Korean cuisine Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠀⠒⠒⠂⠀⠐⠒⠒⠂⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠈⠁⢀⣀⡠⠤⠄⠒⠒⡒⠒⠒⠒⠢⠤⢤⣀⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⢀⡠⠔⠊⠁⠀⠀⢀⣀⣀⠀⠀⠄⡀⠠⡆⠀⡲⠀⣠⠍⠒⠠⣀⠈⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⣠⠖⠁⠀⠀⠀⠀⠉⠒⠤⣀⢩⢉⡗⠢⢬⣵⡧⢠⡦⠈⠥⠀⠀⠀⠀⠙⠢⡀⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⡴⠊⠀⠠⠤⠤⠤⢄⣳⣄⣐⣦⠈⡀⡘⢇⠑⠖⣼⢐⡹⣧⣀⠄⠶⠋⠀⠑⢠⢄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⡠⠋⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠇⢸⠠⡌⡀⡀⢆⠙⠃⡧⣐⣀⡀⠀⠀⠀⡀⠀⠀⠀⡈⠣⡀
⠀⠀⠀⠀⠀⡰⠁⢀⡔⠀⠐⠹⡋⠁⠴⠄⠀⠀⠂⠂⠀⠬⢥⠤⠶⠒⠒⠆⣠⢄⡠⠀⠇⠀⠈⠁⠀⠓⡔⠀⠀⢀⠜⡀⠀⠐⠄
⠀⠀⠀⠀⡰⠁⠀⠌⠀⡠⡄⢀⡈⠒⠤⢈⣁⡀⡀⢀⠈⠀⠀⠦⠀⣁⣀⠐⠜⠀⠀⠀⠀⠀⠐⢈⠀⡀⠒⡆⠐⠿⠀⠠⠀⠀⠈⠄⠀⠄
⠀⠀⠀⢰⠃⠀⡌⡀⠄⠀⠀⠀⠀⠐⢀⠀⠀⠀⠘⣀⠤⠖⠈⠓⠉⠁⠁⠀⠀⠀⠀⠀⠀⠘⠦⠙⠯⡛⠤⣅⠀⠙⠠⣤⠮⠆⠀⠈⠀⠈
⠀⠀⠀⡟⠀⢰⠀⠀⠀⠈⠁⠔⠒⢄⡀⠀⠁⠀⠂⠈⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⣣⣀⠈⠻⢞⣤⠀⠀⠀⠀⠀⢠
⠀⠀⢠⠇⠀⡆⠀⠀⠑⠁⠀⠀⠀⠀⠱⣄⠢⠄⠀⠢⠀⠀⠀⠀⠀⠀⠐⠀⠒⠢⢄⠀⠀⠀⠀⠀⠀⢿⡮⢈⢳⠲⣞⣀⣳⢀⣀⠀⠀⡄⠐
⠀⠀⢸⠀⢀⡇⡄⠒⠀⠀⠀⠀⠀⡀⠄⠈⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠳⠾⡉⠒⠘⠈⡿⠲⣮⡁⠀⠇⠀⡇
⠀⠀⢸⠀⢸⠃⠰⠀⠀⠀⠀⢀⣀⡰⠀⠀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠐⠃⣁⣳⢸⣁⣀⣀⠁⠀⠀⠀⡇
⠀⠀⢸⠀⠀⡇⠀⠃⢠⠔⠐⠁⢀⣠⡲⠃⠶⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠚⠛⠚⠋⠉⠁⠁⠈⠉⠃⠀⡆⠀⡇
⠀⠀⠈⡇⠀⡇⠀⠁⠠⡀⠉⠐⠈⠀⡀⠀⠀⡐⠘⣆⠀⠀⠀⠀⠀⠐⠤⢀⣀⡀⠴⠋⠀⠀⠀⠀⠀⠀⢤⣉⣀⠀⠈⠁⠀⠉⠛⠺⠀⠀⢠⠁
⠀⠀⠀⢳⠀⢸⠀⢄⠀⠈⡃⢂⠴⠊⠁⠐⡎⠈⠁⠃⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢉⠉⠁⠲⠦⠤⠴⠃⠀⠀⡜
⠀⠀⠀⠈⡆⠀⢇⠈⠇⡀⠑⡌⠢⡤⠐⢒⢑⡀⠄⠚⣱⠈⠲⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠴⠒⠉⠒⠒⢎⡠⡅⠐⠂⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠘⡄⠈⢆⠢⡀⠀⠎⡆⠀⠘⠁⠀⣩⠉⢁⠈⠐⠺⠀⢄⠁⠀⠀⢀⡠⠠⠄⣠⡤⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⡁⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠘⡄⠀⢣⡀⠅⢘⠤⠠⢆⠀⢀⡇⢈⢶⣀⣀⠤⠐⠊⠀⢹⠀⠄⡠⠀⠈⠀⠀⡀⠀⠀⠀⢆⠀⢃⠐⠊⠤⠉⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠈⢦⠀⠑⢄⢨⠀⠀⢸⠓⠙⡆⠀⠀⠀⠠⡀⠀⠀⣠⠞⠐⠂⠇⠀⠀⠀⠀⠅⠀⠀⢋⠁⠀⢀⣹⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠐⣀⠀⠉⠀⢨⡇⠀⠀⣁⠀⠙⢪⠉⡉⠀⠀⡀⡘⠆⠀⠀⠀⢃⠀⠂⠊⢠⠢⠊⡠⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠐⠀⡀⠀⠈⠂⠖⠉⡆⠀⣠⠁⠐⠀⠚⠠⠁⢠⠀⠀⠀⠈⡄⠠⠄⣚⠔⠊⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠉⠺⠄⠄⠀⠀⠀⠆⠠⠀⠑⠂⢀⣀⠠⠔⠋⠀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⡀⠈⠁⠐⠂⠀⠄⠤⠄⠄⠀⠐⠒⠈⠁⠀⣀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠢⠤⠤⠤⠤⠤⠤⠄⠒⠒⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⠀⢤⡒⠔⣒⣀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⢠⠉⣗⢖⡀⠀⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⣭⠠⣨⣧⡰⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣤⠘⢺⡶⠩⣁⠟⠂⠀⢨⣀⠀⠀⠀⠘⠧⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡤⣿⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⢷⣽⠇⣈⣁⢮⠁⠽⡆⠒⢇⢌⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⣌⡲⣭⡟⢛⣛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠸⠟⠹⠷⠰⣗⠀⠳⠀⣤⣜⣉⣾⡛⡷⣦⣶⣾⡋⣰⡻⢋⣿⣿⣓⣊⣛⣿⡛⡚⣣⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⢀⠀⠒⠏⣤⡀⠑⣷⣤⣼⣿⣿⣷⢾⣯⣿⣿⢿⠟⠞⣻⢋⣂⣴⢟⣾⡷⠽⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢿⣮⣵⠂⢀⢮⣽⠟⠻⣽⣾⣿⣿⣿⣷⡳⢿⣇⣆⢹⡿⢛⣡⡶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠠⠦⠤⢀⣀⣉⣉⣉⢉⣱⣶⣾⠿⠿⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁




⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣽⣷⣦⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢠⠀⡀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣰⠖⣿⠛⣿⢽⣷⢠⡉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠿⣋⣿⣴⣿⣾⠟⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠊⠔⠀⠀⠀⠖⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⠀⠒⡠⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⠀⠣⠄⠀⠀⠈⠉⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⣀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠴⠉⠀⠀⢁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠁⡁⣁⡂⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⢰⣟⣭⣿⣶⠢⠰⡄⢠⢠⠀⠀⠀⠀⠀⠀⢀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢐⢃⣲⠈⠻⠿⡟⠙⠀⠀⠠⠂⠘⠀⠴⠾⠤⠼⠀⢼⡃⠛⠟⣹⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠀⣢⠄⠅⠙⠱⠇⠀⠀⠀⠀⠀⠀⠒⠐⠃⠀⠉⠁⠀⠉⠁⠀⠀⠐⠀⠐⠀⠂⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠂⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠂⠀⢄⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠴⢖⠀⠀⣠⡙⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⠤⢤⡶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢹⡽⠛⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠖⠀⣸⣯⣽⢧⠀⢸⣭⣳⣿⡆⠻⠿⠛⠟⠃⢀⡀⠀⠠⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⡀


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢐⡀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⡆⠀⠉⠀⢀⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⣆⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠸⠦⠞⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠈
⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⣀⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣐⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠦⠶⠆
⠀⠀⠀⠀⠂⠠⠀⣠⠈⡇⠀⠀⠉⠁⠀⠀⠰⣄⡠⠤⠆⠃⠀⠒⠴⠃⠂⡀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠄⠀⢁⡼⠁⠀⡀⠀⠀⠈⡀⢀⡦⠀⠀⠈⡅⠠⠛⣦⣇⡔⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⢛⡥⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠒⠈⠉⠀⠀⠀⢀⡄⠀⠈⠁⡀⠀⠀⠀⠤⠉⠡⡅⠠⠗⠡⠠⡄⡀⠀⠀⠀⠤⠐⢈⠀⠔⠋⠀⠀⠀⠤⠞
⠀⠀⠀⢠⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⢀⣀⠄⠀⠀⠀⢢⠀⠐⠣⠇⠀⠀⠀⠒⠒⠀⠀⠨⡠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⡡⠀⠃⠀⡠⠈⠇⢀⠆⠀⠀⠀⠀⠀⠀⠦⠂⠁⠁⢠⡴⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠅⠐⠠⠌⡁⣀⠴⠋⠀⠀⣘⡴⠖⠘⣠⠀⠳⠄⠊⠁⣠⢔⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⣤⣄⠁⠀⣀⡐⠀⠉⠉⠁⠀⠠⢂⠆⠌⠇⠀⢀⣼⠀⠀⠐⡶⠚⠁
⠀⠀⠀⠀⠐⢀⠄⠀⠀⠀⠀⢡⠀⢤⡼⠈⠛⠛⠂⠸⣿⣿⠈⠀⠀⠇⠀⠀⠉⠀⠀⠙⠚⠋⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠄⣀⠊⠀⣂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⡀⢤⣾⣿⡆
⠀⠀⠀⠆⡈⠇⠐⠧⠀⢠⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢠⣿⠆⠉⠉
⠀⠀⠀⠀⠀⠁⠈⠁⠀⡞⠀⠀⢬⣾⡄⠀⠀⠀⠐⠓⠁⠹⠰⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠁

⠀⢀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠊⡼⣴⣻⠀⠀⠰⠬⠁⠞⠆⠀⠀⠐⠖⢳⠂⠀⠀⠀⣖⣅⠀⡄⠀⠀⣀⢡⠥⠄⠀⠀⢀⢨⢅⢠⠀⠀⠀⣀⡉⣟⠀⠀⠀⠀⠋
⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⢀⣀⣀⢀⠀⠀⠀⢠⣾⣷⠂⠀⠀⠠⠦⠀⠀⠀⠀⠀⠐⡤⠀⠀⠀⠀⢀⡰⠄⠀⠀⠀⠀⠀⡔⡤⠀⠀⠀⡠⡶⢶⡄⠀⠀⠀⢀⡴⠒⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠊⠀⠀⠀⠈⠉⠉⠁⠀⠀⠐⠘⠉⠑

⠀⠐⠒⠊⠃⠀⠀⠀⠄⠠⠠⠀⠀⠀⠰⣽⡉⢢⠀⠀⢠⣄⡀⣤⡄⠀⠀⣠⣤⣤⣄⠀⠀⠀⣠⡤⡠⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣠⡤⢄⡀
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⣀⠘⠀⠀⠀⠉⠈⠉⠀⠀⠀⠛⠛⠛⠉⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠄⡀⢀
⠀⠤⠤⠤⠤⠀⠀⠈⠁⠒⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠭⠉⠂⠀⠀⠣⠁⡁⠐⠀⠀⠀⠁⠀⠂⠀⠀⠀⠐⠂⠒⠂⠀⠀⠐⠀⠒⠃⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⠐⠈⠁⠀⠀⠀⠀⢐⡥⠀⠀⠀⠀⠀⠖⠒⠂⠀⠀⠀⠊⠁⠀⠄⠀⠀⠂⠈⠀⠀⠀⠀⠀⣐⠀⠅⠀⠀⠀⠆⠂⠚⠰⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣀⠀⡤⠤⢶⣄⡄⠠⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⢀⡤⣢⣵⢅⠀⠀⠠⠒⠀⠀⡀⠀⠀⢄⠀⠀⠄⠀⠀⡠⠄⣶⡆⣤⣄⠂
⠀⠀⠀⡓⢹⠛⠀⠀⢀⢀⠑⢶⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠀⠀⢠⠀⢛⡔⠁⠁⠀⠛⣿⣶⣤
⠀⠀⠀⠁⠀⠫⠧⠭⠄⠆⠀⠀⠈⠀⠀⠀⠠⡔⠂⡀⠀⠀⠰⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠛⢿⣇⡀⠀⠀⢠⣳⠞⡫
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠄⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠉⠉⠉⠁⢀⠔⠁
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠴⣿⠔⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠈⠌⠁⠈
⠀⠀⠀⠀⠐⠁⠀⠀⠢⢔⠄⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢄⣀⠀⠀⠀⠀⠁⠐⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠐⠀⠈⠀⠀⠀⠀⠀⡠⠀⠄⠀⠔⠀⠈⠃⠀⠀⠀⠈⠀⠀⡂⣞⣾⠷⣪⡤⠀⠈⠀⠈⠀⠀⠀⠽⣜⠒⠉⠇⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠖⠁⠀⠀⠙⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣷⠛⢷⡚⣇⡗⠀⠀⠀⠀⢀⣾⣦⣷⠚⠈⣅⢞⡢⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀
⠀⠀⠀⢰⠄⠦⠀⢀⡀⠄⣡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣻⠂⠀⠈⣺⣞⠃⠀⠀⠀⠀⠀⣿⢿⣽⣿⣧⠁⣰⠀⠀⠀⡐⠁⢀⠀⠀⠀⣿⣯⣹⢱⠶
⠀⠀⠀⠀⠅⠀⠠⣈⡄⠬⠃⠠⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠢⡤⠔⠟⠁⠁⠀⠀⠀⠀⠀⠊⠻⢿⡿⡿⠟⠂⠀⠀⠀⠡⠀⠁⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠚⠗⠦⠂⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢿⣋⠀⣿⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣠⡀⠀⠀⢀⠀⢠
⠀⠀⠈⠀⠀⠀⠀⠀⠲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⢄⠀⠀⠀⠀⠀⣾⣴⣦⢡⣤⣤⣶⣦⣤⢠⣵⡶⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣯⣾⡿⠂⠀⠀⠀⡀⠉⠀⢋⣾⣄⣠⣥⣄⣠⡅⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠐⣚⢁⢛⣛⢹⢛⡛⣃
⠀⠀⠀⠀⠒⠧⢴⣁⠔⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠜⠯⠿⠿⣿⠿⡿⠿⠿⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣼⣁⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⢍⠈⣒⣶⣤⡁⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡜⣡⠖⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⣤⢄
⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠗⢪⠹⣝⢺⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠻⠇⣽⣠⣷⡖⣦⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⠠⠀⠀⠀⠀⣴⣾⢭⣿⣿⣴⣆
⠀⠀⠀⢤⣂⡐⢀⡀⠶⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠛⠛⠋⠉⠀⠀⠀⠀⠀⣤⣶⣾⣴⣶⡄⣤⡀
⠀⠀⠀⠀⠉⠙⠐⠂⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠛⠛⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⣿⡿⣿⣧⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠤⢲⣶⣿⣇⣀⣠⡦⠐⠀⠤⢤⠀⠀⠀⠀⠀⠀⠛⠋⠻⠋⠻⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⣀⣀
⠀⠀⠀⠀⡀⢰⠞⢋⢳⠀⢀⠀⠀⠳⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤
⠀⠀⠂⠀⠈⠙⠰⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⡘⠖⠂⣀⡴⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢲⡏⠠⢇⠉⠀⠀⠀⠀⠀⠀⠀⠒⢿⡖⣺⠁⡴⢿⡛⠤⠘⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⣠⣴⠆⠀⠀⠀⠀⠀⠀⠠⠉⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⡀⢀⡀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⢀⡠⣞⣿⠟⠁⠀⠀⠀⢰⠀⡁⠀⠀⠀⠀⡀⠈⠋⢢
⠀⠀⠀⠀⠀⢁⣤⣾⣷⣎⠃⠀⠈⠻⠞⠳⢮⣓⠄⠄⠀⠀⠀⠀⠀⠀⠀⣀⠤⢚⡥⠞⠉⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠄
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣄⡀⠓⠂⠀⢀⡛⣃⣙⠷⣬⡀⠀⠀⠀⢀⣴⢾⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄
⠀⠀⠀⠀⠀⡻⢁⠚⠋⡀⢩⣶⣤⣶⣿⣷⣶⣴⣶⠮⣀⡑⠖⠀⠀⠐⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠙⠦⡈⠓⠀⠿⠿⠿⠛⠛⠛⢩⠞⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣀⣀⡀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⡆⡄⢰⠀⡆⠀⠆⢰⠀⠀⠀⠀⠀⠀⠑⠂⠄⠀⠀⠀⠀⠀⠊⠀⠀⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠃⠈⠀⠆⠐⠁⠘⠘⠂⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⣶⢀⠀⠀⠀⠀⠀⢰⠀⡆⡄⠒⡀⠀⠀⠀⠀⠀⢀⠀⡶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠀⠀⠀⠀⠸⠀⠃⠇⠆⠇⠠⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠠⠤⣴⠦⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⣶⣒⣶⢶⣤⣄
⠀⠀⠀⠀⠀⠀⢰⠁⠀⢠⣞⠁⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠧⣿⠟⣿⣚⣛⡇
⠀⠀⠀⠀⠀⠀⢻⢾⡥⠴⠋⠶⡄⠠⠞⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡤⢖⡐⠒⣒⠶⠶⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⡇⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠠⠀⠂⠼⠛⠒⢒⡉⠘⠀⠄⠂⠠⠀⠀⠀⠀⠀⠀⠀⣞⢁⣩⡕⣾⡿⠽⠖⠒⠚⣄⠀⠀⠀⠀⠀⠀⠂⠄⡁⠠⠄⠠⠤⠀⠀⠀⠒⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠒⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠰⣆⣸⣆⣤⣀⡽⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡉⠋⠁⠠⠤⠈⠒⡒⠡⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢀
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⡁⠀⢀⠒⠲⠴⣐⣠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣼⢴⠾⠉⠀⢃⣀⡤⠀⠁⠁⢠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣠⠲⢓⠀⢈⠴⢚⠍⠁⠀⠀⢀⡄⡀⠀⣡⡈⠁⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢀⡃⠀⡼⢫⠡⠆⠴⠤⠤⢥⡅⠉⠵⠚⢂⡨⠄⠀⠉⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠤⡈⠢⠮⠀⠐⠣⣉⠀⠀⠒⠁⠈⠉⣀⠔⠁⠀⠀⠀⢀⡼⠆⠀⠄
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⡂⠐⡎⠀⠀⢀⣀⠨⠱⠆⠀⠀⠀⠂⠁⠀⠀⠀⢀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠐⠁⣠⠤⠒⠾⠯⣉⠀⠀⠀⠀⠈⠳⣀⠙⠢⡀⠀⠀⠐⠨⠣⠄⠀⠒⠀⡀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠈⠢⣀⠐⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠈⠀⡠⠁⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠘⢷⣀⠀⠀⠀⠀⠀⠈⠉⢖⠦⡤⠀⠀⢲⠀⠀⠠⣄⠀⠀⠀⠄⢀⣄⡠⠔⠒⠊⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⠁⠘⠉⠈⠃⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣂⡀⠤⠌⠙⠒⠋⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢲⡄⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⢸⠀⠀⠀⠀⠀⢈⢻⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠐⠠⣄⠀⠀⠀⢀⢼⡀⠈⠀⢠⣦⣈⣀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠈⠺⠻⣎⡀⠀⠀⠉⠀⣙⢠⡈⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣥⠀⠀⠀⠠⠁⠀⠀⠀⣀⠉⠲⣄⣤⣷⣥⣦⣟⢟⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠤⢤⢀⠏⠓⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⢺⡕⣾⣵⡶⣋⣤⠚⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠆⣝⣥⣽⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢫⡍⠘⣭⡾⣍⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣶⡌⡓⢯⡃⡆⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⡐⣄⡺⠋⡛⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢿⡟⢤⢿⡇⠀⢄⠈⠒⠄⠉⠀⠀⠀⢀⡙⡆⢟⡿⢯⣁⢻⠃⠠⢀⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⣆⣸⠲⠳⡄⠈⠂⠄⢀⣀⣀⢀⣀⣼⠓⣧⠠⡗⢀⡁⠂⢠⠋⠱⠘⠈⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠙⡻⣦⡙⢷⠶⠚⠋⠂⡁⠀⠄⠑⠄⠏⡟⡔⡰⠀⡠⠋⠀⠀⠐⡊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⢿⣷⠂⡿⠻⠀⠀⠡⠂⠠⠀⢐⡞⠪⠃⣠⡎⠀⠀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⠀⣀⢠⠠⡄⠂⢀⠤⠘⣁⣤⡪⠕⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣿⣶⣤⣤⣤⣤⣤⣬⣤⢔⣲⣿⣿⣦⣤⣤⣀⡀
⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⡟⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠄
⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣷⢋⣦⣍⣙⣿⡃⣸⢋⡟⢿⣧⣿⣿⣿⣿⣿⣿⣥⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠉⠉⠉⠘⠉⠉⠛⠛⠿⣿⣿⣿⣿⣤⣀

⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠉⠿⣦⣄⡀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠃⠀⠀⣀⠀⠀⠀⠁⠀⣀⡀
⠀⠀⠀⣀⣴⣤⠆⠘⠿⠷⣾⡦⣄⠀⠀⠁⠀⠀⠀⣀⣤⣾⠟⠉⠁⠀⠀⠀⠅⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⡀
⠀⠀⣾⡿⣿⡧⡀⠒⠀⣨⣛⣿⡳⡧⣀⠀⠀⢴⣾⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠉⠁
⠀⠀⠨⣄⠉⠐⣼⣿⣿⣿⣿⣿⠟⠐⠎⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠤⠊⠁⠀⠀⠀⠀⢠⠀⠀⢠⠀⠀⠄⢠⠀⠀⠀⠀⠁⠀⠤⠀⠀⠀⠐⠁⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠁
⠀⠀⠀⠀⡀⠀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣤⣤⣄⠀⠀⠀⢀⡀
⠀⠀⠀⣠⡀⢰⣎⠀⠀⣀⣠⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣟⣿⣿⡏⠀⠀⢲⢾⣿
⠀⠀⠀⠹⢛⣯⣅⠝⢀⠉⡀⢀⠀⠀⠀⠀⠀⡠⠏⢾⣩⣭⣍⠭⣦⠀⠀⠀⠀⠀⢐⢀⡛⠛⠋⠙⠉⠡⠀⠀⠛⠛⠛
⠀⠀⠀⠈⠁⠐⠂⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⣮⣍⣹⣥⣄⡰⠼⠃⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⡆⠒⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠽⠃⠐⠒⠋⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠻⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣤⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠈⠻⢿⣿⣿⣗⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⢀⣀⠤⠤⠤⠝⢿⣿⡿⣮⣗⠦⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠖⠋⠁⠀⠀⠀⠈⢀⠀⠘⢿⣾⣟⢿⣆⡐⠦⣬⣙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠈⠷
⠀⢤⣼⣷⣦⣼⠻⡝⣀⠠⢞⠋⢻⢷⣼⠽⣷⣮⡙⠻⢦⣌⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴
⣿⣿⣟⣿⣾⣿⠆⠘⣠⠀⠀⠈⠙⠋⢥⣔⢨⡙⢿⡓⣤⡙⠧⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⢋⠥⣢
⣿⣯⡽⣿⣿⡀⠀⠀⠻⢦⣤⣤⠀⠀⠀⢸⠿⠿⣦⡍⠻⣿⣷⣌⡛⢄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⣯⡥⣪⡴⢛⡡
⣟⠿⢾⣿⣿⠟⣳⠦⡀⠀⠀⠀⠀⠀⣠⣾⣤⣤⣶⡤⡷⢦⡙⠟⣿⠶⣌⡓⢄⡀⠀⠀⠀⠺⣛⡷⣛⣵⠾⣯⠔⠋
⢈⢳⡞⡿⠃⠀⣙⣀⣽⣷⣦⣤⣶⣿⣿⣿⣿⣶⣶⣶⣶⡬⢿⣦⣈⠲⢌⠙⠶⣿⠆⠀⠀⠀⠀⢾⢟⡽⠛⠁
⠹⢇⣀⡄⠌⠱⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣫⣴⠟⠁⠈⠳⢶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣟⠂⠌⢉⡓⠂⠾⠿⠿⠿⠿⠿⠿⠿⢛⠛⠉⠡⠒⣻⠟⠁
⡈⠙⢦⣀⣀⣉⠉⠑⠀⠀⢀⢚⣉⣀⢀⣀⣀⣴⢊⣁⠀⢀⠀⠀⠀⡀⢀⢀⠀⠀⠀⠀⣴⣠⡖⠀⣠⣄⡀⢀⣠⣀
⡙⢍⡳⢉⡻⠿⣿⣷⣿⣬⣯⣾⣿⠀⠶⠉⠉⠀⠉⠀⠁⠀⠀⠈⠀⠈⠀⠀⠀⢸⠙⠁⣿⣿⡔⢽⣿⠨⣿⢸⣿⡿⠌
⣵⣾⣿⣽⣶⣿⣮⣭⣭⣽⢻⣏⣍⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣲⡄⣿⡿⣿⢸⣿⢃⣿⡸⣿⣷⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠭⠀⣒⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠁⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⢄⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠐⠀⠀⡀⠀⡀⠀⢀⠀⢀⠁⠆⠀⠀⡠⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠑⠠⡑
⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⢀⠤⠊⠀⠀⠀⢸⠁⠀⠠⠀⠀⠑⢄⠀⠀⠀⡜⠈⠀⢠⠀⠇⠀⠀⠀⠁⠂⠄⠀⠀⠈⢦⠢⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡠⠥⠤⢄⠀⠀⠀⠘⡀⠀⠀⠀⠀⡠⠀⠀⢀⡜⠀⠀⠀⠋⠀⡀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠑⡌⢄
⠀⠀⠀⠀⠀⠐⠀⢀⠔⠉⠀⠀⠀⠄⠈⠢⡀⠈⡇⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⢺⠔⠙⠁⢢⠀⠠⡀⠀⠀⠀⠀⣄⠀⠀⠘⠄⢂
⠀⠀⠀⠈⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠐⡀⠘⠀⢘⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⡠⠃⠀⠀⠠⡆⠀⠀⠈⠢⡀⠀⠀⠀⠀⣀⠀⠈⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠔⠁⠀⠀⠀⠔⠀⠀⢠⠊⠀⠱⠀⠀⠀⠀⠉⠢⠀⠀⠎⠱⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠣⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠐⠁⡄⠀⠀⠆⠀⠠⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢁⢁
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡠⠄⠀⢠⠂⠲⡄⢀⠔⠀⠀⢀⠊⠀⠀⠃⠀⠀⠰⠀⢀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⠀⠀⡐⡐⠁⠀⡘⠘⡄⢀⠘⠆⠀⠀⠀⠁⠀⠈⠂⠀⡀⠀⠤⠃⠀⠆⠀⠀⠀⢃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠊⠊⠀⠀⠐⠑⠀⠰⡄⠀⠐⣄⠀⠀⠀⠐⠂⢄⣀⠀⠀⢀⢄⢀⠈⠆⠀⠀⠸⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⢀⠄⠀⠒⠈⠀⠑⡀⠀⠈⢦⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠁⠸⠀⠀⠀⢳⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠔⠁⠀⠀⠀⢀⠀⠀⠘⡄⠀⠀⢱⡀⠑⠀⡀⠀⠀⠀⠓⣄⣀⠀⠀⡇⣀⡠⣬⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀⡄⠀⠀⠠⠀⠀⠀⠀⢀⡊⠁⠀⠀⠀⡄⠀⠀⠈⠀⠄⠈⠢⡔⣁⠃⢀⠀⢠⠂⠀⠀⠀⠈⢣⡀⠀⠙⠐⠂⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠡⠰⡀⠀⠀⠀⠀⠐⠀⠀⠈⠢⣄⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠄⠀⠘⣆⠀⠀⠀⠢⡀⠀⠀⠵⠐⠐⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢳⡑⡄⠀⠀⠀⡀⠀⠀⡀⠀⠀⠑⠢⣄⠀⠀⠈⠑⠲⠤⢄⣀⡀⡀
⠀⠀⠀⠀⠀⠱⡜⢄⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⣹⠆⠀⠐⠒⠒⢀⣀⡈⢠⠠⠤⠄⠒⠒⠒⡀
⠀⠀⠀⠀⠀⠀⠈⠆⠱⠀⠀⠀⠀⠀⠀⠀⠁⠢⠤⡁⠀⠀⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠐⠐⠒⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀



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

⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⢰⡴⢠⠒⠀⡂⢰⠀⣠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠈⠀⠉⠀⠀⠈⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣀⠀⠈⠉⠒⠢⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠈⠉⠓⠢⢄⣀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠉⠓⠢⠤⣄
⠀⠐⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠲⠤⣄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⢄⡀⠀⠀⠀⠀⠀⢄
⠀⠀⡴⠉⠉⠉⠀⠀⠀⠀⢀⠀⢣⣀⠀⣨⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠂
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢌⢀⣄⣀⣶⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡤⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠈⠑⢟⠹⢺⡍⠀⠀⠀⠀⠀⠈⠛⢀⡀⠀⠙⢚⣡⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈
⠀⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠄⣀⠀⠘⠓⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⡁⠀⠀⢀⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠐⠀⢬⡀⢈⠛⠁⠀⠀⠀⠀⣠⠃⢐⣿⡿⠀⠀⠀⡀
⠀⡃⠀⡀⠡⠀⠀⠐⢠⣉⠄⠀⠀⠀⠀⠀⠀⠐⣲⣲⡦⢀⠀⠀⠀⠀⠀⠀⠀⢄⠂⠐⠁⠀⠀⠀⠀⠀⠀⠙⠃⠚⠋⠀⠀⠀⢀⡀
⠀⠀⢠⠔⠆⠈⠡⢊⢀⠁⠀⠀⠀⠀⠀⠀⣾⡟⢻⣿⣾⠇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡠
⠀⠃⠀⠐⠀⡘⡥⡛⢠⠙⠀⠀⢀⡀⠀⠀⣸⢿⡏⠃⣿⣿⣿⠇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢴⠚⢈⣀⠃⠀⠀⠀⠀⠢
⠦⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢘⠁⠀⠀⠹⠾⠟⢘⠷⠟⠋⠀⠀⠀⠀⢩⣯⡤⠀⠀⠀⠈⢀⣀⡿⠊⠉⣦⠀⠀⠀⠐⢦⠀⠀⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠
⠀⡀⢁⣤⣄⡴⠒⠺⢶⡆⠢⠀⠀⠀⠀⠀⠀⠊⠀⠒⠀⣴⣾⣾⣯⠀⢠⠒⠀⠀⠠⠀⡀⢢⠀⠘⠀⢀⡠⢂⣾⢖⣶⡌⠠⠀⠀⠈
⠀⠀⢸⡟⢯⣣⢤⡤⣶⡏⡿⣆⠀⡐⠀⠠⠤⢄⠀⠀⡀⡀⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⡉⢀⠀⢂⣈⣿⠁⠀⠀⢙⡿⣿⡆
⠀⠀⣀⠀⠁⠋⠛⠓⠋⠁⠀⠀⠀⠀⠀⠫⠹⠂⠠⠀⠃⡆⠒⠂⢲⠂⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠙⠿⠦⢤⠤⠞⠟⢩⠃
⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠠⠀⠂⡁⠀⠀⡆
⠀⠀⠀⢀⣴⣆⠄⠀⠀⠀⠐⢦⠀⠂⠀⠀⠀⠄⠀⠠⠀⠀⠰⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂⠐⠂⣂⠂⠠
⠀⠄⠀⣀⠜⠁⠀⢄⣦⢀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠐⠀⠀⠀⠨⠒⠂
⠀⠀⣀⡀⠀⠄⠀⠉⠙⠀⠉⠀⡀⠳⡀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⠐⠀⠀⠀⠈⠃⠀⠀⠀⠀⠐⠀⠀⠁
⠀⠓⠚⠁⠀⢀⠀⠀⣤⡠⢄⠀⠃⠀⠙⡀⠀⠀⠈⠠⢐⣽⣿⢷⣺⡤⠀⢙⠀⠁⠠⠄⠿⣟⠚⠽⡄⠄⠀⠀⠀⠀⠀⠤⠤⠐⠈⠀⠄
⠀⠀⠀⠀⠰⡃⠀⠀⠙⣃⣠⠁⠀⠀⠀⠀⠀⠁⢠⣺⣿⣏⢻⣟⣿⣟⠀⠀⠀⠀⣾⣷⣿⡋⢸⡶⣿⠂⠀⠀⡈⠀⡀⠀⢀⣀⣀⣀
⠀⠀⠀⢟⠚⠒⠠⠄⢊⡜⡇⠀⠀⠀⠀⠀⡁⠀⠈⠽⣟⠀⠀⣿⣿⡅⠀⠀⠀⠀⢿⣿⣿⣿⣷⣄⠟⠀⠀⠘⠀⠠⠈⡆⠸⢿⣿⡷⠿
⠀⡤⠀⠙⠂⠐⠣⠒⠚⠑⠊⠀⠀⠀⠀⠁⢀⠀⠀⠀⠉⠳⠊⠛⠂⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⠉⠀⠀⠀⠈⠢⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⠿⡿⣿⣿⣳⠄⠀⢰⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⠠⠀⠀⠀⢸⡿⠏⠩⠭⠉⠙⠚⠇⠀⠸⡏⠀⠁⠀⠀⠁⡿⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠠⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢊⣃⡙⠻⠙⠀⠀⠀⠀⠀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⣲⡉⠀⣺⠀⠀⠀⠀⠠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠠⠀⠀⠀⠠⠀⠀⠀⠰⠀⠄⠀⢀⢢⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠠⠈⠍⡤⠥⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡓⠃⠁⠘⣈⡇⠀⠀⠀⡄⠀⠀⠀⡀⠐⡄⠀⢀⠀⢂⠀⢀⠀⢢⠀⠀⠀⣶⡄⣈⠛⠒⠀⠠⡄
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠂⠀⠀⠙⠳⢿⡀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠉⠑⠀⠀⠂⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠈⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠒⢂⢲⠄
⠀⠀⠀⠀⠀⠂⠀⠚⠁⠀⢀⡇⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⣉⣉⠀⠀⠀⠀⠀⠈⠈⠀⠀⠆
⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⠀⠃⠀⠀⠈⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⣤⡄⠀⠀⠀⠀⠀⠠⡠⢤⠠⢄
⠀⠀⠀⠀⠈⠠⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠐⠠⡤⡅⣢⣌⣅⣆⣂
⠀⠀⠀⠀⠀⡀⢷⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⢀⠀⠀⣀⠀⢀⠀⠀⠀⠤⠀⡉⠀⠀⠀⠀⠄⠀⠀⢀⡶⡄⠀⠀⠀⠀⠀⠖⠠⣀⠊⠀⡄⠀⠀⠀⠀⢀⡞⠁⠀⠉⡇⠀⠐⠈⠁⢢
⠀⠀⠢⠄⠠⠀⢰⡶⠼⠦⠤⠤⠤⠴⠷⠤⡀⠀⠀⠀⠀⠀⠀⠈⡠⠒⣿⣯⠉⠑⢎⠂⢄⠀⠀⠇⡀⠀⠀⢠⣏⣀⣀⠀⠀⡇⠐⠁⠀⠂⠆⠀⣀⣀⣀
⠀⠀⠀⠀⠀⢴⣂⠂⠀⠀⠀⠀⠀⠀⠐⠐⢈⣢⠀⠀⢀⡲⣀⢰⣁⠀⣨⠓⢤⣀⣤⡀⠀⠈⠒⠰⠜⢒⡤⠯⠤⠭⣍⡛⢶⡇⠄⠠⠂⠒⢀⠀⠠⠂⠁
⠀⠀⢀⠀⠀⠀⢸⠨⡧⢩⡍⣭⢩⡅⢬⠅⠟⠀⠄⠀⠀⠘⠁⠸⣟⠉⠅⠀⠀⠀⣻⠣⡄⠀⠀⢀⣠⣾⠖⠒⡒⠒⠦⣌⠻⡅
⠀⠀⠀⠀⢀⠴⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⡀⠀⢉⣄⠀⣎⣙⣦⣀⡀⣀⣴⠧⠰⠃⠀⠀⠉⠀⢸⡀⠈⠁⠀⠂⢈⣿⣏⠀⣂⠇⠀⠀⠀⠀⠄⠒
⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀⣤⣀⠀⠀⢀⣄⡀⢸⠀⠈⠚⠀⢈⠔⠻⡝⣄⣸⠏⠉⠢⡀⠀⠀⢀⡠⣤⢹⡦⣤⢤⠴⠋⠉⡈⠁⢀⣄⡀⠀⡠⠠⠃⠈
⠀⠀⠀⠀⠤⠼⠿⠿⠄⠀⣿⣿⣿⠄⠀⠾⠿⠧⠼⠀⠀⠀⠀⡎⠀⡄⠈⢮⣻⣀⣢⣤⣱⠀⡰⠁⡀⢰⢨⢿⠟⡲⡀⠀⠘⠖⠀⠐⠂⠉⠋⠒⠤⠬⠆
⠀⢠⢤⡄⠀⠤⠄⠤⠤⠤⡄⠀⠀⠀⡀⠀⠔⠐⠀⠀⠀⠀⠀⠑⠚⠒⠤⠄⢿⡠⢿⠷⠇⠀⠓⠮⣀⢸⣐⡶⠋⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⢀
⠀⠈⡎⡇⠰⠀⣀⡀⠠⠀⡇⠀⠀⠀⠁⠀⢂⡠⠀⠀⠀⣤⠀⢀⠄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠧⠤⠆⠐⠂⢠⣘⠐⠀⠀⠃⢘⡄⠹
⠀⠀⢡⢡⠀⣮⣤⣿⠄⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠄⠀⢷⡆⠰⢃⡇⢔⡰⡛⠖⠖⡠⢾⡠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠠⠈⡲⠒⠒⢶⠉⡇⠀⠥
⠀⠀⠸⡈⡄⠌⠛⠋⠐⠂⡇⠀⠀⠀⢠⠖⣂⡐⠦⡀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⢇⠘⠋⣠⠛⡇⣠⠂
⠀⠀⠀⡇⢡⠀⠀⠀⠀⠀⡇⠀⠀⠀⢘⡀⠿⠟⢀⠇⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠓⠂⡀⠀⠈⢸⣣⠈⠉⠉⠉⢠⡇
⠀⠀⠀⢰⢸⠀⠀⠀⠀⠀⡇⠀⠀⠄⠀⣈⡛⠂⠉⠀⢰⡟⠿⣻⠟⡻⣿⠛⢿⢟⣛⣿⢟⡻⣿⣷⠀⠀⠋⠉⠉⠉⠃⠀⢠⠚⠉⡏⢹⠹⢩⠍⣿⡆
⠀⠀⠀⢸⢘⡀⠀⠀⠀⠀⡇⠀⠀⠀⣰⣿⠇⠀⠀⠀⢿⡇⡌⢿⠸⠗⣰⢈⢾⡈⣭⣿⢨⣅⢸⣿⠀⢇⠁⠀⠀⠀⠀⠁⠘⠋⡃⠓⠚⠒⠚⠓⠉⠃
⠀⠀⠀⠀⡀⡧⠒⠢⠤⠒⠃⠀⢠⡾⣿⠏⠀⠀⠀⠀⠈⠙⠛⠾⠷⠾⢿⠿⠷⠷⠶⠿⠟⠛⠛⠋⠀⠾⡀⠀⠀⢀⡠⠈⠀⠴⠀⠀⣰⣰⠀⢀⣡⠄
⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⣠⣴⢋⣼⠋⠀⠀⠀⠄⢒⠀⠀⠀⠀⠀⢠⣯⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢉⣹⢀⡯⣼⡀
⠀⠀⠀⠀⡇⡇⠀⢀⡤⠚⣡⣶⠟⠁⠀⠀⣀⡤⣦⠾⣶⣶⣶⣶⣶⢿⠁⠀⠀⢮⣁⡴⠚⢦⠀⠀⠀⡠⠤⢄⣘⡆⠀⠈⠉⡇⠀⠀⣶⢼⠈⡏⢹⠅
⠀⠀⠀⠀⠉⠁⠀⠀⠐⠟⠋⠀⠀⣔⠶⢊⠜⣋⠉⠒⠚⠛⠛⠛⠉⢉⠀⠀⠀⠐⠚⢙⣶⢃⠀⡀⠀⠈⠒⠀⠷⠁⠔⡁⠄⡈⣢⡀⢘⠊⠀⣏⣹⠂
⠀⠀⡔⠉⠁⠀⣷⣦⠀⠀⠀⢀⠔⣡⠔⠁⠀⠹⣧⣀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠤⡼⠘⠤⠇⡖⠒⠿⠛⡆⢸⢸⠀⠀⠀⡇⠀⠸⠀⠘⣟⢻⠇
⠀⠀⢃⠀⠀⡀⠈⣮⢷⡀⠀⠸⠾⠶⠖⠲⠟⠿⠿⡿⠷⠶⠶⠶⠿⠿⠟⠛⠋⠀⠀⢰⠛⠋⠛⢻⣷⡀⠀⢀⡇⢸⢸⡀⠀⠀⠧⡆⠀⠀⠀⢸⠁
⠀⠀⠀⠈⠁⠃⠀⠈⢆⠙⣄⠀⠀⠀⢀⡜⠓⣄⠜⠙⠉⠓⠢⢢⠀⠀⠀⠀⠀⠀⠀⠘⡣⠀⠀⢸⠈⠉⠉⠁⠀⢸⠀⢿⡭⡿⢰⠀⠀⠀⠀⡆
⠀⠀⠀⣀⣄⠀⠌⠢⠈⢣⡈⢧⡀⡠⠚⠀⠀⠘⢇⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠾⠃⠀⠀⠀⠁⠚⠛⠓⠈⠀⠀⠀⠀⠁
⠀⠀⡌⠄⠀⢨⠌⢂⢑⡄⠛⠀⠀⠈⠲⠤⣄⣀⡜⠓⡴⠿⠒⠉⠉⢿⠀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣷⣴⠆
⠀⠀⡆⡀⠢⠌⠀⠀⠛⠉⠠⢤⣀⡤⠒⠉⠉⠀⡱⢲⡓⠦⣤⣀⣀⣸⠔⠀⢲⠀⠀⠉⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣀⣚⣿⣿⣴⡆
⠀⠀⠇⠣⡤⠆⠃⠀⠀⠐⠀⢀⠈⠑⢆⠀⢀⡾⠁⠀⣧⠀⠀⠙⣦⠈⣀⠤⠴⣁⡚⠀⠉⡇⠀⠀⠀⢀⣦⣶⣦⣄⡀⠘⣿⣿⣿⣿⣿⠇⣀⣤⣤⡀⡀
⠀⠀⠆⠤⠀⢼⡆⠀⠀⠀⠀⢀⡀⠈⠻⠒⠁⠷⠤⢄⡊⠣⠤⠊⠀⠐⡄⢀⡞⠘⡎⠙⣂⠁⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠉⠉⠉⠀⠀⠀⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠄⠈⠀⠘⠲⠴⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠐⠁⠊⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣷⣦⡀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠋⢁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣮⠻⢿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠃⡑⣄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⡿⠷⡔⣝⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠋⢳⡀⠉⠚⠁⠀⠀⠀⠀⠀⠀⢸⣳⣄⣠⣴⣾⣟⣿⣿⣿⣿⣿⡿⢋⠁⠀⠀⢘⣎⢳⣬⡻⣿⣷⡄
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣼⣷⣾⠟⠙⣆⠀⠀⢀⣀⣤⡼⣿⣿⣿⣿⣿⠻⣿⣾⢻⣿⣿⡟⣾⣿⠆⣠⣼⣿⣷⡹⣿⣮⡙⢿⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣘⣶⣾⣿⣿⣿⡇⠙⠶⠽⢿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢿⣿⣶⡅
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣦⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⣿⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡟⣽⣾⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣧⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣛⠿⠿⣿⡿⠿⣛⣵⣿⠟⣋⣭⣥⣭⣭⣍⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣇⢾⣿⣿⣿⣿⣿⣿⠗⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣷⣮⣭⣭⣭⣭⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠂⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡸⠀⠁⠀⣼⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢀⠀⠀⣲⣤⢼⠇⠀⠀⠑⢆⠀⠀⠀⠈⠁⠀⠄⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢐⠄⠘⢄⠴⠦⠤⠂⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠀⠀⠀⠘⠓⠁⠁⠉⠀⠀⠀⠀⠀⠘⡄⠀⠀⡀⠀⠀⠀⡙⠢⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⣆⡠⠇⢀⣀⡄⠀⢀⣤⣶⣿⣿⣿⣶⣄⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⠀⠀⠢⣀⠀⠲⠦⣚⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣾⢟⠙⠛⢉⡛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠀⠀⠈⠂⡀⢰⠀⠉⠲⡄⠐⠨⠭⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠠⠀⠀⠀⠀⠉⠀⠄⠀⠀⠆⠈⣛⡷⠀⠀⠀⠀⠀⠀⡐⠀⠈⠉⠀⠀⠀⣈⣢⠄⠀⠀⠀⠘⠢⣣⣈⠢⣀⢑⣄
⠀⠀⠀⠀⠀⡇⠀⠀⠘⣤⠔⠛⢆⠀⠀⠘⢄⠀⠐⠀⢀⣴⣿⡇⠀⠀⠀⣄⠀⠆⠐⠀⢐⣀⠈⠥⠄⠀⠒⢀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠙⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠀⠀⠑⠦⣀⡀⣹⠉⠹⠉⡀⣻⣷⡄⠀⠀⠈⠀⠈⢁⣈⠀⠄⠀⠀⠐⠂⢀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⡰⢋⠔⠀⠀⠉⢿⣿⡆⠀⠀⠀⠁⠀⠀⡂⠀⠈⠁⠈⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⣶⠓⠂⠀⠠⠀⠈⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⡀⠄⣠⠀⢦
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡌⡄⠀⠁⠂⡠⢆⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣨⣥⣶⣿⠇⠀⡆
⠀⠀⠀⠀⢀⠤⠀⠀⢄⡀⠀⠀⠀⠀⠀⢇⡇⠀⠒⢀⡓⢄⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠛⠁
⠀⠀⠀⠔⠀⠀⠀⠀⠀⢱⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠙⠂⠁⠠⠀⠀⠀⠀⠀⠀⠀⣠⡶⠆⠀⢐⡖⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠛⠖⠈⣑⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡂⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠠⠢⠝⠃⠲⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⣠⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢄⠀⠀⠀⠀⡆⡀⠀⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣀⠠⠔⠘⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠑⠒⠒⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠀⠐⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢓⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⢄⠀⠀⠰⣉⠁⢀⠌⢀⠂⢀⣀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⠴⡫⠞⠀⠈⠁⢈⢀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢆⣀⠀⠀⢸⠀⠀⢀⣀⠼⠖⠋⠀⠀⠀⠀⠀⠀⡠⢞⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⢴⡟⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⠉⠛⠐⠶⠘⠛⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢤⣪⠔⠁⠀⠀⠀⠀⠀⢀⠤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣰⣿⣶⣶⣤⣤⣤⣤⣴⣾⣿⠇⠀⠀⠀⠀⠀⠀⠨⠭⠶⡤⠊⡠⠞⠹⡄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⢻⣿⣹⢿⣏⣿⢹⣿⣟⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡒⠉⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⣀⣀⣹⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠒⠛⠛⠓⠲⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢉⣤⣶⢾⢾⡿⠿⠛⢻⣶⣶⣮⣍⠛⠷⣤⡀
⠀⠀⠀⠀⠀⢀⣴⠋⣠⣾⡿⠉⠀⢠⠞⠀⢀⣴⠋⠁⠀⠿⠛⣷⢬⠙⢿⣆
⠀⠀⠀⠀⣠⡟⢡⣾⣿⠃⠀⠰⠖⠉⠀⢄⠊⠀⠑⠖⠀⠀⠀⠃⡀⠱⢌⢪⢷⣄
⠀⠀⠀⢠⠏⢰⣿⡅⠈⠶⢀⠀⠀⠀⢄⠀⡰⠄⡀⢀⠜⠢⡀⠀⠀⠀⡌⢂⢻⣿
⠀⠀⠀⣾⠀⣾⠉⠿⠁⠀⠀⠑⠀⠀⠀⠋⠀⠀⠘⠉⠀⣠⠌⠀⢀⠴⠀⠀⠀⢿⡄
⠀⠀⠀⣷⠀⣿⠃⠀⢀⠴⢀⠀⢀⢖⣄⡀⡴⠒⣶⣦⡐⠀⡀⢴⡃⠀⠀⢺⡇⢸⡇
⠀⠀⠀⣧⠀⣟⠀⠰⠆⠀⠀⢰⣇⠈⠛⠛⠻⣟⣉⣙⢷⣄⠈⠀⢈⡤⣀⠀⣧⢸⡇
⠀⠀⠀⣿⡀⢿⣆⠀⠀⠰⢀⡀⠉⠟⠢⣄⡀⠈⠙⢿⡾⠁⠙⢶⠄⠠⡸⠻⡏⣼⠁
⠀⠀⠀⠸⣧⡈⢧⡳⠂⠀⢀⠝⠁⠀⠀⠈⠁⠀⡠⠋⠀⠀⡀⠀⠀⢀⣄⡞⣰⡏
⠀⠀⠀⠀⠘⢷⡈⠁⢤⡜⠁⠀⠀⠰⠋⢀⣠⠞⠁⠀⣀⠞⠃⡀⣤⡨⠋⣴⠏
⠀⠀⠀⠀⠀⠈⠻⣦⣈⠃⠀⠀⠐⢄⠀⠀⠁⢄⠀⠀⠈⠑⢦⡴⠟⢠⡾⠧⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠐⠛⠦⠤⠤⠟⠐⠒⣀⣡⠴⠚⣉⣀⣀⣀⣀⠀⠉⠙⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⠶⣶⡶⠶⠟⢛⣭⢖⡾⠛⠉⠉⠉⠛⠿⣝⣒⢦⣄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢙⡧⠀⠀⡴⠋⣤⣤⣞⣻⣶⡏⠀⢀⠀⠀⠈⠀⠀⠹⡟⠟⢴⣷⣄⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⣸⠇⠀⡼⠁⠀⣾⣿⣿⢹⢸⡇⠀⠀⠀⢈⢠⡀⠀⠀⣿⡆⠀⠘⡟⣷⡀⠀⢻⡄
⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⡟⠀⢸⠁⠀⣼⣿⣟⣿⢢⡘⣧⡀⠀⠀⠀⠀⠀⣀⡼⠃⢣⠀⢠⢁⡛⣷⠀⠀⣷
⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⡇⠀⣿⠀⢠⣿⡿⠹⢻⣋⣽⣤⣝⠓⢦⣤⠤⣾⢟⣤⣶⢼⣶⣶⡊⣇⠸⡇⠀⢸⡆
⠀⢠⡞⢁⡴⠖⠋⠓⠢⡀⠀⣷⠀⣿⠀⠀⣿⠁⡴⠋⠁⠀⠀⠈⡉⠻⡄⠀⣿⠋⠁⢀⠀⠀⠈⠙⢯⠀⡇⠀⢸⡇
⠀⡿⠀⡾⠀⠀⠀⠀⠀⢡⠀⢹⠀⢹⡄⠀⢿⣾⠁⠀⠐⠠⠄⠀⠀⠀⣻⣼⠁⠀⠀⠀⠀⠠⡄⠀⢸⡧⠀⠀⣼⡇
⠀⣇⠀⢣⠀⠀⠀⠀⠀⠀⠀⣾⠀⠈⣷⠀⠈⣿⠀⠀⠀⠐⠁⠀⠀⠀⢸⢿⡄⠀⠀⠀⠘⠉⠈⠀⣾⠃⠀⣰⣿
⠀⠙⣦⡀⠑⠀⠀⠀⠀⢀⡼⠁⠀⠀⠘⣧⡀⠘⢦⡀⠀⠀⠀⠀⠀⣠⠏⢸⠻⣄⡀⠀⠀⠀⢀⣼⠋⠀⣴⣿⠃
⠀⠀⠈⠙⠲⠦⠦⠴⠞⠋⠀⠀⠀⠀⠀⠈⢷⣄⠀⠙⠷⣶⠤⠴⣾⠁⠀⢸⡆⠈⢙⠛⡒⠛⠋⠀⣠⣾⣿⠃
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠈⠁⠀⠻⠄⠀⠤⠦⠀⠘⠋⠀⢀⡠⢞⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⣤⣀⣀⣀⣀⢀⣀⣠⣴⣾⡽⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡄
⠀⠀⠀⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⡠⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠓⠀⠀⢀⠂⠀⠀⠀⠀⠀⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢴⣦⣤⣤⠐⠿⣿⣤⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠘⠢⡀⠀⠀⠙⡀⠀⠀⠀⢀⠀⠀⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⡀⠀⠀⠐⢈⠉⠀⠀⠠⣾⣯⢨⣿⣦⣾⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠈⡄⠁⢀⠈⠀⠀⠀⠀⠀⠹⣿⠃⠰⣿⣈⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⠀⠄⠀⠀⠀⠀⠈⠉⠹⠉⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠉⠉
⠀⠀⠀⠀⠀⢀⠄⠀⠐⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⢈⡡⠀⣈⠤⠀⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⢰⣶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠿⠙⢿⣧⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠉⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡿⠋⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⣤⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠐⠒⢠⠀⣀⠀⠀⠘⠉⣭⣀⠀⠒⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠉⠉⠁⠀⠀⠀⣀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠤⠤⠤⠔⠒⠄⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣿⡽⢾⢱⠀⠀⠀⠀⡐⣧⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠑⠤⠀⠀⢄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠀⠀⠀⢸⣷⣦⠀⠁⣷⠀⢰⣞⠀⠁⣬⠜⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⡜⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⣿⣟⣽⡀⠀⠈⢆⡼⠁⠀⢀⠏⢢⡀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠀⠀⡞⠀⠀⠀⠀⠀⡰⠁⣠⡟
⠀⢴⣷⠆⠀⠀⠀⠀⠀⣌⠀⠀⡠⠈⠀⠀⠀⠀⠀⠠⠟⠁⠀⠀⠀⠀⠸⡇⠀⠀⠈⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡳⢄⠀⠀⠀⢠⠛⠛⠋
⠀⠈⠁⠀⠀⠀⠀⣠⠖⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⡀⠀⠀⢄⡀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⠘⠋
⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠐⠀⠒⠊⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢦⠀⡠⠀⠁⠀⢲⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠐⠂⠀⠄⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⣠⠐⠲⠀⢤⡄⢠⡗⠀⠁⠉⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠂⠀⠀⠀⠀⠈⠉⢁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣴⣦⣀⣤⡀⠀⠀⠀⠀⠀⠙⠁⠀⠚⠂⠁⠈⠈⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠤⢀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣶⣟⠙⣫⡿⢃⡀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠂⠀⠐⠁⠀⠱⡀⠀⠀⠠⠒⠛⠢⠄
⠀⠀⠀⠈⣿⡿⢾⣿⣿⢿⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠒⠉⠱
⠀⠀⠀⠀⠉⠁⠸⣿⣟⢈⣽⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠁⠀⢰
⠀⠀⢀⣸⡿⢿⣿⠇⠿⠟⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠁⠀⠨⠀⠁⠐⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢠⠀⣀
⠀⠀⠿⢿⣇⣮⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⡀⣀⣠⣾⠛⠋
⠀⠀⠀⠘⠟⠃⠈⠉⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⡟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⡠⠐⠊⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠤⡀
⠀⠀⠀⠀⢀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡀⠂
⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⢠⠔⡡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡠⠂⠂⠾⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠒⠒⠒⠒⠒⠈⢉⠁⡄⠠⠂⠀⠀⠀⠀⢀⢁⠈⠀⠀⠠⠖⠈⢡⠞⣓⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⢂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⡞⠀⠀⠀⠀⠀⢀⡈⠅⠂⠀⠀⡆⠀⢀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠐⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⣴⠟⠣⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠐⠀⠀⠀⢀⡠
⠀⠀⢀⣴⠚⢣⣅⠀⠘⠋⠀⠀⠀⠙⠉⠠⠈⢀⠀⠀⠀⢀⣄⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠸⠀⣀⣧
⠀⠀⠟⠁⠀⣴⣿⡠⠀⠀⠔⠂⠀⠓⠚⠑⠈⠉⢴⣄⡄⠈⠁⠀⠀⠀⠐⠒⠂⠉⢀⣀⡀⢀⡠⠊⠁⠀⠀⠈⡉⠀⠀⣀⠵⠤⠊⠁
⠀⠀⠀⠀⠀⠉⠙⠛⢆⣀⠈⠀⡀⠒⢀⣔⢁⣠⢾⠎⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠈⢡⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠒⠒⠲⡾⠋⠀⣴⡷⠁⠀⠀⠀⠀⠀⠀⠂⠛⠋⠀⠀⠀⠰⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠉⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⢐⡀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⣠⠤⠖⠊⠉⠉⠁⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠦⠐⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⡒⠒⠠⠭⠖⠁
⠀⠀⠀⡴⠋⠁⠀⡀⢤⣶⣤⣖⡒⠠⠶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠀⣀
⠀⠀⡞⠀⢀⡴⢕⣚⣩⡝⠳⠦⣠⣴⠾⣛⢽⣿⣥⡤⠤⡀⠀⢀⠀⠀⢀⢧⡇⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⣀⢀
⠀⠀⠃⠀⣊⣠⠚⢃⡯⣵⢤⡀⠽⠛⡛⠓⠏⣉⠭⠅⠀⢀⠀⡜⠀⠀⣸⢸⠃⠀⠀⠀⡼⠃⠀⡐⡀⠁⠀⠀⢁⡊⠈⠁
⠀⠀⠘⠸⡁⠀⢀⣾⡇⠃⠇⡱⠃⠈⠀⣀⠀⠀⠀⠀⠀⣳⡾⠁⠀⠀⡇⢸⠀⠀⠀⢸⠇⠖⢁⡤⠄⠀⠀⢀⠞⠀⠀⠀⢠⠀⠀⢰
⠀⠀⠀⠹⡦⣐⠺⢟⡀⠀⠒⠀⠀⠀⠘⠁⠀⣀⡠⠴⣺⣵⠃⠀⠀⢰⠁⡎⠀⠀⠀⢨⢲⣀⠍⠀⠀⠀⠀⠄⠀⠀⠀⣄⠮⡀⢄⣼⡆
⠀⠀⠀⠀⠙⠀⢑⡒⠠⠭⢉⣁⣒⣛⣈⣩⠭⠴⣒⡫⡶⠃⠀⠀⠀⡌⠀⡀⠀⠀⠀⠈⡎⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠠⠂⣀⣞⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠲⠤⠶⠦⠒⠒⠉⣩⠔⠁⠀⠀⠀⢠⠁⠄⠇⠀⠀⠀⠀⠃⠀⠀⠐⠩⠠⢠⣄⣀⣠⣤⠤⣾⠟⣡⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⢤⣀⡴⠋⠀⠀⠀⠀⠀⠀⡌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⢀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠲⣼⣆⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠨⠁⠰⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⠀⠀⠀⠠⢀⡠⢤⣀⠀⠀⠘⢆⢑⠍⠅⠑⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠁⠀⠀⡠⠐⠉⢀⣠⠤⠤⠶⡶⠲⢤⡤⢮⣝⡒⢮⡑⠄⠀⠈⠣⡡⡂⠚⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⢀⠀⠀⠂⢀⠔⠋⠀⠁⠚⠁⡀⠀⡠⢎⡀⠱⢢⢌⠑⠮⡙⢦⡙⣄⢦⡀⠈⠄⢔⠐⣌⠳⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢀⠂⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡄⢌⠑⢤⠀⠰⡀⠄⠌⢧⡘⢦⡙⠦⢀⠂⠓⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠤⢀⠀⠀⠈⢆⠐⢄⠡⡀⠱⡀⠢⡠⠙⠲⢬⡙⢦⡀⢄⠠⢀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠁⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠑⡀⠀⠈⡄⠀⢆⠱⣄⠙⠠⢄⡀⠁⢦⡉⢦⠹⡄⢀⠀⠑⡀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠂⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⡁⠀⠀⠀⠌⡑⠢⢄⡈⠓⣄⠹⡌⢧⡙⢦⡑⠢⣔⡄⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠔⠀⠀⢀⠃⠀⠀⠀⠀⠀⠑⠄⠙⢄⠈⢢⠙⡂⣙⠲⣬⠟⠁⠘⡆⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠊⠑⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢣⡀⢅⡈⠣⣌⡁⠀⠀⠀⠀⠂⠀⢂
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠈⠃⠠⣀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠣⡆⠀⠃⢄⡭⠃⠀⠸⠀⠀⠠⠀⠡⡀
⠀⠀⠀⠀⠀⢀⠂⠀⠞⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣀⣉⣉⡡⠄⠀⢤⠤⢠⠄⠠⠤⣀⡀⠀⠀⠀⠀⠀⢀⡖⠀⣁⡲⠊⠀⠀⠀⠆⠀⠀⠀⠑⡀⠐⠄
⠀⠀⠀⠀⢀⠂⠀⠌⠀⠀⠀⠀⠀⠀⠀⢀⣀⠛⠆⠁⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠀⠉⠉⠐⡦⢠⡞⠀⠔⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠐⠄⠈⠂
⠀⠀⠀⢀⠂⠀⠌⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠆⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠔
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠔⠁⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




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

⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⠤⣤⣤⣤⣤⢤⠤⡤⡠⣤⣤⢤⡤⣤⣴⣶⣤⠶⣶⢶⡴⣶⣔⣦⢶⣢⣴⣤⣦
⠨⣷⠛⣹⡏⢻⣷⣹⢿⡛⣏⢾⡭⢿⠓⣿⡛⡽⣏⢺⡏⡿⢹⣍⢹⣯⡿⣿⣻⢿⣻⣌⠻⣏⣻⠍⣿⢠⣗⠾⣭⠷⣭⣐⣿⡀⣻⣧⡌⠻⣆⢺⣯⡜⣿
⢁⡿⣰⣿⠌⣿⣢⣿⢋⣷⣿⠾⣷⡞⣛⣾⢔⣧⠹⣧⣸⠇⣿⣧⡯⢖⣵⢻⣧⢜⣷⣞⣷⡏⢱⣿⢩⣶⡟⠿⢩⣷⠦⠿⢃⣾⣋⣤⣿⣁⣹⣾⠛⣀⣝
⢽⣿⣧⣴⣤⣿⣿⡅⠀⠻⣿⡦⠈⣙⣿⣿⠀⢁⣾⣿⣿⡐⣿⣿⣶⣷⣄⣛⠛⣶⣶⠿⠯⢑⣻⣿⣷⣿⣿⠓⠲⣿⣧⣤⣬⡉⠙⠻⠿⣯⣥⣤⣾⠿⠟
⠀⣥⣼⣿⣿⣦⠤⠀⢺⣿⣿⣟⠂⠙⠻⠿⢶⣿⣿⣏⣉⠵⠿⣿⣿⣿⣿⣤⣾⣿⣟⠒⠀⣬⣭⣽⣿⣿⣿⣧⣤⣄⠈⠛⠛⠛⠛⠛⣣⣾⣿⣿⣿⡇
⣤⣴⣻⣿⣿⣿⣷⠈⠙⢛⣻⣿⣿⣇⣚⠛⠛⢿⣿⣿⣿⣿⠀⣽⣿⣿⣿⣿⣿⣿⣿⡦⠄⠀⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠘⠛⠛⠛⠿⢿⣿⣿⣿⣧⡀
⠉⠉⠉⣿⣿⣿⣿⡀⠉⠉⠻⠟⠟⢉⣭⣥⣴⣿⣻⣿⣿⣧⣤⠄⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠈⠛⢻⣿⣿⣷⣿⣿⣿⣿⣶⣶⣶⠄⠀⠀⢨⣽⣷⣶⣶
⠾⠿⠿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣠⣤⣴⣾⣿⣿⣉⣿⣿⣧⣤⣤⣄⡀⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣀⣿⣿⣿⣿⣿
⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠿⠛⢁⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠛⠛⠻⠿⣿⣿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⣰⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡿⠛⠛⣿⣿⣿⣿⣿⣃⣀⡀⠀⠀⠀⣼⡿⠋⠀⢿⣿
⠀⠀⠉⠉⠹⣿⣯⣿⣿⣯⣍⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣷⣦⣤⣶⣿⣿⣿⣿⣿⡿⠿⠇⠀⠀⠉⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠈⠛⠿⠆⠉⠙⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣥⣾⣿⣿⣿⣶⣶⣤⣄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠒⠛⠛⠛⠛⠛⠓⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠉⠁⢀⣀⣤⣤⣤⣤⣤⡤⢤⣀⠀⠀⠉⠛⢦⣀
⠀⠀⠀⠀⠀⣠⠞⠋⠀⢀⣤⠞⣡⠞⠋⠀⠀⠀⠈⢹⣤⣬⣝⣲⢤⡀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⡴⣤
⠀⠀⠀⠀⣴⠋⠰⣴⣶⣯⣿⠾⣿⠀⠀⠀⠀⠀⠀⠈⢹⠉⢙⠏⠷⣿⣦⡀⠀⠹⣦⠀⠀⠀⠀⠀⢀⡇⢸⡇⠀⠀⠀⡼⢀⡟
⠀⠀⠀⣼⠃⠀⣰⣿⣾⡇⡏⠀⢻⣤⠀⠀⠀⠀⠀⠀⣞⠀⣴⠋⠙⠋⠙⢿⡄⠀⠘⣇⠀⠀⠀⠀⣸⢀⡿⠀⠀⠀⢰⢁⡼⠁
⠀⠀⢸⠇⠀⢰⣿⣿⡿⢷⡤⣠⣞⡿⣶⡶⠒⠚⠋⣷⠻⡞⠉⠀⠀⠀⠀⠀⢿⡀⠀⢹⡄⠀⠀⢀⣏⣸⠃⠀⠀⢀⣿⡿⠁
⠀⠀⣿⠀⠀⣿⡏⠀⠀⠀⠀⠈⣹⣷⠃⠀⠀⠀⠀⠙⣦⣿⣄⠀⠀⠀⠀⠀⢸⡇⠀⠸⣧⠀⠀⣸⢧⡟⠀⠀⠀⣾⣿⠃
⠀⠀⣿⠀⠀⣿⠁⠀⠀⠀⠀⠀⣧⣾⠀⠀⠀⠀⠀⠀⠘⣧⡙⣧⠀⠀⠀⢰⡞⠧⠀⠀⣿⠀⢠⡏⣼⠁⠀⠀⣼⢻⠇
⠀⠀⢻⡄⠀⢸⡆⠀⠀⠀⠀⠀⠘⡏⢷⠀⠀⠀⠀⣀⡴⢻⡁⠳⠶⡦⠞⠋⢁⠁⠀⢸⣿⠀⣼⢳⡏⠀⠀⣰⣯⡟
⠀⠀⠘⣧⠀⠈⢿⣶⣀⣀⣀⣴⡞⣠⣼⣿⣓⣲⣟⣯⠴⢺⣵⣤⢄⣕⢰⡟⡘⠀⢀⣾⡏⢠⣏⡾⠀⠀⢠⣏⡾
⠀⠀⠀⠹⣇⠀⠘⢿⢭⠛⢭⢫⡖⢤⣿⠈⠉⠁⠀⠀⠀⠀⢸⡟⠛⡇⢚⡴⠁⢀⣞⡿⠁⣼⣿⠃⠀⢀⡞⣾⠁
⠀⠀⠀⠀⠹⣧⡀⠀⠻⡀⠀⡏⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⠧⠛⠀⣠⣾⡿⠁⢠⣯⡟⠀⠀⣜⣼⠃
⠀⠀⠀⠀⠀⠈⠳⣤⡀⠈⠛⢧⡄⠀⢘⠳⢤⣤⣀⣀⣀⣴⠻⠒⠀⠀⣠⣖⣿⡟⠁⠀⡞⣾⠁⠀⡸⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀⠀⠀⠉⠉⠀⠈⠉⠉⠁⠀⢀⣠⣴⣞⣵⠟⠋⠀⠀⢰⢳⡏⠀⣰⢃⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣶⣶⣤⣤⣤⣤⣤⣶⣾⣽⠿⠛⠉⠁⠀⠀⠀⢀⡏⡾⠀⢰⢇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⣩⣭⣤⡴⠤⠤⣤⣤⣀⡀⠀⣸⣹⠃⢠⡏⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⢉⣩⣤⣴⣤⣤⣤⣤⣈⡙⠛⢳⣯⣏⠀⡞⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢁⣠⣶⣿⠿⠛⢻⠀⠘⣿⡄⠰⠛⠛⠳⣾⣼⠛⡿⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢁⣶⠟⠉⠀⠀⡄⠀⠀⡃⠀⠀⠀⠀⢀⣀⣰⣿⠟⣿⣻⠟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣠⣿⡯⠥⠴⢖⠙⠑⠀⠀⠠⠀⠀⠒⠋⠀⠀⣿⣽⢠⢿⡿⢦⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⡿⠁⠀⠀⠀⠨⡀⠀⢈⠀⠀⠀⢀⢀⣠⡀⣰⣿⣏⣿⡟⠀⣠⣆⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⣷⡶⠖⢏⠁⠀⢀⡤⠘⠂⠀⠈⣹⣆⠀⣻⣿⣿⣽⣿⠋⠉⠀⠙⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢰⡷⢦⣿⣁⠀⠀⠼⢄⠀⠈⡅⠀⢀⣠⡴⣼⡟⠀⢸⣿⣽⡿⠁⠀⠀⡀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣿⠟⠃⠀⠀⠠⠀⠒⠋⠉⢠⣣⡾⢻⣇⠀⠻⠇⠛⠓⠚⠁⠀⢱⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣧⡄⢹⠊⠛⠠⠀⠀⡀⢀⠤⠠⠘⢿⡄⣰⣿⠀⠀⠀⣀⣤⠴⠆⠀⠀⣿⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⡄⢷⠀⢃⠀⠀⠀⠀⢀⡀⡀⠈⡿⠼⠟⠓⠉⠉⠁⠀⠀⠰⡀⢠⠇⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⡄⠣⠈⠤⠰⡖⠉⠙⢃⠀⠀⢷⠀⠀⢀⣀⡤⢸⡄⠀⠀⡏⠉⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡑⠀⣀⣀⠀⠀⠠⡞⠂⠚⠁⠀⠀⠹⠁⠀⣇⢀⠐⢡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣆⠀⠙⠷⣤⣀⣷⡐⠒⠀⣤⢄⣾⡴⠶⢛⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣍⣉⡁⠈⣉⣉⣉⣤⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⢰⡄⠠⢀⠲⣿⣿⠿⣿⡿⣧⠆⢸⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠙⠟⠲⠶⡦⣤⣶⣦⣤⣤⣤⣤⣤⣤⣀⠀⢀⡿⢁⣰⠂⢴⠊⣴⣿⣾
⣾⡹⣧⣿⣤⣄⢤⣀⣰⠀⢸⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣦⣥⣀⣄⠀⠀⠠⠈⠈⠀⠉⠉⠙⢉⠉⠃⢀⡗⢁⡼⢀⣾⣣⣾⢟⢷⡽
⢽⣷⠹⣿⣿⣿⣿⣿⡟⠀⠸⠀⢸⣿⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣾⣶⡞⠀⣰⢋⢠⠎⡠⡿⢋⣛⣡⣴⠟⢡
⡈⢹⣷⡙⢿⣻⣾⣿⡿⠀⠀⣴⢋⣿⠛⢿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢈⠅⣡⠎⣀⠞⢁⣫⣾⡟⢁⣤⢟
⣷⣬⢹⣷⡈⣿⣿⡿⢧⣤⠚⣿⠵⣾⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡉⢻⣧⣬⣭⣭⣭⣽⠛⣁⠂⠔⠋⠐⢁⢐⣹⣶⢛⣛⡄⢀⠀⣩⣿
⣿⣷⣦⠘⢻⣌⢹⣷⡈⠀⠐⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣟⣤⣤⣿⣿⣿⡿⢋⡠⠈⠀⠀⠄⡀⣰⣴⡟⢛⣁⠔⢂⣿⠨⠞⣛⣿
⣿⣿⣿⣿⡭⠻⣧⡙⠫⡀⡰⣿⡀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⠷⣿⣷⠿⢛⡠⠔⠉⠤⢀⣀⣤⣾⡿⢻⠃⠀⠚⢁⣴⣿⠋⢻⠃⢿⣿
⣿⣭⣿⣿⣿⣷⡘⠳⣄⢤⠟⣳⠞⢀⡈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣶⣞⣻⣟⣲⣚⣳⣼⣭⣿⡿⠩⡤⠔⢓⣢⡿⠿⡟⠧⢸⢉⠁⣶⣿
⣿⣿⣷⣞⣻⣿⣿⣦⡙⢷⣌⠷⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠻⠯⢿⣿⣿⣿⣿⠿⠿⠛⡴⠀⣀⣱⣾⡿⣿⣷⢬⣿⣶⠸⣽⣦⣃⡧
⣿⣿⣿⣿⣿⣷⣿⣻⣿⣦⣝⠷⣌⡛⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡯⠉⢹⡷⠒⢍⣠⣶⣟⠻⠇⣠⣭⣶⣿⠻⣷⣶⣿⣿⡿⠓
⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠋⠁⠀⢹⣢⣷⣿⣏⣾⣿⣶⣮⠀⠛⠉⢀⠔⢉⠀⢉⠁⣰⣦
⣴⣂⠍⡛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢛⠝⢋⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣠⠳⢌⣡⣴⣾⣿⣧⣹⡵⠾⡿⢋⡩⣥⠶⠁⢀⣤⣨⣅⣴⣿⣿⣿⣿
⣿⣿⣿⣷⣇⣦⣌⣛⠻⢿⣿⡵⠞⠉⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣦⣶⣾⣿⣾⣿⣿⣿⣿⣿⠿⡙⢿⣷⣨⡠⣶⣶⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣴⣄⠄⠀⠀⢀⣠⣾⣿⣿⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⢿⣿⠿⠛⠛⣭⡗⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿
⠻⣿⢿⣿⣿⣿⣿⣿⠿⠿⠋⠁⣀⣤⣶⣿⣿⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⣤⠄⠀⠀⣉⢀⡒⠻⣿⣿⣿⣽⣿⣾⣿⣿⣿⣿⣠⣿⣿⣿⣿⣷
⠷⠶⢼⣅⣍⣉⠙⡿⣤⣴⣶⣶⣿⣿⣿⣿⣿⡿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠐⠉⠀⠁⠀⢀⣠⣽⣾⣷⡘⢻⣿⣿⠿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠁⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣷⡆⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠖⠠⠀⠀⠀⠀⠀⠀⣿⣯⡙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣿⠤⡀⠀⣀⠀⠀⠀⢀⠈⠛⢿⣿⣿⣿⡏⠹⠛⢿⣿⣧⡚⠿⠉⠉⠿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⠿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⣿⣶⣤⣄⡈⠙⠛⠿⣿⡍⠀⢀⣜⠛⡿⢫⡽⠵⠀⠰⢾⣟⢻⢿⣿⣿⡿⡇⠰⠖⠚⠉⠀⠀⠀⠀⠀⠀⣿⢻⣿⣟⣿⡿⡅⠀⣼⣿⢻
⠆⠘⠓⠲⠟⠚⣿⣟⣀⣈⣉⣉⠹⣿⣿⣿⣿⣷⣶⣄⠀⠺⢇⡀⠁⠙⠐⣿⣤⡤⠴⠗⠺⠠⠤⠤⠤⠖⢀⠀⣀⣤⡶⠇⠀⠀⠀⠀⣿⠿⣿⢿⣿⢿⣇⣀⣸⣿⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠦⠘⠉⠉⣉⣽⣽⣯⣅⣀⣀⣉⣛⣋⣉⣩⣴⣶⣦⣶⣤⣶⣦⣴⣦⣤⣚⣿⣿⣿⣾⣿⠀⠀⠀⠀⣿⣤⣿⣿⣿⠙⠋⠉⣩⣯⣹
⠛⠋⠙⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠿⣿⣿⠟⠿⡿⠹⢿⣿⣿⡿⠛⣿⠉⠛⣿⣿⠋⠻⠙⣿⣿⣽⣿⣿⣟⠀⠀⠀⠀⣿⢀⣿⣀⡏⠀⢰⢿⣿⣿⣿
⠀⣦⣤⣄⢄⣐⣂⣸⡿⠟⣿⣿⠿⠽⣻⣿⡿⠀⠀⢐⡆⠽⣶⣿⣾⣾⣇⡻⠀⠀⠁⠀⠀⣿⣿⠀⠐⠶⠶⡗⠶⣿⣿⣿⠀⠀⠀⠀⣏⠉⣿⢻⣷⡄⢸⠀⣿⣿⣼
⣿⣿⣿⠋⠸⣟⣲⣽⠷⠿⣿⣟⠓⢀⣻⣿⡏⠀⢀⡨⠄⢶⢴⠻⠞⠾⠿⣶⣄⠀⠀⠀⠀⠇⠀⠀⠘⠶⠶⡷⠶⣾⣿⣧⠀⠀⠀⠀⡷⠶⠿⠿⢿⡇⢸⣌⣿⣇⣹
⢿⣿⣷⡀⣿⣿⣿⣿⠀⠀⣿⣶⠐⠀⢸⣋⡇⠀⢸⣇⠀⠉⠀⠀⠀⠀⠀⠀⠙⠻⢷⣄⣀⡀⡀⠀⠘⠛⠓⠗⠰⣾⣽⡏⠀⠀⠀⠀⣷⣶⣦⣶⣾⡁⢰⠈⢉⠀⢸
⢸⣿⡏⠁⠈⣿⣼⣧⡀⠀⣿⡋⠀⠂⣿⠛⢓⣠⣿⡟⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣶⣞⠀⠠⢀⠲⢮⣄⣛⠀⠁⠀⣨⣿⣧⣿⣭⣿⣿⣏⠰⣿⡶⣿
⣾⣿⣇⣴⣾⣿⠟⡿⡿⢀⣿⣉⣀⣀⣿⢀⠈⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠤⡀⠙⢲⡌⣧⠀⠀⢀⠙⠁⠀⠀⠀⠐⠛⣿⢠⣿⡇⣿
⠉⣹⡟⠋⠁⡧⣈⣿⡞⠁⣿⣿⣿⣿⣿⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡇⢠⣼⠀⠓⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⢈⢹⡉⣿
⢸⣿⡃⣀⣦⡟⣣⣿⣿⣶⠏⠉⠈⠉⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢷⡇⢠⣾⠓⠆⠀⠀⢨⠀⠀⠀⠀⠀⠘⢻⣿⣸⣿⣧⣿
⢸⣿⡇⣿⣿⣿⣿⠿⠛⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢸⣹⠀⠂⠀⠀⢰⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⣠⡶⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠞⠛⠛⠋⠉⠉⣉⣉⣁⣀⣀⣀⣀⣀⣈⣉⡉⠉⠉⠛⠛⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⠋⢉⣀⣤⣤⠶⠶⠖⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠓⠶⢦⣄⡀⠈⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⣀⣤⡴⠶⠛⠋⠉⠀⣀⣀⣠⣤⣤⠴⠶⠶⠶⠶⠶⠒⠛⠛⠛⠛⠛⠛⠋⠉⠉⠛⠛⠛⠿⢿⣷⣄⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⢀⣠⡶⠛⠉⠀⠀⣀⣤⠴⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⢸⡇
⠀⠀⠀⠀⢀⣴⠟⠁⢀⡴⠛⠁⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⣼⠃
⠀⠀⠀⢀⡾⠁⠀⢠⡟⠁⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⣠⡾⠃
⠀⠀⠀⢸⡇⠀⠀⠘⣧⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠁⠀⢀⣠⡾⠋
⠀⠀⠀⠈⢷⡀⠀⠀⠈⠻⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⠛⠋⠁⠀⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠈⠙⠛⠳⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠶⠖⠛⠛⠋⠉⠁⠀⠀⠀⣀⣠⡴⠶⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠛⠋⠉⠁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣛⠛⠛⠓⠒⠲⠶⠖⠒⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⣀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⠤⢖⣚⣿⠭⣝⣛⡒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣄
⠀⠀⠀⠀⢀⡴⣫⣵⡎⠡⣄⢂⡅⠘⠉⠈⠙⠂⢝⠦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣙⠦⣑⢄⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⢠⢎⡜⠀⣰⣽⠶⢦⠰⡌⠀⠀⠀⣀⡀⠀⣷⡝⣆⠀⠀⠀⠀⠀⠀⠒⠒⠒⠺⠷⣮⣿⣿⠟⠁⠀⠀⠈⢻⡿⡿⢡⠆⠙⠉⠑
⠀⠀⢀⡏⣾⡗⠀⠃⠀⠀⣼⡏⢿⣦⣄⣀⣀⡠⢺⡿⢻⡜⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣰⣿⣿⡏⠀⠀⠀⢀⡀⠀⣿⠦⠼⡀⠠⠀⣔⢰⣄
⠀⠀⢸⠃⡏⠁⠀⠀⣴⣋⣋⡏⢻⡤⣮⣿⡏⠀⠀⠀⠀⠇⣧⠀⠀⠀⠀⠀⠀⠀⠀⣧⡻⣿⣿⣿⣾⣧⣾⣿⣶⠟⠀⠀⠀⢹⣤⣼⡶⢏⡜
⠀⠀⠸⡄⣿⣿⣀⣴⡿⣿⡯⢜⡾⣇⣾⣿⠃⠀⠀⠀⠀⡆⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣮⣭⣿⣛⣛⣛⣛⣓⣂⣀⣀⣮⣭⣵⣾⣿⠁
⠀⠀⠀⢧⠹⣿⣿⣿⣯⣟⡶⣶⣿⣿⣿⣇⢀⠀⠀⢀⡸⣱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠳⡝⢿⣿⣧⣿⣶⣿⣿⣿⣿⣿⣼⣀⣤⢟⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠲⣍⡳⠽⣿⣿⣿⣿⣿⡿⢟⣫⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣭⣿⣿⣿⣿⣭⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠲⠶⠶⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣲⣦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤⢶⠓⠐⠀⠉⡡⢛⠀⠢⣄
⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠥⡀⣰⣄⣀⢄⡀⠀⠀⠀⠀⡠⣐⡈⠠⠖⠛⠉⠀⠙⣶⣶⡞⠃⠀⠀⢀⣤⣀
⠀⠀⢀⢰⣿⡿⣿⠿⢿⣿⣻⣿⡿⢿⣿⡿⣿⠿⢧⡀⠊⠉⠉⣿⣿⣦⠂⠀⠀⠐⠋⠉⠇⠀⠠⠤⣤⣴⠞⠉⠀⢀⠀⣀⣠⣼⡿⢻⠄
⠀⠀⠀⠑⢽⣻⠏⢀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣆⠀⢀⡠⢿⣻⠕⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠣⠤⠄⠀⠶⢭⣭⣽⣯⠭⠞⠃⠀⡠⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠒⠯⠭⢭⣿⣶⣶⣶⣮⡤⠥⠭⠗⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠤⠀⠠⠤⠤⠤⠈⠁⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⢀⠔⢻⠏
⠀⠀⠀⢀⣀⣀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⣿⣷⡄⠂⠁⢀⠁
⠀⠀⠀⢸⠀⠈⢉⠀⠀⢀⡠⠀⣤⠠⠦⠼⠖⣲⡆⢀⠠⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠧⠄⠐⠁⠀⠀⠀⠀⢠⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠁⠀⣸⣀⣀⡈⠀⢒⠰⡸⢀⠈⣦⠀⠀⠀⠀⠠⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠑⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢅⡠⠀⠀⠉⢹⡿⣡⣋⣈⣿⣻⡆⠀⠀⢠⣾⠿⠿⣟⣻⣿⠿⠋⠀⢀⣿⢄⢄⢶⡂
⠀⠀⠀⠀⠀⣤⢦⣀⠀⠀⠀⠻⣟⠍⣂⣌⣀⣉⢘⣉⢭⡿⠶⣁⣢⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡞⢿⣼⡏⠸⠀⡀⡀
⠀⠀⢠⣤⣿⣷⣡⡿⡽⠀⠀⠀⠈⠉⠈⠿⠿⠛⠿⠟⠻⠿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢻⣿⠃⠀⣎⠀⠄
⠀⣠⣽⣿⢛⣉⣹⣿⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣅⢶
⠀⣾⡻⢷⣼⣿⡷⣿⣳⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠁⠋
⠀⢹⣿⣿⣿⣿⣿⣹⣯⡗⠀⠀⠀⠀⣄⠔⠉⠀⠀⠀⠀⢠⣶⣾⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠤⠰⠃
⠀⢸⡿⣿⣿⣿⣿⣻⣿⡇⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⠂
⠀⠈⢷⣼⣷⠿⢾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠇
⠀⠀⠈⠙⠻⠯⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠰⠀⣶⠂⡈⠀⠈⠒
⠀⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠸⡛⠛⠃⠄⠀⠀⡘⠀⠀⠀⣾⠛⠛⠉⢀⣶⠀⠀⠀⠀⠀⠀⠊⡉⢻⣿⣦
⠀⠀⢰⣿⠘⠷⡶⠀⠀⠃⠀⠀⢴⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣻⣿⠀⠀⠀⠀⠀⢀⡤⠖⠒⠂⠀⠠
⠀⠀⣶⠿⠁⣶⠉⢠⢃⠀⠀⠀⠘⢆⣠⡰⡀⠲⢀⡀⠀⠀⠀⢸⠿⠷⣿⣶⣽⡏⠀⠀⠀⠀⡔⠀⠀⠖⢓⡺⠀⢄
⠀⠀⣇⣠⡧⣴⢃⠁⠀⠀⠀⠀⢻⣼⡟⠉⢱⠄⠀⠀⠀⠀⠀⡿⠁⢹⣝⠻⣿⡇⠀⠀⠀⢐⠀⣴⠀⠀⢀⡌⠃⠤
⠀⠀⢣⠾⡇⢻⢺⠀⠀⠀⠄⠀⢀⡟⠉⠑⣄⠀⠀⠀⠀⠀⢀⡇⠀⢺⠞⢄⢸⣿⠀⠀⠀⢸⠀⠀⢀⡟⠉⣡⣰⠟⡁
⠀⠀⣟⢀⠛⠉⠀⠀⠀⠀⠀⠀⢨⣧⠀⢠⢫⢳⠀⠁⠀⠀⠸⡇⢇⠘⡄⣷⣿⣿⠀⠀⠀⠀⠀⠀⠺⠥⣶⡘⠇
⠀⠀⠋⢩⠀⣾⢀⠀⠀⠀⠀⠀⠸⡄⣱⣎⣸⢸⠀⠀⠀⠀⠀⠙⢮⣧⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⢀⡤⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢼⡁⢡⠂
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡤⢀⠀⠀⠀⠐⠉⠁⠁⠏
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠁⠀⠀⡈⡂⠢⢀⠀⠀⢆⠀⡀
⠀⠀⠀⢢⠑⢄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠊⠀⠀⠀⠈⠐⠠
⠀⠀⠀⠐⠀⠂⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀
⠀⠀⠀⠀⠐⠀⠈⠢⡈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠑⠄⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠅⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠁⠂⠄⡁⠂⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠦⢀⠀⠀⠀⠀⠁⠂⠠⠈⠐⠋⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⠐⠠⠀⡀⠀⠀⠀⠀⠀⠐⠠⠤⢁⣀⣐⡀⠤⠤⠤⣄⣀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠜⠀⠠⠤⣄⡀⠀⠀⠂⠄⠄⠀⠀⠄⠀⠀⠀⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠅⡀⠀⡠⡈⡦⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⡈⠄⢲⠁⠀⠁⡘⢍⠐⠄
⠀⠀⠀⠄⠀⠄⠀⠤⣖⠠⠔⠖⠁⠀⢤⠂⠶⣤⠰⠑⢶⢪⠒⢬⠒⠄⠠⠀⠠
⠀⠀⠀⡁⣏⡭⠐⠉⣍⠀⠀⣉⠀⢠⣯⠋⠀⣩⠁⠀⣉⢫⣡⢩⠉⠃⣽⣃⢈
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⢀⣠⢤⡀⠀⠀⠀⢀⡀⣴⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠱⠷⢊⠀⢀⠄⠚⡱⠆⠄⠀⠀⣠⡟⠁⠙⡆⠀⠀⠀⠀⢀⣀⣀⣀⣀⠤⣴⣊⠈⡄⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣉⡥⠋⢀⣤⣎⠀⠳⠤⠖⠹⣷⠖⢉⣯⡄⢀⠤⠒⠢⢄⠉⠛⠁⢱⠀⠀⠀⠀⢰⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢃⠀⡀⠀⡀⠐
⠀⠐⣢⠤⣤⣀⣀⣀⣤⣤⡄⠒⠋⡏⠐⠀⡇⠀⠀⠀⠀⣿⡀⠈⠛⠀⡎⢀⣀⣀⣸⣧⠀⠀⠸⡆⠀⠀⢠⣎⣀⣀⣀⡀⣠⡠⣄⣀⣀⣀⣀⣈⣦
⠀⢰⠁⠀⢸⠀⠀⡌⠀⠀⣱⠀⠀⠈⠓⠊⠀⢀⡀⠀⠀⠸⣇⠀⠀⠀⢣⣿⣿⣿⣿⠏⢸⣷⠀⡇⠀⠀⠀⠀⢸⠆⢸⠆⠶⠂⢾⠀⠶⠀⡆
⠀⠀⠙⢒⠁⠀⠀⠘⠒⠚⠁⠀⠀⠀⠀⠀⢢⠋⣶⠀⠀⠀⢿⠀⠐⠿⣷⢉⣛⣛⣉⠀⠤⠔⠊⠀⢠⠂⠁⠉⠉⠁⠈⠐⠛⠓⠛⠒⠉⠈⠉⠉⠉⠁⢢
⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠂⠓⠅⠀⠀⠀⢨⣇⡠⠒⠉⠁⠀⠀⠀⢀⣠⣞⠀⡴⢁⡠⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⡀⣀⣀⣀⣀⡀⠱⠄
⠀⠀⠀⠠⠔⡈⠇⠀⢠⠎⠈⠸⠀⣤⡀⢀⣄⠀⡀⠀⠀⠀⠀⢾⡅⠀⠀⠀⠀⡤⢘⡀⠎⠘⠀⠀⢀⡇⢺⠀⠶⠤⡧⠴⡇⢼⠤⡧⠤⡧⠼⠆⢷⠐⡆
⠀⠀⠀⠀⠁⡀⠐⠀⡈⠁⠢⠅⠀⢇⢣⠀⠈⠀⡝⠂⠰⠄⠀⠘⠷⠀⠀⢀⠃⠰⠎⠁⣠⠁⠀⢠⠞⡉⠉⠍⡙⠿⠿⠿⠷⠿⠿⠿⠾⠿⠋⠉⠉⠉⠜⢦
⠀⠀⠀⠀⠀⠈⠐⡀⣀⠘⠁⠀⠀⠘⡎⡆⢠⠀⠁⠠⠁⠀⡐⠆⠀⠀⠀⢘⠎⣁⣐⠖⠀⠀⠀⠉⠀⠙⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠛⠛⠓⠚⠛⠛⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠸⡹⡈⢀⡐⢁⠔⣉⠤⠔⣛⠷⠀⠈⢀⣠⠴⠒⠒⠋⠉⠐⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠠⢂⠀⡀⠒⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻⣾⠶⣛⡭⠶⠚⠉⠀⠀⢠⠖⠉⠀⠀⣀⡀⢀⣤⡐⢒⣦⠈⢣⠀⠀⡔⠀⠒⠎⠀⠁⢈⠠⣇⠀⢠⠐
⠀⠀⠀⠀⡄⢀⠀⠠⡄⠀⠀⠀⠤⠐⠈⠈⠚⠛⡉⠀⠀⠀⠀⠀⠀⡰⢁⠀⡼⢀⣄⣣⣟⢸⣞⣁⠳⠾⠃⣸⠀⢘⠀⢒⠌⣶⠆⢁⡠⠂⠀⠢⣵⡤
⠀⠀⠀⠘⠀⢧⠃⠀⢳⢠⠂⣠⠆⠁⠧⢀⡀⠀⢰⠀⠀⠀⠀⠀⠀⡇⠈⢧⡧⡸⣄⡽⠯⠓⠈⠁⠀⠀⢰⣃⣀⠀⠑⠠⠐⠙⡄⠘⠃⠀⠛⠀⡼⠁
⠀⠀⠀⠠⠁⠀⢀⣀⢀⣀⠀⠁⠀⢈⡆⠀⠁⠈⠀⠃⠀⠀⠀⠀⠀⠹⢄⠈⠃⠘⠂⠀⠀⠀⠀⣀⠤⠤⠤⠔⠋⠀⠀⠀⠀⢀⣘⢤⡀⠀⣠⡔
⠀⠀⠔⠁⣴⠞⠉⠀⠀⠈⠉⠑⢄⠉⡄⢠⠀⠀⠀⠀⠀⢀⡀⠀⡠⢒⠆⠉⠓⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠈⡀⠆⢠⠁⠌⠈⠒⢄
⠠⠠⠈⡸⢇⠀⠀⢾⣶⠞⠀⠀⢺⡀⠡⠘⠀⠀⠀⡀⢌⠋⠹⠀⢛⣁⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⡈⠧⡜⠀⢀⠀⠈⠆
⠀⠀⠀⡟⢈⡙⠲⠦⠤⠤⠶⠚⣹⡄⠂⠀⠀⠀⢲⣺⣅⠦⠱⣄⠈⠛⠁⠀⠀⠀⠀⠀⢀⠀⠑⢀⠀⡀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘⢶⣾⡎⢻⠀⠀⠘
⠀⠀⠀⣴⢀⡀⠉⠀⠁⠈⢀⠁⣤⡇⠈⡀⠀⣠⢳⢻⣤⣛⣶⠇⠀⠐⠀⠀⠀⠀⠀⠀⣠⠂⣠⡀⠀⣍⠉⢠⡀⠀⠉⠐⠒⠤⠄⠄⠀⠙⠳⠜⠟⠒⠂⠉
⠀⠀⠀⠈⠑⠢⠽⠜⠧⠽⠼⠗⠋⠀⠀⠀⠠⢰⣏⢱⡄⣬⣿⠂⠀⣀⣁⠊⠐⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢲
⠀⠀⠀⡰⣄⢀⡀⢠⢶⠀⠀⠀⠀⠀⠀⠀⠂⠆⠪⣉⣉⠝⡌⣾⠭⠥⠚⣧⠀⠀⠀⠀⠀⠠⣤⡄⠀⣴⡤⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠹⣇⢹⡇⢸⡏⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢰⠁⣿⡀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠘⣧⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣿⢸⡇⣾⠃⠀⡴⢤⠀⠀⠀⠀⠀⠉⠒⠒⠒⠁⠀⠘⠷⠤⠔⠃⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⣿⣸⣇⡿⠀⢠⠃⠀⠳⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠤⠒⣄⡀⠀⠀⠰⠾⠟⢁⠀⠀⠀⠀⠀⠀⢀⢔⠆⠀⠀⡇⠀⠀⠀⢠⠂⠉⠁⢢
⠀⠀⠀⡾⠿⠿⠟⢿⠀⢸⠀⠀⠀⠘⢦⡂⠀⠀⠀⠀⠀⠀⠀⢴⠒⢧⡀⣀⣠⡧⠰⡄⠀⠀⠀⠀⠀⠈⠀⠀⢀⡤⢾⠂⠀⠆⠉⠉⠁⡄⠀⠸⠶⠶⠶⢾
⠀⠀⠀⡇⡄⢠⠀⢸⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⣍⠉⣣⡔⢼⠉⠉⢄⠀⠀⠠⠰⠶⢀⠃⠙⢾⠂⠈⠶⠶⠶⠶⠇⠀⢸⣤⣤⣤⣼
⠀⠀⠀⣇⡇⢸⢸⡟⠀⢸⡀⠀⠀⠀⡰⣧⢤⣤⣄⠀⣀⡄⠀⠘⢴⠟⠀⠙⣷⠁⣠⡃⣺⠉⠐⡀⠀⠀⢀⠏⠀⣰⠎⠀⠈⣦⣤⣤⣤⡇⠀⠀⠣⣉⡁⠃
⠀⠀⠀⢹⣿⣾⣾⡇⠀⠀⠱⠦⡤⠞⠁⠙⠈⠁⠛⠂⠉⠃⠀⠀⠈⠋⠧⠦⡜⠯⢄⢸⡇⢑⡞⠀⠠⠆⠁⠴⠛⠁⢀⠐⠠⠐⢄⣀⠜⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀⣤⠄
⠀⠀⠀⠀⡀⠀⠐⠓⠒⠠⣀⣀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡀⠀⠀⢠⡎⠁
⠀⠀⠀⡠⡝⠁⣠⡖⣰⣀⡄⠋⠀⠀⢸⣿⣿⣀⣙⣣⣠⣷⠀⠀⠘⡆⢀⠀⢀⣀⠀⣀⣀⠀⣀⡀
⠀⠀⠀⠈⡉⢙⡓⢴⣿⣽⡞⠀⠀⠀⠸⣿⣿⡭⠉⠉⡿⠃⠀⠀⠀⠀⠁⠁⠈⠈⠀⠀⢀⡀⣤⢁⠘⠓
⠀⠀⠀⠀⠔⡀⠲⠊⠉⠀⠀⠀⠀⠀⠀⠘⠿⣷⣤⡾⠂⠀⠀⠀⠀⢀⡀⣔⢆⣤⣤⡐⠿⡇⣿⠼⣽⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⢚⣭⣅⣿⢶⢷⡄⠙⠀⠁⠏⠘⣻⣃⡀
⠀⠀⠐⣶⠶⠒⠼⠹⠙⣇⠀⢀⣀⠀⡈⠈⠐⠁⠀⢴⣀⡀⠀⠀⠊⠽⢉⢁⢀⣀⠒⢫⡃⠀⠀⠀⣭⣉⡤
⠀⠀⠀⠃⢠⣲⣄⠂⡿⣜⠀⠈⠸⠤⣋⣀⢴⡢⡱⢈⡼⣡⠇⠀⠂⡀⢯⡖⠂⠐⠉⢺⢷⠁⠀⠀⢩⣩⠄
⠀⠀⠀⠅⠂⢳⡽⠶⠿⠟⠀⢠⠤⠴⠚⠂⠉⠀⡠⠚⠀⠃⠀⠀⢀⡑⠀⠁⠈⠛⢲⡓⡛⠀⠀⠠⠦⠤⠂
⠀⠀⠀⠘⠆⡉⠕⢒⢶⠎⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⡠⠂⠔⠲⢺⠳⠆⠀⢲⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠌⠀⠀⠐
⠀⠀⠀⢉⠉⠛⠓⠊⠒⠀⠀⠀⠐⠓⢉⡅⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⢰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⢄⠈⠁⠀⢀⠀⠀⠀⠈⠁⡤⠀⠀⠀⠀⠐⢀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠜⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⢺⠛⢣⣑⠙⡏⣓⣦
⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣬⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⢰⠛⢃⡠⠫⡼⢄⢾⡧
⠀⠀⠀⠊⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠠⠀⠄⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠈⠀⠙⠛⠯⡵⣶⠖⠒⠉⠐
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⡰⣤⣤⡔⢢⢄⠀⠀⠀⠘⠋⠀⠀⠀⣀⠔⢠⠒⡆⠀⠐⡄⡆⠀⠀⠰⠀⠰⡄⠀⠀⠀⠀⠀⠒⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠞⠉⠀⡀⡛⢄⡛⠀⢧⠀⠀⠀⠀⠀⠀⠀⠛⢄⠸⣀⠇⡰⢆⠁⡇⠁⢠⠉⠃⠀⠈⣤⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠈⣂⣈⣻⣶⡟⠉⢿⡧⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠔⠳⠛⠃⢱⣤⡞⣩⠩⠋⢅⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⢀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠁⠀⠀⠀⡎⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢦⡀⠀⠘⠉⠛⠀⠀⠀⠀⠀⠀⡠⠤⠀⡃⠀⠀⠀⣅⡀⢰⠁⠃⡌⠈⢸⠈⠣⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⡢⡁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠒⠐⠂⠉⠁⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠇⠀⠘⠤⠂⠡⠰⠸⠤⠊⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠱⠀⠀⠰⡀⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⠐⠒⠒⠶⠤⠤⠤⠀⠀⠀⠀⠈⠉⢀⠀⠀⠀⢀⢀⠀⠀⣄⢰⠂⠀⠤⠀⢀⢀⠀⠀⢀⢀⡀⠠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⠀⢠⡄⠀⡄⠀⠀⡀⢀⡀⠀⠑⠀⠀⠀⠀⢜
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠁⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠈⠐⠆⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⢤⠀⠄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠐⠖⠀⠢⢀⠀⠀⢈⠉⠠⡁
⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠒⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀⢈⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠈⠛⢿⣿⣿⣿⣿⣷⣦⣄⣀⣀⣤⣤⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⠄
⠀⠀⠀⢀⣜⣀⣠⣦⣠⣈⠉⠀⠀⠀⠀⠀⣼⡇⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⣩⣭⣭⣭⣭⣀⡀
⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⢠⠠⣠⣤⣄⣀⣀⣠⣤⡖⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣾⡛⣷⡶⣾⡿⢿⣂⣏⣩⠿⠭⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠪⣐⡛⠾⠯⠽⠧⠻⠿⠥⠂⠢⠀⢠⡠⠀⠀⠀⠀⢀⡀⣀⣀
⠀⠀⠀⠀⠀⢄⣀⡐⢲⣮⠩⠏⣈⠀⠀⠈⠑⠷⡶⡒⠂⠀⢀⠀⣠⠐⣿⣄⠀⠈⠉⠉⠁⡄⠉⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠼⢿⣶⣎⡉⠲⠤⠈⠁⠐⢄⠀⠀⠐⠌⣪⣵⢢⠊⡝⠛⠛⣿⣿⡾⠒⠀⠈⠁⠀⠀⠁⠀⠀⠈⢢
⠀⠀⠀⢀⣤⣕⢌⣙⠿⣷⣷⡆⡌⢓⣠⣦⡀⣁⡐⢧⣿⣯⣠⡐⠀⠠⡀⢸⣿⠙⠄⠀⠀⠀⠀⠤⠄⠀⠀⠀⢠⠧
⠀⠀⠀⠈⠉⠛⢿⣾⣭⣝⣛⣛⠓⠛⠻⠭⢁⠙⠛⠀⠉⠻⠿⣍⣂⠤⢄⣤⣿⣶⣦⣄⠀⠀⢀⣠⡄⠈⢁⣺⣅⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠆⣀⡒⣀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠛⠛⠻⠛⠸⠚⠀⠸⠜⠗⠪⠟⠛⠟⠃
⠀⠀⠀⠀⠀⠀⢀⣀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠐⠂⠑⠜⠣⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⣿⣿⡷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠊⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀⡀
⠀⠀⠀⠀⠀⣤⣮⡿⡿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⢼⡎⠳⢴⣤⡄⢳⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⣋⣻⣾⠏⠕⢀
⠀⠀⠀⠀⠈⠚⠓⠟⠛⠋⠿⠛⠡⠒⠂⠀⠀⠒⠛⠻⠳⠿⠿⠷⠲⠟⠛⠓⠂⠀⠀⠀⠀⠈⠙⠊⠀⠛⠛⠓⠐⠛⠋

⠀⠀⠀⠀⠀⢠⣶⣖⢶⡗⡖⡶⣄⠀⠀⠀⠀⠀⠀⣄⣤⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠯⣤
⠀⠀⠀⠈⠁⠞⠸⣼⡜⠟⠧⠃⠛⠟⠁⠀⠀⠀⠀⠄⠌⠀⠨⠃⠀⠉⠉⠀⠀⠤⠀⠀⠄⠘⢄⣤⣤⣤⣄⣁⣀⣌⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠛⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⡆⠀⣰⠒⣦⣟⡛⠓⠛⣷⣴⠁⠀⣤⣄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡗⢦⠄⠘⠿⠞⠁⠀⠘⠶⢿⣿⣷⣤⣶⡿⠋⠀⠀⠹⣿⠞⠀⣰⡀⠒⣒⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⢰⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡀⠨⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠸⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠈⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠲⠊⢄⠀⠀⠀⠀⠀⠸⣉⡀⠠⠔⠀⠷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠶⢦⡀⢠⠀⠀⠀⢨⣇⠀⠀⠀⠀⠀⠑⠦⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠱⡄⠀⠠⠙⠂⠀⠀⠀⠀⠀⠀⠌⢧
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠈⢆⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠓⢄⣀⣜⠁⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢤⣤⣤⣤⣤⠀⡤⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣰⢻⠃
⠀⠀⠀⠀⣶⣿⣿⣀⣿⣏⠷⠀⠘⣛⣩⡅⠰⣖⣤⠆⠀⢀⡏⣷⣄⠀⠀⠐⠀⠀⠀⠀⣠⡾⢃⡏
⠀⠀⠀⠀⠠⡹⣿⣿⣿⣿⣅⠐⠂⣾⡇⠁⠀⠈⢳⣿⠃⢰⠃⠘⣿⣦⡀⠀⠀⣀⣴⣿⠏⠀⢸
⠀⠀⠀⠀⠀⠉⠺⠿⠛⠟⠃⠞⠀⠁⠀⠀⠀⠀⢸⣏⣼⣿⠀⠀⠈⠻⣿⣶⣿⡿⠋⠁⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⡻⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠉⠒⠾⣄⠀⠉⠱⣄⣀⣀⡤⠤⠶⠒⠒⠚⢋⣭⣭⡉⠉⠉⠉⠛⠒⠒⡶⣦⠤⢤⣀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣹⣦⡀⠀⠈⠛⠙⣄⣇⠈⢧⣀⠀⠀⠀⠀⣠⡟⣽⢿⡟⢿⣿⠶⣤⠀⢰⢃⡷⣴⢳⢠⠏⣼⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠸⣀⠀⠈⣇⠀⠀⢀⠘⢾⠂⠈⠈⢧⠀⠀⢰⡟⢸⣇⣾⣳⣤⣿⠶⣾⡇⡜⣸⢠⢃⣾⢋⡜⢉⠗⡹⠊⠑⠦⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣹⡆⠀⠉⠓⠪⣕⢮⡳⢄⣦⡘⢦⡀⢿⣃⡞⢹⣿⡋⠁⢻⣄⣼⣧⣇⢇⡎⣸⢣⢞⡴⡡⢊⣤⣖⣽⠧⢚⣹⡿⠂
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠉⣒⠶⣭⡳⣌⠳⡵⡄⠉⢙⠲⣍⢿⣿⣀⡸⢘⡏⠲⣤⠏⢠⣿⡸⡸⢱⣣⢫⢎⣾⣿⣿⢟⡫⠗⠊⢁⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢡⣖⡺⠟⢮⣧⡹⡿⣄⠀⠙⢮⣇⣟⠻⣤⣾⣟⣦⣾⣖⣻⣿⣷⣷⡿⡳⣳⢟⣽⣫⡟⢉⡴⢤⢴⠋⠈⢳⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣰⢫⢮⢻⡻⣦⣀⣳⡳⣜⠪⣗⣶⣪⠽⡷⢚⠽⠀⠀⠀⠀⠀⠉⠛⢿⠿⢵⣵⣟⠵⢫⡏⠈⡹⠧⡤⢦⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠻⣯⢨⣧⣷⣿⡛⠻⣍⠛⡻⠛⠉⠀⠸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡇⠀⠀⠉⠲⣍⢰⠚⢁⡴⢦⡞⠀⢸⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠺⣿⡏⠳⣉⢳⠈⣷⡁⠀⠀⠀⠀⠈⠙⠒⠒⠶⠶⠶⠒⠒⠋⠁⠀⠀⠀⠀⠀⢈⡏⠐⡅⢀⠞⢓⡶⠋⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠈⠙⠢⣌⣹⢀⡟⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠗⢲⣋⠭⠛⠉⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠦⣀⠀⠀⠀⠈⠙⠓⠾⠧⣝⣛⣷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣒⣾⣽⡿⠭⠖⠚⠉⠀⠀⠀⢀⡠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠈⠙⠒⠶⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠶⠚⠉⠁⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⠙⠲⠤⣄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⠤⠖⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠉⠓⠒⠶⠤⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠴⠖⠒⠋⠉⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⣒⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢌⣉⠉⠙⠛⠒⠒⠓⠛⠋⠉⢉⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠒⠒⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠰⠀⠢⠀⠀⠀⠀⠀⢀⣀⠤⠔⢂⠁⠨⡄⠀⠀⢀⣀⡀⠀⠀⠀⠀⡀⣠⢄⡶⠂⢩⠉⢡
⠀⠀⠀⢼⠨⢽⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠒⠉⠀⠄⢀⣀⡀⠘⠀⡇⠀⠀⠀⢇⠈⠐⡴⡁⠂⠻⠈⠊⠁⣠⣴⡆⠘
⠀⠀⠀⠈⡆⠀⠣⢄⡀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠁⢰⡁⢻⣿⠀⡀⠸⡀⢀⣤⣼⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⣴⣾
⠀⠀⠀⢀⠌⠀⠀⠀⠈⠑⡄⠀⠀⢀⣀⡀⠰⠀⡤⢀⠑⠛⠁⠐⣈⠤⠃⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡀
⠀⠀⠀⢈⠀⠀⣀⠠⣴⠀⠈⡄⢞⢉⣁⡇⠀⢇⠀⠃⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⡨⢧⢠⣬
⠀⠀⠀⠘⡀⠀⢈⡀⢉⠡⠐⢃⠈⠧⠄⠚⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢀⠖⣁⡈⣃⣀⡞⠋
⠀⠀⡀⠀⠹⡀⠀⠀⣀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡆⠀⠤⡀⠀⠀⡰⢉⣚⡹⢧⡿⠐⠚⠊
⠀⠘⠄⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣦⠀⠀⠀⠀⠀⠀⢈⣁⠸⠤⢇⠀⠀⠧⣈⠦⠟⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠘⠂⢲⢦⡀⠉⠲⡄⠀⠉⠐⠁
⠀⠀⠀⡤⠤⢄⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠋⠀⠉⠻⠿⣿⣀⠀⠀⠀⠀⣞⠢⠀⠀⢀⠜⡲
⠀⠀⠘⠐⠒⡄⠙⢆⠀⠀⠀⠀⢠⢼⠛⠋⠁⡄⠀⠀⠠⠆⠀⠀⣋⠇⠀⠀⠈⠪⣁⣀⠤⡊⠒⠈
⠀⠀⢰⠀⢰⠁⠀⠈⡆⠀⠀⠀⠘⠤⢆⠀⠀⠀⠀⣀⡀⠀⠀⡰⠁⠀⢀⠀⠀⠀⠘⣔⠆⠈⠀⠀⠀⡰⠂
⠀⠀⠘⡄⠈⠒⠢⡄⢰⠀⠀⠀⠀⠀⠀⢳⣄⣀⡀⠀⢀⣤⠊⠀⠀⠐⠩⠄⠀⠀⠀⠀⠀⠀⣀⠀⠼⣹
⠀⠀⠀⠘⢄⠀⠀⠈⢸⠀⠀⠰⢄⡀⠀⠀⠛⠛⣇⠀⢹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠺⡁⣀⠀⠀⠙⢆
⠀⢀⡘⠀⠀⠁⠂⢤⡞⠀⠀⠉⠂⠀⠀⢀⠤⠒⣿⢷⡞⣈⡝⠒⢄⠀⠀⠀⠀⠀⢠⣃⠀⠀⠀⠈⠒⠉⠑⠛⡄
⠀⠀⠑⠈⠀⠀⠀⠈⡟⡄⠀⠀⠀⠀⢰⠁⠀⠀⢨⠚⡪⠊⠀⠀⠸⡀⠀⠀⠀⠀⡀⠀⠀⠉⠉⠉⠈⠀⠒⠒⡇
⠀⠀⣀⡀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⡌⠀⢀⣴⠥⠼⢥⣀⣐⡀⠀⠇⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⣼⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠃⢔⢁⡟⣶⠤⠼⠹⡀⠇⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⠀⠀⢀⣀⠴⠃
⠀⣿⣿⣿⣽⣿⣿⣽⣿⣷⢆⠀⢐⠂⠄⠈⠉⠉⠑⠃⠀⢸⡿⡀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠒⠋⠉⠃⠀⠀⠐⠂⠁
⠀⠉⠛⠿⠿⣿⣷⣿⣿⣷⣮⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠪⡀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⢠⡄⠀⢤⡀⢤⣤⠶⣦⢤⡴⢤⡤⣤⢤⡖⣶⣠⢤⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⡎⡌⡆
⠀⠀⠀⠀⣦⡭⠼⠀⠚⠀⠒⠠⠼⠷⠞⠧⠽⠧⠽⠁⠸⠄⠃⢀⡤⠒⢒⣶⣦⣄⠀⠀⠀⡀⠀⠀⠀⠛⠁⠀⠀⣤⢄⢀⡀⣀⡀⠀⠀⠰⡷⠁
⠀⠀⠀⠀⡛⡷⠀⠀⠀⠀⠀⢀⣠⢔⣶⣲⠠⢤⡀⠀⠀⣀⢀⢋⣤⠀⣾⣿⣿⣿⣷⡀⠘⠿⠿⠯⠭⠭⠭⠭⠭⣽⡟⣿⣿⣿⣷⣐⡐⣦⢸⣠⠊⡆
⠀⠀⠀⠀⡇⣵⠀⣏⡭⠥⠭⣝⣚⡅⠀⣀⢨⠟⠁⠀⠀⠋⠸⡀⠁⠀⠘⠿⣧⣤⣿⡇⠀⢶⣶⣗⣀⣈⣀⠀⠠⣿⣧⣿⣿⡿⡷⠶⠶⠆⠀⢻⡧⠃
⠀⠀⠀⠀⡿⣏⠀⠈⢆⣀⡀⠀⡱⠗⠘⠋⠁⠐⠂⠀⠀⠀⠀⠑⢤⡀⠀⢀⣽⣿⠟⠁⠀⠀⢀⠀⠀⠀⠀⢀⠀⢸⣸⢸⣿⡙⡖⠀⠀⢠⠒⢬⡄
⠀⠀⠀⠀⣧⡾⠀⠀⠀⠑⠒⠊⢁⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡈⠉⠉⠉⠀⠀⠀⠀⠤⣼⠆⣔⠰⠦⡾⠀⣣⡁⢸⡄⣿⠃⠀⠀⠈⠂⠽⢧⡖⢲
⠀⠀⠀⠀⡏⣻⠀⠀⠈⠁⠀⡜⠁⠀⠈⠑⠀⡴⡟⠀⠀⢈⡀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⡠⠤⡀⠀⠈⣿⠀⣿⣾⠀⠀⠀⠀⠀⠀⣿⠧⠊
⠀⠀⠀⠀⡇⠷⡆⠀⠀⠀⢸⡇⠀⠀⠀⣠⠞⣱⠟⣇⣠⢿⠶⠖⢧⣀⣾⢁⡴⣇⣀⠾⣅⣠⠖⠀⠀⢇⠀⠹⡄⠀⠃⠀⠁⢙⣆⠀⠀⠀⡵⠀⠣
⠀⠀⠀⠀⡇⣪⡀⠤⢤⣶⠄⠳⠤⠴⠚⠁⠀⠁⠀⢈⡁⠀⠀⠀⠀⠁⠀⠁⠀⠉⠁⢀⠀⠀⠀⠀⠀⠀⠑⢄⢣⡀⠀⠀⠀⢸⡇⠀⢀⣰⣦⣄
⠀⠀⠀⠀⢣⣶⡁⠱⣤⠟⠀⠀⠄⠀⠀⣀⡄⠀⠀⠘⠃⠀⠀⠀⡀⠀⠈⠀⠀⠀⡰⡏⡛⡖⢤⣠⣀⣀⡀⠀⠱⡑⣄⠀⠀⠘⢣⢊⣿⢁⣿⢸⣿⠢⡀
⠀⠀⠀⠀⠨⡚⠁⠀⠀⢀⡀⠀⠀⢀⣼⠋⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣠⡴⢾⣥⣤⣀⠈⡴⣿⣟⠻⡟⠳⣦⡈⢮⣷⡄⠀⢈⢸⣿⢸⣿⢸⣿⠀⡔
⠀⠀⠀⠀⠘⠚⠀⠀⠀⡄⣿⡀⠀⣾⠗⠊⣀⣀⡩⠉⠙⠛⠓⠀⠀⢠⢾⠊⢰⢱⠻⢸⠑⡙⡇⠂⠀⠁⢸⠀⠀⣽⠀⠑⠚⠀⠈⠙⠻⣼⣧⠾⢛⡋
⠀⠀⠀⠐⠀⠰⣶⡀⣸⠇⣸⣧⠞⢶⣌⡉⠀⠉⠻⢶⣤⣄⠀⠀⠀⠸⣮⡀⠸⣄⠀⠘⠀⣡⠗⠤⠤⠔⢃⣀⣸⠏⠀⡀⠠⢀⠀⠀⠀⢸⠁⠀⠈⠂
⠀⠀⠀⠀⡀⠀⠈⢿⣞⠋⠈⣿⠀⠀⠉⠻⢦⣀⠀⠀⠀⠉⠁⠀⣠⣄⠙⠷⢶⣄⣩⠭⣉⠠⣄⣀⣴⣤⠟⡻⠁⠀⠀⢰⢸⠈⠆⠀⠀⠰⠃
⠀⠀⠀⠘⣧⡀⠀⠀⠙⣧⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠞⢏⣿⠂⠀⠀⠉⠙⠙⠛⠛⠛⠛⠉⠉⠁⡤⣄⢀⠴⣄⣀⢄⡀⠀⠀⠀⠀⢮⣷
⠀⠀⠀⠀⠙⣷⡄⠀⠀⠈⢦⡀⣅⠀⠀⠀⣠⣴⡶⡶⢻⣧⠀⠈⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠛⠀⢀⣤⣧⣾⢡⡞⢡⠙⣦⢹⣊⣦⡀⠀⣾⡽
⠀⠀⠀⠀⣠⡞⠛⠒⣄⡀⠈⢷⣿⠀⠐⠋⠁⢀⠜⠀⠸⣿⠀⠀⠀⢠⣿⠀⠀⠀⣼⠆⢰⡆⠀⠀⢰⢻⢧⣟⡿⢿⢇⣊⡴⢫⣾⣙⠁⠙⡄⣎⠘
⠀⠀⠀⢠⡿⠁⠀⣴⡟⠉⠒⢌⣿⡇⠀⠀⢠⢾⡆⠀⠀⠻⠀⠀⠀⠘⠷⠀⠀⠀⠻⠀⠸⡇⠀⠀⠘⢎⡈⠻⣿⣿⠾⡏⢙⢻⠧⠴⢃⡴⢁⡜⢑
⠀⠀⠀⠸⠁⠀⢰⢏⡀⠀⠀⠀⠹⣧⠀⣠⠃⢾⣧⠀⠀⠀⠀⣠⣴⣶⣞⡟⡟⣹⢿⡻⡻⡲⢶⣄⡀⠀⠻⣷⣾⣯⠤⠬⢲⣷⣶⡾⠏⠀⠈⣩⢂⡀
⠀⠀⠀⠀⠀⠀⠙⠘⡄⠀⠀⠀⠀⠻⣶⡇⠀⢸⣿⠀⠀⣀⠀⣷⣷⡿⡻⢾⣰⡛⣧⠹⣵⣵⠙⣼⣷⠀⠀⠀⠀⠉⢉⡉⣭⣥⠤⢄⣀⠀⠀⢷⣾⡇
⠀⠀⠀⠀⠀⣀⣤⢾⡷⣤⣀⠀⠀⣀⢹⣷⠀⢸⡏⠀⠈⠃⠀⣿⣻⣿⣟⣛⣳⣶⣾⣷⡿⠷⢿⣯⡿⠀⠶⠀⢀⡔⢁⣈⣁⡀⠀⢀⡝⠀⠀⢟⡩⡇
⠀⠀⠀⢀⠞⣽⡇⢸⡇⢹⣏⢣⠀⢸⡆⢿⡇⠈⣇⠀⠀⠀⠀⢹⣷⣤⣓⠚⠛⣄⣠⠞⠲⢤⣧⣼⠃⠀⠀⣀⠔⠉⠁⠀⠀⠀⠀⢙⣦⠀⠀⣴⡿⡃
⠀⠀⠀⠘⢆⣿⣧⢸⣿⢸⣟⡸⠀⢸⣷⠘⣧⡀⠈⠀⠀⠀⢠⢆⠹⣌⡙⣛⣛⣛⣒⡛⠛⣋⡽⠃⢀⠀⠀⠛⠢⠬⠥⠤⠭⠤⠔⠊⠀⢠⡀⢱⡄
⠀⠀⠀⠀⢀⡍⠉⠾⡿⠏⠁⠀⠀⠀⣿⡄⢸⣇⠀⠀⠀⠀⠀⠑⠀⠀⠙⠻⠿⣿⣿⡿⠏⠁⠀⠀⠈⠀⢀⡀⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣱⣗⠁
⠀⠀⠀⠀⠀⠁⠀⠀⡼⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡡⢤⠟⣜⣧⣸⣯⢹⣇⢹⠐⣂⣖⠠⢍⠰⠂⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠖⠖⠊⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠐⠂⣠⣄⠀⠀⠀⢀⡀⠀⠀⠀⣠⠤⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⢫⡀⠀⠀⡘⠀⠀⠀⢸⣦⣄⠠⠂⠄⢶⣆⠛⢶⢒⡀⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣀⡴⠃⠀⠀⠀⢃⠸⣹⠗⠚⠿⡭⢿⡟⡳⠵⠏⠅⠃
⠀⠀⠀⠀⠀⠀⠀⣤⡾⣦⣼⠿⠶⠂⠀⠀⠀⠀⠀⠀⠀⣨⠉⠀⠙⣧⡀⠀⠐⢄⣀⠀⠀⠀⠀⠀⢠⣾⠍⠁⠀⠀⠀⠀⠀⠑⢄⠈⠉⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠘⠃⠀⢸⠛⣤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠼⠁⠁⠀⠘⠋⠹⠀⠀⢀⠙⠿⠒⢺⡿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠠⠄⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠴⠶⠲⠖⠒⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢀⠀⢠⣁⡤⢤⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠈⣉⣲⡎⢡⡈⣦⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠂⠐⠚⠻⡷⠂
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠰⡀⠀⠈⠣⡀⠀⠀⠁⠈⠓⠂⠐⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠰⠶⠎⠀⢠⠄⠼⠦
⠀⠀⠀⠀⠀⠃⢚⣦⠀⠀⠀⡀⠀⠀⠑⣄⠀⡀⣠⡞⢂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⡙⢋⡿⢥⣾⣶⢶⠀⣄⡀⠘⠃⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⡈⢷⣄⣴⣼⣦⣶⠶⠛⠛⠋⢉⠁⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠫⠃⣤⢶⣾⣿⠤⠀⣨⠂⠀⠀⠀⠀⢁⠅
⠀⠀⠀⠀⣠⠀⠀⠀⠀⠘⠉⠉⠤⠤⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣴⡆⠀⠀⠀⠀⠀⡀⠴⢦⡞⠀⣀⣠⣿⣇⡏⠃⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⡷⡀⠀⠀⠀⢈⡀⠀⠀⠀⠈⠑⠚⠟⠏⠁⠀⠆⠀⠀⠔
⠀⠀⠀⠀⠀⠀⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⡘⠁⠀⠀⠀⠀⠈⠑⠦⣄⡀⠌⡠⠀⠀⠀⠘⡠⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠉⠒⠟⠁⠀⠀⠀⠀⠂⠀⠀⠠⢠⠆⠀⠈⣡⡶⠦⠴⠀⠀⡈⠀⡀⢉⣉⣀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣄⡀⠐⢈
⠀⠀⠀⠀⠀⠒⠶⠀⠴⠒⠃⠀⠀⠤⠀⠀⠙⠛⠍⠀⠀⠀⠀⠀⠀⠳⣀⠂⠐⠄⠀⣰⣬⠉⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡠⠀⠀⠀⡄
⠀⠀⠀⠀⢀⡤⠖⠊⠉⠈⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⡀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠐⠒⠂⢈⣁⠤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠲⠇⠀⠀⣠⡇
⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢀⡀⡀⢀⢀⣀⣀⣀⢀⡀⠙⢷⡄⠀⠀⠀⢨⣤⠤⠶⠖⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣿⡦⠤⠀⠀⠀⠀⠀⠀⡟⠁
⠀⠀⢘⢡⠁⠀⣀⣠⣔⢾⣟⡉⠛⣼⡶⡬⢉⡀⢈⣁⣤⠿⡿⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠈
⠀⠀⠘⣧⡀⠸⣟⡶⣴⡦⣮⣙⡋⣿⠟⢋⣈⣉⠉⣭⣷⣴⠃⠀⠀⠀⠀⠀⠉⠉⢀⡄⠀⠀⠀⣦⡀⢀⡠⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⢉⠓⠿⣬⣅⠶⡄⡻⠟⢛⣚⠉⣩⣽⠶⠟⡡⠀⠀⠀⢠⠀⠁⠀⢀⣠⠀⠀⠀⠈⠀⣹⠀⠀⠀⠀⣀⣀⠀⠒⠀⠀⠀⠀⠀⡀⠀⠀⠈⠱⣤⡄⠠
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠉⠙⠛⠉⠉⠉⠀⢀⡀⠐⠁⠀⢀⡀⠈⠓⠄⠀⠀⠉⠒⠀⢀⣤⠴⠛⠀⠀⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⠀⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠢⠀⠄⠀⠀⠤⠤⠶⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⡂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣀⡀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢀⣀⣠⣴⠖
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⠻⢿⣎⠉⠀⠖⡒⢦⢤⢤⡤⣤⡤⠤⡤⣤⢤⢤⠒⡒⠒⠈⢉⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠯⠉⠉⠉⠯⠉⠉⠹⠏⠉⠉⠉⠉⠯⠉⠉⠉⠭⠉⠉⠩⠇
⠀⠀⠀⠀⠀⠀⣂⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⣀⡂
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣧⠤⡤⡤⢤⡤⢤⢤⡤⣤⠤⡤⠤⠤⡤⢤⡤⢤⢤⠤⣤⠤⡤⡤⢤⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠄⣤⡤⢸⠿⠀⠀⠀⢿⠄⢠⣤⣤⠀⠸⠇⠀⠀⠀⠿⠀⣤⡄⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠨⠀⠿⠇⠠⠀⠀⠀⠀⢨⡀⠠⠿⠿⠀⣠⠀⠀⠀⠀⠠⠀⠿⡇⠸⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡂⠐⠂⠂⠒⠀⠒⠒⠂⠂⠒⠂⠐⢒⡒⠀⠂⠒⠐⣒⠒⠒⠒⠂⠀⠒⠀⠒⠀⠀⠂⠒⠐⠒⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⣄⢀⡤⣀⣄⢀⣤⡠⡀⠀⣄⢀⢀⣀⣀⠀⣀⢠⡄⢀⣀⣀⣀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠹⠴⠻⠇⠻⠭⠸⠐⠇⠇⠀⠀⣿⢸⣎⢲⠀⡽⢐⠀⠀⠖⢙⢮⠀⡟⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢰⠳⡄⢾⡂⡆⢰⢰⠚⡖⣷⠀⠉⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠼⠈⠈⠑⠁⠙⠉⠈⠀⠁⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠻⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣀⣤⣤⣤⣄⣠⣤⣤⣤⣀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⠉⠋⠉⠉⠉⠉⠋⠉⢁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⢀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⠒⠀⣬⣍⡛⢛⣩⣥⠀⠚⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⣀⠀⠀⠀⠀⣿⡿⠟⠻⢿⣿⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⣤⣤⣭⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⣛⣛⠛⠛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣛⡛⢉⣉⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠉⠐⠋⠉⠙⠲⡀
⠀⠀⠀⠀⢀⠔⢚⠛⠉⡉⠩⠙⠢⡀⠀⠀⠋⠀⠀⠒⠀⡀⠀⢀⠟⠀⠡⠀⢀⣸⡚⠠⠄
⠀⠀⠀⠀⠋⢀⣼⠏⢠⠁⣠⣤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⡄⡀⡠⠈⢻⣷⣵⣔⡀⠒⠀⠀⠙
⠀⠀⠀⠀⠀⠘⠻⣄⠀⢠⠏⠁⠀⠀⡼⣄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣠⠇⠀⠀⠙⣿⣧⣁⢀⠀⠤⠀⠒
⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠙⢷⣄⡀⠀⠀⠀⠀⠀⡀⠖⠋⠀⠀⠀⠀⠈⠙⠛⠈
⠀⠀⠀⠈⠳⠦⠀⠀⠀⠀⢀⡤⠋⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⡠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⣄⠐⠲
⠀⠀⠀⠀⠀⠀⠐⠒⠀⠛⠺⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢴⡀⠒⢯⠤⠄⠂⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠲⠄⠐⠋⠀⠀⢀⣀⣀⡈⢡⠴⠂⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⠀⣀⠔⠚⠙⠀⠀⠐⠀⠄
⠀⠀⠂⠐⠒⠋⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠉⠙⠒⡤⠒⠉⠈⠉⢀⣤⡀⠀⠀⠀⢴⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠠⠤⠤⠖⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠛⠉⢀⣴⣦⢄⣠⣄⣀⣐⡒⠒⠒⠿⠗⠉⠔⠈⢠⠀⢄
⠀⠀⢀⢔⣪⡶⠶⣶⠶⣶⣤⣄⠀⠀⠀⠀⣠⣤⠿⢯⣽⣿⡻⣿⡟⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⢡⣾⠛⢷⣤⣼⣦⣼⠉⠹⣿⡄⠀⠈⠇⠀⠀⠀⠀⠹⡿⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣾⣿⡦⠐⠻⣷⣶⡀⠤⢆⣀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠒⡀⠀⣠⣩⣤⣄⠀⠄
⠀⠀⢻⣿⣷⣠⣆⣿⠋⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⣰⡾⠁⠀⠁⣤⠭⡤⢉⡐⠓⠂
⠀⠀⠀⠙⠿⣿⣏⠉⠓⣤⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠙⠅⠀⠴⠟⣿⣖⠹⢃⢶⡶⠂
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠋⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⣀⣼⡆⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠓⢄⡀⠀⢙⣣⠄⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⡄⠠⣚⡉⠀⢀⡴⠂⠀⠀⠀⠀⠀⢸
⠀⠀⢀⣀⣀⡀⢤⣤⢄⣥⣔⣻⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣛⣧⣶⣠⣤⠄⣀⣀⠀⠀⢸
⡶⢿⣿⣿⣿⣿⣿⣶⣨⣭⣟⣻⣯⣥⣭⣛⣛⡿⢿⣿⣿⣿⣿⡿⢿⣛⣻⣥⡭⣿⣛⣿⣭⣆⣶⣿⣿⣿⣿⠷⣾
⠉⠛⠒⠿⠯⠭⣽⣯⣙⣛⣙⣻⣷⣶⣍⠛⠛⠫⠭⠤⠘⠓⠖⠛⠻⠿⣛⣋⣞⣒⣒⣒⣹⣥⣭⠭⠽⠷⠚⠋⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢠⢠⢀⠆
⠀⠀⠀⠀⣀⢰⠀⠀⠄⠀⠀⠀⠠⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⣁⣠⠈⢸⡆
⢠⠈⠃⠀⠈⠀⠇⠀⠀⠀⠁⠀⠠⠄⠀⠄⠀⠀⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠄⠀⠀⠀⢃⡀⠀⠉⠁⡄⢸⠁
⠈⠂⠀⢒⡂⠀⠀⠀⠀⠄⢠⠀⠀⠀⡀⠀⠀⠠⠀⠃⠀⠀⠐⠂⠠⠐⠆⠀⠀⠀⢈⡀⢤⠀⡀⠀⠀⠀⡀⠀⠀⢀⢫⡽⠀⣀⣄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠁⠀⠊⠀⠑⢀⢀⠀⠀⠰⠇⠀⡀⡛⣀⢰⠀⠀⠀⠀⠈⠛⢦⡕⠐⢤⡀⠀⠈⣴⣁⢤⣖⠙⠋⠁
⠀⢨⣀⡂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠐⠊⠁⠄⠉⠈⡔⠀⠀⠀⠀⠀⠀⠀⢀⠒⠀⠀⠁⠉⠀⠀⠄⠂⡀
⠀⡎⠁⠉⠁⠀⠀⠀⠀⠀⢀⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠈⢢
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠄⠠⢂⣨⡖⠀⠀⠀⠀⡂⠀⠀⣤⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⢀⣌⣀⣠⣥⡀
⠀⠈⠀⠟⠐⢐⠻⠃⠀⠀⠀⠀⠁⠀⠀⠁⠅⡻⠯⠄⠀⠀⠈⠀⠅⠀⠁⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣸⢉⣈⡀⣈⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡎⠂⠀⠀⠀⡼⢰⡆⠀⠀⠀⠖⠀⡃⠐⠆⢠⠕⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⣯⣂⣀⣒⣐⣺
⠀⠤⣀⡢⠄⢀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⡁⠁⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠀⠨⠛
⠀⠀⠈⠕⠃⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠠⠀⠀⠄⠀⡇⠀⠄⠀⠄⠈⠈⠀⠀⠹⠦⡀⠀⠀⠀⠀⠀⠁⠈⢀
⢐⢤⠄⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠤⠀⢄⠃
⠈⠛⡐⠍⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠖⣀⠀⠀⠁⠀⠀⠠⠀⢀⠐⠰⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⢀⣀⠀⡇⠀⣀⠀⠐⠏⠈⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠐⠈⠂⠀⠀⠀⠀⠀⠀⠐⠒⣿⡏⢙⡗⢀⢀⡀⠀⡀
⠀⠀⠜⠆⡤⠁⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⡇⠀⠀⠀⠀⢀⠈⠀⠠⡀⠀⠁⠈⠁⡎⠍⠹⠁⣥⠤⠤⠤⡽
⠀⠀⠈⠔⣥⣧⣤⣤⢐⠐⢂⠀⠂⡁⠂⠐⠐⠒⢀⣠⡪⣦⡶⢶⡗⠀⠐⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠄⠄
⠀⠨⢬⠆⣠⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡆⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣀⣬⣀⡀⠀⠀⢁⣰⣰⣀⢀⣀⣠⡠⣀⢀⣀⣠⡀⡁⢀⡠⠤⣷⣠⠀⠀⠀⠖⠋⠲⠒⠀⠄⠄⠖⠩⠴⢎⠀⠉⠃
⠠⠄⠹⠁⠁⠀⠂⠒⠀⠃⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠔⠀⠉⠋⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠉⡀⠂⢀⠆
⠀⠀⠀⠀⡐⠀⠄⠀⠀⠀⢀⠄⠀⠀⠀⠀⠅⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢠⠀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⠈⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠒⠀⠀⠀⠀⠐⠐⠀⠀⠀⢂
⠀⠀⠀⢀⡀⢀⣀⣀⠀⠀⢠⣀⡀⠀⠀⣸⣀⠀⠀⢀⣠⣀⠀⣀⠀⠀⠀⡀⠀⢀⡀⠀⢀⡈⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⣀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠋⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠘⠉⠛⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⣛⣿⣷⣶⣶⡄⢆⡨⣠⣤⣤⣄⡀⢀⣾⣿⣆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣄⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⡟⠸⣆⡞⠐⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⠀⣶⣶⣿⣿⡏⠛⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠀⠀⠠⠤⢤⣼⣏⣀⢀⠻⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠛⠛⠋⠉⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⣩⠖⠋⠀⣵⣿⣽⡆⠀⠀⠈⠁⠈⠀⠈⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣼⣾⣿⣆
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣿⣿⡿⢿⠟⠻⣿⡟⠀⠀⠀⠀⢻⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠐⠚⠋⠀⠈⢿⣿⠛⢻⠿⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠰⢾⡿⠀⠀⠀⠀⠀⠀⠙⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠄⠠⠀⠀⠈⢀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢼⣶⣅⠀⠀⠀⢐⣾⣦⠄⠀⠸⢆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠾⣿⢷⠂⠀⠀⠀⠀⠀⠀⠚⠹⠃⠀⠀⠀⠈⠿⠛⠂
⠀⠀⠀⠀⠀⠁⢈⣠⣴⣶⣦⠀⠀⢀⠈⠀⢁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣄⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣤⣶⣿⡇
⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⠁⠀⠀⠀⠄⠠⠄⠀⠀⠄⠠⠀⠀⠁⠁⠀⠀⠀⠀⣰⡄⠀⠀⢿⣿⢧⠀⠀⠀⣠⣾⣏⠀⢀⣠⣾⡿⠿⠿⠿⠗
⠀⠀⠀⠀⠀⣿⣿⣿⣏⣀⣀⣤⣤⣤⣶⡾⠁⠀⠂⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠀⠀⠈⠀⠀⢀⣼⡟⠛⠈⠐⠋⠉
⠀⠀⠀⠀⠀⠻⣿⠟⢻⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣥⣤⣴⡶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠔⠀⠴

⠀⠀⢀⠠⠄⠒⠒⠒⠂⠉⠉⠉⠉⠉⠉⠛⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠄⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠠⠤⢤⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠠⠈⠀⠀⠶⠤⠀⠑⠀⠀⠀⠀⠀⠀⠒⢄⡀⣄⠀⠀⠀⠈
⠀⠸⠦⣗⣤⣀⡀⠁⠀⠀⠀⠈⠁⠔⠌⠀⠁⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠔⠀⣈⡀⠒⠄
⠀⠀⠳⣤⡁⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⢀⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠅⠐⠀⠄⠀⠤⣭⡀
⠀⠀⠀⠙⠬⡉⠓⠒⠂⠀⠀⠤⠤⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠅⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠤⠄⠓⠦⠤⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠤⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⣂⠠⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠻⠟⠓⠚⠛⣁⣽⡚⠓⠂⠔⠞⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢄⠀⠂⠀⠀⠀⠀⠀⠀⢸⣷⠇⠐⢀⡀⡐⡈⠁⠐⠮⠀⠉⠉⠉⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈
⠀⠀⣶⠬⢵⠒⠀⣧⡀⠀⠒⠲⡉⠙⣒⠆⡀⠀⠀⠀⠐⡀⢉⠀⠈⠉⠉⠩⠙⠉⠁⠀⡀⠀⠰⠄⠀⠀⠀⠀⠀⠰⠂⠄
⠀⢰⡛⡷⡜⡓⠤⡈⠙⣀⣉⣀⠑⢤⡘⣅⡥⢀⡀⠀⠀⠱⡄⠤⠄⠀⠀⠀⠀⢀⠀⠀⠡⠂⡤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌
⠀⠈⠹⢷⣯⣻⢟⣙⢣⡩⡄⣘⣅⢐⡉⠉⠙⢂⢤⠀⠀⠀⠈⠒⠀⢀⡀⠁⠀⠈⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠘⣿⣨⣙⣃⠻⡞⠀⠈⠁⠐⠒⠉⠅⠄⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠹⢿⣏⠊⢡⡄⠃⠚⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡅⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡉⠀⠀⠀⠀⠀⠈⠉⠙⠒⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣙⣦⣀⣀⣀⣀⣀⣀⡀⢀⡀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠠⣀⠐⢦⠠⢠⡀⠀⠀⠀⠀⠀⣄⢹⠛⢻⠛⠛⠒⠖⠋⢉⠵
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⠤⠀⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⢀⡄⠒⠒⠀⠉⠀⣀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠜⠦⠤⠲⠦⠒⠁
⠀⠀⠀⠀⢀⠀⢀⣠⡤⠄⢈⠉⢉⠙⢻⡿⠟⠳⠀⠉⡄⠀⠈⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠘⡒⠶⠶⠄⠋⠉⠉⠩⠠⠼⠼⠶⠆⢀⠀⠆⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣠⢤⡴⠿⣿⠾⢧⠭⣬⣁⣐⡂⢄
⠀⠀⠀⠀⠀⢀⠙⠒⠂⠤⠤⠤⠤⠤⠀⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢮⡉⠋⠙⡇⢐⣀⣀⣀⢢⣀⢚⠉⠏⢸
⠀⠀⠀⠀⠀⠈⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡨⢤⣁⣈⡀⠉⣧⣘⣁⡀⠹⢅⡀⡐
⠀⠀⠀⠀⠀⣀⠀⠀⠈⠐⠆⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣌⠐⠀⢀⡀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠨⠤⠴⢦⢤⣤⣤⣈⣁⣀⣀⣀⣀⣀⣀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⢯⣅⣂⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠁
⠆⠀⠀⠐⠀⠠⠤⠤⠀⠀⠀⠀⠉⠉⠉⠀⠈⠉⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠥⠤⠤⠤⠬⠭⢉⣀⣒⡒⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠋⠂⢿⣍⡓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠐⠀⠀⠀⠀⠀⡴⠀⠀⢸⠧⡀⠀⠀⠀⠀⡠⢆⠠⠈⠁⠀⡀⢸⠹⡉⠳⢦⡉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠔⡹⠆⠀⠀⠀⠐⠈⡆⢿⠋⠉⡹⠋⠔⠈⣀⠄⠀⠀⠀⢸⠀⡇⠀⠀⠙⠳⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡴⠁⠀⠀⠐⠂⠀⠀⠀⠀⡇⢸⢀⠼⠁⠀⠀⠀⠀⠀⠤⠀⠀⠘⣀⠇⠀⠀⠀⠀⠘⢧⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠚⠁⢤⠀⠀⠀⠀⠈⠀⣀⠀⢃⢿⠣⣀⠀⠋⠀⠀⠀⠀⠀⠐⠂⠀⡏⡷⡀⠀⠀⠀⠀⠀⢳⡄⠘⣦
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡏⠑⢤⡀⠀⠀⠀⣀⠀⠀⠀⠀⢸⢸⣦⣨⠑⢤⡀⠀⠀⠆⠀⠀⠀⠀⣇⢸⠘⡄⠀⠀⠀⠀⠀⢷⠀⠸⡆
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢣⡈⠲⣗⠈⠢⣄⠀⠉⠀⠀⠀⠀⠘⡄⡧⣼⠢⣄⠉⡢⣄⠀⠀⢠⠀⠀⢹⠈⡆⠘⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⡙⢦⡑⢄⡘⠑⢤⡀⠐⠃⠀⠀⡇⢳⡈⠑⢌⡑⢄⡀⠑⢤⡀⠀⠀⠸⡀⡇⠀⡄⠀⠀⠀⠀⢈⡇⠀⢸
⠀⠀⠀⠀⠈⡀⠁⠀⠀⠀⠀⠈⠣⣄⠉⠢⣌⠦⣄⠈⠢⣄⠀⡄⢷⢸⠙⠦⡀⠝⠣⣹⡢⢄⠉⠢⣌⠀⣇⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠹⡗⢏⠈⠑⢷⣝⠢⣀⠑⢦⣸⡇⠀⠀⠈⠲⣄⠈⠙⢦⡉⠢⣌⠑⢾⣇⠀⠀⠀⠀⠀⢀⡾⠀⢠⡟
⠀⠀⠀⠀⠀⠘⣄⠠⡀⠀⠀⠀⠀⠀⠙⢦⡑⠦⡠⠌⠓⢌⠱⡦⣈⡿⡄⠀⠀⠀⠀⠑⢬⡁⠈⠲⢜⣍⠺⢛⡆⠀⠀⠀⢀⡼⠁⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠘⢦⠀⢄⠀⠀⠀⠀⠀⠀⠙⠢⣌⡒⢄⡈⠑⠻⣆⢥⡽⠀⠀⠀⠀⠀⠀⠈⠓⣄⡒⠩⠦⣽⠁⠀⠀⣠⡞⠁⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠑⢄⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠦⢄⡉⠙⣿⣀⣀⡀⠠⠄⠐⠀⠀⠀⠈⠒⠄⣻⠆⣠⠾⠋⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠛⢁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣉⡓⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠋⣁⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣬⣉⣉⣛⡒⠒⠒⠒⠚⢛⣋⣉⣉⣤⣤⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁




⡿⠿⠿⠿⡿⠿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠉⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢿⣦⣀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⢈⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⢙⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢛⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣿⣿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠟⠛⠉⠉⠀⢀⣾⣿⡿⠃⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣀⣤⣤⣶⢶⣿⣿⠟⠛⠛⠛⢛⣛⡛⠛⠛⠛⠛⣛⣻⣿⠿⠶⢶⣦⣤⣄⣀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⣭⣄⣀⣀⠉⠁⠀⠿⢶⠆⠈⢩⡄⠀⠿⠃⠀⠉⠉⠻⠇⢀⣀⣀⣬⣽⡿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⠀⠈⠉⠙⠛⠛⢛⡻⠿⢶⡶⠶⣿⣷⠶⠶⠶⠶⠾⠿⠟⠛⠛⠛⠉⠉⠀⢀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⣦⣤⣤⣄⣘⣋⣀⡘⠛⠷⠈⠋⠀⠀⠸⠇⣀⣀⣀⣀⣤⣤⣤⡶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠄⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠠⣿⠿⠷⣛⣣⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠈⠀⠐⠐
⠀⠀⠉⠂⣄⣀⢀⣀⣀⣄⠀⠀⠉⠓⠚⠋⠉⠁⠀⠀⠀⢀⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠉⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠉⠀⠀⣀⡰⠤⠐⠀⠀⢀⢀⣤⣦⠄⠀⠀⠀⠀⠀⠀⢀⣠⡤⠄⣀⠀⠀⠄⠀⠀⡠
⠀⠀⠀⠤⢀⠀⠀⢀⡤⠀⣆⣀⣠⡤⣀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠡⠀⠀⠀⠀⠀⠀⠿⠞⠀⠀⠀⠀⠀⠀⠀⠙⢼⣬⠞⣧⣧⠀⢀⠀⠊
⠀⠀⠠⠄⠀⠀⠐⠿⠴⣶⣤⣤⣽⠷⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠘⠂⠼⠆⢰⡤⢀⠄⠠⠀⠀⠘⠿⠟⠀⠀⠀⠀⠴
⠀⢠⠘⠉⠀⠀⠉⠓⢄⠀⢀⡀⠀⠠⡀⠀⠰⣷⡛⠛⡻⣿⠁⠀⠄⠀⠀⠀⠀⠳⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂
⠀⠲⠢⠤⣄⡤⠴⠆⠖⠀⠨⡀⠀⢀⡈⠀⠀⠙⠿⣽⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣴⣶⣤⣴⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⡆⠠⠈⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⣤⣠⣤⣄⣄⣀⠀⠁⠀⠀⣀⣠⣤⣤⣤⣀⢀⠀⠀⠀⢀⠴⠀⠂⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠺⠿⠿⠟⠯⠿⠟⠟⠀⠀⠀⣈⠉⠉⠛⠛⠋⠛⡋⠀⠀⠀⠀⠀⠀⡀⣀⣤⡤⠀⠀⠀⠇⠁⠤⣀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⡀⠀⠀⠀⠺⠉⠀⠀⠀⠀⠀⠋⠉⠉⢰⠋⡓⠀⠀⠀⠑⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣁⣄⣀⣀⣾⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⣍⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⠺⠻⠛⠾⠳⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⣠⣀⣰⣦⣤⣤⣤⣤⣤⣤⣇⣀⣀⣤⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠨⠈⠀⠀⠄⠀⠀⠀⠀⠘⢿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠳⣿⣾⣿⣟⣽⣽⣭⣿⣿⣿⣧⣯⣽⣽⣯⣿⣿⡷⠚⡁⢺⡀⠘⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢁⣄⣀⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣠⣀⣂⣸⣀⠊⠂⡨⠀⠀⠀⠀⡔⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣤⣤⣌⣨⣡⣀⣌⣩⣃⣭⣿⣀⣸⣠⣠⣤⣤⣅⣤⣤⣽⣿⠋⠀⢸⡀⢰⡄⠀⠳⠛⡿⠄
⠀⠀⠀⠀⠐⠂⠀⣶⣤⡠⡄⠀⣹⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⢉⡀⡠⣾⣄⣼⠀⢐⡀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡸⠇⢹⡃⣠⣮⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣷⣿⢿⡦⠤⡃⣿⡸⡷⠀⢐⢢⡿⢿
⠀⠀⠀⢀⠀⠀⡇⠞⠛⠓⠀⠯⠽⠏⠈⠌⠋⠉⠉⠿⠄⠹⠯⠤⠼⠑⠉⠱⠀⠀⠈⠇⠸⠄⠀⠘⠋⠁⠛⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠘⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⡤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣀⣀⣀⣀⠤⠤⠤⠤⠴⠒⠒⠒⠒⠚⠉⠉⠉⠉⠁⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠩⠤⠤⠤⠤⠤⠤⠲⠶⠒⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⡀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⡄⢾⣀⠀⠠⣄⠀⣣⡀⣂⣸⢋⡔⢲⠄⡘⠉⠀⠀⣄
⠀⠀⠀⠀⠀⠀⢫⣻⡁⢈⢁⠰⡀⡸⢀⠀⡑⠈⣻⣮⣵⢃⠀⠲⠚⣀⣼⣿⠄
⠀⠀⠀⠀⠀⠀⠀⢯⠉⠉⠛⠛⠛⠲⠿⠾⠷⠶⠷⢿⣿⣿⣿⣿⣿⣿⡿⡗
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣟⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠬⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⣀⣽⡈⠁
⠀⠀⠀⠀⠀⠈⡉⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⢀⣀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡠
⠀⠀⠀⠀⠠⠼⠷⠦⡧⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⢀⠀⢠⠀⠀⠀⠲⣶⣷⣶⣚⣛⣒⣒⣒⣒⡒⣓⣒⣶⣶⣦⠀⠁⠀⢀⡀⠀⠀⢀⢁⠀⣀⣮⣁⣶⡄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⣿⣿⣹⣶⣭⣯⣭⣍⣏⣭⣍⣿⣻⣇⣀⠘⠀⠀⠑⡏⡉⣹⣠⡴⠋⠈⢳⣴⣉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣚⣲⣒⣻⣻⣿⣟⢻⣻⣻⣻⣿⢿⢷⠂⠀⠀⠀⡘⢻⢥⣤⣤⣤⡶⣿⣿⣿⠷⠦⠀⠄
⠀⠀⠀⠀⠰⢀⡀⠈⢙⡿⠿⠝⠯⠟⠹⠋⠽⠋⠿⠩⠝⠹⠿⣷⣞⡄⠀⠀⠀⠄⣸⣼⠿⠟⠏⠹⠏⠹⣏⢰⡀⡈
⠀⠀⠀⠀⢰⣿⣿⠞⠉⠀⡔⠋⠆⠀⢠⠚⠓⡄⠀⡠⠒⢢⠀⠈⠉⢠⠓⠢⣿⠛⠻⣦⣤⣀⠀⡀⠀⠻⠿⠗
⠀⠀⠀⠀⠠⠉⢀⡀⠀⠀⠁⢀⠀⠀⡄⠀⢀⣀⡀⠁⠀⢀⠀⠀⠀⠀⠀⠻⣽⣿⣁⠘⠛⠋⣌⠁⡄⣤⢈⡐⠂⠠⠃
⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠁⠀⠊⠀⡀⠙⠇⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠡⠀⠀⠀⠧⡟⠓⠂⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⠛⢿⠛⡟⢿⡟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⣟⠿⠿⢿⣿⣟⣿⣿⣿⣿⣭⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⣿⣿⣿⠟⠁⠀⠀⠉⠒⠤⠀⠁⢀⠤⠀⠐⠉⢹⠿⠻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣩⣴⣿⣿⣿⡏⠉⠉⠀⠑⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⢉⡷⠇⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⡉⣀⡒⠀⠀⠀⠀⠀⠀⠀⠀⢁⡤⠈⠉⠁⠀⠀⣼⠶⠿⣶⡄⠀⣠⣏⢻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡿⠻⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠰⠙⣿⡆⢁⣰⣿⡽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢟⣼⢿⣿⣿⣿⣿⣿⢿⢿⣾⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠹⠅⠀⠀⢻⣧⣄⠉⠈⠀⠸⣿⣿⣿⣿
⣿⣿⣿⣿⢟⣫⣾⣿⣿⣿⣿⡷⠤⠆⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣶⡿⢠⣾⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠲⠈⠀⠀⢀⣀⣀⣠⡄⠛⠃⠋⠀⠀⠰⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⢺⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣂⡀⡀⠀⢹⣟⣥⣦⡿⣾⡇⠀⠀⠀⠀⠲⣟⣿⣿⣿⣿⣯⣾⣿⣷⣾⡿⢿⣤⢾⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣾⢤⣼⣿⣿⠛⢿⠛⠀⡄⠀⢀⣤⣴⣺⣿⡿⣿⣿⣿⣿⣿⣿⠟⡿⣿⣿⣿⠿⢻⣿⣿
⢿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⢉⡹⣿⡋⠁⢸⡏⠀⢿⡀⠀⣇⠀⠓⠀⠘⣿⣿⣿⡟⣿⡿⠟⠉⢹⣿⣿⣿⠁⢻⠀⠘⣖⣼⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣾⣷⡿⢳⣦⣼⢣⠀⠀⢻⡄⡟⠀⢀⣴⡾⠿⠻⠿⠟⠉⠀⠀⠂⠈⢀⡁⠀⠀⣸⡄⠀⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣀⡋⣴⠻⣾⣿⣾⣿⠦⠁⠀⠾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⣫⣿⣯⣿⣿⣿⣿⣿⣷⣿⣿⡄⠀⠐⢷⡄⣻⣿⡀⠀⠀⠀⠀⠀⠀⡠⠒⢀⣀⡠⣿⣾⣿⣻⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣄⣀⣀⣿⣿⣿⣿⡾⠿⢿⣿⣿⡿⠦⣄⠀⠀⢹⣿⡟⠢⢄⣀⣤⠤⢾⣷⣭⣽⣿⣤⣿⣿⣿⣿⣿⣿
⢟⠉⠉⠀⠉⠙⠹⠛⠙⣿⣷⣌⣩⣿⣿⣿⠿⣏⣀⠀⠀⠘⠛⠛⠛⠀⠂⠀⠀⣿⠻⣿⡤⠤⠴⠶⠚⣿⣿⡟⠛⢿⠿⠿⠿⠛⣯⡿⠋
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠚⢛⣉⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣠⣄⡀⠀⠀⢀⣠⠴⢚⣋⣭⠤⠶⠖⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡛⢭⢼⠖⠗⢋⢻⡶⠞⣫⡵⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⠾⡖⠂⣍⣨⠷⢊⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣞⣉⣭⣥⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠤⠶⠶⠦⠤⠤⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⠫⢅⡶⠬⠖⡀⠵⢠⡤⢈⡓⠦⠄⣉⣙⠓⠲⢤⣄
⠀⠀⠀⠀⠀⢀⣠⢞⠚⠣⡼⢑⣩⣄⢘⡀⠱⡶⠀⠆⡈⢁⡤⠤⡄⠨⢙⠊⢂⡉⡳⣆⡀
⠀⠀⢰⡶⠶⠿⠷⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠓⠒⠒⠶⠶⠶⠶⠾⠿⢶⡆
⠀⠀⠀⠻⣔⠂⠒⠀⠒⠀⠂⠐⠂⠒⠂⠒⠀⠐⠀⠒⠀⠒⠂⠒⠀⠒⠂⠒⠀⠒⠐⠂⢒⡾⠁
⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠓⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣠⣤⣴⠶⡶⢶⣤⣤⣤⣶⢶⣆⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣴⠾⠋⣉⠩⠥⣀⡀⠰⠆⠀⠐⠂⠠⢤⣀⡙⠋⠙⠿⠶⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⢉⠀⢛⣼⡟⠛⠛⠁⣡⠀⠛⠃⠿⠓⢀⣤⡍⠉⠓⢠⠄⡶⣄⡁⢈⡛⠻⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠛⠟⣡⠤⠾⠑⢊⡵⣄⠈⠋⠀⠠⠶⠶⠀⠰⠆⠀⠈⣀⣠⣤⢤⡀⢠⣌⠙⠃⡈⢀⡉⢙⢻⣆⡀
⠀⠀⠀⢀⣀⣀⣀⣾⣿⣋⣐⣉⣘⣀⣘⣀⣈⣉⣡⣭⣥⣭⣤⣤⣽⣧⣤⣤⣬⣥⣤⣥⣤⣤⣤⣧⣤⣤⣬⣥⣀⣈⣁⣈⣀⣉⣻⣆⣀⣀⡀
⠀⠀⠀⠘⣯⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⠁
⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠿⠿⠟⠛⠛⠛⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠶⠶⠶⠿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠹⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣥⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠿⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⣠⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⠉⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣬⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣏⣡⣶⣶⡆⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣾⠿⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⣾⣿⣿⣿⣯⣍⣉⣀
⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢿⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀
⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠈⠁⢠⣶⣶⡜⠛⠛⠁⠈⠀⠀⠆⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠙⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠈⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣷⣦⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⢠⡊⢀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠨⠁⢺⡍⠃⣑⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠂
⡀⢀⠲⠁⠠⠀⠀⠀⠀⠚⠉⠀⠀⠀⠌⠀⠀⠑⠛⠋⠀⠙⠁⡀⠆⢀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠺⠉⠑⠂⢄
⠁⠂⠐⠊⠀⡀⠀⠂⠭⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠂⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠈⠙⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠆⠛⠛⣰⡄
⠀⠀⠀⠀⠀⠀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠉
⠰⠦⢒⢄⠄⠀⠒⠤⢄⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠒⠊⠺⠥⠼⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡄⠀⠄
⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⣤⠐⡀⠀⠀⠈⠀⢁⠀⠀⠀⠀⠰⠌⠂⠀⠀⢀⢡⡀⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢠⠠⠂⠀⠀⣀⠂⠀⢰⡀⠐⠄⠀⡸⠀⢀⡇⢀⡜⠀⠈⣆⠀⢸⠆⠃⡀⠀⠀⠀⠀⢀⠁⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠀⠄⡁
⠀⠀⠀⠀⠀⠐⠶⠄⠀⠀⠀⠀⡄⠀⠀⠀⡀⣠⠀⠓⡄⠀⠀⡠⠈⠲⠀⠀⢀⣉⠑⣆⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠛⠀⠀⠇⠀⠀⡇⠀⠀⠆⠀⠈⠂⠀⠸⡀⠀⠀⠐⢊⡉⠠⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢆⠀⠀⠃⠀⠀⢇⠀⠠⡀⠀⠀⠢⠀⠀⡂⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶
⠀⠀⠀⣠⢀⠀⠈⠑⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡴⠿⠟⠛⠉
⣀⣈⣴⡟⠀⠀⢀⠀⠄
⠛⠋⠁⠀⠀⠈⢀⠀⠠⠄⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠤⢤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⡤⠠⠤⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠠⣀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠜
⠀⡀⠀⠀⠀⡾⠀⠀⠀⠀⠈⠁⠀⠀⠰⠀⠐⠀⠀⣼⠀⠀⠀⠀⠀⠙⠀⠀⡠⠜⠂⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⢀
⠐⢢⣤⣁⢀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⣠⡤⠐⠁⠀⠀⠀⠀⠀⠘⠻⠟⠋⢀⣀⣠⣶⣾⣯
⠀⠈⠛⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⣀⠄⠉⢠⡒⢦⠟⠻⣉⢀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣋⣧⠿
⣀⣀⣈⣀⣀⣁⣀⣀⣀⣒⣀⣛⣀⣀⣨⣀⣀⣀⣀⣀⣀⣈⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣻⣿⣿⣍⣐⣋
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣶⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡏
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠒⠉⠥⢿⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡉⠻⠓⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣳⣿⡄
⠀⠀⠀⠀⠀⣴⢾⡶⣧⠸⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡾⠃
⠀⠀⠀⢠⡀⠁⠀⠺⢖⠑⠤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠉⢷⣄⣀⣤⡒⣷⠞⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠘⠗⠀⠈⠀⢹⠛⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢠⣀⡀
⠀⠐⠈⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣴⡷⢂⠀⠀⠀⠂
⠀⠑⠉⠁⠀⠀⠀⡠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠢⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⢈⠀⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⡙⢀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠄⢸⡄⠀⠀⠀⡴⠇⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠄⠲⡄⢀⠀⣸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡉⠠⠆⠀⠀⠈⠳⡀
⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⡆
⠀⠊⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠁⠀⠠⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡶⠿
⡉⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢦⡠⠈⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠁⢀
⠁⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣁⡀⠐⠋⣠
⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣙⢉⠉⠛⠛⠉
⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⡦⡠⢀⠀⠀⠀⢀⡠⠄⣒⣶⣶⠒⠠⢀⠀⠀⠀⢠⠤⠴⠴⠖⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢄⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠈⠡⠇⠰⠈⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠁⠎⠀⠄⠁⠀⠀⠸⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣯⣉⣩⣩⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻
⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⣄⠠⠤⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⣬⠇
⠀⠀⣠⡼⠁⠀⠀⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣶⡶⠃⠀⠀⣺⠃⠀⠀⠀⠀⣠⡾⠃⠀⠀⠄⢤
⠀⣴⠏⠀⠀⡀⡞⢡⠈⣲⡄⠀⠀⠀⠀⢤⣀⣀⣉⣴⣇⠀⠀⠀⠀⠀⠛⠿⣿⣿⠟⠀⠀⠀⠉⠀⠀⠀⠀⣰⡏⠀⠀⡈⣞⠡⠬⣓⡄⠀⠀⠀⠀⢠⣀
⠈⠃⠀⠀⠀⣿⣷⣗⠛⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⣿⣷⠛⣻⡇⠀⠀⠀⠀⠠⣿
⠀⠀⠀⠀⠀⠻⠿⠿⠶⠟⠁⠘⣷⠀⠀⠀⠉⠉⠉⠁⠀⢀⠠⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠶⠟⠁⠐⢳⡀⠀⠀⠉
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⣶⣌⣐⣐⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢿⣉⣿⢏⠉⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡦⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆⡐⠐⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠘⡧
⢀⣙⣁⡴⠀⠀⠀⠈⢻⠄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠣⢾⡀⠀⢸⡇⢩⣿⡿⢛⡄⠔⠀⠀⠀⠀⠀⠰⣄⣀⣘⣃⣤⠀⠀⠀⠀⠻⡄
⢸⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠳⠈⠀⠀⠙⠾⠿⣇⡂⢠⠍⡕⡀⠀⠀⠀⢠⣾⣿⣿⣿⣷
⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣳⣾⣿⡇⠀⠀⠀⠀⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠿⢿⡿⠿⠃
⠀⣀⠀⣀⠐⠛⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠁⠱⣆⠢⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠛⢀⠄
⢀⣉⡔⠛⣋⡙⢣⣀⡙⣃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢇⠀⣉⠉⢘⣂⠀⠀⠀⠀⠀⠀⠀⣀⡐⢠⣀⣉⡡⠛⢋⡙⠻⣀⣈⣋⣰
⠈⣭⡁⢠⣬⣤⣾⣿⣭⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠙⠀⠀⠀⠀⠀⣷⡤⣬⣤⠐⠋⢩⡁⠠⣤⣤⣾⣿⣭⣿⡿
⢠⣧⣴⣿⣿⣿⠟⠈⠉⠁⠀⠀⠀⠀⠀⠀⣄⡐⠊⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣾⡟⣶⣤⣤⣴⣞⣿⣿⡿⠈⠉⠁⠀⠀⠀⠀⠀⠀⣤
⢸⣿⡿⠏⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠉⠉⠙⢿⣿⣿⡿⠟⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢼
⠀⠁⠀⠀⠀⠀⠀⣐⠷⢕⢄⡀⠀⠀⢀⠤⢘⣛⣻⣛⣛⡀⢄⡀⠀⠀⠰⠖⠶⠶⠒⢶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢷⠖⠤⡀⠀⠀⢀⠤⢈
⠀⠀⠀⠀⠀⠀⠈⠰⠃⠘⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠆⠁⠀⠀⠸⣿⣿
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣦⣉⣱⣤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳
⠀⠀⠀⢠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⣄⠀⠄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢠⣼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⢿⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣷⡀⢠⠐⣷⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣄⠀⠀⣾⣿⣿⣿⣿⣿⣁⣿⣾⣿⣿⣷⣿⡿⣂⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣼⣥⣧⣾⣿⣲⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⠋⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⠊⢻⡇⣿⣿⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣿⡿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣀⣠⣼⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⢀⣧⣲⣿⣘⣿⣿⣿⣗⣛⣿⢹⣿⡿⣿⣟⢻⣍⢉⣯⣹⣽⣿⣿⣿⢞⣿⣿⠟⣿⣷⣿⡿⠡⠿⠃
⠀⠀⠀⠀⠀⠠⣻⣿⣿⣿⣿⣿⣿⣿⡼⣿⠇⣨⣿⣿⣼⣿⣿⣿⣿⣿⣏⢻⢿⣶⡶⠟⠁⠤⣤⡭⡥⠄
⠀⠀⠀⠀⠀⠈⠛⠻⠟⠉⠃⠈⢹⣏⣷⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⡍⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣀⢐⣷⢶⣾⣬⢻⣿⣿⠾⢿⣿⣿⣿⣿⣉⣿⣧⣀⢺⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⣀
⠀⠀⠀⠀⣀⣸⣷⣾⣿⣿⣿⣿⣿⣿⣽⠇⠀⠀⢩⣿⣿⣿⣿⣷⣷⣦⣾⡛⣿⡀⠀⠀⢀⣠⣄⣠⣶⣄⣾⣿⣱⣿⣿⣿⣼⣿⣴⣿⣤⣄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠛⠉⣤⡙⣿⣧⡴⠞⠉⠉⠉⠛⠋⠉⠉⠛⢿⣿⣤⡙⢦⢠⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢂⡸⠁
⠀⠀⠀⠀⠘⠛⠛⠭⣬⠿⠂⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠂⣩⣿⣿⣿⣿⣿⣿⣿⡿⠋⣩⠯⣾⡿⣿⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣿⣿⡿⠿⠛⠻⠟⠐⠦⠼⠋⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣿⣿⣿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⡀⢀⣴⡾⠛⣋⣉⣹⣧⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢠⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⡀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣫⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢻⣶⣦⣒⠉⠉⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⣄
⠀⠀⠀⠀⠀⠐⠒⠻⠿⠿⠿⠿⠿⠛⠻⠟⠿⠟⠛⠻⠿⠿⣿⣿⠿⣿⡿⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠉⠙⠓⠒⠒⠂

⠀⠀⠄⠐⠀⠀⠀⢠⣶⠂⣠⠆⠀⠀⣴⣾⡿⠿⠟⠒⢶⣾⡄⢀⣼⣿⡷⠶⡿⣿⡇⠀⠀⣼⣿⠛⠛⠿⢿⡟⠀⢀⣀⣼⣷⣷⡀⠀⠀⠀⠀⠀⠒⠂⠐
⠀⣄⠀⠀⠀⠀⠀⠸⣿⣾⣯⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⣿⠃⠀⢸⣿⣬⣿⣿⠁⠀⠀⠀⢾⡿⠿⠇⠀⠀⠀⠀⢻⣿⣯⡈⢿⣧⠀⠀⠀⠀⠀⠀⠀⣌
⣈⣿⣧⣄⠀⠀⠀⠀⢿⠁⢹⣧⠀⠀⢠⣿⣆⠀⠀⣀⣠⣿⡆⠀⠀⣿⠋⠉⠻⣦⡀⠀⠀⣼⣇⣀⣀⣀⣀⡀⠀⡼⠁⠙⠛⠿⢿⡄⠀⠀⠀⠀⣠⣾⡿
⠀⣭⣯⣻⣷⣦⣀⠀⠈⠀⠀⠛⠁⠀⠀⠘⠉⠉⠛⠛⠋⠉⠁⠀⠀⠈⠀⠀⠀⠀⠉⠂⠀⠉⠙⠋⠉⠉⠀⠀⠀⠁⠀⠀⠀⠀⠘⠀⠀⢀⣤⣼⣿⡿⣷
⠐⠛⠛⠀⠁⠀⠈⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣹⣶⣶⣤⡄⠀⢀⣀⣀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⣤⠀⠀⠀⠐⠛⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡽⠛⠁⠀⠈⢻⣿⣿⣿⣿⡿⠂⠉⠈⣤⣤⣤⣭⡈⠉⠛⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡅⠀⠀⠀⠀⠀⣴⡿⠟⠋⠉⠀⣀⣠⣼⣿⣧⣿⣿⣇⠀⠀⠀⠈⠛⠛⠛⠀⠀⠘⠀⠠⠜⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡦⡤⠴⠀⠠⠉⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡋⣍⣉⡍⠛⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⠿⣿⡼⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⢻⠋⡛⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣽⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣥⡾⠋⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋⠍⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠂⠀⠀⠀⠀⠐⠆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⢉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣴⣄⠀⠀⡀⠀⠀⢨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡟⠿⢷⡦⣝⣦⡀⢿⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⡾⣶⡝⡻⠍⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣸⣯⢭⢹⡤⢉⣂⡀⢀⠋⣀⣀⣀⡤⣴⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⣀⠀⠀⡐⠘⠛⠛⠰⡀⠀⠀⠀⡤⣐⣀⣀⣀⠤⢄⡀
⠀⠀⠀⠀⣴⣿⣷⡄⠀⠀⠀⠐⡇⠸⢪⠞⠀⠈⠀⠠⠤⠤⠤⠼⠄⠀⠘⡟⠛⠿⠿⠿⠿⠷⢾⠆
⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⢧⡴⠁⠀⠀⠀⠀⠠⣀⡠⡄⠀⠀⠀⠀⠙⢦⣀⠀⢠⣀⣠⠟⣀⡀
⠀⠀⠀⠀⢿⣿⣻⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⢰⠈⢹⢧⡽⣽⢢⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠐⠁⢇
⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⢧⡤⠘
⠀⠀⠀⠀⣿⢿⣻⣷⠀⠀⢠⠊⢣⠔⡆⠀⠀⠀⢀⠄⠀⣄⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠈
⠀⠀⠀⢸⣿⣿⢟⣿⠇⠀⠈⢆⢀⠞⠀⠀⢀⣴⣾⡿⠿⢾⣦⡄⠀⠀⢀⠊⣰⡶⡿⡷⣦⠠
⠀⠀⠀⠀⢹⣾⠏⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠛⠁⠀⠈⠋⠀⠀⠀⢀⠀⢿⣿⣿⣶⠏
⠀⠀⠀⠀⠀⠉⢀⣄⢤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⢷⣤⣂⠀⠀⠀⠀⠀⠢⠀⠉⠉⠁⠀⠀⠀⠀⡀
⠀⠀⢀⢒⡐⢶⣧⣤⣧⣿⡇⢀⣀⠀⠀⠀⠠⠁⠀⠎⣼⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡠⠃
⠀⠀⡄⢪⣿⢸⣿⠓⢻⣿⢁⠀⢿⣷⠀⠀⡆⠀⢀⣼⠏⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⢀⠂⢉⠼
⠀⠀⢣⠑⢃⣾⡟⠒⠛⡇⣾⡇⣿⣿⠀⠀⠙⣸⣿⣥⣶⣶⡮⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⣰⠕⠊⠁
⠀⠀⠀⠉⠉⠉⠀⠀⠀⢃⠙⢡⡿⠃⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⣠⠞⣁⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⣿⣿⠀⠀⠀⠾⠗⠋⠉⢀
⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠁⠿⠿⠀⠀⢀⢤⠴⠒⠉⢁⠠⢀⣈⠐⠠
⠀⠀⠀⠀⢏⠛⡹⠃⢀⢄⣄⢀⠤⠒⡄⠀⠀⠀⠀⠀⠁⠀⠀⠐⢡⢁⠀⡀⠂⣀⣀⡁⠀⡃⠀⠀⠊
⠀⠀⠀⠀⠈⠛⠁⠀⢻⣢⠀⡏⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⢄⠀⠀⠀⠉⠉⠁⣠⠥⠒⣡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠕⠀⠠⠄⠄⠠⠐⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⣀⣀⣀⣀⣀⠈⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⡤⠊⠀⣠⡴⣊⣩⣭⣤⣶⣦⢬⣭⣳⣤⡀⠈⠳⣄
⠀⠀⠀⠀⢠⡞⠰⣶⣾⢽⠟⣿⠅⠀⡇⠆⢘⠀⠈⢹⠘⢿⣦⡀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⢀⡟⠀⣸⣿⢿⣜⢀⣻⡀⠀⡇⠀⢸⡀⠀⣌⠀⢈⠁⣷⡀⠘⣇⠀⠀⠀⠀⠀⠀⣠⠏⠀⣸
⠀⠀⠀⢸⠇⢠⣿⡿⡿⡿⠣⣓⠵⠜⢰⣔⣿⠦⣠⣬⣧⣬⢘⠈⣧⠀⢹⠀⠀⠀⠀⢀⡴⠃⠀⢠⡏
⠀⠀⠀⢸⠀⠘⣿⠁⡜⠀⠀⡇⠀⢸⠉⠀⡟⠋⠉⡛⠉⣿⠘⠃⠰⠀⢸⡆⠀⣠⠔⠋⠀⠀⠀⢸⡃
⠀⠀⠀⠸⡆⠀⣿⠀⣇⠀⢸⠁⠀⢯⠀⠀⡷⠀⢰⡄⠀⡌⢀⡀⠆⠀⣸⢃⡞⢁⡤⠒⠒⠢⡀⢸⡇
⠀⠀⠀⠀⢻⡀⠈⣷⣰⣴⣾⣂⢺⣿⣦⣾⠿⠶⣾⣼⣷⣗⣽⡰⠀⣰⡿⣼⠀⡎⠀⠀⠀⠀⠠⠀⡇
⠀⠀⠀⠀⠈⢳⡄⠈⢏⠈⣿⠷⢛⣫⣤⡶⢶⣶⢶⣶⣦⣅⡛⢷⢶⡿⠁⢻⡀⠣⡀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠙⢦⣠⠟⣡⡾⠛⢻⠃⠀⣜⠃⠠⠉⠠⠇⠘⠒⢝⢻⣷⡀⠻⢤⣈⣀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⣸⠋⣼⡿⠀⣠⠓⠄⡈⠀⠉⠃⠠⢄⠀⠀⠀⠂⠐⡙⣷⡀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢰⠋⣾⢿⡀⠀⠁⠠⢀⣀⠖⠒⠤⠂⢀⡌⠀⡐⠁⠀⢷⠀⣧
⠀⠀⠀⠀⠀⠀⡟⢸⣷⣄⠈⠐⠠⠀⠀⠈⠀⢠⣥⣤⡐⠀⠬⠓⠄⣀⡀⣷⢹
⠀⠀⠀⠀⠀⠀⡇⢸⣇⠍⠀⢠⠀⠀⡰⢴⣶⣷⣞⣋⣻⣷⠦⢤⡬⠀⠝⢻⢸⡇
⠀⠀⠀⠀⠀⠀⢿⠈⣿⠀⢠⡁⠀⠸⢷⣤⢄⡀⡈⠉⢻⠏⠀⠀⠁⠀⣤⡏⣼
⠀⠀⠀⠀⠀⠀⠘⣧⠸⣦⡀⠈⠐⠠⢤⠄⠀⠈⠁⢀⡌⠀⢀⠞⠀⣰⡞⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡙⢧⡲⠀⢠⠊⠀⠠⠃⠠⠞⠀⠀⠉⠑⢲⠞⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣉⠐⠧⠀⠀⠒⠤⣀⠀⣈⡶⠒⢂⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠦⣤⣄⣈⣉⣉⣥⡴⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⣒⣉⠉⢩⣉⣉⣉⣛⡒⠒⠢⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣉⠤⡖⡏⡼⡰⢠⢠⢀⠀⠀⠀⠈⠉⠒⠢⠤⢍⡉⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢁⢴⠏⡏⡜⡜⡸⢱⢁⢃⢎⠎⡜⡔⣠⠀⠀⠀⠀⠀⠀⠈⠙⠢⢌⠑⠢⣀
⠀⠀⠀⠀⠀⠀⡠⠊⢀⠔⠇⡜⡸⡐⡐⢰⢡⢃⣇⣎⣼⡼⠴⠵⠧⣧⣆⣄⣀⠀⠀⠀⠀⠀⠀⠉⠲⣌⠑⢦⡀
⠀⠀⠀⠀⢠⠞⢀⡔⡙⡜⡸⢰⠱⣱⠵⠓⣋⣉⣒⣒⡒⠒⠒⠒⠖⠒⠂⠀⠈⠉⠛⠶⣤⣀⠀⠃⠆⠈⠑⢄⡉⠢⣤
⠀⠀⠀⡴⠁⣠⢻⢡⢣⢱⣡⠗⣋⣀⣒⣒⣒⣒⣒⠐⠂⠐⠒⢂⣀⣀⡀⢀⠎⢭⡍⠒⡄⠘⢓⢦⡘⠀⠀⠀⠙⢦⠈⠻⡥⠤
⠀⠀⡜⠀⡔⡇⡎⣎⡶⠋⣑⣒⣒⣒⣤⣔⣉⠀⠂⠀⠀⠀⠀⢮⡐⠓⣨⠀⠳⣤⣸⠦⠃⠀⠈⠂⠉⠢⣄⠀⠀⠀⠑⡄⠘⢯⠍⠥⠄
⠀⡜⠀⣼⢃⢳⡼⠋⠀⢀⠀⣀⣰⡲⢒⠄⢺⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢰⠉⠏⠿⢱⠄⠶⠀⡔⣈⢑⢮⠳⢄⠀⠀⡌⢆⠈⢯⠭⠭⠭⠠
⢰⠁⡜⠸⣠⠞⠠⠭⠥⠤⠤⠄⠒⠊⠑⢒⠗⠒⢤⠀⠀⢠⢊⣁⢉⡒⡌⠛⠒⠀⢚⣛⠀⢘⣂⣈⠓⠓⠊⠀⣀⡑⢄⠳⠈⠆⠈⢯⡉⠉⣀⣐⡀
⣼⢠⡇⣧⠋⠬⠩⠁⠀⣭⠍⠉⠁⠁⠀⢏⠛⠀⣣⢇⠀⠈⢮⣭⡬⣔⣅⠄⣀⠲⠀⡬⠀⣏⠆⠬⣱⢠⡀⠀⠀⠬⠀⠳⡉⢸⣀⠸⡖⠒⢒⣒⣂
⡇⢸⣧⠏⣒⣒⣒⣒⣒⡒⠂⠀⠀⠀⠀⠀⠈⢛⡣⠋⠀⢀⠀⠋⠙⠋⠀⠀⣉⣀⣀⣐⠂⠀⠹⠏⢁⡔⢂⠐⡲⡄⠀⠁⠙⣜⠁⠈⡧⠤⠤⠤⠤
⡇⢸⣿⢐⡒⠒⠀⠤⠤⠤⠀⠀⡠⠒⠤⢄⠀⠀⠀⠠⠎⡫⣁⠒⠠⣆⢵⠼⣠⡐⠯⢊⡗⠛⠀⡴⡘⣾⣉⡱⢇⡼⠀⠀⠀⢸⡇⠀⣟⣉⣉⣉⣉
⣧⠸⡇⠤⠤⠬⢭⠁⠈⠁⠀⠀⢇⠀⡬⢑⡇⡄⠀⠀⠸⡫⣀⡹⠸⡼⠞⢃⣀⡭⠉⣁⠤⢄⡀⠈⠊⢉⢽⣏⠛⠢⡀⠈⠛⢰⠀⢸⡯⠤⠤⠤⠤
⢽⣆⠱⡠⠭⠍⣐⣒⣀⠀⠀⠀⠀⠉⠉⠙⠊⠀⠀⠀⠀⣬⠒⠒⡟⠉⠙⠢⡀⠀⡜⠑⠶⠰⣌⢣⢀⡸⣀⠀⠺⣣⠇⠀⠀⣜⢠⠇⣟⣀⣀⣈⣉
⢸⠘⢆⠑⣄⠒⡒⣂⣀⣀⣀⠀⣀⣀⣀⠀⠀⠀⠀⡠⢀⡤⠼⣇⣹⢟⣀⡴⢁⣀⠳⣔⡇⣸⡭⠊⠈⠪⠮⠉⢉⣁⡀⢀⠞⢀⠯⣂⡗⠒⠒⠀⠤
⢸⠀⡈⠣⡈⠣⡐⢒⣒⣀⠀⢸⡷⠀⠬⣳⠀⠀⢡⡅⡏⢶⠄⢠⡈⢢⠀⢀⣿⠎⣑⠄⠀⠀⠀⠀⣠⡄⠀⠒⠈⠀⣠⠋⣠⢏⣘⣼⣉⣉⣉⣉⣉
⠈⡆⢸⡐⣙⢦⡈⠢⣄⠤⠄⠀⠉⠀⠨⠕⠁⠀⠈⢗⠕⠦⢄⡚⠥⠃⢰⠉⠾⠙⡄⡤⢚⠀⣠⣄⢤⠀⠀⠀⣠⠞⢁⡼⣻⣿⣷⡗⡒⠲⠶⠶⠏
⠀⢳⡀⢣⡐⠒⢙⣯⣘⠙⠫⣍⡂⠀⠀⠀⠀⠀⠀⠀⠑⠊⠒⠲⠄⠀⠀⠉⠀⠉⡸⣀⠻⠂⣦⠔⣼⣦⠴⠂⣠⠴⡄⣶⣾⢿⡿⠭⠭⠭⣭⡍⠃
⠀⠀⠱⣄⠱⣅⠒⣀⠈⡓⠢⢄⣉⠓⠲⠤⣴⣫⢭⡑⠲⣀⠀⠀⠀⢤⠀⠀⠀⠀⠛⢦⣭⡡⠔⠚⢉⡠⠔⡋⡅⡜⡐⡹⢁⡞⠒⢒⣒⣒⠂
⠀⠀⠀⠈⠢⣈⠳⢄⡺⠯⠀⠀⠈⠙⠒⠦⢄⣈⠍⠉⣉⠉⠒⠒⠒⠒⢒⡶⠆⠉⢉⣉⣠⠤⠖⢪⢁⠆⡜⡜⡴⣵⠟⣱⠯⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠈⠳⢄⡉⠲⢄⡉⠒⠊⠀⣀⠀⠈⠉⠉⠛⠒⠒⠒⠒⠒⠒⠛⠋⠉⣡⡦⡲⡲⡡⢣⢂⢎⢜⡾⢖⣡⣞⣛⣛⣀⣘⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡈⠓⠮⢍⡉⠩⠍⠁⡠⢴⡂⠔⠁⠤⠀⠀⠀⠀⢠⢞⢝⠕⡕⡱⣡⡎⢋⣩⡴⠛⠐⢒⣒⣒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠈⠉⠒⠢⠤⣄⣀⣒⣓⡒⢂⠠⠀⠀⣴⣡⣯⡾⡖⢛⣡⣴⣞⣛⣒⣒⣒⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠤⢄⣀⣀⠐⠀⠩⠉⠝⢑⣲⣫⣥⣥⣖⢚⡃⠀⠠⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠓⣒⣒⠒⠒⠂⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢀
⠀⠀⠐⠀⠀⣀⣴⣀⣀⣀⣰⣀⠀⠀⠀⠀⠀⠪⢂⣤⣤⠤⢈⠀⠂⠀⠀⠀⠀⢀⡜⠁⠀⢸⡀⠨⠀⢀
⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠈⢁⡄⠀⢀⢄⢠⡁⢈⠿⢀⣀⡇⠀⠠⠀⠳⣀⠼⠍⣛⡲⣼⠀⠀⠠⠄⠁⠠⠈
⠀⠀⠀⠀⢈⣁⣇⣭⣹⣸⣀⣇⣋⠀⠀⡀⠁⢈⣏⠉⠀⠀⢸⠓⡄⠀⢀⠴⡟⠐⠁⠒⠬⣻⡄⢀⡀
⠀⠀⠀⠐⠉⠉⠉⠙⠛⠛⠉⠉⠉⠓⠀⠰⠆⠓⡺⣷⡀⢲⠏⢌⠁⠀⠀⠀⠹⣄⠀⣈⡰⠟⠦⠑⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠾⢷⠀⢰⣿⣷⠀⢼⠿⠄⠀⠀⠀⡘⠀⠈⠿⣏⣀⣈⡂⠀⠀⠈⡍⣿⢟⠅⠀⠸⠀⠠⠃⠒⠂⠀⠦
⠀⠔⡆⠀⠐⠒⠠⢤⠀⠀⢠⠀⠂⠀⠀⠀⠀⠉⠙⠒⠂⠫⠸⠗⠃⠈⠚⠄⣥⠖⡃⠀⠀⠀⠀⠀⠐⢀⢀⠀⡀
⠀⠘⢀⠈⣔⣢⠈⢰⠀⠀⠀⠀⢰⠀⠀⠐⢂⡀⢠⢰⣀⢠⣄⣀⢀⡄⠀⠀⠀⠈⠁⠂⢀⡀⠱⢂⡀⢀⡰⡃⢁
⠀⠀⡌⡀⠛⠛⠠⢸⠀⠀⠀⡤⣊⡤⠀⠀⠈⠉⠀⠈⠉⠉⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⢆⠰⠂⠗⠇⡈
⠀⠀⠠⠀⠀⠀⠀⢸⠀⠀⠀⢄⣛⢃⠄⢀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⡀⠀⢀⣈⣁⡀⠀⠀⣡⣌⣉⣉⣠⡇
⠀⠀⠰⢠⠀⠀⠀⢸⠀⠀⠀⣴⡄⠀⠀⣾⠉⣽⢩⡝⠉⣽⠹⣿⠱⠹⣿⢀⠀⠀⠀⠀⠀⠸⠅⣄⣠⣄⡇⠿
⠀⠀⠀⠸⠤⠤⡠⠚⠀⣠⣾⡟⠀⠀⠀⠙⠺⠾⠶⢾⡶⠾⠮⠿⠿⠷⠛⠠⠆⠀⠀⠀⠀⠀⠄⠀⣀⡄⠀⣀
⠀⠀⠀⡇⠀⠀⠀⣠⢔⣯⠟⠀⠀⠄⢐⠀⠀⠀⢀⣾⠖⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠩⡅⣼⣴
⠀⠀⠀⠧⠀⠀⢪⡵⠛⠁⣀⡠⣰⠾⠍⠿⠿⠿⠿⠇⠀⠀⢳⠬⣈⠇⠀⠀⠎⠁⡾⢀⠄⠀⢄⠀⢋⠇⡱⢼
⠀⠀⠀⠀⢠⣄⠀⠀⢀⠔⡡⠊⠀⢧⣀⠀⠀⠀⢀⠂⠀⠀⠀⠀⡑⢢⠔⡤⠴⠶⡄⠀⡅⠉⢰⠁⠀⠀⢿⢻
⠀⠀⠀⢀⠀⢻⠣⡀⠘⠛⠒⠛⡛⠛⣿⣷⡶⠶⠟⠛⠛⠁⠀⢰⡋⠉⢹⢷⣀⡀⠃⠀⣄⢀⡐⡇⠀⠀⢸⠁
⠀⠀⠀⠀⠁⠄⠱⡙⢄⠀⣠⠎⠈⢮⠀⠀⠈⡙⠀⠀⠀⠀⠀⠀⠓⠀⠘⢀⡤⠀⠀⠠⠸⠿⠥⠁⠀⠀⠈
⠀⠀⠈⠉⠄⢀⢠⠑⠌⠁⠃⠄⣀⣨⠂⡤⠎⠒⠂⡆⠀⢀⠀⠀⠀⠀⠀⠀⢰⣤⠄
⠀⢠⡀⠢⠀⠀⠙⠁⠲⢤⡂⠉⠉⣸⠒⡗⠦⢤⠤⠗⠁⢢⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣿⣿⣶
⠀⢀⣀⠈⣄⠀⠀⠀⠐⠀⢽⡀⢴⡁⠀⡷⡀⡠⠃⡀⠚⡡⠮⠤⡀⠀⠀⠀⣾⣿⣿⣶⠀⠿⠿⠛⠛⢰⣶⣶⣦
⠀⠈⠀⠄⠉⠀⠤⠄⠬⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⠁⠜⠀⠁⠀⠀⠀⠉⠙⠛⠃⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⢸⣁⡀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢰⣤⠄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣀⡗⠀⠀⠘⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣿⠏⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡆⠀⠀⠘⢧⡀⠀⠀⢀⡤⠟⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠃⠠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡉⠀⠀⠀⢀⣀⡗⠀⠀⠀⠓⣆⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡆⠀⠀⠀⠀⠀⠀⠀⠠⠴⠞⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡞
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣉⡤⠖⠒⠲⢤⣀⣀⣀⣀⣀⡴⠚⠛⠓⢦⣀⣀⣼⠀⠀⣼⣁⣀⣀⡀
⠀⠀⠀⠀⡿⠿⠯⠭⠭⠤⠼⢥⣤⠄⢤⣬⣧⣤⣤⣤⣼⣥⣤⣤⣤⣤⣷⣤⠧⠤⠼⠧⠤⠭⠭⠿⠟⢷
⠀⠀⠀⠀⡇⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣸
⠀⠀⠀⠀⣷⠀⡞⠉⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⢹⠀⡟
⠀⠀⠀⠀⢹⡀⠹⠤⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢦⡴⠚⢲⡀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠞⢰⠇
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠘⣆⠀⢰⠋⠻⡄⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⡴⠁⠀⠀⠀⠀⠀⠀⢰⠋⠛⡆⢀⡞
⠀⠀⠀⠀⠀⠀⠈⢧⡈⠲⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⢡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣀⠀⠀⠀⢰⣋⣳⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⡇⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡁⠀⠀⠀⠀⠀⠀⠀⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠠⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⡘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⡀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠏⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠂⢀⠌⢂
⠀⠀⠀⠀⠀⠀⠀⢀⡃⠸⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⢀⡯⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠸⠯⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢸⠆⠐
⠀⠀⠀⠀⠀⠀⠠⡿⠄⢘⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⡔⠀⣠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⢘⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣠⣟⠂⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡀⠂⠶⢆⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⣄⡀⠀⠀⠤⠆⠀⣠⠎⠄⠩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⢰⠀⠀⠓⠘⢗⣦⢤⣤⠀⠘⠁⠀⠀⠀⠀⠀⠀⡿⠖⠛⢃⡼⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⡴⠴⣯⠀⠀⠀⠀⠀⠀⠀⣀⡴⢤⡄⠀⠀⠀⠀⠀⢁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠤⣀⠀⠀⠀⠀⠀⠀⠒⠔⠀⠀⡀⠁⠀⡀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠒⠙⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣶⣴⣷⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⣤⡀⣤⠀⠅⢿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠒⠊⠛⠿⣿⣯⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⡀⠀⣴⠒⠒⣾⣿⣿⣿⣟⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⢸⡟⠛⠙⠛⢿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡀⠀⠀⠀⠘⣿⣿⣿⡏⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣆⠀⣀⣴⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡽⠿⠟⢒⣿⣿⣿⣿⢟⢳⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢛⣿⠛⠹⠁⠃⡹⢏⡿⢟⠻⣅⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⢾⠁⠈⣷⢮⡛⢿⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠸⣄⠻⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⡿⠃⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⢤⡑⠀⠈⠀⢠⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⡤⠀⠀⠀⠀⡈⢻⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⡒⠀⡀⠀⠂⠐⡇⠘⠀⠆⠀⠀⠀⠀⡂⠀⠀⠀⠈⡀⠀⠀⣦⠃⠀⠀⠀⠀⠀⢪⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⠀⠀⠀⠩⢅⡁⠲⡄⣤⠁⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠻⡀⡀⢸⡄⠀⠀⠀⠐⠲⢼⣿⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢅⡀⠈⠀⠀⠀⠠⠭⢁⠻⣿⠀⡟⠀⠀⠀⢀⡄⡸⠑⡀⢀⠀⠀⠀⠁⠁⠈⡧⠀⠀⠀⠀⠀⠀⠘⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠉⠀⠴⠒⠒⣋⡷⣷⣯⠀⠀⠀⠀⠰⠋⠁⠃⠁⠀⠀⠁⠀⠀⠀⡐⠶⠓⠲⠄⠂⢠⠠⣾⡦⠻⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⣀⠈⠻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⢠⣄⠀⠀⠀⠀⠀⠀⢡⠍⠘⣷⠘⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠀⠀⠈⠑⠲⠌⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡀⢠⡖⠀⠈⣱⣦⣤⣄⡀⠀⣤⡀⢸⣧⡃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⣬⢦⣤⣤⣤⣀⣀⣀⣁⣬⡹⣷⠞⠷⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⠻⢳⣿⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠔⠲⠊⠉⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣟⠁⠉⡉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀
⠀⠀⠀⠀⡎⠉⠁⠀⠀⠂⠒⠐⠒⠀⠀⠈⠢⠎⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠑⠴⠁⠀⠀⠀⢀⣤⣤⣤⣀⠀⠐⠊
⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠐⠚⠛⢳⣦⣌⣿⣿⡆
⠀⠀⠀⠒⠓⠓⠐⠂⠒⠐⠀⠀⠂⠓⠀⠀⠀⢰⡟⠿⣿⡙⠗⢸⢹⡿⢹⡆⠀⠀⠀⠀⢠⡒⣶⢸⡿⠋⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠘⠠⡶⢶⠇⠀⠀⠀⠀⠀⠀⠸⣷⣶⣿⣤⣶⣧⣮⣷⣿⠃⠀⠀⠀⠀⠀⠀⠁⠞⠉⠉⠉⠉
⠀⠀⠀⠈⠈⠁⠈⠉⠉⠉⠉⠈⠁⠈⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⠿⠟⠁⠄⢀⠤
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡼⠀⠀⠀⠀⣀⡀⣀⣀⣀⣀⠈⣆
⠀⠀⠀⣠⣤⣄⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠆⣲⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⣄⢀⡉⢻⣦⡘⡆
⠀⠀⣾⣇⣽⣿⣷⠀⠁⠄⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠸⠀⠀⠀⠀⠀⣸⠣⠈⠀⢀⣤⠁⠀⠀⣸⡏⠑⠿
⠀⠀⢻⣿⣿⣿⣿⡇⠀⣌⠀⠀⠔⠀⠠⠀⡀⢀⠀⠀⡠⠄⠀⠀⠀⡀⠀⠀⠀⠀⠹⣆⣒⠈⠀⠀⢀⣩⣷⠟
⠀⠀⣼⣿⣽⣿⣿⠁⠀⢘⣷⠀⠁⠀⠁⠀⠁⠀⠀⠀⢳⡈⠀⠈⣰⠇⠀⠀⠀⠀⠀⠈⠓⠋⠉⠓⠚⠉⠀⠀⠀⣀⠄
⠀⠀⣿⣟⣿⣿⡿⠀⠀⠀⠹⠐⠑⠔⡅⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣿⣿⣿⣿⣧⠀⠀⡐⠀⠐⠐⠀⠓⠂⠀⠀⠀⠀⢀⠨⠉⠈⠁⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠘⣿⣛⣿⣿⠀⠀⠣⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠔
⠀⠀⠀⠉⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠈⢳
⠀⠀⣠⡾⢻⠙⡉⡉⡩⡱⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠔⡝⡢⣤⣄⡞
⠀⢰⣏⠄⢀⠊⠀⠉⢰⢧⠂⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐⢲⡤⠀⢩⠀⠀⢀⢖⡬⢍⢂⡱⣤⠀⡆
⠀⠈⢿⡄⠐⠗⢤⡴⠋⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⣜⡷⢽⠇⠀⠀⠸⠃⠀⠩⠒⠐⠈⠠⠁
⠀⠀⠀⠙⠲⠤⢭⡤⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠂⠀⠀⠀⠈⠉⠄⠱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠛⣷⣤⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠀⠀⠀⠀⠀⡀⠂⠐
⠀⠀⠀⠀⢀⣀⣈⣀⣹⣿⣿⣤⢢⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⢤⡾⠟⠋⠀⠀⠀⢐⠉⠀⠀⠀⠀⠀⠀⠛⡆
⠀⠀⢠⣴⣿⣿⡋⠡⣀⠈⠉⣯⣗⢭⣵⠀⠀⠀⠀⠀⣠⡴⣮⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠰⠶⠂
⠀⠀⠘⠿⠩⠿⢛⣢⣄⣠⣴⣷⣾⣷⣽⠉⠢⠄⠀⠙⢿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠈
⠀⠀⠀⠳⣅⠂⠱⠿⠿⠿⠿⠛⡯⠟⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢐⠀⠀⠲⠐⠆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⣄⣀⡀
⠀⠀⠀⠀⡘⠁⢬⡜⠁⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣯⣿⢿⣯⢿⡿⠀⠀⢠⣤⣽⡇
⠀⠀⠀⠘⠿⣶⡾⠋⢶⡀⠶⠒⠛⠀⠀⠀⠀⠀⠀⠀⣠⢶⡒⠲⢶⠶⠦⢄⠀⠀⠀⠀⠀⠀⠀⡀⢹⣷⣿⠞⠿⠿⠗⠀⠀⢸⣷⣿⡇
⠀⠀⠀⠀⠡⠚⣛⡻⠡⠄⢃⠐⠁⠂⠀⠀⠀⠀⠀⢰⣍⠤⠵⠿⠟⠷⢉⠘⡇⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⡀⠀⠀⠈⠁⢈⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⠶⠚⠷⠶⢚⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠁⠐⠉⠁⠉⠉⠁⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⣌⣻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄
⠀⠀⠀⠀⠀⠀⠀⢉⣻⣿⣿⣷⣯⡶⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⣀⡤⠴⠚⠋⠉⠉⠡⠁⠈⠻⣷⣞⣿⣷⣍⡉⢉⡛⠒⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠁⠀⠠⣄⡀⠀⢠⡄⣤⠀⠀⢘⣟⣿⣬⡙⢳⢦⣈⠛⠶⣤⣍⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣛⣿⣻⡝⢷⣧⠙⢏⡠⠐⠚⠌⣀⣹⢻⡶⠟⠿⣿⣦⡈⠙⢿⣦⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⢋
⣿⣿⣯⣽⣛⣻⡿⠄⠈⢠⠀⠀⠀⠀⠉⠑⠲⣎⣁⣮⡙⢝⣓⣦⣌⠻⢌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⢋⠤⣪⣵
⣿⣿⣬⣿⣿⣯⠀⠀⠀⠙⠶⣤⣤⡤⠀⠀⠀⠘⡿⠻⢿⣦⠉⠻⣿⣷⣤⣙⠣⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⣯⡤⢚⣵⠞⢋⡤
⡟⠿⠶⣟⣿⣿⠟⢶⢤⡀⠀⠀⠀⠀⠀⠀⣠⣾⣥⣤⣴⣤⣴⣶⢤⡙⠟⢻⠷⣤⡙⠢⣄⠀⠀⠀⠀⠐⣿⣛⡥⢛⣡⣶⢟⣡⠞⠁
⠉⢳⣴⢻⡾⢁⠀⠛⠀⣹⣶⣤⣄⣠⣴⣾⣿⣿⣿⣵⣤⣤⣤⣤⣨⣷⣦⡈⠳⢌⠙⠷⣦⣽⡆⠀⠀⠀⠈⠉⣴⡿⣉⠶⠋
⢺⣶⠉⠘⢃⠸⢤⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⠏⠙⠶⣤⣙⣦⠈⠉⠀⠀⠀⠀⠀⠀⠘⠚⠁
⢤⣉⠒⠿⢦⣄⢀⣠⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠿⠟⢛⣭⣴⣿⠟⠁⠀⠀⠀⠈⠙⠋
⠳⣦⡈⠀⠒⠠⠬⣍⣉⣉⣉⣉⣉⣉⣉⡉⠴⠀⠒⠈⢁⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣤⣤⣙⢶⣤⣤⣤⣤⡤⣤⡤⣤⠤⣤⣤⠀⠠⣤⣤⠾⢫⠤⠤⠤⠤⠤⢤⡤⠤⠤⠤⠤⠀⢤⣤⣤⢼⣧⣾⢥⢠⣶⢶⣦⡀⣴⣶⣄⢤
⡈⠢⣝⣓⡪⠝⠻⢿⣿⣿⣦⣽⣾⣶⣷⠀⠛⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⡃⢸⡿⣷⡜⢸⣿⡀⣿⡇⣿⣿⢣⢚
⣼⣿⣦⣧⣼⣿⣯⣶⣤⣭⣭⡭⡏⢩⡇⠀⡃⠀⡃⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡀⠀⠀⠀⢸⣂⡷⢸⣿⢹⣧⣸⣿⠁⣿⣇⣿⣿⣏⢺

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠻⠷⣦⣌⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢶⣦⡈⢻⣧⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠿⣶⣄⠹⣿⠀⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⣠⣴⡾⣯⣄⣼⡟⠸⠟⠠⣿⠣⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⢀⣠⣶⠿⢛⣥⡾⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠋⣁⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣼⣿⣌⣻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⢹⣿⠙⠛⠛⠛⠛⠿⢷⣶⣤⣤⣤⣤⣤⣤⣤⣶⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠿⠿⠿⠿⢿⣷⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⢸⢸⡌⣿⠙⢿⣄⣀⣀⣀⣀⣀⣠⣤⣤⣤⣶⠶⠶⠶⠿⠿⠶⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣭⣿⠸⢸⠀⡇⣿⠀⠀⢉⣉⣉⣭⣭⣭⣭⣥⣤⣀⣀⣀⣀⣀⣀⣀⣀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⡞⠀⡇⣿⣤⣴⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⡄⡇⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⡇⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⡇⡇⣿⠀⣀⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⣠⣶⠾⢟⣿⣶⠶⠟⢛⣛⣛⡻⠷⢿⣿⣋⠭⠒⣒⣒⡒⠭⣙⢻⣦⣤⡶⠶⠶⠶⠶⣶⣤⣀
⠀⠀⠀⠀⢀⣾⢋⢔⣿⠟⡩⢖⣊⠭⠥⠒⠒⠪⠭⣐⠪⡻⣿⡭⠤⠤⠭⣱⡾⢛⡩⢖⣒⠬⠭⠭⢵⣒⡪⢝⠿⣦⡀
⠀⠀⢀⣀⣼⣧⣯⣾⣧⣾⣴⣯⣴⣯⣭⣽⣭⣿⣷⣶⣷⣾⣾⣿⣾⣿⣶⣿⣶⣯⣶⣥⣶⣮⣭⣭⣽⣶⣭⣲⣵⣜⣿⣄⣀
⠀⠀⠘⣿⡉⢡⡄⢠⣤⡄⢀⣤⠀⢀⣤⡀⢀⣤⡄⢠⣤⡄⠀⣤⡤⠀⣤⣤⠀⣤⣤⠀⣤⡄⢀⣬⡍⢉⣉⡉⢉⣉⠉⢹⡿⠃
⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠛⠛⠛⣿⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁