⢠⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⢹⣿⢠⣶⢶⣄⠀⠐⣶⣤⣶⣠⡶⢶⡄⣶⡆⣶⠆⠀⠰⣶⣰⣶⣴⡆⣴⡶⣶⠀⣶⣶⣦⢰⣶⣶⡆⣰⡶⣶⡆⠀⠀⣿⣧⡶⠂⣶⣶⣦⢠⣶⣶⡄⢶⣦⣶⣠⣶ ⠸⠿⠾⠏⠘⠿⡾⠋⠀⠀⢸⣿⠃⠹⠷⠾⠇⠻⢷⠿⠃⠀⠀⢿⠿⠿⠿⠀⠿⠷⡿⠀⠿⠾⠿⢸⢿⢿⠇⠹⡷⣿⡇⠀⠀⣿⠿⣷⡀⠿⠿⠿⠘⢿⡾⠏⠸⢿⠟⢿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣄⢸⣿⢀⠀⠘⠛⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⣠⡄⢸⣿⠀⠀⠀⠀⠀⠀⣤⡄⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⢿⣟⣼⡟⣿⡦⣿⡟⣿⢿⣿⢰⣿⣿⡆⢻⡟⢸⣿⢿⡇⢸⣿⢸⣿⣿⡇⣾⡟⣿⠇⠀⠈⢿⡟⢸⣿⣿⡇⣾⡟⣿⡅⣿⡟⠈⠁⠰⢿⣟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠋⠈⠛⠛⠁⠛⠃⠛⠚⠛⠈⠛⠛⠁⠘⠃⠘⠛⠘⠓⠘⠛⠘⠛⠛⠃⢸⣟⣿⡃⠀⠀⠚⠃⠘⠛⠛⠃⠘⠛⠛⠂⠛⠃⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⠀⣀⡀⠀⢀⣀⠀⢀⣀⡈⣉⡉⣀⠀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣼⣿⡄⢠⣿⣿⠠⣿⡿⠇⣿⡿⠇⣿⡇⣿⡇⣿⠇⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⡇⣾⣧⣿⡆⣙⣿⡆⣙⣿⡆⣿⡇⢻⣿⡟⠀⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠃⠛⠓⠛⠉⠛⠋⠛⠋⠀⠛⠋⠀⠛⠃⠈⠛⠃⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠘⠁⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣠⣉⣜⣦⣾⣕⣶⣄⣶⢴⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠀⠀⣀⣾⣿⡟⢿⡟⢻⣿⣿⣻⠟⡿⢿⣗⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠤⣤⡁⢺⣿⣆⢰⡸⣸⡍⣿⢽⡃⡄⠘⢿⡆⠐⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠒⣤⢀⡀⠀⢀⢧⠈⠀⠑⠋⣈⣂⣙⡣⠠⠣⠐⠘⠚⠊⠁⠃⠀⣨⣴⣶⣶⣤⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡐⢫⡞⠀⢈⠆⠀⠀⣰⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢩⢾⡁⢠⠀⣀⣴⢿⣿⣿⣿⣿⣿⠿⣿⣿⢤⣦⣴⣴⣤⣶⣝⢯⢽⣻⢛⣡⣜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠧⣘⣾⣿⢣⣴⣭⣍⣭⣍⡠⢐⠋⠠⢿⣿⣿⣿⣿⣿⣿⠇⢠⡞⠿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣠⣿⣇⠚⢽⣿⣿⣿⡏⠘⡛⠃⠀⠈⢹⣿⣿⣿⣿⡹⠀⠀⠀⠀⢹⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢾⡿⢠⣭⣿⣿⢯⠀⢚⣩⡁⢆⡞⣧⢿⣿⣿⣯⣗⡩⢀⠀⠡⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⣿⣿⣿⠗⠀⠈⢠⠐⢌⡾⣽⢿⡿⣟⠿⢛⢷⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡋⣷⢇⡬⡀⣠⠀⠀⠈⠙⠈⢃⠓⠜⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣻⣿⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢪⣽⣿⡿⣾⣝⣢⢀⡀⠀⠀⢀⡼⣱⡼⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠢⢝⣿⣿⣟⡿⣿⢿⢣⢖⡈⠜⣓⣫⢗⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠶⣄⠸⡙⠿⣿⣾⣷⣧⣞⣹⣞⣏⠣⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣴⣼⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣖⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⣙⢫⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣞⡕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡿⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣻⣾⣵⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣧⣵⣾⣻⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣏⡿⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡕⣞⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢫⣙⡼⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣲⣖⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄⣼⣴⣿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠣⣏⣞⣹⣞⣧⣷⣾⣿⠿⡙⠸⣄⠶⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⢗⣫⣓⠜⡈⢖⢣⢿⣿⡿⣟⣿⣿⢝⠢⣇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡼⣱⡼⢀⠀⠀⡀⢀⣢⣝⣾⡿⣿⣽⢪⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⣿⣻⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⠓⢃⠈⠙⠈⠀⠀⣠⡀⡬⢇⣷⡋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢷⢛⠿⣟⡿⢿⣽⡾⢌⠐⢠⠈⠀⠗⣿⣿⣿⣼⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠡⠀⢀⡩⣗⣯⣿⣿⢿⣧⡞⢆⡁⣩⢚⠀⢯⣿⣿⣭⢠⡿⢾⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡿⢹⠀⠀⠀⠀⡹⣿⣿⣿⣿⢹⠈⠀⠃⡛⠘⡏⣿⣿⣿⢽⠚⣇⣿⣠⢧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⠿⡞⢠⠇⣿⣿⣿⣿⣿⣿⢿⠠⠋⢐⡠⣍⣭⣍⣭⣴⢣⣿⣾⣘⠧⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣜⣡⢛⣻⢽⢯⣝⣶⣤⣴⣴⣦⢤⣿⣿⠿⣿⣿⣿⣿⣿⢿⣴⣀⠀⢠⡁⢾⢩⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡇⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⣄⣶⣿⣿⣿⣿⣿⣰⠀⠀⠆⢈⠀⡞⢫⡐⢣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⣤⣶⣶⣴⣨⠀⠃⠁⠊⠚⠘⠐⠣⠠⡣⣙⣂⣈⠋⠑⠀⠈⢧⢀⠀⡀⢀⣤⠒⢇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠐⡆⢿⠘⡄⡃⢽⣿⡍⣸⡸⢰⣆⣿⢺⡁⣤⠤⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⣗⢿⡿⠟⣻⣿⣿⢻⡟⢿⡟⣿⣾⣀⠀⠀⠀⠀⠀⣀⠀⠐⠀⠀⠀⠀⠀⣆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣶⣄⣶⣕⣾⣦⣜⣉⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠘⣏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⠛⠀⠃⠛⠈⠃⠛⠀⠋⠛⠀⠋⠛⠋⠛⠉⠛⠓⠛⠃⠘⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣟⣿⠀⡟⣿⢻⡇⣿⡆⣿⣙⡆⣿⣙⡆⣿⣧⣾⡇⣿⡿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡟⣿⠇⣿⡇⣿⡇⣿⠇⡿⣿⠇⡿⣿⠠⣿⣿⢠⡄⣿⣼⣇⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⣀⠀⣀⡉⣉⡈⣀⢀⠀⣀⢀⠀⡀⣀⠀⠀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⠛⠘⠀⠀⠃⠛⠂⠛⠛⠘⠃⠛⠛⠘⠃⠚⠀⠀⡃⣿⣟⢸⠃⠛⠛⠘⠛⠘⠓⠘⠛⠘⠃⠘⠁⠛⠛⠈⠛⠚⠛⠃⠛⠁⠛⠛⠈⠋⠛⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣟⢿⠰⠁⠈⡟⣿⡅⣿⡟⣾⡇⣿⣿⢸⡟⢿⠈⠀⠇⣿⡟⣾⡇⣿⣿⢸⣿⢸⡇⢿⣿⢸⡟⢻⡆⣿⣿⢰⣿⢿⣿⡟⣿⡦⣿⡟⣼⣟⢿⠰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⡄⣤⠀⠀⠀⠀⠀⠀⣿⢸⡄⣠⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠛⠘⠀⢀⣿⢸⣄⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⢿⠟⢿⠸⠏⡾⢿⠘⠿⠿⠿⡀⣷⠿⣿⠀⠀⡇⣿⡷⠹⠇⢿⢿⢸⠿⠾⠿⠀⡿⠷⠿⠀⠿⠿⠿⢿⠀⠀⠃⠿⢷⠻⠇⠾⠷⠹⠃⣿⢸⠀⠀⠋⡾⠿⠘⠏⠾⠿⠸ ⣶⣠⣶⣦⢶⡄⣶⣶⢠⣦⣶⣶⠂⡶⣧⣿⠀⠀⡆⣶⡶⣰⡆⣶⣶⢰⣦⣶⣶⠀⣶⡶⣴⡆⣴⣶⣰⣶⠰⠀⠆⣶⡆⣶⡄⢶⡶⣠⣶⣤⣶⠐⠀⣄⢶⣶⢠⣿⢹⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣴⢠