⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢺⣷⡀⢶⢮⣲⡐⣄⣀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⢿⡿⠏⠁⢰⣆⣿⠋⠛⠉⠷⡹⣆⠈⢸⣴⠀⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠹⣿⣿⣾⢦⡼⡌⢿⡜⡎⣯⡀⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⠸⣿⡇⠀⠀⠀⠀⢻⣿⡏⢧⢵⣌⣢⣿⣷⣿⣷⠋⡕⠊⠀⠀⠂⠀⠀ ⠀⠀⣸⣿⡇⣿⠻⠀⣀⠤⠒⠁⠙⢿⡄⢕⣄⣱⣤⣽⣿⣿⠀⣆⡀⠉⠵⠋⠀⠀ ⠀⠀⣿⡏⢻⣿⣇⠁⣠⣤⣤⣦⠀⠐⠙⠢⠻⡟⢻⠁⣿⢺⠈⠋⠛⠓⠲⢽⣦⡄ ⠀⠀⣿⣿⣦⣿⣿⡯⣙⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢼⠛⡆⠀⠀⠀⠀⠀⠙⠁ ⠀⠀⢹⠟⠛⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣇⢱⡀⠀⠀⠀⠀⠀⠀ ⠀⠐⠁⠀⢠⣿⣿⡇⠑⢄⠀⠀⠀⠀⣶⣖⠆⠀⡠⢊⡠⢿⣆⣣⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⡧⠤⠀⠉⠒⣠⡀⣀⣀⠠⠪⠂⠁⠀⠀⠳⢿⣿⣳⣷⣦⠀⠀ ⠀⠀⢠⣿⠿⡿⣼⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣷⡄ ⠀⢰⢏⣿⣶⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡗ ⠀⡏⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃ ⠀⡇⠀⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⡴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠁⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⡜⡜⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣤⣄⣤⣤⢤⢖⡮⠁⠀⠀⠀ ⠀⢠⠀⠃⣿⣿⠟⠦⡤⢀⣀⣀⡠⢄⡒⠶⣖⣋⣓⠒⠚⠯⢄⡴⠁⠀⠉⣏⠕⠀ ⢒⣾⠰⠀⣿⣿⡋⠒⢄⠀⠀⠁⠂⢀⣴⡭⠤⠤⠶⢎⣹⢲⣯⡟⠉⠉⠁⠀⠀⠀ ⣿⡟⠀⠀⠙⢄⣙⣶⢦⡊⠁⠀⣠⠞⠉⡐⠀⠁⠀⣠⡿⠟⡏⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⠀⠀⠀⠀⠻⡌⢆⠑⣄⠜⠁⠀⠀⠀⠀⣀⠸⡁⣠⠔⠑⠦⢄⣀⠀⠀⠀⠀ ⠀⢺⣦⣀⣀⣀⣀⣸⠀⣦⣿⠎⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠄⢀⠀⠉⠐⢀⠀

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⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣾⣿⣧⠀⢰⣄⢦⡻⣦⡄⠠⡄⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣳⣿⡿⣿⣿⣿⢿⠿⠛⢿⠸⣿⡿⣷⣀⢿⣆⣿⣎⢻⣶⡸⠼⠼⡆⢻⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣯⣿⣽⣹⢻⢏⠎⠀⠀⢠⡿⣆⢿⣷⢸⠈⠛⠃⠈⢻⣦⠹⣷⡀⠀⢹⠸⣧⢳⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣇⣿⣼⠈⠀⠀⠀⠀⢹⢻⣾⣿⣇⣧⣱⣤⡀⠘⡎⠳⣮⢳⠀⣾⠀⣿⠸⡆⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡝⢿⣞⠷⣄⠘⣿⣇⢸⡇⣿⣦⡇⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⣿⡜⢿⡈⠻⣄⠈⠳⣜⣿⣆⣷⣿⢹⣷⣀⡿⠓⣢⠴⠋⠁⠀⠈⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⠿⣞⣿⣧⠈⠻⡝⠺⠷⣦⠾⠿⣿⣿⣿⣿⣿⡇⣀⢲⠁⠀⢄⡠⣀⠀⣐⡄⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡆⣿⣿⡟⡇⠀⠀⠀⣀⡤⠞⠁⠀⠈⢯⣿⣇⠐⢮⢢⡀⠈⣑⡤⣤⣽⣿⣿⡟⡇⠀⢾⣀⠀⠀⠠⠬⠷⠟⠁⠀⠀⠀ ⠀⠀⠀⢸⣿⡿⣿⣷⣿⣿⣇⠡⠔⠒⠉⠁⠀⠠⣄⡀⠀⠀⣝⢿⣧⡀⢻⣽⣿⣷⣟⣿⠟⢟⣿⡇⡇⠀⣿⣯⣷⣦⣄⣀⠨⠤⣂⠀⠀⠀ ⠀⠀⠀⢸⣿⣇⠀⢙⣿⣿⣿⡀⠀⣠⣤⣒⣲⣿⣷⣷⡀⠀⠈⠃⠈⠓⠞⠙⢿⠛⠉⣯⠤⣸⢿⣇⣿⠀⠀⠀⠀⠀⠀⠈⠙⢷⣮⣿⢦⠀ ⠀⠀⠀⣼⣿⣿⣷⡀⢹⣿⣿⣿⡿⠛⢿⣿⣿⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢸⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠘⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣾⣿⣿⣷⡉⠒⠶⠛⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣸⡇⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⠿⠛⢹⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣷⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠛⠁⠀⠀⣼⣿⣿⣿⣿⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣠⠏⠀⢯⣧⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠞⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⡾⠿⠟⣻⠂⠀⠀⢀⠜⠁⣀⠴⢿⡿⣦⢈⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠈⠉⠉⠀⠀⣠⠖⡥⠖⠉⠀⠀⠀⠙⣯⡳⣽⣗⢿⣶⣴⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⡿⣹⡿⣿⣿⠙⠒⠒⠢⠤⠠⠤⠭⢝⣒⡢⠤⠤⠴⠊⠱⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⢽⣳⢯⣿⣿⣿⣦⡀⠀⠀ ⠀⠀⠀⠀⢠⣿⣷⣿⢳⣿⢡⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣄⠀ ⠀⠀⠀⣠⡿⣿⣧⠀⣿⣣⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀ ⠀⠀⣰⡿⢱⣟⣿⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡁ ⠀⢠⣿⠁⢸⣿⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇ ⠀⢸⡇⠀⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⡄⠀⠀⢸⡉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣧⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠇⠘⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⣰⢳⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠃⢰⠏⣼⢧⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⣀⠀⠀⠀⢀⣀⣠⣤⣤⡶⣚⣭⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⡞⠀⡏⠀⣧⣜⣧⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠛⣛⣛⣿⣿⠟⠉⠛⣡⠾⠯⠤⣄⣀⣀⠄⠈⠀ ⠀⠀⢀⡇⢰⠃⠀⣿⣿⣿⡏⠛⢷⣦⠤⣀⣀⣀⣀⣀⣠⡤⠴⣒⠺⠿⢶⡟⢓⣉⡉⠛⠛⠛⠫⠯⠤⠄⢀⡞⠁⠀⠀⠀⢠⢞⣡⠖⠁⠀ ⢴⣀⣸⠀⢸⠀⠀⣿⣿⣿⡦⢤⣄⡈⠁⠀⠈⠙⠳⠤⡀⠀⠈⠁⣠⠴⠞⠋⠉⠉⢉⣙⠳⠶⢤⣀⣤⡾⢷⣶⠶⠒⠒⠒⠋⠉⠀⠀⠀⠀ ⢀⢷⣿⠀⡜⠀⢸⣿⡿⢿⣇⠀⠀⠙⣦⠀⠀⢀⣀⣀⣀⣀⣀⣼⣷⣶⠖⠛⠛⠉⠉⠙⢷⣄⣿⡁⢿⣶⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠀⠀⠀⠈⠻⣅⠀⠙⣷⣶⣤⣨⠴⠚⠉⠀⠀⠀⣨⣾⠏⠉⠀⠖⠀⠈⠀⠀⠀⢀⣿⣿⣻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⡇⠀⠀⠀⠀⠀⠘⢷⣷⡌⢿⡇⢹⣦⠀⠀⠀⢀⡴⠋⠀⠀⠀⠚⠂⠂⠀⠀⠀⣴⡿⠟⠋⠁⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠹⡄⠈⢣⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⢀⣠⠴⠋⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢉⢉⣙⣧⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⢹⡀⢀⣿⣥⡞⠃⠀⠉⠁⠀⠀⠀⠈⠉⠉⠈⠀⠓⠛⠳⠆⠀⡀⠀⠀⠀⠉⠙⠲⢦⣄⡀⠀⠀⠀ ⠀⠈⠽⣿⣷⣤⣀⣀⣀⣀⣠⣤⣼⡇⠀⣿⣼⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⢀⣀⠀⠀⠀⢀⢁⣀⡀⠀

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( * ) ( * )

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⠀⢀⠐⠉⠀⢀⠄⠐⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠎⣿⣦⠀⣸⣀⣀⣀⣀⣦⢺⠀ ⠀⠀⠀⠀⣀⢄⠦⠑⠔⣠⡁⠸⣀⠀⠀⠀⠀⠁⠜⣄⠑⢆⡌⠻⠀⠀⠀⠀⣧⣿ ⠀⠀⠀⠀⠀⠀⠀⡏⠟⡿⣠⠀⠁⠀⡐⠉⠞⣠⠀⠁⡊⢦⣶⣙⢄⠙⠀⠀⡟⣿ ⠀⠀⠀⠁⠉⠉⡟⣯⢲⣹⢎⠶⠤⠤⡭⣴⢀⠂⠁⠀⠀⢄⠒⡋⣿⣿⠀⠰⣾⢒ ⠀⠕⣏⠉⠀⠁⡴⢄⠯⠚⠒⣓⣋⣖⠶⡒⢄⡠⣀⣀⢀⡤⠦⠟⣿⣿⠃⠀⢠⠀ ⠀⠀⠀⠁⡮⢖⢤⣤⣤⣄⣤⣷⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣟⡜⡜⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠁⢰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢿⠿⠀⡇⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⢸⡏⠀ ⡗⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⣶⣿⢏⢰⠀ ⡄⣷⣿⠻⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡇⣼⡿⠿⣿⢠⠀⠀ ⠀⠀⣦⣷⣳⣿⢿⠳⠀⠀⠁⠂⠪⠠⣀⣀⡀⣠⠒⠉⠀⠤⡧⣿⣿⣿⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣣⣆⢿⡠⢊⡠⠀⠆⣖⣶⠀⠀⠀⠀⢄⠑⡇⣿⣿⢠⠀⠁⠐⠀ ⠀⠀⠀⠀⠀⠀⡀⢱⣇⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⠛⠟⢹⠀⠀ ⠁⠙⠀⠀⠀⠀⠀⡆⠛⢼⠈⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⣙⡯⣿⣿⣦⣿⣿⠀⠀ ⡄⣦⢽⠲⠓⠛⠋⠈⢺⣿⠁⢻⡟⠻⠢⠙⠐⠀⣦⣤⣤⣠⠁⣇⣿⢻⡏⣿⠀⠀ ⠀⠀⠋⠵⠉⡀⣆⠀⣿⣿⣽⣤⣱⣄⢕⡄⢿⠙⠁⠒⠤⣀⠀⠻⣿⡇⣿⣸⠀⠀ ⠀⠀⠂⠀⠀⠊⡕⠋⣷⣿⣷⣿⣢⣌⢵⢧⡏⣿⢻⠀⠀⠀⠀⡇⣿⠸⣿⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⡀⣯⡎⡜⢿⡌⡼⢦⣾⣿⣿⠹⠀⠀⠀⡇⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⠀⣴⢸⠈⣆⡹⠷⠉⠛⠋⣿⣆⢰⠁⠏⡿⢿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣄⡐⣲⢮⢶⡀⣷⢺⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀

⠀⡀⣀⢁⢀⠀⠀⠀⣀⢀⠀⠙⠈⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣾⣼⣿⠀⡇⣼⣤⣠⣀⣀⣀⣀⣤⣷⣿⠽⠈⠀ ⠀⠀⠀⡀⣄⢦⠲⠙⠉⠀⠀⠀⡀⠀⠆⠳⠛⠓⠀⠈⠉⠉⠈⠀⠀⠀⠁⠉⠀⠃⡞⣥⣿⢀⡀⢹⡀⢻⠈⠀⠀⠀⠀⠀⠀⠀⣧⣙⢉⢉ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢦⠳⠙⠋⠴⣠⢀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣴⣀⢣⠈⡄⠹⡄⢿⠙⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⠁⠋⠟⡿⣴⠀⠀⠀⠂⠂⠚⠀⠀⠀⠋⡴⢀⠀⠀⠀⣦⢹⡇⢿⡌⣷⢷⠘⠀⠀⠀⠀⠀⡇⣿⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⠿⣻⣿⣿⢀⠀⠀⠀⠈⠀⠖⠀⠉⠏⣾⣨⠀⠀⠀⠉⠚⠴⣨⣤⣶⣷⠙⠀⣅⠻⠈⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⣶⢿⡁⣿⣄⢷⠙⠉⠉⠛⠛⠖⣶⣷⣼⣀⣀⣀⣀⣀⢀⠀⠀⣦⠙⠀⠀⣇⢿⡿⣿⢸⠀⡜⠀⣿⢷⢀ ⠀⠀⠀⠀⠉⠋⠒⠒⠒⠶⣶⢷⡾⣤⣀⢤⠶⠳⣙⢉⠉⠉⠋⠞⠴⣠⠁⠈⠀⡀⠤⠳⠙⠈⠀⠁⡈⣄⢤⡦⣿⣿⣿⠀⠀⢸⠀⣸⣀⢴ ⠀⠁⠖⣡⢞⢠⠀⠀⠀⠁⡞⢀⠄⠤⠯⠫⠛⠛⠛⡉⣉⢓⡟⢶⠿⠺⣒⠴⡤⣠⣀⣀⣀⣀⣀⠤⣦⢷⠛⡏⣿⣿⣿⠀⠃⢰⡇⢀⠀⠀ ⠀⠈⠄⣀⣀⣄⠤⠯⠾⣡⠛⠉⠟⣿⣿⣛⣛⠛⠟⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣱⣧⣜⣧⠀⡏⠀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⣭⣚⡶⣤⣤⣠⣀⢀⠀⠀⠀⣀⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⢧⣼⠏⢰⠃⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⢳⣰⠀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠘⠇⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣧⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⡉⢸⠀⠀⡄⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⠈⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⢸⠀⡇⢸⠀ ⠇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣾⣿⢸⠁⣿⢠⠀ ⡁⣿⢻⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣴⣿⣟⢱⡿⣰⠀⠀ ⡀⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣣⣿⠀⣧⣿⡿⣠⠀⠀⠀ ⠀⣄⣿⣿⣿⢿⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢡⣿⢳⣿⣷⣿⢠⠀⠀⠀⠀ ⠀⠀⡀⣦⣿⣿⣿⢯⣳⢽⠾⠙⠈⠀⠀⠀⠀⠀⠀⠀⠋⠱⠊⠴⠤⠤⡢⣒⢝⠭⠤⠠⠤⠢⠒⠒⠙⣿⣿⡿⣹⡿⣿⣾⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣦⣴⣶⢿⣗⣽⡳⣯⠙⠀⠀⠀⠉⠖⡥⠖⣠⠀⠀⠉⠉⠈⠀⠀⡀⣄⠦⠓⠈⠀⠀⠀⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡳⢈⣦⡿⢿⠴⣀⠁⠜⢀⠀⠀⠂⣻⠟⠿⡾⠀⠀⠀⠀⠀⠀⡀⢦⠘⠀⣿⣿⣿⣿⣿⢠⠀⠀⠀⠁⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⠘⣧⢯⠀⠏⣠⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⣿⣿⣿⣿⣼⠀⠀⠁⠛⡴⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⣷⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⢹⠛⠿⣿⢿⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⡇⣸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠛⠶⠒⡉⣷⣿⣿⣾⣿⣿⣿⣿⢻⠀⠀⠀ ⠀⠘⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⣿⣿⢿⠛⡿⣿⣿⣿⢹⡀⣷⣿⣿⣼⠀⠀⠀ ⠀⢦⣿⣮⢷⠙⠈⠀⠀⠀⠀⠀⠀⣿⣇⢿⣸⠤⣯⠉⠛⢿⠙⠞⠓⠈⠃⠈⠀⡀⣷⣷⣿⣲⣒⣤⣠⠀⡀⣿⣿⣿⢙⠀⣇⣿⢸⠀⠀⠀ ⠀⠀⠀⣂⠤⠨⣀⣄⣦⣷⣯⣿⠀⡇⡇⣿⢟⠟⣿⣟⣷⣿⣽⢻⡀⣧⢿⣝⠀⠀⡀⣄⠠⠀⠁⠉⠒⠔⠡⣇⣿⣿⣷⣿⡿⣿⢸⠀⠀⠀ ⠀⠀⠀⠁⠟⠷⠬⠠⠀⠀⣀⢾⠀⡇⡟⣿⣿⣽⣤⡤⣑⠈⡀⢢⢮⠐⣇⣿⢯⠈⠀⠁⠞⡤⣀⠀⠀⠀⡇⡟⣿⣿⡆⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⡄⣐⠀⣀⡠⢄⠀⠁⢲⣀⡇⣿⣿⣿⣿⣿⠿⠾⣦⠷⠺⡝⠻⠈⣧⣿⣞⠿⣠⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⠀⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢦⠈⠀⠁⠋⠴⣢⠓⡿⣀⣷⢹⣿⣷⣆⣿⣜⠳⠈⣄⠻⡈⢿⡜⣿⣿⣾⠹⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠘⡇⣦⣿⡇⢸⣇⣿⠘⣄⠷⣞⢿⡝⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⡆⠸⣿⠀⣾⠀⢳⣮⠳⡎⠘⡀⣤⣱⣧⣇⣿⣾⢻⢹⠀⠀⠀⠀⠈⣼⣿⣇⣿⣿⣿⣿⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢀⠀⢳⣧⠸⢹⠀⡀⣷⠹⣦⢻⠈⠃⠛⠈⢸⣷⢿⣆⡿⢠⠀⠀⠎⢏⢻⣹⣽⣿⣯⣿⣿⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢻⡆⠼⠼⡸⣶⢻⣎⣿⣆⢿⣀⣷⡿⣿⠸⢿⠛⠿⢿⣿⣿⣿⡿⣿⣳⣿⣿⣿⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⠀⡄⠠⡄⣦⡻⢦⣄⢰⠀⣧⣿⣾⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀