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