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