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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠉⠈⠉⠀⠀⠀⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠔⠤⠤⠤⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣳⠽⣦⣷⣆⠫⠙⢣⠈⢗⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⢒⠤⠧⠟⠤⠤⠲⠵⠭⠾⠶⣶⣶⢤⠦⠻⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⣇⢼⠷⣭⣉⣉⡦⠻⠙⠃⣧⠸⠀⠀⠀⠀⠀⠃⡾⣠⠒⡤⣤⣀⣀⢦⠈⠀⠉⠀⣀⠀⠀⠀⠉⠋⠛⣗⡽⣖⡿⢾⠭⠀⠒⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠄⣢⢐⣈⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠁⡾⢀⠀⠀⠀⠀⠀⠃⠟⡮⣶⢠⠉⠛⠶⡴⣤⣀⢀⠀⠀⠀⣀⣄⣤⣶⣻⢝⠪⠐⡉⢀⠄⠤⠒⠐⠀⠀⠀⠀⠀⠍⠫⠾⡴⣢⣿⣽⣋⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠧⠪⠇⠀⡇⠈⠀⠀⠀⡿⢠⠀⠀⠁⠈⠀⠃⣼⢀⠀⣀⡇⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣦⠶⣓⠍⠤⣷⢽⠶⠶⠶⡒⣟⡤⣧⠈⠁⡺⡴⣜⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠁⢸⡀⠀⠀⢹⠀⠀⠀⣾⠛⠖⠮⢂⠁⡞⣠⠀⠀⠋⠔⢀⠉⠋⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⢶⠲⠑⠈⣿⠀⡇⢷⠀⠀⡞⣎⣞⣟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈ ⠀⠃⠛⡕⣦⣗⠻⠑⠈⠀⠀⢀⣸⠀⠀⠀⣷⠀⠀⠀⢃⠉⠀⢠⡮⣠⠀⠀⠁⡾⢒⠅⡯⣶⣤⣄⢤⠳⠙⠉⠈⠀⠀⠀⠁⠉⠛⠛⠒⠛⠉⠉⠈⠈⠂⠭⠚⠱⠀⠀⡀⡆⠸⡏⡹⠋⡼⢉⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠟⠿⠴⣭⣿⣿⣶⣯⢴ ⠀⡀⡤⢦⠕⠘⣄⢳⣦⣬⠳⠈⣿⠀⠄⠀⡃⠀⠀⠀⠀⣦⠳⠈⠑⠉⠞⠶⣠⢀⠄⣠⠉⠀⠀⠀⠀⠀⡁⣿⣿⣿⣿⣼⣀⣄⢈⠀⠀⠀⠀⠀⡀⣧⢿⠛⠉⠀⠀⠀⠉⡟⢿⣾⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⢀⠤⣉⣓⠟⣿⣿⢰⠀ ⠀⠀⠀⠀⠀⣄⠳⠀⢆⢿⠚⣆⣟⠀⠀⠀⡄⢘⠀⠀⠀⠉⣜⣺⣍⢢⠈⠀⠀⠀⠀⡀⠄⣠⠠⠀⠁⠞⣫⣾⠀⡏⣾⢠⠂⠈⢄⠈⠒⠂⠐⠀⠀⠀⣴⣿⣽⣿⠿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⡀⣇⠸⠀⡆⣿⠃⡴⢏⡿⣿⣾⣲⠀⠀ ⠀⠀⠀⠀⡀⣤⣧⢿⠈⣆⢿⠄⣇⠀⠀⠀⠀⢣⠛⠀⠎⣡⡆⣠⣃⢤⡪⢝⠑⠂⠉⠉⠀⠢⠓⡙⢋⡔⣀⠃⡿⣸⠀⠀⠀⡄⡠⠀⠀⠀⠀⡀⠀⠁⡏⢠⠀⠀⠀⡀⣄⣦⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣿⣿⣿⣾⣷⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⢜⠈⣇⢹⡇⠀⠀⠀⠀⡗⣿⠋⢠⡏⢹⢣⠁⠇⢆⡛⣾⣤⠶⡾⠿⣿⣿⣿⣿⣾⠶⣤⣀⠀⠀⠀⠀⠀⠢⠒⠐⠤⠡⠔⢤⢃⢸⢧⠘⠀⠁⠀⠀⠀⣀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣿⣿⣿⢻⡄⣽⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⢆⠈⣷⡿⠀⠀⠀⠀⠀⣧⡸⠃⣸⡄⡈⡽⣿⠀⣿⢹⠒⠞⢀⠀⡀⣀⢤⠠⠒⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠉⠔⣀⠀⠁⡼⠀⠃⡆⠀⠀⠀⠑⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⡏⣿⣿⣿⣿⢻⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢃⡀⣿⠀⠀⠀⠀⠀⡀⢸⡗⢸⠀⠁⡇⣇⠀⣿⢹⠾⢀⠀⠀⠀⠁⠂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⣿⢠⠀⠸⠀⠱⠀⠀⠀⠡⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣠⣄⢷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠉⢱⡇⠀⠀⠀⠀⠀⠀⣯⡇⠀⠀⡄⡄⡼⠸⢻⣴⠁⠂⠒⠀⠠⢒⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⠁⡜⠀⠐⠀⠀⠀⠀⡀⠘⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣷⣿⣿⠉⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡜⠈⠘⠀⠀⠀⠀⠀⣿⡟⠀⠀⡀⠸⣿⢾⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡣⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣿⣿⣿⢻⠉⡟⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⢣⢸⠀⠀⠀⠀⠀⣷⣿⠉⡷⠀⢿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⡿⣿⣸⠁⣾⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠫⠉⢇⠀⣿⡈⢿⠀⠀⠃⠴⠀⡇⣿⣻⣿⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⢿⣾⠭⣺⢴⣧⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣆⣖⣿⠽⡇⢸⣿⠸⠂⡤⠐⠀⡿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⡎⠀⠀⠀⠊⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣽⣞⢀⠀⠀⠀⢾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢃⠆⣿⡏⢣⣿⢸⠀⡈⠀⠁⣾⢠⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠉⡐⠀⠔⢀⠀⠀⢉⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⠾⠶⠿⠿⡿⢨⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣠⡸⣾⠀⡞⢠⠀⡇⣾⠤⣀⠀⠀⠀⠀⠀⠀⠀⣥⠐⠀⠀⠐⠀⠀⠀⠀⡀⢤⠐⠈⠀⠁⠉⠒⠮⣠⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣾⠤⣤⣤⢀⡿⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠘⢸⢹⡰⠀⠀⠀⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡌⠀⠀⠀⠊⢠⠀⠀⠏⣿⣠⢃⡻⡠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⢛⠙⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡤⢠⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠏⢁⠀⠀⡇⠀⢸⣟⣸⠀⠀⠀⠀⢸⠁⠒⠴⠤⠤⠢⠒⠈⠀⠀⠀⠀⠂⢀⠀⠤⣀⠀⠀⠈⠁⣾⢏⠟⣴⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⠟⠾⠻⠛⣿⣶⢝⣽⣷⢿⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⠘⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡾⠀⠀⡇⠃⠱⣿⢠⠀⠀⠀⡇⠟⢀⠀⠀⠀⠀⠄⠢⡈⢄⠙⠐⠆⢀⠀⠀⠂⠒⠄⡀⠁⡾⢏⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠏⣼⣎⣯⣰⡁⣿⢿⣵⢯⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣰⠏⢀⠀⠀⡏⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢻⣆⠻⠀⠸⡇⡟⣼⠀⠀⠀⠀⡾⢠⠀⠀⠀⠀⠀⠀⠀⡀⠡⡆⠁⢠⠀⠀⠁⠀⠄⠠⣀⣄⠗⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡿⣼⣧⢭⢛⠴⣠⣀⢀⡀⢤⡑⣀⣷⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠟⣰⠏⢠⠀⠀⠁⣿⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⠀⣼⢳⣌⢻⢸⡇⣸⢀⠀⠀⠀⠆⢈⠈⠀⠀⠀⠅⠛⠀⠀⠀⠀⠁⡠⠀⠆⡤⣀⠀⠀⠢⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠎⣠⠁⠀⠀⠀⠀⠀⠀⡀⢦⠈⢷⢻⠀⠀⠀⠀⠀⠀⠀⠃⣹⠖⢀⠀⠀⠀⡿⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⢣⡇⡌⢿⣿⢸⡞⠄⠀⠀⠀⠀⠂⢩⠄⠀⠀⠂⡀⣷⠰⠀⠁⠶⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢠⠀⡀⡞⠈⠀⠀⠀⠀⠀⠀⣆⡏⣏⠀⠀⠀⠀⠀⠁⠟⣴⢠⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢂⢫⣆⣻⢸⢠⠀⠀⠀⠀⠀⠆⣿⠢⠀⠉⠀⣀⠀⠀⠈⡁⢂⠠⢄⠐⠀⠀⠀⠀⠀⠀⠁⢰⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⠀⠀⠆⢁⠀⠀⠀⠀⠀⠀⠀⣧⣾⠀⠀⠀⠀⠁⣾⢠⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⣽⣞⢿⠀⠀⠀⠀⠀⠀⢠⣸⠠⠀⢸⠀⠉⠄⣚⠈⠁⠉⠚⠓⠛⡷⠿⠛⠚⠑⠉⢉⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠀⠀⣸⠰⠀⠀⠀⠀⠀⠀⡀⣿⠈⠀⠀⠋⣾⢀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⡞⣮⢸⠀⠀⠀⠀⠀⡆⢀⠀⠃⢹⢒⠬⣁⠔⡶⣿⣻⣿⣸⢻⡿⣹⡾⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⢰⠆⠈⠀⠀⠀⠀⠀⠀⣷⢸⠀⠏⣴⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⢁⠀⠀⠀⠀⠀⠀⠀⡡⡼⠀⡙⠞⣠⠂⠒⠓⣀⣄⠢⣿⣿⣿⢿⡇⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⠀⡄⠈⢰⠀⠀⠀⠀⠀⠀⡘⣿⠏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠰⠀⠀⠀⠀⠀⠋⣿⢹⡟⡰⠀⠀⠀⠀⠀⠃⠀⠀⡀⣧⣫⣯⣿⢻⡿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠀⢃⡇⠀⠀⠀⠀⠀⠀⣧⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡦⠙⠈⠀⠉⠞⢿⡀⣿⢰⠀⠀⠀⠂⠛⠉⡉⠁⠀⠻⠌⣧⣹⣆⢮⢸⣏⠢⠈⣇⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠀⢱⠘⠀⠀⠀⠀⠀⡇⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⡟⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣧⠢⡈⣧⣾⡇⡿⣰⠀⠀⠁⠈⠀⡝⣜⢦⣞⢿⣙⣮⣿⣨⢷⢷⣇⣯⠀⡄⡞⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⡀⡕⠐⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡇⠹⢆⡘⢸⣾⢉⠏⢻⠛⡿⣿⢶⢠⣏⠱⠀⡀⣦⡹⣦⢨⡧⡄⡀⣿⢸⠡⢰⡿⢡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠘⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠕⣵⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣇⠸⢸⣷⣿⣈⣏⣼⣵⠢⡝⠦⣑⠀⢨⢢⠀⠀⡀⢢⢆⡿⠀⠿⣀⢸⡏⡇⣾⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠋⠰⡜⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢷⠀⡀⣿⣷⠏⣿⠻⣌⢦⠀⢄⠑⢄⠀⢌⣗⠈⢄⠈⠀⠀⢂⣇⠀⡅⠸⢳⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠻⠀⠀⠀⠃⣷⣼⠱⠀⠀⠁⠞⢡⡞⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠆⡇⠘⡇⠹⠈⣶⢽⠪⡙⣀⡤⠦⠑⠀⡀⠀⠐⠈⠀⢢⠀⣄⠐⠀⠃⠀⠙⣾⠀⡟⣮⢀⠋⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⠀⠀⢠⡰⢠⡀⠀⠊⡠⠀⠀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢯⡄⡷⣿⡌⣿⣿⠻⣙⠨⠀⠀⡀⠄⠂⠋⠀⢀⠠⢢⠀⡄⠹⠀⠀⣿⢁⡿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣳⠮⠒⠀⠀⠋⡴⢀⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣣⢬⢦⢾⠱⣄⢶⡿⡽⣺⣀⡻⢭⠺⠒⠀⠄⠀⢀⠤⠴⠫⠙⠀⡆⠁⠀⣿⢣⣷⣩⣄⢤⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠙⠀⣀⢀⠀⠀⠋⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠛⣟⠿⡒⠹⠀⠉⡋⣞⣿⠆⣾⠃⣰⠁⡊⣀⠧⠑⠀⠂⠉⡀⢀⡟⣴⠄⢣⡳⣱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣖⠿⠉⠟⡶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⣿⠾⣦⣄⢹⡉⠌⢀⠁⠔⢀⠀⡀⠄⡁⠋⡿⣹⢃⠿⣽⢟⡽⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡤⣀⠀⠀⢣⡄⣿⢢⠟⢉⠤⢀⠀⠅⡊⠟⣴⣩⢶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡃⣶⠓⠉⣉⣜⣤⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⢹⠚⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀