⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠠⠀⠄⠠⡐⡿⣜⣳⣏⠾⡅⠀⠟⠘⠁⠉⠀⢁⠈⠌⣈⠡⠛⠞⣳⣛⣾⡹⣏⡷⣏⡷⣏⣷⢫⡷⣛⣞⣳⣛⣮⢷⡹⢄⠸⣧⣛⢾
⠀⠀⠀⠀⠠⠐⠀⠁⡐⠀⠄⡈⠄⠡⢈⠐⢨⢷⣫⢗⡞⡏⠃⠀⠀⠀⠀⠀⠀⢂⠐⠠⠄⢂⠡⠌⠠⠙⠶⣻⡝⣾⡝⣾⡝⣞⣯⣳⢟⡾⣱⡟⣼⢧⡟⠤⢹⡖⣯⢻
⠀⠀⠀⠀⠄⠀⠠⠁⢀⠐⠠⠀⠌⠐⠠⢈⠰⡻⠜⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⡐⠈⠄⠂⠌⠡⡈⠔⡡⢟⣧⢟⣧⠿⡽⣞⣳⢯⣽⢳⣻⡝⣮⣝⠢⢱⣏⢷⣫
⠀⠀⠀⠀⡀⠈⢀⠀⠂⢀⠂⠁⠄⡁⠂⠄⠂⢁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠁⠌⡀⢣⠖⣅⠺⠑⢊⠺⣽⣚⢿⣹⡳⣏⡿⣜⣯⢳⡽⣳⢮⡑⢸⢮⣳⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠁⠂⡐⠠⢉⠠⠀⡑⠠⠌⢡⠋⡍⠥⢋⠍⡜⡩⢌⣋⠱⣉⠎⠄⡹⢲⡝⣧⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠡⢈⠰⡶⣬⠶⣥⡞⣴⡲⢦⢦⡵⢦⡼⡐⢤⡳⢲⡝⣧⣻
⠀⠀⠀⠀⡀⠄⠂⠀⡁⠈⡀⠄⠈⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡐⡄⢆⡂⢖⡰⢂⢖⡘⣐⠦⢰⢹⢧⡟⣧⢟⡧⣟⢯⣛⡾⣏⢷⡈⢲⡝⣧⣻
⠀⠀⠀⠀⢀⠀⠀⠂⢀⠐⠀⡀⠂⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣢⠱⡜⢢⡙⢦⠱⣉⠦⣙⡔⢪⠔⣸⢏⡾⣝⡾⣝⡾⣭⢷⡻⣼⢳⠌⢲⣏⢷⣳
⠀⠀⠀⠈⠀⠀⠐⠀⡀⠀⠂⠀⠄⠁⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⠣⡜⢆⢫⠔⣣⠒⣌⠣⡘⢬⣻⣝⡮⢷⡻⡼⢧⣻⣽⣣⢟⡌⢲⡽⣎⢷
⠀⠀⠀⠀⠄⠈⠀⢀⠀⠄⠁⡀⠂⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠓⡜⣌⢣⠚⡤⢋⡔⣃⢩⢸⣳⢮⣛⡷⣽⡹⣏⢷⡞⣧⡻⢄⢪⢷⣹⣞
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⡙⠴⣈⠖⣉⠖⣉⠲⣡⢒⠸⣧⡻⣝⢾⣱⡟⡽⣎⣟⢶⣛⠄⢪⣗⡳⣾
⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⢦⡙⢦⢉⠖⡡⠎⠥⠓⠄⠋⡐⢷⡝⣯⡞⣧⡻⣝⢾⣹⢮⡽⡈⢜⣮⢽⣺
⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠐⡄⠒⡄⢒⡐⢢⣾⢾⣳⡿⣯⢿⣻⢷⡇⠐⡈⠄⠡⢀⠻⣞⡷⣹⢧⡻⣝⡾⣭⡻⣵⢁⠺⣜⣧⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡌⠄⡃⢌⠂⡜⡈⢍⣛⡷⣿⣽⣻⡽⣯⠃⡐⠠⢈⠐⠠⢩⢻⣜⢷⣫⢗⡯⣞⠷⣝⣞⠠⣙⠾⣜⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢃⠌⠄⡃⠤⠑⡼⣯⣟⡷⣯⡷⣟⠃⠐⡀⢁⠠⠈⡐⠀⣟⢮⡳⣝⡮⣗⢯⡟⡽⣎⠅⣸⢻⡜⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢃⠔⣈⠒⡜⣳⣾⣻⢷⠻⠁⠀⠀⡐⠀⠄⠂⠠⢁⢸⡳⣽⢣⣟⡼⣻⢼⡳⣭⠒⢨⢷⡹⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠐⠠⢊⣼⢷⡯⠛⠁⡄⠀⠀⠀⠀⡐⠀⠁⠂⠄⠂⡿⣜⣳⢮⡳⣏⢷⡹⣖⠁⢎⡷⣹⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠌⠀⠡⠀⡃⢼⣣⢟⣮⢳⡽⣺⢵⡫⠌⣘⢾⡱⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡀⠐⠰⢨⡗⣯⠞⣧⢻⡵⣫⠵⢂⢸⢣⡟⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⡐⠀⠠⠱⠨⡝⢮⠻⡜⢧⠻⢵⠫⠄⡘⢧⡝⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⢡⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠐⡀⠘⠤⠑⡈⠆⡑⢂⠡⠂⢲⡝⣧⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢂⢁⠢⠄⠀⠀⠀⠀⠀⠠⠀⢀⠈⠸⠸⡍⢟⡽⣹⠽⣩⢏⡷⠁⢸⢭⡳⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠂⠈⠄⠂⠌⢀⠁⠀⠀⠀⠀⠀⢂⠩⡐⢡⠒⢄⠢⢡⢉⠳⣏⣞⠡⢘⣮⠳⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠄⠠⠐⡈⠀⢀⠠⠂⠄⠀⠀⠀⠀⢁⠊⠤⠑⡂⠜⢠⠊⢄⠊⡔⠘⣮⠐⢨⣖⡻⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⠔⠡⢈⠂⠡⠀⠅⢂⠢⠑⡈⠄⡀⠀⠀⡌⢂⠱⢈⡐⢉⠄⠢⠌⢒⠈⠥⢐⠂⣘⠶⣭⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢨⠀⠜⠀⡈⠄⠂⠌⢠⠁⢊⠄⠂⡅⢂⠒⡀⠠⠡⡐⠌⡐⢂⠌⢂⠜⡀⠣⠌⡘⠄⠃⠄⢨⢳⢎⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⠀⠄⢂⠡⠐⡈⠰⠈⠄⡘⠠⢈⠒⡀⠆⢂⠤⢁⢂⠐⢂⠁⠆⠌⢂⠤⠘⡐⢂⠰⢈⠡⠈⢰⣋⢮⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠄⣈⠐⡀⢂⠡⠠⠁⠌⡐⠠⢁⠂⠔⠠⠘⣀⠂⢂⠌⡐⠂⠌⡐⢈⠂⠐⠀⢁⠂⢄⠃⠌⢀⠢⡝⢮⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠌⡐⢀⠂⡐⢀⠂⠡⠘⠠⠠⢁⠂⠌⣀⠃⠡⡀⠌⢂⠰⢀⡉⠰⢀⠂⠀⠀⠈⠄⣈⠢⠘⡈⠀⢸⡙⢦⢭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢂⠐⡀⢂⠐⠠⢈⠐⡁⢂⢁⠂⠌⡐⠠⠈⠔⠠⠘⡀⢂⠂⠤⢁⠂⡡⠀⠀⠌⡐⢀⠢⢁⠂⡁⢰⡙⣎⠶