Alien ASCII Art

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣉⣁⣤⣴⣶⣶⣶⣶⣶⣴⣦⣤⣈⣉⠙⠻⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡉⠻⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣴⠿⠿⢿⢿⠿⢿⣿⡿⠿⢿⡿⠿⢿⠿⢿⡟⠹⠹⢿⡿⠿⠏⢷⡈⢻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣀⣇⢘⢸⢸⢸⣿⡘⢃⡆⣰⡐⢂⣆⣿⣇⠘⢸⣟⡁⡂⣇⢻⣷⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⡿⢻⣿⣿⣿⣿⣿⢿⢻⣿⣿⣿⣿⣿⠟⣿⡿⠿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⡆⡎⡂⠁⣥⢱⢸⢸⢰⠘⣸⡟⢰⢸⢐⣿⡧⡍⣻⣿⣿⣿⣿⠏⣠ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠲⢷⣶⣶⣶⣾⣾⣾⣮⣥⣿⣿⣶⣾⣶⣿⣷⣶⣿⣿⣿⡿⠋⣴⣿ ⡿⠟⣉⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠋⣉⡑⠢⣌⣉⡛⠛⢻⢛⡿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⣁⣴⣿⣿⣿ ⠃⠾⢿⠉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣄⢹⠿⠆⢸⣿⣿⣿⡇⢸⣷⣶⣤⣤⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿ ⣷⣶⠘⡆⠻⠛⣉⣠⣤⣤⣌⡉⠛⠇⠸⠀⣶⣿⣿⣿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡧⠑⡀⣻⣿⣿⣿⣿⣿⣿⡇⠠⠁⢴⣿⣿⣿⠟⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢀⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠈⣿⡋⢡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠘⠛⠛⠻⢿⣿⣿⣿⣿⡿⠛⠛⠛⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⠀⣴⣿⣶⣆⠀⢻⣿⣿⠏⠀⣴⣾⣿⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⠀⢻⣿⣿⡿⠀⠀⣿⡟⠀⠘⣿⣿⣿⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣆⠀⠈⠉⠀⠶⠀⣻⡇⠰⠶⠀⠉⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣤⠀⣀⣤⣴⣿⣿⣦⣄⡀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⡌⠛⠿⣿⣿⠿⠋⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠟⣠⣶⣦⣤⣴⣶⣷⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣇⠐⠋⠉⣿⣿⣿⡟⠉⠛⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢀⡟⢉⡉⢳⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣈⣠⣿⣷⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

i luve Sprite ⣰⣾⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡴⠞⠋⠁⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡤⠶⠒⠒⠶⠞⠛⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⠈⢻⣿⣍⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⠁⠀⠀⣴⠄⠀⠀⠀⠀⢀⣤⣄⣀⣤⡶⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣻⠿⣇⠀⠀⠀⠀⠀⠀⠠⠤⠴⣾⠁⢸⡇⠀⠀⠀⢰⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⢷⣀⣀⣀⠀⠀⠀⠀⠀⠉⠿⠏⠁⠀⠀⠀⠀⣿⠿⠷⣿⣾⣶⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣛⣛⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠲⠭⢼⣧⣀⣽⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⣰⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠤⣷⠮⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠘⣧⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡕⣻⣛⠖⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠙⢿⡙⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡼⠋⢠⡾⠛⢧⡀⠀⠀⠀⢸⡛⠓⠋⠛⠋⠉⠛⠶⢤⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡿⠀⢰⡿⠀⠀⠀⠹⣷⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡿⠀⠀⣾⠁⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡁⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠋⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⬛🟥⬛🟧⬛🟨⬛🟩⬛🟦⬛🟪⬛ 🟪⬛🟥⬛🟧⬛🟨⬛🟩⬛🟦⬛🟪 ⬛🟪⬛🟥⬛🟧⬛🟨⬛🟩⬛🟦⬛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣤⣤⣶⣴⣶⣶⣶⣶⣶⣶⣤⣤⣄⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠙⠛⠛⠿⢿⣿⣿⣦⣄⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣷⣶⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠿⠿⢿⣿⣧⡂⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢿⡿⠃⠀⠀⠘⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠂⠀⠀⢠⣤⣤⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠛⠛⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⣶⣶⣀⠀⠀⢀⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿ ⠀⣄⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠰⢿⣷⣦⣆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⣿⡿⠀⠹⢿⣿⣷⣾⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃ ⠈⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀ ⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋⠁⠀⠀ ⠀⠸⣿⣟⠀⣠⣤⣴⣶⣶⡶⠶⠾⠾⠶⢼⣿⣧⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢀⢀⣤⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣶⣾⡿⠟⠉⠀⠀⠀⠀⠀ ⠀⠈⢻⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠛⢿⣶⡀⠀⠀⠠⣤⣿⣿⣷⣿⡿⠿⠿⠿⣿⣿⣿⣶⣷⣶⣤⣦⣤⣶⣾⣾⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢼⣿⡧⠙⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠹⣿⣀⣤⣾⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠙⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⣷⡂⢩⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠹⣿⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣇⠸⡡⣂⣶⣿⡿⠿⠿⣷⣦⣤⠀⠀⠀⠀⢰⣴⣾⣿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⡞⣹⣿⡟⠁⠀⠀⠀⠀⠻⣿⣦⠀⡲⢸⣿⠟⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⣿⣏⣿⡟⠀⣀⣄⠀⠀⠀⠀⣹⣿⡇⠀⣿⣿⠀⠀⠀⠀⣠⡄⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣹⣿⢻⣿⡄⠈⠁⠀⠀⠀⠀⣿⣿⠃⢀⢹⣿⣇⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣏⢻⣿⣦⣄⢀⣀⣠⣼⡿⠛⣤⣠⡀⠙⠿⣷⣶⣶⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⡅⠈⠛⣿⣿⡟⠛⢫⠀⢠⣿⠋⣥⣤⣤⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠥⠀⣴⣶⣶⡿⠿⠟⢿⣿⣿⣿⡿⢿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⢻⣿⣿⡟⠀⠀⡼⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠀⢿⡹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⣈⣿⣿⠏⠀⡸⠟⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⠷⣶⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀꒰ 𝑳𝒐𝒐𝒌𝒊𝒏𝒈 𝒂𝒕 𝒕𝒉𝒆 𝒔𝒕𝒂𝒓𝒔 ^᪲᪲᪲ ـــــــــــــــﮩ٨ـ♡ ✩‧₊˚ ⁀➴ 𝑨𝒅𝒎𝒊𝒓𝒊𝒏𝒈 𝒇𝒓𝒐𝒎 𝒂𝒇𝒂𝒓. ꒱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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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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⠀⠀⠐⡱⠑⡇⠀⠀⠀⠀⢸⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿ ⠀⢠⠎⠀⢰⠁⠀⢀⡠⢴⠚⠉⠙⠛⠻⣿⣿⣿⣿⡇⢠⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⢰⣋⠀⣠⡞⠀⠠⠋⠀⡇⠀⠀⠀⣠⣶⣿⣽⣿⣿⢱⣟⣿⣿⣯⠀⠀⠀⠀⠀⠀ ⠀⠙⢌⠉⠀⢀⡆⠀⠀⣇⠠⠤⠖⠛⠛⠛⠛⠻⠿⣿⣟⣿⣿⣿⣆⡀⠀⠀⠀⠀ ⠀⠀⢂⠑⢦⠼⠃⠉⠑⠂⠄⡀⠀⡐⠶⠶⠴⢀⠀⠙⢷⣽⣿⣯⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⣀⡭⢢⠈⢻⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⢰⠉⣤⣌⢇⠘⣿⣿⣿⣿⣿⣿⣤⣤ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠛⠋⣼⠀⣿⣿⣿⣿⣿⠿⠿⠿ ⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠉⠉⡜⢀⣿⣿⡿⠟⠋⠀⠀⠀ ⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠑⠠⣀⠀⠀⠀⢀⡀⠊⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠂⠤⠄⣤⣤⣤⣀⣀⣺⣿⣽⣏⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠒⠀⠁⠘⠻⠿⣿⣿⣿⣿⣿⣿⣷⣶⣮⠻⡒⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠀⣀⡄⠀⠀⠀⠀⠀⠈⢙⠟⣋⠉⣽⣿⣿⣷⣵⣀⠑⡄⠀⠀⠀ ⠀⠀⠀⠀⠆⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠸⣜⣛⠑⠋⠹⣿⣿⣿⣿⠄⠈⠀⠀⠀

👺,👽,🦎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⡶⠶⠾⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⠶⢶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠙⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣷⡄⠀⠀⠀ ⠀⠀⣼⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣇⠀⠀ ⠀⢸⡿⠀⠀⠀⠰⣶⡶⠶⠀⠀⢀⣾⡿⠂⢀⣀⠀⠀⢀⣀ ⣿⠀⠀⠀ ⢀⣀⡀⠀⣀⡀ ⠀⠀ ⢀⣀⠀⢰ ⠀⣀⡀⠀ ⣀⡀⢀⡀⠀⢀⣀⠀ ⣿⠀⠀ ⠀⠈⢿⡄⠀ ⠀⠸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠛⣿⠛⢰⣿⣽⡇⢸⣿⣿⠆ ⣿⠀ ⠀⠀⢾⣯⡋⣾⠛⣿⠀⠀⠠⣿⣿⡃⢸⡇⣾⠋⣿⢰⡟⢻⡟⣿⢰⡟⢹⡇ ⣿⠀⠀ ⠀⠀⢹⡇⠀ ⠀⠀⢻⣷⠀⠀⠘⠟⠛⠓⠀⠀ ⠿⠀ ⠈⠻⠟⠋⠘⠻⠛⠃ ⠿⠀⠀⠀⠻⠾⠃ ⠙⠿⠛ ⠀⠈⠿⠟⠃⠸⠃⣙⣟⣿⠘⠃⠘⠃⠻⠘⠓⠛⠃ ⠻-⠀⠀ ⠀⢸⡇ ⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇ ⠀⠀⠀⠀⠀⠙⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⠏⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⢿⣿⠛⢷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣼⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⢻⣿⣿⣮⠉⣿⠉⠉⠛⠛⠛⠛⠿⠿⠿⠶⠶⠶⠶⢦⠤⡤⣤⣤⢤⣤⣤⣴⣤⣶⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣷⣞⢿⣿⠿⢣⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣎⢿⣸⡇⠀⠀⠀⢀⣴⡿⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡁⣨⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣬⣿⡇⠀⢀⣴⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡉⠌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢉⣿⢹⣇⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣠⠏⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣨⣷⣶⠶⠶⠶⠶⠖⠶⠶⠶⢤⣤⣤⣀⣀⡟⠀⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠙⢿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⡼⠹⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠀⠀⠰⣣⢣⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⢸⣀⣿⣿⣿⠿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⣽⣽⣼⣿⠀⠀⠀⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⢙⢿⢿⣿⣶⣤⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡀⠀⢸⣾⣿⣿⡟⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠩⢻⣿⣿⣶⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣍⠙⠻⠿⠿⢿⠁⠀⢠⣤⣤⡤⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣶⣶⣶⣶⣤⣤⣭⣴⣶⠶⣯⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢿⠿⠿⢿⣿⣿⡿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⢷⠀⡙⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣞⣉⠀⠀⠀⠀⠀⠈⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡁⢰⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣷⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⣦⣠⡶⣀⠀⢀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⠇⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠻⣤⡙⢶⣈⣁⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡤⠞ ⠋⢠⡟⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢄⣀⠀⠀⣧⠀⠀⠈⠙⠶⣄⣈⣇⡂⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢄⣀⣤⡤⠴⠚⠁⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣙⠻⣍⣻⣒⢤⣽⠀⠀⠀⠀⠀⠀⠀⠀ This took me 1000+ years

𓍊𓋼𓍊𓋼𓍊

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o o )-( (O O) \=/ .-"-. //\ /\\ _// / \ \\_ =./ {,-.} \.= || || || || hjw __|| ||__ `97 `---" "---'

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠉⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠒⠈⠉⠁⣀⣀⣈⡉⠀⠒⠒⠦⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢣⢳⠀⠀⠀⠀⠀⣀⣤⣚⣉⠀⠀⠀⠀⠀⠀⠀⣉⠤⠀⠠⢍⣢⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⣰⠿⠀ ⠀⡈⠀⢣⡀⠀⣠⠞⡽⢋⠅⠂⠈⠁⠒⢄⠀⢀⠞⠁⠀⡀⠀⠀⠈⠆⠀⠀⣠⠭⠭⢉⡓⢌⠳⣄⠀⠀⠀⡴⠁⡀⡇ ⠀⡇⢆⠈⢧⡰⠋⠀⢃⠎⠀⠀⠀⣠⡀⠘⠆⢸⠀⠀⢠⣷⡆⠀⠀⠰⢀⠖⠉⠀⠀⠈⠁⢘⠄⠙⣄⢀⡴⢃⡴⠃⡇ ⠀⢧⠘⣆⡸⠁⠀⠀⢸⠀⠀⠀⠈⠻⠟⠀⠂⠀⠳⢄⣀⣉⡀⠀⠐⠁⢀⠀⠰⣿⡆⠀⠀⠀⡆⠀⠈⡟⢠⠞⠀⠀⠃ ⠀⠸⡀⠏⡇⠀⠀⠀⠀⡑⠤⠤⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⢀⡴⠀⠀⠀⣠⠇⢰⠀⣸⠀ ⠀⠀⢇⠀⡇⠀⠀⠐⠛⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢁⡀⠀⠀⠀⠃⠀⠋⢠⠃⠀ ⠀⠀⠈⠲⠼⣄⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⢀⣀⣠⣤⣶⢿⡿⣶⣤⣀⣀⣠⡤⠤⠔⠂⠁⠙⠀⠀⡀⠀⠀⡰⠃⠀⠀ ⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠐⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐⠒⠒⠒⠒⠂⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡼⣷⠟⠛⠿⢿⠿⢶⣤⣀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠛⠉⠀⠀⠈⠛⠛⠓⠸⠿⠃⠀⢯⣛⠿⢿⣯⣭⣭⣟⠿⢦⣄⣀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⢾⣿⡏⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⠘⠛⢻⣿⠀⠀⠀⠀⠀⠀⣭⣍⡛⣻⣍⣉⡙⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠿⠃⢺⡿⢷⡾⠿⠁⠀⢀⣤⠾⠟⠻⣭⣿⠉⠩⠙⠛⠶⣄⣀⣼⣿⠁⠀⠀⠀⠀⠈⠉⠻⠛⠁⠉⠈⠉⠁⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠿⠟⢻⣦⡄⠀⠀⠀⠀⠙⢧⣄⣼⠋⠁⠀⢀⣾⣿⣿⣤⣤⣀⣀⣤⡿⠏⠀⢀⣀⣤⡶⢦⡄⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠍⠠⠾⠦⠤⢾⠟⠶⢤⣀⡀⠀⠀⠀⠈⠻⢶⣶⣶⠛⢽⣿⣘⣧⡄⣹⡿⠷⠦⢤⣔⣼⡟⠁⠀⠜⣿⠀⠀⠀⣿⡋⠀⠀⠀⠈⠉⠛⠲⣄⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠟⠙⠳⣦⣄⣀⣴⠟⠹⣿⣿⣿⣿⠟⢷⡟⢿⣧⡀⠀⠀⠙⠋⠁⠂⠀⢾⣿⠶⠶⣶⣌⠻⠶⣤⣤⣠⣾⣷⠀⠉⢷⣄⠀⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⢀⣠⣴⠶⢶⣶⣿⡄⠀⠀⣹⣧⠀⢐⡄⠛⠏⠀⠀⢠⣿⣟⣿⠃⠀⠀⢹⣷⣼⣿⣦⣤⣀⠀⠀⠀⠀⢀⣀⠈⢁⣼⣽⣇⣢⡿⣟⣻⣿⣿⡀⠀⠀⢹⣿⡟⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢀⣴⢟⣿⣂⣭⣿⣿⣿⣃⣴⢾⡿⠛⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣷⠶⢶⣶⣟⣛⣿⣿⣷⡾⠿⠷⡶⢶⣿⣛⡉⣩⣨⣿⣿⣭⣿⣻⣿⣿⣍⣹⠿⣦⣀⣸⡟⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠇⠀⣰⠟⠱⣿⣿⣿⣿⣿⠉⢹⣿⣥⣧⣤⣤⣤⣤⣤⠾⡟⢙⣻⣿⣿⣿⣿⣿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣯⣿⡿⢯⣿⣿⣿⡙⠉⠁⠀⠀⣿⣿⣿⡿⠻⢿⡇⠉⠉⠁⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣾⡇⠀⠀⣸⣿⣿⠻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⠛⠛⠿⢿⣿⣻⣿⣿⣽⢷⣤⡀⠀⣿⣿⡿⠀⠀⠀⢿⣤⣀⣤⣤⣤⡀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠻⢿⣇⣀⣰⣿⣿⣿⣿⣿⣷⠈⠉⠉⠁⣰⣿⢿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣾⣿⢾⣿⠿⣦⣻⣇⠀⠀⠀⠀⠙⠛⠉⠀⠀⢩⣿⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠛⠛⠻⢿⣽⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠈⣙⣿⠏⢩⣿⠋⢙⣿⣿⣿⡇⠀⢀⣼⢛⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⢿⣿⣿⢿⣟⣿⡀⠀⠀⠀⠀⣄⣴⠞⠙⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣤⣥⣀⣀⡀⠈⣿⡯⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⣀⣼⠟⣁⣠⣽⣿⣶⡟⠛⠛⠻⣧⣴⡟⣷⣟⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣒⣲⣀⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⠘⢿⣷⡄⠀⠀⠀⠻⣯⡄⠀⢠⣤⣄⣀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠙⠛⠛⠛⠻⠿⢿⣯⣿⣻⡏⠁⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⢰⣿⣿⠛⠍⠽⠋⠁⠉⠁⠀⠀⣸⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣤⣤⣴⠾⠛⠳⣦⠀⠀⠀⠀⢀⣿⡏⠀⠈⠉⣿⠟⠃⠀⠀⠀⠀⠀⠀⠘⣿⣝⣿⣧⠙⣿⡝⣶⣄⠀⠀⠀⠻⣦⣸⡏⠈⠙⢷⣄⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢶⣤⡸⠽⠻⣦⡀⠀⠀⠀⠀⠀⣴⡾⠟⠁⠉⠙⠻⢶⣤⡆⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢻⣾⡆⠀⠀⠰⢹⡷⠀⠀⠀⠈⢿⡑⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣷⣿⣿⣟⢻⣿⣦⡤⠶⣿⠙⢷⡄⢀⣶⠹⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣶⡄⠊⢹⣦⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣶⠀⣽⣿⡟⠀⠀⠀⠀⠈⢻⣶⣵⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣽⣿⣧⠙⢳⣯⡟⠛⣷⣶⣤⣬⣿⣾⣷⠀⢹⡆⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⣴⡾⣷⣆⣴⡟⠑⢠⣤⡶⠷⣦⢀⣾⠏⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠊⠡⣄⣤⣴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⣿⡄⠀⠀⠉⢛⣷⣾⣿⣿⣯⣿⣿⠇⠘⣷⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⣿⡷⣶⣿⠁⣰⣆⣿⠚⣿⣦⣶⣿⡿⣻⡿⢿⣿⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣐⣒⣒⣒⣲⣤⣤⣤⣤⢶⣶⣿⣿⠿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⣠⣴⣿⣿⡿⠟⢿⣿⡟⢹⣆⡀⠙⣿⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠻⠧⣠⣿⣿⣻⣤⣿⣟⣿⡿⠟⠋⠀⢸⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⠛⠛⠻⠓⠛⠋⠋⠉⠉⠁⠀⢈⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣶⡏⣿⡿⠛⠺⢶⣀⣿⠀⠈⠉⠉⣼⣏⡿⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣀⣤⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠹⣿⣿⣿⣷⣾⣿⡿⣤⣀⡀⠀⢸⣿⣇⣿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⡿⠻⠖⠀⠀⠀⢀⣼⡅⢻⣦⣤⣀⣼⠏⢸⣧⣤⣤⠴⠶⠛⠋⣿⣯⣯⣀⣿⣿⣿⣿⣍⠉⠉ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⢶⣄⢈⣣⡀⠀⠀⢀⣠⣼⣿⣻⠶⢿⣿⣟⣿⡗⠀⠀⠀⠘⠷⣤⣀⠀⠉⠉⣡⣶⠿⠉⠉⠻⣧⣴⣤⣤⣀⣀⣤⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣏⠀⡀⠀⠀⠀⠀⠹⣧⠈⠻⣾⡽⠧⣤⣬⣿⣃⠀⠀⠀⠀⠀⠀⢻⣯⣾⠟⣟⣀⣾⣿⡾⠁⢀⡿⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠉⣽⡿⠛⠛⠿⣽⡷⣾⣻⣷⠟⠉⠻⠮⢿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⣿⣿⡿⠛⠿⢿⣯⠆⠸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⢿⡿⠋⢩⡿⣷⡀⠀⠀⠀⠀⠙⢷⣞⡉⠛⠛⠛⠛⠛⣿⣷⠀⠀⠀⠀⠀⠀⢿⣿⡿⣿⢭⠞⠋⣀⣴⠟⠁⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⣤⡴⠋⠁⠀⠀⠀⠈⠻⣾⣷⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⠋⡀⠀⣠⣼⠋⠀⢠⣿⠘⢿⡆⠀⠀⠀⠀⠀⠀⢶⣿⣿⣃⣿⣦⡾⠁⠈⢳⣄⠀⠀⠀⠀⠀⠙⠻⢶⣄⣠⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠶⠾⠟⠁⠀⠀⢀⣤⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠉⠀⣀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠞⢶⣄⣀⠀⢀⣤⡶⠟⠋⠀⠀⢀⣲⡿⠋⠀⠀⠀⢰⣿⡀⢸⣇⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⠟⠁⠀⠀⠀⠀⠘⢳⣄⠀⠀⠀⢀⣴⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⡶⠛⠁⠀⢄⣠⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠲⠲⠞⠓⠛⠉⠁⠀⠀⠀⠈⠉⣻⠟⠁⠀⠀⠀⢀⣴⠿⠉⠀⠀⠀⠀⠀⢻⣿⡉⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣤⣿⡿⠿⠿⠂⠀⠀⣀⣀⣤⠿⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡾⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⡴⠞⠋⠁⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣯⣅⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⢿⣟⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠈⠉⠛⠛⠒⠲⠚⠛⠛⠋⣿⣿⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠛⠋⠁⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣷⣀⢠⣤⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣢⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣤⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠘⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⠇⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡄⣀⣈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣂⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⠷⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣟⣧⡈⠛⢿⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣾⣶⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠒⠀⠳⠀⠠⡄⠀⠀⢂⠀⠰⡄⠀⣴⡀⠄⠠⢾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢌⠀⠀⢂⠀⡇⠀⢑⡧⠀⠼⡇⠀⣿⠀⢀⢸⡱⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡨⢄⠀⢈⣦⡃⠤⠂⣅⠠⢰⡇⠂⡛⠀⠀⣧⢻⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣾⢰⠀⣟⢤⢚⣷⣿⣟⣶⣷⣎⢠⠀⣿⡦⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢰⠍⢻⣽⢸⢺⣿⣿⣿⣿⣿⣿⣾⣻⣿⡃⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠌⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣢⠑⡎⠈⢾⡺⢀⠛⡃⣹⠯⣿⣿⡿⣯⢻⣾⡇⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠐⢀⠂⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠃⡜⡸⢔⡀⢂⠁⠂⠀⠐⠠⠁⢑⡋⠉⠉⡿⠯⢣⡛⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡈⠠⠐⠀⠄⠀⠀⠀⠄⠀⠐⠀⠨⡾⢤⡛⣜⠣⡍⢳⠈⠀⡈⠄⡀⠀⠀⠐⠀⠁⣸⠑⠆⣛⣦⠙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠠⠁⠄⠡⠀⠀⢀⡀⠤⢀⠀⠉⠐⢉⠲⡙⢬⡃⠅⡆⢡⠀⢐⢩⠆⡠⠀⠀⠠⠁⢨⠀⣴⣾⣗⣯⣷⣻⣿⣿⣿⣿⢿⡿⣟⡿⢿⣿⣿ ⠀⡁⢂⠐⢀⠂⠀⠀⠀⡱⣌⢦⡐⡈⢌⢃⠢⠁⢽⡜⢠⠁⠀⢈⠰⢣⡛⢄⠰⠁⡀⢨⢲⣿⣿⢏⡳⣿⣯⣿⣿⣻⡽⡚⣵⣿⣟⠻⣿⣿ ⠀⡐⠠⢀⠀⡐⠀⠀⢢⣝⠎⡐⠁⢰⢊⠤⡂⢔⡡⡱⣄⠂⠀⠀⠘⣰⢏⡖⠃⠀⠀⡜⣸⣿⡿⢨⢹⢾⣿⡿⣞⣴⣳⠌⡙⣿⣷⣤⣿⣿ ⠐⡀⠂⠄⠂⠀⠀⠀⢸⣮⠀⠠⡉⢄⢛⠮⣜⢎⡶⣡⡛⢦⡀⠀⣔⢫⣞⠐⢀⠀⠀⠀⣽⣿⣃⠐⣀⣿⣿⣿⣷⣿⣿⠦⡁⣿⣿⣿⣿⣿ ⠠⢀⡁⢂⠁⠀⠀⡀⠀⠹⠀⢀⠘⠈⢎⢳⡚⢮⠓⠃⠈⠁⠈⠁⠪⣳⣻⠄⡰⡐⢈⢠⣿⡝⠋⠉⠉⠉⠻⢿⣿⣿⣿⡷⡐⣿⣿⣿⣿⣿ ⢀⠂⠀⠂⠌⢀⠐⠀⠀⠀⠀⠀⠀⠀⡀⣀⣁⣂⠀⠀⠀⠀⠀⠀⠀⠐⠋⡦⠱⣘⣼⣣⣻⠁⠀⠀⠀⠀⠀⢨⣛⣿⡟⠱⠀⣾⣿⣿⣿⣿ ⠠⠈⠄⠂⢈⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠑⡹⢻⢆⣀⣀⣀⣤⣠⣴⡄⠈⠀⠙⠿⢻⡾⠙⠣⣤⣀⣀⣀⣠⣾⣿⣿⣿⣦⢼⣿⣿⣿⣿⣿ ⠠⢁⠀⠌⠠⠀⢀⠀⠀⠀⠀⠀⢀⡝⢦⣡⣀⢦⡶⣗⡛⠛⡠⠡⠄⠬⣦⠀⠀⠠⠡⠘⣀⣖⢁⣠⢥⠿⡟⣮⣍⠛⠙⢎⣿⣿⣿⣿⣿⣿ ⠐⠂⠄⡀⢂⠀⠂⠀⠀⠀⢀⠀⢢⣻⢿⣼⣿⣿⣓⠧⠙⡡⠔⠢⠈⡤⡬⢷⠠⠀⠀⠼⠿⣯⣴⣮⣤⢷⡚⢦⣻⣿⣾⣿⠻⣿⣿⣿⣿⣿ ⠈⠌⡐⠀⠆⡀⠐⠀⠀⠀⠀⠈⢁⠸⣻⣿⣿⣾⣏⡶⣤⡐⢆⠒⣃⢠⠯⡐⠀⠀⠈⢉⡳⢭⡝⣟⣊⣿⢶⡽⣾⣿⡿⢟⠳⠦⣬⢩⡻⢿ ⠈⡔⠈⠌⠐⠀⠄⠀⠀⠀⠀⠀⠈⢂⡡⢟⠩⠳⢏⡟⢾⡙⢆⠼⢁⣎⡳⢆⡥⢓⡭⢲⣙⠶⡌⢧⡻⣼⣯⣿⣿⣆⠀⠈⠻⢐⣨⡳⡼⢿ ⡱⠆⠌⠐⠀⠈⠀⠄⠀⢀⣠⡶⣡⣿⣷⣩⣛⡴⢪⡜⣥⢊⠠⢐⡪⢥⡙⢮⢹⠳⣜⢣⣹⢶⣳⣶⣿⣿⣿⣿⣿⣿⣄⠤⠈⢰⢫⢿⡁⢯ ⠐⡉⠠⠐⠠⠁⣀⣤⣶⣿⣿⣾⣿⢿⣳⢷⣻⣼⢳⡝⣦⣿⣾⣱⣎⣧⣝⣮⣳⣟⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠸⠋⠀⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡄⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣧⣤⣤⣤⣤⣀⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣷⣶⣶⣿⣿⠻⠿⠛⠋⠀⠀⠸⠉⠙⠿⣿⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡿⠋⢉⣀⣀⢐⡀⠀⢀⡀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣶⡿⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀ ⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀ ⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠉⠙⠛⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢻⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⠀⢸⣆⠀⠀⢠⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⢿⡄⠀⢸⣇⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⡏ ⠀⠀⠀⠈⢿⡀⠘⣿⡀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣴⠀⠀⢠⡿⠀ ⠀⠀⠀⠀⠈⢿⡄⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠋⠀⠀⢀⣾⠏⠀⢀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣆⠀⠈⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠀⢀⣾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⢀⣾⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠀⠘⢿⡿⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⢿⣿⢹⣿⣽⣿⠙⢻⡿⣧⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠸⣿⠀⠈⣿⠁⠀⣿⡇⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⡀⠀⠀⠀⠀⣿⡀⢀⣿⠀⢀⣿⠃⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠹⣷⣀⣉⣀⣾⠏⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠉⠛⠿⠛⠉⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣤⣤⣀⣀⣤⣤⣴⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠛⠋⠉⠙⠻⠿⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠿⠿⣽⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠿⢿⣷⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⣿⠀⠀⠀⠀⣹⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡄⠀⠈⢿⣻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⣠⣶⠿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠈⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣼⣿⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠀⠀⠀⠀⣿⣠⣶⠶⣶⣿⣿⣶⣄⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀ ⠀⠀⠀⠀⠀⢀⣤⣤⣤⡶⠾⠿⠛⠻⠿⠟⠛⠁⠀⠀⠀⠀⣼⡿⠋⠀⣠⣿⣿⣿⠛⢿⣿⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⠀⢀⣴⡿⢉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣷⣶⣾⣿⣿⣿⣿⣾⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇ ⠀⠀⣰⡿⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠿⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⣴⡟⠁⠀⠀⠀⠀⢰⣆⠀⠀⠀⠰⣿⣟⡁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⣾⠟⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠀⠈⠙⢻⡇⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣀⣀⣀⣀⣀⣀⣙⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣿⠿⠿⠿⠟⠛⠁⠀⠀ ⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠺⠶⠶⠶⠾⢿⣿⣟⠛⠛⠛⠛⠛⠛⠋⣋⣻⣆⡀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣤⣤⣶⠾⠟⠛⠛⠛⢻⡟⠛⠳⠶⠶⠾⠟⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⢠⣴⣿⠿⠀⠀⢠⣄⠛⡽⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⡶⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣷⣤⣤⣤⣤⣤⣤⣾⠟⠻⠶⠶⠶⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢠⣿⣷⣄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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