Dog Lol Funny Meme Haha Cute Emojis & Text

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

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⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠋⠀⠀⠀⠙⠷⠞⠛⠲⠾⠋⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠹⣦⡄⠀⠀⢿⠗⢀⣀⡀⢿⡿⠀⠀⣠⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⡰⠋⢩⣶⡉⢳⡀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⠀⠀⡇⢀⠈⣍⠀⡀⡇⠀⢠⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⠙⣷⣀⠹⣌⡉⠈⣉⡴⢁⣠⡟⢁⣀⣤⣀⡀⠀ ⠀⣰⡟⠋⠉⠉⠻⡏⠈⠑⠲⠭⠭⠴⠒⠉⠈⣻⠛⠉⠀⠉⠻⣦ ⠠⣿⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿ ⠀⢻⣆⡀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⢀⣴⠟ ⠀⠀⠉⠛⣿⡭⠥⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⣩⡟⠋⠁⠀ ⠀⠀⠀⣼⠋⠀⠀⠀⠉⠳⡀⠀⠀⢀⡴⠋⠀⠀⠀⠘⣷⠀⠀⠀ ⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢹⠀⠀⡼⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀ ⠀⠀⠀⠈⢿⣄⡀⠀⠀⠀⣼⡦⠤⣷⡀⠀⠀⠀⣠⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠳⠶⠛⠉⠀⠀⠈⠛⠶⠶⠛⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠒⠤⣄⣀⡤⠤⠤⠤⠤⠤⢤⣀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⢁⡠⠤⠤⢤⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⠋⢁⣀⣀⣀⣉⠙⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠁⡰⠋⠀⢀⣀⣀⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⣁⣀⣀⣀⠈⠑⣌⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⢰⠃⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡄⠘⣆⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡚⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣤⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢀⣀⣀⣀⣠⣶⡆⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠉⠁⠀⠀⠀⠉⠻⡅⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢾⣹⣿⡆⠀⠀⢹⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠶⣄⣉⣉⡴⠀⠀⡼⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⢤⣀⠀⠀⠀⡤⢶⣲⡿⠒⠚⠓⠲⣽⣿⣶⣴⠎⠁⠀⣀⠤⠚⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠉⠉⢻⢳⡿⠋⠀⠀⠀⠀⠀⠈⠉⢻⣿⠓⠊⠉⠁⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠘⡾⠁⠀⠀⣤⣄⣀⣴⣷⠀⠀⢻⡶⠲⣆⠀⡤⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣼⠀⣿⢿⣞⣧⠤⠼⠓⠬⠽⠟⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣦⠀⠙⢆⠀⠀⠙⢤⡽⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠦⣴⣉⣉⣑⣲⡏⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⢀⣠⣾⡓⠒⢊⣹⠧⠤⠦⠤⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⣏⣿⠚⠟⢉⡵⣾⣷⠈⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀ ⠀⠀⠀⠀⢀⣀⣠⡎⠙⠢⠤⣄⣀⣀⣰⣦⣀⠀⠀⠀⠀⠀⣷⣠⣿⠟⢆⠀⠸⣥⣿⠃⠀⠀⠀⡠⠔⠒⠲⣄⠀⠈⡇ ⠀⠀⣠⠞⠉⠀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠈⠉⡟⠒⠒⠋⢛⡉⠙⡆⠀⠙⠒⠛⠁⠀⠀⣠⠊⠀⠀⠀⠀⢸⠀⢀⡇ ⠀⡼⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢰⠋⣹⣴⠇⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⡜⠀⡼⠁ ⢀⡇⠀⡴⠉⠁⠀⠉⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣘⣺⠿⢧⡀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⠞⢀⡴⠁⠀ ⠀⣇⠀⢣⡀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠉⠒⠖⠒⠋⢀⡠⠊⠀⠀⠀ ⠀⠘⢆⠀⠙⢤⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣀⣀⡤⠤⠒⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⠤⣀⠈⠙⠒⠦⠔⠊⠁⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠤⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

🧸🌻✨

⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⢊⠠⠤⢄⢹⠁⠀⠀⠀⠉⠰⣂⣉⠉⣁⢢⠀⠀⠀⠀ ⠀⠀⠀⠰⢠⠁⠐⠆⠘⠁⠀⠀⠀⠀⠀⠀⠑⠂⢀⠀⢡⠇⠀⠀⠀ ⠀⠀⠀⠰⠘⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡊⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⣠⡄⠀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠋⢁⢤⡄⠈⢃⠀⠀⠀⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢇⠀⠤⣉⡡⠀⡜⠀⠀⣠⠁⠀⠀⠀⠀ ⠀⠀⠀⢀⠊⠁⠂⠤⡴⡽⠋⠉⠉⠙⢿⡯⠤⠐⠈⠀⠑⢄⠀⠀⠀ ⠀⠀⢀⠆⠀⠀⠀⠀⠷⠁⠀⡦⣤⣆⠀⢳⠲⣄⠆⠀⠀⠈⡄⠀⠀ ⠀⠀⡘⠀⠀⠀⠀⠄⠘⣄⠀⢣⡿⠓⠉⠁⠈⠁⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⣇⠀⠀⠀⠀⠈⠒⠒⠛⢧⠆⡀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀ ⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢅⣀⢀⣀⢴⡒⡒⠯⠤⠤⢄⠀ ⠀⠀⠀⢸⠢⢀⣀⠀⣄⠀⠀⠀⢰⣨⡾⡈⢰⣹⠇⠀⢀⠤⢄⠀⢡ ⡠⠊⠁⠀⠉⠂⠀⠀⠀⠈⢋⠉⢙⢍⡁⠈⠐⠁⠀⡔⠁⠀⠀⡇⠸ ⠃⠰⠂⠀⠂⢄⠀⠀⠀⠀⠈⢄⣑⠾⢅⠀⠀⠀⢸⠀⠀⢀⠜⡠⠃ ⢆⠐⢄⠀⠀⠀⢣⠀⠀⠀⢠⠎⠀⠀⠈⠑⠤⡀⠀⠉⢉⡠⠊⠀⠀ ⠀⠑⠄⡁⠒⠐⠊⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣌⠙⣿⣿⣿⣤⣀⣀⣀⣴⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣶⣿⣿⣿⣿⣿⣿⣮⣻⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⣶⣤⣴⣿⣿⣿⣿⣋⣽⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠻⣿⣿⣿⣿⣿⣿⣿⣟⣋⣭⣿⣿⣿⣷⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠶⣤⣀⡀ ⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⣤⣶⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣦⣴⣾⣿⡇ ⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⠿⣿⡿⢿⣿⣿⣧⣿⣿⣿⣿⣿⡿⠁ ⠜⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠊⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⡁⠀⠘⠀⢹⠁⠀⢹⣿⢿⣿⣿⡟⢻⡿⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣋⠁⠀⠀⠉⠉⣸⡤⠤⣀⣸⠀⠀⢸⠁⠀⠉⠈⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⡇⠀⠙⠉⠲⡄⢰⡿⠀⠀⠀⠈⡇⠀⡞⠒⠒⢲⠀⠀⡜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠹⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣷⡀⠀⠀⠀⢸⣽⣧⡀⠀⠀⠀⢸⡼⠁⠀⠀⢸⢀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣿⣿⣍⠉⠒⢄⠀⠘⣧⣤⡈⠒⡶⣆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣷⣦⣘⠉⠁⠻⢿⣿⣷⠃⢸⠒⢤⠀⠀⡞⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣼⠃⠀⢠⣷⣦⣧⡜⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣿⣠⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠈⠋⠙⠛⠉⠛⠉⠿⠿⠛⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠁⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⠟⠻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠒⢤⣠⡤⠀⢒⣲⣬⣭⣭⣭⣶⣤⣤⡤⠤⠒⣼⡅⠀ ⠀⠀⠀⠀⠀⠀⠀⠲⡟⣉⣙⣲⠔⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣌⡳⣴⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⣘⠟⠀⠀⠀⢠⡾⠛⢉⠛⡿⡟⡳⢬⣭⣴⡌⠻⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⢞⣭⠀⠀⠀⠀⢸⣇⠫⠉⢓⡶⠃⢉⢶⣭⡽⢀⠀⢱⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⣇⣾⡿⠀⠀⠀⠀⠹⢿⣿⣿⡏⠀⠁⠀⠀⠹⡀⠈⠉⡟⠀⠀ ⠀⠀⠀⠀⣠⣶⠞⣽⣿⡕⣡⠀⠀⠀⢀⣠⣭⣿⠇⠀⡴⣶⢾⣶⡽⡄⠀⡇⠀⠀ ⠀⠀⣴⣿⣿⠇⣸⣿⣿⠞⣡⠞⡄⠀⠞⠻⠿⢿⣧⣀⢻⡏⣾⡿⠇⣷⣾⡇⠀⠀ ⢠⣾⣿⡟⠁⠀⢼⣿⣿⡟⣡⡾⠃⣠⢶⣶⣦⣜⠿⣿⡦⠥⠿⢋⣰⣿⣿⣿⡄⠀ ⢸⣿⠏⣠⡀⠀⣿⣿⣿⣿⣿⡤⣐⡁⢻⣿⣿⣿⡿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⢹⣟⣼⣷⣿⡀⣻⣿⣿⣿⣿⣿⡿⢠⣄⡄⡁⠈⠘⢁⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠨⠿⡿⢿⣿⣷⣿⣿⠿⣿⣿⣟⣴⣼⣿⣇⣷⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀ ⠀⠀⠀⠈⠹⠉⠀⠀⠀⠘⠙⢻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⠿⡿⠇⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠻⠟⢻⠟⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣰⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⣶⣄⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣦⠤⠶⠶⠶⣿⠿⠛⠛⠓⠒⠲⠤⠴⠃⠀⣼⣿⣿⠄⠀⠀ ⠀⠀⠀⢿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀ ⠀⠀⢀⣼⠟⠁⠀⠀⡀⠀⠀⠀⢀⣲⣦⣀⣤⠖⣂⣀⣀⠀⠀⢙⣿⣿⣷⡄⠀⠀ ⠀⠀⣾⠏⠀⠀⠀⠀⠉⠛⢿⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣴⣿⡿⢿⣿⡄⠀ ⠀⣼⡇⠀⠀⠀⠀⠀⣀⣨⣽⣿⣿⠛⠉⠉⠉⣿⣿⣿⣿⣿⠛⠉⠀⠀⠻⣿⣿⡄ ⢰⣿⠀⠀⠀⠀⠀⠛⣻⣿⣿⡟⠙⠇⠀⠀⠀⠟⠛⢧⣝⣿⣷⣤⡑⢦⣀⠹⣿⣧ ⣼⣿⠃⣷⠀⠀⠀⣰⣿⣿⣿⠀⠀⣤⣶⣶⣦⡄⠀⠀⣿⣿⣿⣿⡛⢷⣽⣿⣿⡟ ⣿⣿⢠⡸⣷⡀⠀⣿⣿⣿⣿⠀⠀⠰⠿⠿⠆⠁⠀⢀⣿⣿⣿⡝⣿⣌⢿⣿⡟⠀ ⢻⣿⠀⢳⣿⡻⣄⠸⡿⣿⢻⣷⣶⠀⣀⣀⡀⣶⣶⣿⣯⣿⣾⣿⣞⣿⣾⠏⠀⠀ ⠘⣿⠀⠈⢿⣷⣌⡁⠀⠹⠈⠋⣿⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠹⣧⠰⡄⢪⡙⠿⣿⣿⣶⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠘⢧⠹⣦⡙⢶⣤⣽⣿⣿⠟⡟⣿⣿⠻⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠳⢦⣿⣦⣌⢻⣿⣿⣦⡀⠀⠀⠀⣠⣿⣿⣿⣿⠿⠿⠿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠿⠦⠤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠶⠀⢰⡇⠀⠀⠀⢀⡼⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠚⠻⠄⠠⠤⠤⠤⠴⠂⠠⠴⠿⠛⠂⠀⢠ ⠀⠀⣀⡴⣤⣀⠀⠊⠀⢸⡇⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⣄⠀⠀⢀⡠⠤⠤⢀⣀⠀⠀⠀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣾ ⠀⠘⢻⣴⢻⠋⡆⠀⠀⢸⣿⣀⢀⠀⢻⡄⠀⠀⠀⣀⡴⠞⠛⠉⠉⠉⠉⠓⠲⢏⠀⠀⠀⠀⠒⠂⠀⠀⠀⠒⠀⠀⠀⣠⡄⠀⠀⠀⠀⢸ ⣐⡣⡿⠿⠇⢰⡇⠀⠀⢸⣿⢠⢸⠂⣿⢿⣦⣴⢞⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡶⠒⢭⡉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠤⠖⠒⠉ ⠖⣼⣿⣿⣧⠏⡇⠀⠀⢸⣿⢹⣿⣷⡿⠛⢩⣯⣾⣋⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡿⢼⠟⡟⠀⡇⠀⠀⠸⣿⣎⣿⡏⠀⠀⠀⠉⠛⠛⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⢸⠈⡇⠀⠇⠀⠀⢠⣿⣿⠟⠋⠉⠽⠓⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠔⠿⠥⠴⠶⠶⠶⠆⠀⠠⠦⠄⠀⠀⠀ ⢹⠀⠘⠀⠇⠀⠀⠀⠀⢨⠏⠀⠀⠀⠀⠀⠉⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⡇⠀⡇⠀⢀⡏⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢸⠀⡄⠀⡇⢣⠀⠀⠀⠀⠀⠀ ⣿⠀⢸⠀⣧⣴⣿⣶⣾⣧⡀⠀⠀⢀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠴⠶⠶⣾⠀⡄⠀⣧⣼⠀⠀⢠⡖⠒⠲ ⣿⣀⣸⣿⣿⣿⠟⣿⣿⣿⣿⣦⣄⣨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣯⡀⠀⠀⠈⠻⠷⠶⠿⠙⠋⠉⠙⠁⠀⠀ ⣿⣿⣿⣿⣭⣍⣴⣿⣿⡟⠛⢛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡟⠛⠻⣿⣿⠿⠿⠚⠉⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣶⣶⣶⣿⣧⣤⣤⣤⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣸⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣻⣿⣿⣟⡛⡛⠻⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⠀⣀⣴⡏⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣛⣛⣻⣿⣿⣿⣿⣿⣿⣛⡛⡻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⠧⠿⠋⠀⠀⠀⢠⣿⣶⡶⡶⠶⠶⢷⢶⣶⣶⣶⣶⠶⠶⠶ ⠉⢉⣙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣻⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣟⣻⣛⣻ ⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠻⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠾⠿⠿⠏⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠉⠙⢺⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣄⡔⠀⠀⢈⣇⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠿⠦⠧⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⢀⣀⡀⣀⣠⣤⣤⠶⠶⠒⠒⠛⠛⠻⠷⠶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢖⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣫⣁⠀⠉⠛⣷⣦⣶⠾⠋⠉⠡⠤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢷⣶⠶⠶⠚⠉⠀⠀⣽⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣿⡿⠟⠛⠷⢶⣤⣄⣀⣀⠴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠘⢷⣄⠀⣠⣶⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⢤⣤⣶⣶⣶⠿⠋⠁⠀⠁⠛⠿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣈⠻⣷⣿⣿⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢿⣿⡿⠂⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠿⠛⠻⣿⣿⣿⡿⣿⣿⣿⣇⠈⠉⠛⠋⣁⣀⠈⠻⢿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠁⠀⠀⢠⠈⠙⢿⠇⡏⠘⣇⠙⠲⢶⣶⣿⣛⣛⣧⠄⠀⠙⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣰⡟⠻⠃⡆⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠐⣶⠚⠋⠉⣳⣦⣬⣴⣇⡀⠉⠳⢦⣴⠟⠛⠉⣿⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⣡⣼⣾⡄⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⣆⣈⡛⠩⠉⠁⣨⡿⠟⢁⣀⠀⢠⠞⢿⣷⣶⡾⠛⢺⢤⢀⢀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡾⠀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣾⠏⠀⠐⠋⠉⠂⠀⠀⠈⠻⡿⠁⠀⠀⠘⠛⠹⢼⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⣤⣽⣿⣿⠟⢀⠄⠀⠀⠀⠀⠀⠀⠀⠚⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣠⣴⣿⠇⣼⣿⡿⢋⣴⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⣩⣸⣿⠀⠀⠀⢀⣠⣤⣴⣶⣶⣦⣄⠹⣷⡀⠀⠀⠀⣽⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠟⢁⣾⣿⣿⣷⡿⢁⣰⡟⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣿⣿⣿⡋⠀⠀⢠⣿⠛⣿⡿⠻⣿⣿⣿⣷⠹⣷⠀⠀⢀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠃⠀⣾⣿⣿⣿⣫⣴⣿⠏⢀⣴⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⢂⠀⠀⢿⣿⡟⢳⣶⣿⣿⢻⣿⠀⢹⡶⣠⣸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⡟⠃⠀⢰⣿⣿⣿⣿⣿⡟⢁⣴⣿⠏⢀⣼⡆⠀⠀⠹⠇⠁⠻⠙⠟⠇⣿⣿⣿⢠⣄⠈⢿⣿⡄⣿⣿⣿⢸⠇⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⣿⠟⠁⣠⣿⡿⠃⠀⢀⣠⣤⣤⣤⣄⣀⠀⢻⣿⣿⣿⣿⣦⣈⠛⢃⣿⡿⠿⠂⠀⣠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢫⣿⣿⣿⣿⣿⡟⢁⣠⣾⣿⠟⠁⠀⣰⡿⠛⣿⣿⣿⣿⣿⣯⡬⠛⠿⠿⠿⠿⠿⠿⠿⠛⠷⠶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⢸⣿⣿⣿⡿⠋⠀⠀⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⠖⠂⠀⠼⠋⢀⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣶⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀ ⢸⣿⣿⣿⠟⠀⣰⡞⢠⠂⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣋⣠⣤⡄⠈⠰⢻⡿⣿⢿⣿⠿⣻⡿⢛⣽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⢸⣿⣿⡟⢀⣾⣿⣱⣿⡞⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⠇⠀⡀⠀⠀⠁⠚⠁⠘⠋⢠⡾⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡀ ⠼⣻⣿⢡⣿⣿⣿⣿⣿⣷⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣾⣿⣀⡿⠀⣠⠄⠀⠀⠀⠀⠀⣤⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠣ ⠀⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣠⡄⣿⣿⣿⡇⢠⣿⡀⣾⢣⣾⣰⣆⢿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⠃⠀ ⠀⠺⠟⠋⣿⠟⠛⣽⣿⣿⣿⣿⣿⣿⢿⡿⠋⠘⣿⣿⣿⣿⣿⣇⣾⣿⣷⣿⣿⣿⣷⣄⢿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠉⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠟⠛⣿⠟⠋⠀⠀⠀⠀⠀⠀⠈⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠹⢿⣿⡝⠿⣇⠙⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠻⣿⣿⠿⣿⣿⡿⢻⣿⣿⠋⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠘⠋⠀⠈⢿⠇⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣻⡟⠁⠂⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⠒⠒⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⢀⡼⠟⠛⠛⠛⠷⣦⡇⠀⠀ ⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⠀⡼⠟⠹⡄⠀⠀⠀⠀⡄⠹⣆⠀ ⠀⠀⢀⠏⠀⠀⠀⠀⣀⣴⣤⣖⣲⡤⠤⠒⠉⠁⠀⠀⠀⠀⠠⢤⣏⣴⠶⠟⠢⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⡀⠀⠸⡀⠀⠀⠀⡇⠀⢹⡇ ⠀⢀⠎⠀⠀⠀⣠⢊⠁⡄⠙⡳⢤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⢦⡴⢳⣀⡤⠃⠀⠀⠈⣷ ⠀⡞⠀⠀⠀⢀⡇⠀⠀⡇⠀⡰⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣿⠯⣷⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢣⠻⡉⠉⠓⢄⡀⠀⢸⣿ ⠞⠀⠀⠀⠀⠈⡇⠀⢠⡘⣴⠷⠊⠁⠀⠀⠀⠀⠀⠀⠀⢸⠟⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⢧⠙⡆⠀⠀⠙⣶⣄⣙ ⠀⠀⠀⠀⠀⠀⢣⠀⢀⡝⠁⠀⠀⠀⠀⠀⢀⡄⠀⡀⠀⠘⡄⠀⠀⠀⠀⠀⢸⠀⢠⠤⠤⠤⠄⣠⠀⢃⠀⠀⠀⠸⠀⢹⣀⠴⡎⠈⠻⠿ ⠀⠀⠀⠀⠀⠀⠈⢳⣏⣴⠂⠀⠀⠀⠀⢀⣞⠀⠀⢹⣤⡄⢳⠀⠀⠀⠀⢀⡇⡰⣷⠀⡇⠀⡠⢻⢉⣇⠀⠀⠀⠀⡇⢸⡇⠀⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⢋⡏⡀⠀⠀⠀⢀⣾⡿⢦⡀⠈⣏⢸⠦⠷⢄⠀⠀⠞⠋⢠⣿⣼⣷⣮⣥⣾⠉⢸⣠⡇⠀⠀⢁⡄⢣⠀⠸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⡇⠀⠀⠀⣸⢻⣧⣴⣿⣷⣯⣿⡆⠀⠀⠀⠀⠀⠀⠛⠛⣡⣤⣤⡈⠛⢷⣞⣿⠀⠀⠀⠈⡆⢸⠐⠋⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣧⡀⠀⠀⢹⣤⣿⠟⢉⣥⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠈⢿⣧⠀⠀⠀⢰⠃⣾⠀⠀⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠞⢧⡈⢳⡀⢀⣈⣿⡏⠀⣼⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⠟⠀⠀⣻⢃⡀⠀⢠⡟⢠⣿⠀⠀⡟⢣⡀ ⠀⠀⠀⠀⠀⠀⠀⡜⠀⡼⠓⣄⠙⢾⣿⣿⠃⠀⠘⠿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠉⠀⠉⣩⠷⢚⡉⢳⡾⠉⡆⠀⣷⣾⣿ ⠀⠀⠀⠀⠀⠀⡸⢀⡜⠁⠀⠈⢦⡞⠘⢾⣆⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⣿⡄⢇⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣧⠎⠀⠀⠀⠀⣼⠃⠀⢸⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣠⠏⢠⠃⡇⢸⠀⢹⣿⣿ ⠀⠀⠀⠀⠀⡼⢁⡴⠀⠀⢀⠞⡟⠀⠀⠈⢧⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡉⢉⣁⣴⡿⠀⡇⠀⡄⢸⣿⣿ ⠑⠦⣀⢀⣴⠵⠋⢀⣠⠔⠉⢸⠁⠀⠀⠀⠀⠙⠻⢦⣀⣠⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⣸⣿⡟⠻⣿⡇⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠈⠻⢇⣤⠖⠉⠀⠀⠀⣾⠀⡠⠤⣄⡤⠤⠤⣔⠋⢀⣠⣤⣤⣀⣉⠆⠀⠀⠀⢀⣠⠴⣿⢃⣽⣿⣿⡃⢠⣿⡇⠀⠠⠀⠀⠘⣿⣿ ⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⣼⠋⠉⢇⠀⠈⢷⣄⠀⠈⢦⠞⠁⣸⡟⠲⠤⢤⠤⠴⠒⠉⠀⠘⣿⣿⣿⣿⣿⣷⣸⣿⠀⠀⠀⡇⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢦⡀⠀⢢⡀⠀⠻⣦⠀⠈⢳⣴⡏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⣿⣿⣿⣿⠀⠀⣸⡇⠀⢀⢹⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠴⢷⣄⠀⠙⣷⣀⢀⣿⡇⠈⠳⣄⠀⠀⠀⣀⡠⠤⠀⢻⣟⠑⢶⠲⣬⠛⠯⣄⣴⡿⠃⠀⢸⠘⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⠀⠈⠉⠀⢹⠀⠀⠈⠓⢤⣉⠀⠀⠀⢀⠞⢹⡀⠈⡇⠹⣶⡄⠈⠉⠀⠀⠀⣿⠀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠈⠙⠢⣤⠋⠀⠀⡇⠀⠸⡀⠈⢿⡄⠀⠀⢀⣼⡇⣠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⠲⢄⠀⠀⠀⠀⠀⡏⠳⡄⢀⣿⠀⠀⢣⠀⠀⠙⢦⣾⣩⣽⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠟⠛⠛⠿⣿⣦⡀⠀⣀⣀⣀⠀⠀⣠⣶⣿⠿⠿⠿⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⠿⠿⠿⠿⠿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠈⠛⠛⣃⣤⡴⠶⢦⣤⣘⠛⠛⠁⠀⠀⠀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⡾⠋⠀⣴⣶⣦⠈⠙⢷⡀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⢀⣿⠀⠀⠀⠿⠿⠟⠀⠀⠈⣿⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠘⣿⠀⣤⡀⢀⣶⡀⠀⣠⠀⣿⠁⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀⠀⠻⣦⡈⠙⠋⠀⠙⠛⢁⣼⠏⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣴⣶⣶⣶⣶⣤⣨⣿⡿⣦⣀⠉⠻⢶⣤⣤⣤⠶⠛⠁⣠⣴⢿⣿⣅⣤⣶⣾⠿⠿⣷⣶⣤⡀⠀⠀ ⠀⣰⣿⠟⠋⠁⠀⠀⠉⠻⣿⡉⠀⠀⠉⠛⠷⠶⠦⠤⠴⠶⠾⠛⠉⠀⠀⠉⣿⠟⠁⠀⠀⠀⠀⠉⠻⣿⣆⠀ ⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄ ⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀ ⠀⠘⢿⣷⣦⣄⣀⣀⣤⡶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⣴⣾⡿⠋⠀⠀ ⠀⠀⠀⠈⠙⢻⣿⣉⣡⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⣿⡟⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⡿⠋⠁⠀⠀⠉⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠁⠉⠙⢻⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣶⣶⣿⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣤⣀⣠⣴⣾⡿⠉⠀⠀⠈⠻⣿⣦⣄⣀⣀⣤⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢀⠖⠁⠀⠀⠀⠀⠈⠢⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠊⠀⢠⠗⠒⠠⠤⠐⠀⠉⠐⡨⠄⠠⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠊⢀⠀⠰⠘⡜⠑⡲⠊⠀⠀⠀⠀⠈⠒⠠⡘⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠃⠀⠂⠠⠃⠀⢸⠊⠁⠀⠀⢀⡄⠀⠀⠀⠀⠀⠈⡞⠄⠀⠀⠀⠀ ⠀⠀⠀⡘⠀⢸⠀⠀⠀⠀⠸⣀⠀⠀⣀⠈⠁⢀⣀⠀⠀⠀⠠⠃⠘⡄⠀⠀⠀ ⠀⠀⢀⠇⠀⠸⡀⠠⠀⠀⠀⠈⢆⠀⢩⠁⠀⠀⡄⠀⠠⠞⠁⠀⠀⠇⠀⠀⠀ ⠀⠀⡸⠀⠀⠀⢣⠀⠆⠀⠀⠀⠀⠑⢶⣀⠠⢀⢰⡐⠁⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠇⠀⠀⠀⠀⠱⣰⠀⠀⠀⠀⠀⠀⠳⢥⠦⠊⡀⠀⠀⠀⠀⠀⠈⢆⠀⠀ ⠀⢰⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢀⠐⠊⠰⠀⠀⠀⠀⠀⠀⠈⢇⠀ ⠀⠘⠀⠀⠀⠀⠀⠀⢀⠜⡄⠀⠀⠀⠀⠀⢘⠀⠀⠁⠣⡀⢀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠀⠀⡠⠊⠀⢣⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⢈⠞⠀⠀⠀⠀⡸⠀ ⠀⡇⠀⠀⠀⢀⡔⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⢂⠀⠆⢰⣧⠀⠀⠀⢀⠔⠁⠀ ⢸⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢂⢰⠀⠀⠑⠑⠒⠊⠁⠀⠀⠀ ⠉⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠓⠀⠀⠤⠤⠼⠾⠀⠀⠀⠀⡤⠠⢤⣶⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣿⣿⣿⣦⣾⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⣋⣽⡟⢉⣷⠞⠉⠀⠺⠛⠛⣻⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣒⣯⣵⠖⠛⢉⡠⠤⣾⡟⢀⠀⠀⠀⠙⣧⡻⢟⣿⡿⣶⣦⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢒⡿⠛⠉⠉⠋⠁⠀⢰⣿⠁⢀⣿⠁⣿⡄⠀⠺⣿⣤⠉⣁⣀⠀⠀⣹⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣳⣾⡟⠀⠀⠀⠀⠀⣸⡇⢸⣿⡀⠈⠿⣧⣌⠙⠳⠀⠈⠁⣼⡟⣿⠟⠿⠛⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢑⣿⡿⠁⠀⠀⠀⠀⠀⢻⣇⠈⠹⣷⣄⠀⠈⠛⠣⣀⣀⢀⣄⣋⣑⡛⠛⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⠏⢉⣁⣠⡤⠤⢤⣀⡠⣿⡿⠀⠀⣦⣍⣷⣦⣶⣾⡿⠿⠟⠀⠀⠁⠈⠙⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣷⡀⢾⣤⡀⠉⠀⠀⠀⠀⢍⡛⢧⡀⠀⠈⢡⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⠻⣷⣄⣉⣛⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠒⠻⢿⣿⡟⠃⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢿⣏⣿⣦⣍⡛⢻⣛⠛⡛⠛⠉⠀⠀⠀⠀⠀⢀⣴⠾⢚⡿⠷⠤⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⢸⣏⢹⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⠲⠷⣄⠀⣡⠾⠋⢡⡘⣦⣧⡙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠗⠁⠀⠈⢿⣆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣨⡷⢦⣴⣽⣶⣿⠟⠋⠻⣦⡝⠢⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣫⠄⠀⠀⠀⠈⠻⣦⠸⡿⢿⣿⣿⣿⣿⣿⠙⠻⠿⣿⠟⢳⣾⣿⣿⣿⣶⣒⡀⠀⠀⠛⢧⡀⠙⢆⠀⠀⠀⠀ ⠀⠀⠀⣽⣡⠂⠀⠀⠀⠀⠀⢻⣄⠘⣄⠉⠛⠻⣿⡟⠀⠀⠀⡀⠀⣸⡅⠀⠙⠿⣿⣿⣿⣧⣤⠀⠈⢻⣆⢸⣄⠀⠀⠀ ⠀⠀⠀⢹⢇⠀⠀⠀⠀⠀⠛⢿⣿⠳⢼⣶⣤⡶⠀⠀⠀⠀⣰⡿⠐⢿⡇⠀⠀⠀⠈⠉⠻⢿⣿⣿⣧⣄⠉⠀⠉⠳⡄⠀ ⠀⠀⠀⢸⠸⣷⡀⠀⠀⠀⠀⠀⠙⣦⡈⣿⡋⠀⠀⠀⢀⣠⡿⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣷⣦⣄⡀⢧⠀ ⠀⠀⠀⢸⡄⠙⢿⣄⠀⠀⠀⠀⠀⠈⢻⣽⣷⣤⡀⠀⠞⠋⢀⢀⣀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⡇⣸⠀ ⠀⠀⠀⢠⣧⡀⠀⢙⠛⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⣄⣼⣿⡟⠋⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠛⠁⠀ ⠀⠀⠀⠈⣿⠇⠀⢾⣤⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣿⡤⠀⢸⡟⠀⠀⠀⠀⢠⣾⢻⣿⣿⣿⣿⡿⠟⠠⠤⣤⣀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣽⠁⣠⠏⠀⢾⣧⣤⣾⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣥⣄⣠⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡾⢁⣼⡏⠀⠀⠀⠀⠀⣼⡿⠋⠛⢿⣿⢿⡯⠤⠤⠖⠚⠉⠉⠙⠛⠃⣠⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠟⠁⠸⠿⢟⣠⣄⣠⣴⣿⢧⡀⠀⠀⠀⢀⡞⠀⠐⠀⢀⣴⡤⠤⠤⢴⣾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⠀⠀⠀⠀⠈⠹⠽⠻⣉⢻⡓⣾⣦⠀⠀⠘⠧⣄⣀⣀⣈⠀⣀⣀⠀⠀⠉⢹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠦⠤⠖⠒⠒⠲⠦⠤⣾⣾⣽⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⡲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⣠⢊⣀⡀⠀⠀⠀⢀⣀⠤⠤⠤⠤⣀⠤⠚⠉⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⡟⠉⠀⠉⠙⠒⠲⠁⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⡜⠀⡇⢏⠓⠦⠤⡴⠃⠀⠀⠀⡆⠀⠀⠀⠙⠲⠤⣀⠀⠘⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡴⠀⠀⡸⠁⠀⠸⡌⠁⣠⠞⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢰⠁⠀⠠⠇⠀⠀⠀⣧⠈⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠱⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠘⠤⡀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠘⠀⡜⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠇⠀⠀⠘⣇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠙⠛⠁⠀⠀⠀⢩⠁⠀⠀⠀⢠⣮⠎⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢻⡄⠀⠸⡇⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢿⠀⠀⠀⠀⠘⡄⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢳⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⠑⢾⡞⠀⣀⣄⣀⡀⢹⢃⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠳⡄⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣠⣤⣤⢃⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠟⠋⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠐⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢠⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡎⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢳⠀⠀⠈⠳⣄⡰⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⡆⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀ ⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢰⠃⠀⣤⣏⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀ ⠀⠀⡿⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡇⠀⠀⢻⡿⣦⡀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀ ⠀⢰⡇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠁⠀⠀⠀⠉⠉⠙⠓⠚⠋⠁⠀⠀⠀⠀⠀⠀ ⠠⠼⠥⠤⠤⠤⠤⠤⠤⠧⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠒⠒⠒⠒⠛⠛⠃⠀⠀⠀⠀⠀⠀⣿⠿⠸⠿⣿⣿⠇⠀⢀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢶⡶⢴⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣔⡾⠕⡛⣼⠏⠀⠈⢅⡯⢷⢤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⢀⣒⡼⠉⠉⠉⡄⣾⠀⣾⠸⢄⠘⠷⣩⣤⣀⡽⠁ ⠀⠀⠀⠀⠀⠀⢠⢪⡿⠀⠀⠀⢐⡇⠙⢦⡈⠛⢆⣀⣀⣛⣛⢢⠀⠀ ⠀⠀⠀⠀⠀⢠⡖⣥⡒⠒⠀⠒⡸⣇⠀⠓⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢷⡻⣮⣭⣀⣀⠀⠈⠉⠁⢈⣻⣟⠉⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⢹⡛⣿⣶⣶⣶⣶⣶⡦⠦⡀⡫⠖⠕⣼⡡⡀⠀⠀⠀⠀⠀ ⠀⢐⡋⠀⠀⢳⡘⣿⣿⣿⣿⡿⣧⣤⢾⣵⣿⣟⠉⠙⠲⡕⠠⠀⠀⠀ ⠀⢸⠄⠀⠀⢀⣣⡐⡌⠛⠿⠃⠀⡄⢨⡄⠙⠻⢿⣧⣄⡙⠆⠧⡀⠀ ⠀⢸⢦⡀⠀⠀⠙⣌⣛⠋⠀⢀⣰⠇⢸⡇⠀⠀⠀⠉⠛⠻⣦⣀⡸⠀ ⠀⢸⠈⠳⠄⠀⠀⠈⢻⣷⣦⡈⣡⡤⠞⢤⠀⠀⠀⠀⠀⠀⠙⢿⠵⠀ ⠀⠨⡇⠐⡦⠀⠀⠀⣠⣿⣿⣿⡟⠁⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢈⡏⡠⠣⣄⣠⣞⣿⣿⣿⣯⣥⣽⢓⣀⡀⢸⡄⠀⠀⠀⠀⠀⠀⠀ ⢠⠞⣼⡅⠀⢀⣴⠛⠉⠛⡻⠒⠒⢉⠀⢉⣡⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠉⠿⢫⢳⣵⡄⠀⠣⠄⠠⠭⠄⣀⣉⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠶⠶⠤⢤⣤⣄⣀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⢮⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠻⣦⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠚⣇⠀⠀⢀⡟⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⣠⠞⠀⠀⠘⣧⣼⠁⠀⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⡤⠒⠂⠀⠀⠀⠀⠀⠹⣿⣿⡄⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠛⠁⠀⠀⠀⢀⣾⠃⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣍⣁⣀⣠⡴⠞⠋⠀⠀⠀⠙⣿⡇⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢠⡶⠶⠶⠋⢸⠀⠀⠀⠿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣀⡤⢶⣶⡴⠲⣦⢤⣀⡀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠋⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⣠⡴⠻⠋⣠⠞⠁⠀⠀⠉⠛⠲⢤⣀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣠⡴⠛⠁⣀⣤⢾⣏⠉⠀⠀⠀⠀⠀⢸⣄⠀⠀⢠⡀⠙⢷⣖⡿⢷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⣠⡾⠛⠒⣶⣫⡟⠙⠀⢻⠀⠀⠀⠀⠀⠀⢸⠹⣦⠀⠈⠻⡄⠘⣾⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⠞⠁⠀⢠⣾⣽⣏⣀⣤⣤⣸⡆⠀⠀⠀⡀⠀⢸⣠⣼⣧⡀⠀⠸⣆⠈⢿⣿⣻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀⠀⠀⢠⣿⡿⠀⣠⣴⣿⣟⣥⣤⣤⣤⣤⣬⡇⠀⠀⢀⡇⢀⣿⣿⣿⣿⣿⣦⣀⣹⡄⠸⣏⡽⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⠟⠛⢿⠇⠀⠀⣼⠃⢸⣿⣿⣿⣿⣟⠙⣻⣿⣿⡆⠨⠻⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢸⠇⠀⢸⣿⢸⡇⢸⠛⣿⣿⣿⣶⡔⣂⣠⣴⡿⠀⣴⣼⡏⣠⡟⢻⡛⠻⠿⣷⣾⣿⣿⠹⢿⡄⠀⠙⣷⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⢠⣽⡿⢸⠁⢸⠀⣿⢙⣛⡉⠉⠉⣠⠞⢁⣾⢟⣿⠟⠉⢳⣤⡇⠀⠀⠀⠀⡇⠹⡆⣴⣧⠀⠀⠙⣷⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⣸⡿⣇⢸⠀⢸⠀⢹⣾⠿⡇⠠⠾⣿⡞⠉⠈⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⡇⠀⡇⡿⢸⡆⣠⠾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢹⠀⢿⣷⣿⡘⣇⠸⡆⠈⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⣿⠇⢸⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡄⠀⠀⠀⠀⠀⢾⢿⣿⡇⢹⠀⢣⠀⢹⠀⢹⡆⠀⠀⠀⠀⠀⢀⣀⣤⣶⠶⢶⡤⠀⠀⣰⠋⠀⣾⠏⣸⠞⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠹⣦⠀⠀⠀⠀⠈⠈⣿⣧⡈⠀⠀⠀⠈⠇⠀⠙⠲⣤⡀⠀⠀⠈⠉⠑⠂⠀⠀⠀⣠⡾⠁⠀⣴⠃⣰⢯⢃⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⢦⡀⠀⠈⢧⠀⠀⠀⠀⠀⠈⣯⡙⠶⣦⣄⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⠀⠀⠀⠀⣠⠞⠋⠀⠀⣼⣣⡾⠁⠛⢾⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠈⠻⡄⠀⠸⡇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠉⢛⣶⣤⡀⠀⠀⠀⠀⠈⢻⣿⡟⠒⠛⠓⠒⠒⠒⠚⣻⡟⢷⡀⠀⠀⠈⠳⠤⣀⠀⠀ ⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢳⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢈⣽⡆⠙⠛⠓⠒⠒⠒⠚⢿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠙⠛⠿⣦⡀⠀⠀⠀⠈⣿⠀ ⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠸⡆⠀⠀⠀⠀⠀⠀⢹⣇⠀⠈⢿⡄⠀⢠⡀⠀⠀⠀⠀⢘⣿⠇⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠈⠻⣶⣤⣤⡴⠟⠀ ⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢀⡿⠀⠀⠱⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⠀⠀⠮⢳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠸⣧⣠⡴⢇⠀⠀⢠⠀⠀⠀⠀⢸⡿⠦⡀⠀⠀⠀⠀⠐⠛⠓⠙⠀⠀⠀⠀⠀⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⢀⠀⠀⠄⢠⡄⠄⡄⢿⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠶⢤⣀⡀⠀⠀⣸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠒⠓⠂⠐⠐⠚⠒⠛⠓⠛⠛⠀⠙⠧⣄⠀⠀⠀⠀⣿⡇⠠⢤⣀⠀⠀⠀⠈⠛⠋⠁⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣷⣹⣿⣶⣤⣾⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⣦⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣷⣾⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀ ⠀⣨⣿⣿⣿⣿⡟⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢟⣛⣿⣿⣿⣿⣿⣟⣶⡦ ⠴⠿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⢹⠛⣿⣾⡿⣿⠃ ⠀⠀⠘⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠋⠤⠀⢸⠂⠚⡀⠅⠀⠀⠇⠀ ⠀⠀⠀⢻⣿⣿⣿⣄⠉⢿⣿⣿⣿⣿⣿⣿⡼⣿⡣⠀⠀⣟⠠⣄⠐⠀⠀⠐⠀⠀ ⠀⠀⠀⠸⠻⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⣙⡿⠈⣔⣄⢡⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣮⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠉⠛⠻⠿⠿⢻⠿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀ ⠀⣀⡤⢀⡠⠔⠂⠉⠉⠁⠒⢡⡄⠘⠄⠀ ⠰⡁⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⠀⠀ ⠀⠑⠰⠀⠀⠀⠠⡄⠠⠖⣴⠖⠀⢠⡀⠀ ⠀⠀⣀⠀⠉⠟⠃⢀⠳⠃⠰⠄⠀⠀⡟⠀ ⠀⠀⢯⡀⠀⠠⠒⡅⠂⡔⠀⠀⣀⡦⠄⡄ ⠀⠀⠀⠀⠂⢀⣐⠂⠀⠒⠈⠇⣉⠀⠉⠀ ⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢈⠁⠀⠀⠀ ⠀⠀⠀⠚⠂⠀⡇⠀⠀⠀⠀⠀⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠁⠀⢠⣤⠠⠤⡀⢢⠀⠀ ⠀⠀⠀⠀⠀⡘⢀⠃⠀⠀⠀⠀⠑⠤⠇⠀ ⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⠀⡑⠀⡇⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠐⠒⠒⠁⠒⠋⠁⢠ ⢀⢻⣾⢳⠀⢀⡧⢀⢸⡄⠀⣀⠔⠚⠉⠘⠒⠺⡁⢀⣙⣂⣀⣙⣉⣁⠍⠉⠉⢹ ⢖⣯⣥⢾⠀⠀⡇⣼⡼⠝⣟⣗⠀⢀⡀⠀⠀⠀⠘⢉⠇⠀⠀⠀⠀⠀⠀⠈⠁⠀ ⡾⢺⠍⢸⠀⠀⣷⣿⠡⣄⡈⠉⠀⠈⠀⠀⠀⠀⠀⠀⢣⢀⣀⣀⣀⡀⠀⣀⠀⠀ ⠃⠀⠀⢀⠀⢠⠋⠀⠀⠐⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⣄⠀⠀⠀⠀ ⡆⢀⢸⣸⣤⣦⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⢤⡇⡀⣇⡆⠀⡤⠤ ⣧⣼⡿⠟⣽⡿⢷⣦⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠄⠀⠉⠓⠚⠉⠉⠁⠀ ⣿⡿⠛⢻⡿⠷⠒⡙⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡷⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⣿⣿⣿⡷⠶⢶⡇⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⣰⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠭⢽⡿⣿⠿⠯⢭⣧⠀⠀⠀⠀⠀⠀⠀⠈⠚⠚⠁⠀⢠⣿⣷⣾⣿⣿⣿⣷⣾⣶ ⠀⠛⠛⠛⠛⠛⠛⠻⢷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠗⠋⠉⠙⠋⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠐⠂⢤⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠴⠤⢼⣄⣄⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⠿⠷⠶⠶⠶⢦⣤⣤⣤⣀⣀⡀⣴⡿⠁⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠉⠉⠛⠻⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠏⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣤⡀⠀⠀⢀⣤⣤⣤⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⡋⠀⠀⠀⠀⠀⠀⠐⢶⣤⣀⣀⡀⠀⠀⠀⠙⢶⣶⣿⣿⣿⣶⣾⣿⣟⣉⣤⣤⣤⣶⣶⣤⣤⣤⣀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣷⣶⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡿⠟⠛⠉⣡⣾⣿⣿⣿⣆⠀⠀ ⠀⠀⢰⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣙⣻⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣄⠀ ⠀⢀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠿⣿⣿⣿⣷⣄⠀⠀⠀⣄⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⡀ ⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠛⣻⣿⣿⣿⣿⣿⡟⠁⢻⡿⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⢿⣦⣈⠛⢿⣿⣿⣷⣦⣀⠉⠻⣦⣄⠀⠀⠀⣿⣿⣿⣿⡇ ⢠⣿⣿⡇⣀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣿⣿⣿⣿⣿⣷⣦⣀⠙⢿⣶⣶⣬⣿⣿⣿⡇ ⣸⣿⣿⣿⡟⠀⢾⣷⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⠃⠀⢸⣿⣧⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠟⢛⣿⣿⣿⣿⡟⠻⠟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣎⢻⣿⣷⣄⠈⢿⣿⣿⣿⣿⣿⣿⡟⠀ ⣿⣿⣿⣿⠀⢆⠀⢿⣿⣷⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⣿⣿⣧⠹⣿⣿⣧⡀⢻⣿⣿⣿⣿⠟⠀⠀ ⢿⣿⣿⣿⠀⠸⣷⡜⣿⣿⣿⣄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣷⡘⣿⣿⣧⡘⣿⣿⣇⢨⣿⣿⡿⠋⠀⠀⠀ ⢸⣿⣿⣿⠀⠀⢹⣿⣿⣿⡹⣿⣧⡀⠀⠻⡏⢻⣿⣿⠛⣿⣿⣿⣿⣿⠃⠀⠀⣀⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣷⢹⣿⣿⣾⣿⡟⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣎⠛⠿⡆⠀⠁⠀⢿⡇⠀⢹⣿⢿⣿⣿⡀⣾⣿⣿⣿⣿⣿⡄⣸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⡀⠀⠀⠀⠻⣿⣿⣿⣷⣄⣀⠀⠀⠀⠈⠗⠀⠘⠏⠈⢿⣿⣷⣹⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⣷⠀⠀⡀⠀⠈⣛⠿⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣇⠀⠹⣦⡀⠘⣦⡀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣆⠀⢻⣷⣄⠈⠻⣷⣤⣀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣦⡀⠛⢿⣷⣄⠈⠻⢿⣿⣷⣶⣽⣿⣿⣿⣿⡟⠸⣿⠙⣿⣿⣿⣿⠏⠻⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠙⢿⣷⣦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣄⠀⠋⠀⠈⠉⠉⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⣾⣿⣿⣿⣷⣄⠙⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢀⣠⣾⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⠉⠉⠉⠉⠛⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠋⡹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⣀⡀⣀⡤⠞⠋⠉⠉⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⢼⡵⠛⠉⠓⠒⠦⣤⣀⣴⠚⠉⠁⠀⠀⠀⠀⠈⠁⢠⡤⠴⠒⠢⡄⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⢠⠀⣿⢀⣤⣀⠀⠀⠀⠀⣀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⠀⠀⠀⠀⢰⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢀⡏⠀⢻⡈⣦⠈⠛⠶⢶⡶⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠲⠦⣀⠀⠈⠣⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⡴⠀⠀⠀⡞⠀⠀⠀⢣⠈⠃⢀⣠⠞⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣄⠀⠀⣯⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣸⠁⠀⠀⢸⠃⠀⠀⠀⠈⣇⠰⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⣧⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡿⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣄⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⢸⠁⢀⡾⠁⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠐⠿⡿⠇⠀⠀⠀⠀⢛⡛⠋⠀⠀⠀⠀⠀⣼⣢⠎⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢀⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⡀⣿⠀⠀⠀⠀⠀⠀⠹⣄⢀⠀⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣽⡟⠀⠀⣀⣀⡀⢀⠀⣹⠃⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣞⠋⡅⠀⠈⡟⠀⣷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣿⣛⣛⣿⣣⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠛⠋⠁⠀⠀⡼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠊⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀ ⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⠁⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠘⢷⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⠀⠀⠀⠀⠙⢧⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀ ⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⡿⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⣼⠁⠀⢀⣟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡟⠀⠀⠈⢻⡽⠳⣦⡀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⠁⠀⠀⠀⠀⠉⠛⠉⠛⠶⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⣷⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢸⣶⡾⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⡤⡄⢀⡀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢉⠉⠁⠀⠀⠀⠀⠀⠀⠨⣿⡻⠇⠋⠗⣻⣟⣧⠇⠸⠠⣜⠃

︵‿︵‿୨♡୧‿︵‿︵

⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠆⢩⠋⠢⠀⠑⠢⡁⠢⡀⠀⠀⠀⠀ ⠀⠀⡜⡌⠀⠊⢀⢆⢡⠀⠀⠈⢄⠙⡀⠀⠀⠀ ⠀⢰⢰⠒⠂⠉⠉⠘⠉⠉⠉⠉⠎⡄⢱⠀⠀⠀ ⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⢈⡀⠀⠀ ⠀⡇⢋⠀⠀⣤⠀⠀⠀⢤⠄⠀⢸⠀⠀⡇⠀⠀ ⢠⢳⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⠀ ⠀⣿⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⠀ ⠀⠹⡾⠳⢒⢒⡖⣶⣴⣿⢟⣿⠻⠀⠠⡇⠀⠀ ⠀⠀⠱⡈⣼⣼⡿⠛⠛⠁⠸⡿⣦⣐⡐⣿⠀⠀ ⠀⣠⣾⣿⢿⣿⣿⡄⠤⠤⣠⣿⡿⣿⣿⣿⣶⡄ ⢸⣿⣿⣿⣿⡑⠫⣻⣿⣿⣟⠕⠉⣼⣿⣿⣿⡇ ⠘⣿⣿⣿⣿⣷⣤⣈⡙⢟⣁⣤⣾⣿⣿⣿⣿⡇ ⠸⣿⣿⣿⣿⣿⣿⡟⠛⠛⢻⣿⣿⣿⣿⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡄⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⡿⠁⠐⣯⡟⢽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⣰⠟⠁⠀⠀⢩⣲⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠇⠀⠀⠀⠀⣀⡤⠞⠋⢀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣿⣟⣿⣿⣿⡿⠿⠿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⢀⣠⡤⠖⠊⠉⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠛⣿⣿⣭⣿⣿⣿⣯⣿⣿⣿⣿⣯⣥⡀⠀⢠⠶⠿⣽⢿⡷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⢉⣀⣤⠴⠞⢩⡟⡉⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⠍⠀⠀⠉⣿⣿⣩⣵⣿⡇⠉⠻⡿⠛⣿⣿⣿⣿⣟⡛⠀⣤⠀⣹⣧⠀⠙⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠛⠉⠉⠀⣀⡴⣯⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠀⠀⢀⣼⠟⣸⣿⡟⢙⢧⣾⡿⠟⠀⠀⠈⢿⣯⠉⠉⠁⠻⣿⣼⡾⠛⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡴⠞⠋⢀⡼⣆⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⢀⣼⠋⢀⣾⠟⠀⠛⢿⣿⣏⠀⠀⠀⠀⢸⢻⣿⣷⡔⣤⡴⠾⣿⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀ ⠀⣾⣝⠀⣠⣾⠋⠀⢸⠗⠀⢀⣾⣿⣵⠀⠀⠀⣰⠟⠁⣠⡿⠁⠀⠀⢠⣿⡟⠛⢿⡶⠶⠶⠶⢾⣿⣿⡇⠁⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀ ⣸⢻⣏⣴⠏⢹⠀⣠⠏⠀⣴⣿⣿⣿⠁⠀⢀⡾⠋⠀⣰⡿⠁⠀⠀⢠⡾⢿⡇⢀⣿⡇⠀⠀⠀⠈⣿⣾⣧⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀ ⠃⢀⡽⠃⠀⠘⢯⡿⢀⣼⡿⠋⣿⣿⠀⢠⡿⠁⢀⣼⡟⠀⠀⣠⡶⠋⠀⣼⠀⣿⢿⡇⠀⠀⠀⠀⢹⣾⣿⡄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⠀⠀⠀ ⣴⡟⠁⠀⠀⠀⠀⠀⣼⡟⠀⢸⣿⡟⣀⡿⠁⢀⣾⣟⣠⣴⠟⠉⠀⠀⠀⣿⣿⡇⢸⣿⡴⢶⣤⣄⠘⣿⣿⡇⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣧⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⣾⣿⣸⣿⣧⣤⣼⣿⠛⠁⠀⠀⠠⢄⣀⠀⢹⣿⡇⠈⣿⣧⠀⠀⠉⠀⢻⣿⣧⠀⠀⣿⠀⠀⠀⠠⡇⠀⣠⣾⣿⡿⢿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⣿⡿⢿⣿⡟⣿⣿⠃⠀⣠⣄⣀⠀⠀⠉⠓⢾⣿⡷⠓⢻⣿⣭⣟⣛⣓⣭⣿⣿⣧⣴⣿⣶⣀⣀⣰⣷⡾⠛⠉⣿⡇⢸⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⣿⡧⣿⣯⣶⣿⣿⡗⠺⢿⡽⣯⣍⠓⠦⠈⠀⣿⡇⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⢹⣿⡧⠀⠀⣿⣷⢸⡏⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢠⣿⣿⣿⣻⣿⣿⣿⣇⣀⣾⣷⣀⣹⣗⠀⠀⠀⠘⢧⠀⠀⠀⣹⠛⠻⣶⡀⠈⠙⠻⢿⣿⣿⣿⣻⢻⣿⡇⢀⠀⣿⢿⣼⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠈⠓⠒⠾⠿⠤⣤⡀⢸⣿⣿⣿⣇⢿⣿⢇⠰⠀⢿⡾⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢸⣿⣿⣿⣿⣿⣿⢸⠀⠀⢸⣷⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠸⣿⣿⡟⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣄⡄⣼⣿⣿⣿⣿⢾⣿⢸⣭⠀⢸⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⣧⣿⣿⢿⣯⣿⠏⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿⢿⣿⣿⣿⣿⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⡟⠀⣿⣿⣿⣿⢻⣿⣿⡆⢸⣿⣿⣦⡀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⡈⢹⣿⣿⣿⠀⢻⠀⢸⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡟⠀⠀⢹⣿⣿⣿⢻⣿⣟⠃⠘⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡌⣵⢾⣿⣿⣿⣶⠥⠀⣾⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡇⠀⠀⠈⣿⣿⣯⣼⡿⣿⣴⣆⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⢽⣿⡿⣼⣿⣿⣿⠙⡋⠀⣿⡿⢿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⡇⠈⠉⠛⠻⠛⠿⣿⣿⣿⢿⡷⣤⣀⣤⣤⡤⠶⠟⠛⠉⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣰⣿⠁⠈⠛⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠻⠗⠛⠋⢻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⢿⣿⣷⣶⣶⣶⣶⣶⣾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣀⣠⣴⣶⣶⣦⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣯⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⢳⣿⠟⠀⠆⠠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⣶⣿⣯⣦⣆⠆⣷⠐⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⠊⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠓⠒⠤⣄⡀⠀⠀⠀⠀⣠⣶⣯⠉⠀⠀⠀⠀⠈⠉⠻⣿⡄⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠊⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⢸⠟⠁⠈⢳⡀⠀⠀⠀⠀⠐⡄⠈⢻⣦⠀ ⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣀⣶⣶⣶⠒⢲⣦⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⡤⣨⣠⣶⣛⣮⡛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⢧⠀⠀⠀⠀⠀⡇⠀⠈⢿⢄ ⠀⠀⢠⠟⠀⠀⠀⠀⢀⡴⠋⢁⠀⠛⠮⣍⣉⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡱⣄⢀⡼⣆⠀⢀⡴⠃⠁⠀⠀⢸⣧ ⠀⢠⡞⠀⠀⠀⠀⢠⡟⢠⠁⢸⠀⠀⡸⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣀⢀⣾⡿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⢻⡤⡞⠻⢯⣀⠀⠀⠀⠀⣸⣿ ⢀⡎⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⡇⠀⣥⠋⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣽⠿⠛⠛⠛⠻⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠘⣆⠱⣌⠂⠀⠉⠳⣄⢀⡐⠻⣿ ⠟⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣦⡛⣰⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠹⡆⠙⣇⠀⠀⠀⠈⣿⣤⣤⣈ ⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢈⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⣤⡤⠤⢤⣄⡀⣄⠀⢻⠀⠀⠀⠀⠀⢳⠀⢹⣄⣠⢴⡞⠀⠻⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣴⠋⣠⡆⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣷⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢰⠃⢠⣾⡀⠀⡇⠀⠀⣰⢻⠐⣮⠁⠀⠀⠀⠀⢸⠀⢸⡟⠀⠀⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢾⡿⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⢹⣿⡝⣆⠸⣄⠀⠀⠀⠀⢀⣾⡴⠋⣿⡇⣰⡇⣠⠞⡁⣸⠰⢻⡄⢰⠀⠀⠀⢸⠀⡘⢹⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢸⠁⡄⠀⠀⠀⠀⢀⣿⣿⠋⠳⢤⡀⠀⣷⡀⡟⠙⠚⠳⠆⠀⠰⠛⠁⠀⢴⣿⣧⡿⠿⠿⣶⣾⣟⡁⠈⣧⣽⠀⠀⠀⠀⢰⠇⢸⡇⠀⣸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⡇⠀⠀⠀⠀⢸⡇⢻⢠⣶⣺⣭⣷⣶⣭⣽⡄⠀⠀⠀⠀⠀⠀⠀⠈⠹⠏⢡⣤⣤⣤⣄⠈⠻⢿⣿⣻⡏⠀⠀⠀⠀⢸⡆⢸⡇⠙⠉⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⢸⣇⢈⣷⡿⡛⢙⣠⣤⣤⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣿⣿⣿⡇⠀⠈⢿⡿⣡⠀⠀⠀⠀⢸⠇⢸⡇⠀⠀⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡏⢙⢷⡀⠀⠀⠀⢿⣿⡿⠁⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡛⣿⣿⣾⡇⠀⠀⣼⣿⠁⠀⠀⠀⢀⡏⠀⣼⡇⠀⠀⣿⢷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢳⣜⠀⠻⣄⢰⣶⣾⣿⡇⠀⠘⣯⣿⣿⢿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣓⣚⣋⣀⡄⠀⣼⣣⢴⡆⢀⣤⣿⡁⣠⡿⢇⠀⠀⣿⠀⣻⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⠟⠈⢳⡄⠈⢿⢿⡝⣏⠃⠀⠀⠘⠳⠶⣛⣫⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⢠⡾⠛⣉⣤⠈⣳⡏⡇⢸⠀⠀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣠⠏⠀⠀⠀⠹⣄⡟⠀⢳⣸⣆⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠐⠸⡇⡇⠸⡄⠀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢠⢇⡴⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⢹⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⣴⠒⢸⡇⡇⠀⣿⠀⢹⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣼⠞⠁⡠⠀⠀⠀⠀⣼⡿⠀⠀⠀⢸⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣞⣠⠾⠁⣠⡿⠀⢳⠀⢹⠀⢸⣿⣿⣿ ⡀⠀⠀⠀⠀⠀⣸⠏⣠⠞⠁⠀⠀⣠⠞⢹⠃⠀⠀⠀⠀⠳⣄⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣤⣀⣠⣤⣾⣿⡇⠀⢸⠀⠀⠆⠸⣿⣿⣿ ⠉⠳⢤⡀⠀⣴⡧⠞⠁⠀⣀⡤⠞⠁⠀⡏⠀⠀⠀⠀⠀⠀⠈⠓⠿⢦⣀⣀⠤⠤⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⡏⣰⣿⣿⠟⠉⣿⣿⠃⠀⢸⡀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠉⠻⣟⣀⣠⠔⠛⠉⠀⠀⠀⣠⡇⠀⣀⡤⢄⣀⣀⠤⠤⢤⡤⠛⠁⣀⣀⣠⣀⣀⠀⢙⣶⠀⠀⠀⠀⠀⠀⣀⡴⢾⣿⠀⣽⣿⣿⣿⠀⠀⣿⣿⠀⠀⠀⣄⠀⢰⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠙⠷⠤⣄⣀⡀⠀⣠⡾⠖⢾⡃⠀⠀⠻⣥⡀⠀⠈⠱⣄⢀⡽⠋⢻⡷⢭⣉⠉⠁⠀⠀⣀⣠⡴⠚⠋⢠⣿⣧⣾⣿⣿⣿⣿⣆⢰⣿⣿⠀⠀⠀⢸⠀⠀⠀⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡝⠻⣄⠀⠀⠳⡄⠀⠀⠹⣷⡄⠀⠀⠙⣏⠀⢀⡶⢷⠀⠈⠉⠛⠛⠉⠉⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡏⠀⠀⢀⢸⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠘⢦⡀⠀⠈⢿⣦⠀⠀⠈⢷⢺⡆⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⢻⡟⠛⠿⢿⣿⣿⣿⡗⠀⠀⢸⣿⠀⠀⢸⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⢾⣷⣄⠀⠀⢻⣷⡀⠀⢸⡇⣧⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⣠⡴⠀⢹⣿⡏⠓⢶⡶⣦⣌⠙⠿⣄⣀⣤⣿⡿⠀⠀⢸⠀⢸⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⡾⠁⠉⠛⠋⠁⢿⠀⠀⠀⠙⠶⣄⡈⠉⠉⠁⠀⠀⠀⣸⠋⢳⠀⠈⢷⠈⢳⡔⡄⠀⠙⠛⠉⠀⠀⠀⣾⠀⠸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⢀⡴⠃⠀⢸⡇⠀⠸⣆⠉⠙⣾⣆⠀⠀⠀⠀⠀⣰⣿⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣅⠀⠀⢠⣧⠀⠀⢻⡀⠀⠘⢿⡀⠀⠀⣀⣴⡿⠟⣠⣾⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠸⠙⠳⢄⡀⠀⠀⠀⠀⠀⢸⡇⠙⡆⠀⢸⣿⠀⠀⠀⣧⡀⠀⠀⢙⠢⣭⣭⣥⣶⣿⣿⣿⠀

⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠃⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀ ⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀ ⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⡆ ⠀⠀⠀⠹⣧⠀⡀⠀⠀⠀⠀⢀⡀⡀⠈⣇⢀⣠⣤⠴⠖⠒⠛⠉⠉⠉⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⡷ ⠀⠀⠀⠀⠘⣧⡽⠶⢦⣀⡞⠛⠓⢦⡄⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⣿⠀⠀⣠⠿⢦⡀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⡷⠀⣏⠀⢀⡗⠚⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡀⠀⠈⣹⡋⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⣽⠒⠛⠉⠙⠲⠖⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠋⠉⠉⠙⠛⠒⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⣰⢏ ⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢶⣄⠀⠀⠀⠀⠘⣧⠀⣰⣿⠋ ⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢻⢰⡟⠁⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⣧⡀⠀⢸⡟⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢨⠏⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⢀⣴⣏⠀⠀⠘⣧⠀⢸⠃⠀⠀⠀ ⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣶⣤⣤⣤⣼⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⢿⠿⣿⠋⠉⠀⠀⠀⠹⠷⢿⡀⠀⠀⠀ ⠀⠀⠀⠀⠘⣏⠀⠀⠀⠀⠀⠰⡟⠀⠀⠀⠀⠀⠹⠏⠻⠇⠉⠀⠀⢰⡞⠋⠉⢉⡗⠀⠀⠶⠫⠞⠁⠚⠁⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⠞⠡⠞⠰⠞⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣆⢀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠴⠚⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠹⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠦⢄⣙⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⣀⣀⣤⡴⠖⠿⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠖⠛⠛⠉⠉⠙⠛⠓⠒⠒⠲⢿⡅⠀⠙⣿⠋⠙⣧⠀⠀⠀⠀⠀⠉⠙⠲⢦⣄⠀⠀⠀⠀⠶⣾ ⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠿⠂⢦⠀⣤⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠆⠀⠀⠀⠀ ⣰⣏⡁⠀⠉⠛⢦⣤⠀⠀⠀⢙⣿⡿⠟⢷⡄⠀⠀⠀⠀⢀⣾⡿⢷⣤⣀⣲⣾⣿⣿⣯⠉⠻⣷⣴⡀⠀⣤⡶⠋⠁⠙⣿⠀⠀⠀⠀⠘

⠀⢨⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⢇⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢀⢠⠃⠀⠀⠀⠀ ⠀⠀⠈⢦⢄⣀⢀⡤⣀⣸⡤⠖⠒⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⢘ ⠀⠀⠀⠸⡁⢨⠯⡄⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠠⡋⠘⣲⠃⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡄⠀⠀⢀ ⠀⠀⠀⠀⡝⠉⠉⠑⠉⠀⠀⠀⣠⠤⠒⠈⠉⠉⠉⠁⠒⠠⢄⡀⠀⠀⠹⡄⢠⡮ ⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢇⠟⠁ ⠀⠀⠀⡇⠀⠀⠀⠀⢐⠞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⡀⢀⣴⠀⠱⡀⠸⠀⠀ ⠀⠀⠀⢷⠄⠀⠀⢀⡎⠀⠐⢶⡶⡾⠇⠀⡠⠤⢄⠀⢈⢟⠟⡉⠀⠀⠛⢣⠀⠀ ⠀⠀⠀⠘⣆⠀⠀⢀⠀⠀⠠⠢⠒⠖⠀⠀⠑⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀ ⠀⠀⠀⠀⠘⢶⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠁⢣⡀ ⠀⠀⠀⠀⠀⠀⠙⠦⣈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡔⠊⠁⠀⠀⠀⠀⠑ ⠀⠀⠀⠀⠀⠀⠀⣠⣤⠛⠛⠛⠒⠒⠒⢲⣏⠙⠟⢙⡅⠀⠈⠉⠒⠤⣀⠀⠀⠶ ⢀⣔⠒⠢⢄⡀⠀⢻⣾⠧⡀⠀⠀⢀⣾⢏⣩⣼⣼⣞⠳⣄⡀⢀⡤⠚⢿⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠀⠀⢀⠔⣪⠊⠈⠷⠇⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠠⢄⣂⡥⠊⠁⠀⢀⡤⠒⣾⢿⡿⣿⣿⣯⣉⡭⠷⡆⢄⠀⠀⠀⠀⠀ ⠒⢉⠠⢊⠀⠀⣠⠶⠋⢀⢔⡽⣯⡵⠊⠈⣿⣉⣙⣷⠃⠀⠑⢆⠀⠀⠀ ⡸⣣⢾⢡⢃⣼⡗⢀⡔⢡⠊⠀⣼⢙⡖⠒⢻⣧⠁⢸⠀⠀⠀⠈⢦⠀⠀ ⡱⠃⠈⢃⡞⣹⢇⠎⣰⣃⠔⠊⢸⡜⣧⢄⡈⣿⠀⢸⠀⠀⠀⠀⣘⡀⠀ ⠀⠀⠀⡾⠀⣿⣿⣺⡏⣠⣀⡐⠸⡧⢹⣦⣆⣽⣦⣼⣄⣰⡔⢻⣙⡇⠀ ⠀⠀⠀⠃⢀⣿⣿⣿⡇⠽⠽⠎⠀⢣⠀⢹⣻⡍⠛⣿⣷⣾⡇⢸⣻⡇⠀ ⠀⠀⠀⣠⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⣿⣿⣿⣧⢸⣿⠀⠀ ⠀⠀⢠⡟⣿⣿⣿⡏⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢁⡟⢿⣿⠸⢸⡟⠀⠀ ⠀⠀⠸⠀⢹⣿⡿⣧⣹⣿⣦⡀⠀⠀⠀⣀⣠⣴⣿⣧⣿⣿⠷⢸⣷⡀⠀ ⠀⠀⠀⠀⢸⣏⡇⠀⠉⠉⠋⣹⣒⠂⠉⠁⡜⠉⠙⠹⠛⠻⡷⠞⠀⠁⠂ ⠀⠀⠀⠀⠀⢻⣷⣤⣤⣤⠄⠉⠉⠉⠉⠉⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣤⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣩⣶⣦⡀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠓⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⣀⡭⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣿⠤⣖⢻⣩⣀⠀⠀⠀⢸⣿⡿⣗⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⠉⠉⠉⠉⣹⣛⣷⡾⠃⣶⣻⣯⣿⣽⠀⢠⣤⣼⡽⠷⠾⠉⣹⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⢰⣶⣚⣋⣩⣉⡅⠀⠀⠀⠉⠉⠉⠁⠀⢻⣯⡙⢴⡶⣶⣫⡝⠁⠀⠙⢯⠓⠒⠲⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣄⠈⠉⢉⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⣡⣴⡀⠀⠀⠉⠙⠙⠶⠤⠤⢌⣷⣶⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠿⣆⣰⠏⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡃⠀⠀⠀⠀⠀⠄⣠⡾⠋⠀⢀⣴⣿⡀⠀⠀⠀⠀⣷⠀⠀⠀⠈⠃⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⠔⠚⡏⠁⠀⠀⠀⠀⠀⣰⣿⠧⠶⢲⣿⠉⣿⢷⡀⠀⢠⣀⣹⣿⡀⠠⠤⢼⡟⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢻⡄⢸⡇⠀⠀⠀⠀⠀⣴⠏⣶⠀⠀⢼⡏⢸⣿⠆⠉⠓⠚⠓⠻⣿⡇⠀⠀⢸⣷⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣸⡃⠀⠀⠀⣠⣾⣋⣀⡿⡆⠀⣿⡇⠰⡿⠁⠀⠀⠀⠀⢠⣿⣇⠀⠀⣼⡿⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢻⠃⠀⠀⠀⡟⣿⠉⠶⣄⠹⣎⣿⣇⠀⠁⠀⠀⠀⠀⠀⢈⣹⣿⡿⢓⣿⠛⡿⢺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠹⢷⣦⣤⣀⣈⡻⠟⠀⠀⠀⠀⣶⡆⠀⠈⣛⣿⣿⣾⡏⠀⢹⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠹⠿⣿⣽⡿⠛⠲⠖⢦⣤⣼⣶⣴⣾⣿⠟⠋⠀⠙⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⣳⠶⣄⠀⠀⠀⠀⠀⠈⠙⠒⠲⣶⠶⠿⠿⢤⣬⡿⠶⠶⠾⠯⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢾⣇⡠⢨⡷⠀⠀⠀⠀⠀⠀⠀⠸⣿⡖⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⣿⢃⡄⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠁⡼⠁⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠹⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⣸⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠹⣦⠀⠀⠀⠀⢻⡌⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⢻⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣏⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠺⠯⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡍⠉⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠉⠉⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢸⠇⣠⠾⢶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣀⣼⡁⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⡾⢧⣤⣌⣿⡖⣻⣦⡀⠀ ⠀⠀⠀⠘⠻⣿⡀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢿⣿⣖ ⠀⠀⠀⠀⠀⠀⠉⠓⠶⣄⣀⣠⠴⠖⢻⣦⠀⠀⠀⠀⠀⠀⣶⣆⣀⣀⣀⣀⣤⣤⡤⠤⠤⠶⠶⠶⠒⠒⠒⠛⠛⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⡀⡬⣄⣒⠉⢱⡶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠴⢺⠍⠈⠉⠉⡐⠟⠯⢶⡋⠲⡂⡠⠄⠀⠀⠀ ⠀⠘⡴⠁⠀⠀⡠⠊⣩⠃⠀⡀⠀⠂⢹⠀⠀⠀⠀⠀ ⠰⡊⡇⠀⢀⡼⠓⠸⣹⠢⠤⢼⡄⢒⡟⡀⠀⠀⠀⠀ ⠀⠱⠀⠀⣾⠖⢃⣦⠘⠀⠀⢘⣧⢼⢧⡇⠀⠀⠀⠀ ⠀⠀⣀⡀⠈⠳⠖⡯⠤⢄⠧⣼⢟⣛⡸⠃⠀⠀⠀⠀ ⠀⠀⠰⢍⡆⠀⠀⠀⢹⠉⠉⠏⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡐⡜⠀⠀⠀⠆⢀⠀⠈⢤⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⢱⠀⠀⠀⠀⠀⠀⠣⡀⠈⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢻⠀⠀⠀⠀⠀⠀⠀⠈⢒⠓⡂⠀⠀⠀⠀⠀ ⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⣁⡀⠀⠀⠀⠀ ⠀⠀⢀⠃⠀⠢⠀⠀⠀⠀⠀⠀⠀⠑⢄⣎⠔⣄⣀⠀ ⠀⠈⠻⢄⡀⢀⡱⡀⠀⠀⢀⠀⠀⢀⣀⣀⣈⠉⠚⠷ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠉⢳⣰⠋⠙⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀ ⡀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠙⠷⠋ ⣰⠟⠉⠙⢦⡀⢀⣾⡟⠉⠳⣆ ⣿⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⡿ ⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃ ⠙⢧⡀⠀⠀⠀ ⠀⢀⡴⠃⠀ ⠀⠀⠀⠙⠶⣄⣀⠴⠋⠀⠀⠀⠀⠀

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

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⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

.　 +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *

⋆౨ৎ˚⟡˖ ࣪🧸🌻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚｡⋆୨♡୧⋆ ˚｡⋆

ੈ✩‧₊˚🎀₊‧✩ੈ

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⣠⠶⠶⠦⣄⠀⠀⠀ ⠀⣀⣤⣄⡀⠀⣠⠴⠛⠉⠀⠀⠀⠀⠈⠉⠺⠁⣤⣀⠀⠈⡇⠀⠀ ⡼⠉⠀⡀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⢀⣰⠇⠀⠀ ⡇⠀⢸⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀⠀ ⠙⠦⣤⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⡶⢀⣠⣴⡄⠀⠀⢧⠀⠀⠀ ⠀⠀⣼⠀⠀⠠⢤⣤⣄⣈⠉⢁⡤⢦⡄⠛⠛⠤⠄⠀⠀⠘⣿⡄⠀ ⠀⠀⢹⠀⠀⠐⢈⡭⠛⠁⠀⢀⡹⠞⠓⠃⢶⠖⡄⠀⠀⠠⣾⠃⠀ ⠀⠸⣟⡃⠀⠀⠈⠀⠀⣠⠒⢉⣠⠤⢤⠀⠀⠀⢧⠀⢀⡞⠁⠀⠀ ⠀⠀⠻⢥⠄⠀⠀⢠⠎⠙⢠⠋⠰⢾⡁⠀⢀⠀⡸⢀⣾⠴⠒⣲⠄ ⠀⠀⠀⠈⠉⠲⣄⠘⠦⢴⣽⣀⣀⣀⡱⠤⠞⣫⠕⠋⢀⡠⠞⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⢙⡶⠤⠄⠀⠀⠀⠀⠀⠈⠁⣠⠴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠴⠋⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠃⣠⠔⠋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⡤⠤⠿⠛⠚⠋⠉⠙⣆⠀⠹⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠤⠿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠥⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣿⣿⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠟⠉⠁⠀⠀⠈⠙⠿⣿⣷⣄⣤⣴⣶⣶⣦⣤⣀⣠⣾⣿⠿⠋⠉⠉⠉⠉⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⠿⠛⠛⠛⠛⠻⠿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡿⠀⠀⠀⠀⠀⠛⠻⠛⣁⣤⣤⣶⣴⣤⣤⣀⠛⠿⠿⠋⠀⠀⠀⠀⢰⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⢉⣤⣤⣌⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⣿⣿⣿⣿⡆⠀⠈⢻⣧⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠘⠿⠿⠋⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠘⣿⡀⢠⣄⠀⠀⣰⣆⠀⠀⢀⣀⠀⣿⡇⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠀⢿⣧⠀⠛⠿⠾⠛⠙⠿⠶⠟⠁⣰⡿⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠈⠻⣿⣷⣄⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⢀⣼⣿⡟⠁⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡿⠛⢷⣦⣄⠈⠙⠻⠷⢶⡶⠾⠟⠋⠁⣀⣤⣾⠟⢿⣿⣷⣴⣾⣿⡿⠟⠛⠛⠿⣿⣿⣦⣄⠀⠀ ⠀⢠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠉⠻⣿⡍⠀⠀⠀⠈⠙⠻⠿⢶⣶⣶⣶⣶⣶⠾⠿⠛⠉⠀⠀⠀⠉⢻⣿⠛⠁⠀⠀⠀⠀⠀⠀⠉⢿⣿⣦⡀ ⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧ ⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿ ⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿ ⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃ ⠀⠈⢿⣿⣶⣄⡀⠀⠀⠀⢀⣠⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⣀⣀⣀⣀⣤⣾⣿⡿⠁⠀ ⠀⠀⠀⠙⠿⢿⣿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⠿⠿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣤⣶⠶⠶⢶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⢶⣶⣦⣄⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠈⠉⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠉⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣤⣤⣤⣤⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣶⣄⡀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠛⠛⠛⠛⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣷⣶⣾⣿⣿⠟⠃⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣶⣶⣶⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⣉⡉⠉⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣁⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠝⠉⠉⠛⠷⣦⣤⣶⣶⣶⣶⡾⠃⠀⠈⢻⡾⠛⠉⠉⢻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⠁⠀⣾⢻⡶⠛⠲⣄⣤⠼⢧⣄⠀⠀⠀ ⠀⠀⠀⠀⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⢙⣿⡀⠀⠀⣹⢶⡄⠀⣹⡀⠀⠀ ⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠒⢺⡛⠛⠁⣰⠏⠀⠀⠀ ⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⢹⡇⠀⠀⠀ ⢠⡶⢼⣷⢤⠄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠾⣿⠖⠶⠆ ⠀⠀⢈⣿⣀⡀⠀⠀⢿⡿⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠸⣿⠇⠀⠀⠠⣴⣿⣄⣀⠀ ⠀⠘⠋⠹⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠯⣦⠽⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⠃⠀⠀⠀ ⠀⠀⣠⡴⠟⠻⣧⡶⠳⣦⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠋⠛⠶⠄⠀ ⠀⠀⠁⠀⢀⡾⠛⠂⣀⡈⠀⢹⣧⣤⣄⣀⣀⣠⣤⣤⣴⣶⣾⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣷⣤⠄⠛⠃⠈⢿⢹⣄⠀⠀⠀⢠⡿⠀⠈⢷⡉⣻⣦⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠏⢿⣤⣴⡷⣶⡟⠀⠙⠳⠶⠶⠛⠁⠀⠀⠈⣿⡋⠀⠈⣿⠆⠀⠀⠀ ⠀⠀⠀⠀⢻⣆⠀⠀⢸⣿⣜⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⣽⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣶⠞⠃⠙⠶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡿⠶⢶⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⡶⢾⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣀⣀⣀⣀⣠⣿⣀⣀⣀⣀⣀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠛⠛⠒⠲⠦⣄⣠⡞⠁⠁⠀⠈⠙⣦⠀⠀⠀ ⠀⢀⣠⣤⡿⠶⢤⡀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢼⡓⢦⠀⠀⢸⠆⠀⠀ ⠀⡾⠉⠀⢀⣀⡀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⢀⣠⡟⠀⠀⠀ ⢸⣇⠀⠀⢾⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀⠀⠀ ⠀⠻⣄⡀⢈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⣀⡄⠀⠀⠀⢿⠀⠀⠀⠀ ⠀⠀⠀⠉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠴⣦⡄⠀⠀⠿⠋⢠⣶⡯⠗⠟⠀⠀⠀⢸⣧⡀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠒⢒⣶⣶⣶⡤⠀⠀⢶⡚⢹⡇⢀⠉⠉⠉⠙⠀⠀⠀⠈⠹⢿⡄⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠋⢁⡴⠞⠉⠀⠀⠀⣠⠼⠟⠛⠉⠉⣯⡟⢶⠀⠀⠀⠀⢶⡿⠁⠀ ⠀⠀⠀⣿⡛⠇⠀⠀⠀⠉⠀⠀⢀⣠⠖⠋⢁⣀⡤⢤⡄⠀⠈⠁⢸⡁⠀⠀⡼⠋⠀⠀⠀ ⠀⠀⠀⢸⣏⣣⠀⠀⠀⠀⠀⣠⠞⠾⢀⡴⠋⣡⣴⠚⠁⠀⠀⠀⠀⡹⠀⣼⣃⣠⠦⢤⡄ ⠀⠀⠀⠀⠉⠹⢍⣀⡀⠀⠀⣇⠀⢀⢼⠀⠀⠀⠘⢦⡀⠀⣶⣤⡜⣡⠾⠟⠉⢀⣴⠾⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠉⠓⠿⠾⠦⠤⠤⠤⠼⠓⠒⢋⣱⠞⠁⢀⣠⡴⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡽⠒⠦⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣠⠴⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣠⠴⠋⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣀⣀⣠⡿⠿⠷⠒⠚⠋⠉⢷⡀⠀⠹⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⢘⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣄⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢰⣿⣿⣿⣮⣷⡾⠭⠽⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⠛⣩⣿⠟⠩⣥⣴⠍⠉⠀⠴⠟⠯⠔⠶⣾⣝⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⣞⣋⣉⣭⡶⠿⠉⠉⣀⣽⣿⠃⠀⠀⠀⠀⠐⣶⡤⣷⣾⣟⠭⢷⣄⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢶⣫⣷⣜⣿⡟⠋⠀⢀⣠⠞⠉⢘⣿⠅⢠⡆⠀⠀⢀⣤⡌⠻⣦⣤⠤⠟⠋⠱⠿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⣉⡵⠋⠁⠀⠀⠈⠀⢀⡀⠀⣾⣟⠀⠀⣸⣿⠀⣿⣧⣀⠀⠈⢿⣿⣶⠀⣀⣀⣀⡀⠀⢀⣸⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⣸⡏⠀⡯⢽⠀⠀⠹⣿⣷⣤⠉⠛⠶⠄⠀⠉⠁⣸⢳⢿⣿⠿⠿⠿⠛⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠛⢿⣧⡀⠀⠀⠙⢿⣿⡄⠀⠀⠀⠀⠀⡷⢇⣼⣿⣦⣶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣠⣾⡷⠭⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⠈⠻⢿⣦⡀⠀⠀⣁⣱⣶⣶⣤⣼⠷⠶⠶⠶⠤⣀⣹⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡴⠇⠡⠤⣤⡤⠴⠖⠒⠶⢦⣄⡸⣿⣿⠀⠀⠈⢿⣦⣼⣿⣷⣿⣿⣿⡿⠛⠻⠙⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢯⣶⠀⢾⣧⣀⠀⠈⠛⠀⠀⠀⠀⢠⣙⠻⢧⣀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠸⢻⣧⡈⠹⠿⠇⠊⠂⠀⠀⠀⠀⠀⠉⠑⠲⠿⠷⠶⠦⠴⣿⣿⣿⣏⡷⠅⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⢿⣆⠸⢾⣿⣿⣟⣷⣤⣤⣔⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⣛⣿⣿⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢳⣿⣼⣿⣷⣦⣍⡩⣝⣄⡀⢬⣀⠁⠀⠀⠀⠀⢀⡀⠀⠀⠰⣾⠿⠋⣡⡭⠙⠉⢳⠬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⣿⠁⣯⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡷⠶⢿⣄⡀⢀⣠⣶⠟⠋⢤⡀⢳⣬⣧⡘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣜⣡⠂⠀⠀⠚⣿⣇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⣳⣦⣅⣀⣴⢲⣤⣿⣾⡿⠟⣻⣦⣝⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣻⠏⠀⠀⠀⠀⠀⠹⣿⣆⠸⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣾⣿⡇⣨⣿⣿⣾⣿⣟⣋⡁⠀⠀⠙⠻⣷⡄⠙⠲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣯⠞⠃⠀⠀⠀⠀⠀⠘⢻⡟⠘⢿⠋⢿⣿⣿⣿⣿⣿⣿⡄⠉⠛⠛⠿⠟⠃⢻⡟⠿⢿⣿⣿⣿⣿⣭⣥⣄⠀⠀⠈⢻⣦⡀⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⢣⣇⡴⠂⠀⠀⠀⠀⢀⠀⠘⢧⣄⠈⢣⡀⠉⠛⠻⢿⣿⡟⠁⠀⠀⠀⡀⠀⢠⡼⡄⠀⠀⠙⠿⣿⣿⣿⣿⣯⠤⠤⠀⠀⠹⣷⡂⢸⣇⠀⠀⠀⠀ ⠀⠀⠀⠛⡿⠁⠀⠀⠀⠀⠀⠈⢻⣾⣿⢮⢣⣌⢷⣄⣀⣀⡬⠉⠁⠀⠀⠀⡰⣿⡀⣰⣱⣿⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣶⣶⣦⣀⠈⠛⠈⠋⠳⣄⠀⠀ ⠀⠀⠀⠀⡇⣾⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠈⣯⢿⣺⡟⠁⠀⠀⠀⠀⢰⣹⡇⠁⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣷⣤⣄⠀⠀⠀⠈⡇⠀ ⠀⠀⠀⠀⡇⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣸⣷⣅⠀⠀⠀⠀⢀⣤⣾⠻⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣶⣦⠀⢳⠀ ⠀⠀⠀⠀⣇⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣿⣿⣦⣄⠀⠀⠜⠛⠀⢀⢠⠀⣠⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⠀⣼⠀ ⠀⠀⠀⠀⣟⣀⠀⠀⠙⡛⠳⠀⠀⠀⠀⠀⠀⠀⠈⣿⣜⣿⣿⣷⣄⣀⠀⣼⣼⣾⠟⠋⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⣻⡿⠞⠁⠀ ⠀⠀⠀⠰⢿⣿⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠉⢓⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⡿⠁⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⢻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢾⣧⡴⠀⠨⢾⡟⠀⠀⠀⠀⠀⢀⣴⡟⣻⣿⣿⣿⣿⣿⡿⠿⠫⠤⠤⠤⣤⣀⠀⠀⠀⠈⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⡿⠁⢀⣴⠋⠠⣾⣅⣀⣀⣴⡾⠋⣷⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⢿⡞⣁⣀⠀⡀⠀⠀⢐⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡿⠋⢰⡿⠂⠀⠀⠘⠛⠋⠛⢱⢻⣷⠿⣿⣿⣿⣿⣿⡿⠛⠉⠚⠛⣋⡭⠕⠛⢿⣿⣷⡀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⡿⠁⣰⡿⣂⡀⠀⠀⠀⠀⢀⣠⡿⠟⠁⠀⠀⠛⠿⠛⣹⠏⠉⢉⠉⠉⠁⢀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⠟⠀⠀⠛⠛⢛⣥⡤⣄⣤⣶⣿⣿⢷⣄⠀⠀⠀⠀⠀⣰⡇⠀⠀⠁⠁⢈⣶⣥⠤⠤⠴⠶⣾⢿⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣟⠀⠀⠀⠀⠀⠉⠉⣟⣹⠶⡏⠳⣿⠓⣌⣧⡀⠀⠀⠀⢻⣄⡀⠀⠀⠀⢉⣀⣀⡀⠀⠀⠀⠈⠉⠻⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣇⡀⠀⢀⣀⣀⣀⣀⣈⡁⠀⢸⣇⣼⢶⣿⣷⠇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠓⠶⠶⠶⠶⠾⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠉⠁⠀⠀⠈⠉⠉⠛⠻⣾⠟⡿⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⡄⠀⢰⡏⠀⠀⠀⠀⠀⣠⣼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠒⠿⢧⡄⢀⣤⣤⣤⣤⣠⡼⠀⢠⣤⣼⡿⠳⠖⠀⠀⢀ ⠀⠀⠀⠀⢀⠄⡀⠀⠈⣱⠂⠀⢸⣿⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⢀⣴⢶⠏⣾⣥⡆⡐⠃⠀⠀⢸⣿⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣟⣛⣶⣀⡀⢀⣴⠖⠒⠛⠙⠒⠒⠒⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠐⠶⠶⠶⠶⠶⠶⠾⢿ ⠄⢈⠚⣾⣺⢃⣏⠌⡇⠀⠀⠀⢸⣿⡦⡄⣤⠀⢘⣿⡄⠀⠀⠀⢀⣠⡼⠟⠋⠁⠀⠀⠀⠀⠀⠈⠙⠻⢅⡀⠀⠀⣀⣀⣈⣁⣉⣀⣀⣀⣀⣉⣀⣀⣀⣀⣴⡶⠀⠀⠀⠀⠀⠀⣸ ⠠⠞⣰⡷⣧⣟⠄⣸⡀⠀⠀⠀⢸⣯⡃⡀⢻⠔⣮⡿⣿⣤⢤⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡤⠬⣭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠤⠤⠶⠤⠞⠩ ⣩⢉⣼⢰⣷⣶⣰⠏⡇⠀⠀⠀⢸⣿⡇⣷⣿⣤⣿⣶⡾⠻⣟⣁⣾⠗⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒ ⠁⣼⡷⢿⣿⣿⡏⢀⡇⠀⠀⠀⢸⣿⠃⢿⣿⣿⠟⠁⠀⠸⣿⣿⣷⣶⠆⠀⠀⢸⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⠷⣿⢋⣿⠁⠀⡇⠀⠀⠀⠸⣿⣿⣬⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠇⠀⣿⠸⣿⠀⠀⢧⠀⠀⠀⢠⣿⣿⡿⠿⠛⠉⠩⠽⠛⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠻⠯⠭⠭⠽⠿⠿⠿⠿⠛⠀⠠⠬⠥⠄⠀⠀⠀⠀ ⢿⠀⠀⣿⠀⣿⠀⠀⡌⠀⠀⠀⢘⡿⠋⠁⠀⠀⠀⠀⠀⠶⠒⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠉⠀⢨⠀⠀⡇⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠂⠀⠀⠀⡄⠀⠒⠒⢶⠶⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⣀⠀⣹⠀⠀⣧⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⡇⠀⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⣿⠀⣿⣀⣼⣿⣾⣷⣿⣧⡀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⠴⠶⣶⣾⡇⠀⡆⠀⢸⣤⣸⠀⠀⠀⢠⡶⠶⠶⠶ ⣿⠀⠀⣿⣶⣿⣿⣟⣿⢾⣷⣿⣿⣷⣄⡀⠀⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⡀⠀⠀⠀⠈⠛⢧⣷⣄⡌⣿⠛⡿⠛⠒⠛⠋⠀⠀⠀ ⣿⣿⣶⣿⣿⣿⡿⠿⠁⣼⣿⣿⣿⣿⣿⣿⣷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢿⡇⠆⠀⠀⠀⠀⠀⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣭⣶⣶⣶⣾⣿⣿⣿⡅⠀⢉⣹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣿⡟⠋⠛⠿⣿⣿⣿⡿⠿⠞⠋⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣤⣥⣤⣤⣤⣿⠧⠠⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⢰⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡛⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢣⡏⠈⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⣿⣷⣿⣿⣯⣿⣿⣿⣯⣭⣩⣩⣉⣫⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢢⣦⠀⣴⣮⡟⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠻⠻⠻⣿⣿⣿⣿⣿⡿⡿⡟⠛⠛⠻⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⣽⣴⠿⠋⠀⠀⠀⠀⠀⣼⡿⡿⠷⠾⠿⠿⠿⠿⠿⠿⠿⢿⢾⠿⠶⠿⠿⠷⠶ ⠛⠻⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⣿⠿⠿⠿⠿⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⠤⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣣⡼⠿⠶⠶⠶⠶⠷⠶⠿⠿⠿⠿⠾⠾⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⣷⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡞⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠈⠉⠓⢶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠇⠀⣀⠀⠀⠀⠞⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣴⣏⣀⣀⣀⣼⣫⠄⢀⡄⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠿⠓⠞⠷⠲⠶⠖⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣰⣯⣿⣀⡄⠀ ⠀⠀⡌⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⢀⠀⣀⠀⠀⠉⠐⠠⣀⠞⠣⠀⠀⢨⠱⡄ ⠀⡘⠀⢀⠄⠊⢻⢺⠍⠀⠀⠀⠀⠀⠒⢋⠁⠁⠀⠀⠀⠀⠀⢑⢄⢆⡀⠜⠀⢳ ⡐⠀⠀⢸⠀⣠⢠⡡⠀⠀⠀⠀⠀⡾⠗⠛⠳⠀⠀⠀⠀⠠⡀⠀⢪⢇⠉⠢⡀⠻ ⠀⠀⠀⠘⡀⡑⠁⠀⠀⠀⠄⢠⠀⡆⠀⠀⠀⠆⡤⠄⠄⣄⡁⠀⠀⡄⡦⢴⠙⠻ ⠀⠀⠀⠀⠸⠺⠀⠀⢀⣼⢄⠈⡆⡔⢄⠀⠰⢊⣇⣦⣈⡔⢣⡀⠀⢃⢳⠀⡆⠀ ⠀⠀⠀⠀⠀⢷⡄⠀⢸⢹⡶⢟⣛⠆⠀⠀⠀⠈⢩⣶⣦⠙⣿⠇⠀⢸⢸⠈⡇⠀ ⠀⠀⠀⠀⢠⠻⡙⢄⣈⣿⠁⣿⣿⡇⠀⠀⠀⠀⠘⣿⠟⡀⣺⡡⢀⡎⡼⠀⠟⣄ ⠀⠀⠀⢀⢂⠌⠘⢄⠟⣩⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠒⢸⡅⡆⢸⣿ ⠀⠀⠀⡸⢂⠀⢀⡼⠀⢠⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠇⠜⡼⢠⠀⢸⣿ ⠂⢄⣰⠕⣁⠔⠁⠃⠀⠀⠙⠢⡀⠤⠤⢄⡀⠀⠀⠀⢀⢴⣹⡖⢻⡇⠈⠈⢸⣿ ⠀⠀⠁⠋⠤⠀⡼⠰⡉⠢⡉⠙⣤⠒⡧⠔⣁⠀⠄⠊⢽⣾⣿⣧⣸⠇⠀⠀⠸⣿ ⠀⠀⠀⠀⠀⠀⠘⠄⣐⡄⠙⣆⠈⣾⠸⡀⠀⠀⠀⢀⢸⡿⣛⡻⢿⠂⣸⡀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡎⠁⠁⡆⠈⠒⠄⡉⠀⡜⢁⠘⡸⢤⠉⠉⠀⡆⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠹⢄⠀⠀⠈⡝⡄⢸⠀⢡⠈⠣⣠⣚⣷⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⣶⠞⠋⠉⠀⠉⠩⣇⡉⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣫⠁⠀⣰⠋⠀⠘⢳⡀⠀⠀⠈⠙⢦⣀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⢋⡾⠁⠀⠀⡏⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠙⢧⡀⠀⠈⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⢃⡼⠁⠀⠀⢸⠁⠀⠀⢸⡂⠀⢷⠀⠀⠀⠀⠀⠀⠹⣆⠀⠄⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠇⣼⠃⠀⠀⠐⢸⡀⠀⢸⠉⢹⣀⣘⣇⣀⣀⣀⣀⠘⠀⠘⢧⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠇⢠⡧⠤⠶⠖⠒⠚⠛⠛⠉⣇⣸⠉⠉⠉⠉⠉⠉⠉⠉⠙⢲⡜⣇⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢻⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⢰⡇⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀ ⠀⢸⠃⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⠀⢠⣾⠀⠀⠀⠀⠀⠀ ⠀⣾⠀⢰⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠆⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀ ⠐⣿⡄⠘⣇⡇⠀⠀⠀⠀⣶⣶⡄⠀⢠⣤⣤⠀⠀⢴⣶⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⣿⡇⠀⠘⡇⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⣷⠀⠰⡄⠀⣾⠀⠀⠀⠀⠀⠀ ⢠⡟⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡇⠀⢺⠀⠀⠀⠀⠀⠀ ⠘⣧⢿⡆⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⡇⠀⣾⠀⠀⠀⠀⠀⠀ ⠀⣿⣸⠀⠠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⡇⠀⢸⡄⠀⠀⠀⠀⠀ ⠀⢻⡏⡇⡀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠘⣿⡇⢹⣧⣷⠶⢶⠶⠶⠶⡶⠲⣶⣶⣒⢒⣯⣿⣿⣿⡏⡟⣿⠿⢻⠁⠀⡇⠀⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⡆⣧⠘⠀⠸⡄⢰⡄⣷⣀⣿⣿⣿⣿⣿⣿⡿⢹⣇⠇⡼⠁⡞⠀⠀⡇⠈⠛⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣷⢿⠀⢷⠀⣧⠰⣷⣿⣿⣿⣿⣿⣿⡿⠋⠀⠘⣿⣷⡇⢰⠇⠀⢰⠃⢠⣰⢻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⢸⠀⠘⡆⣿⣴⣿⣿⡟⠃⠈⠉⠁⠀⠀⠀⠀⠛⣻⡇⣿⣦⣤⣄⣀⠀⠈⣇⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⣼⣤⣶⡟⢻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣿⣿⣿⣿⣿⣶⣿⣽⣄⠀⠀⠀ ⠀⣠⣴⣖⣛⠻⡿⠿⣿⣿⣿⣿⣿⣿⣧⣀⣤⠶⠶⢶⣤⣀⣾⣿⣾⣿⡿⣟⣿⣿⣿⣷⣶⣾⣿⣿⣦⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣾⡿⣭⣛⠿⣿⣿⣷⣶⣶⣶⣶⣦⣽⣿⣿⢟⣩⡾⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⠻⣯⡿⢿⣿⣿⣿⣿⣿⣿⢟⣴⠟⠉⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠙⢶⣝⣿⣿⣿⣿⡽⠟⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⠐⠀⠉⠻⣿⡿⠋⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣈⣡⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁

⡤⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢤ ⢣⡀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⢀⡜ ⢸⡉⠒⠄⠀⠀⠀⢉⡙⢢⠀⠀⡔⢋⡉⠀⠀⠀⠠⠒⢉⡇ ⠀⠉⢖⠒⠀⠀⠀⣇⠀⣸⠀⠀⣇⠀⣸⠀⠀⠀⠒⡲⠉⠀ ⠀⠀⠀⠉⠙⠫⠤⠚⠉⠀⠀⠀⠀⠉⠓⠤⠝⠋⠉⠀⠀⠀

⠀⠀⠈⡇⢸⡆⠀⠀⠀⠈⠙⠦⢤⣄⡀⠉⠒⠤⣀⠀⠀⠉⠓⢦⡀⠈⠆⠀⠀⠀ ⠀⠀⠀⡇⠈⣧⠀⠀⠀⠀⠀⠀⢠⠏⠉⠙⠲⢤⡀⠑⠢⡀⠀⠀⢹⡀⢸⠀⢀⡀ ⠀⠀⢰⠃⠀⢻⠀⠀⠀⠀⠀⣴⠋⢀⠤⠀⠀⢀⡙⢧⡀⠘⡀⠀⢸⠇⡸⠀⡼⠀ ⠀⠀⡼⠀⠀⢸⠀⠀⠀⢀⡼⠁⣐⣁⣤⣴⣾⡭⠇⠀⢧⠀⡇⠀⣾⣴⢁⡼⣁⡴ ⠀⢀⡇⠀⠀⢸⠀⠀⠀⣼⣥⣾⣿⣿⣿⣷⣶⣾⣿⡴⠘⣇⠇⣼⣹⠾⠿⢭⡏⠀ ⠀⢸⠃⠀⠀⢸⠀⠀⣸⠋⠉⠀⠀⣸⣿⣿⡀⢸⠉⠁⢠⣿⠾⠟⢻⣿⣿⢿⠗⠀ ⠀⢸⡀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠸⣿⠿⢿⡟⠀⠀⠀⢀⣀⡈⠺⣿⣿⡞⠀⠀ ⠀⠘⡇⠀⠀⠸⡆⢠⣧⣀⣠⣄⠀⠀⠈⠉⠉⠀⠀⠀⠻⠛⠋⢡⡀⠙⢒⣇⠀⠀ ⠀⠀⢹⡀⠀⠀⠹⣄⠈⢮⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠚⢿⠀⠀ ⠀⠀⠀⢻⣄⠀⠀⠙⢦⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀ ⡇⠀⠀⠀⠙⢧⣄⠀⠀⠙⢦⣈⢳⡀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⢀⡴⢻⠇⠀ ⣹⡆⠀⠀⠀⠀⠙⢧⡀⠀⠀⠈⢷⡇⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⠴⠋⢀⣸⠀⣰ ⠀⡇⠀⠀⣀⡄⠀⠀⢹⡆⠀⣀⣼⡳⢦⡤⠤⠤⠤⣤⠖⠚⠉⠌⠀⠀⣼⣣⠞⠁ ⠈⠉⠉⠉⠹⠥⠴⠒⠛⠓⠋⠁⠀⠙⡟⠀⠀⠀⣠⣿⡆⢠⠎⠀⣠⡞⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣠⠞⠁⢸⣓⣥⠶⠛⠁⠹⣆⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣿⡇⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣷⣦⡀⠀⠀⠀⠀⠘⢶⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡇⠀⢸⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣾⣭⣄⡠⢦⡄⠀⠀⠀⠉⠓⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⠿⣶⣶⣤⣒⡀⠀⠀⠈⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⢙⢿⣧⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠉⠛⠻⢷⣦⣀⠄⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⢸⠀⠀⠀⠀⢀⡀⠀ ⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⡀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⢸⣿⢀⠀⢸⠀⠀⠀⠀⣾⠇⠀ ⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⠏⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡐⠀⠀⠈⢷⠀⠀⠀⠀⠀⢸⣿⠘⠄⣿⠀⠀⠀⣼⡟⠀⠀ ⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣀⣴⣾⣧⠀⠀⠹⣷⡀⠀⠀⠸⡆⠀⠀⠀⠀⣿⡇⠀⣼⠃⠀⠀⣺⣿⠁⠀⠀ ⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠰⠋⠀⠀⣀⣀⣠⣶⡾⠟⣋⣸⣿⠀⠀⠀⠹⣷⣀⠀⠀⣇⠀⠀⠀⣴⣿⣁⣼⠏⠀⢀⣴⡿⠁⠀⣠⡾ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠠⣼⡟⠁⢠⣤⣤⣴⣶⣿⣿⣿⣿⡿⠾⠿⠟⠛⠋⠁⣀⡰⠀⠀⢻⣯⠀⠀⣿⠀⠀⢠⣿⣿⡿⣷⡀⣠⣿⣋⣀⣤⡾⠟⠁ ⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣼⡿⠀⣠⣬⣭⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣃⣠⠀⠘⣿⡆⢠⡟⠀⢀⣿⠏⠿⣷⣽⡿⣿⣟⣛⠛⣿⠁⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⢿⡷⣼⠁⢠⣿⣿⣶⡾⡟⠛⠛⠛⠻⠿⢿⣿⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⡿⠟⠋⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠈⠉⣿⡛⠿⠿⠇⠀⠀⣼⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⡆⠀⠀ ⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣀⠀⢀⣸⡇⠀⠀⠀⠀⢰⣿⣩⣾⠿⠛⢿⠁⠈⢹⣿⣿⣿⣿⠻⣿⣿⠿⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣸⡟⠀⠈⠁⠀⠈⠉⠉⠉⠉⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⣧⣀⣸⣿⣿⣿⣿⣄⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣝⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠉⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⣶⣾⠟⠁⠀⠀⠀⠀⠀⢠⣤⣴⣾⣟⣯⣷⡿⠂⠀⡈⢻⣮⣉⠉⣻⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⢠⣸⣷⣀⣀⣀⣐⣲⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⠿⠿⠋⠉⠀⠀⣀⠀⠀⠀⠙⠻⠿⢿⡏⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣧⡆⠀⠀⠀⠀⠀⠚⣿⣆⠀⠘⠟⢿⣟⢛⣛⣛⣛⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣥⡀⠀⠀⣤⣿⣿⣟⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⢘⣿⣆⠀⠀⠈⢻⣯⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢠⣾⠿⣿⡃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣆⡄⠀⠀⠀⠀⠈⠉⢿⣦⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⡅⡀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠙⣿⣾⡆⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣴⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣗⢄⡀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⣶⡏⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠁⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⣿⠁⠀⠀⠀ ⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣦⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣚⠛⠁⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⢠⣿⠀⠀⠀⢠ ⢀⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣤⣾⠿⠋⠀⠀⠀⠀⣾⡏⠀⠀⢀⣾ ⠟⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡕⠀⠀⠀⠀⠀⠀⠀⣹⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠟⡋⠁⠀⠀⠀⠀⢸⣾⡿⠀⠀⣠⣿⠃ ⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⢀⣼⣿⡛⠿⢷⣦⣤⣤⣤⣤⣄⣀⣀⣠⣤⣤⣴⣶⠿⠟⠛⠁⠀⢀⡾⠃⠀⠀⠀⠀⢴⣾⡟⢀⣠⣾⠟⠁⠀ ⠀⢸⣿⣄⣀⣀⣤⣤⣶⡿⣿⡟⠀⠀⠀⠀⢀⣠⣤⣿⡇⢀⣠⣤⣾⡿⠋⠙⣿⣄⠀⣰⡿⠟⠉⠉⠉⠉⠉⠉⠉⢹⣷⣄⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⣰⣿⣿⣶⠿⠋⠁⠀⠀⠀ ⠀⠈⠉⠉⠉⠉⠉⠉⠁⢰⣿⣥⣤⣤⣴⣶⠿⠋⠻⠿⠿⠟⠛⠉⠁⠀⠀⠀⠈⠻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⠀⠀⠀⣠⡟⠁⠀⠀⠀⣠⣾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⢿⣿⠀⢀⣴⠋⠀⠀⢀⣰⣾⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣧⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⢸⣿⠰⠋⠀⢀⣤⣶⣿⠟⠋⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣷⣄⣤⣴⡿⢋⡁⠀⠀⠀⣾⣯⣤⣶⠿⢿⠛⡉⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⠆⢠⣴⢤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⣀⠔⠋⣴⠃⠀⠈⣯⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡜⠀⠀⠀⣀⠴⠊⢁⡤⠞⠁⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣿⣿⣿⠿⠛⠳⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡧⠔⠚⣉⡤⣤⠞⠋⠀⠀⠀⠀⠀⣠⡴⠛⠉⢽⣿⣿⣿⡿⠿⣿⣿⣿⣿⣦⣤⣴⢛⠚⢹⡝⠲⣄⠀⠀⠀⠀⠀⠀⠀ ⠤⠗⠛⠉⣀⣴⠃⠀⠀⠀⠀⢀⣤⡾⠛⠀⢀⣴⢚⣿⡟⢻⣷⣶⠟⠀⠙⣿⡛⠛⠒⢿⣷⣾⠇⠀⠈⠳⣦⠀⠀⠀⠀⠀ ⠀⣠⡴⠚⢁⡼⢧⠀⠀⢀⣴⠟⠉⠀⢀⣴⠋⣠⡟⠉⠛⣿⣏⡀⠀⠀⠘⣿⣷⡆⡤⠞⣿⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀ ⢠⣿⢀⡶⡿⠀⡼⠁⣠⣾⣿⠂⠀⣠⠞⠁⣴⠋⠀⠀⣼⣿⠉⣿⠋⠉⠉⢻⣿⣧⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀ ⠇⢘⠟⠀⢱⣼⠁⣴⡿⣻⡇⠀⣴⠋⢀⣾⠃⠀⣠⠜⠁⡏⢸⣿⠀⠀⠀⠘⣿⣿⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀ ⡴⠋⠀⠀⠀⠀⣼⠋⢀⣿⣇⣼⠃⢀⣾⣧⠴⠚⠁⠀⠀⣿⡟⢸⣧⠶⢤⡄⢻⣿⡇⠀⣿⠇⠀⠀⠀⠀⠀⣀⣠⣽⠀⠀ ⠁⠀⠀⠀⠀⢸⡏⠀⢸⣿⣿⣿⣶⣿⠏⠀⠀⠀⠒⠤⣀⣿⣧⣘⣿⣆⣠⣄⣘⣿⣧⡀⣿⣀⠀⠀⣆⣠⡾⣿⡟⢿⡇⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⢸⣿⣿⣿⣼⣿⠤⣾⣷⣶⠦⡄⠈⢹⡏⠀⠹⣿⣿⣷⣾⣿⣿⣿⣿⣿⡖⢺⣿⡇⠀⣿⡇⣾⡇⠀ ⠀⠀⠀⠀⠀⠻⠀⠀⣸⣿⣿⣿⣿⣿⣇⡼⠷⣍⣿⡄⠀⠀⢻⠀⠀⢸⡟⢻⣍⠉⠙⠻⣿⣿⣿⣿⣿⡇⡀⢻⣷⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠛⠓⠲⣤⣿⣿⣿⣿⣿⡇⠀⢸⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⠛⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣿⣿⣿⣿⣿⣗⡂⢸⣿⡇⠀⠀ ⠀⠀⠀⠀⢀⣿⡿⣿⣶⣿⣿⣾⡟⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢸⣿⢿⣿⣿⣿⠀⡇⢸⣿⠇⠀⠀ ⠀⠀⠀⠀⣼⡟⠀⣿⣿⣿⣿⣿⡇⢸⣿⣷⣄⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⣄⣾⣿⣿⠀⠇⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⢻⠁⠀⠛⣿⣿⣹⣿⣆⣀⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣷⣾⣹⣿⣿⢿⠁⣻⣿⣆⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⢸⣿⡿⣿⠈⠙⠛⠿⠿⢿⣿⡿⡷⣄⣀⡠⠤⠶⠞⠋⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣿⠁⠙⠦⣀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⢀⣧⣀⣀⣀⣀⣀⣀⣀⡟⠀⠀⠀⠀⠘⠋⠉⠙⠿⠿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⣀⣀⣀⠀⢀⡜⠉⠙⠛⠛⠛⠛⠛⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠈⠉⠒⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣡⡤⡒⡋⠁⠉⢹⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠉⠉⣉⣙⡿⠶⠋⠴⣿⣿⡿⠀⣴⣾⠟⠿⢋⣹⡶⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡘⠿⠦⢴⡶⠀⠀⠀⠀⠀⠀⣠⢕⡊⠛⠛⠷⢯⡀⠀⠙⣍⣉⡹⠖⠀⠀⠀⠀⠀⠀ ⠀⠀⠷⣀⡴⠋⠀⠀⠀⠀⠀⡠⠚⠉⣹⠃⠀⠀⠀⠀⠉⢩⡉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⠁⠀⠀⠀⠀⣠⠞⠁⣀⣴⣇⠀⠀⠀⢰⡀⠀⠀⠁⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⡞⢩⡇⠀⠀⠀⠀⣰⣟⠋⠉⣿⢩⣟⠦⣄⣴⣾⣿⠀⠐⢻⡏⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣸⠃⠀⠀⢀⣾⢃⣸⡀⢠⡇⢸⡗⠀⠀⠀⠀⣿⡇⠀⢸⣷⠘⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⠃⠀⠀⢻⣏⠙⠤⠳⣿⣧⠈⠀⠀⠀⠀⠀⣽⣿⡗⣾⠛⡇⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠙⢿⣶⣤⣯⣏⣀⣀⠀⢿⡇⣀⣽⣿⠿⢧⠀⣷⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠓⢢⣤⡀⠀⠀⠉⠙⠻⠥⢬⣬⣿⣿⣉⣿⣯⣥⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣀⣹⠖⠀⠀⠀⠀⠀⢸⣷⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⡟⡴⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⢰⠁⠀⠀⠀⠀⠀⠙⠀⠠⡄⠀⠀⠈⢗⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠘⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠛⠓⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⡽⢀⣤⡀⠀⠀⠀⠀ ⠀⠀⢀⣀⡾⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣷⠧⣄⣻⣴⢶⣄⠀ ⠀⠀⠈⠛⠧⣀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣙⣻⡷ ⠀⠀⠀⠀⠀⠈⠉⠒⠒⠋⠡⣿⠦⠤⠤⠤⠤⠟⠒⠒⠒⠒⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⡸⠀⠀ ⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠡⠀⡔⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣣⡀⠀⣀⠔⠂⠉⠀⠀⠀⠉⠁⠒⢏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠔⡃⠠⣇⠎⣤⡀⠀⠀⠀⣀⠀⠀⠀⢶⡄⢂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠉⡠⠤⡏⠀⢿⠇⠀⠀⣀⢲⡶⣌⣀⠀⠛⠈⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡎⠀⠀⠱⠀⠀⡠⢔⣩⢴⠋⠈⠁⡄⠈⡐⢤⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣢⠊⣠⡿⠥⢬⠀⠀⠀⣬⣦⠘⡜⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⡘⠀⠀⡇⢰⠿⣾⣿⣟⡛⣻⢀⡸⡸⣿⣿⣹⣿⡈⢣⡀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡆⡇⣽⡍⢡⡧⠺⠋⠱⠇⠀⢸⠁⣷⢀⠟⠁ ⠀⠀⠀⠀⢀⣰⠀⠀⠠⣿⣴⠁⢣⢣⠀⠀⢀⣀⠤⡄⢀⠎⡜⡼⡇⠀⠀ ⠀⠀⢀⠔⠁⠄⠑⡀⠀⠘⡗⠤⡈⠀⠁⠂⢄⡀⢀⠔⠁⣜⠜⠻⡇⠀⠀ ⠀⡠⠃⠀⠀⠈⢢⢃⠀⠀⠘⡄⢰⡇⠒⠀⠘⣷⠀⠀⠀⡞⠳⢄⠈⢱⠄ ⠌⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢹⢀⡇⠈⠀⠀⣿⡀⠀⠀⠧⠄⠀⠻⠀⠀ ⠀⠀⠀⠂⠀⠠⠴⠤⠣⣀⠀⠀⡇⣈⠐⠀⠤⠣⠀⠀⠀⠀⠀⠀⢀⠀⠀

⠀⠀⠀⠀⢸⣷⠀⣹⣷⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⣀⣀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣷⣾⣷⣀⡀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠈⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠈⠉⠛⠻⢶⣄⡀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠙⣷⡀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⡄⠀⠀⠳⡄⠀⠀⠀⠀⣿⡇⠀⡇⠀⠀⢰⡏⠀ ⠀⠀⠀⠀⣼⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢀⡴⠂⠀⠀⠀⠀⣀⡀⠈⢻⣆⠀⠀⢹⠀⠀⠀⠀⣿⠁⢠⠇⠀⢀⣿⠁⠀ ⠀⠀⠀⢀⡿⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⡴⠊⠀⢀⣀⣤⡴⠟⣻⣷⠀⠀⢻⣆⠀⠈⡇⠀⠀⣸⡏⣠⠏⠀⣠⡿⠃⢀⣴ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣾⠏⠀⣤⣶⣶⣾⣿⣿⡿⠿⠟⠛⢉⣁⣀⠀⠈⢿⡄⠀⡇⠀⢠⣿⣿⢿⣄⣴⣟⣡⣴⠟⠁ ⠀⠀⠀⣿⠁⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⣼⣏⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⢸⣇⣸⠃⢠⣿⣉⣿⣿⣿⣿⣯⣭⣿⠀⠀ ⠀⠀⢠⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⣿⡿⠟⠛⠉⠉⠉⣿⣿⣿⣿⡏⠉⠛⢿⡿⣿⡦⠀⢀⣿⡏⣠⣿⣿⣿⣿⣶⣶⣤⣤⣽⣯⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡟⠁⡀⠀⣀⣀⣀⠀⣿⣿⣿⣿⣧⣀⣀⣸⡇⠀⠀⠀⣸⣿⡾⠟⠻⡏⠉⣿⣿⣿⡟⢿⣿⠏⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠁⠀⠀⠀⠱⠤⣿⣿⣿⣷⣼⠇⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⣿⡆⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣭⣭⣿⠟⠁⠀⠀⠀⢀⣀⣤⣶⣶⣶⠆⠀⠻⣿⡛⢻⣿⠀⠀⠀⠀ ⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⣇⠀⢠⣼⣇⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠉⠀⢠⡀⠀⠙⠛⠻⣿⣀⠀⠀⠀ ⠀⠀⠀⢹⣷⠀⠀⠀⠀⠈⢿⡄⠀⠉⢿⣏⠿⠭⠿⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠆⠀⠀⣾⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠘⢿⣆⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣇⡀⠀⠀⠀⠀⠹⣷⣄⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⢻⣿⣤⠀⠀⠀⠀⠈⠙⢷⣄⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⡆⠀⠀ ⣧⠀⠀⠀⠀⠀⠀⠙⢷⣥⣦⡀⠀⠀⠀⠀⠙⢷⣄⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⣠⡾⠋⣿⠃⠀⠀ ⢻⣆⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⠀⠀⠀⠀⠀⠙⢷⣄⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠋⠀⠀⠀⠀⣠⡾⠋⠀⢀⣿⠀⠀⢀ ⣤⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠋⠀⠀⣀⣼⡏⠀⢀⡾ ⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⣰⡿⢦⣤⣀⣀⣀⡀⠀⠀⢀⣀⣀⣠⣤⡶⠟⠛⢉⡇⠀⠀⠀⢀⣽⠟⢀⣴⡟⠁ ⠀⣼⣇⣀⣀⣀⣤⣶⣿⠃⠀⠀⠀⣀⣼⣷⢀⣀⣤⡾⠛⢿⣆⢈⣽⠿⠛⠛⠛⠛⠛⠛⣿⡍⠀⠀⠀⢠⡞⠀⠀⠀⢠⣾⣯⡶⠟⠁⠀⠀ ⠀⠈⠉⠉⠉⠉⠀⢾⣷⣶⡶⠶⠟⠋⠛⠛⠛⠉⠁⠀⠀⠀⠙⣿⠏⠀⠀⠀⠀⠀⢀⣼⣿⣷⠀⠀⣰⠋⠀⠀⢀⣶⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢀⣤⡾⠋⢙⣿⢠⠞⠁⢀⣠⣾⠟⠙⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣠⣴⠟⠋⠀⠀⢸⣯⣤⣴⠾⠛⠋⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⡶⠛⡉⠈⠉⠻⣌⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⠇⠀⡸⠁⠀⠘⣆⠀⠀⠈⠳⣄⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⢱⠃⠀⠠⡇⠀⠀⡆⠘⡄⠀⠀⠀⠈⠳⡄⠀⠹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⢣⠇⠀⠀⢀⣇⣀⣎⢹⣀⣹⣀⣀⣀⣀⣀⠘⡄⠀⢹⡀⠀⠀⠀⠀⠀ ⠀⠀⢰⠃⣸⠒⠉⠉⠉⠉⠁⠘⠚⠀⠀⠀⠀⠀⠀⠀⢹⢻⡀⠀⢧⠀⠀⠀⠀⠀ ⠀⠀⡜⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠸⠀⢰⡇⠀⠀⠀⠀ ⠀⢸⡃⠸⠿⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡇⠀⠀⠈⡇⠀⠀⠀⠀ ⠀⢸⡇⠀⢻⠀⠀⠀⠘⠛⠀⠀⠉⠁⠀⠈⠟⠁⠀⠀⠀⡇⠀⡀⢠⡇⠀⠀⠀⠀ ⠀⣼⢹⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠈⡇⠀⠀⠀⠀ ⠀⢹⣼⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠐⡇⠀⠀⠀⠀ ⠀⢸⣿⡄⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⡇⠀⡇⠀⠀⠀⠀ ⠀⠀⢿⣧⣿⣿⠤⢤⠤⠤⡶⢶⣤⣔⣶⣶⣶⣶⢲⢶⠲⡏⠀⡇⢠⣿⠀⠀⠀⠀ ⠀⠀⠈⢻⣹⡎⡁⢸⠀⣆⣷⣼⣿⣿⣿⣿⠏⢹⣜⣼⢠⠃⠀⡇⠈⣻⡀⠀⠀⠀ ⠀⠀⠀⠀⡿⡇⢸⡈⣇⣿⣿⡿⠛⠟⠛⠁⠀⠸⢿⡿⣼⣀⡀⠁⠘⢿⡇⠀⠀⠀ ⠀⠀⠀⠀⣧⣡⣴⡟⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣼⣧⣿⣿⣿⣿⣶⣾⣿⣀⠀⠀ ⠀⣠⣶⣿⣿⣟⣿⣿⣿⣿⣿⣿⣦⢖⣒⣒⡶⣴⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⡀ ⢠⣿⣿⣿⣿⣿⣿⣿⡟⠳⣯⣻⣿⣿⣿⣿⣿⣿⢟⣵⠟⠉⣼⣿⣿⣿⣿⣿⣿⡇ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⠮⣿⣿⣿⣿⡿⠋⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀⠈⠻⡿⠋⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧ ⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃

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˚ ༘ ೀ⋆｡˚୧ ‧₊˚ 🍮 ⋅ ☆༘⋆🌷🫧💭🐻

🐻✨🌻♡

⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⢤⠀ ⠀⠏⠀⠀⠀⠈⠳⡄⠀⠀⡠⠚⠁⠀⠀⠀⠘⡄ ⢸⠀⠀⠀⠤⣤⣤⡆⠀⠈⣱⣤⣴⡄⠀⠀⠀⡇ ⠘⡀⠀⠀⠀⠀⢈⣷⠤⠴⢺⣀⠀⠀⠀⡼⢁⡇ ⠀⠡⣀⣀⣤⠶⠻⡏⠀⠀⢸⡟⠙⣶⣴⠥⠼⠀ ⠀⠀⢠⡾⠉⠀⢠⡆⠀⠀⢸⠃⠀⠈⣿⣆⠀⠀ ⠀⠀⣿⣠⢶⣄⠀⡇⠀⠀⠘⠃⣀⡤⢍⣈⡀⠀ ⠀⠀⠀⠀⠀⠙⠼⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀

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⠀⠀⢀⣠⠶⠺⢷⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠶⠤⡤⣄⡀⠀⠀⠀ ⠀⣴⠟⠉⠀⠠⣄⠤⣍⠂⠀⠙⠳⢤⣠⣀⣀⣶⣶⠿⠛⠛⢦⣿⣶⠿⠛⠶⣤⣀⣀⣀⣀⣀⣤⠞⠛⠉⠀⠀⢀⡀⠘⠈⢻⣧⡀⠀ ⢰⡟⣥⡖⠂⢀⢈⣦⣀⣙⣀⠀⠀⠀⠀⠈⠻⡿⠏⠄⢀⣠⣀⡉⢥⣲⡆⣀⠻⣿⣿⣏⡛⠯⣧⡀⠀⣀⣤⡴⢿⣏⣁⢄⡀⢙⣷⡀ ⡟⠛⠇⢩⣷⠟⠉⠀⠀⠀⢉⣻⣤⠤⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⢷⣯⣿⣭⠳⣿⡉⠁⠀⠀⠀⠈⢿⣧⣤⣾⣾⠁ ⢻⣶⣾⣻⣻⡀⠀⠀⠀⣰⠋⠁⠀⠀⡀⠒⠂⠁⣥⣀⣤⠤⢦⣠⣤⣾⣾⢁⠐⠛⣯⡙⢺⣭⣳⣿⣿⣄⠀⠀⠀⠀⣸⡻⣿⣿⡿⠀ ⠀⣿⣯⡗⣸⢷⡀⢀⡞⠁⠀⠀⣀⣴⣭⣼⣷⡞⢙⣿⣷⣴⣶⣷⣿⣿⣿⠛⣴⣾⣛⣻⣄⡷⣍⢷⡤⡝⣦⡀⠀⢠⡏⠻⣾⡟⠁⠀ ⠀⠈⢿⣶⣣⠤⣷⡴⠖⡒⠒⣾⢟⢡⣦⣾⣿⣷⣿⣯⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⡿⣿⣿⣫⡗⣥⣭⣛⢿⣶⣿⣯⣭⡿⠀⠀⠀ ⠀⠀⠸⣯⣿⠟⠃⠴⠛⣳⣾⢿⣻⣿⡿⠛⣻⡿⠿⠋⠁⠙⠋⠉⠀⠀⠀⠀⠀⢠⠇⠙⠻⣿⣿⣿⡋⡷⢬⣿⠻⣇⣿⣿⡀⠀⠀⠀ ⠀⠀⠀⠘⣇⡄⣠⢴⣿⣟⣵⣿⡿⠋⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠙⣿⣿⣿⢥⣹⣿⣷⣾⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⣽⣿⣅⣟⣽⣿⣿⠯⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠁⠀⠒⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠉⢻⣷⡶⣿⣛⢿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⡿⠟⢹⣳⢻⡇⠀⣴⣿⣿⣷⣤⠀⢀⡴⠚⠋⠉⠉⠉⠙⠒⢶⡅⠀⣴⣶⣿⣿⣦⠀⢀⣿⣿⣿⣿⡿⢿⡏⠀⠀⠀⠀ ⠀⠀⠠⣾⣏⣠⣾⡟⢹⣼⠁⠀⠟⣿⣿⣿⡟⡷⠋⠀⠀⠀⣤⣤⣄⠀⠀⠀⠙⣦⣥⣿⣿⣿⠇⠀⠀⣧⣽⡿⣿⣷⣀⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣏⢲⣾⣿⣇⠀⠀⠈⠉⠉⠀⡇⠀⠀⠀⠈⣿⣿⡿⠀⠀⠀⠀⢸⡿⠮⠉⠁⠀⠀⠀⣿⡟⢿⣿⢧⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣷⣛⢋⢻⣝⣧⠀⠀⠄⠀⠀⢹⣄⠀⢠⣶⡿⠻⢿⣶⠄⠀⣠⡿⠄⠀⡀⠠⠀⠀⣰⡿⢿⣼⣾⣿⡋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⢸⠸⣿⣏⠳⣄⠈⠣⡄⠀⠙⢷⣤⣄⣀⣀⣀⣀⣤⣾⠟⠀⠀⠀⠀⠀⣠⡶⠫⣠⣾⡿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣽⡿⣷⣌⡛⣲⣾⣿⡶⣿⢿⣿⣿⣿⣿⢻⢿⣛⠻⠷⣶⣶⣴⣾⢏⣿⣫⢿⣿⡧⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⣾⣝⣿⣾⣏⢧⣹⣷⣯⣨⣯⡍⠛⠮⣽⣿⡿⣟⣩⡟⢉⣽⣿⣿⣷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣶⣦⣾⣿⣷⣾⣿⣿⣧⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣻⣿⣿⣿⡿⣛⢛⣿⠟⠋⣥⠿⠿⣯⠁⠉⠉⠉⠉⠙⢿⣿⣿⣻⣿⣻⣾⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣯⠿⠳⠾⢫⣿⣼⣧⡾⢁⠀⢸⣿⠷⠿⢿⡗⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠙⢋⡀⠂⣴⣿⣿⣿⠿⠟⠉⠀⠀⠹⠧⠾⠏⠁⠀⠀⠀⠀⠀⠀⣼⣿⣷⡾⢿⣻⢳⡽⢿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠁⠀⠀⣡⣶⣿⣿⣾⡟⠁⠀⠀⠀⠀⠀⠠⠦⠦⢤⣀⡀⠀⠀⠀⠰⣿⣿⣿⠘⢿⡻⣷⡇⠀⠻⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠃⠀⢀⡴⠋⣠⠿⠋⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⣻⣟⡉⠛⢙⡷⣄⢈⠓⠙⠀⠀⢻⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⣾⠀⢀⡴⢋⣴⡟⠁⠉⠁⠀⠳⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢿⣟⠛⣞⡃⢨⢒⣿⡟⢳⠞⣐⠀⢸⢹⣷⠀⠀⠀⠀ ⠀⠀⠀⠻⣾⣯⣦⠟⣩⠀⠀⠠⠤⠤⢌⠡⢬⣙⡲⣤⡀⢀⣀⣤⢴⣻⠃⣀⡴⢶⣖⡳⢭⣗⢦⡈⠻⣜⣿⡾⠀⣸⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⢹⡅⠀⠀⠀⣠⢆⠘⢷⣴⣌⣿⢾⣻⣿⠛⣁⡽⣟⣉⡻⠵⢆⡨⢥⣀⣘⢷⣹⣦⡾⠟⠲⠗⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡧⢀⣴⣟⡽⢯⣿⢦⣽⣿⣿⣷⡛⢿⣤⡟⣵⠛⠻⢙⣦⡋⠪⣦⠼⢿⣗⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⣏⢙⣤⠜⣧⣀⠏⢻⣿⣿⣷⣾⣿⠁⣴⣇⣰⣿⠋⢻⡖⢛⠗⢺⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣾⡾⠋⣽⡇⠀⠀⢹⡖⠾⡿⣏⢰⡿⠿⢾⣇⣿⣇⣨⡇⠈⠉⠙⣶⠾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣤⠟⠙⢲⢶⠟⠙⠶⣤⣿⡏⠀⠀⠘⣯⣿⡿⠃⣻⣤⣤⡾⠋⢷⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠒⠚⠚⠛⠋⠉⠁⠀⠀⠀⠀⠈⠙⠒⠚⠓⠶⠶⠶⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀꒰ᐢ. ̫ .ᐢ꒱

⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⠟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢼⣿⠀⢿⣿⣿⣿⣿⠀⣾⣷⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠈⠋⢀⣿⣿⣿⣿⣿⡀⠙⠋⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀ ⢀⣀⣀⣀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣾⣿⣷⣦⣤⣴⣿⣿⣿⣿⣤⠤⢤⣤⡄ ⠈⠉⠉⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀ ⠐⠚⠋⠉⢀⣬⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣀⡀⠈⠀⠈⠛ ⠀⠀⠴⠚⠉⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠉⠛⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡜⠻⠿⢾⣷⠹⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡎⠁⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⡠⠞⠛⠛⠻⢽⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⢀⠀⢂⠀⡀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠸⠀⠤⢄⠀ ⠀⠀⠀⠀⠙⣗⣄⠀⠠⡀⢢⠃⠀⢸⠌⠀⡠⢊⠀⠊⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣀⣀⣈⣲⣕⣦⡈⠢⣻⡀⡎⢀⣴⡢⠑⠂⠁⠀⠀⠀⠀⡠⠃ ⠀⣴⠿⠽⠏⠀⠀⠀⠈⠉⢒⣺⣷⣗⣉⣁⣀⣀⣀⠀⠠⠤⠐⠈⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢀⠠⡖⠁⣿⢳⡬⡁⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀ ⠈⢦⡀⠀⠀⡀⠄⠂⠁⠊⠀⢰⣯⡏⠎⢌⠑⠀⠀⠀⠈⠑⢄⠀⠀⠀ ⠀⠀⠉⡻⠀⠀⠀⠀⠀⠀⣲⡟⡟⠀⠀⠀⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢧⣤⡄⡀⠀⢀⡔⣽⠃⢧⡄⠀⠀⠀⠰⣀⠀⠀⣀⠞⠀⠀⠀ ⠀⠀⠀⠈⠳⠬⠥⠔⠋⡜⡌⠀⠘⣿⣦⣀⠀⡀⡇⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠀⠀⠀⠈⠛⠯⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠖⢂⣽⣿⣿⣷⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟ ⠀⠀⠀⠀⣀⣤⡶⢿⣋⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⢀⣠⣾⠿⠋⠀ ⠀⢀⣴⣿⠟⠉⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⡿⠛⠋⠉⣀⣤⠶⠟⠋⠁⠀⠀⠀ ⢰⣿⡟⠁⠀⠀⠀⣷⠀⠀⠀⠀⠀⠈⣿⣿⣟⣀⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⣧⣀⡠⠤⢾⣿⣷⠤⠄⠀⠀⠀⢹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀