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