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