Tree frog Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣭⡉⠉⢉⣍⣉⠩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⣑⠻⡷⣠⣠⣝⠿⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢊⠄⠀⠁⢁⣵⣿⡧⠋⠀⠀⠀⠘⠛⠒⠶⣿⣂⠀⢀
⠀⠀⠀⠀⠀⠀⣾⠠⠀⠀⠀⣴⣿⢿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢢⡦⡀
⠀⠀⠀⠀⠢⠐⢇⠀⠀⠀⠐⡹⢟⠛⠷⠖⠂⠀⣠⣀⡄⠀⠀⣀⠐⢤⣀⣤⡄⠉⡀
⠀⢀⠀⠀⠀⠀⢈⠐⢠⠒⠀⠀⠀⠑⠶⡷⠶⠒⣹⡿⠀⠀⠀⠘⠓⠤⣌⡛⠛⣿⣿⡶⡂⠀⠀⠀⣀
⡆⠀⠁⠀⠀⢐⣯⠄⠁⠀⠀⠀⠀⡞⣒⠤⠤⣾⠏⢀⣀⣤⣄⣀⣀⡀⠈⣛⣷⣾⣷⣢⡁⠒⠀⠀⠀⠱
⡎⠀⠀⠀⡀⠀⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⢶⣉⡘⡛⠟⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠢
⡇⠀⠂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡟⠻⠶⣶⣦⣄⣀⠀⠈⠻⢿⣿⣿⣿⣿⣟⠀⠀⢐⡄⠀⠀⠐⠣⢀
⡇⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣤⣤⣿⣿⣿⣿⣶⣦⣈⠁⠉⠙⢻⣿⣿⡄⠀⠁⠂⠀⡄⠀⠸⣦⡀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⠉⣿⣷⢄⠀⠀⠀⠀⠀⠀⣟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⣻⣿⣿⣿⣿⣿⣿⣿⣭⣧⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⡀⢰⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠙⣫⣯⢾⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉⡰⢇⣿⣟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠹⡀⠀⣄⣸⡏⠺⠟⢿⣿⣿⠀⣿⣿⣿⣿⡖⠻⣷⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡱⡿⣄⠙⡋⣷⣶⣾⣿⣿⠋⠀⣸⣿⡟⣻⣿⣶⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣅⠻⣎⠳⣾⡜⡎⢈⢿⣿⣄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⣷⣙⣷⣸⡄⠘⠁⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠃⠀⠄⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣧⣤⡿⠋⣼⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣸⡿⠋⠀⣼⢻⡿⠁⣤⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣒⡖⠂⠤⠶⣾⡖⠚⣻⣿⡄⠀⠀⣽⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠐⠛⠛⠋⣙⣿⣿⡆⠀⢰⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⢻⣿⣿⣿⡆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡎⢐⡤⠖⠛⢿⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⡭⠌⠋⠁⠀⠀⠀⡟⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠋⠀⠀⠀⠀⠀⠀⣸⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣃⣴⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣖⣲⣶⡶⠶⡒⠦⠤⠤⢤⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢉⡀⠀⢶⣶⣾⣿⣿⣯⣷⡶⣿⡖⡃⣠⣤⡀⠀⠐⣿⣾⣇⠀⠳⠤⡀⠀⠀⣀⣀⣼⣷⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠀⠆⠉⠛⢿⠿⣯⣙⡡⠿⣆⣀⠋⠙⠛⠉⠻⠃⣿⣯⠀⣀⠀⢰⣦⢀⣼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⠀⡴⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠠⠁⠹⣿⣏⠀⠀⢨⣿⣿⣿⣉⠘⣧⣍⠹⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠃⠀⠀⠀⠀⡀⠀⢀⣀⠤⠤⠂⠐⠀⠀⠀⠠⠀⠀⠀⠘⠋⠋⠀⢀⣾⣿⣿⣿⢿⣿⢁⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡀⠀⠀⠀⠠⠄⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⡀⠀⠀⠚⠛⣛⣋⣴⢾⣧⡾⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢶⣶⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣟⡿⣟⡿⠟⡏⣿⣿⣼⠏⠀⠀⠂⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢷⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣅⢻⣿⣾⣻⣿⣿⠟⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡭⠭⣤⣀⣀⣠⣾⣿⣿⣿⣿⣿⡎⠻⣿⣿⣿⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⢀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣙⣿⡿⠋⠀⠀⢠⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣶⠀⠃⠀⣻⢿⠏⠋⠝⡋⢻⢿⣿⣿⣿⠆⠀⠀⢸⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣠⣤⣤⣶⣾⣿⣷⣥⠙⢦⣼⣧⣿⡧⣄⡀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠸⠃⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡟⠀⣾⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣷⣮⣿⣿⣿⣿⣿⣥⠀⠀⠀⠃⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠂⠐⣖⡈⠛⢿⡿⣯⠙⠿⠿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡷⣶⣬⠟⠋⢰⣧⣙⠳⣦⣤⣀⣀⣠⣄⣈⣙⣿⣿⣿⣿⣿⣧⣠⢀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠓⣌⠛⡄⢠⣀⡶⢉⣷⠊⠁⠈⠉⠙⠙⠛⠋⠛⢻⡿⠋⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⠿⠫⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⣋⣿⡿⠋
⠀⠀⠀⠀⠀⠀⡈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣤⣤⡙⣿⣶⣄⠀⠀⠀⠀⢠⣾⣿⡟⢁⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⢁⣿⣿⣿⣷⣶⣶⣾⣿⣿⡿⣧⠈⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣴⠿⠁⠉⢉⠅⠉⢹⣏⠁⣽⣿⣽⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠘⠓⠀⣈⣀⢀⣀⣉⣀⣛⣛⣩⣭⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠿⠿⠿⠛⠛⢋⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⡀⠀⢀⠀⠐⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⣴⠀⠈⠉⠁⠁⠂⡀⠀⠈⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣀⠀⣀⣤⣴⣧⣀⠀⠀⠀⠀⠀⢙⣄⠀⠐⣫⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⠀⠻⠷⠙⠙⢈⣙⡲⠶⠀⣈⠉⠛⠷⡄⠀⢻⣻⢶⣦⣄⡀⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠋⣛⣻⣧⠀⠄⠒⠀⠉⠀⠀⠀⠀⠀⠉⠑⠂⠰⣦⢷⠟⠸⠹⠾⠉⠉⠻⢿⡇
⠀⠀⠀⠀⠀⠀⢐⣒⠁⠣⠤⠒⠉⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡌⠟⠈⠀⠀⠀⠁⠸⣦⠀⠴⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠘⢋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⠀⠀⡀⠀⣿⣿⣿⣿⣿⡇⠀⡀⠀⢰⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢦⣸⣄⡜⠁⠀⣾⣿⣿⣿⣿⡆⠀⠙⣄⣼⣠⠎⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣟⠀⣀⣼⣿⣿⣿⣿⣿⣿⣄⡀⢘⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⢲⢠⣶⣶⣤⣀⣿⣿⣿⣿⣿⣿⣿⣇⣠⣴⣶⣦⢰⠃⢀⡴⠂
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⣳⣾⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⣶⡋⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⡽⠟⠿⣶⣿⣿⣿⡙⠿⢿⣿⣿⠿⠟⣻⣿⣿⣷⡾⠟⠿⣍⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡭⠉⠉⢭⢩⠝⠁
⠀⠀⠀⠀⠀⠀⢀⠐⠀⠂⠀⠀⠀⠈
⠀⠀⠀⠀⢀⡔⠐
⠀⠀⠀⠐⠠⡉⠀⠀⡀⠄
⠀⢄⠀⠀⠀⡀⠀⢠⡾⠁⠀⠀⡀
⡇⠀⠀⠀⢨⡷⠀⠚⡁⠀⠀⠀⠈⠁⠂⠤⠀⢀
⡇⠀⢀⠐⡋⠀⠐⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠀⠐⠒⠂⠦⠤⠄⣀⡀
⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⠠⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠘⠀⠦⢀
⠁⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠻⠿⠿⠿⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣦⣤⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣾⠛⠛⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⢀⠀⠀⠀⠄⣤⠿⠻⣟⣿⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢀⣠⣼⣀
⠀⠀⠀⠀⠀⠀⡀⠐⠀⢀⣀⡀⠚⣿⣷⣿⢶⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠈⠈⡉⢛⣥⡆⠜⠁⠀⢈⣉⠈⠉⠉⠁⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⢦⡼⠋⣷⣼⠗⠦⣄⡀⠙⠂⠀⣄⠀⠀⠀⠀⠀⣰⡿⠿⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠓
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢹⠖⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⠀⠶⠏⠛⠁⠀⠀⠀⠀⢀⣀⣤⠴⠒⠋⠁⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⡀⣼⠟⠛⠒⠂⠀⠉⡀⠀⢀⣴⠖⠀⠀⠀⣀⠴⠖⠚⠉⡉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣽⡇⠀⠀⠀⠀⠀⠡⣠⡶⣤⠤⠖⠛⣠⠞⠁⠀⢀⣀⡠⠅⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠁⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡶⢦⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣯⣁⠪⡲⣶⣤⣀⠠⣴⣿⣧⣼⡇⢘⣿⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢸⣩⣿⣿⣆⣧⠙⢹⡙⣛⡛⠛⠈⣿⣶⣜⡿⠀⢀⣐⣴⡟⠁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢠⣸⣿⣿⣿⣿⠏⠤⠶⠉⠀⢨⢻⣿⣽⣿⡏⢀⣴⣴⣯⡟⢁⣤⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣻⡛⠻⠥⠘⠀⠐⠁⠴⠐⠛⢿⡏⢉⣸⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⢤⣒⣤⣴⢶⡶⢷⣾⡿⢹⣿⣿⣿⣿⣿⣷⣦⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⡀⠀⣠⠀⠀⡀⠶⠯⠷⠶⣶⣶⠶⠿⠿⠿⠛⠋⠁⠈⣠⣾⣿⣿⣦⠙⢿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⢻⣄⣠⡞⠀⠀⠁⣶⢀⡀⠒⠀⠀⢀⣦⣶⣾⠟⠁⠀⣷⣿⡻⣿⣿⣿⣷⣤⣍⢻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣬⡿⠛⣻⠧⢤⣤⣼⡿⣿⡇⠀⠀⣠⠶⠛⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣏⣙⣿⣿⣿⣿⣿⣿⣷⣮⣴
⠀⠀⠀⠀⠀⠀⠀⠀⡺⡟⣹⣴⣾⣧⡄⢸⡿⢛⡿⡣⢁⣴⣟⡍⠀⠀⢀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣏⣼⣹⣿⣿⣿⣿⡿⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡷⢻⣶⣏⣡⡀⣸⣿⣿⣷⢖⣴⣾⣿⣿⣿⣿⣿⡿⠟⣛⣩⣶⣿⣿⡛⠋⠙⠉⠩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⡁⠀⢻⣻⣿⣿⣿⣿⣽⣫⣶⣿⣿⣿⠿⠟⢛⣩⣵⣶⠿⠿⠿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢈⡢⠈⢙⠻⣿⣯⠀⠀⠁⠀⠀⠀⢠⣶⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣷⣦⣄⠲⣍⡳⢬⡛⢧⡀⡀⠀⠀⣈⠹⣿⣿⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣦⣀⠀⠝⢶⣍⡿⣦⣴⢏⣰⣿⣷⣶⣤⣬⣙⡓⠶⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠿⢛⣷⣦⣉⡻⢻⣶⣌⠛⣿⣷⣶⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⡀⠀⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡶⣭⣙⡳⣝⠿⣧⣍⡛⢿⣿⣻⠿⢿⢿⡿⢿⠛⠿⠄⠷⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⠉⠀⠀⢻⣿⠀⣿⣿⣿⣷⣦⣿⣿⣿⣷⣦⣽⠛⢶⣜⠀⠀⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⣿⣿⢿⣿⣇⠹⢿⡁⠀⠙⠛⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠈⠈⠳⡙⢿⡟⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢉⡉⠉⠉⣉⡍⣉⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢊⡘⠉⠀⠀⠀⢔⠆⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⡀⠀⠁⠀⢀⠀⡁
⠀⠀⠀⠀⠀⠀⢴⠃⠈⠁⠀⠀⡀⢀⠔⠁
⠀⠀⠀⠀⠠⢀⣜⠉⠀⠀⠂⢈⠔⠁
⠀⠀⠠⠀⠐⠀⠈⢁⢠⠑⣨⡴⠂
⡄⢈⠂⠀⠀⠀⢼⠦⠑⢀⣿⠀⠀⠀⠀⠈⢢⣀
⡝⠀⠀⠀⠄⢀⡾⠋⠉⠀⠠⡄⠀⠀⠀⠀⠀⠂⠈⠙⠂⠒⠠⣄⣀
⡇⠀⠔⢀⠆⡏⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠐⠀⠀⠀⠀⠉⠓⠒⠒⠶⠤⠤⢄⣀⡀
⡇⡠⠔⠁⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡀⠀⠀⠈⠈⠲⠂⢄
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣄⡀⠉⠛⠛⠛⢋⡼⠁⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⣦⢄⠀⠉⠐⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⠻⠿⠶⠦⢤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⣟⢿⢦⣄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣀⡀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠻⡋⠈⠙⣦⣿⣋⢲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⠒⠒⠓⠦⠤⡀
⠀⠀⠀⢀⠠⠀⠀⠀⡀⠀⠁⠀⣀⣤⣀⡀⣛⣛⣻⣿⡿⢽⣷⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠘⠒⠛⠛⠛⣠⡖⢠⡟⠁⠀⠀⠉⠉⠀⠉⠉⠈⠁⠀⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠤⠃
⠀⠀⠀⠀⡄⠈⡶⠿⣏⣙⣶⣬⣄⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⡤⢾⣁
⠀⠀⠀⠀⠙⠛⠁⠀⠿⠟⠋⠀⠉⠳⢶⣄⣀⡀⠀⠈⠟⠁⠀⠀⠀⠀⢀⣼⠟⠋⠉⠛⢠⣤⣤⣀⠀⠀⠤⠄⠐⠒⠃⠀⠀⠀⠀⢀⣀⡤⠶⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠟⠉⣀⠀⠀⠀⠀⠄⠐⣀⡴⠏⠁⠀⠀⠀⠙⠛⠀⠉⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⠛⠉⠁⠀⠀⠀⠀⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⢀⢀⣾⡿⠛⠛⠒⠊⠀⠈⠁⡀⠀⠰⣀⣴⠶⠀⠀⠀⠀⠀⣠⡴⠖⠚⠋⠉⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⡋⣾⠋⠀⠀⠀⠀⠀⠀⡔⠉⠀⢰⣀⣉⣀⣤⡴⠖⢀⡤⠞⠁⠄⠀⠀⠀⢘⡃⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠒⠄⣀⠀⠀⠀⠀⠀⠈⠋⠉⠹⠯⠀⠰⣤⠴⠋⠀⠀⠀⠐⠰⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡀⢀⢤⣄⡀⣠⣴⣆⡞⢹⡆⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸⣽⣿⣦⡎⢹⡝⢟⣛⣩⣷⣼⠇⠀⣤⣾⠁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⢿⣿⣟⠕⠋⠄⡀⣽⣿⠿⢣⣴⣿⣿⣥⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠉⠀⠁⢀⣄⣤⣤⡶⣿⣾⢻⣿⣿⣿⣿⣅⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣠⠀⠀⠛⠛⡓⠶⠟⠛⣛⣋⠉⢀⣴⣿⣿⣧⡙⢿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢠⣑⣿⢶⡇⣀⣠⣿⣶⠀⠀⣠⠿⠛⠃⠀⣸⣿⣿⣿⡟⢿⣷⣾⣿⣿⣄⣄
⠀⠀⠀⠀⠀⠀⣾⣫⣴⣾⡄⣹⢟⡿⠍⣴⣿⠁⠀⣠⣤⣶⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⠟⠛
⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠛⣿⣯⣴⣴⣿⢿⣫⣾⣿⣿⣿⢿⣛⣭⣶⣿⠿⠋⠁⠁⠐
⠀⠀⠀⠀⠀⠀⠀⢹⣏⠘⠄⠛⢿⣿⡋⠉⠋⠉⠉⣩⣴⣾⡏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣤⡢⠕⠨⡳⢄⡀⠀⡄⢻⡿⠯⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡶⣄⡸⢷⣽⡚⢷⣿⣛⣿⣶⣶⣬⣭⣂⣀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣬⣟⣦⡿⣯⣝⠿⣿⣿⠿⢿⠿⠿⠧⠰⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠈⡿⢸⣿⣿⣷⡿⣿⡿⠷⣿⣹⣦⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠝⢷⣮⣷⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣽⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⡄⠛⠀⠀⠀⢺⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣧⠴⣷⣷⠈⠂⠀⠀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢠⡶⠚⠃⠘⣡⣴⢶⠶⣬⢡⣄⣀⣤⣤⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠃⠀⠉⠁⠀⠀⣼⣷⣿⣿⣿⣿⣶⠧⠖⠛⠁⠀⠀⠀⡸⠓⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢹⡆
⠀⠀⠀⠀⠀⠀⢠⡞⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠻⠁⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡈⣷
⠀⠀⠀⠀⠀⢀⣚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠋⠙⠃⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⢀⣴⡻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠻⠀⠀⠀⠀⠀⠀⠀⣠⠴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚
⠀⠀⠀⠞⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠐⡗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠐⠀⠉⠁
⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡊⠁
⢀⠀⢳⠀⠀⠋⠶⢠⣄⣠⠴⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠁
⠀⠱⣄⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠁
⠀⠀⠈⠛⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⣷⣦⣤⣀⣀⠀⠀⢀⣀⣠⣞⣠⣤⣄⡀⢀⣀⣀⣀⣘⡁⢰⠴⠂
⠀⠀⠀⠀⡍⠙⠳⠦⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣠⠴⠯⠵⠊⠩⠉⢙⣛⣿⠿⠛⠿⠿⠷⠿⢦⣧⣤⡙⢀⢌⣭⡽⠛⠋⠁
⠀⠀⠀⠀⢻⣆⣤⡄⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⠿⣿⣥⣶⠶⢤⡴⢶⠖⠒⠾⠤⠇⠀⠀⠀⢀⣀⣠⠶⠛⠛⠉⠚⠯⠇
⠀⠀⠀⠀⠀⠙⠿⢿⢧⣾⣾⣿⣦⡀⢀⣼⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠉⠉⠁
⠀⠀⠀⡀⠀⠀⠀⠘⠻⠶⠶⣶⡶⠷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⡴⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⣀⣀⣤⣶⣷⣾⣻⣯⣙⠈⠉⠉⠙⢢⣶⣦⠀⢠⡀⠀⠀⠀⠀⢀⣦⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣷⠀⡜⠻⠿⣿⣿⡻⢋⣿⡀⡸⠻⠷⠒⢴⢻⣿⡂⠀⠀⢠⡀⠀⣶⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠁⡠⠀⠀⠀⠀⠈⠉⠁⠀⠁⠙⠀⠀⠀⠠⠀⢻⣶⠉⠀⢸⣿⣿⣟⠩⣯⣙⠲
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡋⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⠀⠀⠀⠠⠀⠀⠀⡘⠙⠀⢀⣾⣿⣿⡿⣿⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣀⣀⣀⣈⣛⡭⣵⡞⣿⠞⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢛⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢻⣿⣋⣇⣿⣷⠏⠀⠀⠁⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣶⣶⣖⠀⠀⠀⣠⣾⣿⣿⣿⣼⢿⣿⣾⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⠉⠁⠘⣾⣿⣿⣿⣿⣿⣿⣤⢻⣿⡷⠆⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢷⡄⠳⠈⣻⢿⠟⠋⠟⠻⢿⣿⣿⣧⠀⠀⠸⠄⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣠⣤⡴⢾⣿⣯⣌⠳⣼⣯⣿⣦⣀⠀⢺⣿⣿⣿⣧⠀⠀⠸⠃⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠻⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡄⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠻⣤⡉⢻⠻⣦⡛⠉⠋⠉⠉⠻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡛⢿⡁⠀⠙⡓⢬⡛⠟⠲⠶⠶⢶⡶⢾⣿⣿⠗⠛⠲⠦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⠟⠁⠈⠂⠁⠈⠻⡥⡛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠩⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠤⠭⠉⠉⣭⡭⠋
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢰⠀⠁⠀⠀⠠⠂
⠀⠀⠀⠀⠢⢀⠀⠡
⡄⠀⠀⠀⣴⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄
⡇⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣿⣿⣷⡶⡖⣠⣾⣿⣿⣿⣷⣾⣦⡄
⡇⠠⠂⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣋⣁⣉⣉⡉⢉⣙⣛⢻⡭⠴⠞⠛⠿⠛⣻⢍⣡⣾⣿⣿
⠃⠀⠀⠀⠀⠀⠀⢠⣤⢝⢁⠼⠾⠿⡉⠻⠿⠿⠿⠟⢁⣀⣀⣴⠅⠀⠀⣠⣷⣿⡏⣜⣵⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣠⠀⣽⣵⢣⡾⠟⣫⣤⣭⣭⣥⣤⣶⣾⡿⠿⠛⠋⢀⣴⣾⣿⠏⢁⣶⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⢀⣾⣿⠆⣴⣶⣷⣤⠀⢿⡿⠛⠉⠁⠀⢁⣀⣤⢂⢀⣴⣿⡿⠛⣫⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⣠⣿⣿⣿⡇⢯⣀⣤⣽⣷⡀⠀⠀⠀⠔⣚⠋⠀⠀⢨⡿⠟⠡⢀⣰⣗⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⣰⣿⣿⣿⣿⣿⡈⢿⣿⠾⢻⡿⠀⣀⠀⠈⠀⠀⠠⣄⠿⠀⠀⣠⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⣿⣿⣿⣿⣿⣿⣷⡀⠳⠈⠙⢿⡇⢹⣷⣿⣧⣶⣶⣷⡇⣀⠀⠿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⢹⣿⣿⣿⣿⣿⣿⣿⣦⢰⣦⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣮⣶⣧⣮⡹⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⢿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠒⣒⣻⡈⡄⡀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣾⡯⠷⠞⠻⢿⣯⠀⠀⠀⠀⠀⠀⠉⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢒⣶⠟⠉⠀⠋⡴⢶⣒⡖⣲⡄⢤⣤⣄⣴⣶⡄⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⠟⠁⠀⠘⠁⠀⠀⠀⣾⣶⣿⣿⣿⣿⣿⣼⠥⠶⠛⠉⠀⠀⠀⠀⣸⠋⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠛⠠⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⣣⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡘⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⡿⠏⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⠁⠹⣇
⠀⠀⠀⠀⠀⠀⠀⣰⣷⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣇⣥⠀⠀⠀⠀⠀⠀⠐⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠠⢿⡄
⠀⠀⠀⠀⠀⢀⣴⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠈⠀⠀⠀⠀⠀⠀⢀⣿⠄⠀⠀⠀⠀⠀⠠⠁⠀⠂⠀⠀⠀⠀⠀⢼⠃
⠀⠀⠀⠀⣠⣾⠿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠙⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝
⠀⠀⠀⠰⠻⠏⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠀⠀⠀⠀⠀⠀⠀⠘⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁
⠀⠀⣀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠤⠀⠀⠉
⠀⢠⠉⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⡁
⠀⠀⢰⡀⠀⠙⠦⣀⠀⠀⠀⠀⣀⣀⡤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠈⠁
⠘⢆⠈⢃⠀⠀⠀⠀⠙⠛⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠀⠠
⠀⠈⠳⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠐⠀⠐⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⢾⣿⣿⣶⣤⣀⣀⣀⣀⣀⣀⣀⣼⣧⣴⣴⣦⣤⢀⣤⣀⣀⣀⣈⣅⣙⡷⠒⠁
⠀⠀⠀⠀⢨⡀⠉⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⣀⡤⠾⠥⠶⠊⠠⠉⢉⣛⣛⣻⠟⠛⠿⠿⠳⠶⠿⣶⣷⣤⡈⠓⢠⢨⣥⡼⠛⠉⠁
⠀⠀⠀⠀⠘⣷⡤⣤⡀⠀⠀⠀⠂⠀⠀⠀⠀⠈⣿⠛⠿⠿⢿⣭⣴⣦⣶⣤⣴⣶⡶⠶⠶⢧⣨⠇⠀⠀⠀⠀⠀⠀⢠⡤⠽⠛⠛⠓⠿⣯⡅
⠀⠀⠀⠀⠀⠈⠿⣿⣿⣶⣠⣣⣦⣶⣄⠀⠀⢀⣿⡶⠖⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⡐⠓⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣝⣋⣉⣉⣙⣣⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠲⠚⠉⠁
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠔⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⡉⡉⠉⠒⢄
⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠖⠉⣁⣈⡑⢆⠈⡆
⠀⠀⠀⢠⣾⡟⠻⠀⠀⢄⠀⠀⠀⠀⢀⣀⠞⢀⠇⢠⣾⣿⠿⠻⣾⠆⢸
⠀⠀⢂⠸⣿⣷⡾⠀⠀⠀⠙⠈⠉⠁⠐⠁⠀⠸⡄⢿⣿⡟⣦⣤⡿⠁⣼
⠀⡠⠔⢋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⣿⣿⡿⠟⠁⠀⡇
⣎⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠶⣄⠀⢇
⠈⠫⢐⡂⠤⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠔⠒⠁⠀⠀⠀⠈⢆
⠀⠀⠀⠈⠙⢒⠒⠂⠀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢤⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⡳⣄
⠀⠀⠀⠀⠀⠀⠈⠢⠀⠜⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠠⠀⠂⠀⠆⡀⠀⠀⡀⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠰⠤⡌⠀⡀⠁⠠⢘⠀⠘⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠈⢢⡀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠘⠀⡇⢸⠰⠁⠑⠊⠀⠀⡸⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠙⣄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⡇⠀⠀⣀⠔⠊⢀⡴⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⣆⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠉⢀⣠⠞⠁⠀⠀⠈⢓⣤⣀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢸⠂⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⠖⠋⢀⠀⠄⠀⡂⠭⢀⠖⡌⠙⠒⡲⠖⠉⠀⠀⢀⣴⡋⠀⠀⠀⠀⠀⠀⠀⢀⠈⠑⢤⡀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠉⠀⠀⢄⠀⢰⠉⠁⡀⡠⡡⢂⡴⠚⠉⠀⢀⣠⠴⠚⠉⠀⢈⠩⡄⢀⡀⠀⠠⣀⠀⠀⠀⠂⠹⢆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠑⠋⠀⢠⡤⠀⠒⠁⠀⣠⠴⢚⠭⠀⡀⢀⠠⠂⠁⡰⡡⠋⠁⠰⠉⠉⠓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢈⣀⡀⠤⠤⠤⠀⢀⠀⣼⠁⠀⠸⡀⠀⠰⠁⠀⠀⡐⡰⠁⠀⠀⢰⠀⠀⠀⠀⠀⠈⠑⠲⢤⣄⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢀⠀⢪⠀⠀⠡⡹⡀⠀⠀⠉⠒⠚⢰⠂⠈⠐⣅⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⢁⠔⠁⠀⠀⠀⠱⡙⠤⢄⠀⠀⠀⠀⠓⠤⣤⠜⠀⠀⡠⠃⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢈⡆⠀⠀⠀⠀⠀⡝⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠴⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣤⣤⣤⣤⣤⣤⣼⣶⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣄⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⣉⣉⠁⠢⡀
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠎⣁⣤⣤⣝⡄⢡
⠀⠀⠀⣿⣧⣴⠀⠀⠠⠠⠄⠐⠖⠁⢸⢰⣿⣿⡁⣹⡇⢸
⠀⡀⠔⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣿⣷⡿⠟⠀⠈
⣎⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠶⠀⢠
⠈⠃⠥⣐⣂⠀⠀⠤⠤⠤⠤⠤⠤⠄⠠⠐⠒⠉⠀⠀⠀⠀⢢⡀
⠀⠀⠀⠀⠁⠠⢉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠂⠤⢄⡀
⠀⠀⠀⠀⠀⢀⠀⢉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠑⢄
⠀⠀⠀⠀⠀⠐⠄⠠⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠈⠉⠓⠤⡀
⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠠⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠈⠒⢂⢠⢠⢀⠠⣀⠄⠈⢣⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⠢⡀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠈⠘⠘⡄⠀⠀⢀⠄⠊⣱⣄⠀⠀⠀⠀⠀⠀⠈⢂⠀⠙⡄⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠐⠀⠀⠈⠐⠊⣀⠔⠋⠀⠈⠳⣤⡀⠀⠀⠀⢀⠜⠀⠀⢸⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⢢⣀⢀⣠⠴⠊⠁⠀⠀⠀⠈⠀⠂⡌⣛⡲⠒⠁⠀⣀⡴⣋⡀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢄⡨⠀⠀⠐⢁⠡⠋⠁⣀⠤⠖⠋⠁⢀⠀⢐⢂⠄⢀⠤⢤⣀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⣈⡀⠀⠀⡴⠋⠱⡈⠀⠠⠊⠀⠠⡢⠃⠀⢈⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠁⠀⠀⡠⠂⢀⢣⠀⠀⠑⠤⠊⡔⠐⠱⡁⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠊⠀⠀⠀⠣⡡⠤⡀⠀⠀⠘⠢⠤⠆⠀⢠⠃⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣀⡼⠀⠀⠀⠀⠀⣅⣠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠁
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡦⢹⣿⣦⣀⣀⣀⣀⣼⣿⣿⠡⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⣀⡾⠾⠿⠿⣿⢿⡿⠿⣿⡿⣧⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠏⣥⠀⠀⠃⠀⠘⠧⠤⠿⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⢶⣶⣶⣶⣶⡶⠶⢿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢠⠀⠈⠛⠃⠂⠄⠀⠀⠹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡀⢀⣀⣤⣼⢄⠀⠀⠀⠀⠀⣡⡀⠀⢺⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣶⠈⠿⠎⠉⢁⣉⠲⠶⠀⣈⡉⠻⢦⠀⠘⣿⣖⣦⣄⣰⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⣉⡉⢿⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠑⣀⢳⡼⠞⠙⠛⠛⠁⠉⠛⡿
⠀⠀⠀⠀⠀⠀⣬⠁⠐⠖⠉⠁⠀⠀⠛⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣶⠘⠃⠀⠀⠀⠀⠘⠷⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠟⠂⢀⡀⠀⠀⠉⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⡇⠀⣰⠀⠀⣿⣿⣿⣿⣿⣟⠀⠀⣆⠀⢸⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣸⣶⣿⡶⠁⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⠈⢶⣿⣶⣇⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣇⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣸⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣄⠀⢸⡀⣶⣷⣶⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣁⣤⣶⣾⣶⢀⡇⠀⣠⠛
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⢳⣾⣇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣸⣷⡞⠁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣹⠿⠿⣷⣾⣿⣿⣯⠻⢿⣿⣿⣿⣿⡿⠟⣽⣿⣿⣷⣾⠿⠿⣏⡉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠉⠙⠛⠿⠃⠀⠀⠈⠉⠀⠀⠘⠿⠛⠋⠉⠀⠀⠀⠀⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠒⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⣤⣤⣰⣤⣄⡀⠀⠀⠀⢀⠀⠀⠄⠠⠀⢻⣆
⠀⠀⠀⠀⢀⡀⢲⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠶⣤⣄⣴⣋⡥⣄⣀⠙⡿⠀⠀⠀⣨⣿⣶⣤⣿⣀⣨⡟
⠀⠀⠀⠀⠀⠙⢶⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣧⡓⠚⢉⣭⣷⡇⣀⣴⠾⠛⠋⠉⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠾⠷⠖⠒⠚⠿⠿⠟⠿⠿⣶⣶⣦⣶⣿⡽⣭⣶⣶⠿⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣷⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢬⠤⢿⠶⠛⠓⠲⢦⣄⣀⡀⠀⢀⣴⣿⠟⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠄⠀⠀⠀⠉⠻⢿⣸⡿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡭⠉⠉⣭⣭⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠐
⠀⠀⠀⠀⢀⡔⠑⠈⠀⠀⠊
⠀⠀⠀⠐⠠⡁⠀⡀⢂⠄
⠀⠐⠀⠀⠀⡀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⡇⠀⠀⠀⢘⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣄⣀⣀⡀⢀⣼⣿⣧⣤⣄⣤⣀
⡇⠠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢾⠿⣿⣿⠿⢿⣿⣿⠿⠛⢍⣴⣿⣿⣿⣿⠿⡟⣿⣻⣧⡀
⡇⠀⠁⠀⠀⠀⠀⠀⠀⣀⣀⡤⢺⣍⣤⣦⣤⣴⣶⣄⣤⣤⡤⠸⠒⠛⡩⠈⠉⠉⢩⣞⣤⣾⢻⡿⣿⣅⡀
⠁⠀⠀⠀⠀⠀⠀⢀⣴⠖⡡⢠⢚⡛⠛⣥⣈⣛⠛⠛⠛⢉⣠⣤⣦⣶⠇⠀⠀⣠⣾⣿⡿⠃⣮⣼⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⣠⡆⠠⠽⢞⣰⡟⠛⣩⣶⣶⣶⣶⣶⣶⣿⡿⠿⠛⠋⠉⢀⣴⣾⣿⡿⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⢀⣴⣿⣿⢠⣶⢾⣷⣦⠀⠻⡿⠛⠉⠀⠀⠀⣀⣤⡤⢂⣀⣤⣿⡿⠟⢋⣰⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣾⣿⣿⣿⡈⣅⣀⣤⣽⣷⣄⠀⠀⠀⠠⠂⣙⠁⠄⠀⢊⣿⠟⠩⠀⣀⣾⡟⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⣿⣿⣿⣷⠸⣿⣿⡾⢿⣿⠆⡀⠀⠀⠁⠀⠀⢠⣄⠿⠀⠀⢀⣴⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⣿⣿⣿⣿⣿⣿⣿⣇⠘⢦⠒⠺⣿⣦⢸⣿⣾⣿⣤⣤⣶⣿⡆⠀⠀⢾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣄⢠⣄⠈⢁⣸⣿⣿⣿⣿⣿⣿⣿⣷⣜⣡⣶⣨⡛⡏⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣬⣿⢿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⡿⢿⡿⣿⣿⡿⣿⠿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁

⠀⠀⠀⠀⠂⡀
⠀⠀⠚⠛⠛⠓⠒⠒⠒⠚⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠚⠓⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣦⢘⣿⣿⣦⡀⠀⠀⠀⠀⣴⢿⣣⣿⠁⣤⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠀⣸⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣆⠈⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣾⠏⠈⠁⠈⠀⠈⠉⣺⡉⠠⣸⣟⣥⣿⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠲⠄⠀⠀⠀⠀⠀⠈⠁⠂⠛⠛⠛⣛⣛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠶⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⠿⠿⢿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣴⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⠀⠠⣤⡤⢀⠀⠄⠀⠀⠙⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠉⠂⡀⠀⠀⠈⢿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡄⠀⣀⡤⣴⢾⡣⡀⠀⠀⠀⠀⠀⠀⢉⣆⡀⠀⠉⣍⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⡦⠀⢻⣷⠜⠋⠃⠈⠑⠲⣶⠖⡒⠊⠉⠟⣵⢀⠀⠀⣿⢻⡶⣤⣄⡀⢰⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠻⠻⠟⣿⡆⠀⠀⠠⠔⠒⠊⠉⠁⠀⠀⠈⠉⠓⠲⡤⠉⣤⡰⣌⣿⢰⣏⣟⡟⠚⠛⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢠⠀⣀⣠⠤⠖⠊⠙⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢶⣌⠿⠈⠁⠀⠂⠀⣥⡀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠨⠶⠀⠀⠘⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠤⡄⣤⡄⠀⠀⠀⠀⠀⢠⡼⠗⠈⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠸⠟⠀⠀⡀⠀⠀⠀⠉⢠⣤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣭⡍⠉⣭⣭⡩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠨⠍⢿⣤⠴⡝⠃⠀⢀⣠⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠄⠄⠀⠀⣠⣾⡿⠏⠀⠀⠀⠀⠉⠉⠙⠛⢤⡐
⠀⠀⠀⢀⠀⡝⠂⠀⠠⠸⡿⢯⣥⣠⠄⠀⠀⠀⠀⠀⠀⣀⠀⠈⠋⠆
⠀⠀⠄⠀⠀⠘⠢⠀⠄⠀⠀⠠⣬⣤⡤⠘⣿⠇⠀⠈⠳⢄⣙⠻⠷⣶⣦⡤
⡄⠁⠀⠀⠀⣎⡄⠃⠀⠀⠀⡴⢒⠤⢤⡾⠃⣀⣠⣄⣀⠀⠈⢓⣦⣿⣷⣌⠰⠀⠀⠈⠢
⡏⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠈⠁⠀⢮⣑⣛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣇
⡇⢀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣙⠛⠲⣶⣤⣄⡀⠙⠻⡿⣿⣿⣿⣄⠀⠠⡀⠀⠀⠉⢠⡀
⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣿⣿⣿⣿⣿⣦⣄⠀⠈⢻⣿⣇⠀⠀⠈⠐⠀⠀⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣷⣖⠂⢸⣿⡕⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣇⠀⠀⠀⢀⢠⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣟⡽⢿⣿⣿⣿⣿⣿⣿⡆⠐⢂⠦⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠣⠀⢠⣘⣯⠸⠟⣿⣿⡇⢹⣿⣿⣿⡜⢾⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡱⡷⣄⢉⢹⣾⣿⣿⡟⠀⠸⣿⣏⣿⣿⣾⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢮⣻⣌⢻⣏⢧⠘⣻⠿⠤⣴⣿⣿⣿⣿⣿⣿⡿⣡⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣞⡞⠃⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣇⣀⣠⡶⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣾⠟⠉⣽⢯⡟⢉⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣲⡦⠠⠴⣶⡖⢒⣾⣯⠀⠀⣽⣾⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⢉⢉⣽⣿⣷⠀⢰⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠸⢟⣿⣿⣻⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢿⠄⠛⠉⠈⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡯⠟⠁⠀⠀⠀⠀⣸⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⡖⢶⠖⢲⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠮⢓⣈⣴⠈⢰⣮⣒⡋⣺⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣲⡄⠀⠀⠷⠞⠀⠀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣾⣮⡿⣸⣿⠋⡀⠄⠹⢿⣧⣻⣾⣟⡒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠘⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣴⢒⡀⠀⠀⢀⠀⠀⠀⠀⠰⣧⡄⠿⣻⢿⣫⡵⡃⡇⣼⣜⣶⢭⣻⣯⡙⠘⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢚⣶⠲⣢⡄⠀⠀⠀⣀
⠀⠀⠀⠀⣔⣢⠀⠀⠈⠛⠁⠀⢸⣭⠁⠀⠀⠀⠀⠉⠀⠀⠚⣩⢞⡵⢡⣏⢸⡜⢮⡳⢬⣉⠙⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⠏⣉⡿⣏⠳⠄⠐⠯⠼
⠀⠀⠀⠀⠉⠉⠀⠀⠀⢠⣠⣀⠄⠀⠀⠀⠀⠀⠠⣮⡲⠶⠶⢾⡋⢁⡾⢸⡇⢳⣄⠹⣻⣶⣛⣫⣵⢷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣈⡳⠬⢿⠟⠉
⠀⠀⣠⢠⡀⠀⠀⡿⣯⡿⠿⣌⢇⠀⠀⠀⠀⠀⢸⣹⠋⣉⣭⠥⠶⢋⣴⣸⣇⣦⣉⠛⠶⠮⣭⠉⢏⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠍⠚⠁
⠀⠀⠙⠚⠃⠈⠭⡱⢿⠗⢊⡿⢸⠀⠀⠀⠀⠀⠀⢳⣄⠉⠙⢶⡄⣿⡇⣿⣿⢸⣿⢠⣞⠉⢁⣠⠞⡄⠀⠀⠀⠀⠀⠀⢀⡤⣬⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⠻⠻⢋⠀⠀⠀⠀⠀⢀⣦⢍⠻⠿⠟⣣⡿⣰⡏⢸⣆⢿⣌⣛⠛⢛⣥⢸⢹⡆⣀⣀⠀⠀⢀⡞⠀⠱⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⡷⠀⠀⠀⠀⣠⠼⣿⢸⢰⣿⡿⢟⣵⠟⠀⠀⠻⣮⡛⢿⣿⣇⢿⢸⣸⣍⡯⡙⣗⣄⠸⣤⢏⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⠟⢦⣰⣿⡏⢾⣇⡿⠸⢫⣴⠟⣡⢊⡖⡰⣆⢮⡛⢷⣍⠻⡌⢸⡇⠻⢧⣬⣬⢮⣓⢖⣫⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡘⡔⠤⢣⢿⣥⡾⢸⡇⢰⡿⢡⣾⣁⢈⠃⡇⢋⠀⣹⣧⠹⣷⢹⣼⣿⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡻⠶⢋⡞⠛⠁⣿⡇⢸⣧⠸⠿⠟⣸⢠⣿⢸⣜⠿⠿⢡⣿⢰⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⢹⣧⢢⣙⠿⠶⠟⣣⣾⣿⣧⡙⠷⠾⢟⣡⡟⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡙⢿⣇⢿⣿⣿⣿⣿⣿⢇⣿⡿⣫⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣝⠓⠶⠤⠍⣹⢿⡉⠥⠼⠶⢚⣫⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⡿⠀⠸⣦⠟
⠀⢀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢰⠋⡀⣴⢋⡌⢧⢀⠉⣦⢹⡟⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⢀⡀⠀⣈⡀
⠀⢿⣰⡦⠀⠀⠸⣅⣴⠀⠀⠀⢀⣤⡤⠤⠤⠤⣀⡀⠀⠀⠈⢮⡍⣼⠏⡼⢿⡘⣧⢉⣵⠟⠀⠀⠀⣀⠤⢔⣾⡿⣯⡙⡷⠀⠀⠸⠦⡗⣀⡿⣰⠁⢠⡔⡄
⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⡄⢿⠡⣾⣫⠽⣦⢰⣻⡖⠀⠀⠸⢳⡟⢰⢱⣦⠃⢿⡜⡟⠀⠀⣀⠨⣳⢪⣟⠉⣻⢞⣾⣿⠇⠀⠄⡾⣹⡿⣟⠊⠀⠈⠛⠁
⢠⠄⣄⠀⠈⢦⣔⢤⡇⡀⠈⠷⣺⣕⡙⢮⣢⣼⣎⣗⢏⠺⡰⣇⢸⡇⣿⡜⣧⣿⢸⡇⣼⣣⢗⡼⣿⡷⣛⠿⣫⣴⡿⢡⢖⡀⣈⣢⢀⠵⠊⠁
⠘⠶⠟⠀⠐⠚⢩⣿⣶⣧⢀⡀⠰⣩⢯⢳⣮⣝⡮⣿⢥⠗⡜⣿⢸⡇⢿⣿⡌⠛⣸⢧⣿⡻⣝⢛⡿⠋⠁⣾⡇⣶⠒⢊⣼⡜⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠩⡛⠎⠃⢠⠹⣇⣀⡐⠆⢿⣮⠓⢜⠦⣿⣧⡳⡌⠻⠟⣠⢏⡞⢩⣖⡽⠋⠀⠀⣸⢛⠥⠟⢸⣿⡷⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡘⣆⡳⣽⣿⣿⣘⣢⢝⣇⠀⠉⠂⠌⠛⠊⠀⠀⠙⠛⠡⠘⠋⠀⠀⠀⢀⡿⢀⡺⣿⡿⡵⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⡝⣿⢻⣿⠟⣩⣬⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠋⣿⢘⡞⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣽⣔⢻⣦⣇⢨⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡴⣣⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⡑⠟⣯⡚⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠐⠚⠓⠂⠀⠀⠀⠳⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⠄⠐⠀⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣶⣾⣾⣿⠄⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠤⠄⠀⡖⠈⠁⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠒⠁⡈⠛⠟⠛⠁⠀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠉⢩⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠄⠁⠀⠀⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠟⡀⠢⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂
⠀⠀⠀⠀⠀⢀⣼⠁⠀⠈⢆⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠠⠀⠂⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊
⠀⠀⠀⠀⢀⡞⢠⠉⢏⣠⠞⡀⢁⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠚⠁⠀⠖⠂⠀⠀⠀⠀⠀⢠⡴⠃
⠀⠀⠀⠀⣸⠁⠀⠑⣴⢋⡈⠡⠄⠀⠉⣠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⡼
⠀⠀⠀⠀⢹⡀⠂⢰⣇⠠⠔⠀⠀⢀⣌⡁⢀⣄⠀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠉⠈⠀⠈⣧⠀⠀⡞⢠⠃⠀⠀⠀⡆⠀⠠⠀⠀⠉⢹⠙⡲⠶⢤⣀⠀⠠⠄⢸⡇⠄⠀⣼⠳⣦⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠆⠀⠃⠀⠀⠀⠑⠄⠑⠄⠀⠀⠀⡆⠈⡆⠀⠈⡟⠺⣆⣸⡇⠀⠀⠙⢷⡀⠉⠉⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢄⣀⣆⠀⣤⠤⢠⠖⠐⠲⡖⠶⠲⠗⡶⠒⢲⠶⠂⢄⠈⠹⡗⠤⣀⠀⠀⠈⠓⠒⢉⠈⠟⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢇⠀⠈⠀⠀⠀⠀⠀⠈⡆⠀⢠⠀⢀⠌⠀⡄⠀⠁⢠⡇⠀⠈⠙⠓⠤⠄⠤⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠰⢨⣄⣈⣄⣀⡇⠀⠀⣊⠀⣐⠚⢀⡃⢰⠀⣀⠠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠤⣬⡄⠃⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠒⠒⠒⠂⠀⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠢⠤⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⡈⠳⠭⢉⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠲⠤⣼⣯⣉⠁⠐⠚⠻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙





⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠐⡇⠀⠃⠀⢠⠂⠀⠀⠈⢸⡇⠀⠀⡄⣀⠀⠀⠀⡀⢀⡀⢀⠀⢀⠓⡀⠀⡀⠀⠀⠀⠃⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠀⠀⠀⣰⠋⠀⠄⠀⠀⢠⡀
⠀⢀⠀⠀⡀⠀⠐⠒⠃⠀⢸⡇⠀⠀⠀⠁⠈⠐⡇⠀⢨⠁⠀⢀⠚⠉⠉⣄⠰⠀⣠⠀⠀⠀⠀⡇⢀⡀⢰⠀⣠⡀⣈⡄⢀⣤⠀⣆⠀⠀⠠⣶⡄⠀⠁⠨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠉⠀⠀⡀⠖⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠡⠈⢁⠀⠀⡈⠀⡀⠀⠠⠀⠀⠀⢠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠐⠀⠠⠦⠀⠀⠒⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠄⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⢀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠉⠀⠀⠐⠀⠀⠀⡠⠤⠀⠀⠀⠀⢣
⣶⡶⠶⠶⠶⢶⢶⣾⢷⣾⣶⣶⣶⣶⣿⣶⣾⣶⣿⣾⣿⣶⣶⣶⣿⣶⣾⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠐⠒⠐⠒⠒⠒⠂⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠐⠠⠀⠀⠐⠄⢠
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⠀⠀⠁⢀⠀⠀⠘⣴
⠀⠀⠀⢀⠤⢶⡶⠄⠡⠀⠺⠇⠀⠄⠸⠃⠀⠐⠛⠂⠀⠂⢄
⠀⠀⢀⠎⠀⢀⡀⠀⠀⠑⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢰⠒⠒⠒⠒⠖⢲⠒⠒⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠸⡄⠀⠀⠀⠐⠠⢀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠄⣸
⠀⠀⠀⠱⡀⠀⠀⠀⠂⡀⠀⠁⠌⠁⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⢏⢠⠃
⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠒⠈⠀⠂⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠠⠀⠀⣀⡢⠈⢤
⠀⠀⠀⠀⠀⠀⠈⠑⡢⠄⢀⣀⣀⣀⣀⠀⠠⡄⠀⠅⠀⠀⠄⠐⠈⠀⠀⢸⠑⡖⠈
⠀⠀⠀⠀⠀⠀⡀⣬⡱⠆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠐⠁⢀⣿⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂
⠀⠀⠀⠀⠄⠀⠆⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢿⠤⠆
⠀⠀⠀⠀⠚⠀⠀⡘⠢⢀⠀⠀⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠘⠠⠊⠀⠀⠀⠈⠖⠀⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠈⠠⠐⠀⠀⠀⠁⢀⠀⠤⣄
⠎⠀⢄⣀⠀⠀⠤⠤⠤⠤⠤⠔⠰⠄⠠⠄⠤⠤⠤⠄⣀⡨⠆⠨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⠿⠟⣻⣿⣿⣟⠲⢶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⠉⠉⠁⣀⣤⣾⣷⣯⣭⣿⣷⣶⣦⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡟⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣤⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⡾⠿⠿⠛⠛⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⣟⣯⣭⡶⠾⢛⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠛⢉⣁⢠⣤⠀⠀⠀⢀⣠⣤⣤⠶⢿⣿⠛⣩⣭⣽⠿⠿⠿⣿⡵⣿⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠈⠁⠀⠀⢀⣰⣿⣟⣵⠶⠖⠚⠛⠉⠀⠈⠁⠀⠀⠀⠀⣩⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⣀⣀⣀⡠⣾⣿⣟⣷⡟⠁⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣵⣷⡆⢀⡀⢾⣿⡟⠿⠟⠛⠁⠀⠉⠀⠿⠛⠛⠀⠀⠀⣀⠀⠀⣴⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠀⠈⣀⣄⠿⠇⠈⠁⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⣿⡟⠀⠀⠘⠛⠁⠀⠀⢀⣀⣀⣨⣭⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠋⢠⡿⠁⠀⠀⢀⣠⣶⣿⣟⣿⣿⣿⣿⠉⢹⣿⣿⡷⠶⣤⣤⣤⣴⡾⣿⣇⠀⠸⣿⣿⣿⡿⠿⠉
⠀⠀⠀⠀⠀⠀⠘⠿⠶⣾⣷⣄⣠⣴⡿⠿⠿⢿⣿⣿⡟⠛⢿⣿⣿⡿⠿⢿⣶⡦⠉⢻⣯⡀⠈⣿⡆⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠀⢀⣀⣠⣿⣿⣿⣗⣂⣼⣿⠿⠀⠀⢸⣿⣧⠀⠀⠹⣷⡄⠘⣿⡀⠀⠹⣷⣄⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣥⣀⣀⠀⣼⣿⣿⠍⠉⣻⣿⣿⣿⣦⣀⣀⣼⣿⣿⣷⣤⣤⡿⠓⠀⠈⠳⣦⣀⣨⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠿⠶⢦⣿⣿⣅⣀⡉⠉⠿⣭⣽⡿⠿⠿⢿⣿⣿⣶⣦⣤⡀⠉⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠻⠛⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⠾⣠⠴⠂⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣞⣃⣀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⢋⣼⣿⡋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⡯⣖⣤⡾⠛⠛⠓⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡆⠀⠀⠀⣴⡶⢄⠀⠀⢀⣴⣾⣿⣏⣤⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠁⢀⣠⣾⣿⣵⠎⢀⣴⣿⣟⣿⣿⣿⣿⣥⣤⣀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⢀⣴⣿⣿⠟⠉⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⣿⣿⣯⣭⣄⣭⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣶⣿⠟⢋⢀⣠⣶⣶⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣟⡛⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⢛⡛⢿⠛⢁⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣣⣼⣿⣿⣿⣿⡿⠻⢋⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠿⢟⣵⣯⡴⢣⠌
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣿⣿⣿⣿⣿⣿⣯⣨⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⠕⠋
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡟⣯⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⢿⣈⣤⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠚⠁
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢻⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣿⡟⠋
⠀⠀⢠⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⡿⠏⠀⡈⣻⣿⣿⠋⠀⠀⣰⣿⠁⠀⢀⡄⠠
⠀⠀⠀⠛⠛⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣶⣿⣿⡟⢁⣀⣠⣼⠇⠌⣣⠴⠟⠛⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢹⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣼⣷⣠⣀⣀⣠⡾⠷⠞
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⣿⣷⣶⣦⣤⣄⠀⠀⠀⠀⠈⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣴⣤⣔⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣦⣶⣶⣦⠂⣠⣦⣃⠉⡉⠛⠻⠶⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣦⣤⣀⡁⠉⠛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡇⢠⣂⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡶⢿⡿⡻⣛⠙⠙⣋⣍⣩⢏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠁⠀⠀⠀⣀⣤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣻⣖⣲⣴⣴⣶⡾⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣿⠟⠛⠉⢁⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣷⣶⣾⠿⠋⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⢆⡀⠐⠒⠰⣤
⠀⠀⠀⠀⢀⣾⣿⢟⣽⣿⢤⣶⢤⢤⠀⣀⡀⠀⠀⣠⡆⠚⢛⣠⣆⣭⣿⠤⠘⡑⠯⠿⢷⠧⢤⣄⣾⠩⠆⠦
⠀⠀⠀⠀⢸⣿⠟⠛⠛⢿⣶⣿⣯⣤⠷⠏⢍⣿⣶⣌⢑⣆⠹⠷⡷⣡⡡⣤⣤⠀⢀⡀⣤⡤⣤⡁⠷⡏⠰⠦⣦⣤⠀⣒⣶⠄
⠀⠀⠀⢀⣾⡟⣀⢠⣼⡆⠀⠟⢛⣭⣷⣶⡆⠚⣡⣄⡚⠻⣤⣦⣄⢽⣿⣟⡛⣻⣮⣃⣃⡘⠿⣁⣢⡔⡀⠀⠉⣀⡄⠐⢏⣗⣦⡡⠲⢄⡀
⠀⠀⡖⠰⠞⠙⠟⣡⣽⣧⣐⣧⣿⣿⣦⣽⡀⢈⡩⠾⣟⣡⣦⡌⠐⡾⣿⣻⡕⢩⣷⣟⣧⡽⡉⠉⢛⣟⡛⠀⠀⣬⣷⢶⣄⣦⡀⣡⣄⠺⠿⠂⣠⢤⡄
⠀⡼⢡⣶⣶⡮⣻⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣍⠿⠿⣿⠆⠐⠊⠛⣀⡘⠄⠙⠃⣀⣄⡻⣿⣥⣿⡶⣼⠶⢿⡇⠌⣉⠫⠃⠸⠗⣦⣼⡄⠄⠀⢀
⠀⣧⡸⣿⣿⡿⢯⣿⢟⡣⢽⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣥⡄⣤⣄⠛⡓⠶⡿⣿⣿⣆⢀⣭⣻⡟⠀⢼⠛⠾⢷⠀⡈⠁⠐⢬⣙⠀⠉⡀⣾⠛⠻⣶⣷⣄⠋
⠀⠙⣿⣿⠏⣴⣦⣥⡈⢉⣨⣿⣿⣿⠟⢿⣿⣽⣿⣽⢟⣿⣿⣿⣷⠀⠛⢳⣣⣽⡇⣡⣿⣿⣿⣷⠀⠀⠙⠀⢴⡔⣿⠿⣧⡈⠃⠀⠃⣹⣥⣀⣄⡈⠻⣿⡓
⠀⠀⠀⠙⠿⣿⣿⣟⡃⣸⣿⣿⣿⠗⠀⠌⢻⣾⡿⡾⣯⡍⣿⣿⣿⣂⠻⣉⡀⠈⢀⡀⠛⠟⣟⠿⠇⠀⠀⣄⢛⡀⠉⠀⠈⠉⢙⠂⠶⡯⠉⠉⠉⠛⠓⣾⢹
⠀⠀⠀⠀⠀⡾⣿⣟⣿⣿⣿⣿⣷⣿⣿⣧⣼⣿⣾⣿⣿⣷⣍⣹⣿⣿⣷⣽⣿⣇⡉⢩⡖⠀⠈⠀⠔⠶⢶⣀⣠⡿⣶⠺⡗⠀⡿⡧⠛⣧⢠⣽⠿⣿⣦⡀⠴
⠀⠀⠀⠀⠀⣟⡜⣋⣉⣻⣿⣿⣛⠳⢦⣮⡽⠷⣺⡐⠃⠙⢿⡁⠛⠻⣽⢿⣿⣿⡷⣬⣴⣤⣷⣶⠀⣶⣾⣯⣷⣾⣿⠀⠉⢰⡟⠀⠚⣻⠻⠿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠽⢁⣥⣰⠟⣿⣿⣿⣿⣷⣦⣄⣤⣊⡡⠀⣲⠬⣜⣡⢖⣠⣤⠂⠉⠛⠰⣿⣿⢿⣟⠁⡉⠻⠿⢏⠈⠁⠀⠀⠘⠀⣀⣽⡿⣶⣶⣟⣿⣹⣿
⠀⠀⠀⠀⠒⠈⣾⣿⡟⢿⣿⣮⣹⣿⣿⣟⣿⣿⣿⣏⡶⢿⣷⣿⡏⣟⣾⣻⣷⡇⠤⣰⣟⣿⣿⣗⣦⣮⣤⣤⣆⠀⣀⢦⣼⣿⣥⣬⡍⡱⢻⣤⡌⢸⠷⠁
⠀⠀⠀⠀⠀⠀⠁⠋⡿⠿⢿⣿⣭⣿⣿⣿⣿⣿⣿⣻⣷⣿⣯⣟⢱⡋⣹⣿⣿⣿⣙⠿⣿⡋⠀⣹⡟⠛⢿⣾⡷⠸⠿⣿⣿⣿⣿⣿⣏⡀⢀⣻⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣏⠿⢿⣟⣿⣿⡍⠉⠳⢿⣬⣿⣿⣿⣿⣿⠿⣦⣬⣤⣻⣿⣐⣿⣿⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢫⣿⠿⣯⣷⣶⠀⣸⣿⡛⡿⠛⠛⢙⣿⢿⣿⣽⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡍⣸⣿⣇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢿⣿⣇⣘⣿⣿⣿⣉⣼⢿⣿⣿⣷⠹⣟⣍⢻⣾⣻⣟⣩⣍⣿⢿⡛⣛⣿⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⡿⣿⣿⣿⡾⠿⢍⡽⠗⠚⠉⠁⠙⠶⠿⠟⠉⠁⢈⠓⠺⠃

⠀⠀⠀⠀⡶⢀⣠⡀
⠀⠀⠀⠈⢷⣘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡆
⠀⠀⠀⠀⠀⣿⣿⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣤⠀⢀⡄
⠀⠀⢠⣤⣄⣿⣿⣯⣤⣀⢠⣠⣤⣀⡀⠀⢠⡏⣴⣦⠀⠀⠀⢀⣀⠀⡼⠀⠀⠀⣴⣦⠀⡿⠀⠈⣧⢰⣶⡆
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⠡⣦⢹⡇⠀⠀⣷⣽⣭⣀⠀⠀⣿⣿⣾⡁⠀⣄⣀⣉⣭⣾⡁⠀⠀⠈⠳⣽⣶⣶⣆
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⡷⠶⣾⡇⠀⠀⢿⣿⣇⡽⠂⠐⠟⢻⣿⣿⣄⠀⠀⠀⣿⣿⣷⡀⠀⠀⠀⢸⣿⡿⠃
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⣇⣋⣼⡇⠀⢀⣼⠟⣿⡀⠀⠀⠀⠸⣿⣿⡿⠂⠀⠀⢿⡿⣿⠃⠀⠀⢠⡿⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣇⠀⠈⢿⣄⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⡇⠸⣧⠀⢠⡿⠁⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣛⣀⣀⣀⣹⣃⣀⣀⣘⣛⣃⣀⣀⣀⣘⣇⣀⣹⣀⣙⣁⣀⣀⣛⣀⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄
⠀⠀⠀⠀⠀⣴⣶⣆⣀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⠀⢀⡛⢛⣁
⠀⠀⠀⠀⣀⣙⣛⣩⡽⠇⠀⠀⣀⣛⣟⣁⠀⠀⡀⣸⢀⣼⣿⣧⣸⣿⡇
⠀⠀⠀⢾⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⡁⣿⠀⠈⢹⣿⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠘⠿⠿⠿⢻⣿⣿⣿⡻⠿⠿⠿⣿⣿⣿⣿⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠿⠿⠃⠀⠀⠀⠀⠀⣨⡿⠟⠦⠀⣀⣀
⠀⠀⠀⢠⣿⠿⡿⢿⣷⠀⠀⢰⣿⠿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣀⠀⣾⣿⣿⡇
⠀⠀⠀⢸⣿⠀⡇⢸⣿⠀⠀⢼⡏⠀⡇⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣄⠀⠀⣩⣿⣿⣮⡛⠛⠁
⠀⠀⠀⠀⠁⣀⣇⣀⠁⠀⠀⠈⢁⣀⣇⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⣿⣷⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣾⣿⣿⣶⣾⣿⣿⣿⣿⣯⣤⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠋⠉⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠉⠀⠀⠀⠀⠘⠛⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⡠⠊⢉⠑⢢⠀⠀⠀⣀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠶⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣽⣿⠀⡇⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠠⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣉⣀⠜⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡺⠟⠁
⠀⠀⠀⢀⣀⣠⠤⠤⠒⠚⢉⡵⠁⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢋⣩⠔⠋
⠀⢰⠊⠉⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢒⡽⠁
⢠⠞⠒⠒⠲⠤⣄⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⠞
⡇⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠀⠀⠀⠀⠀⢠⠏
⢷⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⢀⠀⠀⢠⠋
⠈⢧⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⠑⢦⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠔⠋⠀⣰⠋⠉⣭⣭⣭⣱⠄
⠀⠈⢧⡀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠱⡄⠀⠀⠀⠀⡇⠀⠀⠀⢻⡁⠀⠀⡰⠋⠙⠒⠒⠮⢭⡓⠦⡀
⠀⠀⠀⠱⣄⠀⠀⠑⢦⡀⠢⡀⠀⠀⠀⠀⠈⠳⠄⠀⢹⡀⠀⠀⠀⢹⡀⠀⠀⠀⢳⣀⠞⠁⠀⠀⠀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠈⠢⡀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢳⡀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠉⠒⠲⠦⣄⡀⠀⢀⣼⣀⣀⣀⣀⣤⣔⠻⣄⠀⠀⠀⠑⠶⠴⠖⣒⣫⠭⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣄⣀⣀⡀⠉⠉⠉⠉⠉⠉⠩⢿⣯⡽⠃⠈⠦⣀⣀⣀⣠⠬⠭⣝⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠲⠤⣄⡺⢷⣒⡲⠭⢽⣒⠒⡄⠁⠀⠀⠀⠀⠈⠓⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢛⣛⣛⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠛⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡞⠙⣿⣿⣿⣄⠈⢷⣤⡤⠤⠶⠶⠦⠤⢤⣤⡾⠁⠀⠀⣠⣤⣀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠙⡧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠙⠿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠈⠙⠳⢾⡀⠀⠀⠀⠀⠀⠀⢶⣀⠀⠀⠀⠀⠀⣀⡶⠀⠀⠀⠀⠀⠀⠀⡷⠞⠋⠁⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣠⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢠⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠘⠻⣅⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⣠⠟⠛⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠘⢷⡄⠀⠀⠀⠈⠙⠓⠶⣤⣄⣀⣀⣀⣀⣀⣠⡤⠶⠚⠋⠁⠀⠀⠀⢠⡾⠃⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠙⠷⣄⠀⠀⠀⠀⢠⠀⢀⠀⠉⠉⠉⠀⠀⠀⠀⡀⠀⠀⠀⣠⠾⠋⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⣙⣦⡀⠀⠘⣿⢦⣄⣀⣸⠀⢸⠃⠀⠀⠀⠀⢸⡇⠀⣇⣠⡴⣿⠃⠀⢀⣴⣋⣀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣽⣿⣽⣿⡿⠏⠉⠃⠀⢀⡿⠀⠈⠉⢻⠀⣸⠶⠤⠤⠤⠶⢾⡇⢰⡏⠀⠀⢿⡀⠀⠘⠉⠹⢿⣯⣿⣿⣯⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣟⣛⣯⣭⣴⡶⠓⣠⡴⣾⣯⣤⣠⣤⠴⠾⠀⣿⠀⠀⠀⠀⠀⢸⡇⠘⠷⢦⣤⣈⡙⢳⣤⣀⠺⢶⣶⣭⣽⣛⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣴⣒⣻⡵⠖⠋⠉⠀⠹⣶⣾⣿⢟⣠⡤⣠⠏⠀⠀⠀⠀⠀⠈⢷⡄⢠⣄⠰⣯⣽⣍⣽⠋⠛⠶⣬⣛⠺⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠿⠵⢾⡿⠟⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡙⣿⣦⣝⣻⡄⠀⠀⠀⠀⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡿⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢌⢉⠈⠉⢉⣍⣉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠁⠀⠀⢨⠜⠁
⠀⠀⠀⠀⠀⠀⠀⡠⢊⠄⠊⠀⠀⣠⠈⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣤⣤⣀
⠀⠀⠀⠀⠀⢠⡮⡐⠀⠀⢀⣰⣃⡞⠋⢠⣤⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠛⠁⠈⢇⠀⠀⠀⣤⣀⣀
⠀⠀⠀⠀⠢⠁⢏⠀⢠⣾⣿⡿⠛⠙⠦⡀⠀⠀⠀⠀⠀⠲⠦⠶⢒⡃⡀⢀⠀⠀⠀⡰⠤⠀⠿⠿⠏⠙⠢⢀
⠀⢀⠐⠀⠀⠁⢈⣱⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢲⠔⠒⠀⠒⠀⠀⠀⠈⠒⠄⠉⠦⡀
⡆⡠⠁⠀⠠⢔⣹⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠲⣤⡀
⣏⠀⠀⠰⡦⣱⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢉⡑⢢⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⡄⠀⠁⠄
⡇⠀⠀⠄⢋⡃⠀⢀⣤⣾⣶⠷⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠑⠤⡀
⡇⠔⠀⠀⠈⣿⣿⣉⡉⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠱⢤⡄⣀⡀⠀⠀⠁
⠃⠀⠀⠀⢀⣇⠻⣿⣿⣿⣿⣶⣶⣤⣄⣀⡈⠛⠛⠿⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠄⠀⠀⠀⢸⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠻⣭⣿⡿⣿⣿⣿⣿⣿⡶⠶⠤⢈⠉⠛⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠉⠟⠃⠙⠺⣮⡙⠛⠿⠷⠖⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣁⡀⡐⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⡀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⠄⠉⠀⠀⠀⠀⠀⠐⢉⣉⠉⠹⠅⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⠸⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⡤⠃⢀⡜⠋⠀⠀⠀⢀⡀⠲⢤⣄⣹⣿⡗⠱⠄⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⣀⢈⡀⡤⠋⠀⠀⠶⢀⡀⠈⠀⠀⠀⢹⣿⣿⣿⣄⣬⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠛⠿⠀⠀⠀⠀⢀⠿⠀⢿⣷⣦⣴⣿⣿⣈⣿⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠈⣿⣿⡿⢿⣿⣿⣺⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⢀⣿⡿⠃⢾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⠸⣿⢷⣤⠔⢀⣼⡿⢃⣴⢿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⢀⣾⣭⣶⣿⡷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⣤⡀⠀⠀⣼⡀⠀⠀⠀⠀⢀⣤⡾⠟⣱⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠌⠉⢓⣮⡿⢿⣶⣶⣶⣿⢟⣫⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠶⣤⣀⡀⠘⠃⠀⠀⢰⡭⢡⣶⣿⡿⢋⣭⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢤⣤⣀⣠⡤⣤⡀⢀⡞⣩⣴⣿⢏⣡⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢣⠞⠋⠁⠀⢤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⣀⠠⠶⠖⠛⣡⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⣻⣾⣯⣍⣛⡓⠲⠶⠶⣤⣤⣀⣀⠀⠀⢀⣤⣾⢟⣛⣳⣦⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣠⣊⡀⣠⣽⣿⣿⣑⢺⣝⠛⠿⠟⠻⠷⠶⣯⣭⣿⣿⣿⣿⣿⣿⣗⣛⠿⣿⣿⣻⢿⣽⣿⡿⢹⣿⣿⠖⣤⡀
⠀⠀⠀⠀⠀⠙⢄⠀⠀⠘⠿⣿⣿⡞⣻⣧⡀⠀⠀⢤⣤⣀⣀⣈⣩⣉⣿⣿⣿⣿⣿⣷⣶⣭⣛⠿⢶⣭⣛⡿⣿⣽⡮⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢿⣿⣿⣷⡀⠀⠉⠁⠈⠙⠿⠏⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣶⣾⣭⣟⣷⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⡄⠀⠈⠘⢲⣢⡄⠀⣀⠀⠻⢿⣻⣿⣿⠿⣟⡿⠉⣧⠘⠓⣿⣫⣹⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣆⠀⠀⠀⠀⠉⠻⠀⠠⢠⣬⣹⣿⣇⣤⣤⣴⣿⣟⣭⠀⢷⣶⣖⠀⠀⣴⣾⣿⣿⢫⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣷⡀⠰⣦⢠⠄⠀⡉⢳⣿⣻⣿⣿⣟⡿⣿⠿⢿⣿⠆⠀⠙⣿⣷⣤⣿⣿⠟⣹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⣿⣿⣿⡻⣿⣿⣦⣟⣷⣦⣤⣙⠇⡿⠋⠈⠀⠀⠀⠀⣹⣿⣄⣼⣿⣿⣿⠟⢡⣬⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⠮⣹⣿⣿⣯⣭⣭⣭⣿⣿⣶⣷⣠⣄⡀⢂⣰⣾⣿⣿⣿⠿⠛⠉⣀⣴⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⡻⠿⢋⣁⣤⣴⡾⠿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠉⠛⠻⣿⠟⠛⣛⣫⣭⡽⢷⢟⣩⠴⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠚⠛⠛⠛⠓⠒⠲⠀⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣄⡀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣶⣦⡀⣀⢾⢿⣠⡾⠀⠀⠀⣀⠀⠀⠈⠉⠈⢿⣿⣾⣿⣿⣷⡄⠀⠀⠀⠀⣠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠻⣶⣄⣦⣿⣿⣿⣿⣧⣌⣳⣿⣠⣴⣿⠃⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡀⠀⣠⣴⣿⡿⣿⣿⡟
⠀⠀⠀⠀⢤⣤⣀⡛⢛⠻⣿⡟⢻⣵⣯⣻⢿⣟⡄⣿⢃⣴⣶⣾⡟⠁⠀⠀⣿⣿⣿⣿⣏⢸⣇⣾⣿⣿⣿⣥⣿⣿⠃
⠀⠀⣀⣀⣈⣙⣿⠿⠎⢳⣿⣿⢸⣿⣿⣿⢆⣿⠉⠡⣿⣿⣷⣾⣿⣷⣶⣦⣻⣿⣿⡏⣿⣿⢿⣿⣿⣿⣟⣿⣿⠃
⠀⠀⠈⠙⠻⠿⣿⣿⣷⣦⡹⣆⢸⣿⣾⣿⠿⠳⢂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠻⡏⠸⣿⢟⡿⣿⣾⣋⣄⣼⣵⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣉⣉⣽⡏⢀⡈⠙⠋⢃⣠⣴⣿⣽⣹⣾⣿⣿⣿⣿⣿⣿⣿⡟⠟⠙⠁⠟⠀⡠⢋⡴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣵⣾⣿⡿⢃⣴⣶⡔⣶⠞⣾⣿⠁⣿⣿⣿⡏⣿⣯⣙⣟⣤⣤⡀⣼⠞⠑⠋⠶⢿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦
⠀⠀⠀⠈⠉⠛⠋⣾⣛⣻⣿⡽⠿⠾⠿⢛⣿⣿⣿⡽⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣶⣶⣿⣿⣯⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣮⣭⣭⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣦
⠀⠀⠀⠀⠀⣠⣾⣿⣟⡙⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣜⣿⣧
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⣿⣿⣿⣿⣇
⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠻⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⢹⣿⣿⣿⣿⡿
⣴⣶⣿⣿⠛⠋⠉⠉⠹⣿⣿⡀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢳⣧⣾⣿⢻⣿⣿⣿⣄⣠⣤⡤
⠈⠛⠟⠃⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⢻⣇⡿⠻⠟⣁⣼⢯⡿⢫⠍⣿⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣡⣶⣿⢿⣭⣎⣴⣫⣼⡷⠋⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠸⢿⣷⣿⣿⢇⣾⣛⠉⢶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣌⠉⠙⠉⠁⣼⣿⣿⣿⣿⡟⣿⣿⣿⠇⡈⠉⡙⣟⡋⠉⠒⣚⡛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⡀⢰⣿⣿⣿⣿⣿⣿⣽⣯⡇⣤⡘⢷⣝⠿⣿⣷⣝⡿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⠹⣮⣿⢆⠈⠛⢿⣿⣾⡛⠿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡍⠻⠿⠿⠿⢿⣿⣿⠀⢻⣿⣿⣿⣿⣦⠈⠙⠻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⠿⠀⠀⢻⣿⣿⠙⠿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠟⠉⠀⠈⠻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣨⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠈⠃⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠀⠦⣾⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣿⠠⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⡔⠛⢧⡌⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣄⠙⠳⠤⣄⣀⣀⣀⡈⢀⣠⣤⣶⠊⠙⣆
⠀⠀⠀⠀⣠⡶⠊⠀⣼⣿⣿⣿⣧⢀⣤⣤⣤⣬⣍⡙⠻⠿⠿⢯⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢸⣏⠀⠀⠀⠹⣿⣿⣿⣏⠈⠿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠐⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢂⣠⣶⡟⡇
⠀⠀⠀⠀⠻⣿⣿⣶⣯⡀⠀⠈⢍⣀⡀⠀⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣶⣄⠻⣦⡀⠀⠀⠀⢀⣴⣵⣾⣿⠛⠻⣷⣿⡀⠀⠠⡆
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣾⣿⣿⣿⣧⠀⠀⠀⣀⠟⠙⠛⢿⣿⣿⣿⣿⡆⢮⡻⢦⣀⣠⡏⢸⣿⣿⡇⢰⣿⣦⣵⠑⠄⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⢿⣿⣿⣿⣿⢃⣴⣿⣿⣿⣦⠀⠀⠈⠻⠿⠟⠁⣠⣤⣤⡙⢿⣄⠀⢻⣿⣷⠈⠻⣿⣿⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⣿⣿⣽⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⠀⣀⣴⣿⣿⣿⣧⠀⠙⠷⡟⣿⣍⣀⣀⣸⡿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢻⠿⢿⡀⠉⠻⡿⢛⢉⣄⣉⣀⠀⢰⣿⣿⣿⣿⣿⣿⣄⣀⠀⢸⣿⣿⡿⠿⣿⣅⠙⢛⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⠳⢀⡀⠟⠀⠀⢣⡀⢀⣷⣰⣿⣿⣿⣿⣷⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠘⣷⣀⣼⣿⣷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣠⡶⢤⠀⣻⣿⡿⠟⠿⣿⣿⣿⡿⣠⡾⠛⠁⠀⠈⣉⣿⡿⢿⠃⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢼⣿⣦⣄⣙⣷⣀⠀⠀⠉⢻⡾⠋⢀⣀⣤⣶⣾⡿⣉⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠻⣷⡄⠀⢾⠟⠀⣴⣿⣿⣿⣿⣿⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢠⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣠⣾⣽⣿⠷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⣼⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢤⣀⠀⠙⠿⢿⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠀⠀⠀⣀⡀⠀⠀⠀⠈⠛⠿⠶⣀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢦⣄⡀⠀⠈⠀⢀⣀⡈⣁⠀⠀⠄⠀⠀⢀⣠⣽⣶⣤⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠠⣄⠉⠙⠛⠻⢶⣶⣷⣶⣾⠋⠁⣀⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠠⠤⠤⣤⣽⣿⣿⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⣰⣿⣦
⠀⠀⠀⠀⠀⠀⣰⠆⣻⣾⠞⠀⠀⠀⠘⡛⠃⢰⡄⠀⠀⠀⠀⠀⣾⣿⣻⡇⠀⢸⡇⠀⠀⢸⣷⣿⡷
⠀⠀⠀⠀⢰⠟⢁⡠⠜⡃⠀⠀⠀⠀⣀⣤⠠⠌⣷⣄⣀⣴⠀⠀⠙⠷⣟⣷⣶⣿⠁⠀⠀⠀⠀⢐⣷⣾⣗⣦⣄
⠀⠀⠀⠀⠀⠀⣡⣶⡾⠁⠀⠀⠀⠀⠙⢿⣷⣃⣀⣀⣉⣭⠀⠀⠀⢠⣿⣿⣿⠇⢀⢀⠀⠀⠀⢰⣻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣼⣿⣿⡷⠦⡤⠄⠀⠀⠀⠀⠉⠙⠋⠉⠁⠉⠀⠀⠀⠾⠿⣿⠏⠀⠙⠛⠲⠶⠶⠿⠃⠘⣽⣯⣿
⠀⠀⠀⠀⢧⠙⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣶⣿⡄
⠀⠀⠀⠀⠨⣷⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣿⠀⢸⣇⠀⠀⠀⠀⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠉⣽⣿⡟
⠀⠀⠀⠀⠀⢹⡇⠘⣿⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠈⣿⣷⡀⠀⢿⣿⣷⣤⣤⣤⣦⡀
⠀⠀⠀⠀⠀⠀⣧⠀⡿⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠳⣄⠀⠀⠀⠀⠘⣿⣿⡄⠀⠉⠛⠛⠻⠿⠟⢻
⠀⠀⢀⣤⠤⢤⣤⣠⣇⣤⠤⠤⠤⠀⠬⣽⡷⠦⢀⣤⠤⢤⣤⡀⢀⣼⡥⢤⣝⡇⠀⠀⢠⣖⠛⠛⣤⠀⣤⡀⢤⣤⠤⣤⣉⠀⣤⡤⠤⠤
⢀⣰⠞⠳⣶⡞⠉⣰⡟⠓⠒⠒⠀⠀⣰⡟⠀⠀⣼⡟⠲⢶⣟⠁⢿⣇⡀⠀⣸⡿⠀⠀⠀⠙⢷⣤⣿⠀⠘⣷⡌⢻⣖⠒⠛⣦⣌⠻⣶⡒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⣤⣤⣤⡀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⡀⠠⠔⠂⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⡁⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⡀
⠀⠀⠀⠀⠀⠀⡰⠋⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠒⠤⡀⠀⠀⠈⠁⠂⢄
⠀⠀⠀⠀⠀⠀⢣⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡤⢂⠩⢑⡆⠀⠀⠂⠠⠤⢄⡇
⠀⠀⠀⡠⠄⠐⠃⠀⣀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠀⠠⠤⠀⢀⣀⣀⡀⠀⣀⠄⠊⠀⢿⠅⠠⢤⣏⠔⠀⠀⠀⢀⠜⠁
⠀⠀⡘⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⡁⠖⠋⠁⢀⣠⠤⠒⠁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣀⡀⠤⠒⠁⠀⢀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠘⠂⠉⠀⢠⢊⡠⠔⠊⠁
⠀⠀⠇⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⣠⠚⠉
⠀⠀⠘⡀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⡀⠀⠀⣀⣀⣀⡔⠁⠀⠀⠀⣠⢔⠉⠈⠒⠤⣀⠠⠄⢒⣐⠄
⠀⠀⠀⠣⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢪⡀⠀⠉⠒⢄⠀⠀⠀⢉⣭⣭⠀⠼
⠀⠀⠀⠀⠱⡄⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠒⠒⠂⠠⠠⢀⡱
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠑⢄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠑⠤⢄⣀⡐⠂⢀⡢
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠉⠂⠀⢠⣒⣁⠈⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢄⡀⠀⠭⣅⣒⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢰⠤⢀⡉⠒⠤⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⡉⠒⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠑⡄⠈⠑⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣙⣂⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣔⣭⢹⣿⣿⣿⠐⢉⡜
⠀⠀⠀⠀⠀⢠⠀⠀⠀⣇⡄⡀⢂⠀⠀⣠⣶⣿⠿⠿⣣⣶⣿⣿⣃⡴⢋⣄⣀⡀⠀⠀⢀
⠀⠀⠀⣤⣷⣶⡦⣦⣹⣝⣯⣴⡶⢶⡿⠿⢻⡝⣰⠀⣿⣿⡿⠿⠏⢠⣿⣿⣿⣷⣦⣅⠈⠙⠳⠄⠀⠀⠀⠀⠀⠁
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⢿⣿⢷⡋⠀⠴⢤⡍⠁⠀⠄⢠⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠠
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣥⣾⣾⠓⡆⢿⣾⣿⠾⡄⣼⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠐
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣿⡿⣿⣿⣿⣵⣦⠀⠈⣿⣿⣶⡜⣿⣿⣿⠿⣿⢯⣀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠈⢿⣿⣿⣿⡿⠿⢿⠷⣿⣷⣿⣯⡝⢯⣁⣀⣠⣬⣿⣿⣿⣯⣿⣳⣾⠿⠛⠿⣦⡟⠈⠁
⠀⠀⠀⠈⣿⣿⣿⣿⣾⣧⣼⣿⣿⣷⣾⠿⠞⠉⠉⠙⠛⣉⢯⣽⣭⣿⣧⡀⠀⠀⠐⠁⠁⠀⠃⠁
⠀⠀⠀⠀⠉⠻⠿⢿⣿⡿⣿⣿⣭⣉⣠⣤⡄⠀⠀⠀⠀⢿⠞⡛⠿⣿⢟⡳⠦⣄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣧⣿⣿⣿⣿⠀⠀⠀⠀⢸⣤⣬⣤⣾⢷⣼⣿⣟⢿⣷⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠣⢹⣯⣿⣷⣿⣿⣿⣿⣦⣭⣿⠿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⣀⣠⣤⣿⣿⢿⣿⣷⣏⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣠⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⣾⣿⣿⣟⣿⣿⣿⣿⣿⣯⡿⢿⣿⣷⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⠿⣿⣿⡟⣭⡈⠾⣿⣿⣿⠿⠿⣿⡿⣿⣿⣧⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠠⠤⢶⡶⠶⠖⠂⠀⢀⣛⡠⡬⣄⠀⠀⠚⠡⠀⠭⣿⣿⣷⣾⣿⣧⠿⢿⣷⣿⣿⣿⣶⣶⣿⣾⣿⣿⣿⣿⣍⡿⠩⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠛⠋⠐⠒⠒⠒⠀⠀⢀⣀⣀⡠⣀⣀⣤⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠝⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠉⠉⠙⠛⠿⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣡⣭⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛




⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⣧⠀⢀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣤⡄⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠘⢷⣼⣦⣾⣷⣠⣿⠀⢐⣷⣶⠀⠀⣿⠀⠀⢀⡀⢰⣾⣆⣴⣦⠀⡀⢀⠀⠀⠀⢰⣿⣧⢀⣀⣤⠄
⠀⠀⢀⣤⢴⣿⣿⣴⢿⣿⣿⣿⣿⣯⣶⣾⣿⣯⣶⣾⣻⣷⣶⣏⣿⢟⣾⣿⣿⣏⠀⣿⣿⣷⣆⢀⣠⣿⣿⠋⠁
⠀⠀⠀⠙⣿⣿⣿⣿⡾⢿⣿⣿⣿⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣾⣿⣿⣿⡇
⠀⠀⠀⠘⣿⣿⡿⣳⡇⣿⣿⣿⣿⠈⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⡝⢸⣿⣿⡟⢿⣿⡿⣹⣿⣿⡗⣿⣿⣿⣇
⠀⢀⣠⣤⣿⣿⣿⣿⣷⣿⣿⣿⣿⡎⣻⣿⣿⣿⣷⣿⢽⣿⣿⣿⢀⣼⣿⣿⣿⣹⣿⣱⣿⣿⣯⣷⣿⣿⣿⣧
⠀⢿⡟⠛⠿⣿⣿⡇⢸⣿⡿⢿⣿⡇⣿⣿⣿⣿⣿⢻⢻⣿⣿⣿⡈⢻⣿⣿⣾⡿⣯⡽⣿⣿⣿⣿⣿⡏⠻⣿⣧
⠀⠈⣧⠀⠀⣸⣿⠀⣾⣿⠃⢸⣿⣿⡿⣧⡿⢻⣿⠚⣿⣿⣿⡟⣷⠺⣿⣿⣿⣿⣿⢿⣿⠋⢉⣿⣿⡆⠀⢙⣿⡇
⠀⠀⣼⠃⠀⡏⢿⢂⢹⣿⠇⢸⣿⢻⣿⣿⠁⠈⣿⡇⢙⣻⣿⠁⡧⡐⢻⣿⡿⣿⣿⢿⡇⠀⣸⣿⣿⣿⠀⢸⣿⡇
⠀⠀⠀⠀⢸⠃⢸⡏⢠⣿⢳⠘⢈⠋⣿⡺⡆⠀⢿⡟⠈⣿⡿⠀⠰⠀⠈⣿⡿⢻⣿⣿⡃⠀⣿⠇⠸⣿⠄⢸⣿⡁
⠀⠀⠀⠀⠁⠀⢸⠁⠻⡇⠈⠀⠈⠀⣽⠅⠈⠀⢨⡟⠈⢹⡇⠀⠀⠀⠘⢻⡁⠀⠀⣁⠏⠀⣭⠀⠀⠀⠁⢸⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠸⠃⠀⠘⠇⠀⠀⠀⠀⠻⠁⠀⠀⠈⠀⠀⠙⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡀⠄⠒⠀⠉⠉⠐⠠⠄⠄⠀⠠⠄⠂⠁⠀⠀⠀⠀⢀⠡⢚⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠⣦⣽⡷⠀⢀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠛⠁⠂⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⠔⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠔⣴⠚⠁⢀⠴⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⠀⠀⠘⠀⠀⡤⠚⠀⠁⠋⡀⠊⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠐⢄⠰⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠄⡀⠀⠀⠁⠐⠒⠒⠒⠒⠋⠙⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⣀⢀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠙⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠆⠀⠘⡄⠀⠀⠀⠀⠀⠈⠐⠒⠐⠒⠀⠀⠀⠡⡀⠀⠈⠐⢄⠀⠀⠀⠠⠐⠜⠋⠓⠊⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢦⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⡀⠀⠀⠀⠀⠖⠀⡀⠄⠀⠘⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠠⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠈⠁⠀⠀⠤⢔⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠠⠀⠁⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠁⠠⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⢃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡡


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⠤⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣦⣶⠀⠀⠀⠀⠀⣀⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠛⠁⠀⢀⡠⠔⣪⠕⠁
⠀⠀⠀⠀⠀⠀⣀⣀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠐⠉
⠀⠠⠀⢄⡠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠆⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠄⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠐⠀⠀⠀⠀⠀⠀⢀⡴⠋
⢠⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⢖⠁
⠘⡄⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⡌⠀⠀⠀⠉⠀⠀⠂⠠⠤⠒⠊⠉
⠀⢇⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⢪⡑⠒⠤⣀⠢⢀⠈⠉
⠀⠘⡄⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣐⡥⠂⠀⠁⠀⠀⠑⠄⠙⢦⡀⠀⠁⢂⠉
⠀⠀⠐⠈⢢⡀⠀⠀⠀⠀⠀⠸⠑⠠⠄⣀⣀⣀⣀⣀⡀⠤⠀⠀⠘⠁⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠐⠐⠊⠁
⠀⠀⠀⠁⠀⠑⢄⡀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⢀⠀⠀⠀⢩⢖⠒⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⢰⠒⢡⠊⠁⠀⢸⠈⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠈⠑⠂⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠠⠐⢁⡠⠃
⠀⠀⠀⠀⠀⡸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠤⣀⠀⠰⡒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡈⠓⢤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⡖⠀⣀⠀⢸⣿⣿⣿⣿⡇⠀⣀⠀⢲⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠘⣦⣷⡴⠁⠀⣼⣿⣿⣿⣿⣧⠀⠈⢦⣾⣴⠃⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣅⣠⣶⣿⣿⣿⣿⣿⣿⣦⣄⣨⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠿⠟⣻⣿⣿⣿⣿⣿⣿⣟⠻⠿⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⡇⢾⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⡷⣸⢁⣠⠊
⠀⠀⠀⠀⠀⠀⠠⠤⠤⣬⣿⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣖⣂⣿⣿⣁⠠⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠋⠉⠛⠿⢿⣿⣧⠉⠛⠻⠟⠛⠉⣼⣿⡿⠿⠛⠉⠙⠲⢤

⠀⠀⠀⢀
⠀⠀⠀⡄⢀⡘⣄⠀⢹⡀⢀⣀⠀⣠⠃⠀⠀⠀⠸⡟⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢣
⠀⠀⠀⢷⣿⣷⡾⠀⠀⠳⣾⣯⡾⠁⠀⢀⠀⢰⣿⣿⣷⠀⠀⠀⠹⣦⣶⣦⠀⠀⠀⠀⠘⢷⣿⡶⠃
⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⡆⠀⠀⠀⠙⠛⣿⣿⡟⢧⠀⠀⠀⣿⣿⠟⠲⠶⠄⠄⠀⠸⣿⡇
⠀⠀⠀⢈⣿⣯⠁⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⠃⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⢰⣿⣇
⠀⠀⠀⢸⣿⣿⣧⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠹⣿⣿⡀
⠀⠀⠀⠈⠉⣿⣿⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⣿⢹⡇⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠰⣿⡟⠁
⠀⠀⠀⠀⢰⢣⡃⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠘⠁⡇
⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠛⠀⠤⠀⠀⠀⠀⠐⢆⠐⠤⠀⠀⠀⠀⠀⠀⠀⠐⠑⠢
⠀⠀⠀⠀⠀⢂⠠⡤⠆⠀⠐⠻⢶⡱⣺⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠰⠄⠀⢤⣤⡄⢠⣶⠖⢎⡀⢷⣆⡄⠀⠀⡙⠁⠀⠀⠀⠀⢰⠠⠀⠀⢠⠖⠀⡜
⠀⠀⢤⣀⠀⠂⠠⢼⣄⢠⡇⢠⠀⠟⣼⡿⠂⠈⠀⠀⠀⠐⠀⠀⢰⠀⣤⠀⠀⠀⠄⡰⢀⡄
⠀⠀⠀⠈⠁⠂⠀⠀⣨⣾⣧⣀⣴⡿⠟⢁⡠⠒⠀⠀⠀⠀⢀⣠⣈⡦⣿⣶⣷⠆⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⣨⠿⠛⢟⣻⡅⢠⡆⠀⠀⠂⠰⠤⠝⠻⣿⣻⣿⣟⠉⠓⠂⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠒⢢⠃⠒⢀⣨⠤⠤⠖⠃⠀⠣⣈⠀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠐⠀⡀⠀⠀⠄⠒⠒⠤
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣴
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⠀⠀⠀⠄
⠀⠀⡠⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⡟⣀⣀⣶⢰⠀⣽⡅⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠛⢉⠰⢷⠊⠚⣒⡤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⠀⠀⣀⠐⠀⠀⠀⠀⠀⢸⣄⣁⠀⠾⣃⣶⠏⠁⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠙⠀⠀⠀⠀⢂⠀⣴⣟⠻⡋⠙⠻⡛⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⢨⠓⢹⣷⣄⡈⠃⠤⠬⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⡈⢀⠀⠀⠈⠡⠐⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠢⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣷⠀⠀⠀⠀⣀
⠀⠀⠀⠉⠀⠀⠀⣾⡿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡋⠐⠉⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⢰⡟⢀⣠⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣥⡶⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⠀⠀⠀⠀⠀⣀⠀⠀⢁⣀⣀⣀
⠀⠀⠀⠀⣠⣴⢿⣧⣿⣿⣿⣿⠀⢀⣴⡀⠀⠀⠀⠈⢻⣿⠛⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠄⠋⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠀⢈⠁⠂⣿⣿⣿⣿⣅⠀⠀⠉⠀⠀⢀⡴⠱⣿⣿⣧⡀⣰⡏⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⣼⣧⡀⠹⠟
⠀⠀⠀⠀⠙⠛⠛⢻⣿⣿⣿⣿⡷⠀⠀⠀⠀⢾⠙⠗⣉⠻⣿⣿⣿⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⡿
⠘⠃⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠓⣀⠉⠀⠛⠉⠁⠀⠀⠀⠀⣀⣀⣀⠢⡤⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠛
⠘⠛⠂⠀⠀⣴⣿⡿⠃⣿⣿⣿⠁⠀⠀⠈⡘⠆⡈⠉⣡⡄⠀⠀⣄⠀⠀⠀⠀⠣⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⡀⠛⣓
⠀⠈⠁⠀⠰⠿⢿⣿⣷⣿⣿⣧⣦⠀⠀⠘⠉⡀⠓⣠⡅⢡⡀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⢿⣿⣿⡿⠇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠸⠀⠀⠀⠀⣛⣠⡤⢀⣬⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠒⠀⠀⠀⢸⣿⡆⠀⠶⠀⠀⢸⣿⠏⠀⣾⣿⠃
⠀⠀⠀⠀⠐⠒⠀⠀⠀⠈⣿⡇⠀⠶⠦⠀⠘⣿⠀⠀⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠓⠀⠀⠻⠄⠀⣿⠀⠀⠀⠀⠀⠀⠰⣹⣅⠀⠈⠉⠉⠁⠀⠀⠀⠿⠀⠰
⢀⡤⠤⠀⠀⠀⠀⠀⠒⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡲⠄⠀⠈⠁⠀⢀
⢸⡧⠄⣰⠊⢳⡀⡖⢠⣎⣱⠔⡆⢰⢢⣎⣱⠄⡖⠁⠀⠙⡞⢡⡞⠑⡆⣶⠀⣶⢰⡆⢳⡄⡖⠑⣶⠀⠀⡧⠴⠃⣈⢳⠀⡖⠁⣿⠁⢦⢠⠆
⠘⠃⠀⠘⠲⠚⠀⠃⠈⠳⠶⠀⠘⠃⠈⠳⠶⠀⠃⠀⠀⠀⠃⠈⠳⠖⠃⠘⠖⠛⠘⠃⠘⠃⠓⢖⡇⠀⠀⠃⠀⠀⠳⠚⠀⠃⠀⠙⠆⢈⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⣤⣤⣾⣿⣾⣿⡍⠁⣈⡉⠉⢳⣶⣄⠀⠄⡀⠀⠀⠀⣸⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢰⣷⣿⠗⠐⠚⠛⠿⢿⣝⡥⢷⢨⠛⠛⠓⠲⢹⣿⢀⡀⠰⣆⣨⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠈⢿⣏⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⣿⠇⠀⢠⣿⣿⣧⣤⢷⡌⠁⠂
⠀⠀⠀⠀⠀⠀⠀⣾⠂⠀⠀⠀⡀⠔⠂⠈⠁⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠⠿⠿⢟⣻⣟⡞⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⢤⡶⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣾⣳⠿⡏⣿⣷⠏⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢤⣤⣤⠀⠀⠀⢀⣴⣿⣿⣦⢿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⠛⡐⢶⣿⣿⣿⣿⣿⣦⠿⣿⡷⠂⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⠘⠀⣻⢿⠛⠋⠛⡿⣿⣿⣧⠀⠀⠐⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣶⠞⣿⣿⣧⣙⣶⣷⣿⣦⣄⠰⣿⣿⣿⣷⠀⠀⠚⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠉⣀⠻⣿⣿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⣸⠗⠢⣯⡛⣦⣤⣀⣀⣀⣙⣛⣿⣿⣟⣧⣀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠢⠙⠀⢠⣔⣹⡇⠀⠈⠉⠉⠋⠉⠻⠟⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⠟⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠈⣿⠟⠁
⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡾⠀⠀⣠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣆⣷⠖⢈⣙⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⢤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣵⡧⠤⣤⣤⠤⠐⠚⡻⠖⣶⢦⡀⠘⠷⠴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠁⣈⣤⣴⠖⠋⢠⣠⡴⠚⡁⡀⠙⣿⡟⠒⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⢀⡴⠺⡶⠤⢤⣾⣥⠴⠛⠋⠁⠀⠀⠀⠀⠀⠁⠉⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⢋⣤⠾⠓⢊⣩⢆⢴⠀⣠⢖⠫⣝⡓⢿⣿⠃⠀⠀⢸⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⣠⢞⠡⠚⠉⠀⠀⠀⠀⠀⠈⠁⢠⢳⠁⣿⡎⢻⡎⠃⠀⢀⣤⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣀⡨⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣆⢦⣈⣡⠼⠁⡠⣖⢝⣊
⠀⠀⠀⠀⠀⠀⠀⠰⠃⢠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠘⢋⡉⣤⣴⣽⠞⢁⠎⡼
⠀⠀⠀⠀⠀⠀⠀⠐⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⡾⠟⠿⠻⣿⡿⢿⢹⢀⢎⡞
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣠⢶⠶⢶⣤⡈⡵⠾⢍⠉⣥⣶⣶⠏⠀⠀⢠⣶⠋⢀⠆⣾⢃⣾⣀⣠⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠙⠻⠷⣤⡻⣄⡉⠶⣨⡷⣍⠟⢁⣠⣴⠚⡋⢫⡓⠊⠀⠀⠞⠉⣠⠶⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠉⠙⠻⢿⡿⣿⠋⠀⠈⠉⠀⠉⠉⠉⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠉⠉⠙⠛⠂⠄⠀⠉⠢⡑⠲⠦⣤⣀⢀⣀⣀⣀⣤⠤⠚⠁
⠀⠀⠀⠀⠀⠀⢣⡀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡹
⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣈⠙⠛⠲⠦⠴⣤⣤⣶⣏⣀⡤⠤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⡚⠀⠀⠀⠀⠀⠒⠒⠿⠛⠶⡦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⣄⠀⠦⠄⡴⠚⠛⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⢻⠛⡟⣻⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⣀⠀⢀⣴⡆⠀⢀
⠀⠀⠘⠿⣶⣿⣇⣴⡂⣰⠛⠀⠁⠈⠑⢶⣤⠀⠀⠀⣨⣽⠆⡛⡵⠚⠛⠃
⠠⡶⠶⣤⣻⣿⢿⡿⢺⣇⣀⣠⠁⣤⣤⡼⣞⣷⡀⠖⠋⢡⢎⡇⠙⢿⡆
⠀⠀⢠⣤⡍⣾⢀⠻⣿⣿⠛⠁⠀⠈⠉⠀⠹⣿⡇⠀⠀⠉⠘⡇⠀⠀⠁
⠀⠀⡿⠃⠀⣼⡌⠧⠸⠛⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⠀⣰⠂⠀⠰⡦⠐⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⡇⠀⠀⠀⣤
⠀⠀⠀⠀⠀⣿⠀⠁⠀⠈⣸⠿⠀⠀⠀⠀⠈⠉⠓⢤⠀⢀⠀⣷⢀⡴⠊⠉⠀⠀⠀⠀⠀⠀⢀⣀⢀⠈
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⠋⠀⠀⠀⠆⠀⠀⠀⠀⢸⠀⠀⢡⣿⣯⣾⣷⠀⠀⣠⡄⠀⠀⡠⠾⡦⠀⠈⠁
⠀⠀⠀⠀⠀⣿⠁⠀⠔⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠖⠋⠀⠀⠀⠊⢠⣨⡇
⠀⠀⠀⠀⠀⠇⠀⠀⡷⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⢤⡄⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⡀⣸⢷⣦⣤⣤⡆
⢀⠀⠀⢰⠊⠀⠀⠠⠁⠈⠢⣀⣀⣴⣀⡠⠖⠛⠁⠀⠀⡀⠀⠀⠙⣄⣠⠗⠁⠀⢀⠀⣤⠈⣶⢶⢦⣬⠅⠀⢀
⣿⣟⣤⠆⠀⠀⠀⣼⣧⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠁⠀⠀⠀⣠⣫⠄⢹⣷⣯⢾⣸⣿⣷⣦⣼
⣿⣿⣿⡄⠀⠀⢀⣿⣿⣦⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⢀⣿⣷⣄⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣠⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣩⡍⠉⠉⣩⣍⡩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡚⠌⠉⠀⡀⠀⠫⠂
⠀⠀⠀⠀⠀⠀⠀⠐⡉⠐⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⡠⣏⠀⠀⠀⠀⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠁⠘⣇⠀⡀⠠⣡⠈⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⢴⣿⣯⣯⠻⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⡀
⠀⠠⡈⠀⠁⠀⡀⠈⣴⣿⠃⠐⣾⡶⠒⠲⠂⣙⣋⠙⢨⣽⣿⣏⢘⠛⣛⣟⣫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣤⣆
⣇⠐⠀⠀⠀⠨⡤⠂⢿⡇⠀⠀⠨⠶⠟⠃⢉⣿⠅⠀⠀⠀⠉⢏⠛⣼⣿⡿⢿⡟⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⡇⠀⠀⠀⡀⠀⠀⠀⢈⡷⢴⡿⠛⠀⠀⠀⠈⣠⣂⣠⣠⡀⠀⠈⠚⢿⣿⣿⠫⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⡇⠂⡠⠂⠀⠀⠀⢀⣾⣷⠗⠲⠖⠀⠀⠰⣴⣿⣿⣿⣿⣿⢠⣠⣤⣄⠀⠈⣼⡟⢨⣿⣿⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠿⣿⣦
⡧⠂⠀⠀⠀⠀⠀⢾⣟⠙⠀⣶⡄⠀⠀⠀⠈⠻⠿⡿⠿⠃⠀⠵⣥⢿⠏⠰⠈⠀⠘⡿⣿⣿⣚⣿⣿⣿⣿⣿⣿⣹⢯⣿⣿⣷⣦⣭⠾⢷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠨⣻⠅⠀⡀⠀⠀⠀⠀⡀⣀⣀⡀⣀⣀⡀⠬⠶⠾⣤⢀⣐⣀⠀⠁⠉⢸⢃⠀⠻⢇⣽⢻⣿⡏⢿⡿⠿⠻⢽⣷⣶⣼⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⢶⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⢤⠶⣶⢶⡶⣿⣦⠙⣿⡦⣲⣦⡜⠉⠱⠴⢾⣿⡼⠻⢷⢨⣷⣴⣿⣿⣧⡍⢻⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣿⣿⣿⣿⡿⠟⠉⠉⠀⠀⠀⠀⠀⢀⣴⣿⠟⣿⣿⣷⡉⣱⣾⣿⣷⠶⠚⣡⠞⠁⠀⠂⢀⣥⣍⡟⠛⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣷⣾⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠈⠀⠸⢿⣿⣿⣿⡿⠿⠿⡿⣦⠖⠋⠑⣠⣴⡇⠀⠛⡛⣻⠿⢿⣿⣿
⠀⠀⢀⡔⣀⣤⠎⣉⡽⢿⠟⡿⠉⠉⠉⠛⢷⡢⠉⠦⡄⠀⠀⠡⠀⢀⠀⢠⡿⣿⠿⢷⢿⡄⠀⢀⣀⠴⢺⠿⣋⢧⠀⠀⠂⢳⣶⡞⣻⠃
⠀⠀⠀⠀⠀⢀⡞⠁⠀⡚⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠱⡦⠤⠭⠬⠵⣶⡞⠛⠉⠀⠀⠒⣠⠽⠛⣆⠀⠀⠈⠟⣴⠗⠒
⠀⠀⢸⡗⠳⣬⠷⠀⠀⠙⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣴⣻⡿⠤⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⢹⣷⣤⡤⠎⠘
⠀⠀⠘⠀⢀⠀⠠⠂⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡹⠇⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⡤⣰⠇⠉⠅⢠⢀⢸⠄
⠀⠀⠀⠄⠃⢀⠀⠀⠀⢀⠀⠀⠠⠶⠆⠀⠀⢒⠒⢂⡼⣿⣷⣤⣘⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⡴⠛⠂⢠⣤⡄⣼⣷⢓⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡁⠒⠆⠀⣒⡛⢰⣆⣀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠠⠾⠒⠚⠉⠙⠂⠀⠐⠒⠘⢃⣷⠛⠛⠺⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⠤⡦⠐⢶⠋⠍⢙⣾⣿⣿⡿⠛⣁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠈⠀⠀⠀⠀⢀⠠⠖⢘⣿⠀⠈⣿⣶⡾⠷⠋⠀⠀⠀⢰⡀⠄⠠⡤⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟
⠀⠀⠀⠀⠐⠒⠒⣾⣧⠶⠞⣻⢛⡶⠛⠋⠁⠀⠀⠀⢀⣀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠈⠉⠟⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⢀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⣂⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠰⣾⢿⣿⣿⣿⣧⠀⠀⠀⠀⠠⢀⣀⢙⣫⣴⣾⣿⣀⣾⣿⡿⠂⠶⣆⠀⠀⣠⣾⣿⣿⣷⣦⠀⢰⡶⠀⢸⣿⣿⠿⠓
⠀⣴⣞⣺⣿⣿⣿⣿⣿⣡⣤⣄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠁⠀⠀⠙⢦⡀⢻⣿⣿⣿⣿⣿⣴⠏⠀⠀⢀⣿⣿⣿⣴⣶⣤⡀
⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠸⣿⠿⠛⣿⣿⣿⣿⣿⣦⢠⣤⠀⠀⠈⠛⣦⣍⣻⣟⣿⠟⠁⠀⢀⣴⣾⣿⣿⣿⡿⣿⣿⣿
⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⠙⣹⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡿⢿⣿⣿⡎⣿⡿⣷⡀
⠀⠀⠀⠀⠀⠉⠉⣹⣿⣷⣦⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⢫⣄⠙⠛⠁⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠈⢿⣿⠀⠈⠛⣿⣿⣿⡀⠈⣷
⠀⠀⠀⠀⠠⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⢀⣹⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡟⠁⠀⠀⠀⠀⠀⠘⢿⣀⠀⢠⣿⣿⣿⣷⡈⠏
⠀⠀⠀⠀⠀⣰⣿⡿⢹⣿⡿⠁⢀⣴⣾⣿⣿⣿⣿⣿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠹⠇⠀⢻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢠⡿⠋⠀⣼⡿⠁⠀⠻⣿⣿⣿⣍⠈⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢠⣾⠁⠀⠀⠹⣷⡀⠀⠀⠈⠛⠻⣿⣦⣿⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢡⣿⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠀⢼⣿⣷
⠀⠀⢀⡿⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠿⠃⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⣿⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⠉⠀⠀⠈⣿⡟
⠀⢀⡞⠀⠀⠀⠀⠀⢀⡾⠆⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⢸⢿⣦⡄⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠘⠁⠀⠀⠀⠀⠀⠉⠀⣀⡠⣤⡄⠀⣠⡄⢙⡉⠩⠤⢀⣄⣀⠄⠀⠀⠀⢤⡤⠄⣙⠿⢄⡀⠀⠀⣤⡤⠀⣄⠀⣈⠉⣤⠀⠀⠀⠀⠀⠘⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠙⠋⠓⠉⠙⠋⠘⠓⠐⠂⠐⠋⠉⠓⠀⠀⠀⠀⠚⠀⠘⠓⠀⠚⠁⠀⠀⠘⠃⠀⠙⠁⠉⠃⠙⠃⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣀⣤⣶⣒⡽⠟⣃⣤⠶⢒⣹⡿⠂⠰⠞⣃⡀⠤⣤⣀⠀⠀⠀⠀⢀⣤⠤⢤⣄⠀⣀⣤⣀⠀⠀⣠⡤⠤⢤⣀⠠⠤⣤⡤⠄⠠⣄⣀⣀⣤

⠀⠀⠀⠀⠀⠀⢠⠚⢉⣑⠢
⠀⠀⢀⠤⠒⠒⢱⢋⢤⣄⣙⡥⢀⣉⠉⠉⠐⠠⠤⢀⡀
⠀⠀⠇⠲⠾⢿⣿⣧⣿⣟⣼⣷⣄⠀⠉⠀⠀⠀⢀⡀⠈⠉⠀⠒⠒⠠⠄⡀
⠀⠀⠘⢶⠤⣀⠈⠻⠿⢿⣿⣿⣿⣿⣍⠑⠢⢄⠀⠈⠉⠐⠒⠂⠀⠤⡀⠈⠙⠬⡙⠽⠃⠲⠀⣠⣀⡀
⠀⠀⠀⠀⠁⠒⠭⢓⡢⠤⢄⣈⠙⢿⣿⣆⠐⠠⢈⡀⠀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠈⠉⠀⠡⠼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣑⠤⡈⠁⠀⠈⣿⡀⠀⠈⠈⠁⠒⠒⠬⠥⢒⣂⣴⣄⠠⢄⣀⠀⠀⠑⣄⠤⠔⢁⠤⣀
⠀⠀⠀⠀⠀⠐⣻⢖⡀⠤⢤⡨⠦⣠⠊⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠊⠀⠀⠈⠢⠀⠿⣶⠀⠉⢆
⠀⠀⠀⠀⠀⠀⢨⠄⣀⢠⢌⠀⠀⠨⠐⢢⠀⠀⢃⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⢉⣹⢰⠒⠤⣏⠆⢣
⠀⠀⠀⠀⠀⡠⠤⠵⢀⡉⠀⠉⣽⣤⠿⠥⡀⠀⢸⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢠⠃⢠⢉⠤⠤⠒⣁⣍⡤⠬⣕⢾⣑⠈⡄
⠀⠀⠀⠀⠀⠈⠉⠒⠮⣁⡉⠀⠖⠀⠑⠚⠁⠀⢸⠓⠢⠤⢄⣀⣀⣀⠤⠤⠒⠚⡆⠀⠋⠀⠔⠊⡤⡏⠑⠒⢄⢹⠗⠒⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠤⠤⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡄⡰⢀⠴⢪⡐⢄⢹⢓⠊⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠉⠀⡌⠈⠀⢱⢈⢾⠛⢹⣋⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠡⡆⠀⠀⠉⣘⣷⡾⣿⣋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⣠⠛⢷⣲⣆⣻⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠲⠋⣅⣼⡈⠢⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣦⣾⣿⣿⣶⣶⣾⣿⣿⣿⣶⣶⣤⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣴⣶⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣽⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣫⡿⣿⣿⣶⣤⣤⣆⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣛⣯⣭⣭⣯⣍⠩⠿⢹⣿⣟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣤⡀⠀⢀⣂
⠀⠀⠀⠀⣰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠭⠉⠉⠋⠁⠀⠀⠉⠘⠉⠘⠚⡶⡿⢳⣿⡿⠧⡼⢿⡿⣠⢤⡤⣤⡴⣶⣗⡆
⠀⠀⠀⠀⠻⣿⠟⣿⣿⣿⣿⡿⠿⣿⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⠿⠷⣒⣴⣿⣟⡛⠽⠗⣳⣯⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣗⣦⣍⠻⢿⣦⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣥⣶⡿⢟⣯⡩⣾⣿⣟⣻⣿⠟⠁
⠀⠀⠀⠀⢀⣠⣄⣀⠑⠮⣗⣯⣿⢷⣿⣳⡦⡙⢯⣟⡓⠦⠤⠄⠤⠀⠄⢀⣀⣤⣶⣿⣿⣻⣖⣮⣽⣶⣾⣿⡿⠋⠁
⠀⠀⠀⢠⡟⣝⣿⣿⣿⣷⣾⣿⣿⣻⠿⣷⣿⣿⣮⣻⣿⣿⣿⣶⣶⣾⣿⣿⣿⣽⣫⠿⠛⣿⡿⣻⠿⣟⠟⠧⡀
⠀⠀⠀⠀⢷⢹⣿⣯⣟⡿⣿⣄⣄⡉⠉⠒⠍⡻⣿⣿⡹⣿⣾⣿⠾⣿⣿⣿⣿⣧⢿⣿⡟⠛⠉⠓⠀⠀⠑⡀⠀⠙⠁
⠀⠀⠀⠀⠈⢳⣻⣿⣯⠙⠺⢿⣟⣻⣷⣶⣤⣭⡌⣿⣿⡟⠛⠛⠛⠛⠛⠋⠉⠙⣎⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠙⣿⢿⣷⣄⠀⠀⠉⠛⠓⠾⢭⣭⣻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣿⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣻⣿⢷⣄⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣬⣀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣝⣿⣿⣷⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡍⠛⣯⣿⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣟⠻⣶⣌⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠙⢾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠈⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠈⠯

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢊⣉⡉⠑⠢
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡡⠊⣀⣤⣌⡱⡀⢡
⠀⠀⠀⣼⣿⣉⡆⠀⠢⣀⣀⡀⠀⢤⠎⠀⡇⣼⣿⣿⠋⢻⡇⢸
⠀⠀⢠⡹⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢻⣿⣯⣶⡿⠁⢸
⡔⠊⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢛⣉⣀⠀⢸
⠳⣄⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠊⠸⠀⠘⡄
⠀⠀⠉⠒⠦⠬⠭⠉⠁⠈⠉⣉⣁⡈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠦⣄⣀⣀
⠀⠀⠀⠀⠀⠈⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⡔⠒⢮⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣈⣢⡀
⠀⠀⠀⠀⠀⠀⠓⠀⠜⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⠀⠀⠀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠂⠐⠀⡁⡄⠀⠠⠠⡈⢣⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠓⠲⡀⡁⢀⢀⠥⣀⡔⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠱⡄⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠁⠇⠘⡄⠀⠀⠀⡀⠔⢑⣄⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠈⢆⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠣⠤⠔⠉⣠⠔⠋⠈⠳⢄⡀⠀⠀⠀⠀⠀⢈⠁⠀⠈⡇⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣀⡴⠊⠁⡀⠠⠄⡒⢨⢍⠲⠦⢤⡤⠐⠁⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠓⠒⠒⠋⠁⠠⠁⠁⡒⠀⠁⡠⡢⢊⡤⠒⠁⠀⣀⡤⠖⠋⠉⢛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠚⠁⢘⡄⠀⠒⠁⢀⡤⠖⡋⠁⠀⢀⠄⠊⢀⢂⠞⠁⣰⠉⠙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣀⠠⠤⠄⠢⠀⢀⠠⡏⠀⠘⣄⠀⢸⠁⠀⢠⢣⠋⠀⠀⢡⠀⠀⠀⠀⠈⠙⠒⠤⣤⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠔⡡⠊⠀⢢⠣⡀⠀⠈⠙⠉⢸⠉⠁⠳⡀⠀⠀⡜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠠⡊⠀⠀⠀⠀⢣⡑⠒⡄⠀⠀⠀⠙⠒⠒⠁⠀⣔⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠴⠃⠀⠀⠀⠀⠸⣄⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠑⠢⡀
⠀⣀⠤⠒⠒⠒⠒⠓⠂⠀⠐⠒⠀⠀⠙⠶⠤⣀⡀
⡜⠁⢀⣀⡀⠀⠀⠀⠠⠒⠈⠁⠒⠢⢄⠀⠛⠂⢈⡉⠒⠠⠤⠄⣀⣀
⢣⡀⠀⠈⠁⠀⠀⠀⢠⣊⣉⣈⠉⠑⢄⠇⠀⠀⠀⠈⢱⣦⡤⢄⣀⠰⠆⠉⠉⠈⣾⡎⠉⠉⠒⠢⢄⡀
⠈⢏⠢⡀⠀⠀⢀⠀⠘⣌⠻⠿⠿⠆⡸⠀⠀⠀⣀⠀⠈⠛⠁⠀⠀⠈⠉⠉⠐⠒⠉⠄⠀⠀⢺⣿⣦⠉⠢⣀
⠀⠈⠦⡈⠒⠤⣈⡃⠀⠈⠑⠒⠒⠈⠀⠀⠙⠃⠙⠁⠀⠀⠀⠀⢰⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣈⡑⠦⣀
⠀⠀⠀⠈⠒⠤⢀⣈⠉⠒⠂⠀⠃⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠉⠁⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠻⠃⠀⠀⠑⠂⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠘⠛⠁⠀⠀⠀⣴⣶⣤⠀⠈⠉⠀⠀⢠⣶⣤⠀⠀⠀⠀⣶⣶⣆⠀⠉⠢⠀⠀⣀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⢴⣶⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣈⠉⠁⠀⠀⢠⡷⠊⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⡀⠀⠀⠀⡄⠁⠀⠀⠙⣄⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠘⠿⠇⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⣠⢏⣀⠀⠀⢠⣀⠄
⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠔⠉⠉⠒⠤⣇⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠒⡀⠀⠀⣴⠃⢾⡿⠀⠀⠀⡜
⣏⣀⣈⣉⣁⡀⢈⡩⠀⠀⠀⠀⠀⠀⠀⠀⢸⢆⠀⠉⠀⣀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⣸⠃⠀⠀⠀⠀⠀⠰⠁⡸
⠀⠀⠀⢀⡠⠜⢉⡠⠔⡲⠋⣀⠤⠐⠒⢤⡈⠬⢧⡀⠘⠿⠃⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⣄⢀⠇⠀⠘⠀⠀⠀⢠⠃⢠⠁
⠀⠖⠉⡡⠔⠈⢡⠒⢩⠔⠋⠀⠀⠀⠀⠀⠉⠒⠚⠙⢄⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠋⠈⠀⠀⠀⠀⠘⢠⠃⢠⠃
⠀⠉⠈⠁⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠛⡦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠁⠀⠀⠀⢸⠀⠐⠂⠀⠀⠀⢀⡴⠁⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⣀⡴⠋⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡡⠞⢩⠀⢠⡄⣄⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⡇⠀⠀⠀⠉⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠎⡠⠃⡇⡟⢎⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⢕⡒⠤⠔⠁⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡜⠁⠀⡇⠀⠈⢪⠒⠲⡄
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠤⠒⠊⠁⠀⠀⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠃⠀⢠⠁⢀⠀⠘⠤⠖⠁
⠀⠀⠀⠀⠀⠸⣄⣀⠤⠒⠒⠒⠒⠒⡨⠋⠀⣀⠤⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⢀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠉⣤⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠐⠒⠆⠀⠀⠉⠉⠲⣆
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠺⡄⠀⠀⠀⠈⠀⠀⠛⠈⠁⠉⠁⢂⠀⠀⠀⡅⠀⠲⣀
⠀⠀⠀⠀⠀⣀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠂⡐⠈⣀⣠⣈⠲⠀⢰⡸⠋⠀⠀⠀⠈⠳⡄⢀⠠⠀⡀⢀
⠀⠀⠀⢰⣿⠋⢓⠀⢀⠀⠀⠀⠀⢀⣀⠠⠁⡄⢀⣾⣿⡟⠛⢳⡆⠈⠁⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠈⠁⡄
⠀⠀⠀⢸⣿⠿⠿⠀⠀⠐⠂⠀⠐⠉⠉⠀⠀⢇⠸⣿⣿⣣⣤⡾⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄
⠀⠄⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠿⠿⠿⠋⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢘⠃
⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢳⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⢀⡤⠴⠊
⠀⠑⠊⣡⢀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠀⠉⠀⠀⠀⠀⠀⠑⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠀⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠂⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠤⠼⢦⡀
⠀⠀⠀⠀⠀⢀⠀⠁⠄⠁⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠈⠐⢠⢀⠀⡧⠀⠠⠀⠘⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠈⢦⡀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⠀⠀⠀⠀⠀⠀⠉⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠠⠔⠂⢁⡴⠚⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢱⡄⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⢀⡠⠞⠉⠀⣀⠀⠤⠀⣙⠓⠦⠄⣀⣀⠠⠀⠀⠀⢀⡼⠁⠀⢀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠘⠦⠄⠴⠞⠋⢠⠀⠀⠠⠀⠐⠒⡤⠉⢶⣀⠦⠉⠁⠀⢀⡠⠖⢛⡶⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠈⠀⠠⠀⠀⡀⠉⢠⠄⠈⠀⢀⡀⠒⠊⠁⠠⠒⠉⠀⠀⢃⠰⠀⡀⠔⠶⢄⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢰⡏⠁⠐⠒⠒⠶⠉⠰⠀⠀⠀⠉⠀⠀⠀⢠⠞⠁⢀⡃⠈⠁⠀⠁⠀⠀⣈⠂⠀⢠⡇⠀⡠⠊⢸⠉⠲⢤⣄⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⠠⠂⠈⠉⠀⠀⢀⡄⠂⡸⠁⠉⠉⠑⠤⠤⢃⠶⠶⠡⡞⠂⠂⠰⢰⠎⠀⠀⢸⠀⠈⠀⢈⡏⠙⠛⠉
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠡⠀⢤⡀⠀⠀⠀⠈⠢⢀⣀⡸⠀⠀⠠⠘⠠⡀⠀⢸⠀⠀⢠⠜⡇
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⠀⠀⠈⠉⠀⠀⠀⠣⣀⡠⠃⠀⠈⠀⠰⠁⢀⡇
⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠘⠂⠘⠃⠀⠀⠀⠀⠀⠀⢦⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⡠⠈⡇
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠋⠀⡟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡆⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠎⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⢹⠀⠀⠀⠀⠸⠒⠒⠂⠠⠤⣤⣤⣤⣤⡄⠀⢠⡿⠂⢀⠚⠃
⠀⠀⠀⠀⠀⠀⠇⠒⠂⠀⠠⠤⠤⠤⠤⠤⠄⠀⣸⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠂⠀⡇⠀⠆⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⡏⠀⠀⠀⠒⠒⠒⠓⠒⠂⠀⠤⠤⣿⠀⠀⠀⡇⠀⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠇⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠘⠒⠂⠤⠤⠤⠤⠀⠀⣀⣀⢀⡀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠒⠒⠚⠃⠀⠤⠤⠤⠤⠀⣀⣀⣀⣀⠀⠀⣴⠃
⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶
⣿⣿⣿⡏⠁⠛⠙⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⣒⠀⢀⡂⢄⣀⢔⠠⠍⠩⠭⢐⡢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠊⠁⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠀⠈⠪⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠑⢄⡀⠀⠀⠀⢀⠰⢄⠀⠀⠀⠀⠀⢀⡠⠊⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⠀⠒⠈⢁⡀⠀⣈⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠭⣀⡈⢆
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠰⣈⠆⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀⠀⠓⠘⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⡆⡠⠂⠢⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠁⠈⡄⠁
⠀⠀⠀⠀⠀⠀⠀⢇⠣⢀⠜⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠒⠔⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⢀⣀⣀⣀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠁⠂⠄⣀⠀⠀⠀⡀⠀⠀⠀⠠⠄⠀⣀⠤⠒⠉⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠆
⠀⠀⡠⠄⠒⠀⠀⠐⠐⠎⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠘⡂⠀⠒⠒⠠⣀
⠀⡌⠀⠀⠀⠀⠀⠀⢰⢒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡂⢡⠀⠀⠀⠀⠀⢡
⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠀⠀⠀⠀⠀⢈
⠀⠰⡀⠀⠀⠀⠀⠀⢸⠁⠀⡂⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠁⠀⢱⠀⠀⠀⠀⠀⠸
⠀⠀⠱⡀⠀⠀⠀⠀⢸⠑⠊⠀⠀⠀⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠑⠒⢱⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠆⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⠔⠁
⡔⠂⠒⠀⠂⠒⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠚⠀⠐⠀⠐
⠉⢂⠶⠂⠀⠀⠀⢀⡀⠠⠤⠵⢄⡀⢰⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⡗⠚⠀⠀⠤⢀⡀⠀⠀⠐⠶⠆
⠀⠡⢀⡀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠈⢘⠀⠀⠀⠀⢠⣀⡀⣀⣀⡀⢀⢀⣀⠇⠀⠀⠀⠀⢅⡀⠀⠀⠀⠀⠈⠑⠢⠄⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⢁⠤⠄⠀⢠⠄⠈⠙⢄⠀⠀⢠⠊⠀⡠⠄⠀⠀⠒⠄⡈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⠁⠀⠢⣀⡸⠀⠈⠉⠁⠀⠀⠈⠁⠉⠀⠠⠀⠜⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⢠⣾⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣺⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⢀⣷⢸⡇⠀⠀⣤⠤⣄⠀⠀⠀⠘⣿⠁⠈⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡙⢏⠙⡄
⠀⢸⣡⠟⠂⣿⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⣾⢙⠒⢾⡆⠀⠀⠀⡞⠉⢯⡁⠀⠀⠀⠀⡀⢠⣶⣄⡀⠈⠳⣤⣠⣽⠗
⢀⡼⢻⠶⣟⠁⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠘⠲⣴⣾⠗⣒⠒⣶⣷⡏⡇⢷⠀⠠⣶⣾⡿⢈⣿⡞⠁⠀⣼⢃⣤⣿
⠀⠀⡿⣆⠈⢳⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⡾⣩⣟⡴⣣⢾⡉⡟⡇⢷⣸⣄⡤⠞⣿⠷⠈⡟⢯⡳⣤⡷⠏⢠⢿
⠀⠀⣧⣬⣾⠿⠛⢧⡀⢀⣀⡀⠀⠶⣫⡭⠭⠞⣳⣿⠿⣇⠀⢿⡇⠹⢤⣤⡤⠤⠴⣿⠀⠘⠃⠀⠉⢲⠦⠴⠋⢸⠇
⠀⠀⠉⠉⠙⣆⠀⠈⣟⡉⢀⡇⠀⠀⠀⠀⠀⠀⠈⠀⣠⠞⠀⣼⡇⠀⠀⢸⡆⠀⠀⠛⠂⠀⠀⠀⠀⡾⠤⠶⠶⢸
⠀⠀⠀⠀⠀⢹⡄⢰⠏⣹⣾⠁⠀⠀⠀⠀⠀⠀⣠⠞⣡⣶⣴⢿⡇⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡾⢰⠏⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⢸⣥⣯⡟⠸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣸⠃⡜⠀⡆⡆⣸
⠀⠀⠀⠀⣼⢡⠏⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣿⠀⢸⡇⠀⠀⣾⠀⠀⠀⠀⠀⠀⢠⡏⢰⢣⠀⡇⡇⣿
⠀⠀⠀⢰⢇⡟⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⣦⢸⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⣼⠁⡏⢸⢀⣇⣇⣿
⠀⠀⢀⡏⡞⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⣠⡤⠴⣿⠣⣿⠟⠈⠧⠤⢬⣷⡆⠀⠀⠀⠀⠀⠛⠛⢩⣟⣋⣹⠉⠁
⠀⠀⣼⣽⣁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠰⠿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠺⣿⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣦⣤⣾⣿⢻⢷⡦⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⡿⢛⣿⣿⣎⣘⣯⣍⣰⣿⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣺⣥⣶⣿⣿⣤⠴⢶⣾⠿⠟⠋⠉⠉⡠⢊⣞⣡⣶⣾⣿⣿⣿⣿⠟⣩⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡮⣴⣶⣿⣿⣿⣿⣿⡿⠷⠚⠛⠉⠀⠀⢀⣠⠀⠁⣰⣿⣿⣿⣿⣿⠿⢟⣩⡴⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠄⣪⠿⠁⠀⠀⠉⠉⠉⡉⠉⠉⠄⠠⠀⠀⣐⣊⣉⣤⣴⡾⣱⣿⣿⣿⣿⠟⣡⢶⡿⢋⠕⠁
⠀⠀⠀⠀⣠⠶⣧⠞⠁⠀⠀⠀⠀⢒⣈⠥⠰⠶⢶⠛⠋⠙⠋⠋⠉⠉⠛⢉⣰⡿⠿⣛⣛⡉⢪⡟⣠⠖⠁
⠀⠀⠄⢊⣀⡼⠁⠀⠀⡶⣊⡤⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⡶⢶⡆⠈⣡⠴⣾⣧⣶⣶⡶
⠀⡇⣀⣼⠟⠁⠄⣠⠞⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⣿⣾⣾⣷⣶⣿⠇⢀⣼⣿⣿⣿⢟⠓
⣠⠿⠿⣿⣤⣥⡞⣁⣠⣶⠾⠗⠛⠒⠛⣳⣶⡶⣶⣦⣄⣤⠰⣾⢧⡼⠙⢿⣿⡟⠛⠫⢠⣾⣿⣿⣏⡠⠀⢀
⢇⠀⠀⠀⠀⠈⠙⠋⠉⠈⠉⢸⣷⡖⠛⠻⠧⣤⣈⣈⣩⡿⠷⠬⣀⠳⣴⣌⠙⢿⣦⡴⠿⣿⣿⡿⠺⠗⠊⠁
⠘⠻⢷⣶⣦⣤⣾⠀⠀⠀⠀⠀⢾⣧⠀⠀⠀⠀⣽⠉⠉⠁⠀⠀⣿⣷⣾⣿⣦⣌⣩⡽⠿⠟⠛⠉
⠀⠀⠀⠈⠙⠻⢿⣿⣿⡾⣶⣭⣮⣿⣦⣠⣀⣠⣽⣆⣀⣀⣤⡐⣿⣿⣿⣿⣯⣩⢤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⠿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠤⠤⠄