Wandere 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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⠀⠀⠀⠀⠀⢀⣠⣴⣷⣀⣴⣾⣦⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡯⠙⠛⠿⠋⢅⠛⠩⠿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠊⠀⠀⠰⢱⠀⠀⠂⠀⢈⢂⠀⠀⠀⠀ ⠀⠀⠀⢀⢃⠁⠀⣐⡇⡀⠀⠰⣨⠄⠀⢂⢡⠀⠀⠀ ⠀⠀⠀⠜⡄⠀⡶⢓⣲⡇⢀⡶⣋⢮⢿⠊⡘⢆⡀⠀ ⠠⢔⣁⣠⠀⢸⡿⣿⣗⠧⠋⢰⣿⡿⢿⠀⢠⣀⡈⠆ ⠀⠠⡶⡌⠀⠀⣷⣿⡅⠀⡀⠀⣽⣷⣯⠀⠈⠘⠄⠀ ⠀⠀⣧⠃⠀⠀⣿⣯⣄⣀⢀⣀⣬⣿⡏⠰⠀⢣⡼⠀ ⠀⠀⠸⢀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⠀⣼⡠⠞⠀⠀ ⠀⠀⢠⣯⣆⠐⣸⣿⣿⣿⣿⡿⠿⠛⠉⣏⣢⡀⠀⠀ ⠀⠀⠀⣩⣿⣿⣿⣿⣿⠁⠀⣀⣦⣤⠴⠛⠉⠀⠀⠀ ⠀⠀⠀⠉⠉⠁⠛⠛⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⡠⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⢀⠠⢄⡠⠊⠉⠉⠉⠍⡉⠉⠚⠲⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⡀⠀⠀⠀⠀⡠⢁⡴⠫⠃⢀⠐⠆⠀⠀⠈⠒⡂⠕⢍⣳⡇⠀⠀⠀⠀⠀⠀⠀ ⢟⠛⢤⠀⠀⠀⠑⡞⡡⠁⠀⠀⠁⠢⢄⣀⡀⢀⣀⠔⠚⠡⠙⣦⠀⠀⠀⠀⢀⠁ ⠈⠫⣙⣧⡀⡀⢐⠡⢁⠀⢰⠀⠀⠀⠈⠄⠀⡺⣄⣁⠀⠀⢡⠑⡀⠀⠀⠀⠘⠀ ⠀⠀⠘⣠⣤⠀⢼⠀⢸⡀⠀⠡⡀⠀⠀⣼⣞⣤⡼⢼⠀⢸⠀⠢⠬⠂⠀⠀⢀⠀ ⠀⠀⠀⠟⠁⣰⢞⠠⠈⣴⣭⣵⣜⠢⡤⢘⣍⠛⠛⢰⢀⣿⣴⣂⠚⠀⠀⠀⠠⠀ ⠀⠀⠐⠠⠂⡜⢸⡈⣄⠹⣧⠛⠛⠀⠊⠀⠀⡀⠀⠒⠃⣩⠵⠏⠀⠀⠀⢀⠀⠀ ⠀⠀⡰⢁⡾⠁⠀⠟⠼⠢⣕⠤⠀⠀⡴⠘⠃⢉⠀⢀⣬⠂⠀⠀⠀⠀⠀⠁⠀⡀ ⠀⠐⢁⡞⠁⠀⠀⠀⠀⠀⠀⠑⢀⠀⠑⠀⠠⠊⣠⢎⣷⣄⠀⠀⢀⡀⣀⠀⠀⢰ ⢀⡦⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣷⢂⠤⠊⣠⣿⣿⣿⠖⠊⠀⠀⡠⠁⠄⢡ ⡄⠉⠂⢀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣽⡇⢠⣼⣿⣿⠟⣏⠀⡀⠠⠎⠂⢰⣾⣧ ⢣⢸⣶⣾⣶⡀⠀⠀⠀⠀⢀⢻⣿⣿⠏⠀⣸⣿⣿⣿⣿⣍⣀⡇⢀⣔⣺⣿⡏⠁ ⠀⠀⠈⠻⣿⣿⠀⠐⠁⢠⠥⠞⠛⠻⡿⠼⠿⢁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡻⣡ ⠐⠂⠤⠴⠽⢣⠁⠀⢠⠏⠀⢀⠴⠃⠐⠨⢠⣬⣼⣦⣼⣿⣿⣿⣿⣿⣿⣯⣶⣾

⣷⠁⡠⠀⡰⠁⠀⡰⡁⠤⠐⠊⠡⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⡐⠁⠰⠁⠀⠰⠁⠀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠒⢄⠀⠀⠀⠀⠀⠀⢸ ⡗⠀⢑⢳⣶⢯⠛⠛⡻⠷⣦⢌⠐⠄⠀⠀⠀⠀⠀⡀⠤⠄⡀⠈⠂⠀⠀⠀⡀⢸ ⡇⠀⡌⠀⠙⣶⣤⡼⠤⡬⡥⠯⠃⢘⠀⠀⠀⠠⣤⠶⠦⠶⠾⣶⣦⣄⠀⠀⠰⣸ ⡇⢀⠁⠠⡸⠈⠥⠐⠃⠉⠀⠀⠀⠊⠀⠀⠀⠀⠈⠁⠒⠤⢔⡁⠤⠙⣿⣦⣀⣸ ⡇⠘⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠛⠋⠀⢸ ⡇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⡇⠀⠀⠀⡀⠀⠀⠀⢹⣾⣥⣄⣀⣉⡀⠂⠤⡀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠔⡈⢸ ⡇⠀⢸⣆⠷⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⡆⠀⠀⠀⠀⠈⢀⠞⠁⡠⢺ ⡇⠀⢸⣿⣦⠀⠀⠀⠀⡏⠀⠀⢠⠋⠉⠉⠙⢿⠟⠀⠀⠀⠀⠀⢠⠎⣠⢟⠁⢸ ⡇⢰⠸⠋⢿⣷⡄⠀⠀⠡⡀⠀⠈⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⡠⡏⠾⠁⣸⣴⢺ ⡇⠀⡆⡄⠸⣿⣿⣦⡀⠀⠐⢄⣀⠠⠐⠈⠀⠀⠀⠀⣠⡔⢉⣼⠈⣰⣾⣇⡧⢺ ⡇⠀⢡⢃⠀⢹⣿⡿⡗⣄⠀⠀⠀⠀⠀⠀⣀⣠⠴⣿⠟⡢⠋⣸⣶⣿⣿⣿⠀⢸ ⣧⡀⠀⢻⡄⠸⡟⠜⠦⡟⢷⣤⣤⣤⢶⠿⣿⣿⡿⠓⣈⡤⢞⡕⢱⣿⣿⣿⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠶⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠶⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣸⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⡀⠀⠀⠀⠀⠀⡾⠀⠀⠀⣿⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠾⠟⠛⠛⠛⠛⠛⠛⠛⠿⠶⣤⣀⡀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⢳⠀⠀⠀⠀⢸⡇⠀⠀⢠⣿⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠈⢷⡀⠀⠀⢸⠁⠀⠀⠈⣿⠋⠀⣀⣀⠤⢤⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠳⣄⠀⢸⠀⠀⠀⠀⢿⣠⠞⠁⠀⢠⡟⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡄⠀⠀⠈⠳⣼⣇⠀⠀⠀⢀⠇⠀⠀⢀⣟⣀⠼⠯⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣄⠀⠀⠀⠈⠻⡷⣶⠦⢼⣀⠀⠀⢸⡏⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⡶⠶⠶⠶⠶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠈⢿⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣦⡀⠀⠀⠀⠙⠯⢦⣀⠉⠙⠒⠾⠲⣶⡋⠁⠀⠀⠀⠀⢀⣤⡶⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠶⣦⣌⣻⡄⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠳⢤⣤⣤⡶⠛⠛⠛⢲⠂⠀⠀⠀⠳⣄⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢹⡄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣶⠟⣹⠃⠀⣠⢴⠖⠺⣇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⠟⠁⠀⡇⣠⡞⠁⣾⠀⠀⣽⡗⠦⠤⣶⠒⠚⠃⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡟⠀⠀⠀⠸⢻⡇⠀⠘⣄⢸⣿⣷⠄⠀⣾⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⣼⠁⠀⠀⠀⠀⠀⠙⠦⠤⠼⣿⢻⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⣇⠸⠿⣇⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡞⢳⡴⢾⡏⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⠀⣿⡆⠀⠿⣷⡀⠀⠀⠀ ⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠚⠛⠉⠉⠀⠀⠀⠀⠀⣿⣷⣤⣄⢸⠟⢦⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠈⠀⢛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠻⣄⣀⠀⣼⣀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⣀⣾⠻⠀⢴⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣍⠀⠁⠸⣯ ⢸⣿⠀⠀⠀⠀⠀⣸⠻⢇⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢨⡗⠂⠘⢳ ⠀⣿⠀⠀⠀⢠⡾⠇⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣳⡄⢀⡼ ⠀⢹⣆⠀⠀⢸⡇⠘⢛⡟⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⡇⠀⠉⢸ ⠀⠸⣿⣄⣰⣾⠷⣾⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡏⠁⠀⢾⡿ ⠀⢀⣼⠟⠋⠙⠚⢿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣛⠳⠤⣶⠟⠉ ⠀⢸⣧⡶⠀⠀⡀⢸⡆⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⣀⢿⠂⠀ ⠁⠘⠁⢻⣄⢰⡟⠛⠛⠶⠶⠿⢷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡀⣀⣀⢀⡀⡀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣶⠾⠋⢸⡄⢠⠟⡿⠀⠀ ⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⢠⣤⡄⣧⣤⣤⣤⣶⣼⣟⣛⣽⡆⣇⣤⣄⠀⢀⣤⣤⢀⣤⡄⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⢾⡻⣿⡇⢿⣿⡐⠟⠿⢽⡇⠉⠸⠇⠟⡿⠿⠰⢛⠧⡷⡻⢴⢇⣧⡹⣝⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⢿⣿⣿⣿⣷⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣁⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣷⣄⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣆⢠⣿⣦⡀⠀ ⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠁⣿⣿⠏⢠⣾⣿⣿⣿⣿⣿⣇⠛⢻⣧⠀ ⠀⠀⠀⣠⣿⣿⣿⣿⠋⠀⠀⠈⠙⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⡇ ⢀⣴⣶⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣴⣭⣿⣿⣿⣿⣿⣿⣤⣤⡿⠃ ⢸⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣧⣤⣬⣤⣤⡄ ⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⣷⣶⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⡆⠀⠀⠀⠡⡈⣿⣿⣾⣿ ⠻⣿⡟⠁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠡⠘⢻⠿⠿ ⡾⠻⢀⠎⠀⠀⠀⠀⠀⠀⠃⡀⡠⠊⠇⢀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⢢⠀ ⢤⠁⠆⠀⠀⠔⠀⠀⠀⢰⡨⡊⠉⠹⢦⡄⠸⠀⠀⠠⠀⠀⠀⡀⠔⣆⡇⢸⠀⠱ ⠼⠸⠀⢀⠊⠀⠀⠀⠒⢼⠷⡷⢶⣦⣦⡙⠀⡆⡠⠁⣀⢤⠺⣷⠀⡿⡃⢸⠀⠀ ⠤⡆⢀⠂⠀⠀⠀⠀⠀⢸⠘⠞⠅⡻⠙⠏⠴⠏⣖⠏⠀⡎⠀⢉⠀⠁⢱⢸⠀⠀ ⠤⡇⡈⢀⠀⠄⠀⠀⠘⣄⢆⠀⠀⠀⠀⠀⠀⠀⠙⡳⣦⡇⢠⡌⠀⡄⢸⡈⢒⠰ ⠀⢹⡃⢸⠀⡜⡄⠀⠠⢃⠑⠢⠀⠀⠀⠀⠀⠀⠀⣃⠉⠆⠸⠥⣤⠁⢈⡟⠐⠓ ⠀⠀⡇⠎⣆⣧⠈⣦⠀⣙⡤⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⢀⣿⠀⠀⠃⠠⢀ ⠀⠘⠸⢀⠃⡡⢢⡎⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠈⠀⢸⣿⠀⢸⠀⠀⠉ ⠀⠀⠀⢸⡴⠁⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⢃⠀⠀⠀⣿⣿⡄⡇⢠⡄⠀ ⠀⡐⠀⠃⠀⡰⢋⡄⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣂⠀⣸⡿⢹⣷⣽⣼⣷⣶ ⠊⠀⡜⠀⠀⠀⢄⡁⢁⣚⣕⡢⡀⠑⠠⣀⣠⣤⣶⡏⣠⣿⠿⠁⠀⢿⠓⠻⣷⣿ ⠀⡐⠀⠀⠀⠜⢸⣴⣶⣤⣾⣿⣾⡦⠑⢾⣿⣿⣿⣷⣿⡇⠀⠀⠀⢸⠀⠀⠈⣿ ⠋⠀⠀⠀⢈⢂⠜⠙⣿⣿⡿⠟⣻⣅⢻⣠⣧⣼⣿⠇⠹⡇⠀⠀⠀⠈⠀⠀⠀⢸

╲ 　　╲ 　　　　𒆙

⠀⠀⢀⡴⣪⣶⢿⠟⠋⠁⣀⣀⣉⣑⣦⣀⣀⡩⠽⢷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⡷⣫⠊⢠⣏⡴⠒⠫⣉⠀⠀⠀⠑⠌⣉⠙⠿⣟⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣝⡕⣁⣀⣾⠋⠀⠀⠠⠙⢗⠠⡀⠀⠀⠀⠈⠑⠪⢷⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⡿⠋⢡⡟⡏⠀⠀⠀⡆⠀⠀⠓⢄⡉⠀⢒⠒⣖⠢⣀⠀⠀⠀⠀⠁⠂⠀⠀⠀ ⣿⠁⢀⡾⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⣆⣏⢡⣝⡗⠤⡄⠒⠀⠉⠉⠀⠀ ⢿⠀⢼⠃⢰⠀⠀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡅⠙⡿⣿⠁⠀⣸⠀⠀⠀⠀⠀⠀ ⠚⠦⣿⢀⢸⡄⠀⠀⢂⡆⡝⠁⡀⠀⡀⢀⡷⢀⣴⣞⢮⡾⠁⢀⡗⠂⠠⢄⠀⠀ ⠀⠀⢸⡄⢣⡇⠀⠀⠀⢿⣠⣼⣷⠶⠕⠁⠀⠻⣏⡹⢀⠁⢀⡞⣕⣬⣷⠁⠀⠀ ⠀⠀⠀⢣⡨⠳⠐⡀⠀⠈⢚⢍⣉⠇⠀⠀⠀⠀⠀⠀⣼⡴⢻⠫⣀⡔⠁⠀⠀⠀ ⠀⠀⡠⠊⣀⡀⠵⣔⣄⣀⣀⡑⠀⠀⠀⢔⣊⠇⡀⢴⠗⠁⣼⣀⠈⠢⡀⠀⠀⠀ ⠀⠈⡨⢒⣈⢩⠏⡉⡗⢉⠿⠋⠃⣖⢦⣄⣤⡞⡯⠋⠀⡰⡏⠀⠑⠠⡐⠄⠀⠀ ⠀⠪⠛⠁⣠⠾⣮⣄⠗⠁⡾⠂⠺⡓⢿⣿⣿⣿⠀⣠⡚⢀⣇⣀⣤⣾⢿⠂⠄⡀ ⠤⠧⣖⣈⠉⠉⡜⡁⠀⣸⢧⡀⠠⠣⣀⣼⢷⣬⣄⡇⠀⠈⡟⢍⠈⠁⠸⠀⠀⠈ ⠉⠒⠐⢸⠀⠘⠜⠱⡀⢻⠀⠣⣀⢀⠿⡁⠀⢈⠋⠉⢲⢟⡖⢜⠂⠀⠀⠀⠀⠀ ⠂⠀⠀⠸⠀⠀⠀⢀⣯⢳⡩⡖⣏⠀⢀⠔⠉⠉⠲⠤⢸⢸⣇⠈⠕⢄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠰⣆⠤⠤⠤⣄⣀⠤⣖⠞⢋⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⡾⢗⡪⠯⣭⣹⣨⡁⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢀⠀⠀⡴⠚⢡⡞⠁⠀⠀⡠⢖⢟⠉⠀⠀⢀⡀⠀⠀⠈⢑⣄⢀⠀⠀⠀⠀⠀ ⠐⠄⠑⡀⣳⣴⠏⠀⠀⡠⠊⠀⠂⢸⠠⡀⠢⡀⡈⠲⣄⡠⡀⠹⣟⢒⡀⠀⠀⠀ ⠉⣚⠠⣸⣽⢍⡀⢀⠔⡠⠂⡠⢣⠇⢰⡹⠀⠸⢖⠀⠈⢷⣹⡌⣺⡷⠖⠀⠀⠀ ⠤⣸⢧⡼⢛⠢⣗⠵⠊⢀⣠⣿⢿⣜⣸⢵⠷⡑⠈⢆⠀⠀⢹⣿⣾⢧⠀⠀⠀⠀ ⢰⠓⢾⣢⡰⠻⠳⡾⢻⡿⡟⢸⡊⠀⠀⢸⠀⠙⢦⣸⡀⠀⢾⡎⢻⡄⠀⠀⠀⠀ ⢬⠀⠈⣷⣿⡆⠈⣾⣎⣞⣀⣀⣇⠀⢀⣾⠒⣉⣥⢽⣷⢀⢷⣿⣧⠃⠀⠀⠀⠀ ⠋⠐⠀⣼⢿⡤⣾⡗⡿⡖⠶⠆⡼⣠⢻⠃⠈⠈⠙⢁⠟⣿⣿⣿⣑⡠⣄⣒⣠⠀ ⣀⣀⠜⢹⣾⣧⠹⣷⣧⠀⠀⣰⠟⠁⠁⠀⠀⠀⠀⠀⢠⠻⣿⣟⡗⢻⠿⡏⡙⣆ ⠊⠟⠆⡞⣾⡷⡀⡟⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⣿⣋⢱⣤⣧⡇⡇⠸ ⠀⠀⣸⣇⣿⡈⠀⡠⣺⡿⡑⣄⠀⠀⠀⠀⠀⠀⠀⡠⠁⣸⢹⢻⠘⣿⣿⡇⡇⠀ ⠀⣠⣱⡻⠉⠁⠀⠀⣹⣿⠳⣹⣿⡦⡀⠀⠀⡠⠊⣀⡼⠁⡞⠆⡄⣿⣿⡇⡇⠀ ⢈⣽⠟⠑⡰⣄⢀⣾⣟⡇⣇⠹⣿⣇⠈⢙⣽⠿⣾⣯⡀⣸⠀⠏⠱⣿⣿⣇⡆⠀ ⠅⠂⠉⠉⠁⠲⣿⣿⣾⡇⢹⣿⡷⠻⠴⡛⠰⢷⡷⠣⡵⡇⠀⠀⠀⣿⠿⣿⠇⠀

⠀⠔⡠⠚⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⠫⡉⠑⠂⠀⠀⠀⠀⠀ ⠐⢋⠀⠀⠈⡦⣀⡠⠔⠠⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠱⡈⠀⠀⠑⠀⠀⠀⠀ ⠀⢸⠑⠤⠤⠬⠀⣒⣎⡚⣃⢑⣢⣄⠀⠀⠀⠀⠀⠀⠀⡆⢱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠣⣄⣀⣠⣄⣿⣿⣿⡶⡧⢯⠗⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠈⠉⢁⠆⢉⠿⣋⠟⠉⠔⠡⡀⠤⠂⠀⠀⠀⠀⠀⢠⠀⠀⢧⠀⠀⠀⣧⡀⠀ ⡓⠂⠉⠫⢩⠚⠉⡠⢊⠄⠊⠁⠀⠀⢀⠀⠀⠀⠀⠀⠸⠀⡘⢸⠀⠈⢀⡻⠮⠅ ⠉⢰⠀⡔⡡⠐⣡⡔⠙⠶⡤⣄⣄⠘⢜⣄⡄⠀⡀⠀⡁⡰⠙⢼⡇⡀⠸⠧⣀⠀ ⠀⢈⣭⣪⣴⣿⠁⣆⢠⢸⣧⣘⡹⠑⠖⠛⠹⣦⠁⣴⡮⡤⣤⣼⠃⠇⡆⢲⠉⠆ ⢠⢚⢵⣿⣿⡟⡀⡏⢮⣄⠉⠉⠀⠀⠀⠀⢜⣡⢼⡡⢜⡴⣫⢟⡄⡉⢣⣈⣇⠘ ⣧⢿⢹⡟⣿⢧⠱⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢀⣉⣾⢟⠟⣅⡧⠀⣿⣮⣦ ⡻⢼⣾⡟⠉⠻⣷⣝⣷⣄⠀⠘⠄⡀⠀⠀⢀⠈⠀⢀⣜⡠⠊⢀⡸⢠⢱⡏⠛⣿ ⡗⠁⣿⡻⣷⢶⣻⣟⣿⣛⣷⣄⠀⠀⠑⢈⡡⢔⠺⠛⠉⠀⢀⠞⢤⢺⠋⣧⠖⠛ ⠆⣰⣷⠿⣚⣾⣿⣿⢿⣿⣿⣿⣿⣶⡎⢳⠾⠆⢼⣠⢤⣄⠁⠘⡌⠀⠏⠁⠀⠀ ⣤⢿⣿⡸⡻⠇⡱⣝⣿⣿⣿⣿⣿⣿⠇⣼⠄⡄⢸⡇⠙⡇⢱⡷⢤⠂⡑⠄⠀⠀ ⣿⣯⠟⢻⡇⢀⣶⣿⣽⣿⠛⠉⠉⠉⠳⣷⣼⢁⣮⣈⢙⠇⡌⢨⠸⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⢼⣤⣴⣕⣊⡁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠉⠘⠦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠎⡐⠀⠀⡄⠀⠀⠀⠀⠈⡼⢢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡌⣾⠔⠃⢸⠀⠀⠞⢦⢡⢠⡇⡆⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢻⢾⣤⣇⢸⢤⣪⠄⡀⢻⠸⢰⠁⡄⠀⠀ ⠀⠀⠀⠀⠀⢰⡽⡼⡌⠻⠁⠙⠸⣾⠀⢜⢟⠂⣷⣤⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⢣⡷⡠⣬⠤⠤⡀⠐⠋⡙⣰⠼⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠪⢶⣼⡶⠶⣿⡋⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠠⡲⠣⠙⠓⣠⠤⢓⠨⢅⠀⠘⡀⠀⠀ ⢀⣄⠀⠀⠀⠀⠀⡕⢡⡡⠢⠖⠮⡤⠚⠒⠒⠊⠒⢄⡱⡀⠀ ⣞⢮⡻⡳⡄⠀⡜⡠⠋⠀⠀⠀⠀⠐⡀⠀⣀⠀⠀⠀⠁⡀⠨ ⠘⡕⠕⠉⠉⢛⠫⡐⢄⣄⠠⠄⡀⠀⢥⠀⠇⠀⠀⠀⣴⠁⠀ ⠀⠈⢶⣶⣦⣾⣷⣾⡾⣷⣾⢰⣶⡆⠀⡶⠀⠀⠀⠀⣿⠀⠀ ⠀⣀⠼⡯⢽⡿⣇⣿⣽⣯⣼⣸⣻⣇⠤⠗⠀⢀⢊⡜⠈⠄⠀ ⡞⠈⠢⠤⢖⠔⡇⠑⢄⡠⠃⠀⠁⢢⡸⠀⠀⠑⡱⠁⠀⠀⠠

⠀⠀⠀⠠⠂⠁⡀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢧⢁⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠡⠁⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⣿⠀⢡⠀⠀ ⠀⠀⢀⠂⠀⣯⠇⠀⠀⣀⡤⠲⠎⡇⠀⠀⠀⠀⠀⢀⣤⣼⡀⠀⠀⠸⡇⠈⡀⠀ ⠀⠠⠃⠀⢠⡏⠀⠐⠈⢀⠔⠀⢠⠀⠀⠀⢰⠀⠀⠀⡘⠀⠡⠁⠀⠀⡇⠀⠀⠀ ⠀⠁⠀⠀⢸⠀⠀⢀⠔⠁⡀⣠⠦⢤⡤⢒⡏⠀⠀⣴⣁⢀⠀⠡⠀⠀⡿⠀⠀⠀ ⠀⠀⠀⠀⠸⡠⠒⢁⣠⣶⣾⣿⣿⣅⢀⠎⠀⢀⠜⠉⣠⣾⣿⣷⣵⣠⠇⠀⠀⠀ ⠀⠀⠀⠀⣀⣬⡿⢿⣿⠻⢟⣟⡇⠥⠡⠄⠒⠁⠀⠈⢿⣻⢻⡏⡻⣗⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⢂⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡰⠺⠀⠄⠀⠀ ⠀⠨⡦⡀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣠⡗⠌⠀⠀⠀ ⢶⠑⠮⣉⡐⠠⢨⣘⠲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡠⠊⠀⠀⠀⠀ ⠈⠀⠀⡇⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⢰⠒⠀⣢⠤⢀ ⠀⠀⢸⢠⠀⠘⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢁⠀⠀⠧⠦⡼ ⠀⠀⠘⠀⠄⠀⠘⡄⠈⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⢡⣏⠘⠀⠀⡟⡞⠁ ⠀⠀⠀⠀⠈⠄⠀⠐⡀⠀⠀⠀⠑⢦⣄⣀⢀⠠⠐⣩⢁⠔⠃⠉⡇⠀⣸⠁⠁⠀ ⠀⠀⠀⠀⣇⠀⠀⠀⠐⢄⠀⠀⠀⠀⠙⢿⠏⡂⢀⠔⠁⠀⢆⡸⠀⣠⡏⣀⡀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣒⠦⡼⣁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⢡⡤⠤⠙⠁⠤⢄⠀⠈⠑⠄⡀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠠⢐⢕⣵⠋⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢈⡀⠝⠀⠀⠀⠀⠀⠀ ⢃⠀⠀⠀⠀⠀⢲⢯⣿⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠐⠀⠵⡆⠀⠀⠀⠀⠀⠀ ⠁⠁⠀⠀⠀⡀⢻⣿⠏⠀⠘⠀⠀⠰⢀⣰⣀⠀⠀⠀⠐⢖⠈⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣼⣯⠔⠐⢈⣹⢣⠀⠀⠆⣸⣬⣢⣹⢀⢀⠀⠁⠚⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠚⢁⡄⢲⠛⣿⢿⠻⣄⡈⢽⣿⣿⢹⠆⢰⡟⡍⡉⢂⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠣⡘⣦⡉⠁⠚⠊⠈⠉⠁⢤⢞⡡⠻⠟⠄⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⡄⠃⢹⢅⠀⠀⠀⠆⠀⠀⢀⢼⠁⡸⠀⠀⠐⠤⡃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⠘⡀⠄⠈⣒⣤⣀⠄⠊⢀⠌⢀⣇⡇⠀⠀⢉⠀⠀⠀⠀⠀ ⢀⢀⣀⠀⠀⠀⠀⠀⠀⠐⢠⠰⠿⠿⠿⣿⣿⣧⠴⠿⠛⠣⠀⢀⢼⣀⡀⠀⠀⠀ ⠕⡣⡻⣽⣆⡤⠄⣀⡀⣠⣁⡀⠀⠀⠀⠀⣀⣀⠔⣹⠋⣾⣷⡮⠊⠲⠁⠀⠀⠀ ⢕⢝⣽⠱⡇⠀⠉⢁⠚⠿⠿⢿⣿⣿⣿⣿⣿⣿⠀⢣⢈⠅⢄⣤⣴⣶⣧⡀⠀⠀ ⣦⡑⢽⠀⣀⣀⡠⠙⠸⠀⠀⠀⠁⠀⣌⢀⢣⠁⠡⢀⢀⠝⢿⣿⣿⣿⣿⣧⡀⠀ ⣿⠟⠉⠁⠀⠀⠘⠌⠣⡆⠀⠀⢠⠀⢁⡎⠂⢠⠤⢜⢀⠀⠈⢹⣿⣿⣿⣿⣷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⡈⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠊⠉⠉⠐⢄⠀⠀⡸⠁⢀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⠌⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠌⠀⡐⠁⠀⡼⢀⠀⠀⠀⠀⠀⠀⠧⠆⠀⠀⠈⣴⠀⠀⠀⠀ ⠀⠀⡀⠀⣀⡔⠁⢀⠌⠀⢀⠊⡠⡌⠀⠘⠔⠄⣀⡘⠀⠩⠀⠀⠀⠸⡆⠀⠀⠀ ⠀⠀⠠⠃⢸⠀⠐⠒⢒⠖⠁⢡⠒⢀⠀⠀⡀⠀⠠⠁⠉⠉⠑⡀⠰⠀⠃⠀⠀⠀ ⠀⢠⠁⠀⢸⠂⡠⠐⠁⠀⠠⠃⡰⢺⠀⠰⠀⡐⠓⠀⠀⠀⠀⠈⢢⣾⡄⠀⠀⠀ ⠀⣸⠀⠀⠀⣾⠶⣴⣤⣴⣧⣥⡀⡜⡐⠁⠈⠀⠸⠷⢶⠶⣷⣶⣻⢷⠇⠀⠀⠀ ⠀⡟⡁⠠⠀⢹⠀⠷⠲⢻⡿⡇⠐⡡⠂⠀⠀⠀⠀⠀⠘⣛⠻⠟⠻⠼⠀⠀⠰⠀ ⠀⠹⡰⡀⠡⡀⢃⠀⠷⠆⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠘⡠⠂⠀⠀⣠⠂ ⠣⡀⠑⢕⣄⠙⡢⠵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢮⠄⢂⡠⡞⠁⠀ ⠈⠻⠔⠢⡛⠱⢨⢙⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⣰⣀⠀⢐⠀ ⢀⣤⣾⢷⠬⡀⣩⣦⡀⠀⠀⠀⠀⠀⠀⣀⠤⡀⠀⠀⠀⠀⠀⣠⣼⡇⡐⢀⡅⠀ ⢻⠟⢅⢈⡇⠈⡋⡟⠉⠑⠂⠄⡀⡠⢂⣁⠤⡈⡄⢀⣠⡴⠚⣹⠣⠁⢃⢾⠀⠀ ⠁⠀⠀⢨⡃⠀⡇⢇⠀⠀⠀⠀⠜⠀⠀⢄⠉⠐⠻⠟⠉⢀⡼⢻⠃⠀⡠⡏⠀⠀ ⠀⠀⢸⠸⢀⢦⣰⢹⡀⠀⢀⡾⣧⠀⠀⠀⠈⣉⢐⣤⠞⠁⠀⡆⡄⣰⠃⠁⠀⠀

⠀⠀⠀⠂⠄⠀⠀⢀⠄⢊⡑⠄⠊⠀⠈⠑⠂⠝⠲⢤⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⡐⡡⠠⠋⠀⠀⠀⠀⠐⢄⠀⠀⠑⠄⠙⠀⢄⠀⠀⠑⡄⠀⠀⠀ ⠀⠀⠀⢸⠀⡰⢮⣠⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⢂⠀⠀⠑⡀⠀⠈⠄⠀⠀ ⠀⠀⠐⡑⠁⢠⠏⠀⠀⡐⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⢦⠀⠀⠈⢦⡀⠀⠀⠀ ⠀⠀⠀⠡⡠⠁⢂⠀⠠⠁⠠⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠘⣆⠀⠀⢀⠨⢄⠀⠀ ⠀⠀⢠⠊⠇⠀⣀⡖⠀⠀⢸⠆⢀⠀⠀⠀⠀⢸⡂⠝⠾⣄⡉⡄⠀⠈⣆⢃⡷⠀ ⠀⠀⠈⡀⢸⢮⠈⣆⡀⢀⣦⣙⣬⠀⠀⢠⢀⡞⣰⣾⢻⣿⢺⡧⠀⢠⣿⢸⣱⡀ ⠀⠀⠀⠰⠼⠀⢣⢱⢀⣾⣁⣀⡜⠀⣠⣣⠞⠀⠉⢹⡿⢿⢠⢇⠆⣸⢻⣿⠏⠇ ⠀⠀⠆⢠⠋⠀⠺⡀⣿⠏⣷⣯⣿⠉⠁⠀⠀⠀⠀⠀⠉⠁⠸⢫⣴⣟⣿⣟⠀⠀ ⠀⠀⠀⡬⡆⡄⠀⠐⢄⠣⡘⠣⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⡇⢳⡄⠀ ⠀⠀⠀⣡⢿⣜⡦⢄⡤⠽⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢡⣿⡇⠰⠁⠘⡇⠀ ⠀⠀⠀⠀⠀⠻⢄⡘⡆⠀⠘⢦⣀⡀⠀⠀⠀⠀⠀⢀⠎⢠⣿⢏⠜⢁⠆⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠠⢌⣻⣾⣄⠉⢯⠀⢲⠋⢠⢉⣧⣥⢴⡎⠀⠀⠇⠀ ⣆⠀⠀⠀⠁⠂⠤⣀⣀⣱⡀⠀⠈⠉⢉⡆⢸⡿⠁⠀⠀⠈⠉⢇⡜⠀⠀⠀⠀⠀ ⣿⡄⠀⠀⠀⠀⠀⡠⠌⠑⣛⡢⣄⠈⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀

⠀⡰⠁⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⢣⠠⣄⣌⠑⣄⢷⡈⡁ ⢈⣠⣐⣁⡴⠀⠀⡔⠀⠀⠦⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢳⡈⢻⣿⣮⣿⣿⣶ ⠝⡸⠀⡠⠁⠀⡼⠀⠀⣸⠀⠐⡒⠤⣁⠂⢦⣘⡀⠀⠀⠀⠆⢷⣆⠹⣿⣿⣿⣿ ⢣⠃⡐⠁⣠⣾⠃⡔⣰⠃⠀⠐⠰⠀⠀⠁⠢⣌⢣⠀⠀⠀⣸⢸⣿⣷⣿⣿⣿⣿ ⣾⢼⠴⠚⢩⣂⢼⣶⠋⠀⠀⠀⢃⡆⢀⡴⠊⣁⣹⣤⠀⠀⣿⣾⣿⡿⠛⡻⢿⣿ ⣿⠘⡀⠐⡏⠀⢠⠱⠈⡀⠀⢠⠸⣷⣫⣾⡟⢋⣰⡿⢸⠀⣿⣿⠻⣷⠩⠘⡈⣿ ⣿⢀⠀⠀⣧⠀⡌⠀⠡⠇⠀⠘⣾⠁⠏⠓⠋⠉⠀⣇⢾⣼⣿⣿⠀⢹⡝⡠⣿⣿ ⢿⣿⡆⠀⢇⡦⣗⣶⡶⣿⢀⠇⠸⠀⠀⠀⠀⠀⠀⠏⢸⣿⡏⡏⠀⠀⠋⣰⣿⡇ ⡆⠹⣿⡀⢼⣾⣍⣳⠓⠁⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠁⠀⢼⡽⣿⣿⣿ ⠉⠀⠹⣷⡀⢻⣍⠁⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⢬⣏⠛ ⠀⠀⢰⡟⢿⢪⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠉⠑⢴⠁⠀ ⠀⠠⠋⠀⠘⣏⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠇⠀⠀⠀⠰⠱⣦ ⠀⠀⠀⠀⠀⠘⠐⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⠃⠀⢀⠠⠒⠃⢻ ⡀⠀⠀⢀⠀⠀⠇⠹⣹⣿⣿⠈⠒⠄⡀⠀⠀⣠⠔⠁⠀⠀⠀⡠⠒⠁⠀⠀⠘⠀ ⠇⠞⠳⠛⠛⠂⠈⠂⢫⣿⣿⡆⠀⠀⠈⠁⢁⠨⣷⠄⢀⠄⠊⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⣾⠎⡇⠀⠀⣟⠉⠑⠂⠐⠈⣾⢆⠀⠀⢸⠀⠀⠈⡆⠀⠀⠁⠀ ⢀⠀⠀⠀⠀⣸⠋⠀⡇⠀⢠⠋⠀⠀⠀⣀⠀⣿⠘⡆⠀⠀⡆⠀⠀⠇⠀⠀⢸⠀ ⡈⠀⠀⠀⢰⣏⠠⠄⣿⡛⢻⠀⡇⣧⠀⡟⡄⢻⠛⠛⣦⣀⠸⡀⠀⢸⠀⢀⣾⠀ ⠃⠀⢠⠔⠻⠀⣀⠀⣸⢣⣜⠀⢱⡏⢆⣰⠘⣄⣇⡀⠈⠻⣻⣷⣀⠀⠀⠸⣻⡠ ⠀⢀⢸⣄⣧⡶⠛⠉⣩⠷⢿⠀⠀⢣⠈⠿⠄⣨⣽⣴⡶⢭⣄⡙⢻⢳⡀⠀⣿⠀ ⠀⢸⢸⣿⡇⠉⠀⠐⠛⠓⠞⠀⠄⠀⠀⠀⠀⠸⢧⠤⣿⠀⢈⡿⠅⢹⠙⣦⣽⢰ ⠀⠀⣾⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⣿⠔⠳⣽⣿ ⡆⠀⢻⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠊⢸⣿⣿ ⢠⠀⣘⡧⠕⢊⠇⠀⠀⢸⠷⠖⠂⡀⠲⠶⣦⠀⠀⠢⠀⠀⠀⢀⣤⠡⡣⢺⣿⣿ ⠔⠉⢀⡠⡔⣇⠀⠠⠀⢉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠇⠑⢄⣀⡈⢀⣠⣴⣿⣿⡏ ⠀⡠⠋⠀⠟⡿⣧⣀⠀⠈⠢⢀⠀⠀⠀⢀⢃⠄⡀⢈⣦⠀⠹⣙⠇⣾⠹⣿⠟⠀ ⠀⠃⠀⡘⠀⣄⠈⢿⡗⢄⠀⠆⠈⢒⠖⠁⠃⢠⠘⡝⠁⠱⠄⠈⠑⣿⢠⠏⢀⣦ ⠈⢀⠌⣠⣴⠿⡀⠘⢷⡀⠑⢦⣀⣠⣴⠞⠀⢸⠀⢁⠀⢗⣀⣀⠀⢻⡇⢠⠋⠀ ⠐⠓⠊⡼⠷⠐⠚⢫⣺⣿⣿⣿⣿⣿⣿⣾⢂⣾⣄⠰⠀⢰⠀⠀⠀⠀⢻⡇⠀⠀ ⠀⠀⠀⣀⣠⣔⢶⡏⠙⢝⡛⠻⠿⠿⠿⠿⠾⠀⠈⠢⢳⢢⡆⠀⠀⠀⠀⢿⣶⣦

⠀⠀⠀⠀⠸⣦⠀⠀⠀⠈⢗⠊⠙⡿⣦⡿⣴⡿⠋⠁⠀⠀⢀⡠⠔⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢻⣷⡀⠀⠀⢀⡹⠶⠶⠾⠗⠛⠶⢶⣾⣟⡋⠉⠂⠘⣇⣀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣤⡞⠋⠀⠀⠁⠀⠀⠀⠀⠀⠈⠙⠯⣒⢤⡴⠾⠤⡈⠷⠶ ⣲⠶⠒⠚⠉⠉⢉⡯⡎⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠳⡹⢆⠀⠀⠈⠉ ⠀⠀⠀⠀⠀⢀⡿⡽⠸⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠁⠀⠀⠘⡌⢧⠀⠀⠀ ⢄⣀⣀⣀⣀⣾⢁⠇⣀⠀⠀⠀⠀⠀⠀⡼⠼⣦⠈⡀⠀⠀⠀⠀⠀⢸⡈⠇⠀⠀ ⠀⠀⠀⠓⣺⠃⠊⢀⡛⣄⠀⠀⠀⠀⢰⣧⣴⣭⣷⣼⠀⠀⠀⠀⠀⠀⣇⢹⠀⠀ ⠀⠀⢔⢈⡇⠁⠀⣼⣤⣽⡄⠀⢀⣰⢻⡿⢋⠇⠌⢸⡆⠀⠀⠀⠀⢀⡈⢿⠀⠀ ⠀⠀⠀⡝⡀⠃⡄⢿⢸⣫⣨⡷⠂⠵⠤⠥⠈⢊⡠⠊⠀⠀⠀⠀⠀⢸⠛⢶⠥⠒ ⠀⠀⠰⣇⢞⢄⡀⢚⠖⠃⠀⠀⠀⠀⠀⠀⠨⣭⡿⠤⣲⠀⢀⢀⢀⠏⡆⣽⠀⠀ ⠀⠀⢠⠹⡺⠶⣻⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⡣⣺⡜⢀⠸⣿⠀⠀ ⠀⠈⢪⣆⠐⢄⠀⠻⣿⣦⣄⠀⠀⠀⠀⠀⣀⣤⣴⢿⢾⡏⠐⢹⢆⠈⡆⠈⠂⠀ ⠀⠀⠀⠉⠛⠒⠵⠀⣿⣇⠘⠳⣶⣶⡢⠛⠑⠈⠀⢸⣿⡷⡀⢸⡼⡣⡘⣦⣄⠑ ⠀⢀⠸⠀⠀⡠⠂⠉⠹⡜⠢⠤⣤⠟⢦⡀⠀⠀⠀⠸⣿⠇⠈⠛⣇⢳⡈⢪⣽⣗ ⠀⠀⠀⢀⡴⠥⣴⣤⣀⡈⠚⠿⠭⢕⢦⣙⢦⢠⣄⣀⣽⢀⣾⡇⠈⢺⣷⡈⢿⠣

⠀⣂⡀⠀⠀⣀⡀⠀⢀⣀⠤⠀⠒⠠⠥⠁⠀⠀⠀⠀⠀⠀⠀⠉⠐⠄⠀⠀⠀⠀ ⠛⡷⠈⡏⢹⡦⢤⡋⠉⠉⠕⠋⠩⠍⠉⠉⠀⠀⠀⠀⣀⡀⢤⠒⡉⠁⡢⡀⠀⠀ ⢀⣀⢰⡇⡜⠀⠀⠀⠛⠉⠒⠤⣀⣀⢠⠤⠐⠒⡏⠩⡃⠀⠀⠣⠈⢆⠈⠪⢂⢀ ⠀⡨⠛⠋⠀⠐⡢⣷⣿⣿⡿⠋⠟⡹⠈⠀⠀⠀⠁⠐⡐⠄⠢⡀⠱⡨⣆⠐⢽⠁ ⡶⠵⢄⣠⡤⠊⡰⢁⢡⠻⠀⢸⢠⡍⣶⠀⠀⣇⣸⡀⠔⠐⡑⠱⠀⢵⠹⡄⢸⠀ ⠀⠀⠋⢹⡃⢀⡇⡆⠶⠀⠀⡾⢸⠇⠈⢆⢸⡟⣼⡷⡀⠃⢡⠈⢇⠘⡇⢳⢸⠀ ⢇⠀⢠⣰⡏⢹⡰⠰⠀⠀⣼⠧⡬⣸⣧⠀⢸⡧⠊⢇⠑⠄⢠⡄⠨⠀⢷⠈⡄⠀ ⡈⢿⣿⡋⠀⣮⡇⠀⠂⢀⡇⠀⡇⠀⡟⡗⠌⡇⠀⣈⣄⣈⡄⣇⠀⡆⢰⠁⢰⠀ ⠃⠨⠋⠁⠀⣿⡇⡀⢁⢸⢀⣶⡷⠧⡄⠈⠊⠚⠨⠟⠋⠉⠛⣽⠀⡇⢿⠀⢈⠀ ⢠⠁⠀⠀⠀⣧⡇⡇⠈⣿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡌⡇⣼⠀⡇⢢ ⢸⡄⠀⠀⠀⢸⣷⣧⢇⣿⡆⠀⠀⠀⠀⠀⠀⣀⣀⠀⢤⡀⠐⢹⡧⢇⢿⣾⢧⡾ ⣂⡇⠀⠀⠀⠈⢿⡏⡘⣿⣷⠀⠀⠀⠐⡎⠁⠀⠒⢒⣱⠁⢀⣾⢰⢂⠛⠝⠁⠀ ⢿⢅⣀⡀⡆⠖⠏⠟⢃⡹⣿⢓⢄⡀⠀⠈⢰⠀⠝⠓⠁⠙⠉⡆⣰⠂⠀⠀⠀⠀ ⡼⡇⢱⠈⡟⠂⠀⠀⠀⣧⢻⠀⠀⠛⠛⠙⠉⠀⠀⠀⠀⠀⢰⣰⠁⠀⠀⠀⠀⠀ ⢁⣇⠈⢆⢸⣿⡿⢤⠄⠁⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⣀⣠⡄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢉⢢⡌⠁⢸⠀⠀⠀⠀⠀⠀⠂⠀⠘⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣐⠃⢤⡢⠀⡃⢀⠠⠗⠀⢄⠀⢠⣄⣰⠦⡀⢈⠤⠂⢀⠀ ⠀⠀⠀⠐⡀⠀⠀⢔⠊⣐⢲⠓⠊⠁⠀⠀⢀⠔⠝⣠⡘⠣⠈⠑⢌⢀⢀⡠⡃⠀ ⠀⠀⢔⠁⠠⢭⠤⠽⡑⣾⠒⠀⠀⠀⢀⡤⠊⠉⠛⠏⣈⡁⠚⢧⡀⠡⡡⠀⠇⠀ ⠁⠀⢸⣉⠈⠀⢀⠘⣒⡆⠤⡤⣂⣻⣖⣀⠀⠀⢤⡔⠒⠓⠲⠄⠉⠀⠁⠡⡀⠀ ⠀⠀⢸⡀⡈⢱⠀⠀⠀⢡⠀⠁⢻⣻⣿⣿⡄⠀⠀⢀⣠⣿⣤⠀⠀⠀⠀⠀⢡⠀ ⠀⠀⠂⠉⠑⣼⣏⡀⠀⠀⢣⡄⠀⠈⠁⠈⠁⢀⢴⣿⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⢀⠺⢡⠤⠅⣒⢼⡉⠂⠀⠀⠀⠀⡀⠀⠉⢈⣿⠟⠐⠄⠀⠀⡀⠀⠁ ⠀⠀⢀⠴⠅⠋⣪⣆⠀⠀⡛⢧⡀⠑⠆⣠⣁⡀⠀⡠⠎⡤⣤⡤⠤⣷⡎⠀⠀⠀ ⠀⠠⢺⠉⢋⠀⠀⠉⠀⣰⠃⢄⠷⢄⡀⢀⡀⠄⡾⢢⡚⠝⣁⡔⠈⢀⡈⠆⠀⠀ ⠀⠀⢸⠀⢸⠀⠀⢀⡔⠉⠙⢾⣀⢀⡏⠩⠤⡾⠃⡡⢴⢛⠊⡠⠋⢫⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⢀⠔⠁⢀⣴⠮⢝⠍⠉⠀⠀⠌⣠⠎⠀⣆⠧⢰⠁⠀⠀⠁⠀⠀⠀ ⠀⠀⡀⡠⠋⠀⠀⠀⣓⣧⣀⢜⡜⠀⠀⢸⠘⠁⠀⢸⢸⢄⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠞⠀⢀⡠⡖⠙⡘⠁⠲⢁⠨⣢⡀⢈⡇⠀⠀⢘⢼⢌⡇⠀⠀⠀⠀⠀⠀⠀ ⢀⠃⡠⠒⠁⠡⡈⠢⡈⠒⡈⠔⠈⡠⠑⢾⡇⠀⠀⢰⢺⠄⡇⠀⠀⠀⠀⠀⠀⠀ ⡦⠊⡀⠄⢂⠡⢈⢂⡈⣉⠤⡒⠣⡀⠀⠈⢥⠀⠀⣸⡋⠷⣄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣠⠖⠈⠉⠠⠤⡀⠈⠁⢲⢲⡂⠄⣀⡓⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠊⡐⠁⠀⠀⠀⠀⠈⠢⡀⢠⠀⠑⢄⡙⣧⡀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠌⠀⠀⠀⢀⠁⠀⠀⠀⡖⠀⠐⠠⢆⡀⡸⠁⢘⠰⡃⠀⠀⠀⠀⠀ ⠀⠀⡘⠀⢠⠂⠀⢸⠠⠀⠀⡆⠈⠢⠀⢀⠄⢃⠀⠦⣞⡀⢡⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⠀⠎⡄⠣⡀⢃⠀⠤⠤⠆⠀⠀⣇⡀⠘⣌⠺⠀⠀⠉⠆⠀ ⠀⠀⡀⠀⠇⢀⠜⠈⠙⢄⢛⠢⣢⣤⣦⢼⣤⣼⠆⢉⣉⠀⠐⡣⠀⠀⢸⠀ ⠀⠀⣷⠀⢰⣶⣶⠸⡽⣺⠹⢆⠀⠘⣗⠂⠟⠧⠀⢸⢀⠀⠁⡇⠁⢠⣼⠀ ⠀⢠⣼⠂⠈⡌⢄⠤⠑⠉⠚⠉⠀⠀⠀⠀⠀⢀⡆⣌⠊⠀⢀⠇⠀⠲⣟⠀ ⠀⠘⠉⡔⡀⠈⠂⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠚⣸⢁⠀⣸⠊⡀⠀⠀⠘⠄ ⠀⠀⠌⢸⢯⣢⢀⠀⠙⣤⣀⠐⠀⠀⠁⢀⠄⢪⡝⣨⠊⠀⠀⢰⡀⠀⠀⠀ ⢀⠌⠀⠈⢸⡙⠓⠗⢦⠙⠆⠉⠒⡤⠒⠁⠀⠸⣉⣾⠀⠀⡀⠀⠘⠀⡀⠀ ⠀⠀⢀⡇⠜⡇⠀⠀⢣⣢⠚⠉⠐⢅⠀⠀⡰⠋⠾⡎⠀⡐⡀⢠⠂⠁⠀⠀ ⢀⡠⠂⠇⠀⣷⡀⢂⠘⣎⠁⠀⠀⠀⠢⡊⠀⠀⡘⠀⡘⣱⢁⠆⠀⠀⠀⠀ ⠀⠁⠸⡄⠀⣟⢷⡈⢢⠐⣧⡀⠀⠀⠀⠙⡀⠌⣠⡪⠔⡼⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣆⠇⠀⠈⠐⠳⠭⠒⠤⣀⠀⠀⡩⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀ ⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀ ⠀⢸⣦⡙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢋⣴⡇⠀ ⠀⠈⠻⣿⣦⡙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢋⣴⣿⠟⠁⠀ ⠀⢸⣷⣌⢿⣿⣦⡙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢋⣴⣿⡿⣡⣾⡇⠀ ⠀⠈⠻⣿⣷⡝⢿⣿⣎⢻⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⡟⣱⣿⡿⢫⣾⣿⠟⠁⠀ ⠀⢀⡤⣌⢻⣿⣦⢻⣿⡎⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⢱⣿⡟⣴⣿⠟⣡⢤⡀⠀ ⢀⠘⠶⠟⠀⢹⣿⡇⣿⣿⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⣿⣿⢸⣿⡏⠀⠻⠶⠃⡀ ⠘⠿⢿⠿⠷⢸⣿⣧⣿⣿⣸⣿⡇⣀⣀⣀⡀⢸⣿⣇⣿⣿⣼⣿⡇⠾⠿⣿⠿⠃ ⠹⣶⣶⣶⣦⢸⣿⣿⡿⠿⢿⣿⠁⢿⣾⣿⡄⠈⣿⡿⠿⢿⣿⣿⡇⣴⣶⣶⣶⠏ ⠀⠀⠀⣠⣤⡘⢿⣿⣧⣀⡀⠀⢀⣼⣿⣿⣧⡀⠀⢀⣀⣼⣿⡿⢃⣤⣄⠀⠀⠀ ⠀⠰⠿⠛⠉⣡⣦⠉⠻⠿⣿⣿⣿⣿⣿⡇⢙⣿⣿⣿⠿⠟⠉⣴⣄⠉⠛⠿⠆⠀ ⠀⠀⠀⠀⠐⠛⠁⠀⡿⠂⣤⡍⢻⣿⣿⣿⣿⡟⢩⣤⠐⢿⠀⠈⠛⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡄ ⢿⣟⠛⠛⠁⠀⠀⠀⠀⣠⣾⣿⠋⠁⠀⠀⠀⠉⠛⢷⣄⠀⠀⠀⠀⠈⠛⠛⣻⡿ ⢰⣿⣿⣷⣶⣶⡶⢀⣾⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⣷⡀⣶⣶⣶⣾⣿⣿⡄ ⠸⢿⣿⣿⣯⣀⠀⣾⣿⣿⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⣷⠀⣈⣽⣿⣿⡿⠇ ⠀⠀⠀⣸⣿⣿⣿⢶⣮⣭⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣤⣴⡶⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⡏⢸⣿⢉⣿⠛⠻⡟⢻⡟⠛⣛⢻⣿⠉⣴⡆⢻⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠻⠶⣦⣼⣿⣀⣦⡁⢸⡗⠒⣂⣈⣿⣧⣴⠶⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⣭⣝⣛⣛⣛⣛⣛⣛⣫⣭⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢀⣤⣤⣤⣤⡀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀⠈⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡋⢩⣿⣿⣿⣿⣇⠀⣿⡧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢸⣿⣿⣿⣿⣯⣀⣽⣷⣶⣤⣤⠀⠀⠀ ⣶⣶⣶⣿⣿⣯⣽⣿⣏⢀⣀⣀⣀⣀⣀⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠈⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀ ⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀ ⢀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⣿⡛⠿⠿⠿⠿⠿⠿⣿⠇⠸⣿⠿⠿⠿⠿⠿⠿⢻⣿ ⣿⣷⣶⣶⣶⣶⣤⠀⠿⠶⠶⠿⠀⣤⣶⣶⣶⣶⣾⣿ ⠹⣿⣿⣿⠙⠛⢿⣷⣶⣶⣶⣶⣾⡿⠛⠋⣿⣿⣿⠏ ⠀⠀⠉⣿⣿⠀⠘⣉⣠⣤⣤⣄⣉⠃⠀⣿⣿⠉⠀⠀ ⠀⠀⠀⢻⣿⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⣿⡟⠀⠀⠀ ⠀⠀⠀⠸⣿⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⢹⣧⢸⣿⣿⣿⣿⣿⣿⡇⣼⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣾⣿⣿⣿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣦⠀⣿⣿⣿⠀⠀⣿⣿⣿⠀⣾⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⣿⣦⣴⣿⣿⡿⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣦⡀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⠀⣰⣿⡏⠉⠉⢹⣿⣆⠀⣿⣿⣿⣿⣦⡀⠀ ⣴⣿⣿⣿⣿⣿⣿⢀⣿⡟⠀⠀⠀⠀⢻⣿⡄⣿⣿⣿⣿⣿⣿⣦ ⣿⣿⣿⣿⣿⣿⣿⣸⣿⣇⣀⣀⣀⣀⣸⣿⣇⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢻⣿⡟⠛⠛⠛⠛⢻⣿⡟⣿⣿⣿⣿⣿⣿⣿ ⢿⡿⠟⠋⠀⠈⠉⠸⣿⣿⣿⣿⣾⣿⣿⣿⠃⠈⠁⠀⠙⠻⢿⡿

⠀⠀⢠⣶⠀⢠⣶⡄⢠⣶⡄⠀⣶⡄⠀⠀ ⢠⣶⣾⣿⣶⣾⣿⣷⣾⣿⣷⣶⣿⣷⣶⡄ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁ ⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁ ⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⢸⣿⣿⣿⠋⠉⠉⠙⣿⣿⣿⡇⠀⠀ ⠀⠀⢸⣿⣿⡇⢀⠀⠀⡀⢸⣿⣿⡇⠀⠀ ⠀⠀⢸⣿⣿⡇⢸⣿⣿⡇⢸⣿⣿⡇⠀⠀ ⠀⠀⢸⣿⣿⣇⠘⢿⡿⠃⣸⣿⣿⡇⠀⠀ ⠀⠀⢸⣿⣿⣿⣶⣤⣤⣶⣿⣿⣿⡇⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢠⣾⣯⣍⡒⠒⠒⠒⣒⣒⠒⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠑⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⣦⡀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣵⣶⣶⣶⣶⣶⣶⣶⣤⣽⡄⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠋⠉⠉⠉⣉⣽⣿⣿⣏⡀⠀⠀⠀ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⣴⣿⡿⢿⣿⣶⣄⣀⣠⣾⣿⣋⣉⣙⣻⣿⣄⠄⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠿⠓⠒⠒⠺⠿⣿⡿⠿⣿⠁⠀⠀⠀⠉⢹⣿⠉⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⡟⠀⠈⢣⠀⠀⠀⢀⣾⣿⡄⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣷⣄⣀⣀⣠⣾⡿⠃⠀⠀⠀⠳⣶⣾⡿⣿⣿⣝⡄ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⣸⠂⠀⢸⣿⣿⣷ ⣾⣿⣿⣿⣿⣿⣿⣿⢇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠚⠉⠀⠀⠀⢸⣿⣿⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠀⠀⠀⠀⣼⣿⣿⠃ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡷⣄⠀⠀⠀⠲⣾⣿⣻⠛⣿⣹⠄⠀⣠⣾⣿⣿⠏⠀ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣦⣤⡀⠈⠛⠿⠟⢁⣠⣴⣿⣿⡿⠟⠁⠀⠀ ⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣤⣀⣀⢠⠜⢱⣿⣿⣷⣤⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⠶⣿⣿⠶⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣶⡆⠀⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⢀⣤⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⡀ ⠀⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⣿⣏⣉⣉⣉⣉⣉⣉⠀ ⠈⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠁ ⠐⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠂ ⠀⠀⣶⡆⠀⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⠀ ⠀⠀⣿⣧⣀⠙⠻⢿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⢿⣷⣦⣄⡈⠛⠛⢁⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⣿⣧⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣠⣾⣆⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠋⠉⣿⡏⠉⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⣰⣿⣧⡀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡏⠀⢸⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⡄ ⠈⣿⣿⠉⠉⢹⣿⡏⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⢹⣿⡏⠉⠉⣿⣿⠁ ⠀⠸⠿⢿⣿⣾⣿⣧⣄⣠⣾⣿⣿⡟⠉⢹⣿⣿⣿⣆⣀⣼⣿⣷⣿⡿⠿⠇⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠿⠀⠸⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⠶⠦⠤⢤⣄⣀⣴⣷⣤⣆⣤⣤⣤⣤⣤⡤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠶⠛⠛⠛⠛⠛⠛⠓⠀⠀⠈⠙⠃⠉⠙⠉⠀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠛⠲⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢛⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣽⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠋⠀⢀⣠⣤⣴⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⡋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠋⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⢀⣤⣏⡉⠿⠿⠿⠛⠛⠉⠉⠀⠙⣆⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⣠⣯⣥⣄⡀⠀⠀⠀⣀⣭⣭⣝⡀⠀⠸⡆⠀⠀⠀⠀⣸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀ ⠠⢾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡛⠛⠛⠛⢻⠀⠀⣼⠛⠛⠛⠛⢳⡀⠀⣷⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀ ⠀⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣇⠀⠀⢠⣯⡀⠀⢻⡃⠀⠀⠀⣸⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀ ⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠇⠠⠬⣽⠛⣿⣿⣿⡀⠀⠉⢒⣶⣯⠥⠄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⣐⣒⣛⠉⠀⠛⠻⠿⠗⠋⠀⠈⠛⣛⠒⠂⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⣿⢀⡀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⠀⢸⠁⠉⠉⠉⠉⠙⠛⠛⠒⠒⠛⠛⠉⠁⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣿⠀⠀ ⠀⢿⣿⠇⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⠀⠀ ⠀⠈⢹⡄⠀⠀⠀⠀⢠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⡿⠟⠀⠀ ⠀⠀⠘⣇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠹⣆⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣾⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢧⡀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣀⣀⣰⠟⠙⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⡿⣄⠀⠀⠈⢷⣄⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢾⡿⠋⠀⠀⠈⠙⠻⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠏⠀⠙⣆⠀⠀⠀⠙⠷⣄⣀⣤⠶⠚⠳⣦⡀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠏⠀⠀⠀⠘⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⡼⠀⠀⠀⠀⢀⡾⠏⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⠾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⢀⡇⠀⠀⣀⢴⡞⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⣀⣤⠶⠞⠋⠉⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀ ⠀⠀⢸⡇⠀⢾⡿⠚⠷⠶⠤⢤⣤⣤⣽⣷⡄⠀⠀⠀⢀⣴⣟⣹⣿⣟⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⢀⡴⢿⣇⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣠⡾⠋⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀ ⢾⠇⠀⠈⠉⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⠻⣇⡀⣤⣀⡀⣄⣀⣀⣀⡄⣀⣤⣆⣠⡼⠛⠳⣄⡀ ⢸⡇⠀⠀⠀⠙⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠈⠉⠛⠋⠉⠛⠉⠉⠙⠋⠉⠈⠉⠀⠀⠀⠰⣿⡇ ⠘⣧⡀⠀⠀⠀⠀⢹⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿ ⠀⠈⠻⢷⣶⣦⣤⣤⣿⣿⣿⣿⣿⣿⣷⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣤⣴⣶⣦⣴⣾⣿⣷⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀

⠀⠀⠀⠀⠀⠀⣔⣊⣉⠀⠐⢶⠐⠒⠂⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⢸⡥⠯⠵⠯⣄⣀⠀⠀⠀⠀⠉⠑⠢⣶⣾⣿⣿⣿⡷⠖ ⠀⢀⠀⠀⠠⠴⠃⠀⠀⠀⢀⡤⠀⠚⢟⡦⣄⠀⠉⠒⠀⠀⠙⠻⣇⠁⠀⠀ ⢀⣿⠀⠀⠄⠸⢀⠀⣠⣤⣂⣨⣦⣴⢋⠄⠈⣷⣦⡀⠀⠈⠂⢄⡈⠳⣄⠀ ⠘⣿⠷⠃⣠⡀⣼⡶⠒⠒⠀⣀⣠⡤⢤⠽⠮⠁⠁⠉⢢⡀⠀⠀⠹⠷⠾⠃ ⠘⣿⠀⡾⠟⠛⠙⠓⠌⠁⠈⢉⢭⣀⣠⣄⠀⠀⠀⠀⠀⢿⣆⠀⠀⠈⠄⠀ ⠨⢚⣆⠁⠀⠀⠀⠀⣀⠄⠂⡍⠀⠇⠀⠙⢀⠀⡀⠀⠀⠀⠙⣆⠀⠀⠘⠀ ⠀⠁⠈⠑⠂⠤⠤⡔⠁⠀⠀⢸⠎⠀⠀⠀⡈⠀⠀⠉⠒⢄⢠⠉⢆⠀⠀⡆ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⣸⡀⠀⠀⠀⠀⢈⡿⢇⠈⡄⠀⡇ ⠀⠀⠀⠐⠠⣤⣬⣷⣀⠀⢠⠀⢀⡠⢜⢃⠷⠶⠶⠖⣺⠟⠀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠔⠁⠙⠉⢉⡝⠿⠄⠁⣒⣒⣶⠖⠚⠁⠀⠀⠀⠈⠶⠀⠀ ⠀⠀⠀⠀⠀⡌⠠⠀⠀⠀⣈⠀⠀⢀⠠⢣⠀⢀⣑⠄⠀⠀⠀⠀⠘⠃⠀⠀ ⠀⠀⠀⠀⠀⢧⢂⢀⢆⡀⠁⢀⠀⡙⠀⠀⠀⠎⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠋⠉⠀⠀⠉⢁⣁⠰⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⣤⣤⣤⣤⣤⣤⣤⡄⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄ ⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⠿⢿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿ ⢸⣿⣿⡿⠛⠃⠀⢀⡀⠀⢸⡏⠀⢸⣿⠀⠀⣀⠀⠀⠛⢻⣿⣿⣿ ⢸⣿⣿⡇⠀⢠⣤⣾⡇⠀⢸⡇⠀⢸⣿⠀⠀⣿⣦⣤⠀⢸⣿⣿⣿ ⢸⣿⣿⣇⣀⣀⠀⠀⣀⣀⣸⣧⣀⣸⣿⣀⣀⠀⠀⢀⣀⣸⣿⣿⣿ ⠈⠉⣻⣿⣿⣿⡀⠀⣿⠟⠛⠛⠛⢻⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿ ⢰⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣾⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⠁⠈⣿⣿⣿⣿⣿⣿⣧⣠⣿⡏⠀⢻⣿⣿⣿⣿⣿ ⢸⣿⣿⣏⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⣸⣿⣿⣿ ⢸⣿⣿⡿⠛⠛⠀⠀⣿⠀⠀⣿⣿⣿⡇⠀⣿⡇⠀⠘⠛⢿⣿⣿⣿ ⢸⣿⣿⣷⣤⣤⣤⣴⣿⣦⣤⣿⣿⣿⣧⣴⣿⣧⢤⣤⣤⣼⣿⣿⣿ ⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠹⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⣠⣴⣶⣶⣄⣠⣶⣶⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⡇⠀ ⠀⢸⣿⣿⣿⣿⣿⠀⣿⡟⢻⣿⠀⣿⣿⣿⣿⣿⡇⠀ ⠀⠸⣿⣿⣿⣿⣿⣦⣿⡇⢸⣿⣴⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⠹⣿⣿⣿⣿⠻⣿⣷⣾⣿⠟⣿⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⠙⠿⣿⣿⣄⣿⣿⣿⣿⣠⣿⣿⠿⠋⠀⠀⠀ ⣤⣄⠀⠀⠀⣿⣿⠛⠿⠿⠿⠿⠛⣿⣿⠀⠀⠀⣠⣤ ⣿⣿⠀⠀⠀⣿⣿⣤⣤⣴⣦⣤⣤⣿⣿⠀⠀⠀⣿⣿ ⣿⣿⣀⣴⣾⣿⣿⠿⠛⣿⣿⠛⠿⣿⣿⣷⣦⣀⣿⣿ ⣿⣿⣿⣿⠟⠉⠀⠀⠀⠈⠁⠀⠀⠀⠉⠻⣿⣿⣿⣿ ⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠟⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣀⣀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄ ⣿⣿⣀⣀⣀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣀⣀⣀⣿⣿ ⣿⣿⠿⠿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⠿⠿⣿⣿ ⣿⣿⠀⠀⠈⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠁⠀⠀⣿⣿ ⠻⢿⣷⣦⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣴⣾⡿⠟ ⠀⠀⠉⠻⠿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣷⣾⣿⠿⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⣿⣿⠀⠀⣿⣿⣿⡏⠙⠿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣼⣿⠏⠁⠈⠹⣿⣧⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣯⣤⣀⣀⣤⣽⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠉⠉⠉⠉⣿⣿⠟⠛⠛⠻⣿⣿⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡀⢀⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠛⠉⠀⠀⠙⠿⠿⠋⠀⠀⠉⠛⠋⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⢠⣤⣤⣼⣿⠉⠉⣿⣿⣿⣿⠉⠉⣿⣧⣤⣤⡄⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡄⠀ ⢠⣿⣿⣿⣿⣿⣿⣆⠀⣿⣿⣿⣿⠀⣰⣿⣿⣿⣿⣿⣿⡄ ⠘⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⠀⠀⢹⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⡏⠀⠀ ⠀⠀⠀⢻⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡟⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣶⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⣾⡿⠟⠛⠛⠉⠉⠉⠉⠛⠛⠻⢿⣷⣦⣄⠀⠀⠀ ⠀⢠⣾⡿⠛⠁⢀⣠⣤⣶⣶⣶⣶⣶⣶⣤⣄⡀⠈⠛⢿⣷⡄⠀ ⢠⣿⡟⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⢻⣿⡄ ⣾⣿⠀⠀⣾⣿⣿⣿⣿⡟⠉⠁⠈⠉⢻⣿⣿⣿⣿⣷⠀⠀⣿⣷ ⢿⣿⠀⠀⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠀⠀⣿⡿ ⠘⣿⣧⡀⠈⠻⣿⣿⡟⠀⢰⣿⣿⡆⠀⢻⣿⣿⠟⠁⢀⣼⣿⠃ ⠀⠈⢿⣷⣦⡀⠈⠙⠁⠀⠾⠿⠿⠷⠀⠈⠋⠁⢀⣴⣾⡿⠁⠀ ⠀⠀⠀⠉⠻⣿⣷⣦⣤⣄⣀⣀⣀⣀⣠⣤⣴⣾⣿⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⣿⠋⠙⣿⣿⡿⠀⢸⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠸⣿⣿⠀⠀⣿⣿⠇⠀⢸⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⠀⠀⣿⣿⣿⣷⣾⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠟⠋⠉⠉⠹⣾⣷⠏⠉⠉⠙⠻⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡀⠀⠀⠀⠀⢀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣆⠈⢿⣿⣿⣿⣿⣿⣿⡿⠁⣠⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⠻⣿⣿⣿⣿⠟⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣿⣆⠀⠈⠉⠉⠁⠀⣰⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣶⡄⢠⣶⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⢀⣶⣦⡀⠀⠀⠻⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠟⠀⠀⢀⣶⣶⡀⠀ ⢀⣿⣿⣿⣷⣄⠀⠀⢨⣿⣿⣿⡇⢸⣿⣿⣿⡁⠀⠀⣠⣾⣿⣿⣿⡀ ⣼⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⡇⢸⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⠈⢿⣷⣍⠙⠻⠿⢿⣿⣿⣷⣤⣤⣾⣿⣿⠿⠿⠛⠉⣡⣾⡿⠁⠀ ⠀⠀⠈⠻⣿⣿⣄⠀⢀⣤⠀⠉⢉⡉⠉⠀⣤⡀⠀⣠⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠈⠛⢿⣿⣾⣿⣤⣀⣸⣇⣀⣤⣿⣷⣿⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠛⠻⢿⣿⠿⠿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡸⠀⡄⠂⠤⠙⣷⣶⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡷⠇⠀⢄⠀⣰⠃⠙⣿⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠰⠄⠲⠭⠀⠀⠀⡿⠗⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠓⠦⠇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠔⠒⠒⠒⠛⢲⠀⠑⢤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⡎⡟⢠⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢴⣿⣿⣿⣿⣿⡼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡗⠢⡀⠀⠀⠀ ⠀⠀⡠⠊⠀⠸⣿⣿⠿⣿⠇⢿⣮⡑⠒⠤⠤⠔⠊⠒⠦⣴⠁⠀⠸⠀⠈⣦⡀⠀ ⠀⡰⠁⠀⠀⠀⠙⠁⠀⠈⠦⠜⠻⢿⣦⣄⠀⠀⠀⠀⡠⣫⠊⠉⠒⣧⡄⣿⣷⡀ ⢰⣿⣷⣀⣤⣠⣾⣦⣄⠀⠀⠠⣤⣤⣙⠁⡉⠢⣄⣜⠀⠁⠀⠀⢠⣿⣿⣿⣿⣇ ⣾⣿⣿⣿⣿⡿⠿⣿⣟⢰⠀⠀⢿⣿⣿⣿⣿⣠⣾⣼⣿⣴⣦⠀⣹⣿⣿⡏⠟⢸

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

⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠒⠒⠚⠋⠉⠉⠛⠛⠲⠶⣦⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⢿⣿⠀⠀⠀⠀⠀⠀ ⠸⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠒⠋⠉⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀ ⠀⠈⠙⢿⣟⠛⠛⠛⠋⠉⢁⡴⢚⣿⠲⡄⠀⠀⠀⠀⠀⠀⠀⣿⣧⣦⣤⡤⠶⠂ ⠀⠀⠀⢀⣙⣷⡀⠀⠀⠀⣾⢀⠎⢹⣧⣽⠀⠀⠀⠀⢠⣤⣾⣿⢹⡿⡉⠀⠀⠀ ⠀⢀⠔⠚⠛⠛⠛⣄⠀⠀⣿⣾⡶⠋⢻⣾⠀⠀⠀⠀⠘⢿⣿⡿⡌⠿⢱⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⣿⡋⠀⠀⢈⣿⡀⠀⠀⠀⠀⢀⣉⣴⡏⠑⠊⠀⠀⠀ ⠀⠀⣀⣀⣠⠤⠖⠛⠑⠒⠈⠙⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀ ⣼⠉⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⢉⣹⣿⠀⠀⠀⠀⠀⡠⠀ ⢿⠀⡏⠉⠉⠉⢹⣷⣶⣤⣀⡀⠈⠉⢰⠊⠀⠀⣠⣶⣿⣿⣿⡀⠀⠀⣀⡴⠃⠀ ⠘⡄⠀⠀⢀⣦⢾⣿⣿⣿⣿⣿⣷⣶⣤⣤⣴⣿⡿⣿⣿⣿⣿⣿⣿⡿⢋⠀⠀⠀ ⠀⠹⣤⣴⡟⢹⣾⣿⣿⣍⣙⣻⣿⣿⣿⣿⣋⣁⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⠛⠛⡛⠛⢋⣠⡍⠛⠋⠉⢠⣤⡄⢸⡿⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢧⡘⠿⣷⣤⢽⢤⠤⠴⡲⠛⢁⠕⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠬⢝⣃⣚⣊⡥⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡤⠀⠈⣿⣿⣿⡿⠛⠛⣷⣄⠀⠀ ⠀⠀⠀⠙⣿⣿⣿⡏⠀⠀⢸⣿⣿⡇⠀⠀⢿⣿⣿⣷⠀⠀⣿⣿⣷⡄ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⢹⣿⣿⡇ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠘⣿⣿⡇⠀⠀⠈⣿⣿⣿⠀⠀⢸⣿⣿⡇ ⠀⢀⡀⠀⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⠖⠓⣶⣿⣿⣿⠐⣄⣸⣿⣿⠇ ⠈⢧⣀⠀⣿⣿⣿⣇⣠⣴⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⡇⠈⠛⠉⠀⠀ ⠀⠀⠉⠛⣿⣿⣿⡟⠉⠁⠀⣿⣿⣿⠀⠀⢸⣿⣿⡿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⢄⣿⣿⡇⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⡿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠉⠉⠉⠁⢀⡼⠿⠿⢿⣦⡀⠀⢹⡇⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀

⢲⣿⣄⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀ ⠀⠻⣿⣧⡀⠀⢀⣤⣾⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣶⣄⠀⠀ ⠀⠀⠈⠻⣿⣶⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⡄ ⠀⠀⢀⣼⣿⠟⠿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠟⠁ ⠀⣠⣿⡿⠁⠀⠀⠈⠉⠛⠿⣿⣿⣶⣶⣶⣤⣤⣤⣴⣶⣶⣾⣿⠿⠛⠋⠀⠀⠀ ⠰⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠒⠒⡒⠢⣤⠔⠒⠒⠒⠒⠤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⡠⣲⠦⢴⣶⣌⠜⠁⠀⠚⠀⠀⠀⠀⠘⡄⠀⠀ ⠀⠀⠀⠀⠀⢀⠞⠁⠀⢀⣤⣴⠶⡧⣝⣿⣩⡋⠀⢀⣀⣀⠤⠤⠤⣤⡀⢹⠀⠀ ⠀⠀⠀⠀⡠⠃⠀⢀⡀⠈⠁⠘⠓⠲⣿⠶⢷⣲⠏⣩⣄⣠⣤⣴⡾⠋⠹⠏⠀⠀ ⠀⠀⢀⡜⠁⠀⠀⢻⣶⠀⣀⣒⠂⠀⠀⠉⠁⢹⡿⢋⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠗⠀⠀⠀⡈⠙⠛⠿⠃⢀⣶⠗⠛⡾⠟⢀⣾⡿⠛⣻⠀⠀⠀⠀⠀⠀⠀ ⠀⣜⡀⠀⠀⠀⠎⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠜⠟⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⡿⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠸⢀⡾⠁⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀ ⠸⣠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡆⠃⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⢿⡇⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀ ⠀⢹⢰⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠛⣀⡄⠀⠀⠀⠀⠀⠀⣠⡀⠀⠈⢦⠀⠀⠀ ⠀⠸⣾⡇⡀⠃⠀⠀⠀⠀⠀⢰⠀⣠⣿⣷⣤⠀⠀⠀⠀⡆⢹⣷⣶⣀⠈⢃⠀⠀ ⠀⠀⠙⢻⣧⣴⡇⣄⣀⣤⣀⣷⣾⣿⣿⣿⣿⡄⢰⣰⣤⣼⣾⣿⣿⣿⣷⣾⣆⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠘⠟⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠈⠛⣿⠛⠉⠉⠀⠀⠀⠀⠀⠙⠹⣿⢿⣿⣿⣿⣿⠻⣿⢿⠟⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠿⠍⠀⠉⠀⠀⠀⠀

⠀⣠⣴⣿⣿⣿⣿⣶⣦⣴⣶⣶⣿⣿⣶⣶⣶⣤⣶⣿⣿⣿⣿⣶⣄⠀ ⢰⣿⣿⠟⠋⠉⠻⣿⡟⠻⠿⣿⣿⣿⣿⠿⠟⢻⣿⠟⠋⠙⠻⣿⣿⡆ ⠸⣿⣿⣶⡄⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⢠⣶⣿⣿⡇ ⠀⣿⣿⡿⠛⢷⣀⣀⣿⣿⣄⠀⠀⠀⠀⣠⣿⣿⣄⣀⣴⠋⢿⣿⣿⡆ ⠀⠈⠳⣤⣠⡾⠛⠋⠹⣿⣿⣦⠀⠀⣴⣿⣿⠏⠙⠛⢿⣤⣤⠾⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠉⠉⠁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⠸⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⡏ ⠀⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⢀⣴⡟⠀⠀⠀⠀⢠⣟⠛⠛⠛⠛⠛⠛⣣⡀⠀⠀⠀⠀⠹⣷⡀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀ ⠀⠀⠉⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⣰⣿⣿⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⣿⣿⡀⠀⠀⣴⣿⣿⣿⣿⣷⡀⠀⣼⣿⣿⣿⣿⣦⠀⠀⠀⣿⣿⡿⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣿⣿⡇⠀⠼⠿⠿⠿⠿⠿⠿⠷⠾⠿⠿⠿⠿⠿⠿⠷⠀⢰⣿⣿⣷⣦⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢁⣹⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⠿⠟⠛⠉⠁⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣾⣿⣆⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠉⠛⠻⠿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡿⠋⣸⣿⣿⣿⣿⡿⠃⢀⣾⣿⣿⣿⡄⠀⠿⣿⣿⣿⣿⣯⠈⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠋⠀⢠⣿⣿⣿⡏⠀⠀⢀⣼⣿⣿⣿⣿⣷⡀⠀⠀⠘⣿⣿⣿⡆⠀⠙⢿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠟⠁⠀⠀⣾⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⢿⣿⣿⣿⡀⠀⠀⠙⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⣸⣿⣿⣿⡇⠀⢠⣤⡀⠉⢻⣿⣿⣿⠋⠀⣠⣄⠀⠘⣿⣿⣿⣧⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠀⢠⣿⣿⠃⠀⢸⣿⣿⣿⠀⠈⢿⣿⣇⠀⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⢸⣿⣿⣿⠂⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⠿⠿⠿⣿⣿⡆⠀⠀⠈⢿⣿⠃⠀⠀⠰⣿⣿⠿⠿⠿⢿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⡀⠀⠀⠘⠉⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠛⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣤⣶⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⠤⠤⣤⣤⣤⣤⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⢿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠈⠋⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⠈⠙⠿⠿⠿⢿⣿⡏⠀⠀⠀⡔⠲⡀⢀⠔⢆⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⢠⠁⠀⡇⡌⠀⢸⠀⠀⠀⢸⣿⣏⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠈⡄⣶⡇⣷⡆⡘⠀⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⠟⠓⠀⠀⠀⢑⣛⣛⣛⡓⠁⠀⠀⠘⠻⢿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡍⠀⢀⡤⠀⠀⠠⣿⣿⣿⣿⣿⠆⠀⠀⠀⣤⠀⢹⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢇⠀⠁⠑⢄⠀⠀⠙⠛⠛⠛⠉⠀⠀⡠⠊⠀⠀⠸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠻⣶⣤⣤⣤⣤⣤⣶⠏⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⡹⡏⠉⠝⠛⠻⢋⢀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⢕⣒⡨⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣀⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣼⣿⣿⣿⣾⣿⠀⠀⣷⡄⠀⣀⣀⣀⡀⣴⠇⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⢿⣿⣁⠀⠀⣨⣿⣉⣿⠯⠽⣯⣻⣦⡀⣀⣴⣾⡧ ⠈⡿⠿⠟⠋⣵⣽⣿⣷⣶⣿⣧⣄⣀⡀⣀⣀⣤⣾⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠛⠉⢉⣁⠀⢀⣀⠉⠙⢿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⡏⠀⠊⢁⣌⠀⠤⠤⠀⠠⡀⠀⢻⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣤⣤⣴⣾⠋⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⣤⣨⡀⠂⠀⠀⠀⠀⠀⠀⠄⣈⣁⣀⡤⠀⠀ ⢀⣼⠟⠁⢀⣞⢿⣟⠀⠀⠀⠀⠀⠀⠀⣾⣿⡍⠉⠻⣶⠀ ⠉⠛⠄⠀⠀⣙⠛⠁⠀⠀⠀⠀⠀⠀⠀⢻⣟⡁⠀⠠⠛⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠿⠋⠁⠀⢀⡀⠤⠤⠐⠒⠒⠒⠲⠤⢄⣀⠀⠈⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣋⣁⣀⣀⣀⣈⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠘⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢻⣿⣿⡿⠘⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⡤⣶⡜⢿⣿⣿⣿⣿ ⣿⣿⣿⡿⠀⢹⣿⣧⣴⣿⣿⣿⣿⣿⠃⠈⢿⣿⣿⣿⣿⠃⠀⢿⣿⡌⣿⣿⣿⣿ ⣿⣿⣿⠁⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⡿⠿⠿⠿⠀⠀⣼⣿⡇⢸⣿⣿⣿ ⣿⣿⣿⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣀⣤⡀⠀⠀⠀⣀⣌⢻⣿⡇⣼⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠻⠾⠇⠀⠀⠀⠿⠾⠃⠙⡃⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠁⢀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣠⣾⣿⣿⢛⡛⣿⣿⣿⣦⠀⢠⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢰⣿⣋⣙⣿⣿⣿⣿⣷⣶⣿⡇⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡛⠿⢿⣿⣿⣿⠿⠟⣫⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿

⣀⣤⣶⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⣦⡀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣷⡄ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠋⠈⠙⠻⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⠿⠋⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠻⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀ ⢠⣾⣿⣿⡿⢿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡄⠀⠀⠀⠀ ⣿⣿⣿⣍⠀⠀⣩⣿⣿⣍⠀⠀⣩⣿⣿⣍⠀⠀⣩⣿⣿⣷⠀⠀⠀⠀ ⣿⣿⣿⣧⣴⣦⣼⣿⣿⣯⣴⣦⣼⣿⣿⣿⣴⣦⣿⣿⣿⣿⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⡀⢀⣿⣿ ⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠀⠀⠘⠿⣿⣿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣷⣦⣠⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣦⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣽⣿⣿⣿⠿⣫⣵⣾⣿⣿⣿⣿⣷⣦⣝⠻⡿⣫⣎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⠟⡱⠘⠻⠿⢿⣿⣿⣿⣿⣿⣷⡾⣷⡿⣿⣓⣷⡀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⢫⠊⠀⠀⠀⠀⠀⠈⠉⠉⡉⢛⣿⣿⣮⣾⡌⢿⣿⣿⣦⣀⠀⠀⠀ ⠀⢸⣿⣿⠣⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⡷⠋⠀⢸⣿⣿⡟⡄⣿⣿⣿⣿⣷⣦⡴ ⠀⠀⣿⡧⠁⣰⠖⠂⠛⢶⣄⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠘⡌⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⣿⡇⢹⣷⡆⠀⠀⠀⠑⡇⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⡏⠀⠀ ⢠⣾⣿⡇⠸⠉⠁⠀⠀⠀⡔⠁⠀⠀⠀⠀⠈⠑⠒⠒⠒⠊⠀⠘⣿⣿⣿⣷⠀⠀ ⢹⣿⣿⡇⠀⠣⣀⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀ ⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀ ⢻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢿⣿⠛⠀⠀⠀ ⠈⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠛⣷⡄⠀⠀⠀⠀⠀⠉⠛⠓⠛⠋⠀⠀⠀⠀⢰⣿⣿⠿⠖⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠁⠀⠀⠀⠀⠀