Bass drum Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⢤⡤⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣤⣤⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢀⡀⢰⣿⣿⣿⢿⣿⢎⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⣼⣿⢼⣻⠝⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣧
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠃⣿⡟⢸⣿⠀⢿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⡆
⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠀⣿⠇⠸⣿⠀⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣟⣿⣍⣿⣿⡄
⠀⠀⠀⠀⢠⣿⣿⣿⡿⠀⠄⣽⠀⠀⠿⢀⢸⢿⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣦⣴⣶⣤⣴⣶⣦⣾⣷⣿⣿⣿⣿⢷⣿⣇
⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⢠⡇⠀⠀⠀⠀⠺⢸⣿⣿⣿⣿⣿⠻⣿⡿⠛⠛⠛⣿⡿⠏⠀⠉⠋⠙⠉⠉⠉⠉⠉⠁⠀⠀⠉⣿⠸⣿⣟⣻⣿
⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⣆⠀⠀⠀⠀⠀⠀⡈⢿⡿⣧⠰⣿⡇⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠎⠛⡷⢿⡇⢸⣿⡆
⠀⠀⠀⣸⣿⣿⣿⡏⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠰⠸⣷⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⢻⣇⠀⢹⣇
⠀⠀⣶⣿⣿⣿⣿⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⣶⣛⣙⣷⣶⣾⣈⣿⣦⣔⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣙⣘⣿⣾⣾⣿
⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣥⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⢿⡇
⠀⠀⢸⣿⣿⣿⡷⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⡇⢸⣿⠉⠉⠀⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⡉⠁⠸⣇
⠀⣠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠈⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⢰⣿⢻⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⢠⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢻
⣿⣷⣾⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠈⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇⠀⠀⢸
⣿⣿⣿⣇⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⠀⠀⢸
⢿⣿⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⣿⡄⠀⢸
⠈⢿⣿⣿⣏⣹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡀⠀⠸⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⢻⡇⠀⢸
⠀⢸⣿⠏⠐⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣗⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢿⡇⠀⢸
⠀⣸⡟⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣠⡄⣿⠸⣿⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠀⠀⠹⠛⠺⣿⢾⣧⣬⣬
⠴⣿⡏⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⣴⣿⣿⣷⣿⣴⣿⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣆⣛⣿⣟⣿⣿
⠀⠙⣇⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣿⣿⣿⣿⣶⣶⣶⣴⣶⣶⣶⣶⣶⣤⣤⣤⣤⣴⣶⣶⣶⣾⣤⣬⣿⢿⣿⣿⡿
⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣏⢩⡀⣼⣴⣿⠀⠀⠀⠀⠈⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡷⢾⣿⣬⣴
⠀⠀⣿⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣹⣾⡇⢿⢼⣿⠀⠀⢀⠀⠀⡤⠆⠀⠠⠄⢀⡀⠀⣠⠄⢀⡀⠀⠀⠀⢻⢀⣿⠀⢻
⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣷⣾⣟⢋⣠⣿⣼⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⢀⣤⡀⠠⠀⠀⣿⣹⣿⣘⣿
⠀⠀⣿⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⡧⢤⣿⡿⣿⣿⠠⢄⣤⠤⠶⡤⠤⢤⣤⣤⡤⢤⣤⣴⣿⣧⣤⠀⢄⠀⠾⢼⣿⢻⣿
⠀⠀⣿⡀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⠿⢶⣾⣷⣿⣿⣄⢻⣁⣶⣶⣶⣶⣶⣤⣬⣥⣤⣤⣄⣉⣿⡏⢀⢈⡀⣷⣾⣿⣶⣿
⠀⠀⢸⡇⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⣿⣿⠛⢿⣤⣿⣿⣿⣿⣻⣿⣿⣿⠟⢛⣻⠿⣿⣟⣛⣭⣽⣿⣿⡿⠿⠛⡵⣧⣾⣿⣾⣿
⠀⠀⢸⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠈⣿⣿⣿⣯⡗⣿⣿⣟⣛⣹⣿⣿⣿⣛⣛⣛⣛⣋⣙⣛⣛⣻⣿⣿⠿⠿⠺⣦⣦⣿⣯⣾⣿
⠀⠀⢈⣯⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢴⣿⣧⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣿⣽⣿⢽⣿⣿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡯⣼⣿⣿
⠀⠀⠙⢻⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⣿⣛⣿⣿⣷⣶⣶⣶⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣟⣿⣿⣿⣶⣿⣿⣿
⠀⠀⠀⢸⣧⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⡇
⠀⠀⠀⠀⣿⡇⠀⢸⡆⠀⠀⠈⣇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⢹⣧⠀⡈⣧⠀⠀⠘⠇⠀⠀⠀⠀⠀⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢿⣧⣥⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢠⡟⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠐⢻⣧⣿⣿⣿⣿⡆⠀⠀⢀⡴⢟⡩⣍⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⡿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣥⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠉⠈⣿⣿⣿⣿⣄⠀⠀⣵⣎⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣫⠉⣽⠟⠛⠛⠛⠛⠻⠟⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⡷⠟⠛⠛⠛⠉⠛⠂⠈⠛⠛⠛⠛⠋⠉⠉⠉⠛⠋⠙⠋⠉⠉⠉⠛⠉⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣠⣀⣀⣀⣀⣠⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣤⡾⠋⢀⡠⢊⡵⠚⠛⠛⠓⠲⠶⠿⠷⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠬⠬⠥⢽⢭⣥⠟⡹⠋⠉⢉⡽⠿⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠿⠿⣿⠟⣷⠛⠖⢺⡿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠴⠶⢶⣶⢦⢤⣤⣤⣴⣧⣾⣥⣤⣴⣿⢷⡀⠈⢿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣰⢃⡼⠁⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⣼⢁⡟⠀⠀⢸⡿⠋⠀⢷⠀⠘⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⡸⠁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣼⠁⠀⢀⡟⠀⠀⠀⠘⡇⠀⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢰⠇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢰⡇⠀⠀⣼⠁⠀⠀⠀⠀⣿⠀⠸⡇
⠀⠀⠀⠀⠀⢀⡀⢰⡏⠀⠀⡏⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣿⠀⠀⢠⡟⠀⠀⠀⠀⠀⢸⠀⠀⣷
⠀⠀⠀⠀⠀⣾⣿⣿⣀⡀⣸⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⡇⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⢸⣿⣿⡿⠿⢻⡟⢳⠖⠒⠒⢿⣿⠿⠶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣶⣄⣀⣀⣀⣸⣃⣼⡤⠀⢀⣿⣿⠀⠀⠀⠀⠀⢸⡇⠀⢿⣷⡄
⠀⠀⠀⠀⠘⠛⣿⠀⠀⢸⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⣿⢩⡟⠉⠛⢿⣇⡿⠀⠀⠀⠀⠀⠐⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⡟⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⠇⠀⠀⣼⠿⠃⠀⠀⠀⠀⠀⠀⡇⠀⢸⡟⠁
⠀⠀⠀⠀⠀⣼⠃⠀⢀⠇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⡿⠀⠀⢸⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⢰⡇⠀⠀⢸⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⡇
⠀⠀⠀⠀⢸⠃⠀⠀⡆⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⡇⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⢀⣦⣾⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⣿⡆
⠀⠀⢸⣿⣿⣦⣤⣀⡁⠸⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠁⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⡇
⠀⠀⢸⣿⣿⠛⠛⢙⠉⢻⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣷⣶⣶⣶⣶⣶⣤⣤⣴⣶⣀⣀⣀⣘⣃⣼⣤⣤⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣿⠛⠁
⠀⠀⠈⠁⣿⠀⠀⢸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⢹⡏⣿⠛⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣿⠀⠀⢸⡿⠟⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡟
⠀⠀⠀⠀⢿⠀⠀⢸⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⡇
⠀⠀⠀⠀⢸⠀⠀⠈⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⠇
⠀⠀⠀⠀⢸⡆⠀⠀⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣾⣦
⠀⠀⠀⠀⠸⡇⠀⠀⠇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⣿⣿
⠀⠀⠀⢸⣿⣧⣀⡀⢠⠀⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⡿⠟
⠀⠀⠀⠸⣿⣿⠭⠿⠿⡷⢷⠦⠤⢴⣿⣿⣦⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⢀⣤⡀⠀⠀⢸⡇⣿⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⣸⠁⠀⣿
⠀⠀⠀⠀⠙⠛⣇⠀⠀⣇⠸⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠷⠤⠤⢼⣧⣿⣶⣶⣾⣿⣿⠀⠀⠀⠀⢀⡏⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢿⡀⠀⢸⡄⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⡍⠉⠙⣿⣿⠂⠀⠀⠀⣼⠁⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢷⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⡇⠀⠀⣿⠁⠀⠀⠀⢠⠇⠀⢰⣧⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⢆⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢿⠀⠀⢹⡆⠀⠀⢀⡟⠀⢀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⣼⣦⣀⣀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠸⡆⠀⠈⣧⠀⠀⣼⠁⠀⡼⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠓⠚⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⣤⣠⣿⣟⠀⠀⠘⠇⢹⡀⢀⣹⣦⣴⠃⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⢀⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⣐⣂⣒⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣯⣿⣿⣿⣽⣟⢿⣿⣿⣿⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⡿⣫⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⢈⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠆⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠐⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⡍⢭⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⣤⣄⠀⠀⡀⣀⡀⢀⣄⢀⣠⡤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡷⢒⣵⣾⣿⣿⣿⣧⣤⣤⣶⣦⣾⣿⣿⠟⣫⣾⣯⣾⣿⣿⣿⣷⣦⣌⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⡾⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣼⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠾⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⡀⠀⣜⢃⣺⣿⣿⣿⠉⠉⠻⠛⢿⣿⣿⣿⣿⣿⠟⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠤⣴⠇⣸⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⠇⣤⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⣆
⠀⠀⠀⠀⠀⠄⢸⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢻⡀
⠀⠀⠀⠀⠀⠀⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⣧
⠀⠀⠀⠀⠀⢸⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢻
⠀⠀⠀⠀⠀⣼⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠸⡇
⠀⠀⠀⢀⠀⢿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣇
⠀⠀⠀⠰⠀⣸⠆⢾⣿⣿⣅⣀⣉⡁⠸⣯⣭⣭⣭⣭⣽⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿
⠀⠀⠀⠘⠀⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⡇
⠀⠀⠀⠀⠀⢹⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼
⠀⠀⠀⠀⠀⡀⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⡟
⠀⠀⠀⠀⠀⠡⠘⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠘⣛⣛⣻⡏⠉⠉⠉⢩⡿⣿⣿⣿⣿⣆⠛⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠄⢻⣧⠹⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣶⣾⣆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠹⣧⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢾⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢻⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣌⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⠛⠯⣈⡉⡉⠛⢹⡟⠛⠛⠿⠮⣻⡎⠙⢿⣿⣿⣿⣿⠿⢋⣡⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠛⠛⠛⠛⠓⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡇⠀⣀⣤⣀⢀⣀⣀⡀⢀⣄⣤⢀⣤⣤⢀⣤⣤⣄⢤⣤⣤⣤⣤⣼⣤⡽⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢙⣾⣿⢹⣿⣿⣷⣾⣿⣿⠸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⠀⠀⠀⠈⣷⣾⣿⣞⣉⣠⢠⣤⣤⣼⣤⡼⣿⣿⢸⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⢸⣿⣿⠻⠿⡿⢿⣿⢿⡿⠿⠟
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⡛⣿⢸⣿⣿⣿⣿⣿⣿⣿⣟⡿⢿⣟⠛⠛⠙⠛⠁⠀⢠⣷⣾⣿⣶⣵⡄
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⠁⣌⣡⣿⣿⣿⣧⣀⡄⠁⠀⠀⠀⠀⠀⠀⡇⢸⠁⢸⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠃⣀⣀⣤⠾⠛⠋⠉⠉⠉⠉⠛⠻⢶⣄⣣⠀⠀⠀⠀⣧⣿⠑⣸⠃
⠀⠀⠀⠀⠘⠛⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⢀⣿⡾⣄⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠛⠛⠛⠛⡟⠉⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣴⣿⡋⣿⠉⠙⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⡤⠖⢻⠓⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⢯⣿⡀⠀⠀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠍⣀⠀⢘⡠⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣸⠀⠀⣙⠢⢀⡀⠈⠃
⠀⠀⠀⠀⠀⠀⣠⠔⡋⠀⠀⠀⠀⠈⠉⠀⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢷⠋⠉⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠋⠀⠀⠃⠀⠀⠀⠀⠀⠀⣰⠃⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠉⠳⣦⣄⣀⡀⠀⠀⣀⣀⣤⡴⠟⠉⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠈⠉⠛⠛⠛⠛⠉⠉⠀⢰⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠟⠛⠋⠉⠉⠉⠀⠀⠈⠉⠉⠉⠛⠻⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⣀⣤⣄⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣰⣿⡟⣩⠔⠲⣶⠀⣸⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣀⠋⠀⠀⠀⠀⣿⠃⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⣧⣤⣀⠀⠀⠀⢿⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⢸⣿⣿⣿⣿⣷⡀⢠⣼⠇⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⢸⣿⣿⣿⣿⢋⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇
⢸⣿⣿⣿⡇⠸⣿⣿⣿⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿
⠈⠻⣿⣿⣿⣦⣾⣿⣿⣿⡜⣟⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠈⠀⠙⣿⣿⣿⣿⣿⣿⡘⡆⢈⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣾⣿⣿⣷⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠗⢹⣾⠏⠈⢹⠿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⣾⡟⠀⡰⠋⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⢸⣧⢾⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣯⡿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣭⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢉⡉⢢
⠀⠀⣀⠤⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣡⣇⣼⣜⡀⡀
⠀⡰⢁⡾⠥⠤⠤⡔⣖⡒⠒⠈⠉⠉⠀⢰⠋⠂⠀⠈⢢
⢠⠁⡾⠀⠀⠀⠀⠀⠀⠉⠙⠒⢤⣤⣠⡏⠀⠀⠀⠀⠀⡆
⡜⢠⣧⠀⠀⢀⡄⡤⠐⠒⠋⠉⠉⠀⢸⢁⠀⠀⠀⠀⠀⢰
⡇⢸⠀⠀⠀⠀⠈⠉⠙⠒⠢⠤⣀⣀⣞⠈⠀⠀⢰⠁⠀⠸
⡇⢸⣀⠀⠀⣀⡄⡤⠤⠒⠒⠈⠉⠉⣿⠀⠀⠀⢀
⡇⢸⠀⠀⠀⠀⠉⠉⠑⠒⠦⠤⣀⣀⣟⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⢠⡀
⠇⢸⡆⠀⠀⠀⠀⡀⣀⣠⠤⠔⠊⠁⢹⠠⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠅⠂⠄⠀⠀⠀⠀⠀⢔⠀⡂
⢸⠀⣷⠒⠒⠒⠘⠼⠠⠤⠤⠤⢀⡀⢸⡄⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠠⢅⡒⠥⠂
⠀⢀⠘⣄⠀⠀⠀⣀⢤⠤⠔⠐⠋⠉⠀⢳⡀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢈⠐⠠⢀
⠀⠀⠣⠝⠯⠭⠭⠬⠬⠭⠭⠶⠶⠶⠶⠤⠷⠦⠄⠔⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠰⠂⠉⠃⠄
⠀⢲⠁⠀⠀⠀⠀⢥
⠀⠈⢻⠀⠀⠀⡠⡏
⠀⠀⠀⠛⣢⡮⠂⠱
⠀⠀⠐⢮⠋⡔⣐⡠⢃⠴⢀⣀⠀⡠⠂⠐⡄
⠀⠀⠀⠀⢹⠂⠑⢙⠜⢴⡅⠈⠙⢾⠃⢀⠇⠀⢀⠠⠔⠂⠉⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄
⠀⠀⠀⠀⠈⠵⠆⠀⠰⢦⡻⣄⡀⠞⡷⠚⡀⠉⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⠀⠀⠀⠈⠀⠈⠐⠒⠤⣄⠂⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⡻⠗⢙⡫⠁⠀⠀⠀⠀⠀⠲⡒⠋⠉⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠂
⠀⠀⠀⠂⠀⠒⠄⠘⠤⠁⠐⠂⠈⢿⣄⠡⢂⠄⠀⠀⠀⠱⡀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⡄
⠀⠀⢀⠀⠀⠀⠘⠀⠀⠀⠀⠈⡄⠀⢳⠓⠀⠀⠁⠘⠁⠀⠝⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢠
⠀⠀⠀⠁⠀⠚⠀⠀⠀⠀⠀⠲⣵⣀⣀⠀⠀⢀⡀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⣚⣏⠐⠖⠒⠛⠂⠉⠈⠉⠒⠚⠲⠄⠀⠮⠄⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘
⠀⠀⠀⠀⠀⠱⠸⠖⠢⠤⠤⠄⠀⡀⠀⠀⠀⠀⠀⠀⠈⠃⢚⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠄⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠔⣂⢄⣀⣀⣀⠀⠀⠀⢀⢂⢈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠉⠉⠉⠁⠁⠀⠀⢳⡞⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣊⠔⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢂⣀⣀⠀⠀⠀⠈⠙⠃⡠⠂⠈⠐⠠⠤⢀⡒⠊⠩⠉⠒⠂⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠫⠁⡈⠉⠓⠶⢶⢰⠾⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡶⠾⢇
⠀⠠⣄⡤⠿⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢸⣿⠇⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣁⡤⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣶⡶⠴⡈⡁⠀⠈⠂⠰⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠍⠀⣉⣾⠁⠀⠀⠀⠀⠈⢷⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⠿⣿⣦⡀⠁⠀⡀⢰⣿⠦⡀⢸⣿⣿⠀⠲⠆⢠⣿⡇⠀⡀⠤⢄⠀⣾⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣄⣄⠈⠺⣻⣥⡹⢶⣿⢏⡀⠀⢰⣿⣿⡷⠋⠀⠀⠀⢱⡿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣄⡇⠘⣵⡄⣏⠿⣿⣿⠟⠫⠋⠀⠀⠀⠀⠀⢸⣷⡀⢈⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⣾⠀⠈⠋⠢⠅⡹⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣮⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣻⣴⣶⢦⡀⠲⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢽⡿⠃⠀⢙⠁⠀⠀⠀⠀⠀⠀⠀⣼⡟⠻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⡆⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠐⠠⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣧⣀⠐⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠈⠛⠀⠀⠀⠀⠀⠀⣸⡿⠣⢄⡀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠉⠀⠀⠀⠀⠀⠀⠤⠀⠀⢠⣾⠟⠁⠀⠀⠉⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣰⣿⡇⠀⠀⢀⠄⠀⠀⢀⠇⠀⣚⠟⠉⠐⠠⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⢿⣷⡀⠀⠈⠀⠀⠀⢠⠀⠈⡄⠁⠒⢤⡀⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠁⠃⠀⠀⠀⠆⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⣤⣤⣤⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡷⣿⣯⣉⡉⠉⠉⠙⠳⠤⠿⠛⣒⣆⣶⢤⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⣴⡿⠋⠀⠈⠙⠙⠛⠻⢷⠶⢶⣦⣄⣀⣤⣼⣙⣩⠵⠚⠛⠻⣦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠈⢠⡾⠋⠀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠈⢛⣿⠟⣿⠟⠉⠀⠀⠀⠀⠀⠀⠑⡕⣄⠀⠀⠀⠀⠀⠀⠀⣏⣉⠉
⠀⠀⠀⠀⠀⢠⣆⣰⡟⠁⠀⠀⠙⠛⠻⠯⢼⣟⣷⠂⠀⣴⠟⢁⠜⠁⠀⠀⣀⣀⣄⣶⣾⠀⠀⠘⣻⡇⠀⠀⠀⠀⠀⠀⣥⢠⣤
⠀⠀⠀⠀⢠⢿⣻⡿⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣠⣪⣤⢰⣖⣷⣿⡿⠿⠙⠉⠀⠀⠀⢀⠘⡀⠀⠀⠀⠀⠀⠇⠘⢰
⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠈⠉⠙⠛⠲⢶⣤⣄⣀⣾⣧⡴⠡⣯⣿⠸⠟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡖⢲⢓
⠀⠀⠀⠠⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡿⣿⠃⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠀⠀⠀⠀⠁⠈⠘
⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣰⣶⣤⠀⠀⠀⠀⢘⠌⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡇⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡦⣼⡏⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠦⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠠⠤
⠀⠀⠀⡟⢺⣧⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⠀⠀⠀⡵⠒⠒⠦
⠀⠀⠀⠀⠈⢱⠉⠐⠛⠳⠖⣤⣄⣀⣀⡀⠀⣀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠇⠀⠀⠀⠀⠀⠀⠏⡁⠌
⠀⠀⠀⠀⠀⡸⡇⠀⠀⠀⠀⠀⠈⠐⠛⠳⠶⢤⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡟⠀⠀⠀⠀⠀⠀⠀⡞⢉⣉⣉
⠀⠀⠀⠀⠐⣬⣿⡄⠀⠀⠀⠰⠀⠀⠀⠀⠀⠒⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡸⠁⠀⠀⠀⠀⠀⠀⠀⣧⠤⡄
⠀⠀⠀⠀⠀⠘⠻⣿⣦⡶⠠⣀⣀⡀⠀⠀⠀⣁⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣗⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢦⣄⣐⡆⢀⣹⡄⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠱⠷⢿⣿⢶⣃⡀⠀⠀⠀⠀⠀⠀⢀⡠⢪⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠶⠦⣄⣀⣠⣤⣒⠡⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⢉⣉⣉⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠛⠉⣀⣤⡶⠶⠛⠛⠛⠉⠉⠉⠙⠛⠛⠳⠶⣦⣄⡈⠙⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⢁⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀⠙⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠋⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠈⠻⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠘⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠃⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⢻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⢻⣿⣿⡄
⠀⠀⠀⠀⠀⢰⣿⣿⠇⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢿⣿⣷
⠀⠀⠀⠀⠀⣿⣿⡟⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠘⣿⣿⡇
⠀⠀⠀⠀⢰⣿⣿⡇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣿⣿⣷
⠀⠀⠀⢀⣼⣿⣿⠃⢸⡇⠀⠀⠀⠀⢀⣴⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣄⠀⠀⠀⠀⠀⣿⠀⢻⣿⣿⣄
⠀⠀⠀⠘⢿⣿⣿⡆⢸⡇⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣿⠀⣾⣿⣿⠟
⠀⠀⠀⠀⠸⣿⣿⡇⠸⣇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⡿⠀⣿⣿⡿
⠀⠀⠀⠀⠀⣿⣿⣧⠀⢿⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣸⠇⢠⣿⣿⡇
⠀⠀⠀⠀⠀⢹⣿⣿⡆⠘⣧⠀⠀⠀⠀⠀⠈⠛⠛⠉⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠙⠛⠋⠀⠀⠀⠀⠀⢠⡟⠀⣾⣿⡿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣦⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣌⡙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢠⣾⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣷⣄⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡌⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⢀⣴⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⡈⠙⠷⣤⣀⠀⠀⣠⣾⣿⣿⠟⠀⠙⢿⣿⣿⣦⡀⠀⢀⣠⡴⠟⠉⣠⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⣤⣀⠉⣡⣾⣿⣿⠟⣁⣀⣀⣀⣠⡙⢿⣿⣿⣦⡉⢁⣠⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠟⣡⣾⣿⣿⠟⣡⣀⣀⣉⣉⣉⣀⣀⣠⡙⢿⣿⣿⣦⡙⢿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣾⣿⣿⠟⠡⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠙⢿⣿⣿⣦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⠀⠀⠀⠂⠁⠀⠀⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠖⠛⠛⠛⠛⠛⠛⠛⠛⠲⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⣁⣠⣤⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠓⠶⠦⣤⣈⡉⠛⠶⣤⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⣁⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢦⣄⡉⠻⣿⣝⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢁⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⠙⢿⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡙⢷⡄
⠀⠀⠀⠀⠀⣠⠟⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⣦
⠀⠀⠀⠀⣴⠋⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⢷⡀⢀⡀
⠀⠀⠀⣼⠃⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⢿⣿⠻⣄
⠀⠀⣼⠃⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⢿⡶⠛
⠀⢰⡏⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⣇
⠀⣾⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢻⡀
⢠⡏⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢸⡇
⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣇
⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡿
⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣿⣶
⠈⣧⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢸⣇⣸⡆
⠀⢻⡀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣾⠋⠉
⠀⠈⣧⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢰⠇
⠀⠀⠹⣆⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢠⡟
⠀⠀⠀⠹⣆⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡳⣟
⠀⠀⠀⠀⠙⣦⣨⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣨⠿⣿⣧⡀
⠀⠀⠀⠀⢀⣼⣿⡏⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⢃⡴⠋⠀⠈⠻⣿⣆
⠀⠀⠀⣰⣿⠋⠀⠙⢦⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣴⠟⠁⠀⠀⠀⠀⠈⠻⣷⣄
⠀⢠⣾⠏⠁⠀⠀⠀⠀⠙⢶⣄⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣁⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣌⡙⠳⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⣉⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢦⣄⣉⡙⠛⠲⠶⠶⠶⠤⡤⠤⠶⠶⠶⠚⠛⣉⣡⡤⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⢋⡩⠅⠚⠉⠙⠿⠖⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⢙⠶⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⡿⣶⣤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢠⠂⠁⠀⠀⠀⠀⠀⠀⢀⡀⢀⣴⡖⢫⡯⠟⠓⠉⠀⠁⠈⠉⠙⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠋⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣈⣝⣶⡝⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣡⣀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⣡⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡏⠩⠂⠀⠀⠀⠀⠀⠀⢀⠌⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢺⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡐⡇⠀⠀⠀⠀⠀⠀⠀⠻⠉⢂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣧⢀⠀⠀⠀⠀⠀⠀⠀⠁⢱⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣏⠁⠀⡀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⣼⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣸⠑⡆⠈⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⢰⣍⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣀⠀⠀⠀⠀⠰⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⣀⠀⣠⣿⣉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠏⠙⠲⢤⡀⠀⠸⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠀⠀⠠⢈⡷⣯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠈⠓⠦⣍⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣷⠀⠀⣠⢨⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⡏⠀⠀⠀⠀⠀⠀⠀⠘⢧⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢄⠋⠀⠚⠟⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⣄⡀⠀⠀⠀⠀⠀⠀⢀⠸⠇⠀⠐⠒⢮⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠻⣄⡀⠀⠈⠦⡉⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣌⡉⠑⢤⣐⡿⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣍⣂⡀⢠⡝⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠾⠛⠛⠛⠛⠛⠟⠻⠿⢿⣛⢓⠶⡦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠯⣤⣉⠿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣚⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡕⢀⠹⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⡲⡉⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡔⡀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡐⡀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢺⠓⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⡄⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣘⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡍⠘⣿
⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⣿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⠓⢲⣿
⠀⠀⣾⣿⣿⣿⣿⣶⣄⠀⠀⣻⡄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠘⠀⣿⠃
⠀⠸⣿⣿⣿⣿⣿⣿⣿⡗⢠⣾⣿⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠒⣼⡟
⠀⠀⠈⠻⢿⣿⣿⣿⣿⣶⠞⠋⣡⣳⡜⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠡⢁⣼⠟
⡠⠒⢦⠀⠀⠈⠛⠻⢷⡴⣖⣁⢨⡇⠹⣎⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠥⢠⣾⠏
⢧⣂⡰⠀⠀⠀⠀⠀⠀⣀⣪⣷⡞⢦⣼⣉⠷⣵⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠒⣤⠟⠁
⠀⠀⠙⢦⣀⡀⠀⠀⢰⣿⡿⠟⢻⡆⡅⣹⣦⡙⣷⣵⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⣩⡴⠛⠁
⠀⠀⠀⠀⣏⣳⡠⠄⠠⠈⢀⡐⣹⣿⣉⣩⠄⠻⣆⠠⠙⣮⣵⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡯⠖⠋⠁
⠀⠀⠀⠀⠀⠉⠚⠳⢴⡖⠪⠽⡿⢿⠼⠒⠃⠀⣏⡳⠇⠀⠀⠉⠛⠛⢷⣶⠶⠤⣤⣤⣤⣤⣤⠶⠖⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠠⢤⣼⡶⣿⡶⠛⠋⠁⠲⠤⡀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⡆⠀⠉⠒⠦⣀⠀⠈⣳⣄⡀⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠎⠀⠀⠈⠑⠶⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣤⡌⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⢀⡀⢀⣀⠀⠀⠠⠤⠤⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⣿⣿⣶⣶⣶⠄⠉⠠⠤⠂⠉⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⠀⠄⢴⣧⣤⣤⠄⠀⠈⢓⣒⣶⡖⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇⠀⠀⠀⠐⠀⠀⣵⣟⡈⠀⠀⠀⣀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣷⠄⠀⠀⠀⡘⠀⣰⣿⠟⠀⠀⠀⠀⡅⠀⢸⣶⣖⠂⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢈⣹⠁⠀⠙⢻⠗⠁⠀⠀⢰⡄⣤⣿⣿⠂⠀⠀⠀⠀⠀⢿⡿
⠀⠀⠀⠀⠀⠀⢹⡟⠒⠀⠀⠀⠐⠉⢹⢃⠀⠀⣸⣶⢲⣶⠶⠆⠀⠀⠀⣹⣿⣃⡀⠀⠀⠀⢰⣾⠃
⠀⠀⠀⠀⠀⢀⣬⠇⠀⠀⠀⠀⠀⢀⣼⠴⠒⠟⠿⢿⡞⠃⠀⠀⠀⠀⣤⢿⠉⠛⠒⣶⠶⠶⠾⠛
⠀⠀⠀⠀⠀⠐⣾⡆⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠘⡦⡄⡀⠴⠂⠀⠈⢄⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠻⢧⠄⠀⢀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢀⠀⠀⠀⠀⢸⣆⠀⡇
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣴⣯⠈⢂⣦
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣠⣾⣿⢉⡤⡾⡿⠲⣄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⠣⠏⢱⢳⣇⡴⠉⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⡋⠀⠀⠀⠀⠾⠀⠁⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠛⠉⠁⠀⠙⠦⠀⠀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢚⠝⠋⠀⠀⠀⠀⠀⠀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⠵⠊⠁⠀⠀⠀⠀⠀⣠⠔⡫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⡽⠚⠁⠀⠀⠀⠀⠀⢀⡤⣊⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⢤⣤⢖⣩⢾⣥⣀⣀⣀⣀⣀⢀⡠⢖⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠋⢉⠔⠛⠓⣯⠔⠋⠀⠀⠀⠀⣀⣠⣠⠝⢋⠴⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠸⣄⠀⣀⡜⠀⠀⠀⠀⠀⣼⠁⠀⠈⡟⠁⠀⠀⠀⠀⠀⠉⢳⡀
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠘⠦⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⢸⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⡇
⠀⠀⠀⠀⢸⡷⣌⠙⠲⠤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠖⠚⠉⢀⣠⠔⡇
⠀⠀⠀⠀⠀⡇⠈⢑⡦⢄⣀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢀⣀⡠⠤⡖⠊⠉⠀⢠⡇
⠀⠀⠀⠀⠀⡇⠀⡆⢡⠀⠀⠉⠉⢉⠗⠒⠒⠒⠒⠒⠒⡚⢏⠉⠉⠉⠉⠀⠀⠂⢱⠀⠀⠀⡎⡇
⠀⠀⠀⠀⠀⡇⣸⠀⠘⡆⠀⠀⢀⠎⠀⡇⠀⠀⠀⠀⡰⠁⠘⡄⠀⠀⠀⠀⢸⠀⠀⢣⠀⠀⣇⡇
⠀⠀⠀⠀⠀⣧⠇⠀⠀⢣⠀⠀⡌⠀⠀⢃⠀⠀⠀⡰⠁⠀⠀⠱⡀⠀⠀⢀⠇⠀⠀⠈⡇⢰⢹⡇
⠀⠀⠀⠀⠀⢻⢦⡀⠀⠘⡄⡸⠀⠀⠀⢸⠀⠀⢰⠁⠀⠀⠀⠀⢳⠀⠀⡘⠀⠀⠀⠀⠸⣸⢸⠁
⠀⠀⠀⠀⠀⠘⢦⡙⠢⣄⣁⠁⠀⠀⠀⠀⠇⢠⠃⠀⠀⠀⠀⠀⠈⡆⢠⠃⠀⠀⠀⠀⣀⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣉⠑⠲⠤⢄⣀⣀⡈⠀⠀⠀⠀⠀⠀⠀⢠⣌⣠⠤⠤⠒⣉⠥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⢤⣌⣉⣉⣉⣉⣉⣉⣉⣉⣥⠤⠴⠖⠛⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⣶⠛⣦⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⣴⣿⣷⣿⣿⣍⣿⣾⡛⣻⣿⣉⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣸⠀⠐⢿⡿⠛⠛⠛⠋⠉⠉⠻⣿⣥⣿⣉⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠻⠇⠀⠗⠋⠀⠀⠀⠋⠀⠀⠀⣀⣤⡤⠀⠙⣿⣾⣏⣹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢿⣆⠘⢋⠕⣶⡤⠀⢿⠿⠻⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠈⡹⠀⠀⠀⠀⠀⠀⠁⠖⢰⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡐⠠⠦⠀⠀⠀⠀⠀⢰⣏⡹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣒⠒⠂⠀⠀⠀⣠⣾⣿⠟⣿⣴⡀
⠀⠀⠀⠀⡰⠃⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣀⣀⣤⣴⠞⠋⠸⡏⣴⣩⡷⣿
⠀⠀⠀⢠⠁⠀⠀⠀⠀⣾⣀⣀⣀⣠⣤⣤⣄⣀⠀⢀⣀⢀⣠⣤⣤⣀⠀⠀⣽⡿⠛⠁⠀⠀⠀⢳⣾⣭⣷⠏
⠀⠀⠀⢸⡆⠀⠀⠀⠁⠈⠉⠉⠉⠀⠀⠀⠀⠉⠙⠻⢍⣻⡁⠀⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠙⡿⣷
⠀⠀⠀⢸⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣷⠀⠀⠘⠿⣻⡋⠛⠻⣄⠀⠀⠀⢠⡾⠁⣸⠷⣄
⠀⠀⠀⠀⠉⠛⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⢠⡟⠀⠀⠀⠀⣀⣀⣴⣶⣸⣆⡴⠞⠋⠀⢰⠏⠀⠈⠓⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢶⣤⣤⣤⣹⣻⣿⡃⣘⠀⣶⠀⠀⠀⠉⠉⠀⢸⢧⣿⠞⠉⢻⡄⢾⠀⠀⡠⠀⠀⠀⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣟⣴⡟⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠑⠿⣠⠞⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⢹⡟⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠘⠄⠀⠀⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷⠄⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠙⠀⡀⢸⣿⣀⣠⡤⠶⠶⣄⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢱⡞⠹⡿⠓⠚⣛⣓⠢⢄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠈⢢⠘⣧⠀⠀⠀⠀⠀⠀⠀⢰⡟⢸⣷⣤⠶⠿⠿⣿⣯⡒⢤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢲⡀⠘⡇⣿⠀⠀⠀⠀⠀⠈⠀⣻⡧⠞⠋⠀⠀⠀⠀⠀⠈⢻⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⢄⠘⢦⠘⢾⡀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠛⠄⠀⠀⣃⣠⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠋⠉⠀⠀⠀⠀⢀⣀⣀⣤⠴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⢀⡠⠤⠖⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢶⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠟
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠁
⠀⠀⠐⣧⡈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠁
⠀⠀⠀⠈⠛⢦⣄⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣌⠙⢦⣤⠶⠶⠖⠒⠛⠛⠛⠛⠛⠛⠛⠓⢲⣶⠋⣠⣾⣅⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠑⠦⣉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣡⠞⠁⠀⠀⠉⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠈⠑⠦⣙⠲⣄⡀⠀⠀⠀⢰⠟⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⡙⠓⣆⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⡀⠀⠉⠛⠓⠶⢦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡴⠶⠞⠛⠉⠀⣠⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡌⠙⠳⢦⣄⣀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⣀⣤⠶⠟⢩⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡄⠀⢀⠌⠉⢟⠛⠒⠶⠶⠶⣶⠶⢶⡶⠶⠶⠶⠶⠶⢻⠟⠛⢍⠀⠀⢀⡎⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢱⡴⠁⠀⠀⠈⢦⠀⠀⢀⡔⠁⠀⠀⠑⢄⠀⠀⠀⡰⠃⠀⠀⠈⠳⣄⡼⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡠⠊⢣⠀⠀⠀⠀⠈⢧⡠⠋⠀⠀⠀⠀⠀⠀⠱⣄⡜⠁⠀⠀⠀⠀⠀⣸⢧⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡟⢦⣀⠀⢧⠀⠀⠀⣠⠞⢣⡀⠀⠀⠀⠀⠀⠀⣠⠞⢦⡀⠀⠀⠀⠀⣰⠃⠀⢙⡶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠙⠳⢦⣧⣴⠊⠀⠀⠀⠱⣄⠀⠀⠀⢀⡴⠁⠀⠀⠙⢆⠀⠀⣰⣁⣤⠶⠋⠀⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠉⠙⠳⠶⢦⣤⣬⣦⣀⣠⣎⣀⣀⣀⣤⣤⡤⠷⠞⠛⠉⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⢤⣄⣀⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⣀⣠⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠲⠶⠶⠶⠶⠶⠖⠒⠛⠛⠋⠉

⣿⣿⠛⢿⠛⠿⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⢂⠈⡀⠀⠀⠀⠁⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣾⣼⠁⣶⣶⣆⡄⠀⠂⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣶⣿⡿⢿⣿⣖⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇⠀⠀⠠⠙⠄
⠀⠀⢀⣠⣴⠶⠆⠀⠉⠑⠲⢤⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠠⠀⠀⠀⢠⡇⠀⠀⠀⠀⣂⠈⡄
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠉⠳⠖⠚⠉⠀⠀⠀⠀⠀⠐⢦⡀⠀⢸⡇⠀⠀⠀⠀⣿⡆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣶⡾⣷⡀⠀⠀⣴⣿⣿⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣦⠀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⢻⣦⡀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⢿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⡿⣿⡿⠃⡄
⠀⠀⠀⠀⢀⣠⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠚⠛⠹⠛⠉⢁⣄⠸⣿⣿⣿⣿⣷⡼⠁
⠀⠀⠀⢠⣿⣿⣿⠟⠁⠐⢻⣿⠋⠀⠀⠈⠙⠻⢿⣿⣷⣤⣀⣀⣠⣶⣿⣿⡿⠿⠾⠿⠟⠋
⠀⠀⠀⠉⠁⠛⠋⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠠⢈⠉⠉⢓⣶⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠒⢾⠷⠐⠒⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡾⠁⠁⠀⠉⠢⡀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣈⡑⠒⠒⢺⠒⠒⠉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠉⠀⠀⠀⠀⢠⠀⣾⡹⠀⠤⠄⢻⢈⡆⠀⢸⣀⠠⠤⠧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⣿⣧⣤⣤⣾⣼⣧⠀⡚⡂⠀⠘⠋
⠀⠀⠀⠀⠀⠀⣤⢤⡮⢤⡤⣤⣤⣄⠀⠀⠀⠀⠀⣸⠀⠹⡁⠀⠀⠒⣿⣿⠟⠈⣯⡇
⠀⠀⠀⠀⠀⠐⣿⣿⡇⠀⠀⡟⣸⡗⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⣾⣏⢙⡃⠀⠰⣿⣿⠀⢀⡆
⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⣄⣿⡇⠀⢘⠿⠫⠉⠀⠉⠹⢆⠀⠿⠿⢿⣿⣿⡟⣿⠅⠀⠙⡂
⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⣿⣿⣧⡾⠉⠀⠀⠀⡀⠀⠀⠀⠈⢲⠀⠀⢉⢿⠀⢹⠀⠀⣴⣧
⠀⠀⠀⠀⠀⠀⢹⣟⠋⢺⠋⠋⠛⡿⠁⠀⠀⠐⢧⡀⠠⡂⠀⠀⠀⢃⠀⢀⣏⠀⣿⢆⡔⣾⠂⠱⡀
⠀⠀⠀⠀⣠⠴⢻⢻⢧⣸⠀⠀⠀⣇⠀⠀⠀⠐⠉⠀⠀⠃⠀⠀⠀⣸⠀⠀⠏⡸⢹⠞⢳⡟⠂⠒⠙⡄
⠀⢀⡤⠚⠣⣠⠎⢸⡸⣿⣄⠀⠰⢅⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢉⡦⠤⣶⣤⣸⣀⡼⣿⠁⠀⠀⠈⢄
⡴⠉⠀⠀⠘⠀⠉⠙⠀⠈⠾⢢⠃⠀⠙⠈⠂⢄⣀⣀⣀⣤⡄⠘⠋⠀⢱⠈⣹⠛⠼⠛⠒⠛⡆⠀⠀⠀⠘
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢘⣆⢠⣾⠆⠛⠋⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠠⣾⣆⣀⣀⠀⠀⠀⠀⠸⠿⠃
⠀⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⡞⣷⠀⠀⠀⢀⡤⡞⠿⠗⠀⠀⢀⡾⠿⠂⡼⠿⠆⠀⠀⣾⠁⠀⠀⠈⠙⠿⠟⠁⠀⠀⠀⠀⣀
⠀⠀⠀⢀⡴⣦⠀⠰⣞⡇⠀⠀⣵⠏⠀⠀⠀⠈⠙⠁⣤⠀⠀⠀⡜⠁⠀⡼⠁⠀⠀⠀⠠⡞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣹
⠀⠸⣿⠞⠚⠁⠀⠈⠃⠁⢀⡞⣽⠶⢶⡄⠀⢀⣤⣴⠃⠀⠀⠀⠉⠙⠚⠁⣀⠀⠀⠀⠀⠀⠀⡤⢄⣰⣩⠆⠀⠀⢠⣶⣦⠀⢰⣿
⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠸⣆⠧⢁⣸⠇⠀⠈⠙⠃⠀⡠⠤⡀⠀⠀⢀⣴⣏⠀⠀⢀⡤⣄⠀⠙⠊⠉⠀⠀⠀⣠⠏⠈⠁⠀⠈⠁
⠀⠀⠀⠯⠵⠫⠖⠃⠀⠀⠀⠈⣙⠛⠁⠀⢀⠀⠀⠀⠀⢻⠉⠀⠀⠀⠻⣴⠋⠀⠀⣸⣼⠃⠀⢀⣶⠀⠀⠀⣀⠀⢀⣴⣄⠀⢠⣖⡦
⡀⠀⠀⣀⠀⣀⡴⠛⢦⡀⠀⠀⠉⠋⠀⢠⠏⠉⢹⠃⠀⠸⠀⠀⢀⣀⠞⠁⠀⣰⢞⣽⣄⡀⠀⢘⣧⠀⠀⣼⠻⠃⡼⠉⠁⠀⠸⡇
⠃⠀⠀⠻⠟⢡⣤⣠⠜⠻⣄⠀⠀⠀⣀⡼⢀⣄⡟⠀⠀⠀⣠⣄⠻⡟⠀⠀⠰⡇⠏⠀⢨⡇⠀⠘⠀⠀⠰⢿⣗⣺⠃⠀⣼⠃⠀⠃⠠
⠃⠀⠀⠀⠀⠈⠛⡁⠀⣠⠞⠁⠀⠘⠿⠃⠈⠛⠁⠀⣴⡆⠻⣅⠀⣹⣆⠀⠀⢙⠲⠶⠛⠁⠀⡤⣤⠀⠀⢠⣄⠀⠀⣸⣧⠀⠀⠀⢰
⠀⣠⣖⠁⠀⠀⠘⠿⠋⢁⡀⢠⢞⡆⠀⠀⠀⠀⠀⠀⠹⣄⢀⡼⢾⡥⠞⠁⠀⠙⠓⠁⠀⡔⢠⡟⠁⠀⠀⢸⡸⠃⠀⠈⠉
⠈⠁⠋⣀⣀⠀⠀⠀⠀⠸⠿⠋⠉⠀⠀⠀⣠⢾⡅⠀⠀⠈⠯⠖⠋⠀⠀⠀⠀⢀⠀⠀⠀⠈⣉⠀⠀⠀⠰⣉⠇⠀⢠⠏⠙⢲⠆
⢀⡀⠈⠓⢮⣇⠀⠀⠀⠀⢀⣠⣴⣦⠀⠀⠀⠉⠀⢠⡤⠤⣤⠀⠀⠀⣀⣤⡞⠉⢳⡀⠀⠸⡯⠭⢽⠀⠀⢀⣤⣴⠋⣀⣠⠏
⣻⠏⠀⠀⠸⡿⠃⠀⠀⠐⠋⠀⠈⠉⢠⣶⡄⠀⠀⢸⠋⠉⣿⠀⠀⢺⡁⠀⣳⡀⢀⣷⡄⠀⣷⣦⢸⡇⠀⠀⠉⠁⠈⠛⠋⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠀⢠⣶⡆⢸⠉⠀⢀⣤⡿⠰⣿⠇⠀⠀⠀⢳⡐⠿⠃⠈⠛⠁⠀⢀⠀⠀⠿⠗⠀⠀⠀⠀⡞⣇⠀⠀⠉⠋
⠀⠀⡀⠀⠀⠀⠀⠘⡷⢄⠀⢸⡥⠤⣾⠀⠀⠀⠉⠁⠀⠀⣤⣆⠄⠀⠿⠗⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢀⣤⡀⢈⠽⡄
⠀⣷⣿⠄⠀⠀⠀⠀⠛⠃⠀⠈⠛⠉⠉⠀⠀⠀⢀⣀⠀⠘⠱⠋⠀⠀⣤⡄⠀⠺⣝⣦⠀⢠⣶⡇⠀⢠⣶⡄⢸⠋⠁⠈⠊⠁⠀⣄
⠀⠉⠈⠀⠀⠀⢠⡒⡄⠀⠀⠀⢠⠖⣛⣛⡶⠾⡥⠾⠃⠀⠀⢠⣦⠀⡟⠁⠀⠀⠀⣿⡆⠀⠉⠀⠀⢸⣉⣤⣿⠀⠀⠀⠀⠀⣿⠋
⠀⠀⢀⡞⠀⠀⢸⡇⠀⠀⢀⣀⢿⠈⠁⢛⣷⠀⠀⠀⡄⠀⠀⢸⡁⠀⢻⠀⠀⠀⠀⠈⠀⠀⣤⣄⠀⠘⠒⠒⠋⠀⠀⠀⠀⠟⠙
⠐⣿⡟⠀⠀⠀⠘⠃⠀⠀⠈⠫⠘⠛⠲⠛⠁⠀⠀⣼⣥⡀⠀⠘⣧⠴⠞⠀⠀⣀⡀⠀⠀⠀⣿⣉⠀⠀⠀⢀⡄⠀⠀⢠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠛⠒⡆⠀⠀⠀⠀⠀⠀⠀⠸⢧⡞⠀⢠⣦⡀⠀⠀⠀⡴⠛⠛⠀⠀⠀⠸⠜⠀⠀⣰⡟⠁⠀⠀⣾⠀⠀⡇
⢠⣶⡄⠀⠀⠀⢰⠇⣀⣸⠃⠀⠀⢀⣀⠸⣿⠃⠀⠞⠀⠀⣀⡯⠇⠀⠀⠘⠁⠀⠀⠰⣖⢦⠀⠀⠀⠸⠉⠃⠀⠀⠀⢿⣶⠀⣇
⠋⠉⠁⠀⠀⠿⠟⠀⠻⠛⠀⣠⣤⠸⣟⠀⠘⣦⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⢀
⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠙⣏⠀⢈⣶⣚⡭⠇⠀⢠⠤⣄⡴⣻⠆⠀⢰⠯⣟⣷⠀⠈⠛⡁⠀⠀⢸⡭⠃⠀⠀⢀⡞⠓⢦⣤⣀⠈
⠀⢀⡤⠖⢿⠉⠈⢧⠀⠀⠀⠀⠈⢿⣭⠞⠉⠀⣀⠀⠀⠉⠁⠉⠁⢀⣀⡏⣠⣤⡏⠀⠀⣿⣿⠀⠀⠸⡇⠀⢠⣄⡾⢀⣄⡾⠀⢉⡟
⣀⣈⣧⣀⣈⣧⣀⣨⣇⣀⣀⣀⣀⣀⣀⣀⣀⣼⣻⣇⣀⣀⣀⣀⣀⣻⣟⣀⣈⣉⣀⣀⣀⣘⣀⣀⣀⣀⣁⣀⣈⣛⣁⣘⣛⣁⣀⣼⣁
⣿⣿⠋⡛⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⠉⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠓⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⣀⡽⠋⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⢤⣈⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠒⠚⠛⠉⠀⠛⣆⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠉⠉⠒⠄⠀⠀⠀⠀⠀⠀⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠤⢄⣀⡀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠑⠲⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠴⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠇⠀⠀⣼⣇⠀⠰⠀⠖⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⢑⠚⠀⠀⠀⠀⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡀⠈⠀⠀⢀⣠⣠⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠘⠃⢀⠀⠀⠰⣴⣶⣼⣷⣷⣿⡻⣿⣯⠀⠂⠶⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠠⠄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⠀⡀⣴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠻⠆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠟⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣾⠂⠀⠃⣼⣧
⠀⠀⠀⠀⢀⠞⢻⡇⠀⢹⣿⣇
⠀⠀⠀⠀⣿⣷⣾⡇⠀⠸⣿⣿
⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠙⠿⠇⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣁⡌⠙⣦⠀⠀⠀⠀⢀⣴⠿⣷⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠘⣧⠀⠀⠀⡼⢋⣀⠀⠀⠋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠸⠲⢄⠀⠂⠀⠉⠀⠚⠒⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣷⣶⣬⠀⠀⠈⢧⣀⠘⠟⠻⢆⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣈⣿⠀⠀⠀⠈⢻⣧⣤⣴⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠉⡿⠿⠟⠒⠙⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢹⣿⣇⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⢿⣿⣦⣀⣀⡴⠁⠀⠀⠀⠀⠀⢂⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠈⣽⡯⠰⣿⣦⣄⣀⣀⣭⣿⣦⡐⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠐⠀⠀⢀⣀⣀⡈⠙⠿⣿⣿⣿⣿⠃⠻⣦⣀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠉⠀⠉⠻⢶⣦⣶⡿⣿⠃⠀⠀⠈⠙⠿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣩⣿⣿⡾⠃⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⢶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠲⢦⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠊⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠰⠈⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡎⢦⣤⣤⣤⣤⡰⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠐⣿⣿⣿⣟⢥⡹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⣘⣿⣿⣿⣿⣶⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠙⢿⣿⣿⣟⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⠉⣻⣿⣿⠃⠀⠀⠀⠀⠀⠻⢿⠈⠈⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉

⣶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣧⣃⣻⣤⣭⣭⣭⣬⣥⣭⣥⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠒⠒⠀⠤⠴⠒⠒⠋⢀⣀⣀⣠⡄⣾⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣸⡍⠉⠋⠋⠉⠑⠤⢄⣀⠠⡄⠀⠰⠤⠤⢤⡤⠖⠒⠀⣀⠀⠀⠈⢻⣷⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠉⠀⢀⣤⣇⡀⠀⠀⠀⠀⠈⠰⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡴⠛⠁⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⣤⣀⣀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣠⣿⣄⠀⠀⠈⠸⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⡇⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠺⠀⢹⠀⠙⠢⢄⠀⢂⡤⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣤⢒⡟⣉⣧⣄
⠀⠀⠀⠀⢀⡠⠚⠁⠃⠀⠀⠙⠁⠀⠀⠀⠉⠺⠇⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⡨⢠⣃⣤⠟⠫⠄⡇⠝⠦⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠑⠳⢦⣀⣀⣀⣸⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠄⠈⠀⠈⠠⠀⠄⠠⠀⠀⠀⠀⢀⣤⡀⡀⠠⠀⠀⠀⠀⡤⡀
⠀⠀⠀⠀⠀⠀⢢⡀⠈⠁⡀⠀⠈⠀⠠⡌⡙⢿⡛⢿⡀⢙⣷⠀⢰⣦⡼⢷⣀
⠀⠀⠐⡆⠀⠀⢨⠁⠀⠀⠀⣦⣦⣄⡀⠀⠀⠂⢥⠰⠌⡛⣁⠀⠼⠏⣾⡿⠛⠉⠀⠞
⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⠰⠫⢻⢻⠛⢦⡣⠀⠀⠀⢡⠁⠀⠀⠀⢆⠋⠀⡀⠔⢐⣶⣤⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠡⡄⠎⠁⠀⡀⠸⠦⠀⠀⡄⠈⢃⠀⠂⢁⢣⠂⠁⠂⠀⣀
⠀⠀⠀⠂⣈⠀⠂⠀⠀⠀⠀⠀⠀⠢⠀⠘⠀⡀⠄⠋⠢⢠⠸⡦⠜⠀⠀⠀⠐⠃⠄⠀⠀⠈⣡⠆⢔⠀⠀⠂
⠀⠀⠀⡾⠁⠀⣴⡏⠐⠂⢤⣤⣀⣂⡙⠀⠴⣤⡈⠠⢖⠚⡠⠅⢂⠄⠀⠂⠨⠄⠄⣠⠔⢾⡇⢴⠂⠐
⠀⠀⠀⠀⢶⣤⣿⡇⠀⠀⠈⠛⢻⠋⠀⠄⠀⡀⠈⣂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠒⢺⠇
⠀⠀⠀⢀⣰⣿⡏⠀⡓⠊⠐⢀⣈⠀⠠⠎⠀⠀⠨⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠐⠀⠄⣁⣴⡿
⠀⠀⠀⠈⡿⠋⠀⠁⠀⠀⠀⢀⠉⢠⡄⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⠀⠀⠀⠀⠀⠙⠂⠰⢿⣽⠇
⠀⠀⠀⢷⠔⠀⢀⣤⣶⡎⣤⠜⠁⠀⢀⠄⣀⡂⣀⠀⠀⠒⠀⠀⠀⡀⠀⢀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠨⠄⠀⢸⣏⣌⣁⠙⢶⠀⠀⢸⠀⢇⠀⠀⠀⣠⠧⠀⠀⠐⢃⠀⠘⠠⣁⡀
⠀⠀⠐⠁⠀⠀⡀⠉⣱⠏⠀⠰⠀⠀⠈⡇⠈⠃⠌⠁⣀⠀⠀⠀⠐⣠⢦⡤⠚⠻⢟⡀⠖⡤⠀⠀⡠
⠀⠀⠀⠀⠐⢾⣶⣴⣿⠁⠀⠀⠀⣤⣴⣷⣄⡀⠀⠀⠅⠀⢂⣠⠶⢹⣥⣂⢐⡘⠃⠁⠾⠷⢂⣠⡀
⠀⠀⠀⠶⠀⠀⠻⣿⣃⣀⣀⣀⠈⢨⠟⠉⠉⠍⠈⠀⠸⢂⠯⠀⠩⠀⡟⠟⠅⠈⢢⠲⢟⠛⠋⠉⠀⣠⠀⡀
⠀⠀⠐⠀⢰⠀⠀⠈⡿⠏⠛⠉⠀⢀⡀⠀⡘⢆⠛⠠⠠⢹⣥⢤⠴⣎⠁⠈⢃⡔⠁⠁⡀⣘⡂⣴⡞⠛
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⣰⣾⣿⣗⠀⠄⠈⠦⠤⠀⣸⢕⠥⡊⠀⠑⡤⠋⣀⣤⠅⣬⣭⠃⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⡻⠷⠠⣤⣤⣤⣾⡃⠁⢀⠄⠠⡀⡏⠀⠀⠋⠀⠈⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠛⠛⠉⠢⠁⡡⠠⢴⣶⣶⡞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠉⢹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣮⡻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠋⠀⠀⣠⣾⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠻⣿⣿⡌⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠁⢀⣀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣯⣠⣶⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡁⢈⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠛⣿⣿⣿⠟⠁
⠀⠀⠀⢀⣠⣤⣤⣤⣤⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣿⣷⣴⣿⡿⠋
⠀⢀⣾⣿⡿⠿⠟⠿⢿⣿⣿⣿⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⣠⣾⣿⣿⣧⣀⣼⣿⡿⠋
⠀⠸⣿⣿⣄⡀⠀⠀⣀⣼⣿⡟⠀⢀⣴⣿⡿⠿⠿⠿⣿⣿⣿⡟⠁⢙⣿⣿⡿⠋
⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠁⢠⣿⣿⠋⠀⠀⣠⣾⣿⠟⢿⣿⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⣾⣿⡆
⠀⠀⠀⠀⠀⠈⠉⠁⣀⣠⣤⣴⣿⡿⠃⢀⣠⣾⣿⡟⠁⢀⣴⣿⣿⣿⡀⠀⠀⣴⣶⣾⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⣿⣿⡇
⠀⠀⠀⠀⢀⣤⣶⣿⡿⠿⠟⠛⠉⠀⣴⣿⡿⠛⢿⣿⣶⣿⡿⠋⢸⣿⣷⠀⠀⣿⣿⡏⠉⢉⣀⣀⣤⣤⣤⣶⣶⣾⣿⣿⡇
⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⣠⣿⡿⠋⠀⠀⣸⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠉⣿⣿⡇
⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⠟⠁⣀⣤⣾⣿⠟⠀⠀⠀⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⢸⣿⡏⠀⠀⠀⠀⠰⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠛⠁⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠘⣿⣷⠀⠀⠀⠀⠀⠈⠻⣿⣶⡄⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣿⣿⡇
⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⣀⣀⣀⡀⣿⣿⡇⠀⠀⠀⢀⣾⣿⡿⠿⠿⢿⣿⣿⡇
⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣄⣀⣀⣠⣿⣿⠇
⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⢺⣿⣯⡁⠀⠀⣉⣿⣿⠇⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣶⣾⣿⡿⠟⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢰⣆⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣤⡀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⡿⡿⠯⠽⠿⠛⠿⠿⠿⠿⢿⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠋⠁⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣬⡙⠛⠿⣿⡷⣶⢶⣦⣤⣤⣤⣤⣤⣤⠴⠶⠚⠛⠉⠁⠀⣡⣾⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣶⣄⣒⣘⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⠿⣿⣿⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠏⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡏⢹⠛⠀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠋⢿⣿⣿⣿⣿⣿⣗⡋⠀⠀⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠘⣿⣿⣿⣿⣟⡺⠀⠀⠀⢹⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⢻⡿⣿⡏⠀⠀⠄⠸⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣟⠃⠀⠀⠀⠸⣿⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣹⡇⠊⠀⣿⣍⠐⠂⠠⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⢿⣿⣿⡏⠀⠀⠀⠀⢀⣿⠀⠉⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⠀⠀⠀⠘⣿⣷⢶⣤⠄⠈⣿⣿⠁⠀⠀⠀⠀⠀⠘⣿⡿⠀⠀⠀⣀⡴⠛⡅⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⠀⠀⠀⠸⣤⣉⠛⠿⣾⣤⣽⣧⣄⣀⣀⣀⣀⣀⣀⣹⣧⡴⠶⠛⠉⢀⣴⠇⠀⠀⠀⠀⡸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠘⠷⣧⣀⡑⠈⠉⠙⠩⠍⢉⡉⠉⠉⠉⠀⠀⠀⢀⣤⠶⠛⠁⠀⠀⠀⣠⢄⢳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠲⠶⠤⠤⠶⠴⠶⠶⠖⠒⠋⠉⠀⠀⠀⠀⠀⣠⣾⣿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⠦⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠄⠃⢹⣿⣿⣿⣿⣿⣿⣿⣧⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡇⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢧⠠⢀⣠⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣄⣰⣷⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⢀⣠⡴⠶⠒⠛⠛⠛⠛⢷⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣲⠟⠛⠛⠛⠓⠲⠶⣤⣀
⠀⠀⠀⢧⣅⣀⠀⣠⣖⣀⠤⠔⢺⠥⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠦⢽⠒⠤⢄⣐⣦⡀⢀⣀⣥⠇
⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⡆⠀⠀⠀⢠⠃⠉⠙⠳⢤⡀⣠⠶⠛⠉⠁⠇⠀⠀⠀⠈⡄⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠠⣄⣀⣀⡜⠀⠀⠰⣷⢸⠁⢡⢼⡧⠀⠀⠘⣀⣀⣀⡤⣴⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⣇⠀⠀⡔⠒⠺⠦⢤⣄⡀⠉⠑⠒⢼⣹⠇⠀⠀⣏⡧⠔⠂⠉⠁⣀⣤⠴⠾⠒⠒⡄⠀⢀⣇
⠀⠀⠀⠀⠀⢸⢸⠀⢸⠠⠤⠄⣀⡜⠈⠙⠳⢶⡒⠒⣿⠀⠀⠀⢸⡗⠒⣲⠶⠋⠉⠘⣀⡠⠤⠤⢰⠀⢸⢸
⠀⠀⠀⠀⠀⠘⡾⠀⠀⠑⠤⣀⣠⡌⠑⠢⢄⢀⠏⠀⣿⠀⠀⠀⢸⡇⠈⠇⢀⠤⠒⠉⣤⣀⡠⠒⠁⠀⠸⡞
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡗⠒⠢⠤⠛⠀⢀⣿⠴⠶⠶⢾⣇⡀⠘⠧⠤⠒⠚⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣸⢹⠀⠀⠀⠀⠀⡘⡇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⢻⡀⠀⠀⠀⠀⢸⢹⡀
⠀⠀⠀⢀⡾⠋⡟⠳⣄⠀⣠⠞⢳⡟⢦⡀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣠⠞⣿⠛⣦⡀⢀⡴⠛⡏⠻⣆
⠀⢀⡴⠋⠀⠀⠁⠀⢘⣿⡏⠀⠘⠁⠀⠹⣦⡀⠈⠻⢦⣄⣀⣀⣤⡴⠛⠁⣠⡞⠁⠀⠉⠀⠈⣿⣏⠀⠀⠁⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⢀⠀⠄⠀⠀⢤
⠀⠀⠈⠀⠢⡀⠀⠀⠒⠀⠀⠩⢂⠐
⠀⠀⠀⠀⠀⠈⠙⠋⣩⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣤⠒⢲⣾⣿⣿⡟⢻⡆⠠⢤⣶⣶⣾⡏⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣌⠀⠀⢸⣿⣿⠛⡇⠘⢓⣢⠄⠠⠻⣿⡇⡆⣿⣿⠀⠀⠀⠀⢠⣶⣒⣚⠡⠤⢤⣼⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢹⠀⠀⠈⣿⣿⠀⡿⢸⣾⠁⣾⢠⣿⣿⣇⣧⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀⢀⣀⣸⡿⣧⠿⠼⢿⡇⣿⣠⣿⠿⢟⣚⣾⡿⢃⣀⣀⣀⣀⣀⣀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⡀⠀⢸⡀⣀⣈⣃⣈⡑⠛⠒⠚⠓⠚⠉⠀⣿⣈⣯⡉⠀⠀⢸⠷⣷⡶⠶⠶⠶⢾⢿⣿⣾⡇
⠀⠀⠀⢸⣿⣿⡟⣿⢉⡏⠩⢭⣭⣿⡇⠀⠀⣠⠤⠒⠒⢚⡷⠞⠛⠛⠒⠲⢤⡀⣿⡇⠀⠀⣇⠀⣾⣿⣿⡇
⠀⠀⠀⢸⣿⣿⡇⣿⢸⣇⣸⠘⠻⣿⣇⣴⣯⣄⠮⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⢿⣻⣻⠟⠛⠋⢉⡧
⠀⠀⠀⢸⣿⣿⡇⢿⢸⣿⣿⣰⠀⠏⣿⣿⣿⣿⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢹⡅⠀⠀⠀⠀⡇
⠀⠀⠀⢸⣿⣿⣷⠀⢸⣿⣷⣼⡆⣸⣿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡇⠀⠀⢀⠴⡷⣄
⠀⠀⠀⠈⣿⣿⣿⣀⣸⣿⣿⣿⣇⣿⣿⣿⣿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡇⠀⢠⠏⠀⡇⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠉⢹⡏⠀⠀⠀⠸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡇⣰⠯⢤⣀⣇⣠⠼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢸⣷⠃⠀⠀⠈⡇⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡼⢧⡀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡼⠁⠀⠀⠀⣴⢃⡄⠀⠀⠈⣆
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⠤⣀⣀⡠⠤⠖⠋⠀⠀⠈⠁⠀⠀⠀⠀⡏⢸⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⡶⠶⠶⠶⠶⠛⠛⠿⠿⠻⠿⠟⠛⠛⠛⠛⠿⠶⠶⠶⠶⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⢀⣠⣤⠶⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠶⢦⣤⣀
⠀⢀⣴⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣄
⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠸⣿⡄⠀⠀⠀⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⣸⡿
⠀⠘⣿⡦⠀⠀⠀⠀⠀⣀⠉⠁⠒⠒⠒⠀⠤⠤⠤⠄⢀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠠⠤⠤⠄⠐⠒⠒⠈⠉⢁⣀⠄⠀⠀⠀⠠⣾⡟
⠀⠀⣿⡇⠀⠀⠀⠠⠄⠀⣈⠉⠑⠒⠒⠂⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠤⠤⠤⠀⠒⠒⠒⠉⢉⡀⠀⠠⠀⠀⠀⠀⣿⡇
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠐⠒⠒⠤⠄⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠤⠔⠒⠒⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⡇
⠀⠀⣿⣇⠀⢘⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠘⣄⠌⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⢀⣿⡇
⠀⠀⢿⡏⠢⣘⠀⠀⠀⠀⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡇⠀⠀⠀⢸⡠⠊⣿⠇
⠀⠀⠘⢿⣆⡘⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠃⠀⡠⠔⠈⣀⣾⠟
⠀⠀⠀⠀⠙⠷⣶⣄⣀⢸⠃⠀⠠⠄⢀⡄⠀⠀⠀⠀⠸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣇⠀⠠⠐⠂⢳⠀⣀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢷⣤⣤⣀⣸⣀⠀⠀⠉⠁⠀⠐⠂⠐⠒⠒⠀⠒⠂⠀⠘⠃⠉⠀⠀⠀⣸⣀⣠⣤⣶⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠶⠶⣶⡶⢶⣶⣶⣤⣶⡶⢶⣾⠷⠾⠟⠻⠛⠛⠋⠉⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠲⠀⠆⠀⠀⠀⠀⠀⠂⠐⠐⠀⠀⠀⠐⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠉⠀⢰⠀⡠⢀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡄⠀⠀⠀⠀⠀⠀⢠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⡀⣀⠀⡆⠀⠉⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠀⠀⢄⣉⣡⣍⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠿⠷⠂⠐⠾⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣡⣌⣉⡠⠀⠀⢻⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⡀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢻⣿⣿⣿
⣿⣿⣿⡟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⠢⠧⠴⠜⡆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣿⣿
⣿⣿⡿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠛⢦⣼⣧⡶⠛⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢿⣿
⣿⣿⠃⠀⠀⠀⠀⠀⣿⠿⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠈⠁⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠿⣿⠀⠀⠀⠀⠀⠘⣿
⣿⣿⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣿
⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⣿⣿⣿⣷⣶⣶⣆⣀⠀⠀⠀⠀⠀⢀⣠⠀⣀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣀⠀⣄⡀⠀⠀⠀⠀⠀⣀⣰⣶⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡇⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠰⠀⢸⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⠤⣀⡀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣀⠠⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⣠⠎
⡀⠒⠠⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⣠⠞⠁
⠑⠤⣄⣀⡀⠀⠀⠉⠉⠒⠲⠦⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢠⠞⠁
⠀⠀⠀⠀⠈⠉⠉⠑⠒⠒⠲⠤⠤⣤⣄⣉⣉⠒⠒⠦⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠓⠒⠂⠤⠬⣉⣒⠒⠒⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠊⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡠⠊⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡤⠤⠶⠶⠶⠶⠶⠶⠤⠤⣤⠞⣡⣞⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠋⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⡶⢃⡼⠧⠤⣭⣉⡛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠛⠛⠒⠂⠀⠀⠀⠀⢠⡴⠋⡡⣐⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⢠⠋⠀⠀⠀⠀⠈⠉⠗⣦⣈⠳⣄⠀⠀⠀⠒⠚⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡰⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⣄⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢸⡆⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠻⠿⠿⠶⠶⠆⠀⠀⠀⣿⡀⠫⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢃⣼⡇⠀⠀⠴⠶⠶⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⢦⣄⣁⡀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠀⠀⠀⠀⣤⣤⡤⠤⠤⠤⠤⠶⠖⠒⢋⣉⣤⠴⠛⢹⡇
⠀⠰⠶⠶⠶⠶⠶⠀⠀⠀⠀⠳⣤⡀⠀⠉⠉⠛⠓⠒⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠖⠚⠛⠉⠁⠀⠀⣠⡾⠃⠀⠀⠠⠶⠶⠶⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⡗⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⢹⡇
⠀⠀⠀⠀⣠⣤⣤⣤⠄⠀⠀⠀⢸⣇⢹⡄⠀⠀⠀⠉⠉⠉⠁⣶⠒⠒⠲⠒⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠤⣤⣤⣤⡀
⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⢸⡿⡄⢣⠀⠀⠀⠀⠀⠀⢰⠇⢠⡆⠀⣇⠀⠀⠀⠀⠀⠀⣸⠁⢠⡄⢹⡀⠀⠀⠐⡇⡇⠀⠀⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠆⠀⠀⢸⡇⢳⠈⣇⠀⠀⠀⠀⠀⡿⠀⡾⢸⡀⢹⡀⠀⠀⠀⠀⢠⠇⢀⡞⣧⠀⠇⠀⠀⢸⡇⡇⠀⠀⠦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⠈⣇⢸⡄⠀⠀⠀⢸⠃⢰⠃⠀⡇⠈⡇⠀⠀⠀⠀⡾⠀⡼⠁⠘⡄⠘⡀⠀⢸⠃⣿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠸⡄⣧⠀⠀⠀⡟⠀⡟⠀⠀⢹⡀⢹⠀⠀⠀⢰⠇⢰⠃⠀⠀⢻⠀⢷⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣷⠸⡄⠀⢰⠇⣸⠁⠀⠀⠈⣇⠘⡆⠀⠀⡞⢀⡏⠀⠀⠀⠘⡇⠸⡇⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡆⢧⠀⡾⢰⠇⠀⠀⠀⠀⢹⡀⢳⠀⣸⠁⣼⠀⠀⠀⠀⠀⢹⡀⢻⡇⢸⢿⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡇⠀⠀⠀⢳⠘⣶⠃⡼⠀⠀⠀⠀⠀⠈⣇⠸⣇⠇⢰⠇⠀⠀⠀⠀⠀⠀⢷⠀⢀⣽⠞⠁⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⡙⠲⠦⣤⣬⣇⣉⣰⡃⠀⠀⠀⠀⠀⠀⢹⡀⠉⠀⡞⠀⠀⠀⢀⣀⣀⣤⠼⠗⠋⢀⣤⠞⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠉⠙⠒⠂⠄⠈⠉⠉⠉⠙⠛⠛⠛⠒⠒⠚⠓⠒⠚⠛⠛⠛⠉⠉⢉⡁⠠⠤⠖⠚⢉⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠶⠞⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣽⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠀⠀⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⢷⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⣀⣤⣶⠾⠿⣷⣶⣾⣇⣀⣤⣴⡶⠶⠶⠶⠶⠶⢶⣤⣄⣀
⠀⠀⠀⢠⣾⠟⢉⣠⣴⣶⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⣄
⠀⠀⠀⣿⣥⣶⣿⣿⣿⣿⣿⣿⡿⠁⣀⣤⣶⣶⡿⠿⠿⠿⢿⣶⣶⣤⣀⠀⠀⠙⢷⣦
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠿⠋⣠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣷⣄⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠉⣹⡟⠉⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠈⢿⡄
⢀⣀⡏⠂⠀⢰⡟⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠈⣿⡄
⠿⠿⠃⠀⠀⣾⠃⠀⠀⢀⣿⡇⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠸⣿⡆⠀⠀⢸⣧⣴⡄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣧⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⣤⣿⡇⠀⠀⢸⣿⡿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⣿⣶⣤⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⠀⣾⠏⠀⣿⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⢻⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⢹⢹⣿⣷⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⡟⠀⢠⠇⠀⠀⢀⢜⣥
⠀⠀⠀⠀⠀⠘⣿⡀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣾⡾⠟⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⢸⣇⣴⠋⠀⠀⠀⠘⢌⣡
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠙⠻⢿⣿⣿⣿⣿⠀⠀⠙⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⢋⣴⠿⣿⠁⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⣰⡟⠁⠀⣹⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠀⢀⣾⡿⣿⠛⠻⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠾⠋⢹⣇⠀⠘⣿⠀⢹⡀⠀⠀⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠁⢠⡄⠀⠀⢿⣄⠀⠈⠁⠸⣇⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠙⠿⢶⣦⣤⣿⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⢾⢳⡄⠀⠀⠀⠀⣠⣤⣄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠋⠀⠀⠀⠀⢰⣿⠿⠟⣸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠒⠒⢶⣴⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⣀⣸⠁⢈⣀⣉⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠛⠛⠛⠛⠛⠛⠛⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡝⢁⣀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠁⠀⠀⠀⠀⢱⡞⠁⠂⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⡾⡯⠀⠻⠛⡳⠆⠉⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠤⠤⢼⡇⠀⠐⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⡴⣿⣅⣀⣀⣠⢤⡶⠞⣍⠉⠉⠛⠻⢲⡧⣭⠤⠀⣀⣐⣒⣒⣤⣤⡄⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⣸⠀⠀⢠⠀⠀⡇⠀⣿⠀⣀⠄⠀⠨⡇⠀⠀⢨⠀⠀⠀⠀⠉⢹⠇⢠⣼⣃⠀⠀⠀⠀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠄⠀⢸⠀⢠⡅⠀⢉⣀⣻⣀⣟⢸⠋⠉⠀⣸⠀⠀⠀⠀⡇⢸⡧⠤⠼⡧⠀⠀⢒⣛⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⢸⠀⠀⢠⡆⠀⠙⠿⣷⠿⢿⣿⣂⣀⣀⣤⣤⣀⣠⣤⣼⠁⠀⠀⣇⠀⠀⠁⢘⡂⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⣄⠀⢸⣇⡀⠀⠀⣇⢀⣀⣘⣀⣠⡇⠀⠀⠉⠉⠙⠁⠉⠀⠈⡬⠒⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡄⢀⡾⡿⡄⠀⠉⠙⠛⣸⢿⡍⠉⠁⠀⡨⠙⠓⣀⠀⠀⢠⠀⠆⠀⠀⡇⠀⠀⠀⢀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣼⣁⣧⣨⣆⣀⡀⠀⠑⠚⠷⣂⠀⠀⠀⠀⠀⠙⢿⣆⠰⡄⣇⠀⢀⣟⠀⠀⠀⢸⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠋⢉⣿⡷⠾⠟⠯⠭⣤⣀⠈⠁⠀⠀⠀⠀⠀⣠⠆⢻⣇⠢⣿⡀⢈⣉⣀⠀⠀⠸⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢰⡿⠉⠀⠀⠀⠀⠀⠀⠉⠙⢦⡑⣄⢀⡤⠀⠀⠀⠈⣿⡄⠬⠀⠈⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⠹⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⠎⠀⠀⠀⠀⠀⡿⠃⠀⠀⠴⡆⢀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠍⢐⠃⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢃⠀⣀⠴⢁⡟⠀⠂⣠⣘⣻⠈⠉⠁⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⢀⡄⠉⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢴⡀⠉⠀⠈⠃⢠⠚⠁⡹⣷⠤⠧⠂⢀⡀⠈⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡾⠏⠀⢠⠿⠛⠒⠶⠫⠾⠒⠀⠀⠉⠓⠤⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⢍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠃⢀⠴⠁⠀⠸⠆⠀⠀⢠⣦⠀⠀⠀⠀⠀⠈⠓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠱⢿⣶⠀⠀⠀⡀⡀⢀⣴⠟⠉⢀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠈⠉⠐⠈⠛⠊⠈⠀⠀⠀⠘⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡀




⣿⣟⣛⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣤⠤⠴⠶⠶⠶⢤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡤⠶⠶⠶⠤⠤⣤⣀
⠀⠀⠠⣽⡉⠀⠀⣠⢀⣀⠤⢾⣥⡤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣬⡳⠤⣀⡀⣄⠀⠀⢉⣿
⠀⠀⠀⠀⠈⢉⡟⠁⠀⠀⠀⡌⠀⠀⠀⠸⠉⠙⠓⢦⡀⢠⡴⠚⠋⠉⡅⠀⠀⠀⢡⠀⠀⠀⠈⢻⡉⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠤⠄⠀⣀⡇⠀⠀⣾⣆⠃⠘⣸⡇⠀⠀⢰⣀⠀⠠⠬⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡸⡄⠀⡘⠛⠛⠒⢦⣤⣀⠈⠁⠒⣯⡟⠀⠀⢯⡵⠒⠉⠀⣀⣤⡴⠚⠛⠛⢂⠀⢠⢇
⠀⠀⠀⠀⠀⡇⡇⠐⣃⠐⠂⠠⢎⡀⠈⠙⢯⡀⢻⡁⠀⠀⢸⡇⢀⡽⠋⠁⢀⡡⠄⠐⠂⡸⠂⢸⢸
⠀⠀⠀⠀⠀⢹⠁⠀⠀⠑⠂⢴⣆⡈⠑⠢⡜⠀⢸⡃⠀⠀⢸⡇⠀⢢⠔⠊⢁⣰⡦⠐⠈⠀⠀⠈⡏
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠈⠉⠉⠀⣠⠞⠛⠉⠉⠙⠳⣤⡀⠉⠉⠁⠘⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡜⡆⠀⠀⠀⠀⢸⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠸⡇⠀⠀⠀⠀⠰⢣
⠀⠀⠀⢀⡴⢳⠷⣄⠀⢀⡴⢿⠷⣄⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣠⢶⡿⣆⠀⠀⣠⠾⡞⢦⡀
⠀⢀⡴⠋⠀⠘⠀⠈⣷⡞⠁⠘⠃⠈⢳⣄⠀⠙⢦⣄⣀⣀⣀⡤⠞⠁⣠⠞⠁⠘⠃⠈⢳⣾⠁⠀⠃⠀⠙⢦⡀
⠀⠈⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠅⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣜⣛⠁⠀⣀⣀⣀⡀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢿⣷⠀⢻⠿⣿⠅⠀⠀⣼⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢀⡟⠀⠀⠀⠀⠀⠀⠀⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡼⣿⣧⣶⣶⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡷⠦⠤⠛⠟⠀⢀⣾⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠉⠉⠁⠀⣰⣷⣿⠏⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣶⣶⣤⣾⡿⣯⡝⠀⠀⠈⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⣿⣿⣿⣿⣿⡟⣹⣿⠁⠀⠀⢀⣠⣶⠊⣡⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠇⣿⣋⣩⣽⣿⣿⣇⣿⣿⡶⠤⠴⠟⢻⠃⢰⠇⠀⠀⠀⠙⠓⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠀⠉⠩⠀⢸⠀⠀⠈⠉⠻⣿⣿⠁⠀⠀⠀⢀⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠑⡯⠀⠀⠀⠀⠀⡸⠀⢰⠀⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⢠⡏⠀⠀⡆⠸⣿⡇⠀⠀⠀⠘⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠃⠀⢼⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣾⡷⠀⠀⠁⠘⢿⣷⣀⡅⠀⠀⢣⡀⠀⠀⢠⣷⡀⠀⠀⠀⡜⠀⠀⣿⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠩⣿⣿⣿⡄⠀⠀⠀⠱⢤⣀⣼⣿⡃⠀⣠⠞⠀⠀⢀⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠀⣀⣀⣤⣿⠟⠉⠛⠋⠁⣀⣀⣴⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⢰⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠛⠉⠙⠛⢧⣄⡀⠀⣠⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⣿⡏⠀⠀⣠⣾⣿⣿⣿⣿⣵⣦⣤⣤⣤⣄⡤⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⣿⠃⠀⠀⠁⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣍⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠀⠀⠀⠀⢀⠠⠃⡸⠁
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡅⡼⠁
⠀⠀⠀⢿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⡾⠋⡾
⠀⠀⠀⢸⣇⢰⣶⣶⣄⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⣀⣉⣱⣒⣛⣳⣾⠃
⠀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠚⠉⠉⠉⠀⣿⣿⡿⠟⠛⠉⠁⢠⠉⠻⠟⠻⢿⣿⣿⣿⣿⣿⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠶⠓⠒⠛⠚⠚⠓⠒⠒⠒⠒⠢⠤⠅⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⠤⣌⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⢰⠁⣘⠄⣀⠛⠄⡀⠂⠌⠀⢀⣀⣀⣀⠀⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠌⡘⢀⡏⠔⠂⠚⠂⠉⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠌⡰⠤⠌⠴⠃⣘⠴⡄⠀⡤⣤⠒⣶⣒⢆⣜⣡⣌⡹⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠐⢠⠁⡊⠀⠀⠀⠀⠀⣯⣱⡇⠀⠁⢉⣉⣉⢉⡁⢤⢄⠀⢤⠐⡄
⠀⠀⠀⠀⠀⠀⠀⣀⠂⠌⣑⠦⠄⠀⠒⠚⢶⢯⡇⠀⣭⡿⣼⣛⠾⣽⢃⠎⣐⠢⠌⡁⠀⠉
⠀⠀⠀⠀⠀⠈⡐⠠⡎⠁⠀⣀⡤⣴⡖⣶⣸⢿⡇⠀⣿⣽⣳⣯⣿⢣⣏⡲⢠⠋⠴⠅⠀⡦⢀
⠀⠀⠀⠀⠀⠀⢀⠂⠴⠀⠀⠯⠓⣋⣩⣭⢯⣿⡇⠀⣿⣿⣟⡾⣭⣛⡾⣱⠃⡌⣑⠇⠀⡵
⠀⠀⠀⠀⠀⡀⠂⠌⡰⢇⠀⢰⢏⡟⣼⣟⡿⣽⡇⠀⣿⣿⣿⣽⢧⣟⡳⢧⣝⢰⣁⠄⠀⣇⠂
⠀⠀⠀⠀⠀⢀⠀⠠⢁⠺⡀⠀⢿⡽⠗⠛⠛⠋⠁⠀⣿⣟⡿⣯⣟⡶⠋⠁⠀⠀⠀⠀⠀⡏⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠂⡘⢃⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⡾⣹⠿⣼⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠠⠀⠐⠠⢙⡀⠀⡆⠀⠀⠀⠀⠀⢀⡟⡳⢯⡟⠰⢦⡀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣱⠀⠸⡤⢤⣀⡠⢴⠛⠤⢁⠒⡬⢁⠆⡌⠃⠎⡐⠈⠉⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠉⠀⠀⠀⢇⠂⠬⣑⠂⡌⠑⠎⡜⠠⢌⡐⠠⠉⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⢸⡌⠠⢀⡘⠠⢁⠒⠠⠁⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⡜⠀⠁⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣯⡤⠤⠀⠀⠤⠤⠀⠀⣀⡉⠛⠛⠒⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⢹⡿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⢶⣤⣈⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⣠⣶⣿⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠘⠍⠟⠒⢤⣿⢢⣤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣧⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠐⣥⠃⠀⠀⠀⠉⠻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢀⢁⠕⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆
⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⣶⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣠⡀
⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⠃
⠀⠀⠀⢀⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⣿⣿⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⢻⣿⡆⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⢯⣿⣿⣘⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡅
⠀⠀⠀⠀⣼⣿⣿⣿⣮⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢹⡏
⠀⠀⠀⠀⢹⣇⢿⣿⣯⡟⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣩⣭⠟
⠀⠀⠀⠀⠀⢹⡘⣿⣿⣿⣝⢿⡏⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢁⡴⣿⢠
⠀⠀⠀⠀⠀⠀⡁⡸⣧⣿⣿⣷⣕⠄⡀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣞⣡⢜⣵⡿⠋⡏
⠀⠀⠀⠀⠀⠀⠡⣰⡄⣿⣿⣿⣿⣿⣏⠲⣤⣀⠀⠉⠒⠤⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠐⣐⣾⣿⣼⠿⣫⣷⣿⣿⢳⢾⡃
⠀⠀⠀⠀⠀⠀⠀⠹⡧⣿⡻⣿⣿⣿⣬⣷⡧⣬⣯⣔⡂⢼⣿⡏⠀⠀⠈⠀⠀⠀⠀⠒⠀⠀⠈⣽⣿⣿⠸⢾⣟⣭⣶⣿⣿⣿⣟⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣽⣿⣌⡻⣿⡟⡟⢱⣦⣽⣿⣿⣿⣼⣿⣭⣤⣤⣄⣀⣀⣀⣀⣠⣤⣬⣭⣵⡾⠗⣾⣿⣿⣿⣿⡿⡫⠊⣾⣞⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠛⢿⡍⠎⢷⠷⠸⣛⣿⣿⣿⣗⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣁⣿⣿⡿⢟⡵⠊⡡⠊⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡈⠻⢿⡟⠻⢿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⢛⡩⣶⣯⡷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⢀⠀⠁⠂⣍⣼⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⣟⣛⣫⣭⣏⣼⣿⡇⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠁⠐⠢⣬⣱⡄⠀⠉⠁⠈⠉⠀⠀⠀⠀⢠⣸⣿⡿⢷⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⡀⠀⢀⡶⠀⠀⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡅⠀⢤⡀⢠⣷⣤⣾⠇⠀⠀⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⡀⢹⣿⣿⡇⠀⠀⠸⠛⠋⠉⠀⣤⡀⠀⣿⣿⣿⠁⣠⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣿⣾⣿⣿⡇⠀⠀⣠⡆⠀⢀⣾⣿⣿⠀⣿⣿⣿⣾⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠹⣿⣿⣿⠀⣾⣿⣷⣴⣿⣿⣿⡟⢸⣿⣿⡿⠁⢰⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⣿⣿⣿⠀⣿⣿⣿⠋⢸⣿⣿⡇⢸⣿⣿⡇⠀⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠃⢸⣿⣿⠇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢸⣿⣿⡇⢸⣿⣿⠀⣾⣿⣿⠀⣾⣿⣿⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠈⣿⣿⣇⢸⣿⣿⠀⣿⣿⡿⢀⣿⣿⡏⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⢻⣿⣿⠀⣿⣿⠀⣿⣿⡇⢸⣿⣿⠃⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⢸⡿⠁⠀⣿⡿⢰⣿⣿⡇⠀⠹⣿⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠁⠀⠀⡟⠁⠈⣿⣿⡇⠀⠀⠘⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆





⣿⣿⣿⣻⣛⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣟⣻⣿⣛⣛⣿⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢉⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣋⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢋⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢋⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢋⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⣁⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⢋⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢋⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⡴⠋⣡⣴⣿⣅⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠞⠛⢋⣭⣭⣤⣄⡴⠛⢁⣤⠞⠉⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⣻⡶⠛⠁⣠⣾⣉⡀
⠀⠀⠀⠀⣀⣤⠶⠛⠋⠉⠀⠀⠀⠀⣴⠋⠀⠀⠀⠘⣷⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⠞⠁⣀⣴⠟⠁⠀⠉⠉⠛⠶⢦⣄⡀
⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠀⠀⠙⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄
⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⣀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣿
⣿⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⣿
⣿⣆⠈⠙⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠛⠁⠀⠀⢀⣴⣿
⣿⠈⠳⣄⠀⠈⠉⠛⠳⠶⠶⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⡴⠶⠞⠛⠋⠉⠀⠀⠀⠀⢀⣠⠴⠋⢸⣿
⢸⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠛⠉⠀⠀⠀⡾⣿
⢸⠀⠀⠀⢀⡏⣇⠉⠛⠶⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⡤⠴⠶⠚⠋⠍⢦⠀⠀⠀⠀⠀⠀⢠⡇⡿
⢸⠀⠀⠀⣼⠀⢸⡀⠀⠀⠀⠀⠀⠉⠉⠉⣹⢻⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡟⢯⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠘⣆⠀⠀⠀⠀⠀⢸⢰⡇
⢸⡄⠀⢰⠇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⣰⠃⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠸⣆⠀⠀⠀⠀⡟⢸⡇
⢸⡇⠀⡟⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢹⡄⠀⠀⠀⡇⢸⡇
⠸⡇⢸⠃⠀⠀⠀⠈⣇⠀⠀⠀⠀⣰⠃⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢳⠀⠀⢸⡇⢸⠇
⠀⣇⡏⠀⠀⠀⠀⠀⢻⠀⠀⠀⢠⠏⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠈⣇⠀⢸⠁⣿
⠀⣿⣦⠀⠀⠀⠀⠀⠘⡇⠀⢀⡞⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢹⡄⣿⠀⣿
⠀⢻⡌⠳⢤⡀⠀⠀⠀⢹⠀⡼⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡿⢀⡿
⠀⠈⢳⣄⠀⠙⠲⣄⡀⠘⢀⠇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡷⣻⠇
⠀⠀⠀⠈⠳⢤⣀⠀⠙⠓⠾⣤⣀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⡏⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠈⠙⠓⠶⠦⣤⣀⣀⣈⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣼⣁⣤⡤⠴⠶⠚⠉⠁⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣤⣄⣀⠀⠀⠀⠉⠉⠙⠛⠛⠓⠒⠒⠓⠒⠒⠒⠚⠛⠛⠛⠉⠉⠁⠀⢀⣀⣠⣤⠶⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠲⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠖⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠻⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢣⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⣶⣶⣦⣤⣤⣄⡠⢄⡬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⡀⠀⠀⢇
⠀⢠⣦⢶⠒⣀⣤⡀⢐⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡯⣶⡵⣂⠉
⠀⠀⠀⠀⠈⠻⣿⣿⣶⣬⣓⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠁⠀⠀⠀⠀⢀⣤⣀⡀⠄
⠀⠀⠀⠀⠀⡐⡰⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣶⣿⣿⠿⣻⠂
⠀⠀⠀⢀⢠⣷⣻⣿⡿⢿⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣽⢷⣶⡔
⠀⠀⠀⠶⠿⠿⠛⣧⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⠻⣿⣿⣿⣿⣯⣟⣿⡿⠻⠛⠛⢉⣥⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⡹⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠙⢻⣿⣿⡅⠀⠀⠀⠀⢢⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠐⣿⣿⡇⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣿⣿⣿⣿⣿⣿⡿⣿⠏⠀⠀⠀⠀⣽⣿⡷⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢿⡯⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠭⣽⣿⣿⣿⣿⣟⠭⠊⠁⠀⠀⠀⠀⠀⣽⣿⡗⠀⠀⠀⠀⠀⠀⠀⠉⠚⠩⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠥⣞⡽⣻⠽⡫⠅⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠑⠩⠛⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣴⣶⣶⣿⣿⣶⠄⠀⠀⠀⠀⠀⠸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡑⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢛⣻⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡝⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⢎⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⡷⡳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠵⠫⠊⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠳⣄⠀⠀⠀⠀⠀⠀⠈⢦⣀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠘⣷⡄⠀⠀⠐⠶⠀⠈⢏⠛⢦⡀⢸⣧⣀⠀⠀⠀⢰⡀⣦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢹⣿⡆⢀⣀⠀⠤⠤⠼⠿⠶⣇⢸⣎⠻⣆⠀⠀⢸⢷⡸⡿⢦⡀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣿⣿⠀⡀⠤⠄⠒⠒⠘⡖⠚⠺⡿⢿⣿⠀⡀⢸⠀⢻⢃⠀⠃⢸⢿⣄⢀⡀⢀⡀
⠶⠦⣶⣶⠞⠛⠛⠓⠢⢀⡴⠊⢸⣿⣿⡉⢀⠤⠾⠂⠉⣁⣩⡅⠈⣇⠀⢻⢽⣿⣿⠀⠚⠈⣏⠉⢹⣀⢹⡆⠀⠛⢸⡆
⠀⠀⠀⠈⠉⠓⠢⠤⣠⣋⠀⡠⢺⣿⣿⠛⢧⣴⣶⣾⣥⣈⠿⠁⠒⡧⠠⠉⡐⠄⣺⡐⢨⣾⡷⠀⢺⠂⠘⣥⣐⠛⣻⠴⣆
⠀⠀⠀⠀⢶⠆⠀⢰⢣⣿⣿⣇⠸⣿⣇⢀⣿⡟⢧⡞⠙⢻⡆⠸⠿⠷⠀⠀⠀⢁⣼⠀⠉⡩⢐⣬⣽⢴⣶⣍⣿⠛⠁⠀⠈⢷⡀
⠀⠀⠀⠀⠀⢀⣤⣇⠀⢻⠿⠟⡼⠙⢿⣧⡙⡿⠥⠈⠲⣼⠃⠐⢾⡿⠀⠀⠘⠛⠋⠐⠍⡀⠿⠿⠋⠀⠉⠁⢠⡄⠠⣦⣤⠖⠁⢴
⠀⠀⠀⠀⠀⢸⣿⣿⠏⣻⠶⢤⣇⣀⢸⠉⠻⠷⠖⠒⠋⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠜⢵⣶⠎⠈⢀
⠀⠀⠀⠀⠀⣼⣿⣿⠀⣿⠀⠀⡇⠉⢙⠓⠶⣤⣀⠀⣶⣷⣀⠟⠀⠀⠀⢀⡀⣀⢀⡀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⡞⢉⡟
⠀⠀⠀⠀⠀⣿⣿⡏⠀⢸⢀⡴⣷⣶⣼⡀⠰⣿⣿⡆⠀⠉⠀⠀⠀⠀⠀⢸⡇⣿⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣧⠉⡄
⠀⠀⠀⠀⢠⣿⣿⣧⠀⠈⢿⣴⣶⡀⠙⣷⠀⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣸⣿⢿⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢀⡀
⠀⠀⠀⠀⢸⣿⣿⠘⡆⠀⠘⡄⠀⢱⡀⠘⢆⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⣶⣶⣞⢲⡖⠀⠀⠀⠀⠀⢠⡆⢀⣀⡿⣶⡆⣾⡏
⠀⠀⠀⠀⠈⢉⡉⠙⠛⣖⠒⠻⡦⠤⠷⣤⣌⣢⠀⠸⣤⡀⣀⠀⠀⠀⠀⢸⡇⢿⡿⣿⢩⠿⣧⠀⠀⠀⠀⠀⠈⠁⡘⠻⢿⣤⠁⠉
⠀⠀⠀⠀⠀⠛⠃⢀⣀⡈⢶⣦⠘⣆⠀⢿⣿⡷⠑⣔⠿⠳⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢆⠌⠲⡄⠠⡤⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠨⠿⠶⠈⠻⣃⡠⠷⡌⢉⡱⣶⣾⡧⡀⠈⣢⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠖⠙⣦⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠢⣀⡼⠫⡀⢈⣻⣁⠈⣿⢋⣉⠫⡉⠀⠀⠀⣴⠇⠀⢰⠗⣼⠇⠜⣿⡠⠀⣨⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣿⣧⠖⠉⢢⡠⠚⠻⣿⠿⠓⢷⠾⠛⢄⠀⠑⢄⠀⠀⡄⠀⠀⢢⠜⣄⡠⠊⢣⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⣼⠟⢁⣤⡊⠁⠈⠢⡀⢈⡷⣶⣾⣷⢤⡀⠑⠢⣠⣷⢆⡘⡤⢊⠔⠱⡈⢣⣾⡗⠙⠁
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⢺⣧⠹⣷⡄⣀⠴⠊⠓⢄⠈⠙⠯⡀⠈⠢⣀⠹⠫⡀⢉⢘⣅⣠⡾⠋⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⠀⠀⢻⣧⡜⣿⣄⠀⠀⠀⠀⣙⡦⡖⣿⣿⣷⡌⠑⢧⣈⢔⣴⡿⠋⠀⠀⠰⣤⣼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡘⢿⣦⣠⠔⠊⢁⣀⠈⠛⢍⣩⠗⢆⡘⣷⡿⠋⠀⠀⠘⠃⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⠚⠉⠀⠀⣤⣈⠙⠋⢠⣾⠛⠢⡀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⡇⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⠼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⢀⣀⠤⢄
⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⠤⠐⠒⠂⠀⣀⢀⣀⡠⠖⢊⣁⣤⣒⣻⣤⠤⠔⢒⣋⠁⠤⠤⠀⢀⣀⢀⣀⣀⣀
⠀⠀⠀⠀⢀⣼⡁⠤⠒⠒⠘⠉⠉⠉⠀⠀⠀⡠⠋⠁⠀⠈⠀⡐⠊⠩⠁⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠂⠀⠈⠉⢉⣓⣄
⠀⠀⠀⠀⠈⣷⠨⠥⢤⣀⣀⣀⠀⠀⢠⡤⠬⠀⠀⣀⣀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠀⠀⠀⠨⠭⣑⣺⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠒⠲⠤⠭⠭⣿⣖⣒⣀⣀⣀⣀⣀⣠⡤⠤⠿⡧⠤⣤⣤⣄⣤⣤⣤⣴⣶⣾⣷⣖⣒⡚⠋⠭⠭⠤⢺⡅
⠀⠀⠀⠀⠔⢻⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣸⡁⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⡇⠀⠀⠐⠂⠀⠀⠀⠸⠇
⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡀⠀⠀⠀⠀⠀⠀⠶⠐
⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠰⣆⡉⠁⢀⡀⢰
⠀⠀⠀⠀⢧⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠂⡇⠈
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠇⠀⠀⠀⠀⡄⠀⢱⠁
⠀⠀⠀⠀⢼⡧⢄⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢐⣶⣺⣽⣺⠄
⠀⠀⠀⠀⠈⠉⠁⠟⣛⣻⠶⠶⣶⣤⣿⣥⣒⣒⣒⣒⣒⡒⠒⠂⢠⣷⣤⣴⣶⡒⠀⠀⠐⠲⠶⠶⢾⡷⠶⠯⠭⢹⣿⣿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠀⠀⠀⠈⠭⠉⠩⠭⠭⠭⠿⠀⠠⠤⠀⠠⠤⠄⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠉⠑⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠒⢦⡀⠈⢁⡔⢁⢍⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢨⣀⡠⠶⠖⠚⣛⣛⣉⣉⣉⢭⡽⠃
⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⣇⠐⡩⢦⡘⠒⣡⡈⠢⡀⡰⣡⠔⣒⣒⢠⠃⠀⠀⠀⠀⠀⠰⠯⣥⠶⡖⠉⠙⢉⠁⠀⠈⢸⡄⠀⡇
⠀⠀⠀⠀⣶⡋⢻⡆⠙⠲⠤⢤⠔⡡⣊⡴⣛⣳⣄⠉⢶⠄⠈⠳⡇⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠠⠈⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠘⢎⡴⣫⣾⢟⣵⣿⣦⡀⠀⠀⡤⠜⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠠⠄⣿⠀⡇⠀⠀⢸⠃⠀⠀⠀⠃⢠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⢔⣹⠿⣋⣴⡷⡄⠀⠘⢆⠀⠻⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⣀⣀⣰⣦⠦⠤⠚⠛⠉⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠈⠻⡥⣪⢟⣭⡾⢟⣦⠀⠀⢳⣀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠰⣟⣉⣉⣉⠥⠤⠤⠒⠒⠚⠋⠻⣧⣤⣤⣤
⠀⠀⠀⡠⠂⠀⠀⠐⠄⠄⠀⠾⠿⠀⠀⠀⠘⢷⠟⡫⣴⡿⡫⣣⡀⠀⠉⠀⢱⣀⡀⠀⠤⠠⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⢀⢀⠠⠇⠀⠀⠀⠀⠀⣀⠤⠤⠒⠒⠈⠉⡂⠀⠻⣊⢕⡪⣞⣭⣷⣂⠀⠀⠀⢷⢓⠲⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿
⡎⠀⠀⠀⠀⠀⠀⠀⠸⣴⡀⠀⠀⠀⠀⢠⠇⠤⠤⢽⣯⡪⢟⣫⣶⣷⠂⠠⣶⢸⠀⠀⠀⢔⣢⠒⣼⡂⣀⠀⠀⢀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡇
⠈⠀⠀⢒⢀⡀⠀⠀⠀⠈⠙⢶⣤⡀⠤⡼⢦⠤⣤⣃⠘⣾⣟⠟⣋⢼⡧⠤⠒⠉⠀⢰⠒⣤⠿⣋⡡⠄⠈⢷⣾⣷⣄⠈⠉⠏⠀⠙⢯⡁
⠀⠀⠀⠈⠁⠙⠦⣄⣀⠀⣰⡪⠛⢧⢠⠇⠈⠲⠃⠈⠉⢙⣶⣿⣿⡉⠀⠀⢀⡤⠒⠉⠱⡜⢧⠀⠐⠂⢀⡼⠈⢿⣿⣆⠎⠀⠀⠀⠀⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡹⠒⠒⠒⠢⣤⠀⣾⣿⣿⠋⣡⠴⠊⠁⠀⠀⠀⢀⣵⢈⡧⢴⠊⡿⣦⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠘⠂⠤⠼⠁⠀⠀⠀⠀⢹⠀⢻⡿⠗⠉⠀⠀⠀⣀⠴⠒⠉⠉⠈⢋⠀⠛⠃⠈⠁⠀⠀⡟⣠⡆⠀⠀⠀⠀⠀⡟⠫⠯⠃
⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠒⠉⠀⠀⢀⡤⠖⠛⠁⠀⠀⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠰⣟⠄⠃⠀⠀⠀⠀⠀⠃⠀⢀⣤
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⢰⠃⠀⠀⣠⠴⠚⠉⠓⠦⡄⡀⠀⠀⢰⣿⢋⠽⢻⣾⣧⡀⠀⣀⠀⠄⠀⠈⠀⠀⠀⠀⢸⣶⣤⡀⠉
⠀⠀⠀⠀⡄⠀⣀⡀⠀⣬⠀⠀⠹⡆⠀⠀⠀⠈⠳⣍⣉⠀⠀⠀⠀⠀⢄⠈⠳⠀⠀⠸⣷⣝⠊⣠⣿⡴⠋⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡷
⠀⠀⠀⠀⣷⠈⣿⣇⠀⠙⠧⣄⠼⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⣶⣶⣬⣉⠀⠀⠃⠀⠀⠈⠓⠶⠿⠿⠅⠀⠰⠆⣉⠢⣄⠀⠀⠀⠀⢠⡿⠿⠟⠁
⠀⠀⠀⠀⢸⡆⢹⣜⡄⠀⠀⠀⠀⠀⠀⢀⠔⠉⢱⣶⣿⣿⣿⣿⣿⠟⠉⠛⢷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⠳⢄⠀⠀⡜
⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⢀⣿⠿⠿⠻⣿⣿⣄⣀⣀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠀⠒⠒⠾⢷⣈⠀⢀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠉⣀⡤⠔⠊⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣄⣠⣤⡶⠖⠉⠉⠀⠁⠢⣀⠀⠀⠠⡖⠒⠢⣝⢆⠀⠀⢱⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡀⠀⠀⠰⠋⠈⠀⠙⢦⠀⠘⣿⣿⣿⣿⣿⣿⣿⠟⣉⣀⣀⠤⠤⠀⢠⣤⣈⡑⢦⡔⠋⠀⠀⠀⠀⢣⠀⠀⠀⠠⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄⠀⢣⠀⠀⠀⠀⡀⡇⠀⠘⢿⣿⣿⠿⠋⠀⠀⠹⡄⠀⡰⠁⠀⢸⡿⠋⠁⠀⡍⠓⠢⠤⠤⠴⠋⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠑⠤⠤⠤⠜⠁⠀⠀⠈⢟⠁⣀⠤⠤⠤⣄⠘⣴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠠⡄⠀⠀⠀⢀⠏⠒⠲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⡠⠤⡄⠀⠀⠈⢎⠃⠒⠒⠒⠊⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠓⠤⠂⠀⣀⣠⣼⠀⠾⠭⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣤⣤⣴⣾⡿⠿⠿⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣹⣛⣩⣙⣙⣟⣩⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢴⠲⣄⡀
⠀⠀⠀⠀⠈⠙⠦⣝⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣍⡳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢍⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢌⠐⠤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢚⡩⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡌⠉⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⣊⡡⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⡤⠞⠀⠀⠀⠀⠀⠀⣀⡤⠖⣋⡥⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠂⠒⣋⡥⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣀⣀⣀⣈⣁⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⢰⢆⠀⠀⠀⠀⠆⠀⠀⠀⢀⡶⠀⠀⠀⢀⢶⡀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠘⡆⠀⢀⠇⠈⠆⠀⠀⠆⠀⠀⠀⠀⡞⠀⢀⠀⠀⡜⠀⢣⠀⠀⡼⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠀⠌⠀⠀⠀⠀⡌⠀⠀⠀⡆⡼⠀⠀⠀⠄⠐⠀⠀⠀⠆⠠⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⢐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠓⠒⠒⠒⠚⠛⠓⠚⠓⠒⠒⠚⠚⠚⠒⠒⠒⠛⠛⠛⠒⠒⠒⠚⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣷⣄⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⣿⣿⣿⠷⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⢀⣤⣾⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠁
⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⣤
⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⢠⡏⠉⠉⠉⠉⠉⠉⠉⠙⠳⣄⠀⠀⢰⠏⠉⠉⠉⠉⠉⠉⠉⠙⢦⣀⠀⣼⠉⠉⠉⢩⣿⡆⠀⢸⡏⠉⠉⠉⣽⣷⡏⠉⠉⠉⠉⣿⡆⠀⢀⡾⠉⠉⠉⠉⣽
⠀⠀⣼⠁⠀⠀⠀⣀⣀⠀⠀⠀⠀⠘⣷⡀⡼⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢿⣦⡟⠀⠀⠀⣸⣿⠁⠀⣾⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⢹⣷⣠⠟⠀⠀⠀⠀⢀⣿
⠀⢀⡟⠀⠀⠀⢸⣿⠛⢳⡄⠀⠀⠀⢹⣷⡇⠀⠀⠀⣸⣿⣻⠇⠀⠀⠀⣼⣿⠁⠀⠀⠀⣿⡏⠀⢠⡏⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠸⣿⠋⠀⠀⠀⠀⠀⢸⣿
⠀⢸⠇⠀⠀⠀⣿⡟⠀⢸⡇⠀⠀⠀⣼⣿⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⣰⣿⡟⠀⠀⠀⢸⣿⠃⠀⣸⠃⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⣿⡟
⠀⡿⠀⠀⠀⢰⣿⠇⣠⡟⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢛⡇⠀⠀⠀⢸⣿⠀⣠⠇⠀⠀⠀⣸⣿⡟⠀⠀⠀⢰⡇⠀⠀⠀⢠⡞⠀⠀⠀⢰⣿⠇
⢰⡇⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀⣾⣧⠀⠀⠀⠀⢿⡇⠈⣇⠀⠀⠀⠈⠛⠚⠁⠀⠀⠀⣰⣿⢿⡇⠀⠀⠀⣾⣧⠀⠀⣠⣿⠃⠀⠀⠀⣼⣿
⡼⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠋⡿⠀⠀⠀⢰⣿⠛⣆⠀⠀⠀⢘⣿⣾⣿⣿⣿⣿⣦⡀⠀⠀⢀⣠⣾⡿⠃⣾⠀⠀⠀⢰⣿⡟⠻⠿⠿⣿⠀⠀⠀⢠⣿⡇
⠻⢶⣶⣶⣶⣶⣶⣿⠿⠟⠛⠉⠀⠀⠳⣶⣶⣶⣿⠿⠀⠙⢶⣶⣶⣿⣿⡃⢴⠄⣿⣿⣿⣿⣶⣿⠿⠛⠉⠀⠀⠻⢶⣶⣶⣾⡿⠀⠀⠀⠀⠻⣶⣶⣶⠾⡿
⠀⠀⠀⣰⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠳⢦⡀⠀⠀⠀⠀⢀⡶⠓⢻⣿⣿⠃⣀⠘⠟⢹⣿⣿⣧⠴⠚⠛⠉⠉⠛⠛⠲⢦⣀⠀⠀⢀⣠⠶⠛⠛⠉⠉⠛⠓⠶⢤⡀
⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⢀⡾⠁⠀⠀⢿⣿⣄⣙⣃⣀⣙⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⢸⠃⠀⠀⠀⢠⣶⣶⣶⡄⠀⠀⠀⠀⣿⡇⠀⢀⡞⠁⠀⠀⠀⠀⠙⠿⣿⣿⡿⢿⠏⠀⠀⠀⠀⣴⣶⣦⣄⡀⣠⣾⡟⣹⠃⠀⠀⠀⢠⣴⣶⣦⣄⡀⣰⣿⠟
⠀⠀⣿⠀⠀⠀⠀⠘⠛⠷⠛⠁⠀⠀⢀⣼⡿⠁⢀⡞⠀⠀⠀⣰⠀⠀⠀⠀⣿⡇⠀⢸⠀⠀⠀⠀⠀⠈⠙⠲⢮⣝⡻⠋⠀⣿⠀⠀⠀⠀⠀⠉⠙⠲⢬⣝⠻⠋
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠁⢠⡟⠀⠀⠀⣰⣿⠀⠀⠀⠀⣿⣇⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⣼⠁⠀⠀⠀⣰⣶⣶⣶⡄⠀⠀⠀⠈⣿⣤⠟⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⢸⣿⠀⢠⣤⣙⠶⣤⣄⡀⠀⠀⠀⠀⠀⣿⡇⣠⣬⡛⠶⣤⣄⡀⠀⠀⠀⠀⠀⣿⡆
⢀⡏⠀⠀⠀⠀⠻⠿⠴⠞⠃⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⠋⠀⠉⠛⠛⠿⠟⠀⠀⠀⠀⢀⣿⡿⠁⠀⠉⠛⠻⠿⠛⠀⠀⠀⠀⢰⣿⠇
⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠏⠀⠀⠀⢀⣿⡿⠛⠿⡇⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠟
⢷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⠿⣯⣤⣤⣤⣤⣾⡟⠀⠀⠀⢧⣤⣤⣤⣤⣿⡟⠶⣦⣤⣄⣀⣀⣠⣤⣴⣿⠿⠋⠉⠻⢶⣤⣤⣀⣀⣀⣤⣤⣶⣿⠟⠋
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⢠⣾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⢀⣠⣾⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠟⠉⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⠰⢾⣿⠶
⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟

⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣶⣾⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⠿⣿⣿⣿⡿⠷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣠⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠴⢿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣧⡆⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⢀⣤⣴⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡦⡷⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⡷⠀⠀⠀⣿⡂
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡷⢶⣶⣶⣿⣿⣷⡶
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠛⠛⠿⣯⠀⡇⠀⠀⠀⣿⣿⣿⠿⠟⠛⠛⠿⣧⠀⡇⠀⠀⠀⣽⠋⠁
⠀⢠⣶⣿⣁⣀⣀⣿⣿⣿⣷⣾⣿⣶⣶⣿⣤⣷⣶⣶⣴⣿⣿⣿⣷⣾⣿⣶⣶⣷⣤⡷⠀⠀⢠⠿
⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⠿⠟⠛⠉⠈⠁⠉⠉⠛⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠺
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣴⢟⠝⠁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠈⠪⣻⣿⣿⣿⠿⠿⠿⠿⢇⡀⢸
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⠃⠀⠀⠀⠀⢀⣴⣿⣶⡆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣶⣶⣶⣾⣧⡼
⠀⣿⣿⢿⠛⠛⠛⠛⢻⣿⠃⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠰⣿⡉⠉⢹⡟⠉⠉⣿
⠠⣿⣿⣿⣷⣷⣿⣷⣾⡇⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠰⣿⡇⠀⢾⡷⠀⡰⡿⣆
⠀⠙⠿⣿⣿⣿⣿⡿⢻⣿⡄⠀⠀⠀⠀⠀⠘⠠⣟⣿⠠⠇⠀⠀⠀⠀⠀⢠⣿⡧⡀⣸⣧⠞⠁⠿⠈⠳
⠀⠀⠀⠀⠀⠈⠉⡄⠀⢻⣶⡀⠀⠀⠀⠀⠀⠐⠿⠿⠀⠀⠀⠀⠀⠀⢀⣷⡟⢈⣮⠛⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠻⣞⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⠟⣴⠟⢉⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⣴⣇⠀⠀⠀⠈⠻⣷⣢⠄⣀⠀⠀⠀⠀⢀⢠⣰⣽⠟⠁⠚⠋⠀⣰⣦⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠾⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢠⣤⠴⠞⣛⣉⡙⣦⡀
⠀⠀⠀⠀⠀⣾⡟⠛⠉⣉⣉⣻⣾⠹⡆
⠀⠀⠀⠀⢀⡟⠴⠂⠀⣀⣀⣈⣿⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠤⠤⠄⠀⠀⣀
⠀⠀⠀⠀⢸⡇⠐⠋⠡⣤⣀⡈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⠀⠠⣤⣤⣤⣤⡴⠞⠁
⠀⠀⠀⠀⢸⠁⠀⠀⠈⠙⣯⣴⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⢸⠀⣰⠀⠀⠀⣸⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠸⣇⠘⠓⢶⣚⣫⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⠞⣳⣒⡫⠍⠂
⠀⠀⠀⠀⠀⢻⡄⠀⠈⠙⠽⣄⠻⣄⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠖⠺⠿⢶⣤⣾⣤⣄
⠀⠀⠀⠀⠀⢸⡇⠘⣆⠀⠀⠘⢦⠙⣦⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣌⢳⡄⠙⢶⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠹⣆⠀⠀⠀⠀⠈⢷⣄⠀⣸⠏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢻⣄⠀⠻⣦⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⠻⣿⢠⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠳⢦⣈⠻⢶⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠘⣧⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢰⠀⢀⠈⢷⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣿⠰⣄⠈⣿⡷⣄⢀⣀⠀⠀⠀⠀⠸⣇⠹⡆⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠈⡇⣸⠀⠘
⠀⠀⠀⠀⠀⠀⠸⣇⠚⠀⣿⠈⠚⠛⠒⠂⠀⠀⠀⠀⣿⡿⡅⠦⣤⣤⣤⣴⠾⠋⢀⣴⡣⠀⠀⣧⡏
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠸⣦⡀⠀⠀⠀⠀⠤⠤⠞⠁⣧⠀⠀⠀⠀⠀⣀⢄⣀⢯⠏⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⡛⠛⠶⠶⠶⠖⠂⠀⠀⠏⢀⡆⠀⠀⠀⠈⠳⠥⠬⡇⠀⠀⣾⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠙⢦⡀⠀⠀⠀⠀⢠⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠃⠀⠈⠻⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣙⠓⠒⠒⠀⢀⣠⣤⣤⣤⣤⣤⣤⣶⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆

⣷⣷⣿⡟⠁⣠⡶⣿⣿⣿⣿⣮⣷⡍⠻⣿⣶⠶⣖⣻⣻⣛⣰⡆⠦⣬⢈⡛⢲⢤⡙⠑⠆
⣿⣿⠏⢀⠞⡙⠂⠘⢹⣿⣿⣿⣿⣿⣿⣮⣻⣿⠁⣇⠉⠈⠹⠙⢋⠗⡶⣍⡑⠦⠛
⣿⡟⠀⡞⠰⠀⠀⠖⢙⠟⠛⢯⡿⣿⣿⣿⣿⣿⠿⠛⠿⠛⠙⠟⡶⢦⣤⣀⠛⠓⠲⢄⠀⠀⠀⠀⠀⢀⣤
⢭⠇⠀⣧⠁⠀⢻⠎⠁⠀⠀⣾⡿⢿⣾⣿⢿⣿⣯⡙⠿⢦⡘⠷⣷⣿⣭⣇⠀⠀⠀⠀⢣⠀⢀⣠⢾⣿⣽
⣧⣾⡀⢲⡀⡐⠀⠀⢰⣿⡆⢀⣴⣾⣿⣕⢌⣿⠟⣮⡢⡈⠟⢶⣽⠿⣿⣿⣿⣤⠀⠀⢠⠐⢿⣿⣿⣿⣿
⣷⣿⣇⠀⠛⠀⣠⡤⡀⠉⣰⠟⣵⣯⣙⣿⢿⣟⠻⣿⣺⡯⡢⣈⠻⣷⣜⠿⣿⣿⣷⣤⠜⠃⣀⢿⣿⣿⣿
⣿⣿⣿⣷⠀⠀⠻⠷⠇⣼⡇⣽⣿⣿⣻⣼⡻⣿⣷⣝⣻⡮⡪⡻⣅⣍⠙⢳⣞⠻⣿⣿⡄⠀⠉⣈⣿⣿⣿
⣿⣿⣿⡇⣠⡖⢦⠀⣸⠿⠗⣿⡿⠛⠛⣿⡿⠿⢿⣟⣛⣿⣛⠊⠪⡳⠕⢌⠹⣷⣮⡉⠙⢄⠀⢀⣸⣿⣿
⣿⣿⣿⠀⠻⣿⠿⠃⣿⠃⠘⣿⣁⣴⣾⡟⢂⣴⡌⣿⠿⠿⢿⣯⣦⡁⠀⠈⠳⣌⠿⡿⠀⠀⠀⠀⢼⣿⣿
⠿⣿⣿⠀⠀⡠⢄⠀⢿⡀⠀⢻⣿⣿⣿⣷⣿⣿⣷⢸⠀⠀⢀⣿⣿⣼⡢⡙⣆⠈⠀⠀⠀⠀⠀⠀⡀⣿⣿
⣷⡿⢿⡄⠸⣷⡾⠂⠸⣧⠀⠈⣿⣿⣦⢿⣿⣿⣿⣤⣷⣤⣾⣿⣿⣿⣿⣮⡺⣷⠄⠀⠀⠀⠀⠀⠑⢎⡛
⡟⣷⣾⣇⠀⠀⣠⠤⠀⢻⣇⠊⠈⢿⣿⣷⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢮⠀⠀⠀⠀⠀⠀⣇⣀⠑
⣟⡿⣿⣿⡄⠐⣿⣷⣶⠀⠁⠀⢀⡀⠀⠙⠿⣿⣾⣿⣿⣿⣄⣀⣽⣿⣿⣷⣤⣼⡇⠀⠀⠀⠀⣨⡃⡝⢴
⣿⣿⣿⣿⣿⣄⠈⠉⠁⠀⢀⣾⣯⣀⣡⠀⠀⠀⢀⣩⡿⠿⢿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢀⡪⣻⣮⡓

⠀⠀⠀⢰⠛⠙⠒⢦⣀
⠀⠀⠀⠘⢦⡀⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠉⠳⣄⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠙⠦⣼⣭⣽⠦⠴⠶⠶⠶⠶⠒⠒⠒⠒⠚⢓⣶⠿⠶⠶⠤⢤⣤⣄⣀⣠⡒⢢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⢤⣀⣤⠴⠟⠓⢦⣄⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠉⣷⠀⠀⠀⠀⠀⠀⠈⢉⡽⣿⠓⠶⣤⣀⣤⠶⠚⠛⠉⠉⠙⣧
⠀⠀⠀⠀⢀⡼⣗⣋⠉⠀⠀⠀⠀⠀⣈⣙⣶⣄⡀⠈⠳⢶⡶⠶⠒⠒⠒⠒⠒⠒⠛⠛⠳⠶⠶⠶⠤⢤⣤⣄⣿⣤⠼⠗⠛⠉⠀⠀⠀⠀⢀⣀⣤⠾⠃
⠀⠀⢠⡾⠋⢠⡏⠈⣷⣤⠴⠖⠛⠉⠉⠁⠀⠀⠙⠳⢤⣀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠉⠁⠀⠀⣀⣀⣤⣤⣶⣶⠋⢹⠿⣦
⠀⢰⡏⠀⢀⣤⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠙⠲⣄⣀⣠⡤⠶⠚⠋⠉⢀⣀⣤⠤⠶⠒⠛⠉⠉⠀⠀⠀⠈⠙⠻⣏⡀⠈⣷
⢰⠏⠙⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠉⠓⠦⠼⠗⠚⠉⢉⣀⣤⣴⠶⢾⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⠉⣧
⢸⠀⠀⡟⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⢀⡤⠶⠚⠋⠛⢦⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⡇⠀⣽
⢸⠀⠀⡇⠀⠀⠉⠓⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠘⠧⣤⣠⡴⠟⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⣀⡟⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠋⠁⠀⠀⡇⠀⣿
⣸⡤⣤⣇⡀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣶⠛⢳⡤⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣛⣚⣭⡴⠒⣦⠶⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⢾
⢧⠀⠀⠈⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏⠁
⠘⣇⠀⠀⢸⠋⠳⠦⣤⣀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠙⡇⠀⠀⣸
⠀⠘⢧⣀⣾⡀⠀⠀⠀⠉⠙⠓⠶⣶⠛⠛⠺⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣤⢼⣀⣀⣠⣤⠴⠖⠛⠉⠁⠀⠀⠀⢰⣷⣀⡼⠃
⠀⠀⠘⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣼⠛⠛⠓⠒⠒⠶⠶⠦⠤⠤⠤⠄⠴⠶⠶⢺⡇⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣹
⠀⠀⠀⣿⠀⢿⠀⠀⠀⠀⠀⠀⠀⣸⢧⣀⡴⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⠀⢀⡾⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣿
⠀⠀⠀⣿⡄⢸⡆⠀⠀⠀⠀⠀⢰⡇⢠⡏⢷⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢈⡿⠛⣆⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⣿
⠀⠀⠀⡟⣇⠈⣧⠀⠀⠀⠀⢀⡿⠀⣾⠀⠸⡆⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡼⠁⠀⠘⣦⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣼⢻
⠀⠀⠀⡇⢻⠀⢻⠀⠀⠀⠀⣼⠃⣸⠃⠀⠀⢻⡀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣼⠃⠀⠀⠀⠘⢧⠈⢷⡀⠀⠀⠀⠀⠀⢠⡏⢀⡇⢸
⠀⠀⠀⡇⢸⡇⢸⡇⠀⠀⢰⡇⢠⡏⠀⠀⠀⠈⣧⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠇⠀⠀⠀⠀⠀⠈⢧⠀⢳⡀⠀⠀⠀⠀⣸⠁⢸⠃⢸
⠀⠀⠀⡇⠀⣧⠀⣷⠀⢀⡿⠀⣾⠀⠀⠀⠀⠀⠸⡄⠸⡆⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠳⡀⠀⠀⠀⡿⠀⡿⠀⢸
⠀⠀⠀⡇⠀⢹⡀⢹⡄⣼⠃⣸⠃⠀⠀⠀⠀⠀⠀⢳⠀⢹⡀⠀⠀⠀⠀⠀⢰⠏⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠱⡀⠀⢸⡇⢰⡇⠀⢸
⠀⠀⠀⡇⠀⠸⡇⠘⣷⠏⢠⡏⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⣧⠀⠀⠀⠀⢠⡟⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠹⡄⣼⠁⣸⠁⠀⢸
⠀⠀⠀⣇⠀⠀⣷⢀⡿⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⡆⠀⠀⢀⡞⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠹⣟⠀⡿⠀⠀⣼
⠀⠀⠀⡟⠳⣄⢸⣾⣇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢻⡀⠀⡼⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡽⢾⡃⣠⠞⢻
⠀⠀⠀⡇⠀⠈⢻⣅⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⣇⣸⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣼⠟⠁⠀⢸
⠀⠀⠀⢷⡀⠀⠀⠉⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣸⠃⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠈⠉⠓⠶⠦⣤⣄⣀⡀⠀⠀⠈⣷⠟⢦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠖⠊⠉⠀⠀⠀⠀⢀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠳⣤⠾⠷⠶⠶⠶⠶⠖⠒⠚⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠚⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣙⣛⣒⣒⣶⣶⣶⣤⣤⣤⣤⣤⣤⣴⣶⣶⣒⣒⣛⣋⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⠛⢛⠿⣿⣿⣖⣒⣲⣷⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⢶⣶⡶⠶⠶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⢶⡵⢯⣤⣦⣤⣤⣥⣭⣭⣭⣭⣭⣭⣍⣉⣉⣭⣭⣉⣉⣉⣹⣫⣞⣀⣠⣾⡉⠙⣧
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⣠⢋⡞⠁⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢸⢫⠏⠉⢹⡿⠃⢹⡀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⢀⡾⠁⢠⢃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡞⠀⠀⡏⠀⠀⠀⣧⠘⣿⠁
⠀⠀⠀⠀⠀⠀⣼⠃⢀⡏⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⠃⠀⣸⠃⠀⠀⠀⢹⠀⢹
⠀⠀⠀⠀⣴⣶⠇⠀⣸⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡞⠀⠀⣿⠀⠀⠀⠀⢸⡀⢸⡆
⠀⠀⠀⢰⣿⣿⠿⢿⠟⡶⠒⠲⢶⡶⠶⠶⠶⠶⠤⠤⠴⢶⣦⣤⣤⣤⣤⣦⣀⣀⣀⣸⣰⣅⠀⣰⣿⠀⠀⠀⠀⢸⡇⢸⣷⡄
⠀⠀⠀⠈⢹⡇⠀⢸⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⡏⣽⠉⠙⣿⣼⠀⠀⠀⠀⠈⡇⠘⣿⡇
⠀⠀⠀⠀⣼⠁⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡏⠀⠀⡏⠁⠀⠀⠀⠀⢀⡇⠀⡏
⠀⠀⠀⠀⡟⠀⠀⠇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡇⠀⢸⡇⠀⠀⠀⠀⠀⠸⡇⠀⡇
⠀⠀⠀⢰⡇⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⠁⠀⢸⠁⠀⠀⠀⠀⠀⢠⡇⠀⡇
⠀⠀⠀⢸⠁⠀⢸⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣾⠀⠀⠀⠀⠀⠀⢸⡇⢀⣧⡀
⠀⠀⣾⣿⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸⠀⠀⡿⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⡇
⠀⠀⣿⣿⠿⠛⠗⢲⠲⠶⠾⠿⠶⠶⢶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣀⣠⣤⡀⠀⠀⠃⣇⣀⣠⣿⡇⠀⠀⠀⠀⠀⢸⠁⢸⡿⠃
⠀⠀⠉⣿⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢹⡏⡟⠻⢿⣿⡇⠀⠀⠀⠀⠀⢸⠀⢸⠇
⠀⠀⠀⣿⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡇⠀⢸⡟⠁⠀⠀⠀⠀⠀⣾⠀⣼
⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⡟⠀⣿
⠀⠀⠀⢸⠀⠀⢁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡇⠀⢸⡇⠀⠀⠀⠀⠀⢠⡇⢀⣯⡀
⠀⠀⠀⣸⡇⠀⠘⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡇⠀⢸⡇⠀⠀⠀⠀⠀⢸⠁⢸⣿⡇
⠀⠀⢸⣿⣷⣤⣤⡄⡇⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡇⠀⢸⡇⠀⠀⠀⠀⠀⡟⠀⣾⠛⠁
⠀⠀⠀⠿⢿⡉⠉⡏⢩⠉⠉⠛⠛⠛⠛⠛⠛⠿⠷⠶⠶⠶⠶⢦⣤⣴⣿⣄⣀⣀⣇⣧⣀⣸⣿⡆⠀⠀⠀⢰⠃⢠⡏
⠀⠀⠀⠀⠘⣇⠀⢸⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⢻⠙⠛⣿⡷⠀⠀⠀⡞⠀⣸⠁
⠀⠀⠀⠀⠀⢹⡄⠀⠇⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠀⠀⣿⠁⠀⠀⣸⠁⢠⣯⡄
⠀⠀⠀⠀⠀⢠⣿⣦⣘⣆⢳⡀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡇⠀⢸⡄⠀⢠⠇⠀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⣿⣿⣶⣾⣿⣶⣶⣶⣤⣤⣤⣤⣄⣀⣀⣀⡀⢠⣶⠀⠀⢳⠹⠀⠈⣧⣀⡞⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠓⠶⠶⢾⣿⣿⣿⣿⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣯⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠛⠛⠉⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠛⢁⣀⡀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⡄⠀⠀⠈⠉⠉⠈⠉⠄⡰⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠈⢀⣷⡀⠀⠀⡀⣴⢶⣴⣿⣶⣄⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⢸⣿⡿⠂⣤⣄⢀⣼⣿⣿⣿⣿⣷⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⢈⡿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⣿⣿⣿⣿⣿⣯⠀⠈⠉⠛⠉⣿⣹⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⡼⣾⣿⣿⣏⣿⣿⣿⠟⠀⠀⠀⢠⣇⠘⠇⠑⠁⠂⠠
⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⣽⣿⢣⣾⣿⣿⣿⠏⠉⠁⠀⠀⠀⢀⠜⣿⣦⢀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠸⢃⣿⣿⣿⢹⡧⢀⣠⡤⣶⣶⡾⠃⠀⠈⠻⣿⡀⠀⠀⠘⢿⣇
⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⠠⠂⠀⠀⠈⢘⡟⣻⣿⡿⠟⠋⠀⠀⠀⡀⠀⠀⠀⠀⠈⠳⡀⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠙⠀⠀⠀⠀⠠⠞⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢦⢠⡖⠀⣀⣴⡟⢠⡾⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠐⠿⠛⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣾⣷⣶⣶⣴⣴⣶⣾⣷⣶⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣼⣿⣿⣛⣿⣿⣿⣿⣿⣋⣽⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢋⣙⠉⢿⠿⠹⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢏⣀⢾⣿⣧⣇⢰⣷⣿⣿⣿⣯⢿⡗⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣗⢿⣿⣿⣿⣿⣾⣿⣿⣿⡏⠛⠇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠛⢷⣝⣿⣿⣿⡿⠻⠿⠎⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣭⣭⡽⠟⠛⠉⠉⠁⠀⠀⠀⠈⠉⠉⠙⠛⠲⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⡖⠀⠀⠀⠀⠀⠀⠀⢠⡖⣶⡄⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡇⢠⠇⠀⠀⠀⠀⠰⣌⣳⠛⠁⠀⠀⣀⠤⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⣀⣴⣞⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣀⣠⣤⠴⠶⡒⠒⠒⠂⠹⣦⡈⢧⠀⣄⠀⠀⠀⠀⢀⡔⠋⣠⡶⠿⠛⠉⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⣿⣿⣞⣻⡭⣟⡨⣀⣤⠄⠙⢿⣦⣧⡈⠙⠲⠒⠀⠸⣧⡾⠟⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠻⢿⣿⣷⣿⣿⠟⠉⠀⠀⠀⠀⠈⢙⣛⣶⣤⣤⣤⣤⡶⠶⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠀⠀⠀⣠⣴⣾⣟⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢠⡶⢊⠄⠀⢠⣾⠟⢻⣶⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⢠⣏⠜⡱⡡⢰⡿⣧⡀⠠⡙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢻⣾⠞⠀⣿⠁⢻⢱⣰⡇⠀⠙⢿⣿⣿⡆⠀⠀⠀⠀⢀⡀⣠⣤⣴⣶⣾⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⢻⡄⠀⠙⠉⠀⠀⠀⠀⠈⠉⠑⠒⣒⡒⠻⣆⠩⠭⣷⣷⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠀⣿⢀⣘⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠤⠽⣿⣷⣦⣤⣀⣀⣀⣀⠀⠀⠀⢀⡟⠐⠒⢒⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⠻⢿⡯⠉⠉⠙⠛⠲⢿⣭⣙⣛⠶⠶⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃






⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡀
⠀⠀⠀⢤⣴⣧⠄⠀⡀⠀⠀⠀⠀⠀⢀⣠⡴⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣳⣾⡅
⠀⠀⠀⠘⠉⢃⣴⣿⣿⣿⣦⣤⡶⠞⠋⠁⠀⠀⢀⠀⠆⠀⠂⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⣔⣾⡯⢤⡿⡝⠛
⠀⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘⠄⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⣷⠿⣿⢾⡇⠙⠁⠀⢰
⠀⢿⣿⣿⣿⣿⡿⠛⠿⠿⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⣀⣀⠔⠈⠈⠐⡌⠧⠉⠁⠀⠀⠀⡠⠃
⠀⠀⠛⠿⠿⠋⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⣣⣤⡀⠸⠟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣰⠾⣶⡶⢶⠿⣶⢶⡶⠶⢾⡿⢼⡿⠛⢷⡄⠀⠀⣠⡎⠀⠀⠀⠀⠀⢈⠠⠠⠃
⠀⠀⠀⠀⠁⠀⠀⠀⡄⠀⠀⠀⠀⣿⢀⡈⡀⣸⢠⣧⠈⠱⣯⣼⡇⢸⢁⡿⠛⠃⠀⠛⠋⠀⢀⡀⠀⠀⠀⠠⠒⠒⢢
⠀⣀⣠⡄⠀⠀⡀⠀⠀⠀⠐⠂⠀⣿⢸⣿⡇⢹⠈⠋⢸⣷⣄⠙⡇⢸⡀⢿⢶⡄⠀⠀⠀⠀⠈⠡⠀⠘⠁⠠⠟⠒⢲
⠀⠘⠿⢁⡄⢦⠙⠀⠀⠀⠀⠀⠀⢿⡼⠛⠷⠾⢷⣴⠟⢷⣤⠾⢷⡾⠷⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡭⣅
⠀⢀⠔⢤⠙⠀⡀⠀⠀⠀⢰⡆⣾⠀⠀⢰⡆⣶⢠⣶⠀⠀⣶⠀⡷⠀⠀⣶⠀⣶⢰⡇⠀⠀⠀⠠⠀⠀⠀⠀⠔⠠⢬
⠀⠈⠙⠀⠀⠀⠀⡠⠀⠀⠸⠇⠻⠀⠀⠸⠇⠿⠘⠟⠀⠀⠻⠐⠇⠀⠀⠛⠀⠛⠘⠃⠀⠀⠀⠀⣠⣄⠀⠠⠖⠒⢦
⢰⠆⠀⠀⠐⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠠⠧⠤⠤
⢀⡚⠀⠖⠄⠀⡄⠀⠀⠀⢀⣠⣄⣠⣾⣶⠀⢠⠀⠀⢀⠀⠰⠶⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣄⣈⣤
⠀⠉⠉⠲⠒⡑⣉⠤⠖⠦⢺⣿⣿⣿⣟⡟⢀⣾⣿⡖⠈⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢡⣙⢻⢒⡀⠀⠀⠙⠿⣿⠏⠀⠀⠈⠹⠀⠀⠀⠀⠛⠀⡿⠀⠀⠀⢀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠒⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣒⠀⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡿⢟⢷⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⠳⠞⢿⡟⠫⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣷⣦⢺⣿⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣏⡡⠄⢺⣿⣿⣿⣿⣷⠹⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢠⡀⣀⡀⠀⢀⡾⠿⣿⣷⠀⡆
⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠈⠉⠐⢴⣦⣿⣿⣿⢟⣋⠑⠢⠒⠋⠉⢐⣢⣤⡤⠶⠒⠒⠶⣖⣉⡀⠀⠀⣤⣶⣾⣷⣿⠿⢶⣶⠮⣵⣿⣯⡼⠁
⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⢀⣠⠀⠀⠀⠀⠹⣿⢇⣼⣿⣶⡦⠀⢰⣶⣎⠉⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⢸⣿⡃⠀⠀⣠⣾⣧⡀⠀⠀⠀⣠⠟⡿⢿⣿⡿⣰⠓⣸⣿⣿⡷⠦⢴⣶⡿⠟⠋⠀⠉⠉⠁
⠀⠀⠀⠀⠈⣿⡇⠀⠰⠟⠀⠘⣿⣶⣄⣼⣵⣷⣿⡿⠿⢷⣡⣾⠟⠉
⠀⠀⠀⠀⢸⣿⢧⠀⠀⠀⠀⠀⣿⠿⠋⠀⣨⡝⠉⠀⠀⢠⣿⠏
⠀⠀⠀⠀⢸⣿⣷⣄⠀⠀⠰⠋⠀⠀⠀⣸⡿⢳⣶⣦⠴⠋⠁
⠀⠀⠀⠀⠀⢿⣿⣿⣷⡄⠀⡔⠀⠀⣼⡿⠁⠈⣿⠃⡜
⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣤⣤⣀⣴⠿⠚⠂⢀⣿⡜
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠋⢉⡴⠶⠒⠀⣾⠁
⠀⠀⠀⠀⠀⢈⣿⣿⣿⣯⠀⠀⡰⠶⠦⢤⣏⡟
⠀⠀⠀⠀⢀⣾⣭⣽⣛⣛⣿⠿⢗⠒⣒⣻⡋
⠀⠀⠀⠀⠋⠀⠀⠈⠈⠃⠛⠙⠛⠙⠙⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠠⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠛⠻⠛⠓⠚⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠊⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⣶⣾⣶⣶⣶⣶⣶⣦⣤⣤⣶⣶⣦⣤⣤⣴⣶⣶⣴⣶⣿⡷⠾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣷⣶⣿⣷⣶⣦⣿⣿⣤⣤⣤⣴⣿⡷⣤⣾⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⣰⣿⡏⠀⠻⣿⠏⣩⠝⠉⢹⣿⠉⠙⢻⣿⣙⣿⣿⣿⣿⣿⣬⡇⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠃⢹⣿⡇⠀⠘⣿⠇⠁⠀⠀⢸⣿⠀⠀⠽⢿⣩⡿⠟⢹⣿⣿⣯⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠸⣿⡇⠀⠈⣿⠀⠀⠀⠀⢸⣿⠀⠀⢼⣿⣤⠴⠚⢹⣿⣿⢋⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠄⠀⣿⡇⠀⠀⣿⠀⠀⠀⠀⢸⡿⠀⠀⣸⡟⠀⠶⡶⢼⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡤⠀⣿⡇⠀⠀⣿⠀⠀⠀⠀⢸⣇⠀⠀⢹⣿⠒⢶⡦⢸⣿⡿⣦⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣧⠀⣿⡀⠀⠀⠿⡇⠀⠀⠀⢹⡿⠀⠀⢸⣿⢰⠞⠀⣼⣿⡇⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢉⣿⠀⠀⢰⡇⠀⠀⠀⢸⡇⠀⠀⢸⡟⢀⣿⣴⣿⣿⣤⣮⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠸⣿⡄⠀⢸⣧⠀⠀⠀⣾⡏⠀⢀⣿⣿⣋⣿⣿⣿⣿⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢹⣷⠀⢹⣷⠀⠀⠀⣿⡇⣤⣸⣿⠏⣛⣩⣿⡟⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠸⣿⡄⢨⣿⡅⠀⠀⣿⣿⡂⣾⣿⣰⣿⣿⣿⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣹⣷⣤⣽⣧⣤⣤⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡟⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠻⢶⣿⡏⠹⢿⣿⣿⣿⣿⣏⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠤⠀⠉⡿⠟⢿⣿⣿⣟⡵⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣀⠀⠀⠀⠉⠀⣛⣛⣿⣿⣿⣿⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠳⠛⠶⠶⠶⠦⠾⣿⣿⣿⣿⣿⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢠⡤⠰⠿⣿⣿⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣇⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠞⣿⣿⣃⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⠟⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣿⡿⢂⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠺⣟⣿⣏⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠻⣶⣦⣤⣄⣀⣀⣀⣀⣠⣤⣧⣶⣿⣿⡿⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠙⠯⣹⣿⣿⣶⡁⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢲⣤⣿⣯⡄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠈⠋⠐⠲⠛⠋⠹⠟⣻⣧⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⠶⢦⣤⣬⡥⠾⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣴⣾⣿⣦⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠈⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⣠⠴⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠴⠛⠁⠀⡇⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣢⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡿⠻⠿⠿⣿⣿⠿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⠤⢤⣀⡀⢀⢔⣁⠀⠰⡄⠙⢦⣀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⡇⠀⢀⠄⠘⠓⠂⣀⣀⣀⡀⠒⠂⠀⢄⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠉⠳⣟⣡⡘⠢⠈⠂⣀⢹⢙⠂⢸⡇
⠀⠀⠀⠀⠀⡇⠀⠸⡗⠀⡆⢠⡌⢩⠉⣤⠀⡆⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⡅⠀⠀⠢⡨⢣⠊⠀⢸⡇
⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠁⠈⠁⠈⠀⠈⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢹⣄⡹⢊⡔⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡇⠀⠐⢇⢀⡇⢠⡄⢠⠀⣠⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣯⠔⢻⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⡇⠈⠁⢺⠃⠉⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡇⠀⢸⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣠⠾⡿⢦⡀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⢀⡞⣰⠃⠀⢸⠀⠀⠀⢀⣼⣷⡄
⠀⣠⠞⠁⠀⡏⠀⠙⣶⣿⡻⣄⠀⢸⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⠁⣠⠎⣰⠃⠀⣠⣿⣧⡀⣠⡟⢹⡏⠻⣦
⠀⠀⠀⠀⠀⠃⠀⠞⠁⢹⡇⠈⣷⢿⢷⡄⠀⠀⠀⠈⣳⣄⡀⠀⠀⠀⠀⣀⡠⠔⢊⣠⡞⠁⢀⡼⠋⢸⢈⣿⣏⠀⢸⡇⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠞⠁⢸⠀⠙⢦⠀⣠⡾⠛⠁⠉⠓⠲⠶⠤⠶⠖⠚⠉⠈⠻⣦⣘⠁⠀⠸⠈⠁⠙⠀⠸⡇⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⢀⣈⣦⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣦⣴⣾⠛⠓⠛⠉⠹⡍⠉⠉⠉⠉⠙⠛⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠈⠉⠓⠤⣀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣄⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠻⠶⣶⣤⣤⣤⣀⣀⡀⡠⣤⣤⣴⡶⣾⣿⠵⣋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⣯⠉⠓⠲⠤⢭⣭⣩⣭⣍⡩⠭⠵⠗⠛⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡟⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠁⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⡇⠀⢐⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣹⣤⣀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⣰⣠⠓⣞⡹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠪⠭⢿⣒⣶⣾⣹⡶⣖⣒⣚⡉⠥⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⢀⡀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢹⡧⡷⢿⢿⡇⠀⡇⣿⠄⠀⠀⠀⠐⠒⠒⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣷⡀⢰⡇⠀⢰⣴⢿⣧⢰⡶⣦⠀⢶⡆⣴⣶⡄⢠⡾⣷⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠛⢻⡿⠛⢿⡿⢸⡿⣿⡄⢹⡇⢸⣿⡏⢸⡇⣿⠃⢻⡆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠁⠀⢸⡇⠀⣸⡇⣼⠇⢹⡇⢸⡇⢸⣿⠁⢸⡇⣿⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢻⡆⠀⢸⡇⠀⣿⡿⠋⠀⢿⡿⣾⡇⢸⡟⠀⣾⡇⣿⡐⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⣾⡟⠀⠘⣧⡀⢹⡟⠲⠀⠘⢧⡿⠉⢸⡇⠀⠿⠇⠸⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⡏⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢧⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡎⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⡆⠀⠀⠀⠀⠀⣼⠁⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠉⢧⠀⠀⠀⠀⠀⡼⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠹⡀⠀⠀⠀⠀⣿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢸⠀⠀⠀⠀⢰⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳⠀⠀⠀⠀⢹⡀⠀⡀⠹⡄⠀⠀⣀⡀⠀⠀⠀⢀⡞⠀⠀⠀⠀⡼⠀⠀⠀⢠⠇⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⢧⠀⠀⠀⠀⢣⡀⠀⠀⣹⢒⠛⠅⠜⠒⢄⣠⠎⠀⠈⠀⢀⠞⠁⠀⠀⢀⡞⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⣶⡒⣄⠀⠀⢙⡦⠘⢧⣂⠴⠠⠀⠀⣨⡇⠀⠀⣀⡴⠋⠀⠀⢀⣀⡼⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣆⠸⡁⢘⣦⣀⡞⢠⡀⠀⠈⠉⠉⠉⠉⠁⠀⠀⣞⠁⠀⠀⠀⢠⠏⣠⣹⡞⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⠚⣡⠊⠀⡞⠀⠀⠁⢤⣤⠀⠀⠞⠉⠀⠀⠀⢸⡄⠀⣠⠞⠻⣄⣇⡸⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠁⣠⠞⡇⠀⠀⠀⡐⠐⠒⠀⠀⠀⠀⠀⠀⢀⣧⠾⡅⠀⠀⠈⠳⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡜⠁⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠱⡄⠀⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠉⠳⢤⣀⡀⠀⠀⠀⢀⣀⣤⠞⠀⠀⠀⠀⠘⢆⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⡶⠀⠉⢹⡛⠛⠉⠉⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⠤⠶⠶⠶⠿⠶⠤⠤⣤⣍⣐⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⣄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⡇
⡠⠤⣧⠙⠲⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠚⢡⡷⠤⡀⠀⠀⠀⢻
⢇⣠⠋⢳⡦⣀⣀⠈⠉⠉⠋⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⣠⢠⡴⠋⢣⣀⠏⠀⠀⠀⢸⡄
⢰⠟⠶⣆⢀⡎⠉⠉⡟⠓⡖⠶⢶⠖⠲⠶⠶⢶⠂⢲⠚⠋⠉⢹⡀⣸⠴⠚⢳⠿⡆⠂⠀⠸⡇
⢸⠀⠀⠀⠈⠉⠛⠛⠓⠰⠷⠦⠾⠤⠴⠤⠤⠼⠦⠾⠶⠒⠛⠉⠉⠀⠀⠀⢸⠀⠛⠲⡞⠛⠁
⣿⠀⢠⢂⣭⡐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣨⣅⢢⠀⢸⡆⠀⠀⣧
⢻⠀⡞⡼⠼⢯⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢊⠿⠼⠝⠇⢸⣁⣀⣀⢸
⢸⡄⠘⠓⠠⠐⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡗⠄⠔⠻⠘⣸⠁⠀⠉⠻⡄
⠈⣧⠡⡑⠤⠴⣣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡳⠤⠔⡡⢃⡏⠀⠀⠀⢠⡇
⠀⠸⡄⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⡼⠓⠒⠒⠒⠉
⠀⠀⡟⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⡇
⠀⠀⠳⣄⠈⠛⠒⠶⠤⣤⣤⣤⣀⣀⣀⣀⣀⣠⣤⣤⢤⠴⠖⠚⠉⢁⡴⠃
⠀⠀⠀⠈⠙⠲⠦⣤⣄⣀⣂⡀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⡤⠶⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⣄⣐⣲⣶⣶⣶⣶⣶⣶⣖⣂⣀⣤⣄⠀⣀⡀
⠀⠀⢀⠔⢀⠀⡔⠢⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⣢⣬⣷⣾⣿⠿⠿⠿⠛⠛⢛⣛⣛⣛⣛⡛⠛⠛⠻⠿⠿⢿⣿⣾⣯⣴⣢⢄⡀
⠀⠀⠈⡗⠜⠀⢻⠐⠀⠀⠀⠀⠀⡠⢒⣵⣾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⢸⡿⠿⢿⣿⠿⠿⣧⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣮⣕⢄
⠀⠀⠀⡇⠀⠀⣼⢀⠀⠀⠀⠀⡜⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠈⠙⠻⠿⠬⠿⠛⠋⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠉⠻⣧⢱
⠀⠀⠀⡇⠀⠀⣿⢸⠀⠀⠀⢠⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠲⠦⣤⣀⣤⡴⠶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢆
⠀⠀⠀⡇⠀⠀⣿⢸⠀⠀⠀⡇⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡶⠶⠛⠋⠉⠈⠉⠛⠳⠶⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣠⣦⢘
⠀⠀⠀⣇⠀⠀⣿⢸⠀⠀⠀⠸⡉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠋⢉⡏
⠀⠀⠀⣿⠀⠀⣿⢸⠀⠀⠀⢀⣿⣦⡀⠀⠀⠀⢰⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⡆⠀⠀⠀⢀⣴⣿⡄
⠀⠀⠀⣿⠀⠀⣿⢸⠀⠀⠀⢸⢸⣿⣿⣷⣦⣤⣀⡀⠉⢹⣯⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⢵⡏⠉⠀⣀⣠⣴⣾⣿⣿⡇⡇
⠀⠀⠀⣿⠀⠀⣿⢸⠀⠀⠀⠘⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣦⣤⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠃⡇
⠀⠀⠀⣿⢀⠀⣿⢸⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣟⣗⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣇⡇
⠀⠀⠀⣿⢸⠀⣿⢸⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿
⠀⠀⠀⣿⢸⠀⣿⢸⠀⠀⠀⠀⠱⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡜
⠀⠀⠀⣿⢸⠀⣿⢸⠀⠀⠀⠀⠀⠑⢄⡀⠙⠻⢿⣿⣿⣿⣿⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⡿⠟⠋⠁⡠⠊
⠀⠀⠀⣿⠸⠀⣿⢘⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠈⠉⠛⣻⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠛⠉⠁⣀⡠⠔⠋
⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢭⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡭⠖⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢠⣶⡀
⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⡷⠃⣿⣿⣿⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⢸⣼⡇⠀⠀⢰⣄
⣿⣿⣿⣿⣿⣦⣶⣶⣿⣿⠋⣀⣾⣿⣿⠟⢹⣿⣿⡟⢙⣿⡇⠀⠀⠀⠀⠀⠀⡟⠉⢹⡀⠀⣴⣿⡋⠀⠀⢠⣼⠈⠀⢰⣶
⣿⣿⣿⣿⠟⢻⣏⣁⣿⡇⢸⣥⣦⠘⣿⣷⣿⣿⣿⠗⣿⣿⡇⠀⠀⠀⠀⢀⣤⡇⠰⡿⠇⢸⣯⡞⡟⢻⡄⠈⠉⠀⠀⣾⡇
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡮⢿⣹⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢙⡦⢷⠞⠁⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣘⣹⣿⣿⠉⣹⣏⣀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠻⣿⡾⠀⠀⣾⡷⢰⠿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⠿⠟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣇⣀⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠳⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠆⠨⣠⡈⠧⠙⠆⠀⠀⠀⠂⢀⣀⣨⠀⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠴⡾⡛⢡⣾⠦⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠦⠁⠡⠐⡀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠀⠀⠀⢳⡀⣀⠘⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠂⠀⠀⠐⠀⠀⠀⠀⠻⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⣀⡀⠀⠀⠀⣤⠄⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠤
⠀⠀⠀⠀⠈⠐⠋⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⠙⠣⢶⠄⣌
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠇⢐⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠶⠴⡤⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠐⠂⠀⠀⠀⠀⠀⠀⠠⣀⠀⠉
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠃⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈
⠀⠀⠀⠀⠚⠀⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠈⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠀⠘⠛
⠀⠀⠀⠀⢀⣤⠀⠼⠂⠀⠀⠀⠀⣀⠀⢀⠀⡄⠀⠆⠈⡀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⡜⠀⠐⡀⠄⠣⠇⠃⠀⠀⠀⠒⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣦⠀⠀⠙⠂⠀⠀⠀⠐
⠀⠀⢀⣤⣦⣤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⡜⠃⠀⠀⣾⠁⠀⢀
⠀⠀⣾⣽⡉⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡨⠄⠀⠀⠀⠀⠀⢀⡘⡏⠰⢆⡀⠀⠀⠀⠑⠢⠀⠁⠀⠀⢀⡀⠇⡀
⠀⠀⠈⠻⠿⠷⠃⠀⠀⠀⠀⢀⡀⢀⠀⠀⠘⠉⠀⠀⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠣⠘⠂⠐⠁⠀⢀⣤⣤⣤⡀
⠀⠀⡀⢀⠀⠐⠀⠀⢤⢠⠴⠄⣤⡤⠀⠀⠐⠀⠀⠸⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⣻⣻
⠀⠀⠙⠹⠥⢶⠀⠀⢸⣩⡭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⠜⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠏
⠀⢀⠀⣀⠀⡀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀
⠀⠘⠚⠃⠙⠁⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠲⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠺⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣬⢿⣤⠤⠤⣤⠤⠤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣤⣖⡺⠭⠷⠶⠟⠉⠻⣏⠉⠉⠉⠉⠍⠛⢛⠚⠻⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠛⠿⢦⣄⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠈⠙⠲⢄⣀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠄⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⣦⣬⣑⠲⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⢀⣠⣴⣾⠟⣻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠻⢯⣾⠛⠿⢯⣿⣒⣲⠦⠤⠤⢤⣤⠤⠤⠤⠤⣖⣒⣾⡭⢷⡏⣿⡴⢛⣥⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢘⡏⠙⠳⠶⣤⣌⣉⣉⣉⠙⢻⢸⡛⠋⣉⣉⣉⣤⠧⠿⠛⢻⡃⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡇⠀⠀⠀⠀⠀⠀⠉⠩⠭⢹⢻⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢞⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠖⣦⠀⢐⢂⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠠⠄⢠⣽⣠⠴⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠶⣏⡛⠲⠦⣭⣔⣀⡀⠀⠀⣠⣄⠀⠀⠀⠀⣀⣐⣲⠭⠷⢿⣀⡷⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠥⣭⣩⣿⣿⣇⣸⢟⣛⣋⣉⣉⣤⠤⠴⠒⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠤⠤⠀⠀⠀⡀⠄⠀⠀⠀⠀⠄⢀⠀⠄⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠐⠂⠐⠒⠀⢀⠐⠀⠀⠈⠐⠠⡀⠀⢀⣀⣤⣤⠀⢈⠀⠀⠀⠐⠀⠀⠀⠀⠀⣠⠞⠂⠐⠠
⠀⠀⠀⠀⠀⠒⡄⠄⡰⡋⠄⠂⠀⠀⡀⠀⠀⢠⡾⣶⣄⡀⠀⠘⡈⠛⠻⣿⣿⣷⣶⡀⠀⠀⡀⠀⠀⠀⠀⢐⠁⠀⠈⠈⠀⠀⡀
⠀⠀⠠⠀⠀⡈⠀⠀⢁⠀⠄⠀⢡⠀⠡⠄⠠⣈⠀⠀⠀⡄⠀⢁⠑⠀⠀⠈⠉⠁⢻⣿⡀⠊⠀⠂⢀⠀⠀⡜⢂⠀⠀⢀⡂⠀⢄
⠀⠀⠀⠀⠈⠀⠀⠀⢰⠀⠀⠀⠀⠄⠀⠒⠀⢎⠙⣧⣀⠀⢀⠌⢣⠀⠀⠀⠀⢀⣸⣿⠇⠀⠀⠀⠂⠈⠞⠀⠄⠠⠀⠒⠉⠀⠄⠢
⠀⠀⠀⠀⠈⢃⠁⠀⠀⢡⠀⢠⠀⠐⠀⠈⡈⠀⢠⡈⠻⣿⠀⡀⢀⠋⠀⠡⡈⠛⠉⠉⠀⠈⠀⣘⣁⠜⢀⠀⠀⠀⡇⢄⠐⠀⡀
⠀⠀⠀⠀⠂⢈⢂⠱⣿⣿⣆⠀⠄⠀⠁⡀⠀⠠⠀⠕⣄⠙⡆⠁⡀⠇⢀⠀⠈⠀⠀⡠⠋⠙⣠⢠⡀⠀⠄⢀⠠⢀⣇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣠⠈⣷⡙⠿⠿⡦⠐⠀⠀⠀⠀⠀⢀⣼⠟⣠⣿⠂⠀⠀⡌⠐⠠⠀⢀⡂⠀⠀⢄⠶⢀⣀⡴⠁⠀⠀⠀⡀⠀⢀⠐⠰
⠀⠀⢀⠀⢀⠀⢤⡜⢹⣄⠲⣤⠠⣄⣀⣠⡥⠶⠟⣡⡔⠙⢿⣤⣤⡌⠀⠑⠠⠀⠐⡆⠀⠀⡘⠐⣼⠁⢺⡈⠀⠀⠴⠁
⠀⠀⠂⠀⣴⠰⣿⣇⠻⢿⣧⣘⢂⣿⣟⣿⠟⠒⠓⠈⡙⢢⡰⠟⢅⣠⢶⡷⢠⠀⣰⠁⢁⢀⠃⠼⠳⠞⠉⣿⡶⡃⠀⡀⢠⡠⠀⠀⡀
⠀⠀⠐⠀⠘⣧⡙⠿⣿⣿⠿⢫⡜⣿⠟⠁⠀⠀⠀⠀⠀⠂⠔⠁⣠⠁⡸⠃⡢⠔⠁⠀⠀⠒⠌⠀⠀⠀⣠⡿⠁⢊⠕⠄⠅⠀⠠⠁
⠀⡄⠀⠐⠄⠹⢿⣶⣶⡶⠾⢿⡷⠀⠀⠀⠀⠀⠠⠊⠄⠀⠀⠀⠌⠉⠀⠊⠐⠀⠀⢀⠀⠈⠀⠀⡠⣾⡟⠁⠀⠈⠐⢂⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⣴⡆⣧⡈⠃⠀⠀⠀⠀⠀⠀⠈⠁⢂⠀⠱⠀⠀⠂⠀⠀⢀⠁⠀⠰⢰⣷⡌⡄⠀⡔⡀⠞⠁⠀⠘⣷⡀⡀
⠀⠀⠀⠀⠀⠀⣿⡿⠓⠄⠙⠛⠋⣡⣄⠀⠀⠀⠀⠨⠀⠀⠀⠐⠀⣰⡀⠀⠀⢄⠀⠀⠁⠀⠀⠈⣭⡇⢸⡰⢧⣴⣉⢂⠀⣰⡿⠃⠁
⠀⠀⠀⠀⢀⠀⡛⠁⠀⠖⢢⢻⡿⠛⠋⠁⢄⠈⠂⢀⠒⠄⠀⠀⠦⠐⠈⢤⡀⠀⠀⠀⠀⠁⠀⣸⡿⢁⠇⠘⡦⡙⣇⣠⢸⠉
⠀⠀⠀⠀⠀⡐⢤⣴⡊⠀⢀⡌⠀⠀⢀⡀⠀⠐⢢⡤⠓⠀⠁⡅⡈⠉⠂⢔⠙⠒⠦⡄⠀⠦⢮⠩⠔⢍⠃⠠⣌⣷⢨⠄⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠸⢋⡵⠋⡰⠀⠀⠄⡛⠋⠀⠀⢁⠀⠁⠀⠀⠛⠀⠀⡷⠄⠰⡀⢀⡁⠀⠀⢀⢀⡀⠐⢄⡔⠛⢶⢸⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡴⠁⠆⠈⠣⣀⠀⠀⠀⢀⠁⣶⡞⠀⠀⡀⠀⠀⠀⠠⠄⠂⡱⠁⠀⣘⠼⠀⠙⣄⠔⠃⠂⠁⡜⡀⢀⠀⠂⡄
⠀⠀⠀⠆⠀⡉⢐⠂⡆⠀⠠⢁⣾⣿⣶⡾⣿⠸⣿⠁⠀⠀⠘⠿⢀⠀⠀⠀⢨⡀⠀⠠⢉⠇⠀⠙⠏⣤⣤⡤⢊⣼⠃⠀⠀⠀⠄
⠀⠀⠀⠀⠂⡑⠘⡃⡇⠀⢀⠸⢻⡿⠛⠛⣿⣆⢻⣷⠄⠀⠈⠠⠀⠀⣤⣄⠀⣼⣦⣄⠁⠀⠠⠒⠦⢩⣭⣶⡿⠁⠠⠁⠀⠀⠈
⠀⠀⠈⠈⠀⢀⠜⠡⠈⡀⠀⠂⠹⠵⠾⠃⣾⣿⣦⡀⠨⣁⣶⣶⣶⡿⠟⢁⣼⣿⣿⣿⣷⣦⡈⠀⠀⠊⠈⢉⠀⢠
⠀⠀⠈⠂⠠⠄⠀⠁⠀⠐⠦⣄⢀⠀⠀⠄⠙⠋⣹⣿⡶⠤⠍⠩⠄⠀⠀⠀⠈⡣⠊⠉⠻⢿⣿⣿⠇⠰
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠈⠀⠒⠀⠠⠀⠀⠀⠈⠀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠊⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠂⠉⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⢀⣤⣶⣿⣿⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣠⡎⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣶⣶⣶⣦⡀⠀⢀⣈⣩⣭⡣⠀⠀⠀⠀⢻⠏⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡫⠂⠀⠀⠀⢀⡼⠁⠀⠈⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠔⡵⠋⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣉⡛⠀⠀⠀⠀⠉⣷⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⡼⢣⠞⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠉⠁⠀⠀⠀⠀⠀⢋⡞⠻⣿⣿⣿⠁
⠀⠀⠀⠀⣠⡟⣰⠏⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣄⠀⠀⠀⠀⠀⠚⠋⠀⠀⠈⠉⠁
⠀⠀⠀⢠⠏⢠⠏⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠴⠆⠈⠀⠀⠀⠀⢀⣠
⠀⠀⢠⡟⠀⠈⠀⠀⠀⠀⠀⢀⣼⡇⣀⡴⠶⠒⠛⠒⢦⡀⣀⠤⠖⠒⠒⠒⠒⠒⠦⢄⡀⠐⣖⢀⣀⡤⠿⠛⠁
⠀⠀⣼⠀⠀⠀⢠⡄⠀⠀⠰⠿⠟⠚⠁⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠐⢶⠤⡽⠖⠋⠁
⠀⠀⣿⠀⠀⠀⢸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷
⠀⠀⢻⣄⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁
⠀⠀⠀⠙⠳⢶⣤⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠌⠳⢦⣄⣀⡀⠀⠀⢀⣠⣴⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣄⡀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠶⣶⣶⣶⡶⠶⠟⠛⢳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠐⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠃⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠘⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣽⣾⠟⠛⠛⠛⠛⠛⠾⣯⣉⣱⠶⠤⣄⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢛⣿⡿⠛⠉⠛⠿⣷⢦⣤⣤⣄⡀⢐⡀⠀⠉⠐⠂⢻⢾⡡⠿⣔⣲⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣠⣿⠋⠀⠀⠀⠀⠈⠁⠀⠈⠉⠛⠉⢛⣿⡶⣶⣶⣿⣿⣧⠴⠛⠉⠁⠈⠉⠻⢟⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠌⢀⣼⠟⠁⠀⣠⣶⣶⢤⣤⣀⣀⠀⠀⠀⠀⠀⢨⢾⠝⢣⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⣦⡀⠀⠀⠀⠀⠀⠀⠀⣽⠶⠆
⠀⠀⠀⠀⠀⠀⢠⡦⣠⣾⠏⠀⠀⠀⠙⠋⠛⠳⠧⢼⣽⣹⡷⠀⠀⣴⡟⠁⣠⠊⠀⠀⠀⣀⣀⣠⢰⣶⣸⠀⠀⠀⠙⣹⡧⠀⠀⠀⠀⠀⠀⠀⣭⠄⣠⠤
⠀⠀⠀⠀⠀⢠⠿⢟⣿⢯⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣾⠏⠀⡔⣡⡀⢤⣆⣇⣿⣩⣾⣾⠹⠛⠀⠀⠀⠀⢃⠙⡀⠀⠀⠀⠀⠀⠀⠻⠀⠟⢰
⠀⠀⠀⠀⠀⡘⢘⣿⡏⠀⠁⠈⠙⠛⠷⠶⢦⣤⣄⣀⠀⠀⢀⢾⣇⣀⠞⣼⢛⣷⢸⢼⠻⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠀⣤⠦⣴⠦
⠀⠀⠀⠀⢰⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠿⢶⣿⣿⣶⠏⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠀⠀⠀⠀⠀⠀⠻⠀⠛⢰
⠀⠀⠀⠀⡄⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠾⣍⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣞
⠀⠀⠀⠀⠀⢰⣻⠀⠀⠀⠀⠀⣾⡻⣷⡆⠀⠀⠀⠀⢰⠘⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡮⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠠⠦⣜⡏⠀⠀⠀⠀⠀⠈⠉⠛⠁⠀⠀⠀⠀⡃⠆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡅⠀⠀⠀⠀⠀⠀⣿⠀⠐⠂
⠀⠀⠀⢸⡷⢾⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢱⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣬⠶⠶⠶⠦
⠀⠀⠀⠈⠒⢚⢿⠙⠌⠹⠖⡤⠤⣀⠀⠀⠀⠀⠀⠸⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡞⠀⠀⠀⠀⠀⠀⠀⢿⠒⢂⠐
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠉⠈⠻⢕⣲⣶⣆⣀⠒⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣴⠁⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠶
⠀⠀⠀⠀⠀⠄⢂⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⢉⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠒⠒⠒
⠀⠀⠀⠀⠀⠈⣦⣮⣧⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠈⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠘⠳⢽⣷⣶⡖⠂⣄⣀⣀⠀⠀⠀⠀⡎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠻⢿⣦⣄⣀⢠⠤⠀⣰⣇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⣓⣲⣽⣻⣧⠼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢝⣿⣢⡀⠀⠀⠀⠀⢀⣀⠴⢊⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠾⢿⠿⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⠀⠿⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⡾⠁⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠹⡆⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡞⣠⡟⠀⠀⠀⠀⠀⢀⡴⢟⢡⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣴⠟⠀⠀⠀⠀⢀⡴⠋⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣱⠏⠀⠀⠀⣠⠾⣋⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡾⣵⠃⠀⠀⣠⢞⣱⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠖⠚⠛⣛⣋⣉⣉⣉⣉⣿⣽⣋⣙⣿⣿⡵⠿⢥⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢡⣤⡤⠶⠚⠛⠉⠉⠉⠉⠉⢹⡏⣸⢯⡟⢉⡿⠛⠓⠶⣤⣌⣙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠛⠶⢤⣤⣀⣀⣀⣀⡀⠈⠛⠋⠈⣙⣍⣰⣠⣦⣾⠷⠞⠉⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢰⣤⣄⣀⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⣀⡀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢶⡿⢞⣥⠟⣩⠟⣻⡷⢲⡶⢶⠀⢰⡶⢲⠞⢛⡿⠛⣹⠋⣹⠿⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⡴⢋⣵⠞⣡⠞⢁⡴⠋⢀⡾⠳⢞⡵⠋⣰⠟⢀⡼⢁⡼⠃⣰⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡴⢋⣠⠞⢁⡴⠋⢀⡴⠋⢀⣴⠋⢀⡾⠁⣠⠟⣠⠞⠁⣴⠃⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⣶⠛⣡⡴⠋⢀⡴⠋⢀⣴⠟⢁⡴⠋⢀⡼⢃⡴⠋⢀⡾⢁⣼⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠿⣾⣉⣠⡶⠋⢀⣴⠟⢁⣴⠿⣤⣰⠏⣠⠞⠁⣠⠟⢠⣞⡿⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⡉⠙⠛⠒⠿⠷⠴⢿⡿⠀⠸⠧⠾⠧⠶⠾⠟⠚⠛⠉⣁⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠶⠶⠦⢤⣤⣤⣤⣤⠤⠤⠶⠶⠶⠒⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢃⡴⠋⣠⡾⠃⣠⠞⢀⡾⠁⣠⠟⢀⡴⠃⣠⠟⠀⣰⠏⢀⡾⠃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠚⠋⠀⠞⠁⠰⠋⠀⠞⠁⠠⠟⠀⠚⠁⠀⠚⠁⠀⠋⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⣾⣤⣤⣄⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⡴⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⢳⣿⡤⣤⣭⣉⣉⣉⢹⡟⠛⠋⠉⠉⣉⣀⣽⣶⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠛⡇⣿⠋⠁⠉⠉⠙⣿⢹⡿⠛⠋⠉⢉⣭⣇⡿⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣷⢻⠀⠀⠀⠀⠀⣿⣾⠀⠀⠀⠀⠀⢸⠇⠇⠐⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣸⡄⠀⠀⠀⠀⢹⢻⠀⠀⠀⠀⠀⢸⢸⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⡏⡧⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⣸⠸⠀⢠⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢷⢣⡄⠀⠀⠀⢸⣸⠆⠀⠀⠀⠀⣿⡇⠀⣸⣿⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠸⣼⠀⠀⠀⠠⠸⣿⠀⠀⠀⠀⠀⣿⠃⠀⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡄⢷⡧⢀⠀⢀⠀⣿⠀⠀⠀⠀⠀⣿⡀⣠⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣧⡸⣿⠘⠐⠶⠀⣿⡁⠀⠀⠀⠀⡿⣠⣿⡿⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣿⣄⣀⣀⣀⣻⣇⣀⣀⣀⣸⣿⣿⠟⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣩⣉⣉⣉⣙⣛⣋⣋⣉⣩⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⣴⣿⠉⣈⣅⡉⢩⣿⡉⣿⣿⡀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣿⡀⢛⢋⣾⡷⠺⣿⡌⣯⣸⣿⣿⢷⡀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⢸⣇⠛⣸⣿⠀⡛⢸⣏⠁⣿⣿⣿⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠻⣿⠀⣿⣿⢸⣿⠸⢸⢀⣿⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣡⣘⠛⠀⡛⠋⢘⣋⣘⢛⣠⣟⣁⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠛⠻⠻⠿⠏⠿⠿⠿⠿⠻⠟⠛⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣶⣤⣠⢄⣄⣤⣴⣀⣠⣤⣤⣤⣤⡴⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢙⣋⣵⡿⣽⣿⣻⡯⣿⣽⣿⣿⠛⢿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣷⣻⣗⣿⣿⣿⣿⣿⣾⡿⣳⣿⣦⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣁⣉⣉⣉⣉⢉⣉⣉⣉⣉⣥⣥⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠛⠛⠛⠛⠛⠛⠓⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣬⣶⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⠷⠤⠀⠙⠓⠚⠉⠀⠀⠀⠀⠀⠈⡉⠛⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣧⣾⡋⠙⢿⡏⠁⠀⠀⡀⠘⠋⠁⠀⠀⣀⣤⣤⣶⣤⣀⠀⠀⣀⡀⡄⢀⡤⠀⠈⠁⠂⠤⣁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣿⣿⠿⣿⣷⣤⡉⠰⠛⠁⠀⠀⠀⠀⣴⣾⣿⢛⣿⣿⣿⣿⣿⣯⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⡌⠛⢿⠟⠀⠀⠀⠀⠀⠀⣾⠟⣿⣿⡿⠧⠀⢀⣿⣿⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠰⢶⣿⣿⣮⣿⣀⡐⣦⣀⣻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡛⠳⡄⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⠿⣿⣿⣿⣿⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠹⣆⠀⠂⠀⠺⢿⣿⣿⣿⣡⣾⣿⣿⣿⣿⣶⣬⣿⣿⣿⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢆⠀⠀⠀⣼⣿⣧⣄⡘⠖⠿⢟⡿⠿⠰⣃⣠⣼⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠁⠀⢀⣿⣿⣿⣿⣿⣶⡄⠄⠠⢤⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠲⣦⣿⣿⣿⣿⣿⡷⠿⠶⠶⠿⢿⣿⣿⣿⣿⣿⣥⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣀⡤⣤⣷⣄⠈⠻⣿⣿⣿⣿⡛⠋⠒⠂⠙⢛⣿⣿⣿⣿⣿⣿⢹⣷⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣦⡠⠸⠟⢻⣿⣷⣤⣤⣤⡤⠾⠛⢛⠉⣩⠀⣻⣿⣿⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠋⣙⣿⣿⣿⣿⣿⡇⢰⡆⢘⠋⣉⠀⡀⢸⡇⢸⠀⣿⠀⣿⠀⣿⣿⣿⣿⣿⣿⣝⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡽⣿⣿⣿⣿⣿⠇⢘⡃⢸⠀⢴⣿⡇⢸⡇⠸⠀⢻⡀⣹⣄⣼⣿⣿⡿⣿⠟⣿⣏⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⣼⣿⣉⣹⣿⡇⠘⠁⣸⠄⣸⣿⣧⣴⣶⣾⣿⣿⣿⡿⢿⣿⣿⣤⣽⣿⣶⡿⣿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣽⣿⣿⣿⣿⣿⣿⠟⠳⣶⡀⢡⡄⢹⡿⠛⠻⡿⢫⣀⣛⠁⣤⠶⣿⣿⣿⣿⠟⡟⠃⠀⠂⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠿⣿⣿⣿⣿⣿⢘⠋⣿⠂⠘⠀⢾⠿⣃⠀⣆⣈⡍⢹⡤⠶⠀⣹⣿⣿⣿⡂⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠾⠟⠀⠀⠀⣹⣿⣿⠘⣃⣿⠄⢸⡆⠀⠀⠿⠀⣏⠉⣡⣴⣦⣴⣾⣿⡟⠳⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣆⡈⠰⣿⣴⠾⠸⡟⠉⢿⠛⠛⠛⠛⠛⠛⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠈⠛⠉⢉⠀⠈⠛⠀⣴⡀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⡤⠤⣄⣀
⠀⠀⠀⠀⠓⠢⠤⣌⣉⠓⠲⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠦⠬⣉⣓⠲⠤⣀⡀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⠒⠛⠉⠑⠒⠮⢭⣛⡾⠛⢯⡉⠉⠉⠓⠒⠲⠤⢤⣀⠀⣀⣠⠤⠴⠒⠊⣱
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠁⠀⣀⣀⣠⠤⠤⠴⠖⠒⠒⠒⠛⠒⠚⠳⠦⠤⣤⣤⠤⠴⠒⣋⣉⡥⣤⠖⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⢰⡇⣠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢔⣒⣪⠭⠴⠒⠒⠉⠉⠓⠦⣄⢸⡆
⠀⠀⠀⠀⠀⠀⢠⡟⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢻⡇
⠀⠀⠀⠀⠀⠀⢨⡗⢄⡈⠙⢒⣦⠤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⣴⡒⠋⢁⡠⢺⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠑⢻⣬⢧⣀⣀⣀⠈⠉⠉⠉⡽⢯⠉⠉⠉⠁⢀⣀⣀⡼⣥⡟⠊⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⢸⠀⠀⠀⠈⠉⠉⠉⠉⣿⣿⠉⠉⠉⠉⠁⠀⠀⠀⡇⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⠧⡀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⢀⢼⡇
⠀⠀⠀⠀⠀⠀⠈⢧⡈⠓⠢⣼⢼⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡧⣧⠴⠚⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣽⣴⡋⠉⠉⠑⠒⠒⠒⠒⡟⢻⠒⠒⠒⠒⠚⠉⠉⢉⣦⡯⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠲⠶⠿⠿⠶⠖⠒⠒⠒⠋⠉⠉