Glove Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢰⣿⣿⡂⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣧⠸⣿⣾⣿⠀⢿⣽⣇⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⢠⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⢺⣿⣿⡇⢹⣿⣿⡂⢛⣗⣟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠃⣿⣿⣿⡇⣰⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢐⣿⣿⣇⠘⣿⣿⡇⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⢸⣿⣿⣿⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⣽⣽⣿⠀⣿⣻⡆⠸⣿⣿⠀⠀⣠⣦⡀⠀⠀⢸⣿⣿⣿⠃⣿⣿⣿⡇⣼⣿⣿⡇⣰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⣿⣿⣿⣷⣿⣿⢷⣾⣿⣿⠂⢠⣿⣿⣷⠀⢀⣿⣿⣿⡏⣸⣿⣿⡿⢠⣿⣿⡿⢠⣿⣿⡟
⠀⠀⠀⠀⣿⣿⣦⠀⠀⣿⡯⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⡟⠀⣸⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⢡⣿⣿⣿⠁
⠀⠀⠀⠀⢻⣿⣿⣇⠀⢹⣿⣿⣿⣿⣿⣿⢿⣿⣽⣿⣿⣿⣟⠀⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠃
⠀⠀⠀⠀⠸⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢻⣿⡿⣽⣾⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣗⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢻⣷⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣷⣿⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⣿⣿⡿⣿⠛⣯⠉⢿⠀⢺⠀⢰⠀⠀⠀⠙⡿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠹⡆⠸⡇⠸⡇⠸⡇⢸⡀⠀⠀⠀⡏⠀⡇⠀⡿⠀⡾⠉⡿⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢿⠀⢿⠀⢿⠀⢿⠀⣇⠀⠀⠀⡇⢸⡇⢸⡇⢸⠇⢸⠇⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣘⣧⠼⠖⠚⠛⠉⠉⠉⠀⠀⣼⣅⣾⣀⡾⠀⣾⠀⣿⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠧⣴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢠⡄⠄⣤⢠⡄⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣂⣷⡼⠞⠓⠓⠛⠾⣾⣧⣿⡀⠁⣠⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠹⣶⡿⠋⠀⠀⠀⢀⡀⠀⠀⠀⠈⠙⢳⣏⡛⠀⠀⠬⢹⡗⠈⠻⢦⣄⠤⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣷⠸⣽⣄⣀⡀⠀⠀⣀⣀⣠⣤⡔⠒⠻⢿⠋⣧⠀⠀⢱⣍⡌⠀⢐⢄⡛⠀⠀⢻⣷⠐⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣧⢸⡇⠀⢿⣿⣿⡇⠀⢀⣿⣿⣿⣿⡇⠀⠀⢸⢀⠉⠀⠀⠀⠀⡛⠀⠈⠗⢵⠀⢸⣦⠂⠀⠀⢺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠁⠀⢸⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⣿⠞⠃⠀⠀⠀⢸⡇⠀⠀⠀⣰⠀⠀⡙⠃⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠘⢻⣃⠀⠀⠀⠂⠀⠀⠀⢀⣀⣭⡿⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⡄⠀⡇⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⢸⠀⢸⣿⠋⠉⣿⣿⣿⣿⡇⠀⡀⡈⠁⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⡇⠀⢸⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⢸⠇⢞⣿⠖⠀⢁⡀⠀⠀⠈⠉⣙⣟⢠⠇⠀⠀⠀⢸⣿⠀⠀⠀⠀⣾⠃⠀⡇⠀⢸⡃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⡇⠘⣦⠘⣷⠶⡀⠀⠀⠀⠀⣀⣠⣤⡯⢸⠀⠀⠀⠀⣾⡿⠀⠀⠀⢀⣿⠀⠀⠀⠀⢀⡇⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣷⠀⣸⠀⣿⡟⠁⠰⣾⣿⣿⣿⣄⡨⠁⡊⠀⠀⠀⢠⣿⡇⠀⠀⠀⣸⡟⠀⠀⠀⠀⣾⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⣧⠈⢁⢨⣿⣄⡀⠻⠛⠛⠉⠉⠁⠰⠇⠀⠀⠀⢻⣿⠃⠀⠀⢸⣿⠇⠀⠀⠀⠀⡋⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣷⡼⠆⠻⠀⠀⠀⠀⠀⠀⠔⣵⠂⡀⠀⠀⠀⠈⠁⠀⠀⠀⠸⠋⠀⠀⠈⠀⣴⠁⠀⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡶⠆⠀⠀⠠⡤⠀⢤⠄⠰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣠⣤⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣠⢳⣬⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣭⡵⠆⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⠀⠼⢰⡕⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣟⣛⡲⠆⠀⠀⠀⠈⠉⠓⠀⠀⠆⠠⠤⠀⢀⣀⣀⡀⠀⠀⣘⢿⣿⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⠦⠲⡖⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠒⡶⣾⣷⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⣿⣿⣷⣚⣽⣃⣤⢶⡆⢀⡴⡆⠀⡴⡆⢀⡏⣷⣷⣹⠟⣿⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⣿⣿⣴⣿⣷⣏⣴⣷⣞⣵⢿⣿⣧⣿⠟⠁⠀⠘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠖⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠈⡇⡇⠀⠀⡇⡴⠲⢄⠀⠀⠀⠀⣀⣀⢸⠀⠀⢹⢸⠁⠀⢳
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠢⡀⡇⠀⠀⣿⠁⠀⢰⣿⠀⠀⢸⠀⠀⠀⢸⠀⠈⢇⣇⠀⠀⢿⡆⠀⠘⡆⡞⠉⠱⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣷⠁⠀⠀⡿⠀⠀⢸⡇⠀⠀⡎⠀⠀⠀⠘⡄⠀⠈⣿⡀⠀⠘⣷⠀⠀⠱⣧⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣿⠀⠀⢸⡇⠀⠀⣸⡇⠀⠀⠇⠀⠀⠀⠀⢣⠀⠀⢸⡆⠀⠀⢹⡄⠀⠀⢿⡀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⣸⠃⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠈⡆⠀⠀⣿⠀⠀⠈⣷⠀⠀⠘⣧⠀⠀⢻
⠀⠀⠀⠀⠀⠀⡞⠀⠀⣸⠃⠀⠀⣿⠀⠀⢀⡏⠀⠀⡜⠀⠀⠀⠀⠀⠀⢹⠀⠀⠸⣇⠀⠀⠸⡆⠀⠀⢹⡄⠀⠈⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡿⠀⠀⢀⡇⠀⠀⢸⠇⠀⠀⡇⠀⢀⣴⣒⠐⢦⡈⡇⠀⠀⢻⡀⠀⠀⢿⠀⠀⠀⣧⠀⠀⠸
⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠀⠀⢸⠃⠀⠀⣼⠀⠀⢀⠁⢠⠊⠁⠈⠑⣄⡇⠸⡀⠀⠈⣇⠀⠀⠘⡇⠀⠀⠸⡄⠀⠀⢁
⠀⠀⠀⠀⠀⡸⠀⠀⠘⠁⠀⠀⠸⠀⠀⠀⡟⠀⠀⢸⢠⠛⣄⠀⠀⠀⠈⠣⡀⢣⠀⠀⠸⡀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠈⠦⠀⠀⠀⠀⠙⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⠓⣄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠇
⠀⠀⠸⠤⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠒⠒⠐⠂⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠖⠒⠈⠁


⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⡖⢆⠀⢸⠀⠘⡄⠀⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡏⠀⡇
⠀⠀⠀⠀⣀⠀⡇⠈⡄⢸⠀⠀⡇⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⢸⠀⠀⡇⢀⠞⠢
⠀⠀⠀⢾⠀⢳⢱⠀⢣⠸⡀⠀⡇⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⣾⠀⠀⠃⡼⠀⡆⣠⢄
⠀⠀⠀⠸⡀⠈⠇⡆⠘⡄⡇⠀⢇⠀⡇⠀⡇⠀⠀⠀⠀⢀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⣿⠀⢸⢀⠃⢰⣱⠁⢸
⠀⠀⠀⠀⢇⠀⠀⣠⠀⠱⠇⠀⠘⠞⠀⠀⡇⠀⠀⠀⡰⠋⢀⠇⠀⠀⢠⠖⢤⠀⠀⠀⠀⢸⠀⢸⡀⡏⠀⡀⡀⠀⡀⠇⠀⡜
⠀⠀⠀⠀⠸⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⡜⠀⢀⠎⠀⠀⠀⠀⢇⠀⠑⡄⠀⠀⢸⠀⠀⠉⠀⠀⠙⠁⠰⠟⠀⢀⠃
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠞⠀⢀⠎⠀⠀⠀⠀⠀⠈⢣⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⣀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡶⠄⠐⠒⠉⠉⢡⣄⠀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⢉⠐⠂⠠⠤⠀⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣇⡦⠠⠷⠊⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠛⠆⠀⠄⣖⠀⣀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣍⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢤⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿⠀⠀⢱
⠀⠀⠀⠀⠀⠀⢠⠋⠉⢳⠀⠀⠘⡄⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡴⠒⢦
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡇⠀⠀⢷⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢹⠀⠀⢠⠃
⠀⠀⠀⠀⠀⢀⣀⣃⠀⠀⢹⠀⠀⠘⡄⠀⠀⢇⠀⠀⠀⡠⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡇⠀⠀⡜⠉⠉⢣
⠀⠀⠀⠀⠀⡏⠀⠘⡄⠀⠀⢇⠀⠀⢱⠀⠀⠸⡀⠀⢠⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸⠁⠀⢀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢳⠀⠀⢱⠀⠀⢸⡀⠀⠈⡆⠀⠀⢇⠀⢸⠀⠀⢸⠀⠀⡠⢤⡀⠀⠀⢀⠇⠀⠀⡎⠀⠀⡸⠀⠀⢰⡥⢄
⠀⠀⠀⠀⠀⠈⡆⠀⠘⡆⠀⠀⢇⠀⠀⢱⠀⠀⠘⡀⡸⠀⠀⠘⡀⢰⠁⠀⢣⠀⠀⡸⠀⠀⢰⠁⠀⢀⠇⠀⠀⡌⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢹⠀⠀⢱⠀⠀⠸⠀⠀⠈⠀⠀⠀⢣⠇⠀⠀⠀⡇⢸⠀⠀⢸⠀⠀⡇⠀⠀⡎⠀⠀⣸⠀⠀⢰⠃⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠘⡄⢸⠀⠀⢠⠃⠀⠀⡇⠀⠀⡼⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢧⡇⠀⠀⠈⠀⠀⠰⠀⠀⢀⠇⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣀⣠⠤⠔⠒⠉⠉⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⠤⠤⣄⣀⡀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡐⠉⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠣
⠀⠀⢀⠒⠀⠢⡀⡀⠀⠀⠘⠀⢀⠔⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠢⠀⢀⠁⠀⠀⠰⢀⠔⠀⠐⠄
⠀⠀⠀⡀⠀⠀⢠⠁⠀⠀⠀⡆⠌⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⢸⠀⠀⠀⠐⡌⠀⠀⠀⡆
⡀⢀⠀⢡⠀⠀⠀⡈⡀⠀⠀⠇⡆⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢘⠀⠀⢀⠃⠀⠀⠀⡐⠀⡀⠄
⡇⠀⠑⡄⢂⠀⠀⠃⠡⠀⠀⢀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠸⠘⠀⠀⡌⠸⠀⠀⠠⢁⠎
⢃⠀⠀⠘⡌⡀⠀⠘⠔⠀⠀⠉⠀⠀⠀⠀⡔⠉⠑⠀⠀⠰⠁⠉⢆⠐⠀⠀⠀⠉⠀⠀⠓⠂⠀⠀⢃⠎⠀⠀⢠
⠈⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⢀⠀⠀⢡⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠆
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⢠⠃⠀⠀⠀⠡⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡀⢤⢪⠀⠀⠀⠀⠀⠀⠀⠀⢀⢓⠤⢀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠏⠑⠂⠂⢒⠀⠈⠅⠀⠀⢣⠱⠀⠀⠀⠀⠀⠀⠠⢁⠊⠀⠀⠨⠉⠁⠒⠀⠐⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢡⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠠⣜⠀⠀⠀⠂⠀⠀⠅⠀⠀⡅⠀⡄
⠀⠀⠀⠀⠀⠢⢀⣄⣀⣀⣄⠀⠬⠄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠰⠤⠀⢠⣀⡀⢠⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⠀⢀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⢀⡏⠈⠉⣿⠛⠁⠀⠀⠀⣉⣿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣤⣼⣇⣀⣼⠷⠦⣤⣄⣤⠞⠋⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣄⠀⢸⠉⣹⠃⠀⠀⣠⠟⠙⠳⣄⠀⠀⠀⠀⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⣀⣨⡷⠾⠿⠳⠦⣄⣰⠏⠀⠀⠀⠈⢻⣶⠖⠋⠉⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠛⠳⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠷⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⢀⡴⠋⠈⢷⡀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠚⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠈⢷⡀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⠛⣯⠛⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠘⣧⣀⣠⣼
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠈⠙⠲⠦⠬⣭⣍⣙⣛⣋⣠⣤⣤⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⠚⠛⢻⡏⠁
⠀⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⢚⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠶⠶⠶⠞⠛⠋⣉⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠦⣤⣤⣷⡴⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣚⣽⠿⢦⣄⣸⡇⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠉⠀⠀⠀⠀⣀⣤⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢖⣫⡵⠞⠋⠁⠀⠀⠉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⢀⣤⠞⠋⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⡴⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⢀⣠⣾⠋⠀⠀⠀⠀⠀⢀⠀⣠⠟⠁⢀⣴⠏⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⣀⡴⢋⡿⠁⠀⠀⠀⠀⢀⠔⢡⡾⠃⠀⣰⠟⠁⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⡿
⠀⢀⣼⠋⠀⣾⠁⠀⠀⠀⢀⡴⢋⣴⠏⠀⣠⡾⠁⠀⠀⠀⠀⢀⣼⢫⡟⠀⠀⠀⠀⣰⢿⠇⠀⠀⠀⢸⠇
⢠⡿⠁⠀⠀⣿⣀⣀⣠⠶⢋⣴⠟⠁⢀⣴⠋⠀⠀⠀⠀⠀⢠⡿⢡⡟⠀⠀⠀⠀⣸⠏⣾⠀⠀⠀⠀⢸⡆
⣾⠁⠀⠀⠀⠘⠿⣭⣴⣶⠛⠁⠀⢠⡾⠁⠀⠀⠀⠀⡀⣠⡟⢁⡿⠀⠀⠀⠀⢠⡟⠀⣿⠀⠀⠀⠀⢸⡇
⢻⣆⣀⣠⣤⡶⠟⠋⣴⠃⠀⠀⢀⡿⠁⠀⠀⠀⢀⡞⣰⡟⠀⣾⠁⠀⠀⠀⠀⣾⠁⠀⡇⠀⠀⠀⢸⢸⡇
⠀⠉⠉⠉⠀⠀⠀⣼⠃⠀⠀⠀⢸⠇⠀⠀⠀⢀⡞⣰⡟⠀⢰⡏⠀⠀⠀⢠⢰⡏⠀⠀⡇⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢻⡄⠀⠀⣠⠟⣴⠏⠀⠀⣼⡇⠀⠀⠀⡏⣾⠁⠀⠀⣷⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⡾⢷⣶⣚⣵⣾⠃⠀⠀⠀⢿⡇⠀⠀⢸⢣⡏⠀⠀⠀⣿⠀⠀⠀⡼⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⡴⠛⠀⠀⠈⠉⠀⣿⠀⠀⠀⠀⣸⣷⣀⣠⢟⣿⣇⠀⠀⢸⠛⢷⣀⣰⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢀⣴⠏⠀⠙⠛⠛⠁⠙⣦⣠⡟⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⣀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠁⡀⠉⣸⣿⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠳⣤⣾⠟⣷⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆⠸⠀⠀⠀⠀⢹⡟⠁⢸⡀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⣙⣶⠟⠁⠘⠶⠀⠀⠀⣰⡞⠀⠀⢸⣧⡀⠀⠀⢀⡾⠣⠊⠀⠀⠠⡲⠁⠀⠀⠰⠁⡀⠀⢀⡤⠖⠁
⠀⠀⠀⠀⠀⢀⣞⡽⠁⠀⠀⠀⠀⡀⠀⠀⣹⣇⠀⠀⣸⣿⠵⡀⡺⠋⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⣀⣠⠾⠋⠀⠀⣀
⠀⠀⠀⠀⣡⡿⠋⠀⠀⠀⠀⠀⠀⠐⠀⠀⠿⣿⠀⢸⣿⣷⡖⡳⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁⠀⣀⠴⠚⠁
⢀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠀⢸⣿⣷⣿⡅⢀⣔⠀⠀⢀⠀⠀⠀⢀⡤⠾⠁⠀⠀⡶⠚⠁
⠈⠐⢼⠗⢀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠀⠀⢀⣿⣿⠿⠋⠠⠜⠁⠀⠀⠔⠀⣠⠶⠃⠀⠀⠀⢀⣠⡤⢂
⠀⠀⠀⠀⢸⡄⡀⠀⠀⠀⠀⠀⢀⣁⣠⣴⠟⠀⡾⠟⠁⠀⠀⠀⠀⠀⠀⣠⠂⠈⠀⠀⠀⠀⡰⠖⠋⠁⠂⠁⠀⠀⣀⢀⠄⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠘⡇⠀⠀⠁⠐⠀⣠⢾⣹⣿⣅⢲⣤⡞⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⣀⠀⠊⠀⡀⠀⠀⠀⠀⣀⠰⠋⠀⠀⠀⠠⠐⠂⠈
⠀⠀⠀⠀⠀⠣⣀⢀⠀⢀⠔⠁⣾⣿⡝⣿⣿⣷⡀⠈⠀⢀⡤⠞⠋⢀⡀⠀⠐⠀⠉⠁⠀⣀⠔⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢸⣟⠀⠁⠀⢰⣿⣿⣏⣹⣿⣿⢲⣦⣶⡉⠀⣀⠐⠋⡠⠀⠁⠀⠀⠀⠀⠉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣸⣏⡛⠓⠲⢦⣿⣿⣿⣼⠋⣰⡿⢑⠙⣷⠀⠀⠺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢠⣞⣿⡌⠳⢦⡀⣿⣿⣿⣽⣿⣦⠟⣱⠋⠁⣿⣶⡻⠂
⠀⠀⠀⢠⣿⡟⢻⠋⠠⣾⠿⣿⣿⣷⣯⣬⣥⣶⣿⣄⢀⡿⠉
⠀⠀⢠⣿⡟⢀⣿⣦⣏⣡⣰⣅⣽⣿⣿⣿⡻⠉⠀⠋⣽⠃
⠤⢤⣿⣟⢀⣿⣿⣶⣤⡴⢏⢍⣥⣼⣿⡁⠀⢀⣠⡾⠁
⠀⣼⣿⢿⡟⣿⣭⣟⣃⣭⡿⠟⠛⠉⠙⠛⠛⠛⠁
⢠⣿⣧⠞⣰⣿⣿⠿⡛⠉
⠘⣿⣇⡴⠛⠉⠉
⣶⡾⠿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣽⣷⣶⣶⣶⣦⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⣠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⣴⠀⡰⢁⠞⠁⠀⠀⠐⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡟⠀⠀⠀⠀⣠⣿⣿⣿⠇⣜⠵⠋⠀⠀⣀⢀⡷⣫⡤
⠀⠀⠀⢠⣶⣷⠀⣀⠀⠀⠀⠀⠀⠀⢀⢆⡿⣱⢇⢠⣾⣴⣿⣵⣿⣃⠴⠀⠀⠀⢀⠔⣱⣯⡾⠋⣀⡀
⠀⠀⠀⠸⣿⣧⠌⢿⣿⡀⠀⠈⠐⠂⠞⠼⣰⢧⣿⢿⣾⣿⣿⣿⣿⡟⠀⠀⢀⠔⣹⣿⣿⣫⣠⣴⠏⠁
⠀⠀⠀⠀⠈⣿⣶⣿⣿⣿⠀⡄⠀⠁⡀⠀⠙⣿⣿⣿⣿⣿⣿⣿⢟⢁⣤⠖⣡⣿⣿⣋⣉⢼⣯⠖⠁
⠀⠀⠀⠀⠀⣿⡟⠉⠙⠻⠀⢸⣶⣾⡷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⢃⣴⣾⠟⣻⣿⢿⡥⣚⡡⠄
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣿⣿⣿⡗⠀⢸⣿⣿⣿⣿⣿⡝⣻⣴⣿⢟⣷⣿⣿⡷⡿⠚⠉⣀⣤⡦
⠀⠀⠀⠀⢏⠀⠀⣴⠳⠀⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣾⣿⣿⢿⣷⣿⣟⡩⠟⠁⢀⣴⣛⣫⣥⠒
⠀⠀⠀⠀⠘⣠⣼⡉⠀⠀⣠⣿⣿⣿⣷⡀⠙⣿⡿⣻⣿⣿⣿⣿⣿⠿⠎⠉⣠⣴⣾⣿⣿⣿⠿⣩⡄
⠀⠀⠀⠀⠙⠃⣿⠦⣄⣠⣹⣿⢿⠻⣿⣿⠀⢘⣴⣿⡿⢷⣾⠋⢛⣠⣶⣿⣿⣿⡿⢛⣉⡤⠖⠋
⠀⠀⠀⠀⠀⠀⣿⠋⣻⣏⣻⡿⠤⣬⣟⣾⣇⠀⢄⣍⡻⣿⣿⡾⢿⣿⣿⣿⣿⣯⣶⠉⠁⠀⢤⣆
⠀⢀⣠⡴⠶⢾⣿⢤⣁⠊⣿⣇⠀⣿⣿⣿⣿⡄⠹⣟⣳⠘⣿⣟⣯⣿⣿⣿⣿⣭⣼⡿⠛⠛⠋⣀
⢠⡿⠁⠀⠀⢸⣿⠀⠉⢻⡿⢋⣳⣯⣿⣟⡻⠇⣼⣿⢑⡆⣿⣿⣿⣿⣟⣿⣿⣿⣿⠴⠔⠞⠁⠁
⣿⠁⠀⠀⠀⣸⣿⠀⠀⠀⢻⣿⣿⣿⡿⣿⡵⢞⣩⣌⣿⠇⣿⣽⡿⠟⠃⠈
⢿⡀⠀⠀⠀⠛⠈⠀⠀⠀⢸⣿⣿⣿⡿⣾⣿⣷⣽⣿⣥⠾⠋⠈
⠘⢷⣄⠀⠀⠀⠀⠀⠀⣠⣿⣿⢿⣿⠿⠋⠉
⠀⠀⠙⠷⣶⣤⣤⣴⠾⠋⠀⠈⠉
⣿⡯⣟⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠲⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡋⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣧
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⢀⡞⠁⠉⠳⣄⡈⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠘⢦
⠀⠀⣀⡴⠛⠉⠀⠀⠀⠀⢉⡟⠳⣄⠀⠀⠀⠙⠦⣄⠀⠈⠙⠒⠲⠶⠒⠋⣹⠁⠀⠀⢈⡷⣖⠋⠉⠉⠉⠙⠓⠦⣄
⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠈⢳⡄⠀⠀⠀⠈⠓⢦⡀⢠⡖⠀⠀⢰⠇⠀⠀⡴⠋⠀⠈⠳⡄⠀⠀⠀⠀⠀⠈⠳⡀
⣼⠁⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠙⠲⣽⡦⠶⢯⡀⣀⣼⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⢹
⡇⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡏⠉⡏⠉⠓⠲⠦⣤⣀⣸⡆⠀⠀⠀⠀⠀⠈
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠺⣅⠀⣧⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢰
⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⣀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠛⣛⣛⣛⣛⣛⣛⣃⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⣿⡿⠿⠿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⣿⣟⣛⣛⣛⣛⣛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣿⡷⠶⠶⠶⠶⢾⣿⡇⠀⠀⠀⠀⠈⣿⣿⠀⣿⣯⣭⣭⣭⣭⣭⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣿⣟⠛⠛⠛⠛⢻⣿⡇⠀⠀⠀⠀⠀⠸⣿⠀⣿⣯⣤⣤⣿⣿⢛⣛⡃
⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⣿⣟⣛⣛⣻⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⢻⡀⢿⣿⣿⣿⣿⡿⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⡇⢸⠟⠀⠀⠀⠀⠀⠀⠀⠈⣷⣶⣶⠶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡏⣩⠭⠭⠭⠭⠭⠭⠭⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣀⣀⣀⡀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⡇⣿⢰⠒⠒⠒⠒⠒⠒⠒⠒⡆⠀⠀⠀⠀⢠⠖⠚⠁⡇⢈⣉⣉⣉⣉⣁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠐⠒⠒⠒⠒⠂⠀⡇⠀⠀⠀⠀⠈⣇⠀⠀⡇⠠⠤⠤⠤⠤⠤⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠒⠒⠒⠒⠒⠒⠀⡇⠀⠀⠀⠀⠀⠸⡄⠀⡇⠀⠖⠒⠀⠀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠘⠙⠛⠋⠛⠃⠀⡇⠀⠀⠀⠀⠀⠀⢳⠀⣇⣀⣀⣀⣀⣀⡧⠊
⠀⠀⠀⠀⠀⠀⠀⠃⣿⢸⠀⠉⠉⠉⠁⠀⡖⣶⠇⠀⠀⠀⠀⠀⠀⠈⣇⠀⣀⣀⠤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠤⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣒⣒⣒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⠃⠀⠀⠀⠀⠀⠀⠀⠠⣖⡒⠒⠚⠋⠉⢉⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠽⠂⢰⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠰⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡖⢀⡈⠢⡀
⠀⠀⠀⠀⠀⣠⠴⠒⠉⠉⡉⠉⠓⠲⠞⢀⣄⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡜⠙⢆⠙⢤⠴⠒⠋⠉⣉⠉⠑⠲⢤⡀
⠀⠀⠀⡴⠋⣠⠔⠊⠉⠉⠉⠉⠙⢲⠀⠈⠢⡳⣄⠑⢄⠀⠀⠀⠀⠀⠀⢀⠇⢰⠃⢀⡴⠃⡀⢰⡊⠉⠁⠈⠉⠉⠒⢤⡈⠳⡄
⠀⢀⠎⢀⠞⠁⠀⠀⠀⠀⠀⠀⢠⠇⡰⠙⣄⠘⡌⠢⡈⠳⡄⠀⠀⠀⠀⡜⠀⡏⢀⡎⢠⠎⠉⢦⠑⣄⠀⠀⠀⠀⠀⠀⠙⢆⠈⢆
⠀⡜⠀⡎⠀⠀⠀⠀⠀⠀⢀⡴⢁⠜⠁⠀⠘⡆⠸⡀⠘⢦⡈⠢⣠⡤⣴⠁⡸⠀⡸⠀⡎⠀⠀⠀⠱⡌⢢⡀⠀⠀⠀⠀⠀⠈⡆⠘⡄
⠀⡇⢸⠀⠀⠀⠀⠀⠀⣞⢁⡔⠁⠀⠀⠀⠀⠃⠀⡇⠀⠀⠑⢄⠙⠇⠃⢠⠃⠀⡇⠀⣇⣀⡠⠤⠤⠞⠂⠙⡆⠀⠀⠀⠀⠀⢸⠀⡇
⠀⡇⠈⡆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡇⢀⠇⠀⠀⠀⠈⠳⡄⠀⠘⠋⣉⣁⠀⣤⠤⠴⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⡌⠀⡇
⠀⠸⡄⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡜⠀⠀⠀⠀⠀⠀⠳⡄⡞⠉⠁⠘⡄⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡼
⠀⠀⠙⢄⠘⠢⣀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⣵⢣⡀⠀⠀⠘⢆⠈⠢⣄⠀⠀⠀⠀⠀⠀⢀⡠⠚⢀⠜⠁
⠀⠀⠀⠀⠑⠦⣈⠉⠒⠒⠒⠒⠊⢁⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠙⠦⣀⠉⠒⠒⠒⠒⠊⢁⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠋⠉⠀⠀⣉⠉⠉⠉⠛⠛⠛⠛⠛⠳⢶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⣉⣩⡽⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠛⠋⠉⠀⠀⠀⠀⠠⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢛⣡⡴⠶⠻⢯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⣶⣶⠿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣴⣿⣷⠾⠿⠷⠶⠶⢶⡶⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣻⣿⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀⣀⣴⣿⣿⣵⣶⣶⣶⣶⣾⡿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠀⢀⠈⠙⠻⣿⣶⣤⣀⠀⢄⡀⠀⠉⠙⠋⠁⠀⠀⠀⣠⣶⣿⣾⣥⠶⢍⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢶⣿⠛⠛⠛⢛⣛⣛⣛⣛⣛⡛⢿⣟⡶⣌⡁⠀⠀⠀⠀⢀⣠⣾⣿⠿⠛⢉⡰⢜⠃⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠾⣧⣤⣬⣤⣀⣀⣀⠒⠀⠒⠤⠻⠶⣹⣦⣄⢀⣴⡟⠯⢑⢠⡔⠊⠁⠈⠀⣀⡭⣷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣠⣤⣤⠠⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡭⣿⣁⣤⡶⠿⠃⣀⣤⡶⢾⡛⠉⠀⠼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡍⠻⡶⢦⣌⣉⠛⠛⠛⠶⢶⣦⣤⣤⣀⣒⣰⣟⣉⣤⣴⣶⣟⡋⠁⠀⢀⣹⣶⣤⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠶⣿⡀⠈⠄⠈⠉⠛⠷⢦⣤⣀⠀⠈⠙⠛⠿⠿⣿⡿⣿⡿⠛⢉⣠⣴⠾⠟⣛⣫⡭⠴⠶⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢷⡈⢿⡀⠀⠀⠀⠀⠀⣀⣀⠉⠛⠶⣤⣀⠀⠀⠀⢉⣠⣴⣾⣿⣿⣷⠾⣿⣿⣶⣦⣀⠘⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⢳⡈⠛⠛⠛⠛⠛⠙⠛⠛⠛⠷⠶⣤⣍⣛⣶⠶⢛⣽⠟⠋⣉⣤⣤⡒⠀⣀⣤⢼⡏⠙⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣞⣁⣀⣀⡐⠒⠤⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦⣤⣼⣿⣿⡿⠷⠛⢋⠛⢉⣠⣴⠾⢻⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣏⣉⣉⠉⠛⠓⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⢀⣴⠏⠉⢹⡇⡄⠀⢀⣴⠶⠟⠋⠉⠀⠀⠘⡿⠛⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡈⠉⠙⠓⠶⢶⣭⣍⣛⠶⣦⣄⣴⣿⣧⣴⣶⣾⡧⠶⠚⠉⠀⠒⠒⠒⠀⠀⠀⢠⣷⠀⠀⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡹⠛⠛⠛⠓⠶⠦⣤⣌⣉⡛⠛⠿⢷⣿⡃⢄⡸⢦⣑⣲⠿⠿⡛⠛⠛⠛⠻⠶⣦⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣷⣶⣤⣀⠀⠀⠀⠙⣯⠙⠛⠳⣶⣟⡉⠛⠿⢿⣶⡵⠞⡩⠐⢉⠄⠂⠀⢀⣠⠿⣍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣿⣿⡍⠛⣷⣤⣄⠘⠓⠛⠛⠉⠉⠙⠷⣦⣤⣀⠀⠀⠀⠊⣁⣤⣶⣿⣯⣉⣠⠬⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣠⠟⠙⠛⢷⣤⣾⣿⣿⣶⣤⡀⠀⢀⣤⠾⠿⠬⣿⣷⣶⣶⣿⡿⠟⣋⡩⢬⡐⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⣀⣀⣀⠉⠛⠻⠿⣷⣾⣿⢾⣏⣁⣀⣠⣴⡾⠜⠛⣉⠵⢞⣋⣽⣾⣃⡴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⣻⣿⢿⣶⡶⢦⣤⣤⡴⠟⠉⠛⣻⣗⠤⠔⠒⢊⣽⠿⢋⣵⣯⣼⠻⡶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢸⠁⠈⣷⡈⠙⠛⠷⢦⣤⣀⢖⣚⣿⡍⠑⣲⢛⣻⠶⣞⣛⣭⠴⠾⠃⠘⣆⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠉⠲⢤⣀⢻⣤⣴⠶⠋⠉⠉⠹⠷⢮⣿⣿⣭⠷⠞⠛⣉⣥⠄⠂⠀⠀⠀⢹⡆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠐⠦⢄⡈⠛⠿⣤⣀⠀⠀⣰⡷⠲⣤⡉⠉⠀⠀⠐⠉⠁⢀⣀⣤⡶⢾⣛⣛⣡⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣶⣤⣀⠀⠉⠓⠀⠀⠉⠛⣶⣟⠀⠀⡏⢻⣄⠀⣀⣤⡶⠿⠟⠛⠋⠉⠉⠉⢨⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣌⡝⠳⢦⣄⡀⠀⠀⢰⣿⠙⣿⠸⣧⠀⠹⠿⠋⠁⠀⣠⡀⠀⠀⠀⠀⠒⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠈⠱⠤⠉⠛⠷⣦⣼⣿⣿⠃⠀⣹⠆⠀⠀⠈⣉⣡⣤⠴⠖⢊⡽⠋⠁⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣿⠃⠀⠀⠀⠀⠀⣀⡀⠀⢁⡀⠀⠀⣿⡤⠴⣚⠋⠉⠁⢀⣠⠞⠋⠠⣦⡴⠴⣿
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣶⣤⣍⣛⠶⢦⣤⣀⠀⠀⠈⠉⠙⢶⢧⣤⣾⢁⠤⠄⠉⠓⠾⠋⠁⠀⠉⠉⢀⣰⣤⣿⠃
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⡿⠿⠿⣶⣮⣭⣻⣶⣄⣀⠀⠉⠑⣺⣏⢀⡀⠒⣀⡠⠤⠔⣒⣠⠶⢟⡛⠉⠁⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣷⣦⣄⡀⠀⠀⠀⠀⠙⠻⢿⣶⣦⣬⣿⣠⣄⣠⣤⠴⠖⠋⠡⠔⠊⣁⡤⠐⠀⠀⢀⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣶⣤⣀⠀⠀⠀⠈⣙⢛⣿⠛⠛⣯⠳⣄⠀⠀⠀⠀⠊⠁⢀⣠⠤⠚⠋⠁
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣦⣤⣈⣉⢻⣀⣤⣬⢷⡌⣳⡀⠀⠀⠔⠚⠉
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠾⠛⠋⠐⠉⠉⠁⠛⠊
⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣷⣼⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣠⣤⡤⠄⠀⠀⠻⢿⣿⣻⠟⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧⣀⣴⣿⣶⣦⣄⡹⣿⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⡿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⡻⣿⣿⣿⣿⡿⠋⠁⠀⢀⣟⠻⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠉⣠⣿⣿⣦⡙⡿⠋⠀⠀⠀⣠⣾⣿⡄⠀⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⠻⡄⠀⠀⠀⠉⠙⣿⡅⠀⠀⠈⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣦⡁⠀⠀⠀⠀⠀⠙⣧⣄⠀⠀⠀⠀⠈⠳⣦⣰⣤⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠙⢷⣤⣄⣴⡏⠹⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠉⠛⢿⣿⣷⡄⠀⠀⠀⣀⠠⠄⠐⠚⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣠⣾⣥⣿⠛⠃⠀⠈⠁⠀⠀⠀⠀⡠⠂⢻⣿⢿
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠶⠶⣶⣦⣤⣀⠀⠀⠀⠀⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⢳⣸⣆⢥⣤⣤⣤⣄⣀
⠀⠀⠀⠀⢀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⢟⣷⢖⡠⣾⠿⣯⠁⠀⢰⡆⠀⠀⠀⠀⢀⠜⠁⠀⠀⢀⣴⡿⣻⣿⣾⠓⠂⠘⠉⠛⡷⣦⡀
⠀⠀⠀⣴⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢞⣴⣟⢿⣆⠀⢹⡆⠀⢸⣧⠀⢀⠀⡰⠃⠀⠀⠀⢠⣿⠋⠀⠘⣿⢿⡄⠀⠀⠀⠀⠈⠪⡻⣦
⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣯⢻⣆⠈⡷⠀⠸⠿⠀⣁⠎⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠹⣎⢿⡀⠀⠀⠀⠀⠀⠀⠽⣧
⠀⢠⣿⡁⠀⠀⠀⠀⠀⠀⣠⣶⢂⣥⠀⠀⠀⠙⢿⣿⡿⣿⠄⢕⣦⡤⠀⠀⠁⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢿⣼⣧⣀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⢸⣿⠄⠀⠀⠀⠀⠀⠀⢿⡿⠿⠿⠀⠀⠀⠀⠙⠛⣋⣛⣶⣿⣿⣷⣤⣴⣿⣷⣶⣤⣤⣄⢸⣧⠀⠀⠀⠀⠀⠈⠻⠿⠟⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠂⠀⠛⢻⡇⠀⠀⠀⠀⠀⢰⣿⠀⢻⣿⣿⣿⡿⠿⣿⡿⠿⠟⠉⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⡇
⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⣀⠀⣀⣤⣿⠇⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠙⢿⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠁
⠀⠀⠀⠀⠀⠙⠿⣶⣤⣄⣀⣀⣀⣀⣠⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣦⣤⣤⣤⣶⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⡉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣀⣀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠆⠠⠀⠀⠃⠀⠑⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⢰⠐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⢀⠀⠐⠂⡰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠐⠚⠁⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠳⠤⢄⠀⢀⠠⠊⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡋⠀⠀⠀⢐⠂⠀⠀⠀⠀⠸⠶⢖⠒⠲⠦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠠⠀⠐⠒⠦⢤⠁⠀⠀⠀⢀⡀⠀⠀⠀⢀⡃⡀⠀⠐⠄⢀⡀⢈⡒⣄⠀⠀⠀⠀⠀⠀⠀⠈⠒⣕⢄
⠀⠠⢂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡀⠙⠢⡀⠀⣠⡁⠀⠀⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠔⠃⣄⡄⠀⠉⠒⠤⢁⣴⠋⠀⠀⠀⠀⠐⠄⢀⠀⠀⠀⠀⠀⡄
⢰⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠹⠂⠀⠀⠘⠭⢶⠏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠈⡈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠊⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠱⡐⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠈⠃⡀⠀⠀⠀⠀⠀⢀⠀⡢⠂
⠀⠀⠈⠪⠐⠄⢀⠀⠀⠀⡀⠡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠒⠉
⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣭⣿⣯⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠙⠻⡿⠿⣿⢿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣈⡄⠨⠄⠀⠿⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣆⣀⣀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⠛⠿⠿⣿⡿⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⠿⠀⢀⠀⠀⠀⠀⠂⠘⠿⠿⣿⣿⢿⠶⠎⠙⠿⠿⠹⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠭⠉⠋⠽⣶⡖⠒⠞⠠⡈⠀⠀⠀⠀⣀⡀⣀⣀⠐⠤⠤⠴⠲⠤⠄⠀⠠⠼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠔⠒⠒⠉⠉⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠚⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣍⡉⠉⠁⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣷⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣖⣛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⢀⣨⣿⣿⣿⣿⠀⠈⠉⢛⡿⠿⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢏⣿⣿⠟⣸⣿⣧⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⢻⣿⣿⣿⣿⡟⠁⣰⡿⣻⡿⣯⠉⠉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠠⢻⣿⣿⣿⢻⣿⣴⡿⢱⡟⣧⠸⡆⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣅⢨⣿⣿⣹⣾⣻⡿⠁⣿⠀⢹⡄⢻⡀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⠿⠭⣿⣿⣿⣿⡿⠁⠠⣿⠀⠈⢧⣤⠧⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⠃⢠⣿⣿⣿⡿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⢈⣿⣿⣿⡅⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠉⠉⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⣀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⠀⢀⣀⣀
⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠘⠟⠋⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⠀⠈⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⢉⠄⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠙⠂⠀⠀⠈⠉⠀⠠⠤⠼⠀⠀⠀⠀⠀⠀⡠⠂⠈⠤⠀⠂⠀⠀⠀⠀⢀⠄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠀⠐⠈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠽⠀⠀⠤⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠐
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠤⠃⠀⠀⠀⠀⠀⠀⠀⡆⢰⠀⢄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⣠⣤⡤⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠂⠀⠀⡐⢢⠀⠑⠁
⠀⠀⠀⠀⣚⠟⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠄⠁⡀⠀⣀⡏⠀⠀⠀⠀⠀⣠⠀⠀⡠⠀⡄⣰⣠⢂⠔⡀⡄⣠⢀⠆⣰⠀⠀⠀⢤⠀⠀⠀⠀⠀⠻⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠎⠂⠀⠀⠀⠀⠀⠓⠑⠑⠊⠑⠚⠂⠘⠐⠃⠈⠁⠁⠀⠉⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠁
⠀⠀⠀⠀⠀⣹⠟⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡠⣴⣿⡶
⠀⠀⠀⠀⠀⠌⠸⢷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠉⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠀⠀⠀⣤⣦⠀⠀⠀⡀⠀⠀⠀⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⠁⠀⠀⠀⢒⠀⠀⠉⠟⠃⠉⠈⠀⠛⠃⠌⠀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⢰⣿⠇⠈⠻⠛⠀⠀⠀⢀⠀⠀⠤⠀⠠⠀⠉⠉⠉⠉⠁⠈⠈⠥⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢣⢩⣬⡄⢘⠈⠑⠘⡁⢘⢓⠓⠃⠀⠀⠘⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠏⣥⣀⠠⣀⠀⣀⡂⣖⢒⡒⠁⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠂⠀⠀⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⡀
⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠀⠀⢀⣠⠔⠙⠓⠛⠀⠀⠀⠰⠅
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠄⠀⠀⠀⣀⣴⣋⠀⠈
⠀⠀⠀⠀⠀⠂⠈⠀⠀⠈⠁⠒⠀⢤⢀⢀⠀⠀⠀⠀⠀⣀⠄⠊⠁⠀⠀⠈⠀⠀⡠⢔⡾⠋⠁⡠⢔⡫
⠀⠀⠀⠀⠀⠀⡀⠄⠒⠤⢄⣀⠀⠀⠀⠀⠁⠉⠉⠋⡉⠀⠠⠀⠀⠀⣀⠠⠂⣩⠔⢁⡠⢒⠍⢚⠵⣺
⠀⠀⠀⠀⠀⠀⠀⠐⢠⣄⢀⢀⠉⠒⠠⠤⣀⡀⠀⠀⠀⠀⣀⡠⠔⢊⡠⠖⡁⢔⡪⠔⠉⢀⡤⠖⠋⠩
⠀⠀⠀⠀⠀⠀⠤⣀⣀⣀⠀⠈⠈⠙⠒⠒⠤⠤⣍⣑⣒⡋⢁⡠⢖⡡⣐⠥⠒⠁⣀⠴⠚⠉⠀⣠⡠⡇
⠀⠀⠀⠀⠀⠀⠗⠀⠒⠂⠈⠭⠅⣒⣀⠤⠄⣀⠀⠀⠈⢈⠤⣒⠅⣊⢄⣨⠵⠊⣁⣠⢤⡺⠟⣋⣶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠈⠩⠀⠚⠩⠭⠕⠊⣔⡯⠑⠉⢥⢴⣛⡽⠚⡹⢖⡯⠗⣻⠃
⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠁⢀⣨⠴⢞⠍⠀⣀⠥⠚⡡⠔⡋⢸⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢺⣷⡾⣫⠕⠋⠄⠒⠉⣠⡔⠬⠐⠁⢠⣻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠁⠐⠆⣭⠝⠊⠁⠂⢀⣠⠶⠛⠁⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠦⣄⣀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠄⠂⠀⢀⠤⠚⠉⡀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠢⠄⣀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠠⠄⠀⠈⠀⠠⣐⡼⠞⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠄⣰⠿⠭⠄⠀⠀⠀⠀⠒⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠵⠋⠀⠒⠒⠒⠒⠦⠄⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢠⡇⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⠄⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣄⡄⠀⠀⢀⠀⠀⠀⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⡀⠀⠠⠄⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣤⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⠤⠀⠀⠀⠀⠄⠂⠒⠂⠤⢄⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠔⠂⠉⠉⠡⠂⢀⠑⢄⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠐⠁⠈⠁⠙⡁⠀⠉⠀⠀⠀⠀⠀⠈⡄⠀⠑⠈⠎⠐
⠀⠀⠀⠀⠀⠀⠀⢨⢀⣀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠒⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⢠⠤⠠⠤⠌⡀⢰⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⠀⠀⠀⠀⠀⠐⡔⠈⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⢁⣀⣤⣤⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢸⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠞⠉⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢀⠚⡄⠀⠀⠀⠀⠀⡆⢠⠀⠔⠁⠌⠀⢀⡇⠇⠀⠀⣠⠴⠖⠒⠢⣄⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢁⠀⢀⠠⠠⡀⡇⠈⠁⠀⢂⠀⢀⠞⠁⠸⠀⠚⠁⢸⠆⠀⠀⠈⠳⡄⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠈⠀⡊⠀⠀⠸⡇⠀⠀⠀⠀⢄⡎⠀⠀⣴⡆⢠⠀⠘⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⢆⠀⣷⠀⠀⠀⠀⠰⠀⠀⠀⠀⡟⠀⠀⢰⠁⢱⠈⡐⡇⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠑⠾⠀⠀⠀⠠⠘⠓⠒⠁⠀⠇⠀⠀⣿⠀⠀⡆⢁⠓⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⡜⠀⠀⠀⠀⠀⠀⠘⡆⢸⠀⠀⠀⡏⠀⠀⠛⡀⣀⣁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠀⢸⠀⠀⢰⡇⠀⠀⠀⠑⠈⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠪⣁⣠⠇⠀⠀⠘⡄⠀⠘⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⢧⡀⠀⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠉⠓⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⢀⣀⣠⠴⠚⠁

⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠠⠤⠒⠈⠈⠀⠀⠰⠇⠠⠐⢁⠀⠀⠆⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠀⠀⠀⡰⠁⡀
⠀⠀⡠⠞⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠠⠀⠀⡠⠈⠑⠄⣀⠠⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣠⠀⠀⠀⡐⢊⡤⠈⠀⠀⢀⠄
⠐⠉⠀⠀⠀⢀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢈⠁⠎⠀⠀⡄⢂⠠⠋⠀⠀⢀⠔⠊
⠀⢀⣀⡀⠀⠀⠀⠀⣀⡐⢄⡠⠒⠀⠀⠀⠀⠀⠀⡄⠀⢀⠂⡀⠴⠗⠂⠂⡀⠀⠀⠀⠀⢀⣼⠘⠀⠀⠉⠀⠀⠀⠠⠒⢀⢀⣀⣀⡀
⠀⠈⠀⠈⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣴⠊⠘⠀⠂⠀⠀⠈⠀⠀⣀⠤⠋⡁⣀⠀⠀⠠⢂⠀⢰⣿⣿⡿⠹⣿⣿⡷
⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣶⠆⣄⢀⡄⠸⠀⡋⠀⠈⠉⠀⠒⠂⠀⠠⠴⠊⠁⡠⠚⠀⣿⡀⠀⠀⣿⠂⠈⠛⠋⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠐⠀⠀⠠⠀⠀⢈⠀⠀⠄⠀⠈⠁⠒⠀⠤⠀⠀⠀⠀⣠⠔⠋⠀⠀⣼⣿⣷⣶⣾⣿⣧⠀⠠⠀⠀⠀⠀⠠
⠀⣀⠀⠀⠨⢀⠀⠀⠀⢀⠃⠀⡄⠀⠀⠰⠀⠠⢀⠄⠀⢀⣀⠀⠄⠤⠄⠄⣀⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠏⠀⠀⢂⠀⠀⡐⠀⠃
⠀⡀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠈⠀⠀⠁⠐⠀⠀⠂
⠈⠸⣿⡿⠀⠀⠺⣿⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⡰⠀⢰⠀⠀⠀⠀⡀⠀⠀⣼⣿⣿⣿⣿⣿⡀⠀⡀
⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⠀⢄⠀⠀⠀⠀⢀⠀⠀⠀⢇⠀⠀⠆⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠛⠿⣿⣿⡿⠿⠇⠸⡀⠀⠀⠁⠀⠀⡸
⠀⡈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡀⠀⠀⠀⠐⠀⠈⠁⠎⠀⠀⠀⢀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠤⠀⠄
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠛⡀⠀⠀⠐⠀⠂
⠈⢀⠀⠀⠀⡇⠀⠀⠀⠐⠀⠁⠐⠂⠀⠒⠈⠠⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⡐⠀⠀⢂
⠀⠀⠈⠀⡈⠈⠀⠀⠀⣀⡀⠀⣴⣶⣆⠀⠀⠄⠀⠁⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠡⠀⠀⡜
⠀⡀⠀⠀⠀⢀⠑⠀⠻⣿⠿⠀⠈⠛⠁⠰⡁⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠢⠀⠂⠀⠀⠈⠀⠀⠒⠀⠐⠂⠀⠁⠀⠅⠀⡆⠀⠀⠀⠃
⠀⠑⠠⣀⠀⠙⠃⠠⡀⠀⠠⠄⠀⠀⠀⠐⠈⠂⢨⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠜
⠀⡄⠀⠈⠑⠠⠄⣀⠨⠀⠀⠀⣀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠐⠀⠀⠀⠐⠁⠀⢀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠐⢠
⢀⠈⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⡀⠀⠀⡄⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⢃⠀⠀⠀⢁⠀⠀⣀⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠆⠀⠀⠀⢀⠆
⠀⠀⠠⡀⠀⠀⠀⠀⡌⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠆⠀⠀⠈⣀⡀⠀⠤⠄⠀⠀⡤⠠⠀⠤⠀⠀⠀⠂⠀⠀⠀⡄
⠀⠀⠂⠈⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠀⠀⠈⠀⠀⠘⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠆
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠃⠘⠀⠀⠀⠀⠁⠠⠠⠄⠠⠂⠀⠀⠀⠑⠂⠀⠘⠁⠀⠒⠈⠁⠀⠀⠀⠁⠈⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠒⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢉⡀⢉⣉⣁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠞⡶⢄⡶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡤⢏⠉⣠⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢠⡤⢉⠤⡴⡩⠏⣀⠠⡾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡕⢠⠤⠤⢠⠄⢐⣈⠃⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⢀⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣤⣄⡈⠋⠴⠨⠛⠐⠒⠏⠠⣄⢎⡟⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡶⣧⡤⠃⡒⢠⠔⢲⣠⡦⠜⠒⡒⠲⠎⠁⠀⠀⠀⠀⠀⠀⠀⡖⠤⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡜⠁⠀⠀⠉⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣴⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣁⣀⣀⣀⣀⣀⣀⣀⣈⣉⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡿⢷⣄⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠛⠛⠻⠷⣾⣟⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢙⣷⡾⠟⠛⠋⠛⠛⠿⣶⣄
⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⢠⣿⠛⣷⡌⠻⣧⡀⠀⠀⠀⠀⣸⡏⠀⣰⡿⠋⠻⣆⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠘⣿⡀⠈⠻⣦⡀⣀⣠⣿⠁⢠⣿⠁⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠰⡿⠋⠀⠀⠀⠀⣿⡇⠀⠀⠈⢻⣾⣿⡇⢀⣸⣯⣤⣤⣴⠶⠾⠿⠇⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⢿⣿⠟⠛⠙⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣤⣤⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣶⣶⡶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⣠⠖⠛⠉⠉⠉⠙⠳⢤⡀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠉⠉⠙⠓⢦⣄⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⢉⠉⠛⠲⣄
⠀⠀⢠⡞⠁⠀⠁⠂⠀⠀⢈⠀⠀⠹⡄⠀⠀⠀⣴⠋⠀⠀⠀⣠⣖⣒⣖⣶⠙⣦⠀⠀⠀⢠⠏⠀⢰⠂⠈⠉⠉⠉⢹⡏⢳⡀
⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢻⠀⠀⢸⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠸⡇⠀⠀⡏⠀⠀⠸⣀⣀⣀⣀⣀⣸⠇⠀⣷
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡄⠀⣴⣶⣦⣿⣿⣿⣿⣿⠀⢠⡇⠀⠀⡇⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⢧⡀⣿⣿⣿⠈⠉⠉⠉⠉⢀⡼⠁⠀⠀⢻⡄⠀⣠⠞⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠘⠷⣄⡁⠀⠀⠀⢈⣠⡴⠋⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠙⢦⣋⡀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⣀⣤⠴⠶⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠴⠶⠦⣤⣀
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⢀⡾⢋⠀⠀⠀⢀⣠⣤⣽⢷⡀⠀⠀⠀⠀⣴⠋⠁⠄⠀⠠⡀⠀⠉⠳⣄
⠀⠀⣰⠃⠀⣶⣶⣶⠀⠀⠀⠀⠀⠈⢷⠀⠀⢠⡟⠀⣿⡇⠀⠈⣿⣿⣿⣿⠀⢻⡄⠀⠀⡾⠁⠀⡾⠀⠀⣰⡆⠀⠀⠀⠘⣇
⠀⠀⣿⠀⠀⠿⣿⠿⠀⠀⠀⣴⡆⠀⢸⠀⠀⢸⠁⠀⠙⠁⠀⠀⠈⠹⣿⠿⠀⠈⡇⠀⠀⡇⠀⠀⠁⠀⠀⢻⠀⠀⠀⠀⠀⣿
⠀⠀⢻⡀⠀⠀⠉⠀⠀⠀⠀⠙⠁⠀⣼⠀⠀⠸⡆⠀⠀⠀⠄⠀⠀⠀⠉⠀⠀⢸⠇⠀⠀⣧⠀⠀⠷⠶⢶⠞⡆⠀⠀⠀⢀⡟
⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠹⣆⠀⠓⠄⠄⠀⠀⠀⠀⣰⠏⠀⠀⠀⠘⢧⡀⠀⠶⠶⠶⢿⠶⠖⣠⡞⠁
⠀⠀⠀⠀⠈⠳⠦⣤⣤⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣤⣤⡤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣤⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⣠⠖⠛⠉⠉⠉⠙⠳⢤⡀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠉⠉⠉⠓⢦⣄⠀⠀⠀⠀⠀⢀⣤⠞⣋⣉⣉⣉⣛⡷⣤⡀
⠀⠀⢠⡞⠁⠸⠿⠿⠀⠀⠿⠿⠆⠹⣄⠀⠀⠀⡴⠋⠀⠀⣶⣾⣷⣶⠀⠀⠙⣦⠀⠀⠀⣠⠏⠀⠀⣿⣿⣿⣿⣿⡏⠈⢳⡀
⠀⠀⣾⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⠇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠸⡇⠀⠀⡏⠀⠀⠀⣿⣿⣿⣿⣿⡇⡀⠀⣷
⠀⠀⣿⠀⠀⠐⢷⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢀⡇⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⣿⡇⠇⠀⣿
⠀⠀⠸⣆⠀⠀⠈⣁⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⢧⡀⠀⠀⣿⣿⣿⣿⠀⠀⢀⡼⠁⠀⠀⢻⡄⠀⠀⣿⣿⣿⣿⣿⡇⠀⣰⠇
⠀⠀⠀⠘⠷⣄⡀⠀⠉⠉⢁⣠⡴⠋⠀⠀⠀⠀⠈⠳⢤⣀⠉⠉⠉⠉⣀⡤⠞⠁⠀⠀⠀⠀⠙⢦⣄⡙⠛⠛⠛⢛⣡⠾⠃
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠛⠛⠛⠛⠘⠛⠘⠙⠛⠛⠛⠛⠉⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣶⣦⣤⣄⣀⣀⣀⡀⣀⣀⣀⣤⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣄⢘⣿⣷⡍⠶⡌⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣀⡴⠊⠝⢊⡡⠔⠚⠉⠈⠙⢾⠿⣨⣟⢢⣌⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠴⠊⠁⠀⠀⠉⠁⠀⠀⠀⣠⣴⣀⣀⢻⣙⢫⣶⣯⠱⣦⡈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠛⠓⠦⣜⣫⣶⣮⠸⠿⣇⣼⡷⢀⣈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡠⣄⠙⣋⡺⣿⢗⣝⡛⣥⣮⡛⢡⣄⡉⠻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⡿⣗⣉⣋⣾⣿⢝⠻⢟⣦⣽⣿⣧⣮⣩⣾⣷⢏⡱⣶⡄⠙⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠋⠁⢀⣠⣼⣕⡿⠟⠋⠀⠀⢈⡿⠛⠁⠙⢧⠻⡿⣇⣜⡷⢆⡈⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠚⠋⢹⡿⠋⠀⠀⠀⠀⠒⠉⠀⠀⣠⠖⠛⠻⣆⣙⠿⣣⣮⣟⠗
⠀⠀⠀⠠⢄⣠⣤⠴⠶⠒⠛⠁⠀⢈⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣤⡿⡿⣟⣭⡛⢵⣶⣦
⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢛⠿⣿⣃⡽⢿⢟⣤⣍⠁
⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠟⠋⠉⢁⣤⣾⣮⡛⠋
⠀⢦⣤⡈⠳⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⣿⠇⣙⠿⠋
⠀⠀⠙⢿⣦⠈⢦⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣀⣴⣄⡻⣿⣷⣦⡀
⠀⠀⠀⠀⠹⣷⡄⠙⠲⠂⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠙⠿⢟⡁⠈⠻⠿⠋
⠀⠀⠀⠀⠀⠈⠳⣄⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠙⢿⠶
⠀⠀⠀⠀⠀⠀⠀⢈⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣉⣹⣉⣉⣉⡭⠿⢓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣤⣀⣀⡀⠀⠀⠀⠀⢠⠖⣚⣯⡥⠴⢒⣛⣿⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⣀⣠⠤⠭⠓⠀⠀⠀⢀⣉⠥⠴⠒⣋⡩⢤⡾⡌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣀⣠⠤⠖⠒⣉⣡⠤⠖⠊⠉⢀⡴⠋⡠⢯⠉⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⡴⡇⢸⣡⠤⠖⠚⠉⠁⠀⠀⠀⢀⡴⠋⡠⠊⠀⠈⢏⢱
⠀⠀⠀⣠⠔⠚⠉⠉⠉⠉⠉⠓⠢⣄⡴⢋⡰⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡠⠊⠀⠀⢀⡤⠾⡌⣏⠉⠉⠉⠓⠲⢄⡀
⠀⢠⠞⠁⣠⠔⣞⠉⣿⠉⢹⠶⡴⠋⡰⣎⠀⡇⢸⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠁⠀⢀⡴⠋⢀⣤⢳⠸⣽⡏⠙⡶⢤⡀⠙⢦
⢰⠃⢀⣞⠁⠀⠸⡄⢿⢠⡿⠊⡠⠺⡀⠘⣆⡇⢸⠀⠀⣀⣤⣴⠋⣠⠞⠁⠀⠀⢀⡞⠀⣰⠋⠀⠳⣇⢻⠀⡜⠁⠀⠙⣄⠀⢣
⡏⠀⣼⠀⠙⠲⢄⣳⠼⣏⣠⣾⡶⠯⠷⠒⠛⠋⠉⠉⢹⠁⡶⣌⡟⠁⠀⠀⠀⠀⢸⠀⢰⠋⠙⠒⠦⣽⡼⢿⡤⠔⠚⠉⢹⡄⠈
⡇⠀⣯⠉⠉⢉⡩⢷⣤⡿⣤⠤⠤⣤⣀⣀⣀⣀⣀⣀⣈⣷⢿⣜⢧⡄⠀⠀⠀⠀⢸⠀⢸⠒⠒⢋⡩⢿⢦⣼⠻⢍⡉⠉⢹⡇
⢹⡀⠘⣤⠔⠋⢠⠏⣧⠳⡈⠙⠢⣤⠇⠀⡞⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠘⡆⠈⢧⠚⠉⢠⠏⢸⠘⡄⠀⠈⠓⡞⠀⣸
⠀⠳⡀⠈⠢⣄⡞⠀⢸⠀⢹⣤⠔⠁⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠈⠳⢤⡃⠀⡾⠀⢹⣀⡠⠊⠀⡰⠃
⠀⠀⠈⠢⣄⡀⠉⠉⠛⠋⠉⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠉⠙⠛⠚⠋⠁⣀⡤⠚⠁

⠀⠀⠀⠀⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⢰⠀⠀⢠
⠀⠀⠀⣀⠀⢰⣏⡇⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⣴⠃⠀⡄⠀⠀⠈⠋⡄⠒⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠹⣿⡃⠛⠆⢠⠃⠀⠚⠀⠀⠀⣀
⠀⠀⠀⠠⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠒⠀⠀⠀⠀⠸⠿⠍⣓⠀⠀⠀⠰⠀⡀⠀⣨⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠲⠀⠘⠀⢎⠀⢀⠔
⠀⠀⠀⠀⠀⠓⠄⠀⣀⣠⠀⡀⠀⠀⠀⠀⠈⠁⠎⠀⠀⠀⠀⠀⣄⣁⣁⠈⠈⠉⠐⠳⠐⠁⠀⠁⠀⡀⠤⠀⠀⠀⠠⠀⠀⠠⠐⢀⠀⠀⠰⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠢⠤⠅⠠⠄⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠠⠴⠀⠠⠄⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠆⠐⠀⠠⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢤⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠤⠀⡄⠀⠀⠀⠀⠀⡰⠋⠁⣁⠀⡤⠉⢲⡀⠀⠀⠀⢀⡄⢀⠀⠀⠀⠀⠀⢀⣼⣿⠏⡴⡁⠀⠰⠀⠀⠀⠀⠀⠀⠔⠒
⠀⠀⠀⠀⡀⠀⢀⠀⠇⠀⢰⠀⠀⠀⡏⠀⢠⠇⠐⡇⠀⢨⠇⠀⡆⠀⠐⠀⡜⠀⢠⠀⠀⠖⠻⡿⢃⣼⣿⠏⠀⠀⠀⠀⠀⠲⠤⣄⡀⠀⠐⠄⠀⡀
⠀⠀⠀⠰⠁⠀⡸⠀⠇⠀⠸⠀⠀⠀⠐⠄⠁⠀⠀⠡⠀⠁⠀⠀⠀⠀⠸⠐⠁⠀⠘⠀⠀⠀⢐⠖⠚⡟⠉⠀⠀⠰⠀⢰⡥⠭⢿⠟⣘⣶⣄⠀⠛⢀
⠀⠀⢀⠀⠀⠐⠃⠀⠠⢤⠀⠀⠀⠀⠸⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⣠⠴⠟⠓⠚⠏⠟⠒⠂⠒
⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠀⠐⠊
⠀⠀⠐⠒⠐⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠐⠒⠒⠀⠈⠁⠉⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠀⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠌⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠜
⠀⠀⠀⠀⡆⠀⠀⠀⠸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⢀⠌
⠀⠀⠀⠘⠀⠀⢀⡀⠠⠀⠀⢨⠀⠀⠀⠂⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠒⠂⠀⠀⠀⢀⠀⠀⠀⠀⢠⢠⠀⠀⠀⠀⠋⠀⢐⠁⢀⢠
⠀⠀⠀⢠⣴⣦⡸⠀⠸⡀⢀⠜⠀⠀⢄⠀⠈⠒⠶⠒⠒⠒⠀⣀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⡤⡴⢾⠤⠤⠠⠤⢜⣾⠦⠄⠀⣁⠂⠀⠀⠀⠀⠙
⠀⠀⡀⠀⣿⠟⠗⠀⢠⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⣀⢈⢉⣀⡀⠀⠠⢤⠀⠍⢁⢐⣒⡀
⠀⠀⠁⠁⡏⢶⢷⣼⠟⠉⠌⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠈⠉⠀⢀⠀⠀⠀⠱⠒⠐⢀⡂⠀⣀⣀⣀⢀⣀⢈⣂⢐⣒⣘
⠀⠀⠰⢡⡁⠀⠈⣿⡇⠀⠈⠀⠀⠀⠀⡀⢤⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⠀⠡⡀⠀⠹⢌⣤⣑⡀⢃⠀⠒⡂⢢⢀⡒⣒⢒⠂⠀⠀⢀⡀⢀
⠀⠀⠀⠐⠃⠀⠀⣿⣷⠀⠐⠀⠀⠙⠌⠁⠠⠄⢀⠀⠀⠀⠀⢀⠃⠀⡄⠈⡀⢈⠁⠀⠀⠭⠤⡤⡀⢐⣀⠤⠦⣐⢰⣒⣒⠛⠀⠀⠊⠀⢀⡏⠀⢸
⠀⠀⠠⠀⠈⠀⠀⣿⣿⠀⠀⡀⠀⠂⠀⠃⡀⢖⠦⢀⠀⠀⠀⠀⣀⣠⠀⠀⣿⣿⢸⠀⠀⠀⠉⠏⠉⠨⠀⠀⠀⠸⢘⠒⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡷⣸⣿⡄⢰⠋⠉⠰⠀⠀⠀⠀⠀⠠⠆⠁⢁
⠀⠀⠀⠀⠀⠀⠀⠜⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠈⡛⠀⠃⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣂⣰⠤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⢠⠗⠈⠉⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⢀⣀⣀⠀⠀⠤⠤⠤⠤⠀⠐⠒⠲⢲⡀⢀⠀⠄⠂⠀⢸⠊⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⠀⠀⠀⠀⠀⠸⡀⣷⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⡜
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠐⠐⠈⠀⠀⠀⠙⢦⣀⡠⠤⠒⠁⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⡆⠀⠀⠀⠀⣀⢀⠀⣀⠀⠀⠀⠀⠀⠀⢏⡇⠀⠊⠁⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠤⠤⠖⠚⠉⠙⡄
⠀⠀⠀⢡⠀⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⢸⢹⠀⠸⡏⠙⠒⠦⢌⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡆⢲⡒⠒⠀⠀⠠⣭⣉⠓⠢⢤⡠⠤⠤⠔⠒⠊⢉⠏⠸⡀
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢇⢬⡡⠀⠀⠀⡇⡇⠈⠙⠢⢄⣀⠀⠀⠀⠀⡴⠁⠀⠀⢣
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠐⠂⠀⠀⠀⠳⠃⠀⠀⠀⠀⠈⠉⠓⠦⠊⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠸⠄⣠⣤⠄⡀⠒⠒⠒⢒⣒⡒⠒⠒⠒⠒⡟⠒⠒⠒⠒⠒⠛⢀⠐⢢⣤⡄⠀⠠⡄⠈⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠐⠒⠚⠓⠛⠛⠒⠓⠓⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠓⠒⠛⠒⠚⠛⠓⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠁⠀⢹⣿⣿⡟⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⣤⡴⠋⠉⠘⢈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠅⠀⠀⠀⠀⣿⠉⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢃⡀⠀⠀⠸⠁⢀⠔⠀⣰⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠘⢓⠖⠁⢀⣴⣿⣻⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣰⡿⠛⠉⠀⠀⠙⢷⣼⣦
⠀⠀⠀⠀⢠⣾⣿⣿⣷⣦⣲⣾⣿⣯⣷⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠏⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣽⡄⠀⠀⠈⣓⠂⠁⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⢠⡀⣿⣿⣿⡆
⠀⠀⠀⠀⡏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣠⠏⢀⠀⠀⠱⠀⢀⡄⣠⣀⡀⠀⠀⠈⣿⡿⠀⠀⠀⠀⠀⠀⣿⡇⡟⣿⣿⣇
⠀⠀⠀⠀⢷⣶⣶⣶⣶⣾⣿⣿⣿⣿⡿⣿⣿⣿⡻⣮⣿⣶⡣⠄⣤⠒⠺⡙⠈⠠⠴⠤⣶⡄⠹⡇⠀⠀⠀⠀⠀⣰⡟⣹⢳⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡵⠀⡇⠀⠀⠀⠀⠒⠤⣄⣘⡆⣰⠁⠀⠀⠀⠀⢠⠋⣰⢯⣿⣿⣿⣿
⠀⠀⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡆⠃⢄⣀⠀⠀⠀⠀⠀⠈⠁⢝⢦⡑⠀⠀⣠⣿⣞⣱⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⡟⠉⠁⠀⠀⠈⠙⢦⡀⠀⠀⠀⢰⠌⠧⠁⠀⣴⣿⣿⣿⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⢀⡜⣿⣿⣿⣿⠟⠿⡟⠈⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢠⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡶⣶⣤⣄
⠀⠀⠀⠀⠀⢶⡦⢀⣀⣀⡀⠀⠀⠀⠠⠴⠋⢈⡉⣻⣷⠀⠀⠀⠀⠈⠿⢇⣤⣤⣤⠀⠀⠀⠄⠐⠋⢀⡤⣈⣿⠇
⠀⠀⠀⠀⠀⠀⣰⠿⠛⠙⢻⣦⠀⣀⠀⠐⢒⡿⣾⡋⢀⣀⡀⣀⣀⣀⣠⣟⣋⡉⢉⡟⠀⡒⠒⢢⣉⣹⠻⣯⣄⠀⠠⡄
⠀⠀⠀⣠⠠⠾⠿⠞⢉⡽⠛⠀⢴⣶⡆⢀⣿⣿⡇⣷⣬⣿⣿⢹⣹⣿⣛⠛⠉⠴⠛⢁⣴⣄⢀⠺⠛⠛⠒⠿⡈⠁⠀⢸
⠀⠀⣠⠴⠶⢿⣃⣴⣶⠀⣶⡷⠶⢭⣿⡿⠿⠛⠛⢿⡻⢿⣧⣿⣿⣿⣿⣴⣿⡇⠐⢿⣿⠿⠏⢀⡤⠶⠶⢶⡌⣷⠶⡅
⠀⢰⠃⠀⠀⠀⠙⡆⠀⢹⢇⠁⣠⡾⠋⣇⢀⣀⠀⣡⣿⠀⡞⠀⠀⠀⠀⠘⡆⠀⢄⠀⣀⠶⠛⢀⣇⡤⢖⣀⣾⠇
⠀⠸⡀⠀⠀⠀⢀⠇⠀⠘⢧⠚⠡⠶⣶⡿⣧⣴⡿⠟⠃⠀⠹⣄⠀⠀⠀⠜⠁⠀⠈⣂⣁⡚⢹⡿⠛⣶⣿⡟⢉⣀⣀⣀⡀
⠀⠀⠉⠲⠶⠂⠀⠀⢠⡴⠚⠛⠓⢶⡏⠀⠸⣿⣓⠶⡚⠋⠛⠻⢯⡉⠀⠀⠀⠴⠋⠉⠈⠉⠻⡅⠀⠸⣿⡽⠻⣅⠀⠈⠙⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠹⡆⠀⠙⣏⠀⠈⠂⠀⠀⠀⣧⠀⠀⢸⠃⠀⠀⠀⠀⠀⢸⡄⠀⢹⡇⠀⠀⠁⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠃⠀⠀⠀⠀⠀⢀⠏⠀⠀⠸⣆⠀⠀⠀⠀⠀⡸⠁⠀⠀⠣⡀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⠄⠊⠀⠀⠀⠀⠑⠤⣤⡤⠴⠋⠀⠀⠀⠀⠈⠳⠦⠤⠖⠈⠀⠀⠀⠀⠀⠈⠒⠖⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢰⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⠤⢦⡄
⠀⠀⠀⠀⠈⢹⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢥⠤⠼⠴⡅⠀⠀⠀⢰⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢀⡆⡈⢘⢀⡄⠀⠀⠀⠀⠒⠒⠒⠒⠀⠀⠀⠀⠀⠐⠐⠀⠀⠂⠃⠀⠀⠀⢨⠁⠂⠀⠀⠀⠅⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⢇⣈⣈⢈⢈⡨⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⠠⣀⠀⠀⠀⢠⠐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠖⠂⠒⢄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⡇⠀⠀⠀⡈⡷⠂⠀⠂⠀⠀⠐⠀⠀⢉
⠀⠀⠀⠀⢠⡀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈
⠀⠀⠀⠀⡀⢈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⠁⠀⠀⠀⠀⠀⠈⢉⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢀⣰⢼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣄⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠈⠉⠘⠖⠀⣤⠸⣿⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠄
⠀⠀⠀⡄⠌⠇⣈⡜⠄⡘⠁⠀⠀⣿⡏⠉⡅⠀⣟⡽⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⣴⡉⢳⠀⠀⠀⠀⠀⠂
⠀⠀⠀⣏⢨⣿⠾⣢⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⣻⣸⢻⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣯⣿⣿⡻⡆⠀⠀⢰⠤⣀
⠀⠀⠘⠛⠺⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⢀⣤⣤⣦⠀⠀⠀⣸⡟⠀⠀⠀⢉⣿⠀⠀⠈⠃⠻⣽⡇⠀⠀⠀⣀⣀⡀
⠀⠀⠀⢀⠠⠀⠀⠀⡤⠄⣀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⢈⠥⠤⠤⠀⠀⠀⢹⠁⠀⠀⠀⠈⡍⠀⠀⠀⠀⠀⠀⢡⢀⣽⣾⣿⡿⠗
⠀⠀⠀⠀⠀⠈⠀⢠⡛⠱⡎⠀⠀⠀⠘⠓⠓⠋⠀⠀⠀⠈⠓⠓⠻⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠺⠦⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⣀⡀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⣶⣿⣯⣵⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠒⠒⣄⣀⣠⠒⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⡀⡞⠁⠄⡈⢣⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⡀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡥⠥⠤⠤⢤⣤⣤⣤⣤⣤⣤⠤⢤⣵⡞⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢵⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠘⣧⠐⠀⠀⠀⠀⠈⠐⠂⢄⣄
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠨⢷⡀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣇⠀⢹⡄⢣⠀⠀⣠⠞⠁⠀⠀⠂⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣤⣤⣄⣀⣀⠐⢾⠀⠀⣿⡼⣤⠞⠁⠀⠀⠀⣨⠀⠀⠀⠀⠀⠙⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠉⢉⣙⡛⠛⣺⠛⢿⡾⣿⡛⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠻⠁⠂⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠏⠀⠘⠳⡧⠝⠁⠀⠀⠀⠀⢹⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⢹⣦⣄⣀⡀⠀⣀⣀⣠⣶⣯⣀⣀⣀⠀⠀⠈⢁⠀⠀⣀⡀⢀⣀⣀⠀⠈⣿⣴⣢⠤⠀⠀⠤⠤⣀⣶⠿⡁
⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⠟⠛⠛⠛⠟⠛⠛⠏⠛⠁⠐⠒⠐⠀⡂⠀⠘⠷⢏⡞⠉⠉⡙⢃⠙⠺⠿⠟⠛⠿⠟⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⢠⢀⠄⠖
⠀⠀⢀⣀⣀⡀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠂
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡠⠤⠶⠤
⠀⠀⠀⠀⡞⠉⠉⢁⠀⠀⠀⠀⠀⠀⠠⠆⠀⢀⠀⠀⠃
⠀⠀⠀⢰⡋⠀⠀⢹⠄⠀⠀⠠⠀⠠⠁⠠⠄⢠⠠⢤⠀⠢⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠈⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠂⠂⠀⠀⠐⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣠
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢽⠃⠀⢚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢰⡤
⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠠⠠⠌
⠀⠀⠠⡤⠄⣀⣀⣀⠒⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⢀⡠⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⣀⣠⣤⣶⡆
⠀⠀⠀⠀⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠘⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠻⠁⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡛⠉⠉⣿⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⣿⣿⣿⣿⣿⡙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⢿⡿⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣀⣀⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠽⠛⠉⣿⠁⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣹⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⢿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣷⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢳⣰⡏⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠋⠄⠸⠿⠿⠿⠛⠙⠛⠛⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣆⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠘⠿⡃⢸⣿⣿⣿⠿⠿⠿⠿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡈⠈⣤⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢻⣴⡇⢠⣤⣤⣤⣤⣤⣤⣤⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠂⠁⢂⠘⠛⠛⠛⠉⠉⠉⠉⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢧⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢜⣛⠅⢸⣻⣿⣿⠛⠛⠛⠛⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⠊⠢⠘⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⢀⣀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢸⠾⠿⠿⠿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡞⠐⣛⣿⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠊⠱
⠀⠀⠠⠘⢄⠀⠼⠀⠀⢾⡄⠀⠀⠀⢸⣿⣷⣞⣽⠇⠀⠀⠀⠀⠀⣀⣀⡂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⣼⣇⠀⠀⠒⠔⠂⠸⢣⠀⠀⠀⠈⠳⡭⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⢁
⠀⠀⠙⡟⢀⠀⠀⠀⡠⠇⠈⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢸⠄⡅⠒⠊⡠⠃⠀⠀⠀⠴⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠛⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣴⣶⣶⣦⣤⡀⠀⠀⠈⠂⢄⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡞⠙⣴⣿⠧⠤⢄⠉⠻⣷⡀⠀⠀⠀⠜⠻⣟⠒⠆⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢧⣁⣿⠁⠀⠀⠀⢣⠀⠘⠗⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠐⣦⡐⢺⣷⡞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣀⡄
⠀⠀⠀⠀⠄⠠⠄⠀⡀⠀⠔⡲⠀⠈⠀⠀⠀⠀⠈⣿⢾⣿⣽⡈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠋⠀⠁⠁⠹⠂
⠀⠀⠀⡀⢄⢐⣠⠤⢐⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣈⣝⠿⣟⠣⠤⠄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⢠⢤⠀⠀⠀⠃⠀⣦
⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⢧⣀⣀⢀⠆⠀⠀⠀⠀⠀⠞⠃⠀⠀⠄⠀⠀⠀⠀⠀⢘⠇⠚⠀⠀⣀⠀⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⢀⠀⠀⠈⠀⠀⠾⠰⠄⠀⠘⠁
⠀⠀⠀⠀⣄⠀⢰⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁
⠀⠀⢎⠁⠆⠀⢀⠀⠨⠔⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢸⠀⠀⠄⢠⠉⢃⠁⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣞⠇⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⢀⣈⠆
⠀⠘⠀⠠⠤⠬⠽⠥⠤⡼⠄⠀⠀⠀⠀⠀⠀⠀⠠⢤⣆⠀⠀⠀⢀⡄⣴⡄⠀⠀⠈⠉⠴⠋⠀⠀⣄⠀⠀⠀⠀⢀⠠⢀⣀⠠⢁
⠀⠀⠀⠠⠂⣶⡴⠦⣄⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠈⠀⣤⠀⠀⣄⠀⠀⠰⡶⠎⠀⠀⠀⢠⢡⣾⡿⠿⣶⣆⠑
⠀⠀⢢⠀⠀⠜⣦⡴⠃⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣅⠀⠀⠀⠀⠸⠘⡿⣧⣀⣼⣟⠀⡦
⠀⠀⠀⠁⠀⠀⢈⠐⠓⠒⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠁⢉⠛⠍⢛⠡⡲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄⠁⠀⠀⠀⠀⠀⠀⠐⠄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⡷⠀⠀⠀⠀⡈⠄⠴⠦⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⠀⣁⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣇⢀⡐⠡⠄⠒⡸⢏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡘⠓⢄⠀⠠⠀⣠⠞⠀⠀⠐⢄⠀⠀⠀⠈⣽⠃⠀⠀⠀⠀⢀⢿
⠀⠀⠀⠠⠂⠀⠀⡼⠁⠑⡇⣇⢀⠎⠀⠈⢃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠨⡇⡄⠜⠁⠀⠀⠀⠀⠀⠇⠀⢀⡼⠁⠙⡄⠰⣠⠔⠁⠀⠂⠀⠈⠂
⠀⠀⠐⠀⠀⠀⠼⠁⠀⠀⢴⡤⠃⠀⠀⠀⡄⢦⠀⠀⠀⠃⠀⠀⠀⠀⠀⠾⠀⠀⠀⢐⣧⠟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠁⠀⠀⡇⣴⠛⡄⠀⠀⡈
⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠎⠑⠒⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠉⠒⠁⠀⠀⠀⠀⠀⢀⠜⠀⡀⠀⢀⣰⠃⠁⠈⠁⠀⠀⠀⡀⠔⠁
⠀⠀⠀⢀⣂⣤⣠⣤⣖⡉⠠⠤⠤⠤⠤⠤⠠⠀⠀⠊⠀⠀⠀⠀⠲⠴⠶⢒⣚⡉⠀⠀⠤⠤⠤⠀⠀⠒⠐⠊⡀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠀⠈⠈⠁






⣷⣶⡶⠶⢾⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢪⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠠⢤⣀⠀⠀⠀⠀⠀⡠⠤⣄⠾⣶⠄⠠⣤⣀⡀
⠀⠀⡠⢾⡾⠿⣿⡦⣀⠀⠀⠀⠀⠀⠀⢠⡾⠉⢀⣀⠀⠀⠀⣀⠘⣷⡀⠀⠀⠀⢁⠀⠙⢫⠑⣣⡼⠶⢳⣤
⠀⢘⡜⠁⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⢸⡽⣎⠁⠀⠀⠀⠀⠀⢱⡏⠃⠀⠀⠀⠀⠑⠶⠋⠐⣇⠀⠀⠀⣘⠇
⠀⣼⠁⠀⠀⠀⠀⢀⡘⣷⠀⠀⠀⠀⠀⠈⢣⡏⡗⢢⠀⠠⣤⠚⣇⠝⠀⠀⠀⠀⠀⡠⠄⠀⠀⠈⠉⠉⠉⠁
⢰⠡⠆⠀⠀⠀⠀⠀⠁⠘⡆⠀⠀⠀⠀⠀⠀⠈⠓⠺⡳⣦⠿⠓⠁⠀⠀⠀⠀⠀⠀⠅⢠⠇
⠘⢦⣀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣹⠀⠀⠀⠀⠀⢸⠋⢹⠀⢼⣁
⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⡄⠀⠀⠀⠀⠀⠳⡌⢰⠛⠃⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠄⠀⠀⠀⠀⠀⠀⢸⣶⣶⡇⠀⠀⠀⠀⠔⠲⣿⡘⠢⠤⠔
⠀⠀⠀⠀⠀⢀⢴⢒⡳⢿⣶⡿⢖⣒⡲⡀⠀⠀⠀⣀⣀⣀⣠⠀⠀⠀⠀⣀⠀⣰⠇⠀⠀⠀⠀⡤⠀⠀⠠⡄
⠀⠀⠀⠀⡠⢃⠎⠬⣥⡯⠭⠽⣬⠥⠑⡱⡀⠀⠀⠏⠉⠉⠙⡄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡿⠤⡠⢤⠄
⠀⠀⠀⠘⡍⠉⠀⠒⠒⠒⠒⠒⠒⠒⠒⠓⡇⠀⢰⠛⠛⠛⠛⢳⠀⠀⣼⣿⡧⠀⠀⠀⠀⠀⠀⠠⢀⢀⢰
⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠘⢤⣶⣶⣶⠞⠀⠀⡿⠿⠷⢀⠀⠀⠀⠀⠀⢀⢀⢀⢰
⠀⠀⠀⠀⠀⢇⣀⣀⣀⣀⣀⣀⣀⣀⡰⠀⠀⠀⠀⠈⢢⡤⠊⠀⢠⢊⠂⠉⠉⢢⢱⠀⠀⠀⢀⣆⣀⣁⣰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⡀⠀⠀⣸⣻⠃⠀⠀⣼⡿⠛⠛⡻⣿⡀
⢰⢫⠝⢋⠳⣶⡲⡖⢭⢉⡐⠎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠥⠤⠼⠇⠁⠀⠀⢸⡟⠘⠶⠾⠋⢸⣿
⠸⣄⠖⢠⠌⣽⠾⣣⣶⢠⠁⣃⠇⠀⠀⠀⣠⠤⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢮⡄⠀⠀⢴⣾⠁
⠀⠻⣴⠖⢾⠎⠀⠈⠺⣱⡞⠋⠀⢀⡴⣫⣒⠟⠁⠀⠀⢀⣴⠊⢲⢃⠀⣺⡊⢦⡀⠀⠀⠀⠰⠝⠋⠙⢹⠎
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡰⡫⠊⠘⡜⠀⠀⣀⢀⣝⣁⣀⠈⠁⠀⠉⣁⣀⣙⣂⡀⠀⠀⠐⠐⠒⢸
⠀⠀⢀⠀⠄⠒⠈⣧⠀⠀⣠⣪⠞⠓⠢⡀⡇⠀⡶⢻⣿⣿⣿⣿⣿⣄⣼⣷⣿⣿⣿⣶⡽⡆⠀⠠⠴⠢⢸
⣤⣤⣼⣤⣤⣤⣤⡼⠷⣪⠗⠁⠀⠀⠀⢣⡇⠀⠉⠻⡻⢿⣿⣿⣿⡤⢼⢿⣿⣿⡿⢟⠝⠁⠀⢀⠠⢄⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⡄⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣠⡀⢧⡤⠒⠉⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢳⣀⡠⠔⠒⠒⢦⡀⠀⠀⠀⢸
⠀⠀⢀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢙⣦⡀⠀⠸⡤⠤⣤⣀⡀
⠀⡔⠃⠓⣠⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⢠⠔⠂⠀⠒⠢⡀⢀⠤⠐⠒⠀⠐⢢⠔⢋⣠⠽⠆⠀⠀⠀⠀⢀⣨⡆
⠀⠈⠓⢋⠠⠒⠢⣠⠖⠲⠀⠀⠀⠀⠀⠙⢆⠀⠀⣠⡀⡘⢁⠀⠀⠀⢀⡴⠇⢠⡏⣄⢤⠤⠤⠶⠾⢭⣁⣀⣀⠀⠀⠐⠂⠤⢄⣀
⠀⡠⠀⠁⢔⠈⠉⠒⠃⠐⣆⠀⠒⠒⠒⠒⠒⠛⠓⡋⠉⠈⠛⠃⠀⠒⠁⡶⠀⠀⠘⣡⠋⠀⢀⠴⢄⠀⠀⠈⠉⠉⠙⢲⠆⠀⠀⢈⣱
⠈⠁⠒⠂⠀⢬⠐⣠⠀⠀⠀⠙⠒⢤⡤⠤⠄⠒⠉⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀⠎⠉⠈⠒⠚⠁⡠⣈⢢⠀⣴⠀⠀⡰⠃⠀⠀⣠⡞⠁
⠀⠀⠤⣀⣉⡐⠮⢀⠀⠀⠡⠀⠀⠀⠉⠒⢤⣀⠀⠀⣀⣀⠤⠔⠊⠀⠀⠀⣸⠖⢤⣀⣀⠤⠊⠀⠈⢦⣩⠞⢢⠎⠀⠀⢀⣼⠋
⠀⠀⠀⣀⡤⢄⡋⠔⠁⢔⡩⡹⠦⣄⠀⠘⣿⣧⣌⠉⡰⠒⡶⠠⠤⣤⠤⠊⠀⣠⠀⢀⡀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⣠⡿⠁
⣤⠊⠉⠀⢾⡁⠀⠀⠀⣜⡩⢔⢀⠦⢒⠥⠊⠉⠁⠛⢁⠈⠲⢶⣉⠀⠀⢀⣼⡟⠳⠭⣉⠒⢄⠀⠀⠀⡔⠁⠀⠀⣜⠟
⠀⠈⠉⠐⢒⢤⣀⡀⠂⠉⢠⠸⠄⡎⢠⢲⣊⣍⠦⡀⢀⠠⢚⡿⠟⠻⠶⠛⠛⠤⢀⣀⠀⠈⠈⠓⡀⠜⠀⠀⢀⣾⠎
⣴⠦⣒⠪⢽⣼⣶⣗⣦⣅⠂⠝⡒⠁⠈⡭⡌⡗⠂⢋⠅⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡉⠒⢢⣜⣊⠀⠀⠀⢼⡎
⠀⠉⠂⠍⡒⠭⡛⠿⣿⣽⡯⢶⣦⣈⡐⠧⠍⠴⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠵⣀⠀⡿⠈⠉⠓⠺⠞
⠀⠀⠀⠀⠀⠑⠢⢕⡢⢍⠛⢽⡯⢷⠷⣒⣄⣀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠋⢑⠢⣀⠀⣀⣤⢔⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢍⡲⢌⠛⠉⢋⠉⣤⠶⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣽⡪⠔⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣶⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠐⠋⠀⠀⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⠉⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠀⠀⠀⠀⣀⡀⠀⠐⠁⣀⣈⡠⡤⠶⠥⠚⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢉⣹⣋⣀⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢰⡏⡠⠊⠉⠀⡼⠁⠀⢈⠆⡷⠖⠒⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠧⡠⢤⠞⠙⠓⠒⠛⠚⠧⢤⡀⠒⠠⠀⠒⠠⡁⢶⣀⡂⠤⠬⠍⢰⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠒⢏⣀⡀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⣄⢀⠀⠀⡀⠍⠀⠀⡀⠀⠀⣭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⠀⠀⠀⠰⠁⠀⠀⠀⠃⠀⠉⣹⡖⢒⡒⢠⣖⢚⡛⠲⠦⢄⣂⢭⣀⣒⠢⠭⡅⠹⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠤⣀⠀⠀⠀⠀⠀⠀⢰⠦⠬⠃⠀⢀⠇⠀⠀⠀⠈⠀⢀⡴⢉⠁⣿⡏⠹⠼⠁⢹⣶⣤⣤⡈⠁⠀⠀⠀⠀⠈⡦⠤⠄⣀⡀
⢹⡿⣭⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠒⢢⣤⠀⠀⠈⠒⠒⠣⢄⡜⠀⠀⠀⠀⡷⠖⠉⠀⢸⠀⣿⡇⠀⠀⠀⣸⣿⠀⢸⡿⠀⠀⠀⣤⣀⠀⠇⠀⠀⠀⠙⡇
⠈⣿⠷⣿⣷⣦⢄⡀⣀⣀⣠⢤⣴⠶⢮⣛⠯⣻⠆⠀⠀⠀⠀⠀⢰⠁⢀⠠⡴⠶⠁⠀⠀⢠⡎⢸⣿⣧⣤⣶⣶⣿⣿⠀⣼⠇⡄⢸⠙⠛⠈⣠⠀⠀⠀⠀⢀⠁
⠀⢻⢔⠽⣿⣝⠑⢫⣉⡢⠼⠓⠂⠉⠀⠀⠀⢘⡇⠀⠀⠀⠀⢀⠃⠀⢀⠜⠁⠀⠀⠀⠶⣡⠁⣾⣿⣿⣿⣿⣿⣿⣿⢀⣿⢠⢠⠺⡄⠀⠀⢙⣤⠀⠀⠀⡜
⠀⢸⡗⠦⣦⢝⣳⠜⢢⡄⠀⠠⢄⡀⠠⠤⣀⣻⠀⠀⠀⢀⣀⡎⢀⠔⠁⠀⠀⠀⠀⠀⣠⡞⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⠆⡌⠀⠓⢒⣋⡅⠀⠀⠀⢠⠃
⠀⠀⣇⡈⠀⠝⢿⣛⡴⢶⠛⠻⢟⣛⠛⠋⢭⡿⠀⠀⠀⢹⠟⠴⣿⠄⠀⠀⠀⠀⠘⠊⣰⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⣇⣀⣀⣈⡅⢿⠀⠀⣠⠃
⠀⠀⣯⢻⢮⣔⣽⣯⠑⠒⠛⠉⠀⠀⠈⠉⢻⡇⠀⢀⠤⢿⠂⢴⠁⢀⡀⠀⠀⠀⠀⢠⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡷⠛⠁
⠀⠀⣟⠡⡳⢊⣛⡲⠤⠄⠒⠢⠤⠬⣤⣀⣿⡇⢀⡟⡧⡇⠀⣿⠀⡸⠀⠉⠒⠂⠤⠧⢈⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⣉⣉⠁⠈⠁
⠀⢈⡷⣮⣮⢥⡿⠿⠛⠛⡛⠛⠒⠒⠶⠴⣿⠀⡸⣤⡽⣤⡤⢭⡶⠥⠤⠤⠔⠊⠙⢦⣀⠙⠶⢦⣬⣉⣙⡛⣿⡿⠿⠾⢄⠀⡠⠊⠀⠀⠉⠒⠠⠄⣀
⠀⢸⢟⠗⡻⣷⠮⣍⣓⠒⠤⠉⠉⣉⣈⠀⣿⡀⠁⣈⣵⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣲⣆⡀⢋⠉⠁⠀⠀⠀⠀⠀⠫⡀⠀⢀⡀⣀⠔⠓⠂⠬⣀
⠀⣿⡭⡫⢺⠶⢿⡶⠾⠟⠛⠓⣂⣀⠌⠭⢿⣇⠼⠿⣦⣞⠳⣄⣀⣀⣀⡤⠤⠴⠂⣺⡋⠠⢚⡅⠈⠉⢣⡀⠀⠀⠀⠀⠀⠀⠙⢶⡁⠀⠉⠑⠒⠦⠤⣄⣉⠒⢠
⠀⠀⠀⠀⠻⠛⠲⠜⠛⢛⣛⡉⠥⠖⠓⠚⠋⠉⠑⢤⡀⠙⠯⣢⣄⣉⣑⣦⣤⣀⡴⣍⠂⠉⠉⠉⢁⠟⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⣠⡚⠕⠊
⠀⠀⠀⠀⠀⠀⠈⢫⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠉⠁⠀⠀⠀⠀⠀⣉⡵⢂⡴⠁⠀⠀⠰⠀⠑⢦⣀⣀⣠⡤⠀⠂⠂⠉⡀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣀⠀⠀⠀⣀⣀⡠⠴⢒⠩⠒⠙⠢⣀⣠⣤⠴⢖⡒⠉⢀⠔⠉⠉⠙⠲⣖⠃⠀⠀⢀⡨⣖⠉⠈⠁⠐⠛⠁⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁⠙⢏⠉⢉⡡⠐⠛⠀⡀⠀⠀⠀⠈⢁⡠⠔⠚⠉⠛⠁⠀⠀⠀⣠⠊⠈⠲⡤⠚⠁⠀⠀⠈⣁⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠳⣤⠔⠊⠉⠁⠒⠒⠤⠄⣀⠀⠀⡔⠣⡀⠀⠀⢀⣀⠠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠙⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀
⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡷⠀⢴⣶⡶⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠁⠄⡀⠀⠀⠀⠀⠀⠔⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠄⠀⠀⠠⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠤⠒⠉⡠⠃⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⢙⠀⠀⢀
⠀⠀⠀⠀⠓⠆⠀⠀⠈⠉⠋⠉⢀⣀⡀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢉⡀⠠⠐⠈⠀⠀⠀⠀⠀⡠⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠈⠉⠰⠀⠀⡤⠄⡀⠀⠀⠀⠀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⡀
⠀⠀⠀⠠⠀⢤⢊⠃⠀⠀⠙⠁⠀⠡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠒⠚⠀⠀⠀⠈⠀⠀⠀⠀⠀⠇⠀⠇⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠘⠧
⠀⠀⠀⠀⠀⠀⣠⣤⣴⠎⢡⡂⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠂⢠⠀⠀⠂⠀⠀⠆⠀⠀⠀⠒⠀⠀⠀⡔⠲⡀⠈⠈
⠀⠀⠀⠀⢀⢞⣿⠋⠀⠐⠈⣷⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠘⣛⠄⠀⠀⢀⢰⡿⠀⠀⠀⠀⠀⠈⣈⠀⢀⠉⢁⡀⠀⢀⡀⢀⠀⣠⡀⣀⡁⠩⠀⣀⢀⡀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠒⠂
⠀⠀⠀⠀⠈⡁⠈⠐⢀⠶⠺⠁⠀⠀⠀⠀⠀⣆⢼⡠⡁⠰⡃⢠⣏⠜⡗⢻⠞⣡⠖⠹⠀⠣⠸⠃⢌⠁⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠶⠆⠀⡀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠎⠀⠀⠀⠀⠡⠀⠁
⠀⠀⠀⠀⠀⠀⢻⡾⠷⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⣶⣶⡤
⠀⠀⠀⠀⠀⠀⡙⠡⣤⣄⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠉⠛⠛⠃
⠀⠀⠀⠀⢀⠄⡄⠈⠉⢿⣧⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠐⠦⡀
⠀⠀⠀⠀⠀⠁⡆⠀⠀⢸⣿⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡇⣀⡀⣀⡀⣷⣿⢒⡂⢀⡀⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⢘⠠⠄⠭⠈⠚⠃⠀⠀⠀⠀⡙⢙⠒⠀⠀⠍
⠀⠀⠀⠀⢈⠀⠀⠀⠀⢸⣿⣧⠀⠐⠀⠀⢾⣿⡿⠀⠹⠿⠟⠀⠀⠀⠀⡀⠀⠀⣐⣀⡀⠠⠀⠉⠩⠍⠉⠉⠅⠨⠉⠭⠭⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢲⡐⣂⣒⡀⢸⠖⠒⠤⠰⠃⠰⡧⠼⠤⠇⠀⠀⠂⠆⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⢀⠀⠀⠀⢀⣠⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⠚⣚⠃⠀⠂⠀⢀⠂⡁⣐⡀⣒⣲⠀⠀⠀⢀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠈⠛⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢷⡶⡀⢒⠂⡐⣒⡂⣒⣐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣸⣳⠂⠀⠀⠀⠀⠀⣠⠾⠓⠚⠷⣄⠀⠀⠀⠀⠀⠀⣶⠀⢰⠆⠀⠀⠀⠀⠀⠀⢀⣼⣿⣦⣀⣀⠀⠀⠀⠀⠀⡠⠖⠲⢦⡀
⠀⠀⠀⡴⠋⠉⠙⣆⠀⠀⠀⠀⢨⡟⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢀⣿⡄⣼⣇⠀⠀⠀⠀⠀⡴⠋⠀⠀⠈⢿⠃⠀⠀⠀⠀⢸⠁⠀⠀⠀⢱
⠀⠀⠀⣇⠀⠀⢀⡟⠀⠀⠀⠀⠘⢻⣄⡀⢀⣠⡿⠃⠀⠀⠀⠀⢸⣏⡷⣏⣿⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠘⢦⡄⢀⡤⠃
⠀⠀⠀⠈⠙⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠈⠑⠀⠀⠚⠁

⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠤⢄⡀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠞⠏⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢀⣶⣿⣶⠀⠀⠀⠀⠀⠀⣤⣿⡤⢤⣽⣦⡄
⠀⠀⠀⠀⡼⣿⡇⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⢠⡀⠀⠀⠀⠀⠀⠁⢒⣶⣖⠂⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⢠⣍⣙⣓⣚⣛⣩⣥
⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠈⠲⠊⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢠⣯⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣶⡀⠀⠀⠀⠀⢀⠀⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⣷⣎⡀
⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⣿⣿⡅⠀⠀⠀⡀⠿⢿⣿⣿⠿⠇⡀⠀⠀⠐⡀⠀⡸⠐⢇⠀⢸⠂⠀⠀⠀⢰⡏⠀⠀⢹⣆
⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠈⠙⠻⠷⠶⠶⠿⠛⠁⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠘⢧⣀⣀⡼⠃
⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⡿⠿⢿⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⡴⠚⠛⢲
⠀⢰⣿⣿⣿⠸⣿⣿⣷⠀⠀⠀⢾⠉⢉⡿⢻⡉⠉⣿⠀⠀⠀⠀⡏⠀⠠⠀⢹⡄⠀⠀⠀⠀⠀⢸⡿⢋⣿⡗⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠈⠛⠛⠁⠀⠙⠛⠛⠀⠀⠀⠨⠛⠋⠀⠀⠉⠛⠅⠀⠀⠀⠀⠣⣄⣀⣀⠜⠁⠀⠀⠀⠀⠀⢸⣷⣽⣿⡇⠀⠀⠀⠀⠀⠀⣧⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠙⠓⠘⠋

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⣰⠈⠛⠋⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣶⠀⣴⠀⠀⠀⠀⠀⠀⣈⢠⡄⠀⠀⠀⠀⢀⣀⠀⢰⡖
⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⣿⣿⠇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⣼⣽⡆
⠀⠀⠀⠖⠉⠉⠉⠲⠀⠀⠀⠀⠸⠛⠛⠛⠇⠀⠀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣠⣌⣄⡀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠁⠀⠀⠀⠀⠀⢴⣶⡆
⠀⠀⠀⠀⠎⠀⠱⠀⠀⠀⠀⠀⢸⣏⣭⣭⣧⠀⠀⠀⠀⠈⡏⣷⣤⡀⠀⠀⠀⠀⠀⣿⣾⡇⠀⠀⠀⠀⠀⢰⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠸⣿⣿⣿⠗⠀⠀⠀⠀⠀⠿⣭⡿⠃⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠉⣾⣿⡆⡇⠀⠀⠀⠀⠀⢈⡤
⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠸⠻⠦⠄⠀⠀⠀⠀⠙⠯⠿⠵⠃⠀⠀⠀⠀⠦⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⣤⡴⣶⣤⣤⠀⠀⠀⠀⢠⣤⣯⣧⣤⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣶⠀⠀⠀⠀⢰⣶⣶⣶⡄
⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠀⠀⢸⢿⣿⡿⡿⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠸⣿⣿⠿⠀⠀⠀⠀⠸⠿⠿⣷⠇

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⢀⡠⠀⠂⠉⠐⠐⠀⠉⠛⠻⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠀⠂⢐⣶⡶⠶⣤⣤⣄⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⢬⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⢀⡖⠈⠉⣍⢳⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣄⢁⡀⠤⡀
⠀⠀⠀⠐⠀⠉⠀⠀⠀⠀⠺⠶⠶⠀⠠⠘⠀⠈⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⣄⡀⠀⠀⠀⠠⠆⠠⠀⠄⣀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣓⢾⡧⠀⠀⠀⠀⣺⣿⣿⣿⡿⢿⣿⣿⡀⠀⠀⠀⡀⣀⣀⣭⣭⡏
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⢠⠤⠤⠤⡇⠀⠀⠀⠁⠭⢾⣷⠶⠷⠛⣛⢹⠶⠠⠀⠉⠉⢛⣭⡶⠯⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢔⣀⡀⠈⠧⠀⠢⠤⠀⠀⠀⠤⢄⣀⣶⣶⣿⡃⠀⢈⠀⠤⠒⣒⠚⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠍⠉⢅⣲⣇⠀⠀⠀⠀⠩⣔⣟⣻⣯⠽⣾⣿⣤⠀⣪⢠⡀⢠⠄⠬⠔⠓⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠛⠛⠛⠛⠛⠚⠰⠆⢰⣿⣿⣿⣛⠛⠉⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠚⠭⠍⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠠⠍⢉⡋⠒⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣸⠀⠀⠲⠴⠆⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣷⣶⡶⠿⢿⣋⣭⣬
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⠏⠀⠒⠒⠒⠂⠉⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠐⠒⡊⠅
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠆⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠙
⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠦⠤⣤⣀⡀⠀⠀⠀⠄⠀⠈⠢⡀⠀⠀⠀⠀⠈⠑⠀⠀⠠⢢⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠋⠂⠒⠒⠒⠒⠒⠒⠒⠒⠤⠤⢤⣀⣰⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠔⠂⠀⠀⠂⠘⠃⢀⠈⠖⠀⠀⠰⠆⠀⠀⣤⠀⠀⡌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠁⢀⠀⠉⠀⠀⠀⢸⠁⡏
⠀⠀⠀⠀⡀⠀⠂⠦⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠘⡇
⠀⠀⠀⢤⠄⢂⠈⠉⢁⠐⠀⣠⡳⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠋⠛⠛⠒⠲⠶⢤⣤⣤⣀⣀⣀⣀⠀⠀⠂⠉⡇
⠀⠁⢠⠀⠀⠀⡀⠀⠀⠀⠂⠈⠀⠐⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⣹⣿⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠢⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⡀⠀⠀⠉
⠀⠀⢃⠠⡀⠀⠀⠀⠀⠠⠂⡀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉
⠀⠀⠀⠱⡤⣀⣀⠀⠀⠄⠊⡀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠉⣁⠠⠄⠀⠀⠂⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⠉⠡⠤⠔⢒⣀⠀⠀⠍⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠒⣒⠀⠁⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠥⠀⠂⠀⢡⠤⠀⠐⠀⢈⠉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢉⡁⠤⠄⢀⠐⢃⣈⡡⠄⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠶⠃⣀⣀⡀⠀⠀⠀⠨⠤⠔⠒⢂⣀⠈⠀⠀⠀⠀⠀⢠⠂⠰⠋⢙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠠⢐⠂⢶⡇⠀⣴⠒⢅⠀⢀⣀⡤⡖⢢⣤⣤⣴⣦⣕⣒⣚⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡇⣸⣿⢤⣴⣥⣾⣿⡟⠻⡁⢴⢊⣧⣴⢿⡯⢹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⣿⢿⣿⣿⣿⣧⡺⢷⣤⣾⣿⣯⡾⢃⣾⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣧⠘⣿⣿⣟⣉⣽⣿⣷⣯⣭⣭⣥⣶⣿⣿⣿⡿⢿⣟⣿⣙⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⡹⣿⣿⣿⣿⣿⡿⢿⡛⣿⢩⠟⣼⣛⡾⢩⡟⠨⠃⡚⢹⣏⡻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣜⠿⣿⡓⠾⢄⣛⠸⢅⡿⢼⣟⣾⡥⠶⢜⣓⣪⣭⡼⢫⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣮⡻⢷⣤⣖⣁⣚⡛⣭⣤⢶⣶⣿⣿⣿⡿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣽⣿⡿⠿⠿⠛⠛⠋⠉⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⠊⠢⠚⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⢀⠀⢀⣀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢰⠾⠿⠿⠿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⢀⡞⠠⣋⢿⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠊⠱
⠀⠀⠀⠘⢄⠀⠘⠀⠀⢾⡄⠀⠀⠀⢸⢿⣷⣞⣽⠇⠀⠀⠀⠀⠀⢀⣀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⣼⣅⠀⠀⠲⣔⠐⣸⣣⠀⠀⠀⠈⠳⡭⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⢡
⠀⠀⠘⣟⢄⠀⠀⠀⡐⠃⠋⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠂⠊
⠀⠀⠀⠸⠄⡇⠒⠎⡄⠃⠀⠀⠀⠴⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠙⠘⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣴⣶⣶⣦⣤⣀⠀⠀⠈⠂⢄⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡞⠙⣴⣿⠧⠤⢄⠉⠻⣷⡄⠀⠀⠀⠜⠻⣟⠒⠆⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⣧⣁⣿⠁⠀⠀⠀⢣⠀⠘⠗⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣘⢿⣷⡖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣀⡀
⠀⠀⠀⠀⠄⠀⠔⠀⡀⠀⢔⡲⠀⠈⠀⠀⠀⠀⠈⣿⢾⣿⣽⡌⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠀⠁⠀⠹⠂
⠀⠀⠀⡀⠄⢐⣠⠤⢐⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣀⣝⠿⡟⠣⠤⠄⠀⠀⠀⠀⢠⡄⠄⠀⠀⠀⠀⠀⡀⠀⢠⢤⠀⠂⠀⠃⠀⢦
⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢧⣀⣀⢀⠄⠀⠀⠀⠀⡚⠛⠳⠆⠐⠴⠒⠆⢰⠃⠀⣿⣿⡿⠓⣊⣴⡀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⡁⠠⠂⠀⠆⠀⠀⠁⠻⠀⠀⠙⠻⠥⠿⠿⠿⠼⠟⠃
⠀⠀⠀⠀⢄⡀⢠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠒⠈⠉⠀⠀⠀⠈⠁
⠀⠀⣌⠁⠆⠀⢀⠀⠨⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠄⢠⠉⢣⠁⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣞⢇⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⢀⣈⠆
⠀⠐⠀⠠⡤⠬⠭⠥⠤⡴⠄⠀⠀⠀⠀⠀⠀⠀⠠⢤⡆⠀⠀⠀⢠⡄⣴⡄⠀⠀⠈⠈⠔⠋⠀⠀⢄⠀⠀⠀⠀⢀⠠⢀⣀⠀⢁
⠀⠀⠀⠠⠂⣶⡴⠤⣄⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡤⠀⠀⣤⠀⠀⠰⡶⠆⠀⠀⠀⢠⢡⣾⡿⠿⣶⣆⠑
⠀⠀⢢⠀⠀⠜⣦⡴⠃⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⣇⠀⠀⠀⠀⠸⠐⡿⣧⣀⣼⣟⠀⡆
⠀⠀⠈⠀⠀⠀⢀⠑⠓⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠁⢉⠛⠍⢛⠡⡠⠃
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣲⡤⢤⣤⣤⣤⣤⣼⣟⠃⠀⠀⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣵⡆⣠⣶⡿⠋⠀⠀⠀⢀⣠⣾⣿⣿⣿⣄⠑⢌⠰⣌⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣾⣿⣿⣧⢳⡙⢿⣷⡈⢃⠈⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣉⠓⠀⢒⣩⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣮⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⣿⣿⡿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣞⣿⣿⣿⡦⠉⠁⠻⣿⣿⣿⣿⣧⠀⠀⠈⣿⠿⠛⠓⠀⡰⠿⣿⣿⡄⠀⢂
⠀⠀⢀⣴⣶⠶⠶⣶⣦⣙⣿⣿⣿⣿⣧⠄⠀⠈⢻⣿⣿⣯⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠂
⠀⣴⡿⠋⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣅⣀⣀⣀⣿⣿⣿⣁⣀⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⡻⢿⡟⠻⡀⠀⠀⠹⣷⣆⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠹⣷⠈⠳⣄⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠴⣢⣄⣀
⣿⡇⠀⠀⠀⠀⣀⣴⣶⠋⠀⠀⠀⢻⣇⠀⢨⣗⠀⠐⠀⡜⢻⡀⠀⠈⠳⣤⣀⠀⠀⣀⣀⠀⠀⢀⣤⣶⠾⠋⠹⣿⣷
⢻⡇⠀⠀⠀⢼⣿⣿⣿⠧⡀⠀⠀⠘⣿⠀⣾⡟⠀⠀⡰⠁⠀⠙⠀⠀⠀⠈⠻⣿⣶⣟⡛⣿⣶⡿⠋⠀⠀⢀⣤⣿⠿
⠘⣿⡀⠀⠀⠈⣿⡁⠙⠳⣬⡓⢤⡀⣿⢀⣿⠃⠀⡜⠁⠀⠀⢀⣀⠀⠳⣤⡀⠀⢉⢻⣿⣿⣯⠀⠀⠀⠀⠈⠉⠈
⠀⠹⣷⡀⠀⠀⠈⠑⠢⡀⠈⠛⢶⣽⣿⣼⡿⠤⣼⣤⣴⣶⣿⣿⣿⣇⣀⣬⣿⣇⠚⠙⠻⣿⣿
⠀⠀⠙⣷⣄⠀⠀⠀⠀⠈⠲⢄⠀⣽⣿⣿⠏⢹⣿⣿⣿⣿⣿⠿⠿⠛⠉⠁⠀⠙⣆⠀⠀⣿⣿⠿⣶⣤⡀
⠀⠀⠀⠈⠻⣷⣤⣀⠀⠀⢀⣠⣿⠿⣿⣿⡄⠘⢿⣿⠋⠁⠀⠀⠀⠀⠰⣦⣀⣼⣿⣤⣴⡟⣿⠀⠀⠙⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠟⠋⠁⠀⠨⣿⣷⣆⡈⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠿⠏⢸⣿⣿⡆⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠿⠤⠖⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠈⣿⠹⣧⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢹⣇⢻⣆⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⣤⣤⣴⡿⠋
⣶⣶⡶⡶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⢡⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠋⠈⢿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠘⠛⢿⠟⠀⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡅⠀⠀⠀⠀⢰⢾⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠱⡴⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠘⠢⡀
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣠⠖⠙⠛⠧⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠖⠋⢻⡤⠀⠀⡠⠀⠀⠀⠈⠢⡀
⠀⠀⠈⠉⠉⠁⣀⣠⡴⠞⠉⠀⠀⢀⣠⣴⣾⡿⠧⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠒⠈⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⣀⠤⠒⢩⣏⣁⠀⠀⢀⣤⣶⡿⠛⣭⡷⡙⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⢿⣷⣦⣿⣿⣿⣷⣾⡿⠋⣑⡬⠛⠉⠟⢽⣮⣍⠃⠀⠀⠀⠀⠀⠐⠒⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠘⠿⢿⣿⣿⡟⠛⣻⡷⣿⣥⣍⠃⠀⠀⠘⡿⠟⠻⠿⢿⣿⣴⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠈⠙⠛⠦⠀⠉⠛⣿⣿⣿⠀⠀⠀⠃⠀⠀⣠⡞⠋⠙⠀⠒⠢⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣀⠀⠀⠠⠞⠉⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣾⠿⠛⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠑⠤⢄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣰⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⠘⠀⠀⠈⠀⠀⡠⠋⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⡠⠊⠁⠀⠀⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣉⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⢀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠀⢐⣧
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣸⣷⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⣠⣶⣿⣿⠛⠛⠛⠿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢡⣿⠃⣼⣿⣿⣯⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠁⠀⢼⣿⣿⣿⣿⡿⠋⠉⠉⠁⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⣀⣴⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠛⠻⣿⡿⠿⠋⠉⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣟⡎⠀⠘⠓⠤⠤⠤⣤⣠⣤⣤⢐⣿⣛⢲⡆⡰⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⣅⠀⠆⠀⠱⡄⠀⠀⠀⠀⠀⢼⣿⠉⣽⠾⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠙⠂⠀⢄⠀⠙⠀⠀⠀⠀⠀⢸⣅⡼⠃⢠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠘⢧⣀⣠⡿⢦⣄⡀⠀⠀⠀⠀⠀⢉⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢰⡏⣇⣧⠀⠈⢙⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⠀⠀⠘⠃⠛⠁⠀⠀⣸⠷⠶⣶⣶⣿⣿⡿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠋⠀⡹⣦⡈⠳⠒⠒⠀⠒⠘⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⣴⡄
⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠋⠁⠀⠀⠀⢤⠈⠻⣦⣄⠀⠀⠀⠀⠗⠲⠀⠀⠀⠀⢀⣿⣿⢟⣿⠋
⠀⠀⠀⠀⢶⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠉⠓⠦⠀⠘⠀⠰⡄⠀⠀⠀⢸⣿⣟⣾⠃
⠀⠀⠀⠀⢠⣜⢿⣿⣿⣿⣿⣶⣤⣄⡀⠈⠆⠀⠀⠀⠀⠀⣴⠰⡀⠀⢵⡄⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠙⢷⣝⡻⢿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠻⣾⡇⠀⠈⢇⠀⠀⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣯⣭⣿⣛⡿⢿⣿⣿⣶⣄⠀⠀⠸⡿⠇⠀⠀⠸⣦⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⠽⢿⣍⠉⠛⠛⠷⣤⡀⠀⠀⠀⠀⠀⠈⣸⠃
⠀⠀⠀⠀⠀⣀⡤⠶⠖⠶⠦⣤⣈⠀⣤⠀⣸⣧⡄⠀⠀⠈⠙⠳⠦⢤⣄⣀⣠⠃⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠸⣁⠀⠀⠀⠀⠀⠀⠉⠙⣿⠛⠉⢸⠃⣖⣦⢰⠀⢰⡗⠀⠀⠠⣾⠀⠴⠄⠺⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠁⢈⡁⠠⠄⢄⠀⠀⢹⣧⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠴⠛⣿⠁⣤⡦⢠⡄⢿⣆⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠛⠀⠀⣀⣴⡿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣤⣤⡤⠶⠟⠉⠀⢀⣠⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⣄⣀⣀⣀⣀⣀⣠⣤⣴⠶⠞⠛⠉⠁⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄

⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡟⡭⣭⡟⠛⠛⠛⠛⠛⠛⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣀⣀⣀⡠⠤⠤⠤⠤⠶⠶⠒⠒⢒⣒⣋⣉⣩⠭⠤⠤⠤⠤⠄⠐⠒⠒⠒⠒⠀⠤⡄⠀⡸
⠀⠀⠀⠀⠹⡀⠀⡠⠤⠖⠒⠒⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢰⠃
⠀⠀⠀⠀⠀⠱⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡏
⠀⠀⠀⠀⠀⠀⢳⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸
⠀⠀⠀⠀⠀⠀⠀⢣⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢇⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠱⢤⣀⣀⣀⣤⠤⠤⠤⠤⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠒⠒⠒⠒⠒⠒⠚⠉⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣰⢚⣉⣉⣉⣭⣩⠭⣍⣭⢭⣉⣭⣭⢭⣭⡍⣽⡍⢹⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠙⠒⡊⢉⣉⣈⣭⣭⣨⠭⣤⢤⣤⣠⣴⡆⣖⡶⢸⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⢸⣭⣿⢟⡜⡱⢋⣽⣭⠿⡽⣿⡌⢯⢻⠢⡴⢲⠀⡇⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠃⣹⣴⠃⠘⠰⢡⢏⢞⣩⠯⡵⢌⢻⣦⠃⠃⠙⡄⡆⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢳⠇⠀⠀⠀⢠⣣⢋⠞⢉⢅⣾⣧⠉⠀⠀⠀⢸⠃⢇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢸⠀⢸⠀⠀⠀⠀⠈⢁⣞⣤⡬⢵⠦⣄⠀⠀⠀⠀⠀⡇⢸⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣀⡎⠀⠀⠀⠀⢀⠮⠬⠭⠭⠭⠤⠬⢆⠀⠀⠀⠀⢧⠼⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡼⠀⠀⠀⠀⠀⣎⣀⣀⣀⣀⣀⣀⣀⣸⡀⠀⠀⠀⠘⣤⠤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡽⠁⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⡀⠄
⠀⠀⠐⠀⠀⠒⠒⠄⠀⠀⠀⠀⠓⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⢀⡀⠀⠀⡖⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⡀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠒⠀⠀⠀⠀⠀⡰⠋⠀⠁⠀⠀⠀⠀⠀⠉⣉⠉⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠢⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠠⠤⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠈⠀⠀⠀⢋⣂⢐⢾⠛⠀⠀⠀⠀⠈⠀⠲⠁⡁
⠀⢰⠀⠀⠀⠂⠀⠀⠀⡀⢀⠀⠀⡠⢄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠠⠤⠄⠀⠀⠀⡀⠐⠄⠐⠀⡀⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⢀⠂⠀⠀⠀⡠
⠀⠀⠒⠒⠒⠀⠀⠁⠀⠀⠊⠀⠉⠀⢸⠀⠀⡀⠀⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠒⣚⠡
⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠀⠀⠉⠑⠀⠀⠒⠀⠀⠐⠠⠰⢰
⠀⠀⢀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣠⣄⠀⠀⠀⠀⠀⠁
⠀⠀⢂⠀⠂⠃⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠸⠀⠄⠀⠀⠀⣓⣀⣀⣀⣸⣀⠀⢰⣶⣤⣿
⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⢢⣠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡶⢦⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⡔⠷⠶⠶⠶⠿⢶⡄⠀⠀⠘⠄⠃⠀⠀⠀⠔⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠆⠀⠀⠀⠈⠉⠁⠉⠉⠁⠀⢀⠁⠀⠀⣀⣈⡄⠈⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⡀⡤⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠤⠤⠀⠁
⠀⠀⠈⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢉⠉⢧
⠀⠀⠀⠀⠀⠀⠀⢠⣶⢖⣶⡶⠶⠶⠋⠰⢯⠗⠈⠳⢶⣶⣖⣶⣲⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣹⣿⡽⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣫⣿⠁⣠⠤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢯⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢟⣽⠀⣿⢼⣹⠆⡏⠀⠀⠉⠉⠉⠛⠀⠀⢸⡵⡳⡧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⡟⠊⠉⠓⡇⠀⠘⠋⠉⠉⠁⠀⠀⢸⣞⢟⡷
⠀⠀⠀⠀⠀⠀⠀⣼⣣⣿⠀⠙⠛⠋⠉⢁⡀⠐⠛⠛⠛⠓⠀⠀⢸⣫⢞⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡫⣿⠀⣰⢶⣲⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⡿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢟⡿⠀⠙⠚⠋⠐⠒⠒⠒⠒⠒⠒⠒⠒⠀⢸⢟⣼⡇
⠀⠀⠀⠀⠀⠀⠀⡷⣫⡇⠀⢸⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢟⡇⠀⠈⠉⢩⠄⠛⠛⠛⠛⠛⠒⠂⠀⠀⣿⣿⢿⠇⠀⠀⠀⠀⢀⣤⣶⠆
⠀⠀⠀⠀⠀⠀⢰⡿⢻⡇⠀⣾⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣵⣿⠀⠀⠀⣀⡴⠋⣠⡏
⠀⠀⠀⠀⠀⠀⢸⡷⣻⠁⠀⢉⡉⠁⢉⡿⠟⠓⠒⠒⠒⠒⠀⠀⣿⡫⢿⢀⣠⠞⢁⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⢸⡟⣽⠀⠀⣿⣽⡶⣋⣀⣀⣀⣀⣀⣀⠀⠀⠀⣟⣴⡿⠋⣠⠶⠟⠋
⠀⠀⠀⠀⠀⠀⢸⣟⢾⣤⣤⣬⣭⣤⣄⣉⣉⣉⣉⣉⣉⣀⣀⣠⠟⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⢸⣧⣫⢎⣞⡵⣱⣫⣫⢞⡝⡵⣱⣣⣫⣯⠞⣁⣴⣋⡿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⡧⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠒⠋⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠓⠒⠒⠒⠒⠶⠤⠤⠤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣲⠶⠛⠉⠉⣉⣈⠭⢟⣠⡀
⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⡤⠖⠋⠀⢰⡇⢀⡠⠔⠊⣡⠴⢒⣉⣼⠃
⠀⠀⠀⠖⢻⡷⠶⠶⠶⠶⠶⠶⠶⢶⣶⣦⣤⡤⠤⣤⣤⣤⣤⣤⣤⣤⠴⠯⠬⠷⣖⣋⣻⡏⠉⣉⣉⠽⠋⡡⠴⠚⣉⠴⠊⠁⡗⡏
⠀⠀⢰⠶⠟⠒⠒⠒⠚⠋⠉⠍⠍⠀⠀⠀⣀⠀⣐⣂⣀⣀⣀⡀⢒⣀⣀⣀⣐⣒⡒⠒⠀⠤⠭⠭⠭⣶⡡⠔⢂⠩⢛⠨⢙⡩⠷⢇⣀⣀
⠀⠀⢸⡄⠀⢀⢀⣀⣀⠤⠿⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠬⠭⠭⢉⣉⣙⣻⡂⢩⣰⠼⠒⠊⠁⠀⠀⠀⠀⠈⣉⣳⡦
⠀⠀⣼⠀⣀⣉⣁⣤⠤⠤⠤⠶⠶⠒⠒⠒⢒⣛⠛⣛⣛⣒⣒⠒⠒⠒⠒⠒⠲⠦⠤⠤⠤⠤⠤⠴⠶⠾⠗⠉⠀⠀⠀⠀⣀⣤⣤⠒⠚⠉⠁
⠀⠀⠉⡠⠋⠁⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⠤⠤⠤⠤⠤⠬⠥⠭⠭⠽⢶⣶⣶⣦⣤⢤⣄⣀⣀⡀⠀⠀⠀⠀⣀⠤⠖⠩⢑⡒⠊⣻
⠀⠀⠚⠉⠉⣩⠉⠀⠀⠀⠀⠀⠐⠐⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠐⠒⠒⠒⠒⠒⠛⠂⠀⠀⠀⠉⠉⢹⡲⠭⢀⣒⠤⠍⠀⣒⣀⡽
⠀⠀⠀⠒⠂⡇⠀⣀⣀⣀⣀⠀⠈⠉⠉⠉⠉⣉⣁⣒⣛⣛⣒⣒⣒⣒⣒⣒⣶⠦⣤⣤⣤⣭⠍⢉⡀⣼⠐⣊⡡⠴⠒⠊⡉⠉⠀⠠
⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠭⠛⠉⠉⠉⠩⠭⠍⠁⠈⢨⠔⠂⠀⣈⠠⠀⠀⠀⡇
⠀⡰⠁⠀⠤⠤⠐⠒⠒⠒⢈⣉⡉⣉⣉⣉⣉⠉⠉⠭⠷⠶⠶⠶⠶⠶⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⡀⠄⠒⠀⠠⢀⣰⣇
⠀⠀⠀⠀⠀⢹⠉⠁⠀⠀⠀⠤⠤⠤⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠐⠒⢸⠀⠀⠐⠚⠣⠤⠤⣼⣄⣱⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠒⢺⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠙⠛⠛⠋⠙⠋⠡⠤⠤⠤⠤⢀⣀⣀⡀⠀⠈⠉⠉⠉⡝⠀⢸⠀⢈⡀⠄⠀⠂⢁⡏
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠬⠭⢍⣉⣙⣛⣁⣀⣼⢈⠠⠀⠀⠈⢁⣰⠇
⠀⠀⠀⠀⠄⠚⠑⠠⡤⠤⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣈⣙⣛⣛⣁⣒⠒⠒⠒⠢⠤⠤⠄⣇⢀⣀⠤⣔⡻⠿⡟
⠀⠀⠀⠀⠀⠀⢹⢎⡀⢤⡤⠄⠒⠒⠒⣊⣩⠭⠽⠛⠋⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⡉⢉⣙⠛⣋⠥⢒⣋⡁⠄⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠉⠓⠀⠈⠁⠀⠀⠀⠀⠀⢠⣤⡤⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⡇⣈⡥⠤⠖⣂⢹⠇
⠀⠀⠀⠀⠀⠀⠀⡸⠤⠤⠤⠤⠄⠰⠶⠶⠶⠶⠶⠒⠐⠲⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⠁⠀⠐⠘⠋⠉⡟⠀⠀⠀⡀
⠀⠀⠀⢀⡠⠀⠀⢳⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢶⣶⡶⠶⠶⢶⣶⣤⣤⣄⣀⡀⠀⣽⠀⣀⣡⣤⣤⣶⡧⢀⡴⠊⡀
⠀⠀⣉⠤⢒⣩⠔⢊⡹⠗⢒⡲⠖⠒⣶⠶⠶⢶⡶⠶⠶⠶⠶⠶⡶⠶⠶⠶⠶⠶⠶⠦⠶⠤⣤⠤⢤⡿⠭⢗⠟⢉⠵⣪⠔⣉⠴⢊
⠀⢀⠥⠒⣉⠤⠚⢡⠔⠊⠉⠀⠔⠉⠀⠔⠊⠁⠀⠂⠁⠠⠐⠉⠀⠠⠐⠁⠠⠒⠁⣀⠔⠊⣠⠖⠉⠠⠊⠡⠚⠵⠊⡤⠊⠁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡠⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣽⣶⢶⣶⣆⡆⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣋⣬⣴⠺⡿⢷⠛⡉⠉⠉⠉⠛⠳⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⠇⠉⢾⣇⣸⣶⠀⠀⠀⢰⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣠⠿⠛⠟⠈⢧⠀⠀⣿⣷⠦⣤⣄⡀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣀⣶⣶⣾⡆⠀⢹⣿⣷⣶⣶⣶⣶⠦⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⠁⠉⠉⣧⠀⢸⡿⣿⣿⡿⠋⠀⠀⠀⣶⡄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⢀⡞⠀⣸⣇⣾⡿⠁⠀⠀⠀⣼⣿⣷⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠧⢠⣿⡀⢀⠞⢀⡴⢋⣾⣿⠃⠀⠀⣠⣾⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢷⣶⣶⣴⠗⢋⡴⠋⢠⣿⣿⠇⠀⠀⠞⣿⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡞⡓⠤⢒⢿⡿⢋⣿⠾⣅⣀⣼⣷⠦⠿⠿⣿⡀⠀⠀⣼⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢱⢛⣟⡛⠊⢠⠞⠁⢠⡇⠀⢿⡛⣿⣿⣿⣿⣧⡀⠀⠹⣷⡆⠸⡇⠀⢀⡠⢴⣖⣒⣶⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⢧⣩⡿⠿⣷⣶⡾⣧⢲⣦⡙⢮⣿⣟⣿⣿⣧⠀⠀⢻⣇⢠⣬⡲⢯⣾⣿⣿⣿⣿⣿⣷⣮⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣽⣾⣿⣿⣿⣿⣿⢰⣿⣻⣦⡉⠻⣿⣿⣿⣧⠀⠈⣿⣸⡏⣿⣶⣝⠿⣿⠿⠛⠻⠿⣿⣿⣷⡝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⣾⣿⢟⡵⠞⠛⣿⣿⢸⣿⣿⣿⡽⣷⣌⠛⢿⣿⣧⠀⢸⣿⣽⣿⣿⣿⣷⣮⡓⢄⡀⠀⠀⠙⢿⣿⣞⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡏⣾⣿⢣⠎⠀⠀⢠⣿⡏⣿⠙⢿⣿⣿⣞⣟⢷⣄⡙⠻⣷⠈⢿⣿⣿⣿⡏⠻⣿⣝⣶⡝⢢⡀⠀⠀⢻⣿⡼⡆
⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⣿⡌⠀⠀⠀⢸⣿⣷⡇⠀⠈⢿⣿⣿⡞⡆⠙⢿⣦⠜⠁⢀⣿⣿⣿⠷⠖⣛⣭⠷⠚⠉⠀⠀⠀⠀⣿⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⣿⠁⠀⠀⠀⢿⡿⠿⠃⠀⠀⠀⠸⣿⣿⢹⠀⢾⣥⣴⣾⣿⣿⣩⣴⡾⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⠀⠀⢿⠛⠿⠿⢻⢯⡹⣿⣮⡳⠀⠀⠀⠀⠀⠀⠀⣰⣿⢧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣸⠀⠀⠈⠙⠒⠒⠋⠀⠱⣌⠻⣿⣦⣤⣀⣀⣀⣤⣾⣿⢋⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⢿⣷⣄⡀⠀⠀⠀⠀⠀⣠⣿⣿⢣⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣍⣛⠻⠿⠿⢛⣫⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠻⢿⣷⣶⣶⣶⣿⣿⢟⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠭⣭⠭⠵⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⣀⣠⣤⣄⣐⣦⣤⣴⣶⣾⣿⣶⣶⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣴⣦⣤⣴⣴⣶⣾⣿⣷⣾⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣴⣶⣾⣶⣾⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⣿⡿⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠁⢀⣀⣀⣀⣀⣤⡤⠤⢤⡤⠶⠖⠂⠀⠀⠀⠀⣼⣿⣿⡛
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠀⢴⣶⣤⣴⣶⣶⣾⡿⠿⠆⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣸⣿⣿⢳⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡻⣿⣿⣄⠀⠀⠋⠉⠭⠅⠀⠀⢒⣐⣘⣢⣀⣀⣀⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢏⡞
⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠝⣿⣿⣦⠀⠀⠀⠘⠚⠊⠉⠁⠈⠉⠁⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣟⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⢿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⣋⣉⣉⡉⠊⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠾⠿⠻⠛⠛⠛⠛⠛⠛⣛⣋⣉⣩⣩⣥⣤⣤⣦⣶⣶⢶⣺⠿⠿⡟⢿⣟⣛⣛⡅⠘⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣧⠁⢰⣶⡶⢾⠽⠿⢿⡟⣻⣋⣛⢫⣭⣭⣬⣽⣷⣶⣶⣶⣿⡿⢿⣿⢿⣿⣛⣿⣇⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡟⠀⠀⣶⣿⢞⣿⠟⣁⣼⠟⣩⣤⣿⣟⣿⣯⣿⣿⣾⣿⣱⡛⠻⣶⣍⡙⢿⣿⠻⣿⠀⠁⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠂⠀⣿⢇⣾⠃⣸⡿⠣⣸⣿⣛⠿⠻⠛⣿⣽⣿⣾⣿⣿⣿⣦⣌⡻⢿⣦⠙⢷⡙⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢿⠀⠀⠘⢸⠇⢰⡿⠁⣸⡿⠏⣁⣲⣶⣿⣿⣼⣿⣭⣟⡁⡙⠻⣿⣆⠈⠻⡆⠈⠁⠐⣀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⠃⠀⠀⠘⠁⠀⠟⠁⣰⣟⣻⣿⣽⣿⣭⣿⣿⣿⣻⢿⣦⡄⠙⠂⠀⠀⠀⠀⠀⠘⢸⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⢋⣤⣻⣿⣧⣿⣿⡾⠿⠶⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⡗
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⡧⣿⠀⠀⠀⠀⠀⠀⠀⠸⠁⢀⡾⠛⠛⠛⠋⠉⠉⠑⠚⣶⣤⡄⠳⡄⠀⠀⠀⠀⠀⠀⠸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⢸⡞⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠓⠛⠛⠛⠛⠉⠉⠉⠉⠉⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠟⠀⣦⠀⢠⣼⠁⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⣤⣀⣀⣤⣤⣴⣾⣿⣶⣿⣿⣶⣄

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠀⠀⠀⠀⢀⡿⠛⣛⣛⣛⣿⠇⠀⠀⠀⢀⣾⡟⣽⠿⣿⣿⠟⣿⣿⢿⣿⢷⡀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⡍⠀⡄
⠀⠀⠀⠀⠘⢿⣷⣿⢟⠻⠿⠆⠀⠀⠀⢸⣿⣾⣿⣿⣷⣽⣿⣽⣿⣷⣦⣿⣧⠀⠀⠀⠀⠀⠀⠸⡄⠀⠸⡆⠀⠀⠀⠀⠀⡥
⠀⠀⠀⠀⠀⣠⣼⣿⠦⣿⠟⠒⠠⠄⠀⠸⣿⣯⢿⣧⣸⣆⣾⣆⣾⣘⣇⢸⠏⠀⠀⠀⠀⠀⠒⠠⠙⢦⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠠⣄⡸⠃⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⣸⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⡆⢠⡄⠀⠀⠑⢄⠀⠀⠀⢠⣤⣀⠀⢀⣀⡀⢀⠀⠠
⠀⠀⠀⠀⠀⠠⠋⣈⠁⠀⠀⡆⠀⠀⠀⠀⠀⡄⠀⠀⢠⠀⠀⣀⡀⠀⠀⠀⠀⠀⠑⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⣿⣧⡳⠄
⠀⠀⠀⠀⠀⢀⣾⣿⡧⠀⠀⡇⠸⣄⡀⠀⠀⢹⡀⠀⡾⠀⠀⠨⣭⢼⡟⠻⠇⠀⠀⠀⠈⠛⠿⠶⠶⠖⠁⠀⠀⠀⠁⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠿⠟⠃⠀⠀⡇⠀⠀⠉⠓⠢⠀⢧⠀⢥⣀⣀⠘⠿⠷⠏⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⣤⣦⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⡿⠀⠀⠀⠀⠀⠀⢠⠛⣷⡀⠀⣿⠉⠉⠙
⠀⠀⠀⠀⠀⠘⠁⠀⣶⠄⠀⠀⠀⠀⠐⠒⠀⠉⢁⣤⡀⠀⡀⠐⠀⠀⢀⠀⠀⠀⠸⣄⢸⠃⠀⠀⣤⣤⣄⠀⠀⠂⢹⠃⠀⡿⣿⣿⠇
⠀⠀⠀⠀⠘⠇⠀⢰⣿⢋⡄⠀⠀⠀⠀⠠⡈⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿⠀⠀⠀⠀⠻⣿⣿⣰⡄⠀⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⡃⠀⠀⠀⠸⠃⢘⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢿⣿⣿⣿⣇⣶⡀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠟⠃⠀⠀⡐⠀⠀⠸⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠳⣈⣿⣿⣿⣟⣸⡆⠀⠳⠾⢶⣄
⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠒⠒⠒⠠⠼⠓⢦⡀⠀⠀⢠⣍⣙⣏⣛⣟⣿⠃⠰⣷⣿⢊⣿
⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⢰⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠈⠃⠀⠀⠀⠀⠀⠁⢝⡀⠀⠀⠻⣿⣿⣿⡿⠁⠀⠀⠈⠉⠉
⠀⠀⠀⠀⡈⢻⡟⠀⠀⢄⠀⠈⠀⠀⠀⠀⠀⠠⠒⠐⠐⠀⠀⠑⠄⠁⠀⠀⠀⠀⠀⠀⠀⢠⠍⠻⣴⡄⠀⠀⠉⢿⠀⠀⠀⠀⠰⢄
⠀⠀⠀⠀⠁⠀⠀⠠⡀⠀⠁⠀⠀⠀⠀⠀⣤⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣼⣯⣤⡄⠀⠀⠀⠀⡀⠀⢠⡂⠀⠘⡄⠀⢠⣆⣀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡧⡄⠀⠀⠀⠉⠒⣄⠀⠉⠉⠛⠻⠋⠀⠀⠀⠀⢇⡀⠀⠁⠀⠀⠐⠀⠀⠉⠉⢫⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠀⠀⠀⠀⠀⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣀⣤⣄⣠⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⣠⠠⡉⢉⡉⠉⠉⠉⡉⡉⢉⠉⠉⠉⠉⠉⠉⡉⠑⣤⡶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠘⠀⠀⠀⠂⠨⢄⢋⢍⢜⢘⠂⠂⠀⠑⠂⠀⠀⠘⠀⠘⢿⣗⡀⠠⠄
⠀⠀⠀⠀⠀⣠⡤⠃⡀⠊⠀⠀⠀⠀⠀⠀⠀⠊⠈⠈⠀⠀⠰⠄⠓⠀⠀⠀⣠⠀⠠⣌⢧⣭⣍⢩⡄
⠀⠀⢀⣤⠶⠾⣥⡾⠲⣄⢀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠣⡑⣀⢼⠾⠿⣿⡝⠛⠁
⠀⠀⠉⠀⠀⠔⠛⠂⠀⣨⡿⠯⠶⠤⠴⢤⣤⠤⢀⣀⣀⠀⠀⣀⣀⣀⣀⣠⣴⡜⢿⡄⠉⠀⠊⠉⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉

⠀⠀⠀⠀⠀⣯⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠤⣄⣀⠶⣶⡄⡀⣀⣀⢀
⠀⠀⠀⣠⣮⢿⣽⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠋⠁⠀⠀⣀⡀⠀⠈⢻⢆⠀⠀⠀⠀⢸⠀⠈⢗⡎⠡⢇⡥⣧⡾⢭⡀
⠀⢠⢫⠖⠉⠉⠈⠉⠑⢮⢢⠀⠀⠀⠀⠀⠀⢸⢛⣤⠖⠊⠉⠀⠀⠀⠉⠑⣼⠺⠀⠀⠀⠀⠀⠱⢄⣠⡞⢠⡟⠉⠀⠀⠉⢻⡄
⠀⢸⡏⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠘⣿⢸⠶⣄⡀⠀⠀⠀⣀⣴⠛⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠤⠴⠊
⠀⡿⣃⠀⠀⠀⠀⠀⠐⠆⠹⡇⠀⠀⠀⠀⠀⠀⠈⠻⣼⡁⢹⣄⠈⣿⣇⡸⠎⠀⠀⠀⠀⠀⠀⡰⠋⢱⡄
⢸⠀⠋⠀⠀⠀⠀⠀⠀⠀⠁⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⣝⣳⠟⠉⠀⠀⠀⠀⢀⢄⣄⠀⠙⣀⡼
⠈⠳⢄⣀⣀⠀⠀⠀⣀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣬⡀⠀⠀⠀⠀⠀⢸⡁⢈⡃⢰⢯⠄⡀
⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⠉⡇⠀⠀⠀⠀⠀⠀⠳⣄⢠⠋⠛⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣧⠀⠀⠀⠀⠀⠔⢲⣾⡄⠢⠤⢤⡔
⠀⠀⠀⠀⠀⠀⠀⣤⠤⠧⣴⣥⣸⣦⡤⠤⢤⡀⠀⠀⠀⠀⡎⠀⠉⠹⠀⠀⠀⠀⢨⠀⠀⢀⣾⠀⠀⠀⠀⠀⣤⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡠⠊⡼⢐⡎⣴⠟⠛⣦⠙⡂⢣⠳⡀⠀⠀⢠⠿⠿⠿⠿⡇⠀⠀⠀⠀⠛⠒⠚⠁⠀⠀⠀⠀⠀⣾⣀⠀⢀⡚
⠀⠀⠀⠀⡼⠥⠾⠀⣉⣙⣉⣉⣉⣉⣋⣉⣀⣧⣱⠀⠀⢸⣤⣤⣤⣤⣽⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⡋
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡌⠀⠀⠀⠀⢀⡇⠀⢘⣿⣽⣏⠀⠀⠀⠀⠀⠀⠀⠘⠐⠂⠒⠃
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠙⢿⠛⠛⢻⠟⠀⠀⡠⢛⣛⣛⠢⣄⠀⠀⠀⠀⠀⠰⠠⣤⠄⡇
⠀⠀⠀⠀⠀⠈⢇⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼⠀⠀⠀⠀⠀⠀⠳⡶⠃⠀⠀⣜⣔⠁⠀⠀⠙⡎⣆⠀⠀⠀⣠⣂⣀⣀⣀⣗⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢁⠀⠀⠀⢀⢇⡟⠀⠀⢀⣿⡿⠛⠉⢙⢿⣯
⢠⢫⡍⠛⡑⠶⣤⠲⡖⢫⡉⣁⠶⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣥⣤⣬⠅⠈⠀⠀⠀⣼⡟⠰⢶⣴⠿⠃⣿⣿
⠸⡀⢰⠄⣉⢘⣹⣼⢇⣰⠄⡉⠰⢦⠇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣔⡀⠀⠀⢀⣴⡼⠉
⠀⢿⣀⣤⣭⣞⡝⠀⠙⣭⡺⣅⣴⠏⠀⠀⢀⡴⣋⢥⠞⠀⠀⠀⠀⢀⡤⡚⣷⡄⠀⣴⣐⢄⠀⠀⠀⠀⠀⢘⣳⠦⠦⠿⣏⡇
⠀⠀⠙⠷⠤⠋⠀⠀⠀⠀⠑⠛⠀⠀⢀⡴⡡⢺⢇⠎⠀⠀⠀⢀⢔⠝⠈⠀⠧⠃⠀⠾⠆⠙⢷⣄⠀⠀⠀⠀⢁⢀⣀⡀⡏
⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⡰⣫⣎⡀⠸⢸⠀⠀⣠⡞⣵⣳⣶⣶⣦⡀⠀⢀⢤⣰⣶⣶⣓⠴⣄⠀⠀⠈⠀⠀⠀⡇
⠀⠀⠀⡔⠒⠈⠁⠀⢷⡄⠀⡠⢎⠜⠁⠀⠙⢆⢸⠀⠸⣋⣾⣿⣿⣿⣿⣿⣿⠤⣳⣿⣿⣿⣿⣿⣿⢙⠇⠀⠘⠚⠉⠂⡇
⣦⣶⣶⣧⣤⣤⣤⠤⠴⠟⣫⠔⠁⠀⠀⠀⠀⢸⣸⠀⠀⠈⠫⣛⠿⢿⣿⡿⣿⠒⣟⠿⣿⡿⠿⣛⡵⠃⠀⠀⢠⠤⠢⠄⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⡞⠙⠢⣀⠀⠀⢠⠏⠱⣤⠎⠈⠙⠲⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠑⢦⣸⠁⠀⠀⠈⠳⢤⡏⠀⠀⠈⠑⠦⣀⠀⠀⠀⠈⣉⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⠂⠠⡉⠳⣄⡀⠀⠀⠀⠉⣻⠂⠀⠀⠀⣨⠗⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⠢⣈⠳⢄⡉⢓⡆⠀⢰⡟⠀⠀⠀⢰⠃⠀⠀⡾⣄⣀⠀⢀⣀⣀⡤⠔⣄
⠀⠀⠀⠀⠀⢠⣖⠒⠒⠒⠳⣄⠐⢄⡑⠢⡀⢸⡶⠀⠈⣧⠀⠀⠀⣿⠀⠀⢸⣇⠀⠉⠉⠉⠁⠀⠀⠀⠈⠑⠢⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠈⣿⣿⣶⣄⣀⠈⠓⢤⣈⠓⠄⠸⣧⡅⠀⠈⠳⣄⠀⢻⡀⠀⠈⣏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣟⣀⡀
⠀⠀⠀⠀⠀⠀⠙⠻⢮⣟⣿⣿⣦⣄⠈⠙⠲⣄⡈⠳⣄⣀⠀⠙⢦⣀⠱⣄⡀⠘⢎⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣯⣤⣶⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⢝⣿⡿⣿⣦⣄⠀⠉⠙⠚⠻⠿⣶⣤⣬⣟⣶⣿⣶⣦⣽⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⡶⠶⠾⢿⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⡺⣷⣝⢷⣤⣖⠭⢭⣿⣿⣿⡿⣿⡿⢿⣿⣿⡿⠷⠶⢟⣛⡶⠾⠿⠛⠛⠚⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢽⢵⣛⣚⢩⣭⣦⡶⠮⠿⠟⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠋⠉⠁




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣯⣮⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣷⣿⣿⣿⣿

⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡂⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⡀
⠀⠀⠀⣰⣿⣿⡄⠀⠀⠀⠀⠀⠀⢿⣿⣏⣿⣹⣿⡇⠀⠀⠀⠀⠀⢸⣿⡆⣴⣿⡇⠀⠀⠀⠀⠀⠸⣿⡿⠒⢿⣿⠇
⠀⠀⢠⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿
⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣠
⠀⠀⠿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣸⣿⠏⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠉⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣬⣏⣹⣴⢤⡀⠀⠀⠀⠀⠀⢤⡦⢏⡡⢴⡄⠀⠀⠀⠀⠀⠀⠠⠨⠀⠀⠂
⠀⠀⠸⣎⣿⣱⠆⠀⠀⠀⠀⠀⠀⠙⢻⢻⢻⢻⠋⠀⠀⠀⠀⠀⠀⠀⠈⢹⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄
⢠⡴⠿⠾⠿⠷⠿⢦⡄⠀⠀⠀⠀⠀⠘⠘⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⣀⠔⣀⣀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠉⠉⠐⢄⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⡥⢤⡤⠏⠁⠉⠙⣄⠀⠀⠀⠀⡞⠀⠀⡀⢀⠀⠀⣇⠀⠀⢠⡶⠛⠛⢦⡰⠶⣶⡄
⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢹⡀⠀⠃⠘⠀⢀⡏⠀⠀⣿⠀⠀⠀⢀⡷⠀⠈⢿
⠀⠀⠀⠀⠻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠦⠏⠀⠀⠀⠀⠀⠙⠢⠤⠤⠖⠋⠀⠀⠀⠈⠢⠄⠤⠞⠀⠑⠤⠞


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣄⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀
⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣠⣀⣥⠀⠀⠀⠀⠀⠀⣿⣧⣿⡿⠀⠀⠀⠀⠒⢿⣿⣿⣿⣿⣷⣄
⠀⠀⢹⠿⣦⣄⣠⣶⣄⠀⠀⠀⠀⠀⠐⠉⠉⠙⢽⡍⠀⠀⠀⠀⠀⠀⢹⣏⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⠿⠆
⠀⠀⠸⠀⠈⠻⠿⠿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⣾⡆
⠀⠀⠀⣿⣇
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⠀⢀⣰⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣦⣄
⠀⠀⢰⣿⣿⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡒⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⢸⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠈⣿⣿⢽⣿⡗⠀⠀⠀⠀⠀⠀⢴⡟⣿⣿⣿⣿⣿⣿⠿⠿⠈⢹
⠀⠀⠸⣿⣿⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡿⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣬⣙⣛⣛⣛⣛⣤⣠⡼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉


⠀⠀⢠⣦⣶⣤
⠀⠀⣾⣿⣿⣿⡇⣴⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⢰⣿⣿⣿⡿⣼⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⢠⣤
⠀⣸⣿⣿⣿⣷⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⣿⠂⣰⡿⣿⡇
⢰⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢸⡏⣰⡿⠀⣿⠁
⠺⠿⢿⣿⣿⣟⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣿⣷⣶⣶⣶⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣋⣠⣯⣿⡿⠁⣼⢿
⠀⠀⠀⠘⠃⠈⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⢿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⡀
⠀⠀⣀⣞⣉⣉⣉⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠋⠁⠀⠈⠑⢳⣄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠁⠀⠀⠀⠀⠀⠀⣱⡄
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣶⣶⡤⣴⣶⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⢈⣯⡀⠀⠀⠀⠀⠀⠀⣼⡅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡀⣸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠛⣴⣦⠀⣀⡀⣠⣦⡝⠁
⠹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⢺⣿⡗⠛⠋


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠒⠛⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠁⠀⠀⡈⣷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠦⣄⠀⢹⣿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⢿⠿⠛⠛⠻⠶⣦⡀⠀⡀⢀⣈⠛⠶⣿⣿⣷⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠁⠀⠀⠀⠀⠀⠀⠁⠠⣴⠆⠙⢿⣷⡶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⡟⠁⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢉⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⣆⢸⠀⣌⡼⠀⠀⠀⠀⢹⣦⡀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣭⣷⠀⠰⢤⣾⣿⠶⠛⠁⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣝⣷⣾⠇⠀⠀⠀⢿⠁⢀⡀⠀⠀⠀⠀⠀⠀⢰⡎⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⢾⣿⢏⠃⠀⠀⢀⣾⣿⣿⣾⣷⣿⣾⣿⣾⡷⠘⢿⡄⠀⠀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠒⢾⡟⣾⡀⠀⣀⣸⣿⡿⣿⣿⣟⢿⣿⣿⡏⣄⡀⠀⠃⣠⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⠰⣷⣜⠇⣼⣿⣿⣿⣿⣷⣾⣿⣶⣿⡿⢷⣍⠻⣦⠈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣂⠀⠉⠺⡿⠀⠈⠛⠿⢿⡿⢿⣿⣯⡉⠉⢀⣀⣹⣿⣮⣁⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⡀⠀⠀⠀⠀⠘⢛⣂⣙⣃⠁⠀⢀⣁⣴⠷⡍⢙⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠉⠀⣾⢡⣶⣶⣾⣿⣭⠽⠿⠷⠆⠀⣠⣿⣿⠿⠀⠀⢹⠃⠙⣿⡷⣿⣦⣤⡖⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⢿⠀⠀⣠⠞⠋⠉⠉⠉⠁⠀⠀⢀⣤⠖⢀⣴⣿⣿⣧⠀⠀⠀⠈⢠⣴⣿⣧⣈⢿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠀⢠⣾⠏⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⣴⣿⣿⡏⠘⠛⠁⠀⠀⠀⠸⣿⣿⣿⢻⡆⠻⣱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠁⠀⠀⢀⣾⠃⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⢀⡴⠟⢁⣴⡿⣿⣿⠛⠛⠀⠈⠻⣿⣷⣦⡀⠀⠉⢻⣿⡶⠚⠛⠁
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⣼⠇⠀⠀⣰⢋⣴⡇⠀⠀⠀⣠⠶⠋⣠⣾⠟⠉⢰⣿⡏⢀⡄⠀⠀⠀⠈⢿⣿⣷⡀
⠀⠀⠀⠀⣠⣿⣿⠟⠁⠀⠀⢀⡤⠂⢰⠏⠀⠀⠐⢱⣿⣿⣴⠞⠋⠉⢀⣴⡾⡋⠀⠀⠀⣼⡿⢰⣿⠇⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠀⢀⣼⣿⡿⠋⠀⢀⣠⠞⠉⠀⠀⠚⠀⠀⠀⠀⣾⣿⡇⠙⠆⣀⣴⠟⢉⣾⠁⠀⠀⢀⣿⠃⢸⣿⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⢀⣾⣿⡿⠁⠀⣴⣿⣷⣆⠀⢀⠀⠀⠀⢀⣤⣶⣿⣿⣀⣤⣾⠟⠁⢠⣾⡇⠀⠀⠀⣸⡟⠀⢸⡿⠀⠀⠀⠀⠀⢸⣿⣿⠁
⠀⣼⣿⡟⠁⠰⠾⣿⡿⠿⠛⢣⡞⠀⠀⣰⣿⣿⣿⣿⣿⣿⠟⠁⠀⢠⣿⡟⠀⠀⠀⢠⣿⡇⠀⢸⡇⠀⠀⠀⠀⢀⣿⣿⡏
⢰⣿⣿⠁⠀⢀⣴⠏⠁⠀⢀⣾⣉⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣿⣿⠁⠀⠀⠀⠈⠛⢁⠀⣸⡇⠀⠀⠀⠀⣼⣿⡿
⣾⣿⡇⠀⠀⠀⠉⠁⠀⣴⣾⠇⠀⠀⠀⣿⣿⡿⠿⠟⠁⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⢀⣼⣿⡿⠁
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⣠⡌⠉⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠁
⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣀⡄⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠘⣿⣿⣿⣶⣦⣤⣶⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡿⠋
⠀⠈⠻⠿⣿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣄⠀⠀⠀⢀⣠⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⡠⠀⠀⠀⡠⠒⠉⠙⠛⠉⠙⠒⢦⡀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠉⠐⠂⠶⠈⣀⠀⠀⠀⠀⠤⠐⠀⠀⠀⠀⠈⠉⠐⠲⠤⢀
⠀⠀⠀⡠⠚⠠⢐⣀⡞⠁⠀⡀⠤⠊⢡⡄⠀⠀⢹⡿⡎⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣠⠴⢛⠢⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⣴⣶⡂
⠀⢀⣼⠀⠀⢀⠚⠋⠐⠒⠀⠀⠀⡀⢉⣦⠀⠀⣸⣿⡧⢀⢀⠠⣂⣵⣶⣾⡄⣀⢔⠩⣶⠿⠟⣁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣿⣿⣿⣯⡥⠔
⠈⠀⢬⣑⠈⠁⠀⠀⠀⠙⠲⠒⠋⠁⠈⠉⠂⠰⢿⣿⣷⣏⣵⣾⣿⢿⣿⣿⢻⣫⠵⣾⣶⣿⣟⡍⢿⣦⣤⣴⣶⣿⣿⣿⣿⣟⣽⣿⣿⣿⠗⠊
⠀⠀⢚⠾⠷⣦⣄⣀⠀⠀⠀⠀⣀⣠⢴⣶⠶⠴⠒⣘⡿⣿⣿⢿⣧⠸⡿⠿⠾⣛⣲⣋⣫⣭⡖⠌⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠟⠛⠛⠛
⠀⠀⠀⠠⣒⣲⣦⣉⠝⠒⠦⣝⡫⠶⡅⣴⣢⠾⢛⣋⣐⣼⣤⠬⠽⠿⠷⠖⠛⠛⠛⠛⠉
⠀⠀⠀⠸⠶⠾⢭⣟⣢⠤⣄⠀⠚⣳⢞⡩⢒⡽⠿⣿⠿⠛
⠀⠀⠠⣠⡍⢙⡛⠒⠚⠉⠓⠦⠄⠖⠁⢈⣡⡾⠉⠁
⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠉⠉⠁