⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡸⡲⢚⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡫⢊⣝⠂⠀⠀⠀⠀⠀⠀⢀⢮⢵⢔⠠⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣬⣪⣴⡁⣅⡄⠀⠀⠀⠀⠀⡌⠄⣞⠁⣊⡧⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠰⡻⢏⣻⣁⣴⠒⠂⠨⠭⣐⣲⠀⡸⡷⣶⡞⠪⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠸⣢⠇⠀⠀⡘⢍⠉⠉⠐⠒⠃⠰⢗⠲⠻⠀⢑⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⡫⡞⠀⠀⠀⣪⡒⢕⠯⡢⡚⢠⢗⡡⢒⡁⠀⠈⠢⡁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣼⣛⣩⡭⠵⠒⣻⠮⠤⣵⣠⠂⣖⠅⡲⢷⡀⢢⡒⠕⢌⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣘⢝⡏⠀⠈⠉⠁⠒⢦⡤⠤⡍⢈⣅⡡⢳⠃⠀⢢⠣⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⡽⠀⠀⠀⠀⠀⠀⢍⡪⠰⠀⣖⡩⢒⡝⠀⠀⠀⠀⢈⢊⠢⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣫⠕⠓⠤⠤⠄⣀⣀⠀⢐⢬⠃⢰⠣⢊⢵⠁⠀⠀⠀⠀⠀⢕⠕⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣶⣳⠽⠽⢖⡖⠂⠤⠤⢉⣉⠏⢀⣧⣆⢕⠆⠀⠀⠀⠀⠀⠀⢦⠉⢃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢨⢟⡟⠀⠀⠀⠀⠀⠀⠉⠉⡞⠀⡜⣺⠞⡿⢕⠄⠢⡤⡀⢠⡀⡀⢕⢄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⣮⣽⠤⠤⣀⡀⠀⠀⠀⠀⠐⠀⡸⡫⠔⡸⡉⠂⠓⠐⢌⠪⡢⣝⢌⠢⠡⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣐⣻⠴⢏⣵⡒⠪⠭⠝⣒⣲⠄⢠⣫⢔⣩⣏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⢕⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⢟⡎⠀⠀⠀⠀⠉⠐⠂⠤⡜⢀⣯⣋⣽⡼⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡫⢽⠁⠀⠀⠀⠀⠀⠀⠀⢠⠁⠠⢔⡨⡶⠀⠺⡊⠂⠂⠀⠀⠀⠀⠀⠀⠀⠠⣕⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⢖⣒⡒⠠⠤⣀⣀⠀⠀⠆⢀⢖⠥⣪⠁⠀⠨⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡸⢚⡾⠓⠥⠮⣉⡒⠢⠤⠍⡙⠀⣞⣱⣪⠇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⡯⢱⠃⠀⠀⠀⠀⠀⠉⠐⠲⠁⣸⠟⠘⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣸⣥⠛⠢⠤⣀⣀⠀⠀⠀⢀⠃⢰⢗⠤⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⣰⢟⡶⠼⣍⡒⠒⠤⠍⣑⡒⡆⢀⢟⠥⢊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢢⡻⢵⠀⠀⠀⠈⠉⠒⠂⠤⢬⠁⣜⣗⣩⣣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢈⣮⣪⡅⠀⠀⠀⠀⠀⠀⠀⢀⠆⢰⡥⢒⠥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢠⣾⣿⣳⢆⠬⠅⣐