Songbird Emojis & Symbols

⣶⡟⢿⡇⣠⣿⣿⣿⣶⠁⠀⠀⠀⠀⠀⠉⢛⣿⣯⣉⡛⢺⡟⠋⠀⠀⠀⣤⣄⡀⣀⠀⠀⠠⠻⠷⣿⣿⡿⠿⣿
⣿⣿⠙⣇⡉⢛⣿⣏⣁⣀⡀⠀⠀⠀⠀⠀⠀⠹⠏⢿⣽⣾⣭⣭⣻⢤⠄⠙⠉⠉⠙⡓⠤⠀⠀⠙⠛⠁⠀⢀⣼
⡟⡡⠊⠙⢿⣿⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡽⠟⡋⠓⠚⠓⠀⠀⠀⠸⢿⣿⣷⣾⣶⣀⠀⠀⠈⠇
⢣⣾⣥⡿⠧⠌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣯⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣟⠿⠿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡗⠀⠐⠠⣀⣀⢀⡀⠀⠀⠀⠀⣀⡀⠉⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⠄⠘⢂⠈⢁⣤⡄⠈⠉⠉⠙⠋⠉⠁⠀⠀⣸⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠉⠀⣘⠃⢤⠈⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢦⣀⣨⣽⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢦⣍⠛⡿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣬
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⣼⣻⠄⠀⠀⣴⡀
⠀⣠⣽⣿⣿⢶⡄⢨⠃
⣶⡿⠻⢎⣅⠘⠿⠟
⢠⣶⣞⣹⠄⠄⠷⡀⣠⠀⣀⣾⣷⡄⠰⠾⡗
⢸⡿⢋⣥⣶⣇⣀⣀⣿⡀⡹⣿⠏⠀⠀⣠⡴⢄
⠈⠀⠉⢹⣿⣿⣿⣿⠂⠣⡘⣿⠀⠀⠀⠉⠀⣽⠀⠀⠀⢀⡘⣻⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃
⠀⠀⠈⠉⠁⠙⠁⢀⣴⣶⡍⠻⣇⢀⣀⠀⢠⡏⠀⠀⠀⢠⡋⢹⢃⡄⡀⣀⡀⠀⠀⠀⢻⣯⣤⣼⣶⣇⣀⢀⣦
⠀⠀⢠⣾⣲⣾⣄⣴⠛⠋⠀⠀⠹⣿⣍⢻⡟⢸⣶⣬⡹⣟⠋⣿⡿⢛⣯⠿⠁⠀⠀⠀⠈⠻⢿⣿⠛⠉⠀⠀⠈
⠀⠀⣿⣿⣿⡟⠁⠋⠀⠀⠀⠀⠀⢸⣿⣿⡗⠦⣉⣺⣿⣟⣳⠙⠿⠿⠉⠀⢀⣴⣶⣇⡀⠀⢈⣡⣴⣿⢂⡀
⢻⣾⣿⠛⠛⠿⠂⠝⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⣶⠿⣥⣼⣯⡠⠀⠀⠀⠀⠙⠏⠀⠀⠈⣵⠋⠿⠿⠟⠋⠉
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠉⠂⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⡔⢢⣴⣄⡤⣤⣧⡃⡄⣠⡆⣠⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠈⢉⣽⠧⠃⠉⠁⠓⠙⠙⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠀⠀⠈⠑⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢁⣈⡀⠀⠁⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⣠⠔⠂⠉⠙⢤⡻⠿⠿⠂⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠅⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣠⠔⠒⠈⠁⠀⠀⠀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡐⠀⡆⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡝⡆⢇⠸⢿⡀⠀⠀⠀⢀⡀⠀⠀⠑⠦⡤⠜⠁⠒⠚⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡣⣘⠦⣧⡑⢄⡀⠀⠀⠈⠑⣦⣤⠤⠯⣉⣒⠒⠶⠶⠖⠒⠛⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠁⠈⠘⢄⠈⠉⠀⠒⠮⡀⠈⠉⠒⠂⠤⠭⢉⣉⡉⠀⠀⡈⢉⣳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠉⠀⠀⠀⠀⠈⠉⠒⠒⠤⠤⠤⠤⢤⠤⠬⠭⢭⡤⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠲⠂⠤⠤⣤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠤⠤⢀⡀⢝⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⠴⡋⠀⢀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢝⢮⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⡺⠋⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠢⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢮⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠈⡀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣶⣿⣿⡇
⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣀⣾⠿⠿⠟⠁
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠺⠟⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⣀⠀⢠⠃⠀⡀⠂⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡜
⠀⠀⠘⣀⠏⡠⠈⠀⠀⠀⠐⢄⠀⢘⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠑⡎
⠀⠀⢀⡏⠔⠀⠀⠀⠀⢀⠀⠀⠀⢺⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰
⢣⡀⡼⠛⠀⠀⠀⠀⠈⠁⠀⠀⠀⠸⠆⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⠃
⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠈⠳⡀⠀⠀⠀⠀⠀⡰⠚⠁⠀⠀⣀⡀⠧
⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠈⠢⡀⠀⠀⣰⠃⠀⣀⠔⠊⠁
⠀⡷⠂⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢢⡴⢁⠴⠊⠀⠀⠀⠀⠀⠀⠂
⣸⠁⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣸⠶⠏⣀⠀⠀⠀⠀⠀⣀⠁
⠇⠀⠀⠀⠀⠀⡄⠑⢄⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠘⠉⠑⠀⢀⡠⠔⠂
⡀⠀⠀⠀⠀⠀⠙⢦⡀⠢⡀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⢀⣃⠤⠐⢊⠁
⠀⢹⠀⠰⠀⠀⠀⠀⠈⠢⡐⢄⢀⡿⠄⠀⠀⠀⡀⣴⠟⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⢀⠔⠁
⠀⠀⠆⠀⢀⠀⠀⠀⠀⠀⠈⠘⢿⣴⡇⠀⠀⠀⣸⠏⠂⠀⠀⠀⠀⢀⠔⠁⠀⢀⠴⠐
⠀⠀⠸⡀⡞⠀⠀⠀⠄⢀⠀⠀⣹⠈⣿⠀⠀⣰⠿⡄⠀⠀⠀⢀⠔⠁⠀⢀⠔⠁
⢠⠀⢀⣷⠃⠀⠀⠀⠀⢻⠀⠀⣿⠀⠸⣦⡾⠁⠀⢳⠀⢀⡴⠧⠤⠤⡴⠓⠂⠀⠀⠒⠂
⢀⡆⢺⢸⠁⠀⠐⠀⠂⠬⢥⠀⡇⠀⣼⠋⠀⠀⢀⣼⠞⠉⠀⠀⢠⠞⠂⠉⠁
⡜⠁⠺⣼⠂⠆⠢⠀⠀⠆⠀⢸⢇⣼⡿⠀⠀⠀⠘⡇⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠄⠂
⠀⠀⠀⢹⢆⢩⢰⠀⡟⠀⠀⣼⡾⠙⡇⠀⠀⣀⠴⡇⢀⡴⠛⠒⠒⠒⠒⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣶⣶⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣾⣿⣶⣶⡶⢾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡂⠀⠀⠀⠀⢀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣷⣶⣦⣴⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠈⠙⣻⣿⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⢀⣠⣀⠀⠀⠰⢄⣘⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢸⣿⢿⣾⣦⢧⣾⡝⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⣶⣾⣿⣿⣧⣼⣗⣿⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣷⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠿⠋⠈⠛⣿⣿⣿⣿⣿⢿⣦⡀
⣶⣶⣦⣤⣤⣄⣀⣠⣾⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⢻⡿⠋⠉⠛⠳⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣦⣤⣤⣀⣀⣄⣠⠴⠚⠉⠀⠐⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢹⣦⡀
⠉⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣯⠉⠀⠀⠀⠀⠀⠀⠀⠘⣶⣿⣀⣀⠀⠀⢀⣾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠿⢿⡄⠀⠀⠀⠀⠀⠀⠀⣄⣿⠟⠋⠁⠀⠀⠙⢿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣿⣯⠄⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣺⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡻⠿⡿⠋⠟⠉⠉⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⡽⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣄⠀⣄⡀⠀⠄⠀⡈⠒⢄⡀⢀⠀⠤⠸⢆⠀⠀⡸⣾⡳⣈⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡤⠀⠈⠁⠀⠈⠀⠈⠉⠉⠉⠀⠀⠀⠀⠙⣶⡀⠛⡽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣤⣶⣦⡄⠀⠀⠀⠀⢀⡀⠀⠄⠒⢄⣙⡇⢸⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠿⢿⣿⣷⣿⣷⣾⣿⣿⠟⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠿⠿⣿⣡⠴⠋⠉⠉⣙⣾⣶⣦⣄⣀⡀⠀⠀⣸⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠋⠁⠀⠀⠛⠑⠋⢉⣀⣀⣀⣍⠻⣽⣿⣿⣿⣮⣿⣿⡟⢿⡀
⠀⠀⠀⠀⠤⠄⠰⠦⢤⡶⠖⠒⠋⠠⡄⠁⠀⠀⠀⠚⣰⠃⠀⠈⠉⠁⠈⠙⠉⠉⠉⠹⣿⣿⣿⣟⣿⢸⡇
⠀⠐⠁⠀⠀⢀⡀⠐⠠⠀⠀⠀⡠⠂⠀⠀⢀⡄⠀⠰⠃⠀⠀⠀⠀⢀⠨⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣏
⠀⠀⠀⠑⠀⠀⠂⠁⠀⠀⠀⠀⠀⠰⠀⠘⠀⠀⢀⡶⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡟⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣦⠀⢨⡟⠇⠳⠾⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠛⠁
⠀⠀⠀⠀⢀⣴⠖⠇⠉⠈⠳⣤⣀⣠⣤⣴⡶⣶⣒⠲⣦⣶⣄⡤⣤⣤⣾⣿⠿⠛⠁
⠀⠀⠀⠈⠫⠩⠏⠲⡀⠀⢰⣿⣷⣶⢿⣶⣿⣏⣽⣛⡀⣰⡀⣴⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠁⠚⢻⣷⠸⠹⢳⢹⣛⣿⣾⣿⣿⣷⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠠⣿⣾⣿⣿⣾⣿⣿⡿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢃





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

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠀⣀⠀⠀⣰⠆⠀⠀⠀⠈⠓⠲⠶⣦⡤⣄⡀
⠀⠀⠀⠀⢀⣷⣥⡶⠿⠋⠀⠀⣺⠈⠀⠀⣄⣀⣀⣀⣀⣈⣹⣿⣿⣷⣦⣄⡀
⠀⠀⠰⠖⠚⠛⠛⠁⠀⠠⠠⠀⡽⠀⠀⣀⣞⣲⣿⣿⣒⣲⣿⣿⣭⢿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣲⣞⣶⣿⣿⣿⣿⡿⣯⣭⡝⡯⣽⣿⣷⣾⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣵⣌⡘⡳⣿⣷⠵⣿⣿⣿⣽⣶⣿⣿⡷⠶⢤⠤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠻⠶⠶⠶⣶⠾⠿⠿⠶⠖⠒⠛⠋⠉⠙⠓⠶⠦⢴⣒⣒⣂⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠄⠀⠀⠀⠀⠀⠐⣦⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠠⠀⡐⠉⠀⢀⡀⠀⠀⢀⣠⡿⠏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⢄⠀⠀⠀⠀⣀⠤⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠄⠚⠁⠀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⡶⠶⢶⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠷⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣀
⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⡀
⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣶⣶⢂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⢛⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⣠⠆⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⡛⠁⠈⠂⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⣧⠀⠀⠀⢀⣀⣠⣤⣤⣤⠀⠀⠀⠀⠀⢠⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⣿⠀⠀⣀⣈⣻⣿⣿⣿⣿⣦⡀⢦⠀⠶⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⣿⡤⣿⣿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣠⣄⠀⠀⠀⢸⡇
⠀⣿⣧⡿⣛⣷⣼⣼⣇⡙⡿⢁⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣒⣽⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡀⢀⡀⠀⡀⢸⡋⠃⢠⠀⣿⡇
⠀⣿⣿⣦⣿⣿⣿⣿⣏⣿⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣶⡀⠀⠀⢀⣿⣟⢃⣰⢿⣿⣁⡀⠆⢸⣿⡇
⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢰⣾⣿⣇⠀⢰⣿⣿⣿⡶⠛⢏⣷⣼⡟⢰⣷⣿⡇
⠀⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⡾⢶⣿⣿⣿⣿⣿⣿⣿⣷⣠⡶⣼⠏⠴⢠⠟⢿⣿⡇
⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⠷⡿⢀⣿⣿⠿⢿⣿⣯⣭⣯⣤⣿⢇⣴⣿⣷⣿⣿⡇
⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣆⡙⠛⠃⠀⠀⠿⢿⣶⣿⣿⣿⣉⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠋⠐⢺⣶⣾⣿⣿⣏⣽⣿⢿⣿⠟⡏⢻⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣏⣻⣿⣟⠛⣶⣤⠞⢿⣿⣿⣿⣿⣿⠀⠀⢀⣀⡀⢀⣀⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡷⠒⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠶⣾⣷⣮⠻⠳⣿⣿⣿⣿⣿⣿⠟⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠋⠁⠐⠾⣿⣿⠟⠟⠉⢻⣿⣥⣾⣿⡿⢿⣿⠓⣤⠿⣿⡷⡾⢿⣿⡿⠻⣿⣿⣶⣿⣿⡾⠛⠹⢿⢿⣿⣿⣿⣿⣿⡇
⠈⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡀⡀⠀⠀⢀⣹⣿⣿⣷⣿⣿⣿⣯⣿⣿⣷⣾⣿⣿⣿⡗⠛⠀⠀⠀⢹⣿⣶⣿⣿⣿⣿⣿⠃⣤⠂⠀⠀⠉⢛⡿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡋⠉⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⡿⢹⡿⠲⠆⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡖⠺⣷⣿⣿⡇
⢀⣿⣿⣿⣿⣿⣿⣿⠋⠻⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦⣍⣀⣸⣷⣴⣾⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡇
⠈⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣾⣿⣿⣿⣿⣿⡟⠉⠁⠈⣿⣿⣿⡇
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣼⣿⣿⣋⣻⣿⠋⠁⠀⠀⢀⣼⢿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣭⣏⣩⣏⣹⣿⣿⣿⣿⣿⣷⣄⣠⣤⣿⣯⣤⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠟⠻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⣿⣿⣿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣄⣤⣤⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠐⠿⠃⠐⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣆⠀⠀⡀⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠁⠲⠀⠒⠐⠖⠠⠐⠂⠀⠐⣿⡟⠀⠀⠀⠠⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠳⠒⠤⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⠀⡀⠀⠀⠀⠀⠙⠡
⠀⠀⠀⠀⠀⠀⡀⠄⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣦⠀⠀⠀⡰⠁⠀⡟⠀⠎⠂⠄
⠀⠀⠀⡤⠐⠦⣀⠘⡆⠃⠀⠀⡀⠀⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠌⠷⣿⣧⡀⠜⠀⠀⡀⠀⠀⠈⢳
⠀⠀⠀⠀⠐⠄⢀⡳⢄⠀⠀⠀⠱⠀⠀⠀⠀⠀⠈⡉⠛⠑⠲⠖⠐⠀⠀⠀⢨⡀⠀⠀⠈⠀⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠤⠊⠀⠀⡀⠀⣰⣾⣧⡀⠈⠀⠀⠤⣀⡀⠂⠀⠐⠀⠀⠸⣦⠀⠳⠦⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⠀⡄⠀⠀⠙⠅⣑⡀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠘⠹⠃⡲⢟⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⣤⣇⠔⠀⠀⠀⠀⠀⠓⠿⠂⠒⠁
⠀⠀⠀⠀⠀⠀⢒⠀⠂⠑⡞⢦⢀⠀⠸⢊⠀⠀⠀⠈⠙⢿⣕⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠸⡀⠀⠐⡸⠀⠀⠀⠀⠀⠉⠀⠑⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡐⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠿⠛⢻⣿⣿⡟⠛⠿⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠁⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠈⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⢀⣴⣿⣿⡿⠋⢸⣿⣿⡇⠙⢿⣿⣿⣦⡀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏
⣴⣦⣄⢇⣰⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣴⣿⣿⡿⠋⠀⠀⢸⣿⣿⡇⠀⠀⠙⢿⣿⣿⣦⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣆⡸⣠⣴
⠙⠻⠿⢿⡿⠛⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡋⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢙⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿⠿⠟
⢠⣤⣤⣀⢣⢠⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⢸⣿⣿⡇⣀⣀⣤⣶⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡄⡜⣀⣤⣤
⠘⠻⠿⠿⠿⢿⠛⠉⣠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⠉⠛⡿⠿⠿⠿⠟
⠀⢠⣤⣤⣄⣈⢧⢰⣿⣿⡿⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⢿⣿⣿⡆⡼⣁⣤⣤⣤⡄
⠀⠹⠿⣿⣿⣿⡷⠿⡟⠉⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠉⢻⠿⢾⣿⣿⣿⠿⠏
⠀⠀⠀⠀⣠⣤⣄⣀⡘⢦⡸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢇⡴⢃⣀⣠⣤⣄
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡿⢿⡋⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⢿⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠙⠺⣿⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⢺⣷⣀⠔⠋⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠟⠛⢻⣷⠀⢀⣀⣀⠀⠀⠀⠀⣀⠀⠀⣠⣤⣄⠀⣿⣭⡿⠀⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠲⣶⣾⣋⣠⣿⣧⣿⠇⢰⣿⠛⣿⠇⠰⣿⡀⠋⣀⣿⠿⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠉⠉⠉⠻⠷⣦⡶⠿⣷⣾⠿⣧⣤⡿⠛⠛⠋
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡀⠈⡂⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠂⠀⠀⠂⠖⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠄⠛⠈⠐⢂⣀⣼⠯⣼⡀⠀⠌⠁⠀⣸⠆⠐⠴⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢧⠄⣤⠀⠐⠎⠀⠀⠳⠀⠈⡁⠀⢀⡴⠔⠀⠈⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣍⠀⠀⠛⠀⠀⢰⠂⢂⠩⡀⠀⠠⠀⠀⠰⠉⠂⢀⢓⠀⠀⠀⠀⠀⡁⠀⠀⠐⠘⠳⠦⠄⢀⠔⡀⠀⣠⠀⠀⢀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠰⠄⢊⠀⠂⠀⡇⠂⠁⣶⣀⠀⠠⠀⠀⠀⢠⠀⡀⠀⠐⠒⢦⣀⠀⠀⢀⡀⠀⢀⣀⡀⠼⢇⣀⡀⣈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⣠⣄⠈⠀⠀⣰⣾⠉⠀⠐⠠⡄⠦⠀⠀⠀⡠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢸⡆⠈⡁⠁⠈⡠⠊⠁⠈⠑⠀⠀⢀⢁⡀⠋⠈⠩⠁⠀⠀⠥⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⠂⠀⠀⠀⠅⡆⠀⠀⠀⠥⠀⠀⠄⠄⠀⠀⢤⡀⠠⠀⠀⠀⠀⠁⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠒⠶⠦⣠⢀⠀⣡⡈⠀⠀⠀⢀⠀⣀⠀⠃⢀⠀⠀⣰⣀⠀⢀⡀⠙⠆⠀⠀⠀⠀⠧⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆⠆⠈⠋⣃⠉⠀⡀⢰⡟⠀⠁⠀⢀⠍⡀⠊⠁⠀⠀⠚⠄⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠠⣗⠀⠀⠀⠀⠀⢭⡀⠰⠛⠸⠇⠀⠀⠀⠉⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⢠⢠⡖⠡⣄⠠⠀⠙⡠⠀⠀⠈⠪⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⡄⠐⢶⠀⠱⠆⢸⠂⠀⠀⠉⢈⡁⠂⣴⠆⠀⠀⠐⠲⡈⠀⠐⡊⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠤⣁⣀⣀⣀⠀⠀⠀⠀⢧⡀⠈⠫⠁⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠉⠙⠛⡦⠴⠖⠒⠋⠀⠀⠀⢠⠀⠀⠠⠐⠀⠀⠂⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⡀⢉⠴⠡⠄⠀⡠⠀⠑⠄⠀⡀⠀⠈⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠄⠀⠀⠀⡤⠀⢀⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠿⠀⠄⠀⡁⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠈⡄⠁⠀⠄⢦⡰⠀⠙⠂⠉⠀⠴⢠⡀⣀⠀⠚⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣈⠀⢢⡀⠀⠀⡀⣘⡄⠀⠀⠀⠀⠀⢆⡇⠀⡀⠀⡀⠸⠋⠶⠆⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⡐⠋⡉⠉⠐⠉⠑⢳⣦⣴⣤⣚⡉⠀⠀⢈⡁⢆⠀⠀⠀⡅⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠋⠔⡲⠦⠄⢸⣇⢧⠙⡇⠐⠀⠉⠀⡈⡗⢀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡠⡀⠤⢀⣐⠀⢀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣋⠑⡟⢉⣛⠧⠤⠍⠰⣼⣿⠆⡔⣻⠁⡫⢄⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠈⡰⢷⣹⢆⡊⠀⠀⠀⠘⠁⠀⠚⡴⢷⡎⢟⠲⣷⢀⡄⠲⠫⠄⢄⡀
⠀⠀⠀⠀⠀⣠⣖⢽⡆⢭⣤⡁⢉⡐⠀⠊⠈⠀⠀⡀⠀⠀⠈⠀⠀⠒⠚⠂⡦⡄⠗⠀⢈⡡⣀
⠀⠀⠀⢀⠀⣽⣟⣏⡱⣇⠏⠁⠀⠀⠀⠀⠀⠸⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠈⠍⣀
⠀⠀⠀⠎⠀⣴⡭⡩⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠌⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⢂⡰⠀⠀⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢠
⢀⡯⠦⠱⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⢀⣀⣍⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠋⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡀⢣⠄⢠
⠀⠀⠂⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠈
⠀⡀⠀⠥⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⡄⠠
⠀⢋⠁⠄⡜⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠰⠁⠀⠀⠳⠂⠀⠠⠘⢃⠀⠄⠀⠀⡄⠀⠀⠀⠠
⠀⠈⢧⣀⠀⠉⠶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢁⣾⠃⠀⠀⠀⠟⠠
⠀⠀⠀⠂⠀⢡⣡⢀⣠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠋⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠟⡇⠆⣸
⠀⠀⠀⠀⠄⠀⢻⠟⡚⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⢜⢰⡀⠀⠀⠀⠀⠀⠠⠂⠂⠄⠳⢁⣠⡧⠄
⠀⠀⠀⠀⠈⠀⠨⣀⡀⠀⠀⠀⠀⠉⠀⠠⠄⠀⠀⠤⠷⠇⡠⠀⠀⠈⠀⢀⠈⠘⢃⡑⠀⠹⠂
⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠐⠍⡀⡀⠘⡂⠂⠁⠀⡴⠆⠀⠀⠂⠀⠐⠀⠈⡀⠹⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢈⣀⠸⠋⢣⠠⠀⡕⠀⠀⠓⠀⣩⠇⠈⠁⠌⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠲⣀⣉⢀⣤⢀⠂⠃⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⣰⡅⠀⣴⡀⠀⠀⠀⠀⠰⠂⠀⠀⠸⠂⠀⠀⣀⣤⠁⠀⡤⠀⠐⠀⡴⣃⠉⠀⠀⠀⢸⣶⣧⡠⢻⡷⠀⠸⠀⣆⢻⠘⡄
⣤⡀⠀⠤⠂⠀⠚⠀⠈⣆⣀⠉⠏⠸⣿⣿⣤⡀⣰⣿⣶⠀⠀⠘⠁⠀⠀⠊⠀⢀⠀⠃⣀⠀⠀⣰⠱⠁⠀⠁⠁⠀⠀⠰⠟⣰⡆⡖⠛⠈⡇⢱⠈⡇⢸
⠁⠀⠀⠀⠀⠐⢂⡀⢸⣿⣿⣷⡀⣀⣤⡽⠟⠁⠚⠛⠛⡄⠀⠀⠐⠃⠠⠆⠀⠀⠀⠀⠐⢶⡾⠃⠀⠀⠀⠀⠀⠀⣢⣤⡅⠀⠈⡇⠸⠀⡇⢸⠀⢷
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠉⠿⠿⠿⠟⣀⠀⠀⠀⠁⠀⠟⠀⠀⠀⠀⠀⠈⠀⠀⠠⡔⠋⠀⠀⠀⠀⠀⠺⢣⠈⠛⣫⠀⠀⣸⡀⡆⢀⡇⢸⠀⢸
⠈⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠚⠁⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢄⠀⠀⠀⠀⠀⢂⠀⢠⠁⠸⠚⡿⠻⠟⢸⠃⢙⠢⢼⡀
⠀⠀⠀⠀⠀⠈⠉⡽⠟⠋⠀⠲⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡋⢰⠟⠀⠂⣼⠁⠀⡀⣸⠀⠐⠀⣾⠙
⠀⠀⠀⠉⣀⣠⠀⠀⠀⠐⠁⠐⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⠄⣀⠀⠀⠀⣰⣶⣦⡀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⠞⢤⣿⢄⠏⠀⠀⠈⣧⣠⣄⠀⡿⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠤⡤⠊⠡⠀⠀⠀⠀⠠⢋⣵⡾⠋⠀⢠⣾⣿⣿⣿⡧⠀⠀⠀⡠⠁⠔⠀⠀⢀⠎⠀⢈⡯⡜⠀⠀⠀⢸⠿⢿⡋⢠⡧⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⢦⠀⠀⠀⠁⠀⠀⠀⠀⠀⡞⠀⠀⢂⣠⠿⣿⣿⣿⣿⣃⣀⣀⣄⣠⣊⡀⠀⢠⠊⠀⠀⠀⣰⠁⢀⠀⠀⣯⣾⡿⠈⢾⡀⢹
⠀⠀⠀⠀⠀⠀⡤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⣰⣿⢟⡴⠂⡐⣀⣈⢿⣿⣿⣿⣿⣿⠿⢢⠃⠀⠀⠀⢠⠃⠴⠾⠀⣼⠛⢅⠀⠀⡟⠙⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⢟⠔⢀⠌⣁⠀⠀⡰⠁⠀⠀⠀⢠⠏⠀⠘⠀⢰⢿⠠⠬⣣⣼⠇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠛⠻⠋⠩⠟⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡋⠁⡸⣧⣴⣿⠉⠁⠀⡐⠁⠀⠀⠀⢀⠎⠀⠀⠀⢀⡞⠀⢳⣿⣿⣿⣆⣠⠇
⠀⠀⢀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠉⣤⣤⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢰⣿⣿⣿⠿⢃⠜⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⡼⠁⠀⠈⠛⢻⠿⠟⣿
⠀⠀⠉⠀⠀⠀⠀⠀⠐⢟⠀⠊⣰⡿⠿⠊⠀⠀⠀⠀⠀⣠⣶⠀⢀⠔⠁⡡⠊⡀⠀⠀⢠⠎⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢴⠃⠀⠀⠀⠀⡾⠀⠀⡇
⢠⣤⡤⠄⢀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢀⡼⠿⠁⡰⠋⣠⠜⠀⠀⠃⠀⡰⠃⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢠⠏⣳⣠⡀⠀⢰⠇⠀⢸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⢰⣦⠀⡟⢦⣠⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠑⣤⡭⠧⣧⡚⠁⠀⢹⠁⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠲⣦⣄⡀⢇⠀⢰⠍⠀⠀⠀⠙⢆⠀⠀⠀⠀⢨⡦⡴⢤⣀⣀⢀⣀⠤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠓⠦⣀⠀⠈⢇⠈⢻⣄⣸⣆⠀⠀⠀⠀⠈⠀⣄⣆⣠⠋⠀⠀⠀⠋⠘⢿⣇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⣾⣧⡴⠚⠿⣿⣿⡿⠿⣄⣖⠙⠢⣄⠀⠉⠛⢿⣦⡀⣠⠖⠛⠛⠻⣿⠓⠒⠲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⡿⠁⠀⣠⠿⣯⠄⠀⠘⠫⠿⢶⢤⣿⢿⣇⠀⣠⣄⣠⣾⣥⠴⠚⠋⠉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠛⢷⡀⠀⠀⠇⠀⠞⠁⠀⡼⠷⢖⣰⣋⠙⢻⡀⠁⠀⠈⣾⠃⠀⠈⠛⠖⣤⣴⡊⠉⣻⠟⠉
⠀⠀⠀⠀⠀⢀⣠⣤⠒⣾⠀⠀⠀⠀⠀⠁⠐⢓⡀⠀⣀⡤⠾⢧⠀⣜⠉⠉⠉⢢⠱⣄⠀⢀⡎⠀⠠⠄⠀⠈⠉⠛⣇⠴⠁
⠀⠀⠀⠀⠀⠈⠉⢉⣲⣿⣄⣀⡠⠲⡤⣥⣚⣛⣉⠵⠿⠀⠀⣰⠋⣹⣤⠶⣦⣸⣶⠿⣶⣿⣦⠀⠀⣀⣠⣤⣤⣴⣧⠤⣀⡀
⠀⠀⠀⢀⣤⣴⣞⣁⠬⠿⠛⠛⢣⡄⡠⠋⠁⠀⢀⠀⠀⢀⡾⠁⠀⠙⢦⣴⠄⠌⠃⠲⣶⣾⠻⡏⠉⠁⠀⠀⠹⣿⣏⣀⣀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠔⠋⠉⠓⠋⠀⠀⠀⠀⠀⠙⠶⢦⣖⡆⠄⣅⣸⡧⠀⢀⣀⠀⠀⠀⣽⣿⣿⣋⠉⠉⠉⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠾⠿⢤⡀⠀⢘⡇⠀⠀⣿⣿⣯⠛⠻⣕⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠧⠴⣾⣿⣿⣷⡀⠀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠌⢿⡌⠙⠒⠒⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⢘⡔⢁⠀⠀⡠⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣶⣾⣛⠀⠈⠢
⠀⠀⠀⠀⢀⡈⠀⡜⢀⠴⠡⣚⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠂⠄⠐⠖⠋⠀⠘⣿⠋
⠀⠀⠀⢠⣼⣧⡄⠀⠀⠀⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠰⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠏⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⡗
⣶⣤⣾⠂⠀⠒⡄
⠉⢻⡿⠃
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⠦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⣉⠊⡆
⣀⣴⣄⣠⠔⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣁
⠀⣽⣿⡏⠁⠐⠄⠀⠀⡠⠊⠠⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣷⣶⡾⠆
⠴⠋⠀⠀⠀⢀⡁⢀⣌⠀⢐⠀⠀⠠⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣿⠟
⠀⠀⠀⠀⡠⠜⢻⣿⡇⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣦⠀⠀⠀⠀⠀⠸⣶⣤⢁⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢀⣀⠘⡈⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⣀⣙⣛⠳⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⣀⣴⠟⠉⣉⠙⠻⠷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠉⠀⢀⣴⠾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠶⣶⣶⣶⣶⣶⡶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠐⠷⠶⣶⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⠶⠛⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⣼⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣿⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⡿⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢀⡇⠀⠀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢸⠁⠀⠀⣾⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⢀⡏⠀⠀⢰⠇⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⡜⠀⠀⢀⡞⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⡰⠁⠀⠀⡼⠁⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠐⠀⠀⢀⡜⠁⠀⢀⡞⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠠⡘⠆⢠⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢠⠎⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣤⡙⠆⠰⢫⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡐⠁⢀⣾⣿⡏
⠀⠀⠀⠀⠀⢀⡈⠳⢄⠠⠏⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⣸⢃⣴⠾⠿⢷⣶⣄⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠟⠀⠒⠂⠀⠈⠻⣷⣄⠠⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠈⢿⣦⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠹⣷⡈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢀⡶⢶⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠈⠻⣌⣿⠀⠀⠀⠀⠀⠀⠀⢐⣿⠏⢀⡾⠁⠸⠁⠠⠞⠉⣩⡿⠛⠳⢶⣶⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⢀⡾⠋⢀⡞⠀⠀⠀⠀⠀⠐⠋⢁⣠⡴⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠠⠏⠤⠔⠊⠀⠀⠀⠀⣀⡠⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣄⣀⣀⠀⠀⠀⣀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣷⣿⣿⠂
⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⢿⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⣾⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⣠⣿⣿⣿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢹⡀⠀⢀⣰⣾⣷⡄⣀⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣾⣦⣄⣀⣠⣿⣇⣶⣿⣿⣿⣿⣧⣼⣿⣾⣿⣿⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠁⠈⠛⢿⣿⣿⡿⢁⣴⣿⣟⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣷⡿⣿⡟⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠳⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⡤⠄⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣾⡿⢛⣿⣿⣿⣿⣧⣄⡁⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣷⣤⠔⠊⣙⠒⠦⣄⡀⠀⠀⢻⣆⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣆⠈⠿⣷⣦⣾⢁⣴⣾⣟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⢽⣿⣤⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣿⣿⣿⣿⣿⣿⣦⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠂⠁⣰⣴⣭⡝⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣛⣿⡿⠟⠡⠛⠻⣿⣿⣿⣏⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠘⠋⠉⣹⣷⣶⣾⣿⣿⣿⣿⠟⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣥⣄⡀⠀⠀⠛⠟⠋⠛⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⢶⣨⣿⣿⣿⣿⠟⣻⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢈⣤⣿⣿⣿⣿⣿⡟⣠⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣱⣾⡟⢫⡼⠃⣼⣿⣇⠘⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠿⢶⣧⣤⣾⣯⣿⣿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢉⣿⣿⣧⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠃⠀⠀⠀⢠⣿⣿⣿⡿⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣟⣁⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⢠⣼⠟⠋⠁⠀⠀⢻⡿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣟⣩⡙⢿⣿⣿⠿⠛⠛⠙⠛⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠉⠀⠀⠀⢀⠀⠉⠁⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⣠⠀⠀⠀⠈⠶⣶⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣷⣦⡀⠀⠰⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⠿⣿⡷⠀⠀⡆⠀⡤⣠⣴⡟⠏⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⡇⠀⠁⠉⠉⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠈⢿⣿⣿⣿⣿⣿⣧⠀⢀⣠⣄⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡏⠹⣷⣾⣿⡉⢉⡉⢉⢁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠰⣤⣼⢿⣿⣿⡏⠻⢛⣿⠟⠛⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠈⠠⣶⣼⣿⣾⠏⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⢖⣞⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⠿⠋⠉⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠙⢏⠛⠃⢤⠀⠀⠉⠉⠳⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠳⠀⢄⣠⣄⡈⢦⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⢺⠝⣧
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢦⣀⣃⠀⠉⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⠞⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⣨⠟⠒⢀⣀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠘⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠗⠒⠛⠉⠀⠈⠲⢝⢢⡀⠀⡀⠀⠀⣀⠀⡼⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠳⡑⡾⠁⠀⠀⠈⢏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠂⠛⠐⠒⠢⢄⣀⠀⠀⠙⣜⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠘⣞⡄⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡏
⠀⠀⢀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠤⠤⣄⡀⠀⢀⠀⠀⠀⢳⡀⠘⢂⡔⠓⠂⠀⠀⠀⠀⠠⠶⠊⠁⠀⣷
⠀⠀⠈⠑⠤⣄⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀⢳⠀⣄⢹⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡇⢰⠸⠀⠀⣠⠚⠁⠀⡀⡠⠊⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⢲⣄⣀⠠⣄⡰⠖⠛⠁⠈⠛⢦⡀⡆⢰⠃⠀⢀⢀⠟⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡤⠧⢤⣿⠀⠀⠈⠿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠑⠚⠛⠒⠦⣄⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡦⣾⠤⠖⠛⠛⠛⠲⣄⠀⣀⣀⣀⡈⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⠉⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠃⠀⠀⢀⡀⠀⠀⠀⣼⢰⡖⣪⡅⠪⣽⢃⠀⢀⡤⠀⠀⠀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣆⠀⣀⡇⠉⠓⣤⡾⢻⣌⠳⢭⣠⠞⠉⢧⠞⠁⠀⠀⠀⠀⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣨⠟⠋⠀⠀⣼⠋⠀⠀⠉⠳⣄⠟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠤⠐⠒⠠⡏⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⡏⠀⠀⣠⠞⠒⣒⢦⡄⠀⣠⡶⠶⠋
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠹⣦⡀⠀⠀⣀⣉⠤⠞⠁⣠⠎⠹⣄⠀⢠⠏⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⡠⠞⢋⠟⠉⠀⠀⠀⣀⡾⠁⠀⠀⠀⠉⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⢤⣄⠀⠀⠀⠀⠰⢟⣁⢀⣠⢞⠟⠒⠒⠉⢩⠑⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣤⣀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⣉⡩⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠶⠚⠉⠂⠈⠙⠓⠛⠛⠲⠶⠴⠖⠚⠁

⠀⠀⠀⠀⠀⢀
⠀⠠⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡤⠶⠚⠛⠉⠉⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉⣀⣙⣤⣤⠤⠤⠶⠶⣦⣤
⢀⠠⡠⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠚⣉⣤⠴⠚⢋⣉⠀⣀⣀⣀⣀⣤⣤⡇
⠈⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢚⡡⠽⠛⣁⡤⠴⢶⣿⠟⠉⠉⠉⠉⣿⣿⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⡩⠖⣫⡴⠾⢋⣁⡤⠤⠶⠒⠒⠚⠛⠓⠲⠾⠷⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠄⡨⢔⣽⡖⣉⠤⠖⢋⣉⣤⠤⠤⠶⠶⠶⠶⠦⢤⣤⣄⣀⠀⠀⠉
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢘⠡⠐⠥⢒⠡⢘⣉⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢦
⠀⣠⠆⠀⡀⠀⠀⣀⠀⠀⠀⠶⠀⠀⣥⠐⠿⠐⠊⠁
⠘⠟⡳⠸⠉⠀⠀⠁⠀⠘⠁⠀⠀⠈⠋
⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠢⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⠀⢸⠀⡏⠀⠀⡰⣡⠔⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢌⢇⠘⠀⠀⢀⣾⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡈⠓⠄⢀⠼⠚⠓⠒⠲⡟⠁⠠⠊⢀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡏⠀⢛⢀⠘⠃⢸⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢒⣒⠭⠛⠧⡀⠘⠚⠀⢀⡼⢍⠑⠒⠤⣄⣀⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠁⢀⠤⠀⠀⢨⣷⠒⠒⠁⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠴⠁⡰⠁⢀⣿⣿⠀⢰⠀⠳⡀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠻⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡿⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡸⢰⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⠤⠒⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠳⢄⡀⢀⡰⠁⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡠⠊⢁⡠⠖⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⠣⡀⠀⢀⡠⠴⠊⠁⠀⣠⠊⢀⠴⠋⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⢀⠜⢁⡔⠁⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠣⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡠⠃⠴⠋⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠢⣄⠀⠳⡄⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⠜⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡈⠁⠀⠈⠢⡀⠀⠀⠀⠘⡌⡄⠀⠀⠀⢠⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠈⢦⡀⠀⠀⢃⢱⠀⠀⢠⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠈⠢⣀⠸⡈⡆⢠⠇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡓⢧⠱⣎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣤⠏

⣶⡶⠒⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⢢⢹⣧⢷⡄⣤⠀⢹⡷⠀⠍⠀⠀⢀⣄⣀⣠⣴⣿⣿⣿⣹
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⠀⣦⡀⡀⢸⣿⡌⢡⡟⠀⡄⢓⡀⣒⣂⣉⠀⠀⠀⠁⠈⠉⠈⠉⠛
⠀⠀⢤⣀⣠⣤⣤⣤⣶⣿⣿⣗⡖⡆⠀⠀⠀⢹⣿⣿⣦⣿⣶⡿⣸⣿⣿⠟⠀⠀⠉⠕⠚⠉⢉
⡀⠀⠀⠛⠉⠉⢉⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⢻⡁⢿⣿⣿⣿⠇⣿⣿⣷⡶⠀⠀⢤⣤⣆⣀⡠⠟⠀⠀⢀⣴⣶⣄⣀⣀⡀
⠻⠗⠛⠛⠉⠉⠁⠀⠀⠀⠉⠙⢦⠀⠀⠀⢰⢸⠃⠀⢹⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠈⠽⠃⠀⠀⡠⠔⠉⠹⠛⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠿⠛⠙⠛⠿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⣒⣒⣛⣓⣒⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠊⠀⣀⡀⠀⠀⠀⠀⡀⠐⠀⢀⣠⣤⣄⣈⡉⣉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⡀⠀⠤⠔⠉⠀⠉⠒⠀⠀⠊⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣿⣦
⣛⣛⠀⠀⠀⠲⠦⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠙⠋⡙
⢿⣾⣗⣦⣄⡀⠀⡀⠈⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠐⠉⠿⣿⡻⣿⣮⣿⣷⣦⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⢀⣄
⢀⡂⢠⡈⠳⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣄⣴⣔⠒⠂⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⣴⠀⠉
⠀⡅⠛⠢⢤⣄⡉⠻⢿⡿⣿⣟⣛⠿⣿⣿⣿⣛⠻⣦⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠑⣶⣶⡇⠀⠀⠀⠀⠀⢀
⣶⣆⠀⠀⠀⠈⠙⠦⢄⣉⠒⣝⣿⣧⡀⠀⠹⣿⣆⣛⠿⠶⠶⢶⣶⣖⠚⠓⠒⠦⠀⠀⠀⠀⠀⠀⣽⠟⠃⠀⠀⠠⠊⠁⠈
⣿⣿⣷⣤⣀⣀⠀⠙⠳⢿⣧⠘⢿⣿⡗⠤⠄⡈⠉⠛⠋⠛⠋⠉⠙⠋⠉⠳⣤⣀⣀⠀⠀⠀⠀⠀⣿⣶⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⢄⣴⡄⠒⠲⠗⠚⠉⠉⠤⠂⠀⡀⢠⡈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢄⠀⠉⠒⠔⠀⠀⠀⠀⢀⣶⠉⡀⠄⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⢀⣀⣠⣄⣯⣨⠇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⢀⣠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢊⡁⢀⠊⢣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⢛⣉⣀⣠⣤⣄⣀⣀⢀⣤⣴⣶⡾⠿⠿⠁⠘⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢈⠉⠁⠈⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠲⡀⠌⠔⠀⠀⠀⠀⠀⠀⠀⡀⠡⠀⠀⠀⠀⢰⣦⣄⡀⠀⠀⠐⢠⠁⠀⢀⠂⠀⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠊⢬⡀⠀⡄⠀⣤⣤⣤⡄⠂⠀⠒⠀⠀⠀⢨⠀⠈⠭⠀⢀⠁⠺⠬⠄⠘⠓⢠⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢐⠀⢙⣉⣉⡉⡈⠀⠀⠀⠀⠀⠈⠛⠂⢰⣤⠀⠀⠀⠀⠀⠀⣀⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠉⠈⠁⠙⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠞⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⡄⠀⢀⣦⡶⠀⠀⠀⠄⠀⢀⠋⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⠇⠀⢨⡷⡟⠀⠀⠐⢀⣀⣀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢏⠀⠀⠀⠉⠀⠀⠀⠺⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⠿⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠄⢷⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⢶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢎⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠋⠁⠀⠀⣿⣿⠀⠀⠈⠙⠻⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦
⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇
⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⣿⣿⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀⠀⠀⢀⣴⣿⣿⠟⠁⠀⣿⣿⠀⠈⠻⣿⣿⣦⡀⠀⠀⢀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣀⣴⣿⣿⠟⠁⠀⠀⠀⣿⣿⠀⠀⠀⠀⠲⣶⣷⣆⣀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣄⡀⠀⠀⣿⣿⠀⠀⢀⣠⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⣀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢠⡄⠀⠀⠠⠤⠤⠀⠀⠀⠛⠐⠒⠒⠒⠒⠚⠉⠳⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠾⠐⠒⠒⠂⠀⠀⠈⠘⠇⠀⠀⠀⠴⠧⠤⠤⠤⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣹⠀⠀⠀⠀⢀⣠⠄⠀⠠⠀⠀⠀⠀⠐⠒⠒⠒⠲⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡤⠀⠀⠀⠌⢦⡄⠀⢀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠉⠁
⠀⠀⠀⠀⠀⢀⣠⠧⠀⠒⠛⠒⠒⣶⠖⠲⠶⠤⠤⢼⣏⣀⣀⡉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠶⠆⠀⠀⠀⢀⣀⣠⣴⠒⠁
⠀⠀⠀⠀⠀⠁⠸⣜⣉⡂⠀⠀⠈⠉⠉⣩⡟⠓⠒⠒⠦⠤⠬⣭⣍⣍⣉⣙⣛⣛⣛⣛⣛⣻⣛⡉⠉⠉⠉⡿⠀⠀⠁⠀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠐⠺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡤⠤⠶⠒⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⣤⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣱⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣧⣤⣤⣤⣤⣴⡶⠯⠭⠭⣄⣀⡾⠃⠀⠈⠉⠉⠙⠒⠒⠦⠾⢏⣀⣀⠀⠒⠒⠂⠀⠐⠒⠒⢒⠋⠉⠀⠀⢀⡀⠘
⠀⠀⠀⠀⠀⠀⠁⠀⠘⠮⠴⠋⠀⠀⠀⠈⠉⠙⠒⠲⠤⢬⣉⣙⠒⠲⠤⣄⣀⠀⠠⠂⠀⠀⠈⠉⡉⠉⠐⠒⠂⡶⠞⠉⠁⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠶⠶⠬⠭⣙⣒⣶⣤⣤⣘⣁⣀⠀⠀⠀⢀⢀⣀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⡿⠀⠈⠁

⡿⢿⡿⣿⡿⢹⡇⠩⠝⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿
⠁⠤⠀⠸⠃⠈⠀⠄⠀⠠⠿⠇⠿⠛⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠠⡄⠀⠀⠀⠀⢃⡀⡀⠀⢀⣤⠀⡆⠀⢀⣿⣿⣿⣽⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣯⠁
⠀⢻⣦⣴⣶⡄⠀⠀⢃⠀⣾⣿⠤⡆⣦⣼⣿⣿⣿⣿⠀⠀⠻⠼⣿⣿⣿⠛⣿⠇⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠿⢿⡿⠋⠉⢳⠖⠚⣶⢾⣿⡶⠛⢿⣿⣿⠟⠉⣿⣷⡦⠀⠀⠁⠀⠁⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⡆⢀⡙
⡦⠀⠀⠀⠀⠀⠈⠀⣀⠀⠸⢣⡀⠿⠺⣿⣿⣶⣦⣽⣿⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠘⣶⣦⣠⣦⣤⣾⣷⣷⣿⣸⣷
⠁⠀⠀⠀⠀⠀⠀⠈⠿⣄⣀⣽⠃⠀⢠⣿⣿⣿⣿⣿⣦⣼⣇⣠⣾⣷⣶⣶⣿⣶⣤⣤⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⣶⠄⠀⠀⠀⠀⠀⣿⣿⡟⠺⣷⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⠛⠋⠀⠈⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣣⣄⣻⡀⢳⣄⣶⣶⣾⣿⣿⡗⢀⣿⣿⣿⣿⣿⡿⣿⣿⠿⢿⣿⣿⡿⠿⣿⣿⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣼⣿⡘⢤⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣷⠋⠻⠀⠀⢻⣿⣧⣄⣸⡅⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿
⣿⡏⡻⢃⣤⠛⠛⠋⠀⠙⠿⢿⣿⣿⣿⣿⣿⠁⠁⠀⠀⠀⠀⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣻⣿⣿⣿
⣿⣿⣡⡆⢻⡆⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣷⠀⠀⠐⠆⠀⠀⡰⠘⢧⣿⡏⠙⣿⣿
⣿⣿⣿⣷⠘⠃⠀⠀⠀⠀⠀⠀⠀⠙⠿⠽⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢆⣄⠀⠀⠀⠀⠀⠀⠀⢠⡀⢹⣿
⣿⣷⣿⣿⣿⣿⣤⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠿⢋⣽⡇⠈⠒⠀⠀⠀⠂⠀⠀⢠⣷⣾⣿
⣿⣿⣿⣿⣿⣿⣿⠃⡿⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢱⣤⣠⡾⣧⣶⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠈⠛⢿⣿⡿⠿⠃⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⢰⣶⡟⠈⠹⠿⢠⣸⣿⣿⣿⣿⣿⣶⢀⣴⠶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣆⢀⣀⣰⣾⣧⣼⡿⠃⠀⠠⢄⣿⣿⣿⣿⣿⡿⠟⠉⠛⠋⠀⠘⠻⠿⠿⢻⣿⣿
⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠰⠃⠀⠀⣬⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢾⡿⠻⠿⣿⣿⠟⢿⡇⡀⠀⠀⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣃⡀⠀⠛⠁⣠⡌⠡⠟⠣⡄⡀⠀⡈⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣰⣿⣿⣟⣀⡀⠈⠀⠀⢠⣿⢿⣿⣷⣾⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣟⠁⠈⣿⡛⠁⠀⢀⣀⠛⠋⠘⣿⣿⠃⠀⠀⠀⠀⣠⣤⣤⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣻⣿⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠿⢿⣿⣿⡿⠿⢿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠁⠀⠀⢸⣿⣿⡇⠀⠀⠈⠙⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⢀⣴⣿⣿⠟⢹⣿⣿⡏⠻⣿⣿⣦⡀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣴⣿⣿⠟⠁⠀⢸⣿⣿⡇⠀⠈⠻⣿⣿⣦⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣅⡀⠀⠀⢸⣿⣿⡇⠀⠀⢀⣨⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣷⣶⣾⣿⣿⣷⣶⣾⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠛⠛⠉⠁

⠀⠈⣷⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇
⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣶⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡄⢀⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠘⠛⠀⠉⠙⣿⡏⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⢡⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⠉⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠈⣩⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⣿⠟
⣀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟
⣿⣿⡿
⡟⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣤⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢿⡄⣯⣝⠛⢻⡶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⣸⣧⣼⠇⠀⡀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡀⠀⠀⠀⠀⠀⢰⣾⣿⡅⠀⠸⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠻⢿⣼⣿⣦⣤⣄⣰⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⣀⣿⡆⠀⠀⠀⠀⠀⠘⠿⠟⠃⣰⣶⠀⠀⠀⠈⠿⠛⠁⠀⠀⣰⣶⣤⣦⡀⠀⠀⠀⠀⠀⠀⠹⡇⢸⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣭⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣍⣛⣛⡹⢯⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡏
⠀⠀⠀⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⢠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⠁
⠀⠀⢀⣿⠿⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⠀⠸⠿⢿⣿⠀⠀⠀⠀⠀⠀⠰⣿⣷⠀⠀⠀⠀⠀⢸⣿⡇⣼⠇⠀⠀⣿⣿⣿⣿⣿⡿
⠀⠀⢸⡇⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢻⣿⣷⣄⡀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⢠⣾⡇⠙⠀⠀⢰⣿⣿⣿⣿⣿⣧⣀⡀
⠀⠀⢸⡇⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠙⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⢶
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠈⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⡟⣳⣾⣫⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠿⣿⣽⠏⢀⣴
⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣦⣤⣾⣭⣶⣷⠘⠋
⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣯⣼⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠛⠉⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⣻⢿⣿⣯⡟⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠠⢀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⢳⣭⣶⣺⣮⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠚⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣸⡿⣼⣿⡿⣿⡿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠉⠙⡿⠁⠉⠉⠙⠛⠛⠛⠛⠛⠛⢻⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣯⣽⣭⣿⣿⣧⣻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠿⣿⣯⠿⣏⣙⣯⣽⣷⣾⣾⣷⣿⣿⣽⣿⣿⠇
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣯⣷⣽⣶⣾⣿⣿⣿⣿⣿⣿⡿⣿⠛⣻⣷⣝⣿
⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣿⣿⣿⡿⣿⣿⡟⢿⡿⢯⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡞⣽⣷⣿⣿⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⢿⣿⣿⣿

⡤⢶⡶⢶⣿⡭⠿⠛⠛⢉⠩⠉⠉⠉⠉⠛⠛⠻⠷⠶⠾⠯⣭⣤⣴⣶⠿⣟⣯⣥⣴⣾⣿⣿⡿⠟⠉⠀⠊⠁⠀⠀⣠⣾⣿
⠞⣩⣴⣿⣷⣶⣶⣶⣿⣿⣾⣭⢤⣒⣩⣭⣿⣷⣶⣶⣭⣄⣒⣂⣠⣴⣿⣿⡿⠿⠿⠿⠛⡭⠀⠀⣠⠔⠀⠀⣠⣶⣿⣿⠿
⣠⣿⣿⣿⣿⣿⣿⠿⠏⠁⣴⣊⣵⣿⣿⣿⣿⣿⣿⣿⡟⣴⡿⣷⣾⣿⠿⣿⣙⠷⢛⣡⠎⢀⡤⠚⢁⣤⣴⣾⣿⣿⣟⣥⡶
⣿⣁⣿⣿⣿⣿⣿⣠⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠟⣽⠻⣿⣡⣭⢤⠖⠥⠒⢛⣉⣤⠶⠋⢠⣾⣿⣿⣿⣏⣋⣛⢋⡥⢞
⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⡿⣶⠶⣿⣿⢟⡕⠁⣶⣾⠟⠋⠉⠀⣠⣴⡿⠛⣹⠿⣿⣿⠟⠃⢈⡴⠋
⠟⠉⠉⠓⠀⠐⠀⠀⠒⠹⢶⡆⠙⢻⣿⢿⡦⣤⡭⣠⣶⠟⠁⠋⠀⣸⠟⣁⣨⣶⡾⠿⠛⣡⣶⡾⠷⠛⢉⣀⠤⠚⠋
⢟⡻⢻⣍⣻⣿⠆⠀⠀⠀⣋⣀⣤⣿⣿⢿⣟⣫⣾⡟⠋⠀⣀⣤⠞⣫⣾⠿⣫⡷⡈⠤⠾⠛⣉⠤⠒⠉⠁
⣩⣤⣾⠟⠋⠁⠀⠀⣚⡭⠖⢋⣉⣤⣴⠾⣿⡺⠟⠁⢀⣴⡿⣡⡾⠛⠁⠀⠀⠀⠀⠠⠐⠊⠁
⠋⣉⣀⣤⠴⠖⠚⢉⣡⡴⠞⠛⠉⠉⠀⠀⠀⠀⢀⣴⢿⡯⢊⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢋⣉⣠⣤⣴⣶⠾⠉⠁⠀⠀⠀⣠⡄⠐⣒⡠⢴⣢⣵⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣴⡶⢟⡫
⠛⠛⠉⠉⠉⠀⠀⠀⠀⢴⣴⠟⣯⠚⠯⠥⠴⠿⠟⠉⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢀⣠⣴⡶⠿⢛⣛⠛⣛⡿⠯⣒⣪⣥⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⣿⣴⠟⠋⠛⠁⠀⠒⠁⢀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⡫⠕⢒⡉⠉⠀⠒⠶⠞⠛⠋⣉⣀⣤
⠀⢀⡀⠀⣠⠤⢤⠰⠈⣟⡊⠀⠄⠀⣀⣤⡴⠖⠋⠁⠀⠀⠀⠀⣀⣴⣿⠟⡋⠔⠉⠀⠀⠀⢀⣀⡤⠶⠶⠶⠞⢿⠿⠿⢿
⠀⠈⠉⠐⠀⠀⠀⠀⠀⠏⡡⢔⣶⢟⠏⠁⠀⠀⠀⠀⣀⣤⣶⣿⡿⢋⠕⠊⠀⠀⢀⣤⠶⠛⠉⠐⠚⠙⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋⠀⢀⣠⣤⣶⣶⣿⣿⠿⢟⡫⠕⠊⠁⠀⠀⣠⡶⠋⠁
⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣾⣷⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠉⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⡀⠀⠀⠈⠌⠀⠄⠀⡌⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⡀⠈⠄⠀⠀⠠⠀⠀⢠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⡤⠂⠒⠀⠀⠂⠀⠀⠀⠀⣀⣀⠀⠀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠩⠀⡠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠴⠛⠄⠀⠈⠀⠀⠀⡨⠙⡀⠖⠰⠂⢒⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⠀⢠⠔⠁⠀⢀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⣀⡀⢀⣤⣤⠤⠶⠒⠚⠉⠟⠁⠀⠀⢀⠴⢁⡀⠉⠅⠀⡀⠀⠀⠨⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠔
⠀⠀⠈⠐⡤⠛⡩⠉⠄⠀⠀⠀⠀⠠⢒⡰⠤⢤⠊⠀⠒⠀⠀⠀⠀⡂⠠⠀⡀⠐⠀⠀⠀⠀⠀⠀⠄⠈
⠀⠀⠀⠀⡣⢀⠀⣀⢀⡄⡀⠤⠐⠊⠀⠀⠐⠁⠈⠂⡀⠁⠀⠀⢁⡀⠒⠁⠀⠀⠀⢀⡀⠄⠂
⠀⠀⠀⡚⠀⢀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠄⠂⠈⠀⠀⠀⡉⢠⠂⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠤⠤⢚⣀⠂⣀⠠⠀⠀⠔⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢀⣔⣀⠄⡮⠀⠛⠲⠦⠔⢥⣂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡛⠗⠉⠂⠀⠀⠀⠀⠀⠀⠀⠈⠓⢕⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⡋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠐⡈⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⡉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣾⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣩⠶⡀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠆⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⡴⠀⠈⠐⣀⣧⢞⠁⢠⠀⠀⢀⠠⠀⠀⠄⠚⢢⡄⠊⠉⠹⡄
⠀⡲⠐⠄⡀⠀⢀⣼⣗⠇⠈⠀⠀⠈⠀⠀⢧⠀⢀⢸⠏⠜⢈⣶⡋⠈⠓⠀⠀⣠⠞⠀⠀⠀⡁⠀⠀⢠⢃⠄
⠀⠸⡂⠬⣟⣴⡯⠦⠯⠋⠀⠀⠀⠀⠀⠂⠈⠿⣿⣴⣮⠜⠉⠜⢁⠠⠀⠀⠀⠘⢄⡢⣀⠢⠁⣀⣀⡜⠁
⠀⠀⠄⠀⡐⡿⠗⠀⠀⠤⠀⠀⠀⠀⠀⢀⡴⠚⢹⠋⠟⣛⣿⢣⡀⠀⠀⠀⠀⠀⠀⣉⡻⠛⢻⠛⠓⡀
⠀⠀⠀⠈⠁⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠜⠀⠀⠀⠈⡆⠀⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⣄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⣏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢦⡘⢶⡿⢈⣷⣫⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣾⣆⠃⠋
⠀⠀⠀⢠⣴⣶⣶⣶⣾⣶⣦⣸⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠀⠀⠀⠀⠀⠀⠀⣀⠛⠶⠟⠀⠀⠀⠀⠀⠀⢲⣤⡀⠀⣥⣭⣿⡆⠺⠟⠁
⠀⠀⠀⢼⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⠘⠻⢋⢻⣷⣶⠆
⠀⠀⠀⢾⣿⣸⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⢰⣿⣿⣿⠟
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠙⢿⡿⡾⠿⠛⠁
⠀⠀⢰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⣿⣿⣆⠀⠘⢀⣐⣒⢢⣄⡀
⠀⠀⠀⠙⠺⣬⣿⣿⣿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⡟⢿⣿⣠⣴⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣭⣿⡟⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⣏⡿⣿⣿⣿⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⠃⣴⠀⠀⠀⢀⣴⣤⣄⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⡜⢿⣿⠟
⠀⠀⠀⠀⠠⣤⡀⠀⢀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠓⠀⢸⡿⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⢿⣿⣷⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⠁⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠻⠿⢧⠄⠀⠀⠀⣾⣤⠀⠁⠀⠀⠀⠀⢀⣿⣿⠿⠃⢸⣿⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⢤⣤⣶⡚⣠⣶⠀⣠⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣾⣿⣿⣿
⠀⠀⠀⢴⣦⡈⢻⣿⣿⡟⠁⠈⠁⢠⡜⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣿⣿⣿⡿⠀⠀⠀⢠⣼
⠀⠀⠀⠸⣿⣿⡄⠈⠛⢿⠟⠃⢤⣜⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡟⣿⣿⣿⣿⠇⢠⢀⣴⠿⡟
⠀⠀⠀⠈⢻⣿⣿⡏⢀⣰⣾⣆⡰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠈⣿⣿⣿⣿⠟⢀⣼⣿⡿⠞
⠀⠀⠀⣀⣼⣿⣿⣷⡀⠈⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢄⠹⣌⠛⢃⣴⣤⣤⣤
⠀⠀⠀⠉⠻⢿⣿⣿⣇⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠉⠁⠈⢉⣥⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠠⠼⠿⠂⢸⣿⣿⣿⣿⡿⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠻⠛⠀⠠⠀⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠿⠿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⣠⡶⠆⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡉⠉⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈⠀⠘⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠁⡀⢀⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⢀⣾⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣫⠵⠦⠄⠄⡀⠁⠀⠁⠠⣤⣀⣀⣰⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢀⠠⠂⢀⡼⠋⡤⠀⠀⠀⠺⠿⠟⠻⠿⠿⠛⠛⠋⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠴⠈⢉⠠⠊⣠⠀⠀⠀⠴⠷⠇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣣⣲⠶⣂⠀⠀⠀⠚⡠⠔⠁⡰⠊⢠⣾⣡⠄⣠⠟⠀⠀⠂⠀⠈⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢊⣥⣦⡤⡖⠢⠛⠙⣠⢖⣀⠴⢚⡡⠈⡽⣷⡟⠁⠀⠀⠀⠐⠀⢠⠀⡤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⢞⣛⠭⣖⠯⠂⠀⢀⣠⣼⣏⣑⣚⠽⢚⡭⠖⠋⠀⠀⠄⠀⠀⢀⠀⢀⣆⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⢍⠀⢈⣠⣤⣴⣾⣛⣻⣿⣿⣿⣖⣪⠟⠁⠀⠀⠀⠀⠀⠀⢀⠀⢳⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣋⠤⠶⠤⠭⣥⣭⣿⣷⣿⣶⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⣪⣭⠟⠁⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣇⣩⣤⣶⣶⣀⣶⣤⣤⢤⠤⠐⠒⠂⠉⠁⠀⠈⠀⠀⠀⠀⠀⢠⣤⡵⠗⠀⠀⠀⡀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠟⠛⠟⣫⠽⠿⡟⢛⣭⢁⡆⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣾⡥⢀⣀⣀⠜⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⢀⡠⠔⠛⠁⠊⠉⠉⠑⠶⠓⠳⢆⡄⠐⠀⠛⠀⠀⠀⡀⠀⠀⠀⠠⠔⠛⠉⠀⠈⠉⣹⣿⡞⣡⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣪⠝⠁⢀⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣶⡈⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣥⡶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣺⠕⠋⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⣠⢖⣭⠟⠋⠛⠛
⠀⠀⠀⠀⠀⠀⣀⠴⣊⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣦⡀⢐⣡⡶⠛⠁
⠀⠀⠀⣀⠴⣊⡵⣚⢥⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣽⣵⣾⣿⡅
⢀⣴⣿⡿⢞⡵⢊⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣲⣿⠿⣧⡭⠿⠛⠉
⠈⠱⣿⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣭⠶⠛⠉
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⣿⣷⡄⢸⣿⡇⠀⠀⠀⣿⣽⡇⠀⢸⣿⠀⢺⣿⡿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣿⣟⠁⢸⣿⡇⠀⠀⠀⣿⣿⡇⠀⢸⣿⠀⢸⣿⣷⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣈⣿⣿⡇⣸⣟⣇⣀⣠⡄⣿⣿⣧⣀⣼⣿⠀⢸⣿⣏⣀⣈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠋⠀⠛⠚⠛⠛⠓⠃⠈⠛⠛⠿⠛⠁⠀⠚⠚⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠛⠛⠃⠀⢠⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢠⣄⣀⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣷⣶⣴⣿⣿⣿⣦⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⣠⣴⣿⣿⠿⠛⠹⠛⠿⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⢀⣠⣶⣿⣿⠿⠋⠁⠀⠀⡁⠀⢠⢫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠻⣿⠟⠁⠀⠰⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⡿⠟⠋⠀⠀⠀⠀⠀⢀⡃⢠⣯⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⢀⣶⣶⣾⣿⣷⡀⠀⠀⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠔⠀⠀⠀⠀⠀⠀⢀⡿⣽⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣀⡼⣹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠘⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⣿⣿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢰⢷⡀⣸⠧⠞
⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⠶⣦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠉⠉⠙⠳⣦⡀⠘⠾⣳⢏⣠⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿⠶⣶⣦⣄⡀⠀⠀⠀⠀⣼⠋⠀⠀⠀⢠⣦⠀⠈⠻⣦⣤⡏⠻⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⠀⢰⡟⠀⠀⠀⠀⠈⠉⠀⠀⣰⠏⢸⢣⡴⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠿⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⣴⡶⠀⠀⠀⠀⣠⡾⠋⠀⠀⠈⠉⠛⠛⠻⠶⠶⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣠⣴⠾⠋⠀⠀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢠⡞⡉⠁⠈⠙⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢰⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣠⡶⢶⡄⢠⡟⠉⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡧⠶⠶⠛⣡⡶⠶⣦⠀⢠⡾⠋⠉⣼⡆⠀⢰⡏⠀⠀⠀⢿⣤⠾⠋⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣟⣀⣴⠏⠀⣿⡇⠀⣠⣿⣦⣠⡼⢷⣤⣤⠶⠛⠛⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠈⠻⣭⣤⡴⠞⠋⠙⠛⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋


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

⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠎⠀⠴⣾⣿⣿⡇⠈⠃⠉⠛⠂⠀⠀⠂⠀⠀⠀⠰⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠤⠒⠚⣸⣿⣿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠈⡇⠀⠀⢀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡿⠋⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼
⠀⣀⠔⠂⠀⠦⢄⠀⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠠⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡄⢀⣾⡟
⠴⠁⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠈⠙⢂⣀⣀⣀⡀⢀⡠⠐⠒⠦⢄⠀⠀⠀⠑⠇⡀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⣾⡿⠋
⠆⠤⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢡⠀⠀⡀⠀⠐⢄⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⢤⣶⣶⣼⣷⣷⣤⣾⣿⣿⣿⠖⠈
⠀⠀⠀⠀⠠⠀⠀⠐⠠⠀⠄⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⢳⡎⠀⠁⠈⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠛⢛⣟⣿⣿⣿⣷⣶⣖
⣦⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠎⢳⠀⠀⠀⠀⣠⠤⠀⠠⠤⢺⣿⣿⠘⠻⠟⠿
⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠊⠁⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣆⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣻⣷⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⡄
⠀⠀⠀⠈⠀⣦⢄⡀⣀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠐
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠤⠱⠶⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⡇⠀⣾⡇⠀⢀⠔⠀⡠⠊⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠢⣀⣀⣀⠀⠉⠙⢿⣿⣿⣇⢰⣿⣷⣾⣿⡵⠄⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠘⠛⠛⠛⢻⣿⣾⣿⡿⢿⡅⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠂⠸⡄⠀⠀⡼⠀⠀⣠⡄
⠀⣠⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁⠈⠁
⠀⠠⢀⣸⣆⠀⠀⠀⠀⠀⢉⡂⠀⡀⠀⠀⠀⠀⠀⠀⠠⠶⠒⣈⡽⠟⠉⠉⠻⣧⠀⠉⠀⠀⠀⠶⠤⢄⠀⢀⠌⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣠⠂
⠀⠀⠀⠀⠹⠞⠀⢀⠂⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠴⢒⢀⠝⠉⠡⠚⠐⠆⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢠⠀⠀⠀⠀⠀⠀⣠⣄⡀⢸⠀⠀⠀⠀⠀⢀
⠀⣀⠀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠋⠉⠉⠻⢟⢿⣇⣠⡀⡀⠀⠀⠀⠀⠐
⠊⠁⠀⠀⠀⢀⠀⠀⢀⠈⠈⠲⠤⢶⡀⠀⣀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡄⠀⠀⢀⠀⢠⠀⠀⢀⣴
⠀⠀⠀⠀⡤⣈⣀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢳⣇⠀⢸⣧⣤⣤⣶⡿⠛
⣀⠀⠀⠀⡎⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠿⠿⠛⠂
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡄⠀⡌⠀⠀⠀⢀⣴⣾⡥⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣍⠀⠀⠀⠐⠊
⠀⠀⠀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠀⠀⠀⠤⣄⡀⠀⠀⠀⣹⣿⣿⣄⣄⡆⠀⣴⣾⣿⠯⢀⡄⠀⠂⠐⠀⠀⠲⠀⠠⠁⠈⠀⠈⠳⣍⡀⠒⠒
⠒⠠⢀⠀⠀⠀⠁⠀⠀⠢⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠙⢿⣿⡏⠃⢠⣿⣿⣯⠖⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣷⣶⡅⣤⠛⠲⣹⣿⣣⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠆⠀⠀⠀⠐⠚⠋⠉⠁⠘⠞⠛⠙⠋⢻⡿⢿⠅⣀⣶⠋⣵⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⣿⣧⣭⡍⠀⠀⠁⡆⠀⣀⢀⡀⠀⢸⠦⠄⠴⠶⣤⠀⠆⠀⠀⠀⠀⠀⢀⠀⡀⠀⢰⡀⠰⣦⣄⣀⠀⢠⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⢀⣿⣾⣿⡄⠘⠋⠀⠁⠀⠛⠰⠆⠐⠛⠀⣤⡄⠀⠀⠀⠀⠀⠶⡇⠀⠀⠙⠀⡅⢀⣼⠉⠀⠃⠈⢹⠀⢸⠀⠻⠄⢛⠀⠘⠓⡄⣙⠛⢳
⠀⠀⠀⠀⠀⢨⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⣀⣘⠀⠈⠀⠀⠀⠀⠀⠶⠀⢀⡒⠐⢲
⠀⠀⠀⠀⠀⢸⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠉⠐⠒
⠀⠀⠀⠀⠀⣹⣧⣤⣤⠀⠀⠀⠀⠀⠀⠐⠞⠁⠀⠶⠀⠀⠀⠶⠄⣤⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠉⠀⢠⡀⠀⠀⢤⠌⣃⠀⡠⠶⢦⠀⠀⣀
⠀⠀⠀⠀⠀⣿⣶⣦⣶⠆⠠⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠰⠿⠃⠀⠀⠀⠰⠆⠈⠃⠀⠀⠀⠀⠀⢰⣤⣧⣘⣋⠀⠟⠀⡶⢨⡅
⠀⠀⠀⠀⢀⣿⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠲⠷⢶
⠀⠀⠀⠀⢸⣿⣾⣥⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠶⠂⠀⠀⢠⡋⢰⠆⢀⣤⠀⣒⡀⠀⠀⠤⠀⢠⠀⠀⠌⠉⠟⠻⠷⢶⠶⢤⣤⣤⠀⠀⢀
⠀⠀⠀⠀⢸⣯⣭⣭⣠⣬⠀⠀⠀⠀⠐⠏⠀⠨⠁⠀⠀⠀⠀⠀⠈⠛⠻⠶⣤⣄⣀⡏⠀⡛⠃⠰⠆⢈⠀⣤⠅⠛⠀⠶⢠⡌⠀⠀⠀⠈⠀⠀⠨⡥⠀⠈⣥
⠀⠀⠀⠀⣻⣯⣭⣉⠛⠉⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠶⡆⠀⠘⠀⠀⠀⠀⠀⠑⠀⠀⠸⠥⠘⠛⠀⠀⠀⣥⣀⣶
⠀⠀⠀⠀⣿⣍⣉⣻⠲⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠰⣿⣉⣭⣏⣀⠂⠀⠃⠹⠉⢛⠛⠲⠀⠄⠀⠀⢀⡀⢰⠖⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡄⢀⣀⠀⠀⢀⡄⠀⠐⠒⢀
⠀⠀⠀⢸⣟⣙⠛⠉⠉⠀⠋⠰⠆⣠⡄⣀⠀⠀⠃⠰⠶⠘⠃⠘⠀⠛⠁⢀⣄⠀⢈⠉⢂⣀⡀⠀⠀⢸⠀⠀⣠⠑⠗⠈⠋⠀⠀⠨⠉⠈⡟⠀⡇⠰⠆⡂
⠀⠀⠀⢼⡟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠶⠾⠶⠚⠚⠓⠀⠀⠲⠂⠐⠀⠛⠛⠀⠉⠀⠀⠦⠀⠰⠶⠷⠾⠷⠾⠟⠻⠛⠛⠋⠀⠇⠸⠛⠻⠿⠆
⠀⠀⠀⣾⠟⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈
⠀⠀⢀⣿⢿⣶⣶⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⠶⠿⠛⠟⢩⡭⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢠⣿⣶⣶⣶⠀⠀⢀⣍⠀⠛⠀⡶⠀⣤⠄⣀⠀⠺⠃⠀⠀⠀⢀⠉⣠⡉⠴⠆⠀⠀⠶⠂⡀⠐⠓⢰⠖⣠⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡤⠈⠉⣤⡄
⠀⠀⢸⣷⣶⣦⡄⠀⠀⠀⠙⠛⠛⠷⠷⢶⣧⣤⣭⣀⡀⠀⠀⠘⠟⠨⠁⠉⠀⠀⠀⠀⠀⠀⠀⠄⠘⠷⢶⣦⣽⣀⣛⠁⡖⠀⣶⠄⡀⠐⡛⠀⡀⢀⡀⣨⠀⠰
⠀⠀⢹⣧⣌⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉⠛⠛⠷⢦⡄⢀⠀⠀⠛⠛⠛⠛⠋⠉⠀⠈
⠀⠀⣿⣉⣉⡉⠀⠀⠤⠖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠢⡴⠶⠹⡁⠀⠀⢠⡄⢀⣥⠤⣤⣤⣔⡀
⠀⠰⣿⠿⠿⠟⠀⡟⠁⡶⠆⣤⡌⢑⡆⠀⠰⠦⠀⠀⠒⠀⠀⠀⡂⠀⡏⢙⠛⢛⠛⠛⡟⠶⠆⠰⠀⠀⠀⠆⠀⠀⠁⠀⠀⣠⣌⠀⠀⠅⠈⢨⡥⠘⠏⠀⠶⠂
⠀⢠⡿⠿⠿⠧⠀⠷⢦⣧⣄⣇⠀⡌⠁⢸⠛⢠⣶⠄⢰⣶⢀⣄⠐⠖⢀⣀⠀⣀⡀⣀⢀⣀⠀⠀⠀⣴⣶⢀⡀⠀⠈⠀⠀⠛⠋⠉⠀⠁⠀⠈⠅⠈⠁⠀⠁
⠀⣸⣷⣶⣶⡄⠀⠀⠀⠀⠉⠙⠛⠿⠶⢶⣤⣴⠀⠀⠈⠉⠠⠤⠀⠀⢨⡁⠲⠶⠀⢫⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠉
⠀⣹⣷⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢭⠀⠀⠀⠀⠀⣠⡄⠀⣀⡀⠀⠀⠀⠀⠀⠀⡐⠃
⠀⣿⡟⠉⠉⠉⠉⠍⠙⢻⠁⠨⠀⠈⠳⠀⠀⠦⠀⠀⠶⠀⠀⣈⠘⠊⢐⣶⠀⠀⣺⠙⣁⣶⣉⣇⣶⡀⢐⣆⡀⣠⡵⠒⠀⠠⠀⠠⣤⣤⣤⣤⣶⠶⠶⡆
⠀⠈⠻⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠶⠿⠶⢶⢿⣶⣶⣿⣶⣶⣾⣿⣶⣶⣾⣿⣿⣧⣿⣴⣯⣿⣴⣿⣿⣼⣤⣶⣧⣬⣤⣤⣤⣤⣥⣀⣨⣀⣀⣁⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣐⣲⣞⣛⣛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣿⣿⣿⣿⣿⣿
⣀⣤⣤⣤⡤⠀⠀⠀⠀⢠⣤⣤⣶⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣭⣿⣿⣿⣿⣿⣿
⢶⣶⣾⣷⣶⣒⣀⠂⠀⣀⢸⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡍⢻⣿⣿⣿
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⡀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣋⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣦⣤⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⣦⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠯⠀⠉⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣤⣀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣠⣿⣿⣶⡤⠄⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣶⡄⠀⠀⠀⠀⠀⠀⠰⠶⢤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠃⠀⠀⠀⢀⡀⢀⣰⣾⣿⣿⣿⠟
⠰⢤⣄⣀⣀⠀⠀⠀⠈⠛⠛⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⡅
⠀⠀⡙⢿⣿⣿⣷⣶⡀⠀⠀⠙⠿⣧⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠘⠛⠉⠉⠛⣿⠿⠟⠋⠉
⠀⠀⠀⠸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⣴⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⢿⣿⣿⣿⡷⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣿⣿⣷⣦⠀⠀⠀⠀⠈⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⠏
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢨⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠚⠉
⠐⠲⢶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠘⠻⣿⣷⣦⣄⠀⠀⠘⠒⠲⢾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⠀⠀⣀⣀⣀
⠀⠀⠀⠻⢿⣿⡿⠟⠀⠀⠀⠀⢀⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⢻⠿⡟⠋⠀⠀⠀⠀⠀⠀⣧⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠁⠈⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠝⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡿⠓⠀⠀⠀⠀⠀⠀⣸⣿⣿⣄⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⣾⣷
⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠠⠔⠚⠛⠻⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠀⠀⠀⠀⠀⠀⠙⠿⣿⠿⠋⠉⠉⠁⠀⠀⠀⠴⠿⡿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⣿
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢻⡀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⡇
⣿⣷⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠈⢷⡀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠘⢿⣿⢸⣿⡄⢠⣄⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢣⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⣠⣤⣬⣾⣿⡟⢸⣿⣷⡀⠀⠀⣀⠼⠤⣄⡀⠀⠀⢠⠞⣡⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠈⠛⠿⣿⠟⢧⡘⣿⣿⡇⢀⠌⠁⠀⠀⠀⠹⣦⣰⠋⡼⠁⠀⠀⠀⠀⠠⠴⢶⡍⠁
⠀⠀⢀⣤⣶⣶⣾⣿⡿⣤⣸⢤⠸⠗⠀⠀⠀⠘⠃⠸⠀⠀⠀⠀⣀⣠⡤⠴⢋
⠀⠀⠙⠿⣿⣿⡿⠋⠀⠀⠗⠚⠗⠦⣄⡀⠀⠀⠀⠀⠀⠀⠒⠚⠉⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⡙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣀⡈⢳⡀⠀⠀⢀⣀⠴⠊⠁⠘⠀⡄⣧⣹⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⡏⠉⠉⠀⠀⠀⠀⠀⠙⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣃⣀⠚⣛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠙⢿⣻⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⣶⣿⣿⣿⣿⣷⣤⣀⠀⠀⣿⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⢷⡼⢿⠀⠘⠁⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣯⣙⣻⣿⣿⠛⠃⠁⠀⠀⣀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣾⣿⣿⣿⣦⣽⣿⣿⡟⠃⠀⠀⠀⢀⣾⠿⠃
⠀⠀⠀⠀⠀⠶⠞⠛⠛⠛⠉⠉⠉⠉⠉⢉⣠⣤⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⢁⣿⣿⡿⠟⠻⠿⠁⠀⠀⢀⠀⠀⠀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⡾⠁⣰⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⣤⣿⡿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠃⠐⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢛⣻⣿⣾⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣤⣶⣿⣿⡏
⠀⠀⠀⠂⠉⠁⠀⢀⣴⣷⠿⠿⠿⠛⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢄⠙⠿⠿⠏⠵⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣻⡿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣷⣤⣒⡜⠻⢭⣿⣿⣿⠿⣿⣿⣿⣾⣿⣿⣿⣍⣉⣷⣬⣙⠂
⠀⠀⠀⠀⠀⠀⠀⠛⢛⣿⠿⣿⣿⣿⣿⠥⠸⠒⡛⠛⠛⠸⣛⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠿⠷⣤⡁⠀⠈⠉⠀⠭⣥⣽⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠙⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠀⠀⠀⢀⡉⠓⠶⣶⣶⣶⣶⣿⠃⣾⣷⣠⣤⣶⣶⣴⡄⠀⡠⠊⠁⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠺⣿⣿⣿⣿⡶⠀⠝⣿⣎⣻⣃⢨⣿⣿⣿⣏⠉⠛⠃⠈
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢰⣿⠷⠈⣉⣹⡟⡻⢿⣿⣿⣿⣾⣿⣿⣿⣿⣽⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣶⣾⣿⣿⣿⡏⠈⠁⠀⠀⢈⣉⣿⣿⠛⣟⠻⠿⣿⣿⣿⣟⡒⠀⠀⠀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠋⠉⠐⠀⠀⠀⣤⣾⣿⣿⣿⠁⠸⡆⠀⠀⠙⠻⣿⣿⣷⣄⡊⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣽⣧⠘⠋⠀⠀⢹⡀⠀⠀⠀⠈⡻⢿⣿⣿⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠙⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣦⠤⣄⣀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢀⠀⠀⠀⣀⠊⠀⠠⠀⠙⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢀⡀⠀⡿⠉⠑⣶⠟⠀⠀⠀⠀⠀⣅⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠁⠈⣾⠇⠀⠀⠀⠀⠀⠢⠐⠀⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⡀⢀⠂⠀⠀⢠⡟⣇⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠐⠀⠀⠀⠠⣧⡄⠀⣺⣵⣷⠆⠀⠀⢀⢁⠎⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠙⢯⠁⠀⠀⠘⣿⡏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠺⠟⠯⡀⠀⠀⠈⠓⣄⣀⠀⠹⠧⢂⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠓⡄⢸⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠜⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠉⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠤⠄⠀⠤⠀⠀⢀⡀⠀⢀⡀⢠⡔⠋⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⡀⡘⠁⠀⠼⣇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⢀⠀⠠⠋⠉⠦⠄⠀⠀⠀⠀⠀⢇⠀⠀⣀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢲⣾⣿⣿⡟⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠉⠀⠀⢀⠀⠀⠀⠀⢀⣰⡿⠁⢻⡏⠈⠉⢄⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠚⠁⢁⠀⠀⠀⠐⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤
⠀⠀⠀⠀⣤⠀⠀⠡⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⢄⡀⢿⣧⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠉⢘⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡾⠿
⠀⠀⠀⠀⠈⠀⠉⠙⠛⠛⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⣠⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆⣘⣿⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣟⣿⠛⣿⣿⣿⣿⡄⣹⣿⣿⣿⡷⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠋⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣇⣴⠿⣿⣿⣿⣷⣤⣶⣿⣿⣿⣿⣿⣶⣾⣷⣿⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⠟⠉⠛⠻⠿⠿⠏⠉⢬⠻⣦⣙⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛⢷⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⣷⣿⡗⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣤⣤⡄⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣀⡀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠻⢿⣿⣿⣿⣿⣿⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⡬⠻⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣭⣿⣿⣶⣾⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢰⡋⣳⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠇⠀⠉⠁⠀⠿⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄
⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⢲⠀⠀⠀⠀⠀⢰⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⡼⠁⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠹⡄
⠀⣸⠁⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠹⡀
⢠⠇⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢧
⣼⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢸⡆
⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢸⡇
⣇⠀⠀⠀⠀⠀⢻⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢸⠃⠀⠀⠀⠀⢀
⢹⠀⠀⠀⠀⠀⠘⡆⣠⠞⠁⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠙⢦⡀⡞⠀⠀⠀⠀⠀⢸
⠈⣇⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⢀⡴⠋⢸⠀⠀⠀⠀⠀⢸⠈⠳⣄⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢀⡏
⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠉

⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⣀⣀⠀⣀⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⢀⡀
⠀⠄⠀⠁⠀⢠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠲⣊⡖⠂⠀⣯⡽⠂⣿⠍⢰⣿⣧⢰⡟⠀⣿⠍⠀⠀⢿⣦⣿⠃⠠⠄⠀⠉⠀⠙⠀⢴
⠀⠭⠀⠀⠀⠃⠀⠀⠀⠀⠀⣤⣖⠗⠀⢀⣀⣤⣈⠀⠁⠀⠀⠛⠀⠀⠛⠛⠘⠛⠓⠈⠛⠃⠛⠛⠀⡂⠀⠻⠏⠀⠀⠀⠀⠀⠀⢀⠀⠈
⠀⠀⠡⡀⠀⠀⠀⠀⠐⠀⡶⠉⠀⠀⡴⢋⠀⡇⣀⡙⡄⠈⠁⠀⠀⠀⣶⣀⠀⠢⠀⠀⠀⠦⠀⠀⢰⡷⠀⠀⠀⠰⠆⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠈⠒⡄⠀⠀⠀⠀⠀⢀⡀⠀⣇⢀⡴⣷⢤⣀⡟⠀⠀⢀⠤⢼⠉⠸⠇⠀⠀⠀⢠⡄⠀⠀⠀⠃⠀⠀⢠⡠⠀⠠
⠀⢤⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠯⣄⣿⡠⠞⠁⠀⠀⠀⣀⣀⣀⡀⠀⠠⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⢶⠄⠀⠀⠀⡀⠀⢾⣿⣷⣴⣿⣿⠀⠀⠀⠀⡄⠀⣠⣾⣿⣿⣿⣿⣿⣷⣤⠀⠀⢶⡶⠂⠀⠀⠀⠀⠀⢶⣶⠆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠐⠂⠀⠀⠑⠈⠻⣿⣿⠟⠁⠐⠁⠀⠀⠀⣼⣿⣿⠛⢟⠛⡋⡏⢿⣻⣷⠀⠀⠀⠀⠀⠼⠧⠀⠀⠀⠁⠀⠤
⠀⠐⠢⠤⠀⠀⠀⠃⡀⠀⠀⠈⠃⠀⠀⠀⠘⠀⣴⠀⣿⣿⣿⣶⣷⣿⣿⣶⣾⣿⣿⠀⠙⠀⠛⠙⠋⠓⠋⠛⠠⠆⠀⠀⠀⠀⠀⠂⠀⠶
⠀⠀⣀⡤⢶⡶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣟⠂⠀⢿⣿⣿⢲⣔⣃⣛⣃⣿⣿⣿⠁⣴⢦⡀⠐⠃⣀⣀⠀⠀⠠⠀⠀⠀⠀⠠
⠀⡼⠁⠀⢸⡇⠀⠈⢧⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣽⣿⣿⣻⣿⣿⡿⠃⠀⣧⠀⠙⣶⠛⠉⣹⠂⠀⡀⠀⠀⠀⠀⠀⠀⠠
⠀⡇⠀⣠⢼⣧⣀⠀⢸⠀⠃⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⣀⠈⠙⠛⠛⠛⠋⠉⠀⡀⠀⠘⣶⢺⡿⣦⡴⠋⢀⠀⠀⠀⠀⠀⠉⠀⠀⠁
⠀⠹⣏⠁⢸⠇⠈⣳⠏⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣶⣿⠏⠈⣷⣄⠀⠈⠓⠀⠈⠻⠟⠉⠀⠀⠈⠀⠀⠀⠀⠀⣀⣀⣀⠀⡠
⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⡀⠀⢿⣟⠙⠀⣀⣿⣭⡆⢀⠀⠀⠀⠂⡀⠀⠀⠂⠀⢀⣀⣠⣬⠿⣿⣯⣍⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠈⢁⠀⠈⣷⡀⢘⢻⡷⠀⢿⣿⠟⢁⣜⠁⠀⠐⡿⢇⠀⠀⠀⠀⠀⠛⠽⢫⠟⠛⠱⠋⠀⠆
⠀⠀⢀⠄⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⢃⡄⠉⠈⠠⠜⠉⢠⣘⠂⠀⠀⠀⠀⠀⢠⣤⡄⣤⠀⢠⠀⢠⡄⣤⡀⢠⡤⡀
⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠘⠃⠀⠀⠘⠻⠉⠛⠀⠸⠟⠿⠁⠿⠧⠸⠿⠄

⣿⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣿
⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠐⢄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⣄⠀⠄⠀⠑⢄⠀⠀⠀⠀⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠈⠐⠈⠃⢄⠑⠄⠀⠑⢄⠀⠀⠠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠐⢄⠀⠀⠐⡀⠑⢄⠑⢄⠀⠑⢤⠁
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡀⠀⠤⠄⢀⠑⠄⠀⡘⢄⡀⠑⢄⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠄⠂⠁⠀⠀⢠⡢⡀⠈⡄⠙⢷⢤⣀⡁⠀⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⠂⠀⠀⠀⠀⡠⢼⣍⢷⠼⠀⢸⠀⠀⠑⠄⢈⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠊⠀⠀⠀⠀⠠⢮⠨⠕⡙⠉⠀⠀⡀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠁⠀⠀⠀⡠⣾⠍⣐⡌⠉⠀⠀⠀⡰⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠠⠁⠀⠀⡠⠤⣣⢣⠌⠂⠀⠀⠀⠀⡔⢁⠔⠁
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠃⠀⡠⡾⢜⢣⠽⠋⠀⠀⠀⠀⡠⢊⠔⠁
⠀⠀⠀⠀⢀⠔⠁⠀⠐⢄⠀⠀⡀⠀⢌⠂⡩⠉⠀⠀⠀⢀⠠⢊⠔⠁
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠠⡐⠄⡀⠀⠀⠀⡀⠄⠂⢁⠔⠁
⠀⠀⠀⠀⠈⠢⡑⢄⠀⠀⠐⡀⠈⠢⡀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠢⡑⠄⡀⡈⠢⠄⠈⢢⡀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡘⠻⡲⠤⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠶⠟⡻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠛⠜⣀⠋⡞⣆⡛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢦⡀⠀⠀⡴⣣⠴⠣⠀⢠⡏⠂⠀⢀⢀
⠀⠀⠀⠀⠀⠀⡴⠉⠀⢸⠀⠀⠈⠒⢼⣿⣅⠀⡼⠀⢸⢀⢃⠔⠉⠀⠙⢦⡀
⠀⠀⠀⠀⢀⡞⠀⠀⣠⢼⣲⠂⠀⠀⢸⣍⠻⠛⣦⡀⡎⢸⣷⠖⠲⣠⠤⢄⠘⣄⠀⠀⠀⢰⢆
⠀⠀⠀⠀⠠⡇⠀⠀⠀⢸⣷⡡⠀⠀⡘⢇⠀⢀⠉⠙⡿⠋⠁⠀⢀⠏⠀⠀⠻⣄⠱⡀⠀⠈⠀⡗⢄
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠸⢿⣿⠖⢩⣷⡮⠭⠉⢷⣦⣇⠀⠀⠀⡏⠛⠁⠀⠀⠈⡶⠃⢐⠀⢸⣷⡬⠖⠋⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠃⠀⠊⠉⢻⣷⣶⠳⠤⢍⠳⡄⢾⠀⡄⢀⣠⣶⠟⠓⠤⢄⣆⢸⠋⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⠀⢀⠄⠚⡝⢻⡠⠀⠀⠓⠛⢻⣿⣿⡿⠋⢻⠀⠀⠀⠀⢿⣬⡝⠛⠛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢲⡀⠀⠉⢸⠇⠀⢀⡄⢠⠞⠍⡞⠀⠀⢸⣖⣄⣀⣴⠋⠉⠓⢦⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠔⠉⠉⣽⠁⠀⠈⠛⠚⡇⠀⠀⢘⣟⠛⣿⢸⣤⠢⠈⣢⡇⠀⠀⠀⢤⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠬⠷⣄⡀⣀⣧⣸⣄⠀⣾⣷⢰⣿⢸⣤⣟⠻⡁⠀⣀⡄⠀⠀⣧⠴⠂⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠂⠲⢿⡟⠳⡌⢙⠟⠀⠘⣿⠿⣷⢦⣿⣦⡃⣸⣿⣄⣠⡼⠯⠥⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠁⠱⣄⣼⠸⠀⠀⡼⡇⢠⠃⢀⡿⠀⢻⢷⡄⣀⣀⡔⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠷⣹⠙⠻⣿⡁⠀⠾⠞⢿⣟⣉⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⠇⠀⠀⠀⠈⢧⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⡴⠃⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏

⣿⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⠛⠛⠛⠛⠛⠛⣿⣿⣿⡇⣾⠛⠛⢻⣿⣿⣿⡟⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⣼⣿⣿⣿⡇⣿⠀⠀⠀⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⢀⣾⣿⣿⣿⢻⡇⣿⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⠁⢸⡇⣿⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⠁⠀⢸⡇⣿⣶⣤⣀⡀⣸⡟⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣶⣿⡇⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠈⠙⠿⣶⣤⣀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠈⢙⣿⠿⢿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠉⠻⢿⣾⣿⣿⣿⣿⡿⠟⠋⠙⣿⣿⡇⣿⠀⠀⣾⡏⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣷⣦⣤⣀⢸
⣿⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⢿⣥⡀⠀⠀⠀⠈⢻⡇⣿⠀⣸⡟⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠃⠀⠉⠛⠷⣦⣀⠀⢸⡇⣿⢠⡿⠁⠀⠀⠀⣀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠟⢋⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠙⠻⣾⡇⣿⣿⣧⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠁⢸
⣿⠟⠉⠀⢀⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠀⠀⠘⣿⣿⣿⣆⠀⢸
⣿⠀⠀⢠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⢸
⣿⠀⣰⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣼
⣿⣾⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⠇⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠔⢃⡀⠠⠐⠀⣀⣥⡀⠁⠀⠀⠀⢤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⢀⣄⠖⣉⣤⣶⡦⠃⠐⡟⢿⠀⠀⠀⠀⠀⠀⠉⠹⠿⢿⣷⣶⣤⣀
⠀⠀⠀⠀⢀⣸⣿⣾⡟⠛⠁⠀⠀⢠⣿⡌⠀⡀⠶⡴⢶⣴⣤⡦⠤⣼⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠘⠛⠋⠉⠉⠑⠄⠀⠐⠒⠂⣱⡟⢀⠒⢤⠿⣭⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠹⢿⣦⣽⣟⣳⣿⣿⣿⣿⣿⡿⣿⣿⣯⢿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣶⣿⣿⣿⠶⢦⣤⢤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠛⠿⢿⠿⠿⡤⣿⣶⣶⣶⣿⣯⡭⠭⠷⠾⠿⠛⠛⠛⠷⠶⢤⣴⣒⣀⠵⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣋⣼⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠐⠠⣄⣀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⠤⠒⠋⠉⠀⠀⠀⠀⠠⣤⡤⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⡁⠒⠃⠀⠀⠐⠒⠀⠀⣀⡴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠐⠦⠠⠤⠀⢀⡤⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠂⠀⠩⠀⠉⠊⠈⠀⠲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠇⠀⡄⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠷⣦⡀⠀⢀⣼⣿⣿⠗⣀⣀⣀⣀⠀⠀⠀⠰⠷⡞⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡅⠀⠀⠀⠈⢻⡄⣾⢟⣩⠖⠛⠉⠉⠉⠉⣹⡷⠂⠀⠐⡿⢀⣠⠞⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣿⡇⣦⠀⠀⠀⠀⡧⢫⠞⠁⠀⣀⣤⠄⠀⣼⠏⣤⠀⠀⢀⡗⣉⠀⠀⣼⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢻⣇⣿⣧⢰⠀⠀⠃⠀⢀⢦⣾⣫⣤⡄⣴⠋⢠⣿⡆⢀⢈⡾⠃⠀⡰⢃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠝⠻⣿⡆⣇⠀⠀⣄⣾⣾⡿⠟⠁⠊⠀⠀⢸⣿⣿⣼⣨⣾⠁⠈⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠛⠛⠂⠀⠈⢃⡿⠴⠚⣿⡏⠉⠀⠀⠀⠈⠙⠓⢮⣻⠇⣻⣿⣷⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣠⡴⠦⣬⣶⣏⣀⣤⣾⡿⢁⡶⠒⠈⠡⢤⣀⣀⢰⣽⣾⡿⠀⠀⣴⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣤⣀⠤⣬⣽⡿⢿⠟⢃⣤⣭⣍⠉⠉⢠⣛⡳⠦⣤⣤⣶⣾⣿⣿⣷⠟⣠⣤⣤⠸⣷⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⣻⣿⣱⢟⣵⢸⠁⠀⠀⢸⣿⣿⡷⠀⠀⢈⣩⣤⢶⣿⡽⣿⡻⣿⣧⡿⠀⠀⢀⣿⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣿⡿⣿⡈⠀⠀⣸⠘⠿⣟⣥⠀⠀⢉⠛⠧⣽⣦⡀⠀⠈⠊⣿⡇⠀⡄⣾⢏⣴⡿⠿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡏⢏⣿⣬⣁⣀⣠⠏⠀⣀⣭⠷⠾⢿⡜⣷⡀⠀⠙⠿⣧⠱⡄⡏⢠⣾⠱⠏⢚⣵⡾⠿⠟⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣀⣉⣉⠁⠈⠳⢿⣿⣵⢋⡴⠞⢩⣶⠾⠿⢸⡇⣿⣷⠀⠀⢀⣈⠃⠚⣵⠛⣇⣀⣚⡛⠛⠛⠉⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⣍⠉⠉⠉⠙⠓⢦⡀⠈⢀⡞⣴⣧⡞⠁⠀⠀⢸⡇⣿⣿⠀⣴⣿⣿⠇⡀⠻⣤⣿⡟⢷⣤⣴⣆⣀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠸⣇⣿⡀⣤⡠⣀⠀⢀⠁⠀⠀⣸⣿⢋⠔⠀⠀⠀⣼⢇⣿⢃⣠⣿⠟⢡⣾⡇⣷⢬⡙⠛⠶⡀⠉⠉⠻⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡻⡸⣷⣿⣷⣌⢳⡌⣆⠀⠀⠿⣵⡿⠀⠀⢀⣼⣫⡾⣣⣿⡿⠉⡏⡿⠛⠈⠁⢀⡇⢸⣷⡍⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣙⢮⣟⣻⣿⣳⡿⢋⡴⠖⠶⣦⡙⣦⠖⠋⠚⢩⣌⣛⠋⠀⠀⣧⠀⠀⠀⣠⡞⣷⢈⢷⣍⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣶⢯⡀⢌⣉⣛⡛⠃⣿⡀⠀⠀⢸⣧⢐⠚⠛⠻⠿⢓⣮⣝⢶⣄⠹⠷⠾⠟⠉⢸⣿⣯⡳⣮⣳⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢤⣴⣾⣿⣿⣿⢟⡿⣫⣶⣿⣿⡟⣡⣆⠹⣿⣶⣶⣿⠇⣼⣿⠶⠦⠬⠭⠍⠙⠓⠹⣆⠀⠀⠀⠀⠀⠙⢿⣿⡎⠙⢦⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢫⡿⣁⣠⣤⠞⠩⠞⠁⣸⡷⢠⣭⣭⢡⡈⠻⢦⣄⡀⠀⠀⠀⠀⣀⡴⣛⣤⣶⡟⠀⠀⠀⢀⠙⠃⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⡿⠋⠁⠀⠀⠀⣰⡿⢁⡿⠉⣿⢸⣿⣆⢀⢯⣝⣛⣛⣿⠍⠀⠾⠿⣟⣻⣃⣀⣀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠻⠇⠀⠀⢀⣠⡾⣟⣵⢺⡇⠀⠸⠸⡿⣿⡌⡇⠿⠿⠛⠁⠀⠂⠉⠉⠉⢛⣿⡟⠛⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠁⢸⣿⣿⡸⣇⠀⠀⠀⠃⢹⢧⡇⠐⢶⣤⣤⣤⣤⣴⣶⣾⠟⠋⠀⣠⡟⣴⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠙⢆⠀⠀⠀⠞⣾⠁⠀⠀⠛⠿⣦⣉⠉⠉⠀⠀⣀⡴⠋⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠈⠳⣦⣠⣾⠃⠀⠀⠀⠀⠁⠒⠤⠤⠴⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃

⠀⠉⠉⠉
⠀⠑⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⡀⠀⠀⠀⢀⣠⡄
⠀⢀⣀⣀⣤⣤⡤⠶⠶⠶⠶⠶⢶⡷⠦⠤⣤⣀⣛⠈
⠿⣿⣿⣏⠹⣇⠀⠀⣀⣀⣀⣴⣟⣀⣀⣀⡀⠀⢈⣩⣷⠶⣾⣄⡀⠀⠀⠀⠄
⢀⣹⣿⣿⡶⢿⡟⠉⠉⣩⡿⠋⣇⠀⠈⢩⡯⠉⢻⠷⠾⢯⣀⡀⢉⣷⡤⣀
⠛⠉⢹⣿⣷⣘⣧⣤⠴⣿⠒⡶⢻⡛⢷⠒⠒⠲⠶⠤⣄⣀⢠⣿⠓⠢⢄⡀⠙⠢⣄⠘⠛
⣀⣤⡶⢿⣿⣏⢹⡆⢀⣻⣄⣷⣤⣧⡼⠤⠤⣤⣴⣆⡘⠋⠉⠑⠒⠤⣀⡸⠷⠦⢄⠉⢢⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠋⠁⠀⣈⣿⣿⡞⢿⡉⠁⠈⠉⠉⢙⣆⣀⣀⡀⠉⠀⠉⠉⠓⠢⠤⣤⡄⣉⡑⠢⢀⠈⠘⠅⡉⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠄
⣤⡶⠛⠉⠘⣿⣷⣼⠷⠖⢺⣿⣿⣩⡟⠉⠉⠉⠉⠉⠒⠒⠦⠤⢀⣀⠈⠉⠓⠠⣀⠀⠐⠶⠋⠀⠠⠤⠈⠀⢀⠀⠠⢀⡀⠀⠀⠀⣃⡁
⠁⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⣭⣐⠒⠠⢙⡳⠀⠀⠀⠀⠀⡤⢤⢀⡉⠘⠀⠀⡔⠀⠀⢠⠈
⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠁⠘⠂⠀⢠⣤⣤⠆⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡂⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⡀⠄⣠⠂⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠉⠙⠑⠐⠇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣷⡀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡂⣀⣠⣾⡟⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⣰⠥⣦⣿⣿⣿⠋⠀⠀⢀
⠀⠀⠶⢶⣶⣶⣶⣶⣶⣶⣾⣷⣿⣷⣿⣿⣿⠋⠊⠀⣀⡴⠋
⠀⠀⠀⠀⠈⠉⠛⠉⠉⣿⡿⢿⣿⣿⣿⣿⣿⣷⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⡀⢀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠒⠛⠈⠉⠀⠀⠈⠙⠲⣶⣿⣟⣉⣿⣿⣿⡷⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣦⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⣿⣯⣿⣾⣿⣏⡽⣟⡿⡌⣿⣿⣿⣿⣿⣿⡦⢶⢻⠷⠤⡀
⠀⠀⠀⠀⠀⠀⠀⡀⢠⡤⡌⢹⣿⣾⡿⠟⠉⠀⠀⣶⢿⠿⣯⡆⠈⠉⠙⠱⢝⣿⢏⠺⠇⢸⣦
⠀⠀⠀⠀⠀⠀⠘⣷⣈⡛⣁⡼⠋⠁⠀⠀⠀⠀⢀⣿⣿⣿⣻⡇⠀⠀⠀⠀⠀⠉⠟⣷⢿⣟⣗⣓⣄
⠀⠀⠀⠀⠀⣦⡠⣿⣽⣿⠋⠀⠀⠀⠀⠀⠀⠀⢠⡝⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠉⢿⢨⣽⣿⣿⣆
⠀⠀⠀⠀⢐⠐⣧⡻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣫⣯⡹
⠀⠀⠀⢠⣭⣞⣳⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢶⣿⣡
⠀⠀⠀⣸⣟⡿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣏⡙⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡋⣸⡙⠄
⠀⠀⠀⣿⡿⣷⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣵⣺⡎⣋⡅
⠀⠀⠀⡏⣒⢸⣿⣣⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⡇⢶⠆⣘⣻⣾⣷⠄⠀⠀⠀⠀⠀⠀⠀⢀⢻⣌⣰⣿⠅
⠀⠀⠀⢱⠗⣀⢻⣟⡀⠀⠀⠀⠀⣀⣴⣿⣯⣾⠻⣿⣦⢞⡿⢯⢚⡿⠶⡳⣄⠀⠀⠀⠀⠀⣼⣿⣷⣶⣾
⠀⠀⠀⠀⠹⣱⡾⣿⣷⠀⠀⢀⣴⣿⣏⡛⢻⣿⡵⣯⣳⣮⣽⡿⢿⡗⣮⢅⣿⣷⣄⠀⠀⠴⣛⢻⢻⣟⡏
⠀⠀⠀⠀⠘⣟⣷⣿⣿⣷⣴⣣⣽⣿⣮⣭⠴⠃⠀⣿⣿⠻⣿⡇⠀⠻⣼⣷⣼⡻⣿⢇⢈⡿⣙⣠⣿⡟
⠀⠀⠀⠀⠀⠘⣿⣟⣿⣿⡿⢻⡞⢻⡟⠁⠀⠀⠰⣿⣡⣥⢹⡏⠀⠀⠀⠻⣿⣷⢾⣿⣶⢾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⡟⣸⣿⣿⣤⣀⠀⠀⠐⣿⡽⡛⢞⡃⠀⠀⠀⢀⠄⣿⡟⣛⡛⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢌⡡⠛⠾⢿⣿⣿⣷⣶⣿⣧⣴⣿⣷⣾⣟⣿⡾⢻⣿⢧⣙⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⠔⢨⣿⡛⢬⢘⣻⣭⣷⣿⠁⣶⢞⡿⡽⡛⠷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠾⠿⠽⠿⠿⠷⠲⠚⠁

⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡙⠛⢻⣭⣤⢾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣊⣥⣷⣶⣶
⠀⠀⠀⢿⣿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⢸⣶⠖⢚⣻⣧⣤⣄⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⣋⣠⣠⣥⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠁⠴⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠸⢿⡿⠿⢿⠟⠑⠃
⠀⠀⠀⠀⠀⠀⠠⣰⠄⠀⠀⠀⠀⠀⠀⠀⡤⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣒⣲⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠕⠓⠊⠕⠪⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠡⠄⠙⠉⠀⠀⠀⠀⠀⠀⠀⢠⡄⣀⢀⡀⣆⠰⢰⡄⣄⠰⠠⢐⠴⡄⠀⡆⡄⠒⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣾⡄⢘⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡶
⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠉⣻⠇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠷⠄⠀⠀⠀⠀⠀⣴⣶⣶⣦⡀
⠀⠀⠀⠐⠾⠿⠿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠌⢻⣇
⠀⠀⠀⠀⢠⣠⣴⣶⣶⣴⠆⠀⠀⠀⠀⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣦⣬⣼⡿⠃
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⠀⠀⠀⠐⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋

⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠁⠸⠀⠀⣤⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡄
⠀⠀⠀⣠⢀⣥⢄⠀⠀⠀⠀⠀⠀⠀⠳⠟⢀⡀⠀⣠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⡉⣀⡀
⠀⠀⠀⢷⡘⠀⢠⠇⠀⠀⠴⠆⠘⠋⠀⠀⣐⠙⠀⠈⠀⠀⢠⡄⠀⣰⣖⠀⠸⠇⠛⠃⠉⠁
⠀⠀⠀⠀⣭⠉⠀⠀⠀⠀⣤⡴⠆⠀⠀⠈⠋⠀⠀⠀⠀⣤⡌⠁⠀⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⡏⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣰⠟⠀⢸⠁⠀⠀⠂⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⣧⠀⠀⢀⣴⣿⣿⣿⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠑⣤⣄⠀⠀⣸⣆⣠⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣧⣄⣀⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠁⠙⢿⣿⣿⣿⣫⣾⣟⣿⣿⣟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡶⠊
⠀⠀⠀⠀⠀⠀⠐⠻⢿⣿⣿⢿⡿⣻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣿⣿⣿⡯⢍⢒⠒⠤⣄⡀⡀⠘⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣿⣄⠛⢾⣶⣾⣣⣴⣾⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⢿⣿⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⣀⡡⠼⡾⢖⣺⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⠛⠁⠉⠙⣿⢿⣿⣧⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠀⢆⡎⣿⣿⣿⣿⢿⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣶⣀⡀⠈⠃⠀⠈⠁

⠀⠀⠀⠀⣠⠖⠚⢻⠛⠒⢦⡀⠀⠀⠀⠀⠀⢀⣤⠶⠛⣿⠛⠲⢦⡀⠀⠀⠀⠀⠀⢀⣴⠾⠛⣿⠛⠷⣦⡀
⠀⠀⢀⡞⠁⠀⠀⢸⠀⠀⠀⠙⣆⠀⠀⠀⢠⡞⠁⠀⠀⣿⠀⠀⠀⠹⣆⠀⠀⠀⢰⡟⠁⠀⠀⣿⠀⠀⠀⠻⣆
⠀⠀⢸⠀⠀⠀⠀⣸⡀⠀⠀⠀⢸⠀⠀⠀⣾⠀⠀⠀⠀⣿⡀⠀⠀⠀⢻⠀⠀⠀⣿⠀⠀⠀⢀⣿⡀⠀⠀⠀⣿
⠀⠀⠸⡄⠀⣠⠞⢹⠙⢦⡀⠀⡼⠀⠀⠀⢹⡄⠀⣠⠞⣿⠛⢦⡀⢀⡿⠀⠀⠀⢿⡄⢀⣴⠟⣿⠻⣦⡀⢀⡿
⠀⠀⠀⠙⢾⡁⠀⢸⠀⠀⣹⠞⠁⠀⠀⠀⠀⠻⣾⡁⠀⣿⠀⢀⣹⠞⠁⠀⠀⠀⠈⠻⣿⡁⠀⣿⠀⢈⣿⠟⠁
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⢀⣴⠿⠛⣿⡟⠻⢷⣄⠀⠀⠀⠀⠀⣠⣶⠿⠛⣿⡟⠻⣷⣄⠀⠀⠀⠀⠀⣠⣾⠿⠛⣿⡟⠿⣷⣄
⠀⠀⢰⡟⠁⠀⠀⣿⡇⠀⠀⠙⣷⠀⠀⠀⣰⡟⠁⠀⠀⣿⡇⠀⠀⠻⣧⠀⠀⠀⣼⡟⠁⠀⠀⣿⡇⠀⠈⢻⣷
⠀⠀⣿⡃⠀⠀⢀⣿⣇⠀⠀⠀⣿⡇⠀⠀⣿⡃⠀⠀⢀⣿⣇⠀⠀⠀⣿⡇⠀⢰⣿⠁⠀⠀⣠⣿⣇⠀⠀⠈⣿⡇
⠀⠀⢹⣇⢀⣴⠟⣿⡟⢷⣄⢀⣿⠁⠀⠀⢿⣇⣀⣴⠟⣿⡿⣷⣄⣠⣿⠁⠀⠀⢿⣇⣠⣾⠿⣿⡿⣷⣄⣰⣿⠁
⠀⠀⠀⠹⢿⣅⣀⣿⣇⣀⣽⠿⠁⠀⠀⠀⠈⠻⣿⣅⣀⣿⣇⣨⣿⡿⠁⠀⠀⠀⠈⠻⣿⣥⣀⣿⣇⣬⣿⡿⠁
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣭⣯⣼⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄⠀⠀⠀⠄⢰⡞⠠⡯⠩⡬⠉⡏⠁⠒⠠⢀⡀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠱⠂⠀⠀⠀⠴⠆⠒⢐⡆⠀⠀⣗⡒⠠⣷⡄⢈⡓⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⢀⠀⢠⣤⠀⠀⠊⠁⠀⡀⠤⠀⢺⡇⠒⠒⠿⠧⢀⡀⠉⠛⠣⠄⣛⠁⠈⢁⠂⠒⢒⠤⠴⡇⠀⠀⡀⠀⠐⠀⠀⠤⠤⢤⠉
⠀⠀⠀⠀⠀⠀⡀⠈⠥⣤⡤⠀⠁⠺⠇⠠⠄⠘⠒⠒⠒⠀⢤⣴⡉⠁⠂⠄⣠⠀⠉⠑⠺⠵⠄⠀⠀⠈⠁⠀⠀⡅⠾⠟⠀⠀⠃⠀⢀⠀⠰⡇
⠀⠀⣼⠀⡆⠈⠋⠀⠂⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠴⣏⡉⠐⠂⢤⠨⢀⣀⡴⠴⠀⠀⠀⡁⠀⣀⠀⠿⠃⠐⠟
⠀⠀⠚⠀⡇⠀⠀⠛⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠐⠚⠧⠄⣀⣠⡅⣨⠉⠉⣚⠇⠀⠹⠀⣀⢚
⠀⠀⢀⣤⡇
⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠤⠤⠀⠤⠤⠥⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠴⠶⢶⠠⠐⠈⠁⢸⠀⣀⡀⣴⣦⣶⣰⠖⠼⠏⠒⠤⣀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠈⡷
⠀⠀⢀⣤⡀⠀⢀⡄⠀⣀⠀⠀⢀⣤⣽⠀⢸⣕⠀⠀⠀⢀⣈⠁⠒⠤⣀⠀⠉⠐⠢⠤⢀⣀⡀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠩⠀⠀⢠⡀
⠀⠀⢸⠀⣿⠀⠙⠁⠘⠋⠀⢀⡸⠟⠛⠀⠙⠉⡉⠉⢉⡉⢒⡂⠤⣀⠀⠙⠛⠫⣅⡀⠀⢀⡉⠉⠘⣶⠀⠀⠀⡶⠀⢀⣬⠀⢀⣤⠀⠀⠸⢎
⠀⠀⣸⡾⠃⠀⠀⢀⡦⡀⠈⢠⡾⠄⠒⣶⡾⠉⠉⠉⠉⠁⠛⠢⠄⣀⣉⡗⠤⣠⡄⠀⠙⠛⠑⠒⠀⠤⠤⠦⠀⠇⠀⠀⠁⠀⠈
⣠⠞⢹⣄⠀⠀⠀⠀⡀⠔⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠤⣉⡀⠉⠒⠺⠿⠿⠿⡀⢀⣀⠀⢈⠉⠩⠉⠁⠀⠀⢠⣶⠆
⣿⠀⢸⡅⢣⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠲⠶⠶⢖⣀⣤⡅⠠⠖⠰⠦⠠⠖
⠈⠳⠤⡷⠊⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠁
⢠⣶⡆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣇⣀⠀⣤⣤
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠈⠁⠀⠀⢈⡇⠀⣈⠉⢐⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⡣
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⠀⠀⠀⠀⣿⡓⠀⢀⣼⣾⠃⠉⠉⠒⠫⢄⣀⡏⠑⠒⢤⣾⡀⠀⠀⠀⠠⠤⠤⢤⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠆⠀⠀⢀⡤⠤⠄⠚⠛⠋⠒⠒⠢⣾⠄⣀⠈⣇⡂⠤⣀⡟⠀⠉⠀⠒⠰⠀⠀⠰⠀⠀⠀⠀⠀⠀⡷⠄⠀⠀⣤⡆
⠀⠀⠀⠀⠀⠘⠀⢠⡾⠀⠀⠀⠠⣶⡆⠤⠀⠂⠀⠒⠒⠒⠂⠿⢄⡀⠙⠗⠧⣀⠀⣈⣁⠒⠂⢴⠶⠀⢰⣶⣀⠀⠀⠟⠄⠀⠀⢀⠀⠀⠈
⠀⠀⠀⠀⣤⡄⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⣀⠈⠉⠛⠤⠄⢀⢀⣶⡀⠀⠀⠀⠀⡀⠀⠀⠀⢾⠁
⠀⠀⠀⠀⡳⢎⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠑⠚⠠⠄⠀⣀⡀⠀⠀⠀⠐⠿⠁⠀⠀⠀⠚⠁
⠀⠀⠀⠀⡁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠰⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠄⠉⠆⠜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣰⠞⠛⠷⣆⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢿⣀⣠⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠉⠀⠀⢀⡟⣠⡴⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢣⣏⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⡛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢶⣄⡀⢠⡟⠀⠠⣄⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠊⢳⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣾⠟⠛⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣧⣀⠀⡄⢻⡄⠀⠀⠀⢀⣠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣱⢠⡅⡐⠁⣸⠁⢀⡤⢞⣫⣥⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠂⠀⢠⡟⣰⣟⡔⡩⡦⣾⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠙⠏⠈⠀⢣⣿⡟
⠀⠀⠀⢀⣀⣤⠤⠴⠶⠴⢤⣄⡀⠀⠀⠙⢶⣤⣴⠇⠀⠀⠀⣘⣠⡾⠋⠀⠈⠲⡄
⠀⠀⠀⠈⠻⣦⠸⣏⣽⠿⢷⣮⣥⡀⢀⡀⢼⣿⣿⠓⣶⠖⠚⠉⠙⣧⡀⠀⠀⢀⡆⣀⢀
⠀⠀⠀⠀⠀⠈⠳⣌⠨⠳⣄⡀⠩⠃⠀⠀⠀⠹⣇⠸⠇⠀⠀⠈⠀⣿⣷⣶⣶⣟⡃⠉⠉⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡌⠛⢧⡀⠀⠀⠀⣴⠋⠀⠀⠀⠟⠻⢿⣿⣿⣶⣿⣏⠀⠀⠀⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⣦⣶⣾⣧⠀⢀⣀⣀⠂⠀⠔⠒⠉⠛⣟⠛⠳⣄⣠⠾⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⣷⣾⣟⡏⠀⠀⠀⠑⢼⠀⠀⠀⠀⠀⠁⠀⠹⠛⠻⢶⣍⠛⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠁⠀⠹⣬⠀⠀⠀⠈⠀⣸⣧⠀⠀⣀⡄⠀⠠⣎⠤⠄⠴⢒⣙⣤⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⡿⢃⣤⠠⠶⠶⣾⣿⣟⣿⠇⠀⠀⠀⠈⠶⣤⢤⣤⢤⣤⢤⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢋⣽⣤⢄⣀⠐⡛⠁⠀⠀⠀⠀⢻⣿⢿⣿⡀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣰⢟⢟⣀⣠⡴⣪⡇⠀⠀⠀⠀⢀⡼⠁⠀⠏⠛⡦⢤⣤⣮⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢰⣏⡼⠭⠍⠒⣈⡴⠿⠁⠂⠄⠀⠚⠀⠀⠀⠀⠀⠐⡂⠻⢿⡿⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣤⡴⠶⠞⠛⠋⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⣀⣴⡳⣄⣃⢳⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⢷⣝⢮⣝⣸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣮⣍⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇