Snowcore Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡄⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢀⠀⠐⠂⠀⠀⠀⢀⠔⢀⠀⠀⢈⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠈⠀⠀⣀⣠⠴⠋⠀⠐⠐⠆⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠂⠀⠁⠂⠀⠀⢀⠄⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡄⠀⠀⠀⠀⠀⠀⠄⠀⢀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠐⠁⠀⠀⢀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠈⠀⠈⠒⠤⢀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠁⠂⠀⠀⠄⠀⢀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠁⢀⡀⠀⠀⠀⠀⠀⠲⠀⠀⠀⡠⢄⠈⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⣀⠠⠄⠁⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⢠⠄⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠐⡠⠄⠂⠈⠈⠀⠠⠀⠀⠁⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⢌⣃⠀⢀⡠⠗⢀⢒⢂⠂⠀⠠⠄⠀⢈⠙⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣀⡀⡀⠀⠁⠘⠛⠚⠈⠉⠉⣉⣉⣁⣾⣄⣇⠘⣠⠁
⠀⠀⠀⠀⠀⠄⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠠⠤⠤⠤⠭⢾⢒⣤⣤⣄⣀⣀⢀⡀⠄⡄⡀⠉⠁⠁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡁⠍⡁⠉⠉⠙⢿⣤⡌⠀⡇
⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠨⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠆⠆⠖⠶⠀⠔⠂⣠⠚⣀⠐⠀⠀⠀⠀⢸⠃⠀⠰⠇
⠀⠀⠀⠀⠊⠀⠐⠂⠒⠤⢄⡀⢠⢄⡀⠀⠁⠠⠀⠠⠔⠒⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠄⣠⣾⠕⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠡⡀⠤⣤⡀⢀⡀⠀⠀⠀⠀⡜⢦⣯⠖⠃⠤⢥⣮⠙⠛⠀⠀⠀⠀⠀⠀⠀⢀⠀⡟⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠠⢫⣄⣢⡇⠀⠀⠂⠨⣯⣹⣆⡐⠀⠀⠀⠀⠀⠂⠀⠄⠁⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠙⠃⠶⣤⣳⣽⣿⠯⣼⣦⢀⡀⠀⠀⠀⠈⠀⠀⡰⠤⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠛⠿⠟⠨⠙⠪⠽⣤⠠⠀⣰⠀⠀⢈⡀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠉⠂⠼⠌⢠⣾⣗⣠⡮⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠈⠀⠠⣗⠒⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠶⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠛⠛⠋⢾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⣼⣦⡀⠀⣠⣄⢤⠀⣔⣦⣀⡠⠀⠠⠀⠁⠀⣠⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡸⢒⠀⠀⠀⠀⠀⠀⠀⠐⣺⡘⣿⣿⣶⡟⠉⠈⠀⠁⠈⢻⣇⠀⠄⣠⠀⠘⢣⡀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠠⢻⠑⠶⠆⠀⠀⠀⠀⠀⠀⣠⠁⠛⠹⠋⠙⢧⣐⣘⡀⠀⣀⣉⡉⣐⣴⣧⠀⢀⣸⣿⠟⢁⣺
⠀⠀⠀⠀⠀⠀⠈⣹⠆⣰⣦⠀⠀⠀⠁⠀⡄⠙⠿⠅⢿⠇⠞⣉⠈⠉⠉⠞⠻⣷⣾⣿⣾⢿⣤⣿⡿⠃⠀⢸⣿
⠀⠀⠀⠀⠂⠀⠻⡟⡀⣠⠛⠀⠀⠀⡼⠗⠀⠠⠤⡥⠀⣻⣿⢯⣰⢻⡄⣿⣦⣈⣭⣏⣿⣿⣿⡿⠀⠀⣠⣼⣿
⠀⠀⠀⠀⠖⣠⢼⡃⣸⣿⣢⣬⣤⢤⣠⣄⣀⡄⠀⢁⣮⠟⢡⣠⡌⠈⠀⠀⢽⣿⣿⢛⡉⣽⠛⠁⡀⠀⢙⣛⣿
⠀⠀⣼⠀⢢⣿⣿⢁⣈⣹⡟⠋⠀⠀⠛⠁⡈⣲⡎⠀⢁⣴⣿⠋⠀⠀⢸⣾⣮⠙⣿⣿⣿⣿⣶⣾⣷⣶⣿⡷⠏
⠀⠫⣟⠀⠛⣹⢟⣹⣿⣾⣷⣸⣾⠃⣤⣼⡃⢈⣿⣿⣿⠛⡛⣴⡆⣾⣼⣿⡟⠳⣿⣿⣾⠿⣿⣥⣾⠋⠁⣀⣸
⠀⣿⣟⠔⢛⣿⣸⣿⣿⣿⠟⣉⣷⠈⠛⡉⡷⠊⢻⣿⣿⣿⣿⡏⠀⠀⣹⣿⡇⠠⠙⣿⣿⢳⣿⣁⣽⣧⣼⣽⣿
⠀⣿⠯⣾⣿⣿⣿⣿⣿⣧⣾⣿⡇⠀⢀⣿⣿⣦⣼⣿⣿⣛⣿⡵⣾⣶⣟⡟⠀⣰⠆⣿⣿⣾⣿⣿⣿⣿⣿⠿⠟
⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣦⣾⣿⣿⣿⣿⣻⣭⣴⡾⣿
⠀⣿⣿⣿⣿⡿⣿⣿⣏⡄⣰⣷⣧⣸⣯⣿⣻⢛⠻⣿⣟⣿⡿⠉⢻⣿⣿⣿⣿⣿⠷⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿
⠀⣿⣿⣿⣿⣴⣿⣿⣿⣧⠈⣽⣿⢃⣾⣷⣌⣿⢦⣿⣿⣿⠃⠀⢺⣿⣿⣶⣿⣯⣦⣼⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⢈⢹⣷⣶⠏⢹⣯⣿⣸⣿⣿⣿⠄⢠⣴⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠠⣿⣿⣿⣿⣿⣿⣿⡟⠁⣮⣿⡏⠁⢰⣾⣿⣿⣿⣿⣿⣧⣾⣾⣿⣿⣿⣿⡿⠿⣿⣿⣿⣾⣿⣿⡟⠈⣩⣻⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠅⠀⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢉⣀⣀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠎⡙⠋⢁⡁
⠀⠀⠀⠀⠀⠀⠀⠆⠀⢻⡦⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣆⠰⠤⢀⠸⠗⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠲⣉⠁⠛⢁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢰⣶⣦⣄⢄⣀
⠀⠀⠀⠀⠴⠂⠀⡶⢴⠏⢠⠖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⢀⠄⡀⣰⣿⡟⠛⠙⢯⣸
⠀⠀⠀⠐⠀⢠⢠⣠⡀⣲⣦⣤⡄⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠉⠉⠁⠘⠏⣁⣀⣠⣤⣿
⠀⠀⠀⡀⢣⣾⡟⡻⠋⠁⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⠀⠀⡤⠀⠐⠂⠠⣴⠿⠛⠉⠉⠉
⠀⢀⠰⠶⣿⣿⠿⠁⢠⣷⢤⣼⣒⡐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠂⠚⠷⠟⠃⠢⣶⣤⣤
⠀⠰⠶⠴⠿⢁⠤⠋⢸⣷⣄⣀⢈⣿⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣴⡆⠀⢀⣤⣤⣤⣶⡂⢀
⠀⠀⠠⠶⠂⠀⠀⠀⠈⠁⠙⠿⢩⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣟⠶⠚⠉⡭⠞⠀⠄⠈⠁⠙⢫
⠀⠠⠂⠀⢰⣖⣁⣤⣤⡴⣴⣄⠀⠑⠌⣐⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠋⠀⠦⠀⠀⢶⡾⠇⠀⠀⠉⠀⠀⡀⢴⣧⣀⣖⡀⠀⠛⠂⠚⠁⣈⠿⣀
⠀⠊⠴⢺⠟⠋⠙⠋⠉⠉⠛⠫⡤⠄⠀⣤⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢴⡶⠒⠂⠀⠠⠔⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠉⠉⠡⠂⠠⠜⡶⣿⠀⠙
⠀⠀⠀⠀⠒⡶⠒⢰⠈⠛⣷⠤⣀⢨⣧⡀⠈⠉⠂⠀⠀⠀⠀⠀⠀⢶⠉⠉⢛⣟⠁⢸⠃⠀⠐⠀⠀⠀⠀⢠⠐⠀⠀⠀⠀⠐⠂⠐⢠⡴⣷⣶⡶⠀⣈⠀⠋⠀⣤
⠀⠨⠀⠀⢠⠀⠀⠉⠛⠁⠉⠢⠈⠀⠉⠁⠘⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠋⠙⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠒⠋⠩⢉⢋⠴⠿⡿⠀⢶⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣰⢷⡔⢮⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠃⡼⠃⠀⠉⠈⠻⣿⣿⣿⣦⣀⠀⢀⣤⠾⠫⠞⠉⠁⣙⣳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠞⠀⠈⠀⠀⠀⠀⠀⠀⠙⠏⢿⡙⢿⡿⣟⠁⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⡿⣶⣤⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠉⠙⠳⠦⣀
⠀⠀⠀⠀⠐⠁⠀⢠⣇⣸⣧⣤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⣤⣤⣤⣀⣀⠀⠀⣾⠀⣀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⢀⡠⠴⣚⣫⡭⠥⠶⠶⢒⣲⣶⡶⠶⠶⠶⠦⠤⣤⣀⡀⠈⠉⠙⠛⠻⠿⢷⣿⣄⣀⣼⣿⣼⡇⠀⠀⣸⡄⣾⡆⢀⣀⠤⠂
⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠒⠀⠀⠀⠀⠠⢄⣀⡉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠒⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠛⠦⣄⠀⠀⣀⡤⠖⠛⠛⠋⠉⠛⠛⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣇⠀⠀⠀⠀⠀⠀⠈⢳⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⡤⠤⢤⣄⡀
⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠘⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢀⡤⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢶⣶⢤⣤⣴⣶⡞⢛⡷
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣆⠀⠀⠀⠀⠀⣠⡿⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡏⠁⢾⡄⠀⠀⢹⡿⢦⡄
⠀⠀⠘⠳⠤⢤⣤⣤⠤⠴⠖⠛⠉⠀⠈⠙⠓⠒⠚⣿⢷⡀⠈⠙⢿⢳⡶⢶⣶⣶⢾⡛⠾⣱⠏⢩⣅⠀⢀⡼⣣⠾⠇⣠⢟⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁⣙⣛⣛⣛⠁⣙⣛⡃⢘⣛⡋⠀⣛⣿⡉⢨⣭⣍⢠⣭⣭⣭⣥⠨⣭⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠶⠋⢰⡒⢫⡞⠁⠀⢹⣯⡼⣡⠿⡜⠦⣽⠞⠁⠈⢧⠻⣤⡄⠈⠳⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣾⣇⠀⠀⢘⡷⣠⡽⠼⣧⣄⢿⡀⠀⠀⣼⣥⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⣨⣭⣭⡍⢸⡃⠀⠀⠀⣸⢊⢩⣽⣛⢉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⠞⡼⣧⠳⣤⣤⠼⢡⠟⢦⢳⣘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣒⠋⢾⡉⠳⠦⠟⢿⣤⠼⠃⠈⡷⠉⣭⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡾⠾⠇⠀⠀⠀⠀⠀⠀⠀⠘⠷⢷⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠛⠲⣄⠀⢀⡤⠶⠒⠛⠛⠛⠓⠒⠦⣄
⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤⣧⡀⠀⠀⠀⠀⠈⠳⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠒⠒⠒⠲⢄
⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⣈⡽⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢤⡤⣤⣤⣴⡖⣻⡆
⠀⠰⡇⠀⠀⠀⠀⠀⠀⢀⣠⠼⣄⡀⠀⠀⣀⡠⠷⣄⣀⠀⠀⠀⠀⠀⢀⣾⡏⣱⣧⠀⠀⢹⠿⣦
⠀⠀⠉⠓⠒⠶⠖⠒⠛⠉⠀⠀⠀⠉⠉⢉⣿⠳⣄⣈⣹⡝⣟⣳⡾⣟⣏⠛⣼⣩⠷⣄⣠⠞⣴⣿⣤⠫⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⣢⠖⣒⡶⣠⠖⠲⣤⢶⡆⣄⢶⡲⣤⡖⠲⡴⣖⠒⠒⢦⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢷⣼⡇⠀⠀⢿⡍⣸⣩⣇⢹⡇⠀⠀⣹⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⢙⣒⣒⠋⡞⠉⠀⠉⡷⠙⣒⣒⢛⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⢯⢶⡹⢤⣤⠞⡵⠳⡹⣜⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣯⢁⢯⠙⠲⠛⠻⠶⠛⠀⡽⡈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠛⠛⠁⠀⠀⠀⠀⠀⠀⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠀⠀⠈⠀⢀⠀⠀⠈⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⣿⣏⠀⠀⠀⠀⠀⠀⠀⡀⠉⡉⣙⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠾⠲⠀⠀⠀⢀⠠⡄⠀⣀⣍⡈⣌⣙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠒⢀⠠⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⡀⢩⢀⡉⠡
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠔⢁⡠⠏⣤⠠⡨⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡄⢠⢉⠈⡃⢄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⢰⠏⠀⢄⡽⠯⢇⣠⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣱⢈⡁⣍⣍⠛⡀
⠀⠀⠀⠀⠀⠀⡀⢀⣀⠤⠽⠡⢠⣤⠀⠀⠀⣀⡀⠀⠑⡴⢊⠰⠔⠀⢸⣮⣭⠄⡛⠛⠿⠻⠄⠒⠀⠐⠀⠒
⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⢀⡤⠙⠛⠓⠃⠰⠿⠗⢀⠧⠿⠯⢷⠐⠈⠀⠘⠛⠚⣇⣈⠔⠀⠒⠔⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⠈⠉⠒⠊⠉⠐⢼⠀⠈⠠⡖⠊⠉⠀⠀⠀⠀⠀⠈⢰⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠳⠔⠲⠤⠠⣀⠠⠤⠤⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⡀⠀⡄⠠⣮⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢳⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠄⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠻⠂⠩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣫⣽
⠀⠀⠀⠀⠀⠀⢘⡼⠈⠵⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢐⡏⠘⡇
⠀⠀⠀⠁⠀⣠⠟⠁⠲⠇⠀⠒⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⣇⠀⡄
⠀⠀⠀⠀⠀⠅⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠻⠊⡏⠀⣥
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠃⠺⠿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⠀⢈⢻⣼⠀⠀⢠⡞⠃⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠈⣬⣿⣄⣻⡆⠀⡾⢀⣠⣷⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡐⠀⠀⠀⠈⠁⢠⠌⣿⡇⠀⢻⠟⠀⠊⢶⠁⠀⠢⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠈⠠⠄⠂⣀⠀⣀⣠⠿⡇⣀⠘⣤⡄⡤⠚⠀⠀⠀⠈⢸⠀⠀⠀⠢⡀⠀⣀
⠀⠀⠀⠠⠠⢀⠀⠀⠒⠄⠀⢀⡀⠀⠀⢀⢠⠀⡄⣿⠀⡇⠈⢩⠼⠀⡇⠀⠀⠀⠀⠂⡸⠀⠑⠀⠀⠈⠂⠀⡑⠀⠀⠐⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠔⠃⠂⠀⠀⠀⢸⡐⠂⡛⣦⣇⡀⢙⡿⠓⠛⢠⡆⠀⠀⢀⡃⠀⠀⠀⠈⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⡀⡀⠀⠀⠄⠀⠀⠀⠀⢰⠀⠀⠀⣿⡁⠠⢀⣿⣏⠀⣼⣇⠀⢂⣏⣿⡀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄
⠀⠀⠈⠛⠛⠿⢷⣶⣮⡍⣖⣲⡆⣶⣤⣒⣾⡥⢠⣸⣿⣮⣦⣿⣯⣉⠭⢤⡟⣣⠄⣴⠀⣠⢠⡐⣤⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⣤⣥⢬⠀⠀⡇⢸⡿⢹⡁⠀⠀⡇⢹⠀⠀⠀⠀⢠⠉⠉⠋⠉⠉⠙⠷⢾⣧⣰⣢⡐⣠⢄
⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠉⠉⠋⠉⠘⠛⠀⠉⠉⠉⠁⠓⠛⠻⠾⠷⠶⡤⠆⠀⢄⡀⢀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄

⣎⣹⣿⡽⠛⣷⣤⣗⢘⣋⣩⣉⣍⢩⣽⢦⡤⡾⡟⣶⢂⡤⣒⢐⡤⣶⠶⣗⡴⠶⡤⣴⢴⣤⠶⠴⢶⢶⡶⠶⠶⠲⢶⣒⣲⣒⢲
⣟⣿⣿⣳⣴⣿⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⣙⣿⣟⣹⣿⣾⣥⣿⣿⣿⣚⣃⣘⣛⣓⣆⣹⣟⢪⣫⣿⡝⢛⣿⣽⢿⣫⣡⠀⣜⣻
⡏⣿⣯⣽⣿⣿⣿⣿⣿⣟⣿⣿⣯⣿⣿⡿⣷⣿⡯⣭⠿⡿⢿⠿⠟⠙⠘⠉⢉⠉⢡⢤⢀⣌⣁⣁⣶⣿⣿⣿⣶⣿⣬⣯⣞⣿⣼
⣟⣻⣟⣻⣿⢿⡽⡯⣭⠿⣉⠿⣏⣙⣘⣃⣁⢠⡉⣄⣠⡀⡠⡖⡚⠤⣾⢽⣭⢿⣿⡿⡿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾
⣇⣾⣿⣿⣿⣿⣷⡷⡶⣶⠻⣿⣴⣾⡿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣲⣾⣛⡾⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⣿⣿⣯⣽⣿⡿⣯⣿⡟⣿⣮⣏⣿⣷⣿⣾⣿⣷⢿⣿⠻⣽⣿⣿⣿⢻⡛⠛⢋⠹⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⣟⣿⣿⣿⡿⣾⣿⣗⣿⢿⡿⣿⣿⣽⣶⣿⣿⣯⡿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣾⡿⣿⡿⠻⠿⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡿⣭⡍⠠⢍⢉⠡⡥⡨⢄⣶⠂⣄⣼⣿⣿⣷⣭⣧⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢼⣿⡵⣷⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⠿⢥⢿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣽⣿⣿⣿⣿⣽⣿⣾⣿⣿⣿⣷⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠮⢭⡾⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢹⣿⡿⡿⠿⠿⠟⠻⠛⠿⢿⣿⣷⣯⣼⣿⣿⣿⣿⣝
⣿⣿⣿⣿⣿⣿⣿⡿⢿⠓⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠃⠀⠉⠁⠀⠀⠀⠀⠀⣠⣿⣆⠻⢿⣟⣥⣾⣯⣍⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⡸⣿⣿⣿⣿⡟⢿⣿
⢿⣿⣿⣻⣛⣿⡿⠛⢻⠿⠿⠿⠿⠯⠟⠿⣿⢿⣟⢽⣋⣱⢿⣃⣤⣄⣤⣤⣶⣤⢤⣤⣤⣴⣟⢟⣿⣟⣿⢧⣼⣿⣗⢿⢍⢷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⡿⣿⡼⢿⣿⣿⣿⣿⣿⣿⣘⣚⣿⣿⣿⣉⣿⣿⣿⢸⣿⡿⠛⣸⠟⡋⢙
⣿⣿⣿⠻⠟⢻⣿⠈⡛⠉⠋⠉⠉⠁⠉⠁⠉⠉⠁⠁⠙⠘⠃⠛⠁⠉⠿⠿⡯⠝⠛⡛⣧⡟⣿⢽⣿⣿⡿⣋⣽⣶⣷⣾⣿⣿⣿
⣷⠿⢁⣗⣠⣾⠏⠁⠁⠀⣸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⣀⠘⠆⠛⠓⠛⠛⠻⠛⣿⣧⣿⢙⡻⣿⣻⣏⡛⢛
⡏⢀⣙⡟⠁⠀⢠⣔⠀⢠⣺⣿⠶⠀⠀⠘⠃⠀⠀⠀⠀⠈⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠍⠉⠻⢄⡉⠛⠘⠦
⡧⢀⠀⠋⠀⠀⣻⣧⠄⠀⢟⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣼⣷⠀⠀⢀⡄⢠⠉⠀⠀⠀⠀⠀⠀⠁⠂
⣡⠆⢘⠁⢀⢠⣿⣿⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠐⣿⣿⣦⢟⢄⣷⡤⠀⠀⠀⣰⠄
⠀⠀⠀⠀⠀⣉⣽⡧⠒⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠶⢾⣿⣯⣿⣾⢿⡁⠀⠀⠀⢛⠀⠀⠀⡀
⡅⠀⢁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠺⠿⢧⡌⠛⠀⠁⠢⠀⠀⡅⠀⠀⣸⣧⡀
⡇⠀⠀⠀⠀⠀⠀⠀⢰⠒⠀⠀⠀⠀⠀⠀⣀⠁⠰⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢀⣼⣻⣿⠅
⠁⠀⠂⠀⢀⡄⠀⠠⠏⠀⠀⠀⠀⠠⠆⠰⠉⠀⠀⠀⢀⡀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣹⣿⣻⠄
⠀⠀⠀⠀⠠⠂⢤⡔⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⡀⠀⠆⠀⠀⠀⠀⡖⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠿⠿⣄
⡄⠀⠀⠀⠐⠀⠀⣀⡀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⡈⡄⠠⢀⡈⠀⠀⠀⠈⡧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⡇⠀⠀⠀⠀⠀⢀⡈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢶⠀⠙⠀⠀⠉⠀⠀⠀⠀⠠⠀⠰⠀⠀⡄⢠⠀⠀⡄⢀
⢃⠀⠀⠀⢀⣠⠀⢡⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠃

⠀⠀⠀⣤⣀⣀⡀
⠀⠀⠀⠈⠉⠉⢉⠀⣄⡷⠦
⠀⢀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣇⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠹⣽⠺⠂⠀⠀⠀⠀⢤
⣿⢰⣤⣠⡝⠛⠛⠀⠀⣴⢠⣰⣶⠄⡀⠈⠠⢧⠘⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⣿⣄⣿⣿⣿⠀⠀⠤⠾⡟⠋⠉⠀⠀⠀⠀⠑⠰⠀⢈⡟⢿⣯⣀⡀⠂⠁⠠⣄⣠⣤⠤⠀⠐⣤⣀⣁⠐⠄⠀⢰
⣿⣿⣛⠀⣃⢴⡆⠆⠘⠈⢓⠒⠀⠀⠳⡀⠠⢄⡀⠀⠀⠐⠈⠉⠥⢤⠀⠀⠀⠀⠀⠑⣿⣶⣦⡙⠛⢿⣗⡀⠘
⠙⠉⢳⣾⣻⠛⡛⢀⣃⢙⠉⣅⣀⠀⠚⠃⠈⠛⠻⢧⣦⣲⣤⡀⠀⠀⢀⠀⢰⢦⡀⠀⠀⠙⡍⠛⠛⢸⣿⣧⠀⠀⢰
⠀⠀⢸⡿⣷⠶⠗⣿⣿⣿⣛⡍⠋⠁⠀⡀⠀⠀⠀⡀⠀⠁⢙⡗⢶⠆⠈⠐⠻⣞⣀⣀⠀⠀⢋⠑⠂⠸⣿⣿⣿⣷⣾
⣀⣦⡮⣴⣆⣠⣅⣿⣹⢹⠏⠁⠀⠀⢰⠀⠘⠀⠀⠀⠀⠀⠀⢡⣤⣬⡛⢷⣂⠌⠙⠛⠂⢸⠀⠹⣆⡸⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⣿⡏⡏⡄⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠓⠉⢻⠂⣠⢠⠸⠇⠀⣎⣷⣼⡿⢿⣿⣿

⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣾⣴⣂
⠀⠀⢀⣙⣷⠾⢶⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠟⠿⠻⠍
⠀⠀⠈⢩⠿⢳⠛⢯⡁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⡞⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣳⡾⢷⣟⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠴⠂⠦⢀⡠⢀⠀⠀⠀⠀⠀⢠⠾⢳⡛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠈⠀⠓⠐⠒⠀⠁⠀⠈⠒⣄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠫⠵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠌⠃⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠐⠂⠠⠤⠤⠄⠒⠈⠀⠀⠀⠀⠐⡀
⠀⠀⢀⣸⣶⢳⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣢⡼⣦⣆
⠀⠀⠀⠘⠉⠏⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⢳⠛⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠇⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣀⠊⡑⡛⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠰⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠄⠈⡀⡐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⣀⠀⠀⢀⡈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⢀⠴⠊⠀⠀⠀⠠⢀⠀⠀⠑⠠⡀⠀⣀⠀⠄⠠⠄⠀⣀⠀⠀⠀⠀⠀⢀⡠⠚⠁⣀⠄⠀⠄⠁⠦⣄⡀
⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠒⠁⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠀⣀⠀⠁⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⡌⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠄⠂⠀⠀⠀⠀⠀⠀⠀⠓⢄
⠀⠀⠸⠀⠀⠀⢠⠎⠀⢀⠀⠂⠍⠀⠀⠠⠀⠘⠦⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣈⡀⠀⠀⠠⠄⠀⠀⠀⢡
⠀⡠⠆⡀⠀⡠⠁⠀⠔⠉⠢⠌⠀⠀⠀⠀⢠⣤⠁⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠄
⠀⡀⠀⠁⢀⠁⠀⡌⢀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡘
⠀⠈⠂⠂⢅⠀⠀⠇⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠂⣤⠀⠀⢈⠙⠀⠀⠀⠀⡀⠆⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡁⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠠⠄⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⡌⠀⠉⠀⠢⠀⠀⠀⠀⠀⢀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⡄⡠⠄⠊⣀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡲⠀⠁⠀⣤⠀⠈⠋⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠓⠄⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣠⡁
⠀⠀⠀⠤⡀⠀⡀⢀⠀⠈⠁⠀⠀⠁⠀⢀⠀⡆⠀⠈⠈⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡠⠓⢄⠀⠀⠀⠀⠀⠀⠑⠔⠀⠀⠀⠠⠀⠀⠈⠢
⠀⠀⠀⣄⠈⠀⠁⢂⠀⠀⠀⢀⡄⠠⠀⠐⠈⠰⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠁⠀⠀⠀⠠⡀⠑⠰⠊⠀⡆⠀⠀⠀⢀⠄⠀⢤⠆⠀⠀⣠⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠐⠄⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠉⠂⠀⠈⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⡠⠄⠂⠀⠀⠐⠠⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠒⠀⠀⠁⠐⠀⠀⢀⣀⠠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠐⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣈⠀⠡⢀⡀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠔⠈⠀⠠⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⡀⠀⠀⠀⢀⠠⠀⠊
⣤⣄⣤⣤⣤⣤⣄⣤⣠⣤⣤⣤⣤⣤⣤⣤⣌⣀⣀⣩⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣄⣠⣤⣠⣤⣤⣤⣤⣤⣠⣄⣠⣄
⣿⣛⣛⣟⣻⣯⣛⣻⣛⣛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣭⣽⣿⣯⣽⣽⣿⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢻⣿⣿⡳⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣀⠀⠀⣼⡇⢀
⠀⠀⠀⠀⠀⢰⡄⠀⠀⢀⣴⣿⣿⣿⡛⠛⢿⣿⣲⣄⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡀⣀⣴⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣸⡄⡀
⠀⠀⠀⠀⣦⣼⣇⣰⢴⣿⣿⢻⣻⣻⣷⣦⣀⡀⣄⣽⣷⣆⣾⣿⣼⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⠾⣿⣯⣛⡛⠛⠻⠿⠏⠻⣿⣿⣿⣧⣧
⠀⣀⣀⣀⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠈⠙⠛⠿⠿⣿⣟⣺⣿⣿⣷⣤⢀⡀⠀⠀⠐⣚⣛⣿⣿⣿⣿⣿⣿⣦⣤⣉⣉⣉⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢶⣿⣿⣦⡀
⠀⠀⠀⢀⠀⠀⢀⣴⣀⡀⠀⣀⣤⣾⣫⣾⣿⣿⣆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣴⣿⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣤⣄⣤⡀
⠀⠠⠴⢾⣷⢶⠿⠿⢿⣿⠿⠿⠿⢿⣿⣿⠿⠿⠿⠿⠿⣤⣶⣾⣷⣄⣀⠀⠀⠀⠀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠼⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠙⠋⠉⠉⠀⠀⠀⠐⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡠⢲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁
⠀⠀⠀⣠⣶⣯⣴⣮⣿⣿⣷⣄⠀⠀⠀⠀⠀⣠⠾⣦⡞⠀⠈⠋⠑⠄⠀⠀⠀⠀⠀⢀⠴⠞⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⡰⠂⢀
⠀⠴⠿⠿⠿⠿⠿⠿⠿⠷⠶⠾⠷⠄⠀⠀⠐⠁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡀⠀⠠⣾⠀⠀⣠⠂
⠀⠀⠛⠀⠀⠊⠁⠀⠈⠛⠒⠀⢢⡄⠀⠀⢀⣤⣀⣤⣴⣿⣄⣠⣾⣤⣤⣤⣶⣦⣀⠀⠀⠀⠀⠠

⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠒⠶⠶⠶⠶⠒⠒⠒⠒⠒⠀⠐⠶⠲⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠘⣯⣟⠉⠙⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⡋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⡞⠈⡒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣾⣿⣿⣿⣿⣿⡀⠀⢀⣻⣦⣄⠀⠀⠒⠒⢀⣠⠀⢘
⢀⠀⢀⣤⣤⣵⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠆⠀⠠⠵⣻⣷⣆⣀⢞⣭⣁⣀⠺
⠸⢿⣿⡟⠋⢡⣾⣷⣿⣤⣄⡀⠀⢀⣘⣻⣴⢻⣿⣿⣿⣿⣟⣟⣿⣼⣿⣿⣿⣷⣶⣤⣤⡘⠛⠿⠿⣿⣿⣷⣿⣷⣺
⢰⣿⣿⣿⣿⡾⣯⠙⡼⠉⣼⡿⠶⢌⠉⠙⠓⠛⠽⣿⣿⡿⣡⡘⠿⠋⠉⠉⠛⠿⢿⣿⠟⠁⠀⠀⢀⣈⠉⢻⣿⣷⣽
⢸⣿⣿⠏⣁⠤⠃⣴⣾⣿⣟⠁⠀⢀⣉⣀⣠⡄⠀⢨⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠽⣿
⢠⣽⣿⣿⡧⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿
⢸⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⢸⣿⣿⣶⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢋⣠⣤⡤⠒⠂
⢸⣿⣿⠿⠿⠿⠻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠈⠓⠈
⠘⠋⠁⢀⣀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⢸⡿⠚⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠑⠢⣄⢀⡤⠖⠚⠋⠉⠙⠓⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠾⠄⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⡤⢾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣆⡀⠀⠀⣀⠼⣄⣀⠀⠀⠀⠀⢀⣼⡏⣹⡅⠈⢹⡿⢦
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠚⠉⠁⠀⠀⠉⠉⣭⡟⢦⣬⣽⠝⢯⡿⢯⣿⠛⣾⡭⠶⠤⠞⠵⠯⠴⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢯⠞⣹⢟⡴⠋⢳⣞⢟⣴⡻⣽⡾⠉⢧⢯⣉⠙⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡾⢧⣀⣨⢗⠼⠒⠷⡼⣅⣀⣼⣧⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⢻⢧⡼⣄⣀⡰⣣⣔⣖⠦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠫⡟⠧⠼⢻⡤⠗⢘⡎⢳⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠁⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢻⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠔⣪⠿⠋⠀⠀⠀⠀⠀⠀⣠⠄⠂⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⣉⡼⢋
⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣨⡇⠀⠀⠀⠠⠚⠁⠈⡙⠀⠀⠀⢀⡤⠔⠊⠡⠉⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⢰⡆⠀⠀⠀⢼⡇⢨⣡⣶⣮⠈⠒
⢠⣾⠴⣻⠇⣸⠀⠀⠀⠀⠚⣍⡄⢦⠀⠀⠀⠄⣦⠐⠀⠀⠐⠚⢻⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⣾⣧⠀⠀⣠⣿⣿⣈⣋⡼⠟⢶⠶⣶⢀⣆
⣿⡿⣊⢃⣲⣼⣇⣤⡶⠚⢈⠉⢰⢌⣁⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢸⡆⠀⠀⣫⣜⠅⠀⡜⢛⡎⢉⣻⣀⣤⠈⢃⡀⠙⢿⣀
⣿⠞⣹⣈⡽⢌⣿⣿⡷⠂⠀⠈⡃⠀⠀⢣⠀⠈⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡷⠂⠘⣁⡙⢶⡀⠟⠁⡴⣄⡘⣿⡏⠳⡌⠙⠷⣾⣿
⠿⠓⣅⡟⢘⣦⣹⡿⠗⠚⠶⠖⠉⠛⠧⣌⠳⣦⣦⣴⣀⣴⣠⡠⢼⡿⢄⣀⣰⣄⣦⣦⣾⣷⣶⣏⢜⡁⢸⠞⢉⡅⢸⡡⠒⠉⠻⡀⠻⣌⣗⣦⣤⣀⠈⠻⣿
⣰⡎⠀⣿⢺⣏⣠⡤⢾⣀⣤⠾⢶⢸⡆⠘⠷⣿⣿⣿⣿⣿⣿⡗⡹⡟⢺⣿⣿⣿⡟⢹⣿⣿⣿⡥⢟⠙⠓⠛⣩⢸⢛⣀⠀⠂⣧⠘⣤⣼⣿⣇⠀⠙⠷⢴⣿
⠴⠳⣀⣿⣶⠟⠉⣀⢀⣉⣇⠀⢨⡽⡟⢦⣀⠸⣿⡟⡟⡿⡿⣉⣠⠉⢈⢻⣿⣿⡴⢊⣻⣿⠋⡠⠴⠗⠶⣦⣽⣇⣼⠡⠤⠖⠛⢿⡀⠘⢯⠉⠁⣄⠀⠀⢹
⢀⣶⡟⣹⣷⡞⠋⢀⣬⠋⠀⡖⠈⠀⢀⡀⠙⠳⣾⣿⡏⣿⠯⠎⣀⢧⡼⠨⢿⡵⡁⠊⢉⡟⢋⠀⣠⢤⠦⣀⢹⣿⣅⠀⣠⡀⠀⢹⣉⠉⠺⣆⡀⠈⠂⢤⣀
⣾⣁⣼⣿⡯⠀⠚⢻⣁⣠⡞⠀⢠⡀⠘⢳⡄⣀⠈⡿⢿⡅⠀⠈⡇⢸⠀⠀⠠⡾⠁⠲⢎⠁⣣⣤⡇⢀⡷⣄⣉⣿⣿⠜⠛⣧⠀⢠⡏⠶⣄⡘⢧⣠⠂⠀⢻
⠀⠀⡽⠃⠀⠀⣀⡤⠞⠉⠀⠀⠀⠛⣆⢨⡗⠛⠓⠇⠘⠓⠐⠋⠙⠛⠒⠀⠀⠈⠀⠀⠀⠁⠀⠀⠑⠁⠀⠘⠛⣁⠆⠀⢈⠉⠓⠃⠀⠀⠀⠙⠻⣯⠁⢀⢈
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠒⠲⠀⠀⠀⠙⠻⠇⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠁⠀⠠⠾⠴⣄⡀⠀⢠⣀⣣⡀⠈⣻⠿⠿




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢀⡠⡆⠀⢀⠛⠃⠀⠀⠀⠐⡀⠂⢄⠈⡆⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠉⠀⣠⣤⣤⡄⠀⠀⠀⠡⠄⠤⡔⠀⠀⠀⣀⠹⢼⣦⡔⣤⡌⠳⣌⡇⠈⠁⠒⢼⣆⡿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣆⢰⣾⣿⣿⣿⣷⣄⡀⢀⠀⠠⠀⠀⠀⠀⠀⠙⡀⠶⠦⠿⣾⣿⠆⠈⠻⡄⠀⠛⠿⣿⡇⠈⢣⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠒⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠲⢞⣫⠉⠃⠤⣄⠀⢰⣿⠟⠁⠈⢳⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣤⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⢳⡀⢈⠙⣿⣿⡄⢣⡀⠀⣿⡇⡀⠀⢅
⠀⠀⠀⠀⠀⠀⣀⣴⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠉⠓⠀⢀⠀⠀⢅⠠⠦⢀⡭⠙⠒⠲⢼⣿⣇⠀⣿⡀⣘⣧⡅⢠⡏
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠒⠶⢄⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡷⠿⣧⠀⢿⡆⣸⣇⡠
⠀⠀⠀⠠⣼⣿⣿⣿⡿⠛⡻⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠚⠶⠒⠲⢦⣄⣀⣀⡀⣠⣴⢶⡞⢻⣿⣿⠄⠈⣷⣾⣿⣿⡟⣀
⠀⠀⠀⠀⣻⣿⠟⠋⠀⠀⠉⠙⢻⣷⡆⠈⠙⣿⣿⢿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⡶⣆⢀⣠⠜⠉⣹⡿⠛⠛⠻⠿⠷⣾⣿⣿⡀⢠⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣾⠃⠀⣀⡀⠀⠀⠀⣧⣿⣿⣦⠀⣷⣿⠿⠻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣏⡄⣔⠒⣚⡙⢀⠀⢀⣄⠀⠀⠀⣿⢿⣷⠈⢸⣿⡿⠁
⠀⠀⠀⠘⠷⠶⠛⣷⣯⣴⣿⣿⣿⣿⡿⠟⠠⠛⢟⡄⠁⢹⣻⣿⠛⢿⡿⠿⢿⠿⠟⠛⠛⠻⠊⠒⠾⠓⠐⠂⠒⢿⣋⠘⢷⣿⡾⢿⠀⡷⠈⠊
⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⣦⣤⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠃⠒⠂⠀⠀⠀⣸⣽⣷⣿⣟⡇⠀⢿⣧⠄
⠀⠀⠀⠀⠀⠀⠀⡀⢙⡹⠟⠏⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⢰⣴⣶⣶⣶⣾⣿⣿⡿⠋⠈⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠳⠿⢿⡷⠶⣶⣶⣶⣶⣶⣤⣤⣤⣴⣦⣤⣤⣤⣶⣬⣾⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⠟⠉⣉⡥⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠊⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠄⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⠀⠀⡉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⢶⡀⢀⡼⣿⣬⣀⠀⣤⣈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠘⣷⡟⠸⠋⢨⠉⠿⠈⠉⠙⠿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⢻⣤⣾⢋⡀⢡⡆⠁⠀⢀⠈⢀⡔⣰⠃⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠊⠂⣬⠟⡇⢠⢊⠉⠀⡀⠀⢡⣭⡎⢳⣟⠀⠀⢷⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣤⠞⢿⣏⠀⢹⣠⣖⡀⡢⢸⡼⢏⣿⡇⠾⣧⢤⣤⣼⠷⣧
⠀⠀⠀⠀⠀⠀⢠⣤⣿⡶⣾⢹⡆⣸⣇⣀⣸⡇⢻⣷⢃⣼⠁⣾⣿⣷⡶⠟⠻⠉⠛⢶⣏⣷⣰⡆
⠀⠀⠀⠀⠀⡰⠿⢸⢏⣤⠿⠿⠛⠿⠾⢷⣿⣷⡿⠙⣦⢿⣶⡿⠋⠁⠀⠠⠖⠃⠀⢀⠹⣮⣟⢳⡄
⠀⠀⢀⣠⣼⣅⣠⡾⠛⠰⠋⠀⠠⠄⠈⠑⠂⢄⠙⠻⣿⣯⣉⣀⠁⠘⠀⠀⠤⣄⡀⠀⠁⠬⠻⢦⣷⣄⣀
⠀⠀⠀⠀⠈⠉⠁⠀⠒⠀⠁⠀⠀⠀⠂⠔⠀⠀⠀⠀⠀⠀⠙⠉⠀⠈⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⣿⠆⠀⠀⠀⣠⣴⣾⠏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡏⣇⠀⣸⣶⣝⣠⢴⣾⡿⠛⠁⠀⠀⠀⠀⠀⣀⢠⠖⠈⠁⠀⠀⠲⣻⡶⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⡰⢧⠀⢠⡀⠀⣄
⠀⠀⠀⡀⠀⠀⠀⣦⡀⣀⠀⢞⠛⠋⡼⢡⠿⣞⣏⠌⢉⡅⠀⠀⠀⢀⣤⠆⠉⠁⠂⠀⢸⡧⠀⠀⣿⢉⣦⡄⠀⠀⠰⢿⠆⠀⠀⠀⣝⡄⠶⣷⡀⡶⣷⢴⣿
⢠⣦⣸⣷⠀⣶⣜⣍⣁⣿⣶⣯⠼⣷⢶⢿⡀⢈⠛⠁⠈⠀⠠⠔⠪⢿⠇⠀⠀⠀⠀⠀⣻⡟⠄⠘⣻⣾⢧⣀⠀⠀⠶⢻⣼⢠⡄⢸⣏⣹⢼⡀⢻⢧⣼⣌⣿
⢸⣿⣵⢾⣿⣯⠼⡯⣤⢿⣃⡞⠀⣿⠂⡸⣧⣰⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢤⡇⠿⠠⠶⣿⣌⡟⠀⠰⡶⣿⣄⠚⠄⠚⣿⣥⡾⠷⠾⣧⣏⢸⣹
⢸⣿⢿⡤⣿⣁⡠⢆⣦⣤⣿⣧⣾⣿⡿⢀⣾⣷⡀⢦⣠⣀⡆⠀⡀⡀⠀⠀⠀⠀⠐⣸⠟⣿⢼⣤⠚⢻⠉⠉⠀⠠⠖⠻⠎⢃⡄⠘⠻⣯⡴⣦⡀⢹⣽⢻⣿
⢸⣷⣿⣿⡀⣠⠀⣈⣧⣀⠙⣿⣿⣿⣽⣿⡏⣿⣷⣾⣿⣿⣿⣿⣿⡿⣿⠶⣾⣶⣋⢼⡴⢿⠶⣴⣦⣼⣤⣤⢺⣧⣤⡖⣲⠃⠑⣊⠻⣿⣾⣿⣿⣿⣷⣼⣿
⢸⣿⣿⡿⠉⢉⡶⠏⠈⢻⡟⢻⣿⢿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⢷⣷⣯⣿⣿⣿⡵⢚⣇⢘⠧⣜⣦⣿⡿⡄⣩⡐⢿⣋⠉⡇⢸⡅⢙⣻⣿⣿⣿⣿⣿⣿⣿
⢸⡿⣿⡿⠑⢺⡀⠈⡧⣀⣷⡖⠟⠘⠁⠹⡇⠁⠈⠋⠛⠁⠀⠀⠀⠉⠙⠛⢻⡡⠒⠻⠋⠀⠴⠗⠀⣿⠁⢯⠡⠅⠐⠵⡎⢁⣏⠙⠦⢭⢹⠟⠛⠉⠀⠙⠻
⠀⠀⡈⢛⠚⠉⡉⢁⣄⠀⠈⠿⠒⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠃⠘⠃⠀⠚⠂⠉⠁⠀⠀⠀⠐⠈⠘⠃⠋⠸⠀⠆⠀⠦⠴
⠀⠀⠉⠉⠀⠈⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣭⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⣄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣷⣄⠀⠚⠻⣥⢤⡄⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠘⠟⠿⠿⣿⣿⣿⣿⡄⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣮⣅⠀⠐⢿⣶⡂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠰
⠀⠀⠀⠐⠶⣶⣦⣄⣠⣴⣿⡏⣿⡿⡇⢀⣴⣿⣿⣍⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⢀⣹⣿⣿⣶⡄⡀⠀⠀⠄⠸⡇
⠀⠀⠀⠀⠀⠀⢈⣉⣽⣿⣿⢿⣿⣿⣿⣾⣿⣿⣿⠁⠀⠀⢡⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄⢨⣿⣿⣿⣯⠀⠈⠀⠈⠄
⠀⠀⠀⠉⠳⠶⣾⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣟⠀⠳⡄⠄⠒⢓⠢⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠠⢄⡀⠀⣼⣿⣿⣿⣿⣷⣾⠿⣿⣿⣿⠿⠁⠈⠀⠀⠀⢰⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣤⢀⡀⠀⠘⠀⡇⠀⠀⠀⠰
⠀⠀⠀⠀⠘⠋⠙⠛⣿⣿⣿⣿⣿⣷⣿⣿⣿⠶⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣠⣀⣀⣀⡀⠈⣿⣿⣿⣿⠈⠁⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠸⣿⣿⡟⣿⠁⡿⣿⣿⣿⣿⡽⡏⡏⢘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡆
⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠟⠀⠃⠙⢙⢻⣛⡣⠁⠷⠿⢺⣿⣿⣿⣿⣿⣿⡇⠀⣦⠡⠄⢀
⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠆⠀⠀⠀⠀⠀⠒⠻⣿⣾⢷⣼⣿⢠⣄⢠⠄⠘⠀⡆⠟⡋⠹⣿⣿⣿⣷⢀⣿⣀
⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠿⠿⣶⣦⣶⣶⣶⣶⣮⠞⢹⡅⠐⠒⠺⣟⠳⢠⡴⠊⠐⠀⠀⠉⣀⣀⠀⠀⠉⠉
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠋⠡⠶⠚⠛⣒⠒⠀⠀⠀⠀⡀⠈⠹⣏⠉⢀⣼⣿⡀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠚⠻⠿⠷⠂⠀⢐⠂⣀⠈⠁⠀⠀⠀⣼⣷⡀⠐⠈⠰⠖⠿⠿⠣
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠶⠾⠿⠿⠿⢧⣀⠐⠀⠈⠉⠉⢁⣀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⢤⣄⣤⣄⣀⣀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀
⠀⢀⠀⢘⡅⠀⢀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣦⢼⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡆
⠀⠞⡞⢻⡏⠰⣿⣶⢖⡶⡞⣃⣤⣤⡌⢗⣆⣄⢘⠏⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡀⢠⣿⢯⢿⠓⠒⣦⣀⣤⡔⢄⣤⣼⣰⣇⢰⡆
⠀⣛⣥⠘⠉⢻⠿⡟⢙⡄⠁⣭⢸⣗⢩⡍⢹⡟⢊⣩⣨⠇⣀⠀⠀⢀⣤⠀⠀⣀⣀⣀⠾⢠⡮⢳⠈⣼⠨⣯⣳⡍⢿⣿⠯⡁⠛⡚⢇⠤⢳⠼⣧
⠀⡯⠘⢦⣸⢓⣖⢹⣅⣷⠚⡣⢘⣵⠈⣓⡭⠶⣤⠒⣶⡂⢿⣿⢻⡏⠛⣿⣿⣯⣿⡿⣺⣛⢈⢫⠀⣶⡠⢿⢧⠱⠶⣿⣆⠩⢠⡈⢻⠒⠽⢷⡼
⠀⠈⢀⣯⡜⠸⣆⡰⡿⣠⠋⣥⡬⡄⢟⣿⣖⡱⢋⣾⠉⡍⠺⣻⡴⠃⠡⠈⢿⣁⡹⡋⡩⠌⢹⡯⣹⠀⢣⠐⢄⠱⢦⣬⡁⠲⡄⠓⠘⣅⡛⠜⠳
⠀⠀⠀⠙⠀⠺⠤⡘⢀⠀⠈⠉⠘⠉⠛⢡⣄⢱⡏⠀⢢⣸⡛⠎⠁⠐⠒⠀⠈⠀⠀⠈⠁⠉⢚⡙⠉⠱⠏⢉⠚⢏⣠⡃⠍⠠⠆⠨⠢⣌⠔⢠⡉
⠀⠀⠠⠇⠐⠁⠄⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡇⢈⡧⡀⠘⡟⠀⠭⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣷⡶⣤⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⠀⣀⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⣸⣟⣿⣿⣇⡤⢛⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣻⣽⢿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣿⣿⣿⣿⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⣿⣿⣿⣷⣿⣸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣾⣿⢿⣻⣿⣿⣿⣻⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠟⠻⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⡏⢉⣉⠀⢰⢖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⢻⣿⡟⠛⠓⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢽⣿⣿⡏⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⡇⠀⠀⠀⣴⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣹⣿⠟⠀⢀⣀⣶⣀⠀⠱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣿⣷⣿⣷⣶⣶⣶⣿⣿⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠁⠀⠈⠉⠉⣿⡏⢉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣟⣿⣷⣿⣿⡿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⡋⠁⠀⠀⠀⠀⠀⠀⣞⢽⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⣟⣿⣟⣻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⠀⠀⠀⢀⣖⣿⣸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⢀⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠋⠉

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠦⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠄⠀⠀⠀⠁⠀⠐⠀⠀⢀⠀⠀⠂⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠤⢆⡑⠀⡴⠜⢃⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⢰⠸⣿⠒⠒⣶⠂⣄⣤⡖⡇⠀⡀⣄⠀⠓⢴⡚⢚⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠒⠚⠓⠛⠀⠀⠁⠒⠕⠊⠇⠀⠠⡅⠹⡤⠀⠀⡠⠞⠒⠓
⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠀⠈⠟⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠴⠖⠒⢲⠀⠀⠀⢀⠆⠀⠈⠙⠒⡐⠈⠱⢲⡷⠄⠀⢢⣄⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⡀⢀⡀⠀⠠⢜⡁⠀⠀⠁⠀⠀⣀⠀⠀⣗⠀⠀⠁⠀⠀⠀⠓⠛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠶⠀⠈⢄⠀⠄⡀⡀⠀⠀⠀⡰⠁⠉⠀⠀⣀⡠⠴⠒⢉⢄⡂⢼⠤⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠁⠀⠀⠀⠀⠉⠒⠢⠅⠀⠀⠀⣇⣄⣠⠶⣻⢶⠦⢖⠋⠁⠀⣤⡁⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⠸⡍⠉⠒⠶⣄⠁⠂⣬⡇⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡇⠀⠀⠈⠢⠄⠀⠀⠙⠢⡈⠑⢤⣀⠀⠀⠙⠀⠀⠀⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣉⣠⣤⡠⡼⠶⠂⠀⠈⠓⠦⣈⣉⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠠⠔⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⣠⠤⡤⠊⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⠁⠀⠀⠀⣀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁
⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠁⠀⠀⠰⠄⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠆⠀⠀⡤
⠀⢀⡄⠀⢀⣄⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠀⡠⠀⠠⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡀⠉⣄⠑⠀⠁⢀⠀⠀⠀⠀⢀⣿⠀⠐⠀⠀⠀⠺⠀⠀⠐⠀⠀⢢⠀⣰⡄⠊⠀⠠⠀⠈
⠀⠀⠀⠈⢀⢃⠈⠀⣠⣤⣤⣵⠀⠀⠖⠢⠂⠒⠆⠀⡌⣂⠀⣐⠩⠁⢀⢠⣆⠰⢃⠱⡀⠤⣼⡇
⠠⣾⡀⠀⠐⠐⠰⠛⠛⠛⠃⠌⠶⠒⠀⠓⠐⠃⠘⠘⡖⠿⠀⠿⠀⠗⠀⣤⠈⠻⠫⠛⢋⠈⢀⠃⣠⣤⡀
⠈⣾⡅⣠⠨⠺⠀⠰⠂⠗⠀⡂⡄⠚⢀⠄⠄⠄⠘⠃⡇⠀⣏⡅⠀⠀⣶⠀⣶⠀⠿⠿⠀⢠⡄⢘⢁⣤⠉
⠐⠛⠂⢸⠐⠾⠀⠐⠂⠂⢸⠽⠃⠀⠀⠂⡀⠂⠀⠰⡇⠰⠃⢧⠈⠘⠛⠀⠛⠂⠿⠽⡄⠘⠃⢸⠀⠅⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠶⣤⡀⠀⠀⠀⠀⣠⡴⠞⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠈⢻⡄⠀⠀⣼⠋⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢀⣠⣼⣆⡀⠀⣿⠀⠀⠀⠀⢀⣠⡴⠞⣿⠀⢸⡇⠀⠀⠀⠀⣀⣤⠶⢻⡇⠀⣀⣾⣦⣀
⠀⠀⠀⠀⠀⠀⣾⣥⣤⣬⣷⠀⣿⠀⣀⣤⠶⠋⠉⠀⠶⣿⠀⢸⡇⠀⠀⠀⠀⢉⣠⡴⢾⡇⢰⣯⣤⣤⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠀⣿⠟⢋⣠⡄⠀⠀⠀⠀⣿⠀⢸⡿⠛⣀⣤⠶⠛⠉⠀⢸⡇⠈⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠾⠛⠁⠀⠀⠀⠀⠀⣿⠀⢸⡷⠟⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⣀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣿⠀⣴⠟⠋⠙⠻⣦⠀⣿⠀⢸⡇⢠⡾⠛⠉⠛⢷⡄⢸⡇⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⢸⣧⣤⣤⣤⣤⣼⡇⣿⠀⢸⡇⣿⣤⣤⣤⣤⣤⣿⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⢸⡇⠸⠷⠾⠏⢸⡇⣿⠀⢸⡇⣿⠈⠿⠶⠿⠀⣿⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⢸⡇⣿⠀⢸⡇⣿⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⢸⡇⣿⠀⢸⡇⣿⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⣿⠘⢷⡀⠀⠀⢀⣾⠃⣿⠀⢸⡇⢻⣆⠀⠀⠀⣰⠟⢸⡇⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠈⢙⣛⣛⡋⠁⠀⣿⠀⢸⡇⠀⠉⣛⣛⣛⠉⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⢀⣉⣉⡀⠀⠀⣿⠀⢸⡇⠀⠀⣈⣉⣁⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠉⠀⠀⠀⣿⠀⢸⡇⠀⠀⠈⠉⠁⠀⠀⢸⡇⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣤⡶⠛⣿⠀⢸⡇⠀⠀⠀⢀⣠⣴⠞⢻⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⢀⣠⡴⠞⠋⣡⣴⠞⣿⠀⢸⡇⣀⣤⠶⠛⠉⠀⠰⢻⡇⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠛⣉⣤⠶⠛⠉⠀⠀⣿⠀⢸⡟⢋⣡⡴⠞⠋⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⡞⠋⠁⠀⠀⠀⠀⢀⡿⠀⠸⣷⠛⠉⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢸⡇
⢾⣛⣛⢛⣻⡟⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⣀⣤⠞⠁⠀⠀⠙⢦⣀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠘⣿⣛⣛⣛⣻
⣤⣭⣽⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣭⣥
⣿⣿⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⠛⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣏⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠄
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠂⡠⠀⣤⡀⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⡄⠈⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⣠⠛⠄⠀⠀⠀⠀⠀⣸⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⣷⣶⠁⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠛⠻⣿⣿⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⡟⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣷⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⣏⣉⡉⠀⢰⡄⠀⠀⠀⠀⣿⣉⣹⠆⠀⠀⠀⡀⠀⢀⡀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⢸⡆⢸⡀⢸⡇⠀⣦⢸⡇⠚⠙⣶⠿⣄⠰⢤⣀⣾⠷⠺⠬⣀⠀⠈⠉⠉⣷⢸⡷⡀⣷⠠⠄⣏⠉⣧⢰⡼⠶⡇⢹⡆⡏⢹⣰⠶⠿⢸⡇⢹
⠀⠀⠀⠀⠘⠹⠞⠀⠀⠳⠶⠿⠸⠇⠘⠶⠃⠤⠾⠃⠴⠟⠳⠆⠀⠤⠿⠀⠠⠦⠶⠟⠸⠂⠇⠟⠀⠀⠟⠀⠹⠟⠶⠀⠇⠸⠇⠇⠘⠋⠲⠖⠘⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠶⠆⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⣀⣀⡀⠀⠀⣠⣤⣼⣇⣤⣤⡀⣀⠀⠀⠀⠀⣀⢀⣤⣄⠀⣉⠀⢠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⢀⡀⠀⠀⠀⠈⠉⠉⠙⣧⣸⠇⠀⠀⣇⠀⠈⡇⢹⡆⢠⡄⢰⡇⣯⣤⣬⡇⣿⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢸⣉⣷⣿⠛⣯⠁⠀⠀⠀⣀⣀⣀⣠⡿⠹⣇⣀⣀⣏⠀⠀⡇⠀⢱⡞⢻⡏⠘⣧⠀⠀⡀⣿⠀⣠⡟⠀⠀⠀⠀⠀⠀⣿⠀⡎⢹
⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠁⣀⣀⣀⣀⣉⠉⠉⠉⠀⠀⠈⠉⠉⠀⠀⠀⠁⠀⠈⠁⠈⠁⠀⠈⠛⠛⠁⠉⠀⠛⠛⠛⠛⠃⠀⠀⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣍⣉⣉⠉⠀⡀⣀⣀⠀⠀⢀⣀⠀⠀⠀⢀⡀⠀⢰⡆⢰⡆⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠈⠀⠀⣿⠉⠙⡧⢰⠋⠈⢻⣇⣾⣋⣙⣧⢸⡇⢸⡟⠉⢻⡆⢰⣏⣉⣻⡄⢸⠋⠉⢰⡟⠙⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣿⠀⠀⣯⢸⠀⠀⢸⣿⣟⠉⠉⠉⢸⡇⢸⡇⠀⢸⡇⢸⡋⠉⠉⠀⢸⡆⠀⢿⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣤⣤⣤⠀⠿⠀⠀⠿⠘⠷⡴⠾⡇⠹⢦⣴⠖⠈⢷⠀⠿⣤⡾⠃⠘⢷⣤⡶⠀⢸⠇⠀⠘⢷⣤⠶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠐⡄⠰⠆⠀⣦⢲⡄⠀⠀⢀⣠⣤⣤⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢀⠀⢀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠴⠶⣶⣶⠶⣶⠶⢶⣶⠶⣶⠶⠿⠷⠾⠿⣿⠿⠿⠿⠿⠿⠉⠁⠀⢸⢀⠃⠘⡇⢸⠠⡆⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⣿⡄⡟⣤⡂⠀⠀⠀⠀⠀⠈⣿⣽⣿⣭⣽⣯⣭⣭⣭⣿⣯⣭⣭⣭⣽⣭⣿⣿⡇⠀⠀⠀⠀⠸⠈⠳⣶⠇⠸⠀⢧⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠚⠛⠓⠒⠒⠒⠓⠒⠶⠶⠿⠶⠒⠶⠖⠲⠖⠒⠂⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀
⠀⡀⣐⣇⠀⡀⠀⡀⢀⠀⠀⢀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⣿⡁⠀⠀⠀⢀⠀⠀⢠⡄
⢀⡿⢙⡧⣹⣿⣿⠿⠯⡴⣶⡮⢥⣴⣸⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⣇⠸⠟⢿⡍⢹⣦⣶⠎⡔⣾⠿⡇⣧
⢰⡞⢇⢠⢌⡽⡔⣇⠴⠱⣇⠺⣌⣣⣐⢟⡇⣶⡶⣤⢾⣤⣴⣶⣶⡥⠏⢽⠀⡇⣹⡞⢆⣻⡏⠦⠐⢼⠍⣿⣙
⠀⠂⣼⡙⢼⣀⠿⡼⢚⡬⠉⢾⡧⡠⢳⡞⣛⠺⣧⠟⠠⠙⣟⣹⢗⠫⠙⣿⣾⠙⡈⢍⠲⢨⡏⢰⠘⠘⣆⡇⠻
⠀⠀⡈⢀⠓⢄⠀⠀⠈⠘⠉⠃⠴⠹⠇⠘⠼⣟⠊⠀⠈⠀⠀⠀⠈⠈⣙⡍⢉⠙⢠⡙⢧⣬⡘⠐⠀⠓⠮⠂⠤
⠀⠀⠁⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠓⠀⠃⠀⠃

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⡀⠀⠀⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢘⣿⣻⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡃⠀⡄⠀⢠⣯⠄⠀⠀⠀⠀⣸⠀⠀⢀⠀⠀⠀⠀⣨⡆⠀⠀⠀⠀⢀⡀
⠀⠀⠠⣿⣿⠿⣿⣄⡀⠀⠀⠀⢰⣧⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢢⢠⣇⠀⣰⣿⡇⢰⠀⠀⣴⣿⡷⠀⢀⣆⢰⣿⣇⠀⣾⠀⠀⡀⠀⣼⡆⢀⠀⠀⢀⣼⣧
⠀⠢⢼⣿⣿⣶⣉⡶⢿⣤⠀⠀⣼⣿⣇⠀⢰⠀⠠⣿⠀⠨⠀⢠⣿⣾⣿⣤⣼⣿⣿⣿⠀⢴⣾⣿⡟⠂⢼⣿⣿⣿⣿⣿⣿⣦⣠⡆⠀⣼⣧⣾⡆⠀⢠⣿⣿⠄⢰
⢠⣾⣾⣿⡿⢿⠯⢹⣿⣿⣷⣾⣿⣿⣿⣶⣿⣶⣼⣿⣦⣾⣄⣸⣿⣿⣿⣾⣿⣿⣿⣿⣀⣿⣿⣏⣼⣷⣿⣿⡿⠟⢟⡛⢿⣿⢿⣿⢈⣿⣿⣿⡇⠀⣼⣿⣿⣇⣾
⠘⢿⣿⣿⡿⣌⣴⣿⠿⠉⣿⡿⠿⠿⠟⠛⠙⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⢿⠟⠓⠚⠛⣵⡎⢿⣾⣿⢾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿
⠀⠛⠻⠿⣤⣿⣿⢡⠤⡤⠠⠀⡦⠰⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠀⠉⠀⠂⠀⠀⠀⠀⠀⠉⠋⠉⠉⠙⠛⠛⠿
⠀⢺⠙⠇⠉⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⣤⣤⣀⣀⣠⣠⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⡄⠤⠀⠀⠦⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣶⣶⣶⣤⣄⣀⣀⣀⣀⠀⠀⢀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⣀⡀⠀⣀⣤⣤⣴⣶⣶⣾⠂⠀⠀⠀⠀⠀⡠⢆⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣫⣭⡶⠿⠛⠛⣉⡻⣧⡀⠀⠀⠀⠀⠀⠀⢠⣾⢞⣩⣖⡡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣏⠀⠀⠳⠂⣦⣝⡃⣼⡇⠀⠀⠀⠀⢀⠔⣸⠟⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣤⠀⠀⠀⣠⣽⠟⠁⠀⠀⠀⢀⡵⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡞⠁⠀⠀⠀⢀⣄⠀⠉⠑⢦⡀⢀⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠈⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⣿⠄⢀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣦⠤⠀⠀⠀⠠⠶⠶⠾⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠉⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣽⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠋
⠀⠀⠀⠀⠀⠤⠶⠚⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠲⠶⠾⠿⢷⣤⣤⣤⣤⣄⡀


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠋⠁⠀⡄⠈⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⠠⡄⢀⠀⠉⢻⣶⡄
⠀⠀⠀⠀⠀⠀⢠⡟⡿⠁⠀⠀⠀⠇⠸⠇⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢉⡱⠶⣉⠁⠀⠀⢿⠹⡄
⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⠀⢠⣄⡀⢀⣠⡿⠁⠀⠀⠀⠀⢀⣠⠤⡴⢶⣶⣤⣄⣠⣤⣶⣶⡶⢤⢄⡀⠀⠀⠀⠀⠈⠻⣌⡐⠓⣈⡄⠀⠀⢸⡇⢱
⠀⠀⠀⠀⠀⠀⢿⠀⢷⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⣠⣴⣞⣭⣶⣿⡇⣾⣿⣷⠈⣿⣿⠟⢿⣧⢸⣷⠉⣳⣦⣄⡀⠀⠀⠈⠉⠋⠉⠀⠀⠀⣼⠃⣸
⠀⠀⠀⠀⠀⠀⠸⡆⠈⢧⣀⠀⠀⠀⢀⣠⣴⣶⣿⡇⣿⣿⣿⣿⠋⢡⣿⣿⣿⡆⣿⣿⡀⢀⡉⢸⣿⣀⣿⣿⠀⣹⣶⣤⣄⣀⠀⠀⠀⢀⡼⠃⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠻⣿⣿⣿⣿⣟⣋⣉⣉⠁⠀⠀⣿⣿⠀⣸⣿⣾⣿⡿⢻⣿⣿⣿⡿⢸⣿⣿⣿⣿⠀⠻⣿⣿⣏⣙⣉⣉⣭⠉⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣉⣉⣛⣛⣿⣿⣿⣷⠀⠀⣿⣿⠀⣿⣏⡼⠋⠀⠀⠙⠿⣍⡁⢸⣿⠈⣿⣿⠀⣾⣿⣿⣟⣛⣋⣉⣉⣄⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣏⣀⣠⡿⠿⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠒⠯⢤⣿⣿⣄⣻⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⠆⣿⢀⡄⢸⡀⠀⣶⣀⣴⠀⣠⣄⠀⣴⡄⠀⢶⣄⣶⡀⡶⢠⣤⡄⢠⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⠇⣿⠻⣆⢸⠇⠀⢿⠉⢿⠀⢷⡼⠇⢿⡄⠀⠘⣿⠋⣿⠃⢼⣿⡿⢰⠿⣧



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⡀⠀⣿⣿⣿⣿⣀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢈⣿⣿⡄⢹⣿⣿⣿⣿⣿⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣴⣿⣿⣿⣇⠘⠿⠿⢿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣿⣷⣄⠀⠀⠈⠻⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⡄⠙⢿⣿⣿⣷⣄⠀⠀⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠙⢿⣿⣿⣷⣄⠘⠿⠿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣦⡀⠀⠀⠙⢿⣿⣿⣷⣶⣶⣤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣶⣶⡄⢹⣿⣿⣿⠟⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⣿⣿⣿⣿⣿⣇⠘⣿⣿⡁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⣿⣿⣿⣿⠀⠈⠛⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⡀⢰⠣⠀⠀⠀⢀
⢣⡾⠁⢴⡃⠀⣿⠀⢀⡆⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣾⣥⡋⣠⠝⠀⢃⡘⣿⠄⣼⣴⠁⣾⣄⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡛⣷⣄⣐⡒⠀⣴⠀⣺⠆⣿⣏⣁⠸⣷⣴⣧⢄⡄⡠⠀⣶⣠⢀⣠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣄⣠⣆
⠉⠑⠓⠊⠀⠐⠧⣖⠎⢉⢿⠀⣐⠂⢻⣯⡐⢻⣿⡟⣼⠃⢻⣿⡏⣴⣿⣠⣤⠀⠀⠀⣠⣴⣴⣾⣿⣿⣟⣿⣛
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⡃⣤⠄⠀⠘⣿⠀⠐⣿⠀⢸⣇⣐⣿⠃⠸⣇⣘⣿⢿⣾⠿⠟⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠚⠒⠛⠧⢬⣹⣆⠈⢿⣒⣺⣆⣤⣻⣆⣿⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣾⣀⡤
⠀⠀⠀⠀⠰⣦⣀⢘⡇⣀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⣿⣭⣿⡗⠒
⠀⠀⠀⢤⣤⣬⣾⠋⠙⣯⣡⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠟⠈⠙
⠀⠀⠀⠀⢀⣴⠽⢻⡋⠯⣦⡀
⠀⠀⠀⠀⠈⠁⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣽⣟⢛⣿⡥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠀⢿⢀⣠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠙⡟⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣵⡟⠛⢳⣮⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⡔⠐⢦⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⡶⡻⢵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠛⠃⢰⣀⣀⣈⡄⠘⠃⠈⠑⠢⢄⠀⠀⠀⠀⠀⠉⠀⠀⠻⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠣⠴⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠣⠘⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠈⠑⠒⠤⠄⣀⣀⣀⣀⣀⠠⠤⠒⠋⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⣄⢀⣦⢀⣠⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠠⠴⢿⣟⣹⣿⠧⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⣈⣿⡾⢷⣾⣋⣀
⠀⠀⠀⠀⠐⠋⠹⡏⠙⠓⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠿⢻⡟⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀
⠀⠀⠀⠀⠙⠢⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⣸⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠉⠉⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠀⠀⠈⠉⠉⠉⠁⠀⢸⠀⠀⢠⠀⠀⠀⣠⠎⠁
⠀⠀⠀⠀⠀⣀⣀⣀⣈⣦⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⠀⣠⠞⠥⠀⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡆⠀⠀⡸⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠔⠁⡜⡉⠉⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⡜⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠠⠁⠀⠡⣀⠀⠀⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠓⠤⢀⣀⣀⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⢀⡀⠤⠤⠀⠀⠤⠤⠄⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣁⠀⠀⢀⣀
⠀⠀⢀⡴⠮⠅⠀⠀⠤⠄⣀⡀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⣀⡠⠤⠤⠬⢑⣢⣄⡀
⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠀⠀⠽⠖⠂⠉⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⠄⣀⣀⣠⠔⠉⣀⡀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀
⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡶⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⡟⠄
⠀⠀⢀⣤⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⢴⠋⠀⠀⠀⠀⠠⠠⠎⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⣼⠀⢴⢎⡠⢤⡀
⢠⣆⣼⡗⣠⠀⠀⠀⠴⠂⠠⠀⠀⠈⢀⡀⠀⠀⠠⠠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⢀⣼⡆⠛⠛⠿⣤⣠⡄⣀
⣿⣿⡟⣷⣿⣠⣠⠔⢐⠁⡄⣀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠐⣆⠀⠀⣯⠃⠀⡜⢛⠉⣻⡁⣀⠹⣀⠠⣿⣀
⣸⡿⢀⢻⣿⣿⣿⢞⠁⠈⡁⠀⠡⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠕⢀⢘⣤⠓⣄⡔⠀⠶⢌⣯⠈⠣⠈⢳⣮⣿
⢨⡿⢛⢰⣿⠟⠃⠌⠁⡀⠀⠀⢂⢘⣿⣷⣿⣶⣼⣤⣄⣀⡀⣠⣤⣤⣷⣤⣼⠴⠅⣘⣋⠀⣀⡥⠋⣁⠀⠈⢿⠀⠀⠠⡀⠈⣿
⢠⡀⠊⢈⣥⠖⠋⠀⠚⠀⠀⣄⡀⠑⢿⣿⣟⣹⣽⣽⣿⡿⠟⠟⠿⠿⣿⣿⠟⠀⡀⣈⡑⡆⢈⡶⢋⡠⢦⠜⢦⡂⠀⠀⠉⠙⢿
⠘⠋⠀⢯⡥⠀⠁⠚⠁⢤⡜⢳⡀⠱⠦⢷⣀⢼⠷⠛⣡⠤⣄⠀⠀⠀⠈⠻⠀⠀⣀⢉⠻⣄⣾⢉⢁⠀⠀⡁⠂⢄⡀⠀⠢⢀⠠
⠀⠀⢠⡎⠀⠂⣏⡀⠔⠀⠈⠤⠷⠀⣀⢀⠀⠈⠰⣭⡼⠏⢿⣽⠶⠾⠟⠁⣨⠈⢁⣁⣉⣻⣿⡷⢛⣧⣀⣿⣷⢄⣻⣇⣧⠈⢿
⠀⠠⠋⠀⣀⡤⠶⣅⠀⠀⠈⢳⡠⠲⡍⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠤⠀⢩⠉⠛⠙⢦⠠⠉⠻⣏⢠⣼
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠠⠀⠊⠁⠐⠄⠀⠠⠳⠄⠸⠿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⢀⡴⣿⠃⠀⠀⠘⣿⢦⡀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠾⠡⡟⠀⠀⠀⠀⢻⠌⠷⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⣤⣼⣀⣀⡀⢀⣀⣀⣧⣤⣤⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡏⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⢹⣏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣀⠀⠀⠀⠀⢠⡶⢶⡀⠀⠀⠀⠀⣠⣾⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡶⠤⠶⠛⠁⠈⠛⠶⠶⢶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠊⠉⡍⢨⠉⠉⠁⠄⠉⠉⢉⠨⠉⠑⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢸⠀⠀⠀⠵⠘⠀⠀⠀⠂⠰⠐⠄⠽⠀⠀⠀⠃⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⣘⣒⢮⣿⡿⠃⠄⠀⠀⠀⠄⠠⠙⢿⣿⠵⣒⣂⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣶⠀⠀⠀⠀⠀⠀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⠀⠀⠠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠇⠀⠀⠀⠀⠸⠿⠏

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠂⠉⠉⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠈⠉⠀⠂⠒⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠮⠤⠤⠤⠤⠤⠦⢄⡀⠀⠀⠀⠀⠀⠰⠚⠒⡢⠀⠤⠤⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⡧⢀⣠⠁⠀⠀⠀⠀⠐⠁⠀⠀⠉⠉⡰⠒⠀⠢⠤⠠⣀⣰
⠀⠀⠀⠀⢀⣜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠣⠀⠎⠀⠀⠀⠉⠉⠒⠒⠂⠦⠤⠀⢀⣀⢠⡀⠀⠀⠀⠀⢀⠊⠀⠁
⠀⠀⠀⢀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠀⠈⠉⠉⠀⠐⠚⠒⠐⠇
⠀⠀⠀⡸⠤⢤⡤⠀⠐⠒⠒⠰⠂⠉⠉⠉⠈⡘⠁⠀⠀⠀⠀⢸⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠢⡀
⠀⠀⢸⡀⠀⢸⠀⠀⠀⠀⠀⣀⠀⡀⢀⣀⣀⠧⠀⠠⠤⠤⠄⠺⡒⢺⡀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⢋⠋⠉⠈⠀⠀⠀⠉⠁⠀⠀⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡼⣀⠒⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣪⣱⠀⠀⠀⢠
⠀⠀⢎⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡹⠙⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⡀
⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠉⠐⠂⠐⠒⠂⠀⠊⠁⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠒⡇
⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣽⠒⠂⠠⡴⠶⠆⠀⠒⣊⠁⠀⡀⠀⠀⡰⢤⣄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⢇
⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⣿⡀⠀⢰⠄⠀⠠⠤⠤⢆⠀⠀⠈⢢⡜⢁⠆⡆⠀⠀⠀⠀⡇⠀⢀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠰⢏⠀⠉⡙⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠑⡌⠀⡇⠀⠀⠀⠀⠇⠀⢨⡀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠍⠲⡀⠀⠀⠁
⠀⠀⠀⠀⠌⠀⠀⠀⢀⠃⠈⠉⠈⠁⠥⠕⠀⠀⠀⠀⠘⠀⠀⠀⠀⢡⠀⠱⠤⢀⡀⠤⠃⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⢲⢄
⠀⠀⢀⡎⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢱⠤⠀⠔⠁⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⠑⠤⣀⣀⣀
⠀⢀⠊⠈⠙⠐⠂⡼⠀⠀⠀⠀⠀⠀⢙⡁⠀⠀⠀⠀⠀⠘⣄⠤⠐⠐⠈⠉⡄⠀⠀⠀⠀⠀⢈⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠈⠢⡀
⢀⠎⠉⠐⠂⠤⣀⠂⠀⠀⠀⠀⠀⠀⠣⠜⠀⠀⠀⠀⠀⠀⢰⣀⡠⠤⠐⠊⠙⡄⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡌⠀⠀⠀⠀⠀⠈⠢⣄⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⣠⠜⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢇⠀⠀⠀⠀⠀⡠⣀⡸⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢆⡀⣤⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠰⡁⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠈⠒⠤⠀⠔⠊⠀⢸⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠑⠢⠄⠀⠔⠋⠀⠀⠀⠀⠀⠉⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠉⠁⢹⡁⠀⠀⠀⠈⠉⠉⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠁⠀⠀⠀⢈⠁⠀⠉⠉⠀⠀⠀⢁⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⢀⡠⠒⡇⠀⢀⣀⣀⣀⡀⢸⠀⢀⣀⣀⣀⣀⠀⢸⠃⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⢀⡴⠛⠈⠉⠉⠉⠑⠢⢄⡀⠀⡙⠈⠀⠀⠀⡀⠤⠈⠛⠒⠀⠤⠌⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠉⠉⠐⠻⢦⣄
⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠂⠀⠤⠄⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠚⠉⠉⠉⠉⠉⠉⠉⠓⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⣀⠀⠀⠀⠀⣠⣄⠀⠈⠁⠀⣀⠤⠴⣀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠋⠀⠀⢠⠞⠡⠈⢳⣴⠋⠉⠁⠀⣀⣀⡱⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢀⠤⣀⠀⢀⡴⠛⠲⠚⠲⠋⢸⢃⣞⠉⢉⣥⠛⠢⡀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣠⣏⠀⠀⢑⣏⡀⠀⠐⠖⠀⠀⣨⣌⢀⣟⣉⡈⠶⠲⠟⢆⠐⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⡴⠁⠈⠛⠑⠋⠀⠙⠦⡀⠀⣰⡎⢧⡼⠉⠀⠀⠙⣄⠂⠀⠈⠣⡀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠎⠀⠀⠃⠀⠀⠁⠀⠀⣠⢬⡞⠁⢧⠀⠀⠀⣀⣀⣠⢬⠇⠀⠶⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡍⠓⢄⣀⣠⠤⠴⠶⠶⠤⠮⣀⣻⢩⣿⢹⠒⠚⠉⢱⣳⣄⣸⢑⣦⣀⣀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠒⠓⠚⠒⠚⠉⡉⠀⠀⠊⠁⢀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⠀⠀⠐⠃⠀⢀⣀⠤⠤⠴⠦⠤⣀⠀⠀⠀⠀⠀⣀⣀⣤⣀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⣡⠔⠛⠋⠉⠁⢛⠃⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠐⠀⠁⠀⠀⠁⠀⠀⡀⠀⠈⠀⠀⠀⠄⠀⠀⠉⢀⣀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠒⠒⠒⠶⠤⠤⠤⠤⠤⠤⠤⠶⠒⠒⠒⠚⢉⣉⡠⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠉⠉⠙⠛⠒⠒⠒⠒⣒⡒⠒⠒⠒⠒⠒⠛⠉⠁⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠐⢏⣀⣉⡱⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢬⣓⣀⠀⠠⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠤⠤⢄⣀⡠⠤⠒⣋⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠤⠬⣭⣉⣉⣙⣛⣛⣛⣛⣛⣛⣛⣛⣁⣈⣩⡭⠥⠖⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠠⠀⠀⠀⠀⢠⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⣄⠆⠀⠀⠀⠀⠀⠐⠬⡄⣸⠿⠁⠀⠠⠀⠀⠀⠰⡀⢀⠄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⡛⠀⠀⠂⠀⠀⠀⣂⣢⡄⢤⡤⣀⡀⠀⠀⠀⠈⠀⢑⠺⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠂⠂⠈⠌⠨⠩⠽⠂⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠈⠘⠛⢍⠀⠀⢀⢀⠔⢀⠀⠀⠀⣠⠖⠀⠀⠀⢀⠀⢠⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⢠⠊⠳⡄⡀⣠⣞⡠⠆⠀⣠⠚⠁⠀⠀⠀⠐⠀⢀⠀⢉⢉⡑
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢁⡀⡀⠀⣀⠀⠁⠀⠀⠂⠌⠀⠀⡇⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⠐⠰⠦⠦⢜⢀⢉⠉⠉
⠀⠀⠀⠀⠀⡛⠒⠚⢂⢈⣉⡍⠛⠁⠀⠀⠀⠀⠀⠀⣠⠄⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠤⠦⠤⢦⢝⠋⠊⠛⠓⠀⠀⢀
⠀⠀⠀⠀⢘⠃⠛⠑⠎⡉⢉⠉⠉⠙⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⢠⡤⡠⠤⡤⣼⠟⠜⠚⠳⠎⠁
⠀⠀⠀⠀⠐⠛⠒⠛⠫⠁⠓⠊⠂⠙⠄⠀⠀⠀⡀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⣤⣠⡀⣤⣀⣈⢹⡆⠀⠐⠀⠁⠀⠁
⠀⠀⠀⠀⠓⠛⠊⠚⠯⠶⠤⠦⠴⠴⡶⠁⠀⠀⠀⠁⠀⠀⠀⠀⠠⠄⠐⠈⠀⠀⠀⠀⠀⠠⠀⢄⠀⠀⠈⢙⡇
⠀⠀⠀⠀⠁⢱⠇⠘⠔⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠐⠃⠀⠀⠀⠒⠢
⠀⠀⠀⠀⠀⠘⠃⠀⠄⠀⣀⢻⠈⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣌⠄⠀⠀⠐⠠⢀⠀⠀⠉
⠀⠀⠀⠀⠀⠘⠷⢄⡀⠀⠄⠈⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠠⠮⠂⠀⠀⠀⠀⡀⠀⠀⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠅⠀⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢋⣀⣀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠰⠊⡙⠋⢁⡁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⢻⠦⠒⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣄⠴⠄⢃⠸⠗⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠒⢉⠉⠛⢁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣰⣶⣆⣄⢄⣀
⠀⠀⠀⠀⠰⠂⠀⡶⢴⠇⢠⠂⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⢀⠄⣀⣰⣿⡟⠋⠙⢯⣼
⠀⠀⠀⠒⠀⢠⢠⡠⡄⣶⣦⣤⡄⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠉⠉⠁⠘⠏⣁⣀⣠⣤⣿
⠀⠀⠀⡀⢣⣾⡟⠻⠋⠁⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠂⠀⠀⡤⠀⠐⠂⠠⣴⠿⠛⠉⠉⠉
⠀⢀⠰⠶⣿⣿⠿⠁⢠⡷⢤⣹⣒⡘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠂⠚⠷⠟⠃⠢⣶⣤⣤
⠀⠰⠶⠴⠿⢁⠤⠊⢸⣷⣄⣀⢈⣿⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⡆⠀⢀⣤⣤⣤⣾⡂⢀
⠀⠀⠠⠶⠂⠀⠀⠀⠈⠁⠙⠿⢭⣧⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣟⠖⠚⠉⡭⠎⠀⠄⠉⠁⠙⢫
⠀⠠⠂⠀⢰⣞⣁⣤⣤⡴⣴⣄⠀⠑⡌⣐⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠀⠦⠀⠀⢶⡾⠇⠀⠀⠁⠀⠀⡀⣴⣧⣀⣖⡀⠀⠓⠂⠚⢁⣨⠿⣈
⠀⠊⠴⣺⠟⠋⠙⠋⠉⠉⡛⠫⡤⠄⠀⣤⣉⠉⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠠⢠⡖⠒⢂⠀⠤⠖⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠉⠉⠉⠱⠂⠠⠜⡶⣿⠀⠙
⠀⠀⠀⠀⠒⡶⠒⢠⠊⠛⣷⠤⣀⢨⣇⡀⠈⠉⠂⠀⠀⠀⠀⠀⠀⢴⠉⠉⢛⣿⠁⢸⠃⠀⠐⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠐⠂⠐⢠⡴⣶⣶⡶⠀⣈⠀⠋⠀⣤
⠀⠈⠀⠀⠠⠄⠀⠉⠛⠁⠉⠢⠀⠀⠉⠁⠘⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠋⠙⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠒⠉⠩⢉⠃⠴⠾⡿⠀⢶⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠁

⠀⠀⠀⠀⡙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡿⠃⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡞⠋⠐⠐⠒⠒⠐⢷⢸
⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸
⠐⢀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻
⡀⣠⠃⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠛⢻⡄⠀⠀⠀⠀⠀⠀⣶⠛⠒⢠⣤⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠉⣤⢾⣷⡈⠀⠐⠀⠀⢠⡗⠀⡄⡀⠹⣄⡀⠀⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡾⠛⠳⡒⠀⢸⣀⣽⣷⣦⣀⣠⣶⢿⠅⣰⢸⡵⡖⠉⣙⣳⣤⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠵⠤⣄⢈⣂⣾⣉⡄⠉⣻⣡⡟⣦⢸⢡⣿⣿⣿⣾⡷⠛⠉⢹⣷⠀⣸⠁
⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⡆⡁⠀⠀⠀⠀⣿⠄⠀⠀⠈⠟⣹⣿⠋⠙⢿⣿⢹⡟⡇⡌⣾⣻⡿⠂⠁⠀⠀⢠⣾⣿⠂⡁⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠹⣤⡀⠀⢠⠈⠀⣉⣓⣦⣼⣿⢸⢸⣤⣾⠟⠉⠉⠻⣦⠀⣬⣾⠿⠋⢀⡇⠀⠀⠀⠀⠀⠐⡇
⠀⢈⠀⠀⠀⣄⠀⠄⠳⡀⠀⠀⢀⣀⠀⡄⠀⠙⠻⣦⣿⣤⡾⠁⠀⠈⢁⡉⢙⣛⡛⠃⠀⠀⠀⢀⡿⠛⡋⢡⣀⡀⠘⠓⠶⢶⣦⣤⣤⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠀⠀⠀⠁⠀⠀⠀⠈⠛⠛⢿⡄⠀⠀⢀⣤⣬⣍⢁⡀⢀⡀⢠⡞⠁⠀⠀⠀⣹⣦⣄⣤⣤⣤⡴⢤⣿⣿⣧⣄⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡤⣤⡅⣠⣴⠛⠀⠀⠀⠀⠞⣡⣤⣴⣶⡿⣶⡿⠿⠮⣟⠿⠟⠛⠿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⡟⣏⡤⢞⣵⡾⣭⡐⠈⠀⢀⣀⣀⣘⣿⣿⣿⣿⣶⡞⠠⢉⠛⢶⣇⠀⠒⠤⠤⡄⠉⢻⣿
⠀⠀⠖⠃⢤⠇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⣉⡿⠞⣋⣘⠛⢉⡔⣠⡿⠀⠀⠈⢀⣈⣿⣿⣿⣇⠈⠯⣉⡑⠢⣬⠉⠲⠈⡉⠁⢀⡀⠠⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡸⠛
⠀⡀⣴⡆⠀⠀⠀⢀⡀⠀⠀⠀⠊⠀⠙⠀⠀⢠⠄⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⣤⠀⠀⢸⡇⣼⣵⡇⠐
⣾⣿⣿⣰⣇⡀⡀⠩⠆⠁⠀⠀⠀⡇⠀⠀⠁⠈⠀⠀⠀⢠⠀⠀⠀⠀⡄⠀⠀⣿⡄⠠⡿⠳⢶⠊⠉⡏⠉⣸⡀
⢹⡏⠹⣿⣿⣿⠴⠂⠐⠁⠑⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠐⡙⢤⣨⠄⡡⡙⣗⠑⢌⠲⣬⣷
⢩⡗⠃⣿⠿⠛⡈⠀⠀⠀⠐⠈⣿⣷⣾⣤⣶⣤⣀⡀⣀⣤⣤⣦⣤⡥⠀⣸⣋⢁⣨⠝⢉⠀⠘⢷⠀⠀⢀⠈⣻
⢰⠀⠁⣽⠖⠋⠐⡊⠀⢠⢄⡁⢻⣿⣏⣿⠿⣿⡿⠟⠛⠛⠿⣿⡿⠁⠠⣈⡑⠄⢹⠚⡡⠲⡘⢦⠀⠀⠈⠙⠻
⠈⠁⠘⡵⠀⢁⠈⠁⠶⡏⢧⠈⠒⠿⠄⢚⢛⡡⣖⣦⣀⠀⣀⣈⠃⠀⠠⡨⢙⣾⣏⠁⡄⠀⢉⠐⠠⡀⠐⠀⣐
⠀⢀⡜⠂⠀⠡⡄⠃⠀⢨⠊⢂⢤⣀⠀⠀⠙⠚⠓⠚⠚⠛⠛⠁⠠⠐⠀⠖⠤⡽⠛⠈⠵⢀⠞⠃⠠⢹⡴⠀⠘
⠀⠈⠀⠀⠚⠉⠳⢤⠄⠀⠷⠈⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⢠⠦⠀⠀⢁⠐⡀⠳⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠄

⠀⠀⠰⡿⠛⣶⣤⡀⠀⠀⠀⠀⠀⢠⡶⠛⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠛⢦⡀⠀⠀⠀⠀⠀⠐⣿⠛⣷⣤⣀
⠀⠀⢸⡇⠀⣿⣸⠛⣦⠀⠀⠀⢠⡟⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⣿⠀⢸⣸⡟⣧⡀
⠀⠀⠰⣏⠀⣿⢸⡆⠘⣧⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⢸⢹⡇⠈⣷
⠀⠀⢘⣧⣀⣿⠘⣇⠀⢹⡆⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣿⣀⣼⠈⣧⠀⢸
⠀⠀⠈⣿⢹⡇⠀⠙⠳⠛⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⡏⣯⠀⠘⠳⠞
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⡿
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⣯
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡶⠋⠙⢷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡞⠋⠻⣶⡇⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⣿⢀⡇⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢸⡀⡇
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⣾⠁⣠⡶⠶⣤⡈⣷⠀⠀⠀⠀⠀⠀⢠⡟⢀⣴⠶⢶⣄⠸⡇⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠛⢿⠃⠀⠀⠈⣿⠛⠀⠀⠀⠀⠀⠀⠘⠛⣿⠁⠀⠀⢹⡟⠋⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⣟
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣧⠶⠶⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠶⢦⣼⡇⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⣠⣼⠃⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⢀⣤⣿⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⢀⡟⢸⡇⠀⠀⠀⣿⢹⡄⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠸⠇⢸⠁⠀⠀⠀⣿⠸⠇⠀⠀⠀⠀⠀⠸⠁⣿⠀⠀⠀⢸⡇⠻⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣾⡇⠀⠀⠀⠀⠀⠀⢸⡇⣟
⠀⣀⣤⣿⢸⣷⣤⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣤⣾⡇⣷⣤⣀
⠛⠛⠛⣿⢸⡟⠛⠛⠓⠀⠀⠀⠀⣸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠚⠛⠛⢻⡇⡿⠛⠛⠛
⠀⠀⠀⢹⣾⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣷⡇
⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣆⣀⣀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣼⠇⠀⠀⠀⠀⠀⠀⠈⣿⡇
⣤⣤⣤⣤⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣼⠀⠰⠀⠀⢰⠄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠸⠀⠀⢀
⠀⠀⠀⣼⣿⣝⡆⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡆⠀⢠⣿⡆⣘⠀⠀⣺⣗⡀⠀⢀⠀⣴⡇⠀⢠⠀⠀⠀⠀⢺⠃⠀⠀⠀⠀⣴⡀⠀⢸
⠀⡀⢸⣿⣿⣹⢿⣲⣄⠀⠀⠀⣿⣦⠀⢀⡀⠀⣾⠀⠠⠀⠀⣵⣸⣷⠐⢺⣿⣥⡆⠀⢘⣿⣿⣅⠀⣿⣄⣿⣷⣤⣾⡆⠀⠂⠀⣿⡇⣴⠀⠀⢰⣿⡗⠀⣸
⠀⣈⣹⣿⣿⣷⠮⢏⣿⣧⣀⣼⣿⣿⣆⣸⣇⢠⣿⡄⣨⠀⢸⣿⣿⣿⣻⣿⣿⣷⡗⢀⣽⣿⠟⣤⣨⣿⣿⣿⣿⣿⣿⣿⣾⣧⠠⣿⣿⣿⡀⠀⢼⣿⣯⠀⣿
⢸⣿⣿⣿⣏⢙⢡⣾⡿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢟⣩⣴⢆⡘⣿⣹⣿⣸⣿⣿⣿⣧⣀⣿⣿⣿⣾⣿
⠀⣽⣿⡿⢉⣿⡿⢛⢀⠘⡛⢉⡉⣁⠀⠀⠀⠠⠤⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠋⠉⠉⠈⠉⠉⠉⠉⠇⠠⠴⠆⠸⠃⠘⠛⠋⠙⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿
⠀⣴⢰⡌⠟⠻⠷⠘⠈⠁⠁⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⡀
⠀⢀⡀⣀⠀⢠⣀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣶⣶⣶⣤⣠⣤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠟⠛⠋⠉⠉⠉⠙⠛⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠛⠉⠛⠛⢲⣾⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠉⠀⠀⠈⠉⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⣀⣤⡤⠴⠶⠤⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⢠⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧
⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣿
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⣿
⠀⠀⣿⣇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⣾⠏
⠀⠀⠘⢿⣦⠂⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠀⠄⡀⠂⡀⢂⣥⡾⠋
⠀⠀⠀⠀⠙⢷⣦⣥⣈⣀⠄⠀⢀⣰⣤⡶⠏⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠾⣤⣥⣀⣤⣥⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠉⠙⠲⣥⣬⣈⣠⣂⡄⣐⣀⢀⣅⣈⣤⡬⠿⢷⣬⣄⢄⠀⠄⠤⢀⢠⠠⣠⣴⠟⠋⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠈⠙⠛⠳⠿⠶⠶⠛⠛⠉⠀⠀⠀⡀⢀⠀⠀⢄⢡⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠤⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⣣⠆⠀⠪⠃⠊⠠⡆
⠀⠀⠀⠀⠀⠀⢈⣐⡸⠀⠙⠋⠈⢀⢩⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠁⢬⠳⠀⢀⠠⠐⠕⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⢂⡐⠀⠤⡀⣱⠩⡈⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠒⢌⠂⠐⡀⠭⠌⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡔⠮⠂⠄⠌⠔⠀⠙⠈⠃⠀⠀⠀⠀⠀⠀⢀⢐⠔⡎⠄⠒⠠⢑⢄⡀⢀⠁
⠀⠀⠀⠀⠀⠀⠡⢰⠢⠀⠂⠖⠕⢀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠂⠄⡬⠆⡠⡆⢌⠀⠀⠀⠀⠀⠀⠀⠀⠃⢁⠀⡤⠀⠀⡞⡕⢂
⠀⠀⠀⠀⠀⠀⠈⠤⠁⠠⣦⠦⠀⢁⠅⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡨⢲⠁⢠⣤⠀⠰⡰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠂⠂⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡏⠑⠂⠀⠀⠀⠀⠀⠀⡀⡐⠀⠀⠀⠀⠀⠀⠁⠀⠊⠰⠐⠩⠒⠂⠀⠀⠀⠀⠀⡉⠠⠀⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡆⠐⠭⠊⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢄⠑⠨⠃⠀⠀⢼⠡⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠚⢀⢠⠀⡀⢄⢒⠏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠲⣁⠄⠄⠒⡕⠀⢁⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣒⡄⠀⣡⢀⡒⠀⢀⣁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⣀⠘⠠⠰⠂⠠⠩⡎⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢂⠜⢀⣀⣄⠀⠐⣑⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣒⡆⠀⠤⡔⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢚⠢⠤⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠚⢈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠶⠶⠶⣤⣄⣴⠞⠉⠁⠀⠀⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⣀⣀⢀⣠⣤⣼⡋⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠶⠶⠶⢤⣄
⠀⠀⢀⣠⣴⠛⠉⠉⠛⠁⠀⠈⠿⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠷⣦⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠈⠳⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⠞⠋⠉⠛⢷⡴⠶⠶⠶⣤⣸⡇
⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢶⣄
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠈⠙⠳⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡶⡶⡶⡶⢾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢟⡟⣟⠇⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢽⡮⣥⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠸⠷⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠃⠀⠀⠀⠀⢼⣿⡧⠀⠀⠀⠀⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠼⢳⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠸⣺⢿⡺⠂⠀⠀⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣴⣷⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⠻⡟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡣⠄⠀⠀⠀⠲⠆⣤⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠾⠰⠀⠀⠀⢀⡄
⠀⠀⢀⣃⠀⠀⠀⢨⡑⢣⠀⠀⠠⠄⣄⠳⠆⠀⠀⢓⡀⠀⠀⠀⢀⡀⠀⠀⠀⣐⡁⠀⢠⠀⠀⡭⠋⡲⠍⡀⠀⣐⠓
⢠⠀⢐⠊⠀⠀⠐⠌⠠⢃⣀⢀⣤⠴⠆⣄⡃⠀⢰⠰⠂⠀⠀⠀⠸⡇⢀⡆⢘⠂⠌⠀⡬⠀⣄⠐⠫⠅⣨⣁⠠⢄⠊
⣸⠀⡄⠠⢁⣳⠖⠪⡥⢠⡠⠀⠤⠀⢀⣈⠁⠀⣚⠓⠾⠀⣶⡀⠯⡀⣸⡔⠢⠌⣒⣠⡚⡂⠰⠚⠀⠀⣀⣬⡐⢀⠉
⡠⡧⠄⣁⢀⣺⠻⡤⠊⠠⠜⠃⠀⡛⠀⠉⠐⣧⠖⡈⢊⡥⢉⣟⠓⣃⢿⣨⠁⢢⠤⠴⣪⢳⣤⡄⠻⠃⠀⢀⡴⢐⠉
⢌⣬⡃⢁⡛⠧⠆⠶⠀⠔⢘⠛⠉⠉⠷⠂⠶⠘⠚⢀⡈⠡⢵⡮⠉⢰⢮⢅⡡⠄⠛⡤⢓⠽⣯⢄⣠⡄⠛⠛⠀⠛⢤
⡥⠂⡄⠂⣼⡛⠁⠶⠐⠲⠛⡶⠖⠃⣀⠀⢠⣄⣨⡵⡀⢁⣯⠙⠉⠀⠉⠩⠹⠄⠦⠐⠛⠓⢀⢈⣁⢠⣤⡄⠙⠓⡞
⢽⡉⠏⣨⠞⠛⣁⠐⠐⢿⡆⠀⢀⣀⡈⠟⠀⠀⢈⣙⣧⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠉⠁⢨⡄⣤⠶⣤⡿
⠀⠀⠁⠉⠻⠶⢖⡂⢶⠂⠚⠃⠈⠉⠁⠦⣀⣀⡌⠁⠚⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠻⠖⠠⠔⠂⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⠄⠴⠛⢦⡴⣉⡈⢤⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠚⠞⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷
⠀⣠⢠⣽⠤⣀⣄⣀⢄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣇⡽⣯⣀⢀⠀⠀⢠⠦⠀⢀⢸⡇⢀
⠀⣽⠃⣳⠦⣽⣿⡿⡚⠟⠶⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠨⠿⢰⡄⡸⣆⡸⢟⢫⡷⡠⢼⣷⣾⠟⣱⢻⡞⢺⣗⣾⡄
⠠⡞⣥⡀⣤⢮⠽⣖⣧⡠⣏⠀⣰⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⠀⠈⡼⠏⡾⠀⡗⢘⣱⠺⣌⣿⣎⠰⡀⠢⣽⣅⣾⣍⡧
⠀⠑⢠⡏⠇⣮⠁⡿⠼⣶⠃⣰⣿⣿⣧⠀⠀⠀⠀⠀⠀⢰⠿⠿⠿⢻⣆⠀⠀⠀⠘⣾⡞⢶⠛⡆⢿⠑⣬⢉⡟⠠⡌⢧⠸⡰⡇⠹⡄
⠈⠀⠙⠭⠀⣮⣩⠀⠀⠘⣶⠛⠀⣩⠙⢧⣀⣤⣤⣤⣤⣮⡉⠉⣉⣉⣉⣐⣶⣿⣿⢾⠅⠚⢢⠏⠂⢵⡂⡙⢹⠄⣡⢚⢄⣙⠅⢁⠂
⠀⠀⠼⠀⢴⣠⠥⠤⢢⣅⢸⠿⣿⣿⡇⠀⣟⣻⣿⡟⠉⢸⣿⣿⠋⢻⣿⣿⣿⣿⡷⠋⣇⢘⣆⡀⢻⠂⢙⡿⠘⠉⠉⠀⠈⠁⠁⠀⠁
⠀⠀⠀⠀⠀⠐⠠⣩⠊⠠⣉⠙⠻⠭⠧⠈⠿⠿⠿⠧⠀⠚⠛⠻⠧⣼⡏⠉⠙⠉⠈⠉⠉⠉⠉⠁⠀⠉
⠀⠀⠀⠀⠀⠐⠊⠑⠄⠑⠯⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠑⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠂⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠈⠀⠀⠀⠤⢡
⠀⠀⠀⠀⠀⠀⠀⠐⣁⣀⠤⡀⠀⠔⠒⢷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠘⠐⠒⠚⠐⠢⠄⣀⠀⠈
⠀⠀⠀⠀⠀⠀⣰⡎⠁⡁⠀⢱⡀⣈⣄⣈⣀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⢄⡀⠀⣰⠁⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠠⣀⠠⠀⠀⠀⠀⠀⠉⠐⠁
⠀⠀⠀⠀⠀⢀⡧⠆⡠⠖⠚⠉⢁⣀⣀⠀⠀⠁⠷⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣯⣾⢤⡀⠀⠀⠀⠀⠀⢀⣠⠗⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⡀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⣞⠁⠀⠆⠀⠠⠀⠀⢀⠀⢀⡉⡢⡽⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠁⠈⠙⠫⣗⢤⡀⣠⢔⣋⢀⣀⠀⠀⢀⠂⠐⣠⠀⠀⠀⠀⠈⠢⣀⠀⠈⢂
⠀⠀⠀⠀⠀⠈⢦⠤⢤⣠⠉⠁⠀⠁⠐⠀⠠⡀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⠵⢮⣳⡁⠘⣌⠆⠳⣄⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠋⠀⠀⢃
⠀⠀⠀⠀⠀⠀⡇⠰⠀⠁⠀⠀⠀⠀⠈⠈⠁⠸⡀⠀⠀⠀⢰⠁⠀⠀⠀⠀⣴⣶⠀⣠⣤⠐⡄⠀⠈⠉⠀⠸⣀⡀⡀⠙⠣⣄⠀⠀⠀⠀⠀⡠⠋⠀⢀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠈⠓⠚⡇⠀⠁⢀⠀⠀⠀⠀⢀⠇⠀⠀⠀⡌⠀⠀⠀⠀⢀⠨⢅⠀⠉⠁⠀⠈⠢⠤⣤⠴⣀⢈⠁⠈⠢⣀⠀⠙⠁⠀⠘⠻⠛⠃⠂⠥⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣄⠀⠀⠀⣀⡤⠊⠀⠀⠠⠂⠁⠂⣀⣉⣀⡀⠀⢀⡇⠀⠀⣀⡀⠀⠀⠈⡇⠊⠥⣀⠀⠀⠀⠉⠳⢄⣀⢀⡠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡀⡸⠈⠢⠄⠀⠸⠅⠐⠀⠀⢠⠀⠀⠉⡂⠀⠀⡇⢴⠆⢀⣤⢠⡶⠉⠀⠀⠀⡰⠃⠀⠀⠀⠙⠲⢤⡀⠀⠀⠉⠁⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠐⡨⠊⡩⠓⠀⠤⠀⠀⠠⠀⡧⠄⠊⠀⠱⡀⢀⡕⠀⠊⡀⠀⠀⠈⠁⠀⠀⠀⠀⡠⠊⠠⡀⠀⠀⠀⠀⠀⢀⡉⡳⣄⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⡀⠊⡐⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠇⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⢸⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⢯⡀⠔⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠸⡤⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼
⠀⠀⠘⢤⡀⠀⢔⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⡓⠠⠤⠤⠤⠤⠒⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠃⠙⢀⠀⢀⡴⠀⠀⠀⠤⠎⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠶⠒⠂⠀⠀⠀⠀⠀⠀⠘⠀⢨⠦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢱⠀⠀⡀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠊⠀⠀⠀⠀⠀⢠⡠⠞⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢏⠀⠀⠀⠀⠀⠀⡆⠀⠰⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⡀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠑⠒⠙⠒⠋⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⢀⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⡇
⢀⣀⡀⠀⠀⢀⣸⡤⠄⠀⠀⠀⣄⣀⠵⢠⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠑⠞⠉⠙⣎⢙⠢⡴⠤⠤⠤⠐⡟⠣⢄⣀
⠀⠀⠉⠙⠋⠁⠀⡇⠀⠀⠀⢀⡀⡇⠐⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠀⢀⠇⠀⠀⠀⠀⠸⣯⠄⣧⠒⠀⠀⠀⢇⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠰⠠⡇⠍⢻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣠⠟⠁⢹⣉⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⠧⢄⣀⠀⠉⠑⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢣⠀⠀⡠⠚⠁⣀⠴⠋⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠐⠧⠤⠤⣀⣀⣀⣀⣀⣈⣉⠿⠁⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣠⣟⡒⠯⣠⣔⣊⣁⣀⡠⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⠒⠉⣑⠲⢤⠉⠉⡉⠑⠂⠀⠀⣠⠤⠤⠾⠯⣄⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠻⠟⠛⠿⣿⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠕⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠠⣾⣾⣿⣶⣄⠀⠀⠀⠀⠀⠘⢷⣌⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⢀⠸⢿⢙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣧⣀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⢤⡟⢸⣃⣬⠻⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢠⡶⠀⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡄⠀⠀⣉⣦⡆⣿⣾⠓⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣴⣶⣫⣅⣀⠀⢾⡇⣽⢾⣦⣻⢿⣞⣿⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⢛⣼⣋⢠⡀⢰⣛⣸⡇⣉⢋⣹⣻⣿⣍⣭⣦⡀
⠀⠀⠀⠀⠀⣄⠀⡀⠘⠖⣿⢠⡀⠐⠂⣀⡀⠀⠀⣀⡄⣂⡾⣻⢷⢋⣿⣿⣻⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠄
⠀⠀⠀⠀⠀⢬⡻⢤⠤⢼⠿⣏⡀⣤⡄⠀⠀⠐⠂⠉⢙⣋⡶⣉⡄⠙⣿⣿⡟⠿⢟⣫⡿⢟⡿⣿⣿⣿⣿⣋⣥⢼⣇⣶⣄
⠀⠀⠀⠀⠀⠀⠠⠈⣤⣤⡤⣿⣧⡄⠳⢄⣤⣤⣀⠲⣾⣿⣴⠏⢠⠟⠹⣿⣤⣦⣟⣉⣷⢟⣿⡟⣿⣷⣾⣿⢻⣿⡿⠿⡝⣄
⠀⠀⠀⠀⠀⠀⠀⢾⣄⠐⠂⠞⢻⣧⣀⢀⣍⠛⢋⣴⣿⣛⣥⡆⠀⣠⣾⠛⢻⣟⣿⣿⣷⢬⣿⣼⣿⣿⣿⢿⡼⣿⡇⣶⣷⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⢄⣠⠼⢿⣿⡿⢃⣥⣿⣁⡿⢧⣿⣀⡾⢻⣇⣵⠟⢉⣽⣿⢿⡿⣿⣿⣿⣾⢛⣼⣇⣻⣿⣿⣧⡿⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣮⣳⣶⣊⣿⠿⣿⣾⣯⣿⣟⣷⢿⣯⢥⣿⡟⣻⣆⢸⣯⣴⣎⣾⣯⣿⣻⡿⠿⣿⡛⣿⣣⣼⣽⣷⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣭⣿⠟⣽⣾⡟⣻⡿⠿⢿⣣⡾⣻⡾⢻⣿⡿⣿⣼⣯⡿⢿⣿⠏⣹⡿⣷⠿⣿⡿⢿⣿⣿⡿⠻⣾⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣻⣾⣋⣷⣿⣍⣛⠻⣻⣿⣿⢛⣿⣿⣧⣴⣋⣿⣏⣴⢦⢶⣾⣻⣶⣏⣤⣾⣵⣶⣿⣶⣶⣾⣿⣿⣿⣯⡛⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣟⣻⢶⣿⣿⣹⣷⣾⣏⢛⣿⣿⣩⣿⣿⣻⣿⣽⣯⣶⣿⠛⡿⡟⣿⣿⡿⢿⣿⢿⣏⢉⣿⣽⣿⣿⣿⣿⣽⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣯⡽⣿⣿⣯⠵⣿⣿⣽⣿⣿⣏⣴⣿⣿⣿⣿⣏⣴⣤⣧⡆⢩⣼⣀⠀⣼⢛⢿⠻⢿⡛⠛⣍⢿⣿⣷⡿⣯⠛⠩⣣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠱⠶⢻⣷⡺⣿⡋⢷⣅⣭⣿⣿⣿⣿⣿⣿⣿⠛⢿⡛⠿⣿⡟⣿⣿⡾⢿⣿⣴⣿⣤⣿⣿⣿⣼⣿⣿⣷⣄⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣿⣿⣾⣿⣮⣿⣽⣿⣿⠿⣟⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣻⣿⣎⣻⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⠿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣛⣯⣟⣹⣷⣿⣷⣶⣛⣿⡼⢿⣵⣿⣿⣿⣿⣿⣿⣿⣟⣭⣿⣯⣷⣿⡿⣿⣿⣿⣿⣿⣿⣯⡢⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣡⣯⣍⣬⣯⣙⣿⣿⣋⣶⠾⢿⣿⠟⣫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⣭⣿⣟⣿⣾⣷⣤⠶⠶⢿⡾⢫⡜⢻⣿⣿⣯⡀⠙⠻⢿⡿⠿⣿⣿⣷⣿⡿⡏⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⡿⠋⠙⢿⣯⣷⣶⠞⣻⡅⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⢇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢀⣾⣿⡟⠀⠀⠈⢀⣀⣀⠀⠀⠀⠀⠈⠛⠟⠀⠀⠉⠉⠹⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⢻⡏⠙⠃⠀⠀⠀⣼⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣻⣷⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⣽⣿⡇⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⠸⣶⣄
⠀⠀⣽⣿⡇⢸⡏⠻⣧⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⢰⡟⠹⣷⡀
⠀⠀⣽⣿⡇⢸⡇⠀⠹⣧⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⢸⡇⠀⠹⣷
⠀⠀⣾⣿⡇⠘⣿⠀⠀⢻⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡇⠸⣷⠀⠀⢹
⠀⠀⠘⡛⠃⠀⢻⣧⣀⣸⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛⠃⠀⠹⣷⣄⢈
⠀⠀⠀⣿⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠙⠛
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢁⣤⣀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣠⣄⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠉⣉⡉⠙⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⣉⣉⠉⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣴⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣀⣀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢸⣿⣿⣿⣿⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢰⣿⣿⣿⣿⡇⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⢸⣿⣿⣿⣿⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⢸⣿⣿⣿⣿⡇⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢸⣿⣿⣿⣿⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢸⣿⣿⣿⣿⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠰⣿⣿⣿⣿⡇⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠠⠶⠂⣿⠒⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠂⣿⠸⠶
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠇
⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣀⣀⣀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠐⠂⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣀⣀⢈⠀⡠⢀⠄⡠⢀⠈⠐⠤⡀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠈⡉⠁⠀⠈⠉⠙⠒⠦⣠⠂⠄⠀⢢⡄⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠆⠀⠀⠀⠀⠘⢖⡠⢀⣲⢐⢀⣠⣠⣁⣀⣀⢁⢀⠂⠄⡀⠙⢢⣼⠘⣃⣶⡄⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⣈⠛⠥⣀⠀⠀⠠⠈⠉⠙⠚⢶⣄⡠⠀⠹⣸⠀⠀⡹⠈⠣⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠳⣤⣀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⢄⡋⠀⠀⠃⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡷⠟
⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⡭⠃⠀⠀⠀⠐⠂⠀⠀⠀⢀⠘⠦⡀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠐⢎⣢⡀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠉⠐⠒⠒⠒⠈⠁⠀⠀⠌⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠇⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠄⠉⠒⠤⣤⣤⣤⢀⡀⠀⣀⣠⣾⠤⡄⠀⠀⠀⠀⠀⢔⡢⠀⠀⢀⢔⡡⠗⠖⠟⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣦⡀⠀⠀⠘⣠⢀⠀⠀⡀⠀⡄⠀⠈⠻⣿⠛⠋⠠⣨⡄⠀⠀⠀⠀⠀⠀⢀⣔⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠄⠀⠀⠀⠀⠈⢻⡢⡀⡰⠉⠛⠲⠦⢥⣄⣡⠀⠀⠀⢸⡁⢶⡵⠟⢦⡀⠀⠀⠀⢀⠀⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠟⠀⢀⠤⡄⠀⠀⠀⠙⠀⠀⡀⠀⣯⠀⠆⠀⠠⠙⣄⢀⣴⠗⠋⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠈⠙⠃⠀⠀⠀⠐⠀⠀⠂⠀⣿⠄⠘⢄⠀⠠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣇⠐⡀⠈⠑⠠⠅⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢠⣼⠆⠀⠀⠀⠀⢸⠀⠀⠕⢀⣋⢧⡀⠁⠄⠀⣬⢀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⢸⡅⠁⠉⠀⢤⠼⠃⢘⠁⠀⠀⠐⠯⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⢸⠐⠀⢼⣣⠀⠀⠈⠋⠱⠈⡉⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠀⠀⠢⠟⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠀⠀⠀⠀⠘⢃⠋⠀⠀⡐⠋⠉⠙⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⠔⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⢄⡤⠴⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣈⣆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠐⢨⠀⣨⢄⣄⣦⠖⠊⠉⠉⠉⠛⠔⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠔⠉⠀⠀⠈⠢⣉⠂⢀⣀⢠⣀⢄⡄⡤⣀⢠⣤⡂⠀⠀⢈⣰⠃⠀⢈⠁⠀⠀⠀⣠⡤⣤⣀⠀⢀⡠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠁⠀⠀⠀⠀⠂⠀⠄⠁⠅⠬⠟⠁⠀⠀⠉⠋⠀⠀⠀⠀⣀⣀⣁⠀⠀⠈⠉⠒⢤⢂⠁⠃⡗⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⡠⠊⠁⠀⠀⠉⠣⠔⠈⠁⠀⠀⠑⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⣀⣀⠀⠀⢀⠀⢄⢀⠄⠀⡀⡀⡀⢀⠀⠀⠀⠀⡀⠀⠀⠈⠌⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣀⠀⠀⠀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠁⠘⣈⠛⣶⣤⣾⠆⢄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠉⠉⠀⢀⠀⠈⠁⣙⠄⠀⠛⠦⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠄⠀⣦⡘⠶⠂⠀⠀⠀⠐⠚⠛⠃⠠⡞⠯⢠⣀⠈⣥⣢⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠣⠀⡀⣿⣧⡀⠀⠠⡀⠀⠀⠀⠐⠀⣿⣿⣄⡚⠉⠘⠁⠃⢳⡀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⢿⣿⣷⠄⠈⢸⣶⣴⠇⠀⠀⢿⣿⣿⣿⣀⡀⢰⣤⠀⢁⡄⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⢻⣿⡿⠃⠢⣌⡛⠉⠀⠀⠀⠀⠉⢩⣿⣿⡟⣄⠠⡔⠟⣿⢂⡀⠹⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠂⠅⡂⠉⠛⠀⠠⠐⠃⠐⠐⣀⠠⡀⣠⠘⣿⣿⣦⢿⡄⢣⣌⠈⠸⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⢤⠔⠀⠀⠠⠀⠀⢀⠀⠰⠖⠃⠀⠀⣻⠉⡇⠺⠁⠈⡉⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⠘⠂⠀⠀⠀⢀⡈⠀⠀⠈⠁⠀⠀⠀⠐⠆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⡶⠚⠻⠿⣿⡿⢯⣽⣿⣿⣿⣿⣶⣶⣤⣄⣠⣤⣤⣴⣦⡴⣦⡠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣸⣿⣿⣿⣿⡿⠟⠀⠀⢀⡊⠉⡛⢿⣿⣿⣿⠋⠁⢾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⠿⠛⠙⠋⣿⠁⠀⣾⡀⠋⠁⠀⠀⣀⣬⣿⣿⣶⣾⡿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠏⠁⠀⠀⠐⠟⠉⢠⡆⠘⠙⠶⣶⣴⣾⡿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡇⠀⠀⠠⡻⣇⡠⣠⡿⣗⣌⡀⠀⠈⠛⣫⣵⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣧⠀⠀⠀⠻⣶⣠⣤⣶⣾⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⢢⡈⢿⣿⣿⣿⣿⡿⣦⣀⣻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣍⠢⠈⠿⣿⣷⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⣿⡿⢿⣿⣷⣬⣽⣿⡟⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠟⠿⠿⠿⢿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡀⢀⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⠠⢠⣤⠀⣀⡀⠀⣠⠴⠀⠀⡉⠻⣀⠯⠤⠶
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠃⠀⠘⠤⠧⠽⠀⠀⡁⠣⡀⠀⡁⠜⠐
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠃⠀⠀⠀⢰⡀⠀⠀⠀⠖⠒⠒⡀⠀⢀⡐⠀⠈⠑⢂⠂⠁⣸⠷⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠠⠄⡀⠢⠅⠀⠀⠀⢀⠤⠀⠘⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠚⠁⠀⠑⠬⢀⡀⠀⠀⢠⠃⠀⣀⣤⣒⡉⠥⠀⠐⠸⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠋⠙⡗⠛⠥⣌⠀⠄⣸⠃⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠈⠠⠀⠀⠑⠢⡉⠢⣄⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠤⠴⠟⠂⠀⠈⠑⠠⠈⣈⠁⠉⠀⠀⠀⠀⠀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⡀⠄⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⢄⠀⠀⠀⠀⠀⠀⠀⡌⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢱⠄⠀⠀⠀⠀⠈⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⡀⠀⢁⠆⠀⠀⠁⠆⠀⠀⠀⠁⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠇⠤⠀⠀⠀⠀⠀⠀⠀⠀⢑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠑⡠
⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⠀⠀⠀⡆⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠌⠢⡀⠀⠈⠃⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇⡏⠀⠀⡠⠂⠀⠀⠀⠈⢆⠀⢀⡀⡨⠓⠀⠀⢀⣀⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡆⠀⡀⠀⠀⢠⣮⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⣰⠀⠀⠀⠀⠈⠸⡁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠈⠉⠀⠸⠀⠠⠀⠀⡀⠀⠀⢀⠀⠀⠀⢰⠀⠀⠀⠀⢀⡀⠀⠍⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠀⠀⠠⠀⣀⠀⠀⠰⠀⡠⠀⣀⡠⠜⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠑⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠑⢄⠀⢱⡁⠉⠀⢀⣀⡀⠄⠁⠀⣠⠂⠀⠀⡀⢠⠀⠀⡈⢁⡀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠠⠆⠀⠀⠀⡀⠀⢀⠀⢅⠊⠓⠤⣄⣀⣀⡠⠤⢚⠀⠠⠒⠉⠁⣈⢀⠀⠘⢇
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠁⠈⠐⠐⠀⠉⢄⡰⠁⠀⠀⠑⠂⠤⠀⠤⠤⠵⠒⣉⠒⠤⠤⠤⠚⢉⠀⠄⠀⠀⠉⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢁⠠⠄⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡣⣀⠐⠁⠎⠐⢀⠂⠈⠀⠀⢠⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠊⡑⠒⠒⠒⠚⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠎⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⠧⢄⡠⠤⠤⢀⣰⡦⢄⣰⡖⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠔⠁⠀⠀⠠⠤⠤⠀⠢⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄⠸⠤⠆⡆⠀⠎⠀⠀⢐⣈⢉⡁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠐⡆⠘⡔⠀⠀⠀⡠⠄⢘⡛⢦⠧⠔⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠀⠀⡠⠎⠆⠀⠀⣀⠱⠴⠊⢉⡠⠐⠈⠋⢐⡬⡑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⢀⠌⠀⠀⢦⠄⠐⡞⠉⡀⢠⡄⠀⠀⠤⠌⠙⡷⠞
⠀⠀⠀⠀⠀⢀⠄⠂⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠄⣤⣌⡆⡆⢀⠁⢈⡄⠀⠄⠀⢇⠀⢠
⠀⠀⠀⠀⠀⠈⠔⠈⢀⠠⠀⠀⠀⠬⢀⡄⠀⠀⠄⠀⠀⡔⠀⠈⡆⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠐⠀⠦⠤⠼⠤⠼⠄
⠀⠀⠀⠀⠀⠈⢀⠊⠀⢀⠀⠀⢀⡠⠀⡘⢆⠀⠀⠀⡠⠒⡀⠉⠉⢀⡢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠓⠂⠘⠋⠀⠒⠙⢦⠀⢀⡼⡨⠄⣂⠀⠀⠀⢐⡈⢦
⠀⠀⠀⠀⠀⠠⡄⠸⠁⠀⠼⠆⠀⠀⠿⠀⠰⠀⢈⢊⠔⡡⡔⡤⠀⠠⢆⡐⠨⠄
⠀⠀⠀⠀⠀⠀⠙⠄⠄⠀⠀⠰⠀⠂⠀⢀⠀⠀⢋⠀⠌⠐⢠⡆⠀⠀⣀⡀⠈⠁⠀⠀⡔⠋⠀⠈⠑⢄
⠀⠀⠀⠀⡀⠠⠄⠼⡃⠶⠤⠤⡤⠄⠂⠁⠀⠀⠘⡌⠀⠀⠀⠁⣀⠀⠛⠀⢠⠀⢀⠮⠤⠀⣀⠀⠀⣤⠒⡄
⠀⠀⠀⠘⠓⠀⠀⠒⠚⠒⢶⢰⡆⠀⠀⠀⠐⠀⠀⢀⠀⢀⣀⠀⠒⠀⠀⡠⠚⡰⠁⠨⡄⡐⠂⠉⢲⠏⠀⠁
⠀⠀⠀⠀⠀⠀⠌⠀⡀⠐⠚⠘⣸⣲⠀⠀⠀⠀⠀⢀⠗⡼⠬⠉⣁⠼⠁⣴⠀⢻⣀⡐⠬⠄⢂⣀⡸⠀⠀⢀⠀⠀⠦
⠀⠀⠀⢀⡀⣀⡃⠄⠉⠈⣺⢺⢨⠁⠀⠀⠀⠀⠀⡘⡜⠀⠀⢄⣤⢀⠑⣾⣆⠬⠄⣉⣀⣀⣀⡄⡸⡀⣀⣢⣤⠴⠃
⠀⠀⠀⢺⡀⠀⠈⡢⠤⠔⢇⡈⠀⠱⡀⠀⠀⠀⠀⠙⢃⠀⠒⠐⠜⠨⠁⠀⡏⠀⠀⠰⠀⣜⣰⠀⠃⠈⡄
⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠁⡴⢋⠝⠀⠀⠀⠀⠀⠈⠖⠒⢒⠒⢚⠀⠀⡄⠀⠀⠂⠘⠊⢛⣤⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣾⠒⣎⠀⠀⠑⢄⠀⠀⠀⠀⠘⠚⢃⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠋⠉⠈⠀⠀⠀⠀⠙⠂⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠂⢀⡀⠀⠀⠐⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⢄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠒
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠁⢤⠀⠀⠠⡒⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠖⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⡀⠀⠢⠠⡤⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠒⠠⠈⠀⠀⠀⠀⠈⠐⠄⠀⠷⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⡠⠒⠀⠀⠀⣶⣾⠚⠳⢦⣀⠠⠈⠒⠤⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⡴⠋⣰⡇⢙⡍⣱⠈⠋⠙⡀⢀⡀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⢂⠔⠀⠀⠞⠵⠃⠀⠋⠸⣿⢳⡭⠀⠄⠀⠁⡿⠹⠳⡄⠄⡀⠈⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⡠⠂⣀⡆⠟⠁⣀⣀⣀⠀⠀⠉⡌⢁⠀⢂⠀⠠⡀⠀⠀⣄⣶⣌⡀⠐⠄⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠸⠁⠛⠀⢰⠈⣿⣉⡢⠀⠀⢀⣄⠖⣩⣗⣦⡈⢢⠀⣏⣿⣿⢱⠰⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⠀⠀⠀⠸⠛⠟⢫⠁⢀⠀⣸⡟⣒⢻⣛⣿⢡⣶⠋⠋⠋⠉⠈⠇⠀⠀⠁⠀⠀⠀⠛
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠉⠱⢌⠉⠉⡁⠤⣀⠀⠅⢍⣿⡬⣿⡀⢻⡀⠀⠤⠀⠠⢀⡈⠀⠀⠀⣀⠀⠀⠈⠁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠁⠉⠠⠄⠀⠉⠺⠊⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀
⠀⠀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠀⠃⠀⠀⠀⠄⠠⣀⡀⠀⣀⡠⠴⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠂⡐⠁⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠈⠐⢀⡀⠠⠀⠀⠐⠠⣀⢀⡀⠀⠁
⠀⠀⠀⠀⠂⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠂⠄⠄⠈⠑⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⢀⣖⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⣾⠁⠀⠀⡿⠇⠀⡀⢏⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣤⠄⠐⢶⡀⢘⣚⣿⡆⢀⠀⣽⡆⢠⡶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠸⠄⠀⢲⢆⣼⢭⡎⢁⡂⠐⠍⠙⠊⠁
⢠⣷⡄⠀⠀⠀⠀⠀⠀⢐⠃⠐⢄⣿⣿⣿⠀⠠⠀⠀⣿⣿⣿⠀⠀⠀⡀⠀⠠⠜⢳⣦⣌⣷⠿
⣿⠟⠃⠀⠀⠀⠀⠀⠀⢙⡃⠂⢀⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⠀⠀⠀⠃⠚⠓⠶⠘⠉⠉
⡀⣤⠄⠀⠀⠀⠀⠣⠀⠀⠀⡖⣿⣿⣿⣿⣧⠀⠀⠈⢻⣿⣿
⠟⠀⠀⠀⠀⠀⠀⡀⢴⠓⠆⢹⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡴⠆⠀⠀⢸⡇⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣿⣿⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣸⣿⣿⠀⠀⠀⠀⢸⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⢘⢡⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢠⣴⣀⡀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣯⣿⣷⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠘⠿⠆⠀⠀⠀⢠⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⡠⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠀⠀⠀⠀⣤⣀⣠⡄⠀⠀⢀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣤⣤⣴⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢹⣷⣾⠀⠀⠀⠸⡇⢹⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢇⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣤⠀⠀⠀⢠⣼⣿⣿⠀⠀⠀⢠⣇⣬⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠻⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠀⠀⠀⠀⢸⣿⣿⡀⢤⣔⠚⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⠟⠛⣁⡀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡗⠦⠀⠀⣠⣼⣿⣿⢀⣼⢿⢿⡇⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⢡⠄⠀⠀⠀⠀⡐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣤⡤⠚⠛⠀⠸⠿⠛⢃⡤⠟⠂⠁⠿⠿⠛⠿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡭⠉⠁
⠈⠁⠀⠀⠀⠀⠀⠿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣤⣤⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢸⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⣀⠀⠀⡰⠾⠀⢺⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢬⢺⣁⠀⠀⣰⠀⠀⠀⣂⢠⣭⢀⣶⣠
⣤⣤⢧⢰⣆⡋⣼⣶⠦⢶⡶⢧⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠺⣾⢅⡀⠀⢺⡦⢀⢐⣏⡷⡎⢻⢼⣞
⣿⣿⠛⡿⠊⡓⠚⣧⡇⣼⣡⠚⣶⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⣣⣇⡃⢺⡿⠬⠁⠘⣻⡧⠑⢈⣿⠞⡓⠛⡿⣴
⣿⣥⣷⠓⠋⢸⡏⠙⣿⣿⣧⣾⣿⣦⣿⣷⣷⣴⣶⣦⢤⣤⠒⣧⠯⢝⣄⡀⣀⢠⣌⡠⢥⠘⢄⢴⣯⣿⣦⣿⣈
⢸⣿⣟⠉⡱⢋⠙⣟⢻⡿⡿⣿⢻⢿⣿⣿⠿⠿⢶⣿⣿⡯⠔⣣⠘⢦⠷⣿⢇⡨⡚⣧⢉⠄⣍⢸⣿⣿⣿⠿⢿
⠘⠹⢏⡨⠦⠈⠓⠛⣍⡁⠀⠸⠀⠀⠈⠀⠀⠀⠀⠀⠩⠃⠁⠭⠀⠉⠠⠓⠐⠀⠀⠠⡇⠘⠀⠓⢊⣃
⠀⠐⠒⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠂⠂⠠⠤⠤⠤⠤⠀⠄⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣩⣶⣤⠠⠄
⠀⠀⠀⠀⠀⣀⣰⡀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠈⠡⠔⠂⠀⡴⠆⢞⠿⡿⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡠⠤⠤⠤⠤⠷⠾⠳⠲⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠠⠴⠶⠛⠡⠈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿