Christmas Tree Dot Art

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⢿⣷⣶⣭⣻⡿⣿⣿⣿⣿⣶⣿⣋⡛⠶⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠒⠛⠋⠀⠀⠉⠉⠋⠉⠙⠛⠳⣾⣿⡿⠿⠿⣿⣿⣷⣬⢻⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⣯⣻⣿⣿⣷⡝⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⡘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⢿⣧⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡃⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⡇⢻⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠿⠐⠚⠋⠉⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⣧⢘⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡾⢏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠲⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣴⠞⠃⠈⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⣀⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⢀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⢈⣼⣿⣿⣿⣿⣃⣀⠀⠀⠀⠀ ⢀⣴⡟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⠿⠶⢿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⣴⠛⠀⠀⠀⠀⠀⠀⠀⠙⢳⡄⠀ ⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠉⠀⠀⠀⢠⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄ ⢿⣤⡀⠀⠀⢀⣠⣴⡶⠖⠛⠛⠲⠶⢦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢫⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡇ ⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠳⠦⣤⣤⣄⣀⡀⢀⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠄⠀⢠⡄⠀⢀⡤⠔⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⡀⠀⠀⣀⣠⣤⠶⠶⠿⠿⠷⢤⣤⣀⣀⣸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠶⣶⣶⠋⠳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⡰⠻⡅⠙⠲⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠖⠚⠉⠉⠛⠲⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⢀⣠⣤⡤⢤⣤⣤⣀⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠻⣍⠳⠖⣃⣘⠓⠖⣩⡟⢦⠀⠀⠀⠀⠀ ⠀⠀⢰⡇⠀⢨⠿⠺⣇⣸⠗⠿⡅⠀⠘⡇⠀⠀⠀⠀ ⠀⠀⠈⣧⠀⠛⠶⠚⠧⠼⠓⠶⠛⠀⣸⠧⣄⠀⠀⠀ ⠀⠀⣰⠋⠹⡄⠀⠀⠀⠀⠀⠀⢠⠯⣥⣶⡮⡷⣄⠀ ⠀⣸⢡⠞⠀⠙⠲⠤⣤⣤⠤⠖⠋⠀⣏⣀⣗⡷⠸⡆ ⣰⢓⡟⠒⠶⠤⠤⢴⣻⣟⣶⠤⠤⢶⡏⠉⢻⠀⠀⢷ ⢹⢻⣓⠲⠤⠤⠤⣼⡻⣟⣿⠤⠤⠬⠟⣛⡏⠀⠀⡾ ⠈⢻⣌⠉⠓⠒⠶⠤⠭⠭⠥⠶⠒⠚⠉⣁⡟⠀⡴⠃ ⠀⠀⠈⠻⣟⠒⠒⠦⣤⣤⠶⠖⠒⣻⣿⠥⠖⠋⠀⠀ ⠀⠀⠀⠀⢨⣏⣉⣉⡇⢸⣉⣉⣹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⣀⣀⣀⡇⢸⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⣴⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⢦⡀⠀⠀⣀⡘⣧⠙⠚⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢧⣀⣴⠃⠀⠘⢯⣭⠉⣤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⢲⣸⠄⢧⡼⣫⠇⢀⡼⠉⢉⣛⣒⣶⣫⠾⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣄⣀⣀⣠⢮⣙⣒⣾⠴⠊⠉⠉⣈⠉⣷⢞⡽⠋⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⢀⣠⣤⣤⣧⣀⡴⠚⠉⠉⠉⠃⣾⡤⠞⠁⠀⠀⢰⣲⣶⣵⣄⠀ ⠀⠀⠀⠀⠀⠈⠻⣍⣙⣒⣮⡍⠀⠀⡀⢀⣀⠀⠈⢧⡀⠀⠀⠀⣞⣿⡏⡿⡷⠁ ⢠⡤⣴⣶⠀⠀⠀⠀⠈⠉⢹⠀⠀⠘⠿⠘⠋⠀⠀⠀⢳⡀⠀⠀⠀⠹⠝⠊⠊⠀ ⢰⡕⡊⣻⣿⠃⠀⠀⠀⠀⢸⠀⢀⡤⠖⡺⢯⠉⠉⠓⢆⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⠷⠛⠛⠀⠀⠀⠀⠀⢸⢰⠏⠀⠀⠓⠋⠀⡀⠀⡼⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣯⣧⣄⣈⣒⣒⣩⠴⢚⣵⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣏⣳⠻⠿⡷⠲⠛⣋⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣰⠃⠉⠉⢙⡿⡟⠋⣭⠍⢇⢳⡀⢀⣀⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠀⢻⠉⡏⠀⠀⠀⣏⡼⢉⣠⡗⠒⢹⠈⡏⢉⡏⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡀⣾⠀⡇⠀⠀⠀⣏⠓⠦⢞⣯⣩⠜⠀⡇⠸⡇⢰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠧⠖⢳⡖⠋⠉⢹⡶⠶⣾⠉⠉⠓⢶⠓⠦⠗⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠛⠁⠀⠘⠓⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠊⠉⠉⠉⠉⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠢⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⣁⠤⠒⠊⠉⠉⠉⠉⠉⠑⠒⠦⢄⡈⢇⠘⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡆⠈⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⢸⡆⠀⠀⠀ ⠀⠀⠀⢠⡇⠀⠀⣠⣴⣚⣯⣉⡉⠉⠉⠉⠙⠒⠦⢄⠀⠀⠀⢹⡀⣧⠀⠀⠀ ⠀⠀⠀⣸⠀⢀⠞⢿⣋⡤⠤⣄⣹⠄⠀⣞⣉⣉⠁⠢⣽⣦⠀⠈⡇⢹⠀⠀⠀ ⠀⠀⠀⢿⣀⣾⠀⠈⠀⣿⡷⠀⣀⠤⢤⡈⠉⣿⡍⠙⠛⠸⡆⢀⣧⣼⠀⠀⠀ ⠀⠀⢀⡞⠁⠘⣧⣀⣀⡨⠷⠺⢤⣀⣀⡸⠦⣉⠁⠀⠀⣰⠿⣾⠋⠉⠑⣆⠀ ⠀⠀⡞⠀⠀⠀⠱⣄⠀⠀⠀⠀⢀⣴⡀⠀⠀⠈⠉⠒⣻⠃⠀⠘⣧⡀⢀⡼⠀ ⠀⡸⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⠚⠛⠒⠤⠤⠤⠚⠁⠀⠀⠀⢸⡟⠛⠁⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀ ⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠈⠀⠀⠀ ⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⣀⣠⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⣀⡀⠀⠀⠀⠀ ⠓⡛⠒⠛⠙⡻⠋⠓⠟⡛⠟⠃⠒⢻⣻⠃⠀⠀⠊⠻⠛⢻⠛⠛⠛⠛⠘⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣶⣤⣀⣀⣀⣠⣤⣤⡶⠶⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠶⠿⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣧⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⡿⠀⣴⢫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠴⠲⠶⠖⠒⠒⠒⠒⠦⣤⣀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⡿⠁⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⡽⠗⠒⠓⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣦⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⢁⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣫⠞⠁⠀⠀⠀⠀⠀⠈⢷⢰⡄⠀⠀⠀⠀⢠⣾⠛⠉⠛⢦⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⠁⢸⡇⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⢠⠋⠀⠀⢀⣤⣶⣦⣤⣤⣿⡼⠃⠀⠀⠀⢀⣼⢿⣤⣀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣷⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⠀⠀⡟⠀⣠⠾⠛⣹⣆⣀⣀⠀⠉⠀⠀⠀⠀⠀⣿⣷⣤⣀⠈⢻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢹⣿⢠⠏⠀⠀⠀⢀⣤⠶⢤⣤⠟⠁⡇⠀⠀⠇⠚⠁⢠⣶⠿⠛⠛⠭⡇⠀⠀⠀⠀⢀⣀⣽⣿⣿⡊⠝⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⡀⠈⠉⠲⢿⡀⠀⣿⡏⠀⠀⠀⠀⣼⡇⠀⢸⡿⡀⠀⢿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⠁⠀⠀⠀⠙⢷⡀⠀⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣫⠅⠀⠀⠀⠀⠘⠛⠓⠾⣇⠀⠀⠀⠀⣿⡆⠀⢸⢇⢷⠀⠈⢧⣤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⢀⣀⣼⡇⠀⢸⡄⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢘⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⢿⡇⠀⠘⣾⠈⠀⣠⠏⢀⡴⠊⠉⠀⠀⠀⠀⠀⣀⡞⠻⣦⣤⠶⠚⠳⠿⠿⠿⠿⠿⢄⣀⠿⠃⣀⡴⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡹⢧⣀⠀⢘⣷⡀⠀⠸⡄⠀⡏⠀⢺⠀⠐⠦⠶⠶⠶⠶⣾⣯⠖⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠈⠉⠉⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡇⢠⣭⣿⣿⠏⠛⢦⣀⠘⡆⢿⠀⠈⠻⢦⣤⣤⣤⠶⠚⠉⠀⠀⣀⣤⡤⣤⣠⡤⠚⠓⣤⣄⣀⣀⣀⣠⣤⣶⠟⠁⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣤⣀⠀⠀⠀⣰⠇⠀⢠⣯⣿⢧⡿⠻⡿⠃⠀⠀⠀⠀⢹⡇⠀⠷⣄⠀⠀⠀⠀⠀⠀⣀⡤⠴⠻⣧⡀⠉⠉⠉⠉⠉⢱⠟⠀⠈⠉⠉⠉⠀⠶⠤⠤⠴⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠛⠳⣚⣡⣤⣶⡿⠿⠋⣼⠁⢸⠁⠀⠠⢤⡀⢠⣿⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠙⢢⣄⣀⣀⡠⠎⡄⠀⠀⠀⠀⠀⠀⠐⠴⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠸⣦⠘⠦⠀⠀⠀⣷⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⠀⠀⠀⢀⣴⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠁⡀⠀⠀⠀⠀⠀⠈⠳⠦⠤⠤⠾⠃⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠓⠦⠈⠙⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡏⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀ ⠀⠀⠀⠀⠀⢿⠀⡇⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀ ⠀⠀⠀⠀⠀⢸⠀⣇⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇ ⠀⠀⠀⠀⠀⠈⠀⠘⢿⣆⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠳⣄⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣝⠷⣦⡓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈⠛⠿⠷⢦⣄⣀⠀⠀⠀⠀⠀⣶⠋⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⠶⠶⠿⣦⣀⣀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⣰⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣼⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⣀⣴⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⢀⣀⣴⡾⠋⣀⡴⠋⢦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣯⠴⠾⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢛⠛⠿⡥⠶⠛⠉⠀⠀⠀⢙⠻⢿⣶⣶⣶⣾⠿⠛⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢿⣦⣼⣿⣿⣿⣿⣿⣿⣟⡲⢶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚⠋⠁⠀⠈⠉⠀⠉⠛⠻⢿⣿⣟⣿⣿⣷⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣟⢻⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣎⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢀⣀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠘⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠢⠤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⢹⣷⣿⣿⠇⠀⠀⠀ ⠀⠀⣠⡿⠏⠁⠀⠀⠀⠀⠀⣾⣿⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⢠⠿⠿⠿⠿⠄⣀⠀⠀ ⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⠦⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠓⣲⠋⠀⠀⠀⠀⠀⠀⠹⡄ ⢿⣇⠀⠀⠀⢀⣀⣠⡴⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠰⣏⠀⠀⠀⠀⠀⠀⠀⢠⣾ ⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⠶⠤⣤⣀⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⢀⡀⠀⠀⠴⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢻⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠤⠤⠶⠒⠋⠉⠉⠉⠙⠓⠲⠾⡏⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⡾⠛⠻⢶⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠉⠉⠁⣠⣴⠿⢿⡇⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⢠⡾⢿⣄⠀⠈⠻⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣠⣤⣴⠶⠶⢶⣮⣤⣀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣧⣴⣾⠛⠛⢻⡿⠉⣿⡟⠛⠻⣷⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣶⠻⣿⡀⠙⢻⡟⠛⢁⣀⡈⠛⢻⠟⠉⢨⡿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠁⠀⠈⠻⣶⣤⣤⣴⠟⠛⢿⣦⣤⣤⡾⠟⠁⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⣠⡾⠋⠉⢻⣦⣤⣼⠏⠉⠛⢷⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡀⠀⠀⢿⣤⣤⣴⣿⣏⣉⣹⡷⣦⣤⣼⡟⠀⠀⢰⣿⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣷⣤⡀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⣀⣴⠟⠉⠙⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠁⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣥⣤⣴⣶⠶⣮⡿⣧⠀⠀⠀ ⠀⠀⠀⣼⠏⢠⣶⠀⠘⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⢸⡟⠋⠙⣷⡈⣷⠙⣷⡀⠀ ⠀⠀⢸⡏⢠⡿⠁⠀⠀⠀⠈⠛⠻⠶⢶⣶⡶⠶⠟⠋⠁⠀⠀⠸⣧⣀⣠⣾⣡⡿⠀⠸⣧⠀ ⠀⣠⣿⣦⣿⠷⢦⣤⣄⣀⣀⣀⣠⡶⢶⣶⠶⣶⣄⣀⣀⣀⣤⣴⠟⠋⠙⢿⣏⠀⠀⠀⢻⡆ ⢸⣿⣀⣾⣇⠀⠀⠀⠈⠉⠉⠉⢹⡇⣿⢻⣷⣿⡏⠉⠉⠉⠉⣿⣤⣤⣤⣬⡿⠀⠀⠀⢸⡇ ⠀⣿⢻⣿⡛⠻⠶⢦⣤⣤⣤⣀⣼⡇⠿⢾⡟⣿⣧⣠⣤⣤⣤⠶⠾⠛⢛⣿⠀⠀⠀⠀⣼⡇ ⠀⠻⣾⡏⠛⠷⣶⣤⣄⣀⣀⡀⠈⠻⠶⠾⠿⠛⠁⢀⣀⣀⣠⣤⡶⠞⠛⢻⡆⠀⠀⢠⡿⠀ ⠀⠀⠘⢷⣤⣀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⢀⣀⣴⡿⠁⢀⣰⡟⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⡿⠶⢶⣤⣤⣤⣀⣀⣀⣠⣠⣤⣤⣴⠶⠶⣿⡿⢋⣁⣠⡶⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣀⣠⣩⡿⠻⣿⣍⣁⣀⣀⣠⡾⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⠀⢀⣀⣹⡗⠀⣿⣁⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠛⠉⠉⠉⠉⢹⡇⠀⣿⠉⠉⠉⠉⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣼⡇⠀⢿⣤⣤⣤⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

🎄🎅🏻🦌☃️❄️

❄🌨️🎅🏼🦌🎁🎀☃️☃⛄⛸️🎄✨🎋🍪🥛

* * * * * 🦌🛷* * * * * * 🌲 🏠🌲 🌲 🌲 🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠛⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀ ⠀⢀⡏⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠖⠋⠉⠉⠙⠓⠒⠒⠒⠦⠤⠬⠷⣄⣀⠀ ⠀⢸⠁⢂⠀⠀⡰⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻ ⠀⣿⠀⢈⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⣿⢠⠋⠀⠀⠀⠀⢀⣠⠤⠴⠟⢲⠟⠉⠉⠓⠛⢏⡟⠋⠉⠉⠓⠲⡖⠒⢲⡞ ⠀⢿⠸⡀⠀⢀⣠⡞⠉⠉⡆⠀⠀⡇⠀⠀⢰⣾⡖⠈⡇⣶⣷⡆⠀⠀⣽⠀⠀⡇ ⠀⢸⠀⠉⠻⡏⠠⠐⠄⢰⠀⠀⠀⡵⢶⢤⣌⠚⢊⡼⣅⠑⠚⢁⣀⠴⣇⠀⢰⠋ ⠀⢸⠀⠀⠀⣇⠡⣀⠇⠀⡆⠀⠀⠑⢲⢆⠙⠚⠉⠀⠈⠉⢉⡀⠠⠴⠋⠀⣏⠀ ⢠⡞⠓⠒⠳⣿⡆⠀⠀⣀⢠⠀⠀⠀⢸⠀⠉⠐⡶⠲⡖⡖⢲⡟⠂⢀⣀⠀⡟⠀ ⣾⠀⠀⠀⠀⢸⠹⡄⠸⡀⠈⡇⠀⠀⢸⠀⠀⠀⠉⠈⠀⡗⠈⠀⠀⠁⠀⢹⡇⠀ ⠙⢦⣤⣀⣠⠞⠀⡻⢄⠈⠈⡇⡔⠢⡘⢍⡉⠋⠉⠢⣄⠇⠀⠀⠀⠑⠠⢂⡇⠀ ⠀⠀⠀⠈⠁⠀⢰⠃⠈⣇⠀⢃⠣⠠⠃⠐⠬⠭⠝⠫⠥⣜⣀⣀⡩⠜⢀⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢳⢶⣿⣽⣿⣭⣿⣿⣿⣿⣷⣶⠾⢿⠭⠼⠬⠽⠿⢻⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀⠀⢹⠉⠉⠉⠉⠀⠀⢸⡅⢼⠁⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠊⢟⠲⡼⣤⠤⢤⡤⠤⠤⠤⠿⠿⠴⠶⡶⠶⣶⡾⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣷⠀⡦⠃⠑⢢⠤⠚⠁⠀⠀⠀⠀⢹⠒⠚⠁⠰⣷⡌⡦⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣤⠀⠀⠀⠈⠙⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡇⠀⠀⠀⠀⠀⠀⣸⣻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠒⠤⡀⠀⠀⢰⣁⠀⠉⠉⢲⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢤⣤⡤⠇⠀⠀⠀⠉⠈⠙⠛⠋⠀⠀⠀⠀⠀

⢰⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀ ⢸⣆⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠹⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⡼⠃⠀⠀⠀⠀⠀⠀ ⣠⣤⣿⠀⢹⡆⠀⢠⣤⣄⠀⠀⠀⠀⣀⣀⠀⠀⢰⡏⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⢿⡀⠀⢀⣀⣙⠛⠋⠀⠹⣄⠀⠀⣼⠋⠹⣧⡴⠟⠀⠘⠓⢲⡄⠀⠀⠀⠀⠀⠀ ⠈⠙⠛⠋⣉⣩⣿⣶⡴⠞⠛⠛⠿⣧⡀⣠⡴⠖⠒⢶⣤⣠⡾⠃⠀⠀⠀⠀⠀⠀ ⣠⠴⠚⠋⠁⠀⣼⠋⠀⠀⠀⠀⠀⠀⠹⡟⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⢄⡀⠀⠀⢸⡇⢀⣔⡆⠀⠀⢀⣀⠀⢹⠀⠀⠙⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠙⠒⣿⠀⠘⠟⠁⠀⠀⢸⡾⠀⡼⠀⠀⠀⣀⡸⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣄⠀⠀⢠⠚⠑⡦⠀⢸⡟⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡏⠻⠶⣄⣉⣋⣥⢶⣋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠲⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠛⠻⢯⡄⠀⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⣦⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠏⠀⠈⣻⣿⠀⠀⢸⣀⣀⣀⣀⣠⣷⡀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠙⡿⠀⠀⣾⠉⠉⠉⢻⡍⠀⢿⢦⡀⠀⠀⠳⢤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⢰⡇⠀⠀⡇⠀⠀⠀⠀⣷⠀⠈⢢⠙⠳⣄⠀⠈⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠘⣧⠀⢸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣾⠀⠀⠀⠀⢀⡇⠀⠀⡟⠀⠀⠀⣿⠀⠈⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣰⠇⠀⠀⠀⢀⡾⠀⠀⣼⠃⠀⠀⢀⡟⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠀⠀⠀⠀⠈⠛⠛⠛⠡⠬⠥⠽⠾⣥⣀⣀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣶⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠊⠁⠉⠉⠛⠻⢿⣻⣶⣿⣿⣶⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡾⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⣠⠾⠠⠐⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢿⢹⣿⠃⠀ ⠀⠀⢀⡤⠊⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⣹⣿⡿⠀⠀ ⠀⡴⠋⠀⠀⠀⠀⠛⠐⠢⠦⠄⠀⠀⡀⠀⠀⠈⠣⡴⠋⠉⠁⠐⢄ ⠘⠧⠀⠠⠄⠒⠒⠢⠤⢀⣀⡀⠀⠈⢫⠀⠀⠀⠐⢇⠀⠀⠀⢀⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡁⠀⠀⣀⣠⣄⡀⠹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⢷⣦⠸⣿⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠹⠿⠟⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣿⠆⠀⠀⠀⣴⡿⠿⠶⠾⠃⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠈⠿⣦⣤⣴⣟⠀⠀⠀⠀⠙⠷⢶⣶⠃⢰⣶⡶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣶⣄⢸⣇⠈⣿⢀⣴⡿⢻⣧⠀⠀⢀⣿⠋⠙⠛⠷⠶⢶⣤⣄⣼⠏⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⣿⠀⠻⠿⠟⠀⠙⠛⠋⣤⣾⠃⠀⣠⡿⠃⢀⣠⣤⣤⣶⢶⣮⣿⣿⡾⠋⣀⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⣀⣴⣤⣈⡛⠛⣿⣿⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⢹⣷⡾⢋⣽⠟⠁⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠈⠙⠛⠛⢻⡿⠁⠀⠀⣠⣤⡶⠾⠿⠿⠶⣾⡟⢠⡿⠁⣀⣾⠏⠀⠀⠀⠀⠀⢀⡀⣀⣠⠶⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠶⠶⣾⣿⣄⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠁⢿⣷⠾⠛⠁⠀⠀⠀⠀⠀⠐⣯⣽⢷⣽⣿⣟⣦⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⡛⠛⠷⢶⣤⣌⣙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠙⢿⣽⣷⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣦⣤⣤⣿⡟⠀⠀⠀⠀⣤⢦⢀⣿⣷⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠛⠻⣿⣟⣸⠯⣽⢿⡀ ⠀⣠⠤⣴⠶⣯⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢿⡿⠀⠛⠟⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠹⠥⠟⠛⠉⠋⠀ ⠀⣹⢒⣉⣿⣯⣿⣾⣲⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⡶⠶⠶⣶⣤⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣛⡇⣩⠄⣐⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣴⡾⠛⢋⡽⠶⢶⡆⠀⠀⠀⠈⠻⣦⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠳⡿⢶⣽⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢰⡟⠁⠀⠀⠈⠳⠶⠛⠁⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⡇⠀⠀⠀⣀⠀⠀⠀⢀⣠⠎⠀⢀⣼⢟⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣜⢿⣤⣀⠀⠈⠙⠛⠛⣋⣁⣤⡾⠛⣡⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠻⣷⣯⣝⣻⣿⡟⡛⣛⣋⣉⣥⣴⡾⠋⢹⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣀⣽⠉⢹⡟⠛⡟⠉⢹⡁⢀⣿⣤⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠉⠙⠛⠛⠿⣿⣶⣿⣿⣟⣛⣋⣉⣿⡄⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠿⢶⣦⣤⣤⣾⠃⠀⠀⠀⠀⢀⣾⠋⣹⣇⡀⢀⣿⠋⠀⢈⣷⠈⣿⣦⣤⣴⣶⡾⢷⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣷⠀⢸⡟⠀⠀⠀⠀⠀⢸⡇⣴⣏⡀⠉⢹⣿⠓⠉⠁⢹⡄⢸⡇⠀⢰⡟⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡿⣧⡀⠈⢉⣿⣿⠤⠴⠒⣻⠇⠈⡇⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢸⡏⠀⢸⡇⠀⠀⠀⠀⣀⣸⣇⠈⠉⠛⠛⢹⣿⣦⣴⠞⠋⠀⢰⡇⠀⢸⣇⠀⣸⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⣿⣅⣤⡾⣿⣤⡶⠟⠛⠛⠛⢿⣦⣤⣤⣤⣾⠛⠛⠛⠻⢷⣤⣾⠷⣤⣄⣿⡶⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⣿⡀⠀⠀⠀⢀⣼⡏⠀⠀⠸⣷⡀⠀⠀⠀⢀⣹⡏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠾⠛⠋⠀⠀⠀⠀⠈⠛⠷⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢀⡠⠤⡀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠤⡀⠀⠰⠀⠈⡄⠀⠀⠀⠈⠃⠤⢌⠊⣄⣊⠀⢠⠔⠉⡇⠀⠀⠀⠀⠀ ⠀⢸⠀⠘⢄⠀⠣⠀⢠⢠⠋⠒⡀⠠⡒⠒⠀⡠⠘⠀⠇⠀⢀⠇⠀⠀⠀⠀⠀ ⠀⠀⢣⠀⠈⠢⢀⣱⠘⡀⡃⠀⢡⠀⠉⠒⠀⣨⠖⠊⠀⠒⠮⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⢄⠀⠀⠀⠀⠈⠀⠀⠀⠑⠒⠒⡺⠁⠀⠀⠀⠀⠀⠑⣄⠀⢀⡀⠀ ⠀⠀⠀⠀⠀⠈⠒⠠⠤⠀⠀⠠⠄⠂⡡⠒⠉⠉⠀⠀⠰⢿⣢⠀⠀⢸⠁⠀⡃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠁⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣽⡦⣀⣀⡠⠄⣳⠤⠤⠜⠀⠀ ⠀⠀⠀⢠⠋⢘⠀⠀⠀⠀⠀⠀⠀⢠⡠⠎⠀⢠⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠰⠇⢠⣾⠇⡏⠀⠀⠀⠀⢠⡒⠠⣆⠀⠀⠀ ⠀⠀⠀⠸⡀⠀⠈⠒⠤⢀⣀⣀⡀⠸⡄⠀⣠⡑⠲⣀⣀⣄⠟⠀⡀⢸⡀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣌⠀⠀⠀⣤⡄⠀⠘⠚⣸⠁⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠦⠤⣀⡠⢤⢄⠂⠙⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⢎⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠁⠀⠙⢆⠀⠀⠀⠀ ⠀⡔⠁⠀⠀⠀⢀⡞⠀⠀⢹⠉⠁⠐⠒⡆⠀⠀⢫⠀⠈⢆⠀⠀⠈⢣⠀⠀⠀ ⢸⠀⠀⠀⢀⠔⠁⢡⠀⠀⠈⡄⠀⠀⠀⢇⠀⠀⠀⢣⠀⠈⠆⠀⠀⢈⡄⠀⠀ ⢸⠀⠀⠀⣇⠀⠀⠀⢆⠀⠀⣸⠀⠀⠀⠘⡀⠀⠀⠀⠑⢄⠸⠤⠔⠊⠀⠀⠀ ⠀⡄⠀⠀⢈⠆⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠻⣿⣿⠇ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⢀⣴⣾⣿⠿⠀⠀⣹⣿⣷⡄⠀⠀⢠⣾⣿⣏⠀⠀⠿⣿⣷⣦⡀⠀⠀ ⠀⣰⣿⡟⠋⠀⠀⠀⠀⠻⠿⠛⠃⣀⣀⠘⠛⠿⠟⠀⠀⠀⠀⠙⢻⣿⣆⠀ ⢠⣿⡟⠀⠀⠀⣾⣶⡀⠀⠀⠀⠺⢿⡿⠗⠀⠀⠀⢀⣶⣶⠀⠀⠀⢻⣿⡄ ⢸⣿⣷⣶⡆⠀⠘⢿⣿⣶⣤⣄⡀⠀⠀⢀⣠⣤⣶⣿⡿⠃⠀⢰⣶⣾⣿⡇ ⠈⠉⠙⣿⣧⣀⣤⡀⠈⠙⠛⠿⣿⣷⣾⣿⠿⠛⠋⠁⢀⣤⣀⣼⣿⠋⠉⠁ ⠀⠀⠀⠙⢿⠿⠿⣿⣶⣤⣀⠀⠀⠙⠋⠀⠀⣀⣤⣶⣿⠿⠿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠑⢦⠀⠀⠀⠀⠀⠀⠀⠠⡾⠉⠀⠉⠲⡀⢠⠖⠉⢙⡦⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣀⠀⠀⠀⠀⡇⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣤⡀⠈⠁⡴⠒⠉⠀⠀⠀⣰⠞⠉⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡾⠁⠈⠳⡀⠀⠀⠸⡄⠀⠀⢸⠀⠀⣠⠤⣄⠀⠀⠀⠀⣀⣀⠈⡇⠀⠙⠋⢹⡇⠀⣼⠃⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢷⠀⠀⠀⠹⡄⠀⠀⠙⣆⠀⠈⡇⠀⡇⠀⠀⠱⡀⠀⠸⡁⠈⠉⠁⠀⢰⠊⠁⠀⢠⠇⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⠀⠀⠀⠈⠢⡀⠀⠈⢆⠀⢇⠀⠹⡄⠀⠀⢧⠀⠀⠈⠳⠤⣀⣀⣈⣙⡶⠶⠚⠓⠲⠦⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⡄⠀⠀⠀⠈⠓⠒⠛⠀⠈⠦⡴⠃⠀⠀⠘⢆⡀⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⣋⡿⠷⠚⠃⠀⠀⠀⠀⣠⣤⢤⡀⠀⠀⠉⠛⢻⠟⠉⠉⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠶⠒⠒⠉⠁⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠮⠽⠀⠀⠀⠀⠸⡀⠀⠀⢠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠓⣺⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠤⣄⣀⣀⡤⠴⣞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢀⣄⣿⠲⣄⣀⢀⣀⣠⠴⠖⢚⡟⠶⠴⠶⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠛⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠀⢸⠀⠀⠈⠉⠁⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠃⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡦⠚⠁⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⣠⣼⣿⠤⣿⡁⠀⠀⠀⠀⠀⠀⠀⢰⡗⠣⠤⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠻⠏⠉⠀⣿⡁⣀⠀⠀⠀⠀⠀⠰⡾⠇⠀⠀⠈⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⣀⣀⣀⣠⡤⢼⣇⠀⠀⢠⡤⡄⠉⠹⣄⢀⡀⢠⣄⣼⠃⠀⢀⠀⠀⢸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡈⠛⠃⠀⠀⠈⠉⢉⡁⠀⠀⠀⠀⣏⣹⠠⣴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⡀⠀⠀⠀⢯⡽⠃⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⣆⣀⣀⡀⠀⠀⣀⣀⣀⢠⠞⠉⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠶⠋⠀⡼⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢠⠗⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢯⡀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀ ⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⣏⠉⠉⠉⠉⠛⠛⢻⡇⠀⠀⠀⠀⢧⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀ ⢀⡏⠀⠀⠀⠀⠀⠀⠀⣠⠜⢹⡇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠘⢧⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢧⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠸⡄⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀ ⢸⡄⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⢷⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀ ⠈⡇⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠘⢦⣀⣀⠤⠔⠋⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠧⠤⠤⠴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⡠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠁⠈⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠖⠒⠂⠀⠀⠀⠒⠒⠦⢄⣀⠀⠀⠀⠀⣄⠀⠈⢳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⠀⠸⡇⠀⠀⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣇⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⠤⡤⠤⠤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⡟⠀⠀⠀ ⠀⠀⠀⠀⢷⣄⣈⣧⠎⡴⠂⠉⠉⠐⠦⡈⠻⠟⠛⢲⣦⣄⣀⠀⠀⠀⠀⠀⠀⠈⢧⢠⡇⠀⠀⠀ ⠀⠀⣀⡀⠘⡆⢹⣿⠀⡇⠀⠀⣴⣯⣶⣷⢠⣞⣛⡉⠉⠑⢯⠓⣦⣀⠀⠀⠀⠀⣸⢾⠀⠀⠀⠀ ⢀⡾⠁⠉⣻⣧⣿⠉⢦⡈⠲⠤⢹⡿⡿⣃⢸⣿⣿⡿⠀⠀⠀⡇⣟⡟⢷⣦⠀⢠⣏⡾⠒⠲⣄⠀ ⢸⡇⠀⢿⣷⢛⡏⠀⢀⣍⠓⠒⠒⠒⠉⠉⠣⣙⠻⠤⠤⠤⣊⡴⠿⠥⢄⣸⣷⣾⣏⠀⠀⠀⢈⡇ ⠀⢧⠀⠘⣿⣾⡀⠀⠀⠈⢳⣤⣀⡀⠀⠀⠀⠈⠉⢒⠒⠋⠁⠀⠀⠀⠀⡿⠀⠙⢿⣶⠤⠤⠚⠁ ⠀⠈⢧⡀⠈⢻⡈⣢⣄⠀⠀⠙⠢⠬⣉⣉⠽⠿⠛⠉⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠹⣧⡀⠀⠀ ⠀⠀⠀⢳⣄⡸⠙⣿⠋⠉⠒⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡟⠀⠀⠀⠀⠀⠏⢳⡀⠀ ⠀⠀⠀⢸⠥⡇⠀⠀⠀⠸⠉⣲⣦⠤⢀⣉⠉⠙⠒⠚⣏⢭⠉⠀⣀⣼⡁⠀⠀⠀⠀⡀⡆⠀⢧⠀ ⠀⠀⠀⢸⡞⠀⠀⠀⠀⢧⢸⣿⣽⣿⠀⣠⠃⠀⠀⠀⢹⡿⠟⠛⠲⢇⡙⣧⠀⠀⢸⠟⠁⠀⢸⡄ ⠀⠀⠀⠘⣧⠀⠀⠀⠀⠈⢦⣙⣛⡡⠞⠁⠀⠀⠀⡰⢏⣤⠀⢀⠀⣄⡝⠙⡇⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⢀⣈⣷⣄⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⡇⠚⠿⢶⣿⠞⠻⠥⠴⠃⠀⠀⠀⠀⠀⣼⠁ ⠀⠀⠀⠸⡉⠙⢿⣿⠶⣤⣸⡀⠀⠀⠀⠀⠀⠀⠀⠱⠄⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀ ⠀⠀⠀⠀⠙⢦⡄⣻⠗⠋⠈⠉⢻⣒⠒⠲⣶⣶⣶⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠤⢔⣶⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢯⣍⣉⣩⣽⡎⠛⠷⣄⣀⠀⠀⠀⣀⣀⡤⠖⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠶⠒⠒⠚⠛⠋⠙⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀⣠⠤⢤⣄⣀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣠⣴⣤⠤⠞⠛⠋⠵⠚⠁⠀⠀⠀⠙⠛⠙⠖⠺⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⢀⡾⠁⠀⠀⢀⣠⣴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⡾⠁⠀⢀⢴⡿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣸⠇⠀⣰⠞⠙⠋⠁⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣠⣴⠤⠶⢶⣆⣠⢤⡀⣄⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣿⢀⣾⡗⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠟⠚⠛⠳⣄⠀⠀⠀⠀⡴⠛⠛⠻⢿⣦⣤⠀⢸⣟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⣶⠏⠀⠀⠀⠀⠀⢀⣄⣼⣿⣃⠤⠶⠲⠶⠶⠋⠀⠀⠀⠀⠓⠒⠚⠓⠮⣿⡟⢧⣴⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⢁⠀⠀⠀⠀⠀⢠⣼⠿⣿⠟⠁⡤⡶⠒⠦⣄⠀⠀⠀⠀⣰⣿⣿⣏⠓⢦⠘⡇⣾⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⢿⡀⡀⠀⠀⠀⣸⠋⢠⠏⠀⡞⣘⣿⣷⡄⠘⣆⠀⠀⠀⣿⣷⣾⣿⠃⠀⣷⣧⠻⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠚⣿⣇⠀⣸⣿⣏⠀⠸⣄⣸⣧⣝⣿⣫⣀⣠⠼⠀⠀⠀⢿⠓⠾⠶⠚⣹⠛⠛⠓⢾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⣿⢿⡟⢳⣬⣓⣶⡿⣁⠼⠛⠦⡀⠀⠀⠀⡠⠶⠖⠚⠛⠳⡄⢠⠟⠒⣄⠀⠀⢱⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⢰⠒⠚⢁⣾⡴⠊⠀⡟⠁⠀⠰⡏⠓⠀⢀⡠⠷⠤⢤⣄⣤⠴⠛⠲⠤⠴⠛⠀⠀⢸⡇⠙⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠘⢦⣀⡴⠋⠀⠀⣻⠇⠀⠀⠀⠙⠲⠖⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠈⢳⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣄⣦⡀⢀⡀⠀⢀⣀⣀⠴⠋⠈⠀⠀⠀⢻⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠘⠦⣀⡀⠀⢀⣀⣠⠼⣿⡛⠛⠿⢿⣿⣿⡏⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⠙⠉⠀⠀⢠⠙⠲⠤⠤⠽⠟⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⢶⣄⣠⣾⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈ ⠀⠀⠀⠀⠀⠠⠰⣀⠟⢣⣤⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯ ⠀⠀⢐⡂⠉⠀⠀⠀⠀⠀⠀⠙⠿⣧⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏ ⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡸⠀ ⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⡿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠁⠀ ⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠃⠀⠑⢄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀ ⠀⠙⠾⣢⣀⡀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠑⢿⡳⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⣤⣾⡕⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠻⠤⠶⣤⣖⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣿⡢⣄⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⢦⣧⠀⢾⣿⠁⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣸⣦⡀⠀⠠⡀⠀⠉⠉⠉⠁⠀⣸⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⣤⣈⣓⣲⣤⡤⠴⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢴⣤⣌⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠴⠶⠶⠒⠒⠚⠉⠛⠲⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢀⣀⣀⣀⣀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡴⣯⠿⠛⣋⡽⠛⠉⠉⠀⠈⠻⠿⡧⠶⣤⣤⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢐⣻⡷⠟⠉⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⢽⣗⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⢀⣀⡶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣾⠇⠀⠀⣤⣬⢺⡿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⣠⣤⢤⠀⡀⠀⠀⢀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢸⡏⠀⢀⠴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡖⣻⣿⣿⠒⠛⠟⠋⠁⠈⠙⠛⠒⣿⣛⠶⣼⣆⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⡇⢠⢟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⠛⠉⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⣴⠋⠉⠈⠙⠻⣝⣷⣰⡄⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣷⣺⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡟⡿⠁⣤⡤⠶⠤⠤⠤⠞⠃⠀⠀⠀⠀⠀⠙⠒⠒⠛⠓⠲⣜⣿⡟⢷⡄⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠋⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣶⡒⠦⣄⠀⢹⡇⢠⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣇⣤⠀⠀⠀⠀⠀⠀⠀⣷⡟⠁⢹⡟⠁⣠⢟⣭⣤⣄⠈⠻⣆⠀⠀⠀⠀⠀⣾⡾⠛⣿⣷⡄⠈⢳⡄⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠛⣿⣀⣀⠀⠀⠀⣀⢠⡟⠀⢠⡟⠀⢀⡏⣀⣽⣿⣿⡇⠀⠘⣇⠀⠀⠀⠀⣿⡇⢿⣿⠿⠃⢀⣈⣟⣷⡌⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠊⣿⣿⠀⠀⣰⣿⣾⡁⠀⠸⣇⠀⣸⣄⣘⣛⣿⣋⣀⣀⣠⠾⠀⠀⠀⠀⢿⠓⠶⠷⠶⠞⢉⡿⠛⠉⠓⠲⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠉⣿⣶⣇⣿⢿⣌⠱⠦⢤⣼⡟⠁⣸⡿⢏⡉⠉⠉⠉⠁⠀⢀⣀⣀⡤⠼⠷⠶⣤⠀⠀⣸⠷⢤⡀⠀⠀⠈⢶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⢀⣙⣋⣿⠇⢸⠏⢓⡲⠟⢿⡵⠊⠁⠀⣀⢽⣆⠀⠀⠀⠀⣎⠁⠀⠀⠀⠀⠀⢘⣦⡀⠃⠀⠀⣹⠀⠀⠀⠈⡍⢷⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⢸⠉⠉⠁⠠⣾⡶⠋⠁⠀⡸⠁⠀⠀⠀⢿⡀⠁⠀⢀⣠⠖⠛⠓⠒⠲⠦⣴⠶⠋⠉⠉⠓⠒⠊⠉⠀⠀⠀⠀⣇⠀⠙⢷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠈⠳⣀⣠⣾⠋⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠙⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠹⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⣈⠟⠁⠀⠀⠀⠈⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠉⠆⠀⠀⠀⠹⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣴⣦⣿⣷⣿⣷⣦⣽⣦⢤⣀⣰⡶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⣀⣠⡤⠖⠛⠿⣆⡈⠉⠉⠻⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠈⠉⠉⠉⠉⠀⠀⠀⢰⡈⠙⠶⠤⠤⠤⠿⠟⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⣤⡄⠀⢀⣶⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣿⡇⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠾⠵⠖⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦ ⠀⠀⠀⠀⠀⠀⡠⠊⠈⠢⠞⠀⠙⠶⣺⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⢀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⣷⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀ ⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠠⠃⠀ ⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢼⠇⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀ ⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡾⠀⠀⠹⣄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀ ⠀⠻⣇⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⠃⠀⠀⠀⠀⠈⠳⣄⣹⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⢮⣦⣤⣀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⠽⢷⣄⠀⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡞⠀⠀⣴⣞⡻⢾⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠷⠶⠾⠧⠴⣫⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣯⡳⣦⡀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠹⣌⣇⠀⠸⣯⡿⠀⠀⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠳⢦⣄⣀⠀⢻⣦⠀⠀⠀⠀⡀⠀⠈⠉⠉⠉⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠞⠳⢤⡀⠀⠙⠦⣄⣀⠀⠀⠀⢀⣠⠼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠤⠤⠭⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠰⠶⡖⡒⢦⣆⣀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠁⠂⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⢐⠠⠒⠀⠀⠀⠐⠢⢄⣃⠣⠀⠀⠀ ⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢣⠀⠀ ⠀⠀⢠⠃⢠⡴⠬⠭⡉⢉⠉⠒⡠⡀⠘⡸⠀⠀ ⠀⠀⢸⣠⡃⠋⣿⢉⠡⢈⢲⣖⠚⢱⠀⣧⡀⠀ ⠀⠀⠌⠀⢑⠀⠚⠙⢂⠐⠑⠤⠠⡜⠹⡁⠈⡆ ⠀⡘⠀⠀⠀⠁⠒⠒⠋⠓⠠⠤⠊⠀⠀⢹⠚⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀ ⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀ ⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠑⠦⣀⣀⡤⠴⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⡦⠴⢦⠄⠤⠤⠆⠤⡤⠀⠰⠦⠶⠶⡶⠶⠆

⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠔⢁⠠⠤⠤⠤⠤⠬⢁⡒⠂⠄⡀⠀⠀⣀⠀⠀⠀ ⠀⠀⡼⠊⠀⠀⠀⠀⠀⠀⡄⡀⠀⠁⠢⡑⢴⠚⠉⠙⢶⡄ ⠀⡎⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⣆⡀⠄⡰⡤⠭⠂⠀⠀⣇ ⢸⠀⠀⠀⠀⡔⢈⣘⡝⠖⠤⠜⢹⠔⠒⢵⠧⣄⣀⣀⣾⠋ ⢸⠀⡀⠠⢏⠷⠁⣠⣈⠀⠀⠀⢠⣶⡆⣞⡀⠈⠉⠉⠀⠀ ⠈⢄⠫⠁⠼⠐⡨⠟⠻⠄⡨⠛⢻⡅⠀⠀⢸⢳⠂⠊⡆⠀ ⠀⠈⡻⠂⡵⡈⠀⠀⢀⡸⠒⠒⠊⠉⠀⠀⢁⡜⠀⠐⢙⠀ ⠀⢰⠀⠀⠘⢌⠉⠉⠁⠀⣀⣔⣗⡖⠒⠒⠊⠀⠀⠀⠹⠀ ⠀⠻⠀⠀⠀⠀⠐⠒⠉⠉⠀⠈⢚⠁⠀⠂⠄⠀⠀⠀⢀⠀ ⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠈⢷⠁⠀⠀⠀⠀⠀⡌⠀ ⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀ ⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀ ⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀ ⠀⠀⠀⠀⠀⠁⠂⠤⢀⣀⣀⠀⠀⣀⡀⠀⠰⣈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀

⢰⡏⠛⢦⡀⢸⠏⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠋⡇⠀⣠⠞⢙⡦ ⠀⠙⢦⡀⠻⣼⣆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣧⠞⢁⡴⠟⠁ ⠀⠀⠀⣙⣦⠞⠁⠀⢷⡀⣰⢤⡀⠀⠀⠀⠀⠀⣠⢦⡀⣼⠃⠀⠉⣰⣏⡀⠀⠀ ⠀⢻⡉⣀⣀⡤⣤⡀⠀⠻⠃⢠⠏⠀⠀⠀⠀⠘⣧⠀⠛⠁⠀⣠⣤⣄⣀⡉⣽⠀ ⠀⠈⠉⠁⠀⠀⣈⡽⠆⠀⠀⠸⣆⣤⠤⠤⠤⣤⡟⠀⠀⠀⢾⣽⠀⠀⠈⠉⠁⠀ ⢰⡖⠒⠀⠒⠲⣽⣄⣤⡴⢦⡀⠙⠀⠀⠀⠀⠻⠀⣰⠶⣤⣤⣟⡴⠒⠚⠁⠒⣶ ⠀⢷⡀⠀⠀⠀⠈⣿⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢻⡏⠀⠀⠀⠀⣠⠇ ⠀⠀⠙⠲⠤⠤⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠤⠤⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠰⢿⠿⠀⠀⠀⠀⠸⠿⠟⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢠⡖⡒⢦⡄⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⡈⠛⡟⠛⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠙⠒⠓⠒⠁⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡼⠛⠶⠤⣤⣤⡤⠤⠖⠻⣏⠱⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠋⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠹⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⠤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠤⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡴⠛⠉⠙⡆⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣀⣠⠇⠀⠀⠀⢿⡀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠖⠒⠶⠶⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣦⣤⣤⡀⠀ ⠀⠀⢀⡴⠿⣤⠀⡀⢀⠀⡀⢀⠀⠀⢀⠀⡀⢠⡤⣾⠁⠀⠈⢻⡄ ⠀⠀⣼⠁⠀⠀⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠀⠀⢻⣄⠀⢀⡼⠃ ⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡏⠉⠀⠀ ⠀⠀⣹⡟⠓⠶⠶⠤⢤⣤⣤⣤⣤⣤⣤⠤⠴⠶⠖⢻⣏⠁⠀⠀⠀ ⠀⣞⠉⠀⠀⠀⢀⡴⠶⢦⣤⠶⣄⡤⠶⢦⡀⠀⠀⠀⠉⢻⠄⠀⠀ ⢀⣽⠞⠳⣆⠀⢸⡅⠀⢨⡇⠀⢸⡅⠀⢈⡇⠀⣠⠞⠳⣿⡀⠀⠀ ⣼⠁⠀⠀⠹⡷⠦⠽⠟⠻⣦⣄⣤⠟⠻⠿⠴⢾⠏⠀⠀⠈⢷⠀⠀ ⣧⠀⠀⠀⠀⠙⢦⣀⣀⣀⣴⠛⢧⣀⣀⣀⡴⠋⠀⠀⠀⠀⣸⠀⠀ ⡾⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⢻⡀⠀ ⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀ ⠀⠈⠉⢿⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡼⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠛⠶⠦⠤⠴⠶⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣄⠀⢰⣿⠛⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠈⢻⣷⣈⣿⠀⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠛⠛⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠙⠛⠋⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣴⡿⠿⢷⣶⣾⠟⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣀⢀⣠⣾⠏⠀⠀⠀⠀⠀⢻⣧⣤⣤⣤⡆⠀⣤⣤⣤⣴⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣿⠛⢻⣷⠀⠀⢀⣤⣤⣤⡀⠀⠈⠙⠛⣿⡿⠿⣶⣤⣄⣀⣀⡀⠀⠈⠉⣹⡿⠀⣰⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡿⢿⣧⠀⣿⡆⢸⣿⣄⣰⣿⠏⠁⣿⡇⠀⠀⠀⣴⡿⠁⠀⠀⠉⠉⠛⠛⠿⢷⣶⣾⠟⢁⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡁⠈⠻⠿⠿⠃⠀⠙⠛⠛⢁⣤⣾⠟⠁⠀⢀⣾⠟⠁⠀⣀⣤⣴⣶⣶⡶⣶⣶⣿⣿⣿⠟⠋⢀⣠⣴⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠙⠻⠿⣷⣶⣿⢏⣤⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⢿⣦⣶⡿⢋⣵⡿⠟⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠿⣦⣤⣤⣤⣴⡾⠟⠛⠿⠿⣶⣦⣴⣾⣿⡿⠋⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀⣸⡿⠃⣠⣿⠏⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⣀⣴⣾⠿⠟⠛⠉⠉⠉⠙⠻⢿⠁⣴⡿⠁⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⡤⣆⡶⢶⣏⣙⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠶⠾⠷⠶⣾⣿⣧⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⣝⢷⣦⡝⣟⣉⣷⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣟⠛⠻⠿⣷⣶⣤⣤⣀⠙⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣭⣿⣿⠝⢻⣛⣻⣯⡤⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⣀⣀⣉⣛⣛⣿⡟⠀⠀⠀⠀⠀⣀⣀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⣩⣿⢻⣶⠆⡤⡟⢾⣯⠟⠀ ⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠟⢻⣿⠁⠀⠀⠀⠀⢰⣿⣉⡇⢸⣷⣼⡇⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⠷⢶⣝⣹⣿⣉⡷⠀ ⠀⢰⠖⠲⣾⠛⢿⣦⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠈⠉⠀⠁⠀⠀ ⠀⢨⠿⢒⣉⢿⣧⣽⣿⣾⠞⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣤⣤⡀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡼⢷⠝⢚⣓⠈⢩⣶⣟⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣠⣴⡾⠿⢛⣫⣭⣥⣄⠀⠀⠀⠀⠈⠛⢿⣦⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠳⢾⡁⣿⣋⢸⣷⣿⡿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⡿⠏⠉⠀⠀⣿⣉⣀⣠⡿⠁⠀⠀⠀⠀⠀⠈⢿⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣟⢹⡷⠷⠟⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⡟⠁⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⢀⡀⠀⠀⢀⣼⠇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⣿⣇⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⣤⠞⠀⠀⢠⣾⠟⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡘⣿⣆⡀⠀⠀⠈⠙⠲⠶⠾⠟⠛⢁⣀⣴⣾⠟⢁⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣷⣬⣛⠿⢷⣶⣤⣤⣤⣴⣶⣶⠾⠿⠛⠉⣀⣴⡿⢿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠈⣟⠻⢿⣶⣾⣭⣭⣭⣭⣥⣤⣴⣶⣾⠿⢻⡏⠀⢸⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣤⣀⣧⡀⠈⣿⠉⠉⣏⠁⠀⢹⡀⢀⣸⣷⣴⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠉⠉⠙⠛⠿⠿⠿⠿⢿⣶⣿⣾⣿⠟⢛⡛⠉⢉⣿⡇⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣀⣀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⣀⣶⠿⢻⡿⠉⠉⠉⣿⡟⠚⠉⠘⣷⠀⠹⣿⣀⠀⢀⣀⣀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠻⣿⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⡾⠛⠦⠤⢤⣿⣇⣀⣤⡴⢿⡆⠀⣿⣿⠛⠛⠋⣿⠟⠉⠙⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⣿⡇⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⢸⡏⣠⣿⣥⣀⠀⠀⣼⣿⠃⠀⠀⠀⢸⣷⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⣿⡇⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣄⠀⠈⠉⢩⣿⣿⠤⠤⠶⠞⢹⡿⠀⠀⣿⠀⠀⢸⡟⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⣿⠃⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢸⣷⠈⠙⠿⠶⠶⠿⢻⣿⣄⣀⣀⣴⡿⠃⠀⢀⣿⠀⠀⢸⣿⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⣼⡿⠀⠀⢸⣿⡄⠀⢀⣤⣤⣴⣶⣾⣿⣄⠀⠀⠀⠀⠀⣾⣿⣿⣭⣭⣥⣄⡀⠀⣼⣿⠀⠀⠘⣿⡄⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣧⣴⡶⠟⢻⣧⣾⠟⠋⠉⠀⠀⠀⠙⣿⣿⣶⣶⣾⣿⡟⠉⠀⠀⠀⠉⠛⢿⣦⣿⠛⠿⣶⣤⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⡀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢶⣶⣶⣶⡾⠿⠉⠀⠀⠀⠀⠈⠻⠿⣶⣶⣶⣶⠾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡶⣆⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀ ⠀⠀⠳⡸⣄⣀⡇⡇⠀⠀⠀⠀⠀⢠⣯⣇⣀⡴⢻⣏⡀ ⠾⠭⠽⠒⠒⠪⣅⢣⣀⣳⠾⣦⣔⣫⣼⣿⣛⠒⠒⠚⠃ ⠀⠀⠀⢏⣿⣳⣮⠏⠁⠀⠀⠀⢹⡿⣛⣷⡼⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⢩⠇⠺⠂⠀⠠⠿⠋⢻⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⢧⠒⠉⠉⠉⢲⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⠈⠣⣀⣠⠔⠁⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡌⢺⡀⢁⠀⠀⢐⡆⠀⣰⠃⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠙⠢⢝⣚⠦⢐⣊⡤⠚⠙⠋⠉⠀⠈⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⢀⠀⢰⢧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⣦⢤⣸⡄⡏⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⢹⠇⣯⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢸⡇⠘⡄⣿⠀⢱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠧⠤⡾⣄⡠⢷⣿⣠⠼⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⠚⠀⠧⢠⡞⠙⠶⠞⡃⠀

⠀⣴⣾⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡏⠀⠀⠙⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⡄⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠏⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣿⣆⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣦⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⡆⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⢀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⣀⣀⣿⣿⠀⠀⢸⣿⣧⠀⠀⠀⠀⢠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⠛⠛⠛⠛⠁⠀⠀⠈⢻⣿⣦⣄⣀⣠⣿⡟⠙⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣿⣶⡀⠀⠀⠀⢠⣿⡿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠸⣿⣧⣀⣤⣶⣿⠟⠁⠀⠀⠘⠿⠿⠿⢿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⣦⣀⣀⣠⣴⣶⣾⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⣻⣿⣄⣀⣀⠀⣰⣾⡟⠁⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠛⠿⠿⠟⠛⠉⠀⠀⠀⠉⢛⣿⣿⣦⣤⣴⣾⣿⣿⠿⠿⠿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣶⣤⡀⠀⠀⢀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⠿⠿⠟⢛⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣦⣠⣾⡿⠿⠋⠁⠀⠀⠀⠈⠛⠿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣶⡶⠿⠛⠉⠉⠀⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠈⠛⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠿⣷⣄⣀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⢀⣞⣉⣹⡇⠀⠀⠀⠀⠀⠀⢠⡶⣦⡀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⢿⣶⣶⣦⣤⣾⣿⠃⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣤⣾⡇⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⡟⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣤⣀⠈⠉⠁⠀⠀⣿⣧⣄⣀⣀⣠⣤⣶⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣀⠀⠀⠀⠀⠀⠀⣾⠉⠀⠀⠈⢻⡇⠀⠀⠀⢀⣿⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣷⣦⣀⠀⠀⠀⠻⣦⣤⣤⣤⠾⠁⠀⠀⣠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠙⠻⢿⣿⣦⣀⠀⠀⠘⢃⣀⣠⣤⣶⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠿⠿⠛⠉⠁⠘⠿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣤⣄⣠⣾⡿⠋⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠛⠛⠻⣿⣿⣧⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⢀⣰⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢻⣿⣷⣄⠀⢸⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠃⠀⠀⠉⠻⣿⣷⣼⣿⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⣼⡟⣿⣿⠀⠀⠀⠀⠀⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⢿⣧⣿⡟⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⢙⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⣿⡿⣿⣦⣄⠀⠀⠀⠀⠀⠈⠻⢿⣷⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠹⣧⡈⠛⠿⣷⣦⣀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⣿⣿⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠙⢿⣦⠀⠉⠻⢿⣷⣄⠀⠀⠀⠀⠘⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣼⣿⠇⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⢹⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠈⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⢿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠈⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣏⡀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⢀⣀⣀⣀⣰⣿⣇⣀⣀⣀⣀⣀⣀⠀⣰⣿⡇⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⢿⣇⣛⣝⣝⣁⡀⢈⣀⡙⣀⣘⣡⣄⣘⡇⠀⠀⠀⠀⠀⠀⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡉⠉⠉⠉⠉⠻⡿⣿⣷⣦⣤⣤⣶⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣇⣀⣿⣀⣀⣿⣀⣸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⢶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀ ⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⣶⡀⠀⢀⣄⠀⠀⣀⣀⠀⠀⣠⡀⠀⢀⣶⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⢸⡏⠀⠀⠀⣿⠻⣶⠟⠙⢷⡾⠋⠙⢷⡾⠋⠻⣶⠟⣿⠀⠀⠀⢹⡇⠀⠀ ⠀⠀⣾⠃⠀⠀⢰⣿⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⣿⡆⠀⠀⠘⣷⠀⠀ ⠀⢰⡟⠀⠀⠀⣼⣿⢷⣤⠞⠛⢦⣴⠟⠻⣦⡴⠛⠳⣤⡾⣿⣧⠀⠀⠀⢻⡄⠀ ⠀⣼⠇⠀⠀⢀⣿⣿⠀⠁⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠈⠀⣿⣿⡀⠀⠀⠸⣧⠀ ⢀⣿⠀⠀⠀⣸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣇⠀⠀⠀⣿⡀ ⠈⣻⡶⠶⣶⠟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠻⣶⠶⢶⣟⠁ ⠀⠿⠷⠾⠏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠹⠷⠾⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢄⣀⣀⡤⠤⠶⠶⠶⠶⢶⣦⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠈⠉⠁⠒⢠⡀⠀⠀⠈⠙⢷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢢⠀⢀⠈⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠀⢀⠠⠀⠒⠒⠒⣀⣤⣀⠀⠀⠀⠀⠀⠀⢥⠸⡄⢸⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡔⠉⣢⠀⠀⢶⡊⣀⡀⠙⠕⢤⠀⠀⠀⠀⠀⢳⣱⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠥⣴⡇⠀⠈⠁⠠⣭⡃⠼⠀⡷⣄⣀⠀⠀⢀⡿⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⢄⠂⣎⠀⠀⠁⠠⡀⠀⠀⠁⡀⣠⠁⠮⠀⡇⠀⢸⠣⠌⠀⠀⢤ ⠀⠀⠀⠀⠀⣕⠊⠑⠉⠉⡉⠁⠒⠹⣤⠄⠀⠁⡌⡆⡀⢀⡇⣠⠾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢧⡈⠕⠒⠒⢺⠈⠒⢒⠦⢌⣁⠀⢉⡠⢹⠒⠁⠩⠳⣴⣆⠀⡀⢀⠐ ⠀⠀⢀⠠⠒⠉⠀⠀⠀⢰⣑⣂⠡⠀⠀⠀⠀⠀⠀⠀⡷⡂⠠⣣⠇⠉⠑⡍⠁⠀ ⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⠉⠀⠀⠀⢠⣸⠀⠀ ⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⡇⣸⠻⠀⠀ ⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⢀⢂⢔⠔⠁⠀⠀⠀ ⠘⣧⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⠀⣰⣀⡠⠤⠒⠋⠉⠁⠀⠀⠀⠀⠀ ⠀⠙⢷⣄⠘⡀⠀⠀⠀⠀⢀⢡⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠓⢦⣤⣤⠴⠊⠓⡽⠶⠤⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠲⠤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⠁⠀⢀⣠⣤⡤⠶⠖⠒⠒⠚⠛⠒⠖⠲⡦⢤⣤⣀⠀⠀⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣡⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⣄⠀⠀⠙⣄⠀⠀⣀⣮⣶⢿⣿⣶⡆⣦⢀⠀⠀ ⠀⠀⠀⠀⣰⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢤⣀⡀⠀⠀⠀⠀⠈⠉⠦⣄⠈⠳⣶⠟⠉⠁⠀⠀⠀⠉⢻⣿⣦⠀ ⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠙⢦⡀⠀⠀⠀⠀⠀⠸⣦⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⢸⣿⡧ ⠀⢀⡾⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠟⠀⠀⠀⣧⠀⠀⣠⣤⣀⠈⠹⡷⠢⠤⠤⠞⠃⠀⠀⠀⠀⠀⣽⣯ ⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣦⣼⣉⡀⠉⠁⠀⠀⠀⣴⡿⣹⠋⠁⠀⠈⢳⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿ ⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠁⠘⠙⠻⣄⠙⠾⣗⡤⠤⠤⠴⠞⢰⣇⡴⠒⠛⠓⢄⢻⣾⣧⣤⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁ ⢸⡇⠀⠀⠀⠀⠀⠀⢀⣤⣾⠀⢀⡴⠒⠒⠲⢾⣦⡀⠀⠀⠀⠀⠀⠀⠘⠏⢀⠀⠀⠀⠈⣿⡏⠉⠙⠿⣶⣶⣧⣶⣿⢿⠟⠃⠀ ⢺⡇⠀⠀⠀⠀⠀⢀⣾⡋⢸⣶⡎⠀⠀⠀⣀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⣲⣦⣀⢸⡟⠀⠀⠀⠀⠀⠁⠁⠉⠀⠀⠀⠀⠀ ⠸⣧⠀⠀⣾⣄⣠⠞⠉⢳⠀⠙⠀⠀⣠⣴⡿⣟⢦⡀⠀⠀⠀⣀⢀⠀⠀⣿⢿⢿⣻⠄⠚⠛⠦⣄⣀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀ ⠀⢻⡀⠀⢿⣄⠀⠀⠀⣸⠀⠠⠤⠄⠘⣻⣿⣿⣯⡁⠀⠐⠛⣡⠾⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⡯⣟⠦⠤⠠⠼⠛⢧⠀⠀⠀ ⠀⠀⠻⣆⢸⡍⠀⠀⢉⡝⠀⠀⢈⠴⠋⠉⠁⠀⠉⠉⢀⡴⠚⠁⠀⠀⠀⡿⠳⡄⠀⠀⠀⠀⠀⢠⠇⢸⡆⠀⠀⠀⠀⣸⣄⠀⠀ ⠀⠀⠀⠙⠿⣽⣷⠶⠛⣷⣀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠸⣄⣠⠴⠦⣤⠾⠛⠚⠓⠒⠒⠒⠒⠋⠁⠀⣸⠇⠀⠀⠀⠰⠟⠻⡀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠸⣟⠻⣄⠀⠀⠀⠀⠀⢀⣀⠤⠚⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⣤⡇⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⢸⡀⠈⠑⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⢀⣼⣷⣤⣀⣄⣀⣀⣀⣀⣤⠔⠋⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀ ⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⣿⣻⣗⡼⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀ ⠀⠀⣾⢰⠄⠀⠀⠀⠀⠀⠀⠈⠳⠤⣄⣀⣠⣬⠿⠿⠟⠁⠀⠀⠳⣬⣉⡥⠾⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢄⠀⠀⠀⠙⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢱⢳⡌⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀ ⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠈⣦⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀ ⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠸⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀ ⠀⠀⠈⢿⡇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠈⠹⣜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠚⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠶⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠤⣤⣶⣤⣄⣀⠀⠀⠀⠶⣦⣤⣀⡀⠀⠀⠀⢛⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣤⣴⡶⠶⠶⠶⠤⠤⣄⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⣠⡔⠂⠀⠉⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠏⠀⠀⢠⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⡸⢠⠇⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠐⠀⠤⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢰⣡⠃⠀⠀⠀⠀⢀⠔⠝⠁⣀⠈⣦⠀⠀⢠⠚⠂⡜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠸⡇⠄⠀⢀⡀⡰⡇⢘⡀⣪⣯⡍⠉⠀⠀⣿⣭⠚⠁⠀⠀⠀⠀⠀⠀ ⢀⡄⠀⠘⡤⣻⠀⠀⡇⢸⡆⢃⣀⡀⠁⠀⠀⡠⠀⠉⠀⢑⡄⠢⢄⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⢘⢆⠀⣇⠘⡀⡌⡔⠍⣄⣠⡴⠑⠒⠉⡟⠋⠂⠧⠐⡇⠀⠀⠀⠀ ⠰⣀⠀⠠⢀⣴⣶⠿⠋⠑⢸⠣⡈⠒⠒⣉⠠⡔⠲⠶⢡⠒⠐⠒⠏⣠⠆⠀⠀⠀ ⠀⠀⠉⡗⠋⠁⢧⠃⠀⣢⡇⠀⠀⠉⠁⠀⠀⠠⣑⢒⡱⢀⠀⠀⠈⠛⠠⡀⠀⠀ ⠀⠀⢸⠱⠀⠀⠀⠉⠉⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⠀⠈⢢⡀ ⠀⠀⠸⢰⡀⡆⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧ ⠀⠀⠀⠀⠱⢔⣄⢄⠀⠀⠀⠀⠈⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠉⠙⠓⠤⣄⣀⣰⡀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠁⠀⠀⠀⣠⢀⠀⠀⠀⠀⠀⡀⢀⣰⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠤⡚⠅⠊⠢⣤⣀⣤⠔⠓⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠙⣛⣻⡶⠦⠴⠶⠒⠛⠛⠓⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⠁⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠁⠀⣄⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡏⠀⠀⣼⠀⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⣤⡤⠤⠤⠤⢄⡀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⣼⠁⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠓⠒⠢⡀⠀⠀⠀⠀⠀⠈⢑⣢⡀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⢸⢇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢩⠏⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⣸⡋⠁⠙⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡇⢸⣾⠇⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⡆⢀⣤⠖⣿⠉⠉⠛⠋⠀⠀⠀⣴⣏⡉⠒⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠈⣿⣀⠇⠀⠀⢀⡤⠤⣤⠏⢹⠀⠰⠄⠊⢠⡾⠿⠿⠥⠀⠀⠀⠀⣀⡻⢿⣿⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡤⠄⠈⠙⢻⣄⣸⡟⠀⠀⠀⣾⠁⠀⡟⡄⠘⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠤⠈⠀⠀⠀⠈⢳⡀⠰⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡟⠃⠀⠀⠀⠀⠉⠉⢿⡀⠀⠀⣿⠀⠀⣿⠁⠀⡽⠊⡩⠖⠀⠀⠀⠀⢀⣾⣄⣀⣠⢤⣤⣤⣶⣾⡁⢰⡇⠀⣱⡄⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⢨⠳⣄⠀⢸⣆⠀⠹⡀⢸⠀⢜⠀⠤⢴⣦⠤⣶⡿⠄⠈⠉⠀⠀⢰⡆⠀⠀⠈⠙⠒⠉⣠⠇⠀⠀⠀⠀⠀⠀⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⢀⢰⡆⣼⣿⡿⠉⠳⠄⣹⠘⡄⠈⠳⠶⠶⠶⠚⠉⢀⣀⠤⣴⣤⣴⢛⢲⠤⢤⣤⣤⡴⠾⠋⠀⣵⠀⠀⠀⠀⠀⠀ ⠀⠙⠲⢤⣀⡴⢁⣠⣾⡿⣿⠋⡟⠀⢀⠀⠀⡾⠀⠈⠢⠤⠤⠤⠤⠔⠒⠉⠙⢦⣀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢑⣲⡾⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣹⠋⠉⠀⠀⢻⡀⠧⠀⠀⢱⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⠉⠉⢁⣜⠀⠀⠀⠀⠀⠀⠈⠁⠒⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠇⡀⠀⠀⠀⠀⠙⠲⠤⠖⠋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠒⠈⠉⠢⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀ ⠀⠀⠀⠀⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀ ⠀⠀⠀⠀⡿⢸⣄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇ ⠀⠀⠀⠀⠁⠈⢿⣄⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⣦⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠻⣷⣤⣀⠀⠀⠀⠀⠀⡤⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠴⠷⣄⣀⡞⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⢀⣠⠞⢁⡼⣁⠀⠀⠀⠀⠀⠀⢀⣰⣃⣤⠾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠶⠶⠾⠿⠥⠖⠉⠀⠈⠻⢶⣦⣤⣴⡶⠛⠉⢁⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⠋⠉⠉⠉⠉⠙⠛⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⡷⠶⠖⠒⠛⠋⠉⠉⠉⠙⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣠⣶⣟⣩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠆⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠈⣩⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀ ⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠃⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀ ⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣿⠀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⣧ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⢀⡈⣿⡾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣴⡟⢹⣿⣷⢿⡅⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢠⣿ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⢸⣿⢿⣏⣷⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢠⠿⢹ ⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⢹⠏⠈⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣴⠏ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⢸⡇⢀⣤⣤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⡼⠋⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠻⣦⠀⠀⠀⠀⠀⠀⢸⣇⣼⣻⣬⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣠⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣴⣿⡉⠘⣧⡀⠀⣸⣷⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⣠⠞⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣹⣤⣤⣄⣀⣿⡆⠀⠀⠀⠀⠀⢸⠏⠈⠳⣄⠘⢷⡄⣏⣿⣿⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣇⣀⠀⠀⠀⣀⣴⣏⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠉⠝⢿⣦⡀⠀⠀⠀⢸⡄⠀⠀⠈⠳⣤⣻⣿⣿⣿⣧⠀⠀⠀⠀⠀⣽⡿⠛⠛⠉⠉⠀⠀⠀⠻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠈⠛⠀⠀⠀⠀⠈⢻⡾⠽⠛⠟⢀⣤⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡏⢻⣦⡠⣄⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠿⢶⣶⡶⢞⣫⣿⠖⠋⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡇⠀⠙⠳⠿⠻⠶⠶⠶⠞⠻⣇⡀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⣀⣀⡤⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢺⣧⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠲⠶⠶⢺⡟⠀⢀⣴⡛⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣧⡀⠀⠐⣷⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⢀⣤⣾⡍⠃⠐⠋⠈⠻⣄⠀⢀⡼⠿⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠷⠦⠼⠷⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡚⠁⠻⣄⣠⢟⡿⠋⡴⠀⠀⣄⡀⠀⢘⡷⠛⢠⣄⣐⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠟⠓⠲⣆⠀⠛⣾⠀⢸⡇⠀⠀⢨⡿⠲⢮⣥⣴⠿⣷⣬⣍⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡤⠴⠒⠛⠛⠉⠁⠀⠀⠀⠀⠈⠛⠛⣿⠀⠘⠃⠀⠀⢸⡇⠀⠀⠀⣠⡾⢋⡿⠀⠀⠉⠙⠛⠓⠲⠦⢤⣤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⠛⠓⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⢸⣧⠀⠀⡴⣫⣄⡼⠃⠀⠀⠀⠀⠀⠀⠀⣠⡴⢿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣀⣀⣭⣍⣓⠶⢦⣄⣀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠙⢷⣾⣿⡽⠟⠁⠀⠀⠀⠀⠀⣀⡶⠛⠁⢠⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⡯⡅⠀⠀⠈⠙⣶⣄⠈⠉⠛⠿⣤⡀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⣰⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⡇⠀⠀⠀⢿⣤⣿⢤⡀⢠⡞⠉⢹⠇⠀⠀⠀⠀⠉⠛⠦⣤⣀⠀⠀⣼⠃⠀⠀⠀⢠⡴⣿⣧⠤⠤⠤⠾⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣴⣞⣋⣉⣀⠀⢀⡇⠀⠀⠀⠈⠿⠿⣿⢷⣸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣅⣀⠀⣠⠾⠋⢰⠟⣻⡆⣀⢀⡐⢚⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⣿⠀⠙⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡟⠉⠀⣰⢯⣴⣿⣷⣿⣿⣧⡼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣰⠃⣸⠃⠀⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠒⠒⢺⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣰⠇⢰⠇⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢠⡏⠀⡞⢀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣼⠁⢸⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠦⣤⣿⡀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⣯⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⠀⠀⠀⠀⠀⢀⡾⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⢸⣣⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢦⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⢳⡀⢹⡲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠘⡈⡇⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣄⠀⠀⢸⠘⡆⠀⡇⢻⢠⠇⢸⡇⠀⡠⢲⠄⣤⣶⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠈⢇⠘⡇⠀⡸⠀⣧⣴⠃⠘⢿⡄⢸⡦⠞⢱⡏⡜⣸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢻⣆⣸⠀⠿⠦⡇⠀⣿⣠⡤⢶⣾⠃⠈⠳⠶⠬⠟⣠⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⢣⠀⢻⣏⢀⣠⢶⡇⠀⠈⠙⠒⠉⠀⣀⣀⣀⣀⡀⠘⠿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡧⠤⠤⠧⡄⠉⠛⠛⠉⢀⣀⣀⣤⡤⠶⠛⠋⠁⠀⠀⠉⠓⠦⣈⠳⣤⡄ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⢹⠀⠀⣰⠞⠉⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠷⣏⣀⢀⣿⠤⠔⠉⠁⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡴⠟⠉⣠⣄⠀⠈⠁⠀⠀⢀⣀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⠖⠛⠁⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠘⢯⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣏⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢶⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠓⢛⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⠶⠚⠉⠉⠳⡄⠀⠀⠀⠀⢀⠜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠶⠶⠶⢶⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠟⣻⡟⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠠⠟⠁⣸⡏⠀⠀⠀⠀⠀⠀⣀⣄⣀⣠⣤⡤⢤⡤⣤⣄⣀⣀⣸⣿⣿⣿⣄⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⢀⡄⣿⣇⣤⡿⠛⠛⠛⠛⠉⠈⠋⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠿⣿⣦⣤⣽⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⢀⣘⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠉⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⣀⣼⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⢰⢲⣶⡖⠒⠒⠒⠊⠓⠒⣦⣄⣀⣤⡀⠀⠀⠀⠀⠀⣧⠴⠋⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣸⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⡇⡏⢣⠤⡟⢹⡏⣧⠀⠀⠀⠀⣀⣸⠁⡇⢹⠟⣏⠙⢶⣤⡀⢠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⡔⠋⠀⠸⠟⠑⡄⠸⡆⠀⠀⣀⡤⠖⡎⠉⢸⡀⠀⣿⣇⣸⣤⣇⡈⠀⣸⡞⡇⠀⢠⣧⣇⣀⣧⣟⣀⣸⡀⣸⠀⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⣹⠀⠹⡤⠞⠁⠀⠀⡇⠀⠀⢳⣆⣿⡏⣽⣿⣿⣿⣿⠛⠻⢷⢀⡾⠟⣿⣿⣿⣿⣿⢻⣧⡇⠐⡾⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⠀⠀⠀⠀⢀⡟⠀⠀⢷⠀⠀⠀⠀⡃⠀⠀⠀⠹⣿⠀⢛⣻⣿⣿⣿⠀⠀⢸⠟⠀⠀⣿⣿⡿⣿⠀⡟⡿⠁⢸⡟⢿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢦⣄⣤⠖⠋⠀⠀⠀⣸⢰⠀⠀⠀⢱⠀⠀⠀⠠⣿⠀⠈⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⢸⡇⡇⠀⢸⡇⠀⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢿⡀⠀⠀⠘⡆⠀⠀⡆⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⣿⠁⢠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⡇⠀⠀⠀⢿⠀⠀⢸⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⡿⢀⢢⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡇⢦⠀⠀⠈⣇⠀⠘⣧⣷⣄⣀⠀⠀⢿⠛⠲⡦⠀⣀⣠⡤⢾⠟⠀⢰⠇⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⡀⠀⠠⠈⠷⡄⠸⣿⣞⠙⠛⢿⣗⡒⢲⣾⢿⣍⡀⠀⣿⡀⠀⡏⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⣿⡀⣠⣶⣷⣿⣶⣿⣿⣦⡀⠀⠈⣿⣼⣷⡀⢹⣿⣶⣿⣧⣾⣸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣦⣰⡏⢳⠀⢳⣿⣽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡋⠳⡀⠀⠀⠀⠀⠀⣠⣿⠿⠿⠃⠈⢿⣿⣿⣿⡟⢪⠻⣧⣼⣆⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⠖⠛⠛⠛⠛⡇⠀⠹⢦⣴⣤⡀⢰⣿⣧⣀⣀⣀⣀⣀⢿⣿⢿⣿⣿⣟⣛⣻⣿⣷⢸⣿⣿⣿⡟⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣉⣉⠀⠀⠀⠃⠀⠀⣰⣿⣿⣿⣾⣏⠈⠛⠛⠛⠉⠉⢸⣿⣿⣛⣛⣿⣿⢟⣩⣽⠿⣿⣭⢿⣧⠈⣿⡆⠀⠀⣀⣤⣤⣠⠤⠤⢤⢤⡀⠀⠀ ⠻⣭⢤⡄⠠⠖⠀⠀⣰⣿⣿⣿⣿⡿⠛⢷⣄⠀⠀⠀⠀⢸⣿⡋⣩⣽⣿⣻⡽⠟⠁⠀⠸⣿⡀⣿⡀⡟⣿⡶⠿⣿⣿⣿⣿⣦⠀⢘⢯⡁⠀⠀ ⠀⠹⠭⠴⠶⣦⣴⠾⣿⠛⣾⣿⡿⠁⠀⠈⢻⣷⣄⠀⠀⣿⣿⣶⣿⣿⡏⠉⠀⠀⠀⠀⠀⣿⡇⣸⡇⠁⢹⣿⡀⠹⣿⣿⣿⣿⣷⡀⡰⠿⣦⠀ ⠀⠀⠀⠀⠰⣿⣿⠆⢁⣴⣿⡟⠁⠀⠀⠀⠀⢿⣿⣷⣿⣿⠿⠋⣡⣿⣿⣠⣤⣤⣤⣤⣶⡿⣧⢿⡇⠀⢸⣿⡇⠠⠌⣿⣿⣽⣿⠧⣽⣦⣼⠇ ⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⢻⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡏⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠈⡇⠀⢸⣇⠀⣾⢻⣿⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣴⣄⠀⠀⢀⣼⠋⢹⣿⡄⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⡁⠘⣿⣅⠋⠉⣽⣷⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⣴⠟⠁⠀⣸⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⣿⣀⣶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣯⡁⠀⢀⣀⣿⢿⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠂⠈⠻⢦⣬⠉⣿⡿⠷⢶⣤⣄⣀⣠⣼⣿⡋⠁⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⠶⠶⠶⠶⠶⠷⠿⠿⠷⠶⠦⠴⠾⠿⠿⠿⠿⠶⢶⢿⢿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢠⣶⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⠀⠸⣆⢹⡄⠀⢸⠙⡇⠀⠀⠀⠀⠀⠀⠀⢀⡖⣶⠀⠀⢀⣾⣿⠇⠀ ⣀⣤⠤⢼⡈⠛⠲⠾⠇⣇⠀⢀⣀⣠⡄⠀⢀⡼⠛⢷⣶⣶⣋⣁⠛⢲⣦ ⠛⠓⠒⠋⣉⣉⣉⠓⢦⣘⣦⠤⠿⠛⠿⣶⣏⣴⣾⣿⡿⢥⡀⠉⠉⠉⠁ ⠀⠀⠀⠸⣇⣻⣟⡻⣶⠟⠁⠀⠀⠀⠀⠀⣿⡿⢛⣹⣷⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⢻⠏⢸⡆⠀⠀⠀⣾⡶⠘⢿⠟⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣃⡤⠔⠒⠒⠢⢄⠈⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠉⢯⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠁⠀⠈⠳⣄⡤⠔⠋⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣆⠙⣏⠀⢸⠀⠀⠀⠐⡶⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠦⣈⠳⠼⣦⣀⢤⠞⢁⣤⠞⠓⠖⠒⠉⠉⠉⠳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⢾⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡄⠀⠀⠀⠀⢰⡀⢠⣏⣳⡦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢿⠀⢷⣒⣲⣿⡇⢸⠈⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⠀⢸⣽⢸⢹⠃⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣸⡆⠈⡇⠀⢸⠀⠸⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⣿⠃⠀⢸⣀⣿⠀⠀⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡙⠒⣻⢻⠶⠖⠚⣿⣿⠶⠚⣹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⠛⠁⠈⠦⠤⣼⠋⠈⢓⠚⢋⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠉⠒⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠚⠀⠉⠉⠉⠀⠒⠤⡀⠀⢤⠈⢢⠀⠀ ⠀⠀⠀⠀⡠⠜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣼⠀⢸⠀⠀ ⠀⠀⠠⡀⢃⢝⠍⠉⠭⡐⠶⠤⣄⡀⠀⠀⠀⠈⢆⡘⠀⠀ ⠀⡤⢄⣇⡿⡸⣀⠰⣿⡇⣾⣥⠈⠙⣱⢦⡀⠀⡜⣇⡀⠀ ⢸⠀⣾⣻⠁⠨⡒⠚⠚⠘⢝⡫⠤⣰⠼⠦⢽⢦⣏⠀⠈⡆ ⠀⢣⠈⢻⢠⡀⠘⠔⣂⣀⠤⠔⠂⠀⠀⠀⡜⠀⠙⣯⠉⠀ ⠀⠀⣱⡈⠙⠁⠅⡒⠠⠤⠀⠀⡀⠤⠄⢰⠁⠀⠀⢰⢡⠀ ⠀⠀⢧⠁⠀⠰⣰⣭⡆⡹⠀⠀⡸⠓⠚⠯⣢⠀⠰⠂⠀⡆ ⠀⠀⣘⣆⠀⠀⢱⠒⠊⠀⠀⢰⠵⢧⡦⠷⡡⠇⠀⠀⢀⠇ ⠀⠀⠡⣉⢿⡲⠼⢤⢀⣀⣀⣈⡢⠔⠁⠀⠀⢀⣀⣠⠎⠀ ⠀⠀⠀⠈⠈⠀⠀⠀⠧⠤⠽⠕⠣⠀⣀⣀⠠⠤⠊⠁⠀⠀

⢀⢄⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⣠⣄ ⠈⠢⡑⢤⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⢊⡴⠋ ⠠⡐⣚⣁⡀⠳⠊⡆⠀⠀⠰⡛⠞⠁⣀⣚⠒⡄ ⢀⡁⢀⣠⡛⢀⡀⢧⠒⠒⢲⢁⣀⠚⣇⡀⠈⣀ ⠸⣄⠀⠈⡻⠁⠈⠀⠀⠀⠀⠈⠈⢻⠁⠀⢀⠜ ⠀⠀⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠁⠀ ⠀⠀⠀⠀⡇⠀⠘⠛⣀⣀⡘⠋⠀⢀⠇⠀⠀⠀ ⠀⠀⠀⠀⠘⡄⠀⠀⡓⡗⡁⠀⢀⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠼⡲⠄⣈⣈⡠⠴⡚⢄⠀⠀⠀⠀ ⠀⠀⠀⡠⠃⡜⠀⠀⠀⠀⠀⠀⠘⡄⢣⠀⠀⠀ ⠀⠀⢀⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀ ⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠆⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢆⠀⠀⠖⠑⡆⠀⢀⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⢚⠀⠀⠘⣒⠁⠀⠀⠀⠀⠀

⠀⠖⠀⢠⠀⠀⠀⠀⣠⠀⣠⡄⠀ ⠦⠑⣚⢩⣆⠰⠆⣔⣽⠟⠒⠛⠂ ⠀⠈⠙⡻⡇⠀⢤⠸⠟⠁⠀⠀⠀ ⠀⠀⠜⠂⠉⠉⠂⠀⠂⠀⠀⠀⠀ ⠀⠀⡔⠆⡅⠀⠔⢀⠁⡀⣀⠀⠀ ⠀⠀⠀⠈⠁⠘⣀⠁⠀⠀⢀⢆⠀ ⠀⠀⠀⠀⠀⠀⠸⢃⢶⢲⢈⠉⠀ ⠀⠀⠀⠀⠀⠀⠃⣸⠸⢸⠘⡀⠀ ⠀⠀⠀⠀⠀⠸⠤⠛⣀⠟⠦⠇⠀

⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣴⠶⠦⠴⠦⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀ ⠀⣸⠋⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠄⠀ ⢠⡏⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀ ⣼⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⣄⣤⠶⠾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠛⠉⠉⠉⠉⠉⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⢦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣀⣤⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠀⠀⢀⣤⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⠴⠶⠶⣶⣤⡀⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⠇⢠⣶⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣒⣛⣋⣩⣽⣦⣀⠀⠀⠀⠀⡏⢹⡟⠉⠉⣿⡏⠀⠀⠀⠀ ⣠⢶⣤⣴⡿⣫⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢚⣋⡵⠛⢹⡍⠉⠁⠀⢸⠀⠉⠙⠒⠶⢼⡁⠀⢳⠀⠐⣿⡇⠀⠀⠀⠀ ⠀⠈⣿⣥⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠉⣽⢿⡍⠀⠀⠀⠀⢷⠀⠀⠀⠸⡆⠀⠀⠀⠀⣸⢧⠀⢸⠀⠀⠙⠁⠀⠀⠀⠀ ⠀⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣋⠁⠀⣠⠞⠁⠀⠙⢦⠀⠀⠀⠘⣇⠀⣀⣠⣇⠀⠀⠀⢠⠇⠈⢧⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡏⠁⠀⠉⠛⡿⢧⣀⠀⠀⠀⠈⢷⣤⠤⠞⢻⠉⠉⢰⠉⠓⠦⢤⡞⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣧⡄⠀⠀⠀⠀⢠⡴⠋⣹⣿⣇⣤⣤⣶⣾⠟⠒⠺⢷⣦⣄⣴⠏⠻⡄⠀⠸⡄⠀⢸⠀⠀⢀⡼⠻⣄⣰⠃⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣸⡇⠀⠀⢀⡼⢋⣀⣴⣿⣿⣿⣻⣯⣭⣭⡅⠀⠀⣐⣚⡻⠿⣶⣄⡹⣄⣠⡷⠴⢾⢦⣤⡞⠁⢀⣾⣥⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣇⠀⢰⣿⡿⠋⠁⠸⠿⢿⡛⠉⠉⠉⠙⣿⠛⠛⠛⢻⣿⣿⣷⣾⣿⣿⣥⣿⣷⣤⣾⣿⣿⣿⣛⣻⡇⣚⡟⠒⠒⠒⣶⣖⠀⠀⠀ ⠀⠸⣿⠟⣶⣾⡿⢿⡄⠀⠀⠀⠸⡇⠀⠀⠀⠀⣿⣤⠴⠖⠛⢿⡄⠀⠀⣹⡿⠛⣿⠿⠿⡟⢿⡛⠉⠛⢿⣟⢻⠃⠀⠀⠀⠺⣿⡆⠀⠀ ⠀⠀⠉⣴⣿⡇⠀⠈⣿⠀⠀⠀⢸⡇⢀⣠⡴⠞⠙⢷⡄⠀⠀⠀⢳⣤⠞⠋⠙⢶⣯⣤⣤⣷⠶⢻⡄⢰⠏⢙⣿⠀⠀⠀⠀⠀⠈⠉⠀⠀ ⠀⣠⣼⣿⣿⣧⡄⠀⢸⣧⠀⠀⣸⣿⠋⠁⠀⠀⠀⠀⣽⡄⠀⣠⠞⠻⢦⡀⠀⡼⠁⠀⠀⢹⠀⠀⣹⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢞⣿⣟⣁⣿⣿⡇⠀⠀⣿⣠⡾⠋⠙⣧⡀⠀⠀⠀⠀⠀⣷⡞⠁⠀⠀⠀⠹⣾⣧⣤⣤⣀⣸⣶⠞⠉⢹⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢁⣽⣿⡁⣿⣿⣷⡀⢻⣟⠀⠀⠀⠈⢿⡆⠀⠀⢀⡼⠛⠻⢦⡀⠀⠀⢠⡟⠀⠀⠀⠀⠹⡇⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⠁⠘⣿⡟⠀⢻⣿⠏⠙⣦⡀⠀⠀⠀⢿⣄⣰⠟⠀⠀⠀⠀⠙⣦⠀⡾⠁⠀⠀⠀⠀⠀⡇⢀⡴⠋⡽⠒⠒⠒⠦⣤⡤⠀⠀⠀⠀⠀ ⣿⣄⣤⠾⠛⣿⡄⢸⣿⣧⡀⠈⢻⣄⠀⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠈⣿⠧⠶⠶⠶⠤⢤⣤⣷⠋⠀⣰⠃⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀ ⣿⢿⣯⡁⠀⢿⣿⡞⠉⢻⣷⣄⠀⠹⣦⠀⠘⠁⠙⠳⣄⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⠃⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀ ⡇⠘⣿⣷⣤⣿⡏⢻⡆⠀⣿⣿⣿⣶⣿⣷⡄⠀⠀⠀⠈⠻⣦⡀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣧⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠷⣤⣿⣿⢿⣼⡇⠘⣿⡆⠈⢿⣿⣿⣿⡿⢿⡛⠓⢦⣄⠀⠈⣻⣯⡤⠤⠤⠤⠤⠤⣤⣤⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⡈⣿⣤⠞⢋⣿⣦⣼⣿⣿⠋⣾⡿⠀⠀⠀⠈⠙⠻⢷⣤⣉⣳⣄⣀⡀⠀⢀⣰⠛⠛⠒⠒⢶⡶⠒⠂⠀⠀⠀⠀⠀⠀⠐⣷⠀ ⣀⡀⠈⡿⣷⣿⠷⣄⡛⠀⢸⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡟⢻⡟⢻⣿⡆⠀⠀⠀⠀⠀ ⠀⣀⣀⠀⠀⠸⣿⣿⣻⣟⣿⣿⠇⠀⠀⣀⣀⠀ ⣾⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣷ ⠘⠛⠁⠿⠿⣿⣿⣿⣇⣸⣿⣿⣿⡿⠿⠈⠛⠃ ⠀⠀⠀⠀⠀⠈⣿⣿⡟⢻⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣷⣾⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⠇⠸⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢰⣦⣭⣉⠋⠀⠀⠙⣉⣭⣴⡆⠀⠀⠀ ⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⠻⠿⠿⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠁⠀⠈⠁⢲⠤⠤⠄⠀⠠⠄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⡀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀ ⠀⠀⠀⠀⡰⠃⠀⠀⠀⢠⠃⢠⣖⠅⠀⠀⠀⠀⠀⢀⣠⠄⠀⠈⠱⡀⠀ ⠀⠀⢀⠎⠀⠀⠀⠀⢀⠋⡀⠖⠁⠀⠀⠀⡀⢀⡴⠁⠀⠑⢄⠀⠀⠈⢆ ⠀⠀⢸⠀⠀⠀⠀⢠⡧⠊⠀⠀⠀⠀⣸⣀⡷⡟⠁⠀⠀⠀⠈⢂⠀⠀⢈ ⠀⠀⢸⠀⠀⠀⢀⡾⠀⠀⠀⠀⢀⡟⠁⠟⢽⢧⠀⠀⠀⠀⠀⢸⠀⠀⠞ ⠀⠀⠀⡄⠀⠀⡜⠀⠀⠀⠀⠀⡜⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⡜⠀⠀⡜ ⠀⠀⠀⡇⠀⢰⠁⠀⠀⣀⠴⡊⢢⡀⠀⠀⣶⣿⡇⠀⠀⠀⡐⢁⠤⠊⠀ ⠀⢀⡠⠗⠒⠼⣄⠀⠀⡃⠳⢕⣼⣷⠀⠀⢹⡿⠷⠀⠠⡾⠊⠁⠀⠀⠀ ⢠⠋⠀⠀⠀⠀⣸⢆⣀⠁⠀⢀⠟⠋⢴⣶⢶⡤⠄⠀⢀⡇⠀⠀⠀⠀⠀ ⠘⢿⡀⠀⠀⢀⡟⠀⠉⠉⠂⠉⠢⠤⠤⣬⠁⡠⠒⠂⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⠄⠣⠎⠀⠀⠀⠀⢀⡤⠲⣠⡾⡋⢈⡈⡦⢊⣱⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⠤⠐⠚⠉⠑⢸⠁⠃⠀⠉⠀⡹⡖⠒⠂⠤⠤⣀⠀ ⠀⠀⠀⠀⠀⠀⡇⠈⢉⡐⢶⡤⢀⣸⠀⠀⠀⠣⡾⠖⠁⠀⢀⠔⢨⠃⠀ ⠀⠀⠀⢀⡀⠤⠇⠀⢸⣦⡀⠞⡆⠈⠁⠢⠄⣀⠇⠀⡠⣶⠥⠴⡅⠀⠀ ⠀⠀⠀⠉⠀⠐⡆⠀⠀⢹⠙⠀⠇⠀⠀⠀⠀⠈⢱⠊⡐⡽⣷⠶⠃⠀⠀ ⠀⠀⠀⠓⠒⠒⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠃⠰⠸⢠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠣⠀⣀⡄⠀⢠⠀⠀⠀⠀⠀⠎⠀⣃⠗⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠼⣀⠀⠀⠀⡘⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣠⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣤⡀⠈⠛⠛⠁⢀⣤⣤⡀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⡀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿ ⣿⣿⠀⠸⠿⠟⠙⠻⠟⠋⠻⠿⠇⠀⣿⣿ ⣿⣿⠀⢠⣤⣴⣶⣤⣤⣶⣦⣤⡄⠀⣿⣿ ⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠉ ⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠤⠾⠧⠤⠤⠼⠷⠤⣄⡀⠀⠀⠀ ⠀⠀⣴⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣦⠀⠀ ⠀⢸⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⡇⠀ ⢀⡟⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢻⡀ ⣼⠁⢀⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⡀⠈⣧ ⣿⠀⢸⡇⣿⣦⡴⠷⣤⣤⠾⢦⣴⣿⢸⡇⠀⣿ ⣿⣀⣸⡇⣿⣈⣀⣀⣈⣁⣀⣀⣁⣿⢸⣇⣀⣿ ⣿⣭⣽⠇⣿⣭⣭⣭⣭⣭⣭⣭⣭⣿⠸⣯⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢀⠀⠀⡀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠻⠃⠘⠟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣀⢀⠘⣧⡀⠐⠢⠔⠂⢀⣼⠃⢀⣀⣀⣀⣀⡀⠀ ⢠⡿⠉⢈⡟⠉⠛⠛⠻⠿⠂⠀⠀⠐⠿⠟⠛⠛⠉⢻⡁⠉⢿⡄ ⠘⢷⣄⣾⡃⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⢘⣷⣠⡾⠃ ⠀⠀⠈⠉⠙⠛⠿⣶⡀⠀⠀⠈⠁⠀⠀⢀⣶⠿⠛⠋⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢾⡷⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣠⣄⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⢠⡟⢻⡄⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣧⣤⣀⢠⡿⠀⠀⢿⡄⣀⣤⣼⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⠀⠉⢉⣿⠁⠀⠀⠈⣿⡉⠉⠀⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠳⠶⠛⠁⠀⠀⠀⠀⠈⠓⠶⠞⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⠷⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠁⠠⡦⠀⠀⢴⠄⠈⣿⡇⠀⠀⠀⠀⠀ ⠀⣀⣤⣤⣄⣘⣿⣆⠀⣠⣀⣀⣄⠀⢰⣿⣃⣀⣤⣤⣀⠀ ⣼⡏⠁⠈⠉⠙⠛⠿⠂⠈⠛⠛⠁⠐⠿⠟⠛⠉⠁⠈⢹⣧ ⢻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡟ ⠀⠉⠙⠛⠿⢷⣶⡆⠀⠀⠘⠃⠀⠀⢰⣶⡾⠿⠛⠋⠉⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⡄⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠈⠁⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡟⠁⠀⠀⢀⣴⣶⡀⠀⠀⠈⢻⣦⡀⠀⠀⠀ ⠀⠀⢀⣾⠏⠀⠀⠀⣠⣾⠋⠙⣷⣆⠀⠀⠀⠹⣷⡀⠀⠀ ⠀⠀⢸⣇⠀⠀⠀⣼⡟⠁⠀⠀⠈⠻⣧⡀⠀⠀⣸⡇⠀⠀ ⠀⠀⠈⠻⠷⣶⠾⠋⠀⠀⠀⠀⠀⠀⠙⠿⠶⠾⠟⠁⠀⠀

⠀⠀⠀⠀⠀⠀⣠⠶⠞⠳⠶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠃⢀⡀⢀⡀⠘⣷⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣿⡀⢈⡁⢈⡁⢀⣿⣀⣀⣀⡀⠀ ⢠⡟⠉⠉⠙⠛⠓⠈⠙⠋⠁⠚⠛⠋⠉⠉⢻⡄ ⠈⠿⢦⣤⣀⣀⠀⠀⢠⡄⠀⠀⣀⣀⣤⡴⠿⠁ ⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⠀⠀⣿⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠀⠀⠘⠃⠀⠀⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⣠⡞⠁⠀⢀⡾⢷⡀⠀⠀⢻⣄⠀⠀⠀ ⠀⠀⢰⡏⠀⠀⣠⡟⠁⠈⢻⣄⠀⠀⢹⡆⠀⠀ ⠀⠀⠘⠷⣤⠶⠋⠀⠀⠀⠀⠙⠷⠶⠾⠃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡟⣿⠛⠛⠛⠛⣿⢻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⡾⢿⣿⣿⣇⣿⣦⣤⣤⣴⣿⣸⣿⣿⡿⢷⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⣶⠛⠉⠀⠀⠈⢻⣿⣿⣷⣤⣀⣀⣤⣾⣿⣿⡟⠁⠀⠀⠉⠛⣶⠀⠀⠀ ⠀⠀⢸⡏⢰⣆⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⣰⡆⢹⡇⠀⠀ ⠀⠀⣼⠇⠀⣿⡀⢠⣄⡤⠀⠀⠀⠈⣭⣭⠁⠀⠀⠀⢤⣠⡄⢀⣿⠀⠸⣧⠀⠀ ⠀⠀⣿⠀⠀⢸⡇⠰⠛⠗⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠺⠛⠆⢸⡇⠀⠀⣿⠀⠀ ⠀⢸⡏⠀⠀⢸⡇⢀⣾⣦⡀⠀⠀⠀⣴⣦⠀⠀⠀⢀⣴⣷⡀⢸⡇⠀⠀⢹⡇⠀ ⠀⣼⡇⠀⠀⣾⢧⣾⣿⣿⣷⡀⠀⢸⣿⣿⡇⠀⢀⣾⣿⣿⣷⡼⣷⠀⠀⢸⣧⠀ ⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⢀⣿⣿⣿⣿⡀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⠀ ⢸⡟⠀⠀⠀⣿⣿⣿⠃⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⣿⣿⣿⠀⠀⠀⢻⡇ ⣼⠇⠀⠀⠀⣿⣿⠃⠀⠀⠹⣿⣿⣿⠏⠹⣿⣿⣿⠏⠀⠀⠘⣿⣿⠀⠀⠀⠸⣧ ⠻⣶⣤⣤⣴⣿⠃⠀⠀⠀⠀⠹⣿⡟⠀⠀⢻⣿⠏⠀⠀⠀⠀⠘⣿⣦⣤⣤⣶⠟ ⠀⣿⣿⣿⣿⡇⠀⢘⣷⣏⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣹⣾⡃⠀⢸⣿⣿⣿⣿⠀ ⠀⠈⠉⠉⠉⠛⣿⠿⣷⣷⣶⢶⣶⣶⡶⢶⣶⣶⡶⣶⣾⣾⠿⣿⠛⠉⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⢿⣤⣿⣿⣿⣼⣿⣿⣧⣼⣿⣿⣧⣿⣿⣿⣤⡿⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦ ⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠙⠛ ⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇⠀⠀ ⠀⣠⡾⠟⠀⣿⣷⠀⠀⣾⣿⠀⠻⢷⣄⠀ ⣾⠏⠀⣤⡄⠉⠁⣶⣶⠈⠉⢠⣤⠀⠹⣷ ⠿⣶⡆⠈⠻⢶⣦⣄⣠⣴⡶⠟⠁⢰⣶⠿ ⠀⠘⠟⠻⣶⣤⣀⣙⣋⣀⣤⣶⠟⠻⠃⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⠓⣆⠀⠹⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠘⡆⢹⡄⠀⢳⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢷⡀⠀⢱⠘⣇⠀⣸⠁⢹⡄⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡙⠳⣦⠀⠀⠀⡇⢸⡇⠀⣼⠀⢿⣀⡏⠀⣼⠇⠀⣠⠎⣽⠇⡴⣻⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⠀⠀⢻⠀⢹⡆⠀⢸⠃⢸⣿⣴⠏⠀⠈⠻⣧⠀⢿⡷⠾⠃⣾⡇⡜⢀⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠙⣷⡄⢸⡆⠘⢷⡤⣼⠀⠘⣿⣁⣤⡤⢶⣾⡟⠀⠘⠿⣶⣤⡼⠟⢁⣼⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠘⣿⡟⠁⠀⣀⣤⣾⠀⠀⠙⠻⠤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠈⣧⡀⠘⠿⣦⣾⣯⠽⠋⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠛⠛⠛⠓⠦⣤⡀⠉⢷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⡒⠊⠉⠻⣦⠀⠀⠀⠀⣀⣤⠤⠤⠶⠖⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣹⣿⡶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆⠀⣿⠀⠀⠀⣾⠋⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣾⣏⣀⠀⣰⣧⣤⠴⠋⠉⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⢁⣀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣤⠶⠛⠉⠀⠀⠰⠿⠿⠃⠀⠀⠀⠀⠀⠀⠰⣶⡶⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡶⢟⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣇⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⣍⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠛⠛⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢷⡶⠖⠛⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⢀⡼⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣴⠶⣦⡀⠀⠀⢰⠶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⣶⠀⠀⠀⣠⡶⣶⡄ ⠘⢷⣄⠈⠻⣦⡀⢸⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⣠⡾⠋⢐⣾⠏ ⠀⠀⠙⢷⣀⠈⠳⣾⣤⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣿⡾⠋⢀⣴⠟⠁⠀ ⠀⠀⠀⠀⠙⣶⣤⠞⠁⠀⢻⣆⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⢠⣿⠁⠀⠛⠀⣴⡟⠁⠀⠀⠀ ⠀⢠⡖⠚⠛⠉⠁⠀⠀⠀⠀⠹⣶⡟⠈⢻⡆⠀⠀⠀⠀⠀⠀⣿⡉⠙⣷⠞⠁⠀⠀⡀⠈⠉⠙⠓⠲⣶⠀ ⠀⠀⣷⣤⠶⠶⠟⠋⠻⣦⡀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡾⠋⠛⠲⠶⢦⣼⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠂⠀⠀⠀⢿⣤⠴⠶⠶⠶⠶⢦⣼⠃⠀⠀⠀⠺⠷⣬⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⣶⠛⠛⠛⠛⠳⢦⣽⣆⣀⣤⡴⢶⡄⠈⠻⠀⠀⠀⠀⠀⠸⠇⢀⣰⠶⣤⣄⣠⡿⣠⡶⠛⠛⠛⠛⠳⣶ ⠀⢿⡄⠀⠀⠀⠀⠀⠙⢯⣽⠏⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠈⠻⣯⡿⠁⠀⠀⠀⠀⠀⣰⡇ ⠀⠈⢳⣄⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢀⣴⠟⠀ ⠀⠀⠀⠈⠙⠓⠶⠶⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⠶⠶⠚⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣦⠀⠀⠀⠀⠀⢠⣿⣿⡦⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠉⠉⠉⠀⢀⣀⣀⡀⠀⠉⠉⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⢰⣟⢩⡉⣿⡆⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⡁⠙⠿⠾⠋⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠹⢄⡼⢦⣠⠇⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢠⡾⠋⠉⠛⠒⠲⠶⠶⠖⠒⠛⠉⠙⢷⡄⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠸⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣆⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⣴⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣴⠞⠉⠉⠳⣆⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⢀⣿⠀⠀⠀⠀⣿⡄⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⠤⠾⠋⠀⠀⠀⠀⠘⠷⠤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⣦⠤⠤⠴⠖⠒⠒⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡾⠀⢀⣠⠔⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠙⣻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⢯⡀⠀⠀⠀⠀⠀⠹⣄⠀⠀ ⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⡼⠃⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠳⡄ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡴⠊⠀⠀⠀⠀⠀⠀⠀⣆⠀⢾⣇⣼⡿⠁⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢳ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣼⡵⠋⠀⠀⠀⠀⠀⠀⢀⣄⣴⢻⢰⣼⡏⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣸⣯⠄⠀⠀⠀⠀⠀⠀⠀⣸⡾⠁⢸⡾⣧⣳⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡼⢹ ⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢸⡟⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⡞⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢀⡾⠃ ⠀⠀⠀⠀⢸⡀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣀⡴⠻⣤⠀⠀⠀⠀⠀⡇⣰⣯⣹⡧⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⣠⠞⠁⠀ ⠀⠀⠀⠀⠈⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⡴⣎⠙⣇⠀⢨⣧⡀⠀⠀⠀⢿⣿⣿⣿⣯⠀⠀⠀⠀⠀⡴⢁⡤⠞⠉⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠿⠶⠦⠤⣿⡀⠀⠀⠀⢸⠁⠈⢦⡈⢳⣸⣿⣧⠀⠀⠀⠈⢿⣿⣿⡷⠤⠀⠀⣤⣾⠜⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠸⠇⠀⠀⠈⠳⣟⣿⣿⠇⢀⣀⣀⡉⠉⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠃⢀⠀⠀⠀⠀⠀⠀⢀⣀⡟⢦⡀⣄⠀⠀⠀⠀⣰⠃⠀⠀⠰⢯⣶⠴⣛⡶⠒⠂⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⢿⠀⠀⠀⠀⠀⠀⢀⡟⠇⠈⠛⠿⠓⠲⠖⠚⠻⣄⡀⠀⠀⠀⣙⡉⠁⠀⣀⠤⠴⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠹⣆⠀⠀⣀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠉⠉⣩⢽⠁⡰⠿⡄⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⠤⣈⣧⡞⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⠜⠹⣀⣠⢾⠞⡥⠀⢀⠀⠘⣦⠴⣍⣉⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⠟⠒⢦⠘⢣⡇⢰⠁⠀⠈⡗⠦⠥⠴⢯⣭⣍⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣶⣒⠋⠉⠉⠀⠀⠀⠀⠀⠉⢹⠃⠈⠁⠀⠀⡇⠀⠀⡴⠋⣼⠀⠀⠀⠉⠉⠓⠲⣶⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⠉⠉⠓⣦⠤⣀⡀⠀⠀⢸⠄⠀⠀⠀⠀⢷⣄⣾⢖⡼⠁⠀⠀⠀⠀⣠⠴⠊⡽⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢠⣞⡉⠉⠙⠺⣍⠙⠒⠾⣅⡀⠀⠀⠀⠀⠙⣏⠁⠀⠀⠀⢀⡠⠞⠁⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⡴⠖⣿⠀⠀⠸⣶⣷⣆⢠⡞⠉⡇⠀⠀⠀⠈⠑⠦⣄⡀⣠⠏⠀⠀⣀⠴⣿⠶⠶⠶⠾⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠾⠭⠤⠤⠤⣿⠀⠀⠀⠙⠹⡟⢾⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣤⠞⠁⡼⢉⣿⣠⣤⡁⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡇⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡜⢹⠛⠛⡿⠛⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠒⠒⠶⠶⠶⡿⠀⠀⠀⠀⢸⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡼⢀⠏⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢰⠃⣸⢠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣀⠀⡟⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡿⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⣰⡇⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⣸⠃⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⢀⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⡆⠹⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡠⡀⢘⢱⢰⢸⠐⢸⢀⢔⡄⡶⠀ ⠀⠀⠀⠀⠀⠓⣄⡁⠠⣈⠸⣏⣀⡽⠘⢭⡸⣠⠃⠀ ⠀⠀⠀⢰⣄⣠⡘⠧⠶⠋⠀⢀⣀⠤⠒⠒⠠⣙⢄⡀ ⠀⠀⠀⠀⠑⢢⣸⠀⢰⠊⡉⠁⡀⠀⠀⠀⠀⠀⠉⠉ ⠀⠀⢀⡠⠖⣩⠉⠁⠉⢀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀ ⡴⡾⠁⠀⠀⠁⠀⠀⠀⢈⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⣇⠠⢄⡀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡁⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠙⠲⣄⠀⠀⠀⣠⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠈⠳⣤⠾⠁⢀⣀⡴⠏⠀⠀⠀⠀⣀⣤⠶⠾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠶⣤⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠶⠶⢤⣀⠀⠀⣾⣉⣁⣀⠀⠀⠀⢀⣾⠏⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠃⠀⠀⠹⣆⠀⠀⠀⠀⢳⡀⠀⠀⠀⣷⠀⠀⢀⡴⠦⣄⡀⠀⠀⠀⠀⠀⣀⣀⠀⢹⠄⠀⠉⠉⠉⣹⡇⠀⠀⣾⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⢳⡀⠀⠀⢹⠀⠀⣿⠀⠀⠀⠙⣆⠀⠀⠀⣟⠉⠉⠛⠛⠀⠀⢀⡴⠛⠁⠀⠀⣸⠃⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠻⣄⠀⠸⡄⠀⠙⣆⠀⠀⠀⠹⡄⠀⠀⠙⠶⣄⡀⠀⠀⠀⠘⢧⣄⣀⣠⣠⣿⣀⣀⣀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠈⠳⣄⡀⠀⢹⠀⠀⢳⡀⠀⢹⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⣶⠾⠋⠉⠀⠀⠀⠉⠉⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠻⠶⠟⠀⠀⠀⠀⠈⠷⣀⡀⠀⠀⠀⠀⣀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠶⠶⢶⣾⣤⠤⠶⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⠛⠶⠶⣶⠖⠚⠓⢶⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢄⣀⣀⣀⣀⣀⢀⣀⣀⣀⠴⠖⠉⠁⢀⣴⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠿⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠋⠀⠀⠀⠀⠀⠈⠳⣄⡀⢀⣀⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣀⣀⣀⣀⣀⣀⡤⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⡀⣹⣷⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠼⣿⣦⣀⣀⣀⣠⡼⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡶⠤⠶⠿⠾⣧⠙⠻⠶⠦⠶⠶⠞⠋⠉⠀⢰⡟⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠏⠁⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⠶⠛⠁⠀⠀⠀⠀⣼⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠈⠀⢀⣰⣾⣶⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢶⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣇⠀⠀⣞⣿⠷⠏⠀⣽⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡇⠀⠈⠉⠹⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠉⠉⠀⠀⠀⠛⢷⡴⣶⠀⠀⠀⠀⠀⡀⠀⣹⡏⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠤⣤⣀⣀⣀⣤⠤⠴⠶⠖⣿⣄⠀⠀⠀⣶⣶⣆⠀⠀⠹⣦⣀⣤⣀⣠⣶⡤⠟⠁⠀⢀⣀⡀⠀⠸⣧⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⡀⠙⠟⠃⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣸⣉⣽⠠⢰⡾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢶⣀⠀⠀⠀⠀⠀⠀⢴⣟⣿⡆⠀⠀⠀⠀⠈⠉⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠙⠶⣄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⠾⢿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠶⠶⢦⣀⠀⣀⡴⠶⣶⢦⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠿⠃⠀⢠⡟⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠏⠁⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠛⠶⠶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠘⣇⠀⠈⠉⠉⠉⠉⠉⠉⢻⡇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀ ⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢻⡇⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀ ⢸⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠘⣧⣀⣀⣀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠻⣆⣀⣀⣀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣇⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣆⠀⠀⠀⢀⣀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠤⠤⠶⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⣾⠿⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⡄⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣆⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣧⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⢸⣿⡄⠀⣿⣷⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⡟⠛⠛⠛⠀⠀⠘⢿⣧⣄⣀⣾⡟⠙⢿⣆⠀⠀⠀⠀⠀⢀⣴⡿⢿⣶⠀⠀⠀⣰⣿⠁⠀⢸⣏⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣧⡀⠀⠀⠀⣀⣀⣀⣉⠛⠛⠋⠀⠀⠘⣿⣄⠀⠀⠀⢀⣾⡟⠀⠀⢿⣷⣴⣾⠿⠃⠀⠀⠘⠛⠛⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠿⣶⣶⠿⠟⠛⠛⠛⠿⣶⣄⣀⣠⣤⣾⣿⣶⣶⣴⣿⣋⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠟⣻⣿⡿⠛⠉⠉⠀⠀⠉⠉⠛⢿⣶⣄⣴⡾⠟⠋⠉⠉⠉⠛⠿⣶⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⡾⠟⠋⠉⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⠳⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⡋⠁⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣦⣄⠀⠀⠀⠀⠀⣿⡏⠀⠀⡜⢙⣷⠀⠀⠀⠀⠀⣠⣤⠀⠀⠘⣷⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠛⠷⠶⣦⣴⣿⠁⠀⠀⣿⣿⠇⠀⠀⠀⠀⢰⣧⣼⡇⠀⢰⡏⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠉⠁⠀⠀⠀⢀⠀⠘⠿⠿⠀⢠⣿⠁⠀⠀⠀⣀⣠⣴⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⣴⠛⠉⠙⢷⡄⠀⠀⢸⡟⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣦⣄⠀⠀⠹⠦⣤⠤⠞⠀⢀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠉⠛⠿⣦⣤⣤⣭⣤⣶⠾⠻⣯⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢀⣾⡿⠋⠙⠻⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠿⠿⣷⣿⣏⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⢀⣰⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⡀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠈⠻⣿⣦⣀⣿⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠈⣽⢿⣿⠀⠀⠀⠀⣧⣀⡀⠀⢀⣀⣀⣀⣠⣴⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⢿⣼⡏⠀⠀⠀⢰⡿⠿⠿⠿⠿⠿⢿⣿⠛⠛⠉⢿⣦⡀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⣽⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢸⡟⠻⣶⣄⡀⠀⠀⠀⠙⠻⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⢠⣿⠁⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠻⣦⡈⠙⠿⣦⣄⠀⠀⠀⠸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣼⡟⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠈⢿⣦⠀⠀⠀⢻⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⣿⡇⠀⠀⠸⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢹⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠶⣤⣤⣤⣤⣾⡟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣤⡖⣶⣶⡟⠓⠲⠲⠖⢲⣂⢰⢟⠁⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠑⠚⠛⠛⠛⠛⠻⡷⣶⣤⣤⣤⣼⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣴⡾⠿⠿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠾⠟⠛⠛⠛⠛⣛⣯⣿⡏⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⠁⠀⠀⠀⠀⣀⣶⡿⠟⠉⠻⣷⣄⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⢀⣼⡿⠻⣿⡄⠀⠀⠙⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣀⣠⣤⣤⣤⣤⣤⣬⣭⣀⣀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡾⠟⠋⠉⠉⠀⠀⠈⠉⠉⠛⠻⢷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣤⣾⡿⠛⠛⠛⣿⡟⠛⢻⣿⠛⠛⠻⢿⣶⣤⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠋⠻⠷⣶⡶⠾⠿⠃⠀⠘⠿⠶⣶⡶⠿⠋⠙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡿⠃⠈⢿⣦⣀⠀⠻⠇⠀⣠⣴⣶⣦⣄⠀⠻⠃⠀⣠⣾⡟⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠙⠻⢿⣶⣶⣾⡿⠁⠀⠙⣿⣶⣶⣶⡿⠟⠉⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⣶⠿⠋⠁⠹⣿⣄⣀⣴⡿⠁⠉⠙⢿⣦⡀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⣿⣏⠀⢀⣀⣴⡿⠛⠛⠻⣷⣤⣀⡀⠀⣻⡷⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠙⠛⠛⠛⠛⠙⠻⣷⣶⣾⠟⠙⠛⠛⠛⠛⠁⠀⠀⢀⣾⠿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⣽⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡿⠋⠀⠀⠈⠻⢿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡿⠋⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣄⣠⣶⣶⠶⣶⣶⣽⣿⣄⠀⠀⠀ ⠀⠀⠀⢀⣾⠏⠀⣠⡄⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⣹⡿⠿⠻⣿⣆⠘⣿⡘⢿⣇⠀⠀ ⠀⠀⢀⣾⠏⠀⣼⡿⠁⠀⠀⠈⠻⢿⣦⣤⣀⣀⣀⠀⣀⣀⣠⣤⣶⠿⠋⠀⠀⠀⣿⡅⠀⠀⢈⣿⠆⣿⡇⠈⢿⣦⠀ ⠀⠀⣸⡿⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠟⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠻⣷⣤⣴⣾⣯⣴⡿⠁⠀⠘⣿⡄ ⢀⣴⣿⣷⣾⡿⢷⣶⣦⣤⣤⣀⣀⣀⡀⢠⣾⠿⢿⠿⠿⢿⣦⡀⠀⣀⣀⣠⣤⣤⣾⠟⠉⠉⠻⣿⡅⠀⠀⠀⠀⢻⣧ ⣸⣿⠀⢠⣿⠃⠀⠀⠈⠉⠉⠉⠛⠛⠛⢻⣿⢰⣿⠿⣿⠀⣿⠟⠛⠛⠋⠉⠉⣿⣏⣀⣀⢀⣀⣸⣿⠀⠀⠀⠀⠸⣿ ⢸⣿⣶⣾⡿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⢸⣿⢸⣿⢀⣿⠚⣿⠀⠀⠀⠀⠀⠀⣙⣛⣻⣿⡿⣿⡟⠉⠀⠀⠀⠀⢸⣿ ⢸⣿⢀⣿⣧⣈⡉⠙⠛⠻⠿⠶⠶⠶⠶⢾⣿⡘⠛⢻⣛⣀⣿⡷⠶⠶⠶⠾⠿⠛⠛⠋⢉⣠⣾⣷⠀⠀⠀⠀⠀⣾⡏ ⠈⢿⣾⣿⠉⠛⠿⣶⣶⣤⣤⣀⡀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠋⠀⠀⠀⣀⣀⣤⣤⣶⡾⠟⠛⠉⣿⡆⠀⠀⠀⣰⣿⠁ ⠀⠀⠸⣿⣦⡀⠀⠀⠈⠉⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠉⠀⠀⠀⣀⣴⡿⠃⠀⠀⣴⡿⠁⠀ ⠀⠀⠀⠈⠛⠿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣿⠿⠋⠀⢀⣴⡾⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣝⠛⠛⠿⠿⠿⠿⢶⣶⣶⣶⣶⣶⣾⠿⠿⠿⠟⠛⢛⣭⣿⣛⣡⣤⣴⡿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣤⣤⣤⣤⣤⣾⠟⠙⢿⣦⣤⣤⣤⣤⣤⣴⡿⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⣿⡇⠀⢺⣟⠉⠉⠉⠉⠉⣻⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠶⠶⠶⠷⠾⣿⡇⠀⢸⡿⠷⠶⠶⠶⠾⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣤⣤⣤⣤⣤⣤⣿⠇⠀⢸⣷⣤⣤⣤⣤⣤⣤⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠉⠀⠀⠀⠉⠉⠉⠁⠂⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⢼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀ ⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣄⠀⢀⣠⣧⠀⠀⠀ ⠀⠀⣀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠈⢢⡟⠿⠹⣶⣤⠀ ⠀⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⡏⠁⠀ ⠀⢠⠯⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⢀⡆⣾⣏⣢⣄ ⣀⢟⣶⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠉⢰⡋⢹⡿⠟ ⢸⣿⣿⣿⡿⣻⣆⣀⢤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⢿⣟⣫⠿⣾⢿⣷⡦ ⠀⣸⡿⣿⢧⣴⣿⣽⣾⢇⠀⣆⡀⠰⣄⡀⠀⣵⢀⣶⢾⣽⣿⣾⣿⣿⣭⣀ ⠀⠉⠋⢹⣿⣿⣯⣿⣿⣾⣽⣿⣧⡀⣙⣿⣿⡟⣿⣿⣗⣛⣼⣿⣽⣿⡿⠟ ⠀⠀⠀⢀⣬⣿⣿⣿⡟⣻⠛⠻⣿⣿⣤⣿⣧⣿⡟⠛⣿⣿⣿⣯⡆⠉⠁⠀ ⠀⠀⠀⠀⠉⠻⣿⣤⡛⣳⢦⣼⡿⡁⢈⢻⣧⣼⣷⣿⡟⡷⠻⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⠘⣦⡟⠛⠻⠏⠪⢵⣿⡽⠛⡅⢿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠶⢤⣤⣤⣄⣀⣀⣀⣀⣡⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠉⠉⠉⠙⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⣀⣀⠤⠤⠤⠤⠤⢤⣄⣀⡀⠀⠀⠈⢷⠈⢳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣄⡈⣇⠀⠹⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⢹⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⣀⡤⡤⠖⠒⠒⠒⠒⠒⠶⠤⢤⣀⡀⠀⠀⠀⠀⠀⠹⡄⠸⣇⠀⠀⠀ ⠀⠀⠀⠀⢰⡾⠀⠀⢀⣴⣾⣭⠦⠓⠒⠲⣤⡀⠀⠀⢀⣠⣤⣌⡉⠳⣦⡀⠀⠀⠀⣷⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⢠⡾⠢⣿⡤⠤⠶⠦⠤⣬⡇⠀⢰⣏⣀⣠⣄⠈⠑⢶⠻⣆⠀⠀⢸⡆⣿⠀⠀⠀ ⠀⠀⠀⠀⢸⣇⢀⣾⡁⠀⠁⠀⣿⣿⡆⠀⢀⣠⣀⣀⠉⠉⣽⣯⡉⠛⠚⠃⢽⡆⠀⣼⣇⣿⠀⠀⠀ ⠀⠀⠀⠀⢸⡿⠉⢹⣇⠀⠀⠀⠘⣯⣁⣾⠉⠀⠀⠉⢱⣄⠻⠿⠃⠀⠀⠀⢸⣷⣤⣿⠛⠛⠲⣄⠀ ⠀⠀⠀⣰⠏⠀⠀⠀⢹⠛⠒⠒⠛⠉⠀⠈⠻⠶⠤⠖⠛⠉⠓⠦⣄⣀⣀⣴⠏⠀⠹⣧⠀⠀⠀⠘⣇ ⠀⠀⢠⠏⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠀⠉⣡⡟⠀⠀⠀⠹⣧⣀⢀⣼⠏ ⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠶⠾⠿⠳⠶⠦⠤⠴⠞⠋⠀⠀⠀⠀⠀⢻⠋⠉⠁⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠄⠀⠀ ⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠈⠀⠀⠀ ⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣶⣶⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣰⣄⡀⣠⣀⣀⣀⣀⣀⢀⣀⣀⣀⣤⠀⢀⣀⣀⣀⣀⠀⠀⠠⣦⣤⣀⣠⣠⣀⢤⣤⣄⣤⢤⣄⣤ ⠘⢛⡛⠓⢛⢃⢚⡚⠓⣘⠛⢚⠛⡓⠛⠒⠑⢚⢚⡋⡇⠀⠀⠀⠋⡒⠛⠛⡒⠛⠚⡓⡛⠚⢘⢙⡛

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠒⠂⠀⠈⠉⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠌⠀⢀⠜⠀⠀⠀⣀⣀⠴⠖⡲⠒⠀⠲⠦⠬⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠊⠀⢠⠃⠀⣠⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⡎⠀⢀⠇⢠⠜⠛⠀⠀⠀⠀⣀⣤⣀⡤⠤⢄⡠⣀⡀⠀⢺⡀⠀⠀⠀ ⠀⠀⠀⢰⠀⠀⠸⣰⠏⠀⠀⠀⠀⣴⢊⡁⣉⡡⠀⠀⠰⠉⠍⣳⢦⣘⡅⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⣁⠀⠀⠀⣴⢻⠏⣡⣒⠢⡄⠀⠀⡶⣶⡐⢌⣴⠉⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠹⣆⠀⣦⡃⢈⣠⣰⣿⣃⡰⠀⠀⡯⠯⠄⡾⠣⢵⠀⠀⠀⠀ ⠀⠀⠀⠈⣇⠀⠀⠀⣘⡻⡱⡪⢻⠕⢉⠦⠀⠀⡆⠀⠉⣱⣐⢉⡆⠀⡗⢄⠀⠀ ⠀⠀⠀⠀⠘⡄⠀⠀⠣⡠⠋⠀⠚⠀⠀⠑⠐⠁⠀⠈⠉⠀⠀⠀⠀⠀⣧⠀⠣⠀ ⠀⠀⠀⠀⠀⢡⠀⠀⡰⠁⠀⠀⠘⢄⠀⠀⠀⣠⡤⠶⢾⣦⡆⠤⠒⠈⠀⠀⠀⢡ ⠀⠀⠀⠀⠀⡞⠀⢀⠃⠀⠀⠀⠀⠐⠈⠉⠉⠀⢈⠐⡒⢛⢠⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⢀⠀⠀⠣⢤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠉⠁⠀⠀⠀⠀⠀⠀⢐ ⢀⠀⠀⠀⠀⠀⠀⠉⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂ ⢀⠀⠀⠀⠀⠀⠀⠀⡭⠃⠣⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀ ⠀⠙⠦⣄⣀⣀⣠⠟⠁⠀⠀⠈⠋⠳⣄⣄⡀⠀⠀⡀⠀⠀⠀⠐⢀⣶⠫⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠤⠴⣄⠀⢀⠉⠀⠁⡠⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢉⡒⠒⠋⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠀⠀⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⢶⡞⡏⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠇⠈⣴⡧⠖⠒⠊⠒⠉⠉⠉⠒⠛⠻⢦⠤⠀⠀⠀ ⠀⠀⠀⣰⣇⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀ ⠀⠀⣰⣿⠇⠀⠀⠀⡀⢤⢖⡰⡶⠀⠀⢰⠆⣤⠤⡀⠰⠊⠀⠀ ⠐⠁⠈⢡⠠⡠⠂⡅⠱⣸⢺⣷⣴⢿⠰⢷⣶⡶⣶⢨⡅⠀⠀⠀ ⠐⠄⠤⠊⠀⣇⠀⠂⠀⢸⠘⠛⠃⠈⠁⠘⠛⢱⡇⠸⠑⠀⠀⠀ ⠀⠀⠀⠀⠰⠙⠀⠘⡀⢛⡁⠀⢀⡀⠀⠀⣠⢜⠁⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠀⣑⣜⣿⠐⠲⣺⢪⣅⣇⣬⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⢄⠀⠀⠈⣿⠿⢿⣿⡷⢼⣁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⣆⡉⠉⠀⢱⣶⣼⠃⠤⠒⣻⣿⣿⣟⡿⣿⣟⢻⠀⣀⣀⠀⣀⠀ ⠘⠧⢤⡤⢿⣿⠋⠱⣤⣀⣿⣾⣟⠉⠀⢹⣸⠈⣏⠻⣿⣧⢨⢄ ⠀⠀⠈⠓⢾⡇⠀⠀⢹⣿⠃⠸⣯⠉⠉⢹⢹⡠⢻⣀⣿⠿⠉⠉ ⠀⠀⠀⠀⠀⠈⠣⠔⠁⣼⠀⠀⣿⠀⠀⢸⠀⢣⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣞⣈⣳⣿⣟⣒⠦⣾⣏⣨⡆⠀⠀⠀⠀⠀

⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀ ⢀⠏⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠈⣽⡅⠀⠀⠀⠀⠈⢗⠀ ⡜⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣘⠁⠀⠀⠀⠀⠀⠀⠀ ⠓⢖⢺⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠉⠉⠁⠀⠈⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣷⠀⠀⠀⠀⠀⣀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⣀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⢤⡀⠁⠀⠀⠀⠀ ⢀⡀⣠⢞⣴⠟⠉⠀⠀⠀⠀⠀⠀⢀⡠⣴⢶⠭⠍⢺⠢⢄⣀⡈⢸⠁⣹⡅⠀⠀ ⠁⢻⡵⠋⠀⠀⠀⠀⠀⢀⡠⠔⢨⠷⡉⠀⠈⡄⠀⢸⠀⠀⠀⠷⡀⡄⠘⠁⠀⠀ ⢀⡟⠀⠀⠀⠀⢀⣤⠚⠛⢢⢔⡁⠀⠘⢄⡠⢴⠒⢺⠢⢄⡘⠀⣱⡇⠀⠀⠀⠀ ⠀⢳⠀⠀⢠⠖⣩⣿⣴⡶⠾⠉⠙⣲⣴⡉⢆⠈⣄⣸⠀⡰⠙⡴⠉⡇⠀⠀⠀⠀ ⠈⣿⡀⢰⡗⠉⠛⢻⠛⠋⠙⡖⠚⣻⡶⠿⣿⣯⣷⣤⣿⣶⣾⣏⣻⠒⠂⢶⡀⠀ ⠀⠋⣼⡋⠹⡄⠀⢸⠀⣀⠴⢿⡉⠀⢣⡠⠞⢧⣏⣹⡽⢆⢠⠓⡅⠀⠀⠘⠃⠀ ⣠⡾⢻⣷⠀⢳⢀⡼⣏⠀⠀⠀⢳⣠⠞⠑⢄⡘⠀⠀⡇⡨⢆⢘⠃⠀⠀⠀⠀⠀ ⣎⡽⣏⡿⣦⣸⡏⠀⠈⢦⠀⢀⠜⠳⢄⠀⢨⠋⠉⠉⠋⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⣏⣠⠞⣇⢸⣧⠈⢦⠀⠨⣷⡋⠀⠀⠀⢳⡯⠤⠄⢀⣠⠔⠱⠁⠀⢩⡏⠀⠀⠀ ⡟⣿⡀⣿⣏⠙⣷⣄⣳⡀⠁⠙⢦⡀⢀⡞⠀⠀⠀⠀⠀⡠⠃⠀⠀⠘⠃⠀⠀⠀ ⠧⣽⡿⡿⢸⣦⠹⣿⣿⢿⡖⠢⢄⣙⠾⣤⠤⠤⠤⠤⣖⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⡀⠘⣧⡿⣡⠞⣻⠿⠃⠛⠀⠀⠀⠈⠓⠾⠷⣶⠤⠊⠀⠀⢹⡅⠀⠀⠀⠀⠈⠡

⠀⢷⣿⡿⠟⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠢⢀⡀⠀⠀⠀ ⠀⠀⡤⠒⠟⠻⠛⠛⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀ ⠀⠠⡄⠀⢄⠀⠀⠀⠀⠄⠈⠂⠀⠀⠀⠀⠀⢀⣀⣀⡤⢤⣈⠂⠀⠀ ⠀⠀⣘⣆⠀⢁⡠⠸⢠⠄⠀⠀⠀⠀⠸⣉⠀⠁⠀⢀⡈⠸⣿⢹⣄⠀ ⠒⡎⡸⠠⡦⠞⠀⠀⢯⠀⠘⠋⠀⢀⡰⠿⢦⣀⡀⢈⣡⠔⣿⠀⡛⠃ ⠀⢷⠁⠀⢇⠀⠀⠀⠀⠉⠉⣹⠟⠋⠀⠀⣸⠇⠀⠀⠁⠀⣸⢠⠃⠀ ⠀⠀⣱⡄⠸⡀⠀⠀⠀⠀⡞⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⣾⠊⠀⠀ ⠀⠀⣿⠈⢱⠀⠀⠀⠀⠘⢇⣀⣀⠔⠋⠀⠀⠀⠀⠀⠀⡸⡙⠀⠀⠀ ⠀⠠⡿⠀⠈⡆⠀⠀⠀⠀⠀⠀⢲⡤⠤⢤⠤⠀⠀⠀⣰⠁⡇⠀⠀⠀ ⠀⠀⡇⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢰⢹⠀⠃⠀⠀⠀ ⠀⢸⠇⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡈⢸⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⡇⢸⠀⠀⠀⠀ ⠀⡬⠀⠀⠀⠀⠀⠀⢀⠗⠢⠤⠀⣄⣠⠊⠁⠀⠀⢰⢰⢸⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠶⠶⠶⣶⣤⣄⣀⣤⡶⠾⠿⠿⠟⠛⠛⠛⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠲⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣉⣳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⠀⠀⢀⡀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⣿⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠄⠀⠀⠀⢀⣠⠴⠒⠒⠛⠉⠉⠒⠒⠒⠒⠒⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⢧⡀⢿⣆⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣠⣞⣉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠉⠉⠓⠺⣝⡶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⣹⣆⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡞⠁⠀⠉⢳⡄⠀⠀⠀⠀⢸⡗⡞⠀⠀⠀⠀⠀⠀⠀⠙⣎⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡭⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢀⣠⠤⠾⢧⡀⠀⠀⠀⠈⢷⣷⠤⠴⠶⢶⣦⣄⠀⠀⠘⡆⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣸⡇⠀⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡏⢀⣤⣤⣤⣷⠄⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡉⠳⢄⠀⢹⠀⠀⢹⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⠁⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠋⣛⣿⠿⠯⣤⡀⠀⠀⠀⠀⠀⠁⠘⠛⠛⠽⣄⠈⠛⠸⠂⠀⢸⠀⠹⣦⠴⠲⣶⡀⠀⠀⠀⠘⣆⣿⡟⠀⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡞⠁⢠⡞⠁⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡏⠀⢰⣏⡧⠀⠘⣷⠀⠀⠀⠀⢹⡿⠀⡀⣸⠀⠀⠀⠠⢤⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⢰⡇⠀⢸⣧⣄⣀⣀⡀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⢠⡖⠒⢦⡼⠀⠀⡼⢹⠀⠀⠀⣿⠀⠀⠀⠀⣼⠗⠛⠋⠁⠀⠀⠀⠀⠀⠈⠳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠷⣄⣈⣗⣠⠴⠛⠛⠿⠿⠛⠋⠙⠶⠶⠶⠋⠹⣆⡀⠀⠀⠀⠀⠀⠉⠳⡄⠙⣆⠀⠁⢸⠀⠀⢠⡿⠀⠀⠀⣴⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠛⢾⣟⡛⠭⠭⠥⠖⠃⢀⡽⠀⢸⠀⣰⠏⠀⣠⣾⣁⢀⣠⠾⠋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⠀⠈⠛⠷⣦⣤⣤⣤⣤⣤⡴⢆⠙⠦⣤⣤⣠⣤⣤⡀⠀⠈⠙⠓⠶⠶⠶⠞⠋⠀⢀⡾⢸⣁⣤⠖⠋⠘⢿⣻⣧⣄⢸⣇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡶⠦⠶⠞⠀⠀⠀⠀⠀⠀⠹⡆⠈⠉⠉⠉⠀⣠⠾⠛⠓⠦⣄⣀⡀⠀⠀⠀⣀⡠⠞⠀⢘⣇⠀⠀⠀⠀⠈⢳⡈⢻⣏⣿⣞⣆⠀⠀⢦⠀⠀⢀⣀⡠⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⠽⠚⠃⠀⠀⠀⠀⠀⠀⢠⠙⢦⣄⣠⡤⠞⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⣿⡆⣠⡴⠂⠀⠀⣷⠀⣿⠈⠛⠻⠷⢦⣬⣿⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢷⣄⡀⠀⣀⣠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⡀⠀⠀⠶⢋⣼⠏⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠛⠲⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀ ⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢲⢸⣿⠀⠀⠀⠀ ⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢸⢸⠀⣿⠀⠀⠀⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣸⣼⠀⡿⠀⠀⠀⠀ ⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡞⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣰⠏⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣎⣴⢾⣥⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⡇⠀⠀⠀⢀⣀⣠⣤⠴⠿⠛⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⠾⠛⠒⠚⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢿⣧⣄⡀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠿⣶⣄⣀⠀⠀⠀⠀⠀⣀⣤⠞⠙⢷⣄⡙⠻⣶⣤⣀⡀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡻⠿⣿⠿⠿⠿⠛⠁⠀⠀⠀⠈⣙⠛⠒⢛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠁⠀⠀⠀⠈⠉⠉⠋⠉⠓⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣤⡴⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣟⡋⠙⠿⣦⠀⢀⣠⣾⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⠿⠟⠀⠀⠀⠰⡘⡟⠿⠿⠙⢷⣶⣶⣦⠀⠀ ⠀⠀⣠⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢃⠀⠀⠀⣸⣿⠿⠟⠀⠀ ⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣸⡀⠀⢠⣿⡅⠀⠀⠀⠀ ⠀⠀⠀⣨⣉⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢧⠀⣸⣿⡟⠳⠀⠀⠀ ⠀⠀⣼⡏⠉⠙⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣤⣤⠾⠐⣿⣿⣷⣴⣿⣿⣷ ⠀⣀⣟⢻⣒⣾⣟⣻⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠋⠀⠀⢸⡏⠉⢹⣿⣿⠿⠟ ⠸⣷⣤⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣈⣤⣴⡶⢶⣿⣿⣦⣾⣿⣤⣄⠀ ⠀⣛⣿⣿⣿⣿⣿⡿⢯⣿⣿⣤⣤⡒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠈⠻⣿⣿⣉⣠⠞⠻⣿⣿⢻⣿⣿⡿⠇ ⠀⠉⢙⣿⣿⣿⣿⣶⢀⣴⣿⣟⢿⣷⣾⣧⠀⠀⣠⠀⠀⠀⢠⡄⠀⠀⠀⠀⠘⣇⠀⢠⣤⣠⣼⣻⣟⢿⣦⣾⣿⣿⣿⣏⠉⠁⠀ ⠀⠐⣿⣿⣀⣹⣯⣻⣿⣿⣿⣏⣿⢳⣿⢿⣇⣠⣿⣿⣦⠀⠈⢿⣿⣤⣤⣠⣼⣿⣆⣾⣿⣏⠻⣿⡿⢶⣿⣻⣿⡿⣷⣿⣿⣶⡆ ⠀⠀⠈⠉⠉⠉⢿⣿⣿⣿⣷⣿⣿⣿⢿⣿⣏⣿⣿⣿⢧⣄⠀⠀⠛⣿⣿⣿⣿⡿⢿⣿⣿⣿⢻⡿⢳⣼⣿⣿⣮⣿⣿⣿⡿⠿⠏ ⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣷⡞⠉⣻⣿⡜⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⡏⠉⠿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠋⣽⡿⠀⠀⠸⣿⣿⣿⣿⣶⣿⣿⣿⣶⣿⣿⠉⠈⢹⣿⣿⣿⣿⣿⣷⣋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠋⠿⢿⣻⣇⣀⣽⠿⢿⣧⣄⢀⣶⣿⣿⠉⠁⠹⣿⣿⠏⢀⣼⣿⣤⣶⣾⢿⣯⣥⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⡷⠀⣸⣋⣻⣿⣯⣽⡍⢦⣤⠄⣸⣿⣿⣿⣽⡿⢿⣿⣿⣤⠇⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢷⣤⡭⠙⠋⠉⢿⣿⠙⠳⠶⣾⣿⣿⣭⠙⠉⣇⠘⢿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃⠀⢀⡿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣶⣶⣶⣶⣂⣀⣀⣀⣀⣀⣤⣤⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

🎄🎁🎅🏼🦌❄🎊⛄

⠀⣼⣶⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⢿⣿⠟⠉⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⡁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠟⠟⠋⠉⠁⠀⠀⠀⠙⠂⢤⣄⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⠀⠤⢾⣿⣿⣿⣿⣿⣿⠿⠛⠿⠟⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀ ⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠀⠀⠀ ⠀⠀⢸⣦⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠴⣤⣠⣄⠀⠁⠀⠀⠀ ⠀⠀⠀⠹⣦⠀⠀⠘⢄⠀⠀⠁⠄⠁⠀⢈⠀⠀⠀⠠⠀⠀⠈⢀⠤⠥⠆⣠⠔⠋⠉⠉⠉⠑⠢⣙⣿⣿⢶⣄⠀⠀ ⠀⠀⢀⣠⣼⣧⠀⠀⠐⣴⡴⠀⠘⢢⢖⠋⠀⢀⣀⠀⠀⠀⠀⠈⢳⣤⠎⠁⠀⠀⠀⠀⣤⣤⠀⠈⣿⣷⠀⣿⣧⠀ ⠤⢴⡋⢁⡿⠀⢣⢀⣴⠏⠀⠀⠐⣿⠋⠀⠀⠿⡿⠃⠀⠀⠀⠀⣼⣿⣦⡀⣀⠀⠀⠀⠛⠛⠀⣠⢿⣿⠀⠸⣿⠿ ⠀⢸⠁⡾⠁⠀⣿⡈⠁⠀⠀⠀⠀⠈⠷⣄⣀⣀⣀⣀⣀⣠⡼⠞⠋⠉⠙⢿⡟⠲⠤⠤⠴⣶⠟⠁⠸⣿⠀⠀⣾⠀ ⠀⠸⣾⠁⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣿⠟⠛⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠈⠀⠀⠀⣿⠀⣼⠃⠀ ⠀⠀⠙⢦⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⢀⣼⠏⠁⠀⠀⠀⠀⠀⠀⠀⢘⣿⣴⠋⠀⠀ ⠀⠀⠀⢸⣿⡂⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀ ⠀⠀⠀⣼⡇⠉⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢰⡇⠀⠀⠀⠀ ⠀⠀⢸⣿⠇⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠶⠴⠤⢤⣤⡤⠀⠀⠀⠀⠀⢠⣿⠁⣸⠁⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠦⠴⠜⠁⠀⠀⠀⠀⠀⢀⣿⣿⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡇⠀⡏⠀⠀⠀⠀⠀ ⠀⠀⢸⡟⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢸⠃⢠⡇⠀⠀⠀⠀⠀ ⠀⠀⣼⡇⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⣼⠀⢸⠃⠀⠀⠀⠀⠀ ⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⢰⢿⡀⢸⠀⠀⠀⠀⠀⠀ ⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠛⠶⠦⠀⠴⢦⣠⡟⠁⠀⠀⠀⠀⠀⠀⣸⢸⡇⢸⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠿⠷⢶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣴⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⠉⠉⠉⠛⠛⠛⠿⠶⠶⠶⠶⣦⣤⣄⣀⡀⠙⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⢰⣿⠀⢀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠶⠛⠛⠛⠓⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠻⠷⠶⣦⣀ ⠀⠀⣼⡇⠀⠸⡀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠐⣿⠁⠀⠈⢻⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⣿⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⣿⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣴⢿⠟⢲⣾⠟⠉⠉⠉⠛⠛⠛⢿⡍⢩⡿⠋⠉⠉⠉⠙⠛⠛⢶⣶⠶⠖⠲⣦⣾⢿ ⠀⠀⣿⠀⢸⠁⠀⠀⠀⠀⠀⠀⣠⣴⠶⠿⢧⡀⠉⠉⠁⠀⡾⠁⠀⠀⠀⠀⣀⣀⣀⠀⠻⣿⠀⢀⣀⣀⡀⠀⠀⠀⠀⢹⡆⠀⠀⠀⣿⠀ ⠀⠀⣿⠀⢸⣆⠀⠀⠀⣀⣤⣾⠟⠁⠀⠀⢈⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⢱⣷⡆⢳⠀⣿⠀⡯⣾⣶⢹⡆⠀⠀⠀⢠⡇⠀⠀⠀⢸⡇ ⠀⠀⣿⡀⠀⠻⠷⢶⣾⠏⠁⡠⠤⢄⠀⠀⣼⠀⠀⠀⠀⠀⢷⣠⣀⣀⡀⠘⠦⠽⠵⠋⣰⡟⠀⠳⠬⠵⠞⠀⠀⠀⢀⡾⠁⠀⠀⢀⣾⠁ ⠀⠀⣿⡇⠀⠀⠀⠀⣿⠀⢸⠀⠀⠘⡄⠀⣇⠀⠀⠀⠀⢰⡟⠙⡧⠍⢝⢷⠀⢀⣠⡾⠋⠙⢦⣀⠀⣀⣠⡤⠶⠚⠉⠙⡇⠀⠀⣼⠃⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⣿⡄⠸⡀⢀⡸⠃⠀⠘⡆⠀⠀⠀⠀⠙⠒⣿⣶⡄⠸⠛⠛⠁⠀⠀⠀⠀⢉⣉⣁⣀⣀⣀⣠⡴⠞⠁⠀⠀⣿⠀⠀ ⠀⠀⣸⣷⣄⣀⣠⣄⣿⣷⡀⠈⠉⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⣿⠈⠻⠦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠉⠻⣤⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⣾⠏⠉⠉⠉⠁⠙⢿⣎⢷⡀⠀⠀⠀⣀⣀⢸⡄⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⢹⠉⠉⣿⠉⡟⠉⠉⣿⠉⠁⠀⢀⣠⣀⡀⢰⡏⠀⠀ ⣸⡏⠀⠀⠀⠀⠀⠀⠀⣿⢸⣇⠀⠀⢺⠁⠀⠙⢿⡀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠘⠒⠒⠋⠀⢷⠖⠚⠁⠀⠀⢰⠁⠀⠀⠙⣾⡆⠀⠀ ⣿⣧⠀⠀⠀⠀⠀⠀⠀⣹⡆⠹⣦⠀⠘⢦⡀⢀⣼⠀⠀⠀⠀⠀⣷⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡀⠀⠀⢠⠟⣇⠀⠀ ⠈⠻⣦⣄⣄⣀⠀⣀⣼⡏⠀⠀⣿⠶⣄⠀⠈⠁⢸⠀⡤⠚⠒⡄⠹⢧⣀⠈⠙⠂⠀⠉⠳⣤⣠⡟⠀⠀⠀⠀⠀⠀⠙⠤⠤⠋⢸⡏⠀⠀ ⠀⠀⠀⠉⠈⠙⠛⠋⠁⠀⠀⣸⠋⠀⢹⡆⠀⠀⢸⡆⣇⠀⠀⢸⠚⢄⡉⠛⠲⠶⠶⡶⡶⠞⠋⢀⡷⠀⠀⠀⢴⠋⢲⡀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣄⡀⢀⣇⣈⡓⠒⠁⠀⠀⠙⠒⠒⠛⠉⠉⠉⠙⢛⣋⣤⣤⣤⣄⣈⣓⣊⣀⣠⣴⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⣶⣶⣿⣿⣙⣻⣻⣉⠛⠿⣿⣛⣛⣛⣿⣻⣷⣶⣶⠾⠟⣿⣉⣀⣨⣇⣈⣭⣿⣭⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠛⠛⠫⠭⣿⠽⠿⠿⠿⠿⠯⠯⠯⠯⠿⠽⣯⣉⡉⣽⡯⠭⠤⠤⠤⠤⠤⠔⠰⢾⡯⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢻⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠤⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⣷⣤⣄⡀⢸⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣘⣷⣶⣾⣁⣀⣀⣀⣀⣀⣀⣀⣤⣼⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⢻⣌⠙⢿⠻⠷⠖⠛⠛⢻⣿⠛⠛⠛⠛⠛⠛⠛⣿⡋⠉⠉⠉⣹⡏⠉⠉⣿⠩⣋⠙⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡧⠀⣦⣼⠇⠈⠳⢦⣤⣤⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢹⢻⠟⠛⠉⠀⠀⣾⣡⢂⠜⣦⣬⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣀⡇⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠙⠿⢼⣆⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠾⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠉⠳⠶⢤⣄⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠈⠉⠉⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠈⠫⢽⣒⣦⣤⣄⣀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢶⣶⡶⠞⡁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠒⠒⠖⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢿⡟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠛⠀⣿⠀⣀⣀⣀⣀⡤⣄⣤⠤⠶⠶⠦⣤⣄⣸⣿⣿⣆⠠⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⢠⣾⣿⠾⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⠒⠓⢤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⡇⢀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⢳⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡼⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⢀⡦⣿⡏⠉⠉⠁⠈⡹⡖⢶⣦⠤⣀⠀⠀⡷⠊⠀⠀⠀⠀ ⠀⡠⠒⠘⠿⢋⠁⡄⠀⠀⢀⠠⠔⠚⡁⠀⣿⢸⣹⡁⠃⣸⣶⠀⢀⣶⡁⣇⡜⠈⡆⠸⠙⡶⠁⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⡆⠘⡤⠊⠁⠀⡇⠀⢻⣶⡿⢽⣿⣿⣿⠟⠻⣆⡼⢻⣿⣿⣿⢿⣷⡇⢰⣷⠀⠀⠀⠀⠀⠀ ⠐⢄⠀⠀⢀⡼⠁⠀⢻⠀⠀⠀⡄⠀⠀⢘⡇⠨⣽⡿⠿⠀⠀⠋⠀⠰⢿⡿⠟⢸⠿⠀⢸⠙⠧⠀⠀⠀⠀⠀ ⠀⠀⠉⠋⠁⠀⠀⠀⣾⣇⠀⠀⢰⠀⠀⡌⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡆⠀⡜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠏⢸⠀⠀⠈⡇⠀⢡⢧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠇⣰⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⢳⠀⠀⠸⣄⠘⣿⣶⣤⣄⣘⣉⣛⣦⡤⠔⢺⠏⠀⡼⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣦⠀⣠⣬⣦⣼⣿⣄⠈⠙⢢⣼⡍⢻⣦⣼⣇⣰⡽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠹⣿⣿⡿⣿⣿⣿⣿⣷⣄⡟⡏⠹⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣘⡍⢣⡀⠀⠀⠀⣼⡟⠛⠁⠈⢿⣿⣿⣯⣈⣷⣿⣼⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠧⠀⠀⠀⠃⠀⢙⣿⣷⣤⡟⠳⠶⠶⠶⠚⣿⣿⣿⣿⣿⡿⣻⣾⣿⣿⣿⠙⣯⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀ ⠸⣯⣥⠠⠄⠀⢀⣾⣿⣿⣿⠛⢦⡀⠀⠀⠀⣿⡛⣫⣿⣿⠿⠋⠀⢹⣏⢻⣄⡿⣶⠶⣿⣿⣿⣄⠀⠻⡁⠀ ⠀⠘⠓⠒⣲⣶⠻⠊⣿⣿⠃⠀⠈⢿⣦⣀⣸⣿⣿⢿⣿⡁⠀⠀⠀⢘⣿⣼⡇⠀⣿⡄⠹⢿⣿⣿⣇⢠⠛⣆ ⠀⠀⠀⠀⠛⠿⣤⣾⣿⠁⠀⠀⠀⠈⢻⣿⣿⠋⠀⢺⣿⡛⠛⠛⠛⢻⡟⢹⡇⢀⣿⣧⠈⢸⣿⣿⡏⠙⠛⠋ ⠀⠀⠀⠀⠀⠀⠈⠙⠾⣤⣄⠀⠀⣠⠟⢻⣯⠀⠀⠈⣿⡇⠀⠀⠀⠸⣗⠈⣷⡚⠃⢿⣦⡼⠟⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠞⠁⠀⣼⣇⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠀⠹⣧⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠷⣄⡰⢾⣿⣇⣀⡀⠀⠀⣿⡴⠆⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣤⢤⣬⣷⣾⡿⠤⣬⠽⠿⠿⡿⠧⣤⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠒⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠙⠋⠛⠒⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣴⡴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢾⡍⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡻⠋⠋⠻⢿⣷⡀⠀⢀⣀⣴⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⢻⣿⣿⡆⠀⠀⠈⠁⣆⠘⡿⣯⣿⣿⠟⣯⣥⣦⣄⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣄⣠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠘⡇⣧⠀⠙⠙⠀⠘⣿⣿⣿⣿⡓⠀⠀⠀ ⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢹⡀⠀⠀⠀⢰⣿⡿⠿⠋⠀⠀⠀⠀ ⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡘⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⡛⠛⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢹⡀⠀⢠⣿⣿⣿⢦⠄⠀⠀⠀⠀ ⠀⠀⠀⢤⣾⠷⠶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠁⠀⠀⠈⣷⢠⣾⣿⣿⡀⠈⢠⣤⣄⡄⠀ ⠀⠀⠠⣿⣇⠀⠀⢨⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⢿⣿⣶⡶⠞⠛⠨⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆ ⠀⢀⣸⡉⢻⣗⣲⣾⣛⣻⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⡾⠋⠀⠀⠀⣸⡟⠈⠉⣽⢿⣶⣿⡿⠟⠀ ⢸⣻⣄⣉⣳⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⣋⣀⣠⣤⣤⣴⣿⠹⣆⣠⣿⣞⡁⢀⠀⠀⠀ ⠀⣻⣿⣿⣿⣿⣽⣿⣿⡿⣿⢻⣿⣷⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠙⢿⣿⣶⣶⣿⠾⠛⢉⣿⣿⣿⣾⣷⣾⣿⣿⣯⣾⡀⠀ ⠀⣤⣽⣿⣿⣿⣿⣿⣿⡟⠛⠻⠷⣿⣿⣾⣷⡈⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠙⢿⣿⡵⣤⣴⠋⠉⢙⣿⣿⣏⣿⣿⣿⣿⠓⠃⠀ ⠀⠀⠀⣙⣿⣿⣿⡿⣾⣶⠂⢠⣶⣿⣿⠛⣿⣷⣾⣿⡆⠀⠀⢀⡦⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣤⣦⣰⣬⡍⢻⣎⢿⣷⣶⣾⣿⣿⣿⣿⣍⠉⠀⠀⠀⠀ ⠀⠀⠴⣿⣿⠍⠘⣿⡙⢿⣿⣿⣿⣽⣿⢻⣾⢫⣽⣾⣻⣆⠀⣸⣷⣶⣆⠀⠀⠘⣿⣶⣆⣂⣀⠀⣀⣾⣿⡆⣬⣿⣷⡞⢿⣿⣿⣿⣦⣻⡿⢿⣿⣿⣿⣨⣿⣿⣆⣤⡄⠀ ⠀⠀⠘⠛⠿⡿⠿⠿⣿⣷⣶⣾⣿⣍⡻⣿⣷⡾⣿⠣⣿⡿⢺⣿⣯⣿⡟⠁⠀⠀⠙⢹⣿⣿⣿⣷⣿⣿⣿⣿⣎⣿⣼⣿⣧⣭⣿⣍⢸⣿⣿⣿⡛⢿⣮⣯⣿⣿⣿⣿⡧⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣏⣾⡿⣶⣿⣿⣿⣿⢛⣶⣄⠀⢀⣀⣘⣿⣿⡏⣿⣿⠈⢹⣿⣾⣿⣿⣨⡟⣉⣱⣿⡷⣽⣿⣿⣾⣿⣿⣿⡽⠛⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⣻⣿⣿⣼⣿⣿⣧⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣵⡟⠉⠉⣿⣿⣇⢹⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠿⡍⠀⠙⠿⠿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⢉⣽⣿⠀⠉⠀⣿⣽⣿⣿⣿⣿⣦⣶⣿⣿⣿⣷⣼⣿⣿⡏⠉⠉⢿⣿⣮⣿⣿⣿⣿⣿⡶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢿⣿⣿⢿⣿⠛⠛⢿⣦⣼⣿⠋⠀⠀⢀⣠⣽⣿⡿⠿⠟⠺⣿⣿⣿⣿⠛⠛⣿⣿⡁⢀⣀⣴⣿⣿⡿⠛⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢿⣼⣿⣦⣤⡿⠋⠙⣿⣿⣿⣄⣼⣿⣿⡿⣅⠀⠀⠀⠿⢿⣿⣏⣀⣴⣿⣿⣿⣿⣿⣿⡟⢿⠷⠾⠶⢿⣿⣿⠻⠅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡿⢿⡿⠀⡄⣿⣉⣙⣿⡿⢷⣼⣧⠨⣵⣤⡶⢀⣼⣿⣿⣿⣿⣾⡿⠻⣿⣿⣿⣥⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠘⣷⡀⣐⡟⠛⠛⠋⠛⣿⣿⡍⠳⣦⣤⣴⣿⣻⣿⣙⡛⠛⠛⣇⠀⢿⣿⣿⡟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠹⢿⡿⡆⠀⠀⠀⠀⠘⠉⠁⠀⠀⠈⠸⠿⢿⣿⣿⡁⠀⠀⣿⠀⠈⠘⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⣟⣃⣀⣀⣀⣤⣤⣤⣤⣴⣶⡶⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣴⠟⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠹⢿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠒⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣦⡀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀ ⠀⠀⣰⡿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣧⣄⠀⠉⠀⠈⠉⠙⠛⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀ ⠀⢠⡿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⣷⣄⠀⠀⠀⠀⠀⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⢷⠀⠀ ⠀⣾⠁⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢾⣷⣦⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠁⠀⢀⢀⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡶⠶⠿⠿⠿⠶⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠶⣶⠞⠛⠉⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⣦⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡴⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣀⣐⣶⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣴⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠶⠶⠶⠶⠶⠶⡶⣶⣀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⣴⣶⣾⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠶⠿⠛⢉⣩⣿⣄⠀⠀⠀⠀⠀⠀⢰⡇⠊⣿⠟⠉⠉⢻⣷⠂⠀⠀⠀⠀⠀ ⠀⢀⣀⠀⢀⣴⡿⠋⣠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⣻⡿⢻⡗⠶⠖⠛⠋⠉⢸⠉⠛⠶⣤⣤⣀⣀⣸⠁⠀⢻⡄⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀ ⠚⠛⣿⣿⠿⢟⣰⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⣿⣥⣤⠶⠛⠉⠀⠀⢿⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⣿⡄⠀⠀⡇⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⣴⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠀⣰⡟⢻⣆⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡏⢳⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠏⠀⠀⠀⣠⡾⠃⠀⠀⠙⢷⡀⠀⠀⠀⠀⢹⡆⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⣼⠁⠈⢷⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠉⠉⠛⠷⣶⣾⡋⠀⠀⠀⠀⠀⠀⢿⣄⢀⣀⣠⠾⣿⠛⠛⠉⢽⠛⠶⣤⣀⣀⣸⠇⠀⠀⢈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⣿⣿⡇⠀⠀⠀⠀⣀⣼⣌⣙⣷⣦⡀⠀⠀⠀⣀⡿⣯⠉⠁⠀⢻⠀⠀⠀⢸⠀⠀⠀⠉⢹⣿⡀⠀⢀⡾⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣷⡆⠀⠀⠀⠀⠀⣠⣾⠟⠁⢰⣿⣿⣧⣶⣾⣿⣿⣿⣏⠉⠉⠉⠛⠿⣷⣦⣶⡟⠀⠙⣧⡀⠀⠘⣇⠀⠀⣸⠀⠀⠀⣠⡟⠀⢻⣤⡞⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⢠⣾⠟⢁⣀⣴⣿⣿⣿⣿⣿⣭⣭⣭⣭⣥⠀⠈⠀⣀⠛⠛⠛⠿⢿⣷⣤⡘⣧⣀⣠⣿⢦⠶⡿⣦⣄⣴⠏⠀⢀⣴⣿⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⣿⡇⠀⠀⢰⣿⣿⠟⠋⠉⢹⣿⣿⣿⠟⠛⠛⠛⠛⠛⢿⡟⠷⠶⠶⠿⢿⣿⣿⣷⣬⣽⣿⣿⣟⠉⣿⣷⣄⣠⣼⣿⣿⣶⣾⡿⠿⠿⠋⠸⢿⠇⠤⠤⠤⣤⣶⡤⠀⠀⠀⠀ ⠀⠀⣿⢻⣿⣄⣀⣻⣿⣿⡀⠀⢀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⢸⣷⠀⢀⣀⣠⣾⣷⠛⠛⠉⠛⢻⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠿⣿⣿⡿⣧⣾⣿⠀⠀⠀⠀⠘⣽⣿⣄⠀⠀⠀ ⠀⠀⠻⡿⠁⣽⣿⠻⠋⠛⣿⡀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⢀⣸⣿⡞⠛⠉⠁⠀⠙⣷⠀⠀⢀⣼⢿⣏⠀⣿⠋⠉⢻⡇⠙⣷⡄⠀⠀⢨⡿⣦⣨⡇⠀⠀⠀⠀⠀⠙⢷⣿⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⡄⠀⠀⢻⣧⠀⠀⠀⠀⣼⡧⠀⣠⣴⠾⠛⠉⠈⢿⣦⠀⠀⠀⠀⠙⣧⣴⠟⠁⠀⠙⣷⣯⣤⣤⣼⣿⠾⠋⢿⡀⢠⡟⠁⢈⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀ ⠀⠀⣀⣾⣿⣿⣿⣁⡀⠀⠀⣿⡆⠀⠀⠀⣿⣷⠿⠋⠁⠀⠀⠀⠀⠀⡹⣧⠀⠀⢀⣴⠿⢷⣄⡀⠀⢀⣿⠁⠀⠀⠈⢹⡀⠀⠈⢿⣼⠁⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣯⡿⠋⣻⣿⣿⡇⠀⠀⢹⣧⠀⣠⣼⠟⢿⣦⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⣴⠟⠁⠀⠀⠉⢻⣆⣸⠃⠀⠀⠀⠀⢸⡇⣠⡾⠛⢻⡄⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣥⡾⠻⣷⣶⡿⢻⣿⣇⣄⠀⢀⣿⣴⡟⠁⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⢀⣼⣿⣁⠀⠀⠀⠀⠀⠀⢹⡿⠚⠛⠛⠛⠲⢾⡿⠋⠀⠀⠈⣧⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠄⣠⣿⣿⣄⢸⣿⢿⣿⣦⠀⣿⣯⡀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⣠⡾⠋⠈⠙⢷⣦⡀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡾⠛⠁⠈⣿⣾⡇⠀⢿⣿⣼⠏⠙⢷⣄⠀⠀⠀⠀⠈⢿⣆⢀⣴⠟⠀⠀⠀⠀⠀⠈⢿⣄⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⠟⢩⡟⠒⠒⠒⠤⢤⣤⣤⠤⠀⠀⠀⠀⠀⠀ ⣿⡅⢀⣀⣴⠿⢿⣧⠀⠀⣿⣿⡄⠀⠈⠻⣧⡀⠀⠀⠀⢾⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣇⣀⣀⣀⣀⣀⣀⡀⠀⣿⣴⠟⠁⠀⡾⠁⠀⠀⠀⠀⣨⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡟⠍⠀⢸⣿⣧⣰⡿⢿⣿⣆⠀⠀⠹⣷⣄⠀⠀⢠⡟⠻⣯⣀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠉⠉⠉⠉⠉⠉⠉⠉⠛⣿⠃⠀⠀⣾⠁⠀⠀⠀⠀⠀⣹⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⣿⠛⣿⣷⣄⠀⢘⣿⣿⣿⠀⠀⢿⣿⣷⣄⡀⠈⢿⣆⠀⠈⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠹⠟⠃⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⢻⣿⣿⣤⣼⣿⡏⢻⣷⠀⠸⣿⣿⣿⣿⣷⣾⣿⣶⡀⠀⠀⠀⠀⠀⠙⢿⣦⡀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⣄⣘⣿⣿⣿⡇⣿⡇⠀⣿⣧⡄⠈⢿⣿⣿⣿⣿⣿⣿⣿⡟⠶⣦⣤⣀⠀⠀⠙⢷⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢼⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠙⠻⣿⣿⠌⢿⣿⠃⣠⡿⢿⣧⡀⠈⣿⣿⣿⣿⠟⣥⣼⠇⠀⠀⠘⠛⠷⣤⣴⡟⡉⠙⢦⣄⠀⠀⠀⠀⠀⠉⠉⢹⣟⣤⣤⣀⣀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀ ⠀⠀⠀⢺⣿⣆⢸⣿⡾⠋⢀⡴⠟⢿⣾⣿⣿⡿⠀⠰⠿⠟⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣶⣦⣭⣳⠤⣤⣤⣀⣀⣴⠟⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⡀ ⣀⣀⠀⠀⣿⢿⡾⠟⠿⣶⣉⠁⠀⢸⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⢸⣟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⣸⣴⣶⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⡿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠿⣟⣅⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠿⠟⠋⠉⠉⠉⠙⣧⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⡿⡿⡿⠟⠽⠋⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣤⠀⠾⠚⢿⣿⣿⣿⡿⢿⠿⢟⠿⠟⠙⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣦⠀⠀⠀⠀⠘⠶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣗⡀⠀⠀⠘⣄⠀⠀⠀⠀⣄⠀⣄⡀⠉⠲⠄⠀⠀⠈⠑⠀⠁⠀⠠⡄⠀⠀⢤⡀⢀⣀⠀⣠⡴⠦⠤⣭⣭⣉⠛⠶⣿⣤⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠈⠳⣄⠀⠀⠀⠱⡀⠀⠀⢠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣖⡳⠒⠛⢀⡴⠛⠁⠀⠀⠀⠀⠀⠈⠻⢦⣹⣿⡟⠿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣸⣷⡀⠀⠀⠘⢆⣦⡴⠆⠘⠓⣠⠞⠛⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢳⣀⣴⠋⠀⠀⠀⠀⠀⠀⣤⣤⣀⡀⠀⢻⣿⣷⠀⣾⣿⣆⠀⠀ ⠀⠀⣀⣀⡴⠟⢁⣿⠀⢳⡄⠀⢠⣾⠏⠀⠀⠀⣴⣯⠞⠀⠀⢰⣿⣿⡧⠀⠀⠀⠀⠀⠀⣙⣿⣧⠀⠀⠀⠀⠀⠀⠀⢽⠿⠿⠄⠀⣸⣿⣿⠀⠉⣟⣿⣶⠄ ⠈⠉⠉⢹⡷⠀⣼⠃⠀⢦⣷⠴⠟⠁⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⢄⣴⡿⠟⠿⣿⣦⣓⠄⠀⠀⠀⠀⢀⣀⣤⡞⠉⣿⣿⠀⠀⠈⡿⠈⠀ ⠀⠀⠀⢸⠀⣼⠏⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣶⣤⣤⣤⣤⣤⣤⣤⡾⠟⠉⠀⠀⠀⠈⢿⣏⢉⡛⠒⠒⠒⠻⣿⠋⠀⠀⢻⣿⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠸⣶⡏⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣹⣿⠿⠙⠂⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣱⣿⠀⣠⡿⠀⠀⠀ ⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢀⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣔⡀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡿⣧⡀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⡇⠈⠉⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⢀⣤⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣧⡇⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣴⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣼⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠛⠛⠛⠛⠛⣛⡿⠛⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⠷⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢸⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣯⡏⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢸⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⢠⣿⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡞⠁⠀⠀⠀⢸⣿⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣼⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡷⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⢠⡟⢸⡆⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢐⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠟⠁⠘⠛⠛⠓⠖⠀⢚⣿⣤⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⠿⠛⠋⠁⠀⠀⠀⠀⠉⠙⠛⠻⢿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⠶⢶⣶⣶⣤⣀⣈⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⡿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠉⠻⣷⣶⣶⣄⣠ ⠀⠀⠀⣿⡿⠀⠀⢧⠀⠀⠀⠀⠀⠀⣼⠟⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿ ⠀⠀⣠⣿⠇⠀⠀⢸⣧⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷ ⠀⢀⢹⣿⠀⠀⠀⠀⢹⣷⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯ ⠀⢸⢸⣿⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿ ⠀⢸⢸⣿⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣰⡿⣿⠷⣶⣶⡿⠟⠉⠙⠛⠻⠿⠶⠾⣿⣟⠛⢛⣿⡿⠟⠛⠛⠛⠛⠻⠿⠷⢶⣶⣦⣤⣴⠶⢦⣄⣤⣾⣿ ⠀⠸⢸⣿⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⡟⠛⠛⠛⠛⠚⠁⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠙⢿⣇⠈ ⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠋⠉⠻⡄⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⣠⢴⣒⠲⣄⠀⠘⣿⠀⢀⡤⢶⠒⢶⣄⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠘⣿⡀ ⠀⠀⠸⣿⠀⠘⣿⡄⠀⠀⠀⢀⣤⣶⣾⡿⠋⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢰⡇⢸⣿⣷⢈⡇⠀⣿⠀⢸⣵⣿⣿⡇⣿⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⣿⠀⠀⠙⢿⠷⣶⣶⣾⠏⠉⢀⣠⣤⡀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢸⣇⢀⠀⠀⠀⠀⠘⢷⣌⣻⣵⠾⠁⣰⡟⠀⠸⢧⣌⣯⡶⠋⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⣰⡿⠁ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⢈⢻⣿⠀⢠⠟⠀⠀⢸⡆⠀⢰⡏⠀⠀⠀⠀⠀⠀⣴⣿⠻⣟⠛⢛⠷⣦⡀⠀⠀⠀⣀⣴⠟⢿⣤⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠿⢷⣤⠀⠀⠀⢠⣿⠃⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⢸⠀⠀⠀⢠⡇⠀⠈⢷⡀⠀⠀⠀⠀⠀⢿⡀⠀⣻⣛⠈⠱⢹⣧⣀⣴⡾⠟⠁⠀⠀⠙⣿⣦⠤⠴⠖⠛⠉⠁⠀⠀⠀⣠⡿⠀⠀⠀⣿⠃⠀⠀ ⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⡀⠈⢧⣀⣀⡼⠃⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣟⡀⠸⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣀⣠⣤⠶⠾⠋⠀⠀⠀⠀⣿⡀⠀⠀ ⠀⠀⠀⣿⣿⣤⣀⣀⣠⣄⢸⣿⣷⠀⠀⠉⠉⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠻⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⢰⣿⠟⠛⠛⠛⠛⠉⠛⢿⣷⡻⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⢻⡟⠛⠻⣿⠟⢿⡿⠛⠛⢻⡿⠛⠛⠉⠁⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀ ⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⢹⣷⠀⠀⠀⢠⡶⠒⠒⢦⣻⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣿⠀⢸⣇⣀⣀⣿⠃⠀⠀⠀⣠⠖⠊⠓⠲⣤⣿⡃⠀⠀⠀ ⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣄⠀⠀⢸⡇⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⣿⠉⠉⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀ ⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠈⢿⣆⠀⠀⠻⣄⡀⠀⣠⡟⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣄⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣠⠟⣿⠀⠀⠀ ⠈⠹⣷⣄⡀⣀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠸⣿⣦⣀⠀⠈⠉⠉⠉⣇⠀⢀⡴⠶⢦⡀⠘⣷⣄⠀⠉⠙⠲⠀⠈⠉⠳⢦⣀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⣀⡠⠋⣰⣿⠀⠀⠀ ⠀⠀⠈⠛⠿⠛⠿⣶⣶⣶⠿⠛⠀⠀⠀⣼⡏⠉⢻⣆⠀⠀⠀⠀⣿⠀⡜⠀⠀⠀⢹⣄⡌⠛⢷⣦⣄⣀⣀⠀⠀⠀⣀⣽⣷⠟⠡⣄⠀⠀⠀⠀⢀⣤⣤⡀⠀⠉⠀⠀⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣰⡿⠀⠀⠈⢻⡆⠀⠀⠀⢻⠀⢸⡀⠀⢀⡼⠀⠙⢦⣄⡀⠈⠉⣉⣽⣿⣿⣍⣁⣀⣀⣴⠟⠀⠀⠀⠀⠹⣅⠀⢸⠄⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣄⣀⠀⣸⣄⣀⣙⠛⠋⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠀⠀⠉⢉⣉⣀⣤⣤⣤⣤⣄⣀⣈⣙⣁⣀⣠⣤⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣧⣤⣴⣾⣟⣿⠛⠿⣟⣿⠙⠻⠿⠶⣶⡾⠿⠿⠿⣿⡿⢶⣶⣶⣶⣶⡶⠾⢿⣟⠉⣉⣉⣿⣉⣉⣉⣿⣟⣛⣿⣿⣭⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢿⣿⣿⣿⣿⠿⢿⣿⡿⣷⣶⣶⣿⣿⣿⡿⣿⣿⢿⣿⣿⢛⣿⠓⠒⠒⢺⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⢉⣹⣿⠓⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠈⠉⠙⣿⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⢻⡗⠀⠒⢺⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⢹⣿⠈⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠒⠲⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠸⣿⣷⣤⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣶⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⢻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠹⣯⠙⠻⢿⣶⣿⣦⣤⣤⣶⣶⣶⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠟⠛⠛⠛⠛⢿⡟⠛⠛⢿⣿⢛⠿⠛⣾⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⡀⠀⢀⠙⢷⡄⠈⣿⣄⠉⠉⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⣀⣀⣴⡿⠁⠀⢀⣼⢏⠈⠳⣦⠀⠻⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⢸⡷⠾⠇⠀⠈⠙⠻⣶⢶⡶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡏⢻⠉⠉⠁⠀⠀⠀⣼⣇⣼⢡⡆⠙⣶⡶⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣷⣄⣸⡇⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠈⠻⢿⣼⣇⣀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠓⠻⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠛⠛⠛⢷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠉⠉⠛⠛⠳⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⢸⡷⢦⣤⣀⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣷⣤⡀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠚⠛⠛⠯⠤⠤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠛⠿⠿⣭⣭⠿⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⠉⠉⠀⠀⠀⠀⠈⠉⠉⠛⠶⠦⣄⡀⠀⠀⠀⠀⢰⣀⡀⠀⠈⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⢻⡇⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣯⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠸⡇⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣿⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⢸⡇⠐⢒⠖⠒⠒⠒⠒⠲⠶⠶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⢰⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣦⡀⠈⣷⣴⠃⣴⠞⠉⠉⠉⠙⠢⣄⠈⢷⡼⠟⠛⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣸⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢯⠉⢻⣯⡇⢸⡇⠀⠀⠀⣤⣶⣦⣸⣆⠀⣠⡶⠞⠛⠛⠲⢭⡛⠶⣤⡀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀ ⢀⣴⠖⠲⣄⣸⡆⣼⡟⣇⠈⢷⣀⠀⠈⣿⣿⣿⢯⡏⢸⢱⣾⣷⣦⠀⠀⠀⠙⣄⢸⣿⣶⣤⠀⠀⠀⠀⣿⢃⡏⠀⠀⠀⠀⠀ ⣾⠃⠀⠀⣨⡿⣿⣽⠃⠙⢧⣀⠉⠒⠲⠼⠟⢛⣉⣴⠘⣞⣽⣿⡟⠀⠀⠀⢀⡟⣼⢀⠏⠻⣷⣆⠀⢰⣧⡾⠋⠉⠉⠳⣄⠀ ⣿⠀⠀⢿⣿⡖⢋⡇⠀⠀⢀⡉⠙⠓⠒⠒⠚⠉⠁⠈⢳⣌⠛⠶⠤⣤⡤⢶⣋⣴⠿⠿⢤⣄⣠⣿⣧⣾⣿⠀⠀⠀⠀⠀⢹⡄ ⢻⡄⠀⠸⣿⢷⣾⠀⠀⠀⠀⠘⢦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⠤⠶⠛⠋⠀⠀⠀⠀⠀⣸⡇⠙⠳⣿⡧⣀⣀⣀⣠⠟⠀ ⠈⢿⡀⠀⠙⠿⣿⢦⣄⠀⠀⠀⠈⠻⣍⠓⠲⠤⠤⠤⠤⣤⣤⡤⠾⠄⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠈⢻⣦⡉⠉⠀⠀⠀ ⠀⠈⢷⡄⠀⠀⣿⣄⡭⣳⣤⡀⠀⠀⠈⠙⠒⠲⠶⠖⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢻⣳⣄⠀⠀⠀ ⠀⠀⠀⠻⣦⡀⡟⠙⢏⡟⠀⠉⠙⠲⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⡟⠀⠀⠀⠀⠀⠀⠀⡇⠻⡆⠀⠀ ⠀⠀⠀⢰⣇⣠⡇⠀⠀⠁⠀⢰⠓⠲⢤⣀⣀⠉⠉⠉⠒⠒⠶⠶⠶⡖⢒⡋⠉⠉⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⡄⠀ ⠀⠀⠀⢸⡀⡼⠀⠀⠀⠀⠀⣿⢀⣴⠿⠻⣦⡉⠙⢓⡦⠀⠀⠀⠀⢳⣳⣾⣠⣤⣚⣻⡟⢷⣄⠀⠀⠀⠀⡞⣼⠃⠀⠈⣧⠀ ⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⢿⡸⣿⣻⣷⣿⠇⢀⡞⠁⠀⠀⠀⠀⣰⡟⠋⠉⠉⠉⠙⠢⣤⣻⣦⠀⠀⠐⠟⠁⠀⠀⠀⢿⠀ ⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠈⢳⣌⡉⢉⣡⠔⠋⠀⠀⠀⠀⠀⡴⢿⣠⡇⠀⢀⡄⢰⡄⡿⠉⢻⡀⠀⠀⠀⠀⠀⠀⠀⣼⠀ ⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⣶⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠓⠮⣝⣷⠤⢾⣥⡾⣿⣁⣠⡾⠃⠀⠀⠀⠀⠀⠀⢀⣿⠀ ⠀⠀⠀⢸⡛⠿⣿⢿⣦⣀⡀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠈⢹⡿⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀ ⠀⠀⠀⠀⢷⣄⠈⠳⣝⣌⢙⣷⠾⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢓⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⣒⢹⡿⠛⠁⠀⠀⠈⢿⣉⠙⠛⢒⣲⣶⣶⣟⠛⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⣺⡽⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⣯⣭⣉⣙⣉⣩⣶⠙⠷⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠙⠓⠶⠶⠶⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

🎁🎄🎀🎉

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

🎄🎁🎅🏻☃️

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠈⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⡞⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⠒⠉⠉⠉⠙⠲⢤⡀⠀⠀ ⠀⠀⠀⢀⡾⠋⣹⡇⠀⠀⡼⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀ ⠀⠀⠀⣼⠁⢠⠏⠀⠀⢰⠃⢠⡇⠀⠀⠀⠀⠀⠀⣰⢶⡄⠀⠀⠀⣶⢳⡀⠀⠀⠀⠀⠀⠀⣀⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇ ⠀⠀⢰⠇⠀⡞⠀⠀⠀⡟⠀⣼⠀⣀⡴⠦⣤⣤⣠⠇⣸⠟⠳⣆⢸⠃⡼⡏⠻⣆⣰⠛⢲⣼⠉⢹⡆⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⡞⠀⣸⠁⣀⣠⡼⠃⢠⡇⣰⠋⢠⡷⠀⣸⡿⠀⢠⣾⠀⢹⡟⠀⣰⢿⠀⣿⠇⢠⣿⠃⢠⡟⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⢰⠇⠀⠛⢉⣉⣠⡶⠀⣼⣴⠃⣠⣿⠁⢰⡿⠃⢠⢏⡞⢀⣾⠁⣰⢣⡏⢀⣿⠀⡼⠃⠀⡞⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏ ⠀⡞⠀⣰⠛⠉⠀⢸⠁⠀⡇⡇⢀⡿⢁⡤⠾⣁⢀⠻⣞⣡⡾⡟⢠⡛⣏⣠⠟⠸⣆⣠⡆⢸⠃⠀⠀⠀⠀⠀⠙⢦⣄⣀⣠⠴⠚⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀ ⢰⠃⢠⡇⠀⠀⠀⠘⠶⠞⠁⢧⣈⡴⠋⠓⢺⡏⢸⠛⠚⠉⢸⠇⣸⠉⠉⣥⣄⠀⠀⢸⠀⣸⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀ ⣾⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡞⠀⠀⠀⡾⢀⡇⠀⠀⢿⡘⠓⠶⢏⣠⠟⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⣀⣠⠴⠚⠁⠀⠀⠀⠀ ⠈⠉⠁⠀⠀⠀⠀⢀⣠⠤⠤⠤⢤⣀⠀⠀⡏⢰⡇⠀⠀⠀⡇⢸⣇⢀⡀⠀⠙⢳⠾⣏⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠛⠛⣉⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠋⠀⣀⣀⡤⢤⡙⢧⡀⠙⠚⠃⠀⠀⠀⠉⠉⣽⠏⣹⣆⣰⡏⢠⠏⠀⠀⠀⠀⠀⣰⠖⢾⡇⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢀⡼⠉⢙⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⠀⣸⠉⠀⢀⡼⠁⣠⠇⠀⠀⠀⠀⢠⡖⠋⢉⡉⢠⣄⣤⡄⢨⡿⠀⠀⠀⠀⠀⢰⠏⢀⡞⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⡼⠁⠀⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⢠⠇⣠⡴⠋⣀⡴⢫⡞⢛⣧⡴⠲⣤⣭⣉⡿⠁⡾⠀⡼⢀⡞⣀⣀⠀⠀⠀⢀⡟⠀⡾⠀⣀⡀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢰⠃⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠇⠀⠞⠋⠁⠐⠛⢧⡀⣼⠛⣿⢻⠄⡀⠉⢠⣿⠃⢰⠃⣸⠣⣼⡟⠁⣸⣤⠞⠉⣻⠁⣸⣡⠞⠉⡙⠗⢶⣀⡴⢿⣤⡴⢦⡄⡏⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠀⣠⠶⠒⠒⠒⣶⠀⣿⠇⢰⣇⡟⢠⠇⢠⡏⡟⠀⡞⣰⠃⣸⢏⠀⢠⣿⠋⢀⣾⠏⢠⣿⠃⢠⣾⠏⠀⣼⡟⠀⣸⡿⠀⣠⢿⠇⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⢠⡏⠀⠀⣠⠞⠁⣰⣿⠀⣾⡾⣡⣿⠀⣼⡟⡁⢠⣷⠃⠀⢃⣿⠀⡾⠃⢀⣿⡏⠀⣸⡇⢠⣿⠋⠀⢸⡿⠁⢰⡿⠁⢰⠃⣼⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠀⣸⣀⡤⠚⢁⣠⠞⠁⢹⡀⣻⡴⠃⠸⣤⣨⠶⠳⠤⠴⣆⣠⠟⠹⠦⠴⣆⠘⢋⡴⣄⣉⣅⠘⣁⣴⡄⢛⣠⣄⠈⡀⠀⣯⣠⠿⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⡀⢉⣀⡤⠖⠋⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⣈⣽⠿⠛⢻⣍⠁⠉⢹⡇⢸⠻⣇⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⣀⣠⡶⠞⠋⠀⠀⠀⢸⡘⠧⢤⣼⠁⣸⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⢋⣀⣤⡴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⡛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⛄˚｡⋆୨୧˚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⣠⣾⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣯⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣀⠀⠀⠀⠀⠀ ⠀⠀⠸⡿⢡⡿⠁⣰⡿⠛⣇⠀⢸⣷⡞⣿⡄⢻⣷⠛⣷⢸⣷⢸⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⢾⣵⠞⠹⣧⣼⣿⣴⣺⣿⣠⡿⠟⣽⣧⣰⠟⠋⠙⠛⢸⣿⡾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⣿⠉⠀⣸⢻⣿⠀⠀⠀⠀⣰⢿⣿⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠸⣧⡿⠀⠀⠹⣦⡟⠀⠀⠀⠰⣿⣼⠏⠀⠀⠀⠀ ⢠⣀⣼⠟⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀ ⢨⣿⣟⡛⠉⣤⡀⠀⠀⠀⠀⣤⠀⣴⡟⣷⠀⢸⣿⢹⠆⠀⠀⠀⡀⢠⣄⠀⠀⠀ ⣾⠟⠉⣿⣽⡟⠠⣶⣀⡐⣾⡿⣴⣿⣞⠁⠀⠀⣿⡟⠀⣴⢶⡄⢻⡄⣿⣷⡄⣤ ⠙⠳⠾⢻⣿⣴⣶⢋⣿⢀⣿⠀⢸⣿⢻⡏⢰⡞⠛⣷⣼⢿⣤⢿⡼⠙⠉⢸⣿⠁ ⠀⠀⠀⠀⠉⠉⠁⠸⣧⠏⢿⡶⠋⠉⢸⡵⠋⠓⠚⠉⠁⠀⠀⠀⠀⠀⢰⡏⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠀

⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠒⠒⢤⡀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣾⣾⠟⠛⠢⣄⠀⠀⠙⣦⣤⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡴⠋⠹⡟⠁⠋⠀⠀⠀⢈⣷⠶⠿⠭⣥⡤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⠀⢸⡀⠀⠀⣀⠴⠚⠉⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢣⠀⠀⠀⣧⡴⠊⠁⠀⠀⠀⣼⣅⠀⣰⣅⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣄⣠⡾⣋⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠁⠀⠀⣾⣿⣿⡷⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⢹⢷⣿⣶⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣾⣿⣿⣿⣿⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣡⠴⠊⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⠀⠙⠲⠤⠤⠤⠤⢤⣶⣿⠋⠉⠁⠀⢻⡗⠀⣞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⡏⠙⠓⢦⡀⠀⠀⣴⣿⡿⠁⠀⠀⠀⠀⢿⡇⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠻⠋⠀⠀⠀⠀⢻⣤⣴⣟⠉⠀⠀⠀⠀⡴⣶⣾⠿⠤⠷⠿⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠘⣆⠀⠀⢀⠶⣧⣼⠻⢿⣤⠀⣠⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠐⠢⠾⠿⠛⠛⠂⠛⣩⡗⢾⣿⠳⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢀⣀⡀⣥⣷⣀⣁⣀⣈⣣⡼⠀⠰⣤⣄⣢⡴⠋⣙⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠓⠒⠉⠉⠙⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣹⣿⢾⣗⣀⣍⢹⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢻⢿⡧⠀⠙⠿⠿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣆⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣀⠀⠀⠀⣤⠀⠠⡈⠙⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣋⣉⠽⠛⠉⠳⣤⠀⢠⡀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⡽⠖⠤⠦⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠘⣧⣀⣸⣦⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⡤⠒⠋⠉⠀⠀⠀⠀⠀⡀⢩⡙⢦⡠⡌⢳⡀⠀⠀⠀⠀⠀⠀⠻⣀⣿⣧⣤⠴⢤⣤⠀⠀⠀⠀⠀⠀ ⠀⠒⠾⠟⠛⠿⠿⠛⠛⠛⠳⠤⠤⠤⠤⢤⡤⢤⠤⡷⠤⠷⠖⠳⠟⠚⠡⠤⢶⡾⣿⡿⠿⠿⣿⡿⠶⠾⠽⣿⣿⣷⣦⡤⣤⡀⠀ ⠀⠀⠀⠀⠀⣠⣶⣾⣍⣥⣶⣶⣶⣤⣤⠖⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠶⠿⠿⠿⠶⠶⠶⠶⠶⠶⠿⠿⠷⠂ ⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠁⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣿⣿⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠁⢀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⣀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⣻⣿⣿⠦⠀⠀⠀⣠⣤⣤⣄⣀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⡀⠀⠀⣄⣀⡀⠀⣠⣤⣤⡄⠀⠀⣾⣶⠀⠀⣿⣟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⢠⣿⣿⠃⠀⠀⢠⣾⣿⡿⠿⢿⣿⡄⠀⠀⠀⢹⣿⣿⣴⣿⣿⣿⣧⠀⠀⢹⣿⣿⣾⡿⠿⣿⣷⡀⠀⣿⣿⡆⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠿⠃⢠⣿⣿⠏⠀⢀⣤⣿⣿⠏⠀⠀⣸⣿⡄⠀⠀⠀⢸⣿⣿⣿⠃⠈⣿⣿⡆⠀⢸⣿⣿⡿⠀⠀⣿⣿⡇⣠⣿⣿⣇⠀⣾⣿⣿⣿⣧⠀⠀⢀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⣠⣴⣿⠏⣿⣿⡄⠀⣠⣿⣿⡇⠀⣦⡄⢸⣿⣿⡇⠀⢠⣿⣿⣷⡾⠃⣿⣿⡇⠀⢠⣿⣿⣿⠟⠉⠿⣿⣿⡿⠃⢿⣿⣿⣠⣾⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠁⠀⠘⢿⣿⣿⣿⣿⣿⣇⣼⣿⣩⣿⣿⣿⡇⣠⣿⡿⠟⠉⢠⣾⣿⣿⣇⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠻⣿⡿⠟⣽⣿⠛⣿⣿⡟⠛⠉⠀⠀⢀⣿⡏⢿⣿⣯⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⣸⣿⠃⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⠇⠀⠀⠀⠀⢿⣿⡄⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣴⣿⣿⠀⠀⠀⠀⠀⠸⣿⣷⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡀⠀⢠⣾⣿⣿⠟⠁⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢼⣧⣠⣿⣿⡿⠁⣀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⣿⣿⣿⣶⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣴⣿⣿⢿⣿⣆⠀⠀⠀⢸⣿⡏⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⡿⣄⣀⡀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⣼⣿⣿⠃⢠⣿⡟⠀⠀⠀⢸⣿⣇⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢺⣿⣶⣄⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⠿⢿⣿⣶⢶⣾⣿⠛⠁⠀⣠⣶⡄⠀⠀⠀⣤⣤⣾⣿⡏⠀⢰⣿⣿⢃⣴⣿⠟⠁⠀⠀⠀⠸⣿⣿⣼⣿⠃⠀⠀⠀⣀⣠⣄⠀⠀⢿⣿⡀⠀⢻⣿⣿⣷⡀⠀⠀⠀⠀ ⢿⣿⡿⠉⠀⠀⠀⣿⣿⣾⣿⣿⠉⠁⠙⢿⣿⣇⣀⣀⡀⢉⣿⣿⣿⢿⡇⣸⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⠁⠀⠀⢠⣿⡿⠛⢿⣇⠀⠘⣿⣷⡀⠈⣿⣿⣿⣿⡄⢀⣾⡷ ⣿⣿⣦⣀⣀⣠⣾⣿⣿⣿⣿⠇⢀⣀⠀⣾⡿⢻⣿⡿⠀⢠⣿⣿⠋⠀⠘⣿⣿⣿⣾⣿⣿⣶⠄⠀⠀⣠⣤⣭⣿⣿⡄⠀⢠⣿⣿⠁⠀⢸⣿⡆⠀⣿⣿⣷⣾⡿⠀⢻⣿⣿⣾⡿⠁ ⠀⠈⠛⠿⠿⠿⠟⠋⣿⣿⣏⣴⣿⣟⣼⠟⠀⣼⣿⠃⠀⢸⣿⣿⠀⠀⠀⢹⣿⣿⡟⢠⣿⡟⠀⠀⣾⣿⠟⠙⠻⣿⣿⣄⣾⡿⣿⣧⣠⣼⣿⣷⣼⣿⠀⠉⠉⠀⠀⠈⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⣿⠏⠀⢠⣿⡿⠀⣴⣾⣿⡿⠀⢀⣴⣿⣿⣿⠁⣸⣿⠇⢀⣴⣿⣿⡀⠀⢠⣿⡿⣿⡟⠀⠈⠛⠛⠛⠙⠛⠛⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠃⠀⠀⢸⣿⣧⣾⡿⢹⣿⣿⣶⣿⡿⠁⠀⠀⠀⣿⣿⣠⣿⠟⠈⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠈⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠁⠀⠻⠿⠟⠁⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣴⠂⠀⠀⡀⠀⠀⢀⣄⠀⠀⡀⢀⡀⠀⠀⣰⣷⠟⠀⠀⠀⠀⠀⠀⠀⢠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⡇⢰⢃⡴⢀⡾⠁⢰⡇⣸⢣⠀⠀⢻⢸⠇⠀⢰⣿⠏⠀⠀⠀⠀⡀⠀⢀⡿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢧⠀⠀⠘⢧⡞⣾⢁⡟⠀⠀⡾⢀⣷⡏⠀⠀⢸⢸⠀⢠⣿⠇⠀⣴⠃⢸⢻⡇⠀⢸⢿⠇⣰⠆⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⣞⣧⡄⡀⠘⣹⢡⠞⠀⠀⢀⡇⠸⣼⠁⠀⠀⠸⠈⢀⣾⡟⢀⡾⠁⠀⢸⣾⠀⢠⡟⡞⣠⠋⣠⠞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢨⡿⢦⡙⢷⣄⠀⠀⠀⠀⠀⠀⠹⣎⢘⣿⠈⠁⠀⠀⠀⠀⣸⠁⢠⠇⠀⠀⠀⠀⢠⡾⠉⠀⠞⠁⠀⠀⢸⡿⠀⠈⢱⠏⢁⡼⢫⠞⠁⠀⠀⠀⠀⠀⢀⡤⠄⣠⡴⠃⠀⠀ ⠀⠀⠀⠘⢷⣄⠙⢦⡙⢦⡀⠀⢠⡆⠀⠀⠘⣾⠋⡇⠀⠀⠀⠀⠠⠿⠀⠈⠀⠀⠀⠀⣰⣻⠇⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⣿⡄⢘⡴⠋⠀⠀⠀⠀⠀⣠⡴⣋⡵⠛⠉⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠉⠳⣄⡙⢶⡝⢢⣿⡇⠀⠀⠀⠹⣾⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⣧⡟⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⣾⣸⠃⠈⠀⠀⠀⠀⠀⣠⡞⠁⠀⢉⣀⣠⡤⠴⠶⠀⠀ ⡀⠰⠶⣄⣀⠀⠀⠀⠙⢶⡀⢿⢨⡇⠀⠀⠀⢲⣮⢿⡇⠀⠀⠀⣾⢷⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⣼⢻⡄⠀⠀⢀⣽⣯⡆⠀⠀⠀⠀⢀⡼⣿⠀⠘⠉⠭⠶⠶⠶⠶⠿⠂⠀ ⠛⠓⠦⠤⣌⣙⣓⠦⡄⠀⠀⢸⣿⣃⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠻⣸⡇⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⢷⣸⠇⠀⠀⠘⡟⢹⡇⠀⠀⠀⠀⣼⣴⠇⠀⢠⣀⣀⡀⠒⠒⠦⠤⠤⠄ ⠀⠀⠀⠀⠀⢈⣉⣙⣲⡄⠀⣿⠿⢻⡄⠀⠀⢸⡇⢸⡇⠀⠀⠀⢤⣿⣧⡀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⣮⣿⣤⠀⠀⠀⡇⢸⠃⠀⠀⠀⢸⠿⣽⡄⠀⠸⣍⡉⠉⠉⠛⠒⠒⠒⠶ ⠐⠒⢒⣛⣯⣭⠭⠝⢋⡀⠀⢻⠀⢸⡇⠀⠀⢸⡇⢸⡇⠀⠀⠀⢸⠉⢿⡇⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⢻⠉⣿⠀⠀⠀⡇⢸⡆⠀⠀⠀⣿⠀⣿⠀⠈⠓⠮⣭⡓⠲⢦⣄⠀⠀⠀ ⠈⠉⠉⠀⣀⣤⠶⠒⠉⠁⠀⢸⠀⢸⣇⠀⠀⠘⡇⢸⡇⠀⠀⠀⢸⠀⢸⡇⠀⣀⢀⡇⠰⣧⠀⠀⠀⠀⢼⠀⢻⠀⠀⠀⡇⢸⠇⠀⠀⢀⡇⢰⡿⠀⠀⠀⠀⠀⠉⠙⠶⢧⣦⣀⡀ ⡤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⢸⡄⠘⣿⣀⣠⣤⡇⢸⣷⠖⠚⠛⢻⠀⢸⡏⠉⠉⠉⡇⠀⣟⠉⠛⠛⠛⣿⠀⣸⠷⠶⣤⡇⢸⣆⡀⠀⢸⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⣇⠀⣿⠀⠈⢿⣻⣾⣿⡷⠀⠀⢸⠀⢸⡇⠀⠰⣾⢿⣼⣟⣶⠀⠀⠀⢸⠀⢸⠀⢸⣜⡇⢸⣇⣉⠙⣿⠀⣿⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⢀⣿⠀⣿⡀⠀⠀⠉⠉⠉⠀⠀⠀⢸⠀⢸⡇⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⢸⡄⢸⡀⠈⢷⣿⣿⣷⠛⢠⡿⢠⡇⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢿⡙⠶⣟⣿⠇⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣇⣸⣷⡀⠀⠀⠀⠀⢰⡾⣇⣼⣧⡄⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠻⣍⣳⣿⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣭⣿⣾⠓⠀⠀⠀⠀⠘⠷⠮⠿⠾⠇⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡟⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⢠⡷⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣶⡿⠋⢱⡏⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣠⣶⣶⣴⡶⢶⡀⣠⣴⡶⠖⠲⣤⣄⠀⠀⢸⣿⠁⠙⠳⣼⠇⢻⡿⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠉⠉⠉⠁⠀⠈⠳⣤⣄⣤⣶⠿⠋⠁⠀⠉⠳⣄⠀⢀⣴⡿⠃⠈⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠉⠳⢦⣼⡿⠀⠀⠀⠀⠀⢸⣯⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡅⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⢀⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣴⢿⣿⣾⣝⡶⢤⣀⣀⡀⠀⠰⣖⠺⠻⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠿⠘⢛⣿⣧⡤⢤⢤⣞⣿⠽⠿⠉⣿⠐⠛⠉⠉⠉⠉⠙⠛ ⣤⠶⠛⠉⠀⠀⣼⣿⠀⠙⠻⢦⣯⣭⣉⣿⣿⣿⡇⣀⠻⡿⣯⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡿⢻⡄⣀⣸⣷⡺⠿⠟⠛⠛⠁⠀⠀⠀⢻⢺⡇⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⢻⡿⣆⠀⠀⠀⠀⠀⠉⠉⠉⠻⠟⠋⠳⢿⣧⣿⣝⢻⡖⠶⢶⠤⢤⣤⣤⡤⠤⠶⢖⣺⣋⣭⣗⣯⣾⣴⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⣼⡷⠀⠀⠀⠀⠀⠀ ⡿⠿⠛⠀⠀⠀⠀⠙⢿⡻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠿⠿⢿⣿⣶⡶⢶⣻⣿⡿⠿⣿⡿⠃⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⡽⠾⠏⠀⠀⠀⠀⠀⠀⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⣭⣳⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢶⣛⣹⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⡼⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⠾⢯⣝⣿⣶⣤⠤⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⣤⣤⢴⠚⣛⣫⣭⡶⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⣤ ⠀⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠦⠾⠻⢿⣯⡽⠿⢿⣭⡽⠛⠳⠶⠶⠚⠉⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⡿⠃⠀ ⠀⠀⠙⠓⢶⣶⣤⣤⣶⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⣀⣠⣴⡶⠛⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣀⣀⣀⣀⣀⣀⣠⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⣿⠶⠶⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠻⢶⣤⣄⣀⣀⣀⣀⠀⣀⣀⣠⣞⣿⠗⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⡻⣧⣤⣤⣤⣤⣤⡤⠴⢟⣛⢻⡦⠦⠤⠴⠶⢾⠛⠛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢼⡿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⡟⠥⣛⠽⢢⣄⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⠿⣿⣷⠊⡡⢚⡽⠛⣉⣷⣮⣀⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣯⡴⢩⢖⡿⠟⠉⠀⢻⡍⠳⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠉⠙⢷⠋⠀⠀⢠⣦⠀⠹⢶⣼⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠈⢹⣿⡾⠉⠻⣿⢿⠈⡎⠙⢷⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡼⢠⠇⠀⠀⠉⣿⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⢿⣶⣋⢠⠎⠀⠀⠀⠀⣼⠸⡧⠤⢤⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣟⠓⠖⠒⢲⡶⠦⠤⣀⠙⡣⣿⣆⣠⢶⣿⣿⣿⣀⣗⢒⣶⠶⣋⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠱⠦⣤⣝⠃⠹⣿⣿⣿⣿⣿⣏⣩⠥⠔⠒⠊⠈⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠇⢠⠀⠀⠀⠀⠀⡴⠋⠉⠓⠒⠛⠛⠛⠛⢣⡀⠀⠀⣀⡀⠤⠊⣽⠃ ⠀⠀⠀⠀⠀⠀⠠⣯⡀⠀⠑⢤⣀⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣹⣿⣭⡤⠔⠒⠉⣽⣦ ⠀⠀⠀⠀⠀⠀⠀⢸⠉⠓⠤⣀⡈⠉⠳⢽⠓⢒⣶⠶⡶⣴⠒⠋⠀⠀⠀⠀⢀⣠⠴⠊⣡⠟ ⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⡇⢻⣿⣿⣿⣻⣏⣹⣥⡴⠶⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⢀⣀⡤⢄⣀⠀⠀⠀⢀⡇⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠋⠉⠳⣼⡀⠀⠀⡖⠉⠀⠀⠀⠈⠙⠲⢤⣈⡜⢀⠴⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡞⠁⣦⡀⠀⠀⠙⢦⣀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠉⢲⠇⡰⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠈⢻⢤⣀⠀⢀⣈⡹⠖⠛⠢⠤⢄⣀⠀⠀⠀⠸⢠⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢣⣀⣠⠏⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⠸⠃⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣴⣶⣖⣶⣶⣶⠶⠾⠿⠿⠿⠿⢿⣿⣿⡿⠿⢿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢾⡟⠒⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠻⠆⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⢠⡄⠀⠈⣏⡾⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠴⢿⣁⢸⡷⢿⢀⡼⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⡋⢀⡴⠋⢈⠗⢤⣀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠋⢀⠴⠁⢀⡼⠛⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠴⠋⢀⠴⠋⢀⠔⣉⣽⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣖⣩⡤⠶⣿⣯⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠀⠀⠀⢻⣿⣿⣿⣿⡛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⣠⣶⣿⣿⣷⣦⡀⢠⠶⣴⠁⠈⡇⠀⢀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⢸⡅⠀⣠⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣧⢸⠀⡿⠀⢠⡇⣴⠏⠉⡇ ⠀⢀⣠⣴⣒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠦⡄⠀⠀⠀⢸⣿⣿⠟⠻⠀⠟⠛⠲⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⠀⠃⢀⡾⠛⠁⢀⡼⠃ ⢠⣾⠛⡽⣿⡇⣽⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠙⣆⣀⣤⢤⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿⠙⢿⣿⣿⣿⣿⡿⣡⢧⢀⡄⠀⠀⠀⣠⠞⠀⠀ ⢸⣵⣄⠙⠚⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠹⡄⠹⡄⠙⢷⣄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⣿⠟⠀⠀⢀⣉⣉⣽⣿⡛⠧⢽⡿⠃⠀⢠⠞⠁⠀⠀⠀ ⠈⠳⣄⣉⠛⠛⠒⠒⠶⡤⡤⣤⣤⡤⡤⡤⡤⡼⣷⡴⣷⣤⣸⣆⣠⣟⣻⣿⡿⣿⣟⣹⣂⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠠⠯⣄⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣍⠉⠀⠀⠹⡄⢁⣤⠤⠇⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠙⠒⠚⢷⠒⢤⡀⠈⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠄⠀⢠⡏⠀⢀⣠⣾⣿⣿⠏⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠦⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠉⠙⠻⢿⣦⡹⣍⣳⣴⣦⣄⡀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣯⣄⣀⣼⣿⣿⣿⣗⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣿⣿⡿⠿⠿⣿⣿⣿⣿⡿⠏⢹⡦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠉⠀⠀⠈⣻⡿⠟⢶⣿⣿⣯⠄⠀⠀⠉⠀⠈⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠉⠉⠂⠀⠀⠀⣠⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢤⣀⣀⣀⣀⡠⠤⠒⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡉⠛⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⣀⠀⠀⣦⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠖⠯⣀⡶⢿⡠⠛⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠔⢁⠜⠑⣦⣾⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠔⠁⡠⠊⣠⠛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣴⣊⠤⢾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠈⣿⣿⣿⣏⠉⠀⣀⣀⡀⠀⠀⡀⠠⠲⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡎⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣤⣾⣿⣿⣿⣧⢸⠉⡇⠀⡅⣠⠖⡆ ⠀⢀⣠⣤⢤⡀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⢸⣿⣷⠿⠀⠟⠦⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠠⠁⡰⠟⠁⣠⠃ ⢠⡿⠋⣿⣇⡇⠀⠀⠀⠀⠀⠀⠸⡄⠘⣤⢤⠠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠙⠿⣿⣿⣿⣫⢷⣠⡄⠀⢀⠔⠁⠀ ⠈⣟⠦⠍⠉⣀⣀⣀⣀⣀⣀⣀⣀⣘⣄⣸⡀⢣⡈⢳⠤⣀⣀⣰⢦⠀⠀⢀⣴⣯⣀⣤⣤⣤⣾⣿⣍⠚⠋⠀⣠⠃⠀⠀⠀ ⠀⠀⠙⠒⠒⠒⠒⠒⠒⠚⠒⠓⠒⠒⠻⡒⠋⠙⢿⠙⣉⣩⠍⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠧⠴⣦⠄⡈⠙⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡄⠀⣴⣁⣀⣴⣿⣿⠋⠻⣿⣿⣿⡿⢋⡀⠀⠀⠀⠀⠀⢘⠆⠈⠲⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠟⠋⠁⠀⠀⠀⠈⢛⣷⣾⠮⢿⣷⣦⣄⣀⠎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣴⣶⠲⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⢙⡿⠿⠾⣿⣯⡍⠀⠈⠀⠙⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⡜⠁⠀⠀⠀⠀⠀⠉⠀⠀⢀⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠳⢄⣀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠚⠉⠉⠙⠛⠓⠒⠶⣿⣏⣉⣉⡉⠉⠉⠉⠉⠉⠙⠛⠛⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣑⡢⢄⠀⠀⠀⠀⠀⠀⠈⠛⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⡤⠀⠘⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⡠⠤⠴⠒⠂⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⣧⠀⠀⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣠⣾⣁⠀⠀⠀⠀⠀⠀⡤⠒⠚⠛⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢘⣧⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡞⠀⠀⠙⡆⠀⠀⠀⢺⣿⡁⠀⣀⡀⠀⠀⠱⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣻⡀⢸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡖⢊⣉⣹⡆⠀⠀⠀⠙⠋⢉⣉⡙⠳⢄⠀⢱⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢙⡻⠿⠧⣄⠀⠀⠀⠀⠁⠛⠻⠷⡀⠙⠸⠀⠀⡇⠳⡤⠴⢦⡀⠀⠀⠘⣼⡟⠀⡸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢴⠁⢰⠋⠀⠀⠀⠀⠀⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢸⡽⠀⠈⡇⠀⠀⠀⣿⣁⣤⠇⠀⠀⠀⠤⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⢇⡀⢻⠀⣸⠷⣶⣶⠤⠤⢤⣀⣴⢧⡀⠀⠀⠀⠀⠛⢍⠙⢇⠀⠃⡇⠀⢀⡇⠀⠀⣠⡏⠁⠀⠀⠀⠀⠀⠀⢈ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠉⠉⠉⠀⠀⠀⢰⡀⠀⠀⠀⠀⠰⢿⣲⠦⠤⠤⠂⢀⡇⠈⡆⡠⠃⢀⣼⡁⢀⡴⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣇⠀⠙⠳⠦⠤⠤⠤⢶⡊⣙⣦⣴⠶⠦⣄⡀⠈⠙⠒⠒⠒⠋⠀⡸⢫⡤⠔⠋⠈⢿⢷⣄⢸⣄⡀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠻⢷⣮⠁⠀⠀⠀⠀⠀⢣⡀⠀⢀⡠⠞⠉⠉⠓⠲⠤⠤⠤⠤⠚⠁⠀⣧⠀⢀⡀⠀⢣⠘⡿⢿⣷⣄⣈⣦⣤⠤⠒⠁ ⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⢀⡀⢧⡈⠉⠉⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⣏⠀⠠⠜⣠⠇⠀⠀⠀⠹⣯⠁⠀⠀⠀ ⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠒⠒⠚⠁⠀⠀⠀⠀⡀⢹⣇⠀⠀⠀ ⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣿⠀⠀⠀ ⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⡇⣿⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⣴⠟⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣠⠜⣡⠞⠁⠀⠀⠀⠀⠀⠀ ⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡏⠀⠐⢆⠀⠀⠀⠀⣀⣠⣴⠾⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢰⡅⠀⠀⠀⠀⠀⠀⠣⣄⡴⠿⠶⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣦⡀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠷⢤⣹⣄⡀⠀⠀⠀⠀⠀⢀⡼⢦⡘⠷⣤⣀⠀⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⣶⡶⠞⠋⠀⠀⠉⡓⠺⠿⠛⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⠛⠛⠋⠉⠉⠉⠉⠙⠛⠓⠲⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠿⠶⠶⠶⠶⠶⠿⠿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⢀⣹⡿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⣴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢼⡇⠀⠤⣄⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣄⣄⢀⣀⠀⠀⠀⢸⣿⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⡀⠐⠛⣏⠀⠀⠀⠀⣀⣴⣶⣶⡶⠿⢁⣤⣶⣶⣷⣶⣯⠉⠉⢙⣿⣿⣷⣤⡾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⢿⠀⠀⠠⣾⠻⣿⣧⠀⢷⠀⠉⢠⣶⣛⣿⣶⠈⠀⢰⣿⣿⣶⣾⠟⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⢻⡄⠘⣧⣀⣴⡿⣄⡀⢉⡆⢸⣧⠄⠀⠈⠙⠙⠋⠀⢀⣸⡟⠛⠛⢻⡀⠘⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⠾⠶⣦⣸⡇⣰⠟⣿⠏⠀⢨⣿⡟⠀⠈⣇⠀⠀⠀⢀⣠⣯⣀⡀⠀⣹⡀⠀⢸⡇⠀⡿⠀⠀⠀⠀⠀ ⢀⣰⡟⠁⠀⠀⠀⠈⢿⣵⠋⠀⢻⡆⠀⢸⡿⠀⢀⡴⠛⠳⢶⠖⣩⣤⣀⣀⣹⣏⠀⣷⡴⠚⢿⣸⡇⠀⠀⠀⠀⠀ ⠀⢹⡄⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿⠀⠈⣧⠀⠈⠀⠀⠀⠀⣧⣟⠒⠦⠤⠤⢾⣴⠋⠀⠀⠀⣿⣿⠂⠀⠀⠀⠀ ⠀⠈⡇⠀⠀⠀⠀⠀⠀⢈⣷⠀⢠⡏⠀⠀⠙⢧⡀⠀⠀⡀⠀⠀⣸⠿⠶⠶⠾⠛⣿⠀⠀⢦⣠⣿⣍⠻⣆⠀⠀⠀ ⠀⠀⢿⣄⣀⣀⣀⣠⣴⠟⠁⣀⡼⢧⡀⠀⠀⠀⠙⣦⢠⠇⢀⠞⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠙⣧⡽⠗⠛⣧⠀⠀ ⠀⠀⠀⠙⣩⡿⠋⠀⣈⡿⠋⢁⣠⣼⡇⠀⠀⣠⡾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣆⠀ ⠀⠀⠀⢰⣿⠁⠀⠀⠉⠉⠉⠁⠴⠯⠤⠴⢾⠋⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⠛⠂⠀⢿⡀ ⠀⠀⠀⢸⣿⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⣾⣀⡴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠻⣧⡀⠀⢰⠁⠀⠀⠀⠀⠀⠘⠋⠁⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣠⡿⠃⠀⠀⠀⠀⠀⠀⣷ ⠀⠀⠀⠀⠀⠈⢿⣦⡏⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⠉⠛⣿⣦⡀⣇⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⢀⣀⣀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠉⠻⢿⣄⠀⠀⠀⠀⠀⠀⢿⡿⠛⠉⠁⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⢷⣄⡀⢦⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠶⠶⠶⠶⢶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠈⠻⢾⣆⠀⠀⠈⠻⣦⡀⠀⠀⠀⣴⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣶⣤⣀⠀⠀⠀⠙⠳⣦⣄⣀⣀⣹⣦⣠⡾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠛⢷⣦⣄⠀⠀⢸⡁⠀⠀⣠⣾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣿⡇⢀⣴⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣿⠏⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠶⠖⠚⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠶⢶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⣀⣀⣀⣉⣙⠻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣴⡶⠶⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⠶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⣀⣤⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⢀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠈⠉⣳⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠶⠖⠛⢛⣛⢛⡛⢻⡿⠶⣷⣤⣶⣦⣤⣀⠀⠀⣸⣷⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠉⠁⣿⡀⠀⠀⠀⠀⢀⣠⣾⣿⠿⢿⣿⠛⠋⣰⣶⣿⣿⣿⡿⠿⣷⣦⠀⠀⣈⣵⣶⡷⢿⣿⣶⠿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⢸⡇⠀⠀⠠⣴⡟⢛⣿⡿⡄⠀⣿⡀⠈⠁⣠⣶⣞⣻⣿⣶⡄⠁⠀⢠⣿⡵⣿⣶⣬⡿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠘⣿⡄⠀⠀⣿⣧⠀⠉⠻⢳⠀⢸⣇⢀⠀⠈⠙⠻⢟⠻⠿⠃⠀⠀⠘⡿⣿⣛⡻⣿⡇⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⢿⡇⠀⢙⣿⣶⣾⠟⠙⠳⣦⣤⡾⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⠒⢧⡀⠀⠀⠈⣷⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⡴⠾⠟⠛⠻⣷⣿⡇⢠⡟⠉⣿⠏⠀⠀⢸⣿⡿⠁⠀⠀⢻⡀⠀⠀⠀⠀⣠⡾⠿⠦⢄⡀⠀⣰⣧⠀⠀⢀⣿⡀⢀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠸⣿⣰⡟⠀⠀⢿⡇⠀⠀⢸⣿⠁⠀⢀⣴⠟⠻⠷⢶⡞⠋⣀⣤⣀⡀⠀⣸⣋⠀⢘⣦⡴⠚⠻⣧⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠀⠀⢿⠀⠀⠘⣷⠀⠠⠞⠁⠀⠀⠀⠈⣇⢸⠯⣤⣌⣉⣙⣋⣹⡇⣼⠋⠀⠀⠀⠹⣧⣷⡤⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⣼⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠚⠛⢶⣤⣈⠉⢉⣩⣼⣿⠓⠀⠀⡄⠀⢀⣿⢿⣦⡄⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠠⡇⠀⠀⠀⠈⠹⣧⡀⠀⠀⢠⡄⠀⠀⣠⡾⠛⠛⠛⠛⠛⠁⢻⡇⠀⠀⠙⣆⣾⣿⣦⡈⠻⣦⡀⠀⠀⠀ ⠀⠀⠈⣿⣄⣀⣀⣀⣀⣀⣠⣶⠟⠋⠀⣀⣴⢷⡄⠀⠀⠀⠀⠈⠻⣦⠀⣾⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠈⢻⣧⣭⡿⠗⠹⣧⠀⠀⠀ ⠀⠀⠀⠀⠽⠟⣻⣿⠟⠉⠁⠙⣻⠟⠛⠉⠀⣸⣿⡄⠀⠀⠀⢀⣼⣿⣿⠏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠹⣇⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⠃⠀⠠⠴⠾⠥⠤⠤⠞⠛⣹⠟⠀⢀⣠⣴⠟⠃⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣠⣤⣄⣀⠀⢿⡆⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠛⠒⠛⠋⢹⡇⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⠁⠀⠀⠀⢸⣷⠀ ⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⣾⠃⣠⡼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠴⠟⠋⠁⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆ ⠀⠀⠀⠀⠀⠀⠘⢿⣧⣀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠶⠦⣼⣿⣦⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⣨⣿⣿⣦⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣀⣀⣀⣠⣤⠤⠤⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠁⠀⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⣆⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣤⣹⡄⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⣸⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠻⠿⠿⢿⣿⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣄⡀⠀⠀⠀⠙⠷⣦⡀⠀⠀⢀⣼⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣤⣄⣀⣈⣿⡆⣴⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣶⣄⡀⠀⠀⠀⢸⠃⠈⠉⠉⠉⣡⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠘⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠉⠻⣿⣦⣄⠀⣾⡇⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⢀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣤⣤⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⠉⠛⢿⣷⡀ ⠀⠀⠀⠀⣰⡿⠛⠛⠿⠷⠆⢠⡄⠀⣤⠀⢀⡀⠀⣀⠀⢀⡀⠀⣤⡀⢠⣄⠀⡶⠿⢿⣿⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠘⠃⠀⠛⠁⠘⠋⠀⠋⠁⠈⠁⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⢀⣿⠇ ⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⣤⣤⣴⠿⠋⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠈⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣼⡟⠀⠉⠉⠙⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠉⣿⣦⣄⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠉⠀⠀⠀⠀⠀⠀⢀⣤⣷⣶⣦⡀⣠⣴⣶⣄⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠈⠉⢻⣷⠀⠀⠀⠀ ⠀⠸⣿⡀⣀⣀⡀⠀⠀⠀⢀⣿⠋⠀⠀⠈⣿⡿⠁⠀⠹⣿⠏⠁⠀⠈⢿⣇⠀⠀⠀⠀⣀⣀⡀⣸⡿⠀⠀⠀⠀ ⠀⢀⣽⠿⠛⠙⢿⣦⠀⠀⠘⣿⡀⠀⠀⠀⣼⡇⠀⠀⠀⣿⡄⠀⠀⠀⣸⡟⠀⠀⢠⣾⠟⠙⠻⣿⣅⠀⠀⠀⠀ ⢠⡿⠃⠀⠀⠀⠈⢻⣷⣤⣀⣙⣿⣶⣶⣿⣿⡀⠀⠀⠀⣸⣿⣷⣶⣾⣟⣀⣤⣴⣿⠃⠀⠀⠀⠀⠻⣷⡀⠀⠀ ⣿⠇⠀⠀⠀⠀⠀⠀⢿⣏⠛⠛⠛⠋⠁⠀⠙⠿⣷⣶⡿⠟⠁⠈⠉⠛⠛⠛⢋⣿⠇⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀ ⣿⡄⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⢀⣴⡿⠻⣷⣄⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀ ⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠷⠶⠶⠿⠛⠀⠀⠙⠻⠿⠶⠶⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠀ ⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀ ⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀ ⠀⠻⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡿⠋⠀⠀⠀ ⠀⠀⠀⠉⠉⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠟⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⠿⠷⠶⠿⠿⣶⣤⣀⡀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠿⠷⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⠔⠒⠉⠉⠉⠉⢉⣉⣑⣒⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠞⠁⠀⣠⠶⠒⠊⠉⠁⠀⠀⠀⠀⠈⠉⠒⢄⠀⠀⠀⠀ ⠀⠀⢠⠏⢀⣠⠋⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⡀⠀⠰⣇⠀⠀⠀ ⠀⠀⠈⢧⡈⢹⠀⢀⣤⣶⠲⡚⠴⣶⣿⡺⠄⣩⣿⣳⡞⠃⠀⠀⠀ ⠀⠀⢀⠀⢳⠘⣆⣼⠧⣙⡆⣧⠀⠉⠋⡃⠀⢟⠛⢻⠈⡆⠀⠀⠀ ⣠⠒⠉⠉⢾⡜⠹⡇⠀⡟⢀⠼⠤⡤⣊⣁⢢⠚⣄⠼⡆⡃⠀⠀⠀ ⢳⠀⠀⠀⠀⢧⠀⡅⠀⢇⠀⠀⠀⠑⢥⣒⣲⣷⠁⡀⢸⢧⡀⠀⠀ ⠸⣤⣀⡠⢴⣋⡠⢧⠀⠀⢱⣤⠃⠔⠁⠀⠀⠘⠄⠈⢻⠵⠻⡄⠀ ⠀⢠⡏⠀⠒⠑⠒⠝⠠⠴⢋⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⠄⢹⠀ ⠀⠘⣇⠀⢀⠃⠀⠀⢀⠧⠚⣇⠀⠀⠀⠀⠀⠠⠀⣰⠃⠀⠀⠈⡇ ⠀⠀⠈⢧⡎⠀⠀⠀⠐⠒⠚⢚⣷⣄⡄⠀⠀⠀⢻⣁⣀⡀⠀⠀⡇ ⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠠⠊⠀⠈⠳⢄⡀⡀⠈⢏⠀⠀⠀⠀⡃ ⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠲⠶⢤⣄⡀⠀⠙⠳⣄⠈⠓⢄⢀⡴⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀⢈⡏⠉⣩⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡾⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠒⠒⠒⠒⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠎⠁⢀⣀⣤⠤⠤⠤⠶⠦⠤⢤⣤⣀⡈⠉⠑⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣮⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⡀⠈⢢⡀⢀⣴⡶⠿⠷⢦⣄⡀⠀ ⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠒⠤⡀⠀⠀⠀⠈⠳⡄⠙⢿⡁⠀⠀⠀⠀⠛⣿⡄ ⠀⢠⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠘⡆⠀⢀⡀⠀⠻⣦⣀⣈⡳⠂⠀⠀⠀⢘⣿ ⢀⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⣾⣉⡉⠁⠀⠀⢰⣟⡟⠉⠈⠑⣄⢳⡀⠀⠀⠀⠀⠀⠀⣼⣿ ⢸⠁⠀⠀⠀⠀⠀⠀⡞⠁⢀⣀⣙⢦⠙⠛⠓⠒⠒⠉⢸⡖⠋⠉⠑⣼⡿⢷⣄⣀⣀⣀⣠⣾⣿⠁ ⣸⠀⠀⠀⠀⠀⣰⠋⣇⡴⠉⠀⠈⠙⠓⠀⠀⠀⠀⠀⠈⣠⣤⣀⠀⣾⠃⠀⠈⠙⠛⠛⠛⠉⠁⠀ ⢸⡄⠀⣶⣄⡜⠛⣆⠙⠁⠀⣤⣾⣶⣄⠀⠀⢀⣀⡀⢰⣿⣿⡿⠐⠛⠦⣄⡀⠀⠀⠀⣀⠀⠀⠀ ⠈⢧⡀⢻⡄⠀⣠⡏⠐⠂⢀⣹⠿⠿⠧⠀⠈⣡⠞⠋⢳⣄⠀⠀⠀⠀⠀⢹⠫⡓⠂⠐⠉⢃⠀⠀ ⠀⠀⠳⣼⣦⣀⢴⡅⠀⠔⠁⠀⠀⠀⠀⢰⡊⢁⣀⣀⣼⠭⠧⠀⠀⠠⠤⠊⢀⡇⠀⠀⢀⡾⡆⠀ ⠀⠀⠀⣠⠟⠁⢸⡟⢇⠀⠀⠀⠀⢀⣀⠔⠋⠁⠀⢨⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⣽⠀ ⠀⠀⡰⠁⠀⠀⠀⢳⡀⠉⠙⠒⠉⠉⠀⠀⠀⠀⣀⣼⡷⣤⣤⠤⠤⠤⠤⠚⠁⠀⠀⠀⠀⠸⡅⠀ ⠀⢠⣧⠀⠀⠀⠀⠀⠙⢦⡀⠀⢀⣠⣤⣤⠔⠚⢻⡾⠷⣻⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀ ⠀⠈⡻⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢉⡉⠁⢀⠀⠈⠓⠤⡀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣶⣎⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀ ⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠘⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀ ⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀ ⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀ ⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠛⠒⠒⠤⠤⠬⠿⠒⠒⠤⠤⠬⠓⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⡿⠿⠿⠿⠿⠛⠛⠛⠻⠿⠿⠿⠿⠿⢿⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣦⣠⣤⣤⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠛⠛⢿⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⡟⠁⠀⠀⠀⠀⠀⠙⢿⣿⡄ ⠀⠀⠀⠀⠀⠀⣾⡿⠋⠉⠉⠉⠛⠋⠀⢾⡷⠀⢰⣶⠀⠀⣶⡄⠀⣶⣆⠀⣰⣦⠀⢰⣶⡆⠀⣿⠇⠀⠹⠛⠋⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠁⠀⠉⠉⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⢀⣾⡿⠁ ⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣤⣤⣤⣶⣿⠟⠁⠀ ⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡋⠋⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢻⣿⡿⣷⣶⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣶⣶⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣾⡿⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⢻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⣀⣤⣤⣄⡀⠀⢀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠋⠙⠻⣿⣶⣿⠟⠉⠻⣿⣶⣿⠟⠋⠙⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠈⢻⣷⣴⣶⣶⣶⣄⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠙⣿⡏⠀⠀⠀⢹⣿⠉⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⣠⣶⣶⣶⣦⣾⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⡿⠋⠉⠈⠹⣿⣇⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⣴⣿⠁⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⣼⣿⠟⠁⠈⠛⢿⣷⣄⠀⠀⠀⠀⠀ ⠀⣰⣿⠋⠀⠀⠀⠀⠀⠘⣿⣷⣤⣀⣀⠙⢿⣷⣶⣶⣿⣿⣏⠀⠀⠀⠀⠀⣹⣿⣿⣶⣶⣾⡿⠋⣀⣀⣤⣾⣿⠃⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀ ⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⠻⠿⠿⠿⠿⠛⠋⠉⠻⢿⣶⣶⣤⣶⣶⡿⠏⠉⠙⠛⠿⠿⠿⠿⠟⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⣀⠀⠀⠀⣀⣴⣿⠟⠀⠿⣿⣦⣀⠀⠀⠀⣀⣠⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀ ⠈⣻⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡁⠀⠀⠀ ⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀ ⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀ ⠈⢻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀ ⠀⠀⠙⠻⣿⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣾⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣶⣶⣶⣶⣾⣷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣷⣶⣶⣶⣶⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣿⣶⣶⣦⣤⣤⣤⣴⣶⣶⣾⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀