Industrial robot Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣏⡀⠀⡀⠀⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠷⣾⣿⣿⣷⡶⠟⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣷⠀⠀⠀⢀⡴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⣿⣿⡟⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡏⠻⢶⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢛⠆⠀⢰⣿⣿⣇⠀⠀⡟⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡍⠉⢍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠛⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣁⠀⣀⣀⡀⢀⣹⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣾⣿⣦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⢻⣿⣿⣿⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⢌⣱⡄⠀⠈⢳⣾⣿⣿⣿⣶⡟⠀⠀⣰⣏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣿⠁⣿⣿⣇⠘⣷⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣼⣿⣿⣿⣦⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠃
⣿⣿⣛⣛⣿⠏⣛⡉⠛⣉⡛⡛⣋⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣉⠹⣏⣉⠉⢿⡉⣉⢹⣟⠛⣿⢙⡉⢻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⡞⡛⠳⡤⢄⡤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⡇⢧⢃⣀⠇⠀⠀⡏⠀⢻⠐⠒⠒⠘⢿⠉⠙⡍⠉⠉⠉⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠦⠙⠦⣥⡥⣤⣤⣀⠁⠀⣼⣶⣤⣤⣀⣼⠃⢀⡇⠀⢀⡔⠐⠀⣼⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢗⡶⣄⠈⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠉⠉⠒⢿⡷⢦⣼⠀⢠⠸⢿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡏⠛⠳⢿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠉⠀⢀⣿⣦⡜⠁
⠀⠀⠀⠀⠀⠠⠖⣾⠿⠗⠿⣿⣶⣤⢼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡆⠀⣼⣿⡿
⠀⠀⠀⠀⠀⣄⣸⠀⠀⠀⠀⠀⠈⠉⠻⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⢀⡔⠁⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠣⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠐⠁⠀⠀⢀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠂⢀⣴⠦⠦⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⠀⡆⣰⣽⠃⢠⠄⠈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⡇⢿⠃⠀⢿⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠸⡄⠳⠘⢆⠀⠀⠀⡠⠋⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣵⣄⠀⠤⣤⣴⡏⠀⠀⠀⠈⠙⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠻⣿⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⠄⢀⡀⠀⢀⣀⣠⣬⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣖⠈⠉⠙⠁⠀⠐⣶⣿⣷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣏⠙⠿⠯⠗⣶⣶⣒⣲⣾⠯⠙⢛⣽⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⣿⠿⠿⣿⢿⠦⠤⠤⢤⣤⡤⠤⠤⠤⢤⣤⡼⠿⠿⢿⣻⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡂⠁⠐⠒⠒⠚⠛⠓⠒⠒⠒⠚⠃⠁⠀⢰⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠧⠤⠤⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠼⠿⠟⠛⠛⠉

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

⠀⠀⢀⠐⢢⣴⠋⠂⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠐⢶⣶⣶⠆⠀⠀⠀⢶⠶⠶⢶⢶⣶⠶⠶⢶⡆
⠀⠀⠐⠴⣿⠟⠚⠛⡳⡗⠻⠿⠀⠀⢸⣿⣧⣤⣤⣄⠀⠀⢸⠁⠀⠀⠀⠀⢸⠀⠀⠿⣿⡿⠇⠀⢸⡇
⠀⠀⠀⠠⠁⠀⠀⣐⣴⠿⠀⠀⠀⠀⠸⠿⠃⠄⣀⠈⡷⣀⡾⠁⠀⠀⠀⠀⢸⠀⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠐⠲⣾⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠥⠛⢉⣭⡉⠀⠀⠀⠀⠀⠀⢸⠀⠀⡔⠙⠉⢦⠀⢸⡇
⠀⠀⠶⠶⠶⠤⠿⠿⠿⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠌⠩⠡⠀⠀⠀⠀⠀⠀⢿⠀⠈⢳⠀⠠⠎⠀⢸⡇

⠀⠀⠀⢠⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣤⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠻⠻⢿⡦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠁⢰⡯⡩⠀⠀⠀⠀⡀⠀⣸⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⣴⡄⠀⠀⠀⠠⠀⢸⣿⣷⢦⣾⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢹⣬⣛⣄
⠀⠀⠀⠀⠀⠾⠿⠃⠀⠘⠉⠀⠀⠀⠀⠀⢤⣼⣿⣯⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢹⠿
⠀⠀⠀⣴⠆⠀⠀⠀⣺⠇⠀⠀⠀⠀⠀⢰⡻⡏⢽⠍⢹⠏⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⣁⣟
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢹⣿⡍⠉⠉⢻⣿⡿⠉⠀⠀⠀⠀⠙⢷⣦⣤⣄⣤⣤⣶⠝⠃⠀⠀⢀⣴⣶⣤⣤⣤⣀⢀
⠀⠀⢸⣿⡇⠀⢶⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢩⣭⣉⠹⠀⠀⠀⠀⠀⠀⠈⠉⢠⡤⠔⠚⠙⠁
⠀⠀⢸⣿⡇⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⣿⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⣤⣤⣶⡄
⠀⠀⢸⣿⡇⠀⠀⠒⠑⠆⠀⠀⠀⠀⠀⠀⠀⢇⣀⠘⣀⡸⢀⠀⠀⠀⠀⠠⣶⢶⣾⣷⣶⣶⣶⣶⢶⡂
⠀⠀⠘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠛⠃⠀⠀⠀⠀⠀⠀⠙⠚⠛⠛⠓⠚⠛⠛⠒⠃

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⣠⠄⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠋⠈⠚⢻⢭⡀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠻⠛⠛⠉⠩⠘⣆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⣀⡀⠐⠀⠁⠀⠀⠠⢖⠒⠒⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣀⠀⠀⢀⠀⠈⠀⢈⠑⠄⢈⡴⠯⠅⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠁⠀⣀⡀⣨⠇⣠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⠀⠂⠀⠀⢠⡌⠉⠁⠤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⢠⠀⠒⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠴⠂
⠀⠀⠀⠀⢀⠔⠛⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣠⠖⠀⠀⠀⣀⡬⢴⠦⣤⡀⠁⠂⠠⠀⠀⠠⡀⠤⠒⠐⠈⢐⣀
⠀⠀⠀⢀⠀⠀⠀⠑⠀⡀⠁⢈⠀⣀⠤⠴⠟⣉⠀⠀⠀⠁⠒⠙⠷⠂⠤⣀⠉⠂⠤⠀⠀⠀⠀⠀⠉⠐⠢⡀
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠈⠉⢀⣠⠤⠀⠀⠀⠁⠐⠀⠤⠄⣀⠀⠀⠙⠉⢳⠀⠀⠀⠀⠀⠢⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⠚⠉⠀⠀⠀⠈⠻⡀⠀⠀⢠⣤⠀⠀⡁⠀⠒⠋⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠁⠀⠀⡀⠀⠈⠪⠵⠰⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠀⠀⠐⠒⠓⠚⠒⠋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⢄⣀⣀⢀⣄⣀⡄⢀⣒⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⢿⣿⣿⡿⠟⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠉⠙⠻⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⣠⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠑⡖⠰⠀⣆⠀⠀⠄⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢨⠯⠃⢲⡀⠀⢸⠠⢿
⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣋⠉⢉⠔⢈⠠⠈⠀⠀⠀⠀⠈⠉⠉⠀⢸⡤⠤⠭⠌
⠀⠀⠀⠀⠀⢀⡞⡝⢁⠀⡠⠂⢠⠖⠁
⠀⠀⠀⠀⠀⢈⡴⠒⠢⡝⢾⠟⠁
⠀⠀⠀⠀⠀⠘⢦⣒⡠⠇⠀⢀⢀
⠀⠀⠀⠀⠀⠁⠀⢤⠀⠀⠀⠙⠀⠈⠁⠒⠠⠄⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⠀⠀⣀⡀⠀⠀⠀⠉⠐⠂⠀⠀⠀⣠⠖⠋⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢄⠀⠀⠀⠀⠀⡀⠀⣴⠃⠀⠀⠀⠀⠈⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⢧⣀⠀⠴⠚⠶⠶⠻⢆⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠙⠛⠿⠒⠚⠛⠁⠘⣛⠓⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⣀⣀⣀⣁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠆⢈⠁⠀⠀⠀⠀⢀⢁⠁⡀⠉⡈⣀⡟⠡⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠔⠋⢀⠙⣻⠗⠃⠀⠖⢒⠖⠀⡀⠖⢂⠶⠂⢐⠖⢒⠞⢂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠂⠚⠐⠀⠚⠖⠰⠁⠆⠼⠢⠖⠡⠤⠄⠡⠤⠅⠤⠺⠷⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡋⠀⣸⡇⠀⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⠀⠀⠀⠀⠤⠀⠐⠀⠈⠙⢛⠉⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣨⣭⠥⠀⠉⠀⡀⠀⠀⠀⠀⠀⢀⡠⠶⠚⠡⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⠟⠁⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⣠⠐⢩⢯⠀⠀⠀⢀⡤⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠄⠃⠁⠡⢔⠄⡀⠁⠀⠰⠋⠀⠀⠀⠃⠀⠀⠀⡇⢠⠧⠀⠀⠀⠀⠀⠀⣀⠀⢀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⣄⠁⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠀⠀⠃⠀⠁⠠⠀⠀⠀⠀⠈⠁⠀⠈⠘⣹
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⠃⢀⠃⠀⠀⠀⠀⠀⠠⣦⣘⠹⠁
⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠤⠀⠤⠊⠀⠀⢘⠀⠇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⡸⠤⠤⠜⠒⠀⠀⠘⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠣⣄⠀⠀⠀⠀⠀⢀⣔⠁⠀⠀⠀⡀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣶⣤⢴⠡⠁⠀⠀⠀⠀⠈⠺
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠐⠀⠐⠀⠀⠀⠀⠀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀⠀⡀⣀⢀⡀⢀⢀⣀⣠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠊⠉⠁⠒⠠⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠂⡐⠀⠀⢠⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣐⠤⢉⡑⠤⠀⠐⠂⠀⠀⠂⠂⠀⠀⠀⠀⣀⠀⠀⠄⠤⠖⠳⢬⣹⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⢸⡇⣉⡀⠙⠀⠒⠦⡀⡀⣰⡱⠃⠣⡳⠁⡉⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⢀⠀⠠⢀⣦⣬⣇⠠⠀⠀⠀⠀⠋⣄⠀⠊⠀⠀⢠⣐⠢⣀⡉⠀⠀⠀⠀⠀⠁⠒⠒⠒⠒
⠀⠀⠀⠀⠀⢀⢡⠊⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⢦⣄⠉⠂⠤⡀⠂⠄⡀
⠀⠀⠀⠀⠀⠈⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠤⣀⠂⠀⠉⠀⠀⠈⠁⠠⣀⡀⣀⠁⠢⢕⠶⠒⠙⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣁⣰⠂⢀⡔⠋⠙⠆⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⣀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡠⢆⡤⢄⡠⠟⠋⠁⠀⠘⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⠍⠚⠁⢀⠀⠀⠀⣀⣄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠍⠁⠀⡾⠜⠊⠁⢀⠠⠄⠂⢐⠀⠀⠀⣧⠊⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠈⠀⣀⡠⠐⠊⢀⠀⠀⠀⠀⣀⠄⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⣀⢤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠠⡂⠁⠀⠀⠂⠀⠀⢀⡠⠞⠋⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⢡⠖⠋⠉⠛⣦⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠏⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⢰⡇⠀⠀⠀⠀⢘⡆⠁⠀⠀⠀⠀⠀⠀⠀⣸⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠡⠘⣇⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢬⡙⡒⡊⡉⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠠⣀⣀⢀⡀⢀⢀⡀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⠀⠤⠀⡠⢀⣰⣤⣀⣤⣠⣦⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠋⠉⠛⠛⠛⠛⢛⠛⠛⠛⠛⠛⡛⠂
⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⢉⣀⣀⡁⣀⠀⡀⠀⠀⠁⠉⣑⡞⣲⣂⣳⣓⣓⣂⣢⢯⡤⢠⠓⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠁⠈⠁⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⢤⣄⠄⠂⢀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠦⠥⠤⠤⢴⡤⠁⠀⠀⠐⣌⢲⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠞⠉⠁⠀⠀⠀⠀⠀⣀⣄⠈⢌⠤⠤⢚⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡞⠀⠀⠀⠀⢀⡠⢔⡋⠔⠁⠀⣣⣉⣉⣭⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣤⣃⡀⢀⡀⠶⠛⠀⠀⠀⢀⡤⠀⠈⠀⠂⠈⢀⠀⠀⠉⠀⠀⡜⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠉⠈⠀⠀⠀⠈⠁⠀⠀⣀⠠⠐⠈⠁⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⣸⢀⣧⠴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣹⡇⠀⡀⠀⠀⠀⠀⢀⣴⠊⠁⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⢠⠇⣼⡥⠔⠁⣀⠀⠀⣀⣠⣤⢀
⠀⠀⠀⠀⠀⢀⠀⠈⠡⠤⠀⠤⢈⠑⢄⠀⠀⠓⠑⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠉⠀⡀⡔⢢⠟⠉⠁⢙⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡔⠀⠉⠢⠑⢦⡀⠀⢀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠢⠘⡆⠁⠀⢼⣿⡤⣤⠤⠆⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡞⠁⠀⠑⠀⢡⠀⠑⢎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⡤⠇⣧⣿⠤⠒⠋⠉⠳⠆
⠀⠀⠀⠀⠀⡀⢄⠀⣠⠋⠀⠀⠀⢀⢆⡦⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠵⠶⠿⠇
⠀⠀⠀⠀⠀⠐⠤⣑⠂⠠⠀⠀⣀⠕⠝
⠀⠀⠀⠀⠀⠑⢄⠀⠉⠉⠋⠉⠀⠀⠀⠀⠀⢀⢀⢀⣀⣂⠆
⠀⠀⠀⠀⠀⠀⠀⣇⡉⠉⠁⠉⠀⠀⠑⠒⣚⣒⣿⣖⣶⣞⣤
⠀⠀⠀⠀⠀⠀⠀⢁⠈⠉⠈⠉⠁⠈⠈⠉⠀⠀⠉⠈⠁⢸
⠀⠀⠀⠀⠀⠀⠀⣚⣀⣀⣀⣀⣀⣀⣀⣀⢈⣈⣛⣛⣻⣹⡆⠀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠤⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣧⣼⣧⣽⣿⣿⣥⣿⣬⣿⣸⣿⣿⣿⣼⣧⣽⣶⣿⣿⣧⣿⣼⣿⣸⣿⣧⣿⣿⣿⣧⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣝⠿⣶⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠟⠉⠻⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⡿⠋⠀⠀⠉⠻⠿⠃⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡚⠻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⢰⣿⣷⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⠟⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣧⡘⠿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠛⠛⢿⣿⣿⣿⣿⣿⣧⣠⠗
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠛⠛⠛⠛⠋⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠻⣿⣏⠁
⠀⠀⠀⣤⣤⣤⣤⠶⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠷⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⢀⣼⣿⣷⡄
⠀⠀⠀⣿⣿⣿⣿⣄⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⢶⡟⠁⠀⠀⠈⠙⠻⠿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡄
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠘⢣⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠺⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣿⣿⣽⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣇⣽⣩⣿⣼⣧⣿⣸⣧⣿⣉⣯⣽⣧⣿⣸⣇⣿⣽⣿⣯⣿⣝⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⣶⠟⣣⣶⣾⣻⣭⠝⡻⢟⠳⣤
⢒⠄⣠⡤⠶⢟⣥⣾⣋⣴⠟⠋⠛⠶⣮⢺⡆⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⢀⣀⡀
⠀⡸⣿⣟⡳⢠⣂⡠⠭⠋⣠⣤⣐⡀⠼⠯⢷⣀⣾⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⢀⠤⣪⢟⣫⠭⠭⡭⡭⣭⣍⣛⠷⣖⢄
⠀⢱⣶⣧⣤⣤⣀⣈⡇⠸⠯⠬⣭⣙⣛⠓⠶⢦⠀⠈⠉⠀⠂⠒⠠⠤⠀⣀⣤⣪⢕⣭⠶⠛⠉⠉⠀⠀⠈⠉⠑⠒⢝⣪⡳⡳⡄
⠀⠀⡀⠂⡌⣿⡿⠉⠻⢶⣦⣔⣂⠄⠈⡉⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢉⠉⡓⠲⠤⢄⣤⡚⠛⠳⢖⠤⡀⠀⠑⡕⣼⣱
⠀⠀⢱⣄⣰⣾⡀⠀⠀⠀⠀⠉⠉⠛⠻⢶⣬⣤⣐⡀⠀⠀⠀⠀⠀⠀⢀⡆⢒⡡⣔⠾⠉⠃⣁⡤⠾⢭⡻⣐⢻⠪⡳⡀⠘⣿⣿⡇
⠀⠀⠈⡍⠉⣿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠶⠶⣬⣅⣾⣕⡫⠁⠪⡁⢈⠰⢘⣏⢊⠌⢻⢹⡎⣿⡧⢹⣳⣰⠟⣽⠁
⠀⠐⠄⠑⠒⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣾⣶⢶⣥⣌⣿⣷⢷⣫⡾⣱⢿⢣⣿⣛⡩⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺⠃⠀⢙⠓⠾⠯⣿⣿⢿⣞⣷⡿⡳⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢄⠠⠋⠀⠀⠀⠠⠎⠈⠢⡱⠆⢍⢉⡽⡻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⠶⠟⠛⠛⠛⠿⣶⣴⣯⠀⠀⠀⠐⣠⠄⠢⠒⣱⠏⢂⣴⡿⠋⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠗⢩⣴⢶⣶⠾⣿⣹⣿⡿⠛⠁⠀⠀⠀⢌⢂⡺⡑⣰⢏⢢⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⣀⢾⠁⣼⠃⡴⠻⢟⣋⣀⣀⠀⠀⠀⠀⢢⡞⡑⠔⣰⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠃⠈⠈⠩⠞⠛⢾⡿⣄⢊⣤⣤⣤⣄⠑⢆⠀⠀⡍⠜⣌⢼⡷⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣄⣆⡘⠙⠇⠠⠀⠀⠀⣿⡇⣿⡏⠁⢸⣿⡟⢈⡅⠘⢌⡾⡻⠋
⠀⠀⠀⠀⠀⠀⠄⡀⠀⠈⠉⠋⢫⡟⣳⣶⡖⠛⠳⡾⢿⣶⡿⠯⢊⣼⢁⣼⣻⠟⠁
⠀⠀⠀⠀⠀⠐⠄⠈⠁⠒⠒⢲⣤⣤⣬⣿⣿⣦⣀⠉⠳⠲⠖⠞⣋⣴⣫⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⠿⢲⣿⢷⣤⡝⠛⠳⠶⠮⠿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡚⢔⠂⠤⢀⡀⢀⣃⣉⢉⠉⠉⠉⣇⣅⣄⣧⣄⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⡠⠐⠒⢺⡲⢤⡀⠀⠈⠀⠒⠛⠫⠿⠿⠿⠿⠯⠿⠿⢚⣟⠿⢿⣿⣶⡳⣤⣤⡀⣀⡀
⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠙⢻⣆⠣⠴⠇⠀⣀⣀⣀⣠⢀⣀⣀⡀⠀⠣⠶⠃⣰⡟⠅⠀⠈⢷⣄⢀⠉⠉⠉⠁
⠀⢠⣔⣁⢀⢀⡀⠀⠀⠀⠀⠀⠢⢉⡟⣏⣭⣭⠖⠚⠚⠚⣓⣓⡀⠭⠭⠩⠭⠿⠗⣲⡐⢒⣀⣙⣧⡒⢒⡒⠒⠶⣤⡀⠀⢀⢀⣁
⠀⠸⡬⢭⣩⣩⣿⠣⠯⢿⣿⢿⣿⣿⠏⠟⢽⣛⢟⠙⠙⢛⠝⠑⡩⡋⡉⢉⢈⢈⢍⡁⣉⣩⣡⣨⣾⠯⠿⠇⠀⠂
⠀⠀⠀⠀⠀⠀⣌⣃⣰⣻⣛⣻⣿⣿⣿⡿⣸⢛⠟⠉⠉⠉⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠳⣦⣶⠟⠛⠳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠈⢿⡄⠀⠀⠀⠙⠷⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⠀⠀⠀⢀⣾⣧⡀⠀⠀⠀⠀⣯⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢉⣿⠷⠶⢶⣟⢹⡏⢻⣦⡀⠀⠀⠈⠁⠠⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⣴⠟⠁⠀⠀⠀⠙⢿⡇⢸⡏⢻⣦⡀⠀⠀⠀⠀⠙⠃⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⢸⡏⢻⣦⡀⠀⠀⠀⠘⠃⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⢿⣅⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⢸⡏⢻⣦⡀⠀⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡁⠀⢀⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⢸⣟⢻⣶⣴⠶⢶⣤⣌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠉⠻⠶⠟⠋⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⢁⣤⣶⣦⣄⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢰⡟⠁⠀⠀⠹⣧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣇⠸⣧⡀⠀⢀⣰⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠻⣦⣈⠛⠛⠛⢉⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠈⣹⡿⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣾⣯⣀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠁⠀⠀⠀⠀⠀⠈⠙⢷⡄⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⣤⠀⠀⠀⠀⠘⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣧⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣿⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⢀⣴⠾⢛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢶⣄
⣾⠃⣾⠋⠻⣧⠀⠛⠀⠘⠛⠀⠘⠛⠀⠘⠛⠀⠘⠛⠀⠘⠛⠀⠘⠛⠀⠘⠛⠀⠘⠃⠀⠘⠃⠀⠛⠃⢠⡾⠛⠻⣦⢹⡇
⢻⣄⠻⣦⡴⠟⠀⠶⠀⠰⠶⠀⠰⠶⠀⠰⠶⠀⠰⠶⠀⠰⠶⠀⠰⠶⠀⠰⠶⠀⠰⠦⠀⠴⠆⠀⠴⠆⠈⠿⣦⡼⢏⣼⠇
⣀⣙⣳⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣛⣁⣀
⣿⣿⢋⣙⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣋⣉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠳⠜⢀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣠⠶⡁⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠛⠲⣄⠀⠀⣠⠞⠁⠀⠙⢆⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡴⢦⠀⠘⡶⠊⠀⠀⠀⠀⠀⠈⠳⣤⢞⣉⡓⣦⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠙⠋⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⠦⢇⡼⠉⠳⡙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠶⠶⠚⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⡼⢹⠛⠉⠀⠀⠀⡝⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠣⣀⣀⣀⠘⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣀⡤⢬⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⡤⣄⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠓⠊⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠒⠒⠒⠒⠒⠒⠻⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠯⠤⠤⠤⠤⠤⠤⠤⠤⠷⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇


⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠓⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓
⠀⠀⠀⠀⠀⠀⢰⡂⡖⠲⣰⠐⡖⢰⡄⢰⡢⠀⠀⣖⡂⠠⡂⠐⡖⢰⡢⡴⠒⡄⣤⠂⣖
⣤⣤⣤⣤⣤⣤⣤⣤⣷⣼⣼⣤⣧⣯⣽⣼⣼⣴⣤⣧⣤⣤⣼⣤⣧⣼⣴⣵⣴⣥⣭⣦⣧⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠏⡆⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⢦⡀⠀⠀⠀⠀⠀⠀⡜⡎⢰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠙⢆⠳⡙⢆⠀⠀⢀⡤⡞⡜⠀⠚⠂⣿⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡜⠀⠀⢀⡱⠬⠖⠛⠉⠈⣻⣰⡥⠤⠖⠊⢫⢳⠉⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠴⠗⠒⠉⠁⣀⡠⠤⠖⠒⠉⠉⠈⢷⡀⠀⠀⠀⢇⢇⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠖⠒⠉⢁⣀⠤⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⢀⣀⡬⣧⢀⣀⠤⢾⣿⣠⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⡳⣤⡴⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⣀⣠⡤⣖⡺⠯⠗⠓⡏⠀⠀⠀⢸⣼⣿⡿⠟⢡⡾⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠜⣧⠼⢄⡀⠳⠗⠀⠀⠀⠀⠀⣀⡤⡴⣖⡹⠷⠛⠋⠁⠀⠀⠀⠀⣇⣀⣠⣴⣾⠟⠋⢀⡴⠋⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⣠⣾⣷⡜⠌⠓⢖⣉⡹⠀⢀⣤⢴⣲⣹⠓⠛⠉⠀⠀⠀⠀⣀⡠⠤⠔⠒⠻⡍⠳⡜⢯⠁⣠⠴⠋⠀⠀⠀⠀⠀⢀⣴⣷⡄
⠀⠀⠀⠀⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠘⠚⠉⠁⠀⢀⣀⡤⠴⠒⢎⠉⠀⠀⠀⠀⠀⠀⠈⢦⡈⢢⡙⣅⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⣽⡄
⠀⠀⠀⠀⠻⢿⣿⣿⣿⠀⢀⠀⢀⣀⣀⡠⠤⠶⢶⣯⣭⣭⣭⣭⣭⡭⠭⠶⣒⡤⠄⣀⠀⠀⠀⠑⣄⠙⣌⣳⡀⠀⣀⣴⣿⣿⠟⣡⣾⡿⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡿⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠈⠁⠒⠫⠵⠶⠶⠮⠍⠚⢉⣤⣾⣿⡿⠋⣁⣾⠟⠁⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠟⠉⣠⡾⠋⠁⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⡿⠛⠉⣀⡴⠚⠁⠀⠀⠀⠀⢀⣴⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⠿⠟⠋⠁⣠⠴⠊⠁⠀⠀⠀⠀⠀⢀⣤⠿⠋⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⣶⣶⣶⣿⣿⣿⣿⠿⠿⠛⠋⠉⢀⡠⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⢀⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠛⠛⠛⠉⠉⢁⣀⣠⡤⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⣠⣶⡿⠋⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠶⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⣀⣴⡾⠛⠁⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠖⠋⠁⠀⢀⣠⣴⠾⠛⠁⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣤⣤⣶⡶⠶⠞⠛⠋⠁⠀⠀⣀⣠⣴⡾⠟⠋⠁⠀⠀⠀⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⢄⣀⣀⣀⣤⣴⣶⡾⠟⠛⠉⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠯⠥⠄⣀⣀⣀⣀⠠⠤⠴⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⢀⠔⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⣍⠀⠁⠀⢂⠲⢀⡀⠀⠀⠐⡡⢂⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⢊⠈⠁⠀⠀⢠⡀⣋⠀⠈⠉⠚⠠⠅⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠐⠐⠀⠄⢀
⠀⠀⠀⠀⠀⡀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠀⠀⠀⣼⢤⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⢀⡀⠉⠀⠂⠀⣀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣀⣀⣸⡀⠀⠀⠀⠈⠈⠐⠘⠀⢰⣠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⡐⠈
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢇⠀⠀⠀⣠⡿⢛⡿⠈⠐⡠⢄⣠⠀⠀⠀⠀⠀⠈⠉⠚⠃⢇⡖⡤⣀⠀⠀⠀⠀⠀⠑⠀⣀⠔⢢⠜⢠⡀
⠀⠀⠀⠀⡠⠸⣽⣿⠿⠗⢛⣴⣵⢄⢘⡶⣶⡇⢀⠄⡀⠀⠀⠉⠀⠀⠒⠠⠀⡀⠀⠀⠀⠀⠁⠙⠽⢃⢂⢤⠀⠀⠄⠠⠃⠀⠂⣴⣿⣦⡀
⠀⠀⠀⢠⠽⡺⢁⡰⣢⣿⡶⢣⡇⠘⡻⢀⣍⡗⠀⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠈⠈⠀⠀⢄⣀⡀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⡆
⠀⠀⠀⡾⠄⢡⣳⠉⠹⡿⠂⢴⡟⢲⠁⠀⢖⠅⢀⡐⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠠⠀⠀⠀⠀⠠⠿⠿⠿⠛⠁
⠀⠀⢰⣄⠀⣘⠉⢠⡔⠂⢹⣿⠰⠈⠓⠊⠀⠁⠀⠀⠐⠀⠀⠀⠉
⠀⠀⢸⠀⠩⡇⢐⡺⠋⠸⠃⢐⣤⡟⡄⠀⠀⠈
⠀⠀⠀⠀⠴⠇⢈⡟⢶⣤⠶⢦⣟⣴⠇
⠀⠀⠀⠈⠠⢺⡞⢛⠻⠮⡶⡾⢞⣁⠈
⠀⠀⠀⠀⠘⠿⠗⠀⠀⠒⢃⣍⣄⣠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠘⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡁⠄⠀⡦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣡⡀⢠⠴⠴⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢠⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠄⠞⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⡟⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠉⠁⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⢲⠞⠉⠙⣦⠀⠀⠀⠰⣾⣭⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄
⠀⠀⢀⣠⣤⣴⣶⣭⣭⣥⣖⠚⠉⠹⣄⣠⠈⠉⠀⠀⠀⡀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠻⣿⣿⣟⠓⠦⣄
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠀⠀⠀⠀⢻⣿⣶⣶⣶⣾⡿⠃⠀⠀⠀⠀⣯⣭⣷⠴⠊⠁⠁⠈⠑⢤⡈⢹⣶⣤
⠀⠀⠈⠛⠛⠛⣿⣫⠉⠙⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢿⣝⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣯⣿⣭⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢸⣿⣿⣷⣤⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣀⣘⣿⣿⣿⣿⣿⣿⣿⣀⣀⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣇⣀
⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⣀⠤⠢⣀⠀⠀⣠⠖⠒⠦⠀⠀⠀⣰⣿⣷⡆⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⣀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣴⣶⣦
⠀⠀⠀⠃⡿⢟⢈⠟⠛⣇⠀⠀⢀⠀⠀⠀⢉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⡛⠙⠁
⠀⠀⠀⠑⢮⠁⠘⡆⠀⠈⠑⠒⠉⠀⠀⠀⠀⠛⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⢣⠀⠘⡆⠀⠀⠀⠀⠀⣴⣷⡝⠷⠟⢡⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠳⠶⠞⣱⣶
⠀⠀⠀⠀⠀⣀⣣⣀⣘⣄⣀⡀⠀⠀⢻⣿⠇⠀⠀⠸⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⡐⠶⠶⢶⠶⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠟⢣⢰⣶⣦⣸⣿
⠀⠀⠀⠀⢸⣿⣿⣿⠩⡍⠉⠉⠀⠀⠘⠻⣷⡶⣶⣾⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿
⠀⠀⠀⠀⢸⣿⣿⣿⠐⡆⠺⠂⠀⠀⠀⠐⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣌⣡⣄⣤⠀⠀⠀⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠉⠃⠛⠁⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠠⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣻⠀⠀⠀⠀⠀⢰⣿⣷⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⢀⣤⣴⢟⣌⣿⠀⠀⠀⠀⠀⠸⣿⡿⣿⠀⠀⠀⠀⢠⣿⣾⣿⣿⣿⣾⣿⣦
⠀⢰⣿⣶⣾⢸⣿⣿⣿⡇⠀⠀⠀⢸⡫⣶⢰⣵⣿⠀⠀⠀⠀⠀⢤⣤⣴⣿⠀⠀⠀⠀⠀⢛⣌⣿⣿⣯⣼⠛
⠀⠘⠿⠿⠿⠷⠙⠛⠋⠀⠀⠀⠀⠘⠷⠶⠿⠿⠿⠀⠀⠀⠀⠀⢀⣀⣴⣿⡀⠀⠀⠀⠀⠸⠟⠛⠛⠛⠿⠂

⠀⠀⠀⣶⣷⣆⣠⢤⡀⠀⠀⠀⠀⢀⠀⢰⣾⣷⡄⠀⠀⠀⠀⠠⠞⢧⣄⠀⠀⠀⠀⠀⠀⠀⣀⣦⠰⢦⣄
⠀⠀⢀⣹⣿⣹⣕⣃⡟⠀⠀⠀⢀⡞⠁⡘⢿⡟⡀⠀⠀⠀⣼⣆⠀⠘⠙⠳⣄⠀⠀⠀⠀⠀⠈⠻⣦⡊⠉⠃
⠀⠀⢸⣿⣿⣿⠍⠉⠀⠀⠀⠀⠺⢿⣾⣇⣿⣇⣿⡄⠀⠀⠀⠉⠳⣤⡀⠀⠈⠁⠀⠀⠀⠀⣠⡾⠋⠻⣦⡀
⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠘⠻⣟⣿⣏⡿⠟⠀⠀⠀⠀⠀⠙⠻⡄⠀⠀⠀⠀⠀⠘⠋⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⣿⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣠⣴⣴⣧⡄
⠀⢀⠂⣠⣶⣶⣶⣤⡀⠂⠀⠀⢶⣀⣠⠀⠿⠿⠿⠿⠀⠀⠀⢸⠀⣀⣠⠀⢸⠀⠀⠀⠀⢀⣾⣿⣽⣿⣿⣷
⠀⠘⡛⠿⣿⣿⣿⠿⠛⠋⠀⠀⣼⠯⠷⠤⣬⠀⠀⠀⠀⠀⠀⣸⠼⠿⠿⠤⣼⠀⠀⠀⠀⠈⢿⣾⣿⣟⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣤⣤⣤⣼⣧⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠠⠛⣿⠻⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣴⡤
⠀⠀⠀⠀⠀⢅⠕⡨⠀⠀⠀⠀⢠⣦⣶⣿⣷⣶⣦⠀⠀⠀⣿⢸⡇⢀⣠⣤⣤⣄⡀⠀⠀⠀⣿⣿⡿⢿⣿⣿
⠀⠀⠠⢐⠢⣀⠉⣀⣤⣤⡀⠀⢸⣯⡿⢿⢿⣫⣿⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⣿⠛⣾⡎⣻⣿
⠀⠀⠰⠜⠤⠁⠀⠘⠿⠿⠃⠀⠘⠿⠿⠷⠎⠿⠛⠀⠀⠀⣿⣿⣿⣿⣛⣟⣻⣛⡇⠀⠀⢀⣿⣷⣾⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠦⠔⠒⠒⠢⠴⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢀⣠⢤⣔⣒⣒⣈⣉⣭⣭⣭⣀⣒⣒⡢⠤⣄⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠛⠉⠙⢻⣿⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣻⣿⣿⡀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣧⠘⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣀⣥⣭⣭⣅⢉⣾⣥⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⠟⣷⣄⠙⠻⢿⣿⣷⣶⣤⣤⣄⣀⣀⣠⣤⣤⣶⣿⣿⣷⡧⠄⣠⣴⠬⠶⣾⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣄⣀⣿⣿⣷⡄⣀⡉⠙⠿⢛⣻⣿⣿⣿⣿⣛⡛⠿⠛⢉⣀⣴⣾⣿⣿⣀⣠⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⠿⡿⣿⣿⣿⣿⣗⡏⠉⠑⠒⠲⠶⠤⠤⠤⠤⠶⠒⠒⠊⠉⢹⣿⣿⣿⣿⣿⢿⠿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⢻⡆⠇⢱⠀⠀⠙⠿⢿⣴⣒⡠⠀⠀⠀⠤⠄⠀⠀⠀⢄⣒⣾⡿⠿⠋⠀⠀⡎⠸⢰⡟⠙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⢸⡇⢰⠈⡄⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⢠⠀⡇⢸⡇⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠈⡇⢹⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠋⢸⠃⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠸⠀⠀⠀⡰⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⢦⠀⠀⠀⠇⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠛⢿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠘⠀⠀⠀⠐⢁⣤⣦⣤⠈⢂
⠀⠀⠀⠀⣴⣴⣿⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢽⢷⣴⢿⠇⠀⠀⠀⠀⠀⠀⣼⡟⠛⢻⣧⠀⠀⠀⠀⠀⠸⣏⢀⣽⠆
⠀⠀⠀⠘⠛⣋⣈⡛⠓⠀⢀⠀⠀⠀⡀⠀⠀⠀⣀⠁⠀⠀⠆⠀⠀⠀⢠⠀⠸⠷⣶⠾⠇⠀⠀⠀⠀⠀⠐⠉⠛⠉⠨⣀
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⡀⠀⠀⠃⠀⠀⡀⠀⠀⠀⠀⢀⣄⣠⣶⣶⣀⣠⡀⠀⠀⠀⠀⠀⡠⠐⠀⠀⢢⡴⣦⡄⠀⠀⠀⠀⠀⠀⠔⡆
⠀⠀⠀⠀⠀⣥⣶⣤⢀⠀⠀⠀⠀⠀⣻⣿⣿⠿⠿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢡⣶⣶⣻⣄⣼⡟⠀⠀⠀⠀⠀⠀⠘⠓⢦⡀
⠀⠀⠀⠀⡘⣧⣤⣿⠡⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠈⣿⣿⡧⠀⠀⠀⠀⠀⠘⣿⡟⠄⠨⠁⠀⠀⠀⠀⢤⣄⣛⠃⠀⠀⡇
⠀⠀⠀⠀⠈⣤⣁⡔⠁⠀⠀⠀⠀⠀⣹⣿⣦⣤⣤⣾⣿⣏⠀⠀⠀⠀⠈⡀⠀⠈⠀⣴⠶⡄⠀⠀⠀⠀⠀⠐⠬⣠⣤⡔⠁
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠙⠛⠙⣿⣿⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⢳⣹⠟⠚⠁⠀⠀⠀⠀⠀⣤⣤⣴⣤⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⣠⣀⣴⡖⠒⡂⢄⠀⠀⠀⠀⠀⡠⢸⣿⣿⡗⢄⠀⠀⠀⠀⠀⠂⠀⢐⢀⠀⠀⣠⣶⡦⠀⠀⠀⠀⠀⢀⣶⠂⢀
⠀⠀⢸⣿⣿⠿⠧⠤⠰⠊⢡⠀⠀⢀⠈⠀⢸⣿⣿⡇⠀⠑⡀⠀⠀⠀⠈⠒⠀⢨⣠⣾⡿⠋⠁⠀⠀⠀⠀⡀⠸⣿⣷⠿⠁
⠀⢸⣿⣿⡇⠀⠤⠤⠤⠤⠤⠄⠀⣦⣤⣤⡄⠉⠉⢠⣤⣤⣤⠀⠀⠀⠀⠁⠑⢜⠿⠿⡀⠀⠀⠀⠀⠀⠈⢀⣾⡏⠁
⠀⠀⢸⣿⣷⣤⡖⠀⠠⢄⡐⠀⠀⠈⣹⣿⣷⣤⣤⣾⣿⣏⠁⠀⠀⠀⡀⠐⠚⠁⠑⢄⠈⠢⡀⠀⠀⠀⠹⡿⠏⠀⠀⠈
⠀⠀⠈⠛⠉⢿⣇⡠⠁⠊⠀⠀⠀⠀⠙⠟⠛⣿⣿⠟⠛⠋⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠑⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⣤⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠈⠙⢦⡀⠀⠀⠀⡀⢨⠀⠀⠀⠀⠀⠀⠀⢀⣿⣙⣶⣿⠃⠀⠀⢰⡄⢠⡄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⣀⠛⠃
⠀⠀⠀⠀⠀⠙⢦⡠⠊⠀⢸⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠉⠀⠀⠀⠀⢸⡇⢸⡇⠀⣿⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡠⣊⠀⡁⠀⢨⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠚⠓⠚⠓⠀⠛⠘⠂⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠓
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠆⢸⠀⠀⠰⣏⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠘⠛⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣴⢂⣴⣾⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⣠⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⣠⣴⣾⡟⣼⡇⣾⣿⣿⣿⡇⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠚⢿⠟⠂⠀⠀⠀⠀⠀⣀⡤⣷⣿⣿⣿⣇⣿⣇⢿⣿⣿⣿⣿⣦⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⢖⣵⣿⣷⣾⣿⣿⣿⣿⣿⡸⣿⡌⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⣠⣶⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣿⣦⡙⠿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢠⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣝⠿⠶⣤⠄
⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠓
⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⢿⣿⣿⣇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣷⣿⣿⣿⣷⣌⠻⣿⣿⣿⡿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⢰
⠀⠀⠀⣾⣿⠀⠀⢀⣰⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⣿⠀⣶⣿⣿⣿⣿⣿⣿⡿⠟⢩⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⣿⡀⠙⠟⠉⠁⠈⠉⠁⠀⠀⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⣼
⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⣼⣿⡟⠀⠈⠙⠉⠸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣀⣰⣦⣀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⢹⣿⣧⠹⣿⣆⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⣰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠹⣿⡆⠀⠀⠀⠀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠙⣿⣇⠀⠀⠀⢻⣦⣤⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣷⣶⣶⣶⣾⣿⣶⡶⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠃⠀⠘⠀⠘⠃⠀⠛⠀⠀⠀⠸⠀⡂⠀⠀⢀⠀⠁⠘⢀⠀⠠⠀⠀⠐⠂⢐⠀⠀⠀⠐⠟⠀⠘⠃⠀⠃⠀⠐

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣬⣽⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣯⣿⣽⣿⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⣿
⠀⠀⠀⠀⣠⣦⡀⢀⣤⡴⠶⠟⠀⠀⠻⠶⢦⣄⡀⢀⣴⣄
⠀⠀⠠⣾⡋⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⢙⣷⠄
⠀⠀⠀⢈⡷⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⢿⡁
⠀⠀⢀⡿⠁⠀⠀⠀⣠⡾⠋⠁⠀⠀⠈⠙⢷⣄⠀⠀⠀⠈⣷⡀
⣤⣤⣼⠇⠀⠀⠀⣸⠏⠀⠀⠀⢸⡟⠛⠛⠛⢻⣆⠀⠀⠀⢸⣧⣤⣤⠀⠘⠛⠛⠛⠛⣛⡛⠛⠛⠛⠛⠛⠛⠛⣿
⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣾⠋⢻⡆⠀⠀⠀⠀⠀⠀⣿
⠛⠛⢻⡆⠀⠀⠀⢹⣆⠀⠀⠀⢸⡇⠀⠀⠀⣸⠏⠀⠀⠀⢸⡟⠛⠛⠀⠀⠀⠀⣨⣿⠶⢾⣧⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⣷⡀⠀⠀⠀⠙⢷⣄⣀⢸⡇⣀⣠⡾⠋⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢈⡷⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⣠⡿⠀⠀⠀⠀⠀⣿
⠀⠀⠐⢿⣅⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⣨⡿⠂⠀⠀⠀⠀⠀⠀⢸⡟⠻⠻⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠙⠟⠁⠈⠛⠳⠶⣦⠀⠀⣶⠶⠟⠋⠁⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⢹⡆⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠇⠀⠀⠀⠀⣿⣀⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠛⠛⠛⠛⠛⠛⣿⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⢶⡶⠾⠷⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠁⠀⠘⠛⠛⢻
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇⠀⠀⢀⣬⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⣸⡇⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠻⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⢀⣠⡾⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣤
⣿⣿⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠈⠉⠉⠉⠐⠒⠢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⢋⣷⢄⡀
⠀⠀⠀⠀⢀⣀⠠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠛⢁⣴⠟⠁⠀⠉⠢⡀
⠀⠀⠀⠻⣥⠄⠒⠒⣉⣱⢤⡀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠛⠉⢀⡴⠋⠀⠀⠀⠀⠀⣠⣿⣄
⠀⠀⠀⠀⠀⠑⢯⣁⡩⠶⣔⠛⢢⣀⠀⠀⠀⠀⡜⠀⠀⠀⣀⣠⣤⣶⣿⣿⡿⠟⠋⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⣠⣾⣿⡿⣩⣆
⠀⠀⠀⠀⠀⠀⠀⠉⠢⣖⠊⣛⣥⡨⠷⢄⠀⣼⣶⣶⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⢉⣼⡿⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢤⡤⠝⠶⣊⠙⣻⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠟⢁⣴⠟⠁⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⣠⠒⠉⠉⠙⠿⣖⣒⡭⢿⠤⠤⢐⣒⡺⡍⠑⡔⢢⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠋⣠⠶⠋⠀⠀⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠙⡹⣆⠈⠆⢿⠿⣿⠛⢸⠀⢱⠴⠁⢀⣠⣤⣶⣿⣿⠿⠛⠉⣀⠴⠊⠁⠀⠀⠀⠀⢀⣼⠟⢉
⠀⠀⠀⠀⠀⠀⢈⠀⣀⣀⠤⢄⠀⠀⢡⢻⠀⢸⠘⢃⣉⣶⣼⣤⣾⣶⣿⣿⡿⠟⠛⠉⣀⡤⠔⠋⠀⠀⠀⠀⠀⠀⣠⡶⠋⢁⣴⡿
⠀⠀⡠⢤⣤⡲⢯⠭⠔⠒⠊⠉⠀⠀⢸⡿⠄⢺⣿⣿⠿⣉⡩⠷⢤⡚⢫⣄⡠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⢀⣴⡿⢛⠇
⠀⠀⠑⠉⠀⠀⠀⠣⡀⠀⠀⠀⠀⢠⠟⠀⠀⠀⢣⣤⣤⣼⠶⣖⠊⢙⣧⣤⠵⢤⡀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⣠⣶⠟⠋⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⠤⠖⠁⠀⠀⠀⠀⠀⠫⡀⠀⠀⠀⠙⢤⡤⠜⠳⣎⣉⡦⣤⠔⠚⠉⠀⢀⣠⣴⠟⠋⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣤⣤⣤⡼⠶⣉⣉⠹⠤⠘⠓⢤⣴⠾⠛⠉⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢍⣀⣀⣀⣬⣷⣤⠴⠖⠚⠉⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠫⠥⠀⣀⣀⣀⠠⠤⠔⠒⠉⠁

⠀⠀⢠⣾⣿⣿⣿⣿⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢄
⠀⠀⢸⣿⣿⡙⠛⠉⠉⠉⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⡾⠃
⠀⠀⢸⣟⣛⣿⣿⣿⣿⠿⡿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠙⢿⠗⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋
⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋
⠀⠀⠘⡟⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⣀
⠀⠀⠀⠀⠀⢀⣤⣴⣤⡙⢆⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⣠⠞⣡⠞⣠⠖⣀⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣾⣿⣷⣄
⠀⠀⠀⢀⣴⣿⡿⠛⠻⣿⣾⠛⢤⠀⠀⠀⠀⠀⠀⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠞⣁⠖⣁⠶⢋⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡁⠈⠻⣆
⠀⠀⣰⣿⡿⠋⠀⢠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⠞⣡⡞⢡⠾⢉⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠉⠻⢦⡄⠈
⠀⠀⣿⣿⣁⠠⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⡾⣫⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛
⠀⠀⠈⠙⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡀
⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⣴⣇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣽⣿⣷⡄
⠀⠀⠀⠈⠳⣄⠀⠀⢠⣴⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠙⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣱⣾⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣇⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠛⠛⠁
⠀⠀⢀⣀⣠⣾⠿⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⣸⠟⠳⠶⠶⠆⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁
⠀⠀⠟⠻⣿⡇⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⡶⠃⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣦⣶⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠋⣹⣏⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠉⢙⣿⣿⣦⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠿⠛⠃
⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠸⣿⣿⣶⢉⣶⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⣤⣶⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠁
⠀⠀⠁⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣄⡀⠸⢀⣄⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⣀⣴⣾⡯⠤⠾⠛⠁⠀⠀⠀⢠⣿⣥⣿⣿⡷⠀⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠛⠛⠋⠂⠈⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣿⣿⣇⠄⠈⣾⠇⠀⢀⣀⡀⠀⠀⠀⠀⠀⣸⠀⠀⢠
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠏⠈⡄⠀⡠⠔⢏⠉⢹⣇⣇⣦⠖⠁⠀⣴⣿⣿⣿⡆⠀⠀⠀⠤⣿⡀⠃⣼⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢵⣢⣇⣴⠿⣦⣤⣼⣿⠾⣷⣆⠀⠹⣿⣿⡿⠃⠀⠀⠀⡖⣿⣏⣹⣿⢸
⠀⠀⠀⠀⣀⣀⡀⠀⠀⠄⠄⠀⠀⠈⠁⢻⣄⣽⣿⡿⠧⠤⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⡇⢸⣿⣹
⠀⠀⡤⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⢰⠀⠀⢻⣥⣽⣷⠀⣠⣴⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⡷⡿⡇⢸⢿⢾
⠀⠀⣤⣀⣴⡇⠀⠀⠈⠉⠛⠶⢶⣾⣄⣤⡀⠀⠈⢿⡏⠀⣿⡓⣶⣵⡀⠀⠀⠀⠀⠀⠀⣿⠃⡇⢸⡎⢿⡀
⠀⢾⣿⠋⠙⠳⣄⠀⠙⠓⠶⠟⠋⠀⠈⠉⠉⠀⠀⠈⢿⣤⣴⡝⢿⣟⠁⠀⠀⠀⠀⢀⣾⣹⡿⢹⣾⢹⣿⣷⡄
⠀⢠⣿⣦⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡋⠁⠘⣉⠀⠀⠀⠀⠀⠀⠁⣟⣷⢿⣿⢾⣘⠆⠁
⠀⠉⠀⠀⠉⠳⢴⣄⣀⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠻⢥⡑⣄⠀⠀⠀⠀⠘⠁⠈⠁⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣈⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢂⠀⠀⠉⠁⠀⠀⠀⠀⣠⡖⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠈⠙⠲⢕⢄⠀⠀⠀⠀⠀⠀⠀⢹⣤⡆⠀⠀⣰⠃⠀⠘⠋⠉⠠⠂⡀⠐⠀⣆
⠀⠀⠀⠠⠐⠄⠀⠀⠀⠀⠀⠔⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠉⠀⢀⢈⠀⠀⠀⣄⠁⠰⠆⠀⡀⣐⣰⣿
⠀⠀⠀⠀⠘⢠⣤⡀⠀⣠⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣲⣤⠶⠷⠛⣨⠀⠀⠈⣶⣴⣰⣾⣥⣿⣿⠃
⠀⠀⠀⠀⠀⠈⠛⠃⠀⠛⠏⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⡤⠚⠋⠀⣀⣴⣾⣯⣄⣀⠀⠈⠙⠛⠛⠛⠛⠁⠀⡀
⠀⠀⠀⡀⠀⠀⠀⢀⢀⠀⠀⠀⠠⠀⠀⠀⠀⣤⠚⠋⠀⢀⣤⡼⢟⣋⠥⠭⠯⠥⠭⠵⠖⠀⠈
⠀⠀⠈⡄⠀⠀⠀⠈⠁⠀⠀⢀⠐⠁⠀⣠⢾⠀⣀⣴⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠤⣶⣾⠛⠁
⠀⠀⠀⠀⠀⠔⠂⠄⠀⠄⠒⠐⠁⠀⠰⠿⠷⠛⠋⠉⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢠⣶⠴⠾⠿⠿⠦⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⢿⣶⠊⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⡞⠉⠉⠙⣦⠀⠀⠹⣷⣀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠻⣦⡀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⡶⢇
⠀⠀⠀⠀⠈⢧⡀⠀⢀⡞⠀⠀⠐⣿⣿⡇⠀⠀⠀⠀⣴⣿⣥⣤⣄⣈⣻⣷⣄⠀⠀⠀⠀⢻⡄⠀⠀⠀⣷⠼⡆
⠀⠀⠀⠀⠀⠈⠙⠙⠉⠀⠀⢀⣸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠂⠀⠀⠀⢻⡄⠀⠀⢸⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠘⠀⠀⠁

⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡄⢠⡀
⠀⠀⠀⠀⠀⢯⣠⡇⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠙⢻⡄⠀⠀⠀⠀⠀⢀⣤⣶⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢻⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢰⣶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠸⠟⠇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠘⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠠⠴⣶⠖⠢⠄⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠂⣠⠶⠛⠒⠆⡀⠐⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠒⠒⠁⡄⢠⡄⢠⠈⠒⠒⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢱⡦⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⢴⡎⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠌⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢡⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠐⠀⢀⣀⣅⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⡀⠀⠆⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⠁⡌⠈⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⢰⠀⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠄⠀⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡄⠠⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⠔⠁⠀⠸⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠃⠀⠈⠢⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢁⠔⠁⠀⠀⡠⠂⠀⠀⠋⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠀⠀⠘⢤⡀⠀⠈⠢⡈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⢀⠔⠁⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠢⡄⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡠⠂⠁⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠈⠐⢄⠈⠳⣄
⠀⠀⠀⠀⢀⡴⠊⠁⡠⠊⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠧⠤⠄⠠⠤⠤⠠⠤⠤⢸⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠑⢄⠈⠑⢦⡀
⠀⠀⠀⣰⠋⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠦⠀⠠⠠⡔⢢⠤⠄⠀⠸⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠈⠢⡀⠙⣆
⠀⠀⠀⢹⠀⠃⠒⠀⠒⠒⠒⠀⠒⠂⠀⠒⠒⠒⠒⠒⠒⠂⠖⠁⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠈⠲⠐⠀⠒⠒⠒⠒⠀⠐⠂⠒⠂⠒⠒⠒⠂⠒⠘⠀⡏
⠀⠀⠀⠺⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠆⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠰⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⡇
⠀⠀⠀⠀⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣀⡀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠠⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠄⠚⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠃⢤⣀⣀⡀⣴⢿⡿⢠⣀⣀⣀⠠⡞⠒⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣅⣠⣀⣭⣹⣯⣨⣅⣀⣈⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⡿⠋⣍⣀⣀⣀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⣠⠤⠔⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠀⠀⢠⡤⣼⢾⢚⢚⡹⠀⠀⠀⠀⠀⢀⣀⠠⠆⠀⢠⠛⠠⣤⣄⣀⣀⠀⠀⠀⠀⠙⠃⠀⠚⠁
⠀⠀⠀⠀⣆⣏⣥⡦⠶⠒⠒⠀⠀⠀⠀⠀⠀⠘⠊⠉⠉⠀⢀⣠⠴⣺⠟⠋⠉⠀⠒⠀⠀⠀⠠⠞⢈⣹⠎⠍⣳⡄⠀⠀⠁
⠀⠀⠀⠀⠏⡧⠖⠗⠁⠀⠀⠳⣶⣤⣶⡏⠀⠀⠀⠀⠀⠀⢺⣧⣀⠈⠓⠒⠖⠒⠶⠒⠶⠒⠚⠋⢉⣀⣤⡾⠟⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠔⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠶⠶⠶⠶⠶⠶⠿⠿⠛⠛⠋⠉
⠀⠀⠀⠀⣀⢤⠶⠋⠁⠀⠀⠀⠀⢀⡀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⢀⣀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⢀⠠⠀⠫⡽⢀⠘⠋⠀⣠⣀⠀⠀⠠⡀⠀⠀⣖⢻⢻⠚⡗⣦⡄⠓⠋⣼⡏⠇⢹⠸⠸⡇
⠀⠀⠀⠴⠶⠚⠃⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⣵⠀⢸⣸⣸⡤⠷⠋⠀⢀⠘⠀⠙⠛⠚⠒⠗⠃
⠀⠀⠀⠀⠀⠀⣀⣬⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠋⠀⢀⠝⠀⠈⠈⠀⠀⠀⠀⠀⣸⣣⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠔⠐⠒⠀⠀⣀⡀⢀⣀⣀⡀⠀⣀⣘⠁⠀⠀⠀⠸⡀⠀⠀⠀⠺⡄
⠀⠀⠀⠀⠀⠀⠉⠓⢤⣸⣷⣦⠀⠀⠀⢀⣴⣶⣦⣰⡆⠀⣾⣷⠿⣿⡟⠃⣾⣯⣭⡍⣿⣏⣽⠇⠀⠀⠀⠀⡗⠒⠒⠀⡖⠀⠂
⠀⠀⠀⠀⣤⣀⠀⠀⠈⠀⠀⠙⠣⠀⠀⢼⡇⣸⣿⠹⣿⣤⣿⠇⠀⣿⡇⠀⣿⣥⣤⡀⣿⡟⠻⠦⠀⠄⣀⠀⢹⠚⠓⢺⡃
⠀⠀⠀⠀⠀⠈⠙⠡⠀⠀⣠⢤⡀⠀⠀⠘⠛⠛⢁⣀⡈⣩⣥⣄⠀⣬⣤⡀⠀⣠⣶⡄⣠⡴⠶⠆⠀⠀⠀⠀⣼⠦⠤⠼⣇⡈⠄⠤
⠀⠀⠀⡤⢤⣤⡄⡀⠀⢸⡁⢀⡽⠀⠀⠀⡀⠀⠿⣤⣅⢹⣧⣾⠗⣿⡾⣇⢸⣏⠀⡀⢿⡷⠚⠃⠀⠀⠀⠀⠀⠁⠒⠀⠉⠁
⠀⠀⠀⠀⠠⢶⣷⣤⡄⠀⠉⠉⠀⠀⠀⠁⡀⠀⠶⠶⠿⠸⠿⠀⠀⠛⠀⠉⠈⠛⠛⠁⠸⠷⠚⠛⠀⠀⠀⠀⠐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠘⠈⢀⡄⠂⡂⠠
⠀⠀⠀⠀⠰⠄⣀⡉⠀⠀⠀⠀⠀⣀⠤⠆⠚⠀⠈⠒⠂⠀⠓⠲⣄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢰⡁⠀⡀⠧⠖⠀⠀⠤⠀⣀⢀⡼⠀⠀⠆⠂⠀⢀⠀⡐⢶⡀
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠑⠦⠦⣄⣀⡑⠠⠤⠠⠚⠉⢀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠃⠀⠀⠰⠀⠑⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠈⣶⠆⠀⢤⠒⠈⠳⣤⡀⠀⠀⠀⠀⠐⠒⠘⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠑⠀⠀⠸⣦⣄⡒⠀⠠⠤⠀⠀⠂⣀⡜
⠀⠀⠀⠸⠇⠀⠀⠘⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠳⠶⠖⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⡀⠃⠐⠒⠀⠀⠀⠀⠀⠒⠘⢀⠃⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠎⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠒⠒⢰⣏⣀⣀⣹⡤⠀⠒⠂⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⢀⠀⢘⠠⢨⡿⠭⡓⠆⠃⠀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⡀⠈⠁⠁⠰⠆⠌⠈⠁⢀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⢹⡖⠂⠐⠂⠀⢲⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠀⠰⢀⣾⡇⠀⠀⠀⠀⢸⣷⡀⠂⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⢿⡃⠐⠀⠀⠀⢘⡻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣰⡏⢸⡇⠀⠀⠀⠀⢸⡅⢹⣆⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡿⠘⢙⡏⠉⠉⠉⠉⢹⡋⠃⢿⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣠⢖⠁⠁⡆⢘⡃⠀⠀⠀⠀⢘⡁⢸⠈⠨⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠕⠁⡠⠊⠀⢨⡇⠉⠉⠈⠉⢸⡇⠀⠑⢄⠈⠪⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢋⠔⢁⠄⠊⠀⠀⠀⢸⣇⢀⡀⢀⡀⢸⡇⠀⠀⠀⠁⠠⡈⠢⡙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⡞⡡⠂⠀⠀⠈⠀⠀⠀⠀⠀⠸⠃⠀⢴⡦⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⢳
⠀⠀⠀⠀⠀⠀⠀⣧⣉⣉⣉⣉⣭⣉⣉⣍⣉⣩⡇⠀⠀⢸⡇⠀⠀⢸⣍⣉⣉⣉⣉⣭⣉⣉⣩⣉⣼
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠤⠀⢀⡤⠀⣀⠀⠀⠀⠄⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⣀⠀⢠⡀⠀⠤⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠤⣤⠤⠬⡆⢲⠤⢤⣾⡷⣤⠤⠾⢰⠏⠤⣬⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢁⠈⣿⣿⡿⠿⣿⣿⡇⠘⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⣶⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣶⣤⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠁⡘⠁⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢨⠀⠀⠀⡌⠀⠑⡄⠀⠀⠀⠀⠴⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠣⠔⠒⠁⠀⠀⢡⡐⠋⠢⠴⠚⠀⠀⠂⠤⠞⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡶⠶⠶⢦⡄⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠘⠧⠇⠂⠒⠀⠀⢀⣀⣀⣬⡤⠄⠀⠀⢀⡀⠀⠉⠑⡀⠀⠈⠃⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠋⠀⠤⠤⢀⡀⠈⠀⠢⠀⠀⠉⠐⠢⣅⠀⠀⡤⠤⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠑⢾⡀⡔⠢⠞⠀⠣⠴⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⠀⠀⠐⣆⠀⠡⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠼⠤⠄⠤⠟⠀⡰⠚
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠦⠜
⠀⠀⠀⠀⠀⡔⠀⠀⠀⡠⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⢸⠀⠒⠄⡰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠐⠒
⠀⠀⠀⠀⠈⠂⠠⠴⠥⠤⠤⠤⢤⣤⢄⣀⣀⣀⣀⣀⠈⠉⠒⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠾⠤⠃⠂




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠭⣽⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⠿⠟⠋⡁⢄⣤⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⡛⢉⡁⢀⣢⣤⢶⣿⣿⣿⣿⣿⠿⠟⠟⣩⣝⢿⣿⣿⣿⠟⠡⠀⠂⣀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣏⠰⠟⣡⣾⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⡝⢏⢷⣻⣿⠰⠀⢀⠰⡆⠀⣂⣿⡇
⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠛⣿⣿⣷⣨⣿⣿⣿⣿⠛⣉⡀⠀⠀⢀⠀⠀⡄⣇⢸⡄⣏⣿⣷⣄⣈⣐⣆⣬⣿⣿⣷⡄
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⣶⣿⣿⣿⡟⠋⠉⠁⣌⢰⣉⣽⢀⠀⢸⡄⠀⠸⡜⢾⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣾⣿⣿⣴⣿⣿⠉⣟⣡⣴⣧⣤⣤⣶⣿⣼⣇⢹⣿⣿⣿⣿⣶⣶⣾⣢⣭⣿⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⢏⠉⠛⢿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⡿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣽⣿⡿⢻⣿⠟⠿⣿⣿⡻⣿⣿⠛⢻⣿⢍⠚⠀⠈⠉⠑⠈⢻⣿⣿⣿⡄
⠀⠀⠀⢸⡿⣫⡟⠡⠤⠖⢀⠀⠀⠘⢻⣯⣻⣿⡿⣿⣧⣽⣶⡇⢰⣿⣿⣷⣜⠪⠐⢾⣿⣇⠠⠀⠀⠀⠀⠉⢈⣭⡛⢿⠁
⠀⠀⠀⠈⣱⣏⠀⠠⠀⠀⠀⠀⠀⣀⣤⠹⠷⢻⣷⣿⣿⠿⢿⣳⡊⠛⢿⣿⣿⣷⣧⣶⣦⣍⡛⠳⠶⢦⣤⣤⡄⠀⠐⡀⢄
⠀⠀⠀⢠⣿⠒⠖⠀⠀⢀⢀⣀⣠⡟⠈⢘⢸⣿⣿⣷⡝⣅⣀⣭⣭⣁⣟⢡⣿⣟⢻⣿⣿⣄⠙⠛⠳⢶⣦⣬⣤⣀⢀⣠⣾⣫
⠀⠀⠀⠸⣿⣳⣖⡻⢿⣿⡿⠟⠋⠀⠁⠀⣺⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⠘⣿⣿⢿⣿⣿⣿⣿⣶⣿⣿⣿⡟⢿⣿⡿
⠀⠀⠀⠀⢻⣅⡀⠉⠀⠉⠀⠀⡀⢀⣢⣞⣿⣿⣿⡇⡌⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣷⠛⠛⠛⢻⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠙⠿⣤⣀⠀⠠⠀⢶⣯⢷⣿⣿⣿⣿⢡⢿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⠿⣛⡀⠀⣸⣿⣿⣷⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢬⣭⣭⣭⣶⣿⣿⣿⣿⡏⣌⣾⣿⣿⡿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣾⣿⣿⣿⢶⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢦⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⡟⣼⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣧⢻⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠙⠛⠛⠛⢇⠛⠛⠛⠛⠉⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣧⠀⣠⣄⢀⣼⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢹⣿⣷⣽⣧⣾⣿⠉⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⠇⢀⣴⣦⣴⣿⣿⣷⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⢀⣿⣿⠋⠉⠉⠉⠻⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠉⣿⣷⣄⠀⠀⢀⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⡿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠘⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢐⡢⢀⡄⡂⠒⢰⡆⢀⢆⢀⠀⢐⠠⢤⢐⡂⠰⢤⢔⢠⡂⣴



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⢋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠈⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠛⠀⠀⠀⢘⠃⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⡦⠀⠀⠀⢸⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢄⠀⠀⠀⠀⣇⠀⠀⠀⢀⠀⠀⠀⠈⠈⠓⢄
⠀⠀⠀⢄⠀⠠⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⢀⠃⠀⣶⠀⠹⡀⠀⠀⠀⡁⠀⠀⡑⡀
⠀⠀⠀⠈⠐⢌⠲⣅⢄⡀⠀⠀⠁⠀⠉⠑⠒⠒⠒⠒⠒⡊⠉⠁⠈⠒⠀⡚⠀⠀⣿⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠐⢬⡓⣎⣢⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠴⣤⣤⣿⣤⢤⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠹⡶⡞⠀⠄⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠛⠛⠛⠿⠿
⠀⠀⢀⡤⠴⠀⠀⠃⠀⠿⠐⠀⢞⠻⣕⠢⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠐⠀⠀⠊⠀⠀⠀⠀⠉⠂⡙⢭⡣⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠈⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⢀⣶⡀⢀⠀⢀⠀⣀⣄⠀⠀⠀⠀⠀⠀⣠⣴⣶⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⢉⣿⣿⣿⣧⣿⣾⣿⣏⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠟⠋
⠀⠀⠀⣯⣾⣿⣿⣿⣿⣮⡅⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣨
⠀⠀⠀⣿⣽⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣼⡇⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠿⠷
⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠿⠿⠄⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣎⣍⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡍⠓
⠀⠀⠀⠀⠀⣠⣾⣿⣷⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣻⡿⠋
⠀⠀⠀⣠⢾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡎⠈⠪⡻⣿⡗⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⢾⡙⢦⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠀⠀⠈⠢⠜⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀
⠀⠀⠀⠀⠀⣤⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠉⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣤⠄⠀⠀⠀⣠⣾⣿⡿⣿⣿⡀⠀⣠⡀
⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣄⡈⠛⠁⠀⠀⠀⠠⠤⠤⣶⣶⢶⣾⣿⠟⠁⠀⠀⠀⣼⣿⠟⢏⢀⣽⣿⣿⠞⠉
⠀⠀⣿⣿⣿⡿⣟⣫⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣴⠟⠛⠿⠋⠀⠀⠀⠀⠀⠐⠾⣷⡆⠉⠉⣿⠟⠁⠀⠀⠀⠀⠀⢻⣿⣿⣴⣿⣿⠟⠁
⠀⠀⠙⠙⠉⠙⠉⠉⠉⠉⠋⠁⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢶⡄⠀⠀⠀⠀⠀⣴⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡄
⠀⠀⠀⠉⠢⡀⠀⢀⣴⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠻⠶
⠀⠀⠀⠀⠀⣈⣶⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠛⠉⠀⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⣠⣤⣾⠟⠉⠻⣿⣦⣄⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋
⠀⠘⠋⢹⡟⠀⠀⠀⠙⢿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣾⣿⡶
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣛⣟⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣦⣄⡀⡀⠀⠀⣠⣶⣿⠿⣷⣦⣄⠀⢠⣴⣶⡿⢿⣶⣦
⠀⠀⠀⣼⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⡟⢸⣿⣿⣇⢹⡇⠀⠀⠀⣀⣤⣤⣸⣿⡿⢻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠙⠿⠿⠿⠿⠿⢿⣤⣿⣛⠿⠿⠿⠿⠛
⠀⣴⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠁⣿⡏⢹⣿⠈⠁⠀⠀⠀⠹⣿⡿⠟⣿⣿⣸⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠏
⠀⠛⠛⠿⣿⡿⠛⠛⠃⠀⠀⠀⠀⠀⠘⡿⠁⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠⡅⠀⠀⠀⣤⠀⠀⠀⠀⣥
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠛⠂

⠀⠀⠀⠰⣀⣀⢰⣂⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠙⣤⡄⠀⢀⣀⡀
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠫⣿⡯⠋⣠⣤⡝⠆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢘⣶⣿⣿⠛⣿⣿⡛⡄
⠀⠀⠀⠈⢻⣿⣅⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⢠⣾⣿⣿⠇⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⡿⠽⣿⣿⣏⣀⠿⣿⠃
⠀⠀⠘⠀⣿⣿⣿⣿⣿⣿⠀⠃⠀⠀⠀⠀⠀⠰⣜⠿⠟⢁⣾⣿⣦⣄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢈⣿⣧⣞⣙⠿⣿⣿⠖⠁
⠠⠮⠀⠀⠉⠉⠭⠍⠉⠉⠀⠀⠥⠄⠀⠀⠀⠀⠈⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⠀⠈⠛⠿⠿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠈⠛⠴⠿⠟⠂⢾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗

⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠤⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⡀
⠀⠀⠀⣍⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣯⡀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠘⠳⣦⠄⢠⣴⣶⣶⣦⡀
⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⡷⠘⣿⣿⠷⣟⢀⡤⣾⡇⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠈⠑⣿⣿⢿⣿⣿⣿
⠀⣤⣾⣿⣻⣿⣦⡄⠀⠀⠀⠀⣰⣿⣿⣯⡻⠿⠤⠼⢟⣶⣿⣿⣆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠯⣰⣤⣀
⠀⣿⠋⢸⣿⠈⢻⡇⠀⠀⠀⠀⠙⢿⣿⠟⠀⠀⠀⠀⠀⠻⣿⡿⠇⠀⠀⠀⠀⠀⠘⠛⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉
⠀⠃⠀⠀⠇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀
⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣷⣦⣤⡀
⢀⣾⣿⣿⣿⣹⣿⣶⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⢿⣶⣤
⠸⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⢿⣟⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⢀⣀⣴⣹⣛⡟⢻⣛⣏⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢧⠀⠈⠉⠙
⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⢻⣽⣽⢿⣿⣿⠄⠀⠀⠀⠀⠿⣿⣿⣷⣿⣿⣿⣷⣾⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⡸⠠⡄⢆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⣼⣧⣬⡉⠁⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠉⢹⡏⠉⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⡆

⠀⠀⠀⠀⣤⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣀⣀⣀⣠⣤⡀
⠀⠀⠀⢾⠋⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢉⣿⡥⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷
⠀⠀⠀⠻⢧⣤⣴⡟⣧⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣸⣿⢭⣿⣀⣀⣀
⠀⠀⠀⠀⣠⠵⢦⢺⣇⠀⢀⡷⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⣡⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠻⣤⠀⠀⠀⠀⠀⠀⠀⠉⠏⠉⡏⢹⣿⣿⣿⠉⢹⠉
⠀⠀⠀⠈⢧⣀⣼⠋⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠘⠛⠛⠋⠀⠈
⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠴⣶⡖⠒⠒⢲⡷⠒⢲⠀⠀⠀⠀⠀⠀⠀⢴⡶⠞⠛⠳⣶⡆⠀⠀⠀⠀⠀⠀⠀⠻⢆⠀⠀⠀⠀⢰⣧⡤⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⢸⣿⣿⣿⠀⠀⡸⢻⡀⢸⠀⠀⠀⠀⠀⠀⢰⣾⡦⠀⣶⠀⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⢛⣛⡛⠛⠛⠛⠛⡆
⠀⠀⢨⣿⣿⣿⠀⣰⠁⡀⢳⣸⠀⠀⠀⠀⠀⠀⢠⣿⣶⣾⣶⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⣤⣷⠤⡀⠀⠀⡇
⠀⠀⢸⣿⣿⣿⠴⠧⠤⠤⠤⠯⠀⠀⠀⠀⠀⠀⠀⢹⣿⢹⣿⠉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠶⣶⠏⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣈⣒⣁⣀⣠⡇
⠀⠀⠈⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠛⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠋


⠀⠀⠀⠀⠀⠀⡆⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣶⣆⠀⡀
⠀⠀⠀⠛⠃⢸⣿⠉⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⢠⣿⣜⣛⢸⡻⣿⡇⠀⠀⠀⠀⠀⠀⠀⡆⢸⡇⠈⠀⠁⢹⠀⣼⠀⠀⠀⠀⠀⠀⠀⢺⣟⣫⢍⢩⣛⣿⠂
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣮⣵⣿⣷⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⡿⣻⢶⣾⢰⠇⠀⠀⠀⠀⠀⠀⣶⣿⠀⠄⠠⠀⠄⢸⣷⡆
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⡚⡽⣮⣿⢨⠀⠀⠀⠀⠀⠀⠀⠀⣹⣆⡳⠘⠰⣃⣾⡁
⠀⠀⠀⠀⢀⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠺⠿⠿⠿⠿⠿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠿⠟⠉⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣙⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠞⣻⡓⢶⡦⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⣒⡖⠒⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡈⣳⣦
⠀⠀⠀⠀⡐⣿⣿⣿⣿⣷⢂⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⣀⣛⣁⠀⣷⣆⠀⠀⠀⠀⠀⠀⢸⠀⠈⢧⣼⡠⣄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛
⠀⠀⠀⠤⠀⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠈⢹⣆⣿⣿⡿⣧⣏⠁⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣳⣊⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠈⠉⡍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⣿⡇⠙⠁⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⠯⣭⠩⠿⠿⠿⠦⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣦⣠
⠀⠀⠀⠀⢠⣿⣿⣽⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣴⣶⣶⣤⣴⣶⣶⣶⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢾⡣⡆⣻⠦
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⣬⠉⠉⠉⠉⠉⣿⣿⣿⠋⠉⠛⠛⠛⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⢻⡶⢛⢛⠶⣿⠘⠛⠾⣻
⠀⠀⠀⠀⢸⠉⠉⣀⡀⠉⢹⠂⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⠐⡁⢈⡇⣿⠶⣸⣿⡛⡿⣿
⠀⠀⠀⠀⠈⢷⣶⣿⣷⣶⡎⠀⠀⠀⠀⠀⠀⣿⣿⣇⣀⣀⣀⣠⣿⣿⠇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⣭⣭⡴⣯⠈⢻⣴⣂⣦⣿⠃
⠀⠀⠀⠀⠀⠈⡻⠿⠿⣋⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠈⠉⠛⠉⠉
⠀⢀⣠⡄⣤⣴⣿⣿⣿⣿⣤⠄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⢄
⠀⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⣿⡦⠀⠀⠁
⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⢀⣤⠶⡶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢸⣻⣿⣿⣿⣿⣿⣿⣿⢸⢸⠉
⠀⠈⠛⠻⠸⠿⠿⠿⠿⠿⠿⠸⠛⠋⠀⠀⢀⣠⣤⡄⣾⠀⢀⣇⠀⠸⡇⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡝⣟⢛⣿⣟⣿⣿⣋⣿⣌⣨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠉⠁⠻⣞⠉⠉⢙⣾⠃⠉⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠉⣬⣿⣿⣿⣿⣾⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⢸⣿⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⢤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢟⣻⢿⣯⣿⡆⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣠⡴⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⢿⣿⠟⠙⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⡾⠿⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣯⣶⣤⡀
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠤⡤⠤⢜⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢴⠒⢲⣶⣶⣶⡶⠶⢶⣶
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣸⠇⢻⣿⣿⣿⡇⠒⢠⣿⠉⠉⢱
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣼⢛⣛⢛⣛⡛⠻⣿⣿⣿⡟⠀⢨
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠛⠋⠉⠀⡀⠀⠀⠀⠀⠀⣽⢨⣿⠿⣿⠋⠀⣿⣿⣿⠛⠀⢸
⠀⠀⠀⢀⡴⠖⢒⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⢿⡘⠓⠒⠓⠒⣈⣿⣿⣿⢀⣠⣘⣄
⠀⠀⣰⢣⠊⠀⠀⠈⢲⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣤⣶⣶⣴⢒⢲⣿⡿⠶⢶⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿
⠀⠀⢿⢠⠀⠀⠃⠀⠠⢅⡇⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣶⣿⣿⣿⣿⣴⣸⣿⡕⠯⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠘⢦⡃⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢻⣬⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣷
⠀⠀⠀⠀⠉⠛⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠘⠛⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⠞⣡⣴⡆⢠⡙⢦⠀⠀⠀⠀⠙⢿⡿⠋
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⡿⠀⠀⠀⠀⠀⠇⣼⡿⠿⠁⣿⣿⡀⢇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠿⠿⠿⢿⠀⠀⠀⠀⠀⣆⠰⣶⣶⣶⡘⠿⢁⡇⠀⠀⠀⣿⢸⡇⡇
⠀⠀⠀⠀⢠⣤⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣶⣶⣶⣶⣾⣦⠀⠀⠀⠀⠈⠢⣈⡙⢛⣋⡤⠊⠀⠀⠀⠀⣿⣼⣧⡇
⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⠶⠶⢶⣶⡶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⡄⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠱⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠆⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢰⠀⠘⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠰⠀⣇⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠠⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⢡⡃⠀⠉⠉⠀⠀⠀⢹⠁⠀⣧⠁⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⡏⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⣰⠏⠈⢧⢸⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠂⠀⠀⠘⡇⠀⢰⠏⠀⠀⠀⢿⠀⠀⡟⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢀⠃⠀⢀⣀⠀⠀⠆⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀⣀⣀⣀⡇⢸⠰⢩⡿⠯⢏⠡⢸⠀⣇⢀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⡀⠁⠱⠦⠦⠄⠁⢹⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡍⠙⡖⠒⠒⠒⠒⠒⣿⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠒⠒⠂⠒⡀⣾⡇⠀⠀⠀⠀⠀⣿⡆⡗⠐⠂⠒⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡀⣠⠀⠖⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⡿⠈⡇⠀⠀⠀⠀⠀⣷⠸⣧⡀⠀⠀⠀⣸
⠀⠀⠀⠀⠈⠃⢤⠀⠒⠀⠈⣀⡈⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠁⠈⢈⡟⢳⠚⡗⠒⠒⠒⠒⠚⣟⢲⠛⣅⠁⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠑⠦⡉⠁⣙⢶⣤⠄⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠴⡫⠀⡀⢈⡇⠀⠀⠀⠀⠀⣿⠈⡈⠩⠳⣄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠌⠳⣶⡀⠉⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠞⡡⠊⢀⠔⠁⠸⡏⠉⠉⠉⠉⠉⣿⠀⠑⢄⠈⠢⡑⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⠴⠈⠛⢷⣀⠈⡡⢄⠀⠀⠀⠀⠀⢀⡴⢊⡵⠋⡠⠒⠁⠀⠀⠐⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠑⠤⡈⠢⣝⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠲⡂⠈⠉⠳⣄⣀⠱⠆⠀⢀⡴⣋⢔⣁⠀⡎⠀⠀⠀⠀⠀⢸⡇⠀⣀⣄⢀⠀⣿⠀⠀⠀⠀⠀⠈⡆⠈⠑⢌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠈⠉⠻⣧⣉⡡⠬⢷⠦⠄⠐⢚⣁⡙⠦⠀⠐⡗⠲⣖⠒⢒⢒⡎⠀⠀⢸⣿⠀⠀⠈⣖⠒⠒⠒⠒⠒⠓⠒⡒⠒⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠐⡉⢷⡀⠀⢂⢻⣿⡷⡾⠟⠃⢃⠀⢡⠤⠋⠉⠉⠉⡇⠀⠀⢸⣿⠀⠀⠀⡏⠉⠉⠉⠉⠉⡏⢉⣉⠉⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣧⠀⠸⠀⠷⠀⠛⣤⡀⡘⢀⡜⠓⠀⠠⠤⡄⣇⣀⣀⣸⣿⣀⣀⣀⡧⡄⠤⠀⠐⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠤⠀⠒⣈⡉⠆⠀⠀⠀⠀⡿⠀⢰⠤⠤⠀⢒⣊⠹⢧⣝⠛⠫⣯⠉⠉⢃⠸⣯⣭⣿⣿⣿⣭⣽⢀⠉⠈⠹⠉⠉⠹
⠀⠀⠀⢀⠀⡶⠖⠙⠒⢂⠈⠉⠀⠀⠀⠀⠀⠀⠀⡾⠋⠉⠀⠀⠀⠀⠙⢤⡄⠒⠙⢻⣄⡈⠵⢄⣘⠀⠉⠉⠉⠉⠉⠉⠉⢘⣀⣀⣀⡀⣀⣀⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣉⠁⢈⠻⣦⡄⠙⠢⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠙⠋⠛⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀⡀⡀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣈⣻⣌⣀⠀⠙⠶⣄⠋⠓⣄⠀⠀⠀⠀⣃⣀⣀⣀⣀⣀⣀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡤⠀⠛⠻⠎⢀⣑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢖⠀⠉⠀⣀⣀⠨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁