⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡙⣿⣙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡂⠤⠤⠤⠽⠛⠋⢁⠈⠙⠢⡱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢐⠈⠁⠀⠀⠀⠀⢀⠀⠀⠈⠐⠄⠀⠈⠛⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢁⠞⠁⠀⠀⠀⠀⠀⡰⠁⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⡈⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢊⡏⠔⠎⢠⣖⠬⡀⠀⣠⡼⢁⢠⢃⠀⠀⠀⡄⢠⠀⠀⢸⢰⠢⢌⢺⢺⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡐⠸⢼⡞⠀⠈⠉⢁⠄⣼⣾⢃⠆⠸⡘⠄⠀⣤⣱⠰⡑⡄⢸⢠⠂⠀⠉⠣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡿⠀⠇⡨⢋⠁⠀⢀⡆⣼⠟⢻⢸⠀⠀⠱⡀⢠⣿⡿⢧⣙⢌⠣⣜⠀⠀⠀⠀⢌⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣵⣺⡭⠔⠁⢀⢤⣻⢰⠇⠒⠼⡎⠀⡀⠀⢐⢸⡿⠒⠒⠪⠷⣗⣦⠕⣢⣄⠀⠘⢷⡹⡄⠀⠀⠀⠀⢀⣴⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢧⠄⠀⠀⣼⡗⢹⠎⠀⠀⠀⢧⠀⠇⠀⢸⠨⠀⠀⠀⠀⠀⠹⣍⡆⠀⠀⡇⠸⡌⡟⠁⠀⠀⠀⠀⡌⡏⠒⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⢠⠀⢀⡟⠀⣨⠴⠒⠒⠦⣼⡼⢸⡀⡈⡆⣨⡽⠟⠓⠦⣄⠹⣇⠀⠀⡏⣆⡙⢧⡀⠀⠀⠀⠀⡇⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣿⣿⣿⣟⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢠⢸⢁⣾⠁⡠⠶⠶⣤⠈⡇⡆⡵⣱⣣⠁⣠⢶⡶⢦⡈⢷⣿⡆⠼⡄⣼⣯⠑⠚⠒⠀⠀⠀⡇⡇⠀⢸⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠟⠋⣻⣿⣿⣿⣿⣟⡿⠀⠉⠙⠺⣝⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢣⡿⠘⣼⢿⡇⠰⠁⠸⠟⠊⡗⠜⠱⣰⠑⠛⠂⡇⠛⠃⠀⣣⢸⣿⠃⣰⣧⣞⡉⠁⠀⠀⠀⠀⠀⡇⡇⠀⠈⡇⡰⢋⠈⠉⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣿⣿⣿⣿⠏⠀⠀⠀⢃⣿⣿⣿⡿⢸⠇⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣧⠳⠀⠀⠀⠀⠀⠀⠰⠞⡲⣇⢿⠆⢁⠘⢦⣄⣠⡴⠃⠀⠀⠈⠃⠀⠀⣑⠤⣀⡤⠇⠀⡌⣠⡿⠛⡟⠳⠀⠀⠀⠀⠀⠀⣇⠇⠀⠀⠿⠷⡆⣀⣀⡧⡴⠲⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠁⠀⠀⣀⡀⠸⠹⠿⠿⠇⠚⡀⠤⠄⠀⠀⠀⠈⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⠱⠈⠪⣆⠀⠉⠘⠋⠉⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠉⠚⠁⠘⢋⠏⠀⠀⢸⠀⣀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠣⢧⢸⡔⠀⢀⡜⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⡿⠃⠀⠀⠀⢀⠈⠑⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡟⠇⠀⠀⠀⠀⠀⠀⠀⠈⢧⠑⢴⣿⣆⠀⠀⠀⠀⠀⢀⠎⠉⠀⠉⠉⢢⠀⠀⠀⠀⠀⢀⣮⡀⡀⢀⣞⣓⡄⠉⠑⠢⣀⣸⡇⠀⠀⢀⠀⠀⠀⠀⣼⡔⢤⠚⠳⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡧⣤⠶⠛⠛⠓⢯⡢⠀⠀⠀⠀⠀⢐⡿⠟⠛⠛⠷⣦⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣍⣹⣆⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⣟⣩⠭⠒⠉⠀⠀⠉⠒⢤⡀⠀⠁⣀⡤⢾⣉⣧⠀⠀⠀⠈⠦⡧⡋⢀⡼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣇⢹⠀⠀⠴⣷⡆⠸⡄⠀⠀⠀⠠⠏⠠⣾⣦⠀⠀⣿⢻⣿⠿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠸⠁⠀⠀⠀⠀⠀⢀⠇⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠞⠀⠀⢀⠡⠃⠀⠀⠀⠀⠘⣎⣜⡹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠚⣿⠀⠇⠀⣶⣿⣿⠀⠁⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠇⢠⣿⢻⡌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠞⣟⣶⣤⣀⠀⠀⠀⣀⣬⣶⠺⣏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡀⠀⢸⠁⡄⠀⠂⠄⡀⠀⠀⠀⣸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠸⡀⠀⠀⠼⠿⠯⠀⠀⠀⠀⠀⠀⠀⠸⠿⠯⠀⠀⠀⡜⠙⢀⠇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠔⠳⠿⠯⠿⠿⢿⣿⣏⢞⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣸⡰⠀⠀⠀⠀⠀⢀⣠⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠶⢄⠀⠀⠀⠀⠀⠀⠀⠣⣒⠤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡤⢊⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣀⢀⣤⣤⡴⣒⢤⡀⠀⠀⢀⣩⡿⠤⠤⢤⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⡤⡏⠉⠆⠸⢳⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠟⠋⣜⣁⣀⠉⠙⠳⡢⢼⣿⣷⠶⠶⢻⣿⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣸⠿⡄⠀⠀⠀⠀⠀ ⠀⢰⠃⢸⠀⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⢠⡊⠉⠉⠑⢦⡀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣮⡿⢿⠋⠀⠀⠀⠀⠀⠈⠉⠁⠈⠛⢌⡉⢣⠀⡿⢿⣷⠢⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡗⠀⢳⠀⠀⠀⠀⠀ ⠀⢸⠀⡆⠀⠄⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡑⠒⠒⠂⣞⣥⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢽⡿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⠐⠛⣆⢃⠀⠀⢻⡉⢱⣦⠤⣀⡀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⣏⠀⠸⡄⠀⠀⠀⠀ ⢀⠇⠀⡇⢸⠀⠃⢸⠀⠀⠀⡴⢶⡆⠀⠀⠀⠀⠀⠀⠀⣄⣀⣸⡟⠻⢾⣿⣯⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻⢃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠋⠈⠒⢤⣸⡌⡆⠀⠀⢣⣸⡿⠀⠀⣽⡄⠀⣼⠃⠀⠀⠀⠀⠀⠀⣧⠀⠀⢧⠀⠀⠀⠀ ⡎⠀⣸⣄⡬⠔⠊⠙⣄⠀⠀⠇⠈⡇⠀⠀⠀⠀⠀⠀⣾⢟⠉⠉⠹⢹⣿⢈⣩⠭⣿⣿⣶⣆⠀⠀⡴⢒⢦⠖⡆⠀⠀⠀⠀⠀⠀⢠⠏⣸⡏⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⣤⠾⣿⣿⣰⠀⠀⠘⣿⠇⠀⢰⣿⣷⣀⣿⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⢧⠀⠀⠀ ⣷⠈⠉⠀⠀⠀⠀⡀⢸⠀⡠⠃⠀⡇⠀⠀⠀⢀⡰⠋⠿⢷⡱⡀⢧⡟⠉⣿⣷⣅⢄⠙⠿⣽⣄⣀⡧⠮⢞⠇⠸⠉⢲⡀⠀⠀⠀⠸⢸⡿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⣠⡟⠁⠀⠀⠈⠉⠓⠢⠤⣼⣀⣀⣼⡟⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣆⠀⠀ ⢸⡄⠀⠀⠤⠐⡺⠁⠈⠛⠁⠀⡼⠁⠀⣤⠶⡫⠔⠋⠀⠀⠱⡟⣾⣟⣒⣻⣿⣽⡌⡄⢠⣿⣿⠋⠀⢴⣿⣷⣨⡓⢸⠈⣕⠀⢀⡽⢚⡇⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⢠⢪⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠚⠃⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠘⣆⠀ ⠀⣧⠀⠀⠀⡰⠁⠀⠀⠀⢀⣾⣡⠔⣋⠕⠉⠀⡖⠢⢤⣀⠀⠈⠙⣷⣂⣙⣒⡿⠳⣴⠛⠿⡏⣇⠀⠈⠛⠻⢿⣷⣸⣔⡇⡱⡿⠁⢸⡇⠀⠀⠸⡈⠢⣄⠀⠀⠀⢠⣿⠟⠀⠀⠀⡰⢡⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢸⡄ ⠀⠸⡆⠀⢰⠁⠀⠀⠀⠀⣸⢏⠤⠊⠀⠀⠀⢸⠁⠀⠀⠀⠈⠁⠀⢹⣲⣾⣻⠀⠀⠀⠀⠀⠘⣾⠀⠀⠀⠀⠀⡇⠀⠙⢻⢇⢹⠀⢸⡇⠀⠀⠀⢣⠀⡔⠓⣦⣠⣿⠏⠀⠀⠀⡰⢱⣿⠿⠟⠛⢛⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⣳⠀⠀⠤⠤⡤⠄⡾⢻⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢸⣌⢯⣇⡿⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⡆⠀⠀⡌⠘⡄⠀⠀⡇⠀⠀⠀⠈⣖⠀⢰⣇⠈⠙⢤⡀⠀⠰⢡⡏⠀⠀⢀⡴⠋⠉⠙⠛⢻⠙⡉⠙⠒⣤⣀⣀⣀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣧⡀⠀⠀⠀⠀⢸⡇ ⠀⠸⡅⠀⠀⠀⡘⠀⢰⠇⠈⡄⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⢩⢨⡇⠀⠀⠀⠀⠀⡄⠀⠙⢦⡀⠀⠡⣀⠀⡇⡆⡇⠀⠀⢷⠀⠀⠀⠀⠘⣆⣼⠹⠀⠀⠀⠈⢶⣇⣿⣠⡤⡶⣿⣇⠀⠀⠀⠀⠘⡆⠇⠀⠀⢳⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠒⠒⠦⠤⠼⠇ ⠀⠀⡷⠀⠀⠀⠁⠀⣼⠀⠀⢃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢸⢸⣷⠀⠀⠀⠀⠀⢹⠀⠀⡟⢱⡀⠀⠀⢀⠇⡇⡇⠀⠀⠸⡄⠀⠀⠀⠀⢘⡏⡇⠀⠀⠀⡘⡜⠀⠙⢿⡇⡇⢸⣟⠀⠀⠀⠀⠀⣷⢸⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⢀⡏⠀⠀⠸⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⡘⡆⠀⠀⠀⠀⡈⡇⢀⡇⠀⢧⠀⠀⢸⡀⡇⡇⠀⠀⠀⢧⠀⠀⠀⠀⣼⢳⠁⠀⠀⠀⣳⠁⠀⠀⠸⡄⡇⣿⣿⠀⠀⠀⠀⠀⣿⡀⡇⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⡇⡇⠩⠭⠭⠭⠤⢷⣸⠀⠀⠸⡄⠀⢸⡇⡇⡇⠀⠀⠀⠘⡇⠀⠀⠀⡿⠆⠀⠀⠀⢸⡇⠀⠀⠀⡇⡄⡇⡗⣿⠀⠀⠀⠀⠀⣿⡇⢠⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠇⠀⠀⠀⠀⣾⡇⠀⠀⠀⢹⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠈⡆⡇⣇⠀⠀⠀⠀⠀⠘⡿⡗⣢⣾⢧⠀⢸⡇⡇⡇⠀⠀⠀⠀⢻⡀⠀⢰⠃⠀⠀⠀⠀⡼⠀⠀⠀⠀⡇⡇⡇⡇⣿⠀⠀⠀⠀⠀⣿⣧⡘⡀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠀⠀⠀⠀⠀⣿⡛⠻⢷⣤⡈⡆⠀⡇⠀⢄⠀⠀⠀⠀⠀⠀⠀⢉⢰⠀⡇⠇⢸⠀⠀⠀⠀⠀⠀⢳⢸⣿⡷⣿⡄⢸⣿⠁⢰⠀⠀⠀⠀⠈⣷⠀⢯⠀⠀⠀⠀⢰⠃⠀⠀⡀⢸⠃⡇⠁⡧⢽⠀⠀⠀⠀⢠⣿⢿⡟⣄⣤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⠀⠀⠀⠀⠀⣿⣄⡀⠀⠙⢻⣧⢰⡁⠀⠘⡀⠀⠀⠀⠀⠀⠀⠂⢸⠀⡇⢂⢸⠀⠀⠀⠀⠀⠀⢸⣿⡿⡇⣯⣧⠈⣿⢸⠘⠀⠀⠀⠀⠀⠸⣧⠘⣆⠀⠀⣠⠎⠀⢀⡖⠁⢸⢰⢲⢀⢻⢸⠀⠀⠀⠀⢸⡏⢰⡇⢹⣤⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡇⠀⠀⠀⠀⠀⣿⢿⣿⣷⣦⠀⠙⣿⡇⠀⠀⢃⠀⠀⠀⠀⠀⠀⡃⢸⠀⡇⢸⢸⡄⠀⠀⠀⠀⠀⢸⡟⢧⣏⣿⡟⡄⣿⡇⠠⡇⠀⠀⠀⠀⠀⢹⣷⡟⠛⢿⡇⠀⢠⠎⠀⠀⢸⢸⢸⢸⢸⢸⠀⠀⠀⠀⢸⠃⢸⠃⣾⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠸⣏⢸⢻⣿⣷⣼⠃⡇⠀⠀⠈⠆⠀⠀⠀⠀⠀⡁⢸⠀⡇⢸⢸⠆⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⡅⢧⢸⡇⡇⣇⠀⠀⠀⠀⠀⠈⠻⠛⢶⡿⠀⡠⠃⠀⠀⠀⣿⣾⣾⣸⣼⣾⠀⠀⠀⠀⡾⠀⡿⢀⣿⣧⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢹⣏⣿⣿⡿⢻⡄⣇⠀⠀⠀⠘⡀⠀⠀⠀⠀⡇⢸⠀⡇⢸⢸⡇⠀⠀⠀⠀⠀⠀⡗⡿⢿⣿⣿⡘⡌⣷⢁⢻⡀⠀⠀⠀⠀⢠⠃⠀⣼⠀⡴⠁⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⡇⠀⡇⣼⣿⢹⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣇⠀⠀⠀⠀⠀⠀⣠⠟⠉⠉⠀⠈⣿⣸⠀⠀⠀⠀⠰⠀⠀⠀⠀⡇⢸⠀⡇⢸⢸⡇⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣭⣝⡀⢿⡼⠘⣇⠀⠀⠀⠀⡎⠀⢠⡟⡸⠁⠀⠀⠀⢀⡄⣿⣿⣿⣼⣿⡿⠀⠀⠀⢸⠇⠸⣷⣿⠏⠀⡇⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣧⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢣⠀⠀⠀⡇⢸⠀⡇⢸⢸⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢾⣇⠇⢩⡆⠀⠀⡼⠀⠀⣿⠃⠀⠀⠀⢀⠴⠋⠀⠙⠿⢿⣿⠟⠁⠀⠀⡰⢹⠀⡤⢹⡏⠀⠀⢏⣉⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⠤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢂⠀⠀⣷⣬⣄⡇⢸⣸⡇⠀⠀⠀⠀⠀⠀⣿⣶⢭⣍⣛⣻⣿⡄⣿⠸⡈⢞⡀⢰⠁⠀⣸⡟⢀⡀⠤⠊⠁⠀⠀⢀⣀⠄⢸⠟⠀⠀⢠⠎⠀⡏⠜⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠈⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣷⣌⣐⢹⣿⣿⣿⣇⢹⡇⢣⠘⣵⡐⢭⡱⣿⣇⡁⢀⣀⣤⣴⣒⢛⣛⣉⠠⠤⠤⠐⠒⢓⣒⣉⣉⣉⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⡇⠀⠠⡢⡀⠀⠀⠀⠘⣿⣿⣆⣼⣿⡿⠀⠀⠀⠀⠀⢠⠈⢻⣿⣿⣿⣿⣿⣿⡌⣿⣌⡆⠰⣣⡎⣶⠓⢛⣛⣁⣁⣀⣤⣭⣴⢒⣲⣾⣟⣿⣟⠋⣿⣿⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢷⡐⠕⢔⠔⠀⠀⠀⠀⠘⠿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢸⠀⢸⣿⣿⣟⣿⣿⣿⣷⡽⣿⣿⡀⠡⡱⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⢤⣛⣛⣿⣿⣿⠀⣾⣿⣇⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠈⢣⠈⢫⢹⠋⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⢰⠻⠤⣀⡀⠀⢀⡴⢋⡿⠉⢀⣴⡵⠋⠁⢰⣿⢀⡏⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠓⠀⡏⠀⠀⠀⠀⢀⠞⡟⠀⠀⠀⢠⠇⠀⠀⠀⣨⠝⠓⢤⣞⢀⣴⠿⠋⠀⠀⠀⣼⣿⣾⡇⢠⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡸⠀⠀⠀⠀⢀⠏⣸⠀⠀⠀⠀⡜⠀⠀⣠⠞⠁⢀⡴⢃⡰⠟⠳⠤⣀⠀⠀⠀⣿⣿⣿⠀⡾⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠠⠀⢠⠃⠀⠀⠀⢀⠏⣸⡏⠀⠀⠀⢰⢁⣠⣎⣁⣀⣠⣮⣔⡛⠲⠤⢄⣀⠈⠙⠲⣄⣿⣿⣿⢰⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠉⠳⡌⠀⠀⠀⠀⡎⠀⡏⠀⠀⠀⠀⣿⠟⠛⠛⢻⡿⠛⠛⣿⣿⣿⣷⣶⣾⡛⠦⡀⠀⣿⣿⣏⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠑⣴⠃⠀⠀⠀⡼⠀⢰⢠⠀⠀⠀⢀⠁⢠⠎⠑⠋⠉⠁⣽⣿⣿⣿⣿⣿⠻⣿⡇⠀⠀⣿⣿⣿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⠀⡌⠀⠀⡆⣰⠁⠀⢸⣸⠀⠀⠀⢸⣰⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡟⠁⠈⢻⠀⢀⣿⣿⠏⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⢨⠃⠀⢰⢁⠇⠀⠀⡟⡇⠀⢸⠀⣼⠃⠀⠀⠱⣤⡀⠈⣗⠻⢿⣿⡿⠁⠀⠀⡞⢀⣾⢿⡟⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠂⢸⠀⠀⢸⡸⠀⠀⠀⡇⢇⠀⠈⠀⢸⠀⠀⠀⠀⠈⠻⢦⣜⣿⠾⠋⠀⠀⢀⡜⣡⡟⢁⡟⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠘⠁⠀⠀⠀⡇⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣀⡴⠿⠞⡹⢡⠏⢀⡴⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⡀⠀⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣴⣷⡯⢖⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢆⠀⠀⠀⠀⠀⠀⠀⡜⢇⠀⡇⠀⠁⣧⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠛⠉⠴⠛⠋⠀⠀⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⠀⠀⠀⠀⠀⠀⢠⠁⢸⠀⠸⠀⣦⡏⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⠀⠀⡞⠘⡄⣆⠀⣇⡏⢿⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⠀⢠⠁⠀⠹⡸⡀⠘⣧⠈⢧⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⠀⡜⢆⠰⡀⠙⢷⡀⠹⠀⠀⠑⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⠀⠇⠈⠀⠳⡀⠀⠳⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠸⣸⠀⠀⠀⠀⠙⢄⠀⠘⢮⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠳⣄⠀⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿