⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠛⠋⠉⠉⠀⠀⠈⠉⠙⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⠄⠠⠤⠤⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⢀⣀⣤⠶⠖⠒⠒⠶⠦⣤⣀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠉⠁⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠉⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠋⠀⠀⣀⣴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⣀⣤⠶⠒⠋⠉⠉⠉⠉⠉⠙⠓⠲⢤⣀⠀⠈⠙⢦⡀⠀⠀⠀⠀ ⠀⢀⡾⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⠀⠉⠛⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠈⢳⡀⠀⠀⠀ ⠀⣾⠁⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡶⢤⣀⠀⠀⠈⠉⠙⠓⠒⠦⠤⠤⠄⠤⠤⠤⠞⠋⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣠⣾⣄⣸⣆⠀⠈⢷⠀⠀⠀ ⣸⠇⠀⢰⣧⠤⠤⣴⣶⣿⣾⣿⣿⣿⣿⣿⣿⣷⣷⣶⣦⣤⣀⣀⠀⠀⠈⣷⠀⠈⠙⠳⠶⢤⣄⣀⣀⣀⡀⡀⠀⠀⠀⠀⢀⣀⣤⡾⠁⠀⠀⠀⠀⠀⣀⣀⣤⣦⣶⣾⣿⣿⡋⠉⢁⣀⠿⠟⠛⢹⡆⠀⠘⡇⠀⠀ ⣿⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⡏⠉⠉⠛⢶⣄⣽⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠉⠉⣿⠁⠀⠀⣤⣠⣶⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⣿⠀⠀⡧⠀⠀ ⢂⠀⠠⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠶⠾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣀⣴⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣟⠀⠀ ⣹⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣭⣼⡿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣯⠀⠀ ⠸⡇⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣧⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠇⠀⢰⡇⠀⠀ ⠀⠹⣄⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠙⣧⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⢀⡟⠀⠀⠀ ⠀⠀⠘⢦⡀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣼⣦⣄⠀⠀⠀⠀⣠⣽⠇⠀⠀⠀⠎⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠀⠀⣠⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠳⢄⣀⠀⠀⠉⠛⠛⠒⠖⠛⢿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⠶⠾⠋⠘⠀⠝⠛⠳⣾⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠷⠦⣤⣤⣀⣤⣠⣤⣤⠤⠶⠚⠋⠁⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠶⠤⠤⣤⣀⣀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢀⣀⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢷⣆⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠙⣧⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢿⣆⠀⠀⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠈⢷⣄⠀⠀⠂⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⣿⠇⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠈⢹⣷⡄⠀⠀⠱⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠻⣦⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⣄⢸⣿⠀⠀⠀⠀⠀⢻⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⢶⢀⣿⠋⢻⣦⡀⠀⠈⠳⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠙⣷⡄⠀⠀⠁⠀⠀⠠⠐⠀⠀⢠⣾⠋⢸⡏⠀⠀⠀⠀⠀⠉⠻⣦⠓⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢂⣾⡟⢀⡇⣿⡿⣦⠀⠀⠘⢧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠈⢷⣄⠀⠈⠠⠀⠀⠀⠀⢠⣿⠃⠀⣰⡇⠀⡄⠀⠀⠀⠀⠀⠹⣷⡈⢠⣄⠀⠘⠁⠀⠀⢀⣴⡿⣋⣀⡟⣿⡿⢀⣨⠻⡦⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠌⢻⣆⠀⠀⠄⠐⠀⢠⣿⠃⠀⠀⣼⡇⠀⡶⠀⠀⠀⠀⠀⠀⠿⣿⣆⠋⣧⡀⠀⠶⠞⠋⠁⠀⠁⢰⣾⠿⣡⡏⠀⢸⡇⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢻⡆⠀⠠⠀⠀⣾⡇⠀⠀⠀⣯⣇⠀⠃⠀⠀⠀⠀⠀⠐⠃⠘⣿⣦⠀⠲⡀⠀⠀⠀⠀⠐⠞⠛⠁⠊⠁⠀⠀⢸⡇⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢸⣿⡄⠀⠀⢐⣿⠁⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠩⣿⣿⡛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣷⡁⠀⠈⢸⣿⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢿⣷⣄⠙⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⣿⢃⠀⠐⠸⣿⠀⠀⠀⠀⠀⢿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠐⣇⡐⡈⣿⣿⣆⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠤⠀⠂⠀⣿⡄⠀⠀⠀⠀⢸⣧⠀⢹⣷⢠⡀⢀⠀⠠⢈⢻⣷⣈⠆⣿⣿⣧⡀⠀⠻⢦⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠁⠠⠀⣹⡇⠀⠀⠀⠀⢸⣿⡄⠘⣿⡠⣍⢦⡉⠆⣅⠪⢽⣿⣼⣘⠿⣿⣷⡄⠀⠈⢷⣀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠁⠀⠡⠀⢸⡇⠀⠀⠀⠀⠀⣹⡇⠀⣿⣗⣮⢳⣜⣧⠆⡓⢼⣿⣷⣯⣟⣿⣿⣿⣮⠀⡀⠙⣧⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⡐⠀⡘⣿⠀⠀⠀⠀⠀⠙⣿⠀⢸⣿⣧⣟⣮⢿⣎⡵⢪⡝⣿⣿⣿⣿⣽⣿⣿⣷⣁⠀⠈⠳⣄⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠠⠁⢀⢻⣇⠀⠀⠀⠀⠀⢹⣧⠐⢿⣿⣻⣾⣿⣿⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣦⢀⠁⠀⠄⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⢄⠁⢂⠈⣿⡀⠀⠀⠀⠀⠀⢿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡲⠀⢀⢺⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢨⡄⡈⠄⢂⢹⣇⠀⠀⠀⠀⠀⠈⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠀⣼⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠾⠷⠿⠾⠶⠾⠿⠷⠤⠦⠤⠄⠀⠸⠷⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠇⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢀⠞

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