⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⠝⠊⣉⣠⡤⠶⣖⣒⣪⣑⣫⡆⠀⣠⣊⣁⣤⠤⢀⡀⠀⠈⠲⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣁⡴⠞⢉⡥⣶⢟⣫⣽⣮⠗⢋⠅⢻⡈⣏⠉⠚⠯⣖⢬⡑⠦⡀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣡⡾⠉⣠⣶⡿⢋⡴⣫⣿⡿⠃⢠⡾⠀⠈⣷⢳⠀⠒⠲⢤⡉⠻⢦⡈⠢⡀⠱⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⠟⣠⣺⠟⢁⠔⡡⢪⢟⡟⠀⢀⠎⡆⠀⠀⢿⢸⠀⡄⠀⠀⠈⠑⠢⡙⢦⡙⢄⠸⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⢡⢞⡼⠃⡰⢋⡔⣱⢋⡞⠀⠀⡜⢰⠁⠠⠀⢸⡿⠀⣧⠀⠀⠀⠀⠀⠈⠁⠙⣎⢦⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⡱⢁⡾⢁⡞⣠⡟⣴⠇⡼⠁⡄⡸⡇⢸⢠⠀⠀⠀⣧⠀⣿⠀⢤⣀⠀⠀⠀⠀⠀⠈⢯⣾⣄⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢹⡿⢡⣿⣁⢞⠞⡾⣰⡻⢰⡇⣴⢱⣿⠁⢀⣨⠀⡀⠀⢸⠀⣿⡀⠈⠙⠧⠒⣤⣀⣀⣀⣠⣿⣿⠹⠙⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢸⣇⡟⡏⣾⠛⢴⢣⢹⡇⣾⢸⡇⡄⣿⢸⣾⣿⠀⡃⠀⢸⠀⢺⡗⠦⢀⣀⣀⣀⣀⣠⣾⣿⣿⣿⡇⡇⣯⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡀⣸⣷⣇⡏⠀⢼⡏⡾⠀⣿⢿⢣⠃⢹⠈⣿⡿⠀⡇⠀⢰⢀⢸⡏⠀⠒⠒⠛⠉⣱⡿⣿⣿⣿⣿⣷⠇⣹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣇⣿⠙⠋⠻⣷⡸⡇⣿⡀⡿⢸⢸⠀⢸⡮⣧⣇⣄⡇⠀⢸⢸⣸⡇⠀⣀⣀⣤⣾⣟⣽⣟⣿⣿⣿⣿⠀⣾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡍⠀⠀⠀⠈⠧⠁⠘⠃⠇⠘⡖⣤⣄⣇⣟⡿⣇⡏⠓⢸⡞⡏⠋⠉⠉⢀⣤⣟⣻⣿⣿⣿⣿⡏⡸⢰⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⠊⡝⣻⡿⣿⣿⣧⠀⡌⠇⢹⣉⣭⣿⣟⢋⣽⣟⣿⣿⣿⣿⡇⣿⡜⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡃⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⣈⠻⣛⡿⠏⣿⣗⠀⢣⢸⣾⠚⢉⣴⡖⣯⣾⡞⣸⣻⣷⡿⢡⢏⡇⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠏⣼⠿⡇⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⣿⠀⡜⣞⡷⢹⢉⡵⣿⢏⡞⠀⡟⣿⣿⠇⣼⣼⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⢀⣷⡀⠘⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⢃⣹⡓⢓⣩⣾⢃⡞⠀⢰⡇⡇⣯⠀⡇⢻⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⣿⣷⠀⠳⣌⠑⠦⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⣸⡟⢸⣼⣿⡟⣿⣳⡟⡘⠀⠀⣼⣿⣇⣿⢠⢸⠈⣼⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⣿⣿⣿⣧⠀⠀⠉⠀⠀⠀⠀⠸⠿⠆⠀⣀⡴⠚⢹⣿⣿⣿⣿⣿⣿⡿⢱⠇⠀⣸⡏⡟⣿⠃⢸⡿⠀⢻⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣀⣀⡤⢼⠀⠘⡏⠀⠀⠀⣿⠈⢩⢿⢹⣿⢫⠇⡞⠀⢠⣿⢁⣿⢿⡇⢸⡇⠀⠀⢻⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⠟⠋⠀⠀⠈⡆⠀⢠⠀⠀⢠⣿⠀⢸⡏⡼⡟⣸⢰⡇⠀⣬⡇⢸⡇⡟⣿⣼⠇⠀⠀⠀⢧⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠁⠀⢿⡀⠀⠀⠀⠀⢰⠀⠈⡆⢀⣼⣿⠀⢸⠘⢷⠁⡏⢸⠇⢰⡛⢠⡟⣷⡃⣷⡉⡆⠀⠀⠀⠈⠃ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⣿⠀⠀⠘⣿⣶⣤⣤⣤⣤⡇⠀⢸⣿⣯⡇⠀⢸⠀⠀⠳⡇⣾⡄⣌⣯⠞⠀⣿⠀⡇⢳⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏⠠⣿⠀⠀⢰⡇⠉⠉⠛⢛⠻⣧⠀⠀⢿⣻⠃⠀⢸⠀⠀⠀⠙⢾⣧⣿⠁⢘⠀⣿⠀⡇⠀⠱⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠏⠀⠀⢸⠀⠀⣿⠃⠀⠀⠀⡆⠀⢸⣤⣶⣿⣿⣶⣿⣾⡀⠀⣐⣤⣾⣿⣿⣀⣀⠀⣿⣷⡇⠀⠀⠙⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⠀⠀⠈⡆⠰⠋⠀⠀⢠⢖⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠋⠉⢁⣠⢿⡿⢿⢻⠀⠀⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠇⠀⠀⠀⡎⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣴⣿⣿⣜⡆⢸⠘⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠚⠙⠒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣧⢸⣇⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⡎⡄⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⡸⡀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣧⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢳⣆⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡤⣄⡒⠶⢆⡤⣤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⣽⠐⢮⠫⣌⠳⣄⠄⠉⣻⣷⡒⢖⠪⢷⡢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠎⢻⠘⡠⣧⠈⢧⠘⢆⠹⡊⢦⠘⢹⣱⡀⢣⠀⠑⣌⠢⠀⠀ ⠀⠀⠀⠀⠀⢠⢿⡀⠰⡁⠐⡻⣧⠈⢧⠈⡄⠱⠘⣧⢸⡇⢳⠀⢃⠀⠈⢧⠡⠀ ⠀⠀⠀⠀⠀⢻⠸⣇⠀⢣⡀⠈⠙⢷⡈⢇⠰⠀⠀⢹⣜⣇⠈⡈⠜⠀⠀⠈⠇⠃ ⠀⠀⠀⠀⢀⣟⠀⠹⣧⡀⠳⡠⢀⡠⢭⣾⡄⠀⠀⠘⣟⣿⠀⠁⢰⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡏⡌⢦⣈⠚⠥⠉⠀⠃⠸⡿⠳⠀⠀⠸⡇⢸⠀⠀⠀⣶⠀⠀⠀⠀ ⠀⠀⠀⢰⢠⠟⣽⣦⠗⣢⡀⠀⠀⠀⠈⠀⠀⠇⠀⠀⢠⣾⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣸⡌⢟⠢⠝⠃⠀⠀⠀⠀⠀⠀⠘⡀⠀⣯⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⣀⣽⡿⢻⠘⣡⠀⠈⠂⠀⡀⢠⠀⠀⠀⠃⠀⡿⡇⡇⠀⠀⠀⠀⠀⠀⠀ ⠨⠀⢠⣾⣟⠀⠈⣇⠘⣧⡀⠀⠙⠒⠂⠀⠀⠀⢸⠀⡇⢀⠇⠀⠀⠀⠀⠀⠀⠀ ⠒⡆⢸⣙⣢⡑⣰⠛⣇⠈⠎⡦⣄⠀⠀⠀⣀⡴⠋⡄⡇⢸⢠⠀⠀⠀⠀⡄⠀⠀ ⡄⢰⣙⣬⢻⣭⡏⠃⠽⡆⠈⣅⡇⣯⢲⡿⠟⠁⠀⣇⡇⠈⡿⡀⠀⠀⠀⢀⠀⠀ ⣠⢸⣿⣿⣿⡝⠀⠀⠀⠹⡄⠘⣷⡕⣾⣥⠀⠀⠀⣿⠀⢀⣬⣿⢶⣢⣤⣜⡀⠀ ⢸⣻⣿⣿⡟⠀⠀⠀⠀⠀⠘⢄⢸⡇⣙⠟⠀⡀⠤⠗⢴⢻⡿⣡⣿⣿⣿⣿⣷⡀ ⠈⢬⣛⣿⠇⠀⠀⠀⠀⠀⣀⣀⡮⠋⠉⠀⣈⡀⠐⠣⠼⠟⣴⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⢶⣾⣟⠛⢻⡩⣍⠉⠉⠛⠻⠿⣍⡙⠳⣶⣾⡟⠿⠭⢛⠲⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⡏⠀⣄⢦⠙⢯⡳⣄⠉⢿⣷⣄⠀⢠⠀⠈⠙⠻⣿⣿⣿⣄⣀⣤⣤⣤⣀⡉⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠇⠀⡾⣽⡀⠈⢿⣷⡀⠹⣿⣆⠀⠙⢯⢦⠀⢳⡀⠀⠀⢨⣿⢿⣿⣧⡈⠙⢦⡈⠉⠛⢶⣝⢏⠳⣆⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢫⡇⣿⠸⡄⢧⢹⣧⠀⠀⢻⣿⡀⠈⢻⣧⠀⠈⢿⣳⡀⢳⡠⠀⠘⣿⠸⣿⡝⣷⡀⠀⠹⣦⠀⠀⠈⠻⣦⡈⠻⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⡇⣿⠀⢳⠘⡌⣯⣇⠀⠀⠹⣿⡄⠀⠹⣇⠀⠀⢷⡳⠀⢳⢳⡄⠘⠀⣿⣷⠸⣷⡀⠀⠙⣆⠀⠀⠀⠘⢿⣆⠈⢳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⡇⠀⠀⢷⠹⡀⠀⢷⡘⣜⣾⣇⠀⠀⠹⣿⡄⠀⠸⣆⠀⠈⢷⡀⠈⣧⢧⠀⠀⢿⣾⡀⢹⣷⠀⠀⠸⣇⠀⠀⠀⠈⢻⣧⡀⠙⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢳⢿⡇⠀⠀⢸⡄⡇⠀⠈⢳⡘⣞⣿⣦⠀⠀⠹⣿⡄⠀⠹⡄⠀⠀⢣⡀⠸⡾⣆⠀⢸⣿⡇⠀⢿⡇⠀⠀⢹⡀⠀⠀⠀⠀⠻⣷⡀⠘⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⠈⣼⣹⠀⠀⠀⢻⣱⠀⠀⠀⠹⣌⢿⣾⣧⡀⠀⠘⣿⡀⠀⢻⡀⠀⠀⠁⠀⢳⣿⠀⢸⣿⢧⠀⠘⡇⠀⢧⠀⣷⠀⠀⠀⠀⠀⠹⡿⡄⠘⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢧⠀⣷⣟⣇⠀⠀⠈⢧⣄⠀⠀⠀⠈⠃⠙⢿⣿⣄⠀⠙⣧⠀⠈⡇⠀⠀⠀⠀⠘⣏⡇⡆⣿⢸⠀⠀⢹⡀⠈⣇⠸⡆⠀⠀⠀⠀⠀⠹⣿⡄⠙⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣾⠀⠘⣾⣿⣄⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⢹⣇⠀⠀⠀⠀⠀⠀⠀⢻⣿⢃⣿⣿⡆⠀⠀⣧⠀⢸⡀⣇⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠻⡇⠀⠘⢿⣻⣧⡀⠀⠈⢿⣷⢤⣀⠀⠀⠀⣀⣀⣬⣙⡷⣿⡄⠀⠀⠀⠀⠀⠀⡈⣿⣟⠻⣿⡇⠀⠀⠘⠀⠀⣧⢸⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⣆⠀⣀⠀⠀⠻⣷⡿⠢⣄⡀⠹⣧⡉⠙⢲⣿⠟⠉⣤⣿⣿⣯⣷⠀⠀⠀⠀⠀⠀⣷⢿⣿⢶⢿⡇⠀⠀⠀⠀⠀⠸⡽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣷⢹⡄⠘⢧⡀⠀⠈⠻⢶⣶⣉⠙⠉⠙⠓⠀⢻⡇⠀⢻⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⢹⢸⢡⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⣟⣟⡄⢿⣄⠈⠻⣷⠢⠤⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⣀⣻⠟⠋⠀⢹⠀⠀⠀⠀⠀⠈⡏⣿⠀⣸⣇⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢸⢹⣿⢳⡘⡿⣦⣀⣽⡷⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⡇⢹⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡏⣸⢸⠋⡆⡿⣽⣽⣟⡿⠀⢶⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣇⢸⣾⢸⣻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⡟⠀⢧⢇⠘⣿⣿⣳⡀⠸⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢹⢸⢹⢾⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⢱⣴⣿⡾⡀⠸⡧⡉⠓⠒⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸⢾⣾⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⣧⣷⠀⢻⡹⡆⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⣿⢹⡟⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣀⣀⡀⢠⢿⣿⣿⠏⠘⡾⡄⠀⢧⡸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢴⡖⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⣿⠸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⠀⠀⠀⠀⠀⣹⣿⡿⡻⠋⠀⠀⢻⢧⠀⠀⢳⣳⡀⠀⠀⠀⠀⠀⣴⣛⠉⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⣿⠀⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⡷⠒⠒⠒⢶⣾⠹⣿⣼⠃⠀⠀⠀⠈⢿⡆⡀⠀⢳⣳⣦⠀⠀⠀⠀⠈⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢸⣿⠀⣿⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠁⢀⡄⠀⠘⣿⣄⣿⠈⠛⢦⡀⠀⠀⣼⣿⢷⡀⠀⠹⣎⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⡇⠀⢸⡿⠀⡿⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⢾⡇⠀⢀⡟⣸⠛⢷⣄⠀⠙⢳⣾⡟⠙⣏⢧⠀⠀⠘⣆⢸⡿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⢇⠀⢸⡇⠀⢻⢧⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⠀⠸⡇⣀⣼⡟⣿⣿⣦⣝⣳⣦⣾⠿⣷⠀⠸⡞⣆⠀⠀⠸⡆⢷⢈⣧⠙⣶⣄⡀⠀⢀⣠⣴⣾⣿⠟⠁⠀⠀⢸⠀⢸⡇⠀⠸⡿⡄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀ ⣆⠀⠀⣿⠁⡼⢁⣀⣙⢿⣏⣣⣬⣿⠀⠙⠳⣄⠹⡽⡄⠀⠀⠹⡈⡎⣿⠀⣧⣧⠉⢻⣿⣿⣿⡿⠃⠀⠀⠀⠀⢸⡄⣿⠃⠀⠀⢹⡻⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀ ⡿⡀⠀⢸⣾⡃⣿⣿⣿⣤⣾⡿⢹⡏⠀⠀⠀⠈⠉⠻⣵⡀⠀⠀⠻⣵⢸⡆⢸⡞⡆⠸⡿⡟⠁⠀⠀⠀⠀⠀⠀⢸⡇⡿⠀⠀⠀⠀⠳⡙⢷⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀ ⠂⣃⠀⢸⣿⣿⣿⣿⢿⣤⣿⢃⠏⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⢻⡏⣧⢈⡿⣽⡄⣧⢻⡀⠀⠀⠀⠀⠀⠀⢸⢱⠇⠀⠀⠀⠀⣀⣽⣦⣿⣧⣤⠤⣤⣤⣤⣤⡀⢧⠀⠀⠀⠀ ⢺⣿⡀⢸⣿⣿⣽⣿⣿⣭⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠈⢷⣿⢸⡇⢹⣷⣿⣾⡇⠀⠀⠀⠀⠀⠀⣞⡿⠀⠀⠀⣠⣾⡿⣯⣿⡿⢋⣵⣾⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠘⣾⢸⡇⢸⠻⣿⣽⠃⠀⠀⠀⠀⠀⢀⣿⡥⢤⣰⣿⡿⣫⠞⡵⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⠀⣿⣷⣿⣿⣷⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢿⣿⠇⣸⣤⠞⠋⠀⠀⣀⡤⠖⠛⠉⢸⡇⠈⣿⢋⣴⢫⡞⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀ ⠀⠹⣎⢉⡻⣷⣽⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠘⣯⠞⠛⠉⠁⠀⠀⢘⣁⣀⣀⣀⣴⣿⣇⠀⢸⣿⣱⡟⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦ ⠀⠀⠘⡳⣕⣠⣝⣻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣾⢇⡇⠀⠀⠀⠀⠀⠀⣼⣁⣀⡀⠀⠀⠀⠽⠛⠋⠙⣏⣀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣄⣀⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⠛⡛⢿⣧⠙⢶⣦⡀⠉⠙⠲⢮⣽⣿⣏⠉⠉⠉⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⣼⡆⠐⢿⣄⠹⣷⡀⠙⢿⡄⠱⡀⠀⠈⣿⣿⣿⡉⠻⣍⠑⠲⢽⣿⠶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⢸⠁⡆⠙⣿⡀⠈⢿⣆⠘⢿⡄⠈⢿⣆⠱⡀⠀⢻⠸⣿⢻⡄⠈⢳⡀⠀⠙⢷⡈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⡿⡄⠘⡄⡸⣷⡀⠀⢻⣆⠀⠻⡄⠈⢯⠀⢱⣷⠀⠀⣿⡆⢿⡄⠀⢳⡀⠀⠀⠻⣦⠈⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⠀⠀⢇⢃⠀⠱⡜⣿⣷⡀⠀⢻⣆⠀⢱⠀⠈⢧⠀⢿⣆⠀⢸⣧⠈⣷⠀⠀⢧⠀⠀⠀⠙⣷⡀⢳⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢸⣿⡆⠀⠘⣜⠀⠀⠙⢎⢿⣷⣄⠀⢻⣆⠀⢇⠀⠀⠀⠘⣿⡀⣿⣿⠀⢸⡀⢣⠘⡆⠀⠀⠀⠘⣷⡀⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠀⢿⣷⠀⠀⠘⣦⠀⠀⠀⠁⠙⢿⣦⡀⢻⡄⠘⠀⠀⠀⠀⢻⣷⢨⣿⡀⠀⢧⠀⢇⢻⠀⠀⠀⠀⠘⠷⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⡀⠈⢿⣷⡄⠀⠘⣷⣄⡀⠀⠀⠀⢙⡛⣦⣷⠀⠀⠀⠀⠀⠘⣿⠾⣿⡇⠀⠘⠀⠸⡜⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢇⠁⡀⠈⠻⣿⠶⣄⡘⢷⡉⠒⢶⡟⠉⣽⣿⣿⡇⠀⠀⠀⠀⢸⣿⡷⡾⡇⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⡘⣆⠘⣦⣀⠈⠳⠷⣍⠉⠉⠁⠈⠇⠀⢿⣿⣿⠿⡀⠀⠀⠀⠸⣯⡇⠀⡇⠀⠀⠀⠀⠸⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⢿⣿⢧⢻⣦⡈⣿⣍⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⢣⠀⠀⠀⠀⡟⡇⢸⣷⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⢸⡟⡏⣧⣿⣿⡿⠀⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⡇⣧⣿⣿⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠁⣹⣃⠹⣿⣷⡀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢹⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡀⢻⢦⠉⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡿⣿⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣀⢀⣿⣿⡟⢹⣇⠈⢎⢇⠀⠀⠀⠈⠁⠀⠀⢀⣀⣤⠄⠀⠀⠀⠀⢸⠀⠀⢸⡇⡟⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠏⠀⠀⠀⣸⣿⣿⠟⠀⠀⢿⡄⠈⢿⣆⠀⠀⠀⠀⢴⣋⣁⣠⠏⠀⠀⠀⠀⠀⠀⣇⠀⢸⡇⢱⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠋⠉⠉⢻⡇⣿⠯⡀⠀⠀⠘⣷⡄⠈⢻⣷⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣠⣿⠀⢸⡇⢸⡆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠾⢦⡆⠀⢸⢛⠿⣄⠈⠓⢤⣼⠿⣿⡀⠀⠹⡈⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠹⠀⢸⠇⢸⣇⢰⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀ ⠀⠀⢇⣠⣾⢻⣿⣮⣳⣦⣾⢿⡄⠹⣷⡀⠀⢱⠸⡈⡏⢳⣤⣀⣀⣠⣴⣾⡿⠁⠀⠀⡇⢸⠀⠈⣿⣸⡀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⣇⠀⢸⣠⣇⣤⣼⢻⣷⣶⡇⠀⠙⠦⣹⣧⠀⠀⢣⢃⣷⠸⣿⠈⢿⣿⡿⠋⠀⠀⠀⠀⣇⣿⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀ ⠉⠀⢸⣿⣾⣿⣿⣻⡟⡼⠁⠀⠀⠀⠀⠹⣧⠀⠀⢿⣼⡄⢻⣧⢸⢹⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢙⣾⣷⣄⣀⣀⣀⣀⡀⣇⠀⠀⠀ ⢾⣇⢸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠹⣧⠀⠈⢷⡇⡏⢻⣾⢿⡇⠀⠀⠀⠀⢰⡿⠀⠀⣀⣴⣿⣿⡿⢛⣵⣿⣿⣿⣿⣾⡄⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠸⣿⡇⢈⢻⣿⠃⠀⠀⠀⣀⡼⡗⢲⣾⠿⣻⣿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀ ⠀⣿⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢿⣣⠾⠿⠁⠀⠰⠚⠉⠀⣠⡆⠈⣯⡞⡽⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄ ⠀⠈⢻⣇⣝⣻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣽⢾⠁⠀⠀⠀⠀⣜⣉⣉⠉⠉⠹⠒⠛⢻⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣠⣴⡶⠛⠉⠉⢹⣿⣿⣶⣶⣟⣭⣴⣶⣶⣦⡶⠛⣿⠟⠁⠀⠀⠀⣀⣰⠏⠀⠈⢷⠘⣆⢷⡘⢿⣧⡙⢯⢷⡌⢿⣶⣀⣤⣤⣀⠀⢸⠞⠉⠉⠉⠉⠉⠛⠊⠀⠀⠈⠉⠀⠀ ⣴⣿⠟⠁⠀⢀⡤⣰⣿⣿⣿⣿⣿⠿⠉⠀⠀⢠⡞⠀⡐⠋⠀⠀⠀⡴⠋⠀⡿⠀⠀⢰⠘⡄⠹⣼⡗⠈⢻⣷⡈⢳⡙⣌⢻⣿⣿⣎⠉⠛⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡽⠁⠀⠀⣰⣿⠟⠉⠉⠙⣿⣿⠳⡀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⡞⠁⠀⢰⠇⠀⠀⢸⣶⢧⠀⡇⡇⡀⠀⢻⣷⡀⠑⡜⣧⢹⣿⣿⠷⣄⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⣴⡿⠋⠀⠀⠀⢠⢿⣿⠀⠙⠂⣰⡏⠀⠀⠀⠀⠀⢀⡾⠁⠀⢠⡟⠀⠀⠀⣾⣿⢸⠀⢹⢹⢹⡆⠀⢳⢷⡀⠀⠘⢷⢿⠙⢳⣜⢧⡀⠘⢾⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⣰⢫⠇⠀⠀⠀⠀⣸⠘⡿⡀⠀⣰⡟⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⡟⠀⠀⠀⠀⣟⡇⢸⡀⢸⢸⠀⢳⡀⠘⣷⢧⠀⠀⠈⣟⣇⠀⠙⣮⢧⠀⠘⢯⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠏⣾⠀⠀⠀⠀⢠⡏⠀⣷⠓⢰⢯⠃⠀⠀⠀⠀⢀⡾⠁⠀⠀⣾⠁⠀⠀⠀⢰⢿⠀⣸⡇⢸⢸⡄⢸⣷⠀⢹⡾⡄⠀⠀⠸⣿⠀⠀⠈⣯⣧⠀⠈⣽⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡟⢠⡇⠀⠀⠀⠀⣼⠁⠀⢯⢧⡞⡞⠀⠀⠀⠀⠀⡼⠁⠀⠀⣼⠃⠀⠀⠀⠀⣿⡏⢠⠇⡇⡇⠀⡇⢸⣘⡆⠀⣷⣿⢣⠀⢰⣽⡄⠀⠀⢸⣿⡆⠀⠈⣟⣧⠀⠀⠀⠀⠀⠀⠀ ⣸⠀⢸⠀⠀⠀⠀⠀⡏⢠⡇⢸⢨⡗⠁⠀⠀⠀⠀⣸⠃⠀⠀⣼⠇⠀⠀⠀⠀⣸⡿⢀⡟⠀⣿⡯⢀⡇⣸⠉⢇⠀⣿⡸⣾⡄⠀⢻⣧⠀⠀⠀⣿⣿⡄⠀⢸⢹⡆⠀⠀⠀⠀⠀⠀ ⡏⠀⣸⠀⠀⠀⠀⢰⡇⢸⠀⠸⣿⠰⠀⠀⠀⠀⢠⠇⠀⢀⣼⢟⣀⣀⣀⣀⣼⠿⠛⠛⠂⠀⡟⠃⠘⠛⢻⣾⣾⣄⣇⣇⡇⡇⠸⡾⣿⠀⠀⠀⢻⢹⡇⠀⢸⡈⣧⠀⠀⠀⠀⠀⠀ ⡇⢀⡇⠀⠀⠀⠀⢸⠃⣼⡇⠀⣿⣰⠀⠀⠀⠀⣾⠀⣠⣾⣯⣽⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣟⣿⣫⣿⣷⠁⠀⢳⣿⡇⠀⠀⢸⡛⡷⠀⠀⡗⢹⠀⠀⠀⠀⠀⠀ ⠂⢸⡇⠀⠀⠀⠀⣸⠀⣿⣿⡀⣯⢹⠀⠀⠀⢸⡇⢸⡏⠘⣿⣿⣿⠇⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠘⡏⠁⢹⡆⠀⢸⢸⡇⠀⠀⠀⡇⢹⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⡟⠀⣿⣿⣷⣯⡏⠀⠀⠀⣸⡇⠘⢧⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⢍⣤⠀⠀⢸⡇⠀⠸⠸⡇⠀⠀⠀⡇⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⡇⢸⡇⠀⠀⠀⠀⡇⢰⣿⡏⢿⡟⡇⠀⠀⠀⣿⠇⠀⠈⠛⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⢸⡇⠀⠘⠀⣿⠀⠀⠀⣿⢀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⣇⠸⡇⠀⠀⠀⠀⡇⣿⣿⠀⢸⣧⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⠀⠀⠀⢹⠘⡇⢰⠃⢸⠀⠀⠀⠀⠀⠀ ⢹⠀⣇⠀⠀⠀⢸⡇⣿⣿⣇⢸⢸⠀⠀⠀⢸⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸⠀⠀⠀⢸⣄⡇⣸⠀⣾⠀⠀⠀⠀⠀⠀ ⠈⣇⢹⠀⠀⠀⢸⡇⣾⣼⣿⣿⠸⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⢠⠀⢸⠀⠀⠀⢸⣿⢡⡇⢰⡇⠀⠀⠀⠀⠀⠀ ⠀⠹⣾⠀⠀⠀⢸⡇⣿⡿⡟⣿⣌⠀⠀⠀⣿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⠀⠀⠀⢸⠀⠀⠀⢼⣿⡾⠀⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣧⠄⠀⢸⡇⣿⢹⣷⣿⣿⠀⠀⠀⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⢶⡟⠀⠀⠀⠀⠀⠀⢀⢠⣿⢹⡿⠀⠀⠀⢸⠀⠀⠀⣸⣷⠇⢠⠇⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠘⣿⡄⠀⣻⡇⣿⢨⣿⣿⣿⡆⠀⠀⢻⣿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⡀⣠⡤⠀⠀⠀⠀⠀⢀⣴⡟⣿⡟⡇⠀⠀⠀⢸⠀⠀⠀⣿⡟⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⣿⡇⠀⣿⡇⣿⣸⣿⣯⣻⡇⠀⠀⠀⣿⢸⣿⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢀⣴⡞⣿⡇⣿⣿⡇⠀⠀⠀⡼⠀⠀⣰⣿⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⢿⣯⠀⢿⡇⣿⠘⣿⢹⠻⣿⠀⠀⠀⢸⣾⢻⠀⠀⠙⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⣿⠁⣯⡇⣿⣿⡇⠀⠀⢠⡇⠀⢠⣿⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡄⠀⢸⡟⠀⢸⣧⣿⡎⣿⢸⠀⢻⡆⠀⠀⢸⣿⡾⠀⠀⠀⠀⠈⠻⣿⣷⣦⣤⣀⡀⣀⣠⣶⣿⣿⣹⡇⣿⠀⢻⡇⣿⡿⠁⠀⣰⣿⠁⠀⣾⣿⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢷⠀⣸⡇⠀⢸⣿⣿⢃⣿⠸⣆⣸⣇⠀⢀⠘⣟⡇⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣄⣼⡇⢿⡇⠀⢠⣏⣿⠀⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢸⡆⣿⠃⠀⢸⣿⣿⣾⢸⣧⣿⣿⣿⣧⠘⡆⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⣿⣆⠀⠈⢻⣷⣽⡾⠀⠀⣾⣽⣾⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⣧⠏⠀⠀⣞⣹⣿⣿⡾⢱⣿⣿⣿⢻⣷⡹⡜⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡆⠀⠀⢻⣿⠁⢀⣾⡿⢟⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣸⣿⣶⣶⣶⣿⣿⣿⡿⢠⣿⣿⣿⣿⠀⢻⣷⣿⣿⣏⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⡀⠀⣰⣇⣴⣿⡿⣿⣾⣾⣯⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⣸⣿⣿⣿⣿⠃⣾⣿⣿⣿⡿⠀⠸⣿⣷⡍⠻⣿⠿⣿⣶⣿⣿⣿⣿⣹⣿⣿⣿⣏⣿⣿⠟⠹⣿⣧⠺⠋⣿⣿⣿⣿⣮⡻⣿⣿⣿⣩⣙⠛⠳⠶⢶⣶⣤⣀⠀⠀⠀⠀⠀ ⣇⡀⠀⢠⣿⣿⣿⣿⠃⣼⣿⣿⠿⠋⠀⠀⠀⣿⣿⣷⡀⠈⠁⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠀⠀⠸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣮⡻⣿⣧⡻⣷⣄⠀⠀⠈⢻⣿⣿⣆⠀⠀⠀ ⣿⣿⣦⣿⣿⣿⣿⢇⣾⡿⠛⠁⠀⠀⠀⠀⠀⣿⣿⡼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣷⣮⡻⣷⣻⣿⣧⠰⡄⠀⣿⡿⣿⡆⠀⠀ ⣿⣿⣿⣿⣿⣿⢣⣿⣯⣄⣀⠀⠀⠀⠀⠀⠀⣽⣿⡇⢸⣯⠉⠉⠒⠲⢤⡄⠀⠀⠀⠀⠀⠀⠤⠚⠁⢘⣷⣾⡇⠀⠘⠿⣿⣿⡿⠋⣀⣈⣽⠉⠻⣿⣿⣿⡇⢻⣄⣿⡇⣿⣿⡀⠀ ⣿⣿⣿⡿⣿⣏⣠⣤⣿⣿⡿⠿⠷⠶⠤⣤⣾⣿⣿⣿⡀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⡀⠀⠀⣠⣶⠾⠿⠛⢋⣭⣍⣉⣡⣼⣿⣿⢸⣿⣿⠇⣿⣿⣧⠀ ⣇⢻⣿⣷⣤⣤⣤⣴⣴⣶⣶⣶⣶⣶⣶⣶⣦⣉⠻⢿⡷⢦⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣿⣿⣶⣿⣭⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢠⣿⣿⣿⡀ ⣿⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠓⢦⣿⣄⣙⣻⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣻⣧⣾⣿⣿⣷⣾⠟⠺⠯⠛⡛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠁⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⣄⡈⠙⠲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣉⠀⠀⠀⢀⡴⢞⣡⠤⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠁⠈⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⢒⣙⣿⣿⡿⠋⣁⣀⣀⣤⣤⠶⠶⢶⡾⠧⠤⠤⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢞⣷⣤⣶⡶⠶⢶⣲⣶⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢞⡡⠖⠋⣡⣿⣿⠧⠚⠉⢀⡄⢀⠜⠁⢰⢣⠋⢠⠏⢠⠀⢰⠉⣳⢶⣏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣉⣙⠓⠪⣅ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡵⣋⠴⡣⢚⣽⠟⡁⢀⠀⡴⠋⣠⢿⠆⣼⣿⠃⠀⣼⠀⡸⠀⢸⡘⢮⠳⣳⡍⠳⣤⡀⠀⠀⠀⣀⣀⡠⠤⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⣿⣧⡙⢿⣶⡀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⣫⠊⣡⡞⡵⡿⣣⠞⢠⡞⡜⠁⢰⣟⡟⢰⣳⠃⠀⠀⣿⠀⣷⠀⠀⣇⡆⠳⣽⣵⡀⠈⢿⡷⣌⢉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠻⣿⣿⣿⣿⣟⢿⡷⣝⢧ ⠀⠀⠀⠀⠀⠀⣸⡟⠜⠁⣌⣮⣸⢞⡞⠁⠀⡿⡟⢀⡞⠠⢿⠀⢺⡿⠀⠀⢸⣿⠀⡏⠀⠀⢿⣇⠀⠱⣵⢷⠀⠀⡽⣍⢮⡳⣄⠀⠀⠀⠀⠀⣠⡾⠁⣔⣻⣿⣷⣻⠙⣦⢳⡈⢳ ⠀⠀⠀⠀⠀⢰⡟⠀⠀⠈⣼⡿⣡⠞⠀⠀⣸⡟⢀⡟⡇⠀⡏⢰⡘⡇⠀⠀⠈⣿⢀⠇⠀⠀⠸⣼⡄⠀⠹⣏⣇⠀⠸⡝⢆⢳⠘⢧⠀⠀⣠⢾⠿⠁⣼⠞⡥⣿⡾⠻⣇⠘⡆⢷⠀ ⠀⠀⠀⠀⠀⡿⡄⠀⢀⣞⡞⢠⠋⣀⠀⠀⣿⢁⡼⣇⡇⠀⡇⡾⡇⠀⠀⠀⠀⢻⢸⠀⢸⠀⠀⣧⢣⠀⠀⢻⣸⡀⠀⢻⡈⢣⢳⡈⣧⠘⣡⠏⢀⡼⠋⢰⡇⡟⢧⠀⢻⡀⢳⠘⡆ ⠀⠀⠀⠀⣸⣡⠀⠀⣞⡼⢀⡏⢀⢇⠀⠀⡟⡜⠁⣼⠃⠀⡇⡇⠇⠀⠀⠀⠀⠸⡟⠀⠘⠀⠀⡏⠹⡄⠀⠀⢧⣧⠀⠀⣧⠈⢏⢣⠸⡟⠁⢠⠞⠀⢀⢿⢳⠁⢸⡄⢸⢷⠘⡇⢻ ⠀⠀⠀⠀⣿⡟⠀⢸⣻⠃⡞⠀⡾⢸⠀⠀⢠⠃⠀⢘⣿⠀⢱⡇⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⢰⡀⢣⢠⠀⠘⡼⡄⠀⢸⡆⠘⡎⣇⢹⡔⠃⠀⢀⡞⠂⣸⠀⠘⣿⠸⠈⡆⢱⠘ ⠀⠀⠀⠀⡇⡇⠀⣯⠇⢰⠁⢸⠇⢸⠀⠀⣿⠀⠀⢸⡘⣆⠈⣧⢸⡆⠀⠀⠀⠀⡇⠀⠀⡇⢸⠈⣇⠘⢟⡄⠀⢻⡇⠀⠀⢳⠀⠹⢹⡄⣷⠀⢠⠎⠀⢠⡇⠀⠀⢹⠀⠀⠇⠘⡦ ⠀⠀⠀⢸⡇⣷⢸⣿⡀⡜⠀⠈⠀⠘⡄⠠⢿⠀⠀⠘⠇⠘⢆⠘⡄⣷⠀⠀⠰⡄⠇⠀⠀⡇⠀⣇⠸⣠⠘⢿⠀⠈⣾⠀⠀⢸⡀⠀⠀⢇⠘⡆⠋⠀⢀⡏⠀⠀⡀⠸⡀⠀⢠⠀⢣ ⠀⠀⠀⢸⣧⡉⣼⣿⣿⠇⠀⡄⠀⠀⢧⠀⠈⡆⠀⠀⣿⡀⠘⡦⠰⠘⡄⠀⠀⢣⠀⢀⠀⢰⠀⣿⡆⢻⣇⠈⡆⠀⢻⠀⠀⠀⡇⠀⠀⢸⡀⢧⠀⣰⠟⠀⠀⠰⡇⠀⡇⠀⠀⠀⢸ ⠀⠀⠀⢸⣿⣇⢹⣿⣻⠀⢸⠇⠀⠀⢈⣆⠸⣡⠀⢰⡜⣗⠀⢲⠀⠀⠹⠀⠀⠘⣆⢸⡀⠘⡄⢫⣿⡀⠛⣆⢳⠀⠈⡇⠀⠀⡇⠀⠀⠀⣧⢸⣴⠃⠀⡇⠀⠀⡇⠀⡇⠀⠀⠀⠘ ⠀⠀⠀⠈⣿⠙⡜⣏⣯⠀⢸⠀⡄⠀⠸⡞⣆⢫⣇⠀⢷⣜⢦⠈⡆⢀⠀⠁⠀⠀⠙⣶⣻⡰⣳⢸⣯⣧⡀⠹⡼⡆⠀⣷⠀⠀⢰⠀⠀⠀⣿⢸⠃⠀⠸⡇⠀⠀⡇⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠁⢻⣟⠀⣸⠀⣿⡄⠀⣟⢮⠻⣯⠄⢸⣟⣎⡳⣼⡀⢳⡴⣕⢄⡀⠹⠿⣷⣝⣮⢷⠙⢷⣄⠹⣿⠀⣿⠀⠀⢸⠀⠀⢰⢸⡟⡆⠀⡹⡇⠀⢀⡇⠀⠀⠀⠀⢰⠀ ⠀⠀⠀⠀⠸⣄⠀⠈⢿⠀⣿⠀⢹⢹⣀⢻⣾⡷⢽⣧⡈⢿⣼⡛⠲⠿⣬⢻⡮⣷⣯⣗⢦⠬⣟⣽⣿⡷⣦⣹⢦⣹⠀⢹⠀⠀⢸⡆⠀⢸⢸⡇⣟⠀⢠⡇⠀⢸⣇⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠹⡄⠀⢸⡇⡇⠀⢸⣸⡟⡎⢿⡇⣼⣿⣟⢬⣿⡗⢄⠀⠘⠪⣯⡀⠀⠙⠳⡌⡿⢑⣿⣟⠀⡈⠻⣿⡆⢸⠀⠀⢸⠀⠀⠸⣸⡇⣿⠔⣉⡇⠀⢸⢹⠀⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠱⡄⠀⡇⡇⠀⠀⣿⡇⣽⠈⠃⢸⠛⡻⣷⠹⣿⡆⠁⠀⠀⠈⠑⠆⠀⠀⢹⡁⢸⡿⢿⣿⣿⠀⠈⡇⢸⠀⠀⠸⠀⠀⠀⣿⠁⢿⢿⡏⡇⠀⡜⢸⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠙⠆⢰⡇⠀⠀⣿⠀⣟⣇⠀⢾⣷⣤⣬⣦⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⣀⠀⣹⢆⣠⡇⢸⠀⠀⠀⠀⠀⠀⡞⡇⣶⢸⣯⣿⠀⣧⣼⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⠀⠀⢻⡄⢸⣆⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠛⠉⠀⡇⢸⠀⠀⠀⠀⠀⠀⠟⡇⣿⣿⣟⢿⣼⢻⣿⠀⠀⠀⠀⠀⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢸⡇⢸⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⡇⣯⠏⠀⣼⢙⣿⢺⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣱⠀⠈⣧⢸⡄⣇⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠈⠀⠀⠀⠀⣿⣏⣄⣼⣿⡛⣽⡄⠀⠀⠀⠄⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠀⠀⢻⠀⡇⢹⡆⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⠀⠀⡔⠀⠀⠀⢠⣿⠛⡿⣿⣸⡇⠹⡇⣰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠘⡆⢷⢰⠹⡄⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⡏⠀⠀⡇⠀⠀⠀⣼⢸⢸⡇⢻⢿⡿⢀⠁⣿⠀⢰⢮⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢧⠀⠀⢹⡘⢸⡇⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡇⠀⠀⠀⡿⢸⣾⣷⣾⣿⡇⠈⢸⣿⠀⣼⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⣇⠀⠀⢧⡌⡇⠁⠙⢦⡀⠀⠀⠀⠀⠙⢷⣤⠤⠤⠤⠒⠒⠛⠃⠀⠀⠀⠀⠀⣿⠀⠀⢰⠁⠀⠀⢸⡇⡟⢹⡏⠈⢿⣿⢠⣿⣧⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡸⡄⠀⠈⣧⢣⠀⠀⢾⡝⢦⣀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⠀⠀⣸⠀⠀⢀⣾⠀⡇⣿⡇⠀⢸⣿⡌⢹⣸⢰⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠹⡄⠀⠘⣿⡀⠃⢸⢻⣧⠉⠳⣄⠀⠀⠀⠻⣄⣀⣀⠔⠀⠀⠀⠀⠀⠀⣾⣿⠀⢠⣇⣀⣀⣸⠻⣸⠀⢿⠇⠀⢘⡟⣇⢀⠁⡞⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠱⡄⠀⠘⣇⠀⠈⡏⢞⣦⣖⣉⣷⠤⠤⠶⠖⠂⠀⠀⠀⠩⣉⣩⣽⣿⣿⣯⣭⣏⣉⣀⡈⠉⠤⢯⡀⠀⠀⢀⣈⣴⣿⣿⣿⣇⡿⣧⠀⠀ ⣦⣄⣀⡀⠀⣀⣠⠤⠴⠖⠒⠒⠲⠤⠼⢦⣙⣄⠤⠈⠷⠛⣋⣉⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣶⣿⣿⣿⠟⠋⠀⠙⢧⠻⠀⠀ ⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⢀⣀⠀⠀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣀⣴⣿⣷⡞⣡

⠀⣠⣴⠞⠋⠉⣹⣿⣿⣶⣯⡵⠶⠶⣶⠚⣽⠋⠀⠀⡀⢠⡟⠀⠘⡆⢳⣧⠹⣷⡙⢿⣎⢻⣦⣤⣤⣄⡀⠛⠉⠉⠉⠉⠉⠁⠀⠉⠀⠀ ⣾⠋⠀⢀⣶⡶⠿⢿⣿⣿⠉⠀⠀⡼⠁⠀⠀⠀⢠⠎⠀⣸⠁⠀⣰⣳⠘⣿⠀⠘⣷⡈⠪⢳⡹⣿⣷⣄⠙⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⢠⡿⠋⠀⠀⢰⣿⠀⠳⢀⡾⠁⠀⠀⠀⢀⠎⠀⢰⠇⠀⠀⣿⠋⡄⣿⠙⡆⠘⣷⡀⠁⠹⣿⠛⢬⣳⡀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⢿⠃⠀⠀⠀⡇⢹⡇⢀⣾⠁⠀⠀⠀⢠⠏⠀⢀⡏⠀⠀⢰⣿⢠⡇⣿⡇⢹⡀⢹⣷⠀⠀⢻⣇⠀⠻⣷⡀⠹⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⡞⡼⠀⠀⠀⢰⠃⢸⣇⣼⠏⠀⠀⠀⢀⠎⠀⢀⡞⠀⠀⠀⣸⡏⣸⢇⡟⢷⢸⢷⠀⣿⣇⡀⠀⣿⠀⠀⢹⣧⠀⠹⣷⡀⠀⠀⠀⠀⠀ ⡸⠁⡇⠀⠀⠀⡞⢰⢸⣙⡟⠀⠀⠀⠀⡞⠀⢀⡾⠁⠀⠀⢠⡿⢠⠇⢸⡇⣸⢸⠻⡆⢻⣿⣧⠀⢿⡆⠀⠈⣿⡇⠀⢹⣧⠀⠀⠀⠀⠀ ⡇⢠⠀⠀⠀⠀⡇⣾⠀⣿⠆⠀⠀⠀⡼⠀⢠⣾⣃⣀⣀⣤⠿⠛⠋⠀⠚⠀⠛⣻⣾⣧⣼⣏⡇⠀⣾⣧⠀⠀⢻⣷⠀⢸⢹⡄⠀⠀⠀⠀ ⠃⢸⠀⠀⠀⢠⠇⣿⡄⣽⡜⠀⠀⢠⡇⡴⢻⣷⣿⡿⣿⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣿⠟⣇⠀⠹⣿⠀⠀⢸⢸⡀⠈⠁⡇⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⢸⠀⣿⣷⣿⠆⠀⠀⢸⠁⢧⠀⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣃⡉⠀⢻⠀⠠⢹⠀⠀⠸⡌⠀⠀⡇⡇⠀⠀⠀⠀ ⡆⢸⠀⠀⠀⢸⢸⡿⢿⣿⡆⠀⠀⣿⠀⠈⠓⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⢸⠀⠀⢸⡇⠀⠀⡇⡄⢸⠁⡇⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⣼⣿⣷⠀⣿⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⡇⡇⢸⢀⡇⠀⠀⠀⠀ ⠸⡘⠀⠀⠀⣿⣼⣿⣧⡿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡇⠀⠀⣷⡇⡆⢸⠁⠀⠀⠀⠀ ⠀⢻⡇⠀⠀⣿⣿⣿⢻⣇⠀⠀⢸⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣰⣿⡄⠀⠀⡇⠀⠀⣿⣿⠀⡏⠀⠀⠀⠀⠀ ⠀⠈⣷⠀⠀⣿⣿⢿⣿⣿⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠛⠋⠀⠀⠀⠀⠀⣰⣿⣿⠁⠀⠀⡇⠀⠀⣿⠇⣸⠁⠀⠀⠀⠀⠀ ⡆⠀⢻⡇⠠⣿⣿⣿⣿⢿⡇⠀⠈⣿⣿⠷⣤⡀⠀⠀⠀⠀⠀⠘⠒⠒⠃⠀⠀⠀⣠⣾⡏⢹⣿⠀⠀⢀⡇⠀⣸⡟⢰⠃⠀⠀⠀⠀⠀⠀ ⣧⠀⢸⡇⠘⣿⣿⣿⣿⡿⣧⠀⠀⢹⣿⡇⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⢹⡇⢸⣿⠀⠀⣸⠀⢀⣿⢱⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⢸⡏⠀⣿⣿⢿⡟⡇⢹⠀⠀⢸⣿⠃⠀⠀⠀⠙⠻⣿⣶⣤⣤⣴⣾⣿⣿⣿⡟⠈⣇⣸⡇⠀⣼⡟⠀⣼⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢣⢸⠃⠀⣿⣿⡾⣧⣷⣾⣦⠠⡄⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⢿⣏⠙⠻⣾⣿⣹⠀⢠⣿⣷⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢸⡞⠀⢠⣿⣿⣷⢏⣿⣿⡿⣷⣱⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠙⣿⠃⣠⣿⣟⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠷⠾⠷⢶⣿⣿⣿⠇⣾⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⡄⣠⣧⣶⣿⣿⣿⣾⣿⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⡀⠀⢀⣾⣿⣿⡏⣼⣿⣿⠟⠁⠈⣿⣿⡈⠛⠋⠛⠛⠿⠿⠿⠿⠿⠿⠟⠋⠀⣿⣇⠀⣿⣿⣿⣿⣮⡻⣿⣷⣦⣄⠉⠙⠻⣷⣦⡀⠀⠀ ⣿⣦⣼⣿⣿⣟⣼⡿⠛⠁⠀⠀⠀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠀⢻⣿⣿⣿⣿⣿⣮⣿⣾⣿⣷⣠⡀⢹⣿⣷⠀⠀ ⣿⣿⣿⣿⡟⠺⢿⣤⣄⣀⠀⠀⢀⣾⣿⡈⣿⡉⠉⠑⠢⠀⠀⠀⠀⠀⠐⠃⠀⣿⣾⡆⠈⠛⠿⢟⣁⣤⣼⣏⣿⠿⣿⡇⣷⣿⡏⣿⣇⠀ ⡿⣿⣟⣛⢒⣾⣛⣛⣉⣉⣉⣛⣛⠿⣿⣧⡘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⣷⣄⣤⡞⢋⣩⣥⣼⣷⣶⣶⣿⣿⣿⣿⢃⣿⣿⡀ ⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠦⣽⣌⣛⣷⣀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣾⣿⣿⣿⠿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢒⠖⡿⡛⢉⢟⠟⠲⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠤⡐⢆⣤⣤⢪⢫⠢⠁⣼⡑⠀⢸⠸⡯⣂⠨⠳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠕⢁⢄⣾⢿⢣⢣⣇⠃⢠⣿⠃⢸⢸⠀⢻⡗⠂⠡⠈⢦⣤⠄⣀⠀⠀⠀ ⠀⡼⢁⠔⡡⠓⣛⠂⢂⡞⢸⡆⢸⣿⠀⣾⠘⡆⠘⡏⣭⠀⢃⠈⡿⣢⡈⢊⢊⠉ ⢸⢡⠊⢰⠃⠀⡟⠘⢸⣧⣸⣳⣼⣿⢸⡟⣆⠛⢄⢹⡸⡄⠘⣰⢰⠈⢿⡀⢂⠄ ⣇⠃⠐⣿⠀⢸⡇⠀⡟⣴⣿⣿⠌⠃⠃⠉⢀⣿⣿⣧⣧⡇⠀⣿⢸⠀⠈⡇⠈⣸ ⡟⢀⠛⣿⠀⠈⡇⠀⡇⠐⠾⠓⠀⠀⠀⠀⠀⠈⠛⠊⠹⠈⠀⢹⢸⠀⠀⣷⠀⠉ ⡇⢸⡇⠸⡄⢰⢀⢰⣇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡄⠀⢾⣼⠀⠀⡿⠀⠀ ⢀⢸⡇⠀⠀⢸⠈⢼⡇⡄⠀⠀⠀⣔⣒⡄⠀⠀⠀⠀⠀⡇⠀⢸⢻⠀⢀⡇⠀⠀ ⠈⢼⡅⠀⠀⠈⢃⠈⡇⢘⣄⠀⠀⠑⡂⠚⠀⠀⠀⢀⡜⣧⠀⢸⠀⢀⡼⡇⡰⠀ ⠀⠈⠳⡀⠀⠀⡆⡆⠹⡞⡏⡷⢄⠀⠀⠀⢀⣠⡴⠁⣇⣽⠀⣿⡆⠘⢀⡷⠁⠀ ⠤⠐⠒⠒⠒⠲⣴⢹⣢⡐⣿⣧⣤⣈⣉⡉⠁⠀⣇⡇⢹⡁⢀⢿⠇⠀⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣧⢂⠀⡌⠙⠻⡿⠿⢿⣿⣿⡿⢡⠋⠇⠌⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⡀⠙⠻⡒⠤⢈⡀⠀⠀⠈⠉⡋⠰⠠⢐⣃⣀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⢀⡠⢄⡀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⣈⠑⠢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣤⣤⡤⠖⠛⠃⠀⣀⣀⣾⣟⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⣀⣀⣀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⣊⠥⠒⣾⣿⠯⠒⢈⠉⢩⠋⣠⡠⢁⡆⡀⠉⡒⣦⣴⡒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣯⣛⠋⠽⡋ ⠀⠀⠀⠀⠀⠀⣰⡿⡫⢕⣖⣹⢛⠅⣀⡰⠋⣴⡇⣰⡟⠀⢸⠀⡇⠀⣏⢟⢿⣏⠳⣤⡀⣀⣀⡠⠤⠀⠀⠀⠀⠘⣿⣿⣿⣿⣯⣝⢷⡄ ⠀⠀⠀⠀⠀⣼⣯⠎⢰⢟⣾⡷⠋⣰⡿⢠⢸⣿⢠⣿⠁⠀⣼⠀⡏⠀⢹⡀⢻⣿⡄⠈⢿⣦⡤⡀⠀⠀⠀⠀⠀⡠⢈⣿⣿⣿⢷⣻⡙⢕ ⠀⠀⠀⠀⣰⠋⠀⢈⣾⢟⠟⠀⢠⡿⢠⡏⠈⡇⠸⡇⠀⠀⢻⢸⠁⠀⢸⣇⠀⠹⣿⡀⠹⡷⡕⡝⣄⠀⠀⣠⡾⢁⡾⣯⣿⠿⣇⢻⢱⠈ ⠀⠀⠀⢀⠇⠀⢠⣾⢃⠏⡀⠀⢸⢁⠿⡇⢰⠁⡇⠁⠀⠀⠘⡎⠀⡇⠀⣿⡄⠀⢻⣇⠀⢱⠘⣷⡈⣆⣪⠎⢠⠟⢡⡿⠛⡄⢹⡄⡎⣧ ⠀⠀⠀⣾⡆⠀⣿⠃⡞⢠⠂⠀⠘⡎⠐⣿⠀⡇⠁⡀⠀⠀⠀⠇⠀⠃⠀⡃⢣⠀⠀⣿⡀⠀⢇⠸⢳⠘⣅⡰⠁⢀⢾⢳⠀⢧⡸⢧⢱⠸ ⠀⠀⠀⣿⠁⢸⡏⠸⠁⡏⠀⠀⢸⠀⠀⡟⡄⠸⡀⡇⠀⠀⠀⠀⠀⡄⢠⢰⠈⢮⡀⠸⣧⠀⠸⡀⠃⢧⠹⠀⢠⠎⠀⡎⠀⠸⠀⠘⠘⣆ ⠀⠀⢸⣿⣇⣾⣁⡇⠀⠁⢨⠀⠾⠀⠀⢣⠘⢄⠃⢳⠀⠀⠀⠀⠀⢰⠈⡆⢧⡘⢧⠀⢿⠀⠀⠇⠀⠘⡄⡇⠁⢀⡜⠀⠀⠀⡄⠀⠀⢸ ⠀⠀⢸⣿⡸⣿⡽⠀⡀⠀⠀⡆⠀⡃⠀⠸⡆⠘⠂⠘⢆⠀⠸⡀⡄⠘⡄⣿⡈⢷⡈⡄⠘⡆⠀⢀⠀⠀⢣⢰⢀⠎⢀⠀⢐⠀⡇⠀⠀⠘ ⠀⠀⠘⣿⢧⢿⣷⠀⡇⠀⠀⢾⣆⢿⡀⢳⡱⡀⢀⠀⠀⠀⠀⢳⣼⡄⣅⢻⣷⡀⢳⣧⠀⠇⠀⢨⠀⠀⢸⣸⠋⠀⣾⠀⢸⠀⠃⠀⠀⠀ ⠀⠀⠀⣿⠈⠻⣟⠀⡇⢸⡄⢸⣮⡻⣇⠸⣟⣎⡶⡄⢣⣠⣂⡀⠿⢿⣿⣼⡍⣳⡄⢻⠀⠀⠀⠸⠀⠀⡆⣿⡄⠸⢳⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡄⠀⢹⠀⠃⢸⣿⣌⣿⡿⣿⣦⡹⣿⡉⠛⢮⣿⠟⠿⢿⡖⣿⢿⣿⡟⠿⣾⡇⢰⠀⠀⠂⠀⣿⡇⣇⡠⢾⠀⠸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡄⠘⠰⠀⠀⣿⣿⡜⠇⢿⢿⣟⢿⣍⠂⠀⠉⠣⡀⠀⠙⡏⢼⣿⣶⡆⠘⡇⢸⠀⠀⠀⠀⢸⡿⣿⣶⢿⠀⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠂⢿⡄⠀⣿⢸⡧⠀⢾⣤⣽⡤⠁⠀⠀⠀⠀⠀⠀⠀⠃⢈⣄⣈⣿⣠⣇⢸⠀⠀⠀⠀⢸⠃⣄⣽⣿⣠⣧⡇⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⠀⢷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⢸⢸⠀⠀⠀⠀⠈⠀⣿⡿⢿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢸⡀⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⣸⣏⢀⣾⡾⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⡇⠃⢹⡀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⣿⢻⣿⣿⡇⢻⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢱⠸⠰⢳⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⢸⠀⠀⢰⠁⣻⣏⣟⡇⠀⣼⠀⢰⠄⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⢇⠸⡀⠳⣄⠀⠀⠀⠀⢤⣀⣀⣀⣀⠠⠤⠀⠀⠀⠀⣿⡇⠀⡄⠀⠀⣼⠽⢿⡟⢻⣇⢠⣿⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠈⢷⡇⠀⢸⡳⣄⠀⠀⠀⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠇⠀⢠⡿⡆⣿⠀⠘⣿⡞⣿⣠⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢣⠀⠘⣧⠀⢸⣿⡆⢑⣄⠀⠀⠑⠤⠤⠂⣀⣀⣀⣀⣰⣿⣀⣼⠤⠤⡞⠇⠁⠛⠀⠀⠟⣧⣀⣿⣿⠀⠀ ⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⣆⢣⡀⠈⢆⡼⠦⠟⠓⠒⣛⣩⣭⣭⣤⣤⣤⣴⣶⣿⣿⣿⣿⣷⣶⣤⣤⣽⣦⣀⣠⣶⣿⡿⠟⠻⡟⡆⠀ ⣿⣿⣷⣶⣯⣁⡀⠀⢀⡀⠀⣈⣉⣭⣴⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢀⣤⣾⡦⢂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠈⡡⡄⠦⠀⠀⠀⠀⠉⠐⠨⠑⢦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡐⢝⣶⠿⢓⢂⠔⡭⢫⠁⢐⣤⣔⠂⠀⠀⠀⠀⠀⠀⣽⣿⣟⣋⠗ ⠀⠀⠀⣴⠋⣜⣵⠕⣔⠂⡾⣸⠃⢸⠐⠘⡗⣷⡙⢶⡒⠀⠀⠀⢀⢹⣿⠿⣺⢧ ⠀⠀⠰⠁⣨⠫⠃⢸⢣⠃⣇⠛⠀⢸⠇⡀⣧⠘⣧⠘⡪⠕⡀⠴⢃⢞⡿⠻⣡⢆ ⠀⠀⡇⢰⢇⢣⠀⢘⠃⡇⢇⠀⠀⠘⠀⠁⠋⣄⠸⡆⢡⢙⡼⡡⠁⠜⡆⠧⢃⡞ ⠀⢸⣇⡟⡈⠈⠀⢸⠀⠟⠘⢸⠀⠀⠀⠂⡞⡘⡄⢣⠀⡄⠱⢁⠊⡐⠀⢐⠘⢐ ⠀⢸⣟⣷⠁⠀⢘⡀⡄⡽⠈⠀⠂⠐⣀⠰⢻⡑⣰⠘⠀⠁⠀⡾⡜⡀⠈⢸⠀⠈ ⠀⠈⡏⢻⢠⢰⡀⣿⣷⢸⣗⣅⢦⣤⣹⢿⣾⣳⡘⡆⠀⠀⠀⣱⡄⠃⢠⠀⠀⠀ ⠀⠀⠱⡀⠯⠈⣿⡿⢹⢷⢿⡀⠙⢍⠙⢻⢹⣯⡙⠇⡇⠀⠀⣯⣷⠅⠸⡇⠀⠀ ⠀⠀⠀⠁⢰⠀⡇⡇⠘⠖⠊⠀⠀⠀⠀⠈⠠⠤⠧⠂⡇⠀⠀⠟⣿⣷⣶⠃⠀⠀ ⠀⠀⠀⠀⢸⡆⢁⡈⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⣏⣼⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠘⡠⢥⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡌⣼⣿⠈⡄⢠⠀ ⠀⠀⠀⠀⠀⢫⡄⢡⡃⠑⣄⠀⠐⢦⠄⠀⠒⠀⠀⢸⠀⠇⢀⡿⡿⢹⡤⡇⣾⠀ ⠀⠀⠀⠀⠀⠈⠖⡀⢳⠀⣷⣑⢄⣈⣢⠄⠀⠀⣠⣿⡴⠤⠜⡀⠃⠸⣣⣹⣿⠀ ⣶⣤⣄⡒⠀⡀⢚⣚⣲⣵⣭⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡿⠋⢉⣭⣀

⣠⠖⢉⣩⣿⣷⠗⠒⡲⠹⠉⢀⠄⡇⢈⡌⣵⠻⡝⠮⣳⣶⠢⢌⠀⠉⠉⠀⠀⠀ ⠁⢠⠟⠀⠸⡏⠂⡜⠀⠀⠠⠁⡘⠀⢸⢣⢹⢂⢹⡄⠱⣟⢻⣄⢳⡄⠀⠀⠀⠀ ⢠⠻⠀⠀⡆⣗⣼⠁⠀⢠⠁⢠⠁⠀⡟⣸⡘⣼⡄⢿⡀⢹⠀⢹⡄⠻⡄⠀⠀⠀ ⡆⡇⠀⢰⠰⢫⡃⠀⢀⠃⣰⠃⠀⣰⡣⢁⡇⣿⣱⢸⢿⢘⡇⠀⣿⠀⡿⠀⠀⠀ ⠁⠁⠀⠘⣾⢸⡄⠀⡌⡔⣿⡿⠏⠁⠀⠀⠀⣾⣿⠿⢫⠈⣿⠀⠋⡆⠁⡄⠀⠀ ⡀⠀⠀⡇⡿⡿⠁⠀⡇⠡⠬⠅⠀⠀⠀⠀⠀⠈⠵⠂⢸⠀⢸⠀⢰⡀⡄⡇⠀⠀ ⠇⡀⠀⡿⣷⣸⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡅⢇⠁⠀⠀ ⠘⡇⠀⣿⣿⣧⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣼⠀⠀⠀⢸⡟⡸⠀⠀⠀ ⡀⢻⠀⣿⣽⣿⡀⠘⣿⢄⡀⠀⠀⠀⠧⠼⠀⠀⣠⡞⣿⠀⢀⠀⣸⠣⠁⠀⠀⠀ ⡇⢸⠄⣿⣿⠟⡇⠀⣿⠀⠙⠲⣤⣀⠀⣀⣤⣾⡇⡇⡿⠀⡼⢠⡯⠁⠀⠀⠀⠀ ⡟⢸⠀⣿⡿⣴⣶⡤⢹⡀⠀⠀⠈⠙⠛⠿⢻⡝⢳⣯⠇⣸⣧⠘⠃⠀⠀⠀⠀⠀ ⡤⠧⣴⣿⡟⣾⣿⢹⡿⣿⣶⢶⣤⣤⣤⣤⣾⣷⢀⣝⣴⢿⣿⣄⣀⠀⠀⠀⠀⠀ ⣄⢠⣿⡟⣼⠟⠃⠈⣿⡌⠉⠉⠛⠛⠛⠛⠉⢸⡇⢸⣿⣷⣝⣷⣲⡄⠙⣷⡄⠀ ⣿⣿⡟⢺⣥⣄⣀⣠⣿⡹⡀⠒⠀⠀⠀⠀⠂⢸⣷⠈⢛⣛⡭⡯⠿⣿⣱⣿⣻⡀ ⣟⣷⣿⣷⣶⣶⣶⣾⠝⣗⣵⡄⠀⠀⠀⠀⢀⣼⣼⣷⡿⠶⠿⣿⣿⣿⣿⣇⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⡦⣴⠶⣶⢶⣶⣶⡦⣄⡀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢾⡋⢁⡜⠁⣼⣳⠋⡼⠁⢠⡎⢷⡝⢦⠙⠛⠿⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣻⡿⣩⠞⣰⠏⠀⣰⢳⠇⡼⠁⠀⢸⡇⠸⡿⣌⢳⡀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⢒⣶⠶⣶⡶⣦⣴⡾⠁⣼⠏⣠⠃⡴⠁⠀⢰⡿⡾⣰⠁⠀⠀⢸⣧⠀⢹⢿⢧⠹⡄⠀⢠⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⣡⠴⠊⠉⠀⣴⣿⣱⡿⣵⠃⡸⠁⣰⠋⣸⠁⠀⠀⣿⣇⠇⡇⠀⢀⣀⠘⡇⠀⠘⣯⣏⢳⡹⡄⠈⠳⡀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⢞⡵⠚⠁⠀⢀⣠⢼⣿⣿⡟⡼⠃⡼⠁⣰⡟⢠⡇⠀⠀⢰⣿⢿⢰⠁⠀⢸⣿⠀⡇⠀⠀⢻⣽⣦⢳⠹⡀⠀⢱⡄⠀⠹⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⣿⠋⠀⠀⣠⠔⢁⡴⣿⣿⡏⡼⠁⡸⠁⢰⣻⡇⣾⠀⠀⠀⢸⢸⢸⣼⠀⠀⣜⡏⠀⣷⠀⠀⠀⣏⣯⣇⢧⢃⠀⠀⢹⡀⠀⠘⣿⣿⣏⠙⠛⠲⣤⠤⣄⣀⣀⣀⣀⣀ ⠀⠀⢀⣾⠟⠁⠀⢠⠞⠁⣰⡯⠖⢻⡿⢰⠁⣸⠃⢰⣿⢻⠀⡿⡆⠀⠀⢸⢸⢸⡟⠀⢀⣿⠀⠀⢻⡄⠰⠀⢸⡹⡜⣎⢞⠆⠀⠀⣷⠀⡄⠸⣿⣟⢧⡀⠀⠈⢳⡀⠻⣄⠉⠉⠉ ⠀⢀⣼⠏⠀⢀⡴⠋⠀⣴⠋⠀⠀⢸⣱⡇⢀⠇⠀⣾⡏⢸⢀⣷⣧⠀⠀⢸⣾⢸⠃⠀⣸⣟⣇⠀⢸⣿⡄⠀⠈⣿⡇⠹⡼⡄⠀⠀⢸⡆⢹⡀⢿⠙⡷⣿⡶⡄⠀⠹⡄⠘⣆⠀⠀ ⠀⣾⡏⠀⢠⠞⠀⠀⣼⡏⠀⠀⠀⣿⣿⠀⣼⠀⢸⣿⡇⢸⠀⣧⣿⣄⠀⢸⣿⣼⠀⢠⣿⣿⣻⡄⠀⣯⣿⡄⠀⠹⣹⠀⢳⣣⠀⠀⠀⣇⡄⡇⠈⡇⠃⠘⢿⣵⡄⠀⠹⡄⠹⡄⠀ ⢠⡟⠀⣰⠇⠀⠀⢰⡿⠁⠀⠀⢠⡏⡇⠀⡇⠀⡾⣿⠿⣼⡄⢿⠘⢿⡦⣼⢻⣿⠀⡸⣿⡇⠳⣷⣄⠙⠄⠙⣄⠀⢏⣧⠘⡿⡀⠀⠀⢸⢹⢹⠀⣧⠀⠀⠈⣷⣱⠀⠀⠹⡄⢻⠀ ⢸⠁⢰⠋⠀⠀⡴⣻⡇⠀⠀⠀⣼⢻⠀⠀⠀⢰⣿⡏⢀⣽⣿⣿⡿⣇⠙⠲⣟⠇⢳⡿⠙⠿⠀⠛⠈⢿⣿⣷⣮⣗⠮⣿⡆⢹⡇⠀⠀⢸⡈⣿⠀⡿⠀⠀⠀⠸⡟⡆⠀⠀⢧⠈⡇ ⣼⢠⡏⠀⠀⣾⢁⡇⡇⠀⠀⠀⣿⢸⠀⠀⠀⣸⡿⠠⣽⣿⣿⣿⣿⣿⣧⠀⠈⠀⠋⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣽⣷⣌⣧⠘⣼⠀⠀⠘⡏⣿⠀⡇⠀⠀⠀⠀⢻⢿⠀⠀⠸⡇⢳ ⢿⡼⠁⠀⢰⠇⣾⢻⡇⠀⠀⠀⡇⢸⠀⠀⠀⣯⡇⠀⠻⠘⠿⣿⠿⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠸⢿⣿⣿⡟⢹⡿⢿⡆⡿⠆⠀⠀⡇⣿⠀⣧⠀⠀⠀⠀⢸⢸⠀⠀⠀⢣⢸ ⣾⡇⠀⠀⡾⣰⢹⣾⡇⠀⠀⢸⠃⢸⠀⠀⠀⣿⡇⠀⠀⠻⠷⠾⠷⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠷⠿⠆⠀⠘⡇⣇⠀⠀⠀⠍⣿⠡⣿⠀⠀⠀⠀⢸⡇⡇⠀⠀⢸⠀ ⢸⠀⠀⠀⡇⡟⠈⣿⡇⠀⠀⢸⠀⢸⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⡀⣿⡇⣿⠀⠀⠀⠀⠘⡇⡇⠀⠀⠈⠀ ⢸⠀⠀⢠⢇⡇⠀⠘⣷⠀⠀⠘⡇⠈⡇⠀⢸⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢼⠀⠀⠀⢖⣿⣇⣿⠀⠀⠀⠀⠀⣇⠇⠀⠀⠀⠠ ⢸⠀⠀⢸⢸⠃⠀⠀⠹⣇⠀⠀⣇⠀⢿⠀⢸⢺⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠩⣿⣾⢾⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢘ ⠸⡄⠀⢸⢸⠀⠀⠀⠀⠘⠆⠀⣿⠀⠈⡆⢸⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⣿⡏⡏⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠐ ⠀⣧⠀⢸⠸⡆⠀⠀⠀⠀⠀⠀⣿⡄⠀⠸⣼⢸⠁⢸⡄⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢰⠀⠀⠐⣿⠁⡇⠀⠀⠀⢀⣾⣏⠀⠀⠀⠀⠀ ⠀⢸⡆⢸⡀⡇⠀⠀⠀⠀⠀⠀⢻⢧⠀⠀⠙⣾⡇⠀⢻⣦⠀⠀⠀⠀⠀⠀⠿⢯⣀⣀⣀⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⡇⡸⠀⠀⢰⣻⠀⡇⠀⠀⠀⣼⡏⡏⠀⠀⡀⠀⠀ ⠀⠀⠹⣌⣇⣇⠀⠀⠀⠀⠀⠀⢸⡎⣧⠀⠀⣏⣧⠀⢸⣹⣧⡀⠀⠀⠀⠀⠀⠠⣬⣭⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⠀⡇⡇⠀⠀⢸⣿⠆⡇⠀⠀⣼⡿⢀⡇⠀⣰⡇⠀⠀ ⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⡇⠘⣆⠀⢸⣾⡀⡄⠟⡇⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠹⡇⢸⢱⡇⠀⠀⣾⣼⢠⠇⠀⢾⡟⠀⢸⠀⣰⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⢳⠀⣏⠃⠀⢳⣷⣿⠀⡇⠘⡿⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⡟⠀⠀⢀⣸⣾⡇⠀⠀⣿⣿⢸⠀⠀⠋⠀⠀⣾⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣙⣒⣀⣀⡀⠀⠀⠸⡄⢹⣧⡀⠀⠘⢇⠀⣿⣼⡇⠀⠀⠉⠓⠶⢤⣄⣤⡤⠶⠾⠿⠟⠋⢹⡇⣧⠀⠀⣿⣧⢻⡇⠀⢀⣿⢿⣿⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀ ⣀⡤⠴⠚⠋⠉⠉⠉⠉⠛⠛⠻⢷⣦⣷⠈⣷⠙⢦⡀⠈⢶⣟⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀⠀⣿⣹⢸⠀⠀⢸⢹⡼⡟⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⣿⣿⣆⠘⡟⠒⠛⠂⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣄⣀⣿⢸⣿⠀⠀⣿⣧⡏⠀⠀⡞⣸⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠹⡄⠀⠀⣶⡀⠀⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⠁⡇⣼⠃⢧⠇⠀⣸⠃⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃⠹⣦⣀⠘⢷⠀⠀⠀⠀⠀⢦⣄⠈⠉⠉⠛⠿⠿⢿⣿⣿⣿⣏⠀⢸⠏⠀⢾⠀⢠⠋⢰⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠈⠳⠽⢻⣷⠤⣄⡀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠧⠀⢠⡏⢀⠀⠀⣼⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⡂⠀⠀⠀⠀⢻⢆⡀⠙⠛⠲⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡀⠙⠀⠘⠒⠶⣮⣼⣧⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣄⠀⢰⣒⠒⣒⣤⢖⡂⡈⡉⠉⠙⠻⡴⣢⢄⠀⠒⠈⣉⣉⡙⠄⠀⠀⣀ ⠀⠀⠀⠙⢤⠃⡤⢊⡞⢉⡇⠀⡄⠙⠢⢀⠀⠈⠳⣕⢕⠲⣿⣀⠀⠀⠉⠒⠰⣆ ⠈⠙⣆⠀⢀⡌⡠⠋⠀⢸⠁⠀⢸⡄⠀⢑⡱⣄⠀⠘⣆⠑⠙⢧⢙⠣⢆⠄⣄⠈ ⢀⠠⠊⢉⡿⢠⢁⠀⠀⡾⠀⠀⠀⣾⡀⠈⣖⠘⣧⠀⠘⠦⡀⢸⢣⠈⠑⣌⠢⠣ ⠂⠀⡴⢹⠇⡎⢰⡇⠀⢷⣣⠀⠀⠸⢟⢄⢸⡆⠘⣇⠀⠜⣧⢸⣏⣄⠜⠎⢻⢆ ⢀⡎⣠⢹⠀⠃⡌⣯⡀⠺⡗⠷⠢⠀⠙⢒⣑⣛⣦⣹⠀⠠⢹⠉⠘⡇⢀⠼⠈⠇ ⡞⡐⢁⢸⢰⠀⡷⣋⣥⣆⡀⠀⠀⠀⠀⠸⢻⣿⣏⠞⡇⠀⡌⣦⠀⢻⠕⠀⠀⣸ ⠓⠀⠈⢸⠸⡀⡇⠇⢿⣿⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠇⠀⡇⢫⠁⠸⣦⠆⠀⡸ ⠒⠒⠒⢸⡀⡇⣷⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣇⢀⠘⠀⢇⠀⠚⡁ ⠀⠀⢸⠀⡇⢠⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡟⢸⣀⠃⢸⠀⢰⠃ ⠀⠀⠀⡷⣟⠈⡈⣿⢢⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⣾⠀⠁⢸⡟⡘⠀⠷⠃⠴ ⠣⢦⣴⡁⢸⠀⢁⣹⡉⣗⠄⡀⠀⠀⠀⠀⠀⢀⠴⠛⡝⠘⠀⣾⠀⢇⢡⢰⠖⠀ ⡀⠘⡄⣷⠀⢆⠀⢿⣧⠘⡄⡌⠷⣦⠤⠒⠊⣀⣀⣀⠇⣸⢀⡏⠀⠸⡄⠆⠆⠀ ⢔⡀⢰⠘⢦⡘⣄⠈⢻⣆⠰⣱⠈⣷⣾⣿⡿⠿⠿⢟⠰⡟⡼⢧⣁⡀⠿⣄⣐⣄ ⠀⠀⢄⠧⠼⣧⠼⣦⣄⢻⣦⣔⠉⠉⠁⠀⠀⠀⠠⠋⣐⡿⠄⠒⠀⠉⠉⢹⡇⠀

⠀⠀⠁⠀⢀⡀⠀⠀⠀⣤⠖⠦⠤⠤⠤⣄⣀⣤⡴⠖⠚⠋⠉⠉⠙⠻⢿⣷⣒⡦⣤⣀⠀⣀⣀⠤⠤⠒⠋⠉⠉⠉⠙⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣆⠀⢀⡿⠶⠤⢀⡤⢚⣟⣋⣥⠖⠙⠒⢼⣦⡀⠀⠀⠀⠈⠙⢝⣷⢮⡓⢦⡀⠀⢀⣠⡶⠶⠒⠒⠤⣌⣇⠀⠀⠀⡀⠛ ⠀⠀⠀⠀⠀⠈⠻⣀⡞⠀⣠⡶⢋⣴⠟⠁⣰⡟⠀⠐⡄⠀⠙⠛⢄⠀⠀⠀⠀⠀⠙⣷⡉⠳⣝⠲⣿⣿⠆⠀⠀⠀⠀⠀⠈⠙⠲⢶⣿⣉ ⠒⠦⣤⣄⡀⠀⠀⠈⡇⡴⠋⢠⣾⠏⠀⠀⡏⡇⠀⠀⢻⣆⠀⠀⠈⢣⠱⣤⡀⠀⠀⠈⢿⣄⠈⠢⠈⢿⣿⠯⢶⣲⠤⣀⠀⠀⠀⠀⠈⠛ ⠀⠀⠀⢱⣄⠀⠀⢀⣿⠃⢠⠃⠁⠀⠀⢠⡇⠁⠀⠀⠀⢿⡄⠀⠀⠰⡱⡘⢿⣤⡀⠀⠀⢻⣆⠀⠁⠀⠹⣶⠤⣈⡉⠲⢭⡒⢕⢆⠀⠀ ⠀⠀⢀⡼⠛⠋⢹⣿⠇⢠⠃⠀⠀⠀⠀⡼⡇⠀⠀⠀⠀⠸⣿⡄⠀⠀⢳⣵⡈⢻⣿⡀⠀⠀⠻⣆⡀⠀⠀⣏⢣⠀⠉⠓⢤⣈⠲⣄⠱⡄ ⢀⠔⠉⠀⠀⣠⣾⡟⠀⡾⠠⢾⠀⠀⠀⢇⢹⡀⠀⠀⠀⠀⣿⣿⡄⠀⠈⣿⡁⠀⢻⣷⡀⠀⠀⠹⣱⡀⠀⣿⡌⣇⠀⠀⢰⢻⣷⣌⠃⠈ ⠋⠀⠀⢠⡾⠁⣿⠁⣸⠇⠆⣾⡇⠀⠀⢻⣇⢧⠀⠀⠀⠀⠸⣿⡟⢆⠀⢸⣷⡀⠀⢿⣇⠀⠀⢀⢫⢷⠀⣿⣷⢸⠀⢠⢃⠎⠈⢿⡷⡀ ⠀⠀⣰⠏⠀⡼⣿⠀⣿⠀⡇⢿⡵⠀⠀⣸⣿⢯⣷⣄⠀⠀⠀⢳⡻⣄⣳⣄⣿⣷⡀⠘⣿⡄⠀⠸⠈⣾⡶⠹⠏⣏⡗⠁⠈⠀⡤⠈⣧⠘ ⠀⣼⠃⢀⡾⢀⡇⠀⡇⠀⣇⢸⣿⣦⣀⠈⠿⠧⠙⠋⠉⠂⠀⠀⠉⠈⣠⣤⣬⣭⣽⣶⡼⡇⠀⠀⠇⢸⠃⠀⠀⢹⣷⠀⡠⢊⠏⠀⠘⡆ ⣼⡏⢠⠛⡇⢸⡇⠀⡇⠀⣿⣤⠟⢋⣩⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⡟⢳⠝⣿⠀⠀⢸⠈⣧⡀⠀⠈⣿⣏⠔⠀⠀⠀⠀⣽ ⡽⢠⠃⠀⢳⢸⡇⢸⡇⠀⡟⢡⣶⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⣿⣿⣧⠄⠀⢸⠀⠀⠀⡇⢸⢹⡄⠀⢹⡇⠀⠀⠀⠀⠀⢾ ⢣⠃⠀⠀⢸⠀⡇⢨⡇⠈⣷⠈⠇⠸⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡇⠘⡼⢁⠀⠈⣷⣠⡾⠀⠀⢀⡼ ⣂⣀⣀⣀⣸⠀⡇⠀⢸⠀⣿⡀⠀⠒⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡇⠀⠇⠈⡄⠀⢻⠃⠀⠀⣴⡟⠀ ⠉⠉⠁⠀⢸⠃⢷⡄⢸⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣷⠀⡇⠀⢱⠀⠘⡇⠀⠈⠉⢀⠈ ⠀⠀⠀⠀⢸⠀⢸⡇⠀⡇⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⢳⠀⠈⡆⠀⢷⠀⠀⢠⣷⠀ ⠀⠀⠀⠀⠘⣆⢸⣷⠀⢣⠀⣿⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⢸⣾⡆⢸⠀⢸⡄⠀⣸⠃⠀ ⠀⠀⠀⠀⠀⢹⢿⣿⡆⠘⡄⢹⣿⡷⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⢸⠀⠀⢸⡏⢳⠀⠇⠀⢿⠞⠁⢀⠼ ⣄⢠⠀⠀⢀⡏⠀⢹⠁⠀⢣⠈⣿⣷⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡿⠀⣜⠀⢀⢼⠃⢸⡆⠠⠀⠸⡀⡀⡁⠀ ⠈⠿⣷⣶⣿⡆⠀⠘⡆⠀⠈⡄⡼⣇⠀⢧⡙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠋⠁⢰⡇⠀⡸⠀⢸⡄⠀⠀⣷⠀⢇⠀⢿⠋⠀⠀ ⠀⠀⠘⣏⠸⡿⡄⠀⢧⡀⠀⠸⣱⣹⡆⠘⣧⠀⢂⠙⡳⣦⣄⣀⣀⣠⠴⠚⠁⠀⠀⠀⠀⣸⠀⢀⡧⠀⣾⠇⠀⠀⠸⣇⠈⡄⠸⡀⠀⠀ ⢧⠀⠀⠸⡄⢻⣜⠀⠈⣷⠀⠀⠹⣿⣷⠀⠘⢆⢸⡄⠰⣹⡟⠛⣉⣀⣠⣤⣤⣤⣶⣶⣶⡇⠀⣼⡇⢰⣿⠀⠀⠀⠀⣿⣄⠘⠀⢣⠀⡀ ⢀⣱⠀⠀⣿⠀⠹⣧⡀⠘⣇⠀⠀⠉⢿⣧⠀⠘⡆⢣⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⢀⠾⣿⢇⣾⣝⣆⢠⠀⠀⢸⢿⣦⡀⡈⣴⠃ ⠀⠁⠀⠀⠋⣇⠀⠹⣿⠀⢸⣧⡀⠀⠘⣿⣧⡀⠈⢸⣦⠾⠿⠛⠛⠛⠉⠁⠀⠀⠀⢠⡿⠁⢀⣿⣾⠁⠀⢉⠉⡹⠶⠒⠒⠻⣿⡟⠋⠉ ⠀⠀⠀⢐⡠⠿⠓⠒⠻⣷⡞⠿⣿⣾⣦⣈⣷⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣀⣨⡿⠗⠚⠉⠁⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠖⣩⠟⣹⡽⢫⠋⢈⢻⡻⣝⠻⢷⣬⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣿⢫⠏⡔⠁⣠⡿⢡⠃⠀⢸⠀⣿⣎⢦⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠖⣉⠭⠛⣹⣟⣿⣟⢁⡞⢡⠏⡞⠀⢠⣿⢧⠏⠀⠀⢸⠂⠸⣿⢧⢣⠀⠠⡈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣎⠔⠋⠀⣀⣴⣿⡿⣻⢃⠎⢠⡏⣸⠀⠀⣸⣿⣾⠀⢀⣷⢸⠀⠀⢻⣷⢣⢣⠀⠱⡀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠟⠁⢀⡠⢊⡴⣿⡿⡱⠁⠎⢠⣿⢁⡇⠀⠀⣿⣿⡇⠀⢸⡏⢸⡆⠀⠘⣿⣧⢣⠃⠀⢱⡀⠈⢿⣿⡏⠑⠲⣦⠤⣤⢀⣀⣀ ⠀⢀⣾⠋⠀⡠⠋⢠⠞⠋⢹⣡⠁⡜⢀⣿⢹⢸⣷⠀⠀⣿⣿⠇⠀⣾⡇⠀⣷⡈⠀⢻⡏⢧⣏⠀⠀⢇⠀⡈⣿⣯⣦⣀⠈⢣⡘⢦⠀⠀ ⠀⣼⠃⢀⠞⠀⢰⠏⠀⠀⣾⡏⢰⠁⢸⣿⢸⢸⣿⡆⠀⣿⣿⠀⢰⣿⣷⡀⢹⣳⡀⠘⣿⠈⣯⡀⠀⠸⡀⠃⢹⡸⠙⣿⣆⠀⠳⡈⡆⠀ ⢰⠇⢠⠋⠀⢀⡿⠀⠀⢠⣿⠀⠈⠀⣿⡿⣾⣌⣏⣻⣦⣿⣿⢀⣿⣯⠹⣷⣈⠋⠳⣄⢻⣧⠸⡇⠀⠀⣇⣿⠘⡇⠀⠘⣿⡄⠀⢳⠸⡀ ⡾⢠⠃⠀⡰⢻⡇⠀⠀⣸⡿⠀⠀⢸⡿⢠⣾⣿⣿⣯⡈⠙⠏⡹⠃⠙⠂⠁⣸⣿⣿⣿⣗⢻⡄⣷⠀⠀⣿⣻⠀⡇⠀⠀⢸⣧⠀⠀⡆⢳ ⣧⡞⠀⢠⢇⣿⡇⠀⠀⡟⠀⠀⠀⣾⠇⢹⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⢿⣿⣧⢹⡀⠀⢸⣿⠰⡇⠀⠀⠀⣿⠀⠀⢰⢸ ⣿⠁⠀⡞⡼⣿⡇⠀⠀⡇⠀⠀⠀⣿⠀⠀⠲⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠂⠀⢸⢸⠀⠀⠈⣿⢰⡇⠀⠀⠀⣧⡇⠀⠈⠀ ⣿⠀⠀⣷⠃⠸⣇⠀⠀⡇⢰⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠀⠀⠀⣿⣹⡇⠀⠀⠀⢻⡇⠀⠀⠀ ⢧⠀⢸⢸⠀⠀⢻⡀⠀⡇⠘⡄⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐⣿⣿⡇⠀⠀⠀⣸⠃⠀⠀⢨ ⢸⠀⢸⢸⠀⠀⠀⠑⠀⢹⠀⢣⢸⣿⢠⡀⠀⠀⠀⠀⠀⠀⡠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡷⡇⠀⠀⠀⣿⠀⠀⠀⠘ ⠀⡇⢸⢸⠀⠀⠀⠀⠀⢸⡆⠀⢻⣿⠀⢧⡀⠀⠀⠀⠀⢸⣷⠖⠾⢷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⢰⠀⠀⣿⢀⠇⠀⠀⣸⣿⠀⠀⠀⠀ ⠀⠸⣼⣬⡀⠀⠀⠀⠀⢸⣷⠀⠀⣿⡄⢸⢳⣄⠀⠀⠀⠀⠙⣒⡒⠚⠁⠀⠀⠀⠀⠀⠀⣠⡟⠋⡆⠀⠀⣿⢸⠀⠀⢰⡟⣻⠀⢰⠀⠀ ⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⡇⢳⡀⢸⣇⡈⣿⠙⣧⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣠⠞⢹⡇⣷⡇⠀⢠⣿⣼⠀⢰⡟⠀⡇⣠⠏⠀⠀ ⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⢣⢸⡅⠀⠻⣿⠠⣇⣹⠛⠦⣄⡀⠀⠀⠀⠀⣀⣤⣶⣿⠟⠀⢸⣤⣿⡇⠀⢸⣿⡿⠀⠈⠀⣰⡗⠃⠀⠀⠀ ⠀⣀⡤⠴⠶⠶⠶⠶⢤⣤⣸⡄⢿⢦⡀⠘⣄⣿⣿⣄⣀⠀⠉⠙⠚⠋⠉⠉⠁⠀⣸⢸⠀⠈⣿⣿⠁⠀⣾⣿⡇⠀⠀⠴⠋⠀⠀⠀⠀⠀ ⠋⠁⠀⠀⠀⠀⠀⠀⠀⢾⣿⣧⠘⡖⠻⠆⠈⠿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣀⣀⣟⣾⡇⢀⣿⣿⠀⢠⢟⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡹⡄⠀⢰⡀⠈⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡏⢡⡼⠉⡇⠀⡜⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠘⢷⣤⣷⣀⠀⠀⠀⠳⠀⠀⠀⠉⠉⠛⠛⠻⢦⡼⠁⢨⠃⠘⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠘⢯⡉⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠋⠀⠢⢤⣭⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⢤⣤⣄⣀⣀⣀⡀⢀⣠⣤⣤⠤⠔⠛⠛⠉⠛⠛⠻⢿⣿⣷⡒⠦⣤⣄⠀⠀⠀⠀⠀⣀⣠⣤⠖⠒⠋⠉⠉⠉⠙⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣶⡄⠀⠀⢸⡷⣉⣀⠁⠀⠀⣡⡶⢞⡭⠛⣉⡤⢤⣄⡰⣄⠀⠀⠀⠀⠀⠈⠙⠯⣝⢶⣬⣙⠶⣬⡉⠉⠁⠀⠀⠀⢀⣠⣤⣤⣀⣀⠀⠙⣆⠀⠀⠀⠀⠀⢠⣦ ⠀⠀⠀⠀⠀⠀⠀⢷⣷⠀⠀⡼⠋⠉⠉⣁⡴⠟⣡⣾⠷⠒⣿⠋⠀⢀⠀⠉⠾⣕⣄⠀⠀⠀⠀⠀⠀⠈⠳⣵⣍⠳⣎⡙⢦⣀⠀⣠⣾⡿⠋⠉⠀⠀⠈⠙⠓⠾⣦⣀⠀⠀⣰⣇⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⣆⣼⠃⠀⣠⡾⠋⢀⣞⡟⠁⠀⣴⢻⠀⠀⠘⣆⠀⠀⠘⠊⢳⡀⠀⠀⠀⠀⠀⠀⠈⢯⣷⡀⠙⢦⡙⢿⣿⣿⠚⠃⠀⠒⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣆⣀ ⠳⢶⣤⣤⡀⠀⠀⠀⠀⠀⢹⠀⣴⠋⠀⣠⣯⠏⠀⠀⢠⡿⡏⠀⠀⠀⢹⣧⠀⠀⠀⠀⠙⣎⠳⣤⡀⠀⠀⠀⠀⠻⡽⡄⠀⠙⣄⠙⢿⣿⣽⣛⣒⡦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠙⠻ ⠀⠀⠈⠙⢯⡁⠀⠀⠀⠀⡾⣼⠁⠀⡴⠓⠋⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⢯⣆⠀⠀⠀⠀⡝⣆⠙⣾⣆⠀⠀⠀⠀⠙⣝⣄⠀⠈⠂⠀⠻⣿⣄⡉⠉⠓⠮⣭⡓⢦⣄⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣆⣀⣠⣤⢿⠇⠀⡼⠁⠀⠀⠀⠀⠀⢸⡇⠃⠀⠀⠀⠀⠘⡾⣆⠀⠀⠀⢹⡌⢦⠈⢿⣯⢦⠀⠀⠀⠘⡾⣄⠀⠀⠀⠀⢹⡻⡍⠓⠶⣤⣀⠉⠳⣄⠑⠋⢦⡀⠀ ⠀⠀⠀⣠⠶⠋⠁⠀⢰⡿⡏⠀⣰⠃⠀⡀⠀⠀⠀⢰⡻⣧⠀⠀⠀⠀⠀⠀⢳⣹⣆⠀⠀⠀⢻⣫⢣⠈⢻⣯⣣⠀⠀⠀⠘⡾⡄⡀⠀⠀⢸⣇⠹⡄⠀⠀⠈⠳⣦⣀⠙⢦⡀⠹⣄ ⠀⣤⠞⠁⠀⠀⠀⣠⣾⣿⠀⢠⡿⡀⣴⡇⠀⠀⠀⠠⡇⢿⡀⠀⠀⠀⠀⠀⢸⣏⣿⣆⠀⠀⠈⣟⣇⠂⠀⢻⣯⣆⠀⠀⠀⠀⢳⡸⡄⠀⣼⣿⡀⢷⡀⠀⠀⠀⡼⣿⡳⣄⠙⠄⠈ ⠞⠁⠀⠀⠀⣠⡾⠉⣿⡏⠀⣼⠃⡇⣧⣿⠀⠀⠀⠰⡿⡌⣧⠀⠀⠀⠀⠀⠀⢻⣿⣟⣤⠀⠀⠸⣿⡄⠀⠀⢻⣿⡄⠀⠀⢠⠈⣧⣇⡄⢃⣿⡿⡘⡇⠀⠀⡼⢃⡟⠹⣝⣷⣄⠀ ⠀⠀⠀⢀⣴⠟⠀⢠⣿⠁⢸⣹⠀⡅⣿⡟⡇⠀⠀⠀⢧⣿⡜⣧⡀⠀⠀⠀⠀⠈⣏⢿⡈⢣⡀⠀⢻⣿⡄⠀⠈⣿⣧⠀⠀⠀⣇⢸⡘⡇⣼⢸⡇⡇⢻⢀⠞⢁⡞⠀⠀⠹⣵⡘⣆ ⠀⠀⢀⣿⠃⠀⣰⢋⣿⠀⣦⡏⠀⡇⠘⣷⡻⠀⠀⠠⡼⣿⡹⣜⢿⣦⡀⠀⠀⠀⠹⣎⠻⣤⠽⠦⢼⣏⣿⣄⠀⠘⣿⡄⠀⠀⢸⡀⢣⣿⠇⠸⠃⢹⣼⡃⠀⠈⠀⣠⢞⠀⢹⣇⠘ ⠀⣰⡿⠁⢀⣼⠃⢸⡇⠀⢸⠇⠀⣇⠀⣿⣿⢦⡀⠀⠘⣿⣧⡈⠳⠗⠉⠛⠀⠀⠀⠈⠉⠈⣡⣴⣤⣤⣤⣝⣷⣦⣸⣷⠀⠀⠈⢇⢸⡏⠀⠀⠀⠘⣇⡇⠀⢀⡴⣣⠏⠀⠀⢹⡀ ⢠⣻⠃⢀⡞⣿⠀⢸⡇⠘⣸⠀⠀⣿⡄⢹⣾⠗⠛⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡿⣿⣿⣿⣿⣿⢻⣌⢳⣿⠀⠀⠀⢸⠀⢣⡀⠀⠀⠀⢹⣻⡴⢋⡠⠁⠀⠀⠀⠀⡷ ⢿⠇⢠⠟⠀⣿⠀⢸⡇⠀⣿⠀⠠⣿⡝⢋⢀⣴⣾⣿⢭⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢻⣿⣿⣿⣿⠀⠿⠈⢿⡆⠀⠀⠘⡆⠸⡟⡆⠀⠀⠘⣿⡗⠋⠀⠀⠀⡀⠀⠀⡇ ⡼⢠⡎⠀⠀⠘⡇⢸⠁⠀⣿⡀⢰⢹⠀⣮⡟⢹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣭⣭⡥⠞⠁⠀⢸⡇⠀⠀⠀⣇⠀⣧⢹⢲⠀⠀⢳⣧⠀⠀⢀⠀⠀⠀⠉⣧ ⢇⡏⠀⠀⠀⠀⡇⢸⡀⢠⢸⡇⠘⣾⠀⢹⠇⠸⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣿⠀⢿⢸⠘⡀⠀⢸⣿⢀⣴⠏⠀⠀⠀⢀⡇ ⡜⠀⠀⠀⠀⠀⡧⠈⡇⢸⠘⡇⠀⣿⡆⠀⠠⢤⣭⣿⡷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⣿⠀⢸⡇⠀⡇⠀⠀⢿⡟⠁⠀⠀⢀⣾⡿⠀ ⠶⠶⠶⠖⠛⠛⣧⠀⣇⢘⠀⡇⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡇⠀⠀⣿⠀⠈⡆⠀⢸⡄⠀⢸⡇⠀⠀⢰⠿⡟⠀⠠ ⠀⠀⠀⠀⠀⠀⡏⠀⣿⣼⠀⢸⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡇⠀⡇⠀⠈⢇⠀⠀⣷⠀⠀⠀⠀⢀⡜⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⢼⣿⠀⢸⡀⠸⡾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡇⠀⣧⠀⠀⢸⠀⠀⢹⡇⠀⠀⢠⣾⡇⠀ ⠀⠀⠀⠀⠀⠀⣧⡀⢸⣿⠀⠀⣇⠀⣿⡏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⡿⠀⠀⣿⣴⣆⠀⣇⠀⠸⣧⠀⠀⢀⡿⠁⠀ ⠘⠀⠀⠀⠀⠀⢸⣿⡬⣇⡇⠀⢻⠀⠸⣷⢻⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⠇⠀⠀⢹⡏⣼⡄⢸⡄⠀⢻⣠⣣⠾⠁⠀⣠ ⠀⠇⠀⠀⠀⠀⢀⡟⠳⣽⢳⠀⠈⡇⠀⣿⣿⡎⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⢸⠀⠀⠀⣸⣷⠀⢧⠀⢣⠀⠈⣿⠃⠀⢠⠖⠛ ⣦⠸⡆⠀⠀⠀⣸⠃⠀⠸⡄⠀⠀⢹⡀⢸⣿⡿⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⢹⠃⢀⡞⡄⠀⡀⣿⠉⠀⡿⡀⠸⡄⠀⢻⠀⡰⢡⠀⠀ ⠘⢷⡹⣶⡶⣶⣷⡀⠀⠀⣇⠀⠀⠈⣧⢠⢷⡇⠀⢹⣌⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠉⢠⡟⠀⢸⢹⠁⠀⡇⡇⠀⠀⢸⣇⠀⢣⠀⠈⡿⠟⠃⠀⠀ ⠀⠀⠀⢿⡾⠋⡿⣇⠀⠀⢹⡄⠀⠀⠘⡎⣏⣿⡄⠀⢳⣆⠀⢨⡻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⢈⡇⠀⢀⡞⠀⢠⣧⡇⠀⠀⠀⣿⡆⠈⢇⠀⢻⠀⠀⠀⠘ ⡄⠀⠀⠀⢧⠀⢳⡝⣆⠀⠈⣧⡀⠀⠀⢹⡽⡸⣷⠀⠈⢿⡄⠀⣆⠀⢮⢻⣿⣶⣤⣤⡴⠞⠛⠁⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⣸⡟⠀⢸⣾⢠⠀⠀⠀⢸⣷⠀⠘⡄⠘⡆⠀⠀⢠ ⢳⡀⠀⠀⠘⣦⠈⣿⣌⠁⠀⠸⣷⠀⠀⠀⢳⣣⢹⡆⠀⠈⢣⠀⢿⠀⠘⣎⣿⠟⢉⣁⣀⣠⣤⣤⣴⣶⣶⣶⣶⣿⣿⠏⠀⢠⣿⡇⢠⣯⡏⠈⡄⠀⠀⠈⣷⢧⠀⠘⠀⢻⠀⢀⠅ ⢀⠹⡄⠀⠀⣿⡆⠈⢻⣷⡀⠀⠹⣇⠀⠀⠀⠉⢯⣿⡄⠀⠘⣦⠈⣇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣰⣿⣿⡇⣼⣏⢿⡄⠸⡀⠀⠀⢸⢿⡷⡄⠀⠀⢇⣸⠃ ⠈⠣⠱⠀⠀⣿⢷⡀⠀⠻⣿⡆⠀⢹⣦⠀⠀⠀⠘⣿⡿⣄⠀⠘⠆⢿⡄⢀⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠉⠉⠀⢀⣧⠞⠁⢰⡿⣰⡏⠛⠛⠿⠾⠧⠤⣀⣈⣃⣙⣿⣦⣧⡼⠧⠴ ⠀⠀⠀⠀⠀⡆⢸⣧⠀⠀⢧⣻⠀⢠⡿⣷⣄⢀⡀⠙⢿⡙⣄⢀⣀⡼⠗⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⢠⣾⣿⡿⠀⣀⣠⠤⠐⠚⠋⠉⠀⠀⠀⢙⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⢐⣡⠜⠛⠛⠛⠛⢻⣿⡟⠓⠿⣿⣦⣷⣤⣈⣿⣾⣿⣛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣀⣠⣴⡿⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀