⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠀⠀⣀⣴⠖⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠒⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⢀⣤⠞⣫⡤⠶⠚⠉⠀⠈⠛⠲⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠞⣻⣬⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⡟⣿⣍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣗⡿⢹⡀⠀⠀⢀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠳⠯⠷⠋⣀⣀⢠⡴⠶⠶⠚⠉⠉⠙⠳⠲⠶⠀⢤⣤⣀⣀⠸⣏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣠⡤⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠙⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⠆⢀⡴⠋⠉⠀⠀⢐⣦⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠘⠷⠂⢹⣆⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠖⠚⠉⠁⣠⠏⢀⡞⢠⠀⠀⠀⠐⠛⠁⠀⣤⠖⠛⠉⠉⠀⠉⠁⠈⠛⠂⠀⠀⠀⢀⠈⠉⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠴⠛⠁⠀⠀⠀⠀⠀⣰⠏⠀⣼⣡⡟⠀⠀⠀⠀⢀⣴⠞⠁⣀⣴⠾⢻⡟⠙⣿⠳⠶⢶⣤⡀⠀⠘⠶⢤⣀⣀⡀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠸⣏⣽⠇⠀⠀⣠⠾⠋⣀⣴⠟⠉⠀⢀⡿⠁⠀⠹⣧⣾⡄⠘⠉⠳⠶⣤⣀⡀⠈⠉⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠋⠀⠀⢠⡶⠟⠁⣀⣀⣀⣈⠿⠻⣦⠀⠀⠀⠀⠈⠙⢷⣦⣤⣀⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢀⣤⠞⠁⣠⣴⠞⠋⠁⢀⡀⠀⣰⡟⠀⠀⠈⢉⣉⣉⣤⡀⠀⢻⣿⣆⠀⠀⢠⠀⢸⡇⢿⡛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡁⠐⠚⣉⣥⣶⠟⠉⠀⠀⠀⠀⣾⠃⣰⡟⠁⢀⣿⣍⠉⠉⠁⠀⠴⠛⠛⠇⣿⠀⠀⢹⣧⣸⡇⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢭⣿⡟⠋⣿⠁⠀⣴⠀⠀⠀⠀⠀⣸⡟⠰⢞⣉⣁⡀⠀⢀⡠⠶⣦⡶⠾⡶⣿⡇⠀⠀⠙⣿⣷⣨⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣿⠀⣸⣏⡄⠀⠀⠀⠀⣿⣥⠶⠛⣉⠉⣻⡆⠀⠀⠀⣟⣠⣼⣧⣼⣷⣿⡄⠀⢹⡏⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⣿⠇⠀⠀⣿⠀⠿⠋⠀⠀⠀⠀⠀⣿⠃⣠⣴⣿⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⡿⠟⠿⣧⠀⠘⣷⠀⣹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣰⡏⢀⡶⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣈⠋⢻⣿⣿⣿⠃⠀⠀⠀⠀⢹⣷⢿⢣⡄⠘⠻⣇⠀⢻⡄⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣰⡟⠀⢾⢷⣄⢹⡇⠀⠀⠀⠀⠀⠀⠀⡟⠈⠉⠙⠋⣹⣿⡿⠷⣦⠰⠿⠿⠏⠀⠛⠒⠶⣄⣻⡄⢸⡇⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠉⠈⣿⣺⡇⠀⠀⠀⠀⠀⣇⠀⣠⡶⠛⠁⠀⠀⠀⠸⣛⡀⠀⠀⠀⠀⠀⠀⠙⠏⣇⠈⣿⠀⠀⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⠀⠀⠀⢸⡆⢸⣇⠀⠀⠀⠀⠀⠀⣿⠾⠃⠀⠀⠀⠀⠀⠀⠈⠉⣃⣀⣠⣤⣴⣶⣶⡆⠀⣿⣼⡟⠀⠀⢋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⢀⣾⣧⡄⢿⡆⠀⠀⠀⠀⣠⣿⣤⣤⣤⣤⣤⣴⣶⣶⣾⣿⡿⣿⣿⣿⡿⠿⠟⠃⣠⡿⢿⡇⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠒⢤⡀⠀⠀⠀⣠⠴⠛⠙⢲⡆⠀⠀⠉⢸⣇⠘⢷⡄⠀⠀⠀⣿⠉⠿⠿⠿⠿⠿⠿⠭⠿⠭⠶⠚⠛⢉⣥⣤⡴⠖⠛⠉⢀⣿⡇⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠀⠀⠀⠀⠙⣦⣾⠿⣦⡀⢰⡟⠛⠛⠒⠲⠶⠒⠒⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⢀⡾⠋⣧⣦⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣏⠀⣀⡀⠀⠀⠘⠃⠀⠈⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢿⣿⠀⠀⣿⣿⣥⣅⣀⣀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣤⠴⠞⠛⠁⠀⠛⠿⣿⣇⠀⠀⠀⠀⠀⠀⣴⡟⠉⠛⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠾⠛⢁⣀⡀⠀⢠⣿⣧⣰⡟⠋⠀⠀⠈⠉⠛⠒⠿⠤⣄⣀⡀ ⣀⠠⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣆⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⢩⣟⠓⠒⠒⠶⠶⠖⣻⣿⠉⠉⣿⣶⠾⠟⠛⠁⢠⣾⠋⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡈⠿⣦⡀⣼⣿⣄⣀⠀⠀⠀⠀⠀⠙⢷⣤⣄⠀⠀⢀⡛⠋⠁⠀⠀⠀⠀⠀⢠⣀⣼⠃⠀⠈⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣽⣿⠋⠀⠉⠙⠻⠶⣦⡀⠀⠀⠀⠀⠙⠷⠀⠈⢷⡄⠀⠀⠀⠀⢀⣶⡿⡟⠃⠀⢀⣼⠏⠀⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣄⡀⠀⠀⠈⠙⠛⠷⣦⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣼⠏⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⠤⠖⠒⠒⠂⠀⠀⠀⠀⠀⠀⠈⢙⠳⣦⣄⡀⠀⠀⠈⠛⠻⠶⣤⣴⣄⡀⠀⠀⢀⣼⠋⠀⠀⠀⢀⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀