Mushroom ASCII Art

Copy & Paste Mushroom ASCII Art Emojis & Symbols

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