Patrick Star's Nudes Emojis & Text

⢣⡙⠤⠓⡌⢓⠸⡀⠆⢤⠡⢌⠰⠰⣀⢒⣰⡀⢆⠰⢂⣄⣦⣶⣴⣄⠢⠐⡄⠢⠌⠤⣁⠆⡰⢄⡒⠄⠇⠀⠀⢀⠀⡀⢀⠀⡀⢀⠀⡀⠀⡀⢀⠀⡀⢀⠀⢀⠀⠀⡀⢀⠀⡀⠀ ⢣⠘⡰⢉⠔⡉⢆⡑⢊⡄⠣⢌⠢⣑⠠⣺⣹⠃⢤⣶⣟⠿⡄⢀⣠⣿⠃⡰⢈⡱⢉⠒⡄⢚⡐⢢⠘⠌⢄⡣⠌⠀⠠⠀⠄⠠⠀⠄⠠⠀⢁⣤⣄⠐⠀⠠⠀⠂⠀⠁⡀⠠⠀⠐⠀ ⡅⢎⠰⡡⠌⡜⡠⢌⠂⡌⠱⢈⠒⡄⠢⣅⣶⡿⣽⣽⣧⠜⠺⣯⠉⡄⠰⡁⢎⠰⢁⠎⠰⠡⠘⠤⡉⡐⣟⠀⠠⠈⢀⠐⠀⠂⠐⡀⠁⡐⢨⣧⡿⣧⠈⢀⠐⠀⡁⠠⠀⠄⢈⠠⠁ ⠜⡂⠱⢠⠉⠴⡁⢊⠱⣈⠱⠌⡒⠤⢹⡟⢻⠇⠘⠋⠁⢢⡀⢻⡔⢨⠑⡌⢂⠣⠌⡌⢡⢃⠜⡐⠤⣁⠻⣦⡔⠀⠂⢀⠡⠈⠀⠄⠐⠀⣾⠀⢧⣼⣦⣀⠂⠐⠀⡐⠠⠈⠀⠄⡀ ⢣⠌⡡⠃⠬⡑⢌⠢⡑⢄⠣⡘⠄⡃⠌⣿⡞⣶⠂⠀⠀⠀⠙⠮⢿⡄⠃⡜⢠⢃⡱⢈⠂⢆⠒⢾⡒⠒⠳⢦⣇⠀⠌⠀⡀⠂⠁⡐⠈⢰⡇⠀⠀⠻⣿⡧⢴⠀⡁⠠⠐⠀⠡⠀⠄ ⢣⠘⠤⣉⠢⡑⢌⠢⡑⢌⠢⡑⡘⢄⣽⣋⣳⠷⠒⠒⠀⠀⠀⠀⢠⡟⠷⣦⡅⢂⠦⢁⠎⡌⢢⠘⢧⡀⠀⠀⠈⢳⡆⠁⠠⠀⡁⠠⢐⡼⠃⠀⠀⢀⡀⠙⣿⠀⠠⠐⠀⠡⠐⠀⠂ ⠣⠜⠰⡠⠑⡌⢢⠑⡌⢢⠁⠆⣡⡞⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⠾⢞⠣⠐⡌⢢⠘⡄⢡⠊⡈⣷⠀⠀⠀⢰⢿⣆⠁⠂⢄⡵⠋⠁⠀⠀⠀⠀⠉⠉⠚⢷⡀⠂⢁⠐⠠⠁⠂ ⢣⡉⢆⡑⠌⠴⡁⢎⠰⡁⢎⢰⡏⠀⢀⣧⠀⠀⠰⣦⣤⣤⠴⠖⢛⠠⡑⠢⠌⢣⠘⡄⢣⠘⡠⠃⠔⣿⠀⠀⠀⠈⢳⣈⡧⡈⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠀⠂⠄⠂⠄⡁ ⢣⠐⠢⢌⡘⠤⢃⠌⢢⠉⡔⢺⣁⣴⠛⡉⠷⣄⢀⡏⢄⠰⡈⠜⢢⠡⢌⠱⡈⢆⠱⡈⢆⠱⣀⠃⣼⠃⠀⠀⠀⠀⠀⣽⣇⣠⠹⣆⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⣾⠠⠁⠌⠡⠄⠄ ⢣⠉⢆⡡⢘⠰⡉⠜⡠⢃⠰⠉⠟⠡⠘⡄⢣⠘⠛⡉⠤⡑⣈⠒⡄⠣⢌⠢⡑⠌⢢⠁⢆⠒⣄⡼⠃⠀⠀⠀⠀⠀⠐⠛⣿⠟⡛⠽⣛⣛⢻⠛⢻⢛⣛⣛⣛⠻⣹⠁⠋⠘⣡⠋⡖ ⣃⠎⠰⣀⢃⡒⢡⠊⠔⡁⢆⠱⢈⠂⡱⢈⠆⡱⢈⠴⢁⠒⡄⠣⢌⡑⢌⠒⣈⠰⡁⠎⣀⣶⠞⠀⠀⠀⠀⠀⠀⢀⠈⠙⠛⣧⡙⡬⢱⠌⣎⢄⡠⣃⠖⣲⡼⠛⠻⡄⠀⠈⢀⣍⠲ ⠦⢌⠱⣀⠒⡌⢢⢉⠜⡨⠄⣺⠷⣮⠄⢣⠘⡄⠣⢌⠢⡑⠌⡑⠢⠌⢠⣁⣦⣥⠴⠶⠏⠁⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠸⣷⠡⢏⡜⠲⣌⠲⣭⠞⠁⠀⢀⣴⠷⡁⠯⠖⡨⢑ ⠣⡌⠰⣀⢣⠘⡄⣊⠰⡁⠌⣽⠀⠼⣧⠌⢣⡐⠣⢌⠢⡑⢌⠰⣁⣾⠞⠉⠀⠀⠀⠀⠈⠓⢤⡀⠰⠀⣀⠀⠀⠀⠘⣆⠀⠀⢹⡂⠱⣈⠳⣌⣳⠏⠀⠀⠀⢸⣷⣂⣡⠂⠑⠄⢃ ⢣⠐⣡⠂⠦⣁⠲⡀⢆⠑⣜⡿⡗⡟⣿⣇⠲⣁⠱⢈⠰⡁⠎⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣋⠉⠁⠀⠀⠐⠢⣜⡄⠀⢸⡇⠀⠐⠃⢸⠏⠀⠀⠀⠀⣠⣿⣿⡿⠁⠈⠈⠀ ⠅⡊⠔⡨⢑⡀⢣⠘⡄⢊⣿⠱⣽⣏⡿⢻⡔⠢⠑⡌⢢⠙⢄⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⠁⠈⠁⠀⠀⠀⠀⠀⠈⢻⡀⢨⡇⠀⣀⣤⣿⡀⠀⠀⠀⢀⣾⣿⠯⣆⠀⠀⠀⠀ ⠈⡔⢡⢂⢃⠐⡁⢂⣰⡿⠟⠀⠀⠀⠀⠈⠛⢦⡑⢨⢂⠘⣼⠏⡀⠀⠀⠀⠀⠀⠀⢀⢎⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢰⡇⣾⠉⠀⠀⠈⠀⠀⠀⠀⠿⡇⠀⢹⠐⡘⠌⢂ ⠈⠴⡁⢌⠢⡘⠄⣩⡏⢀⡖⠀⠀⠀⠀⠀⢀⠘⣧⢂⠩⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⡞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠁⡝⢦⣀⠀⠀⠀⠀⠀⠀⣰⣧⣄⣼⠃⡜⡈⠄ ⠈⢆⠱⡈⢆⠑⡈⣼⠁⡼⠀⠀⠀⠀⠀⠀⠀⢧⠹⣇⢂⢹⡇⠀⠀⠀⠑⠢⠤⣀⣀⡿⠁⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⡯⠘⠤⢂⢉⠛⠓⠶⠶⠶⢾⣿⠿⡿⢃⠡⠰⣁⠊ ⠈⢆⡑⠨⠄⢣⣼⠋⣸⠃⠀⠀⠀⠀⠀⠀⠀⠘⣆⠙⣦⢹⡇⠀⠀⠀⠀⠀⠀⠀⢼⡀⡇⠀⢹⠂⠀⢀⡀⠀⠀⠀⠀⠘⠁⠈⣷⠈⠦⡁⠎⡌⢃⠒⠤⣈⠰⣀⠒⡠⢌⠒⡡⢂⠌ ⠈⠆⡌⡑⢨⡾⢣⣾⡁⠀⠀⠀⠀⠁⠀⠀⠀⠀⢉⣷⡞⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣹⠛⠒⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⢃⠜⠰⡈⠤⣉⠒⢄⠣⢄⠣⠰⡈⠔⡡⢊⠐ ⠈⢆⠱⠠⣿⡽⠁⠀⠉⢹⠶⠦⠤⠤⠤⠤⢶⠚⠉⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⣱⠟⣇⠀⣸⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡐⢡⠊⡱⢈⠒⠤⣉⠢⡑⢌⠢⡑⢡⠊⡔⣁⠊ ⢈⠂⢆⠣⣿⣁⣀⠀⠀⠈⠛⣄⡀⠉⣤⡴⠋⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⣴⢏⢂⡙⠛⢃⠒⡉⢷⣀⠀⠀⠀⠀⠀⠀⠀⢸⠄⡃⢆⠱⡈⠜⡐⢄⠃⡜⢠⠑⡘⡄⢣⠰⣀⠃ ⠠⢉⡐⢢⣿⠁⠸⣆⠀⠀⠀⢻⡱⣄⢾⡇⠀⠀⠀⣴⠋⢶⣷⢻⡀⠀⠀⢀⣼⠏⡤⢒⠈⢆⠡⠊⡅⢂⡙⠶⣄⠀⠀⠀⠀⠀⣾⢠⡁⠊⠴⡈⠆⡩⠄⢣⠘⡄⢣⠘⠤⡁⠖⡠⠡ ⢀⠣⠄⡃⣿⡀⠀⠛⢦⡀⠀⠀⠙⡟⠉⠀⠀⢀⠴⠳⠀⣼⢇⠃⡝⠲⠶⠛⠡⢂⡔⢨⠘⢄⠣⡑⡈⢆⠰⢂⠌⠳⢦⣄⣀⣾⡿⠛⠻⣧⠂⢱⢂⠱⡈⢆⠱⡈⢆⡉⢆⠱⡈⠔⡡ ⢀⠃⡆⠡⠹⣟⠦⣤⣤⣇⣤⡤⢴⠧⣤⣀⣀⣿⣀⣤⢽⡟⢈⠒⡄⢣⠘⠌⡁⠆⡠⢡⠘⠄⡃⠴⡁⢆⡘⠰⣈⠣⠔⡈⢥⣾⢓⣂⣈⢹⣧⠂⡌⢆⠱⢈⠒⡌⠤⠘⡄⢢⠑⠌⡐ ⢀⠣⠘⡄⢣⠙⣯⡀⡉⢉⡠⠖⠉⢉⣰⠤⠴⠶⠤⢬⡟⢁⠎⡔⡘⠤⡉⠆⡑⠢⣡⡶⠳⠶⢶⣄⡡⠂⣌⠱⡀⢆⠣⠁⣾⠏⡎⠈⠀⡏⣿⡆⠱⡈⢆⠩⡐⠤⡑⢊⡐⢤⡨⠴⠃ ⢀⠣⢡⠘⢄⠢⠌⣿⣘⣩⠤⠔⠚⠉⡠⠖⢚⣓⣲⡏⡐⢎⡐⠤⡑⢢⠑⡌⠰⢡⢸⡁⠀⠀⠀⠈⠙⠳⣆⠤⡑⠌⡢⢑⣿⢀⣣⣴⣤⣦⡽⣧⠣⢘⠠⣂⠱⣠⣱⠖⠋⠁⠀⠀⠀ ⢀⠃⢆⡉⢢⠐⡡⣼⣎⢁⠰⠒⢚⣯⠡⠚⠉⡔⣸⡇⢌⠢⠌⣂⠱⣈⠒⣈⠑⡂⠼⣇⠀⠀⠀⠀⠀⠀⠈⠻⣤⣂⢡⡾⠏⠀⠉⠛⠋⠁⢀⣽⣶⡅⠡⣀⡷⠛⠁⠀⠀⠀⠀⠀⠀ ⠠⡉⠆⡰⠁⡆⢡⣿⣿⣿⣷⣠⣟⡏⢿⣄⣵⣿⣿⣿⢀⠣⠜⣀⠣⢄⠣⠤⡉⠔⣂⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠀⠀⠀⠀⣀⡠⠞⠉⢀⣢⠟⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠠⡑⢌⡐⢡⠐⣸⣿⣿⣿⣿⡿⠡⢘⠸⣿⣿⣿⣿⣿⢂⠑⣊⠄⢣⠌⢢⡑⠤⢃⠆⡰⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⠀⣠⡞⠀⣀⡤⠞⠼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋ ⠠⡑⢢⠘⠤⠑⡸⣿⣿⣿⣿⠃⢡⠊⡐⢹⣿⣿⣿⡿⢂⠱⡀⠎⣡⠊⡔⢠⠃⠬⡘⢄⠂⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠈⠉⢹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢏⠐ ⠠⡑⢢⠘⠤⡑⠰⣿⣿⣿⡇⠊⢄⠡⠌⡐⣿⣿⣿⡇⢡⢂⠱⡈⡄⢣⠘⠤⡉⢆⠱⡈⠜⠠⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠌⢂ ⠠⡑⠢⢉⠒⠌⡡⣿⣿⣿⣿⣁⠂⢆⢂⣽⣿⣿⣿⠇⠢⢌⠢⡑⢌⠂⡍⢢⠑⡌⢢⠑⡌⡑⢂⠹⣤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⣼⠃⡜⠨⠄ ⠠⡑⡡⢊⠜⡠⢁⣿⡏⢹⣿⣿⣌⣢⣼⣿⠟⣹⣿⡈⠒⢌⠢⡑⢌⠒⢌⠢⡑⢌⠢⡑⡄⠣⠌⡂⠽⣆⡀⣀⠴⠃⠀⠀⠀⠀⢀⣴⢤⣄⠀⠀⠀⠀⢄⡈⠉⠉⠉⣹⠇⡘⢄⠣⠌ ⠠⠱⠄⠣⡘⢄⠣⢄⠂⣥⣐⢉⡁⢋⣉⣦⣐⠂⡉⢄⠩⠠⡑⢈⢂⠩⣀⠣⠌⢂⠱⠐⡨⠑⡈⠔⠂⣍⡙⠳⠦⡴⡤⡴⠶⢞⡛⢡⢂⡌⠛⠲⢦⣤⣤⣤⣤⠴⡾⠛⢠⠁⠊⡔⠡

⠀⠀⠀⠀⠀⢴⢀⡤⠒⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢶⠻⠃⡹⡀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⡀⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡫⠅⠀⠈⠡⢄⠀⠀⠀⠨⡉⠐⡄⠀⠀⢀⠇⢈⠳⡂⠀⠀⠀ ⠀⠀⠀⠰⢁⡄⢠⠤⠤⠞⠉⠀⠀⠀⠀⡇⠀⠹⡆⠰⠁⠀⠀⠀⠱⠀⠀⠀ ⠀⠀⠀⠐⠁⠈⠒⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⣷⠚⠂⠀⠀⠀⢚⠀⠀⠀ ⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⣀⠠⠤⠊⠀⠀⠀⢂⠈⠆⠀⠀⢀⠖⢩⠇⠀⠀ ⠀⠀⢀⣷⣿⡀⠀⠀⠀⠎⠀⠀⠀⢈⠖⠂⠀⠈⡆⢠⠀⢀⠃⠀⢸⡶⠀⠀ ⠀⢀⠜⠉⠉⠓⡄⠀⡸⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⡸⢔⠉⠀⠀⢻⠙⠀⠀ ⠀⡘⡌⠀⠀⠀⡴⡀⡇⠀⠀⠤⡜⠠⠀⠀⠀⠀⡠⡇⠈⠑⠒⠠⠾⠟⠀⠀ ⣴⠽⣀⠀⠀⢀⡰⢵⡇⠀⠀⠀⣹⠒⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⡀⠘⣄⢠⠊⠀⣀⣷⠀⠀⡰⠉⠒⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣆⠑⡀⢈⡋⠀⠜⣠⠃⠑⠚⠁⠀⠀⠀⠀⠈⠂⠤⡗⢲⡀⠀⠀⠀⠀⠀⠀ ⠘⢄⠍⢂⠍⡙⣋⠊⠀⠀⠀⠀⡖⠒⠤⡀⠀⠀⢸⣈⣙⣇⠀⠀⠀⣀⠄⠀ ⠀⣸⣅⢠⢇⢈⣼⠀⠀⠀⠀⠀⢃⠀⠀⠈⠳⡤⠃⠉⢉⠼⣢⡠⠊⠀⠀⠀ ⠀⣿⣿⠋⠈⣿⣿⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠈⢂⠔⠠⠎⠋⠀⠀⠀⠀⠌ ⠀⢹⣿⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⢆⠀⢀⠀⠀⠁⠒⠂⠀⠀⠀⢀⠄⠀ ⠀⠘⠙⠓⠘⠋⠓⠀⠀⠀⠀⠀⠀⠀⠈⠢⠔⢀⠠⠴⠒⠤⢀⣂⡀⠜⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠁⢀⠔⠀⠒⢤⡔⠈⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠀⡇⠀⠀⠂⢀⠂⠀⠂⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠑⠤⠀⠠⠊⠐⠤⠤⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠀⠀⣀⣴⣶⣿⣿⣷⣦⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡎⠀⠀⠛⠻⠿⠿⠿⠿⠿⣿⣿⠛⠛⠛⠉⠀⢰⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀ ⢠⠇⠀⠀⠀⣠⠆⠀⠀⠀⠀⢁⣀⡠⢤⣼⣛⣲⣯⣭⣭⣭⠿⣆⠀⠀⠀⠀⠀⠀ ⡎⠀⠀⠀⡰⠃⠀⣀⡤⣖⠪⢿⣶⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠘⡄⠀⠀⠀⠀⠀ ⣇⠀⠀⡼⣁⢴⡪⠗⠉⠀⠀⠀⠻⠟⢋⣿⣿⣿⣿⣿⡆⠀⠀⠀⢳⠀⠀⠀⠀⠀ ⠘⢤⣼⣋⠗⠁⠀⠀⠀⠀⠀⠀⠀⣤⣘⣿⣿⡿⣿⣟⣥⠖⠀⠀⢨⣿⣦⣀⠀⠀ ⠀⢸⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⡿⠟⠋⠁⠀⠀⠀⡼⠁⠀⠈⠑⢆ ⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⣠⣦⡀⢠⣄⣠⠤⠷⣀⡠⠶⢄⣀⣼⣀⠀⠀⣀⣀⠜ ⠀⠀⠀⠈⠉⠒⠤⠄⣀⣰⣿⣿⣷⣿⡟⠁⠀⠀⠈⠱⡄⠀⠀⠀⠉⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠤⢀⣀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

───────────────▄████████▄──────── ──────────────██▒▒▒▒▒▒▒▒██─────── ─────────────██▒▒▒▒▒▒▒▒▒██─────── ────────────██▒▒▒▒▒▒▒▒▒▒██─────── ───────────██▒▒▒▒▒▒▒▒▒██▀──────── ──────────██▒▒▒▒▒▒▒▒▒▒██───────── ─────────██▒▒▒▒▒▒▒▒▒▒▒██───────── ────────██▒████▒████▒▒██───────── ────────██▒▒▒▒▒▒▒▒▒▒▒▒██───────── ────────██▒────▒▒────▒██───────── ────────██▒─██─▒▒─██─▒██───────── ────────██▒────▒▒────▒██───────── ────────██▒▒▒▒▒▒▒▒▒▒▒▒██───────── ───────██▒▒█▀▀▀▀▀▀▀█▒▒▒▒██─────── ─────██▒▒▒▒▒█▄▄▄▄▄█▒▒▒▒▒▒▒██───── ───██▒▒██▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒██▒▒██─── ─██▒▒▒▒██▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒██▒▒▒▒██─ █▒▒▒▒██▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒██▒▒▒▒█ █▒▒▒▒██▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒██▒▒▒▒█ █▒▒████▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒████▒▒█ ▀████▒▒▒▒▒▒▒▒▒▓▓▓▓▒▒▒▒▒▒▒▒▒▒████▀ ──█▌▌▌▌▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▌▌▌███── ───█▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌█──── ───█▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌█──── ────▀█▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌▌██▀───── ─────█▌▌▌▌▌▌████████▌▌▌▌▌██────── ──────██▒▒██────────██▒▒██─────── ──────▀████▀────────▀████▀───────

⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⣿⡟⠛⢿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⠁⢀⣸⣿⣿⣷⣤⣠⣿⣿⣿⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⣼⣿⣿⠋⠀⠀⠈⢻⡟⠁⠀⠀⠙⣿⣿⣧⠀⠀ ⠀⢀⣿⣿⡟⠀⢠⣤⠀⠀⠀⠀⣤⡄⠀⢻⣿⣿⡀⠀ ⠀⢸⣿⣿⣷⠀⠘⠛⠀⢀⡀⠀⠛⠃⠀⣾⣿⣿⡇⠀ ⠀⣼⣿⣿⣿⣧⣀⣀⣠⣾⣷⣄⣀⣀⣼⣿⣿⣿⣧⠀ ⢀⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡀ ⢸⣿⣿⣇⢀⠀⠛⠿⠿⣿⣿⠿⠿⠛⠀⡀⣸⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠈⠟⠋⠻⠭⠀⣼⣷⣦⡄⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⠶⣲⠢⣄⠀⣀⣀⡀⠙⢿⡿⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⢿⣿⣸⡿⠛⣩⡌⡙⢳⡈⠁⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠿⣏⣿⣿⣿⣿⢡⣌⣿⣷⣿⡄⢷⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠳⣄⠀⠀⢸⡟⠿⠿⢻⡌⣿⣿⣿⣿⡷⠾⠳⢤⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠳⡄⣸⠛⠶⠖⠋⠳⣌⠉⠉⣾⠀⠀⣠⠴⢭⡈⠉⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢻⣸⣷⣦⣀⡀⠀⠈⢉⣩⠿⢤⡞⠁⠀⠀⢹⡄⠀⠀⠈⠙⢶⡤⣀⠠⢶⠞⠻⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠁⠀⠀⠀⢘⠹⣿⣯⣤⣿⣿⣿⣿⠋⢠⡏⠀⠀⠀⠤⣞⠀⠀⠀⢆⠀⠀⠻⣎⠳⣌⠀⠀⠀⠹⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡞⢱⠇⠀⠀⠀⠀⡾⠀⠙⢿⠟⢻⣻⠟⠁⠀⣼⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢳⡄⠀⠹⣆⠘⢧⡀⠀⠀⠹⣧⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠋⢰⠏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⢻⡄⠀⢻⡄⠈⣷⡀⠀⠀⢻⡆⠀⠀ ⠀⠀⠀⣰⠋⠀⣰⠏⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠳⣄⠀⡀⠈⣿⡀⠘⣧⠀⠸⣿⢦⣄⠀⢷⠀⠀ ⠀⠀⢰⠇⢀⡴⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⠀⢸⡇⠀⣿⠀⠀⢻⡆⠈⠳⣜⠆⠀ ⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡿⠀⠀⢸⡇⠀⠀⠘⢷⡀ ⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⠇⠀⠀⠘⠁⠀⠀⠀⠘⡇ ⣴⣾⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣾⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇ ⠻⢿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣾⣥⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣤⣄⣀⣀⣠⣼⣧⣭⣀⣀⣀⣀⣀⣀⣀⣤⣾⣿⠟ ⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⣠⡴⠚⠋⠉⠆⠀⠀⢨⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⣼⣿⣿⣿⣿⣿⡿⢇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⣠⠟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣨⣿⣿⣿⣿⣿⣿⣿⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣠⠖⠋⠀⠀⠀⠀⠀⣤⣄⣰⡀⣀⣀⣰⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠻⡟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⢠⣼⠃⠀⠀⢀⠀⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⠀⢸⣿⡇⠘⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠛⠋⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢠⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠡⡄⠀⠀⠈⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣧⣀⡀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠛⠿⢶⡇⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢧⠀⠀⠀⠀⣀⣼⠷⠶⢶⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾⡿⠿⣻⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿ ⠉⠉⠁⠉⠙⠛⠛⢻⡖⠲⣾⣆⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢿⣄⡴⢟⣹⠇⠀⠈⡏⢛⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣧⡴⠋⠙⠦⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡥⠤⠶⠚⠁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣄⣿⠛⠋⠉⢹⡆⠀⠀⠀⠀⠀⠀⣰⠶⣶⠒⠚⠉⠁⠀⠀⠀⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢍⠛⠳⡶⠾⣤⣤⣤⣤⣤⣤⣤⠿⠀⠙⣟⠛⠛⠛⠛⣻⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⣦⣼⠂⠀⠀⠀⠀⠈⠳⠦⠤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠲⠶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⣏⣉⣀⠴⠖⠒⢲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⢿⠖⠉⠉⠉⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣘⣁⠆⠈⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢀⠀⡀⢀⡀⠀⣴⡚⠲⣴⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠾⡟⠀⠾⣿⣦⣿⣿⡆⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⠀⢃⠀⢿⢿⣿⠻⣿⢇⠔⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡘⠀⠀⠜⠒⠚⣗⠟⢀⣈⠽⠤⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠃⠀⠀⠀⠒⠈⠙⠫⣀⡜⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀ ⠀⠀⢀⠎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀ ⠀⢀⠆⢠⠁⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀ ⢀⠏⠀⠸⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡇ ⢋⠓⢄⣰⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⡠⡖⠲⡔⠒⡩⠔⢀⠇ ⠘⠍⠀⠈⢆⠀⠀⢠⠋⠈⠉⠉⠉⠁⢀⣰⡤⠶⣾⣷⠀⠀⣜⠀ ⠀⠈⢆⡀⠀⠑⡂⠅⠒⠒⠒⠠⠄⡀⢸⠿⠗⠋⠉⡅⡠⠊⠀⣱ ⠀⠀⠀⠉⠂⠼⡀⠀⠀⠀⠀⠀⠀⠌⠙⡄⢀⣀⠔⠛⠒⠒⠈⠁ ⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⣿⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣀⡴⠃⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠈⠁⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡞⠋⠉⠉⠉⠉⠙⠛⠲⢦⣤⣀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣠⡴⠛⠉⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣤⣀⣀⣀⣀⠀⠀⣀⣀⣸⣤⡤⠶⠛⡁⠀⠀⠈⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⢉⣉⣉⣉⣉⣉⡉⡁⠀⠀⡀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣦⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠋⠉⠉⠉⠀⠈⠉⠉⠙⢻⡶⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⢠⣬⣧⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣁⣀⣼⡇⠀⠀⠀⠘⠟⢛⡩⠤⠤⢄⡀⣀⠼⠛⠻⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠁⠀⠀⠀⠀⡰⠃⠀⠀⢀⣄⠙⣇⠀⢀⡀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢰⠃⠀⠀⠀⠸⠿⠀⢸⠀⠻⠟⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡍⠛⠒⠦⣄⠀⢸⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⠠⠤⠊⠉⠒⠂⠐⠒⠁⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣦⣄⣀⣼⣷⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣰⠂⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣶⣟⣉⠁⣀⣈⣽⣁⣏⠈⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⠞⠁⠀⠀⠀⠀⠀⣹⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣩⣟⡋⠁⠀⠉⠙⢦⡀⠀⠀⠉⠙⠒⠦⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠶⢚⣥⣾⠉⠙⣏⠓⠲⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠉⠓⣄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠘⠉⠀⡿⠀⠀⠈⢧⠀⠀⠙⢦⡀⠀⠀ ⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠈⢧⠀⠀⠀⠱⡄⠀ ⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠹⡄ ⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⢠⠾⡇⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢳ ⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣈⣙⣲⣤⣀⣀⣀⣴⣋⣀⣧⣀⣀⣀⣀⣀⣀⣀⣧⣀⣀⣀⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠶⠒⠶⢶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠈⠀⢀⣠⣤⣤⣤⣤⣴⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⣶⣴⣾⠛⢉⣀⣀⣠⣄⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⢫⣿⣿⠖⠛⠉⠁⠀⠀⠀⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⠟⢻⣷⠋⢰⠏⠀⡄⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣘⣁⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⣄⣠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⣄⠀⣤⠶⠒⠲⣤⡀⠀⢠⣿⡷⡀⠀⠙⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠐⢯⣿⠁⠀⢠⣿⣽⣿⣆⣼⣿⣿⣿⣤⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠉⢙⢹⠀⠀⢠⣬⣿⣿⣿⣾⣿⣿⣿⣿⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡀⠀⠸⣿⢿⣿⣿⣯⠛⣿⣿⡿⢃⡴⠚⠓⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⣧⣀⣀⣙⠮⠭⢿⡏⠀⠈⠻⠤⣞⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡞⠀⠀⠀⠀⠛⠁⠀⠀⠈⢹⣤⠞⠀⣀⣀⣤⠞⠛⠛⠛⠀⠈⠳⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⠀⠀⠀⠰⠶⠶⠶⠚⠉⠙⢿⡉⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠙⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⠀⠀ ⠀⠀⠀⢠⠏⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀ ⠀⠀⢠⡏⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢻⠀ ⠀⣠⣿⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⣠⡟⠀ ⠙⣇⠉⠲⣄⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠢⣤⠴⠒⠋⠁⣠⠔⠊⠁⡇⠀ ⠀⠹⡗⠤⠀⠉⠒⣧⠀⠄⠀⠀⠀⠀⢀⣾⣀⣀⠤⠤⠤⠤⠤⠤⠶⠒⠚⠉⢹⠃⢀⣀⣘⣦⣀⣈⠉⠀⠀⠀⣸⠃⠀ ⠀⠀⠹⡀⠀⠀⠀⠘⢆⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣯⣴⠿⡾⢛⣶⣶⣿⠀⠀⠀⣰⣇⠀⠀ ⠀⠀⠀⠻⡄⠀⠀⠀⠈⠳⢤⣀⡤⠞⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⣛⡿⣧⣴⡾⠟⠛⢹⠀⠀⢀⡴⠃⠈⠻⣅ ⠀⠀⠀⠀⠘⠢⡀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⡀⢸⠛⠊⠉⠀⠀⠀⠀⣞⣀⡴⠋⠀⠀⠀⣀⡿ ⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⢧⡀⠀⠀⠀⠀⢀⡴⠛⠓⠒⠒⠒⠚⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⣷⠤⠖⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠒⠒⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠿⠷⢶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠁⠈⠀⠀⠀⠀⣭⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢾⠏⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠁⠀⢀⣠⣴⡶⠶⠶⢶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠓⢖⣶⣾⡏⢉⣀⣤⣤⠤⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣾⣭⣿⢿⡿⠋⠁⠀⠀⠀⠀⠈⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⢉⣹⠟⠁⡼⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠤⠬⠤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⠦⣖⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⣄⣰⠚⠉⢙⣶⣄⠀⢸⣿⣷⡄⠀⠙⢗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⡼⠠⡽⢶⠇⠀⠀⠿⢾⣿⣷⣼⣿⣿⣷⣷⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢼⡆⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣇⠀⠀⢿⡙⢿⣿⣿⠈⢿⡯⠎⡰⠋⠉⢹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡞⠀⠀⠀⣀⠼⠖⠒⠲⢽⠛⣻⠇⠀⠀⠉⣹⣧⣀⠀⠙⢿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢶⠇⠀⠀⠀⠀⣀⠀⢀⣀⡼⢿⣥⠤⠶⠚⢻⠁⠀⠀⠀⠀⠈⠳⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠘⢦⣀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀ ⠀⠀⠀⢀⡞⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀ ⠀⠀⢎⡞⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢦⠀ ⠀⠀⡾⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟⢀⣜⠀ ⠰⡏⠳⣄⠄⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⢤⣀⣀⣤⠴⠚⠉⣀⠔⠋⡇⠀ ⠀⠱⣤⣈⠙⠲⢼⡆⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⢀⣀⣠⣤⡤⠶⠒⡿⠀⠀⠙⣇⠀⠀⠒⠉⠀⠀⢰⠃⠀ ⠀⠀⢧⠀⠉⠀⠀⢳⡈⠀⠀⠀⠀⢠⠏⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣰⣇⣴⡾⠷⣿⣿⣵⠄⠀⠀⢀⡏⠀⠀ ⠀⠀⠈⢧⡀⠀⠀⠀⠙⢄⣀⣀⡴⠋⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣾⢷⣿⣡⣤⣶⠿⠛⡏⠀⠀⣠⠟⠓⢶⡂ ⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⡤⠖⠋⠉⠀⠀⠈⠉⠙⠒⠦⣄⡀⠈⢻⠿⠟⠋⠁⠀⠀⢰⠃⣠⠞⠁⠀⠀⢰⡇ ⠀⠀⠀⠀⠀⠈⠙⠦⣄⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣇⠀⠀⠀⠀⠀⣠⡾⠯⠥⠤⠤⠖⠚⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠘⡦⠤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠢⠤⠤⠤⠤⠤⠤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢉⠏⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠇⠘⠁⠀⠀⠈⢆⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠋⠀⠀⠀⠈⠙⠒⠼⣀⣀⠀⠀⠀⠀⢸⣀⡠⠔⠋⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠠⠀⣈⣉⡩⠭⠭⢍⣅⡀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠢⣀⠀⠀⠀⠀⡖⠉⠀⠀⣀⠀⠀⠀⢀⣏⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠒⠒⠴⡇⠀⠀⢉⠕⠒⠒⡄⠊⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡆⠀⠀⠟⢘⠐⠇⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⡖⠤⢄⠀⡘⠀⠀⠀⠑⢄⣀⡀⠎⠄⠀⠔⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠭⠦⢤⢷⢧⡀⠀⠀⠀⠀⠰⡀⠀⡠⠂⠀⠀⢆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢁⣲⡊⠉⠛⢄⠈⠑⠂⠤⢀⣀⣈⣉⣀⣀⡠⢔⡪⡏⠲⡂⢄⡀⠀⠀ ⠀⠀⡠⠒⠁⠀⠈⢣⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠁⠀⠱⠀⠈⢆⠀ ⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⢣⠀⠀⢃ ⡜⢀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣸⢈⡓⢤⣀⣀⣀⣎⣇⣀⣀⣀⣈⡆⣀⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⢭⠁⢹⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠅⢁⠠⢠⡿⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠃⠀⠀⠅⡿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡇⢀⣤⠀⠀⠸⣫⠑⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⠀⠘⠻⠟⠀⢠⣿⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡲⡶⣴⣄⠀⠀⠀⠀⠀⠀⠀⢀⡞⢝⡈⡱⠾⠋⠛⣤⡀⠈⡿⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⡀⠈⠙⢯⡂⣆⠀⠀⠀⠀⣾⠁⠽⣿⡣⢾⣧⠌⡅⡇⠀⣇⠈⡀⠀⠀⠀⠀⢀⣠⠖⠊⠉⣧ ⠹⡖⡀⠀⠀⠉⠲⣅⠕⠦⣄⢹⢦⣀⡰⢯⣄⣀⡴⡋⠀⠀⣷⠕⠀⠀⢀⡠⠖⠉⠀⠀⠀⣰⡯ ⢀⠹⡔⠀⠀⠀⠀⠀⠑⢦⣷⠏⣄⡀⠀⠀⣀⣠⣤⣿⠓⠀⢸⡂⣤⠔⠋⠀⠀⠀⠀⠀⣼⠯⠀ ⠀⠀⠝⡅⠀⠀⠀⠀⠀⢦⠏⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⡸⠟⠁⠀⠀⠀⠀⠀⣀⡟⡫⠀⠀ ⠀⠀⠀⡚⣇⠀⠀⠀⣼⠏⠠⣤⣿⠟⠛⠟⢋⡽⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡰⢫⡂⠂⠀⠀ ⠀⠀⠀⠀⠙⢦⢠⡼⠃⠀⠀⠈⠙⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠑⡆⠅⠀⠀⠀ ⠀⠀⠀⠀⡀⣒⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠀⠿⡐⠀⠀⠀⠀ ⠀⠀⠀⠈⢁⡏⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢹⡿⡝⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣺⣎⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠫⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⢿⣦⣄⠄⠀⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣻⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡬⢹⠛⣿⣷⣮⣍⡁⡀⠀⠀⠀⡀⡀⣀⣀⣠⣴⣾⠟⠍⠋⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⡉⣻⠋⠀⠉⢻⡛⠛⢿⠿⠿⠿⠛⠛⠋⠉⠀⠀⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢯⡓⠦⠤⠼⠙⠒⠋⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣇⡂⠈⠓⠦⢤⣀⣀⠀⠀⣀⠀⠀⠀⠀⣠⢍⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡷⠢⠤⠤⢤⠼⠈⠉⠉⢻⡄⠀⠀⠀⡇⢀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⢀⡞⠀⠀⠀⠀⠀⠙⣏⠓⠚⠉⢩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠉⠁⠀⠁⢀⠜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⠀⠤⠤⠀⠀⡔⠁⠀⠀⠀⠀ ⠀⠀⢀⠄⠂⠉⠁⠐⠂⠤⡀⠀⢀⠔⠊⠀⠀⢀⠔⠂⠲⣀⣀⡟⠀⠀⠀⠀⠀⠀ ⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⣲⡄⠏⠀⢛⢱⡦⠀⠆⠀⠀⠀⠀⠀⠀ ⠀⢣⣈⠠⠐⠈⢢⡄⠀⠀⠀⠀⠀⠀⣼⣿⣷⣈⠉⠡⠀⡠⠊⠀⢀⡠⠔⠂⠈⠱ ⠀⠀⠀⠀⢀⡜⠁⠈⠂⠀⠀⠀⠀⠀⠩⡙⠿⣿⡿⠒⢀⡥⠐⠊⠁⠀⠀⢀⠔⠁ ⠀⠀⠀⠀⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀ ⢀⠎⢉⣺⡈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡇⢀⠄⠊⠀⠀⠀⠀⠀ ⢸⠀⡔⢹⠈⠂⠩⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀ ⠸⡀⠀⠖⠤⠎⠀⠈⠘⢴⣦⢀⡀⠠⠢⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⠷⡁⠀⠀⠀⠀⠀⠇⣄⠍⠙⡛⠒⡶⠶⠒⠚⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠈⠉⠢⠜⡢⠤⢤⠈⣊⠤⠄⠠⢄⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣾⠀⠀⠀⠀⡸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡅⠠⠀⠀⠉⠒⢤⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠥⡀⠀⠀⠀⠀⢽⣴⡄⠀⡰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐⡀⢰⡿⣃⡈⡵⣒⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡎⢠⣾⣼⣿⣷⢈⠗⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⢰⠓⢜⠻⠋⡨⣁⢼⣤⠎⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⣀⣀⢀⠔⠊⠉⠔⠁⠑⢌⢖⣊⢁⠰⣽⢏⠀⢀⠡⡀⠀⠀⠀⠀⠀⢸ ⠀⠌⠇⠘⠀⡔⢡⠐⢆⠎⡍⡅⠀⡌⡈⠛⠿⠿⠃⢸⠀⠀⠀⡈⣢⠀⠀⠀⠀⠸ ⠀⢸⠀⠀⣼⢁⠇⡈⡌⢌⠌⠀⠀⠀⡇⠀⠀⠀⠀⠘⡆⠀⠀⠰⡱⡑⡀⠀⠀⠀ ⠀⠈⣠⡾⠃⢸⠀⢁⢌⠎⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠑⠈⢰⠀⠀⠀ ⠀⣜⠁⢁⠀⠀⢸⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢸⡳⢄⣀⣀⣠⣜⣛⣒⣒ ⣀⣇⠃⣜⣀⣀⠀⡧⠶⠶⠶⡾⠟⠻⠓⠚⠛⠉⠉⢉⢉⡉⠉⠈⠀⠀⠀⠀⠀⠀ ⡐⣨⣉⢉⠡⠤⠤⠀⢀⡐⠒⡒⢒⡂⢠⣀⣉⢁⣉⣬⣀⣶⣤⣠⣀⣀⡀⠀⡀⠀ ⣄⣐⡂⠊⢋⡓⠊⢱⣯⣿⣿⣿⠷⠿⠶⠲⢶⣶⣶⣿⣿⣿⣯⣭⣭⣭⣹⠤⣔⡕

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠃⠳⣄⠸⢰⣤⣖⡊⣝⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣹⠀⠑⠀⢠⡟⣙⣶⢞⡛⠀⣈⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠙⢷⣄⢀⡼⡟⣿⡝⣮⣝⢿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⣤⠀⠀⠀⠀⠙⣿⣤⣇⡿⢷⣝⣛⣣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣦⠀⢀⣀⣀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡋⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣦⣿⣿⣴⣿⣟⣿⣷⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⣿⣿⣿⣷⣿⣿⣿⠿⠋⠀⠀⢠⣿⠀⠀⢀⣤⡄⠀⠀⠀⠀⢠⣦⣀⡸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢻⣿⣿⣿⣿⣿⢿⡟⢿⣿⡆⠀⠀⣸⡏⠀⠈⠿⠋⠁⠀⠀⠀⠀⠀⢉⣋⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣁⣼⣿⠙⠿⣿⣿⡿⠃⠀⠀⣿⠃⠀⠀⣠⠞⠉⠉⠓⣦⣠⡞⠉⠉⠳⡄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣻⣿⣿⣋⣀⣀⣀⣀⣀⣀⣀⣸⣿⠀⠀⢰⡇⠀⠀⣤⣄⢸⣿⠀⣷⡄⠀⢻⠀⣿⣀⠀⠀⠀⠀⠀⠄⠐⠈⠉⠉⠉⠓⠂⠖⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⡇⠀⠀⠘⣧⠀⠀⠙⠁⢸⠿⡆⠉⠀⠀⣸⠀⢻⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠈⠳⢤⣀⡴⠏⠀⠙⠦⣤⣴⡋⠀⠈⣿⡖⠂⠀⠀⠀⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠈⠒⠒⠒⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠐⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣴⠦⢤⣄⣀⣀⡤⠴⣻⠇⠀⠀⠹⡟⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠆⠒⠒⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⣶⣴⣶⡿⠋⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠗⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⣿⣻⣿⣿⣷⣦⣄⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡿⢿⣿⡷⢾⣿⣿⣿⡞⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡾⠋⠀⠀⠈⠛⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠏⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣟⣿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠃⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⠿⠿⠷⠶⢾⡿⢿⣦⡼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⠀⠀⠀⠀⠀⠀⣼⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⣼⣧⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣰⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⠋⠀⠀⠀⠈⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣲⣄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⢆⠀⠀⠀⠀⢀⣤⠀⠘⣿⡿⠿⠇⢀⡠⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⢦⠀⢀⣾⣿⠟⠃⠀⠀⣠⠖⠂⠘⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠁⠀⠙⢡⠖⠋⢙⣳⠇⣴⣿⣶⣄⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⡏⠀⢰⣿⣿⣷⣿⣿⣿⣿⠀⣼⠉⠋⡳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢀⢼⣧⣄⠸⣿⣿⣿⠃⡈⠉⠁⢀⣇⠀⣰⠟⢂⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠼⣦⢾⣀⠈⠳⡄⠉⠀⣠⠟⠓⠒⣋⣽⣿⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⠴⠋⠉⠀⠀⡴⠁⠀⠈⠳⣄⢿⣟⠋⠁⠀⡀⢎⣼⡿⣿⠀⠀⠠⡀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⢠⢖⡏⠙⡶⠋⠉⢙⠞⠁⢀⢀⠀⢀⠞⢢⢤⡀⠀⠀⠘⡆⠻⣿⣿⣾⣧⣶⣿⠃⢹⡀⠀⠀⠁⢀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠃⡾⠀⠀⠁⠀⣰⠃⢀⡞⠁⡜⢠⠃⢠⠎⡰⠃⠀⠀⠀⣧⠀⠈⠙⠻⠿⠛⠁⠀⢸⡇⠀⠀⠀⠀⢦⠀⡻⣆⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⢠⡇⠀⠀⠀⣼⡏⢀⡜⠀⣸⢁⠎⢠⠋⡴⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⢇⠹⡌⠳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠃⠀⢀⣼⡿⠁⣮⠁⠀⠇⡜⣠⠃⡼⠁⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠈⢇⠘⣄⠹⡀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⣰⣿⡿⠃⠀⢿⠀⢸⢀⡷⢃⡞⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠈⠢⠈⠁⢣⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⠉⢿⠀⠀⠀⠘⡄⡜⠈⢀⠞⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣖⣐⣂⣀ ⠀⠀⣿⡀⠀⢸⡀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣨⣿⣦⣀⣀⣀⣀⣠⣞⣉⣉⣉⣩⣥⡤ ⠀⣠⠆⠳⣄⣠⠇⠀⠀⠀⠀⠘⣆⢠⢤⣤⣤⣶⣶⣶⣾⡿⢿⣿⢶⡶⠿⠷⠖⠛⠛⠛⠛⠛⠋⠙⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠞⢷⣤⣤⣭⣴⡶⠒⠒⠛⠛⠏⠙⠉⠉⠉⠉⠛⠉⠘⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⣀⠠⠄⠴⠆⠐⠘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠠⠅⠉⠉⣉⣁⣠⣤⣤⠤⠀⠄⠀⠀⠒⠀⠉⠉⠉⡙⣁⡉⣡⣀⠀⠀⠀⠀⠀⢀⣶⡀⢀⣻⣭⣤⠀⢀⡀⣀⣀⠀⠀⠀⢀⠀⠀⠀ ⠛⠚⠋⣉⠉⡁⢡⣤⡠⣀⣠⣤⠄⠀⠼⣷⣤⣤⣾⣷⣦⣩⣷⣖⣛⡛⢛⣛⣃⣈⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⢷⠀⢈⠃⣤⠀ ⣿⣥⣬⣤⡄⢈⣉⠁⣤⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⡿⠿⠟⠻⠿⠋⣉⠿⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣷⣤⡼⠛⢿⣿⣽⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠤⣶⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢦⣤⡄⠒⠋⠁⠀⠀⢻⡝⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⢀⡀⠀⠀⠀⠀⠀⢷⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⣸⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠉⢳⣴⢻⣽⣟⢦⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠐⠉⠙⣿⢿⡇⠀⠀⣀⡀⠀⠀⢀⡴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣄⠀⠀⠀⠀⠀⣰⠟⣽⠁⠀⣀⠓⠃⠀⢠⡞⣱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣧⣦⣤⣤⡔⢋⠈⠁⠀⠀⠀⠀⠀⠀⠏⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣻⣿⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢠⡀⢠⡄⠀⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⡾⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣸⢸⢠⡆⠀⠀⠀⠀⠀⠰⠞⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡽⠛⠘⢿⣥⣤⣤⣤⣀⠀⠤⠠⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠶⣿⡛⠁⠀⠉⠉⠉⠙⣿⣦⢠⣰⠚⣋⣉⣁⣀⣤⠤⣶⣫⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠚⠿⠯⠭⠭⠭⠤⠼⠏⢹⢾⠿⠿⠟⠓⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣼⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠘⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣤⠏⠀⠀⠀⡿⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⡦⢤⣀⡴⠋⣥⣍⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣾⣷⣷⣶⡝⠂⠈⠀⠘⠓⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣔⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠹⣆⠀⢠⡆⠀⢀⡀⠈⠁⠀⢸⠐⣿⣿⡀⠀⠀⠀⠀⢀⢠⣶⣟⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠫⢘⢧⣼⣷⣂⡈⠉⠀⢀⣀⡌⢧⠻⣿⣷⡀⠀⠀⠀⠨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⡟⠿⠥⣶⣟⣉⣁⣠⡤⠴⠖⠙⠟⣴⣀⠀⣽⡿⣳⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣈⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⣷⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠖⠒⣦⣄⠀⡴⠋⠀⠀⠀⠈⠝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠠⣾⡀⣰⣦⠀⠀⣀⡀⣇⠀⠰⣶⣀⢀⢰⣿⡀⣸⡷⢳⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⢻⣿⣧⣿⣿⣸⣾⣿⣧⣿⣷⣰⣿⣿⣿⣾⣿⣿⣿⣣⢿⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⡟⠈⠉⠛⣟⠙⠿⠟⠉⠋⠉⠛⡏⠻⠿⠋⠉⠀⠈⠉⠉⠉⢩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀⢠⡞⠁⢀⡾⠁⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡤⠖⠒⢿⡀⠀⠀⠙⢿⠆⠀⠈⡇⠀⠀⠀⠀⠀⠀⠱⢄⡀⠀⠀⣠⠞⠈⠳⢄⡀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡇⠀⠀⠀⢻⡄⠀⠀⠈⠆⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢸⣉⠽⠍⠠⠤⠤⠶⠤⣉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠘⣿⣀⡀⠀⠀⢻⣆⣴⠶⡀⡄⠀⢸⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣇⠀⠀⠀⢻⣿⡀⠺⡇⠀⠀⢧⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢳⣆⠀⠀⢈⢿⣆⢀⣄⣀⣿⣧⡀⠘⠆⠀⢸⠀⠀⠀⡼⠀⠀⠀⠀⣀⣶⡤⠤⢤⠶⢤⣀⠀⠀⠀⠀⢌⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠻⣷⠀⢠⣸⣿⣿⢯⠀⠈⢻⣷⡜⢮⠀⢸⠀⠀⢰⣳⣀⣠⡶⠚⠋⠉⠙⠛⠛⠂⠘⠛⠛⠀⠀⣀⠀⢱⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡽⣄⠙⣷⣻⣧⠈⢻⣿⣆⠀⢦⠉⠻⠦⠖⢸⠀⠀⠈⢇⡩⠏⠀⠀⠀⢀⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⣉⠍⡹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣦⡘⣿⣿⣦⠈⢿⣿⣟⠈⢣⠀⠀⠀⢸⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢙⡚⠁⠀⠀⠀⠀⢀⠴⣚⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠛⠿⢿⣾⣿⣿⣦⠀⠘⣿⣆⠀⠧⠤⠤⢼⡄⠀⠀⠀⡏⠈⠒⠀⠈⠉⠉⠉⠉⠉⠐⠛⠛⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠛⠛⠷⠀⠀⠙⠗⠂⠀⠀⠀⢹⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣺⠥⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣼⠃⠀⠀⠀⠀⠈⠙⠻⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢧⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⢦⣄⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣹⣨⣳⡦⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠹⡄⠀⠀⠀⠀⠀⠀⣠⡄⠀⠠⣻⣿⣿⣿⣷⠀⣀⣀⡤⠄⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⡀⠀⠀⢠⣴⣾⣿⣷⠆⠀⠈⠉⢠⣤⠤⠤⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⠒⠲⣄⠙⡆⠀⢸⣿⡿⠋⣀⣤⣤⣄⣰⠏⢁⣤⣀⠀⠈⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⢠⡞⠉⠀⣠⣉⡻⢰⣿⣿⣿⣷⣄⠀⢹⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠂⠀⠀⡏⠀⠀⣾⣿⡿⣿⣾⣿⣿⣿⣿⣿⠀⢠⣿⠁⠍⡙⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠂⣘⡇⡀⠀⢻⣿⣿⣿⣿⠈⠙⠛⠛⠃⠀⣸⠀⠀⠀⡿⠦⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠊⣹⠟⠛⢶⡌⠛⠿⠟⠋⠀⣼⣄⣀⣀⣴⢿⣦⢠⡾⠃⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠖⠚⢻⡼⠳⣤⡀⠀⠹⣆⠀⠀⢀⣴⠏⠈⠉⢩⡥⣸⡏⡿⠀⠀⠋⠁⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠶⠋⠁⠀⠀⠀⣰⠋⠀⠀⠈⠙⢦⡀⢿⣍⠉⠉⠀⠀⢀⡰⣋⣴⣿⠰⡇⠀⠀⠀⢠⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⢀⡤⠶⠛⠶⣤⠾⠛⠛⠷⣴⠟⠁⠀⠀⠀⠀⢀⡼⢄⣀⣀⠀⠀⠀⡈⢻⡌⠻⣿⣷⣶⣤⣾⣃⣤⣿⡏⠀⣿⠀⠀⠀⠀⠣⡀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⢠⡟⢠⠟⠀⠰⠏⠠⠀⢠⡞⠁⢀⡠⠖⢰⠆⢠⡞⠀⣸⠁⣹⠀⠀⠀⣁⠈⣧⠀⠙⠿⣿⣿⣿⣿⣿⡿⠁⠀⢹⡆⠀⠀⠀⠀⠐⢀⠀⢙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠈⠀⡟⠀⠀⠀⠀⠀⣰⡏⢀⢀⡾⠁⢀⡏⢠⡏⠀⣰⠃⣠⠏⠀⠀⠀⠘⠀⣿⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠘⣦⠈⣆⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⢠⡇⠀⠀⠀⠀⣰⢿⠇⡌⡼⠀⠀⡾⢀⡞⠀⣰⠃⣰⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠘⣇⠈⣦⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠇⠀⠀⠀⣰⣏⡏⠀⣇⠃⠀⢸⠇⡸⠁⡸⠃⣴⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠘⣆⠘⢧⠀⢻⡀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⣾⠀⠀⣠⣾⣟⡼⠀⠀⣿⠀⠀⡜⠀⣇⡼⠁⡸⠋⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⠳⡄⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢀⣴⢟⣽⠋⠃⠀⠀⢿⠀⠀⡇⣠⠞⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡞⠁⠚⣿⠀⠀⠀⠀⠘⡆⢠⠃⠁⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡶⣒⣀⠒⣀⡀ ⠀⠀⢰⢟⡀⠁⠁⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⣎⣷⣄⡀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠉⠉⠉⣉⣉⣉ ⠀⠀⢸⠘⣧⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣼⣿⠤⢤⡄⣀⣠⣖⣦⣀⣠⣤⣤⣤⣶⣶⣶⣾⢾⣿⠶⠾⠿⠿⠿⠛⠛⠛⠛⠛⠉⠉⠙⠉⠉⠉⠉⠉ ⠀⠶⣾⡀⠈⠳⠤⡾⠀⠀⠀⠀⠀⣀⣀⣸⣦⣐⣿⣿⣿⣭⣭⣿⣷⣿⢿⡟⡛⢻⠿⠛⠻⠛⠛⠋⠉⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢒⣛⠛⣿⣤⡤⢶⢶⣖⣒⠚⠛⠛⠉⠉⠭⠍⠉⠉⠉⠈⠈⠈⠘⠃⠀⠀⠁⠀⠈⢀⠈⠀⠀⣀⣀⣀⡤⢤⡤⠤⠄⢶⠖⠶⠒⠒⠈⠈⠁⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠊⠐⠃⢈⣃⠚⠉⠙⠉⠁⠀⢒⣀⣀⣀⣀⢠⡄⡀⠀⠀⠒⠒⠒⠒⠚⠓⠚⠋⠁⠉⠉⡁⠀⠈⠀⠀⠀⠀⠈⠉⢩⣤⠀⠀⠘⣛⣒⣀⡀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⠶⠦⠴⠒⠒⠛⢛⠋⡉⠉⠙⠉⠀⠀⠀⢰⣶⣆⠀⠀⣈⣥⣤⣀⠺⢖⣋⣁⣼⣿⣷⣤⣶⣤⠤⠴⠦⢼⣿⣿⣷⣴⣿⣿⣿⣿⣧⣤⣿⣷⣾⣿⣷⣤⣤⡀⠀⠲⣤⠀⠀⠀ ⣀⣀⡈⠠⠴⠀⢰⣊⣩⣟⠳⠭⠤⠾⠛⠛⢀⣤⡍⠛⣿⣿⣿⣯⣽⣿⣭⣥⣭⣭⣥⣴⣤⣤⣴⢶⣶⣤⣶⣾⣶⣿⠿⠿⣿⠿⢿⣿⣿⠛⠛⠛⠛⠻⢛⡋⠉⠛⣧⣀⣤⣀⣜⣣⣤ ⠿⣭⣴⣬⣤⣤⠨⣀⣀⡉⣤⣤⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠋⢀⡰⠿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣿⣶⣶⠟⠛⢿⣿⢤⣭⣀

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⠀⠀⠀⠀⠀⢀⣷⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠚⢫⡉⠉⠉⠉⢳⡆⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢻⣾⣿⣿⣿⣿⣿⣿⣿⣤⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣀⣴⠾⠋⠉⠀⠀⠀⠈⠁⠀⠀⢠⡿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣐⣴⣾⣿⣿⣿⣿⣿⣿⣿⡟⠉⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⣿⣦⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠟⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣶⣷⣀⣤⣤⣴⣿⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠈⠁⠀⠉⢻⡏⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⢰⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡸⣧⡀⠀⠀⢸⣿⣶⡇⠀⣶⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡙⢷⣦⣀⣠⡿⢿⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠻⠿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣃⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⣷⣦⣤⣤⣤⣤⣄⣠⣄⣀⣠⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⡿⢟⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠛⠻⠛⠿⢿⣿⣿⣿⣿⣆⣠⣄⣸⣦⠀⠀⠀⠀⢸⣾⠏⠉⠉⠉⠉⠉⠉⠉⠛⣿⡛⠛⣛⣻⠟⣿⠛⠋⠉⣿⠻⣦⣠⣾⠏⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠋⠀⠈⠋⠛⠙⠋⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢈⣿⠻⣆⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠾⢋⣥⡾⠋⠀⠀⣀⣽⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡟⠁⠀⣈⣛⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⠶⠖⠛⠋⠉⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣸⡏⠛⠋⠉⠉⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣝⠻⠷⣶⣤⣤⣟⣀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢃⠈⢻⡿⠶⠶⠶⠶⠶⠶⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠻⣍⠉⠛⠛⠛⠛⡛⢛⡟⠛⠋⠁⠀⠀⠀⠻⣦⣀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⣀⣘⣫⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢉⢉⢉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠲⠉⣦⡷⠝⠳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⠀⠑⢄⡟⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣿⣽⣤⣶⡆⠀⣸⠀⠀⠀⠰⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⡿⠿⣿⣿⡅⢠⡇⠰⠃⠀⠀⠓⠚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠷⠇⠈⠉⠁⣼⠀⠈⠀⡌⡊⠦⢀⢱⠀⠀⠠⠐⠀⠐⠐⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠐⠠⠄⠈⠠⡄⠈⣗⠀⠐⠒⠀⠀⠀⠒⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠘⠓⢶⡟⠃⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢘⣿⣷⢦⣄⡔⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀ ⠀⡰⠋⠀⢹⠟⠁⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀ ⢰⠁⠀⠀⠎⠀⠀⠀⢀⡴⠉⠉⢹⠹⡞⠀⠀⠀⠀⠀⠀⠈⢆⠑⡄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡶⢒⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣴⠟⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⠀⡟⢠⣠⣤⣶⣦⠀⠀⠀⣴⣶⣦⣤⣀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠛⠀⠀⠀⠻⢿⣿⣿⠿⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠦⠤⣠⡤⠾⠃⠀⠀⠀⠀⠀⠀⣸⢉⡿⠿⠻⢤⣀⠀⢀⡤⠖⠒⠲⢥⡀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠙⣶⠏⠀⠀⠀⠀⠀⠱⡄⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢱⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠷⣄⣤⡾⠀⠀⠀⠀⠀⠀⠀⡼⢸⠁⢰⣾⣿⣿⠀⡇⣼⣿⣻⡄⠀⠀⠀⠀⡇⠀⢃⠈⠳⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⢸⡀⠘⢿⣿⡿⠀⣷⠹⣿⣿⠇⠀⠀⠀⢰⠇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⡌⣇⠀⠀⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⢀⡾⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠹⢾⣁⣀⣀⣤⠾⠛⢿⣤⣀⣀⣠⡴⠋⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢠⣤⠶⠖⠛⠉⠉⠉⠙⠒⠒⠦⢤⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣀⡀⠠⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢄⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣄⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠦⣄⢀⡴⠒⠒⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⠃⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠠⠀⠀⠀⣀⠈⣷⠀⠀⠀⠀⠲⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⡠⢾⡋⠀⠀⠀⠀⠀⣤⠶⠿⠧⠿⠶⠒⠲⣄⠀⠈⠳⠀⠙⠢⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀ ⠀⡀⣠⠏⠀⠀⠀⢀⡠⠖⠊⠁⠀⠁⠀⠀⠀⠀⠀⠰⣿⡄⡀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⣀⠀⠀⠀⠀⠀⠀⠘⣄⠀ ⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡲⣤⢀⣴⠏⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠄⠀⠀⠀⠘⣆ ⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠟⠋⠉⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸ ⢸⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠀⢤⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⣤⣤⣶⣶⣶⣶⣾⣶⣶⣶⣦⣦⣦⣶⣶⣶⣶⣶⣶⣶⣦⣦⣦⣦⣦⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣦⣤⣶⣾⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⠻⣿⣿⣿⣿⣿⢿⠟⡻⠿⣝⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠀⠉⠉⠻⢳⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⣶⣆⠈⢻⣿⣟⠳⠂⠂⠀⢃⡨⢟⣻⣿⣿⣿⣿⡖⠁⠀⠀⠀⠀⠚⠠⠘⣗⢰⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣧⣄⣿⣷⡀⠹⣿⣿⣷⣴⣾⣤⣼⣿⣿⣿⣿⣼⣿⣷⣇⣚⠿⣿⣿⢆⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⠟⠛⠻⣷⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢩⣿⣟⣅⠈⠁⣀⣶⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⠀⠀⠀⣻⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣾⣯⣄⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣤⣈⣵⣶⣿⡇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣨⣷⣿⣿⣿⣿⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⣽⣷⠿⢿⣿⣿⣇⣀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⢛⣿⣿⣿⣿⣿⣞⣆⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣧⢈⠙⠻⣿⣾⣿⣿⣿⡿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⢳⡌⢿⣿⣿⣿⣿⠒⠈⠉⠙⢫⡝⠛⠋⢉⣻⣶⣋⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣀⠈⣿⣿⣿⣄⢺⣿⣇⣤⡟⢮⣽⣿⣿⣿⣆⠄⠀⠀⠈⠄⠀⠀⢈⣡⠉⠉⢡⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣶⣿⠃⠈⢻⣿⣿⣿⣿⣷⢪⡿⣮⣿⣿⡗⠄⠀⠀⠀⠀⣶⣾⣿⣿⣮⣤⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠰⣦⠉⡟⠻⣏⣹⣴⡿⣮⡻⢿⣿⣶⣤⡀⢀⢒⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣿⣿⢻⣧⣤⣤⣴⣿⣷⣿⣶⣿⣿⡟⢷⡜⣧⡐⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⣿⣎⢿⣎⢿⣆⢿⢻⠻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⢿⢻⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣜⣿⣆⣿⣶⣘⢿⣿⡆⠈⢹⡄⠈⠉⠛⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢸⢸⣇⣿⣿⣿⣿⣿⣽⡿⣿⡿⣟⠿⣿⣎⠻⣯⡙⢿⠸⣿⣧⣄⣀⡇⠀⠀⠀⣰⡏⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⠟⣽⣇⢸⣿⣾⣿⡿⢻⡏⣿⡉⠀⢀⠸⡇⠹⣧⠹⣿⣧⡙⣷⡘⣷⣿⣿⣿⣿⣷⣤⣀⣼⠋⠈⠛⠦⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⡿⠋⢠⣶⡿⣿⣾⣸⢻⣿⢃⠟⢸⣿⠃⠀⠘⠀⣿⡀⠹⣿⣾⣿⣷⣸⣷⣿⣿⡟⡿⠈⢻⣾⣟⢯⡀⠀⠠⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠿⣋⣠⣴⣿⣿⣿⣿⣿⣿⢸⣯⠠⢀⡈⣿⠁⣀⣤⣼⣿⣧⣘⣿⣿⣿⣿⣯⣿⣿⣯⣼⣿⣿⣿⣿⡿⣿⣿⣷⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢘⣵⡿⣿⣿⣿⡿⠛⣹⣿⣿⣿⡾⣿⣝⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠿⠛⠿⠿⠿⠿⠷⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠲⠒⠲⠲⡶⠒⡖⠒⡒⠒⠀⢹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠊⠀⠈⠁⠒⠁⢒⡋⠂⣀⡾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠲⠶⠮⠭⠍⠍⠉⠉⠉⠉⠭⠉⠉⢯⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠶⠒⠒⠒⠒⠒⢲⠒⠑⡒⠒⡄⣦⢐⠲⠒⠀⡄⠐⠒⢲⡆⠒⠖⢒⠂⠀⠀⢸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣐⣒⣂⣀⣂⣈⣐⣒⣀⣀⣁⣈⣈⣒⣈⣁⣀⣀⣉⣈⣀⣀⣀⣈⣁⣁⣁⣨⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉

⢀⣤⣶⣶⣶⣶⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⣶⡶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⣀⠙⢿⣿⡿⡟⠋⠉⠙⣿⣿⣿⣿⣿⡻⠉⠋⠁⠀⠀⢩⡇⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⠐⣦⣙⣷⡄⢻⣷⣶⣤⣤⣠⣴⣾⣿⣿⣿⣷⠀⠶⣶⡦⣀⠀⠁⢩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠛⠛⢿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣟⡀⠁⣠⠆⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢾⠀⠠⣘⣻⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣇⣾⣷⡆⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢛⣿⣿⣿⣿⣧⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣬⣈⣿⣿⣿⡿⠿⡾⢿⣿⣿⣿⣿⠿⠿⢿⢿⣿⡿⣿⣿⡟⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⠁⣤⣄⣘⣮⣿⣿⣿⣇⠀⠀⠘⠃⠁⠀⠎⠛⠆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣼⡏⠙⢿⣿⣿⣿⡦⣿⣿⣿⣿⠀⠀⠀⠀⣴⣶⣿⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠐⣦⣹⣛⣯⣷⣿⢾⡛⣿⣷⣦⣀⣰⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣷⣿⣿⣿⣿⣿⣿⢿⣜⣮⢷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢿⣜⣷⣝⢿⣿⠉⢻⡉⠛⠻⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⡿⣏⡏⣷⣿⣿⣿⣿⠿⢿⡿⣿⢿⣧⡻⣯⢻⣘⣿⣤⣠⡇⠀⠀⣴⢃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⡿⢛⣹⣷⣸⣿⣿⠟⡿⣽⡄⠀⠄⢧⠘⣧⣻⣷⡙⣧⣻⣿⣿⠿⣿⣶⣾⠁⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣋⣠⣾⣿⣿⣿⡇⣿⠈⠁⢿⡀⣀⣠⣾⣆⣼⣿⣿⣿⣿⣿⣏⣿⣦⣼⣿⣿⣷⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢘⣽⣿⣿⣿⡟⢛⣿⣿⣷⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⡀⣤⣄⣤⡀⢤⠍⠙⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣒⣀⣘⣀⣑⣘⣐⣀⡾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢖⣒⣒⣒⣒⠒⣒⣒⣒⢒⢒⡒⠒⠂⢀⡀⠀⠀⠀⣀⠈⠳⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠈⠉⠩⠉⠉⠙⠠⠀⠀⠊⠖⠌⠠⠐⠀⠀⠝⠀⠁⠠⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢰⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠣⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣴⡄⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠒⢤⣀⠖⠉⠉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡌⠀⠀⠀⠀⠀⣣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡠⣺⣤⣇⣠⡤⣧⣀⣦⣄⣾⣤⣟⣆⣴⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢀⠀⡔⠁⡜⠀⠀⠣⠉⠀⠀⠈⢎⠁⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀ ⠀⢠⠒⠘⢆⠀⠙⡇⠀⡇⠀⠀⠀⠑⡤⢤⠔⢁⣑⠤⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣆⡀⠈⢆⡴⢄⠀⢁⠀⠀⠀⡠⠋⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⠀⠘⣧⢀⣘⣷⡈⢆⠈⠀⠀⡜⠀⠀⣠⡀⢀⢄⡀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀ ⢌⢳⣠⡼⢿⡇⢈⠷⣝⡀⡇⠀⡥⡴⠋⠉⠉⠉⠀⠉⠁⠀⠤⠾⠄⠀⠀⠀⠀⠀ ⣿⣦⣻⣷⡘⢿⡇⢣⠀⠀⡇⠀⢹⢀⠀⢀⣑⣃⡀⣀⣈⣔⠞⠊⠀⠀⠀⠀⠀⠀ ⠀⠉⠙⠿⠷⠄⠙⠦⠉⠁⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠰⠀⢣⠀⠀⢀⡀⠤⡄⠀⠄⣰⣿⣿⣿⣿⣷ ⠀⣤⣿⣿⣿⡿⠳⠀⠀⠀⠀⠀⠀⢠⠀⢘⡤⠒⠉⠀⠀⠀⡠⣳⣿⣿⣿⣿⣿⣿ ⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠐⡏⣰⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⢀⣇⠔⠁⠀⠀⢠⠦⠤⣤⢴⣠⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⠟⠁⠀⠀⠀⢠⡇⠀⣀⡁⣀⢹⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣴⠟⠁⠀⠀⠀⠀⠀⠈⠙⠦⠝⢣⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠃⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠂⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡛⠶⡇⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠛⠻⠿⢷⠤⣧⠀⠀⡶⠉⠉⠛⠛⣟⡻⣻⠛⢻⢫⡝⠉⠉⠉⠙⠛⠋⠙⠛⠛ ⠀⠀⠀⠀⠘⣖⠁⢵⠚⠀⠀⠀⢀⣀⡀⠼⠓⠒⠉⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠓⢲⠾⠤⠤⢤⠤⠇⠑⣖⠒⢒⡖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠠⠜⠋⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⠀⠀⠤⠤⠄⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟⠀⠘⠳⢶⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢀⠀⣀⣀⣀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣀⣀⣠⣎⣀⡀⣀⣵⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠌⠉⠄⠃⠍⠀⠠⠊⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣀⣀⣀⡀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠇⠉⠒⠄⡀⠀⠀⠀⠀⢀⡀⠤⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠒⠈⠀⠀⠀⠀⠈⢆⠠⠒⠉⠀⠀⠀⠙⠒⠠⢄⠀⣀⣀⠤⠔ ⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅⠀⠀⠀ ⠀⡔⠁⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀ ⡘⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠷⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢄ ⡥⢀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣶⠆⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀ ⠱⢄⣈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⡀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠲⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⡄⢸⣿⣿⣇⡀⠘⠁⢀⣠⣴⡾⠛⢻⣿⣶⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣇⣸⣿⣿⢻⠉⣷⣾⢟⠋⠉⠀⠀⠀⠈⢻⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣽⣽⣿⣿⣸⣦⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠏⠀⠀⠀⠀⠀⣤⠀⠀⠀⣰⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣩⣿⣿⡄⠀⠀⢀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⠉⠀⠀⠐⣿⣷⠀⠀⠀⢸⢻⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠶⣤⡀⠀⠀⠀⠻⠟⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣸⠟⠋⠙⢳⣆⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢤⣄⡀⠀⠀⠀⣾⣿⠄⠀⠀⣼⠋⠀⠀⠀⠀⢹⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠈⣷⣤⣄⠀⢸⡛⠳⠶⢿⣿⣶⠀⠀⢀⣠⣾⠆⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠁⡜⠁⠀⠀⠀⣿⠀⢹⣇⡘⢧⣀⠀⣸⣇⠉⠙⠛⠛⣻⠋⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠇⢸⠀⠀⠀⢠⠀⣻⠀⢸⠟⠋⠉⠉⠉⠉⠙⠶⠤⠤⠞⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⢠⠏⢀⠀⠀⣸⠀⡿⢠⠈⠀⣟⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣳⠾⢤⣾⠀⠀⡇⢰⠇⣼⣄⠀⠙⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢹⠀⠀⠀⠀⠀ ⠀⢠⣶⠋⠀⠀⠀⠀⠙⢳⠾⠷⣾⣾⠟⠛⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⡆⠀⠀⠀⠀ ⢰⣿⠃⠀⠀⠀⠀⠀⣴⠃⠀⠀⣷⠟⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⢿⣀⣠⢇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⣇⠀⠀⠀ ⠀⠻⣷⣄⠀⠀⢀⣰⣿⢿⣷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡹⣄⠀⠀ ⢠⡞⠹⣏⠙⠿⠟⠛⣡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⢧⠀ ⣾⡇⠀⠈⠓⠶⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠂ ⢿⡇⠀⠀⠀⢀⣠⣤⣤⣤⣐⣢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛

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⢠⣶⣶⣶⣷⣶⠶⠶⣶⣶⠶⠶⣶⣶⣶⣶⠶⠖⠒⢗⢦⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣇⣦⣳⡙⣿⣤⣔⣽⣿⣿⣧⣰⣦⠀⠁⢻⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⢹⢀⢷⡸⣿⣿⣿⣿⣿⣿⣾⣷⣠⣇⣸⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣼⣟⣿⡇⠹⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣟⣧⣝⣿⡿⠷⡽⣿⣿⡿⠿⡿⡿⢿⡟⢿⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⢡⣍⡿⣴⣷⣜⣿⣿⡆⠀⠀⣀⣥⣉⣾⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣟⣀⣮⣯⣿⣟⢟⣿⣦⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣸⡿⣿⣿⣿⣿⣯⣿⣫⡻⣿⠻⡛⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡿⣿⣻⣷⢿⣟⢋⢋⢯⢷⡷⡱⣿⣶⣅⣠⠃⢤⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣫⣾⣿⣿⣎⣁⣏⣠⣼⣬⣿⣿⣿⣯⣧⣽⣿⣦⣼⠀⠀⠀⠀⠀⠀⠀ ⠐⠛⠛⠓⠚⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠒⠒⠒⢲⠂⣡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣒⣒⢒⡒⠒⠒⠒⠚⠉⢉⠉⠉⠙⢅ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠉⠈⠀⠉⠀⠈⠁⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠉⣀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠉⠀⠀⢌⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡀⠀⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠐⠋⠁⣔⠉⠉⠉⠥⠂⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠔⠒⡤⠻⡛⡣⠄⠀⠀⠡⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠒⠚⡆⠺⡟⠷⡇⡇⠸⡀⠀⠀⠱⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣕⡞⠅⣠⠧⠴⠁⡇⢀⡇⠀⠀⠀⣧⠀⠀ ⠀⠀⢀⠔⠀⠐⠒⠢⠄⡀⣴⡏⢀⠕⠨⢳⢋⠆⠀⠀⢿⡥⠀⠀⠀⢠⠁⠀⠀ ⠀⢠⠊⠀⠀⠀⠀⠀⠂⠈⢻⠘⢜⠵⠥⠚⠉⠀⠀⠀⠌⡁⠀⠀⢀⠎⠀⠀⠀ ⠀⡆⠀⠀⢠⠴⣄⠀⠀⠀⠀⠑⠢⢁⡒⠠⢤⣖⠶⣞⠔⠁⠄⢠⠊⠀⠀⠀⠀ ⠀⡄⢀⠀⣷⠀⢈⠕⠄⠀⠀⠀⠀⠀⠈⢩⢋⠝⠛⠯⠱⠀⠈⢇⠀⠀⠀⠀⠀ ⠀⠑⠤⠤⠋⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠘⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠀⠀⠈⠐⠄⢀⠀⠀⠀⠀⠀⠀⠀⠮⠂⣀⠔⠊⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠈⠑⢀⠀⠀⠈⠉⠀⠐⠒⠂⠀⠈⠁⠀⠀⡘⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⢃⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡍⠒⠤⠤⡎⠉⠙⠒⠤⠤⠤⠤⠤⠖⠊⢹⠤⠤⠐⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⣿⠇⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⢸⡇⠀⠀⠀ ⢠⠤⣔⡂⠁⠀⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣀⠂⠈⠁⠒⣤ ⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠁⠀

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⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⡠⠄⠀⠤⣀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠚⠛⠛⠒⠦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡠⠀⠀⢼⠀⢀⣀⡀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⣀⠴⠚⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣀⣌⡄⠘⠿⠇⠀⠀⠸⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀ ⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠙⠻⠊⠢⢄⡀⠀⢀⠘⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⢳⠀⠀ ⢎⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⢀⡜⠀⠀⠀⠀⣠⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠉⠒⠤⣀⠀⠀⠀⣸⠀⠀ ⠈⢣⡀⠀⠀⠀⠀⠀⠈⠑⠒⢤⣀⠀⠀⠀⠈⢯⠈⠁⠀⠀⣀⣤⣾⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠙⢦⡀⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀ ⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⣸⠀⠀⠈⠙⢿⣿⣿⣿⠿⡟⠁⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢀⣿⠟⢁⡀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢈⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡌⠸⣄⣠⠤⠶⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⠜⠀⠀⣏⠀⢀⠀⠈⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⠊⢀⣴⣿⣿⣷⣄⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡩⠊⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⢡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢊⠅⠊⠀⠀⠀⠘⣿⣿⣿⡿⣿⣿⣷⠀⠀⡎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠐⠁⠀⣀⡠⠄⢒⣩⣴⡊⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⢠⣼⣿⣿⠀⣰⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡔⠫⢔⣒⠠⠤⠤⠤⠤⠤⠐⣒⣈⣥⣴⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣇⠔⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠈⠉⠉⠉⠉⢿⣿⣿⡿⣿⣿⣿⣷⣦⣬⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⣀⣀⠀⠀⠈⠛⠋⠀⢾⣿⣿⣿⣿⣿⠟⠀⣀⡤⠚⠉⠙⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⡖⠉⠀⠀⠀⠀⠉⠐⠢⢄⠀⢠⠉⣉⣉⡠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣇⠀⠀⠀⠀⠀⠀⠀⠀⡰⠱⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⣗⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⠒⠒⠒⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢢⡀⠈⠁⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⣀⠀⠄⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⢤⡄⠀⠀⠀⠀⠈⠂⡤⠔⠈⠁⠀⠀⠀⠀⠁⢄⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢠⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠆⠀ ⠀⠂⠀⠀⠈⠐⠠⢀⠈⡆⠀⢠⣴⣿⡿⠳⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠁⠀⠁⠀ ⠀⠀⠑⠠⡀⠀⠀⠀⠈⠁⠀⠈⠟⠡⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠂⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡤⠄⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢂⣴⣷⡀⠈⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠠⠀⠀⢸⣿⠿⣷⠀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⢀⣀⣠⣴⣶⣷⠀⠀⠀⠀⠀⠸⣟⠌⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠻⠋⢿⣿⡷⠆⡀⠐⠀⠀⠐⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢈⠀⠀⠀⠀⡢⡂⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⡀⠃⢲⣸⠰⣖⡬⢭⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠚⠳⢥⡀⠀⣿⣴⢏⡻⣥⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣀⠀⠀⠀⠻⣎⣹⣸⢟⠿⢎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠯⣷⡄⣀⣤⣀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⡀⠙⣯⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣶⣺⣿⣷⣿⣻⣿⣽⣾⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠁⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠿⠽⣯⣿⣷⣿⣿⡿⣿⣄⠀⠀⣿⠁⠰⡾⠃⠀⠀⠀⠈⠛⠋⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣻⣁⣿⡏⠻⠿⡿⠟⠀⢰⡏⠀⢀⡴⠋⠉⠲⣄⡞⡉⠙⡄⢹⡄⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠤⠽⠿⠯⠤⠤⠤⠤⠤⠤⢾⠇⠀⢸⠀⠀⢶⠆⣿⡀⠷⠀⢸⠘⣷⠄⠀⠀⠀⠂⠈⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀ ⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠣⣀⢀⣰⠋⠳⣀⣀⡞⠀⢹⡦⠄⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠤⠤⠤⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠈⡏⠀⠀⠀⠀⣴⡤⠤⢀⡀⠤⢖⡇⠀⠈⣿⠒⠒⠒⠒⠒⠒⠒⠂⠤⠐⠒⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠈⠛⠿⠾⠾⢟⠋⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣶⣶⣦⣄⡀⠀⠀⢀⡤⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⠿⣽⡿⣿⣿⣶⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠟⠁⠀⠈⠙⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠃⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣛⣛⣻⣾⣙⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠇⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⣿⠈⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠘⢦⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠳⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠋⠉⠉⠉⠉⠓⠒⠒⠢⠤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣿⠀⠀⠀⠽⣷⣦⣤⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠈⢑⡶⠚⠉⠉⠉⠙⢢⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣄⣀⣀⣀⣤⢶⣿⠧⣤⣤⡤⠤⠤⢶⣿⡀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠉⠉⠁⢀⡼⢄⠉⠉⠀⠀⠀⣠⠋⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠉⠒⠒⠊⠁⠀⠀⠉⠓⠐⠒⠉⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠛⠦⣄⡀⠋⠉⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⣯⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠖⠃⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⣀⠴⠒⠉⠁⠀⠀⠀⠀⠹⠧⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣠⣤⠶⠞⠛⠉⠁⠀ ⡀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣉⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀ ⠀⠀⠀⣰⠋⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀ ⠀⢠⠇⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣ ⠀⢸⣄⣀⡀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣧⠀⠈⠑⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠘⠳⢦⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠒⠒⠢⢄⣀⡰⠋

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣣⡄⠀⣬⣀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠁⠀⠈⠛⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⢢⠔⠒⠒⢄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⠒⠶⠚⣻⠳⠇⠀⣻⠂⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⠉⠀⠉⠀⠈⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠒⢲⠏⠀⠒⠀⠀⠒⠀⠀⠀⠀⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢄⣀⠀⠀⠀⠀⣀⣠⠤ ⠀⠀⠀⣠⠎⠁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠳⡖⠊⠉⠀⠀⠀ ⠀⢠⠞⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀ ⣰⠋⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⢄⠀⠀ ⡇⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠈⡆⠀ ⠳⣄⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⣠⡟⠲ ⠀⠈⢳⠻⢦⣄⣀⠀⠀⠸⠷⠆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣀⣠⠶⠋⠀⠀ ⠀⠀⢸⠀⠀⠈⠉⠟⠛⠲⠤⠶⠶⠶⠶⡶⠖⠚⠛⠉⠈⠁⢀⠏⠀⠀⠀⠀⠀ ⠀⠀⢘⡄⠀⠀⠀⠢⠔⡰⠀⠀⢖⠢⠤⠃⠀⠀⠀⠀⠀⣀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⡀⠀⠀⠀⠀⠢⠤⠤⠜⠀⠀⠀⠀⠀⠀⠀⢎⢠⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠈⡇⠀⠀⠀⠁⠒⠤⡤⠤⠤⢴⠂⠀⠀⠀⠰⠂⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠓⡦⠤⠤⠤⢤⡶⠁⠀⠀⠸⢤⠤⠤⠤⠼⢴⠚⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⢄⣀⣠⠞⠁⠀⠀⠀⠀⠀⠧⣀⣀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠂⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣼⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢙⠿⢅⡩⠟⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠁⢠⣄⢳⢰⣦⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⠘⠟⢸⠘⠛⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠑⠤⠤⠋⠂⠠⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠔⠒⠉⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡇⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠴⠚⠓⠂⠠⠒⠉⠉⠉⠉⠙⠒⠄⠐⠚⠚⠛⢍⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⢳⣘⣆⠀⠀⠀ ⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣳⠺⡗⣄⠀ ⢰⠋⢃⠔⠋⠀⠀⢀⣠⠀⠢⣄⣀⠀⣀⣀⡤⠔⠋⠀⠀⠈⠑⠒⠚⢻⡠⠬⠈⣇ ⡸⠀⠈⢀⣀⣀⢀⡴⠃⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⡆⠀⠀⡘ ⢳⣄⠀⠀⠀⠈⠙⣄⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠠⣶⡶⠀⠀⣠⡇⠀⠐⢀ ⠈⢧⡰⣄⣀⠀⠀⠈⢳⡶⣶⣖⣢⣤⣤⣤⣤⣴⣶⣶⣶⡿⠷⠟⠛⣻⡤⠤⠔⠊ ⠀⠀⠉⠒⠢⡵⠒⢂⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄⠀⣰⢛⡆⠀⠀⠀ ⠀⠀⠀⠀⠘⠦⡤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣠⢾⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⡠⠤⠤⠚⠉⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⠦⠄⣀⣀⣀⣀⣀⠞⠈⣇⣀⣀⣀⣀⣠⡤⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠤⠀⡔⣠⠏⠀⠀⠀⢸⠸⡀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠀⣀⠔⠁⠀⠀⠀⠀⠀⠣⣄⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣺⡟⢳⣌⢲⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⡶⣦⣤⣀⣀⡸⠉⠀⠀⠈⢳⡊⠀⣠⣴⣶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣛⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⠏⠁⣀⣤⠀⠀⢨⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣻⠀⠀⡜⠉⢩⡵⣭⡍⠱⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⣪⡞⠀⠀⠳⣀⡀⣠⢇⣀⡴⣇⣀⠀⠀⠀⠀⠀⠀ ⣬⣭⣭⣥⣤⣤⣤⣬⣿⣟⣿⣿⢅⣀⠀⠀⠀⠺⣀⡠⠃⠀⠘⣷⣿⣿⣿⣶⣦⠀ ⡿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣄⠈⢷⣌⡙⡲⠶⠤⠤⠤⠴⠖⠋⡟⠈⢏⠛⠿⣿⠀ ⣿⣿⣿⣿⣿⠟⠉⡀⠀⠁⣸⡄⠀⠁⠻⢷⢄⡀⠀⠀⠀⠀⣸⠃⠀⠈⣇⠀⠀⠉ ⣉⣉⣉⣹⠧⠤⡈⠠⡀⢣⣼⠃⠀⠀⠀⠀⢸⠈⢱⠢⠤⠼⠹⡄⠀⠀⠘⡄⠀⠀ ⠀⠀⢀⡇⠀⣀⣼⣶⡏⠉⠁⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⢀⣀⡇⠀⠀⠀⢳⠒⠀ ⠀⠀⠀⠈⠉⠁⠀⠘⢄⣀⠀⠀⠀⠀⠀⠀⢸⣩⠏⠉⠉⠹⣭⣇⣀⣀⣤⣞⣀⣀ ⠒⠒⠒⠚⠛⠛⠛⠁⠈⠉⢏⠉⣹⡾⢿⣿⣿⣷⣦⢤⣤⣴⣾⣿⣿⣿⡏⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠶⠄⠀⠀⠛⢻⠟⠀⠈⠻⡛⠛⠛⣹⠛⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠀⠒⠀⠀⠀⣸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⢀⣤⣤⣤⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣠⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠉⠙⠒⠦⣄⡀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⣀⠔⠋⠍⠉⠱⣄⣀⡀⣨⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠉⠓⢴⡋⠀⠀⠀⠀⣠⣄⠀⢠⠏⠀⢰⣿⡷⢤⡇⠀⠉⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣼⣿⡍⠹⣄⠀⠀⢁⡤⢻⡿⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠀⠙⠀⣀⡤⠚⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣷⡄⠈⠉⠉⢹⡀⠀⠀⢀⠜⠁⠀⠀⠀⠀⣀⡤⠖⠊⠉⠉⢱ ⠀⠀⠘⠓⠒⠋⠁⠀⠀⢀⡴⠛⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⢿⣿⣿⣿⣦⣄⣀⠀⠉⠁⡟⠁⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⣠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢹⠻⢿⣿⣿⠟⠉⠁⢸⣁⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠌⣻⢧⠤⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⢷⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀ ⠀⢀⡼⠉⠛⢶⡿⠈⢎⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⠀⠀⢃⣼⡷⢄⠈⢮⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡇⠀⢀⠎⢰⣇⠀⠳⡀⠱⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡇⠀⡜⠀⢘⡹⠀⠀⡇⠀⠈⠓⢭⡲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⠀⡇⠘⢧⠙⠤⠞⠁⠀⠀⠀⠀⠉⢳⣬⣓⠤⣄⣀⠀⠸⠬⠧⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⣸⡤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢈⣉⠓⠪⠭⢖⣲⡤⠤⠤⠤⢤⣤⣲⠮⢟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠦⣀⡀⠀⠀⠀⢀⣀⠀⠀⠉⡩⠽⠚⠁⠀⢠⢄⠀⢨⡏⠉⠉⠉⠀⠀⢴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⠳⢤⣀⠳⢤⣀⣀⣀⣸⠈⠓⠋⣀⣀⠤⠤⣄⡀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⢤⡏⣠⠔⠋⠁⠀⠀⠀⠀⢸⡶⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣋⡇⠀⠀⠀⠀⠀⠀⢸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⡘⠉⠃⠠⣶⣄⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣵⣧⡗⣊⠑⢆⠉⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⡉⠉⢻⢿⡿⢰⣿⣿⣨⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠈⢢⢌⠒⠊⠣⠉⢹⢀⡴⠺⠍⠙⠢⣄⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠁⠀⠘⢺⣯⣰⣶⡶⢋⠏⠀⠠⡌⠀⢀⠈⠻⡪⡉⠀⠱⡄⠀⠀ ⠀⠀⠀⡰⢊⠆⠀⠀⠀⠀⠻⠽⠝⠁⢸⠀⠀⠀⠡⠀⠀⠱⡀⢣⠘⢆⠀⠸⡀⠀ ⠀⢀⠎⢠⠋⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠑⡄⡀⢳⠈⡇⠘⡶⢄⢣⠀ ⠀⠘⠐⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠁⢸⠀⡇⠀⡇⠀⠱⡄ ⢀⣥⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢸⠰⠁⠀⠁⠀⠀⡀ ⠻⢿⣷⣦⣤⣀⣴⣥⣄⣀⣀⣀⣤⣤⣴⣶⣿⣿⣦⣤⣤⣤⣧⣥⣄⣀⣠⣤⡾⠟ ⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⡿⠿⣦⡠⠗⢤⣽⣬⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡶⠟⠀⠀⢸⣷⠄⢻⡟⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⣄⣀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠹⣧⠏⠀⠀⢀⣠⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣿⣤⣤⣀⣀⠀⠀⠀⠀⣻⣦⣤⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠽⠿⠿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢤⣴⣾⣃⠀⠀⠀⢰⣾⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⠀⠀⠀⢠⡟⠉⠁⢩⣛⣾⠉⣄⠀⠙⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⡏⠀⠀⠀⣿⠀⠀⠀⠸⠟⠈⡿⠟⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣄⣠⠚⣧⣼⠁⠀⠀⠀⠙⣦⡀⠀⠀⢀⣴⣇⡀⢀⣠⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠤⠤⠤⠤⠄⠠⠀⠀⠀⠀⠀⠤⣤⣼⣿⣿⡿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉⢹⡟⠉⠀⠀⢭⠩⠁⠀⢻⣿⣟⣳⣶⣶⣶⣤⣄⣀⣀⠀⠀ ⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣽⣿⣿⣿⠷⣤⣀⡀⠀⠀⠀⠀⠀⠻⣦⣐⡴⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠁⠀⠘⢿⣦⡉⠻⡷⠶⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⡴⠟⢻⡏⠈⢿⡛⠿⢿⣿⣿⣿⠀⠀ ⣿⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⣀⠸⢷⡄⠀⠙⢿⣿⣦⣄⢢⠛⠀⠉⠉⠉⠉⠉⠁⠉⠁⠀⠀⣾⠃⠀⠀⢻⡄⠀⠈⠙⠻⢤⣀ ⣿⣿⣿⣿⣿⣿⣟⣛⣿⠟⠁⠀⣀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠈⠛⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠙ ⣿⣿⣿⣿⣭⣽⣿⡟⠁⠀⢠⠞⠁⠀⠀⡤⠚⢉⣿⠀⠀⠀⠀⠀⠀⠈⠁⢻⠙⠶⣤⣀⠀⠀⠀⠀⣰⢿⡇⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣰⡿⠔⠒⠦⣄⠀⠰⣄⠀⠹⣤⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡟⠛⠶⣴⣾⠃⠰⣧⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀ ⠉⠉⠉⠋⢹⣿⠁⠀⠀⠀⠈⣳⣀⣼⠶⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⣷⠀⠀⠀⢸⠀⠀⢿⠀⠀⠀⠀⠀⠀⢿⡄⢤⣄⠀ ⣀⡀⠀⠀⢸⣿⣀⣀⣠⣴⣾⣿⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣀⣀⣇⣀⣀⣀⣸⣄⣤⣼⠀⠀⠀⠀⠀⠀⢸⡇⠐⠊⠉ ⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢙⣿⠛⠉⠉⠉⠙⣯⣀⣹⠀⠀⠀⠀⢀⣠⣼⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣾⣿⡟⠉⠀⠀⠀⠀⠀⠙⣿⣿⣶⣾⣿⣿⣿⣿⠓⠒⠒⠒⠚ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠘⣇⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠉⠉⠁⠀⠈⢻⣿⣿⣿⡿⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⣋⡉⠉⠉⠉⠉⠉⣡⡟⠁⠀⠀⠀⠀⢳⣀⠀⠀⠀⢀⣴⡏⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠟⢷⠀⠀⢀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣸⣿⡖⣤⡴⠚⠋⠈⢻⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⢿⣿⡷⠋⠀⠀⠀⠀⣸⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠏⠀⠀⠀⠄⠀⣰⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠂⠀⣶⡀⠀⠸⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠓⢦⠤⢄⠛⠁⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠤⢤⡀⠀⢰⣧⢀⣰⠃⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⡕⠀⠀⡟⢳⡸⣌⠉⣟⠓⠤⢶⠏⠀⠀⢿⠀⠀⠀⠀ ⠀⠀⠀⡸⢰⠀⠀⡆⡇⠸⢩⣁⠉⠉⠒⠒⠁⠀⠀⠀⠀⡄⠀⠀⠀ ⠀⠀⡰⠷⠧⣆⢰⢡⢣⣆⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⠀⠀⠀ ⢠⡟⠀⠀⠀⡰⠉⢩⠏⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡄⠀⠀ ⠸⣇⠀⠀⠀⡣⣜⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣱⠀⠀ ⢠⠚⣕⠲⢛⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡱⡀ ⢸⠀⠀⢉⣁⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⣿⠛⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⣰⡟⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠠⡶⠞⠋⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣶⠟⠋⠉⠁⠁⠈⠉⠉⠙⠛⠷⢶⣤⣀⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠛⠷⣿⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣀⣠⣴⠾⠛⠉⠀⠈⠘⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣧⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠳⠶⠶⣶⣶⣶⡶⠶⠾⠛⠟⠉⡁⠀⠀⠃⠀⠀⠀⡀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣧⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⣀⣀⣀⣤⣤⣦⣤⠤⢤⣤⣴⣤⣤⣄⡀⠀⠂⠀⠀⢰⠈⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣧⡌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠷⠀⠀⠀⠈⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⣀⣻⣆⢀⣀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣤⣀⣀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⣴⣶⠿⠟⠃⣀⡀⠀⠀⠀⠀⢠⣿⣿⣿⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠶⣶⣿⡇⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠙⠲⣤⠖⠋⠁⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢠⣶⡀⢘⣦⠀⢀⣴⡀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠸⠿⠇⠀⢸⠀⠘⠿⠇⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠽⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠶⣤⣄⣀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢀⡼⠧⣄⡀⠀⢀⣠⡴⠋⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠈⠉⠛⢶⣄⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠚⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣷⣤⣄⣀⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣶⡟⠋⠉⠁⠀⠀⢉⣿⠁⣿⠉⠉⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⢘⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢛⣲⠿⠛⠉⠙⠛⠻⣦⡀⠀⠀⠈⠙⠳⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⣡⡿⠛⠲⣦⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠟⠷⠤⣄⡀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠳⠶⠤⠤⠤⠤⠤⠤⠤⠴⠶⠛⠛⠋⣡⣴⠟⢻⡇⠀⠀⠙⢦⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⡇⠀⠀⠀⠈⢷⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⣠⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠙⣦⠀⠀ ⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠘⣧⠀ ⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠘⡆ ⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢹ ⢸⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣇⣀⣀⣀⣈⣙⣛⣶⣤⣤⣤⣤⣴⣞⣁⣀⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣈

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▔▔▔▔▔╲ ▕╮╭┻┻╮╭┻┻╮╭▕╮╲ ▕╯┃╭╮┃┃╭╮┃╰▕╯╭▏ ▕╭┻┻┻┛┗┻┻┛ ▕ ╰▏ ▕╰━━━┓┈┈┈╭╮▕╭╮▏ ▕╭╮╰┳┳┳┳╯╰╯▕╰╯▏ ▕╰╯┈┗┛┗┛┈╭╮▕╮┈▏

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⢾⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣴⣶⣿⣿⣿⣿⡇ ⠈⢿⣿⣿⣿⡛⠛⠈⠳⣄⠂⠀⠀⠀⠀⠀⣠⠞⠉⠛⢻⣿⣿⣿⡟⠀ ⠀⠸⣿⣿⣿⠥⠀⠀⠀⠈⢢⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⣿⣿⣿⠁⠀ ⠀⠀⣿⣿⣯⠭⠤⠀⠀⠀⠀⠃⣰⡄⠌⠀⠀⠀⠀⠨⢭⣿⣿⣿⠀⠀ ⠀⠀⠹⢿⣿⣈⣀⣀⠀⠀⠠⢴⣿⣿⡦⠀⠀⠀⣀⣈⣱⣿⠿⠃⠀⠀ ⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠘⣻⣿⣶⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⢂⠀⠀⠀⠀⠘⢸⡇⠆⠀⠀⠀⢀⠰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣷⣿⣆⡀⠀⠀⠁⠈⠀⠠⠀⠀⢀⣶⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣷⣴⡜⠀⠀⠀⠀⣦⣤⣾⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠛⠿⠿⠛⠁⠀⠀⠀⠀⠘⠿⠿⠿⠿⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣤⠟⡇⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⡃⠀⠀⢀⡾⡃⠀⣿⠀⠀⠀⠀⢠⡼⠋⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⠟⠋⠁⣰⡟⣠⡇⠀⢻⡀⠀⢀⣴⠏⢀⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⣶⣿⡇⠠⠸⣧⣠⠟⠁⢀⣾⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠐⣧⡀⠀⠀⠀⣸⠏⢾⠿⣿⡇⠀⠀⠙⠃⠀⢠⣾⣿⡇⠀⣿⡆⠀⠀⢀⣀⠀⠀ ⠀⠀⠙⢦⣀⡾⢿⣶⣮⣅⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠅⠀⢹⣇⣠⠶⠛⠛⠀⠀ ⠀⢠⣄⣀⣹⡇⠘⣿⣿⣿⠿⠆⠀⠒⢻⣾⣶⣶⣤⡀⠀⣠⣼⡟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⣧⠀⠀⠀⠀⠰⡆⠀⠀⠈⠿⣿⡿⡟⠻⠞⢯⣼⣇⣀⠀⠀⠀⠀⠀ ⠀⠠⡾⠛⠁⠘⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠉⠛⠶⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣶⣶⣶⣶⣶⣶⠶⠛⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠛⠛⠛⢻⣇⠀⠀⠀⠀⠉⠳⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡆⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢸⠇⠀⠀⠀⣷⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⠴⠞⠛⠛⡆⠀⠀⠀⢸⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣋⢀⣀⣠⣴⣾⠇⠀⠀⣰⠟⠙⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⢁⡴⠋⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡇⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠉⠀⠘⠻⠟⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⡈⡱⠮⠉⠙⡄⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣾⠀⠼⣿⠃⢼⡧⠄⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣠⠖⠊⠉⣣ ⠹⡆⠀⠀⠀⠉⠲⣄⠀⠀⠀⢸⢦⣀⡰⢧⣀⣀⡴⡁⠀⠀⣷⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⢰⠇ ⠀⠹⡄⠀⠀⠀⠀⠀⠑⢦⣠⠏⣄⡀⠀⠀⣀⣠⣤⣿⠓⠀⠸⡀⣠⠔⠋⠀⠀⠀⠀⠀⣰⠃⠀ ⠀⠀⠙⡄⠀⠀⠀⠀⠀⢠⠏⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⡠⠟⠁⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀ ⠀⠀⠀⠘⣆⠀⠀⠀⣠⠏⠠⣤⣿⠟⠛⠟⢋⡽⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢦⠀⡴⠃⠀⠀⠈⠙⠓⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡏⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⠿⣦⣄⠀⠀⣴⣤⣀⠀⠀⠁⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡄⢹⠛⣿⣶⣬⣉⡁⠀⠀⠀⠂⠀⠀⠀⣀⣠⣴⡾⠟⠉⠀⡎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⡈⣻⠋⠀⠉⢻⡛⠛⢿⠿⠿⠿⠛⠛⠋⠉⠀⠀⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢯⡓⠦⠤⠼⠙⠒⠋⠀⠀⠀⠂⠀⠀⠀⡰⠋⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣇⠀⠈⠓⠦⢤⣀⣀⠀⠀⣀⠀⠀⠂⠀⣠⢍⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡷⠢⠤⠤⢤⠼⠈⠉⠉⢻⡄⠀⠀⠂⡇⢀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢀⡞⠀⠀⠀⠀⠀⠙⣏⠓⠚⠉⢫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⢀⠞⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣁⠀⠀⠀⠀⠀⠀⠀⠁⠂⠂⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢘⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣿⣿⣿⣿⣟⢿⡿⠿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢠⡾⠋⠀⠈⠻⣾⡃⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢠⡿⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⣴⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣾⠃⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠉⢻⡿⠀⠀⠈⣹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⣼⠁⠀⣀⣠⠿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣤⡴⠞⠛⠛⠛⠋⠁⠀⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⣤⠾⠒⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢠⡾⠁⣂⣴⠟⠉⠀⠀⠀⠈⠉⠓⠶⣤⣄⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⢺⡇⠈⢋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣧⠀ ⠀⠀⠀⠀⠀⣀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡆ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇ ⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇ ⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇ ⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇ ⢰⡟⠀⠀⠀⠀⠀⠀⠀⢀⡴⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⡇ ⠘⣿⡀⠀⠀⠀⠀⠀⣰⠟⣧⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢸⠀ ⠀⠘⢿⣄⣀⣠⣴⠞⠉⠀⠈⠳⣤⡈⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⢀⡾⠀ ⠀⠀⠀⠈⠉⠁⣟⠀⠀⠀⠀⠀⠈⠛⠶⣤⡈⠙⠓⠲⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢾⡟⠀⢀⡾⠃⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠉⠙⠛⠓⠲⢦⣤⣤⣤⣤⣤⣤⣴⠶⠞⠛⠛⠉⠁⣰⡿⠳⠶⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡷⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣷⠦⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⣤⣶⡶⠶⠖⠚⣻⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠈⣩⡿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣴⣴⣦⠁⠀⠀⠀⢈⣝⡀⢀⣴⠇⢀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠇⠀⠀⣴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡞⠉⠉⠉⣱⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡀⠀⠀⠉⠛⠋⠉⠻⣦⠀⠀⠀⠀⢀⣾⣇⣀⣀⣀⣈⣻⣦⣤⡶⠏⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⣷⣄⡀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⡾⢹⡏⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠛⠦⣤⣤⡴⠟⠁⠀⠀⢀⣾⠃⠘⣿⠶⢤⣄⣀⣀⣀⣀⣀⣀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠉⠛⣲⣦⣄⣀⣼⠇⠀⠀⣿⡆⠀⠀⠀⠀⠉⣹⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢀⣴⠟⠀⠀⠉⠁⠀⠀⠀⠸⣧⣀⣀⣀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

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

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈⠛⠿⣿⣿⠿⠛⠉⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⣷⣶⣶⣶⣿⣿⣷⣶⣶⣾⠿⢋⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠛⠋⠛⠛⢿⣿⠛⠛⠉⠛⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣀⣀⣀⣀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⣿⢿⡆⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢰⣏⣥⡼⠃⠀⢹⡦⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⣠⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣤⣤⠶⠚⢋⣹⡄⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⡟⢿⠈⣉⣻⣦⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠁⠻⡆⢹⡀⠀⠀⠀⠀⠀ ⣄⡀⠀⠀⣾⣿⢿⣽⠟⠲⡿⠼⠇⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⣷⠘⡇⠀⠀⠀⠀⠀ ⠈⠙⠳⣦⣿⡷⠚⠛⠒⠛⠃⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠿⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⣀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢶⣤⡄⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣀⠀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠳⢦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠀⠀⠀⣀⣠⠔⠊⠁⠀⠀⠀⠀⠈⠙⠳⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠠⣢⣀⣤⡶⠧⠬⠷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡜⢋⣠⡤⢤⠶⣤⣀⠫⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠒⠺⠀⡯⣀⣷⣼⣶⢷⣼⣿⣯⣛⢷⣦⣤⣤⠀⠀⠀⠀⢀⣠⡶⡏ ⠀⠀⠀⠀⠀⠑⡇⣴⠣⣿⠻⠿⠧⠿⠿⠿⢿⣿⣿⣿⣷⠋⠀⠀⢀⡴⠋⡸⢱⠀ ⠀⠀⠀⠀⠀⠀⢧⢿⣙⣧⣶⡍⠃⡀⠀⡆⣈⣿⣿⣿⣿⣶⣶⢾⣽⠁⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣶⣿⣿⡎⠀⠀⢠⠤⡌⡿⠛⠉⠉⢹⢣⢣⠃⡇⠀⠀⣇⠀⢀ ⠀⠀⠀⠀⠈⢃⠀⠙⣿⣿⢷⣤⣠⣤⣡⣼⠁⠀⠀⠀⠸⡜⡌⢆⠘⠆⠀⠈⠢⣈ ⠀⠀⠀⠀⠀⠈⡄⠀⣿⣿⡿⠟⠛⠛⢿⠋⣐⡒⠖⠒⠛⠛⣿⠦⣉⣲⣦⣤⠤⠼ ⠀⠀⠀⠀⠀⠀⢱⠀⠀⡜⠁⠀⢀⡴⣳⠏⠬⠦⠀⠀⠀⠀⢻⡷⠋⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢃⣼⠀⠀⣰⢟⠾⣡⠖⠂⠉⠉⠉⠉⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣀⢠⣞⠭⢷⣴⡷⡫⠊⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡌⠫⡓⣍⠒⢔⠀⢂⣽⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠀⠈⠈⢢⠀⣷⣧⣿⠋⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⡄⠀⢸⡿⣻⡿⠁⠀⠀⠀⢰⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣼⡧⠔⠋⠉⠉⠃⠀⠀⠀⠀⠀⣶⡼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠚⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⣌⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠳⣣⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠭⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⢀⣾⠤⠀⠀⢀

⠀⠀⠀⠀⢀⣀⣠⣤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⠾⣻⠾⠛⣀⣠⠤⠜⠛⠓⣦⣄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⢞⣥⠖⠋⠁⠀⠀⢀⠴⠋⠁⠈⠑⡶⠋⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣯⢾⠃⠀⠀⠀⠀⡴⠋⠀⠀⢀⣠⡜⠁⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡟⠁⡟⠀⠀⠀⠀⡼⣡⠀⣠⠾⠋⠁⠀⠀⢀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠇⠀⠀⢀⣼⠟⣏⣼⡷⠒⠒⠲⣾⣠⠞⢠⡮⠔⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⣠⣤⣟⣿⠁⠀⣿⣿⣿⡇⠀⠀⢹⠤⢠⣿⠀⢀⡏⣀⡴⠚⠋⣹⣦⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠋⢹⣻⣿⡏⠀⠀⢸⣿⣿⣷⡤⠀⠀⠀⣼⢸⠀⣼⠞⠉⠀⢀⡴⠋⠁⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡏⠩⢀⠀⠀⠀⠙⣛⡛⠡⠀⢀⡼⢃⣿⠼⠃⠀⠀⣰⠋⠀⢀⣴⡯⠴⠒⠋⠉⢛⡶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣦⡞⠀⠀⠀⠀⠀⣀⣤⢴⣛⢀⠞⢸⠀⠀⢀⣼⠗⢾⡴⠋⠁⠀⠀⠀⣀⡴⠻⢕⢄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⡖⠛⠉⢉⡽⣻⠋⠀⣾⢀⣀⡿⠁⣡⠟⠀⠀⣀⡤⡖⠋⠁⠀⠐⢄⠱⡻⣷⣦⣽⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣾⢟⡁⢀⣾⡏⢉⡞⠁⠴⠛⠉⢹⡏⠉⠉⠉⠉⢲⠀⡄⠈⡆⢱⢱⣿⡌⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣸⢡⣾⢁⡞⣹⠃⠋⠀⣀⣀⣠⣴⣛⣀⣠⠤⠴⣖⠋⢀⠘⡄⠸⠀⡇⢿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣿⡟⢸⡞⢰⡏⢤⣄⡀⣹⡇⠀⠈⣻⢹⡀⠀⠀⠸⡆⠘⡆⢡⠀⡇⠀⢈⣹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠿⠀⢸⡄⡿⠀⠀⠀⠉⢹⡙⢻⡏⠁⠀⡇⠀⠀⠀⣷⢀⠸⡸⠀⡇⢰⠘⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠰⡄⢻⣷⡄⠀⠀⠀⠀⢳⣄⠙⠆⠀⡇⠀⠀⠀⢸⣸⠀⣇⠀⠇⢸⢀⡇⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠙⡇⠀⠓⠸⡦⠤⣶⠚⠛⠛⢧⡀⠀⠻⠦⡄⠀⢼⣿⠀⢸⡇⠀⠀⢸⣇⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣧⠀⠀⠀⢻⠀⠸⡄⠀⠀⠈⣿⡄⠀⠀⠘⢦⠚⢸⡆⢸⡀⢰⠀⢸⣿⣾⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⠀⠀⠀⠘⡇⠀⣷⠀⠀⠀⢸⡙⡆⠀⠀⠈⢧⠘⣷⣸⣿⣼⠘⡄⢿⡸⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣸⠀⠀⠀⠀⢻⠀⣿⠀⠀⠀⠀⡇⢹⡄⠀⠀⠈⣧⠹⣿⡏⢷⣇⢷⡈⢧⠀⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡿⠀⠀⠀⠀⢸⠀⡏⠀⠀⠀⠀⣧⠀⣷⠀⠀⠀⠘⣧⠙⣷⠀⠻⣮⣷⣌⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢰⠇⠀⠀⠀⠀⢸⡾⠁⠀⠀⠀⠀⡿⠀⢸⠀⠀⠀⠀⠘⡆⠈⠁⠀⠀⠙⠻⠽⠛⠳⠦⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠚⣿⠀⠀⠀⠀⠀⣸⠋⠙⠒⠒⠛⠉⠁⠀⣾⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⠟⢛⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⡄⠀⣀⡀⠨⣙⣏⣉⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⢿⣿⣿⣿⡿⣟⣿⣯⣿⣷⣿⢾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣒⡛⢫⠤⣠⢤⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣯⣿⢿⣿⢯⣿⣯⣿⣿⣻⣞⡷⣿⣽⣻⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢮⣭⣉⡓⠺⠊⢉⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣻⢿⡿⣯⢿⣷⢯⡷⣯⣟⠷⣯⡗⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣩⣿⣿⢿⣷⣄⡙⢮⠭⡁⢠⣬⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣯⢿⣽⡿⣾⣻⣽⣳⣞⣟⡧⣟⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡴⠹⢿⣿⣀⣿⣿⣯⣍⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡿⣯⣿⡽⣟⡾⣵⢫⣾⡱⢯⡜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣞⣰⣀⣾⡷⠘⣿⣿⣟⣩⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⢷⣟⣿⢯⡷⣏⡟⣶⡹⢇⡞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⢯⣾⣿⣿⡿⠁⠀⠀⠼⢿⣿⠥⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡾⣟⣯⢿⡼⣹⢶⡹⢣⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⡽⣯⣟⢾⡱⣏⠵⣋⠎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢬⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣳⢯⣏⡗⣎⠳⡌⠆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⢻⡗⣮⡝⣬⢳⠉⡎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣯⢷⣫⢗⡭⢎⢧⡙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣯⣟⣧⡟⡼⣉⢆⠣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣿⢿⡟⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡂⠭⢊⠻⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣻⣞⡽⣲⢍⡎⢇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠒⠐⢀⠀⠠⠐⡆⢯⡹⡹⢛⡯⢭⡹⣿⣿⣿⣿⣿⣿⣿⡿⣾⢯⣷⣻⣜⡳⢎⡜⠦ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢎⢦⡹⢄⡄⣌⣩⣝⠾⣡⢃⠡⠃⡘⢧⠿⣽⣻⣿⣿⣿⣿⣿⣽⣿⣟⣷⣻⡼⣝⢮⡙⡖ ⣿⣿⣿⣿⣿⣿⣿⠃⣾⣷⣄⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢉⣩⣁⣳⣶⣦⣤⣤⣈⣥⢛⡞⣶⣿⣜⣫⢝⣶⣫⢞⣡⣀⣒⣀⡴⣨⡽⣎⣿⣿⣿⣿⣿⣿⣿⣿⢾⣯⢷⣻⡜⣮⢱⢣ ⣿⣿⣿⣿⣿⣿⣿⡇⣿⢻⠇⠛⢧⠀⠀⠁⠀⠀⠀⠾⠛⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⢾⣯⢷⣻⣼⢣⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⠀⣶⣿⠃⠀⠂⠀⠀⢰⣶⡾⠟⠫⣈⢿⡿⠟⣨⣿⣿⣿⢿⡆⠀⠈⣿⣿⣿⣿⣿⡟⢹⣯⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⢯⣿⢯⡿⣟⡾⣏⣞ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡀⢿⡃⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣉⣛⠶⣿⣿⣿⣿⠟⣿⠃⠀⢠⣿⣿⡏⢿⣯⣭⠷⣭⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣯⣟⣯⡿⣽⣻⢞⡵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠱⡈⠹⡄⠀⡁⠀⠀⠀⠀⠀⠈⠙⠋⣙⣹⣿⣿⡿⠋⠀⠀⠀⠀⢺⣿⣿⣿⣆⢻⣿⣻⣶⣷⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣾⢯⡿⣽⡷⣯⢿⣹ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢲⡾⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠜⡹⠟⠉⠀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣞⡽⢿⣿⡿⢿⡟⢶⣡⣿⣿⣿⣿⣿⣿⣿⣳⣯⢿⣯⣟⣷⣻⣽⡳⣏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡀⣀⡆⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣠⣾⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠱⠂⠄⣙⢣⣟⣮⣿⣿⣿⣿⣿⣿⣿⣟⣷⣻⣟⡾⣽⣞⡷⣯⡽⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⢈⣿⣿⣿⣿⣍⠣⡉⠴⣌⢷⣾⣻⣿⣿⣿⣿⣿⣿⡿⣞⣯⢷⣯⡟⣷⣫⡽⢶⡻⣵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⢺⡿⢏⢀⣠⣀⠀⣦⣀⢻⣿⣿⣿⣿⣣⣝⡳⣎⣿⣽⣿⣿⣿⣿⣿⣿⣟⣿⡽⣯⣟⢶⡻⣵⢣⡟⣯⢳⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⢰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⢢⣏⣷⢿⣭⣻⢷⣿⣿⣿⣿⣽⣾⣳⣟⣷⣫⢯⡷⣭⢳⡝⣮⢛⡼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣞⡿⣎⡶⣿⣿⣿⣿⣿⣿⣞⡷⣟⣾⡳⣏⡷⣹⢎⡷⣙⢦⣋⠖ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣽⢳⢏⣾⣿⣿⣿⡍⣉⣛⣻⡿⢿⣾⣽⣝⣳⣝⢮⠳⣍⠶⣉⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣧⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠾⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣞⢿⣺⣿⣿⣿⣿⣿⡉⢿⣿⡙⠲⣤⣈⡙⠻⠮⣽⣙⡌⢣⠱⣊ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣆⠠⡀⠀⠀⠀⠀⠘⠉⠁⠀⠀⢀⣠⣶⣿⢿⡛⣴⣿⣻⢻⡽⣷⢯⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣡⡄⠀⢢⠉⠱⣄⠀⠉⠈⠐⠃⠄ ⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⠹⣄⠙⣄⡀⠀⠀⠜⢢⠳⣾⣿⣿⣿⣿⣿⣷⣯⡷⢭⡷⣯⢿⣯⣿⢾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠉⠢⠈⢦⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢱⡙⢧⡈⠻⣦⣄⠘⠀⠠⠀⠈⠁⠀⠀⠀⠀⠀⢌⢧⡻⡽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⡄⠀⠀⠃⠈⣷⡀⠀⠀⠀ ⣿⣿⣧⣿⣿⣧⣿⠟⠀⠀⠀⣠⠀⠀⢀⣠⠀⠀⢿⠛⠻⢤⡘⠻⣤⡀⠀⠀⠀⠀⢀⣀⣠⣤⡼⣼⢧⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡄⠀⠀⢀⠸⡇⠀⠀⠀ ⣿⣷⡿⣿⣽⠟⠁⠀⣠⡏⢰⡇⠀⠀⢸⣿⠀⠀⠘⣧⠤⠄⠙⢶⣌⠛⢶⣤⣶⣶⣿⣾⣿⣯⣟⣯⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣳⢯⣿⡄⠘⠤⢂⠙⢦⡀⠀ ⣟⡾⣽⠟⠁⠀⠀⢠⡿⠀⣾⡇⠀⠀⠹⢿⣀⣤⡀⠙⢆⡰⣳⣦⣈⡛⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣷⢫⣞⢿⡃⠄⢂⠀⢣⢳⡀ ⣯⡟⠃⠀⡰⠀⠀⣿⠃⢸⣿⡇⢀⠀⡀⠀⠈⠻⢿⣷⣮⠵⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⣿⣟⡿⣷⣿⠿⣝⡷⣎⠲⣅⠀⠀⠈⠀⠡⢓ ⠋⠀⣀⠔⠁⠀⢀⡇⠀⣾⣿⡄⠈⣆⠘⡀⠀⠀⠀⠹⢿⣿⣿⣟⣯⣙⣌⣙⡻⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⢯⣟⣿⣿⡿⣿⡽⣾⣽⣻⣿⡹⣌⢳⣍⡒⠈⠄⠀⠀⠀⠀⠈ ⠀⠀⠀⠠⣆⠀⢸⠀⢠⠿⣿⡇⠀⢸⣧⠑⢦⠀⠁⠀⠀⢈⠛⢿⣿⣽⣶⣯⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣻⣞⡷⣿⢯⣟⣷⢳⣿⣯⡕⢎⠲⡡⠌⠐⠠⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠈⢆⡇⠠⠊⠀⣿⡇⠀⠀⣿⡷⣄⠳⣤⠀⢠⠀⠀⠀⠘⠻⠿⣿⢿⡿⠟⢉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣟⣾⢿⣽⡻⢾⡭⣟⣿⡗⢮⡡⠂⠑⣂⠀⡲⢱⠀⠄⡁⠀ ⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣿⣷⠀⠀⢸⡷⠜⢧⡈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡾⡽⢧⠿⣜⣿⡟⢢⠑⡤⠘⢤⠣⢌⢣⠘⠠⠀⠂ ⣾⣦⡀⠀⠀⠀⠀⢙⣦⠀⣿⣿⠀⠀⠀⠀⠆⠐⠛⣦⣄⠠⣄⠀⠰⠀⠀⠀⠀⠀⡐⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢯⡿⣷⣿⣻⠯⣷⣎⡿⡍⢦⡙⠴⡁⠎⣇⠫⢄⠊⢀⠁⠀ ⠀⠀⠉⠲⣭⣯⣿⣾⣿⣷⣽⣿⡀⠀⠀⠀⠁⠀⣨⡇⠸⣷⣄⠁⠄⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣟⢿⣿⣿⣿⣿⣿⣿⡣⢿⡱⢎⡝⠻⠶⣾⡽⣙⠦⡙⠤⠃⢘⠀⢳⡈⡐⠀⠀⠀ ⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣇⢠⠐⡁⢰⣿⠿⡷⠀⠹⡙⣶⣄⡀⠀⢠⡄⢀⣾⡿⣟⢣⠟⡼⢫⣿⢿⣿⣿⣿⡿⣿⣷⣏⠂⢜⡱⣌⡄⢣⣝⠂⡉⠒⡁⠀⠀⠂⠐⠈⠀⠠⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡔⠒⢺⠁⠒⡔⠒⠲⠄⠠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠠⢎⠢⠧⠀⠘⠀⠀⢐⠀⠀⠀⠜⠀⠈⠨⢦⠀⠀⠀⠀⠀⠀ ⢀⠔⠛⠋⠀⢀⡏⢃⠀⠂⠀⠀⢠⠀⡀⢸⠀⢀⡎⠀⠠⠔⢁⡸⡀⠀⠀⠀⠀⠀ ⣸⠣⡀⢣⡄⠈⠃⠘⢦⠀⡇⢡⢺⠀⠁⢰⠀⠘⠀⠔⠁⡀⠋⣴⠤⠶⠠⡀⠀⠀ ⡆⠁⠀⠀⢩⣦⡀⠀⡘⣄⠻⣌⢢⠀⡆⡘⢠⢃⠌⡠⠊⣀⡼⠁⠀⠀⢐⣉⡄⠀ ⠘⣦⠀⣀⠀⠙⢿⣦⣝⣬⣮⣾⣿⣿⣻⣿⣷⣥⢊⡤⠮⣊⡤⠐⠁⠀⠉⠀⠈⡆ ⠀⢹⠄⢀⣁⡀⠒⣚⣛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣏⡠⠐⠉⠀⡠⠶⢂⡤⠖⢈⡇ ⠀⠈⢔⠀⣀⠬⢛⠛⡉⠙⡻⠿⣿⣿⣽⣿⣿⣾⡿⣗⣒⡒⠒⠒⠈⠁⠀⠀⠀⠇ ⠀⠀⢀⡋⢀⢔⠅⠀⠠⠜⡔⠀⠄⠀⢸⠁⠉⠀⢣⠈⠂⠤⠄⡀⠈⠐⠒⡲⠊⠀ ⠀⠀⠀⢆⡁⠥⠤⠤⠠⢎⣀⣼⠄⣀⡀⡇⠓⢰⢰⠮⠵⢒⣒⣖⣨⠭⠟⠁⠀⠀ ⠀⠀⠀⠀⠈⠘⠚⠓⠤⠀⠦⠤⠰⣄⠩⠷⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⢦⣤⣀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⣇⡀⠈⢻⡄⠀⠀⠈⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠁⠘⡌⢢⠀⢻⡄⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠀⠂⠀⠰⢸⣧⠈⣧⡀⠀⠈⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠁⠢⡀⠀⠞⣻⡂⠘⣧⠀⠀⠀⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⡉⠀⢼⠃⣩⡿⠀⠀⠘⣧⡄⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢶⣈⣴⡿⠁⠀⠀⠀⠘⣷⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⢸⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀