Sweetkin Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⡺⡻⢿⣄⡒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠄⠠⡤⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⠀⠀⠀⠀⢠⠋⠔⠉⡰⠁⢸⠘⡌⠢⡈⡆⠀⠀⠀⠀⠀⠀⢰⣀⡀⡄⠀⠀⣀⣸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⡌⠜⣰⢆⠀⠀⠀⢘⣼⡀⣀⣇⣀⣸⢀⣸⣀⣥⢇⠀⠀⠀⠀⠀⠀⡎⠈⠉⠉⡏⢫⠉⡀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠙⠻⡯⠐⠊⠀⠀⠀⠯⢀⣉⣁⣀⣈⣉⣁⡀⠤⠔⠚⠇⠀⠀⠀⠀⣔⢣⣤⣀⣄⣄⣠⣤⣧⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠈⠛⠀⢀⡀⢰⠀⠀⠀⠀⠀⢇⠀⠀⡉⠀⠀⠀⠀⢀⡀⠀⠸⠀⠀⠀⠀⠀⠈⡄⠉⠽⠁⠀⠀⠹⠀⢰
⠀⠀⠀⠀⠀⠀⣀⣄⠀⠐⠀⠀⡠⠃⠀⠀⠀⠀⠀⠘⡄⠀⠛⠀⠀⠀⠀⠈⠁⠀⠇⠀⠀⠀⠀⠀⠀⠘⠢⠤⢀⣀⣀⠠⠔⠃⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠮⣔⡝⣹⡖⠒⠈⠀⠀⠀⠀⠀⠀⢀⠀⠱⣄⠀⠀⠀⠀⠀⣀⡀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠐⠈⣦
⠀⠀⠀⠀⠀⠀⠈⠙⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠈⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⣀⣴⣿⡆⠀⠀⢠⡋⠢⠀⢄⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⠒⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢹⠿⠛⠋⠀⠀⠎⠐⠈⠃⡀⠳⢨
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠦⢤⠻⡈⣦⠤⠒⡄⠀⠀⠀⠀⠀⣠⠒⠉⠀⠈⠑⢄⠀⠀⠀⠀⠓⠤⢢⣤⣤⡒⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠑⢠⠋⢢⠀⠀⠀⠀⠀⠀⠀⣇⡣⠴⠒⠉⠀⠀⣀⠸⣄⠀⠀⠀⠀⣃⡀⠙⠂⠠⠄⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⠁⠀⣉⣃⠀⠀⠀⠀⠀⠘⡅⠀⢀⡠⠴⠒⠉⠀⠀⠈⡆⠀⠀⢀⡇⢳⡞⢧⣴⢠⠜⠀⠀⠀⢀⡴⢖⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠤⠤⠤⣌⡄⠀⠀⠀⠀⠀⢸⠈⠀⠂⠀⢰⡄⠄⠂⠁⢣⠀⠀⣸⠚⣅⠴⣪⠋⠁⠀⠀⠀⢠⠮⠄⡴⣏⣠⡋⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡂⣐⡲⠇⠀⠀⠀⠀⠀⠈⢦⠤⠒⠈⠁⠀⣀⠠⠔⠊⠀⠀⡿⢆⣹⡶⠁⠀⠀⠀⠀⠀⣧⠤⠐⡆⢸⠷⠛⣅⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⡀⠀⠀⠣⠤⠐⠒⠉⠀⠀⠀⠀⠀⢸⠕⣈⠏⠀⠀⠀⠀⠀⠀⠀⢣⡠⢊⡌⠃⣤⠻⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠐⡀⢴⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⠠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠄⠁⢴⢃⠗⣢⡤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠓⠄⡳⠞⠃⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠶⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡠⠤⣤⣀
⠀⠀⠀⠀⠀⠀⢸⡿⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡁⠉⠀⠀⠈⠂⠛⢦
⠀⠀⠀⠀⠄⠀⢸⣿⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣄⡀⠀⠀⣾⡏⠀⠀⡴⠲⣄⠀⠀⢀⡎⠁⠀⠴⠀⣠⣄⠀⠦⠀⠘⣥
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⢠⣶⠂⠀⢀⣀⠀⠀⡀⠀⢀⡉⠑⣾⣿⣀⣀⣀⣀⡴⠟⠀⠀⢸⡃⠀⠀⠠⠊⠀⠀⠱⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⢀⣿⠇⠀⠀⠺⣷⢠⡾⠁⣰⣿⠃⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⡄⠀⠀⠳⠄⡠⠔⠀⠀⠀⡾⠁
⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⢻⣷⢸⣿⠀⢰⣦⢀⢁⣿⠃⠀⣿⠃⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠈⠓⠤⣤⣤⣤⣴⡿⠏⠸⣿⣤⠾⣿⠎⠘⣿⠠⠘⢿⢀⠔⢹⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠦⢤⠤⠦⠖⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠠⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣀⠀⠀⠀⣠⣉⠦⡉⠁⠢⡀⠀⠀⠀⠀⠀⠀⠶⢲⣨⠀⣠⠷⠀⠀⠀⠰⠁⠈⢡⠀⠀⠀⠀⠀⡰⠭⠤⠀⢠
⠀⠀⢀⣀⡄⢂⣁⡘⠀⠀⠁⠀⠄⢠⠀⠀⠀⠀⠀⠀⠰⢻⣞⠟⣅⠀⠀⠀⠀⡤⠁⡲⣤⡀⠀⠀⠀⠼⠀⢄⠤⠔⠂
⠀⠀⠘⠤⠀⠀⠐⠦⠶⠒⠂⠀⠊⡀⠀⠰⠀⠀⢀⢟⡖⠓⡿⠽⠙⡄⠀⠁⠀⠀⢠⠁⢈⡁⠀⠘⠀⠠⢀⠘⠀⠇
⠀⢔⠉⠑⠂⠀⠀⠐⠐⠒⠀⠉⢀⡀⠔⠁⠠⠄⠀⢎⠵⠀⠁⠐⡽⠁⠀⠀⠀⠂⠠⢠⠄⠃⠀⠀⠀⡊⠡⠀⠀⢔⠠
⠀⠋⠁⠀⠀⠒⠒⠒⠀⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⠀⠄⠀⠀⣀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⡈⠁⠀⠈
⠀⠀⠀⠀⢀⢄⠀⢀⡤⢀⠀⠀⠀⠀⠀⡤⠀⠒⢀⣐⢄⠀⠀⠀⢸⠀⠁⡆⠁⠀⠀⠉⠀⢐⠑⠃⢀⠄⠀⠀⠀⡀⠉
⠀⠉⠀⡐⣡⠯⡉⠍⣎⡦⢥⠀⠀⡐⠀⠀⠊⠀⠀⠐⢠⠄⠀⠙⠠⢄⡄⠘⠢⠀⠀⠀⢀⠹⠅⣠⠌⠰⠀⠀⠀⠁
⠀⠀⠀⡧⣅⣮⠀⠀⡸⣧⠈⠀⠈⠀⠊⠀⠀⠀⠀⠈⡘⠄⠀⠀⠀⠀⢄⢀⡴⠐⠂⢀⠀⠉⠂⠈⡠⠠⢄⡩⠠⠢⡀
⠀⠀⠀⠐⢜⠤⢮⢉⡱⢛⠇⠀⠐⢤⡁⢄⠀⠀⠀⠀⠈⠌⠢⠈⠁⠀⠀⠀⠦⡤⢍⡢⠀⠀⠀⡐⠔⠁⠄⠐⢄⠁⢺
⠀⠰⠀⠀⠀⠁⠀⠉⠉⠐⠀⠀⠀⠀⠈⢧⡡⢀⣀⠠⢂⣡⠞⠀⠀⢀⠀⠀⠐⠃⠀⠀⠀⠀⠀⢙⠠⠘⢄⣀⠐⠀⣇
⠀⠘⠀⠀⠀⠀⢀⣀⠠⢤⠤⢀⠀⠠⠄⠀⠱⣄⣠⠴⠋⢀⢀⠐⠋⣦⠄⠂⠀⠀⠀⠀⠀⠰⠀⠀⠢⠂⠂⢄⡐⡠⠋
⠀⠀⠀⢀⠠⠒⠄⠑⡆⠈⠃⢈⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠘⡔⠚⠳⡄⢤⠀⢤⡥⠤⣤⢤⡤⢄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡐⠫⣆⠀⠃⠀⠀⠠⡠⠊⠀⠀⠀⢀⢰⠌⡉⢁⠢⡀⠀⠈⠀⠀⠃⠚⠒⠒⠓⠀⠒⠂⠓⠈⠀⠀⠀⢰⠆⠀⠈
⠀⠀⡀⠀⠈⠀⢀⠰⠑⠊⠀⠀⠂⠀⣀⠓⠃⠀⠃⠀⠓⠐⢀⡄⠀⠀⢀⠔⠂⠀⠀⠂⢄⠀⠀⠐⠀⠀⡠⠂⠠
⠀⠀⠊⠀⠈⠁⠀⠀⢀⢀⠀⠀⡀⠀⠑⢖⠐⠂⠒⠒⠒⡰⠁⠀⠀⢀⠃⠠⠊⡀⠄⡁⠀⠂⠰⠀⠀⡠⠀⠀⠀⢑
⠀⠀⠀⠀⡐⠂⠀⠪⠀⠀⠘⡁⢀⠀⠀⠀⠀⠉⠉⠉⢉⡀⠀⠀⠀⠀⡀⢀⠀⠒⠀⡀⠀⡄⠀⠀⠀⢄⡀⠀⠀⡀⠆
⠀⡀⠀⢰⡀⠀⠀⠀⠑⠀⢀⠌⠀⢀⠄⣢⡆⢀⡠⡀⠀⠀⠀⠀⠀⠀⢑⣄⠑⠒⠊⡀⠔⠀⠶⠀⠀⢸⣽⠎⣟⠁
⠀⠀⠀⡌⠀⠑⠠⠀⡠⠋⠀⠀⠰⠅⠮⡀⠎⠌⠙⠐⠀⠤⠀⠉⢀⢔⠕⠁⠀⡀⠀⢀⠀⡄⠀⠀⠀⠐⢛⡘⢩⠀⣀
⠀⠀⠀⡕⠀⠀⠔⠀⠀⠆⠀⠀⠘⠢⡐⡐⡈⠌⢦⡅⠀⠀⠀⡀⡁⠀⠀⠀⣅⡨⡀⠣⠝⢢⡀⠀⠀⠀⢗⠶⡇⠀⠉
⠀⠀⠀⠑⠂⠀⠀⠀⡀⠀⠀⠀⠠⡑⠄⣜⡈⡼⢌⠔⠀⠀⠬⠊⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢠⠀⠀⠀⠸⠭⢁⡀
⠀⠀⠐⠂⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠁⠀⠂⠂⠁⠀⠀⠀⠀⠀⠒⠂⠀⠀⠐⠂

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀⡀
⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢄⣀⠌⠉⠠⣃⠀⠀⠀⠀⠀⠸⠉⢶⠃⡇⠀⠀⠀⠀⠀⠐⡧⠶⠤⠴⠯⠭⠍⠠⠤⠬⠟
⠀⠀⠀⠀⠀⢏⠀⠉⠂⣾⢡⠀⠀⠀⠐⠂⠄⠀⣹⠀⠚⠀⣨⠃⠀⠀⠀⠀⠀⠑⢠⠞⠀⠀⢀⠀⡄⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶
⠀⠀⠀⠀⠀⡰⠁⢀⠀⣿⠀⡀⠀⡁⠀⡀⢀⡄⢸⣄⡈⠀⠝⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡌⠀⠀⣀⡀⠀⠀⠠⠤⡀⠀⡇⠉
⠀⠀⠀⠀⠀⢈⡆⡀⢀⡽⢆⡀⠀⠀⣀⣀⣠⡤⠞⠀⠉⠓⠲⠚⠀⣀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢰⠃⠀⡀⠣⢟⡀⠴⢐⠐⠁⠀⡇
⠀⠀⠀⠀⠀⠸⣨⠔⠋⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢄⢣⠈⡇⠀⠀⠀⠀⡜⠀⠀⠚⠀⠥⠝⠰⣉⠇⣴⠂⣷
⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠒⠃⠙⠲⡄⠀⢠⡇⠀⢎⣨⠂⢜⠂⡶⠀⠘⠔⠁⢻
⠀⠀⠀⠀⠁⠀⠀⠀⣠⠀⠀⠀⠐⢮⡁⠀⢯⠀⠀⠀⠀⠀⠀⠀⢰⠒⠠⡀⢠⠀⠀⠀⠀⣰⠃⠀⠈⠓⠒⠶⠶⠶⠶⠶⠶⠶⠒⠒⠲⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⢔⠒⠁⠀⣰⠃⠀⠓⠶⠖⠋⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠖⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⡨⠆⠀⠀⠀⠀⠀⠸⠧
⠀⠀⢐⡆⠀⠀⠉⢀⠴⠂⠉⠀⡤⠉⠙⠦⡀⠀⠀⢀⢒⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⠓⠁⠀⢀⣀⠀⣀⡀⠀⠁⠔⠒⢢
⠀⠀⠈⢠⢢⠄⡔⠁⠘⣀⡤⠤⣄⡀⠀⠄⠙⢦⠀⠈⠁⠀⠀⠀⠀⠀⠀⡠⠔⠢⡄⠀⢀⠔⠊⠁⠀⠀⠀⠈⠓⣎⠀⠀⡞⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠆⠀⡞⠀⠀⡼⠁⠀⠀⣄⠙⢦⠀⡤⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⠈⢦⠏⡀⡜⠀⡐⡐⠀⡀⢀⢘⡇⠀⠈⠓⡆⠀⠀⣹⡗
⠀⠀⢰⠀⢸⡃⠀⠐⡇⠀⠄⠀⢸⠂⠘⡇⠀⠀⢸⡄⠀⠀⢴⡞⠀⠀⠀⣏⠅⠀⠐⢿⡔⡜⠀⡔⡰⠀⡰⢡⢃⣼⣁⠀⠰⡞⠁⠀⠈⠓⠃
⠀⠀⢸⠀⠈⣇⠀⠄⠈⠲⠤⠴⠋⠀⢰⠇⠘⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢈⡆⢈⠈⡴⠻⢤⣜⣜⣀⣔⣴⠷⠋⠀⠙⠣⣀⡟
⠀⠀⠀⢧⠠⡌⠦⣀⠀⠀⠀⠐⢀⡰⠋⠠⠀⢀⡟⠀⠀⠀⠀⣠⠀⠀⠀⢯⡐⣡⠞⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠈⠳⣄⠀⠈⠙⠒⠒⠛⠉⢀⡀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢔⠖⠀⠀⠀⠀⠕⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⣤⣤⣤⡭⠴⠛⠁⠀⠀⠀⠀⣀⣠⠎⠉⠐⠉⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣍⡉⠙⢳⡄
⠀⠀⠀⡰⠤⠆⠀⠀⢴⡄⢰⢸⠀⠀⠀⠀⠀⠈⠃⠀⠈⢆⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢠⡞⠡⣠⡞⠉⠉⡇⠈⣿
⠀⠀⠘⠢⡤⠷⠀⠀⠀⠀⢸⢸⡆⢀⠀⠀⠀⠀⢀⣀⠀⠀⠖⠲⠶⠞⢣⡀⠀⠀⠀⠀⠀⠠⠗⠀⠀⠀⣰⠋⣄⣰⠋⠀⢠⡞⠁⣸⡟
⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⢸⠸⡇⠘⠇⠀⠀⠀⠬⠄⠀⡐⠀⢀⢀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣼⠁⣧⡜⠁⠀⠀⠈⠙⠛⠋⠀⠀⡀
⠀⠀⠀⠀⢠⢄⠀⠀⠈⠃⢸⡆⡇⠀⠀⠀⠀⠀⠀⢠⠞⠃⠐⣒⢋⣀⠀⢀⡆⢳⡀⠀⠀⠀⠀⢠⢾⠘⣦⠋⠀⠀⠀⠀⣠⡂⠀⠀⠀⠘⠃
⠀⠀⠠⠒⠇⢸⠀⠀⢀⠀⠈⡇⣧⠀⠀⠀⠀⠀⢠⠃⣈⠣⠐⠊⢀⠂⢂⢠⠀⣸⠃⠀⠀⠀⡰⢧⢀⡿⠃⠀⠀⠀⠀⢀⡽⣓⢦⡀
⠀⠀⠀⠁⠀⠞⠀⠏⢏⠇⠀⡇⢿⠀⠀⠀⠀⠀⠘⠦⣌⣃⡈⠀⠚⢀⣑⣨⡴⠋⠀⠀⠀⠀⠳⠼⠟⠁⠀⠀⠀⠀⠀⢾⡘⠀⡇⢱⠀⢀
⠀⠀⠀⠀⡄⠀⠀⠀⠉⠀⠀⢧⠜⠀⠀⠀⠰⡷⠂⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠫⠭⠴⠃⣠⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠃⠀⠁⠀⠹⡄⠐⠙⠲⢤⣄⠒⢎⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠜⣦⡀⠠⣠⠘⣻⣾⣾⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡁⢀⣀⡠⠜⢀⣟⠘⢋⡁⠠⠐⠋⠀⢼⣿⠁⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⠴⠶⠩⠚⠾⡤⠔⠚⠉⣩⡴⠛⠈⠳⡀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⡗⠠⡾⠁⠀⠀⠀⠀⢰⣶⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠀⠀⠂⢤⣄⣀⣄⣠⠟⠁⢀⡇⠀⠀⠀⠀⠀⣿⠁⣯⡩⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⠾⠁⠀⢀⣠⡴⠚⠏⢀⢸⣁⢀⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠣⣄⣠⣤⢤⣄⣄⠤⠴⠤⠤⠀⠊⢉⣠⠴⠒⠛⠛⠉⠁⠀⠀⣔⣸⣿⡵⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠈⠛⢦⣃⠀⠀⠀⠠⠀⣠⡴⠞⠉⠀⠀⠀⣀⣀⣶⣶⡿⣿⣿⠟⡟⠿⠟⡭⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠈⠓⠶⠶⠶⢿⣿⣷⢶⢤⢴⣶⠿⣿⠛⠻⠋⡀⠋⢠⣯⣤⣼⣵⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠲⣦⣀⡀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠒⠈⢎⡴⠀⡔⣉⣴⣶⣸⣿⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢣⠹⡏⠙⣿⠆⢺⠷⢾⠷⠿⡿⠿⡿⡿⣿⠿⢻⠛⢻⡋⣽⣿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⡆⢿⠀⢿⠀⠸⡇⢸⡆⢠⡏⠀⡗⠀⡏⠀⣾⢀⣿⣧⣿⣿⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠱⡸⣇⢸⣧⠈⣷⢈⡧⡘⣷⠀⣇⢰⡇⣰⡿⣴⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠰⣿⣿⢾⣧⠁⣿⣮⣧⣻⣿⢰⡷⣼⣷⣿⣷⣾⣿⣿⣟⣿⣿⣿⣧⣤⣤⣄⣀⣀

⠀⠀⣀⣠⠤⠤⠔⢒⣒⣂⣌⣉⠉⠭⠭⠭⠭⠭⠉⣉⣁⣐⣒⡒⠂⠤⠤⣄⣀
⡴⢊⡥⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠲⢬⡙⢦
⡗⠮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⢺
⡗⠒⠤⢌⣉⠓⠒⠒⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠒⠒⠚⣉⣩⠤⠒⢺
⡇⠀⠀⠀⠀⠉⠉⠐⠒⠒⠒⠤⠤⠤⠤⠤⠤⠤⠤⠤⠒⠒⠒⠂⠉⠉⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⢤⡠⠞⠁⠀⠈⠳⢄⡤⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⢠⠖⠒⠲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠖⠒⠲⡄⠀⠀⢸
⡇⢀⣀⡆⠀⠀⡴⠤⡤⠀⢠⠖⢲⠀⢀⡔⠂⢄⡀⢀⢀⣀⣀⠤⠤⢤⠀⢽⣀⡀⢸
⣷⠋⠀⠀⡠⠤⡽⠀⣧⣤⡬⠆⠸⠤⣄⣉⠙⠒⡫⠒⡿⢻⡄⣾⠭⢥⠀⠀⠀⠉⣾
⡿⣄⠀⠘⠓⠒⢶⢠⣉⣉⣉⡇⢸⠉⠙⠯⠭⠲⣷⢰⡇⢸⡇⣿⠀⢸⠀⠀⠀⣠⢿
⡇⠸⣄⠀⠀⠀⠈⢀⠂⠀⠚⡃⢸⠀⢀⣀⡤⠞⣥⢰⣇⣡⣬⣽⠂⡆⠀⠀⢠⠇⢸
⡇⠀⡇⠀⠀⠀⠶⣈⡉⠭⠭⠥⠜⠀⠸⣄⣀⡜⢨⣛⣣⣤⣤⣼⣁⡇⠀⠀⢸⠀⢸
⡇⠀⠙⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠋⠀⢸
⡇⠀⠀⠀⠀⠑⠒⠲⣄⣠⡄⠀⠀⢀⠤⠄⠤⡀⠀⠀⢀⣄⣠⠖⠒⠊⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠓⠉⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣷⢻⡼⠂⠀⠀⠀⠀⠀⡤⢤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⢸
⡯⠽⠚⠁⠀⠀⠀⠀⢸⡹⣉⠖⡄⠀⡠⢢⠤⡀⠀⠀⠀⠀⠀⡜⣖⢱⢼⠀⣾⡹⣿
⣯⠿⣱⠄⣜⡽⣗⡆⠀⣙⣖⣉⠀⠸⣙⢭⢗⡇⢀⢎⠽⣑⡆⠈⢢⠕⠊⠈⠣⣓⣿
⣏⣀⠔⠈⠢⣓⡯⠇⢰⢳⠚⡬⡄⠀⣈⢖⣉⡀⠘⢮⣑⠥⠃⡴⡥⢫⣱⠀⣴⣲⣾
⣗⣶⢢⡀⡰⣲⡶⡄⠈⢳⡽⠒⠁⢰⡳⣊⡦⡇⠀⣔⣲⠲⡄⠑⢍⡪⠜⠐⢏⠧⣿⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⡟⢴⣫⠔⢅⠧⣏⡥⢠⢯⠽⣙⡀⠀⠙⡎⠚⠁⠘⣜⠦⣋⠇⣠⣊⣖⡢⠤⠐⠛⣛⣉⣉⠩⠭⠭⠭⠤⠤⠤⠤⠤⠤⠭⠭⠤⠍⣉⣉⡒⠒⠢⠤⣀⡀
⡯⣭⢄⠀⢠⢭⡥⡀⠘⢮⣺⠴⠃⢠⢯⠜⣍⡆⠀⡨⢭⢤⡀⠣⡟⢁⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⢤⠉
⡿⡩⢞⠡⣃⢏⡗⡣⢀⣖⣳⠲⠀⠈⠳⡭⠕⠃⠰⡹⢍⠗⡇⢸⡏⠛⠦⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠾⠋
⣗⣚⡉⠀⢈⣒⣋⠁⠸⢜⢴⣩⠇⢀⣞⡱⡒⡄⠀⢘⣒⣉⠀⢯⡻⣄⡀⠀⠀⠈⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠉⠉⠉⠁⠀⠀⢀⠴
⢧⡙⠚⠦⣮⡞⡧⠇⠀⡴⣣⢤⠀⠘⢮⣓⡣⠇⢰⢳⡚⡮⠇⢀⡹⣋⣙⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠈⠑⠢⠤⣈⡉⠛⠚⠿⠤⠶⢦⡀⣴⣷⡤⣄⠤⠷⠬⠶⠓⠚⢉⣡⠤⠔⠊⠉⠒⠦⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠐⠒⠲⠶⠒⠀⠀⠀⠒⠶⠖⠒⠂⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠰⠯⣉⣉⠉⠉⠙⠛⠛⠉⠉⢉⣉⡉⠵⠂
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤⣀⠀⢠⠛⠱⠢⠲⡒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡰⠱⡄⣀⣀⣜⠓⠊⢠⠐⣌⠁⠙⢦⢃⡴⢀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉⣦⢀⡔⢮⠻⡉⠻⢫⠙⡛⣦⣰⠈⢩⠃
⠀⢹⠂⠑⠛⠑⢬⡷⡄⠈⠁⢁⠐⠢⡲⡏⢀⠰⠤⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠐⠢⢬⠠⠀⣧⢁⠀⡆⠀⡇⣿⣤⡀⢈⡆
⡔⠁⠀⢀⡀⢤⡊⠘⠀⡀⢀⡈⠢⠚⢠⢟⠳⡄⢰⠃⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⡄⡠⢦⣸⢫⡀⣟⡌⣠⣿⣠⡧⠟⠸⠼⠁
⠑⠤⠜⠋⠳⡀⢈⣵⣳⡣⠤⢃⢒⡩⠋⠈⠓⠒⠊⠀⠀⢀⡤⠔⠂⠻⢍⣉⣝⣛⠒⠒⢤⡀⠀⠠⣇⡟⠁⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠈⠉⠀⠈⠙⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢤⣤⣙⣋⣉⣉⣉⣢⣉⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠉⠀⠀⢈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠉⠐⠢⢤⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⢸⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠙⠁⢛⠩⡢⣄
⠀⠀⠀⠀⢀⠔⡞⠁⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠐⠐⠇⠤⠤⠼⠤⠤⠜⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⡄⠀⢀⠐⠤⠜⠈⣆
⠀⠀⠀⠀⢸⡄⠘⢆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠊⠀⠐⠤⠃⠀⣀⠹⣬
⠀⠀⠀⠀⠘⡉⠢⡀⠑⠢⢄⣀⠀⣀⣠⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⠒⠠⠤⢀⡀⠀⠀⠀⠀⠀⠈⢆⠢⠀⠀⢢⠐⠤⠜⣀⠄
⠀⠀⠀⠀⠀⠑⢄⠈⠑⠒⠤⠤⠀⢄⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⢀⡴⠚⠀⠀⠉⠑⢒⢤⠀⠀⠈⠒⠄⣀⣀⣀⣤⠼⣙⠢⡄
⠀⠀⠀⠀⠀⠀⢀⠟⠲⡤⢤⠤⠴⠊⠁⠀⠀⠀⠀⠀⢀⠴⢆⣪⠀⠀⠀⠁⠈⠖⠀⢀⣀⣀⠀⢀⠤⠂⠁⠀⡆⠀⠀⠀⠀⠀⢀⠩⠠⣰⠙⡍⠁
⠀⠀⠀⠀⠀⠀⡜⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠓⠒⠠⠌⢢⡤⡀⠀⠀⠀⠀⠀⠀⠠⢊⡄⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⡄
⠀⠀⠀⠀⠀⡰⠁⡜⠀⠀⠀⠀⠀⠀⢀⠴⣚⠁⠀⠀⠀⠀⢀⡠⠊⠐⠙⠒⠲⢠⣔⠙⢦⠀⠈⣇⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘
⠀⠀⠀⠀⡸⠁⡸⠀⠀⠀⠀⠀⠀⠀⢨⠓⠤⣑⠢⠄⢀⣔⠤⠦⢄⣀⠤⢤⡐⠁⠐⠃⢀⡇⠐⠁⠀⠀⠀⢀⡠⠔⠒⠒⠒⡲⢄⡀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠣⠤⠃⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⡈⣇⢀⠀⡇⢀⣀⣘⠁⢀⡀⢸⠀⢀⠜⠒⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⠁⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠀⠀⠈⠋⠀⠈⠙⠈⠁⠀⠀⠀⠀⠀⠀⡾⠡⠀⢀⡴⡋⠩⠙⡧⠉⡒⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⡆⠀⠀⠀⠀⠀⠀⠀⠐⡇⠑⠒⡏⠀⢚⡉⣠⠧⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠤⡗⠁⠈⢳⠄⠀⠀⠀⠀⠀⠀⠳⡤⢠⡷⡤⢚⠉⠀⡃⣡⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⣖⠉⠁⠉⠢⡘⡄⠀⣹⣾⠀⣪⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠬⠷⠶⠖⠻⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⣔⠂⠉⠀⠀⠐⢄⢣⠀⠀⠀⣱⣰⠔⠁⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠱⡀
⠀⠀⠀⠀⠂⠲⠦⢄⣀⣋⠀⠲⡄⠙⢆⢂⠀⠀⣈⡤⠶⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⢦
⠀⠀⠀⠐⡦⠄⠑⢤⣤⣀⣔⠀⠀⣀⣨⠾⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⡳
⠀⠀⠀⢸⠀⢀⡶⡤⠴⠁⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠉⠁⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠛⠛⠛⠛⣛⠛⠛⠛⠳⣦⠀⠀⠀⠀⠀⠀⠠⡦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢶⠞⠋⠛⣶⠆⠀⢸⡇⠀⠀⣠⠴⠶⠾⠃⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⣼⠛⠛⠛⢿⡀⣀⡼⢃⣤⠴⠧⠤⠤⠤⠤⠤⠤⠷⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠉⠉⠉⠉⠙⡇⠸⠃⣴⢸⡟⠉⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⡼⠁⣀⣀⣿⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣾⣅⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠉⢿⠉⠉⢹⡏⠉⠉⠉⢹⠋⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠸⡇⠀⠘⡇⠀⠀⠀⣼⠈⣯⠉⠉⠹⡏⠉⠉⣿⠉⠉⠉⢉⡏⠉⠉⡟⠉⠉⢹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢿⠀⠀⣷⠀⠀⠀⡿⠀⢸⣆⠀⠀⢷⠀⠀⢿⠀⠀⠀⢸⡇⠀⢸⠃⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⡇⠀⣿⠀⠀⢀⡇⠀⣾⠹⡆⠀⠸⡆⠀⢸⡀⠀⠀⢸⠁⠀⡟⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢿⠀⢸⠀⠀⢸⡇⢰⡇⠀⣿⡄⠀⢷⠀⢸⡇⠀⠀⣾⠀⢸⠇⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣸⣇⣸⣇⣀⣸⣁⣾⣀⣼⠃⢷⡀⢸⡇⠘⡇⠀⠀⡿⠀⡿⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⣧⣀⣷⣀⣷⣀⣠⣧⣸⣇⣰⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⡄
⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿
⠀⣠⣾⣿⣿⣿⣿⠿⠛⠋⠉⢻⣿⣿⡟
⣼⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀
⠈⠻⢿⣿⣶⣶⣦⣤⣄⣀⠀⠸⣿⣟⠀⡄⢠⠀⢴⣞⠂⣸⠯⡇⠉⡗⠀⢠⣴⣶⡄
⠀⠀⠀⠀⠈⠉⠉⠉⠛⠿⣿⣶⣭⡘⣦⠷⣼⠂⢣⣴⣁⣉⣈⣥⣤⣶⣾⣿⣿⣿⠁
⠀⢰⣦⣤⣀⡀⠀⠀⠀⠀⠈⢙⣿⣿⣦⡠⣤⣶⣾⣿⣿⣿⠟⠛⠉⠉⠀⣿⣿⠏
⠀⠀⠈⠙⠛⠿⢿⣶⣤⣤⣶⣿⣿⣿⡿⠃⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⣭⣁⣀⣀⣀⠠⣤⣿⣿⣿⡿⠿⠿⣗⣦⢠⡀⣀⠄⠀⣦⠐⡶⣜⣆⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⡿⠋⠉⠙⢻⣶⡼⣿⣿⠀⠛⠸⡁⢘⠘⢟⠹⡇⠠⠟⠀⠃⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣇⣀⣤⣾⣿⠟⠁⠻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⢛⡛⠉⣁⣠⠀⢀⣀⠀⡀⢀⢀⣀⢀⡀⠀⣀⣤⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⣸⡇⢾⡁⢋⠈⢹⠃⢸⣇⣼⠠⡗⠺⡅⣴⠛⡮⢘⠫⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠼⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠀⠘⠲⢄⣀⠌⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠢⠀⠀⡈⠦⠀⡀⠘⣿⡟⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣁⡰⢁⡐⡠⠤⢖⣨⠛⢄⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢡⠆⢴⠋⠀⠀⠀⣦⣴⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠤⠛⠀⡴⠀⠀⠀⣠⠏⢨⡄⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣀⡀⠀⣀⢄⡀⠀⠀⢐⣩⠤⠤⠖⠋⠁⢀⣴⣧⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠛⢀⡈⠁⠀⠀⣠⡴⠚⠉⠀⢀⣀⣤⣶⣾⡿⠻⠛⠋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢀⠀⠀⠈⠛⠛⠛⠛⠛⠒⢒⠛⠻⠋⠉⠀⠁⣶⣴⣶⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢛⢲⠢⣦⠀⣤⣤⣤⣦⣤⣤⣾⡴⡶⢾⡟⣿⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⡘⡆⢻⠀⣧⢸⠀⣼⠀⡇⣾⠀⡇⣸⣷⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢠⣷⣸⡇⢹⡨⡧⣿⢠⡇⣿⣸⣳⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⡽⣷⢸⣿⡇⣿⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣖⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠋⠉⠉⠉⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡏⠐⠀⠄⢈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠋⠀⠀⠀⡀⠐⠈⠀⠀⠀⣠⣾⡦⠀⠘⣿⣿⣿⣿⣿⣿⣿⣟⠈⠁⠓⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠰⠀⣤⣤⣤⣤⣤⡾⠋⢁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⢁⣈⣴⡏⠲⣄⡀⡀⠘⠏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠻⡀⠀⠰⠀⠀⠀⠀⢀⠘⡇⢀⢳⠀⠀⠀⠀⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢿⣿⣿⡇⠀⠀⠔⠠⡄⠀⠀⠀⠀⠁⠀⠹⡀⡸⠀⠀⠀⠀⠀⣾⠿⠛⠻⢿⣿⠿⡿⠿⠛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢠⠜⣿⣿⣧⡀⠀⠀⠀⠁⠐⠆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠂⠘⠇⢀⣾⣿⣿⣿⣶⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣾⣿⣿⣿⣿⡿⠿⠦⠀⣦⠀⠀⠀⠀⠀⢀⠄⠀⠤⠀⡐⠀⡋⠢⡀⠀⠀⠀⢠⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⢄⡀⡀⠠⠀⠁⠀⣀⡄⠀⠀⠀⠀⠀⠈⢢⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⠿⠧⠀⠀⠀⠀⠀⠀⠀⡇⠐⢄⠀⠀⢀⠀⠀⠐⠒⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠰⡿⠟⠃⠀⠀⠘⠀⠀⠀⠀⠀⡐⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⢀⣮⣤⣤⣴⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠢⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠿⠿⠿⠿⠿⠿⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣤⠄⠀⢀⢎⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣾⣉⡀⣈⣉⢉⡉⣭⡍⣴⣛⡟⢋⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⡼⠏⢿⡿⡜⢙⡟⡵⢿⡵⣧⠏⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⣄⣸⢷⢫⢇⣤⢄⡤⡞⡤⡤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⣋⠀⣹⡁⢘⢛⠘⣜⡘⢛⣉⢃⡃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣉⡽⠛⣧⢧⢿⡾⠺⣥⣧⣟⣽⢻⡧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁⠠⠚⠶⠻⠶⠳⠴⠳⠄⠀⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⢀⣐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠐⣲⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⢤⠠⢄
⠀⠀⠀⠀⠀⠀⡮⠃⠈⡖⠋⠀⠀⠀⠀⠀⠀⢀⠖⠛⠛⡲⡀⠀⠀⠀⠀⠀⠀⠸⠈⢉⢢⡏⡆⡇
⠀⠀⠀⠀⠰⡐⢣⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⣎⣄⣀⣀⣡⣡⠀⠀⠀⠀⠀⠀⢈⢎⡵⠷⢌⢲
⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠉


⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢀
⠀⠀⠀⠀⢀⣼⣜⣒⣤⣄⡀⠀⠀⠀⠀⠀⠀⢠⠼⠄⠠⠧⡄⠀⠀⠀⠀⠀⠀⢠⣃⡠⠤⡀⠱
⠀⠀⠀⠀⢸⣶⣴⣞⣦⣴⡇⠀⠀⠀⠀⠀⠀⠈⡢⠀⠀⢔⠁⠀⠀⠀⠀⠀⠀⠘⡀⠐⠒⠉⡹
⠀⠀⠀⠀⠘⠚⠛⠒⠚⠓⠃⠀⠀⠀⠀⠀⠀⠘⠤⠊⠱⠤⠃⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠈


⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣰⡫⡑⢕⡄⠀⠀⠀⠀⠀⠀⢠⡞⢲⡆⢳⡀⠀⠀⠀⠀⠀⠀⢠⠄⠈⠠⠠⢀⡀
⠀⠀⠀⠀⠀⢀⢕⢌⡮⠞⠀⠀⠀⠀⠀⠀⠀⣜⣢⣀⣂⣔⣣⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠰⡧⠃
⠀⠀⠀⠀⢎⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⠤⠤⠤⠤⠬⠄⠀⠀⠀⠀⠀⠠⡓⣂⣐⣚⠄

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⣞⠓⠼⣄⠀⠀⠀⠀⠀⠀⠀⡠⠚⠚⠢⡀⠀⠀⠀⠀⠀⠀⢸⣇⣠⢄⣨⡆
⠀⠀⠀⠀⠀⠀⠈⠻⣎⡓⢏⡟⠁⠀⠀⠀⠀⠀⠀⣸⣀⣉⣉⣻⡀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠉⢲⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣝⡾⠁⠀⠀⠀⠀⠀⠀⠀⢻⡤⠤⠤⣴⠃⠀⠀⠀⠀⠈⠲⡞⡳⠶⡛⡶⠊⠀⠀⠀⠀⠀⠘⠤⣀⣀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠓⠞⠒⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⡴⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠢⣄⠀⠀⠀⠀⠀⠀⣠⠴⢧⣤⡼⣄⠀⠀⠀⠀⠀⢠⠎⠉⠁⠙⡖⠁⠀⠀⠀⠀⠀⠀⡤⠷⠾⢤
⠀⠀⠀⠀⠀⡔⣋⣀⠀⣀⡀⢀⣈⡓⣄⠀⠀⠀⡏⣉⣉⣉⣉⣉⣹⠀⠀⠀⠀⠀⠺⡤⠤⠤⢤⠟⠀⠀⠀⠀⠀⠀⣸⠓⠒⠒⠚⡄
⠀⠀⠀⠀⠀⠉⠣⠬⠭⠤⠬⠭⠤⠋⠁⠀⠀⠀⡟⠛⢛⣛⣋⣉⣹⠀⠀⠀⠀⠀⠀⠙⣶⣖⠎⠀⠀⠀⠀⠀⠀⠙⠯⠭⣍⣩⠭⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠯⠵⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣄⠀⠀⠀⠀⠀⠀⠀⡠⢖⣒⡲⢄⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡤⣤⣤
⠀⠀⠀⠀⠀⠀⡴⢚⣉⡒⢦⡀⠱⡄⠀⠀⠀⠀⢸⢱⢡⢒⡌⡆⣧⠀⠀⠀⠀⠀⡼⠁⠀⠂⠀⠈⣆⠀⠀⠀⠀⠀⢸⣿⣻⣟⣿⣿
⠀⠀⠀⠀⠀⢸⡁⡏⣄⠙⡆⢱⠀⡇⠀⠀⠀⠀⠘⣜⢮⣓⣊⣴⠏⠀⠀⠀⠀⠰⡏⢳⠉⡞⢙⠎⣹⠀⠀⠀⠀⠀⣸⢭⣍⡋⢉⣽
⠀⠀⠀⠀⠀⠀⠣⡱⢌⣛⣁⡼⠊⠀⠀⠀⠀⠀⠀⠈⠑⣿⠋⠁⠀⠀⠀⠀⠀⠀⢱⠸⡀⡇⢸⢀⡇⠀⠀⠀⠀⠀⣿⠉⠉⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠓⠓⠛⠚⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⡀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠲⡀
⠀⠀⠀⠀⠀⠀⡼⢀⡄⠀⠐⠆⢳⡀⠀⠀⠀⠀⠀⢀⡴⢺⡙⢦⡻⠀⠀⠀⠀⠀⢀⣈⡆⠒⢸⣁⡀⠀⠀⠀⠀⣠⠴⣏⠉⠉⣹⠦⣄
⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⢠⠀⢀⠇⠀⠀⠀⢀⡠⡏⠸⡀⢧⡜⠀⠀⠀⠀⠀⠀⠑⢤⠀⠀⢀⡴⠋⠀⠀⠀⠀⡟⢦⡸⢄⡠⢇⡴⢻
⠀⠀⠀⠀⠀⠀⠑⠤⣄⣀⡠⠤⠞⠀⠀⠀⠀⠀⠳⣌⡲⠓⠉⠀⠀⠀⠀⠀⠀⠀⢠⠞⢀⣄⡀⠣⡀⠀⠀⠀⠀⠙⠺⠇⠀⠀⠰⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠀⠙⠒⠃

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡂⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠇⠙⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢀⢈⠂
⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠚⠁⠀⠀⠉⠀⡺⢤⡄⠀⡀⣠⠞⠁⠈⠳⣄⠀⠀⠀⠀⡎⠉⠱⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠑⠎⠁⠀⠀⠀⠀⠀⠀⠊⣀⡷⠈⠓⣸⠁⠀⢀⡀⠀⠈⢣⠀⠀⢀⠇⠀⠁⠀⡀⠀⠈⠳⣤⡀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⣀⣀⣀⣘⡬⠖⠨⠿⠀⢄⠀⣴⢤⡀⡤⠂⡀⠈⠀⠀⣈⣇⠀⠔⠁⠈⠢⠀⢸⡃⢰⢫⡆⠀⠀⠈⠉⢀⡴⠤⢷⠟⠉⢀⡘⣆
⠀⠀⠀⢀⠀⢰⠀⢠⠖⠋⠁⠀⠀⠉⠳⣌⠄⣐⠉⡁⠡⠼⣆⠙⢦⠀⢀⡰⠧⠀⠈⣍⢢⣄⡀⠀⣀⣄⡋⠙⢣⠚⡇⠀⠀⢠⠖⠉⠁⢀⠀⠀⠀⢸⡉⠉
⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⠀⡀⠀⠀⠀⢸⡄⠈⠣⠀⠀⠀⣽⠀⠈⢧⡀⠀⣄⡠⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⢸⠇⢧⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠀⠀⠀⢸⡧⠤⠖⢲⡶⠞⠁⠀⠀⠀⠉⠉⠛⢻⡶⠦⢤⣤⠄⠀⠀⠀⠔⠢⣼⠂⠸⣆⠛⣷⠀⠋⠀⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠐⠂⠀⠀⢸⡀⠀⠀⠀⠀⢡⠀⠂⠀⠀⠂⠀⣀⠂⠀⠀⠀⠈⠑⢦⣀⣠⣄⣀⣿⡀⠀⠘⢧⣉⣧⣀⠀⢰⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠈⠙⣆⠀⠂⠀⠚
⠀⠀⠀⠀⠀⠀⢠⠈⠀⠙⠲⣄⣀⠀⠀⠀⠘⠦⣄⡁⢀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠸⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡰⠦
⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠀⠸⡉⠉⠛⠛⠛⠛⡏⠁⢨⣤⣤⠀⠀⠀⠰⠶⠶⠄⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠉⠳⡄⠂⠀⠀⠀⢀⠀⠀⡏
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡬⠠⣾⣉⢉⣷⣥⠤⢤⡄⠀⠄⠐⠒⠒⠂⣤⠖⠚⠓⢦⡀⠀⣜⠀⠀⠀⠀⠀⠀⣹⣤⡀⠀⢀⠀⠁⢾⠁
⠀⠀⠀⠀⠐⠤⠀⠐⠒⡞⢈⠉⠹⣴⠋⠀⠀⢸⣷⣤⣌⡷⠀⠠⢘⠀⢀⡞⠁⠀⠀⠀⠀⠙⢾⠁⠀⠀⠀⠀⠘⠄⠣⣁⡏⠐⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⠂⡀⠁⣿⠐⠀⠀⠚⡇⠀⠀⡇⠀⠢⣸⣠⠟⠠⠤⠄⠀⠀⠠⠤⠘⢧⣀⣶⠀⣀⠀⣴⡄⠀⢹⡀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⠀⣿⠀⠀⠀⢀⡇⠀⠀⢷⡀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠁⠀⠀⠀⠀⠐⣧⡤⢶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢈⣠⢀⣿⠀⡤⠖⠉⠀⠀⠀⠀⠉⠓⢾⡁⠀⠀⠒⣀⣄⣠⣀⠂⠀⠀⠸⡄⠀⢠⠞⠉⠙⢦⡂⢃⣳⠺⢋⡒⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠂⠉⠈⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳⡄⠠⠤⠉⠉⠉⠉⠤⠀⠐⠈⣟⢳⠏⠄⠀⠠⠄⠳⡀⠐⠢⢄⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⢸⡇⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡤⠄⢲⣇⡏⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢰⠟⢖⠒⠦⠤⠤⠾⢄⠀⠀⢀⠽⡧⠤⠀⠀⠀⠀⠄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠈⠀⠃⢂⠀⠀⠀⣀⡴⠃⡃⠄⣀⠐⠀⠄⠀⢡⠀⠅⠀⠀⠉⠓⠶⠤⠶⠶⠚⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠚⠉⠁⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠐⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣴⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣿⡿⠿⠿⣿⠉⠛⠋⠀⠰⠞⠛⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠛⠛⠀⠀⠀⠀⠀⠤⠤⢆⣀⠀⠀⠀⠈⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡇⠀⠀⠀⠀⠀⠀⠲⡤⠀⠀⠣⠄⠀⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡐⠄⠀⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣄⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣴⣿⣶⣦⣦⣄⡀⠀⠀⠈⠻⣿⣿⣦⡀⠠⢼⣇⠀⢀⠀⠀⡄⠀⠀⢀⣀⣤⠖⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡿⠋⠀⠀⠈⠛⠀⠈⠻⠛⠛⠻⢷⣄⡀⠈⠻⢿⣿⣾⣷⡌⠉⠛⠁⠛⣭⡀⠛⠉⡿⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣧⠀⠀⠀⠀⠀⠂⠀⢀⡀⠀⡀⠀⠈⠙⢦⠀⠀⠈⠉⠀⠙⠛⠀⠤⠶⠿⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣇⣹⠾⠻⠛⠀⠀⠐⠆⠉⠈⠙⠖⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⢀⣤⡴⣺⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⣀⠀⠐⠒⠒⠞⠲⢌⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠿⠁⣾⣿⣿⣿⣿⣿⣿⣧⣻⣦⣀⡀⠚⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⢦⣼⡄
⠀⠀⠀⠀⢴⠆⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⣻⣷
⠀⠀⠀⠀⢸⣧⡈⠻⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣦⣄⣀⠀⠉⠁⠐⠀⠒⠚⣥⣶⣿⡿
⠀⠀⠀⠀⠘⣿⣟⠳⣄⣙⠻⢿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣽⡟⠿⠿⣿⠿⠿⠟⠋⠁⠈⠉
⠀⠀⠀⠀⠀⠈⢿⣿⣶⣬⡃⢤⣈⡙⠿⠿⠿⠿⠿⠛⠛⠋⢉⡋⠰⢲⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣾⣿⣿⣏⣃⣀⠳⠴⠦⠶⠖⢀⣠⣶⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠉⠉⠛⠲⠶⠿⠿⠟⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢖⣛⣛⣓⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣵⣿⣿⣿⣿⣿⣿⣷⣭⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣱⣿⡟⠛⢻⣿⣿⠟⠛⢿⣿⣷⡹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⣿⣿⣷⣤⣼⣿⣿⣧⣤⣾⣿⣿⣧⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡼⣿⣟⠻⣿⣿⣿⣿⣿⣿⡟⢻⣿⡟⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠘⣧⢻⣿⣦⣌⠛⠿⠿⠛⢋⣴⣿⣿⢣⡟⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣫⣭⣭⣭⡛⠳⠦⣤⣀⡀⠈⢷⣝⢿⣿⣿⣷⣶⣿⣿⣿⢟⣵⠟⢀⣀⣤⠴⠞⢛⣭⣭⣭⣝⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣼⣿⣿⣿⡿⣛⣼⣿⣶⣯⣽⣛⠶⠿⠇⠛⠻⣿⣿⠟⠛⠱⣿⠶⢞⣫⣭⣶⣿⣧⣘⢻⣿⣿⣿⣧⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢻⣿⣿⣿⠗⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠉⠉⠄⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⡰⢿⣿⣿⡟⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣝⡻⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣾⣷⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣛⣫⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢮⣭⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⢟⣛⣭⡵⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣮⢻⣿⣿⣿⣿⣏⠀⠀⢈⣿⣿⣿⣿⣏⡴⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⡏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢏⣾⣿⣿⣿⣿⣧⣀⣀⣠⣿⣿⣿⣿⣿⡜⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣭⢭⣍⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⣿⣷⣬⣍⢻⣿⣿⣿⣿⡿⢋⡼⠋⠀⠀⠈⠻⣮⠻⣿⣿⣿⣿⣿⢫⣭⣴⣿⣮⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢿⣿⣿⣿⣷⣌⣛⢻⡿⢋⡴⠋⠀⠀⠀⠀⠀⠀⠈⠳⣌⢿⡿⢛⣋⣼⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣜⢿⣿⣿⣿⣿⡿⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢸⣿⣿⣿⣿⣿⢏⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⣭⣭⣥⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣭⣭⣭⠶⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣾⣿⠿⣛⣿⣿⣛⠿⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠿⡿⠿⣿⣟⣛⣫⣾⠟⠿⣿⣿⣷⣴⣶⣮⡝⣿⣛⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⣫⣵⣾⣿⣿⣯⡉⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣦⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢟⣫⢶⣿⣿⣿⣿⣿⣿⠃⠀⠀⣠⣴⠀⠀⠀⠈⠉⢉⣿⣧⣿⣿⣿⣿⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢟⡵⠋⠀⠸⣿⣿⣿⠉⠽⠋⠠⠖⢋⣁⣀⠀⠀⠀⠀⠀⣾⣽⣿⣿⣿⣿⣿⣮⡛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣱⠋⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⢠⣾⣿⣿⣋⣿⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣼⣿⡟⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⡿⠋⠀⠀⣠⣴⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣀
⠀⠀⠀⠀⠀⢰⣿⡿⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⢠⣿⣿⣿⣿⢿⣻⣿⣿⣿⣟⣻⠿⣿⣷⣆
⠀⠀⠀⠀⠀⣾⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⡄
⠀⠀⠀⠀⠀⣿⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿
⠀⠀⠀⠀⠸⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢤⣄⣀⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡏
⠀⠀⠀⠀⠀⣿⣿⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⠁
⠀⠀⠀⠀⠀⠸⣿⣷⢻⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣯⢧⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⢳⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣎⢧⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣳⣿⣿⣿⣿⣿⡿⣳⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡳⣄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣮⡳⣄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣮⣓⢦⣀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣵⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣮⣝⡲⢤⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣵⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣾⣭⣭⣽⣿⣿⣿⣭⣭⣷⣶⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠿⠿⠟⠛⠛⠋⠉

⠀⣠⣤⣄⣤⣤⣤⣄⣤⡀⣠⡄⠀⣤⣤⡄⢀⣤⡀⢠⣄⡠⠠⢄⠄⠀⠀⠀⠀⠀⡀⡀⠀⠀⠠⡀⢠⠄⠀⠠⠄
⢰⣿⡛⠛⠉⣿⡏⠁⣿⠁⣿⡇⢸⣿⠉⠁⢸⣿⣷⣿⠛⠀⠁⠊⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠄
⠀⢻⣷⡀⠀⣿⡇⠀⣿⡇⣿⡇⣼⣿⠀⠀⢸⣿⣿⡃⠀⢂⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠠⡀
⣠⡄⢻⣷⠀⣿⡇⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⡿⣿⡆⡀⠂⠀⠀⡇⠀⠀⠀⠀⠀⠂⠀⢠⠀⡀⠀⠀⠦⠐⢄
⠹⣷⣾⠟⠀⢻⡗⠀⢻⣷⣿⠇⠈⢿⣷⣿⠇⣿⡇⠈⢧⣀⠀⠀⠀⠃⠀⠀⠀⠁⢀⠀⠈⠀⠊⠀⠈⡀⠀⠀⢀⠣
⠀⠀⠀⠀⠀⣴⣷⡆⠀⡈⠁⢀⢄⣤⡌⠁⣄⣬⣄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣤⡄⠀⣄⠤⣤⢠⡀
⠀⠀⢶⣷⠀⣻⣿⡏⠀⣿⠿⠈⡤⠃⠀⠀⠸⠰⠞⠎⠁⠀⠄⡀⠀⠀⠀⠀⠀⡀⠈⠘⠄⠃⠀⠀⠸⠸⠞⠎⠁
⠀⠀⠀⣿⣧⣻⣿⣇⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢀⠀⠀⢀⡄⡀
⠀⠀⠀⠈⠻⣿⣿⣿⢿⡇⣀⣄⢀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢸⡄⢰⣇⣀⣄⢀⣠⣀⣤
⠀⠀⠀⠀⠀⢸⣿⡣⢀⡠⠤⠤⠬⢄⡀⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠸⢿⠊⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠰⡩⢉
⠀⠀⠀⠀⠀⠀⢘⠰⠒⠦⢴⣦⡦⢼⣗⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠈⢮⡀⠰⠴⠛⠦⠆⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠈⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⢐⡂⠉⠑⡒⠒⠒⠚⢉⢀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡒⠀⠀⡀⢀⠀⠀⢉⢀⠦
⠀⠀⠀⠀⠀⢀⡌⠀⠉⠂⠁⠈⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠈⠂⠁⠈⠀⠘⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⢀⠂⠀⣀⠀⠀⠀⢠⣢⡘⠋⢈⠷⣣⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⢃⡸
⠀⠀⠀⠀⠀⢤⣈⠂⠀⠀⠎⠁⣏⠹⢗⣋⢁⠙⠧⢔⡄⠀⠀⠠⠺⠇⢀⠀⠀⠀⠀⠈⠁⣠⣞⠱⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠙⠁⠛⢣⣄⣓⢬⠄⣬⡒⠇⠀⠠⠀⠀⡀⠀⢉⠖⠀⠀⠾⢿⡟⠉⠁⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⢶⢄⣤⣼⢀⠁⠾⠧⠕⡀⡄⠀⠀⡀⣠⢴⠛⢋⠠⢂⠀⠤⣀⡄⠀⠀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠡⠐⠂⢌⠉⠰⠆⠁⠀⠈⠉⢿⡁⠊⠁⠀⠀⠀⠀⠈⠉⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠂⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢃⡄⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠀⠀⠈⠑⠂⠤⡀⠀⠀⠁⠈⠼⠀⠀⠀⠈⠙⠷⠤⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠢⣄⠉⠒⠄⣐⠂⠀⣆⡀⠀⢀⠀⣀⠂⠀⠀⠀⠀⠀⠈⠓⠶⢤⣀⠀⠄⡠⠀⠀⠤⠀⠀⠀⠠⢠⠐
⠀⠀⠀⠀⠉⠀⣠⣿⡟⠓⠚⢷⣾⡚⠛⠋⠙⠲⠀⠀⠀⠠⡀⣠⡆⠀⠈⢹⣦⡇⣀⠀⠂⠠⠠
⠀⠀⠠⠊⢀⠾⠛⣿⠷⠒⠂⠀⠀⠘⠯⠶⠲⢾⠆⠀⠐⣎⠂⠀⠀⠀⠀⠈⠨⠛⡧⢶⣠⣇⣰
⠀⠀⠀⠈⠁⠜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠁⢀
⠀⠀⠀⠀⠘⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⠖⠦⢀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⢡⣶⡀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⣦⠀⠉⠀⣐⠆⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠉⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠤⠤⠤⠄⢀⣀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠉⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠉⠐⢤⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡁⢀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠁⠀⠀⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡁⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⢀⡤⠤⠴⠾⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⢿⣠⣇⣤⣄⡀
⠀⠀⠀⢀⠒⠀⠀⢠⠒⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢰⡇⣰⡖⠲⣶⣜⣿⠳⠙⠛⠛⠉⠛⠛⠛⠛⠉⠉⠉⠑⠃⢉⣿⣿⠇⠨⠛⠷⡄
⠀⠀⠀⠨⣄⠀⠈⠈⠉⢐⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡾⢇⠀⣄⠀⠘⠿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡿⠁⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠈⠑⠂⠓⠚⠉⠀⠀⠄⠀⠂⠄⠀⢠⠀⠀⠀⠀⠁⠀⠙⠶⢬⣄⣀⣒⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡗⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠇⠁⠀⣴⠞⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠉⠉⠙⢿⢿⣶⣄⠀⠀⠀⠀⢀⣠⡶⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠒⠊⠁⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠜⠋
⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠛⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠐⠒⠛⢉⢻⡭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⡠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠭⣥⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣹⣧⠆



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠁⠀⢸⠀⠀⢀⠇⠀⠈⠉⠉⠉⠀⠘⡄⠀⠀⡰⠉⠣⠤⠧⠤⠊⠱⠀⠀⠀⠸⠀⠑⠛⠒⠚⠁⢱⠀⠀⢸
⠀⠃⠀⢸⠀⠀⢸⠀⠐⠒⠠⡄⠊⠂⠀⡇⠀⠀⠇⠀⠤⢀⠀⢤⠀⠀⡇⠀⠀⡇⠀⠀⢀⠀⠠⠀⠀⡆⠀⢸⢀⠘
⠀⠀⠀⣎⡀⠀⠸⡀⠀⣀⠊⠁⠁⠀⢀⠇⠀⠀⠀⠁⠀⠚⠓⠀⠈⣀⡀⠀⠀⢇⣀⠀⠈⠁⠀⠀⡰⠀⠀⠘⡄
⠀⠀⢠⠃⠙⠤⠤⠥⠜⠉⠆⠀⠀⠀⢨⠓⣄⢀⡇⡠⠓⡄⠀⠀⠰⠁⠑⠤⠤⠞⠁⢱⠀⠀⠀⡔⠙⣄⢀⣸⠔⠱⡀
⠀⡔⠁⠀⣀⠀⠀⠀⣀⠀⠈⡆⠀⠀⠇⠀⡈⠈⠉⡀⠀⢡⠀⠀⠃⠀⣤⠀⠀⢠⠀⠀⡇⠀⢰⠁⢀⡀⠀⢀⡀⠀⠇
⠀⡇⠰⠀⠀⠀⠶⠠⠀⠀⠀⠘⠀⠸⡀⠄⢁⣰⣀⠁⠀⠸⠀⠀⡄⠂⠀⢤⡣⠀⠀⢀⠃⠀⢸⠀⠈⠁⠒⠈⠁⠂⡀
⣀⣣⣠⠊⠳⡀⠀⠀⠀⡴⢢⣎⣀⣀⡗⢢⠀⠀⠀⠀⠀⡆⠀⠀⠇⠀⠀⠀⠀⠀⠀⡜⠣⣀⣠⣠⠒⢄⠀⠀⠀⠰⠓
⡀⠀⠀⣄⠀⠃⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠎⠙⠤⠴⠤⠎⠙⡄⠀⠀⠸⠀⣀⡀⠀⠀⠀⠈⠆⠀⠀⡇
⠁⠀⠧⠀⠀⢰⠀⠀⢰⠀⠌⠁⣰⠀⠁⠀⡀⠀⠀⢸⠀⢠⠄⠀⠀⡄⠀⢃⠀⠀⠾⠐⠀⠤⠓⠄⠀⠂⡄⠀⠀⡇⠠
⣀⠀⠀⠀⢀⠗⢄⠀⠈⣆⠔⢆⠀⠀⠀⠀⣇⡀⠀⢨⠘⠀⠀⠛⠖⠀⠀⢸⠀⠀⠘⠆⠀⠀⠀⠀⠀⢰⣁⡀⠀⡅
⠈⡆⠀⠀⡌⠀⠈⠉⠉⠉⠀⠀⡆⠀⠀⢀⠋⠈⠦⠼⠤⠄⠀⢀⠀⠀⠀⢸⠛⢄⢸⡀⡴⠑⡄⠀⠀⢸⠃⠘⠒⠓⠒
⠀⢰⠀⠠⠀⠀⠛⢀⡄⠘⠀⠀⡇⠀⠰⠁⠀⣀⡀⠀⠀⡠⡀⠀⢣⠀⠀⡇⠀⠀⡀⠀⢀⡀⢸⠀⠀⡆⠀⠤⠀⠀⠰
⠀⡘⠀⠀⡇⠈⠀⠈⠁⠀⠁⢰⡁⠀⡇⠀⣀⠀⠀⠼⠄⠀⠀⠀⢘⠀⠀⡄⠀⠈⠁⣰⠈⠡⠀⠆⠀⢣⠀⠀⠐⠓
⠎⠑⠤⠤⠕⠉⢆⠀⠀⠀⢰⠁⠑⠀⠚⠊⠀⢣⠀⠀⠀⠠⠒⣄⣘⢀⡔⠳⡀⠀⠀⠀⡤⢄⢸⠀⠀⣸⢤
⠀⣀⠀⠀⡄⠀⠈⡄⠀⠀⡇⠀⣠⠀⠀⠤⠄⠈⠀⠀⢀⠃⠀⡀⠀⠀⡀⠀⢣⠀⠀⠈⠀⠀⠉⠉⠉⠁⠀⢃
⠀⠠⠼⠤⠀⠀⢀⠄⠀⠀⢇⠀⠀⠒⠓⠂⠐⢠⠀⠀⢸⠀⠌⠁⣰⡀⠉⠄⢸⠀⠀⡇⠀⠚⠀⣤⠀⠃⠠⢸⠀⠀⢘
⡆⠀⠀⠀⢀⠖⢾⡄⠀⡰⠻⡄⠀⠀⠀⢀⠀⢱⠀⠀⠀⡇⠀⠀⠀⢀⠤⡀⠇⠀⢀⢇⠀⠀⠈⠀⡙⠉⠦⠸⠤⠤⠋
⠈⢆⠀⠀⡌⠀⠀⠉⠈⠀⠀⢱⠀⠀⢠⠁⠑⠼⠄⠤⠊⠘⡄⠀⠀⡎⠀⠉⠉⠐⠋⠀⢇⠀⠀⡜⠁
⠀⠈⠀⠀⡇⠀⠒⢠⡄⠒⠀⠀⠂⠀⡎⠀⢠⠀⠀⢠⡄⠀⢱⠀⢸⠀⠘⢀⡄⠰⠀⠀⢸⠀⢰⠀⠀⠐⢒⣠⣆⡐⠊
⠀⢰⠀⠀⡱⠀⠀⠀⡀⠀⠀⠜⠀⢀⡇⠀⠀⠀⡧⠀⠐⠀⢸⠀⠈⡆⠀⠉⠁⠀⠈⠀⡜⠀⠘⡄⠀⠀⠀⠈⢁⡀
⣦⣴⣭⣷⣥⣤⣤⣼⣭⣦⣤⣼⣴⣧⣷⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣧⣤⣤⣤⣤⣶⣤⣧⣤⣴⣷⣦⣤⣤⣤⣧⣽⣦
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠤⠶⠖⠒⠒⠒⠚⠛⠛⠛⠒⠒⠲⠶⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⠴⢖⠚⢻⡟⢿⡓⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⣷
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢧⣸⠇⠀⠀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⢸⡇
⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠤⠶⠶⠖⠛⠛⠉⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡴⠟
⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⣼⠉⠁⠉⢹⡇
⠀⠀⠀⢸⣿⠆⢠⠶⠤⣄⣄⠀⢀⠀⡔⠚⠛⡆⠀⠀⠀⢰⠉⡆⢸⠀⠀⠀⢆⢀⡴⣿⠀⠀⠀⣾
⠀⠀⠀⠀⢿⣆⡾⢠⠀⠈⠫⡁⢀⠤⡿⠀⠀⣧⠀⠀⠀⣸⠀⠙⠞⠀⠀⠀⠘⠦⠾⠃⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠈⠁⠀⢧⠀⠀⠈⠓⠚⠁⠀⠀⠘⢦⣠⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣠⡤⠶⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠒⠶⠖⠒⠒⠒⠚⠋⠉

⠀⠀⣀⠀⠀⠀⣤⠀⠀⠀⣄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⡀⠀⠀⠀⠄⠀⠀⠀⢸
⠀⠘⠿⠃⠉⠈⠁⠀⠀⠀⠿⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡤⡄⠀⣀⠀⠀⢸
⠀⠈⠢⠀⠀⠀⠀⠀⠁⠀⠰⠄⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠁⠀⠤⠀⠰⡦⠀⠀⠀⠻⠀⠀⣶⠀⠺⠃⠀⠀⣴⠀⠘⠟⠀⠀⠀⠘⠋⠀⠀⡀⢀⣀⠀⠀⠀⠠⠄⠈⠃⢸
⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠈⠋⠀⠀⠀⠀⠀⠈⠀⢸
⠀⠀⠠⠄⠘⠃⠀⠁⠀⠀⠀⠀⠂⣄⠀⠀⠀⠘⠃⢀⠀⠀⠀⠀⠗⢀⠀⠀⠀⠀⠀⠀⢴⣶⠀⠀⠉⣀⡀⢴⡆⠀⢸
⠀⠁⠀⠀⠀⠀⢀⠐⠆⠀⠁⠀⠀⠉⠀⡤⠀⠺⠆⠀⠀⢠⠀⠰⠷⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⣀⡁⠤⠀⠤⠐⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠉⠁⠈⠉⠒⠀⢀⠨⠄⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠄⡪⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠈⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡈⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⢀⣀⠤⠔⠊⠊⠁⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⠎⠀⠀⠀⢀⠀⠠⠐⠉⠈⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⢀⠠⠐⠂⠒⢉⡉⠉⡉⢸⠉⠉⠉⠙⠒⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⢤⡄⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠲⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠠⠐⠈
⠀⠀⠀⠀⠁⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠁⠀⠀⠀⡀⠁⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠈⡔⠄
⠀⠀⠀⠀⠀⠀⡠⠄⠒⠒⠙⠒⠈⠉⠉⠉⠁⠛⠛⠲⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈
⠀⠀⠀⠀⢄⠰⠤⣬⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠈⠁⠒⠂⠠⠤⠤⠤⠤⠤⠤⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⢠⠀⠀⠂⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠈⠂⠀⠀⠈⠄⢀⡀⠂⠀⠉⡜⠀⡀⣓⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠄⠲⠶⠶⠶⠶⠤⠤⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠐⠂⠀⢀⡉⠛
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠃⠔⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠒⠒⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⣠⡤⠤⠤⢤⣤⣤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣰⢀⡒⣎⠜⣁⠦⣤
⠀⠀⠀⠀⠀⣿⡂⠀⠀⢸⣿⣇⣀⡀⠀⣿⠀⠀⠀⠀⠀⢠⡿⠿⠿⠚⣿⣶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⡿⠿⠿⢿⣿⡾⢷⣦⣌⣔⠁⡸
⠀⠀⠀⠀⠀⣿⡿⠿⠿⢿⣿⡿⠿⠛⠛⣿⡀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣿⣿⣀⣀⣀⣀⡶⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⢸⣿⡇⠀⠀⠉⢹⡇⣘⠋
⠀⠀⠀⠀⠠⣿⣀⣀⣀⣸⣿⣇⣀⣀⣀⣿⠂⠆⠀⠀⠀⢠⡿⠿⠿⠛⣿⣷⡿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠐⣶⣿⠿⠿⠿⢿⡿⠛⠿⠿⢿⢿⡇⢉
⠀⠀⠀⠀⠈⠿⣿⣿⠿⣿⡏⢛⠛⠛⠛⠿⡡⢘⠂⠀⠀⠸⣇⣀⣀⣀⣿⣿⣀⣀⣀⣀⡿⠀⠀⠀⠀⠀⠐⣯⡵⠀⢀⡠⠸⡄⠀⠀⠀⠀⢠⠀⡶
⠀⠀⠀⠀⢠⣾⣿⣿⠿⠛⠀⠀⠀⠀⠠⠄⠳⡇⠀⠀⠀⢀⡿⠛⠛⠛⣿⣿⠿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠘⠓⠀⠀⠀⠀⠀⣟⣰⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣿⣿⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⣿⣾⠟⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣿⣷⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢠⣾⠋⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⢰⡟⠛⠋⠙⣿⣿⠛⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠤⠀⢀⣴⣿⣅⡀⣸⠏
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢒⡒⠛⠙⠀⠀⠀⠀⠀⠸⠧⠤⠤⠤⠿⠿⠤⠤⠤⠼⢇⣤⡴⠓⢄⠀⠀⠀⠁⠀⠀⢀⣼⣿⡟⠙⠻⣿⡏
⠀⠀⠀⠀⠀⣇⡀⠀⢀⡀⣀⣐⠤⢩⡿⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣿⠟⠁⣠⠼⠃⠀⠀⠢⠀⢴⣋⣾⡟⠀⣠⣰⠏⠘
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡶⣾⣿⠏⠙⢾⣻⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢤⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣿⡇⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠞⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⣏⣀⣀⣀⣀⣀⣀⢸⡄⠀⠀⣴⠀⠀⡎⠉⠢⡔⠉⠀⢱⠀⢰⠊⠙⢤⠀⠠⠂⠀⠀⠀⠀⠀⡀⢬⡉⠙⢦⠠⠀⠀⣀
⠀⠀⠀⠀⣌⠒⠉⠉⠉⠉⠉⠛⠛⠁⠐⢄⠀⠈⠀⡀⡆⠀⢸⠀⠀⠀⡇⠀⡘⠒⢤⠁⠀⠁⠀⠀⠀⠀⠀⢘⢴⠆⢸⠀⠀⢯⡀⠀⠓
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡋⠉⢃⠀⡇⠀⠀⢰⠆⠉⢨⠇⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢸⡄
⠀⠀⠀⢠⠇⠀⠀⠸⠟⠀⠀⠸⠟⠀⠀⠸⡇⠀⠑⡀⢘⠀⠁⠀⢀⡇⢀⣎⣁⠀⠠⠃⠀⠑⢤⣄⣀⣀⡀⣀⣀⡤⠒⠀⠀⢨⡱⠀⢠
⠀⠀⠀⢸⠀⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⠀⡇⠘⢏⢷⢸⡆⠀⠀⡼⢠⢋⡨⠼⠃⠀⢌⢉⠆⠀⠡⢈⠀⠉⠀⠉⠀⠀⠀⠠⣘⡢⠀⠡
⠀⠀⠀⢸⠀⢀⠔⣳⠤⡤⣄⣐⣹⡄⢄⠀⡇⠀⢈⠿⠤⠧⠤⠴⠧⠿⢁⠀⠣⠅⠰⠆⠀⢀⢀⡤⡀⠀⠉⠉⠈⠉⡄⠀⠀⢻⢲
⠀⠀⠀⠸⡠⣈⠉⠑⠚⠓⠓⠮⠔⠁⣁⢄⠇⠀⠠⠉⠩⠍⠭⠍⠍⠉⢱⠀⠀⡠⠊⠉⣠⡀⢀⣄⠈⠫⢁⡅⠀⠊⠇⢮⠄⠀⠈⢛⣦⡀
⠀⠀⠀⠀⠈⠑⠋⠉⠀⠖⠒⡂⠈⠁⣀⣁⢀⡀⢸⠀⠀⠀⠠⠀⠀⠀⠸⠀⠎⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⢱⠀⢠⠆⢀⠀⠀⠀⠈⠸⣇
⠀⠀⠀⠀⠀⠀⠟⢃⠀⠀⢶⡀⠇⠘⡘⠂⢃⠏⠀⠢⢀⣀⣀⣀⣠⠤⠂⢀⠣⡐⠉⠂⠀⣀⣀⡀⠀⣀⠀⡘⠀⡀⡀⠏⢀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠤⡀⠘⢆⢦⠀⠀⠤⠤⢄⡈⠲⠃⠰⠅⠀⣈⣑⣚⣀⣁⣀⣀⣉⣀⣈⣉⣉⣀⣀⣀⠀⢅⠀⠉⠀⢢⠐⢔⢄⡒⠤⡀⢠⠀⡇
⠀⠀⠀⢰⡄⠈⣠⠤⠤⠤⠤⠤⠤⠤⠬⠶⡄⢀⣾⠛⢻⡿⠙⡟⢻⣿⢹⡏⢻⠛⣿⡟⢻⣿⣿⣷⡄⠀⠶⠈⠁⠰⠮⠬⢀⡽⠃⢸⠘⠛⠁
⠀⠀⠀⢸⠑⠊⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⠀⠘⡇⠀⠃⠈⠙⢸⠀⠘⠀⣿⣧⣴⣶⠌⣿⠇⠀⠀⠀⣀⡀⠀⠄⠈⠡⢀⡁⢀
⠀⠀⠀⢸⠀⠀⢀⠀⠀⢀⡀⠀⠀⢀⠀⠀⡇⠀⢿⣤⣄⣁⣦⣴⣤⣤⣾⣰⣦⣄⣿⣿⣯⣵⡾⠏⠀⠎⠊⢹⠃⠀⠀⠀⠀⠀⠀⠹⠀⠊⡄
⠀⠀⠀⢸⠀⠀⢸⠀⠀⠿⠿⠀⠀⠻⠇⠀⡇⠀⠀⠈⠉⠉⡉⠉⡁⢠⠤⣄⠀⢀⡈⠉⢁⠠⡄⠀⠀⢷⡄⠸⠀⠀⠶⠀⢴⠆⠀⠀⢀⢴⠃
⠀⠀⠀⠸⡀⠀⢸⠀⠀⠀⠀⠒⠒⠀⠀⠀⡇⢀⠠⢀⣂⠥⠒⠐⠲⢍⣂⠢⢀⠘⠃⣀⠏⠄⠈⠢⢄⠀⢹⡆⢄⠀⠀⠤⠀⠀⢀⠆⡼⠁
⠀⠀⠀⠀⠘⠢⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⢺⠉⠀⣀⠀⠀⢀⣀⠈⠹⠚⠃⡞⠁⠀⠀⠀⠀⡀⠑⠀⠫⠬⠗⠄⠀⢀⠔⠯⠦⠃
⠀⠀⠀⠀⠀⢀⡈⠁⠉⣁⠀⠀⢀⠀⠩⠩⠤⡀⢸⠀⠈⠋⠀⠀⠈⠋⠀⠀⠀⢠⠋⠀⠀⠻⠃⠘⠟⠀⢄⠀⠀⠀⢠⠀⢀⠀⠀⣤⠒⡄
⠀⠀⠀⠀⢔⠕⠈⠀⠈⠐⠕⠄⢠⣀⣀⣀⢀⠄⠸⠤⠤⠀⠀⠀⠀⠠⢤⠼⠀⢸⡀⠀⠀⠀⠂⠀⠀⠀⣠⠀⠠⠊⠠⠀⠀⠈⠦⠙⠒⠁
⠀⠀⠀⢰⠈⠀⣶⡄⣴⡆⠈⢸⢀⡤⠤⠖⠐⠂⠀⠀⠀⠀⠀⠂⠒⠒⠒⠤⣄⠀⠉⠒⠢⠤⠄⠀⠀⠊⡁⣀⣀⡤⠤⠴⠖⠦⠩⣙⢳⢄
⠀⠀⠀⠈⡐⡀⠀⠄⠄⠀⡀⡘⠸⠀⠀⠚⠃⡔⠈⠉⠀⠈⠈⠐⡆⠛⠃⠀⠈⠀⣴⢚⣋⣉⣉⡓⣶⠀⡏⠁⠀⠀⠀⢀⠀⠀⠀⡅⠈⠀⡆
⠀⠀⠀⠀⢈⠂⠅⡀⡢⠍⠊⠀⠈⢠⠄⠠⡄⠇⠀⣶⠄⢰⣦⠀⠇⢸⡣⡢⠀⠁⡇⠈⠉⠉⠉⠉⠀⠀⡇⠀⠛⠃⠀⠻⠃⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠨⠃⢰⠁⢳⠀⡠⡀⢀⠈⠡⠌⠀⡇⠀⠠⠤⠤⠀⠀⡅⠁⠑⠷⢀⠀⡃⠰⠿⠀⠺⠇⠀⠀⡇⠀⠀⠀⠀⠂⠀⠀⠀⡧⢠⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠈⠀⠈⡁⠉⠑⠀⠡⠤⠤⠤⠤⠤⠤⠂⡔⠉⠁⡹⠀⠣⣀⡀⠒⠂⣀⠔⠀⠋⠫⠗⠒⠢⠤⣄⣀⣀⠃⣰⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⡖⠒⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠔⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡇⠀⣇⣀⠀⠀⢈⠀⠀⠀⢸⠀⠀⠀⢰⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠇⠀⢧⣤⡄⠀⢠⣤⡄⠀⠸⣤⣤⠀⠈⢦⣠⠞


⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⡤⠤⣈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢂⡡⠤⡈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠙⢢⡈⠳⠤⠤⠴⠦⠤⠤⠔⢉⠔⠊⠁⠀⠀⠰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⡄⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢀⠃⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠐⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⡞⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠐⢿⠇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⢶⡶⠀⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠈⠳⡊⢑⡞⠁⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⣀⣀⠴⠀⣀⡀⠠⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⣀⣀⣤⣤⣾⣿⣷⣤⣴⣶⣶⣿⣯⣀⡀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣷⣦⣤⣾⠟⠀⠀⠀⠀⠀⠀⢀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⡀⢀⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄⠀⠀⠀⣠⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣶⡿⠋
⠀⠀⠈⠙⠷⣦⣤⣀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⢀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠰⣶⣶⣶⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⣀⡀
⠀⠈⠉⠉⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠛⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⣠⣶⠿⠟⠋⠉⠙⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠉⠛⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠛⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠈⠙⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣶⣦⣤⣤⣀⣀⣀⣤⣤⣴⣶⣾⣿⣿⣿⡁⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠉⠙⠛⠛⠛⢻⣿⡿⠛⠉⠉⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠈⠻⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⢘⢿⣿⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⣫⡶⢋⣞⢼⡟⢮⡝⠦⡈⠿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⡡⡆⠀⢩⡴⠺⠋⠀⣷⢸⣇⠀⣽⡄⢻⡿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣄⣷⡶⠿⠥⣶⠶⢚⣁⣼⣏⣠⣟⠁⣸⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠉⢉⣡⠤⢶⠶⠚⠛⠿⠍⠁⣀⡀⠠⠚⡿⢃⣼⣷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠴⠊⠉⠀⢀⣀⣤⣴⣶⣶⣿⣧⡤⠤⣤⡴⢶⡿⢻⣿⡿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⣠⣶⠾⠟⠛⠻⢏⣁⣀⡠⠴⢶⠞⣋⣴⣟⠧⢸⣿⣿⡜⣿⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⣀⣶⠞⠉⢀⣤⠴⠒⠈⠁⣁⡤⠴⠒⠊⠉⠉⠰⠋⢠⡿⣿⣿⠇⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢰⡟⠀⢠⡴⠋⠀⣀⣤⠖⠋⠁⢀⣀⡤⠤⠐⠚⠛⢋⣡⡾⠛⣃⣼⣿⣹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠘⣿⣇⢰⡏⠀⠀⣰⠋⠀⢀⣠⠖⠉⠁⢀⣠⡤⠶⠒⢋⣩⠐⠋⠉⠈⢠⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⡀⠀⠈⠻⢌⣧⡀⠠⡇⠀⢠⡞⠀⣀⣴⠾⠋⠀⠀⣠⣶⣿⣥⣤⣤⣴⣾⣷⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣛⠳⠤⢄⢠⡉⠙⠲⠷⠤⣿⣥⣴⣿⣯⣤⣴⠶⣾⠛⣛⣗⣴⣾⣽⣿⢿⣟⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠄⠀⠈⠀⠁⠉⠙⠒⢶⠶⠶⠶⣦⣽⡶⣿⡿⢿⡟⢻⡛⠏⣿⢸⡇⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠀⠷⠀⡏⢰⡇⢸⡇⣼⣿⢀⡇⣼⢳⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢰⠀⣇⢸⠁⢸⢀⡇⣾⣼⣧⡏⡸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢠⠐⠀⠀⠀⠀⠀⠀⢸⡄⣟⢠⠀⣿⢸⡁⠦⡿⢸⢃⣷⣿⣿⣿⣵⣄⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢰⡄⣇⢝⢾⠠⡀⢠⠘⠀⡇⣟⢼⢰⡇⣼⣿⢲⡏⣿⣾⣿⣿⣿⣟⣿⣿⣿⠳⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⣯⠿⡜⣾⣇⠱⠈⡅⡇⣿⣻⣿⢸⣯⣯⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣮⠛⢓⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠿⣿⣤⣧⣃⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠙⠫⠷⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⡿⣿⣿⡿⣿⣿⣿⡿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣁⣀⣀⣈⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⡀⢁⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣭⣭⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠋⣠⣤⡌⠛⣨⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠉⠸⠷⠿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡈⠀⠗⠘⢛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⢿⣿⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⣄⣰⣀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⡟⢻⣿⡟⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢐⢐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠸⠘⠇⢨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⡇⢸⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠀⠄⡀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⢀⠀⢀⡀⣀⣀⠀⢀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⣿⣀⣿⣸⢿⡃⣿⣹⣿⣼⠀⣽⠿⣿⣿⡀⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣦⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣄⠀⠀⢀⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣠⣴⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠸⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣄⠀⠈⠙⢿⣿⣿⣆⠈⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠈⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⢀⠝⠛⠳⠦⣀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠟⠋⠁⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡔⠁⠀⠀⡘⠀⠀⠀⡄⠀⢠⠀⠀⠀⠈⠀⠈⢢⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢃⠀⠀⠑⡀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡘⠀⠀⠀⢠⠀⠀⠀⢠⠀⠀⠀⠈⡄⠀⠀⠈⢆⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠐⢤⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡌⠀⠀⠀⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⢆⠀⡠⠒⠘⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠇⠀⣀⢀⣘⡀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠐⢠⡀⠀⠀⠀⠀⠀⠀⠰⡎⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡇⢰⠒⠒⠒⠒⠒⠒⠒⠠⠤⣀
⠀⠀⠀⠀⠀⠀⣀⠗⠤⢻⡟⣛⣁⣀⣀⣀⣀⣀⣀⣀⠠⠜⣆⡀
⠀⠀⠀⠀⠀⣎⡘⠤⠤⠄⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠤⠤⠞⣈⡆
⠀⠀⠀⠀⠀⠗⠺⠭⠴⢒⣒⣀⣐⠶⠶⠶⣖⣀⣐⣒⠲⠬⠵⠚⠇
⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡧⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⢉⡅⠐⠒⠒⠒⠒⢂⣈⠉⠉⠀⢠⠀⠀⣀⠔⠒⠢⣄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡞⠹⣆⠀⠀⠀⢀⡾⠹⣆⢀⡠⠜⠒⠚⣓⡦⠤⠤⡬⠶⠶⠮⠾⣛⣁⡉⠙⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⢀⠜⢁⢤⡴⠮⠛⠁⠀⠀⣀⣈⣦⣤⣒⣒⠒⠢⠬⣉⣒⣠⣈⠫⠑⣄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢿⡏⣹⠃⠀⣮⢞⠕⠉⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠀⠉⠉⠓⠲⢤⡀⠀⠈⠉⠣⣨
⠀⠀⠀⠀⠀⠀⠀⠛⠐⠒⠂⠤⠤⠤⠭⠥⠤⡴⠱⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⢀⡾⠁⠀⠀⠀⠐⢤⣀⡀⠀⠀⠀⠀⣀⣠⠔⠀⠀⠀⠀⠈⢧⡀⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠊⡾⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠈⣷⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢅⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⠤⠤⠤⠤⠤⠤⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠶⠖⠒⠚⠋⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣄⠀⠠⣶⠀⠀⠀⣠⣤⣤⣶⡶⢦⣀⡴⠟⢂⣥⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠘⢷⡀⡿⠀⠀⣸⣯⣼⠛⣫⣷⣾⣿⣷⣾⣿⠛⡹⢉⣿⡄⠠⢦
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⢦⡀⠉⣼⣯⣭⣿⣿⠍⠁⠟⣧⣝⢿⣌⠟⣿⠇⠀⠀⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⢳⣄⣿⣉⡟⣱⣟⡀⠀⣅⣘⣿⡆⣷⠰⣟⡄⢀⡄⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠾⠏⢻⣷⢋⣹⣿⣟⠻⠞⢻⣿⣷⣧⡌⣿⣯⣩⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠘⣿⣿⡜⠿⣿⣷⠠⠈⠽⣿⣿⣇⣽⠋⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡀⢠⡘⣿⣿⣿⣿⣿⠦⣖⡴⢿⢿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⡟⠁⠛⣿⣯⣿⣿⢿⣿⣿⣿⣶⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠈⢻⣿⠇⣸⣿⣿⠻⠽⠻⢿⣟⠹⢾⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠦⠘⢿⣦⣹⣿⡏⠀⠀⠀⠈⠛⣶⣛⣻⡟⢉⣷⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠙⣿⣿⡿⣄⠀⢀⣤⣴⢿⣼⣿⠃⣾⣯⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣯⣥⣞⣱⣏⣴⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣽⢿⣿⣿⡛⢻⣿⣿⣦⡈⣻⣿⣿⣷⣾⣿⠿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣾⠃⢻⣷⣾⠋⢿⣟⠛⢿⢿⣿⣿⣿⣿⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⡇⠀⠀⣻⣧⡀⠘⣿⣧⠀⢸⣿⡿⠋⠙⠿⢿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⣥⣼⣿⣿⣦⣼⢿⡷⣿⠛⠀⡀⠀⠀⠀⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣬⢉⣰⡿⠈⣯⠁⠀⢹⣿⠀⠨⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠈⣹⡇⠀⢿⣤⣄⠘⣿⠀⢐⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⣶⣿⡇⠀⢸⡏⢡⣤⣿⠀⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⣤⣾⠁⠀⠀⣿⢶⣾⣿⣄⢢⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⡉⣿⠀⠀⠀⣿⣿⣿⠶⣿⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡈⣳⣿⡀⠀⠀⢮⣿⣿⠀⣹⣿⣄⠀⠐⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⡛⢻⣿⣿⣧⠀⠀⢺⣿⣿⣃⢸⣏⣛⣷⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣇⣾⣿⣿⣿⠀⠀⠈⣿⣿⣿⣀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠾⠛⠟⠻⣿⣿⣿⣿⢿⣴⠶⠶⠞⣿⣿⣿⣿⢏⠤⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠛⠛⠛⠃⢈⢋⢀⡀⠀⠛⠛⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⠀⠛⠂⠀⠸⠈⠐⠀⠀⠀⠉⠉⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡤⣄⠀⠀⠀⡠⢤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢂⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠃⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣤⠀⣀⠈⢧⠀⠐⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⣞⠀⠀⠀⠀⠀⠱⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠍⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣠⡍⠠⠇⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠤⠀⠀⠐⠉⠀⠀⢀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒⠀⠀⢘⠂⡢⠀⠀⠀⣇⣸⠁⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄⠀⠀⠔⠀⠀⠀⠀⠀⠈⠱⠀⠀⠄⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⠀⠀⢠⣀⠀⠁⠀⡀⠀⠀⠀⢀⣀⠀⠀⠄⠁⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣅⠀⠀⠀⠚⠋⠀⠀⠄⠁⠀⠀⠀⡀⠀⠀⠠⠀⢠⠀⠀⠈⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠈⠀⠀⠎⢀⡀⢀⠀⠆⠀⣀⣀⠇⠀⠀⠄⠂⠀⠒⠐⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⢀⠔⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⠀⠒⠒⠶⠒⠒⠚⠋⠁

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

⠀⠀⠀⠀⠂⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠉⠉⠀⢠⡄⠀⠀⠉⠉
⠐⠄⠄⠀⠀⠀⠀⠀⠀⡤⠔⢇⠀⠀⠘⠀⠀⠀⠀⠀⠐⠄⠄⠀⠀⠀⠀⠀⠀⡤⠔⣇⠀⠀⠘
⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠎⠀⢀
⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠄⠈⠉⠁⠀⠀⠀⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠄⠈⠉⠁
⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⠄⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠄⠀⣀⠆
⠂⠀⢐⠘⠙⢢⠄⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙⢢⠆⠀⢘⠘⠉⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙
⠀⠀⠈⠓⠒⠉⠀⢠⡄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠒⠉⠀⢠⡄⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠
⠀⠀⠀⠀⠢⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉
⠐⠄⢄⠀⠀⠀⠀⠀⠀⡬⠔⣃⠀⠀⠘⠀⠀⠀⠀⠀⠐⠄⠄⠀⠀⠀⠀⠀⠈⡭⠔⣂⠀⠀⠘
⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠆⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠊⠀⢀⠀⠄
⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠊⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠄⠀⢀⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⡀⠀⠀⠈⠄⠀⢀⠆
⠀⠀⢈⠘⠙⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙⢀⠄⠀⢐⠘⠉⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙
⠀⠀⠈⠑⠒⠉⠀⢠⡄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠒⠉⠀⢠⡄⠀⠀⣿⡄
⠀⠀⠀⠀⠀⡀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⡏⢹⠀⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⡷⢹⡀⠀⢰⠁⠈⡆⠀⢀⡠⡎⡟⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢓⢤⡀⠀⠀⡇⡄⢧⡀⡸⠀⠀⢇⡰⢉⠊⡜⠁⠀⢀⡤⡚⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡑⢌⠓⢤⣧⣘⠤⢽⣇⣠⣄⣸⡧⠼⣀⣇⡤⠚⡡⢊⠞
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠙⣄⠑⢄⣈⠗⠊⠉⠀⠀⠀⠀⠉⠑⠺⣁⡠⠊⣠⠋⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢖⢍⠒⠒⢺⢦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡴⡟⣉⠭⠉⣙⣫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢌⣉⣇⡎⠀⠐⣋⣭⡛⢦⡀⢀⡴⢛⣭⣙⠂⠀⢱⣸⣠⠞⠉⠁
⠀⠀⠀⢀⣀⣀⡠⠤⠔⠒⠒⠊⠉⣹⠀⠀⠸⢯⣿⠟⠀⡇⢸⠀⠿⣿⡿⠇⠀⠀⣏⠉⠑⠒⠒⠢⠤⢤⣀⣀⡀
⠀⠀⠀⠈⠉⠉⠓⠒⠢⠤⠤⢄⣀⣹⠀⠀⠀⠀⠀⠀⡰⠁⠈⢆⠀⠀⠀⠀⠀⠀⣏⣀⡠⠤⠤⠔⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⡏⢇⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⠀⠀⠀⠀⡸⢹⣉⡑⢢⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣫⣍⣀⣒⣉⣼⠞⢣⡀⠀⠀⠈⠩⠭⠭⠍⠁⠀⠀⢀⡔⠳⡧⠤⠤⣑⠵⢄⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣠⠊⡠⠊⢉⡶⢄⣀⠀⠀⠀⠀⣀⡠⢴⡉⠑⢄⠙⣄⠀⠈⠉⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡡⢊⡤⠚⢹⠉⡖⢺⡏⠙⠋⢹⣗⠒⡍⢻⠓⢤⡑⢌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡬⠚⠁⠀⢀⡜⡠⣁⠎⢱⠀⠀⡎⠈⢳⠘⢸⠀⠀⠈⠓⢥⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⣼⡸⠊⠁⠀⠸⡀⢀⠇⠀⠈⣇⢾⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⣇⡸⠀⠀⠀⠈⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⡀⠤⠀⠀⠀⠐⠀⠠⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠁⠀⠀⠀⠀⠀⠃⡄⠀⠀⠀⠀⠀⠑⠂⡀⠀⠀⠀⠀⠀⢀⠡⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⡀⠀⠈⠁⠸⠛⠂⠈⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⡠⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣀⡜⠁⠀⠀⠀⠀⠀⠙⣂⠀⠆
⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠐⡇⠑⠀⠀⠀⠐⠋⠀⠘⠃⡆⠀⠐⠄⠀⠀⠀⠠⢀⠒
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠘⠇⠀⠀⠤⠄⠀⠀⠀⠤⠀⠅⠂⠀⠀⠀⠀⠀⠀⠂⠈⢀
⠀⠀⠀⠀⠀⠈⠉⠉⡄⠈⠁⠉⠁⠀⠀⠀⡖⠥⠀⠀⠀⠀⠀⠀⠉⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁
⠀⠀⠈⠒⠰⠄⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠶⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠃
⠀⠀⠀⣀⠄⠀⠀⠀⠂⠐⠌⡁⢀⠀⠀⠀⠀⠩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠒⠈⢠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⡡⢄⠀⠀⠐⠀⢀⠀⠁⠀⠀⢀⣁⠠⠠⠄⠤⠤⠤⠈
⠀⠀⠈⠠⢄⠀⠀⠁⠠⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⣀⡀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠐⠀⠀⠈⠈⠐⠀⠀⠁⠀⠐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⢀⠀⡀⣾⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠦⠀⠀⠀⡀⠄⠀⠠⠀⠀⠀⠀⣀⠍⠅⠀⡅⠈⠉⢁⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⢉⡿⢦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠁⠀⢀⡴⠋⣠⠎⠙⠳⣤⣈⣉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢫⡟⠁⠀⢀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠈⠉⠛⣶⣤⡉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢃⣴⠏⠀⠀⢠⠞⢠⠞⠁⠀⠀⠀⠀⠀⠀⣀⡤⠞⢁⡜⠛⢦⣀⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣰⠋⠁⠀⠀⣰⠋⣰⠋⠀⠀⠀⠀⠀⢀⡴⠚⣁⡴⠚⠉⠀⢠⠞⢉⠟⠛⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⢰⡇⠀⠀⢀⡼⢁⡼⠁⠀⠀⠀⠀⠀⡴⠋⡴⠚⠁⠀⠀⠀⢠⠏⢰⠏⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⡴⠋⠀⢀⡴⠋⣠⠞⠀⡤⠖⣲⡶⠶⠾⠷⠾⢧⣤⡀⠀⠀⢀⡟⢀⡏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⢠⠏⣠⠞⠁⠀⣾⢀⡾⠋⠀⠀⠀⠀⠀⠀⠉⢻⣷⣤⠞⢀⡞⠀⠀⠀⠀⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡏⣰⠃⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡝⣷⠋⠀⠀⠀⠀⠀⠀⢀⡿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⣠⠏⣠⠏⠀⢀⣠⠞⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠻⣿⣁⠴⣁⠴⠒⢋⣠⠴⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣵⠟⠀⠀⠀⠀⢀⡴⠋⣹⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢳⠚⣡⠴⠛⠉⠀⠀⠀⣿⢷⣄⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢀⣠⠴⠋⡴⠛⠁⢹⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⡿⠛⠁⠀⠀⠀⠀⠀⠀⠘⢷⣌⣙⠲⠶⠶⠶⢛⡇⠀⠀⢀⡴⠚⢉⣠⠶⠋⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣿⠦⠤⠶⠟⠁⠀⣠⠏⣠⠞⠉⠀⠀⠀⢀⣠⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⡼⠁⠀⠀⠀⠀⢀⡴⠃⡴⠃⠀⠀⠀⠀⣰⠏⢡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⣤⡤⣤⠀⠀⡠⠞⢉⡴⠋⠀⠀⠀⣀⡤⠖⢋⣠⠞⠁⠀⠀⠀⠀⠀⣿⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⡇⡾⠁⡴⠋⠀⠀⢀⡴⠚⣁⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡇⣸⠁⣀⣤⠴⠟⠛⠛⠛⠶⠶⢤⣀⡀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠙⠛⠲⠶⠶⠤⠤⠤⠴⠶⠞⠛⠛⠒⠶⠛⠉

⠀⠀⠀⠀⢷⡀⢣⠘⢷⡄⠀⠐⣄⠀⠀⠸⡇⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣿⣤⢀⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⠀⢀⣤
⠀⠀⠀⠀⢀⠙⣆⠳⡌⢿⣦⡀⠈⡆⠀⠀⡇⠀⠀⠀⠀⢸⣷⠀⠀⠀⣰⣿⣷⠈⠂⠀⠀⢰⠏⠀⠀⠀⠀⠀⢠⠤⠀⡀⢀⣴⠏⢠⡿⠁⠀⠀⢀
⠀⡄⠀⠀⠈⢣⠘⠀⣿⠸⣿⣅⠆⠀⠀⠀⠹⣄⠀⠀⠀⢸⡟⠀⠀⠀⢹⢈⡟⢢⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣀⡰⠁⣾⠁⣠⠎⡄⠀⢀⣴⣿
⠀⠀⡀⠠⠀⠀⠑⣸⠋⢤⣟⠉⠺⣦⠀⠀⠀⠈⠃⠀⠀⠈⣷⠄⠀⠀⢨⢘⣿⡆⠐⠀⠀⡇⠀⠀⠀⠀⠀⠀⡸⠋⠀⢰⡏⠰⠈⠆⠀⣴⡿⠛⢡
⠀⠀⢀⣤⠀⠀⠀⠀⢇⠈⢹⣆⠐⠟⢷⣀⠀⠀⠀⠀⠀⠸⣏⠀⠀⠀⠀⢸⠸⣇⠴⢀⡾⢃⠀⠀⠀⠀⠀⠴⠁⡄⢠⡟⠀⣧⡘⠀⣸⠏⣀⣴⣿
⠀⠠⡀⠀⠈⠳⣌⣠⣿⡀⠀⠻⡄⣇⠈⢳⡄⠀⠀⠀⠀⠀⣸⡇⠀⠀⢠⡾⣰⠏⢸⣼⡧⠀⢠⠜⠀⡀⠐⠀⠀⣰⣿⠇⢀⣿⠁⢠⡏⣰⢋⣼⠇
⠀⠀⠈⠂⠐⠢⠤⢁⡍⢻⡄⠠⡘⡀⡆⠀⠗⠀⠀⠀⠀⠀⢹⣧⠠⠀⠀⡆⢹⠀⣧⣿⠁⣄⠄⠀⢰⣰⠃⠀⢠⣿⠏⠀⣼⠋⠠⢋⡴⣧⠟⠁
⠀⠀⠀⠠⡄⠀⡀⠀⠘⡄⣿⣄⡐⢰⡷⢄⠐⠀⠀⠀⠀⠀⣿⡁⠀⡄⢠⠃⣼⠀⢻⡅⠀⣇⠀⢀⡟⠀⣠⠀⢫⠇⣰⣟⣡⠎⢠⠋⠘⠁⠀⠔
⠢⣄⠀⠀⠘⣂⠈⢦⠀⠘⢬⡛⢿⡄⠳⣈⡇⠀⠀⢀⠀⠀⢈⣿⣶⠑⠈⢾⢃⣴⠿⢃⣼⠟⢀⡾⠃⢾⠁⡠⠋⣠⡷⠋⡸⢀⡄⠀⠀⠐⠂⣄⡴
⠀⠘⡃⠈⠀⠹⢆⡀⠂⣀⠀⠉⣿⠃⠀⠠⡉⢦⡀⠀⠀⠠⣿⣿⣇⡀⠐⢹⣿⡇⠀⣼⠁⢠⡿⢀⡶⠃⠈⢠⡾⠋⠀⠀⢠⡟⠁⡰⣂⣤⠞⡝⢣
⠀⠀⠈⠲⣐⠀⠀⠙⠂⠙⢦⡄⣿⣇⠀⠀⠈⠜⠽⣢⠐⠀⠈⠙⣿⣿⣦⠈⠹⣿⡀⣿⣴⡿⠁⡀⠁⢲⣶⠟⠃⠀⠀⣠⢞⣠⠀⣴⢋⡤⣞⡶⠆
⠀⠈⢢⣁⢨⣇⡀⠀⠐⢦⠘⣯⠈⠻⣷⣦⣄⣀⠠⣽⣀⠁⠀⠀⣼⣿⣿⡇⠀⣿⡇⢹⣿⠁⠰⣁⣠⣾⠃⠀⠀⢀⠞⣁⣾⡥⢾⣿⣩⡶⠋⡠⠖
⠀⠀⠈⣏⠉⠙⢿⣅⠀⠈⢣⠙⠲⣤⣀⠈⠻⢿⣷⡌⢻⣷⢇⣴⣿⣿⡿⢠⣾⣯⣎⣾⡿⠀⠀⣿⠉⡠⠀⠀⡀⢀⣴⣾⣏⣴⠾⠛⢁⡀⢈⣤⣾
⠀⠶⢤⣈⡛⠛⢆⠨⠳⣄⠘⠳⣄⠀⢸⡇⠀⠘⣿⡿⢸⡟⢻⣿⡟⣿⢡⣿⣿⣿⣿⣯⣤⣾⣤⡿⠀⠃⡠⢂⣤⡾⣻⡿⠏⠁⣤⠔⢃⣼⣾⠷⠉
⣄⡀⠀⠀⠙⠶⠾⣟⢿⣉⢓⣦⠸⣄⣀⣙⣶⣴⣿⠁⣾⣷⠙⣿⣇⢿⣿⣿⣿⣿⣿⣿⡟⣛⣉⣡⡾⠋⣰⣿⠍⣰⡟⠀⠴⣉⣤⣿⡿⢋⡁
⠀⡉⠑⠄⠀⠀⠀⠘⢦⣙⣿⣿⣷⣤⣄⠀⢹⣿⣿⣧⡘⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⢋⣭⣭⣥⣾⣯⣥⠾⠫⢤⣾⠿⠿⢛⡿⠛⠋⠁⠀⡠
⢦⣄⡀⣈⠁⢀⡀⣄⠀⠀⠀⠙⠛⠛⣿⣇⢿⣿⣿⣿⣿⣿⠟⠋⠩⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣟⣁⢠⣶⣶⣟⣡⡶⠾⠋⣀⣠⡔⣂⣻⣷
⣀⡀⡀⠀⠈⠁⠉⠛⠷⠶⠶⠾⢶⣄⡹⢿⣬⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣤⣼⡿⢿⣛⣿⣭⣭⠿
⣋⡉⠁⠂⠉⠛⠶⠶⠶⣦⣤⣤⠶⣿⣿⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣟⣿⣭⡿⣧⠿⠶⠟⣉⣉⡄⠐⠂
⠙⠾⠶⣿⣁⠴⠶⣤⣤⠴⢦⣄⣀⣬⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡛⢛⣉⣹⣧⣤⣴⡚⢛⣷⣾⣧⣄⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⣏⠉⠛⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⠟⣿⠟⣛⣛⠋⣻⣿⣟⢉⣉⠙⠿⠿⢛⣁
⠠⠀⠄⠤⣀⣀⣀⡀⣀⣽⠷⣦⣌⣛⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡟⠛⢿⣛⠛⡿⠿⢿⠿⠿⣟⣛⣛⣋⣩⣍
⢀⡤⠌⠀⠉⠛⠑⣉⠉⢡⣶⣄⠉⢉⣼⣿⣿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⢻⣬⡟⠲⢦⣉⠛⠛⠳⠾⠓⠚⠛⠛⠓⠢⠀⠄
⣀⣀⣤⢶⠾⠟⠾⠛⠳⠿⡥⠈⠟⠿⣿⣼⣟⣿⣿⣿⣿⣿⣿⣶⣤⣶⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣮⡛⠿⣦⣉⡉⠛⡢⣤⢀⣀⡀
⠋⠉⠀⠀⠀⠀⠀⠀⠐⠀⣁⢀⣶⠶⢿⢠⣼⡿⣿⡏⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣌⠉⠻⣿⣿⣷⣌⡙⢻⣶⣤⣠⡀⠀⠈⠛⠿⠛⢣⣶
⠀⠀⠀⠐⠉⠁⠀⢀⡄⣴⠏⠉⣁⠔⣤⢶⣿⣴⣟⣸⡏⣿⣏⣿⠏⢘⣯⢿⣿⡟⢧⡻⣿⣿⣧⣀⠈⠙⠳⠦⡷⢶⡍⢻⣯⡉⠤⡀⠠⢀⡈⠀⠈
⠀⠀⠀⠀⣠⡤⠴⠏⠀⠀⠔⠉⠰⠞⣁⣼⡏⢁⣼⠏⢀⣾⣏⣿⠀⢻⣇⢨⣿⢃⠸⡋⣿⣯⡛⢻⣷⣄⡀⠀⠀⠁⠙⠦⠹⣿⣤⡈⠉⠠⠀⣀
⠀⣄⡲⠿⠋⠀⠀⠀⠀⣠⢴⠿⣋⣾⣿⠛⠐⡏⠁⠀⣿⢹⣿⠃⠀⠸⣯⠹⣷⡘⢆⠙⣋⢿⠿⣿⣿⣿⣿⣌⡲⣦⡀⠑⠢⣝⠻⡿⢶⣶⣄⡀
⠚⠁⠀⠀⠀⠀⠀⠀⢈⣡⣁⣼⣿⠏⠉⠂⡔⢁⠀⢀⣾⣦⣿⠀⠀⢰⣿⡇⠈⢻⡎⡆⠹⡈⠀⠈⣿⣿⡏⢿⣷⣜⢷⡄⠀⠻⣄⠘⠊⢻⣏⠻⣆
⠀⠀⠀⠀⠀⠀⣰⠟⠋⢉⡟⢻⡉⠠⠀⡠⠃⠀⠀⢸⣿⡟⠁⠀⠀⠀⣿⠇⣀⣾⡃⢨⡀⠁⠀⠀⢻⣎⡳⣤⣙⠿⢷⡍⠻⣦⠀⠙⣦⡈⠉⢷⡌
⠀⠀⠀⠀⡀⢨⣿⢀⣸⡏⢀⣭⠋⠀⣼⠀⠀⠀⠠⢾⣿⡅⠀⠀⠀⠈⢻⣤⡙⡯⣿⠘⣧⡀⠀⠘⠙⢈⠙⢦⠈⢇⠀⠰⡆⣹⢷⣄⡘⠷⣄⡀⠈
⠀⠀⢠⣤⣤⣿⠁⢾⣩⣾⠟⠁⢀⢾⡏⠀⢀⣦⣴⢾⣿⠟⠀⠀⠀⠀⠀⣿⠟⠁⣼⠃⠈⣿⣦⡀⠀⠈⠀⠈⠂⡀⠐⠄⠀⠘⠷⣄⡙⠳⡀⠹⣧
⠀⢀⣿⠁⠀⠀⢈⣾⠛⠋⠀⢀⡟⢸⡇⢠⢻⠉⠀⢀⣿⠀⠀⠀⠀⠀⠀⣹⣷⡄⡈⠃⠄⠈⠚⣿⡆⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢌⠻⣆⡡⠀⠻
⡰⠟⠋⠀⠀⢠⣞⠅⠀⡀⢠⠊⢠⡇⠀⠸⠀⣧⠀⢸⠇⠀⠀⢀⡠⠖⠈⢿⡟⢧⣁⠀⣴⡀⠐⠿⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠌⣻⢷⣄
⠁⠀⠀⠁⠀⠼⠃⠀⢠⡸⢀⡤⢿⠀⣠⣴⠾⠛⠀⡞⠀⠀⢀⡏⠀⠀⠀⣟⢧⡘⠏⠐⠨⣿⣄⠀⢦⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙
⠀⠈⠀⠀⠃⠀⠀⢤⠋⢠⢸⡴⠃⢸⡏⠀⠀⠀⠸⠇⠀⠠⠊⠁⣄⠀⠀⢹⠆⠣⠈⢠⡄⠀⢻⡆⡘⠌⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠈⠛
⢠⠄⠈⠀⡀⠀⠰⠃⠀⢸⣼⠃⠀⢼⡇⠀⠀⠠⠀⠀⠠⠀⠀⢠⡁⠀⠀⠹⢦⡀⢣⠈⠉⢦⢼⡇⣶⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠁⠀⠀⠀⠀⠀⠀⣠⠞⣱⠏⢀⠔⡘⠀⠀⢠⠀⠀⠀⣰⠀⠀⣸⡇⠀⠀⠀⠀⡅⠈⢄⠀⠸⡈⢿⠻⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⡞⠁⡼⠃⠐⠁⠖⠁⠀⠀⠃⠀⠀⡀⢙⠂⢀⢳⠈⠇⠀⠀⠸⡃⠀⠀⢠⡀⢸⡇⢣⠀⡄⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣜⠷⠈⢰⠀⢿⠀⠀⠀⠑⠀⠀⠀⠇⠸⢷⡠⡋⠡⡀⠁⠀⠀⠀⠀⠈⠋⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣿⠀⠙⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⣾⡄⠻⡀⠀⠀⠀⠀⠀⡃⠰⠒⠂⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡷⣦⡀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⢀⣿⣿⣿⣎⢿⡜⠏⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⢠⣬⡻⣿⣿⣿⣾⣿⢀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⢻⣷⣿⡗⣭⣶⣶⣾⣍⡈⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣮⢱⣾⣿⣿⣿⣿⣿⣷⡉⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⢰⣶⣶⣶⣶⣶⣶⣶⢴⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⡿⣵⣶⣹⣿⣿⢸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣭⣵⣿⣿⢾⣿⣿⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⢺⣿⣿⢸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣧⣽⣥⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣿⣿⣿⣿⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠁⠀⠀⠀⣶⣶⣆⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠈⠻⣿⠿⠛⢁⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣤⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣴⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠾⣿⣿⣿⠁⠀⠀⠈⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣯⣿⠿⣿⣿⣿⣿⣿⣤⣴⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣦⣤⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡈⠙⠻⠿⣿⣿⣿⣿⠋⠀⢠⣶⡄⠀⠀⠀⠀⢠⣶⡄⠀⢙⣿⣿⣿⣿⠿⠟⠋⢁⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠈⠙⠛⠀⠀⠈⠙⠋⠀⠀⠀⠀⠈⠩⣿⡷⠀⠘⠿⠃⠀⠀⠀⠀⠘⠿⠃⠀⢾⣿⠍⠁⠀⠀⠀⠀⠙⠋⠁⠀⠀⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣶⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⢛⡻⢿⣿⠇⠀⠀⠀⠘⣿⣿⠿⠿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣷⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠛⠀⠀⣄⣠⡄⠀⠈⠻⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣉⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠉⠉⠐⠢⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⣄⡠⠊⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⢀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⢠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⣫⣭⣶⣶⣶⣦⣤⣀
⠀⠉⣵⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⢟⣵⣿⣿⡿⠿⠿⠿⢿⣿⣿⣷⣄
⠀⠀⠙⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣶⣶⣾⣿⣿⣿⠿⢋⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⡆
⠀⠀⠀⠈⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣭⠽⠟⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⣿⠛⠛⠿⢶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣃⣀⠀⠀⠀⠀⠉⠙⠻⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠞⠁⠈⠉⠉⠛⠲⠦⣤⡀⠀⠀⠙⢿
⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠈⠓⠤⣀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣧⠀⠀⣸
⠀⠀⠀⠀⠸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣾⣫⣥⠴⠞⠉
⠀⣠⣤⡀⠀⠘⢿⣿⣿⠆⢠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠭⠿⠻⢛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁
⠀⠹⣿⣿⣄⠀⣴⣿⣥⣄⠈⠻⣿⣄
⠀⠀⠈⠛⠋⠀⠈⣻⣿⠿⠛⠊⠉⠹⣆
⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⢀⣴⣿⠇⠘⢧⡀
⠀⠀⣴⠟⠁⠀⠀⠀⠀⠐⠿⠟⠋⣀⣄⠈⠻⣄
⢀⣾⠋⠀⠀⠀⠀⢀⣀⡀⠀⢠⣾⡿⠋⠀⠀⠈⠳⣄
⣼⡇⠀⠀⠀⠀⠀⠘⠿⢿⠿⠈⢹⣶⣦⣄⠀⠀⠀⠈⠳⣄
⣿⣇⠀⠀⠀⠀⠀⠰⣿⣦⣄⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠁
⢹⣿⣆⠀⠀⠀⠀⠀⠈⠻⠿⠇⣰⣿⣷⠄
⠀⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏
⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠈⠙⠿⣿⣷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣷⣶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠶⠶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠴⠖⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣶⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⣿⣿⣿⡿⠿⠿⠿⠟⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣰⣾⣿⣿⣿⣿⣦⣤⣶⣦⣤⣀⣠⣶⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣷⣄⣀⣤⣴⣶⣤⣤⣾⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⡀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠉⠙⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠛⠻⣿⣿⣿⣿⣿⣿⠟⠛⠻⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⠛⠛⢿⣿⣿⣿⣿⣿⠟⠛⠛⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠔⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠜⠄⠆⠢⠂⠄⠴⢣⠄⠄⡐⡡
⠀⠀⠀⠀⠀⠀⠀⠱⣌⡢⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣌⠙⣷⣄⠄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠐⢲⣴⠄⠒⢢⠀⠀⠀⠀⣀⡀⢀⡠⠤⢤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡀⠠⠒⢊⡂⡀⠀⠀⠀⠀⢸⣷⠶⢾⣿⡶⠶⢾⡀⠀⠀⠀⠈⠁⠈⠃⠒⠐⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣶⡚⢻⣯⠆⠀⠀⠀⣾⣧⣄⣸⣿⣤⣤⣼⡇⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⣀⣀⣀⠉⠀⠐⠁⠀⠀⠀⣉⣿⣿⡿⠃⠉⠉⢉⢇⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢤⡄
⠀⠀⠀⠀⣤⣐⡒⢚⠳⠶⠞⠳⠛⠓⠶⠿⠦⠦⡄⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⣈⠂⢀⣠⣵⡆
⠀⠀⠀⠀⠈⠛⠩⣙⣛⠛⠚⠳⠖⠒⠒⠛⠺⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⠠⠤
⠀⠀⠀⠀⠀⠀⡀⣠⡄⠂⢠⠰⠐⠀⣀⣤⣶⡿⠃⠀⠀⠀⠠⠀⠀⠀⠀⠐⢄⡉⡃⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣄⠀⠀⢀⣐⣀⣴
⠀⠀⠀⠀⠀⠛⠛⠶⢷⣼⣶⣶⣾⣿⡽⠟⠋⠀⠀⠀⠀⠀⠘⠂⠀⠐⠲⠂⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄⠀⠈⠉⢠⣈⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣌⢄⡒⠂⠒⡀⢀⠀⠀⠀⠀⠠⠀⠐⢀⡉⠀⠂⡤⣔⡾⠟⠀⠀⠀⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⠀⡀⠀⠀⣌⢀⡜⠊⢛⠀⡳⢄⠀⢉⣮⣤⠶⠂⠀⠺⠯⣎⣤⢡⡄⢶⡤⠚⠁⠀⠀⠀⠀⠀⢤⣀⢀⠀⠀⠀⡀
⠀⠰⣦⠉⠀⠙⢌⠚⣀⠀⠀⠄⢈⣢⣤⡶⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠉⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠁⠀⠀⠲⡐⡖⠂⠄
⠀⠀⠈⠿⠂⠢⠂⠱⣍⣤⠼⠟⠛⠉⠀⠀⠀⢀⣄⠤⠀⠐⠂⠀⠀⢠⡄⣀⣒⠦⠀⠀⠀⠀⢀⡀⠀⠉⡔⠀⠈⢄⢐⡜⣏⠉⠂⡀⢤⣰⡂
⠀⠀⠀⠀⠐⠷⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠘⠂⠀⠀⢴⣤⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⠘⠞⠢⣤⠔⠂⠙⠈⠃⠼⠷⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡸⠻⠿⠿⠿⠿⠿⠟⢇
⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⠿⠛⠛⠛⠻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢸⠂⠉⠒⠢⠤⠤⠤⠤⠒⠉⡙⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⢁⡤⠤⢤⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣦⣤⣶⣶⣶⣦⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⢸⠀⣦⢰⡄⡄⢠⠀⢰⡠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⠻⢤⣤⣤⠟⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⠀⣿⣼⠀⡇⣶⠀⣾⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⢸⣄⠁⠸⠁⠁⢯⡀⠎⠓⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣶⣶⣶⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢸⠈⠑⠒⠤⠤⠤⠤⠔⠒⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠒⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠿⠔⠶⠶⠶⠤⢤⣀⠉⠙⠲⣄
⠀⠀⠀⠀⣠⠴⠛⠛⠛⠒⠒⠛⠛⣋⣋⣳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⣀⣾⠦⣄
⠀⠀⠀⡔⠛⠃⠁⠉⠉⠉⠉⠉⠉⠉⠉⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣞⣹⣄⣀⣀⣀⣀⣀⣀⣀⠀⣴⣿⠛⠛⠀⠀⠸⡆
⠀⠀⠀⠸⣄⣀⣠⣤⣤⣤⣤⣤⡤⠤⠤⠤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠥⠤⠤⠶⠶⠶⠶⠶⠦⠤⠤⢤⣤⣉⡉⠋⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⣶⣤⡀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣶⣶⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⣿⠛⠁⠀⡇
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠘⠛⠛⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢸⠀⠟⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⢀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⢸⢹⣹⢳⠀⡾⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⣀⠀⠀⠀⠀⠛⠉⠛⠈⠛⠟⠃⣠⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⢠⠠⠄⠀⠠⠀⢠⠀⠤⠠⠀⠀⠀⠀⡀⠄⠠⠠⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢸⠠⢠⠀⠀⡀⠀⠠⠀⢀⠀⠐⠀⠠⠀⠀⠀⠚⠚⠉⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠐⠀⠩⣌⣁⡀⠀⠉⠑⡠⠀⡅⠤⠉⢈⡡⢐⡄⡀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠅⠐⠒⡁⠠⠀⠸⠂⢓⢎⡤⠀⠶⠈⠰⢩⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠨⠀⠈⠆⠄⢀⠀⠉⠏⠻⡤⢒⠀⡛⠆⢋⠬⡃
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠉⠀⠒⠐⠀⠀⠘⠀⡏⠒⠂⠄⠁⠀⢋⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠤⠀⢨⡁⣤⠀⠐⠁⠀⢀⠀⠀⠀⠀⠀⠢⡀⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠂⠐⠓⢢⠶⠥⢍⡀⠁⠶⠌⡳⠀⠂⠀⢰⠀⠁⢈⡇⠀⢇
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⢀⠆⠁⡀⠀⢈⠀⢇⢰⡄⠀⠀⠂⡀⠀⠀⣼⢣⡝⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⣂⠙⠀⡀⠑⡀⢊⠘⠁⡛⠚⠄⠂⠀⠀⠇⣀⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠨⠉⠘⠀⠈⡏⠁⠈⠀⠐⣨⠀⠉⠘⠀⠡⠀⠀⠙⠘⠀⢰⠛
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⢠⠄⠀⠀⠈⠀⠀⠀⠀⠐⠈⠀⠈⠂⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢴⡄⠀⢠⠑⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠈⠀⠀⠀⠄⠡⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠍⠢⣈⠀⠀⠀⠀⠀⣄⠤⠀⠁⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⢁⠀⠄⠀⢀⡀⠀⠌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠈⠀⠀⠐⠈⠁⠉⠀⠀⠐⠂⠐⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⢀⣴⠦⠳⡤⠷⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⡾⣤⡀⠀⠀⠀⠀⠀⠀⠀⣘⠡⢲⢎⢳⢢⢱
⠀⠀⠀⠀⠀⡠⢸⡁⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡎⡀⠀⠀⢇⢱⠀⠀⠀⠀⠀⠀⠀⠰⡰⢞⣮⡛⢎⡜
⠀⠀⠀⠀⠀⠑⢤⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣓⣓⣒⣒⣚⣒⠆⠀⠀⠀⠀⠀⠀⠘⠕⠋⠭⠜⠢⠇



⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠠⠤⣀
⠀⠀⠀⠀⠀⣠⣣⣜⣒⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⡠⠼⠌⠡⠧⢄⠀⠀⠀⠀⠀⠀⠀⢰⣁⣠⠔⢄⠈⢧
⠀⠀⠀⠀⠀⣷⣦⣴⣳⣦⣴⣟⠀⠀⠀⠀⠀⠀⠀⠑⡆⠀⠀⢰⠊⠀⠀⠀⠀⠀⠀⠀⠸⡀⠘⠢⠊⢉⡏
⠀⠀⠀⠀⠀⠋⠛⠋⠀⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠮⣀⠖⠢⣀⠵⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠒⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⡖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒
⠀⠀⠀⠀⠀⠀⠠⡓⢝⢮⣲⠃⠀⠀⠀⠀⠀⠀⠀⢸⠭⠝⠫⠭⡇⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠉⠉⣓⢢
⠀⠀⠀⠀⠀⡠⢖⡝⠢⠓⠃⠀⠀⠀⠀⠀⠀⠀⢰⠭⠕⠭⠭⠪⠭⡆⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢀⡵⠃
⠀⠀⠀⠀⠘⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠰⠭⠥⠬⠭⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠶⠒⠒⠶⢶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠻⣷⡄⠈⠉⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡉⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠉⢻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢻⣏⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⡀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠈⣿⡄⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠹⣷⡄⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⢹⣷⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣿⡄⠀⠀⣀⣠⣤⠿⠷⠶⠶⠒⠲⠾⠿⠦⢤⣤⣀⣀⡀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⣠⣤⠽⠟⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠶⠦⠤⠤⠿⠷⠚⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡂⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⡀⠀⠀⠀⢀⡄⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡶⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠓⠚⠚⠓⠛⠛⠛⠒⠛⠛⠉⠉⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⠈⠠⠠⠊⠀⠀⠀⡀⢀⡄⠀⠀⠀⠀⢄⠠⠀⣂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣀⣀⣈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠔⢈⠇⠀⠀⠀⢘⡆⠀⢸⣄⠀⠀⠀⠀⡁⠢⡀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣉⠳⣌⡠⠔⠁⠀⠀⠀⡔⠁⠙⠋⠉⠀⢱⠀⠀⠀⠀⠤⡀⣊⠴⠓⣄⠀⠀⠀⠀⠀⠀⠀⠠⠂⠄⠀⠂⠀⠀⠠⣄⣀⣀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⢑⠎⠀⠀⠀⠀⠀⢘⠉⠉⠁⠉⠉⠉⠉⡂⠀⠀⠀⠀⠈⠡⢔⠩⠈⠀⠀⠠⠀⠀⠰⠂⠠⠀⠀⠂⠀⠀⠀⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢉⡉⠉⠉⠉⠉⡉⡅⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠀⠤⠀⠂⠀⡆⠐⠀⠀⠀⠀⠀⠈⢠⡌⠀⠘⠁⠌⠃⠀⠀⠀⠀⠀⢀⠂⠀⠀⠖⠀⠀⠀⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠈⢷⠀⠀⠀⠠⠤⠥⠤⠁⠤⠀⠼⠄⠂⠀⠀⠀⡇⠘⠀⢀⡇⠨⠅⢈
⠀⠀⠀⠀⠀⠀⠀⠤⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠣⠄⠄⠀⠒⠚⠒⠒⠒⠂⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠶⠀⠀⠌⠀⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡤⠔⠉⡄⠀⠀⠀⠀⠠⠈⠂⠈⠀⠀⢰⠅⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⢰⠠⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠟⡠⠔⠊⣁⠴⠀⠀⠀⠐⠁⠈⠀⡤⣃⠀⡀⢀⡀⣀⢀⡀⢀⠀⡀⠀⡁⠀⠀⠀⠀⡀⠠⠄⠘⠀⠐⡀
⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠱⠖⠂⠉⠂⠀⠀⡐⠀⢀⠀⠠⠄⠁⠉⠀⠀⠀⠀⠁⠈⠈⠉⠈⠁⠈⠁⠉⠉⠁⠁⠀⠆⠰⡀⠀⠐⡀
⠀⠀⠀⠀⠀⢭⣩⣉⣉⡁⠀⠀⠁⠀⠀⠀⠀⡜⢠⠀⠞⠁⠀⢠⢄⡀⠀⠄⠤⠤⠤⠠⠄⠤⠠⠀⠤⠠⢄⠤⠠⢄⠀⠀⠀⠹⠄⠤⠐⡄
⠀⠀⠀⠀⠀⠲⠤⢤⠠⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠄⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢠⠂⠀⠀⠤⠁⢀⡆⠀⠠⠆⠀⠀⠀⠀⠈⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠘⢤⠀⠡⠀⠀⠘⢂⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡⠈⠀⠀⠀⢀⠔⠁⠂⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠈⠤⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⠀⡠⠊⠀⠀⠀⠀⠀⣀⠀⠀⠸⠁⠀⠀⠀⢰⠀⠀⠀⢼⠀⠀⠀⡀⠀⠀⠈⠣⠀⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡔⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡄⠀⠀⠘⠀⠀⠀⠀⠀⣀⠀⠇⠀⠀⠀⠀⠐⡄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀⠀⡜⠀⠀⠀⠀⠀⠰⠒⠀⠒⠐⠀⠂⠀⠂⠐⠄⠢⠤⠄⢄⠠⢄⢤⣠⠀⠀⠀⠀⠀⠀⠘⡄⢀⠀⠀⡡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⡀⢀⡜⠀⠀⠀⠀⠀⠀⢠⠤⠠⠤⠤⠠⠠⠤⠄⠀⠀⠄⠤⠠⠄⢤⢠⡤⡘⠀⠀⠀⠀⠀⠀⠀⠐⡤⢀⠉⠐⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢁⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡎⠀⠅⡠⠂⠀⠐⠃⢀⠀⡆⠈⠠⠁⠘⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⣠⣾⡛⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠶⠶⢶⣦⡄
⠀⠀⠀⠀⢠⣿⠀⠙⣄⠀⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⣰⠋⠈⣿⡀
⠀⠀⠀⠀⢸⣿⠀⠀⠈⢧⡀⠀⠀⠈⠻⣦⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡰⠋⠁⠀⠀⠀⠀⢀⡞⠁⠀⠀⢹⡇
⠀⠀⠀⠀⠸⣷⠀⠀⠀⠈⢷⡀⠀⢀⡤⠾⠛⠋⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠛⠓⠶⣤⡀⠀⣠⠏⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠃⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢹⡆⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠻⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠇
⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡶⠛⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⡴⠚⠛⠳⣦
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⠓⠀⠀⠀⠙⣿⠃⠀⠀⢰⠏⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸
⠉⠙⠛⠓⠶⢦⣿⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠰⣄⠀⠀⣠⠿⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⣀⣿⠤⠶⢶⡾⠓⠒⠒⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⢹⡏⠑⠂⡠⠐⠀⠀⠀⠀⠀⠀⠈⡏⠉⠁⠀⠈⠉⢙⡇⠀⠀⠄⠒⠒⠀⠀⠀⠀⠀⠉⢸⡏⠀⠀⣸⠃⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠔⠊⠉⠉⠉⢺⠁⠀⠀⢄⠀⠀⠀⠀⢰⠀⠀⢠⡿⠁⠀⠀⣿⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⣀⡼⢿⣏⡀⠀⠈⠁⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣳⣿⣅⡀⠀⠀⣿⠀⠀⠀⢰⠏
⠀⠀⠀⢀⡴⠚⠁⠀⠀⠉⠻⠶⣤⣄⣀⡀⠀⠀⠀⠀⠈⠙⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⠈⠙⠷⣄⣿⠀⠀⠀⣿
⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⡛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦⡀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⢀⡟⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢄⡀⠀⡆⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⣠⠟⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠉⣻⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠋⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠎⢠⠄⠀⠀⡾⠀⡀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢀⣼⠧⠤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠾⠤⠴⠚⠳⣼⣀⣾⣀⣠⡴⠿⣀⣀⣀⣀⣀⣐⣒⣚⣩⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⡠⠐⢄⠀⠀⠸⣧
⢀⣶⠟⠛⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⠊⠀⠀⠀⠆⠀⠀⣿
⣾⠃⠀⠀⡀⢀⠈⠻⢷⡄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠶⠶⢶⠶⠶⠿⢤⣤⣁⠀⠀⠀⠀⢠⠀⠀⣿
⣿⠀⠀⢰⠀⠀⠑⢄⠈⠻⣦⡀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠘⠀⠀⣿
⣿⡀⠀⢸⠀⠀⠀⠀⠑⢀⣸⠟⠋⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⢰⡟
⢸⡇⠀⠈⡀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠻⠿⠦⠀⠀⠘⣦⣾⠃
⠈⣿⡀⠀⢡⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠀⡀⠀⡀⠀⠀⠈⢿⡀
⠀⠸⣧⠀⢀⡾⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠔⠁⠀⠀⠀⣠⣖⡊⠙⠓⢴⠁⠀⠀⠀⠘⣷⡀
⠀⠀⢻⡆⢸⠁⠀⢠⡿⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣠⡆⠀⢇⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢿⣾⠀⠀⠈⠀⠀⢀⣱⢄⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⢿⣿⠿⠃⢀⡎⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠈⣿⠀⠀⠀⠐⠢⡞⣿⣿⣄⣠⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠠⠴⠊⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⡇⢿⣿⣿⡿⠃⢀⠇⠀⠀⠀⣀⡠⣤⣄⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠘⢦⣈⣁⣀⡠⠊⠀⠀⣀⠾⣷⣶⣿⠏⠀⠀⢠⠀⠀⠉⠑⠢⡀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠈⣧⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠘⢤⡀⢀⡴⠃⠈⠉⠉⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠠⠂⠀⠀⣀⡤⠞⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣤⣄⣀⣁⡀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠶⠚⠋⠙⡄⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⡏⡙⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠸⣧⣀⡀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⡏⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⠟⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣇⣴⠟⠁⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡟⠋⠁⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠛⠒⠒⣾⣤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢰⣃⣀⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⡀⠀⠀⣰⢋⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣠⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⣿⣦⣤⣅⣀⣠⣤⣇⠀⠀⡄⠀⠠⠀⢀⣇⣀⣀⣤⣴⠾⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣛⣿⣶⣷⣶⣿⣾⣟⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠱⢃⡴⠖⠶⢤⣀⠀⠀⠀⠀⠀⢠⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡀⠀⠀⢌⠳⢄⡀⠀⢀⣼⣜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⠏⠉⠉⣩⠍⣓⠳⢤⣵⡒⣮⠻⠟⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣆⣀⣈⡴⠲⢤⣵⢤⠤⠃⣼⡷⠖⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣴⡙⠷⣤⡗⣿⠁⠈⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⡄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣛⡷⡟⢸⠀⠀⠀⠀⠀⠀⣴⣋⠭⠖⠒⠂⠈⠁⠀⠉⠀⡨⢿⠿⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠟⠀⠛⠀⠀⠀⠀⠀⠀⢸⡷⠛⠛⠓⠶⠶⠶⠶⠶⠶⠶⢦⡀⠀⢀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣥⣤⣄⣁⣀⣀⣀⣀⣀⣀⣸⣇⠀⠠⣺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡉⠙⠯⠍⠉⠙⠛⠛⠛⠉⠉⠩⠽⣶⣬⢹⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠑⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡓⠆⠀⠀⠀⠀⣀⠤⠤⠶⠤⣄⣀⡀⠀⠸⣧⠿⢽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⣤⣀⣀⣠⠞⠁⢀⣠⣤⡀⠀⠙⣦⠀⠀⢰⢾⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⣴⣿⣿⣿⣿⣷⡄⠘⣿⣿⣿⣛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⡿⢭⣿⣧⠀⢿⣿⣿⣿⣷⣿⠁⢠⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣒⡢⠔⠛⣦⣬⠉⠛⠿⠋⠡⣪⠟⢩⠤⢌⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣗⡀⠀⠀⠙⠳⠶⠶⠖⠛⠁⠀⠠⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠐⠩⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⣄⣀⣀⣤⣤⣄⣀⣀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠶⠶⣤⣌⡒⠦⣄⡀⠀⠀⠀⠀⠀⠸⣯⣀⣉⣛⠙⠛⠛⠛⠉⢙⣻⣿⠇⠐⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠤⠬⠙⠓⠶⣭⣓⠦⢄⡀⠀⠀⠀⠈⠉⠙⢛⣛⠛⢛⣛⣋⣉⣁⠀⠀⣀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢙⡻⢶⣮⣀⠤⢤⣤⣄⣀⡀⠀⠀⠀⠀⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠢⡈⠙⠽⠳⢶⣄⡀⠀⠀⠈⠑⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡈⢦⣄⣐⣐⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣄⣭⣤⡁⢂⣡⡼⣁⣉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣿⠛⠋⠥⠤⠤⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠆

⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠈⣿⣄⡟⢸⠉⠙⡇⠀⢸⡷⠾⣧⢼⠉⠙⡆⣟⣹⠦⣯⠁⠀⢸⣉⣽⢸⠋⠉⣧⣿⣙⡆⣾⢸⣷⣸⡇⣿⣩⡇
⠀⠀⠀⠘⠇⠙⠃⠘⠷⠾⠃⠀⠸⠃⠀⠟⠘⠶⠾⠃⠟⠳⠀⠷⠄⠀⠸⠶⠟⠈⠳⠶⠃⠿⠻⠀⠻⠸⠃⠛⠀⠦⠼⠁
⠀⠀⠀⠀⡀⠀⠀⣀⠀⣠⣄⠀⣀⣀⠀⣀⡀⠀⢀⣀⠀⠀⣀⣀⡀⠀⣀⠀⢀⡀⠀⡀⢀⠀⢀⡀⣀⡀⣀⡀⠀⢀⣀
⠀⠀⠀⠀⢿⣶⣴⡏⢸⡁⠈⣷⣿⣩⠇⡏⢉⡇⠸⣏⠁⠀⣿⣤⡟⢸⣿⣆⢸⡿⣦⡏⢸⢷⣼⢻⡷⠀⣯⣽⠇⠻⣍
⠀⠀⠀⠀⠘⠋⠛⠀⠈⠓⠚⠁⠛⠛⠂⠛⠋⠀⠛⠛⠀⠀⠛⠒⠃⠛⠀⠙⠈⠃⠘⠁⠘⠀⠛⠈⠓⠂⠛⠓⠈⠛⠋
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⢠⠀⢔⠀⠶⠎⠢⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠈⢡⢤⢀⣀⣀⣢⡄⠤⠖⠽⠂⠀⠈⠀⠀⠐⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⢈⡤⠤⠴⠲⠛⠑⠈⠂⢉⠉⠈⠤⣄⣠⡤⢤⡄⠀⡄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠁⠀⢠⠠⢄⠁⠀⠀⠀⣠⠀⡒⣤⣷⠆⠸⠰⠚⠚⠀⠈⠉⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠤⠀⠤
⠲⠶⠤⠤⣤⣥⣀⣀⡀⠀⣤⠬⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⢀⣀⣀⣤⡤⠴⠶
⠀⠀⠀⠀⠀⣾⣿⡟⣹⢻⡇⠀⠀⠀⢸⣿⡏⠻⡛⢛⣽⢛⣿⣿⣿⢛⣻⡟⢿⡟⡻⣿⣿⣿⠀⠀⠀⢸⣿⠿⢿⣿⡅
⠀⠀⠀⠀⢀⣿⣿⣧⣤⣿⡇⠀⠀⠀⢸⣿⣷⡷⠷⠶⠽⠮⢿⣿⣿⣐⣼⣰⣎⣇⣧⣿⣿⣿⠀⠀⠀⢸⣿⣀⠳⠟⠃
⠤⠤⡀⠀⣀⠀⡀⠉⠉⢹⡇⠀⠀⢠⡄⠐⠢⠐⠲⠄⠠⠤⢼⠛⢛⠛⣋⣉⠉⢉⣉⢉⠀⠀⠀⠀⠀⢸⣅⣀⣀⠠⢤⠦⠆⠂
⡀⠀⠀⠀⠀⠁⠈⠉⠈⢻⠁⣐⠒⠀⡅⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠁⠀⠀⠀⠀⠀⠃
⠁⠈⠄⠀⠀⠀⠀⠀⠀⣸⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡃
⠀⢀⠀⠀⠀⣀⣀⣠⣤⡿⠴⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣦⣼⣄⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⣧⣤⣤⣤⣤⠤
⣛⣿⢿⢿⢿⣿⡁⠀⠀⠀⠀⣿⣿⡧⢺⣠⣿⣯⠙⢫⢉⡏⠿⣛⣻⣿⠋⠉⠙⠛⠛⣿⣈⠇⢿⠸⣿⣿⠀⠀⠀⣿⣻⣿⣿⡆
⣿⣿⣼⣈⣤⣻⡇⠀⠀⠀⠀⠸⠿⠛⠛⢻⠟⠛⠛⠿⠾⠷⠶⠧⠿⠿⠀⠀⠀⠀⠀⡿⠿⠿⠿⠟⠛⠛⠀⠀⠀⣧⣩⣾⣿⡇
⠿⠿⠿⠿⠛⠛⡇⠀⠂⠀⠀⠀⠢⠄⠒⣾⠀⠀⠈⠑⠈⠒⠂⠠⠤⠤⠀⠀⠀⠀⢸⡇⠤⠤⠤⠀⠀⠀⠀⠀⠀⣏⣉⣀⠀⠠⠄
⠀⠰⠀⠈⠘⠈⣿⠐⠀⠀⠠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠠⢶⠄⠀⡏⠀⠀⠀⠦⣀
⠀⠠⢥⠀⠀⠀⢻⠀⠀⠀⠐⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡧
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠊⣸⠀⠀⢀⣤⣄⠀⠀⠰⢤⠤⠀⡇⢀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠄⣀⣀⡀⠀⠀⡀⢀⣀⠀⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⡆⠀⠀⠀⠀⢨⠅⠊⠀⠀⠀⠀⠀⠀⠀⠀⡨⠁
⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠿⠶⠶⢶⣶⠶⠶⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠶⠶⠶⠟⠛⠛⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⢀⣤⡶⣶⣦⡀
⠀⠀⠀⢠⣾⣟⣿⣶⡀⠀⠀⢠⣾⣿⣿⣿⣦⠀⠀⣾⣿⣧⣿⣿⡇⠀⠀⠀⣾⣿⣷⣿⣿⣿⠀⠀⢀⣴⡶⣶⣤⠀⠀⠀⢀⣴⣿⢻⣷⣦
⠀⠀⠀⢸⣿⣿⢻⣿⠇⠀⠀⠸⣿⣿⢻⣿⡿⠀⠀⠹⣿⣯⣽⣿⠇⠀⠀⠀⠹⣿⣿⣹⣿⠟⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⠿⣿⣿⠂
⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠙⠻⠓⠛⠛⠀⠀⠀⠀⠙⠛⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣤⡴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⣠⡶
⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣛⣉⣀⣀⣀⣀⣀⣀⣀
⠀⢼⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣦⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠄⠰⢂⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢳⣼⣿⣿⣧⣶⣀⣶⣢⣀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠙⣳⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣦⣤⣶⣾⣿⣆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣴⣾⣆⠀⠀⠀⠀⠀⠀⠀⢀⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⠀⠀⣸⣿⣿⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠈⢀⣴⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣀⣀⣠⣿⣿⣿⣿⣿⣿⡖⠐⠀⠀⠀⠀⣀⣴⣦⠝⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⢻⡿⠿⠿⣿⣿⣟⠛⡿⠋⠉⠀⠈⠳⠶⠍⠉⠁⠀⠀⠀⠀⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⢈⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⢸⣷⣀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⣿⣿⡗⢶⣾⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⢹⣿⣿⣯⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠈⣿⣧⠀⢈⠁⠀⠀⠀⠈⣾⣄⠰⡄⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⠈⠀⠀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣷⡿⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢹⣿⣿⣧⣴⣶⣼⣿⣄⣶⣿⣿⣿⠸⣦⠀⠀⠀⠀⠀⣿⣿⠏⢀⡞⢠⢯⣿⣿⣿⣿⣿⣿⣿⢟⡡⠀⠀⠀⠠⠔⢤⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢿⣷⣤⣀⣠⣶⣿⣿⣷⣞⣷⣏⡾⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠢
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣠⣄⣲⣥⣙⣿⣿⣿⣿⣿⣿⣿⡾⡻⠂⠈⢻⣿⣿⣿⣿⣿⣿⢿⡆⠀⠀⠀⠀⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡋⠀⠀⠊⠁⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⡿⠚⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡇⠐⣄⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⠄⠀⠀⠊⠹⢿⣿⣿⣿⣿⣿⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣆⠉⠑⢀⡀⠀⠀⠀⠀⠀⠈⠛⢿⡃⠀⠀⣀⣀⣤⠾⢿⣶⣿⠿⠍⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⠄⢀⣠⠎⠉⢷⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡰⡞⠈⠀⠀⠀⢀⠈⠵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢧⢱⠀⠒⠂⡀⠈⠀⢀⠉⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡀⠈⠓⠂⠀⠀⠀⡀⠀⠉⠀⠙⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠐⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⣀⣹⠀⠀⠀⠀⠀⡀⠤⠀⡂⠱⠌⡰
⠀⠀⠀⠀⢀⠔⠊⠒⠒⠀⢄⡀⠀⠰⠈⠈⠉⠀⠀⠀⠁⠀⠈⠈⠀⠉⠁⠠⠀⠀⠀⠀⠘⠰⠈
⠀⠀⠀⠔⠃⠈⠀⠀⠀⢀⠀⠀⠁⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡄⣆
⠀⠀⡎⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠡⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡔⠈⠠⠀⠀⠀⠑⢢
⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠨⠀⢀⡴⠒⠒⠒⠲⢄⡀⢠⠀⢸⠀⠀⠈⠀⠀⠀⠂⠀⡇
⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢸⡧⠀⠀⣿⠆⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⡀⠀⣤⠀⠀⠀⠀⠹⠃⠀⡇⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠙⡒⠒⠠⠤⠤⠤⠴⢤⠂
⠀⠀⠀⢱⠀⠉⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠈⠲⠤⠤⠤⠴⠚⢡⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠤⠄⠒⠒⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠐⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠁⠀⠀⠀⠀⠊⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠴⠀⠀⠰⣯⡿⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠆⠢⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠖⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢁⡀⠤⠘⠱⠕⠂⢄⠀⡄⠀⠀⠀⠀⠀⠀⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠙⢁⠀⣀⠐⠀⠀⢀⠀⡌⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠁⠌⠠⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀
⠀⠀⠀⠀⢀⡀⢀⡀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠐⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣴⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣾⣷⣤⣤⣤
⣠⡄⠈⠃⠉⠘⠁⣦⡄⠀⠀⠀⠀⠀⠀⠀⡸⠏⠀⠻⠙⠉⢧⠀⠀⠀⠀⠀⠀⠀⠸⢉⣤⡀⢀⣤⡙⠃⠀⠀⠀⠀⠀⠀⢻⡿⠋⠁⠀⠀⠈⠻⢿⣤
⢸⣏⠁⢐⣀⡀⢈⣹⠁⠀⠀⠀⠀⠀⠀⠠⣯⣁⣤⣤⣤⣄⣽⡆⠀⠀⠀⠀⠀⠀⠇⣾⠟⠃⠈⠻⣿⠸⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⣀⣀⠀⠀⢸⡟
⡀⠲⠂⠀⠉⠁⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣿⣿⣾⠟⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠙⠛⠀⡠⠃⠀⠀⠀⠀⠀⠰⣿⣷⣀⠀⠈⠉⠀⣠⣾⠿
⢛⠀⣘⠀⠐⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⡿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣷⣶⣶⣿⠛⠃
⠘⣴⡇⢠⠄⡤⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⠭⢭⢭⠽⡄⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⣶⢰⡆⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⠠⠃
⠈⠛⠆⣸⡀⣇⠰⠛⠃⠀⠀⠀⠀⠀⠀⠀⣾⢉⣻⣛⣼⡉⠷⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⢿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⢿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢶⣆⢀⣶⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠈⠁⠀⠉⠙⢿⠟⠀⠀⠀⠀⠀⢀⣠⣄⠀⣀⡀
⠀⢀⠀⠐⠒⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣠⣤⣤⣤⣀⣈⠀⠀⠀⠀⠀⢠⠋⣸⣾⠿⠿⠿⣷⣄
⠣⠁⠀⠀⠀⠀⠀⠡⠇⠀⠀⠀⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢰⣿⢻⡟⠁⠠⠀⠀⠀⢻⡛⣷
⠠⠀⠀⢿⣿⠿⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⢩⠉⠀⠀⠀⠀⠀⠀⠀⠹⣏⠳⢄⠀⠀⠀⡀⠈⢛⡯
⠀⠑⠤⠀⣀⠠⡔⠁⠀⠀⠀⠀⠀⠸⢿⣿⣷⣄⠀⠀⠀⣠⣾⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠐⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡏⠉⠹⣷⣄⢿⣞
⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠈⣬⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⢀⣿⣜⡞
⢠⠂⠀⠀⠀⠀⠀⡓⡄⠀⠀⠀⠀⠀⠀⠀⢸⡿⢃⣴⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢘⠀⡄⣤⢚⠎⠀⠀⠀⠀⠀⠀⠐⢿⣿⣷⣤⣾⣿⣿⣿
⠈⠉⠺⠭⠶⠭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠖⠲⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠓⠻⠆⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠀⠠⠀⠀⠀⡄⢠⢿⣷⡀⠁⠀⠁⠀⠐⡀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣤⡀⠀⠂⠀⠀⠀⠿⠸⢿⣇⠀⠀⠀⠀⢀⡴⡫⣷⠈⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠀⠹⡌⢎⢳⣤⠐⠀⢀⢸⠁⠀⣆⢹⡀⠀⠀⣰⠞⢱⢣⡟⠀⠀⠀⠈⡐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⢀⠀⠐⠀⠀⠀⠸⡇⠈⢄⠟⣷⡆⠀⠇⠀⠀⡇⣼⣷⠀⡴⠃⢀⣏⢎⡟⠀⠀⠀⠈⠀⣀⠈⣴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⢿⡳⣴⣄⣀⠀⠐⣇⠀⠘⣞⣰⣽⣿⠤⠤⠶⠻⠿⠿⡿⣅⢀⡞⡿⣜⡟⠀⢁⣠⠤⠚⣡⢾⡿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠙⢮⠪⣝⣗⢶⣾⣀⠴⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢾⣿⠔⠋⠁⣠⢞⣵⡏⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠄⠐⠠⡀⠀⠘⢧⠀⠙⠪⣪⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣠⣞⢕⣿⡏⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠘⢧⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⣀⡄⣠⡤⠤⠶⢦⣴⡶⠂
⠀⠀⠙⠻⣿⠯⣟⣻⢏⣓⠿⣖⣻⠿⠀⠀⢀⡤⢴⠶⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⣀⣀⠀⠀⠀⠹⡅⠀⠀⣀⠤⢒⣭⠾⠛
⠀⠀⠀⠠⠉⠓⢦⡉⠙⠛⠿⢶⡿⡀⠀⠀⠀⢀⣤⣤⣤⣤⣶⣟⢷⡀⠀⠀⢀⡴⠟⣥⣀⣀⣴⣉⣀⠀⠀⠀⠀⠸⣦⠛⣠⣴⠞⠋⠀⠄
⠀⠀⠤⠄⠀⡀⠀⠉⠳⢤⡀⣼⠁⠀⠀⠀⠀⠁⠀⣻⣿⣿⣇⣽⣿⣷⠀⠀⣼⠻⠓⠛⠹⣿⣿⡟⣨⡗⠠⠀⠀⠀⢻⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⣿⡄⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠠⠀⠸⡅⠉⠙⠓⠶⠆⣠⣀⠀⠁
⠀⣀⣠⣶⠶⠞⠋⠭⣭⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣧⣤⣤⣶⣶⣶⣶⣴⠿⠖
⠀⠉⠿⠏⠩⢉⣀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣵⣶⠖⠚⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠉⠑⣲⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⠢⣄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠀⠀⢐⣰⢿⡿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡄⢀⠈⠲⢦⡀⠀⠀⠐
⠀⠀⠀⠀⠀⣠⡴⣏⡬⠗⠋⠉⠙⡄⠈⠀⠀⠀⠀⠀⠀⠀⠲⠔⠓⠒⠦⠤⠚⠛⠛⠒⠒⠀⠂⠀⠀⠀⠀⠀⢠⣿⣷⣿⣟⣾⣥⣂⣽⣷⣄⠂
⠀⠀⠀⣠⣾⣗⣋⡥⢤⠤⠴⠖⠶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣄⣀⠋⣤⢊⠂⢀⠀⠀⠀⠀⢀⡴⠉⢻⡀⠁⠀⠉⡁⠉⠙⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣼⠫⡫⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠠⠐⠀⠀⠀⢀⣴⢿⡢⡀⠀⠩⡄⠈⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠐⢀⠄⠊⠀⢀⣼⡋⣠⠞⠁⢀⣹⣷⣦⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⣀⡤⠞⢿⠷⣴⣝⢮⡲⢄⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⠞⢁⣠⢖⠋⠘⣯⢋⣻⠋⠛⢳⣶⣦⣤⣤⠤⠴⢶⣶⣿⠋⠄⠀⢸⡄⠌⠉⠻⠿⢦⣕⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠵⠞⡁⠀⠀⠀⢸⢇⢈⠇⠀⣰⠋⢸⡏⢿⠀⠀⠀⡜⠘⠿⣆⣌⠄⠈⣏⠂⠀⠀⠀⠀⠁⡉⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⢀⠀⠀⢸⡏⡌⠀⡞⠀⠀⠈⣿⢸⠈⠀⢰⠁⠀⢠⠘⢿⡌⠄⢧⠀⠀⡀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⣾⡝⡰⠃⠀⠀⠀⠀⠘⣷⢠⢀⡇⠀⠀⠀⠀⠀⠹⣤⣬⠀⠠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⡀⠀⠐⠀⠀⠀⠀⢻⣼⡘⠃⠀⠂⠀⠠⠈⡄⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⠂⠈⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠄⢣⣶⢶⡄⠀⠀⣰⣿⣷⡀⠀⠀⠀⠀⠀⠻⠆⢣⣾⠻⣆⠀⠀⣰⡿⣷⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣎
⠀⠈⠻⡾⠃⠀⠀⠙⣻⠟⠀⠀⠀⠀⠀⠀⣾⣿⣧⣛⣚⠃⠀⠀⠈⣛⠛⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠏
⠀⠀⠟⠉⠀⣀⣀⢾⡁⢰⠄⠀⠀⠀⠀⠀⠙⠛⠃⠛⠁⠂⣤⣄⢺⣁⢰⠆⣀⣀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠈⠺⣉⣹⠆⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣽⠃⠉⠁⢺⣏⢹⠂
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⡄⣄⣼⣗⠶⠖⠒⠒⠒⠒⠒⢦⠒⠒⠚⠓⠖
⠀⠀⠀⠘⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣤⣇⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⢀⡆⠈⠁⠀⠀⠈⠉⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⢷⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈
⠀⠀⠀⠀⠀⢈⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠀⠀⣀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣤⡠⢄⡀⣤⣶
⠀⠀⠀⠀⠀⢿⠶⡄⠀⢘⡃⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄⣀⠉⠀⠈⠛⣀⡄⠀⠀⠀⠀⠲⣿⡵⠂⠀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠰⠋⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠉⢁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠾⡇⠀⢀⠀⠀⠠⠐⠊⠁
⠀⠀⠀⢠⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠈⣄⠀⠀⠸⣿⡂⠀⣀⠀⠀⠀⢰⣾⠚⢗⠀⠀⠀⠀⠀⠀⠀⣴⣂⣽⠒⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⢰⣿⣷⣰
⠀⠀⠀⠀⡅⠀⠀⠀⠘⠻⠃⢻⠀⠀⠈⠉⠿⠶⠞⠁⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠰⣤⢧⠆⠀⠀⠀⡉⢟⣿⣻⢏⠛
⠀⠀⠀⠀⠛⠀⡀⠀⠀⠀⠀⡘⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠛⠞⠀⠀⠀⠀⠀⣼⠈⢑⢕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⢠⡄⠀⠀⠀⠀⠀⠀⠘⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⡀⠄⠠⠄⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣀⡀⠔⡆⠀⢀⣤⡀⠀⠀⠀⢀⡤⠒⠒⢦⠀⠈⠁⠀⠀⠀⠀⠀⡼⢤
⠀⠀⠀⠀⠶⠀⠀⢀⡠⠔⡶⠔⠉⡆⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣗⢚⣄⣠⡾⠉⠁⠀⠀⠀⠰⢁⡀⢀⠀⠇⠀⠀⠀⠀⠀⢀⠔⠋⠉⠁⠒⡔⠃
⠀⠀⠀⢀⣤⣐⣈⣁⣀⣀⡁⠈⠭⠤⠄⠐⠒⢈⡆⢀⠀⠀⠀⠀⠀⢀⠤⠾⢽⣯⠗⢳⢄⠀⠀⢀⠀⠀⡶⠆⡆⡏⠦⣼⠀⠀⠀⠀⠀⠾⠠⠤⣠⠦⠜⠣
⠀⠀⠀⢸⣄⡂⠄⠀⠒⣒⣒⣖⣒⠂⠤⠘⠛⢀⠀⠀⢱⠀⠀⠀⢀⡟⣶⠚⠓⣿⣙⡏⠭⡄⠀⠈⠁⠀⡇⠀⣇⠃⠀⣿⠀⠀⠀⠃⠀⢂⠱⠀⠇⠀⡇
⠀⠀⡤⠚⠦⠄⣀⣀⡁⠀⠠⠤⠤⠤⠀⠒⠒⠉⢀⡠⠊⠀⠀⠀⠈⡄⡓⠄⢰⠢⠀⠔⢳⠃⠀⠀⠀⠀⢇⠀⠙⠀⠀⣹⠀⠀⠀⠀⢀⠔⢆⠁⠐⠀⢀⠁⢈
⠀⢨⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠒⠉⠀⠀⠀⠛⠀⠀⠘⠪⠬⢈⠀⠈⠔⠋⠀⠀⠀⠀⠀⠈⠈⠩⠈⠃⠀⠀⠀⠀⠀⠘⠤⢀⣁⡐⠠⠥⠒⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠘⠀⠀⠀⢠⡀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⢠⣄⠤⠐⠒⠀⣐⠢⡀⠀⠀⠀⠀⢛⡢⠌⢰⡈⠁⠀⠀⠈⠉⠀⠀⢨⠑⠞⠄⢀⠌⠀⠀⠀⠀⠀⠈⠃
⠀⠰⠆⠀⢀⠎⢰⠊⠓⡊⢯⠱⣈⢢⠀⠀⠀⠀⡤⠊⣁⡠⠊⠒⠈⢀⠂⢰⠀⠀⠛⢄⡁⠈⠀⠀⠥⡀⠀⠀⠀⠀⢠⠒⣏⠢⢄⠀⠓⢤⡀⠀⠀⠈⠃
⠀⠀⠀⠀⡆⡾⠅⠠⠋⠉⠘⣷⠌⡙⠇⠀⢠⠊⢀⡌⠀⠀⠀⠀⠀⠸⡀⡞⠀⠀⠀⠀⠈⠁⡏⠀⠀⠈⡆⠀⠀⠀⠈⠢⢌⠙⠲⠏⠉⢈⣀⠀⠀⣀
⠀⠀⠀⠀⡗⠢⡸⠣⡀⠀⣀⠟⣗⡇⡄⠀⡆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠠⡐⢄⠀⠀⣀⠀⠀⠱⠄⢠⠖⠀⡉⢑⣲⠄⠀⠀⠉⠊⢠⠆⡵⠲⡤⠒⠒⡍⠢⡀
⠀⠀⠀⠀⠘⢄⠣⠥⢎⡉⡉⡮⢚⠜⠀⠀⠘⣦⣈⠑⢄⠀⠀⠀⠀⠀⠀⠘⡌⠢⡀⠉⠀⠀⠀⠀⠈⢦⢠⠌⣉⣢⠀⠀⠀⠀⢀⢡⠒⠁⡠⠄⠦⣄⠉⠒⣷
⠀⠀⣀⠀⠀⠀⠑⠢⠤⠥⠯⠒⠩⠄⠀⠀⠀⠀⠉⠳⣄⢣⠀⠀⠀⠀⡠⠔⢁⡴⠃⠀⠀⠀⠀⠀⠀⠨⡼⠀⠉⠁⠀⠀⠀⠀⢸⢎⡀⠰⡀⠀⠀⢨⠀⢰⢸
⠀⢀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡉⠐⠒⢉⣠⡾⠋⠀⠀⣀⠤⡐⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢸⠀⠈⠒⠂⠁⣀⢜⠌
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢔⠒⢲⡆⠒⢄⠀⠀⠓⠀⠀⠈⠻⣶⡢⠛⠉⠀⣤⢀⡊⠀⠑⡻⠖⠚⠀⠀⠀⢀⡀⠀⠀⠀⠋⠀⠀⠀⠑⠭⣈⡓⣤⡊⠔⠋
⠀⠀⠀⠀⠀⡠⢖⡛⠄⠈⢲⠀⠀⠃⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠘⠋⠑⣶⠠⣤⠀⢤⣬⠥⠤⣤⡤⣤⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣠⢎⣣⠀⠐⡆⠀⠈⠀⢀⠄⡠⠂⠀⠀⠀⠀⠀⡠⣔⠚⠑⠒⠦⡀⠀⠀⠈⠑⠠⠄⠿⠤⠽⠤⠤⠽⠤⠀⠤⠥⠨⠧⠤⠃⠀⠀⠀⠀⣠⠄⠀⠀⠉
⠀⠀⠐⠀⠀⠘⠇⠀⠀⢀⡠⢔⡡⠚⠁⢀⡀⠀⠀⠀⢌⡴⠋⢠⡇⠘⢷⡌⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⢀⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⠻⡀
⠀⠀⠠⣀⠀⠀⢀⢒⡪⠅⠊⠁⠀⠀⠀⠈⠁⠀⡠⢄⠀⠀⠀⠀⠁⠀⠀⠀⡈⢢⠶⠀⠀⠀⢀⠔⠁⢀⣀⡀⣀⡈⠳⡄⠀⠀⠀⠁⠀⠀⡔⠁⠀⠘⡀
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠑⡆⠉⠓⠒⠊⠒⠒⠉⡹⠁⠀⠀⠀⠀⡎⠀⡔⠁⢀⠤⢄⡀⠀⠘⡄⠰⠆⠀⠀⡰⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⡤⠒⠒⠠⡊⠁⠀⠑⢎⠁⠈⡆⠀⠀⠈⠉⠀⠉⠁⠘⠈⠉⠀⠀⠀⠀⠀⠀⡇⠈⡀⠀⢇⠄⠀⡱⠀⠀⡇⠀⠀⠀⠸⡀⠀⠉⠀⠀⠀⣱
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⡀⠀⠀⠘⡤⠚⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠱⡀⠑⢄⣀⣀⠴⠁⠀⡜⠀⣀⠀⠀⠀⢩⠶⣔⢶⣲⠞⠁
⠀⠶⠀⠀⢈⠦⢀⠀⠀⠀⠀⠰⣀⡠⠞⠀⠀⢀⠔⡩⠰⠒⡐⡶⣕⢆⠀⠀⠀⠀⢀⡀⠀⠀⢠⢞⠦⠤⠀⠀⠤⠔⠊⠀⠀⠉⠀⠀⠀⢸⢲⡋⣹⢥⠆
⠀⠀⠀⠀⡆⠀⠀⠑⠢⢄⣀⠔⠁⠀⠀⠀⡐⡅⢺⠣⡀⢣⠱⡐⡘⡆⠆⠀⡤⠀⠈⠀⢀⠔⡱⠃⠀⢀⡀⠀⠀⢠⠔⣠⡄⠀⠀⠀⠀⠈⠉⣯⡝⢰⠀⢀⡀
⠀⠀⠀⠀⡱⢄⠀⠀⡠⠂⠀⠠⡄⠀⠀⢀⠀⠦⡀⢣⠱⡀⢣⠱⣁⡀⠐⠀⠀⠀⢀⡔⡡⠊⠀⠀⠰⡁⠈⡃⠀⢏⣩⠕⢂⠀⠀⠀⠀⠀⡧⢦⢼⡎⠀⠈⠁
⠀⠀⠀⠀⢇⣀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⢆⡘⢄⢣⠑⡌⠆⣸⢃⠃⠀⠀⠠⢊⠜⠀⠀⠀⠀⠀⠉⠉⠉⠒⢄⡀⠀⠉⠀⠀⠀⠀⠀⢰⡵⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠈⠢⢌⠒⠷⠧⠜⢋⡥⠋⠀⠀⠀⠓⠁⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠁⠰⠆
⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠃⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢀⠲⡄⠀⠀⡠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⠢⡜⢱⠀⠣⠤⠧⣤⠎⠙⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⣧⠈⢧⠀⠀⡴⠙⢄⣀⡎⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢫⢣⡀⠑⢌⡲⢤⣀⡼⠀⠀⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠳⣝⠢⢄⣉⠑⠚⢒⣚⡩⠥⢺⡤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣀⣠⣀⠀⠀⠀⠀⠉⠒⠂⠬⠝⠓⠚⠉⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⢤⣀⠀⠀⠀⠀⡇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠼⠶⠠⠤⡀⠀⠀⠀⠑⠐⠷⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⡇⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠈⠳⠀⠀⣀⠄⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⡼⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡠⢾⠀⡰⠃
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡷⡖⡏⠀⢸⠀⡧⣂⠢⣄
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⣇⠀⢸⠀⠳⠽⠃⠈⡆
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠉⠒⠚⠀⠀⠘⡆⠈⢧⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠵⢖⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠲⠤⠄⠀⠀⠀⢸⠤⢄⣀⣋⣻⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⣠⡃⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡦⠤⠤⠖⠚⡗⠒⢶⠒⠋⠀⠐⢲⡏⠣⣌⡉⠓⠚⠉⢉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⡸⠁⠀⢸⡀⠀⠀⢀⡜⠙⢦⣀⠈⠉⠉⣉⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠙⠲⠖⠋⠀⠀⠀⠈⠉⠛⠉⠁

⠀⠀⢔⡬⠑⢠⡾⠿⣶⣀⣿⠀⠀⢠⡾⠿⣦⣰⣿⠿⣶⣰⡷⣼⣦⠀⣸⣇⢔⠤⢕⠀⠀⠀⣾⡟⣷⡄⣴⡿⠿⣦⢠⣾⠿⣷⡄⣿⣠⣾⠇
⠀⠸⢘⠀⠀⣸⡿⠆⣸⣿⣿⠀⠀⣿⡷⠆⣹⣿⣿⣤⣿⢻⣟⢻⣿⣷⣿⢹⢸⠦⢌⠆⠀⠀⣿⠷⢿⣧⣿⡷⠀⣿⣿⣿⠆⣸⡿⣿⣿⣁
⠀⠀⠪⠲⠬⠙⠿⠶⠟⠁⠿⠿⠛⠙⠷⠶⠟⠘⠿⠻⠷⠘⡿⠸⡇⠹⠇⠀⠢⠑⠫⠂⠀⠀⠿⣷⡾⠋⠹⠷⠾⠋⠘⠿⠶⠟⠁⠿⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠙⢦⣀⣀⣀⣀⡴⠋⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢠⠏⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠱⡄⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⢟⡾⢯⡝⠛⠛⠛⠛⠛⠛⢻⡽⢿⡻⣴⣾⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠸⠋⠉⠳⣀⣀⣀⣀⠜⠉⠙⠇⢹⢸⢸⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡹⣄⣠⠤⣺⠷⢿⡿⠾⣗⠤⣄⣠⢎⣾⠏⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡉⠙⠉⠉⠁⢰⣿⣛⣒⣚⣛⣛⣛⣋⡥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⡀⠀⠀⠙⠉⠀⠈⢉⣩⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⡀⠉⠉⠛⠓⠚⠛⠉⠉⢀⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢀⣠⠤⠶⠗⠒⠒⠒⠒⠒⠒⠒⠒⠺⠶⠤⣄⡀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠒⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠒⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⡼⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⢧⣀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⠉⠉⢹⠋⠙⡏⠉⠉⢉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⠀⠀⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠳⠶⠞⣹⠀⠀⣯⠳⠶⠞⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⡰⢻⠀⠀⡟⢦⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⠓⠋⠀⢸⠀⠀⡇⠀⠙⠚⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠲⣄⡤⠤⣼⡀⢀⣧⠤⢤⣠⠖⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠄⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣾⣿⡿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣘⣭⣭⣭⣭⣭⣷⢟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠻⢭⣉⣿⣏⣿⣧⣽⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⡿⠿⢿⣟⠛⠯⣑⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣾⣷⣶⣶⣾⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡍⢛⣛⣛⣻⣿⣻⣿⣯⣭⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠸⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡹⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣾⣿⣝⣚⣛⣽⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡨⣦⣭⣽⣿⣿⣿⣿⣿⣿⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣤⡀⠀⠀⣄⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣦⠀⢹⣷⣄⠀⣿⣿⣿⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⡈⢻⣿⣿⣿⡆⣾⣿⣿⣴⣿⣿⡏⠀⢀⣾⡇⠀⠀⣠⣾⣿⠋⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⡿⠀⣀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠙⢿⣶⣶⣾⣿⣶⣤⣀⠀⠹⣿⣿⣿⢿⣫⣽⣶⣶⣶⣾⣭⣟⠿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⢿⣿⣿⣷⣾⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢿⣿⡿⠟⠉⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣭⣿⣿⣏⣾⣿⣭⣥⣭⣝⣿⣿⡿⠿⠻⠿⣿⣧⢻⣿⣿⣷⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠿⠿⠿⣿⣿⣿⢹⣿⣿⣿⣟⣧⣿⣿⣿⣾⣿⣿⣻⣾⣿⡟⣿⣿⣛⣉⣀⣀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣯⡉⠉⠙⠛⠛⠋
⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠟⠉⢁⣴⣾⣿⣿⣯⡻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⣾⡿⠟⠛⢋⣿⣿⣶⣽⣛⣿⠿⠿⣿⣛⣭⣾⣿⣿⣿⣿⡛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⣠⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢿⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠃⢸⣿⣿⠏⣿⣿⣿⠏⢿⣿⡆⠀⠀⠻⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠸⣿⠃⠀⣿⣿⣿⡄⠀⠉⠛⠶⠄⠀⠀⠀⠀⠉⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠹⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏

⠀⠀⠀⠀⠀⢀⢀⣀
⠀⠀⠀⢀⠔⠁⢀⡸⠉⠒⢄⠀⠐⠗
⠀⠀⠀⢎⠄⠚⠉⢀⡀⠤⠚⠆⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⢠⠚⠛⢢
⠀⠀⠀⣧⠔⠒⠋⠁⠀⠀⣀⡔⢾⡏⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⢈⠟⠚⠑⠒⣉⠦⡀
⠀⠀⠀⠈⠦⣤⠄⣒⠊⠩⢀⢱⣀⣹⣆⡀⠀⠀⡄⠀⠀⠄⠀⡠⠚⠀⠉⠉⠉⠀⠀⢹⡀⠘⠃
⠀⠀⠀⠀⡐⢩⣆⠀⢰⠶⠋⡥⠤⠤⠒⢌⣉⡒⢄⠀⠈⠀⠠⠋⠉⠉⠉⠐⠒⠒⠒⠋⢹⣌⣉⠲⣄
⠀⠀⠀⠀⡇⣿⡇⣷⢋⠔⢊⠀⠲⠀⠐⠂⠀⠡⣀⢱⠀⠀⢰⠒⠊⠙⠋⠑⠊⠑⠛⠖⣞⡛⢿⣷⠈⡆
⠀⠀⠀⠀⢃⠹⣷⡇⡜⠀⠀⠀⢈⣒⡊⠀⠀⠀⢨⡀⡇⠀⢸⠀⠀⠀⠃⠀⠐⠃⡤⠞⣣⠼⠼⢿⣃⠇
⠀⠀⠀⠀⣀⠑⢬⡇⡱⠀⠀⠀⢪⣀⡱⣀⣀⣀⠰⠥⠷⠤⠾⢄⣄⣀⡒⠤⠔⠀⠺⣴⠁⠘⠃⢀⠙⡄
⠀⠀⠀⠈⠛⠃⠀⢣⠘⡆⠀⠂⠀⡜⢩⣄⣦⣴⣿⣿⣿⣿⣿⣶⣶⣦⡌⠙⡤⢒⣐⡣⡧⣌⠒⠈⢀⠏⢹
⠀⠀⠀⠀⢰⢒⠉⣻⠉⠛⣧⠤⣀⡏⠒⠊⠭⠿⠻⠿⠿⠿⠿⠛⠯⠍⠒⠉⡟⣁⡎⢘⢸⠀⣉⡊⠉⠢⠋
⠀⠀⠀⠀⡧⠠⠊⠀⠰⠀⠘⡖⠂⠻⡀⠀⠀⢠⣦⠀⠀⠀⠀⣤⠀⠀⠀⢠⠁⠁⣀⠎⡜⠀⠙⠋
⠀⠀⠀⠀⢣⡀⠀⠂⠀⡠⠀⢸⠀⠀⠳⡀⠀⠀⠠⣄⠀⢀⡠⠀⠀⠀⢠⠏⠭⠭⠔⠊
⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠴⠃⠀⠀⠀⠈⠲⢤⣀⡀⠀⠀⢀⣀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣰⢿⣿⣦⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⣄⣁⣀⣀⣵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡥⠊⡡⠃⢨⠙⡝⠢⡈⢢⠀⠀⠀⠀⠀⠀⠀⢠⠁⡀⠀⠁⠉⠈⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡝⢱⠤⡄⠀⠀⠀⠀⢇⢸⠀⢠⠃⠀⢸⠀⢸⠀⠑⣜⠀⠀⠀⠀⠀⠀⠀⡸⠙⠓⠞⠦⠶⠒⢒⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠒⢷⣵⡡⣊⡩⠆⠀⠀⢠⠊⠙⠖⠊⠁⠒⠲⠒⠋⠉⢉⣉⣧⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠃⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠋⢰⡄⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⠉⠀⠲⠖⠒⠒⠒⠒⠂⠩⠅⠀⡆⠀⠀⠀⠀⠀⢳⠘⠛⢿⠗⠛⠛⢻⡛⠛⢹⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠲⠂⡸⠀⠀⠀⠀⠀⠈⡆⠀⢠⣤⠀⠀⠀⠀⠠⣦⠀⢰⠁⠀⠀⠀⠀⠀⠀⢧⠀⠈⠁⠀⠀⠈⠁⢀⠇
⠀⠀⠀⠀⠀⢀⡠⢚⢦⣀⠀⡀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠒⠊⠁⠀⠀⣤⠒⢦⡀
⠀⠀⠀⠀⠀⠈⠲⢵⣡⢿⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠑⠤⠤⠤⠀⠠⠤⠤⠔⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣜⠀⠈⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠒⢤⣴⣿⣷⠀⠀⠀⡼⠀⢡⡀⠀⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀⣀⢸⠿⠛⠉⠀⠀⢰⡃⠀⠈⢡⠄⠙⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠤⢴⠓⡌⣥⠤⠒⢦⠀⠀⠀⠀⠀⠀⡰⠊⠁⠀⠀⠉⠢⠀⠀⠀⠀⠈⠚⠯⠷⢒⣒⠦⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠰⡉⠉⣉⠉⢲⡀⠀⠀⠀⠀⠀⠀⠸⣈⡦⠼⠒⠉⠀⠀⢀⡨⢆⠀⠀⠀⠀⢸⣀⡀⠙⠃⠠⡄⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣉⣀⣀⡈⣣⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⣀⠠⠀⠉⠀⠀⠀⣁⠀⠀⠀⢸⡅⢳⡼⢇⣰⢀⡠⠁⠀⠀⠀⢀⠤⡖⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠤⠤⢄⣙⡄⠂⠀⠀⠀⠀⠀⢖⠊⠉⠀⠀⢠⣀⣠⠄⠚⠙⡀⠀⠀⣾⠶⣉⡱⣈⠟⠈⠀⠀⠀⠀⣰⠅⣀⣸⡋⢉⠓⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠤⠠⢬⡇⠀⠀⠀⠀⠀⠀⠸⣄⡀⠤⠒⠊⠁⠀⢀⣀⠤⠃⠀⢀⣧⡔⢫⣤⠋⠀⠀⠀⠀⠀⢠⣁⡀⢼⠁⢹⣩⠵⡋⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠀⠀⢀⣀⣀⠀⠀⠀⠘⢄⡀⣠⠤⠐⠊⠁⠀⠀⠀⠀⣸⣧⢻⡝⠁⠀⠀⠀⠀⠀⠀⠘⡁⡠⢚⠳⢇⣨⢶⠉⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠁⢈⡱⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅⡈⠁⠄⠙⢀⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠶⠈⡳⢸⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠈⢠⢈⣧⠞⠉⠙⠚⠛⠷⠶⢶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⡆⠀⠀⠀⠀⠀⠀⠑⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢆⠝⠋⠙⢖⠢⣀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⠅⠀⠀⠀⠀⠀⠀⠡⠉⣷⡀
⠀⠀⠀⠀⠂⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⡀⠀⣾⡟⠀⠀⠴⠋⢹⣆⠀⠀⢠⡇⠀⠀⠚⢂⡠⠶⢄⠘⠂⠀⠘⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⣰⣿⠃⠀⠀⣠⡄⠀⣀⠀⠀⣀⡄⠉⢻⣿⠧⠤⠤⠤⠤⠞⠁⠀⠀⢸⡁⠀⠀⠀⡈⠀⠀⠀⢱⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⢀⣿⡏⠀⠀⠘⢿⡇⣴⠏⠀⣼⡏⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠦⠀⠀⠈⠦⢤⠤⠊⠀⠀⠀⣿
⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⣿⣧⢸⣿⠁⢰⣶⠀⡌⣸⡿⠀⢸⣿⠁⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠙⠦⣤⣄⣀⣤⣴⣿⠇⠸⣿⣤⠼⢿⡶⠁⢻⡇⠠⠸⣇⠀⠔⢹⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠋⠷⣄⣤⡤⠤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⣠⠀⣿⣿⣿⣦⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⢀⠈⡇⠀⠀⠀⠀⣿⡀⢘⣿⣿⣿⡃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⡿⠿⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡑⠄⣁⡀⢠⠟⠃⠈⠀⠌⢹⣧⠄⣌⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀⣉⠈⣄⣀⣴⢫⣭⣭⢟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠈⠁⡖⠉⠌⠻⢈⣀⡁⡠⠀⠛⢿⣬⣿⣿⣿⣷⣾⣷⢶⣷⣶⡾⣷⣿⡿⠁⢈⣬⠀⠈⣿⣬⣿⣿⢾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠐⠄⠀⠀⠄⠻⣷⡇⠄⢘⣿⣿⣷⣀⠛⠘⢿⣿⣿⣿⣿⡟⠡⢬⣿⣿⣇⡤⠙⣿⣶⣿⣿⡿⠶⠿⠿⠟⣫⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⡀⠀⠀⣼⣄⢨⠈⣿⡿⣟⡉⢶⣽⣿⣝⣿⣿⡟⠀⠂⠤⢸⡟⠠⠒⠄⢸⡟⣻⣦⠷⠿⣛⡛⢻⣿⠟⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⠷⠀⠀⠻⢿⣦⣴⣿⣟⡿⠁⣼⢿⡟⠁⠀⣻⣧⠈⠄⢢⠘⡇⠤⠀⡀⢠⣿⣙⡵⣿⡟⢩⣧⢜⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣥⡞⠉⢻⡟⠌⠀⠛⣿⣦⣀⣀⠀⠁⣀⣀⣤⢪⣿⣿⣉⣼⡿⣿⣽⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠘⣰⣿⣿⣿⣯⣿⢁⣰⠚⠓⠦⣤⣤⣾⣏⠉⠉⠤⠔⠉⠉⣹⣶⣿⣥⣍⣀⣶⣿⣿⣿⣿⣿⣿⣿⣉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⣻⠛⠡⢽⣿⣿⣿⠀⠀⠀⢛⠛⠍⠛⡷⠂⠒⡚⠁⠿⠛⠋⠛⣛⣿⣿⢿⡷⢿⡏⣿⠿⣿⣿⣭⣤⠂
⠀⠀⠀⠀⠀⠀⠐⡠⠄⠀⠀⠀⠃⢀⠀⣠⠀⡀⠀⣴⠌⢐⠊⣻⣿⣿⠷⠄⠀⠘⠣⣄⡀⠓⠀⠸⡷⠀⠃⢀⡀⠘⠁⠈⠓⢛⣿⣿⣿⣿⣿⣿⣿⣯⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢈⢶⡐⣆⠈⠀⢀⣀⡬⣤⢤⡄⠙⢧⡘⢛⣿⠇⡋⠀⢇⠻⢢⡀⠈⢿⣷⠂⠀⠀⠀⢻⡏⠀⠀⠶⠆⡋⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠐⡧⢬⡶⣸⣷⣶⠏⣽⣇⡀⣠⡽⠐⠾⡇⠈⣁⠀⢳⡄⠈⠑⠊⠁⡀⠸⠛⠛⣧⣠⡟⠛⠃⣀⠛⠀⠊⠀⣰⠇⠈⠙⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣾⣴⠟⠛⣿⢂⡉⣁⣩⣭⣀⣀⣹⣦⠐⠈⠀⠀⠙⢦⣤⣤⣴⣦⡄⡁⠚⠁⠟⠙⠂⠃⣾⣤⣤⣤⡴⠋⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣟⠓
⠀⠀⠀⢀⡠⠐⢐⣃⡹⠋⠴⢂⠃⣬⣟⣿⣿⣿⣿⣿⡿⠇⠀⠛⠀⠆⠀⠀⢀⣿⠛⠂⠛⠐⣋⡅⠀⣍⡓⡰⠌⠻⣯⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣭⣀⡄
⠀⠀⠀⠉⠂⢀⣠⠖⢉⠀⠠⢼⠄⠈⣿⠛⡉⢹⣿⠫⠂⠳⠀⠀⠀⠀⠀⠀⢸⠏⠉⠑⢆⠀⠀⠤⢠⠄⠚⡴⠊⠉⠙⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠀⠀⡈⠀⠆⠘⠃⠄⢠⠀⠀⣿⠿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⣀⣀⠀⠊⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠉⠶⠁⠰⢾⡏⠀⠀⠀⣴⣤⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢸⡿⢿⣶⣾⠿⣷⠀⠀⠀⣀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠲⠮⠤⠞⠈⠀⠀⣾⣿⠟⠂⠀⠀⠀⠀⠀⠀⢸⣆⡀⠀⠛⠰⢿⠿⠐⠋⠀⢀⣼⠇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠄⢁⠀⠀⠈⠀⡐⠒⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢈⡐⢀⠀⠘⣧⡆⠴⠶⠚⠳⠶⠤⢠⡼⠃⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣧⡤
⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⣠⠊⠁⠀⢀⡀⠀⠈⡀⠀⠀⠀⠀⢀⣴⣯⠀⠈⠀⠀⠈⡇⣴⠞⠓⠛⠳⣦⢸⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣭⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡄⠂⠀⠁⠀⠰⠀⣰⣤⣠⣴⣿⣵⣿⣆⢐⠀⠀⠀⠹⣏⠘⠓⢖⡛⢸⡟⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢃⣿⣿⣿⣿⣿⣿⣿⠋⠻⣆⠀⠀⠉⠛⠿⠿⠟⠃⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡈⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡞⢻⣿⣿⣿⡏⠁⠀⠀⠀⣀⠀⠀⠀⣠⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡝⢧⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⡿⠋⠀⠀⠀⡀⢀⣽⣃⠙⡀⠀⠀⠈⣿⣿⣿⣿⣿⡿⣿⡎⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢠⡀⢿⡞⠋⠰⠁⠀⠀⢸⣿⣿⣿⣿⡌⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⠉⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⣿⣿⠿⣿⡿⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⢹⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⠒⠒⠂⠀⠐⠒⠠⠤⢄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢹⠆
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡀⠀⠒⠒⢤⡀⠀⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡼
⠀⠀⠀⠀⠀⠰⡄⠆⠀⠀⠀⠰⡆⠀⠀⢀⣀⢉⢲⣄⣄⢀⣀⣠⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢰⠃
⠀⠀⠀⠀⠀⢀⠇⠨⠧⠦⠆⠦⠽⠶⠤⠤⠰⠒⢳⣳⣋⡭⠶⠷⢿⠛⠿⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡜
⠀⠀⠀⠀⢰⣅⡰⢀⢠⣀⠴⢬⣀⢀⣠⢀⡴⠖⠉⠈⣃⠀⡀⡄⠈⡆⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣸⠁
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠱⠚⠓⠊⠉⠓⢳⢹⣔⣃⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⡇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡼
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢰⠃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⣠⠶⠒⠒⠛⠶⢦⣀⡋
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡴⠛⠂⠉⠒⠀⠤⡀⠈⠑⢆
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣸⡅⠤⣠⣤⡀⠀⠀⠀⠐⠢⣈⡇
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⣼⣁⡀⠀⠀⠀⠀⠉⠙⠢⣀⢀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⢀⡟⠉⠉⠉⠑⠒⠂⢤⡀⠀⠀⠹⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠶⠴⠶⠒⠐⠋⠁⠀⠀⠀⠀⠀⠀⢸⣀⣀⣤⣤⣀⠀⠀⠀⠈⠒⢴⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⠀⠀⠀⠀⠉⠒⠤⡂⠄⢈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠈⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠠⠄⣀⣤⣈⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠳⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠐⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢤⠂⠁⠠⠀⠐⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢑⠆⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠑⢦⠀⠀⡀⠀⠈⢀⠀⠰⡆⠁⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⠤⠚⠃⠀⠀⠁⠀⡃⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡞⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⠀⡇⢀⠀⠀⠀⠉⠛⠛⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⠛⠉⠉⠉⠉⠙⠀⠀⠏⠀⢀⡤⠔⠀⣀⣀⣀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠉⡡⠴⠊⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢷⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⠴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢤⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠈⠙⠳⢦⣾⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⣛⡙⠁⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⣠⠞⠁⠠⠒⠉⠁⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⣿⠟⠁
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢶⡶⠤⠶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⢤⡀⠀⠘⠀⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠁⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⠚⢁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡾⠁


⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠱⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⣧⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣴⢯⣉⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠛⣦⡼⠟⠛⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠳⠶⢿⠁⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠳⠦⠤⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⣴⠎⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣱⣾⡄⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⢿⣯⡼⠛⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠘⣃⡀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡿⣶⡛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⡾⣿⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠈⢧⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢉⣿⣾⠟⠣⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠟⠷⠟⠈⢇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢀⣠⠴⠖⠛⣛⣛⣛⣋⣉⣉⣉⣉⣍⠩⠭⠭⠽⠯⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠥⠤⠤⠤⠴⠶⠶⠶⠶⠶⢶⣟⣛⡳⢶⣤⡀
⢠⡞⢻⡷⠖⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡿⠉⠙⡆
⢻⡄⠈⠳⢦⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣤⣤⡤⠴⠶⠞⠋⠁⠀⠀⠀⢹
⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠲⣄⠀⠀⢀⡤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⢠⡇⠀⠀⠀⠀⣠⠛⢳⡀⠀⣸⠀⠀⢧⣀⣠⠟⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢶⡄⠀⠀⠀⢰⠋⠉⢻
⢸⡇⠀⠀⠀⠀⣿⠆⠈⠳⠞⠃⠀⠀⠈⠉⠁⠀⠀⠀⢨⡇⠀⠀⠀⣠⠞⠋⠛⠳⣄⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⣿⠀⠀⠀⢀⡄⢀⡼
⣾⠀⠀⠀⠀⢸⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢠⡇⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⢸⠇⠀⠀⣀⣹⣦⣤⡴⠾⠛⢻
⡿⠀⠀⠀⠀⣿⠿⠦⠤⣤⠤⠤⠤⠶⠶⠶⠶⠶⠖⠂⣾⠀⠀⠀⠘⡷⠒⠒⠲⠖⠛⠷⢶⡄⠀⠀⣿⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡆
⠱⣄⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⣿⡿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢹⠀⠀⠀⠀⠀⣀⣀⣤⠴⡇
⠀⢹⠶⣮⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⠤⠤⠤⠤⢾⡀⠀⠀⠀⣸⠓⠚⠛⠛⠉⠉⠁⠀⠀⢸
⢀⡟⣁⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠁⠈⠁⣈⡉⠉⠉⡁⠀⢠⡀⢀⣀⡀⢀⡀⠛⣷⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⣿⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⡆⠀⡟⠉⢹⠀⠘⡛⠳⣼⣇⢸⡦⠀⠀⠙⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡶⠁
⠀⠈⢳⣾⣥⣀⣀⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠛⠀⠙⠶⠞⠀⠀⠁⠀⠈⠋⠈⢉⣉⣀⡀⣥⣤⣤⣤⣤⠤⠄⠶⠶⠒⠉⠉⠀⠀⡇
⠀⠀⡿⠂⠀⠈⠉⠉⠉⠛⠋⠙⠛⠛⠒⠋⠘⠀⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠰⣟⡡⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁
⠀⠀⠈⠙⣿⢤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠤⠤⠤⠤⠤⠄⠒⠛⠋⠉⠹⡆
⠀⠀⠀⠸⣧⠀⠈⠉⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠀⠈⠉⠉⠉⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠸⣧⠔⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠃
⠀⠀⠀⠀⠀⠈⢹⡷⢦⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⠤⠶⠶⠶⠖⠊⠉⠉⠸⠁
⠀⠀⠀⠀⠀⠀⠘⣶⡠⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣋⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠒⠒⠚⠛⠛⠙⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡤⢂⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⡟⣩⣉⣐⣀⡜⣁⠀⣠⣀⡜⣠⠆⣠⠆⣤⣤⣼⣷⠷⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢳⡀⠀⠀⠀⠀⢠⠏⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠲⡄⠀⠀⠀⠀⠀⢸⡀⠀⣧⠀⠀⠀⠀⢸⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠹⡄⠀⠀⠀⠀⠈⣇⠀⡟⠀⠀⠀⠀⣿⢀⡞⠀⠀⠀⠀⠀⢀⡴⠚⠉⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢤⡀⠀⠀⠀⠱⣄⠀⢳⡀⠀⠀⠀⠀⠸⣀⡇⠀⠀⠀⠀⢹⡞⠀⠀⠀⠀⢀⡴⠋⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⢆⠀⠀⠀⠈⢦⡀⢇⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⣴⣫⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⢧⡀⠀⠀⠀⠙⠾⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⣳⡀⠀⠀⠀⢀⡠⠖⠋⠉⠁⠀⠀⠀⠉⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⣠⠖⠉⣀⣀⡤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⢀⡴⠒⠒⠒⠒⠲⠤⢤⣀⡀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⣤⡖⠒⠒⠓⠒⠚⠓⠲⡄
⠀⠀⠀⠀⠀⠈⠓⠲⠶⠶⠒⠒⠒⠋⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠉⠙⠒⠲⠶⠤⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡄⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠠⣶⠶⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠀⣀⠴⠋⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠉⢲
⠀⠀⠀⠀⠀⠀⠀⠘⠲⠶⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠲⠶⠶⠶⠖⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣰⠃⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⡶⡀⠀⠀⠀⠀⠀⢧⠀⠈⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡴⠁⠀⠀⠀⢠⠏⢸⠀⠀⠀⠀⢸⠃⠙⡄⠀⠀⠀⠀⠈⢳⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⣠⠞⠀⠀⠀⠀⢀⡎⠀⢸⠀⠀⠀⠀⢸⠀⠀⢹⡄⠀⠀⠀⠀⠀⠙⠦⣤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠁⠀⠀⠀⠀⠀⣼⠀⠀⡞⠀⠀⠀⠀⢸⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡼⠁⠀⠀⠀⠀⠀⢧⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠁⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⢂⠭⢪⠋⡛⡆⢌⠢⠀⠀⠀⠀⠀⠀⠐⠉⠙⠙⠙⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠉⠖⣀⠀⠀⠀⢄⡈⠀⡃⠀⡇⢘⡀⣣⡀⠀⠀⠀⠀⠀⠛⠓⠒⠖⡒⠊⠑⠄
⠀⠀⠀⠀⠀⠀⡠⢊⠁⠙⠳⡬⠐⠁⠀⢰⠥⠉⣁⣀⣉⣉⠀⠤⠄⢺⠀⠀⠀⠀⣔⣤⣄⣄⣄⣤⣤⡴⡧
⠀⠀⠀⠀⠀⠰⠀⠈⠀⠠⠄⡄⠀⠀⠀⠀⡄⠀⣀⠀⠀⠀⢀⣄⠀⡄⠀⠀⠀⠀⠱⡀⠘⠀⠀⠐⠂⢠⠁
⠀⠀⠀⠀⡠⢘⣦⣀⡀⡠⠜⠀⠀⠀⠀⠀⠰⠀⠈⠀⠀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠐⠂⠁⠀⡤⠒⠄
⠀⠀⠀⠀⠈⠓⢴⣯⠀⠀⠀⠀⠀⠀⠀⠰⡀⠁⠂⠀⠀⠐⠒⠈⠁⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⠀⠀⠀⡜⠁⢀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡢⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢹⡿⠟⠃⠀⠰⠁⠘⣆⠰⠈
⠀⠀⠀⠀⠀⠀⠀⡒⠢⣈⠀⠀⠀⠀⠀⠀⠠⠧⢤⠺⣑⠤⠐⢄⠀⠀⠀⠀⠠⠚⡉⠉⠙⢄⠀⠀⠀⠙⠲⠧⠶⠤⠟⠃
⠀⠀⠀⠀⠀⠀⠘⡅⠥⠭⢥⠀⠀⠀⠀⠀⡰⠜⠒⠉⠁⣀⠠⠘⢦⠀⠀⠀⡧⡄⣉⠀⠂⢠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠱⡒⠒⠒⠇⠀⠀⠀⠀⠐⡄⠄⠂⠉⠀⠀⡀⠴⡃⠀⠀⣫⠝⣍⢾⠕⠁⠀⠀⢠⠊⢑⠬⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡤⠬⣹⠀⠀⠀⠀⠀⢇⣀⠠⠐⠋⠁⢀⡠⠔⠀⣸⡤⢛⡽⠁⠀⠀⠀⢀⣁⠈⡏⢱⡻⢖⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡠⠤⢄⠀⠀⠣⠤⠄⠂⠉⠀⠀⠀⠀⡿⣞⠏⠀⠀⠀⠀⠀⠈⣅⠔⡑⠣⡔⢎⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡀⢎⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡻⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⣀⣪⠜⠓⠒⠦⠤⣤⢤⣀⣀⡀
⠀⠀⠀⠀⠀⣠⡶⢲⠄⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⠉⠀⠀⠀⠀⠀⢀⡤⠖⠝⠋⠙⠖⢤⡀
⠀⠀⠀⠀⠀⢻⣧⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⢰⡿⠀⢀⡤⣄⠀⠀⢠⠟⠁⣠⠀⣀⠀⣠⠀⢹⡄
⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⣰⡆⠀⢀⡀⠀⡀⠀⢈⡑⠲⣿⣇⣀⣈⣠⠞⠀⠀⢸⠀⠀⠀⠊⠀⠁⡄⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⢸⣿⠀⠀⠘⠆⣴⠃⢰⡟⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠘⡑⠀⠀⠑⠄⠔⠁⠀⢠⡏
⠀⠀⠀⢎⡀⠀⠀⠀⣸⡗⢸⡇⢸⣿⡰⢸⡏⠀⣿⠁⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁⠈⠛⠁⠉⠁⠈⠃⠀⠉⠂⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠖⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⣰⠲⡄⠀⠀⠀⠀⠀⠀⠀⢀⣞⡅⠀⠀⠀⠀⠀⠀⠀⡴⠂⠒⢦
⠀⠀⠀⠀⠀⠀⢮⣀⣄⣄⡼⠀⠀⠀⠀⠀⠀⡰⠣⠭⢽⡀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠦⡀⠀⠀⠀⠀⢀⠷⠔⠒⢺⡄
⠀⠀⠀⠀⠀⠀⠈⢟⠢⡱⠁⠀⠀⠀⠀⠀⠀⣗⢒⠒⢒⡇⠀⠀⠀⠀⠪⣀⢤⣀⡠⣀⡼⠀⠀⠀⠀⠸⡀⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠃⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⢸⠁⠀⠀⠀⠀⠀⠸⣴⣤⣦⠇⠀⠀⠀⠀⠀⠀⠈⢹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⢠⢾⣱⠦⡀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠢⡀⠀⠀⠀⠀⢀⡠⠚⣧⣼⣦⠀⠀⠀⠀⠀⡰⠁⠉⠉⡖⠁⠀⠀⠀⠀⠀⡴⠷⠞⢄
⠀⠀⠀⠀⢰⣫⢤⣀⠤⣄⡠⢌⣲⠀⠀⠀⣏⣩⣭⣤⣤⣤⡇⠀⠀⠀⠀⠳⡒⠒⢲⠞⠀⠀⠀⠀⢀⣠⣏⣙⣉⣹⣄⡀
⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠊⠀⠀⠀⠀⠯⠭⠭⠭⠤⠴⠃⠀⠀⠀⠀⠀⢹⢻⠏⠀⠀⠀⠀⠀⠈⠑⠒⣢⣖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠽⠦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⠤⠶⠭⡉⠑⣄⠀⠀⠀⠀⢰⠣⢢⢔⢮⢣⠀⠀⠀⠀⠀⡔⠉⠀⠈⠱⡄⠀⠀⠀⠀⢸⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⡏⡞⡉⠳⡈⡆⢸⠀⠀⠀⠀⠸⡰⣐⣾⣮⡾⠀⠀⠀⠀⢰⠳⡖⢶⢲⡖⣷⠀⠀⠀⠀⢸⣿⣿⡛⢻⡇
⠀⠀⠀⠀⠀⠱⣱⢌⣒⣁⠷⠊⠀⠀⠀⠀⠀⠉⢲⣿⠃⠀⠀⠀⠀⠀⠈⣇⣧⢸⢸⢧⡏⠀⠀⠀⠀⢸⠋⠛⠻⠿⣯
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡔⠋⠀⢙⠲⡀⠀⠀⠀⠀⠀⠀⢀⣠⡓⢤⠀⠀⠀⠀⠀⠀⡞⡁⡙⡆⠀⠀⠀⠀⠀⠀⣀⣄⣤⣀
⠀⠀⠀⠀⠀⡜⠡⠆⠀⠈⠀⢳⠀⠀⠀⠀⠀⡴⡏⢣⠈⡞⠁⠀⠀⠀⠀⡖⠚⠈⠘⠒⡆⠀⠀⠀⣰⡎⢱⡀⢀⠎⢑⡆
⠀⠀⠀⠀⠀⢸⣀⠀⠀⠙⢀⠎⠀⠀⠀⠐⣮⠣⣸⡤⠋⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢏⠀⠀⠀⠀⠙⢌⡏⠙⠋⢹⣡⠃
⠀⠀⠀⠀⠀⠀⠈⠙⣾⠉⠁⠀⠀⠀⠀⠀⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠋⠳⠬⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠜⠁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠔⠢⡀⠀⢀⠔⠉⠀⠀⠀⠉⠢⠤⠊⠉⠒⠨⠕⠢⡀
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠇⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠉⠘⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢠⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⡆⡇
⠀⠀⠀⠀⠀⠀⠸⡸⡀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠑⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢎⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠔⠊⠁⠀⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠋⠑⠒⡄⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡒⠤⠤⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⠜⠀⠀⣆⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠂⠉⠀⠈⠑⠂⠤⠐⠂⠁⠀⠀⠀⠈




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⠶⡠⡟⠁⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⣏⣻⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⠓⢰⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢹⡤⠄⢀⠀⠀⢲⠖⣽⡃⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣬⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢻⣤⡶⠤⠄⠀⡀⢸⣿⣧⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡿⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⢤⠃⠀⠀⠀⠜⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⣰⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠖⠀⠀⠊⠀⠀⠠⡀⢀⠠⣀⡀
⠀⠀⠀⢀⣀⣰⠀⠠⠀⠀⠺⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⣫⣼⠛⠯⠀⠀⢀⠠⠛⠡⢀⣾⡇⠈⢢⡀⠀⠀⠀⢤
⠀⠀⠀⠘⡿⠋⠴⠀⠈⠢⠐⣾⡄⠼⣴⣆⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠁⠚⠀⠀⠔⠁⠀⠀⠀⣸⣿⣇⠀⠀⠇⠀⠀⢈⣀⢱⡀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⡈⡗⢀⠃⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠈⡉⡇⢀⠔⠃⠀⠠⡀⠀⠀⠹⣿⣿⣶⣤⠂⠀⠀⠈⢛⠿⣿⡗⠈⠁
⠀⠀⠀⠀⠀⠀⢠⡈⢱⡄⠈⠻⠇⠈⠀⠀⠀⠀⣶⢠⠀⠀⠀⠈⠁⠀⠀⣵⡄⠀⠃⠀⠀⠈⣄⠀⠀⠀⠉⠉⠀⠀⠀⠂⢤⣤⡑⡿⠁
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⣶⢀⠔⠈⠀⠠⣹⡆⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⢀⣘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠱⡟⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡷⠁⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠐⢀⠆⠀⠀⠀⠀⣴⣿⠁⠙⢦⠀⠀⠀⠀⢀⠀⠀⣤⣐⢻⣁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⢰⣶⣿⡆⠀⢈⡇⠀⠀⠀⠀⠈⠀⠙⢛⠏⠁⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡜⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠻⡛⠂⣾⡷⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⠀⠀⠀⠀⣀⣴⣴⠁⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠟⢻⡤⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⣓⠺
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢸⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣁⡀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠈⠀⠀⡄⠀⠀⠚⠋⠉⠀⠀⠉⠉⠛⠛⠓⠒⠲⡾⢯⣹⠿⠓⠻⠷⠶⠦⢤⡤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠁⠀⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠠⢄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⡙⣿⣉⡛⣻⡛⣻⣟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⣀⠀⠀⣸⣿⠀⠀⡀⠀⠀⠀⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠸⣿⣇⠀⢿⣤⡄⣿⣿⠀⢰⣇⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠈⢳⣔⣦⣿⣿⣦⣼⣿⣿⣿⣿⣦⣿⣿⣧⣿⡿⠁⢀⡄⠀⠀⠀⢀⣠⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⣻⣿⣿⡿⠿⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣇⣴⢟⡆⢀⣤⣶⡿⠟⠁
⠀⠀⠀⠠⣤⣤⣀⣀⡀⠀⠀⠐⢦⣔⡶⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣿⠟⠋
⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣦⣤⣀⡈⣻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣇⣤⡶⠚⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣟⣀⣤⣤⣤⣶⣶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣶⡶⠦
⠀⠠⠴⠶⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⣽⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠿⠿⠿⢿⣿⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⢶⣤⣀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⠿⢛⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣏⡉
⠀⠀⠀⠀⠀⢀⣴⠿⠛⠋⠉⠀⠀⣨⡿⠛⢹⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣯⡉⠙⠻⣿⣦⣄
⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⣰⣿⡿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠮⠻⢦⠀⠈⠙⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⢻⡟⠀⣿⣿⢿⣿⡟⠻⣿⣿⢿⣻⣆⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠚⠀⢠⣿⡟⠈⢻⡇⠀⢻⣿⠀⠁⠹⠄⠀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠃⠀⢸⣿⡆⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳