Apple tree Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠄⠠⠐⢒⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠘⠀⠀⠀⠑⠒⠆⠉⠀⠀⠀⠈⠀⠈⠖⠢⣀⠠⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠆⠀⠑⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠠⢂⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠐⢄⡀⢀⠀⠀⢀⠀⠀⡼⠉⠀⠉⠁⠀⠃⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⣀⠀⠈⠑⠂⠑⡀
⠀⠀⢀⠀⠀⠀⡀⠆⠀⠀⠀⠈⠁⠀⠡⠀⠀⠀⠀⠀⠀⣹⡀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠘⠤⠠⠀⢠⡀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠀⠄⠀⠜⠒⠶⠖⠋⠀⠀⠀⠁⢴⢀⠀⠀⡔⠒⠒⠖⠒⠦⡀⢤⠀⠀⠪
⠀⠀⠄⢀⠁⠀⠀⠀⠀⠃⠀⠠⠀⠐⠀⢨⠁⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⠀⠀⡇⠀⠀⠀⠀⢀⡇⠀⠀⠆⣠⠃
⠀⠂⠀⡎⠀⠀⠀⠀⠤⠀⠃⠀⠀⠀⠀⠘⠀⠐⢄⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠘⠦⣀⣠⡤⠊⠀⠀⠆⠀⠈
⠐⠀⢀⠊⠀⠀⡔⠒⠲⠖⠒⢄⠀⠀⠀⠈⠢⠤⠴⠾⠁⠀⠀⣄⣠⠞⠓⡏⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠠⠶⢤⠂⠀⢠
⠀⠀⡜⢠⠀⠰⡀⠀⠀⠀⠀⢨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⠀⢷⠀⢱⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢂⠀⠀⠉⠈⡀⠀⢀
⠀⠀⠈⡄⠀⠀⠱⣤⣀⣀⡴⠋⠀⠴⠀⠀⠀⠀⠀⡤⡄⠂⠀⠀⠀⠘⡇⠸⣧⠀⠀⢀⡎⠙⠦⠒⠁⠀⠀⠰⠤⣎⠀⢠⠀⠀⠀⠀⠀⠄
⠀⠀⠀⡇⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠒⠊⠑⠋⢰⡇⠀⠀⠀⠀⠀⣷⠀⠹⣆⢀⡼⢁⠀⠆⠐⠢⣞⠀⠀⠀⠀⠛⠇⠀⠀⡠⠀⢸
⠀⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⢀⠀⢀⠂⠀⠀⠀⠀⠀⠳⢤⡤⠴⠞⠋⠁⠀⠀⠉⠋⠁⠀⠀⠃⠀⠀⠈⢣⣀⣀⡄⠀⠀⠐⠀⠀⢀⡊
⠀⠀⠀⠀⠀⠗⠀⠀⠀⢦⠤⠈⡡⠬⣁⡀⣀⡀⠀⠀⠀⠀⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⣸⠀⢥⠈⠙⠀⡄⠀⡡⢻⡄
⠀⠀⠀⠀⠀⢤⠀⠀⠠⠀⠀⢈⠀⠀⠀⠀⠀⢹⠀⣠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠚⠁⠀⡟⢐⣧⢄⣁⠈⡀⢸⠆
⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⡀⠈⣆⠀⠀⠀⣠⠞⢀⠀⢀⠀⢀⡀⣸⠃⠀⠀⠀⠃⢀⠰⠀⠶⠤⣤⠤⠤⠶⠚⢠⠋⠀⠈⠀⠀⠸⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⣀⡄⠀⠙⠛⠋⠁⢑⠉⠀⠀⠉⠈⠁⠎⠀⠀⠀⢀⠀⠀⠀⢠⡇⠀⠈⠳⠤⠲⠤⠚⢧⡀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠚⠐⠀⠐⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠃⠘⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠄⠀⠀⠀⠀⠀⠀⢸⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⡇⠀⠀⠀⠀⠀⠀⠀⠸⠈⣎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡇⢀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡈⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀⡇⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠓⠐⢮⡀⠉⠲⢠⣤⠄⣀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢘⠀⢨⡀⠛⣚⠦⠶⠐⠦⢉⠢⠄⣀⡦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠄⢰⣀⣢⢘⠂⢴⡤⡅⠼⣂⡠⠀⢠⣦⣉⣼⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣴⠌⠫⠷⡄⠙⢨⣼⠐⠶⠝⠉⣖⣀⠙⠁⠀⢀⡀⠀⢠⡴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠯⠈⠛⠁⣦⡐⡶⢦⡌⢖⣠⠄⠷⣦⠍⢱⠄⠀⢨⡍⠀⠀⠁⠟⣀⠁⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⣎⡙⢲⢨⣉⠙⣈⡁⣭⠰⡈⠁⠀⠈⢸⢛⠒⣌⢉⠻⣃⣜⠠⠄⠀⠠⠐⡾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡘⣾⠃⠰⠄⠛⢤⠄⢮⣭⣄⠷⣔⣳⡊⠂⠀⡸⠈⢆⠈⢈⡥⠤⠨⠵⢤⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠉⣯⠠⣦⠄⠀⢼⠀⠀⠀⠀⣖⢌⡙⠉⠀⠀⡇⠀⠀⢠⡞⠀⢣⠒⡤⢀
⠀⠀⠀⠀⠀⠀⠀⢴⢜⠉⠶⠈⠀⠀⠈⢣⡀⠀⠀⢻⡇⠟⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠹⠈⣃⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⠀⠸⠁⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠰⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⠏⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠂⠒⠂⠀⠀⠀⠀⠀⣸⣏⣸⠀⠀⣀⢀⠀⠀⡀
⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⡌⡀⠩⠜⡻⠟⠷⢢⡭⠦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠄⣀⠠⡄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⠀⠦⠀⡇⠀⠔⣦⠀⣀⠔⠂⠀⠀⠀⠏⠈⠰⣀⠄⠀⠀⡀⠠⠀⠀⠀⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣈⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠃⠈⠆⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⡀⠀⢲⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⠀⠀⠠⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠈⠁⠈⣀⠄⠀⠀⠀⠀⠀⠀⠀⠠⢀⣘⣀⣈⡡⢄⡀⠈⠀⠀⠀⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⡅⠀⣈⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⡼⠀⠀⠀⢀⡸⠤⣀⠀⡀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠁⠀⠀⠹⠀⠀⠀⠀⠀⠄⠀⠰⠈⠀⢀⠀⡠⠀⠀⠀⠙⠀⢡⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠬⠀⠀⠈⠀⠉⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠑⠀⠤⠀⢀⡄⠁⠀⠈⠉⢣⡀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠈⢨⠓⠦⣤⠴⢞⠁⠀⠀⠈⠀⣰⠀⠀⠁⢀⡔⠒⠢⡆⠲⢦⡀⢀⢀⠀⠀⢼⠁⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡸⠀⠀⡆⠀⠀⠄⠒⡛⠙⠋⠁⠉⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢤⠚⠁⠀⢈⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡄⠀⡆
⠀⠀⠂⣀⠒⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠂⠀⠀⠀⠘⢆⡀⠀⠀⠀⣠⠏⠀⢠⠀⠁⠚
⢐⠀⠀⠁⡀⠐⠀⠀⠀⠒⠂⠄⠀⠰⠀⠀⠀⠘⣃⠀⠀⠓⢤⡔⠁⠀⠀⠀⠀⢠⣄⣀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠈⢙⡒⠒⠊⠁⠀⠀⠘⠁
⡈⠀⠀⡆⠀⠀⠰⡎⠀⠉⠋⠉⠉⢢⠀⠀⠀⠀⠈⠑⠓⠛⠉⠀⠀⠀⣰⠤⢶⡇⠈⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢺⠉⢻⠁⠀⢠⠇⡀
⢀⠀⢰⡉⠤⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⢷⡀⢘⡆⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠
⠀⢀⠀⠈⠀⠀⠀⠑⢤⣀⣀⣠⠔⠃⠀⠰⠀⠀⠀⠀⠀⠀⡦⡤⠊⠀⠀⠀⠀⠘⣇⠈⢿⡀⠀⠀⠀⡆⠉⡷⠒⠈⠀⠀⠀⠑⠢⢮⡐⠀⡘⠀⠀⡀⠀⠀⠰
⠀⠀⠀⢳⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠠⠶⠋⠐⠊⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠘⣷⠀⠀⡼⠀⠀⡆⠀⠠⢤⡖⠀⠀⠀⠀⠙⠳⠁⠀⠀⢉⠀⠀⠆⠀⢀
⠀⠀⢁⠈⠁⠲⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⡆⠀⢷⣄⣀⣀⣠⠴⠚⠋⠀⠀⠘⠳⠞⠃⠀⠀⡇⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠋
⠀⠀⠀⠀⠀⠀⣤⠀⡀⠀⣰⠀⠀⠆⠂⠐⠦⠄⠀⠀⠀⠐⢄⠀⠉⢉⡁⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠉⢲⠙⠢⢆⠀⠀⠀⠒⠤⣞⠈⠁
⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠈⠉⠉⢠⠊⠉⠒⠒⠓⠲⡄⠀⠀⠀⠀⠀⠀⠙⣆⠨⠀⠀⠀⢁⠀⠀⠀⠀⠀⢧⣀⣀⣀⣠⡟⠀⢸⠀⢰⠀⢠⡁⠄⠂⠂⣟
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠐⠂⠀⠁⢄⠀⠀⠀⠀⠀⠀⡼⠀⠼⠀⠀⠀⠀⠀⢹⡂⠀⠀⠀⠘⠀⠀⠀⡀⠁⠂⣀⡀⠉⠀⠀⢀⡞⢀⠝⠒⢢⠔⠒⢂⣀⠙
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⢰⠀⠈⢦⣀⠀⢀⣀⡼⠃⣀⢀⢀⡄⠀⣠⢠⣼⠁⠀⠀⠀⢃⠀⠀⠀⡀⣻⠷⠶⣶⠶⠖⠛⠋⠀⡇⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠈⠉⠉⠁⠀⡙⠀⠈⠀⠈⠀⠀⢠⠃⠀⠀⠀⠀⡄⠀⢠⠀⢢⡇⠀⠀⠙⠳⠖⠲⠴⠞⠳⣄⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠘⠀⠢⠠⠊⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠘⠀⠃⠈⡐⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠀⠀⠀⠀⡄⠀⢀⢁⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠆⠀⠀⠀⠀⠀⠀⠈⢸⡇⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⡄⠀⠀⠀⠀⠀⠀⠀⢠⠘⠷⡈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠳⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠰⣠⡟⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡃⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢸⠀⠈⠄⠀⠀⠆⢀⠀⠀⠀⠘⠁⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢁⠁⡘⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⢨⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡌⠀⠇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⢠⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⠥⣤⡀⣼⡀⠀⢠⣟⣀⣀⠀⠀⢀⠀⠀⡀⠀⠀⠀⣠⡤⣤⠶
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣀⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠰⠐⡷⠀⠀⢠⣄⠐⡿⠂⢠⣦⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠁⡐⠃⠲⠃⣀⠘⢻⡔⠀⢠⣘⠋⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣴⠄⡘⠗⡈⢋⣁⢫⡴⠛⢤⡄⠰⢼⠛⠀⠀⠈⠛⣚⡁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣠⣿⣦⣝⢦⣩⢱⡇⣬⠛⢻⠁⣿⣿⣿⡆⣼⠛⠀⠀⠿⣾⣩⡄⠀⠀⠫⡀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠡⡹⣿⣿⢏⠠⠟⠉⢹⢷⣠⢘⡇⠙⠛⠋⢠⣿⡟⢡⣤⣠⡏⣨⣴⣯⡀⣤⣸⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢷⠀⣦⠐⠟⠀⣄⢸⣷⠀⠀⣤⢠⣬⣹⡇⢦⠐⠂⢠⣄⣣⣦⠙⣟⠀⢻⣿⣿⠇⠠⣼⡷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣊⠀⠀⣠⡞⠉⠿⠙⢒⡶⣟⠁⢉⢹⣷⣣⣤⢀⠀⣤⣻⡷⠞⠛⠁⠀⡉⣁⠻⣢⠾⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠉⢀⠀⠶⣀⠮⡁⢸⣴⠝⠿⢿⡟⠉⠘⢃⢉⣹⣇⣴⡆⠀⠸⣷⣸⠾⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠈⢛⣤⣹⣇⠰⠠⣄⢺⣋⣙⣶⣿⢸⣿⠀⠀⣤⡱⠻⢿⡉⢠⣦⢠⡞⠁⣤⠀⢀⣰⡿⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡄⠀⢠⡀⠙⠋⢴⡿⠁⢰⡏⠩⡅⠸⠏⢻⣿⣿⡇⢸⣿⣿⡧⠈⣿⣤⡽⠾⠳⣾⠉⠹⠯⠉⠳⣄⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣄⣿⡿⠀⠀⠀⢠⡄⠐⠛⣄⣉⠽⠶⣾⣿⣿⡇⠈⠻⠟⢁⣼⠟⠁⠀⡾⠂⣶⠀⢰⡶⠂⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢭⡙⡇⣠⡆⠰⡆⠁⠀⢰⣿⣷⣶⠀⠈⣿⣿⣧⢀⣠⣴⠟⢱⡄⠀⠀⢂⣠⠋⠀⠀⠀⠀⠙⡻⠟⣱⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣆⡉⢷⣫⡅⠀⣠⡖⠳⡈⠿⠿⠃⢠⣄⢻⣿⣿⣿⠟⠉⢰⣷⠀⢀⣀⣼⣁⣤⣸⠇⠀⠀⣾⡏⣠⣞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠘⢿⣥⣾⠁⠀⡀⠹⡄⠀⡀⢨⣍⢾⣿⣿⣧⡾⠃⣴⠟⠛⠛⢋⣥⠀⢻⠯⠉⣩⡍⠉⠣⣤⡏
⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⡤⠉⣉⣀⠀⣠⢹⣦⣀⣀⣻⣴⣿⣜⡇⠈⠛⣿⣿⣿⣏⣠⣾⣁⠸⡇⢸⣿⣿⡷⠈⠓⣴⠛⠁⠰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠲⢀⢀⣱⠾⠚⣻⡋⠉⠉⣩⣿⣿⣿⣿⣾⣿⣿⣿⣿⠏⢠⣍⢁⣴⠎⠛⠛⣁⡀⠀⢠⡄⣠⡄⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠿⠟⠁⢤⡠⠞⠁⠟⠐⡿⠃⠀⠸⠿⠋⠀⣙⣿⣿⣿⣿⣿⡟⠀⣹⣷⠊⢰⡿⠀⣸⠿⠃⣀⣀⣥⢟⣃⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠃⠹⣿⣿⣿⣿⣿⣿⡿⢿⣟⡛⠛⣿⡟⠛⠛⠠⢄⣀⠛⠆⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠁⠀⠘⠿⣿⠀⠉⠋⠀⠀⢰⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣉⢣⣈⣿⣶⡶⣦⢶⡤⢶⣻⣖⣠⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⡟⢿⣶⣿⣾⣷⣿⣽⠸⠋⣘⠷⢩⠿⡽⣟⠼⢿⣽⠿⡔⢠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢻⣟⢿⣾⡍⣹⡽⣻⢻⣷⣧⣼⣗⣴⠋⣰⣾⣟⡤⡘⢸⡿⣿⣻⣯⡴⠶⣯⡀
⠀⠀⠀⠀⠀⠀⢠⡶⡷⡁⡛⡼⢥⣷⠣⢼⣆⢸⣿⣾⠋⣹⢾⣻⣿⣿⣚⢿⣴⣿⣹⡇⢱⣺⣞⣲⢷⠛⠶⣠⢀
⠀⠀⠀⠀⢠⡺⣟⣿⣽⣷⣹⡋⣞⣿⣶⣿⡊⢻⣽⣿⣿⣿⣻⡿⣿⡿⡝⢷⡯⣘⡿⣿⣱⣼⣟⡿⠒⣄⢔⢲⣿⡄⡖
⠀⠀⠀⠀⣐⡻⣲⣁⣸⡏⡟⣻⣾⣯⢿⣿⣽⣿⡝⠳⠓⢻⠷⣏⠼⣿⣿⡈⣤⢌⢻⣽⣟⢿⣿⣋⣴⢻⡈⣹⣶⡿⣷⡾
⠀⠀⢀⣶⣛⠙⢟⣙⠾⣄⣼⢩⣿⣯⡟⢸⠶⣿⢿⢧⡼⢵⣴⣟⣆⡻⣿⢡⣿⠟⢫⣜⣻⡿⣍⣯⠛⠿⣍⣿⢻⡷⣛⣂⡒⠂
⠀⠀⢈⣻⡦⢿⠛⢹⣿⣿⡿⣿⣿⠎⡷⠺⣬⣶⣶⣾⣧⢹⣿⣿⣯⡿⣴⢱⡿⣲⣾⣾⡿⠛⢼⢁⢭⣽⢯⣳⢿⣤⡼⡤⠷
⠀⠀⠰⢧⣼⡯⣷⢹⡟⢏⣀⣔⣓⣾⡟⢶⣮⠛⢿⠳⢿⠋⢻⠹⣽⢷⣾⣟⢽⣿⣸⢿⣯⣶⣧⠈⠷⣷⣴⣿⡛⢇⣴⢿⡍
⠀⠀⠀⠜⢷⠟⣿⣾⣿⣮⣿⣿⣭⣷⣴⢿⣯⢴⢳⣾⣿⣣⣬⢍⣿⣿⠯⣛⣷⢺⣮⣿⢷⣿⣳⣿⠿⣷⣿⣶⡇⡜⢡⣸⡏
⠀⠀⠀⠀⠛⡟⠹⢏⣁⣿⣬⡝⢿⡮⠛⣿⣿⣿⡷⣝⢿⣯⠛⠿⢏⠕⠺⣿⣿⣿⣽⠌⢿⣿⣽⣶⣿⣿⣴⠿⢯⢿⡟⠡⠅
⠀⠀⠀⠀⠀⠛⠇⢦⣷⠾⡿⠿⠿⣾⣶⣧⢺⣻⠳⣿⠑⢌⠁⣀⠸⠀⣀⡈⠚⠿⣿⣦⡚⠛⠋⠸⠿⣷⢎⠱⡎⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠈⠉⠁⠀⠀⠡⠈⠀⢡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⠩⠛⡀⠂⡶⠀⡬⡷⠖⠠⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠀⠆⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⡸⡾⢿⡛⠃⠀⠀⠠⣀⠆⠀⢀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣻⠛⣷⣻⣾⣏⠠⠠⠀⣠⠅⠀⢸⣜⠋⠤⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣇⡤⢉⣐⢠⣅⠹⡹⣷⠂⠀⠈⢀⢠⡾⢿⠛⣄⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣾⢿⡍⢃⡎⠹⣿⣿⣾⣆⡘⠟⠙⠆⢹⡟⠃⣧⡀⠀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣴⣿⣿⢻⣷⣶⣃⡽⢷⣦⣉⣿⣿⡿⢿⣿⣿⣌⠁⡀⠀⢩⠻⠀⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢿⢺⣭⣾⣟⣷⢼⣟⢉⠴⠗⠀⣻⣏⠳⠨⠀⠀⢁⣿⠇⡀⠀⠀⠁⠀⠀⠠⡑⢥⠀⠀⠀⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢀⣟⣿⣽⣿⣿⡟⣺⣿⣆⡟⡀⠈⠹⠉⠓⠛⢡⣬⡡⣿⡀⠠⠀⢸⠂⠒⠀⠀⠀⠀⢀⠄⡌⠀⠀⠀⠁⠰
⠀⠀⠀⠀⠀⠀⠀⠿⠟⣳⣾⣟⣻⠟⣿⣏⠀⠑⢿⣿⣀⣠⡘⠓⣶⠉⢿⡋⢹⣦⣠⣬⣛⣁⠀⠀⠀⠀⣠⠄⠀⠀⠀⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠐⢻⣴⣿⣿⠟⠁⠈⡙⢿⣶⣯⠿⢿⣿⣅⡐⠀⢭⠁⡀⠉⠀⠚⢛⠛⡻⢻⡶⢤⡄⠂⢉⠄⠀⠰⠴⠰⠀⢀⡃
⠀⠀⠀⠀⠀⠀⡰⢿⣦⣿⣏⢹⣿⣾⣸⣾⠏⠍⠠⣠⠸⣧⣭⣦⡰⠶⠤⠠⠖⣾⣯⡄⢉⠨⣆⡤⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⣀⣿⣷⣿⣿⣿⣍⢰⣶⣺⣿⡰⠂⠘⠒⠁⣈⠉⠛⢿⣳⣏⡷⢿⣿⡿⣹⣷⡌⣁⠀⠀⠀⠀⢸⡇⡐⣌⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠋⣼⣿⣿⣿⣤⣼⣿⡟⢿⣿⣷⣓⢲⣔⣦⣽⣄⣦⡞⢿⣿⠙⠁⣿⠁⠹⢳⣿⣧⡖⣀⠄⢀⢤⠓⣄⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠟⢿⣿⣽⣯⣙⣿⣽⣤⣛⣟⡭⣉⣻⣤⣿⡿⢻⡅⠈⣿⡄⠀⡏⠀⠀⠀⠀⠀⠙⠟⠶⣏⠈⠁⠿⣏⠨⠆⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠍⡽⠻⠛⠛⠻⣟⠫⠐⠃⡜⢵⡤⠀⠀⠹⠷⣿⣵⡼⠃⠀⠀⠀⠀⠀⠀⠀⠯⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣣⠈⠁⠀⠀⠀⠀⡛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠰⠑⣁⢄⣠⣀⡇⣀⠀⠎⢸⢠⡀⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠘⠚⢻⠚⡷⠛⠚⠃⠀⠀⠘⠈⠚⠃⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡄⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢠⣰⣯⣄⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠯⠅⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⣤⣴⠒⠀⣴⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⣛⣬⣝⣳⣜⢑⡯⣾⡯⠿⣶⣟⡤⢠⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣍⣾⣧⣜⢇⣷⡙⣭⢑⣠⢗⡶⢻⠓⠲⣿⢿⣶⠤⣼⣴⠴
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢿⣼⣿⣿⡏⡯⠿⢦⠴⢭⣟⡦⡗⠛⢾⢉⣴⠧⣙⢶⣿⣿⠃⣦
⠀⠀⠀⠀⠀⠀⢐⣦⡛⣭⣿⣿⣿⣷⢹⢧⡤⣷⡋⠙⡏⢿⣽⣗⡍⢉⠿⣷⢮⢮⡩⡞⢿⢷⡇⢀
⠀⠀⠀⠀⠠⠷⠾⣢⣿⣿⣦⣼⣟⠿⣼⠓⣆⣰⣽⣻⣞⡿⣿⣷⣯⣇⢼⣬⣾⣇⣸⣽⣏⢉⣿⣯⡀
⠀⠀⠀⠀⢰⣼⣮⣿⠛⣿⣿⣿⣽⣧⣏⣲⣽⣧⣀⣿⣴⣈⣿⣿⣿⣻⣏⢙⣿⣿⣵⣿⣿⡿⣯⣗
⠀⠀⠀⠠⣭⣺⣿⣿⣿⠿⣿⣤⣾⣻⣿⡋⢻⣿⣿⣿⣿⣿⣿⣿⣦⣿⢛⣷⣽⣿⢻⡿⣏⣶⡁
⠀⠀⠀⠀⠹⣻⢿⣿⣿⣤⣿⣿⡿⣛⣿⣿⡟⢿⢿⣍⢹⣤⢿⠺⢹⣏⠽⣏⡳⣟⠿⣧⣜⠃
⠀⠀⠀⠀⠘⠹⢫⣿⣨⠿⠫⢋⡈⠻⣇⠚⠓⡖⠐⠛⠀⣿⣤⠞⠋⠁⠀⠉⠛⠧⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠉⠉⠙⢷⡀⡇⠀⠀⡼⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⢸⢏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣌⠛⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠁⠺⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠠⠄⡀⠤⢀⠀⢀⢀⠤⠄⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢀⡠⠤⠤⢀⡡⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⢺⡇⠒⠄⠀⠘⠀⣀⠤⣔⡤⢄⠀⠀⠀⠀⠈⠢⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⡠⢒⡿⢈⠑⡀⠀⠀⠠⠐⠀⠀⠀⡀⠀⠀⠐⠁⠀⠉⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⢥
⠀⠀⠀⠀⠀⠀⠀⢠⠂⠉⠀⠀⠀⠀⡄⠀⠀⠈⠁⠀⠀⠀⠀⡑⠠⠀⠊⠀⠀⠀⠀⠡⣀⠀⡰⠔⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠑⡀
⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠈⠂⠔⠒⠈⡀⡄⠁⠁⢀⠤⢤⣧⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⢊⠩⠿⠉⠑⡀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⣀⠜⠋⡉⠐⠂⠑⢄⣀⠀⠀⢀⢢⣨⣀⠀⠀⠀⢊⢀⡄⠁⠀⠀⠁⠀⠀⠀⠀⣀⠀⢀⠸⡘⠆⠀⠀⢠⠣⢄⠀⠀⠀⠈⠱
⠀⠀⠀⠀⡊⢀⠔⠐⣴⢃⠲⠄⠀⠀⠎⠁⠘⠚⠀⠈⢳⠐⡀⠈⠢⣀⠀⠀⠈⠀⠀⢠⠤⠎⠀⠉⠃⠀⠈⠀⠐⠀⠁⣀⠀⡍⠉⠀⠀⠀⢇
⠀⠀⠀⢀⠅⠈⡄⠀⠀⢠⡁⠄⠀⠀⡀⠑⡀⠀⠀⠀⡘⠀⠉⠂⢀⠄⡀⠠⠀⠀⠀⠀⢄⠀⠀⠀⢀⠠⢴⡤⢄⠀⠊⠀⠹⠏⠙⣦⢄⠀⠀⠇
⠀⠀⠀⠸⡀⠀⠈⠢⠐⠒⠊⢀⠀⠀⠈⠂⠌⠄⠠⠚⠀⠀⢠⠒⠁⠀⠀⠀⢀⠊⠀⠽⠎⠁⠢⠀⡆⠀⠈⠁⡀⠁⢠⡀⠀⠈⢂⠃⠀⠁⠚⡀
⠀⠀⠀⠀⠇⠀⢀⣀⡠⠄⡠⢬⡎⠉⠑⡀⠀⠀⠀⠀⠀⢰⣾⠒⠢⠄⠀⠀⣸⡀⠀⠀⢀⡓⢠⠁⠐⢄⢀⣀⡠⠂⠀⠈⠉⠉⠁⠀⠀⠀⠐⠥⡀
⠀⠀⠀⠀⠱⠀⡇⠈⠀⢸⠐⠄⠀⠀⢀⠇⠀⠀⠀⢠⠉⡀⠋⠀⠀⢸⠋⠛⠀⡑⢠⠄⠬⠴⣧⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⣀⣄⡀⡀⠀⠀⡀
⠀⠀⠀⠀⠸⠊⠀⠀⠀⠀⠑⠂⠀⠒⡚⠀⠀⠀⠁⢈⠠⡑⠂⢀⢀⠌⢀⠐⠊⠠⠁⠀⠠⠊⡠⠑⡄⠀⠀⠀⠀⠠⡜⠀⢠⠫⠈⠛⠀⢸⠀⠀⠱
⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠡⠀⠉⢇⠈⡄⠈⠀⠀⠠⠐⠁⡠⠊⡀⠘⢣⣀⠀⠀⢀⠔⠀⠀⠀⠢⢗⣀⣀⠜⠀⢀⠜
⠀⠀⠀⢐⠁⠀⠀⠀⠀⠤⠰⣸⠆⠠⡀⠀⠀⠀⢠⠈⠡⡀⠀⠈⡄⠰⡟⠀⠀⠀⢀⠌⡠⠊⢀⠔⠁⠈⠑⠒⠁⠀⠀⠀⢀⠀⠀⠀⡠⡀⢀⠜
⠀⠀⠀⠈⠢⠤⡄⠀⠀⠀⠀⠉⠀⠀⠁⠀⡰⠒⠃⢄⠀⠈⠶⡉⠃⠀⠀⠀⠀⠀⠟⠋⢀⠔⠁⠤⠂⠤⠤⠔⠀⠂⠤⠐⠁⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠣⢀⣠⣀⠔⠉⠋⠀⠀⠀⠀⡱⢄⠀⠉⠒⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠀⠊⠀⠁⠈⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠃⠉⠓⠊⠁⠊⠉⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⠒⢴⠶⡲⢏⠣⢄⣀⢠⠦⣤⢀⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⣒⠣⣤⠑⢿⡉⢁⠼⣟⠢⢾⠂⡴⣤⢰⡋⡻⡝⠏⣌⠱⠦⠤⢠
⠀⠀⠀⠀⠀⠀⢠⠔⠒⠚⣇⡀⣉⠶⡈⡄⢭⠏⡴⡀⡰⢆⡤⢦⢞⣢⠐⢚⡴⢋⠐⡀⠒⠷⠄⡅
⠀⠀⠀⠀⠀⠀⢨⠒⢛⣫⣡⣍⣨⡋⣱⢙⣪⠹⣍⢿⠐⡬⣴⡜⢶⡙⣗⢂⡤⢝⡛⠛⠯⡄⠳⠰⣄
⠀⠀⠀⠀⠀⢠⢀⣈⣰⢦⠛⡵⢙⣨⣏⡀⠛⡝⠻⣌⣿⠆⡐⡚⢛⡿⣥⢾⡻⢭⡿⣤⢳⠤⡯⣰⠋
⠀⠀⠀⠀⠀⡼⢁⢳⢯⢁⣀⡽⠀⢀⢝⢶⡰⠃⠄⢎⣻⢼⢉⣷⣮⣾⡵⠈⢗⠜⠠⢜⣷⡼⡗⠽⣈⡅
⠀⠀⠀⠀⠀⢩⡚⠹⣁⠓⠿⣴⣈⣑⣦⠖⡩⢳⣤⣆⣿⡎⣽⣣⣾⢫⢒⣸⣿⣀⣫⣨⠴⣊⢳⡆⢧⡑
⠀⠀⠀⠀⠀⠀⣟⣠⠉⡅⠉⣁⠄⡲⢉⠹⠷⠶⢶⣬⣻⣧⣿⣣⣴⡿⢍⡉⠣⠩⠟⢒⡐⡯⠬⠙⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠒⠀⠀⠀⠀⠉⢿⣿⣿⡟⠁⠀⠀⠁⠀⠐⠀⠀⠐⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠿⢿⣦⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠰⣆⠀⢀⡀⠻⣿⣷⠀⠀⠀⠀⠀⣿⡆⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣤⡄⣾⡿⠀⢀⠴⠟⠁⠀⠉⠛⠃⠀⠀⠀⠀⢈⡱⢡⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⣼⣿⠀⠀⠀⠀⢈⣙⢉⠀⠀⡈⠀⠀⠚⠛⣩⣼⡎⠙⠲⣤⠖⠛⢦⠀⢈⣙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠈⠻⠧⠿⣃⣤⠀⠀⠀⠀⠀⠀⢣⡜⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⢹⡄⠀⠀⠁⢿⣥⡀⠀⠀⢠⣄⠀⠀⣠⣴⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠘⠟⠋⠀⠀⠀⠀⠀⣷⠀⠀⢶⣦⡈⠁⠀⠀⣈⣛⣀⡐⣛⣁⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠿⠟⣧⠈⢈⡉⠉⠒⠲⢤⣀⠀⠀⠀⠀⡇⠶⠿⠋⠀⠀⠀⠶⣄⡠⠖⠒⠒⢿⡄⠀⠈⠻⣿⡄⣠⠎⠉⠀⠉⠗⠠⠐⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⣿⠃⠀⣠⣤⣤⣬⡝⠲⣤⡈⡇⠀⠀⠀⠀⠀⣠⣤⣬⣤⣄⠀⠀⢸⡇⠀⠀⠀⠀⠠⡏⠀⣰⣿⣿⣾⣷⡄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣋⠈⠁⠀⠀⣿⣿⣿⣿⡿⠀⠈⠙⢿⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠘⣧⠀⠀⠀⠀⠀⡇⠀⠸⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠃⢠⡀⠀⠘⠟⠛⠟⠁⠀⠀⠀⠀⠙⣷⡀⠀⠀⠘⠿⠿⠟⠃⠀⠀⠀⣿⠀⠀⢰⣄⠀⡷⠀⠀⠈⠉⠉⠁⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠠⣄⠀⣿⠀⠀⠈⠻⢠⡇⠀⠀⠀⠀⢠⡴⠀⠀⠸⢃⣴⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢠⣤⠀⢈⣻⠶⠖⠺⠛⠉⠉⠉⠙⠳⢤⡘⣿⡀⠀⣠⣤⠀⠀⠀⠙⢰⡇⠀⣀⣀⣠⣾⣥⣤⣤⣤⣤⠬⠴⠒⢲⣬⣍⡉⠁
⠀⠀⠀⠀⠀⠰⢦⠀⢸⠏⠀⢀⣴⠎⢁⣤⡤⠠⢡⣦⣤⡀⠀⠀⠀⠀⠙⢿⣧⠾⠿⠋⠀⠀⠀⢀⣾⣷⠟⠋⠹⣦⡀⠀⠀⠀⠀⠰⣷⡄⠀⠈⢿⣿⣿⣆
⠀⠀⢰⣦⠀⠀⠀⠀⠙⠲⣄⠈⠁⠀⠘⠋⢠⡆⠀⠻⣿⣿⡄⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢀⣴⣿⣋⡁⣀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⠉⠙⠛
⠀⠀⠸⣿⠀⣼⣿⣿⣿⣷⠘⢦⡀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣾⠟⠉⠉⠉⠉⠉⠙⠟⢦⡀⢠⣶⠶⠀⠀⠀⠀⠀⡀
⠀⢰⣶⣍⠀⠹⣿⣿⣿⡟⠀⠀⠹⣆⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣶⠀⠀⣿⣧⠀⠀⣼⡟⠀⠀⢀⣴⣶⡶⠀⢀⡀⠙⡐⠒⠂⣀⣀⢠⠀⣸⣿⠀⢀⣄
⠀⠀⠈⠁⠉⣒⠪⠤⣥⡤⠤⠖⠚⠛⠋⠉⠉⠉⢩⠟⠛⠻⢷⣶⣄⡻⠀⠀⢿⣿⠀⢰⣿⠁⠀⠀⠈⠉⠁⠴⢢⣿⣿⣿⣿⡇⠀⠈⠉⢉⠀⣿⡿⣰⣿⠏
⠀⠀⢀⣶⣿⡟⠀⣄⠀⠀⠀⠀⠀⠀⠀⢛⣛⠐⣣⡀⠀⠀⠀⠉⠛⢿⣦⡄⢸⣿⣇⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃⠀⠀⠀⢨⠀⣨⠕⢭⣦
⠀⠀⠺⠟⣋⣀⠤⠭⠤⣀⡀⠀⠀⠀⣴⠿⠋⠀⢿⣿⠀⠀⠀⠀⠀⠀⠙⣿⣾⣿⣿⣿⠃⠀⠀⠀⠀⠠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠞⠉⠀⣐⠾⠟
⠀⠀⠀⠾⠿⠃⢠⣤⣤⣤⣬⠓⢦⡀⠀⠀⠀⠀⠈⠛⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⣿⣶⣶⣿⣿⣿⣷⣶⣶⣦⣤⣤⣄⣄⣀⣀⣴⣟⡁⠀⣠⠄⠹⣷
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠃⠀⠉⠓⠦⣤⣄⣀⣀⣠⡶⠟⠋⠉⠉⢻⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⠉⢻⡉⠉⠉⠉⠉⢀⣀⣀⣋⣘⠃
⠀⠀⠀⠀⠀⠀⠈⠻⠛⠿⢋⣤⡶⠐⠒⣒⠚⠛⢋⣉⣁⣀⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣦⠃⢠⣄⠀⠀⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⡿⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⠏⢸⡌⠙⠃⠀⠘⢿⡿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⢿⠿⢿⠟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠘⣻⣿⣶⣉⢆⡤⠀⠀⠀⠀⠠⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠛⢲⣿⣻⣻⣿⢣⠼⢢⡧⡀⢀⡀⣠⣴⠕⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⣾⡧⢻⣦⣻⣿⣟⣿⣔⠶⣷⣿⣿⠿⣿⣿⡃⠤⡄⠀⠀⢀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠈⣷⡿⠋⢿⣿⡿⣿⣧⣈⠖⠉⠒⣉⠗⠙⣳⣤⣶⣷⡠⢀⣎⣻⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣈⠷⣿⣿⣿⣿⠆⢙⠙⣿⣏⡱⠞⠠⠨⢈⣷⣿⣷⣼⣷⣿⣧⣷⣸⠑⢏⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠜⠐⠺⢧⢋⣷⣬⣿⣿⣿⡻⢾⠿⣏⡝⠐⠐⢠⣾⣰⣿⢍⣶⣟⣹⣥⠐⣌⠼⠶⣾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠪⢢⣊⡿⢾⣷⡛⣿⠛⡄⣘⣟⣴⣟⣿⣉⢡⡼⠿⢿⣿⣿⣿⣿⣏⣟⣓⡚⠇⣄⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣧⡀⣨⣿⡈⢁⡑⡦⠹⠒⢦⡧⢿⣿⣿⣛⢻⡿⢿⣿⣶⣶⣌⣿⡃⢀⢈⡐⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠌⢹⡇⠋⡞⢷⣊⣡⣩⣴⣿⣦⣇⣾⣾⣟⠈⡿⢿⣷⣻⣿⣿⣏⣋⢜⠛⡈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠐⢀⠀⠠⠠⠀⢐⠣⣈⢙⠳⡴⢿⡱⢿⡟⣟⣿⣿⣛⣿⣏⣛⢉⡗⢛⣟⢫⣿⣭⢿⣏⣰⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣤⣼⣿⣷⢦⣶⢌⡈⣼⢲⣶⢿⡝⢋⣼⡦⠸⣄⠼⠶⣿⣿⣿⣿⣗⣴⣿⣥⡀
⠀⠀⠀⠠⡄⠀⠀⣀⠼⣛⠙⢿⣥⣿⣽⣛⡽⣿⡷⢈⣟⡃⡾⣏⠋⢉⣹⠞⢫⣔⣶⣾⠿⠿⡏⢿⣿⣿⡟⠊
⠀⠀⠀⠀⠀⠀⠙⠉⣿⣯⣿⣼⣧⣴⣿⣿⣗⣛⣿⢟⣬⣿⡓⣿⣴⣶⡐⠆⠀⡈⣿⣿⡸⢧⠹⣍⣧⢋⣽⣦⣦
⠀⠀⠀⠀⠀⠀⣀⠀⣾⣿⢿⣞⡷⢿⡟⢥⣖⢻⠚⢿⣿⣿⣿⣿⣿⡯⢁⢰⡷⢿⢾⢿⣿⡿⢛⣥⣼⠂⣿⣵⣿⣖⡆
⠀⠀⠀⠀⠀⠴⣿⣿⡟⡍⠸⣿⡴⡮⣾⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠁⢠⣷⣶⣿⣿⣿⣽⣿⠖⢲⡜⡅⣧⣿⣉⡀
⠀⠀⠀⠀⠀⣤⢉⡝⣻⣧⡿⣌⣷⣿⣿⡟⣜⣿⡛⢻⣏⣿⣿⣿⢿⣏⠠⣷⠾⠛⣿⡻⣟⣤⢉⣎⣳⣞⡿⡖⣿⣽⡏⢿⠥
⠀⠀⠀⠀⠀⠉⠛⡑⢿⣿⣇⣼⠓⡌⣻⡻⣭⢗⣰⣇⠀⢸⣿⣿⣶⠿⣠⣤⣿⣤⡾⠶⣿⣏⣽⡿⢷⣤⡄⢻⠉⣰⠷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠈⠉⣿⣿⠏⠀⠉⠓⢁⠊⣽⣿⠋⠀⠓⠀⠁⠈⠁⠀⠩⠿⢟⠨⠼⢿⣿⣿⠦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⢩⣫⡄⠀⠀⢀⠀⠃⠀⠀⠀⠀⠌⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⢠⣤⠀⠀⠀⠶⢀⣦⢰⡟⢻⡄⣶⣴⡒⠒⠒⠃⠀⠐⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠾⣷⣶⣶⢾⠟⠉⠐⣿⠿⢽⡇⠈⣧⡼⡯⢼⣷⣶⣾⢿⣋⡁⢀⡈⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⢲⠶⢌⢻⠙⡇⢌⣿⣋⣁⠀⣉⠉⠙⠙⡛⠛⠉⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠱⠁⠛⠒⠒⠓⠨⠋⠃⠗⠐⠁⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⢀⣀⣀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⢻⣶⣄⢀⣾⡷⠀⠀⠀⠀⣀⣀⣀⣹⠁⣀⣛⠛⠉⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⠀⠀⠋⣡⣤⣶⡆⠈⠛⠻⠿⠟⠁⠀⠲⣄⣎⡀⠀⠀⠙⣆⠘⠿⣿⣦⠀⠀⢸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠷⢂⠚⠛⠛⣉⣀⣀⠀⠀⢤⠀⠀⠀⢰⣾⣿⣷⡄⠀⠀⢸⡆⢷⣴⠚⠙⢳⡌⠁⡀⠀⢀⣼⡗⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀⢙⣿⠟⠛⠉⠉⢻⠻⠾⣧⣄⣀⠘⢿⣿⡿⠁⠀⠀⢸⣷⣿⣿⣿⠀⢠⡏⠀⠙⢦⣾⠟⠁⠀⢀⣿⡇
⠀⠀⠸⣦⡀⠀⣰⣿⣿⡟⠀⠀⠀⠀⡾⠁⣠⣤⣤⣀⠸⢃⡤⠖⠩⡝⠻⣶⣄⠀⠀⠀⢀⡾⠁⠛⠛⠋⣠⣞⣁⣀⣀⡠⠀⣠⣤⣀⠈⣿⠁⢸⣦
⠀⠀⠀⠘⠿⣴⣿⠿⠋⠀⠀⠀⠀⠀⣷⠀⠀⠉⠛⠛⠃⣞⠀⢠⣤⣿⣶⣌⢻⣷⣄⣠⠟⠀⠰⠟⣦⡴⠟⢉⣴⠈⠉⢷⣄⣩⠛⠛⠉⢣⠀⢈⠟⢴⣶⣿⣷⠶
⠀⠀⠀⠀⠀⢀⣤⣴⣧⡀⠀⠀⣠⣶⡿⠷⣄⣀⣠⠴⠁⢻⣄⢻⣿⣿⣿⡏⠀⢹⣿⡟⠀⠀⣠⣾⠋⢰⣦⣿⠋⠀⢼⣿⣿⣷⠀⢀⣠⠞⠂⢁⣴⠀⠈⠉⠁
⠰⣶⣶⣶⣧⠘⣿⣿⣿⠃⠀⢸⠿⠟⠁⣠⡶⠛⠓⣢⣼⡄⢻⡆⠙⠛⠋⠀⠀⠀⣿⣿⣶⣿⠟⠁⢸⠆⠛⢁⣠⡀⠘⠿⠿⢏⠜⠉⠉⢻⣷⡿⠃
⠀⠈⠉⠁⠈⠳⣬⣉⣁⣀⣀⣠⣤⣀⣸⡟⠀⠀⢸⣿⣿⣿⢠⣿⠞⠋⢉⡙⠳⣄⢸⣿⣿⡏⡠⣒⡒⢾⡀⢻⣿⣿⠀⠀⢀⡞⠀⠀⢾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣯⣹⠟⠉⠀⠀⠉⠻⣷⡀⠀⠈⠻⠿⢋⡿⠁⠀⠀⢸⣿⡀⢸⣾⣿⣿⠀⢏⣿⠟⠀⡧⠀⠉⠁⣀⣤⠞⠀⣸⣷⠘⣿⣿⣿⣿⢃⣦⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣦⠀⠀⠀⣠⠈⠻⢦⣤⣤⣤⣸⡇⠀⠀⣀⣈⣻⡇⠀⣸⣿⣿⠀⢸⠄⣀⣼⣷⣶⣶⣟⣉⠀⠀⠀⠹⣿⠀⠈⣋⣙⠁⠈⣿⢀⣴⣿⠇
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡏⠘⠳⠦⠋⢀⣠⠀⢶⡍⠉⠙⠿⣦⡈⠛⠋⠁⠀⣠⣿⣿⣿⣄⣠⡾⢋⣙⣴⡖⢀⡤⠈⠙⠒⠦⠄⠂⠰⣶⣌⠻⠿⠶⠅⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠻⠿⠿⠋⠀⠀⠀⡆⠾⠿⠋⠀⠘⢃⣴⠟⠁⠈⠻⢷⣶⣶⣾⣿⣿⣿⣿⣿⠏⠀⢻⣿⣿⣿⡆⢀⣴⠞⠛⠛⠓⢦⣄⠀⠉⠀⠀⠀⡬⠀⠀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣄⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣄⡀⠈⠛⢛⡻⣣⡟⠁⢀⠀⠀⢤⣄⣽⠛⠲⠶⠒⠛⠓⠢⡘⠛⠁
⠀⠘⠿⠶⣄⠀⠀⠀⠀⣀⣴⠞⠉⠉⠉⠙⢛⣻⠯⢭⣉⠙⠛⠛⠻⠷⣦⣄⠀⣿⣿⣿⣿⡟⠉⠙⠛⠛⠉⣰⡟⠀⠀⢸⡇⢀⣴⣿⣿⣿⣄⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⣰⣶⠒⠒⠛⠻⢃⣴⠆⠀⠀⣰⠋⠀⠀⠘⠻⣧⠄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣠⣾⠏⠀⠙⠻⠾⠃⢸⣿⣿⣿⣿⣿⠀⠀⣻⣄⣂⠁
⠀⠀⠀⢰⣿⣿⠀⠀⠀⣶⣿⡇⠀⠀⠀⣿⠀⠀⠀⢰⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣷⣤⣤⣤⠴⠊⠀⠀⠻⣿⢿⡿⠃⠀⢸⣿⣿⣿⠃
⠀⠀⠀⠘⡿⠋⠀⠀⠀⠘⠛⣁⠀⢀⣀⣹⣆⡀⠀⠈⢿⢿⡿⢁⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⣫⣯⣭⡉⠉⠛⠶⣄⠙⠷⣄⣠⣶⣿⣷⠆⠀⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣷⣋⣀⠉⠛⠻⢶⣦⣶⣶⠾⠟⠛⠉⠉⠻⣿⣿⣿⣿⣿⡟⠀⠀⢻⣿⣿⡟⠀⠀⣴⠈⠙⢦⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠉⠉⢤⣤⣀⠍⠀⠀⠈⡷⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⣩⡷⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⢛⠿⢛⠻⠻⣿⠟⣿⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢀⣠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⣹⣦⠂⡀⠀⠀⠀⠠⣀⠀⠒⣈⠳⢎⡐⠣⣆⠴⣗⠦⣀⡴⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣧⣤⣤⣰⡏⣤⡀
⠀⠀⠀⠀⠀⢹⣿⣤⣤⠆⠀⠠⣀⠫⢴⣋⢹⡍⣅⠛⠚⠀⢈⡣⣄⢹⠾⢥⣾⣷⣄⣄⣈⡀⢄⠄⠀⠀⠀⠈⠀⠹⠉⠟⠁⠁⠉
⠀⠀⠀⠀⠤⠚⠉⠉⠁⠀⠀⣀⡋⡷⣿⣯⠾⣞⢾⣁⣡⣚⡏⣄⡣⠬⣐⠀⠈⣌⠹⣄⡸⢾⠇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠇⢸⢿⣷⣯⡙⢰⣁⣀⣎⠔⠀⡽⣶⣣⡤⡜⠚⢛⣄⡐⡠⠟⡈⢗⣊⡰
⠀⠀⠀⠀⠀⠀⢠⣄⠾⣑⣶⣿⡉⢳⢽⡏⣸⠌⡁⣩⠦⣤⣻⣿⣿⣗⣗⡆⢀⡚⣂⡖⠓⡮⣤⠵⢟⠴⠅⠀⠀⠀⠀⠀⠀⠠⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣥⢴⣿⠟⣾⣿⣯⡣⣐⣗⣰⢗⡊⠙⣞⣓⠋⣿⢿⣻⣽⡽⠳⡿⣻⢖⣻⣻⣦⣾⢺⠓⠀⠀⠀⠀⠀⠀⠀⠛⠑⠢⡄
⠀⠀⠀⠀⠀⠀⢚⣻⣿⣧⣤⣿⡎⠉⣿⣽⣖⡞⣾⣻⣶⢿⣟⢶⣿⣿⡉⣾⣷⣦⣻⣿⣿⣾⣷⢋⡙⠛⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠉⡷⣾⣿⣿⡏⠙⣿⣟⣿⣾⣿⣤⣼⣿⣿⠿⢻⠛⣿⢛⠻⡿⢴⡿⣞⣿⣦⡟⠘⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⡵⣏⢿⡟⢻⣻⢿⠞⠹⣾⡗⣻⡆⡋⢈⢖⠘⣷⠉⣀⡴⠗⠉⠹⢢⡗⠈⠹⠟⠀⠀⢀⡄⠀⠀⠐⠀⢀⣀⣀⣤⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠺⠓⠎⠁⠉⠲⠦⢬⣧⡀⠸⡇⠀⠈⢀⢟⡟⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⠀⠀⢠⡏⡎⠀⠀⠀⠀⠀⢀⣀⣤⣤⠒⠉⡏⢠⣶⣤⣄⡀⠀⠀⠀⠀⣴⡦⢄
⠀⠀⠀⠀⠀⠀⠀⢠⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢀⣸⢠⠀⠀⠀⠀⣠⣾⣿⠿⠟⢸⡿⠛⠛⠛⠿⣿⣚⣿⡄⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⢘⠀⠀⠀⢠⣿⣿⢻⢀⣀⡜⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠉⢀⣹⡇⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⣿⡄⠸⠀⠀⠀⢸⣿⣿⠼⣚⢿⣇⠀⠀⠀⠀⠀⢠⣿⣯
⠀⠀⠀⢀⣤⡾⣿⣷⣄⠀⠀⠀⠀⣠⡾⠇⠀⠀⠀⣰⣻⠃⢀⠀⠀⠀⠈⠉⠀⣰⣿⣿⣿⣷⣶⣤⣴⠟⠀⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣿⣿⡶⠟⠋⠀⠑⠒⠶⠞⠋⠀⠀⠀⠀⠀⠁⠉⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⠎⣡⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠹⠶⣽⣭⣍⡱⠆⣤⢬⣴⢦⣀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠈⠤⠎⣡⣴⢏⡳⠄⠠⣿⣿⢦⡟⠴⣮⠓⣤⣿⢡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡵⢄⡄⣐⣢⠴⣀⣶⠳⡌⠶⣼⣰⣥⣿⣀⠜⡶⣿⡔⠿⢷⣽⣒⣾⣷⣋⣙⣿⣿⣉⠡⡄⠀⠀⢀⣀⠀⣀⡠
⠀⠀⠀⠀⠀⠀⣷⡶⣤⣛⠳⢞⣿⢿⡎⣙⣿⣛⣁⢲⣶⣼⣛⣧⣀⣾⣯⣟⢭⣻⣿⣞⣿⣿⣷⣾⠟⢭⣿⣛⣩⣥⡚⣻⢯⣢⣌⡚⠏⠁⡀
⠀⠀⠀⠀⠀⠐⠿⣣⠽⢇⣱⣽⣿⢁⣿⣭⣽⣿⣿⣿⣽⣶⡿⢿⣿⣶⣿⣷⣼⣿⣿⣷⢿⣫⣾⣾⣿⣿⣿⣿⣯⣿⣿⢿⣏⣵⣿⡧⠟⠋⠁
⠀⠀⠀⠀⣾⡆⠀⣭⣽⠺⣯⣿⣻⣿⣾⣿⡿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣷⣿⡯⣽⣿⣿⣟⢿⣿⣿⣿⡿⠾⣾⣝⠼⣿⣶⣆⠀⢀
⠀⣠⠴⣦⣿⣷⣋⣡⣉⠿⣿⡿⣿⣿⣿⣿⣿⠿⣯⠱⠿⣋⣿⣿⡿⣿⣿⣿⣿⣿⣝⣿⣿⣳⠿⣿⠾⢿⣻⣼⡟⠿⣲⣶⣯⣿⣾⡟⠐⠂⢰⡿⢗
⠀⠀⢐⣳⠉⣹⣿⡿⣬⣻⣿⢶⣬⣿⣿⣿⣿⣷⣏⠘⢿⣮⣠⣝⣿⣍⣿⢰⣿⣿⣿⣟⠟⢿⢇⣩⠆⣻⣷⣿⣧⣿⡿⢻⣷⣿⣧⣿⣷⣾⣧⣽⡄
⢀⡀⢤⢼⡿⠻⣾⡗⣾⠿⡿⣜⠸⠿⣁⣯⣭⣽⢏⡷⢦⣞⢿⣇⢘⣿⣼⢟⣛⡍⣥⡙⢾⣟⣽⡿⣛⠦⢯⡷⠿⣿⠷⠻⢿⣟⠛⠿⠿⣿⠃⠈⠁
⠉⠙⠿⠝⣛⣽⠻⣇⣹⣟⣿⡿⠟⢷⣿⣯⡉⣌⠛⣗⣾⣻⡴⣏⣸⢮⣳⣾⣭⣾⡿⢟⡳⢿⠉⠁⠘⠓⠲⡷⣊⢁⣶⣿⣿⢿⣐⣶⣆⡿⡘
⠀⠀⣀⣤⣿⣿⣟⢻⣦⠼⠋⠁⠀⠀⠹⢻⣿⣿⡋⢻⠘⠛⣻⢥⢽⣿⣉⣿⡏⡿⣩⣺⡹⣶⡔⣧⣤⣤⢤⣤⡬⠿⠵⣶⢿⣻⡏⣻⢺⣵⣰⡄
⠀⠶⠿⠋⠿⣧⡾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡋⢧⠀⣈⢿⣿⣿⣝⠺⣟⢁⣉⣽⣒⢗⣌⢤⡀⠻⡏⠙⠲⢦⡤⢄⠟⣼⠷⢯⣟⣻⣯⠠⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢻⡝⢾⣿⣿⠇⠚⠥⠄⠑⠈⢹⢀⡉⠀⠀⠀⠀⠀⠀⠀⠈⠀⣷⣛⠿⢈⡯⣯⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠁⢸⣽⣿⡀⠀⠀⠀⠀⠁⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣟⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠡⢴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡻⠱⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⣤⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⢧⣿⣿⠇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠂⣸⣿⣿⡄⣶⣶⣿⢿⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠐⢀⠆⢀⣼⣿⣿⣿⣆⠃⠀⠀⢘⣀⠖⠚⢂⢀⣖⣴⣆⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠬⠰⠶⠷⢴⡼⢶⢿⣶⣿⢿⣿⠻⣿⠿⠶⡆⡞⠛⣶⣶⠖⠀⣀⣿⣄⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣀⠻⢾⣷⡄⣠⡤⢉⣤⣴⣶⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣰⣿⣿⣇⡈⠟⠻⡟⠉⣄⢛⠡⡶⢾⣉⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣆⡈⣡⢉⣭⡝⣵⠏⣴⡖⢠⣾⣿⡆⢻⡾⡻⣿⡿⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⣿⣿⣿⣇⡿⣫⢀⣰⠆⠼⣷⠎⢻⣿⢃⣸⣿⣣⣼⠏⢨⣙⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡼⣿⢲⣾⡟⢫⣾⠅⠟⢸⣿⣿⣦⣾⠈⣿⡷⣂⣛⣨⣭⣰⣿⣿⣿⣙⣯⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣖⠶⣌⠻⢿⣷⠟⣷⣞⢛⣻⡛⢹⣿⣐⠻⡆⣩⢭⡇⣬⣿⠻⣿⡏⢉⣽⣴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣿⣿⣷⣘⡩⠾⣃⣶⣼⣏⢀⣼⣿⣗⢠⣅⣿⣴⣿⣿⡼⠟⣿⣧⢙⡏⣱⠟⣡⣥⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⡋⢿⣜⢻⡇⢾⣿⣿⡷⣛⣽⣟⣁⢸⡟⣿⣧⠹⣿⡿⠷⠗⢈⣁⣉⣰⣭⠼⣿⣿⡿⢠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⢈⣘⡡⢬⠉⣭⣴⣤⢛⠯⣥⣎⣰⢽⢋⣴⣶⢂⣾⣡⠄⢩⡉⣉⡹⢶⣤⣭⣘⢻⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⣧⠞⣈⣉⣍⠘⠓⣠⣾⡟⡏⢳⣿⣿⣿⣠⢆⡄⠩⣬⡁⣴⣾⣿⣿⡻⠖⢤⣽⣛⡻⠥⠍⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠏⣌⣽⣿⣿⡆⢛⣫⠄⣾⣢⡴⣼⢖⡋⣿⣿⠠⣬⣉⠻⣿⣿⠟⢘⣛⣋⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⣻⡛⡡⠛⣥⣴⠶⣅⢰⣦⢸⡇⢙⣃⣝⠎⣩⣼⡳⠤⠼⡿⠟⣭⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢉⣵⣾⠷⣠⣤⣮⣯⠻⣤⣿⠸⣿⡙⠏⢏⣴⣿⣼⣦⣀⡻⠧⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠙⠙⣷⣄⠁⣿⣆⣀⣁⣴⣿⡏⠈⠃⠈⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠿⠿⠿⠿⠿⠷

⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⣄
⠀⠀⠀⠀⢰⣿⠭⠵⠖⠲⣌⡷⣄
⠀⠀⠀⠀⢸⢫⠄⠀⠚⠛⢻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⠀⠞⠂⣉⣉⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⢁⣀⣀⣀⣠⡴⠊
⠀⠀⠀⠀⡇⠀⠀⠐⠻⣭⡼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⡇⢰⡂⠀⠀⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⣀
⠀⠀⠀⠀⢷⡈⠙⢛⣯⡵⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠰⣫⠿⠭⠋⠁
⠀⠀⠀⠀⠈⣇⢀⠀⠈⠘⣆⠻⡄⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠙⠛⠾⣷⡶⣄⠀⢤⡀
⠀⠀⠀⠀⠀⣿⠀⢷⡀⠀⠈⠃⠹⣦⡀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⡀⠹⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠈⢧⠀⠀⠀⠀⠈⠻⣦⡿⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡈⠻⣦⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠻⣶⣀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠳⣄⠉⠛⠛⠒⠒⠒
⠀⠀⠀⠀⠀⢻⡰⡀⠘⣽⢦⠀⠀⠀⠀⠀⠀⢹⡍⢷⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⡇⣸⠀⠛
⠀⠀⠀⠀⠀⠘⣧⠫⠀⣿⠙⠿⠟⠂⠀⠀⠀⢨⣷⢾⠠⢤⣤⣤⣤⠞⠋⣠⣴⠄⠀⣧⡏
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠹⣆⡀⠀⠀⠀⠠⠴⠚⠸⡇⠀⠀⠀⠀⣀⢄⡰⡝⠁⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠨⡉⠛⠛⠒⠒⠀⠀⠘⢁⡼⠀⠀⠀⠀⠑⠒⠺⠀⢀⣼⠋⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⢦⣀⣀⣀⠀⠔⠋⠉⠀⠀⠀⠀⠀⢀⣀⣤⡴⠟⠁⠀⠈⠙⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣬⣉⢁⣠⡴⠶⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣽⣿⣿⣿⣦⡀⢀⣾⣿⣿⣿⣿⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣟⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣻⣿⣯⣵⣶⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣽⣿⣿⣷⣝⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣾⢿⣿⣿⣿⣿⣿⢻⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡷⠶⢟⣼⣿⣿⣭⣭⣭⡾⢿⣾⣻⣶⣿⣽⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢏⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⡇⣿⣿⣿⣯⣿⢧⣿⣿⣻⣿⣿⣿⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⣻⣵⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⢿⣿⣻⢿⣾⣽⣿⣿⢋⣾⣿⡿⣿⣿⣿⣿⣴⢿⣛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣶⣯⣿⡷⣾⢯⣿⣿⣿⡎⣿⣇⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣷⢿⣧⣟⣻⣿⡿⣯⣾⣷⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣽⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣯⣽⣟⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡄⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⣀⠀⠀⠀⠴⠓⠂⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠂⠀⠀⠀⠀⠀⠴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠐⣀⡀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⢄⡀⠀⠀⡄⠀⠀⠀⠈⠁⠠⠧⠀⠀⡀
⢀⠀⠀⠀⡀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡆⠀⠀⠀⠀⠠⠠⠀⠀⠀⠊⠀⠁⠀⠈⢣⣠⠆⠀⠀⠀⠀⠀⠀⠀⠻
⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣠⣄⠀⠀⠀⠀⠌⣡⡄⠀⠀⠀⠈⠱⠍⠀⣀⠀⠀⠀⠀⠈⠓⠢⢰
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣄⠽⢠⠄⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠈⢄⡀⠰⡂⠀⠀⠀⢀⣡⡤⠀⢠⠀⠀⠀⠀⠀⣡⣄⡆⠀⠠⡆
⠀⠀⢀⠀⠀⠀⠙⠁⠀⠀⠘⠃⠀⢀⠀⠀⠀⠀⠀⠒⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠥⡄⠀⠀⠀⠀⠀⠀⠵⠂⠀⠀⠀⠀⠀⠀⠀⠚⠢⠄⣠⠄
⠀⠀⠹⢳⡄⠀⠀⠀⠀⠀⠀⠀⣀⠉⠁⠀⠀⠀⠀⠀⠀⢀⡤⠒⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⣴⠒⠀⡀⠐⠉⠀⠀⠀⠀⠁⢻⠋⠁
⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠲⠷⣦⣀⠀⢀⡤⠀⠀⠀⠀⠀⠀⢻⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠳⠠⠀⠀⠀⠀⠈⢆⠙⣼⡇⠠⣄⠀⠀⠀⠀⠒⠛⠒⠃
⢠⡄⠀⠀⠴⣿⣁⠀⠀⠀⠀⠀⠀⠐⠁⢀⠈⠃⠀⠀⠀⠀⠀⠀⠙⠿⠀⡀⠀⠀⠀⠀⠀⢒⢔⢁⡀⠀⠀⠀⠀⠀⠀⠉⠘⡳
⡆⠁⠀⠀⠀⢬⡟⠀⠓⠀⠀⠀⠀⠀⠀⠹⠀⠄⡆⣀⡄⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃⣪⢧⠠⡀⡤⠀⠀⠀⠂⠀⠉⠛⠁
⠴⠛⠃⠀⠀⠀⠠⠞⡴⠀⡀⠀⠀⠀⠀⠀⠁⠀⢠⡈⠀⠀⠀⠀⠀⢀⠶⢀⠀⠈⠂⠉⠀⠀⠀⠁⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣲⠀⠀⠀⠀⠀⠀⠀⠡⡾⠀⢠⠐⠀⠀⠀⠠⠶⠾⠀⠃⠂⠀⠀⠀⠈⠈⠈⣠⡄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠛⠈⠁⡀⠀⠀⠀⠀⠀⠖⣁⠰⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠶⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣽⡄⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠡⠄⠈⠄⠀⠀⠀⠀⠀⠀⠀⡾⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠌⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠉⠈⠉⠟⠀⠀⠀⠀⠈⠀⡀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠉⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢀⣤⣤⠀⡆⠀⢀⠔⠀⠀⠀⠀⠔⣠⣤⣄⢠⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⡑⠛⠀⢀⣤⣾⣦⣠⣶⣦⡀⠀⠙⢂⣿⡆⠄⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠙⠻⠶⢿⠟⠋⠉⢈⡁⠉⠙⠻⡿⢶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠂⠄⠜⠣⠀⠄⠊⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣈⡄⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠘⠛⠛⠛⠢⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠛⠛⡄⠀⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⣀⣀⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⠛⠛⠛⠛⠛⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠸⠉⠉⢹⠀⠯⠉⠉⠽⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠠⡀⠀⡈⠀⠰⠀⠀⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣠⣄⣠⣄⣀⣀⣥⣀⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⣿⣿⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠸⠟⠋⠁⠀⠀⠀⠈⠙⠻⠷⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠄⠀⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠃⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠀⠘⠁⠄⠀⠀⠆⠀⠂⠁⠀⠤⢀⠁⢆⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠆⢘⡄⠀⠀⡙⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠁⠀⠀⠀⠐⠐⠄⠀⠀⠀⠀⢄⠀⠇⠀⠀⠈⠀⠀⠀⠀⠀⠈⠘⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠊⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⠀⢠⣧⡀⣹⢿⡇⠠
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡳⠀⠀⣆⡀⢀⠀⠀⠆⠀⠀⠀⠀⠀⠙⢏⠙⠌⣷⠀⣦⠂⠀⠀⠀⢀⣀⠠⠄⠀⠤
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠶⠀⢂⠀⢸⣷⠇⢠⡴⠚⠁⠀⠠⢦
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⠋
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⡀⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠠⡤⠀⢀⡀⣀⡈⠁⠀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⣨⠷⠦⢥⣄⠀⠀⠀⢠⡆⠀⠉⠿⠀⠀⣀⣤⣴⡦⣤⣤⣄⡤⠄⠈⠀⠀⠈
⠀⠀⠀⠀⠳⠀⠀⠀⠀⡤⠀⠄⢀⠀⠀⠈⠀⠀⠐⢊⡀⠀⠀⠀⠉⠑⠦⣀⠉⠁⠀⠀⠀⠀⠀⠟⠉⠉⠁⠣⠀⡀⠈⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⢄⣈⠀⠀⠘⠸⣇⠀⠀⠀⠀⠀⣿⡆⠀⣴⢦⣀⡀⠀⠀⠀⠀⠀⠂⠀⡁⠠
⠀⣤⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠑⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠑⠀⠏⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠘⠀⠐⠂⠀⠀⠀⠀⡠⢿⡋⠙⠋⠉⠉⠉⣒⣶⡶⣞⡓⠂⠀⠀⠀⠒⠿⣤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⣤⠁⠈⠃⠀⠘⣁⠔⠁⠀⠀⠉⠑⠦⣤⠀⠀⠀⠉⢲⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈
⠀⠀⠀⢰⡀⠀⠀⠀⠄⠀⠁⠀⠀⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⢿⡜⠀⠀⠉⡉⠁⢈⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⣅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠃⠈⠁⢀⣈⣉⠀⠀⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢈⣄⡀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⡉⠁⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠘⠅⠢⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⣽⢇⣆⡀⠀⡀⠀⠐⠲⠛⠛⠛⠗⠤⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⡀⢀⡀⠀⠀⠀⣈⡻⠂⣠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠿⣃⡀⢀⣠⣉⠁⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡜⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⡄⣠⡆⠀⠀⠀⠀⠀⠰⠿⠗⠀⠉⡤⢠⡉⠉⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠴⠮⠀⠐⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠉⠴⠂⠀⠀⠀⠀⠀⣴⣶⣶⡤⠀⣬⢃⢂⡀⢈⠉⠁⠀⠀⠀⠀⢠⣤⣰⡇⡠⣤⣶⣦⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡛⠀⣠⡀⠀⠀⠙⠿⠟⠁⢇⡰⠃⠘⠇⠿⢀⣀⠀⠀⢀⠀⣤⡛⣧⡜⠁⠻⣿⡿⠁⠀⣷⡄⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠐⢄⠟⣡⡤⠀⠀⠀⠻⠗⣼⠘⠛⠛⢀⡄⠘⠁⢰⣄⠻⣃⡴⠚⢁⣛⡸⠄⠀⣀⠶⠦⠈⠀⢶⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠴⢆⡑⢭⡀⣴⠀⠀⠚⠃⠹⣌⡻⠆⠉⠀⠀⡼⠀⣱⡾⠛⠋⣉⣉⠀⣼⠇⠈⠛⠇⢀⢎⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⣀⡙⠦⣝⠀⣾⠀⡶⢪⡿⣦⠈⠛⢛⡱⣄⡟⠰⡆⢾⣿⣿⡇⢀⣤⠀⣾⢀⡞⠸⣿⣿⡟
⠀⠀⠀⢀⣠⣤⡀⢠⡄⢀⡄⠀⠀⠀⠀⠀⣿⣿⣿⠆⠈⣙⠦⣄⡰⡆⢠⡿⣤⡬⢉⣡⣼⡗⢀⡀⠈⠙⢉⣀⣛⣣⣤⠶⢛⡰⡆⢀⡀⢰⡇⣴⣾⠿⠂
⠀⠀⠀⠈⠙⠛⣋⡈⠁⠿⠃⣠⠀⠀⠀⠀⠈⠙⢉⣀⠘⡋⠰⠈⠻⣶⣿⢀⣠⡶⢛⡉⢵⣄⠈⠓⣴⡿⠟⠛⠛⠻⠷⢦⣌⣀⣀⣺⣣⠌⢡⣦⡀
⠀⠀⠀⠀⠀⠚⠛⢱⡆⠈⠲⢥⡀⢹⣦⠀⣠⡜⠃⠙⠃⠛⢀⣈⣳⣘⣿⣿⡏⠀⠘⠃⠀⣉⡀⢸⣿⢀⣛⠇⢠⣶⣶⡄⢰⣎⠉⣉⠀⠸⡇⣉⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣆⠙⠳⣥⣀⠉⠀⠞⠀⢶⡄⠀⠖⢀⣩⠻⣿⣧⠛⠁⠀⠀⠘⠛⣼⣿⣬⣭⣀⠘⠿⠿⠃⠀⢉⣀⣟⣘⣃⣀⠟⠰⠟⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⣰⠿⠀⣍⠛⠛⣛⡓⠲⠶⣶⡄⠘⠋⢼⠊⢿⣧⠀⠀⣠⣴⣿⣿⠟⠁⣨⠙⡛⠛⠛⣋⡍⠉⢉⣁⡀⠠⣄⠀⠰⣦⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢰⡄⢠⡆⠉⠤⣶⠍⣡⡾⠛⠻⠿⣶⣶⣦⣤⣈⣿⣧⣼⣿⠟⠉⠀⠀⠈⠉⠸⡿⠀⠐⠛⠁⠀⣿⣿⣿⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣌⠛⠈⠵⠒⠓⠒⠶⠶⠿⢫⣄⠀⠀⠀⣶⢠⡍⠛⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⡾⠿⠋⠀⠻⠆⢠⣶⣿⣶⠀⠺⣦⠉⠁⠀⠀⠀⠈⠃⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀⠀⣀⣀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠘⣿⣦⡀⣴⣿⠀⠀⠀⠀⣀⣠⣄⣹⠋⢀⣛⡛⠋⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⠀⠘⢉⣤⣶⡶⠂⠈⠛⠻⠟⠋⠀⠘⢦⣾⡁⠀⠀⠙⢦⠈⠻⠿⠷⡀⠀⢸⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠓⢖⡛⠛⣉⣀⣀⣀⡀⠠⡄⠀⠀⢠⣾⣿⣿⡆⠀⠀⠘⡆⢻⣴⣋⠉⢳⡌⠁⣄⠀⣠⣾⡇⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠀⠀⠀⠀⣹⠿⠛⠉⠉⢉⡟⠻⠿⣦⣤⣀⠻⠿⠿⠃⠀⠀⢰⡿⣿⣿⣿⠂⢰⡇⠀⠙⢧⡿⠋⠀⠀⢸⣿⠃⣀
⠀⠀⠸⣷⣄⢀⣾⣿⣿⠇⠀⠀⠀⢸⡏⠀⣴⣶⣤⣄⠃⡴⠒⠛⣯⠙⢿⣦⡀⠀⠀⢀⡾⠁⢙⠛⠋⣰⣿⣤⣤⣄⡔⢠⣤⣤⣤⣸⠏⠀⢿⡆
⠀⠀⠀⠈⠻⠼⠿⠛⡁⠀⠀⠀⠀⢘⣇⠀⠀⠉⠉⢉⢸⡃⢠⣶⣿⣷⣶⠙⣿⣦⣴⠏⠀⠐⢋⣧⡾⠋⣠⡶⠀⢈⣳⣦⠼⠉⠁⠈⡂⢀⡬⠓⢾⣿⣿⠿⠃
⠀⠀⠀⠀⡄⢰⣶⣾⣷⠀⠀⢠⣾⣿⠋⠳⠤⣤⠖⠃⡈⢷⡈⢿⣿⣿⡟⠀⠘⣿⣿⠀⣀⣴⡿⢋⡸⣷⡿⠁⠀⢿⣿⣿⡷⢀⣤⢴⣋⢀⣴⡏
⠘⠿⣿⠿⢧⡘⢿⣿⡟⠀⠀⠟⠛⠁⢠⡾⠋⠉⣩⣶⣷⡈⣿⣈⣉⣭⣄⣀⠀⢹⣿⣿⣿⠋⠀⡸⢧⠉⣠⣴⣄⠘⠛⠛⡱⠃⠀⣀⣽⣿⣫⣀
⠀⠀⠀⠀⠀⠙⠶⢦⣤⣤⠶⠶⠶⢤⣿⡇⠀⠀⣿⣿⣿⢧⡿⠋⠁⢀⣦⠉⢳⣸⣿⣿⡇⡜⣽⣭⠹⡄⠹⢿⠟⠀⠀⣰⠃⢠⡀⢿⣿⣿⣿⣿⢀
⠀⠀⠀⠀⠀⢀⣀⣷⣾⣅⡀⠀⠀⠀⠙⣧⡀⠀⠈⠉⠉⣾⠁⠀⠀⠸⣿⡇⢀⢿⣿⣿⡇⢱⡟⠋⢀⡗⢀⣀⣠⡴⠞⠁⠀⣿⣷⠘⢿⣿⣿⠏⢸⡇⠀⣀⣤
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣤⣀⢰⡇⠀⠙⠛⠶⠶⢶⣿⡀⠀⣤⣶⡾⠓⠀⣼⣿⣿⡇⠘⣃⣴⣿⠛⣛⠛⠲⠦⣄⣀⠀⠙⠻⣀⡀⢦⣤⣀⡸⢇⣼⣿⠏
⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠁⠈⠉⠋⣠⣶⠖⠈⣷⠀⣠⡌⠻⣦⣄⣀⣀⣀⣴⣿⣿⣿⣷⣾⠋⢠⣶⣿⣧⠰⠃⢀⣠⣭⣭⣉⠀⠙⠻⠦⠉⠉⠉⡈⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣄⠉⠁⠀⠀⠨⡚⠋⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡃⠀⠸⣿⣿⣿⣇⣴⠟⠁⠀⠀⡈⠙⣦⣄⣀⣀⣠⣴⣁⡀⣴⡿
⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠾⠶⣤⣤⣤⠤⠷⠦⠤⣤⣤⣤⣀⠀⠈⣿⣿⣿⣿⣿⠿⠶⣤⡤⠴⢋⣾⠃⠀⣶⡄⠀⢻⣷⣧⡄⠉⠉⠀⠀⠀⠹⡄
⠀⠀⠉⠉⢡⣀⣀⣤⣴⢾⠏⣀⠀⠀⠀⣠⠖⠋⠉⢿⣦⢀⠀⠀⠉⠻⣿⣦⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⡾⠁⢦⣤⣹⠇⣼⣿⣿⣿⣿⣧⠀⠰⣄⠀⠼⠃
⠀⠀⠀⢠⣿⣿⠀⠀⠀⣼⣾⡋⠀⠀⢠⡇⠀⠀⠀⣠⣽⣧⣄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧⣀⣤⣴⣾⣏⣀⠀⢀⣀⡕⠀⠸⣿⣿⣿⣿⠃⠀⣴⣿⣷⣦
⠀⠀⠀⢸⣿⡟⠀⠀⠀⠿⠿⠃⠀⠀⠘⣧⠀⠀⠀⢻⣿⣿⡿⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣟⠻⠿⢯⣅⠀⢶⣄⠈⢉⣭⣥⣤⡀⠹⣿⡿⠃
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⢳⣤⠞⠛⠻⢷⣦⣄⣀⣩⣭⣴⡿⠿⠿⠿⣿⣿⣿⣿⣿⡿⠋⠀⢿⣿⣿⡷⠀⠀⣬⠛⢦⡬⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠘⠛⠛⣁⣀⠀⠛⠀⠀⢹⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠛⢛⣦⣀⣠⠜⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣼⠥⠀⠀⠀⠈⠑⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣿⠾⠃⠀⠀⠀⠀⠀⢀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣴⣶⣶⡶⠶⢶⢶⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⣼⢸⡇⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠃⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⠛⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠇⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⣴⠶⠿⠛⠷⠶⣦⣀⡏⠈⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⢰⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠛⢧⣄⣀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢀⡴⠞⠛⠒⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠺⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠉⠁⠂⠉⠀⠀⠐⢀⡀⠀⠀⢀⠄⠤⠆⠠⠤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⡀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⡠⢄⡀⠢⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠐⠀⡠⠂⠴⠘⣆⡠⠐⡤⢄⡠⠖⠂⠀⠀⠀⠃⠉⢢⡀⣀⠀⣀⠀⠤⢀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣈⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠀⠳⠆⠀⢀⣀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⢘⡀⠀⢴⠎⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⡄⠀⠀⠠⠈⠐
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⡆⠈⠁⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣀⣋⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⢘⡀⢀⣄⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠐⠀⠀⠀⢀⠾⠀⢀⠀⢀⠹⢤⡀⠀⡀⠀⠀⢠⠀⠀⢾⠁⠀⠀⠁⠀⠀⣷⠀⠀⠀⠀⠀⠆⠠⢆⠁⠐⡀⢀⡄⠀⠀⠈⠃⠀⣀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⣀⠦⠀⠀⠈⠀⠉⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⡀⢀⡀⠈⠐⠣⠤⢄⠀⢠⡀⠀⠀⠈⠑⢄⠀⠀⠈⠐⢀
⠀⠀⠀⠁⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣄⠃⡜⠳⠦⠤⠴⠋⠁⢄⠀⠈⠠⡌⠀⠀⠁⣠⠒⠒⠶⠔⠦⢤⠀⢀⡄⠀⠠⢎⠀⠀⠀⠀⢸
⠀⠀⠄⠀⡐⠉⠈⠀⠀⢀⡺⠄⣐⡇⠀⠠⠤⠒⡏⠉⠋⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠢⠝⠋⠀⠀⡇⠀⠀⠀⠀⠀⠈⡗⠀⠀⢠⠀⢈⠀⠀⠀⠀⠀⢰
⠀⢠⠢⣀⠃⠀⠀⠀⠀⠀⠀⢲⠀⠈⠁⠀⠀⢰⠅⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠐⠂⠀⠃⠀⠰⣄⠀⠀⠀⢀⡼⠃⠀⣀⠉⢀⡇
⢀⠀⠀⢱⡄⠐⠀⠀⣀⡙⠀⣀⠀⠼⠀⠀⠀⠈⡄⠀⢈⣒⣤⠎⠀⠀⠀⠀⠀⣰⣁⡤⠀⠀⠀⠀⠈⠀⠀⠀⡠⠉⣛⠖⠛⡉⠀⠀⢀⠉⠀⠈⠀⠀⢀⡀
⠆⠀⠀⡆⡀⠀⠰⠏⠀⠈⠋⠀⠙⣦⠀⠀⠀⠀⠈⠉⠙⠟⠉⠀⠀⢀⡶⠶⢾⡁⠈⣇⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠈⠀⠀⠓⠀⠘⣋⠙⡋⠀⠀⡼⢀⠀⠀⠀⠘
⢠⠀⢸⡉⠦⠀⠸⡀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠈⣧⠀⢻⡄⠀⠀⠀⠈⣦⣀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠘⠀⡇⠀⠀⠀⠀⡇⠀⠀⡄
⠀⢀⠀⠈⠀⠀⠀⠹⢦⣀⣄⡠⠞⠁⠀⠻⠀⠀⠀⠀⠀⠠⢶⠆⠀⠀⠀⠀⠀⢸⡆⠘⣷⠀⠀⠀⢠⠃⠙⠖⠚⠉⠀⠀⠀⠲⠴⣥⠂⢰⠁⠀⢀⠀⠀⠈⠆⠀⢀
⠀⠀⡁⢻⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠐⠚⠁⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⡁⠀⠘⣆⠀⢀⡆⠀⠀⠀⠀⠦⢴⠃⠀⠀⠀⠈⠛⠃⠀⠀⠉⡌⠀⠸
⠀⠀⢁⠈⠒⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠠⠀⠀⠈⠀⠀⢧⡀⣀⣀⠠⠄⠛⠁⠀⠀⠙⠓⠊⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⡀⠀⠀⠀⠄⠀⠀⠐⡞⢀
⠀⠀⠀⠀⠀⠑⣤⠀⡀⠀⣤⠀⡀⠖⠋⠘⠲⠄⠐⠀⠀⠁⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣟⠑⠲⡄⠀⠀⠲⠢⢴⡁⠉
⠀⠀⠀⠈⠐⣎⠀⠠⠂⠀⠈⠙⡉⣴⠊⠉⠛⠋⠙⠲⡄⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠄⣀⣀⣀⡴⠏⠀⣿⢀⡄⠀⣬⠤⠐⠀⢺⡁
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠘⠀⠈⠀⣮⠀⠀⠀⠀⠀⠀⡗⠀⠛⠀⠀⠀⠀⠀⣿⠀⠆⠀⠀⡆⠀⠀⠀⡀⢀⠀⢀⠀⠀⠀⢀⣰⠃⡤⠛⠓⠶⠒⠒⢄⡨⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⠀⢴⠀⠘⢦⣀⡀⣀⣠⢞⢁⣄⡀⢠⡀⢀⣤⢠⡟⠀⠀⠀⠠⠙⠀⠆⠘⠈⡟⠓⢶⡖⠒⠛⠋⠁⢸⡃⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⡀⠀⠈⠉⠉⠀⠈⠇⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⡀⢀⠀⠀⠀⠀⣸⡅⠀⠀⠙⠒⠚⠳⠖⠙⢧⣀⠀⠀⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠐⠂⠐⠊⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⠋⠀⠇⠸⢸⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⡰⠁⠀⠀⢠⠀⠀⠀⡏⢱⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠁⠀⠀⠀⠀⠀⠀⢀⢹⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⡟⢣⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠂⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⢷⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⠀⡄⠀⠀⣰⠀⠀⠀⠀⠀⢀⠀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣼⢻⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡿⠄⡻⠀⠸⠀⠀⢠⠁⠀⠀⠀⠀⠾⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠐⢀⠇⠀⠀⠐⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⠁⢸⠀⠀⠀⣄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠇⠈⠀⣸⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠤⢦⣠⣾⣀⣀⣼⣣⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⠤⠶⠗
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡶⣶⠶⢻⠶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⣶⣶⣿⣿⡷⢉⣠⣬⣝⣢⣉⢵⣦⠚⠉⠻⢿⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⢻⡛⠿⣬⣷⣾⢻⡿⣿⣿⣿⣿⣫⣷⣿⣯⡿⢻⣟⣴⢆⣐⢺⣷⣿⣿⡿⣝⢷⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢾⡻⣏⠻⣌⢆⠓⣴⡏⢠⠔⢫⣾⣿⣿⣿⣿⣿⣽⣻⡿⣿⣿⣿⢛⣷⣷⡶⣾⣷⣯⠀⣋⣷⡈⣡⠟⡻⢶⣤⡀
⠀⠀⠀⠀⠀⢀⣴⣞⠻⣭⡢⢝⢮⣳⠝⠦⣰⣿⣶⢄⢠⣼⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣯⣿⡿⣯⣦⣽⡇⢈⡴⣋⡴⠛⣳⣄⡀
⠀⠀⠀⢀⣴⣟⡓⠮⣝⡢⣝⡳⢥⡈⠳⣰⣯⡼⣷⣏⣽⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣵⣾⣿⡇⠡⢚⣡⠶⠛⢝⣚⣿⣦⡀
⠀⠀⣴⣿⣷⣮⣝⡓⠦⣍⡓⠭⣒⢭⡓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣧⣼⣿⡏⢹⣿⣿⣿⣿⣿⣾⡟⠻⣿⣭⣿⠇⠚⢉⣠⡴⠾⣻⠯⠥⠬⢿⣄
⢀⡼⠟⠛⠻⢯⣭⣍⣙⡒⠮⢤⣀⡉⠒⢬⣿⠿⣿⣿⣿⣿⣿⡍⠻⣿⣾⣩⣿⠛⣿⡟⡠⢻⣿⣿⠛⢻⣿⣿⣷⣾⣿⣿⠏⢒⣋⣩⡤⢶⡞⠁⠀⠠⠈⠐⠹
⡼⠁⠀⠀⠀⠀⢷⣒⢾⡭⠿⠖⠋⠉⠉⠒⠦⣍⣂⢹⣿⡛⣻⣧⡔⢌⠻⣿⣿⣿⠏⠀⣰⣿⡿⢿⣿⡿⣋⣽⣋⣼⣟⣉⠞⠛⠧⢶⡒⢛⠇⠀⠀⠀⠀⠉
⡇⠀⠀⠀⠀⠀⠀⠙⠏⣀⣀⣀⣤⣄⡀⠀⠀⠄⠹⣄⢿⣿⣿⡛⣷⣴⣭⡀⠉⠁⢀⣮⣿⣿⣷⣴⡟⢀⣿⠿⠋⠠⡇⠀⠀⠈⠙⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠙⠉⣤⣼⣷⠀⠀⠀⠀⡼⠦⣌⣿⣿⣿⣿⣿⣧⡀⠀⠊⣿⣿⣿⠟⢡⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⡀⠀⠀⠀⠀⠀⢐⣿⠶⠃⢠⣆⣠⣮⣽⣿⣆⠀⠀⠀⣀⡀⣂⣀⣀⣙⣿⣿⣷⣱⣸⣼⣿⡶⡏⣿⠁⠀⠀⣤⣾⠍⠛⠲⣄
⣇⠀⠀⠀⠀⠀⢸⣿⣷⣿⣠⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠈⣿⣽⢸⣿⡟⣿⣷⣏⠀⠀⠐⣿⣿⣷⣄⣬⣿⠀⠀⠀⣀⣀⣀⣠⡤⠤⠶⠶⠒
⠹⣄⣀⣀⠀⠀⠀⢻⣿⣭⡽⣿⣷⣺⣿⡿⠤⠶⠶⠶⠶⠖⠒⠤⠴⠦⠤⣤⣿⢸⢸⡇⠟⣿⣿⣏⣀⣀⣀⣉⣛⣿⣽⣿⣿⣶⣿⣏⣩⣭⣤⣶⣶⣶⣶⣿⣿
⠀⠹⣿⡭⠍⠛⠛⠾⠿⣿⣿⣿⣿⣿⣋⣈⣁⣄⣐⣶⡖⢔⣖⣶⣶⡶⠶⢾⡿⡄⠜⠘⣴⣿⢿⣿⣭⣭⣬⣭⣭⣥⣭⣦⣬⣿⣿⣿⡿⠿⠿⢯⣏⣹⣿⣿⣿
⠀⠀⠘⢷⣶⣤⠤⣀⣀⠀⢸⣿⣿⡛⠿⠿⣯⣆⣉⡋⠉⠉⢉⠭⡉⣰⠾⣾⢇⣇⠀⢸⣿⣽⣿⣿⣿⡟⠛⣿⣿⡿⢟⡛⣟⠛⠛⣳⣾⣷⢾⣿⠿⢿⣿⠟⠁
⠀⠀⠀⠀⠙⢶⣶⠦⣭⣍⡛⠒⠢⠽⣶⣾⣷⣾⣭⣝⣛⡿⣭⣴⣠⣼⣵⣿⣾⣿⢶⣿⣿⣟⢿⣿⣿⣿⣟⣛⣛⣋⣉⣉⣉⣉⠛⠛⠛⠛⠒⠶⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠉⠻⣭⣓⣺⠿⢦⣤⢀⣀⢉⣀⣈⡭⠴⠛⠛⠉⣁⣴⠿⣛⣿⡿⣿⣿⠻⣮⣿⡭⣿⠿⣿⣙⠿⠶⠶⠿⡿⢿⡿⠟⠻⣋⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣤⣨⡉⣉⠉⢉⡥⠀⡤⠀⡀⠀⢀⠄⠉⢉⠀⠀⠀⠉⢉⠁⢈⣙⠈⠉⠀⠉⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠿⣿⣥⣶⣈⢤⣂⠴⣽⢢⠄⢱⠷⠂⣰⣪⠅⠖⣡⡕⠁⣀⣑⣐⣤⣤⠴⠞⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⡶⢿⣭⣿⣽⡿⢶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⡓⠀⢼⣿⠿⠿⠿⠟⠛⢶⣿⣻⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠶⢀⠇⠃⠀⠀⠛⠀⠀⠀⣀⣀⠀⠻⣯⣿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⡄⠚⠙⢶⠤⠐⡿⠟⢿⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠍⠀⠀⠀⠀⠀⢐⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣘⣃⠀⠀⠀⠀⣻⣦⣿⠁
⠀⠀⠀⠀⡄⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣀⣤⠞⣿⢇⡽⣿⣦
⠀⠀⠀⡈⠀⠀⠀⢠⡇⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⡀⠀⠙⣾⠿⠋⠀⠀⠸⣼⣛⣯⡟
⠀⠀⠀⡧⠀⠀⠐⠀⠉⠉⠉⠉⠉⠉⠉⠛⠻⣝⣟⠁⠈⢹⣷⣾⣿⣄⠀⠀⠀⠀⠙⣿⢯
⠀⠀⠀⣧⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡆⠀⠈⠻⠿⠉⠛⢦⠀⠀⢀⡴⠃⣰⠷⣄
⠀⠀⠀⠀⠉⠙⠲⠤⣄⣀⣀⠀⠀⠀⢠⣴⣾⡟⡼⠁⠀⠀⠠⣤⠴⢻⡞⣷⣞⣉⡀⢰⡇⠀⠈⠙⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣷⣶⣿⣿⣦⡆⣸⠇⠀⠀⠀⠀⠘⢻⡿⠁⠀⠳⣸⠁⡠⠂⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠻⠛⠿⢾⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠇⠀⠘⠟⠒⠒⣤⠶⣦⣶⣶⣿⣷⢔⠤⣄⣄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡄⠀⢚⠃⠀⠀⠀⠀⠀⠐⠟⣿⢛⣻⣿⣿⣯⣗⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠙⠄⢻⡅⠀⠀⠀⠀⠉⠉⣼⢣⣏⣭⣵⣾⣯⣟⠭⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠠⡄⠸⡘⡇⠀⠀⠀⠀⠀⢸⣧⠜⠋⠁⠀⠀⠀⠙⢷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡈⠣⠐⢧⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠉⢂⣀⡨⠤⠖⠋⠁⠀⠀⠀⠀⢀⣠⡴⠖⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⣀⠀⠤⠤⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⣠⠆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⢰⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠥⡀⠀⠀⡀⣤⡂⠀⢀⣀⠐⣴⠤⣂⣤⣀⢀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠄⠀⠀⠀⡀⠁⠀⠄⠙⣹⣿⣤⣄⠬⢿⣯⠙⣷⣴⣧⠠⢀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⢈⣸⣦⣄⡀⡀⠀⣀⡔⢠⡃⠀⠀⠀⠩⢹⡶⣿⣿⣿⣿⢿⡷⣶⣏⢡⣤⣠⣏⣰⠰
⠀⠀⠀⠀⣀⠀⠀⠃⡴⠉⠉⠉⢸⣿⣷⢆⠃⢼⣦⣶⠶⠀⠀⣩⣛⣻⣽⣿⣞⠟⣿⣿⣿⣽⣿⣍⣈⣶⣶⡘⠄
⠀⠀⠀⠀⠞⢷⠋⠩⠟⣃⣘⣷⣾⡿⢿⣵⡖⢻⢏⠀⠀⣀⣤⣿⣿⡾⢿⣿⣶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡵⠄
⠀⠀⠀⠀⢠⣄⠘⠀⠀⣤⠉⠙⡹⠀⠰⣠⡝⢏⣏⢿⠟⣋⣟⡟⢻⣿⣶⡀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣵⡋⡇⢀⠤
⠀⠀⠀⠀⠞⠁⠤⡾⠇⢰⣇⣤⢉⣄⡠⠘⣧⣾⣿⠞⠃⠀⠿⠙⢳⣿⣿⣿⣦⣻⠟⢿⣿⣿⣿⣿⣿⣣⠞⣻⠇⡀
⠀⠀⠀⠀⣴⢦⡐⠚⣿⣿⢿⣇⢸⣿⢀⣸⣿⣿⣍⣠⠄⠈⠀⣾⣧⣿⣏⡻⠿⣿⣷⣿⣿⣿⣿⣿⣿⣯⣠⡝⠬⠇⡂
⠀⠀⠀⠀⡤⠚⣥⠛⣛⣛⣺⡷⢉⡡⠇⣙⣶⣿⣿⣿⣾⣦⣶⣿⣾⣿⠿⣧⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⡖⠷⡛⠂
⠀⠀⠀⠈⠀⢀⡚⢥⠟⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⣆⣻⣽⣿⣿⣿⣿⣿⣿⣿⡌⠻⣿⣟⢉⠂
⠀⠀⠀⠀⢤⠼⠁⠋⠞⢡⣿⣿⣻⢫⣿⢿⣻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣽⣿⣿⣿⣿⣿⣿⠶⡯⠡⣾⣉⡀
⠀⠀⠀⠀⠀⠀⠀⣉⣠⢟⡁⣍⠰⠟⠉⠘⠉⠈⡷⠯⢀⣿⠟⠉⠛⢋⢿⠛⠹⣍⠻⣿⣿⣿⣷⣿⣿⣿⣶⣤⣴⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠤⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢠⢿⠋⠀⠀⠀⠀⠂⠂⠀⠬⢅⠀⠗⡬⡈⣿⠛⢛⡿⢿⢏⠳
⠀⠀⠀⠀⠄⠠⠠⠀⠀⠀⠀⠀⠀⠀⡀⣤⢤⠠⣀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡃⠀⠀⢐⠚⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠸⠀⠐⠒⠒⠂⠒⠊⠒⠒⠚⠚⠛⠿⠿⡿⠿⠿⠿⠛⠽⠿⠮⠽


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁⠀⠀⠀⠀⢀⣀⣠⣄⣀⡰⣶⠇⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠀⠀⠐⠋
⠓⠆⠓⠒⠂⠩⡤⠄⠒⠂⠸⠀⠀⠀⠀⠀⠀⠸⣤⣼⣧⡝⢁⣤⠀⠀⠀⣴⣯⣭⣶⣋⡱⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢐⡶⠾⣇⡔⠓⠀⢀⡈⣻⣿⣿⠟⠁⠀⠀⠀⣩⣿⣹⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃⢾⣷⣶⠿⠿⣿⣇⠀⡄⠐⠒⠁⠀⠀⠀⠀⠀⠈⠟⡀⠀⢠⣦⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠀⡃⠶⠋⡋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣶⡒⢛⣶⣧⠤⠆
⠀⠀⠀⠀⠀⠀⡀⠀⠀⣶⣼⣿⠲⢦⣄⣘⣁⠀⡀⠀⠀⢡⠄⠀⠁⠀⠀⠙⠋⣿⣏⢛⡿⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢀⡉⠄⠘⣿⣁⣴⡄⠀⠙⢿⣿⣿⣅⠒⠚⢂⡀⢻⡆⠀⠄⠀⠀⠈⠉⠉⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢈⡁⢀⠀⠉⠉⠉⠁⠀⣀⣶⢾⣿⣿⡷⣾⣿⡟⠻⡏⠀⠀⠀⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⢄⠀⠀⠻⢿⣬⡽⠉⠀⠀⠿⣷⠚⢁⠀⠀⠀⠀⠀⠀⠢⢴⣖
⠀⠀⠀⠀⠀⠀⠀⢊⠀⠠⠀⠀⠀⠀⠐⠚⠙⠒⠀⠂⣠⠶⣴⣷⣧⣶⣄⣠⠀⢐⡒⠀⣏⢀⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⢋⠀⠀⢶⣲⣏⣋⠀⢀⡤⠚⢛⢧⠸⡟⠋⢀⠘⠉⠃⠡⠀⠹⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⣹⢻⠿⢪⣦⣓⠲⠄⠀⠀⢰⠛⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠛⢯⣄⣀⠀⠀⢼⠄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣦⣄⣀⢀⣆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⣴⡏⣧⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠞⠉⠀⢀⠀⣠⡀⢀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢰⢀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠁⠀⠀⠀⠀⢸⣿⣄⠈⡟⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢻⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⠤⡄⠀⢾⣿⣿⣆⡄⣀⢠⡷⠄⠀⠀⠀⢠⣶⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣰⠇⠀⠈⠈⣿⡇⠅⠉⠀⠀⠀⠀⠀⠀⡸⡿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠠⣶⠲⠀⠀⠟⠀⠀⠀⠀⠀⠀⢠⡏⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠷⠖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠒⠐⠂⠂⠉⠁⠂⠉⠐⠀⠐⠂⠒⠉⠐⠒⠒⠒⠄⠤⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢑
⠀⢀⡀⠄⢀⡀⠀⠀⠈⠀⠀⠈⠁⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠔⠀⠒⠒⠀⠉⠓⠢⠜⠀⠐⠲⣄⡱⠀⢀⡀⢈⢉⣀⠀⠀⠠⠂⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠹⠯⠉⠳⡀⠀⠀⠀⡠⠀⣎⡷⠠⢄⠀⠀⠀⠀⠀⠀⠀⠚⢄⠀⠀⠀⠀⠈⠂⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢀⠄⢳⡿⢈⠉⠆⠀⠀⠀⢣⠘⠀⠀⠀⢀⠃⠀⠀⠰⠀⠀⠉⠁⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⠈⢢
⠀⠐⠂⠈⠐⠃⠠⠊⠉⠀⠀⠀⠀⢸⠀⠀⠀⠈⠂⡘⠀⠀⠀⠀⠑⠤⠀⠐⠁⠀⠀⠀⠀⠣⡀⠀⠸⣤⠌⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⡀⡄⠒
⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠑⠄⠤⠀⠐⠀⠀⠂⠐⠊⠁⡀⠄⣴⡀⡤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠖⠒⣾⠗⠒⢄⠀⠀⠀⠀⣇⠀⠀⠀⢀⠁⠈
⠀⠀⠀⠀⠀⡱⠐⠒⠄⠠⠠⣄⠀⠀⠀⠀⢀⡀⢠⠂⠁⠀⠀⠀⡌⠀⠀⠛⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⣀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠉⠲⣤⠂
⠀⠀⠠⠊⠉⣀⡄⢢⠤⢄⠀⠈⠋⠑⡤⠒⢺⣘⡊⠑⢢⡀⢀⠀⠱⡀⠃⠀⠀⠀⡜⠀⠀⠀⠀⡠⠒⠒⢤⠊⠉⠣⣅⠀⢀⠰⠁⠀⠑⠄⠠⡀⠀⠀⢸⠐⡁⠢
⠀⠀⢀⠀⡎⠀⠘⠋⠐⠄⢡⠀⠀⠘⠀⣄⠈⠀⠀⠀⠀⠀⠈⠤⡀⠈⠒⠂⠀⠉⠀⠀⠀⠸⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⣔⡧⢤⡇⠀⠀⠈⢢⠀⠁
⠀⢠⠊⠀⠱⡀⠀⠀⠘⢀⠆⠀⠀⠘⢄⠀⢦⠀⠀⠀⡰⠀⠀⠀⢁⡀⠒⠐⠂⠂⠀⡀⠀⣀⢲⠀⡀⠀⠀⡄⠒⣾⡗⠒⠄⢈⠀⠀⠉⢡⠄⢱⠒⢤⢀⡘
⠀⠘⢄⠀⠀⠈⠑⠁⠀⠁⢀⠄⢀⡀⠀⠑⠒⠂⠈⠉⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⡌⠀⠀⠚⠃⠀⠈⢂⠈⡀⠀⠀⠀⠤⢸⠈⢦⣀⡀⠀⡠⠂⠀⠀⠈⢱
⠀⠀⡊⠀⠀⣀⣀⠄⠀⠀⠀⠭⠀⠀⠱⠀⠀⠀⠀⠀⠀⣀⢫⣖⠂⠒⢄⠀⠀⢀⢇⠀⠀⠀⢀⠌⠁⡜⠀⠑⢄⣀⣀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡄
⠀⠀⢸⠆⠈⠀⠀⠀⢸⠐⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⡚⠀⠘⠉⠀⠀⢘⢻⠙⠁⢠⠓⢤⠔⢬⠥⢮⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣀⣤⡀⢀⠀⠀⠀⡸
⠀⠀⢈⠖⠁⠀⠀⠀⠀⠑⠤⢀⠄⠒⠆⠠⠔⠈⠁⢂⠠⡘⠺⠀⠀⢀⡜⢸⠀⠦⠃⡰⠁⠀⣀⠔⢁⡘⢢⡀⠀⠀⠀⠀⠀⡠⠊⠀⠠⢋⠀⠛⠂⠀⠃⠀⠀⢣
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠒⠈⠑⠒⡏⠘⡀⠈⠀⠀⠀⠁⠠⠊⢀⡴⠃⣀⠾⣀⠀⠀⠀⠀⣀⠘⠀⠀⠐⢄⠤⠀⠀⢀⠆⠀⠀⡈
⠀⠀⠜⠁⠀⠀⠀⠀⢀⣀⡰⣂⣀⠀⠀⠀⠀⠀⠀⠤⠴⡁⠀⠀⢰⠀⢡⣼⠀⠀⠀⠀⠀⡠⠊⡠⠞⠁⡠⠊⠑⠄⠠⠔⠁⠀⠀⠀⠀⠀⠉⠂⠉⠁⠀⠀⡃
⠀⠐⣄⠀⠀⠀⠀⡐⠁⠀⠾⠇⡀⠙⡄⠀⢀⣀⣴⠀⠀⠘⢄⣀⡠⡇⠀⠛⠀⠀⠀⠀⣴⡤⠊⠀⡤⠊⢀⡀⠀⠀⢀⢀⡀⠀⠀⡠⠒⠤⠀⡠⠞⠑⠒⠊
⠀⠀⠈⠀⣱⣄⣀⣡⡀⠀⠀⠀⠊⢠⣁⡠⠏⠀⠀⠑⢄⠀⠀⠑⢄⢠⠀⠀⠀⠀⠀⠈⠁⠀⡠⠊⠀⠀⠁⣨⠉⠉⡠⣶⡄⠈⠈⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄
⠀⣀⠀⠀⣀⣔⡄⣠⠙⠢⠴⡦⠔⣁⠀⠀⢀⡀⠀⠀⡠⠓⢄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⣴⣇⡃⠀⢀⣿⣛⠠⠤⠀⠀⠒⠒⠂⠀⠑⢬⣷⡎⢈⠉
⠀⠀⠀⠀⠐⣺⢷⢅⡦⢠⡄⠀⠀⠀⢡⣀⣉⠀⠈⠀⠂⠤⠈⣣⠀⠀⠀⠀⠀⠀⠀⠀⣎⡄⢤⠀⡴⡂⠿⠏⠉⣧⡆⣉⡁⠀⢀⣀⣀⠀⠀⠀⡄⢤⣰⣿⣉
⠀⠀⠀⡀⠀⠀⣋⣿⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⠀⣀⡀⠈⢧⠀⠀⠀⠀⠀⠀⡜⠀⡰⢰⣹⣇⠉⠀⣤⣑⡜⠘⢫⠁⠀⠈⠁⠀⠀⠀⠀⢐⠠⣿⠁
⠐⢈⣿⡷⠂⢌⠁⠉⢀⣀⠀⠠⠄⠀⠀⠀⠀⠛⡼⢿⡐⡀⠀⠀⠈⡄⠀⠀⠀⠀⢀⠁⢰⠠⠀⠁⠀⠜⠈⠿⠉⠙⡆⠀⠘⣰⢀⣠⡔⠦⡀⠀⠈⣍⠛⠉⠁
⡀⠤⠾⣸⡟⠛⠺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠸⠑⠒⠤⠤⠦⠥⠤⠤⠐⠓⣉⠥⠛⠃⣘⢈⠰⡈⡢⢠⣏⣆⡀
⠀⠀⣤⣿⣡⠈⣰⣲⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠙⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠇⠠⣀⠀⢀⣀⠀⢀⣠⡎⣁⠤⠸⠀⢩⠤⢰⡿⢁⠀⠻⠛⡄⠀⠠⠄
⠀⠀⠀⠀⠀⡜⠀⠘⠎⠁⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠘⡀⠀⠰⠂⢤⡀⠀⠁⠀⠀⠀⣇⠠⠤⠐⡇⠘⡦⢈⣁⣦⣕⣢⣄⢖⠢⣬⣼
⠀⢠⠤⣠⣤⠰⠤⡀⠀⢂⠜⠀⠀⠀⠀⢆⢤⡒⡤⠤⢄⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡇⠀⣨⠄⣼⡽⠀⣔⠀⠀⡀⢱⠀⢀⡀⢸⡄⢻⠁⠈⠛⡌⢻⠁⡌⠐⠟⢺
⠀⠀⠙⠉⠛⠃⠒⢸⠃⠁⠀⠀⠀⠀⠀⠘⠉⠓⠃⠠⣀⠁⠀⢰⠁⠀⠀⠀⠀⠀⠀⠸⣰⠁⠀⠘⠁⠰⠈⡃⠈⠁⠈⡁⢿⣦⠀⢼⡄⣱⣄⡘⣢⠊⠢⡀⠀⢀⡰
⠀⠀⠣⡀⠀⠀⠓⡼⠀⠀⠀⡀⠀⠀⠀⠰⣄⠀⠀⠀⣡⡄⢰⢃⠀⢀⡀⠀⢀⠀⡀⣀⣹⣆⠀⠀⠀⠇⡰⠁⠀⠀⢈⠠⠈⠉⠀⠀⡁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⣤⢀⡈⠁⠊⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈⠁⠘⠉⠉⠀⠉⠉⠋⠁⠉⠉⠉⠉⠀⠁⠈⠛⠉⠉⠁⠉⣀⡄⠀⠀⠈⠢⣙⣀⣀⠴⠁⠀⠀⠀⠀⠛⠚⠖⠲
⣴⣤⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣯⣧⣿⣦⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣈⣁⣠⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⢰⡆⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠐⠉⣠⠶⢋⣼⠖⠂⣩⣿⠯⡐⠒⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠖⣘⡛⠋⠙⠿⢇⣀⡴⠊⠁⣰⠟⡁⢀⡾⠉⢙⣦⠉⠳⣶⡂⠀⠙⢾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣄⠉⠑⠚⣔⣤⠙⢶⡤⡾⠛⢄⣠⠟⠠⣴⠛⠙⣦⡙⢦⠙⠲⣤⣀⢙⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣤⠛⢁⣙⢷⣯⡀⠀⠉⠻⣦⣰⡇⣿⣆⠻⣶⢚⣡⠶⢋⠉⡳⣮⢂⣀⡈⠛⣆⣰⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣊⡿⢿⡗⠚⠿⣥⡼⢁⣽⠿⢧⡾⠦⣭⣿⣿⣈⢶⣤⠍⠑⢾⢾⡟⠹⣛⠉⢟⣳⣦⣬⣽⡿⢯⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⢾⡟⠻⠒⠚⠁⠀⠀⢸⣇⣸⣦⡞⠛⠛⠂⢤⠾⢿⣇⠢⡙⢦⡁⠀⠸⣿⠀⣹⠟⠉⠹⠇⠀⠈⠙⣶⡃⠨⢻⡄
⠀⠀⠀⠀⠀⠀⢠⢏⢺⡧⠲⠀⠀⠀⠀⠀⢸⣿⣻⠏⠀⠀⠰⠛⠛⠀⠀⠙⣶⡉⠄⠙⢦⣄⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠉⢳⡀
⠀⠀⠀⠀⠀⠀⣿⠂⢸⣧⣤⣘⣠⡐⠦⢠⡾⣷⣿⡄⠀⠀⠀⡀⠀⠀⠀⠀⣿⢻⣤⣀⠀⢻⣌⠏⠻⣇⠐⠀⠀⠀⠀⠀⣈⠏⢱⠆⠩⡗
⠀⠀⠀⠀⠀⢀⣯⣤⣿⣤⣙⡙⣿⠟⠲⣎⡃⠈⢻⣷⣥⠀⠀⡁⠀⠀⠀⣴⢿⣿⠛⠛⠷⣧⣽⣶⣆⡈⢻⣦⡄⢠⣤⡴⢿⡶⡄⢻⡄⣿
⠀⠀⠀⢠⣤⣼⠋⠀⠀⠰⠏⠙⢿⣧⢖⡈⠓⢤⡀⠸⣿⣿⡴⣶⣧⠶⢾⣧⢏⣠⣴⡟⠑⣿⠁⠉⠽⣿⣄⠉⢻⣤⠉⣀⡤⠤⢈⣋⡱⡿⢠⣴⠂
⠀⠀⠀⠘⣧⡿⠀⠀⠀⠀⠀⠀⠀⣿⢦⣁⠠⠈⢿⡀⢏⡉⠛⠖⠶⣦⡀⠙⢻⣿⠉⠉⠀⠀⠀⠀⢀⣿⣦⣑⠄⠻⣦⠋⣀⣴⠟⠁⣀⡴⠋⡴
⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⢠⣟⡀⠙⠳⣮⣤⡙⣜⠳⡄⢀⠙⢤⠉⠳⢾⣿⠃⠄⠀⠀⠀⠀⢠⣿⠾⠛⡷⣶⣬⣿⡟⠁⠄⣰⠋⡠⣤⠃
⠀⠀⠀⠀⠀⢻⡷⣤⣀⡀⣀⣴⢟⠉⣻⠷⢞⣶⣾⣿⣟⡆⠙⢦⡁⠈⣷⢦⣤⡍⠻⢶⣾⣤⠐⣨⡿⠷⠚⡍⢻⡏⢡⡏⢀⣱⠞⠁⡬⣲⠏
⠀⠀⠀⠀⠀⠀⠛⢆⣉⠋⠹⣧⢸⡇⠘⣶⡞⠁⠀⠀⣽⠙⠳⣀⠙⡴⠛⡀⣠⠶⢋⣴⠋⣩⠟⠁⣶⠖⠉⣴⣿⠀⣾⢠⡾⠁⢀⣠⠼⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠙⢳⣴⣬⣳⣤⠀⣿⠃⠀⠀⠀⠀⠀⠀⢻⡎⢠⡬⠎⠁⣠⡞⢛⡟⢁⡤⠚⠁⢠⡞⢯⣹⢀⣿⣎⣴⣶⠛⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠙⡋⠤⣬⡁⠈⣙⠰⢿⡁⠀⠀⠀⠀⠀⠀⣬⡖⢋⣠⣤⣼⠿⡄⣋⡴⣋⣤⠶⠞⡿⠇⣨⠿⠋⢉⣤⡤⠤⢈⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠑⠶⢷⣄⠑⢆⣀⠀⠀⢀⡼⠿⢋⣽⠟⢋⣀⣐⣿⣟⡓⠉⢀⡴⠏⣰⡞⢁⣤⡾⠋⠁⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⡀⠉⠳⢼⣿⠻⡙⢯⡁⠀⠙⣴⠟⠉⠉⣩⡬⠉⠉⠳⣏⠔⠚⠉⣡⢀⣹⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠻⢿⣗⠒⠿⠳⣜⡀⠙⢷⣬⠏⡀⠀⠘⡀⠀⠀⠀⠀⢿⢠⠿⠃⣀⡾⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠑⢳⢤⣈⠳⣄⠀⠹⡷⢀⠀⠀⠉⠀⠀⠀⠀⣼⢁⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠛⠳⠶⣜⣷⣤⣀⡀⣀⣀⡰⡶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠙⠳⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠆⠀⠙⠦⠀⠖⠀⠱⠶

⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣉⣟⣛⣛⣙⣋⣻⣎⣛⣹⣋⣋⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣭⣿⣭⣭⣭⣿⣿⣭⣭⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⢀⣠⣿⠀⢹⣇⣀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢺⣏⠉⠛⠋⠉⠀⠀⠀⠈⠉⠛⠋⢉⣿⠂⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⠛⠛⠶⠶⠶⣤⣤⡟⠀⠀⢀⣿⠃⠀⠀⣠⡴⠶⢶⣤⡀⠀⠀⢻⡇⠀⠀⠀⢿⣤⣤⠶⠶⠶⠛⠛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⣠⣤⠾⠇⠀⠀⣾⠋⠀⠀⠀⠈⢻⡄⠀⠀⠿⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⢿⣤⣄⡀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣤⣿⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠙⢷⣄⣀⣠⣴⠟⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣿⠧⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠾⣧⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡶⠟⠳⢶⣤⠀⢠⡴⠾⠛⠷⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢉⣩⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠉⠉⠻⣦⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠉⠙⢳⣄⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⠛⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⣶⠏⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠹⣶⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠀⣿⣤⡀⠀⠀⠀⠀⢀⣠⣼⡇⠀⠀⢸⣷⣄⡀⠀⠀⠀⠀⣀⣤⣿⠀⠀⠀⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⢿⣤⣤⣤⠿⠈⠙⠳⣦⣤⠶⠛⠉⠸⣧⣤⣤⣼⠇⠈⠛⠶⣤⣴⠞⠋⠁⠿⣤⣤⣤⠿⠀⠙⠻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⢀
⣿⡟⡋⣻⠿⠿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣶⣄⠀⠀⠀⢰⡄⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⣄⣿⠃⠡⠞⢁⣈⡛⢀⠀⠀⢈⡱⢭⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⡀⢰⣄⣿⠇⠀⠀⠐⠎⢀⢀⠀⠀⠉⣡⣾⠀⠙⣖⠉⠱⢀⡬⠉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠉⠀⠋⠀⠀⠀⠀⢠⠇⠀⠀⠸⠟⠃⠀⠀⠸⡄⠀⣬⡙⠂⠀⠘⢇⠀⠞⣱⡿⠁
⠀⠀⠀⠀⠀⠐⠛⠷⢀⡍⠁⠒⠢⢄⡀⠀⢸⠘⠛⠀⠀⠐⠦⠔⠂⠒⣧⠀⠘⠿⢄⡞⠁⣈⣑⡀⠰⣦
⠀⠀⠀⠀⠀⠀⠲⠦⠸⠁⢰⣿⣷⣷⠈⠳⢼⡀⠀⠀⠀⣾⣶⣿⡆⠀⢿⠀⠀⠀⢸⠀⢸⣿⣿⣿
⠀⠀⠀⠀⢀⣴⣾⡿⠂⡀⠀⠻⠿⠟⠀⠀⠀⠙⣆⠀⠀⠻⠿⠟⠁⠀⢸⠀⠀⣤⢸⡇⠀⠉⠙⠁⠀⢠⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠦⣀⣀⣀⡤⠤⣤⣀⠘⣧⠀⠀⠀⠀⠀⢦⣸⠀⠀⠙⣸⠁⠀⠀⢠⠖⣀⠘⠵⠿⠋
⠀⠀⠀⠀⣤⠀⣿⠀⢉⡄⢂⣉⠀⢡⣀⠀⠀⠈⠑⢾⡆⣾⠟⠀⠀⢀⣿⡴⠖⣟⡉⠉⠉⠉⣭⡁⠀⢿⣷⣄
⠀⢰⣦⠀⣀⣈⣑⢄⠉⠀⠘⠁⠆⠘⢿⣷⠀⠀⠀⠈⣧⠀⠀⠀⣴⣿⣉⣀⣀⣈⠁⠀⠀⠀⠈⠃⠀⠀⠉⠛
⠀⣈⡻⠸⣿⣿⣿⠊⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡀⠀⣼⠏⠀⢀⣀⡀⠉⠑⠔⣛⠁⠀⠀⢀⣤
⠀⠉⠉⢒⠩⠭⡩⠤⠴⠛⠛⠛⠛⡻⠓⠶⣦⣌⡇⠀⣿⡇⢰⡟⠀⠀⠙⠋⠵⣴⣶⣶⡆⠀⠛⠊⢸⡿⣴⠟
⠀⢀⣾⡟⠁⠆⠀⠀⠀⠀⢀⣭⠀⣤⡀⠀⠀⠙⠻⣦⣸⣷⣼⠇⠀⠀⠀⣀⠀⠙⠿⠿⠃⠀⠀⢠⣠⠂⢲⣂
⠀⠀⣱⡶⢉⣉⣑⣒⢤⡀⠉⠁⠀⠻⠇⠀⠀⣀⣀⣹⣿⣿⣿⣠⣤⣤⣤⣭⣄⣀⣀⣀⡀⢀⣴⠋⢀⡀⢾⠁
⠀⠀⠀⠀⢸⣿⣿⣿⠀⠉⠒⢦⣤⣀⣠⠶⠛⠉⠙⣿⣿⣿⣿⠟⠉⠁⠀⠉⠉⠹⡉⠉⠉⠉⣡⣄⣭⡂⠈
⠀⠀⠀⠀⠀⠉⠉⠱⠞⠉⣩⡏⠉⣴⣶⣶⡄⠀⠀⢹⣿⣿⣿⡄⠀⠀⠀⠀⣴⣿⢁⠶⡄⠐⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠻⣿⣿⠃⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠰⠟⠁⠘⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄

⠆⠙⢻⣿⡤⠤⠀⢤⠃⣀⠀⢻⠇⠀⠁⠀⠀⡉⠄⠈⠰⠀⠀⠀⠈⢰⣦⡀
⠀⣠⣄⡀⠀⠖⢦⡀⠀⢻⣧⢨⠀⠈⠃⠌⢀⠀⠀⠀⠀⠀⠐⢃⠀⢈⡿
⢸⣤⠀⣃⠀⢀⡤⠷⡄⠨⠇⣁⠠⠄⠀⠀⠉⢵⣤⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⣿⠟⠃⣧⡀⠀⣠⣿⠖⠑⡀⠐⠦⡀⠀⠀⢈⡿⠃
⠐⠒⠀⠀⣻⠃⢄⠙⠻⠀⠀⠀⠀⠄⠘⢳⣤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⣴⣶⠦⢶⣦⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠘⢩⣦⠀⠆⠰⢟⡓⠀⠈⣶
⠀⢀⣤⠀⠀⠠⣄⠐⠀⢀⣾⣭⣿⡇⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡄⢀⡛⠀⢀⣾⣟⢀⣠⣶⢾⡇⠀⢠⡿⠁
⠀⠈⡟⠲⢽⠆⠛⠐⠀⢸⣿⢙⢹⡧⠶⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⣀⣀⡀⣨⣁⣀⣏⣁⣶⣀⣿⣠⣧⣗⣀⣤⣴⣦
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡌⣀⣀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣉⠑⠂
⣒⠢⢌⣂⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡢⣔⠠⣐⠤⡀⢄⡀⣈⣡⡦⠤⠞⠛⠛⠛⡶⠆⠤⠀⠀⠠⠄⠈⡿⠹⣿⢻⡟⣿⠻⠃⠂⠀⠀⠃
⣲⠭⢗⣒⡬⢕⣒⡢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣙⡮⠷⠚⠛⠉⠁⠀⠀⠀⠀⠄⡈⠉⢃⠆⠀⠀⠀⠀⠀⠀⡇⢸⡇⢸⡇⡿⣀⢠⢂
⣒⣫⠵⣒⣫⠭⣒⣪⠥⢒⣂⠥⠀⣀⡤⠴⠒⠋⠉⠀⠀⠀⠠⢤⣤⡀⠀⠀⠀⢀⡀⠀⠀⢈⣿⠒⠀⠀⠀⠂⠀⠂⠸⠗⣾⠗⠻⠠⣿⢟⡀
⡭⢖⣫⡥⢖⣫⠥⠖⣋⡥⠶⠚⠉⠁⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠹⠇⠤⠄⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠄⠀⣂⠒⠾⡅⠀⠀⣿⡆⠀⠀⠒
⢚⣩⠴⢚⣩⡴⠞⢋⡡⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠐⠀⠀⠀⠀⢀⣆⠀⠐⠀⠀⠀⢀⣄⡀⠐⠀⠁⠀⠎⠀⠀⠸⠛⠐⠗⠀⢀⡀
⣫⡥⠚⠋⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠘⠁⠀⠀⠠⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⡄⠰⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠂⠀⠀⢀⠔⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⢌⠒⢀⢁⠀⠣⠀⠰⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠤⠎⠀⠒⠐⡡⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣁⠀⠀⠉⠀⠃⠀⡀⢦
⠀⠀⡀⠀⠀⠫⡑⢄⠀⠀⠀⠀⠀⠆⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠄⢊⠔⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠂⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡴⠀⠄⠡⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠨⢀⣀⠀⢀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠃⠀⠑⠈⠀⡤⡄⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠁⢉⠔⠁⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⡠⠂⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠐⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠤⠆⠐⡀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⡄⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠢⡈⠢⠀⢂⠀⢀⠖⡀
⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠠⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠈⠀⠀⠐⠂⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡅⠐⡑⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡂⠀⠀⠀⣀⠄⢢⠎
⠀⠀⠈⠀⡀⠀⠀⠀⠀⢨⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠅⠀⠀⠀⠠⠊⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠
⣀⡀⣀⣀⣀⣀⣀⣀⡀⣀⣉⣉⢉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⣀⠀⠀⣠⠀⠀⠀⠀⠹⢿⡄⢀⣤⡤⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢋⣀⡀⠻⢿⣴⡿⠀⣄⣠⠒⠒⠲⡀⢶⣧⣄⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠙⠻⠿⠦⡐⠟⣛⣁⣀⠀⢀⠀⠀⣰⣿⣷⡄⠀⢹⡰⣤⡛⠲⣌⢁⡀⢀⣶⠀⠀⣠
⠀⠀⡀⠀⠀⣠⣶⡆⠀⠀⢨⠟⠉⠉⠉⡟⠛⢶⣤⣜⠿⠟⠀⠀⣸⢻⣿⡿⢀⡏⠀⠙⠞⠋⠀⢰⡿⢀⡀
⠀⠀⠻⣦⣼⡿⠟⠀⠀⠀⣿⠀⠛⠿⠶⣱⠋⣉⣷⣈⢻⣦⡀⣰⠋⢠⣄⣠⠟⣒⠒⢶⣀⡻⠷⠚⠃⠘⣇⣠⣤⣤⠄
⠀⠀⠀⠀⣭⣴⣆⠀⢀⣴⡾⠢⣤⡤⠞⠸⣄⢿⣿⣿⠃⠹⣿⠃⢀⣴⢟⢱⣼⠏⠀⣾⣿⡇⢀⣤⡒⢈⡴⠈⠉⠁
⠘⠿⠿⢧⡹⠿⠏⠀⠘⠋⢀⡶⠉⢩⣷⣧⢹⣎⡭⠥⢄⡀⣿⣿⡿⢁⣘⣃⢡⣴⣤⠙⠛⡕⠁⢠⣽⣿⣥
⠀⠀⠀⠀⠉⣟⡲⠛⠋⠙⠺⣇⠀⠘⠿⠟⡾⠁⠀⣼⡆⠱⣿⣿⠃⢸⡷⢘⡄⠛⠃⣀⡼⢁⣶⠸⣿⣿⣿⢡
⠀⠀⠀⠀⣾⣿⣿⣷⣀⡀⣤⠙⠳⢤⣤⣼⣇⠀⣠⣼⠷⠈⣿⣿⡇⠾⣠⡾⠶⠶⠯⣁⡀⠈⠻⠅⠉⣍⣁⠸⢀⣾⠏
⠀⠀⠀⠀⢻⣿⣿⠏⠈⠉⢡⣴⠆⢸⢆⣤⠙⢶⣬⣀⣠⣼⣿⣿⣷⠞⢡⣾⣿⡔⠂⣠⡭⠭⣅⠈⠳⠌⠉⠁⠉⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣆⠀⠀⢀⣊⡁⠀⠀⠈⠙⠻⣿⣿⣿⣿⣀⡈⠻⣿⣧⡞⢁⡀⠠⣌⣿⠢⠤⠴⠚⠢⡼⠛
⠀⠛⠓⢄⠀⣀⣠⡴⠋⠁⠉⢉⡽⠛⢯⡍⠉⠙⠛⢶⣄⣿⣿⣿⡏⠉⠉⠉⣡⠟⣄⣸⡇⣰⣾⣿⣷⡄⢀⡀⢀⠇
⠀⠀⢠⣾⡏⠁⢀⣷⡏⠀⠀⡏⠀⠀⣨⣿⣦⡀⠀⠀⢻⣿⣿⣿⣧⣠⣴⣾⣏⣀⣀⡩⠀⠹⣿⣿⡿⠁⢰⣿⣶
⠀⠀⠸⠿⠁⠀⠈⠛⣁⠀⣀⣳⣄⠀⠘⠿⠟⣁⣤⣶⣾⣿⣿⣿⣿⡿⢻⣿⣍⠛⠳⢤⡘⢦⣠⣼⣶⠖⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⡈⠙⠛⠲⠛⠛⠉⠉⠈⢻⣿⣿⣿⡏⠀⠸⠿⠟⠀⠀⠇⠈⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠈⠛⣲⣄⣀⠜⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠉⠛⢻⣿⣷⣿⢿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⡿⣛⣵⣴⣦⣀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⠿⠟⣷⣿⣿⣿⣿⣦⣀⡀⠀⠀⢽⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣿⣿⠅⠒⠄⣶⣍⡻⢿⣿⣿⣿⣿⡄⠀⠀⠹⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⣿⣿⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⢼⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣧⠀⠀⠐⡟⢡⡿⣻⣿⣿⣿⣿⣿⠶⣄⣀⡲⢿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠆⠀⢘⢆⡾⣱⣿⣿⣿⠻⣿⢿⠑⠈⠹⣙⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣏⡿⠃⡭⡸⣿⣿⡿⠋⠙⣿⡝⠧⡄⣰⡀⣻⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣧⡞⣹⡇⢠⡶⠐⠻⣿⣿⣧⣶⢹⣼⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣹⣿⣿⣿⠟⠁⢹⣿⠜⣸⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⡟⠉⠀⠘⣸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠸⠯⠀⠀⠀⠀⠿⠼⠻⠿⠿⠿⡿⠿⠿⠿⡿⡿⠿⠇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢀⠠⠤⠔⠉⠐⠈⠀⠀⠀⠀⠉⠐⠈⠈⠀⠈⠐⠀⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠤⢄⠀⠀⠌⠁⡀⡠⡀⠀⠉⠁⠀⠘⠆⢣⡄⠐⠂⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⡴⠒⢀⠀⠀⠨⠀⠈⠀⠀⠄⠀⠀⡊⠀⠛⠀⠈⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠂⠀⠐⠠⠊⠁⠀⠀⠀⠄⠀⠀⠘⠀⠀⠀⠀⠑⠀⠀⠊⠀⠀⠀⠑⢀⠀⡢⠄⠀⠀⠀⢀⠀⠀⠀⠀⠁⢂⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠐⠐⠀⠁⠠⠈⠉⢀⠄⢠⡧⠀⠄⠀⠀⠀⠀⠀⠀⠀⠔⡉⠛⠋⠑⠀⠀⠀⠠⠀⡀
⠀⠀⠀⢀⠄⠈⠁⢄⠀⠁⠁⠀⢀⠀⢄⠠⠆⢀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠢⡐⠀⠀⡠⠓⢄⡀⡀⠀⠈⠂⡀⠄
⠀⠀⠀⢀⢠⠀⠑⠂⠀⢡⠀⠀⠀⢀⠈⠁⠀⠈⠁⠠⡀⠑⠀⠂⠀⠀⠀⠠⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠤⣄⡄⣈
⠀⠀⠀⠀⠀⠢⠀⢀⠒⠀⠀⠀⠠⡀⠆⠀⠀⠐⠀⠀⢀⠔⠐⠂⠀⠀⠄⠠⡰⠀⡀⠀⠔⠰⠷⠒⢄⠁⠀⠉⢠⠈⠒⠢⢀
⠀⠀⠀⡢⠀⠀⠀⢀⠀⢀⡢⠠⢄⠀⠀⠀⠀⠀⠀⣰⡀⢀⠀⠀⠀⠀⠀⠈⠁⠀⢘⠀⢄⠀⠀⠘⡐⠈⠠⠤⠀⠂⠀⠀⠀⡇
⠀⠀⠀⢢⠀⠂⠈⠀⠈⠄⠉⠀⠀⠀⠀⠀⠀⡐⠂⠟⠀⠀⢱⠂⠔⠐⢄⣀⡐⣡⡊⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠡
⠀⠀⠀⢘⠆⠀⠀⠀⠀⠠⠀⠄⠐⠀⠄⠀⠠⠡⡀⠀⠀⣀⠄⡀⠀⠂⠔⠀⡀⠔⡉⠢⡀⠀⠀⠀⠀⡈⠀⠠⠊⠙⠃⠈⠄⠀⠣
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠌⠀⠃⠀⡀⠅⠀⠈⠄⠊⠀⠊⡠⠘⢤⡀⠀⠀⠄⠃⠀⠈⠠⠂⡀⠠⠁⢀⠄
⠀⠀⠀⠁⠀⠀⠀⠠⠀⢂⡗⠀⠄⠀⠀⠀⡆⠉⢄⠀⠈⡄⠱⠃⠀⠀⢀⡔⠠⠊⡠⠀⠀⠀⠒⠈⠀⠀⠀⣀⠀⠀⠠⠄⠀⠄
⠀⠀⠀⠑⠒⣄⠀⣁⠀⠀⠀⠀⡀⢀⠌⠉⠀⢄⠀⠙⢄⠡⠀⠀⠀⠀⠘⠁⠀⠊⠀⠀⢐⠀⠀⣤⡁⠒⠈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡅⡈⠑⠐⠄⡊⠀⠀⢀⠄⡀⠀⠓⡀⠀⠁⠀⠀⠀⠀⠀⡐⠁⠀⠀⢰⣅⣀⠀⣿⡧⠀⠀⠀⠀⠀⠀⠁⢼⣖
⠀⠀⠀⠀⠀⠈⡻⣔⢂⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⡰⠰⠐⣠⠣⠙⠃⢨⣆⣤⣄⠀⠤⠄⠀⠀⠂⢢⡿⠂
⠀⠀⠀⣴⡤⠀⠒⠛⠀⠀⠀⠀⠀⠀⠠⠦⣶⡠⠂⠀⠸⠀⠀⠀⠀⢠⠀⠈⡙⠋⠠⠄⣿⠚⠅⠉⠀⡀⢀⡀⡀⠀⠐⠺⠧⠄
⠀⠀⠠⠍⣷⠞⠲⠂⠈⠀⠀⠀⠀⠀⠀⠐⠗⠉⠀⠀⠀⡇⠀⠀⠀⠈⠀⡓⠀⠤⠤⠠⠤⠤⠒⢒⠈⠓⢹⠁⢤⢠⠀⣏⣄
⠀⠀⠀⠤⠯⠄⡸⢴⣄⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⡇⠀⠀⠀⢀⠀⢙⠀⠄⠀⠀⠀⠠⢌⠠⠐⢂⢸⠀⢾⠇⠀⠛⠣
⠀⠀⠀⠀⠀⢀⡀⠈⠠⢸⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠸⠀⠈⡁⡳⡀⠀⠀⢀⢰⠀⠀⠉⠀⢫⠀⢾⠯⢷⠊⠍⣷⡂
⠀⠀⠈⠨⠻⠇⠠⢰⠐⠁⠀⠀⠀⠠⠚⠾⠀⠈⠀⠀⡄⠀⠀⠀⠀⠀⢇⠀⠁⠛⠁⠙⡂⠘⠘⠃⣶⡄⢱⡈⢄⠀⢄⠜⡈⠀⠀⡨
⠀⠀⠀⠢⡀⠀⠀⠌⠀⠀⡀⡀⠀⠐⢄⠀⢀⣩⡄⣈⣀⢀⡀⢀⠀⣀⡌⣦⡀⠀⠐⡀⠀⠀⠠⠀⠈⠁⠀⠁⠈⠁⠁⠀⠀⠀⠈
⠀⠀⠴⠠⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠤⠆⠀⠀⠑⠡⠀⠐⠀⠀⠀⠀⠉⠁⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠈⠁⠀⠁⠀⠠⠀⠠⡀⠀⠀⢀⠀⠠⠆⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠢⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠐⠊⠓⠀⠔⠢⠤⡠⠘⠂⠀⠀⠀⠋⠉⢠⠠⢄⠀⣀⡀⠂⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠅⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠓⠂⡀⠠⠤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⠥⡬⠄⠠⡄⠀⠀⠀⠀⠀⠀⠂⠐⡄⠀⠀⠀⠀⠀⠸⢀⡠⢄⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠀⠀⠀⠠⠓⠀⡀⠀⡤⠓⠢⠀⠀⠀⠀⠀⠀⠀⠐⡅⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂⠀⠃⠀⢀⡀⠠⠂⠀⠀⠀⠁⠀⣄⡀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⢀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⠷⡀⠀⠀⠀⣠⡎⠀⠀⢀⠀⠀⠄⠠⠤⠀⠀⠑⠐⠂⠀⠦⠀⠐⠀⠀⠈⡄⠀⠀⠀⠁
⠀⠀⠐⠀⠀⠀⠸⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠴⠤⠴⠀⠰⠉⠙⠒⠚⠃⠀⢠⠀⠀⠀⠆⣀⠀⠀⡔⠉⠉⠛⠉⠙⢢⠀⠤⠀⠀⠚⠄⠀⠀⠀⠀⠅
⠀⠀⡀⠀⡎⠀⠀⠀⠀⠀⠃⡀⠐⣀⠀⠒⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡊⠁⡀⠀⢇⠀⠀⠀⠀⠀⢠⠄⠀⠀⠧⢀⠄
⠀⠐⠀⠔⠁⢀⠀⠀⠀⣀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠘⢄⠀⢀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⠀⠠⠀⠀⠀⠈⢦⣄⣀⣀⠴⠋⠀⡀⡆⠀⠘⠂
⠰⠀⠀⡸⠂⠀⣀⠤⠠⢤⠤⠤⣄⠁⠀⠀⠀⠐⢄⣠⣤⡭⠇⠀⠀⢀⠀⣀⡜⠳⡖⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠁⠀⠀⠀⢀⠤⣤⠤⠀⠀⡄
⠠⠀⠀⢧⠀⠀⣸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⠞⠉⠙⣆⠀⢱⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⢀⡀⠀⠐⠁⢠
⠐⠀⠘⠠⠉⠀⠘⣄⠀⠀⠀⠀⣴⠃⠀⡄⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠸⡄⢈⣇⠀⠀⠀⠀⠗⢢⣀⡀⠆⠀⠀⠠⣀⢀⠜⡀⣀⠁⠀⠀⠀⠘⢀⠀⠈
⠀⠀⠀⢤⠀⠀⠀⠈⠙⠒⠒⠉⠀⠀⠀⠁⠀⣀⡰⢄⡤⠊⡏⠀⠀⠀⠀⠀⠀⣧⠀⢻⡆⠀⠀⣸⠀⠀⡇⠀⡀⢀⠄⠀⠀⠈⠣⣴⡝⠀⠀⠒⡄⠀⡌
⠀⠀⠀⠸⠠⣄⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣀⡤⠿⠀⠀⠿⣦⡼⠃⠀⠀⠀⠀⠈⠙⣄⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⢀⡇⠀⠄
⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⡀⠀⢁⠀⠀⢠⡀⠀⠀⠀⠀⡀⠈⠛⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠤⡴⢄⣠⠀⠀⠀⢠⣀⡼⠀⠂
⠀⠀⠀⠒⠀⡀⠁⠀⠀⠀⠣⠒⠂⡠⠐⠠⠤⠤⠤⣄⠀⠈⠁⠀⠀⠀⠲⡄⢀⠀⠀⠀⡄⠀⠀⠀⠀⢀⡄⠀⠀⠀⣠⠇⠀⡇⠀⠈⠀⡀⢀⡠⠀⡹
⠀⠀⠀⠀⠀⠑⢆⠀⠀⠠⠀⠐⢈⡇⠀⠀⠀⠀⠀⢸⠄⢠⠄⠀⠀⠀⠀⢹⡄⡀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠀⣰⠇⣘⡥⢄⡉⠤⢄⠀⡹
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⡄⠀⢣⡀⠀⠀⠀⣠⠞⢀⠀⠀⡀⠀⢀⠀⣼⠀⠁⠀⢀⠁⠀⠀⠐⠑⡶⠤⣤⡤⠤⠴⠞⠁⢸⠁⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⣁⡀⠀⠈⠓⠒⠋⠁⠰⠈⠉⠉⠉⠂⠉⢉⠇⠀⡀⠀⠀⠀⠀⠂⠀⢠⡁⠀⠈⠳⠤⠤⢦⠤⠻⣄⠀⠀⠀⠀⣠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠢⠤⠀⠀⠂⠀⠀⠀⠀⠀⠀⡘⠀⠐⠀⠀⠘⠀⠆⢰⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠈⠀⠀⠀⠄⠀⠀⡜⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢃⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠂⣸⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣧⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⠣⢰⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢂⠛⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡄⠀⡄⠀⠀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢰⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣓⣲⣤⣼⣦⣤⣴⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣒⣛⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⡿⠿⡿⠛⠿⠿⠿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣶⣷⣾⣷⣶⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠟⠻⣷⣶⣤⣄⡀⠀⠀⠀⣀⣠⣴⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠈⠻⡏⠙⢿⣆⢀⡴⠋⠁⠀⠈⠉⠛⠻⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢹⡇⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⡾⠛⠛⠛⠳⢤⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣤⡴⠾⠋⠉⠉⠻⢦⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠈⠙⣄
⠀⠀⠀⠀⢀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⢷⣄
⠀⠀⠀⣠⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠉⠙⠛⠿⠶⣤⡀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣿
⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣁⣀⣀⡀⠀⣀⣴⣿⠃⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⠦⣤⣄
⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⢻⣿⠁⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⢠⣿⣧⣄
⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠁⠀⡹
⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣤⣤⣀⣀⣠⣤⡶⠟⠋⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⠀⢹⣿⡏⠁⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⡿⣿⣷⣿⣿⣿⣄⡀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⡿⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠀⢸
⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⢰⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⣿
⢹⣿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡿⣧⡈⠙⢿⣿⣶⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⣴⠿⠻⠿⠁⠀⠀⣿
⠈⢿⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡈⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣶⣤⣄⣠⣍⣷⠶⠀⠀⠀⠀⢠⣿
⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢻⣿⣿⣿⡌⠻⣿⡙⠛⠛⠿⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠘⢿⡟⣿⡉⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣇⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢿⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡰⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠒⠒⠓⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠸⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠓⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣾⠏⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡉⠃⠀⠉⠿⠁⢀⡞⠉⠉⣹⡅⠛⢐⣧⡿⢋⡿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡻⢟⣛⣿⢛⡛⣛⣛⣛⠛⠻⣿⠛⠛⠛⠛⠻⠟⡛⠻⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⠀⠀⠉⠍⢅⣤⠂⠃⢸⣶⡀⠉⠐⠢⠀⠀⠂⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣠⡋⣑⠠⠀⠈⣳⡄⠀⢻⠃⠋⠀⠀⠀⠉⠶⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⣿⢸⣿⡼⢢⡀⠉⠉⢹⣄⡨⡴⠁⣨⠁⠀⡄⠀⠹⣿⠁
⣿⢠⡉⠀⢸⡷⠀⠲⣿⡏⠀⠈⠀⢀⡉⢢⣌⢉⠞⠉⠀⠀⠀⠀⠀⠀⠀⠠
⣿⠀⠀⠀⠸⠇⠩⠂⠀⠁⠀⠀⠀⢨⠀⠀⣿⡇⠂
⣿⠀⠤⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⡌⠛⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⣀⣀⣀⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣄⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣦⠐⠠⠶⣙⠛⡀⢙⣿⣇⠀⠰⣀
⣿⡤⠀⡀⠐⠦⠄⠀⣰⣿⣶⣿⠄⢳⠃⠀⠀⠀⠀⠀⠀⣀⠀⠈⢿⠀⠀⣼⡯⠁⠀⣨⡱⡆⠀⠀⣿⣇
⣿⠰⠗⢽⠂⠃⠀⠀⣿⡇⠅⣿⠶⠿⠶⣤⣄⠀⠀⠀⠀⣁⡕⠐⠘⠂⠒⢻⠓⠀⣟⠛⣹⠓⣤⠈⡏⣀⠀⠀⣀
⣿⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠢⢌⣷⡊⠀⠀⠀⠀⠀⠀⠓⠐⢿⣶⣿⣾⣏⠀⠐⠛⠛
⣿⣓⡂⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠑⢮⡒⢅⣢⣔⣬⠦⠭⢩⠉⠂⠀⠀⠀⠀⠀⡖⠒⣶⢻⡟⢹⡏
⣿⣒⡪⠭⢕⣒⡈⠤⢀⣐⣠⠤⠴⠖⠒⠉⠉⠁⠂⠀⡤⠴⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⡯⢸⡇⣸
⣿⠶⣒⣫⡭⠶⠒⠋⠉⠁⢀⣀⣀⠀⠤⠂⠀⠀⠄⠀⠃⠀⠳⣄⠠⠀⠀⠀⠀⠀⡇⢨⣇⣸⣇⣿⠔⣠⡄
⣿⠋⠉⠤⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⡀⠀⠢⠶⠀⠀⢀⠐⡿⢄⠀⠀⠀⡀⠀⣀⣀⣸⡏⠀⠉⣬⠛⠁⠀⠠
⣿⠀⠀⠄⠀⠀⠀⣰⣴⡄⠀⠀⠠⠄⠁⠀⠀⠀⢀⠐⠀⢀⠀⠀⠀⠀⠀⠀⡁⠠⠊⢈⡽⠇⠀⣰⡿⣭⣄
⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⡠⠐⠀⠀⠚⠁⠀⠀⠀⠀⠠⠾⠶⠀⠀⠀⠄⠈⠀⠀⠀⠩⠄⠀⠀⠀⠆
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠐⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣄⠀⢬⠀⠀⠠⢀⠀⠄
⠀⠀⠀⢠⠠⠄⠃⠠⢦⠉⠐⣦⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡄⢰⠀⠀⣿⠄⠀⠠⠀⠉
⠀⠀⠀⠀⠈⠄⠀⣠⡆⠀⠀⠛⣿⣷⣉⠐⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣨⠁⠀⠀⠀⠈⠂⠀⠋⠀⠀⢈⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡓⠉⠹⠶⣽⣅⣝⢃⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠛
⠀⠀⠀⢰⡄⢤⡀⠘⠁⠀⠀⠀⣉⣺⣽⣦⡟⠁⡄⣶⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⢴⣯⣀⠀⣾⣇⣾⣶
⠀⠀⠀⠈⠁⢈⡏⠀⣡⢰⠟⠀⠉⠻⢿⣿⣷⣼⣾⣗⠊⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⣴⡖⠀⠀⠀⡄⣻⣿⣖⡇⢀⣀
⠀⠀⠀⠑⣾⠻⣿⠟⢈⣅⠠⣴⣦⡛⣻⣿⣿⣷⣽⣿⣷⣾⣷⠠⢿⣧⣤⣴⡀⠀⢻⡿⢠⣄⠀⠀⠀⣀⠈⠉⠀⠀⢀⡘⠻⠿⡛⡽⠻⠏
⠀⠀⠀⢆⣀⣠⣌⣤⣶⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣌⠱⠆⠘⠳⣄⠀⣡⣤⠀⢀⠂⠀⠀⠀⠀⣐⢷⣟⠓⢰⣾⢷⡆
⠀⠀⠀⠙⠻⣿⣿⡿⠿⡿⢿⣿⡻⠿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡭⣭⡔⣶⣶⣿⣧⣿⣿⠿⢿⣿⣶⣿⣿⣧⣿⣿⣿⣷⣾⡷⠺⠁
⠀⠀⠀⠐⠒⠸⡿⠓⠒⠒⠀⡿⠀⠀⠸⠇⠸⠃⠯⣤⣧⣼⣤⣤⣴⣶⣦⣤⣤⣤⠀⠀⠜⠻⠽⠡⠤⢬⣿⡥⡬⣾⣛⠓⠒⣚⣿⠛⡂
⠀⠀⠀⠈⠁⠉⠉⠓⠲⠶⣮⣭⣥⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣍⣁⣤⣬⣽⣿⣉⡋⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠙⠋⠙⠛⠛⠋⠙⠛⠉⠉⠙⠛⠛⠛⠛⠛⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂