Fishcore Emojis & Symbols

⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠰⣆⡀⠢⡄⠦⢴⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈
⠀⠀⠀⠀⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠲⣠⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠋⠀⠉⠲⣄⡄
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⢹⠖⠧⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠑
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠔⠠⠄⠀⠀⠀⠠⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰
⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⠠⠄⠦⠖⠁⠀⠀⠀⠀⠀⠀⠀⠠⠐⠊⠁⠁⠀⠀⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⣾⠀⠀⠀⠀⠠⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠤⠒⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⡔⠁⠀⠀⢰⡆⠀⣠⢰⠁⠅⠠⠉⠴
⠀⠀⠀⠀⠀⠀⠀⡆⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡤⣀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠠⡀⠀⠀⡞⠀⠀⠀⠀⠸⣧⠄⠀⠘⠓⠷⠜⠔
⠀⠀⠀⣷⠀⠀⡘⠀⢠⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡉⠉⠉⠉⢁⠎⠀⠀⠀⠀⠑⡀⢰⡇
⠀⠀⠀⡟⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣠⠃⠀⠀⠀⠀⠀⠀⠈⠚⠃
⠀⠀⠐⠀⠀⠀⢡⠀⢡⠀⠀⠀⠀⠀⠀⠀⢠
⠀⢀⠁⠀⠀⠄⠀⠑⠀⠑⠀⠀⠀⡐⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⠀⠀⠀⠀⠀⡀
⠀⠸⠀⠐⠀⠀⠀⠀⠀⠄⠀⢠⡐⠁⠀⠀⠆⠀⠈⢂⠀⠀⣀⡠⠀⠘⠂⠀⠉⠑⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⢀
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠣⢄⡀⠀⠀⠀⠀⠀⡇⠀⠛⢀⠱⠀⠀⠀⠀⠀⠈⠉⠽⣗⠸⣏⠙⣲⠲
⠀⠀⠀⠀⢄⠀⠀⠀⠐⠇⣀⠀⠀⠀⠀⠃⠀⠀⠐⠀⠀⠀⠀⠀⠠⠙⠓⠒⠲⠒⠒⠒⠊⠁⠀⠀⠀⠀⢰⡆⠀⠀⢚⣿⠐⣯⠀⣺⢴
⠀⠀⠀⠀⠀⠐⠠⢠⠤⢤⠙⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡷⣨⡗⠀⠟⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢳⡗⠉⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠾⠃⠜⠋⣘⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⡀⡀
⠀⠀⠀⠀⠐⠗⠀⠀⠀⣀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠦⣶⠁⠀⠀⠀⠀⡀⠉⠁⠖⠀⠀⠀⠀⣤⣴⣶⣤⣤⣠⡄
⠀⠀⠀⢠⣄⠀⢄⡴⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠘⠂⠀⠀⠀⠘⠛⠀⠘⠃⠀⠀⠀⠀⠈⠙⠋⠉⠁
⠀⠀⠀⠀⠁⠀⠀⠀⣀⡠⣤⣶⠖⠀⠀⠀⡀⠀⠀⢀⡄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠠⡆⠀⠲⠃⠀⣀
⠀⠀⠀⠀⢀⡤⣾⢉⣿⡇⣿⡟⠀⢀⣴⣿⠃⠀⠀⣀⠀⠀⠶⣿⣿⣿⣿⣿⠶⠶⠾⠀⠀⠀⠀⠐⠖
⠀⠀⢀⣴⣿⠁⣿⢰⣿⡇⣿⣇⣠⣾⣿⠃⠀⠀⠀⠉⢀⠀⠀⠀⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣇⡀⠀⠀⠀⣀⣀
⠀⠀⠘⣿⣿⠀⣿⠘⣿⡇⣿⡿⢿⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣟⡋⠉
⠀⠀⠀⠈⠻⣇⣿⡇⣿⡇⣿⡇⠈⢿⣿⣇⠀⠖⠀⠄⠑⠀⠀⢀⠤⠂⠀⠂⠰⢂⠀⢀⠀⠀⠀⠀⠉⢻⢿⡛⠛⠛⠛⠋⠉⠁⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠈⠻⣧⣿⣇⣿⡇⠀⠀⢻⣿⡆⠀⡆⣠⠀⡀⠀⠁⠀⢴⠁⡰⠤⣎⠄⢁⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡀⠀⡆⠀⣄⠄⡘⢤⢠⠖⠁⡄⠀⠈⡔⠁⡀⠇⠀⡉⢡⠐⢇⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠶⠘⠃⢭⠘⢂⠤⢱⠉⡄⠘⣤⠁⡘⢰⢰⠀⡧⠂⠓⠱⠀⠀⠂⠐⣀⠂⠀⡀⠈⠂⠄⠀⡀⡀⠀⠐⡀⠀⠀⠁
⠀⠀⠀⠀⠀⢠⠐⡴⢤⡄⠂⣲⡀⢈⢢⠇⠀⠉⢠⠀⢰⠋⢀⠳⢆⠃⠐⠀⠚⠃⠈⠇⠈⣤⠁⠃⠀⠲⡄⡄⠁⢀⠂⠁⠀⢀
⠀⠀⠀⠀⠀⠀⢊⠀⠢⢈⠲⠄⠉⢄⢨⡠⠆⡇⠈⠦⠀⢱⠎⡠⢸⠇⠐⢄⢱⠐⠘⣃⠀⠂⠃⠱⠆⠀⠀⠃⠰⡏⠀⠀⠆⢦⠚⠨⠀⠁⠆
⠀⠀⠀⠀⠀⠀⠋⠠⡀⠙⠣⣀⠒⠂⠘⣇⠀⢠⠴⠃⡄⠎⡠⠐⡡⠂⠀⠀⡙⠀⠀⣁⡀⠋⣀⠈⢀⢈⠇⡀⠀⢀⠀⡆⠄⠸⠔⡠⠖⠒⡀
⠀⠀⠀⠀⠀⠀⣈⡁⠚⠓⢠⡀⣉⠍⠀⠌⠑⢯⡀⠰⣀⡯⠤⠀⠤⠥⢐⡀⠃⡄⠠⠈⠇⠃⡘⠔⠂⠃⠀⢃⠀⠃⠱⡇⢊⡀⠈⡤⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢄⠀⠨⠍⣀⡇⠀⢈⣝⠐⢂⡀⠝⠦⣼⡀⠂⠁⠰⡀⠢⠈⠂⠀⢀⠆⠀⠀⢄⣣⣈⣲⡉⠀⠙⡆⠚⠀⠀⠂⠁⠠⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠂⢀⠠⢤⠽⡃⢱⣄⢰⡴⠧⠠⠀⠤⠋⡉⠂⠀⠉⠀⢁⢙⠢⢈⡃⠀⠐⢂⠀⠶⠈⣇⠤⢎⠐⢆⠇⠀⠁⡈⢀⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⢣⣴⠙⠣⡈⠢⡀⢀⠱⠊⠁⣲⠯⡁⠀⣷⠈⠑⠠⢦⢠⠙⠠⣰⢀⠔⣂⠉⣠⡤⠤⣴⠆⠶⠒⡚⠡
⠀⠀⠀⠀⠀⠀⠀⢀⠘⢤⡟⠂⠁⠀⠀⠠⡀⢀⡶⠚⠍⠀⠀⢸⠀⣿⡴⢁⠂⢀⡁⠂⡀⠈⡏⢀⠼⡁⢀⡀⠀⠀⢀⣴⡶⠛⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣌⢐⡖⠀⠀⠀⠀⠠⣀⡬⠂⠁⠀⠈⠀⢠⠀⡀⣫⣀⣼⢀⣸⣡⠀⢁⠐⣷⠍⢶⠿⠏⠀⠀⠀⢄⠉⠀⢠⣶⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠠⢸⡅⠀⠀⠀⠀⠀⡸⠁⠀⠠⠂⠀⠀⣼⠋⣉⠓⢠⠍⢙⣧⣀⢒⠚⣤⡄⠶⣆⠀⠀⠰⠟⠀⠀⢀⣀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠠⠄⠤⡤⠯⢤⡀⣠⣤⡀⠀⠏⠛⣍⣟⠀⣘⡧⠐⡒⠯⣠⡞⡋⢲⣛⢓⣾⢟⣃⡐⠶⣟⠋⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⢞⣃⢒⣾⡁⠐⠀⣈⡟⠀⠈⠙⠢⠤⠙⠢⠤⠥⠤⠚⠀⠘⠞⢣⡌⠡⣆⠉⢹⠂⠩⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠹⠃⠈⠀⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣤⠤⠔⠂⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡯⣠⡞⢉⡀⠈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⣡⠞⠥⠀⠀⠀⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⢛⣃⡼⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⣼⣿⢃⣴⠟⢡⠔⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣾⣿⢣⣾⠋⣀⠏⠀⠀⠀⢀⣤⣶⣿⣶⣥⠤⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡘⢿⣿⣿⣿⠏⠠⣼⠀⠀⠀⠑⣾⣿⣿⣿⣿⡴⠀⠀⠀⠀⠀⠢⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⣥⣴⣿⣿⡿⠀⢲⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠙⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠯⠇⢈⣽⣿⣷⡀⠄⠀⠻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⡿⠿⠛⠛⣋⡃⠐⠀⠀⢹⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⡆⠀⠂⠰⣆⠗⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠛⣲⣿⢣⣴⡌⠃⠀⠀⠀⠑⠫⣿⠀⠀⢀⠔⣻⣿⣿⣿⣷⣴⣷⡄⠂⢲⠀⠴⢁⣿⣴⡀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣾⣿⢿⣾⣿⡇⠀⠀⠀⠀⠀⠀⢹⢇⡴⠋⢀⣿⣿⣿⣿⣿⣿⣿⣿⡔⠂⠆⠠⠂⢼⡇⡗⠠⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠘⣡⣤⣧⠀⠀⠀⠀⠀⠀⠀⡿⠀⢠⣿⣿⣿⣿⠏⠸⢿⣿⣿⣷⠁⠃⠰⠂⠸⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⣴⡷⠀⢸⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣏⡀⠀⠀⢠⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣦⡀⠀⠀⠀⣼⠁⠀⠀⠹⢿⡿⢿⣆⠀⠀⣿⣿⣿⡏⠀⠀⠄⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠟⠛⠿⢿⣠⡤⠜⠉⠒⠀⠀⠀⠀⠀⢹⣿⣷⣾⣿⣿⣿⣧⠈⠱⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠕⣛⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠛⢪⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⣹⣿⢟⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡿⠋⣾⣿⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠋⠀⠀⣻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⠀⠀⢀⡼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠋⠀⠀⠀⠘⣇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠋⠀⠀⠀⡀⠀⠙⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠰⣄⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣚⣺⣿⣷⢮⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡏⢿⠄⠉⣹⣿⣝⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢹⡎⣿⠠⣄⠀⠘⠿⣽⣳⣜⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⠤⠻⢸⡀⠈⠀⠀⠀⣒⣃⣹⡆⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠹⣷⣤⡴⠿⡿⢛⡹⠿⢿⠿⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠾⢏⡙⢿⡄⠀⢾⣿⡶⢿⣶⣤⣼⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢛⣴⣮⢀⡈⣷⢴⡀⢀⣦⠀⣸⣿⠿⢿⣻⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⣾⠄⢸⡇⠀⠈⠛⠉⠙⢉⣷⣦⡱⣟⠻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⢻⣿⠟⣠⠀⣿⠚⠂⠰⠧⠠⠈⠙⢾⡇⠻⣻⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢺⣿⣾⣇⡀⣿⢄⣀⠢⣤⠌⣤⠀⠀⣿⠿⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡯⠘⣿⣯⣾⢃⣿⠈⠉⢀⣀⡀⠠⢶⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠐⣿⡿⢁⢸⡿⢠⣆⠈⣉⠃⠴⠆⣸⠇
⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣵⠃⣾⠇⡀⢀⠀⠛⠀⠠⢀⡟
⠀⠀⢸⡿⡿⡟⠳⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢼⣿⡟⣸⡟⠀⣀⡈⠸⠧⠔⢀⡾⠁
⠀⠀⠀⣿⢧⠙⣟⢱⡾⣽⣄⠀⣀⣠⡾⢾⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢳⡟⠀⠉⠛⠡⠀⡶⢀⡾⠁
⠀⠀⠀⠘⡷⣆⠸⡀⣧⣼⢩⢱⠏⡙⠀⣼⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣱⠟⠐⠀⠑⠞⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠐⣄⣄⠳⡸⣿⣾⣾⣷⣥⢜⠃⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⢤⣤⡔⢀⣠⡾⣫⠞⠁⣀⠰⠆⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠈⠳⣄⣝⣮⣿⣿⣿⡿⠷⠊⠀⠀⠀⠀⠀⠻⣿⢶⠦⠀⠀⠈⣠⣾⠿⠋⠡⠠⣄⠉⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⠇⠀⠀⠀⢠⣀⣀⠀⠠⠤⠤⠴⠒⠚⠉⠁⠀⠠⠈⠀⠂⠀⢀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀⡀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢆⣠⡜⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠛⠛⠛⠻⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⣴⠟⣥⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃
⠀⠀⠀⠀⢀⡾⠋⠐⣧⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⣠⡴⠋⢠⡏
⠀⠀⠀⢠⡟⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣤⠞⠉⠀⠀⣼
⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠻⣧⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠈⠳⣄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣻⡿⣿⢻⣻⡿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠈⠻⣭⡛⢽⣶⣄⠀⠀⣀
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⢿⣿⣶⣤⡀⠀⢀⠀⠀⠀⢻⣟⣯⣻⡽⡽⣷⢷⣿⣽⡿⡿⡿⣿⣦⡀⠈⠀⠀⠀⠈⠻⣶⡽⢿⣧⠐⢙⡆
⠀⠀⠀⢸⣿⣷⣄⠀⠀⠀⠘⢯⡻⠿⣿⣆⠈⢦⡀⠄⠀⢿⡾⣷⢷⢿⡻⡞⣟⣷⣻⣻⣝⣽⣾⣷⣄⠀⠀⠀⠀⠀⠉⠀⠀⠀⡇⠀⠁
⠀⠀⠀⣾⣿⣿⣿⣧⡀⠀⠀⠠⠿⠛⠉⢻⠀⠸⠇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⠘⠛⠛⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣀⠜⠀⠀⣀⣤⣶⢿⣿⢿⣿⡇⣿⣟⣩⣿⣡⣿⣇⣼⣿⣡⣿⣯⢿⣾⣿⣿⣿⣦⣄⡀⠀⠆⠚
⠀⠀⠀⣟⢿⣷⡝⣿⢿⣿⣆⠀⠀⠀⠀⢀⣤⠾⣻⡿⠞⣿⡷⢾⣿⢥⣿⣿⣨⣿⣩⣟⣩⣿⣥⣿⣋⣏⣿⣿⣿⡿⠛⠛⢿⣿⣦⡀
⠀⠀⠀⡿⣿⣿⣶⣟⣳⣿⣿⣆⠀⣀⣴⣿⡷⢤⣿⣇⣼⡿⢑⣿⣯⢸⣿⢥⣿⣟⣽⣟⣼⣿⣣⣿⣫⢽⣿⣿⣿⠀⢾⣿⠂⣻⣿⣿⣄
⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣟⢯⣦⣿⣶⢺⡿⠲⣿⠏⣻⣿⡖⢾⣿⡞⣿⡥⣿⣧⣼⣿⢸⣯⣥⢸⣿⣿⣿⣷⣤⣤⣴⣿⡿⢛⣙⡀
⠀⠀⠀⣿⣿⣿⢿⣯⣿⣿⣧⠼⡷⠲⣧⢺⣶⠾⣿⡛⣿⠏⢻⣿⡖⢿⣷⢶⣿⡷⣿⡶⣫⣾⣿⣿⣿⡿⣿⣿⣿⣿⡿⢿⣿⣿⠰⢛⣩
⠀⠀⠀⣿⣿⣿⣟⣻⣿⣿⣷⣶⣟⠚⡷⢺⣷⢴⣷⠶⣿⣿⢿⣿⡶⣿⡾⢴⣷⢶⡟⣽⢿⣾⢽⣻⣿⡇⢻⣿⣿⣿⣿⣾⣿⣿⣿⡿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠻⣿⣷⡾⡗⣾⣧⡴⣿⣭⣼⣿⡥⣿⡯⣼⣿⣠⣷⣿⣿⣟⣯⢗⣿⣷⠀⢝⢿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⢿⣾⣿⣿⣿⣯⢿⡟⢀⠀⠈⠙⢿⣶⣝⡯⣥⣿⣽⣡⣿⢥⣾⣥⣼⣧⢾⡿⣿⣻⣭⢶⣻⠵⣻⣷⣔⠍⣋⠟⣻⠟⠁
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠘⠀⠀⠀⠀⠉⠻⢿⣷⣯⣥⣻⣯⣤⣿⡝⣬⣯⡴⢷⡹⣿⣿⣽⣶⣿⣿⣿⣿⣷⠶⠛⠁⢠⡄⠲⠴
⠀⠀⠀⢸⣿⣿⣿⣷⣿⡏⠀⠀⠀⢲⡅⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣾⣧⣽⣿⣿⣾⣿⣶⣽⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⢵⣄⠄⠈
⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⡿⣿⠋⠀⡀⠐⠀⠀⢀⡤⠤⡄⠀⠀⠈⢷
⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⠀⠘⠙⢢⠀⠀⢀⣿⣿⣿⣿⣿⠿⢋⣾⡿⣫⣾⣟⡿⣽⡿⡽⠃⠀⢳⠇⠀⠀⠀⠈⠀⠀⣿⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢹⡿⠋⠀⠀⠀⠀⢀⣴⣿⠀⠀⠛⠛⠛⠋⠉⠀⢀⡾⣫⣞⡵⣻⢟⣞⣾⠟⠁⠀⠀⠈⠀⠀⢀⣤⣴⡶⣻⡿⠀⠘
⠀⠀⠀⠀⠘⠀⠀⠀⢲⣶⣾⡿⣩⡇⠀⠀⡀⣀⠂⠀⠀⢠⣞⣿⣷⢟⡾⣳⣿⠟⠁⠀⠄⣂⠂⠀⢠⣾⣿⣿⠟⣱⡿⠃⠀⢼⡎⠈
⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⣯⡾⠋⠀⠀⠁⢸⡇⠀⠀⣰⣿⣿⣿⣷⠿⠚⠉⠀⠀⠀⠠⡾⠃⠀⠠⠿⠿⣯⣽⡾⠋⠀⠀⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠘⠋⠛⠻⠏⠀⠀⠀⠀⠀⠘⠀⠀⠘⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠃⠄⠈⣀⡠⠶⠏⠀⠀⠉⠀⠀⢠⠤⠤⠖⠚⠛⠋⠉⠁⠀⠀⠀⠛⢁⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠠⠀⠀⠀⠀⠀⠀⡀⠂⠀⠇⠀⠀⠀⠀⠈⠀⠂⠀⠀⠄⢀⠀⠀⠂⠀⠀⠀⢀⣀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⡄⠈⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⡀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠰⠂⠀⠀⢀⡀⠛⠛⠁⠄⠀⠀⠀⠀⠐⠀⠀⠁
⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⡀⠀⠌⠁⢀⡀⠀⠀⠀⠤⠒⠀⠉⠁⣀⠀⠀⠀⠀⡀⢈⠁⠀⠀⠐
⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⠈⠀⠀⠀⠘⡈⢁⠄⠀⠀⠀⢀⠀⣤⢀⠀⠀⠀⢄⠀⠀⠉⠀⠠⠀⢀⢀
⠀⠀⠀⠀⣤⠂⠀⠁⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠟⠁⠀⠀⠀⠀⠀⠀⠢⠀⢎⠀⠀⢀⢂⠰⠂⠀⠀⢀⠀⠿⠛
⠛⠂⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠒⠙⢓⠆⠀⠈⠃⠒
⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠠⠆⠃⠉⠐⠀⠂⠁⠠⠀⠀⠀⠀⠀⠀⢠⣄⠤⠤⠠⠤⣤⣄
⢉⢉⡉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠄⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠓⢦⡀⠀⠂⡀⠄⠀⠀⠀⠀⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠞⠛⢓⠆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠂⢀⠀⠀⠀⠉⠀⠀⠀⠀⠄⠈⠀⠠⡄⠁⠀⠈
⠀⠀⠀⠀⢀⣢⡘⠃⠢⠢⠀⠃⠠⠄⠀⠀⠀⠀⠃⠀⢠⠀⠀⠀⠀⠐⠛⠿⠀⡀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢢⡀
⠀⡀⠀⠀⠉⠀⠀⢦⢤⠀⠀⠂⢀⠠⠄⠀⠀⠀⠀⠀⠈⣀⠄⠐⠛⠁⠀⠀⠀⠀⠀⠑⠂⠐⡀⣀⣀⠥⠶⠀⠀⠐
⠀⠁⠀⠀⠀⡀⠀⠀⠀⠙⠃⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠦⠤⡀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠈⠫⠉⠙⠿⣆⠀⠀⠀⠀⠈⠀⢀⣀⣸⡇⠀⠀⠀⠠⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠃⠀⠂⠀⠒⠚⠰⢀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⢀⡀⢀⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂

⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠉⠀⢀⣀⣀⣀⡲⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠳⠲⠦⡀⠀⢀⠤⡶⠀⠀⠀⢣⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠭
⠀⠀⡠⠊⡉⠀⢉⠀⠍⠉⠢⡀⢀⣤⠂⠀⠀⠀⠀⠰⢋⡀⠆⠀⠀⠂⠁⠉⣤⣔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣒⣒⣦⡀⠀⠀⢀⣀
⠀⠠⣄⠀⠀⠀⠠⠁⢀⠀⣠⣌⣆⣀⡁⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⢀⠙⢮⡇⠀⠀⠀⠀⢀⡤⠖⢊⠉⠉⡉⠀⠀⠉⠙⢲⣷⡊
⠀⠀⠀⠉⠉⠒⠒⠶⣒⠟⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠳⢤⣀⡀⢀⣀⡤⠋⠀⠀⠁⠀⠀⠀⠘⠳⠤⣄⣀⣀⣀⣂⣁⣀⡤⠖⠁⠈⠁
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⢭⡄⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋
⠀⠀⠈⠁⠀⠀⣀⣔⣓⣲⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢀⠔⠉⠀⠀⠱⢤⣌⡑⢦⠀⠠⢁⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⢀⡤⠥⣌⡡
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠶⣬⡱⢮⡣⣴⠥⠇⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⡀⠀⠀⠀⠠⠁⠀⢀⡀⠙⠀⡠⠚⠁
⠀⠀⢢⡀⠄⠀⠀⠀⠀⠒⣤⢉⣦⠟⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠄⠀⠈⢀⠀⣿⣒⣉
⠀⠀⠀⠉⠢⠤⣀⣀⣀⣻⣤⠋⠁⠀⠈⠁⠀⠀⠀⠀⠀⠰⠆⠀⠀⠁⠀⠀⠈⠳⠀⠖⠂⠀⡒⠀⠀⠀⠈⢣⠀⠀⠀⡆⠀⠀⠀⠀⢨⣦⡤⡝
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢤⣀⡜⠀⠀⠀⠀⣅⣀⠀⢄⣠⠌⠀⠀⠀⠱⣄⠀⠀⠀⡸⠛⠽⠃
⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⠿⠃
⠀⠀⠸⠤⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⣀⡬⠥⢭⢵⣆⡀⠀⢠⣶⡦⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁
⠀⠀⠀⠔⠉⠀⠀⠀⠀⠶⢀⡉⠢⡏⢘⡇⠀⠀⢀⣀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠉⠻⣟⣀⠀⠀⠀⢀⡠⠖⡲⠆⠀⠀⠀⠀⠀⢀⠀⠠⢄⠀⡠⢤
⠀⣖⠀⠀⠀⠚⠀⠀⢰⢠⡀⠀⢄⢧⣲⠇⠀⠀⠘⠚⠀⠀⠠⠊⢀⠀⠀⠀⠀⠀⠀⡈⠈⢍⢢⡀⠊⢀⠋⠀⠀⠀⠀⠀⠠⠒⠉⠉⠙⠛⢶⠃⡹
⠀⠈⠣⡀⠀⠀⠀⠀⠆⡌⠀⢂⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⢲⠆⠸⠀⢙⠀⠙⣋⣉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣜⡐⠆
⠀⠀⠀⠙⠲⢤⣀⣀⣠⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠐⠆⠀⢸⠀⠘⢀⣼⡂⠄⢅⠀⠀⠀⠀⠀⠳⣄⡀⡐⣠⡴⠓⠬⠇
⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢦⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⢀⠅⣠⡥⠊⠀⠈⠙⠚⠀⠀⠀⠀⠀⠀⠀⠙⠿⠓⠃
⠀⠰⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠀⠀⠀⠀⠀⠈⠹⣿⠖⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠂⠐⠉⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢘⣡⣆⣀⣠⠂⠊⠈⡀⠀⠔⠀⠐⠀⠀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣤⠠⠄⠀⠀⠀⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠻⣿⣿⣿⣿⣿⣿⠋⠙⠛⠀⠀⠉⠉⢻⡟⢿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄
⠀⠀⠀⠀⠀⢀⡴⠿⠛⠘⠃⣹⣿⣷⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⣿⠈⢿⣿⣿⣿⣿⣿⣷⡿⢿⡿⠁⠀⠀⠀⡀⡀⣢⣿⡟
⠀⠀⠀⠀⢀⡞⠁⢰⣷⣦⣾⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣀⣄⣀⢸⣿⠀⣿⠀⢾⡏⣹⡿⣿⡿⣿⣷⣦⣤⣤⣤⣴⣾⡿⠓⣻⣿
⠀⠀⠀⠀⡞⠀⠀⠐⠋⢹⣿⣿⣿⣿⣟⠀⡀⠀⠁⢈⣻⣿⣿⡿⢸⡏⠀⣿⠀⢸⡇⢸⡇⢹⡟⠻⠏⠳⠎⡻⠿⠿⣿⣷⢿⣿⣿
⠀⠀⠀⠈⠷⣄⢀⣽⣿⣿⣿⣿⣿⣿⢳⣿⣇⠀⢀⣼⣿⡿⠋⠀⣸⡇⠀⣿⠀⣾⠇⢸⡇⣿⠇⢀⣤⠖⠛⠻⠿⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⣵⣶⣾⣿⣿⣿⡟⢨⣿⣏⣴⣾⡿⠋⠀⠀⠀⣿⠃⢸⡏⢀⣿⠀⣿⢁⣿⣶⣿⣿⣿⣿⠀⠀⠈⠙⠿⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣟⠛⡋⠀⠀⠈⠌⠉⠙⠈⠀⠀⠀⠰⠋⠀⠞⠁⢨⣉⣴⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠉⠛⠿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⢠⣤⣦⣄⣀⣄⡠⠀⠀⢀⣤⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡽⢿⡛⠛⠛⠋⠻⢿⣿⣿⣿⣿⡿⣿⣿⣿⣽⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣠⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣯⣌⢻⣿⣾⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠉⠉⠙⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⣨⡴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣤⣆⣰⣱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠛⠻⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⡏⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣿⠟⣿⣿⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢻⣿⡷⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠁⠊
⠀⠀⠀⠀⠀⢀⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣿⣯⡾⠃
⠀⠀⠀⠀⠀⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠛⠋
⠀⠀⠀⠀⠀⣿⣿⡉
⠀⠀⠀⠀⠀⢻⣿⣿⣷⣶⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⢫⡛⢿⣿⣿⣿⣿⣷⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠗⣤
⠀⠀⠀⠀⠀⠀⠀⣹⣦⣼⣟⠋⣻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢁⣾⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣾⣏⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⡿⠁⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠋⠙⠻⠗⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⣠⣴⠿⠛⠻⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢫⣾⠟⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣤⠴⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠃

⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠐⠂⠀⢠⠀⠀⠀⠀⠐⠂
⠀⠀⠀⣠⣶⣿⣋⣹⡿⠛⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⣦
⠀⠀⠀⠈⠙⠛⣿⡿⠓⠀⠀⠀⢀⣼⣧⣴⣿⣷⡀⣄
⠀⢀⣴⣾⣿⣿⣿⠇⠀⠀⠀⠀⣾⡟⠯⣉⢻⣿⠇⢈⠀⠀⠀⠀⠀⠀⠰⠀⠀⢻⡄
⠠⣿⠟⢿⣿⣿⣥⣶⣿⣦⣤⡀⠉⠁⠀⢿⣼⢏⣶⣦⣴⣾⣷⡶⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠘⠟⠉⠻⠁⠀⠀⠉⠁⠀⠦⡀⠀⠁⠈⠁⠀⣽⣿⣿⣿⣶⣦⡀⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⠋⢉⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⣤⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠘⠛⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣶⣤⣉⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⡀⠰⡆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣧⣤⣤⣄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠻⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡜⠀⠉⠡⠀⠀⠀⣸⣿⣿⠇⠀⠠⠄⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠈⠀⠘⢣⡀⠀⠀⠀⠀⠹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠹⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠐⠀⠈⠃⣤⠀⠀⠀⠻⣿⣿⡰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡜⠁⠀⠀⠁⠀⠀⢠⣤⣷⡄⠀⠀⠘⢿⣷⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣄⠈⠉⠃⠀⠀⠀⠀⠈⢁⣤⣿⡛⢿⣆⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣦⠓⠂⠀⠀⠈⠁⡀⠀⣀⠀⠙⠂⠀⡀⠀⠀⠾⣿⡟⣾⣿⣶⣿⣦⠀⠀⠘⣿⡗⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠈⠉⠉⠉⠙⠓⠀⣀⠀⢀⣀⠠⠀⠀⠀⠀⠆⠀⠈⣀⢿⣶⣏⠻⣿⣹⣿⣿⣿⡄⠀⠀⢹⣿⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠁⢀⡴⢶⣤⣈⣢⡉⠛⠱⣶⢾⣆⠈⠰⢶⣴⣿⣿⣿⣯⣷⠟⠛⠉⢡⠀⢣⡀⠀⢸⣿⡇⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠿⠿⠃⣀⡤⠀⢸⣿⣄⠈⠿⠳⠿⠛⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠐⠂⠀⠐⠚⠉⠁⠀⠀⠠⣏⠐⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢀⣼⡏⠀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⡻⢀⣾⠟⠀⣀⣠⣤⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⢀⣰⣟⠙⠀⠀⠀⠀⠀⣸⠃⣾⡏⣠⡾⠛⣯⣝⢻⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⡿⣿⣿⣿⡿⢿⣛⣻⣿⣀⣿⣋⡀⢿⣾⣿⡄⢤⠘⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣤⣾⣿⣿⣿⣧⣿⣟⣿⣯⣽⣧⠉⣿⠇⣽⡿⠿⢿⣿⠀⠀⠸⠛⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣇⢿⣶⠟⠟⢃⠈⣱⡾⠁⣼⠿⠀⠀⣼⣿⡇⢀⡀⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢋⣀⠀⠀⠀⢈⣾⠋⠀⠄⠀⠀⠀⢰⣿⠏⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⢸⣟⠀⠀⢰⣿⠁⠀⠀⠀⠀⢀⡀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⢼⣟⢿⣤⣾⡏⠀⣰⣷⠛⢀⠀⢹⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⠀⠀⢠⣾⣏⣹⢿⣿⡅⠀⣿⠾⠛⠿⠀⡀⠈⠓⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢠⣷⣰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠂⠀⠀⠀⠛⢻⣇⠘⡉⠈⠉⠁⢄⣀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣏⠀⠀⠀⠀⠷⠀⠀⠀⠀⠻⣿⣦⣿⣄⠰⣦⣼⠿⠀⢀⣤⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣷⣤⣤⣾⣶⡆⣀⠀⠀⠀⠀⣿⣇⠀⠀⣿⣧⡀⣴⡿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⢿⠀⣾⣿⣿⣳⠌⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⠿⠋⠁⣼⣿⣿⣿⣦⡄⠀⠀⣾⠀⠈⣷⡟⣿⣿⣧⣴⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⣰⠛⠿⢯⣷⠀⡠⠛⠀⢀⣿⠿⢿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠂⠁⠀⢁⣤⣤⣿⣿⣄⣾⡟⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠘⢻⣿⣿⠟⣹⡟⣿⣷⠰⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣾⡿⣿⡁⠶⠋⠀⠿⣿⣷⠞⢿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⠈⠁⣰⣿⠻⣿⠛⠛⠛⢷⣾⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢀⡀⠀⢹⣿⣆⠙⠶⣿⣦⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⢀⡀⠀⠠⠀⢹⣷⣦⡤⠀⠀⠀⠀⠀⠀⠀⠐⢀⡼⢃⣾⣿⣿⠛⢷⣄⠈⠉⠀⠘⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠉⠀⢀⡀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⠿⣿⣽⣿⠇⠈⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠁⢀⣀⣹⣇⠀⠀⠆⠀⠀⠀⣀⠀⠀⣿⡟⣠⣾⣟⠛⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠀⠂⠀⠀⠐⣠⡏⠀⢸⣿⣿⣟⠙⣿⣆⠀⠀⠹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠖⠀⡀⠀⠀⣾⣿⣿⡄⠀⠂⠀⠀⣿⣇⠀⢸⣿⣿⣿⣄⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠾⠀⠀⠀⠀⠀⠙⣿⣿⡀⠀⠀⢠⢸⣿⡀⠀⣻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠉⠸⣿⣷⣤⣿⡙⠋⠻⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣦⣴⡿⠛⠿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⠀⠃⡘⢿⠋⠿⠏⠹⢿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠙⠿⡄⠁⠈⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢶⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠟⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢈⠀⡠⢹⣢⣠⣀⣀⠀⠀⠀⠀⠀⢀⣤⠞⠉⡡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣾⣭⣅⣠⠟⠀⢀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢡⡇
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⡿⣿⣿⣿⡿⣿⣟⣿⣿⡿⣹⡿⣿⠿⣿⠿⣿⡿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣶⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢠⠟
⠀⠀⣀⣤⡶⢿⠿⣭⣽⠋⠙⠿⣿⡓⠛⠉⠙⣚⣛⣿⣙⣋⣙⣏⡸⠏⣸⠏⢾⠟⠱⠟⡽⠋⣿⠏⢹⡿⢻⣿⠿⣿⣷⣿⣴⣆⣤⢀⡀⢀⣾⣥⣤⡾
⠐⠿⣏⠁⠀⢦⣾⣿⢗⠀⠀⠀⠨⣿⢿⣿⡿⠿⠿⠹⠟⠻⠏⠉⠙⠻⣻⣿⠖⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠉⠛⠈⢉⣙⣛⣿⣿⣿⣿⣿⢽⠁
⠶⣴⣘⡣⣰⣦⠉⠁⠀⠀⠀⡃⢠⣿⠬⣆⠀⢀⡀⠤⠤⠴⠖⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠟⠻⠋⠉⠉⠉⠻⣿⢷⡿⣇
⠀⠈⠉⠛⠿⢶⣤⣄⣀⣀⢹⣿⣼⣷⣚⣿⣿⣯⡤⠤⠤⠭⠄⠐⣛⠀⡀⣤⡄⣀⢀⡀⢀⣀⣂⣠⣴⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣭⣷⣶⣿⣿⠿⠯⠽⠿⠿⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⡿⣿⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⠛⠟⣻⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠙⠿⣍⡁⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠚⠛⠻⠶⣤⡀⠀⠀⠀⢀⡤⠐⠒⠂⠒⠢⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠰⠀⠀⠀⠀⠙⢄⡀⠀⠀⠈⠉⠛⠂⠤⠴⠂⢙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣢⣤⠰⢋⣀⣀⣀⣀⣀⣉⣨⡥⠄⡐⣚⣩⢱⠀⠀⢀⣀⡀⠀⠀⢀⠔⠁⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠿⠛⠘⠻⣤⣀⠀⠀⠒⠀⢠⠀⣠⣼⢧⣵⠎⠀⠀⠉⠁⠉⠀⠀⡂⡐⠀⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣋⢒⠤⠤⢤⣴⣮⠵⠟⠁⢠⣄⡠⠖⢠⣤⡤⠀⠘⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣤⢤⠀⠀⠀⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣠⡖⠂⠂⣄⠀⠀⠀⠀⢠⠔⠀⠙⡻⠀⠀⣌⡓⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣶⣁⡀⣦⠀⢰⡀⡇⣀⠔⠁⣀⡀⢀⣈⠑⢀⠀⡁⣀⠀⠄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠻⣾⣀⣸⠀⠀⠳⣔⣊⣒⡎⠁⠀⠀⠈⢠⠄⡧⣡⠇⠀⠐⡤⠀⠤⠤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠦⠧⠄⠂⠀⠀⠀⠈⣉⣩⣿⡦⡀⢀⣠⣾⣟⠚⠁⠀⠀⠀⠃⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠁⣤⠍⠀⠀⠁⠙⢳⠈⢳⡀⠀⠀⠀⣽⣷⣧⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠠⠴⠶⠦⠤⣤⣁⡀⠙⠄⠀⠀⠀⠀⠼⠃⠈⠀⠀⠀⠀⣿⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⠂⢤⣄⡀⠀⠀⢠⣠⣞⣫⠿⠃⢀⡀⠀⠀⠀⠀⠴⠮⣽⡀⠀⠀⠋⢻⠀⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⠋⠉⠉⠉⠁⡠⢐⡉⠀⠂⠁⠀⠀⠀⠉⠁⠢⢉⠂⠶⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠭⠇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠲⡤⠤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⢴⡠⠶⠤⠄⠀⠈⠐⠀⠴⠁⠀⣯⡟⢿⠆⢠⣶⣶⣤⡒⣒⣰⣴⠐⠻⣞⡅⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠵⠏⠀⠈⠙⠛⠀⠀⠈⠙⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠶⢶⣾⣿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠛⢻⣿⠁⠀⠀⠀⠀⠸⠿⣯⠏⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠀⠀⠀⣠⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⣀⣿⣿⣟⣿⣿⣯⣤⣤⡙⡀⠀⠀⢠⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⡶⠶⠿⣿⢿⣿⢟⣿⣿⣿⡿⣿⣿⣟⠀⠄⢀⣼⢷⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠇⠉⣹⢀⡀⣸⢿⣿⣿⣿⣿⣿⣧⠒⢛⣿⣝⣶⣿⠸⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⣿⠀⠀⢹⡆⣠⣿⣿⢻⡾⣿⣿⣟⠃⠐⢿⣿⣿⣿⡟⠠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠈⢻⡅⢹⣧⣿⣿⣿⣿⣿⠙⠻⣿⣤⣴⣿⣷⣿⣿⣿⣷⠈⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢺⣿⣦⣿⣿⣿⣿⣿⣿⣾⡷⣉⠛⠿⣿⣿⣿⣿⣿⣿⠀⠆⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣧⣭⣍⠛⢿⣿⣶⣦⠘⣏⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠏⢼⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣉⣻⣆⡿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠉⠀⠛⠛⠛⠋⢹⡿⠛⣿⣿⠉⣿⣿⣿⡇⣸⡏⢸⡇⣿⣽⣿⣷⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢀⠀⠀⠀⠀⠀⠁⣸⣿⣿⣆⢹⣿⣿⢣⣿⠃⢸⣧⡧⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡆⠈⢧⠀⠀⠀⠀⢾⣿⣿⣿⢹⣮⣿⣿⣿⣿⣇⠈⣿⣣⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣅⣷⡤⣄⢨⡛⠂⠀⣼⣿⣿⡇⢸⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣼⣀⣷⣤⣴⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡏⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠛⠷⣦⡙⣏⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⠇⠘⠛⠻⠙⠋⠕⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⡼⠁⠹⢷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⣇⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⣿⣿⡆
⠀⠀⠀⠀⢀⡾⠋⠛⠳⠀⠀⠈⠛⠛⠶⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢸⡇⠹⣿⡇
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣾⣇⣼⠟
⠀⠀⠀⠀⠀⠘⠷⣶⢀⣠⠂⠀⠀⠀⠈⣩⣿⣿⣿⣿⡿⢷⠀⠀⠀⠉⠻⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⢨⣰⡏⣄⠸⠿⠃⡴⠋⠉⣿⣿⣿⡁⠈⠀⡀⠀⠀⠀⠙⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠻⠀⠀⡜⠁⠀⢠⣿⣿⣿⣧⣴⠀⠁⠀⢠⡄⠀⠘⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢀⣠⣿⡿⠻⣿⣿⣿⠀⢠⠀⣸⣿⣇⣀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⢉⠧⢶⣿⢀⡇⠈⠛⠻⢿⣦⣤⣨⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣻⣟⣛⣻⣯⣙⣛⣟⣛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣯⣭⣿⣿⣯⣭⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⢠⣀⠀⠀⢠⡀⠀⠀⠀⣀⣶⠤⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⣤⠘⢦⡴⠊⠁⠠⠟⠉⢺⡁⠀⣀⡶⠟⠉⢀⡠⠒⠒⠤⡀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠘⠐⢓⠚⣓⠐⣟⠀⠀⠀⠀⢀⡤⠞⢿⣾⠋⠀⠀⢠⠃⠐⢠⠀⠀⠈⢳⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠁⠄⠻⠉⣆⠀⠀⠂⠈⢀⡤⠾⡿⠀⠀⠀⠁⠀⠀⣰⣀⠀⢀⣰⢷⡀⠀⡇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣧⠀⠀⢀⣀⠀⠁⠚⣲⠿⢷⣄⠀⠀⠀⠀⣀⣴⣀⡴⠾⠤⠤⢾⣿⣿⣿⢿⣿⡄⠑⡀⡷⠀⡬⡀
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠂⢹⣷⣀⣀⣽⢶⠒⣨⣶⣈⣤⢿⣷⣄⠀⠁⠀⣿⣏⠉⢈⣀⣴⣄⣿⡉⢁⠀⠈⠙⣦⣼⡧⠤⠴⠃⠠⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠟⣀⢽⣿⡄⣼⣿⣿⣿⣿⣿⣀⣀⠽⢧⣙⣰⠛⢻⣷⣼⣿⣻⣅⣠⣈⠟⣠⡄⠀⠹⢧⡴⠀⡀⠒⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡑⢰⣧⣤⣈⠻⠛⠙⠛⠉⠉⠉⡀⠠⠛⢿⡟⠛⢿⠛⠛⠻⣏⣭⡉⠃⠈⠁⠀⠀⠀⢠⡌⠁⠰⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠡⣀⣠⠀⠐⠛⢙⡆⠀⠀⠀⠀⠘⡀⠀⠀⠉⠓⠲⢾⣷⢄⢲⡄⠀⠀⠘⢻⡄⠀⠀⠖⠀⠀⠀⠀⡀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⡁⢀⣆⠀⠁⠀⠀⠀⠀⢈⣴⣶⣶⣶⣦⣄⠈⢿⡄⠀⡃⠰⠀⠂⡼⡇⠀⠀⠀⠀⠀⠀⠈⠁⡈⠀⠈
⠀⠀⠀⠀⠀⡐⠂⠀⠰⠤⠀⠀⠁⢠⣾⣿⣿⡆⢆⠈⢿⣿⣿⣿⣿⣿⠂⠀⣿⣤⣙⠘⠃⣷⣾⠇⡀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡄
⠀⠀⠀⠀⠀⠉⠨⢋⠴⠂⠀⠀⢰⡌⠛⣻⠿⢳⣶⡄⠈⠳⢿⠿⠃⡼⠀⠂⢠⢈⡅⠒⢠⣾⠃⠀⡆⠀⠀⠀⢀⡃⢀⠁⠂⠁⣰
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣤⣼⣇⠰⡁⢀⡘⢻⡿⣦⡴⠏⡠⠙⠑⠦⠀⣼⠉⠀⣷⠉⡏⠀⣼⣶⡦⠀⠀⣌⣀⠀⠁⠀⡰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠉⠀⠘⣿⣇⡊⠀⠋⠙⠛⠁⠂⠄⡄⠇⣸⣿⡹⠀⠘⣿⡎⠀⢠⣿⠟⠀⢀⣼⡿⠋⠀⢠⣾⡀⠁
⠀⠀⠀⠀⢸⠀⠀⣀⢰⣿⣆⠀⠀⠀⠀⠀⢸⣤⣘⣄⠁⢦⠐⠖⠞⢋⠐⡿⠁⠀⠀⠎⠀⢀⣿⠃⠀⢠⡿⠋⠀⠀⣴⣿⠟⠃⠀⣠⠎
⠀⠀⠀⠀⠸⡄⠀⡉⠙⣾⠉⢄⢠⣈⣰⢲⣾⡀⠈⠈⠀⢀⡦⠾⠊⣡⠌⠀⠠⠄⠈⠀⠀⠘⠁⠀⠀⠊⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠱⡔⠻⢃⠙⢴⠃⠀⠀⢮⢀⣼⠿⣞⠋⣀⣉⡃⠤⠂⠁⠀⣰⠃⢀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠰⠋⠀⢀⡤⠎
⠀⠀⠀⠀⠀⠀⣴⠖⠚⠓⠛⠀⠀⠀⢀⣁⠀⠑⡄⠀⠀⠀⠀⠀⠄⠀⣿⠏⣀⠴⠲⠒⠒⠒⢠⡀⠀⠀⠀⠀⠀⡤⠊
⠀⠀⠀⠀⠀⡀⣇⣀⠀⠄⠀⣠⡀⠀⠈⣡⣴⠀⠣⣓⢲⣶⡆⢠⠀⣷⠋⠔⠁⣤⣴⡶⢶⣶⣾⡷⠃⠀⠀⢀⣼⣅
⠀⠀⠀⠀⠀⠀⠁⢀⢃⣀⠤⠤⡁⠀⠘⠛⠉⠀⠀⢃⣀⣉⡑⠈⠷⠖⢋⣠⡿⠋⠀⢀⣠⡉⠉⠰⠔⠂⣠⠊⠈⢹⣧⠀⠰⠁
⠀⠀⠀⠀⠀⢀⠘⠱⠈⠁⣴⣾⠇⠀⠀⠀⠀⠀⠈⠉⠱⣾⡝⢷⣶⠚⠛⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠰⠿⠧⢤⡴⢿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢠⣀⠀⠈⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠠⠄⠀⠀⠀⢀⠐⠘⠀⠀⣿⣯⡌⣤⣤⠾⢿⣆⠀⣠⣤⣤⣀⣀⣀⣠⣤⣴⣶⡟⠉⢻⡷⣦⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣾⣦⡀⠀⠁⠀⠀⢀⣴⣿⣿⣡⣿⣉⠞⢿⡿⡻⢿⣿⠉⢿⡏⠀⠀⢿⣿⠟⠁⢀⡾⠤⠀⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠛⢿⣿⣷⡾⠿⢿⡟⡉⣿⣷⣾⣟⣿⢻⣷⠀⢻⡅⢺⡇⠀⠀⢸⠁⢀⣤⠞⢀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠔⠉⠀⠀⣀⣀⣘⣿⣧⣤⢿⡟⣿⣟⣟⣛⣿⣤⣦⣍⠁⠂⢀⡾⠖⠋⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃⢀⡀⠀⡀⠸⣿⣋⡼⢷⣟⡏⣹⣿⠿⡛⠛⠁⠀⢀⡞⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⠀⠈⠛⣿⣿⣬⠿⡏⠁⠀⠁⠀⢓⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢷⡀⠈⠳⡖⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠠

⠀⠀⠈⠐⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠋⠀⠀⡤⠊⠀⠀⠠⠤⡐⠀⠾⠓⠒⠒⠈⠀⠀⢀
⠁⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈
⢤⠖⠀⠀⠀⢠⣀⠄⠀⠀⠀⠌⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⣄⠀⠀⠀⢶⠄
⠀⠀⠀⠀⠀⠋⠀⠀⠔⠛⠀⠀⠀⠀⠀⠢⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠱⡁⠀⠀⠈⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⡄⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢆⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠂
⠀⠀⠀⠀⠀⡈⠄⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠘⡎⠂⠀⠀⠀⠀⠀⠀⢄⡇⡀
⠀⠀⠀⢆⠀⠁⣦⠀⠀⠀⠀⠀⠀⠀⠳⡇⠀⠀⠇⠀⠀⠀⡇⠀⢀⠀⠈⠃⡃⠀⠀⠀⢀
⣄⠀⠐⢾⡔⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢣⠃⠀⡠⠂⠁⠀⠀⠀⠀⠀⠈
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⠀⢀⡴⠀⠀⢄⡀⠀⠈⠀⣠⡆
⠀⠀⠘⠀⠘⠀⠀⠀⠀⣠⠀⠀⠀⠇⠀⠀⠀⢀⠀⠊⠙⠀⠀⡠⢺⠀⠀⠀⡘⠁
⠀⠀⠀⠀⠀⠀⢀⣀⡊⠔⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠉⠝⠋⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡠⠊⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠐⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠞⠋⠀⠀⠰⠀⠀⠀⠘⠄
⠐⠠⢀⣀⠀⠀⠀⠈⠉⠉⠁⠌⢠⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠑⠓⠀⠀⢀⡀⠀⠀⡀⠀⠀⡀⠈⠚
⠀⠀⠀⠀⠀⠠⠄⡐⢀⣀⡀⠀⠀⠑⠀⠀⢠⣧⠀⠀⠀⠀⠀⠐⠢⢤⣤⠀⡠⠋⠀⡠⠊⠇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠑⠹⠯⡁⠀⠀⠀⠀⠀⠈⠃⢀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠈⣢⣀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠗⠀⠀⠀⠀⠀⠉⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⢀⡀
⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣐⣛⣛⣉⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⢻⡷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡛⠛⠋⠉⠉⠁⠀⢐⣤⢴⣤⣀⠀⠛⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⢀⣯⣀⡴⣤⡈⠃⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⣿⣤⡍⢡⢛⣋⡇⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⡇⢿⡼⢤⣌⣿⡇⡀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢼⡇⢀⣸⣇⣸⣿⣦⣿⣿⢁⠈⡤⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⡏⡿⢯⡻⣿⣿⠇⢇⠎⠞⣵⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⢀⡙⠾⣿⣼⣯⣾⣀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢻⡎⣿⣿⣦⡀⠙⢿⡿⣯⣲⣶⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢸⣷⢸⣿⣞⢿⣆⠀⡀⢈⠉⠻⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣹⣿⣿⠀⣿⡄⣿⣿⣆⠹⣷⣼⣶⣷⣄⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡅⣿⣿⢹⠀⠘⣧⢹⣿⣿⣦⡘⢧⠉⡛⠛⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢣⣇⡟⣿⠈⢠⠀⠹⡆⠻⣿⣿⡳⣄⠱⣌⠃⢸⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢇⣾⣿⡇⢿⠀⣿⢰⠀⢻⣆⠹⣿⣿⣌⢓⢬⡛⢸⡇⠘⡖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣾⣿⢹⡇⠀⠀⣿⠸⣧⠀⢻⣷⡙⢏⢻⣿⣝⢦⢻⣧⠀⢹⡘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢰⡟⣿⢸⡇⠀⢸⣿⠀⣿⣆⠀⢻⣟⠦⠀⢿⣿⣮⢻⣿⠀⣼⡇⡈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⣿⠘⠁⠀⢸⣿⡄⠘⣿⡄⢠⠙⣦⠀⠈⣿⠈⠋⠃⣴⡟⢇⢻⡀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣿⠀⠀⠀⣿⣿⣇⠀⢹⣿⡀⢳⡄⠀⠀⣿⠀⢠⣾⢿⠁⠀⠈⣧⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢱⠀⠀⠀⣿⡏⠹⡆⠀⢹⣧⠀⢻⣆⠀⠁⢀⣿⣷⡈⠀⠀⠀⠸⣇⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠙⣆⠀⢻⡄⠀⠹⣷⣄⠘⢻⡿⣷⡄⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠘⠂⠀⢧⠙⣿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣿⣏⢽⣟⠻⣿⢟⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢾⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣼⣇⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⣸⠀⠸⣧⣸⣦⡀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣠⠀⣿⣿⣿⡇⢰⡀⣷⡀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣼⣿⢰⡄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⢰⡄⣿⣷⣾⡟⣼⠁⣿⣿⣿⡧⣸⣴⠀⢀⣼⣿⠃⢠⡆⣿⣤⣿⣿⣿⣀⣾⡷⣸⣷⠀⣦⠀⠀⢀⠀⣼⣿⣿⣿⣿⣎⣿⣾⣿⣦⠄
⠀⠀⠀⠀⣄⠀⣴⣿⡇⣿⣿⣿⣿⣿⣤⣿⡿⣹⣿⣿⣿⣷⣿⣿⣿⣴⣿⣃⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣄⢷⣌⣷⣿⣿⣿⡟⣹⣿⣿⣿⣿⣿⣀⣦
⠀⠀⠀⠰⣿⣿⣿⢻⣷⣟⠹⡙⢿⣿⣿⣿⠰⣿⣿⠟⣿⣧⣿⣿⠙⢿⢻⣿⣿⡏⣿⠃⢿⠙⣿⡟⠠⣿⣿⢹⣿⡿⣿⣿⠻⣿⣿⠐⣿⣿⡿⠃⠟⢛⣿⣷⠏
⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠉⠁⠈⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠠⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠇⠀⠀⠀⢂⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠈⠠⠂
⠀⠀⠀⠀⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠈⠐⠀⠀⠄⠀⠀⠀⠀⠘⡀⠀⠀⠄⠀⠀⠀⠀⠆⢀⠠⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠂⠀⠀⣤⠀⠀⠀⠒⠂⠀⠀⠄⠀⠀⢠⠀⠀⠀⠀⠈⠀⠀⡄⠂⡄⠀⠀⠂⠀⠄⢦⡀⡀⠄⠄
⠀⠀⠀⠡⡳⠀⠀⠠⠐⠩⠀⠀⠀⠀⠀⢃⠀⡀⣀⡈⠎⠀⠀⠀⠈⠒⠜⠄⠤⠊⠀⠀⠀⠐⠆⢠⠃⠠⠂⠠


⠀⠀⠀⠀⠀⠀⢄⢀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢀⠀⠁⠸⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠠⠄⠐⠀⠂⡄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⡐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠩⠤⠊⠄⠈⠀⠀⠀⠈⠂⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠔⠤⠀⠂⠁⠂⠀⠀⠀⠀⠀⠂⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠦⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠠⠤⠄⡤⠤⣶⣶⣶⣶⣄⣀⣤⣄⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣿⣶⣲⡆⠈⠙⣿⣿⣿⣿⠛⣍⣩⣽⣉⣝⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⡽⠃⠀⠀⠁⠙⣿⠿⢷⣿⣿⣿⣿⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⡜⠃⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣍⠐⠁⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠸⣿⠀⠉⠛⠿⠀⡀⠀⠀⠀⠀⠰⠿⠿⠷⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⡄⢀⡀⠀⠀⠀⢀⣴⢣⢼⡇⠀⠠⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⢀⣀⣤⠀⣽⣿⠟
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣠⠃⠈⢻⡌⣡⠺⣿⡿⠗⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠐⠉⠀⡰⠧⡄⣦
⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⣴⣿⠀⣢⣾⣏⡛⠁⠠⠁⠰⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢘⠀⠑⢾⠆⠐⣑⣿
⠀⠀⠀⠀⢠⠃⠀⠀⢠⡞⠁⡟⣰⣿⣏⠛⠁⠶⠤⠄⠠⣴⡂⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢤⣼⣶⡶⠚⡏⠸⡟⠉
⠀⠀⠀⠀⠸⠀⠀⡰⠋⠀⠀⡃⣿⣦⡍⠀⠚⠒⠒⠂⠀⠄⠈⠈⠉⠀⠀⠀⠈⠉⠉⠉⠉⠛⠃⠂⠼⠀⠀⠀⠀⡼⠏⠀⢀⡆
⠀⠀⠀⠀⣠⠤⠚⡁⠀⠀⢸⢠⡿⠶⠤⡀⣛⣗⠀⡇⠀⡑⠦⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠤⡆⠀⢸⠁
⠀⠀⠀⠸⢆⠄⠠⠀⠀⠀⡸⢸⣿⡷⣡⠭⠈⡉⠀⠀⢆⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⣀⡾
⠀⠀⠀⠰⠼⠀⡅⠀⠀⠀⡇⠰⣶⢤⣙⣤⡠⣌⠲⣀⠀⡅⢀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⣼⡼⠀⢹⡇
⠀⠀⠀⠀⣧⠄⣀⠈⠀⢰⠇⠰⣿⡙⠷⠈⠋⠈⠑⠚⠁⠋⢁⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⡀⠀⠄
⠀⠀⠀⠀⢹⠀⡇⠀⠀⢸⠀⠐⣿⡁⢜⠠⠀⠀⠀⠤⣐⠺⢿⠛⠉⠀⠚⠴⠦⠀⠀⡌⠀⠀⢀⣠⠄⠋⠀⠰⣿⡈⠁
⠀⠀⠉⠁⢸⡀⡇⠀⠀⡄⢸⣦⣌⠳⠠⠀⠁⣿⣿⡦⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠈⠀⣁⣴⡖⢀⡰⣄⠀⠗
⠀⠀⠀⠀⠘⡇⢀⠀⠀⠇⠘⣿⣿⣷⡀⠀⠀⣼⣿⣟⠀⠐⠀⠀⠀⠀⠀⠀⣁⣤⡀⠶⠚⠛⠿⠁⠈⠉⣤⠀⠀⢰⠀⡀
⠀⠀⠀⠀⠀⠹⠀⡀⢸⠀⠀⢸⡿⠓⢄⡈⠀⠘⡷⠛⠀⣠⣦⡤⠴⠒⠋⠉⠁⠀⠀⢀⣠⣤⣶⣶⣦⣼⣿⠁⣜⣷⣾⠃⠀⠃
⠀⠀⢀⣤⠶⣷⠂⠙⣿⢠⣾⣿⡷⠀⢸⣧⣠⣆⡐⠆⠘⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⢸⡇⠀⠀⠈⠉
⠀⣄⠀⠀⠀⠈⠆⠐⠋⠈⠛⢿⣧⡀⣠⣈⠉⠉⠉⠲⠲⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⣿⣷⡀⢤⣀⠀⠀⡄⠀⠀⠀⠀⠈⠉⠙⠻⣿⡶⢤⣄⡀⠀⠈⠹⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡀
⠀⣿⣻⣧⠻⠿⠘⣿⢆⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠈⠉⠙⠒⠦⢤⣄⡀⠀⠀⠀⢀⠀⠀⠀⠀⣾⢠⠃⠁
⠀⣿⣟⢿⠉⠁⢸⡇⢸⣄⣦⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠈⢇⠀⣀⠑⠎⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⢀⡆
⠀⢽⣾⣧⡀⠀⢸⠀⠘⠿⠿⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⡀⠃⡈⠉⠒⠃⠀⠀⠀⢸⠁⡄⠀⠀⠀⠀⠀⢸⣷⣄
⠀⠈⠉⢿⠇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢀⡠⢖⣩⠔⠉⣤⠶⠶⠀⠀⠀⢠⠏⠀⠁⠀⠀⠀⠀⠀⠒⢹⠁
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣸⠀⢀⠴⣊⡬⠞⡋⠄⠒⠉⠹⣆⠠⠀⡀⠀⡷⡄⠴⡀⠀⢀⣦⡀
⠀⠻⣿⣿⣇⢠⠇⢀⣷⠀⠀⠀⠸⠧⠀⢀⡀⢀⣠⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⡠⠺⢿⣿⣆⠈⡄⠉⠛⠻⠷⠶⢦⠤
⠀⠀⠀⠈⠉⢸⠀⣿⣄⣀⡀⠠⠀⢀⡚⢁⣄⠉⡀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⠦⢭⣝⣧⣈⠠⠄
⠀⠐⢤⡀⠀⡇⠀⠸⣿⣿⡏⠘⠛⠿⣇⠀⠈⡏⠀⢈⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠘⠔⠂⠠
⠀⠀⠀⠙⠲⠀⠀⠀⠀⠙⠻⢶⣤⣤⣠⣦⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠷⠶⣧⠤⠦

⠀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⡐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣜⠱⠟⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣷⢿⡄⠀⢸⣿⣯⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿⣿⣿⣿⣿⣿⢹⡆⠀⠀⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣹⣿⣿⣿⣿⡏⣾⠁⠀⣰⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣸⣿⣻⡟⣿⠇⣯⢀⣼⣿⣿⠟⠻⣿⣷⡝⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢸⣿⡏⣿⣿⣿⡿⠀⢻⡟⠻⣿⠁⠀⠀⠈⢳⣿⣦⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠘⣿⢀⢿⣿⣿⡇⡷⢸⡇⠇⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⡇⡂⣿⢸⢸⣿⡿⢸⡇⣾⢿⠀⡆⠀⠀⠀⠀⠀⠀⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠃⢸⡟⢸⣿⣧⣿⠃⣿⢸⢸⡇⠀⡄⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣧⠀⠈⡗⠘⣿⢹⡿⢰⡿⢸⢸⡇⠀⡄⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢰⠀⡇⡆⣿⣸⠇⣾⡇⡆⢸⡇⠀⡿⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⣿⢸⠀⡇⡇⣿⠛⣸⣿⠇⡇⢸⡇⠀⣷⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⣿⢸⠀⡇⡇⣿⡄⣿⣿⢠⡇⢾⣧⠘⡟⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⢸⠆⠃⡇⣿⠀⣿⡟⢸⡇⣼⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠙⠃⠀⠀⠀⠀⠀⢠⣿⠀⣿⢸⡃⠂⡇⣿⢰⣿⡇⢸⡇⣿⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⠹⠆
⠀⠀⠀⠀⠀⠀⠒⠲⠔⠐⠒⠒⠲⠛⢢⡆⠀⠀⢠⣿⠛⠀⣿⢸⡇⠁⡇⣿⢸⣿⠁⣾⣿⣿⣇⡄⣿⣄⠀⠀⠀⠀⢲⠛⠔⠂⠘⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠖⠐⠶⠀⠀⠂⠀⣨⢏⣾⢰⡇⢸⡇⡄⡇⣿⢸⣿⠀⣿⣿⣿⣏⣽⣻⠏⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣐⣒
⠀⠀⠀⠀⠀⠓⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠈⠁⣸⣧⢸⡇⡇⡇⢻⢸⣿⠀⣿⡿⣻⣿⢸⠷⠀⠀⠀⠀⠀⠀⠀⠛⡤⠀⠀⠀⠀⠀⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠐⠛⠂⠀⣼⠏⠀⠀⠀⠛⣿⢸⣧⡇⡇⣸⠸⣿⠀⣿⡇⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⢲⡆⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠛⠛⠈⢙⣿⢇⠀⠀⠀⠀⠀⡹⣸⣏⡇⡇⢹⠀⣿⠀⣿⡇⣿⣿⠀⠴⠆⠀⢀⠀⢠⡀⠀⠀⠀⠉⠀⢘⡁
⠀⠀⠀⢀⠀⠛⠒⠒⠒⠋⠁⠀⠀⣴⢻⠏⠀⠀⣀⠀⠀⢠⡀⣿⡀⡇⡇⢸⠀⣿⠀⢹⣷⢸⡿⡇⠀⣠⠈⠛⢀⣤⠉⢁⠄⠀⠒⠞⢋⣡⡖⢀
⠀⠀⠀⡄⠀⠊⠠⠴⢶⠶⣤⡤⢾⣷⣾⠀⠐⠚⠛⢁⡀⢸⡇⣿⢰⠇⡇⣼⠀⣿⡇⢸⣿⡘⣧⣿⠀⠀⠒⠒⣿⣀⣀⣀⠐⠲⠶⢶⡞⠉⢛⣉
⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⣠⠀⠸⢿⡿⠀⠀⠀⠀⠀⢀⣾⢹⣿⢸⠀⡇⣿⠀⣿⡇⠈⣿⡇⢻⣾⣷⡀⠴⠊⠉⠙⠳⣿⡿⠷⠶⠚⠛⢱⠿⠛
⠀⠀⠀⠀⠤⠄⠁⠤⣤⠤⠤⠆⠀⣸⣇⠀⠀⠀⠀⠀⣼⡟⣸⡇⢸⢠⡇⣿⠀⣿⣷⠀⢿⣿⠈⣷⣹⣷⡀⠀⠀⠀⠀⠛⠓⠀⠀⢀⣠⣧⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣴⣶⣜⣣⡏⠀⢀⣀⣠⣾⡿⢁⣿⠁⡏⢸⠁⣿⠀⣿⣿⡀⢸⣿⣇⠸⣷⡹⣷⣔⠀⡀⠀⠀⠀⠈⠻⠟⠁⠀⠈
⠀⠀⠀⠀⠀⠈⠉⠉⠀⢺⣿⡏⠈⠁⠀⠸⢿⣿⣿⣟⣡⣾⡟⢸⠃⣾⢀⣿⠀⣿⣿⣇⠀⢿⣿⣆⢹⣷⣽⣿⣷⡤⠆⠀⠉⠐⠦⣾⣶⡤⠐⠊
⠀⠀⠀⠀⠀⠄⠀⠀⠄⢸⣿⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⠟⣠⠇⢰⡇⢸⣿⡄⢿⣿⣿⡄⠘⣿⣿⣾⣿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⢠⣿⠏⠠⣿⣶⣏⣴⡿⢀⣾⣿⡇⣸⣿⣿⣿⣤⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠀⠀⢠⣿⠃⢠⣿⠏⠉⠿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⡷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣴⡿⠁⣰⣿⠃⠀⠀⠰⠟⣿⣿⠛⠛⢻⣿⣿⣿⡁⠈⢿⣦⠀⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣴⢤
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⡠⣯⠟⢀⣼⡿⠃⠀⢀⣶⣤⣤⣿⣿⣦⣾⣿⣿⣿⣿⣷⣄⠀⠹⣿⡄⠀⠈⢻⣓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡿⠃⢐⣏⡹⠀⠀⠀⢸⣿⣿⣿⢻⡏⠀⣤⣈⡿⣿⣿⣿⣿⠀⠀⠘⢏⣵⠀⠀⠈⢹⣛⣦
⠀⠀⢀⢀⡤⠀⠀⠀⣔⠛⠿⠉⠀⣰⣛⡏⠁⣀⠀⠂⠈⢁⣽⡿⠼⠷⠠⣿⢻⡀⠀⠨⠀⣀⣤⡄⠀⠀⠹⡛⣆⠀⠠⠈⠩⡟⢢⡀⠀⠉⠛⠀⠐
⠀⠀⠈⡜⠀⢀⠴⣾⠟⠋⠀⢀⠶⣿⠉⠀⣾⣿⣷⣦⣰⣾⣿⣄⣠⣤⣴⣾⣿⠟⢲⣾⣿⡿⠋⢀⣶⣦⡀⠈⠿⠛⣆⠀⠀⠀⠉⢻⠟⠀⡀
⠀⠀⢀⣤⣤⡿⠖⠋⠀⠀⣠⣾⠟⠂⠀⣠⠟⠻⠟⠋⣿⣿⣿⣿⣿⡦⣀⣸⣿⣀⣀⣼⣿⣿⣿⣿⡿⠟⠓⠀⣄⠚⢿⣤⡀⠈⠁⠈⠀⠶⢿⣤⡄
⠀⠀⣾⡀⠋⠀⢐⠂⠀⢾⣤⠋⠀⠀⣴⣯⣤⣄⣠⣴⡿⠟⣿⣿⣍⣀⠹⣿⣏⢉⡛⢻⣿⣿⣿⣧⣤⣤⢀⣀⣤⣷⣞⢀⣼⡀⠀⠐⠀⠀⠈⠳⣀⡀
⠀⠀⠈⠀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠀⠀⠉⠁⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣔⣶⣒⣒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⢉⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣽⣶⣶⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⠋⣿⣏⡉⡺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠛⣿⠀⠈⣹⡏⠀⠀⢀⣀⣤⣴⡶⠿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⣧⣴⣿⣿⡄⠘⠻⠶⠶⠾⣋⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠉⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⣀⣀⣠⣴⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢛⢻⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⢿⠈⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⣿⣛⠻⠿⢿⣭⣽⣭⣿⠣⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⡀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠟⠻⡉⠑⡀⣤⣤⣤⣤⣷⠀⠀⠀⠠⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠈⣇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣛⡁⠀⢀⣿⣶⣿⣿⣿⣿⣿⣿⢰⣷⣦⡀⠀⠈⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣆⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣿⣾⣷⣸⡟⠻⣦⡀⠀⠀⠀⠀⠀⡜⢠⡀⣽⣦⢻⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⣆⠀⠀⠀⣼⢁⠸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡄⠈⣻⠓⠾⠁⣠⣷⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣷⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⠀⡀⠀⢀⢀⠄⣀⣄⢀⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠠⣙⠶⣿⠃⢾⡿⠫⢈⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⡇⠶⣄⠈⢁⠀⠚⢣⣿⣿⣿⣿⠉⠛⠿⢿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠻⢢⣼⣿⣯⡐⠒⣸⠏⢝⣿⣿⡇⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣴⣂⣱⣾⣾⣿⠀⠀⠤⠀⠙⠃⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣤⣶⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⡇⠹⢿⡇⠹⠈⡏⠏⠿⠿⠙⠿⠿⠿⠙⠏⠁⠈⠁⢠⠈⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⢃⣤⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⡴⢁⠤⠂⠀⠀⠀⠀⠀⠀⠀⢀⢸⠅⠘⡻⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⣉⣧
⠀⠀⠀⠀⠀⠀⡔⠁⣴⠋⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠂⠀⠝⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⢣⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠐⣠⠞⠡⠂⠁⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⢠⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠐⠢⠜⠋
⠀⠀⠀⠀⣠⣾⡫⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣞⡛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣡⠄⠊⣀⡀
⠀⠀⠀⢀⠔⠉⠀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⠙⠘⠁⣟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠀⠀⢿⣷⡴
⠀⠀⠀⠈⣆⡀⠸⢰⠄⢸⠂⣃⡈⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡀⣠⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⠿⠀⠀⣼⢧⡀
⠀⠀⠀⠀⠀⠑⠀⠍⠀⠠⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠁⣟⡄⠀⠀⠀⠀⠀⠀⠰⡇⠠⠈⠓⢬⠇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢤⠀⠒⢀⡧⠄⠀⠀⠀⠀⠀⠀⠀⠁⢢⣠⠇⠐⣾⠿⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⣀⡠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⣀⢠⠀⠀⠀⠐⠄
⠀⠀⠀⠠⡄⠄⠽⠞⠛⠒⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⣷⢉⣹⣿⣄⣌⢠⣤⡇⠀⠀⠀⠀⠀⣴⠁⠀⠄⠂⠀⠐⠂⠀⠠
⠀⠀⠀⠀⠁⢠⡖⣤⣀⢢⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣟⠃⠀⢽⡄⠀⠈⠁⠀⠀⠀⠀⠀⠁⢴⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠆⠈⠈⢙⣏⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠔⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⢤⡄⣁⡀⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡧⠤⢤⠝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣤
⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⣂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⣾⡅
⠀⠀⠈⠀⠀⠸⡇⠄⢀⠰⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣆⢰⡌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⣴⠿⢿⣤
⠀⠀⠀⠀⠀⢠⡇⠀⠨⠄⢻⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡸⠛⢠⠈⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠻⠁⠀⠨⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠠⢥⣝⣀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢰⣶⣛⣛⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⢤⡤⠾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠄⢀
⠀⠀⠀⠀⡠⠈⠁⠁⣀⣠⡶⣆⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠐⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⡄⠀⠀⠐⢢
⠀⠀⠀⠀⣇⣈⡤⠞⠋⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣾⣿⣦⣤⣦⣼⣤⣶⢴⡆
⠀⠀⠀⠀⣿⠃⠀⠐⠀⠠⣶⡏⠀⠀⠀⠀⠀⠀⠀⢈⠛⠀⠊⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠤⠲⣦⣀⡟⠒⠒⠿⣶⣦⠉
⠀⠀⠀⠀⠈⠀⢀⠀⠀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠠⠆⠀⠐⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠉⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠶⢒⣊⣉⣩⣭⣭⣥⣤⣤⣤⣤⣤⣭⣭⣍⣉⡁⠒⠶⠦⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⣉⣭⣤⡶⠶⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠈⠉⠓⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣊⣩⣴⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡤⠤⠤⠤⠴⠶⠒⠒⠶⠤⠤⠤⠤⢤⣤⣤⣄⣀⣀⣈⠉⠓⠢⣤⣀
⠀⠀⠀⠀⣤⣤⣴⡞⣩⣴⠾⠛⠉⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠤⠭⢷⣦⡄
⠀⠀⠀⢺⣏⢿⣿⣷⣉⠀⠀⠀⠀⣀⡠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⡀
⠀⠀⠀⠀⠻⡾⢿⣿⠉⢷⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⡼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠊⣿⣷⠀⠀⠀⠀⠀⠀⠀⣸⣟⣾⣿⣿⠟⢋⣤⣶⣶⣶⣦⣌⠙⠿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⣿⣇⠀⠀⠀⠀⠀⢰⣿⣿⡿⢛⣡⣾⠟⠉⠀⠀⠀⠈⠙⢿⣦⣌⠻⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣿⡆⠀⠀⠀⢀⣿⣿⢏⣴⣿⠋⢁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡈⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⡀⠀⠀⢸⣿⢡⣾⣿⡟⢰⣿⣇⣰⣤⡄⠀⣤⣆⣸⣿⡧⢻⣷⡌⢻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣷⠀⠀⢸⠉⣾⣿⣿⣧⠈⠻⠿⠿⠟⠀⢀⠛⠿⠿⠿⠁⣼⣿⣿⡈⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⣿⣧⠀⢸⠀⣿⡟⣿⣿⣷⣄⡀⠀⢠⣿⣿⡆⠀⢀⣀⣼⣿⣿⣿⡇⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⡆⠸⡇⢸⣿⢹⣿⣿⣿⢸⡀⠀⠁⠈⠁⣰⣯⣸⣿⣿⣿⣿⡿⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢿⣿⡄⢱⠈⣿⡌⣿⣿⣿⠛⢿⣧⣤⣄⣥⡿⠋⣿⣿⣿⣿⣿⠇⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣨⢿⣷⣈⣧⠘⣧⠸⣿⣿⣦⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⣋⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡜⣿⣿⣿⣆⠹⣧⠹⣿⣽⣿⣶⣾⣷⣶⣾⣿⡿⢛⣡⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⠹⣿⣿⣿⣦⠙⣇⠹⣿⣮⡻⣿⣿⣿⡟⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣷⡈⢧⡘⢿⣿⣿⣿⡿⣴⣿⣿⣿⣿⠟⣩⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣦⣳⣌⠻⣿⣿⣷⣿⣿⣿⡟⢡⣾⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣩⣭⣭⣽⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⡀⠸⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠟⢛⣛⣛⣧⡼⣿⣿⠿⣿⣿⣿⣿⣷⣄⡹⣿⣿⣿⣧⠀⢹⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⢁⣴⣿⣿⣿⣿⣿⣧⢻⣿⣷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⢠⣿⣿⣿⡿⠿⠛⠟⣩⣌⠿⠛⢠⡆⢻⣿⣿⣿⣿⣿⣿⣿⡿⠃⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⢠⣶⡿⠀⢉⣠⡴⣾⠿⢁⢸⣿⣿⣿⣿⣿⣿⣏⣴⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣏⠀⠈⢋⠉⢠⠴⣶⠟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⢿⣿⣿⣤⣄⣀⠀⢒⢸⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠸⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⠜⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠸⣿⣿⣿⣿⣿⡿⣱⣷⠹⣿⣿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣿⣿⣿⣿⣿⡇⣿⣿⣧⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⣿⣿⡿⠂⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡟⣸⣿⠁⠘⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢇⣿⠃⠀⠀⠁⡼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠟⡼⠃⠀⠀⠀⠀⠠⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠿⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⢿⡿⢿⠿⢿⠿⠋⠿⠿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢻⠟⠛⠻⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿
⣿⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⡀⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⣷⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⡀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⢠⣿⠁⠀⠀⢀⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⢰⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⢀⣾⠃⡀⠀⣴⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡏⠀⠀⢠⡇⠀⠀⠀⣰⣿⣿⠏⠀⢠⠀⣼⡟⢀⠃⣼⠟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⠀⠀⣠⣿⠀⠀⢀⣼⣿⣿⡟⠀⠀⡄⢰⣿⡇⢸⠠⠏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⣿⣿⣿⠀⢀⣼⣿⠃⠀⣴⣿⣿⣿⡟⠀⠀⢰⡇⢸⣿⠇⣾⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣼⣿⣿⣿⡇⢠⣾⣿⠏⢠⣾⣿⣿⣿⠏⠀⠀⠀⣾⠃⢸⠟⣰⢇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢰⠃⠀⠀⠀⣰⣿⠟⣿⣿⣇⡞⣿⡟⣴⣿⣿⣿⡿⠁⣰⢣⠆⣼⠟⠀⠈⣰⢏⡟⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢺⠀⠀⠀⢠⣿⠃⠀⣿⠟⣿⢀⣿⣿⣿⠋⣼⡟⠀⢰⣷⣿⣾⠏⠀⣠⣾⣿⠏⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢀⠀⣻⡄⠀⠀⣼⡇⠀⠀⡇⠀⡏⢸⣿⡿⠃⣼⣿⢡⢇⣿⣿⣿⠏⢀⣾⣿⠟⠁⠀⣠⡾⠀⠀⠀⢸⡇
⠀⠀⢸⠀⢿⣿⠀⠀⣿⠃⢰⣴⠇⠀⠀⢸⣿⠁⢰⣿⡏⣾⢸⣿⣿⣿⢠⣿⡿⠋⢀⣴⣿⡿⠃⠀⠀⠀⢸⡇
⠀⠀⢸⡄⠈⢿⡇⠀⣿⠀⣼⣿⠀⠀⠀⣼⡇⠀⣼⣿⢧⣿⢸⣿⣿⣿⣾⣿⠃⢠⣿⡫⠋⣠⡜⣡⠆⠀⢸⡇
⠀⠀⢸⣇⢠⣞⣿⠀⠁⢀⣿⡟⠀⠀⠀⣿⠀⠀⣿⢻⢸⣿⣸⣿⣿⣿⣿⡇⢠⡿⠁⣤⣾⡿⠛⠁⠀⠀⢸⡇
⠀⠀⠸⣿⣆⣿⣿⠀⠀⣸⣿⠃⠀⠀⠀⠉⠀⢀⣯⡏⣿⣿⢹⣿⡇⣿⣿⡇⢼⠁⣾⡿⡋⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢻⣿⣿⣿⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⢱⣿⡟⣼⣿⡇⣿⣿⡇⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢻⣿⣿⢠⣾⠏⠀⠀⡆⠀⠀⠀⣰⣿⢇⠏⡿⣹⣿⣿⣾⣿⡿⠁⣼⡿⠋⠀⠀⠀⠀⣠⠀⠀⢸⡇
⠀⠀⠀⠀⠘⣿⡇⣼⠏⢠⠃⣴⡇⠀⠀⢠⣿⡏⢀⠀⣽⢿⣿⣿⠿⠋⡀⠞⠉⠀⠀⢀⣀⣴⡾⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠋⣼⠏⢠⠇⣰⣿⠃⠀⢀⣾⠏⢀⣾⡼⣿⣿⠟⠁⢀⡠⠔⠀⣠⣴⠾⠛⢡⡞⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢰⡏⢀⣾⣴⣿⠏⠀⢀⣾⠃⠀⣼⡇⣿⡿⠁⢀⣴⠋⠀⣠⡾⠋⠀⣰⣾⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡿⠀⣸⣿⣿⠏⠀⠀⡾⠁⠀⣰⣿⣧⢹⠇⢠⣿⡏⠀⠞⠁⠀⣠⣾⣿⣿⠃⣸⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠘⠁⠀⣰⢿⣿⡏⣻⢠⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⠏⢀⢻⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⡴⢋⣾⣿⢳⣿⣾⣿⠃⠀⠀⢀⣾⡿⣭⣿⠏⠀⠎⢸⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⡜⣡⣿⣿⣢⣿⣿⡿⠁⠀⠀⢠⣾⣿⣿⡿⠃⠀⠜⢀⡾⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢈⣼⣿⣿⣿⠿⠋⠁⠀⠀⠀⣰⣿⣿⠟⠋⠀⣠⣎⣤⣿⠇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡆⠀⢀⠞⣵⠿⠋⠁⠀⣀⡀⠀⣠⠾⠟⠋⢁⣀⣤⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣶⠀⠀⢂⠞⠁⠀⣠⣶⠿⠋⠛⢋⣠⣤⣶⣾⣿⣿⣿⣿⣿⣻⠟⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⢀⠀⣠⠞⢉⠀⠀⡠⢚⣩⣭⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢠⣿⡿⠃⠀⢀⡴⠁⠔⣡⡖⠁⠀⢀⣴⡿⠿⠿⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⣿⠋⢀⣤⣶⠟⠁⣠⣾⠋⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠜⢁⣴⡿⠟⠁⠠⠾⠋⠁⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡇
⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠛⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠄⠀⠠⠤⠠⠄⠼⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠈⡉⠉⠉⠉⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠐⠂⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⣀⣀⣀⡀⣀⣀⣀⣀⣈⣁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⡂⠉⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠤⣄⣀⣈⣠⣤⠤⠀⠌⠥⠴⣺⠁⠀⠀⠀⠀⢀⠀⠔⠁⠀⠀⠀⢀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠀⠀⠀⠀⠐⠂⠀⠣⠁⠎⠀⠀⠀⡸⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠰⠤⣀⠀⠀⢀⡴⠁⠀⠀⠀⣀⠤⠊⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⡠⠖⠉⣀⡤⠒⠈⢁⡠⢀⠔⠀⠀⠉⠉⡁⠀⠀⠁⢉⠁⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡴⠃⠀⡠⠊⠁⠀⢀⠔⠉⣠⠃⠀⠀⠀⠄⢠⠀⠸⠀⠀⠸⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⠞⡑⠀⣠⠊⢀⠂⠀⡰⠃⠀⡴⠁⠀⡜⠀⠀⠀⡎⢠⠃⡇⠀⢠⡙⡄⠈⣆
⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⡔⠁⠀⠀⢀⠜⠁⡠⠊⠀⢰⢰⠁⠀⠀⡜⠀⡜⠀⣻⠀⢸⢡⠸⡄⠘⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠎⠀⢀⡠⠚⠁⠀⠀⡠⠨⠀⠸⢸⠀⠀⡜⠀⡜⠀⢈⠉⡆⢸⢸⠀⢣⠀⠸⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠐⠁⡰⠁⢀⡰⠋⡰⠁⠀⡇⡆⠀⢈⠀⡜⠀⠀⢸⠀⡇⠸⢸⠀⠸⡀⢠⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠜⣁⠔⠉⢀⠜⠁⢀⠜⢰⠁⠄⣡⠞⠀⡀⢀⣾⠀⡇⡇⢸⠀⠀⡇⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⢀⠔⢃⠠⠔⠁⣠⠃⡠⠊⠁⠀⡜⠀⡜⢸⢠⢡⠁⡌⠀⠀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⡇⢰⠁⠀⠀⠌⠀⡼⠀⢸⠀⠆⢠⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠃⠀⠐⠀⠘⠀⠀⡆⠈⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⡀⠀⠀⠀⠀⠰⠁⢀⠊



⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠶⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢹⣸⡏⢹⡛⠛⠻⡟⠶⠶⢶⠶⠶⠶⡶⠶⠶⣶⠶⠶⢲⡖⠞⠻⡟⠋⢻⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣧⣇⣀⣇⠀⢘⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⣸⠀⠀⢸⡇⠀⢘⡇⠀⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣉⣙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠈⠉⠉⠉⠉⠙⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣸⠇⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠟⠀⠀⠀⠀⢸⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⡀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡍⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢹⡟⠀⢸⡏⠀⠀⠀⢸⡀⠀⠀⠈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡴⠟⠀⠀⠸⠷⣤⣤⠶⠾⠷⠶⠶⠶⠋
⠀⠀⠀⠀⢠⡴⠶⠶⠶⣶⠶⣤⣤⣈⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣴⠶⠲⢶⣄⡀
⠀⠀⠀⠀⣿⠀⠀⠀⢰⠃⠀⠀⠀⠉⢻⡄⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠉⠀⠈⣿⣄⠀⣠⠞⠛⢶⣄
⠀⠀⠀⠀⠙⢷⣄⣀⣸⣄⠀⠀⠀⣀⡾⠃⢀⡀⠀⢰⡟⠁⠀⠀⠙⣳⣦⣀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠉⠳⣄⣴⠟⠙⢷⣇⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⣛⣯⡶⠛⠋⠙⢷⡈⠻⣄⠀⣠⠞⠁⠀⠙⢷⣄⠀⠀⠀⢸⡅⠀⠀⢀⣴⠟⠁⠀⠀⠀⠙⠷⣤⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠳⡄⠀⢀⣼⠇⠀⠈⠻⣧⡀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠙⠶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣀⣿⠶⠟⠁⠀⠀⠀⠀⠈⠻⣦⣀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉

⠀⠈

⠀⢐⡀⠀⣂⠀⠀⠀⠄⠀⠀⠀⢜⠀⠀⠆⠀⠀⠀⢤⢀⠠⡀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠠⠄⠄⣠⢀⠄⡀
⠠⠈⠂⠐⣈⠂⠀⡄⠂⠄⠀⠁⠉⠀⠂⡥⠆⠑⣈⢰⣇⡠⠋⠢⡀⣿⣰⣧⣝⣀⣇⣷⣅⣿⢀⠔⠀⠀⡤⠀⠠⡄⠀⢠⡔
⠀⡀⢀⠀⠄⠄⡀⢔⢊⠌⠀⡨⣀⠀⠀⠰⠀⠰⠢⢓⠀⢳⡄⠐⠀⠙⠛⠛⢻⡿⢛⡛⠛⠁⢨⠀⡳⠆⠀⣼⡄⢡⣶⡄⠁⢳⡇
⠀⠁⠁⠂⠀⠸⠅⠃⠀⡂⢀⠦⢀⠀⠁⢉⠀⠀⠾⠂⢠⠂⠀⡠⠊⠖⠀⡀⠈⠀⢠⡄⠀⠈⠀⠁⠠⠘⠠⣀⠔⠢⣀⠄⠁⠤
⠀⡠⢂⠅⠰⢈⢐⠀⡨⠇⣀⠪⠂⠁⢀⠰⢁⠀⠀⠠⠂⢰⡁⠄⠀⠀⠀⢧⢀⠀⡇⢩⠀⡞⢰
⠠⠠⠠⢐⠀⠂⠂⠂⠰⠃⠀⠄⠡⠂⠂⠀⠠⠃⠠⠄⠠⠊⠧⠤⠤⠀⠂⠈⠄⠀⠀⢸⠀⠇⢸⠀⡀⡤⠀⠠⡢⠀⠀⢰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⡀⠐⢖⠂⠡⠀⠁⠀⠀⠔⠀⠈⠀⠀⠈⣹⡄⠀⠀⠐⠤⠘⠀⡄⢼⠀⠀⠈⢀⠀⠀⠀⢀⠅⠘⢂
⢀⠄⠀⢠⢀⠀⠀⣉⣂⠐⠻⠲⡶⠲⡶⠆⠀⠰⢆⠂⢒⠶⡀⠁⡁⠈⠁⡀⠀⡐⠈⠀⠁⢀⠀⠀⠀⣄⠀⢠⠀⠀⠌⠈⡀
⢀⣤⣤⣄⡏⢄⢾⣿⣿⠀⠀⠀⠹⠜⡀⠈⠤⠂⠈⠳⠎⠀⠈⠒⠀⠀⠂⠂⠀⠀⠀⠀⠀⢀⠀⠀⣄⠈⠘⠈⠑⠠⠆⠀⠀⠠⠘
⠀⢿⣿⡟⠀⠀⠈⠋⠙⢆⠀⠀⠀⢀⢆⠀⠀⠠⠀⢀⠀⠲⠲⠒⠒⠒⠖⡤⢄⠀⠀⠀⠀⠞⠉⠀⠐⠄⠀⠀⠆⠀⠀⠀⣀⡀
⠀⠀⢖⠀⠀⠀⡠⠒⡀⠘⠣⢀⠠⠼⠸⠄⢀⠀⠀⡞⠀⢀⠀⢀⠐⠀⡆⠀⢘⠆⠘⠋⠁⠀⠀⠀⡀⠈⢆⠈⠀⠀⠃⡀⠉
⠀⠂⠛⠑⠀⠀⠅⠀⠀⢂⠀⠔⡀⠀⠀⠀⢰⡀⠀⡁⢈⠁⠄⠁⠈⠀⠁⠀⠀⠀⠀⠀⢢⡀⠀⠀⡀⡀⠀⠁⠀⠈⠂⠁⠀⠐
⠀⠀⠀⢰⡄⠸⡀⠀⠀⡘⢸⠠⠄⣁⠀⡀⠡⢸⠀⢃⢄⠀⠐⠐⠢⠀⠠⠄⢀⠇⠀⠀⠀⠀⠀⠤⠀⠸⠄⠀⠀⡀⠈⠁⠈⠂
⠈⡐⢠⠃⠱⡀⢡⠀⢀⠀⡸⣀⠀⠀⠀⠀⢐⠸⠀⠀⠘⠀⠤⠤⠤⠤⠄⠐⠁⠀⠰⠆⢰⣶⠞⠉⠁⠀⠙⢶⣶⠀⠀⠐⠈⠄⠁
⠀⠀⠎⠀⠀⠰⠀⠉⠈⠀⣈⠂⢩⠄⠀⠬⠀⠊⠀⣄⠀⠀⠀⢀⠀⠢⠉⠁⢐⠀⣀⠀⠀⠙⠀⠀⠀⠀⠀⢸⠁⢀⠠⠀⠒⢐⠢
⠀⢸⢀⡀⣀⠀⢇⠀⣸⠀⠉⠀⠙⠁⠀⠀⣠⠊⡀⠊⡀⣀⡂⠘⡬⢄⣲⠅⠈⡀⠓⠁⠀⠈⢀⡀⠀⠀⣠⠊⠀⢀⠘⠂⢒⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⢀⢐⠀⠀⡰⠁⠀⠀⢠⡅⠃⠀⠀⠀⠀⠀⡀⢀⠅⠀⠴⠢⠀⣤⣬⣷⣯⣤⣇⠀⠀⠑⠀⠐⢂⠁
⠀⢀⡀⠙⢋⢄⠀⠈⠢⠈⠈⠈⠀⠀⠐⠧⠐⠂⠉⢀⡀⡀⠀⠀⠀⠉⠐⠒⠁⠐⡿⠠⡤⠤⡄⡉⠉⣉⣉⣀⣀⢀⠀⠠⠄⠺⠃
⢀⢮⣈⠻⠧⣔⠢⡄⠐⠠⠀⠀⠀⢀⠆⢀⠀⢠⠞⠁⠀⠰⠞⠉⠁⠀⠀⠀⠂⡀⠀⢠⣀⣀⡃⠀⠀⠀⠀⣰⠀⠀⠀⡀
⠘⠉⠀⠤⠀⠐⠀⠅⠐⠀⠊⠀⠈⢂⣀⡈⠀⠐⠀⠁⠂⢐⠆⠼⠀⠷⠀⠀⠀⠁⠀⠀⠀⠈⠁⠁⠈⠁⠈⠁⠉⠀⠁
⠈⠢⡀⠀⠀⣀⠤⠀⠚⠒⠀⠀⠂⠀⠙⠀⠀⠃⠒⠀⠀⠌⢸⠀⣇⠀⠍⠀⠀⠀⠘⠄⢱⠀⢉⠀⠀⠎⠂⠰⡰⢢⠚⠁
⠀⡠⠬⠉⠀⠀⢄⠀⢀⢆⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠌⠀⠀⠲⠀⢀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠂⠐⠃⠀⠊⠀⠐⠂⠀⠈
⠀⠀⠀⡖⠲⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣰⣰⡌⢄⡸⠀⠀⡂⢀⠀⢀⠂⡂⠀⠚⠈⠇⢹⠈⠐⠄⠀⠡⠀⢡⠋
⠀⠒⠀⠀⠀⠀⠚⠀⠁⠂⠤⠁⠁⠀⠈⠉⠈⠒⠒⠒⠒⠒⠀⠂⠀⠁⠀⠑⠀⠈⠂⠘⠑⠃⠐⠂⠐⠁⠊⠐⠒⠀⠀⠀⠂⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢡⠠⠀⠄⠆⠀⠀⠀⠀⠀⠉⠣⡀⢀⢦⠀⡠⠛⠁⠀⠀⠀⠢⣄⢀⠤⠝⠛⠯⠤⣄⣠⠄
⠀⠀⠀⠢⣔⢤⡄⡒⠰⢠⡤⣂⠤⠂⠀⠀⠀⠰⡛⣭⣠⡝⢳⠆⠀⠀⠀⠀⠀⣙⡃⢰⣶⡶⣶⣆⣽⢋⡀
⠀⠀⠀⠀⠚⠘⢷⡍⠣⡾⠛⠛⠀⠀⢀⣀⣤⣶⣿⢘⣓⠓⣿⣶⡄⠀⠀⠀⠉⠙⣻⣢⢍⣉⡹⢾⣻⡛⠉⠁
⠀⠀⠀⠀⠀⣿⣷⣿⣾⣛⣿⠁⠀⠀⠈⠉⠁⢸⡟⠉⠈⢿⣿⣿⠃⠀⠀⠀⠀⠈⡀⠀⢀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠉⠑⠛⠚⠛⠉⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣤⡴⢾⠿⣿⣷⣄⠀⠀⠀⠀⣸⡇⠀⠀⢠⣾⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⡶
⠀⠀⠰⠶⠟⠒⠒⠛⠛⠛⠛⣿⣇⣤⣇⣿⣿⣟⠒⠈⠀⠀⢸⠀⠀⠀⢿⣿⣿⣿⣿⣵⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠙⠋⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠙⠛⢻⣿⣿⡇⠀⠀⠀⠹⣿⠁
⠀⠀⠀⠀⠀⠀⡀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⣀⣷⡿⢿⣧⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⡜⣿⣿⣦⣤⣼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢤⡄⢲
⠀⠀⠀⠀⣾⠿⣟⣁⣈⣻⠿⣶⠀⠀⠙⠛⠛⠛⠛⠻⣿⡏⠉⠍⢿⠿⠛⠛⠛⠛⠛⠁⠀⠀⠀⠐⣾⡼⢷⣯⡄
⠀⠀⠀⠀⣿⣦⣋⣋⣙⣛⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢻⣥⣬⡟⡋
⠀⠀⠀⠀⠻⣿⣠⣤⣦⣄⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⢛⡒⠻⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣄⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⢶⣤⣤⡀⢠⣄⡄⣠⣤⠄⣠⣤⣴⡆⠀⠀⢀⣿⣿⣿⣿⣿⡿⠤⠤⠤⠤⠤⠤⢶⣦⣤⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⣿⣿⡁⢸⣿⣿⣇⣿⡄⢹⣿⡟⠀⠀⠀⠘⣿⣿⠿⠻⠿⠇⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠈⠻⣿⣶⡶⢦⡴⣶⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠓⠒⠒⠚⠛⠛⠻⢿⣿⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣖⢲⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⡐⠟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣎⣭⡛⠫⠭⠙⠉⠒⢄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠹⣆⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠉⠛⠢⢄⠠⣴⣵⡄
⠀⠀⠀⠀⠀⢸⡷⠲⠶⢶⠒⣿⠀⠀⠀⣀⣹⣄⠀⠀⠘⡿⠿⠿⠿⠶⣶⡶⠶⣤⣧⣀⡏⠉⠁⠒⢲⠀⠈⡆⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣧⣀⣠⣸⠀⢋⡄⠀⣾⡟⠙⠻⣇⣀⣴⠗⣤⠀⠀⢀⣀⣈⣲⡀⠈⣿⣿⠀⠀⠀⢸⠀⠀⡇⣿⣿⡇
⠀⠀⠀⢠⡞⠉⠛⠾⠭⠭⠷⣿⠙⠓⠛⢻⡷⢾⠿⠿⣥⣾⣷⣤⡤⠴⠿⠿⠿⣿⣿⡿⠋⠀⠀⠀⢸⠀⠀⣟⣿⣿⡇
⠀⠀⠀⢸⠉⠓⠒⠒⠀⠐⢺⣿⣿⠛⠉⢹⡇⣧⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡇⢀⠀⠀⠀⢸⠀⠀⣿⣿⣿⡇
⠀⠀⠀⢸⠀⡖⠲⠤⠤⠤⠞⣿⣻⡶⠶⣾⡇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠈⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣤⣿⡛⣉⣃⡨⡳⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣃⡉⠉⠀⢀⣲⡄⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⣼⣽⣿⣷⣿⣿⣯⠨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠉⠉⠉⠉⠁⡇⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⡟⠻⠿⠿⠿⠿⠿⠂⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣉⡓⣒⣒⣛⣩⡵⡀⠀⠀⢸⢿⣿⣇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⡇⠀⠰⢤⡰⡶⠶⠀⢸⣷⢄⣀⠀⠀⠀⠀⠀⢀⣷⢤⣄⣈⣉⣉⣁⣤⢴⡟⠋⠉⠙⠛⠻⠷⢤⣄⣀⡀
⠀⠀⠀⢸⠀⠧⢄⣀⣀⡇⠀⣴⠋⠀⠈⢲⠄⠀⣿⣿⠟⠻⠿⠿⠿⠿⠓⡏⠙⠓⠒⠶⠒⠒⠊⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢓
⠀⠀⠀⠘⠦⣄⣀⣀⣀⡇⠀⣈⡳⣤⡔⣁⠀⠀⣿⡟⠀⠠⡤⠒⠚⢿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠈⠉⠉⠉⠉⢀⣠⡟⠧⢤⣀⣷⣷⡶⡟⠟⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣤⡴⠊⠁⠀⢀⡤
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣿⠿⠿⣿⣿⣿⠇⢿⠇⡀⠀⣠⣯⣧⠤⠂⡼⣿⠢⢤⣄⣀⣀⣠⠤⠖⢻⠿⣿⣿⣿⣿⣿⠀⢀⡤⠞⠉
⠀⠀⠀⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠒⠊⠁⠘⠿⠾⠉⠉⡟⠒⠚⠋⢻⡀⠀⠀⠀⠀⠀⠀⣀⡟⠀⠀⠉⠉⠛⠻⠖⠉
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠼⣧⣤⠴⠠⡄⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠚⠋⠁
⠀⠀⠀⣿⠤⠤⠤⠀⠐⠒⠒⠒⠒⠂⠉⢻⠀⠘⠶⠒⠊⠉⠁
⠀⠀⠀⠹⠴⠶⠒⠒⠒⠒⠒⠒⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢰⣿⡇
⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⣸⣿⣧
⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠙⣿⠄⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠹⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⠀⠀⢠⣾⡿⠃⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⣿⡿⠁⠀⠀⣸⣄⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢻⣿⣿⡟⠇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣠⣴⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⢠⡀⠹⣿⣿⣾⣿⣆⠀⠀⠀⢀⠀⠀⠀⣼⣇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡟⣠⣾⣿⣿⣿⠏⠀⠀⠀⣄
⠀⠀⢀⡀⠀⠀⣸⡗⠀⠙⢿⣿⣿⣿⡆⠀⠀⠘⣧⠀⢸⣿⣿⣶⣤⣴⣿⣿⣿⠀⠀⢻⣦⡀⠀⠀⠙⢿⣿⣿⣿⠟⢰⣿⣿⣿⣿⣿⣆⡀⠀⣰⣿
⠀⠀⠀⢻⣷⣼⡟⠀⢸⣆⣨⣿⣿⣿⡟⠀⢀⣼⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣼⣿⣿⡆⠀⠀⠀⠙⠿⢣⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⡆⠀⠀⣿⡿⠀⠀⠈⢿⣿⣿⣿⣿⢃⣴⣿⡟⠁⢀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣾⣿⣶⣾⣿⡇⠈⣷⡄⠀⠛⢿⡿⢡⣿⣿⣿⣧⣤⣼⡧⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠙⣶⡘⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠋
⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀⢸⣇⢿⣿⣿⣿⣿⣿⢃⣶⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⢀⠈⠹⣿⣿⣿⣿⣿⠏⠀⠀⢸⣯⣿⣿⣿⣿⣿⡿⠁⣾⣿⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣤⣾⣿⣿⣿⠏⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠙⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⣀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⢠
⠀⠐⠈⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢀⠀⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣦⣤⣤⣤⣤⣤
⣿⣿⣴⣭⣦⣥⣽⣥⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢌⣆⠤⢆⡄⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠰⠀⠀⠀⠌⠢⠈⠢⡈⠂⠂⠚⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡵⡇⠀⠄⣀⠂⢄⠢⠀⢈⠀⣀⠠⠄⠤⢱⣄⣣⡀
⠚⠁⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠳⢄⡀
⠀⠀⠀⠀⠓⠤⢄⡀⠈⠙⠢⢤⣀⠀⠀⠀⠀⠘⣠⠴⠊⠁⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠁⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⣁⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⠀⠀⠀⠿⠘⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡜⠃⠀⡠⠖⠀⡠⠒⠀⠀⣏⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡠⢹⠀⠀⠀⠀⠀⠨⠭⠄⡠⠾⢑⠟
⠀⠀⠀⠀⠀⠀⢸⠤⠒⡉⡀⢀⠌⠀⠀⠀⠀⢣⠄⠀⡀⠀⠄⠈⠙⢁⡘⠤⠐⠈⠁⠀⠀⠑⢌⠠⠀⠐⠄⡴⠊⣠⠔⠁
⠀⠀⠀⠀⠀⠀⣁⡠⢊⠊⢠⠊⠀⠀⠀⠀⠀⢹⡒⠁⢀⣀⣀⠴⠈⣡⢀⠄⠠⠠⠴⠄⢀⣀⢀⡉⠀⡄⠐⠒⠉
⠀⠀⠀⠀⠀⠀⡝⡰⢁⡴⠁⠀⠀⠀⠀⠀⠐⠓⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⣠⣟⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠹⡈⠀⢀⡀
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡴⠂⠀⠀⠀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠊⠀⠀⠀⠀⡠⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣶⣄⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣶⠖
⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣶
⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠃⠀⠀⠀⣀⣀⣀⣴⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠿⠟⠋⠀⠀⠀⠀⢠⣖
⠀⠀⠀⣈⣿⣁⠀⠀⠰⣤⠉⠀⠰⣿⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠿⠿⠿⣿⣇⠀⠀⠘⠀⣆⣀⠠⠀⣤⡄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠰⠟⠉⢹⡇⠀⠀⠀⠀⠀⣼⠁⢸⡏⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠉⠃⡈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⢀
⠀⠀⠀⠀⢀⠀⠀⣴⣤⣤⡀⠀⣿⣠⣤⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠛⠂⠀⠀⠀⠀⢙⠇⠀⠀⠀⠀⠀⠀⢳⡆⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⣠⣷⣦⣄⡘⢿⠿⢷⠀⣿⣿⣿⠏⡀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⣿⡇⠀⠀⠀⠀⠀⠀⣬⣁⣴⡿⠋⠁⠀⠀⠀⠀⠀⠸⣿⠄⣿
⠀⢠⣴⢛⡛⠛⠛⠁⠀⠀⢀⡀⠉⣶⣤⣶⣷⣤⡀⠙⢿⣧⡀⠀⠀⠿⠀⢸⣦⠀⣴⣦⣼⣃⠀⠀⠀⠀⠀⠀⠛⣙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠛
⠘⣿⣿⣾⡏⢀⠀⠀⠀⠀⠀⠃⠀⠉⠘⠛⠉⠁⠀⠀⠀⠈⠻⠞⢿⡗⠀⠀⠋⣀⣿⣿⠟⠛⠻⣦⠀⠀⠀⠀⠘⣿⡦⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰
⠠⣿⣿⣿⡿⠛⠛⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⡄⢷⠀⠀⠀⠀⠘⠀⠀⠀⠀⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠛⢿⡗⠀⠀⠀⠿⣿⣆⣰⣜
⠀⠀⠉⠻⠀⠀⠀⠀⠀⠰⣾⣿⡇⠀⠀⠀⠀⠀⠀⡀⣧⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠠⠬⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠙⠃⠀⠀⠶⠂⠀⣠⣷⣼⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢸⣶⢦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣠⣾⣿⠟⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢶⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘
⢸⡁⠀⠀⠁⠀⣀⣠⣤⣤⣀⠀⠀⠀⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⣼⠃⠀⠀⣤⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠛⠃⠀⢶⡄⠀⠀⠀⠀⠀⣰⣆
⢸⣷⡀⠀⠀⠀⣽⣿⣿⣗⠀⠀⠀⠀⠸⠛⣿⡟⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠆⠈⠁⠀⠀⠀⠀⠸⣿⣿⡆
⠈⢹⣷⡆⠀⠀⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇
⢀⣾⡁⠀⠀⠀⠀⠘⢻⣿⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒
⢸⣟⢁⣌⣅⠀⠀⠀⠈⠻⢷⣦⢴⣿⣸⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢟⠁⠇⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠋⠁
⢈⣉⠉⠻⢿⡇⠀⠀⠀⠀⠀⠀⠘⠋⣩⡄⠀⣀⡠⠘⠉⠀⣹⣿⠿⠿⠗⣀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠐⣷⠀⠘⢠⠄⠀⢈⣿⣂⠀⠀⠀⠀⠀⠀⠐
⠸⠿⣿⣦⣀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⢠⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⠀⠀⠀⠉⠆⢩⡄⠀⠀⠀⠀⠙⠉⠛⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠹⣿⢻⣧⠀⠀⠀⠀⠠⣤⣄⠀⢾⠁⠀⠀⠀⠀⠈⣥⡀⢀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡇⢰⣶⣶⣷⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡿⢸⡇⠀⠀⠀⠀⠀⠀⢹⣷⣾⠇⠀⠀⠀⠀⠀⣿⣷⡈⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣍⣛⡛⣧⠟⠉⠛⠿⢿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠹
⠠⠀⠀⢀⡄⠀⢀⡀⢀⣀⣀⣀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣴⠏⠉⠈⠉⠻⣿⡿⠛⠿⠃⠀⠀⠀⠀⢹⣏⣽⡆
⠀⠀⠀⣼⣣⣶⣾⣿⣿⣿⣿⣿⣷⡶⠈⡅⠀⠀⠀⠀⠀⠀⠀⠈⢁⣄⣤⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⣿⣠⣤⠀⠀⠀⠀⠀⠀⣁⣀⡴⣶
⠀⠠⢾⡿⠿⠿⠿⠿⡿⠿⠟⠋⠁⠙⠰⠀⠀⠀⠀⠀⠀⠀⢾⢿⠿⠿⠿⢶⡦⡤⠏⠀⠀⠀⠀⠀⠸⠹⡿⣿⠀⠀⠀⠀⠀⠈⠉⠻⣧⢷⠀⠀⠀⠀⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠁⠒⠤⢤⡀⠀⣀⣀⣰⡿⢯⡙⠃⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⠞⠀⠀⠀⠁⠀⡀⠀⠈⠜⢇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠉⡆⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⢀⠃⠀⢠⡇⡟⠁⠀⠀⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀⡴⠫⣤⣤⡀⠀⠀⠀⡎⠀⠀⣸⠁⠩⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠩⠀⠀⠈⠁⠂⢀⣀⣼⡄⠀⠒⠋⠀⠀⠈⠁⡄⠀⠀⠀⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠑⠀⠀⠀⠁⠀⢀⡰⣄⠀⣀⡔⣇⠀⠀⠀⠈⠀⡐
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡤⠈⠁⢏⠲⢶⡶⠸⢇⠀⣀⡀⠀⠸⠋⠙⠉⠀⡞⠓⠀⠣⠔⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡁⠀⢀⣨⡷⡾⠀⠀⠀⢢⡿⠿⠶⣾⣦⣶⠖⠛⠛⠂⠀⠀⠄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠢⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠧⣤⠼⠷⣶⣿⡏⠀⠈⢤⠞
⠀⠀⠀⡀⣠⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⣾⣶⣿⢶⡄⠀⠈⠓⡄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠈⠀⠀⠀⡀⠈⠀⠀⢻⠀⠒⠀⠄⠤⠄⠑⠒⠊⠘⠉⡉⠹⣭⣠⡦⠴⠉⠒⠈⠓⠀⠈⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡨⠀⣠⡆⠀⠀⠂⠈⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡠⠖
⠀⠀⠀⡠⠄⠀⠀⠐⢾⣆⠀⠀⠀⠀⠀⠀⡘⠁⠀⠃⠁⠀⠀⠈⣀⠄⠀⠀⠠⠄⠀⠀⠀⠀⠠⠊⠀⢄⠀⠈
⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠜⠋⠔⠀⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣸⠶⠞⠋⡄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢧⣸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⢀⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡄
⠀⠀⠀⠀⠘⣿⣝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡫⣿⠇
⠀⠀⠀⠀⠀⣹⢗⢿⠙⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣹⢷⢟
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣄⠙⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⢁⣼⣷⣿⡟
⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡷⢿⣿⣿⠲⢦⣀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣿⣿⣶⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠙⣿⡫⣙⣿⣦⣾⣧⣙⡲⣾⣇⠀⠀⠀⢹⣷⡀⠀⠀⠀⡀⠀⠀⠀⣀⡀⠀⠀⠀⣴⡯⠴⢋⣿⣍⣴⠿⣻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣍⣲⣤⢀⣁⠛⣿⣦⡀⠀⠈⣿⠿⠶⠾⠀⢸⣆⣀⣴⣿⠇⠀⠀⣴⡿⠿⠟⠋⣩⡽⣋⣽⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡛⠦⢭⣿⣤⡨⠭⣽⣿⠟⣆⠀⣸⡇⠀⠀⣺⡏⠛⠶⠾⡏⠀⡰⢾⣿⣓⡒⠃⣚⣟⣋⣽⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⠷⣤⣬⣛⣁⣙⠶⢧⢤⣾⣦⣿⠀⠀⠛⢻⡿⣷⠇⠀⢷⣼⣧⣂⣿⣭⣒⡻⢟⣛⣩⣗⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢆⠹⣭⣤⣜⡒⢲⣯⣿⡟⠀⢀⣤⣼⣧⡄⠀⠀⠘⣯⢯⠤⠥⠀⠐⣻⠟⣹⡅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠡⠶⠀⠛⣾⡿⠇⠀⠀⠈⢹⡇⠀⠀⠶⠀⢻⡯⠓⢨⣍⠽⠻⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣹⡄⠀⠠⣿⣾⣟⡇⠠⠀⡸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣀⠀⠙⢿⡦⢀⣉⠉⠉⠁⠀⢂⣱⠏⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠿⠓⠆⠀⢀⡉⢓⣒⠐⠒⠚⠉⣠⡜⣆⠈⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡄⠀⣸⠚⠁⢸⣼⠇⠀⢿⡱⠹⡼⠌⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢹⠀⣴⡿⠛⢂⡴⢸⡲⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠷⠖⠋⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠎
⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣻⠋
⣀⣤⢤⣶⣾⡿⠿⢻⡿⢋⣭⠉⠁⣀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠛⠛⠻⠿⣶⣦⣤⣤⣤⣴⣿⣿⡽⠃
⠻⣿⠀⠫⢥⣀⠒⠛⠳⣿⣿⡀⠀⠀⠀⠌⠉⠁⠃⠀⠁⠀⠁⠁⠉⠉⠁⠀⠄⠀⠠⠀⠤⠰⠨⠭⠭⠭⣼⣿⣏
⠀⠈⠓⠦⣠⠒⠒⠾⡶⠠⠒⠂⠀⠠⡄⠀⡀⠀⢂⠉⢀⣀⣀⡄⠀⣀⣀⠀⠀⠈⠀⢀⣀⡤⣶⠟⠛⠓⢾⣿⣿⣦
⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣴⣶⣶⣤⣤⣤⣤⣤⣄⣤⣤⣤⠤⠤⠤⠤⠤⠤⣶⣖⣚⣩⣵⠞⠁⠀⠀⠀⠀⠙⢮⣋⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡏⠀⠀⠀⠀⠀⠈⠻⢿⠀⠀⠀⠀⠀⠀⠀⠙⠾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⡬⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⣁⡃⠀⠀⠀⠀⠀⢱⠚⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠺⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠀⠀⠁⠀⡀⠀⠀⣀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⢀⠠⠀⠀⠐⠀⠑⢄⠈⠂
⠀⠀⠀⠀⠀⢀⠀⢤⠤⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠔⢁⠄⠀⠈⠀⠀⠄⠀⠀⠠⠀⠔⠀⠀⢸⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢫⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡠⢂⡄⠀⢈⣨⡄⠉⠛⢄⠀⠀⠀⠀⢀⡀⠀⠀⠰⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣐⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠈⠀⣀⡣⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠈⠀⠀⠀⠠⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠐⠞⠉
⠀⠀⢀⠂⠁⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠁⠈⡆⠀⡠
⠀⠀⡀⠁⠈⠀⠐⠀⠀⢳⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠄⠀⠀⠀⡯⡊⢀⠴⠁⠀⡀
⢸⡂⠧⠀⠀⠀⠀⠀⠀⢄⠁⠠⡄⠀⠀⠀⠗⢄⠀⢀⡀⠀⠀⠊⢀⡌⡀⠀⠀⠀⠀⢀⠇⠀⠁⠀⠈⠀⠀⡀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⠀⠀⡀⠔⠑⠐⣦⣤⠀⠘⡀⠐⠁⠀⠀⠀⡠⠊⠉⠀⠐⠀⠀⠒⡤⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⢑⠶⠀⡀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣦
⠀⠀⢻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣬⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀
⠀⠀⠘⣿⣿⣿⣿⣆⣀⣀⣀⣰⣶⣶⣶⣶⣾⡿⠿⢿⡟⠛⣿⠛⢛⠉⠻⠏⠁⠉⠙⠟⠛⠛⠿⠻⢿⢿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⠿⠭⠿⠀⠠⠾⠀⠀⠒⠒⠒⠂⠀⠙⠀⠀⠀⠉⠀⠀⠴⠀⠐⠇⠚⠛⠛⠿⠻⠿⠿⠩⣿⣿⣿⣶⣤⡀
⠀⠀⠀⣿⣿⣿⣷⡤⠄⠀⠀⠀⢀⣀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⠠⠄⠀⠤⣤⠀⣈⠉⠹⠯⠄
⠀⠀⣸⣿⡿⠟⠋⠀⠀⠀⠀⠀⠈⠿⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠛⠋⠉
⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁

⠀⠀⠀⠀⠀⠀⠐⠒⢶⣦⣤⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢰⣤⣤⣽⣿⣿⣿⢖⣦⣾⣿⡿⣿⣿⡟⢸⢞⢲⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠠⣤⣭⣽⣿⡿⢋⣵⣾⣿⣿⣿⢳⣿⡿⡇⠹⣙⡢⠋⠁⡬⠛⠁
⠀⠀⠀⠀⠀⠤⠶⣾⡿⢋⣴⣿⣿⣿⣿⣿⠃⠙⡛⠀⠀⠠⡀⠀⠀⠈⠉⢙⠇
⠀⠀⠀⠀⠄⠲⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⡀⠀⠀⠨⡀⠀⢁⠤⠃
⠀⠀⠀⠠⠶⢾⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⡀⠀⠂⠈⠳⠤⠝⠁
⠀⠀⠀⢀⣴⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠋
⠀⠀⠀⢠⣼⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⢀⡠⠄
⠀⠀⠀⢀⣼⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⣴⣤⣶⡿⠋
⠀⠀⠀⠁⣽⠨⣿⣿⣿⣿⣿⣿⣝⡛⣿⢕⣣⢴⠟⠛⠉
⠀⠀⠀⠀⢰⡆⣿⣿⣿⣿⣿⣿⡀⠅⠈⠉⠉⠁⠀⠀⠀⢀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠐⠀⠱⠹⣿⣿⣿⣿⣯⢢⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⠻⠿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠸⣄⢣⢽⣿⣿⣿⣿⣫⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢯⠙⢿⣧⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠹⡆⣬⡻⣿⣿⣿⣷⣷⣄⢀⣠⠾⠟⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠉⣿⠑⣮⠿⣿⣿⣿⣿⣀⠉⠋⠉⠙⠶⠆⠀⠀⠀⠀⠀⠀⠐⣘⣧⣤⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠜⡓⢮⡛⢿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠀⢤⣄⣉⡛⠿⠿⣿⣶⣶⣶⣶⣾⣷⡶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⢀⣴⡞
⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄
⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⢸⣿⡟⣧⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⠀⠀⢀⠀⢸⡇⠀⢸⠀⢱⢰⣿⣇
⠀⠀⠀⠀⠀⡜⠉⢠⣸⣇⠀⢀⣼⣇⠀⠀⢀⣿⣿⡀⠀⡘⢦⣈⣿⡄⢸⣧⣾⣿⣯⠻⡄⠀⠀⢱
⠀⠀⠀⠀⠈⠀⠀⠸⣿⠙⠳⡾⠉⣿⣦⣴⠟⢻⡿⢻⣦⡇⢸⡟⢹⢇⡞⢿⣯⡾⠋⠀⢿⣾⠀⠚⠀⢠⡀
⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠰⡀⢻⡇⠉⠀⠘⠇⠀⠀⠁⡞⠀⠀⠊⠀⠊⠀⠀⠀⠀⠈⠟⠁⠀⠀⢼⠁
⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣶⣦⡀⠀⢀⡴⢶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡶⣶⡄⠀⣿⠈⠀⠘⣿⠀⣾⠑⠁⠀⠈⠒⢀⡟⠄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠁⠀⢀⡿⠀⢿⡄⠀⠀⣿⠀⢿⡄⠀⠀⠀⠀⣼⣷⣛⡫⠭⠵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠶⣿⣅⣁⠈⠻⠶⠾⠵⠃⠈⠿⣶⣶⣂⢴⢏⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠉⠉⠋⠀⠀⠀⠀⡔⡄⠀⠀⠀⠀⠈⠋⠀⢟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣶⣄⡀⠀⢀⣤⣤⡀⠉⣀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠎⠀⢸⡷⠶⣟⠞⠉⢿⡄⣿⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢏⠽⣷⢶⣛⡇⠀⢹⣀⡄⣸⠃⣿⡄⠀⡴⠙⠂⣿⣄⣤⣴⣾⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠹⣯⠀⢧⠀⠈⢧⡴⣟⠔⣿⣷⣶⣶⣶⠦⠼⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢙⣒⣸⡆⠀⠘⠏⠑⢾⠏⠭⣤⠀⠀⣶⣦⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⣴⣿⣿⣿⣿⡀⢀⣀⡀⡠⢀⠀⠙⠀⠐⣿⣿⣿⣷⡌⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣼⣻⣿⣿⣿⣿⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣻⡆⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣼⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢂⠀⠀⠂⠀⠀⣿⣿⣿⣿⣷⢿⡄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣿⣻⡿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣻⡇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣯⡿⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⢡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣌⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⢬⣉⣉⣉⣉⣉⣩⠤⠖⠊⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢽⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣀⠀⠀⢀⡄⢀⡇⡇⠀⣄⠀⠀⠀⣠⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠛⢶⠻⣅⣸⡇⣷⡀⣹⠟⢶⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⣿⣿⣿⣿⠀⡿⣧⣿⡿⡻⣿⠿⡟⠀⣿⣿⣿⣿⣿⡿⠿⣷⡄
⠀⣤⣀⡀⠀⠀⣄⣀⠀⣠⣼⣿⣽⣿⠀⣧⠈⣿⠠⣇⡅⢾⡇⠨⣧⣿⣿⣿⣿⣤⡀⢀⣀⡄⠀⠀⣀⣠⡄
⠀⠀⢙⣻⣿⠰⣼⣿⣿⣿⣻⣻⣽⣿⡆⠻⠷⢾⠷⣛⠛⡞⢳⡾⢾⣿⣟⣽⣻⣻⣿⣿⣯⡴⢹⣿⣛⠁
⠀⠀⠀⣉⣻⣻⣾⣏⡹⢿⣷⣞⣽⣸⡇⢸⢟⣼⣷⢟⣥⠀⣸⠁⢺⣿⣸⣝⣶⣿⠿⣙⣿⣾⣛⣋⡁
⠀⠀⠀⠈⣽⣿⣿⣿⣧⢿⣿⡿⣾⢻⡇⢸⡀⢹⡇⣬⣸⠀⡿⠀⣿⣿⢻⡾⣿⣿⢧⣿⣿⣿⣿⡍
⠀⠀⠀⠀⠀⠈⣉⣩⣽⣿⣿⡷⢧⣮⣷⣾⣷⠊⢀⣀⣀⣹⣿⣤⣿⣯⣮⠷⣿⣿⣿⣭⣉⠉
⠀⠀⠀⠀⠀⠀⠉⣩⣴⠶⠟⠻⠟⢹⣿⣿⣡⡶⠦⢠⢰⣶⡭⢿⣿⣿⠙⠿⠛⠷⢶⣬⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢏⠉⠀⠀⡀⠈⣃⣄⣼⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠒⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠤⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⢠⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⢸⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⡰⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⠀⠀⣼⡿⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⢀⠃⠀⠀⠀⠀⢠⣾⣿⡿⠀⠀⠀⠀⣼⡿⠁⡀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⣠⡞⠀⠀⠀⠀⣴⣿⣿⡿⠁⠀⢀⠀⣸⣿⡃⣸⠁⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠀⠀⢀⣴⣿⠁⠀⠀⣠⣾⣿⣿⡿⠁⠀⢠⡄⢰⣿⣿⠃⡿⢰⠋
⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠁⠀⣰⣿⣿⠃⠀⣠⣾⣿⣿⣿⡿⢁⠀⠀⣸⡇⢸⣿⡿⢀⠳
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡏⢀⣼⣿⣿⠃⣠⣾⣿⣿⣿⣿⠋⢀⠂⠀⢠⣿⠁⢨⡿⢁⡿⣈
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣼⣿⡿⠙⡿⣿⠇⣼⢡⣿⢇⣴⣿⡿⣿⣿⠟⠁⣰⢋⡞⣠⣾⠋⠀⠈⣠⣟⣼⠃
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢰⣿⠏⠀⢰⡇⣿⢸⠇⣸⣿⣾⣿⠋⣴⣿⠏⡌⣰⣧⣞⣴⡿⠁⠀⣠⣾⣿⡞⠁
⠀⠀⠀⡄⠀⣿⣆⠀⠀⠀⣿⡏⠀⠀⢸⠃⠋⢸⠀⣿⣿⣿⠁⣸⣿⡏⣼⢠⣿⣿⣿⡿⠁⣠⣾⣿⡟⠉⠀⢀⣤⡾
⠀⠀⠀⡇⠀⢿⣿⡄⠀⠀⣿⠁⢠⡇⣾⠀⠀⠈⢀⣿⡟⠀⢠⣿⣿⢰⡏⢸⣿⣿⣿⠁⣼⣿⡿⠋⢀⣠⣶⣿⡟⠁⠠
⠀⠀⠀⣧⠀⡘⣿⣷⠀⠀⡿⠀⣸⣿⡟⠀⠀⠀⢸⣿⠀⠀⣼⣿⡇⣾⣇⢸⣿⣿⡿⣸⣿⡿⠁⢀⣾⣿⠟⠋⣠⠶⣡⠔⠁
⠀⠀⠀⣿⡄⠱⣍⢿⡆⠀⡇⢀⣿⣿⠇⠀⠀⠀⢸⡇⠀⠀⣿⢩⢣⣿⣿⢸⣿⡟⣿⣿⣿⠁⢠⡿⠋⣠⣴⣿⡷⠞⠁
⠀⠀⠀⢿⣿⡄⣿⣿⣷⠀⠃⣸⣿⡿⠀⡀⠀⠀⢸⠀⠀⢸⡇⡾⣸⣿⣿⢸⣿⣧⢹⣿⣿⠀⣿⢀⣼⣿⢟⠁
⠀⠀⠀⠘⣿⣿⣿⣿⡿⠀⢠⣿⡿⠁⠀⡇⠀⠀⠸⠀⢸⣼⣸⢣⣿⣿⢇⣾⣿⡇⣼⣿⣿⠀⠁⣼⣿⡿⠋
⠀⠀⠀⠀⠘⣿⢿⣿⡇⢠⣿⡿⠁⠀⢀⡇⠀⠀⠀⠀⣾⣿⢇⡞⢹⢟⣾⣿⣟⣴⣿⣿⠟⢀⣴⣿⠏⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠸⣿⣿⢁⣿⠟⢀⡞⢀⣼⡇⠀⠀⠀⣸⣿⠏⢌⢀⢫⣾⣿⣿⣿⢿⠿⠋⣠⠞⠋⠀⠀⠀⠀⣀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠘⠇⣼⠏⢀⡞⢀⣼⣿⠁⠀⠀⣰⣿⠋⠀⣼⣠⣟⣵⣿⠿⠋⠀⢀⣈⠄⠀⢀⣤⣴⠾⠛⣩⡟
⠀⠀⠀⠀⠀⠀⡈⣾⠃⢀⡾⣠⣾⣿⠇⠀⠀⣼⡿⠁⠀⣼⡇⣏⣿⡟⠁⢀⣠⠞⠋⠀⣠⡾⠋⠉⢠⣴⣾⡟
⠀⠀⠀⠀⠀⠠⢰⠏⠀⣼⣿⣿⣿⠋⠀⠀⣼⠟⠀⠀⣼⣿⣇⢻⡟⠀⣠⣾⡏⠀⣠⠞⠉⠀⣠⣶⣿⣿⡿⠀⣾
⠀⠀⠀⠀⠀⠀⡎⠀⢠⣿⣿⡟⠁⠀⠀⢼⠋⠀⠀⣰⣿⡿⢻⢸⠃⣰⣿⡿⠀⠀⠀⠀⢀⣼⣿⣟⣾⡿⠁⢠⢻
⠀⠀⠀⠀⠀⢠⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⢀⡼⠋⣾⡷⣄⣾⣰⣿⣿⠃⠀⠀⠀⢠⣿⣿⢻⣾⡿⠁⢠⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⢠⠏⣰⣿⡟⢇⣿⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⣿⣿⠏⠀⢠⠊⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠰⢣⣾⣿⣿⣿⣾⡿⠟⠋⠀⠀⠀⢀⣾⣿⣽⡿⠛⠁⢀⡴⠁⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣶⠀⠀⠀⡴⢋⣽⣿⠿⠋⠁⠀⠀⠀⠀⢀⣴⣿⠿⠟⠉⢀⣠⣶⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠠⢸⣇⢰⡇⠀⢀⠞⣰⠟⠋⠀⢀⣀⣤⡶⣮⡤⠞⠋⣁⣀⣤⣴⣾⣿⣿⣿⣿⡿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⡟⠀⠀⢀⠞⠁⠀⣠⡶⠟⠋⠁⠀⣀⡴⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠁
⠀⠀⠀⠀⠀⠀⢠⣡⣿⡟⠀⠐⠀⣠⠄⢀⡾⢋⡠⠆⠀⠀⢊⣥⣶⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⢀⣠⡾⠁⠐⣡⡴⠋⠀⠀⣠⣴⠿⠛⠋⠉⠉⠁
⠀⠀⠀⠀⢰⡿⠋⢀⣤⣶⣿⠋⠀⣠⣾⠟⠁⠀⣠⠾⠋⠁
⠀⠀⠀⢀⠟⢠⣾⠿⠟⠋⠀⠐⠚⠋⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⡀⢀⣤⣦⣶⣷⣾⣿⣶⣿⣿⠟⡠⠖⠈⠀⠀⡀⠀⢰⣤⡤⢀⠜⠉⢀
⠀⠀⣠⠔⠒⠀⣀⣽⣿⣏⣴⣿⠿⠛⣋⡶⣊⠤⠒⠐⢚⡛⠉⠉⠉⠩⠍⢛⡀⠂⠠⠤⢀
⠀⠀⠀⠀⠚⣉⣿⡿⠟⣋⣡⡴⠚⠋⢁⡄⣀⣀⣤⣀⣀⣤⣀⡀⠀⣀⡄⠈⠀⠀⠉⠀⠐⢆⢁⣒⢦⡀
⠀⠀⠀⠀⢀⢁⣭⣶⠟⣋⣠⡴⠊⠉⣁⣘⣋⣵⣿⡿⡿⠻⠏⡻⠋⢁⠉⠑⠒⠚⠧⣄⡀⢠⣾⢩⣯
⠀⠀⠀⢀⢰⣿⣿⣣⣶⡿⠗⠀⠠⣴⣟⣿⣿⣶⣶⣾⣿⣿⣵⡃⠀⠈⠈⠑⠂⠀⠀⠀⠁⢈⡿⠓⣿
⠀⠀⠀⣼⣿⣿⣿⢿⣿⠃⠀⣀⠶⣊⣿⣫⣿⣿⣯⠭⠘⠉⣂⡀⠛⢗⡢⣄⡀⠂⠀⠈⠀⠀⡟⢐⡃
⠀⢀⡼⢀⣿⣿⣧⣾⡇⡄⠀⠔⢪⣿⣿⢟⡭⢀⡤⠖⣋⣉⠉⢍⣛⠲⢌⢪⡙⢦⠀⠀⣀⣠⢷⡾⢃⡀
⠀⠋⣠⠞⡿⣿⣿⣿⢃⠁⣠⠾⣿⠿⠣⠏⡐⢁⡴⣛⠣⠩⢉⣹⡇⡌⢲⡄⡌⢈⡆⢐⠚⢹⡞⠋⣸⡇
⠀⠊⠠⠚⣱⣿⣿⣿⠛⠀⠀⠀⣀⣞⠀⡟⣰⢟⡃⢻⢤⣷⡆⡁⢿⠘⡆⢡⡸⣸⡄⠙⠁⢸⠈⢰⠍⠃
⠀⠀⢀⠴⣿⡿⢋⣭⣜⡀⠀⠚⡟⡞⣰⢡⣿⣶⣶⡌⠈⠉⠀⠀⠈⢣⡀⠺⡅⢸⠁⠀⠀⣿⠘⡟⠁
⠀⠀⠀⡖⣾⣿⡿⢿⣿⢰⡀⠞⡐⡇⢸⡟⠿⣿⠿⢃⠈⣤⣶⣤⣰⢎⡗⠂⣯⡆⣤⠐⢁⠏⢸⠃⡄
⠀⢠⠎⢈⣿⣿⣷⣾⣿⣷⡞⡵⢳⣇⣾⠀⡦⣤⣾⣿⢇⠻⣿⣿⣿⣿⠙⣸⣽⠠⠀⣀⣼⢄⡎⠀⠈
⠀⠀⣴⣫⣿⣿⡿⢹⣿⡟⡜⢡⠟⢹⣿⣇⠀⡛⠻⡿⢠⠦⠈⠩⢡⠇⠀⢿⣏⠴⠦⢤⠏⢸⠃
⠀⠀⣠⠴⢾⣿⣷⣿⢏⡞⣡⡏⠐⢺⡿⣏⠛⢦⣤⣤⣶⠓⣢⡝⡝⢠⢃⡼⠘⠖⢠⠏⢠⡿⠁⠲⢦
⠀⠀⣴⢿⣿⣿⡟⣡⠛⣴⡿⠁⠂⠀⡖⠈⣍⣓⣖⣿⣠⡿⢟⣠⣶⠇⡉⢓⠶⢲⡟⢀⡞⠀⠀⡀⠼
⠀⠀⠁⢘⠿⢁⡞⠡⣼⢿⣧⣤⣾⠛⣧⣄⣀⢙⣉⣤⠋⢐⡻⢟⠔⠁⠘⢣⡴⠋⢠⢟⡼⠃⠸⠒⠁
⠀⠀⠰⢇⣤⠏⢠⡾⠟⡿⢉⡶⢿⡔⢛⣛⡻⠥⢄⣐⣋⡭⠶⣧⣦⢀⣴⠾⢁⡔⠁⠸⣶⠠⡄
⠀⠀⢠⠞⠀⢀⡞⠁⡼⠃⣾⣧⣿⠒⣯⡴⠟⡯⠉⣽⣇⠿⣛⣭⣿⡶⠁⣠⡿⣦⣀⠶⠬⣁⠈⠓
⠀⠀⠘⢤⣤⡿⠁⣾⠇⢸⢃⣼⣿⠈⣧⣿⠾⠗⠟⣋⣭⢾⣿⣾⠿⣁⣰⣟⠓⣤⡙⡄⠀⠸⡟⢉⡇
⠀⠀⠀⡰⠛⣀⢄⡟⠀⡿⢸⡏⢻⣶⣿⣽⡶⢛⠿⢉⡱⣻⣏⣱⣟⠳⢮⣿⠀⣿⠇⡼⢀⡀⣈⣁⠠
⠀⠀⢰⠃⠈⢵⣾⠁⢰⡗⢸⢿⡇⢹⣏⣤⣿⣾⡾⢋⣼⣏⡶⠳⣍⣽⡻⣿⡄⠻⣾⡁⠈⠉⠀⣥⠆⣀⡀
⠀⠀⠘⣿⣦⣾⠃⠀⢸⠇⢸⡾⣿⠈⣿⣿⡇⠀⠉⠙⠛⣿⡇⢀⣿⣿⡇⢻⣿⢦⣀⡋⢉⡐⠒⠤⣄⡀
⠀⠀⠰⠋⢰⣇⣀⡀⣿⠆⢸⠃⢻⠀⢻⣧⠉⡻⣶⣶⣴⡿⠀⢸⣿⣷⣱⣿⣿⢣⢹⠿⣿⡙⠯⣤⣾⠟
⠀⠀⡗⠀⢺⢿⣿⠏⡟⠐⠸⣆⣿⠀⠈⢻⣎⠯⠻⠻⣿⠀⠀⣾⣿⣿⠷⠞⢋⡴⡿⢸⠹⣿⣀⠛⠻⡷
⠀⠁⠟⣄⡄⣸⢿⡟⢠⡦⣤⡏⢿⣦⠀⢼⣿⣀⠀⠂⢸⠀⢰⢻⣿⣥⡴⠶⠟⢁⡥⠾⢅⠛⠛⣷⡄
⠀⠀⠀⢨⣿⣿⡜⠁⠉⠠⢿⣯⣲⠟⠀⠈⠻⢥⠔⠆⠈⠓⠊⠚⠻⠯⠤⠰⠖⠀⠀⠀⠀⠛⠾⠞⠋

⠀⠀⠀⡀
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡠⠀⠀⠀⠀⢀⡦⢄
⠀⠀⠀⢸⠀⡸⠁⠙⢉⠇⠠⠀⣠⢐⠚⣓⠢⢀⠴⠂⠀⣴⢿⡭⠭⡻⣧⠀⡀⠀⠀⠇⢰⠙⠒⡉⡂
⠀⠀⠀⢸⣰⠁⠀⠀⣌⠀⠐⠄⡁⠬⣶⡟⠁⣇⡄⠀⠸⢟⡸⡀⠀⡀⣸⠀⠀⠒⠊⢊⠓⠘⠉⢏⡿
⠀⠀⠀⢀⠏⠀⠀⠀⠘⡄⠀⠀⠉⢄⡀⢀⡜⠁⡂⠁⡄⠑⢯⢮⣯⠾⠋⡀⡀⠀⠀⠈⠦⠀⠠⠼⠃
⠀⠀⠀⠈⠉⠉⠉⠉⡉⢁⠀⡀⢠⣤⣄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⡤⡌⣳⡁⢸⠂⡒⠄⠀⠀⠀⠒⡱
⠀⠀⠀⠀⠀⡲⢠⡀⠂⠠⠃⢱⡟⣷⡎⡆⠐⠂⢰⠀⢰⠅⠀⠀⠀⠈⠁⠉⠁⢸⠀⡃⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠄⢵⠐⠃⠀⣀⢀⢀⢉⡒⠊⠀⠀⠀⠈⠀⠀⡀⠀⡀⢀⠀⡀⠀⠀⠀⠰⠥⠤⠤⠤⠤⠤⠱
⠀⠀⠀⠀⠀⠀⠤⣸⣆⠹⢯⣟⡿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠇⠑⠈⠠⠥⠀⠀⠀⠀⠀⢀⠰⠄⡀
⠀⠀⠀⠀⠀⢀⣀⡈⣁⡀⠀⠀⠀⡀⠀⠀⠙⠰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⡍⣔⠁⠀⠀⠈⡴⡆
⠀⠀⠀⠀⡊⠁⠀⠀⠀⣈⠄⢀⠙⢋⡇⠀⠳⠀⣉⣀⣀⠈⢸⢓⣲⢀⢨⣿⣔⡁⠀⢿⠀⣴⣶⡀⠃⣤
⠀⠀⠀⠀⠀⠁⠉⠉⠉⠁⠀⠸⠤⠼⠆⠀⠀⠂⠡⣀⡠⠒⠉⠉⡀⠘⠿⠟⠉⠀⢁⠀⠈⠛⠞⠁⡀⠽
⠀⠀⠀⢸⡑⢒⠒⠠⢂⡄⠀⠰⢪⢍⢢⠀⠀⢶⠀⡀⠀⠀⠀⡼⣁⣥⠀⠀⠐⠉⠂⠉⢢⣀⣀⡜⠁
⠀⠀⠀⠘⠁⠀⠒⠒⠂⠝⠀⠰⢌⡈⠜⠐⠟⠀⠐⠘⠀⠀⠀⠀⠃⠔⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢄⠀⢸⡏⣻⡆⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠡⠀⠀⠈⠀⠂⠈⠀⢸⣿⣏⢀⣶⣶⣄⣴⡾⣦⢸⡇⣠⠄⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠉⠂⠀⠂⠀⢸⣇⠙⣿⣧⣼⡟⢻⣤⣤⢸⡿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠜⠂⢉⠅⠁⠐⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⠈⠀⠈⠁⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠞⠻⠜⠀⠀⠀⠀⠀⢰⣶⣦⡀⠀⠒⠯⠙⠀⣤⡄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⢀⢀⡄⠀⠀⠀⢸⣧⣿⠇⠀⣠⣤⣄⠀⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⣶⣾⣿⡣⠀⠀⠀⢸⡟⢷⣄⠰⣿⣈⣿⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⡏⠙⠛⠛⢛⠀⠀⠀⠀⠘⠃⠈⢻⡷⠙⠛⠁⠀⠋⠀⠿⠃





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢤⠄⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠐⠂⠀⠉⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠂⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠊⠀⠀⣠⠀⢀⠴⢀⣴⣤⣀⡉⠓⠀⠀⠀⠘⢷⢶⠖⠐⣊⡉⠴⠒⠉
⠀⠀⠀⠀⠀⠀⣴⠁⠸⣿⣿⣦⡑⠀⢀⡀⠈⢹⡿⠯⣆⠉⠛⠛⠫⠁⠀⠀⠀⠀⠀⠴⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠙⠀⠀⣿⣿⣿⠇⢰⢿⣽⣶⣾⣿⣷⡇⠠⣁⠤⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢿⠾⣿⣿⠅⡀⠈⣸⣿⣿⣿⣿⡿⠁⠀⠀⠓⠀⠐⢢⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⣘⠂⠀⠀⡜⠁⠀⠁⠀⣿⡆⠋⠄⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⢀⡃
⠀⠀⠀⠀⠀⠀⣤⣄⠀⢠⢖⣹⠀⡀⠀⠄⠀⠀⣄⠀⠁⠀⢀⣐⠓⠄⠘⠂⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⠈⢹⡟⡀⠀⠸⠋⣠⠽⡖⢀⢊⡄⣴⣹⣺⠃⣿⢿⣷⠀⠀⡀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⣾⣷⡁⠀⣀⣾⣧⠀⠀⠀⠘⠈⢻⣿⣿⣠⣿⣦⠹⣧⡇⠘⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠙⠿⣷⠀⢿⠃⠀⠁⠀⠘⠀⠀⢸⣿⣿⣿⠻⣟⠀⣿⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⢄⡀⢰⣄⠀⠀⠀⣿⣿⡇⠙⠟⠙⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⠉⠀⠀⣸⠏⡋⠀⠀⢠⠸⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢸⠀⠀⣿⠇⠈⠀⠀⢈⠢⡟⠄⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢺⣀⣼⠏⠀⢀⡀⠀⣸⠃⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣏⠀⠀⠈⣠⣞⡰⣇⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣿⠋⠀⠀⠙⠿⠆⢹⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠣⠽⠯⢿⣛⡯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠉⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣦⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣏⣼⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⡿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⡀⠑⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⡄⢹⣿⡏⠀⢸⣿⡆⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⣿⠁⠀⡏⢰⣈⡃⠰⣿
⣿⣿⠀⠃⢸⣿⡇⢀⠸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⣿⣿⣿⣏⠻⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⠀⠛⢀⡀⣃⠘⢉⡃⠘⣿
⣿⣿⠙⠙⡟⠙⣟⠉⣿⢩⡟⠉⣿⣿⣿⣿⣿⣿⡛⠿⢿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⠀⠹⣿⣿⣿⣿⣿⣿⣯⢩⣿⣿⢹⣿⣿⠉⠉⣿⣿⠩⣿
⣿⣿⠶⢶⣷⠴⣷⣶⠿⣾⡷⠶⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣿⠁⠀⠘⢿⣿⠟⠀⠀⢻⣿⣿⣿⡿⣿⣿⣼⠿⣿⠼⣿⠿⢴⢴⠿⣿⡬⣿
⣿⣿⡇⣾⣿⠀⣿⡇⡀⣿⣇⡀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⡠⠢⡄⣸⣿⣿⣿⡇⢸⣷⣾⣾⣾⣶⣿⣶⣶⣶⣶⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡇⠙⠿⠿⠋⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢻⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⡧⡠⢭⡛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢀⡾⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉⠀⠳⡀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠃⠀⠀⠀⠀⠐⣿⣿⣿⠏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣆⠀⠀⠀⠙⢶⡆⠑⢄⠀⠀⠀⠀⡠⠒⠢⡄⠁⠰⡟⠀⠀⠀⠀⣀⣀⠈⠉⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠃⠀⣸⡿⢹⣿⣿⣧⡀⠀⠀⠀⠙⢶⡀⠁⠔⠋⠉⠣⠀⠀⠱⡦⠠⡄⢀⡤⠚⠉⠀⢀⡩⠆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⠀⣸⣿⣷⠘⢿⣿⣿⣷⡄⠀⠀⠀⠈⢻⠋⠘⣦⡀⠀⠀⠀⢀⡀⠀⠀⠁⠀⣠⠶⠊⠁⠀⠀⢀⣿⡟⣿⠁⠈⠉⠉⠻⣿⣿⣿⣿
⡿⣻⣿⢃⠀⠀⣰⣿⣿⣿⣆⠈⠻⢿⣿⡷⠀⠀⠀⠀⠘⡄⠈⠙⢷⣤⠼⣶⡿⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠛⢁⣿⣷⣶⡀⠀⠀⢨⣭⣻⣿
⢱⣿⣿⡏⠀⢀⣿⣿⣿⣿⣿⣦⡀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠙⠋⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⣷⠀⠀⡿⣿⣿⣿
⠘⣿⡟⠁⠀⠈⠁⣾⣿⣿⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⣀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣇⠙⣯⠀⠀⠁⢸⣿⡿
⠀⠈⠁⠀⠀⠀⠀⠈⠛⠁⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢳⣤⣤⣾⡿⠻⠿⣿⣿⠀⠀⠀⠀⣀⢀⠀⠀⠀⠘⢿⣿⡿⠃⠀⠉⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣀⠉⠥⠄⠒⠂⠛⢋⡀⠉⠁⠀⡠⠂
⠀⠀⢠⠀⠀⢤⣧⠄⠀⢠⡄⠀⠙⠿⠟⠁⠀⠀⢰⠀⠀⢠⢲⡆⡷⢀⣠⡀⣠⠦⣸⣧⡆⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠠⣶⡤⠀⠠⡄
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣼⢹⡇⣿⣨⠻⣧⡤⠿⠘⠷⠀⠀⡈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢋⡘⠁⠉⠁⠤⠀⠐⠒⣶⣿⣿⣿⣷⣶⠦⢤
⠀⠀⣿⢠⣿⢸⣷⢸⡇⢸⡇⣾⡆⣿⡇⢸⠀⠀⠈⠛⠛⠿⣿⡀⠀⠀⠄⠐⠀⠀⠂⠉⠉⠉⠀⣰⠀⠀⠀⠀⢸⣷⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⡄⢀⠀⡀⢠⢠⡀⢀⢀⡄⢠⠀⢤⠀⠀⠀⢀⣤⡭⠆⠀⠀⣀⠀⣶⢀⡏⣠⠐⢆⡖⣺⢃⡿⠀⠀⠀⠀⢀⡄⢀⢀⡀⡤⢠⡀⣀⢠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⢄⠀⠃⣾⠒⣴⡹⢀⢻⣠⣏⣸⣁⣿⡔⠹⠧⠻⠚⠓⢀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠠⠏⠀⠛⢒⠙⢋⠈⣭⡬⠀⠐⠂⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠒⠀⠀⠉⠀⢹⡇⠀⢠⣿⣧⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣾⣿⣿⣧⣀⠀⢀⣼⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣻⣶⡤⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢉⢻⣿⣷⣿⣦⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠘⠸⣿⣿⣿⣿⣷⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡟⣱⣄⢀⠀⡀⠀⠀⠀⣨⣼⣿⣿⡿⠀⣀⣴⣾⣶⣤⣀⣀⠀⣠⣤⣘⠦
⠀⠀⠀⠀⠀⠀⠀⢱⢈⠻⣿⣶⣥⣀⣷⣺⣿⣿⡿⠋⢀⢸⣿⣿⣿⣿⡟⠉⣉⠻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢯⢧⡙⠛⠿⢿⣿⣿⣿⣿⠇⠀⠸⣜⠿⠿⠿⠏⠃⠀⠘⣶⡼⠿⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣳⣌⠃⢻⡿⠛⠛⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡼⣷⣨⣵⠓⣦⣤⣤⣤⢤⣄⣀⠀⠀⠀⠸⡌⠿⠋⠀⡶⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣧⡐⠿⢛⣵⡷⣿⣿⣷⡄⠀⠀⠀⠀⠂⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠾⢿⣧⠀⠘⢿⡇⣿⡟⠈⠡⠰⢤⠀⢰⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡿⢫⡾⢁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⠀⠀⠐⣦⡘⠿⠋⠒⠀⠐⠀⠐⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⣴⣏⡼⢛⣡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣧⣿⣄⠐⠀⠹⠃⠈⠂⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣽⣷⣏⢻⣼⣟⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢻⣿⣿⣿⣿⣿⣷⣤⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣽⣿⠿⢯⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠘⣷⣈⢙⣿⣿⣿⣿⣿⠎⢿⡷⠦⣤⣀⣀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢙⡾⠖⣾
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⢰⣿⡌⠻⠾⣿⣯⣿⣏⡀⠀⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣞⠓⡴⠁
⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⢸⣿⣿⡀⠀⠀⠀⣿⣿⣿⡆⣨⣿⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠘⠻⣼⣇
⠀⠀⠐⠋⣼⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⡀⠀⠸⡻⢿⣿⣅⠀⢹⣿⣿⣿⣿⣶⣎⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣤⡀⠉⠃⢀
⠀⠀⠀⠀⠉⠉⠟⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⡀⠀⠈⢸⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣷⡹⣆⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣤⡀⣈⡀
⠀⠀⠀⠀⠀⠠⣘⣽⣿⣿⣿⣿⡧⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⣧⢻⣿⣿⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⢽⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⡟⣻⣾⣿⣿⣿⣿⣿⢹⡆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣶⣼⣽⣿⣿⣄⢻⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⡆⠃⠀⠀⢀⣿⣿⣿⣿⣿⣿⡟⠋⢿⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⠟⣱⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠁⠙⠿⠋⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣏⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢿⣿⣿⠿⠿⢿⠏⠘⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⣿⣿⣿⣿⣿⡻⣿⠛⠃⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠋⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⢠⣾⣿⡟⠀⠀⢠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⢿⠀⢠⣿⣿⡿⠀⠀⢠⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⠏⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⡀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠈⣿⡀⣸⠏⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⢸⣿⣿⣿⣿⣦⠀⠀⠸⡇⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠹⣷⡈⢿⡆⠈⣿⣿⣿⣿⣿⣷⡀⠀⠁⠀⠀⠀⠀⣾⠏⠀⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠈⠁⠈⠿⠀⢹⣿⣿⣿⣿⣿⣷⠀⠀⠀⣤⠀⠀⠏⠀⠀⠀⣴⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⢀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⣾⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠙⣿⣦⠀⠸⣿⣿⣿⣿⣿⡇⠀⣿⣿⣧⠀⠀⠀⠸⢏⣼⠟⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄⠀⠀⢻⣿⡇⠀⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡆⠀⢀⣀⠸⠁⠀⠀⣠⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣸⣿⣧⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠁⢰⣿⠃⠀⢠⣶⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣤⠀⠀⣿⣿⣿⣷⣿⣿⣿⠀⠀⠹⣿⣿⣿⣧⣠⣾⣿⡄⢰⠟⣹⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡙⣷⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⠀⠴⢋⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠘⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠒⠫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠀⢹⣿⣿⡇⠙⢿⣿⡀⠀⠀⠀⠀⣿⣿⣿⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠉⠙⠀⠀⠀⢀⣿⡿⠃⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀⠀⠘⠋⠀⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣦⣀⠀⠀⠀⠀⣀⣴⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣠⣤⣤⠤⠤⠤⣤⠤⣤⣀⡀⣀⣤⣰⣦⣴⠆
⠀⠀⠀⠀⠀⠀⠀⣰⠿⡿⣍⠻⣗⡒⠰⣟⡳⢉⣽⣟⢿⣿⡿⣶⣭⣟⠯⣫⡿⢿⣶⣆
⠀⠀⠀⠀⠀⠀⠀⢿⢸⠐⣽⡧⠹⡿⠑⠺⡻⡿⠻⠍⡣⢛⢿⣿⡿⣿⣿⣮⣔⢩⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢘⣏⣶⣘⣿⡀⠇⢠⢀⡇⠀⠀⠐⠀⢸⣆⡠⢃⣿⣿⣿⣿⣷⣻⣽⣿⡀
⠀⠀⠀⠀⠀⠀⣴⢛⣭⣍⣉⡉⠘⠒⠋⢙⣷⠦⠤⠤⢔⣘⣠⠔⣨⠀⢛⣹⣿⣿⣿⣞⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠦⣦⡐⠀⠀⠉⠉⣛⣯⣤⣤⣄⣤⣾⣉⣁⠚⣠⣿⣿⣾⣽⣿⡿⣿⡾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⣴⡖⠮⢿⣿⡿⢿⡛⠷⠊⠁⠀⠙⢿⣿⣿⡿⢛⣭⣬⣿⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⣴⣤⣄⣀⡀⠀⠈⠁⠀⠙⢛⣫⣿⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣤⡀⠀⠙⣿⣯⡹⣿⠀⠀⠀⠀⠐⣿⢿⢿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⡿⠓⠦⢼⣾⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠘⢿⣿⡄⣤⣄⡀⢰⣾⢷⡏⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢀⣀⣀⣀⣀⣀⡼⠃⣽⡿⣷⣝⣯⣿⡾⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠿⣿⣿⠀⠀⢹⣤⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡯⢿⣿⣤⡐⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⣽⢿⣿⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⣡⢿⡿⠁⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⣁⡤⠶⠖⠛⠛⠛⠛⠛⠛⠛⠓⠲⠶⣤⣄⡀⠉⠙⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢟⣡⠞⠋⠁⠀⠀⠀⢀⣴⣾⣿⣿⣷⣤⡀⠀⠀⠀⠈⠉⠛⠦⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⡵⠋⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣼⠉⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⡟⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠟⠋⠉⠉⠙⠻⢿⣿⣿⣿⣿⣦⠀⢰⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡇⢸⠇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢠⣤⣤⣤⣤⠀⠀⣴⣶⣤⣤⡄⠈⣿⣿⡇⣼⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢸⣿⣿⣿⡿⠀⠀⢿⣿⣿⣿⠇⢸⣿⣿⠁⣿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⠉⠛⠋⠀⡴⢦⠈⠙⠋⠁⣠⣿⣿⡏⢀⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡀⣠⡄⢠⡄⣰⣄⣠⣿⣿⣿⡟⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡏⠙⠋⠙⠋⣹⣿⣿⣿⠏⠀⠀⢸⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⣾⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣇⣠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣯⣡⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⠧⠤⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡏⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣇⠀⠀⠀⠀⠾⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣬⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⠶⠶⠶⠶⠶⣶⠖⠂⠀⢀⡀⠀⠀⠀⠀⠀⢿⡿⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢫⣟⣵⢠⣄⡀⠀⠀⠀⠀⠀⠘⠛⠓⠀⠀⠀⠀⠈⢻⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣏⠶⡱⢎⡷⣻⢖⡤⣤⢀⡀⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⣻⣽⣫⣟⣽⢫⣝⣭⣻⣝⣯⣿⣼⣿⣿⣿⠀⠀⠀⠀⣤⣴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⣻⢾⡳⣟⢾⡱⢎⡷⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣽⣫⣝⣯⣻⠝⠋⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡱⢎⡷⡉⠀⠀⢠⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣫⣟⣥⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⢁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠿⠿⣿⣿⣿⣿⣿⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠰⣶⣿⣿⣿⡟⠀⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡡⡀⠀⠛⠋⣤⣀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⡁⠀⠀⠀⠀⣹⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣤⣾⡏⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣿⣟⡛⣋⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣴⣿⣿⣷⣤⣀⡀⠀⢤⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠀⠛⢿⣿⣶⣶⣶⣤⣤⣄⣀⡀
⠀⠀⢀⣠⣴⣾⣿⣿⣟⣡⣆⣾⣿⣿⣿⣿⣿⣿⣿⣶⡄⢀⠀⠁⠀⠟⠛⠻⣿⣿⣿⣿⣿⡿⢿⡿⣦⣄⡀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⢠⣾⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠀⠀⠤⠀⠀⠀⠂⠀⠈⠻⢿⣿⣿⠂⠀⠀⠛⠿⢿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣿⣿⣿⣶⠿⠃⠀⠀⠀⠀⠀⠀⠙⠿⣷⡄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠐⢂⡄⠉⠉⠉⠁⠐⠒⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣊⣥⣄⣀⠀⠀⠺⣿⢶⣿⣿⠄⣠⣶⣶⠀⠀⠉⠑⠢⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣼⣿⣿⣿⣿⣧⠀⢀⣠⣀⡠⢋⣾⣿⣿⡿⣣⣼⣿⠟⢠⣄⣤⣬⡉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⡴⠀⣼⠟⡿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠙⠉⠉⠋⣾⣿⣿⣿⠙⠿⠿⠜⠛⠛⢂⠤⣜⡂⠤
⠀⠀⠀⠀⠀⠀⠀⣰⣫⣾⣿⢃⣼⡟⡌⠁⠋⢻⣿⣿⣿⠏⢰⠰⣴⡀⠀⠰⠀⠁⢀⠴⠒⠒⠒⠒⠀⠀⠀⢴⣿⣿⣶⡶⠖⠒⢷
⠀⠀⠀⠀⠀⠀⡼⣱⣿⣿⣷⣾⠛⢡⠀⠀⠀⠸⣻⣿⠃⢀⡟⣧⣿⣧⡀⠀⠀⠠⠃⠀⠀⡀⠊⠐⠀⣠⣶⣿⣿⣿⣿⠿⣆
⠀⠀⠀⠀⣠⣴⣷⣿⣿⣿⣿⡏⠀⢠⠀⠀⡀⡀⠈⠃⢰⣼⡇⠸⣿⣿⣷⢀⠀⠀⠀⡠⠊⠉⠀⢢⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰
⠀⢀⡴⢋⠝⣫⣿⣿⣿⣿⣿⠇⠀⢸⡀⠀⠱⡐⣄⠀⢸⣿⣿⣄⠈⠛⠿⣿⣦⠀⢸⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⡏
⣰⠋⠀⠀⠊⣡⣿⣿⣿⣿⡵⠂⢀⣾⡇⠐⢄⠘⠮⡳⢎⢿⣿⣿⣷⣦⣄⣀⠈⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⡃⡜⠀⡞
⢻⣀⠀⠀⠀⠺⣛⣭⠞⢁⣠⣶⡿⠃⠘⡄⠈⠓⢤⣘⣆⠳⢍⡻⠿⠿⠿⢿⣿⡦⠀⠀⠀⡈⠉⠒⠄⡈⠙⠻⠿⣿⠞⠀⡸
⠀⠈⠙⣶⡾⠟⠋⠀⠀⣿⡟⠉⠀⠀⠀⠈⠦⡐⢤⣈⠉⢅⣀⠈⠉⠉⠉⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠤⣉⡒⠇
⠀⠀⢸⡇⠀⢀⣴⣾⣷⠋⣽⣗⡀⡀⢀⣠⣤⣌⡒⠤⣉⠉⠩⠕⠲⣄⡀⠀⠀⠀⠉⠒⠦⠤⠤⣤⣀⣀⣀⣀⠀⠀⠀⠉⣢⠁
⠀⠀⠘⣇⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣤⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠭⠀⠀⠐⠊⠁
⠀⡴⠋⠁⠩⠾⠟⣻⣿⣎⣝⣛⣷⣆⣀⣈⣉⠉⠛⣿⣿⣿⣿⣿⠀⣶⣤⣄⣀⣤⡤⠤⠄⠒⠈⠁
⠾⠒⠒⢶⡠⡄⣍⠹⣿⠟⢿⣿⣿⣿⣫⡞⠁⠀⢸⣿⣿⣿⣿⡏⢸⣿⡟⢿⡿⠙⠀⢀⠁
⠀⠀⠀⠀⠳⡱⣌⢷⡅⠀⠸⢟⢭⣻⡿⣷⣄⠀⠀⠈⠙⠿⠟⢀⣿⣿⣿⢸⣷⡦⢔⡀⢀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⣠⣤⠄
⠀⠀⠀⠀⠀⠙⢾⡶⠇⡠⠶⣶⣦⣬⣉⡛⠻⢷⡀⣤⣀⠀⠠⣿⣿⣿⡟⣼⣿⣷⢰⣍⣾⣿⣿⣿⣿⣿⣿⠧⣀⡴⣨⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠂⢬⣛⣶⣮⠉⠛⠛⠛⠚⢻⣦⣝⢷⣤⡀⠈⠉⠰⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⡇⢰⢋⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣶⣦⣽⣿⣿⣿⣿⣶⣄⣀⠈⠁⠀⠹⠟⠙⠿⢿⣿⣿⣿⢧⣓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠁⠙⠋⠁⣠⠞⠉⠻⢿⣿⣿⣿⣷⣦⣄⡀⠀⣠⣴⣿⣿⣿⠛⡗⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠹⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣯⣻⣿⣷⣿⡏⠒⠄⢹⡈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣝⢷⡝⢟⢮⡋⠓⠤⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠠⣀⠙⠦⡀⢨⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢔⡀⠑⢄⣸⠿⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⠅⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢴⣶⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢹⣿⣿⣿⣿⣏⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⡀⠀⠀⢀⢀⡷⢠⣼⣿⣿⣿⣿⡟⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣾⣿⣿⣿⣿⣿⣶⣶⣾⣶⣦⣄⣒⣒⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⣿⣿⣿⢿⣟⣿⣿⣿⠿⢿⡏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠊⠙⣿⠛⠛⠛⢫⣿⣿⡇⠀⣼⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠣⠄⢀⣈⣓⠈⠳⣠⣴⣾⣿⣿⣯⣿⣷⡀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠚⠒⢀⣈⣭⣛⠷⡹⣿⣯⡙⠿⠭⠿⢿⣿⣦⣄⡙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠊⠀⢀⣈⠄⠂⢀⣡⡶⢟⣫⡥⠀⢀⢀⠻⣯⠈⠄⠀⠀⠀⠀⠈⠙⠻⣦⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢛⠃⠀⣠⠞⠋⣀⣴⢞⣫⡵⠞⣫⡿⣧⣿⣾⣿⡆⢹⡆⠙⢆⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢻⢶⡶⠔⠁⡠⠞⠋⠊⠈⠁⣠⣾⣫⣾⣿⣿⣿⡟⢿⡄⢳⡀⢆⡱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠈⠀⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠺⢷⡔⠈⠀⠀⢀⣤⣴⣾⣿⡿⢫⣾⠇⣿⣿⣿⠘⣿⡀⣷⠀⠙⢮⡓⢤⡀⠀⠀⠀⠀⠀⠀⠠⠭⠃⡄⠀⠀⠀⢠⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠴⠿⣿⣇⡙⢿⣿⠿⠟⠋⣭⣴⣿⡟⢸⣿⣿⢹⣇⢹⣧⠘⡄⢢⡀⣹⠞⠃⠵⠤⡀⠀⠀⢢⣄⣴⣖⣷⣤⣀⡁⢀⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇⠐⡲⠞⢿⣟⣿⠦⠤⣤⣿⣿⣿⣿⡇⣼⣿⣿⡿⣿⠈⣿⠀⠘⡄⠻⠃⠀⢀⡀⠀⠤⠚⢛⣀⠀⠀⠀⠀⠉⠤⠶⢛⣋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢠⡆⠙⢿⣾⣟⣧⣀⣠⣾⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣠⣾⣷⣾⣿⠉⠁⠘⠂⢡⣠⣤⣴⠾⠛⠉⠓⠒⠠⠟⠃⠬⠩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣷⡴⠸⣿⣿⣿⣿⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⡿⣧⣤⣴⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢯⢼⡇⣿⣿⣿⣿⣧⣟⢻⣿⣿⡿⠿⣿⣭⣽⡿⢴⠟⠔⢷⣹⡇⠻⢿⣿⠇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣽⡿⣶⣿⣿⣿⣿⡟⡌⢸⡟⣽⣿⣿⡟⣿⡿⣿⣴⡦⠄⠶⠋⠑⠈⠁
⠀⠀⠀⢀⠀⠀⡐⠀⠀⡼⠀⣿⣧⣿⣿⣿⣿⣿⡅⠀⢸⢃⣿⣿⣿⢱⡜⢷⠘⢿⣿⣆⠀⠀⠢
⠀⠀⠀⠀⢀⠀⢈⡦⠊⢀⣠⣿⠃⢻⣿⣿⣿⣿⠁⡇⣿⢸⣿⣿⣿⠈⣿⣦⡀⠀⢻⣿⣷⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⣄⠀⠠⡀
⠀⠀⠀⠈⠂⣄⠉⣠⣾⣿⡟⠁⠀⣼⣿⣿⣿⡇⢀⣇⠀⢸⣿⣿⣿⣇⢻⣿⢷⡼⣆⠻⣿⣦⡙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⣀
⠀⠀⠀⣐⡤⠜⣹⣩⡟⣫⠀⠀⠀⠹⣿⣿⣿⣧⣼⣯⠀⠰⣿⣿⡞⣿⣦⡙⠧⢻⣜⠆⠹⡻⣿⣶⣄⡙⠃⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠋⠀⠠
⠀⠀⠀⠈⠉⠛⠋⠉⠁⡉⠀⠀⣠⣮⣙⣿⡏⢻⣿⣿⣧⠀⢻⣿⣧⠹⣿⣿⣦⢤⣛⣦⡀⠱⡈⢻⠛⣿⡷⠦⣌⡁⠀⠀⠀⠀⠀⠀⠚⠁⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⢉⢻⣿⣟⢷⣸⣿⣿⣿⣷⡌⢿⣿⣶⣿⣿⣷⣶⣮⡙⠻⣦⠰⡸⠂⡿⢻⣆⠀⠠⣀⡀⠀⠀⠀⠀⠠⠖⠁⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣮⡻⣿⣄⢘⣿⣿⣿⣿⣿⡜⣿⣏⣿⣿⠟⣥⣝⢿⣷⡈⢧⠹⣶⣄⠀⣹⡶⡀⠀⠉⠓⠦⠀⠀⠀⠀⢒⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠙⡙⠃⡽⠋⣴⢿⡿⢛⣭⣿⣿⣿⣿⢻⣧⣼⣷⡜⢎⢿⣷⡈⣇⠹⠻⣮⢿⣧⡿⠄⠈⠑⢦⣀⠀⢤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠛⠀⠸⣦⣉⣤⣤⣾⣿⣿⣿⣿⣿⣿⡙⢻⣿⣿⡌⢮⣿⣷⣹⣦⢳⣬⣿⣿⣇⠸⣆⢢⡀⠉⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠡⡄⠘⠛⠿⠿⣿⣻⣿⣿⣿⣯⣾⠃⠀⠈⠙⠛⠦⣜⣈⣛⣛⣳⡛⠛⡧⣻⣆⣿⣦⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠿⡿⠄⠀⠓⠒⠊⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡗

⠀⠀⠀⠀⣠⡄⠐⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⣤⠀⠀⠀⣶⠀⠀⠀⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠈⠂⢀⡄⠀⠀⠀⢠⠀⠀⠀⠿⠀⠀⠀⠀⠈⠓⠀⠀⠘⣿⣦⣾⡏⠀⠀⣠⣡⣄
⠀⠀⠀⠀⣠⣄⠀⠀⢡⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠙⠿⠁⠀⠀⡒⠄
⠀⠀⠀⣰⣿⣿⡀⠀⠀⠀⠈⠉⠀⣴⣶⣶⠀⠀⢸⣿⡇⠀⠀⠰⢿⣿⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡆
⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⣿⡏⣿⡇⠀⠈⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣿⡇
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢹⡇
⠀⠀⠀⠀⠀⢄⠀⠀⠤⠀⠀⢀⠀⢻⠀⢹⡇⠀⠻⠛⣇⠀⠀⠀⡀⡀⠀⠀⢀⠀⠀⠀⢀⡀⠀⣀⠀⡀⠀⠟⠀⠸⠇

⣶⣶⡶⣶⠶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡀⠀⠀⠀⠀⢀⡀⠀⡏⠈⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠙⡆⠀⠀⠀⢨⢷⡀⠰⢈⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⡟⠀⠀⠀⠘⣕⠙⠢⡀⠁⠪⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡀⠀⠀⠀⠀⠀⠱⡨⢀⠌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠊⣣⠀⣴⠀⠀⠀⠀⠘⢤⡀⠀⠂⠑⣄⠀⠀⠀⠀⢠⠜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⠌⡠⢁⡿⢸⠹⣄⢀⡀⠀⠀⠀⠙⣬⠀⢑⠙⡆⠀⠀⡔⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢂⠅⡢⠰⡇⠀⠑⠬⣢⠹⡳⣄⠀⠀⠸⡆⠐⠂⢻⠀⠀⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠐⠁⣄⠀⢷⡀⠀⠀⠈⠀⠇⡈⣷⠀⡸⠂⡷⠀⢹⠀⠀⣴⡇
⠀⠀⠀⠀⠀⠰⣀⠀⠀⠀⠀⢸⡨⠀⡄⠣⡀⠑⢄⠀⢀⡬⠁⠀⣾⡼⠃⡐⢨⠀⡵⠀⢸⡇⣷
⠀⠀⠀⠀⠀⠘⡈⠑⢢⡀⠀⠀⢣⠀⠸⡄⠈⠢⡈⢳⡞⢀⠞⠀⠍⢀⠞⠀⠎⢰⠃⠀⡸⡁⢸⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠂⠀⣙⡀⠀⠀⠑⣄⠐⡄⠀⠐⡀⢠⠃⠀⣇⠔⠁⠀⠌⢠⠏⣠⡞⠃⠀⠀⡇⠀⠀⠀⣠⢷
⠀⠀⠀⠀⠀⠀⠈⠹⢖⠤⣁⠀⠀⠀⠘⡆⠈⠀⠀⢱⡎⠀⠀⠋⠀⠀⡜⢠⠿⠚⠉⣀⡤⠀⢰⠇⠀⢀⠌⣁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡈⠙⢦⠀⠀⢿⠀⡆⠀⠀⠃⠀⠀⠀⠀⠀⠁⢀⠄⠒⠉⡔⠀⢰⠏⠀⠀⠧⢊⡁⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⢦⡀⢳⢀⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡖⠁⠀⢀⠎⢀⡴⠃⢀⡀⢀⡔⢉⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⡀⠰⡈⡟⢁⠌⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⡞⢡⣴⡏⢰⠋⠈⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠃⠀⠆⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇⠀⣷⠟⠲⣇⡟⡰⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠘⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⡀⠇⠸⠀⠟⠱⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢴⠀⠱⣄⡃⠘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠔⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⢀⠀⠀⠀⠈⠀⠀⠤⠀⠀⢀⣀⣀⣀⡀⠀⠔⠈⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠈⠀⠈⠐⠠⠐⠨⠀⡂⠄⡀⠄⠠⠀⡠⢀⠐⠀⠠⢐⠀⢀⠀⡠⢔⠢⢀⡐⢀⠔⡢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢦⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡀⠀⠀⠉⠉⠛⢶⣄⡀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢻⡇
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢳⡀⠀⠀⠀⠀⠀⠉⠳⢌⠀⣠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠹⠃
⡼⠁⠀⠈⢆⠀⠀⣀⡀⠀⠀⠀⢶⠘⠻⣆⠀⠀⢀⡤⠂⠀⠀⠙⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠂⠀⠀⠀⠁
⢷⡀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠓⠀⠁⠀⠀⠀⠀⠀⠀⠈⢄⣤⣀⣄⣦⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒
⠈⢷⡀⢦⠀⣈⣆⠀⠀⠀⠀⠀⢰⣲⡀⠀⠀⢠⣤⣄⠀⠀⢄⡀⠀⠀⢘⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⢀⣠⣤⡶⠏⠀⠀⠀⠀⠀⣄
⠀⠈⣷⣾⣇⠹⣿⣧⠀⠀⠀⢀⣿⢿⠆⠔⠛⠃⠊⠚⠻⣶⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣴⡾⠛⢉⣡⣴⠀⠀⠀⣀⡤⠞⠃
⠀⠀⠘⣿⣿⣆⠹⣿⣆⠀⠒⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠉⠉⠉⠫⠶⡀⠀⠀⠀⠀⠀⢷⣠⣶⣾⣿⣿⣿⠶⠚⠋⠁
⠀⠀⠀⠘⣿⣿⣦⡟⡿⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠛⠛⠃⠀⠸⣍⠀⠀⠀⠠⣙⣦⣄⠀⠀⠀⢀⣀⡀⢠⠤⠖⠁⠀⠀⣠⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⠳⢦⣄⣠⣜⠻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠹⡇⢸⣧⡀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⡀⠀⠀⠀⠀⢀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠙⠻⣿⣶⣌⠙⠿⣿⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢣⠀⠈⠻⢿⣷⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠹⢦⣄⣠⣀⡤⡤⢒⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠙⠾⣿⣷⣴⠿⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⢰⡿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢠⢿⡅⠀⠀⠀⠀⠀⠀⠀⠸⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢻⡆⠀⣼⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⡟⢸⡇⠀⣿⠈⣇⠀⠀⠀⠀⠀⢀⠀⠀⢹⡄⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣇
⠀⠀⠀⠀⠀⠀⣸⠃⢸⠃⠀⢹⠀⢻⡀⠀⠀⠀⠀⠀⢷⡄⠀⢳⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢰⠇⠀⣼⠀⠀⢸⡇⠈⣇⠀⠀⠀⠀⠀⢸⢹⡀⠈⢧⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢿⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⡞⠀⠀⡏⠀⠀⠀⣇⠀⢸⡄⠀⠀⠀⠀⣸⠈⡇⠀⠈⣇⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⡿⡇⠀⢸⡆⢻⡀⠀⠀⠀⠀⠀⠀⠀⡏⣿
⠀⠀⠀⠀⢰⠇⠀⠀⡇⠀⠀⠀⣿⠀⠀⣧⠀⠀⠀⠀⡟⠀⡇⠀⠀⠸⡆⠀⠀⢻⡀⠀⠀⠀⠀⢰⠃⡇⠀⠀⣧⠈⣇⠀⠀⠀⠀⠀⠀⠀⣇⢹⡀
⠀⠀⠀⠀⢸⠀⠀⠀⢿⣤⣀⣴⠏⠀⠀⢻⢠⣇⠀⠀⡇⠀⣇⠀⠀⢀⣇⠀⠀⠀⣇⠀⠀⠀⠀⡟⠀⡇⠀⠀⢹⠀⢸⡄⠀⠀⠀⠀⠀⠀⢻⠈⣧
⠀⠀⣄⠀⢸⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⡿⢸⢹⡄⠀⣧⠀⢻⡶⠶⠾⡟⠀⠀⠀⡿⢠⡄⠀⢠⡇⠀⣧⣀⣀⡼⠀⠀⣧⠀⠀⡄⠀⠀⠀⠈⣇⠘⢧
⠀⠀⣿⡇⠸⡆⠀⢀⠀⠀⠀⠀⠀⠀⢠⠇⠘⡆⢳⡀⠸⡄⠀⠙⠀⠀⠁⠀⠀⢀⡇⣿⡇⠀⠸⡇⠀⠘⠿⠋⠁⠀⠀⢹⠀⠀⢹⣆⠀⠀⠀⢹⡄⠈⢳⡄
⠀⢀⡇⣿⠀⢧⠀⡾⣆⠀⠀⠀⠀⢀⡟⠀⠀⢻⡈⢧⠀⠹⣆⠀⠀⠀⠀⠀⠀⣼⠁⢷⢻⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡟⡆⠀⠀⠀⢷⠀⠀⠙⣆
⡀⣸⠁⣿⠀⠸⣶⡇⢸⡄⠀⠀⠀⡾⠀⠀⠀⠀⣧⠈⣧⠀⠘⢦⠀⠀⠀⠀⢠⡇⠀⢸⡆⢳⠀⢹⡀⠀⠀⠀⣶⠷⣦⣸⠀⠀⠸⡇⢹⡀⠀⠀⠘⡆⠀⠀⠘
⡇⡏⠀⣿⠀⠀⢹⡇⠀⡇⠀⠀⢰⡇⠀⠀⠀⠀⣿⠀⢸⡄⠀⠈⢷⡀⠀⠀⢸⣇⠀⣸⡇⠘⡇⠀⢷⠀⠀⠀⡇⠀⢸⡏⠀⠀⢸⡇⠈⡇⠀⠀⠀⢻
⣿⣷⠀⢻⣄⠀⠀⠀⢠⡇⠀⠀⠸⣧⠀⠀⠀⣠⣿⠀⢘⡇⠀⠀⠘⣧⠀⠀⠘⣿⠛⠉⠁⢠⡇⠀⠈⢧⠀⠀⢳⡀⠀⠀⠀⠀⣸⠁⠀⣷⠀⠀⠀⢸⡆
⠹⣿⡄⠀⠻⣷⠶⠾⣿⠃⠀⠀⠀⢻⣿⠷⠿⠻⠃⠀⢸⠃⠀⠀⠀⣿⡆⠀⠀⠈⠀⠀⠀⢸⠁⠀⠀⠈⢧⠀⠀⠻⢶⣤⣴⡾⠋⠀⠀⡟⠀⠀⠀⣸⡇
⠀⠈⠻⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢠⣏⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠻⣦⣤⣤⣴⣿⡇⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⣀⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⣼⠻⠿⠛⠉⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠈⠉⠉⠉⣿⠃⠀⠀⠀⠀⠀⠀⠘⢿⠛⠛⠋⠁⠈⣇⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣹⣷⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⢀⠴⢉⣿⣍⢳⣦⠖⣊⣭⣭⣭⣿⡯⢠⣾⠟⠁⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⠂⣼⣯⠏⣼⣿⣶⣿⢉⣭⠭⣿⠃⣾⠛⣶⠄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⣧⣾⡏⢰⢟⣵⣾⡟⣱⣷⢹⢃⣾⣴⠋⢠⢹⣿⡿⣤⠀⠀⠀⠀⠄⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠁⣿⠈⣿⡸⡁⣿⢇⣼⣘⣟⣵⣤⣿⣦⣿⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⣸⡿⣷⠾⣾⡿⢾⣿⢿⢟⣿⡟⣹⢽⡟⣽⢿⡿
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠛⡻⢫⠁⣼⣟⡇⢸⣯⣾⣼⡟⢰⣯⡟⢰⢯⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣴⡟⢰⡿⣋⣴⡿⢻⣝⢿⠃⣿⣾⠃⣿⣿⠏⣿⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠁⡎⢸⣟⣻⠁⣿⡏⣼⠠⡿⣫⣐⣿⣫⣾⠟⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠄⠀⠀⢠⠏⢸⣿⣤⣛⣧⣦⣭⣾⠿⠿⠿⠟⠛⠛⠛⠁⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢿⣶⠿⠃⠉⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠜⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠀⢶⣾⡎⢀⠀⠀⢰⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠉⣙⣿⠀⡄⠈⠀⢿⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⡟⢀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣦⡀⢀⣶⣾⣿⠁⡙⠀⠀⠀⠈⣳⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠈⡿⠧⣴⠈⣩⡿⠙⣖⠁⠀⠐⠀⠂⠈⢀⣀
⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⠀⣶⠀⢀⣠⡄⢀⣄⣿⠿⢛⢛⡷⢀⡥⠀⠀⠀⠀⣴⣾⣿⠛⠿
⠀⠀⠀⠀⠀⠀⠆⠀⣠⣄⣠⣤⠆⢠⡿⠛⠋⠁⠕⠈⠀⠁⠄⠈⣧⠠⠄⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⣸⠟⣻⠿⢿⡲⠋⠀⠀⠒⠀⠀⢈⡀⢌⠠⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠄⠀⠒⠱⣤⠞⣡⡁⢠⣴⣛⠤⠘⠢⠈⠉⠀⠀⣀⣀⣀⣈⡀⠀⠂
⠀⠀⠀⠀⠘⣦⣀⠀⠀⢠⠀⠁⠀⠄⠂⢠⡞⠀⠌⢁⡽⠛⠁⠙⢷⣿⡷⠗⠀⠛⠋⠉⠉⠁⠉
⠀⠀⠁⠀⣼⡿⣿⡷⠈⠋⠀⠀⠀⠀⣥⡊⠠⠂⢴⡋⠀⠀⠀⠀⠀⡍⠰⠄⡀⠀⢼
⠀⠀⠀⠁⠉⠀⢍⢀⡖⠀⠀⠀⠀⠁⠸⣇⠶⡤⡍⣡⣀⡀⠀⢤⡀⣶⡀⣤⠵⠊⠀⠂
⠀⠀⠀⠀⠀⠀⠈⡘⢃⠀⡀⠀⠀⠠⠀⠙⣷⡄⠘⠻⠿⠁⠀⢸⣿⣿⠟⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢴⣶⢧⡤⠀⠀⠀⠢⠀⠀⠀⠘⣡⠀⠀⠀⠀⠀⠙⠛⠃⡴⠚⠄⠀⠀⠀⣠⣄⠀⠀⠂
⠀⠀⠀⠀⠀⠰⢿⣿⡆⠄⠀⠀⠄⠆⡀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⢀⣴⣿⢿⠀⠀⡀
⠀⠰⠀⠀⠀⠀⠀⡈⢣⡈⠐⢄⠠⠀⠀⡀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⡁⣶⣰⣾⡟⠀⢀⣀⣴⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠆⠀⠀⠈⠀⠀⠈⠅⠀⠀⠀⠛⠢⠄⣀⠀⠀⠀⠉⠻⣿⣷⣤⣴⢿⣿⣿⣿⠟⠁⠀⠀⠀⢀⣤⣾⣷⣿⣦⣴⡿⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢀⣀⡄⡀⠁⠀⠀⠀⠄⡀⠀⠂⠌⠉⠒⠠⠆⠀⠄⠉⣽⡿⠛⣿⣿⣯⡀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡟⠋⣀⣾⣿⣿⡍
⠀⠀⠀⠀⠀⠀⣈⠀⣿⡄⠀⢀⠁⠦⠀⠁⠀⠀⠁⢀⢠⠁⠀⠀⠀⠀⢀⠀⠀⠀⠐⢠⠘⠁⠲⣿⣿⣿⣿⣶⣿⣿⣿⡿⠏⠉⢿⠟⠋⠀⠋⠳⣤⠀⢡
⠀⠀⠀⠀⠀⢤⣽⣷⣿⣇⠐⠎⠀⠢⣤⡀⠀⠀⠠⠀⠀⠀⠂⠀⠈⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠛⡿⠃⠀⢆⠠⠘⠀⠸⠋⠀⣸
⠀⠀⠠⣶⣤⡄⠈⠉⠉⠁⠀⠀⠀⠀⠀⠙⠂⠘⠀⡀⠊⠀⠀⠠⠀⡴⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣿⡇⠀⠀⡀⠀⠀⠀⣤⣢⣤⡚⠁⠀⡄
⠀⠀⠂⣨⡿⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⢀⠂⠀⠄⠀⠀⠀⠀⠐⠎⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡟⣁⡈⣆⡈⠀⠒⠀⠀⢀⠉⠉⠉⡿
⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢡⣾⣿⣌⠲⠀⢢⣜⠁⢱⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣿⡿⡿⠁⣀⣾⣿⣧⣴⣶⡀⠀⠁⣀⡞
⠀⠘⠛⣻⣏⠀⠀⠀⠒⠀⠐⣀⣾⣿⣿⣿⣷⣄⠄⣽⠀⢀⡤⠌⠀⠀⠂⠀⠀⢀⠀⠀⠲⣄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣣⣾⣟⣩⣿⡿⠏⠉⠋⢴⠆⠋
⠀⠀⠘⠛⢿⣆⠀⠀⠀⠈⡀⠉⠿⣧⡉⢻⣿⣿⣷⣾⠀⠈⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⢀⠀⠀⠀⠀⠀⠘⢋⣼⣿⡟⣁⣽⣭⣿⠁⣀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⢈⣿⣆⠀⠀⠀⠁⠉⠀⡌⢿⠀⣿⣿⠏⢹⣷⣄⣀⠄⠀⠀⠀⠰⢮⣶⡿⠀⠀⠄⠉⠀⠀⠀⠀⠀⠘⣻⣿⢟⣋⣭⣴⠿⠃⠀⠙⢣
⠀⠀⠀⠀⠸⠿⣿⣷⡀⠠⠀⠀⢰⣿⣎⣴⠟⣋⣤⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣾⣿⠿⠛⠉⠁⣴⠂⠀⠲⡄⠀⡗
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣼⡀⣿⠟⡿⠁⠟⢛⡛⢿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣔⢀⡀⠀⠀⠀⠀⠐⢀⣠⣴⣿⣯⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠿⠃⠈⠙⠓⠁⠀⠄⠄⢰⣟⡛⢿⣿⡿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣡⣾⣿⣷⣾⣿⣿⣟⣉⠉⠁⠀⠀⠀⠀⠀⠤⢀⠠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⠋⠈⠻⢀⣴⣟⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠄⠀⠀⠐⠛⠻⣿⣿⣷⣼⡍⠙⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠂⡀⢀⡀⠀⠀⠀⠀⠙⣿⣥⡾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠀⠘⢻⣶⣶⣷⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⢫⣉⡿⠟⠻⠿⠿⠿⠛⠿⠛⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡀⢻⡅⠈⢇⡴⠛⠻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⡀
⠀⠀⠀⠈⣛⣓⣚⣓⡰⢦⣴⣚⣵⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠻⢿⠿⠛⠿⠷
⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⣀⢀⣀⡄
⠀⠀⠀⠀⠘⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⢠⣶⣶⣄
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⣠⡝⠒⠶⠶⠶⠶⠶⠖⠒⣄⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣌⠙⠟⠁
⠀⠀⠀⠘⠿⢿⣷⣶⣦⣤⣤⣴⣶⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇
⠀⠀⠀⠈⠉⠙⠗⠲⠶⠶⠶⠶⠲⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉
⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠘⠀⠇⡇
⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡓⠂⠀⢠⡿⡀
⠀⠀⠀⠰⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠠⢦⣉⣉⣠⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣴⣤⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠻⢦⣬⣭⣭⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⣤⣤⠾⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡇⠀⠀⠀⠀⠀⠀⡔⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡀⠰⡇⠒⠒⣒⡒⠒⠂⠀⠠⡗⢀⠀⠀⠈⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡖⣭⠁⢸⡇⣠⣯⠀⢠⢷⣟⡀⢠⡆⠀⣷⠈⢉⣷⣦⣔
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⠤⠖⢻⠿⠆⢿⣿⠀⢸⣧⣤⣾⣀⣘⡶⠻⠆⢸⡇⠒⣏⠀⣾⣸⢇⡾⣿⠲⠦⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣿⢶⡴⣏⢻⡜⣇⣰⡜⠏⠳⢸⡿⠯⣽⡁⠐⢻⠊⠭⢾⣧⣤⣯⠸⠫⠏⣼⢡⡟⣼⠃⠀⡶⠉⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⠸⣦⣷⢹⣬⠗⣩⠵⠒⠋⢩⡏⠀⣀⠈⠋⣹⢾⠀⠀⣼⠯⠍⡟⠈⠛⠒⠮⣟⢱⣏⠀⣸⠃⠀⡞⢦
⠀⠀⠀⠀⠀⠀⠀⣰⠁⠉⣇⣛⣘⣡⠴⠊⢁⠀⠀⢀⡞⠀⢀⣸⣿⡏⠁⣾⠀⢤⡏⠀⠀⢿⠀⠐⠀⠀⠀⠙⠮⣅⣛⣒⣰⠛⠈⣇
⠀⠀⠀⠀⠀⠀⠀⡿⠔⣦⠀⠋⣹⠃⠀⠻⣿⣧⡀⢸⡄⠀⠈⠉⠻⣇⣀⣸⠀⢠⡇⠀⠀⢹⠀⡀⣰⣿⡿⣁⡀⢘⢯⠙⠅⣰⠲⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡼⠁⠀⠀⠠⣼⣿⣷⡈⣇⠰⡆⠀⠀⠹⣤⠿⡞⣾⠀⠀⡀⣼⠀⣴⣿⣿⡤⠀⠀⠀⠈⢧⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠁⠀⠀⠀⢠⣬⣿⣧⡀⠘⣄⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⢁⡏⠐⣠⣿⣯⣤⠀⠀⠀⠀⠈⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠙⢿⣯⠁⠀⠈⢹⡖⠒⠀⠀⠀⢀⣀⣀⡤⡞⠁⠀⢹⡿⠋⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠙⠇⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠏⠀⠂⢀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⢀⠀⠁⠀⠀⢿⣧⣤⣀⣀⣀⣀⣀⣀⣠⣷⠄⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠉⠛⣿⣿⣽⣿⣿⣿⣿⣿⣯⣿⣟⠳⠆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠛⠛⠻⠛⠛⢻⣏⠀⠀⠀⠠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠶⠖⠒⠒⠒⠒⠒⠲⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⣉⣡⣤⣄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠁⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣩⠔⠒⠛⠛⠓⠒⠤⠌⠉⠛⠛⢗⠒⠒⠲⠶⠦⣤⣀⡀⣼⠁⢀⢀⣴⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠠⠊⠀⡠⠁⣼⠿⠋⠑⢦⣀⠀⠀⠠⡀⡄⠀⠑⣄⠀⠀⠀⠀⠈⠙⠣⠶⣾⣿⠇⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠐⢀⠔⠋⠁⣸⡣⠀⠀⠀⠀⠉⠟⠦⢀⠈⠻⡀⠀⠈⢦⡀⠀⠀⠀⠀⠀⢀⡿⠑⢦⡀⠀⠀⣠⡿⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣟⡇⠀⠀⢀⡠⢔⣦⣀⠼⢷⡄⠈⠀⠀⠀⢳⡄⠀⠀⠀⠀⣼⠁⠀⠀⠙⠶⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠟⢯⡅⠀⠐⢿⣿⡯⠃⢰⣿⣆⠀⠀⠀⠈⣿⡄⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⢻⠟⢱⣦⠈⣉⠁⣠⡯⢻⣿⡄⢠⡆⠀⢹⠏⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣷⣶⣆⠀⠀⠀⢈⣽⣿⣷⠹⣿⡇⢨⡇⣰⠘⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡸⣿⣿⣧⣶⡞⠀⢠⠟⠉⠀⣿⢣⠟⢁⡿⠀⢸⣿⣾⣷⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡻⣞⢿⣿⣿⠡⠄⠂⠀⣰⡟⠁⠀⠀⠘⠃⢠⡿⣿⡟⠻⡄⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣕⣈⠻⣇⣠⣀⣼⠏⡔⠀⡄⠀⠀⢠⣿⡟⢻⡇⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⣿⣿⣽⣮⣝⠿⡟⣸⡇⠀⣿⠀⠀⣿⠋⠀⢸⠃⠀⠀⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⠀⠀⠇⠁⣿⡇⢹⣶⡇⣿⡇⠀⡔⠀⣼⠇⠀⠀⠘⠀⡆⠀⠁⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⢰⠟⢠⠸⡆⠀⠀⠀⡫⢷⡞⡓⠀⢛⣃⡰⢁⣼⢿⠃⢠⠀⠀⢠⡇⠀⡀⡄⠈⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠀⢗⣠⠎⠀⠀⠊⡞⠁⢀⢠⣾⡑⢿⣿⣿⣤⣿⣄⣺⣾⡇⠘⣸⣧⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⢀⡭⠖⠉⠇⠀⢀⠀⢀⡱⡀⣰⡟⢦⣙⡶⡹⣿⡿⢿⣿⠿⣿⣿⣾⡿⢿⠏⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠀⡀⢀⠀⠀⠀⢸⠀⢸⠹⠿⠧⢙⢳⣞⠓⠁⡌⠃⠀⢀⡄⠀⠉⠁⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠚⣧⣾⣗⠄⣠⡿⣦⡟⣦⠀⠐⠀⠙⠀⠀⠰⡇⠀⠀⠈⠁⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠁⠉⠛⠉⠀⠀⠀⠿

⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠘⡈⣇⠀⠀⠀⠀⠀⠀⠀⠠⢲⠀⢇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀
⠀⠀⠀⢣⠸⡄⢀⢀⢀⡀⠀⢠⠁⠏⠀⠘⡄⢳⡀⠀⠀⠀⠀⠀⠀⡠⠁⠏
⠀⠀⠀⠈⣤⣽⡇⢀⡿⠀⣷⠃⡔⠀⠀⠀⠁⠈⢧⡞⠈⣶⠃⢠⡠⠋⡄
⠀⠀⠀⠀⠎⠀⣀⣉⡇⣴⡋⢰⡇⠀⠀⠀⠀⡟⠛⢣⠰⡏⢀⣼⠇⣸⠁⠀⠀⠀⠀⢀⡤⠒⠒⠒⢤⡀
⠀⠀⠀⣼⠀⢴⠛⠷⣾⠛⠀⠀⡇⠀⠀⠀⡜⠀⢀⣦⣴⠃⣾⡗⠂⢻⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠘⢧⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠘⠁⠀⠛⠀⠙⢻⠇⠀⠀⢸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠈⢳⣀⠔⠠⠔⠃⣴⠁⠀⠀⠀⣧⣐⣀⣀⠀⠀⣀⣀⣂⣼⠀⠀⠀⢸⣄⣂⣀⡀⠀⢀⣀⣐⣠⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⢘⣿⣿⣿⠟⠸⣿⣿⣿⣇⠀⠀⠀⢀⢿⣿⣿⡿⠀⢿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠋⠓⡆⣿⣿⠰⡞⠑⠁⠀⠀⠀⠀⠙⠙⠲⢼⣿⡇⠖⠋⠋
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠦⢀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⢀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⢠⣾⣶⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⣶⣶⢶⡀⠀⠀⠀⠀⠠⣶⣶⣦⠀⡀
⠀⠀⣰⣶⣏⣡⠶⡄⠀⠀⠀⠀⠀⣿⣽⡍⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡛⠁⠀⠀⠀⠀⠀⣷⣶⢀⣾⠎⠀⠀⠀⠀⠄⠀⠰
⠀⠀⠿⠯⢿⣿⡿⠀⠀⠀⠀⠀⠀⠉⢩⣥⠟⠃⠀⠀⠀⠀⠘⣿⣿⣯⠁⠀⠀⠀⠀⠀⠛⠶⠆⠛⠃


⠀⠀⠀⠀⠀⠐⠒⠄⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣀⠀⠀⠀⠀⠀⢰⣶⣶⣾⣧⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⢀⣾⣯⡟⠋⠀⠀⠀⠀⠀⠀⠛⢶⣷⣄⠀⠀⠀⠀⠀⠰⣯⡌⢱⣽⠆⠀⠀⠀⠀⠈⠻⣏⠻⡉⠀⠀⠀⠀⠀⠀⠀⠉⣿⣦⡀
⠀⠀⠻⠟⠛⠀⠥⠓⠀⠀⠀⠀⠀⠀⠀⠙⠑⠀⠀⠀⠀⠀⠀⠸⠇⠸⠇⠀⠀⠀⠀⠀⠀⠀⢠⠒⠄⠀⠀⠀⠀⠀⠐⢤⣼⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢰⠆⣀⡀⠀⠀⠀⠀⠀⠀⠀⣶⣛⢫⣷⡄⠀⠀⠀⠀⠀⠰⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⠆⠀⠀⠀⠀⠀⢰⣿⡆
⠀⠀⠺⢶⣿⣯⣴⡆⠀⠀⠀⠀⠀⠈⣽⣯⠉⠀⠀⠀⠀⠀⠀⢰⣾⣿⣧⡀⠀⠀⠀⠀⠈⠂⠉⣶⠆⠀⠀⠀⠀⠀⢀⣾⠟⣻⣷
⠀⠀⠀⠺⠿⢿⣿⣦⠀⠀⠀⠀⠀⣾⣯⣿⣶⠀⠀⠀⠀⠀⠀⠻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠄⠀⠀⠀⠀⠘⠛⠿⡿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⣤⣄⠀⣾⣀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⡀⠀⠀⠀⢀⣤⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣦
⠀⠀⠈⣻⣟⣠⣴⠛⠀⠀⠀⠀⠀⠀⡤⢀⡀⠀⠀⠀⠀⠀⠉⡀⠒⠀⠀⡀⠀⠀⠀⠀⠿⢿⣽⢿⣿⣤⡄⠀⠀⠀⠀⢛⣛⡛⠋
⠀⠀⢾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣻⣯⠁⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠻⠆⠀⠀⠀⠀⠀⠈⠛⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢰⡋⢹⡆⠀⠀⠀⠀⠀⠀⠀⣿⣇⣷⠂⠀⠀⠀⠀⠀⠀⣀⣾⣿⡃⠀⠀⠀⠀⠀⢀⣄⠰⣆⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿
⠀⠀⢠⡀⣩⣍⢀⡄⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⢴⣿⢿⠿⠀⠀⠀⠀⠀⣾⣿⠩⢴⡻⣧⠀⠀⠀⠀⠰⣮⣿⣿⣿⡆
⠀⠀⠈⠻⣾⣷⠟⠀⠀⠀⠀⠀⠐⢬⣿⡶⠀⠀⠀⠀⠀⠀⠠⠾⠟⠟⠀⠀⠀⠀⠀⠐⠿⠿⠁⠻⠸⠧⠄⠀⠀⠀⠀⠿⠯⠽⠿⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠄⠀⠁⠐⣤⡀⠀⠐⡆⠀⢰⣧⠠⠤⠄⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⢰⣶⣶⠚⠀⠀⠁⠀⠸⣿⣆⢀⠂⠠⠈⢃⡀⠀⠀⠀⠀⠙⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⡀⢰⣿⣿⣀⠀⡠⠋⠀⡀⠀⣿⣿⠀⡀⠰⡇⠈⣅⠀⠀⠀⢦⣄⣤⣿⡿⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠢⣄⢘⣿⣿⣿⣿⡟⢹⠃⢀⡶⠀⠀⣿⣿⡄⠀⠊⣿⠀⠸⠀⠀⠀⣼⣿⣿⣯⠀⢠⣿⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢰⣿⣿⣿⣿⣿⡿⠅⣸⠀⡆⢶⠀⠀⣿⣿⡌⠀⠀⣿⠀⢠⠠⡆⠸⣿⣿⣿⣷⣠⣿⡟⢐⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡏⠈⠉⢟⠋⢻⣿⣿⣷⡾⠁⠘⡇⢸⡆⢸⣿⣟⡟⠃⠈⣷⠀⠼⢠⡇⠀⣿⣿⣿⣿⣿⣿⠃⣾⡇⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠓⠀⠀⠀⣠⠄⠸⠷⣌⡇⠀⠀⣁⣸⡄⣼⣿⣿⡇⠃⠀⢿⡀⠘⢺⠁⠀⡿⠟⠻⣿⣿⣿⣷⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣄⡴⠶⠞⠁⠲⢲⣀⠈⠳⣤⡀⠰⣾⡇⢹⣿⣯⣇⠀⠀⡿⠀⠀⠃⠀⡘⠁⠀⣹⣿⣁⣉⢛⣻⢿⣾⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠻⣦⣀⠑⠀⣯⣇⣼⣿⣿⣿⣥⣀⡇⠀⠀⡇⠠⠁⢀⡴⠋⠁⠀⠙⠟⠛⠛⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⢳⣀⡗⢿⣿⡟⢯⡟⢿⣽⣷⡀⠀⡇⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⡾⠧⣀⠀⠀⡠⣠⡄⠀⣸⣿⣇⣬⠅⠻⢿⣥⣿⢟⣯⢟⡀⣷⡏⠀⢠⠀⠀⠀⠰⠃⠀⠀⢀⠀⠀⠛⣷⣄
⠀⠀⠀⠀⠀⢰⠂⠀⠸⣁⠀⠋⠀⠀⠀⠐⠆⠀⠀⠀⢀⣾⣿⡏⠠⠀⣹⣲⣿⣿⡒⡳⣾⣿⣾⡇⠀⠘⣄⠀⠀⠀⠀⠀⠀⠈⠁⢄⡠⢾⣿⣇
⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠀⠀⡀⠀⠀⠀⣤⠀⠀⢺⣿⣿⠃⡠⢾⡟⠉⠉⣉⠛⠿⢄⠙⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡙⣧
⠀⠀⠀⠀⡀⠀⠀⠀⠔⠻⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⣿⣿⣿⠊⠀⠌⣷⡇⡟⠶⣶⡣⠄⠡⠈⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣼⢿⣿
⠀⠀⠖⠀⠡⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⣀⠙⢶⣤⠐⢬⣅⡀⠀⠀⣸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣟⡫⣧
⠀⢐⠃⠀⠀⠀⠁⠀⠀⠆⠀⠀⠐⠀⠀⠀⡆⠀⠀⣾⣿⣵⣿⡤⣿⣯⠀⠠⣿⠀⠀⣸⣿⣼⢶⣽⣿⡗⢄⠀⠀⠐⠀⣀⠀⠀⠀⡇⠀⠈⠈⢰⠹⡇
⠀⠒⠰⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⠁⠀⣸⠗⢿⡧⠘⢰⠏⠀⠀⠀⣿⠀⠒⢈⣿⡿⠀⠈⠛⠀⠀⠀⢀⡀⢀⣼⠂⠀⠘⠣⠀⠀⠀⣾⠁⠻⡄
⠀⠂⠀⡄⠀⠀⢀⠀⠀⠀⠀⢀⣀⣠⠴⠃⣠⠴⢡⣴⡿⠏⡤⠊⠀⠄⢠⠀⣿⠀⠀⠀⣄⡙⢄⣸⣧⣤⡗⢐⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⡟⠆⠀⡿
⠀⡉⠀⠀⠀⠀⡆⠀⠀⣠⠖⠁⠀⠀⠀⠀⣴⠞⠋⠁⠐⠊⡁⠀⠀⠀⡿⠀⢛⠀⠀⢠⣿⡿⣾⣿⣿⣌⡛⠿⣄⢰⡀⠀⠀⠠⣶⠀⠀⢸⡿⢃⠀⣹⠇
⠀⠀⠀⠇⠀⠀⢹⡀⠀⠀⠀⠀⢀⣤⣾⠛⣉⣀⡁⣀⣰⣯⡊⣠⠴⢶⠎⡉⡛⠁⠑⠾⣗⠙⠃⣈⣷⡙⠣⠁⠋⠻⣷⣄⠀⠀⠀⢨⣘⠿⣯⣧⣽⣿
⠀⠀⠀⠈⢄⠀⣸⠃⠀⣠⣶⣿⡿⡟⡽⡟⡏⢹⢿⡿⣿⣍⠻⠇⣠⣤⡇⠀⠦⠀⢤⣀⣿⡷⠊⠁⢨⣿⣶⠈⢱⢴⢮⣍⣷⣄⠀⠀⠈⣻⣿⣿⣿⡿
⠀⠀⠀⠀⠘⡗⠁⢀⣴⢿⣿⡟⠁⠀⠠⡏⠇⠀⠀⠐⡘⡮⡁⢤⡩⣤⣼⠀⠁⠀⣌⣀⣿⡥⢒⣥⣾⠏⡞⢠⠀⠀⠀⡜⠁⠋⠻⣷⣾⣿⢟⣽⣿⠁
⠀⠀⠀⠀⠀⠹⣦⣾⣳⣿⣿⠁⠀⠆⠄⠈⠊⢄⠀⢶⣲⣑⣿⣆⠳⡉⠙⠀⡅⢐⢋⣿⡟⣰⣿⡿⠋⣠⠁⠎⡃⡄⡀⣅⠀⠀⡧⢹⣭⣽⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠄⠀⡴⣤⠀⠠⠘⣦⣀⣽⣿⣿⣿⣇⢥⠀⠀⢇⠨⣸⡿⣼⣟⣛⣥⣾⣯⠈⡰⡹⠃⢇⢅⠀⢀⡟⢸⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣍⣿⣿⡆⡄⢷⡘⢗⡀⠄⢀⠈⢻⣟⣿⣿⣿⣠⡄⠀⡀⢠⣿⣿⣿⣿⡿⠿⠟⢁⣸⡟⠁⢠⡾⡀⠀⣾⣧⣘⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⡌⠿⣟⢿⣿⣷⣦⣆⣠⢬⣙⠿⢿⣿⡇⢀⣲⠺⣿⣿⣿⣿⣿⠷⠛⣫⡏⣠⣠⠞⠁⡁⣰⣿⢳⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣟⡳⢮⣽⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣴⣶⣿⡿⣿⣿⣿⣷⡾⠷⠾⠟⡉⣠⢠⣷⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣬⣍⣛⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⢁⠀⣠⢂⣔⣴⣧⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣝⡛⣿⣿⣿⣿⣿⣿⣿⠟⠘⣿⣿⠻⢿⣿⣿⣿⣾⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠛⠉⠀⠀⠈⠛⠷⠿⠿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡂⠀⢀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⡿⠂⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠰⣶
⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠈⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠆⠀⠀⠠
⠀⠀⠅⠀⠀⠀⠀⣶⡶⠸⡆⠀⣸⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⠀⠀⢦⡀⠀⢻⠟⠀⠙⢦⣽⣥⠾⠁⠀⣦⠀⢀⣇⠀⢰⠆⠀⣦⠀⢀⣆⠀⠀⠀⢠⡄⠀⣠⣇⠀⣾⠀⠀⢰⣀⠀⠀⣀⠀⡀⠀⠀⢀⣄⠀⢀⡆
⠀⠈⠀⣀⣻⣋⣠⠏⠀⠀⠀⢸⣿⣿⠀⠀⠀⠘⢦⣙⣟⣤⠟⠀⠀⠘⢦⣙⣟⣠⣄⡀⠀⠹⣦⣙⣯⡴⠃⠀⠀⣙⣿⣤⠴⠋⠀⠙⠶⣤⣘⣟⣠⠞⠁
⠀⠀⢸⡍⣿⣿⠀⠀⠀⠀⢀⣼⠋⠻⣄⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⡇⠀⠙⠂⠀⠀⢹⣿⡇⠀⠀⣞⠹⣿⣧⠀⠀⠀⠀⠀⢰⣿⣿⡇⢀⡀
⠀⠀⠀⠙⣿⣿⠀⠀⠀⢠⡾⠁⠀⠀⠙⣧⠀⠀⠀⣿⢻⡅⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠙⠀⣿⠻⣆⠀⠀⠀⠀⣿⣿⣿⡇⠀⠁
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⢸⠇⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⡿⡏
⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠁⠀⠀⠀⠀⠀⠛⠘⠃⠀⠀⠀⠀⠀⠘⠃⠃⠀⠀⠀⠘⠃⠘⠋⠀⠀⠀⠀⠘⠋⠃

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠻⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⠐⠀⠀⠐⠠⠌
⠀⠀⠀⠀⢠⡾⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣵⣄⣀⣠⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⣿⢋⡿⠋⠙⠁⠀⠀⠀⠀⠀⢐⣯⣽⡛⣿⡏⠛⠁⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠳⠀⠘⠀⢰⡃
⠀⠀⠀⠀⠀⠀⣿⡌⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⠛⢷⣄⠀⠠⠄⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿⡄⠄⠀⣠⣤⡀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⣿⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢠⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣼⡀⠀⢈⣻⡆⠘⢿⣿⣿⣿⣷⡿⠁⠀⠂⠉
⠀⠀⠀⠀⠀⠘⠋⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠟⠁⠀⠀⠀⠀⣾⣿⡄⠀⠀⣾⣿⣇⠀⠀⡌⠻⣷⣶⣸⣿⣿⣏⣀⡀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠿⣦⣤⡻⢿⣋⣠⡄⢟⢆⢸⡿⣿⣻⡟⣿⣿⣿⠀⠀⢀⣠⣾⠇
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠐⢿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣯⡿⣧⣬⣭⣥⣴⡶⠟⠋
⠀⠀⠀⣠⣧⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣶⣿⣿⣟⣯⣴⣮⣥⣼⣿⢿⣿⠀⣿⣿⣿⣿⡀
⠀⠀⠀⢙⣛⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢸⣿⣻⣷⣸⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⡷⠶⠶⠾⠀⠀⠸⠶⠶⢶⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢸⣿⠙⣿⣹⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⡿⠿⣿⣿⣿⢸⣿⢸⣿⢹⣿⢻⣿⠟⠘⠿⠘⢛⣿⠟⣿⡏⠁
⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⡿⠿⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⢸⣿⠁⠉⢸⣿⢸⣿⢸⣿⢸⣿⠀⠀⠀⠀⠀⣿⡇⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⢸⣿⠀⠀⠈⠉⠀⠉⢸⣿⢸⣿⠀⠀⠀⠀⠐⠿⠃⠿⠃
⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠸⠿⠘⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠈⠛⢿⣶⣶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⢸⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⠟⠻⢷⣦⣄⡀
⠀⠀⠀⠀⢻⣧⠈⠉⠻⢷⣦⡀⢀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠈⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢀⣴⣦⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠛⠛⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⢀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⣴⡟⠁⣀⣤⣾⠟⠋⠈⠛⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⢸⣿⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣦⣴⡾⠟⠋
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⣠⣴⡿⠻⠿⠿⠿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⢄⠈⢷⡄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣸⠃⢻⡀⠀⢀⣾⠀⠀⢹⡆⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⣸⠇⢰⠀⠀⠀⠀⠀⢠⠈⢻⡄⠀⡄⠀⢠⣿⠀⠈⣷⠀⢸⣷⡀⠀⣸⡇⠀⠀⠀⢠⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢀⠀⣿⠀⠘⣧⠀⠀⠀⠀⣼⠀⠀⣿⠀⣧⠀⠀⢿⣷⣶⡿⠀⠸⣿⣿⣿⡿⠀⣧⠀⠀⣾⠀⠀⠀⣿⠀⣇
⠀⠀⠀⠀⢸⡄⠀⢀⣾⠇⢾⡀⣿⡄⠀⢸⣧⠀⠀⣼⣇⠀⣠⡿⠀⢻⣧⠀⠀⢻⣿⡇⠀⠀⢻⣿⣿⠁⠀⠹⣆⠀⢹⣷⣤⣶⡏⠀⢹⡄
⠀⠀⢀⣴⡿⠁⠀⣾⡟⠀⠈⣷⠘⣿⣷⣿⠇⡄⠀⢿⣿⣿⣿⠁⠀⢀⣿⠀⠀⠈⣿⣧⡀⢀⣾⣿⣿⡀⠀⠀⣹⡆⠀⢻⣿⣿⡀⠀⢀⣿
⠀⢀⣾⡟⠀⠀⠀⣿⣷⣄⣤⡟⠀⠘⣿⡟⠀⢳⡀⠈⢻⣿⣿⣄⣠⣼⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⡿⠁⠀⠀⣿⣿⣷⣶⣿⣿
⠀⠈⣿⣇⠀⠀⢀⣿⣿⣿⣟⠀⠀⢀⣿⡀⠀⢘⣇⠀⠀⢹⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣿⣷⣶⣿⣿⣿⣿⣿⣦⣤⣾⣿⣷⣶⣾⣿⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠠⠀⠈⠛⢦⡞⠁⠀⠀⠀⠀⠃⠰⠆⠀⡤⠐⠂⠂⢀⠤⠠⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠄
⢀⢀⠀⠁⠁⡀⠀⠀⠀⠀⢠⠀⠀⠀⠄⠼⠀⠀⣀⠀⠀⠄⠀⠆⠀⣤⠀⠀⠀⠀⠠⣶⣶⠀⠬⠀⢠⠀⠰
⣀⠀⠑⠀⠀⠀⠀⣤⠂⠀⣈⡳⠀⣷⡄⠀⠄⠀⠉⠀⡀⠂⢴⣸⡰⠋⠴⣟⠅⠀⠥⠬⠁⣚⠉⠀⠀⠠⠀⢀
⠉⠀⠀⠄⢠⣶⢴⡳⠶⠀⠈⠀⢠⡉⠍⠀⠀⠀⠁⠀⠀⠀⡈⠋⠀⢀⣘⠁⠉⠀⠀⠀⠀⠈⠁⠀⠀⠄⠀⠴
⠄⠤⠒⢸⣞⠁⠀⠀⠀⠀⠀⠀⠀⢈⢢⢳⡀⢀⡀⠀⠀⠐⠁⣀⠀⠚⠳⠄⠈⡠⠀⢀⠂⣀⠠⣶⡆⠀⢀⣁⠑
⠀⠀⠀⣦⣿⡏⢷⣀⠀⠀⠀⠀⠆⡈⢻⠟⠇⣿⠃⣀⡀⠀⠀⢠⠄⠀⠁⢀⡀⠀⠤⠒⠀⠖⠂⠉⠀⠀⠘⢯⡻
⠀⠀⠀⠈⠹⠀⠘⡇⠀⠴⠀⠠⠀⢼⡦⠀⠀⣇⣊⠀⠐⠠⢀⡠⠀⣸⡉⠉⣧⠀⠀⠃⠈⠀⠀⢸⠀⣀⡄⠀⠈
⠐⠸⢥⣲⣀⠀⠀⣨⡦⠤⠐⠀⠀⠀⠁⠀⠀⠋⠉⠀⡀⠀⠈⠡⡀⠈⠙⠞⠁⠀⠀⠀⠀⠀⠀⠘⡇⣿⡻⡆⠔
⣀⠀⠈⠛⢛⠀⠀⠚⠋⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠈⠂⠠⠄⠐⠀⠀⠀⠀⡀⢠⢋⠀⠀⡀⠀⢀⣯⡇⠎⠂
⠁⣆⠐⠀⠸⠀⠐⠀⠀⣀⣀⣹⠂⠀⠀⠀⠀⠀⢀⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣌⡌⢉⡷⠛⠟⠙⠀⠂
⠀⠀⡀⢀⠀⠉⠑⠀⠀⠈⠢⡉⣦⣌⠇⢤⠨⢾⣖⠀⠀⢀⡀⠐⠀⠀⠀⠀⠀⠇⠹⡟⠀⠋⠁⠀⠀⠀⢀⡖⠛
⠁⠀⠁⢄⠀⠘⠁⡈⠀⠀⠀⢀⠉⠉⡀⠈⠈⠉⣭⡴⢚⢹⡇⠀⢠⠂⠀⣖⡠⣣⠀⠀⠀⠀⠀⠀⢀⡀⠈⠳⣤
⡤⣄⠀⢨⠀⠀⢀⡇⠀⠀⢀⠀⠠⡄⠤⣄⠀⠀⠉⠀⡬⠂⠀⠀⠸⠷⠘⢫⠟⡁⠀⠀⠀⠀⠀⠀⠠⠈⠀⠅
⠀⠂⢀⠀⠀⢀⣀⣗⡞⠀⠀⠢⢀⠐⠀⢀⡤⣤⠀⠀⠀⠀⠠⠂⠀⠀⣠⢄⠚⠛⠁⠀⠀⢼⠀⡀⠀⠡⠀⠔
⠀⠄⠂⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠂⠠⢧⡀⣸⠇⠀⠀⠀⠀⠀⠂⠈⠻⠆⠉⠰⠄⠀⣠⣼⠿⠁⠀⠀⠑⠠⣀
⠀⠀⠀⠀⠀⠘⢇⣷⡒⢦⡄⠀⠀⢠⡄⠀⠙⠁⠀⠐⠁⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⣙⢇
⠀⠀⠀⠀⠀⠀⠳⠾⠯⡀⠈⠂⢀⣋⡁⠸⠂⢢⠀⠡⠀⡐⠀⢻⠟⠀⠀⡐⠀⠀⠀⠀⠘⠢⣿⡝⠻⢦⠀⠀⡴
⠀⠀⡀⠄⠐⠀⢀⣀⣀⣀⡀⠀⠹⠟⠀⠈⠂⠀⠄⠈⠀⠠⢤⡖⡀⢀⢞⢷⠀⠀⠀⠀⢀⠙⠛⠳⠄⠀⠁⢴⣧
⠀⠀⠀⠠⠆⠀⠉⠀⠳⠾⠓⡄⠀⠄⠀⠀⢙⡄⢀⣒⣂⢢⣵⢟⠵⡾⠐⣔⠀⢀⠀⠀⠀⠈⠐⢤⢤⣦⠀⠀⠁
⠀⠀⠑⠀⠒⠀⠀⠀⠀⠀⠀⠐⠀⠁⠐⠛⠉⠥⠾⢿⠊⠆⡂⠀⠋⠀⠀⠈⠀⢐⠀⠀⠉⠀⠠⠜⠉⠉⠰⡀⠘
⠀⠀⡀⠀⡔⠒⢺⡀⠀⡀⠀⠀⢀⠀⠂⠄⠀⠀⠀⢀⠐⠊⠉⠀⠠⠃⠀⠀⠀⠀⠑⠄⡀⠠⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣤⣡⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠛⣿⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢰⣿⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢟⢣⡞⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⣿⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⢺⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⣾⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠡⡷⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⡾⠗⣺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⣤⠀⠀⡘⣦⣠⣯⣷⣿⣶⣶⣦⡀⡜⠒⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣿⣯⣻⣿⣿⣿⣿⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⢻⣿⣿⣿⣿⡿⠛⠉⠹⣿⣿⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠸⣿⣿⠁⠈⠁⠀⠀⣠⣏⣀⣿⣇⠀⠀⣀⣤⠾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠏⠀⢀⣠⣴⣾⣟⣿⣯⡝⠿⠿⠿⠟⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⣿⣷⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣴⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⣃⣭⣿⣿⣿⣿⣿⣻⠟⠛⠃⠀⠀⠀⢰⣿⡿⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⡶⣿⡟⢿⣿⣿⣿⣟⣿⢿⢦⡄⠀⠀⠀⠀⣿⣿⣄⣀⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⣿⣿⣶⣿⣏⣺⠿⣿⠇⣄⡐⠿⣢⣄⠀⣿⡟⠿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢹⠿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣮⣡⣤⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⣻⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠙⠻⣿⣭⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⠉⠙⠻⢿⣿⣿⠏⠀⠎⢁⡈⢑⡀⢹⣿⢿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⢸⣿⡍⢱⣶⣦⣶⣥⣴⣦⣾⡇⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⣦⠀⠀⠀⢸⣿⡅⠀⠙⠿⣿⣿⣿⠋⢸⡇⣾⡁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⢸⡇⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⠋⡇⠀⢸⡇⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇⠀⠀⠀⣸⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⠀⡇⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠛⠉⠉⠩⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣀⣀⡀⠀⠀⣾⣿⣿⣦⠘⡏⣿⡀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⣿⣿⣷⠀⠀⠻⣿⣿⡿⠀⠃⣹⡇⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠻⠿⠃⢰⣤⡄⢨⣭⢀⡎⢐⣿⣷⠀⠀⠈⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣾⡇⠘⠛⠃⠀⢡⣿⣿⡿⢻⣿⣷⡀⠀⢠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⢰⠘⣿⣿⠇⣼⣿⣿⠟⠀⠸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠉⠛⠀⠐⠉⢉⣾⠛⢃⠀⠀⠀⠀⠃⠉⠉⠑⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢿⣿⣿⣇⠀⢀⣀⣀⣴⣿⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢀⣄⠉⠁⠙⠏⠻⢿⣿⣿⣷⣿⠃⡰⠈⠀⠀⢀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠈⠁⠀⠀⠐⣄⠀⠉⠛⣿⣿⠀⠀⠀⠀⢠⠾⠄⠄⠠⠤⠄⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⠀⠐⠚⢿⡄⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢸⠤⠤⠦⠤⢿⣄⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⢸⡇⠈⣠⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠄⡠⣠⣤⣤⣘⣦⡀⠀⠀⠈⠀⠀⠀⠀⠀⠈⡓⣷⣿⠋⠻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠏
⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠘⠀⠀⠈⠀⢀⣝⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠁⣤⣷⣿⣆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢹⡎⠉⠉⠉⣠⣾⡛⠉⠂⠀⠀⠀⢄⠠⠀⠃⠁⠀⢠⠆⢰⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⢈⡇⠀⡐⠀⢠⡏⢀⡇⠀⣿⠈⠻⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠉⠀⠀⠀⠀⡟⠿⠇⣶⠀⠀⠈⠀⠸⠀⠀⢿⣄⣀⣈⠹⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣀⠀⠀⠈⠛⠛⠧⠀⢀⠀⠀⠀⠀⠁⠀⠀⠸⡇⢸⣷⠀⣶⠂⣠⣾⣿⣱⣿⡆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⣀⡀⠀⠀⠀⢀⠠⠈⠀⠀⠀⠀⠀⠁⠈⠽⠀⡟⢰⠏⠀⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣟⢛⣿⣿⣿⡿⠀⠀⢰⡾⡀⠰⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠁
⣹⣿⣾⣿⣿⢏⡇⠐⠛⢺⠃⠓⠘⠐⠃⠃⠀⢀⢀⡶
⣿⣿⣟⣿⣿⣾⡅⠀⠀⣬⣦⣶⣵⣷⢂⢸⢧⡾⣿⡇
⢻⣿⣿⣿⣿⣿⡇⠀⠠⢹⣏⢻⢿⣿⠈⣿⢻⡿⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⣿⡏⢸⣿⣿⣿⠇⠀⠀⠜⠁⢹⠈⠘⠀⠿⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦
⣿⠇⠀⣿⣿⣶⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠈⣻⠀⠀⠀⠀⠀⡁
⡿⠀⠀⢿⣿⣿⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣶⠀⠀⠯⠀⠀⠀⠀⠀⣿⡿
⠁⠀⠀⠀⢹⣿⣧⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⡈⠥⠖⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⣿⠋⠁⠖⢦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣀⡀⣀⣀⣀⡀⠤⠤⠾⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣾⡧⢹⡖⠂⠃⠀⠀⠀⠀⢠⠀⠀⠀⣰⣶⣮⣤⣶⢆⣤⣶⣾⣷⡐⠳⠮⠙⠉⠨⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⢀⠟⢀
⠀⠀⠀⣼⣇⠈⢠⣤⠀⠀⢰⣶⣠⣸⡄⠀⠀⠀⢈⣭⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⢰⣆⣦⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡌
⠀⠀⣸⣧⠟⣆⣿⢿⡆⠀⣾⢻⣿⡍⢷⠀⠀⠀⠸⢿⡏⠀⢀⡀⢠⡄⠀⣿⡇⠀⢸⣾⣿⡀⠀⠀⣿⡇⠀⢀⣀⡀⠀⠼⠃⢀⣠⠄⠉⢸⠃
⠀⠀⣿⠿⠇⢸⡯⠀⠃⠀⢁⣈⣿⣇⠀⠀⠀⠀⢰⠾⣧⡀⠛⠁⣼⢷⣰⣽⠿⠆⢹⣯⣽⠁⠀⣰⣯⣁⣤⣶⠒⢀⣠⡆⢠⣾⠷⣦⠀⠃
⠀⠀⠀⠀⠀⢸⡇⠀⣴⡆⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⠃⠀⠠⢹⡿⣿⣿⣶⣆⡾⣻⣿⣤⣴⣿⣿⠛⠛⠛⠛⠶⠄⠁⠀⠀⠰⠇⢸⠐⡀
⠀⠀⠁⠀⠀⢼⡇⣴⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⣤⡀⢸⡆⠀⠀⢈⡁⢤⣿⡞⢁⡴⠿⠻⠟⠛⣿⡄⠀⠀⠀⠀⡤⠆⠀⠀⡤⠂⠀⣌⣞⣃⡀⢀
⠀⠀⠀⠀⠀⠙⠃⠿⣿⡿⢿⣿⣷⣶⣾⣿⣦⠀⠻⠇⠺⠃⠀⠀⠈⢃⡀⠘⣿⢸⡇⠀⠀⠀⠀⣿⠁⠠⠀⠀⢀⡀⠀⢀⣠⠀⠀⠀⣿⣿⣿⡯⠋
⠀⠀⣶⡷⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⡇⠀⢀⣶⡄⢐⣥⡘⠛⢻⡇⠀⣌⢹⡇⡠⠀⢀⡄⣿⢲⡀⠄⢉⣁⣝⣿⡏⣿⣾⣷⡀⣿⣿⣿⣯⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡿⠟⠈⠉⠉⠁⠀⠀⣸⣿⣅⣤⣥⡀⠀⠼⠇⢀⣿⣿⣧⣀⣀⣠⣤⡟⠋⣉⣽⣾⣿⣿⡿⢃⣿⣿⣿⣧⠘⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢶⣶⣦⠀⠀⠀⠀⢰⣿⣿⣿⣘⣿⣿⡆⢶⠏⠀⠹⣟⣿⠿⠿⠿⢛⣧⣾⣿⣟⢿⡿⣫⣴⢿⣿⣿⣿⣿⣧⠹⣿⣿⡯
⣀⣐⣀⣀⢀⣀⡴⣚⣛⣛⣛⢟⣛⣀⣀⣀⣐⣈⣙⣛⣻⣟⣻⣛⣇⣀⣉⣁⣈⣀⣀⣀⣀⣔⣻⣿⣋⣁⣁⣀⣾⣟⣛⣺⣿⣿⡿⣿⣿⣂⣙⣋⣀
⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠉⠉⠉⢉⣭⣭⠉⠉⠉⠉⠉⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡀⠀⠀⠑⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠁⠀⠀⠠⠃⠀⠀⠀⠐⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠒⠀⠀⠀⠢⠀⠀⠈⠢⣄
⢄⠀⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠨
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⡀⠐⠅⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡠⠀⠀⠀⢠⢄
⠀⠀⠀⠐⠂⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠘⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⡀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣄⠀⠀⡀⠀⠀⠀⠆⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢀⠀⠀⠈⠠⡀⠀⠀⠐⠂⠛⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠄⠘⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢁⡐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢦⠀⠀⢀⠠⠀⠀⠀⠀⠀⠠⠀⠒⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠈⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠤⢴
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⢁⣀⡀
⣀⣀⣀⣆⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣊⣥⣠⣄⣀⣀⣠⣀⣀⣀⣀⣀⣀⣰⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠢⠀⠀⢀⣀⣤⣤⣤⣤⣤⢃⣶⠄⠀⠀⠀⠊⣈⣀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠒⢀⣶⠞⡋⠝⣊⠒⣿⣿⢡⣿⡟⢀⣶⡤⠤⠌⢂⠤⠆⡀
⠀⠀⠀⣀⣀⣄⣀⣀⠀⢎⠈⢁⡶⢋⣄⣱⣦⣼⡤⣺⡾⠃⠞⠋⣠⣾⣿⣧⣄⣤⠛⠤⠴⠁⠀⡀⠀⢀⣀
⢀⡴⠟⠉⠁⠀⠈⠙⢷⠞⠛⠿⣿⠋⠉⠉⠻⡋⠙⣳⣤⣰⣴⣾⣿⡿⠟⠛⠉⠉⠛⢿⡛⠻⢾⡟⠛⠻⡟⠛⢶⣄
⠻⢦⡄⠀⢀⣿⡇⠀⢸⠀⠀⣤⢹⠀⢠⣄⠀⢡⠀⡿⠃⠙⣿⣿⣿⣷⡦⠀⢰⣶⡆⠀⣳⢠⡄⢁⠀⢸⡇⠀⢸⡇
⠀⠀⡇⠀⠀⠁⣀⣴⠋⠀⣼⠇⢸⠀⡏⣼⣴⠋⠈⠁⢀⡴⢧⣸⠁⣿⡇⠀⠾⠛⠁⣠⠏⣾⡇⢘⠀⣸⡇⠀⢸⡇
⠀⠀⣇⠀⢠⡀⠈⠙⡄⠰⣿⠂⡆⠀⣿⡟⠙⠀⠀⣾⡟⢱⢀⠹⠀⡗⠁⠀⠀⠒⢿⡁⠀⣿⠇⡆⠀⣿⡇⠀⢸⣥⣀
⠀⠀⣧⠀⢸⡿⣆⣰⣦⣀⣁⣾⠻⣄⡀⣀⣜⢀⣄⠈⢳⣾⣸⣦⠼⣳⠀⢸⣷⣄⠀⣇⠀⠛⣰⣀⠀⠉⢣⠀⠈⠈⠙
⠀⠀⣷⡴⠟⠁⠈⠋⠀⠙⣿⣿⣷⣮⣍⣉⠙⠛⠛⢳⣾⣉⣠⣴⣾⣿⣶⣿⣿⣿⣾⡿⠛⠛⠋⠉⠙⠳⠾⠛⠛⠛⠛
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠹⣟⢋⣹⣟⠫⣻⡟⡿⠿⣉⣿⡷⣭⠽⠛⠻⢿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⡀⢈⣇⡟⣼⢣⠤⣭⣿⣧⢿⠷⠸⡒⢛⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣝⣛⣫⣞⡛⠁⠨⣿⣿⣷⡶⠛⠃⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠒⠊