Black and white duck Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣟⢹⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠉⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠿⠟⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠀⣀⣀⣠⣤⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠛⠉⠉⠉⠉⠙⠚⠻⠿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⡛⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠑⢶⡶⠶⠶⠤⠤⠤⠴⠶⠒⠚⠉⠁⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷
⠀⠀⠙⢷⣶⣤⣭⣓⣦⣤⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠒⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿
⢨⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⣾⣿⣿⣿⣿⣿⡟
⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡲⢤⣀⢀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠶⠒⠢⠤⠄⡀⠀⣀⣠⣀⡶⠋⢑⡵⣫⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣝⣛⠿⢿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⠶⠟⠋⠁⠀⠀⠀⢔⡽⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠈⠙⠻⣝⡛⠛⠛⠛⠛⠛⠿⠿⠛⠛⠛⠒⠢⠌⠉⠉⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡪⢾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⡽⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠵⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⢠⠞⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⡟⠛⣇⠀⠄⠀⢖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠁⡀⢀⡀⠀⠸⠃⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠀⠤⠤⠤⠤⠄⠀⡀⢃

⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢀⡀⠀⠀⢠⠨⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠐⢋⣉⠀⠈⠁⠀⣩⡙⠄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣿⣿⠟⠻⣿⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠚⣻⠇⠀⠒⠌⡹⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡿⢿⣿⣿⣧⡴⠛⣉⣉⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠤⠄⠊⠀⠠⠂⠉⠉⠁⢣
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣭⣭⣥⣾⣿⣿⣽⡧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠄⠐⠄⡀⡀⠄⠒⡅⠀⡁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⡿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⢀⣸⡄⢀⠈⢷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣛⣫⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠙⣍⠁
⠀⠀⠀⠀⠀⠀⢠⡟⠢⢄⣀⣠⣴⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⠄⠀⠀⠠⠊⠀⠀⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠸⣿⠀⣠⠶⠚⠛⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠄⠂⠂⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⣿⣾⣇⠀⠀⠀⢀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠔⡋⡀⠀⠀⠀⠸⠀⠀⠀⠀⡀
⠀⠀⠀⢀⡀⠀⠠⠾⣿⣿⣷⣤⡴⠞⠻⠿⠿⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢥⣀⣃⣄⡠⠔⠉⠀⠂⠐⠐⠁
⠀⠀⠀⠉⠒⠒⣤⠁⠙⠻⠿⢿⣦⣤⠴⠶⡾⠍⢁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠒⠠⠀⠄⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⠄⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡭⠿⢿⣿⡟⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣶⣶⣤⠀⠀⣠⣬⣽⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠛⠓⠋⠀⠀⠀⠀⠛⠓⠚⠦⠭⣽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣤⠃⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠠⣀⣀⣠⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⣻⣇⣻⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⣀⣤⣠⡤⠒⡊⠉⠉⣉⠉⠘⠀⠀⠈⠉⠈⠁⡀⠀⠉⣻⣿⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠶⠾⠟⠋⠉⢀⣠⣤⢆⡨⠀⣠⣴⢀⣡⣀⣠⣆⣠⣤⡆⠀⣤⣾⣿⣟⣏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠔⠀⣋⣉⡓⠦⢿⣾⣷⣶⢿⣷⣭⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣞⣿⣽⣿⣿⣟⢟⡿⣿⡟⡳⠘
⠀⠀⠀⠀⠀⣀⣤⣾⣦⣤⣀⠀⠲⠮⣍⣳⣻⣿⣿⣿⣿⣿⣯⣟⠻⣿⣿⣷⣿⣾⣿⣿⣿⡿⣿⣯⡼⠛⢛⣻⡭⢯⠖⢠⠃
⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣝⢿⣿⣿⡻⢻⢿⣿⣮⣉⠛⣿⣿⠿⠟⡻⠿⠛⢋⡀⣐⡬⠤⢖⠑⠈
⠈⠉⠉⠉⢉⣩⡿⣻⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⣿⣿⣯⣝⣯⡯⣤⣖⣴⣒⡙⢁⣦⠖⠋⢉⠙⠁
⠀⠀⣠⡴⠛⠁⣠⢿⣿⣿⣿⢿⣻⡟⠯⠛⠛⠛⣛⢿⡾⠿⠛⠁⣡⡤⠒⢧⡈⠠⠄⢊⠀⠤⠄⠊⠁
⠀⠈⠁⣀⣴⢾⣿⣿⣿⣿⣶⣮⣟⠳⡖⡆⠀⠀⠈⣅⠰⠶⠭⢭⣥⡶⠶⠼⠉⠠⠠
⠀⣀⡽⢿⡿⠿⠛⠩⠶⠀⣠⠍⣉⣠⣝⣶⠁⠐⠄⠚⠛⠓⠂⠲⠼⢒⢂⡉⠀⠄⠀⢀
⠀⠀⠀⣤⡄⠈⠀⠒⠁⠀⠀⠀⠉⠉⠉⠉⠉⠛⠪⠄⣀⡀⣀⡀⢠⣤⣾⠚⠷⢲⣾⢙⣒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⢿⣿⣛⡋⢿⡇⠤⢈⣁⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢁⣼⣷⣧⡤⠶⠖⠛⠛⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⠿⠿⠷⠶⠞⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠀⠀⡀⠀⠉⠲⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠀⢣⡀⠈⠁⠀⠀⠀⢹
⠀⠀⠀⠠⢒⣉⣤⡤⠶⠥⣄⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠈⠋⠁⠀⠀⠀⡰⠈⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⢶⠉⢦
⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠤⠤⠤⠤⢄⣀⣠⢀⠜⠀⠀⠀⡼⢺
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⢀⡴⠉⣠⠞⢓⠀⠀⠀⠈⣠⠃
⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠠⢤⣀⡤⠋⠀⠀⠀⠤⡿
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⠀⠀⠈⢉⠟⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠰⣄⠀⠀⠀⠀⠔⣊⠀⠤⠤⠊⠀⠐⣊⠝⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⣀⣔⡊⠁⣠⣤⣚⣁⣀⡭⠃⠀⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠈⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠢⠤⠤⡄⢠⠄⣀⣀⡀⣀⣀⣀⡠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠁⡞⠀⠀⡸⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣉⣀⣀⠜⠁⣀⡠⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⢁⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠛⠛⠛⠛⠛⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⣤⣄⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠖⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠛⠛⠒⠒⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣠⡶⠶⠓⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⡀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⠞⠉⠀⣀⡀⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠏⠀⠀⠈⢿⣿⣷⡀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⣠⣶⣿⠃⠀⠀⠙⣧⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣿⠀⢰⣶⣴⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣷⣄⣴⡆⠀⣿⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣆⠀⠻⣿⣿⣿⠟⠁⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢿⣿⣿⣿⣿⠃⠀⣿⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠙⢧⣄⠀⠀⠀⣀⣴⠏⢀⣤⠶⠛⠛⠛⠳⠶⣤⡀⠹⣦⡀⠉⠛⠉⠁⣠⡾⠁⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠉⠙⠛⠋⠉⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠙⠶⠶⠶⠞⠉⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠇⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠙⢾⡻⢦⣀⣀⠀⠀⠀⠀⣀⣠⠴⢛⡵⠋⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⡀⠀⠀⠙⠶⣌⣉⠛⠛⠛⠋⣉⣥⠶⠋⠀⠀⠀⠀⣀⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡷⠶⣤⣄⣈⡉⠛⠛⠛⠛⠉⠀⣀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⠚⠛⠛⠛⢳⡟⠁⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁⠙⣷⠶⠒⠲⠶⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠉⠻⢦⣀
⠀⠀⠀⠀⢠⡾⠉⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⣼⠃⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠸⣇
⢰⡏⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⢹
⣾⠁⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⠀⠀⠀⠀⠀⠈
⣿⡀⠀⣀⣤⡶⠛⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠻⢦⣄⡀
⠈⠙⠋⠉⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠈⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠛⢻⡶⠶⠶⠶⠶⠶⠶⢶⡖⠛⢛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡾⠁⠀⠀⠀⠀⠀⠀⠈⢷⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢞⣉⡀⣠⣍⡳⣄⠀⠀⠀⠀⠀⠀⣠⣶⣋⣄⢈⣙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣋⣩⡇⢸⠉⢻⣎⣷⠀⠀⠀⠀⣴⣿⡟⠉⣯⢸⣏⣛⣮⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣧⣶⣷⠿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⢾⡏⠁⠀⠈⣿⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣔⣊⣁⡤⠴⠒⠻⣤⣴⣾⣯⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡸⠋⠉⢹⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠁⢀⣤⣿⣿⡇⢀⣠⣶⣿⣿⡿⠿⠿⠿⠿⠿⠿⠶⣦⣤⣀⣀⣤⣄⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣁⣭⠔⠻⠿⢿⣿⣷⣿⠟⣫⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡞⠁⠀⠀⠀⠀⢺⣿⣿⢁⡀⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡇⠀⠛⠀⠀⠀⠤⠣⠟⣿⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⣀⣠⣤⠴⢖⡂⠈⠣⣀⡀⡀⠀⠀⠀⠀⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠴⠶⠶⣶⡶⠒⠒
⠀⠀⠀⠀⠀⠈⠳⠬⠓⠲⠦⠤⢬⣝⠻⢷⣴⣦⣀⣴⣵⣺⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣉⣤⠈⣲⠄⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣍⣀⣀⣈⣉⣙⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠒⠒⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠤⠄⠒⠒⠒⠒⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⡿⠋⢁⣀⣤⣄⡀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠈⠁⠀⠀⠀⠙⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⣴⠄⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠲⡄⠀⠀⠸⣽⠃⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⣏⠙⠓⠚⠛⠋⠀⠀⠾⠃⠀⠀⠀⠉⠉⠙⣲⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⡄
⠀⠀⠀⠀⠀⠈⠙⠲⣦⠤⣤⣀⣀⡀⠀⢀⣀⣠⣤⠖⠋⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⡼⢇
⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣠⡭⠽⠿⠿⠛⢉⡇⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣖⣴⢿⣿⠃⢸⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢻⣠⡤⠶⠖⠛⠛⠛⠋⠉⠉⠸⠿⠛⣡⢸⠃⠀⠈⡼⡇⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠼⢡⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠒⠲⠶⠦⣤⣀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡣⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠰⠯⠥⢤⡄⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⡆⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠀⢀⠞⢀⡞
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠸⣆⠀⠳⣄⡈⠙⠲⠦⣷⣦⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠙⠷⣦⣄⣙⠛⠶⠦⣤⣀⣉⠛⠓⠶⠶⠶⠶⠶⠾⠛⠉⠁⢀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠦⠍⠉⠛⠛⠒⠒⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣽⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣿⣿⡻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣟⠳⢬⡀
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠙⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢃⣀⣠⣤⣤⣤⣀⣸⣿⣿⡿⠿⠿⢷⣀⣱
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠢⠀⠀⢠⠋⠀⠀⠀⣀⣀⣤⣤⣶⣶⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣶⣿⣟⠻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣴⣾⣿⣿⠿⠛⠋⠁⠀⠀⠀⡒⠴⠖⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠉⠁⠐⠶⣶⣶⣶⣾⣿⣧⣶⣿⣿⣿⣿⠿⠛⣛⣿⣿⣿⣿⣿⣟⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣴⣿⣭⣥⣴⣶⣒⣒⠛⠛⠻⠿⣿⡿⠿⠿⠯⡉⠿⣷⣶⣾⣿⠿⠟⠹⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣿⣿⠿⣟⣿⡏⣼⣿⡿⠿⠷⠶⠾⢷⣿⣷⣶⣦⣼⣄⠹⠛⠉⠀⠀⠀⢸⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⠁⣿⡅⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⢀⣀⣀⣠⣴⣾⣿⠿⠛⠁
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⢿⣤⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠙⡿⢿⣷⣤⣀⡀⠀⠀⠀⣀⣤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢸⡆⣤⢀⡡⣀⠨⠉⠛⢻⡿⢻⡟⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣙⠲⢿⢁⣿⢸⣿⣇⣦⠾⣠⠠⠅⠸⠇⠇⢀⡄⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣃⣿⣿⣶⣮⣳⣝⣿⣿⠿⣬⣟⣿⡶⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠠⠚⠓⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣟⣯⣿⣿⣿⣯⣭⣥⣤⣤⣤⣿⣻⣶⣆⣬⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⠿⠿⣿⣿⠭⣿⠿⠛⠻⠿⠶⠿⠗⢺⡇

⠀⠀⠀⠀⢀⡀⢠⡄⢀⡄⠀⠀⠀⠀⠀⠀⣦⠀⣇⠀⢠⡄
⠀⠀⠀⣄⢸⡇⣾⣧⣸⣇⣾⠀⠀⣷⡀⢀⣿⢸⣿⠀⣿⠁
⠀⠀⡀⢿⣾⣿⣿⣿⣿⣿⣿⣧⡀⢿⣷⣘⣿⣿⣿⣿⣿
⠀⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⡿⢧⠻⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠰⣼⣿⣍⠛⠆⠀⠈⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣩⣿⣟⠓⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠈⢙⣿⡷⠆⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠛⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⢠⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠛⠦⠤⣀⣀
⠀⠀⠀⠀⠀⠀⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠀⠀⠀⠀⢀⡾⣻⣿⣿⣿⣿⣿⣿⠿⠿⠐⠒⠒⠛⠛
⠀⠀⠀⠀⠀⠀⠛⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡀⠀⠀⢠⠞⠑⠻⠿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣶⠾⠋⢠⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⠋⠁
⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠋
⠀⠀⢀⣾⣿⡷⢠⣄⣀⠀⠀⠀⣀⣠⣤⣶⠶⠟⠛⠉⠁
⠀⣠⡿⠟⠋⣀⣈⣿⠿⠃⡠⠚⠋⠉⠁
⠘⠉⠐⠚⢛⣿⣿⣿⠿⠟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠿⠛⠛⠛⠻⠿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠻⣦⠀⠀⠀⠈⢿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢀⣿⠃⠀⠀⠀⠘⣿⣿⣿⠛⠛⠛⠛⠛⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⢀⣼⣿⣿⡿⠛⠿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⣠⣿⣿⠃
⠀⠀⢀⣾⣿⣿⠟⠀⠀⠀⠈⠙⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣃⣀⣠⣴⣾⣿⠟⠁
⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⡈⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⡿⠿⠿⠟⠋⠁
⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇
⢰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄
⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿
⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇
⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁
⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏
⠀⠀⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿
⠀⠀⠈⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁
⠀⠀⠀⠈⢻⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣶⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡁⠀⠀⢀⡀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠋⡀⠀⠘⠁⠀⠀⠀⠀⢻
⠀⠀⠀⠀⢀⡤⠖⠊⣁⣠⣤⣂⣉⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⢯⡴⠾⠛⠋⠉⠉⠀⡙⠓⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣄⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠳⠁⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠤⠤⠤⠤⠤⢀⡀⢀⡄⢀⠞⠀⠀⠀⢠⠗⢻
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠤⠴⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢉⡽⠯⢥⠀⠀⠀⠐⠉⣠⠏
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⠀⠀⠊⠀⣠⠃⠀⠀⠀⠀⢚⡏
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⢀⣉⣽⣤⠚⠁⠀⠀⠀⠀⠊⣩⠃
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠒⠋⢀⠀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⢐⠟
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⢦⠀⠀⠀⠀⠀⠤⠖⣋⠀⠀⠤⠔⠋⠀⠀⠊⣩⠏⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠁⠀⠀⠀⠠⠤⠚⠁⠀⣀⡤⠖⠁⠒⢚⡽⠁⠀⠀⠀⢀⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠓⠒⠒⠚⠛⠒⠒⠚⠋⠁⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⢲⠎⢱⠆⠤⢤⣄⣀⣀⣤⣤⠤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞⠀⣸⠀⠀⠀⡾⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠁⠀⢀⡴⠁⠀⠀⣠⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠛⠋⠉⠉⡠⠴⠚⠉⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠧⠤⠴⠖⠒⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠴⠊⠉⠉⠉⠁⠒⠒⠒⢶⡄
⠀⠀⠀⠀⡰⠁⠀⠀⠴⠄⠀⠀⠀⠀⠀⠀⠹⣀
⠀⠀⠀⢀⣇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⡾⣡⠘⣧⣐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⡼⡅⠛⢀⣠⠞⠛⠛⢻⡟⠳⠀⠀⠀⠀⠀⠀⡆
⢠⢚⠖⣀⠴⠋⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⢰⠃
⠧⠔⠚⠁⠀⠀⠀⠀⣠⠞⠡⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⡸⠁⠐⠠⠀⠀⠀⠐⠀⠀⠀⠈⠉⠉⠉⠑⠒⠚⠒⠶⢤⣀
⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀
⠀⠀⠀⠀⢸⠀⠀⠐⢀⠂⠁⠢⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠤⢀⣀
⠀⠀⠀⠀⣾⠀⠂⠁⠈⠈⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠒⠦⠤⢄⣀⡀⠀⢀⣀⣠
⠀⠀⠀⠀⢰⠈⡠⠀⠀⠁⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣽⣿⠟
⠀⠀⠀⠀⢰⠌⡣⠀⠀⠐⠀⡀⠐⠂⠀⠈⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠳⣈⢦⠀⣀⣀⡀⠀⠀⠀⠀⠈⠐⠂⢀⠄⣀⣿⠟⠁
⠀⠀⠀⠀⠀⠳⣄⠠⠀⡀⠂⠁⠀⠐⠀⡀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡈⠑⠮⣄⡈⠉⠀⠠⡞⠩⢄⡀⠄⠀⣸⠋
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⡌⠁⠀⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠀⠀⠉⠩⠐⠉⠀⠀⠁⣀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢥⣤⡤⢀⠐⠈⠀⠢⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣶⠎⠠⢄⡀⢔⣋⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠺⠥⣤⣀⣄⡀⢀⣀⠘⠆⠀⠑⠀⠀⠀⠉⢶⡀⠀⠁⢺⣄⣨⡴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣷⣶⢶⣤⣤⣜⣀⠀⢀⣶⠿⠷⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⡿⠊⠟⠋⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⡟⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣺⣿⣯⣿⣯⣵⣾⣿⣿⣽⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣩⣿⣿⣿⣛⣿⣾⡿⠖⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣽⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣅⣅⣥⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠀⠀⡀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⣠⠞⠀⢣⡀⠈⠁⠀⠀⠀⢹
⠀⠀⠀⢠⢒⣩⣤⠴⠶⠥⣄⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠈⠋⠁⠀⠀⠀⡐⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⢶⠉⢦
⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠤⠤⠄⠀⢀⣄⣠⣀⠜⠀⠀⢀⡞⢻
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⢀⡴⠁⣠⠞⢳⠂⠀⠀⠈⣠⠃
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠠⢤⣀⠴⠃⠀⠀⠀⠴⡟
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠀⠈⣉⠟⠀⠀⠀⠀⢰⠎
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣇⠘⢄⠀⠀⠀⠀⠐⡊⠀⠤⠔⠊⠀⠀⣩⠟⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⣀⣀⣒⣊⣀⣠⣴⣊⣀⣈⠽⠃⠀⠀⢀⠌⠁
⠀⠀⠀⠀⠀⠀⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠠⠤⡄⢠⠄⢀⣀⣀⣀⣀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠜⠁⡎⠀⠀⡸⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣁⣠⠤⠞⠀⣀⠤⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡉⣀⣀⠜

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠶⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢳⡀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠑⠄⡀⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡀⠄⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠈⠓⠤⠤⣤⣤⣀⣤⡤⠄⠄⠒⠛⢒⡸⢇⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠈⠁⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠓⠒⠒⠒⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⠄⠁⣈⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠠⠃⡼⠁⠀⠊⠈⠀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡰⣌⠢⠐⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠈⠳⡄⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡈⠁⠀⠀⠀⠀⠀⠀⠙⠾⣶⢤⣀⡀⠀⠀⠀⠤⢄⣀⡀⠀⠀⠉⣫⠉⠉⠁⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠓⠒⠒⠒⠒⠒⠲⡖⠚⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠳⡀⠀⠀⠀⠀⢱⠀⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠎⠁⠀⠀⠀⠀⠀⢀⡴⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠠⠄⠀⠀⠀⠀⠀⢀⠤⠚⠉⠁⠀⠀⠆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠴⠓⠢⠔⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠉⠁⠀⠈⠉⠙⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⣾⠉⢙⡆⠀⠀⢹⣿⣷⣶⣶⣶⣶⣶
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠁⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸
⠀⠀⠀⣠⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⢠⣿
⠀⠀⣼⣿⡟⠁⠈⠙⠿⣿⣷⣄⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⣀⣠⣴⡿⠋
⠀⣼⣿⡟⠀⠀⠀⠀⠀⠈⠻⣿⣷⣀⣀⣀⣀⣠⣹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠛⠛⠛⠉
⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇
⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄
⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿
⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠈⢿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⡿⠁
⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣶⣶⣤⣤⣤⣄⣀⣀⣀⣠⣤⣤⣤⣴⣶⣾⣿⣿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⡀⠀⠀⣠⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠘⢡⡀⠀⠉⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⡠⠒⣋⣡⣤⣴⡮⠥⣄⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠳⠚⠋⠉⠀⠀⠀⣠⠈⠁⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢦⣀⠖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠹⠀⢸⣀⡄
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠘⢢⡀⠀⠀⠀⢀⣀⣤⠤⠤⠒⠒⠒⠒⠒⠀⠀⢀⡴⠦⢴⡦⠜⠁⠀⠀⢀⠞⢁⡇
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⡰⠛⢉⡇⠀⠀⠀⠁⣠⡎
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠤⢤⢀⡠⠎⠀⠀⠀⠀⠤⢾
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠐⠒⢋⡟⠀⠀⠀⠀⠀⢠⡴⠃
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢤⠀⠀⠀⠀⠀⢀⣀⡴⠂⠀⠀⣀⡴⠀⢀⠠⠖⡟⠀⠀⠀⠀⠀⣰⠊
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⠓⠀⠀⠀⠀⢀⣠⠞⠀⠈⠉⣡⠀⠀⠤⢴⠏⠀⠀⠀⠀⡤⠚⠁
⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠬⠭⢤⣤⡤⠾⠭⠤⠤⠴⠒⠁⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠦⠤⠤⡤⠂⡤⢀⣀⡀⠀⠀⢀⣀⣀⣠⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⢰⠇⠀⠀⢹⢩⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠊⠉⠀⢠⠞⠀⠀⠀⡎⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠒⠚⠛⢁⡠⠴⠒⠉⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠮⠤⡤⠤⠴⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⠉⠛⠿⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⠈⠛⠿⢦⣈⠙⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⢳⣤⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⠿⡿⢿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣯⣅⣀⢀⣀⣠⣤⣤⣤⡙⣿⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠾⠿⢻⢏⠉⠁⠉⠘⡁⠉⢹⣷⠞⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣝⠻⢿⣦⡈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣶⣤⣟⣩⣽⠿⠶⢒⣀⣫⣄⣡⣠⡀⠀⠘⠁⠀⠴⠂⢀⠀⠁⠂⠁⠛⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡭⢀⠈⠓⠄
⣀⣀⠀⠀⠀⠀⢀⣈⣙⣧⣟⣃⠠⣾⣷⣾⣿⣛⣛⣛⣉⣩⣤⣭⡽⠛⠉⠁⠈⠀⠀⣀⡴⢊⡁⣠⡄⠀⠀⠀⠀⠈⠁⡻⢛⣧⡼⠏⣿⠛⣿⢿⣿⣿⣷⠀⠙⠒⠒
⠙⢿⣿⣶⣶⠒⠒⠚⠻⣿⣿⣿⣷⡌⠹⣿⣿⣿⣿⣿⣽⣶⣾⣿⣿⣡⣤⣀⡴⠀⣼⣿⠟⠋⠀⠉⢀⣴⠀⠀⠰⠀⠠⣰⣨⡿⠃⠀⠀⢼⠘⢃⣸⡿⣿⣇
⠀⠀⠈⢿⣛⡓⠃⠈⠿⠿⠿⣿⣯⣿⣷⡌⠛⠯⣀⣰⣿⣿⠿⠿⠟⢋⣵⡿⢇⣼⣿⣁⡴⢾⣄⣠⠿⠛⠉⠀⠄⢀⣠⣿⠏⠀⠀⠀⠀⠀⡠⢾⣥⠅⢿⣿
⠀⠀⠀⠀⠈⠻⠷⣦⣤⣤⣄⣨⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⡿⠿⠶⠿⢥⣤⣬⣚⣛⠉⢠⠿⠛⠐⠀⢠⣾⠁⢾⡿⠛⠋⠀⠀⠀⠀⠄⠀⣡⡾⣿⣳⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⣠⣶⣤⣀⣀⠈⢽⣿⢿⠿⣶⣶⣤⣶⣿⣿⣿⣿⣵⣀⣾⣿⣿⣿⠶⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⢉⣴⣿⣧⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣦⣬⡙⢻⣿⢟⡃⠟⠈⣙⡉⠣⠝⣻⡿⢿⡿⠋⠉⠉⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣰⣺⣧⣶⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣵⣾⣿⣴⣯⣶⠟⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⠀⡀⠐⠀⡠⠚⣽⣡⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣷⣿⣷⣶⣦⣦⣄⣠⣠⠤⣄⢀⢠⣼⣿⣾⣧⣶⣴⣶⣾⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⢻⡟⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣎⢧⣄⣤⣤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⠐⠿⢿⣶⣿⣻⣻⡟⡛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠑⠒⠢⠤⠉⢉⣛⣉⠉⠉⠉
⣿⣿⣿⠿⣿⠿⢿⢿⡿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣶⣶⣶⣶⣿⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠒⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠳⡀⠀⠿⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⡤
⠐⠥⢀⣀⣀⣀⣀⣀⠀⠠⠤⠤⢔⣇
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠉⠁⠈⠙⠁⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠉⠓⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡀⠀⠀⠀⠀⠀⡠⢲⠀⠀⡠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠐⠀⠋⠀⠀⠀⠀⠤⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⢄⡠⠀⠀⠰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⢦⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠂⠀⠀⠀⠀⠀⠑⠦⣦⣄⡀⠀⠀⠀⠀⢀⣀⠀⠀⠉⢻⡒⠒⠁⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠒⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡍⠉⠉⠉⠉⢫⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠈⠀⠀⠀⠀⡨⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣉⠀⠀⠀⠀⠀⠀⡠⠔⠛⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⠬⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠚⠋⠒⠲⠆⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠈⠉⠁⠀⠁⠀⠀⣀⣤⡀⠀⢐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠓⢀⣀⣀⡀⢀⣤⡤⠤⠌⠁⠀⠰⣶⣤⣤⣤⠀⣠⠌⠁⠀⢀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠛⠟⠁⠀⠈⣅⠀⠉⠉⠢⡐⢦⣐⠲⠤⢝⠊⣉⣙⣥⣶⡟⢋⣩⣽⣿⣶⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣾⣧⠂⠀⠀⠦⠠⠶⠆⠂⠀⠐⠛⠂⠉⢀⡁⠈⠁⠉⠀⠉⠹⢿⣻⡵⠞⠛⠉⠉⠉⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⡐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣀⡀⡓⣀⣤⡀⠀⠀⠀⢀⣰⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠈⠛⠀⠐⠲⠟⠓⠒⠲⣶⣴⠶⠂⢒⣓⣒⣒⠒⠓⠒⠛⠛⠛⠿⠋⠭⢿⡝⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠠⠀⠀⠀⠈⠉⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⣀⣖⠀⠘⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⣀⠉⠀⢀⡀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠒⠂⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠛⠓⠀⠉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⣤⣀
⠀⠀⠀⠀⣀⡴⣿⡿⠿⠿⠛⢿⣿⣆
⠀⠰⠊⠭⠭⠤⣿⣷⣤⣀⣱⡎⣻⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⠋⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡷⠶⠤⠄⢠⠤⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠉⢋⠋⠄⡀⠉⢠⡍⠽⢖⣒⠲⢯⠬⣽⡗⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠶⢄⡀⠈⠀⠬⣟⠷⠶⢭⣷⢶⣍⣛⣶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠓⠈⢟⡊⠙⢻⢿⣍⡳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢙⠢⣄⠑⢤⡙⠦⣓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡘⢱⣟⢻⡑⣀⢠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⠟⠛⠒⠢⣿⣷⠮⠛⢷⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⢏⢁⠚⡷⠐⢖⡞⠠⢀⠆⠀⠀⠈⠁⠀⠀⠀⠀⣈⣿⣅⣀⠀⢀⠑⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠠⠤⢄⣨⣤⡤⡄⢀⠀⣤⠤⠀⠚⠉⠉⠉⠉⠀⠀⠀⠀⠁⠉⠉⠓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠉⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣴⣿⣆⢤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⠮⣿⣟⠟⠋⠁⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⠞⢉⠉⠉⠙⣿⣷⡀
⠀⠀⠀⠀⠀⢀⣼⠇⠈⠋⠀⠀⠀⠀⣽⣿
⠀⠀⠀⣀⣴⣾⣿⡀⠀⠀⠀⠀⠀⠀⢽⣿
⠴⡾⠿⠟⠛⠛⢻⣷⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⣰⣿⡃⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⢰⣿⣿⣁⣀⣤⣴⡶⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⠶⣄⡀
⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣽⠇⠀⠙⠲⣄
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠾⠛⣡⣾⣿⠀⠀⠀⠀⠈⠳⣦⣀
⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣀⣴⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⣁⣤⡶⠟⣋⣿⡏⠀⠀⠀⠀⠀⠈⠻⣿⡿
⠀⠀⠀⣿⠀⠀⠀⠀⢠⣾⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢉⣡⣴⠞⢋⣿⠃⠀⠀⠀⠀⢰⣾⣿⣿⠷
⠀⠀⠀⣿⡆⠀⠀⢀⣿⣿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠋⣉⣥⡶⢛⡿⠀⠀⢀⣤⡶⠛⠋⠉
⠀⠀⠈⢹⣿⣾⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠛⠉⢀⡤⠋⣀⣠⡾⠛⠁
⠀⠀⠀⠈⠻⣿⣿⣾⣿⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⣤⣞⣡⣴⠿⠛⠁
⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣥⣄⣀⠀⠀⠀⠤⠤⠔⢒⣉⣥⣶⣾⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁⠉⢀⠁⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡎⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠤⠀⠤⠤⠜⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠲⠤⢤⠴⠖⠡⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⡤⠀⡠⢄⠀⠀⢁⡂⢀⡀⠀⠀⣀⠀⠊⠀⢀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⢤⠠⠀⠀⠀⠀⡄⠀⢬⠖⠀⣀⢀⠤⠤⠌⠍⠀⠈⢳⡆⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠰⠐⠘⠐⠀⠀⡈⠀⢰⡀⡈⠉⠅⠀⠐⡆⠈⠃⠐⠐⠀⠀⢠⠆⠀⠀⠈⢙⣶⡦⠶⢤⡶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠁⠲⠖⠲⠚⠄⠀⠀⠉⢠⣤⣤⠔⠋⠀⠀⠀⠑⠤⠴⢊⠀⠀⠀⠀⠀⠘⣌⣄⣀⠈⠻⢦⣤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠾⠟⠛⠛⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⣴⡆⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠻⠃⠀⠀⢀⡴⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠉⠓⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢸⡇⠀⢀⣀⣠⣤⣤⡶⠶⠶⠶⠶⠿⣷⠄⠀⠀⠀⠀⠀⠘⣿⡿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠘⠷⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⣀⣠⠤⠤⠶⠾⣷⠀⠀⠀⠀⠀⠀⠐⣇⡀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠚⠉⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⣠⡀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠠⣀
⠀⠠⣤⣀⣀⣤⢦⣄⣿⡄⠀⠀⠀⠀⠀⠈⠛⠶⠞⠛⠳⢶⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⠀⠙⢢⠀⡀
⠀⠀⠀⠉⠀⠀⢀⣀⣈⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠑⠀⠀⠀⠀⢣⠹
⠀⠀⠉⠛⠛⠛⣉⣀⡤⠤⣬⣳⣦⣀⣠⣦⣀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⣤⠶⣤⣴⡿⠗⠀⣀⠔⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠙⠛⠋⠉⠀⠉⠛⠛⠛⠋⠉⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⡴⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠤⠀⠒⠒⠉⠁⠀⠀⠀⠀⠀⣀⡴⠊⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠒⠋⠁⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⠤⠤⠤⠒⠒⠂⠉⠉⠀⠀⠀⢀⣀⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠒⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢠⡄⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⠾⣇⠀⠘⠃⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠈⣳⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢯⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⡀⠀⠀⠀⢀⣀⡤⠞⠉⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⠉⠙⠛⠋⠉⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣠⠞⠉⠁⠀⠉⠉⠛⠛⠛⠛⠙⣧⠀⠀⠀⣼⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠒⠲⠀⠄⢲⠏⠀⠀⢀⡏⠀⠀⠀⠈⠋⠀⡤⡀
⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠸⡇⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠠⠤⢄⣠⠴⠋⠀⠀⠀⡼⠁⠀⠀⠀⡤⢤⡀⠑⠁
⠀⠀⠀⠀⠀⠉⠁⡠⢄⠀⠀⠀⠹⣄⠀⠀⠀⠀⠙⠲⠦⠤⠤⠶⠖⠋⠁⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠳⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠧⠤⠃⢀⠔⠒⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠉⣱⠖⠒⠉⠉⠉⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠖⠋⠉⠑⠢⠄⠀⠀⠈⠙⠲⠦⢤⣤⣤⣤⣤⡤⠴⠖⠋⠁




⣿⣿⠛⠿⢻⠿⡿⢻⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠟⠛⠛⠷⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⣠⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠈⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⣿⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣬⣿⣦⡀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢿⣤⠶⠾⠛⠋⠉⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⢀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⣠⠖⠋⠉⠁⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⣳⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀
⠀⢀⠀⠀⠀⠀⣀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣠⣾⣆⣀⣀⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠒⢤⡀
⠀⠈⠛⠒⠚⠛⠉⠛⠚⢿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠳⡄⠀⠀⠀⠙⡌⢆
⠀⠀⠤⣤⣤⣤⡴⠖⠶⠶⠻⣦⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣴⡋⠀⠀⣸⠀⠀⠀⠀⣱⠈
⠀⠀⠀⠀⠀⠀⠒⠒⠚⠉⠙⠾⣿⣷⠶⠛⠻⢦⣤⣤⣤⠤⠲⢦⣤⣤⣤⣤⡴⠞⠛⠛⠛⠛⠉⢀⡤⠞⠁⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠚⠉⠀⠀⠀⠀⢀⡰⠋⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠚⠉⠁⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⣀⣠⠤⠖⠋⠁

⠀⠀⠀⠀⡠⠒⠉⠉⠉⠈⠐⠒⢲⡀
⠀⠀⠀⡜⠀⠀⠘⠃⠀⠀⠀⠀⠀⠱⡄
⠀⠀⢠⠟⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⢀⢏⠻⢀⡭⠓⠒⢺⠖⠄⠀⠀⠀⠀⡅
⡀⠻⣣⠔⠁⠀⠀⠀⡜⠀⠀⠀⠀⠀⢠⠃
⠑⠉⠁⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠤⠤⠠⠤⣄⡀
⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⢄⡀
⠀⠀⠀⢸⠀⠀⢀⢂⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⣀
⠀⠀⠀⠘⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠲⠤⠤⣤⣴
⠀⠀⠀⢸⠰⡁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⢤⡠⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⣴⡿⠉
⠀⠀⠀⠈⢢⡁⠄⡀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡉⠛⠀⢠⠒⡀⠀⠀⢁⠞⠉
⠀⠀⠀⠀⠀⠙⢦⡀⡀⠈⠠⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠩⠐⠁⠀⢁⡀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠲⠶⣦⣌⡀⠈⠂⠁⠀⠀⡄⠀⠄⠀⠀⢀⡀⠀⠸⢃⠀⠀⢀⡥⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠺⠶⢴⣆⣀⣀⣀⠄⠀⠀⣽⣦⡬⠼⠗⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⢿⠛⠓⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢼⣿⣻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣽⣿⢿⣽⣾⣿⣿⣿⡗
⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠒⠚⢻⣿⣾⢛⢛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⣿⣿⡙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⠑⠦⡀
⠀⠀⠀⠀⠀⠀⣠⠂⠀⠉⠳⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣀⣤⣤⣤⣶⣦⣤⣼⣿⣿⣟⣛⠛⣳⣤⣴
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣀⣠⣤⣴⣶⣾⠿⠿⠛⠛⢛⠛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣏⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠟⠋⠁⠀⠀⢀⣀⡜⠘⣋⣙⣛⡿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠋⣑⣀⣀⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣉⣭⣿⣿⣿⣿⣿⣧⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⣴⣿⣿⣶⣷⡟⣿⣥⣭⣉⣉⣙⣟⣿⣛⡛⠋⢢⡙⢿⣿⡿⠟⠛⠁⢸⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢛⣻⣯⣿⣿⢰⡿⠟⠉⠉⠉⠙⠛⠛⠿⢿⣿⣿⠧⠈⠁⠀⠀⠀⣀⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⢾⣿⣿⣿⣿⣿⡇⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⣶⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠉⠉⠉⠛⠿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣆⠀⡀⠹⡉⠛⠿⢷⣦⣤⣤⣤⣴⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣠⡿⢰⡇⣾⣵⢠⢡⡄⠀⠟⠀⣿⢸⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢻⣶⣌⣏⣾⣷⣿⣿⣾⣿⣽⣦⣧⣤⡁⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⣤⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢿⣾⣿⣿⣿⣿⠿⠚⣙⠋⢈⢻⢿⣏⣉⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠙⠛⠛⢟⣿⣿⣿⣿⠿⣿⣿⡿⣿⣧⣽⣷⣦⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠢⣤⠋⣌⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠛⠈⠀⠀⠀⠀⠈⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠴⠚⠛⠲⣄⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⢀⠰⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⠒⣿⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⢩
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠓⢦⡀⠀⠀⠀⣿⠀⢀⣤⣤⣄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⢀⡶⠶⣤⠞⠋⠀⠀⠀⠀⠀⢳⡀⠀⠀⢯⣀⣾⣥⣿⣿⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠳⣦⠈⠁⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠈⠙⠻⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠱⢄⡀⠀⠀⠀⠀⠀⠀⠀⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⡙⠗⢶⠤⣤⡴⠖⠃⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠠⣏⡠⠟⠉⣀⡠⣴⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡔⠁
⠀⠀⠀⠀⠀⠀⠐⠤⠤⠒⠉⠁⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠦⠤⠤⠤⠤⠖⠚⠙⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⠀⠀⣠⡴⠞⣻⠶⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠉⠉⠉⠉⠒⠒⠶⠶⠶⠶⠒⠚⠋⠉⠁⠀⠀⢈⠗⠈⠁⠐⠋⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⢀⡆⠀⠀⠀⢀⠴⢃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠁⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⢀⠇⠀⠀⠀⢀⠔⢡⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠐⠃⠀⡼⠁
⠀⠀⠀⠀⠀⣀⣠⣤⡤⠀⠐⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠒⢊⡽⠁⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⢠⡎⠁⠀⠀⠀⡀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣄⣀⡀⠀⠀⠀⠀⣀⣀⣤⠴⠞⠉⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠈⠧⣀⠀⠀⠀⠉⠛⠲⠾⠛⠲⣄⣀⣠⡴⢦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⡀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠔⠚⠢⣄⣀⠀⢀⣀⡤⠖⠒⠦⠤⠤⠤⠒⠉⠉⠒⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠙⠢⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⡠⠤⠄⣀⠀⠠⠄⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠉⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠁⠢⢄⣀⡀⠀⠀⢀⣀⣀⠤⠤⢄⡀⠀⠀⠀⠀⣀⡠⠤⠒⠒⠒⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠓⠄⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡵⣞⡭⢞⣡⡶⢖⣠⣤⠄⢀
⠀⠀⠀⠀⠀⡀⠀⠤⠈⣧⣈⣘⣏⣻⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢐⣮⣕⣺⠭⠶⣚⡭⡭⠶⢛⣻⣿⣷⡄
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠻⠿⠿⣿⣥⣭⣻⣶⣶⣴⣶⣾⣯⣴⣿⣿⣦⡻⡭⠦⣕⢲⣏⣿⣽⣿⣿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣭⣽⢿⠿⠿⢿⠟⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣋⣈⣉⠈⠉⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣭⣉⣉⣀⣀⣀⣰⣿⣥⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣷⣦⣬⣭⣍⣛⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣿⣿⣿⣿⣿⣝⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣷⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢿⡟⣿⡹⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣧⣻⣮⡿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⡙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠚⠉⠉⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣅⠀⠀⠀⢀⣀⠀⠀⠀⠈⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⠼⡀⠀⠀⠑⠋⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁⠀⢀⣠⠝⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⡔⠋⣡⣤⣶⠶⠿⠿⠖⠒⣧⡄⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠓⠛⠋⠁⠀⠀⠀⠀⠀⡰⠀⠁⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⢤⡀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⠁⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⡀⠀⣠⠏⠀⠀⠀⠀⣸⡷⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⢀⣀⣤⠤⠶⠒⠚⠋⠉⠉⠉⠉⠉⠁⠀⠀⢀⡠⠟⠒⢻⣧⣞⡁⠀⠀⠀⢀⡴⠃⢀⡟
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢀⡴⠋⠉⣩⠁⠀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⣠⡉⠀⢀⡴⠃⠀⠀⠀⠀⣀⣩⣾⠅
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠀⣀⣡⡤⠿⡖⠉⠀⠀⠀⠀⠀⠀⠉⣡⠞
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠒⠋⠀⣀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⢐⡿⠁
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢳⡀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠁⢀⣀⣀⣠⠖⠁⠀⠠⠔⠚⣹⠃⠀⠀⠀⠀⠀⠀⣺⠋
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠙⠂⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠉⠉⣀⠔⢀⣀⡤⢴⡞⠁⠀⠀⠀⠀⢠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣀⣈⣛⣉⡁⠀⢀⣰⣖⣋⣁⣀⣀⣤⠴⠋⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠢⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠶⠶⡆⠁⣶⠦⠤⣄⣀⣀⣀⣀⣀⣀⣠⡤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡇⠀⠀⠀⢸⠇⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚⠉⠀⢀⡴⠃⠀⠀⠀⡼⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⣀⣀⣀⣤⠤⠞⠁⠀⣀⡠⠔⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠒⠋⠁⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠷⠦⠤⠶⠒⠒⠃

⠀⢀⠄⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⣀
⠀⠈⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠁
⠀⠀⠀⠀⠀⠰⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠁⠀⠀⠉⠑⠲⢄
⠀⠢⣀⠀⠀⠀⠢⡄⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⢖⠀⠀⠀⠀⠀⠀⠀⢄⠀⠠⡂⠀⠀⠀⠀⠀⠀⠂⠀⡠⠂⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠨⡀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢘⠀⠠⠐⠀⠀⠀⠀⠠⠤⠃
⠀⠀⠈⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⢠
⠄⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠥⡀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠉⠈⠀⠀⠀⣀⡀⠀⠀⠐⣉
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠁