Explore Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⢆⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠁⠀⠀⠎⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⢠⣤⣀⣠⢀⣀⡈⠄⠈⠈⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠅⠾⠋⠁⠚⠷⠸⠙⠃⠀⢀⣀⡀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⡎⠀⠀⡀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠈⠄⠀⢇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠸⢃⡀⣰⠃⠀⠀⠀⠠⠈⠀⠌⠁⠠⠀⠀⠐⡀⠐⢛⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠀⢉⡳⠎⠀⠂⠀⡠⠄⠤⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⢥⠐⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢇⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠤⠀⠀⠀⠀⠀⢀⡠⢀⣡⠖⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⢆⠀⠀⠀⠀⡤⣉⡉⠁⠸⠀⠀⠀⠀⠇⢠⣀⡀⠤⢀⡠⢀⡄⠄⠀⠀⢐⣂⠐⢆⠀⠀⠀⣄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠑⠢⠀⢀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠠⣍⠺⠀⡁⠈⠉⠏⠉⠀⠂⠄⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡠⠊⠀⠀⠀⠀⣀⠔⠀⠉⠩⢥⠖⠃⠀⠀⠐⠢⡀⠀⠆⠀⡆⣀⠦⠀⠠⠀⠠⠤⢤⠀⠀⠠⠤⠃⠀⠀⠀⠀⠀⠔⠀⢚⠖⠈
⠀⠀⡐⠞⠖⠃⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠤⠀⠀⠈⠰⡄⡀⠉⡐⢀⠂⠁⠀⠀⢁⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣀⡔⠁
⠀⠀⠸⡆⠀⠀⢐⠀⡀⠠⣀⠀⠀⠀⢠⣦⣰⡧⢀⣠⣀⠀⡌⣀⠀⠀⠄⡀⠁⠈⠅⠄⠀⠄⡀⠄⢈⠆⠰⢀⠒⠰⠂⠀⡀⠀⠐⠂⣁⣤⠞⠈⠑
⠀⠀⠀⠈⠀⠀⠀⠀⠣⠀⠀⠐⠛⠀⠊⠁⠤⠀⠋⠑⣏⠀⠀⣀⡁⢀⣀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠉⡀⡀⠀⠀⢀⡄⣀⠠⡖⠒⠀⠈⠀⠀⠉⠐
⠀⠀⠀⢠⠀⡠⡤⣠⠀⠀⠀⠀⠀⠠⠚⠂⠀⣀⠀⠮⠀⠄⠀⠀⠂⠄⣉⡟⠻⠯⢉⠝⠋⠉⠉⠉⠉⠉⠉⠉⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⣀⡀⠋⠑⢢⡀⠀⠠⠤⠇⠀⠀⢰⡉⠐⠄⢀⠀⠀⠀⠀⡨⠛⠛⠐
⠀⠀⠀⢆⡀⠀⠀⠀⠀⠈⠰⠁⢀⢠⣤⢆⢄⡁⠈⠚⠄⣀⠁⠀⠀⠀⠀⠐⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢋⠀⠀⠀⠀⡄⠀⠀⠂⠋⣗⡡⠿⠀⣻⣳⣄⣠⠃⠀⠀⣀⡀⣀
⠀⠀⠀⠊⢀⠀⠀⢀⣑⠦⠀⠀⠈⠁⠀⢼⠀⠋⡩⠋⠈⠐⠠⠀⢌⣀⠈⠁
⠀⠀⠀⠀⠈⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡔⢒⠀⡘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣺⡎⠱⠄⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢡⡾⣻⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠙⠀⠀⠘⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠤⠄⠈

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⢀⣀⣀⣀⣀⣴⣾⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢀⡐⢊⡑⠀⠀⠒⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⠁⠋⠛⠀⠀⠛⠓⢀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣅⡤⠤⠀⠀⠔⠲⠌⢻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠖⣷⠆⠀⠾⠿⠓⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⣈⠀⠠⠀⢀⠉
⠀⠀⠀⠀⠠⠀⠁⠁⠀⢀⠈⡀⠈⠈⠁⠂⠀⠀⠀⠀⠀⠀⡰⢀⣀⡀⠀⠈⠠⠄⡀⢠⠀⠁
⠀⠀⠀⠐⠀⠀⠀⠀⢴⠈⢢⣹⠒⠀⠀⠀⢰⠀⠀⠀⠀⠠⠌⡜⠀⠀⠒⡒⠀⠀⠀⡸⠋⠆⣄
⠀⠀⠀⠂⠀⠀⠀⠀⡠⠷⢞⣿⠃⠠⠀⢀⠀⠀⠀⠀⠀⢈⠀⠁⢤⠖⣋⠀⠈⢲⠎⠀⡄
⠀⠀⠀⠀⠐⠓⡬⡄⠁⢀⠀⢻⠄⠀⠀⠀⠁⠀⠀⠀⠘⢍⣈⡤⠈⠆⢣⣄⣠⠌⠀⠀⠀⡀⠀⠀⠂
⠀⠀⠐⠀⠀⠀⠪⠃⠀⠉⠉⠃⠀⡀⠠⡄⠀⠠⠀⠀⠀⠀⠈⠁⠀⢀⡍⠀⠀⠀⠀⠀⠀⠁⢐⠃⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⡀⠤⠐⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠒⠁⠈⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⡄⠨⠃
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠀⠒⠀⠀⠀⡨
⠀⠀⠀⠀⠰⡄⠀⢀⠀⣠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠐

⠀⠀⠀⠠⠄⢐⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢘⢀⠺⠀⠀⠀⠀⠆⠠⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⡀⠀⠀⠀⢸⠀⠛⡆
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⡄⠀⠀⠉⠉⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡴⠀⡁⠀⠀⠀⠈⠒⢾⡿⣔⢄
⠀⢠⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠛⢋⡤⠆⠃⠀⠀⠀⠀⠀⠢⡉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⣉⣉⣱⡤⢤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠛⠜⠁⠈⠁⠐⠄⡀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡎⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢀⣤⠤⠴⠖⠛⠉⠈⠉⠀⠀⠀⠉⠉⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⠖⠊⠁⠀⠐⠁⠀⠀⠀⠠⠀⠀⠀⠒⠒⠒⠒⠚⠒⠒⠂⠠⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣶⣶⣶⡖⠶⠶⠶⠦⢽⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠈⠁⠀⢀⣀⣠⣤⣶⠶⠿⠛⠻⢿⣿⣿⠿⠿⠟⠛⠻⣿⣿⣄⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣠⣴⣶⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣀⣤⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡴⠚⠉⣹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠐⡀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⠘⠰⣿⠂⠀⠀⢻⡄⠀⠀⠀⠀⢀⠔⠡⠛⠳⡉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⣷⠀⠀⠀⠀⠎⡐⠁⠀⠀⢡⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠤⠴⠀⠀⠀⠀⠀⢹⠀⠀⠀⠸⢀⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠁⠀⠀⠀⠀⠀⢨⣀⠂⠄⠀⠀⣀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⢿⣿⣶⡆⠈⠉⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠁⠠⠉⠤⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢳⠦⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠘⠈⡄⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠚⡀⠀⠑⠠⠉⠉⠓⠚⠛⠻⢯⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠡⡐⣀⣀⠜⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⠖⠉⠀⠀⠀⠀⠙⡄⠀⠀⢀⠐⡆⠀⢀⠔⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠺⠿⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢸⠁⠀⠀⠀⢀⡄⠀⠀⠈⠢⣠⠇⠀⢁⡀⠃⠀⠈⠳⡎⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠘⠇⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠢⡀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢸⡀⠀⠙⠶⠲⠎⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⠈⡲⠁⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣱⣀⠠⠤⠀⠀⠑⠀⠀⠃⠀⠠⢀⠠⡎
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠈⠳⡀⠀⠀⠀⠀⡐⠀⠈⢻⣦⣀⡼⠁⠀⢨⡤⢠⡀⠀⣘⠁⠀⠀⠀⠀⢋⠉⢀⡀⢤⠇⡇⠀⠀⠀⠀⢀⡴⢦⠀⠀⢠⠠⠄
⠀⠀⠀⠀⡐⠀⠀⠀⠈⠀⣀⠙⢆⡀⠀⠴⠀⠀⠀⢠⠟⢹⠁⠀⠀⠀⢀⢘⠁⠀⠉⠀⠀⠀⠀⠀⠈⠄⠈⣇⡠⠀⢹⠀⢀⣠⠔⠋⠀⢸
⠀⠀⠀⠈⠀⠀⠀⠐⠠⠈⠀⡀⠂⢁⠀⠀⠀⠀⠐⢏⠀⡇⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠀⠀⠀⠀⠈⠀⠀⠂
⢣⡀⠀⠀⠀⠀⠀⢀⠀⠀⠜⠀⠀⠀⠀⠀⠀⡀⠀⢄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠛
⠀⠑⠄⢠⠀⠀⠀⠈⡄⠀⠘⠶⣀⣀⠀⠀⢸⠑⠦⣤⠻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠸⡀⠀⠀⠀⠂⡀⠀⠀⠈⠉⢠⠴⠟⠁⠀⠀⠀⠍⠙⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢴⠞⠁
⠀⠀⠀⠀⠈⠦⠀⢀⠀⠀⠀⠀⠀⠀⠘⠖⠐⠀⠀⠀⠀⠀⠀⠇⠀⠉⠉⠉⠛⠛⠓⠒⠒⠲⠒⠒⠚⠋⠉⠁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠀⠀⠰⠀⠁⠀⠀⡔⠀⠀⠀⢠⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠰⡆⠀⠀⠀⠀⡐⠀⠀⠀⠀⢸⠀⠀⠉⠐⠂⠤⠄⠀⠀⠀⠤⢶⡤⠤⠄⠐⠒⠂⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠗⠒⠒⢶⣄⡀⢸⠛⢿⡛⠉⢹⡋⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡙⠁⠰⠄⠊⢹⢡⣄⠃⠀⠀⠄⢀⡸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠉⠷⠤⠄⠦⠤⠛⢠⡋⠈⠓⠒⠒⡈⠙⠠⢤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⠠⢄⠂⢈⢀⠄⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠁⠢⡔⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠑⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⢄⣀⣀⣀⣀⡀⠀⠀⠠⠀⠠⠐⠒⠈⠁⠸⠆⠀⠀⠀⠈⠉⠉⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡲⣄⣀⡤⠊⠐⣨⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠈⠻⢮⣙⡯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣳⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡾⢋⡝⠋⠀⠈⠑⢝⢏⠉⠓⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡞⣰⠋⠀⠀⠀⠀⠀⠀⢣⣣⣀⣀⣀⣙⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡞⣰⢃⣀⠤⠤⠖⠒⠚⠛⠉⠉⢉⣉⣁⣉⣉⣉⣉⡛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣯⠴⠖⠚⠉⠉⣁⣀⣤⠤⠶⠖⠒⠛⠉⠉⠉⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⣀⣤⠴⠒⠛⠉⠉⠀⠀⠀⠀⠀⢀⣤⡀⢀⣴⣶⡀⠬⡿⠛⣻⣟⠿⡿⠟⢻⢿⣒⢦⡀
⠀⠀⠀⠀⠀⢀⡴⢋⣠⣴⣶⣿⡿⠒⠲⠀⠈⠻⠆⠀⠀⠀⠀⢰⠏⣸⣏⣭⡵⢲⡄⣸⠃⡘⠁⠈⡏⢺⢠⠃⠀⢻⠀⣇
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠠⡿⠏⠈⠁⣼⠃⡏⠀⡇⢸⠇⡿⢸⢾⠰⠟⢸⠇⡏
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠘⠦⢷⡄⠀⠀⢷⣀⣇⠀⢣⡀⣠⡇⡞⠸⣄⣀⡼⣲⠇
⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠋⠉⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⡴⠛⣩⠏⢙⡶⠶⠿⠛⠋⠳⠤⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋⠀⠈⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⣀⡴⠋⣀⡞⠀⢀⡤⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⢸⡟⠻⣤⠞⠉⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⣉⣛⡿⠁⠀⠻⣤⣿⣷⠶⢤⣤⡤⣶⡏⠉⣻⠋⡿⠲⠶⠖⠒⢒⣲⡖⣩⣤⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⠁⠀⠀⢸⡃⠀⠀⢀⣟⢹⡏⢧⡤⠴⢶⡏⣧⠀⡏⢰⡏⠙⠛⠛⠓⠛⡛⢠⡮⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡿⠀⠀⠀⢸⣧⡤⠞⠉⡏⣼⠀⠘⡆⢀⡼⡇⢿⠸⠧⠼⠇⠀⠀⠀⠀⠐⠷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⣇⠀⢀⡼⢡⠇⠀⠀⢷⡞⠀⠱⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⢀⣿⠴⢋⡴⠃⠀⠀⠀⣟⢤⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠤⠘⡿⠚⠉⠀⠀⠀⠀⠀⢻⡐⡀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡤⠴⠶⢾⡇⠀⠀⠀⠀⣀⡀⠀⢸⣧⣵⣶⣾⡇⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⡷⠖⠚⠉⠉⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡼⢿⡿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⡞⠙⠋⠁⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡔⢢⢀
⠀⠀⠀⠀⠀⢀⡀⢀⡂⠀⠀⡼⠀⠨⠛⢯⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣉⣷⡄⠀⣤⠴⣶⣾⣤⡀⠀⢀⢾⣿⣧⣤⡀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠰⠉⠩⠍⠉⠹⠎⠹⠄⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠻⠋⠀⠈⠉⠉⠻⠀⠀⠀⠛⠻⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⣀⣀⣠⣀⣠⣤⠀⠀⢰⣺⣇⠀⠀⢸⣇⠀⠶⠏⠉⠁⢀⡀⠀⠀⠀⠀⡠⣾⠃⢀⣾⡧⠄⠀⠉⠀⠀⢤⠤⡀
⠀⠀⠀⡿⠯⠭⠿⠿⠿⠾⢷⠄⢀⡤⣿⠃⠀⢹⣿⠀⠀⠀⠀⠀⣿⣿⠀⢀⡄⠀⢉⡿⡇⠈⣹⣧⠀⠸⡻⣄⠀⠭⠭⠇
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⠀⠈⠈⠛⠀⠀⠘⠛⠀⠀⠒⠀⠀⠙⠋⠀⠑⠠⠆⠚⠀⠃⠐⠃⠙⠀⠐⠓⠂⠀⠛⠛⠁
⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠸⠿⠿⠟⠀⢸⣼⡇⣽⣭⣿⠀⠠⢶⣷⣶⠷⡍⡿⠃⢀⣀⣤⣶⣶⡿⠿⠗⠀⠀⢰⣛⣛⣳⠀⠀⣠⠟⣐⣧⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠁⠀⠀⠀⢿⣿⡾⠃⠀⢠⡾⢿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠑⠀⠀⠙⠁
⠀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠑⣤⣄⡀⠺⢿⣿⠏⠙⠉⠁⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⢀⠀⣠⣇⣀
⠀⠀⠀⠘⣷⣤⠾⠁⠀⢰⣿⣶⣷⣿⠄⠀⠀⠀⠀⢹⠟⠁⠀⠘⠟⠀⠀⠀⠰⣶⠄⠀⠀⠀⣼⠓⢻⡆⠀⠈⠉⠹⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⢤⣴⣶⣶⣶⠀⠀⡠⠀⠐⢀⠀⠀⣤⡄⠀⢀⣠⣀⡀⢀⣤⡀⠀⣶⡀⠀⣀⣤⡀⠀⢰⣖⣒⣶⠀⠀⢠⣤
⠀⠀⠀⠘⠿⠛⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠉⠉⠁⠀⠿⠀⠀⠛⠁⠀⠉⠉⠁⠀⠸⠿⠿⠿⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀
⠀⠀⠀⡞⠉⢓⠀⢀⣀⣀⣐⠀⠀⠀⢰⠫⣭⢳⠀⠀⣋⣋⣃⠀⠀⠟⠛⠏⠀⢰⣷⠀⠀⠀⠀⠁⡀⠀⠀⣷⡶⢿⣿⡆
⠀⠀⠀⠙⠶⠋⠀⠈⠉⠙⣿⣷⡷⠀⠘⢄⣡⠜⠀⠀⡻⠿⡏⠀⠀⡅⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠿⡿⠿⠿⡇
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠙⠁⠀⠀⠘⠟⠀⢀⡀⠀⠀⢀⠀⢀⠀⣠⡟⢀⠾⢧⠀⠸⣥⠀⠀⠶⠀⠀⣀⠀⢀⠈⠋
⠀⠀⠀⠀⣶⣶⣀⣰⣶⠀⠉⣷⠀⢘⢉⠀⢸⠘⠿⣷⠀⣷⡇⠀⣬⣽⠀⠀⣠⣦⠀⢨⣿⣧⠀⣠⣦⠀⠀⢀⣖⣲⣲⣀
⠀⠀⠀⠀⠯⠿⠀⠹⠽⠀⠀⠇⠀⠺⠶⠇⠿⠀⠀⠿⠀⠻⠇⠀⠿⠹⠀⠰⠿⠿⠇⠸⠿⠿⠀⠿⠿⠗⠀⠛⠿⠛⠿⠛⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⣿⢿⡯⢻⠛⣿⣏⠙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⣻⠃⠄⠏⢈⣯⣱⡻⣬⢯⣸⣧⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣖⢻⣽⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣶⣿⣿⠟⠉⠉⠉⢉⣉⣭⣿⣿⣿⣷⣀⣀⣤⠤⠤⠴⣶⠆⠀⠈⠹⡏⡇
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠁⢢⠉⢿⣿⡀⠀⠀⠀⠁⢴⠛⢻⣿⡉⠀⠄⠀⠀⠀⠀⠀⢼⣒⠂⠀⠀⣗⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⣿⣿⣿⣿⡆⢘⡅⠈⠻⠆⠀⠀⠀⠀⠈⠿⠚⠿⠶⠶⢦⣤⣤⣤⣴⣶⣮⣾⣀⣀⣀⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⣴⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⡰⠀⠀⣿⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠏⠀⠀⠀⠀⠀⢀⣀⡜⠁⢀⣥⡇⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⡟⠁⠀⠀⠸⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡁⠀⠀⠀⣠⣿⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠄⠙⠿⣮⣅⡒⠠⠤⢀⣀⣿⣟⠂⠒⠈⠀⠀⠠⠐⡴⡿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣶⣴⣾⣯⣽⣶⣤⡀⠀⣨⠟⣇⠀⠀⠀⠀⣁⠰⠞⠁⣸⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣄⡀⢸⡄⠀⠀⠰⠃⠀⠀⣼⠋⠈⢾
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢿⠹⢇⠀⢳⡣⢝⣻⣿⣧⢼⡿⢦⣷⡀⢀⣸⡄⠀⠀⠘⠶⡆⠁
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡱⣿⣧⢻⣷⡁⡑⣉⣻⣿⣿⣿⢬⣮⣿⣿⣿⣟⠷⣀⠰⢦⢀⠃
⠀⠀⠀⠀⠀⠀⢰⣿⡿⣯⣕⣌⣿⣿⡻⣽⣆⢽⣟⢿⣿⣿⣷⣽⣾⣿⣿⣿⣶⣼⡹⠳⣿⡀
⠀⠀⠀⠀⠀⠀⣾⣿⢿⣬⣾⡶⢳⣿⣷⣟⠾⣯⣽⣿⣿⣟⣼⣿⡿⢛⢿⣿⣮⢻⣿⢿⣿⠇
⠀⠀⠀⠀⠀⢰⣿⣿⣏⣳⣯⢹⡷⡝⣿⣿⡇⡹⣿⣿⡿⣿⣿⣿⣫⡿⡽⣿⣫⢿⣧⢿⠏
⠀⠀⠀⠀⠀⢸⣻⣿⡿⣿⣿⣶⣿⡽⡞⢿⣿⣎⠘⣿⣿⣽⣿⣞⠟⢿⡿⣿⣟⣿⢯⠞
⠀⠀⠀⠀⠀⢸⢽⣿⣿⢿⡵⡏⣱⡿⣿⣾⣿⣿⣯⣎⢿⣿⣿⣏⡄⠀⡻⣿⣿⢮⠏
⠀⠀⠀⠀⠀⠘⠗⠛⠃⠈⠘⠈⠈⠋⠉⠛⠻⠛⠻⠛⠂⠋⠛⠛⠓⠓⠲⠘⠻⠃

⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠐⠂⠐⠂⠔⠀⠂⠀⠒⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⣿⣿⣿⠀⠀⢸⣿⣿⣿⡤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⢤⠤⡤⣤⡤⢤⠤⡄⡄⠀⢀⣀
⠿⡿⠁⠀⠀⠈⠉⠁⠉⠀⣿⠀⣯⣿⣿⣾⣷⡆⠚⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣫⠄⠡⠀⠌⠰⠤⢾⠶⠲⠃⠛⠀⠘⠑
⣒⠛⠺⡷⠟⢓⣛⡖⢛⣉⠟⠀⠣⠤⠤⢤⠀⠀⠀⢤⠄⠖⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡀⠀⠄⠀⠀⠀⢀⠘⠐⠐⠃⠐
⣽⣿⣿⣧⣀⣾⡿⠿⣿⣿⣶⣶⣶⣶⣶⣆⣀⣀⣀⣀⡀⣀⠃⡂⠀⠀⢀⢀⠀⡛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠨⠝⢡⣿⣿⣿⣿⣽⣿⣀⠀⢰⡆⣴⣴⣤⡀
⠉⠍⠻⠀⠠⡈⠙⠉⣉⣉⠉⠉⣉⣉⣉⣙⡉⡋⡙⢻⣏⣏⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠞⠨⢡⠁⠀⠂⠂⢰⡆⠀⠘⣿⣿⣿⣻⣿⣿⡁⠀⠀⠁⠛⠙⠋
⠠⠀⡀⣦⠰⠇⢀⠀⣀⡉⢀⣶⣮⠈⠁⢈⠁⣡⠉⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠂⠀⠀⠀⠀⠀⠸⠀⠀⠓⠛⠛⠛⠛⠛⠋⠁⠀⠀⠐⠂
⠀⠀⠨⠃⠤⠤⠶⠸⠯⠥⠨⡭⠥⠠⠄⠿⠿⠏⠠⠤⠄⠤⠠⠤⠤⠠⠄⢤⠀⣸⣇⠀⡀⢀⠀⠂⢰⠖⠃⠚⠀⠀⠀⢤⠀⠾⢺⠀⣓⣀⣒⣀⣃⣐⣘⣃⣙
⣿⡆⠀⠀⠀⠀⠒⠀⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠈⠀⠤⠬⠄⠀⢸⣿⣿⣿⠀⢸⡇⠐⠀⡄⢘⢸⣿⡟⣿⣿⣿⡍⣿⣻⢛
⣿⡇⠀⣀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠆⢸⡇⠀⠀⢁⢸⢸⣿⣿⣿⣿⣿⣦⣿⣿⢹
⠏⢁⣠⡿⡿⠀⠀⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⡀⠉⠫⢍⣙⢠⡀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠘⠘⠛⠧⠛⠛⠛⠛⠛⠛⠛
⠀⣭⣭⣼⢇⠀⡂⠓⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠁⠀⠏⠀⠄⠘⢆⣤⠶⡆⣴⠒⠗⢰⣿⣷⠤⡦⣤⣤⣤⣤⡄⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠂⠈⠍⠅⠘⠀⡅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠒⠁⢩⡴⠤⠦⡆⡶⠄⠾⡕⠢⠶⠐⠀⠂
⣤⣠⡤⠧⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⣀⣠⣴⡄⠀⠀⣤⣴⣶⣦⠀⠇⣤⣀⡈⣥⢠⠘⡇⠀⠐⠀⣿⣻⣿⠃⡀⣄⣀⡀⣤⣴⠂⠉⠀⠀⠀⠀⡀⠀⠁⠈
⡿⣉⢁⣒⡂⣀⢰⡀⣀⢀⠀⡀⢠⠐⣈⢊⠻⡃⠀⠀⣿⣿⣿⡇⠈⠳⣿⣾⣗⣿⣿⠉⡇⠀⠀⠀⣿⢯⡴⠀⠔⡁⠂⡜⠸⣿⠈⡉⡉⠉⠉⠉⣉⣉⣉⣁⣉
⡏⠁⠈⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⡀⠉⠀⠀⠀⣿⣿⣿⡗⠀⣀⣿⣾⡿⣿⣿⣺⡇⠀⠰⢠⣿⡟⠀⠁⠀⠁⠈⠁⢀⡶⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿
⡇⠀⠀⣿⣿⣿⠉⠉⠉⠙⣿⠙⡗⠙⣿⡇⠀⠀⠀⠀⡿⠿⠿⠗⢸⣿⣤⢠⡌⠸⣿⣿⡇⠐⢀⣽⣿⣇⠀⢸⣿⡿⣿⢿⣿⣟⠀⠁⠀⢈⠀⠀⣟⣿⣿⣿⡿
⠃⢠⣤⣿⣿⣿⣀⣀⣀⣀⡟⡟⢇⣠⣿⡇⠀⠀⠀⠀⠀⢀⣘⣇⣻⡦⠷⠒⠓⠰⣇⣼⡷⢾⠢⠀⢸⡿⠀⢸⣿⣿⣿⣿⣿⠯⠀⠄⠀⠠⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠁⣿⣿⣿⣤⣄⣤⣤⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠟⠛⠛⠀⠛⠀⠭⠀⠀⠀⠘⠉⢸⡇⠀⢹⣿⣿⣿⣿⣿⡗⠀⠂⠀⢰⡶⢿⣍⣿⣿⣿⣿
⡀⡈⠀⠙⠛⢉⣉⣉⣉⣉⣙⣁⣀⣉⣋⣉⠂⠀⠀⠀⠀⠀⠀⠀⢸⠠⠄⢀⣀⢠⡆⢰⣤⣰⣤⣤⣾⡇⠀⠈⠉⠉⠉⠄⠛⢻⠀⠁⠀⠈⠉⠙⠟⠛⠛⠟⠿
⠤⣤⢤⣶⣶⢸⣏⣿⣿⣟⣽⣟⣋⣻⡏⣿⣾⣷⡆⠀⠀⠀⠀⠀⢸⡀⢘⣟⡏⠀⠁⢸⣿⣿⣿⣿⣿⡷⠐⣲⣶⠿⣶⡟⢻⣿⡶⢶⡖⠒⣶⡖⢲⣶⠒⣶⡆
⣠⣤⣴⣿⣿⠈⠟⠛⠛⠛⠛⠛⠛⠻⠛⠿⢙⣿⡇⠀⠀⡀⣦⡀⢸⠀⠻⡿⡟⠀⠀⢺⣟⣟⠉⠻⠋⡇⠀⠹⣿⣼⣿⣦⣼⣿⣦⣾⣧⣤⣿⣧⣿⣷⣤⣿⡇
⠀⠀⠀⠉⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⣅⠉⠀⢸⠀⠸⣗⣧⠀⢀⠘⠉⠁⠀⣀⣀⠉⢰⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠐⡦
⡀⠀⠀⠀⣇⣀⡀⣀⠀⠀⡀⢀⠀⠀⠀⠀⠀⢰⡄⠀⠀⣿⢠⣤⣤⣷⣾⠋⢁⠔⠁⠀⠃⠀⠐⣿⣽⡇⢸⢿⢿⠿⢿⣾⡿⠷⠿⠷⣾⣿⠀⠀⠀⠀⠀⠀⣌
⠄⢶⣾⡦⣯⠁⠅⠀⠀⠀⢰⠄⠀⠄⠀⠤⢤⣼⡇⠀⠀⣿⢸⣧⣽⠏⢂⠆⠉⠀⠄⠀⠀⠀⠀⣧⣼⡇⠀⠰⠾⠿⠴⡴⠿⠄⠀⠂⠀⠟⠀⠀⠀⠀⠀⠀⢀
⠀⢺⣿⡷⣿⠛⡃⠀⠀⢠⣤⣴⣆⣶⣶⡀⢸⣿⡇⠀⠘⣿⢨⣿⣿⡖⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⡇⠀⢠⠀⠀⣤⠄⠀⠀⠀⠶⡿⠟⠀⠀⠀⠀⠀⠀⠨
⠀⢼⣿⣿⡷⠶⠆⠀⠀⠀⣤⣈⣀⣩⣬⡀⣼⣟⡇⠀⠠⣿⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⢛⣻⡇⢀⠘⠀⠀⢼⣿⣷⠀⠀⠸⡷⣾⠀⡀⡀⡀⡆⠀⢠
⠀⢸⣿⣿⡟⠛⠃⠀⠀⠺⢀⣀⣀⣠⣤⣄⣘⠀⠀⠀⠀⠘⢻⣧⣾⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⢸⣶⣿⣾⣿⣴⣿⠒⠂⠐⢒⣗⠀⠀⠠⠤⠄⠀⠘
⡀⠉⠙⠉⡇⠀⠀⠀⠀⢀⠉⡉⠉⢙⡉⠉⢹⢠⡄⢠⡈⠁⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⣿⠁⢸⣶⣿⣶⣶⣾⣿⡀⠙⠒⠉⡉⠀⣀⣀⣀⣀⣀⡀
⠀⠒⠐⠐⡇⠀⠀⠀⠀⠛⠛⠋⠛⠻⠛⠛⠛⠀⣼⢿⣿⣿⣿⣿⣧⠀⠀⠐⠀⠀⠀⠀⠀⣀⠀⠈⠋⠀⢸⣶⣶⣶⣾⣿⣷⣄⠀⠀⢸⡇⠀⣿⡏⢻⠏⢹⣇
⠄⠀⠀⠐⡇⠀⠀⢀⠀⠀⡀⠀⢀⢠⡀⢈⠀⠀⢘⣿⡏⡉⠉⢉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠔⠇⢸⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⠗⠘⠿⠿⠿⠷⠾⠟
⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠐⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⣀⠀⠤⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠁⠀⢀⣀⣹⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠦⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⢀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠈⠻⠀⠀⠀⠀⡀⠀⢀⠀⠀⠠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⡀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠛⠿⠿⠛⠛⡄⢰⣶⠀⠻⠇⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⡠⢀⠀⠀⠀⣀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠰⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠡⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⢰⠋⠀⢠⡞⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠐⢠⠀⠴⠁⢀⠐⡏⠀⠀⠀⠀⠀⠀⠃⠈⠃
⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⠀⠠⠀⠀⠀⠀⠂⠄⢀⠐⠀⠀⠀⣠⠀⠀⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢸⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠈⠀⠀⠀⠀⠇⠀⠀⠀⠀⡀⠴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡠⢇⡀
⠀⠀⠀⠀⢸⠀⠘⢦⣀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡄⠀⠒⠊⢁⡤⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⢠
⠀⠀⠀⠀⣼⠀⠀⢠⠿⠛⠲⣶⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⣰⠏⠀⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣿⡀⠀⠀⠺⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠈
⠀⠀⠀⠈⢙⡇⠀⠀⠀⠀⠀⣴⣧⣤⣤⣤⣤⣤⡔⠀⠀⠀⢰⣶⣶⡏⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⡀⠀⠀⢀⣤⠆⠰⡄⠈⠉⡏⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢧⠀⣠⡾⢻⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠟⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡠⠆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠢⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠈⡿⠛⠛⠛⠛⢶⠞⠀⠀⠻⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠆⠀⠼⠒
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠉⠂⠀⠀⡄⠃⣀⡀⢀⡜⣦
⠀⠀⠀⠀⠀⠀⠀⢰⠁⣄⢀⡠⠈⢱⠀⠀⢱⠄⠀⠀⠀⢠⡋
⠀⠀⠀⠀⠀⠀⠀⢘⣄⠀⠀⠀⠀⠇⠀⠀⠈⡄⠀⠀⠀⠈⠀⠂⠀⠤⠤
⠀⢀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠻⠦⣤⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠁
⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠙⠒⠒⠒⠚⠃
⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠏⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠛⠋⠉⠙⠛⠛⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⡀⠀⠀⠀⡠⡀⠀⠀⢀⡀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⡀⠘⠀⠀⢀⠀⠁⠀⢀⠀⠑⠊⠀⡀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠘⠜⠀⠀⠀⠠⠂⠀⠀⠢⠀⠀⠀⠘⠜⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠗⣚⣉⣭⣭⠤⠶⠶⡶⠖⠒⠒⠒⠒⠶⡶⠶⠤⢤⣭⣍⣙⣓⠻⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡩⠖⢺⡋⡩⠔⠀⠀⣠⠤⠄⠑⢄⠀⢠⢄⡀⠀⡇⠤⢤⡀⠀⠓⠬⡉⣿⠓⠮⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡋⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠈⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣸⠀⠀⠀⠀⠰⠖⠒⠒⠄⠀⠀⠀⠀⠀⠀⠔⠒⠒⠶⠀⠀⠀⠀⢸⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢀⣰⣀⠀⠀⠀⢀⣰⣀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠋⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠓⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠐⠁⡀⢴⣀⣀⠀⠹⡓⠶⠤⣤⣄⣄⣀⡤⡤⠴⠖⡻⠁⢀⣀⣲⠄⡀⠑⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠪⡠⢰⠆⢀⠕⠀⠀⡇⠀⠀⠈⠑⠠⠔⠁⠀⠈⠑⠤⠐⠁⠀⠀⠀⡅⠀⠐⢅⠀⢶⠤⡨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠤⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠔⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠀⠐⠒
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠃


⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢘
⠐⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠀⢀⣀⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠈
⡀⠀⠀⠀⠀⠀⠘⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠚
⣥⣤⣴⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣗⡀⠉⠹⡏⠉⢘⣋⣁⣒⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠈⠙⠛⠉⠑⢶⡲⢭⡄⣈⠉⠢⡄
⠀⠀⠀⡠⣒⡉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡁⡢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠯⠄⠀⠀⠀⠤⠤⢀⡀⠀⠑⡀⠙⢀⠱⡀⠈⢂
⠀⠀⢰⠏⠀⠀⡏⢀⣟⣛⢖⣀⡄⠀⣈⣉⡹⠟⣄⠈⠁⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢊⠤⠐⠂⠉⠉⠉⠉⠉⠀⠒⠨⣢⡀⠀⠀⠈⡆⢰⠀⠈⡄
⠀⠀⠀⡀⠀⠀⢁⢸⠠⣿⣦⡜⠃⠉⠈⢉⣉⣑⠉⠆⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⢀⣀⢀⠠⠄⠀⢀⣀⠈⢻⡆⠀⠀⠀⠈⠀⠀⡇
⠀⠀⠀⠱⡀⠀⢸⡻⡄⠈⠛⠁⠀⠀⠀⠛⠇⠉⠴⡾⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⠞⣡⣽⣍⢀⡈⢶⣌⣳⡾⡇⢷⡀⠀⡀⠀⠃⠀⡇
⠀⠀⠀⠀⠈⠢⣼⢖⢣⠀⢀⣀⠀⠀⠀⠀⠀⢀⠟⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣭⣷⣦⡄⠉⠘⢷⣿⣷⣾⡄⢻⣶⠁⢠⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢄⠈⠀⠀⠀⣀⣴⠜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠃⢠⠁⠈⠉⠀⠀⠀⠀⠉⠁⠈⠁⢠⢿⠀⠘⠀⡌
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⢒⡟⠐⠚⣿⠉⢬⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠉⠄⠀⠀⣀⣀⣀⣤⡄⠀⣠⡤⠂⠘⠀⠀⠰
⠀⠀⠀⠀⠀⢀⡏⠁⠈⡁⠈⠣⡀⢀⠉⠁⠀⠀⠈⠗⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⢢⠀⠀⠀⠀⠈⠢⣀⡙⠛⠋⢉⡠⠞⠋⠁⠀⠀⠀⢀⠇
⠀⠀⠀⠀⡠⠃⢁⠀⠀⢷⡀⣀⠼⣾⣰⢷⣀⡇⠀⢰⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡰⠢⠈⡟⠁⠒⡄⠀⢀⡔⠉⠈⠛⠀⠩⣿⢿⡀⠁⠀⢠⠀⠘⠀⠀⡄
⠀⠀⠀⡔⠀⠀⢸⠀⠀⡇⠈⢿⡀⠰⢧⣾⠉⠛⡀⠸⠀⠀⠰⢤⡀⠀⠀⠀⠀⠀⠀⠓⠒⣼⠁⠀⠀⠀⣉⣬⠀⠀⠀⠆⢀⡜⠁⠀⢋⠿⠄⠸⠀⠰⣀⠠⢱
⠀⠀⢀⠗⢄⠀⠀⡄⠀⠇⢀⣸⠷⣶⢯⣿⠙⠀⠃⢸⠀⢀⠃⠀⠑⢄⠀⠀⠀⠀⡠⠋⠐⠊⠑⣤⡶⢻⠋⠀⠀⠉⠲⣶⠃⠐⣂⠄⠎⠀⠈⠲⣇⠀⠉⠃⡎
⠀⠀⠎⠀⠀⣙⣦⣅⠀⢀⠜⠁⠈⠠⢹⢿⡄⢐⠀⡮⠁⠉⡒⠁⠀⠀⡇⠀⠀⢰⣔⡓⠒⢄⠀⠼⣇⢸⡏⠉⠑⢆⠠⠃⠀⠀⠉⠀⠀⠀⠀⠀⣹⠂⠐⠊
⠀⠸⡀⠀⠀⠀⠉⢹⣋⡇⠀⠀⣠⣎⣁⡸⠗⠉⠀⢠⠀⠰⠀⠀⠀⡰⠁⠀⠀⠀⠛⢿⣶⣾⠊⠀⢋⠂⡹⠶⠯⠿⠃⠀⠀⠀⠀⠠⡄⡀⠀⠔⡉⠢⡀
⠀⠀⠑⠒⠂⢰⠒⠚⠲⠓⠠⠚⠀⠉⠉⡁⠀⠀⠔⠲⣄⠁⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⣹⠋⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⣇⠀⠀⠀⠀⠀⠀⣀⢀⣸⠎⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠔⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡴⠁⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠘⡄⠀⠀⣉⡏⢉⠉⢙⡉⢙⣇⠸⠖⠺⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡟⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠁⢲⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢤⠀⠀⠸⡆⠀⠀⡀⡴⠋⠐⠀⠘⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠒⠃⠐⠒⠉⠀⠘⠠⠅⢂⠰⢙⠇
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⡄⠀⠀⠀⠀⠊⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠘⡈⠁
⠀⠀⠀⠀⠀⠀⡰⠄⠀⠀⠃⠀⠀⠀⡈⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠒⠠⠄⣀⠀⠈⠀⠀⠀⠀⠀⢀⡀⠷⠄
⠀⠀⠀⠀⠀⠰⠁⠀⠀⠰⠀⠀⠀⠈⠀⠀⠀⠀⠀⢐⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠸⠗⠒⠒⠀⠉⠁⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠒⠒⠒⠁⠀⠀⢀⠁⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠒⠀⡴⠆⠀⢀⡀⠀⠠⠰⠎⠁
⠀⠀⠀⠀⠀⢈⠖⠐⠀⢀⡤⠀⠼⢠⡄⠄⠀⣀⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢋⠀⠀⠀⠡⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⡆⠀⠀⠀⡜⠀⠀⠀⠄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡄⠀⠀⠀⠠⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠁⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠀⢃⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⡘⠀⠀⠀⠀⠀⠆⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡄⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠾⠦⢠⡁⠀⠀⠀⠀⠀⢠⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠁⠀⠀⠀⠀⠀⠈⡄⠀⢠
⠀⠀⠀⡜⡦⢤⡰⠄⠀⠀⠀⠀⠀⣀⣀⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⣠⡆⠀⠀⠀⠀⠀⠀⣷⠀⣸⢧
⠀⠀⢀⢇⠷⡎⡐⠀⠀⠀⠀⠀⠐⠀⠀⠈⠑⠳⠖⣤⠤⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⠀⡠⠷⠀⠀⠀⠀⠀⠀⣧⡉⠁⣸⠡⣄
⠀⢀⠎⢘⢠⠀⡇⠀⠀⠀⠀⠀⠀⠷⠀⠠⠤⠤⠤⠤⠔⠀⠈⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⠔⡱⠊⠀⢀⡄⠀⠀⠀⠀⠀⠘⢌⠙⢁⠑⢢⠑⢄⡀
⠀⣮⠔⠂⢄⢀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠣⣘⠃⠊⢀⣠⡞⠔⠁⠀⠀⠀⠀⠀⠀⠀⢢⡀⠑⠊⡠⠚⢳
⠀⠑⠄⢀⠠⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠤⠬⠝⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠖⡁⠤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡛⠛⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠆⠀⠀⣀⣠⣀⣀⣀⠀⠀⠀⠉⠛⠛⠻⢧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⣤⡀⠀⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⢀⡀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠾⠿⠛⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢉⣤⠖⠂⣀⡀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠶⠶⠖⠀⠀⠀⠲⣶⡶⠈⠀⠀⠀⠀⠉⠲⣆⡈⠙⠶⢀⡀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠎⠉⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠄⠀⠈⠙⠦⣀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⠁⠀⢀⣀⠀⠀⠀⢀⡀⠴⠶⠟⠀⠀⠀⣀⡀⢶⣦⡀⠀⢀⠀⠿⣆⡀⠀⠀⠈⠁⠀⠘⡿
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢀⣠⠶⠈⠉⠁⣀⠀⠀⠈⠉⠐⢶⣦⠉⠁⠀⣶⠀⢀⡠⠶⠉⠠⣄⡈⠉⠙⠛⠷⣦⠈⠣⡄⠀⠀⠀⠀⠐⣶⣄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣰⠞⠁⣠⣴⠆⠈⠉⠙⠿⠟⠀⢦⡀⠉⠢⣀⠀⢰⡶⠈⠁⣠⣾⠷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⢆⠀⠀⠀⠀⠘⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢾⡆⠀⠀⢀⡘⠁⢠⡄⠛⠃⢠⡞⠉⢀⣀⣀⣀⠀⠈⠣⡀⠉⣠⠀⠀⠀⠀⠛⠃⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⢃⡀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡆⠀⠸⠃⢀⡄⠀⠀⠀⠈⠁⣰⡿⠿⡿⠿⣷⣦⠀⠋⠀⠸⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠸⢿⡀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣄⠀⢸⡇⠀⠀⠀⠀⠀⠏⠀⡄⠀⣀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⠟⠋⠉⠁⠀⣰⣶⡟⢿⡆⠀⠀⠠⡇⠀⢃⡀⠀⠀⠀⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠈⠁⠀⠀⠆⠀⠀⠀⠠⣇⡈⠻⣿⡿⢿⡟⠀⢀⠀⠀⠀⠀⠠⠀⠀⢠⠈⢿⣿⣿⠇⣸⡇⠀⠀⠀⠃⠀⠈⢳⡤⠙⠋⠙⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡀⠘⢷⣆⠀⠀⠀⠀⠀⠘⠛⠀⠈⠁⡦⠁⢀⠛⠀⠀⠀⠀⠀⠀⠀⠛⠓⢠⣤⣄⠘⠋⠀⠀⠀⡀⠀⢀⡼⠋⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡜⠛⠻⣷⣄⠀⠙⠃⣤⣄⠀⠀⠀⣠⣤⠐⠁⢀⣤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⡄⠋⠀⣀⡞⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⢀⡈⠀⠈⠙⠂⣀⣀⠙⠿⣦⣤⠀⠀⠀⠀⠀⠀⢀⣤⡴⠛⠋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⡦⠀⠀⢀⠟
⠀⠀⠀⠀⣠⠞⠛⠓⠀⣀⠀⠀⠀⠙⢣⡀⠘⠏⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟
⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠻⢧⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⡀⠐⢶⣿⣇⣀⣴⠃⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⢀⣤⡴⠟⠁
⠀⠀⠀⢾⠁⠀⠀⠒⢀⣤⡀⠀⠀⢠⡶⠂⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⢀⣀⡀⠘⠒⠀⠀⢀⡹⠃⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠈⠁
⠀⠀⠀⠀⣶⣄⡀⠀⠀⠉⠳⢄⣀⣼⣧⣤⠾⠉⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠛⠁⢀⣀⡀⠶⠋⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠀⠀⣀⡀⠀⢀⠿⣦⣀⠈⠉⠹⠏⠁⠀⠀⠀⠀⠉⠷⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠀⠀⣀⡴⠾⠋⠁
⠀⠀⠀⠀⣉⠓⠲⠿⠆⠉⠉⣀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠶⢄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠶⠊⠉⠁
⠀⠀⠀⢀⡟⠀⠀⠀⢀⡶⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠰⣶⠖⠒⠀⠈⠉⢻⠃
⠀⠀⠀⡿⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡶⠆⣀⠀⠀⠀⠀⠀⢿⣶⡶⠦⣀⡀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠶⢶⣾⠋⠀⠿⣀⠀⠿⠀⠀⠀⠀⡀⠼⠋⠀⠀⠉⣿⣇⡀
⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠀⠉⠉⠀⠀⠀⠛⡀⠀⠀⠙⠿⠀⠀⢠⡴⠈⠉⠀⠀⠀⢠⠚⠁⠉⠉⠲⣦
⡀⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣴⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠷⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠀⠙⢃⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣧⠀⣾⠀⠀⠀⠀⠺⠀⠀⢀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠙⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯
⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠙⠳⣤
⠀⠈⢷⣤⡀⢀⣤⣤⣤⡤⠔⠛⠛⠛⠻⠇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠘⠛⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⡘⠋⠀⠀⢀⡴⠛⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡼⠟⢀⣀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡴⠋⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⡀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠃⢠⠞⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡀⠀⠀⣀⣀⠀⠀⠲⠶⠖⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠲⠶⣶⣄⠘⢧⡴⠃⠀⠀⠀⠀⢀⣀⠴⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⡊⠉⠁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⣏⠰⠎⠀⠀⠀⠀⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠷⠶⠶⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠰⢿⡟⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠠⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠶⠂⠀⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣶⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠺⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⢠⣿⠀⠀⣶⠀⠀⢀⣀⣠⣄⡀⠲⠾⢿⡟⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠁⠈⠉⠁⠀⠙⡿⠁⠀⠁⠀⠀⠛⠓⠺⣿⠁⠉⠁⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠸⣇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⣿⠟⠁⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢾⣿⡷⢠⣤⠄⠈⠋⠀⣿⠀⠀⠀⠀⠀⠀⣤⡴⣿⡦⠤⠄⠀⠈⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠛⠀⠀⢀⡀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢈⣤⠀⠀⠀⠀⢀⠘⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢘⣇⠀⢀⣤⡞⠛⢷⠀⠀⠀⠀⣴⠛⠛⠁⠀⠀⠀⠛⢃⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠻⠧⣤⣤⠀⠀⣘⠛⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⣠⣼⣇⡀⢠⣄⣴⣶⡀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠉⠉⠉⠙⠓⠀⡀⠀⠀⠻⠿⠶⠟⠛⠛⠻⣿⠁⠀⠀⠀⠀⠀⠉⣿⠟⠓⠀⠀⠀⠀⠙⠃⢀⠙⠋⠁⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⣿⡄⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠒⠾⠛⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⣀⣀⣀⣤⣄⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠲⠖⠘⠛
⠀⠀⠀⠀⢿⣇⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠴⠶⠶⠖⠈⠉⠀⠀⠀⠀⠀⠀⠀⠙⠷⢦⣀⡀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⣠⡿
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠶⠆⠀⣀⣀⣀⣀⣀⣀⣀⡀⠰⠶⠖⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠶⠿⠛⠛⠛⠛⠛⠛⠿⠶⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡔⢦⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠪⣠⠇⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠺⣀⠇⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⡴⠢⡀⠀⠀⠀⢠⠖⣤⠀⠀⠀⠀⡴⠲⡀⠀⠀⠀⢠⠖⣤⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠈⠓⠃⠀⠀⠀⠀⠘⠚⠁⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣀⣠⣤⣤⡶⠶⠶⠟⠛⠛⠛⠛⠋⠉⠉⠉⣉⣉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠷⠶⠶⣦⣤⣄⣀⣿⡄
⠀⠀⠀⣀⣠⡴⠞⠛⢉⣉⣠⣤⣤⣴⣶⠶⠚⠛⠛⢿⠛⠛⠛⠉⠉⠉⠉⠛⠛⠛⡿⠛⠛⠓⠶⣶⣶⣤⣤⣄⣉⣉⠛⠳⢶⣤⣀
⠀⣠⠾⢋⣡⡴⠶⣿⠋⠉⣡⡴⠚⠁⠀⠀⣀⣤⡀⠈⢣⡀⠀⠀⢠⡀⠀⠀⠀⠀⡯⢀⣤⣀⠀⠀⠈⠓⢦⣌⠉⠙⣿⠷⢶⣬⡙⠳⣤
⣾⣧⡾⠋⠁⠀⠀⣿⠴⠊⠁⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠙⠦⣄⣸⠈⠑⠒⠤⠤⡧⠀⠀⠉⠓⠀⠀⠀⠀⠈⠑⠢⣿⠀⠀⠈⠙⠷⣼
⢻⣏⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣸
⠀⠙⢷⣄⡀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢤⣶⠴⠶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⣶⡤⠀⠀⠀⠀⠀⠀⢸⠅⠀⣀⣤⠾⠋
⠀⠀⠀⠈⠙⢻⣶⣷⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣼⣶⡟⠋⠁
⠀⠀⠀⠀⢠⡟⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠈⢻⡀
⠀⠀⠀⠀⠀⢷⣄⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣠⡾
⠀⠀⠀⠀⠀⠀⠈⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣄⡀⠀⠀⠀⠀⢀⣠⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣁
⠀⠀⠀⠀⠀⠀⢀⡤⠚⠋⣿⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⣯⠙⠓⢤⡀
⠀⠀⢀⣀⣠⡴⠋⠀⠀⣀⡿⠀⠀⠀⠈⢻⠳⢦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡴⠞⡟⠁⠀⠀⠀⢿⣀⠀⠀⠙⢦⣄⣀⡀
⡠⠞⠉⠁⠀⠀⠀⠰⡏⠉⠓⠂⢾⠀⠀⠀⠑⠦⣀⠈⠉⠉⣙⠟⠛⠛⢿⡙⠉⠉⠁⣀⠴⠋⠀⠀⠀⡷⠀⠛⠉⢹⠆⠀⠀⠀⠈⠉⠳
⠑⣤⠖⣉⢿⠀⠀⡴⠃⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠉⠒⠞⠁⠀⡄⠀⠀⠈⠲⠒⠉⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠘⢦⠀⠀⡿⣉⠲⣤
⠀⠀⠛⠁⠈⢦⣀⡵⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢮⣀⡴⠁⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠒⠀⠤⠤⠀⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣀⠀⠤⠤⠀⠒⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠦⠤⠀⣀⣀⣈⠁⠀⠀⠀⠓⠀⠀⠚⠀⠀⠀⠈⣁⣀⣀⠀⠤⠴⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⢀⣀⡀⢀⣀⡀⠀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⢀⠀⢀⢀⢸⡏⢹⡇⡀⠀⠀⠀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠉⠉⠉⠉⡏⠀⠀⢹⠉⠉⠉⠉⢹⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠤⠤⠤⢴⡇⠀⠀⢸⡦⠤⠤⠤⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠁⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠈⠑⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣤⣤⣤⣤⡶⣿⣿⣿⣿⠇⠀⠀⠸⣿⣿⣿⡿⣶⣤⣤⣤⣤⣽
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣀⣀⣀⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢆⡉⣩⡦⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠩⠋⠀⠀⠀⠐⠄⠀⠉⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠁⢀⣀⣀⠠⠤⠴⠦⠤⠤⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⡠⠔⠚⢉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠋⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⡤⢤⣬⣄⣓⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⣀⣤⣤⡶⠶⠿⢿⣿⣿⣿⠿⠟⠻⣿⣷⡀⠀⠀⠀⢈⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⣀⣤⣴⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣤⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣊⡴⠊⠁⢹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣈⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠽⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣀⠀⡀⢠⡄⠀⠘⢇⠀⠀⠀⠀⠀⠀⢀⠤⡄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠠⣄⠉⠁⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠊⠁⠀⠀⠘⣇⠀⠀⠀⡀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⣿⠀⠀⠰⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠊⠀⠀⠀⠀⠀⣌⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⣿⠿⡖⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⡀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⡴⠋⠀⠀⠀⢠⠐⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠙⠁⠢⠤⠠⣤⣤⣤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠐⠀⠀⠀⢢⡀⠀⠀⠀⢄⠀⠀⡤⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢶⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠀⠀⠀⢀⠀⠀⠑⢄⡰⠁⠘⣀⠊⠀⠑⣤⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠺⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠢⡀⠀⡔⠁⠀⠀⠀⠀⠁⠀⠀⠙⠀⠀⠀⠘⣆⠀⠀⠀⠀⡄⠀⠘⠶⠶⠃⠀⠜
⠀⠀⠀⠀⠀⢀⠀⠐⣄⠀⠀⠀⠀⠀⠀⢾⣧⠀⠀⢈⠎⠀⡤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⢸⡆⠀⠂⠁⠈⠀⠀⠁⠈⠄⠀⢲
⠀⠀⠀⠀⠠⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠘⣷⣤⠎⠀⠀⠖⠠⠤⠀⡌⠀⠀⠀⠀⠡⠀⢤⠐⠂⢲⠀⠀⠀⣀⠜⢱⠀⠀⠒⠐
⠀⠀⠀⠐⠀⠀⠀⠀⠄⠂⢙⠆⠀⠁⠀⠀⣰⠋⡜⠀⠀⠀⠐⠠⠄⠐⠀⠀⠀⠀⠀⠀⠂⠘⠂⠀⢸⡤⠔⠚⠁⠀⠀⠀⢠
⢄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⡈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠠⠘
⠈⠢⠀⡀⠀⠀⠀⡀⠀⢦⡄⠀⠀⠀⠘⠠⣈⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢇⠀⠀⠀⢁⡀⠀⠈⠉⠠⠴⠗⠐⠈⠀⠉⠰⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⡜⠁
⠀⠀⠀⠀⠑⠀⠠⠀⠀⠀⠀⠀⡈⠂⠀⠀⠀⠀⠀⠀⡄⠈⠉⠉⠙⠛⠛⠒⠒⠒⠓⠒⠉⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠧⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⡀⠀⠀⠀⠀⠸⣄⠀⠀⠁⠀⠀⠀⠀⠀⠈⡗⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⣤⣤⣤⣄⠀⠀⡧⣤⠤⠴⢶⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⠂⠠⠀⠞⡆⣀⠠⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠱⠄⠄⠤⠤⠂⡘⠀⠒⠲⠆⠙⠂⢄⡠⠄⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠀⢄⠀⣁⠠⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⡀⠰⠡⠤⠀⠀⢀⣀⣀⣀⠀⠠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠐⠒⠂⠀⠀⣀⢀⠉⠁⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⠀⠘⢷⣤⣀⣀⣀⣠⣴⣾⠋⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢦⡠⠀⠾⠿⣿⣽⣛⣿⣧⣼⠃⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢛⣿⡗⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣾⡷⠀⠀⣀⣤⣷⣶⣽⠁⠙⢉⣽⡆⠀⢀⣤⣄⢠⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢼⣿⣛⣓⣲⡾⣍⡮⡯⣻⣻⣾⡀⢸⣿⡇⠀⠙⣿⣿⣿⣿⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢀⠀⠀⠀⢾⡟⣿⣿⡟⠿⠶⠧⠂⠉⠛⠛⠙⢮⢻⡇⠀⠀⠈⠛⢿⡿⠿⢏⠉⠃
⠀⠀⠀⠀⠀⠀⡀⢳⡄⠿⠹⠖⠀⠀⠈⣿⣮⣍⣛⣻⣶⣤⣄⣀⣀⠀⢒⣳⡞⠀⠀⠀⠀⠀⠀⢤⣼⢣
⠀⠀⠀⠀⠀⠀⣿⣆⢹⠿⣶⣶⠏⠀⢸⣿⣿⣙⡋⢿⣿⣿⡿⠿⠿⠿⢟⡝⣿⣄⡀⠀⠀⠀⠐⠾⠓⠋⠀⣀
⠀⠀⠀⠀⠀⢰⣧⢩⣠⣤⢆⣠⣤⠆⠘⣇⣻⢳⣧⣐⠒⠓⠒⠀⠅⠘⣀⣶⣿⣿⡻⣦⡀⠈⢳⣶⣦⡐⣸⡇
⠀⠀⠀⠀⠀⠈⠻⠇⠟⠉⠟⣉⣡⡖⢸⡿⢷⠏⠿⣿⠿⣇⠂⢌⡄⡰⢫⣿⣿⡟⣧⣻⣽⣆⢦⣈⠉⠃⠻⠁
⠀⠀⠀⠀⠀⠀⠀⣰⣠⠄⠚⣿⠟⠀⠀⢿⣟⣦⢶⡊⠚⣿⠹⠟⠃⡷⢏⣿⣿⣻⢿⡽⢻⣿⡼⣇⠙⡦⢄
⠀⠀⠀⠀⠀⠀⣊⠁⢀⡁⠀⠋⣆⠀⠀⠈⣿⣿⣾⢸⡄⠁⠆⣐⣛⡕⣻⡿⣤⡿⣫⣿⣷⣿⠷⡜⢁⠄⢀⡑
⠀⠀⠀⠀⠀⠀⠫⢀⠀⠛⡞⠻⣿⣶⡄⠀⠹⣿⣿⣌⡓⠀⠊⣿⠷⢞⣻⣤⣤⣤⣿⣿⣿⣿⠦⣝⠁⣀⠠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⡫⠀⢇⢠⡘⣿⠁⠀⠀⠙⢿⣿⣿⣷⣦⣸⣿⣿⣿⠷⠶⢯⡙⢻⢿⣿⠱⠿⠥⣇
⠀⠀⠀⠀⠀⠀⠀⠈⡦⠘⣿⣾⣷⣾⢿⣶⣷⡀⠈⢿⣿⢿⣿⣿⣿⣮⣽⣇⠀⠄⣳⣀⠘⣷⡠⠂⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠞⢎⡻⣿⣿⣿⣯⡿⠤⠜⠛⠓⠛⠛⠛⠓⡿⣿⣷⣶⣀⣹⣶⡿⠶⠶⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠿⢤⣟⠋⣀⣀⣰⠦⢤⣤⣄⣀⣀⣀⣠⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠈⠙⠲⠬⣍⡛⠛⠶⠶⠾⠿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣉⠉⣵⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⡍⠁⠀⠀⠐⠀⡀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠘⠀⠀⣀⣀⠠⠤⠴⠤⠤⠼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠤⠒⠊⡉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣄⣈⣁⣲⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠀⠀⠀⠀⣀⣠⠤⠤⠒⠚⠋⠉⠉⠉⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣀⣠⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣡⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠒⠐⠓⠂⠤⢈⣓⠀⢐⠤⢄⠀⢤⡀⠙⠂⢔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠉⠉⠙⡗⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠱⢀⡌⠂⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠄⠀⠀⠀⠀⠃⠀⠂⠀⠀⠀⠀⣠⡜⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠀⠀⠀⠠⠈⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢠⠄⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢈⠠⡀⠲⢀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠛⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠈⠒⠐⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠈⠁⠀⠀⠀⠈⠉⠛⢢⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣤⠔⠋⠀⠀⠀⠀⠘⢆⠀⠀⡠⠈⡂⠀⠀⠋⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠲⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠘⡁⠀⠀⠀⢀⡔⠀⠀⠈⠓⢤⠁⠀⠁⡄⠁⠀⠀⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⡰⠚⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⢄⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢹⡄⠀⠀⠀⢀⠄⠀⠙⠦⠐⠀⠈⣄⠀⠊
⠀⠀⠀⠀⠀⠀⡀⠀⠱⣄⠀⠀⠀⠀⠀⠀⢠⢾⣧⠀⠀⠀⡹⠁⠀⠤⠀⢀⢀⣀⡀⠀⠀⠀⠀⣀⣀⣀⠀⠤⡷⠄⠀⠂⠁⠀⠀⣀⠀⠀⠀⠐⣀⣀
⠀⠀⠀⠀⠀⡔⠀⠀⠄⠈⠢⡀⠀⠀⠀⠠⠂⠀⠉⢷⣤⣼⠃⠀⠘⡆⢤⡠⠄⢤⠁⠀⠀⠀⠀⢡⠠⢤⠄⠐⠐⡆⠀⠀⠀⢀⡴⠋⠐⠂⠀⠐⠁
⠀⠀⠀⠀⠊⠀⠀⠀⠀⡀⠀⠘⢦⠄⠈⠁⠀⠀⢠⠞⢡⠅⠀⠀⠀⠃⡤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠠⠄⠀⠀⣵⣀⡤⠖⠋
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠉⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠑⡄⠀⠀⠀⠀⠀⠔⠁⠀⡇⠀⠀⠀⠉⠀⣤⡀⠘⣄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠀⣰⠀⠀⠀⢠⠀⠀⠈⠑⢠⢇⠀⢀⡄⠈⠲⠍⢂⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠈⢆⠀⠀⠀⠐⠂⠀⠀⣀⣈⢵⠏⡀⠀⠀⠀⠉⠀⢉⠁⠛⠠⠦⠄⣀⣀⡀⠀⡀⣀⣀⣀⣀⡤⠶⠚⣻⠁
⠀⠀⠀⠀⠀⠑⠀⠆⠀⠀⠀⠀⣀⡠⠀⠀⠀⡠⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⢀⠀⠁⠀⠀⠀⠰⠀⠀⠀⢸⡇⠙⠢⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠞⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠔⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠐⠂⠐⠂⠀⢹⠃⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⢤⣄⣀⣀⣀⠀⠀⢘⣦⣤⠤⠤⢶⠦⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠺⠅⠀⡀⡽⢳⠀⠈⡄⠁⠒⠐⠚⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢆⠀⡀⢁⠀⣬⢈⠗⠴⢀⢀⡄⠘⠎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠠⠐⠆⢈⠉⠉⠉⠁⠀⠘⠢⣄⠀⠀⠑⠂⣄⡈⠋⠉⠀⠈⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠉⠢⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢉⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⡉⠉⠉⠁⣀⡀⠤⠀⠀⠂⠒⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠁