Among us updated Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠛⢿⣦⠀⠀⠀⠀⣀⣠⣴⡾⢿⣇
⠀⠀⠀⠀⢠⣴⣟⣋⣁⣀⣀⠀⠻⣧⣠⣴⠾⠛⠉⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⢻⣧⠀⠙⠋⠀⣶⣠⣦⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣤⣤⣼⣿⣿⠁⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢹⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⢰⣶⠶⠶⠶⠶⠶⠶⠶⣾⠟⠀⢸⠀⠀⠀⠀⠀⠀⢸⡿⣶⣶⣶⣶⣶⡶⡶⢶⣶⠄
⠀⠀⠀⠀⠀⠀⠻⢷⣤⡀⠰⢶⣖⡾⠋⠀⠀⠘⢦⣀⣀⠀⠀⠀⣸⠁⠻⢒⣶⠖⠀⢀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣬⣉⣙⠒⠒⠦⠤⠤⠭⠭⠭⠭⠥⠖⠊⢉⣠⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠟⠛⠻⢿⣿⣿⠷⠾⠷⠶⠿⠿⠿⠛⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⢶⣿⠀⠀⠀⠸⣿⠈⠦⣀⡀⠀⠀⠀⢀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⡏⠀⠀⠀⠀⣿⡀⠀⠀⠈⠉⠉⠉⠉⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢸⡇⠀⠀⠀⠀⠈⠻⠷⣶⣶⣴⣶⣶⠶⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⣶⢾⣷⠀⠀⠀⠀⠀⣤⣤⣤⣤⠤⠴⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢸⣿⠁⠈⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢸⣿⠀⠀⢿⣆⣀⣀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢶⣶⠾⠟⠋⠀⠀⠀⠉⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡍⠻⣦⡀⠀⠀⠀⠀⣿⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⡬⢿⣆⠀⠀⠀⢿⣄⡶⠽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠹⣧⠀⠀⠸⣧⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠹⣧⠀⠀⢻⡆⠀⠀⠘⣷
⠀⠀⠀⠀⠀⢠⡏⢳⡄⠀⠀⠀⠀⠈⢷⡀⠀⠀⠹⣇⣀⣈⣿⣄⣀⣀⢹⡆
⠀⠀⠀⠀⠀⣼⠀⢦⠹⡄⠀⠀⠀⠀⠈⠻⣄⠀⠀⠹⡍⠉⠉⠉⠉⠛⠛⠿⣦⡀
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠹⡄⠀⠀⠀⠀⢀⣿⢧⡀⠀⠀⠀⢀⣠⣤⡤⠤⠤⣬⣿⣆
⠀⠀⠀⠀⠸⢦⣄⣤⣀⠴⠻⣆⠀⠀⠀⣾⠇⠀⠀⠀⣠⠞⠋⢁⠄⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⢀⣭⠿⢃⡠⢟⣠⣤⣴⡿⠀⠀⠀⣼⠇⢠⠀⠈⠦⣄⣀⠀⠀⠀⠀⢀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠙⠳⢦⣈⣿⠟⠉⠁⢸⡇⠀⠀⠀⢿⠀⠈⢧⡀⠀⠀⠈⠉⠉⠙⠋⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⣼⡇⠀⠀⠀⠘⣧⡀⠀⠙⠲⠤⣤⣤⡤⠴⠖⠚⢁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⣀⣀⣀⣀⣀⣤⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⢸⡷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣬⣿⠀⠀⠀⠀⠀⠀⢠⣶⣶⠾⠋⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣼⠇⣇⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⢀⣴⡟⠀⠻⣦⣄⣀⣠⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠈⠉⠉⠉⠁

⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠻⢿⣇⠀⠀⠀⠀⠈⠻⢿⣯⣤⣦⣶⣶⣤⣤⣄⣀⠀⠀⣄
⣿⣿⣄⡂⠀⠀⠀⠀⠀⠀⠀⣠⢰⣿⣾⣿⣿⠂⠀⠋⠶⣶⣿⣶⣶⣶⢆⣠⣤⣬⣭⣭⣭⡽⢿⣿⣿⣶⣿⡀
⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⢿⡄⠀⠀⠀⠢⠉⣽⠟⠑⠀⣀⠀⡈⢿⣿⣿⣿⣶⣮⡙⢿⣿⣧⡀
⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣤⡾⠁⠀⠀⠀⠀⠀⠀⠈⢬⣛⠿⢿⠿⣧⢸⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠛⠻⣿⠙⠿⠿⠟⠁⠀⠘⢻⡅⠀⠀⠀⠀⠀⠐⠂⠀⠀⢈⠙⠒⠚⠋⢸⣿⣿⡿⠿⠳⢦⣄⡀
⠛⠻⠿⣿⣿⣿⣿⣿⣯⠝⢈⠑⠢⠄⠀⠀⠀⠀⠀⢠⡄⠈⢿⠹⢟⡛⠛⠓⠲⠶⠦⣤⣀⣀⠀⠀⢀⣾⣿⣿⡇⢀⣸⠖⠹⣿⠁⢀⣤⣤⣤
⠀⠀⠀⠀⣉⣛⣛⣭⣭⣤⣴⣦⣾⣿⡿⠿⠿⠿⣷⣾⣤⡶⠀⠂⠀⠠⠿⣷⣶⣦⠡⠦⠌⠭⡝⣻⠿⠛⢿⣿⡇⠀⠈⠀⢠⡏⢀⣥⣿⡿⠻
⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠙⠿⣷⠀⠀⠀⠀⠀⠉⢿⣿⣖⣤⣥⣶⣿⡀⣄⠀⢸⣿⡇⠀⠀⢠⣼⠁⢈⡛⠃⢠⡶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠈⢙⡉⠉⣽⣟⣯⣤⣿⣷⣾⣿⣟⡿⠒⢛⣶⢦⣿⡿⢦⣬⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣶⣮⣦⠦⠴⠦⠤⢴⡇⠀⠀⠀⠀⠀⠀⡠⠶⠾⣿⣿⣿⣿⡿⢯⣽⣿⣿⣿⡇⢠⣀⣸⡻⠅⣙⠣⣵⠟⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡈⠁⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣽⣿⠗⠖⣿⣶⠊⠳⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠈⣷⣿⣦⣤⣤⣀⣀⠀⠉⠈⣿⣿⣿⣿⡿⣿⣿⣿⣽⣿⣷⣿⣇⣤⣶⣮
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣹⣿⠿⢿⣿⣿⣿⣿⣷⣶⣼⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣿⠏⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⠀⠀⠀⠀⣀⣤⣤⣤⣤⣴⣶⣦⣬⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠁⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⣽⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⣿⠇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⡿⠿⠛⠛⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⣾⣿⣇⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣤⣤⣤⣤⡤⠀⠀⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢻⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡿⠻⣿⣿⡟⠉⠀⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⣠⣿⣿⠇⠀⢻⣿⣷⣤⣤⣤⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣶⣿⣿⣿⠟⠀⠀⠀⠉⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠛⠉⠉⠉⠉⠛⢯⡛⠲⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠉⠉⠉⠉⠉⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢸⠀⠀⢾⠁
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢸⠀⠀⠈⠓⡆
⠀⠀⠀⠀⠀⢸⠤⣄⣀⠀⠀⠀⠀⠀⡇⠀⠀⣀⠤⠶⠶⣤⣄⠀⠀⠀⣀⠤⠶⠶⣤⣄⠀⠀⢸⠇⠀⠀⠀⢸⠀⠀⣀⠀⡇
⢀⡖⠚⠓⠒⣿⢤⣀⡈⠉⠙⠓⠒⠒⢻⠀⢰⡃⠀⠀⠀⢸⠈⡇⠀⢰⡃⠀⠀⠀⢸⠈⡇⠀⣸⠀⠀⠀⠀⢸⣄⡼⠉⠙⡇
⢸⠀⠀⠀⠀⣷⠀⠀⠉⠉⠙⠓⠒⠒⠺⡆⠀⠙⠲⠤⠴⠟⠊⠀⠀⠀⠙⠲⠤⠴⠟⠊⠀⢠⡇⠀⠀⢀⣀⣸⣀⣀⣀⣠⣇⣀⣀
⡿⠦⣄⣀⣀⡏⢣⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣠⣶⣄⠀⢀⣴⣦⡀⠀⠀⠀⢀⡞⠀⠀⡴⠉⠉⠉⢢⣀⣀⣀⣀⣀⡿
⡇⠀⠀⠀⠀⡇⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⠛⠋⠀⠀⠛⠛⠀⠀⠀⢀⣾⠀⠀⢸⠁⠀⢠⠀⠀⢷⠀⠀⡹
⡇⠀⠀⠀⠀⡇⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⢰⣿⣷⠀⢰⣿⣷⠀⠀⣠⠎⢸⡄⠀⢸⠀⠀⠈⣦⡤⠾⠒⠛⣧
⡇⠀⠀⠀⠀⡇⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠉⠁⠀⠀⠉⢁⡠⠞⠁⣠⠞⡇⠀⠸⡆⠀⢀⡷⠶⠤⠶⠚⢧
⣧⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠚⠋⠁⠀⣠⠞⠁⠀⡇⠀⠀⠳⣄⠀⠓⢦⠤⠴⢶⠋
⢹⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋⠀⠀⠀⠀⡇⠀⠀⠀⠈⠓⠒⢾⣀⣀⣸
⠈⣇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠈⠉⠋⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠛⠉⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⣠⠴⠖⠒⠒⠒⠒⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠸⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠒⠛⠉⠁⠀⠀⠀⠀⢰⡚⠁⠀⠀⠀⢀⣀⡤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠩⠭⠽⠟⠛⠛⠓⠒⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠠⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣟⡋⢀⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⢀⠔⠊⠉⠉⠁⠒⢄⠀⠀⠀⢠⣾⣿⣿⣶⣯⡲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⣸
⠀⠀⠀⢀⡯⠖⠚⢯⡑⠲⡄⠈⢆⠀⢠⠏⠀⠳⡀⠈⣝⣻⣦⡱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⡏
⠀⠀⠀⠀⣤⠀⠀⠀⠳⡀⠀⠀⠈⣆⣘⣼⣣⠀⣰⡄⠘⠁⠙⣧⠈⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠠
⠀⠀⠀⠀⢸⡄⠀⠀⡘⠳⡀⠀⠀⢄⠈⠸⣾⠍⢁⣰⠆⣧⠀⠸⣇⠘⠀⠀⠀⣰⣿⣿⡀⠀⠀⠀⠀⠀⠀⣷⠚⡆⣟⠋⠉⠉⠙⢛⣲⣤⡀
⠀⠀⠀⠀⢸⡜⠛⠁⠄⠈⠱⣄⣀⠀⠉⢉⣠⣾⣾⣥⣶⡿⢧⠀⣿⠀⠁⠀⠀⢹⣿⣿⠇⠀⠀⠁⠀⠀⢀⡇⢀⣙⣉⣠⡴⠖⠛⠋⠉⠀⠙⣄
⠀⠀⠀⢀⠞⡇⠀⠀⠀⠀⠀⠠⢋⠝⠋⠁⠀⠀⠉⠉⠛⡴⢄⠀⡿⢰⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠈⡇
⠀⠀⠀⢸⠀⢄⠄⡶⠒⠲⠤⢴⠁⠀⠀⢀⣀⡀⠈⢳⣾⠁⠀⢰⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⢸⡀⠈⢰⠀⠀⠀⠀⣶⠀⠀⠃⢹⣻⠟⢶⠔⠁⣱⠖⣫⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢳⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠳⡄⠀⢆⠀⠀⠀⠸⡀⢀⡀⠀⣟⠛⠶⠾⠟⠓⠋⠁⠀⠀⠀⠀⢀⣀⣠⠤⠖⠒⠈⠘⡆⢸⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠈⠲⣌⢢⠀⠀⠀⠸⢄⠑⢄⠉⠒⠲⣤⡤⠤⡄⠒⠒⠒⠚⢛⠉⠄⠃⠀⠀⠀⢀⡠⠞⢻⣧⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢰⠀⠈⢳⡆⠀⠀⡀⠀⠑⠢⣑⣄⠀⠘⢧⠀⡇⠀⠀⠀⠀⠨⡤⠥⣴⡴⣞⠿⠝⠛⠉⠀⠙⠻⣷⣶⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠈⢱⠀⢀⠇⠀⠀⠀⠀⢽⣧⡀⡼⠀⠀⠀⠀⠀⢀⣠⢶⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⢠⡀⠀⠀⠀⡇⠀⠀⠀⠑⠊⠀⠀⠀⠀⢠⡿⢼⣷⡁⠀⠀⠀⠐⠚⠉⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠄⢹⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢘⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⠐⠀⠉⣉⡉⠉⡇⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⠁⠀⠀⡾⣧⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠈⡄⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢰⠉⣷⢰⠇⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁⠀⠀⠀⠀⠘⠁⠸⣧⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢃⢱⠀⠙⢦⣀⢧⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠸⣤⡏⡾⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠱⡄⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢧⠐⠀⣟⠀⡱⠀⠀⢀⢴⣿⠀⠀⠀⠀⡠⢄⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠄⠈⠣⡀⠈⠳⢷⡄⠀⢸⠀⣿⠀⢀⡴⢞⠙⣆⡇⠀⡇⠀⠰⣦⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠙⢦⡈⡆⢸⣠⡏⠀⡰⠺⠟⠁⠀⢻⠀⠀⢈⠻⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹

⠀⠀⠀⢀⡤⢄⡀⠀⠀⠀⠀⡠⠔⢢⠀⠀⠀⠀⠀⢀⠤⡀⠀⢀⢤⡞⠉⢢⡀⠀⠀⠀⢀⣠⡤⠤⡀
⠀⠀⢠⡧⢴⣶⣷⠄⠀⠰⣪⠴⣶⣿⡆⠀⠀⠀⡴⢾⣶⣧⠀⠈⠛⣭⢬⣠⣼⡀⠀⠀⢸⢀⣤⣦⣅
⠀⡠⢾⠸⡁⠈⣙⠆⢀⠴⡇⢎⠀⠉⣱⠀⢠⢴⠁⣏⠀⢉⡇⢀⠴⡇⢏⠀⢉⡳⠀⢠⢼⠱⡍⠉⢉⡆
⠀⡇⢸⠀⠉⠉⢹⠀⢸⠀⡇⠀⠉⠉⡇⠀⢸⢸⠀⠈⠉⠉⡇⢸⠀⡇⠈⠉⠉⡇⠀⣏⢸⠀⠈⠉⢹⡅
⠀⠙⢾⠀⡴⡄⡸⠀⠈⣷⠧⣤⢄⡘⠣⡄⠈⠚⣄⠀⣶⡞⠀⢈⡟⠃⡠⠤⡔⠳⡄⠘⡾⠄⢰⠤⡜⠁
⠀⠀⠈⠙⡁⠈⠁⠀⠀⠈⠙⡡⡀⠈⠒⠋⠀⠀⠙⠷⠋⠀⠀⠀⠑⢚⠁⡀⠈⠚⠁⠀⠉⢉⣙⡒⠁
⠀⠀⣔⣉⣬⣵⠀⠀⠀⠀⠞⣉⣉⣲⠀⠀⠀⠀⡔⠟⣓⡄⠀⠀⠰⣞⡩⢥⣀⠀⠀⠀⣎⣩⠀⣡⡀
⠀⣸⡏⡞⠉⠙⢳⠀⢀⣤⠋⡏⠉⠙⣆⠀⢀⣴⠩⡏⠉⠙⡆⠀⣠⡇⡞⠉⠉⢳⠀⢀⣠⠇⡞⠉⠛⣦
⢸⠀⡇⠈⠒⠚⣏⠀⢸⢸⠀⠙⠒⠚⡇⠀⡞⢸⠀⠙⠒⠚⡇⢸⠀⡇⠈⠒⠚⣏⠀⢸⢸⠀⠙⠒⠚⡇
⠘⢦⡇⢀⣄⠀⡟⠀⠸⣼⣄⣀⡀⠰⣅⠀⠹⢼⡀⠀⣤⡴⠁⠘⡦⠇⢀⣀⣠⠿⡀⠸⣼⣄⠀⣄⣠⠇
⠀⠀⠳⠞⠉⠚⠁⠀⠈⠓⠞⠋⠉⠳⠤⠇⠀⠀⢻⣤⠟⠁⠀⠐⠧⠴⠋⠀⠙⠤⠃⠀⠙⠖⠺⠥⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣾⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣭⣴⣶⣿⣿⣿⣿⠋⠿⡏⠉⠉⠉⠉⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣿⣿⣿⣿⣿⣿⣿⣷⡶⢶⣤⣤⣤⣤⣤⣤⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢸⣿⣿⣿⣿⡟⢀⡞⠙⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢸⡇⠀⢸⣿⣿⣿⣧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠓⠚⠁⠀⠀⠉⠛⠛⠛⠊


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣬⣭⣬⣭⣯⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠟⠛⠛⠛⠻⠿⢿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⣴⣿⡿⠛⠉⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⡟⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆
⠀⠀⠀⠀⠀⢠⣿⣿⠛⠉⠀⢸⣿⣿⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠘⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⣿⣿⠋⠁⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢿⣿⣧⣤⣤⣤⣤⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣶⣦⣤⣴⣾⣿⡟⠀⠀⠈⠛⠿⠿⠿⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢰⣶⡆⢠⡀⠀⠀⠀⠀⠮⢑⣛⣋⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⣉⣙⣦⡀
⠀⠀⠀⣾⣷⠞⠛⠛⢾⡿⠆⠀⠀⠀⣰⠋⣩⡭⢷⣄⠀⠀⠀⠀⢀⣀⠘⢍⠈⢀⡄⠀⡄⠀⠀⣠⢼⡇⢸⡁⠀⠀⣹⠄
⠀⠀⠀⣄⣿⣧⠒⢶⣿⣆⡄⠀⢠⡖⡏⠈⣿⣤⣤⣼⠇⠀⠀⠀⠈⠀⠈⠉⠁⠀⠀⠀⡇⠀⠀⣿⢸⠇⠀⠙⠛⠛⣿
⠀⠀⠀⠙⢟⢳⣤⡿⢟⠟⠁⠀⢸⡇⡇⠀⠀⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⠀⠃⣀⣀⣿⡼⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠷⡇⠀⢠⣠⡤⡾⠀⠀⠀⠀⣸⣀⣀⣧⣄⣀⣼⡀⠀⠈⠳⠤⢤⡀⠀⣠⣤⡼⠃
⠀⠀⠀⠀⣀⣠⠓⠖⠆⠀⠀⠀⠀⠀⠻⠤⠞⠹⠶⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣉⠋⠁
⠀⠀⠀⠀⠈⣦⠖⢛⣛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⣲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣩⣭⣽⣦⡀
⠀⠀⠀⢀⣤⡏⠰⣯⣉⣉⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣴⠶⠿⢦⡀⠀⠀⠀⠀⠀⢠⡖⡿⠀⣿⣦⣄⣠⡿
⠀⠀⠀⢸⠰⡇⠀⠙⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⢰⡏⡇⠀⢿⣶⣶⣾⠃⠀⠀⠀⠀⠀⢸⠄⡇⠀⠈⠉⠉⠉⡇
⠀⠀⠀⠸⣤⡇⠀⠀⢀⡀⡿⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣧⡇⠀⠀⡀⣀⢰⡇
⠀⠀⠀⠀⠈⢧⣀⡿⢿⣡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠓⣇⠀⣠⣤⠖⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣸⢻⣅⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠋⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠋⠉⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⠶⠛⠶⣦⣄⠀⠀⠙⣷⡾⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠙⢷⡄⠀⠈⢻⣄⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠹⣦⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣷⡀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠛⠉⠙⠛⠛⠻⠷⣦⣄⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⣀⡾⠃⠀⠀⠀⠀⠀⠈⢷⡄⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠈⠛⠷⢶⣶⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⢀⣴⠶⠾⠛⠛⠛⠛⠛⠿⢷⣄⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⣠⣖⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠒⢶⣟⠋⠻⣦⠀⠀⠀⣸⡇
⠀⠀⠀⢠⣶⠟⠛⠛⣿⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⢹⣧⠀⠙⠷⠶⠟⠋
⠀⠀⠀⢸⡇⠀⠀⢸⡏⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠟⠃
⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠛⠻⠷⠶⠶⠶⠿⠛⠛⣿
⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⢸⣇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠻⠷⣶⣾⣷⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⠤⠔⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢸⡟⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⡇⠀⠸⣧⣀⢀⣀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣤⣴⡶⠟⠁⠀⠀⠉⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣴⣶⣶⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⢠⣶⣿⣿⣿⡿⠿⠟⠟⠛⠛⠛⠻⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⣿⣿⠁⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠉⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠛⠉⠀⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣀⣀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢱⣿⡟⠉⠀⠀⠉⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⣤⣴⣦⣤⣤⣤⣤⣤⠶⠖⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣿⡇⠘⣿⣧⡀⠀⠀⣀⣼⣿⠇⠀⠀⠀⠀⣿⣿⡟⠛⢻⣿⣿⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⣿⡇⠀⠘⠿⣿⣿⣿⠿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣿⣿⡇⠀⠘⣿⣿⣤⣤⣤⣤⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣿⡇⠀⠀⣴⣶⣶⡶⠀⣿⣇⣀⣀⣀⣤⣾⣿⣿⠃⠀⠀⠘⠻⠿⠿⠿⠿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡇⠀⠀⣿⡇⣿⣇⣀⣿⣿⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣶⣿⠃⠙⠻⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠁⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⣴⣶⣶⣤⣄⣠⠞⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠙⢮⢢⠀⠀⠟⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣥⡤⣶⠗⠀⠀⠀⢸⢠⢀⡠⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣄⣷⣴⣤⡤⢴⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠉⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⢐⣀⣠⣤⣄⣀⠀⡸⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠈⠓⢦⣀⣤⣄⡀
⠀⠀⠀⠀⠀⢠⡾⠋⠉⠉⠉⠙⢯⡣⠀⠈⠗⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠈⠙⢆
⠀⠀⠀⠀⠀⢪⡧⡤⣶⠆⠀⠀⠀⣅⣀⡠⠴⠊⠀⠀⢀⣤⡶⠋⠉⣆⠀⣹⠶⠷⠶⠶⠖⠺⢯⡀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠘⠲⢤⠷⢤⠤⠴⠾⠛⠁⠀⠀⠀⢀⡤⠞⠋⢁⠀⣴⠋⣼⠁⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⡇⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⠚⠛⠒⠃⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣷⠀⠀⣇
⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠛⠉⠛⠲⢤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠲⠤⠤⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢻
⠀⠀⢀⡀⣠⠎⠀⠀⢀⡀⠀⠀⠀⠀⠀⠹⡍⠉⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣀⠞
⠀⠒⢉⣰⡧⠤⠤⢤⣄⡉⠂⠀⠀⠀⡤⠀⠹⡄⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠁
⠀⢠⠋⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⣨⣅⢱⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠸⣄⠀⠀⠀⠀⠀⠀⣀⠇⠀⠀⠀⢰⣇⠸⣌⡆⠀⠸⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠈⡟⠓⠒⠒⠒⠛⠁⠀⠀⠀⠀⢸⠻⡄⢹⣧⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⣰⠋⠉⠉⠀⠀⠈⣇⠀⠀⠀⠀⠘⣆
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣻⡴⠟⠳⣄⡟⠀⠀⠀⠀⠀⠸⣤⢤⣤⠏⠀⠀⠀⠀⠀⠀⠘⠶⠤⣤⣀⣠⡇
⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⣀⣤⠟
⠀⠀⠀⢸⡄⠀⠀⠀⠀⣀⣀⣀⣤⣤⡞⠁⠈⠙⠳⡏
⠀⠀⠀⢸⠁⠀⠀⠀⢰⠋⠀⠀⠀⠀⠱⡄⠀⠀⠀⢱⡀
⠀⠀⠀⣟⠀⣀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠙⠲⠒⠚⠋⠁
⠀⣠⠞⠛⠻⣭⠁⠀⠀⠀⣶⠀⠀⢀⣶⠀⠀⡴⠓⣆⠀⣶⡄⠀⢰⡆⢀⡶⠛⠂⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡆⢠⡞⠛⠲
⢠⣿⠚⠋⠳⡈⣷⣄⠀⢠⢿⡄⠀⢸⢻⠀⢠⡇⠀⢸⡄⣿⢳⠀⢸⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢐⡇⣾
⢼⠙⠦⠤⠴⠃⢻⢸⠀⢸⠀⣧⠀⣿⠸⡇⢸⡇⠀⢸⡇⣿⠘⡇⢸⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠘⢦⣀
⡟⠀⠀⠀⠀⠀⢸⣨⠇⡟⠀⢹⠀⡇⠀⡇⢸⡇⠀⢸⡇⣿⠀⢿⢸⡇⡇⠀⠀⣤⠤⠄⠀⠀⠀⠀⠈⡇⠀⠀⢸⡇⡀⠀⠉⠳⡄
⡇⠀⣴⠶⣦⠀⢸⡏⢠⡇⠀⠸⣾⠃⠀⣷⠈⡇⠀⢸⠃⣿⠀⢸⣾⡇⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⠁⣿⠀⠀⠀⣿
⣧⣀⡿⠀⢸⣀⣨⡇⢸⠁⠀⠀⣿⠀⠀⢸⠀⢻⣤⡟⠀⣿⠀⠀⢿⠁⠹⣤⣤⠇⠀⠀⠀⠀⠀⠀⠀⠸⣦⣠⠏⠀⠹⣤⣠⡴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠶⠶⠶⠶⠦⠤⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣳⡦⠤⠶⠒⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠉⠉⠙⠛⠒⠶⠤⣄⣀⣠⠤⠴⠚⠉⠀⠀⠀⠀⣀⣀⣀⡀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣰⠟⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⢀⣠⣤⠶⠖⣿⠛⠉⢉⡽⠛⢷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣰⠏⠀⠀⣰⠟⠁⠀⢠⡾⠋⠀⠀⡴⠋⠉⠉⠛⢲⣤⣶⡋⠁⠀⢠⡞⠁⠀⣠⠏⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠛⠛⡿⠀⠀⣰⠇⠀⠀⣰⠋⠀⠀⢠⡞⠁⠀⢀⡤⠞⠉⠀⠈⠙⠶⣤⠟⠀⠀⣼⠃⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⡇⠀⠀⣿⠀⠀⣼⠃⠀⠀⣰⠏⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⣼⠃⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠒⠚⣧⠀⠀⢻⡄⢸⠇⠀⠀⢠⡏⠀⢠⠟⠀⠀⠀⢀⡴⡟⢻⠛⣦⡀⠀⢻⡏⠀⣀⣠⣤⣴⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠹⣆⠀⠀⠻⢿⣀⣤⠶⠛⠛⠛⠛⠶⣄⠀⢠⣿⡆⣧⢸⡄⣿⢷⠀⠈⣷⠞⠉⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠙⢷⣀⠀⠀⡏⠙⠳⣄⠀⠀⠀⠀⠘⣧⢸⡿⡇⣿⢸⡇⢿⢸⡆⠀⢹⡄⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠖⠛⢹⡇⠀⠀⠀⠀⠀⠀⠉⠓⠶⣷⠀⠀⠘⣧⠀⠀⠀⠀⢸⠚⠿⠷⠿⠴⠷⠾⠟⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⣼⠋⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠘⣧⠀⠀⠀⣿⣄⣀⣀⣀⣀⣀⣀⣤⡤⠶⠛⣧⡀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢹⠄⣠⡾⠁⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⢻⡦⣤⠾⠋
⠀⠀⠀⠀⠀⣿⠹⣦⡀⠀⠀⢸⡏⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⢰⡏⠀⠈⠛⠦⣤⣸⡇⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⢹
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣦⠤⣄⣀⣀⣀⣀⢀⣀⣀⣀⣠⠤⣶⠾⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠉⠉⠉⠉⠁⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠖⠛⠋⢻⣥⣀⣀⡀⠀⠀⢀⣀⣀⣀⣤⡴⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢹⠛⠶⣶⠶⠶⢤⣤⠴⠶⠶⠛⢻⡇⠀⠀⠀⢸⠀⣿⠉⠉⣿⠉⠉⠉⠉⠉⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠀⠀⠘⢦⣿⣀⠀⣿⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠦⠿⣤⣤⣤⣤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠚⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠙⠛⠁⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⡤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⢸⡃⠈⡷⠴⡏⠀⢹⠀⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⠀⠙⠛⠁⠀⠉⠛⠉⢀⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣦⡀⠀⠀⠀⠀⠀⢀⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠈⡟⠒⠶⠶⠶⠚⡏⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⣇⠀⠀⠀⠀⢀⡇⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⣻⠇⠀⢻⠉⣻⠿⡏⢹⠃⠀⢿⡳⠤⣄⣀⡤⠖⠚⠛⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢴⡃⠀⠀⠈⣇⢳⣶⢋⡏⠀⠀⠀⣹⠄⣰⠋⠳⡄⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠙⢦⣀⠀⢹⡞⠘⣿⠀⠀⣠⠞⠁⢠⡇⣾⠁⢿⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⢷⢰⢇⡴⠋⠁⠀⠀⠘⡇⠉⠀⢸⡄⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠇⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣤⣤⠴⠞⠙⡶⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣽⣛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣋⣉⣉⣽⣿⣿⣿⣿⣿⡿⣿⣿⡛⠛⠛⠛⠛⠛⠛⠛⠾⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⡤⣬⣿⣿⣿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧⡴⠏⠀⠀⠀⠙⠻⠿⠿⠿⠿⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠈⠉⠻⢯⡉⠙⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⣀⣀⣤⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣴⠚⠁⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⠀⠙⢦⠀⠀⠀⠀⠀⢈⡷⣄⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⣸⠀⠀⠀⠀⢠⣯⡤⠬⢧⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣈⣧⠀⠀⠀⠀⠈⠙⠲⠶⠤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢠⣞⣁⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠈⠓⠦⠤⠤⠤⠤⠤⠤⣄⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠤⣀⠀⠀⠀⠀⠀⠙⣦⠚⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣠⣌⠳⡄⠀⢠⣄⠀⠙⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠻⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⣇⠀⣰⠃⢸⡀⣹⣰⠃⢹⡀⠀⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁⠀⠀⢹
⠀⠀⠀⠀⠀⠀⣴⠞⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠁⠀⢰⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⢻⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣤⣤⣤⠴⠞⠁⠀⠀⠀⠈⠷⣄⣀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡿⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢟⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣯⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣯⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣻⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣟⣽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣾⣦
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⡇⠀⢸⣿⠟⠿⠿⠿⠿⠿⠿⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣥⣦
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡀⠠⡀⠀⠤⢠⠄⢸⡇⠀⢸⣿⠀⠀⠄⠀⠠⡄⡤⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣸⡷⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠛⠱⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠛⠁⠀⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠉⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⢹⣿⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⣸⣿⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠻⣷⣤⣀⣀⣀⣤⣶⣿⡏⠀⢱⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣦⠀⠙⢿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣿⣿⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⢻⣿⣇⠀⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣿⣿⡄⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⡀⠈⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⢻⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣇⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡀⢸⣿⣿⡇⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠈⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣇⠘⣿⣿⣷⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⣿⣿⣧⠀⠀⠀⠀⠹⣿⣿⠃⠀⠀⢀⣴⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣧⣤⣤⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣻⣿⣿⡄⣾⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣤⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⣤⣀⣀⣹⣿⣿⣿⣿⣿⠿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠙⢿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⢟⠉⠁⠀⠀⠀⠀⡟⠉⠛⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠁⠀⢀⡷⡖⠶⠒⠒⠋⡟⠲⠤⣤⣀⣈⡽⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣠⠞⠀⠹⣄⣀⣀⡤⡷⠤⠤⠤⢤⣯⣉⠓⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠥⢤⣤⡞⠁⠀⢀⡼⠻⣄⣀⣤⣽⣤⣤⣤⣾⣤⣬⣭⣍⣉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⡇⠉⠳⣞⢉⣴⠾⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⢰⠇⠀⢀⡇⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⣠⣶⠟⠛⠛⢿⡇⠀⠀⣸⠀⠀⡸⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⣼⠏⠘⢦⠀⠀⣾⣧⣄⣠⣏⠤⠾⡗⠋⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⣸⡏⠀⠀⠈⡇⢀⣿⠀⠉⠻⣧⡀⠀⠹⡄⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⣿⢣⡀⠀⢀⠿⢥⣿⠀⠀⠀⠈⢻⣆⠀⣇⡤⠚⠛⢷⣤⣄⣀⣀⠀⠀⠀⠀⢀⣀⣀⣠⣤⢾⣿⣿
⠀⠀⢰⣿⠀⢳⡴⠋⠀⠀⣿⠀⠀⠀⠀⠀⠹⣷⠛⠲⣄⢀⠞⠁⢉⡟⠋⠛⠛⡟⠛⠛⠙⢯⠉⣰⡿⠁⣿
⠀⠀⢸⡇⢀⠞⠓⢦⡀⠀⣿⠀⠀⠀⠀⠀⠀⢻⡆⠀⣸⠿⠤⣄⣾⣤⠤⢤⣄⣷⠤⠖⠒⠚⣿⡟⠀⠀⣿
⠀⠀⢸⣷⡏⠀⠀⠀⠱⡄⣿⠀⠀⠀⠀⠀⠀⠘⣷⣰⠃⠀⠀⣸⠁⠀⡀⢀⠀⣿⠀⠀⠀⢠⡟⠀⠀⠀⣿
⠀⠀⠸⣿⠙⢦⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡧⠤⣄⣀⡏⢸⡀⣇⣿⡗⣿⣰⢀⣀⣾⠃⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⢳⢀⡜⠁⣿⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢹⡟⣩⢿⢿⣿⣿⣿⣏⠉⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⢻⡆⠀⢸⡟⠀⠀⣿⡶⣦⣤⣤⣀⡀⠀⢸⣇⡀⠀⢸⡇⠇⠃⢻⣿⡿⣾⢸⠀⢐⣿⢀⣀⣤⣴⣿
⠀⠀⠀⠘⣷⡀⡜⠉⠙⠲⣿⠀⠀⠀⠈⠉⡟⠳⣾⡏⠉⠙⠺⡗⠚⠚⠚⠛⠣⡿⠖⠚⠙⠿⠛⠉⣁⣸⡇
⠀⠀⠀⠀⠘⣿⡁⠀⠀⠀⣿⠛⠻⠷⠶⠾⢷⣤⣤⣤⣤⣤⣴⣧⣤⣤⣤⣤⣴⣷⠶⠶⠶⠾⠛⠛⠋⣹⡇
⠀⠀⠀⠀⠀⠈⠛⠷⢶⡶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⡶⠆⠀⠀⠀⢀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⣇⣀⣠⣤⣤⣴⠶⠾⠛⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⣿⠶⠶⠶⠶⠶⠟⠛⣿⠀⠀⠀⢸⡏⠉⠉⣀⣀⣀⣤⣄⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠙⠢⣿⠤⠤⠤⠤⠤⣤⣀⣿⠀⠀⠀⢸⡗⠋⠉⠁⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⡇⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⢿⣄⣀⠀⠀⣀⣀⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣧⣤⣤⣤⣤⡶⠞⠋⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⠀⣀⣀⢀⠀⡀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠰⡄⠇⡰⢄⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⡿⠁⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⠊⠀⠀⠀⠀⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠂⠀⠀⠀⠀⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠠⡀⡆⢠⠄⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠈⠀⠘⡶⠁⠀⠀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠇⡠⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢠⡀⡇⢠⡀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠈⢰⠂⠐⠂⠁⠬⠐⠀⠁⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠈⠂⠀⠱⣶⠃⠈⠂⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠂⠀⠀⡨⠠⠞⠀⠆⠇⠀⢀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠁⠦⠀⠅⠀⠔⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠠⠈⡌⡔⠀⡤⠤⠤⢤⣀⠀⠀⠈⠀⢳⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣃⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⠭⠭⣙⣒⠀⠸⣿⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡪⠭⢝⣒⣂⠀⠰⠿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣊⣩⣍⣙⣓⣒⠦⠥⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⣛⣛⣒⣒⣒⠭⠭⣓⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣒⣒⣒⣒⣒⡦⠭⢭⣒⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⠉⠙⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣁⣉⣀⣉⣉⣉⣉⣓⣒⣤⣼⣤⣤⣐⣀⣀⣀⣀⣀⣀⣀⣈⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠉⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⠿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⣀⠀⠀⣀⣹⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠛⠃⣀⣴⠟⠹⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⠏⠻⣦⣀⠘⠛⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣥⡤⠶⠛⠉⣀⡴⠂⠘⣿⡄⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢠⣿⠃⠐⢦⣀⠉⠛⠶⢤⣬⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠈⢉⡠⠖⠀⠘⣿⡄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⣿⠃⠀⠲⢤⡉⠁⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⢠⠖⠋⣀⠘⣿⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣿⠃⣀⠙⠲⡄⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠰⠛⣁⡄⠘⣿⣆⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣠⣿⠃⢠⣈⠙⠆⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠚⣁⡤⠆⠘⣿⣆⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⣰⣿⠃⠰⢤⣈⠓⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠉⠀⠀⠀⢨⣿⠂⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠐⣿⡅⠀⠀⠀⠉⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⣀⣤⣾⣿⠃⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⣿⣷⣤⣀⠀⠀⠀⢠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⡶⣿⡟⢿⡌⢿⣦⠀⠈⠻⠿⣶⣶⣶⣶⠿⠟⠁⠀⣴⡿⢩⡿⢻⣿⢶⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⢻⡌⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢡⡟⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠘⣿⣆⢻⡌⢻⣧⠀⣀⡀⠀⠀⢀⣀⠀⣼⡿⢡⡟⣰⣿⠃⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡈⠉⠛⠛⠿⣶⣦⠀⠀⠘⢿⣆⢻⡄⢻⣿⢛⣿⡇⢸⣿⡛⣿⡟⢠⡟⣰⡿⠃⠀⠀⣴⣶⠿⠟⠛⠉⢁⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡷⠀⠀⢀⡴⢻⣿⠀⠀⢠⣾⣿⡆⢻⣠⣵⡿⠋⠀⠀⠙⢿⣮⣄⡟⢰⣿⣷⡄⠀⠀⣿⡟⢦⡀⠀⠀⢾⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⡀⢀⣴⣯⣀⣸⣿⠀⠀⢿⣷⣶⡾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣾⡿⠀⠀⣿⡇⣀⣽⣦⡀⢀⣹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⠉⠛⠻⠿⣶⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣶⠿⠟⠛⠉⣿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣇⢠⡆⣰⡄⠉⣩⣍⠛⢛⣛⠛⠛⠛⠛⠛⠛⠛⡛⢛⣛⣛⣉⠉⡥⢤⡄⣶⡄⢾⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢻⡾⢠⣧⣽⣸⡇⠈⢣⡏⠉⠓⣼⢸⢷⣸⡇⣼⢳⡈⢹⠁⢸⢸⡇⢀⡟⣿⠙⡿⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢷⣶⣬⣄⣈⡋⠓⠶⠋⠳⠤⠗⠿⠸⠀⠻⠧⠟⠛⠇⠸⠀⠘⠈⢛⣋⣠⣤⣶⡾⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠋⠉⠉⠉⠉⠛⢯⡛⠲⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠉⠉⠉⠉⠉⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢸⠀⠀⢾⠁
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢸⠀⠀⠈⠑⡆
⠀⠀⠀⠀⠀⢸⠤⣄⣀⠀⠀⠀⠀⠀⡏⠀⠀⣀⠤⠶⠶⣤⣄⠀⠀⠀⣀⠤⠶⠶⣤⣄⠀⠀⢸⠇⠀⠀⠀⢸⠀⠀⣀⠀⡇
⢀⡖⠛⠓⠒⣿⢤⣀⡈⠉⠙⠛⠒⠒⢻⠀⢰⡃⠀⠀⠀⢸⠈⡇⠀⢰⡃⠀⠀⠀⢸⠈⡇⠀⣸⠀⠀⠀⠀⢸⣄⡼⠉⠙⡇
⢸⠀⠀⠀⠀⣷⠀⠀⠉⠉⠙⠓⠒⠒⠺⡆⠀⠙⠲⠤⠴⠟⠊⠀⠀⠀⠙⠲⠤⠴⠟⠊⠀⢠⡇⠀⠀⢀⣀⣸⣀⣀⣀⣠⣇⣀⣀
⡿⠦⣄⣀⣀⡏⢣⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣠⣶⣄⠀⢀⣴⣦⡀⠀⠀⠀⢀⡞⠀⠀⡴⠉⠉⠉⢣⣀⣀⣀⣀⣀⡿
⡇⠀⠀⠀⠀⡇⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⠛⠋⠀⠀⠛⠛⠀⠀⠀⢀⣾⠀⠀⢸⠁⠀⢠⠀⠀⢷⠀⠀⡽
⡇⠀⠀⠀⠀⡇⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⢰⣿⣷⠀⢰⣿⣷⠀⠀⣠⠎⢸⡄⠀⢸⠀⠀⠈⣧⡤⠾⠒⠛⣧
⡇⠀⠀⠀⠀⡇⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠉⠁⠀⠀⠉⢁⡠⠞⠁⣠⠞⡇⠀⠸⡆⠀⢀⡷⠶⠶⠶⠚⢧
⣧⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠚⠋⠁⠀⣠⠞⠁⠀⡇⠀⠀⠳⣄⠀⠓⢦⠤⠴⢶⠋
⢹⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋⠀⠀⠀⠀⡇⠀⠀⠀⠈⠓⠒⢾⣀⣀⣸
⠈⣇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠈⠙⠋⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠓⠛⠉⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⣠⠴⠖⠒⠒⠒⠒⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠺⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⢰⡚⠁⠀⠀⠀⢀⣀⡤⠞

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⢀⣤⣄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠐⠒⠊⠉⠊⢀⠒⠺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡀⠀⠠⠤⠓⠂⢒⣸⠓⠂⠀⠠⣭⣥⣤⠀⠀⠀⢄
⠀⠀⠀⠀⠀⡠⠒⠀⢈⣩⡭⠭⠤⢈⡁⠈⠛⢍⠭⠉⠷⢻⠁⠀⠒⠂⠀⠀⠀⠐⢒⠂⣭
⠀⠀⠀⠀⠀⠛⠂⠀⠠⠬⠬⠉⠭⠭⠤⠀⠐⣁⡄⠀⣨⢾⡀⠀⠀⠀⠀⣜⢜⢕⠥⠪⠞
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠔⢔⠔⠐⠀⠀⢺⣠⣆⠠⠀⣹⠷⠲⠤⠴⠤⠷⠚⢶⡕⠄
⠀⠀⠀⠀⠀⠀⠃⣤⣀⡀⠐⠐⠅⠔⡕⣑⢹⣛⡙⠂⣠⢸⠁⠀⠈⠉⠉⠉⠉⠁⡀⢀⠀⡄
⠀⠀⠀⠀⠀⢀⠜⠉⣁⡈⠉⠉⠋⠉⠁⢋⠓⠷⡀⡄⠀⠈⠀⠀⠀⠀⠀⠠⠪⠦⠨⠘⣀⡇
⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠉⢉⢉⢉⠄⢀⠤⠂⣇⡂⠀⡂⠀⢨⡉⠀⢒⠒⡒⢂⡉⣉⢰⡇
⠀⠀⠀⠀⠀⡟⠢⠤⢀⡀⠀⠁⠀⠀⠐⠉⣉⠁⡇⣀⠀⡇⠀⢸⡈⡄⠽⣘⠀⢀⠀⡏⢻⡅
⠀⠀⠀⠀⠀⣷⣴⡆⡄⠄⣉⠉⠉⡉⢉⠡⠂⠀⡇⠀⠎⡇⠀⢸⣹⣶⡠⠭⠂⠨⠄⠒⠚⠄
⠀⠀⠀⠀⠀⠯⣈⠁⢆⠸⣀⠠⠀⠑⣌⢈⡁⠀⡇⠀⡀⠅⠀⢸⠀⡫⠑⣋⣉⡀⠀⣒⠀⡆
⠀⠀⠀⠀⠀⣾⠶⣭⡒⢒⠂⠤⠤⡤⠄⢒⠊⠁⡖⠒⢛⡀⠀⠀⠲⣦⠍⡀⠂⠀⠀⣀⠤⡇
⠀⠀⠀⠀⠀⢲⣅⣒⠀⠈⠝⠉⠀⠇⢸⡗⠀⡆⡏⠉⠉⢙⠀⠀⠀⠀⢉⣒⣒⣎⠩⠀⠀⡏⠀⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⡙⠪⢕⡀⠸⠓⠂⠀⠀⠈⠀⣀⠃⡧⠀⠀⠈⠢⡙⢤⣐⠛⡬⣍⣸⣶⠟⣸⣒⢒⣒⡂⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠁⡀⠀⠀⡉⠐⠒⢒⠂⢀⡊⣠⠂⣗⣒⡂⠀⠀⠈⠑⠪⢥⣬⣬⣬⣴⡛⠠⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠘⢜⡦⣀⠨⠲⠃⠔⣤⢦⣴⠟⡾⠀⠀⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠪⢍⣊⠗⠒⠚⢉⢠⠚⣁⠀⠀⡀⠠⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠉⠠⠤⠠⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠶⠟⠛⠛⠛⠛⠛⠻⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠋⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡉⠹⠀⠀⠀⠀⠀⠀⠴⠃⠀⠈⠀⠀⠉⠀⠀⣀⣀⡀⣀⡠⢉⡛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⡙⢧⡴⢆⠈⠲⢶⡴⡇⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⡽⢋⡙⠊⣠⠞⢱⠞⢹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠸⢷⣄⠰⢎⠑⠤⠈⠙⠧⠴⢻⣄⠀⠀⢀⣰⢿⡷⠤⠛⢁⡀⠚⣀⠜⢃⡔⠃⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠁⠘⠛⢳⣤⡙⠠⣝⢓⠦⢠⢀⣈⣀⣀⣈⢁⣀⢠⡄⢲⣈⠵⠀⣡⡶⠟⠑⠀⠀⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠲⠠⠇⢸⡄⡬⠀⠷⠐⠃⣈⡀⠒⠉⠁⠀⠀⠀⠀⢈⠁⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢱⣀⣀⣠⣤⡤⠀⠀⠀⠐⠚⠛⠓⠒⣒⣤⣴⣶⡶⠿⠿⠟⠛⠛⠛⠛⠛⠿⠿⠿⣷⣶⣤⣌⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣠⣠⡤⠟⣋⣉⣥⣤⡴⣶⢶⠞⠿⠭⣻⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠐⣋⣤⡔⣿⠿⢻⠛⣄⢀⣅⢸⣦⣴⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣵⣾⠟⢫⡃⢳⣤⣿⣄⣿⠿⠛⠊⣹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠿⠙⣦⣼⠷⣬⠿⠋⣉⡠⣔⡾⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣿⣀⣷⣀⣫⠴⠋⣡⣴⠚⣻⠹⣟⣻⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⣶⢟⣛⣭⣥⣭⣿⡿⢹⣥⠟⢁⣴⢛⡑⡄⠻⣿⡄⠙⠏⢀⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⣴⣿⣿⡏⣉⣷⣮⣅⣿⣿⠞⣡⡶⢻⣆⠹⣾⠳⠀⢐⢀⣼⣦⣾⠿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⣼⡯⢄⣉⣉⣉⣉⢉⡉⣻⡏⡰⢏⠻⣾⡿⠆⢈⡴⣤⣿⠿⠋⠉⡠⠀⣀⡞⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⢶⣿⡏
⠀⢰⣿⢿⣮⣽⡏⢀⣱⣿⡟⣿⣿⣵⣿⣦⡀⢁⣤⣼⡾⠋⡁⠀⠒⠄⢲⣶⣿⠀⠘⣷⣌⣙⠿⠷⡶⣶⣦⣤⣤⣤⣤⣤⣤⣶⣶⠶⠾⠿⠛⠋⣁⣴⠟⢸⣇
⠀⣿⡗⣺⡏⠘⣿⣾⡋⢝⣻⣿⣿⣀⠙⠁⢀⣿⡿⠋⠀⣾⠻⣿⣿⡀⢸⡟⠛⠀⢂⠀⠈⠻⠤⠾⠛⠻⠏⢠⣟⠻⢷⣤⣤⡎⠀⠀⢠⣤⣤⣾⣿⡇⠀⢸⣿
⢸⣿⢿⣿⣷⣾⣁⠿⣿⣾⠇⣿⣿⡍⢀⣾⡿⠋⠀⣸⣠⣿⡀⣀⠛⠻⠾⠃⠀⢁⣀⠀⢤⣤⠤⣴⡦⠄⠤⣄⣀⡀⠀⠙⠿⢧⡀⣠⠿⠛⠉⠁⠈⠳⠀⠸⣿
⢸⡟⣿⠛⠝⣿⣿⣶⢟⣿⠀⣿⡧⣴⣾⡟⢁⣤⣤⣅⡸⡟⠁⠄⠋⢀⣤⣶⢉⠻⠁⠀⠈⠁⠆⠀⠀⠀⠀⠉⡄⠛⠋⠐⣦⣄⠈⠑⠆⠀⠀⠀⠀⠀⠀⠈⣿
⣾⡇⣿⡁⠌⣿⡟⣿⣿⣿⠗⣿⣧⣿⠏⠀⣿⡉⠙⢟⠛⠟⢀⡴⢾⡅⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠄⠀⡀⠀⠉⠍⢿⠦⠄⠈⠳⣤⣤⡄⠂⢠⣿
⣿⡇⢸⡽⣿⣿⠘⣿⣿⣿⢴⣿⣿⡏⣀⠗⠙⢷⡤⠏⠁⠔⠛⠇⠀⡀⠀⠀⠀⠀⠤⢀⡀⠤⡂⠀⡒⠓⠖⣠⣄⠀⠀⠀⠂⠀⠀⠀⠀⡷⢄⠈⠻⡇⠀⠀⣿
⣿⡝⡏⠀⢀⣿⣾⣧⠙⣿⣽⣿⡏⢠⣠⣶⡤⠾⠇⢠⣶⠀⠀⠀⠀⢁⣠⠶⡜⠁⠀⢁⠐⠈⠀⣠⠁⠀⠻⠀⠙⠣⠛⢖⣤⡀⠐⢀⡀⠂⠼⠷⡄⠙⢦⠀⣿
⣿⣏⠻⣄⣾⠁⢸⣿⣵⣾⢿⣿⠁⢿⡌⠉⣥⠀⢰⣆⠠⢄⠀⠀⠀⠂⠀⡄⠐⢂⠀⣄⡤⢂⣀⡃⠀⠀⢺⣤⣄⣀⡀⠋⢀⢫⡄⠀⠀⠀⠀⠀⣴⣆⠈⢠⣿
⣿⣏⡿⠋⢷⣸⡎⢁⢹⠏⢸⣿⢧⡴⢿⡂⠃⢀⡉⠀⠀⠈⢀⡀⠀⠀⠁⡄⠀⠈⢿⠋⠀⠃⢸⠀⠀⠀⢸⡘⣝⡿⠁⠀⢸⢃⡉⢠⣄⠀⢀⠠⠂⠼⣦⠘⣿
⢹⣏⢦⣀⣼⠛⣿⣆⡈⣶⣬⣿⠏⣥⣤⡿⠀⡘⠃⠀⠀⠀⣼⠁⠢⡀⠁⠏⠀⠀⠈⢆⠀⠘⡄⠀⠀⠀⢸⢈⡞⠀⠀⠀⡞⣤⣿⣫⡤⢆⠀⠄⠀⠀⢀⣤⣿
⠘⣿⡹⡋⣿⠸⢀⣿⢿⣏⢼⣿⡞⠋⢣⡄⠀⠟⠀⠈⠁⢰⠁⢂⠀⠈⠲⣿⡆⠀⠀⠘⢋⡉⠇⠀⠀⠀⢸⣿⠁⠀⠀⣸⢯⡶⠋⠁⣠⠜⡀⠀⠀⠠⡍⣹⣿
⠀⢿⣷⣡⣹⣷⣾⢳⣶⣛⢸⣿⡍⣷⡄⠂⠀⣄⠀⠀⠀⣬⠁⣬⢃⡀⠀⠈⠳⠀⠀⠀⠸⣴⠀⠀⠀⠀⢸⠀⠀⠀⢠⡟⠁⠀⠀⣰⣿⣦⣧⠀⠀⠀⠀⢹⣿
⠀⠘⣿⣿⡿⠷⠿⠿⠾⠿⠗⣿⡇⠋⠳⠄⠀⠋⢀⣀⣀⣀⣀⣀⡈⠉⠀⠀⢄⠀⠀⠀⠀⣿⠀⠀⠀⠀⡿⠀⠀⠀⠎⡠⠀⠀⠛⣁⣀⣀⣀⣀⠉⠀⠠⢿⣿
⠀⠀⠘⣷⣴⣶⣶⣶⢶⣶⣶⣿⡵⠟⣁⠴⣶⠉⠹⡏⠀⠙⠁⢈⡿⠋⢱⣦⠄⠉⠂⠀⠀⠹⠀⠀⠀⠀⠁⠐⠀⠄⢈⡠⣶⠊⢻⡏⠀⠛⠁⠘⠟⠁⣦⣼⡇
⠀⠀⠀⠘⢿⣾⣛⠶⣋⣩⣽⣿⡧⠾⡇⠀⢸⣄⣰⡧⠤⠿⠤⠼⠆⣠⣮⠀⣠⠟⢂⡀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡔⠻⡀⠀⣄⣠⣦⠠⠷⠄⣼⣀⣠⠁⣸⡇
⠀⠀⠀⠀⠀⠉⠛⠿⠿⠛⠋⢹⣇⠀⡸⠆⠉⢁⣀⣠⠤⣤⠤⠤⣄⣀⠁⠙⠳⣤⡜⠛⣄⠑⡀⠀⠀⢰⠃⣴⠉⢡⣄⠿⠛⠉⣀⣀⣀⣤⣀⣀⡈⠙⠶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⣠⠰⠎⡋⣹⠉⣷⠙⢀⢠⡍⠠⡝⢳⣦⡈⠱⣎⢹⣄⠀⠀⠀⠁⠶⣀⡱⠞⢁⣴⣾⣿⠙⣿⡿⠉⣿⢺⣯⠳⣄⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣪⠐⡄⣱⢸⠁⠀⣻⣀⠇⣼⢠⡟⠀⠘⣥⠘⣆⠈⣥⠼⠀⠀⠀⡘⢣⠜⢁⣴⣿⡇⠘⣧⢸⣿⡇⠀⢻⣌⣿⡞⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢩⣆⢈⡤⠈⠀⠐⡅⠈⢧⡙⠉⠓⢃⠴⠣⢈⢸⣶⡾⠶⠿⠿⠿⠿⣿⣦⣿⡿⣿⠁⢈⣟⣸⡿⣅⣀⣸⣿⣹⠇⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢨⠋⠲⡅⡀⢠⠞⣠⠖⠉⠉⠲⣿⡾⢃⠀⠙⣼⣿⠀⠀⠀⠀⠀⠀⣿⡇⢿⠱⣿⢦⠼⠋⢻⣏⣸⣭⡄⠿⢋⡃⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣠⠗⠚⠛⣷⣡⣊⠴⠀⠀⠀⠀⢷⡈⠣⠞⠛⠻⣿⠀⠀⠀⠀⠀⠀⣿⡇⣸⠿⢿⡀⢶⡟⠉⠉⠙⣶⠶⡶⠋⠉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠈⠁⠹⡀⠀⠀⠀⠀⣸⠉⠛⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢿⡇⣉⣦⣼⠶⣋⡅⠀⠀⠀⠛⠶⠇⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡴⠀⠀⠀⠀⠀⢳⠄⠀⠄⢠⡏⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⢸⣧⠁⠀⠈⠛⢯⡀⠀⡀⠀⣰⡆⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠠⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠸⠝⠂⠀⠀⠉⠁⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⢶⣤⡶⠶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣤⣀⣀⣀⣤⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠞⠛⠛⠛⠛⠛⠻⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⠛⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡛⢆⠁⣀⠀⠀⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⣤⠄⡠⠆⣠⣉⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢫⣦⠙⢈⠲⣀⠙⠷⣇⣠⣖⠀⠀⠀⢀⣦⡀⢀⡥⠂⣠⠘⣠⠜⣡⠛⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠐⠰⠷⣮⡑⠎⣱⠤⣈⠁⠉⠀⠀⠐⠊⠁⣈⡠⠄⢢⡀⢚⣠⡞⠄⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠈⠉⠐⠈⠘⠂⠮⠬⠋⣏⣈⡉⠧⠸⠂⡉⠥⠒⠉⠁⠀⠀⠀⡀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠘⣂⣀⣠⣤⠄⠀⠀⠀⠚⠓⡒⢂⣠⣤⣴⠶⠾⠿⠿⠟⠚⠛⠻⠾⠶⠷⣦⣤⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣤⠤⠚⣋⣩⡥⢤⢶⡔⡚⠋⠉⣭⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⢈⡥⢖⠙⠛⢁⠈⣤⣰⣄⣿⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⢏⠉⢡⡈⣗⣺⠷⠛⢋⣩⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⡏⣌⠀⣋⡫⠝⢋⡤⡶⢮⢾⡈⢿⡃
⠀⠀⠀⠀⣠⡶⠟⠛⣛⢛⣿⢟⢋⡷⢋⣰⢎⡛⢶⣿⡀⢻⠃⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢀⣾⣯⠛⢨⣉⣥⢸⣿⡴⢃⡴⢿⡙⢦⡿⠄⠉⢀⣴⣴⡷⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟
⠀⢀⣾⡅⣉⣉⣉⣉⡉⢙⣟⡰⢏⠻⢮⠷⠀⣡⣤⣾⠟⠋⢁⠄⢠⡞⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⢶⣿⠁
⠀⣼⡟⣧⡼⣆⢀⡽⣿⢻⣿⠷⣦⠧⠈⣠⣴⡿⢋⣀⣀⡁⠀⣶⣿⠁⠘⠷⣬⡝⠛⣿⣶⣶⢶⣶⣶⠶⠶⠶⠞⠛⠛⠋⠉⣠⡶⠃⢹⡀
⢠⣿⣠⣿⢀⠿⣿⡄⢨⢿⣿⡧⠈⣀⣴⡟⢁⠀⣽⠙⢻⣷⣄⡿⠉⠀⠑⠀⠈⠓⠚⠋⠚⠂⠰⠍⠛⣷⣶⡃⠀⢀⣶⡶⠟⠻⡄⠀⢹⡇
⢸⣟⣿⠟⣿⡇⣠⣿⡯⢸⣿⢃⣠⣿⠋⠀⠀⠐⣿⠆⠂⡄⠉⣁⡠⣴⠆⠀⠻⠋⠛⠋⠉⠱⠶⢢⣤⠄⠉⠛⠶⣟⠁⠀⠀⠀⠈⠀⢹⡇
⣼⡇⡷⠀⢸⣿⣿⢐⣷⣼⣯⣸⡿⠁⣞⠛⢿⠶⣿⠀⢀⣴⠈⠙⠒⠀⠀⠀⠀⠈⠀⠀⠠⠀⠘⠀⠀⠀⠹⠓⣤⡀⠀⢤⣀⡀⣀⠄⢸⡇
⣿⡃⣟⢶⣾⠁⢟⣿⠃⣸⣿⡿⠀⠆⠿⣦⣠⠂⠠⠾⠇⠍⠀⠀⠀⠀⠀⠠⠀⣀⢀⣀⠤⠤⠀⡀⠀⠀⠄⠁⠉⠉⢰⣄⠙⢿⡇⠀⢸⡇
⣿⢰⡁⠀⣸⣷⣯⠙⠗⢻⡿⠁⣨⣤⡤⠿⠀⣴⠀⠀⠀⠈⠀⡴⢦⠀⠀⠀⠀⠀⠀⠆⠀⡁⠈⠀⠁⠀⢤⡀⠠⣀⠐⠠⠷⡀⠻⡄⢸⡇
⣿⡎⢣⣴⠁⠈⡷⣴⡟⢻⡇⠘⣌⠉⠴⠀⣾⡠⢄⠀⠀⠀⠀⠀⠀⢀⢀⡀⡠⠄⠒⠀⠀⣵⢤⣀⣀⠊⠀⠃⠀⠀⠀⠀⠀⠴⣆⠀⣼⡇
⢿⡷⠋⠙⣦⣇⠀⠸⠃⢾⣷⡔⠻⣅⠁⣤⠀⠀⠀⢠⡂⠀⠀⢠⠀⠀⢃⠀⠀⠀⠁⠀⠀⢀⠢⡹⠃⠀⢨⠰⠀⡀⡀⠀⠀⠀⠺⠆⢸⡇
⢸⣧⢦⣴⠉⠸⣧⣤⡶⢾⣇⣴⡶⠋⢠⡍⠀⠄⠀⠈⠀⠁⢄⣠⡀⠀⠀⢢⠀⠶⠀⠀⠀⢸⡸⠁⠀⠀⡆⣄⡷⠔⠙⡀⠀⠀⠀⣴⣾⡇
⠈⣿⡉⠘⣦⣁⢾⣻⡄⢾⡿⣄⡀⠃⠈⠁⠀⠀⠈⠄⠠⠀⠀⠙⢧⠀⠀⠈⠖⠂⠀⠀⠀⢾⠃⠀⠀⢸⡝⠋⠀⣠⠇⠀⠀⠀⠈⠰⣿⡇
⠀⢹⣧⣶⢟⣿⣤⣴⣮⣼⡷⠘⢧⡀⠸⠂⠀⠀⠘⠀⠉⠒⠄⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⡏⠀⠀⡠⠃⠀⠀⠜⠊⠛⠙⠀⠐⠀⢠⣾⠇
⠀⠀⢻⣄⣤⣤⣤⣤⣤⣼⣏⠶⢂⣠⡴⠐⣿⠁⠙⠋⢹⠷⠂⣤⡈⠐⠄⠀⠀⠇⠀⠀⠀⠁⠀⠀⠀⢂⣤⠐⢾⠋⢹⠋⠘⠗⢠⣄⣿⠁
⠀⠀⠀⠻⣯⣛⢛⣭⣑⣽⣧⠴⡏⠀⣡⣀⡾⠤⠾⠤⠼⢀⣴⠁⢀⠟⢂⡀⢀⠀⠀⠀⠀⠀⠀⣠⠚⠃⠀⣄⣸⡄⠼⠄⣴⣀⡬⠁⣿
⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⣿⣀⠼⠂⠉⣀⣤⡄⢢⠀⠀⡄⢀⠈⠛⢤⡞⢙⡄⠢⠀⠀⠰⠁⣶⠉⣤⠜⠋⣁⣀⣤⣤⣤⢤⡀⠙⢺⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⠤⠘⠁⢰⠃⢸⡈⡀⢱⢀⡒⠙⡓⠄⠘⢧⠽⡄⠀⠀⢀⠛⣤⠛⣠⡴⢺⡏⢸⣿⠀⢻⡈⣧⢙⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡀⠀⠂⠤⠀⡼⠣⡁⠦⢤⣀⠀⣓⠀⢢⣀⣞⣃⣠⣄⣬⣼⢁⣼⣿⠇⠈⣧⣸⡿⠀⢈⣧⢸⠎⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠷⢐⠆⠀⢄⡀⠀⠼⠃⣄⢄⡬⠀⠰⢸⣿⠉⠉⠉⠉⠉⣿⠷⡟⢸⣇⢠⠷⣾⠙⡖⡊⢻⠿⠄⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⡦⠌⢷⡀⡠⢐⡅⠀⠀⢠⡑⠀⡠⠖⢿⡟⠀⠀⠀⠀⠀⣿⠀⣷⣾⠉⢥⡶⠘⠒⢭⣥⣬⠲⠳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠉⠙⠆⠀⠀⠀⠀⡝⠲⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠆⣡⣀⡅⢒⡁⠀⠀⠸⢧⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡔⠀⠀⠀⠀⠹⠄⠠⠀⣸⠃⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠙⢫⡀⢀⠀⢠⣦⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠃⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠘⠋⠀⠀⠀⠁⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⡀⠀⠀⠀⢀⣠⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡁⠀⠀⠀⠀⢀⣴⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠒⠒⠷⣿⡖⠐⠢⠀⠀⠀⢀⠀⢀⣀⣀⠀⠀⠀⠀⡠⠒⢒⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠈⠙⠲⣶⣶⣦⣀⢈⡿⠶⠴⠁⠀⠀⢻⣦⣤⣤⣄⣍⣑⠖⠀⣠⣤⡿⠋⠁⣠⡑⣀⢀⡀
⠀⠀⠀⠀⠀⡠⠊⠉⠉⠛⠲⢶⣿⣀⠀⠈⢻⣿⢿⠟⠁⠀⠀⠀⠀⠀⠘⠿⢿⠿⠟⠻⡇⠀⣸⡿⠋⢀⣼⣿⡟⠋⢉⣁⣌⠃
⠀⠀⠀⢀⠊⢀⣼⣿⣶⣤⣤⣾⣿⣿⣷⣶⠾⢱⢺⠀⠀⠀⠀⠀⠀⠀⣴⣤⣾⣦⣼⠘⠀⣠⣿⠇⠀⣸⣿⠏⠀⣰⣿⣿⣿⡀⠆
⠀⠀⠀⢘⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⡧⣼⡦⠤⣄⠀⠀⠀⠀⡖⠒⠀⠀⢺⠘⠶⠋⢰⠀⣰⣿⣿⣤⣾⣿⣿⣿⣟⣳⠈
⠀⠀⠀⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⠄⣰⠊⠀⠀⣠⠞⠀⠀⠀⠀⡆⠀⠁⠀⠙⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢡
⠀⠀⠀⢘⠈⠋⠹⢛⣿⣿⣿⣿⣿⢿⣿⣶⣯⣤⣴⡿⠁⠀⠀⠀⠀⠀⢷⣶⣶⣶⣾⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⡆
⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⡿⣳⣿⣿⣿⣿⣿⢻⠃⠀⠀⠀⠀⠀⠀⢾⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢱
⠀⠀⠀⠠⠀⢿⣿⣿⣿⡟⣿⠁⣿⣿⣿⣿⡟⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠛⠛⠛⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠸⡆
⠀⠄⠀⠘⣣⣉⣿⣿⣿⣇⢻⡄⠻⡟⠋⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡘⡻⣿⣿⣿⣿⣿⣿⣯⣤⡈⡇
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣷⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⢾⣿⣿⣿⣿⣿⣿⣷⣿

⠀⠀⠀⠀⠀⠀⢠⣶⡿⠟⠛⠻⠿⠿⢿⣶⣄⣀⣀
⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⢀⣀⣀⣀⣈⣻⣿⣍⠙⢦⣠⠞⡧
⠀⠀⠀⠀⠀⣿⡇⠀⠀⢰⡿⠛⠛⠋⠉⠉⠛⠻⢿⣷⡾⢁⣼⡃
⠀⢀⣴⣶⣾⣿⠁⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡟⠁⠹⣆⣀
⠀⣿⡟⠀⢀⣿⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠀⢀⣠⣿⠇⠙⢦⡀⠀⠹⢦⡀
⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠙⠻⠿⠷⠶⠿⠟⠛⣻⡏⠀⠀⠀⠳⣄⠀⢸⠇⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣦⣤⣀
⠀⣿⠇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠳⡾⠀⠀⠀⢠⣶⠟⠋⠉⠀⠀⠀⠀⠀⠈⢻⣷
⠀⣿⡆⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠶⢦⣄
⠀⣿⡇⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣶⠿⠿⠿⠛⠛⠛⠛⠻⣿⣇⠀⠀⢹⣧
⠀⠘⢿⣦⣴⣿⠀⠀⠀⠀⢠⣤⣤⣤⣤⠄⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⣠⣴⠶⠶⠞⠳⠶⣤⡀⠈⣿⣆⠀⣸⡏
⠀⠀⠀⠈⠈⣿⡄⠀⠀⠀⢸⣿⢹⣿⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢀⣾⣭⣴⡾⠿⠿⣧⠀⠈⣿⠀⢸⣿⣠⣿⠁
⠀⠀⠀⠀⠀⣿⣇⠀⠀⢀⣼⡿⠀⢿⣦⣤⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡟⠉⢉⡉⠀⠠⣤⣿⠀⢀⡾⠃⢸⣿⡿⠃
⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠛⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⣤⣾⡁⠀⠀⢸⣿⠶⠾⠃⣠⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣶⣿⣧⡴⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠿⠿⠿⠿⢶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠸⠇⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣿⣿⠿⠿⢶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⢀⣀⣤⣴⣶⠿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣤⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣄⣀⣀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⠶⠶⠾⠿⠿⠿⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣾⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠿⣿⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢸⣇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣿⣄⠳⡄⢠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣤⣀⡈⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇⠙⠻⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠙⠛⠻⣿⠿⠿⠿⣿⡿⠿⢿⡿⠿⠟⢿⣿⢻⣿⠋⠀⣿⠃⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠈⠻⢶⣌⣿⣶⣶⣾⣿⡿⠁⠀⣰⡟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣤⣝⣿⣷⣤⣿⣯⣤⡶⠟⠋⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⡍⠉⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣴⣏⣀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⣿⠛⠛⠋⠉⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⣀⣠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣦⣤⣤⣤⣤⣤⣤⣶⣶⡾⠁⠀⠀⠙⣿⡟⠻⠿⠿⠛⠛⢛⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣉⠉⠉⠉⠉⣉⣼⡿⠁⠀⠀⠀⠀⠈⠻⠷⣶⣶⣶⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⠄⠤⣤⢀⡴⠀⣤⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠀⡃⠘⠃⠻⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠢⢈⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠛⢄⠀⠀⠈⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⢴⡁⠀⠀⠀⠈⢺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠑⠢⡀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⠤⠄⠠⠄⡀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠰⠁⡠⠐⠢⡀⠙⡄⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢃⠀⢠⡀⣀⠄⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠈⠢⢀⣈⣁⡠⠊⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠈⠐⠠⣤⠀⠀⠤⠔⠚⠣⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡃⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣙⠳⣤⡀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠐⠤⠠⠄⠤⠄⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣭⠆⠀⠈⢩⠋⠝⣋⡛⢍⢫⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⢁⢠⠸⡘⢅⠸⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⢀⠔⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⡜⢠⣤⡄⠊⠀⡈⢆⠢⢍⣒⣒⡡⠊⠳⡀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢄⠁
⠀⠀⠀⠀⠀⠀⡜⠠⠁⠀⠀⢀⠀⠘⡌⢆⠀⠀⠉⠢⡀⠀⠈⠢⡀⠀⢀⠊⠀⠀⠀⢠⠊⠉⠑⡄⠀⠀⠈⢢
⠀⠀⠀⠀⠀⡼⠠⠁⠀⠀⠀⠑⠃⠀⠘⡌⢆⠀⠀⠀⠈⠦⡀⠀⠈⢦⡌⠀⠀⠀⠀⠐⢄⣀⡠⠃⠀⠀⠀⠀⡆
⠀⠀⠀⠀⡰⢡⠃⠀⢠⡆⠀⠀⠀⠀⠀⠘⡜⡆⠀⠀⠀⠀⠈⠢⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⡰⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⣦⠀⠀⠀⠀⠀⠈⢢⡇⠀⠀⠀⠀⠀⣀⡀⠀⢤⣄⣀⡠⠤⠿⠐⠒⠺⠄
⠀⠀⡰⢁⠂⠀⠀⠀⠀⠀⠀⡔⠉⡆⠀⠀⠀⠱⡘⣄⠀⣀⣀⡀⠤⢤⣗⠒⠦⠭⠙⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢰⢃⠂⠀⢠⢢⠀⠀⠀⠀⠈⠛⠁⠀⡠⠠⡀⠱⡘⡏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⢠⢃⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣⠴⠁⠀⠡⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⣣⣤⣭⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣍⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡀⢀⠀⣠⢀⠀⠤⢠⠀⡠⠀⠀⠀⠀⠀⡠⠂
⠀⠑⠂⡇⠉⡌⠀⠀⠞⠀⡇⢀⠀⠀⠀⠀⡑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠌⠣⠐⠀⠃⠀⠒⠀⠘⠁⠄⠀⠀⠐⠄⠁⠔⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠋⠉⠉⠙⠻⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣶⣶⠶⠶⣶⣦⡀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⢸⡿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠶⠶⠶⠶⠾⠿⠛⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠛⠛⠛⠛⠛⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⣤⣤⣤⣶⣶⠶⠆⠴⠦⠤⠶⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣟⣻⣆⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠟⠒⠂⠐⠒⠲⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣀⣀⣀⣀⠀⠀⠀⠀⢸⣧⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⡏⠉⣿⠀⠀⠀⠀⢸⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢛⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣸⡇⠀⣿⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠁⠀⠻⢶⣶⡶⠾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⢉⣓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⡇⠀⢀⡤⠂⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡇⠐⠣⣀⣘⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡉⠙⠇⡈⢻⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡴⠛⡆⣠⠁⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠀⢀⡔⣁⠤⠼⠒⠲⠤⣄
⠀⠀⠀⢀⣞⣀⣠⡇⠘⢦⣀⣠⠞⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⢰⣀⠞⠊⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⣠⠊⠉⢰⠃⠀⠀⠀⣀⠯⠂⠀⠀⠈⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⡴⠁⠀⠀⢀⡱⠖⠂⠉⠀⣀⠀⣀⡄⠀⠀⠈⢆⠀⠈⠀⡗⠂⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⡼⠳⣶⠖⠈⠀⠀⠀⣀⠔⠊⠁⠙⠳⠇⠀⣏⠛⠢⢦⠀⠀⠛⠀⠀⠐⡎
⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⣦⠐⠀⠀⠈⠣⣀⠀⠀⠀⢀⠇⠀⠀⠂⠀⢸⡎
⣀⣀⡠⢴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠳⡌⠂⢄⣀⡼⠓⠢⣀⡸⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠈⡦⡀⠀⠨⡃⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠀⠀⢠⠃⠈⠢⢄⠘⠤⣀⢀⡎⠈⠒⢄⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣿⠀⠀⡼⠀⠀⠀⠀⠑⠒⠈⠉⠀⠀⠀⠀⠈⠢⡀

⠀⢌⠸⣄⠀⠀⢀⣎⠢⠀⢄⠸⡂⡜⣃⡘⣆⠀⠀⢠⡓⠌⢳⠸⣧⠀⣠⡏⡤⠛⢧⠀⠀⣱⠶⢎⡀⠀⠰⣡⣀⣝⡄
⠠⡇⢎⣉⡇⠀⠰⠈⡁⠋⢈⠇⠉⣧⣀⠀⣇⣀⡀⠉⢻⠉⠁⠀⣧⢸⢩⡇⠑⠒⢺⢀⢴⠁⡎⠉⢱⢄⣨⠃⡖⠚⢳
⠠⡇⢀⠀⡇⠀⠀⠔⢉⡀⡁⠀⠀⠈⠑⡇⢠⢄⡸⠀⠸⣀⢆⣀⠀⠘⢾⡂⢠⡄⣸⢸⢸⠀⠈⠉⢹⢸⢸⠀⠉⠒⢻
⠀⠑⠉⠍⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⢈⡁⠀⢀⡀⠀⠀⠀⠀⢀⡤⠲⡑⠁⠉⠁⠈⢻⡀⡴⣆⡼⠘⢺⡄⢠⡄⣸
⠀⡐⡭⠲⠀⣀⠀⡀⠀⠀⠀⠀⢀⡀⠰⡅⣄⣀⣠⢟⠉⠢⡀⡀⠸⣳⡾⣿⡤⣀⠀⠀⠀⣩⠔⠚⣙⡦⠠⡻⣧⡉⠁
⠀⡀⠈⢈⠐⠚⢁⠥⠉⠰⢨⠢⠤⠃⡤⠼⢅⡲⢈⣿⠇⢀⣄⡸⡤⣎⢿⣁⣈⣉⣱⢀⣴⡝⣶⠚⠙⢣⠀⢄⡵⠇⢤
⠀⠐⢎⣊⠀⢀⠀⡀⠀⠀⠃⠀⠀⠀⠉⠣⠜⠉⠙⠒⠒⠉⠀⠀⡇⡟⠤⣭⣽⡇⠀⢸⢰⠍⠙⢖⢺⠯⢉⢿⡑⠒⠉
⢀⢶⢾⣈⣱⠘⡾⣷⢂⠔⢆⠀⠀⢠⠴⠚⠙⠓⣆⡀⠀⣠⢤⣤⣌⢳⢠⣾⣁⠃⠀⠘⠼⡆⢀⣄⢇⡆⠀⠫⣷⡀⡤
⠸⣼⠀⡀⠸⠀⠀⢽⠈⢐⠺⡄⠀⡿⢚⠭⠭⡛⢏⢹⠀⣸⣬⣤⡼⢌⠉⢀⣤⠴⡦⠀⠀⠛⠚⠈⠚⠁⡰⠂⠺⡖⠛
⠀⠘⠚⠑⠁⡠⣀⠘⠀⠀⠁⠀⠸⡕⠓⠠⣇⡼⣸⠏⢘⣲⢃⠖⠚⠫⠀⣸⡤⠰⣞⠂⠀⢀⣀⠀⠀⣠⠛⢞⠉⠙⡆
⠀⢠⣔⡊⠢⡁⠀⠀⠤⢄⠀⠀⠀⠈⣛⣶⣟⠛⠁⠀⡘⢸⠀⠓⠒⢺⠸⣁⣀⡰⢸⠢⠰⠃⠄⡅⢠⢻⠀⠈⠉⢸⠁
⠀⢸⡘⠀⠐⠁⠐⠒⢐⡀⠉⣄⡶⣦⣿⣦⣾⣤⠀⠀⡳⠼⡄⢠⡄⡸⠀⡇⠀⠀⠀⣦⣈⠦⠓⠂⠈⠺⡀⢰⢖⢸
⠀⡼⠋⠀⢘⣳⡔⠟⡝⠁⢠⠏⡇⣿⠀⠀⠀⠀⡇⠀⠑⠒⠓⠃⠓⠃⡠⠬⡧⣤⠤⠶⠃⠀⠀⠀⠀⡀⡉⠉⠀⠁
⠀⣡⣤⠄⠄⠟⠀⠒⠃⡊⢁⠀⠓⢿⠀⡴⡆⢸⠀⠀⠀⠀⢀⣄⡀⠀⡧⢠⠼⡀⠀⠀⠀⠀⠀⠀⠈⣾⢟⢦⣞⡤⢤
⠈⠁⡯⢿⠄⠀⣀⠀⢼⠇⠅⡗⠀⢈⡉⠁⠈⠁⢈⠳⡀⠀⢸⢬⡇⠘⣇⡁⠤⡜⠀⠎⠵⡀⠀⠀⠀⠀⠀⡹⠋⡨⢾
⠈⠿⢦⡘⣚⢻⠁⠄⡀⢀⡀⡗⢀⣇⣸⠤⡄⢀⡾⠤⠷⣴⠛⢰⣧⡰⡇⢨⣮⡅⡞⠁⡊⢸⡄⠀⠠⠤⢸⠃⠀⠑⠄
⠀⠀⡠⠓⠩⢍⠈⡀⠀⠁⠈⠁⠓⡞⡭⠻⡁⣯⠀⠓⠐⡞⠒⠚⢛⡔⠘⢫⣈⡀⠈⠉⠀⢸⣰⠀⣘⣃⠀⠂⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠤⠤⠤⠶⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠈⠻⢷⣶⣤⣴⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⣤⣦⣠⣤⣤⣤⣬⣭⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠉⠑⠂⠀⠀⣸
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠒⠒⠲⠶⣤⣤⣀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⢻⣿⣿⣿⣿⡟⠩⠐⠆⢻⣿⣿⠇⠀⠀⠀⠐⠛⠻⢷⣤⣄⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⣆⣴⠀⠸⣿⣿⠀⠀⠀⠀⠀⠲⠆⠀⢸⠛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⢸⣿⣿⣿⣿⡆⠸⠇⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠠⠋⠀⠈⠙⠻⢿⣿⣿⣿⡿⠠⡄⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⠆⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⣀⣠⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡟⠲⠄⠀⠀⠀⠀⠀⠀⣈⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣄⠀⠉⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠓

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⡀
⠀⠀⠀⠀⠀⣤⡄⠀⢠⣄⠀⢸⡿⠂⠀⠀⠀⠀⠀⠀⠀⣢⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⣿⢿⣄
⠀⠀⠀⠀⠀⠙⣧⡤⢞⣛⣒⣚⣷⣤⣶⠆⠀⢀⠀⠀⠠⣿⣿⣿⡿⠄⠀⠀⠀⠀⢴⣄⢀⣞⣵⣿⠟⠁
⠀⠀⠀⠸⣷⠞⣵⣾⣿⣿⣀⣹⣿⣿⣿⣦⣤⠿⠗⠀⠀⠉⠟⠛⠀⠀⠀⠀⢀⡴⠋⠙⢷⣝⠟⠁
⠀⣶⣦⣠⢏⡾⢿⣧⣾⣿⣿⣿⣧⡿⠛⢻⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠐⢦⡀⠀⣹⢷⠄
⠀⠀⠀⢸⢸⣧⣼⣿⣁⣨⣿⣋⣿⣷⣤⣼⣿⡟⠃⠀⠀⠀⠀⠀⢀⡴⢋⠀⠳⡄⠀⣠⠞⠁
⠀⠀⠻⠻⣼⣿⣏⣽⡟⢻⣿⣿⡿⢻⣿⣏⣿⠷⣶⣦⠀⠀⢀⡴⢋⡀⠈⠳⠀⣠⠞⠁
⠀⠀⣠⣤⠿⣿⣿⡟⣻⣿⡏⠀⢹⣿⣿⣿⣧⡀⠀⠀⢀⡴⠋⢤⡀⠙⠂⣠⠞⠁⢠⠤⠤⠤⠤⠤⠤⠤⢤
⠀⠀⠙⠃⠀⣼⡿⢿⣿⣿⣿⣿⣿⠿⣏⠀⠉⠀⢀⡴⢋⣄⠻⣿⣾⣿⠟⠁⠀⠀⣿⢸⡇⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠀⢀⣾⠉⠉⠿⠆⠀⠿⡷⢀⡴⢋⣴⣝⢿⣿⣿⠟⡁⠀⠀⠀⠀⠈⠛⡟⠛⠋⠉⠉⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢀⡴⣯⣴⣦⣙⣿⣿⠟⠁⡜⡉⢆⠀⠀⠀⡠⠞⠁⠈⠉⠉⠁⠙⠲⡄
⠀⠐⢦⣰⣼⣡⡄⡀⠀⠀⠀⠀⠀⠀⡟⣵⣿⣿⣿⣿⠟⠁⠀⣸⢸⠁⠸⡄⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠤⣽⢾⡿⣾⣟⢻⡅⠀⠀⠀⠀⠀⢤⣝⢿⣿⣿⠟⠁⠀⠀⠀⢯⠄⠀⢀⡇⠀⡇⠐⠀⠒⠒⠒⠒⠒⠒⠒⠂⡇
⢐⣻⣿⣿⡿⣿⣿⠲⠀⠀⠀⣀⣵⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠀⢫⡀⠀⡇⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠈⠀⠛⡟⠻⠛⠌⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⢃⣀⣀⡙⡄⡇⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⣿⣿⡇⡇⡇⢻⠀⢿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⣿⣿⡇⡇⡇⣾⠀⣾⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣼⣿⣿⡇⡇⡇⣿⣦⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⠿⠿⠿⢇⠇⢧⡙⠿⠿⠿⠿⠿⠿⠿⠟⣣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠠⠀⠭⠉⠉⠍⠩⠭⠭⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢹⣇⢰⡟⢠⡿⣷⠀⣼⠟⠛⠃⣾⠟⠛⠃⣿⠄⣿⣧⣸⡇⠀⣾⢿⡄⠛⣿⡟⠃⣿⢠⡾⠛⢻⣆⣿⣷⣄⣿
⠀⣻⣿⢀⣾⠛⢻⣧⠻⣷⣶⠆⠻⣶⣶⠆⣿⣂⣿⡈⢻⣇⣼⡟⠛⣿⡀⣿⡇⢀⣿⠈⢿⣦⣾⠃⣻⡇⢻⣿⡀
⣿⣿⠛⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠋⠉⠉⠉⠉⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠉⠉⠉⠉⠉⠉⠲⢄⡀⠀⠀⠀⠀⠀⣇⢠⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⡟⠋⠹⠬⡑⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢠⡀⢠⠀⢦⡀⢰⡄⢰⣄⠀⠀⠀⢣⠀⠀⠀⠀⠇⠀⣀⠀⠀⠀⠀⢣⠤⢤⠀⠈⡆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠦⠼⠙⠚⠈⠉⠉⠉⠉⠉⢤⡉⠉⠀⢈⠀⠀⠀⠀⣠⡀⢿⡇⣀⠤⢶⠁⠀⢸⠃⠀⢰⠀⠀⢰⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠐⠉⠁⠀⠀⠀⠀⠀⣀⠀⠁⠀⢰⡼⢄⠀⠀⠸⡀⠈⠉⠉⣀⠄⠸⠀⢰⡇⠀⠀⠘⠀⠀⢸⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢾⣄⠀⠀⢾⣧⠀⠀⠀⠀⣿⡆⢀⡠⠚⠃⢨⠀⠀⠀⠑⡄⠉⠉⢀⡠⠀⢳⠆⠀⢸⠀⢸⠀⣠⢃⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣈⡀⡗⠒⠚⣓⣊⡉⢉⣉⡉⠍⠀⢡⡰⠒⠁⠀⠀⠀⠀⠱⣈⠉⠁⢀⠴⠃⠀⢿⠈⣠⢆⡰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠤⠤⠤⡤⠤⠔⠒⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⡲⠀⣠⠚⢳⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠶⢖⣶⣖⣲⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⠟⢁⣠⠃⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⡏⠉⠈⠙⡀⡠⢖⡒⣀⡶⠴⠤⡀⠀⠀⠀⠀⡜⣨⠃⢒⠁⠞⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠖⣍⣭⣵⡀⣀⠷⣛⣩⣽⠋⠑⠢⠀⠀⡏⠑⠒⢴⡱⢁⢔⡥⠐⢦⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠐⣤⠁⠀⠈⠻⡓⢻⠁⠙⠯⠿⠖⠒⠉⠰⣅⡀⠀⣾⠔⡡⠊⠀⠀⠈⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠢⡀⠀⠀⠱⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣧⠎⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⢤⣤⡖⠘⠦⣀⠀⠀⢀⣀⡤⠤⠖⠒⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⣯⢕⣂⠀⠀⠉⠁⢙⡀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⢦⠙⠒⠒⢎⠉⠧⠄⠒⠒⠂⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

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

⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄
⠀⠀⠀⠀⠀⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣎⡲⣴⢟⢦⣂⠄⠀⠀⣀⢤⣶⠃⣶⠀⡀⠀⠀⠀⢢⣴⣶⣾⣤⠂⣀
⠀⠀⠀⠀⢰⠷⠊⠃⠀⠀⠀⠀⠀⠀⠀⣀⣱⣾⣷⠐⢀⡫⣷⣃⠀⢰⣿⣿⣿⣍⣙⣿⣅⠀⢠⢨⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠠⠼⠀⠀⠀⠀⠀⠀⢀⠀⠀⠖⣯⣿⣿⣷⣶⣶⣻⡀⠀⠸⣿⣿⣾⣝⣶⣿⡟⠀⠠⢀⠹⣿⡅⠁⠀⠈⠀⠁
⠀⠀⠀⠀⠀⡌⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠊⡝⠿⡿⠷⡛⠃⠀⠀⠀⠘⠻⠿⠿⠿⠋⠀⠀⠀⠈⢠⠋⠀⠐⡌⠂
⠀⠀⠀⠀⢠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢀⡩⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠃
⠀⠀⠀⠀⢸⣾⣷⡆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠁⠠⠂⣃⢁⡀⠁⢁
⠀⠀⠀⣤⢽⣿⣿⣯⣄⠀⠀⢐⣟⠂⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⢸⠛⣿⣿⣿⡇⠀⠠⠀⢠⡚⠡⢟⠈⠃⠀⡆
⠀⠀⠀⠀⠸⢹⣟⠇⠀⠀⠀⢀⣿⠇⠀⠀⠀⣾⡥⢿⣿⣭⡄⠀⠀⠀⠛⡶⠻⡿⠟⠃⠀⠀⠀⠀⢂⡀⠢⠖⢠⠙⠁
⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠆⣿⡄⠀⠀⠀⠸⠗⠾⠿⠟⠁⠀⠀⠀⡠⠋⠀⠹⠀⠀⠀⠀⠀⠂⠀⠄⠋⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⢸⡟⠃⠀⠀⠀⡊⣿⡆⠀⠀⠀⣂⣀⣀⣀⢀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⢸⣧⠄⠀⠀⠀⡇⣿⡅⠀⠀⠸⡟⠛⠛⠿⠿⣟⠀⠀⢠⣶⣦⣖⣾⣷⣶⠀⠀⠀⢀⣀⣦⣴⣢⣶⠀⡀
⠀⠀⠀⠀⠀⢸⡋⠆⠀⠀⠀⠏⣯⡄⠀⠀⠰⠆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠉⠀⠈⠀⠀⠠⢤⣿⣿⡿⢏⢛⣎⡁
⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⣀⣦⣿⣇⣀⠀⠀⡄⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⢒⣯⣿⢕⡡⢁⣛⡒⠂
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠙⣿⠀⠉⠀⠀⣇⣀⣀⣀⣼⣿⠀⠀⠀⣄⣀⠀⣀⣁⡀⠀⠀⠈⢉⢿⣿⣮⣥⡣⣟⠉
⠀⠀⠀⠀⠠⠟⠓⠀⠀⠀⠀⠾⠛⠦⠀⠀⠀⠋⠛⠻⠟⠛⠋⠀⠀⠀⠛⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠃⠘⠀⠁

⣶⣾⠿⣶⠶⢶⣶⡶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⠉⠙⠉⠉⠠⠦⠄⢀⣀⣀⣀⣀⣀⣀⣀⢀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠈⠉⠙⠉⠛⡀
⠀⠀⠀⠀⠀⠀⢀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠰⠧⠤⠄⣀
⠀⠀⢀⣠⡄⠒⠛⠓⠒⠒⠒⠒⠒⠂⠀⠀⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠒⠒⠒⠒⠒⠒⠂⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠑⢢
⣀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠛⠦⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣌⠳⠆⠈⠉⠉⠉⠉⠠⠾⢋⡴⢆⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠴⠖⠉⠁
⠀⠀⠀⠀⣿⠛⡟⠀⠠⠤⠤⠤⠤⢀⡴⣛⡾⠁⣀⡀⣀⠀⢀⠀⠀⠀⠀⠀⠠⠴⠶⢌⡷⡄⠚⠛⠋⠁⠈⠻⢄⣘⡷
⠀⠀⠀⡌⢿⠏⠀⠀⠀⠀⠀⠀⢀⢮⡙⠁⠀⠀⠀⠀⠀⢰⠄⠀⢴⠄⠀⠀⠀⠀⠀⠈⠳⣡⡄⠀⠀⠀⠀⠀⠀⠹⠇⣴
⠀⠀⣴⠃⠘⠀⠀⠀⠀⠀⠀⢠⡙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠋⡸⠂⠀⠀⠀⠀⠀⠀⢸⠉⡆
⠀⠀⣅⢠⡆⠀⠀⠀⠀⠀⠀⡈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣴⠀⠀⠀⠀⠀⠀⢸⠀⡘
⠀⠀⠈⠲⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠟⠁
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠻⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⢰⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⢴⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡝⠃⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠙⢾⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⠓⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣀⠀⠀⠀⠀⠙⠿⣦⣤⣀⣀⠀⠀⠀⠀⣀⣀⣠⣴⠷⠋⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢄⡀⠀⠀⠀⠈⠛⠛⢷⡾⠷⠾⠟⠛⠉⠀⠀⠀⠀⢀⣠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠂⢤⣤⡄⠀⢸⡂⠀⠀⣿⠂⢠⣤⡤⠰⡖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢹⠃⠀⠀⣟⠀⠀⠀⠀⢀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣼⡁⠀⠀⠉⠉⠉⢹⡇⠀⠀⣿⣉⡉⠉⠉⠀⠙⣧⡀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢸⠉⠳⣄⠀⠀⠀⠘⣇⠀⠀⠟⠈⢡⠀⢀⡴⠛⠋⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢀⡌⠀⠀⠈⢳⠄⢀⡜⠛⠳⠤⠀⠀⠈⠾⠯⠤⢀⣸⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣼⣧⣤⡤⠰⠛⠲⠞⠙⠲⠀⠀⠀⠀⠸⠀⠀⠀⠈⠉⠑⠒⢠⣄⠀⠀⠘⣆
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠷⠶⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠶⠆⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡦⠤⠤⠀⣾⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠈⢤⠤⠀⠀⠀⠀⢀⣀⡀⣀⣀⣀⡀⠀⡀⠀⠀⣇⣀⣀⣀⡈⠉⠿⢂⠒⠒⠀⢤⣤⣄⣀⡀⡀⢀⡀⢀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠉⣟⠉⠉⢻⠋⠹⠟⠛⢩⣽⠛⠏⣭⡅⠴⡉⢹⠖⠒⠐⡟⠈⢿⡁⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠒⠋⢉⠉⠹⢇⠿⠲⠶⢶⡄⠀⠀⣰⠴⠶⢧⣸⠇⠀⠈⠙⠆⠛⢃⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⣰⣄⣠⣾⡦⢾⣿⣦⡀⠀⠀⠀⣠⡟⢹⡟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠠⣿⡟⠛⠿⠀⠙⠁⣠⡛⠀⠱⠀⠀⠀⡛⠁⡾⢷⡄⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢿⣥⠄⠒⠒⠈⢀⣍⠉⠀⢿⠀⠀⣠⠃⢸⠀⠀⠳⡀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠲⠂⠈⠉⣹⠏⠉⢹⣿⠀⢠⡋⠀⠿⢢⡄⠀⢣⣀⡬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠶⠛⠉⠠⠷⠤⠰⠾⠛⠳⡄⠙⠾⠆⠾⠇⠀⠈⠁⠖⠁⠶⠶⠄⠀⠀⠀⠀⠠⠶⣷
⠀⠀⠀⠀⠀⠀⢰⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠
⠀⠀⠀⠀⠀⢀⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡄
⠀⠀⠀⠀⠀⡌⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠘⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢡⡀
⠀⠀⠀⠀⠀⠏⠀⠀⠱⢆⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠸⡇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠈⢃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠸
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠧⠤⡤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠤⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⡀⠐⠀⣠⣄⣠⣀⣀⣀⣀⣀⡀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠤⢞⣛⡿⢿⠿⣛⣛⣫⣿⣬⡁⣿⡏⣨⣿⣯⣛⣛⣛⠿⠿⢿⣛⠢⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡷⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢥⠶⢂⣀⣀⣀⣀⡰⠶⠬⠓⠉⠘⠫⡴⠖⣀⣀⣀⣀⣀⠶⢦⠝⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡞⠉⠀⣀⣭⣽⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⡿⠀⠀⣼⠋⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠻⣄⣀⣀⣀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁⠀⠀⠀⠀⠉⠉⠉⢿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡄⠀⠀⠀⠀⣤⡀⣀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠻⣦⡀⠀⠀⠈⣿⠻⠶⠦⠾⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠈⠙⠶⣤⣴⠏⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠶⠖⠲⠶⠶⠾⣧⣀⠀⢰⡏⠹⠶⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣶⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⢷⣀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣉⣉⠈⠉⣿⠁⠀⠀⢰⡏⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠙⣧⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⢠⡏⢸⡇⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠳⢾⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⢤⣤⣀⣀⣀⣀⣀⣀⣤⡤⣶⠟⠁⣠⠴⠾⢯⣉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⣿⠀⣸⠁⠀⠀⠀⠙⣧⠀⢹⡖⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣦⣀⡀⢀⣠⠏⠀⠈⣇⢸⡇
⠀⠀⠀⠀⣠⣴⡶⠶⠶⢦⡀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⣤⣿⠀⠀⣿⠉⠉⠉⠁⠀⠀⠀⣿⠸⡇
⠀⠀⢀⣰⡏⣿⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡏⢀⣴⠖⠛⠙⢻⣦⣤⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⢰⡏⢹⡇⠻⢦⣤⣤⠴⢿⠀⠀⠘⢷⣄⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⠃⠸⣇⠀⠀⠀⢀⡇⠉⠙⠻⠶⣤⣄⡀⠀⠀⢸⡶⠃
⠀⢸⠃⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠘⠓⠶⠖⣿⠀⠀⠀⠀⣠⡶⠟⢻⡆⠀⢸⠇
⠀⠈⠷⣼⡇⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣆⣸⡆⠀⠀⠀⠀⠀⠙⠓⠶⣄⠘⠃⠀⠀⢸⡷⠤⠞
⠀⠀⠀⢸⡇⠀⠀⣴⣾⠃⠀⣿⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡿⣷⣦⡀⠀⠳⢶⡆⠀⠀⣸⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠘⢧⣀⣰⠇⠘⠳⠶⠟⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⠀⠹⣇⠀⠀⢈⡟⠒⠺⢯⣤⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠓⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⣀⠀⠀⢀⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣰⣆⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⡿⠿⢿⣿⡿⣿⣦⡤⠀⠀⡴⣄⠀⢀⡽⣮⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣧⣀⣼⣿⣷⣿⣿⣇⠀⢀⡝⢮⡳⣏⠔⠁⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⣿⡏⠉⢹⠟⢁⠔⢁⠐⠀⠙⢮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⠖⢁⠴⡉⠢⠀⠀⢀⡴⢋⣉⣁⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⢁⠔⠁⠄⠈⠀⢀⡴⠋⢀⣾⡿⣿⣁⣹⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠣⡀⠁⠀⢀⡴⢋⠀⠀⠉⠹⣷⣾⣿⡿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢦⡀⢀⡴⠋⠀⢻⣷⡒⠀⠈⠁⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠓⠊⣉⠉⣴⣷⣤⣾⣿⡧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣸⣿⣇⣀⣸⣿⣏⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⡻⠿⣿⣿⠿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠠⣄⣼⣤⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⡾⠛⠻⡆⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠚⠓⠂
⠀⠀⢺⢿⡿⠋⠀⠀⢿⣿⣿⠗⠀⠀⠀⠁⠀⠀⠁⠀⠀⡰⠋⠀⣭⠀⠀⢠⣶⣷⡆⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠶⠶⠶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠛⢦⣀⢀⡴⣆
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣴⣶⠾⠿⠿⠛⠿⠿⣿⣷⣄⣽⠋⣰⠏
⠀⠀⣀⣀⣤⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣥⡶⠛⢲⡀
⠀⣼⣿⠋⠉⣿⠃⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢧⡀⠈⠙⢻⣀
⠀⣿⡇⠀⠀⣿⠀⠀⠀⠀⠙⣿⣶⣤⣤⣤⣤⣴⣶⣿⡟⠀⠀⠙⢦⡀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⣿⡇⠀⠀⠀⠈⠳⣄⣸⠇⠀⠀⠀⢀⣤⣶⠿⠛⠛⠛⠉⠉⠛⠻⣶⡄
⠀⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣀
⠀⣿⡇⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣴⣿⠟⠉⠛⣷⡄
⠀⢻⣧⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠋⢉⣉⣉⣀⣀⠀⠈⠉⢻⣦⠀⠀⢸⡷
⠀⠈⠛⠿⠿⣿⡇⠀⠀⠀⠀⣾⣿⣶⣶⠖⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⢁⣴⠾⣛⣩⣭⣍⠉⠛⢷⣄⠀⣿⡇⠀⣾⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⢻⣏⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣠⣾⣷⣾⠟⠋⠉⢻⣧⠀⠀⣿⠀⢹⣧⣼⡟
⠀⠀⠀⠀⠀⢻⣷⣄⣀⣠⣼⣿⠃⠈⠿⠷⠶⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⢀⡤⠀⠀⠺⣿⣇⠀⢰⠏⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣾⣇⠀⠀⢀⣿⠟⠛⠋⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠶⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠁⠀⠀⠂⠀⠀⠀⣀⡀⢀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠀⠀⠤⠤⠤⠀⠀⢀⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠩⠉⢉⣁⣀⠀⠠⢼⡯⡀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠉⠐⢄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣒⣒⡒⠒⠆⠀⠀⡜⠧⡀⠰⠀⠀⠀⠀⠀⠌⠀⠀⠁⠀⠀⠄⠀⠠⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠤⠀⠤⠭⠭⢀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠁⠀⠀⠐⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠉⠉⠉⢁⣐⡒⠢⠠⠭⣁⣺⢀⣀⠀⠀⠀⡂⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣒⣒⡒⠒⠢⠬⠍⣉⣒⠒⠼⣿⠉⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⡠⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠤⠤⠤⠭⠍⣁⣒⠂⠠⠬⢹⠿⠀⠀⠀⠀⠀⠂⠁⠂⠀⠀⠀⠐⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠉⠉⠃⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠉⠙⠒⠂⠤⢤⡨⣄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣄⠀⣠⡶⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠹⣿⡋⠀⢀⣤⡿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢋⣤⡶⢷⣄⠈⢻⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⣁⣴⠟⠙⠷⠀⣹⡇⠀⣹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⣠⡾⠋⠻⠆⢀⣠⡾⠋⣠⡾⠋⠁⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢉⣴⠟⠙⠷⠀⢀⣴⠟⢉⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣡⡾⠛⠻⠆⠀⣠⡾⠋⣡⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣾⠋⠀⣾⠛⠷⠀⢀⣴⠟⢋⣴⠾⠋
⠀⠀⠀⠀⠀⣀⣄⡀⠀⢰⣿⣷⠀⢴⣷⠄⢸⣿⣿⡿⠀⠀⠀⠀⢹⣧⡀⠙⢷⣤⡶⠟⣡⡶⠟⠁
⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠙⣿⠀⠘⡟⠀⢸⣿⠏⢰⣾⡆⢀⣶⠛⣉⣿⣦⡀⢉⣤⠾⠋
⠀⠀⠀⠀⢀⡀⠉⠙⢷⣄⣠⣼⣷⣶⣿⣶⣾⣧⣠⠟⠉⢀⡵⠛⠞⠋⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠿⢿⣦⣀⣼⣿⡿⠿⣿⣿⣏⣹⣿⣿⡿⢣⠔⠉⢀⣤⣤
⠀⢠⣤⣤⣄⠀⠀⣿⣿⣿⡀⠀⢸⣿⡟⠉⠈⠉⢠⣴⣿⡶⠿⠿⠟⠁
⠀⠘⠿⠿⠟⠻⢾⣿⣿⣿⣿⣾⣿⣿⣧⡀⠀⣀⣿⡟⢻⣿⠤⠴⢾⣿⠇
⢀⣶⣿⣶⣶⣦⣾⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣶⣆
⠈⠻⠿⢟⣋⣁⣨⣿⣿⣿⣙⣿⣿⡟⠉⢹⣿⣧⣠⣿⣿⣇⡀⠉⠛⢿⡿⠏
⠀⠀⠐⢿⠿⠋⢀⣼⠿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⠋⠈⠻⣿⣿⡆
⠀⠀⠀⢠⣾⣿⡿⠁⠀⢈⡿⠻⣿⣿⣿⡿⠿⡟⠉⠻⣦⣀⠀⠈⠉
⠀⠀⠀⠘⠛⠛⠁⢀⣴⣿⡇⣴⣇⢸⣿⡀⠀⢳⡀⠀⢻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠻⢛⣾⣿⣧⠀⢸⣿⡆⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠟