⠀⠀⠀⠀⠀⠀⠀⢠⢴⠚⠃⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢂⠣⠀⠈⠨⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠱⡢⡀⠐⠨⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠑⢄⠄⠐⣮⢳⡄⠀⣀⣀⣀⣠⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣱⢦⠿⢍⣯⡽⢷⠟⢛⠫⡎⠀ ⠀⣀⡤⣀⠀⠀⠀⠀⠀⠀⣀⡤⣚⣯⡽⣞⣛⡉⢦⣶⣼⣾⣿⠋⠳⠄ ⠈⣿⣿⣿⣵⣀⢴⣶⣾⣯⠿⠛⢉⡀⢝⣶⣾⣮⡉⠉⠉⠘⠗⢵⡀⠀ ⠀⠘⣿⣿⣿⣿⣿⠯⠙⠐⠒⠚⠉⠉⠁⠀⠀⣸⣷⣓⠪⠴⠤⠄⠋⠀ ⠀⠀⠀⠈⠛⠿⠤⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⢸⠃⠀⢹⣟⠛⢿⣿⡀⠀⠀⣿⠀⠀⠐⠛⢿⣿⣿⣿⣿⡋⢁⣴⣶⣿⣿⣿⣿⠿⠟⠛⣛⣛⣛⣛⣟⣛⣛⣛⣛⣛⣛⣋⡘⠓⠛⠓⢾⣿⠏⣽⣿⣿⣿⣿⣍⣛⣛⣛⣛⡻⢿⡿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿⣿⣛⣛⣹⣩⡱⢄⡲⣦⣉⢷⣍⡚⢦⠙⣿⣿⡉⠛⠛⠉⠂⠀⠐⠂⠈⠛⠛⠉⠁⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢻⣧⠀⠀⣼⠃⠀⠀⠀⠀⠙⢿⣿⣿⣷⡘⢿⣿⣿⣿⡏⢹⣾⣿⣿⡿⠟⠛⠛⠛⠋⠙⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣼⣿⡿⠿⠿⠷⠶⠾⣿⣿⣿⣯⣭⣽⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣛⣟⣿⣻⣿⣿⣶⣷⣿⣶⣬⣿⣶⣹⣟⣛⠿⢧⣦⣴⣤⠀⠄⠀⢀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢿⣦⡐⠿⣷⣤⣀⠀⣀⠀⠀⠀⠙⠛⠿⣶⣍⠻⠿⣿⣦⣛⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢋⠛⣙⢛⣿⣿⡿⠻⠿⢿⡿⣿⣿⣿⣿⠧⡹⠜⡭⢛⣛⢻⠻⠿⠿⠿⠿⣶⣶⣷⣶⣤⣤⣤⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣄⣀⣀⣀⣤⣤⣄⣀⣀⡀⠀⠀⠀⠺⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢻⣷⣦⣀⡙⣿⣿⣷⣻⣶⣾⣶⣶⣆⣨⣿⣷⣶⣾⣭⣿⠷⡏⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠘⣦⠜⡸⢛⠣⡑⢌⠢⠐⣄⠢⢍⢒⠢⡑⢌⠰⣁⠢⢌⡱⠈⣄⠡⡀⠄⠀⡀⠉⢉⠩⠉⠛⢻⡟⠀⠀⠐⠀⠀⠁⠀⠀⠀⠄⡀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣀⣠⣤⣤⣤⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⡿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡁⡔⢠⢀⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⢀⠠⠁⢂⠄⣀⢂⠈⠄⠀⠂⠁⠤⠀⠀⢠⡟⠠⢁⢂⢂⡑⢊⠒⡱⢈⠱⢊⠤⢃⠜⡠⢓⠤⢡⠒⠤⢡⠐⠡⡐⢊⠒⣁⠈⡔⡀⠤⠀⠘⠃⠀⠀⡐⠀⢀⢀⠀⡀⠄⠀⢀⠀⠀⠂⠈⠠⠁⡈⠔⡀⢆⠒⡌⠔⠢⢐⠠⠀⠀⠀⠀⡀⢀⡀⡀⠖⡠⠠⣴⣿⣾⡿⣿⣿⣿⢿⡿⣟⡿⣿⢿⣟⡿⣿⣿⣿⣻⣿⣿⣾⣿⣿⣷⣳⢞⡭⢯⡽⢭⣟⣿⣿⣿⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣶⣯⣽⣿⣿⣯⡙⠛⢿⣷⣿⣿⣲⡱⣌⠧⣎⢜⡻⣿⣿⣿⣶⣶⣦⣄⣤⣿⣿⣿⣏⢄⠣⢆⡑⢢⠠⣁⠂⠌⡀⠄⡈⡐⠠⡀⠀⠀⠀⠰⠏⠁⢂⠁⣂⠆⢆⢣⠣⡜⠬⣑⠪⣌⠣⢎⡰⢃⡌⢣⡘⢆⡡⢎⡱⢄⢃⠲⣀⠣⠄⡑⣀⠂⡡⢀⠐⠠⢠⠁⢄⡊⠤⡑⡘⢠⠂⡔⢈⠰⣀⠆⢠⠀⠀⠰⣈⠷⡐⣌⠒⣌⠰⢃⠎⡱⢌⠱⡡⢌⠱⡠⢀⠄⡙⢛⠫⢔⡛⡻⡜⡯⡽⣭⣛⣞⡻⢾⣝⡷⣻⢿⡿⣿⢿⢿⠿⡿⢿⢿⣿⣾⣷⣾⣷⣿⣿⠟⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣿⣻⣦⡀⠀⣿⣿⣿⣿⣯⣿⣾⣾⣷⣧⣿⣼⣳⣮⣽⣿⡿⣿⣹⢏⡿⣎⡳⢭⣸⢡⡓⣌⢣⠚⡤⢣⠔⡡⢃⢵⣦⡀⠀⠀⣶⣈⢄⠣⡔⢪⠜⣂⠳⣌⠳⢌⠳⡌⣓⢣⠜⡱⢌⠣⡜⢢⡑⢦⢑⡊⡌⢱⠈⡆⠱⡐⠄⣷⡐⠌⢢⠑⢢⠉⡔⠬⡑⠴⡉⢖⡹⢰⢡⠚⢥⠚⡤⢣⠌⡴⣠⢧⡹⢤⣋⠴⣃⠎⡜⡰⢊⡕⢢⢍⠲⣁⠎⣴⣡⢛⢣⢎⡼⡱⣝⢶⡹⢶⣹⢮⡽⣯⡾⣝⣯⢯⣽⣾⣟⣮⣿⣵⣯⣶⣾⠿⠋⠉⠙⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣽⣿⣧⣿⣼⣧⣿⣵⣧⣟⣴⣭⣚⣿⣇⠀⠉⢻⣿⣮⢳⣜⣣⢞⣬⠳⣌⡳⢎⡵⣚⠴⣫⣜⣱⣋⠶⣩⠖⣭⢒⠧⣜⠼⣡⢏⡼⡱⣜⢣⣿⡷⣌⢧⣙⢦⣹⣐⣣⣝⡲⣝⢎⣖⣣⢇⡻⢦⣏⠷⣭⣞⣵⣫⣶⣽⣳⣎⣷⣮⣜⣶⣵⣷⣼⣷⣮⣷⣽⣾⣷⣿⣭⣻⣾⣿⣷⣿⣾⡿⡿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠻⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣬⣿⣿⣿⣾⣷⣿⣾⣿⣷⣿⣻⣾⣿⣿⣷⣾⣷⣾⣿⣷⣿⣾⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠻⠿⣿⣷⣿⣿⣿⣾⠟⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠙⡿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⣄⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠁⠀⠈⠉⠉⠉⠀⠀⠈⠉⠙⠿⣯⡉⠉⠉⠉⠉⠋⠙⠉⠙⣏⠙⢛⡋⠛⠉⠋⠉⠉⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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