⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠈⠛⢻⣿⣿⣿⣿⣿⣷⡄⠀⠀ ⠀⠀⠀⠿⠛⠛⠛⢿⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣽⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣿⣿⣿⣷⣄⣀⣤⣶⣶⣶⣄⢀⠀⠀ ⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣧⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⢠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡡⠀⠀⠀ ⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀ ⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠿⠛⠋⠉⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣆⢻⣿⡗⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀

⠀⠀⠀⠀⠄⠀⢉⠠⠤⠅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠂⠀⢰⠃⠔⠀⠀⠂⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣷⣤⣈⠈⡔⠒⢦⠠⡀⣀⠀⠀⠀⡀⠀⣀⣀⣤⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣯⠎⠀⠀⠀⠀⠈⠀⠈⠢⢭⡄⠀⣷⣾⣿⣥⡙⠷⣦⡍⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡆⠤⠀⠀⠠⠤⠒⣀⡀⠘⢹⣿⣿⣻⣿⠿⠛⠀⠀⠈⠀⡀⣌⡄⠀⠀⠀ ⠀⠀⠘⢣⡀⣀⠀⠀⠑⠉⠋⠀⠀⢿⡟⡞⣩⡀⠁⠀⠀⢉⠭⢅⠈⣽⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⣷⡇⠩⠃⠀⠀⠀⠉⠀⠀⠀⠋⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣀⠄⠞⠘⣿⠁⠀⠀⠀⠀⠀⢀⠀⠀⢀⡠⢲⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣶⠞⠁⠀⡀⠀⠈⣿⣆⠀⠀⠉⠉⠀⠀⡀⠺⡇⡈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠄⣏⢹⣿⣒⡤⠄⡒⡎⡏⠀⠧⢃⠀⠀⠀ ⠀⠀⠀⠀⠒⠙⠋⠄⠀⠀⠀⠀⠀⠀⠠⣧⣀⡌⠿⠿⠿⠿⠾⣃⢏⠀⠀⠀⠀⠀ ⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡾⠉⠀⠠⠀⠀⠀⠈⠱⣾⠘⠴⡀⠀⠀ ⠀⠂⠀⠋⠁⠀⠀⠉⠙⠻⢿⣿⣿⣿⠏⠀⠀⠀⢀⠀⠀⠀⠀⠀⢹⣇⠀⣣⠀⠀ ⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⢿⣎⠀⡄⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠤⣿⡇⠑⡡⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⣖⣆⠀⠀⠀⠀⣀⠀⠀⣐⣢⣶⠿⠋⠀⠀⢧⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠛⠛⢒⣺⣒⣚⡛⠛⠉⠀⠀⠀⠀⠀⠀⠘

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣿⠿⠛⠉⠁⠀⠉⠻⠛⠉⠁⠀⠀⠈⠉⠙⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣾⣿⡿⠛⢁⡀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⡟⠍⠉⣻⣁⣴⠚⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠠⠔⠛⠉⠓⠒⠶⣤⣀⠘⣿⣿⣯⣿⢿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⠋⠙⠳⠶⠀⡀⠙⣷⡄⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠠⠀⡠⠀⠀⠀⠀⠀⠀⠈⠛⢾⣿⡿⣽⡿⣿⣻⣽⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⣾⠳⡞⢃⣀⡀⠀⠀⠀⠀⢻⣦⣀⠀⢈⠀⠄⠀⠀⠀⠀⢠⠋⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠙⠿⣿⣽⣟⡿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣿⠃⣼⡇⠂⡌⠙⠛⠒⠀⠀⠀⠙⠻⢷⣶⣎⠄⠀⠀⠀⣴⠂⠀⠰⣮⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠘⢿⣾⣟⣿⣳⣿⣽⣾⣿⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣿⣻⣾⣟⣾⠃⢸⡟⢠⠁⢄⣀⣠⣤⠦⠶⠀⠀⠀⠀⠈⢻⣦⠀⠀⣼⣃⠀⠀⠀⠈⢷⡐⠀⠤⢄⡀⠀⠙⢦⡀⠀⠦⢻⣿⢾⡽⣷⢿⣻⣾⣿⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣼⡿⣿⢧⣿⣿⡿⢼⡧⠄⠛⠘⠛⠃⢀⣠⣤⣿⠿⠿⠿⠧⣤⡿⠤⠼⣇⣿⣤⠀⠀⠀⠘⠿⣄⡀⠀⠀⠀⠀⣀⢧⡀⢀⠸⣿⣿⢿⣻⣿⢿⣻⣼⣿⣿⢿⣿⣿⣿ ⣿⣿⣿⣿⣷⣿⣯⣿⣟⣿⣳⣿⠁⢸⣟⠬⢡⡷⠌⢱⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠻⣷⣤⣀⠀⠈⠳⣽⡄⡄⢿⣿⣿⣳⣯⡿⣟⣯⣿⢿⣿⣿⣿⣿ ⣿⣿⣿⣷⡿⣷⣿⣳⢿⡾⣽⣿⣤⣾⢋⡴⠋⢀⣴⡿⠃⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠘⣿⣏⡳⢦⡀⠈⢻⣷⢸⡇⢻⣟⣾⡽⣟⣯⣿⡿⣟⣯⣿⣿ ⣿⣿⣿⣽⣿⣟⣾⣟⣯⣟⣷⡟⣽⡿⢋⠤⣑⣾⣿⠡⢃⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠸⣿⡟⣶⣄⠠⢀⣈⡉⢁⣿⡿⣾⣽⣻⣽⣾⢿⣿⡿⣿⣿ ⣿⣿⣿⣻⣾⣟⣷⣻⢾⡽⣾⣯⣿⠃⢌⣶⣿⣿⢇⣫⣿⣿⣿⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣤⡴⣶⣦⣄⠀⠹⡇⠈⠙⢷⣾⣧⣾⢿⣻⡽⣳⢯⡷⣟⣾⣿⣻⣿⢿⣿ ⣿⣿⣟⣿⣽⡾⣯⣟⣯⢿⣽⡇⢻⣘⣼⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠰⠿⢛⣯⣿⣿⣿⣿⣿⣯⣷⠀⢿⣆⠀⠀⣿⣿⣏⡟⣾⣹⢯⡿⣽⣻⢷⣻⣯⣿⣿⣿ ⣿⣿⡿⣯⣿⣽⢷⣻⣞⣟⡾⣷⡘⣿⣿⡟⣱⡏⢽⣿⡟⠋⣿⣿⣿⣻⣿⣿⡂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⠙⢻⡿⠀⠘⠻⣧⠀⣿⣿⢧⡻⣵⣫⢷⣻⢷⣯⢿⣯⣷⡿⣷⣿ ⣿⣿⢿⣟⣷⣯⢿⣳⣟⡾⣝⣻⣿⠹⣿⡗⢸⡇⡘⢿⣧⣀⠻⣿⣿⡿⠁⣿⠇⠀⠀⠀⠀⠀⠀⣿⠙⢿⣿⡿⢫⣠⣾⠁⠀⠀⠀⣿⣧⡟⠸⣿⢿⣿⡳⢯⣟⡾⣽⣻⢾⡷⣿⣿⢿ ⣿⣿⣿⣻⣟⣾⣟⡷⣯⣟⣭⢷⡻⣷⣞⣧⠚⡇⢸⣀⠋⠙⠛⠛⠒⠒⠲⠟⠁⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⢈⣿⣧⣤⣿⢿⣳⢻⣛⡾⣽⣳⢿⣯⢿⣿⣽⣿ ⣿⣿⣾⡿⣽⡷⣯⣟⡷⣯⣞⢷⣫⢗⣿⡽⣇⢯⢸⣿⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣸⣻⡟⣼⢣⠿⣜⣯⣻⢽⣳⢯⣿⢾⣟⣯⣿⣿ ⣿⣿⣷⡿⣿⣽⢷⣯⣟⡷⣞⣯⢾⡹⣞⢷⡝⢿⡄⢻⣷⡈⠆⡄⠀⠀⠀⠀⣴⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣴⢇⣿⠽⡜⣯⢻⡵⣳⢯⢿⣽⣻⢾⣟⣯⣿⢿⣽ ⣿⣿⣾⢿⣯⣟⡿⣾⡽⣾⡽⣞⣧⠿⣜⢯⣿⣼⣿⡌⢻⣮⠱⡌⢡⠀⡀⢀⢻⣟⣿⡿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣄⣼⠛⠉⠁⢸⣿⡯⣝⡞⣧⠿⣭⣟⣻⢾⣽⣻⣾⣟⣯⣿⣿ ⣿⣿⡿⣿⣯⣿⡽⣷⣻⢷⣻⢾⡼⣏⡟⡾⣼⡇⢻⠹⣎⡻⣷⡘⠤⡑⢶⣯⣼⣾⣥⣴⣤⣤⣤⡶⠖⠀⠀⠀⠀⣤⣾⣿⡄⠀⠀⠠⢸⡿⣼⡹⣞⣽⣳⢯⣟⡿⣾⣽⡾⣟⣿⡿⣿ ⣿⣿⣿⢿⣳⣿⣻⣷⣻⢯⣟⣾⢳⡯⣽⢳⣭⣿⡀⠂⠘⡳⣮⡙⠦⠑⣄⠢⢉⡙⠫⠿⠯⠉⠀⠀⠀⢀⡤⣷⣽⣿⣿⡷⣄⠀⠀⢰⣿⣿⡖⣯⡽⣶⢯⣟⡾⣽⡷⣯⣿⢿⣟⣿⣿ ⣿⣿⣿⣿⣿⣻⣷⢿⣽⣻⢾⡽⣯⢷⣫⢷⡺⣜⡿⣦⣁⠼⢉⠿⢷⣅⡢⠑⣂⠐⣀⡀⠀⠀⠀⠀⣰⣿⣾⣿⣿⣽⠏⠙⢿⣳⣆⣾⣿⣯⢻⣵⣻⢞⡿⣾⡽⣷⢿⣻⣽⣿⣿⣿⣿ ⣿⣿⣿⣿⣾⣿⢯⣿⣯⣟⣯⣟⡷⣯⣻⢞⡽⣧⢻⡭⢿⡆⠳⢈⡜⣿⡛⢳⠲⡌⠤⣈⠛⠚⠛⠀⠙⣿⣿⣿⣿⠋⠀⠀⠈⠀⠈⠻⠿⣯⣟⡶⣯⢿⣽⣳⢿⣻⡿⣟⣿⣯⣷⣿⣿ ⣿⣿⣿⣿⣯⣿⣿⡟⣾⣯⣷⣯⡟⣷⣯⡟⣽⡞⢳⣯⠛⣿⣦⠈⠁⣿⣧⠁⢣⠈⠂⠀⠀⠀⠀⠀⢠⡏⢻⣿⠃⠀⠀⠀⠀⣶⠀⠒⡄⢸⣯⣿⣽⢻⣾⣽⣿⢻⣽⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣟⣿⣿⣽⣻⡾⣟⡷⣯⣟⡷⣻⣛⣮⢿⣱⢯⢿⣶⢿⣧⠉⠠⠈⠀⠀⠀⠀⠀⠀⢸⠃⣼⡿⠀⠀⠀⠀⠚⣷⠀⠀⠙⣮⣿⣾⣽⣻⡾⣿⣽⡿⣿⣻⣿⣽⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣯⣿⣻⣽⢷⣯⣟⣷⣻⢾⣭⢷⣫⢿⡏⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠠⣿⠁⠐⠀⠀⠀⣻⠟⢧⡀⠀⠃⣿⣿⢾⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣽⣿⣽⡿⣾⡽⣾⣽⣻⣞⣯⣿⠟⠁⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿⡤⣿⢀⡀⠀⢠⣴⢏⠀⠈⠷⣄⣀⣿⣿⣻⣿⢾⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⢿⣽⣿⣽⣷⣿⠷⠛⠉⠀⠀⢰⡟⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢰⣿⡸⠁⠀⠘⣽⡦⠀⠀⠀⠈⡿⠿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠿⠟⠛⠉⠀⢀⠂⠀⠁⠀⢸⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣸⡿⠁⢠⡆⠀⣹⣧⣰⠀⠀⠀⠁⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⠃⡠⠛⠀⣠⡿⣌⠳⣄⠄⢀⠀⠠⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⡀⠀⠂⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠻⣿⢰⣁⣀⣴⡿⠖⠈⠀⢻⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⠠⣀⡁⣀⣠⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢂⣿⡿⠁⠀⢸⣷⡄⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠚⠛⠛⠛⠲⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⢶⣶⠞⢛⣶⠟⠁⠀⠀⠀⠀⣀⣤⣤⣀⡈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⢠⡟⠀⢠⡞⠁⠀⠀⠀⢀⡴⠟⠉⠉⠉⠙⠻⢷⣄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣞⣿⡀⠀⢸⠃⠀⡟⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠉⠁⠀⠈⠙⠛⠷⣤⣸⡄⢸⠁⠀⠀⠀⢰⠏⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠙⠿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⠶⠶⠶⠶⠶⠶⠶⠦⢤⣽⣻⣿⣄⠀⠀⠀⣿⡤⠤⠶⣾⡛⠉⠉⠉⠛⠻⢦⣀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢀⣀⣤⠴⣶⣚⣛⣛⣛⠿⣦⠀⢸⣋⣀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠁⠀⠀⠀⣀⣫⠵⠖⣻⠽⠟⠛⠛⠛⠛⠋⠁⠈⠉⠉⠻⣆⠀⠀⠀⢻⣦⣀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡟⠛⠛⠉⠉⣠⢶⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠙⣎⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣻⠶⢶⣾⠟⢁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣀⠀⠈⠳⣽⡻⣦⡀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠇⣰⡿⠁⣰⢫⡇⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⡠⠤⢬⣭⢭⣝⠛⣧⠀⠙⢦⣀⠀⠀⠀⠈⢍⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢰⡟⠀⣴⠃⣸⣡⣾⣏⡛⠛⠛⠛⠓⠲⡁⠀⠀⠀⠀⠈⠉⠉⠉⢉⣡⣬⣭⣍⡓⢽⡆⠀⠀⠙⠷⣦⣤⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡿⠀⣼⠃⢀⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⢹⡀⠀⠀⠀⠀⠀⢀⣴⣿⣻⣟⠻⢿⣿⡆⣿⣆⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⢠⡇⢀⡾⣿⣿⣿⠋⣯⣿⣶⣿⡷⡀⠈⡇⠀⠀⠀⠀⠀⡿⡽⣿⣷⣿⠀⠀⣿⠁⢻⡎⢷⣄⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡇⢸⣠⣿⠁⣯⠉⣧⡀⠳⢿⣻⠞⠀⢣⠀⠳⠀⠀⠀⠀⠀⣇⣈⣚⡻⠥⠤⠞⠋⠀⢸⣿⠈⡿⣦⡀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣸⠃⣿⠀⣿⠀⠈⠉⠉⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⢣⢿⠳⣄⠈⠳⣶⠖⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⢀⣿⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⡞⠘⣾⡛⠚⠷⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣏⣧⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢾⣥⣀⠀⠠⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠋⠀⣰⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠓⠒⠚⠁⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠛⢷⡄⠀⠀⠀⠀⠀⢠⡶⠯⠭⠤⠶⠾⢟⡿⠇⠀⠀⠀⠀⢀⣾⠧⢤⣀⡀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠻⣦⡀⠀⠀⠀⠀⠈⠉⠑⠒⠊⠉⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠈⠙⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣥⣀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⡴⠋⠙⡟⠶⢦⣤⣤⣤⣤⣤⡤⠶⠛⠉⣸⠁⣀⣭⣿⣦⣄⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⡁⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⣞⣉⣤⣀⠉⠙⠻⢦⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⡿⠋⠀⠀⠘⣧⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⢹⠃⠀⠀⠀⠀⠀⠀⠀⢠⣏⡟⠀⠀⠀⠀⣠⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⡧⠶⠶⢴⠛⠁⠈⢳⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢸⡇⠀⠀⠀⣿⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢀⡼⣅⠀⠀⠀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣴⡶⠟⠛⠉⠁⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣀⣴⠋⠀⠈⢷⡀⢠⡿⠈⠙⠻⢶⣦⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⣠⡶⠟⢯⣟⡉⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢠⡿⣧⠞⠋⠁⢸⠆⠀⠀⠈⣧⡾⠒⠶⢶⡏⠉⠉⣉⣉⣽⠟⢶⣤⠀ ⢀⣾⠉⠀⢰⠶⠾⠟⠓⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⡾⣽⠃⠀⠀⣠⣿⠀⠀⠀⢠⡿⠁⠀⣴⠿⠖⠚⠉⢉⣼⣣⢴⣟⡟⣧ ⣼⠉⠙⠦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣼⢹⡏⠀⢀⡼⠋⠘⡆⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠠⠟⠉⢠⠎⡼⢹⣹ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣸⠇⢸⡇⢀⡞⠀⠀⠀⣿⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⡼⠁⢸⣿ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠒⠒⠒⠒⠒⠒⢺⠋⠀⢸⡟⠋⣿⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡿⠁⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣿⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⣿⡗⠁⠀⠀⠀⠀⣦⡈⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣤⠀⠀⠘⢿⣟⣲⣿⠿⢦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⢀⣴⠭⣍⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣶⣠⠀⣴⣿⣾⡆⠀⠀⠀⠲⠾⠟⠛⣯⣍⠓⢤⡀⠀⠀⠀ ⠀⠀⣠⠀⠀⢸⣣⣤⢤⣖⣛⡓⠒⠮⡳⡄⠘⣯⠳⣄⠀⠀⠀⠀⠀⠀⠈⢿⣧⣿⣷⡏⢿⣿⣁⣠⣄⠀⢀⣤⡤⠤⠽⠈⢦⡀⠙⣶⡀⠀ ⠀⢰⢻⣀⣀⠤⣫⠟⠉⠀⠀⠉⠓⢄⠸⣇⠀⢸⡄⠈⣦⠀⠀⠀⠀⢠⣦⣽⣿⠿⠍⠁⠘⠻⣿⣟⣿⡽⠏⠉⠉⠉⠙⠢⠤⣉⡿⠟⡇⠀ ⠐⣾⡄⠀⢀⡜⠁⠀⣀⣀⣀⣀⡀⠈⢆⢸⢀⠞⢀⡴⢻⡀⠀⠀⠺⠯⣿⣾⣿⣷⡄⣀⣘⣿⣟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⡇⠀ ⣴⣿⣽⢶⠏⣠⠖⠉⠁⣀⠤⠤⢬⣶⣘⣿⣷⣊⣁⣠⡼⡄⠀⠀⠀⠀⠀⠁⣼⣿⣶⡿⢿⣿⣿⣯⡀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠇⠀⡇⠀ ⠁⠻⠿⠵⠊⠁⠀⣴⣿⠗⠉⠉⢉⣽⠿⠟⠉⠀⠀⣸⣟⣾⠀⠀⠀⠀⠀⠀⢿⣿⡯⠃⠈⠛⠳⠿⠇⠀⠰⣶⣴⣿⣀⡀⠀⡼⠀⢠⠃⠀ ⡄⠀⠀⠀⠀⡠⠊⡿⠁⠀⣠⡶⠉⠀⠀⠀⠀⠀⣸⣵⣽⣿⣀⣶⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⣾⣯⣭⣻⣟⠉⢰⠇⠀⠰⠀⠀ ⣷⣤⠤⠔⠋⢀⣾⠗⢁⣞⡟⠀⢀⣀⣠⡴⠀⠀⡟⣿⣷⡿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠛⠛⠀⡏⠀⠀⣦⠀⠀ ⢾⢻⣀⣀⠴⠚⠁⣠⣏⣿⡶⢚⣿⣯⣭⡄⠀⠀⢣⠟⠋⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠠⣿⠀⠀ ⠸⡀⠀⠀⠀⠀⡰⣡⣿⠩⣴⣿⣿⣿⣇⡽⠃⠀⠀⠳⣄⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠔⣿⠀⠀ ⠀⠹⣦⣀⣠⣾⣿⠯⡻⣧⡀⠈⠉⠉⠁⠀⠀⠀⠰⠤⢐⡽⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠛⠁⠀⢀⣰⡟⠀⠀ ⠀⠀⠀⠹⡿⡏⠙⡶⢭⣷⣿⣄⠀⠀⠀⠀⠠⠴⠶⠾⠽⠃⡿⠯⠭⠝⢶⡒⠒⢦⡀⠀⠀⠀⣀⣤⡶⠖⠋⠁⢴⣶⢀⡴⢁⡾⣱⠁⠀⡀ ⠀⠀⠀⠀⠹⣮⠿⡇⡄⡇⠀⣏⠑⢶⠤⣤⣤⣤⣤⣤⡔⠊⠀⠀⠀⠀⠀⢳⡀⠀⠹⣶⣯⡯⣻⠟⠀⠀⢀⣺⣿⣿⣯⣧⠚⠋⠀⠀⡼⡼ ⠀⠀⠀⠀⠀⠀⢸⠀⣷⠁⠀⢸⠀⠈⢢⡀⠀⠀⠀⠀⠈⠲⠤⠤⠤⢤⡒⠚⠓⠤⢄⣿⠛⣯⠁⢐⣊⣉⣭⡿⠟⢻⠘⠢⠤⠔⢒⡩⣼⢗ ⠀⠀⠀⠀⠀⠀⠘⢧⣿⡀⠀⠸⡄⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢉⡗⠦⡴⣞⡛⢧⠘⣯⣭⠝⠋⠁⠀⠀⠸⡀⠀⠀⠰⣤⣤⡥⠖ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⠳⣄⣀⣙⡦⠤⠤⣧⠀⠀⠀⠀⡠⠚⠁⠀⢀⠎⠀⠀⡷⠼⣾⠷⢷⣿⡟⢧⡀⠀⠀⠀⢀⣧⠴⡚⡫⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡠⠊⠀⠀⢀⡴⠁⠀⣀⣠⠇⠀⠛⣿⣿⣿⣇⠀⣿⠀⠀⠀⡼⠁⢠⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠈⠁⠀⢀⡴⢋⣠⠔⠉⢳⡀⠀⠀⠀⠘⢿⣿⣿⢀⠿⠀⢀⡴⠁⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⣴⣿⣿⡿⠁⠫⣷⣟⣧⠀⠀⠀⠀⠘⣇⠻⣾⣄⢠⠞⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⡠⣶⣿⢟⢿⣿⣅⡀⠀⠈⠑⠻⡀⠀⠀⠀⠀⣿⠀⠑⡿⠋⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣼⡗⡿⢋⠏⣿⠀⠉⠓⠦⣄⡀⡇⠀⠀⠀⠀⣿⣠⠞⠀⠀⢰⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢜⣡⡎⢸⡻⠁⢧⡀⣄⠀⠉⠛⠢⢤⣀⡀⡼⠃⠀⠀⢤⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠉⠳⢧⣻⠀⠀⢻⣌⠳⣦⣰⢆⣀⣀⠽⠁⠀⣀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠙⢏⠒⠦⣷⣷⣌⣻⣉⣠⣴⠶⠚⠉⣉⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠘⡿⣿⠉⠓⠓⠦⠤⣶⣟⣺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡄⠿⣿⠉⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡝⠀⣸⡏⠀⢸⠀⠀⡇⢹⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠓⠦⠿⡧⠤⠾⣀⣸⡃⢸⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠈⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢸⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

🟦🟦🟦🟦🟦🟦⬛⬜⬛⬜⬜⬛⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦 🟦🟦🟦🟦🟦⬛⬜⬛⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦 🟦🟦🟦🟦⬛⬜⬜⬛⬜⬛⬜⬜⬛⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬜⬜⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦 🟦🟦🟦⬛⬜⬜⬜⬛⬜⬛⬜⬛⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬛🟦🟦⬛🟦🟦🟦🟦🟦🟦 🟦🟦🟦⬜⬛⬜⬜⬛⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬛🟦⬜⬛🟦🟦🟦🟦🟦 🟦🟦⬛⬜⬜⬜⬜⬛⬜⬜⬜⬛⬜⬛⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛⬜⬜⬜⬜⬛🟦⬜⬛🟦🟦🟦🟦🟦 🟦🟦⬛⬜⬛⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬛⬛⬜⬜⬜⬛⬜⬜⬛🟦🟦🟦🟦 🟦⬛⬜⬛⬛⬜⬜⬜⬛⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬛⬛⬜⬛⬜⬜⬛🟦🟦🟦🟦 ⬛⬜⬛⬜⬜⬛⬜⬜⬛⬜⬛⬜⬛⬜⬜⬜⬜⬛⬛⬜⬜⬛⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛🟦🟦🟦🟦 ⬜⬜⬜⬛⬜⬜⬛⬜⬜⬛⬜⬜⬛⬜⬜⬜⬛🟧🟧⬛⬛⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟦🟦🟦🟦🟦 ⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬛⬜⬜🟧🟧⬜⬛🏼🟧🟧⬛⬜⬜⬛⬛⬛⬛⬜⬜⬜⬛⬛⬜⬛🟦🟦🟦🟦🟦 ⬜⬜⬛⬛⬜⬜⬜⬜⬛⬜⬜⬛⬜🏼🏼🏼🟧⬜⬛🏼🏼🟧⬛⬛⬜⬜⬜⬜⬛⬛⬛⬜⬜⬛🟦🟦🟦🟦🟦🟦 ⬜⬛⬜⬜⬜⬛⬛⬛🟧🟧⬜⬜🏼🏼🏼🏼🏼🟧⬜⬛🏼🏼🟧🟧⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬛🟦🟦🟦🟦🟦 ⬛⬜⬜⬜⬛⬜🟧🟧🏼🏼🟧🏼🏼🏼🏼🏼🏼🏼🟧⬜🏼🏼🏼🏼🟧🟧⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬛🟦🟦🟦 🟦⬛⬜⬛⬜🟧🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🟧🟧⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛🟦🟦 🟦🟦⬛⬜⬜🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🟧⬛⬜⬜⬜⬜⬜⬜⬜⬛🟦🟦 🟦⬛⬜⬜⬜🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🟫🟫🟫🏼🏼🏼🏼🏼🏼⬛⬛⬜⬜⬜⬛⬜⬛🟦🟦 🟦⬛⬜⬛⬜🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🟫🟫🟧🟧🟧🟫🏼🏼🏼🏼🏼🏼⬛⬛⬛⬛⬜⬜⬛🟦🟦 🟦⬛⬜⬛⬜🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🟫🟫🟧🟧🟪🟪🟪🟪🏼🏼🏼🏼🏼⬛⬜⬛⬛⬜⬜⬛🟦🟦🟦 🟦🟦⬛⬜⬜🏼🟫🟫🟫🟫🏼🏼🏼🏼🏼🟫🟫🟧🟧🟪🟪🟪⬛⬛⬛🏼🏼🏼🏼🏼⬛⬜⬛⬜⬛⬜⬛🟦🟦🟦 🟦🟦⬛⬜⬜🟫🏼🏼🏼🏼🟫🟫🏼🏼🏼🏼🟧🟧🟪🟪⬛⬛⬛🟦⬜⬛🏼🏼🏼🏼⬛⬜⬜🟧🏼⬛⬛🟦🟦🟦 🟦🟦⬛⬜⬜🟫🟪🟪🟪🟧🟧🟧🟧🏼🏼🏼🏼🟧🟪⬛🟦⬛⬜🟦⬛🏼🏼🏼🏼🏼⬛⬜⬜🟧🏼⬛⬜⬛🟦🟦 🟦🟦⬛⬜⬜🟪🟪🟪🟪🟪🟪🟧🟧🏼🏼🏼🏼🏼⬛⬜🟦⬛⬛🟦⬛🏼🏼🏼🏼🏼⬛⬜🟧🏼🏼⬛⬜⬛🟦🟦 🟦🟦🟦⬛⬜⬛⬛⬛⬛⬛⬛🟪🟧🟧🏼🏼🏼🏼⬛⬜⬜🟦🟦⬛🏼🏼🏻🏻🏼🏼🏼⬛🏼🏼⬛⬜⬜⬛🟦🟦 🟦🟦🟦🟦⬛🟦⬛⬜🟦⬛⬜⬛🟧🟧🏼🏼🏼🏼🏼⬛⬛⬛⬛🏼🏻🏻🏻🏻🏼🏼🏼🏼🏼⬛⬜⬜⬜⬛🟦🟦 🟦🟦🟦🟦🟦🟦⬛⬜⬜🟦⬛⬛⬛🟧🏼🏼🏼🏼🏼🏼🏼🏼🏼🏻🏻🏻🏻🏻🏻🏼⬛⬛⬛⬜⬜⬜⬜⬜⬛🟦 🟦🟦🟦🟦🟦🟦🟦⬛⬛⬛🟧🟧⬛🏼🏼🏼🏼🏼🏼🏼🏼🏼🏻🏻🏻🏻🏻🏻🏻🏼🟧🟧⬛⬜⬜⬜⬜⬜⬛🟦 🟦🟦🟦🟦🟦🟦⬛🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏼🏻🏻🏻🏻🏻🏻🏻🏼🏼🟧⬛⬛⬜⬜⬜⬜⬛⬜⬛ 🟦🟦🟦🟦🟦🟦⬛🏼🏼🏼🏼🏼🏼🏼🏼🏻🏼🏼🏼🏼🏼🏼🏻🏻🏻🏻🏻🏻🏼🟧⬛⬜⬜⬛⬜⬜⬜⬛⬜⬛ 🟦🟦🟦🟦🟦🟦⬛🏻🏻🏻🏼🏼🏼🏼🏻🏼🏼🏼🏼🏼🟧🏼🏼🏻🏻🏻🏻🏼🟧🟧⬛⬜⬜⬛⬜⬜⬜⬛⬜⬛ 🟦🟦🟦🟦🟦🟦🟦⬛🏻🏻🏻🏼🏼🏼🏼🏼🟫🟫🏼🏼🟧🟧🏼🏻🏻🏻🏼🟧🟧⬛⬛⬜⬜⬜⬛⬜⬛⬜⬜⬛ 🟦🟦🟦🟦🟦🟦🟦⬛🏻🏻🏻🏻🏼🏼🟫🟫🏼🏼🏼⬛🏼🏼🏼🏼🏼🏼🏼🟧⬛⬜⬜⬛⬛⬜⬜⬛⬜⬜⬜⬛ 🟦🟦🟦🟦🟦🟦🟦🟦⬛🏻🏻🏻🏼🏼🏼🏼🏼⬛⬛🟪🏼🏼🏼🏼🏼🏼🟧⬛⬛⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬛ 🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛🏻🏼🏼⬛⬛⬛⬛🟪🟪🏼🏼🏼🏼🏼🏼🟧⬛🏼⬛⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬛ 🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛🏼🏼🏼🟪🟪🟪🟧🟧🏼🏼🏼🏼🏼🟧⬛🏼🏼⬛⬜⬜⬜⬜⬜⬜⬛⬜⬛⬛🟦 🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛⬛🏼🏼🟧🟧🟧🏼🏼🏼🏼🟧🟧⬛🏼🏼🏼⬛⬜⬜⬜⬜⬜⬜⬜⬛⬜⬛🟦 🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛🏼🏼🏼🏼🏼🏼🏼🟧⬛⬛🏼🏼⬛⬛⬜⬛⬜⬜⬜⬜⬜⬜⬛⬜⬛🟦 🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛🏼🏼🏼🏼🟧🟧⬛🏼🏼🏼⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬛🟦🟦 🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛⬛⬛⬛⬛⬛🏼🏼🏼🏼⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬛🟦🟦 🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛🏼🏼🏼🏼🏼🏼⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬛🟦🟦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠖⠊⠉⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡟⢀⠎⠀⠀⡠⠒⠉⠙⠓⢬⣳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠚⠛⠳⢧⣀⡀⡎⠀⠀⡸⠁⠀⠀⠀⠀⠀⠑⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠓⠒⠒⠒⣒⣺⣿⣧⡀⢠⠗⠒⠻⣍⠉⠉⠓⢄⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⢰⣁⣀⣀⠬⣛⠾⠛⠛⠓⠃⠈⠙⠢⡀⠈⢳⣄⡀⠀⠁⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⡧⢤⡴⢪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠑⢽⢦⡀⠀⠀⠈⣄⡀⠀⠀ ⠀⠀⢰⣡⠏⡰⡹⢀⣤⣤⣤⣤⠄⠀⠀⠤⠤⠶⠾⠿⢍⣇⠙⢦⣀⣀⣩⠇⠀⠀ ⠀⠀⢸⡏⡸⢀⣿⣿⣷⣶⣤⠀⢃⠀⠀⠀⢠⣶⣿⠻⣷⢼⣆⠀⠈⡏⠁⠀⠀⠀ ⠀⠀⠘⡀⣧⡞⡟⢏⠸⣿⡟⢡⠸⠀⠀⠀⠌⢻⣟⡡⠜⠀⡏⢳⡄⠸⡀⠀⠀⠀ ⠀⠀⠀⢳⠃⡇⡇⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡼⣯⣢⣹⠖⠀⠀ ⠀⠀⠀⠀⠻⡧⣡⠀⠀⠀⠀⠀⠦⠄⠠⠴⠀⠀⠀⠀⠀⢸⠋⡠⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⡼⢧⠀⠀⠀⢀⣤⡴⢶⠶⡤⠀⠀⠀⣠⢏⡉⢀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠈⠳⣄⠀⠀⠀⠉⠉⠁⠀⠀⣀⡔⠁⠀⠈⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⢀⠜⠛⡲⠤⠤⠤⠤⠔⠊⡟⣩⠷⣤⡀⢀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢠⡇⠀⠀⠀⠀⠀⣴⡿⠒⠒⡄⠈⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡇⠀⠀⠀⠀⢰⣟⣀⣀⠴⢧⠀⢸⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣹⠀⠀⠀⠀⠀⡼⠁⠀⢸⠀⠀⢣⠎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⡤⠖⠚⠉⢀⡏⠀⠀⠀⠀⢰⠃⢀⡠⠋⢢⠀⡜⠲⢤⣄⣀⠀⠀⠀ ⢀⡴⢛⣛⣥⡀⠀⠀⠀⣸⠀⠀⠀⠀⢠⣿⠊⠁⡗⠀⠀⡷⠑⣺⣋⠤⢬⢟⣳⣆ ⡎⠑⠼⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢀⢿⠇⢀⠞⢳⠀⡸⠁⠀⠀⠀⠀⠋⡹⡝⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⡸⠤⠤⠤⠤⡞⢘⠖⢧⠀⠈⡖⠁⠀⠀⠀⠀⠀⠜⡟⠀⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣿⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⡀⠘⢦⣿⣶⣄⠀⠀⠀⠀ ⠀⠀⠀⢠⠂⢀⣰⣋⢍⠲⡤⡀⠀⠀⠀⠀⣷⣶⣰⣿⡧⠀⠀⠚⠛⢛⠅⠢⡀⠀ ⠀⣎⣀⢜⠟⠉⠉⠢⡙⡇⢰⠈⡄⠀⠀⣠⣼⡿⠋⠘⣿⣿⡶⠋⠙⠓⠨⣲⢾⠀ ⣸⣧⡴⡁⠄⠒⣒⣢⡐⣥⠇⣚⣐⠀⠈⠙⢛⣿⣦⣾⣷⡌⠀⠀⠀⠀⠀⠸⢸⠀ ⠉⠛⠋⢀⢴⠛⢉⡩⠛⠋⠀⡸⣿⡆⡀⠀⠈⠿⠋⠈⠙⠓⠀⣲⢾⣤⠄⡆⠘⠀ ⣧⠤⠐⢡⠗⣰⠏⣀⣠⠄⠠⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⠓⠘⠀⢠⠀ ⠋⠒⠊⢁⢜⡟⣩⣿⡟⡦⠀⢋⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠿⠀ ⠈⠦⣤⡾⡻⣷⡈⠉⠉⠀⠀⣒⣼⢻⡀⣀⣀⡀⠀⠀⠀⠀⣀⠠⠔⡚⠀⡠⡆⠀ ⠀⠀⠸⠵⣯⡉⠹⠢⡤⠀⠁⠉⡕⠋⠉⠀⢡⠈⢢⣶⣶⠏⣀⣠⣿⣷⠱⠋⢁⡴ ⠀⠀⠀⠀⣿⡇⠀⡆⠈⠄⠀⠀⠈⠰⠀⠐⣍⣁⡺⠏⢧⡬⠶⠛⠉⡎⠀⢈⣓⣛ ⠀⠀⠀⠀⠈⠓⠤⠴⠆⢸⠀⠀⡠⠊⠀⠐⠁⢐⢻⣾⣾⡗⠄⠀⠀⡧⢂⠞⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⣠⣊⡔⢂⠉⠀⠸⣿⡇⡼⠀⡌⢠⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⣠⣾⣿⠃⠙⠿⡆⠀⠀⢹⠹⣦⠎⢠⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⡛⡛⣿⠈⠒⠤⣀⠀⠀⢸⡔⠁⢰⡍⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠑⠴⣻⠈⢮⣢⣠⢈⣑⠎⢀⣀⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠈⢫⠘⣷⡯⢵⣒⣉⣤⡔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⢀⡇⢹⡇⡀⢀⢸⡍⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⡠⠛⠥⢼⠀⣇⣸⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠘⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠔⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡼⠄⠀⠀⠾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⢀⡀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⢠⠏⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⣴⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠆⠀⢀⣠⡤⡷⠴⠶⡦⠤⣄⡀⠀ ⠻⣄⣀⡀⠀⠀⣄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣏⡀⠛⠓⡒⠒⠚⣁⣠⠇⠀ ⠀⠈⠉⢳⡀⠘⠁⠀⠀⠀⠀⢰⣿⡿⠀⠀⡀⡾⠛⢹⢸⡟⠦⠏⠉⠘⡆⠀ ⠀⠀⠀⠀⠳⡄⠀⠀⠻⠇⠀⠀⠀⠀⠀⣰⠃⣇⣀⣼⣏⡁⠀⠀⠀⠀⣿⣄ ⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠉⣩⠗⠋⠉⢧⠀⠀⢳⠀⣀⣠⠴⠃⣸ ⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠈⣇⡴⠋⢻⣩⡿⠖⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠚⢻⠋⠣⠀⠀⣤⣤⣶⣚⡥⠤⠤⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣠⠤⠖⠛⠉⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡖⠖⡶⠀⠀⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⡽⠺⣅⣀⣀⡴⠃⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠠⣷⢀⢸⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠀⠀⣿⢸⢸⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⡧⢠⣿⣿⣾⣿⡇⡆⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⣾⣿⣿⣿⣿⣏⣿⡀⠀⠀⠀ ⢀⣇⢀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡆⣸⠀ ⢿⣿⣿⣿⠿⠛⠻⣿⣿⣿⠟⠛⠿⣿⣷⣿⣷ ⢸⣿⣿⠃⠀⠀⠀⠸⠿⠇⠀⠀⠀⢸⣿⣿⡇ ⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣧ ⣿⣿⡿⢿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠴⠆⠀⠀⠀⠘⣿⣿⠀⣤⠀⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⣿⣿⠀⣄⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠀⠀⠀⣿⣿⢠⣿⠀⢸⣿⣿⡇⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⡀⠰⡆⣿⣿⣾⣿⣧⣸⣿⣿⡇⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢰⣇⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢼⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣟⠀⠀⠀⣠⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣟⠀⠀⠀ ⠀⣴⣿⣄⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢰⣿⡄⠀⠀ ⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣶⠆ ⢻⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠀⠉⠙⢿⣿⣿⣿⣿⡿⠋⠉⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀ ⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀ ⢸⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣷⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⠀ ⠀⠉⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⠉⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠸⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠵⠒⠛⠛⠂⠀⠹⢿⡿⣿⠟⠀⣿⠟⠧⣬⣻⡿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣮⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠙⢿⣿⠟⠁⢀⣴⣺⣭⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⣿⣿⠈⣷⡘⠋⠀⠀⠘⢿⣿⣿⣿⠂⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡧⢻⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠿⠀⠀⠀⠀⠀⠀⠉⠻⠧⠤⣾⡆⠀⠀⠀⢀⣀⣀⠀⠀⣾⣟⣴⠏⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⡃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠉⠁⢰⣏⠛⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⡼⠃⢰⣇⡠⠤⠲⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡘⡏⠀⠀⠀⠀⠀⠀⠀⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣇⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠛⠚⠓⠀⠀⠀⣠⠞⠁⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⢲⡀⠀⠀⠀⠠⠚⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⠀⠀⠸⣧⣉⡉⠑⠒⢲⠖⠒⠲⠶⠶⠶⢶⡤⠄⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⢀⣠⠶⠖⠋⠉⠋⠀⠀⠀⢸⡇⠀⠀⠀⠈⠑⢢ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣿⣧⡀⠀⠘⢦⡙⠒⠒⠾⣄⠀⠀⠀⠀⣠⠏⠀⠀⢀⣾⣿⣿⣿⣿⣷⣀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⣴⠏⠁⠋ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⣿⣿⣦⣄⠀⠙⠲⣤⣀⣸⣃⣀⡤⠞⠁⠀⣠⣴⠿⠟⢿⡏⠉⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⠉⠳⠦⠤⢈⣉⣉⡡⠤⠴⠖⠊⠹⡄⠀⠀⢨⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠟⠛⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠒⠒⢏⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⣀⣀⣤⡤⠛⠁⠀⠀⠈⢳⡀⢻⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⣄⣀⡀⠈⢷⡈⡷⠛⣿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠁⠀⠀⠀⠀⠀⠈⠉⣲⣌⣷⣴⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⢠⣶⣯⣭⣭⣛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣼⠗⠀⢸⠁⠀⠈⠙⠳⢤⣄⡀⠀⠀⠀⠀⠀⠈⠹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠙⠶⣄⣀⡀⠀⠀⢀⡏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠙⠷⢦⣀⡀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢠⠟⢻⠛⠛⠋⠀⠀⠀⠘⡇⠀⠀⠀⣦⠀⠀⠀⠀⠀⠉⠛⠦⣄⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣀⡀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠉⠙⣦⠀⣄⠀⠀⠀⠈⠳⣀⠀⢯⢧⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡟⠀⠀⠀⠀⠹⡄⣯⠑⢤⡀⠀⠀⠈⠑⢾⣮⠳⣄⠀⠀⠀⠀⠘⢿⡲⠾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⣿⣿⣿⡧⣄⠀⠀⠀⠀⢻⢸⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠚⠋⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢸⠂⣾⠃⠙⢦⡀⠀⠀⠈⣿⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠀⢐⠀⣀⠴⠚⠉⠉⣧⣘⡄⡏⠀⠀⠈⠻⣦⠀⠀⠁⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⢹⣧⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⢣⣀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⢸⠁⠀⠀⠀⠀⢀⣀⡴⣶⠒⠲⠤⣄⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢨⣙⣒⡲⠶⠀⠀⠀⠈⠁⢀⡞⠀⠀⠀⣠⠞⠉⠉⠉⠻⠆⠀⠀⠈⠙⢆⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠳⣤⣀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⢰⡇⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠈⢳⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⡛⣦⡀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠘⣧⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠶⠦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠛⠃⠀⠀⠀⠀⠉⠷⣦⣀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢈⣙⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠈⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠾⢥⣤⣤⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣦⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⠤⠶⠶⠦⣄⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣖⣒⠒⠚⠉⠀⢀⣀⣠⣶⣞⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣄⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣶⣴⡾⠛⠛⠋⢉⣩⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣭⣿⣶⣮⣷⣦⣤⣀⣐⣚⠿⠀⠀⠀⠀⠀⣀⣀⣠⣤⠴⢶⠋⣩⠚⠀⠀⠒⢦⣼⣧⡽⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⣀⡄⢀⠀⣀⠉⠉⠓⣯⣉⡿⡹⠏⠉⠉⠉⠉⠉⠉⠁⠉⠳⢾⣚⠁⠒⠲⠦⠶⠋⣉⣳⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠉⠁⠳⠤⠧⣄⣤⠔⢉⣭⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠲⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠤⢤⠤⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠄⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⠋⠉⠀⠀⠀⠀⢸⣿⣷⠀⠛⢷⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⢸⣧⣤⣼⣿⣿⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀ ⠀⠀⢠⣾⠋⠀⠀⠀⢀⣷⠀⣸⡀⣼⣿⣿⣿⣿⣿⡀⣾⡀⠀⡄⠀⠙⣷⡄⠀⠀ ⠀⢰⡿⠁⠀⢀⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⠇⠀⠀⠈⢿⡆⠀ ⢠⣿⠁⠀⠀⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡄⠀⠀⠈⣿⡄ ⣸⡇⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⢸⣇ ⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿ ⠛⠃⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⢄⠀⠀ ⠀⡰⠊⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢃⠀ ⢰⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣤⠴⣄⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡄ ⡔⠁⠀⠀⡇⠀⠀⢀⠤⠂⠉⠀⠀⠀⠀⠈⢐⠤⡀⠀⢸⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⠃⠀⡰⠉⢠⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⢂⢸⠀⠀⠀⢀⠇ ⠱⠀⠀⠀⠰⣜⣤⣤⡀⡇⠀⠀⠀⠀⠀⠀⢀⡾⢻⣶⣯⠀⠀⠢⡈⠀ ⠀⠣⡀⠀⢠⢿⣿⣤⣿⣤⡠⠐⠒⠒⠂⢄⣿⣷⣾⣿⡏⡇⢀⠜⠀⠀ ⠀⠀⠈⠢⢸⠜⢿⣿⣿⢿⡄⠀⠀⠀⠀⢸⠛⣿⣿⡟⠔⡏⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⢂⣡⠿⠯⠁⣈⣢⣀⣠⣔⠡⠤⠒⢉⠱⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠖⠲⠂⠀⣤⠀⠐⠒⢈⠋⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠇⠀⠺⣆⠀⠀⡎⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⠀⠀⠉⠀⢠⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠤⠼⡇⠀⠀⠸⠀⠀⠀⠀⠘⠀⠀⠀⠹⢄⡀⠀⠀⠀⠀ ⠀⢀⠎⠉⠉⢣⠀⡇⠀⠀⠀⡄⠀⠀⠀⡇⠀⠀⠀⠀⢠⡬⠒⠦⣀⠀ ⠀⠘⡁⠀⠀⢠⠃⢡⠀⠀⠀⣷⣤⣤⣤⠀⠀⠀⡜⠀⡆⠀⠀⠀⢹⠀ ⠀⠀⠈⠐⠒⠈⠈⠉⠱⠢⡞⠂⠀⠀⠘⢢⡤⠎⠑⠒⠓⠤⠤⠄⠃⠀

⬜⬜⬜⬜⬜⬜⬜⬜🌫️🌫️🌫️🌫️🌫️🌫️🌫️⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🌫️🌫️⬜⬜⬜🌫️⬜⬜⬜🌫️⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🌫️⬜🌫️⬜⬜🌫️⬜⬜🌫️⬜🌫️⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🌫️🌫️⬜⬜🌫️⬜🌫️⬜🌫️⬜⬜🌫️🌫️⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🌫️⬜🌫️🏻🏻🏻🏻🌫️🏻🏻🌫️⬜🌫️⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🌫️⬜🏻🏻🏻🏻🏻🏻🏻🏻🏻⬜🌫️⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🌫️⬜🏻⬛⬛🏻🏻🏻⬛⬛🏻⬜🌫️⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🌫️🏻⬛🟦⬜🏻🏻🏻⬜🟦⬛⬜🌫️⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🌫️🏻🏻🟦🟦🏻🏻🏻🟦🟦🏻⬜🌫️⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🌫️🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬜🌫️⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🌫️⬜🏻🏻🏻🏻🏻🏻🏻🏻🏻⬜🌫️⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🌫️🌫️🏻🏻🏻🏻🏻🏻🏻⬜⬜🌫️⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🌫️🏻🏻🏻⬜🌫️⬜🌫️⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🏻🏻🏻🏻🏻🌫️🌫️⬜🌫️⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🌫️🌫️⬜🌫️🟦⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🌫️⬜🌫️🌫️🟦🟦⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🌫️🌫️⬜🌫️🟦🟦🟦⬜⬜⬜⬜ ⬜⬜⬜🟦🟦🟦🟦⬜🟦🟦🟦🟦🌫️🌫️🟦⬜🟦🟦🟦⬜⬜⬜ ⬜⬜🟦🟦🟦⬜⬜⬜⬜🟦🟦🟦🟦🌫️⬜⬜⬜🟦🟦🟦⬜⬜ 🏻🏻🟦🟦⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦⬜⬜⬜⬜🟦🟦🏻🏻 🏻🏻🏻⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜🏻🏻🏻 ⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟦🟦🏻🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟦🟦🏻🏻🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟦🟦🏻🏻🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟦🟦🏻🏻🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜⬜ ⬜⬜⬜⬜🟦🟦🟦🏻🏻🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜ ⬜⬜⬜⬜🟦🟦🟦🏻🏻🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜ ⬜⬜⬜⬜🟦🟦🟦🏻🏻🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜⬜ ⬜⬜⬜🟦🟦🟦🟦🏻🏻🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜ ⬜⬜⬜🟦🟦🟦🟦🏻🏻🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜⬜ ⬜⬜🟦🟦🟦🟦🟦🏻🏻🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜ ⬜⬜🟦🟦🟦🟦🟦🏻🏻🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢰⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡁⠀⠀⠀⠀⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⠀⢀⣼⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣅⣴⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⡾⢋⣾⡿⣿⠟⣿⠿⣿⡟⠉⢻⣿⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣿⠟⠰⠃⠀⣥⣾⠏⠀⣀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⢠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡟⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣤⣴⣶⣶⠶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡿⠟⠛⠉⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠖⠒⠒⠒⠒⠒⠶⠤⣄⠀⠀⢸⡇⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⣗⠲⠦⣄⡀⠀⠀⠀⠀⠀⠙⠲⣄⣇⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡳⢄⡀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠙⠲⢤⣠⠤⠤⠤⠤⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠭⣗⣲⠬⠷⣄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣟⣲⣿⡦⠖⠀⢀⡴⠖⠒⢶⡄⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠼⠟⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠂⣀⣤⠤⣄⡀⢀⠇⢠⣖⣶⣤⡀⠀⠽⡄⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢀⡞⠁⠀⠀⠀⠹⣿⢀⠏⢿⣿⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡼⠀⠀⠀⠀⠀⠀⠻⣿⣀⣶⢟⡜⢸⠀⠀⡇⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⠀⠀⠀⠀⠀⠀⠀⢻⠬⠗⠋⢀⡏⠀⣼⠀⠀⠀⠀⠀⠀⣼⣼⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡠⠊⢀⡼⠁⠀⠀⠀⠀⠀⢰⢧⠗⢶⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠉⠤⠒⣉⣀⠀⠀⣠⡿⠃⠀⢎⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠉⠛⣯⠉⠉⠙⣦⡟⠁⠀⠀⢸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠳⠦⣄⡀⠀⠠⡤⣖⠋⠀⠀⠘⡄⠀⣠⠟⡆⠀⠀⣠⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠠⠤⠞⠓⠒⠷⣌⡲⢤⠤⢤⡌⠉⠁⣠⡇⠤⠞⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⠖⢿⣟⡋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠤⠽⠧⣤⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⡳⡀ ⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠉⣳⠶⣄⣀⠀⢀⣀⣠⢴⠞⠋⠀⠳⣄⡀⠀⠈⢻ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣠⠞⠁⠀⠀⠈⠉⢉⠀⣠⣎⠀⠀⠀⠀⠀⠉⠙⠊⠉ ⠀⠀⠀⠀⣿⣒⠒⠒⠦⠤⠤⠤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⣀⡴⠯⠞⠃⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣖⠋⠁⠹⢦⣤⣘⢦⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⡻⠋⠛⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⡠⠊⠀⠈⠲⢄⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⢤⣀⡠⢄⡀⠀⠀⠀⠀⠀⣠⣾⣞⣉⣀⣀⣀⣀⣤⠴⠖⠯⠥⠤⠤⠤⠔⠊⠀⠀⠀⠀⠀⠀⠙⣄⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠉⠒⠒⠒⠒⠚⠉⠀⠉⠉⠉⠉⠁⠈⠉⠉⠓⠒⠒⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢹⣿⣷⣤⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⠿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢻⣿⡿⠈⠀⠀⠀⠀⠀⢠⣄⡈⠻⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣾⣍⣻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⢠⣴⢻⣇⠀⠀⠀⠈⢛⣒⣺⣿⡭⠭⠿⠷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⣼⠿⠶⣤⡀⠉⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣿⣳⡀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠘⠛⠛⠋⠉⠹⡷⣄⠈⠛⢦⣀⠀⠀⠀⠀ ⠀⠀⠀⣴⠀⠀⠀⣟⠧⣀⣠⢤⣶⣟⣛⠛⠳⢦⡙⣆⠀⠘⢿⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣾⣿⣿⣿⢹⣿⣿⡏⢀⣀⡀⠀⠀⢀⣠⣀⣀⣀⣿⠈⢷⡄⠀⠙⣷⡄⠀⠀ ⠀⠀⣼⡏⠀⠀⠀⣨⠟⣻⠗⠋⠉⠉⠙⠲⣄⠀⠙⣾⠀⠀⠸⣆⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣄⣚⣿⣿⣿⡚⠛⠀⢿⡿⣿⣿⣿⡿⢳⣶⠛⠛⠛⠒⠒⢶⣄⡀⠙⠒⢶⣾⣿⠀⠀ ⠀⣀⣯⠻⠶⠶⠋⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠱⡄⠘⡇⠀⢠⠟⠀⢀⣿⡄⠀⠀⠀⣀⣤⣿⣿⣿⣶⣯⡩⠀⠀⠀⣀⣬⣽⣿⣟⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡏⠁⣿⠀⠀ ⠀⣻⣿⡄⠀⠀⡴⠃⠀⢀⣠⣤⠤⠤⠤⢤⣀⠀⠹⡄⡇⣠⠏⣀⣤⠞⢹⣧⠀⠀⠀⠉⠛⢺⡿⣿⡿⣿⡿⠆⣠⣄⣬⣿⣿⣄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⣿⠀⠀ ⣴⣿⣯⣽⣶⡞⢁⡴⠖⠉⠁⢀⣀⡠⠤⠤⢌⣷⣀⢿⣿⣿⣛⣉⣀⣤⣼⣧⠀⠀⠀⠀⠀⠀⠀⠁⣠⣿⣿⣶⣾⠿⣟⣿⣿⣯⣅⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣼⠇⠀⣿⠀⠀ ⠋⠻⣿⡧⣊⡴⠛⠀⠀⢀⣴⣿⡥⠖⠚⠛⠛⢻⣿⣿⡿⠛⠉⠀⠀⢹⡿⣮⣧⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⠿⠀⠹⠿⣿⣭⣧⡁⠀⠀⣦⣤⣠⣾⡆⠀⠀⠀⠀⡟⠀⠀⡿⠀⠀ ⠀⠀⠉⠉⠉⠀⠀⠀⣰⢿⡿⠋⠀⠀⢀⣠⠶⠋⠉⠀⠀⠀⠀⠀⣴⠟⢿⣸⣿⠀⣀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⣸⣿⡿⢿⣷⣶⠶⠀⢸⠃⠀⠀⡇⠀⠀ ⡆⠀⠀⠀⠀⢀⣠⠞⢉⡾⢀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣧⣿⣿⣿⣿⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣷⣮⣿⣆⠀⢀⡟⠀⠀⠈⡇⠀⠀ ⣹⣦⣤⣤⠖⠋⠁⢠⣾⡿⠉⣠⣟⡟⠁⠀⠀⢀⣠⣴⠖⠀⠀⣼⣻⣿⣿⣽⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠉⠉⠋⠀⣼⠁⠀⠀⢰⡇⠀⠀ ⢸⠸⣇⠀⠀⣀⡤⠟⠉⠀⣴⢻⣿⣥⡶⢿⣿⣟⣋⣡⠀⠀⠀⠸⡸⡿⠟⠁⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢀⣾⡇⠀⠀ ⢸⡀⠙⠛⠛⠋⠀⠀⢀⡾⢑⣿⠟⠁⣠⣿⣿⣿⣟⠛⢦⡄⠀⠀⢳⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢠⣿⡇⠀⠀ ⠘⢷⡀⠀⠀⠀⠀⢠⣎⣠⣾⣇⠐⠻⢿⣿⣿⣿⣿⠶⠋⠀⠀⠀⠀⠙⠶⣤⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠉⢸⠁⠀⠀ ⠀⠈⢿⡦⣤⣤⣴⣿⣟⠻⣽⠻⣧⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠲⠄⢈⣿⠟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠛⢻⠁⠀⠀⢀⣴⣾⠀⠀⠀ ⠀⠀⠀⠈⢳⣿⣷⠛⠙⣦⣌⣓⣾⣿⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣖⣻⡿⢀⣷⣞⣉⣙⠳⣶⠶⠶⢶⣄⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠾⠋⠉⣠⣤⣴⠀⣠⠖⢠⡿⣻⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣜⢦⣤⣿⡀⢹⡏⠉⢻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠁⠀⠀⠀⠀⠘⢷⠀⠀⠘⢷⣤⣤⣤⡶⣺⣯⡿⠃⠀⠀⠀⣠⣼⣿⣿⣾⡇⢀⣿⠗⠋⠀⠀⣼⢳ ⠀⠀⠀⠀⠀⠀⠙⠛⢫⡟⣿⢸⡇⠀⠘⡆⠈⠻⡍⠙⠒⠒⠒⠒⠒⠚⢯⡁⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠈⣿⣿⣾⣯⡽⠋⠀⢀⣠⣤⣴⣾⣿⣿⡾⣿⠞⠉⠀⠀⠀⢀⡴⣳⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⠀⠀⠀⣧⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠤⠴⠶⢾⡛⠉⠉⠻⠦⢤⣼⣇⠙⢧⡀⠀⢉⣁⣀⢤⣤⠿⠛⠙⣇⠈⠓⠶⠶⠛⢋⣥⢶⡿⢏ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣿⠀⠀⠀⣿⡀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠉⣳⢦⣤⣴⣾⠛⠟⡆⠸⣿⣉⣩⠿⠟⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⢤⣀⢀⢈⣠⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣆⠀⠀⠘⢷⣀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⠀⢀⡴⠃⠀⢸⣇⣸⣝⡦⣽⣦⣸⣿⣷⡄⠀⠀⠀⠀⠀⠀⢸⡇⢀⣠⠤⢶⡻⠟⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠳⠤⠤⠖⠛⠛⠛⠛⢿⠀⠀⠀⠀⢠⠖⠋⠀⠀⠀⢠⠞⠁⠀⠀⢸⡏⠉⢻⣿⣿⣻⣿⣿⠈⠙⢦⠀⠀⠀⠀⠀⣼⠟⠉⢀⡴⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢀⡴⠋⠀⠀⠀⢀⡴⠋⠀⠀⣀⡤⠾⠇⠀⠈⠉⣿⣿⣿⣿⡀⠀⢸⡇⠀⠀⠀⣰⠃⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠉⠀⠀⠀⢀⡴⠋⣀⣤⠖⠋⠻⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⢀⣿⠇⠀⠀⣰⠋⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣴⣿⣶⣾⡟⢵⡶⢤⡴⢿⡀⠀⠀⠀⠀⠀⠸⣿⠹⣿⣼⠃⠀⠀⡼⠃⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⣶⣿⣿⣿⣿⡏⠀⠀⠙⢿⡟⣦⣧⠀⠀⠀⠀⠀⠀⢻⡆⠹⣟⣷⢠⠟⠁⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣀⡤⢞⣿⣿⢿⡿⣿⣿⠦⣤⠀⠀⠀⠀⠉⢻⡄⠀⠀⠀⠀⠀⢸⡇⠀⢈⡹⠋⠀⠀⢠⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⣴⣿⠞⡿⠋⡼⢡⣿⠀⠈⠙⠳⢦⣀⡀⢸⡇⠀⠀⠀⠀⠀⢸⣇⣠⠞⠁⠀⠀⢰⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣋⡾⠁⡼⠁⣾⣿⠂⢦⠀⠀⠀⠈⠙⠚⢷⣄⡀⠀⠀⠀⢘⣿⠋⠀⠀⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠳⢾⣇⢠⢿⣿⠀⠈⢷⣌⠳⣤⡀⠀⢀⡀⠉⠛⠲⢦⡾⠁⠀⠀⠀⠈⣻⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠉⠻⣦⣿⣀⠀⠀⢻⣷⡘⢿⣦⣼⣃⣤⣤⠤⠚⠃⠀⣀⣤⣤⠾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠈⠻⣏⡙⠶⠤⣷⣽⣦⡙⢻⣍⣁⣤⣴⠶⠞⠋⢉⣉⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠸⣿⣿⣿⠛⠯⢿⣭⣄⣀⣤⢶⠯⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧⠀⣿⣿⣿⣤⠀⠀⠀⠉⠉⠙⡟⣷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠂⠘⣿⡏⠀⢠⠀⠀⢠⡀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣳⠋⠀⢸⣿⠁⠀⢸⠀⠀⢸⡇⠀⣿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠿⠤⣄⣼⣼⣀⣀⣼⠀⠀⣼⠇⠀⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⢀⡿⠉⠉⠉⠛⠛⠛⠢⢴⣿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡢⡍⢉⡉⠉⠉⠒⠄⣸⠀⠀⠈⠑⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠵⣤⢉⡢⡀⠀⠀⠈⠑⠤⠐⠒⠺⢄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢺⡿⡶⠤⠀⡠⠆⢄⠀⠀⠀⠈⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⣁⡀⠀⠎⣀⣀⠀⢡⠀⠀⠀⠀⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠡⠊⠀⠈⢻⡼⢻⡟⡆⢘⠀⠀⠀⠀⣼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠈⢧⠿⠂⠇⠸⠀⠀⠀⢠⡯⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠈⠲⣪⠔⡁⠀⠀⢀⡾⠙⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⣸⠐⢆⠉⢲⡟⠀⢀⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢉⠰⠤⢯⣧⣀⣈⠒⢊⡇⠠⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠀⠀⠈⠲⡊⢿⡅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠉⠉⠢⡀⠀ ⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⢄⡀⠀⢀⣀⠤⠒⢀⠀⠸⡄ ⠀⠀⠀⣜⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠊⠀⠈⢉⣁⠼⡀⠀⠀⠉⠈⠁ ⠀⢀⠔⠋⠀⠀⠉⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠈⠳⢴⠊⠣⣠⣢⡅⠀⠀⠀⠀⠀ ⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⢀⡀⠤⡷⠂⢄⡀⠀⠀⠀⠀⠀ ⠀⠈⠆⡀⠀⠀⠀⠀⠀⢀⡠⠎⠀⠀⣀⣠⡔⠂⣁⠠⠊⠀⠁⠢⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠁⠒⠒⠒⠉⠉⠉⠉⠉⠁⠒⠒⠂⠤⠤⠤⠤⠤⠒⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠶⠾⠿⠿⠿⠿⠶⢶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣤⣤⣤⣤⣤⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠋⠉⣽⡟⠋⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠿⣶⣶⣤⡀⠉⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⢰⡟⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣏⢿⡇⠀⠀⢸⠃⠀⢠⡏⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠉⠉⠉⠙⠻⢿⣷⣄⠀⢸⡀⠀⣿⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣀⣀⣀⣀⣀⣀⣀⡈⠙⠻⢿⣷⣤⡏⠀⠀⠀⠀⠀⣼⠃⠀⠀⣀⣠⣤⡴⠶⠶⠶⢶⣤⣤⣀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⣛⣓⣾⣽⣿⣦⡀⠀⠀⢰⣿⠞⠛⠛⠛⠛⢷⣄⠀⠀⠀⠀⠀⠉⠛⢷⣆⠀⠀⠀⠀⠀⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⢿⣟⣋⣉⣉⣙⣛⠿⣿⡄⠀⣸⣃⣀⣀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⣊⣩⡴⠶⢛⣫⠿⠿⠛⠛⠛⠛⠛⠛⠁⠀⠉⠉⠉⠻⢷⣄⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⣦⣤⣤⠴⠶⠛⠋⢁⣤⡞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠻⣯⡻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⣀⣠⣤⡶⠋⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠘⢷⡌⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢨⡟⠛⢛⣿⡿⠋⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⡀⠀⠙⢾⣧⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⢿⣆⣠⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⣴⣿⠏⠀⣰⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠤⠤⢬⣭⣭⣭⣍⠛⢻⡇⠀⠙⢿⣦⡀⠀⠀⠀⠀⠈⠉⣹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⣸⡿⠃⢀⣾⠁⢰⡏⢀⣴⣖⣯⣭⣭⣭⣭⣯⣭⣽⠏⠀⠀⠀⠀⠀⠈⠛⠒⠒⠚⠉⠉⠉⣉⣉⢙⡛⢷⣜⣿⡄⠀⠀⠙⢿⣶⣤⣀⣀⣠⣾⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣥⣿⠃⢠⡾⠃⠀⣿⣷⣿⣏⣿⣶⣤⣄⡀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣷⣌⢹⣷⡀⠀⠀⠀⠈⠙⢿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⣼⠇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣛⠿⣿⣦⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⣾⣿⣄⠉⠻⣿⣿⠊⣿⣻⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⠀⢰⡏⠀⣠⠿⣿⣿⣿⡿⠉⡜⣾⣿⣯⡟⣿⢷⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡸⢧⡸⣿⣿⣿⡿⠀⠀⢹⡏⠀⢹⣧⠹⣷⣄⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡄⢸⣇⣼⣿⠀⣿⠈⠻⣇⠀⠹⣞⣿⣿⡵⠃⠀⣧⠀⢸⡆⠀⠀⠀⠀⠀⠀⣇⠈⠑⣾⣷⣋⣀⡤⠶⠋⠁⠀⢸⣿⠀⢹⣿⣦⡀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⢸⡟⢹⣏⠀⣿⠀⠀⠙⠷⠤⠤⠭⠭⠤⠤⠠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⣿⢷⣄⠀⠻⣷⣄⣀⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣾⠁⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡿⢿⢹⣦⣙⢧⣄⣠⣽⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣾⣿⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡼⠁⠈⣿⣯⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡹⣆⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣠⡀⠀⢠⠤⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠋⠁⢀⣴⢟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠙⠓⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡷⣶⡶⠞⠁⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⣤⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠔⠒⣒⣒⣢⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠛⢿⣟⣛⠛⠛⠛⣛⣫⡥⠛⠋⠀⠀⠀⠀⠀⠀⣠⡿⠋⠙⠓⢶⣤⣄⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠈⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣟⣁⡀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⣨⡿⠻⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⢻⡟⠈⠙⠻⢶⣄⡀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⢀⣼⠃⠀⠀⠙⡇⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⢀⣾⢀⣤⡶⠟⠛⠻⠿⣷⣤⡀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣿⣡⡤⠶⣤⡀⠀⠀⠈⠻⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢣⣿⠟⠁⠀⠀⠈⢻⡆⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⡟⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠁⣀⣀⡀⢀⣴⠞⠛⢳⣄⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⠋⠉⠉⠉⢻⡁⠀⠀⠀⠘⣷⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⣦⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡾⠟⠁⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⢀⣼⡁⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⠿⠛⠛⠁⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⢀⡴⠋⠈⠙⣦⡀⠀⠀⣾⠟⠻⢷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣤⣶⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⢀⣤⡤⠖⢻⡆⠀⠀⠀⠘⢷⡀⣸⡟⠀⢀⣀⣠⣭⣿⠿⠿⠷⣶⣤⣤⣀⠀⠀⠀ ⠀⠀⣠⣶⠿⠛⠑⠿⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣿⠟⠁⠀⠀⣸⡇⠀⠀⠀⠀⢸⣷⡟⠈⠛⠛⣿⠏⠀⠀⣀⣀⣤⣶⡿⠋⢻⣿⣦⡀ ⠀⣼⡟⠁⠀⢰⡶⠶⠾⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⣿⠃⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⣼⡏⠀⠀⢠⡾⠿⠶⠚⠋⠉⠉⣠⣟⣠⢶⡿⣽⡿⣇ ⢸⡏⠙⠶⣤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣾⠃⠀⠀⢀⣼⠟⠙⣦⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠉⢁⡟⣰⠟⡇⢻ ⣿⡇⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣿⠀⠀⢠⡞⠁⠀⠀⢻⡄⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣠⠟⠀⢿⣾ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⣿⣠⣤⣿⡀⠀⠀⠀⠸⣿⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⠟⠀⠀⢸⣿ ⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⠉⠉⠉⠉⠉⠉⢩⡟⠁⠀⢀⣿⠋⠀⢹⡇⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢠⠟⠀⠀⠀⠸⠹

⠀⠀⢀⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣄⠀⠀ ⠀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄ ⢰⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣷ ⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡍⣿⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠀⠉⠙⢩⣿⣿⣿⣿⣿⠸⠇⢿⣿⣿⣿⣯⠛⠉⠁⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡏⠹⠀⠁⠈⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⠻⠃⠀⠀⠀⠀⠙⠻⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠐⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⠀⠀⠀⠙⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣋⢹⣿⡄⢸⢛⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠸⣿⡇⠀⢸⠀⢸⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡟⠁⠀⠀⠀⠸⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣻⣿⠀⠀⠇⠀⠀⠀⠀⠈⠀⠙⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠃⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠉⠉⠉⠉⠉⠓⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢶⠦⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠙⠾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡶⠤⣀⠀⠀⠀⠀⠈⠑⠒⠢⠤⢤⣤⣄⣀⣀⣠⣤⠤⠤⠖⠋⠁⠀⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⣼⣅⠀⠀⠉⠓⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⢀⡜⢻⣿⣿⣦⣀⠀⠀⠀⠀⠈⠉⣹⣶⣶⣤⣤⣤⠤⢤⡤⠤⠤⠔⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢀⡴⠋⡝⠀⠈⠻⣿⣿⣿⣿⣶⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣇⣀⡤⠤⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⠎⠀⡜⠀⠀⠀⢀⣀⣍⣛⠛⠛⠁⠀⠈⠛⠛⠁⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⣹⠁⠀⠀⠀⠉⠲⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡜⠀⡸⠁⠀⢀⡔⠉⠀⠀⠈⠳⡀⠀⠀⠀⣀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠘⢦⡀⠀⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡆⣰⠁⠀⢀⡞⠲⣄⡀⠀⠀⠀⢳⠀⢠⠎⠁⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢳⠀⠀⠀⢳⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢠⠃⠀⠀⣼⢦⡀⠺⣿⣿⡟⠒⢻⢠⢧⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢸⠂⠀⠀⡼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡏⠀⠀⠀⢿⠀⠈⠑⠒⠤⠤⣤⠇⣸⠀⠈⣿⣶⣤⡤⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡼⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⠀⣀⡤⠤⠤⠤⡼⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⣠⡮⠤⣿⠒⠤⣈⡛⠉⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⠊⠀⠀⢠⠎⠀⠀⠀ ⠀⠀⣰⠋⠁⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠑⠒⢒⠞⠁⠀⠀⢹⣆⠀⠀⠈⢉⡹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣠⠔⠁⠀⠀⠀⠀ ⠀⠀⡇⠀⠖⢲⡒⠦⡼⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⣷⠙⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⡄⠀⠀⢳⡀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⡟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⢄⠀⠀⢹⡇⠀⡠⠤⠒⠒⢶⡏⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠘⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣄⠘⡇⡴⠓⠚⠛⠛⠒⢧⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⡀⠀⠀⠙⢦⡀⠀ ⠀⠀⠀⠀⡰⠋⠀⠀⣿⢧⣀⣀⡤⠒⠊⠉⢹⢤⣀⠀⠀⠀⣀⣴⣶⡴⠧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣉⡵⠦⢄⠀⠈⠢ ⠀⢠⡤⠖⠁⢀⡴⢃⣿⡄⠈⢯⠀⠀⢀⡔⠁⠀⢸⠉⠉⢫⠀⠱⣄⠈⠳⡄⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣇⣠⡔⠉⢠⢋⡏⠘⣄⠀⠙⢲⣺⡀⠀⠀⡎⠀⠀⠈⡇⠀⠈⣆⠀⠘⣤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠠⡶⡚⣿⢭⣉⠉⠉⠉ ⠀⠀⠀⠀⠉⢛⡳⠾⣤⠶⠾⠦⡀⠀⠙⢯⡒⠒⠳⣀⠀⣠⢧⡀⠀⣸⢤⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠻⡀⢱⡹⣍⠒⢿⠀⠀⠀ ⠀⠀⢀⡤⠒⠻⢄⡀⠀⠙⢦⡀⠈⠢⣄⠀⠈⠙⠒⠒⠛⠓⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠧⢤⣧⣀⣙⣎⣹⠋⠀⠀⠀ ⠀⢠⠚⠳⢤⡀⠀⠈⠢⡄⠀⠑⣄⠀⠀⠙⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⣠⠖⠉⠀⠈⣙⣯⡀⠀⠀⠀⠀ ⢠⠃⠀⠀⠀⠉⢦⠀⠀⠈⠣⡀⠈⢆⠀⠀⠀⠀⠈⠉⠓⣶⠦⠤⢤⣤⣤⣤⣤⠤⠤⠔⠒⠋⠁⠀⣠⠞⠁⢀⡤⠒⠉⠀⠀⣨⣦⠀⠀⠀ ⡌⠀⠀⠀⠀⠀⠀⠱⣄⣀⣠⠿⡄⠈⡆⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢀⡜⠁⢀⠔⠁⠀⠀⡠⠖⠉⠀⠀⣧⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢠⠀⢹⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡞⠀⡰⢧⣀⠀⣀⠞⠁⠀⠀⠀⠀⢸⡄⠀ ⠙⠲⠤⢤⣀⣀⣀⣀⣀⣸⣀⣀⣸⣀⣨⣀⣤⡤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⢸⠁⢰⠁⠀⢀⠟⠁⠀⠀⠀⠀⠀⠀⠀⡃⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠲⠤⢬⣤⣤⣀⠀⠘⠒⠒⠒⠒⠀⠀⠀⢀⣠⠁⠀

⠀⠀⠀⡠⠄⠒⠒⠲⠖⡢⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠑⠕⡄⠁⠂⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠧⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⠝⢅⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⠙⠒⠒⠒⠒⠀⠩⠉⠀⠂⢵⡀⡀⠈⢆⢢⠀⠘⡀⢀⣀⣤⡴⡶⠂ ⠀⠀⠀⡆⠤⡄⠀⠀⠀⣀⠀⠈⠀⠀⡀⠰⣡⠀⠈⡀⣆⠤⣋⠝⠛⡶⠊⠀⠀ ⠀⢠⠄⢿⣶⠇⠀⢠⠊⡀⠹⡄⠀⢀⠃⠀⢡⢣⣀⡇⢸⢊⡀⠔⠈⠀⠀⠀⠀ ⠰⠛⡄⠀⠙⢄⠀⢿⣺⣿⡞⠀⠀⢸⠀⠀⠀⡆⢋⡇⠸⡜⠀⠀⠀⠀⠀⠀⠀ ⢣⠘⡈⠢⠀⠜⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠈⡅⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡆⠸⡢⣀⣀⣀⣰⡀⠀⠀⠀⠀⠘⣉⠐⡄⡇⠀⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣄⠫⣉⠩⠋⠁⠈⠀⠀⠀⡀⠀⠀⡰⢡⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠫⢐⣀⣀⣀⡀⠤⠄⣒⠡⠭⣥⡐⠁⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠉⢲⢹⡀⢀⣠⣃⠑⡄⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⠇⠀⢨⠒⢢⠞⠁⠀⡇⠈⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢇⡼⠀⡠⡇⠀⡆⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠁⡠⢰⠛⢸⠘⠀⠀⢸⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠾⠊⠁⠀⠀⢇⠀⠀⢘⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣾⣿⣿⣿⠛⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⠿⠅⠀⠘⠿⠟⠿⠯⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⣻⡟⢡⣶⣦⡀⠀⠀⠀⠀⢠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣧⠃⠀⠀⠙⠣⠗⠀⠠⠤⢠⡯⢻⡟⠁⠀⠀⠀⠀⠀⡠⡂⠀⠀ ⠀⠀⠀⣿⣿⡀⠀⠀⠀⠐⠀⡀⠀⡨⠂⢸⣷⠀⠀⠀⠀⢰⠉⢀⠉⠀⡁ ⠀⠀⠀⣿⣿⣧⡀⠫⠭⢐⠀⠒⢒⠖⢀⣿⣿⡀⡠⠐⠊⠉⠀⠸⠀⢠⠡ ⠀⠀⠀⣿⣿⣿⣿⡦⠍⡂⣓⣐⠡⢴⠋⢫⡝⠁⠀⠀⠀⠀⠀⡠⠊⠁⠀ ⠀⠀⠀⢸⣿⡿⠋⠉⠐⠠⠀⣀⠀⠜⠉⠡⠰⠀⠀⢀⣀⠠⠊⠀⠀⠀⠀ ⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⢀⠔⠀⠉⠀⣢⣷⣽⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⠣⡀⠀⠀⢠⠆⡆⠀⠢⢄⡈⠉⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠁⠀⠀⠈⠐⠖⠊⠀⠡⠀⢠⠀⠈⠑⠢⣘⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠂⠀⠀⠀⣀⠜⠉⢆⡄⡀⠑⢌⡧⠀⠀⠠⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢺⢻⢢⡀⠈⡇⠐⡄⠀⠀⠀⠐⠂⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠂⠉⠊⣆⠀⠑⢄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⢂⣠⠄⠈⠂⡸⠀⠠⠐⠺⠍⠒⢄⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠑⠒⠒⠊⠀⢀⣧⡈⠂⢄⠀⠀⢾⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡈⠉⡑⠤⠀⠀⠀⠀⠈⠆⠀⠀⠀⠙⠦⡘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠗⣄⠉⠉⠐⢄⠀⠀⠀⠈⢂⡄⢀⠄⠀⢘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢂⣬⣃⣄⠀⢀⡆⠀⠀⠀⢀⡉⡴⠖⠊⣩⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠄⢄⡉⠹⡽⠋⠉⠉⠉⠁⠳⠀⠐⠪⠝⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡄⠀⠸⡀⠀⠀⠀⠀⡎⠈⡄⠀⠀⢀⣤⣤⡒⠶⠒⠒⠒⠚⠟⢷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠉⠀ ⠀⣾⣤⣀⡟⢻⢠⣤⡷⡄⠀⠀⢠⠁⠀⣇⣴⡾⠛⠉⠉⠉⠛⢦⠀⠀⠀⠐⠲⠬⣳⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀ ⠀⢘⡆⢈⡤⡬⠉⢰⠃⠘⡶⢄⡈⡄⡰⢋⠎⠀⣀⣤⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠄ ⠻⣏⡅⠸⠤⠵⠀⡼⢤⡀⠙⣄⠈⡝⠁⡼⢀⣾⣿⣿⣹⡇⢀⠇⠀⠀⠀⠀⠀⠀⠀⢠⢼⡄⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⡘⠀ ⠀⠀⠉⠲⡖⠚⠀⠀⠀⠈⠓⢌⢹⠁⠀⢳⡸⣿⣿⣿⡿⢁⠎⣠⠴⢶⣻⣿⡇⢀⠞⠉⠻⡗⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡰⠁⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⠀⢻⢆⠑⠭⣉⣻⡷⢁⣎⠀⠀⠀⠀⠙⣷⡎⣠⣤⡀⡇⢀⡴⢺⠃⠀⠀⠀⠀⠀⡜⠁⠀⠀ ⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢇⠘⡄⠉⢲⣬⣉⠀⠘⣿⡀⠀⠀⠀⢀⣾⣿⣿⣿⡧⡗⠉⢠⠃⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠘⢆⠙⢯⣄⠈⠓⠭⢷⡾⢷⣦⣤⠾⢿⠿⣿⣿⠟⡸⠀⡰⠃⠀⠀⣄⣀⠔⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⡇⠀⣠⣾⠓⢄⡙⢽⡆⠀⠈⠏⠑⢮⠹⡲⣌⡳⠤⣤⣾⡥⢮⣤⣄⡀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣰⠱⠁⠀⠀⢈⡓⠬⣙⡒⠤⠤⠾⠧⢤⣚⠽⠋⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠐⣾⡟⠀⠀⠀⠈⡹⢿⠀⠈⠉⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡇⠀⠀⢻⡀⠀⠀⠀⡰⠁⠘⡄⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢘⠶⠊⠉⠉⠓⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢰⠃⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢇⠀⠀⠀⠀⢀⣀⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⢦⡀⠀⠈⠱⠞⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠘⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠈⠉⢖⡒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⣾⣷⣿⣷⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⣾⣿⣿⣿⣿⣿⣶⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡿⣿⣿⣿⢿⡤⡠⣈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢀⣻⣿⣿⡄⠁⠿⢷⣄⠳⡉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡜⢹⠟⣙⠙⢿⡄⢰⣒⡮⠂⠹⣄⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⢀⣼⡇⠋⢸⣷⣓⠂⡇⠘⣾⡿⢳⠀⣯⠳⢄⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⢀⠴⠋⡞⢧⠀⢸⠿⢸⠀⢻⡦⠘⢦⠾⡀⢻⣦⠀⠙⠢⣄⡀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⣠⠴⠊⠁⢀⠞⠀⡸⢆⠘⠒⡎⠀⠀⢳⣀⣀⣉⣁⡀⠳⡑⢄⡀⠀⠙⠲⣄⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⢀⡤⠊⠁⠀⢀⠔⠁⠀⣰⠃⠘⡎⠉⠀⡠⠖⠉⣷⡀⠀⠀⠈⠑⠚⢒⣯⠲⢤⡀⠈⠳⡜⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⡴⠋⠀⠀⡠⠚⠁⠀⢀⠴⠃⠀⠀⡇⣠⠋⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠘⣿⠀⠀⠈⠲⢄⠈⢾⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⠀⢀⡴⠋⠀⠀⢀⠔⠁⠀⠀⠀⣠⠗⠃⠀⠀⠀⠀⠀⠀⢣⠀⠰⠇⠀⠀⡸⡀⠀⠀⠀⠀⠱⣜⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⡴⠋⠀⠀⠀⣠⠋⠀⠀⢀⣀⣀⡙⢿⠁⠀⠀⠶⠄⠀⠀⠘⡆⠀⠀⠀⢠⠃⢱⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⣴⠊⠁⠀⠹⡟⢮⢦⡀⠀⠀⠀⠀⠀⠐⡇⠀⢀⡴⠃⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠁⢁⡀⠀⠀⠀⢱⠈⡆⠙⠒⠤⠤⠤⠤⠤⣷⣾⡩⠃⠀⠀⢰⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⡇⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠒⠛⠉⣠⠞⠁⠀⠀⠀⢸⡄⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⠀⠀⠀⢠⣴⢾⡒⡾⠜⢓⣪⣧⠀⠀⠀⣸⢠⢷⠀⠀⠀⠀⠤⣲⠟⡸⠀⠀⠀⠀⢀⠇⡇⢸⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀ ⢠⡿⢿⡝⠒⠢⣄⠙⢶⡿⠓⠺⡉⢃⠀⠱⡀⢈⣟⠞⡎⠀⠀⠀⠐⠋⡞⠀⡇⠀⠀⠀⠀⡜⠀⡷⣼⠀⠙⢆⢀⣀⣠⠔⢋⡵⠈⠇ ⢸⣇⠈⠙⣄⠀⠀⠳⡎⠀⢀⡠⢧⣼⡀⠀⠉⢈⠏⣰⡡⡶⡆⠀⠀⢸⠁⢸⠀⢀⡀⠀⣼⠁⢠⣧⠃⠀⠠⠊⠉⠛⠁⢴⠋⠀⠀⢸ ⠈⠣⡣⠀⠸⡆⠀⠀⠀⠀⠘⡇⠈⠑⠫⢶⣤⠮⢴⡯⠊⣰⠁⠀⠀⢸⠀⣸⡀⠀⢈⣉⡽⠀⠴⠛⢦⠀⠀⠀⠀⠀⢰⠃⠀⠀⢠⠇ ⠀⠀⢻⣕⠂⢹⡀⠀⠀⢠⡤⠿⡀⠀⠀⠀⢀⡇⢰⡀⠐⠳⡄⠀⠀⣘⡄⠲⠂⢠⠗⠉⠑⢦⣄⡀⠀⠙⠢⣄⣤⡴⠃⠀⢀⣴⠋⠀ ⠀⠀⠈⢧⣀⠀⠙⠲⣒⣋⢧⡶⠋⠀⠀⠀⣩⣿⣾⣶⣀⢠⠏⠉⠉⠁⠙⢄⡱⣄⡀⠀⠀⠀⢣⠈⠙⠒⠤⣀⡉⠀⠀⢀⡸⠃⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠾⠤⠤⠤⢔⣪⣿⣿⣿⣿⣿⣯⣀⣀⠀⠀⠀⠀⠉⠓⠛⠛⠯⠕⠚⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠿⣻⠿⠿⣿⡿⠿⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⡀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠛⠛⠛⠛⠻⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢿⣄⠀⠀⠀⠀⣠⡾⠛⠁⢀⣀⣤⡤⠤⣤⣤⣀⠀⠙⠻⣦⡀⠀⠀⠀⠀⣼⠟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠻⣦⠀⣠⡾⠋⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠙⠻⣦⣄⠈⠻⣦⡀⢀⣾⠋⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣹⣿⠟⠁⣠⠞⠁⣀⣠⡤⠶⠶⠲⠶⠦⣤⣄⡀⠙⢷⡄⠘⢿⣿⡁⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣠⣾⣿⠏⢀⡾⣃⣴⣟⡯⠴⠒⠒⠚⠛⠓⠒⠲⠬⣝⣷⣄⣹⣦⠈⢿⣿⣦⡀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣾⠏⣿⠃⢠⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣧⠀⢻⡟⢻⣆⣸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠁⣸⠃⢠⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⢻⡄⠙⣿⣅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⢠⠇⢀⡟⠁⠀⠀⠀⠀⠀⢀⡤⠶⠛⠛⠛⠛⠓⠦⣄⡀⠀⠀⠀⠀⠀⠙⣧⠀⢣⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠃⠀⢀⠌⠀⣾⠁⠀⠀⠀⠀⢀⡴⠋⠀⢀⣤⣶⣶⣦⣄⠀⠈⠻⣄⠀⠀⠀⠀⠀⢸⡆⠈⠆⠀⠀⠹⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣾⠁⠀⢠⣿⣿⣿⣿⣿⣿⣧⠀⠀⢹⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀ ⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⡷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀ ⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⠀⠀⢻⣄⠀⠀⠙⠻⠿⠿⠿⠛⠁⠀⢀⣼⠃⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀ ⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀ ⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣆⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⢀⣾⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀ ⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇ ⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣙⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣾⡇⠀⠀⠀⣀⡤⠤⣶⠦⠤⠄⠀⠀⠀⠀⠈⠓⠦⣌⣉⠛⠛⠛⠛⠛⠛⠛⠛⢋⣉⡥⠖⠋⠀⠀⠀⠀⠠⠤⠴⠶⡦⠤⣄⡀⠀⠀⠀⢿ ⣿⠀⠀⠀⠉⠀⠀⠀⢻⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢺⠇⠀⠀⠀⠀⠀⠀⢸ ⣿⡄⠀⠀⠀⠀⠀⠀⠈⣧⠈⢿⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢾⠟⢠⡟⠀⠀⠀⠀⠀⠀⠀⣸ ⢿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣧⡈⠳⣄⠈⠉⢻⡗⠲⠶⠶⣦⠤⠴⠶⠶⠶⠶⢶⡶⠶⠶⠒⣾⠋⠉⢀⡴⠋⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⢈⣿⡶⠾⠛⢦⡀⠀⡾⢦⡀⢀⣆⠀⣀⠾⣇⠀⣠⠞⠛⠦⢾⣏⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿ ⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣌⣷⡞⠓⢦⡉⠉⣀⠀⠙⢋⣈⠛⠁⢀⡈⠋⢡⠖⠛⣶⣋⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇ ⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣄⣳⡎⠉⢙⠞⠁⠈⢳⡞⠉⠉⣶⣋⣤⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀ ⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠓⠛⠛⠚⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀ ⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀ ⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢶⣶⣦⣤⣤⣤⣤⣤⣶⣶⠶⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢇⣀⡆⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⠀⠈⣧⠀⠀⠀⠀⡠⠐⠁⠀⠀⢠⠁ ⠀⠀⠀⠀⠀⡴⠛⠀⠉⢀⡀⠈⢿⡇⠀⢀⠔⠁⠀⠀⠀⠀⢀⠇⠀ ⠀⠀⠀⠀⠀⢻⣼⣧⣠⣿⣷⡀⣼⣇⠔⠁⠀⠀⠀⠀⠀⢀⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⡿⠆⠘⠃⣼⢫⡇⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢲⠮⠔⢫⣷⡋⠑⠄⠀⠀⢀⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣵⣀⣀⠀⢱⡇⠀⢸⠤⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡸⡈⠁⢸⠀⣸⡓⢈⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡓⣻⡦⠆⢠⠣⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢶⡧⠒⠛⠻⠥⢤⠎⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡘⢃⠀⠐⢄⠀⠘⢆⡄⠀⢰⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠁⠘⡀⠀⢸⡱⠒⢀⣤⠓⠮⠤⠜⠲⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡎⠀⡠⣳⠀⢸⠀⡎⠀⢀⣈⣆⣐⣦⢔⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢀⠎⠀⠯⡆⢸⠡⢯⠀⠀⠀⠘⡏⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⢠⠒⢣⢼⠀⠀⠀⠼⢤⢳⡎⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠶⠞⠁⠀⠶⠿⣦⣴⠿⢀⣀⣀⣀⣀⢠⣾⣾⠟⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣬⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢀⣠⠖⠚⠉⠉⠙⠒⢦⡀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠳⣄⣰⠋⣠⠖⠉⠉⠈⠉⠓⢤⡙⢦⣀⡼⠁⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⢀⣤⡾⢡⢞⣤⡒⠭⠭⠭⠭⠕⣦⣙⣆⠻⣦⡀⠘⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⠞⡝⢠⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠹⡝⢦⡇⠀⠀⠀⠀ ⠀⠀⠀⢀⡼⠁⡘⢠⠋⠀⠀⠀⡠⠔⠒⠒⠒⠤⡀⠀⠀⠈⢇⠱⠈⠳⡄⠀⠀⠀ ⠀⠀⢀⡞⠀⠀⠁⡎⠀⠀⠀⡞⠀⣴⣿⣿⣷⡀⠙⡄⠀⠀⠘⡄⠁⠀⠹⣆⠀⠀ ⠀⢀⡞⠀⠀⠀⠀⡇⠀⠀⠘⡇⠀⢿⣿⣿⡿⠃⠀⡇⠀⠀⢀⡇⠀⠀⠀⠹⡄⠀ ⠀⡾⠁⠀⠀⠀⠀⣿⡀⠀⠀⠙⠦⣀⣀⣀⣀⡠⠞⠀⠀⠀⡼⡆⠀⠀⠀⠀⢹⡀ ⢰⠇⠀⠀⠀⠀⠀⠐⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⠝⠀⠀⠀⠀⠀⠀⣇ ⣼⠀⠀⠀⢀⣀⠀⠀⠈⠪⢕⡲⢤⣤⣀⣀⣠⡤⠴⣚⠕⠁⠀⠀⣀⣀⠀⠀⠀⢸ ⡏⠀⠀⠉⠈⡷⢄⡀⠀⠀⠀⠈⠁⠒⠒⠒⠒⠊⠉⠀⠀⠀⠀⣀⢔⡇⠈⠀⠀⢸ ⣷⠀⠀⠀⠀⠘⡌⢮⡑⠲⡤⠤⢤⠀⠤⠤⠤⠤⠤⠤⡔⠒⡩⢋⡞⠀⠀⠀⠀⢸ ⢸⡀⠀⠀⠀⠀⠈⢦⡜⣖⢍⠢⠼⠣⠠⠦⠔⠣⠤⡊⣑⠟⡤⠋⠀⠀⠀⠀⠀⡾ ⠈⣧⠀⠀⠀⠀⠀⠀⠉⠛⠤⣕⣎⣰⢊⡑⣔⣙⣖⡥⠞⠋⠀⠀⠀⠀⠀⠀⣰⠃ ⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀ ⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣤⣄⣀⣀⣀⣤⡤⠴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡰⢂⣾⠿⠛⠒⠚⠛⠃⠺⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡣⠋⠁⠀⠀⠀⠀⠀⢀⡐⠒⢙⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢄⠉⠀⠐⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠁⠀⠀⠄⠂⢈⣠⠎⠀⠀⣸⣿⡿⠓⢬⡇⠀⠀⠀⠀⠀ ⠀⠀⢸⡟⠀⠔⣁⣤⣶⣿⠋⢰⠀⠀⣿⡟⠻⣦⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⣷⡇⢠⣾⢟⢭⣭⡭⡄⠀⡆⠀⣿⣷⣶⠺⡆⢸⡄⠀⠀⠀⠀ ⠀⠀⠇⡇⠛⠡⣑⣈⣛⠝⢁⡀⠇⠀⣿⡿⠛⠒⣡⠇⣧⣀⠀⠀⠀ ⠀⠀⢠⠁⠈⠐⠤⠄⠀⣠⢸⠈⠢⠀⣿⡇⠀⠀⠠⠚⣿⣿⠀⠀⠀ ⡄⠀⢾⠀⡆⠠⣴⠞⠯⡀⠈⠙⠲⣶⣿⡇⠑⣦⡄⠀⣿⣿⠀⠀⠀ ⠈⠺⡮⠀⢡⠀⠀⠀⠀⠀⠁⠐⠒⠒⠛⠃⠈⠛⠇⠀⡏⡏⠀⠀⠀ ⠀⢰⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢷⠀⠀⠀ ⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀ ⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⡳⡀⠀ ⠀⠀⠀⠑⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣯⣼⡇⠑⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡗⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠎⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠑⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣠⣶⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⣾⣿⣿⠿⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠹⡄⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣀⣼⠃⠀⢸⣿⣿⡏⠀⠀⣠⣴⣦⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⣰⠟⡡⠦⣠⡟⠀⠀⠸⣿⣿⣧⡀⠐⣿⣿⣿⡇⣿⣿⣿⣿⣿⠟⣉⣀⠀⠈⠙⣿⣿⣿⣷⠀⠀⠀⢸⡆⠀⠀ ⠀⢰⠃⠞⠀⠀⢹⠀⠀⠀⠀⠉⠻⢿⣿⣷⣾⣭⣭⣾⣿⣿⣿⣿⠃⣾⣿⣿⣷⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⡇⠀⠀ ⠀⠘⣆⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⠉⠉⠙⢿⣿⣧⣜⡻⠟⠋⠀⢀⣼⣿⣿⡟⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠘⢦⣀⢀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⢉⠛⠻⠿⠿⣿⣿⡿⠿⠋⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⢒⡲⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⢀⣀⡈⣿⣿⣶⣶⣶⣿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢹⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⢠⠞⠭⣶⣛⡓⠢⠝⢧⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠏⠁⠀⠀⢾⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣼⠏⠀⣰⠿⠭⠍⠀⠀⠘⡆⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⡠⠞⣇⠀⠀⢀⣠⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠀⣼⣿⡀⠀⠙⢦⣄⠀⠀⠀⠀⣿⣤⡔⠋⠉⠉⠙⢷⡶⠛⠉⠀⠀⠈⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠹⣿⣿⣶⡶⠚⠉⠳⣤⣤⣾⣿⠏⠙⠲⡤⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⣹⠃⠀⠀⠀⣿⠛⠋⠁⠀⠀⠀⠸⡌⠦⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⣀⣀⡠⡞⠁⡄⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⡾⠀⠀⡇⠀⠀⠀⠀⠈⢧⣀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠚⠁⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣤⡀⠀⠀⠀⠀⣠⡴⠺⡇⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢀⣠⣤⡤⠖⢚⡉⠁⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⠀⢹⠹⡄⣠⠖⣏⠉⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠖⠁⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀ ⣇⡆⠈⣇⠙⣇⠀⠀⠉⠲⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⢹⡌⠢⠹⡀⠈⠇⠀⠀⠀⠘⢦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢀⣀⣀⡀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣄⠀⠹⡀⠀⠀⣀⣀⣀⣀⣈⣈⣳⣦⣀⣀⠀⠀⠀⠀⣰⠃⠠⠵⣻⠽⠚⠒⠿⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠓⠒⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⠧⠴⠚⠉⠀⠀⣀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠈⠉⢉⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠶⠶⠶⠶⠶⠶⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠤⢤⣀⣀⠀⠀⣠⠖⢦⡙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⢀⡤⠖⢉⣀⣀⣀⣀⠀⠀⠀⠉⠉⢲⠃⠀⠀⠹⣄⠈⠻⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⣀⡴⠿⠒⠉⠉⠉⠀⠈⠉⠉⠙⠒⠦⢄⡟⠀⠀⠠⣤⡿⠙⡶⠞⠉⠻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⢀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢿⠀⡼⠶⠄⢀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠤⠤⠴⢻⠾⣅⠀⠀⢀⡟⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡄⠈⠳⠤⠞⠓⢆⡀⢹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢉⣩⠶⠋⠉⠉⠉⠉⠉⠉⠙⠒⠒⠒⠒⠒⠒⠋⠁⠀⢳⡀⠀⠀⠀⠀⠀⠙⣾⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠠⠞⠀⢀⡾⠁⠀⠀⠀⠀⣀⣀⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠸⣩⠀⠀⠀⠈⠙⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⡄⣶⣻⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠷⣦⡀⠀⠀⡼⠁⠀⠀⣸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠻⣟⡿⢿⠟⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⣠⡄⠘⡇⣠⠞⠁⠀⢠⡾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡶⠟⠉⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠉⠓⠒⠚⠃⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⣿⢷⣶⣺⡟⠁⣀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠯⠥⢇⣾⣽⠏⢲⡞⠛⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⡇⠀⢸⡇⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀ ⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠛⠲⠆⠀⠀⠀⣀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢦⡀⢀⡾⠀⠀⠀⠀⠀⢠⡇⠀⠘⡇⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀ ⠘⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⢸⠀⠀⠴⡄⠀⠀⠀⠀⠀⠀⠀⢶⢤⡤⠤⠤⢄⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢸⠇⠀⠀⣷⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀ ⠀⠘⠿⣝⠳⠶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢸⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠈⣦⠻⢍⠙⠲⢭⣒⣲⡀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢠⡏⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣦⣀⠈⡉⠛⠻⠶⣦⣄⣀⠀⠀⠈⠙⠲⠤⣼⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠈⠷⣀⠑⠒⢊⡽⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⠟⠁⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠈⠙⠻⣶⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠊⠀⠀⠀⣀⣠⣖⣋⣀⣠⠴⠞⠁⠀⠀⠀⠀⣠⣴⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠈⠻⣧⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠉⠶⢄⣀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠹⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣀⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠶⠾⠷⣄⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⢰⡿⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣀⣀⡟⠁⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢦⠉⠳⢤⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢧⡀⠀⢀⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⢤⣀⠈⠳⣄⠀⠙⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⢧⠀⠀⢳⣤⡀⠘⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠇⠀⡸⣆⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⠳⢄⡈⠳⣄⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠘⣧⠀⠀⢫⡙⢦⡀⠙⠳⣆⡀⠀⠀⠀ ⠀⠀⠀⢰⡏⠀⢰⠇⠘⢆⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠙⣆⠈⠙⠦⣄⠀⠙⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠋⠀⠀⠀⢸⡇⠀⠈⢇⠀⠙⢦⡀⠈⠳⣆⡀⠀ ⠀⠀⠀⢸⠇⠀⢸⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠘⡆⠀⠀⠙⣦⠀⠀⠀⠉⠉⠒⠲⠶⠶⠶⠶⠶⠖⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠸⡆⠀⠀⠹⡆⠀⠘⢷⡄ ⠀⠀⠀⣾⠀⠀⢸⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⡿⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡀⠀⠀⢱⠀⠀⠈⢷ ⠀⠀⢰⢿⠀⠀⢸⡆⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⡄⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠹⢄⣀⠜⠀⠀⠀⠸ ⠀⠀⠀⣸⡆⠀⠀⠳⣄⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⢀⡏⢹⡆⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠀⣀⡠⠤⠴⠶⠶⣏⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⢸ ⠀⠀⠸⣇⠈⢯⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⣀⣀⣀⡀⠈⢧⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⠒⠦⣀⠙⡆⠀⠀⠀⢠⡏ ⠀⠀⠀⢹⣆⣸⠇⠀⠀⠀⠳⠶⡶⠚⠉⢀⡴⠒⠉⠁⠀⠈⠉⠳⣼⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠈⢳⡇⠀⠀⣰⠏⠀ ⠀⠀⠀⠈⢿⣅⠀⠀⠀⠀⠀⢸⡇⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣇⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠘⣇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠤⠴⠞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢶⣤⡀⠀ ⢀⣤⣤⣤⣀⣤⡴⣤⣤⣴⠶⢶⡌⠉⢻⣎⢻⡄ ⣿⠁⠀⠈⠀⠀⠀⠀⠈⠁⠀⢨⡿⠀⠀⣿⠈⣷ ⠘⢷⣤⡀⠷⣦⡀⠀⣼⠏⢰⡟⠁⠀⢠⡿⢀⣿ ⠀⠀⠈⢿⡄⠈⠻⠿⠋⣠⡾⠿⠿⠿⠛⠁⣸⠇ ⠀⣠⣴⠟⣁⡀⠲⠶⠟⠋⢀⣴⠆⠀⠀⢰⡟⠀ ⢼⣯⣴⣾⠟⣡⡶⠻⠿⢶⣾⠇⠀⠀⣰⡟⠀⠀ ⠈⠉⠸⠷⠾⠋⠀⢠⡶⠞⠋⢀⣠⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠋⠉⠀⠈⢳⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⢀⣠⠴⠚⠉⠁⢉⣷⣀⡀⠀⠀⠀ ⠀⠀⣀⣤⣤⠤⠤⢤⣄⣀⢀⣧⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⣹⠀⠀⠀ ⣴⣿⡿⠋⠀⠀⠀⠑⢄⠉⠻⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡿⠀⠀⠀ ⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀ ⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠘⡗⠉⠀⠀⠉⠐⠢⡀⠀⠀⠀⢳⠀⠀ ⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢈⢴⠇⠀⠀⢀⡀⠀⠀⠈⢄⠀⠀⢸⠆⠀ ⠀⠀⠙⢦⣄⠀⠠⠤⠤⠀⠊⣡⠏⠀⢀⠎⣀⡀⠈⠢⠀⠀⠄⠀⠘⣿⣷ ⠀⠀⠀⠀⠈⠙⠒⠶⢶⠒⠋⠀⢃⠀⠸⡎⣴⣶⡧⠀⡇⠀⣸⠔⠉⢸⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠑⢄⡑⠛⣛⡓⠨⠐⠈⠋⢢⡴⠋⠀ ⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠈⠳⢤⣀⣀⠀⠀⢀⣀⣀⣠⠼⠞⠉⠀⠀⠀ ⠀⠀⠀⠀⣸⠃⠇⠻⡄⣀⣀⣀⣀⣤⡽⡹⠉⠉⠉⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⡀⠈⢢⣝⡡⠤⡤⢠⠀⢪⢀⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢶⡄⠑⠴⠴⠃⠘⠒⠊⠁⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⡇⢀⣸⠀⠀⠀⡏⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠴⢻⠟⠋⢹⡀⠀⢸⢇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⢸⣧⠀⠸⡆⠀⠈⡇⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣀⣸⡟⢦⣀⣹⡀⠀⢻⣠⣼⣾⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⡷⠈⠛⠿⠇⠀⠈⠻⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒⠂⠐⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠴⠒⢶⠓⠒⠒⠒⠂⠠⠄⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⢔⠖⠀⠀⠈⠀⠀⠢⠤⠀⠑⠦⠦⠤⠤⣀⠀⠀⠀⠀ ⠀⠀⡀⠈⠈⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀ ⢀⠌⠀⠀⠀⢠⠇⠒⠒⢒⡶⢂⣤⣬⠫⡉⠀⠀⠒⠠⠀⠀⠀⠀⢡⠀ ⠘⠀⠀⢀⢼⡗⠲⢄⠀⠀⠀⡿⢿⡿⠀⠈⢑⠤⢀⠀⠀⠀⠀⠀⠀⠇ ⠘⠄⠀⠸⠀⠱⢿⣿⣷⠀⠀⠁⠁⠀⠀⡐⠁⠀⠀⢂⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠠⢀⠀⢘⡌⠁⢃⡀⠀⢀⡄⠀⢧⣀⣀⣀⠨⠀⠀⠀⠀⠀⡆ ⠀⠀⠀⠀⠀⠈⡇⠈⠢⢀⠴⡿⡻⠁⠠⠃⡆⠀⠀⠀⠀⠀⠀⠀⠰⠀ ⠀⠀⠀⠀⠀⠀⠑⢠⡐⠂⣉⢲⠀⠂⠁⠀⢡⡀⠀⠀⠀⠀⠀⢠⠃⠀ ⠀⠀⠀⢀⣤⠔⠊⠀⠈⢹⢹⠁⠀⠀⠀⡀⠔⡸⠒⠒⠀⢄⢀⠃⠀⠀ ⠀⢀⠔⠁⠱⡀⢀⠂⠀⠀⢆⢑⣀⡉⠥⠒⠈⠀⠀⠀⠀⠀⢇⠀⠀⠀ ⠀⠚⠄⠀⠀⠜⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠚⠠⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠒⠒⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣤⡤⠤⠤⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠈⠙⣷⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠦⣄⡀⠀⠈⣇⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣷⠃⠀⣀⠔⠂⣨⠜⠒⡓⣖⡲⡤⣤⣀⣀⠤⠀⣀⠀⠀⢀⡀⠀⢲⡤⢽⡦⠀⡀⠀⠀⡀⠀⢻⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣚⣉⡁⠀⠀⠉⠰⣿⠀⠰⠁⠀⢸⠀⠒⣀⡥⠟⠓⠲⠷⠶⣮⠍⠉⠉⠉⠉⠁⠀⠀⠀⢳⡀⠀⢀⠇⠀⡼⢀⡠⠋⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠛⠋⠉⠁⠀⠀⠉⠉⠉⠛⠓⠀⠘⣦⢰⠀⠀⠀⢳⡸⠁⠀⢀⠔⢋⣄⡞⠉⠀⠀⠀⠀⠀⠀⢀⣤⠤⣬⣿⣿⠭⢴⡾⠞⠉⣀⡴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣀⣀⣀⣉⡲⠀⠀⠀⣸⠎⣀⣄⣀⠀⠀⠀⠀⠀⠚⠁⠀⠀⣿⢀⡴⠉⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣩⠴⠒⠒⠒⠒⠒⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⡇⠀⢀⣴⢫⠞⢉⢀⠉⠀⠀⠀⠀⢠⣶⣞⣿⡶⣿⡏⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠿⠿⢖⣶⣶⣤⣦⣦⣴⣶⡛⠁⠀⠀⠀⢀⡇⠀⣾⣿⡄⠠⣾⣿⣿⣦⡀⠀⠀⣾⠻⣿⣿⢃⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡤⠀⠀⠀⠀⢀⡞⠀⠰⣿⣿⣿⡀⡝⢿⡿⠟⣧⠀⠀⢷⠧⠤⠶⠋⢹⣄⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣰⠷⠋⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⢳⡙⣏⡙⠦⠶⠞⠉⠀⠀⠈⠃⠀⠀⠀⠘⡏⠀⠀⠈⢱⡶⠒⠚⠉⣩⠴⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣶⡤⠴⠚⠋⡉⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠐⠲⠄⠐⢳⣮⣇⠀⠀⠀⠀⠸⠷⠶⣚⣀⡀⠀⢀⡇⠀⠀⣠⠟⢀⣸⠴⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⡤⠤⢒⠒⠋⠉⠑⠀⠀⣀⡴⠊⢀⡤⣀⡴⠊⢁⣀⣠⠤⠤⠤⣤⣖⡶⠶⠛⠁⠘⣆⠀⠀⢰⣶⣒⣛⣫⣭⡇⠀⡼⠁⢀⡼⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⠴⠚⠋⠁⠀⠈⠀⠀⠀⠀⢀⣠⠴⠊⢁⡤⠚⣡⠞⣡⠔⠊⣁⡤⠴⠒⠋⠉⣀⣠⣤⣤⣴⣶⣶⣾⣷⣄⠀⠙⠻⢯⣽⠟⢀⡾⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⢉⡔⣡⠖⠁⠀⡴⠡⢊⡠⢒⡽⠋⠀⠀⣠⠶⢛⣩⣿⠿⣿⣯⣿⠟⠉⠀⠈⠙⠲⠤⣤⣤⠴⡿⠁⠀⣠⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⢀⡴⣫⠞⠁⠀⠀⣸⠀⡰⠋⣠⠏⠀⠀⠀⣾⡇⠐⣾⠋⠀⢐⣿⣿⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠚⠁⠀⡰⠧⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠞⠁⠀⢀⡔⢁⡜⠁⠀⠀⠀⠈⡏⠹⠁⢰⠃⠀⠀⠀⠀⠣⢳⡀⢿⡀⠀⢠⠏⣿⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⣼⠇⠀⢦⣸⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀ ⠀⢀⣴⠛⠁⠀⢀⡴⠋⢀⡞⠀⠀⠀⠀⠀⠀⢿⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠙⠲⢵⣤⡸⡆⠘⠆⠀⠀⠀⣴⣣⡤⠴⠒⠒⢒⡿⠧⣤⠤⠚⠁⠀⠀⠀⠀⠀⣰⣿⠂⠀⠀⠀⠀ ⣠⠞⠁⠀⠀⣠⠟⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⠓⠦⠤⣀⣀⡀⠀⠀⠀⠈⠙⠻⢦⣀⠀⠀⢼⣏⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢹⡀⠀⠀⠀⠀ ⠋⠀⠀⠀⣰⠃⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠲⠤⣀⠀⠈⠙⠦⣌⣏⠓⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠁⠈⣇⠀⠀⣆⠀ ⠀⠀⠀⢰⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠒⠋⠉⠉⠉⠲⣄⠀⠀⠀⠀⠀⠈⠓⠦⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠙⣆⡸⢻⠀ ⠀⠀⠀⣸⠀⠀⠀⠀⠘⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡨⠻⣷⣄⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡏⠁⢄⡓⢦⣄⠹⡅⠸⡇ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⢳⡙⣆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠳⢵⣦⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡀⠀⣍⠲⣌⠙⣷⠀⡇ ⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠳⣌⠳⣤⣀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠈⢙⡓⠦⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡛⠦⠌⠲⣤⡁⠈⢹⠹⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣁⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠀⢀⡎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠈⠙⢮⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠀⣼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⣀⡀⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⣀⠴⠚⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠶⠖⠚⠉⠁⠀⠈⠙⢶⣾⣿⠁⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⣠⡀⠀⠀⢀⣦⣴⠀⠀⠘⡿⢿⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⣿⣿⡄⢠⢾⡿⠯⢆⠀⢠⣹⣿⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣟⡋⠉⢽⣷⠊⢣⣿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠺⡗⠀⠈⠉⠀⣶⠏⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡬⢤⠖⢀⡼⡿⢲⣧⡗⠒⠢⡄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡭⠛⠻⠁⠀⠿⣟⡽⡇⠀⠀⠘⡆⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⠆⠀⠀⠀⠀⠈⢧⢻⠀⠀⠀⢱⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⡶⠛⠑⣶⠀⠀⣸⡜⠀⣀⠤⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⡀⠀⠀⠀⡏⠀⠀⣿⠋⠉⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⣿⣄⠀⢰⠁⠀⣸⡃⠉⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢾⣧⣀⣭⣿⠗⠻⠄⢀⠇⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣶⣿⣅⡠⠾⠚⢿⣿⣍⣄⣀⣀⡞⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⡏⠀⠀⣀⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⣷⠀⠀⠈⠑⣄⠀⠀⠀⠙⣇⣠⡖⠀⠀⢨⡯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⠸⡄⠀⠀⠀⢸⠦⠤⣀⣀⠘⠁⠉⣲⣄⡜⠁⠈⠙⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⢳⠀⠀⠀⢀⣇⠴⠁⢈⣉⠿⢭⣁⠉⠓⠒⠒⠋⠁⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠇⠀⠀⢀⠞⣇⠀⠀⢸⠀⠀⡔⠁⠀⠀⠀⠀⢱⡀⢀⠴⢦⣄⣤⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⡰⠫⣰⣹⡀⠀⣸⣤⠤⣵⠤⠤⠔⠒⠒⠚⢳⣖⡦⠝⣋⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠃⢀⠜⠁⠀⠳⢔⣷⠀⢹⠤⠤⢿⡄⠀⠀⠀⠀⠀⠈⢻⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⡇⠀⣿⡀⠀⠀⠀⠀⠈⡆⠈⣿⢍⢹⠃⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠁⠀⢱⡞⣹⠃⠀⠀⠀⢠⠖⠉⠲⡇⡼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣵⠤⢤⡪⠊⠁⠀⢰⣶⣞⠽⣄⣀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣼⣗⣦⢿⣟⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠀⠀⠀⠀⠈⠙⠉⠉⢽⡯⢷⣋⣈⣙⠒⠦⠤⠤⠤⠤⠖⠛⠻⠽⠿⠽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣿⣿⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣻⣿⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠒⠒⠒⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⡒⠒⠒⠒⠢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⣀⠀⠈⢇⠉⠑⢦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢴⠶⣿⠀⡠⠀⣠⠔⢲⣲⣒⠢⡤⢄⣀⣀⣀⣀⣠⠄⠐⡦⠵⠂⡄⠀⠠⠀⢹⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠴⠯⠥⠤⠤⠀⠈⢿⠀⠀⠀⢣⢈⠔⠊⢉⡭⠉⡽⠂⠀⠀⠀⠀⠀⢀⣸⣄⡤⢃⣰⡣⠔⢡⠇⠀⠀⠀⠀ ⠀⠀⢀⣠⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠙⠤⠀⠁⢰⠏⣀⡀⠀⠀⠀⠀⠞⠁⠉⡏⢩⠟⣉⡤⠚⠁⠀⠀⠀⠀⠀ ⠀⣴⡫⠔⠒⠒⠒⠒⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠉⠉⡇⠀⣰⣻⠚⣉⣉⠀⠀⠀⢠⣶⣿⡶⣷⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠒⠷⠚⠋⠀⠀⠀⢠⠇⢸⣿⣆⢸⣿⣿⣷⡀⠀⣽⡙⢻⣳⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⡰⠃⠀⠈⢻⠻⡒⢌⣭⠴⠃⠀⠹⠍⠉⠀⢸⠒⠃⠒⣤⡠⠤⠒⣂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠤⠒⢊⠁⠀⠀⢀⠴⠋⠀⠀⠐⠢⠐⢳⣿⡀⠀⠀⠀⠷⣖⣂⣠⠀⢸⠀⠀⡰⢋⡠⠔⠊⠀⠀⠀⠀ ⠀⠀⣀⡠⠤⠒⠒⠉⠉⠀⠀⢀⡤⠚⡡⢔⡴⢊⡡⠤⠒⣒⡲⠶⠟⠛⠉⠀⢱⣄⠀⠸⣯⣭⣶⡟⢀⠏⢀⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠖⠉⠁⠀⠀⠀⠀⢀⡠⠔⡪⣁⠔⠉⡴⠡⢊⢥⡶⠊⠁⣀⠤⢲⣿⣿⣟⣿⠿⠛⠳⠄⣈⣉⣉⣴⠏⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠒⠁⡠⣪⠞⠁⠀⣘⢀⠔⣡⠊⠀⠀⣾⠁⢺⠋⠀⣸⣿⠁⠀⠀⠀⡄⠀⠀⠀⠋⠀⡼⠍⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⠉⠀⡠⠊⡴⠁⠀⠀⠀⣿⠈⠀⡃⠀⠀⠀⠙⠣⣸⣄⠀⡏⢿⠀⠀⠀⢀⠇⠀⠀⣀⢀⡼⠃⢰⡼⠀⠀⠀⠀⢀⡄⠀⠀⠀ ⢀⠜⠁⠀⢠⠎⠀⡜⠀⠀⠀⠀⠀⢹⠀⠀⠓⠄⣀⡀⠀⠀⠈⠙⠳⠷⣄⠁⠀⢠⡟⠚⠉⠉⢉⠟⠉⠉⠁⠀⠀⠀⠀⢠⡟⡇⠀⠀⠀ ⠋⠀⠀⣰⠃⠀⢠⠁⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠈⠉⠁⠒⠂⠤⢀⠀⠙⠢⣜⡟⠢⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢣⠀⢠⡀ ⠀⠀⢰⠃⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠘⣷⣔⠉⠉⠉⠓⢄⠀⠀⠀⠀⠙⠂⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣀⠈⢧⠌⣇ ⠀⠀⢸⠀⠀⠀⠈⡿⣄⠀⠀⠀⠀⠀⢠⠈⠻⢧⣄⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠑⠮⡓⢬⡆⢹ ⠀⠀⢸⡀⠀⠀⠀⠘⢌⠲⣄⡀⠀⠀⠸⣄⠀⠀⠉⠓⠦⢤⡃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⡸⠧⠅⠤⣑⠈⢲⠇⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠛⠛⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢏⠔⡒⠲⠆⠀⠤⠔⣿⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⠀⠻⠿⠗⠀⠀⢾⠯⠿⡄⠀⠀⠀ ⢀⣠⣾⣿⣿⣿⣿⣿⣯⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⡠⠭⡀⠀⡘⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⢄⠀⠉⠉⢁⣴⠃⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠒⠒⢹⠏⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠣⡑⢄⠀⠀⠀⢯⠣⡢⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⠢⡉⠐⠒⠒⠃⢓⡕⡀⠀⠀ ⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⡈⠙⡏⠠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠂⣠⠔⡲⣤⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⣠⠔⠊⠣⡋⠮⠾⡏⠣⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡠⠊⣀⠄⠂⠉⠉⠉⢉⡀⠀⠀⠀⠑⢆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡐⢠⠊⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠔⠊⠀⠀⠀⠀⣀⣀⠤⠚⠁⣲⣄⡀⠀⠀⠀⣆ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡀⣴⣦⣭⡙⠃⠀⠀⠘⣻⣤⠞⡄⠀⡰⠃ ⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠠⠊⢀⠆⢹⠿⠷⠀⠀⠀⣔⢿⣿⠀⠀⡜⠁⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣰⠋⠰⡀⠈⠁⠀⠀⠀⠁⠀⢈⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢀⠃⠀⠀⢣⡀⠀⠄⠠⠤⡥⢀⡎⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠈⠢⠄⢠⠞⠈⠢⠈⠒⠚⡑⠡⠁⠀⢀⡇⠀⠀ ⠀⠀⠀⠀⡼⡆⠀⠀⣀⠠⠤⠤⠐⢏⢄⠀⠀⠀⢱⠈⠀⠀⠀⢀⡜⠀⠀⠀ ⠀⠀⡠⡂⢁⠻⣄⠎⠀⠀⠀⠀⠀⠈⠢⡑⢄⣀⠆⠑⠤⣀⡠⠞⠁⠀⠀⠀ ⠀⣰⠋⠀⠀⠂⢼⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⣐⡟⠀⠀⠈⠑⡄⠀⠀⠀⠀ ⢀⠃⠀⠀⠀⠀⡸⠤⠄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⢪⡀⣀⠀⣀⣀⢀⠀⠀⠀⣆⢠⠁⠀⠀⠀⠀ ⠸⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢆⠔⠉⠈⢃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠀⣲⡒⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠈⠀⡀⠄⠒⢻⣫⠄⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⠀⡠⢊⠠⠒⠈⠁⠀⠉⢉⠉⠉⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠆⢠⡕⠡⠀⠀⠀⠀⠀⢀⠮⣀⠀⡀⠀⠀⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠔⠈⠁⠀⠀⢀⣀⣠⠶⠾⠁⢀⣾⣭⡏⠈⠀⡘⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠎⠀⠀⠀⢀⠠⠂⣽⠹⣳⣷⡄⠀⢸⣿⠿⢅⠀⡐⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⣌⠀⠀⠀⠀⠀⡠⠊⠀⣂⠉⠉⠁⠀⣀⢤⡂⣱⣯⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡄⠀⠀⠀⠐⠅⣐⣮⣿⡀⠀⠲⣖⣾⣾⠝⡀⠈⢀⡛⢳⣖⣰⠶⡄⠀ ⠀⠀⠀⠘⣆⠀⠀⠀⠀⣠⢫⠀⠈⠐⢤⠈⠽⠉⢢⣃⣠⣀⢧⡤⣸⠉⠁⢰⠀ ⠀⠀⠀⡠⠺⢑⢠⠔⠊⠀⠣⡑⠄⣀⣾⠄⡀⠀⡸⢿⣿⣿⣟⡌⢢⠀⠀⠀⡆ ⠀⠀⡎⠀⠀⢠⠁⠀⠀⠀⠀⠈⠚⠾⠟⠀⠈⢂⡇⠀⢀⣙⠉⠁⠀⡝⠀⠰⠀ ⠀⠀⢧⠀⠀⠈⡆⠀⠀⠀⠰⠀⠀⠀⠀⠀⢰⡊⡇⠀⢸⠋⠀⡀⠜⠀⠀⠆⠀ ⠀⠀⠀⠢⡀⠀⢰⡠⠤⠤⠀⣖⠉⠉⠐⠶⠁⢸⠃⢠⡃⡠⠊⠀⠀⠀⠌⠀⠀ ⠀⠀⢀⠠⠏⡐⠚⢄⠀⠀⢀⡀⣁⠀⠀⠀⠔⠁⠀⡆⠎⠀⠀⠀⢀⠎⠀⠀⠀ ⠀⡰⠁⠀⠀⠈⠉⠡⢴⡂⠁⠀⠈⢆⢠⠊⠀⠀⢠⠁⠀⠀⠀⡰⠃⠀⠀⠀⠀ ⡘⠀⠀⠀⠀⠀⡀⠀⠀⢘⡄⠀⠀⠨⠁⠀⠀⠀⠎⠁⠢⠔⠊⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠁⠒⠀⠘⠘⠂⠀⠤⠤⢀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠐⠒⠀⠈⠉⠏⣟⡧⢉⠆⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠍⠁⠉⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠳⠴⠒⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠤⡀⠈⢣⣀⣀⡀⠀⢀⣀⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⢄⣀⠈⢲⡼⠛⠻⠿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣉⢹⣬⣦⣀⣀⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠁⢀⣼⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠋⠁⠀⠙⠟⠁⠀⠉⢻⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠙⣿⡀⠀⠀⢸⡆⠀⣿⠀⠀⠀⣸⡏⢻⣄⠀⠀⠀ ⠀⠀⣠⣿⠇⠀⣿⡇⠀⠀⠙⠃⠀⠛⠀⠀⢀⣿⡇⠀⢿⣦⡀⠀ ⠀⣰⣿⣿⠀⠀⡸⠟⠂⠉⣭⣾⣿⣯⡁⠐⠚⢿⡀⠀⢸⣿⣷⡀ ⢠⣿⣿⡇⠀⢰⠁⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⢱⠀⢸⣿⣿⡇ ⠘⣿⣿⣿⠀⠈⢦⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⠎⠀⢸⣿⣿⡇ ⠀⠈⠛⠃⠀⡤⢤⣉⣲⣦⢤⡤⢭⣤⢤⣶⣋⣡⠤⡀⠈⠛⠋⠀ ⠀⠀⠘⣭⠉⠀⠘⡇⣰⠃⢸⠃⠀⢳⠀⢣⠀⡏⠀⠈⢉⡝⠀⠀ ⠀⠀⠘⠥⡖⢠⠔⢳⡇⠀⣾⠀⠀⢸⡀⠀⣷⠓⢤⠀⡦⠝⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠸⢤⣤⡟⠒⠒⠚⣧⢤⠼⠀⠀⠙⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⣷⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠒⠲⠗⠢⣼⠘⡦⠐⠾⠒⠒⠲⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠧⠄⠀⠠⢤⣀⠷⠀⠇⣠⠤⠄⠀⠠⠇⠀⠀⠀⠀

⠀⠀⣀⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⣿⣿⣿⣿⡘⣿⣿⣿⡟⢄⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⢻⣿⣿⣿⢿⣿⠻⣿⡳⢀⠀⠉⠑⠢⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀ ⠈⣿⣿⡟⠘⠿⡀⡎⠑⠘⣻⢶⢶⣄⠈⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣿⡟⠀⠀⠀⡹⠁⠀⠀⠻⢿⡀⠘⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠚⠁⢠⠀⢤⠸⡀⣀⡄⠀⠀⠀⠀⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣣⠀⢛⠦⢄⣀⣀⣀⡀⠀⠀⣴⠟⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣿⣷⡀⠈⠐⠒⠂⠉⠁⠀⡜⢀⠔⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⠿⣿ ⠀⠀⢸⣿⣿⣧⡀⠀⠀⠀⣀⠠⠔⠛⠠⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠒⠒⠛⠛⠓⠒⠒⠲⠶⣦⣄⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⣶⡤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀⢿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣈⠳⣄⠀⠉⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣌⡳⠦⣀⣀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡵⠶⠖⠛⠛⠛⠛⠚⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢾⣭⣙⡒⠾⢷⣦⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣓⡦⣽⣷⣤⡶⠀⠀⢀⣤⠶⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣧⠉⠉⠁⠀⠀⠀⣴⠋⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣛⠉⠈⠀⠀⠀⠀⠀⠀⣼⠁⠀⣀⣀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠚⠁⣠⡴⠖⠒⠲⣦⡀⣸⠃⢀⣾⡿⣿⢷⣦⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢠⡞⠁⠀⠀⠀⠀⠈⢻⣿⢀⡿⠀⣿⣿⠈⣿⡆⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⠁⠠⣾⡿⣸⠃⡇⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣙⣛⣫⡴⠃⢰⡇⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢠⡟⣾⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠉⠁⠀⢀⡞⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣸⢃⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡴⠋⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢰⢇⡞⠉⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡉⠁⠠⠞⠋⠁⠀⠀⠀⢀⣰⣿⠏⠀⠀⣎⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠲⢶⣖⠉⠉⠉⠳⣦⢸⡿⠃⠀⠀⠀⢿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⢹⡄⠀⠀⠀⣸⣟⠁⠀⠀⠀⠀⣾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠈⠙⠛⠦⢤⣀⠀⠻⡟⣯⡀⠀⠀⠀⠀⠻⣄⣠⡤⠟⢹⡇⠀⠀⣠⣾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠠⠴⠶⠞⠛⠓⠺⠷⣮⣻⠶⠤⠤⠤⣤⠈⠁⠀⣠⣾⡡⠴⠞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⠶⠿⣿⡛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠙⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠉⠉⠉⠙⠛⠛⠛⠳⢦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⣹⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠲⣤⣤⡀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠞⠋⠉⢧⣄⠀⠀⠀⠈⠻⣧ ⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⣠⠞⠁⠀⠙⠛⠓⠒⠚⠛⠋⢉⡿⠀⠀⠀⠀⠀⠈⠓⠦⢤⣤⠴⠟ ⠀⠀⠀⠀⠀⢀⣾⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⣠⠄⣠⠾⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣭⡍⠉⠙⠒⠶⠶⠒⠒⠒⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⣠⣴⠞⠓⠛⠉⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡞⠛⠁⠘⠳⣄⣠⣄⠻⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⣷⠶⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⢀⡴⠋⢀⡀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁⠀⠀⢀⡴⠋⠀⠀⠀⠉⠳⢤⡀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⣄⡀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣼⠋⠁⠀⠀⢀⣀⣀⣠⡤⠶⠿⠯⣅⣀⣀⣀⣠⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠛⠓⠶⠤⠤⠤⠤⠶⠞⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠚⠲⠶⠦⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⠤⠖⠒⠚⠓⠒⠲⢿⣓⠒⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢌⡻⣍⠑⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡑⠄⠀⠀⠉⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠱⣌⠻⡉⠉⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⡦⣄⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠙⢦⠀⠀⠀⠀⠈⢆⠘⢆⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠁⠀⠉⠉⠉⠉⠉⠁⠀⠤⠦⢤⡀⠀⠈⠑⢦⢷⡀⢀⠀⠀⠈⢆⠈⢆⠀⠀⠈⣇⠀⠀⣀⣤⣴⣖⡾⢿⡿⠋ ⠀⠀⠀⠀⢀⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⢸⠀⠱⡌⡄⠀⠀⠘⡆⠘⡆⠀⢀⡼⠖⢋⣿⣿⣯⢥⠴⠋⠀⠀ ⠀⠀⠀⠀⠈⣧⡞⠉⢧⠀⠀⠀⠀⢀⡠⠤⢤⡀⠀⠀⠀⠀⠀⡼⠀⠀⢹⡽⡄⠀⠀⢳⠀⢹⡴⢋⡠⠔⠉⠀⣀⠼⠋⠀⠀⠀⠀ ⠀⠀⢠⠴⠶⣿⣶⣶⡟⠀⠀⠀⢠⠏⠀⠀⠀⢹⡄⠀⠀⠀⢠⠇⠀⠀⠈⢷⠹⣄⣀⣸⡄⠸⡗⠉⢀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⣴⢿⠀⠀⠈⠻⢿⡀⠀⠀⢰⡏⢰⣾⣿⣆⡸⠁⠀⠀⠀⢸⠀⠀⠀⠀⠘⡆⢻⡟⢻⡇⠀⡏⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⠁⠈⢣⡀⠀⠀⠀⠙⡆⠀⠘⢷⣸⣿⣿⣿⠃⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢧⠀⢣⣸⠀⢸⢃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⠀⠻⡀⠙⢄⡀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⠀⠀⣟⠀⣸⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡆⠀⠱⡄⠀⠉⠉⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⠀⠀⢸⠀⠀⢸⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡀⠀⢻⠲⢄⣀⡀⣀⣀⣀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣀⠈⢳⠀⣼⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⡀⠘⡗⠘⠟⠛⢛⡿⠟⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢁⡼⢀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣦⡈⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⣀⣀⣀⡤⠞⠁⡜⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢮⣁⡀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠴⢲⠟⠦⠤⢬⣤⠤⠒⠊⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⡽⢯⣉⡽⢻⠁⠀⠀⠀⠀⡞⠳⣄⠀⠀⠈⠉⠒⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢻⠀⠻⣄⣀⣠⢤⣾⡷⣄⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⢈⡧⠤⢤⣄⡴⠋⠁⠀⠘⡆⠀⠈⠳⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠋⢀⡇⠀⠀⢀⡾⠀⠀⢠⠏⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠈⠉⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣀⡾⠃⠀⣠⠞⣇⠀⢀⣾⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣽⠁⠀⠈⣀⣴⡿⣄⣸⠙⣆⠀⠀⠀⢰⡾⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢀⡤⢊⡡⠊⠀⠀⢹⡆⠈⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠿⡷⠶⠋⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡋⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡶⠶⠿⠿⠿⠿⠶⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠘⢿⣦⠀⠀⠀⠀⣠⣾⠿⠋⠀⢀⣠⣴⠾⠟⠛⠛⠛⠛⠻⢷⣦⣄⠀⠀⠙⢿⣦⡀⠀⠀⠀⢀⣼⡟⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠈⠻⣷⣄⢀⣼⡿⠋⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀⠀⠹⣿⣆⠀⣠⣿⠏⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢈⣿⣿⠏⠀⢀⣾⠟⠁⠀⣀⣤⣴⡶⠶⠶⠶⠶⢶⣤⣄⣀⠀⠉⢻⣦⡀⠈⢻⣿⣟⡁⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣠⣴⣿⣿⠋⠀⣴⠟⢁⣤⡾⢛⣋⣥⣤⠤⠴⠶⠶⠦⢤⣤⣬⣙⠻⣶⣄⡘⢿⣆⠀⠻⣿⣿⣦⡀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⢀⣼⡿⣻⡿⠁⢀⡼⣣⣾⣿⡵⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢼⣿⣶⣻⣦⠀⠙⣿⡽⣿⣦⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣴⡿⠋⢰⡿⠀⢀⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣧⠀⠘⣿⡌⠻⣷⣄⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠟⠁⢠⡿⠁⢀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⠀⠘⣷⡀⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⡼⠁⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠾⠛⠛⠛⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠀⠘⣇⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⣸⠃⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⣀⣀⣀⡀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠸⡆⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀⢰⠃⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⣰⣾⣿⣿⣿⣿⣷⣄⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠹⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀ ⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣷⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⢠⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀ ⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⡀⠀⠀⠀⠀⢀⣀⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣾⡏⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀ ⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀ ⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆ ⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⢋⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡙⠛⢷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⠿⠛⢉⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⢸⣿⠀⠀⠀⠀⢀⣠⣤⡤⣶⠶⠶⠤⠤⠄⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⣁⣤⡴⠛⠋⠀⠀⠀⠀⠀⠀⡤⠤⠶⠶⢶⡶⢤⣤⣄⠀⠀⠀⠀⠈⣿ ⣾⡇⠀⠀⠀⠚⠉⠀⠀⠀⢹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠒⠒⠒⠒⠒⠒⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⠹⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠋⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠘⢮⡙⠛⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⠞⠛⢉⡼⠃⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠈⠻⣦⡀⠀⠀⢹⣿⠛⠛⠛⠛⢿⡖⠒⠒⠛⠛⠛⠛⠛⠛⢾⠗⠛⠛⠛⢛⣿⡁⠀⠀⢀⡴⠋⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿ ⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠈⣙⡶⠦⣼⠟⢧⣀⠀⠀⢸⢷⣄⠀⠀⢱⡀⠀⠀⣠⢿⡀⠀⠀⣠⠞⠹⡧⠴⢾⡋⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⡉⢻⣄⣰⠶⣄⠉⠳⠶⠏⠀⠙⠷⣴⠏⠿⠴⠞⠁⠈⠳⠶⠚⢁⣰⢶⣄⣰⠋⣹⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣽⡃⠀⠈⢿⡄⢀⡴⢦⣄⢀⡤⠶⢦⡀⢀⣠⠴⢦⠀⣠⠟⠁⠀⢹⣧⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀ ⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣙⡟⠀⠀⢨⠏⠀⠀⠀⢻⡏⠁⠀⠀⣿⣣⣤⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀ ⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠷⠿⠿⠿⠾⠿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀ ⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⠿⢿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⠿⠿⠿⠛⠛⢉⠁⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⡃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⠒⠒⠚⠁⠀⠰⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡐⠁⣼⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣄⡀⠀⠙⢄⠀⠀ ⠀⠀⢀⣀⡰⠁⢸⣿⠋⢀⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⡆⠀ ⠀⡜⠕⠢⡇⠀⠸⢿⣦⣘⣿⣯⣿⣿⡟⣩⣤⡀⠙⣿⣿⠀⠀⡇⠀ ⠀⢇⠀⠀⡇⠀⠀⠀⠈⠉⠉⡏⠙⠻⢧⣝⣛⣁⣠⣿⡟⠀⠀⡇⠀ ⠀⠀⠑⠒⢱⡀⠀⠀⠀⠀⢠⡀⠀⠀⢀⡌⠉⠉⠉⠉⠀⠀⢠⠥⢄ ⠀⠀⠀⠀⠀⠱⢄⠀⢀⢤⣼⣿⣶⢞⠟⠀⠀⠀⠀⠀⠀⢀⠔⠉⣹ ⠀⠀⠀⠀⠀⢀⡨⣵⠁⡼⠯⠀⠀⠇⠀⣀⣀⡀⠀⣀⠔⢅⢀⡠⠟ ⠀⠀⠀⠀⡔⠁⠐⣿⣄⡨⠒⢄⣠⣾⠮⢄⡀⠘⡍⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠈⡹⠁⠀⠸⡉⠁⠀⠀⠊⢀⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠂⠐⡽⠀⡀⠀⠀⠱⣄⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠁⠀⢃⠀⠀⠀⠀⠉⠉⠀⢸⡀⠀⠀⠀⠀⠀⠀ ⡠⢤⡀⠀⣀⠔⢺⠀⠀⠀⠃⠀⠀⠠⢤⠔⡪⠉⠁⠑⠄⠀⠀⠀⠀ ⡧⠘⠑⡊⠐⠢⡈⠂⠀⠀⠀⠀⠀⠔⢡⠊⠀⠀⠀⠀⣸⠀⠀⠀⠀ ⠱⡁⢣⠈⠀⠀⠈⠢⢄⡀⠀⠀⠀⢠⠃⣤⣤⠖⣄⡰⠃⠀⠀⠀⠀ ⠀⠙⠒⠒⠈⠁⠀⠀⠀⠀⠉⠉⢀⠧⠐⢈⡀⠀⢨⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠐⠒⠊⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠔⠂⠉⠁⠉⠉⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠈⠺⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠉⠒⠠⠄⢀⣀⣀⣀⡀⠀⠜⠊⢂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠐⠒⣴⣧⣀⠉⠐⠂⠠⢄⣀⠀⠀⠀⠀⠀⣀⠠⠚⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠊⠀⠔⡰⠁⠻⢿⣷⣶⠀⢰⣿⠿⢿⣷⠈⠁⠀⢸⡠⠤⢀⠀⠀⠀ ⠀⠀⠀⠀⡌⠀⡌⠰⠁⢀⠔⠀⠢⡀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠘⠀⢄⠀⠑⡄⠀ ⠀⠀⠀⠀⢡⠀⢠⠁⢀⡋⢢⣤⣀⣡⡰⠁⠀⠀⢣⠀⠀⠀⠀⠀⡇⠀⡆⠀⠁⠀ ⠀⠀⠀⠀⠀⢑⠇⠀⠸⠈⠘⠫⠥⠆⡇⠱⣦⡤⢼⠀⠀⠀⠀⠀⠂⢀⠃⠀⠇⠀ ⠀⢠⠒⠈⠉⡈⠀⠀⠀⠁⠤⡤⠊⠉⣏⠑⠂⢀⠃⠀⠀⠀⠀⠀⢸⣁⡠⠊⠀⠀ ⠀⣇⠀⠣⢐⠃⠀⠀⠀⠀⡐⠁⠀⠀⢸⡁⠈⠀⠀⠀⠀⠀⠀⠀⠜⠢⡀⠀⠀⠀ ⠀⠈⠢⡀⢹⠀⠠⣐⡰⣧⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⢄⠀⠀ ⠀⠀⢠⠘⢸⣎⡀⡀⠄⠛⣄⠀⠀⢀⣤⡰⣁⠀⠀⠀⠀⠀⠀⠀⢰⢒⣠⢄⠑⠠ ⠀⡖⢁⠔⣱⠧⠘⢄⣀⠊⠀⠏⠉⡄⠣⡈⢢⢱⠀⠀⠀⠀⠀⠰⠉⣀⣤⠤⠤⠤ ⠀⠈⠁⡒⠮⢄⠑⢄⠑⠕⡒⠄⣀⢧⣀⠡⠴⠁⠀⠀⠀⠀⠀⠠⢃⠡⡪⣺⠀⠀ ⠀⠴⢅⠉⠂⢀⠑⠄⠑⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⡡⠙⠒⣞⠊⠀⠀ ⡈⠀⠀⠑⠄⠀⢢⡈⠄⠀⠀⠈⢱⠒⠒⠒⡖⠒⠒⠀⠁⡠⠊⡠⠂⠁⡠⠘⡄⠀ ⡇⠀⠀⠀⠀⢩⠁⢡⢸⠀⠀⠀⡘⠀⠀⠀⠃⠀⠀⠀⡐⢀⠪⢀⡠⠂⠀⠀⢸⠀ ⠀⠉⠐⠒⠒⠚⠒⠒⠒⠀⠈⠉⠀⠀⠀⠀⠈⠀⠤⠄⣃⣀⠀⠮⠤⠤⠀⠀⣐⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣭⣛⠿⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠉⠛⠿⣿⣷⣌⠻⣿⣷⡀⠀ ⠀⣠⣶⣿⣿⣿⣿⣶⡄⢴⣿⣿⠿⠿⠿⣿⣿⣷⣿⡿⠟⠛⠻⣿⣷⡄⠀⠀⠈⢻⣿⡆⠘⣿⣷⠀ ⣼⣿⠟⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠈⣿⣿⠀⢸⣿⡇ ⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿ ⠘⢿⣿⣄⡀⠀⠀⢠⣶⣤⣄⡀⠀⠀⠀⠀⢠⣾⣿⠇⠀⢠⣾⣿⠏⠀⠀⠀⠀⢀⣿⣿⠀⠀⣿⣿ ⠀⠈⠻⢿⣿⣿⣦⡈⠙⠻⢿⣿⣦⠀⠀⢠⣿⡿⠋⠀⠀⣻⣿⡁⠀⠀⠀⠀⢀⣾⣿⠇⠀⢸⣿⡏ ⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠹⣿⣿⣿⣿⣿⠇⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣾⣿⠁ ⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠈⠉⠛⠛⠁⠀⣠⣾⣿⠟⠉⠛⠛⠛⠉⠉⠀⠀⠀⠀⣸⣿⡏⠀ ⠀⠀⠀⠀⢀⣤⣾⣿⠏⠀⠀⠀⣰⣦⣤⣴⣶⣿⡿⠛⠁⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀ ⠀⢀⣤⣾⣿⡿⠛⠁⣠⣴⣶⠀⠈⠛⢛⣛⡉⠁⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀ ⢠⣿⡿⠋⢁⣠⣴⣿⣿⡿⠋⠀⣠⣶⣿⣿⣿⣷⣤⣀⣰⣿⣿⠁⠀⠀⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀ ⠸⣿⣷⣶⣿⣿⣿⡿⠋⠀⣠⣾⣿⠟⠉⠉⠛⠛⠻⠿⣿⣿⠇⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀ ⠀⠉⠛⠉⢹⣿⣿⣠⣤⣾⣿⠟⠁⠀⠀⢀⣠⣴⣶⣾⣿⠏⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠿⠿⠟⠋⠁⠀⠀⠀⠀⣼⣿⡟⠉⠁⠀⠀⢀⣀⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠉⠓⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠋⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠉⠓⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⣠⡤⠒⠋⠁⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡶⠤⣄⡀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠃⠀⠀⠈⠙⠲⠤⣀⣀⣸⡇⠀⠀⢀⡴⠋⢁⣀⣀⣠⠤⠤⠤⠤⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡷⠶⠚⠉⠉⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣴⡿⠷⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠶⢤⣴⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⠏⠀⠀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⢠⠇⢰⠋⣠⣾⡷⣶⣄⡈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢀⣤⣶⣶⡄⢈⣇⠚⡇⠀⠀⠀⢀⡴⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣧⣄⠀⠀⠀⣾⠀⣿⠀⣿⠁⣜⣬⣭⣿⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣠⣏⣉⠁⠈⢿⠈⢹⠀⣇⣀⣴⡾⠛⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠈⠛⠿⣶⣴⠃⠀⠹⡄⣿⣸⢿⣿⣓⣾⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⣷⡶⣝⣦⡾⢀⡞⠀⢹⡋⠁⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢠⡇⠀⠀⠀⠻⢌⣿⣜⣿⣿⣻⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡽⣿⣿⣿⡿⣡⠞⠁⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠸⡇⠀⠀⠀⠀⠀⠉⠙⠻⢯⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣿⣲⠿⠟⠋⠁⠀⠀⠀⠠⣾⡇⠀⣀⣀⡤⠦⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡆⠀⠀⣿⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡤⠚⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⡀⢸⣇⠀⠀⠹⣧⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⠀⠀⢰⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀ ⠀⠀⣧⢸⣸⠀⠀⠀⢻⣄⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⢀⡜⢹⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣇⢳⡀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀ ⠀⠀⣿⣿⣿⡄⠀⠂⠀⢻⣆⠀⠀⠈⠳⣄⠀⠀⠀⠀⢸⠀⠈⠻⢄⡈⡉⠒⠶⣦⠶⠖⠋⢡⣤⠞⠁⠈⡗⡀⠀⢠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇ ⢀⢠⣏⢏⢻⡇⠀⠀⠀⠀⠻⣦⡀⠀⠀⠈⠳⣤⡀⠀⢸⡄⠀⠀⠈⠙⠺⣦⣀⣿⢀⣤⠾⠋⠀⠀⠀⣰⠇⢁⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠈⠃⠻⣼⡆⣿⣴⣀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠈⢻⣦⡈⢷⡀⠀⠀⠀⠀⠀⠈⣿⠉⠀⠀⠀⠀⠀⣠⡏⣠⢟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀ ⠀⠀⠀⠀⠀⠀⠁⠿⣤⣀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠙⢿⣜⢷⣄⣀⣀⣤⡴⠚⠛⠓⢤⣄⣀⣀⣠⣿⠟⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀ ⠀⠰⠀⠀⠀⠐⠦⠀⠉⠉⠉⠉⠉⠉⠹⣧⠀⠀⠀⠀⠀⢹⡆⠈⠉⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⢡⡟⠳⢶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠀⡀⠀⠘⣧⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣿⡀⠀⠀⠀⠀⠙⠳⢤⣄⣀⣀⣀⣀⣠⣤⠴⠛⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⡀⣠⡾⠁⠀⠀⢠⡾⠛⠶⢦⣀⣀⡴⠿⠦⣌⠉⠹⣏⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣍⣁⣀⡀⠀⣼⣽⠁⠀⠀⢀⡏⠀⠀⠀⠀⠀⡾⠁⠀⠀⠈⠳⠄⣿⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣭⡆⠀⠐⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠛⠷⢿⣯⣬⣭⣽⡃⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣼⣆⠀⠀⠘⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⡴⢫⣤⡀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠚⠳⠤⢤⡤⠴⠿⢦⣤⣤⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠴⠶⠒⠒⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠒⠒⠶⠤⠤⠀⠠⠤⠄⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠤⠀⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⢀⡤⠔⠋⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢸⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠘⣇⠀⠀⠀⢸⠗⠒⠂⢀⣤⠶⠿⠥⠤⠤⠤⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿⠀⡠⠞⣉⣁⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⢰⡟⢋⡴⠚⣉⡊⢁⣠⠤⠴⠆⠀⠀⠀⠀⠀⠀ ⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣼⠀⣠⠏⠀⣨⣒⣀⣱⡾⢭⡶⠒⠒⠒⠒⠒⠒⠒⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⠾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⣠⡞⠛⠉⠁⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠤⠤⠤⠄⠒⠒⠢⠤⠤⠽⠷⢤⣤⣤⣤⣤⣤⠴⠞⠉⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠑⢄⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡀⠤⢀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠄⠄⡀⠀⡰⠀⢀⠠⠊⠁⠀⠀⠀⠈⠀⠀⠀⠀⢡⣀⡀⣀⠀⠀⠀⠀ ⠀⠀⡆⠀⠀⠀⠉⠑⠴⠓⠈⠉⠀⠀⠉⠉⠐⠢⠔⠂⠉⠉⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⡅⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀ ⠀⠀⢳⠀⠀⠀⢄⢋⣤⡙⠆⠀⠀⠀⠀⠀⡠⢋⣄⢱⣠⠀⠀⡰⡅⠀⠀⠀⠀ ⠀⠀⠘⠓⢤⡜⠸⢸⣴⣾⣼⠀⠀⠀⠀⢠⢣⣧⣬⢇⠇⡖⠋⠀⠘⠆⠀⠀⠀ ⠀⠀⠀⡇⠀⡇⠀⠑⠛⢿⣿⠀⠀⠀⠀⠀⣿⡿⠟⠊⠀⣴⢀⡀⠄⠈⢄⠀⠀ ⠀⣸⡀⢱⠀⢃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢡⡀⠀⠀⢠⠋⠁⠀⠀⠀⠀⠀⢄ ⠀⡿⡇⠀⢣⡀⠱⣄⠀⠈⠐⠄⡐⠠⠐⡨⠋⢱⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢸ ⠈⠛⠳⡄⠀⠑⡄⠈⠱⡜⡄⠀⢈⣸⡉⠀⢠⡧⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠐⠀⠐⢈⣉⠀⠙⢆⠀⠈⡎⠉⠉⠉⠉⠉⠹⢓⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⠀⠀⠀⠀⢀⣈⡄⠀⠡⢄⡀⠀⢀⡠⠂⡜⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀ ⠀⠀⣤⣒⡒⣰⠃⠀⠊⠁⢢⠊⠐⠹⡄⣠⠎⠀⠀⠀⠀⠀⠀⠀⢀⣞⠁⠀⠀ ⠀⠀⠉⠁⠈⢿⡀⠘⡀⠀⢸⠀⠀⢀⠟⠁⠀⠀⠀⠀⠀⠀⣀⠔⠁⢀⡀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠏⠄⠐⠒⠂⠀⠀ ⠀⠀⠀⠀⠀⠄⠠⠀⠀⢀⠔⠈⡀⠐⠂⠀⠀⡔⠀⢰⠀⠀⣀⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠁⠀⠀⠀⠰⠀⠀⠀⡇⢰⡤⡪⠥⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣸⠀⠀⠀⠀⢢⠀⠀⢠⠧⠮⠼⠬⠾⠦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠓⠒⠒⠒⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠖⠲⣄⠀⠀⠀⠀⠀⡀⠹⡋⠓⠒⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡀⠀⠈⠓⠖⠋⠀⠀⠀⠘⠦⣙⣷⣷⠀⠀⠀⢿⣧⠈⡏⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⠟⢲⡄⠀⠀⠀⠀⠀⠀⣀⣦⣼⣿⣿⡧⠀⠀⢸⣿⠀⠀⣸⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⠤⠜⠁⠀⠀⠀⣠⡶⠋⠉⠀⠈⠻⠿⠧⠴⠦⠼⢿⣦⣀⣿⠃⠀⡸⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣴⠄⠀⢀⣼⠿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡈⢷⢢⣤⣔⣩⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄ ⠀⠀⠘⠿⠟⠁⠀⢀⡞⠁⠀⠁⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢿⠀⢸⡀⠏⠹⣇⠀⢳⡀⠀⠀⠀⠀⢀⡴⠉⢀⠃ ⠀⠀⠀⠀⠀⠀⠀⡞⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡇⠀⠀⠀⠀⡸⠀⢀⡇⣷⠀⣿⡟⢦⣳⡀⠀⠀⣠⠋⠀⣠⣾⠀ ⠀⠀⠀⠀⠀⠀⣸⣾⢋⡏⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡇⠀⣸⠀⡟⠀⡏⣇⠈⡿⡷⣤⠾⣇⣴⣿⡿⡇⠀ ⠀⣠⠖⠊⢛⣛⢻⣿⡿⠁⠀⠀⡠⠚⠛⢿⡆⠀⠀⠀⠀⠀⠀⣼⠁⢠⠃⢸⠀⡜⠀⡇⢰⠁⠷⠇⠀⢿⣿⣟⣻⡇⠀ ⣸⠁⠀⡴⠁⠀⠙⠻⠧⡀⢀⣼⡀⠀⢀⡟⠁⠀⠀⠀⠀⠀⢠⡇⡔⠁⢠⠇⡼⠀⢸⢀⠎⠀⠀⠀⠀⡜⠁⠀⢸⠀⠀ ⢺⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠻⣧⡔⠋⠀⠀⠀⠀⠀⠀⠀⣺⡿⠁⠀⣏⡴⠁⠀⠘⠋⠀⠀⠀⠀⢠⡧⠤⢄⣸⠀⠀ ⠘⡆⠀⢻⡄⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠓⢦⣼⠀⠀ ⠀⠹⣆⠀⠓⢄⡀⠀⠀⠀⠦⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⢯⣀⠀⠀⠀⢹⡀⠀ ⠀⠀⠙⢧⡀⠀⠉⠱⡖⠲⣶⡾⠿⡿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠈⠑⢦⡀⣸⠃⠀ ⠀⠀⠀⣠⢿⣦⡀⠀⢳⡴⠁⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣿⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀ ⠀⡠⠚⣡⣿⢇⡇⢱⡘⠓⠒⣉⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡧⢊⡶⢛⠞⠀⠀⠉⠉⠉⠉⠉⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⢹⡌⣷⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⠶⠞⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢻⣧⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⣿⡄⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿⣧⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡏⢻⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡆⢸⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣩⣤⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⢀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⠿⠟⠛⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⣿⣿⠿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠉⢀⣤⡀⠀⠁⠐⠂⠀⠠⣴⣿⣿⡿⠀⠹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⢻⣿⣿⣦⣄⣀⣀⣤⣴⣿⣿⣿⠇⠀⠀⠹⣿⣿⣿⣿⣷⠀⠀⠀⠀⣰⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠹⣿⣿⣿⣿⣿⣿⣟⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠹⣿⣿⣿⣿⢹⣿⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠁⠀⠙⠛⠛⠁⠘⠋⠒⢾⣿⣻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⡿⢿⣿⡿⠋⢀⡤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠈⣦⠛⠁⠀⠘⢿⣿⡟⠹⡄⠀⠀⠀⠀⠀⠀⢠⣾⢽⣽⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣆⠃⠀⠀⠀⠀⠀⠙⢓⡺⠇⠀⠀⠠⠤⠤⠀⡾⡷⠎⢹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣋⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣏⣷⡆⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⢳⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⡏⢳⠞⠁⠘⠒⠉⠈⢇⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⠀⠀⠀⣀⣀⠀⠀⠘⠒⠒⠄⠀⢀⡴⠋⠀⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠠⡀⠀⠀⠠⠚⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣧⡀⠀⠳⡬⣍⠉⢹⠊⠐⠓⠒⢒⡶⠂⠀⣼⣿⣿⣿⠀⠀⢀⡴⠒⠋⠁⠀⠀⠀⣠⠇⠀⠀⣈⢁⡆ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡽⣷⣄⠀⠙⢮⡉⠉⢢⠀⠀⡠⠊⠀⣀⣼⣿⡿⢿⡿⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠁⣀⡠⠜⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢻⣿⣿⠒⠤⣈⣉⣉⣉⣉⡠⠴⠚⡏⠀⠈⡷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠟⠛⠒⠤⣀⠀⠀⠀⠀⠀⠀⢀⡏⠒⠪⡀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠑⠲⠶⠶⠒⠉⠀⠀⠀⠙⡄⢧⣀⣀⣀⡤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠉⠉⠉⠉⠒⠤⣸⣌⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢘⣯⠀⠀⠀⠀⠀⠀⠀⣠⠀⢰⠃⠀⡀⠀⠀⠀⠠⠾⠭⢍⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠋⠈⠢⣀⠀⠀⠀⠀⢀⠟⠀⡇⠀⠀⠈⠑⠲⢤⣀⠀⠀⠀⠈⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠈⢑⡲⡤⠤⠞⠀⠀⢱⡀⠀⠀⡀⠀⠀⠉⠓⠦⣄⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣰⣁⡀⠀⠀⠀⠀⠳⡀⠀⢹⡄⠀⠀⠀⠀⠀⠉⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡠⠎⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠈⢆⢠⣄⠀⠀⠑⢤⡘⡟⡄⠀⠀⠀⠀⣄⣀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠉⠀⠀⠀⠀⠀⠀⣠⣾⣿⣇⡀⠀⠀⠸⡜⠀⠱⣄⠀⠀⠈⠙⠊⠲⢤⣀⣀⠼⠟⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠄⠀⠀⠀⠀⢀⣀⡀⡏⢩⠃⠳⡄⠀⠀⢱⠃⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡠⠖⠉⠀⢇⣱⣾⠀⠀⠙⢦⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣄⠀⠀⠀⠉⠢⣄⠀⠀⢨⠆⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣓⣦⣤⠄⠀⠀⠙⠂⣸⠀⠀⢀⡴⠛⠛⠻⠄⠀⠉⠢⡄⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠢⢄⣀⣀⣀⡠⠔⠁⠀⠀⣾⠀⠘⠦⣀⠀⠀⠀⠀⠘⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⣳⠀⠀⠈⠳⢄⡀⠀⠀⢹⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠴⠭⠭⢉⣀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠈⠳⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⣄⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⢩⣒⣊⠉⣰⠄⠀⠀⠀⣸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⠈⠳⣄⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣄⣤⡴⠶⠝⢓⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣉⣲⣶⣵⣤⣀⣀⣖⠯⠀⠀⠀⢀⣀⣀⡤⢴⡒⡩⠋⠁⠐⣄⣷⡽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠧⣆⣠⢠⠀⠈⢑⡦⢝⡟⠉⠉⠉⠉⠀⠀⠉⠚⢽⣉⣁⠒⣒⣩⠥⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣈⣉⣓⣚⣡⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠖⠒⠒⠒⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⣠⠔⠊⠉⠉⠉⠉⠑⠒⢤⠃⠈⢢⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⢀⡠⠎⠒⠈⠉⠉⠉⠑⠒⠢⢄⡎⠀⠠⣤⡏⢢⠞⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣧⡰⠓⠂⢈⣗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣟⠑⢄⢀⣼⡀⠙⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏⠀⠀⠀⠀⠀⠀⢀⡤⠒⣲⠽⠓⠒⠒⠒⠒⠢⠤⠤⠤⠤⠔⠊⠘⣆⠀⠉⠀⠈⠢⡸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⣾⠁⠀⠀⠀⠀⠀⡴⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡄⠀⠀⠀⠙⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣿⠀⠀⠀⠀⠀⠚⠀⢰⠃⠀⠀⠀⡤⠴⠒⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠸⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⢠⡰⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣦⠀⠀⣰⠃⠀⢰⠇⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠶⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠻⣟⡟⠋⣽⠀⠀⠀⠀⠀⠀⢀⣄⣤⠤⢈⣇⡴⠃⠀⡰⠋⠀⠀⠀⠀ ⠀⠀⣀⡴⠋⠁⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⣶⡿⢟⡟⣿⡽⣋⡤⣖⠉⠀⠀⠀⠀⠀⠀ ⢀⡼⠋⠀⠀⠀⠀⠀⠀⠙⣆⡀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠚⢹⠁⢸⠀⠀⠙⢦⡀⠀⠀⠀⠀ ⢸⣁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡝⠲⠄⠀⠀⣀⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⢀⡖⠀⠀⠀⠀⢸⠀⠘⡆⠀⠀⠀⠳⡄⠀⠀⠀ ⠘⢿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢸⠀⠐⢆⠀⠀⠀⠀⠀⠘⡶⡖⣒⡢⢄⡀⠈⠀⠀⠀⠀⠀⡞⠀⠀⡇⠀⠀⠀⠀⢳⠀⠀⠀ ⠀⠈⠳⣍⠙⠻⠶⣦⣄⣀⠀⠀⠈⠳⢤⡀⢸⠀⠀⠘⣆⠀⠀⠀⠀⠀⠱⡌⠢⣈⡱⡶⠃⠀⠀⠀⢀⠞⠁⢀⡼⠁⠀⠀⠀⢀⡿⠀⠀⠀ ⠀⠀⠀⠀⠙⠶⣄⠀⠈⠉⠙⠲⣦⡀⠀⠈⣹⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠈⠢⠤⠜⠁⠀⢀⡠⠔⠁⣀⡴⠚⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠻⣆⢠⠏⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⣠⠔⠋⠉⠉⠉⠉⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠹⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣔⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣧⡀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣀⠀⠀⠀⠀⢰⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠉⠲⣄⣀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⢀⡏⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣀⠀⠘⣌⠓⢬⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣇⠀⢠⠀⠈⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠏⢀⡀⠀⠀⠀⠀⠀⡌⠑⠤⡈⠢⣀⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣆⠀⢳⠦⡈⠳⣄⡀⠀⠀⠀ ⠀⠀⠀⡟⠀⡜⠱⡄⠀⠀⠀⠀⠙⣄⠀⠈⠲⡈⠓⣄⡈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠸⡄⠀⢧⠈⢢⡀⠑⢦⡀⠀ ⠀⠀⢸⠇⠀⡇⠀⠙⢄⠀⠀⠀⠀⠈⠓⢄⠀⢱⠀⠀⠱⡄⠀⠈⠙⠒⠲⠤⠤⠤⠴⠒⠒⠊⠉⠀⠀⠀⠀⠀⢳⠀⠘⡄⠀⠙⡄⠀⢻⡄ ⠀⠀⢸⠀⠀⡇⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠱⣰⠃⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠸⡀⠀⢸⠀⠀⢻ ⠀⠀⢻⡀⠀⢳⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠃⢀⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠒⠃⠀⠀⠈ ⠀⠀⣸⢳⡀⠀⠑⠤⠔⠃⠀⠀⠀⢀⣀⣀⠤⢴⡊⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠑⠢⣀⠀⠀⠀⠀⢸ ⠀⠀⢿⠈⣇⠀⠀⢀⠀⠀⢀⡠⠚⠁⣀⠤⢤⣀⠱⡀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠒⠢⡈⢳⠀⠀⢀⡞ ⠀⠀⠘⣦⠞⠀⠀⠈⠙⡞⠉⢀⠔⠉⠀⠀⠀⠈⠳⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠈⢿⠀⣠⠎⠀ ⠀⠀⠀⠹⣧⡀⠀⠀⠈⡇⡴⠁⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⠊⠁⠀⠀ ⠀⠀⠀⠀⠈⠛⠦⠤⠤⠼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀

⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢆⠈⢱⣄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠺⡉⠙⠀⡰⠃⢠⢁⣦⠀⣠⢺⡏⢒⡤⢚⡟⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡄⡡⠂⠳⡄⠿⠊⠈⠂⠓⠈⠈⠂⠯⠔⡗⢒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⡇⠀⠈⣇⠃⠀⠈⠐⠢⡀⠲⢄⠀⠀⠐⢟⣀⡇⢀⡄⢰⠲⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠀⠀⠈⡧⡀⠀⠀⠀⠘⠶⠂⠉⠒⠂⠀⠀⣱⠟⣇⠂⢀⠉⠀⠉⡱ ⠀⠀⠀⠀⠀⢳⠀⢠⠓⢝⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⡰⠁⢱⠐⢀⠀⠢⡀ ⠀⠀⠀⠀⠀⠀⠳⡆⠀⠀⠑⠨⣑⠢⠤⠤⠤⠤⢔⣲⠉⠉⠀⢀⠜⠒⠈⠀⠒⠁ ⠀⠀⠀⠀⠀⠀⢸⢄⠀⠀⠀⠀⠀⠈⢩⣿⣯⠝⠁⢸⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⢄⠑⠢⢄⡀⣀⡠⠾⠿⠟⠀⢀⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠉⠐⠰⣀⡀⠈⡇⠀⠈⠉⣁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⡌⠉⠉⠉⠉⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠒⠱⡀⠀⠀⠀⡇⠀⠀⠀⠀⡠⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠃⠀⠀⠀⠉⠁⢈⠭⡁⠀⠀⠉⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠋⠁⠀⠈⠑⠲⠤⠤⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡞⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀ ⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠸⡄⠀⠀⠀⠀⠀⢰⠃⠀⡇⠀⠀⠀⢀⣤⣔⣚⣛⠛⠟⠛⠛⠉⠉⠙⠛⠻⢭⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡄ ⠀⠀⣾⣦⣀⢰⡿⢿⡆⣀⣠⣷⡄⠀⠀⠀⠀⣼⠀⠀⢹⣀⣴⡿⠟⠋⠉⠉⠉⠛⠷⡄⠀⠀⠀⠀⠤⠤⢤⣙⢦⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠃ ⠀⠀⠸⣅⠈⠛⠁⠈⠳⠏⢙⡇⠙⣦⣀⠀⠀⢿⠀⢀⡞⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⢠⠀ ⢠⣤⡤⡟⠀⡼⠋⢹⠀⠀⣿⠀⠀⠘⣎⠓⠦⢼⣤⠎⢠⡏⠀⣠⣾⣿⣿⢶⡄⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⡌⠀ ⠀⠻⢧⣴⡀⠛⠦⠼⠂⠰⠛⠲⢤⡀⠘⢦⡀⢠⠏⠀⢸⠀⣰⣿⣿⣿⣇⣼⡇⠀⡾⠀⠀⠀⢀⠀⣀⠀⠀⠀⢀⣐⡲⣷⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀ ⠀⠀⠀⠈⠛⢶⠶⠚⠁⠀⠀⠀⠀⠉⠳⣄⠙⡿⠀⠀⠸⡄⢿⣿⣿⣿⣿⡿⠀⡼⢁⣀⣼⣗⣚⡯⣾⣗⠀⣠⠋⠉⠻⣿⡇⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡇⠴⢶⡆⠹⣌⣛⠿⢿⣿⡁⠞⣴⠋⠀⠀⠀⠈⠙⢾⣳⣤⠇⠀⠀⠀⢸⡇⠀⢀⡤⢺⠃⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢸⡙⠢⣄⡉⢛⣺⠿⠃⢰⢷⡆⠀⠀⠀⠀⠀⠀⢹⣏⣴⣿⣿⣷⢸⣅⡴⠋⢠⠏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢧⠀⣀⣹⣷⡦⣄⡀⠈⢻⣧⠀⠀⠀⠀⠀⣀⣿⣿⣿⣼⣿⡟⡼⠁⠀⢠⠏⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⢿⣡⡀⠀⠙⠶⠬⢿⠲⢯⣷⣤⣤⣶⠿⣿⠿⣿⣿⣿⡟⢱⠃⠀⡴⠋⠀⠀⠀⣄⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠸⡆⠀⠀⢀⣼⡷⣄⠙⢿⡒⣆⠀⠀⠘⣟⠒⠮⣝⠲⡦⣄⡘⢦⣉⣋⣉⡠⢋⣠⣞⠁⠀⠀⠀⣼⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣇⠀⣰⢫⠎⠀⠈⠓⠦⣍⠻⠤⣄⣀⠈⠀⠀⣸⡆⠙⠒⣛⢶⣌⡽⠛⠛⠫⠦⠚⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠇⡏⠀⠀⠀⢀⣤⠎⠉⠒⠦⣬⣉⠓⠛⠓⠛⢋⣭⣵⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠇⠀⠀⢻⣷⠏⠀⠀⠀⠀⠀⢨⠿⡍⠉⠉⠉⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⢰⠋⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⡏⠀⠀⠈⢧⣀⣠⠤⠒⠲⢤⡀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣤⠟⠁⠀⠀⠀⠀⠉⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢧⡀⠀⠀⠀⠤⢖⣚⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣧⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠙⠦⣄⣀⡀⠈⠋⢈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠘⣆⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣯⣉⢉⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠒⠒⠁⠀⢀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⣤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠴⢶⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠄⣀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠽⠷⠖⠒⢤⡉⠊⠲⣝⣦⡀⠀⠀⠀⠉⠲⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠟⠁⢀⡴⠶⣤⣄⡙⠾⣦⠘⢹⢿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⣠⠄⠐⠒⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣁⡤⢤⣖⡥⠖⠚⠛⠉⠉⠙⠛⠛⠾⠾⡼⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀ ⠀⠠⢄⢀⡤⠄⠀⠀⠀⠀⠀⠀⣠⣾⣧⠞⡡⣞⣽⠞⠂⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢣⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⣠⠄⠂⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡾⣿⢫⠆⠀⡼⡽⠁⠀⢸⣤⣀⡉⠙⠛⠀⠀⣴⣶⣦⣼⡄⠰⡻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠐⠢⣄⡴⠒⠂⠀⣼⢋⣿⢃⣴⡾⠿⣅⡇⠀⠈⠻⠿⠟⠇⠀⠀⠀⣴⡿⣿⣿⢣⡀⠈⢺⣧⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⣿⠋⡏⡎⡼⠀⠀⡼⢣⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⠛⢋⡏⠀⠑⡄⠰⣽⡑⢆⠀⠀⠀⠙⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣼⠁⣰⠃⠀⡞⢀⡌⢣⡀⠀⠠⢬⣍⣓⣒⣃⠀⣠⢞⠁⠀⠀⢹⠀⠙⡷⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢰⠇⢰⠃⠀⢠⢇⢸⠀⠸⡝⠢⣄⠈⠑⠛⠋⣡⠞⠁⢻⡀⠀⠀⠸⡄⠀⢹⠲⢽⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠢⢄⡤⠒⠃⢀⡇⠘⣆⢸⡀⢠⠋⣯⢯⠇⣰⣇⠀⠀⠉⠓⠒⢻⡀⢧⡀⢣⡙⡄⠀⠀⢹⡀⠈⢳⡈⢯⡉⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡿⣰⠃⣧⠼⠗⠛⠛⠁⠙⠻⢦⣀⣀⠀⢀⡍⢿⠛⠓⠿⣼⡄⠀⠀⣿⠀⠀⠳⡈⠛⢶⡳⢤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣴⣵⡷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⣠⣼⡀⠀⠀⠀⠙⣆⠀⠘⢆⠀⢳⢌⡢⡀⠳⣌⢣⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡿⢛⡦⡤⣠⠀⠈⠣⡀⠈⠳⡈⢣⠙⢮⡀⢸⣷⠽⣦⠀ ⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣤⣴⣶⣯⢹⣶⣇⣹⣾⣧⣿⣿⣳⠀⠀⠙⠦⡀⠱⢜⣆⠈⠓⣄⢫⢦⡀⠀ ⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡞⢿⣴⣏⢻⣿⣦⣿⣿⣿⣿⣿⣿⣟⡛⣟⣛⣻⠇⠀⠀⠀⠈⠲⡄⢻⡆⠀⠘⡞⢧⠇⠀ ⠀⠀⣟⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⢻⣁⣆⢱⣺⣿⢽⡻⣽⣷⠿⠛⠚⠉⠉⢁⢀⢀⡀⡁⣽⣄⠀⠀⠀⠀⠀⠹⡼⡽⡀⠀⢽⡘⠄⠀ ⠀⠀⠳⡀⠀⠀⠀⠀⢺⡉⠀⠀⠀⠀⠙⢮⣆⡳⢿⡚⡩⡱⡲⡲⣶⣷⣻⣻⠯⠮⠮⠾⠿⣇⡸⠀⠀⠀⠀⠀⢠⠇⢹⡉⢠⢸⡟⠀⠀ ⠀⠀⠀⠹⡄⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠈⠳⣿⣿⡾⠦⣍⣽⠟⢳⣶⡟⢹⡶⣿⡉⣹⣯⡇⠀⠀⠀⠀⢠⠏⠀⠀⢧⡸⣾⠀⠀⠀ ⠀⠀⠀⠀⣹⣦⡀⠀⠀⠀⠘⢏⠲⢤⡀⠀⠀⠀⠀⢹⣷⣴⡯⠽⠶⠾⠽⠿⣿⡶⠓⣻⣾⣿⠀⠀⠀⠀⢠⠏⠀⠀⡑⠶⢿⣽⣷⡄⠀ ⠀⠀⢠⡞⠁⠀⠙⢦⡀⠀⠀⠀⠑⠤⠽⠦⢤⣀⣀⣼⠛⠉⠑⠒⠋⠉⠉⠉⠉⠉⠉⣸⣇⡇⠀⠀⠀⣰⣃⡤⣉⣓⣿⠏⠉⠉⠉⠀⠀ ⠀⢠⡟⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⣰⣿⡛⠵⣲⡤⢤⣀⣀⣀⠀⠀⠀⢠⣯⠟⠀⠀⢀⡼⠁⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⣼⠑⢺⣽⠶⠤⠭⣍⣓⣒⣊⣉⡩⠿⠿⣾⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⣿⣤⡾⣟⠓⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠬⠽⠹⠶⠶⠾⠮⠭⠭⠍⠈⠉⢉⡿⡽⠁⡏⡇⣟⠳⢤⣀⠀⠉⠉⠉⠉⠉⠉⠉⢹⡴⣋⣉⣉⣉⣉⣉⣉⣉⣛⣛⠛⠛⠛⠛⠋⠉ ⠀⠉⠉⠉⠉⠉⣉⣁⡠⠤⠤⠴⢦⠞⢰⠃⠀⡇⠃⠸⡄⠀⢈⠉⠓⠢⠤⣄⣀⣀⣠⡾⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠂⠀⠀⠀ ⣤⣤⣒⣲⠾⠭⠥⠖⠉⠉⠉⢁⠎⠀⡞⠀⠀⡇⠀⠀⢳⠀⠈⠳⡀⠀⠀⠀⠤⠖⠋⠀⢱⠠⠤⠶⠶⠶⢖⣒⠠⠒⠒⠒⠒⠲⠶⠤⠀ ⠀⢀⣀⣐⣒⣒⠒⠒⠒⠒⠂⣿⣟⣳⣧⣼⢤⣷⣀⣠⠼⡇⠀⠀⠮⣲⡄⠀⠀⢀⣠⣴⣾⡀⠀⢠⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⢷⣿⣷⠛⠻⣟⢲⡋⠀⠀⠀⢀⣩⡷⣶⠯⣏⣿⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⣹⣿⣸⣿⣷⠋⢹⡷⠶⡇⠀⢷⣴⢶⡞⢿⣝⣧⣾⠾⣿⣾⣿⡛⡿⣶⣝⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⠒⣿⠙⠉⠈⠘⠣⠿⠀⠀⢠⠃⢈⣿⡴⣿⣽⡿⣿⣿⣇⠈⣿⠛⠃⣾⡄⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣠⢞⣡⠋⠀⢸⡁⣹⡗⠾⣧⣿⡏⠉⠛⠋⠀⠀⠠⣯⣋⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠒⠋⠉⠉⠉⠉⠉⠉⠓⠲⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⢣⡙⢲⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠈⠉⠒⠶⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠟⠋⠁⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠙⠲⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠑⠒⠒⠚⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠛⠲⣤⢿⣷⣄⠀⠀⠀⠀⠉⠙⠒⠶⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠀⢠⠏⢻⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⢉⣽⣿⣶⣦⣤⣤⡤⠤⢤⣤⣤⠤⠤⠴⠒⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣠⠞⢩⠏⠀⠈⢿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢠⠞⠁⢠⠏⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⠟⠛⠉⠛⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣷⠞⠉⠀⠈⠉⠳⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢠⡏⠀⢠⡏⠀⠀⠀⠀⣠⠴⠖⠲⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣄⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡞⠀⢀⡟⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⣠⠴⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠙⢧⡀⠀⠀⠀⠈⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢰⡇⢀⡾⠁⠀⠀⣠⠟⢦⣄⡀⠀⠀⠀⠀⠘⡇⠀⠀⣴⠋⠁⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢳⡀⠀⠀⠀⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠘⠃⡼⠁⠀⠀⢀⣿⠀⠀⢸⣿⣶⣦⣤⣤⣤⡷⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣸⠃⠀⠀⠀⣾⡏⠛⢦⣄⡙⢻⠟⠋⠀⢀⡇⢸⠉⠳⢤⣄⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠿⣇⠀⠀⠀⠉⠛⠒⠲⠤⡼⠁⣸⠀⠀⠀⣿⣿⣿⣶⡖⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⡿⠀⠀⠀⢠⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⡟⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⢀⣼⣥⣴⣿⠓⠦⣄⣈⠛⠛⠁⠀⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡴⠋⠀⠀⠀⢠⠏⠀⠀⠀⠀ ⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣠⢤⡴⠋⠁⠀⠈⢻⣄⠀⠀⠉⠉⠑⠒⢲⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⢀⡏⠀⢀⣀⣀⣀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠘⣿⠶⣄⣀⣀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠋⠉⢻⡉⠙⢺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⣿⣇⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣷⠆⠀⠀⠀⢳⡀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠀⠹⣿⠀⠀⠀⣀⣤⠤⠤⣤⣴⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣿⠀⢰⣏⣡⣤⣤⣤⣄⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣨⠷⠀⣿⢴⠋⠁⠀⠀⠀⠀⢀⣈⣳⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠶⠦⢄⣀⠀⠀⠀⠙⠦⣀⠀ ⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣿⡌⢧⣀⣀⣠⠖⠋⠉⠁⠀⣨⠷⣄⣀⡀⠀⠀⣀⣠⣴⣛⣶⡞⠳⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⣠⠬⠿⠶⢄⠀⠀⠈⠳ ⠀⠀⣀⣠⠴⠋⠀⢀⣰⠋⣴⣿⠀⠀⢹⡁⠀⠀⠀⢠⠞⠁⠀⠀⣼⠉⠉⢻⡍⠈⠳⣄⠀⠙⢦⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⠀⠀⢀⡴⠋⢀⡾⣽⠋⢧⡀⠀⠑⢦⣤⣤⣿⠀⠀⠀⢠⠇⠀⠀⠀⢳⠀⠀⠘⢦⠀⠀⠙⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⢀⣠⢤⣶⡶⠒⠶⠶⠶⠶⠖ ⠀⠀⠙⠓⠚⢯⣄⣠⡜⢀⡟⠀⠀⢳⡄⠀⠀⠘⢦⡻⣄⠀⠀⣸⠀⠀⠀⠀⢸⡆⠀⠀⠈⣇⠀⠀⢸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠹⡄⢧⠹⣏⠛⣶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣨⠭⠟⠶⣟⠛⠛⠛⢦⡀⠀⠀⠙⠦⣍⠉⠉⠳⣄⣀⣀⡜⢣⣀⠀⣀⡿⠦⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣧⠀⠻⣌⢣⣌⠙⣿⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠔⠻⢧⣄⠀⠀⠀⠙⢦⡀⠀⠙⠢⣄⠀⠀⠈⠙⠓⠒⠒⠛⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠥⣄⣙⣆⠀⢈⣷⠈⡿⠋⠀⠀⠀⠀ ⠀⠀⣠⠿⢧⣀⠀⠀⠈⠙⢦⡀⠀⠀⠹⣄⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢀⡤⠖⠋⠉⠙⠿⣍⠉⠁⠀⠀⠀⠀⠀ ⠀⢰⠋⠀⠀⠉⠳⣄⠀⠀⠀⠉⠢⡀⠀⠈⢳⡀⠀⠀⠀⠈⠉⠓⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⠖⠋⠀⢀⠴⠋⠀⠀⢀⣠⠴⠖⠋⠳⢦⡀⠀⠀⠀⠀ ⢠⡏⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠘⢦⡀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠑⠒⠲⠶⠶⠶⣶⠶⠶⠖⠒⠋⠉⠉⠀⠀⠀⢀⡴⠋⠀⢀⣠⠖⠉⠁⠀⠀⢀⣠⠼⠷⡄⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣀⣀⣀⡼⢷⡀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢀⡴⠋⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⣻⠀⠀⠀ ⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⣇⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣠⢿⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀ ⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⠃⠈⠛⠓⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠉⠙⠓⠲⠶⠶⠤⠤⠤⠤⠧⠤⠤⠤⠿⠶⠶⠷⠒⠒⠒⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⢸⠁⠀⡿⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠲⠶⡤⠤⣿⣀⡀⢀⡇⢸⠉⠉⠋⡉⠁⠀⠀⠀⢀⣠⠏⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⣄⡒⢽⣷⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⣿⡙⢿⣿⣿⣿⠛⢿⡆⣸⣿⣿⣿⣿⣿⣿⠁⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠸⡇⠀⢹⣾⠇⠀⢸⣿⡇⠈⠀⣽⣇⣙⠋⣀⣐⣻⣬⣾⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣠⠤⣼⠿⣧⣠⠞⣛⠉⠉⠀⠀⠀⠀⠀⢹⣦⣤⠿⠿⠿⠛⢋⡝⠋⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⣷⣄⠀⠤⠿⢷⣏⡀⢡⢀⣀⣀⠀⠀⢀⣀⠈⠋⠀⠀⠀⣴⠭⠀⠀⠀⣼⢿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣿⡯⠜⠋⡀⠤⠤⠌⣙⡿⢿⡉⣿⣅⣴⣉⣠⢱⣄⡀⠀⣄⣀⣀⠀⠀⣰⡏⠈⠙⠣⢼⣶⣿⣿⣿⣿⣿⣿ ⠀⠀⣠⠿⡋⠀⠀⠀⣀⣤⠒⠊⠉⡇⢀⡏⠀⣿⡙⠛⠭⣍⠉⠉⠉⠁⠉⠙⢻⣿⣿⠇⠀⠀⠀⠸⠛⠏⢠⣸⣍⡟⠻ ⢀⣶⢿⣯⢤⣤⢬⡿⡏⠉⠳⣄⠀⢿⠋⠘⠤⠃⠈⠑⢄⠀⠉⠢⡄⠀⠀⠁⠀⢌⢿⡓⠀⠀⠀⠀⠀⠀⠲⠁⠿⣟⡗ ⠀⣇⠀⠀⠀⠀⠹⡇⠁⢀⠀⠈⣧⠘⣄⠀⠀⠀⠀⠀⠀⢑⣤⠴⠚⠚⠛⢲⠤⢈⣶⣷⡀⠄⠀⠀⠀⠀⠀⢐⣾⣷⠓ ⠀⢻⠀⠀⠀⠀⠀⠉⡶⠋⠀⠀⣹⠆⠈⠀⠀⠀⠀⠀⣠⡞⠀⠀⡄⠀⠴⣺⠤⠤⣿⡿⠀⠀⠀⠀⠀⠀⡀⣿⣋⣿⢯ ⠀⠈⣇⠀⠀⢀⣴⠞⠀⠀⠀⠀⣿⣄⡀⠀⠀⠀⢀⣠⡿⠀⠀⠀⢸⠤⠽⠃⠀⣰⠏⠠⠀⠀⠀⠀⠀⠀⠈⠈⠇⣿⡯ ⠀⠀⠘⣦⣰⠟⠁⠀⠀⠀⠀⢸⠙⢿⡉⠉⠉⢉⣡⣾⠁⠀⠀⠀⢸⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿ ⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⢀⡇⠀⠀⠉⠛⠛⠉⢀⠇⠀⠀⠀⠀⠘⣷⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⣀ ⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉ ⠀⠀⠀⠙⢦⡀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀ ⠀⠀⠀⠀⠀⠙⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⣠⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠸⠁ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⡄ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇ ⠀⠀⠀⠀⠀⢀⡟⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⣸⠁⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⠄⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡧⠌⠒⠚⠐⠢⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣨⠞⠁⠀⠀⠀⠀⢀⢰⠀⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡡⢺⡏⠁⢀⣀⠤⠒⠈⠁⠀⢡⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠚⠢⠤⠊⢈⣤⡝⠀⠀⢀⡸⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⣢⠱⡀⠀⠈⠙⠀⠀⣾⡶⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠘⠢⡐⡀⠀⢤⣀⡐⣡⠃⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠐⡈⡢⠀⠍⡚⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⣀⡠⢴⠉⣷⡀⠀⡃⠀⠀⠀⠀ ⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⡰⠋⠁⠈⠑⢜⠋⣷⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⢇⢀⡀⠀⡀⠈⡆⢈⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠂⢤⣀⡀⠄⡍⠀⠉⣊⡠⡆⢨⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⠊⢂⣿⠁⠀⢀⠃⠠⠁⠸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡧⠀⠀⢮⠔⠁⡠⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣰⢀⡠⡫⠓⢄⠀⠀⠱⣅⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠠⡂⢚⠝⠉⠈⠁⠀⠀⠀⠈⠐⢄⠀⠈⠪⡢⡀⠀⠀⠀⠀⠀ ⠈⢣⠈⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠂⢄⠈⢌⢂⠀⠀⠀⠀ ⠀⢈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠀⠈⢄⠱⡀⠀⠀ ⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣷⣔⣿⡆⠘⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠁⠘⡏⠛⠀⠈⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣁⠀⠈⢵⡀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⢀⠀⣀⣠⠃⠀⠀⠀⠈⢄⠔⠁⠀⠀⢱⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⢷⡣⢻⢀⠇⣰⣯⡃⢉⣯⡹⠁⠐⣪⠆⠁⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠿⢳⠈⢹⠀⣹⣯⡃⣼⡀⢱⡀⠀⠑⠒⡤⠀⠤⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠟⠀⡼⢶⡴⠛⠛⠛⠻⠁⡤⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⠀⠀⠠⢺⡡⠛⢾⣧⡐⢄⠀⢀⠌⠀⠀⠀⠀⣰⡀⠀⠀⢀⠁⠀⠀ ⠀⠀⣸⠸⡄⠀⠀⠀⢣⡀⠜⠲⣾⡉⠀⠅⠀⠀⠀⡠⠖⠁⢀⠋⠉⠉⣀⢀⣦ ⠀⠰⢠⠀⠘⡀⢀⠴⠭⢤⣀⠀⠀⠉⠒⠒⠒⠂⠁⠀⠀⠀⣆⠀⣤⠞⠁⠀⠀ ⠀⢂⠘⠀⢀⢠⠊⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⢤⠘⠋⠀⠀⠀⠀⠀ ⢠⠏⠀⠀⠞⡌⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀ ⠘⢤⣠⣜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⠺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣤⣀⣀⣀⠠⠔⠊⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣗⠶⠒⠉⠉⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⠤⠤⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠶⠦⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠋⠁⠀⠀⠀⠀⢠⣿⣧⡀⠈⣙⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⣠⣼⣎⢯⣷⠋⠁⠈⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁⠀⠉⣷⣍⠳⠦⠤⡴⢿⡏⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⣠⠞⠉⠀⠀⣀⣤⠶⠒⠉⠉⠉⠓⠲⠾⠗⠻⠿⠿⠿⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⢠⠞⠁⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠈⠉⠓⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣰⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡇⠀⢰⢧⠞⣁⣠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠿⣦⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⠴⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁⠀⠈⢙⣿⣶⣶⣶⣶⠒⠲⢦⡀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠴⢾⣿⣷⠇⠀⠀⠀⢀⣿⣿⣬⡤⣼⡇⠀⠀⠀⠙⠄⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡿⢿⣯⡶⠿⢦⣄⡉⠀⠀⠀⠀⠀⣾⣿⣿⢿⣿⡿⠇⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⣰⡇⠈⢿⠛⢶⣶⣯⣷⠀⠀⠀⠀⠀⢿⢿⣿⣿⡿⡦⣀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⢀⡴⠛⢷⡄⠈⠳⣼⣾⣿⣿⣷⠀⠀⠀⠀⢸⡟⠉⠁⠀⣧⠈⢧⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠀⠀⠀⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡟⠋⠉⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⢠⣷⣽⡄⠀⠀⠀⠀⠀⠀⠀⠘⠶⡾⠇⣸⣧⣤⠠⠟⠙⢿⣷⠾⠿⣶⣦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⣀⠀⢀⢶⣚⣉⡼⣿⡇⠀⠀⠀⠶⢶⣶⡴⢶⣶⣿⣟⢿⣎⠛⠓⠀⠀⠘⠁⠀⠀⠾⠯⠽⣯⣳⡦⠤⢴⣦⣴⣶⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠛⠲⠦⠤⣤⠶⠻⠷⣄⠀⠀⠀⠀⠳⣿⡢⢾⣿⣿⣿⡋⠁⢴⠇⠀⠀⠀⠘⠳⣦⣤⣤⡤⠾⢲⣠⢾⣟⣁⡀⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡃⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠈⢁⡿⠋⠈⢿⣄⠘⠂⠀⠀⠀⠀⠀⣿⣀⣀⡀⠀⢸⡏⠛⣿⠀⠀⠘⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⣷⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⠀⠳⣄⠀⠀⠀⠀⠀⠀⣨⡟⠛⠛⠛⠁⠀⠀⠀⢙⣷⣤⣰⣿⣿⣶⣚⣹⣿⠧⣝⢦⣸⡇⠀⠀⠀⠀⠀⢻⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣇⠉⠲⣄⣀⠀⣠⠴⠞⠉⠀⠈⢷⡀⠈⢧⣄⠀⠀⠀⢠⣿⣄⡀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣄⡽⣿⣿⣾⡟⢹⡀⠈⢧⡀⠀⠀⠀⡄⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠈⠳⢤⣀⡽⠋⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠳⢤⣀⣾⠀⡇⠙⠓⢤⣄⠀⠀⢠⠏⠈⠿⠿⠿⢿⣿⣷⡻⣥⡇⠀⠀⠳⣄⣀⠀⠧⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣝⠶⣤⣼⣆⠇⠀⠀⠀⠙⢦⠀⢸⠀⠀⠀⠀⠐⠛⠛⢿⠙⠛⠇⠀⠀⠀⢈⣹⠀⠀⠀⠀⣼⠃ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠯⠾⠀⠀⠀⠀⠀⠈⢷⢸⠀⠀⠀⠀⠀⣤⡤⣸⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⢠⠏⠀ ⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣤⡾⢾⠀⠀⠀⠀⠀⣿⡥⠿⠀⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⡾⠀⠀ ⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣏⠀⢸⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⣴⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣠⠴⠛⠛⠓⠲⣤⠲⡀⣰⠏⠁⠈⢳⣼⠀⠀⠀⢠⠟⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢈⣧⠴⠶⠖⠒⠒⠒⠶⠤⣼⣇⠀⠀⠀⠀⠀⠈⠙⠿⠃⠀⠀⠀⣼⠃⠀⠀⢺⣇⡀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠳⢤⣀⡀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⡞⠈⣳⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡴⠋⠻⣄⠀⠀⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⢸⡇⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠈⠙⠓⠲⠤⠤⡏⠀⠀⠀⣠⠴⠚⠋⠉⠀⠀⠹⣆⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣰⣻⡁⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡞⠀⠀⠀⠀⠀⠀⠀⠀⡿⠳⢤⡀⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠙⠓⠢⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⡿⠙⣦⡀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠶⠶⠶⠷⠶⠾⠷⠶⠶⠶⠶⠤⢤⣀⣀⣀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠷⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠲⠶⠶⠶⠶⠒⠒⠒⠋⠉⠉⣩⡟⣫⡭⢍⣶⡀⠈⠙⡆⠀⠀⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⣿⣴⣶⡷⠃⠀⣰⠇⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠈⠉⠛⠓⠛⠋⠁⠀⣀⣼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠶⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

👩‍🦳❄️❤️👩‍🦰

❄️🏰✨

👸❄️👩‍🦰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡞⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⡤⠀⠀⢙⣦⣀⡠⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⡖⠒⠲⢿⠃⠀⠀⣸⠋⠀⢠⠎⢀⡀⠀⠀⠀⢀⡤⡤⠤⣄⡀⠀⣠⡤⣶⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣄⡀⡀⠀⢀⠞⠀⠀⢰⠇⢀⣿⢳⠀⢀⣴⠋⢸⣷⠀⢈⡯⡏⠀⣳⣆⡈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢧⡀⠈⢀⡴⠚⢻⣄⡞⢸⢸⡴⠋⠈⠒⠒⠟⠒⠉⠀⠙⠢⢬⣋⣀⡴⡯⠗⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢧⣴⠋⠀⠀⠀⣽⠁⣈⡞⠀⠰⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⣴⣀⢙⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠻⣇⠙⠁⠀⠀⠀⠈⠉⠒⢶⠒⠛⠭⢖⡀⠀⠀⠀⠀⠑⢍⡃⢈⡇⠀⠀⣤⡀⠀⡏⠙⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠙⠲⡀⠀⠀⠀⠀⠀⠀⠀⢑⢤⣤⡤⠼⠓⠦⣄⣀⡀⠀⠉⠉⢹⣤⢞⡇⡇⣰⠃⠀⡝⠒⠉⠐⠒⠲⣄ ⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠸⡙⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⢜⡵⠁⢸⣿⡇⠀⠀⡇⠀⢀⣀⣀⣠⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⡼⠱⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⠀⣠⠏⠀⠚⡆⠠⠃⠀⠸⠲⢤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⣾⠁⠀⠈⠣⣀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢮⣤⠞⠁⠀⠀⠀⣽⠀⣀⣴⣀⡀⠀⣹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠃⠀⠀⠀⠀⠈⠑⠦⣌⡙⠓⠲⠶⠤⠤⠦⠴⠶⠖⢋⣩⡇⠀⠀⠀⠀⠀⣀⡼⠉⠉⠁⠀⠀⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⣶⣶⡒⠒⢷⠋⠁⢸⡇⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣽⣾⣿⡗⠁⠀⠀⢸⡇⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠈⠑⠢⢄⣀⠀⠀⠀⠀⣀⢾⣿⣿⣏⡿⠁⠀⠀⠀⣼⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠲⢤⣀⠀⠀⡏⠉⠙⠒⠳⢥⣄⣉⣉⡠⠤⠤⠔⠋⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⠙⠒⢧⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠛⠉⠙⠒⠒⠒⠋⠉⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠙⣄⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠈⠓⠦⠤⣄⣠⠤⠼⠤⣄⣀⣀⣀⡤⠴⠚⠁⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⣀⣠⣤⣤⠴⠖⠋⠁⠀⠀⠉⠳⢦⣤⣀⣀⠀⠀⠀⢀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠈⢣⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠃⠀ ⠀⠀⠀⢀⡴⠋⠉⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⣆⠔⢦⡠⠒⠒⠨⢆⠀ ⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⡇⠀⠀⠀⣀⡀⠀⢰⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⡀⣀⢸⠀ ⠀⢀⠼⠀⣠⣾⣿⠻⠟⡿⢥⡤⠤⢄⠀⠀⠀⢰⠎⠁⠉⠉⠀⠀⠈⡆ ⢠⠃⠃⢰⡿⠋⠃⠀⠠⠊⢸⠀⢦⣤⣱⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣇ ⣿⣦⠤⡼⠡⠊⢉⠑⠂⠀⠀⠘⡄⠙⠛⠣⠀⠉⢖⠰⠒⣦⠴⠬⢱⠃ ⣿⣿⡀⡇⢃⠀⠋⠻⣿⣦⡀⠀⠐⡀⠀⠀⢣⡀⢈⣦⢤⢤⡤⣤⠊⠀ ⠘⠀⠑⢷⠈⠀⠆⠀⠀⠁⠈⢂⠀⠈⢆⣀⣼⠴⣸⠘⣪⣟⣧⠾⠀⠀ ⠀⠀⠀⠀⠣⡀⠈⢂⠀⠀⠀⠀⢣⠎⠕⣩⣶⣿⠅⠉⣉⣋⠬⠵⠀⠀ ⠀⠀⠀⠀⠀⠙⠦⣀⡱⠤⠤⠤⠂⠈⠤⢄⢹⢛⠼⣾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣈⡷⢨⠕⠒⢌⣒⣒⢥⠊⢸⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢔⠂⠐⠒⠋⠪⡪⣂⠢⣀⠈⠉⢲⠚⠒⠚⡄⠀⢀⡀⠀⠀⠀⠀ ⠀⠐⠭⡤⠀⠀⢸⣶⣷⡿⡊⠁⠣⢤⡢⠔⠈⢹⢳⠂⠁⠈⠐⡄⠀⠀ ⠀⠀⠘⠓⠊⠈⠚⣽⠀⠁⠀⡨⠍⠤⢤⠀⠀⢸⠬⢆⠀⠀⠀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠓⢇⡋⠀⠀⠀⠸⢀⡰⠥⠤⠌⢄⣀⠜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣁⡀⠀⠀⠀⠠⡤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢄⠀⠓⠚⠀⠀⠂⢵⣥⠀⠸⢃⠹⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠇⠔⠀⠀⣀⠔⠚⠺⣿⠁⠀⣿⣀⡦⠀⡕⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⠖⠀⡴⠻⠀⠀⠀⠀⠀⠀⠀⢳⠜⢢⢴⠝⡄⠀⠀⠀⢀⠤⡆ ⠀⠀⠡⠀⣘⡀⠀⠀⠀⠀⠊⡖⠀⠀⢸⠀⡏⡄⣷⢼⡄⠀⡠⠂⣠⠃ ⠀⣀⢤⢴⣯⡌⠀⢀⢤⣄⠀⠁⠀⠀⡆⢠⠸⢁⢻⢨⢋⡖⢣⣾⢽⠀ ⡜⢀⠊⠁⠻⠄⢠⡅⢀⠏⠀⠀⠀⢰⡡⠁⢆⠆⢈⠌⠀⠀⠘⠉⡏⠀ ⢡⠸⣄⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠘⠁⠸⠂⠀⠀⠀⠀⢠⠫⢅⡇⠀ ⠈⢆⠐⠤⢀⡀⢢⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠣⢀⠀⢣⠀ ⠀⠀⣱⣄⠈⡬⠋⡹⠁⠀⠀⠀⠀⢠⣴⢀⠔⠉⠀⠀⠀⠀⠀⠱⠃⠀ ⢠⣪⡺⡛⠰⠭⠬⠆⣀⣀⣀⣀⡠⠬⡿⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠞⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢷⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⢡⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⣏⡀⠀⠀⢿⡚⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠘⣟⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡔⠛⠀⠚⢻⠻⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣭⣤⣿⣤⣤⣀⣤⣫⠊⠈⠛⢿⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠙⢿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠹⣿⣧⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠃⡈⠓⠄⠀⠀⢈⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠂ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡾⢿⣦⡆⠀⠀⠀⠀⡀⠄⡙⢿⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⠀⠀⢀⣤⣹⣿⣿⣿⠓⠼⣿⡇⠀⠀⣠⠮⠖⣲⣶⠴⠻⣿⣿⣿⣿⣿⣿⣆ ⠀⠀⠀⠐⠚⢋⣽⡿⢻⢿⠀⠀⢠⠀⠀⠀⠓⠀⠠⠟⠋⠀⣠⣿⣿⣿⣿⣿⣿⣿ ⣤⣤⣶⡶⠿⢛⣉⠀⡟⢸⡄⠀⢠⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣬⣝⣛⣛⣋⣥⣾⡿⣘⣳⡄⢰⣤⣤⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡟⡿⠡⢀⠇⢸⣿⣿⣿⣿⣿⠏⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠟⣻⠁⡇⠀⢸⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠏⢀⣿⠀⡇⡇⠀⠀⢹⣿⣿⠟⡏⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣼⣿⡀⠀⠀⠀⠀⠀⢉⠌⠀⠇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣿⣿⣷⣦⣀⡀⠀⠠⡁⠀⠀⠢⠤⡤⠤⠤⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⡇⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⢣⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠆⠁⠂⠀⠐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢃⠀⠀⡌⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡸⠀⢰⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⢄⠀⠉⠛⢟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠁⠀⠑⣤⡠⠀⠆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⢸⣦⠐⣀⣮⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢳⡤⠀⢠⠞⠁⠀⢰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠁⢲⣭⡎⠀⠀⣠⣾⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠰⠣⠼⢣⡠⡠⢣⠛⡄⢘⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢁⠧⢾⣄⠈⠾⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⠓⠨⢍⣉⡉⠉⠉⡄⠀⠀⠸⡀⣘⡡⣱⣤⣤⣤⣦⠈⢻⣿⣿⣿ ⣿⣿⣿⣿⠏⡄⠀⠀⠀⠀⠉⠉⢉⠝⢙⠀⠀⠙⢯⠉⠒⠀⣀⡠⠔⢻⣾⣿⣿⣿ ⣿⣿⣿⡏⠆⡇⠀⠀⠀⠀⠀⠔⠁⠠⠁⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⡌⡇⢸⣿⣿ ⣿⣿⡟⢸⠀⠇⠀⠀⠀⢀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠁⠇⠀⢻⣿ ⣿⣿⣇⡘⠀⢰⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠸⠀⠀⠀⠈⢿ ⣿⣿⣿⣧⣀⠀⠆⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡄⡀⠀⠀⠀⣼

⠀⠀⠀⠀⠀⡖⠲⡴⣝⣿⣿⣟⢻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⣇⠀⣃⣘⡿⠁⠸⢎⠉⣿⣙⣃⣽⡭⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣪⡙⠹⣦⡓⠂⣀⠀⠀⡀⠛⠉⠉⡔⠁⠀⣿⣿⢿⣿⣿⣿⣿ ⠀⠀⡼⠗⠉⠐⡒⠨⠟⡭⢣⢮⡤⠦⠤⠦⠤⣄⣼⠉⠉⢺⢿⡛⢿⣿ ⢠⠾⠮⢤⡴⡋⠢⡀⠗⠑⠌⠑⠀⠑⠢⢀⡀⠨⣳⠂⠀⠀⠀⠘⢻⢖ ⠘⡆⠀⠀⠙⡤⠂⢸⡈⠂⠀⠀⢀⠟⢉⠀⢬⠁⣿⠇⠀⠀⠀⣠⣿⣷ ⠀⠱⡀⡤⠊⠀⠀⡼⡢⠤⠤⢄⡏⠀⠀⠒⠋⢠⠃⠂⠀⠀⠀⠀⢃⣿ ⠀⠀⡏⠀⠀⠀⢠⠁⠉⠒⠊⡹⠀⠀⠀⣦⠔⠋⠀⠀⠀⠀⠀⠀⠈⣏ ⠀⠀⢣⠀⠀⡠⠂⠀⠀⠀⠀⡅⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠉⢹⠀⠀⠀⠀⠀⠀⠀⠂⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡃ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢘⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃ ⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢨⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⡴⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡸⠀⠐⡀⠀⠀⠀⢀⠜⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢐ ⠀⠀⠀⡇⠀⠀⠐⠄⠀⠠⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠤⢤⠤⠐⠠⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⢙⡄⠠⢃⠖⠂⠀⠀⠱⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠐⡏⠑⠠⠱⠵⠅⠊⠙⢄⠀⠀⠳⡀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⢣⡀⡧⠤⠀⠀⠀⠠⢖⠢⠄⣗⠤⡄⠃ ⠀⠀⠀⠀⠀⣠⡞⢹⠇⣿⣿⠀⠀⠀⠑⣷⣷⣦⡀⠀⠰⣿⣿⠀⡏⠢⠘⡇ ⠀⠀⠀⠀⠀⠇⡀⢀⡀⣼⠛⠀⠀⠀⡌⡘⠙⠋⠃⠀⠁⠛⠉⠀⢸⡄⠀⡀ ⠀⣀⢰⣦⠀⠀⠠⡀⠿⢻⠃⠀⠀⠀⠈⢣⠀⢐⣀⣀⣀⠀⠀⣰⠚⢁⠜⠁ ⠀⢻⣿⡙⠣⣠⡳⣿⡟⠁⠀⠀⠀⠀⠀⠀⠑⢄⠻⠬⠉⢀⢼⣷⠊⠡⠀⠑ ⠀⠀⠙⠦⣄⡀⠁⠪⠙⠠⠀⠀⠀⠀⠀⠠⣐⡾⠑⠒⠊⡁⢼⠻⣎⣢⣠⠊ ⠀⠀⠀⠀⠈⠑⠍⢢⠀⢸⠀⠀⠀⣰⡡⢊⡈⢤⠶⠛⠒⠒⢴⡃⢉⠿⣵⡀ ⠀⠀⠀⠀⠀⢠⠂⢸⠀⢸⣀⣴⣼⣯⣂⡡⠊⠀⠀⠀⠀⠀⠈⡗⡄⠠⠹⡇ ⠀⠀⢀⡠⡔⠣⣀⡦⠀⡨⡤⠃⢒⡖⠈⠀⠀⠀⠀⠀⠀⠀⢠⠁⡹⠄⡦⠁ ⠀⡠⠃⠀⠈⢲⠎⠑⠒⠒⠋⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣠⡽⠔⠁⠀ ⢰⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⣔⡡⠣⢮⡄⠀⠀⠀⠀ ⠈⢆⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠔⡡⠊⠈⠐⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠒⠒⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⡀⠀⢀⡀⠤⠂⠁⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⠄⣒⣒⣲⣤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠀⠡⠊⠀⠀⠈⠃⢽⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠳⡊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠔⠈⠁⠀⠈⢶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⡠⡴⠃⠀⠀⠀⠄⢂⣺⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣪⠥⠊⠁⢠⡇⡀⠔⠀⡠⠖⠉⣇⠑⢄⠀⠀ ⠀⠀⠀⠀⡠⡿⠁⠀⠀⣴⠓⠛⢾⠀⡜⠒⠀⠢⠿⡀⠈⡗⡄ ⠀⠀⠀⢸⢰⠀⠄⢀⣾⣻⣿⣶⠀⣿⢀⣶⣿⣿⠀⠐⡀⢇⢱ ⠀⠀⠀⠈⢣⢸⢠⣿⣿⡜⠛⠛⠀⠹⠘⠻⠛⢹⡀⠀⠰⣰⠎ ⠀⠀⠀⢀⢜⡇⠟⢻⡏⡇⠀⠀⠐⠤⠀⠀⠀⣼⣇⠀⢂⢻⠀ ⠀⠀⢠⠂⡌⡇⠠⡈⢃⢴⡄⠰⡾⠿⡶⠀⣴⠿⣼⣆⠀⢫⡄ ⠀⠠⠹⠀⠁⡧⠀⢳⡄⢺⠏⠢⡙⠛⡡⡾⠁⠀⠠⢑⡇⠀⢣ ⢠⠇⡇⠠⢆⠁⠑⢼⣧⠐⠳⡀⠈⠉⡞⣤⣒⢒⠒⢄⠇⠀⢸ ⠘⡀⠇⠠⡱⠑⠒⠚⠏⢦⠀⡜⣄⡀⢳⠁⠀⠀⠈⣗⠚⢁⠾ ⠀⠡⡈⠰⠁⠀⠀⠀⢀⠈⠶⡸⡀⠀⠀⠇⠀⠀⠀⡤⢄⡾⠁ ⠀⠀⠐⠇⠀⠀⠀⠀⡘⠀⣇⢸⠇⠤⠠⢠⡼⢄⠀⡧⠘⠁⠀ ⠀⠀⡜⠀⠀⢀⡮⠕⢁⠎⠈⢘⡀⠀⠀⠀⠉⢹⠀⠃⠀⠀⠀ ⠀⡘⠀⡠⠔⠉⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡀⢄⡂⠀ ⢰⠁⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠘⡱⠗⡇⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡰⣮⠞⡩⢍⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠫⠖⠀⠀

❄️🏰👸🏼👩🏻‍🦰

👑❄️🏰✨

❄️👸⛄️

❄️💙👑

❄️✨ᥫ᭡🧊

👸🏼❄️✨💙

❄️👸🏻⌨️🤡

👑❄️✨

🦎🔥❄️

❄️👑⛄️

❄️👸🎤🎶

❄️👸⛄🎶🎤

❄️👸👑

👓🛸🦖🦕➡️🧒👧

🐸🏹🌸❄️

❄️☃️👑🎶

❄️👸🏼☃️

💎🏞️❄️🌊✨🗣️

❄️👑🦌⛄

❄️❤️👭

🏜️🙏💧

⛄👑❄️👸🧡

👸❄️⛄️

👑❄️🏰✨👸🏼

👭🍁🌲🔍

❄️🗣️🎶➡️❓

❄️🐴🌊

❄️🍁🌬️🔥💧