⠚⠓⠛⠚⠓⠛⠚⠓⠛⠚⠓⠛⠚⠓⠛⠚⠓⠛⠚⠓⠛⠚⠓⠛⠚⠓⠛⠚⣷⢻⡞⣷⢻⡞⣷⢻⡞⣷⢻⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢽⣫⣽⣫⢯⣟⣭⢻⡝⣮⣛⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢳⣏⢷⣎⠷⣯⢞⡼⣣⢟⡶⣹⢾
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣊⡾⢯⡞⣯⢞⡻⣜⢯⡞⡵⠋⢀⣿⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢀⣾⡹⠞⠩⠛⠈⡶⣽⠋⠃⠀⠀⢠⡞⣾⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠎⡰⠀⢀⠴⡤⠛⠀⡀⠀⢄⠀⣼⠙⣠⡜⠎⠀⢬⡳⣝⢮⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠔⠁⠠⠑⠊⠀⢀⠀⠄⢂⣐⠜⣁⢶⣡⣞⡵⠋⠀⢠⣏⣷⢫⡟⣼
⠀⠐⢖⠃⠛⠀⠑⠘⠈⠙⠃⠓⡈⢁⠁⠂⠈⠄⠠⠐⠀⠠⣀⠶⠎⢡⣼⢫⢳⣳⠞⠁⢀⡴⣫⢞⣞⡿⣞⣽
⠀⠀⠀⠁⠄⠀⠀⡀⠂⠦⠁⠆⡀⠂⡈⠄⠡⠐⠀⠂⠡⣴⢫⠏⣰⢏⠎⢰⡯⠝⠀⣠⢯⣟⡳⣏⠾⡵⣯⢾
⠀⠀⠀⠀⠀⠁⠢⡀⠁⠂⠁⠂⢀⠁⠄⢂⠐⠠⠈⣤⠛⡜⠃⢰⣏⡟⠀⣯⢟⠀⢠⡛⠎⠁⠉⣠⢞⡽⣳⢻
⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠡⠈⠄⡈⠐⡀⢂⡴⠛⠠⡘⠀⠠⣸⢎⡇⠈⢋⡟⢀⡴⠒⠀⠄⣢⣏⣿⣹⡽⣻
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡁⢂⠁⠆⢦⠑⡈⢁⠠⢈⠐⠀⠌⣰⠏⣼⡚⠀⣾⣡⢞⡵⠂⢠⣜⡷⢾⡵⢧⡻⣽
⠀⠀⠀⠀⠀⠀⢀⠃⡐⢀⠂⡜⢀⠂⠄⣐⢠⡜⠀⢂⢡⠞⣳⢖⡆⠁⡼⣧⢟⡯⠀⡴⣯⣞⡽⣛⣾⣫⡽⣺
⠀⠀⠀⠀⠀⠀⠀⢒⠈⡄⢢⠐⢠⢈⡴⣫⠗⢀⠁⠢⢉⣶⡹⣞⠄⣰⢏⡟⠏⣀⢾⣹⢳⡞⣽⣽⣲⢭⡻⣽
⠀⠀⠀⠀⠀⠀⠀⣹⠊⢈⠅⣈⢶⡫⢊⠱⢊⠁⠌⡐⣽⣲⣽⠺⣄⡯⢯⠝⢠⡞⣯⢞⡳⣟⢶⣹⣏⡯⣽⢺
⠀⠀⠀⠀⠀⠀⢀⠎⠧⢋⡰⣎⢷⡃⠄⣱⠏⠐⠠⠘⣧⠓⠈⠕⣻⠞⠁⣰⢏⡾⣭⣟⡽⣹⣏⣷⢺⡵⣫⢿
⠀⠀⠀⠀⢀⠀⡜⢨⡑⣦⢻⡜⣫⠐⣈⠣⡄⢳⠀⢡⠆⢈⠐⠠⢙⡾⢁⣾⡹⠞⢡⢊⡴⣳⢎⡟⣯⡝⣧⢻
⠀⠀⠀⠀⢀⡼⢡⣳⡝⣮⢳⠃⢄⠒⠈⠀⡅⠇⡈⠄⢂⠄⡼⣚⣮⠓⠈⠄⢃⠄⢢⡞⣵⢫⣞⡽⢶⣹⢮⣻
⠀⠀⠀⠀⡎⢐⡿⣞⡽⣎⠿⢀⠎⠀⠀⠷⡨⠅⡐⢨⡄⠎⠀⢀⡿⢀⠡⣜⢣⣞⡳⣟⡭⣟⣼⢫⡷⡽⣞⣽
⠀⠀⠀⢰⠀⢮⡳⣝⠾⣭⠣⠁⠀⠀⢸⠅⡟⠠⣐⠋⠀⠀⠀⣸⠃⠄⡻⣞⢧⣟⣳⣏⢷⣫⢞⣧⠿⣵⣫⢾
⠀⠀⢀⠃⠈⣯⢇⡯⠛⡴⠣⠀⠀⢠⡛⢼⢃⠴⠂⠀⠀⠀⣰⠇⢌⡰⣳⡝⣯⢾⣱⢞⣳⢟⡞⣷⢻⡵⣫⢞
⠀⠀⠘⠠⠠⠌⠦⠑⠉⠀⠀⠀⠳⢆⣹⠋⡕⠀⠀⠀⠀⣰⠏⣼⠾⣵⢳⣻⢷⣫⣽⣫⢽⣫⡽⣳⢻⣞⣳⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢌⠥⠊⠀⠀⠀⣠⣜⡧⣟⡳⣟⣞⣧⢟⣮⢳⡞⣭⣳⢽⡻⣭⢻⡼⣭⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣱⢮⢿⡵⣻⡜⣯⢞⣯⢞⡯⣽⢎⡟⣧⣻⢭⡻⣜⢧⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣜⡧⣏⢿⡜⣧⣟⣼⢫⡞⣯⡝⣯⢻⣼⣣⢟⣮⢳⡝⣮⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⣫⣽⡹⢯⣝⣳⣞⣭⣻⣝⣧⢻⣼⣫⣖⣻⢞⣮⢳⡝⣮⢻
⣦⢶⡶⣶⢶⡶⣶⢶⡶⣶⢶⡶⣶⢶⣦⣟⡷⣞⡷⣾⣽⣳⣞⡷⣞⣷⣳⣟⣾⣻⢶⣻⣞⣷⣻⣞⣷⣻⣞⣯