Turtle Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣶⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠁⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣼⣫⣽⣙⣦⣄⡰⢻⢻⢷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡗⡭⠴⢭⠁⢀⣺⣻⡿⠉⠙⢟⡾⢻⣷⢰⣏⢷⡯⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⡂⣾⣧⠛⠉⣷⣿⠟⠋⢳⣤⠲⢻⣷⣄⣙⣮⡃⡫⣝⣥⢛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣭⣞⢹⠟⠁⠀⣠⣽⡿⠀⣀⣸⣟⠅⠀⡫⣿⠏⠛⣿⡗⠈⠳⣱⢆
⠀⠀⠀⠀⠀⠀⠀⢘⠾⠏⠀⠀⠀⠀⣶⣾⡿⠟⠋⠉⠉⣴⣿⠻⣿⣆⣀⣹⡷⣿⠀⠈⠚
⠀⠀⠀⠀⠀⠀⠀⠸⠊⠀⠀⠀⠀⠀⠙⠻⣿⣥⠀⢀⣀⣛⠏⠀⠠⣿⠛⠟⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠟⣷⣾⡟⠉⠙⢻⣾⠿⢷⣄⣠⡿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠿⣿⣶⡼⠖⠘⠣⣀⣘⠛⢻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠿⠷⣮⣞⣉⣭⠽⢶⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠟⠋⣽⡿⣧⣤⣼⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠲⠖⠛⠛⠋⠛⠋⡙⠛⠒⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠖⠒⠶⠤⢤⣀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⢲⣄⠀⠀⠀⠀⡼⠁⠀⠀⠀⢨⣥⡤⠈⣷
⠀⠀⠀⠀⡴⠃⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠄⠀⠈⢣⣄⡤⠚⠀⠢⡀⠀⠀⠀⢀⠀⣤⠟
⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠀⠈⣀⡴⠶⠞⠛⠁
⠀⠀⢀⡞⠀⠘⠐⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⢄⠀⠀⠀⠀⢀⣤⠞⠉
⠀⠀⠘⢦⡆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠤⣀⠀⠤⠀⡀⠈⠀⠀⠄⠀⠀⠂⠑⠀⠰⠀⠄⡀⠺⣏
⠀⠀⠀⣠⠟⠀⠦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⠀⠀⠀⠐⠀⣽
⠀⢀⡴⠞⠃⠀⠀⠀⠀⠈⢂⣤⣤⣤⣀⡀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡄⠀⢁⣠⣄⠀⠀⠀⠀⠀⡏
⢰⡟⠀⠀⠀⢀⣀⡀⣾⡟⠉⠀⠀⠀⠉⠉⠉⠉⠙⠓⠶⠶⠦⠭⠤⠭⠴⠖⠒⠛⠋⠉⣹⠀⠀⠀⠀⣴⠇
⠘⢧⣀⡀⠈⢺⡏⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⣤⣦⠶⠇
⠀⠈⠉⠙⠉⠉

⠀⠀⠀⠀⠀⠀⢠⠔⣛⢋⡉⢛⣿⣦⣄
⠀⠀⠀⠀⠀⣀⠋⠸⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠙⣿⣶⣍⠛⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠸⣿⡀⠑⠻⣿⡿⢿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⡒⢀⠷⡿⢋⣻⠿⢿⣯⡿⠷⡉⠐⢀⣀⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡽⣿⣿⣤⠜⠛⠳⠇⢺⣿⣿⣿⣿⣿⣷⣯⣕⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣿⣿⣾⣿⣿⣿⠁⠐⢀⡀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣦⡌⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⣛⣋⠙⠿⣿⣿⣿⡄⢸⠇⠀⠀⣂⣽⣿⣿⣿⣧⣽⣿⣿⣿⣦⡀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⢀⡾⠃⢰⣿⣿⣿⣿⣶⣿⣿⣟⣿⣷⠤⣀⣀⣘⣡⣿⣿⣿⣽⣯⣿⣛⣿⣿⣿⣶⡄⠈⠓⣄
⠀⠀⠀⠀⠀⠀⢺⣀⣀⣿⣽⣿⣿⡿⠟⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣷⡿⠿⣿⣿⣷⣄⠈⣳⡀
⠀⠀⠀⠀⠀⠀⢸⣏⣛⣿⣿⣿⠇⠀⠀⠀⠀⠹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣼⣿⣻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢸⢤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣷⣿⣾⠀⠀⠉⢿⣻⣿⣿⣿⣿⣿⣿⣦⣭⡿⡿⣟⣩⣿⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⠁⠀⠀⠂⠀⠀⠀⠀⠘⢯⡻⣾⣦⡀⠀⠻⣭⣛⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣟⣿⣦⣄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⡈⣤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠙⢮⡻⢶⣶⣟⠀⠈⠙⢿⣭⣽⠷⠿⣥⣾⠛⠷⣛⠯⣿⡿⢿⣷⣮⣙⢻⣿⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢭⣻⠿⣶⣠⣄⣹⣿⣥⣴⣿⣿⣿⣾⣿⣿⣾⣿⣿⣧⣽⣿⣿⣿⣶⡛⢻⣷⣶⣦⣰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⢿⣿⣿⡽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⢿⣿⣿⣄⠉⠉⠛⠯⠽⣟⣷⣽⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣀⣹⣿⠈⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠉⠀⣌⡛⠿⣿⣿⣿⣏⡉⠙⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠟⠁⣀⡤⠒⠊⠁⠀⠀⠙⢿⣯⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣥⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠇


⣀⣀⣀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠈⠀⡶⠆⠠⡈⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠈⠁⣎⠰⡷⢽⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠚⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠃⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣴⡀⡀⠀⠀⠀⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⡾⠯⡤⠀⠤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠤⠀⢀⠀⠀⠀⠀⡄⠀⡀⠠⠀⢁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠽⣏⡹⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⢃⠃⡳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣻⣯⡿⣏⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢶⣴⢬⡱⡨⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⢷⣥⢷⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣭⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⠛⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣉⠵⠠⠖⠛⡳⠤⠀⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣖⠟⣚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣾⠖⢈⣰⢖⡋⠀⠀⠀⠀⢀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣰⡟⡘⢃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡽⠛⠁⢀⠘⠁⠀⠈⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢏⠳⢐⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣂⣠⠔⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢠⠌⠂⠉⠉⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⣤⡏⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠾⣯⣤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⡀⠈⣧⡀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣀⡤⢳⡤⠶⣎⠉⠲⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⡷⣀⡜⠛⢾⠁⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠠⢀⣿⠹⣽⡗⣿⢙⣴⣶⡄
⠀⠀⠀⠀⠀⠀⣀⣼⣿⠽⠷⣿⣿⡿⠀⠀⠀⠴⠀⠀⡀⠀⠀⡀⢀⠋⠀⠀⢀⠀⠀⠀⠉⠁⠀⠀⠤⠐⣿⡇⠸⢐⠪⣋⣭⠴⠊⠉⠾
⠀⠀⠀⠀⠀⠉⠛⠛⠙⠃⠈⠉⠙⠈⠁⠘⠳⢄⡀⠀⠀⠀⠈⠁⠘⠃⠀⠀⠉⠀⠀⢀⣀⠄⣐⣲⠀⣽⠋⠀⠀⠀⠁⠀⠀⠐⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠄⠀⢤⣀⣀⡠⠀⣒⡵⠞⠋⠁⠀⠀⠹⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠶⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠘⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣹⡃⢻⡁⢤⡰⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⣶⡗⣢⡽⠀⣸⢣⣿⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠽⣇⡸⢗⢳⣍⣳⣿⡶⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣞⣿⣿⣦⣿⢿⠷⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡀⠀⡉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠆⠀⠀⠀⠰⢟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣠⣆⣄⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢉⡻⢤⠤⠤⠤⢿⣒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠈⠉⢒⡶⠛⣴⠋⠀⠀⠓⠂⠀⠀⢈⡟⢦⢹⣖⢖⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠕⠀⠀⡄⢼⢀⡾⠉⠓⠶⠤⣤⣦⣶⣒⠋⢀⠞⢿⠙⣆⡉⠀⡙⡄
⠀⠀⠀⠀⠀⠀⠀⠳⠤⠞⠋⢩⠋⣿⠋⠛⢢⣴⡏⠁⠀⠀⠈⢳⣼⠀⠈⣇⡸⠉⢧⣑⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡧⢆⡀⠀⡗⡇⠀⣶⡷⠀⢸⣿⠀⣠⡏⢱⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⣟⠠⠀⢀⡏⣗⠀⠙⠀⠀⣼⣯⠀⢩⠇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⡀⢀⡼⠁⠸⢤⣄⣀⠤⠏⠹⣄⡼⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡖⢳⡋⢀⠔⠚⠙⠉⠉⠛⠛⢲⡸⠁⡼⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠊⢳⡀⠙⣯⣀⡀⢠⢆⡒⣀⡤⢾⣡⠞⠁⠠⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠂⠀⢀⠟⠒⠳⢌⣉⣉⣹⣉⠥⠴⠚⠉⠲⡀⠀⡅⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠄⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠠⢁⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁


⣏⣈⣯⣿⣿⣯⣿⣽⣽⣿⣏⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣯⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⢉⣵⠿⠋⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠘⣿⣃⢴⣶⣶⣿⣝⣯⣿⣹⡛⢿⡟⡶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣰⣾⣿⣿⣤⣯⡽⣿⣿⣦⣼⣿⣿⣿⣟⣳⡿⣿⣿⣻⣶⣦⡀
⢀⣀⣀⡤⣤⢠⡀⠀⠀⠀⠴⡿⢻⡿⣿⣿⡟⠛⡿⢿⣿⢿⠿⢻⣿⣯⣿⣿⣶⣽⣿⣦⣿⣻⣿⣦⠠⢦⣶⣶⠖⠚⠁
⠋⠉⠛⡧⢿⡿⠁⠀⠀⢠⣿⣷⣿⣷⣻⢽⣿⣾⡿⣏⣩⣽⣧⣾⣧⣤⢾⣯⡔⢉⣿⣿⣿⣿⡋⣿⣿⡉
⠀⠈⠚⠿⢿⡇⠐⠀⠀⣻⣿⣿⣉⣙⡿⣿⣿⣿⣿⣮⣿⣫⠿⣿⣾⣿⣿⣿⣿⣿⡟⠻⣿⠯⣽⣿⣬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⡿⣤⣝⠉⢛⣿⡟⠉⣿⢶⣿⣿⣴⡏⢉⡿⠹⣋⣵⠿⣶⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣿⣟⣯⣴⣾⣿⣿⣷⣿⣻⡿⢹⣿⣶⣿⣿⣾⣿⣴⣡⣽⣿⢁⣹⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⢠⣾⣷⢀⣀⡙⢿⣿⣾⣿⣏⣴⡿⢁⣿⣻⣿⣡⠆⣿⡿⠏⠿⢽⣿⣿⡿⢛⣷⣿⣿⣷⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢺⣿⣿⣌⠻⣷⡀⠉⠻⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⠙⠛⠿⠿⢿⠿⠿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣯⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⢶⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣠⣉⢻⣂⢀⡀⣠⣼⡇⢀
⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡼⡿⢟⣛⣿⣿⣿⣿⣍⠻⣴⣿
⠀⠀⣠⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣯⣀⣬⠞⠁⠘⠵⠠⣾⣿⣾⣻⣷⣿⠃
⠀⣰⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣶⣬⡙⠺⢊⣿⣿⣿⣮⣿⣿⡷⣻⡿⢳
⠀⢿⣿⣷⣿⣿⣷⡀⠀⠀⠀⠀⣀⣴⣈⡙⠛⠿⢿⠿⡿⠋⠛⢓⣾⣝⢻⣿⣿⢉⡶⣽⣷⣿⣋⠟⠉⢦⡀
⠀⣾⣿⡿⢻⣿⣿⣷⣄⠀⠀⢰⣿⣿⣿⣯⣿⡿⢢⢞⣤⡶⠞⣿⠇⠈⠳⣟⠁⢸⣬⣾⣿⣿⣿⠂⠀⠀⣳
⠀⢻⣤⣿⣯⢿⣿⣿⣻⢦⣤⣯⣭⣭⡭⡍⣩⢤⣝⡛⢦⡀⢠⡿⢀⡤⢞⣿⡏⣧⢹⣿⣿⣿⣟⡧⠔⠊⠁
⠀⠸⠟⢛⣿⣾⣷⣟⣟⣿⡷⢲⠏⡶⣰⡘⣣⣠⣌⠝⣲⣌⠻⠚⠉⢀⢨⣿⣷⣿⢜⣽⡿⠉⠁
⠀⠀⠑⣿⡟⣻⣿⣿⣿⡷⠥⠼⠮⠖⣁⡻⢼⣿⣿⣿⣕⣪⠇⡐⣷⣧⣮⣝⡿⣫⢾⣽⡇
⠀⠀⠀⠈⠻⣿⣻⣿⣿⣿⣿⡿⣣⣊⠭⠎⡓⣺⢿⣟⣯⣯⣾⣷⢹⣿⣽⣯⣾⠷⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠁⠛⠷⣿⢿⣿⣿⠿⣿⣦⣴⠒⠂⣁⣿⣿⠿⢟⣤⡟⣿⡿⡿
⠀⠀⠀⠀⠀⢀⢠⡚⣮⣿⣟⣛⣛⣿⣮⢻⣿⣮⣴⣿⣯⡶⠺⢏⣾⡟⠓⠋⠁
⠀⠀⠀⠀⠠⠬⣵⣿⣿⣿⣯⣁⢰⣾⣿⠟⠉⠿⢿⣿⣿⣿⣿⣿⣿⣏⣦⡀
⠀⠀⠀⠀⠈⠉⠻⠿⣿⣿⣿⣿⠿⠋⠀⠀⠀⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠑⠀⠀⠤⠴⠛⠁⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣿⣿⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣙⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⠿⠿⣿⣿⣿⣻⣿⣿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠒⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⡤⣀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢉⡿⣏⣨⢿⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢫⡽⣯⣦⢖⡠⠞⠛⠙⣠⠟⠋⠉⠀⠁⢀⡴⠚⠉⠉⠙⠙⢉⣱⣶⣄⡀⠀⠈⣧⡞⢳⣾⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣳⠟⠥⠴⠋⠀⠀⠀⠔⠁⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⢠⠞⠉⠀⠀⠈⠀⣁⣸⣅⡿⢽⢼⡯⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠥⠤⠀⠂⠀⣀⡴⠦⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠬⠃⠀⠀⠀⠀⢠⠏⠁⠈⠉⠓⣞⢙⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⠆⣠⠞⠁⠀⠀⣰⠞⠋⠉⠈⠃⠀⢀⡤⠖⢇⠀⠀⠀⠀⡠⠈⠁⠀⠀⡠⠚⢉⣸⢿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠕⠒⠳⠘⠁⠀⠀⠀⢐⠊⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠁⣀⡴⠛⢀⠀⠰⠀⡸⢠⡞⠉⢛⠁
⠀⠀⠀⠀⢀⣀⡤⡤⡴⣧⠀⣸⣄⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⢀⡇⣾⢁⣾⣿⡷⠆⠀⢤⡄⢀⣀
⠀⠀⣠⣎⣿⣗⡿⣏⣳⣟⣻⣤⣈⢳⠬⣀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢁⢿⡇⠚⠛⠻⠁⢠⣧⠾⡱⠚⢎⢁⠄
⠀⣞⣷⣟⣷⣟⣳⣞⣳⣏⡿⣾⡻⠷⣄⡈⣳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⢞⡟⠀⠀⠀⠀⠀⠀⠙⠴⠟⠖⠓⠉⠻
⠀⠉⠃⠛⠓⠛⠓⠚⠃⠒⠉⠀⠀⠀⠀⠙⠷⣤⣀⣽⠉⠑⢄⡀⠀⠀⠀⢀⡀⠀⠀⠀⣠⢴⣏⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⢯⣽⣿⣉⣥⣀⣈⣭⣿⣗⢿⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣻⣾⣛⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣾⣻⣾⣟⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣞⣧⣾⢿⣾⣻⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⡾⣯⡽⢿⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡷⣯⡿⣟⣹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣛⣶⣟⡷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⡶⠿⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⣷⣱⣳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣽⣿⡽⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣶⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢠⡽⡴⡯⣵⠃⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢀⣤⡞⣽⣿⠷⡝⢿⣿⠢⠀⠀⢀⣈⣉⠡⢉⣩⣀⠀⠀⠠⢺⣿⡟⡵⢿⣿⡝⣦⣄
⠀⠀⠀⢀⣼⣟⡻⣧⡻⢭⡭⢇⣿⣏⡹⣂⠐⠒⠉⢁⣠⣀⠉⠀⠒⢀⡺⣉⣿⣇⠫⣭⡿⢣⡿⣛⣿⣄
⠀⠀⣰⣏⣟⢯⡽⡿⣿⣾⣬⠝⠁⠁⢂⣷⢻⣿⣶⣿⢻⣻⣷⣾⣿⢢⣇⠢⠁⠙⢭⣼⣾⡿⡿⣭⢟⣏⣷⡀
⠀⢰⣾⣟⡯⣓⣚⣽⡿⠋⠀⡠⣭⡼⣽⢉⣻⠻⣛⣪⣥⣋⡘⣿⢻⣋⢩⡽⣬⡥⡀⠈⠻⣿⣝⣒⡫⣿⣿⣦
⠀⣾⣻⣛⣿⣟⣛⠍⠀⠀⡄⣖⣛⣶⣽⣾⣟⢶⢫⣾⠉⢻⣇⢿⣜⣿⣾⣵⣞⣓⡀⡄⠀⠈⢝⣻⣿⣟⡻⣻⡆
⢀⣿⡿⣿⣿⣿⠃⠀⠀⠰⢘⡿⠟⢧⣛⡠⢹⣏⣱⡝⠿⠏⣭⣈⣿⠥⣜⣫⠟⠿⣟⠰⠀⠀⠈⢻⣿⣿⡿⣽⣇
⠰⡯⢨⣿⣾⠃⠀⠀⠀⡄⣻⡞⢉⢽⡧⣽⠿⢽⡯⠏⣩⡝⢮⣿⠽⢿⡥⣿⢍⠙⣾⡃⡄⠀⠀⠀⢻⡾⣯⠸⡧
⠈⡿⣾⣷⠃⠀⠀⠀⠀⠎⣋⡿⣯⣿⣾⣶⣿⣛⡼⢿⡋⢻⡿⣩⢻⣷⣾⣿⣹⡾⣏⡋⠄⠀⠀⠀⠀⢳⡿⡿⡇
⠀⠻⡾⠁⠀⠀⠀⠀⠀⠠⡁⡷⣏⢽⠓⢼⣉⣹⣯⣻⣫⡛⣃⣷⣋⣹⠔⢻⢍⡷⣾⡡⠀⠀⠀⠀⠀⠀⠹⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠌⡹⡞⣻⢴⣦⣷⠽⣯⢪⣭⣋⡈⣿⢥⣿⣢⢴⡋⣶⡋⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢡⣡⣾⡿⠯⣛⣺⢹⣾⠉⣻⣇⡿⣳⡻⠿⣿⣦⣩⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡰⠿⣽⠻⢆⣿⣷⣅⠿⠫⢷⣷⣇⠾⢻⡽⠷⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣌⠩⡿⣏⣹⢋⣦⣻⣣⣎⢻⣉⡿⡯⢉⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣎⡲⠌⠚⣍⣾⣷⡟⣧⣿⣏⡝⠊⠴⣊⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⡍⡿⣽⣮⡁⠤⢛⠺⢿⠿⢚⠣⠄⣩⣾⡽⡏⡍⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⣴⣿⣿⣯⡿⠁⠀⠈⠐⡂⡒⠈⠀⠀⠹⣯⣿⣿⣷⡾⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣇⢻⣿⠿⣿⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⢸⡯⢿⣿⢃⣧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣟⣿⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢽⣟⡯⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢿⠗⠶⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠉⠋⠚⢞⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠐⢚⣛⣛⣳⣧⣀⡐⠌⠀⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣦⣤⠾⠚⣋⣛⡳⣿⣿⣟⣹⣯⣤⣝⣧⡀⡀⢀⣿⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣭⣴⣶⠻⠿⠿⠍⢉⡉⢸⣿⣍⠉⣹⡇⡵⢾⠟⣋⣁⡸⠃⣾⢗⡚⠠⢿⠉⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣿⡍⠀⠀⠀⡅⢷⣶⠀⠀⣼⢇⠠⢙⣿⣿⣿⠇⢸⡇⣼⣓⠈⠀⣢⠄⠎⢡⣴⡶⠸⣇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡽⠋⢡⣄⣻⣇⡀⣠⡞⣿⣇⠉⠓⣊⢁⣹⣿⣷⡍⠅⣤⣷⢙⣻⡏⠃⠀⠀⠀⠀⠀⣘⠩⢄⡜⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣤⣾⣯⣿⡇⠈⢿⣸⣴⣿⡇⠀⠀⣿⠋⢻⣿⣿⡇⣶⣿⡟⣤⣾⡇⠀⠀⠀⠀⣀⣉⠨⠔⠉
⠀⠀⠀⠀⠀⠀⡀⣻⣿⣿⠁⢠⣿⠀⠃⠀⢻⣾⣿⡿⣇⠀⣤⣿⠀⣷⣿⣿⣷⠛⢉⣴⠟⡉⠀⠀⠒⠂⠈⠁
⠀⠀⠀⠀⠀⣰⡇⠻⠛⠻⢶⣼⣿⡀⠀⠀⠈⣿⣿⡇⢹⣶⣿⢻⣿⣿⣿⡿⣋⣤⢛⡁
⠀⠀⠀⠀⠀⠈⢹⡏⣲⣦⣸⣿⠉⣻⣶⣤⣴⢸⣿⣿⣿⣿⣿⡿⢿⡿⣭⣆⣾⣿⡂⢅
⠀⠀⠀⠀⠀⠀⢀⡸⠷⡾⢝⠉⠻⣾⣿⣿⣿⠟⣿⠿⠛⢛⢉⣶⢾⣶⠿⢋⡜⢻⣯⠆⢢⡀
⠀⠀⠀⠀⠀⡀⡟⠂⠀⢙⠸⠿⢾⣮⣭⣥⣀⣥⣴⣤⣿⢵⠿⠛⠈⠁⠠⠛⢤⡼⠃⠀⠼⣷
⠀⠀⠀⣰⠞⠱⢈⠉⠇⣫⠄⠀⠀⠀⠀⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠰⠠⣼⡎
⠀⠀⠀⣼⣧⢀⣤⡰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⢩⠬⡐⠱⣾⠃
⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠇⠁⠄⢂⣕⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⢾⡟⠧⢈⠘⣬⢁⣤⡸⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⡃⢰⠆⣰⡁⢨⣤⠺⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧⢿⣤⣿⠧⠿⠛⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⢀⣤⢜⠳⢿⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠠⠴⠲⣼⣯⠁⢻⣷⡠⣴⣦⡤⣰⡞⣯⠂⠉⠚⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣆⠀⢘⣿⣷⠄⠀⢰⣿⣯⣾⣿⠿⠟⠿⠋⠀⠢⠔⠰⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠇⣼⡿⠀⢰⡻⡏⢀⣴⣴⣿⠟⠻⡃⠀⠀⠐⠒⠀⡾⠧⢴⣋⣙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠗⢀⣷⣤⣐⣾⣿⣿⡿⣛⣻⡵⠂⠀⢽⣳⡀⠀⡠⠬⣫⠀⠀⠘⡯⠂⠈
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⢿⣿⣿⣛⣿⠽⠖⠻⠩⠴⠚⠁⢴⣿⢿⡞⣑⣣⣋⠿
⠀⠀⠀⠀⠀⠀⠐⠋⢽⡛⠟⠉⠭⠉⠀⠈⠀⠀⠀⠄⠀⠀⣷⣿⢏⣋⠞⣵⣡⡎⠀⠀⠀⠀⠀⡞⠄
⠀⠀⠀⠀⠀⠀⢀⣈⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡴⣯⣞⠞⠃⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣎⡱⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⡶⡿⣯⠿⢿⣿⣭⡭⣾⣺⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡹⣿⣾⠻⣧⡀⠀⠀⠀⠀⣴⣿⣙⣿⣽⡗⢯⣽⣾⣽⣾⣯⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣨⣭⡸⣷⡓⡀⠀⠀⠸⣿⣯⡇⣿⣻⣿⡾⠟⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣶⣝⢟⣣⣾⣝⠿⢄⠀⢀⡷⢤⡭⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢊⣋⢿⣷⢟⡛⠀⢈⡞⢁⣠⠼⠦⣄⣼⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡁⠉⢀⡤⠚⢁⡱⠺⡇⠀⠀⠀⠉⠛⣶⣇⡈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣲⣤⠀⡠⠞⠒⣇⣠⠔⠋⠀⠀⢻⣀⠀⠀⢀⡴⠁⠀⠙⢯⡈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣯⣽⣓⢭⡏⣟⣀⡴⠚⢯⣀⠀⠀⣠⠔⠋⠉⠉⠉⡟⠀⠀⠀⠀⠀⠹⡎⠙⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⣻⢾⣿⣿⡷⢷⠁⢹⠁⠀⠀⠈⢳⠋⠁⠀⠀⠀⠀⢰⡃⠀⠀⠀⣀⣤⠴⠻⣦⠼⡄
⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⡿⣷⡿⠋⠀⢨⡗⢺⡀⠀⠀⠀⡏⠀⠀⠀⢀⡠⠖⠉⠉⠉⢻⠋⠁⠀⠀⠀⢻⠀⢱
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣯⣿⠏⠀⠀⠀⠀⣇⣼⣧⠤⠖⠚⠙⠒⠒⡶⠉⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⠀⢸⡗⢻⡄
⠀⠀⠀⠀⢠⡿⣣⡾⣿⠿⠃⠀⠀⠀⠀⠀⢳⠀⢻⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠤⠊⠉⠉⠙⡶⠒⠚⢻⣇⣸⠇
⠀⠀⠀⠀⣾⣽⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢷⠙⢧⠀⠀⠀⣠⠞⠉⠙⠒⡞⠁⠀⠀⠀⠀⢀⣇⠀⠀⢸⠉⢹⠤⢤⣀⡀
⠀⠀⠀⠀⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡼⠳⣤⠞⠁⠀⠀⠀⢠⣇⠀⠀⠀⣠⠖⠋⠉⠳⣤⡿⢤⠏⢀⠂⡓⡭⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣸⠷⣄⡀⠀⠀⡼⠉⠉⠛⡏⠀⠀⠀⠀⢠⣟⢀⡞⡈⢸⣦⠗⠜⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣈⣹⠳⠾⣅⣀⣀⣀⣹⣀⣀⣤⠴⠋⢈⠏⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢼⣁⣈⣹⣍⣁⣈⠧⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⣅⢦⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣵⡷⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠒⠶⣄⡀⠀⠀⠀⢀⣀⣿⣀⣀⣀⣀⣀⣼⣃⣀⠀⠀⠀⠀⣠⡴⠖⠒⠒⠶⢤⣄⡀
⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠈⢳⣤⠖⠛⠉⢋⠁⠀⠀⢸⠀⠀⠀⢩⠋⠙⠳⢦⣴⠋⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⢦⣀⡤⠖⠻⡟⠋⠉⠉⠉⠉⠛⡿⠓⠦⣄⡠⠟⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⣠⠟⠁⠀⠀⠀⠀⣀⣤⠶⠚⢛⡟⠁⠀⡰⠁⠀⠀⠀⢡⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠳⡀⠀⠹⣟⠛⠲⢦⣄⡀⠀⠀⠀⠀⠙⢧⡀
⣰⠏⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⣸⣅⣀⣰⡁⠀⠀⠀⠀⠈⣆⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⣱⣀⣀⣽⡄⠀⠀⠈⠙⠳⣦⡀⠀⠀⠈⢷
⣿⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⢀⡏⠀⢨⠋⠉⠁⠂⠠⢤⣤⠞⠛⠓⠛⠛⢤⣤⠤⠀⠂⠉⠉⢋⠀⠘⣇⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⢸
⠹⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡌⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠘⡀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⣇⣀⠀⠀⠀⠀⠀⢱⣄⡀⠀⢀⣀⣼⠀⠀⠀⠀⠀⢀⣠⡏⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⠏⠉⠉⠉⠉⠉⠉⠹⠋⠀⠀⠀⠈⢻⠉⠉⠉⠉⠉⠉⠉⢇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢺⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢸⠂⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡄⠀⠀⢀⣀⠠⠤⠴⡷⠶⠶⠶⢶⡷⠤⠤⢀⣀⠀⠀⠀⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠂⠉⣿⠛⠉⠁⠀⠀⠀⠰⠃⠀⠀⠀⠀⡳⠀⠀⠀⠀⠉⠛⢿⠏⠀⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⡸⡄⠀⠀⠀⠀⠀⠀⢡⣀⠀⢀⣰⠁⠀⠀⠀⠀⠀⠀⡼⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⠈⣦⡀⠀⠀⠀⣀⠞⠉⠁⠉⠙⢄⠀⠀⠀⠀⣠⡎⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⣴⠁⠉⠒⣶⣾⣁⠀⠀⠀⠀⠀⢀⣿⣶⡖⠊⠁⢱⡤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠈⠓⢦⣤⣄⠀⢈⠟⠒⢲⠒⠚⣏⠀⢀⣤⣤⠞⠉⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⢸⠃⠈⠙⠻⣦⣤⣼⣠⣤⡾⠛⠉⠀⢹⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⡀⠀⠀⣼⠃⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⣤⡴⠃⠀⠀⠀⠀⠘⣇⠀⢠⡟⠀⠀⠀⠀⠀⠳⣤⣀⠀⠀⠀⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣒⣚⣋⣀⣀⣀⣀⣀⣀⣀⣀⣘⣶⣟⣁⣀⣀⣀⣀⣀⣀⣀⣈⣛⣒⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⣤⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠅⣰⠀⠀⣤⠀⠀⢳⣀⠀⡆⠈⠁⡀⢶⠂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠶⡘⢃⣤⡘⠊⠷⢿⣽⢶⡗⡈⢠⣼⡇⠉⣿⡆⢆⡀⣴⠆⠀⢸⡀⠀⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀⠀⠤⢻⠇⠀⢀⠰⣿⡁⠐⣴⣇⣈⡈⢸⡯⣠⣿⣠⣾⣿⡵⣾⢷⠿⢃⡆⣈⡅⠰⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⠉⡀⠀⠈⠁⡼⣄⠀⢾⡄⢰⣾⣽⣿⣧⣾⣷⢙⡿⢿⣿⣿⣿⣷⡛⡷⣾⠁⢻⡅⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⢰⠛⢙⣻⣯⣿⣸⣷⣎⣿⣿⣿⣿⣿⢿⣿⣿⣾⢿⣿⣾⣿⣿⣴⢄⣴⡮⣱⣦⢀⡔⠀⠈⠁⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢀⡀⢀⣿⣿⢾⣿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⠿⢿⣾⣿⣷⣾⣿⣿⣿⣿⣷⣏⠈⠁⠀⣀⠘⠆⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠰⡟⢻⠀⡉⢽⣀⣽⢛⣼⣿⣿⣿⠿⣿⠇⠀⠠⠆⠀⠀⠀⠙⢿⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠾⠋⠲⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⠾⣣⣴⡞⢿⣩⣿⢻⣿⣿⣏⣶⡀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢿⣿⣿⣿⣿⣿⣿⣿⣼⣯⡘⣷⢻⡿⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢹⡍⠳⠛⣏⢰⡟⣻⣷⣿⣿⣾⣿⣁⣀⣀⣀⠀⠀⢠⣾⣿⣤⣶⣊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢰⣆⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢢⠓⢶⠲⣷⣸⣽⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⡆⠀⡿⠿⢿⡿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣭⣿⡿⣠⣤⣀⣔⡂⠰
⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠀⠐⣤⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣥⣿⡿⠋⠀⠀⠀⠀⠀⠁⠀⠀⠾⣿⣿⣿⣿⣿⣽⣟⣹⠏⢿⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡦⣄⣶⣎⣿⣿⣷⣿⣿⣿⣿⠆⠉⠛⠉⠀⠀⠀⣤⣴⣶⡶⠆⠀⠀⠀⠀⢻⣿⣿⣿⢿⣿⡟⣥⢸⡿⠁⠈⠢⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠈⡏⠩⠞⠙⠶⢿⣿⣷⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠈⣉⣹⣤⣤⣤⡔⠁⠞⢻⣿⣿⣿⣿⣿⣿⡟⠟⠓⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠘⠂⣠⡼⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣧⣂⡄⢠⠀⠀⢀⣾⣟⣛⣩⣤⡶⢀⠂⣤⣼⣿⣿⣿⣿⣿⣿⢉⡆⠊⠀⠀⠀⠀⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠠⢄⠀⢡⣼⡶⣽⢲⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠴⠛⠿⠟⠛⠲⡾⠇⣸⣿⣿⣿⣿⣧⠙⠷⠼⣧⡾⠃⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢿⡷⣟⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡄⠀⠀⠀⠀⠀⠲⣾⣤⣾⣿⣿⣿⣿⣹⣿⣷⣠⡄⠈⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢞⡉⢛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣞⣶⡴⠿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣛⣉⣡⠾⣴⠦⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠒⠈⣡⠿⠏⠉⠙⠉⠙⣛⣛⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⠛⠻⠆⠀⠄⠈⠈⠉⢻⣿⣿⡉⠛⠿⠋⣁⠘⠸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠉⠉⣙⣿⣿⣿⢿⣿⣿⣇⣀⠘⡷⠄⠀⠀⠀⠀⠀⠀⣹⣿⣇⠙⠀⣤⠀⠉⢠⠆⠀⠀⠘⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢛⣿⣿⣿⢎⠛⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⣸⠧⡎⠁⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⣿⣷⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠉⠉⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢡⠏⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠑⠒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠳⣄⠤⣤⠶⠚⠛⠋⡰⠖⠋⠉⠀⠀⠀⢀⡠⠝⠋⠉⠉⠉⠻⡒⠦⣤⣀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⣠⠖⢊⡱⠊⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⠴⠋⠉⠉⠉⠉⠲⠤⣠⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠎⠁⢨⠋⠀⠀⠀⠀⣠⡎⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⢀⠔⠓⠚⠳⢄⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⢲⠃⠀⠀⡠⠖⠉⠀⠱⡀⣀⡠⠤⠐⢇⠀⠀⠀⠀⠀⣀⠎⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⣀⡹⢦⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢸⢀⡴⠊⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠈⢢⣀⡤⠒⠉⠀⢣⠀⠀⠀⣀⠴⡏⠀⠀⠀⢀⡔⠋⠀⣀⠴⢃⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠔⠒⢺⠊⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⢆⡠⠞⠁⠀⢃⠀⠀⠀⡎⠀⣠⣊⠽⡚⠁
⠀⠀⠀⠀⠀⢀⣀⠠⠤⠼⡄⠀⢀⣆⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠈⡆⠀⢰⠀⠀⡟⣰⣾⣿⣶⡤⠠⠄⢀⣀⡀
⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠈⢲⡁⠀⠑⢄⠀⡰⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢸⠖⢹⢦⣸⣿⣿⣿⣿⠃⣀⠀⠀⠀⠀⠉⠑⠢⣄
⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣠⠋⠉⠳⢄⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⠎⢀⠎⢀⡿⠒⣤⠜⠉⠒⠹⡀⠀⠀⠀⣀⣀⠀⠈
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠳⢄⣀⠞⠉⠒⠤⣤⢤⣜⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⣬⠔⠋⣠⠞⠓⡞⠑⠦⣄⡀⠀⠈⠒⠒⠉⠰⠊⠓⠔
⠀⠉⠈⠓⠀⠐⠂⠀⠋⠈⠉⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⣠⠃⠀⠈⠓⣤⣀⠀⡀⢀⣀⣇⣀⣀⣀⣠⠴⠊⣃⡠⢾⠃⣠⠜⠁⠀⠀⠀⠉⠓⠒⠦⠭⠭⠿⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⠴⠥⢀⣀⣏⣀⣀⣀⣀⣀⣠⡴⠒⠈⠉⠑⢮⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⢀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⡠⠔⠊⠁

⠀⠀⠀⠀⠀⢠⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⡤⣀⢀⣠⡄
⠀⠀⠀⠀⠀⢠⣿⣟⢻⣿⣿⣯⣹⣿⣿⣿⣾⣯⡿⣖⡿⣿⢿⣿⣏⣿⡷⣯⣯⣹⣿⣻⣿⢿⣿⡷⣟⠻⣿⣷⣦⣤⡄
⠀⠀⠀⠀⠀⢘⡛⢯⣽⣿⣿⣯⢣⢇⣦⣳⣸⣯⣿⣯⣟⣿⡮⣿⣻⣯⣿⡮⣻⠛⢫⣿⣓⣱⢇⡨⢙⢯⣞⢿⣾⠃
⠀⠀⠀⠀⠀⢘⡹⡟⣉⣟⣿⣿⣏⣸⣿⣿⡿⣜⠋⣿⣿⣾⡷⢹⣿⣿⢟⣿⢃⣼⣛⢿⣿⡉⣿⢿⢻⣷⣿⡿⣾⣷
⠀⠀⠀⠀⠀⠸⣏⣻⣿⢉⣿⢃⣹⣽⡿⠙⢃⡠⠚⣹⣿⣿⣥⣈⣯⣵⣯⣧⢟⢶⡣⢴⠊⣴⢟⣿⣾⡾⣷⣿⢖⣭⠁
⠀⠀⠀⠀⠀⢸⣿⣿⢯⣿⣯⣿⡷⣃⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣚⣿⣯⡷⢿⣱⡾⠅
⠀⠀⠀⠀⠀⠀⠙⡘⠐⣷⠻⣿⣴⣿⣿⣛⢛⡙⣿⣿⣿⣿⣿⡟⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⠻⣯⡝⣫⣿⡿⣏
⠀⠀⠀⠀⠀⠀⡀⠅⠀⣿⠀⠇⣿⣿⣿⠈⠉⠛⣿⣿⣿⣿⡟⠉⠋⢹⡎⣿⣿⣿⣷⣦⣿⣿⣿⣿⣾⡋⠉⠁
⠀⠀⠀⠀⠀⠸⡄⣠⠀⠀⠄⢘⣿⣿⠿⠦⢐⠐⠿⢿⣿⣿⣷⣄⡀⠘⠿⠟⣿⡿⠛⣿⡿⣽⠿⢟⡽⠗
⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⢀⠘⠉⠀⠀⠀⠈⠂⠀⠀⣿⣿⡉⠀⠘⠃⠀⡀⠈⠁⠰⣿⢃⣾⠿⠛
⠀⠀⠀⠀⠀⠸⠉⠑⠂⠠⠸⣷⢤⣀⣂⠀⠀⠀⠀⡀⢽⣿⡷⠀⠀⠀⠀⡟⠀⠠⣷⣽⡸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣿⠏⠛⠙⠛⠉⠁⣸⡿⠁⠀⠀⠀⠀⠁⠀⠸⣿⣿⠧⠉⣀⣄⠀⡀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⣸⡄⠀⢰⣥⣞⡀⡠⠤⣀⠠⢄⣤⡒⠉⠙⠿⠰⡿⠁⠐⡼⣀⠛⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠘⠿⠿⠿⠃⠀⠛⠄⠈⠿⢿⣷⣄⠀⠀⣇⠀⠀⠀⠈⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠋⠑⡀⠸⢿⣳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡆⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⣷⡟⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⣾⣷⣆⠀⡃⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢠⠠⢻⡿⣿⣿⣁⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⢛⣾⣿⣏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠙⠻⣯⡟⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠚⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠠⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⣀⣀⣀⠀⢨⠇⠂⠀⠀⠀⡇
⠀⠀⠀⣾⠿⢛⡥⢤⣬⡉⠉⠓⢤⡀⣠⠧⠒⠲⡏⠉⠉⠉⠉⠲⣄⣀⡀
⠀⠀⢠⠋⠻⢨⡣⠿⠿⠀⠀⠀⠀⠙⣄⣠⠴⠒⠙⢦⡀⠀⠀⡰⠋⠈⠉⠓⠦⣀
⠀⠀⠈⢦⣀⢤⣉⣀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⡠⠊⠉⠒⢺⠀⠀⠀⠀⠀⠀⠘⢗⠢⣄
⠀⠀⠀⠀⠑⠤⣀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⢳⡃⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠈⣆⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⡆⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⣀⠴⢧⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡒⠀⠀⠀⠀⢀⠀⢀⣐⢮⣣⡀⠀⠙⢄⠀⠀⠀⠀⠈⡇⠀⠀⠀⠹⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣖⠀⠀⡜⠁⠀⠀⠈⠑⣇⣇⠀⠀⠀⡵⣄⠀⠀⠀⢣⠀⠀⠀⠀⢣⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢣⠀⠀⠀⠀⠀⠀⠀⠗⣤⠎⠀⠈⠳⣄⣀⣸⡀⠀⠀⠀⠈⡆⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⡀⠀⠀⠀⠀⠀⠀⠩⢶⠤⣀⣀⠏⠀⠀⠑⠦⣀⡀⠀⠸⡀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠈⠑⣆⠉⠑⠲⠤⣄⣠⡃⠈⠙⡶⠓⢦⠴⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⣳⡤⢄⠠⠤⠬⠭⠵⠦⢼⣤⣈⣢⡙⡽⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠉⠁⠀⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢄⡀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠖⠊

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢟⡻⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⠉⠉⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣥⣾⣷⣬⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣄⠀⠀⣠⣄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢞⡷⣭⠨⢎⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡱⠅⣭⣟⡱⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣰⠖⣮⡃⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢘⣕⠺⢆⣿⣄
⠀⠀⠀⠀⠀⠀⢀⣬⢛⢯⡟⠉⠉⣼⣿⣿⣿⣿⣯⡿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣧⠉⠁⢻⡽⡛⣤
⠀⠀⠀⠀⠀⢠⣜⠛⡞⠟⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠻⢷⠛⣣⡄
⠀⠀⠀⠀⢠⠟⠙⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠙⠋⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⣿⣿⣿⣿⣿⣿⣿⣷⣻⣟⣾⣿⣿⣿⣿⣿⣿⣿⡷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢎⡻⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⢿⡱⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢎⣛⣿⣿⣿⣿⣿⣿⣻⡱⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠹⠃⣿⡿⢿⣿⠘⠏⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣘⢗⡤⠈⠁⠈⠁⢮⠺⣓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡉⡆⠂⠀⠀⠀⠀⠐⢐⣉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠂⠵⠀⠀⠀⠀⠀⠀⠮⠐⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣾⡘⡟⡷⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⣿⣿⣿⣿⣿⣿⣿⢹⣧⣳⢃⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣿⢣⢿⣿⣿⣿⣿⡿⢃⣾⢧⣏⢸⣿⡿⣿⣿⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢷⣸⡇⢸⣾⣿⣿⣿⢏⣶⣫⣿⣿⣿⢸⣿⣽⣿⣿⣸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢰⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣷⣿⣿⣿⣿⢹⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⣼⣧⣸⣿⣿⣿⣏⡿⣿⣿⣿⣿⣿⣿⢹⣿⢿⣿⣿⣼⣿⣈
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣧⣻⡌⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⡻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⡟⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣷⣾⣿⣿⣿⣟⣿⣿⣯⢻⣿⣿⣿⠟⢳⣿⣿⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣿⡿⣿⣿⣿⣿⣿⡟⣿⣿⡿⠁⣼⣿⣿⣿⣿⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠛⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣥⣾⣟⣿⣿⣿⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠻⣿⢿⣿⡿⢛⠯⠋⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⣿⣷⡾⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢔⠒⠲⡄⠤⠤⠤⠤⠤⠤⠤⠤⠐⠒⠒⠀⠉⠉⠉⠉⠉⠉⠁⠒⠒⠒⠠⠤⠤⠤⠤⠤⠤⠤⠄⡔⠒⢒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢱⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠒⠒⠒⠒⠒⡖⠒⠒⠒⡖⠲⠒⠒⠂⠐⠂⠒⠀⠐⢺⠁⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⡀⠀⢰⠀⠃⠀⠀⠀⠘⠀⡇⠀⠀⠀⡇⠀⡇⠀⠀⢰⠀⠃⠀⠀⠀⢰⠀⡄⠀⠀⡈⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡇⠀⠈⡀⢰⠀⠀⠀⠀⠀⢁⠀⠀⠀⡇⠀⡇⠀⠀⠘⠀⠀⠀⠀⠀⡄⠀⠃⠀⠀⡇⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⡇⠀⠀⡇⢸⠀⠀⠀⠀⡇⠸⠀⠀⠀⠁⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠧⠤⠔⠃⠚⠒⠒⠒⠒⠓⠚⠒⠒⠒⠒⠒⠚⠒⠒⠚⠚⠒⠒⠒⠒⠓⠚⠒⠒⠒⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠐⠒⠂⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠒⠒⠠⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⢀⠎⣀⠤⠤⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠠⠤⢤⡈⢇
⠀⠀⠀⠀⠀⢸⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠐⠒⠒⠒⠖⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⡒⠒⠒⠒⢲⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠳⠤⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠂⠐⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⢲⣶⡤⠀⠀⠀⠀⠀⠠⠀⠀⠔⠠⢀⣶⠖⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡖⢀⣠⡤⠛⢲⢆⣠⠤⢄⢿⣿⡏⠀⣠⡟⡕⠊⠁⠀⠀⢀⠒⠊⠁⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⣤⠲⣶⣼⣿⣿⠀⠀⠀⡾⠛⠀⠀⢰⣝⠿⠛⢹⣿⡆⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠘⢋⣶⣿⠋⠀⣿⣏⠁⠉⠀⠀⡄⠀⠀⠀⣠⡾⢣⡎⢀⠀⠉⠁⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣸⡿⠁⢨⡿⠟⠃⠀⠸⡿⠈⠀⠀⠀⢰⢇⠀⣠⣾⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣼⣟⠀⣠⠋⢤⠀⠀⠀⠀⡇⠀⠀⢀⣠⣾⣾⠿⠛⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⡠⠋⠉⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣟⢹⣷⣳⢫⡄⠀⣠⣃⣀⣀⣀⣴⠾⣛⠉⢱⡮⠅⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠂
⠀⠀⠀⠀⠀⠀⠁⠆⠀⣾⢙⡷⣿⣷⣴⣶⢞⣏⠋⢛⣍⣩⢀⡾⠇⢂⣁⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢥
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠛⠲⠧⠼⠧⠶⠿⠻⢀⠻⠭⠷⠒⠉⢀⣀⣀⣀⠠⠐⢲⠿⢧⡄⠀⠀⡀⠴⠶
⠀⠀⠀⠀⠂⠤⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢼⣦⡀⠀⡈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢂⠀⠀⠤⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢊⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁

⠀⠀⠀⡀
⠀⠀⣉⡟⡀⢀⣤⡼⣿⢷⣦⣄⡀
⠀⠀⢻⣷⣜⣽⣭⣰⡏⢻⡿⢯⡿⢦⡀⠀⣀⣤⣶⣶⣫⡝⢛⠛⠛⢁⡿⢃⣐⣶⣶⣤⣤⣀⣀
⠀⡀⣨⠈⠛⠛⠎⠉⢤⡟⣽⠇⣤⡸⡛⠿⡙⣿⣿⣿⣿⣧⡶⠶⣶⣀⡀⢩⣽⣿⠛⠻⣿⣫⣿⣟⣶⡦⣤⡀
⠀⠈⠻⣿⣷⣦⣄⣠⣆⣤⠠⡀⣿⣽⠃⠀⠁⢨⡛⠛⠀⠻⠂⠀⠉⣿⣿⣿⣯⢔⣠⠬⠞⢻⣿⣿⣷⣶⠶⠮⠷⡂⢤⡀
⠀⠀⠀⠀⠉⠛⢿⣽⣼⣾⣿⣿⣿⣏⠀⠀⠀⢸⡃⢄⣀⣄⡀⠀⠀⠈⢙⣿⣿⣿⣥⣄⢀⠿⢿⣿⣷⢿⣿⡗⠀⢵⢿⣿⢶⣦⣄
⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⣿⣿⣿⣿⡠⠀⠀⢀⠈⠀⠀⠉⠉⠙⠒⠢⠬⣏⠀⠈⠉⠻⣧⣀⠀⠉⠀⡄⠙⢣⡾⠀⠀⠈⣤⠹⡿⠿⠶⣄
⠀⠀⠀⠀⠀⣠⣽⣶⣶⣿⣿⣿⡿⣿⣥⣂⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢸⣿⣿⣶⣦⣄⣼⣜⣷⣤⡄⠁⠀⠁⠈⡀⢈⠋⠓
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⠁⠘⣿⣿⡟⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠓⣠⣸⠿⠛⠉⠻⣿⣿⣿⣿⣿⣿⣤⣔⣀⡀⣾⡾⣀⢠⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠟⠀⠀⠀⠈⠃⠀⠀⠀⢀⠎⢽⣿⡿⣋⣧⣖⡀⡀⠀⠀⠈⠉⠲⣦⣤⣤⣤⣍⣙⣋⠉⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠏⠀⠈⠙⠿⢻⢿⣿⣿⡿⣷⣦⣄⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣯⣭⣍⣉⣛⣻⣯⣿⣯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⢤⠀⠶⣾⢿⣿⣿⣿⣿⣿⣿⣿⣞⠙⠳⠼⠿⠛⠙⠿⠛⠛⠋⠉⠉⠀⠀⠈⠫⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠛⢀⠔⠛⣻⢿⣿⣻⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⢞⣩⣙⡻⣧⢿⣿⣛⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠭⣙⣿⢿⣼⣿⣽⣽⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢿⣿⣿⣛⣽⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣟⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣷⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣶⣶⣦⣤⣤⣤⣄⣀⠀⠀⠀⠀⢀⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣼⣿⣿⣷⡀⣀⣀⣀
⠀⠀⠀⠀⠀⣠⣤⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⣷
⠀⠀⠀⠀⣾⣿⣿⣿⣷⠿⠛⠉⠻⠿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠉⠉⠊⠉⠉⠁
⠀⠀⠀⠈⠻⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠛⠛⠿⠿⠿⠿⠿⠟⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀⢀⣀⣤⣩⣭⣭⣍⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣯⣭⣿⣿⣿⣿⡿⣿⣿⣿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢛⣽⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡜⣿⣿⣿⣿⣿⣿⣣⣶⣿⣾⣿⣿⣿⣿⣿⣿⣆⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠙⣿⣟⣿⣿⣿⣿⣿⣿⣯⣿⣷⣿⣿⣿⣿⣿⡘⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⠀⠀⠈⠛⢾⣿⣟⣟⣿⢿⡟⢿⣿⣟⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠀⠀⠀⠀⠀⠀⠉⠙⠙⠻⠟⠿⠟⠛⢋⣭⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⢿⡿⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣶⠆⠶⣦⠀⠀⠀⢀⡙⠁⡠⠖⠒⣤⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣀⡰⢿⡺⠼⠙⠋⠻⢀⡤⠴⠋⠀⠀⠀⠁⠐⠶⠄⢠⣾⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣮⣾⡷⣿⠙⠛⠉⠠⢈⣟⡟⣾⢏⡁⢳⢄⠀⠀⠀⢀⢠⣴⣿⣿⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠾⠷⠻⠓⠮⠀⠀⠀⢠⠖⣰⢽⢏⣶⣹⡉⣠⣾⢷⣀⠠⣄⣤⣿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣾⠿⠏⠋⠀⠀⠀⠈⠀⢀⠴⠋⣰⠿⣯⣬⣽⣻⡅⣰⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣥⣄⠤⣂⠀⠀⠀⠀⠀⠀⠀⢠⣂⣴⣻⣳⢱⠿⠷⢼⠔⠋⠁⠸⠿⡿⠉⢁⣀⡀⣀
⠀⢀⡀⡀⠀⠠⠄⠛⢿⣯⣄⡠⢰⠜⢚⠤⠰⠀⠀⡀⢬⣩⣾⠷⣯⠱⢿⠟⣴⣶⣶⠶⣶⣎⣰⠖⢠⣿⣿⣯⠃
⣶⢿⠿⢻⡍⡂⠠⢀⡤⠾⠾⠛⢷⢤⢷⣖⣢⡁⠤⢾⣿⣿⣟⢲⣿⠛⣂⣾⣉⣑⣾⠿⠟⠋⠁⠀⣾⣿⣿⣿⠇
⣯⠷⠟⠃⠁⠈⠈⠀⠀⠀⠀⠀⠀⣼⣶⣶⣶⠶⠻⠋⢩⢽⢹⣾⠍⠀⠈⠉⠉⠁⠀⠀⠀⠀⣀⣴⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣽⣳⠄⢠⣶⣧⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢁⣸⣝⣯⡛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⣯⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠶⠚⠛⠛⠉⠉⠁⠀⠈⠉⠉⠉⠛⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⣤⣄⡀⠀⠀⣠⡴⠚⠉⠉⠲⠀⠀⠀⠀⣀⠀⠐⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢸⡏⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⠠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠀⡉⠿⠿⠟⠛⠿⡲⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⣠⣤⣭⣀⠀⠀⠀⠀⠀⠀⠘⣏⢿⡈⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠉⠻⢿⣿⣷⣦⡀⠀⡀⠀⠀⠙⡎⢳⡘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⢿⡍⢻⣿⡄⣿⡖⠆⠀⠃⠸⠁⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠸⠃⠈⣋⡇⠸⠁⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⣿⡇⢆⠀⢀⠀⣠⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠚⠉⠨⠀⠈⢻⣄
⠀⠀⠀⠀⢀⡼⠋⢀⣶⣿⣿⣿⡆⢹⣤⣿⣿⡄⠀⠀⠀⢠⡾⠻⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⡞⠁⠀⢈⣿⣿⣿⢿⣷⡌⠉⠛⠻⠃⠀⠀⠀⠋⠀⠊⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠈⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠘⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⣾⠀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣧⡀⠙⠿⣷⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣉⣠⠄⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡗⠀⠀⠀⠈⠙⠏⠑⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠑⠓⠒⠦⠤⣤⣤⡤⠞⠁
⠀⠀⠀⠀⠀⠘⢷⣆⠐⠀⠀⢀⢿⣿⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠈⠀⡷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠠⠀⠀⢰⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠐⣿⡿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⣿⣏⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠈⢷⣼⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣧⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⣿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣷⣴⣿⣶⣶⣤⣤⣴⣾⣿⠋⢻⣿⣶⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⠿⢿⣿⣿⡀⣹⣿⣿⣿⣿⣷⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣶⣾⣿⣿⣿⢿⣿⣿⣿⠿⠿⢿⠛⢿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠛⠛⠋⠀⠀⠁⠈⠀⠀⠀⠀⠙⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⢀⡀⠀⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠞⠀⠉⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟⠁⠀⠀⣴⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠁⠀⢀⣾⣿⣿⡿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⣼⣿⣿⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠘⠟⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⡈
⠀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⡷⠆⠀⠤⠀⠠⠂⠀⠀⠀⠀⡰⠒⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⡇⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠠⠃⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠰⢻⠃⠀⠘
⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠈⠙⠧⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢸⠀⠀⢀⠄
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡠⠃
⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠄⢠⠑⠤⢀⠌
⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⣀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠁⠂⠀⠀⠄⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣠⣿⣿⣿⠋
⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠁
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡟
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⠄⡊⠶⠆⢹⣿⣿⣟⡓⢶⣦⣄⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠖⠱⠀⠀⠀⡐⠏⢁⠘⣋⡁⢿⣿⣷⣤⣭⡉⣁⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢋⣄⠴⠂⠈⠀⠀⠀⢀⠅⠀⠈⣀⡉⡁⠘⠚⢶⡾⣤⡿⣦⢁⡀⢽⠃⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣤⠖⠈⠁⠀⠀⠀⠀⠀⠀⡈⠀⠓⠀⠙⠋⠇⣶⣦⡀⢤⠁⠁⠈⢿⣧⣴⡆⠄⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣡⢤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠸⣷⢠⠙⣿⣿⣆⠁⠀⠀⣸⣿⣿⣆⠁⠲⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⢉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣈⠱⢈⠙⠛⡀⠀⠸⢃⣈⡛⢟⣧⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠁⣂⡀⠀⠀⢀⡀⣀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠃⠀⠁⠁⠀⠀⠀⠈⠛⠁⠘⡡⠀⠿⠹⠓⢀
⠀⠀⠀⠀⠂⠈⠡⠐⠀⠀⠐⣤⡛⣟⣧⡯⠐⠀⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀⠀⠀⠀⠀⠐⣦⣿⣼⣿⡿⡏⠅⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣄⠈⣿⣼⣿⣿⣏⠰⣐⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠟⠃⠈⠑⢶⣶⣿⣿⡽⠿⠷⠚⠛⠓⠂⠒⠒⠒⠋⠉⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠿⠶⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡑⢄⣀⣀⡀⠈⠉⠙⠛⠲⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢈⢀⣀⣈⠉⠑⠒⠦⢤⣀⠀⠈⠙⠛⠶⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠖⠛⠛⠓⢊⠔⠉⠀⠀⠀⠢⢄⡀⠀⠉⠑⠢⢄⡀⠘⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⣟⠋⠀⠀⠈⠑⠒⠴⡃⡀⠀⠀⠀⠀⢀⠀⢀⠉⠡⢄⠀⠀⠀⠀⠁⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠉⠑⠒⠤⢀⠀⠀⠈⠑⠲⠤⣀⣀⡁⠐⠁⢀⣀⠀⡀⠦⢄⡀⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⢉⣁⠀⠀⠀⠈⠑⡀⣿
⠀⠀⠀⣠⣤⡶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢄⣀⠀⠀⠈⠑⠤⠐⠃⠀⡇⣿
⠀⠀⢸⡏⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠝⣦⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⢸⡟⡉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⣰⠁⣿
⠀⠀⢸⡇⢸⠑⠢⠄⡈⠐⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⠊⠁⡸⠀⣿
⠀⠀⢸⡇⢠⣍⠀⠀⠀⠁⠂⠄⣀⠉⠒⠤⣄⡤⢔⠂⢀⡄⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⣿⠀⢰⡟
⠀⠀⠈⣧⠐⢤⡙⠢⢄⡈⠐⠠⠀⠉⠒⠤⣀⠃⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣤⠶⠟⠀⠈⠛⠛⠁
⠀⠀⠀⢻⣤⣾⠙⠳⢦⣌⡑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣈⠉⠒⠤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⡇⠀⡄⠀⠀⠀⠀⢀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣇⣤⡴⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡄⠀⠀⠀⢠⠀⠀⢰⠀⠀⠀⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣿⣿⣿⡄⠀⠀⠀⠆⠀⠈⡀⠀⠀⢼⣷⠀⠀⢀⣠⣤⣤⣤⣤⣄⣀⠀⠀⣽⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⣠⠿⠃⠿⠿⠿⠿⣆⠀⠀⠰⡀⠀⠁⠀⠀⣾⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢀⠈⠀⢀⣼⣿⣿⡇⣿⣿⣿⣿⣿⣧⡀⠀⠱⡀⠠⠂⢀⣭⣭⣏⣉⣉⣙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠄⠁⠀⣰⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣦⡤⠊⠀⣴⣿⡉⠀⠙⢿⣿⣿⡿⠀⠀⠀⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⢀⣠⠚⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⡟⠠⠂⢸⡿⠃⢤⡄⠀⠀⠹⢿⣷⡄⠀⠀⠀⠈⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⢰⣏⣉⠀⣩⣭⣭⣭⣭⡁⣩⣭⣭⣭⣭⣭⡸⠀⠀⡈⠀⠀⠠⠄⠀⠀⢰⡀⡘⠉⠀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⠀⠀⠀⡆⠀⣀⣀⣀⣀⣿⣿⡇⣿⣿⠿⠿⠿⠃⠛⣻⠿⠿⣿⣿⡇⠀⢀⠀⠀⠤⠀⠀⠀⠐⠀⢐⠃⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠃⠉⠁⠀⠀⠀⠉⠉⠙⠓⠢⢄⡀⠀⠀⠀⠉⢬⠀⠘⢁⡿⠙⠁⢆⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠉⠳⡄⠀⠀⠀⠚⠀⠘⢇⣠⣤⣈⣦⣤⠀⠊⢀⠞⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢻⠵⠶⠷⣖⣛⠃⠚⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠙⢃⠀⣀⣉⡙⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠉⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣋⠄⠀⠀⠀⠀⠀⠑⡅⠐⠴⠀⠀⠉⠙⠝⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠛⢥⢀⣀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⢀⣀⡀⠠⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠠⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢄⣀⡐⣰⡄⠀⠀⡀⠀⠀⠀⢰⣿⠸⢬⣛⣳⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢰⠀⠚⠉⢛⣾⡧⠀⣹⣽⣦⣺⣿⣶⠆⢾⠏⢷⠈⠀⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣅⠀⢨⡿⣾⡦⠀⠀⢾⣿⢷⣿⡿⠿⠏⠛⠛⠁⠈⠑⠉⠐⢀⣈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠠⣿⠟⠀⢸⡻⡟⠀⣠⣦⣾⡿⠟⠻⡣⠀⢀⠀⠓⠊⢰⠞⠧⢶⣋⣉⠉⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠧⠂⣰⣇⣀⢔⣮⣿⣿⡿⠿⢟⣯⡴⠐⡀⣵⢳⡀⠀⠀⡤⡙⢂⠀⠀⠘⣿⠓⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣡⣵⣶⣷⣿⣿⡿⢿⣗⣫⡽⠿⡛⣉⠬⠓⠀⣰⣚⣿⣷⠓⠼⡰⠢⡽⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠿⣛⣿⣾⠶⠛⠻⠛⠉⠛⠀⠀⠂⠀⠀⠀⠰⢦⣾⡿⠿⠣⣖⣐⣉⡙⠀⠀⠀⠀⠀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⣙⠗⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠻⢿⠸⡵⣫⡝⣷⠋⠀⠀⠀⠀⠀⠀⢈⠎
⠀⠀⠀⠀⠀⠀⠀⢸⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢋⢾⡱⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣟⡷⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡶⠂⡀⠈⠑⠨⠭⡯⠋⠀⠀⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢊⣕⠙⢤⣄⣀⣀⣐⣫⠄⠁⠤⣄⡀⠈⢒⢿⢦⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡬⣀⠋⠀⠀⠀⠀⠉⢁⢈⠅⠀⠀⠄⠀⠉⢢⣰⠎⡛⠙⠉⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠗⠠⠤⠤⡄⡀⣀⠵⠂⠀⠐⣠⠀⠀⠀⠂⡊⡈⠛⠀⡈⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⡀⠀⠐⣋⠀⠈⢁⠀⢀⠔⣱⡧⠀⡄⣨⠞⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣣⠐⢰⠂⠀⢴⡄⠀⠀⢸⠅⠀⠀⠉⠤⠊⡁⠜⡈⠙⢇⠁⣧⢰⣟⣨⣌⡅
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡧⢹⣴⢾⡀⢀⣀⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⣠⠾⠁⠀⠘⣀⣡⠙⠓⠊⠉
⠀⠀⠀⠀⠀⠀⠘⠭⣥⣤⣵⣭⣷⡭⢉⣽⣭⠑⠛⣁⠳⢄⠒⠒⠋⠀⢅⠀⠙⡤⡀⣽⠁
⠀⠀⠀⠀⠀⢀⡠⠚⡟⣆⠀⣾⡟⡷⡯⠍⠩⡛⠿⣿⣿⣿⣤⣤⣤⣀⣯⣃⡀⣨⠞⠁
⠀⠀⠀⠀⢠⢺⢒⡎⣶⣮⡠⢎⢿⡀⠀⠀⠀⠀⣃⣴⠋⡄⠀⠸⠟⣛⣉⠟⠉⠁
⠀⠀⠀⠀⠻⣝⢤⢒⣹⣾⡁⠈⢉⠀⠀⡉⠐⢠⣟⣹⣷⠁⠀⠂⡐⠩⣅⢤⣀⡀
⠀⠀⠀⠀⠀⢿⡚⣟⡿⠡⢁⠀⠀⢄⣄⣤⠖⠀⠬⠁⠉⠾⣷⣛⢦⣰⡍⠳⡇⢽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠘⠊⠰⠽⢄⣫⡨⠒⣼⡃
⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠁
⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⢿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠛⠾⣭⣟⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣭⡛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠳⢦⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠙⠳⢮⣙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⠀⠀⣠⣾⠟⡋⠹⠙⠛⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⠙⠳⣬⡻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢿⡛⠙⠳⣤⣀⠀⠀⠀⣿⣥⠂⠀⠀⠀⠀⠀⠀⠈⠙⡻⣷⣦⡀⠀⠀⠀⠀⠈⢻⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠀⠀⠉⠲⢄⡀⠉⠳⢦⣀⠈⠛⢷⣦⣄⡀⠀⠀⢀⠐⣨⠷⢚⣿⣿⠀⠀⠀⠀⠀⢸⡇⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠉⠛⢦⣄⡈⠙⠻⣶⣴⣠⣟⣥⣶⠟⠋⠉⠛⢦⣄⠀⠀⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠈⠙⠶⣄⡀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠛⠶⣼⡇⣿⡇
⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠛⡇⣿⡇
⠀⠀⠀⢸⡿⣥⡀⠀⠀⠀⠀⣴⡟⠙⢀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠈⠛⢦⣄⡀⠀⣠⡴⠛⠉⠀⠀⢀⡿⢹⡇
⠀⠀⠀⢸⡇⠈⠙⢦⣄⠀⠀⢿⡻⣷⢄⡉⠰⣀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣀⣨⣿⡟⠁⠀⠀⢀⣠⠶⠛⠁⢸⡇
⠀⠀⠀⢸⣧⠀⠀⠀⠉⠻⢦⣀⠙⢶⣕⣭⡲⣄⠘⢠⠀⠀⣀⣤⣶⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢻⠁⢸⠇⣀⣤⠾⠋⠁⠀⠀⣀⣼⡇
⠀⠀⠀⢈⣿⣦⣀⠀⠀⠀⠀⠉⠳⣦⡈⠛⢿⣮⣷⣤⣚⡯⣷⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⠀⢸⣠⡼⠟⠋⠀⠀⠀⣠⣴⡿⠛⠉
⠀⠀⠀⠀⣿⠀⠉⠳⢦⣀⠀⠀⠀⠀⠙⠳⣤⡙⠻⠿⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⢀⣠⡴⠛⠁⠀⠀⢀⣠⣶⠿⠋⠁
⠀⠀⠀⠀⣿⣆⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⢀⣤⠾⠋⠁⠀⠀⢀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠈⠳⣦⡀⢀⣠⠶⠋⠁⠀⠀⣠⡴⠞⠋⠀⠀⠀⢀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⡀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠈⢻⠋⠁⠀⠀⣠⡴⠛⠉⠀⠀⠀⣀⣤⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⠀⠈⠛⢦⣄⠀⢸⠀⣠⡴⠛⠁⠀⠀⠀⣀⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠈⠛⢿⠟⠁⠀⠀⠀⣀⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⠀⠀⢸⠀⠀⣠⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣼⣶⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣄⣀⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡇⠀⠲⣤⣀⣤⠴⠂⠐⠦⣤⣠⣤⠖⠀⢸⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠹⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡟⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣧⠀⠀⠀⠀⠀⣀⡷⠀⠀⠀⠀⠀⣼⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣩⡄⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠉⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠛⠛⠛⠛⠛⠛⢻⠀⠉⠀⠀⠉⠀⡟⠛⠛⠛⠛⠛⠛⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⠀⠀⠀⠀⠀⠀⠍⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣚⣋⣻⣒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⣠⠚⠛⠚⣿⡛⠻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠉⠀⢀⣠⣴⣥⣼⠶⠷⠐⠂⠀⠒⠚⠠⣤⣤⡀⠈⢁⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠅⣠⣤⣤⣴⠟⠛⡉⠁⣀⠀⠀⠀⠈⠁⠑⢄⠠⠈⢻⣝⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⢒⣭⠶⠛⠁⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠠⠠⡀⠠⠄⠐⢆⠀⠀⠀⠈⢷⣶⣶⠤⡀
⠀⠀⠀⠀⠀⠀⢀⣼⠉⠀⢀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⢻⣷⡆⠙⣆
⠀⠀⠀⠀⠀⢠⢊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠈⠂⢘⢿⡅⠀⠚
⠀⠀⠀⠀⠀⡈⠁⠉⠀⠀⠀⠀⢀⣀⠄⠂⠀⠀⠀⠀⠰⠒⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠒⠈⠘⢸⡁
⠀⠀⠀⠀⢨⠤⠠⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠑⠀⠀⠈⠉⢼⡛⣇⠀⢀
⠀⠀⠀⠀⢸⡆⢀⠁⠀⠀⠀⠀⠀⠀⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⠀⡀⠄⢠⠾⣳⣇
⠀⠀⠀⠀⠈⡏⠈⢀⠀⠀⠀⠐⠀⠀⠀⠈⠩⠀⠃⠀⠀⠀⢀⠀⠀⠐⠂⠀⠈⠈⠆⢈⣧⣮⠐⡌⢸⡀
⠀⠀⠀⠀⠀⠸⡵⠊⠁⠁⠀⠀⠀⠀⠀⢀⡀⡀⠀⠠⠐⠂⠀⠑⠀⠠⠀⠀⢌⠀⣸⠇⢠⢠⠒⠁⡼⠀⢸
⠀⠀⠀⠀⢀⡠⣶⠀⡈⣄⡀⠀⠀⠀⣀⠀⢓⡸⠐⠐⠄⠀⠑⠠⠐⠆⠐⢫⡴⠮⠉⢄⡡⠃⠀⠀⢿⢠⠏
⠀⠀⠀⡠⠫⢈⢿⣿⠉⠀⢉⠂⠰⣆⢈⣈⣤⣤⣑⣂⣔⣀⣈⡥⠜⠛⢙⢫⠄⢂⠔⠁⠀⠀⠀⠀⠘⠁
⠀⢠⠊⠑⣠⣆⠯⠋⣄⡠⠋⠀⣙⢸⣣⣤⣍⣀⣯⠀⡈⢋⣁⣿⣿⡻⠔⠊⠁
⢰⣣⠤⠒⠁⠀⠀⠀⠀⠈⠚⠉⠁⠉⠉⢉⣟⠿⠿⡿⢿⡏
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠀⠷⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⡠⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠀⡎
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣞⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢨⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⣸⣧⣀⠀⣀⡀⢀⢀⣠⡟⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⢸⣄⡀⠀⣀⡤⣲⡞⠋⠀⠉⠙⠲⣿⠞⠉⠁⠙⠢⢀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⢀⣤⣴⣦⣤⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⣴⡳⠋⠉⠉⠛⠻⣿⠋⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠑⢦⣄⡀⣨⠇⠠⠰⢤⠔⠁⠀⣠⣴⣾⣿⣿⣇⣿⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠒⠒⠒⠛⠀⡀⢸⣿⠟⢿⣿⣿⣿⣿⣿⣿⣯⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⢄⣾⣿⠿⠻⠿⠿⠿⣿⣿⣾⣿⣄⣀⣿⣿⡿⣟⣻⣿⠟
⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣿⣎⣂⣀⣢⣭⣷⣿⣿⣯⣀⠀⠀⠀⠀⢸⣿⣿⠻⣿⣿⣿⡿⠾⣛⠝
⠀⠀⠀⠀⠀⠀⢸⢠⡁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀⣿⣄⠠⠤⠤⢖⣡⣾⣿⣿⣿⡿⠿⠛⠛⢿⡏⠀⠉⠛⠶⣤⣠⣺⣿⡯⠤⠤⠤⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠈⣻⣇⣠⣀⣸⣿⣄⣀⠤⠤⢐⣨⣴⣿⣿⣿⣿⣿⣿⣿⠛⠉⢹⣿⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢀⣿⣿⣶⣆⣰⡄
⠀⠀⠀⠀⠀⢠⠀⣿⠈⣿⠛⠋⣿⠿⠿⣿⣿⡿⠟⠛⣿⠏⠉⠉⠉⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⡄⣀⡴⣡⣾⣿⣿⣿⣿⣿⣿⡟⠄
⠀⠀⠀⠀⠀⢸⠀⡿⠀⡿⠀⢸⡏⠀⠀⢸⡏⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢹⡆⠀⠀⠀⠀⢀⣧⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⢀⣴⣾⣿⣇⢀⡇⠀⣸⠃⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⡇⠀⠀⠀⠘⡇⣤⢖⣫⣴⣿⣿⡿⠟⠛⡛⢿⣿⣿⣿⣿⣿⢯⠹
⠀⠀⠀⣿⣿⣿⣿⡿⠛⠇⢠⣿⢀⠀⢰⡇⠀⠀⠀⢸⣇⣀⣀⠀⣀⣸⣇⣶⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⡶⠿⠋⠁⠈⣿⣿⣿⣿⣿⢯⣀
⠀⠀⠀⠉⠛⠛⠛⠀⠀⢀⣾⣿⣿⣿⣿⣤⣿⣷⣶⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⠱⠆
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣹⡟⠻
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⣼⣀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠹⠏⢻⡍⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣆⠤⣤⣄⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠻⡿⠛⠉⠀⠈⠀⢄⠀⠀⠘⠛⠛⠛⢲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠛⠀⠀⠀⢦⠀⠀⠀⢿⠁⠀⠀⠀⣀⠀⣀⡉⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⢀⡀⠀⠀⠈⠀⠀⡀⠀⢀⡀⠀⠀⠋⠈⠛⠃⠈⠁⠱⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣞⡹⠋⠀⠀⠈⠁⠞⠢⡦⠀⡀⠁⢤⠀⠁⡀⠀⢠⡀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⣄⠀⣅⢠⡀⠰⠆⣩⠀⠀⠁⠀⠀⠘⠃⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠹⠂⠠⠄⠀⠈⠁⠰⠆⠀⠲⢾⣼⡥⣆⠭⠄⠀⠟⠀⠀⡀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣁⡀⠀⠀⠀⠀⢠⠄⢀⡀⢋⠐⢊⠙⠛⣭⡶⢂⠌⠁⡀⠄⠉⠀⠀⠘⠁⠀⠚⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠰⠠⠌⠼⠽⠠⠓⠀⠁⠀⠄⠚⠂⢀⠀⠈⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠐⠋⠁⠀⠒⠀⠐⠂⠀⠆⠐⠂⠰⠀⠖⡀⠃⠀⠏⠀⠀⠀⠈⠉⠂⠀⢣⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠰⠄⠁⢀⠒⠀⣅⠘⡇⠈⠙⠁⠀⠀⠀⠀⢶⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣶⠀⠀⠐⠖⠀⠀⠁⠀⠀⠀⢀⡄⠈⠀⠰⡀⠀⠑⡄⠠⠖⠢⡄⠂⠀⢜⣥⠂⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣄⠀⠀⠀⠀⠀⣀⠰⠆⠈⠁⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⣴⡟⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⣿⣤⡀⠀⣀⠉⠀⠀⠀⠀⢰⡆⠀⠀⠀⡛⠀⠀⠀⠐⣤⠞⠛⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⡦⠀⠀⠀⡄⠀⠀⠉⢻⠾⢿⡠⠶⠄⠀⠀⠀⠀⠀⢀⡀⠀⣀⣤⡶⠉⠀⠸⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⣿⢿⡿⠷⢾⡟⠋⠉⠀⢀⡠⠄⠘⠆⠀⠀⠀⠀⠀⠿⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⡀⢀⣠⠠⠄⠐⠀⠀⠀⠂⠀⠀⠀⢀⣤⠀⠲⠀⠀⠐⠀⠀⠀⢛⠵⠦⠁⡀⠀⠀⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠁⢸⠰⣤⣄⠀⠀⠀⠃⠀⠀⠀⠰⡇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠐⢮⣑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⣶⡟⢻⠀⠀⠁⠀⠀⠠⠀⣠⡔⠀⠺⠁⢀⡀⠀⠀⠓⠀⠀⠰⠆⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⢶⡠⠀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢱⣆⠀⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠉⠀⠀⠇⠀⠀⠀⠀⠀⠀⣿⡟⠛⠸⢯⣷⡆⠀⢀⡜⠀⠀⢐⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠉⠀⠀⠀⠐⠀⠟⠁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠘⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⢰⡄⠀⣠⠄⡄⠀⢀⠀⠀⠸⣷⠀⠀⠰⠄⠀⠛⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠃⠀⠀⠘⠂⠀⠀⠀⢣⠀⠸⠁⠰⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠺⠁⠠⠄⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⠿⠿⠛⠻⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠋⠁⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⢸⡇
⠀⢀⣀⣀⣀⡀⠀⢀⣠⣶⣿⡿⠟⠋⠁⠀⠀⠀⠀⢠⣿⠋⠉⠙⣷⠀⠀⠀⢸⣿
⣼⣿⣿⡿⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⣿⠇⠀⠀⢸⣿
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⣼⠟⠀⠀⠀⢸⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠻⢶⣤⣸⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣤⡶⠟⠋⠉⢀⣀⡀⠀⠈⠙⠻⢶⣄
⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣤⣴⠶⠟⠛⠿⢾⣿⣥⣀⠀⠀⠀⠈⠁⠀⣀⣠⣤⣶⣾⣿⣀⡀
⣿⣿⣿⡇⢀⣠⣴⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣶⣤⣶⠾⠟⠛⠉⠁⠀⠀⠈⠉⣛⣷⣦⣀⡀
⣿⣿⣿⡗⣿⣭⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠟⠋⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠾⠛⠋⠉⠈⠉⠛⠿⢶⣤⣄⡀
⣿⣿⣿⣿⡿⠟⠻⠷⣶⣤⣤⣴⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⣀⣠⣴⡶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⣄⣀
⣿⣿⣿⣅⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⣦⣄⣀
⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⣀⣤⣴⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠿⠛⢻
⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠟⠛⠉⠀⠀⠀⠀⢸
⠀⢸⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⢸⣿⣿⡇⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣤⣴⡶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠾⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠟⠛⠉⠁⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣀⣤⣴⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⠶⠶⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠄⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢠⢼⡑⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⢠⢤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⣰⠈⠱⠀⠀⠀⠐⠐⠀⢀⠀⢸⠀⠐⢎⢥⢈⠀⠀⠀⠀⠁⠉⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠢⠀⡒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⡁⠂⠀⢰⠎⠁⠤
⠀⠀⠀⠀⠀⢠⠁⢀⠀⡆⠀⠀⢀⠀⠀⠀⢀⠀⣤⠄⠀⠁⠀⠀⠖⠠⠀⠀⠀⢰⡀⣀⠄⣀⠒⠬⢠⢀⠾⣈⠀⠀⢀⡀⠀⠀⢀⡤⣀
⠀⠀⠀⠀⠀⡀⠈⠀⡅⡗⢀⣆⡀⢠⡴⠊⠀⡿⠛⠀⠀⠀⣴⡽⠯⠀⠀⢀⠀⠘⠁⣥⡀⠘⠃⠂⠈⠀⠈⢠⣤⣴⢩⣂⣀⣤⡿⢏⣿
⠀⠀⠀⠀⠀⡘⢀⣀⢠⢟⠞⣡⣾⣿⣟⣷⢿⠿⣿⣦⠠⢞⢁⡘⠁⢠⠀⠀⢀⠀⣀⣄⢾⣆⡚⢠⣶⣬⣷⣶⣬⣿⣿⣿⣿⣷⡾⠿⠏
⠀⠀⠀⠀⠘⢹⣱⣫⠇⢀⣾⣿⡿⣷⣿⣾⣋⣴⣾⣟⣿⣤⠀⣤⣢⣤⡄⣀⢈⣸⡎⠈⣷⣞⣿⠛⢧⠈⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠈⠉⠉⡀⠀⢠⣿⣿⣿⣹⣿⣿⣿⣿⣿⢿⣷⣿⣷⣾⣾⣷⣿⣷⣿⣴⣿⣀⣠⣿⠋⠿⢷⣶⣿⣿⡟⢁⣀
⠀⠀⠀⠀⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⢿⣿⣷⣦⢀⣿⣿⠄⡐⣦⡉⠁⠈⠀⢠⡰⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢿⣿⣿⣿⣿⣿⣥⡈⣧⠀⠀⠀⠂⢑⠉⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠵⠟⠋⠉⠙⢿⣿⣿⣿⣩⢆⠀⠐⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣤⣇
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡾⣿⣿⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠁
⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⣯⣭⡟⣿⣿⡿⠿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡦⠶⢶⣤⣤⣤⣼⣟⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⡀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⣠⣴⣾⣾⣿⣭⣽⣔⢻⣿⣿⣿⣜⢿⣿⣧⣵⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠽⠾⣿⣛⣏⣾⣿⣿⣿⣿⣷⡝⣿⣿⣿⣷⣝⢿⣿⣳⢏⣴⣶⣶⣶
⠀⠀⠀⠀⢀⡤⢲⣦⢶⡴⡷⣳⣷⣞⠍⠽⠉⣩⣉⣉⡙⠛⢾⠿⣭⣭⣭⣯⠶⠟⠁⠙⠻⠟⠛⠁
⠀⠀⠀⠸⣗⣾⡽⠿⢨⣧⢿⡻⠉⠈⠀⢰⣼⣫⡥⠗⣋⣈⠉
⠀⠀⠀⠈⠹⣮⠾⠯⠾⢃⠣⠀⠀⠀⠀⠲⣧⢺⣳⣇⣩⡝⣤
⠀⠀⠀⠐⠒⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⠇⣷⣆⣿⣾⣶⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠛⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠠⠀⠀⡏⠐⠁⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢋⠀⠀⠀⢀⣾⠀⠀⠀⠀⢠⠔⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠘⠁⣀⣿⣄⣀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⣠⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡐⣴⣦⢐⣒⣶⣯⣤⣶⣾⣿⣿⣦⣽⣷⣧⣠⣧⡀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢼⣿⣿⣷⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡘⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⢡⣤⡄⢚⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⣯⣿⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣜⣿⡿⣀⣻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠐⠶⣞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠠⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⢻⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣀⣠⣿⣆⠀⠈⢻⣿⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣌⠙⠛⠳⠄⠀⢿⣿⠀⠈⠻⠟⠟⢿⣿⣟⢻⣿⣄⠁⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠻⢿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣧⡀⠀⡀⠀⠈⣿⠛⠀⠀⠀⠐⠿⣿⣿⣀⠈⠙⠿⠋⠀⢙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢸⡏⠻⣿⠶⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⣤⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠸⣿⡇⠻⠿⠇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢻⠷⣶⡆⠀⠀⠈⢿⣿⣿⣦⣄⠀⠀⠲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠠⣿⣿⣦⣿⣿⣿⣿⣷⣄⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⠿⠟⠿⠁⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⢠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠴⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠚⠉⣁⣀⡤⢤⢴⠒⠒⠲⣄⢸⡆
⠀⠀⠀⠀⠀⡴⠊⢁⡠⢴⢺⠉⠁⠀⠀⢼⢸⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⣸⠀⣰⠋⠀⢸⢸⠀⠀⠀⠀⢸⢸⠀⠀⠀⣸⣸⡇
⠀⠀⠀⠀⡏⠀⡏⠀⠀⢸⢸⠀⠀⢀⣀⣼⠼⠖⠛⠛⠛⢮⡑⠤⡀
⠀⠀⠀⠀⡇⠀⡇⢀⣀⣼⣼⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⡆⠈⠓⢤⡀
⠀⠀⠀⠀⡇⢰⣏⠉⠀⠈⢿⡿⡲⣄⠀⠀⠀⠀⠀⣀⡤⢖⣚⡥⠴⠒⠋⠙⠳⢤⡀
⠀⠀⠀⠀⡇⢸⠀⠑⠦⡀⠀⠉⠪⢿⡦⠤⠒⣊⠭⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⡇⠸⣄⠀⠀⠈⠳⢄⡀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⡇⠀⡇⠑⢦⡀⠀⠀⠙⠺⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡭⠷⠒⠋⠉⠉⢲⡀
⠀⠀⠀⠀⢧⣤⠇⠀⠀⠈⠳⢄⡀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⢉⣀⣤⠴⣞⣿⠷⡆⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⢀⡔⠋⢁⣠⡴⣖⣋⣭⡶⢿⡀⡏⣁⣠⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠙⠷⣄⡀⠀⡞⠀⣸⡥⠾⡇⣟⢉⣀⡤⢼⡇⡏⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠈⠙⠿⡇⠀⣯⠠⠴⡇⣿⠉⠀⠀⣘⣇⡧⠔⣚⣹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⡇⠀⡇⠀⢀⣇⡿⠔⢚⣉⠥⠖⠚⠉⠉⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢴⡇⠀⣟⣉⠥⠼⠒⠉⠁⠀⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡤⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣧⣀⣀⣠⣴⠞⠉⠉⠛⢿⠞⠉⠉⠂⢀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣤⣦⣤⣶
⠀⠀⠀⠀⠀⠀⠠⠁⣀⡼⠋⠁⠈⠉⠻⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠙⢦⣤⣞⣀⣈⡖⠁⢠⣴⣾⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢢⠚⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⢀⢸⣿⣧⣤⣤⣴⣶⣼⣏⠈⢻⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣸⣖⣀⣀⣼⣵⣿⣯⡀⠀⠀⠈⣿⣿⠻⣿⣿⡿⠞⠛⠁
⠀⠀⠀⠀⢀⣠⡄⠀⠀⡇⠀⠀⠀⠀⠀⣿⣤⣐⣒⣪⣾⡿⢿⡿⠛⠛⠛⣏⠀⠉⠓⠦⣦⡿⠗⠒⠒⠂
⠀⠀⠀⠀⠀⢸⠳⣶⠶⣿⣶⣬⣬⣴⡾⣿⡿⠻⠿⣿⠋⠀⢸⡇⠀⠀⠀⢹⡀⢀⡀⣸⣿⣿⣷⣿⣤
⠀⠀⠀⠀⠄⣼⢀⡇⢀⡏⠀⢨⡟⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣧⠀⠀⠀⠀⣇⣯⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⢀⣴⣿⣯⣸⠃⢸⠇⠀⣸⠁⠀⠀⡇⠀⠀⠀⢿⠀⠀⠀⢸⠰⣺⣵⣿⣿⢛⣛⡙⢿⣿⣿⣿⡏⠉
⠀⠀⠻⣿⣿⡟⠈⢁⣾⣤⣤⣏⣤⣀⣠⣗⣶⣦⣤⣾⣼⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⢸⣿⣿⣿⣟⠦
⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⡿⠋⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡛⡄
⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣹⠟⡃
⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠷⠧⠄
⠀⠀⠀⠀⠙⢻⡟⣿⠻




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

⠀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⡻⣿⣿⣿⣿⡙⣿⣶⣶⣤⣄⣀
⣼⣷⣝⠟⣽⣶⡽⢧⡟⢿⡆⡀⠀⠀⠀⢀⣠⣴⣾⣿⣿⢆⣙⡻⣿⣿⣮⢻⣿⠿⣃⡹⣿⣿⣿⣎⢿⣿⣶⣤⡀
⢿⣿⣿⣦⡻⢟⣥⠿⢷⠎⢿⣣⣤⣤⣄⠿⠿⣿⡿⠟⣵⣿⣿⣿⣶⣝⡻⠗⣰⣾⣿⣿⣮⡻⠿⣣⣦⡻⣿⣿⡻⣷⣤⡀
⢳⣍⠛⠛⠳⠮⡍⠺⠊⠩⠇⠭⣿⣿⣿⢸⣿⣿⣿⣷⣌⢻⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣮⡙⣯⣜⡻⠿⣶⣄
⠀⠙⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠻⠹⣿⣦⣍⣙⠻⣿⣿⠷⠙⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣧⢿⣿⣿⣶⣝⢿⢟⣶⣦⣄
⠀⠀⠀⠀⠉⠙⠲⠦⠤⣤⣤⣀⠀⠀⣹⣿⣿⣿⣷⣄⢱⣾⣿⣮⡻⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡘⣿⠿⣛⣡⢾⣿⡿⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⣷⣤⣿⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣾⣍⡸⢿⣿⣿⣿⣿⣿⡇⠸⠿⢟⣛⣋⢱⣶⣿⣿⡿⣣⣶⣾⣿⣷⣶⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢻⣝⣏⣿⢿⣿⣯⡗⠆⠈⠛⢿⣿⣿⣿⣷⢰⣶⣶⣶⣶⣆⢻⣿⣿⣿⣿⠗⣈⣭⠵⠺⣿⣿⣿⣿⣯⠿⣿⢎⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣛⣿⣾⣿⡖⣟⣿⡿⢮⣔⡀⠀⠀⠈⠙⠛⠋⠘⠿⠿⠿⠟⣃⣀⣩⣭⣥⣶⣾⡉⠀⠀⠀⠙⢿⣿⣿⡟⣻⣴⡟⣻⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠾⣹⡿⢴⠯⣷⡇⣀⣀⢀⣀⣀⣀⣀⣠⣤⣤⣶⣶⣿⣿⣿⠿⠟⠻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⠻⠿⢩⣷⣶⡜⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡺⣿⢿⣼⣓⣺⠿⢎⡛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠈⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⢾⣻⠿⣭⡹⣶⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣛⣿⢛⣷⡾⠟⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣯⠿⣻⢧⣾⠷⢉⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⠛⣿⠷⡞⣛⣭⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠺⣶⢛⣌⣻⣅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣴⠄⣀⣀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⣠⡻⠫⠙⠋⢠⣷⣬⣛⢓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣴⠀⡴⠶⡄⢿⣾⣶⣖⣾⣦⢩⣿⣿⢺⡧⢸⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣶⣾⣿⣙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠹⠴⡅⠀⠈⠨⣉⠛⢛⢛⣥⣿⣭⠦⢠⣦⠾⣿⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⢇⣬⣍⣉⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠒⠲⢦⣙⠌⠃⠘⣥⠮⣭⢂⢽⡒⠻⠈⢯⣽⡿⣆⠀⠀⠀⣰⣶⡜⢿⣿⣿⣿⣿⣿⣿⡟⣵⣿⣿⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠚⠙⠈⠂⣉⣥⣈⣶⣾⣿⣷⣿⣷⣄⢾⣿⣿⣿⡸⣯⣿⣿⣿⣿⣿⣷⢹⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣾⣿⣿⠿⡿⠟⢛⣿⣿⣿⣿⠘⡿⣋⣉⣤⣌⣭⣭⣉⣉⣙⣋⠘⢿⣿⣿⡝⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣳⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣏⠀⣶⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣆⠛⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣌⠇⣿⢜⣛⣯⣿⣿⣿⣿⣿⣿⡿⣭⣿⣿⣿⡏⢆⠻⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⢡⣶⣤⣙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣶⣷⡶⢻⣏⣁⣰⣿⣿⣿⣿⡟⣣⣾⣟⣼⣿⣹⢟⣎⡓⠜⢿⣿⣿⣿⠇⢸⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠀⢈⢻⡏⠛⢦⣿⢙⠻⣿⣿⡿⠿⠟⠻⣟⢲⣿⣿⠇⠛⣠⢑⣬⢄⠽⡿⠏⢠⣿⣿⣿⣿⡟⣼⣿⢝⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠙⠟⣿⣿⡿⢟⣯⣿⡿⣿⣿⡟⠀⠀⠀⠀⢻⣟⣿⡟⣨⣾⣿⣯⣾⣷⣅⣘⣳⢦⡍⡙⠻⣿⢡⣿⣷⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣄⢸⣧⣼⣽⣿⣧⡿⣿⣿⢶⣿⡟⠀⠀⠀⠀⠀⠘⣟⡿⣬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡌⠉⡛⠷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣉⣽⣿⣿⣿⡿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠙⠻⣿⡛⢫⠉⠀⠙⢿⣯⡿⣿⣿⣿⣤⣤⣀⠀⠙⠻
⠀⠀⠀⠀⠀⠀⠀⣼⣴⣿⡿⠦⣶⡟⣻⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡜⣙⣛⠊⠀⠶⣤⢀⣹⣿⣟⣿⣿⣿⣍⣛⢻⣿⣯
⠀⠀⠀⠀⠀⠀⠀⣷⠉⢹⣧⣼⣿⣾⣿⣦⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢒⣒⡛⠵⠾⠶⠤⠜⢧⢻⣿⣿⣿⣿⡟⣻⡟⠛⢻⣅⣻
⠀⠀⠀⠀⠀⠀⠀⢻⣶⣿⡉⠉⠙⢻⣿⣯⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣭⣭⣽⡮⢻⣿⣃⠀⡂⢼⣿⣿⡿⠟⠛⠿⠷⠦⠿⢼⣻
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⣯⣒⣶⠶⠾⢛⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣥⠤⠶⢒⣛⠠⣁⣂⣹⣿⣿⣿⣷⣤⡀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⠤⠒⠂⠈⠉⠑⠖⠈⠉⠉⠑⠢⢄
⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⣄⠀⠑⣄
⠀⠀⢰⢃⡤⠖⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠂⠀⠀⠪⡱⡀⠈⢆
⠀⢀⠃⣨⠖⣉⠒⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣾⣿⣿⡆⠐⣥⠀⠸⡄
⠀⡘⢸⠃⣾⣿⡿⠊⠉⠉⠉⠉⠁⠂⠀⠀⠸⠘⣿⣿⣿⡏⢀⣿⠀⠀⠘⡄
⢠⠃⢸⡀⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠌⠉⠭⠂⠁⠀⠀⠀⠀⠸
⡆⠀⠈⠁⠂⠀⠂⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⡸
⠰⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⠀⠀⡰⠁
⠀⠙⢆⡀⠑⠠⢀⣀⠀⠀⠀⣀⡀⠤⠀⢂⠞⠃⠁⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠉⠢⢄⡀⠀⠀⠈⠛⠦⠤⠄⠂⢁⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⣤⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠐⠀⠀⠀⠀⠀⠀⠀⢧⢀⡠⠴⠒⠛⠉⠉⠉⠉⠉⠫⡉⠘⠒⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢱⡀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠒⠀⠤⠀⡠⠛⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡃⠀⢀⣀⡀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢰⡏⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⣀⠀⠀⠈⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢪⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡞⠀⠀⠐⠢⢀⠀⡠⠄⢀⡀⠀⠀⠀⢀⠔⠁⠀⠀⠈⠁⠀⠊⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡼⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡈⠀⠑⠄⣀⠀⢀⣀⡀⠄⠒⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠈⠙⠲⣤⠐⠘⠢⣀⠀⠀⠀⠀⠀⠀⡠⢀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠅⠈⠁⠉⠲⢤⠋⠙⢦⡀⠀⠉⠂⢄⠤⠒⠁⠀⠀⠈⠉⠐⠀⠌⠀⠀⠀⠀⠀⠀⠀⡛⠑⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⠈⠑⠆⠠⠤⠤⠐⠊⠡⠂⠀⠀⠀⠀⠀⠀⠙⣄⠀⠙⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣀⣴⠁⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢣⡀⠰⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⡸⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠖⠖⠂⠉⠁⢀⣁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠱⣄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⡀⠈⠛⠤⠤⢤⢠⣤⠤⠖⠚⠉⠀⣀⣤⠜⠒⠛⠉⠉⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠉⠒⠤⣀⣀⣀⣀⣄⣀⠤⠔⣒⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⢑⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠁⠀⣀⣠⡤⠖⠛⠣⢤⣀
⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠶⠶⠖⠒⠛⠚⠉⡿⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠰⣀⣀⡀⠀⠀⠀⠀⠀⢀⡤⠊⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢠⡃⠀⠀⣀⡀⠀⠀⣠⠞⠁⢧⠀⠀⠀⠀⠀⠀⢀⣠⠃
⠀⠀⠀⠀⠀⠀⠘⢄⣀⣢⡤⠖⠋⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠛⠋⠀⠀⠀⠘⢆⠀⢀⣤⣈⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡎⠀⠀⣀⡉⠀⠁⠀⠀⡀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢰⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿
⠀⠀⠀⠀⠀⠘⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠷⠙⢿⣿⣿⣾⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⢛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡸⣿⣿⣿⣿⣇⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣤⠄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣉⣻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢰⡟⢰⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡏⠘⢿⣿⣿⡟⣋⣉⣥⣼⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠻⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣙⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠿⠿⠿⢿⣿⣿⣿⡿⠿⣛⣫⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣋⣥⣴⣶⣦⠀⢠⣤⣤⠄⠀⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣾⡿⠟⠉
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣷⣿⣿⠿⢟⣉⡄⠀⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⡀⠀⠺⠿⢶⣶⣤⣤⣤⣤⡶⠶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠛⣿⣿⣿⣿⣿⠟⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡧⣶⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⡀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⢸⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢶⠞⠋⠀⠀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⠀⠉⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⣀⣀⣀⡀⢹⣿
⠀⠀⠀⠀⠀⠀⣀⣴⣛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢛⣷⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢀⠀⠀⠀⠉⠉⠛⠛⠶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡉⠉⠉⠓⠒⠦⠤⣄⡀⠀⠈⠉⠛⠷⢦⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠧⣄⠗⡢⠒⠒⠒⠠⢀⠀⠈⠉⠒⠢⢄⡀⠀⠈⢹⠋⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠛⠛⠛⠥⢀⡀⣰⠀⠊⠀⠀⠀⠀⠀⠀⠉⠲⠦⠀⠀⠀⠈⠉⠒⠄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠞⠋⠙⠣⠤⢄⡀⠀⠀⠀⠈⠑⠼⣀⡀⠀⠀⠀⡔⢁⠄⠂⠈⠙⠂⢀⠀⠀⠀⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⠀⡀⠀⠀⠉⠑⠒⠦⠧⣨⣤⣤⣤⠤⠤⠈⠉⠒⠤⣇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠠⢄⠀⠀⠀⡀⠀⠀⢸⡇
⠀⠀⠀⣠⣶⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⣀⠀⠀⠀⠑⠆⠈⠀⠀⡁⢸⠃
⠀⠀⠐⡏⣉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⢹⡄⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⣿⢉⠙⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣠⠁⣸
⠀⠀⠀⣿⠈⡍⠓⠢⢄⠉⠐⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡿⠊⠁⣸⠀⣿
⠀⠀⠀⣿⠀⣍⠐⠀⠀⠈⠐⠠⢄⡈⠉⠒⠤⣄⣀⡤⣒⠀⢀⣀⠠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣷⢶⣟⠁⢀⣿
⠀⠀⠀⣿⠐⢬⡙⠲⢄⡀⠑⠢⢄⠈⠑⠢⢄⡀⠙⠀⢸⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⡴⠏⠀⠙⠿⠟⠃
⠀⠀⠀⢸⣇⢰⡟⠷⣦⣈⠑⠢⢄⡀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠋⠉
⠀⠀⠀⠀⠉⠋⠁⠀⠀⠉⠛⠶⣤⣈⠙⠲⠤⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⢹⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⢸⠀⠀⠀⣀⣠⣴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⣷⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢀⡀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠠⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠈⠀⠀⠀⠉⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⣀⠀⠄⠐⠀⠀⠀⡀⠀⠀⢀⠛⠁⢂⠀⠀⠀⠤⠜⠉⠀⠀⠀⠈⠀⠀⠂⠀⠉⠄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠲⠞
⡔⠈⠁⢱⠀⠀⢲⠂⠀⠀⠁⡄⢘⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡀⠀⠀⣌⡀⠀⠀⣄⠀⠠
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡈⠁⠐⠄⣀⣀⣠⢴⠢⢄⠀⠀⠃⠀⠀⠀⠀⠀⢨⠁⠈⠉⠃⠀⠆⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⠀⠘⠁⠐⠀⠀⠈⠛⠁⠠⠖⠀⢀⠀⠀⠠⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠃⠈⠀⠆⠀⠀⠀⠀⠀⠁⠀⠒⠢⡀⠀⢄⠀⢀⠠⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⢀⠈⠁
⠀⠀⠀⡤⠯⠤⠤⠤⠄⣀⣀⣀⣀⠀⠀⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄
⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡓⠀⠂⠀⠂⠀⠀⠆⠀⠀⠃⠐⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠘
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠁⠰⠀⠀⢀⡀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠁⠀⠀⠐⠍⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠰⣀⠀⠠⠀⢀⠀⠀⠀⠀⠁⠘⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢢⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⡀⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠐⠁⠀⠈⠐⡘⡀⠀⠈⡄⠀⠀⠈⢆⠀⠀⠀⠀⢾⡗⡃⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠡⠱⠀⠀⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠆⠀⠀⠐⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡄⠀⠀⢡⠀⢃⠀⠀⠀⠀⠀⢀⠈⠘⠉
⠀⠀⠀⠀⠀⠀⡄⠁⠠⡀⠈⠢⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠀⢡⠀⠀⣠⠷⠚⠁⠀⠀⠀⠌⠉⠁⠁
⠀⠀⠀⠀⠀⠰⠀⠀⠀⡈⠀⠀⠀⡐⠀⠀⠰⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢀
⠀⠀⡖⠀⠐⢇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠰⠀⡀⠀⠀⠀⠀⢀⠀⢢
⠀⠀⠈⠒⠄⢀⣿⡶⣦⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢺⡃⠀⠑⢆⠒⠂⠭⠈⢀⠃
⠀⠀⠀⠀⠀⠀⠠⠀⠈⢻⡉⠁⠒⠀⠀⠠⠤⠠⠀⠐⠐⠀⠁⠀⡠⠃⠀⠐⠒⡧⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠱⡄⠀⣄⠀⠀⠐⢀⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⢇⠀⠀⠫⠄⠠⠎⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠊⠂⠁
⠀⠀⠀⠀⠀⠁⠂⠠⠤⠌⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⡄⣂⢉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⠉⠡⠭⠈

⠀⠀⠀⠀⠤
⠀⣠⣴⡶⠳⣤⣤⡀
⣴⠟⢿⣷⣿⣿⠟⡿⣷⢤⠀⢀⣠⣤⣀⠐⠒⠆⠤⣀⣤⣄⣀⡀
⡆⢴⣿⣟⠉⠁⠚⠹⠳⢾⠙⠉⢿⣿⢿⡖⠺⣦⣤⡼⠟⠙⣿⣿⣿⣖⣦⣀
⡇⠀⠉⠛⠿⣿⣯⣶⣾⣟⠀⠀⠺⠀⣠⡀⠀⠙⢻⣿⣿⣉⠀⠿⣿⣿⣯⠉⠤⣷⣤⣄
⠀⠀⠀⠀⢠⣀⣈⣿⣿⣿⠆⢀⠄⠀⠀⠀⠁⠀⠸⢅⠈⠙⢷⣤⡁⠀⠘⣾⠀⠀⠦⠛⠛⢦⡀
⠀⠀⠀⠀⢻⣿⣿⣿⡟⠘⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡸⠿⠻⢿⣿⣿⣿⣄⣀⡀⣤⣆⢀⣀⣀
⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠈⠀⢀⣀⠘⢿⣯⣷⣦⣤⣀⠀⠀⢲⣶⣦⣬⣭⣉⣙⡛⢻⠿⠿⣿⡿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣽⣿⣿⣿⣷⣶⣅⠟⠻⠿⠛⠿⠿⠛⠛⠛⠁⠲⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⣶⣿⣿⣷⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣽⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⣄⣤⣀⣀⠀⠄⠀⠀⠐⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣲⣿⣿⣶⣿⠿⠗⠛⠛⠛⡛⠄⠀⠀⠀⠐⠶⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠛⠋⠉⠉⠉⠡⠀⠄⠂⠁⠂⠀⠠⠁⠀⠀⠀⣀⠲⡖⣭⠨⠰⣿⢯⠓
⠀⠀⠀⠀⠀⠠⠐⠡⢀⡨⠒⡈⠀⠠⠀⠀⠀⠀⠢⡀⠄⢀⠀⠀⠀⠀⢢⣌⠋⠀⠠⠘⠣⡈⠀⠀⣀
⠀⠀⠀⠀⠐⠁⠐⠠⣌⠑⢄⠈⠂⠀⠑⠀⠀⠀⠀⠀⠢⢀⢑⠸⠄⠓⠈⠀⠠⠀⠀⠂⠐⠀⠴⠂
⠀⡄⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠄⠊⠑⠠⢄
⠀⠀⠁⠐⠒⠀⣠⠊⠀⠂⠤⠤⠤⠤⠤⠀⠀⠀⠀⢀⣀⠀⠀⢀⡁⠀⠊⠁⠀⠄⢀⠀⠈⠵⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠸⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠑⠆⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⢉⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⢀⣤⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⡌⠹⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⢤⣤⠄⡆⠠⢤⠤⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⣠⣿⣿⣿⣿⣧⣿⣿⡆
⠀⠀⠀⣼⣿⣷⣿⣿⣿⣇⠀⠀⠀⠃⢀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠉⠉⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣯⣈⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⠋⢀⣀⠹⣋⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⡏
⠀⠀⠹⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠉⠙⠻⣿⣿⣷⣾⣿⣔⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠟
⠀⠀⠀⠙⠿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⠿⠟⠋

⠀⣤⣤⣤⣤⣤⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣟⢿⣿⣿⣿⣻⣿⣶⣦⣤⣀⡀
⣾⣷⣝⢻⣷⣮⢳⡟⢻⣂⡀⠀⠀⢀⣤⣶⣿⣿⡟⣨⣝⡻⣿⣷⡻⠿⣟⣥⡻⣿⣿⣧⠻⣿⣷⣦⣀
⡻⢿⣿⣾⡛⢷⢛⡻⡧⡫⣷⣶⣶⡘⣻⣿⣿⡉⢾⣿⣿⣿⣷⣝⢋⣾⣿⣿⣿⣮⠛⣵⣷⣽⠿⣿⡻⣷⣦⡀
⠙⢦⣄⠉⠉⠓⠈⠁⠐⠁⢻⣿⣿⣇⠿⣿⣿⣿⣮⡻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡆⣿⣿⣿⣷⣰⣶⣮⣟⢿⣷⣄⣀
⠀⠀⠉⠻⠦⣄⣀⣀⡀⠀⠀⠀⠹⣿⣷⣶⣌⡛⢛⣥⣜⢿⣿⣿⢸⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣇⣿⣿⣿⠷⣹⣽⣿⠿⠆
⠀⠀⠀⠀⠀⠀⠈⠉⠙⢛⣲⣄⣰⣿⣿⣿⣿⣷⡙⢿⣿⣷⣽⡿⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⠿⠿⣨⣭⣶⣿⠏⣫⣵⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣟⣿⣿⣿⣿⣟⠯⠈⠻⢿⣿⣿⣷⡎⣭⣭⣭⣭⣯⢰⣶⣾⣿⣿⠍⢛⣻⠵⣾⣿⣿⣿⣿⣿⡾⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣯⣾⣿⡿⣕⡂⠀⠀⠉⠛⠛⠃⠸⠿⠿⠿⠟⣈⣉⣩⣭⣴⡞⠉⠀⠀⠹⣿⣿⡿⢗⣮⣾⢿⣙
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡽⣯⣿⢷⡏⣷⡇⣀⣈⣀⣀⣀⣀⣠⣤⣤⣶⣶⣿⣿⠿⠟⠻⣿⣿⣿⡄⠀⠀⠀⠀⠉⠿⠏⣿⣶⣎⠻
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢿⣟⣯⣻⣼⠿⣊⠙⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣞⣿⢟⣷⡽⢿⣻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡯⣿⣯⡿⢫⣹⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠈⣽⣽⣟⣭⡼⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠙⢽⣵⡖⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⠿⢿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⠤⠤⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠈⣇⢀⠈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⡉⠁⢀⡇⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢹⠀⠀⠰⠀⠂⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⠀⠀⠀⠰⠀⡄⠀⠀⠸⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡄⠀⠐⡆⢸⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⡆⢠⠀⠀⠀⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⡇⠀⣰⠀⠀⠀⠃⡆⠀⠀⠀⠀⡇⢠⠀⠀⠀⡆⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⠀⠀⠇⠀⠀⠀⠀⠀⢸⠀⡃⠀⠀⠀⣇⠀⢸⠀⠀⢀⡀⣇⠀⠀⠀⢀⡇⢘⠀⠀⠀⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠛⠛⠋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣉⣈⣉⣈⣉⣉⣉⡉⠉⠉⠙⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠗⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⡰⠁⣀⡠⠤⠤⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠒⠂⠠⠤⠤⢄⡀⠱⡀
⠀⠀⠀⠀⠀⠀⣡⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡇
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⣀⢀⣀⢀⣀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⡀⢀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣘⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠁




⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⠶⠶⠶⢶⣶⣶⣶⡶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⣹⣇⠀⠀⠀⠀⠀⠀⠀⠱⣈⣷⡦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠿⣄⣀⣠⠂⠉⠉⠉⠙⠉⢲⣶⠒⠈⠉⠁⠀⠈⠀⢌⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠉⠉⠿⢦⣀⠀⠀⠀⠔⢰⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⡀⡓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣦⡤⠄⠀⠀⠀⠀⠀⡠⠞⠋⠙⠢⣤⡴⠟⠚⠓⠒⠒⢶⡖⠅⠀⠘⠟⣧⠀⠘⡄
⠀⠀⠀⠀⠀⣀⠀⠠⠄⠀⠚⠀⠛⠶⣶⡖⠛⠁⠀⠀⢀⢀⡠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠈⠄⢠⡌⠁⠅⠀⠀⠀⠀⠈⠳⣀⠀⠷⣤⣴⠋⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢗⠀⠀⠀⠀⠀⢰⡀⠀⣇
⠀⠀⠀⠦⣤⢤⣄⣉⣿⠈⠀⠄⡀⠀⡀⠀⠙⢶⡆⠀⠈⠓⣤⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⢸⠀⠀⠀⠀⠄⣨⣿⠻⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠧⠾⠗⠛⡻⠿⣧⣤⡝⢦⣀⣠⡈⠉⠉⠉⠓⣦⡼⢿⣛⠀⠀⢀⠠⢦⣴⠿⠷⠒⢾⢞⠋⢀⣀⣴⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠜⠋⠀⠀⠉⠿⣷⠶⠤⣤⣤⣳⡀⠀⠀⣸⡇⢀⠀⣸⣧⣤⣤⣤⣴⡿⠖⠋⠉⠙⠳⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠎⢰⠇⠀⠀⠀⠀⠀⠴⠿⠒⠀⠀⠀⠘⠋⠉⠉⠉⠉⠉⠉⠉⠀⢀⡤⢐⠛⠓⢠⣐⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠓⠀⠂⠁⠀⠀⠈⠝⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⠾⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠢⡀



⣶⣶⣶⣶⣶⢶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣵⣶⣤⣿⣵⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡠⠒⠊⠉⠉⠑⠢⡀⠀⠀⢀⠄⠒⠀⠀⠐⠢⣄⠀⠀⠀⢀⡠⠒⠒⠒⠲⢄⠀⠀⠀⠀⡴⠊⠉⠉⠙⠲⢄
⡜⠀⣀⠀⠀⠀⡄⠀⢹⠀⠰⠁⠀⠀⠀⢀⠀⠀⠈⢂⠀⢠⠊⢀⠀⠀⠀⣀⡀⢳⡀⠀⡜⠀⠀⠀⠀⠀⠀⠈⢳
⡇⢀⠉⠀⠀⠀⠀⡄⢸⠀⡇⠀⡀⠘⠃⠙⠀⢤⠀⢸⠀⠈⠀⠉⠁⣀⣀⣀⣀⠀⡇⠀⡇⠰⡀⣤⠀⠶⢈⡇⠈
⠱⡀⠓⠤⠤⠤⠊⢀⠜⠀⠰⡈⠃⠂⠔⠢⠒⠊⠀⠌⠀⠸⡄⠻⣽⡯⣇⣳⠟⢀⠇⠀⠱⡀⠑⠤⣤⠤⠚⢀⡜
⠀⠈⠒⠤⠤⠤⠒⠉⠀⠀⠀⠈⠂⠄⠀⠀⠠⠔⠊⠀⠀⠀⠈⠲⠤⠌⠁⠤⠔⠁⠀⠀⠀⠈⠒⠤⠤⠤⠒⠉
⠀⠀⢀⣀⠤⢤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢄⣀
⢀⠔⠁⠀⠀⠀⠀⠙⢆⠀⠀⣠⠊⠁⠀⠀⠀⠉⢢⡀⠀⠀⡴⠊⠀⠀⠀⠈⠑⢄⠀⠀⢀⠔⠉⠀⠀⠀⠈⠳⡄
⡎⠀⠀⠰⠀⠒⠀⠀⡈⡆⢰⠃⢀⡄⠀⠀⠶⠀⠀⢳⠀⡘⠀⠀⠐⠀⠀⢀⡀⠈⡆⠀⡎⠀⣀⠀⠀⠀⠀⠀⢸
⡇⢆⠀⠀⠀⠀⠀⢀⢇⠇⢸⠀⣤⠤⢤⣤⣒⡶⠀⡼⠀⢃⠀⢀⡤⡖⠒⠓⠣⠀⡇⠀⡇⠀⠛⣠⠤⡀⠛⠀⣸
⠘⢮⡒⠤⠀⠠⢔⡪⠊⠀⠀⠣⡈⠛⠥⠤⠚⢁⡴⠁⠀⠈⠢⡀⠈⠁⠀⠀⢀⠔⠁⠀⠘⢄⡀⠀⠀⠀⣀⠔⠁
⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠈⠑⠒⠒⠉⠁⠀⠀⠀⠀⠀⠈⠑⠒⠒⠈⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⢠⠔⠊⠋⠑⠒⢤⡀⠀⠀⠀⢀⠔⠚⠉⠑⠢⣄⠀⠀⠀⣠⠔⠒⠉⠙⠲⢄⠀⠀⠀⠀⣠⠔⠚⠉⠙⠒⠦⡀
⡰⠁⢀⡀⠀⢀⠀⠀⠙⡄⠀⡰⠁⠀⠀⡀⠀⠀⠈⢆⠀⢰⠁⢀⠀⠀⠀⠀⠀⢳⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠘
⡇⠀⠈⠁⠀⠉⠃⠀⠀⡇⠀⡇⠀⠊⠂⠀⠈⠑⠀⢸⠀⢇⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⡇⠀⠀⣀⣀⣁⡠⠤
⠱⡀⠈⠉⠉⠉⠛⠁⡠⠃⠀⢣⠀⠀⠀⠿⠀⠀⢀⠏⠀⠘⣄⠀⢀⠤⠠⠄⢀⡜⠀⠀⢣⡀⠘⣍⠇⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⡗⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣖⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⣿⣾⡉⣻⣿⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⣞⣱⣾⢣⣀⡤⢀⣴⢶⠟⠗⣠⣤⠞⠛⠉⠙⠋⠙⣩⡬⠟⠛⠛⠿⣷⠒⠦⢤⣀⠀⠀⠀⠘⣧⣠⠷⣇⣼⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣞⣳⠾⠛⣳⡾⠋⠁⠂⠈⣴⠋⠀⠀⠀⢂⢀⣴⠟⠉⠀⠀⡠⠀⠀⣠⠾⠛⠛⠛⠛⠂⠄⣀⡟⠻⡖⡞⢺⡆⡞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡞⢉⢉⠭⠋⠄⡈⠀⣀⠊⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⢀⠄⠔⡰⡾⠁⠀⠀⠀⡠⢂⣤⠶⠾⣷⣿⠉⣻⣸⡋⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠒⢲⠂⢉⠄⣈⣴⠞⠻⢣⠐⢀⣀⣤⣴⡌⠀⠢⠀⠀⠄⢂⠜⠋⠀⠀⠠⠊⠌⣴⠟⠁⡠⢂⠄⣈⣙⣧⣨⢯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡂⠐⣠⡾⠋⠀⡠⠡⢀⡿⠋⠉⠀⠀⠻⠀⠐⣠⡴⠟⢻⡀⠀⠐⡠⢀⣡⠊⠁⠀⠈⠀⡵⠊⢁⣐⡼⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡵⠒⢾⠈⢋⠀⠀⠐⠀⢠⡵⠁⠀⠀⠀⠀⠀⠀⢝⠁⠀⠀⠈⠪⢀⢁⣴⠟⢂⠄⠀⠤⠈⡜⢀⡾⠋⠸⠋⠁
⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⡄⠀⠸⣂⢀⠢⠄⠀⠐⡘⠀⠀⠀⠀⠀⠀⠀⢢⠂⠀⠀⠀⠀⠐⡠⡙⠁⠀⠈⢎⠀⠄⠀⡇⢸⠇⣠⣾⣿⣦⡄⠀⢀⣀
⠀⠀⣀⡴⣮⣯⢿⣽⠽⣭⡯⣶⢋⠈⠳⣕⠐⠀⠊⠀⠀⠀⠀⠀⠄⠀⡔⠅⠀⠀⠀⠀⠀⠀⠍⠀⠀⠀⠀⠀⠒⡲⠚⣦⣯⢰⡿⣿⣿⠃⠀⣆⣀⠿⣤⣏⡷⠆⢀
⢠⣾⢛⣷⣟⣳⣿⣙⣶⣋⣗⣿⣻⣷⣦⡎⠙⠳⣄⠠⠀⠂⠄⠌⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢤⢆⡼⣽⠃⠀⠀⠀⠀⠀⠘⢳⡉⣳⣅⣀⣗⠶⢯
⣿⣼⠻⢶⡟⢧⡼⠻⣶⠟⣧⣗⠻⠞⠋⠙⠶⣤⡔⠛⠲⢤⣁⣈⡐⢀⠂⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⣈⡴⢊⡴⠃⠀⠈⠐⠀⠀⠀⠀⠈⠉⠉⡎⠁⠈⠄⠈
⠀⠉⠈⠉⠉⠋⠉⠙⠉⠈⠉⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣤⣏⠀⠈⠳⣄⣀⡀⠀⣀⣈⣄⣁⣀⣀⣀⡥⢾⣿⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠉⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠿⠷⣬⣽⣿⣭⣤⣤⣄⣀⣬⣿⣞⠯⣭⣤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢻⣶⢿⣷⣟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣯⣿⢿⣾⣿⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢛⣿⡏⣷⣾⢻⣷⣟⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⣾⣯⣿⣽⢿⣧⣯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⡿⣷⣟⣽⣿⡻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣿⣿⢿⡿⣯⣼⠿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢶⣿⣛⣟⣾⣿⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⢿⣭⡿⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢹⣿⣿⣿⣿⣿⠿⣿⠿⢻⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⡏⠚⠀⠀⠀⠙⣿⣿⣿⣿⣆⠀⠀⡻⠿⠿⠿⣿⣿⣿⣿⣦⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⢿⣿⣿⢿⣿⡟⠁⠀⠀⠀⠀⠈⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠆⠁⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⡘⠟⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⠄⡄⠀⢀⠄⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠚⠂⠑⠛⠘⠀⠃⠀⠃⠂⠃⠋⠞⠁⠐⠃⠀⠋⠘⠁⠐⠑⠃⠀⠂⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢣⠄⢀⠀⢀⠠⠋⠀⠀⠀⠀⢀⡡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣄⣀⡔⠁⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠤⠄⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠈⡤⠀⠀⠀⠀⠀⡹⠄⠀⠀⣀⠀⡀⠙⠀⠀⣀⠀⢠⠀⠘⠢⡀
⠀⠀⠠⠀⢰⣿⣿⠇⠀⠀⠉⠉⢳⣦⣀⡀⢠⣤⣀⠲⠦⢄⠀⢀⠎⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠈⡇⠀⠀⠀⢈⠂⡀
⠀⠀⠀⠠⠤⣤⣄⣀⠀⠀⣠⣴⣾⢏⡟⠉⢙⠟⢿⣦⡀⠠⠛⡏⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠰⡀⠀⠀⠀⢱⠬⢦
⠀⠀⠀⠀⠀⠈⠓⠲⠾⠷⠿⠿⢿⡯⣀⣀⣀⣀⣿⣿⣷⡄⠀⢣⠀⠀⢀⡀⠀⢀⠴⠃⠀⡀⠀⠀⠀⠈⠁⠀⡀⠀⢀⠔⠉⠓⠂⢠⠃⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣄⠀⠑⢄⠀⠙⠚⠁⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠈⡉⠀⠀⠀⠀⣀⣤⠖⢁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⠀⣈⢻⣿⣷⣤⣈⠉⠒⢦⠠⠤⣤⠤⢤⡤⠥⠤⠖⠒⠋⠑⠒⠒⠒⠚⠀⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⡏⠀⠀⠰⣿⢿⣿⣿⡿⢿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⢠⣀⣠⣤⣴⣶⣤⣤⢤⣬⡿⠶⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢷⠀⠀⠀⠠⠁⠈⠉⠈⠀⠀⠀⠀⠛⠛⠛⠙⠛⠋⠉⠉⠉⠹⣿⣿⣿⣿⣇⠀⡇⠀⠀⡻⢻⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠁⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣽⣿⠀⠈⠳⣌⣠⣀⢠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢽⣿⣿⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⣿⣿⣻⣯⣿⠄⠀⠀⣸⡿⠿⠛⠑⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽⣯⡿⠟⠻⠦⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠠⣼⡧⣀⣰⣌⣦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣼⢢⣖⢰⡴⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⢀⡤⠤⠒⠒⠠⢤⡀⠀⠀⠠⣶⠀⠀⠀⢀⡤⠔⠒⠒⠤⢤⡀⠀⠀⣶⣶⠀⠀⠀⢀⡤⠔⠒⠒⠢⢤⡀
⠀⠀⢀⡔⠉⢀⣀⠀⠀⣀⡀⠈⠢⡀⠀⠀⠀⢄⡔⠉⡤⢤⠀⠀⡤⢤⠉⢪⡀⠈⠁⠀⢄⠔⠁⣀⡀⠀⠀⢀⡀⠉⢢⡀
⠀⢠⠏⠀⠀⣿⣷⠀⠀⣾⣿⠀⠀⠹⡄⠀⢠⠏⠀⠘⠁⠘⠀⠀⠃⠈⠃⠀⠹⡄⠀⢠⠏⠀⠀⣧⡿⠀⠀⣧⡽⠀⠀⠹⡄
⠀⣾⠀⠀⠀⠈⡁⠀⠀⢈⠁⠀⠀⠀⣿⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⡄⠀⠀⠀⡇⠀⣿⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⣷
⠀⠘⣆⠀⠀⠚⠹⠞⠳⠞⠓⠀⠀⢠⠇⠀⠹⣄⠀⠀⠈⠳⠤⠤⠞⠁⠀⠀⣰⠏⠀⠹⡄⠀⠀⠈⠙⠉⠉⠋⠁⠀⠀⣰⠃
⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⢀⣠⠔⠁⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⢀⣠⠔⠁⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⢀⣠⠔⠁
⠀⠀⢀⣤⡀⠉⠙⠛⠛⠛⠉⠀⠀⣴⡄⠀⣀⡀⠀⠀⠉⠛⠛⠋⠉⠉⠀⠀⢀⡀⠀⠀⢀⣀⠀⠉⠛⠛⠛⠋⠉⠀⣀
⠀⠀⠈⠛⠀⣀⡠⠤⠤⢄⣀⠀⠀⠈⠀⠘⢿⠿⠀⠀⣀⡠⠤⠤⢄⣀⠀⠀⠺⠿⠂⠀⠘⠋⠀⣀⡠⠤⠤⢄⣀⠀⠉
⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠈⠑⢦⠀⠀⠀⠀⠀⡤⠊⠁⠀⠀⠀⠀⠈⠑⢦⠀⠀⠀⠀⢀⡴⠊⢁⡀⠀⠀⢀⡈⠑⢤
⠀⢀⡞⠀⠀⢦⣴⠂⠐⢦⡴⠂⠀⢳⡁⠀⢀⡞⠀⠀⠤⠤⠄⠠⠤⠤⠀⠀⢳⡀⠀⢈⡞⠀⢰⣫⣿⠀⠀⣿⣹⡆⠀⢳⡀
⠀⣼⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⣷⠀⢸⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡇⠀⣾⠀⠀⠈⠉⠉⣀⣀⠉⠉⠁⠀⠀⣧
⠀⠸⡄⠀⠀⠙⠶⠤⠤⠶⠋⠀⠀⢀⡏⠀⢸⡄⠀⠀⠀⡴⠋⠙⢆⠀⠀⠀⢠⡇⠀⠹⡀⠀⠀⠀⠸⣅⣹⠇⠀⠀⠀⢠⠏
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⢀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⢀⡀⠉⠛⠒⠒⠒⠒⠚⠉⠀⠀⠀⠀⣠⡀⠀⠉⠛⠒⠒⠒⠒⠚⠉⠀⠀⠀⠿⠇⠀⠀⠉⠓⠒⠒⠒⠒⠛⢉⣀
⠀⠀⠘⠃⠀⢀⣀⠤⠤⣀⡀⠀⠀⠿⠂⠀⠙⠃⠀⠀⢀⣀⡠⢤⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⠤⢤⣀⡀⠙⠛
⠀⠀⡠⣠⠖⠉⠀⠀⠀⠀⠉⠳⢄⢄⠀⠀⠀⠠⣢⠖⠉⠀⠀⠀⠀⠉⠳⣄⢄⠘⠋⠀⡠⡢⠞⠉⠀⠀⠀⠀⠉⠲⣔⢄
⠀⢀⡜⠁⠀⣄⣀⠀⠀⣀⣠⠀⠈⢳⡀⠀⢀⡞⠁⠐⢦⣀⠀⠀⣀⡴⠂⠈⢳⡀⠀⢀⡞⠁⠀⠙⣶⠄⢠⣖⠃⠀⠈⢣⡀
⠀⣸⠁⠀⠀⠘⠋⠀⠀⠈⠋⠀⠀⠀⣷⠀⢸⠁⠀⠀⠀⠛⠀⠀⠛⠀⠀⠀⠀⡇⠀⣾⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠈⣧
⠀⢹⡀⠀⠀⠐⢦⣀⣀⣠⠆⠀⠀⢀⡟⠀⢸⡀⠀⠀⠴⠻⡴⢦⠟⠦⠀⠀⢀⡇⠀⢹⡀⠀⠀⠐⠒⠒⠒⠒⠂⠀⠀⢀⡏
⠀⠀⠱⣄⠀⠀⠀⠈⠁⠀⠀⠀⣠⠎⢀⣤⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢀⣄⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠙⠲⠶⠦⠤⠶⠖⠋⠀⠀⠈⠋⠀⠀⠀⠙⠲⠶⠦⠤⠶⠖⠋⠀⠀⠈⠁⠀⠀⠀⠙⠲⠶⠤⠤⠶⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣒⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣾⢶⢧⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣙⡴⡸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⢿⡣⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⠯⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣽⣞⣷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⢔⢒⣒⢒⣶⣄⣦⢤⣄⠠⣷⣫⠿⢞⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠙⢮⢳⠃⠀⣀⠀⢹⣿⣿⡏⠀⢈⣿⣯⣿⢿⣄⠀⠀⠀⠀⣀⣤⡶⣶⡲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⣀⠀⠀⣠⣶⡼⣷⣿⣧⡤⣀⢼⣿⣦⣀⣼⣦⡿⢥⣀⣨⣡⣾⠟⠙⣿⣮⣵⡟⠒⣶⣾⢻⣻⣾⣛⣿⣴⡿⣦
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⢧⣽⣿⡝⠉⡱⡹⣅⠀⠞⠻⡿⣿⢾⡿⡿⣻⣿⣿⣯⣾⣏⣇⠀⠉⠉⠀⠹⣛⢄⠀⠙⣷⣻⠫⢽⡼⣁⣒⡭⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢀⣴⡿⣟⣿⠟⠀⡹⣯⣅⣒⢞⡵⣿⣭⣊⢾⣿⣿⡿⣷⡟⣿⣾⣟⣿⡋⠁⢀⣻⣿⣧⠴⠛⠛⠛⠏⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣿⣽⣿⣛⣲⡿⣗⣿⣿⣿⣿⣷⡝⣻⣿⢟⡻⢶⣣⣽⣾⣿⣭⣛⣿⣦⣤⡞⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⣿⣼⡫⣫⣿⡷⣮⡿⣲⣿⣽⣿⡟⢯⢛⣿⣿⣿⣧⣟⠋⢿⡏⣩⣿⡿⣯⣽⡟⣓⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⠉⠻⡻⣇⣾⡏⢹⠇⡿⡽⠋⢁⠀⠙⠏⣆⡎⢀⠿⠁⠈⢜⠐⣄⠁⠀⣹⢿⣿⣟⣾⣿⣿⣿⣵⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣻⣄⣴⣹⣷⣤⡞⣰⡀⠀⡿⡇⢀⣈⠻⣶⣌⣇⣬⣷⣾⣿⣿⡻⠋⠲⣿⣿⣽⣷⣛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢾⡿⣯⣿⢻⣸⣿⠀⣹⣿⣿⣧⣿⣿⣁⣠⣿⣿⢫⣿⣶⣟⡻⠋⠀⠀⠀⠈⢿⣽⢶⣭⣟⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⡾⣟⢟⣿⣻⠿⣿⣷⣾⣿⣩⣟⣛⢻⣿⣻⣻⣭⣦⣿⣿⠿⠙⠃⠁⠀⠀⠀⠀⠀⠀⠀⢹⣾⣷⡛⢾⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣻⣯⠿⡿⠂⠀⠈⠙⠛⠿⠽⠿⠿⠻⠿⠿⠿⠿⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣶⡿⣏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣾⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡶⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⣦⡔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠄⠀⠀⠰⡶⠆⠀⠀⣠⡀⡀⠀⠘⠁⢀⠠⠿⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⢡⣄⠀⠀⠀⣴⣾⣿⠀⠀⠁⢀⡀⢀⡤⠂⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢊⣵⠞⠁⣰⣿⣇⠀⠀⢸⣿⠏⠈⠀⢀⣴⣿⠃⢸⡅⠀⠆⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⢀⡄⣨⠏⣰⣿⡯⠀⡸⢿⠟⠩⠀⠀⠀⠈⠀⢀⣶⣄⠘⡷⠒⠉⠂⠀⠀⢀⣴⡞⠁
⠀⠀⠀⠀⠀⠐⢷⠀⡉⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡮⠛⠁⠀⠀⠀⠂⢀⣠⡄⠈⠁
⠀⠀⣠⡽⠊⠁⢺⣾⣧⣤⢀⣴⡤⢠⣤⣤⡄⣰⣶⣾⠚⠛⠉⢐⣠⣀⢄⠑⠀⠀⠦⠁
⠘⠟⡋⠀⣠⣾⠾⠛⠛⠁⠛⠛⠂⠛⠉⠉⠀⠀⠀⠀⠀⠤⠄⠚⠛⠉⠂⠀⠠⠉⣻
⠛⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⢃⡀⠇⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠅⠀⠊⡂⢧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠀⠄⠁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡀⣡⣂⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢑⡲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣬⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⠤⠤⢀⡀⠀⢀⡤⠒⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨
⠀⠀⢀⠤⠊⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠈⢀⢀
⠀⠀⠈⢆⠀⠀⡠⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠂⠀⠀⠈⠑⠒⠄
⠀⠀⠀⠈⠉⠡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠄⠂⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠐⡅⠀⠀⠈⠑⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠤⢐⠈⠀⠀⠆⠀⠀⠀⣀⠀⠀⠀⠀⠈⠁⡀⠀⠁
⠀⠀⡸⠀⠀⠀⠸⡀⠀⠀⠉⠒⠒⠒⠓⠢⢤⡴⢒⣉⠉⠁⢀⡴⠁⠀⠀⠀⠀⠀⠒⠉⠀⠉⠁
⠀⠀⡇⠀⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠃⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠉⠉⠉⠁⠀⠀⠂⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⣦⡀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣤⡀⠈⠃⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠛⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠘⠃⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠠⠠⡀
⠀⠀⠀⠁⢄⠀⠙⠀⡀⢂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠔⠁⢀⠂⡀⠜⠁⢀⠄⠁
⠊⠀⠁⠂⠤⢑⠠⡀⠈⠂⢕⢄⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠠⠂⠀⠀⠔⠁⢀⢔⠅⠊⠀⡠⢐⠡⠄⠂⠁⠈
⠀⠀⢀⠀⠀⡀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠑⠄⠀⢠⡀⠀⣀⣀⠀⠠⠐⠀⡠⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡀⠠⢐⠀⠁
⠣⠀⠀⣀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠂⠀⠠⢀⠀⠀⠀⠀⠀⢀⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⢄⠀⠀⠀⠀⠀⢀⠠⠀⠀⠒
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣬⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣬⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡦⣦⡶⢀⡀⡠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡞⠏⠍⠉⠐⣾⣶⣍⢩⣶⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⣆⢰⠶⢦⡸⣷⣿⣿⣹⣷⢐⣿⡿⢻⡧⢸⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣮⡻⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠹⠾⠄⠀⠁⠤⣌⠉⣍⢵⣟⠧⡃⠀⣶⠛⣿⢙⢿⣷⣄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⢋⣶⣦⣤⣬⣽
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠁⠓⢦⣁⡈⠀⠵⣟⢢⠉⠾⡍⠙⠠⢷⣿⡿⣦⡀⠀⣠⣾⣷⡘⣿⣿⣿⣿⣿⣿⣿⢱⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⢁⣠⣶⣤⣿⣿⣿⣿⣿⣷⡎⢿⣿⣿⡷⠹⢾⣿⣿⣿⣿⣿⠸⣷⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣰⣿⣿⣾⣙⣟⣋⣭⣿⣿⣿⡧⠸⢯⣶⣴⣷⣶⣶⣦⣤⣤⣤⣄⠻⣿⣿⣮⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣷⡌⠙⠻⢿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣷⣚⣸⣯⡵⠞⣿⣿⣿⣿⣿⡟⣫⣾⢻⣿⣿⣇⢢⡙⢿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⢡⣿⣿⣶⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠿⢿⣿⢯⡉⢷⣶⣾⣿⣿⣿⣿⣧⣴⡿⣃⣾⣿⡟⡽⠳⡌⠌⠻⣿⣿⠏⢠⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⢧⣤⣦⣿⣄⣽⢿⣤⣮⣿⣿⠏⠉⠁⠈⣇⣼⣿⡿⠀⣰⣾⠜⣮⡠⠙⣯⣀⠻⢿⣿⣿⡏⣼⣿⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠙⣶⡈⡜⣿⣿⣩⣷⣿⣏⣼⣿⠇⠀⠀⠀⠀⢹⣷⣻⢡⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣴⣌⡙⠳⠿⣿⣏⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⡿⠿⣿⣿⣿⣽⡿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠓⢯⡛⠻⢿⣿⣿⣿⠿⠛⠻⢿⣿⢿⣿⣿⣧⣀⠂⠈⠛⠿⣿
⠀⠀⠀⠀⠀⠀⠀⣄⢙⣿⣟⣛⣻⢿⣿⣿⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄⠨⠿⢤⠇⢀⡀⡀⢛⣿⣿⣿⣿⣿⡻⢶⢦⣦⡆
⠀⠀⠀⠀⠀⠀⠀⡟⠛⣿⣀⣼⣏⣴⣧⣻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠩⢵⣒⣒⣀⡈⢼⡣⣶⣿⣿⣿⣿⢿⡿⠾⣼⠞⢹
⠀⠀⠀⠀⠀⠀⠀⣷⣰⡟⠛⠻⠿⣿⣟⢷⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣒⣛⣆⡱⢦⡶⠈⠠⢉⣿⣿⣿⡿⠿⣾⣷⣂⣴⣻⢿
⠀⠀⠀⠀⠀⠀⠀⢹⣏⣽⠢⢤⣤⣭⡿⢷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣋⣉⡭⠵⠏⡙⠡⠐⣶⣿⣿⣯⣄⠀⠀⠀⠀⠅⠈⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢿⣻⡿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣻⠿⢟⣷⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⠟⣠⣴⡿⠋⠀⢀⣀⣤⢤⣤⣴⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⣸⣿⣦⡼⢿⣿⣿⣾⣷⡿⠾⣥⣿⣈⠻⣏⢹⢻⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⣾⣿⣿⣿⣶⣺⣶⣶⣻⣿⣷⣶⣿⣿⣿⣿⣏⣉⣿⠿⣿⣿⣙⣿⣷⣄⡀
⠀⠀⣀⣀⣤⣀⢠⡀⠀⠀⠀⠀⡴⢾⠛⣿⣿⣿⣿⡿⠛⢻⡿⠿⣿⣿⡿⠟⢿⣿⣟⣫⣿⣷⣦⣹⣿⣦⣽⡻⣿⣿⣦⢀⢤⣴⣲⣶⠶⠚⠋
⢚⠛⠻⢿⣁⣿⣾⠇⠀⠀⠀⢀⣾⣿⣼⣿⡴⢟⣻⣿⣤⣾⣿⡟⢛⣻⣧⣀⣾⡧⣽⣭⣻⣁⡜⠛⣿⣿⣿⣿⣿⠛⣿⣶⡚⠋⠉
⠀⠐⠠⢾⣶⣽⣇⠀⡄⠀⠀⣿⣿⣿⡿⠛⣿⣿⣾⣿⣿⣿⣍⢳⣿⡿⣿⣿⣯⣹⣿⣿⣿⣿⣶⠶⣿⣿⣿⣿⠛⣶⣿⡻⣷
⠀⠀⠀⠀⠉⠙⠃⠀⠀⠐⠱⣿⣿⣿⣷⣦⣼⠛⢿⣟⣿⣿⣿⣿⢿⣾⣛⣻⣿⣿⠛⣿⠿⣿⣿⣿⣧⠤⣽⡏⣹⡟⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣹⣶⣮⠀⠨⣽⣿⣇⡀⣹⣟⣿⣿⣿⣶⠇⣀⣾⡃⢘⣴⡾⣻⢻⣿⣾⡛⣭⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⣿⣿⣷⣿⢏⡷⢶⡿⣿⣿⡿⣿⣿⣯⣿⠏⢼⣿⣾⣿⣿⣿⣿⣿⣶⣧⣴⣿⡿⢁⣸⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡆⢀⣀⡘⢿⣿⣿⣾⣿⡯⣠⣾⡟⢡⣿⢻⣿⢏⣴⢰⣿⣿⠿⠹⠯⣼⣿⣿⣿⠟⢻⣾⣿⣿⣿⣾⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠘⢿⣿⡄⠉⠛⢿⣿⣿⣿⣿⣦⣾⣿⣾⣾⣿⣿⣼⣿⣷⡴⣶⣷⣶⣿⡿⠆⠀⠀⠛⠿⢿⣿⣿⣿⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣶⣻⣿⣂⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠛⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⣿⣿⣿⣻⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⠀⠀⠒⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠁⠀⠉⠀⠒⠒⠒⠒⠒⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⠖⠒⠒⢲⣍⠤⠦⠤⠄⠀⠴⣆⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⡇⢐⣰⠀⢀⠕⠀⡀⠄⠀⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡠⠊⡇
⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⣀⣈⣑⣐⣈⡡⠂⠁⢀⠤⠂⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡡⠋⢀⠎
⠀⠀⠀⠀⡏⡉⠭⠭⠭⠄⠀⠒⠒⠒⠒⡆⣀⠔⣊⠥⠤⠄⠀⠉⠁⠒⠢⡉⠑⠄⠀⠋⢀⡐⠒⢒⠞⠁⠀⡴⡇
⠀⠀⠀⠀⢧⢃⠀⠀⠀⣎⣑⠀⢀⡠⢐⡉⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣠⠊⠙⠁
⠀⠀⠀⠀⢸⠸⠤⠤⠤⣤⣴⠾⠗⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠃⢀⠔⠁
⠀⠀⠀⠀⠘⣆⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⠤⠤⠤⠤⠤⠤⡀⣠⢎⠌⠀⡠⠋
⠀⠀⢀⡠⠒⠉⢸⠀⠀⠀⠈⠉⠩⠀⠈⠩⠭⠥⠄⠒⠒⠀⠀⠐⠒⠒⣒⣒⠒⠚⠁⡘⢀⠞
⢠⠞⠥⠤⠀⠀⠀⠛⠒⠒⠒⠒⠒⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡟⠦⠔⡱⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠊
⠸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⢤⠤⠞⠁
⠀⠀⠈⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⡇⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡼
⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⠔⠉⠑⢎⠉⠉⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⢻⠀⢠⣄⠈⡇⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠸⡀⠿⠟⢀⡇⠀⠀⠀⠙⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠈⠒⠒⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠋⠉⠉⠀⠈⠉⠉⠙⣳⢦⣄⡀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⡠⠚⢽⠦⣤⣄⣀⣀⣤⣤⣤⣖⣫⠛⠁⠀⠙⠳⣄⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠙⢄⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⡜⠁⠀⣼⡞⠉⠉⠙⣶⡏⠉⠁⠀⢻⣧⠀⠀⢀⣠⡾⠳⣄⠀⠀⠀⢷⠀⠀⣠⠖⠲⠶⠿⠷⠛⠋⠁
⠀⠀⠀⠀⠀⣼⠀⠀⢰⡿⠀⠀⠀⠀⢿⡇⠀⠀⠀⢈⡟⠒⣒⢹⠋⠀⠀⠘⣧⠖⠛⢺⡀⠀⣿
⠀⠀⠀⠀⢰⠛⠻⢶⡋⠳⢤⣤⣤⣤⣞⣙⠒⣲⠿⠛⠋⠉⠈⢳⢧⠀⠀⡰⠋⠀⠀⡼⠁⠀⡿
⠀⠀⠀⠀⣸⠀⠀⠀⢹⡼⠉⠉⠉⠉⠉⠈⢳⡇⠀⠀⠀⠀⠀⠀⢫⡷⠊⠀⠀⣠⣞⣉⠙⣶⠃
⠀⠀⢀⠤⡏⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⢀⣀⡤⠞⠉⠀⣀⡴⠚⢭⣀⣸⠞⠁
⠀⣀⣿⣀⠈⠓⠒⠤⠿⢧⣀⣀⣀⣠⡤⠤⠤⠟⠒⠋⠉⠀⣀⣠⠴⢾⠁⠀⠀⠀⠉⠳⣄
⠈⠓⠤⣬⣝⣶⡦⠤⣤⣀⣀⣀⣀⣀⣀⣀⣤⡤⢴⠖⠚⠛⡍⠀⠀⠈⣧⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⣸⣅⡀⣀⣅⣀⣀⣀⣬⢤⣤⣤⠞⠓⠒⠛⠙⣧⡀⠀⢀⠤⢊⣴⠟
⠀⠀⠀⡼⠃⡀⠀⠀⠀⢠⡟⠈⠉⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣬⣤⡶⠛⠁
⠀⠀⠀⠙⠶⣬⣁⣒⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠐⠌⠀⠉⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡪⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣣⡀⣴⠞⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠠⢰⠀⠠⢀⠀⠀⡀⠀⠀⠀⠠⡋⠀⠀⠀⠀⠀⠠⠄⣀⣐⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠠⢤⠶⠄⢘⠀⠀⠠⡀⠀⠀⠠⠂⡠⣤⡀⠉⠙⠛⠉⢠⣆⡀⡀⠀⣀⣄⠠⠤
⠀⠀⠀⠀⠀⠀⣀⡄⠀⣰⠀⠈⠀⠀⠀⠄⢨⠄⠀⠀⠄⢄⡀⠀⠚⠁⣀⡽⢴⡤⢶⡾⣫⠀⠛⠀⠀⠀⣽⣿⣿⣖
⠀⠀⠀⠀⠀⠀⠙⢀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢰⣠⠴⣾⣏⣴⠀⣿⠐⠁⠣⡐⠈⠀⣀⣶⡯⠛⢿⠟
⠀⠀⠀⠀⠀⣀⠞⢽⠁⢀⡇⡄⠀⠀⠀⡇⠀⠀⢘⡠⣴⡾⢉⣁⣮⠄⠀⠈⢳⠉⠘⠖⠠⡂⠌⢽⡟⠙⠁⡀⠙⠂⣄
⠀⠀⠀⡠⣞⣛⠀⡈⠳⣼⣃⠁⠀⠀⢀⡁⣀⡒⠉⠀⢹⡇⣾⠋⠀⠀⠀⠀⢸⡄⣀⣊⣥⡴⢂⠀⣹⣴⠀⠀⠀⢂⡀⡀
⠀⠀⠘⠚⠬⠵⠟⠴⠖⠁⡈⠲⢬⣕⡢⣁⠀⠀⠀⠛⢠⣹⠇⠀⠀⠀⠀⠐⣹⣇⡉⡤⠀⠀⠀⠖⠋⠈⢧⡄⢠⠐⠖⠂⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠉⠙⠛⠛⠂⠙⠀⠀⢠⢆⡀⠔⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⣙⡔⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣃⠠⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠡⠀⠞⢢⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣻⠀⠊⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠁⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⡓⠒⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠕⣷⣂⠂⢀⠄⡄⠀⠀⠀⠀⠰⠁⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⣦⢘⢕⡷⣂⠀⠀⢳⡀⠀⠀⠀⡰
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢱⡆⠸⣝⢯⢠⠀⠀⠙⠲⠖⠚⠁⠀⢀⣀⣠⣄⢶⡦⢀
⠀⠀⠀⣄⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠰⣿⡶⠐⢘⠐⠚⡧⠀⠀⠀⠀⠀⢀⡰⢎⠡⡼⢷⢼⡟⣯⡰⢆
⠀⠀⠀⠰⡀⠀⠀⣠⠇⠀⠀⠀⣀⣴⡶⢖⡽⢿⣿⣶⡿⣰⣏⣹⣶⡶⣄⢔⣏⣭⣜⠂⢰⠩⣖⡾⡛⡙⠻
⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⣾⣯⣽⣣⣝⠂⠿⡤⣡⣾⡏⢀⢔⢫⠛⣼⣷⠇⠛⠁⠀⢰⢴⠊⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢾⣷⡴⡿⠊⡩⣀⣷⠄⠉⠛⠛⠾⣆⡀⢀⡜⡈⢜⣳⡄⠀⠁
⠀⠐⠀⠀⠀⠀⢀⢾⣟⡬⠫⣏⠸⡐⣲⢟⣾⠁⠀⠀⢤⠈⢳⠐⠙⠋⣞⠙⣦⡿⠡⣄
⠀⠀⠀⠀⠀⠀⣸⣯⣫⠖⣉⠉⢳⢆⡤⠾⠯⢵⣦⢄⣀⡠⠎⢀⡴⠛⢿⣷⣻⣷⣷⠽⠭⣓⣤
⠀⠀⠀⠀⠀⡜⣥⣹⠃⢀⣸⠇⣰⠋⠀⠀⣀⠀⠈⢳⡠⣠⣴⠟⡠⡀⠀⡏⣩⠓⣻⣘⢳⣜⡵⣾⠤
⠀⠀⠀⣠⣤⢟⣽⢉⣻⠿⣥⠀⣿⣄⠀⡉⠉⠀⠀⠀⣧⣬⡿⣄⠩⡧⢸⣧⣯⣻⣳⣶⣴⣤⢈⠱⠋⠅
⠀⢀⣚⣝⣇⣫⠋⣞⠐⠠⣷⠚⠉⠋⠓⠻⠦⠤⠄⣠⠋⠀⠈⢆⡡⡤⢟⣿⢸⡏⠉⠉⠘⠂⠻⣿⡈⠤⠱
⠀⣾⡽⢻⣾⣹⢻⢸⣴⣸⡇⢀⡞⠋⠉⠙⢲⣤⣼⣧⠀⢆⠁⠆⡇⣠⣏⣿⠛⠁⠀⠀⠀⠀⠀⠙⠿⣦
⠈⠉⣤⡬⠻⢉⡻⡎⠦⣿⣇⠘⠆⠉⠂⠀⢸⣿⣤⡍⣧⣀⣀⣼⣻⢟⢻⠏⠀⣠⠴⠶⠤⡀⠀⠀⠀⠷⣦
⠄⣀⣾⠂⠀⠰⣟⣽⢷⡙⠻⠦⣄⣀⣀⡤⣿⡛⢛⠇⠿⢟⣫⣾⡿⠎⠁⠀⡾⠃⠀⠀⠀⠈⠀⠀⠀⠀⠋
⢠⣼⡆⠀⠀⠀⢈⢱⣛⠾⣻⢷⠶⣾⣤⡴⣾⢯⣿⣻⣼⠧⠿⠋⠀⠀⠀⠀⢿
⠸⡝⠀⠀⠀⠀⠆⠄⠀⠀⠉⠉⠛⣋⣻⣷⠟⡌⣹⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣌⠋⣷⣫⢹⠟
⠀⠀⠀⠀⠀⠀⠀⣀⢤⡞⠾⠛⠉⡁⣼⠷⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿