⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⡄⠀⠁⠂⢒⢈⠀⢀⠀⠂⠀⠀⡈⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠐⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡠⣲⠜⠃⠈⡀⠘⠂⣄⣬⡤⡄⡄⣈⣢⡎⠀⣂⠠⠄⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⢘⠤⠄⡰⠀⠀⠀⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⡖⣼⢑⣏⡯⡾⢳⡶⡞⣻⢨⠴⢴⠞⣓⠨⢕⠕⠈⠐⠳⠄⠀⠈⢄⠶⠀⠀⠈⢰⡂⢀⠀⠰⢮⣔⠂⠐⠙⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⣿⢿⡌⣤⢻⡇⣿⣇⣿⣼⠇⣻⡯⣟⣿⣯⡿⠷⠈⠀⡤⠴⣐⣅⣤⠴⡀⠐⠀⠀⠐⠿⠜⠎⠈⠀⠀⢀⡁⠀⣤⠂⠊⠀⠀⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡻⡾⣧⡻⡮⣇⢻⣜⡧⠿⠿⡿⡿⣿⣧⣟⣹⢮⢳⣑⣯⠴⡞⡏⠫⣥⣾⢯⣿⠛⠩⢄⠀⣀⢨⠀⠀⢤⣈⠃⠀⠀⢠⠶⢷⣿⣁⢂⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣎⣯⢿⣾⣏⢷⡙⠋⠁⠀⠀⠀⠀⠀⠈⠘⠽⠋⡅⣿⣷⣬⡿⢗⢆⡘⠟⢺⡻⢇⣶⣟⣿⣲⣶⣦⣆⣴⡀⠀⠀⠘⡒⠶⠋⠐⠃⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡜⢧⢻⣽⣟⢳⣽⠃⠀⠂⢔⠊⢾⣤⢤⢀⣀⠀⢀⠀⠚⢻⣽⣚⣭⣥⣴⣾⣿⣯⣿⣧⣝⣩⣼⣿⡿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡰⡽⣞⠷⠷⣝⡳⠊⣰⣄⣐⢠⣯⣽⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⠀⣀⣀⢠⠠⠀⠀⡐⡐⡠⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣤⡳⣻⣜⣷⡳⣯⢧⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠋⠛⠛⠛⠁⠙⠐⠉⠁⠀⠀⠀⠀⠀⣠⣔⠀⢤⠂⠉⡙⢗⠛⠂⠊⠀⠉⠽⠙⡆⠀⠀⠀
⠀⠀⠀⢀⣼⣯⣩⣳⡼⣮⣛⠛⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣒⣤⣐⡄⡒⢀⣠⢿⡥⠒⠂⠔⡠⠆⠀⠤⠌⠬⠏⠀⠀⠀
⠀⠀⠀⣸⣿⡵⢬⡱⡞⠶⣿⠀⣠⣀⡀⠈⠉⠙⢿⣿⣿⣿⣿⡛⢁⡀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⡿⣿⣿⣄⣄⣻⣌⢯⡩⠅⠌⠀⠈⠁⠁⠀⠀⠀⢀⢀⢀⡤⠀
⠀⠀⢀⣿⣿⢟⢤⣝⣿⣿⣛⠛⡉⠁⠒⠂⢀⠀⡀⡘⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠟⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢰
⠀⢀⣾⣿⣿⡯⠷⡌⠷⠶⣦⣶⣀⣀⣈⣽⣿⣩⣧⡭⣻⣿⡃⠉⠉⠹⠿⠿⠿⠿⠿⠿⠻⠟⠛⠉⠁⠀⠀⠉⠈⠁⠑⠀⠀⠀⠁⡂⠀⠐⠮⡃⠇⣣⡧⢀⠀⠀⠀⢾⢍⠅
⠀⠀⣿⣿⣿⡖⠸⢮⣛⣓⣻⣿⣿⣿⣿⣿⣿⣿⡻⢳⣺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣶⣶⡞⢓⡶⠀⠀⠀⠒⢂⢻⡆⠈⠀⠀⠀⠄⠁⡀
⠀⠐⣿⣿⣿⣗⢸⡃⣭⣽⢸⣿⣿⣿⣿⣿⣿⣿⣠⢼⣽⣿⡄⠀⠀⠀⠀⣀⠀⠀⠀⢀⣄⡴⣾⣿⣿⡿⣾⣵⣽⢼⣿⠾⠁⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⣿⣿⣿⠘⣵⠶⠶⢺⣿⣿⣿⣿⣿⣿⣿⠉⠀⠙⠋⠀⠀⠀⠀⠺⣿⣷⡄⠀⠈⠫⡹⡿⣿⣿⠿⠛⠋⠩⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢻⣿⣿⠀⠖⣛⣛⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣠⡤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢿⣿⠀⢣⢬⣭⡅⣿⣿⣿⣿⣿⡿⠻⠿⠋⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠿⡀⢨⡴⠶⠶⠉⠻⣿⣿⣿⣿⣶⡿⠾⠛⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡆⠰⠞⣿⣿⡀⠀⠉⠻⣿⣽⣿⣿⣾⣿⣷⣿⣖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢁⠀⣳⡸⠿⠷⡀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⠿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣛⣛⡃⠀⠀⠀⠈⠛⠛⠚⠋⠙⠚⠙⠃⠁⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⣭⣵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀