⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣲⣆⡆⡤⣰⣶⢺⠀⣮⣦⣤⡴⢆⠆⠀⢠⠐⠢⢦⣲⢀⡀⡶⡴⣄⢰⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣼⢱⡟⣿⣿⡏⢸⣿⡿⠿⣷⣽⠀⠀⡅⠀⠀⠠⡞⠀⢰⣧⠇⠙⣼⢮⢻⣧⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⡏⡇⣿⣏⣿⡿⣨⣩⣉⣀⣰⣿⡅⠀⠗⠶⠀⠀⢠⠃⠀⡼⣹⠐⠜⢹⣼⣴⢿⢖⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⢸⣷⣿⣿⣿⡿⣷⠿⡿⣿⢿⣻⣷⠯⣗⣒⣤⠄⣀⠏⠐⠲⡙⡇⡆⠐⠈⠇⡿⠀⢹⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣰⣿⡵⣻⠟⡋⡥⡼⣶⠼⡻⢿⣾⡾⠳⣷⣷⡖⢟⣌⣹⡛⣮⣖⡄⡟⠁⢀⡆⠈⠸⣧⠁⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠊⠛⠾⠉⠉⠚⢵⠞⢵⡯⢝⢺⠹⠒⡩⡾⣋⠋⠉⠒⠋⠸⠆⣄⡩⣷⣴⢦⣇⡀⡍⣣⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠘⣽⣼⣉⢢⡄⡀⠀⠀⠀⠀⠀⠀⠓⣕⡌⠀⠀⠥⡡⣰⡃⠀⢨⠀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠷⠆⠆⢠⣤⡄⠀⠀⠀⠀⠀⠻⣿⠉⠈⠁⠛⠛⠀⠀⠀⠀⠀⠀⠈⣿⠀⠤⣇⢻⣵⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠐⠄⠀⠀⠀⠈⠉⠉⠛⠋⠚⠪⠯⠮⢿⣟⣽⣂⢄⡂⠄⠀⠀⠀⢹⡇⡀⣷⣮⢑⣌⣤⡃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣶⡷⠟⠧⠼⡽⡖⡤⡀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠐⠐⠀⠟⢇⠼⠁⠀⢚⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣷⣿⡧⣻⡿⣿⡿⣛⣏⢿⣿⡀⢐⣌⣛⣒⣤⣄⣀⠤⢤⢤⣀⠀⠀⠀⠀⠘⣿⢴⣿⣻⣿⣧⢄⠂⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣩⠷⣿⣿⣿⡿⣶⣿⣜⣻⡖⡏⣿⣧⣓⣯⣼⢿⣏⣿⣯⠞⣫⡔⢷⣋⣛⠷⠢⣰⢞⡿⢁⣆⣯⣻⡺⣂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢻⣿⡼⣷⡽⣊⣆⢽⣶⣽⣞⣽⣿⣮⣾⣶⣿⣿⣿⣿⣿⣿⣿⣟⡫⣿⣚⣛⡛⣱⣿⣿⣿⣛⠛⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣧⣾⡯⢿⣿⡿⣿⡽⢗⣟⣯⣿⡞⡂⡿⣯⣿⣿⢿⡷⢽⣗⢮⣷⢿⣾⣯⣿⣯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⣌⢯⣽⠝⢟⣿⡷⣛⡛⣶⡟⠁⠉⠿⡯⣿⠏⡿⣯⣽⣿⣿⣿⣿⣟⣭⡼⢋⡿⠃⡢⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠉⠀⢐⠋⢷⠲⠿⠭⠥⢿⡟⠀⠀⠀⡇⢻⣯⡄⢟⢫⣽⣛⠻⢿⣿⢗⣿⢃⡿⠁⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⡔⢟⠏⣀⣸⣧⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⢬⡙⠯⢯⣇⣽⣿⣾⠿⢟⣅⡿⠁⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡾⠁⢲⠞⢐⣤⡿⠿⠾⢹⣷⣴⣤⣤⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⢀⣾⡿⣿⣆⡀⠀⠪⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠱⢀⡰⢷⣃⡻⠥⠚⠉⠁⠀⣠⠀⠈⣿⡝⠛⢿⣷⣤⣤⡴⠾⠛⠧⣤⣤⣤⡄⠀⣠⣴⣿⣿⠋⡏⠻⢾⣅⡀⠔⣄⣄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣤⠾⠟⠓⠉⢉⠀⠀⠀⠚⡄⠀⡔⡑⠀⠀⠘⣿⣄⠠⣉⠉⠫⠽⡲⠶⠴⠖⠚⠛⣫⡾⣩⡷⠋⣸⠀⣷⠀⠀⠈⠻⢶⣤⡂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⡴⠛⠉⡀⠀⢰⠀⢀⠂⠀⠀⠀⢠⠁⠸⢠⠇⠀⡸⠀⠹⣷⡀⠈⠳⣶⣦⣤⠒⠂⢀⡴⠊⣡⡴⠋⢀⣴⠃⠀⢻⡄⠀⠀⠀⠀⠉⠻⣾⣎⡂⠀⠀⠀⠀⠀⠀⠁
⠠⠋⡇⠀⠀⢧⠀⠀⣆⡜⠀⠀⠀⠀⡌⠀⣇⡞⠀⢠⠇⡇⠀⠙⠿⣦⣀⡀⠀⢀⣠⠴⠋⣡⠞⠋⠀⢄⠝⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⣦⡀⠀⠀⠀⠀
⠀⠀⠸⡇⠀⢸⡀⠀⣿⠀⠀⠀⠀⠰⠃⠀⣾⠃⢀⣾⠀⡇⠀⢠⠀⠀⠛⠿⣿⣿⣶⣶⣿⣧⣤⣤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀
⠀⠀⠀⢡⠀⠀⡇⡄⠸⠀⠀⠀⠀⠀⠀⢠⡏⠠⣫⠏⠀⠀⠀⠀⢇⠘⡄⠀⠀⠀⣯⠉⠉⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⢀⠀⠉⠻⣀⠀
⠀⠐⠀⠀⢣⠐⡁⠁⠀⠀⠀⠀⠀⠁⠀⡾⢀⣣⠇⠀⠀⠀⠀⠀⠈⠀⠘⡄⠀⠀⡜⠀⠀⠀⠀⠀⡠⡢⠊⠒⠤⣀⡠⠔⠊⠀⢠⠎⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠘⢢⡱⠀⠀⠀⠀⡠⠖⠂⢀⡇⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⣦⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠑⡇⠀⠠⠊⡠⠀⠀⢾⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠨⣣⠀⠀⢸⠀⠀⣠⠃⢄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢰⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⢾⠀⠸⡏⢀⠚⠀⠑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠐⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⣣⢰⢎⠀⠙⡠⠂⡄⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⡇⠐⠈⠀⠀⠁⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢐⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀