⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⠤⠖⣛⣛⣤⣙⣖⣂⣀⣒⠒⠶⣦⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣤⡖⢚⣋⣉⣁⣀⣀⠀⠀⠘⠉⡠⢚⠝⠁⠀⢸⡇⠀⠀⠈⠢⡙⠳⣄⡈⠓⠄⠀⣀⣀⣉⣉⣉⡒⣒⢶⡄ ⠈⣿⠀⠀⠙⣳⠀⢀⡄⢹⠇⠠⠊⢠⠊⠀⠀⠀⠘⡇⡇⠀⠀⠀⠐⠄⠘⠗⢄⠘⢏⢄⡀⠀⠘⣣⠀⠐⡽⠁ ⠀⠸⣧⠀⠀⠮⡄⠰⢾⠛⢠⠃⢀⡇⠀⠀⢀⠀⠀⣇⠇⠀⠀⠀⠀⠸⡆⠀⠀⠣⠈⢇⡉⠀⢸⠃⠀⣼⠇⠀ ⠀⠀⠹⣆⠀⠀⠳⢾⠋⠀⡆⢀⣾⠿⡒⠛⠚⠦⠀⢸⠀⠀⠖⠋⠉⠓⢿⣄⣀⢱⠀⠈⡿⠶⠚⠀⣴⠋⠀⠀ ⠀⠀⠀⠙⢧⡀⠀⡇⠀⠀⡧⣼⡣⠤⡳⣄⡀⣇⠀⠀⡆⠀⢰⢦⣇⠀⢸⣇⠸⡘⠀⠀⠸⠀⢀⡼⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⣻⢷⡇⠀⠀⡇⣮⣶⠾⣿⣿⠿⣿⣦⠤⠼⣴⣷⡾⣿⡿⠾⣾⣄⣷⠀⠀⢀⢷⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⢁⠀⠀⠀⢿⣏⠊⣽⢋⡙⣷⠉⣍⣱⡤⢽⠀⡾⢉⡙⣧⠒⣹⡟⠀⠸⠈⣮⢿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡷⢸⠀⠰⡄⠘⡌⠂⢻⣌⣡⡿⠀⠁⠀⠀⠀⠢⢷⣌⣠⠟⠀⡝⠀⢠⠆⠀⡏⢿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⢸⠀⠀⠘⣶⡼⡄⠀⠀⠀⠀⣄⣀⣀⣀⣀⣠⠀⠀⠀⢀⣮⠴⣴⠋⠀⠀⡇⢸⡍⠉⠀⠀⠀ ⠀⠀⠀⣠⡞⢴⠀⡀⡄⠀⡈⡟⠚⠢⠀⠀⠀⣄⡠⠀⠀⢄⣨⠀⠀⠀⠉⠾⢾⠁⢀⠀⢠⡇⢡⣷⡀⠀⠀⠀ ⠀⠀⠀⠛⠛⣿⣄⡇⠸⣤⠱⣥⠀⠀⠀⠀⠀⠘⠲⠦⠴⠖⠁⠀⠀⠀⠀⢀⡌⢀⠎⠀⢸⡇⣿⠙⠓⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡆⣷⡀⠈⠫⡛⢷⡦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣞⣵⢋⠄⢀⣿⣷⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⡿⣷⢄⢠⠈⠳⣽⣮⣍⡓⢲⣀⣤⣤⣤⡗⠛⣋⠘⢻⠏⣡⠎⡠⣾⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠸⣅⠐⠙⢷⣿⣦⠟⢿⣿⣿⠿⠯⣴⣿⣴⣫⡟⠛⢊⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣿⣿⣶⢶⡟⠃⣀⠀⠿⠾⠀⢀⣀⠙⣿⣿⣡⣴⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣈⣙⣒⣨⣓⠢⢍⡁⠈⣉⡤⢞⣺⡿⠟⠛⣩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠛⢿⠋⡟⢻⠉⠉⠙⠛⠋⠒⠚⠛⣗⢲⠲⣾⠋⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠐⡟⡼⠷⠾⠀⠀⠀⠀⠀⠀⠀⠀⡷⠾⣇⢻⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⣷⣷⣶⡗⠀⠀⢐⡲⢖⡂⠀⠀⢶⣶⣾⣾⠁⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢸⣷⣿⣿⣷⣦⣽⡷⢶⣶⣾⣽⣴⣿⣿⣿⣾⡀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⢀⣨⣿⢿⣿⣿⣿⣿⣿⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⡇⣿⣿⣿⣿⣿⢿⣿⣨⢀⠀⡟⣿⣿⣿⣿⣿⢸⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⠀⡀⣾⣿⣿⣿⣴⣽⣾⣶⢶⡷⣽⣦⣷⣿⣿⣷⢸⠀⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠁⣾⣾⣶⢶⠀⠀⡂⢖⡲⢐⠀⠀⡗⣶⣷⣷⢸⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⢻⣇⠾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⡼⡟⠐⡴⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠋⣾⠲⢲⣗⠛⠚⠒⠋⠛⠙⠉⠉⢻⡟⠋⢿⠛⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣩⠛⠟⡿⣺⢞⡤⣉⠈⡁⢍⠢⣓⣨⣒⣙⣈⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣯⣴⣡⣿⣿⠙⣀⢀⠀⠾⠿⠀⣀⠃⡟⢶⣶⣿⣿⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠏⣴⢊⠛⡟⣫⣴⣿⣴⠯⠿⣿⣿⢿⠟⣦⣿⢷⠙⠐⣅⠸⣆⠹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⠟⣾⡠⠎⣡⠏⢻⠘⣋⠛⡗⣤⣤⣤⣀⢲⡓⣍⣮⣽⠳⠈⢠⢄⣷⡿⢷⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠏⣷⣿⢀⠄⢋⣵⣞⣴⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡦⢷⡛⠫⠈⡀⣷⡆⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠓⠙⣿⡇⢸⠀⠎⢀⡌⢀⠀⠀⠀⠀⠁⠖⠴⠦⠲⠘⠀⠀⠀⠀⠀⣥⠱⣤⠸⡇⣄⣿⠛⠛⠀⠀⠀ ⠀⠀⠀⡀⣷⢡⡇⢠⠀⢀⠁⢾⠾⠉⠀⠀⠀⣨⢄⠀⠀⡠⣄⠀⠀⠀⠢⠚⡟⡈⠀⡄⡀⠀⢴⡞⣠⠀⠀⠀ ⠀⠀⠀⠉⡍⢸⡇⠀⠀⠋⣴⠴⣮⢀⠀⠀⠀⣠⣀⣀⣀⣀⣄⠀⠀⠀⠀⡄⡼⣶⠘⠀⠀⢸⡇⢸⠀⠀⠀⠀ ⠀⠀⠀⣄⣿⢿⡏⠀⠆⢠⠀⡝⠀⠟⣠⣌⢷⠢⠀⠀⠀⠁⠀⡿⣡⣌⢻⠂⡌⠘⡄⠰⠀⢸⡷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢿⣮⠈⠸⠀⡟⣹⠒⣧⡙⢉⡾⠀⢽⡤⣱⣍⠉⣷⡙⢋⣽⠊⣏⢿⠀⠀⠀⢁⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⣿⢷⢀⠀⠀⣷⣄⣾⠾⡿⣿⡾⣷⣴⠼⠤⣦⣿⠿⣿⣿⠾⣶⣮⡇⠀⠀⡇⢷⣻⠈⠀⠀⠀⠀ ⠀⠀⠀⠃⡼⢀⠀⠸⠀⠀⡘⠸⣇⢸⠀⣇⢦⢰⠀⡆⠀⠀⣇⡀⣄⡳⠤⡣⣼⡧⠀⠀⡇⠀⡀⢧⠙⠀⠀⠀ ⠀⠀⠋⣴⠀⠚⠶⡿⠈⠀⢱⣀⣄⢿⠓⠉⠋⠖⠀⠀⢸⠀⠦⠚⠛⡒⠿⣾⢀⡆⠀⠋⢾⠳⠀⠀⣆⠹⠀⠀ ⠀⠇⣼⠀⠃⢸⠀⡉⢇⠈⠣⠀⠀⡆⠸⠀⠀⠀⠀⠇⣇⠀⠀⢀⠀⠀⡇⢀⠃⢠⠛⢾⠰⡄⠮⠀⠀⣧⠸⠀ ⠁⡽⠐⠀⣣⠘⠀⡀⢄⢏⠘⢄⠗⠘⠄⠐⠀⠀⠀⡇⡇⠘⠀⠀⠀⠊⢠⠊⠠⠇⢹⡄⢀⠀⣳⠙⠀⠀⣿⠈ ⡄⢶⣒⡒⣉⣉⣉⣀⣀⠀⠄⠓⡈⣄⠳⡙⠢⠈⠀⠀⡇⢸⠀⠁⠝⢚⡠⠉⠘⠀⠀⣀⣀⣁⣉⣋⢚⡖⣤⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣦⠶⠒⣒⣀⣂⣖⣙⣤⣛⣛⠖⠤⣠⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢻⠀⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀