Gardener Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡗⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⡀
⠀⢠⣄⠀⠀⠀⠀⣠⡴⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠦⢤⠠⣠
⠀⢰⣿⡇⠀⠀⢀⠉⠛⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢮⢵⣂⣹⠖⠳⠒⡀
⠀⢸⣿⡀⢀⣴⡿⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠉⠒⡒⢂⡐⣉⠤⠂
⠀⠀⠛⠷⠉⠉⠓⠀⠉⠈⠀⠀⠃⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠀⠑⠀⠄⢠⠖⠁⢀⣿⣷⣶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⢐⡠⢀⣐⠥⠠⣴⣿⣿⣿⡇⢀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⠂⠁⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⣛⣛⣛⠿⢶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣫⣾⣿⣿⣿⣿⣿⣷⣮⡻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⣶⣾⣿⣿⣷⣯⣽⣛⣻⠿⣿⣿⣿⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣿⣟⣵⣶⡍⠉⠛⠻⠿⣷⣾⣭⣝⡛⢃⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠻⠿⠃⠀⠀⠀⣼⣿⣶⣭⣝⡻⣿⣿⣯⡻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢀⣀⣀⣀⣠⣴⣿⣿⣿⣿⡿⣡⣿⣿⣭⣶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢟⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⣛⣵⣾⠿⠿⣿⣌⡻⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⣠⡾⣫⣾⣿⡏⣴⣿⣿⡜⣿⣿⢸⣯
⠀⠀⠀⢀⣼⢟⣼⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣸⣿
⠀⠀⢀⣾⢯⣾⣿⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿⠶⣶⣄
⠀⠀⣼⣏⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣷⣾⣾⣿⣷⢺⣿⣿⡆
⠀⢰⡿⣼⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⣿⡜⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣭⣭⣭⣿⣿⣷⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡆
⠀⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⣀⣿⡿⠃
⠀⠈⣿⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠀⠀⣀⡀
⠀⠀⠈⣿⣮⣙⠿⠿⣿⣿⣿⠿⠟⡋⢼⡟⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡶⠀⠀⢀⣈⠙⠻⣿⣶⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡇⠀⠀⠀⠘⣿⡄⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠈⢀⠀⠀⣿⣿⡻⣶⣿⣿⠿⠛⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠙⢿⣿⣿⣧⠀⠀⠀⠀⢰⡿⠀⠀⢿⣿⣿⣾⣿⠁⠀⣀⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠉⠹⡄⠀⠀⠀⣈⠀⠀⠀⠀⠙⠿⢿⣿⣶⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⢀⣿⣧⣤⣴⣶⣶⠀⠀⠀⣰⣧⣴⣾⣟⣛⡻⣶⣤⣤⣴⣦⣤⣿⣿⠿⠛⠁
⠀⠀⠀⣿⣿⡿⠿⠿⠻⣿⣿⠿⠟⠟⣸⡇⠀⠰⣾⣿⣛⣛⣭⣥⣴⢸⡿⠀⠀⣼⡟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣶⣶⣝⣿⣁
⠀⠀⠀⠈⣿⡟⠛⠛⠛⣿⡟⠛⠛⠛⢿⡇⠀⠀⠹⣿⣿⣿⣿⣿⣿⢸⣷⡶⢾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⣿⣿⣿⣟⡻⣷⡄
⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⢸⣷⣤⣄⠀⢻⣿⣿⣿⣿⣿⢟⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣶⣄⡀
⠀⠀⠀⠀⣿⣿⣦⡀⠀⠙⢿⣦⡀⠀⠀⠀⠈⠙⢷⡄⢿⣿⣿⡟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣹⣿⣿⣿⣿⣿⣿⣶⡝⣿
⣤⣴⣤⣶⣿⣿⣿⣿⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡙⠛⠛⠛⠛⠛⠛⠛⠛⠛⣉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢻⣿⣿⣿⣿⣧⠐⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣆⠙⢿⣿⣿⠟⠀⠉⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⡟⠀⢀⣤⣤⣤⣤⣤⣤⣬⣿⣿⣀⣀⣀⡀⢀⣴⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣷⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣾⣿⡿⠁
⠀⣠⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣏⣀⣀⣀⠛⢿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⣿⣿⣿⣿⣿⣷⣆⠙⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠹⠿⠿⠿⠿⢿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣶⣿⣿⣿⣯⡛⠛⠛⣠⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⣾⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠘⣿⣿⣿⣿⣿⡿⠋⣤⠘⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠈⠛⠛⠋⠉⠀⢸⣿⠄⠀⠙⠛⠛⠁⠘⠻⢿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⢠⣶⣿⣿⣿⣿⠶⠂⣹⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢉⣵⣾⣿⠟⣡⣴⣾⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣄⡚⠿⠟⠁⠀⢹⣿⣿⣿⣿⠏⠀⠘⣿⣿⣿⣿⣿⠁
⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣙⣿⣟⣉⣀⣀⣀⣈⣛⣻⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠋⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡇⠘⢩⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣄⡺⠀⠈⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠁⠀⠀⠑⠦⠴⠃⠀⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⣠⣾⡁⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠈⢧
⠀⠀⠀⠀⣼⠁⠀⠉⠳⣦⡴⣯⢹⡓⠀⠀⠀⠁⠀⠀⠴⣧⡠⠖⠒⠛⡄
⠀⠀⠀⠀⡇⠀⠀⠀⠙⢯⡀⢻⢸⡇⠀⠀⠀⠀⠀⠀⢀⡏⣳⠆⠀⠀⡇
⠀⠀⠀⠀⠳⢽⣲⣤⣀⠀⠙⢾⣄⣉⠀⠀⠀⠀⠀⠀⢸⣴⠃⢀⣠⣾⠗
⠀⠀⠀⠀⠀⠀⠈⠑⠻⢻⢂⠚⠀⢈⣿⣭⣽⣭⣭⢭⣭⠁⠀⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣠⣾⣿⣷⣶⣶⣶⡾⣿⡤⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⡅⢻⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡎⣿⣿⣿⠛⣿⣿⣿⣷⡈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⢻⣿⡟⠀⠸⣿⣿⣿⣆⢸⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡸⣿⠃⠀⠀⢻⣿⣿⣿⣤⡇⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡙⢀⣤⣤⣼⣿⣿⣿⣿⣷⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠻⠋⠉⠉⣿⣿⣿⣿⡿⠑⢬⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⢧⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠙⢿⣧⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠈⢧⡀⠀⣿⣿⣿⣿⡇⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⠛⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠘⢿⣴⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣯⣤⣤⡖⠚⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣀⣤⡼⢿⣿⣿⣿⣿⣼⣿⣿⢿⣷⣬⠿⣿⢿⣿⡿⠿⠿⠶⠶⠾⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣴⡿⠛⣷⣶⣿⣿⣿⣿⣿⣿⣷⠀⢸⣗⠀⣿⢼⣿⣿⡧⠄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⠀⡀⢸⣿⣿⣿⣟⣛⠉⣙⣿⣦⣼⣟⡀⣿⣼⣿⣿⣿⣿⣦⣴⣶⣶⣃⠀⠀⢀⣀⠀⡀
⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡗⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠄⠀⢈⣙⣿⣿⣿⣿⣦⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡄⠀⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⠛⠻⣦⣼⣿⣿⣿⣿⣿⣛⣛⠛⠋⠉⠉⠉⠀⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠶⠒⠀⠈⠻⠿⠿⠿⠃⠀⠉⠻⣿⣿⣿⡇⢠⡄⢹⣿⣿⣿⣿⣿⣿⣿⡭⠽⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣋⣁⣠⡤⠄⠀⠀⠀⠈⠙⢿⡇⠸⠃⣸⣿⣿⣿⣿⣿⣿⣟⣛⣫⣤⣤⣴⣶⣶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣿⣿⣿⣷⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣴⣦⣶⣶
⣿⣿⣏⣀⣁⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⠿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡿⠉⠀⠀⠀⠘⣿⣧⣴⣾⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠘⠛⠿⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⣿⣿⣷⡄
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⡀⠀⠀⣿⣿⣷
⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⣿⣿⠏
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⣿⣿⣷⣄
⠀⢀⣤⣶⣿⣿⣿⣿⣵⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⣿⣿⣿⣿⡇
⢠⣾⣿⣿⣿⣚⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣾⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠹⣿⣿⠁⠀⣸⣿⣿⣿⡿
⣾⣿⣿⣿⣟⣫⢟⣿⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⣡⣶⣾⣿⣿⣿⡿⠃
⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⡄
⢹⣿⣿⣿⣿⣿⣾⣿⢿⣿⣿⣿⢿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣷⣿⠿⣿⣿⣿⢯⣍⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣴⣿⣿⣿⣿⡿⣿⣾⣯⣿⣷⣿⣿⣿⢿⣯⣿⣿⡛⠀⡿⣿⣿⣿⠁⠀⣩⣾⠃⠀⠀⠀⢀⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡋
⢠⣿⣿⣿⣿⣻⣽⣿⡿⣿⣽⣾⣿⣿⡿⣿⣳⣿⣿⡈⢷⠻⠀⠾⠿⣫⣴⣾⣿⡟⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷
⢸⣿⣿⣯⣿⣿⣾⣿⣏⣽⣿⣻⡧⢿⣿⣿⣿⣿⡿⣷⣄⢠⢧⢀⣿⣿⡿⢀⢹⠃⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⠈⢿⣏⣽⢿⣿⣯⡻⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⣾⣿⣯⣿⣾⡟⠀⠀⠀⠀⣾⣿⣿⣧⠀⠀⠀⠀⢿⣿⣿⣿⡿⠋
⠀⢺⣿⣷⣳⣿⣿⣷⣿⣿⡷⣟⠿⢯⣙⢛⡹⠟⠋⠉⠉⢻⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⠆
⠀⠀⠛⡛⢟⣯⣿⣽⡼⣇⡇⠧⠭⠭⢭⠉⠀⠀⠀⠀⢀⡼⠉⡭⡄⠒⢶⣺⠁⠀⠀⠀⡼⠒⣔⡲⠛⠧⠀⠀⠀⠘⣊⡭⡋⣀⡀
⠀⠀⠀⢹⣿⢧⢾⣹⣳⢱⡇⣸⡟⢻⢥⣵⣤⣀⡠⢾⣟⡹⢟⣴⣷⣶⣏⡏⠀⠀⠀⠀⣟⣟⣴⣷⣧⣼⠀⠀⠀⠀⣷⠚⣇⡀
⠀⠀⠀⠘⠟⣿⣬⢿⣿⡌⡇⣼⢿⡳⣍⣿⣿⣷⣉⣼⡟⢣⣾⣡⣷⣿⣿⠁⠀⠀⠀⢸⣿⣌⣿⣧⡿⢻⠀⠀⠀⠀⣿⡿⣿⡇
⠀⠀⠀⠘⣷⣿⠹⣶⣿⣷⠁⣿⣦⣧⡟⣿⣧⣼⡿⣿⣿⢚⣿⣏⣼⣿⡇⠀⠀⠀⢀⣿⡇⢿⣹⢛⣿⣿⡆⠀⠀⠀⢻⣿⣿⠁
⠀⠀⠀⠀⢙⣿⣄⡇⣾⣿⠀⢻⣿⣿⢀⣿⣿⣿⣿⢿⣿⣀⡇⡿⠿⠋⠀⣀⠀⢀⣼⣿⣷⣼⣧⣾⣿⠟⢁⢀⣀⣀⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠚⡩⠉⢉⠡⡀⠈⠐⠨⡑⢄⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡠⠀⡜⠀⠀⠈⠄⠀⠄⠀⠀⠀⠰⣅⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⣀⠀⠀⠀⠀⠘⠀⠈⢆⠀⠑⡀⠘⣇⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣄⠊⢉⠁⠢⡄⠀⠀⠁⠀⡈⢦⠀⢜⠂⠐⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠠⠁⣠⠤⠖⠐⠶⠛⠀⠀⠀⠃⠈⠀⡃⢒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣦⠴⠶⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⣸⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⡰⠧⠤⣍⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⠀⠊⠀⠀⠀⡠⢘⠁⠀⠀⠀⠀⠉⠓⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠒⠀⠀⠀⢒⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢡⡀⠀⠀⡀⠀⠪⠅⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠐⡋⠤⠄⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢀⡤⢤⡀⠀⠸⠀⢀⡀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⢀⠋⠀⣂⡵⠒⠒⣖⠠⡌⠦⢄⢀⠀⠤⠠⠦⡜⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⣨⠂⠐⠚⠁⠀⠀⠀⠀⠀⠀⠈⡄⠒⠀⠀⢲⡢⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄⠀⠀⣀⠀⠀⠀⠑⠚⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢸⠑⠷⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢈⡠⠔⠂⠈⠀⠈⠀⠀⠢⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⠀⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⡠⠊⠁⡠⠄⠂⠀⠬⠠⠀⡀⠀⠀⠈⠐⠠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢐⠦⠊⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠥⣶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿
⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⡇⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⠀⠀⠒⠃⡉
⠀⠀⠀⠀⠀⠀⠀⠁⠈⢄⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠒⠀⠈⠉⠀⠜⠁⠀⢰⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠠⡤⢀⠀⠣⠀⠀⠦⠂⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⣀⡁⢣⣀⣀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⠀⠐⠇⠀⠀⠀⠐⠚⠓⠒⠒⠒⠚⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠠⡃
⠀⠀⠀⠀⠀⠠⠤⠂⠰⠄⠖⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠨⠤⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⠀⡄⢔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⢄⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠤⡱⠈⠃⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠂⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡠⠘⡀⠘⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡀⠀⠈⢀⢀⣤⠤⠚⠁⠒⢛⠆⠈⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠂⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠠⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄⡀
⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠘⣿⣧⡈⠃⣠⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⣈⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣀⡀⡀⠤⠀⢘⡦⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⠶⠞⠋⠀⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠚⡻⠻⠟⠁⠒⣒⠂⡼⠃
⠀⠀⠀⠀⠀⠀⢀⠤⠀⠒⠚⠹⢄⠀⠀⠀⠁⠄⢠
⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠢⠐⢄⠁⠁⠂⠎
⠀⠀⠀⡔⠁⠀⠁⠀⢀⠀⡀⢃⠀⣡⢀⠕⢰⠊⠑⡀
⠀⢀⠎⠀⠀⢀⠀⠀⠈⢠⠰⠈⠖⠹⠿⠷⠎⠀⡐⢰
⢀⠎⠀⢂⠁⢸⣇⠀⠀⠀⠀⠀⠇⠰⠀⠀⠀⢀⠀⠀⠡⡀
⠀⠀⠀⠐⢵⣤⣽⣦⡀⠐⠢⠀⡀⠀⠀⠀⢀⣦⡠⢀⡀⠱⡀
⠀⠀⠀⣀⠀⣨⣿⣿⡉⠀⢀⡄⡈⢆⠀⡤⠘⠻⣿⡲⠄⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦
⠀⠀⠉⠉⣿⣿⣿⣿⣿⡦⣀⠈⠡⢀⡹⢠⡀⠀⠘⣯⣲⢤⡀⠀⠐⠤⢄⠀⠀⠀⠀⢠⣿⣿⣿⣟⠆
⢸⣷⣦⣤⣭⣿⣿⣿⣿⣷⣬⠁⡀⠈⠀⠀⡈⠶⠄⠈⠻⣅⣠⠊⡀⠀⢘⡄⠀⠀⠀⢰⣾⣿⣿⣿⠟
⠀⠉⢻⣿⣿⣿⣿⠿⠟⠉⠘⢏⠀⠀⣠⠊⠀⠀⠀⠈⠀⢻⣿⣿⡧⠊⠁⠈⠐⢠⣤⣸⣿⣿⣿⡿⠋⣀⡀
⠀⠘⠋⢿⣿⣿⣿⡲⠀⡄⠀⡴⡉⠘⢉⠉⠐⠂⠠⣤⣾⡿⠟⠂⢍⠐⠢⠄⡀⣸⡿⢈⣿⣿⣿⡷⢊⣿⣿⣧
⢰⣶⣶⣆⢙⣿⣿⣷⡄⠙⢦⣬⣐⠭⠀⠀⠀⠀⣒⠈⠙⡄⠰⠁⠀⠑⣄⠀⢈⠛⠃⢄⠻⢯⡵⢼⣿⣿⣿⣿⠇
⢸⣿⣦⠄⠉⠀⢙⣿⣷⣄⠀⠹⣿⣿⣿⣟⣋⣡⣴⣎⣉⣯⣴⣲⣂⣄⠏⢨⣧⣤⣬⣁⠐⡂⡀⠄⠋⢹⡏⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡀⠀⢀⡠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⡿⢿⣿⣿⢄⣆⡄⠀⠀⠈⠢⣀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣿⣿⣿⠻⣿⣿⡩⠀⠀⠀⠀⠀⠀⢹⣿⣷⢹⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠽⠿⠉⠻⢷⡿⡏⠛⠓⠲⠀⠀⠀⠀⠘⣿⣿⣿⣿⠛⣳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠣⠑⠀⠀⠀⠀⠀⠀⠀⣨⣯⢴⡿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠁⠀⠀⢙⡿⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣤⣤⠄⣀⢴⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢘⠁⠀⠉

⠀⠃
⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⢀⡀⣠⡀⣤⡄⣤⡄
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⡇⣿⣇⣾⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠋⠋⠁⠋⠉⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣄⣤⢠⠆⣴⢦⢰⣴⢠⢶⡄⣤⡄⣤⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠸⡇⢹⡟⢸⣃⣿⢿⠀⣿⢸⣽⣧⣿⣷⡏⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⢀⡂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣆⣡⣖⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠤⣬⠶⠰⣍⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠞⡉⠫⣙⠌⢷⡁⢠⡤⠀⠀⣠⢆⡠⠤⠤⠄⢴⣁⠴⢢⠔⡱⠋⠈⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠐⡱⡱⣌⠳⢄⢙⣦⡤⠝⠓⡀⡭⢔⣒⡩⠉⠉⠉⡱⠀⣀⢰⢣⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡄⡄⠑⢹⡆⢓⠉⠉⠈⡉⠐⡃⢲⣠⠊⢔⡵⢊⠔⡟⣠⠏⡨⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⡟⢆⠫⡃⠔⠀⠛⡴⠌⡙⢳⣰⠀⣐⣫⠖⠁⢈⠀⠠⢞⣱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣄⡠⠑⠊⠑⠶⠶⠆⠀⠒⠂⠑⠈⠍⣰⡱⡼⠵⡦⡌⠍⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⢓⠋⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⣅⡃⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠃⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣝⢷⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢰⠃⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢈⠈⠀⡄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠈⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡆⠀⠇⠈⠲⠤⠤⠤⠀⠀⠀⠀⠀⠤⠤⠤⠒⠁⠀⢸⡇⢰⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡆⢀⠀⡌⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢡⢸⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡇⠸⡇⠁⡄⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⢇⣸⠘⡄⢻⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠇⡇⣧⠃⠑⢹⠋⣼⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠃⡄⢸⠹⠀⠇⠘⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⡟⡀⠇⠈⣠⠛⠀⢰⡄⠀⠀⠀⠀⠀⢀⡰⣀⡼⣰⣄⣼⣼⣀⢀⡀⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢡⢁⠀⣆⠻⢀⠈⢸⠰⠀⠀⠀⠀⠀⠘⡇⣇⢠⡌⢩⣀⣿⠏⠚⣇⣿⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠇⡇⡆⠙⣰⠀⠆⠀⠀⠀⠀⠀⠀⠐⢷⢰⠆⡞⡆⠶⢰⠒⢻⠟⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠸⢸⢠⡏⠃⡇⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⢹⢃⠄⣿⢀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⡆⠀⡌⠇⡆⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⡆⣼⢰⡏⡼⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⢠⡠⡇⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢸⡄⢸⠸⢁⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡇⠈⣦⢰⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢸⡇⠁⠀⡞⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⡇⠀⠁⠈⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣿⠁⡄⣀⣀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢸⠃⠸⢸⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⣧⡇⠇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠚⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡃
⠀⠀⠀⡀⠀⠀⢄⠈⠃⠀⠀⣾⣶⠄⠀⠀⣾⡁⠂⠀⠀⠐
⠀⠈⠀⠒⠈⠀⠀⢀⠀⠀⠀⠈⠉⠂⠀⢰⠟⠁⣀⣀⡈⠈
⠀⠀⠀⠀⠀⢀⣿⠆⠠⡄⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⠆
⠀⠀⠀⠀⠀⠀⠈⠀⠠⠇⠀⠀⣠⣷⡤⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠋⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠉⠀⠁⠀⣀⣤⠀⢠⣆⠀⠀⠀⠀⢐⣾⣷⡆⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠨⠀⠀⠀⠀⠈⠁⠁⠁
⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⢧⠀⠀⡈⠁⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠁⠀⠚⠁⠀⠀⠀⠀⠛

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⣀⣀⠐⠋⠉⠈⠀⠀⠈⠁⠲⣌⠢⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠙⠳⢆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢆⣤⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⢀⣁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠐⠉⠁⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠰⠏⠴⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠹⣠⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠠⣀⠀⠀⠉⠙⠻⠷⡄
⠀⠀⠀⠀⠀⠀⠸⣦⡡⠀⠟⠀⠀⠀⠀⠀⡄⠀⠙⠿⠿⣿⣿⣿⣓⠄⠀⠀⠀⠀⠀⠀⠚⠛⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠸⠻⣆⣧⠀⡠⠂⠀⠀⠀⠈⠰⢦⣄⣼⠋⠂⠀⢩⠖⠒⢄⠀⢀⣠⡤⢤⣄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢰⠃⡌⡔⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣸⣀⣈⡽⠛⠑⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡸⢵⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢀⡴⠁⠈⠹⡃⠀⠀⠈⠤⡃
⠀⠀⠀⠀⠀⠢⡐⠀⠀⠠⡀⠀⠱⠈⠀⠀⠈⠀⠀⠀⠀⠘⣆⣀⡤⠞⠋⠐⠄⠀⠰⠀⠀⠀⢀⠴⠃
⠀⠀⠀⠀⠀⠠⠙⠦⠦⢤⣸⡿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡤⠒⠃⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡸⠓⠄⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⣿⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⣀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡇⢠⣀⠴⠠⡀⠀⠀⠀⠀⠀⠀⠠⠀⣺⠠⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⣏⠀⠀⠀⡄⠀⠀⠀⠀⠀⢆⡀⠙⢦⠊⠀⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢠⠀⠀⠀⠀⠀⡎⠉⢓⡾⠇⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⢿⡄⠀⣾⠀⠀⠀⠀⠀⢸⣶⡟⢀⣤⡮⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣂⢿⣇⢠⣧⠀⠀⠀⠀⠀⠀⡉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⠋⠘⠀⠀⠀⠀⢀⠈⠀⠇⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠹⠀⠀⢢⡀⠀⣦⡔⣠⠂⢸⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢷⠀⡟⢠⠏⠀⠆⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢀⡄⠀⢀⠀⠰⢻⠀⡜⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⣌⢷⠀⢸⠀⠀⢻⡈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⡅⠀⠉⠉⠉⠉⠉⠛⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠁⠀⢀⣤⣿⣷⡄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣠⠶⠟⠛⠉⠉⠀⠀⠀⠀⠚⢿⠋⠁⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠞⠁⠀⠀⢀⣀⣤⣤⠤⠀⠠⠋⠙⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠙⢿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠡⠀⠀⢸⣷⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢸⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⣎⢻⣿⣿⣿⣿⣿⣿⡟⠲⠤⢧⠀⠀⠀⠀⠀⢀⠎⠀⠀⣀⣤⣶⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢷⡹⣆⠻⣿⣟⠻⣿⣿⣿⡄⠀⠈⠳⣀⡀⡀⠔⠃⠀⠴⢿⡛⠥⠂⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⢻⣝⢧⢹⡘⣧⠻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣝⢮⣳⡕⡌⢣⡑⢿⣎⠻⣷⡒⠤⢀⣀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⢿⣷⣍⡿⣮⡀⠹⣆⠈⠳⠈⠳⢄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠛⢻⡃⡇⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢣⣟⠻⠛⣮⣹⠦⡀⠁⢄⠀⠀⠢⢑⠄⠀⠀⠀⠀⢸⣿⣿⠹⠀⠸⣇⢻⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠏⣠⡴⠞⠋⠉⠙⢿⣄⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠻⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⠟⠁⠀⠀⠀⠀⠀⢈⣿⡄⠀⡀⠀⠀⠀⠀⠀⠊⠑⡄⠀⠸⣿⣷⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠤⠆⠠⠄⠒⣰⢾⣿⣷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠹⣿⡆⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⣀⣠⣤⡴⢶⣫⣵⠿⠋⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠹⣿⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⣋⣩⠤⠶⠚⠛⠉⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⡤⠋⠁⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⢀⡀⠙⣆
⠀⠀⠀⠀⠀⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣜⡆

⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠸⠀⢠⠄
⠀⠀⠀⠀⠀⠐⢄⠀⠀⠄⠀⢠⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠀⠀⠀⣸
⠀⠀⠀⠀⢀⡀⠀⢠⠁⠀⠀⠀⢉⡀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡴⠑⠂⠁⠀⣀⠐⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⢀⠐⠀⢄⠀⠀⠀⠀⠈⡀⠀⢠⠀⠀⠀⡀⠘⡃⠀⠀⠀⠰⠄⠄⢀⡤⠪⠁
⠀⠀⠀⠀⠀⠈⠀⠀⡈⠁⠉⠀⢠⡀⠈⠁⠀⠀⠀⠀⠁⠀⠈⢷⢄⠀⠈⠀⡀⠀⠀⠀⠀⠅⡠⢊⠂⠀⠀⠸⠀⠀⠈
⠀⠀⠀⠀⠀⡀⠀⠘⠁⠀⠸⠀⠀⠁⠀⠀⠀⠐⡂⢄⠀⠀⠀⠈⠳⢐⠄⠀⠇⠀⠀⠀⠀⢸⢀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠌⠖⠀⠐⠄⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠡⠄⠓⠢⡖⢄⠀⠀⠀⡀⠈⠁
⠀⠀⠀⠈⠙⠲⠄⡄⠀⠁⠀⠀⠀⡐⠁⠀⠀⠀⠀⠄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⢅⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠂⠂⠀⠈⠈⠀⠀⠀⠀⠈⠀⣀⠤⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠢⠈⠸⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠂⠄
⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠘⠐⠙⠀⠀⢲⢊⣀⠀⠀⠀⠀⠀⠐⠄⠀⠈⠀⠀⠀⠀⠇⡆⠀⠀⠀⠀⠠⡀⠀⡀⠙⢆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡌⡌⠀⠀⠉⠙⠁⠈⠀⡀⠀⠀⠠⠂⠒⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠣⠄⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠒⠀⠠⢄⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠠⠀⠰⠀⠠
⠀⠀⠀⠀⠀⢀⠊⠀⢀⠄⠀⠠⡀⠀⠄⠀⠂⠀⠊⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡀
⠀⠀⠀⠀⢀⡀⡠⠢⠈⠢⠀⠀⠀⡁⠀⠀⠄⠠⠀⠂⢁⠀⡀⠀⠉⠀⠀⠀⠀⠠⡀⠀⢃⠀⠀⠀⡄⠂⠀⠀⠀⠁⠐⢀
⠀⠀⠀⠀⢰⠀⠃⠀⠋⢀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⡁⠀⠈⠀⠀⠰⠀⠀⠀⠀⠐⡀⠀⠁⠀⠀⠀⢀⠀⠀⠉⠐⠀⠔
⠀⠀⢀⠀⠀⢧⡀⠀⣠⣂⡀⠃⠀⠀⠖⠈⠀⠀⠀⠀⠁⠀⠀⢀⠤⠂⠠⠂⠀⠀⠀⠐⠄⠀⠀⠀⠀⠂⠀⠀⠒⠐⠀⢄
⠀⠀⠀⠠⠀⠐⠬⢉⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⡆⠠⡀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠈⠄⢀⠀⠀⢂⠀⠈⠀⠂
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢄⠀⠈⠂⠀⠀⡠⠔⠒⠒⠒⢄⠂⠀⠀⠁⠀⠀⠁⠀⠘⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠀⠀⠂⠀⠀⣀⣈⠀⢀⣀⡀⠀⠀⠁⠀⢡⠔⠒⠀⠤⠤⠤⠄⠀⣑⣌⠂⠠⠀⠀⠀⠊⡀
⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠂⠐⡁⢄⠨⠁⠩⠀⠈⢙⠀⢣⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠠⡀⢱⠘⢀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠀⡐⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠡⣀⣆⡂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⠀⠤⠔⠀⠀⡠⡀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠤⢀⣒⣀⣀⠖
⠀⠀⠀⠀⡰⠊⠄⡁⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠊⠀⠀⢀⠘⠂⠀⠁⠀⠀⠈⠊⢔⡤⠠⡀⠀⠀⠀⠈⠒⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠶⠶⠶⠶⠤⢤⣤⡤⠶⠒⠊⠉⠉⠉⠉⠙⠓⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⢠⠇⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⢸⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢻
⠀⠀⠀⠀⡏⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⡇⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⣠⣤⡤⠀⠀⣀⣀⣀⣀⣀⣈⣀⠀⠀⠀⠐⠶⢶⣤⠀⠀⢀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠣⣄⠤⠶⠛⠛⢋⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣛⣓⠒⠶⢬⣅⣀⠻⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⠙⠛⢦⡀⠀⠀⠀⢀⡴⠞⠉⠉⠉⠉⠙⠲⣄⠁⠘⠒⠀⠐⠊⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣤⠦⢤⡀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢠⡟⠀⠀⠀⠀⣀⣤⣤⣀⠘⣇⠀⠀⠀⠀⢠⡗⠘⢷⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢧⡀⠈⢡⠀⠀⠀⣿⠀⠀⠀⣴⣾⣿⡿⠷⣄⣷⠀⣾⠀⠀⠀⣠⣿⣿⣿⡟⠛⢷⣿⠀⠀⠀⠀⣾⢀⣠⠟⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠛⣦⠴⣆⠀⠀⢻⡄⠀⠀⣿⣿⣯⣥⣴⣿⠇⠀⢻⡄⠀⠀⣿⣿⣿⣯⣷⣤⣾⡿⠀⠀⠀⣼⠋⠉⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠹⣆⠀⠀⠻⢦⣀⡙⣿⣿⣿⡿⠋⠀⠀⠈⢳⣄⠀⠘⢿⣿⣿⣿⣿⡿⠁⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠙⣦⠀⠀⠀⠉⠉⠉⠉⠁⣴⠒⠂⠀⠀⠀⠙⠛⠶⠶⠿⠿⠛⠉⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠳⣤⢠⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⢦⣄⣤⠆⠀⠀⠀⠀⢀⣠⣤⠞⠛⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡶⠶⠦⢤⣤⣤⠶⠶⠖⠛⠉⠁⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩
⠀⠀⠀⠈⠙⠳⢦⣄⣀⣀⠀⠀⠀⢀⣀⣠⣤⠖⠋⠀⠀⠀⢸⠆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣤⣀⣀⣀⣀⣤⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⡀⠎⠀⠀⡸⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺⠁⠀⠁⠉⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣴⠃⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⢂⠔⠋⠘⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠉⠒⢠⠀⠀⠀⡤⠴
⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣀⠀⠀⠀⠴⠈⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢁⠀⠀⠀⢀⡤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⡠⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣀⣰⡅⠀⠀⠀⠀⠀⠀⠑⠀⠄⠉⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢄⣠⠀⡄⠠⠊⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠂⠙⡉⠍⠉⢉⠋⠟⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠘⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢰⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠘⡇⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠁⠁⠀⠀⢀⣧⡀⠀⠀⢀⠝⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⣉⣁⠢⠜⠋⠁⠙⠶⣆⠁⠀⠀⣀⠼⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢀⣀⣀⣀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿
⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣄⣀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡻⠿⣿⣿
⣿⣯⣭⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⡿⡹⣿
⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠑⠹
⣷⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣟⢿⣿⣿⣷⣿⣿⣿⣿⣿⠟
⣿⠀⠀⠈⠻⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢘⣿⣿⣖⡙⢿⣷⣽⣿⣿⣿⡏
⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣏⠈⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢸⣿⡿⢹⣿⣿⡧⠀⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣧⣬⡿⣚⣁⣠⣿⣿⣿⣇
⠀⠀⠀⠀⠀⢸⣿⣷⣀⣙⣭⣷⣿⠿⠋⠉⠁⣀⣀⣀⣠⣤⣤⣤⣄⣀⠉⠛⠳⢮⣟⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣠⣍⢿⣽⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢸⣿⣻⡿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠉⠿⣿⢿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠤⠀⠀⠀⠀⠀⠐⠚⠷⠶⠛⢿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠐⠲⠖⠂⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠃
⠇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣴⡷⠾⢶⠄⠀⢀⣴⣿⣿⣿⣿⣿⡿⠃
⡄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⠓⠒⠁⣠⣶⣿⣿⣿⣿⣿⣿⣿⠁
⣧⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠿⠿⣿⣿⣿⣿⣿⠋⡇
⣿⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡿⠋⠀⠀⠀⠙⠿⢿⣿⣿⣸
⣿⣷⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠶⠶⢤⡀⠀⠀⠀⣾
⣿⣿⣧⣀⠀⣠⠤⠤⠤⠼⠟⠙⢿⣿⡿⢿⣮⣻⡗⠀⠀⠀⠀⠀⠀⠀⣠⠴⠀⠀⠀⠀⠀⠀⠈⠀⠀⣷⣿
⣿⣿⣿⣿⣪⠁⣠⠞⠁⠀⠀⠀⠀⠙⢷⡀⠈⠉⠻⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣯⣼⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠠⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠃⣿⢀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⣄⡔⠀⠀⣠⠶⠿⠿⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡄⠀⠀⣿⢸⢿⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃⠀⠐⠁⠀⠀⠀⠀⠈⠙⠻⢷⠄⠀⠀⠀⢀⣴⡾⠿⢃⡇⠀⢸⣿⠸⢸⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣴⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠁⠀⢸⣿⣄⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⠀⠀⠰⠶⠟⠉⠁⢀⡺⠹⠆⠀⠀⠀⠀⠀⠀⠀⡴⠛⡄⠀⠀⢸⣿⡇⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⡌⣿⡇⡆⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡏⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⠁⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⡇⣧⡀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⣿⠀⡇⢹⣿
⠀⠀⠀⠀⠀⠀⢰⢹⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠄⠀⠀⠀⡀⠀⠀⢸⣿⠀⠃⢸⣿
⠀⠀⠀⠀⠀⠀⢀⠛⠀⡖⡏⢳⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠇⠀⠀⡾⡟⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡇⢸⣿⣧⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⠀⠠⡀⠀⠀⠀⡧⡏⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⢸⢹⣿⣦⠀⠁⠀⠀⠀⠀⠀⠀⠂⠄⠉⠁⠠⠀⠂⠀⠀⠀⡀⠀⢣⠃⡇⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⢼⢸⣿⣿⣷⡆⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄⠁⠀⡮⠀⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⡇⡇⠀⡄⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⢸⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡇⠀⡇⣾⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠸⠃⢀⡇⣿⢠
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⡄⠀⡀⠀⠀⡇⢸⡈
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣇⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⡇⠀⡀⡇⢻⠃⡄
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣧⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢸⠁⠀⢻⢇⡶⣄⢳⣤⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⣸⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠻⡇⠀⠀⡌⢀⠀⢸⣶⣤⡹⠳⠿⢾⣿⣿⣿⣶⣤⣀
⣶⣾⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢰⠇⠀⢀⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⠀⠠⢸⠇⠀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⢾⣶⣤⡀⠀⠀⣀⣀⣀⣀⣠⢨⠀⠀⠘⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⠿⠿⠿⣿⣿⣿⠿⠿⠟⣿⠸⠀⠀⠀⠀⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣾⣿⠀⡀⠀⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⡇⠀⠇⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣴⣾⣿⣿⣿⣿⣷⣤⡀⠀⣀⣀⣀⣀⣀⣤⣿⣿⣿⣿⢠⠇⠀⢀⡇⠀⢸⣿⣿⣿⣿⣿⡿⣿⡟⣿⣿⢻⣷⣿⣿⡟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⢿⣿⡿⠛⠛⠛⢻⣿⣿⣿⣿⣿⢸⠀⠀⢸⠁⠀⠈⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠐⠐⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠀⠀⠒⢀⠀⠀⠒⠂⠀⠠
⠀⠀⠀⠀⠁⠀⠈⠀⢀⡀⠐⠀⡀⠀⣀⠀⠀⠈⠉⡀
⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠠⠀⠁⡀⠉⡄⠀⠀⠀⢅⠀⠁⠀⠄⠀⠀⠠⠊⢀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠠⠄⣀⣁⡀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⠘⢀⡀⠀⢀⠀⢀⠀⠙⠉⠁⠀⠠⠛⠀⠀⠀⠀⠘⠣⠄⠀⠀⠄⠀⠄⠀⡀
⠀⠀⠈⠀⠁⠀⠀⠁⠁⠤⠤⠐⡀⠡⡔⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠁⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠠⠌⠀⠒⠀⠀⡀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠠⢆⠀⡀⠐⠀⠠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⢠⠎⠀⠁⢈⠒⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠄⠄⢗⡌⠀⠐⠀⠰⠂⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣡⠀⠊⠀⢉⡄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢃⠈⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠘⡀⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⠐⡀⠤⢀⠀⠴⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⡀⠀⠀⠀⠀⠀⠀⢠⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡀⣀⠔⠓⠀⠐⠁
⣶⣶⣶⣶⠶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⣶⣶⠶⢶⡶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⡤⠤⣄⠀⣟⣳⣦⠶⣦⢤⡀⣠⠔⢲⡤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣴⣡⣻⡯⢽⢷⡷⠾⣟⣿⢵⣏⣹⡭⠷⠛⣧⣒⣤⣄⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣉⣯⣶⣉⣏⣽⣿⣻⣷⣦⡿⣯⣙⣿⡯⢿⣶⡟⣹⢻⣭⣿⣓⣿⣿⣿⣟⠉⣿⣦⡀
⠀⠀⠀⠀⣴⠋⢲⠶⣼⠉⡿⢿⣾⣸⠤⣿⣶⡟⣿⡄⢘⣧⣤⢽⡟⣶⠿⠟⠻⣿⣅⡜⠻⣭⣿⣽⣟⣡⣧⡈⠁
⠀⠀⠀⠐⠷⠀⢛⠤⣬⣴⢿⢿⡷⣾⡖⠙⢏⣻⡗⣽⣿⠬⣿⣶⣏⣹⣷⣶⣾⣽⣅⣹⣄⣿⡿⣿⣋⣿⣤⢿⣶⡀
⠀⠀⠀⠀⢀⢴⣿⣦⢹⣚⡾⢿⣽⡟⠫⣳⣎⠉⣹⣿⣤⣿⣾⣯⣾⣿⣿⠿⣶⣹⣿⣿⡉⢢⢹⣯⡥⣾⣿⣾⣿⠿⣾⡋⢳
⠀⠀⠀⢀⡷⠄⢱⢋⡿⣿⣷⣶⣮⣷⣦⣸⠍⣹⠝⢿⣿⣷⡯⠟⣿⣿⠷⣾⡷⣯⡷⣇⣼⢿⣿⣋⣹⣟⡛⣽⢿⣟⣣⣈⠂
⠀⠀⢀⣈⣻⡶⢯⣹⠷⣾⢯⣿⣯⣀⠈⣿⡄⣿⣳⡄⢸⣤⠓⠚⣥⡞⢻⣹⣷⡿⢄⡉⣄⣔⣹⣫⣤⣧⣿⣿⡷⢾⣼⡟⡗⠒⡆
⠀⣰⠁⢠⢿⣗⣦⣽⠷⡷⣴⡿⣿⣻⠭⢿⢛⣿⡿⠃⣟⠂⠀⠈⣉⣻⠞⠟⣯⢱⠶⣿⢁⣏⣉⣽⡟⣼⣿⢽⣿⡞⣿⠷⠴⠞⣳
⠐⡏⠙⣧⠬⡉⡠⡿⣖⣷⣿⣤⣤⡀⠀⠸⣿⣭⠇⠀⠀⠀⠀⠀⣹⢯⠀⢐⣇⠀⠰⠟⢺⠁⠐⣿⣟⠻⢦⡸⣿⣳⣿⣶⣶⢯⣋
⠀⠈⠚⣯⣉⣡⠷⣳⣶⣏⢳⣟⡟⢛⡆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠸⠊⠀⢨⣽⠀⠀⣶⣾⢷⠰⣎⣹⡿⣾⣼⠿⢯⣿⣿⠟⠉⠉
⠀⠀⣜⠁⠈⢱⣤⣟⣻⡿⢾⢶⠭⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢟⢇⣼⣟⣤⣾⣿⣿⡿⣍⣸⣟⣁
⠀⠀⠘⠛⠀⢊⢸⣿⢟⣷⣆⣼⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢋⣯⡤⢾⣿⡷⡶⣿⣋⣏⡁
⠀⠀⠀⠀⠀⢸⣿⠟⠶⠒⣿⣺⡀⠀⠛⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⢛⣗⡿⣻⡿⣇⠟⢣⣬⡏⠁
⠀⠀⠀⠀⠀⢸⣿⣯⠛⣿⢴⠉⢧⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠻⠿⠏⠃⠀⠀⠀⠈⣿⡘⢫⡿⠛⡿⣋⠇⢸
⠀⠀⠀⠀⠀⠲⣀⣿⣶⣶⣚⢦⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠶⣧⣟⣼⣳⣆⣽⡏
⠀⠀⠀⠀⠀⠀⢸⢯⣿⣉⣩⠿⣄⠀⠈⠓⠦⣄⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⣠⠴⠊⠁⠀⢾⣁⡟⠻⢭⠿⡟⠋
⠀⠀⠀⠀⠀⠀⠸⣄⡄⢹⣉⣥⣧⡀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠒⠒⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠚⣸⡄⠰⠦⢶⢳⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢡⠿⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⡆⢀⣤⡞⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⢠⠖⠒⢤⡀⠀⡇⠰⡀⢀⠴⠚⠓⡄⠀⠀⠀⠀⠀⠸⡉⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡎⠀⣄⠀⠉⠒⠁⠀⠈⠁⢀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠛⠀⡇⠀⠈⠳⣤⣀⣀⣀⣀⠴⠊⠀⠀⢸⠀⠀⠀⠀⠀⡞⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⡀⠀⢀⠆⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⡸⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣠⣶⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⣀⢁⠀⠀⠀⠀⠀⠸⣿⣿⡿⠁⡤⠶⠶⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⢸⠂⠀⠀⠀⠀⡄⢿⣿⢣⣄⣤⠶⢀⡀⠀⠀⠀⠀⠀⣀⠲⠿⢿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠄⠀⠀⠀⠀⠙⠷⣯⠈⣿⣿⣷⡄⠈⠀⠀⠀⠀⣼⣿⣦⠀⠀⠙⠿⢏⡤⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢠⠀⠀⠀⠀⢦⡀⢻⡀⠈⠿⠿⠇⠀⠀⠀⠀⠀⠙⠿⠿⠀⠀⠀⢸⠃⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⡄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢡⡀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⢠⣄⣀⡀⣶⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢡⠀⠀⠀⠀⢿⣿⣧⡀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⣀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠑⢤⡤⠄⣸⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢠⡌⠀⠀⠉⠛⠿⠏⠉⢉⣻⡋⠐⠒⠂⢙⠛⢉⠛⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀⠀⡘⠁⡌⠁⠉⠒⠐⠒⠉⠀⠉⢉⠖⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⢤⣄⣠⠁⢴⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇⠈⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠰⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠸⠃⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⣆⠀⠀⡠⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⣶⠁⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠘⢇⠀⢠⢿⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⠦⣼⠀⢁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣉⡆⢸⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢶⠀⢠⢀⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠉⠉⠁⠀⠀⠒⠀⠀⠉⠉⠁⠀⠀⢸⠀⠾⣿⡷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠙⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⡴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⣉⠛⠻⠿⠿⣿⣿⣿⣯⣽⣿⣿⠿⠿⠟⢋⣉⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠐⠒⡤⠠⠤⠤⠤⠤⠤⠀⣴⠒⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⢰⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⣤⠇⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠈⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠙⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣤⠃⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠈⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⢁⡔⠛⢩⣓⣻⣦⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣴⠂⣏⠼⠋⠁⠀⠀⠀⠐⢄⠈⠉⠑⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡀⢣⡾⠋⠀⡀⠢⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠎⢀⡟⠑⠠⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡘⢠⠿⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠅⣸⡇⢌⡑⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠸⠀⠋⡇⢀⣀⠁⠀⠀⠀⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⢳⠆⢱⠀⠀⠀⠀⣀⣀⣈⡙⠛⠂⠀⠀⠰⠶⠖⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡎⠀⠀⠸⣷⣮⠀⠀⠀⠀⠙⠝⠁⠈⠀⠀⠀⠀⠰⠞⠛⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠈⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⡄⠀⠃⢀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠃⠀⡆⠘⠀⠢⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠸⠀⢀⠀⢠⠀⠀⠑⠀⠀⠀⠀⠀⠀⢀⠉⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠃⠀⠆⠀⠀⠀⠸⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⢋⣁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠚⠋⠉⠙⠓⠒⠲⠶⠶⠊⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠈⠉⢉⠛⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠐⠁⠀⠀⡛⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠂⠀⠀⢀⣁⠁⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠣⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠑⢄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠄⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⠀⠀⠀⢀⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⣀⣀⠠⠤⠖⠊⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡃
⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣯⣽⣿⣿⣯⡻⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠿⠿⢿⣿⣵⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡀⠀⠀⠀⣀⣠⡀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⣿⣿⣿⣻⣯⣽⣥⠀⢀⣵⣶⣶⣤⠞⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⡿⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣽⣿⣼⡿⠛⠋⠀⣀⠈⠉⠉⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⡿⣿⣿⣿⣿⣿⣆⠀⠉⠉⠁⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⣻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣿⣿⣿⣿⣿⣿⡟⠒⠒⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣤⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⣿⣦⣄⣀⡀⢀⣀⣠⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢣⣿⡿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠁⠟⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣶⣄⣤⣠⣀⣀⡀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠉⠋⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⣠⠬⠑⠂⠋⠀⠉⠐⠲⠄⢱⣄⡀⠀⠹⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⣀⡚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣦⣀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⠣⣡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠻⣯⠻⣮⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠏⢀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠋⢷⣝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢡⠮⠁⠀⣀⡀⠀⠈⠀⠀⠀⠀⠀⠛⠛⠓⠦⡀⠈⡀⠈⠻⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡔⢀⠇⠀⠻⢯⣽⣿⡢⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠠⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢧⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠛⠃⠀⢰⠷⠥⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃⠘⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⡸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠅⠀⡇⠀⡧⠁⢀⣀⣥⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠘⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡀⠀⠀⠀⣷⢠⢠⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⡇⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⠈⠀⢹⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡔⡇⡀⠀⡇⢸⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⡼⡞⠀⢀⡟⠀⡇⡸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠃⠀⠰⠀⠀⢸⠀⠀⢸⣿⣶⣤⣀⣠⣤⣾⣿⡇⣧⠀⠈⡇⢸⠁⠰⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣞⢄⡇⠀⠂⣾⢸⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⡇⠀⠀⠀⡇⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⢰⡇⢨⢿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢈⠀⠀⠀⠀⠀⠆⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠃⠀⠀⣧⠸⠘⣿⣷⢹⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡀⡀⠀⠀⠀⠀⠀⠇⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⠀⠀⠀⠙⠸⡄⠘⣿⡇⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⡇⠀⠸⠀⠀⠘⠄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡟⢸⠀⠀⠀⢰⡀⢳⡐⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣧⠀⠀⠀⠀⡤⠸⡆⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠐⡆⢸⣷⠀⢧⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠⠀⢠⠀⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠀⠀⣿⢸⣿⣆⠘⣧⢿⣿⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢻⠀⣀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢸⣶⠃⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢰⡇⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠾⠗⠚⠓⠛⠲⠶⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⡠⠔⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⢤⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⣾⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⣦⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢾⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠉⢷⡀⠀⠀⠀⠀⠀⠻⣿⠟⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣄⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠉⡽⠉⠁⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠋⠁⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣳⢦⣤⣄⣀⡀⠀⠀⠀⠀⢀⣀⣤⡴⠞⣋⠁
⠀⠀⠀⠀⠀⣠⠶⣤⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡟⠉⠳⣄⠈⢹⡇⠀⠀⠀⠀⠸⣇⠀⣠⠞⠙⣧⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀
⢻⣷⣶⡴⢛⣥⡀⠈⠙⠶⠞⠋⠹⠖⠛⢦⣀⣴⡛⠀⠀⠈⠛⢾⡁⠀⠀⠀⠀⠀⠹⠟⠁⠀⠀⢻⣄⣀⣠⡴⢦⣤⠞⠁⠈⠛⢦⣤⡴⣾⢿
⠈⣯⠙⠶⠋⠀⠙⢦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢄⣀⣀⣠⠞⠉⠉⠁⢀⣈⠁⠀⣀⡴⠞⢧⡴⠞⠁⡾
⠀⠘⣇⠀⠀⠀⠀⠀⠉⠁⠈⠛⠋⠙⠲⢤⣄⡀⠀⠀⢨⡟⢀⣀⣀⡀⠀⠈⠁⠀⠀⢸⡏⠉⠀⠀⠀⣠⡴⠛⠉⠙⠚⠋⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⠓⠛⠛⠉⠉⠉⠉⢳⣄⣤⣤⣄⣀⣼⠷⠒⢦⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠉⠉⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣛⣲⣶⣶⣶⣦⣤⣤⣤⣶⣶⣶⣞⣛⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠋⠉⠉⠉⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠟⠀⠀⠀⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⣉⣷
⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠶⠚⠛
⠀⠀⠀⣠⠖⠋
⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢀⠎
⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁
⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠈⠛⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⡴⡖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⢈⡟⣇⠀⠀⠀⠀⠀⠀⠀⢀⡟⣇
⠀⠀⠀⠀⠀⣠⣴⡿⢤⡈⠑⠢⠀⠀⠀⠀⠔⠉⢀⡾⠿⠶⢦⡄
⠀⠀⠀⠀⠘⠋⠁⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⠸⠇
⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠋⠛⠛⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡃⠀⠀⢀⣀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣦⠀⣴⣶⣶⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⡿⠟⠀⠛⠿⠋⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣾⣿⣿⣆⠀⠉⠁⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣿⣿⣿⣿⣇⣀⣀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣠⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠋⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠃⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⢄⣤⣄⣀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠐⠀⠀⢀⣆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⠄⠀⠀⠀⣾⠆⠀⠀⠀⠀⠄⠈⡀⠴⠘⡄⠁⠄⠀⠀⠀⠂⣰⠈
⠀⠀⠀⠀⠀⣠⣤⣾⢿⣧⣤⠜⠀⠀⠀⠀⠀⠠⠀⠀⠀⢘⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠄⠀⣴⠁⢌⡱⢐⠀⠀⢀⢈⠇⠈
⠀⠀⠀⠐⠀⢙⣿⣅⣏⣿⡟⠀⠀⠀⠀⠀⠀⡜⠀⠀⢠⠈⠀⠀⢄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡉⢀⠒⠢⢀⠀⠀⠀⢀⠚⡆
⠀⠀⠀⠐⠀⠈⠟⠛⠛⠟⠇⠄⠂⠀⠀⢀⡨⠇⠂⢠⡈⢄⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠈⠀⠠⠈⠃⠀⠀⠀⠀⠀⠐⢧⠀⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠠⠐⠀⠀⠀⠀⣤⠼⠀⠀⠀⠈⢁⠀⠀⢰⣿⠛⠁⠀⠁⠀⠀⢄⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢻⡄
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⣾⠁⠀⠀⠀⢀⣰⢠⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠠⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠀⠀⠁⠦⠘⠘⠸⠁⠀⠀⡀⠀⠀⠀⠀⢀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⢄⠂⠐⣀⢆⠄⠀⠀⠀⣀⣸⣄⠂⠀⠠⠐⣾⡂⠀⠀⠀⠀⠁⠰⡶⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⡀⢀⠀⠀⠀⠀⣰⠇⠂⠀⢌⢄⠂⠤⡩⣚⠌⡄⠀⠈⠔⡷⠾⠉⠂⠀⠀⢸⡇⠁⠀⠀⠀⠄⠀⢰⠀⠀⠀⠀⣠⠁⠀⠀⠀⢀⡴⠂
⠀⠀⠄⢢⠼⢦⠂⠀⠀⠅⠀⠀⠠⠂⢌⠦⠐⡖⠀⢂⡱⡁⠀⠀⠀⠀⠀⠀⠀⠐⠸⣇⣀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⡏⠀⢀⠀⠁
⠀⠀⠨⠜⠓⠋⠁⠀⠀⠀⠀⠀⠠⠎⠎⡜⠨⡰⢁⠃⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⢏⠀⠀⠀⠀⢠⡆⠀⠈⠁⠘⠁⠀⠄⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⡀⢠⡄⠀⠀⠀⠀⠈⠚⠱⠱⠑⠂⠉⠀⠀⠀⠀⠀⡐⠈⡄⠀⡀⠀⡀⠈⠆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠙⠁
⠀⠀⢀⣀⠀⠈⠋⠈⢠⡦⠀⠀⠀⣤⡀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⢥⢀⡖⠀⠀⡀⠁⠀⢀⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠗⣀⠀⢂⠠⠀⢀
⠀⣠⡌⠋⢶⢆⡄⣁⢠⡀⠀⣠⡀⠉⢀⠀⠀⣁⠀⡄⠀⠀⠈⠢⠄⡠⢿⣿⠗⠃⢀⠀⠀⠚⠋⠀⠀⠀⠀⡀⠀⠀⢀⣄⠀⠊⠓⡌⠀⡄⠙
⠀⠀⠁⠨⢄⠈⠁⡄⠈⠳⡶⠙⢁⡀⠀⡔⢆⠉⠀⠁⠜⠠⠀⠀⢠⠀⢀⠋⠠⠀⠀⠄⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠠⣄⠀⠈⡗⠋
⠀⠀⠘⠓⠀⢒⠀⢼⠀⠸⠆⠇⠘⠁⠀⠀⢀⣀⠤⠤⠀⠀⠀⠀⠘⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡰⠖⠀⠀⠀⠀⠈⢈⠑⡼⠂⣀⢰⠆
⠀⠀⠀⣀⡀⣘⠃⠐⢦⠀⠋⠘⠓⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠴⠏⠀⠀⠄⠀⠟⢠⠀⠀⢹⠄⠒⠉⠀⠀⡀
⠀⠀⢠⡝⠃⡛⠀⠛⢀⢡⠀⠿⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⣸⠛⠛⠅⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣇⠄⠀⠀⠀⢀⠇
⠀⠀⠈⠁⠀⣤⠁⠉⠉⠀⢳⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⢀⠀⢸⡀⠀⠀⠄⠀⢀⠋⠉⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡸⠧⠀⠐⠀⠀⡘⠀⠀⠀⠈⠸⡟⠋⠀⠂⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢴⡗⠃⠀⠀⠀⠀⠀⢰⣶⡴⣾⡆⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⢸⠀⠀⠀⠀⠘⣤⢧⡤⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣾⣯⣝⣿⡷⠤⠂⠀⠸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠚⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠻⢅⠀⠘⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠴⣦⠀⠀⢩⣶⣿⣿⠷⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣾⣿⣿⣷⠀⠘⢿⣿⣿⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⡠⠾⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣭⣤⣤⣶⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⢠⡿⠂⠀⠀⢀⣯⣭⡛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣦⡀⠀⠀⠀⢀⣿⣿⣷⢀⣴⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⣉⣤⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣿⢿⡿⢫⣾⣿⡿⢁⣾⣿⣶⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⣙⠻⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⢛⣩⣴⣾⣵⣿⣿⡿⢁⣿⣿⣿⣿⣴⣧
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣬⡛⢿⣿⠟⣭⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⣠⣾⣿⣿⣿⣿⣿⠿⠆
⠀⠀⠀⠀⠀⢀⣬⣉⠻⢿⣿⣿⣿⣿⣎⠻⣿⣿⡿⣿⣿⣿⣿⠿⠿⢛⣥⣤⣶⣶⣶⣿⣿⣏⣛⠛⠛⠻⢋⣴⣶⣦⣄
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣦⣝⠻⣿⣿⣿⣷⡜⣧⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⠿⠿⠟⣿⡿⢛⣡⣶⡿⢫⣿⣿⣿⢠⡄
⠀⠀⠀⣠⣈⡉⠛⠿⣿⣿⣿⣷⣤⡙⢿⣿⣿⠿⡿⢿⣿⣿⣿⠿⠟⣫⣥⣶⣶⣶⣶⣿⣷⣾⣿⣿⣿⣿⠇⣾⣿⣿⠇⣼⣿⡆
⠀⢀⣾⣿⣿⣿⣿⣶⣤⡙⠻⣿⣿⡿⣮⣿⣽⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿⢿⣟⣋⣉⣹⣾⣿⠿⠛⣁⣴⣿⣿⡟⣰⣿⣿⠇
⠀⠚⠛⠿⠿⠿⣿⣿⣿⣿⣷⣦⣿⢰⣿⣿⣯⣴⣽⡿⣿⣿⣿⣌⢿⣿⣷⣌⠉⠙⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⠟⣰⣿⣿⡟
⣾⣿⣿⠷⠶⠶⢺⠟⡿⢱⣿⣿⣿⠘⣿⣿⣿⢹⣿⣧⢸⣿⣿⣿⣎⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢉⡻⢿⣁⣼⣿⣿⠿⠁
⠛⢉⣤⣶⣿⣿⢫⣾⡇⣼⣿⣿⣿⠀⣿⣿⢿⣿⣿⣿⡌⢿⣿⣿⣿⣆⢻⣿⣿⡆⠀⠀⠀⠀⣤⡀⠚⠋⠀⠈⠉⠉
⣾⣿⣿⣿⠟⣵⣿⣿⠁⣿⣿⣿⡿⢰⣿⣷⠀⣿⣿⣿⣷⡈⢿⣿⡿⠿⠀⠉⠁
⣿⣿⠟⣡⣾⣿⣿⡟⣰⣿⣿⠟⣵⣿⣿⣿⡇⢹⡿⠿⠛⠃⠈
⠟⢁⣴⣿⣿⡿⢋⣴⣿⣿⡿⠀⠻⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⢀⣴⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢰⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣤⣄⣶⠖⢦⡾⢻⠆
⠀⠀⠀⠀⠀⠀⢈⣧⠼⠛⠚⠉⠉⠉⠙⠒⠦⣄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⢄
⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣕
⠀⠀⣀⣾⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⣤⡊⠁⡇⠀⠀⠘⠷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠈⣩⠟⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠉⠉⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢏⣀
⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⢸⠛⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠤⣄⣀⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠈⠉⠁⠒⠒⠤⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⠉⠉
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⣶⣶⣿⠿⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣻⡿⠗⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠱⡀⠀⠀⠱⣄⠀⠀⣠⡾⠃⠈⠁⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠾⠗⠛⠁⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡷⠶⠤⢤⣤⣤⣦⣤⣤⣤⣤⠶⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠬⠟⢿⠀⠀⠀⠀⢀⣀⣀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⣸⠀⠀⠀⠀⢀⣤⠬⠭⣷⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠚⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠈⠛⠻⠿⠷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⡀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠈⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⣿⠋⠈⠁⠀⠀⠀⠀⠀⠀⣄⣠⣤⣤⠶⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠋⡀⠁⠀⠀⡟⢤⠀⠀⢀⠀⠀⠀⢠⣤⠾⢛⠏⠀⠑⠁⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠀⠹⣿⣿⣿⡿⣯⣶⣶⣿⣇⣀⡤⠊⠀⠀⠀⠀⠀⠈⠁⢀⡞⠁⣴⠁⠓⢄⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠉⠻⣿⠿⠿⢷⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠁⣀⣼⣿⣥⡀⠩⡀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠓⢄⠀⠬⠷⡆⣅⣹⣵⠤⠤⣶⣶⣤⠤⠤⠖⠛⠻⠉⠿⢝⠋⠢⠅⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠃⣴⠔⠛⠀⠀⠀⠠⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣤⠃⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⢤⠃⠛⠆⠲⡠⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⣅⢀⢺⡑⢊⢇⣶⠼⣀⣸⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣀⡭⠋⣀⠀⠀⠘⣿⡿⣯⣴⣠⡌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠝⣩⠷⠛⠉⠀⠀⠀⠈⠙⠷⡍⢿⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢌⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠠⠄⠀⠀⠀⠀⠀⠠⠄⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡦⡀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣾⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠉⠑⢰⡤⠀⠀⣤⡖⠊⢃⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠄⡠⠘⠻⢤⠤⡋⠗⢀⣮⡟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣹⠳⠈⠃⡀⠈⠁⠀⠁⠀⠘⢿⣷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡿⠀⠰⠀⡇⠀⠀⠀⠀⢰⠀⠆⣾⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⢀⠆⠠⠇⠀⠀⠀⠀⠘⠆⢰⣸⡏⢨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢺⢠⠆⠀⠘⠀⠀⠰⠀⠀⠀⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠒⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠄⠀⢸⡀⠀⠀⠀⠀⠀⠀⣨⠄⠄⠀⠀⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⡜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠲⠟⠁⠀⠀⠀⢠⡀⠀⠠⡀⠀⠀⠀⢘⣿⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⢱⡌⡄⠀⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣘⠀⠸⡄⣿⣷⡀⢢⣻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⠗⠀⠀⠀⠀⢠⣴⠾⣯⣭⡇⠀⢹⣽⣿⣧⠈⢷⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣿⠿⣦⠀⠀⠀⠀⠈⠟⠃⠀⠀⢿⢧⣿⡄⠈⢯⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⣿⣧⠀⠘⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⠀⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠉⠂⠀⠘⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠘⣷⡄⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠉⠹⣦⡀⠀⠤⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠘⢧⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠄⠀⠀⠀⠀⠹⣷⣄⣀⣀⣤⠐⠀⠀⠱⣱⡀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⢀⠘⢗⢿⣿⣿⠃⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⢜⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠰⡘⠦⣴⣤⠿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠂⣠⠖⠀⠀⠀⠀⠁⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠳⣬⡽⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣠⢞⡴⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢁⠞⣄⢄⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⢠⠋⣸⡎⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠤⠤⠔⠒⠋⠁⠀⠀⠀⠀⠐⠏⠘⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣻⣿⣟⣻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢀⠀⢀⣠⣤⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡤⠖⢚⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠡⢋⣠⡶⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⣾⣟⣁⣄⣀⠀⠀⠀⠀⠼⠛⢿⡿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣿⣿⣿⣯⣡⡶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠅⣤⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⣀⣀⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⢤⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⡴⠛⣋⣷⡆⠀⠀⠈⣿⣿⣿⣿⣿⣿⣧⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠙⠿⠿⣿⣿⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣾⡟⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⢹⣿⣿⣿⣿⣿⣿⣿⣷⣶⠤⠤⠤⠔⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢄⡹⡆⢀⣈⣭⣭⣍⣉⣍⡙⠋⣴⡆⠀⠰⠟⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⣿⡟⠉⠙⣿⣿⣿⣿⣿⣽⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⣿⣿⡙⣿⣿⣿⣿⣿⣿⣿⣧⠀⠹⢿⣿⣿⣿⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣾⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣷⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢻⡿⠟⠉⠩⠟⠉⠉⢉⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⢋⠴⡋⠤⠒⠁⠀⠀⠀⠰⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢿⡿⢋⠝⠁⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠚⠉⢛⡽⣒⣔⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠙⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡆⠀⡰⠀⠀⠀⡀⠀⠀⠀⠀⠸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⣠⣴⡩⠊⣁⣴⠟⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⢀⠔⢚⡻⠉⠙⢉⣩⢴⣿⡿⣿⣫⣮⣶⡖⠀⠀⠀⠀⠀⠀⢀⠈⠛⠦⠀⣿⠈⣆
⠀⠀⠀⡐⠀⠀⠀⢀⠞⠀⠀⠐⢭⣲⢟⡝⣠⠿⠋⠁⡉⠁⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⢰⠿⠀⣿⣳⡲⢦⣤⡤
⠀⠀⠀⢇⣠⣄⣤⣊⠀⢀⣠⣶⡿⢁⢾⣿⡥⢊⣴⣾⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣼⠃⣰⢯⡳⣝⠦⡈⠈⠑⠢⠀⡀
⠀⠀⠀⠈⠛⢛⡿⢶⢺⡽⢟⠟⡡⣫⢿⣿⠰⡻⣾⠃⠙⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠃⣰⡿⡀⢧⠹⣷⣬⠢⡀⠢⠀⠙
⠀⠀⠠⡢⣪⠵⣊⠕⠉⣰⠿⠊⡀⣴⠃⣱⣧⢾⣧⠘⡀⠇⠉⠉⠉⠉⠀⢀⠤⠠⣺⣿⠆⢨⡥⠾⢹⡆⢹⣎⢣⠹⡀⠡
⠠⣢⢞⠟⠡⠊⢀⣴⢿⣃⣴⠞⡱⠃⢸⣿⣏⣿⠘⠆⠘⡀⠀⠀⠀⠀⠈⢁⣴⣿⠃⠀⠀⠀⠈⠳⣼⣹⡼⠏⡆⡇⣷⢠⡀
⣵⢡⠏⠂⣠⣾⢿⠟⡿⡏⡀⢰⣧⣮⡾⢿⡶⣏⣆⠠⡠⠸⠀⠀⢀⠀⢠⣿⣟⡽⠀⠀⠀⠀⠀⠀⢻⣝⠅⣾⣣⣿⣵⣿⢄
⡇⣾⢠⣾⣻⠕⢁⡼⣸⠁⣁⡞⠉⢀⢠⡌⢣⠈⣿⡄⢹⣿⠠⠖⣬⢀⣿⡭⣷⠃⠀⠀⠀⠀⠀⠀⠀⣏⣚⡻⠝⢁⢾
⠀⣿⢁⢿⡎⠀⡎⠀⡟⡆⣿⠁⠄⠀⣸⡀⠙⠀⢘⠁⠀⡇⢠⠪⠚⢏⢋⡨⠁⠀⠀⠠⠀⠀⠀⠀⠀⠹⠿⠿⠶⠷⠗⠂⠘
⠀⠸⡘⠘⣷⡠⡇⠀⡇⡡⣿⠀⠀⣄⣾⢽⡄⠄⣾⠀⢤⡇⠞⢠⣶⠹⢒⠁
⠀⠀⠑⢆⠘⢧⣷⡠⢰⣀⣿⠀⠀⠘⠘⢧⠳⢾⣯⢠⡟⠳⣤⠸⣯⡾⠃⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠙⢷⣧⣻⣿⠀⠀⠄⠀⠀⡓⠻⠖⠓⢆⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠀⢀⠀⠀⠀⠃⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⡀⣉⠀⠀⣠⠀⠂⠀⠀⠀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡈⠀⠁⠉⢠⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠠⠄⡄⠀⡩⠄⠁⠐⠂⠀⠀⠀⠀⠠⠇⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠈⠳⣄⠘⠀⣠⠄⢒⠀⠁⠀⠀⠀⠀⢀⠄⠄⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⡈⠀⠈⡁⠤
⠀⠀⠀⠀⠀⠻⠂⠀⡀⠀⠀⠀⠀⠀⠈⠀⠁⠐⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⢃⠀⠭⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠋⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠓⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠠⣀⠰⡌⠁⣀⡇
⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡅⠊⠤⡶⡱⢄
⠀⠀⠀⠀⠀⠁⠀⢰⠄⠀⠀⠀⠀⠀⠐⠀⠈⠂⠀⠀⠂⠀⠀⠀⠀⠀⢠⠀⠀⠐⡈⠛⠁⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠤⠄⠣⠀⠀⠉⠁
⠀⢀⠤⢄⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠢⠀⢠⡀⠀⣀⡀⠤⡀
⠀⡇⠲⣦⡷⠒⡒⢶⠒⡒⡗⣾⠒⡒⢢⠖⡒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠆⠘⠂⠁⠀⠀⠒⢀⡇
⠀⡞⢶⠄⣷⠸⠜⢸⢸⠓⡇⣿⢸⢹⢸⡘⠟⢸
⠀⠈⠒⠚⢃⢰⠚⠉⠛⠀⠙⠋⠊⠙⠺⡍⠃⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡄
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠄⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⢀⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣿⠹⣿⣟⣿⢻⣋⣿⣯⣽⣅⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡯⠁⠁⠉⠈⠉⠙⠋⠉⠻⢿⣿⣇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣽⢶⣿⣿⣶⣤⣤⣤⣾⣿⣿⣤⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣩⣿⣿⣿⠇⣃⡀⣿⣿⣿⣿⣿⣿⡇⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⡟⠿⠃⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢘⠉⢉⡙⠃⠀⠀⠀⠀⠀⠉⠉⠉⢠⣿⣉⠒⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣆⠀⠀⠀⠀⠸⣷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣤⣍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣷⣄⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣦⣤⣾⣷⣶⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠾⠟⠛⠛⠿⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠉⢉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢀⣴⠿⣧
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⠶⠾⠿⠿⢶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣳⠟⣡⡶⠛
⠀⣴⣾⠟⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⡀⠀⠀⠉⠛⣷⣤⣤⣴⠶⠶⠾⠟⠡⢟⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢋⣴⡏⠀⠁⣼⡇
⠀⠙⠻⠿⢿⣿⣃⣀⡀⠀⠀⠀⠀⠀⠀⣰⠀⠀⢸⣇⣀⣤⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⣡⣾⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣽⣇⡄⠀⢿⡇
⠀⠀⠀⠀⠀⢻⣿⣋⣥⣤⠶⠶⠒⠀⠀⠘⢧⣤⣼⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡵⣀⠀⠀⠀⠀⠀⡼⠛⠛⣫⡾⠁⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠙⣿⣯⣤⡴⠶⠛⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⠞⠃⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷
⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⢀⣀⣤⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠩⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠉⠽⢖⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣾⣿⣦⣿⡆⢠⡄⠀⣠⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢩⡟⠡⠖⠰⢦⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣠⣿⠀⣶⠀⣿⠀⣿⠀⣶⠀⠘⣿
⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠴⠶⠶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣾⣿⢰⣿⠀⣿⠀⣿⡇⠀⣿
⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢿⣤⣿⡇⣿⡇⠀⢸
⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡴⣟⣼⣷⢀⣄⠀⣼⡿⠁⠀⠉⠉⠛⠿⣧⣀⡾
⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢟⡿⢛⡵⣿⣏⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⣫⣶⣿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢿⣟⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣄⣀⡀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡟⣿⡿⠿⣷⣤⣄⣀⣀⣀⣀⣀⠐⠶⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠉⠉⠛⠛⠻⣿⣿⣿⠻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⠛⠛⢛⣿⣿⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠻⣧⣄⠀⠀⠀⠀⠀⠀⣠⣴⣿⣥⡴⠾⠿⢭⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡾⢿⣧⠀⣶⠶⠿⠿⠆⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣾⣿⣿⣿⣿⣦⣈⠻⠿⣿⣷⣤⡀⠹⡑⠺⢦⡤⠤⣀⠀⠘⠢⡀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣦⣌⠙⢿⣿⣶⣬⡢⠄⡈⠒⠤⡑⠲⣄⠈⠢⡀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⢻⣿⢧⠀⠈⠂⢄⠈⠁⠀⠉⠀⠘⠂⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⢿⣻⣿⡻⣿⢿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠱⡄⠀⡋⠉⠲⡄⠀⠑⠦⣤⣄⣀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠸⣿⣧⣿⣷⣯⣿⣿⣿⣿⣿⣿⣧⣿⣧⣿⢿⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠢⡀⠈⠖⠀⠀⠀⠀⡇⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⡿⢮⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠢⡀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠈⢢⡀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠰⢿⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠮⠻⢿⣿⣮⣿⢯⠁⠀⠀⠀⠀⠀⣀⡤⠶⠾⠟⠛⠛⠃⢠⣠⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡭⠗⠻⢿⣿⣇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡀⠀⠀⠈⢋⠁⡇⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⢀⠀⢀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠿⠋⠀⠀⠀⠈⠣⣀⠈⠀⠀⠀⠀⠈⢢⠄⠀⠀⢀⣀⣀⡀⠀⠀⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⡒⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠟⢷⡄⠀⠀⠀⠀⠸⡀⠀⡆⠀⢀⠈⠉⠑⠒⠤⠤⠵⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡖⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⣱⠀⠀⠹⣆⠸⡀⠀⠀⠳⣀⣧⠀⢸⠀⠀⠀⠀⠀⠀⡆⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡽⣷⣮⣆⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠓⢈⠆⠀⠀⠸⡆⠡⠸⠀⠀⠙⢼⡆⢸⠀⠀⠀⠀⠀⢰⠃⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠚⣏⠀⠀⠀⠀⢻⠀⢃⢂⠀⠀⠈⢳⣿⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⠈⠓⠲⠤⠤⣄⣀⣀⣀⣀⣀⡴⣿⣷⡀⠀⠀⠀⢣⠈⢆⠣⡀⠀⠀⢻⡀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠙⣿⣿⣦⠀⠀⠀⠀⠈⠀⠈⠀⢢⡀⠳⣄⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠀⠙⢿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡈⠈⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠑⠦⣈⠛⠿⣿⣦⡤⠤⠤⠀⠀⠀⠤⠒⢁⡔⠁⠀⠀⠹⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁⢲⣕⠄⣀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⣏⣀⡠⣤⣦⣤⣉⣑⠛⠿⣿⣦⣀⢀⡀⠤⠄⠒⠁⠀⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣤⡿⠃⠑⠤⡱⣤⣀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢈⣉⣉⣛⢶⣭⣉⠉⠀⠛⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣷⡄⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠘⢄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡠⠤⠒⠛⠐⠂⠐⠒⠢⡉⠢⣄⠢⢄⠈⠻⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡄⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⠛⢦⡑⠢⣈⠉⠻⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠙⢶⡄⠉⠢⢌⠻⣿⣿⣿⣷⢦⣄⠀⠀⠠⣀⠀⠸⢿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠙⠳⣄⡀⠑⠬⣹⣿⣿⣶⣭⠻⢶⣄⡀⠉⠢⠌⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣄⠀⢄⡀⠀⠃⠀⠀⠀⠀⠈⠻⢦⡀⠈⠃⢽⣿⣿⣿⣶⡌⠛⠶⣤⣀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡉⢆⠃⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠈⠙⠿⣿⣿⣦⣀⡀⠉⠓⠦⣄⡙⢿⣆⡀⠀⠀⠀⠀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠘⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠘⠿⣿⣿⣷⣄⠀⠀⠈⠉⠙⢻⣷⣄⠀⠀⣼⣿⡿⢦

⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⡤⣡⢅⠀⢀⠀⠀⠀⠀⠀⠀⢠⢁⠀⠀⠀⠀⠀⢰⣦⣀⡰⣞⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠠⠤⠀⠈⠀⠀⠺⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠱⠌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠂⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠙⣯⣿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠴⠰⠆⠀⠠⠤⠀⠠⠄⠰⠄⠀⠀⡀⠀⠀⠄⠀⠠⠀⠀⢼⡴⣦⡄⢄⡰⠀⠀⠀⠱⠷⠀⠀⡐⠀⠀⠠⡄⣶⣄⠉⠁
⠀⠀⠀⠀⠀⠀⣀⢒⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⡄⠒⣠⠐⢦⡤⠀⠀⠀⠉⠁⠀⠀⡄⠀⠀⠀⠀⢠⢞⣁⠑⠄⠀⠠⠖⠈⠀⠲⠶
⠀⠀⠀⠀⠀⢄⡩⡄⡍⢰⣿⠇⠀⢠⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⢀⠰⠠⠄
⠀⠀⢠⣶⡄⠈⠙⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠁⠀⠁⠠⠀⢀⠀⡀⢀⠈⠀⠀⣤⠀⠀⡀⢀⠀⢀⡐⣨
⠀⠀⠀⢂⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢀⠆⠀⠀⡤⣶⠆⢃⠀⣀⡀⠀⠀⠀⠀⠘⠿⠀⠸⡿⠁⠀⠈⠀⠀⠙⠎⠀⠀⢱⠇
⠀⠰⠶⣷⠶⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⣬⡄⠂⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⡀⢠⣤⡴⠀⠀⠀⡀⢀⡀⠀⠀⠀⣤
⠀⣄⠀⠀⢀⡀⠈⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡠⡊⠉⢠⣀⡦⣴⡂⡄⠀⢠⠀⢠⠴⣄⠀⢾⢟⠀⠈⠁⠀⠀⠻⠂⠈⠀⠀⠀⠀⠀⠏
⠀⣽⣷⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠀⠀⠈⠀⠃⠙⠁⠙⠉⠉⠋⠉⠉⠁⠀⠀⠀⠂⠀⠀⢤⣆⠒⢸⠴⣪⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠈⠀⠉⠀⠀⠤⠀⠀⠀⡶⠶⠎⠀⠀⠀⠀⠢⠀⠀⢀⣺⣭⢸⠷⢺⢶⣂⡆⡶⢤⡦⣖⣡⠀⠐⠂⠀⠀⠀⠠⡐⢾⠀⠓⠃⠄⠀⠀⠀⠋⠀⠀⠁
⠀⢠⡈⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⣹⣉⡱⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣀⠀⠀⢰⣿⣿⠂⠀⠀⠀⠀⢠⡄⠀⣠⠂⠀⠀⠱⡀⠀⠀⠀⠾⠂
⠀⢀⣟⣛⣧⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠿⢀⣤⣄⠉⠉⠀⠀⠦⠀⠀⡾⠀⠀⠐⠰⣿⣾⢾⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢷⣄⡄
⠀⠀⠿⠿⠏⠀⢠⣠⠤⣄⠀⢀⣀⡀⠀⢠⣾⣿⣿⣶⡀⠘⣾⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣌⣠⣦⠄⠀⢠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣀⠀⡄⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢛⠄⠀⠀⠘⠘⠚⠙⠉⠀⠀⢰⣦⣀
⠀⣰⠀⡠⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⣤⣄⠉⠛⠟⠃⠀⠀⠀⠐⠂⠀⠆⠀⡿⣿⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠸⡟⠀⠃⠚⠒⠂⠀⠙⠑⠂⠈⠛⠉
⠀⣿⢰⠃⠐⢃⠌⠀⠀⠠⣿⣿⡇⠀⠛⠋⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⠀⣤⣤⠄⠀⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠒⠲⠤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣀⠀⠀⢀⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢈⡄⣀⠉⠙⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠛⠁⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡞⠀⠀⠀⠀⠀⠀⠀⡠⠖⠲⣄⠈⣆
⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⢸⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠳⡘⡄
⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠙⣜⣆
⠀⠀⠀⠀⠀⠳⠤⠶⠒⠚⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠋⠈⢦⡀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠞⠰⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢦⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠗⠦⠤⠤⠤⡧⠤⠤⠖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣻⢧⠀⠀⠀⠠⠾⡷⠄



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠛⠛⠿⢶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢁⡀⠀⠀⠀⠀⠀⢨⣴⣶⣌⠃⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠳⠗⠲⠘⠀⠀⠸⣿⡟⣸⡇⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣠⡤⠖⠀⠀⠀⠀⠀⠀⠀⠠⠭⠟⠃⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠿⠿⠿⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⣠⠖⠀⠀⠉⠙⠛⠶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠟⠁⠀⠀⠀⠀⠀⠈⠛⠂⠀⢤⡀⠀⠀⠀⢀⡀⣤⢀⡾⣡⠞⠡⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⢛⣉⣁⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣦⡦⠼⠸⠃⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⢀⡄⠀⠙⣦
⠀⠀⠀⠀⠀⢀⡼⠋⣠⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⢀⠀⠀⠀⠀⠀⠘⣿⣧⣦⠀⠘⣧
⠀⠀⠀⠀⣰⡿⠁⣼⣿⡟⣻⠏⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢣⡇⣾⠀⠀⠀⠀⠀⠀⠘⣿⣇⣾⠀⢹
⠀⠀⠀⢠⣿⠁⢰⣿⣿⢁⡿⠀⣿⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡾⢠⠇⡆⠀⠀⠀⠀⠀⠀⠹⣿⣿⣠⢸
⠀⠀⠀⣸⡏⢀⡿⠁⠁⠈⠁⢸⡇⠀⡟⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢡⡟⣰⠁⣠⠀⠀⠀⠀⠀⠀⢻⣿⠏⣼
⠀⠀⠀⣿⠃⡾⠁⠀⠀⡀⢀⣿⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢏⡼⠃⢠⠏⠀⠀⠀⠀⠀⠀⠈⣿⣾⠃
⠀⠀⢰⡟⠀⠀⢠⡀⢸⡷⢾⡿⠀⠘⣇⠸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣴⠋⣰⠃⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⣾⠁⢠⡆⣿⣴⠟⠀⢸⡇⠀⠀⢿⡀⢿⡀⢻⡄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣴⠋⡀⠀⠀⠀⠀⠀⢀⡿
⠀⣼⠃⠀⣼⣰⡿⠁⠀⠀⠸⣇⠀⠀⠘⣧⠘⣧⠈⢷⡀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⠞⢁⡼⠁⠀⠀⠀⠀⢀⣾⠃
⣼⣃⣠⠞⠛⠋⠀⠀⠀⠀⠀⢻⡄⠀⠀⠘⢧⠘⣦⠈⢳⡄⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣠⠞⠀⠀⠀⠀⠀⣠⡾⠃
⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠈⠳⠀⠙⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣡⠖⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣡⠔⠁⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣴⣾⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢿⣦⣤⣀⣀⣀⣀⡀⡀⢀⢀⣀⣀⣀⣠⡶⠛⠉⠋⠙⢯⣹⡏⠘⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡇⣼⠋⠉⠉⠈⠁⠉⠈⠀⠈⠙⠋⠀⠀⠀⠀⠀⢸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣚⣡⡀⠈⣻⠛⢒⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡖⣚⣍⣄⡀⠉⢛⣶⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣧⢼⠏⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢷⣰⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏

⠀⠐⠷⠀⠀⢶⠄⢴⠀⠀⠀⠀⠀⠀⠀⠀⣄⠄⠀⠀⠀⠀⠦⠶⠢⡀⣰⢰⣠⠖⣣⣴⠐⢀⠀⢀⣦⠛⠀⠀⠀⠀⠐⣄⠀⣀⣀
⠨⠤⢀⡂⠀⣠⡄⣔⠂⡈⠑⡄⠈⠐⠋⠀⠀⢦⠀⠶⢃⢄⡃⣎⡐⣢⣿⡿⠁⠉⠰⠇⡘⢋⠞⣁⣒⠀⠀⠀⠀⠀⠀⣾⣿⠿⢿
⠀⠠⠈⢃⢈⠛⠃⢬⠑⢱⠊⠈⣀⠂⠄⠔⠄⠞⠬⡋⢽⢀⠂⠜⠀⠀⠈⠁⠀⠠⡙⠓⣕⠡⠔⡛⠇⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠃⠀⣀⠀⠘⠆⠁⠀⠀⠈⠈⠀⢢⡴⣒⠎⣠⡂⢌⠂⠟⠛⠛⠛⠹⠗⠶⣶⠤⠄⣑⡀⠘⡟⣧⠄⠀⠀⠀⠀⠀⠿⢿⣶⡾
⠶⢂⣠⡄⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠁⡆⠀⠛⠀⠘⠃⠀⠘⠁⠐⠇⠈⣀⣰⣗⠵⣀⠡⠠⠀⠀⠀⠀⠈⠀⠀⠘
⡦⢤⡷⣾⡆⠐⣄⠀⣀⢀⡀⠀⢀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠟⠛⠀⠛⡽⣦⡐⠰⠂
⠃⣸⠍⠈⠅⠀⣼⣿⠿⣿⠳⠆⠀⠸⠆⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⢀⠀⠀⠙⠉⣸⠠⢲⣀⣀⠀⡀⢀
⠀⠈⠀⠀⠀⢀⣿⣇⢀⣠⣵⠶⠆⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠄⠌⠀⣀⡃⢈⣘⣭⢰⠂⠡
⠄⠠⠀⠀⠀⢀⠉⠩⠖⠠⠃⠀⣤⠨⡄⠈⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠃⡀⠉⡃⢉⣂⠘⠤⣀⣀
⠀⠀⠀⠀⠈⠂⡀⠻⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡅⣧⠀⠁⠀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⢤⠎⢯⠛⡟⡄⢚⠏
⠀⢀⠂⠀⢀⠀⠀⢀⡣⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢲⣇⢀⡀⣄⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠁⠊⠉⠖⠃⢈⠒
⠀⠀⢐⠐⠂⠀⣶⣾⢦⠙⡡⠀⠀⠀⠀⠀⢠⠂⠀⡀⠀⢀⠀⠀⣀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡈⠻⠀⠀⠘⠇⠲⡉⢀
⠐⢿⢿⠾⠀⠀⠊⠠⢰⣾⣿⡄⠀⠀⠀⠀⠈⢆⠀⠀⡅⢐⡀⠀⠀⠀⠈⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠒⢨⣄⢀⣠⡗⡀⠈⠄
⣴⡡⠀⠀⠀⠁⠀⣄⣶⡊⢢⠠⠀⠀⠀⠀⠀⠈⠀⡏⠀⠈⠀⠀⢀⠀⠀⠘⢀⠀⡇⠐⠀⠀⠀⠀⠀⠀⠠⠆⠩⢀⠜⢛⠁
⠢⢉⡇⠀⠀⢂⠈⠹⠛⢃⡅⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠘⠐⠀⠰⠀⠀⠀⠘⠀⠱⠔⠀⠀⠀⠀⠀⠀⠀⠈⠄⢠⡄⠈⠢⡄⠁
⠾⠀⠀⠠⠴⠆⠀⠐⡼⡾⣵⢠⠙⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣤⢄⠉⡠⠠⠎⠈⡀
⢀⡀⠀⠀⠙⠂⠀⠀⠈⠟⠢⠁⣀⣧⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣗⢾⢲⣿⠓⠀⢺⣶⠄⠁⠈
⠈⠉⠀⠠⡦⠴⠿⠙⢈⠡⠤⢂⡚⠙⠙⠩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢭⡀⠳⠲⠟⠘⠋⠠⠀⠻⠻⢀⡜⠃
⠀⡀⠀⣤⡄⠠⠄⠶⠀⡔⡰⢓⠂⣠⣦⣯⡶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡆⠢⡊⢧⠙⡤⠄⢀⣤⣮⡱⠀⢀⣡⡀⠉
⢀⣄⠀⠈⠀⠀⠘⠦⠠⣾⠕⠉⢳⠪⠊⠉⠀⠥⠈⠍⠙⠛⠶⠷⠶⠾⠚⠗⡛⠉⠁⠐⠂⠁⠀⠀⠀⢊⠊⠟⠙⠌⠀⢸⠿⡇⠤
⠈⢋⠀⢠⢤⠔⣀⢀⣁⠁⢀⠾⠑⣆⠁⠈⠓⠀⠀⠀⠀⠄⠐⡀⠠⠂⠠⢂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠄⠀⠀⠐
⠀⢀⣤⡄⠂⠠⠈⠉⠈⠁⢸⡏⡀⠉⠀⣰⠆⠀⠀⠺⠂⠀⠸⣶⣦⡂⠂⠈⠀⠀⠀⠀⠱⣄⣤⣤⣄⠁⠀⠀⠀⠀⠀⠀⠆⠠⠈
⠀⠀⠁⠀⠀⠂⠐⢀⣬⢀⠉⢠⡟⣿⠁⠈⢀⠀⠄⢜⠀⠈⠀⠀⠀⠑⠀⢀⠀⠀⠂⠀⣼⣿⠛⠛⢿⣿⡀⠀⠀⠀⠀⠠⠀⠀⢄
⠀⠀⠨⣶⠒⠀⠀⠀⠩⠀⠀⢠⠛⠇⠀⠂⠘⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠯⠀⠀⡼⡿⠅⠄⠀⠀⠀⠀⡜⠇

⠛⠿⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⡿⠉⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⠀⠈⠻⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⣴⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠘⠃⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣵⠿⠿⠟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣧⡀⠀⠀⠀⠘⠛⠛⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠉⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢷⡄⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢿⡄⠀⠀⠀⠀⠀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢋⡿⠁⢠⣿⣿⣿⠟⠉⠁⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣴⡟⠀⠀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣾⡟⠁⢀⣾⣿⣿⣥⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣯⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢿⣿⣭⣾⣿⡿⠋⢉⣀⣤⣤⣌⣉⡛⠛⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠟⠁⣠⣾⣿⣿⣿⣿⠁⠻⣿⡟⠛⣿⣿⣿⣷⡀⠀⠀⠀⢘⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡉⠋⠀⠀⠈⠙⠳⠿⠿⠿⠛⠃⠀⠀⠀⠸⠧⢼⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣭⠛⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⠶⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠉⠛⠿⣿⣷⣄⠀⠀⠀⠀⠦⣤⡶⣶⣶⡤⠀⠀⣰⣿⣿⣿⣿⡿⠋⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢿⣷⣤⣀⠀⠀⠈⠓⠒⠋⢀⣤⣾⣿⣿⣿⣟⠁⠀⠀⠀⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣤⣤⣤⣴⣿⣿⣿⣿⡿⠛⠛⠷⢶⣶⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣼⣿⣿⡿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⣿⣿⣠⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣽⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣽⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠂
⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢏⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣿⣿⣷⣦⡰⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡌⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣿
⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⣆
⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠀⠀⠀⢰⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⠘⣆
⣎⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢀⠀⢁⣿⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠰⠀⠀⠀⠘⠆
⠉⠁⣀⠀⢰⡇⠂⠀⠀⡌⣼⡇⠀⠀⠀⠀⠀⠈⢠⣿⣿⡄⠀⠀⢸⣿⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⢀⠀⠀⠀⢰
⠤⠀⠉⢠⣿⣿⣴⡀⠎⢘⣿⠃⠀⠀⠀⠀⠀⢀⣿⣾⠿⠻⡉⠉⠹⠛⢧⠈⣧⠀⠀⣇⠀⠀⠀⠀⡀⠀⠀⡟⠀⠀⣸⡾⠀⠀⠀⠨
⠀⠀⢀⣾⡟⣿⡿⠃⢀⣾⣿⡀⠀⠀⢀⡆⠀⣼⡏⠀⠀⠀⠐⢄⠀⡇⠀⠂⠹⡆⠀⢹⠀⠀⠀⡸⠁⠈⢸⠃⠄⣠⣿⡇
⠀⠀⢺⣿⣷⡿⠁⣠⣾⣿⣿⡅⢠⠀⠀⣿⣶⣿⠀⢀⣤⣤⣤⣤⣀⠸⡄⠀⠀⠹⡀⢸⣇⠀⣴⠃⣠⢤⡏⠀⣀⡿⡿⠀⠀⡀⢀⡇
⠀⠀⢸⣿⠏⠀⣰⣿⡿⠛⠻⡇⣾⢸⠀⢸⣿⣿⡾⣻⣿⣿⠻⣏⠛⢿⡶⠀⠀⠀⠸⡜⠿⣾⣷⠞⠁⠬⣠⣖⡃⠰⢁⣠⡄⢁⡜⠁
⠀⠀⠘⣁⣴⣿⣿⠏⢀⣶⣶⣅⠻⡇⠀⢸⣿⡏⢡⣿⡿⣿⣾⢿⠇⠈⠟⠀⠀⠀⠀⠈⠇⠹⠃⢀⣴⡿⢿⣿⣄⣹⣿⣿⢀⣾⢡⠃
⠀⠉⢩⣿⠟⢿⡿⡄⠈⠈⣩⣿⢸⡅⠀⢸⣿⣿⠀⠟⠶⡟⠁⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⣻⡆⠈⣿⣿⣿⣧⣾⣿⠅⠁
⠀⠀⢸⡏⠀⠈⢇⣷⠀⠀⣿⢻⣿⡀⠀⠀⠟⠻⠀⠈⠲⠦⡬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⠿⢹⠇⢰⣿⣿⣿⣿⡿⡇
⠀⠀⢘⠀⠀⠀⢸⣿⣷⣌⠊⠙⢿⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢡⣠⠎⢀⣾⣿⣿⢿⡿⠀⠃⠀⠀⢀
⠀⠀⠘⢀⣰⠀⣸⣿⣿⣿⣿⣶⡀⣹⣆⠈⢆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠃⢠⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢿⡇⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡷⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠈⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⢈⢿⡘⠘⣿⣿⡏⠛⢻⣿⣿⣿⣿⡷⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⡀⢀⡀⠀⠀⠀⠀⠀⠀⣠⣿⢻⠃⠀⠀⢀⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠈⢧⣱⣄⡙⢿⣇⠀⠀⠈⣿⣿⣿⡇⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⢀⣠⣾⣿⢃⡾⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠈⠻⣿⡿⣷⣿⣤⡀⠀⠙⢿⣿⡇⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠛⢋⣡⣞⣡⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡌⠙⠿⠿⠿⣿⡷⢿⠁⠀⠀⠀⠀⠙⢿⣷⣤⣀⣀⣤⣶⣿⣿⡿⠟⠛⠛⠛⠛⠛
⣠⣤⡶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⡛⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠋⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⡀
⠋⢹⡁⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣉⣴⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⣀⡤⠶⠶⠶⠶⢦⣄⠀⠐
⢧⣀⠁⣼⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠂⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠉⠻⠇⠀⠀⠀⠀⣠⣾⣿⠿⠋⠉⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠁⠀⠀⠀⣡⠖⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢯

⣴⡶⠶⢦⣤⣤⣤⣴⠶⠟⠛⠛⠻⠶⣦⣄⡀
⢻⡟⢦⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⣤⡀
⢸⡇⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⢳⣠⡜⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⢀⡟⠀⢀⣀⠠⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⣸⠃⠀⡈⣿⡿⣦⡙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀
⠀⣿⠀⠀⣧⠹⣿⣛⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠆⠈⠙⠻⢶⣄
⠀⣿⠀⠀⠈⠓⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠙⢧⣠⣄⣀⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠜⠊⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠉⠛⢷⣤⡀
⠀⢿⡆⡀⡀⡄⣄⣤⠄⠢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⢸⡇⣿⡇⠇⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⢸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠟⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢸⡇⢠⢰⣦⣶⣶⢷⠇⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣠⡤⠿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣋
⠈⣿⡘⣏⢯⡳⠋⠀⠀⢻⡷⣄⡀⠀⠀⡀⠲⠦⣤⣤⣴⣾⠉⠀⠀⢀⣠⡼⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠶
⠀⠘⢷⣌⢦⠑⠀⠀⠀⠈⢳⣌⠉⠛⢿⠛⠳⢤⣤⣤⣤⠿⣍⣛⡉⢉⣁⣠⠴⠋⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁
⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠉⠙⣶⠛⠳⢤⣀⣀⠀⢀⣀⣿⣍⣉⣉⣉⣀⣠⡴⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⡀⠘⠷⣤⣀⣈⠉⠉⠉⣩⣇⡈⠉⠉⠉⠉⣀⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⢻⡄⠀⠀⠉⠙⠛⠛⠋⠉⠉⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣄⣀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣀⣤⣤⡴⠾⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣷⣄⣤⣤⣄⣠⠾⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⣠⣾⣿⡿⢁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣽⣿⣯⣻⣿⣿⣿⠏⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣉⣛⣻⣿⣿⠟⠛⠛⠛⠁⠰⢿⣄⣀
⠀⠀⠀⠀⠀⠀⠘⠿⠿⠷⣶⣶⠖⣂⣤⣶⣴⠶⠶⠶⠾⠽⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⣠⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣉⣟⣻⣿⣿⣿⣥⣾⣿⠦⣭⣋⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠛⠁⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡙⣿⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠙⢿⣿⣿⣷⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠛⠃⠀⠈⠋⢁⣀⡄⠀⠀⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢻⣿⣿⡇⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣿⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⣾⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⣹⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣷⣿⠇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣿⣾⡙⠿⣯⣽⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠂⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡄⠀⠀⠀⠀⠃⠸⣿⡟⠀⣼⠟⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣸⢯⣿⠁⠀⠀⠀⠀⠀⠀⢸⣷⣿⣧⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⡟⠀⠀⠀⠀⠀⠀⠀⢈⡻⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⠘⣷⡀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠈⣧⠀⢿⡟⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠘⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣶⣿⣶⣾⣿⣷⣦⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠿⠿⠛⠛⠛⠛⠛⠋⠉⢹⣿⣿⡿⠿⠿⣿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⢦⠤⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠒⠉⠉⠉⠉⠉⠓⠢⢄⡓⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢮⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣽⡷⣆⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢿⣿⡟⠀⠀⢰⠓⣄
⠀⢠⡼⠂⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠤⠤⠀⠒⠒⠒⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠉⠀⠀⠀⡼⢀⣈
⠹⣔⠆⢱⠄⠒⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠂⠒
⠀⢨⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠲⡎⠁
⠀⠀⣇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⠚⠉⠉⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠘⡄⠀⠀⠀⠈⣹⡖⠤⣖⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠘⡄⠀⠀⠀⠨⠽⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠹⢦⣀⡀⠀⢀⣀⣤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⣀⡀⣰⡆⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠟⠑⠒⠒⠒⠈⠙⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⡤⠶⠖⠢⠄⠀⠀⠀⠀⢈⡷⣶⡒⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢯⣝⠓⠦⠄⠀⠀⠀⠀⣼⠀⠀⠙⢶⡀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢠⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⣀⠔⠂⠀⠀⠀⠀⠀⠀⣀⣄⠀⠲⠐⠂
⠀⠀⠀⠀⠀⢀⡀⣐⡻⠿⡄⣥⠃⠀⠀⠀⠠⠄⠐⠀⠀⣀⣠⠼⠶⠖⠒⠒⠐⣺⢿⠉⠁⠀⠀⢀⣀⡄
⠀⠀⠀⠀⢠⣽⢣⣛⠙⠲⠖⠊⠁⢀⠀⡄⣀⠄⠁⠄⠀⠀⣀⠀⡀⠀⠀⠈⠀⠈⠓⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠉⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⢠⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠠⣞⠇
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠡⠀⠁⠀⡀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈
⠀⠉⠃⠀⠀⠐⠈⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢄⢸⣿⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠚⢤⠄⠀⢠⠀⡀⡀⠠⠀⠀⠀⠀⠔⠀⠀⠀⠀⠁⠀⠀⠂⠰⠍
⠀⠀⠀⠐⠀⠀⠄⠀⠀⠆⠀⠠⠀⠠⠀⠈⡐⠉⠉⠑⡃⠀⠁⠀⠀⠠⠤⠀⠀⢰⣶⡄⠀⠀⢰⣖⡆
⠀⠀⠀⠀⠠⠏⠀⢀⠀⠀⡀⠤⠼⠂⠀⠀⢶⣄⠂⠀⠜⠀⠀⡀⠀⠀⠀⠀⠀⠠⡀⢪⠐⠀⠀⢀⠀⡄
⠆⠀⠀⠀⠀⠀⢀⡛⠛⠁⠚⠒⠀⣤⣠⡄⠀⠹⣤⡠⢀⠄⠀⠛⠀⠀⠀⠀⠀⠋⠜⡄⠁⠀⢐⢠⠙
⠀⠀⠀⠀⠀⠀⠙⠁⠐⠒⠀⢀⢋⠁⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠲⠗⠐⠀⠈⠀⡛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⠧⢾⡝⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡒⢺⢁⠷⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣄⢜⠦⡘⢧⣘⡱⡆⠚⢒⡩⠭⠁⠙⠪⠍⠐⣣⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡉⠊⣧⠖⠉⠉⠀⠀⡂⣆⠙⢁⡴⣢⠴⢂⠏⡃⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠏⢌⢅⡐⠀⠛⠂⠉⠣⡄⣀⠯⠚⢁⠀⠀⣪⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠖⣦⡁⣈⠙⠋⠀⠈⠀⠉⠀⠐⠚⠍⠻⣇⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣢⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡍⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠸⠃⠈⠀⠉⠛⠂⠀⠀⠀⠀⠀⠀⠉⠁⠀⢘⠇⣧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠐⡆⠇⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣶⠏⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⢰⢧⠂⠎⡿⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢸⡟⠸⠈⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡘⠘⠂⢠⠘⠀⣶⠀⠀⠀⠀⠀⡔⠀⠃⢂⠸⣦⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⢸⢈⢠⠀⠋⠀⠀⠀⠀⠀⠃⠀⢿⠸⠆⡧⠀⠰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⢸⢸⠞⡆⢶⠈⠀⠀⠀⠀⠀⠀⢰⠈⣔⡏⠁⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠠⠸⢠⠁⡇⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⢰⢸⢇⢆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⢤⠞⠀⠓⢠⣤⣤⣀⣀⣠⣤⠀⡆⣇⠸⠘⡈⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⡇⠸⠂⠃⡆⢾⣿⣿⣿⣿⣿⣿⢸⢁⡟⠀⠐⠃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠇⡄⡄⠀⢠⢸⣿⣿⣿⣿⣿⣿⡇⣞⢡⡀⠆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠖⠐⠂⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠘⠃⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⡔⠈⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠉⠉⠁⠀⠐⠀⢠⠁⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⡊⠀⠀⠑⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⣲⡄⠀⠀⠀⢀
⠀⠁⠢⣄⡀⠀⠱⡤⠐⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠒⠒⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢜⣷⠃⠀⠠⠂⢉⡒⢄
⢃⠀⠀⠀⠉⡑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡨⠀⠀⠀⠀⡑
⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠉
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡤⠊⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⢀⠀⠤⡀⠂⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢀
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠁⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠂⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠑⠤⣀⡀⠀⢀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠐⠂⠀⠠⠄⠀⠀⠀⠄⢤⡂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⡴⠒⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠒⠤⣈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⠉⠑⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄