⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠟⠛⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠰⠝⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⢰⠀⠠⠀⡀⢆⣻⣦⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣏⣴⣿⣿⣶⣮⣰⣿⣭⣄⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠐⠒⣶⠓⢳⣾⡿⢛⣧⣀⣀⣄⠔⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡬⢿⣟⢭⣿⠟⢿⡉⡀⡟⢩⡇⣛⣛⣿⢟⣛⣩⣭⣴⣿⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢁⣈⣴⣏⣤⣙⠃⢠⣾⢿⡷⣡⣿⣿⡅⢿⣟⠫⣍⣉⡉⠋⢻⣿⣿⠦⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠘⣿⢋⣴⡿⣉⣼⣄⢻⣶⠇⣿⡛⣸⣧⠈⣿⣷⣄⣨⡿⠇⢠⡿⢶⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣧⣿⣏⣿⡿⣿⢿⣆⣭⡀⢣⣴⣿⣿⣆⠙⠿⠿⢛⣁⡀⠈⡟⢦⡙⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⢘⣐⠻⠸⠷⣼⡧⠸⢛⣋⣭⣥⣥⣤⠴⠶⠒⡛⠉⣁⡄⠀⠀⠈⣿⢶⣄⣻⡇⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠈⠉⠉⠛⠒⠤⣄⣈⠉⠅⣈⣁⠓⠲⠌⢋⣡⠤⠛⣀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠶⠛⠩⠴⠶⠀⡈⠉⠛⠦⢬⣁⠖⠒⠋⠴⠒⠤⠅⠀⠀⠀⠀⠀⠀⠠⡈⠻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣿⣤⠰⠖⠒⢒⣂⡠⣤⠶⢚⣀⡠⠌⢑⠒⠦⢢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢢⠙⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⡀⠚⢉⣉⣄⢠⣶⣄⣨⢙⣉⠛⠒⠶⠦⠤⠤⠀⠀⠀⠀⠀⠀⠀⠈⢄⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠹⣿⣌⣷⣿⣿⣿⢼⣿⣶⣼⣿⠟⣰⡖⠀⢄⢀⠀⠀⠀⣆⠐⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣿⣿⣿⡛⢸⣧⣻⠿⣷⣾⡿⠃⠀⢲⣅⣐⣀⡄⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣁⣀⣻⣿⡶⢀⣤⡴⠦⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣧⣸⡏⢻⣷⡀⣿⣿⢸⣿⣿⠇⠄⠀⠀⠈⠙⠋⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣧⣤⣶⣾⣿⡿⢿⣟⣛⣓⣒⣚⠻⣯⣥⣒⠃⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀
⠀⣭⣭⣭⣿⣿⠿⠿⠿⠛⠿⣷⣶⣖⣛⣛⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⣿⠷⠖⢲⡴⠶⠛⠳⡀⠀⠀⠀⠀⠀
⠀⣬⣭⣽⣛⣛⣿⣻⣿⡿⠭⢭⣭⣽⣭⣽⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢟⣛⣻⣿⣋⣩⣵⣶⣮⣽⡗⠀⠀⠀⠀⠀
⠀⣿⣶⣾⠟⣛⣛⣩⣭⣿⣿⣿⣿⠿⠏⠉⠙⠛⠒⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣯⣭⣭⣍⣛⣿⣿⣏⣉⣹⣿⠃⠀⠀⠀⠀
⠀⣉⣩⣿⣿⣿⣭⣽⡶⡤⠍⠋⣡⣶⣬⣽⠶⣿⣿⣿⡿⠷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣛⣛⡛⠩⠤⣶⣶⣾⣯⣛⣋⢉⣙⢿⡟⠀⠀⠀⠀
⠀⠉⠉⠛⠓⠂⠘⠛⠋⣀⣤⣶⣾⣿⣿⣗⣻⣭⣿⣿⣿⣿⣿⠿⢿⣿⣷⣶⣶⣶⣶⣶⣶⡶⠶⠾⠟⢛⣛⣛⣛⣻⣿⣶⠶⠶⠿⠿⠿⠿⣶⣶⡾⢿⣿⠇⠀⠀⠀⠀
⠀⠀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣟⠓⢾⣿⣶⣾⣿⣿⣿⣿⣾⣿⣿⣿⢿⣿⣿⣯⣭⣭⣿⡿⠿⠭⠭⠭⣶⣿⣿⣭⣭⡿⠿⠿⠿⢻⣗⣖⣛⣲⣿⣿⣉⣿⡆⠀⠀⠀⠀
⠀⠀⠘⠛⠛⢻⢿⣭⣿⠿⣯⣭⣽⡿⣿⣿⠿⣿⣿⣿⡷⠶⡒⠒⠒⠖⠚⠻⠟⠉⠉⠙⠛⠉⠙⠛⠓⠲⠽⣿⣷⡶⠶⠻⠿⠿⠓⠿⠟⠛⠛⠛⠛⠉⠙⠁⠀