Primary school Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠆⠀⢴⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢋⡠⠤⠶⠀⢦⡀⢄⡀⠀⠀⠙⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣡⢤⡠⠄⠀⠀⠈⠑⠪⡳⡄⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢻⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠆⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⢀⣤⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢄⣀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠘⢣⠂⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⢉⠽⠛⠛⠲⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡖⢉⠵⢦⣄⡀⠀⠀⠀⠀⠀⠀⣀⠴⣪⡣⢠⠃⠀⠀⠀⠀⢳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠘⠢⠇⡀⠐⠄⣉⣙⣛⣶⣚⡟⢩⠒⡷⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠌⠀⠀⠀⠀⣰⠇⠀⠚⠴⠃⢸⠹⡄⠀⡇⠀⢀⣀⣀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡶⠤⠞⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡼⠀⢱⠘⡇⢯⠭⠭⠵⠲⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⢶⠀⠀⠀⠀⠀⠀⠙⡶⠤⣤⡤⠾⡅⠀⡇⡆⡇⡇⠀⠀⠀⠀⡏⡏⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⢾⠀⠀⠀⠀⠀⠀⠀⢻⠀⣿⠀⠀⢹⡀⡇⢡⠇⢣⠀⠀⠀⣰⠀⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠼⡇⠀⠀⠀⠀⠀⠀⠘⡄⢹⠀⠀⠈⠇⡇⢸⢸⠀⠑⠒⠚⠁⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⣄⠀⠀⠀⠀⠀⠀⠱⡜⡄⠀⠀⢰⠗⢋⣗⣧⡠⠔⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠓⠤⠤⣄⣉⠀⠀⠀⠀⠀⠈⠻⣄⣠⠛⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠈⠙⠓⠦⢤⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⣀⡤⠴⠦⣄⠀⠀⠉⠉⠉⠉⠀⠀⢧⠀⠀⣠⠖⢾⡁⡈⠑⣄
⢀⣀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠘⡖⠋⠀⠀⠀⢧⠒⡍⠘⣆
⡇⠈⠙⠦⣀⠀⠀⢀⡜⠁⠀⠓⠂⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⢸⠉⠀⠀⠸
⠹⣄⠀⠀⠌⠉⡑⠚⣆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⡗⠀⣀⡀⢸⢄⠀⠀⠂
⠀⠈⢦⡈⠀⠀⠀⠀⠈⢓⡦⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⡠⠊⠀⠙⠎⠱⣕⣠⠛
⠀⠀⠀⠙⢦⡀⠀⠀⠀⣅⣡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠉⠀⠀⠀⠀⠀⠀⠈⠣⣠
⠀⠀⠀⠀⠀⠙⠪⢃⣭⡽⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠛⠲⠦⢤⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠲⠦⠤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⠞⠁⠀⢀⠀⠀⠙⢦⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣃⣀⣀⣀⣀⣀⣀⣠⠞⠁⠀⣀⣠⣀⡀⠀⠙⢦⣀⣀⣀⣀⣀⣀⣀⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠉⠉⠉⠉⠉⠁⠀⠀⡼⠉⠀⠈⠹⡆⠀⠀⠉⠉⠉⠉⠉⠉⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡟⠛⡇⠀⡟⠛⡇⠀⢷⡀⠀⠀⣰⠇⠀⡟⠛⡇⠀⡿⠛⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣇⣀⡇⠀⣇⣀⡇⠀⠀⠙⠛⠛⠁⠀⠀⣇⣀⡇⠀⣇⣀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣉⣉⡁⠀⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⡁⠀⣉⣉⡁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠈⡇⠀⡇⠀⡇⠀⢰⡟⠒⠛⣷⠀⠀⡏⠀⡇⠀⡯⠀⡇⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠷⠶⠇⠀⠷⠶⠇⠀⢸⡇⠀⠀⣿⠀⠀⠷⠶⠇⠀⠷⠶⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣿





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠠⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⠟⠋⠙⠻⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣏⠀⡠⠀⠀⣹⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⡏⠉⢹⠉⠉⣿⡏⠉⢹⡏⠉⢹⣿⠉⠉⡏⠉⢹⣿⢡⡅⡡⠍⣌⣍⡥⢍⡨⢬⣡⠈⣿⡏⠉⢹⠉⠉⣿⡏⠉⢹⡏⠉⢹⣿⠉⠈⡏⠉⢹⣿
⠀⠀⠀⠀⣿⡇⠀⢸⠀⠀⣿⡇⠀⢸⡇⠀⢸⣿⠀⠐⡇⠀⢸⣿⠨⠟⠳⠆⠋⠛⡣⡞⠳⠜⠹⡄⣿⡇⠀⢸⡀⠀⣿⡇⠀⢸⡇⠀⢸⣿⠀⠀⡇⠀⢸⣿
⠀⠀⠀⠀⣿⣧⣤⣼⣤⣤⣿⣷⣤⣼⣧⣤⣼⣿⣤⣴⣧⣤⣼⣿⣿⣿⣿⠿⠛⠋⠙⠛⠿⣿⣿⣿⣿⣧⣤⣼⣤⣤⣿⣷⣤⣼⣧⣤⣾⣿⣤⣴⣧⣤⣼⣿
⠀⠀⠀⠀⣿⡿⠿⢿⠿⠿⣿⡿⠿⢿⠿⠿⢿⣿⠿⠿⡿⠿⢿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⡿⠿⢿⠿⠿⣿⡿⠿⢿⡿⠿⢿⣿⠿⠿⡿⠿⢿⣿
⠀⠀⠀⠀⣿⡇⠀⢸⠀⠀⣿⡇⠀⢸⡇⠀⢸⣿⠀⠈⡇⠀⢸⣿⣿⣿⣿⠉⠁⠈⠉⠉⠉⣿⣿⣿⣿⡇⠀⢸⠀⠀⣿⡇⠀⢸⡇⠀⢸⣿⠀⠀⡇⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⢸⠀⠀⣿⣇⠀⢸⡇⠀⢸⣿⠀⢀⡇⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⠀⠀⣿⡇⠀⢸⡇⠀⣸⣿⠀⢀⡇⠀⢸⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿
⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⡴⠒⠉⠉⠉⠉⠉⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⢀⡠⠐⠒⢒⡒⢄⡀⢴⡀⣀⡀⠀⡾⠀⠀⠀⡀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⣠⠖⠉⠀⠀⠀⠈⠙⠟⣧⠀⢹⠉⠉⠙⠛⠛⢛⡛⠛⠛⠒⠤⠼⠏⠀⡒⠶⢤⣤⠤⠤⠤⠤⠶⣤⠼⠃⣤⡤⠤⠤⠤⣀⡀
⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⡄⣱⠖⡆⠀⠀⠀⣠⠾⣡⣴⡶⠘⢳⠀⠀⢰⠛⣵⡶⢶⡙⢶⠀⠀⠀⠀⢸⣠⡼⢷⣦⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡸⠀⢯⠀⢁⠀⠀⠀⠸⠀⣿⣿⣦⡶⠀⠆⠀⢈⠘⣿⣿⣶⡇⢸⠀⠀⠀⠀⣸⠀⡧⠀⢹⡆⠀⠀⠀⠀⠀⠘⢦
⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠓⠺⠀⠀⠀⠀⠣⣌⣉⣉⡠⠞⡤⢤⡈⠢⢌⣉⣁⠴⠋⠀⠀⠀⢠⣿⠴⠃⠀⠀⣷⠀⠀⠀⠀⠀⠀⠈⣷
⠀⡏⠀⠀⠀⠀⠀⣀⠞⠁⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠸⡆
⢠⡆⠀⣠⠶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤
⠘⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠈⣉⡒⠉⠁⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⣀⣲⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⣄⣀⣉⣁⣀⣠⡤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣠⣔⠒⠞⠀⢸⡖⢠⣤⣤⠄⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⣁⣤⠐⠈⠁⠉⣙⣶⠶⢮⡁⠀⠉⠲⢄⡀⠈⠉⠉⠑⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠺⠁⠀⠀⠀⠀⢰⠉⠀⠀⠀⢱⡄⠀⠀⠀⢹⠆⠀⠀⠀⠀⠀⡏⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⢠⡄⠀⠀⠀⠀⠰⣌⠄⠀⠀⠀⠆⠘⣤⠀⡇⢀⢠⠀⠀⠀⠀⠀⢣⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢈⣄⢠⡀⠀⠀⠀⠁⠐⠀⠀⢰⠀⠀⠀⡠⠇⠘⠸⠄⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢡⠀⡄⠀⠀⠀⡇⠀⠀⠀⢸⠄⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⠀⠀⠀⣼⡄⠀⠀⠀⣼⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡈⠰⣄⣀⣀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢦⣤⠼⠉⡅⠀⠀⠀⡇⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡨⠛⢭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠐⢄⠀⢸⠀⠀⠀⡇⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠋⠀⠀⠈⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠙⠁⠀⠀⠀⡇⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⡠⠛⠶⢤⣤⣄⣀⣤⣀⣤⣤⡤⠖⢳⠀⠀⠀⠀⠀⠀⠀⢠⠁⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⣐⢂⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⣀⣀⠠⠎⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⠉⠉⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢎⣡⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⠓⠒⠦⣤⣴⣄⣀⣀⣀⣀⣦⡠⣤⣤⡤⠴⠶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠂⣾⠀⠀⠀⠉⣭⠁⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢻⡀⠀⠰⣴⠏⠀⠀⠀⢀⡟⢀⡀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁⠀⠊⠁⣰⠏⠀⠀⠀⠀⢸⠃⠀⠙⠊⢩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣀⡞⠁⠀⠀⠀⠀⠀⡾⠀⠀⠀⢀⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⢀⣠⠖⠛⠀⠀⢀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢇
⢀⠶⠉⠀⠀⠀⠀⣤⢪⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡀⠈⢳⣄
⡎⠀⠘⠦⣀⡰⢊⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⡡⡄⠀⠈⠓⢤⡀
⢣⣄⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡱⠆⠀⠰⠎⠉⡆
⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣶⠀⢠⡦⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣁⣠⠤⠄⢤⡀⢀⡀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⣉⡀⣀⠀⠀⠀⠉⠑⠬⣳⢄⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⡇⠈⠁⠀⠐⠒⠀⠀⠀⠈⠁⠳⡀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢢⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢧⠞⠛⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⠲⠶⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢀⡏⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣿⡰⢃⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⡄⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣡⠔⠉⠉⠙⢣⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠸⠋⡠⠛⡶⣤⣀⡀⠀⠀⠀⠀⢀⣀⠤⡚⠭⠰⣰⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠈⠓⠞⢡⠀⠑⠀⠈⠉⣉⣽⣟⡿⠋⡔⢚⡇⠀⠀⡏⠀⠀⠀⠀⠀⠀⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⢈⠃⠀⠀⠀⠐⢲⠏⠀⠚⠧⠞⠁⡇⢳⡀⢰⡇⠀⠀⠀⣀⢀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠶⢤⠴⠃⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⢀⡇⠀⢧⠸⡇⢟⣛⣋⣭⠔⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢇⢸⠀⠀⠀⠀⠀⠀⠀⠱⢤⣄⣀⣀⣠⣞⠀⠘⡘⡌⡇⡄⠀⠀⠀⠀⢰⢸⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⢮⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠁⠀⠘⣆⠀⡇⡇⣇⢇⠀⠀⠀⠀⡄⢸⡟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢀⣧⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠀⠀⠀⢸⢆⡇⢸⢹⠈⠦⣄⣠⠜⠁⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⢳⡈⡇⠀⠀⠈⢸⣃⠼⣼⡆⠀⢀⣀⠤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠙⠢⠤⠀⠀⠀⠀⠀⠀⠳⣵⡀⠀⢀⣜⣡⠔⠓⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠉⠙⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠙⠶⠋⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢤⣤⣤⣤⣤⠤⢴⡇⠀⠀⠀⠀⠀⣠⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣀⡤⠶⠾⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⣠⠞⠙⣥⠀⢀⡙⣄
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠘⣟⠉⠀⠀⠀⠸⣆⢁⠁⠘⣆
⡇⠀⠉⠳⣄⠀⠀⠀⢠⠞⠀⠀⠛⠛⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⡏⠀⠀⠡⢹
⠹⣄⠀⠀⡸⠍⡛⠒⠾⡄⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⡟⠀⢀⡀⠀⣷⠀⠀⠀⠇
⠀⠘⢦⡐⡁⠀⠀⠈⠁⠙⠲⣤⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⢀⠔⠉⠙⠶⠛⢌⠢⣠⠗
⠀⠀⠀⠑⢄⠀⡀⠀⠀⢠⠉⣓⡼⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠻⣅⢀
⠀⠀⠀⠀⠀⠙⢮⡢⠄⠄⣛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣤⣤⣤⣤⣤⣤⣤⣬⣾⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣍⣭⣫⣤⣉⣭⣍⣽⣫⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⠷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢤⠀⠊
⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠒⢠⡄
⠀⠀⠀⠀⠀⠛⠀⠘⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣀⠀⠄⠒⠀⢀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠄⠃⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠜⠓⠠⠀⠀⠐⠀⠗⠀⢴⡎⢷⠖⠒⡆⠁⠀⠀⠀⠀⠈⠀⢂⠈⠁⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠈⠙⠀⠀⠀⠤⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠢⠀⠀⠀⢤⡂⠶⡆⠂⢰⡄⠀⠀⢀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠚⠃⡤⡠⠀⠁⠈⡀⠉⠑⠂⠄⢀⠀⠀⠀⠀⠐⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠬
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠁
⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠈⠉⠉⠉⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⠶⠦⠴⠮⠄⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠲⢦⡐⠄⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠚⠁⠀⠀⠀⠀⠹⡌⠄⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢀⡴⠁⡴⠚⠋⠀⠀⠀⠀⠛⠷⣹⡀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣾⠁⢀⡠⢀⣠⣄⠀⠀⣀⠀⢀⡈⢧⡀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣏⠰⠛⣿⣿⣽⡮⡇⣈⣽⣿⣲⢷⡀⠹⡄⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢹⠀⠣⣙⣛⠫⠞⠀⠀⣼⡛⣋⠜⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⠃⠀⠀⠀⠀⠃⢸⡀⠀⠀⠀⠐⣄⠀⣀⣼⠀⠀⠀⠀⢠⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡞⠡⠊⠀⠀⠀⠀⠀⢰⠸⡇⠀⠀⠀⠀⠈⣉⠁⠀⡀⠀⠀⣠⠏⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢻⣄⡀⠀⠀⠀⠀⠀⣤⠀⠀⠹⡁⠀⠀⠀⠀⠀⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⠀⡀⠀⠀⠀⠀⠀⢣⡉⠓⠒⠒⠒⠒⢇⡀⠀⠀⡤⠀⠀⠀⠉⣉⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣀⡀⠀⣩⡗⠀⠃⡀⠀⠀⠙⡶⠚⠀⠚⡛⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠈⠉⠀⠀⠈⠀⠁⠀⠀⠀⠀⢚⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⠳⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠑⠂⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡤⠠⡀⣠⠔⠉⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⡄⢀⡲⠅⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⢀⡀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠀⠉⠩⠞⢱⠂⡣⠠⠀⠀⠔⢀⡉⠀⠀⠈⠉⠉⠐⠒⠂⠠⠄⢀⣀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⡀⠀⠀⠀⢦⡠⠁⠀⠀⠘⠂⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠄⠀⠕
⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠑⢦⡀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⢇⠀⢨⡅⠀⡙⠙⠒⠺
⠀⠀⠠⠀⠀⣀⠒⠀⠀⠀⢀⠀⠀⡁⠈⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢰⠁⠀⠈⠇⠀⢱
⠀⢠⠃⠀⠸⠿⢢⣾⣧⠐⡄⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠈⠀⠀⠀⠀⠀⢸
⠀⠆⠀⠐⣄⡀⠀⠉⠁⣠⠂⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠇⠀⠀⠀⡄⠀⢸
⡘⠀⠀⠀⠄⠁⠘⠛⠁⠀⠀⠌⠀⠀⠘⠀⠀⠄⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⠀⠀⠀⠀⠀⠸
⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢠⠟⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⣆⠠⠼⠄⡀⠀⢢⠄⠒⢐⣠⣀
⠀⠘⢉⠖⠀⠄⣀⠀⢀⡌⠀⣀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⢠⠐⡔⠚⠲⣤⠀⠙⢳⠀⣌⣁
⠀⠀⠀⠀⠀⠀⠀⠉⢯⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣁⣈⣁⣉⣐⠂⠀⣀⣀⣉⣀⠉⠀⠁
⣿⣿⣿⠿⣿⡿⠿⠿⣿⢿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣶⣾⣶⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠿⢧⣤⡿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠐⣠⠀⣠⡀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠈
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠑⠀⢤⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠀⡔⠋⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠲⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠄⠀⡀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⢠⠠⡄
⠀⠀⠀⢀⠀⣀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠄
⠀⠀⠀⠟⠀⣿⠻⡶⠆⡤⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠶⠀⠰⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄
⠀⠀⠀⠀⠀⢠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⣀⠈⠂
⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠁
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀
⠀⠀⠀⠀⠒⠐⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣠⠀⡄⠠⡆⢠⠀⡆⠰⠆⢰⠀⡆⠠⠄⢠⢠⣄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿⣧⣴⣥⣦⣴⣤⣤⣤⣶⣶⣥⣴⣶⣧⣴⣦⣿⣿⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠀⠀⠚⠶⡶⠝⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⡀⢠⠀⡄⡀⠀⡀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⣞⠔⣃⠜⠈⠪⣑⠺⠇⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠉⠁⠀⠀⠀⠀⢀⡉⠒⢄⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⠀⠀⠂⠘⠁⠀⠀⠀⠀⢀⣀⡦⡄⢀⣧⠏
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠅⠀⡆⠂⢀⠀⣮⣶⣦⡁⠀⠀⢾⣿⣷⠇⢸⡇⠂⠰⠉⣩⣭⣭⣭⣭⣭⣥⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢢⠀⠘⠼⣄⠀⠙⠿⠿⠃⠀⠨⠀⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠁⠄⠀⠀⠀⠈⠑⠂⠀⠀⡀⠈⠀⠀⠀⠸⠌⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡓⠤⣤⡀⢰⠂⣦⠄⠐⢆⣈⠀⠀⠀⠀⠀⢠⠊⡾⢮⠂⠀⠀⠀⠀⠀⠀⡟⠛⣻⡆⠀⠀⠀⠀⠀⠀⣿⠀⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢈⠛⠂⡙⣍⠉⣀⣩⣦⠀⠀⡀⡠⠋⢀⠜⠠⠃⠀⣴⡄⠀⠀⠈⡟⠛⠛⣦⠀⠀⠀⠀⠀⠀⣿⠀⡇⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠢⡙⠖⠷⡛⢀⣄⢀⡀⠀⠉⠀⡠⠚⠀⠀⠀⣼⣏⣻⡀⠀⠀⠁⠒⠚⠁⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠦⡠⣦⠐⣆⡵⢾⢛⣛⠓⡁⠒⠊⠁⠰⠀⠀⠸⠁⠀⠀⠷⠀⠀⠀⠀⠀⢀⡤⠖⠛⠃⠀⠀⣿⠀⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣶⠾⠛⠛⣿⡇⠈⠀⠠⠜⢄⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⠀⠀⠀⣿⠀⡇⣇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠨⡌⠛⢤⡤⠇⠀⠉⠁⣠⠄⠘⢢⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠖⠚⠃⠀⣿⠀⡇⠘⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⡴⠖⠚⠁⢀⡄⠀⠚⠀⠀⣀⠀⠔⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⣠⠖⠀⢀⠀⠠⠒⠀⠈⠀⠠⣒⣠⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠃⠇⠀⢀
⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠲⠒⠖⠾⠛⠻⠛⠉⢉⠀⠐⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠗⢸⣀⠀⠀⠈⡀
⠀⠀⢤⠐⠀⠏⠀⣰⠀⢀⡀⠀⠨⠁⠀⠀⠃⠒⠆⠀⠀⠀⠰⠖⠚⡀⠀⠀⠉⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠚⡇⠀⠀⠀⠃
⠀⠀⠐⢤⠄⣀⣫⢉⠀⠸⠆⠄⠒⠀⠀⢰⠄⢀⡀⠀⠀⠀⠀⣄⠀⢡⢀⠀⡂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠆⠜
⠀⠁⠀⠀⠀⠀⠀⠨⠄⠀⠀⠀⠀⠀⠀⠈⠑⠤⠼⠆⠀⠀⠀⠙⠒⠂⠚⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⡆⠀⠀⠤⠖⠈
⠀⠀⠙⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⢀⠀⠀⠀⡤⢄
⠀⠀⠀⠐⣄⠀⠈⠃⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⡀⠀⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠃⠠⠀⠀⠛⠒⠂⠀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⢆⠀⢀⣠⣥⣤⣼⡀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⡀
⠀⠰⠄⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⡀⢂⠐⠤⡠⠃⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⡆⢣⠀⡄⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⢿⣿⣿⠇
⠀⠀⠀⠘⠛⠛⠋⠁⠙⠳⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠟⠘⠀⠸⢇⢃⡀⠄⠈⠹⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⠁
⠀⠀⠆⠀⠀⠀⠀⠀⠐⢂⠀⠀⢦⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠤⠀⡄⠀⠒⠄⠀⡃⢀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⢠⠀⠀⠀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣄⣀⣠⠴⠀⠀⠈⠤⠀⠠⠀⠀⠐⣦⠀⠓⠀⡆⠛⠀⠀⠀⠠⠀⠇⡘⠀⠀⠐⠉⢀⡈⣴⠇⠀⠠⠀⢶⠸⠡⡄⠀⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⠀⠀⠀⠁⢀⡀⠰⠀⠀⠀⢠⠁⢠⠀⠀⢀⣀⣀⣀⡀⢀⠀⢄⠀⢱⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠂⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠺⠃⠀⠀⢰⠀⠀⢨⠃⠀⢀⠀⠀⠄⠀⠀⠀⠀⢀⡎⠠⠀⠀⠀⠀⠀⠀⠀⠁⠹⢆⠈⠀⠘⠀⠀⠀⠀⠀⠀⢠⠀⠄
⠀⠀⠀⡀⠀⠒⠒⠀⡿⠀⠼⠚⠉⠉⡦⡄⠊⠀⠀⠀⡞⠃⠚⡉⠀⠀⠨⠆⠀⠶⡀⠀⠀⠤⠈⡇⠐⣀⣀⡀⠀⠀⠀⢠⡀⠴⠊⢀⠦⠠⠧⠌⠠⢤⣶⠚⠉
⠀⠔⠋⠀⠀⠀⠀⠐⠇⠀⢀⣀⠤⠊⡠⠁⢉⣩⠀⠈⠁⢄⣀⣠⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠘⠶⢅⡀⣀⡰⠀⠀⠈⠇⠀⠆⠀⠀⠀⠀⠀⠀⣀⠀⠐⠄
⠀⠀⠀⠀⠠⣌⠀⠀⠀⠙⠉⢁⣤⠞⠓⠃⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⢡⠀⠀⠒⣄⠀⠀⠀⠈⠑⠤
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠂⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⠀⢀⣀⣀⣀⣀⣙⣦⠀⠀⠠⠀⠁⠀⠀⢠⠖⠂⠀⠐⠄⠈⠳⣄⠀⠀⠀⠠⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠒⠊


⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡿⣿⡿⠿⠿⢿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠠⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⠀⡭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠇
⠀⠀⠸⡀⢅⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢘⠂
⠀⢠⢾⠥⠤⠦⠄⠐⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡤⠦⠤⠤⠤⠀⠂⠀⠀⠈
⡀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠌⠀⠀⠈⠁⠀⠈⠀⠈⢈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣋⣉⣒⣞⣓⣉⣉⣉⣉⣑⢦⡀⠀⠈⠀⠀⠀⠀⠀⠀⢈⣉⣑⣒⣝⣓⣉⣉⣉⣉⣑⣶⡀


⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡄⠛⠒⠛⠹⠈⠙⠒⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⠿⠒⠆⠠⠆⠖⠲⠿⢍

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⢤⣄⣀⣠⠴⠖⠛⠛⠉⠉⠙⠛⠒⠲⠤⣀⢀⡤⠖⠛⠛⠓⢦⣀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⠙⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⢀⣀⣀⣀⡀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⡟⠀⠀⣠⠖⠒⠒⠦⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡉⠁⠀⠈⢹⡄⠀⠀⣇
⠀⠀⠀⠀⠀⠸⡇⠀⠀⢿⡀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣠⡟⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⢳⣄⠀⠈⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⢡⣬⣧⠀⠀⠀⠀⠀⣴⢫⣍⢳⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠀⠀⠀⠀⠀⠘⠿⠿⠋⠀⠀⠀⠀⢀⣾⣀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠹⣦⡀⠀⠀⠀⠀⣀⡠⠤⠒⠚⠋⠉⠛⠲⢤⣄⡀⠀⠀⠀⢀⡾⠁⠈⠙⠲⣤⡀
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠈⠻⢦⣀⠀⠀⣧⠀⠀⠀⢰⣾⣿⣶⡆⠀⢈⡿⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣰⠋⠛⠳⢾⣄⠀⠀⠀⠙⡿⠛⠀⢀⡾⠤⠶⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠙⠓⠶⠤⠴⠷⠤⠖⠋⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢰⠇⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣾⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣏⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣸⣧⡤⣤⣀⣀⣀⣀⣀⣴
⢻⣦⡀⠀⢀⣀⣤⠶⣿⠟⠉⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀⠀⠀⠀⠀⣠⠖⠛⠉⠁⠀⠀⠀⠈⠙⠻⣦⠀⠀⠉⠉⠉⠁
⠀⠈⠙⠛⠋⠉⠀⢰⠇⠀⠀⠀⠀⡴⠢⡄⢠⠶⢦⡀⠹⣄⠀⠀⣼⠁⢀⡤⢦⠀⣠⠖⢲⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⡟⠀⡾⠛⠢⡄⢧⠀⢹⠘⣆⠀⣷⠀⢹⣤⣼⡇⠀⣾⠀⢸⠀⣏⠀⡼⣠⠔⠛⢳⢸⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢧⣄⣀⡿⠈⢓⣛⣀⣈⠛⠁⠀⠀⣇⢸⡇⠀⠙⠒⠋⠀⠈⠉⠁⢿⣀⣠⡼⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠉⡴⠚⠉⠀⠀⠈⠙⠲⢤⡀⢹⠸⡇⠀⢠⠖⠚⠉⠉⠉⠲⢄⠉⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀⣸⠃⢸⠀⢻⡄⠸⣆⠀⠀⠀⠀⠀⢀⡇⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠈⠙⠓⠲⠶⠶⠚⠁⢀⡞⠀⠀⢻⣄⠈⠙⠒⠒⠒⠒⠋⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣤⡤⠴⠚⠉⠀⠀⠀⠀⠙⠳⠶⣤⣤⣤⣤⠶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠁⠁⠁⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⡀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠂⡢⠁⠦⠒⠀⠒⠢⡀
⠀⠀⠀⠀⠀⠀⡔⢡⣶⢤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠈⣢⠀⢰⡲⣄⣽
⠀⠀⠀⠀⠀⠀⠑⢬⣉⡈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠔⡡⢠⣿⢧⣀⣐⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⢼⣼⣿⠇⠀⠀⠀⡫⡈⣾⣽⣶⣡⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡭⠛⠈⣉⣁⣈⡉⠉⠉⠻⣍⢋⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⠀⠀⡎⠀⠀⢸⣥⣾⣿⣿⠆⢰⣶⢻⣵⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⡀⡇⠀⠀⠀⠉⢻⠛⠉⣠⠗⣟⣹⠊⡢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣵⢄⡀⠠⣀⣸⣀⡠⢏⣮⣼⣧⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⠫⡫⢛⠾⡽⣽⣻⣫⣫⢿⣟⢫⡺⠦⡄
⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⢀⠴⣷⠃⠋⠔⠕⡁⠙⠁⠠⡺⢧⠪⠊⠨⡳⢤⡀
⠀⠀⠀⠀⠀⢀⠎⠀⠀⡰⢢⡿⠁⠀⠀⠀⠀⠈⠲⡡⠊⢔⢽⣇⠀⠀⠀⢲⢝⡄
⠀⠀⠀⠀⡔⠊⠀⠀⡐⠡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠨⢐⢕⠠⢩⡇⡀⠀⠐⢕⡱⡀
⠀⠀⠀⣰⣦⢤⡄⢈⡠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡡⡪⠊⣻⡄⠀⠀⡀⢉⠾⢆
⢀⠖⠉⠁⠀⠀⠈⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⡪⠈⢜⢷⡵⠉⠀⠀⠀⠐⠹⣦⡀
⡌⢀⠔⠒⠒⠒⠤⣀⢀⠝⣦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⢔⢕⢕⢵⠃⠀⠀⢀⠤⠤⢌⡂⢝⣄
⡁⡌⠀⠀⠀⠀⠀⠈⠳⡡⣻⡂⣀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢕⢁⣥⡏⠀⢀⠔⠁⠀⠀⠀⠘⢖⠹⡄
⡇⠃⠀⠀⠀⠀⠅⠈⠂⢹⣺⡏⠀⠄⠀⠀⠀⠀⠀⠀⠀⢕⠕⡅⣻⠀⠀⠎⠀⠀⠀⢠⠉⠀⢸⢸⡇
⢀⠸⡀⠀⠀⠀⢑⡠⠂⠌⣅⡿⠠⠂⠀⡀⠀⢀⢀⢀⠔⢡⣡⣾⡇⠀⠜⠀⠀⠀⣐⠀⠀⠁⡾⣾⣀
⠀⢲⣵⡀⠀⠀⢐⠂⡀⢸⣃⣯⣄⣀⣀⣠⡤⣰⣱⣡⣪⣊⢕⣵⣿⠀⠂⠀⠀⠐⠂⡀⠄⣼⣿⠉⢩⡝⠳⠦⠄
⠀⠀⠙⢿⣦⣀⣀⠭⣢⠾⣾⡧⠭⠭⠭⠟⠻⠟⠉⠙⠛⣉⣛⣛⣿⣸⠀⠀⡠⠀⠤⣠⣾⠿⠓⢀⣐⣒⢙⣉⡛⠟⠂
⠀⠀⠀⠀⠙⠛⠻⠟⢟⠛⣁⡂⠀⡤⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠭⢫⣧⣤⣬⣝⡾⠴⠛⢓⣐⠛⠷⠐⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣀⠀⠊⠀⠀⢀⣠⣶⠶⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠿⢦⣀⣤⡶⠟⠋⠁⠀⣀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢽⣧⡀⠀⠉⢣⣀⠀⠀⢸⡏⠉⠉⠓⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠈⠓⢄⠀⠀⠙⢷⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠇⠀⣸⠅⠀⢀⠀⠀⠠⠃⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣠⠠⢿⠀⠀⠀⠂⡠⠁⠀⠀⠀⢀⣄⢿⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣙⣦⣿⣈⣀⠀⡐⠀⠀⠀⠀⠀⣸⣿⠈⠀⠀⠀⠀⠀⠀⢸⣄⣹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⢰⠻⣻⡟⢛⡉⠟⠛⣶⠀⠀⠀⢠⡟⠀⠙⠻⡄⠀⢀⡠⠊⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡞⠛⠉⠶⡉⠙⣄⡴⢻⠄⠀⠀⣼⣦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠐⠂⢤⡈⡆⠈⣶⠋⠐⠂⠴⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⠀⠀⠀⡇⡇⠀⣿⠀⠀⣰⣤⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠵⠶⡄⠀⠀⢠⡂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣤⣀⣙⣩⣼⡏⠀⢀⣿⡇⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⣀⡠⠖⠋⠁⠀⠀⠀⠀⠙⠂⢀⣀⡐⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⠿⠟⠉⠁⢲⠆⠈⢳⡵⠤⠤⠶⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣀⡿⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⡰⠿⠋⠀⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⣸⣙⣧⣤⡤⠞⠁
⠀⠀⠀⠀⢀⣀⠸⠷⠀⠚⢿⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⣾⠹⡎⢌⣹⡆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣾⣿⡇⠓⠲⠃
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⣿⣿⣧⣵⠀⠀⠀⠀⣰⠷⢴⡞⠁⠀⠀⠀⠈⠈⠶⠀⡎⠀⠀⣴
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⣠⠼⠞⢻⣿⣿⣿⢿⡀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇⠀⢠⡟
⠀⠀⠀⠀⠾⣽⣀⣀⣠⣤⣾⢘⠀⠀⠀⠀⠀⠀⣸⢾⣯⣿⠋⠀⠀⠒⠻⠿⣿⣿⣧⣿⠷⠦⣄⡀⠀⠀⠀⠀⠀⠠⢐⣲⣀⣈⢠⡇⢀⣘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠸⠶⠯⣭⠭⠥⠤⢤⣤⣴⡯⠊⠁⠀⠀⠀⠉⠓⠢⠴⠶⠖⠛⠉⠉⢩⠟⢸⠏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⣀⠀⠓⢦⣄⡀⠀⠀⠀⢀⣠⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠙⠢⣠⡴⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⣀⣤⣄⠀⠀⣙⣧⣴⠶⠛⠛⠓⠒⠶⠶⠶⠤⣤⣠⡞⠉⢀⣀⣀⣈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢨⣿⣿⣟⠵⠋⠁⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠈⠙⠾⣿⣿⣦⠍⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⠃⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠹⣄⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⢀⣈⠁⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠠⠴⠟⠛⠓⣤⣾⣿⣿⣻⣆⠿⠿⢥⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⢠⡾⠁⠀⠀⠉⠓⠶⣤⣙⣧⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢀⡇⠀⠀⢀⡄⠀⠀⠀⠀⢀⡼⢁⣠⡤⠶⠖⠒⠒⠲⡄
⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠰⠄⠉⠛⢷⣤⣀⠀⠀⠀⠀⠀⠈⠙⠲⠚⠳⠶⠒⠋⠀⠀⠀⣀⣴⡿⠞⠋⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⢠⠟⠛⠿⣷⡶⢦⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⡾⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠉⠙⠒⣶⡿⣿⢻⣏⣽⣏⠻⡻⡅⠀⠀⠈⢷⡀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⡜⣽⣱⢃⣾⢻⡜⡿⣄⡇⢹⠀⠀⠀⠈⣷⡀⠩⢷⣢⠄⠀⣀⣤⠟
⠀⠀⠀⠈⠙⠻⠶⢤⣤⣀⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠳⠬⠗⢫⠏⣸⠂⣷⠤⠴⠋⠀⠀⠀⠀⠸⣧⣤⣬⡶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣿⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣸⣄⣤⠴⠦⢤⣄⠀⠀⠀⠀⠀⣾⣀⣸⠑⠶⠚⠂⠀⠀⠀⠀⠀⢀⣠⣿⣇⡀
⠀⠀⠀⠀⠀⣰⠋⠁⠈⠉⠲⣌⠛⢦⡀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⡴⠋⣠⠋⠀⠙⢷⡄
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠈⢧⠈⢿⡄⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣼⠁⡼⠁⠀⠀⠀⠀⢹⡆
⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⣷⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⣸⠃⡸⠁⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢹⡇⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢀⡏⢀⠇⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⢸⣿⡄⡆⠠⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⢀⡼⠳⠤⣄⣀⡀⢀⣀⣸⣿⠀⠀⣼⠃⢸⠀⠀⠀⠀⠀⡀⠀⠀⣼
⠀⠀⠀⠈⣿⣧⡇⠀⢨⢰⢠⠀⠀⣸⢠⡿⢀⡴⠋⠀⠀⠀⠀⠀⠉⠉⠉⠀⠙⣷⡀⣿⠀⢸⠀⣸⠸⣸⢰⠟⠀⢠⡟
⠀⠀⠀⠀⠈⠻⣷⣾⣼⣸⣚⣀⣴⣧⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⣧⠸⡀⠉⠃⠉⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢤⣤⡴⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠋⠉⠀⠀⠈⠉⠻⢿⣿⣦⣤⣤⣤⣤⣤⣤⣄⣠⣾⣿⠟⠋⠉⠉⠉⠉⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⠛⠛⠛⠛⠿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠁⠀⠀⠀⠀⠈⠙⠋⣡⣴⡶⠶⠶⠶⣶⣤⡈⠛⠛⠁⠀⠀⠀⠀⢸⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⢠⣶⣶⣦⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢻⣿⣿⣿⠇⠀⠀⠹⣷⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⢿⡇⠀⢶⣄⣀⣴⢿⣄⣀⣠⡦⢀⣿⠃⠀⠀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠈⢿⣄⠀⠉⠉⠁⠀⠉⠉⠉⢀⣾⠏⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⣄⣀⣹⣿⣷⣦⡀⠀⠙⢷⣦⣄⣀⣀⣠⣤⣶⠟⠁⠀⣠⣶⣿⣿⣃⢀⣤⣶⣶⣿⣿⣿⣶⣦⣄⡀
⠀⢀⣴⣿⣿⠟⠛⠋⠉⠛⠻⢿⣿⡿⠛⠁⠉⠻⢷⣦⣤⣀⣉⣉⣉⣉⣁⣠⣤⣶⠿⠋⠁⠙⠻⣿⣿⡿⠛⠉⠉⠁⠉⠉⠛⢿⣿⣦
⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿
⠀⠻⣿⣧⣄⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⡀⠀⠀⠀⢀⣠⣴⣿⡿⠁
⠀⠀⠈⠻⣿⣿⣶⣶⣶⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠉⢹⣿⣇⣤⣤⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⣿⣿⠁
⠀⠀⠀⠀⠀⢀⣾⣿⠟⠋⠁⠀⠀⠉⠙⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⠉⠁⠈⠉⠛⢿⣿⣿⡀
⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⣤⣤⣤⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⡀⠀⠀⠀⢀⣠⣾⣿⡟⠛⠛⠛⠛⢿⣿⣦⣀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣾⣿⣿⣿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢨⡟⠛⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⠾⣇⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠉⠉⠉⠉⠉⠋⠙⣹⠟⢁⡴⠋⠙⢦⡈⠻⣏⠙⠉⠉⠉⠉⠉⠉⠙⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡴⠋⢀⣀⣀⡀⠙⢦⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⣠⠞⢁⡴⠋⠀⡴⠋⢠⡈⠙⣆⠀⠙⢦⡈⠳⣄⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠿⠤⣤⠤⠤⠤⠤⣤⠞⢁⡴⠋⠀⠀⠀⣇⠀⠈⠛⠀⣼⠀⠀⠀⠙⢦⡈⠳⣤⠤⠤⠤⠤⣤⠤⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⠁⠀⠋⠀⠀⠀⠀⠀⠈⠳⠤⠴⠞⠁⠀⠀⠀⠀⠀⠙⠀⠈⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠞⠛⢶⠀⢠⠞⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠳⡄⢀⡴⠛⠳⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⢸⡇⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⢸⡇⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⠦⠤⠼⠃⠸⠦⠤⠼⠃⢸⡏⠉⠉⠉⠉⢹⡇⠘⠧⠴⠴⠇⠘⠧⠤⠴⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠛⠛⢻⡆⢸⠛⠛⢻⡆⢸⡟⠛⢻⡟⠛⢻⡇⢰⡟⠛⠛⡇⢠⡟⠛⠛⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣀⣀⣸⠇⢸⣀⣀⣸⠇⢸⡇⠀⢸⡇⠀⢸⡇⠸⣇⣀⣀⡇⠸⣇⣀⣀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠾⠷⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤
⣶⣶⣶⣶⣶
⣿⣽⠍⣯⣿
⣿⣿⢦⢺⣿
⣿⣿⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠦⣤⣀⠀⠀⣀⣤⡤⠴⠶⠶⠦⢤⣄⣀⠀⠀⢀⣠⠴⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⠐⠂⠒⠂⣹⠷⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣟⣁⠰⠂⠲⢀⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡌⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠈⡥⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠰⠄⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣀⠴⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⡟⠀⠀⠀⠀⢀⣤⠀⠀⠀⣀⣀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣷⣥⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢛⡵⠚⠉⢉⠉⠉⠓⢾⡛⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⡞⠀⠀⠸⣿⣿⠆⠀⠀⢷⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠈⠓⠶⠶⠶⠶⠚⠁⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⡷⣤⡤⢤⣄⣀⣀⣀⢀⣠⡤⢤⡴⢾⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣻⠏⢀⡏⠀⠀⠈⡟⠀⠈⣿⠁⠀⠀⢹⠈⠻⡝⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣼⠃⠀⠈⣧⡀⠀⣀⡿⠤⠴⢿⣀⠀⢀⡼⠀⠀⠹⣆⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣼⠃⠀⠀⠀⠈⠉⠉⠁⠀⡤⠀⠀⠈⠉⠉⠀⠀⠀⠀⠹⡆⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢻
⠀⠀⠀⠀⣠⡴⠶⠶⢤⡀⢠⡾⠃⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢳⡄⢀⡴⠒⠒⠶⣄
⠀⠀⠀⣼⠷⠀⣤⠀⠀⠻⡏⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣹⠏⠀⠀⠴⠐⠞⣧
⠀⠀⢰⡇⠀⠀⠀⠳⠀⠀⢹⣤⠶⠖⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠓⠶⢴⠏⠀⢀⡛⠀⠀⠀⢸⡆
⠀⠀⢸⡇⠀⠀⠀⠈⣃⠀⠀⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⢩⡀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⢸⠃
⠀⠀⠀⣷⠀⠀⠀⠀⢨⡄⠀⠀⠀⠀⠀⠀⠀⢀⣩⠿⠶⢤⣄⣀⣀⣀⣀⣀⣀⣤⠤⠖⠿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⡿
⠀⠀⠀⠸⣆⠀⠀⠀⠰⠆⠀⠀⢀⣀⣤⠶⠚⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣤⣀⡀⠀⠰⠆⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠈⠙⠒⠶⠶⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⠋⠉⠉⠙⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣿⣿⣿⣿⣿⣿⣯⠀⠔⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡆
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⡿⠿⣿⠿⢿⣿⡿⠿⣿⠿⢿⣿⡿⠿⣿⠿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⣿⠿⢿⣿⡿⠿⣿⠿⢿⣿⡿⠿⣿⠿⢿⣿
⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⣿⡇⠀⣿⠀⠀⣿⡇⠀⣿⠀⠀⣿⠰⣗⡔⠒⣦⣦⡖⢢⡖⢢⡆⠀⣿⠀⠀⣿⠀⢸⣿⠀⠀⣿⠀⢸⣿⠀⠀⣿⠀⢸⣿
⠀⠀⠀⠀⣿⡅⠀⣿⠀⠀⣿⡇⠀⣿⠀⠀⣿⡇⠀⣿⠀⠀⣿⣬⣭⣬⣭⣥⣥⣭⣥⣭⣥⣭⣤⣿⠀⠀⡿⠀⢸⣿⠀⠀⣿⠀⢸⣿⠀⠀⣿⠀⢸⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠉⠙⠻⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⡏⠉⣿⠉⠙⣿⡏⠉⣿⠉⠉⣿⡏⠉⣿⠉⠉⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠉⠉⣿⠉⢹⣿⠉⠉⣿⠉⢹⣿⠋⠉⣿⠉⢹⣿
⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⣿⡇⠀⣿⠀⠀⣿⡇⠀⣿⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣿⠀⢸⣿⠀⠀⣿⠀⢸⣿⠀⠀⣿⠀⢸⣿
⠀⠀⠀⠀⣿⣧⣤⣿⣤⣴⣿⣧⣤⣿⣤⣤⣿⣧⣤⣿⣤⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤⣿⣤⣼⣿⣤⣤⣿⣤⣼⣿⣦⣤⣿⣤⣼⣿
⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⣤⣴⣦⣤⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠁⠀⣠⡀⠀⠙⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⠞⠁⠙⢦⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣀⣀⣀⠔⠁⣤⡆⣦⡀⠑⢤⣀⣀⣀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⠀⢰⡆⠀⢿⣷⣾⠇⠀⣶⠀⢰⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠛⠀⠘⠃⠀⠀⠀⠀⠀⠀⠛⠀⠘⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⢸⡇⠀⢰⣿⣷⠀⠀⣿⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠈⠉⠀⠈⠁⠀⠈⠛⠋⠀⠀⠉⠀⠈⠁⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠁⣨⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠐⠿⠜⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣞⢭⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⣠⣾⡫⣦⣽⣾⣿⣧⠴⡖⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⣠⡾⣿⣛⣷⣿⠿⢻⡅⠲⠀⠉⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⢀⡾⣫⢻⣾⠿⢫⡅⠛⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢸⠀⠀⠀⠀⣰⢏⣾⣿⠟⡥⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢸⠀⠀⢀⡼⣳⣿⢟⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢸⠀⢀⡾⣱⡟⠱⠈⠀⠀⠀⠀⣠⣤⣴⣶⣤⣤⣀⠀⠀⠀⣾⣭⣞⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣄⣼⣳⢏⠘⠂⠀⠀⠀⢠⣾⠟⠉⢻⣿⡏⠻⣿⣷⣄⣰⣿⣷⢾⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣭⠾⠏⡏⠈⠀⠀⠀⠀⠀⠈⠿⣧⣤⣾⡿⠃⠀⢹⣿⣿⣿⣿⣿⢻⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣷⠦⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣟⡿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⢿⣷⠂⢨⣳⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣏⡽⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠟⣿⣿⣯⡳⣯⣻⢿⣷⠲⣾⢿⣿⣿⣿⣿⡿⣿⣹⡷⣫⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⡉⠛⠾⣭⣿⣒⣻⣾⣷⣚⣳⣯⠷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡄⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⢺⢩⣿⢛⢟⣿⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⣸⣿⣷⣾⣿⣿⣭⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣟⣻⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢯⣟⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢹⣿⣿⢿⣿⣿⣻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣾⠿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣶⢸⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡟⡷⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣾⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠧⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠉⠒⢄⣀⠤⠔⠒⠒⠒⠒⠒⠒⠤⠄⣀⠤⠒⠉⠉⠉⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣠⠒⠒⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⣄⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡁⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⠃⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠘⠤⠃⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⢰⣶⠄⠀⠀⠀⠀⠀⢠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⠡⠴⠒⠐⠐⠲⠤⢅⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢠⠊⠁⠀⠀⡊⠉⠉⠂⠀⠀⠉⢢⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⡇⠀⠀⠀⠀⠈⢹⠋⠀⠀⡀⠀⠀⡂⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠢⢄⠣⡀⠀⠀⠀⠀⠘⠀⠀⢀⠄⠀⢠⣁⠔⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠉⠛⠦⠄⣀⣁⣀⣀⣀⡠⠤⠞⠋⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡸⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⠈⠐⠠⡀⠀⠀⢇⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠈⡆⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⠰⢧⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡷⠔⠒⠒⠠⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠈⠺⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠗⠁⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠤⠠⠄⡀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⠄⠂⠒⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠐⠀⠀⠀⠀⠈⢂⠀⡗⠢⣀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢺⠀⡔⠀⠀⠀⠀⠀⢁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢠⠀⠀⠀⠀⠀⠈⢠⠓⠤⢀⣈⠀⠒⠒⠒⠂⢉⡀⠴⠚⡄⠀⠀⠀⠀⠀⠀⡄⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢥⣄⡀⠀⣠⠞⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠳⣄⠀⢀⣠⡬⠔⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢀⢀⠀⡀⡀⡀

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠓
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⠐⠈⠳⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⢫⠁⠈⡠⠊⠙⠑⢦⠈⠀⠩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢒⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡀⠑⠒⠊⢁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡤⠚⢢⡠⠓⢤⠜⠢⡤⠓⢄⠜⠣⡠⠛⢄⠜⠣⡠⠛⢄⠔⠣⣠⠚⢦⡄⠓⣄⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡔⠉⣢⠊⢑⡔⠉⣢⠊⢑⡔⠉⢢⠊⡑⠑⠈⢱⡔⠉⣶⠊⢑⡔⠉⣢⠊⢑⡔⠉⣢⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣅⢈⠮⡀⡱⢅⢈⠾⡁⡱⢇⢈⠾⡁⠋⣴⢑⣄⠣⣨⢎⠀⡱⣅⣈⠮⡀⡱⢅⢈⠮⡀⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠔⠣⡠⠞⢄⡠⠣⣠⠞⢄⡠⢣⠔⡡⢎⡠⠓⢄⠦⡀⢠⠛⢄⠔⠣⡠⠚⢄⠔⠣⡠⠞⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⢂⡔⠙⣢⠊⠓⡔⠉⢢⣊⠗⣁⠘⢢⠊⠑⡔⠋⢢⡘⠢⡐⠊⢂⡔⠙⣦⠊⠂⡔⠙⢢⠊⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠉⠉⠀⠉⠁⠈⠉⠠⠏⡡⠊⣭⢀⠭⢡⣈⣉⢦⣉⢭⣨⠉⠂⢌⠯⠈⠉⠁⠈⠉⠈⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠛⠉⠛⠈⠈⠉⠛⠉⠛⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠓⢆⠀⠀⠀⠀⠀⡠⢲⠲⣄⠀⠀⠀⠀⢀⠖⠟⢢⡀⠀⠀⠀⠀⢀⡔⡖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⠴⠦⠼⡆⠀⠀⠀⢰⠧⢼⠤⠼⡄⠀⠀⠀⡾⠤⡦⠤⣧⠀⠀⠀⠀⡾⠤⡧⠤⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⣤⡇⠀⠀⠀⢸⣤⣼⣤⣤⡇⠀⠀⠀⣧⣤⠥⣤⣼⠀⠀⠀⠀⣧⣤⣧⣤⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡤⡶⢤
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⡄⢸⡄⠀⠀⠀⠀⠀⡞⠉⠉⢳⠀⡇⢸⠋⠉⠙⠀⠀⠀⠀⠀⠀⣼⠀⣤⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⣇⣀⣀⡠⠀⡇⢸⣀⣀⣸⠀⠀⠀⠀⠀⠀⣇⣀⣇⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠠⠈⠀⠉⢈⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠈⠡⠉⠠⢉⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠐⠂⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⢤⣄⡀⠀⢀⣠⡴⠶⠚⠛⠛⠛⠛⠛⠓⠲⠶⢤⣄⡀⠀⣀⡴⠖⠚⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠈⠙⠿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣀⣠⣄⣀⡀⠀⠈⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢀⡴⠖⠛⠛⠓⢦⡀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠉⠀⠀⠉⠙⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢸⡗⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⡄⠀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⡟⠁⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠈⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢶⡄⠀⠀⠀⠀⠀⠀⠀⣤⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⢸⣄⣿⣷⡿⠀⠀⠀⠀⠀⠀⢸⣇⣶⣦⣿⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⡄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠃⠀⠀⠀⠀⠀⢀⣾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠛⠛⠛⠛⠶⣦⣄⡀⠀⠀⠀⠀⠀⢀⣾⠃⠈⠉⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⢸⡉⠀⠀⠀⠀⣤⣶⣶⣤⣤⠀⠈⠙⣷⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠈⢹⡷⣦⣤⣈⣇⠀⠀⠀⠀⠙⢿⣿⣿⠏⠀⠀⣼⠁⢀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢰⠉⠉⠛⠻⢦⣀⠀⠀⠀⠈⡏⠀⠀⣠⡾⠋⠉⠉⠙⡞⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢈⡄⠀⠀⠀⠀⠈⠉⠓⢲⠚⠛⢲⠚⠉⠀⠀⠀⠀⢸⠃⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢼⡀⠀⠀⠀⠀⠀⠀⣀⠼⣄⣀⣸⣀⣀⣀⡀⠀⠀⣘⡆⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠉⠙⠛⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣟⣠⡤⠴⠶⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠶⢶⣿⣿⡓⠶⠶⠤⣤⣤⣤⣤⣾⠟
⠹⣷⣄⣀⣀⣀⣠⣴⡾⠟⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠈⠉⠛⠛⠛⠉⠁⠀⣼⠃⠀⠀⠀⠀⢠⡤⠤⣄⠀⣴⢶⣤⡀⠙⣷⡀⠀⠀⣰⡏⠀⢀⣤⣦⡀⠀⣴⠒⢳⡆⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣴⠶⢦⣀⠈⣇⠀⠸⡆⢻⠀⠈⢷⠀⠘⣧⣀⣠⣿⠀⠀⡞⠁⢸⡇⢸⠃⠀⣼⠂⣠⠴⠶⣦⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠸⣏⠀⠀⠘⡇⠹⣄⣤⠇⠈⠳⣤⡾⠀⠀⢸⡏⢹⡟⠀⠈⣧⣀⡼⠁⠘⠷⠶⠋⢼⠁⠀⠀⣸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⠳⠶⠾⠃⣀⡤⠴⠖⠲⠦⣄⡀⠀⠀⠀⣧⢸⡇⠀⠀⠈⠁⣀⣀⣀⣄⣀⡀⠘⠷⠶⠞⠋⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠉⠳⣦⠀⣿⠘⣿⠀⠀⣼⠋⠉⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣾⠀⢹⣆⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠉⠛⠲⠶⢤⣤⠴⠾⠋⠀⢀⡟⠀⠀⠹⣧⡀⠈⠛⠲⠶⠶⠶⠶⠛⠋⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣀⣀⠀⠀⢀⣀⣤⠶⠋⠀⠀⠀⠀⠘⢿⣦⣄⣀⣀⠀⢀⣀⣠⣴⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠿⠿⠟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠠⠄⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢠⣿⡅⣠⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⢠⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠿⣽⡖⠲⠀⠀⠀⠈⠉⠀⠀⣄⠙⠍⠢⣄⠀⠂⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠜⣿⣿⣶⣷⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⡄⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣪⣷⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠘⢓⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣹⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠂⠠⠂⠀⠠⠀⠀⠀⢈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣹⣿⣿⣿⣿⣿⣿⡟⠉⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠛⠿⣿⣿⣿⡇⠀⠀⢀⣠⣴⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⠤⠴⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⡬⠀⠀⠀⠈⠉⠉⢀⣶⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠶⠞⠋⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣧⣤⣤⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣠⣄⡤⠴⡛⠛⠉⠉⠁⠀⠀⠀⠠⣤⢼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣹⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣴⣿⣿⣿⠿⢷⠄⠐⠊⠩⠁⠀⢀⣦⠤⠀⠀⠀⠀⠀⡤⠀⠹⢪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠑⠀⠀⠉⠁⣤⢰⡉⠛⠿⠛⠋⠉⢄⠀⠀⡏⠁⠀⠀⠀⠀⠀⠈⢿⣶⡟⠀⠀⢀⡴⠃⠈⣬⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣦⡰⣧⠀⢠⠉⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠠⠎⠀⢹⠂
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠻⠉⠿⡆⠹⣾⣿⣧⢿⣇⢠⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠁⠐⠀⠄
⠀⠀⠀⠀⠈⠛⠋⠉⠁⠀⠀⠀⠀⠀⠘⠉⠀⠻⢿⣽⡌⠻⠈⢁⡀⠰⠀⠀⠀⣘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠃⠤⠀⢤⡄⣠⡔⠂⣤⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠙⢣⡾⠆⣀⠤⣴⣆⠂⠀⠀⠀⠀⠀⢀⡀⠦⠀⢀⠀⢀⣰
⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⣾⣇⣀⠀⣴⠆⠀⠈⠉⠠⠀⠄⠐⣦⠀⠻⠟⠘⠟⣧⣶⡆⠈⣰⣦⠦⢺⠁⡀⠿⣲⡏
⠀⠀⠀⠀⠀⢀⣾⡿⠋⢰⣿⣿⠟⠡⣴⡿⠀⠀⠀⠀⠀⠀⠀⡄⠈⠃⠀⡾⠛⠖⠃⠈⢡⣆⠓⠳⠚⡏⠀⠉⠓⠀⠁
⠀⠀⠀⠀⢠⣾⡏⠀⠀⣸⣿⠏⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠇⠀⠀⠘⠉⠀⠀⡀
⠀⠀⠀⢠⣿⡟⠀⠀⢰⣿⣿⠆⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀
⠀⠀⠀⣼⣿⣵⣣⢀⣿⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⢠⣿⣿⣿⣿⢰⣿⣿⣿⡀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠇
⣷⣄⢸⣿⣿⣿⣿⠀⣿⣿⣿⣧⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⢀⢉⣿⣦
⠹⣿⣧⢻⣿⣿⣿⣦⣿⣿⣿⣵⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⡴⢦⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠔⠋⠀⠀⠙⢦⡑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠔⠁⠀⠀⠀⠀⠀⠀⠙⠢⡙⢦⡀
⠀⠀⠀⠀⠀⠀⡰⠒⠒⣲⠒⠒⣶⠒⠒⣶⠒⠒⣶⢂⠶⣋⠔⠁⠀⢀⣴⡶⢿⡿⠵⣢⣄⠀⠈⠢⡙⢶⡒⣶⠒⠒⣶⠒⠒⣖⠒⠒⣶⠒⠒⠆
⠀⠀⠀⠀⠀⠀⣇⣀⣀⣟⣀⣀⣿⣀⣀⣿⣀⣀⠟⣡⠖⠁⠀⠀⣰⡿⠁⠀⢸⡇⠀⠈⠻⣷⡀⠀⠈⠢⣌⠻⣀⣀⣿⣀⣀⣻⣀⣀⣻⣀⣀⣹
⠀⠀⠀⠀⠀⢰⠋⠉⣹⠏⠉⢹⡏⠉⢹⡏⠉⢹⡞⢹⠀⠀⠀⠀⣿⣁⣀⣀⣸⣧⣀⣀⣀⣱⡇⠀⠀⠀⢸⢳⡏⠉⢹⡏⠉⢹⡏⠉⠹⣏⠉⠹⡆
⠀⠀⠀⠀⠀⡼⠤⠤⠿⠤⠤⠾⠤⠤⠾⠧⠤⠼⠧⢾⠀⠀⠀⠀⣻⠒⠚⠁⢺⡖⠀⠉⠂⢻⠇⠀⠀⠀⢸⠼⠧⠤⠼⠷⠤⠤⠷⠤⠤⠿⠤⠤⢧
⠀⠀⠀⠀⠀⠓⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣻⠀⠀⠀⠀⠿⡄⣀⡀⣸⣧⢀⣀⣀⡼⡃⠀⠀⠀⢸⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣲⠞
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍
⠀⠀⠀⠀⠀⠀⢸⠀⢠⣤⣤⣤⡀⠀⢠⣤⣤⣤⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣶⢶⡶⣶⠀⠀⡶⢶⠶⣶⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣀⣿⢸⡇⠀⢸⣀⣇⣸⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣯⣼⣧⣿⠀⠀⣧⣼⣤⣿⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⠋⣿⢹⡇⠀⢸⠉⡏⢹⡆⢸⠀⠀⠀⠀⢴⣒⣒⣒⣒⣒⣒⣒⣒⣲⠀⠀⠀⠀⢸⠀⣿⢸⡇⣿⠀⠀⡇⢸⡀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠾⠷⠿⠾⠇⠀⠾⠶⠷⠾⠇⢸⠀⠀⠀⠀⣽⡗⠛⠛⢻⡞⠛⠛⢻⣿⠀⠀⠀⠀⢸⠘⠛⠛⠛⠛⠃⠘⠛⠛⠛⠛⠀⡃
⠀⠀⠀⠀⠀⠀⢸⠀⢠⣤⣤⢤⡄⠀⢠⣤⣤⣤⡀⢸⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⢸⠀⣶⢲⡖⣶⠀⠀⡶⢲⠖⣶⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣀⣿⣸⡇⠀⢸⣀⣇⣸⡇⢸⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⢸⠀⣿⣼⣧⣿⠀⠀⣧⣼⣦⣿⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⠉⣿⢹⡇⠀⢸⠉⡏⢹⡆⢸⠀⠀⠀⠀⢿⠗⠶⠒⠚⠳⠐⠲⠚⣿⠀⠀⠀⠀⢸⠀⣿⢸⡇⣿⠀⢀⣇⣸⡂⣿⠀⡃
⠀⠀⠀⠀⠀⠀⢸⠀⠾⠷⠿⠾⠇⠀⠿⠿⠿⠿⠇⢸⠀⠀⠀⠀⢾⠅⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠈⠋⠉⠉⠙⠁⠘⠉⠉⠉⠙⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣻⠆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⣹⠄⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠐⠛⠂⠀⠀⠐⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠆


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠙⠲⢄⡀
⠀⠀⠀⠀⣀⡀
⢀⣴⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⡀
⣼⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⡆
⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠋
⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⠛⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡏⠀⠀⠀⠀⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⣦⣀⣀⣴⣿⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠉⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⣿⣿⠛⢻⣿⣿⠛⣿⣿⡟⠛⣿⣿⠛⢻⣿⡿⠛⣿⣿⡟⠻⣿⣿⠛⢻⣿⡟⠛⣿
⢀⣤⣤⣤⣤⣤⣤⣤⢸⣇⣠⣿⣿⣄⣸⣿⣿⣀⣿⣿⣇⣠⣿⣿⣄⣼⣿⣧⣀⣿⣿⣇⣠⣿⣿⣀⣼⣿⣧⣀⣿⢠⣤⣤⣤⣤⣤⣤⣤
⢸⣿⠛⢻⣿⡟⠛⣿⢸⡟⠛⣿⣿⠛⢻⣿⣿⠛⣿⣿⡟⠛⣿⣿⠛⢻⣿⡟⠛⣿⣿⡟⠛⣿⣿⠛⢻⣿⡟⠛⣿⢸⣿⠛⣿⣿⡟⠛⣿
⢸⣿⣤⣼⣿⣧⣤⣿⢸⣧⣤⣿⣿⣤⣼⣿⣿⣤⣿⣿⣧⣤⣿⣿⣤⣼⣿⣧⣤⣿⣿⣧⣤⣿⣿⣤⣼⣿⣧⣤⣿⢸⣿⣤⣿⣿⣧⣤⣿
⢸⣿⠉⢻⣿⡏⠉⣿⢸⡏⠉⣿⣿⠉⢹⣿⣿⠉⣿⣿⡏⠙⣿⣿⠉⢹⣿⡟⠉⣿⣿⡏⠙⣿⣿⠉⢹⣿⡟⠉⣿⢸⣿⠉⣿⣿⡏⠙⣿
⢸⣿⣤⣾⣿⣷⣤⣿⢸⣧⣴⣿⣿⣦⣼⣿⣿⣤⣿⣿⣧⣴⣿⣿⣦⣼⣿⣷⣤⣿⣿⣧⣴⣿⣿⣤⣾⣿⣷⣤⣿⢸⣿⣤⣿⣿⣧⣴⣿
⢸⣿⠉⢹⣿⡏⠉⣿⢸⡏⠉⣿⣿⠉⢹⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣿⣿⠉⢹⣿⡏⠉⣿⢸⣿⠉⣿⣿⡏⠉⣿
⢸⣿⣶⣾⣿⣷⣶⣿⢸⣷⣶⣿⣿⣶⣾⣿⣿⣶⣿⣿⣿⣿⣿⠛⠛⠛⢻⣿⣿⣿⣿⣷⣶⣿⣿⣶⣾⣿⣷⣶⣿⢸⣿⣶⣿⣿⣷⣶⣿
⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣦⣄⡀
⠀⠀⢀⣴⣾⣿⠿⠛⠋⠉⠉⠛⠻⢿⣿⣦⣀⣴⣶⣿⡿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣿⣷⣶⣄⣠⣾⣿⠿⠛⠛⠉⠙⠛⠛⢿⣿⣶⣄
⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧
⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⢰⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⢸⣿
⠈⣿⣿⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⢸⣿
⠀⢻⣿⣧⡀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⣠⣿⡿
⠀⠀⠙⢿⣷⣤⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠉⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠟⠀⠀⠀⣠⣶⣿⣿⣿⣿⣶⡄⠀⠀⠸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣼⣿⣿⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣽⡟⠁⠉⠉⠙⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠁⠘⣿⣏⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿
⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⣿⣿⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⢸
⠙⢿⣿⣶⣶⣶⣿⣿⠿⠟⠛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠛⠻⠿⣿⣿⣶⣶⣾⣿
⠀⠀⠀⠈⠉⠀⠀⠀⢀⣀⣴⣿⣧⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣿⣷⣄⣀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⠉⣉⣉⡉⠉⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠉⠉⣉⣉⡉⠙⠻⢷⣦⡀
⠀⠀⠀⠀⢀⣾⠟⣡⡴⠟⠛⢉⠉⠛⠳⣦⡀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠉⢀⣤⠾⠛⠋⠉⠙⠛⠷⣤⡙⢿⣆
⠀⠀⠀⠀⣾⠏⣼⠋⣠⠂⠁⠀⠉⠙⠦⡀⠻⣦⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⣰⡟⠁⡤⠞⠁⠀⠉⠑⢦⡈⢻⡌⢿⡆
⠀⠀⠀⢸⣿⢸⡇⡸⠁⠀⠀⡀⠀⠀⠀⠹⡀⢹⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⡟⠀⡜⠁⠀⠀⠀⠀⠀⠀⠹⡀⣿⣸⡇
⠀⠀⠀⢸⣿⢿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⣾⡇
⠀⠀⠀⠀⢿⣿⡁⢷⡀⠀⠀⠀⠀⠀⠀⣰⠃⣼⣇⣼⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣧⡸⣷⠀⣧⠀⠀⠀⠀⠀⠀⢀⣼⢃⣿⣿⠇
⠀⠀⠀⠀⠈⠻⣷⣤⡙⠶⣤⣤⣤⡴⠞⣁⣼⣿⡿⠟⠛⠻⠿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⠿⠛⠛⢿⣿⣷⣌⡻⢦⣤⣤⣤⡴⠟⣡⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣶⣶⡾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣶⣿⣷⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⡆⠀⠆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢳⢀⠀⣉⣀⣀⣀⣆⢠⠀⡄
⠀⠀⢀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⢄⣳⣾⣿⣿⣿⣿⣿⣿⣾⡇⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀
⠀⠀⠀⢁⠀⠠⠄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣾⣿⣟⢻⣿⡄⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⡀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⠀⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠈⡸⢿⣿⣻⣿⣿⣻⣿⣿⣿⡟⠑⠡⣐⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠈⠿⠛⡿⠿⡿⠛⠋⠡⠈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠘⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠢⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣀⡈⠤⠴⠒⠒⠒⠒⠂⠂⠤⢅⣀⣤⣶⣶⣤⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⣈⣉⣉⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠦⡀⠀⠀⢀⠙⠦⣀⠀⡀⠀⣀⠴⠊⠀⠀⠀⢀⣔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠻⣷⣤⣀⡑⣤⡤⠉⠉⡉⢄⣤⣊⣤⣴⣾⠟⠀⠈⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠻⠿⣿⣿⣶⣶⣾⣿⡟⠛⠉⠁⠀⠁⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠉⠉⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠀⠦⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣠⣬⣉⡑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣁⣤⣤⣤⣌⠲⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣌⠢⠀⠀⠀⠀⠀⠊⣠⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢿⣿⣿⣿⣿⣿⡿⠀⠤⠤⠤⠀⢿⣿⣿⣿⣿⣿⠟⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣈⡙⠛⠛⣉⠠⠀⠀⠀⠀⠀⠀⣉⠛⢛⣉⠡⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⠿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣖⠂⠬⣰⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⢀⣀⠀⢀⠀⠉⠀⠀⠀⠈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡠⠒⠉⠉⠉⠉⠘⠳⠬⣑⠢⣄⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣴⠶⢄⠶⠂⢀⠀⠀⠀⠈⠑⠪⡑⢆⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢷⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢡⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡴⠻⣦⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢤⣀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣔⠃⣽⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⡟⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⡴⠯⢴⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢢⠀⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⢀⡖⠉⠀⠀⠀⠹⡕⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢀⠟⠁⡠⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣛⢍⡳⢠⠏⠀⠀⠀⠀⠀⠀⢱⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠲⣤⡞⠄⠀⠑⢄⠉⠙⠛⠒⢒⡶⠶⣲⠟⣩⠔⢾⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢠⠆⠀⠀⠂⠌⣉⣉⡹⠋⢉⣻⠁⣠⠇⣴⢻⡄⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⠉⠁⠀⣿⠀⢻⡀⢸⡇⣀⣂⣤⣤⣭⠕⡆⠀⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡟⠲⡖⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡟⠀⡈⣧⠸⡇⠹⣬⠥⠤⡶⠞⢱⡀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢧⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣤⣀⣀⣀⣴⢿⡁⠀⢹⢸⡎⡇⢆⠁⠀⠀⠀⠀⠈⠂⣷⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠘⣧⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣿⠉⠁⠈⣧⠀⢸⡜⣇⣷⢸⠀⠀⠀⠀⠀⢰⠀⢻⠲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡇⠀⠀⠀⢸⣦⢸⠇⣿⢹⠈⢧⡀⠀⠀⣠⠞⠀⢸⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢹⠀⠀⠀⠸⡇⣾⠀⢻⡸⡇⠀⠉⠒⠛⠉⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠸⡄⠀⠀⠀⠀⣯⠴⢋⡷⢷⡀⣀⡤⠖⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡀⠉⠒⠢⠤⠀⠀⠀⠀⠀⠀⠈⠳⢷⡄⠀⠀⣸⣅⣴⠊⠑⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠈⠉⠛⠓⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠞⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣦⣄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠸⣇⠀⠀⠀⢀⡴⢦⡚⠁⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠉⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣤⠖⠋⠁⠀⢻⡄⣘⡰⡌⢳⡀
⣠⠶⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⢀⠀⢀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣿⡀⡴⠀⠀⢷
⣇⠀⠀⠉⠳⣄⡀⠀⠀⠀⣠⠏⠀⠀⠈⠙⠉⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⢹⠀⠀⠀⠠⠘⡇
⠸⣆⠀⠀⠀⢨⢉⠛⠲⠦⢿⡀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⠀⢀⠀⠀⢸⡄⠀⠀⠀⠇⢹
⠀⠘⢦⠀⢠⠃⠀⠈⠁⠐⠒⠻⢦⣀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠉⢀⡴⠛⠳⣄⡾⢆⠢⡀⠀⣾⠘
⠀⠀⠀⠳⣄⠡⡀⠀⠀⠀⠀⢀⡤⢭⡛⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⣀⡴⠋⠀⠀⠀⠈⠁⠀⠳⣬⠞⠀⢀
⠀⠀⠀⠀⠈⠳⣌⠢⡀⠀⠀⠸⣄⣸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⡾
⠀⠀⠀⠀⠀⠀⠈⠓⢬⡲⢖⡒⣩⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⡀⢦⠄⢀⣴⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠤⠒⡋⠐⠩⡠⣰⠢⠘⠄⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠊⠔⠠⢁⠑⠈⠄⠠⠀⠀⠀⠈⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠐⡄⠁⠀⠀⠀⠀⡀⢠⠀⠀⢒⠀⠀⠀⡈⠁⠀⠀⠃⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣢⡃⢈⠀⠁⠈⠁⠀⢁⣉⡄⠀⢀⡰⣀⡀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠀⠀⠀⠠⣀⠀⡀⢠⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢆⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠆⠀⠀⠀⠀⠀⠀⠰⠇⣠
⠀⠀⠀⠀⠀⠀⠀⠄⠴⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠈⠁⠀⠀⠂⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠡⢂⠄⡰⠂⠀⠐⠀⠀⠒⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠀⣀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠑⠒






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⡇⠠⠄⠀⢀⣀⣤⣤⣤⣤⣶⣤⣤⣄⣀⠀⠀⠠⠄⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣆⠀⣠⣶⣿⣿⣿⣿⣿⣿⣽⠿⢿⣿⣿⣿⣶⣄⠠⡴⣺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⢿⢃⣾⣿⣿⣿⣿⡛⢿⣿⣿⠃⢔⣛⡝⣿⣿⣿⣿⣷⡘⣿⡇⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢸⣿⣿⣿⣿⣿⣿⣿⡋⠙⠳⣾⣿⣸⣿⣿⣿⣿⣿⣇⢻⢯⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣇⡀⠀⢸⣿⣿⣿⣿⣿⣜⢿⡿⢠⣤⣿⡿⣫⣿⣿⣿⣿⣿⡿⠀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣥⣼⣯⣵⣾⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣦⣦⣧⢻⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⢰⢢⣍⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⣿⠿⠿⣦⡙⠟⣉⡐⠲⠄⠀⣀⣉⠁⠀⠠⣍⣛⡿⠟⣰⢏⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢡⣾⣠⣅⠠⠄⠀⠀⠈⠁⠐⠒⠀⠍⠛⠛⠂⠋⠉⠀⠀⠉⠁⠉⢀⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡤⣇⠘⢻⣿⣿⠲⢦⣇⣐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⢀⣤⣤⣴⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠇⠠⠍⠻⣥⣤⣈⣉⣙⡓⠒⠒⠀⠀⠐⠒⠚⠛⣉⣉⣴⣶⡿⠋⠄⠀⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⠂⠀⣠⣿⣿⣿⣿⣿⣿⠛⠛⣿⣿⣿⣿⠿⢛⣿⣿⣿⣿⣿⣷⡄⠀⠀⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠸⢿⣿⢿⣿⣿⠷⠔⠲⠢⠬⠋⠐⠂⠀⢿⣿⣿⣿⣿⡿⠇⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⣆⠀⠀⢿⠋⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠻⠋⠋⢿⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠏
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣠⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⢰⣶⣴⢦⣶⣠⣦⠀⡏
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠻⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠉⠉⠈⢠⠇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠐⠒⠒⠒⠒⠂⣶⡶⠊⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠐⠂⢀⡀⣀⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢤⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⠂⠁⠀⠂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡱⠂⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠶⠇⠈⠉⠈⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⡀⡀⠌⠀⠀⠀⠄⡐⡂⠀⢀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⣠⠺⡀⠀⠀⠀⠀⢀⡆⠰⠀⠀⠄⠀⠀⠀⣀⠀⠀⠀⡄⠀⢀⠀⠀⢀⠊⠈⠀⣡⢀⠆⠀⡞⠓⠀⠄⣆
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⢡⡴⢧⣀⣶⠀⢠⠎⠀⠌⠀⠐⠀⠀⡠⠖⠀⠠⠐⢋⣀⢐⣄⣁⡀⠄⠀⡔⠀⠋⡎⠀⡰⡗⣠⠀⠀⠈⠙⠒⠢⡀
⠀⠀⠀⠀⠀⠀⡶⢄⡀⠐⠀⠀⠀⠙⡉⠰⡁⢀⠂⢜⣌⣀⣀⡞⠀⠀⣮⠀⢛⡋⠀⢀⠎⡆⠀⠀⡀⠡⠂⠈⢀⠀⠃⠺⠇⠛⢲⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⢤⣁⣸⠉⣃⠀⠀⢀⡀⠁⠁⡨⢸⠅⢈⠑⠉⠀⠀⠄⠀⠀⠠⡌⢀⡴⠃⡘⢙⢢⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠼⠈⣓⠒⠂⠁
⠀⠀⠀⢀⡠⠊⠁⠀⠉⠣⠈⠙⠛⣾⣇⢈⠀⠀⡄⠁⠀⠀⡰⠂⠀⠀⠀⠀⠘⣁⠀⠀⠁⠀⠀⠈⠉⠀⡆⠀⠀⠀⡀⠀⢠⡄⠀⠘⠁
⠀⠀⠀⡎⠀⠀⢀⠀⠀⠀⠳⣠⠔⢉⠋⠀⠁⠀⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⠠⠒⢉⠉⠢⡀⠈⠀⠀⢐⠷⠒⠁⠀⡡
⠀⠀⠀⠄⠀⠀⡝⢉⠁⠀⠰⣛⠢⠘⠓⠒⠀⢼⠉⡲⠀⠁⠀⠀⢀⠀⠀⢀⠄⠀⠀⠰⠀⠀⢠⠈⠀⢠⠀⠘⠀⠠⠤⠄⠀⠈⠀⠈⢄
⠀⠀⠀⢀⠀⠀⠸⠀⠵⠄⠀⠈⠒⠀⠐⠀⢠⠈⠘⠛⢆⢸⣟⠀⣙⣯⠔⠋⠀⠀⠀⠁⠀⢀⠀⠉⠀⡘⠀⠨⠀⠀⠂
⠀⢀⡠⠠⠂⠀⢠⠀⠀⠣⣀⠀⠀⠀⠀⠀⠈⠀⠰⠊⠀⠀⠛⠁⠈⡧⠬⠀⠠⡀⠀⠐⡄⠀⠁⠒⠊⢀⡤⠃⠀⠀⠀⡂⠀⠀⠀⠀⡀
⠀⠸⢀⢀⣀⣀⠖⠂⠀⠀⠀⠛⠂⢦⠠⡀⢠⠤⠂⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⠁⠐⠈⠙⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠿⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⢿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠉⠀⠀⠀⠀⠀⠈⠻⣿⣶⣿⣿⣿⣿⣷⣶⣿⡿⠋⠁⠀⠀⠀⠀⠙⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⡀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠈⠉⣩⣴⠶⠾⠿⠷⢶⣤⡉⠋⠁⠀⠀⠀⠀⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢀⣾⠏⠁⢠⣾⣿⣶⠀⠈⠻⣦⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⣾⠇⠀⠀⠘⠿⠿⠟⠀⠀⠀⢻⡇⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⣿⠀⢀⡀⠀⢀⣤⠀⠀⢀⡀⢸⡇⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠹⣧⠈⠛⠶⠛⠉⠳⠶⠋⢁⡿⠁⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⢹⣿⣷⣄⠀⠙⠷⣦⣀⣀⣀⣀⣠⣴⠟⠁⢀⣤⣾⣿⡃⢀⣠⣴⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠛⠛⠛⠿⣿⣿⠟⠋⠙⠻⢶⣤⣌⣉⣙⣛⣋⣉⣠⣴⠾⠛⠉⠙⠿⣿⣿⠟⠋⠉⠉⠉⠛⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠉⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣶⣤⣀⣀⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣦⣤⣴⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣏⣁⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣼⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠋⠉⠉⠉⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠉⠉⠛⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⢠⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣃⢀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⢀⣼⣿⠿⠿⠿⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣶⣶⣶⣿⠿⠃⠀⠀⠀⠀⠘⢿⣿⣶⣶⣴⣶⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⡠⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣴⣿⡀⢀⡖⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢀⣴⣾⡿⣽⣿⣿⣿⣿⣿⣿⡿⣷⡞⠫⡏⠉⠐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢰⣿⣇⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⠥⠀⡀⠄⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠳⠶⠚⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠀⠀⠠⡿⠿⠿⠟⠛⠋⠉⠉⠀⠀⢀⣀⣤⣴⡖⡀⠀⠀⠀⡄⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣀⣤⣤⣶⣶⣿⣿⣿⣿⠟⢩⣗⠠⠀⢰⣷⠈⢠⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⢠⣀⣿⠀⠀⠋⢀⣤⠀⣀⣍⠴⣍⡛⢿⣿⣿⡿⡟⢿⠿⢿⣿⠛⠍⠀⣼⣿⡀⠒⣸⣿⠀⣤⠆⢀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⢸⣼⡿⠞⠀⢈⠗⠲⣂⠄⢈⡅⠉⢁⡀⠆⣉⡩⠛⠉⠁⢀⠐⠂⡄⠑⠐⠭⣢⡀⡀⢨⠑⠣⠛⠻⢇⠁⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠊⠀⠀⠠⠖⠧⢀⡄⠀⠀⡀⠀⠁⠘⠋⠈⠁⠀⡀⠄⠂⠙⡀⢰⣷⠀⠠⡀⠀⠀⠈⠻⠗⡤⠀⠀⠈⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠔⠃⠀⠀⢀⠂⠠⢸⣇⣾⠀⠈⠁⠀⠀⠀⢠⡆⠈⢀⠀⠂⢠⣇⣸⣿⡀⣀⣀⠄⢀⠅⠀⠁⢠⡀⠀⢀
⠀⠀⡆⠀⠐⠀⠀⠀⠤⣀⣀⠀⢀⣠⣤⡤⣬⣍⠀⠀⠴⠄⠀⣠⡄⣺⣇⢒⠶⠖⠠⡚⠛⠙⠉⠉⢀⠄⠊⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠁⠨⠑⠠⠄⠉⠀⢀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠐⠆⠨⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠂⠈⠘⢿⣿⣶⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⡰⢠⢤⣄⡄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠄⡀⢠⡄⢠⠄⠀⠀⠀⠴⢤⢠⢠⠄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠁
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠀⠀⡄⢠⠀⠀⠀⠀⠀⠤⣤⣠⣤⣄⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣁⣤⣸⣿⣯⣴⣿⣧⣶⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⡄⢒⡀⣀⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⡿⠿⠿⠛⠛⠛⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⡟⠂⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⣿⡇⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⣛⡃⠀⠀⠤⠄⣹⣿⣏⣹⣿⣷⣦⢠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠘⣷⠀⠀⠰⢾⡗⠿⠛⢶⣶⢂⣄⡀⠀⠀⢠⠈⡄⠀⢻⣿⠀⠀⠀⠙⠛⠻⣿⠧⠜⠿⠃⠘⢻⣽⣯⠈⡶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⠀⣿⡀⠀⠀⠀⠀⠀⣀⡀⠉⠑⠈⠁⠀⠀⢨⠈⡁⠀⢸⣇⠀⠀⠀⠀⠀⠀⠛⠄⠀⠀⠠⠂⠈⠻⠓⠿⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣆⢸⣷⣶⣆⠒⠀⢈⣭⣿⡁⠀⠀⠀⠀⠀⠸⡔⢰⡀⠐⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣅⣶⣶⡄⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠹⣾⣿⣿⣷⣷⡿⢯⣉⠁⠒⠀⠀⠀⠀⠀⢘⡚⠾⣇⠀⣿⣿⣿⣿⢶⡚⢼⠗⠀⠀⣀⣠⣾⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠹⣿⣿⣿⣿⣷⣤⣿⡁⠀⠀⠀⠀⠀⠀⠰⣂⠏⢻⣶⣾⣿⣿⣿⣿⣇⣯⣤⣶⣾⠿⠿⠿⠄⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣜⢿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠠⢾⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠻⣷⣶⣄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣦⣄⠀⠘⣿⣆⢻⣿⡟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢾⣆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣷⣆⣨⣽⡟⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄⠀⠉⠻⣧⢿⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣿⣆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢹⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠡⠹⣿⣿⣌⢻⣿⣿⣿⣿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣧⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⡿⣿⣷⡆⢻⣿⣿⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⣇⠀⢀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⡂⠀⠀⠈⠽⢿⣿⡄⢻⣿⠀⠀⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣷⣶⣤⣄⣀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⡇⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⡀
⠀⠀⠀⠀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⣸⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⡿⠟⠛⢡⣿⡇⠉⠉⠛⠛⠿⢿⣿⣿⣧
⠀⢀⣤⣶⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣋⣁⣀⣀⣀⣸⣿⡇⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣷⣦⣄
⢠⣾⣿⠟⣡⠤⠶⠶⡞⠛⢆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣦⡀⠈⢷⡒⠒⣒⣒⣒⣺⣿⡗⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⢻⣿⣷⡀
⣾⣿⡇⡼⢡⠖⠒⠒⢳⠀⠈⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣳⠀⠈⣇⠀⠀⠀⢠⣾⣿⣧⡀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷
⣿⣿⡇⡇⠘⣄⡀⣀⡞⠀⠀⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⠀⠀⡏⠉⠉⠉⠙⢿⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣿⣿
⠹⣿⣷⣙⣀⠀⠈⠉⠉⢉⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⡼⠁⠀⠀⠀⠀⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠀⠈⠻⢿⣿⣷⣶⣶⣶⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣴⣤⠶⠶⡿⢤⣤⣾⣤⣤⣤⣤⣤⣴⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⡿⠋
⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⠋⠀⣸⡁⠀⢿⣿⠛⠛⠛⠛⠛⠛⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⣰⣿⣇⠀⠘⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣃⣤⢠⣿⣿⣿⡄⠀⢹⣿⡆⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠛⣿⣿⡟⠀⢿⣷⣼⣦⣿⣿⡀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⣿⡿⠀⠀⠘⣿⣿⠉⠙⢿⣧⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⢻⡇⠀⠀⠀⠹⠆⠀⠀⠿⠿⢿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡠⠐⠈⣉⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡐⠃⠨⠭⢉⣏⠁⠀⠀⠀⠀⠀⠀⢠⠤⠊⢠⣠⠔⠩⣅⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡠⠴⣄⠛⠀⡄⠀⠀⠠⠜⠀⠀⠀⠖⠲⠁⡠⠳⣖⠊⠙⢡⠂⠀⠀⢤⠜
⠀⠀⠀⢀⠀⠤⠤⠀⠀⢀⡠⢚⣡⠔⠉⢢⡁⠑⢒⣚⠜⢀⠀⠀⠀⠀⠀⠔⠐⠤⡋⠉⡞⣨⠖⠒⡒⡡⣤
⠀⠀⠀⠀⠀⠀⠀⢮⠀⠁⠒⠁⠈⡢⠀⠀⠉⠚⢣⠀⡤⠉⠠⠀⠀⠰⣀⠨⠆⡰⠃⠀⠈⠁⡕⡄⢑⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠂⢀⠈⠀⠀⠀⢀⣀⡞⢄⡘⢠⠂⠀⠀⠀⠀⠀⡜⠀⠀⡠⠤⠔⠣⠯⣁⠔
⠀⢀⠀⠤⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⡌⠀⠉⠒⠔⠂⠀⠀⠀⠀⠀⣸⣀⣀⡠⠇⢀⣀⢀⡀
⠀⠀⠀⠀⠀⡔⠒⠒⠈⠇⣇⣀⣀⡀⠤⠴⠓⡖⠉⠃⠀⠀⠸⠭⡭⢽⠞⠀⠀⠀⠀⠀⢀⠏⡄⠸
⠀⠀⠀⠀⠀⠈⠁⡟⡟⢰⠀⠀⠀⠀⠀⠀⢀⣧⢀⠇⠀⠀⠀⠰⠁⠒⣑⠦⢄⡠⠉⠒⠊⣐⣠⠧⡄
⠀⠀⠠⠄⠀⠀⢠⠀⠉⡀⠧⠤⠤⠒⠉⠉⠀⣆⡼⠊⢩⠂⠀⠀⠉⠉⡀⠄⠀⠀⠀⠀⡄⢏⡠⠐⠁
⠀⠀⠉⠉⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣏⡠⠐⠁⠀⠀⠀⠀⠐⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠚⠛⠲⠦⠀⠄⢀
⣤⣤⣤⣤⣤⣤⣤⣽⣭⣭⣭⣮⣭⣯⣭⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠙⠐⢤⡤⡝⢣⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡗⠀⠀⠘⠀⡼⢀⡤⠒⠀⠀⢀⠀⠀⣜⠻⢦⣌⢱⡏⠳⡞⠀⡶⠁⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢹⣿⡏⠀⠐⠀⣅⣞⣧⢺⣾⡄⠀⠁⠀⢿⣇⡈⢿⡿⢿⣷⣣⣤⠛⢃⣘⣉⡷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢶⣿⣿⡀⠈⢄⠸⣿⢿⣿⣿⡟⠀⠀⠀⠘⣄⣹⣭⠛⢻⡀⢩⠄⠀⠋⠁⣾⣆⣻⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⣘⣛⠿⣷⡀⠘⢯⡛⢧⣿⣿⣦⠀⠀⠀⣰⣿⣧⣭⣦⣤⡁⠹⠹⠂⠀⠀⣴⠘⣏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠂⠎⠀⠈⠁⣼⢿⣿⢦⣄⠀⠀⠀⢈⣁⣀⠴⠚⠉⠈⠁⠈⠲⣝⢻⡧⢰⡄⢤⠀⠬⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠚⡡⠞⠛⣃⠀⡿⠛⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢦⡱⡄⠞⠙⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡼⠻⠟⡁⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠙⣄⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣄⠀⠀⠸⠀⢠⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢱⡆⠀⠀⠀⡄⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠠⢶⡂⠀⢀⡶⠁⠀⠀⢀⡤⢶⡚⢒⣦⠻⠀⠀⠈⠉⠀⠀⣴⡋⡽⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠑⠤⣍⡉⠉⠆⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⠈⠀⢠⡀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢤⣤⣤⣤⣤⣤⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠆⠀⠀⠀⢠⡾⠇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠀⠀⠏⠀⣼⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⡀⢨⣿⣦⠶⣆⡄⠠⠏⠙⠦⠀⠀⠀⠀⠀⠀⠈⢿⣶⣦⡤⠤⣤⣤⣶⣿⡿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣙⠇⠚⠃⣷⢾⣇⠀⢀⡀⠀⠘⠿⣶⠀⢀⣤⣀⡀⠉⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣷⣮⣸⡇⠹⣶⡅⠀⣉⣿⠂⠀⠄⠸⠀⠈⢿⠿⠿⢿⣷⣄⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡟⠋⠁⡿⠈⠉⡿⢚⣛⠰⡮⠀⠶⠆⡀⢀⠀⠀⠀⠈⠈⠉⠛⠲⠠⠴⣴⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠐⣄⠘⠁⠙⢃⡜⠁⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢉⡎⠠⠦⠜⠳⠈⠱⠀⠀⠈⠆⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⢀⠀⠾⢰⣿⠷⠶⠟⢶⡒⠠⠶⠀⡀⠉⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣴⣴⠀⣿⠀⠴⠆⠈⢉⠄⣀⣨⠛⢠⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢇⣨⡟⠀⣤⠄⠶⠛⣤⠻⣥⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠔⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣧⣧⣧
⠀⠀⠀⢠⢶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠒⠀⠀⡇⠀⠀⢸⠀⠁⠉⠉⠉⠉⠢⣀
⠀⠀⣠⠃⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢖⠴⠂⢼⡀⠀⠀⠀⠀⠀⠀⠈⠳⢄
⠀⡴⠁⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢉⡠⠒⠁⠀⠀⠀⠈⠑⠢⢄⠀⠀⠀⠀⠀⠀⠑⢄
⢸⠐⠂⠀⠐⠒⠒⢸⠒⠒⠒⠒⠒⠒⡴⠬⠤⡶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⢻⠚⠚⠃⠉⠁⠉⢻⠁
⢸⠀⠀⠀⠀⠀⠀⢸⢠⣶⡆⢰⣶⡄⡇⠀⢰⠓⢺⠃⢻⠛⡟⠉⢻⠙⡏⠙⡏⢹⠃⣶⡆⢰⣿⡇⢸
⢸⢀⣀⣀⡀⠀⠀⢸⠰⣿⡇⠸⣿⡇⡇⠀⠘⡇⢸⠀⢸⠀⡇⠀⢸⠀⡇⠀⢃⢸⠀⠻⠇⠀⠿⣃⣸⣀⣀
⢸⣿⣿⣿⣿⣶⡀⣸⣀⣤⣄⠀⣦⡄⡇⠀⠀⡇⢸⡤⢤⠀⢣⡔⢶⡀⣶⠳⣞⠈⠀⣿⣷⣴⣿⣿⣿⣿⣿⣿⣦⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣷⣷⣦⠀⡇⢸⡟⣿⡇⢸⣿⠉⡆⣿⣿⢋⣀⣄⠹⠿⠿⠟⠛⠛⠛⠛⠛⠛⠿
⠈⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⢿⣿⣷⡇⢸⠀⡏⡇⠀⣿⡇⠇⠒⡉⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡒⠈⠉⠫⡁⠀⠀⠀⣠⣿⣤⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠑⠤⣐⢛⣿⠹⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⣼⣿⠈⢿⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⢹⠻⠀⣿⠟⠂⠀⠈⠉⠉⠐⠒⠒⠒⠒⠒⠂
⠐⠒⠒⣲⡶⠶⢶⡖⠒⠒⢒⣶⠒⠒⠒⠒⢲⡖⠒⠒⣶⠒⠒⠒⣶⠾⢷⡖⠒⠓⣶⠒⠒⣶⠒⠒⠒⣲⡶⠛⠒⠒⠃
⠀⠀⢸⡏⠀⠀⠀⠀⢀⣀⣾⣙⣧⠀⠀⠀⣿⢷⣀⣾⣿⡀⠀⠀⣿⣀⣼⡏⠀⠀⣿⠀⢀⣿⠀⠀⠀⠻⣦⡀
⠀⣀⣈⣻⣦⣤⣤⣆⣠⣿⣉⣉⣹⣇⣀⣸⣇⣘⣿⣃⣹⣇⣀⣀⣿⣏⣁⣀⣀⣀⣻⣧⣴⣿⣀⣀⣀⣠⣿⣁⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣄⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⢡⣞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠
⠚⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡌⠦⡁⠀⠀⠀⠀⠀⠀⠹⡿⠀⢠⣶⣶⣶⡎⠀⠀⠀⠀⢀⡴⢻⡄⢀⠀⢀⡼⠋
⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠘⣏⡠⠁⠀⠀⠀⠀⠀⠀⠙⠶⣜⠀⠙⠛⠋⢢⠀⠃⠀⡠⠋⠀⢀⠷⠘⠀⠘⡄
⡟⢀⠶⣄⠀⠀⠀⠆⡀⠀⠸⢿⣛⣀⣠⣾⠃⠀⣀⢀⡀⠀⠀⣠⠞⣖⡤⠄⠲⠂⢀⡠⢤⣄⠈⢧⡀⢠⠃⠀⠀⡇⠀⢰⡾
⢀⠎⣀⡼⢃⠤⠀⣀⠉⠀⠀⠠⠥⣷⣶⣋⡀⢺⣹⡏⡋⠠⠤⢘⡷⠻⠁⠀⠏⠀⠑⣄⠖⠩⠄⠀⠻⣼⠀⠀⠀⢳⣰⠟⢣
⣼⠞⠁⠀⠀⠀⠀⠡⣤⠀⠀⠀⠘⡇⠙⠃⠒⠀⠻⠇⠷⠖⠀⠈⠀⡆⠱⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⠳⡎⠛
⠀⠀⠀⣾⡄⣀⠀⠀⠠⢤⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⠿⠛
⠀⠀⠀⠘⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠁⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⢀⠀⠂⠂⠀⠀⠀⠘⠀⠀⠀⢀⠘⠁⠀⡇⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠂⠀⠀⠀⠀⠐⠃⠐⠤⠀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⡀⠀⠀⠀⠰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠄⡤⠀⠐⠂⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢄⣤⢤⣠⠄⠤⢠⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⢻⣿⡟⠿⣿⡟⢻⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠈⠈⠈⠈⠉⠀⠈⠁⠀⠀⠀⠀⠀⡿⠿⠿⠿⠿⠷⠾⠾⠾⠿⠶⠿⠿⠿⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠂⠀⠀⢀⣀⡀⠀⠀⠀⠂⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢾⣿⣿⣿⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⣷⣾⣷⣿⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠙⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠚⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠛⡉⠉⡙⠻⢿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠟⠛⠉⠀⠀⠌⠀⠀⠈⡆⠀⠈⠙⠛⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠁⠀⠀⠀⠀⠀⠀⠈⠒⠀⠊⠀⠀⠀⠀⠀⠀⠀⢹⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⣄⡤⣠⣄⡤⣄⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠁⠉⠀⠁⠉⠀⠉⠈⠁
⠀⠀⠀⢀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣼⠀⠀⡏⢹⠉⡇⠀⠀⠋⡏⢹⠀⠀⡘⢹⠋⡇⠀⢸⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄
⠀⠀⠀⠀⡏⣀⣀⣀⠀⢀⣀⣀⠀⠀⣀⣀⡀⠉⠀⠀⡟⢻⠛⡇⠀⢠⠛⡟⢻⠀⠀⠘⢺⠋⡇⠀⠈⠀⣀⣀⡀⠀⢀⣀⣀⠀⢀⣀⣀⡀⠁
⠀⠀⠀⠀⡇⣯⣥⣼⠀⢸⣼⣼⠀⠀⣧⣧⡇⠀⠀⢀⣇⣬⣤⣅⠀⢨⣤⣥⣸⡄⠀⣬⣬⣥⣥⠀⠀⠀⣧⣧⡝⠀⢸⣼⣼⠀⢸⣤⣧⡇⠄
⠀⠀⠀⠀⡇⣷⣶⣼⠀⣸⣼⣼⡀⢀⣧⣧⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣷⣎⠀⣸⣼⣼⡀⢸⣶⣶⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡤⢤⢤⠀⠈⡏⠛⠛⠛⠋⠉⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⡇⢰⢲⢲⠀⢰⢲⢲⡆⠀⡖⡖⡆⢰⠀⠀⣧⣼⣤⠃⠀⠇⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⡖⡖⡆⠀⣴⢲⢲⠀⢰⢲⢲⠄⡇
⠀⠀⠀⠀⡇⢘⢹⢹⠀⢸⢙⣛⡇⠀⡏⡏⡧⠀⠀⠀⡇⠸⠠⠇⠀⠀⠀⠀⠀⡴⢠⠀⠀⠀⠀⠘⠀⠀⡏⡏⡇⠀⣿⣻⢹⠀⢸⢹⣙⠄⠂
⠀⠀⠀⠀⡇⠚⠒⠚⠂⠘⠓⠚⠃⠐⠓⠒⠓⠈⠀⠘⠃⠐⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓⠓⠀⠛⠓⠚⠀⠘⠓⠚⠂⡀
⠀⠀⠀⠀⠣⠄⠤⠤⠤⠤⠤⠤⠄⠤⠠⠤⠄⠴⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⢤⠴⠄⠤⠤⠤⠤⠠⠤⠤⠠⠤⠠⠤⠤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⣀⣤⣀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⣸⣶⣿⡿⢷⣼⢿⣿⣿⠎⡷⣶⣵⢆⣙⡦⢛⠳⣮⡸⣄⡽⣼⣿⣿⣟⣿⣿⡿⣭⣙⣾⣷⣤⣿⠟⠸⣻⣿⣛⣿⡷⠿⣾⣷⠁
⠀⠀⠀⠀⠀⣸⣿⢿⡟⢂⣤⣆⣻⣿⣧⣀⡌⣹⣬⡞⢯⣦⣏⣠⣯⡗⣭⡙⢻⣿⣿⡟⠸⣿⣗⠈⢹⣿⡙⡯⡙⡦⢔⠱⡅⢻⣿⣟⢶⣿⠿⡆
⠀⠀⠀⠀⠀⢹⣾⢷⣝⠾⣧⣻⣏⣿⡝⡱⣿⢃⣾⡟⠟⢻⡝⣿⣻⣯⣎⣁⣿⣷⡏⠛⣶⡄⣈⠺⣿⣿⠄⠑⠣⠭⣘⣦⢰⡟⣺⣿⣈⡻⣤⡇
⠀⠀⠀⠀⠀⢺⣯⣶⢈⣝⢛⣽⣦⣿⠛⢿⣾⡏⠉⠀⡀⢸⣱⣿⣿⠛⠾⣯⣿⣯⢺⡇⠉⣴⡍⢛⠓⠺⣦⢼⢳⣤⣤⡈⠁⢸⣇⣯⠽⣿⣿⡧
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣽⢫⡯⡿⣿⡷⠺⣿⣿⣀⠀⠀⣠⣿⠿⣿⣛⡂⡸⣿⢜⣯⣿⣶⣿⡓⣾⣦⣴⠻⣆⡵⣿⣿⡾⠄⠈⢿⡇⢤⡼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠿⢻⣿⣿⣧⣿⣿⣾⠾⠁⠈⠏⠀⢈⣡⡖⠉⢋⣁⣹⣋⣿⡏⠛⣹⠿⣧⡘⣫⠿⢻⣿⡟⢿⣼⡗⠾⡆⠉⠿⣮⣥⡜⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣿⣞⢹⣿⣷⣶⣷⣶⣶⣶⢿⣿⣧⡀⠀⢹⣻⡏⠉⣠⣴⡟⣓⡿⢸⡿⠀⡀⠙⢿⣿⠿⣏⢐⢳⣤⡀⠁⢏⣇⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣛⣻⣿⣻⣿⣿⣿⣿⣿⣿⣤⣤⣦⡀⠀⠀⢈⣿⣏⣹⣿⣼⣓⠩⠁⣿⡄⠀⠉⠀⠺⣿⣶⣿⠖⣽⢏⣿⡄⠘⢿⡅
⠀⠀⠀⠀⠀⣶⢻⣿⣿⣿⣿⣿⣯⣽⡻⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢻⣜⡿⡖⢮⠞⠛⢃⣾⣷⣦⣄⠀⣸⠿⠯⢋⣿⡏⣾⣿⠱⠀⣼⠇
⠀⠀⠀⠀⠀⣹⣿⢭⣽⣿⠿⣿⣛⣷⠁⠐⠀⠠⠀⠀⠈⠉⠉⠁⢸⡿⣿⣿⣏⣹⣌⣏⣛⠛⠉⠈⠈⠉⠀⠀⣇⣴⣶⣿⢿⣳⣿⣿⡿⢠⣿⣡
⠀⠀⠀⠀⢈⣿⢠⣎⣡⣿⣯⡓⡽⣄⣀⠤⠀⠰⠀⠀⠀⠀⠀⠀⠈⣿⣯⣯⣷⣌⡿⠟⠁⠀⣀⡉⠈⠁⠉⢹⡏⢀⢃⢹⣿⣷⣿⣿⡄⢿⣯⡏
⠀⠀⠀⠀⠀⠙⣪⢀⠹⣿⡛⢻⣽⠿⠟⢶⣴⣀⣀⣀⠀⡀⢐⡂⢀⣯⣉⣹⣉⣀⣀⣤⡴⠊⠉⠃⠀⠀⠀⡼⠀⡘⠁⠨⣟⠷⣿⡇⠀⠀⣻⡇
⠀⠀⠀⠀⠀⠼⠛⠉⠁⠉⣉⡠⣶⣾⣞⣿⣿⣿⡇⠈⣿⡏⠉⢹⣿⣿⣿⣟⡿⣭⢟⣍⣿⣿⣷⠂⠄⠀⠊⠉⠀⢻⡄⠀⠙⢦⣬⡏⠐⢰⣯⡅
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣇⠀⣻⣿⣾⣿⣿⣿⣷⢀⡿⢿⠀⠸⠿⠿⢿⡿⠿⠾⠳⠾⠿⠿⢿⠇⠀⠀⠀⠀⠀⢘⣟⢦⣀⣈⣯⣿⡘⡎⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣠⡽⠛⣿⡏⠉⢙⡻⢤⣷⠀⠞⢻⡄⡀⠠⢙⡀⠀⠠⠶⢶⣶⠎⠀⠀⢀⡀⠀⠀⢈⡏⠉⠛⠓⠉⢻⠃⣤⠘⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣤⠶⠾⣯⣄⢸⠟⠛⠛⠋⠀⢸⣿⣇⠀⡚⠛⢻⣆⠀⠀⢀⠃⠀⠀⠠⠊⠇⠀⠀⠸⠙⠳⠶⣀⠠⢼⣷⠋⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠈⠀⠀⠀⠀⠈⠙⠓⠶⢦⣄⠠⣀⡉⠁⣤⣣⣖⠁⠈⠀⠀⠞⠀⠰⠎⠀⠀⡄⠀⠀⠇⠀⠀⠘⠻⢦⣠⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠋⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠌⣼⣷⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣀⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡠⣇⢾⣿⢁⣴⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠚⠄⠟⠀⠴⢿⣏⣰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠂⠉⡔⠳⣶⣿⣿⡏⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣾⣿⣿⣥⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣎⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⠀⢈⢀⣙⣋⣩⣿⣿⣿⣿⠟⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢶⡛⠿⠊⠁⠈⣰⡿⠯⣤⣸⣿⣿⣿⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣥⡴⠀⡂⠀⠉⣄⣀⣾⣿⣟⣉⣁⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠀⠈⣳⣊⣿⣿⣿⡿⢲⣴⢟⣿⣿⠟⠛⣯⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣶⡰⣯⣿⠀⣿⣹⣿⣿⣿⣿⣿⣿⠀⣠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠻⠿⣶⣿⣿⠿⠿⠛⠋⠁⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠋⠉⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢂⣴⠟⣡⣾⣷⣌⠻⣦⡐⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⠟⣡⣾⡿⠿⠿⢿⣷⣌⠻⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⠟⣡⣾⡿⢡⣾⡿⢿⣶⡙⣿⣷⣌⠻⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⠛⠛⠛⠛⠛⢋⣴⠟⣡⣾⣿⣿⡇⢿⣿⣧⣬⣽⡇⣿⣿⣿⣷⣌⠻⣦⡙⠛⠛⠛⠛⠛⠛⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣴⣿⣥⣾⣿⣿⣿⣿⣿⣎⡛⠿⠿⣋⣴⣿⣿⣿⣿⣿⣷⣬⣿⣦⣽⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣛⣙⠻⣿⣿⢟⣋⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣙⡻⣿⣿⠟⣋⣛⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣿⣿⡇⣿⡇⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⢸⣿⢸⣿⣿⡆⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⣿⡇⣿⡇⢿⣿⣿⢸⣿⡟⣛⣛⣛⣛⣛⣛⢻⣿⡇⣿⣿⡿⢸⣿⢸⣿⣿⠇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠶⠶⠶⠶⣿⡷⠶⠶⠶⢾⣿⡇⠿⠿⠿⠿⠿⠿⢸⣿⡷⠶⠶⠶⢾⣿⠶⠶⠶⠶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⡇⣿⡇⣿⣿⣿⢸⣿⡇⣿⣿⡇⢸⣿⣿⢸⣿⡇⣿⣿⣿⢸⣿⢸⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣈⣛⣛⣃⣿⣇⣛⣛⣛⣸⣿⡇⣿⣿⡇⢸⣿⣿⢸⣿⣇⣛⣛⣛⣸⣿⣘⣛⣛⣁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣭⣭⣥⣬⣭⣭⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⡇
⣿⣷⠇⢳⣾⡇
⣿⣿⣳⢺⣿⡇
⣿⣿⣿⣿⣿⡇

⠀⠀⢀⣠⣶⠾⠿⠿⠿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠿⠿⠿⢶⣦⣀
⠀⣠⡿⠋⠁⠀⢀⡀⠀⠀⠈⢿⣆⠀⢀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⣾⡟⠀⠀⠀⡀⠀⠀⠈⠻⣷⡀
⣰⡿⠁⠀⣴⣾⣿⣿⣿⣾⣦⣼⡿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣄⣾⣿⣿⣿⣿⣷⡄⠀⠘⣿
⣿⠃⠀⣼⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⡀⠀⢹
⢿⣇⠀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠁⢀⣿
⠈⠻⣦⣌⣻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣋⣤⡾⠋
⠀⠀⠈⠙⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠉
⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡩⠔⠒⠉⣉⡉⠑⠒⠬⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⣾⣿⣿⡇⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣄⣨⣿⣏⢀⡄⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⣧⠀⠀⠀⠙⠋⠁⠉⠋⠀⠀⠀⢰⠇⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣄⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣀⣤⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⢙⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣟⠉⠻⢷⣦⡀
⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠋⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⢰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⡀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⠀⣿⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⢹⡧
⠀⠀⠀⠻⣧⣀⠀⠀⢀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⢀⣠⡿⠃
⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣶⣤⣀⣀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠉⠉⠉⢹⠉⠉⠉⠉⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣄⠀⠀⠀⠀⣀⣴⣿⣦⣄⠀⠀⠀⠀⣀⣴⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠉⠉⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⡔⠋⠉⠓⣄⢹⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣸⣀⣀⡤⠴⠚⠚⠒⠦⠤⣄⡀⡴⣉⣤⣄⡀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡅⠀⠀⠙⡆⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢀⡟⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠭⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣀⡤⠬⣿⣀⣀⡀⢠⣶⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡞⠁⠀⠸⣿⣿⣿⣿⡝⠫⣄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡇⠀⠀⠀⠈⠙⠋⠉⠀⠀⠈⣇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢒⡞⠙⠢⣝⠲⠤⢤⣀⣀⣀⠤⠚⠀⠀⠀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⢀⡞⢀⣀⣀⣀⣉⡓⠲⠤⠤⠤⠤⠤⢤⣶⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⢀⡴⠟⠋⠁⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⢀⡎⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢸⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡴⠒⢶⡲⠤⣼⣦⡀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⣸⠟⢠⣦⣇⠀⠀⠀⢙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⣷⣿⣷⠀⡏⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢹⡿⠋⡼⠁⠀⠀⠀⠀⠘⢷⠦⣀⠀⠀⢀⠔⠊⢉⠉⠛⢶⡦⡀⠀⢸⢻⡀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠒⠒⠛⠋⠉⠙⠮⣝⢲⢿⣶⠄⠻⠟⣠⣄⢱⠹⣄⡟⠀⠉⠙⡷⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⣴⣾⣷⣶⣌⠋⣸⠀⡏⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣿⣿⣿⠷⠃⡰⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⠭⠭⠤⠴⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠻⠛⠻⠟⠿⠻⠿⠟⠟⢿⡿⠿⢻⣤⡿⠿⠟⠻⠛⠛⠛⠻⠿⠟⠻⠿⠟⠛⠛⠟⠛⠛⠿⠻⠿⠛⠛⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⡀⢠⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠶⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁

⠀⠀⠀⠀⠀⠉⠉⠁⣀
⠀⠀⠀⡖⠐⣷⢦⣄⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠁
⠀⠀⠀⠁⠀⠉⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠂
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠀⠆⠰⠀⠆⠰⠀⠚⠀⠆⠐⢀⠆⠰⢠⣆
⣶⣤⣤⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⣦⣶⣶⣴⡿⣶⣶⣶⣷⣶⣴⣶⣾⣿⣷⣶⣾⣿⣶⣧⣾⢿⣦⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠲⣼⣴⣄⠤⠤⠀⠀⠀⠀⠀⠈⠑⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣵⣿⡿⣟⢯⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⢠⠃⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠰⠠⡀⡀⠁⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⢰⢏⠠⡼⠳⣄⣠⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡰⣿⣿⣷⣤⡠⠄⠸⣿⣿⣿⣿⣶⣦⡀⢸⣿⣯⣡⣆⣼⡯⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠿⠁⠀⠈⡹⣿⣿⣿⣿⣿⡗⠈⢻⣿⣿⣿⢹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣦⠀⠈⠻⣿⣿⣿⣿⡿⢁⡤⠈⠻⠛⠃⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⢐⣸⣿⣿⡇⠀⠀⠀⢨⣉⠡⠄⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠟⠋⠙⠛⠁⠛⠃⠀⣀⣤⣤⣙⣧⡀⠀⢀⣠⣴⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⢀⡀⢀⢀⢀⠻⣿⡿⣿⠛⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠈⠈⠈⣈⢁⣀⡠⠋



⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢳⣸⠳⣤⠟⣆⠞⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠒⠒⠒⠒⠒⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⣿⡆⣿⡧⣶⣷⢸⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿
⠀⠀⠀⠀⠀⠀⢰⡶⣦⣰⠲⣧⠖⣤⠶⡆⠀⠀⠀⠀⠀⠀⣿⠘⠛⠁⠛⠃⠛⠋⢸⠀⠀⠀⠀⠀⠀⡔⢆⡰⢲⣿⠒⣶⢲⡀
⠀⠀⠀⠀⠀⠀⢸⡷⠦⠤⠤⠤⠤⠤⠴⣷⢛⣛⡛⢛⣛⠛⣿⢸⣿⡇⣿⡇⣾⣷⢸⠋⠛⠛⠛⠒⢲⡷⠶⠶⠶⠖⠖⠶⢾⡀
⠀⠀⠀⠀⠀⠀⢸⡇⣶⣶⣶⣾⡦⣶⡆⣿⢸⣿⣿⣿⣿⠀⣿⠈⣛⠃⠛⠁⠙⠉⢸⠀⣿⣷⣿⣿⢸⡇⢻⣿⣾⣿⣿⣿⢸⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠛⠛⢙⣛⡃⠛⠃⣿⢈⣛⡋⢛⣋⠀⣿⢸⣿⡇⣿⡏⣿⡿⢸⠀⠻⠋⠙⠋⢸⡇⢹⣟⣙⣿⣙⣋⢸⠆
⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣼⣿⣧⣿⡇⡧⢸⣿⣿⣿⣿⠀⣿⠘⣻⣁⡟⢇⡹⡋⢸⠀⣿⣿⣾⣿⢨⡇⢹⣿⣿⣿⢿⡿⢸⡆
⠀⠀⠀⠀⠀⠀⢸⡇⣭⣥⣨⣭⡅⣭⡅⡧⠈⠛⠋⠛⠋⠀⣿⣴⠗⣴⣾⣿⣮⠓⣼⠀⠛⠛⠙⠛⠰⡇⣴⣶⣴⣶⣶⣦⢸⡅
⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⡧⣿⡇⣧⢸⣿⣿⣿⣿⠀⣿⠈⣾⣇⡫⢍⣸⡆⢸⠀⣾⣷⢸⣿⠀⡇⠿⠿⠛⠿⠛⠟⢸⠇
⠀⠀⠀⠀⠀⣴⣾⣷⣦⡀⠀⠁⠀⠈⢠⡷⠈⠛⠛⠛⠛⠀⣿⠀⣿⣛⣿⣿⣿⣷⢸⠀⠙⠛⠘⠛⢸⡇⠀⠀⣠⣶⣿⣿⣿⣷
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣤⣼⣿⣦⣠⣿⣿⣿⣿⣷⣦⡀⡇⠀⣿⣿⣿⣿⣿⡿⢸⡇⣀⣠⣶⣄⣼⣿⣷⣤⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢇⣀⣿⣿⣿⡿⠿⠿⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠹⣿⠿⠿⠿⢿⡿⠟⠉⠉⠛⠛⠿⠿⠛⠛⠛⠿⡿⠒⠀⠀⠈⠉⠉⠉⠉⠙⢿⡿⠿⠿⠿⠟⠛⠛⠻⠿⠿⠿⠿⠿⠿⣅
⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⢠⣶⣋⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄
⠉⠉⣩⣿⠟⠛⠻⠿⠉⠉⢉⣽⠿⠛⠻⣿⣍⠉⠉⠉⣿⡏⠉⠉⠉⢹⣿⠉⠉⠉⠉⠙⣿⠟⠻⠉⠉⠉⣩⣿⠟⠛⠻⠏⠉⠉⠉⣿⡟⠿⠟⠉⠁
⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⣿⡆⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⢠⣤⣿⣤⣤⡀⠀⠀⣿⠁⠀⠀⢀⣤⠀⠀⣠⣿⣧⣤⣄
⠀⠀⢻⣧⣄⣀⣀⣤⠀⠀⠻⣧⣀⠀⢀⣰⡿⠁⠀⠀⣿⣇⣀⣀⠀⢸⣿⣀⣀⡀⠀⠈⣿⣀⣀⠀⠀⠀⢻⣦⣀⠀⣸⣿⠀⠀⠈⣿⣏⣉⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒⠐⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠒⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠠⠐⠂⠐⠂⢄⠈⠢⠄⠂⠀⠈⠉⠉⠁⠀⠐⠠⠆⣀⡠⠐⠂⠐⠂⠄⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠐⠁⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠄⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡜⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠀⠆⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠀⠀⢰⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠠⠆⠉⠁⠢⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠁⢠⠄⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠘⠀⠀⠀⠀⡔⠀⢡⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠡⡀⠈⠢⢀⠀⠀⠀⢀⠠⠐⠀⢀⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠑⢄⠀⠀⠈⠠⢀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⢀⠠⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠈⠀⡄⢀⠀⠀⠉⠀⠈⠉⠀⠀⡀⠤⠂⠁⠀⠀⠀⠈⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠃⠀⠘⢦⠀⠡⡀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⣀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠂⠉⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⠀⠀⣀⠠⠐⠃⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠘⠂⢄⡀⠀⠀⣀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⢀⡤⠒⠋⠓⠒⢤⡀⠑⢄⠀⠀⠀⠀⠀⠀⡀⠀⢀⡤⠒⠊⠑⠲⢤⠀⠑⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⢀⡜⠁⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠤⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢂⠀⠀⡌⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠤⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⠀⢰⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠁⠹⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠌⠀⠀⢢⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠉⠒⠤⠤⠴⠒⠋⡠⠔⠁⠀⠀⠀⠀⠈⠢⢈⠙⠒⠤⠤⠴⠚⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠐⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣴⣤⣥⣤⣀⣀⣐⣀⣼⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣘⣾⣽⣗⡶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠿⠟⠀⠀⠀⠀⢴⡦⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣽⠟
⠀⠀⠀⢀⣿⡃⢸⡏⠉⠉⢹⡟⢻⡟⢻⡇⡇⠀⠀⠀⠀⠀⢠⣾⣿⡆⢸⣿⡏⢹⣿⣿⠛⣟⠛⡟⠛⣿
⠀⠀⠀⠸⣿⡟⠘⠃⠐⠀⠘⠛⠛⠛⠛⠃⠓⠂⠀⠀⠀⠀⠘⣿⣿⠣⠼⠿⠧⠼⠿⠿⠿⠿⠿⠿⠿⠿⠤
⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⣿⠉⢹⡇
⠀⠀⠀⣸⣿⣧⣠⣤⣤⣤⣾⣿⣿⣦⣤⣤⣤⣤⠀⠀⠀⠀⣸⣿⣿⣷⠶⠶⣶⣿⣿⣿⣷⡶⠶⠶⠶⣶
⠀⠀⢠⣿⣿⣿⡞⡟⡟⣿⣇⣼⣨⣿⠻⠿⠟⡏⠀⠀⠀⠀⣿⣿⣿⣿⠬⠭⣿⡟⠉⠙⠛⠋⠉⠉⠉⠛
⠀⠀⠘⢻⣿⡟⠓⠿⠿⠏⣿⣟⣛⣛⣛⣛⣛⣿⡇⠀⠀⠀⠉⣿⣿⡏⠒⠒⠛⠋⢀⡍⠁⠀⠉⠁⠁⢁⡀
⠀⠀⠀⢸⡿⡇⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⢿⠇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⢀⣀⡀⠀⣀⣠⣤⣄⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦⠄⢀⣀
⠀⠀⠀⢀⡻⣟⡁⠀⣏⣉⣉⣉⣉⣉⣉⣉⣹⠀⠀⠀⠀⠀⢀⡻⣿⡁⠀⠀⢠⣤⣤⠀⢴⡦⠀⢀⣤⣿⣿⠧
⠀⠀⢰⣿⣻⣿⣿⣤⣧⠤⠤⠤⠤⠤⠤⠤⢼⠀⠀⠀⠀⢰⣿⣻⣿⣿⡆⢠⣼⣾⣿⣀⡀⣐⠛⠻⠿⠟⠃
⠀⠀⠻⣿⣿⣿⣿⣿⣇⣀⣃⣓⣐⣃⣚⣀⣸⠀⠀⠀⠀⠸⣿⣿⣿⡿⣷⣾⣿⣷⣿⣿⣶⣿⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⣿⣿⡇⣿⣏⣀⣀⣹⣭⣭⣯⣭⣽⣿⣇⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⢀⠀⠀⠒⠂⢈⠁
⠀⠔⠊⠀⠀⠀⠀⠀⠀⠁⠀⠐⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⡒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠁⠂⢀
⠀⠀⢰⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠺⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⢰⡟⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠻⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⡚
⠀⠑⢌⠀⠁⠀⠀⠀⢈⣉⣁⣈⡐⠀⠀⠀⡪⠈⠁⠀⠀⠀⠀⢨⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠊⠂⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⢐⠀⢤⠤⠄⠀⡰⠛⠉⠀⠀⠀⠀⠀⢀⣤⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣄
⠀⠀⠀⠀⠀⠀⠰⣁⠈⠙⠒⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⢃⠹⡀⠠⠀⠀⠀⠀⣒⠲⠶⠄⠀⠀⠀⡰⢁⠍⠉
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠄⠂⠄⣀⠈⠀⠁⢀⠠⢐⡨⠊⠁
⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠬⣀⠧⠄⠒⠁
⠀⣯⢷⣀⠀⠀⡼⠷⠰⠦⠤⠄⠄⠐⡀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠘⠖⠀⢠⠄⠄⢀⡀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠐⠁⠀⠀⡠⠊⠑⡤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠤⠀⢰⡀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢄
⠀⠀⡀⠆⠣⣝⢎⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠈⠑⠂⠒⠂⡏⡟
⠀⠈⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠠⠄⠒⠊⠉⠉⠉⠉
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠤⡀⠐⢄⣠⢄
⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢎⠔⠋
⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠁⠋⠭⠕⢒⣂⣐⣒⡈⠥⠭⠐⠂⠙⠳⢄⣀⣀⣐
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⢻⣿⣿⠛⢻⣿⣿⡟⠛⣿⣿⡟⠛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡧
⣶⣤⣦⣤⣦⣤⣶⣤⣶⣤⣦⣤⣦⡄⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⡇⠀⣿⣿⡇⠀⣿⣿⡇⢠⣤⣦⣤⣦⣤⣤⣤⣤⣴⣦⣴⣦
⣿⣿⠛⢛⣿⣿⠛⢻⣿⡟⠛⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠛⢻⣿⡟⠛⣿⣿⠛⢻⣿
⣿⣿⠀⢈⣿⣿⠀⢸⣿⡇⠀⣿⣿⡇⣿⣿⣿⠙⢻⣿⣿⠋⠋⠉⠋⠉⢻⣿⣿⡟⠋⣿⣿⡇⢸⣿⣿⠀⢸⣿⡇⠀⣿⣿⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⢀⣿⣿⠀⢸⣿⡇⠀⣿⣿⡇⣿⣿⣿⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⡇⢸⣿⣿⠀⢸⣿⡇⠀⣿⣿⠀⢸⣿
⣿⣿⣦⣴⣿⣿⣤⣼⣿⣧⣤⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣤⣼⣿⣧⣤⣿⣿⣤⣼⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⡀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣧
⠀⠀⣿⣿⡿⣻⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠽⠁⠀⠙⠺
⠀⠀⣿⡿⣿⣿⣿⣋⣙⣝⡫⣿⡭⠿⠟⠛⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⡟⣒⣀⣚⣠⡆⠤⢧⢨⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠿⢇
⠀⢀⣷⢻⣇⣹⣧⠻⣦⣦⠀⢀⣠⣄⡀⠀⠘⢛⠁⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠘⠋⠀⠀⠀⠀⢀
⠀⠼⢷⣊⠹⣖⣙⣭⢧⠁⣴⣿⣿⣿⣿⡆⠀⠀⠀⣭⣩⣤⣌⣨⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣄⡀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣉⡀
⢠⡶⠎⠵⠿⠯⠷⣵⠆⠘⢿⠿⢿⣿⡏⠁⠀⠀⠀⠋⠛⠛⠛⠛⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢰⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢹⣿⣯⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢠⣿⠀⠀⠀⠀⢸⣿⡟⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠐⠀⠰⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⡧⠀⠻⡿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⢠⣿⠋⠀⣼⡇⠀⠸⡿⠁⠀⢿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠤⠄⠀⠀⠀⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠙⠁⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠄⡀⠮⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠓⢦⣠⡴⠖⠚⠛⣩⠟⠉⠛⠛⠲⠶⣯⡀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⡼⠁⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣿⣯⣤⣤⣤⡤⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⠞⠁⣏⠀⠀⠀⣹⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢰⠃⠀⠀⠈⠙⠉⠉⠁⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠸⡄⣀⠀⠀⢰⡀⠀⠀⢀⡄⠀⢀⡇⠀⠀⠀⢀⣴⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢦⣙⠮⣕⣒⣚⣉⣉⣉⣁⣤⠴⠋⠀⣀⣠⠶⠋⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠉⠙⠒⠓⠲⠶⠶⡶⠶⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠰⣯⠀⠹⠟⢋⠆⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠹⣧⣠⠞⠁⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠶⠶⢶⣤⣄⡀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠉⠛⢷⣤⡾⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⠶⠚⠛⠉⠛⠛⠿⣦⡀
⠀⠀⠀⠀⠀⣼⠏⠀⠀⣀⣄⣀⡀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⣀⣀⡀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⡟⠀⢠⡞⠉⠉⠉⠛⢷⣄⠀⠀⠀⠀⠘⢷⡀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⢀⡴⠞⠛⠛⠛⠻⢷⣦⠀⠀⠹⣇
⠀⠀⠀⠀⠀⣇⠀⣾⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠘⣷⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⣿
⠀⠀⠀⠀⠀⢿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣿⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣿⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣇⢻⡀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢠⡟⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⢿⡄⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠙⣮⢷⣄⠀⠀⠀⠀⠀⣠⡟⠀⠀⣠⡿⢁⣰⠦⠤⣄⣀⣀⣘⣦⣀⣠⣤⣤⣾⣷⣼⣆⡀⠀⠀⠀⠀⠀⣀⣴⠟⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣷⣶⡤⠶⠾⠋⢀⣠⡾⠿⠚⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠈⠻⣿⣟⡶⠶⠶⠶⢟⣋⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⢀⢠⣔⢞⡩⠧⠦⠀⠀⢰⠊⢁⢂⠠⠀⠀⠀⠀⡠⠐⢶⠟⠀⡀⠄⠀⢀⡀⠠⠌⠄⠀⠀⢠⠃⠀⠀⠀⠰⠀⠘⢻⠃⠀⠙⠘⠀⠀⡁⠂
⠀⠙⠳⠑⠁⠀⠒⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠇⠀⠠⠀⢀⡸⠆⠸⠐⡐⠈⠁⠀⠀⠀⠀⠍⢐⡂⠀⠂⠀⡠⠈⢆⠀⠀⠨
⠀⠨⠈⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⢒⠄⠀⠈⠆⠀⠀⠠⠐⠀⠀⢀⠀⠀⡔⢠⡆⠊⠀⠐⠈⠀⠴⠑⠂⠀⠀⠀⠀⠀⠅⠘⠄⠀⠀⠀⠀⠄
⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡾⠋⠀⠀⠑⠤⠄⠀⠒⠒⠁⠃⠚⠃⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡀
⠀⠀⠀⠁⠂⠀⠈⠀⠀⠀⠀⠶⡝⠁⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⣀⠠⠀⠀⡀⠀⠁⠀⠀⠀⣎⣀⠀⠐⠉⣀⡘⢁⡃
⠀⠀⢀⡄⣀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⡄⠴⢟⣀⢄⠀⠀⠀⠀⡀⠂⠈⠀⠈⠀⠀⠀⠀⠀⢤⠳⡀⠀⠀⠀⠀⠀⡈⠁⠉⠁
⠀⠀⢢⣿⣍⣪⡓⡄⠀⢀⠀⡴⢂⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠿⡻⠆⢀⠀⠀⡈⠀⠀⠢⠀⢀⠀⠄⢞⠁⠀⠀⠉⠀⡂⠀⠐⠁⡂⡢⠈⠠
⠀⠀⡸⣣⣟⢿⣏⠆⠀⠀⠤⣫⣙⣤⠂⠀⠀⡠⠊⢠⠀⠀⠀⢴⡤⠚⠁⠀⠠⠇⠀⠀⠀⠀⠡⠀⠀⡀⠄⠰⠀⠀⠀⠁⠠⠄⠀⠀⡐⠀⠁
⠀⠀⠀⠈⠉⡍⠘⠋⠀⠐⠀⠋⠹⠦⠁⠠⡊⠀⢎⢀⠀⡀⠀⠀⢀⣀⣠⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠄⠂⠀⠀⠀⠣⠈⠀⠀⠁⠁⠊
⠀⠀⠀⠀⢠⣃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢌⡁⠀⠀⠠⠘⠂⠀⠀⠰⡁⢀⡆⠀⠀⠀⠘⠀⠀⠣⠂⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠑⠲⠀⠀⠀⠀⠀⠘⠀⢀⣇⢀⡀⠀⣀⣄⠀⠄⠂⠀⠀⠀⢀⠀⠀⠀⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⠀⠀⠀⠀⠀⠀⠀⠆⣰⡦⢄⠀⠀⢀⣀⣀⡀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⢤⡠⠔⠀⠀⠨⠄⡠⠊
⠀⠀⠀⠀⠈⠒⠐⠀⠀⠀⠀⠀⠀⠁⠂⠤⣁⠀⠀⠈⠢⠈⢡⠍⠀⢴⣛⠀⠀⠉⠁⠉⠀⠀⠀⡢⠄⠀⠀⠀⠊⠑⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⢀⢀⣠⣀⠐⠀⠀⠎⠀⢃⡀⠃
⠀⠀⠀⠀⠀⠈⠂⠠⠜⠀⠀⠈⠁⠰⠀⠀⠀⠀⠀⠀⡁⠤⠤⠀⠠⠠⠀⠠⠀⠤⠤⠠⠈⠉⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⡄⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⡀⠀⠀⠀⢀⡤⠄⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠁⠁⠂⠶⣀⠀⠀⠀⢰⠀⠀⠀⢘⠀⠒⠀⠀⢣⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢀⠂⠁⠄⠀⠁⠐⣆
⠀⠀⠀⠀⠀⠀⠀⠐⣋⣽⣁⢤⡀⠀⣹⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⡆⠀⠀⣾⡀⠀⠀⠀⠀⠀⡠⠄⠀⠀⡼⠈
⠀⠀⠀⠀⠀⢀⠤⢶⠭⣦⠙⠠⠀⠀⢇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢃⣀⡀⠀⠀⠀⠂⠀⠠⢠⡗
⠀⠀⠠⠢⠀⣀⠀⠨⢙⠀⠀⡀⠀⠐⢨⠄⠀⠀⠈⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉⠉⠛⠶⠶⠶⠶⢦⣼⡰
⠀⠀⠠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣛⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⡟⢛⣙⠛⣻⢛⣿⢻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠿⠿⢿⣦⡀⢀⣀⣀⣤⣤⣀⣀⡀⢀⣴⡿⠿⠿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⣠⣿⡿⠟⠛⠋⠉⠉⠙⠛⠻⢿⣿⣄⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠉⠉⣀⣀⣀⣀⣀⣀⠉⠉⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⢀⡴⠋⠉⣤⣤⣤⣤⠉⠙⢦⡀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⣾⠀⠀⠀⠙⢿⡿⠋⠀⠀⠀⣷⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣦⡀⢿⡀⠰⣤⣀⣸⣇⣀⣤⠆⢀⡿⢀⣴⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠁⠀⣹⣿⣾⣷⣄⡀⠉⠉⠉⠉⢀⣠⣾⣶⣿⣏⠀⠈⠙⠿⣷⣄
⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⢀⣾⡟⠁⠈⠉⠛⠿⠿⠶⠶⠿⠿⠛⠋⠁⠈⢻⣷⡀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠈⢿⣧
⠀⠀⠀⣼⡟⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⢻⣧
⠀⠀⠠⣿⡇⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢘⣿⠄
⠀⠀⠀⢿⣧⡀⠀⣀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀⠀⢀⣼⡿
⠀⠀⠀⠀⠙⠻⠿⠛⣋⣿⣧⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣼⣿⣙⠛⠿⠟⠋
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠉⠉⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠟⠋⠉⠉⠙⠻⣷⣄
⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷
⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⢠⣿⠟⠛⠛⠛⠛⠛⠛⠻⣿⡄⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣤⣤⣤⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣄⣤⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠄⠀⡀⢀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣀⣀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠄⠀⢠⠀⠀⠀⠀⠄⠀⠠⠀⠠⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠐⠂⠀⠀⡆⠒⠖⠒⠆⠀⠀⠂⠐⠂⠒⠀⠀⢰⠒⠰⠂⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠆⠀⠀⢆⠀⡂⡀⠆⠀⠠⠂⠀⠀⢐⠀⠀⠰⠀⠐⠀⠰
⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠤⠀⠄⠀⠀⠄⠀⠄⠀⠄⠀⢠⠄⠠⠄⠠⠄⠀⠠⠄⠠⠄⠠⠀⠀⢠
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠆⠀⠀⡆⠀⠆⠀⠆⠀⠀⠀⠐⠀⠀⠀⠀⠰⠀⠰⠀⠰⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢔⢀⡒⠀⡆⠀⠀⣆⠀⠂⢐⠆⠀⠠⡂⡐⠂⢐⠀⠀⠰⣂⢐⡂⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠤⠀⢄⠀⠀⠄⠀⠄⠀⠄⠀⢠⠄⠠⠄⠀⠀⠀⠠⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠄⠀⠀⡆⠀⠆⠀⠆⠀⠀⠄⠠⠄⠠⠀⠀⢰⠀⠰⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠆⠀⠀⡆⠀⠂⠀⠆⠀⠀⠆⠀⠀⠐⠀⠀⠰⠀⠐⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠤⠤⠤⠤⠤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁⠀⠀⢀⠀⠀⡀⢠⣀⠀⡀⢠⠀⢀⠀⠀⠀⠁⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠑⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⡀⠀⢀⠀⡀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡄⢀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠤⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡢⢄⠠⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⣿⣭⣷⣄⣤⣤⣀⣤⢖⣲⣦⡀⠀⠀⠀⠀⢠⠖⠒⠲⣄⣠⣤⣄⣴⢉⠉⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠘⣯⡷⢚⣭⣶⣶⣶⣮⣵⣯⣹⣿⡇⠀⠀⠀⠀⡇⢰⣉⠆⠀⠀⠀⠀⠀⠉⠲⣇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⡞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠘⣦⠁⠀⠀⡀⠀⠀⠀⠀⣠⡈⢇
⠀⠀⠀⠀⠀⠀⠀⢸⡧⣿⢟⣿⣟⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠟⡀⠄⣲⣖⠩⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠘⣇⣇⢈⣻⣋⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢀⣹⣋⠀⡇⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣭⣭⣤⣾⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠈⣳⣄⡀⠀⠂⠄⠈⠄⣊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⣿⣿⣿⣿⣿⣿⡏⣿⣷⡀⠀⠀⠀⠀⣠⠊⠉⢳⠈⠁⠒⠒⠂⠁⢉⢳
⠀⠀⠀⠀⠀⠀⠀⢠⣞⡿⣼⣿⣿⣿⣿⣿⣿⣇⣿⣿⣷⠀⠀⠀⢰⠃⠀⠀⡌⠀⠀⠀⠀⠀⠀⠈⠎⢧⡀
⠀⠀⢀⣤⣤⣀⢠⣏⣾⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⢳⠀⣠⠤⣄
⠀⠀⣾⡟⠻⣿⣿⣻⣽⡼⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠃⠀⠀⢸⠤⠐⠦⠁⠀⠀⠀⠀⠀⠀⠀⢸⠋⢺⡟⣡⠒⢾⣇
⠀⠀⢻⣇⠀⢿⣿⣿⣿⣷⣝⣿⣿⣿⣿⣿⣯⡾⠛⠻⣿⡇⠀⠀⡎⠠⠒⠢⡌⢡⡀⠀⠀⠀⢀⡠⠉⠀⠈⠁⠇⠀⣾⡇
⠀⠀⠈⠻⣦⣾⣿⣿⣿⠟⠉⠉⠛⠛⢿⣿⣾⠁⠀⣰⣿⠃⠀⠀⢹⡠⠀⠀⠠⠀⣏⡟⠓⠋⠉⠙⠦⣀⠀⠀⠂⣨⠞
⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠻⣽⣦⣶⡿⠃⠀⠀⠀⠀⠱⢕⡠⢘⣠⠏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⢠⣤⣀⡀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⢠⣤⣀⡀⢀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣿⠀⠙⠗⣾⠋⠉⣿⣿⣬⣯⣈⣀⣀⡀⠀⠂⣠⡿⠀⠙⠓⣿⠉⠉⣿⣿⣼⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠿⣄⣀⣀⣴⡟⠀⢰⣧⣰⡷⢈⣽⣿⣿⣿⡿⠟⠯⣄⣀⣀⣴⡏⠀⢸⣧⣸⡇⣩⣽⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢈⣹⣯⣽⡿⢷⣿⣿⣿⣿⣿⣟⣹⡿⠛⠁⠀⠀⣈⣹⣯⣽⡿⢷⣿⣿⣿⣿⣿⣟⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡍⠀⠀⠀⠀⣿⣿⣿⣿⣍⡛⠿⣄⡀⠀⣠⣴⣿⠉⠀⠀⠀⠘⣿⣿⣿⣿⣍⡻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣅⣸⣇⠀⠀⠀⠀⠘⣿⠉⠋⢉⡟⢷⣬⣹⣶⣿⣁⣸⡇⠀⠀⠀⠀⠹⣿⠉⠋⢹⡟⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡟⢹⡇⠀⣀⣀⣠⣤⣼⠇⠀⠈⠻⣿⠀⠀⠀⢸⡏⣹⡇⢀⣀⣀⣠⣤⣼⠇⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⠿⣿⣛⣩⣭⣥⣾⠛⢻⣄⠈⢀⣠⣿⣳⣶⣶⣾⠷⣟⣛⣩⣭⣤⣾⠛⣿⣀⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡉⠙⠿⣇⣀⣿⡃⠈⠉⠹⣿⣿⠿⠯⢿⣿⢻⣿⡉⠛⢿⣅⣀⣿⠁⠉⠙⢹⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⣄⠈⢻⣿⣇⣄⢀⣤⣿⢁⠀⠀⠀⠀⠀⠈⣽⣦⣀⠙⢿⣿⣄⣀⣠⣼⣿⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⡿⠀⠙⠛⣿⠃⠉⣿⣿⡴⣧⣌⣀⣀⣀⠀⠀⣠⡟⠀⠙⠛⣿⠁⢉⣿⣿⡼⣧⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠻⣤⣀⣠⣴⡏⠀⢰⣷⣼⡷⣨⣽⣿⣿⣿⡿⠛⠻⣄⣀⣠⣼⡇⠀⣸⣧⣼⡇⣨⣽⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣽⣧⣼⠿⠿⣿⣿⣿⣿⣿⣿⣹⡟⠛⠀⠀⠀⣀⣽⣧⣽⠿⢿⣿⣿⣿⣿⣿⣿⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣯⣙⠿⣤⡀⠀⣠⣾⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣬⡛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣸⡧⠀⠀⠀⠀⠘⣿⡉⠃⢨⡟⢳⡦⣽⣿⣿⣀⣸⡇⠀⠀⠀⠀⠹⣿⠉⠃⢸⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢹⡇⢀⣀⣤⣤⣤⣼⠇⠠⠀⠻⣿⠁⠈⠀⢰⡏⣹⡃⣀⣀⣠⣤⣤⣼⠃⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⡿⣿⣩⣭⣥⠶⣾⡋⢻⣄⣈⣀⣴⣿⣳⣶⣶⣾⢿⣟⣩⣭⡵⢶⣾⠉⣻⣄⣀⣀⣴⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣅⠙⠻⣇⣀⣿⡃⠈⠉⠙⣿⡿⠛⠫⠿⢿⣻⣿⡈⠙⠿⣆⣠⣿⠁⠉⠉⢹⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡷⣄⡈⢻⣿⣧⣄⣀⣴⣿⢀⠀⠀⠀⠀⠀⠀⣽⢦⣄⡈⢻⣿⣤⣄⣠⣴⡿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣈⢂⣠⡿⠀⠈⠛⣿⠃⠀⣿⢿⡶⣷⣤⣤⣤⣀⣈⢁⣰⠟⠀⠉⠛⣿⠁⢈⡿⢷⡾⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠻⢤⣀⣤⣴⣏⠀⢸⣷⣼⣿⣠⣾⣿⣿⣿⡿⠛⠳⢤⣀⣤⣼⣇⠀⣸⣷⣼⣇⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡷⠾⠿⠻⣿⣿⣿⣿⣿⣿⣵⠟⠋⠀⠀⠀⣠⣽⡧⠾⠟⢻⣿⣿⣿⣿⣿⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⡄⠀⠀⠀⠀⢿⣿⣿⣿⣦⣙⠻⢦⣀⠀⣠⣾⣿⡀⠀⠀⠀⠈⣿⣿⣿⣿⣮⣙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⣼⡧⠀⠀⠀⠀⠘⢿⡁⠁⢨⣟⣻⡶⢽⣿⣿⣄⣼⡇⠀⠀⠀⠀⠙⣿⡀⠁⢸⣟⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠃⠀⠀⠀⠀⠀⠺⠃⠀⠀⠙⠟⠀⠀⠀⠘⠋⠘⠃⠀⠀⠀⠠⠀⠚⠃⠀⠀⠛⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⡩⢍⠲⡀⠀⣀⡠⠶⣆⣀⡀⠀⡔⢉⠭⣉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠨⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⣠⡀⠀⠀⠀⠀⣠⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢛⠗⣥⣶⣬⡑⠻⡁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠈⠀⠛⠿⠛⠀⠀⡅⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠦⣀⠘⢄⣐⠺⢐⡠⠔⢁⡤⠊⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠉⠐⠒⠒⠒⠂⠉⠁⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⢺⡤⠒⠠⣀⠀⠀⠀⠀⠀⠀⡠⠔⠒⢯⡒⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠁⠀⠈⡆⠀⠀⠀⠀⡜⠀⠀⠀⠀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⡄⠀⠀⠀⠀⡇⠀⠀⠀⢀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠃⠀⠈⠉⠀⠐⠒⠂⠀⠀⠒⠒⠂⠈⠉⠁⠸⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡠⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⠤⡀⠀⣰⣿⣶⠀⣠⣶⣦⡀⢀⠔⢢⠀⡼⠁⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⠢⡫⣓⠾⠿⠛⠒⠛⠿⠿⢖⣱⡶⠁⡔⠀⢠⠚⡄⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣙⢎⠀⠁⠀⠀⠀⠈⠀⣰⢋⠤⢊⡠⠒⠁⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⡠⠛⡷⣄⠀⠀⠀⢀⠔⠋⢱⠊⠁⠀⠀⠀⠀⡇⠀⢀⡾⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡌⠀⠀⠈⠪⢑⡒⠚⠁⠀⡠⡏⠀⠀⠀⠀⠀⠀⢧⣰⠏⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡇⠀⠀⠀⠀⡰⠉⠹⢨⠋⢰⠁⠀⠀⠀⠀⠀⠀⢘⢆⠠⡈⠢⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠒⠁⠀⠠⠁⢀⠔⠂⢉⡀⠔⠁⢠⡀⠈⠢⢄⠀⠀⠀⠀⠀⠈⠂⠓⢍⣢⠜
⠀⠀⠀⠀⢀⠄⢺⡁⠀⠀⠀⠀⢀⠔⠁⠀⠘⢤⣀⡬⡶⠤⣀⠀⠈⢲⠀⠀⢑
⠀⠀⠀⡰⠁⠀⠀⠻⣤⠀⠀⡠⠋⠀⠀⠀⡮⢛⠕⠂⡀⠤⠤⠇⣴⣁⣀⣀⡜
⠀⠀⢀⠃⠀⡠⠊⠀⠈⣳⠊⠀⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⡰⠁⣀⠀⠈⡁⢔⡄
⠀⠀⢸⠒⠁⢀⡠⠊⡠⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠑⢄⣸⢈⡼
⠀⠀⠈⠑⠒⠓⠂⠉⠂⠂