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

      †      𓎢𓎟𓎡      ༏ིྀ    𝓫ᥣ᥆᥆dᥡρᥲᥕ᥉ ∔ ,, 𐔌ˇ 🎀 ιᥒtr᥆dᥙᥴtι᥆ᥒ  𓈒 𓈒 haii ! i’m bloodypaws ! ^__^ although i may not be as active as some other people on emojicombos.com ,, im a layout creator here on the website !! im 17 ,, a gyaru / gal , and these are my interests !! i like : roblox ,, discord ,, the sims 4 ,, yansim ( i do not support yandev ) ,, fortnite ,, needy streamer overload ,, minecraft ,, fashion ,, mha ultra rumble ,, my hero academia ,, sabrina carpenter ,, melanie martinez ( i do not support her actions ) ,, sir mix a lot ,, and more !! (ᵕ—ᴗ—) thank u for reading ! ! (๑ᵔ⤙ᵔ๑) now take some symbols !! ^__^ ( CREDITS HAVE BEEN LEFT ON THESE , THEYRE NOT MINE ! ) ♡ ⠀⠀⠀ ⠀ ୨୧ ⠀⠀⠀⠀ ⠀ ୨ৎ ⠀⠀⠀⠀ ⠀ ฅ ⠀⠀⠀⠀ ⠀ ೀ ☆ ⠀⠀⠀ ⠀ ⑅ ⠀⠀⠀⠀ ⠀ ♩ ⠀⠀⠀⠀ ⠀ ◌ ⠀⠀⠀⠀ ⠀ ꕤ 𓋜 ⠀⠀⠀ ⠀ ๑ ⠀⠀⠀⠀ ⠀ ៸៸៸ ⠀⠀⠀⠀ ⠀ ‹𝟹 ⠀⠀⠀⠀ ⠀ ʚ ꔫ ⠀⠀⠀ ⠀ 𓈒 𓈒 𓈒 ⠀⠀⠀⠀ ⠀ 𐂯 ⠀⠀⠀⠀ ⠀ ◝ ⠀ ⠀⠀⠀⠀⠀ ᵎᵎ ꒰ ꒱ྀི ⠀⠀⠀ ⠀ ꒰ ꒱ ⠀⠀⠀ ⠀ ૮ ა ⠀⠀⠀⠀ ⠀ ฅ ฅ ⠀⠀⠀⠀ ⠀ ก ก ‌ ⠀⠀⠀ ⠀ ⊃ ⊂ ⠀⠀⠀ ⠀ ՞ ՞ ⠀⠀⠀⠀ ⠀ ‎ﻌ ⠀⠀⠀⠀ ⠀ ﹏ ❊ ྀ ི ✦ ༽ ༼ ྌ ꒰ ・ ‌ ፝֟‌ ౿ ꘩ ᭥ 𑂅 ☆ つ ⏜︵ ︖ ᧔ ✿ ୧ ꕮ ꣑ ♡ ໒ ၇ ㅤ᭢ ܍ ⪨ ৴ ⌑ ꪆ ୧ ౿ ⩍ ⩌ | ‌ | ‌ | ꒸ ◍ ५ ⑅ ◞ ◟ ೀ ------------------------------------------------------------ ִ ☆゙ ۫ 🦷‌ ֶָ ࣪ ׅ 言 ʾʿ ›‹ ก ࣪ ۪ 𝒜ᱹ ֢ 🦢‌ࣳ 𖧧 ִ ࣪ ⋆ ٫٫ 𝐘ᱹ 🥛᪶ ࣪ ָ 𖦹 ۪ ࣪ ִ さ 𝇃𝇂 ˒ ˓ 我 ⸼ ࣪ ✿◌ ۪ 𖥁‌ ࣪ ִ ⩇⩇ ᭡ 🗯‌ ⬚ ִ ๑ ᘡ 𑁍 ˙ ❀̼ ᨵ ਏਓ 𓈒 ⛽⃝ ࣪ ◍ ׅ ヰ ׂ ♡ิ ݂ ✦ ݁ ﾶ ۪ 🍡 ່ ִ ♡゙ ݂ ⤿ 𝆬 🧃 ׅ ➛ ˒˓ 𖡎 ࣪ ۪ ⬔ 𓈒 ᜃ ˙ ᰍ ִ ױ ࣪ 🩰⃝⃝ ݂ ๑ 𝆬 𝖿ꭤׅ𝗂𝗋𝗒 ⬞ ִ 𓈃 ׂ ‎𐫱 𝂅 숌 ݁ 𔒌 ˒˓ 𓈊 ۫ ᘏ ׅ ≡ ݁ ィ ִ ꕤ 𝆬 𔒱 ݂ ꒷꒦ 🧁 ۪ ᘐ ˙ ᖘ ׅ ❍ ׂ ᳤ ✩᳣ ۪ ᯤ ݁ ઇ 𓈒 ୯ ࣪ ᦾ. 🎀⃞ 𔓗 ݂ ୬ 𔖳 ׅ ২ 𓂅 ࣪ ೨ ۪ ◩ 𝆬 ᨎ ִ 𓈀 ۫ ᨫ̼ ִ ⌇ ׂ ᨯ ׅ ᰋ ݁ ᘛ ݂ ᰌ 𝆬 ◎ ݂ ᨸ ˙ ✿ ˒˓ ᪄ ࣪ ⩁ ݂ ᘐ ݁ 🥟⃝ 𓈒 ᘡ ࣪ ╰ ꞋꞌꞋ ׅ ▭▬ 𝆬 𔘓 ׅ ਕ ۫ ╮ ৬ ۪ 𝇁𝇃𝇂 ࣪ ৯ ◞ ୨୧ ׂ ⤺ ִ ⟳ ʾʿ ◍⃘ ᜔ 🧂 ִ ᡛ 𝆬 𓍯 ׅ 𖣗 ݁ ❏ 𓈑 𓈒 📃 ۫ 𓊌 ˒˓ ▞ ࣪ ۪ 𔓕 ᩧ ✷ ׅ 𓈁 𓄰 ׂ ✻ ݂ ꮚ ׂ 𓋜 ۪ ᘞ ˙ 𓊔 ִ 𓄸 𓄳 𝆬 𓍢🥞 ׅ 𔔡 ʾʾ 𖠇 ۪ 𖣯 ࣪ ꗃ ִ 백지헌 ࣪ 🥯 𓈒 𝇋♡︎𝇌 ׂ 🜸 ׅ 𝆬 ﹫txt ݂ 🜲 ۫ ʬ ᜔ ᄿ ˙ 𝆺𝅥𝆹𝅥 ִ ǂ ݁ ◌ ׅ ᥐ ׂ ⩇⩇:⩇⩇ ׅ ࿂ ݂ ★ ׂ ⍝ . 𓂃 ✿゙ ݁ 𓆩𓆪 ׅ 𔐬 𝆬 𐀔 ִ (:̲̅:̲̅:̲̅[̲̅:♡:]̲̅:̲̅:̲̅:̲̅) ꐑꐑ : 🐄 ׅ ꣹ ۫ 𖨂 𓈒 ᕱ ˓˒ ꨣ ࣪ ʚĭɞ ׅ 𝆭 𑄾𝇂 ִ ᱑ ׄ ׅ 🍭𝆬 ݂ ꭷ ࣪ ☆̸★ ݂ ƸӜƷ ׄ ᱉ ׅ ᱈ ۫ ﹏ 𐀓 = ִ 📁 ࣪ ᰊ ׅ ˙ ⊹ 𓂐 ۪ ▯ ࣪ ꒰ 💭 〢 ⎓ ݂ ఇ ⬭ ࣪ 𔗫 𓈒 ⥽ ݁ ⩩ ˓˓ ᦔ ۪ 〨 ׂ ⩌ 𖫱 ㄔ ִ ∩ യ 𝆬 𓈈 ݂ 👣 ࣪ ੲ⃞⃝ਦ 𝂅 ⩅ ࣪ ⨳ ˒˒ ㅃ ׄ ------------------------------------------------------------- 𐂯‎   ⠀ ⠀ ﾉ  ⠀ ⠀ 𐔌ㅤ  ⠀ ⠀ ೀ  ⠀ ⠀ ᭪ ⼺  ⠀ ⠀ ⺀  ⠀ ⠀ 𓈒۫　ׅ ✧ ⠀˙⠀ ˖ ⁺ ༝ ۫　 ݃ ｡𓃉 ᱖  ⠀ ⠀ ꒰ ⠀꒱  ⠀ ⠀ ྀི  ⠀ ⠀ ⨟  ⠀ ⠀ ᜊ ⁘  ⠀ ⠀ ✎  ⠀ ⠀ ♱   ⠀ ⠀๋  ⠀ ⠀ જ⁀➴ ꒰ა ⠀ ໒꒱  ⠀ ⠀ ฺ  ⠀ ⠀ 𐂯ྀི  ⠀ ⠀ ⠀ ฅ ฅ ೃ𓈒𓏶ྀི  ⠀ ⠀ ౨౿  ⠀ ⠀ ♬  ⠀ ⠀ ‹𝟹 ⠀ ̥°̩̥˚̩̩̥͙°̩̥ 𐐂𐐚  ⠀ ⠀ ๑   ⠀ ⠀ ⪩ ⪨  ⠀ ⠀ 𓉸ྀི  ⠀ ᦏ♡᪔ 𓂋  ⠀ ⠀ 𐚁᭢༘۠  𐙚ㅤㅤ  ⠀ ⠀ 𓄯ྀི  ⠀ ू𑣩𑣨 ♪ྀི  ⠀ ⠀ ꒰੭  ⠀ ⠀ ◟𓋜  ⠀ ⠀ ও  ⠀ ⠀ ⠀∿ ❀ᬊ  ⠀ ⠀ ᶻ 𝗓 𐰁  ⠀ ⠀ 𝗓 ᶻ  ⠀ ⠀ ཻུ۪۪♡⠀  ꩜ྀི｡ ᡣ ︠ 𓈒. .𓈒 ︡𐑠   ⠀ ⠀ 𓈉  ⠀ ⠀ 𖡎  ⠀ ⠀ ✐  ⠀ ♡⃞ CREDITS :: 𝔠𝔥𝔦𝔩𝔡𝔥𝔬𝔬𝔡𝔠𝔞𝔯𝔫𝔞𝔤𝔢 CREDITS :: TSFC 𐔌　𓋫　𓌔　ᛝ　𓏵　໒ྀི　℘　𓎢𓎟𓎡　𓇯　𓉸　◞ ྀི ︶　 ྀི◟　 ͜　˚̣̣̣　｡　 ಿৎ　༻　⊰　⊱　༺　♰　𓂃　ℰ ✟　 ྀི　༏ིྀ　‿　ཁ　ཀ　 ೀ　𓏏𓏏　†　₊　˙　．ㅤ۫　 ݃　𓃉 ⁺　︵　𓏴　⸸　꒱　　╱　　𓍯　ℳ　◌　♱　꒰ྀི　꒱ྀི　ℱ 𝄞　𝒢　𝒞　ℐ　ℋ　✚　❜ㅤ❛　✙　࿐　༢　࿐ྂ　ℛ　ℬ ℒ　✧ ࿐ ༢⠀ㅤ𓈒⠀⠀⠀୨୧⠀⠀˙⠀⠀｡ ⠀꒱ྀི CREDITS :: liqhtscafe ◟ ͜ ͜ ◞◟ ͜ ͜ ◞ ᛪ༙ ◟ ͜ ͜ ◞◟ ͜ ͜ ◞ ~~ᴗ⁠ᴗ⁠ᴗ⁠ᴗ⁠ᴗ⁠ᴗ⁠~~ ⏔⏔ཐཋ⏔⏔ 𓎟𓎟ཐཋ𓎟𓎟𓎟𓎟ཐཋ𓎟𓎟 ◞◟‿‿◞ ୨♱୧ ◟‿‿◞◟ ◞◟ ͜ ◟ ͜ ᧔ ϱ ͜ ◞ ͜ ◞ ◜₊ ͡ ୧‿ིྀˌ͙‿𓉳‿ིྀˌ͙‿୨ ͡ ₊◝ ◟-͜-◞◟-͜-◞◟-͜-◞ 𐙚ྀ ͝ ྀི d᥆ᥣᥣ 🥛ིྀ ͝ 𐙚 𓏵݁ ༏ ྀི ◟‿◞ ◟‿◞ ‎٨ـﮩ٨ـﮩﮩ٨ـﮩ٨ـﮩﮩ٨ـ ◟ ͜ ͜ ◞◟ ͜ ͜ ◞ ᛪ༙ ◟ ͜ ͜ ◞◟ ͜ ͜ ◞ 𝜗 ๋ . ༢ུ . ‿ ✟ ⌣⌣⠀⠀⠀❀  little fleur ﹒ ◟ ͜  𝜗ৎ ‿︵ ◞◞ ◟‿ 𓈒 𓈒◌ text 𓈒ᐟ 𝑠𝑤𝑒𝑒𝑡іe ⑅ ✚ㅤ◜ ͡ ◝ ◜[ emoji ]◝ ◜ ͡ ◝ ㅤ✚ ◞ 🍀 ੭ li𝑡𝑡ᥣ ᥴl𝑜ᴠᥱ ⑅ ݁ 🧁 𓏵 his cupcake 𓋫 𓎢𓎟𓎟୨ ♱ ୧𓎟𓎟𓎡 ♱ྀི◟◞♱ྀི◟◞♱ྀི◟◞♱ྀི◟◞♱ྀི◟◞♱ྀི ᧔◡◡◡◡◡◡◡◞ ◟◡◡◡◡◡◡◡◡᧓ ⏝.‿‿◟꣑୧◞‿◟꣑୧◞‿‿⏝ ˙˖ |꛱ ͜ |꛱ ͜ |꛱ ͜ |꛱ ͜ |꛱ ͜ |꛱ ͜ |꛱ ͜ |꛱ ͜ |꛱ ˖˙ ྀི ◞◟ ͜ ◞ ྀི 𐂯 ྀི ◟ ͜ ◞◟ ྀི ྀི︶˚̣̣̣ ྀི◟ ͜ ◞˚̣̣̣ ྀ︶⸸︶˚̣̣̣ ྀ◟ ◞˚̣ ︶ NO CREDITS ATTACHED ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ,, search bloodypaws for more of my content ! ! ྀི