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