⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢞⣟⣯⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡛⠥⠒⠋⠉⠀⠈⢻⡫⣧⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢠⢄⠀⠀⠀⠇⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⠋⠀⢠⢾⠿⠿⢿⢳⡀⢳⡽⣇⠀⠀⠀⠀⠀⢀⠈⠢⡄⠀⠼⠏⢧⡀⡼⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠇⠀⣏⡧⡴⢳⡄⣾⡇⠀⢣⡺⡆⠀⠀⠀⠀⠀⠈⠲⢌⠃⡟⠀⠪⠳⠥⡥⣤⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⡀⠈⠙⠓⣋⡰⢙⡇⠀⠀⡧⢻⡄⠀⠀⢠⡶⣦⠶⠒⠘⣡⣦⣴⠢⡌⠁⡡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣜⣶⣯⠵⠖⠒⠋⠀⣠⠔⣩⡞⠃⠀⠀⠀⠉⠓⠦⣄⠐⢧⡘⠬⠟⣹⠆⡇⢀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢛⣸⠼⠃⠀⠀⠀⠀⠤⠤⠤⢘⡘⡇⠀⠻⣤⠿⠃⠀⠘⢇⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠁⡰⢀⣀⡤⠚⡖⠦⣤⣠⢊⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠟⠉⠀⢡⠘⡀⠀⠉⠉⠛⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠳⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠄⠊⡱⢄⠀⠀⠀⢠⠀⢠⠁⠀⠀⠀⠀⠀⢀⡀⢤⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠣⠀⠀⠀⠀⠊⠱⣄⠀⡼⠀⡈⠀⢀⣀⣴⠲⢉⠉⠀⠐⠀⡈⡇⠀⠀⠀⠀⢀⡠⢶⣚⠭⠚⠋⣁⡠⡶⢤⣄⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⣶⣄⠀⠀⣟⢷⡇⣠⣦⠚⠍⠂⠀⣤⣴⣶⢿⡄⠀⣈⠅⠀⠀⠀⠀⢹⡅⡏⠀⠀⡴⡫⠑⣩⣬⣑⡚⠼⡛⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣿⣿⣽⣷⣄⡟⠙⠁⠛⠁⠀⣠⣴⣿⢿⠻⣧⡿⠀⠨⡝⠀⠀⠀⠀⠀⢸⠆⡇⠀⢼⢏⠀⢞⡕⢒⠺⡏⡧⠘⢸
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⢻⡯⠖⣏⠻⠷⣄⣀⣠⣴⠿⣟⠩⢦⠪⣞⡿⠁⠀⢰⠁⠀⠀⠀⠀⠀⢸⡇⡇⠀⠘⡊⡌⠶⣍⠽⠁⡇⡇⠈⣸
⠀⠀⠀⠀⠄⡀⠈⠀⠠⣀⠁⣷⣆⡀⢸⣿⣿⢷⣄⠜⠆⣉⠁⣴⣷⣿⠎⡄⣂⣿⠃⠀⠈⡞⠀⠀⠀⠀⠀⠀⠨⡇⢁⠀⠀⠱⡝⠠⠤⣤⣰⣼⠁⠧⡇
⠀⠀⠀⠀⠀⠀⠈⠐⠠⣀⡝⠧⣤⠁⢺⣿⣹⡾⠋⠷⣼⢤⠟⠒⢛⡾⡡⣵⣿⢃⣀⣤⣼⠤⠐⠀⠂⠀⠀⠀⠀⠸⣬⣓⠤⡄⣨⣛⣛⣉⢁⣀⠜⣸⠁
⠀⠀⠀⠀⢀⣠⢴⡲⠉⠀⠉⠳⢈⣠⣿⠓⠈⣇⠀⠀⠀⠀⠀⠀⣰⡇⡼⣽⠃⣋⣉⣭⡇⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠲⠷⠾⠭⠶⠚⠁⠀
⠀⢀⣤⡶⠓⠉⠀⣀⣤⣶⣶⢿⡟⡯⣀⣣⣶⠏⠀⠀⠀⠀⠀⠀⢾⣅⠶⣿⣦⣭⣭⠼⠷⡄⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡜⡛⡂⡀⠀⠀⠘⢿⣿⡷⣟⣯⣋⢖⡿⠽⠏⠶⡆⠀⠀⣠⣤⣀⣀⣚⣳⣜⢋⡿⣦⣀⠀⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠛⠶⠴⣠⣀⠀⠀⠀⠉⠉⢛⠻⠿⢶⣛⡎⡩⢿⣐⣾⠓⣡⢀⣬⡩⣩⣙⠄⢊⡽⣻⢶⡀⠁⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠂⠊⢧⣦⡞⢋⣤⠄⠀⢿⣮⠵⡘⢿⡟⣵⣺⣿⠟⠓⣿⠾⣟⣾⣾⣽⣳⣟⣦⠈⡚⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠛⡇⢰⡄⠈⣷⣯⢱⠘⣮⣯⡟⠁⢸⣧⢹⣶⠀⠀⠉⠛⢻⣯⣽⣿⠈⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⢸⡟⠁⠀⠹⣿⣹⣲⣿⡿⠁⠹⣦⠿⡍⠙⠗⠒⠦⣤⢀⡀⢉⠉⠀⠀⡓⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⢡⠂⠀⠀⣿⣷⣿⡯⠀⠠⣠⡟⡄⠙⡀⠈⠂⠀⠀⠈⠉⠒⠢⠬⠴⠤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⢳⡀⠀⠘⢿⡟⠁⠀⣸⠏⠀⠀⡀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⢀⣰⠏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢢⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣆⡆⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀