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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠶⢲⣶⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠿⢉⣀⣀⣀⣉⡉⠉⠛⠿⣟⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣤⡀⠀⠀⢀⣴⠟⠥⢤⣀⠀⠀⠀⠈⠉⠉⠙⢲⣖⡨⣽⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⠀⠙⠻⣶⡋⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠉⢻⡶⣍⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⢠⠀⠀⠙⢿⣄⣀⣀⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠹⣌⠑⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠘⡆⠀⠀⠀⠃⠀⠀⠉⠛⠲⢤⣀⠰⣤⣙⢄⡀⠀⠀⠀⠀⠹⣆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣷⠀⢳⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡙⠳⣜⣯⠛⠧⣄⡀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣷⡀⠳⠄⢀⠈⠙⡾⠉⠀⢀⡼⠛⠶⣍⢻⡆⠀⢹⡏⢻⡶⠤⣤⣌⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣄⠀⠀⣉⣙⡇⠀⠀⡎⠀⡴⠓⣿⣧⠀⠀⠀⣷⣾⣿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⡟⣇⠀⠀⠀⢣⡀⠀⢇⠘⣇⣀⣿⣿⡆⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢷⡘⣧⠀⠀⠀⠙⢤⡘⣆⠘⢿⣿⣿⠇⠀⠀⠀⠠⠀⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠻⠋⢉⣉⠩⠙⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⣨⢧⡀⠀⠀⠀⠉⠚⠧⠬⠟⠋⠀⠀⠀⠰⣤⣤⠟⠁⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⣠⠶⠏⠀⠀⠀⠒⠒⠢⢭⡑⠲⣕⢤⡀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⡈⢷⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⣤⣴⠚⠙⣄⠀⣠⡴⠚⠉⠀⠀⠀⠀⣸⢿⢷⣶⣤⣤⣄⣈⠉⠐⢄⠀⠈⠢⡈⠳⡙⣤⣄⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣖⠻⣄⠀⠀⠉⠉⠉⠉⠉⠉⢳⡀⡟⢷⡀⢻⡍⠁⠀⢀⣠⠴⠶⢚⣉⠽⠛⢙⣿⡗⠷⣔⣄⠙⢦⡀⠑⣄⠀⠘⡄⢱⠘⣞⢏⠾⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠳⣷⢀⠻⣦⣷⡄⠀⠈⠙⣶⣎⣁⢀⠤⠊⠁⣸⡇⠀⠈⠳⣟⡀⠙⡄⠘⣆⠀⠹⡀⢷⠸⡜⡆⠙⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣿⠈⠛⠂⠀⠀⠀⠀⢹⠆⣀⣤⡾⢃⡇⠀⠀⠀⠙⣵⡀⠸⡄⠸⡆⠀⡇⠘⡄⢣⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⡾⢛⡵⠋⠀⢸⠁⠀⠀⠀⠀⢹⣇⠀⢱⠀⢡⠀⢸⠀⡇⢸⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⢀⣠⡶⣷⠋⠀⠀⢀⡟⠀⠀⠀⠀⠀⠈⣿⠀⢰⣇⢸⠀⢸⠀⠃⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡶⢤⣀⣀⡆⠀⠀⠈⣆⣉⣭⡶⠛⢧⠀⠀⠀⢸⢥⣀⠀⠀⠀⠀⠀⢸⡆⡎⢹⠈⠀⢸⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⢹⠀⠀⠀⢹⡄⠀⢳⠀⠈⣧⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢸⣿⣿⢸⡄⡄⢸⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢸⠀⠀⠀⠀⢧⠀⢸⡀⠀⠘⡆⠀⠀⠀⠀⠸⡄⠀⠀⠀⣾⢁⣿⢸⡇⡁⢸⠀⠀⢸⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡄⢸⡇⠀⠀⢳⠀⠀⠀⠀⠀⣷⠀⠀⢰⣿⣾⣇⢸⡇⡇⢸⠀⠀⢰⣇⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⣿⣸⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸⡀⠀⠘⠋⢸⣿⠐⣇⣧⠸⠀⢨⢸⡟⣇⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⢸⠇⠀⠀⠀⠀⠈⡇⠀⠀⠀⠸⣿⣸⣿⣿⠀⠀⢸⠀⣧⠘⢿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢿⣿⣿⢿⣧⡂⢸⡆⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢿⢿⡀⠹⣿⣌⣇⡀⢻⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣀⡀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⣼⠒⢺⠃⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠈⠳⣷⠀⠈⠻⣿⢳⣤⡙⢷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣏⣀⠀⠀⠀⠀⢀⣀⡴⠇⠀⠉⠓⠒⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠙⠳⠏⠙⠻⠿⠶⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣤⢤⣤⣤⣠⢤⢤⢤⠀⡀⡀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠿⠝⠛⠝⡻⡌⠬⠸⠀⠦⣣⡚⠃

⡉⠻⡟⠁⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡠⣒⠨⢭⠴⡢⡀⠀⠀⠀⠀⠀⠘⣿ ⡵⠚⠁⡜⠀⢄⠁⠢⢄⡄⣠⣤⢱⣠⡿⠛⣉⣐⡰⠙⠀⠰⠷⣢⠀⠀⠀⠀⢨⣿ ⠁⠀⠀⡇⢰⠀⠆⠱⠈⣷⠿⠛⢵⡄⠀⢹⠀⣀⠉⢖⠌⠘⢡⢹⠀⢀⡤⠲⣿⣿ ⠀⠀⠀⣏⠢⢆⠸⠢⡽⠁⣠⡤⡀⠘⡄⣈⠜⠳⡓⠚⡛⠄⠰⣰⠣⡈⠢⢤⢛⠟ ⠀⠀⢀⠘⢥⡬⠆⢤⡇⢸⡘⠿⠓⠈⠉⠀⢀⠠⠐⡒⠀⠀⢣⡈⠁⣒⠛⠂⠁⠀ ⢄⡀⠜⢠⠋⠀⠀⠀⢻⠁⠀⠉⢄⡀⠄⡂⣥⣾⣿⠷⡄⠀⣸⠙⠫⢝⢅⠀⠀⠀ ⠁⠀⢠⠃⠀⢰⢹⠇⢸⡀⡄⠀⠀⠘⣦⣽⡏⠑⢂⣟⠇⢠⡟⠀⠀⠀⢳⡇⠀⠀ ⠀⠀⢢⠀⠀⠘⠦⠤⠋⠜⠂⠐⠢⡄⠈⠙⠬⠭⠅⠊⡠⠋⠀⢸⡁⠇⣸⣼⠀⠀ ⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣤⡤⠒⠤⡐⣎⠣⡤⣤⠪⠃⠂⠉⠁⠀⠀ ⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠉⠀⢀⠔⢺⡟⣪⠊⢀⣄⡀⠀⠀⠀⠀⠀ ⠳⡆⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣰⠋⠄⠀⠔⠘⠉⠀⠚⠂⣄⡀⠀⠀⠀ ⠀⠙⠦⣀⣀⣷⠀⠀⠀⠀⠑⢄⡀⢀⡴⠋⠀⠘⣀⠠⠀⠠⢀⠀⠀⠈⠏⠀⠀⠀ ⠀⠀⠀⠠⠿⠉⠣⢄⣐⣶⣴⣾⠉⠁⠀⠀⠀⠔⠁⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⡀⠀⣴⣮⣄⡀⠈⣇⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀ ⠀⠀⠂⠰⣿⣷⣶⣿⣿⣿⢦⢄⢹⡄⢀⠎⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠒⠲⣶⡦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠀⠀⠀⣀⠀⠀⠈⠻⡺⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⡠⠔⣒⣿⣿⣿⣿⣷⣄⡀⢱⡈⢻⡆⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣡⠖⠉⣠⣾⣿⡿⢿⣧⠉⠉⠉⣿⡶⣧⣀⡿⠋⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡵⠁⣴⣿⣿⣿⣿⡗⢻⣹⠀⠀⡽⢿⣷⡈⠈⠀⢨⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢀⣴⢿⣿⣻⡿⠃⡤⠬⠁⠀⠸⣇⣾⡏⠑⠀⢀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠏⣿⡾⠁⠀⠱⣿⣧⡄⠁⠀⠀⠀⠀⠀⣀⣱⠄⠀⣿⠋⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣀⣿⠃⠀⠀⢠⠏⠀⢻⡀⠻⠷⡄⠀⠀⠀⠀⣠⡾⡿⠀⣀⣠⠴⠖⣫⣵⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⢀⡏⠀⢀⡼⢿⣶⣤⣄⡀⠀⠒⢻⠏⢰⣷⠟⠋⢉⣇⣉⣁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⠇⠀⢸⠁⠀⠙⣿⡀⣠⠖⢀⡏⢠⡏⡟⠀⠐⣟⢠⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠸⡄⠀⢸⠀⠀⠀⠸⣿⠁⠀⣸⠀⡾⣯⣱⣤⠉⢁⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠻⣆⢸⠀⠀⠀⠀⡇⠀⡸⢹⢰⡇⠈⢿⣊⣽⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠈⠻⣆⠀⠀⠀⡇⢀⡇⠘⣾⡇⠀⠀⢙⡷⣿⣷⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⡇⢹⣄⡀⠀⢀⣾⠁⠀⠘⠿⣶⣶⠿⠁⠈⢿⢾⣟⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣧⡾⠈⠛⠛⣽⠋⢿⡆⠀⠀⣠⠀⠀⠀⠀⢸⡆⠈⠻⣍⠉⠉⠛⠒⠦⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢀⡟⢁⡠⠤⡾⠃⠀⠀⠉⠓⢒⣿⠀⠀⠀⠀⠀⢿⠤⡀⠈⠳⡦⢄⡀⠀⠀⠙⢧⡀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⡼⠋⠉⠀⢸⡇⠀⠀⠀⢀⡶⠋⠸⣆⠀⠀⠀⠀⠘⣆⠈⠢⠀⠹⡄⠉⠢⡀⠀⠈⠃ ⠀⣠⢛⠋⠑⡆⠀⠀⠀⣠⠖⢉⣾⠯⠄⠀⠂⠐⠚⢻⡄⠀⠀⠘⣧⠈⠃⠝⠦⠤⢤⣀⠀⠈⢷⡄⠀⠀⠹⡀⠀⠀⠀⠀⠀ ⠰⡇⢸⠀⠀⠀⠀⣠⡞⠁⣠⣚⣁⣀⣀⣀⣀⣴⣿⠟⠁⠀⠀⣴⠟⠀⠀⠀⠈⠐⠂⣿⠀⠀⠈⢳⠀⠀⠀⢣⠀⠀⠀⣀⠌ ⠀⠘⠢⠽⣿⠖⣛⣡⠴⠚⠉⠀⠀⠀⠀⣠⠿⠋⠁⠀⠀⢐⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢧⠀⠀⢸⣠⡴⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠘⡄⢠⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣀⣀⣠⠤⠶⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⣷⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⣆⣴⡛⢡⢑⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠁⢻⡅⠁⠀⢻⠀⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⡠⠟⢧⡆⠀⡐⡁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⠤⡀⠀⠀⠀⣰⡙⠲⠄⠑⠚⠉⠁⠋⠤⠶⠦⡄⠀⠀⠀⠀⠀ ⠀⢊⡾⡢⣄⢠⠋⠿⣷⠀⠀⣤⣄⡀⢠⠀⠠⠊⠀⠀⠀⠀⢀⠀ ⠀⠈⡖⠻⡽⣾⡄⠰⣈⡐⠘⠻⠏⢫⠃⠀⠀⠀⠀⠀⢀⠐⡙⠀ ⠀⠀⠐⢜⠐⠱⢿⣢⢑⣛⣉⣀⠠⠂⠀⠀⣀⠠⠄⠦⠁⠬⡇⠀ ⠀⠀⠀⠀⠁⡂⠏⣹⠀⠀⠀⢆⠀⣠⠲⠍⣄⡈⢒⠊⠒⡼⠀⠀ ⠀⠀⠀⠀⠆⠈⣄⢼⠀⠀⠀⠀⢉⡁⡥⢂⠰⠈⡜⡄⠊⠀⠀⢀ ⠀⠀⠀⢀⠀⠀⢡⣈⢄⢀⠃⡘⠀⡈⠉⢻⢺⣏⢅⢌⠂⠤⠴⣺ ⠀⠀⠀⠸⡆⠐⠆⡅⢀⠃⢀⠓⠰⡚⠢⡀⠀⢞⢦⠢⡁⠀⢈⡟ ⠀⠀⠀⠀⠙⠃⠋⠀⢀⠀⠈⠓⢄⢠⠁⢨⢱⠀⢋⠑⠂⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠠⢈⣆⠀⡨⢳⠀⠈⣢⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠽⠳⠏⠹⢄⡥⠉⠄⢀⢂⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡴⠟⠀⠀⠀⠀

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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢴⣤⣤⣴⣶⠖⣰⣶⡲⠲⠤⣾⠀⢺⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠿⣼⡌⢿⡞⡐⠱⠁⠀⢰⡋⠀⢸⡈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡏⡸⢹⠉⢻⣅⡧⢴⣤⣤⢤⣽⠦⠈⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢁⢃⣴⣶⡉⠁⠀⢸⢌⢿⣾⣿⣆⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣼⠋⠘⠻⣯⣢⠀⠘⡞⢿⣟⠻⠇⢠⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⠤⢄⡀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⠀⠙⣿⠇⠀⠙⠊⢡⣶⣶⣿⢷⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⢉⠀⠐⢌⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠣⠄⣎⡀⣤⣾⣛⣩⡆⢼⣆⠀⣀⡀⢠⠏⣀⣀⡀⣀⠠⠄⡀⠁⢂⠣⠈⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢉⡵⠋⠀⡼⢸⠋⡅⡉⣻⣿⠋⠉⠙⠳⣍⠢⡈⢢⠈⡄⡇⢸⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠸⣄⢀⡔⡜⡸⢀⢢⠃⠈⢹⡄⠀⠀⠀⠈⢷⠹⡀⠀⠀⠀⠸⠹⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⠻⣎⣠⠃⠀⣩⡇⠱⢾⠁⠀⠀⠀⠀⠈⣇⢃⠀⠀⠀⢰⠀⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠢⡄⠀⣀⣀⣀⣦⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⢹⢸⡆⠁⠀⢸⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⠁⠀⡏⠉⠈⠣⡑⢄⠈⠉⠱⡄⠀⠀⠀⠀⢸⣸⡹⠀⠀⣄⣴⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢸⠻⡄⠀⠀⠙⡌⢣⠀⠀⠙⡄⠀⠀⠀⢸⣿⠇⢀⣰⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⣸⠀⢳⠀⠀⠀⢸⠀⡇⠀⠀⠹⡄⠀⠀⣿⣇⡶⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⡇⠀⠘⡀⠀⠀⣸⠀⡁⠀⠀⠀⢱⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢀⡸⠀⠀⠤⠇⠀⠀⠳⠤⡇⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⡚⠛⠉⠉⠉⠛⠓⠦⣄⡀⠀⢀⣠⢞⡥⠴⠾⠷⠶⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⣤⠽⠛⢉⣀⡤⠤⠶⠶⠶⠶⠤⢤⣀⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣠⠞⠉⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠟⠦⣄⡀⠀⠀⠀⣸⢇⡞⢁⢴⣫⠤⠶⠒⠒⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⠀⠀⠀⡿⠀⠀⠈⠉⠛⠛⢛⣵⣾⣴⡗⣩⠴⠒⠛⠒⠦⣄⡀⠀⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⠳⡄⠀⠀⠀⠀⠀⢻⠢⡀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⠻⡅⠀⠀⢀⠀⠀⠀⠙⠲⣄⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠙⢦⡀⠀⠀⠀⣸⠀⢱ ⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣿⠀⠀⡴⢦⡀⢻⣦⠀⠈⢧⠀⠀⠀⠀⠈⢧⡀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠙⠲⢶⡶⠁⠀⢈ ⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⡇⠀⣼⠁⠀⠙⡄⢿⣇⠀⠈⣧⠀⠀⠀⠀⠀⢳⡄⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⣸ ⠀⠀⢰⡏⠙⣧⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⢹⠘⣿⡄⠀⡟⢧⡀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃ ⠀⠀⠸⡇⠀⠘⢧⡀⠀⠀⣷⠀⢷⣀⣀⣠⠃⠀⠀⣙⣾⠧⣤⣝⡲⣤⣀⠀⠘⣷⣤⡀⠀⠀⠀⠈⠓⢤⣀⡀⠀⠀⠀⠀⢀⣠⣴⠞⠁⠀ ⠀⠀⠀⢻⡄⠀⠈⠳⣄⠀⣻⡄⠀⠀⣌⡙⢷⣤⣾⣯⣤⡀⠀⠈⢳⡄⠉⠙⠓⠛⠦⣽⣷⣤⣄⣀⠀⠀⠀⠉⠉⠛⣛⣩⠽⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠹⣆⠀⠀⢈⡿⠋⣧⠀⠠⣬⣛⣿⡿⢃⣤⠶⠿⣦⡀⠀⢻⡄⠀⠀⠀⣼⢏⣨⣽⣦⠉⠉⠙⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣦⡟⠀⢠⣏⠃⠀⠈⢙⡟⢠⣿⣧⣀⣀⡿⢧⠀⠈⣷⠀⠀⣼⣳⢻⡅⢀⣿⡇⠀⠀⢸⣿⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢸⠙⢦⠀⠀⢸⡇⢸⣇⣽⣿⡿⠀⢸⠀⠀⢸⡆⢀⡏⣿⣠⣿⡏⠈⡿⠀⠀⠀⣇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠈⢧⡈⠳⣄⠈⠓⢬⡿⢻⡿⠃⠀⡾⠀⢀⣠⣧⡼⢧⣿⣙⡟⠀⣰⠃⠀⢀⣠⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠑⢄⠈⠳⣄⠀⠈⠙⠛⠛⠛⠓⠚⢩⡅⠀⠶⠀⠈⠉⠛⠛⠓⠒⠋⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⢳⡀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠴⠂⠀⠀⠀⠀⣰⡛⣆⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⣧⠀⢸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁⣡⠼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡦⣄⡀⢀⣀⣤⣏⡀⣸⠉⠉⠙⣿⠓⠒⠶⠶⠶⠶⠶⠶⣖⠒⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡽⣋⡽⣾⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢋⡞⠁⠀⠀⠙⣦⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣣⠞⠀⠀⠀⢠⠀⢸⡏⠀⠀⠀⠀⠀⢠⡆⠀⠀⢻⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⠴⢶⣾⣯⡉⠁⠀⠀⠀⣠⠏⢀⡾⠓⠶⢤⣀⠀⠀⠀⡇⠀⠀⢈⣧⣸⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⢋⡥⠞⠋⠉⠉⠉⢙⣓⣲⠖⠋⣿⠶⠋⠀⠀⠀⠀⠈⢷⠀⠀⣷⠀⠀⠀⢻⡏⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⢏⡴⠉⠀⠀⢀⣴⡖⣻⠟⠛⠻⣆⣠⡬⠤⠥⣤⡀⠀⠀⢀⡾⠀⣀⣿⠀⠀⠀⠈⢷⡀⠀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⣾⠀⠀⠀⠀⠘⠦⣝⡛⠶⢤⣤⣟⣁⠤⠶⠶⢶⣿⢀⣤⠟⠛⣽⠋⢻⡇⣄⠀⣾⠻⣷⢤⣿⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⢿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⢿⠈⣿⠀⠀⠀⠀⠈⠻⡅⠀⣀⡸⠆⠈⣿⠉⢳⡇⠀⠘⣦⣀⣤⡼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⣾⣠⠿⢤⣤⠴⢊⣩⡙⣿⣄⣻⣄⣀⣀⡿⢤⣤⣄⣠⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠦⣭⣓⡒⢶⣶⣶⡶⠟⠉⠉⠲⣤⣤⠖⠋⠉⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢠⠂⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠆⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠒⠤⠤⠤⠾⠿⠿⠿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠏⣉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢚⡭⠶⡴⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⠎⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠙⠛⠻⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢼⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠦⢍⣓⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠿⣄⡤⡆⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠑⠓⣀⣀⣉⡏⠀⠀⠀⣠⢄⣤⣤⣤⢠⣤⣤⣤⣄⣤⢀⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⠀⠀⠀⠀⣿⣾⢻⣯⣍⣼⢿⡇⣿⣸⡏⣸⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠔⡒⠒⠒⢲⣶⢶⣿⣿⣿⣟⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀⢸⠀⠀⠀⢀⣿⠃⣿⣷⣾⡿⣿⣿⡟⣿⣃⣉⠀ ⠈⠁⠒⠀⢀⡀⣀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⣤⣶⡶⠋⠁⠀⢠⠀⠀⠀⠙⢦⡀⠘⣿⣦⣿⣿⣿⣿⠘⣿⣯⣛⢿⣿⣿⣿⡻⣿⣿⣧⠀⠀⠀⠉⠀⠁⠀⠉⠁⠁⠈⠀⠀⠈⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⣼⣿⣿⣿⡇⠀⣠⠶⠛⠉⠹⣷⣦⡈⠑⠦⠸⣿⣿⣿⣿⣿⡀⠸⣿⣿⣷⣼⣿⡿⣷⣌⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁⡼⠁⠀⢸⣄⣰⣿⣿⣷⠀⠀⠀⠈⠛⠛⠙⠻⣧⣀⣹⣿⣿⣿⣿⣿⣻⣿⣧⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⣿⣿⡇⢰⠃⠀⠀⢸⣿⡏⠈⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢀⡾⠉⠀⣿⣿⣿⠙⢿⡛⢻⣿⣿⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢦⠈⣿⠁⢸⠀⠀⠀⢹⠋⠱⢄⣁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⡎⣸⣦⡴⠻⣿⣿⠀⠀⢻⡈⣿⣿⢰⠏⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡷⢿⠀⠈⠃⠀⠀⠈⠳⣆⣸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡿⠛⡀⡰⠛⣹⠀⠀⠀⣇⣿⣿⣾⢇⣰⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡄⠘⢆⡸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⢀⡴⠃⠀⠀⢠⣿⣿⣿⡏⠈⣿⣟⣾⣷⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣄⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⡞⣸⣿⣿⠃⢸⣿⣿⣁⣿⡄⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠇⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠰⠋⠁⠀⢸⡞⣿⡀⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣼⣿⣿⣿⡿⢠⡿⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡃⣠⠴⠞⠉⢸⡇⠹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⣀⠸⣿⣿⣿⣿⡇⢸⡇⣴⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡋⠡⠈⠀⠀⣼⣷⡀⢱⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⢡⣿⣶⣿⣿⣿⣿⡇⢸⡆⠇⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏⠀⣀⣠⣤⣾⣿⣿⣧⢸⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠇⢸⣿⣿⣿⣿⣿⣿⣧⠀⡇⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣉⣩⣵⡀⠸⣿⣿⣿⣿⣧⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣧⠀⢿⣿⣿⣿⣿⣿⣿⡄⡆⠀⠀⠀⠀⠀⣿⣿⡟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢹⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⢳⡈⢻⣿⣿⣿⣿⣿⣷⣳⡀⠀⠀⠀⠀⣿⣿⠁⠀⠙⣟⣶⣤⣤⣤⣤⣤⣴⡶⠞⠉⠉⠀⣰⠟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠿⢿⣿⣿⣿⣿⣷⣳⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⠀⢻⣄⠻⣿⣿⣿⣿⣿⣷⡳⡄⠀⠀⠀⣿⡟⠀⠀⠀⢸⠀⠉⡉⣉⣉⠉⠉⡀⠀⣀⣤⢾⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣡⣴⣄⠹⣿⣿⣿⣿⣷⠧⠀

⠀⠀⠀⠀⠀⣦⣠⣴⣾⡿⢿⣷⣦⣄⣴⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠙⢻⣿⣄⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⡟⠀⠀⣴⡿⠿⣤⡀⠀⢻⣿⣷⡀⠀⠀ ⠀⢀⣾⣿⣿⡇⠀⠘⢿⣤⣤⣿⠃⠀⢸⣿⣿⣿⡄⠀ ⢠⣾⣿⣿⣿⣷⡄⠀⠀⠉⠉⠀⠀⢀⣾⣿⣿⣿⣷⡄ ⢸⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⡇ ⣼⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣧ ⣿⠟⣿⣿⣿⣿⣟⠁⣀⡀⢀⣀⠈⣻⣿⣿⣿⣿⠟⣿ ⣿⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣿ ⢻⡇⠀⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⡏⠀⠀⢰⡿ ⢸⣇⠀⠀⢸⣿⠀⠀⠀⠉⠉⠀⠀⠀⣿⡇⠀⠀⢸⡇ ⢸⣿⣆⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣰⣿⡇ ⢸⣿⡘⠂⠀⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⠀⠐⢃⣿⡇ ⠀⠙⢛⣂⣀⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⣀⣐⡛⠋⠀ ⠀⠀⠿⠛⡿⡟⡟⠃⠀⠀⠀⠀⠈⢻⢻⢿⠛⠿⠀⠀

“s-stop aruguing!” shut the fuck up im trying to find symbols dumbass ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠋⠉⠭⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠋⠁⠀⠀⠀⠁⠹⠝⠛⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢨⠛⢦⣄⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣌⠙⢦⣰⠿⠋⢀⣀⡠⠴⠶⠒⠚⣫⣽⣯⣉⡛⠒⠲⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⢻⣶⠚⠋⠁⠀⢀⣠⢤⣾⡿⠟⠛⠻⢿⣤⣀⣀⠀⠀⠉⠓⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣧⠀⠚⠉⠉⠁⡿⠋⠀⠀⠀⠀⠈⠀⠀⠉⠛⠲⣤⢀⠀⢀⣽⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠿⠻⢿⣿⣗⣆⠀⠀⠀⠀⠀⠀ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢀⣠⣤⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠈⠳⡄⠀⠀⠀⠀ ⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣿⠟⠉⠀⠈⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠙⣆⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠙⢦⡀⠀⠀⠀⠀⣼⠁⠀⠀⡾⠁⠀⣠⣀⡀⠀⠈⣧⠀⠀⠀⠀⣠⡴⠖⠦⣤⡀⠀⠀⠀⠀⠀⠘⣧⠀⠀ ⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⢦⡀⢀⡴⠃⠀⠀⢰⠃⢠⡞⠙⣿⣿⡆⠀⠸⡆⠀⠀⣼⠃⣅⣀⣀⠀⠉⢳⡄⠀⠀⠀⠀⠸⣆⠀ ⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢻⡉⠐⠓⠒⠤⢼⣀⢸⣿⣶⣿⣿⣿⠀⢀⡇⠀⠀⡇⣾⠛⢻⣿⣧⠀⠀⢹⡀⠀⠀⠀⠀⠹⡀ ⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠘⡇⠀⠀⠀⠀⠀⠈⠛⢿⣿⣬⣿⠃⠀⣼⠁⠀⠀⣷⣿⣷⣿⣿⣿⠀⠀⠀⣷⠀⠀⠀⠀⠀⡇ ⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣠⠤⣤⣀⡀⠀⠀⠀⠻⡉⠁⢀⡴⠁⠀⠀⠀⠘⣿⣿⣇⣿⡟⠀⠀⢂⡟⠀⠀⠀⠀⠀⠁ ⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡈⠻⣦⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⢻⡙⠂⠀⠀⠀⢹⠔⠋⠀⠀⠀⠀⠀⠀⠙⢎⡉⠁⢀⣠⠤⠾⠦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢦⡶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⢧⣀⣀⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⢻⣄⠄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢸⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽⣿⣆⠈⠙⠲⠦⣄⣀⣀⣀⠀⠀⠀⠀⢀⣀⣈⡵⠞⠁⠈⠁⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠤⠤⠤⠴⠖⠺⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣷⣄⠀⠀⠀⠀⠀⠉⠉⠉⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡟⠻⢿⣷⣶⣤⣄⣀⣀⣤⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠻⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡽⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣘⣦⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠖⠒⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠷⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀