⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠛⠛⠛⠛⠛⠓⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡤⢶⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣄⠀⠀⠀⠀⢰⠢⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠱⡀⠀⠀⡴⠋⠀⡎⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣌⠑⢄⠀⠀⢸⡄⠈⠢⡀⠀⠀⡜⠙⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢧⢀⠞⠀⠀⢰⠃⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠁⠀⠈⢣⡀⠀⢣⠀⠀⠙⡄⢰⠁⠀⢣⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⢘⡜⠀⠀⡠⠃⠀⣸⠃⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠸⢧⠀⠈⢦⡀⠀⠸⡾⠀⠀⢸⠀⠀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⡎⠘⢄⢰⠀⠀⣸⣀⡤⣚⠥⢲⢆⠇⠀⠀⠀⠉⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢶⠀⡇⡖⠠⢝⠦⣄⣿⠀⠀⢸⢀⠊⢸⠀⠀⠀⠀
⠀⠀⠀⠀⡇⠀⠈⢺⡀⡰⠉⡡⠚⠁⠀⠎⢸⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡞⠁⢨⠇⢁⠘⡄⠀⠉⠢⡉⢣⡀⣵⠃⠀⢸⠀⠀⠀⠀
⠀⣀⠀⠀⢰⡀⠀⠘⡉⣡⠊⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⣤⣎⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣂⣠⡎⠀⠈⡀⢸⠀⠙⢆⠀⠀⠈⢆⠙⡇⠀⠀⡸⠀⠀⣀⠀
⠀⢻⠑⠢⡀⢣⠀⠀⡷⠃⠀⣠⠔⠁⠀⠀⢰⠀⠀⠀⢸⣿⣿⣿⣷⣶⣄⣸⣄⠆⠀⡗⣀⣠⣶⣿⣿⣿⣿⣿⡇⠀⢸⣷⡜⠀⠀⠀⠑⢤⣀⠀⢳⠁⠀⠰⠃⡠⠊⢹⠀
⠀⠘⡄⠀⠘⢆⢦⣰⠋⡩⠋⢸⠀⠀⠀⠀⠀⡇⠀⡄⠈⢿⣿⣿⣿⣿⣿⣿⣿⠂⣀⠀⠙⢿⣿⣿⣿⣿⣿⠟⢀⠀⢸⣿⡇⠀⠀⠀⠀⠘⠈⢎⠉⢇⡰⢣⠎⠀⠀⡏⠀
⠀⠀⠱⡀⠀⠈⠆⠁⡔⠁⠀⢸⠀⠀⠀⠀⠀⡇⣠⡗⠀⠈⠻⢿⣿⡿⠿⠛⠁⢸⣿⣧⠀⠀⠙⠻⠿⠿⢋⠠⠋⠀⡜⢿⠃⠀⠀⠀⠀⢰⠀⠀⠱⡀⢠⠃⠀⠀⡘⠀⠀
⠀⢿⠒⢽⣄⠀⠸⢰⠁⠀⢀⠆⠀⠀⠀⠀⠀⢻⡏⠀⠀⠈⠓⠂⠀⢀⡄⠀⠀⣼⣿⣿⣧⠀⠐⠢⢄⠀⠉⠀⠀⢀⣿⢸⠀⠀⠀⠀⠀⠘⡄⠀⠀⢣⠈⠀⢀⡾⠔⢹⠀
⠀⠘⡆⠀⠈⠳⡼⡏⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠳⣄⣰⠀⠀⢀⡴⠋⠀⠀⠸⠟⠉⠙⠿⡀⠀⠀⠀⠱⣦⡀⠈⣩⡵⠃⠀⠀⠀⠀⠀⠀⠘⢄⠀⢘⡧⡴⠋⠀⢀⠏⠀
⠀⠀⠘⣄⠀⠀⠱⡧⢖⡗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣴⣿⣏⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡗⢮⡟⠀⠀⢀⠎⠀⠀
⢠⠤⠄⣈⡳⡄⠀⢡⢸⠁⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⠁⠿⡗⠲⠟⠛⠒⢶⠒⢺⠿⡟⢹⣻⠉⢥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠇⢸⠁⠀⡴⣁⡀⢤⡄
⠀⠳⡄⠀⠈⠙⠢⡼⢸⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣆⠀⢻⠤⣦⣼⣤⣼⣶⣾⣶⣿⡋⠙⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄⢸⡴⠚⠉⠀⢀⡔⠁
⠀⠀⠈⠢⣀⠀⠀⠈⢌⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⣹⣿⣿⣿⣿⣿⣿⣏⠉⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⡧⠊⠀⠀⢀⡠⠊⠀⠀
⠀⠀⠀⠀⠈⠑⠢⠤⣤⡿⡀⢀⠇⡶⢄⡀⠀⠀⠀⠀⠀⠀⠘⡀⠐⠸⠀⠘⣿⣿⣿⣿⣿⣿⣿⣬⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⡠⢶⠁⡇⠀⣼⣁⡤⠴⢚⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣍⠉⠉⠑⠻⢎⠀⢡⠀⠈⠢⡀⠀⠀⠀⠀⠀⢧⠀⠀⣧⠀⠙⠻⠛⡿⠉⠉⢳⠽⠀⠀⠃⠀⠀⠀⠀⠀⡠⠊⠀⠸⠀⣸⠾⠒⠉⠉⢉⠝⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠑⢌⣧⠀⠀⠘⡄⠀⠀⠀⠀⠈⡄⠀⠘⠻⠆⠴⠀⠧⠰⠀⠛⠁⠀⡸⠀⠀⠀⠀⢀⠞⠀⠀⣰⡣⠊⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⢀⣫⢢⡀⠀⢸⢠⡤⠤⢀⣀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡐⢁⣀⠤⠤⣤⡞⠀⠀⡰⢱⡁⠤⠄⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⡶⠒⠀⠀⠀⠀⠒⠒⠤⣙⠢⡈⠀⠳⡀⠀⠈⠑⠪⣕⠘⠢⣄⡀⠀⢀⡤⢞⡽⠊⠉⠀⢀⡔⠁⣅⡠⢊⠤⠐⠒⠂⠀⠀⠀⠐⢶⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠄⣀⣀⣀⣀⡀⠤⣓⣈⣀⣀⣈⡒⢄⡀⠀⠈⠱⡀⠀⠀⠀⠀⡰⠁⠀⠀⣀⠔⣋⣀⣀⣉⣘⠧⠄⣀⣀⣀⣀⡀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠉⠉⠀⠀⠀⠀⣀⡨⢃⣈⣑⡲⢤⣱⡀⠀⢀⣼⡤⠶⢒⣉⣘⠣⣀⠀⠀⠀⠀⠈⠉⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⠤⠤⠄⣒⠯⠓⠋⠁⠀⠀⣀⡠⡤⢌⡿⢍⠤⡤⣄⡀⠀⠀⠉⠙⠻⢗⡂⠤⠤⠄⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠤⠤⠤⠤⠐⠊⡡⠊⡴⠁⠀⠀⠱⡉⠮⡉⠒⠢⠤⠤⠤⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠊⠀⠀⠀⠀⠀⠑⠦⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀