⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣴⣶⣶⣿⣿⣷⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⡿⠿⠉⠉⠉⠉⠹⠿⣿⣿⣿⣆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠙⣿⣿⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡇⠀⣀⣀⠀⠀⠀⠀⣰⣦⣤⣠⣤⣤⣤⣄⡘⣿⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠘⣿⣿⠇⠀⠀⣴⡿⢁⣉⣭⣥⣤⣼⣿⠇⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢺⣿⣧⠀⠀⠀⢀⣴⡿⢏⣴⣿⠟⢉⣩⣽⠟⠁⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⡆⠀⢀⣾⣏⣴⡿⣛⣥⣶⠿⠋⠁⠀⠀⠀⠀⢸⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣷⠀⣾⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣶⣄⡙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡍⠛⠿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⠀⠀⠀⠀⠈⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠄⠀⠀⠀⠀⠀⠀⠀ ⢐⣿⣿⣿⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠈⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⢸⣿⡄⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⠀⠀ ⠹⣿⣧⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⡀⠀⠀⠀⠀ ⠀⢻⣿⣆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡧⡇⠀⠀⠀⠀ ⠀⢸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣇⠃⠀⠀⠀⠀ ⠀⠘⣿⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⣶⣧⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⣿⣿⡿⡟⣿⣿⣶⣀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠈⠈⢟⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣟⣟⡻⢏⣳⣽⣷⢎⡽⢻⣿⣷⣿⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⠿⣿⣮⡷⣋⢾⡻⣝⣮⣼⣿⣿⡿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣿⣿⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠻⠿⡿⠾⠿⠿⠿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣇⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠿⠿⠻⠛⠋⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⡵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⢕⡒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢩⠖⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡹⡔⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢇⣏⠺⣅⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⣇⠧⣛⠼⡀⠀⠀⠀⠀⠀⠀⡤⢻⡸⣇⡸⢧⣘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠵⠀⠀⠀⠀⢀⢥⡛⣬⢚⡇⠀⠀⠀⢠⠴⡹⢜⠓⠁⡼⣑⠮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡝⣣⠀⠀⣀⠞⣦⣹⠔⣫⡇⢀⠀⢀⠞⣜⡱⠁⠀⣸⢱⡚⠁⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⣄⣄⠀⠀⠀⠀⠀⠀⡴⢪⡕⠆⢰⢩⠞⡴⠁⢛⠴⣃⡸⢢⣸⡙⢦⡟⠀⠀⣇⠧⣍⠀⡰⢣⠀⠸⣌⠦⠀⠀⠀⠀⣠⢻⠀⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢆⢏⠦⡀⠀⠀⣠⢝⡱⢎⠆⡜⢎⣞⠁⠀⠀⢻⠴⣩⢓⢦⡙⢦⠃⠀⠀⠯⣜⢲⡱⣍⠻⣌⠷⣌⢻⠀⠀⢠⠜⣆⣻⢰⣜⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⣞⣁⠀⣘⢦⠋⠸⣎⢆⢸⢪⠜⣄⠀⠀⠈⢞⡥⡛⠢⠝⠋⠀⠀⠀⠈⠊⢧⠚⠬⢳⣌⠇⠨⢧⡀⢀⠠⠟⢸⠬⣖⢣⠙⢸⢢⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡰⢭⡰⢎⠎⠀⠀⢗⠮⣙⢎⡟⠘⠆⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣗⡣⢏⡟⣄⠈⢷⡌⠏⠀⠀⢗⣣⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⣱⢣⡛⣼⠀⠀⠀⠈⢷⢩⢲⡹⠀⠀⠀⠀⠀⠀⢀⠠⠤⠄⡀⢀⠄⠀⠀⠀⢄⠀⠀⠀⠀⠘⠊⢡⢏⡜⣇⠀⠀⠀⠀⠀⠀⢸⡒⢦⡴⠹⡄⠀⠀⠀ ⠀⠀⡷⣦⣀⣰⡽⣆⠧⡹⣜⡀⠀⠀⠀⠈⠣⠧⠃⠀⠀⠀⠀⠀⠔⠀⢠⣶⡄⠈⠁⢠⣶⣶⠄⠀⢡⠀⠀⠀⠀⠀⡯⠎⠈⠁⠀⢸⡿⣦⢞⣿⢳⣻⠿⣜⢣⠇⠀⠀⠀ ⠰⢶⣻⡵⣫⣗⢿⢣⡝⡱⣌⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠈⠉⠁⡔⠂⠠⡈⠁⠀⣀⡼⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣵⡻⢮⣟⣵⠻⣎⠋⠀⠀⣸⠀ ⠀⣼⣳⡽⣳⣭⠿⣮⡘⠱⠮⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⣝⡾⣖⡶⢾⡀⠀⢀⡿⣯⣻⠽⣽⣺⣭⢷⠀⠀⠀⠀⠀⠀⢀⣼⣻⢞⡽⣯⢱⡊⢷⣡⢤⢲⡙⢦⠃ ⠀⠁⠁⣙⡷⣭⣟⣳⣟⣦⡀⠀⠀⠀⠀⠀⠀⣠⣀⣠⡴⣟⣞⣻⣽⣾⣿⣾⣿⣿⣶⣾⣿⣷⣯⣿⣧⣷⣞⢯⣟⡶⣦⠀⠀⣠⣞⡷⡽⡾⡝⠣⠣⠽⠊⢸⢎⡥⣛⠌⢀ ⠀⠀⠀⢰⣩⠳⣞⢷⣺⡵⣻⢦⡀⠀⠀⠀⠘⢿⣝⣳⡟⣽⢮⢷⣻⡟⣿⢻⡟⣿⣻⣟⢿⣻⠿⣟⣿⣻⠽⣞⡾⣵⣻⢁⣾⣻⡼⣝⠗⠁⠀⠀⠀⠀⣠⢏⣎⡖⠁⡠⢞ ⣄⠀⠀⢀⠈⠳⢌⡻⢵⣻⣭⡟⣵⣄⠀⠀⠀⢸⣯⣞⡽⢧⣟⢯⣶⢻⣭⢷⡻⣵⣳⡞⣯⡞⣿⣹⠶⣏⡿⣝⡾⣣⣟⢯⣗⣳⣽⠋⠀⠀⠀⠀⠠⠞⡹⢲⣀⠴⣩⢳⡹ ⢞⡢⡀⠘⡥⢆⡜⣣⢋⠷⣞⡽⣧⡻⣗⣄⡀⠈⠈⢱⣟⢯⣞⢯⣞⣻⡼⣳⣻⡵⣳⢯⣗⣻⡵⣏⡿⣝⡾⣭⢷⣻⡼⣻⣼⡳⠁⠀⠀⠀⠀⠀⢀⡼⣱⢣⢎⡳⢥⠗⠀ ⠣⡳⣩⢆⠼⣪⠜⣅⠋⠚⠉⢳⢯⣗⡟⡾⣽⣤⣀⣸⣞⣯⢞⣯⢞⣧⣟⣳⢧⢿⣹⢾⣹⢮⢷⣫⡽⣞⣽⣣⣟⣶⢻⣵⡳⠀⠀⠀⠀⠀⢠⢖⡫⡵⢆⡏⠖⠉⠀⠀⠀ ⠀⠈⢣⡎⢳⢱⠛⠊⠉⠀⠀⠀⠈⠛⣾⣽⢳⡞⣽⢫⡞⣾⣽⠚⣯⣾⣼⡏⣾⡏⣷⣯⢳⣯⡏⣷⣯⣽⣶⢻⣼⡞⣯⡞⠁⠀⠀⠀⠀⠀⠙⠊⠁⠐⣯⢸⡅⣶⠀⠀⠀ ⠀⠀⠀⠉⢪⢣⡝⡲⢤⣄⡀⠀⠀⠀⠱⢟⣾⡹⣗⡯⣟⡶⣏⡿⣝⣮⠷⣽⡳⢯⢷⡞⣯⢾⣹⡗⣾⢳⡾⣭⣗⣻⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⣬⠣⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢮⡱⢣⠖⡭⢦⠀⠀⠀⠈⢾⣝⣳⡽⣳⡽⣽⣺⢽⣺⢽⣳⣛⣯⢷⡻⣝⡾⣣⢿⣭⢷⣻⡼⣞⣳⠇⠀⠀⠀⠀⠀⠀⡤⢖⡹⡜⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡸⢢⡝⡥⣛⢬⠳⠀⠀⠀⠀⣸⢯⣳⡽⣳⡽⢶⣏⡷⢯⣳⣏⡷⣽⣺⠽⣝⡾⣽⡳⣞⢯⣶⢻⣭⢟⡆⠀⠀⠀⠀⠀⢸⡱⣋⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠋⠓⠘⠒⠉⠒⠃⠀⠂⠐⠀⠚⠋⠓⠙⠓⠛⠛⠚⠙⠋⠓⠚⠙⠒⠋⠛⠙⠚⠓⠙⠋⠛⠘⠛⠘⠋⠓⠀⠂⠒⠒⠂⠚⠓⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀