{"id":"sol-mind","description":"The thinking-Sol flipbook — braille frames exactly as shipped by <AnimatedSol> (apps/web/src/components/sol-mind-frames.ts). Frame 0 is the canonical resting 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⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠀⠀⠀⢀⣴⠿⠋⠀⣰⣿⣿⠟⢀⣿⡟⢠⣿⣿⠇⣿⣿⠸⣿⣿⡄⢻⣿⡀⠻⣿⣿⣆⠀⠙⠿⣦⡀⠀⠀⠀⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⣿⡿⠋⠀⣼⡿⠀⣸⣿⣿⠀⣿⣿⠀⣿⣿⣇⠀⢿⣧⠀⠙⢿⣿⣆⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣰⣿⠟⠀⠀⣸⡿⠁⠀⣿⣿⡇⠀⢻⡟⠀⢸⣿⣿⠀⠈⢿⣇⠀⠀⠻⣿⣆⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢠⡿⠁⠀⠀⣿⡿⠀⠀⢸⡇⠀⠀⢿⣿⠀⠀⠈⢿⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡾⠁⠀⠀⢰⣿⠃⠀⠀⢸⡇⠀⠀⠘⣿⡃⠀⠀⠈⢷⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀","⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⣆⠀⠀⠀⢸⡇⠀⠀⠀⣰⡇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢧⠀⠀⠀⢸⣿⡄⠀⠀⢸⡇⠀⠀⢠⣿⡇⠀⠀⠀⡼⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠘⣧⠀⠀⠈⣿⣷⠀⠀⢸⡇⠀⠀⣾⣿⠁⠀⠀⣼⠃⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢻⣷⣄⠀⠀⢹⣧⠀⠀⣿⣿⡆⠀⣼⣧⠀⢰⣿⣿⠀⠀⣼⡏⠀⠀⣠⣾⡟⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⢻⣿⣷⡀⠀⢿⣧⠀⢻⣿⣿⠀⣿⣿⠀⣿⣿⡟⠀⣼⡿⠀⢀⣾⣿⡟⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⡀⠀⠀⠀⠈⢻⣦⡀⠀⠻⣿⣿⣆⠘⣿⣧⠸⣿⣿⡆⣿⣿⢰⣿⣿⠇⣼⣿⠃⣰⣿⣿⠟⠀⢀⣴⡟⠁⠀⠀⠀⢀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠙⢿⣶⣄⠙⣿⣿⣧⢹⣿⣧⢻⣿⡇⣿⣿⢸⣿⡟⣼⣿⡏⣼⣿⣿⠋⣠⣶⡿⠋⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠠⢄⣀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣀⠙⢿⣷⣌⢻⣿⡧⠛⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠛⢼⣿⡟⣡⣾⡿⠋⣀⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⣀⡠⠄⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⡀⠀⠙⠻⣿⣿⣷⣮⡻⣿⡗⠉⠀⢀⣠⠴⠖⠒⠛⠛⣶⠲⠦⣄⡀⠀⠉⢾⣿⢟⣵⣾⣿⣿⠟⠋⠀⢀⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣙⡻⢿⡿⠊⠀⢀⡴⠋⠀⢀⠠⡤⢀⣴⢮⠀⠀⠀⠙⢦⡀⠀⠑⢿⡿⢟⣋⣤⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠒⠶⣶⣦⣤⣤⣤⣤⣤⣀⣈⣙⠻⢿⣿⡿⠀⠀⣰⠋⠀⠀⠀⡿⣟⢛⡿⢟⠒⡊⢹⣦⠄⠀⠙⣆⠀⠀⢿⣿⡿⠟⣋⣁⣀⣤⣤⣤⣤⣤⣴⣶⠶⠒⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣷⣾⠁⠀⢰⠃⠀⠀⢰⣾⠀⢹⣿⠧⠤⡿⠧⠿⣷⠦⢰⡆⠘⡆⠀⠈⣷⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣭⣭⣭⣭⠀⠀⡜⢀⡀⣠⡎⣘⣇⡄⠌⣧⣼⣷⢶⣿⠁⢠⣌⠀⠀⢣⠀⠀⣭⣭⣭⣭⣥⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⢛⣛⣿⠀⠀⢧⠙⠙⠟⠋⣉⡟⢯⢽⠟⢋⣈⡿⠻⡉⡹⡟⠹⠗⡼⠀⠀⣿⣛⡛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⡿⡀⠀⢸⡌⠁⠘⠲⣿⠒⢺⣿⠲⠚⡄⠐⠒⣿⠇⢿⡆⢠⡇⠀⢀⢿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠤⠴⠶⠿⠿⠿⠿⠛⠛⠛⠋⣉⣭⣶⣿⣷⠀⠀⠳⡄⠀⠀⠙⢳⣎⣀⣷⣾⣆⣱⣼⡀⠀⠙⢣⠞⠀⠀⣾⣿⣶⣬⣉⠙⠛⠛⠛⠿⠿⠿⠿⠶⠦⠤⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⣋⣭⣶⣷⡀⠀⠙⢦⣀⠀⠈⠋⠀⠈⠁⠀⠈⠟⠀⣀⡴⠋⠀⢀⣾⣶⣭⣙⠛⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠉⠁⢀⣴⣾⣿⣿⠟⣩⣾⣦⠀⠀⠉⠓⠦⢤⣄⣀⣀⣠⡤⠴⠚⠉⠀⠀⣴⣷⣍⠻⣿⣿⣷⣦⡀⠈⠉⠛⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠄⠒⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⣠⣾⡿⢟⣵⣿⡷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⣿⣮⡻⢿⣷⣄⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠈⠉⠒⠠⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⢀⣼⡿⠋⢠⣾⣿⡿⢱⣿⡟⣼⣿⡇⣿⣿⢸⣿⣧⢻⣿⡎⢿⣿⣷⡄⠙⢿⣧⡀⠀⠉⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠀⠀⠀⢀⣴⠿⠋⠀⣰⣿⣿⠟⢀⣿⡟⢠⣿⣿⠇⣿⣿⠸⣿⣿⡄⢻⣿⡀⠻⣿⣿⣆⠀⠙⠿⣦⡀⠀⠀⠀⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⣿⡿⠋⠀⣼⡿⠁⣸⣿⣿⠀⣿⣿⠀⣿⣿⣇⠈⢿⣧⠀⠙⢿⣿⣆⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣰⣿⠟⠀⠀⣸⡿⠁⠀⣿⣿⡇⠀⢻⡟⠀⢸⣿⣿⠀⠈⢿⣇⠀⠀⠻⣿⣆⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢠⡿⠁⠀⢀⣿⡿⠀⠀⢸⡇⠀⠀⢿⣿⠀⠀⠈⢿⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡾⠁⠀⠀⢰⣿⠃⠀⠀⢸⡇⠀⠀⠘⣿⡃⠀⠀⠈⢷⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀","⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⣆⠀⠀⠀⢸⡇⠀⠀⠀⣰⡇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢧⠀⠀⠀⢸⣿⡄⠀⠀⢸⡇⠀⠀⢠⣿⡇⠀⠀⠀⡼⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠘⣧⠀⠀⠈⣿⣷⠀⠀⢸⡇⠀⠀⣾⣿⠁⠀⠀⣼⠃⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢻⣷⣄⠀⠀⢹⣧⠀⠀⣿⣿⡆⠀⣼⣧⠀⢰⣿⣿⠀⠀⣼⡏⠀⠀⣠⣾⡟⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⢻⣿⣷⡀⠀⢿⣧⠀⢻⣿⣿⠀⣿⣿⠀⣿⣿⡟⠀⣼⡿⠀⢀⣾⣿⡟⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⡀⠀⠀⠀⠈⢻⣦⡀⠀⠻⣿⣿⣆⠘⣿⣧⠸⣿⣿⡆⣿⣿⢰⣿⣿⠇⣼⣿⠃⣰⣿⣿⠟⠀⢀⣴⡟⠁⠀⠀⠀⢀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠙⢿⣶⣄⠙⣿⣿⣧⢹⣿⣧⢻⣿⡇⣿⣿⢸⣿⡟⣼⣿⡏⣼⣿⣿⠋⣠⣶⡿⠋⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠠⢄⣀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣀⠙⢿⣷⣌⢻⣿⡧⠛⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠛⢼⣿⡟⣡⣾⡿⠋⣀⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⣀⡠⠄⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⡀⠀⠙⠻⣿⣿⣷⣮⡻⣿⡗⠉⠀⢀⣠⠴⠖⠒⠛⠛⢒⠲⠦⣄⡀⠀⠉⢾⣿⢟⣵⣾⣿⣿⠟⠋⠀⢀⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣙⡻⢿⡿⠊⠀⢀⡴⠋⠀⠀⠀⠀⣂⡀⠉⢀⡀⢴⡝⢦⡀⠀⠑⢿⡿⢟⣋⣤⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠒⠶⣶⣦⣤⣤⣤⣤⣤⣀⣈⣙⠻⢿⣿⡿⠀⠀⣰⠋⠀⠀⠀⡷⣶⠒⡛⣟⠒⣺⢿⠈⠁⠀⠙⣆⠀⠀⢿⣿⡿⠟⣋⣁⣀⣤⣤⣤⣤⣤⣴⣶⠶⠒⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣷⣾⠁⠀⢰⠃⠀⠀⢰⣾⠄⠘⣻⠭⠭⠓⠁⣶⣷⡶⠆⠀⠘⡆⠀⠈⣷⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣭⣭⣭⣭⠀⠀⡜⠘⠟⣠⡞⠚⣆⡎⠉⣧⣼⠿⢷⣰⠃⢱⣴⠀⠀⢣⠀⠀⣭⣭⣭⣭⣥⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⢛⣛⣿⠀⠀⢧⠀⠈⠛⣏⢉⠟⢯⠟⠛⢫⡉⡿⠻⣿⣿⠛⠁⠀⡼⠀⠀⣿⣛⡛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⡿⡀⠀⢸⡄⠐⠀⡾⠿⠒⢺⣷⠒⠒⣿⡗⠺⣿⣇⠀⠀⢠⡇⠀⢀⢿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠤⠴⠶⠿⠿⠿⠿⠛⠛⠛⠋⣉⣭⣶⣿⣷⠀⠀⠳⡄⠀⠁⠀⣤⣮⠀⠃⢺⣶⣵⣾⠁⠉⠀⢠⠞⠀⠀⣾⣿⣶⣬⣉⠙⠛⠛⠛⠿⠿⠿⠿⠶⠦⠤⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⣋⣭⣶⣷⡀⠀⠙⢦⣐⠺⠋⠙⠛⠮⠁⠀⠉⠉⠀⣀⡴⠋⠀⢀⣾⣶⣭⣙⠛⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠉⠁⢀⣴⣾⣿⣿⠟⣩⣾⣦⠀⠀⠉⠓⠦⢤⣇⣀⣀⣿⡤⠴⠚⠉⠀⠀⣴⣷⣍⠻⣿⣿⣷⣦⡀⠈⠉⠛⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠄⠒⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⣠⣾⡿⢟⣵⣿⡷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⣿⣮⡻⢿⣷⣄⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠈⠉⠒⠠⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⢀⣼⡿⠋⢠⣾⣿⡿⢱⣿⡟⣼⣿⡇⣿⣿⢸⣿⣧⢻⣿⡎⢿⣿⣷⡄⠙⢿⣧⡀⠀⠉⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠀⠀⠀⢀⣴⠿⠋⠀⣰⣿⣿⠟⢀⣿⡟⢠⣿⣿⠇⣿⣿⠸⣿⣿⡄⢻⣿⡀⠻⣿⣿⣆⠀⠙⠿⣦⡀⠀⠀⠀⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⣿⡿⠋⠀⣼⡿⠁⣸⣿⣿⠀⣿⣿⠀⣿⣿⣇⠈⢿⣧⠀⠙⢿⣿⣆⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣰⣿⠟⠀⠀⣸⡿⠁⠀⣿⣿⡇⠀⢻⡟⠀⢸⣿⣿⠀⠈⢿⣇⠀⠀⠻⣿⣆⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢠⡿⠁⠀⢀⣿⡿⠀⠀⢸⡇⠀⠀⢿⣿⠀⠀⠈⢿⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡾⠁⠀⠀⢰⣿⠃⠀⠀⢸⡇⠀⠀⠘⣿⡃⠀⠀⠈⢷⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀","⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⣆⠀⠀⠀⢸⡇⠀⠀⠀⣰⡇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢧⠀⠀⠀⢸⣿⡄⠀⠀⢸⡇⠀⠀⢠⣿⡇⠀⠀⠀⡼⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠘⣧⠀⠀⠈⣿⣷⠀⠀⢸⡇⠀⠀⣾⣿⠁⠀⠀⣼⠃⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢻⣷⣄⠀⠀⢹⣧⠀⠀⣿⣿⡆⠀⣼⣧⠀⢰⣿⣿⠀⠀⣼⡏⠀⠀⣠⣾⡟⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⢻⣿⣷⡀⠀⢿⣧⠀⢻⣿⣿⠀⣿⣿⠀⣿⣿⡟⠀⣼⡿⠀⢀⣾⣿⡟⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⡀⠀⠀⠀⠈⢻⣦⡀⠀⠻⣿⣿⣆⠘⣿⣧⠸⣿⣿⡆⣿⣿⢰⣿⣿⠇⣼⣿⠃⣰⣿⣿⠟⠀⢀⣴⡟⠁⠀⠀⠀⢀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠙⢿⣶⣄⠙⣿⣿⣧⢹⣿⣧⢻⣿⡇⣿⣿⢸⣿⡟⣼⣿⡏⣼⣿⣿⠋⣠⣶⡿⠋⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠠⢄⣀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣀⠙⢿⣷⣌⢻⣿⡧⠛⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠛⢼⣿⡟⣡⣾⡿⠋⣀⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⣀⡠⠄⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⡀⠀⠙⠻⣿⣿⣷⣮⡻⣿⡗⠉⠀⢀⣠⠴⠖⠒⠛⠛⠒⠲⠦⣄⡀⠀⠉⢾⣿⢟⣵⣾⣿⣿⠟⠋⠀⢀⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣙⡻⢿⡿⠊⠀⢀⡴⠋⠀⢀⠀⠀⢁⡀⠀⠀⡀⠀⠙⢦⡀⠀⠑⢿⡿⢟⣋⣤⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠒⠶⣶⣦⣤⣤⣤⣤⣤⣀⣈⣙⠻⢿⣿⡿⠀⠀⣰⠋⠀⠃⠀⡼⡗⠒⡻⠿⣖⣺⢿⠀⠀⠀⠙⣆⠀⠀⢿⣿⡿⠟⣋⣁⣀⣤⣤⣤⣤⣤⣴⣶⠶⠒⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣷⣾⠁⠀⢰⠃⠀⠀⢰⣾⡤⢤⣴⠥⠼⣷⡧⠠⣷⠆⠀⠀⠘⡆⠀⠈⣷⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣭⣭⣭⣭⠀⠀⡜⣶⠛⣠⡞⠸⣇⡞⠉⣧⣽⠉⢱⣰⠋⢡⣀⠀⠀⢣⠀⠀⣭⣭⣭⣭⣥⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⢛⣛⣿⠀⠀⢧⢀⡈⠿⣏⢻⠟⢯⢉⣽⢫⡉⡉⠱⡉⣻⠛⠁⠀⡼⠀⠀⣿⣛⡛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⡿⡀⠀⢸⡄⠀⠀⠸⣿⡖⢺⣿⡒⠒⣿⡗⠒⣿⠗⣂⠐⢢⡇⠀⢀⢿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠤⠴⠶⠿⠿⠿⠿⠛⠛⠛⠋⣉⣭⣶⣿⣷⠀⠀⠳⡄⠀⠀⠈⣡⣎⣀⣷⣾⣀⣻⣼⡅⠀⠉⢠⠞⠀⠀⣾⣿⣶⣬⣉⠙⠛⠛⠛⠿⠿⠿⠿⠶⠦⠤⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⣋⣭⣶⣷⡀⠀⠙⢦⣀⠀⠉⠁⠀⠈⠁⠀⣈⠉⠀⣀⡴⠋⠀⢀⣾⣶⣭⣙⠛⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠉⠁⢀⣴⣾⣿⣿⠟⣩⣾⣦⠀⠀⠉⠓⠦⢤⣄⣀⣀⣠⡬⠴⠚⠉⠀⠀⣴⣷⣍⠻⣿⣿⣷⣦⡀⠈⠉⠛⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠄⠒⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⣠⣾⡿⢟⣵⣿⡷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⣿⣮⡻⢿⣷⣄⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠈⠉⠒⠠⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⢀⣼⡿⠋⢠⣾⣿⡿⢱⣿⡟⣼⣿⡇⣿⣿⢸⣿⣧⢻⣿⡎⢿⣿⣷⡄⠙⢿⣧⡀⠀⠉⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠀⠀⠀⢀⣴⠿⠋⠀⣰⣿⣿⠟⢀⣿⡟⢠⣿⣿⠇⣿⣿⠸⣿⣿⡄⢻⣿⡀⠻⣿⣿⣆⠀⠙⠿⣦⡀⠀⠀⠀⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⣿⡿⠋⠀⣼⡿⠁⣸⣿⣿⠀⣿⣿⠀⣿⣿⣇⠈⢿⣧⠀⠙⢿⣿⣆⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣰⣿⠟⠀⠀⣸⡿⠁⠀⣿⣿⡇⠀⢻⡟⠀⢸⣿⣿⠀⠈⢿⣇⠀⠀⠻⣿⣆⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢠⡿⠁⠀⢀⣿⡿⠀⠀⢸⡇⠀⠀⢿⣿⡀⠀⠈⢿⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡾⠁⠀⠀⢰⣿⠃⠀⠀⢸⡇⠀⠀⠘⣿⡃⠀⠀⠈⢷⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀","⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⣆⠀⠀⠀⢸⡇⠀⠀⠀⣰⡇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢧⠀⠀⠀⢸⣿⡄⠀⠀⢸⡇⠀⠀⢠⣿⡇⠀⠀⠀⡼⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠘⣧⠀⠀⠈⣿⣷⠀⠀⢸⡇⠀⠀⣾⣿⠁⠀⠀⣼⠃⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢻⣷⣄⠀⠀⢹⣧⠀⠀⣿⣿⡆⠀⣼⣧⠀⢰⣿⣿⠀⠀⣼⡏⠀⠀⣠⣾⡟⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⢻⣿⣷⡀⠀⢿⣧⠀⢻⣿⣿⠀⣿⣿⠀⣿⣿⡟⠀⣼⡿⠀⢀⣾⣿⡟⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⡀⠀⠀⠀⠈⢻⣦⡀⠀⠻⣿⣿⣆⠘⣿⣧⠸⣿⣿⡆⣿⣿⢰⣿⣿⠇⣼⣿⠃⣰⣿⣿⠟⠀⢀⣴⡟⠁⠀⠀⠀⢀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠙⢿⣶⣄⠙⣿⣿⣧⢹⣿⣧⢻⣿⡇⣿⣿⢸⣿⡟⣼⣿⡏⣼⣿⣿⠋⣠⣶⡿⠋⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠠⢄⣀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣀⠙⢿⣷⣌⢻⣿⡧⠛⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠛⢼⣿⡟⣡⣾⡿⠋⣀⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⣀⡠⠄⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⡀⠀⠙⠻⣿⣿⣷⣮⡻⣿⡗⠉⠀⢀⣠⠴⠖⠒⠛⠛⠒⠲⠦⣄⡀⠀⠉⢾⣿⢟⣵⣾⣿⣿⠟⠋⠀⢀⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣙⡻⢿⡿⠊⠀⢀⡴⠋⠀⢀⢠⡄⢀⣠⡄⣀⡀⠀⠙⢦⡀⠀⠑⢿⡿⢟⣋⣤⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠒⠶⣶⣦⣤⣤⣤⣤⣤⣀⣈⣙⠻⢿⣿⡿⠀⠀⣰⠋⠘⠃⠀⡿⣟⠓⡻⢟⠚⣻⢿⠀⠀⣤⠙⣆⠀⠀⢿⣿⡿⠟⣋⣁⣀⣤⣤⣤⣤⣤⣴⣶⠶⠒⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣷⣾⠁⠀⢰⠃⠀⠀⢰⣾⠤⢼⣾⠥⠬⣧⡥⠤⣷⡆⠀⢶⠘⡆⠀⠈⣷⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣭⣭⣭⣭⠀⠀⡜⠀⠀⣀⡊⠘⡆⠚⠉⣧⣼⠉⠳⣰⠃⢱⣄⠀⠀⢣⠀⠀⣭⣭⣭⣭⣥⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⢛⣛⣿⠀⠀⢧⢠⣄⠛⣏⢉⠟⢯⢉⡝⢫⡉⡽⠻⡉⣹⠛⠄⠀⡼⠀⠀⣿⣛⡛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⡿⡀⠀⢸⡄⠀⠀⠸⣿⠒⢺⣿⡒⠒⣿⡗⠒⣿⠇⠀⠀⢠⡇⠀⢀⢿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠤⠴⠶⠿⠿⠿⠿⠛⠛⠛⠋⣉⣭⣶⣿⣷⠀⠀⠳⡄⠀⠀⠈⣧⣎⣀⣷⣾⣀⣱⣼⡁⠀⠀⢠⠞⠀⠀⣾⣿⣶⣬⣉⠙⠛⠛⠛⠿⠿⠿⠿⠶⠦⠤⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⣋⣭⣶⣷⡀⠀⠙⢦⣀⠀⠉⠁⠀⠨⠇⠶⠈⠉⠁⣀⡴⠋⠀⢀⣾⣶⣭⣙⠛⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠉⠁⢀⣴⣾⣿⣿⠟⣩⣾⣦⠀⠀⠉⠓⠦⢤⣄⣀⣀⣠⡤⠴⠚⠉⠀⠀⣴⣷⣍⠻⣿⣿⣷⣦⡀⠈⠉⠛⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠄⠒⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⣠⣾⡿⢟⣵⣿⡷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⣿⣮⡻⢿⣷⣄⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠈⠉⠒⠠⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⢀⣼⡿⠋⢠⣾⣿⡿⢱⣿⡟⣼⣿⡇⣿⣿⢸⣿⣧⢻⣿⡎⢿⣿⣷⡄⠙⢿⣧⡀⠀⠉⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠀⠀⠀⢀⣴⠿⠋⠀⣰⣿⣿⠟⢀⣿⡟⢠⣿⣿⠇⣿⣿⠸⣿⣿⡄⢻⣿⡀⠻⣿⣿⣆⠀⠙⠿⣦⡀⠀⠀⠀⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⣿⡿⠋⠀⣼⡿⠁⣸⣿⣿⠀⣿⣿⠀⣿⣿⣇⠈⢿⣧⠀⠙⢿⣿⣆⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣰⣿⠟⠀⠀⣸⡿⠁⠀⣿⣿⡇⠀⢻⡟⠀⢸⣿⣿⠀⠈⢿⣇⠀⠀⠻⣿⣆⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢠⡿⠁⠀⢀⣿⡿⠀⠀⢸⡇⠀⠀⢿⣿⡀⠀⠈⢿⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡾⠁⠀⠀⢰⣿⠃⠀⠀⢸⡇⠀⠀⠘⣿⡃⠀⠀⠈⢷⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀","⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⣆⠀⠀⠀⢸⡇⠀⠀⠀⣰⡇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢧⠀⠀⠀⢸⣿⡄⠀⠀⢸⡇⠀⠀⢠⣿⡇⠀⠀⠀⡼⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠘⣧⠀⠀⠈⣿⣷⠀⠀⢸⡇⠀⠀⣾⣿⠁⠀⠀⣼⠃⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⢻⣷⣄⠀⠀⢹⣧⠀⠀⣿⣿⡆⠀⣼⣧⠀⢰⣿⣿⠀⠀⣼⡏⠀⠀⣠⣾⡟⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⢻⣿⣷⡀⠀⢿⣧⠀⢻⣿⣿⠀⣿⣿⠀⣿⣿⡟⠀⣼⡿⠀⢀⣾⣿⡟⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⡀⠀⠀⠀⠈⢻⣦⡀⠀⠻⣿⣿⣆⠘⣿⣧⠸⣿⣿⡆⣿⣿⢰⣿⣿⠇⣼⣿⠃⣰⣿⣿⠟⠀⢀⣴⡟⠁⠀⠀⠀⢀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠙⢿⣶⣄⠙⣿⣿⣧⢹⣿⣧⢻⣿⡇⣿⣿⢸⣿⡟⣼⣿⡏⣼⣿⣿⠋⣠⣶⡿⠋⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠠⢄⣀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣀⠙⢿⣷⣌⢻⣿⡧⠟⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠻⢼⣿⡟⣡⣾⡿⠋⣀⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⣀⡠⠄⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⡀⠀⠙⠻⣿⣿⣷⣮⡻⣿⡗⠉⠀⢀⣠⠴⠖⠒⠛⠛⠒⠲⠦⣄⡀⠀⠉⢾⣿⢟⣵⣾⣿⣿⠟⠋⠀⢀⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣙⡻⢿⡿⠊⠀⢀⡴⠋⠀⢀⠀⠀⢀⡀⠀⠀⡀⠀⠙⢦⡀⠀⠑⢿⡿⢟⣋⣤⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠒⠶⣶⣦⣤⣤⣤⣤⣤⣀⣈⣙⠻⢿⣿⡿⠀⠀⣰⠋⠀⠀⠀⡿⣗⠒⡻⢟⠒⣺⢿⠀⠀⠀⠙⣆⠀⠀⢿⣿⡿⠟⣋⣁⣀⣤⣤⣤⣤⣤⣴⣶⠶⠒⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣷⣾⠁⠀⢰⠃⠀⠀⢰⣾⠤⢼⣾⠥⠬⣷⡧⠤⣷⡆⠀⠀⠘⡆⠀⠈⣷⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣭⣭⣭⣭⠀⠀⡜⠀⠀⣠⡞⠘⣆⡞⠉⣧⣼⠉⢳⣰⠃⢳⣄⠀⠀⢣⠀⠀⣭⣭⣭⣭⣥⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⢛⣛⣿⠀⠀⢧⠀⠈⠛⣏⢉⠟⢯⢉⡝⢫⡉⡽⠻⡉⣹⠛⠁⠀⡼⠀⠀⣿⣛⡛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⡿⡄⠀⢸⡄⠀⠀⠸⣿⠒⢺⣿⡒⠒⣿⡗⠒⣿⠇⠀⠀⢠⡇⠀⢠⢿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠤⠴⠶⠿⠿⠿⠿⠛⠛⠛⠋⣉⣭⣶⣿⣷⠀⠀⠳⡄⠀⠀⠈⣧⣎⣀⣷⣾⣀⣱⣼⠁⠀⠀⢠⠞⠀⠀⣾⣿⣶⣬⣉⠙⠛⠛⠛⠿⠿⠿⠿⠶⠦⠤⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⣋⣭⣶⣷⡀⠀⠙⢦⣀⠀⠉⠁⠀⠈⠁⠀⠈⠉⠀⣀⡴⠋⠀⢀⣾⣶⣭⣙⠛⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠉⠁⢀⣴⣾⣿⣿⠟⣩⣾⣦⠀⠀⠉⠓⠦⢤⣄⣀⣀⣠⡤⠴⠚⠉⠀⠀⣴⣷⣍⠻⣿⣿⣷⣦⡀⠈⠉⠛⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠄⠒⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⣠⣾⡿⢟⣵⣿⡷⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⣿⣮⡻⢿⣷⣄⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠈⠉⠒⠠⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⢀⣼⡿⠋⢠⣾⣿⡿⢱⣿⡟⣼⣿⡇⣿⣿⢸⣿⣧⢻⣿⡎⢿⣿⣷⡄⠙⢿⣧⡀⠀⠉⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠀⠀⠀⢀⣴⠿⠋⠀⣰⣿⣿⠟⢀⣿⡟⢠⣿⣿⠇⣿⣿⠸⣿⣿⡄⢻⣿⡀⠻⣿⣿⣆⠀⠙⠿⣦⡀⠀⠀⠀⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⣿⡿⠋⠀⣼⡿⠁⣸⣿⣿⠀⣿⣿⠀⣿⣿⣇⠈⢿⣧⠀⠙⢿⣿⣆⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣰⣿⠟⠀⠀⣸⡿⠁⠀⣿⣿⡇⠀⢻⡟⠀⢸⣿⣿⠀⠈⢿⣇⠀⠀⠻⣿⣆⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢠⡿⠁⠀⢀⣿⡿⠀⠀⢸⡇⠀⠀⢿⣿⡀⠀⠈⢿⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡾⠁⠀⠀⢰⣿⠃⠀⠀⢸⡇⠀⠀⠘⣿⡃⠀⠀⠈⢷⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀","⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⣆⠀⠀⠀⢸⡇⠀⠀⠀⣰⡇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢧⠀⠀⠀⢸⣿⡄⠀⠀⢸⡇⠀⠀⢠⣿⡇⠀⠀⠀⡼⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠘⣧⠀⠀⠈⣿⣷⠀⠀⢸⡇⠀⠀⣾⣿⠁⠀⠀⣼⠃⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢻⣷⣄⠀⠀⢹⣧⠀⠀⣿⣿⡆⠀⣼⣧⠀⢰⣿⣿⠀⠀⣼⡏⠀⠀⣠⣾⡟⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⢻⣿⣷⡀⠀⢿⣧⠀⢻⣿⣿⠀⣿⣿⠀⣿⣿⡟⠀⣼⡿⠀⢀⣾⣿⡟⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⡀⠀⠀⠀⠈⢻⣦⡀⠀⠻⣿⣿⣆⠘⣿⣧⠸⣿⣿⡆⣿⣿⢰⣿⣿⠇⣼⣿⠃⣰⣿⣿⠟⠀⢀⣴⡟⠁⠀⠀⠀⢀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠙⢿⣶⣄⠙⣿⣿⣧⢹⣿⣧⢻⣿⡇⣿⣿⢸⣿⡟⣼⣿⡏⣼⣿⣿⠋⣠⣶⡿⠋⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠠⢄⣀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣀⠙⢿⣷⣌⢻⣿⡧⠛⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠛⢼⣿⡟⣡⣾⡿⠋⣀⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⣀⡠⠄⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⡀⠀⠙⠻⣿⣿⣷⣮⡻⣿⡗⠉⠀⢀⣠⠴⠖⠒⠛⠛⠒⠲⠦⣄⡀⠀⠉⢾⣿⢟⣵⣾⣿⣿⠟⠋⠀⢀⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣙⡻⢿⡿⠊⠀⢀⡴⠋⠀⢀⠀⠀⣀⣀⠀⠀⡀⠀⠙⢦⡀⠀⠑⢿⡿⢟⣋⣤⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠒⠶⣶⣦⣤⣤⣤⣤⣤⣀⣈⣙⠻⢿⣿⡿⠀⠀⣰⠋⠀⠀⢀⡿⣟⠛⡿⢿⠒⣺⢿⠀⠀⠀⠙⣆⠀⠀⢿⣿⡿⠟⣋⣁⣀⣤⣤⣤⣤⣤⣴⣶⠶⠒⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣷⣾⠁⠀⢰⠃⠀⠀⢰⣾⠥⢼⣾⠥⠬⣷⡧⠤⣷⡆⠀⠀⠘⡆⠀⠈⣷⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣭⣭⣭⣭⠀⠀⡜⠀⠀⣠⡞⢘⣦⣞⠉⣧⣼⠉⢳⣰⠃⢱⣄⠀⠀⢣⠀⠀⣭⣭⣭⣭⣥⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⢛⣛⣿⠀⠀⢧⠀⠈⠛⣏⢩⡿⣿⣉⡟⢻⡉⡽⠻⡉⣹⠛⠁⠀⡼⠀⠀⣿⣛⡛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⡿⡀⠀⢸⡄⠀⠀⠸⣿⠒⢺⣿⡗⠒⣿⡗⠒⣿⠇⠀⠀⢠⡇⠀⢀⢿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠤⠴⠶⠿⠿⠿⠿⠛⠛⠛⠋⣉⣭⣶⣿⣷⠀⠀⠳⡄⠀⠀⠈⣧⣎⣀⣷⣾⣀⣱⣼⠁⠀⠀⢠⠞⠀⠀⣾⣿⣶⣬⣉⠙⠛⠛⠛⠿⠿⠿⠿⠶⠦⠤⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⣋⣭⣶⣷⡀⠀⠙⢦⣀⠀⠉⠁⠀⠈⠁⠀⠈⠉⠀⣀⡴⠋⠀⢀⣾⣶⣭⣙⠛⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠉⠁⢀⣴⣾⣿⣿⠟⣩⣾⣦⠀⠀⠉⠓⠦⢤⣄⣀⣀⣠⡤⠴⠚⠉⠀⠀⣴⣷⣍⠻⣿⣿⣷⣦⡀⠈⠉⠛⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠄⠒⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⣠⣾⡿⢟⣵⣿⡷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⣿⣮⡻⢿⣷⣄⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠈⠉⠒⠠⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⢀⣼⡿⠋⢠⣾⣿⡿⢱⣿⡟⣼⣿⡇⣿⣿⢸⣿⣧⢻⣿⡎⢿⣿⣷⡄⠙⢿⣧⡀⠀⠉⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠀⠀⠀⢀⣴⠿⠋⠀⣰⣿⣿⠟⢀⣿⡟⢠⣿⣿⠇⣿⣿⠸⣿⣿⡄⢻⣿⡀⠻⣿⣿⣆⠀⠙⠿⣦⡀⠀⠀⠀⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⣿⡿⠋⠀⣼⡿⠁⣸⣿⣿⠀⣿⣿⠀⣿⣿⣇⠈⢿⣧⠀⠙⢿⣿⣆⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣰⣿⠟⠀⠀⣸⡿⠁⠀⣿⣿⡇⠀⢻⡟⠀⢸⣿⣿⠀⠈⢿⣇⠀⠀⠻⣿⣆⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢠⡿⠁⠀⢀⣿⡿⠀⠀⢸⡇⠀⠀⢿⣿⡀⠀⠈⢿⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡾⠁⠀⠀⢰⣿⠃⠀⠀⢸⡇⠀⠀⠘⣿⡃⠀⠀⠈⢷⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀","⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⣆⠀⠀⠀⢸⡇⠀⠀⠀⣰⡇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢧⠀⠀⠀⢸⣿⡄⠀⠀⢸⡇⠀⠀⢠⣿⡇⠀⠀⠀⡼⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠘⣧⠀⠀⠈⣿⣷⠀⠀⢸⡇⠀⠀⣾⣿⠁⠀⠀⣼⠃⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢻⣷⣄⠀⠀⢹⣧⠀⠀⣿⣿⡆⠀⣼⣧⠀⢰⣿⣿⠀⠀⣼⡏⠀⠀⣠⣾⡟⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⢻⣿⣷⡀⠀⢿⣧⠀⢻⣿⣿⠀⣿⣿⠀⣿⣿⡟⠀⣼⡿⠀⢀⣾⣿⡟⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⡀⠀⠀⠀⠈⢻⣦⡀⠀⠻⣿⣿⣆⠘⣿⣧⠸⣿⣿⡆⣿⣿⢰⣿⣿⠇⣼⣿⠃⣰⣿⣿⠟⠀⢀⣴⡟⠁⠀⠀⠀⢀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠙⢿⣶⣄⠙⣿⣿⣧⢹⣿⣧⢻⣿⡇⣿⣿⢸⣿⡟⣼⣿⡏⣼⣿⣿⠋⣠⣶⡿⠋⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠠⢄⣀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣀⠙⢿⣷⣌⢻⣿⡧⠛⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠛⢼⣿⡟⣡⣾⡿⠋⣀⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⣀⡠⠄⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⡀⠀⠙⠻⣿⣿⣷⣮⡻⣿⡗⠉⠀⢀⣠⠴⠖⠒⠛⠛⠒⠲⠦⣄⡀⠀⠉⢾⣿⢟⣵⣾⣿⣿⠟⠋⠀⢀⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣙⡻⢿⡿⠊⠀⢀⡴⠋⠀⢀⠀⠀⢀⡀⠀⠀⡀⠀⠙⢦⡀⠀⠑⢿⡿⢟⣋⣤⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠒⠶⣶⣦⣤⣤⣤⣤⣤⣀⣈⣙⠻⢿⣿⡿⠀⠀⣰⠋⠀⠀⠀⡿⣗⠒⡻⢟⠒⣺⢿⠀⠀⠀⠙⣆⠀⠀⢿⣿⡿⠟⣋⣁⣀⣤⣤⣤⣤⣤⣴⣶⠶⠒⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣷⣾⠁⠀⢰⠃⠀⠀⢰⣾⠤⢼⣾⠥⠬⣿⡯⠤⣷⡆⠀⠀⠘⡆⠀⠈⣷⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣭⣭⣭⣭⠀⠀⡜⠀⠀⣠⡞⠘⣆⡞⠉⣧⣼⠉⣳⣴⡃⢱⣄⠀⠀⢣⠀⠀⣭⣭⣭⣭⣥⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⢛⣛⣿⠀⠀⢧⠀⠈⠛⣏⢉⠟⢯⣉⡿⢿⡉⡿⢿⡍⣽⠟⠁⠀⡼⠀⠀⣿⣛⡛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⡿⡀⠀⢸⡄⠀⠀⠸⣿⠒⢺⣿⡗⠒⣿⡗⠒⣿⠇⠀⠀⢠⡇⠀⢀⢿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠤⠴⠶⠿⠿⠿⠿⠛⠛⠛⠋⣉⣭⣶⣿⣷⠀⠀⠳⡄⠀⠀⠈⣧⣮⣤⣷⣾⣀⣱⣼⠁⠀⠀⢠⠞⠀⠀⣾⣿⣶⣬⣉⠙⠛⠛⠛⠿⠿⠿⠿⠶⠦⠤⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⣋⣭⣶⣷⡀⠀⠙⢦⣀⠀⠉⠁⠀⠙⠋⠀⠈⠉⠀⣀⡴⠋⠀⢀⣾⣶⣭⣙⠛⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠉⠁⢀⣴⣾⣿⣿⠟⣩⣾⣦⠀⠀⠉⠓⠦⢤⣄⣀⣀⣠⡤⠴⠚⠉⠀⠀⣴⣷⣍⠻⣿⣿⣷⣦⡀⠈⠉⠛⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠄⠒⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⣠⣾⡿⢟⣵⣿⡷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⣿⣮⡻⢿⣷⣄⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠈⠉⠒⠠⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⢀⣼⡿⠋⢠⣾⣿⡿⢱⣿⡟⣼⣿⡇⣿⣿⢸⣿⣧⢻⣿⡎⢿⣿⣷⡄⠙⢿⣧⡀⠀⠉⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠀⠀⠀⢀⣴⠿⠋⠀⣰⣿⣿⠟⢀⣿⡟⢠⣿⣿⠇⣿⣿⠸⣿⣿⡄⢻⣿⡀⠻⣿⣿⣆⠀⠙⠿⣦⡀⠀⠀⠀⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⣿⡿⠋⠀⣼⡿⠁⣸⣿⣿⠀⣿⣿⠀⣿⣿⣇⠈⢿⣧⠀⠙⢿⣿⣆⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣰⣿⠟⠀⠀⣸⡿⠁⠀⣿⣿⡇⠀⢻⡟⠀⢸⣿⣿⠀⠈⢿⣇⠀⠀⠻⣿⣆⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀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⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢻⣷⣄⠀⠀⢹⣧⠀⠀⣿⣿⡆⠀⣼⣧⠀⢰⣿⣿⠀⠀⣼⡏⠀⠀⣠⣾⡟⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⢻⣿⣷⡀⠀⢿⣧⠀⢻⣿⣿⠀⣿⣿⠀⣿⣿⡟⠀⣼⡿⠀⢀⣾⣿⡟⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⡀⠀⠀⠀⠈⢻⣦⡀⠀⠻⣿⣿⣆⠘⣿⣧⠸⣿⣿⡆⣿⣿⢰⣿⣿⠇⣼⣿⠃⣰⣿⣿⠟⠀⢀⣴⡟⠁⠀⠀⠀⢀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠙⢿⣶⣄⠙⣿⣿⣧⢹⣿⣧⢻⣿⡇⣿⣿⢸⣿⡟⣼⣿⡏⣼⣿⣿⠋⣠⣶⡿⠋⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠠⢄⣀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣀⠙⢿⣷⣌⢻⣿⡧⠛⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠛⢼⣿⡟⣡⣾⡿⠋⣀⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⣀⡠⠄⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⡀⠀⠙⠻⣿⣿⣷⣮⡻⣿⡗⠉⠀⢀⣠⠴⠖⠒⠛⠛⠒⠲⠦⣄⡀⠀⠉⢾⣿⢟⣵⣾⣿⣿⠟⠋⠀⢀⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣙⡻⢿⡿⠊⠀⢀⡴⠋⠀⢀⠀⠀⢀⡀⠀⠀⡀⠀⠙⢦⡀⠀⠑⢿⡿⢟⣋⣤⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠒⠶⣶⣦⣤⣤⣤⣤⣤⣀⣈⣙⠻⢿⣿⡿⠀⠀⣰⠋⠀⠀⠀⡿⣗⠒⣿⢟⠒⣺⢿⠀⠀⠀⠙⣆⠀⠀⢿⣿⡿⠟⣋⣁⣀⣤⣤⣤⣤⣤⣴⣶⠶⠒⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣷⣾⠁⠀⢰⠃⠀⠀⣶⣿⡤⢼⣾⠧⠬⣷⡧⠤⣷⡆⠀⠀⠘⡆⠀⠈⣷⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣭⣭⣭⣭⠀⠀⡜⠀⢀⣤⡞⠙⣧⡞⠉⣧⣼⠉⢳⣰⠃⢱⣄⠀⠀⢣⠀⠀⣭⣭⣭⣭⣥⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⢛⣛⣿⠀⠀⢧⠀⠘⠻⣏⢉⠟⢯⢉⡝⢫⣉⣽⠻⡉⣹⠛⠁⠀⡼⠀⠀⣿⣛⡛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⡿⡀⠀⢸⡄⠀⠀⠸⣿⠒⢺⣿⡶⠶⣿⡗⠒⣿⠇⠀⠀⢠⡇⠀⢀⢿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠤⠴⠶⠿⠿⠿⠿⠛⠛⠛⠋⣉⣭⣶⣿⣷⠀⠀⠳⡄⠀⠀⠈⣧⣎⣀⣷⣾⣀⣱⣼⠁⠀⠀⢠⠞⠀⠀⣾⣿⣶⣬⣉⠙⠛⠛⠛⠿⠿⠿⠿⠶⠦⠤⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⣋⣭⣶⣷⡀⠀⠙⢦⣀⠀⠉⠁⠀⠙⠋⠀⠈⠉⠀⣀⡴⠋⠀⢀⣾⣶⣭⣙⠛⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠉⠁⢀⣴⣾⣿⣿⠟⣩⣾⣦⠀⠀⠉⠓⠦⢤⣄⣀⣀⣠⡤⠴⠚⠉⠀⠀⣴⣷⣍⠻⣿⣿⣷⣦⡀⠈⠉⠛⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠄⠒⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⣠⣾⡿⢟⣵⣿⡷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⣿⣮⡻⢿⣷⣄⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠈⠉⠒⠠⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⢀⣼⡿⠋⢠⣾⣿⡿⢱⣿⡟⣼⣿⡇⣿⣿⢸⣿⣧⢻⣿⡎⢿⣿⣷⡄⠙⢿⣧⡀⠀⠉⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠀⠀⠀⢀⣴⠿⠋⠀⣰⣿⣿⠟⢀⣿⡟⢠⣿⣿⠇⣿⣿⠸⣿⣿⡄⢻⣿⡀⠻⣿⣿⣆⠀⠙⠿⣦⡀⠀⠀⠀⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⣿⡿⠋⠀⣼⡿⠁⣸⣿⣿⠀⣿⣿⠀⣿⣿⣇⠈⢿⣧⠀⠙⢿⣿⣆⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣰⣿⠟⠀⠀⣸⡿⠁⠀⣿⣿⡇⠀⢻⡟⠀⢸⣿⣿⠀⠈⢿⣇⠀⠀⠻⣿⣆⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢠⡿⠁⠀⢀⣿⡿⠀⠀⢸⡇⠀⠀⢿⣿⡀⠀⠈⢿⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡾⠁⠀⠀⢰⣿⠃⠀⠀⢸⡇⠀⠀⠘⣿⡃⠀⠀⠈⢷⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀","⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⣆⠀⠀⠀⢸⡇⠀⠀⠀⣰⡇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢧⠀⠀⠀⢸⣿⡄⠀⠀⢸⡇⠀⠀⢠⣿⡇⠀⠀⠀⡼⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠘⣧⠀⠀⠈⣿⣷⠀⠀⢸⡇⠀⠀⣾⣿⠁⠀⠀⣼⠃⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢻⣷⣄⠀⠀⢹⣧⠀⠀⣿⣿⡆⠀⣼⣧⠀⢰⣿⣿⠀⠀⣼⡏⠀⠀⣠⣾⡟⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⢻⣿⣷⡀⠀⢿⣧⠀⢻⣿⣿⠀⣿⣿⠀⣿⣿⡟⠀⣼⡿⠀⢀⣾⣿⡟⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⡀⠀⠀⠀⠈⢻⣦⡀⠀⠻⣿⣿⣆⠘⣿⣧⠸⣿⣿⡆⣿⣿⢰⣿⣿⠇⣼⣿⠃⣰⣿⣿⠟⠀⢀⣴⡟⠁⠀⠀⠀⢀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠙⢿⣶⣄⠙⣿⣿⣧⢹⣿⣧⢻⣿⡇⣿⣿⢸⣿⡟⣼⣿⡏⣼⣿⣿⠋⣠⣶⡿⠋⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠠⢄⣀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣀⠙⢿⣷⣌⢻⣿⡧⠛⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠛⢼⣿⡟⣡⣾⡿⠋⣀⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⣀⡠⠄⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⡀⠀⠙⠻⣿⣿⣷⣮⡻⣿⡗⠉⠀⢀⣠⠴⠖⠒⠛⠛⠒⠲⠦⣄⡀⠀⠉⢾⣿⢟⣵⣾⣿⣿⠟⠋⠀⢀⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣙⡻⢿⡿⠊⠀⢀⡴⠋⠀⢀⠀⠀⢀⡀⠀⠀⡀⠀⠙⢦⡀⠀⠑⢿⡿⢟⣋⣤⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠒⠶⣶⣦⣤⣤⣤⣤⣤⣀⣈⣙⠻⢿⣿⡿⠀⠀⣰⠋⠀⠀⠀⡿⣗⠒⡻⢟⠛⣻⢿⠀⠀⠀⠙⣆⠀⠀⢿⣿⡿⠟⣋⣁⣀⣤⣤⣤⣤⣤⣴⣶⠶⠒⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣷⣾⠁⠀⢰⠃⠀⠀⢰⣾⠤⢼⣿⡧⠬⣷⡧⠤⣷⡆⠀⠀⠘⡆⠀⠈⣷⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣭⣭⣭⣭⠀⠀⡜⠀⠀⣠⡞⠘⣦⡾⠉⣧⣼⠉⢷⣴⠃⢱⣄⠀⠀⢣⠀⠀⣭⣭⣭⣭⣥⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⢛⣛⣿⠀⠀⢧⠀⠈⠛⣏⢉⠟⢯⢉⡟⢻⡉⡽⠻⣉⣹⠛⠁⠀⡼⠀⠀⣿⣛⡛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⡿⡀⠀⢸⡄⠀⠀⠸⣿⠒⢺⣿⡒⠒⣿⡗⠲⣿⡿⠀⠀⢠⡇⠀⢀⢿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠤⠴⠶⠿⠿⠿⠿⠛⠛⠛⠋⣉⣭⣶⣿⣷⠀⠀⠳⡄⠀⠀⠘⣷⣎⣀⣷⣾⣀⣱⣼⠁⠀⠀⢠⠞⠀⠀⣾⣿⣶⣬⣉⠙⠛⠛⠛⠿⠿⠿⠿⠶⠦⠤⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⣋⣭⣶⣷⡀⠀⠙⢦⣀⠀⠉⠁⠀⠈⠁⠀⠈⠉⠀⣀⡴⠋⠀⢀⣾⣶⣭⣙⠛⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠉⠁⢀⣴⣾⣿⣿⠟⣩⣾⣦⠀⠀⠉⠓⠦⢤⣄⣀⣀⣠⡤⠴⠚⠉⠀⠀⣴⣷⣍⠻⣿⣿⣷⣦⡀⠈⠉⠛⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠄⠒⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⣠⣾⡿⢟⣵⣿⡷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⣿⣮⡻⢿⣷⣄⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠈⠉⠒⠠⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⢀⣼⡿⠋⢠⣾⣿⡿⢱⣿⡟⣼⣿⡇⣿⣿⢸⣿⣧⢻⣿⡎⢿⣿⣷⡄⠙⢿⣧⡀⠀⠉⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠀⠀⠀⢀⣴⠿⠋⠀⣰⣿⣿⠟⢀⣿⡟⢠⣿⣿⠇⣿⣿⠸⣿⣿⡄⢻⣿⡀⠻⣿⣿⣆⠀⠙⠿⣦⡀⠀⠀⠀⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⣿⡿⠋⠀⣼⡿⠁⣸⣿⣿⠀⣿⣿⠀⣿⣿⣇⠈⢿⣧⠀⠙⢿⣿⣆⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣰⣿⠟⠀⠀⣸⡿⠁⠀⣿⣿⡇⠀⢻⡟⠀⢸⣿⣿⠀⠈⢿⣇⠀⠀⠻⣿⣆⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢠⡿⠁⠀⢀⣿⡿⠀⠀⢸⡇⠀⠀⢿⣿⡀⠀⠈⢿⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡾⠁⠀⠀⢰⣿⠃⠀⠀⢸⡇⠀⠀⠘⣿⡃⠀⠀⠈⢷⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀","⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⣆⠀⠀⠀⢸⡇⠀⠀⠀⣰⡇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢧⠀⠀⠀⢸⣿⡄⠀⠀⢸⡇⠀⠀⢠⣿⡇⠀⠀⠀⡼⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠘⣧⠀⠀⠈⣿⣷⠀⠀⢸⡇⠀⠀⣾⣿⠁⠀⠀⣼⠃⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⢻⣷⣄⠀⠀⢹⣧⠀⠀⣿⣿⡆⠀⣼⣧⠀⢰⣿⣿⠀⠀⣼⡏⠀⠀⣠⣾⡟⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⢻⣿⣷⡀⠀⢿⣧⠀⢻⣿⣿⠀⣿⣿⠀⣿⣿⡟⠀⣼⡿⠀⢀⣾⣿⡟⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⡀⠀⠀⠀⠈⢻⣦⡀⠀⠻⣿⣿⣆⠘⣿⣧⠸⣿⣿⡆⣿⣿⢰⣿⣿⠇⣼⣿⠃⣰⣿⣿⠟⠀⢀⣴⡟⠁⠀⠀⠀⢀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠙⢿⣶⣄⠙⣿⣿⣧⢹⣿⣧⢻⣿⡇⣿⣿⢸⣿⡟⣼⣿⡏⣼⣿⣿⠋⣠⣶⡿⠋⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠠⢄⣀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣀⠙⢿⣷⣌⢻⣿⡧⠟⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠻⢼⣿⡟⣡⣾⡿⠋⣀⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⣀⡠⠄⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⡀⠀⠙⠻⣿⣿⣷⣮⡻⣿⡗⠉⠀⢀⣠⠴⠖⠒⠛⠛⠒⠲⠦⣄⡀⠀⠉⢾⣿⢟⣵⣾⣿⣿⠟⠋⠀⢀⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣙⡻⢿⡿⠊⠀⢀⡴⠋⠀⠀⠙⠀⢸⡗⠀⠀⡀⠀⠙⢦⡀⠀⠑⢿⡿⢟⣋⣤⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠒⠶⣶⣦⣤⣤⣤⣤⣤⣀⣈⣙⠻⢿⣿⡿⠀⠀⣰⠋⠀⠁⣀⡴⢗⠒⡺⢟⠚⣻⢿⠀⠘⢢⡝⣆⠀⠀⢿⣿⡿⠟⣋⣁⣀⣤⣤⣤⣤⣤⣴⣶⠶⠒⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣷⣾⠁⠀⢰⠃⣀⣀⢐⣻⡯⣼⣾⠤⠬⣧⡠⠤⣦⡆⠀⠛⡘⡆⠀⠈⣷⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣭⣭⣭⣭⠀⠀⡜⠀⠉⣠⡞⠀⣤⡟⠉⠧⣴⠉⢳⣰⢿⢷⠄⠀⠅⢣⠀⠀⣭⣭⣭⣭⣥⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⢛⣛⣿⠀⠀⢧⠀⠈⠛⣟⢋⠇⢤⠀⠀⢫⡉⣽⣻⡉⣹⠓⢶⠀⡼⠀⠀⣿⣛⡛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⡿⡄⠀⢸⡄⠀⠉⣺⣿⠒⢺⡶⠐⠲⢿⡀⣴⠋⠃⠀⠙⢣⡇⠀⢠⢿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠤⠴⠶⠿⠿⠿⠿⠛⠛⠛⠋⣉⣭⣶⣿⣷⠀⠀⠳⡄⠀⠉⠘⣿⣮⣀⡷⣬⣛⣱⣼⠏⠀⠀⢠⠞⠀⠀⣾⣿⣶⣬⣉⠙⠛⠛⠛⠿⠿⠿⠿⠶⠦⠤⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⣋⣭⣶⣷⡀⠀⠙⢦⣀⠀⠉⠁⠘⠓⠃⠀⠈⠹⣶⣀⡴⠋⠀⢀⣾⣶⣭⣙⠛⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠉⠁⢀⣴⣾⣿⣿⠟⣩⣾⣦⠀⠀⠉⠓⠦⢤⣄⣀⣀⣠⡤⠴⠚⠉⠀⠀⣴⣷⣍⠻⣿⣿⣷⣦⡀⠈⠉⠛⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠄⠒⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⣠⣾⡿⢟⣵⣿⡷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⣿⣮⡻⢿⣷⣄⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠈⠉⠒⠠⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⢀⣼⡿⠋⢠⣾⣿⡿⢱⣿⡟⣼⣿⡇⣿⣿⢸⣿⣧⢻⣿⡎⢿⣿⣷⡄⠙⢿⣧⡀⠀⠉⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠀⠀⠀⢀⣴⠿⠋⠀⣰⣿⣿⠟⢀⣿⡟⢠⣿⣿⠇⣿⣿⠸⣿⣿⡄⢻⣿⡀⠻⣿⣿⣆⠀⠙⠿⣦⡀⠀⠀⠀⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⣿⡿⠋⠀⣼⡿⠁⣸⣿⣿⠀⣿⣿⠀⣿⣿⣇⠈⢿⣧⠀⠙⢿⣿⣆⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣰⣿⠟⠀⠀⣸⡿⠁⠀⣿⣿⡇⠀⢻⡟⠀⢸⣿⣿⠀⠈⢿⣇⠀⠀⠻⣿⣆⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢠⡿⠁⠀⢀⣿⡿⠀⠀⢸⡇⠀⠀⢿⣿⡀⠀⠈⢿⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡾⠁⠀⠀⢰⣿⠃⠀⠀⢸⡇⠀⠀⠘⣿⡃⠀⠀⠈⢷⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀","⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⣆⠀⠀⠀⢸⡇⠀⠀⠀⣰⡇⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢧⠀⠀⠀⢸⣿⡄⠀⠀⢸⡇⠀⠀⢠⣿⡇⠀⠀⠀⡼⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠘⣧⠀⠀⠈⣿⣷⠀⠀⢸⡇⠀⠀⣾⣿⠁⠀⠀⣼⠃⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢻⣷⣄⠀⠀⢹⣧⠀⠀⣿⣿⡆⠀⣸⣇⠀⢰⣿⣿⠀⠀⣼⡏⠀⠀⣠⣾⡟⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⢻⣿⣷⡀⠀⢿⣧⠀⢻⣿⣿⠀⣿⣿⠀⣿⣿⡟⠀⣼⡿⠀⢀⣾⣿⡟⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⡀⠀⠀⠀⠈⢻⣦⡀⠀⠻⣿⣿⣆⠘⣿⣧⠸⣿⣿⡆⣿⣿⢰⣿⣿⠇⣼⣿⠃⣰⣿⣿⠟⠀⢀⣴⡟⠁⠀⠀⠀⢀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠙⢿⣶⣄⠙⣿⣿⣧⢹⣿⣧⢻⣿⡇⣿⣿⢸⣿⡟⣼⣿⡏⣼⣿⣿⠋⣠⣶⡿⠋⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠠⢄⣀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣀⠙⢿⣷⣌⢻⣿⡧⠛⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠛⢼⣿⡟⣡⣾⡿⠋⣀⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⢀⡠⠄⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⡀⠀⠙⠻⣿⣿⣷⣮⡻⣿⡷⠉⠀⢀⣠⠴⠖⠒⠛⠛⠒⠲⠦⣄⡀⠀⠉⢾⣿⢟⣵⣾⣿⣿⠟⠋⠀⢀⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣙⡻⢿⡿⠊⠀⢀⡴⠋⠀⢀⠀⠷⢀⡘⠃⠀⣀⡀⠙⢦⡀⠀⠑⢿⡿⢟⣋⣤⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠒⠶⣶⣦⣤⣤⣤⣤⣤⣀⣈⣙⠻⢿⣿⡿⠀⠀⣰⠋⠀⠀⠀⡿⣁⡙⡻⢏⠐⣺⢏⠙⠠⣶⠙⣆⠀⠀⢿⣿⡿⠟⢋⣁⣀⣤⣤⣤⣤⣤⣴⣶⠶⠒⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣷⣾⠁⠀⢰⠃⠀⠀⢰⣾⣤⢼⣿⢁⠬⣷⠁⠤⣷⡖⡶⠷⠘⡆⠀⠈⣷⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣭⣭⣭⣭⠀⠀⡜⠀⠀⠀⡟⢸⣟⡟⠉⣯⣼⠉⢳⡐⠃⢷⣆⠀⠀⢣⠀⠀⣭⣭⣭⣭⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⢛⣛⣻⠀⠀⢧⠀⠈⠛⣏⢩⣟⢀⢽⡝⠻⠟⡽⠻⡉⠙⢻⠁⠀⡼⠀⠀⣟⣛⡛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⡿⡀⠀⢸⡄⠐⠀⠈⢿⠒⢺⣿⢲⡂⣿⡷⡖⣿⠆⠀⠀⢠⡇⠀⢀⢿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠤⠴⠶⠿⠿⠿⠿⠛⠛⠛⠋⣉⣭⣶⣿⣷⠀⠀⠳⡄⠀⢐⣿⣧⣞⣗⣷⣾⣶⣹⣽⢹⡟⠀⢡⠞⠀⠀⣾⣿⣶⣬⣉⠙⠛⠛⠛⠿⠿⠿⠿⠶⠦⠤⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠿⠛⣋⣭⣶⣷⡀⠀⠙⢦⣉⠋⠹⢷⡀⠉⠁⠀⠚⠋⢴⣟⡴⠋⠀⢀⣾⣶⣭⣙⠛⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠉⠁⢀⣴⣾⣿⣿⠟⣩⣾⣦⠀⠀⠈⠓⠦⢼⣇⣀⣀⣠⡤⠴⠚⠉⠀⠀⣴⣷⣍⠻⣿⣿⣷⣦⡀⠈⠉⠛⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠄⠒⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⣠⣾⡿⢟⣵⣿⡷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⣿⣮⡻⢿⣷⣄⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠈⠉⠒⠠⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⢀⣼⡿⠋⢠⣾⣿⡿⢱⣿⡟⣼⣿⡇⣿⣿⢸⣿⣧⢻⣿⡎⢿⣿⣷⡄⠙⢿⣧⡀⠀⠉⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠀⠀⠀⢀⣴⠿⠋⠀⣰⣿⣿⠟⢀⣿⡟⢠⣿⣿⠇⣿⣿⠸⣿⣿⡄⢻⣿⡀⠻⣿⣿⣆⠀⠙⠿⣦⡀⠀⠀⠀⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⣿⡿⠋⠀⣼⡿⠀⣸⣿⣿⠀⣿⣿⠀⣿⣿⣇⠀⢿⣧⠀⠙⢿⣿⣆⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣰⣿⠟⠀⠀⣸⡿⠁⠀⣿⣿⡇⠀⢻⡟⠀⢸⣿⣿⠀⠈⢿⣇⠀⠀⠻⣿⣆⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢠⡿⠁⠀⠀⣿⡿⠀⠀⢸⡇⠀⠀⢿⣿⠀⠀⠈⢿⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡾⠁⠀⠀⢰⣿⠃⠀⠀⢸⡇⠀⠀⠘⣿⡃⠀⠀⠈⢷⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀","⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⣆⠀⠀⠀⢸⡇⠀⠀⠀⣰⡇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢧⠀⠀⠀⢸⣿⡄⠀⠀⢸⡇⠀⠀⢠⣿⡇⠀⠀⠀⡼⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠘⣧⠀⠀⠈⣿⣷⠀⠀⢸⡇⠀⠀⣾⣿⠁⠀⠀⣼⠃⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢻⣷⣄⠀⠀⢹⣧⠀⠀⣿⣿⡆⠀⣼⣧⠀⢰⣿⣿⠀⠀⣼⡏⠀⠀⣠⣾⡟⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⢻⣿⣷⡀⠀⢿⣧⠀⢻⣿⣿⠀⣿⣿⠀⣿⣿⡟⠀⣼⡿⠀⢀⣾⣿⡟⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⡀⠀⠀⠀⠈⢻⣦⡀⠀⠻⣿⣿⣆⠘⣿⣧⠸⣿⣿⡆⣿⣿⢰⣿⣿⠇⣼⣿⠃⣰⣿⣿⠟⠀⢀⣴⡟⠁⠀⠀⠀⢀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠙⢿⣶⣄⠙⣿⣿⣧⢹⣿⣧⢻⣿⡇⣿⣿⢸⣿⡟⣼⣿⡏⣼⣿⣿⠋⣠⣶⡿⠋⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠠⢄⣀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣀⠙⢿⣷⣌⢻⣿⡧⠛⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠛⢼⣿⡟⣡⣾⡿⠋⣀⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⣀⡠⠄⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⡀⠀⠙⠻⣿⣿⣷⣮⡻⣿⡗⠉⠀⢀⣠⠴⠖⠒⠛⠛⠒⠲⠦⣄⡀⠀⠉⢾⣿⢟⣵⣾⣿⣿⠟⠋⠀⢀⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣙⡻⢿⡿⠊⠀⢀⡴⠋⢠⣆⠀⣀⢀⠀⠀⣀⡀⠀⠙⢦⡀⠀⠑⢿⡿⢟⣋⣤⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠒⠶⣶⣦⣤⣤⣤⣤⣤⣀⣈⣙⠻⢿⣿⡿⠀⠀⣰⠋⠀⠀⠀⡿⣗⠛⡿⢟⠓⣻⢿⠀⣠⡀⠙⣆⠀⠀⢿⣿⡿⠟⣋⣁⣀⣤⣤⣤⣤⣤⣴⣶⠶⠒⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣷⣾⠁⠀⢰⠃⠀⠀⢰⣾⠤⢽⣾⠤⠬⣶⡧⠤⣷⡎⠀⠀⠘⡆⠀⠈⣷⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣭⣭⣭⣭⠀⠀⡜⠦⠀⡀⠞⠘⣆⡞⡅⣤⣼⡙⣳⣰⠃⣵⠔⠀⠀⢣⠀⠀⣭⣭⣭⣭⣥⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⢛⣛⣿⠀⠀⢧⠒⠈⡴⣏⢉⠟⢿⡏⠙⢻⣛⡿⠻⡉⣹⠓⠀⣤⡼⠀⠀⣿⣛⡛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⡿⡀⠀⢸⡄⠀⠙⠻⣿⠒⢺⣿⡒⠒⠻⡗⠖⣿⠇⠀⠀⢠⡇⠀⢀⢿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠤⠴⠶⠿⠿⠿⠿⠛⠛⠛⠋⣉⣭⣶⣿⣷⠀⠀⠳⡄⠀⠹⠎⣧⣿⣎⣷⣶⠀⢻⣶⠁⢠⡄⢠⠞⠀⠀⣾⣿⣶⣬⣉⠙⠛⠛⠛⠿⠿⠿⠿⠶⠦⠤⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⣋⣭⣶⣷⡀⠀⠙⢦⣀⠀⠉⠁⠀⢈⣥⠀⠈⠉⠀⣀⡴⠋⠀⢀⣾⣶⣭⣙⠛⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠉⠁⢀⣴⣾⣿⣿⠟⣩⣾⣦⠀⠀⠉⠓⠦⢤⣄⣀⣙⣣⡤⠴⠚⠉⠀⠀⣴⣷⣍⠻⣿⣿⣷⣦⡀⠈⠉⠛⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠄⠒⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⣠⣾⡿⢟⣵⣿⡷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⣿⣮⡻⢿⣷⣄⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠈⠉⠒⠠⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⢀⣼⡿⠋⢠⣾⣿⡿⢱⣿⡟⣼⣿⡇⣿⣿⢸⣿⣧⢻⣿⡎⢿⣿⣷⡄⠙⢿⣧⡀⠀⠉⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠀⠀⠀⢀⣴⠿⠋⠀⣰⣿⣿⠟⢀⣿⡟⢠⣿⣿⠇⣿⣿⠸⣿⣿⡄⢻⣿⡀⠻⣿⣿⣆⠀⠙⠿⣦⡀⠀⠀⠀⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⣿⡿⠋⠀⣼⡿⠁⣸⣿⣿⠀⣿⣿⠀⣿⣿⣇⠈⢿⣧⠀⠙⢿⣿⣆⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣰⣿⠟⠀⠀⣸⡿⠁⠀⣿⣿⡇⠀⢻⡟⠀⢸⣿⣿⠀⠈⢿⣇⠀⠀⠻⣿⣆⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢠⡿⠁⠀⢀⣿⡿⠀⠀⢸⡇⠀⠀⢿⣿⠀⠀⠈⢿⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡾⠁⠀⠀⢰⣿⠃⠀⠀⢸⡇⠀⠀⠘⣿⡃⠀⠀⠈⢷⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀","⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⣆⠀⠀⠀⢸⡇⠀⠀⠀⣰⡇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢧⠀⠀⠀⢸⣿⡄⠀⠀⢸⡇⠀⠀⢠⣿⡇⠀⠀⠀⡼⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠘⣧⠀⠀⠈⣿⣷⠀⠀⢸⡇⠀⠀⣾⣿⠁⠀⠀⣼⠃⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢻⣷⣄⠀⠀⢹⣧⠀⠀⣿⣿⡆⠀⣼⣧⠀⢰⣿⣿⠀⠀⣼⡏⠀⠀⣠⣾⡟⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⢻⣿⣷⡀⠀⢿⣧⠀⢻⣿⣿⠀⣿⣿⠀⣿⣿⡟⠀⣼⡿⠀⢀⣾⣿⡟⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⡀⠀⠀⠀⠈⢻⣦⡀⠀⠻⣿⣿⣆⠘⣿⣧⠸⣿⣿⡆⣿⣿⢰⣿⣿⠇⣼⣿⠃⣰⣿⣿⠟⠀⢀⣴⡟⠁⠀⠀⠀⢀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠙⢿⣶⣄⠙⣿⣿⣧⢹⣿⣧⢻⣿⡇⣿⣿⢸⣿⡟⣼⣿⡏⣼⣿⣿⠋⣠⣶⡿⠋⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠠⢄⣀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣀⠙⢿⣷⣌⢻⣿⡧⠛⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠛⢼⣿⡟⣡⣾⡿⠋⣀⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⣀⡠⠄⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⡀⠀⠙⠻⣿⣿⣷⣮⡻⣿⡗⠉⠀⢀⣠⠴⠖⢒⡛⠛⠒⠲⠦⣄⡀⠀⠉⢾⣿⢟⣵⣾⣿⣿⠟⠋⠀⢀⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣙⡻⢿⡿⠊⠀⢀⡴⠋⡄⢀⠀⠈⢁⡀⠀⠀⡀⠀⠙⢦⡀⠀⠑⢿⡿⢟⣋⣤⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠒⠶⣶⣦⣤⣤⣤⣤⣤⣀⣈⣙⠻⢿⣿⡿⠀⠀⣰⠋⠀⠀⠀⡿⣗⠒⡻⢟⣶⣺⢿⠀⠀⠀⠙⣆⠀⠀⢿⣿⡿⠟⣋⣁⣀⣤⣤⣤⣤⣤⣴⣶⠶⠒⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣷⣾⠁⠀⢰⢃⡀⠀⢰⣾⠤⢼⣾⠁⠬⣿⡧⠤⣷⡆⠀⠀⠘⡆⠀⠈⣷⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣭⣭⣭⣭⠀⠀⡜⠀⠀⠀⡞⠘⣆⡎⠉⣧⣼⠉⢳⣰⠋⢳⣄⠀⠀⢣⠀⠀⣭⣭⣭⣭⣥⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⢛⣛⣿⠀⠀⢧⠀⢸⡖⣏⣉⠟⢯⢉⡍⢉⡉⣽⠻⡉⣹⠛⠁⠀⡼⠀⠀⣿⣛⡛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⡿⡀⠀⢸⡄⠀⠀⠹⣿⠒⢺⣿⡒⠒⣿⡟⠒⣿⠇⠀⠀⢠⡇⠀⢀⢿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠤⠴⠶⠿⠿⠿⠿⠛⠛⠛⠋⣉⣭⣶⣿⣷⠀⠀⠳⡄⠰⠆⠈⣧⣎⣉⣷⣾⣀⣱⣼⣙⠁⠀⢠⠞⠀⠀⣾⣿⣶⣬⣉⠙⠛⠛⠛⠿⠿⠿⠿⠶⠦⠤⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⣋⣭⣶⣷⡀⠀⠙⢦⣀⠀⠉⢁⡀⠈⠁⠀⠈⠉⠠⣇⡴⠋⠀⢀⣾⣶⣭⣙⠛⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠉⠁⢀⣴⣾⣿⣿⠟⣩⣾⣦⠀⠀⠉⠓⠦⢬⣍⣁⣀⣠⡤⠴⠚⠉⠀⠀⣴⣷⣍⠻⣿⣿⣷⣦⡀⠈⠉⠛⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠄⠒⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⣠⣾⡿⢟⣵⣿⡷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⣿⣮⡻⢿⣷⣄⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠈⠉⠒⠠⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⢀⣼⡿⠋⢠⣾⣿⡿⢱⣿⡟⣼⣿⡇⣿⣿⢸⣿⣧⢻⣿⡎⢿⣿⣷⡄⠙⢿⣧⡀⠀⠉⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠀⠀⠀⢀⣴⠿⠋⠀⣰⣿⣿⠟⢀⣿⡟⢠⣿⣿⠇⣿⣿⠸⣿⣿⡄⢻⣿⡀⠻⣿⣿⣆⠀⠙⠿⣦⡀⠀⠀⠀⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⣿⡿⠋⠀⣼⡿⠁⣸⣿⣿⠀⣿⣿⠀⣿⣿⣇⠈⢿⣧⠀⠙⢿⣿⣆⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣰⣿⠟⠀⠀⣸⡿⠁⠀⣿⣿⡇⠀⢻⡟⠀⢸⣿⣿⠀⠈⢿⣇⠀⠀⠻⣿⣆⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢠⡿⠁⠀⢀⣿⡿⠀⠀⢸⡇⠀⠀⢿⣿⡀⠀⠈⢿⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡾⠁⠀⠀⢰⣿⠃⠀⠀⢸⡇⠀⠀⠘⣿⡃⠀⠀⠈⢷⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀","⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⣆⠀⠀⠀⢸⡇⠀⠀⠀⣰⡇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢧⠀⠀⠀⢸⣿⡄⠀⠀⢸⡇⠀⠀⢠⣿⡇⠀⠀⠀⡼⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠘⣧⠀⠀⠈⣿⣷⠀⠀⢸⡇⠀⠀⣾⣿⠁⠀⠀⣼⠃⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⢻⣷⣄⠀⠀⢹⣧⠀⠀⣿⣿⡆⠀⣼⣧⠀⢰⣿⣿⠀⠀⣼⡏⠀⠀⣠⣾⡟⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⢻⣿⣷⡀⠀⢿⣧⠀⢻⣿⣿⠀⣿⣿⠀⣿⣿⡟⠀⣼⡿⠀⢀⣾⣿⡟⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⡀⠀⠀⠀⠈⢻⣦⡀⠀⠻⣿⣿⣆⠘⣿⣧⠸⣿⣿⡆⣿⣿⢰⣿⣿⠇⣼⣿⠃⣰⣿⣿⠟⠀⢀⣴⡟⠁⠀⠀⠀⢀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠙⢿⣶⣄⠙⣿⣿⣧⢹⣿⣧⢻⣿⡇⣿⣿⢸⣿⡟⣼⣿⡏⣼⣿⣿⠋⣠⣶⡿⠋⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠠⢄⣀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣀⠙⢿⣷⣌⢻⣿⡧⠟⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠻⢼⣿⡟⣡⣾⡿⠋⣀⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⣀⡠⠄⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⡀⠀⠙⠻⣿⣿⣷⣮⡻⣿⡗⠉⠀⢀⣠⠴⣶⡖⠛⠛⠒⠲⠦⣄⡀⠀⠉⢾⣿⢟⣵⣾⣿⣿⠟⠋⠀⢀⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣙⡻⢿⡿⠊⠀⢀⡴⠋⠀⢀⠈⠁⢀⡀⠀⠀⡀⠀⠙⢦⡀⠀⠑⢿⡿⢟⣋⣤⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠐⠒⠶⣶⣦⣤⣤⣤⣤⣤⣀⣈⣙⠻⢿⣿⡿⠀⠀⣰⠋⠀⠀⠀⡿⣗⠛⡻⢟⠒⣺⢿⠀⠀⠀⠙⣆⠀⠀⢿⣿⡿⠟⣋⣁⣀⣤⣤⣤⣤⣤⣴⣶⠶⠒⠂⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣷⣾⠁⠀⢰⠃⠀⠀⢰⣾⠤⢼⣾⢥⣈⣷⡧⠤⣷⡆⠀⠀⠘⡆⠀⠈⣷⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣭⣭⣭⣭⠀⠀⡜⠀⠀⣠⡞⠘⠆⡞⠉⢮⣉⠉⢳⣰⠃⢳⣄⠀⠀⢣⠀⠀⣭⣭⣭⣭⣥⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⢛⣛⣿⠀⠀⢧⠀⠈⠛⣏⢁⠔⢯⢉⣝⢫⡉⡽⠳⡀⣸⠛⠁⠀⡼⠀⠀⣿⣛⡛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⡿⡄⠀⢸⡄⠀⢴⡾⣿⡒⢺⣿⡚⠒⣿⡗⠒⣿⠇⠀⠀⢠⡇⠀⢠⢿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠤⠴⠶⠿⠿⠿⠿⠛⠛⠛⠋⣉⣭⣶⣿⣷⠀⠀⠳⡄⠀⠀⠈⣧⣎⣀⣷⣎⣑⣱⣼⡁⠀⠀⢠⠞⠀⠀⣾⣿⣶⣬⣉⠙⠛⠛⠛⠿⠿⠿⠿⠶⠦⠤⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⣋⣭⣶⣷⡀⠀⠙⢦⣀⠀⠉⠁⠀⠈⠁⠀⠈⠉⠀⣀⡴⠋⠀⢀⣾⣶⣭⣙⠛⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠉⠁⢀⣴⣾⣿⣿⠟⣩⣾⣦⠀⠀⠉⠓⠦⢼⣅⣀⣀⣠⡤⠴⠚⠉⠀⠀⣴⣷⣍⠻⣿⣿⣷⣦⡀⠈⠉⠛⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠄⠒⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⣠⣾⡿⢟⣵⣿⡷⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⣿⣮⡻⢿⣷⣄⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠈⠉⠒⠠⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⢀⣼⡿⠋⢠⣾⣿⡿⢱⣿⡟⣼⣿⡇⣿⣿⢸⣿⣧⢻⣿⡎⢿⣿⣷⡄⠙⢿⣧⡀⠀⠉⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠀⠀⠀⢀⣴⠿⠋⠀⣰⣿⣿⠟⢀⣿⡟⢠⣿⣿⠇⣿⣿⠸⣿⣿⡄⢻⣿⡀⠻⣿⣿⣆⠀⠙⠿⣦⡀⠀⠀⠀⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⣿⡿⠋⠀⣼⡿⠁⣸⣿⣿⠀⣿⣿⠀⣿⣿⣇⠈⢿⣧⠀⠙⢿⣿⣆⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣰⣿⠟⠀⠀⣸⡿⠁⠀⣿⣿⡇⠀⢻⡟⠀⢸⣿⣿⠀⠈⢿⣇⠀⠀⠻⣿⣆⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢠⡿⠁⠀⢀⣿⡿⠀⠀⢸⡇⠀⠀⢿⣿⡀⠀⠈⢿⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡾⠁⠀⠀⢰⣿⠃⠀⠀⢸⡇⠀⠀⠘⣿⡃⠀⠀⠈⢷⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀","⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⡇⠀⠀⠀⢰⡇⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢧⠀⠀⠀⢘⣿⡄⠀⠀⢸⡇⠀⠀⢠⣿⡃⠀⠀⠀⡼⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠘⣧⠀⠀⠈⣿⣷⠀⠀⢸⡇⠀⠀⣾⣿⠁⠀⠀⣼⠃⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢻⣷⣄⠀⠀⢹⣧⠀⠀⣿⣿⡆⠀⣸⣇⠀⢰⣿⣿⠀⠀⣼⡏⠀⠀⣠⣾⡟⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⢻⣿⣷⡀⠀⢿⣧⠀⢻⣿⣿⠀⣿⣿⠀⣿⣿⡟⠀⣼⡿⠀⢀⣾⣿⡟⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⡀⠀⠀⠀⠈⠻⣦⡀⠀⠹⣿⣿⣆⠘⣿⣧⠸⣿⣿⡆⣿⣿⢰⣿⣿⠇⣼⣿⠃⣰⣿⣿⠏⠀⢀⣴⠟⠁⠀⠀⠀⢀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀\n⠀⠀⠀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