Cottontail Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠂⣐⠅⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢰⣷⠀⠀⠀⢹⡆⢂⠀⠀⠀⠀⢀⢰⡎⢨⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠃⠀⠀⠀⠃⠐⣀⠀⠀⠀⠆⣾⠁⡟⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢄⠀⠠⡅⠀⣿⠀⠀⡐⣸⡉⠀⣯⠟⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣬⣶⣴⠃⢀⣿⠇⢠⣿⣿⢇⠀⢇⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡟⡰⠋⠁⠀⠀⠀⠀⠉⢢⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣷⡀⠁⣀⠐⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⣠⡿⠛⠃⢰⣿⠆⠁⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⣨⠔⠁⠀⢠⠀⠸⢿⠂⠀⢀⣤⣄⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⠼⠃⠀⠀⢀⠃⠀⠀⡄⠀⠀⣘⠋⠉⢳⠂⠈⡓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⢿⠇⠀⠀⠀⠀⠀⢸⣇⠀⠸⠁⠀⠊⠡⣀⢄⡀⠙⠀⣻⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠙⠀⠐⠀⠀⠀⠀⠀⢻⣷⣆⠁⠀⠀⠀⢉⡏⠀⠜⢁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠙⢻⣶⠆⠀⠀⠘⠂⠀⢀⠞⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⠻⠙⠿⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡗⠒⠲⠾⢧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢠⡦⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠘⡇⠀⠀⠀⠀⢸⣶⣶⣾⡗⠀⠀⠀⣿⣷⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣤⣤⣠⣤⣿⠀⠀⠀⠐⣿⠉⢹⣿⣿⠀⠀⠀⠻⠛⠛⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠄⠄⠠⢦⣼⠀⠈⠈⠉⠒⠳⠾⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⡄⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡈⠂⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⡄⣸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠧⠸⣿⣂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠿⣯⣭⡲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⣐⣾⣛⡀
⠀⠀⠀⠠⠀⢀⠀⠀⠀⠄⠀⠁⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⡋⠁⠐⡆
⠀⠀⠀⠀⠑⢈⠀⢀⠀⠠⠀⠀⠘⠈⠉⣠⣶⣶⣶⣶⣾⣿⣿⠿⠿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⣜⣤⡤⣦⣾⣿⣿⣿⠟⣻⣓⠀⠙⠖⢲⣶⣮⠙⣿⠇⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠂⠀⠀⠀⡄⠈⠀⡎⠀⠀⣰⣿⣿⣿⣿⣿⡛⠉⣿⠅⠀⠨⡟⠿⣿⡇⢸⠀⠀⠀⠞⡠⠀⠀⠈⠀⢀⢁⣐⣋⠉
⠀⠀⠀⠀⠀⠀⠘⡄⠀⡄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣴⣧⢀⣤⢢⣶⣼⢻⢁⠇⣀⠌⠀⠛⣀⣠⠈⠉⠀⠃⠀⡀⢁⡤
⠀⠀⠀⠀⠀⠄⠀⠈⡄⠐⡀⢸⣿⣿⡿⠟⢉⣡⣈⠙⢿⣿⠏⠐⠙⠻⠁⣼⠖⠁⠔⠀⠈⡡⠀⢀⠔⠁⠀⠔⠀⠁
⠀⠀⠀⠀⢀⠀⢁⡤⣇⣀⠀⣿⡿⢋⣴⣶⣿⣿⣿⡆⢸⣷⣿⡞⠀⠀⢸⡇⠀⠘⡀⠂⠩⠖⠋⠁⠂⠀⠀⠀⠲⠶⠄
⠀⠀⠀⠀⠀⠐⠀⠀⢣⣿⣶⣿⣷⣿⣿⠿⢿⣿⣿⡇⣼⣿⣿⡿⠀⠀⣿⡇⠀⠈⠀⠒⢀⠀⠀⣀⠀⣀⡀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠉⠀⠀⠈⡾⠟⢰⣿⣿⡟⢹⠀⠀⣿⠃⠀⠠⠀⠲⣅⢤⡄⠀⠀⠄⠉⠠⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⢀⢠⠀⣋⣠⠀⠀⢀⣿⣿⣋⣀⣈⣇⠀⠩⠄⠀⠀⠀⠀⠈⠂⠈⠈⠀⠈⠑⠤
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣬⣅⣬⣿⣿⣿⣿⠀⠀⣾⣿⣿⣛⣉⣩⠽⡀⠀⠢⠄⡀⣂⣠⣀⢀⣤⡀
⠀⠀⠀⠀⢠⣤⣴⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠉⠉⠉⠉⠀⠀⠀⢙⣤⣀⡠⢸⣿⣿⠿⣿⠻⠇⠂⢶⠤⠤
⠀⠀⠀⠀⠘⠛⠛⠛⠙⠉⠉⠛⠻⠿⠷⠶⠒⠛⠛⠛⠉⠙⠋⠉⠉⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀⣀⣀⣠⣄⣀⣀⣀
⠀⠀⠀⢸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣿⣿⣟⡲⢤⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡳⣄
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣄
⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠈⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠂⠀⠈⡠⠔⠒⠶⠤⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠁⠂⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠠⠤⠴⠊⠉⠉⠉⠉⠉⠁⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣟⣿⠿⠿⢿⣿⣟⣛⣻⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠲⢤⣀
⠀⠀⢀⠈⠲⢤⣀⡀⠀⠀⠀⠀⢸⠀⠓⢄⠈⠳⣦
⠀⠀⠀⠁⢠⠀⠈⠉⠉⠒⠢⢄⡘⣆⠀⠈⢦⠀⠈⢧
⠀⠀⠀⠀⠀⠳⡀⠀⠀⠂⢄⠀⠉⠛⢧⣄⠈⠃⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠙⢦⡈⠀⠀⠈⠢⣀⠀⠈⠳⣦⡀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠈⢢⡀⠀⠈⢳⡀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢍⣄⠀⠀⠑⢄⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠁⠀⠐⠒⠈⠉⠑⢦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠸⠣⠐⡄⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⣄⠠⡀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠈⠐⠐⠀⠰⡈⠐⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢄⠀⠀⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠳⡄⠀⠘⢆⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂⢠⠀⠀⠀⠉⠂⠀⠀⠀⢹⡄⠀⠈⣧⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⣸⠃⠀⠀⣿
⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⡘⠀⠀⣀⠄⠊⠁⠀⣠⠏⠀⠀⣠⠏
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⠤⠞⠁⠀⠀⠚⠁⠀⠂
⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣈⣁⡀⠀⠀⠀⠠⠤⠀⠀⠀⠀⢘⠀⢀
⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠶⢦⣄⠀⠀⠀⡌⠿⣍⠁⠀⠀⠠⡀
⠀⢸⡄⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠈⠓⠦⣄⡁⠀⠈⠳⣄⠀⠀⠘⠆
⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠈⡇
⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡜⠀⠀⠀⠀⢸⠇⠀⠀⡰⠃⠀⠀⠀⠑⢀⠄
⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⣠⠋⠀⢀⠞⠁
⠀⢀⣠⠤⠬⠻⢶⣤⣤⣤⣤⣴⡾⠋⡄⠀⠀⠀⣴⠁⠀⣰⠏
⠀⠋⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⠀⢰⡇⠀⠀⢸⠃⠀⠠⣯⡀
⠀⠀⠀⠀⠀⠀⣀⣀⡿⠀⠀⠀⠀⡞⠀⠀⠀⠘⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠄⠠⠤⠄⢈⠀⠀⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠢⠀⠌
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠊⠀⠀⠄⡀⠔⠈⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠠⠁⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠁⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠠⠄⣀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁
⣈⡀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⡀
⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀
⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠈⠀⡖⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠄⠀⠀⠀⢠⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠌
⠀⠀⠀⠀⠀⡃⠀⠔⠈⠀⠀⠀⠀⠀⡄⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠑⠠⢄⠀⠀⠀⠀⡠⠊⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢗⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠸⣦⡹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠙⠁⠹⢱⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⡥⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢴⡀⠀⠀⢠⠇⣧⠀⠀⠀⠀⠀⢀⡴⢋⡶⠋⠠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠁⠀⠀⢼⠃⣿⡆⠀⠀⢀⣴⠃⢃⣾⢐⡞⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣳⣤⣼⠀⣿⡇⠀⣰⣏⠁⠀⣼⣧⡾⣀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢈⡿⢁⣰⣿⡇⢠⣿⣻⣈⢠⣿⠏⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢁⡬⠉⠉⣉⠉⠙⠻⢿⡨⠋⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡤⠂⠀⠈⠁⠈⠁⠀⠀⠀⠃⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢒⢠⣦⡄⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠀⠀⠀⠀⢃⠀⢀⠐⠃⠀⠀⡀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢥⣾⠜⢂⠃⢠⣾⠗⠀⣴⡎⠃⣀⠀⠃⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⣍⡠⠀⣷⣄⢙⠀⠘⠁⠀⠘⠋⠁⠀⠀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠐⠀⠀⠀⠛⠛⠻⠷⢦⣤⣤⣚⣃⣤⣤⠞⡻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢣⠀⠀⠀⠀⢶⣶⠀⠀⢀⠀⠀⠨⠛⠟⢙⠋⠄⠈⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠡⡀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢼⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⢠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡰⢀⣾⣿⡴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠀⢠⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⠁⠙⠁⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⣸⡟⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠅⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⣿⡇⠀⠻⠀⠀⠸⠀⢀⢠⠀⠀⠀⡠⠈⠀⠠⣴⡟⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⡇⠀⠀⠀⠀⣶⣶⡛⣿⣄⠀⠀⠀⠀⠀⢨⣿⠂⠀⠀⠀⠘⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣸⣿⡗⠂⠀⠀⢸⣿⢃⣼⣿⣿⣇⡀⠀⠀⠀⣾⣟⡀⢠⣤⣤⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡰⠂⢨⣿⠁⠀⠰⠀⢸⣿⣤⣬⣤⡝⣿⠁⠀⠒⢴⣿⣿⡀⣀⣤⢄⠈⠉⢰⡄
⠠⡀⠀⠀⠀⠀⠀⠀⠀⠼⠥⠶⢿⡷⣽⡿⠋⠚⠀⢀⡾⠛⠛⠛⠻⠿⣿⡆⠰⠆⢲⡿⡿⠿⢿⣁⣈⣇⣠⣄⣧⣄
⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠿⠾⠶⠶⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠓⠓⠀⠙⠛⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⡀⠀⠀⠠⡀
⠀⠙⠐⠀⠀⠀⢂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡭⠉⠉⣭⢩⠝⢁⡄
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⡇⠀⠀⢀⠤⢄
⠀⠀⠀⠀⢀⡔⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢱⡀⢀
⠀⠀⠀⠰⠡⡁⠀⠀⢂⠄⠁⠀⠀⠀⠀⠀⠀⠸⣷⣾⡄
⠀⠄⠀⠀⠀⡀⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣗⠀⡀⠀⠁
⡇⠀⠀⠀⢘⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇⡿⠚
⡇⠠⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣿⡟⣉⠻⣿⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⠿⠟⣿⣧
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⡿⣿⣿⣿⣆⡾⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠐⠛⠉⢉⡉⠴⠿⠻⣿⢳⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣯⠉⠀⠀⠰⠁⠸⢶⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⢰⡄⠀⠀⠀⢼⣻⣿⣿⣽⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣄⠀⠀⠀⢸⣿⣻⢼⣿⣿⠿⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠸⠁⠀⠀⢸⣿⡇⢸⡿⠁⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠀⣼⠃⠀⠀⠈⠂⣰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠐⠀⠀⠀⠀⠀⠀⠀⢁⠖⠀⠀⠀⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢀⣐⠆⠀⠀⠀⠊⠀⠀⢀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠇⠘⠻⣧⢀⣠⠂⠀⠀⠀⣼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣄⢠⣄⠀⢿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣀⣴⠀⠀⡀⠀⠀⣾⡿⠈⠋⠉⠋⠀⠈⡏⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⡇⠀⠀⡿⠀⠀⠀⢠⣤⡾⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠚⠛⢁⠀⢀⢙⠛⠋⠉⠛⡀⠄⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⡶⢶⣶⣶⣤⣤⣤⣀⡈⠑⠉⠉⣿⣽⠿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣿⠟⠁⠂⢠⣰⡋⠀⠀⢈⣩⢿⠓⣾⡏⠻⣿⣄⣾⣿⠿⠇
⠀⠀⠀⠀⠀⠀⢀⠖⣳⣦⣤⠎⣠⣿⣯⣅⣴⡶⣿⡿⢁⣤⣴⣾⣧⣿⣦⣈⣷⢀⡛⣿⣿⡀
⠀⠀⢀⠤⡤⢖⠵⣊⣓⣾⣶⣶⣿⣍⣿⠿⠓⠄⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣇⣰⣿⣷⣤⣤⠤⠤⣀
⠀⠀⢛⣶⡖⣡⠞⠉⠀⠀⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠐⠘⠣⠍⣀⣋⠛⠛⡶⢦⣃⡉
⠀⠀⠙⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠈⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠂⠀⠀⠀⠀⠀⠐⠀⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⣠⣶⡷⠀⠀⠀⠀⠀⠀⠀⣞⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⠈⣷⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⣽⠟⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⡠⣿⣷⣻⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣶⡟⠁⠀⠀⣼⡏
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⣿⢧⠆⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢡⡿⠋⠀⠀⠀⢰⡟
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠻⣌⠢⠑⣌⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠉⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡘⢦⠀⠈⢧⡈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⢸⠀⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠙⣦⠈⣿⠀⠸⣿⣿⣷⣄⠀⠀⠀⣸⣿⣟⠀⠀⠀⠀⠀⠀⣿⠀⣿⣷
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠈⠀⢿⡇⠀⢹⣿⣿⣿⣆⠀⢀⣿⣿⣿⠂⠀⠀⠀⠀⣰⠏⢠⣿⡿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⢸⡇⠀⢸⣿⣿⣿⣿⡄⢸⣿⣿⡏⠀⠀⠀⠀⠘⢁⣴⢿⣿⠃
⠀⠀⠀⠀⠉⠛⠿⠿⠷⠙⣿⣿⢸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⢀⡼⢿⡿⠿⢿⣷⣼⣿⣿⣧⠀⠀⠀⢀⡴⠋⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⣧⣞⠤⠄⠀⠀⠀⠹⢿⣿⣿⣿⡀⠀⠰⠋⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣾⡄⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⢙⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⣸⡆⠀⠀⠀⠀⢀⠴⢦⡄⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠤⠴⢶⣾⡿⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⣀⣤⡤⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⣼⣿⣍⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⡿⢃⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠺⠧⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢹⡋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⣠⣿⣦⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⢸⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⢠⣾⣿⠟⠋⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢸⡀⠀⢀⣰⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢠⡿⠸⣇
⠀⠀⠀⠀⢨⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠙⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠴⠛⠁⠀⣿⡄
⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣠⣶⣄⠀⠀⠀⠀⠀⠀⣀⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⣬⠻⠶⠶⠶⠶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠉⣿⡇
⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣿⠇
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡄⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⣠⣴⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⡄⢷⡀⠀⠀⠀⠀⠀⠀⠀⠛⣇⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠹⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣠⣶⣁⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢻⠇⠀⠐⠛⢛⡿⠋⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠹⣦⠀⠀⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠉
⠀⠀⠀⠀⠀⣠⣏⡀⠀⠀⠀⣿⡷⣶⠦⣀⡶⢾⣿⣿⣿⣷⣦⣤⣄⣀⣹⣧⡀⠈⠛⢻⣿⣿⣷⣦⣤⣄⣤⣄⣤⣤⣶⠾⠟⠋⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡙⠻⣿⣿⣿⣦⡀⠈⠁⠀⠙⠛⠉⠈⠁⠘⣿⡄⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠈⠉⠉⣷⡀⠀⠀⠀⠀⠀⣶⠀⠀⣿⡇⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡤⢀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣹⣧⠀⠀⠀⠀⠀⠟⠀⠀⣿⣧⡀⠀⠠⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠦⠔⠛⠋⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣶⠀⠀⣿⠛⠓⠂⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠰⠆⠈⡄⠀⠙⠦⣤⣴⣦⣴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠠⡄⠰⡇⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠔⠛⠘⠋

⠀⠀⢀⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠥⢰
⠀⠀⠀⠁⢀⣝⠲⢤⡀⠀⠀⠀⠀⠀⢀⡴⢫⡞⠀⢀⡟
⠀⠀⠀⠀⠈⢯⢳⡄⠉⠳⡄⠀⠀⢠⠏⢠⣿⣁⠄⡼⠁
⠀⠀⠀⠀⠀⠈⢷⡑⡄⠀⠀⠦⠄⠀⠀⠸⠟⢁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⡇⡦⠀⠀⠀⠀⠀⠀⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⢀⡰⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠑⠛⡀⠀⠀⠀⢠⡁⠈⣿⡿⠟⠛⠛⠋⠉⠉⠉⠉⠓⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠃⢀⡅⡼⠁⠀⠀⠀⠀⠹⡎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⣼⠀⢸⠀⠇⠀⠈⠳⠜⠃⠀⢃⡀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⣧⠀⢹⣣⠄⢀⣀⣠⣀⣀⣰⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠙⠀⠉⠉⠀⠈⠉⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡭⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠠⡄⠀⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⠠⠼⠯⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣼⡿
⠀⠀⠀⠀⠀⠀⢀⣞⠉⠂⠙⣶⠄⠆⠀⡟⠃⠀⠀⢀⣴⠂⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⢀⡖⠋⠁⠀⣠⡾⠃⠀⣀⣇⠀⠀⠀⣴⣿⣉⣀⡀⢀⡴⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠙⣿⣶⣀⡀
⠀⠀⠀⠀⠚⠷⠶⠖⠛⠛⠁⠀⢸⣭⣉⣀⣤⣾⡿⠋⠉⠉⠹⣿⣦⣤⣤⣤⣤⣤⡤⠤⠤⠠⠴⠾⡿⠿⠿⠿⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⠛⠛⢢⣄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠈⠳⣴⣦⣀⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠹⣿⣿⣯⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣽⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⠋⠁⢤⣙⠳⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⡀⠀⠀⢀⢸⣿⣿⡟⠀⢷⣿⣾⢰⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠉⠛⣿⣿⡿⡿⠛⠂⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠲⣆⣂⢀⠀⣀⡤⠔⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⡿⠋⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢾⣞⡏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⣿⠇
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠖⠉⠒⢆⡠⡦⠀⠀⠀⡀⠀⠀⠀⠀⣀⡄⠀⠀⡾⠻
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠘⣿⣥⡤⢴⠊⠀⠀⠀⠀⣔⡛⣷⢀⣠⣶
⠀⠀⠀⠀⢠⣠⡀⠹⣿⡿⣫⠀⢀⣿⣿⣷⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠙⢚⣤⠼⠛⠀⠒⠛⠛⠻⣿⣿⣇⠀⠀⠰⣿⠿⠛⠙⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠠⠤⠀⠖⠑⠙⠛⠋⠀⣀⠈⠄⠂⠀⠀⢀⡁⠀⠠⡲⠶⠀⢠⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠐


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠤⠀⣱⣧⡾⠋
⠀⠀⠀⠀⠀⠀⠀⣠⢟⢸⡿⣊⣿⣧⠀⣦
⠀⠀⠀⠀⠀⠀⢠⡅⠈⣿⠟⡉⢁⡄⣨⣅⢠⣄⡀⡀⣠⠈⠀⣠⠰⡀⠶⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢗⣓⣫⣶⣿⠻⢔⣿⣷⣟⣳⣞⣶⣸⣿⠄⠊⠁⠈⠓⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣧⣶⣾⠢⠄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣟⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠀⠀⠀⠀⠘⣄⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⡿⠿⠛⠛⠙⠛⠛⠿⡇⠀⣮⡤⣐⠢⠄⠀⠈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢿⣿⣿⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣀⡄⢀⣀⣀⣀⠈⢻⣿⣷⡿⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⣠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⣀⣤⠐⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⡄⠀⡄⣿⠁⢀⠄⠀⣼⣿⣿⣿⣿⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣇⣰⣧⢻⡶⠏⠀⢰⠛⠻⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣿⠂⠀⠀⠀⠂⣀⣸⣿⠿⣿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠿⣿⣿⣿⡄⠀⠀⠀⡸⠛⢉⠿⠟⠛⠈⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣀⣀⣼⣽⣿⣏⣷⡖⣻⣿⣿⡇⠀⠀⠰⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⠀⣠⡞⠁⠀⢀⣴⣾⣹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣿⡄⠀⠀⡳⠈⠀⠰⠀⠀⠀⡄⠀⠀⢠⣾⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡇⣠⣿⣿⠀⣴⣿⣿⣿⣿⣿⣟⣿⡀⠀⡉⣿⣿⣡⣼⣿⢿⡀⠈⣧⠀⠀⡀⠰⣄⢀⠀⣠⣄⣿⣧⣟⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡿⢟⣼⣿⣿⣿⣿⣿⣿⠁⠁⠈⠙⠻⠟⠛⠋⠛⠁⠀⡇⠀⠸⣆⠀⠹⣆⢹⠆⣰⡿⠋⠈⠻⢿⣎⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠟⣸⣿⣿⣿⣿⡿⢿⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠁⠘⣶⠀⢸⡞⠀⣻⠀⠀⠀⠀⠸⣿⠃
⠀⠀⠀⠀⠀⢀⣴⡿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣯⣴⣷⣾⣿⣿⢛⣿⣿⠗⢻⣇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠘⢶⢺⣧⠴⠃⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢀⣾⡏⢀⠈⢿⣧⣾⣿⣿⣿⣿⣿⣿⣿⠟⢊⣸⡿⠀⣿⣿⣿⡏⠙⢦⡈⢣⣀⣤⣄⣤⣤⠀⣀⠀⠀⠀⠠⠂⠀⠈⣩⠁⠀⠀⢠⠆⠀⠒⠀⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⢈⣿⣿⣿⡟⠛⠛⠡⣍⣹⣄⡈⠋⠀⣤⢻⣿⣿⠇⠀⣈⣻⢄⣿⠛⠉⠛⠋⢻⠿⠛⠀⠀⠀⡇⠀⠀⠈⠳⣀⣀⣼⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠸⣿⣷⣤⣾⣿⣿⣿⣿⣷⣦⣤⣤⣿⠿⢅⠀⠀⢰⡇⠘⠿⣿⣯⣋⣛⣉⠀⠄⠐⣦⣶⡀⢘⢇⠀⠀⠀⣤⣿⠀⠚⠀⢀⣿⣿⣿⠂⠶⠀⣶⣿⡀
⠀⠀⠀⠀⠀⢘⠟⡉⢿⣿⣿⣿⣉⣩⣿⣤⣀⣬⣠⣾⣗⡙⠊⠿⢮⠵⠮⠿⠿⢿⣧⢤⠤⠌⠈⠉⠉⠉⠙⠛⠒⠒⠚⠛⠓⠒⠒⠛⠉⠙⠛⠒⠒⠚⠛⠋
⠀⠀⠀⠀⠀⠘⠷⠶⠾⠛⠁⠀⠈⠉⠉⠉⠉⠉⠙⠓⠚⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡖⠉⠑⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⢸⡇⠀⠀⡂⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠤⠤⠤⠤⠤⠤⢤⢀⠎⠀⠀⠀⠈⠣⠀⠤⠃⡄⠀⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⣠⢃⣴⠶⠶⠶⠶⠶⣆⠹⣄⠀⠀⠂⠀⠀⠀⠀⠀⠑⠊⠀⣠⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣿⣿⠀⣀⠀⠀⠀⠀⡀⢸⣿⣿⢇⠀⡰⢁⣾⠃⠀⠀⠀⠀⠀⠹⣧⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢻⡿⢸⣿⠀⠀⠀⢸⣿⢸⡟⠀⠀⢳⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢙⣷⢘⡟⢉⣍⠁⠀⠈⢉⣍⢹⡿⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⣀⠀⠀⠀⠉⠀⠀⠂⠈⠉⠀⠀⣄⡠⠎⢢⠙⣧⠀⠀⠀⠀⠀⠀⢀⡾⢁⠾⠃⢸⣿⠀⠀⠀⢸⡿⠘⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡄⠀⠀⣠⠤⠤⠦⣅⠀⠀⢀⠎⠀⠀⠀⠣⡘⢷⣄⣤⣤⣤⣠⡾⢡⢮⣤⠀⠀⠀⠀⠀⠐⡄⠀⠀⢠⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠈⠢⠤⠴⠂⢀⠴⠋⠀⠀⠀⠀⠀⠱⠄⠬⡥⢠⠄⠈⠰⠃⠀⠻⣆⠀⢰⠶⠶⠞⠶⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡗⠂⠚⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠈⠲⢄⠑⠶⠚⣁⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠀⢻⠈⢹⡇⠀⠀⣿⠈⠉⠉⠘⠢⡄⠀⠀⠀⠞⠉⠉⠈⢦⠀⠀⠀⠀⣀⣤⣤⢴⡇⠉⠁⠿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⢾⠀⠈⠉⠒⠊⢹⠀⠀⠀⠀⠀⠘⢆⠀⠈⢆⡀⡠⠤⡿⠀⠀⡰⠋⠀⢸⣿⠀⢇⡀⣠⠂⣿⡟⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⢸⣀⠶⡀⠀⠀⠀⠀⠣⡀⢠⠉⡏⢸⠁⢠⠎⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⢀⡄⣫⠀⢠⣀⣀⡠⠊⠀⠀⠈⢢⠀⠀⠀⣠⢇⢸⠀⡇⢸⡴⡁⠀⠀⠀⠀⢼⣿⣀⡀⠀⢀⣀⣿⣷⠀⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠈⢳⣄⠔⠉⡃⠈⢀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠙⢤⡔⠁⠀⢻⠀⠣⢼⠀⠈⢢⠔⠊⢙⣼⣿⣿⡇⠀⢸⣿⣿⣧⡜⠒⢄⡴⠃⠈⢢
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣔⠁⠀⠀⠀⡃⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠈⢢⠀⠀⡆⠀⠸⣀⠔⠁⠀⠀⢘⠉⠉⠉⣹⠀⢸⠉⠉⠉⢡⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠘⡄⠀⢀⡠⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⣏⠀⠀⠀⠈⠀⠀⢸⠢⠔⠁⠀⠀⠀⠀⣽⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠘⡦⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣉⣀⣇⣇⠀⠀⠀⡆⠀⠘⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⣄⠰⡄⠀⠀⠀⠀⠀⠀⣠⣎⣉⣩⣿⣿⣿⣿⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⢈⡆⠉⠑⢦⠀⢀⢴⣿⣿⣿⣿⡿⢿⣿⣿⣿⠀⠀⢀⡅⠰⢄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠁⠀⠀⠀⡰
⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠘⣄⢀⢄⢠⡿⠃⠀⠉⡉⣉⠉⠀⠈⠻⣿⣿⠀⠀⡎⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡸⢀
⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⢈⡯⠶⠋⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⣧⢻⠰⣇⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⠀⠀⠀⢣⡟⢼
⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠈⠼⠻⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⡀⠀⠀⠈⢸⠾
⠀⢠⡀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⡇
⠀⠀⠑⢄⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡆⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡇⠀⠀⠇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣄⣠⣤⠃⠀⠀⢠⣄⣀⣤⣴⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⣺⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠉⠉⠉⠙⠄⠀⠀⠉⠉⠉⠉⠉⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠿⠋⠈⠉⠁⠀⠀⠀⠀⠉⠉⠀⠻⢿⣿⣿⣿⣷⠀⠀⠀⠀⠰⠋⠀⠀⠀⠰⠿⠤⠊⠀⠀⠀⠘⠤⠼⠂⠀⠀⠀⠈⡆
⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶
⣿⣿⣿⣀⣀⣀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⢁⣴⣾⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠇⢠⣟⠁⠈⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠺⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⡀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣌⡙⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠻⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢾⣿⡄⠀⠀⠀⠀⢀⣀⣠⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠚⠁⠀⠀⢀⡤⡺⠛⠀⠨⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠢⠁⢂⣼⡍⡞⠀⠀⢀⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠉⠄⠄⠀⣾⣿⢀⣿⣆⣀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠤⣴⣹⣿⡈⢿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣦⠬⣅⠽⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣛⣋⠔⠋⢬⣔⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢨⢁⢌⣁⣴⠮⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⠀⠀⠀⠀⠀⢸⣏⠃⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠑⠀⠀⠀⠀⠀⠀⡠⡿⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠡⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⢀⣠⣾⠛⠓⢀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠀⠀⠀⢀⣿⡋⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⡠⠀⠀⠀⠸⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠺⠖⠂⠂⠀⠻⠦⠴⠤⠆⠀⠀⠀⠀⠀⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣻⡟⡛⢻⡛⣻⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣖⣲⣶⣶⣶⣶⡄⢀⣶⣶⣾⣯⣴⣶⣶⣶⣶⣶⣶⣶⣶⠆⡼⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⡿⢟⣵⣿⣿⣿⡿⢿⣏⣭⣭⣿⠟⢻⡿⠿⠛⠛⠀⠈⠁⠚⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡝⢻⣿⢿⣿⡇⠰⣿⣿⣿⣿⠋⠁⢀⣠⠄⢀⣀⠀⠀⠀⣠⣶⣶⣄⣠⣄⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢣⣴⢶⢶⣄⢷⣄⠙⠿⠃⠉⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠸⣿⣿⣿⠟⠀⣻⡷⠀⣸⣷⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⢀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢹⠏⠁⠀⠀⣛⣥⡶⢰⠂⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣿⢠⣶⣤⣾⣿⡿⠙⠘⢀⣼⣿⣿⣿⡟⣿⣿⡏⠀⠀⠀⠀⠘⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣯⠈⠻⣯⣿⣿⠿⠛⠛⠻⣶⠳⠶⢾⣿⣧⣀⠀⠀⠀⠀⠘⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡼⠋⣠⠀⣹⡟⠁⢂⣀⡀⠈⠉⠀⠀⠠⠉⠛⠿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢻⡀⢻⣾⠟⠁⢆⠀⠈⠁⠁⠀⠀⠀⠀⠁⠸⠗⡄⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣙⣡⡮⠨⠀⠈⢀⠀⠀⠀⠁⠀⠀⠀⠐⠀⣀⡐⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⣦⣤⠀⠀⠑⠂⢀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠠⢸⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣼⡇⠀⢿⣿⠓⢄⠀⠀⠊⠻⠷⣤⣤⡤⠠⣾⣷⣆⠀⠀⠙⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⡇⠀⢸⣿⡔⣆⢀⢀⣀⠀⠀⠀⠀⠀⣤⣼⣿⡘⠂⢠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣤⣠⣼⣿⣥⣬⣿⣿⡛⠱⣤⣤⣠⣶⣿⢩⣿⣧⠄⠁⣬⠸⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⡟⣿⣽⢻⣿⣿⣿⣿⣿⣥⣌⣉⣁⡿⠿⣿⣿⣿⢻⡄⣢⠽⠺⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠙⠛⠿⠒⠛⠁⣿⡟⣿⣟⡉⠀⢈⣿⣿⣿⣿⣿⢻⡇⠀⠂⠭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢸⣖⣲⡆⢀⣇⢀⡳⠄⠀⢀⣀⠈⠉⠉⠉⠋⠸⠇⡰⣤⣨⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠉⠉⢡⠊⠉⠁⠉⠀⠀⠉⠉⣻⠀⠀⠈⠀⠀⢈⡟⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣥⣤⣤⣄⡀⠀⠀⠀⢠⡀⢽⣷⣶⣶⣶⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠉⠙⠛⠏⠉⠏⠱⠄

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⡌⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⠁⠀⠀⠈⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠁⠀⠀⠀⠀⣸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠈⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣾⡿⡇⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣾⣧⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⢸⣿⣿⣿⣇⢀⣄⢀⣠⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢻⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⢿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣞⣿⣿⣿⣿⣿⣷⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⠀⠀⠉⠉⠛⠋⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠉⠉⠀⠀⢀⡈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⣠⣎⣀⣀⡀⠀⠀⠉⠲⡄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣤⣤⣤⣬⣉⣉⠓⠲⢤⣢⡈⠀⠠⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠸⣿⣿⣿⣿⣿⣿⣷⣦⣌⠙⢦⡀⠸⡆⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⣧⡀⣷⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢰⠃⢀⣀⡀⠈⠉⠛⠿⣟⣫⡍⣼⣿⡿⢩⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢸⡏⢉⣠⣉⡙⠒⠀⠀⣿⡟⣰⣿⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢿⡩⠤⠤⠄⠀⠀⠀⣿⠁⣩⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⢳⣖⣂⣀⣀⣤⣴⠇⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣈⠨⠿⠿⠿⢛⣸⣿⣿⠟⢙⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⡟⢻⣿⣿⣿⣿⣿⣿⠟⠁⣠⠏⠀⠀⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⡼⠀⢸⣿⣿⠿⢟⣯⣶⣶⡟⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⢰⠇⠀⠀⠀⢠⠖⠉⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣾⡄⠀⠀⣴⠋⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣼⣃⠀⠀⣠⠞⠁⠀⢀⣀⣠⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉⠉




⡶⡶⢶⠶⡶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⢶⣶⣶⡶⠶⣶⢶⣶⣶⢶⣶⡶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠹⣆⠀⠀⠀⠀⠀⣰⡏⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢻⡄⠀⠀⠀⢀⡿⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⣷⠀⠀⠀⢸⠇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⡿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⠤⣤⠀⠀⠀⠀⠀⢀⢤⣄⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⡿⠀⢀⠀⢀⠀⠸⣿⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⢀⡄⠀⢙⣿⣏⠁⢀⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠛⣟⣹⣙⡟⠛⠁⠀⠀⠀⠸⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠋⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⢿⣿⣿⡄⠀⠀⠀⣠⣴⠟⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⢸⣿⡏⠃⠀⠀⣴⣿⠇⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⣿⡇⣷⠀⣸⣿⣿⠘⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣾⣿⣤⡿⢿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⠶⠒⣾⣷⡮⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣸⠎⢩⡇⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣇⣨⣴⣾⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢯⡇⠁⢹⡆
⠀⠀⠀⠀⠀⠠⡬⠁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣧⣤⣾⠁
⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⢠⣾⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡟⠟⠛⠛⠛⢁
⠀⠀⠀⠈⢻⣿⡿⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⠁⠁⠀⠀⠀⠀⠀⠈⠀⢀⠁
⠀⠀⠀⠀⢨⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣾⠟⣧⠂⡀⣀⡀⡀⠀⠀⠀⠟
⠀⠀⠀⠐⠨⣿⣿⣟⣂⣼⣿⣿⣿⣿⣿⣿⣿⣾⣵⣿⣷⣿⣿⣿⣿⠗⢿⡀⢀⡠
⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⢿⣿⣿⣟⣁⠀⣿⣿⣿⣿⣶⢿⠂
⠀⠀⠀⠀⠉⠙⠿⣿⣧⣈⣋⣿⣿⣿⣿⣿⣿⣿⣆⠀⡘⢿⣿⣿⣿⣤⣻⣿⣿⣿⣯⣶⠿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠿⠟⠛⠉⠛⠛⠉⠀⠩⠙⠏⠛⠛⠛⠋⠋⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⣰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⣿⣿⣷⡄⠀⠀⠀⠐⠿⢿⣿⣧⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡿⣰⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣹⣾⣷⣷⣷⣾⣿⣶⣶⣄⣽⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠟⠀⠀⠘⢿⣿⣿⠻⢿⠛⣿⣿⣿⠟⠁⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢠⣿⣿⣦⣄⣶⣿⣿⣷⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⠻⢿⣾⣷⡿⠋⠉⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⣠⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⣤⣤⣶⣾⣿⣿⣷⣶⣴⣶⣾⣿⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠛⠃⠁⠀⠀⠀⠉⠛⠛⠿⠿⠿⠙⠃⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡄⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠙⣿⣄⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⡀⠀⢀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠈⠿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⠟⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠐⢶⡶⠀⠆⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢀⠀⣸⠿⠿⠻⡇⢀⣠⣆⣀⣨⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠈⢀⢄⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⠔⢡⠋⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡎⠀⡆⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⠀⠀⠁⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠠⡀⠀⠆⠀⠠⠃
⠀⠀⠀⠀⢀⠔⠋⠁⡠⠴⠄⠀⠠⡀⠀⡄
⠀⠀⠀⢠⠎⠀⠀⠀⠸⣭⠄⠈⠀⠐⠆⠀⠄⠀⠀⠀⠀⡀⠀⠤⠄⠀⣄⠀⣀
⠀⠀⣠⠟⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠅⠀⠨⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⡗⠒⠁⠀⠀⠐⡀⠀⠀⠀⠀⠈⠀⠀⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠘⠔⠒⠤⣀⡼⠀⠄⠀⠈⠁⡠⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠉⠀⠀⠈⠀⠉⠁⢆⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡁⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠕⣠⠤⣀⠀⠀⠀⠀⣆⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⣂⠀⠀⠀⢀⠌⠌⠀⠀⢀⠙⢆⣀⠊⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄⠀⢀⣁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⠥⠬⠤⠄⠀⠀⠀⠀⠀⠀⠸⠴⠂⠈⠐⠤⠤⠎⢀⣤⠄⠠⠤⠴⠒⠀⠀⠒

⠀⠀⠀⠀⠀⠀⢀⠀⢀⣱⣴⣴⢛⣋⠐⠒⠢
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⠿⣭⡉⠉
⠀⠀⠀⠀⠀⠀⠀⡟⠈⣾⡗⣌⣷⡈⠙⠈⠀⠀⢀⣰⣿⠋⣓⠀⣠⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠶⢻⡇⠈⢻⠙⠠⠀⠀⠀⡾⠁⢻⣷⡌⠸⢳⠏⣦⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠑⢤⡀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠎⠉⠠⢄⠀⠀⠀⠀⠉⠒⠦⢄⡀⠀⠈⠑⠦⡀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⠺⡞⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀⠀⠈⠓⢄⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢦⣀⠀⠙⢶⠀⠾⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢐⠤⡹⣧⣠⣄⡈⠶⣬⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⡤⠖⠋⠉⣀⠀⠚⢑⠻⣮⡾⠛⠓⠾⣧⡘⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⣹⢀⣴⠡⠜⡉⣤⣦⣾⣷⣿⣿⣿⣶⣄⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠖⠟⠳⠿⠿⠾⠷⠷⠛⠁⠁⠀⠀⠐⠀⠐⠈⠁

⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⢀⡀⢸⡇⠀⣀⣴⠆⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⢸⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇
⠀⠀⠀⣸⣟⠚⣿⣿⢷⠀⠀⠀⣤⠿⣤⠀⠀⠀⢀⣬⣯⣄⠀⠠⠁⢸⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠟⣦
⠀⠀⢸⣿⣿⣷⣿⡇⠘⠀⠀⢠⠇⠶⠻⡆⠀⢠⠞⢻⣿⠉⠋⠃⠀⢸⣿⠀⠑⡄⣤⣀⡀⠀⠀⠀⠋⡇⠀⢻⠑
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⠀⢠⢓⡿⣿⡿⠟⠀⠀⠀⣳⣾⡏⠁
⠀⠀⠈⠙⠉⠹⠹⠀⠀⠀⠀⠀⢱⢲⡆⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⠸⠟⠀⠈⠉⠀⠈⠙⣾⡆⠀⠀⢿⢸⠃⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⣠⣤⠀⠀⣠⠶⠋⠀⠰⣶⠀⣼⣿⠀⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⢀⣻⣃
⠀⠀⢀⣼⣯⣬⢿⡙⠂⠀⠀⣿⣿⣷⣿⣿⡇⠀⢺⣿⣿⣿⣿⡀⠀⠰⠆⠀⣨⣯⣤⣀⣶⠀⠀⢠⡾⢻⣿⡿⣦⣸⠁
⠀⠐⠏⢿⣿⠻⠏⠀⠀⠀⠀⢿⣿⡿⠟⠛⠃⠀⠀⢻⣿⣿⣿⡇⠀⠀⠐⠚⠙⣿⡇⠀⠀⠀⠀⠋⢲⣾⣿⡧⠈⠿
⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢠⡶⠛⠻⣷⡀⠀⠀⠀⠈⢻⣿⡇
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⢸⠿⡇⠀⠀⠀⠀⠀⠀⣿⢻⠇⠀⠀⠀⢀⣾⡇⠀⠈⣿⣧⡄⠀⠀⠀⢹⢻⡇
⠀⠀⠀⠃⠀⠃⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠋⠘⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⢰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⡀⠀⠀⡄⠐⣆⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣷⣴⠀⠀⣼⣷⣶⣶⣯⣀⣄⣴⣦⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢦⡖⠋⠀⠀⠀⢈⡁⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠠⡎⠀⠀⠀⠀⣵⠄⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠘⣷⠀⠀⠀⠀⠀⠃⣿⠀⢇⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠉⠀⠈⠀⠀⠃⠀⠉⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⡰⠀⠀⠀⢼⡧⠀⠀⠀⡄⠀⣿⡂⠀⠀⠀⠀⠀⠀⠈⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣟⣽⡄⢂⠀⢀⡐⣼⡷⣂⡀⢀⠃⣰⣿⣷⠀⠀⠀⠖⠀⠀⠀⠘⡉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠝⡶⢆⣀⡀⠉⠛⠛⠉⢀⣄⡴⣿⣿⡿⠀⠀⠀⠆⠀⠀⠀⠀⢣⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣳⡇⠀⠀⠀⠣⠀⠀⠀⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⡃⠀⢀⣰⣴⡃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠁⠀⣾⣿⣷⡧⠄⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠿⣄⡀⠀⣀⣀⣠⠶⠟⢋⣶⣩⣧⣾⣿⡯⠬⠁⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣀⠀⣼⡿⢻⠏⠉⠁⠀⣰⡿⠿⠿⠿⢏⠏⣰⠂⠰⢆⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠮⠴⠤⠴⠋⠀⠦⠴⠤⠼⠴⠋⠀⠀⠀⠀⠛⠒⠛⠓⠒⠋⠉⠁

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠘⠉⠉⠂⠀⠀⠀⠀⠀⡄⠀⢀⡄⠀⠀⠀⠀⠸⠿⠟⠃⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠠⠶⠶⠄
⠀⠀⠀⢀⡀⢤⣴⢄⠀⠀⠀⠀⢀⠠⣶⣾⢃⠀⠀⢀⢘⡮⣶⣴⢄⠀⠀⠀⠀⠀⢐⣶⠀⠀⠀⠀⠀⠀⠀⢠⣠
⠀⠀⠀⣿⠇⢰⡏⢹⡅⠀⠀⠀⣼⣆⡿⠁⣾⠀⠀⠀⠀⢘⠻⡟⢻⠀⠀⠀⠀⠐⢋⣿⡙⠂⠀⠀⠀⠀⡀⠘⡇
⠀⠀⠀⠀⠘⠐⠃⠺⠃⠀⠀⠀⠀⠚⠀⠀⠿⠀⠀⠀⠀⠈⠒⠓⠚⠀⠀⠀⠀⠸⣟⣛⣻⠏⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠘⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⢉⠀⠀⠀⠀⠀⠸⠛⠛⠂⠀⠀⠀⠀⠐⠟⠛⠉⠀⠀⠀⠀⠀⠀⠛⠉⠓
⠀⠀⠀⠁⠄⠐⡞⠀⠀⠀⠀⠀⣠⡾⢶⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣶⣷⡄⠀⠀⠀⠀⠀⠄⠀⡠
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⠿⣿⡾⠟⠛⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠠⠝⠀⢡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠈⠒⠁

⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⢀⡀⣉⡇⠀⠀⠀⠀⠀⣆⠈⣩⠀⠀⠀⠀⢀⢧⣀⣨⡃⠀⠀⠀⠐⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠐⢳⡇⠀⠀⠀⠀⢀⣯⠉⠉⡧⡀⠀⠀⠀⠀⠞⠔⢑⠂⠀⠀⠀⠈⠁⢈⠀⠉⠀⠀⠀⠀⠀⠐⡖
⠀⠀⠀⣆⣀⣀⣾⠁⠀⠀⠀⠀⣸⠈⣄⡔⢻⡁⠀⠀⠀⠰⢈⠧⠈⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠈⠉⠁⠉⠁⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠳⡄⠀⠀⠀⠀⢸⠁⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠂
⠀⠀⠀⠀⠀⠲⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣌⠢⡀⠀⠀⡾⢶⣤⡀⠀⢸⠀⠀⠀⠀⠀⡠⠔⠈⢠⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣍⠑⠒⠤⣀⠀⠀⠀⠀⠀⠀⡇⠚⢉⣁⡀⠈⣢⣞⣀⣠⢤⣁⣀⠀⠣⣀⠠⠐⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠉⠙⠒⠢⠤⠤⢃⡜⠉⠀⠀⠉⠳⣴⠋⠀⠀⠀⠈⢻⡙⠒⢤⡀⠀⠀⢠⠃⠀⠀⠀⣀⠤⠐⠒⠈⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⢀⡴⢻⠁⠀⠀⠀⠀⠀⠘⡄⢀⣀⠀⠀⠀⢣⠀⠀⠈⠳⣄⠺⠤⠐⠂⠉⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢠⠎⠀⢸⡀⠀⠀⣖⣆⠀⠀⢳⢰⣿⡆⠀⠀⢸⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠕⢠⠇⠀⠀⠀⢣⡀⠀⢿⡿⠀⠀⣾⡀⠛⠁⠀⣀⠞⠀⠀⠀⠀⠀⡄⢣⠀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠲⠶⣒⡈⠉⠁⠀⠀⡸⠀⢤⠀⠀⠀⠙⠦⣤⣤⠴⠚⠀⠈⠙⠋⠉⠁⠀⠀⠀⠀⢀⠘⠀⠀⡇⠑⠢⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⡀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢸⠀⠀⠀⢀⣀⠬⠵⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠇⢡⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⢸⢠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠸⡀⠀⠀⠸⡀⠀⠒⠀⠤⠤⠠⠤⠀⠐⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠤⠖⠉⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⣀⠔⠊⠁⢀⣀⣀⠤⠤⠤⠀⠒⣦⠈⢧⠀⠀⠀⠀⠀⠁⠀⠦⠀⣀⡀⠴⠔⠊⠁⠀⠀⠀⠀⠀⢀⡴⢁⠤⠀⣀⡀⠀⠀⠀⠀⠑⠢⣀
⠀⠰⠞⠒⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⡴⠁⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠘⢆⠀⠀⠀⠉⠉⠁⠒⠂⠤⠤⢑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣀⠠⠄⠒⢌⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢁⡤⢄⣀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠗⠊⠉⠀⠀⠀⠀⡆⠀⠀⠈⠉⠓⣒⠲⠲⠶⠖⠒⣋⡉⠀⠀⠀⠀⡁⠀⠀⠉⠒⠤⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡴⠋⠀⢇⠀⠀⢀⠜⠀⠙⣄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡴⠋⠀⠀⠀⠘⡀⢀⠎⠀⠀⠀⠈⢢⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡠⠊⠀⠀⠀⠀⠀⠀⣇⠎⠀⠀⠀⠀⠀⠀⠱⡀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧

⠀⠀⠀⠤⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠥⠤⡀⠀⠈⢢⠀⠀⠀⠀⠀⠂⢀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⢀⣀⣀⡀
⢀⠂⠀⢀⠀⡀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠈⡆⠀⠈⡇⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢾⠋⠁⢀⣍⠉⠒⣄
⠘⢄⣀⡠⠄⢄⣀⡠⠃⠀⠀⠠⠀⠀⠀⢀⠇⠀⢀⠇⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠁⠸⣄⣀⡾
⠀⠄⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⠲⠖⡁⠠⠔⠀⠀⠀⠀⠘⠀⠀⠁⠐⠁⠀⠚⠀⠀⠀⠀⠠⠀⠀⢀⣠
⠀⠑⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠈⠐
⠀⠀⠀⢢⢀⡤⠁⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠁⠂⠀⠀⠀⠀⠀⠀⣀⠤⠒⠲⢄⠀⠀⠀⠀⠀⠂⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⢇⠀⠀⠀⠀⢄⢐⣦⡈⡠⡆⢠
⠀⣤⣤⣤⣤⣄⣀⣤⣤⣤⣤⡄⠀⠑⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⣠⠇⠀⠀⠐⢖⠞⠁⠀⠈⠱⣆⠆
⠀⠸⣿⣿⣿⡟⠹⣿⣿⣿⡟⠀⠀⠀⠀⠑⣄⠀⢠⠁⠀⠀⠀⠀⠀⢹⠉⡉⠈⡽⠀⠀⠀⠀⢃⡼⡀⠀⠀⠀⢀⠧⠐
⠀⠀⠈⠛⠋⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠈⠢⠎⠀⠀⠀⠀⠀⠀⠀⡇⢀⢠⠃⠀⠀⠀⠀⠈⣨⢩⣢⠤⣔⠎⢁⠁
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⠀⠀⠀⠀⠘⣄⡏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠈⠁
⠀⠀⠠⣼⡄⠀⢡⠉⠂⠀⠀⢀⣴⣶⣶⣶⣶⣶⠄⠀⠐⠋⠀⡆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⢁⠀⠀⣠⠁⠀⠀⠀⠈⢦⠂⠀⠀⠐⠐⠃⠀⠀⠀⠀⠀⠀⣴⣾⣷⣦⣀⣹⣦⡀⠀⠀⠀⠀⢰
⠀⠀⠀⠌⠀⠀⢻⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠰⠀⠀⠀⠀⢀⠀⣼⡿⠟⠋⠉⢁⣦⠉⠁⠀⠀⠀⠀⢸
⠀⠀⠀⡀⠀⣀⡼⡀⠀⠀⠀⠀⠸⠀⠁⠈⠀⠂⠀⠀⢐⠨⠊⠀⠉⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⣸⠀⠀⠀⡀
⠀⠀⠀⠈⠘⠓⠈⠀⠀⠀⠀⠀⠀⠁⠐⠐⡈⠅⠀⠔⠁⠀⠀⠀⠀⠀⡀⢀⣾⣿⣿⡷⠀⠀⢠⣤⣶⣿⣤⣤⣴⣿⡄
⠀⠀⠀⠠⢀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠘⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉

⣤⣤⣄⣀
⣿⣽⣿⡿⣿⣶⣦⣄⣀⡀⠀⠀⠀⠀⣀⣠⣤⣴⢶⢾⣿⣻⣿⣷⣿⣿⣶⣶⣤⣄⡀
⣮⣽⣟⣿⡏⣿⣟⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣷⣤⣀
⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⢯⢏⢛⣡⣴⣶⣶⣤⣤⣽⣿⣿⣿⣷⣤⣀
⡛⠿⠿⣿⣿⣻⠿⡿⣿⣿⣿⣿⣿⣟⣿⣿⠛⣲⡦⣀⣁⣭⢷⣾⣿⣿⣿⣿⣋⣿⣿⣿⠌⢟⣿⣿⣿⣷⣦⡀
⣿⣿⣿⣾⣿⣷⣼⣗⡿⣿⣿⡿⣿⡑⠖⣊⢝⢿⠅⣿⣾⣥⣤⡰⣿⣿⡻⣿⣿⡿⢛⠻⢇⣀⣼⣿⣿⣿⣿⣿⣦⣀
⠟⢛⣫⣿⡭⠽⣛⣞⣵⣿⣿⣿⣷⣵⣾⡧⣺⣿⣿⣷⣿⣿⣿⣗⠈⠛⠛⠶⢒⠂⢀⣤⣠⣾⡿⣿⣿⣻⡿⣿⣿⣿⣷
⠉⠉⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⢃⠿⣯⣴⣿
⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡜⠁⢈⠀⠈⣿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠳⠟⠛⠋⣽⣿⣿⡻⢻⡞⠐⢁⠄⡀⠰⠏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣻⠙⠻⠟⠿⣾⣏⣀⣤⡖⣰⢏⣿⡾⣿⣿⣾⣵⣟⣯⣾⡞⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣃⣀⡀⠀⢀⡠⠉⠀⠒⠂⠋⠀⢠⣱⠿⠻⠛⠟⠟⠛⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣚⣿⢉⣔⣀⡀⣀⠀⣠⣤⣰⡟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⡿⣹⣿⣻⡿⣿⡟⠛⠀⠁
⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡂⣹⡿⣿⢽⣛⠛⣐⡉⡨⠛⢳⣸⠀⠀⠈
⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣹⣤⣭⣷⡈⢩⠙⠀⠀⠠⣄⣭⠄⠀⠂
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠿⡗⠀⠀⠒⠂⠀⠠⣷⡏
⣿⣿⢿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⣝⠀⠀⠀⠀⢀⣦⣽⠁
⣿⣿⣿⠩⣿⣳⡻⣉⣛⢛⠻⠿⣏⡿⣿⣿⣿⣿⡻⢯⢣⡄⠀⢀⣿⡿⠋
⣿⣿⣯⣽⣨⠟⠳⠤⡤⢤⡄⠀⢸⡧⠑⢿⣿⣿⣧⡀⢶⠄⠂⣾⣿
⣿⣿⣿⢿⣮⠻⣆⢴⢐⢀⣡⢻⡈⠙⠀⢺⣿⣿⡟⡛⠁⢠⣴⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡘⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢸⠙⡄⠀⠀⠀⠀⠀⠀⠀⢠⠇⡇⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠘⡀⢳⠀⠀⠀⠀⠀⠀⢀⡞⢰⠃⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡇⠘⡄⠀⠀⠀⠀⠀⡼⠁⣸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢳⠀⢳⠀⠀⠀⠀⢠⠇⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⠀⠀⠀⠀⠘⡇⢸⡀⠀⠀⠀⣸⠀⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡇⠀⠀⠀⠀⠀⢻⢸⡇⠀⠀⠀⣟⠀⠀⣇⠀⠀⠀⠀⡔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⠀⠀⠀⠀⠀⢸⠨⡇⠀⠀⠀⡟⠀⠀⢿⠀⠀⠀⢰⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣃⠀⠀⠀⠀⢸⠄⡇⠀⠀⠀⣿⡀⠂⢸⠀⠀⢠⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⣀⡀⢸⣆⣇⠀⠀⠀⣿⢧⣆⣼⢠⣦⢟⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣵⣮⣻⣻⣉⡉⠘⠳⠾⣏⣻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢛⠩⡑⠙⠫⠄⠀⠉⠁⠑⣌⠹⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⡜⠁⠀⠀⢡⠀⠀⠀⠀⠀⠀⠆⣱⣄⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⣿⣿⠣⡀⠀⠀⠠⠀⠀⠀⠀⠀⡼⣿⣿⢹⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠻⣿⣿⠔⠉⠀⠀⠀⠶⠀⠀⠀⠀⠑⠿⢿⠿⠁⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠓⠦⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡀⠀⠀⢀⡀⠀⠘⡁⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⡰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠾⠔⠀⠀⡬⢀⡀⠘⢿⣕⡒⣨⡴⠂⠀⠀⢱⠀⠀⢀⣈⣁⣦⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⢷⣶⣶⣐⣣⢷⠤⠤⣀⠀⠈⠹⠉⠀⠀⡀⡀⣼⡙⣃⠀⡐⣶⡗⠀⠤⠀⠤⠄⢀⡈⠉⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠤⠀⠒⠈⠻⣿⣷⣿⣿⣆⣀⠀⢀⡤⠚⠲⢤⣀⣠⠄⣠⢤⣀⣆⣥⠟⠉⠀⠂⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⢷⣍⣁⣀⣀⢀⣀⣠⣤⣾⠿⠷⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡙⣾⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡌⣷⣴⣷⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠻⢻⣿⡿⣷⡆⠀⠙⢶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠈⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣧⣀⣀⡀⠀⠀⠸⠿⠯⡃⠈⠉⠛⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⡿⠋⠀⢈⡁⠀⠀⠈⠛⠆⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡂⠀⠀⠀⢙⡋⠀⠀⠀⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⠷⢶⣤⣾⣷⣤⡦⢄⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⢿⡿⢿⣿⠿⢿⢿⠟⠋⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡏⠀⠈⠀⣠⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣇⢀⠀⠀⠀⠀⠑⠺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣆⢀⠀⣤⠆⠀⠈⠀⠀⠀⠀⠀⠆⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠙⢿⣿⣿⣵⣴⡏⠀⠀⠀⠀⠀⢀⣴⣀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠈⣿⣿⣿⣿⠇⠀⠀⠀⣦⣠⣼⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠘⢿⣿⣿⣦⠀⠀⠀⠈⢹⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⠿⢿⣄⣀⡀⠠⠼⠟⠛⠛⠲⠔⠂⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠦⣅⠀⠀⠀⠀⠀⠂⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠦
⠀⠀⠀⠀⣀⡀⠀⢀⢀⣇⡈⢙⢣⢂⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣌⢣⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⣹⣷⡀⠼⢾⣯⠟⠛⢛⣛⡭⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡃⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⢰⣿⣿⣧⢠⣠⠿⠠⢽⣿⡁⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⢶⡖⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⠈
⠀⠀⠀⢸⣿⡏⣧⢺⣷⣿⡀⢿⣦⣾⣟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠐⠋⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠰
⠀⠀⠀⠈⢿⡁⠻⠿⢿⠟⢿⣤⣿⡦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡐⠂⡀⠀⠀⠀⠊⡄⢧⡀⠀⠂⣐⠉
⠀⠀⠀⠀⢈⣷⣀⠀⠻⡟⠃⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢂⠀⠂⠀⠀⠀⣁⡄⠸⣆⠈⡅⣘
⠀⠀⠀⣰⣿⡷⣿⠳⡶⣶⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠆⣀⣠⣾⣿⣷⠎⠋⣸⠷⢋⡀
⠀⠀⢸⣿⣿⣷⡀⠉⣶⣿⡄⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣄⣀⣀⡀⡀⠈⠻⠟⠛⠃⠎⡉⠈⠉
⠀⠀⢸⣿⣿⣿⣿⡆⢹⣿⡄⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡉⢁⡤⣤⣤⣤⣤⣶⠛⠄⠀⠐
⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣷⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠈⢻⣿⣿⣶⣄⣌⠛⠋⠋⠠⠠⣄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠈⠉⠛⠉⠉⠉⠁⠀⠁⠀⠉
⠀⠀⠈⠉⠉⠉⠙⠋⠉⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠠⣶⣤⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣷⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⣽⣿⣿⡿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⣤⣞⡋⠁⢸⠏⢸⡟⢿⡄⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣩⣿⡟⣮⠻⡄⠈⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠀⠹⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⡴⢒⣖⣒⡂⢥⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⣀⣤⣽⡝⢻⠁⢩⣟⣿⣿⣷⣬⣄⡀
⠀⠀⠀⠀⠀⢀⣩⣽⣿⠿⠛⠋⠉⠉⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠟⠻⠿⠟⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠈⠛⠟⠥⣤⠀⠒⢲⣾⣿⣿⣒⣒⡒⠲⠶⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⢿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂

⠀⠀⠀⢀⠄
⠀⠀⠀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠉⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣗⣿⢆⢠⣿⣶⣇⡀⠂⡀⢠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠃
⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣄⡀⢈⠐⢿⣿⣿⣿⣷⡀⠀⡀⢤⢄⠀⢀⣠⣾⣷⣄⠀⠀⠐⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠃⠀⠀⡀⠀⠀⣎⣠⣤⣢⣽⣿⣿⣿⣿⣿⣼⣿⣞⣿⣰⣶⣿⣿⣿⣿⣿⣿⡟⡀⠀⠀⠀⠀⢀⠀⢢⠀⢀⡊
⠀⣠⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠐⠀⠀⠀⢳⣄⣸⣷⣻⣿⢋⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⡄⠀⡀⠀⣆⡘⠂⡆⣷⡾
⠀⠧⡞⠀⠀⠀⠀⠀⠀⢢⠈⢷⣅⠀⣛⢌⢢⣧⣌⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣷⣼⡇⣦⣸⣇⣰⣿⣿⣧⣶
⠀⠸⡧⠀⣄⠰⡀⠑⢠⢸⣾⣼⣿⣿⣿⡿⣿⡿⣿⣯⣿⣿⣿⣿⣿⢿⣿⣿⡟⣿⣾⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⣿⣿⣿⢿⣏⡆
⠀⠀⠉⠀⠀⠀⠉⠀⠀⠙⠃⠋⠻⠛⠘⠙⠁⠉⠁⠃⠈⠙⠋⠃⠙⠛⠙⠛⡟⠏⠉⠁⢻⡟⠘⠛⠏⠙⠉⠙⠛⠈⠛⠋⠙⠁⠉⠉⠙⠁⠁⠈⠛⠈⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠞⠁⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢻⣇⣤⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⢿⠷⣤⣴⡞⢿⣿⣿⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⡿⢁⠀⣼⣿⣄⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⡿⢿⣿⣟⣿⠃⠁⣀⠙⣿⣿⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠙⠉⠁⠈⢹⣿⡏⢀⣾⣿⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠸⣿⣿⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡄⠀⠀⠀⠀⠺⣿⠁⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠘⣝⡈⠋⣾⣷⡆⠀⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢶⡈⠻⠟⣁⣼⣿⡟⠶⢤⣤⣤⡁⠀⠀⠰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡸⢿⣿⣿⡿⠿⠓⠀⠀⠀⠺⡿⠟⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠍⠥⠀⠀⠂⠀⢀⣀⣀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⠲⣆⣽⣿⣿⣿⣿⣧⠠⠈⠁⠀⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡇⠀⠹⠛⢛⣙⣽⣧⣿⡽⣻⠿⠟⠂⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠟⠿⠻⣿⠛⠏⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠈⣿⣮⢻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠃⠀⠀⠀⠀⠘⢻⡏⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣴⠛⠚⠿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣆⠀⢻⡅⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠈⠀⠈⡇⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡀⢸⡀⠁⠀⠀⡼⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠱⢸⡇⡀⠀⠀⣥⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⢼⠀⡁⠈⢿⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⣀⡀⠹⣆⠀⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⢻⣷⣦⣠⡌⢿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣴⡇⠿⣿⣟⠘⢓⣾⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠱⠟⠋⠛⠻⣏⠁⠀⠉⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣠⣠⠶⠀⠀⢰⡤⠿⠶⠤⢤⠤⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢾⣿⣯⣾⣿⠃⢘⣠⡶⣄⢀⠤⠖⠋⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠩⣥⣀⡛⠛⠋⠁⠀⢠⠀⠀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠋⣘⠯⠁⡰⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢻⠀⠈⠙⠇⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢄⠀⠂⠠⠄⠘⠂⠲⠀⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⣸⣇⢈⠁⠀⠀⠰⡆⠀⠀⠀⠂⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢻⣿⡈⠀⠀⠁⠠⣿⠀⠀⢀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡼⣻⢷⡄⢿⡁⠀⠠⠀⠀⣿⣿⣁⠀⠀⠀⠘⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠈⣥⠋⠀⢷⡈⢷⠔⠀⠀⠀⣿⣿⡟⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⢈⣶⡀⠀⠁⠘⣤⠴⠂⠀⣿⡿⢳⢠⡜⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠹⢻⡄⠀⠀⢹⡁⠀⠀⡋⠀⠀⡇⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠉⣀⣤⠌⢀⡀⠀⠁⠀⠀⠀⠀⠀⢏⣄⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡵⣶⠇⡠⡴⠞⠑⣰⠈⡀⢠⠀⠀⠀⠀⠀⠀⠀⣠⣾⡴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠙⠃⠉⠀⠀⠀⠁

⠀⠀⠀⠀⡠⣀⡀⠀⠀⠀⣀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⣀⠀⠀⣠⡄
⠀⠀⠀⠀⠱⠕⠃⠀⠀⠀⢆⡼⠁⠃⠀⠀⠀⠠⠡⠁⠐⢀⣀⠤⡠⠀⠀⢬⡳⣀⢇⠇⠀⠀⣖⢆⣸⣿
⠀⠀⠠⠤⡄⠠⠒⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠙⠟⠂⠈⠀⡈⠜⠀⠈⠙⠄⠀⢀⠜⠛⠓⠇
⠀⠀⠈⠲⣈⡶⡤⡁⠀⠀⡀⢸⢓⠀⠀⠀⠀⠀⠔⠀⠠⡄⠀⠀⠀⠀⢀⠆⠀⠀⠠⡂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠤⠀⢸⣄⠀⠀⠂⠶⠄⠁⠀⠀⠀⠀⠸⢄⣀⠀⠘⠀⠀⠘⡀⠀⠀⠎
⠀⠀⠀⠈⠀⠀⠖⠀⡀⠀⠀⠀⠘⣧⠀⣟⠀⠀⠀⡀⢤⢀⢠⡀⣀⡄⢀⠀⢀⠀⠀⠀⠀⠀⠢⠤⠦⠞
⠀⠀⠀⠈⠂⠀⠰⠀⠈⠀⠀⠀⠀⣿⠀⠀⣷⠿⠷⠁⡸⠈⠸⠏⠡⡇⠘⠚⠿⠃⠀⡀⠀⠀⢠⣄⠀⡔⡢
⠀⠐⣄⡀⡤⠀⡀⠀⠀⠀⠀⠀⠀⣿⣄⣰⠟⣼⠃⢸⠁⠀⢠⡐⠘⠁⠀⣼⠀⠀⠀⠌⠔⠀⠹⡨⠷⠤⡅
⠀⢠⢎⣹⠀⠀⠐⠂⠀⠀⠀⢤⡄⠀⠈⡁⠀⢿⠀⢿⡘⠗⡗⠃⠿⢆⡆⣇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢄⠀⠀⠀⠈⠀⠈⣴⣂⣴⢛⡞⠀⠈⠁⠀⠀⠀⠁⠄⠀⠀⠁⠈⠀⢦⠲⣼⣩⠀⠐⢤⡶⠄⢲⡀
⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠰⠁⠁⠈⠫⠠⢶⠀⠀⢀⠀⠀⢀⡔⢅⠀⠀⠀⠀⠀⠕⠋⠋⢂⠀⠘⠀⠂⠀⠁
⠀⠀⠀⡎⠲⣲⠀⠀⠀⠀⡥⠀⠀⠀⢠⠀⠀⠀⠀⠛⠿⠂⠙⠰⠁⡀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⡠⡄
⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⢠⠀⠀⠀⣰⠁⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⡄⠀⠀⠀⠁⠸⠴⠀⠀⠀⢔⣁⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠂⠁⠀⠀⠀⠀⠀⠀⠁⠓⠀⠀⠈⠀⠀⠀⠀⠈⠈⠀⠁

⠀⠀⠀⣀⡀⠀⢠⣄⠀⢠⣤⠀⠀⣠⣠⡄⠀⠀⠀⢴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡠⠄⠲⣶⠄
⠀⠀⣰⣓⣲⠀⢻⠈⢧⣼⣿⠀⢸⣏⠀⣻⠂⣴⡖⠚⠛⣿⠟⠳⢶⣶⡀⠀⢸⢿⣿⡅⠀⠀⠂⢀⣴⢭⣲⡚⠛⢛⣶
⠀⡘⣿⠈⠀⠀⠈⢧⣼⠿⢿⣤⡈⠉⠛⠉⠀⠀⠉⠉⠙⡿⢸⣿⠯⠟⢋⠀⠈⠙⠂⠀⠀⡟⢂⠺⠿⠧⠇⡟⠉⠉⣁⣄
⠸⠎⢛⣾⠀⠀⠀⠸⢳⣿⡆⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣥⣀⣀⣀⣠⣬⣶⡆⠀⠀⠀⠀⠈⠀⢀⠀⠀⢔⠛⢟⠋⠙⠏⠄
⠀⠀⠈⠁⡶⣢⣤⣤⡀⠈⠁⠀⡸⠃⠀⠀⠀⠀⠀⠀⠸⠈⠻⠟⠋⠈⡿⢻⡶⠀⠀⠀⠀⣀⠀⠀⡀⠀⠘⠃⣇⢰⣿⡟
⠀⠀⠀⠸⣼⣿⡟⢿⣍⠛⠻⠇⠀⠀⠀⣴⢶⠀⣀⡀⢠⣀⡀⠀⣀⣀⣇⣸⠇⠀⠀⠀⠀⢿⣷⣔⠁⠺⠍⠶⠥⠭⠽⠁
⠀⠀⠀⠀⢻⣿⠇⢾⡿⢀⡀⢄⠀⠀⢸⠃⣸⣿⡿⠁⠘⠛⠋⠉⠛⠋⠙⠛⠀⣀⡀⠀⠀⢈⣹⣿⢦⣤⡶⠚⢋⣻⠃
⠀⠀⠀⠀⠈⠁⠈⠉⠁⠉⠁⠁⠀⢀⣦⣭⣍⠉⢀⠀⠀⣰⡾⣏⠷⣄⠀⢰⢤⡿⠁⡀⢀⣾⣿⢱⣶⡘⢿⠋⠉
⠀⠀⣠⡲⡶⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣫⢇⡀⠀⠀⢿⣭⢻⣹⡇⠀⠈⠡⣭⠆⠀⠈⢏⠩⠈⠉⢀⣐⣀⡀⢤
⠀⠘⠟⠋⢁⠀⠀⠀⠀⠀⢸⣷⡆⠔⣄⣀⣀⣘⠿⠋⠀⠀⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⣞⢋⣿⢿⣿⣎⡀
⠀⠀⠀⠐⢫⣤⣺⡄⠀⠀⢶⣾⠑⣶⠈⠙⣿⣿⠄⠀⠀⠀⠀⠀⠀⢠⣦⢄⠀⠀⠀⠀⠀⠀⢣⠀⠛⣿⣧⢸⣿⡿
⠀⠀⠀⠸⠯⢀⡀⠀⠀⠀⠘⡷⠿⡛⣤⠔⣿⠟⡄⠀⠀⠀⡨⢭⡆⠀⠛⠿⡷⠀⠀⡀⠀⠀⠓⠘⠓⠘⠓⠂⠘⠃
⠀⢠⢶⠀⢐⣓⣺⡀⢫⣇⣤⠀⠀⠉⠁⠈⠁⠀⠀⠀⡴⣬⠙⠟⠉⣤⡄⠀⠀⠀⢈⣷⡄⣀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠢⡄
⠀⣤⡾⢦⣤⠈⠁⠀⣜⡍⠛⠀⠀⢰⣶⣄⡀⠀⠸⡷⣾⠀⠀⣆⠄⢑⣧⣲⡄⠀⢠⣛⣻⠻⣾⡟⠁⠀⠀⠑⠔⣿⣿⢌
⠀⠈⠁⠈⠁⠀⠀⠀⠈⠀⠀⢿⣉⠉⢓⡦⠘⠄⠀⠀⠛⠃⠠⠂⠀⠺⠷⠀⢠⣶⡄⠀⠀⠘⠇⠀⢀⣾⡆⠀⠐⠄⠄⠁
⠀⠀⠀⠀⣀⠀⠀⣴⡾⣿⠟⠀⠈⠙⠣⣟⣽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡴⠛⡟⠀⠀⢸⣿⡇⢀⡤⠶⣦
⠀⣠⣾⣿⣿⡿⣛⡛⣿⣤⠀⠀⠀⠀⡀⠈⠉⠩⢄⡨⠀⠀⠀⠀⠀⢀⣴⣶⠾⠿⣿⡤⠞⠁⢀⠄⣾⠿⢿⣯⡤⠖⠁
⠀⠀⠉⠁⢘⠉⠿⠧⠼⢿⡇⠀⠀⠀⠻⣷⣶⣶⢆⠀⠀⠀⠀⠀⠀⡾⠻⠧⣿⣇⠽⡆⠀⠀⡌⣼⣿⣿⡶⠛⠂
⠀⠸⣷⣶⣶⡦⣀⣀⣀⠐⠁⠀⠀⢸⣤⡙⡟⣡⣴⠆⠀⠀⢀⢿⣦⣼⣍⣀⠀⣀⣠⠁⠀⠀⠱⠄⡂⢀⣀⣴⣤⣤⣻⠂
⠀⢲⣿⣿⠹⣷⡄⠉⠉⠄⠀⠀⠀⡐⡙⠛⠗⠛⠋⣆⠀⠀⠸⣾⠛⡏⠀⠙⠛⠿⢿⡄⠀⠀⠀⢸⠛⠉⢡⣾⢫⣿⣿⡜
⠀⠈⡿⠛⣘⣿⢓⣤⢘⠄⠀⠀⠀⣧⣅⢀⣀⢀⣠⣏⠀⠀⠀⢻⣀⣇⣀⡀⠀⢀⣠⠃⠀⠀⠀⢠⠢⣤⢸⣿⡘⠿⡿
⣀⣀⣠⣀⣄⣀⢀⡀⣀⠀⢀⡀⢀⡉⢉⡀⠀⠈⠉⠉⠀⠀⠀⠈⠙⠉⠛⠋⠉⠛⠛⠀⠀⠀⠀⠀⢀⣠⣄⣀⡁⣀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣾⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⡀⠈⡄⠀⠀⠠⠀⡠⠆⢀⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠄⠀⠀⠀⠀⠈⠊⠀⠘⠁⠐⠀⠀⠀⢈⠀⠈⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡖⠠⠤⠀⠠⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠀⠢⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⡀⠘⠂⣾⣿⣿⣿⣿⣿⣶⠀⠂⢂⣤⣤⣤⣀⡒⠀⠀⢁⠂⠄⡀⠀⠘⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⡠⠲⣹⣿⣿⣿⣿⣿⡿⣠⡀⣾⣿⣿⣿⣿⣿⣿⣶⢀⡟⠀⠌⠂⡀⠀⠀⠀⡠⢁
⠀⠀⠀⠀⠀⠀⠒⡂⠀⠂⠀⠠⠊⠀⠀⠙⠿⣿⣿⡟⠉⠀⠁⠁⠻⣿⣿⣿⣿⣿⣿⢋⠞⠙⠢⢄⡀⠈⠁⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠠⠈⠀⠀⠉⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠮⠭⠿⠭⠖⠁⠀⠀⠀⠀⠉⠲⢄⣀⣤⠁⠀⣀
⠀⠀⠀⠀⠀⠐⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠁⠋
⠀⠀⠠⢆⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠋⠐⢄⠀⡀
⠀⠀⠄⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⢂⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄
⠀⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⢠⠊⠀⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⠠⠄
⠀⠀⠠⠀⠁⠀⢀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠡
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⡀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠑⠀⢀⠃⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⣁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⢀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⢀⠀⢨⠀⠀⠠⠌⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢠⠀⠀⠀⢀⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⡀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠂⢀⠠⠇⠀⠠⠒⡀⠀⠀⠜⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠈⠐⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠇⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢸⠀⡏⢠⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠁⣀⣀⣀⡀⠀⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠊⠀⠀⠀⠈⢢⠀⢁⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢸⠀⠀⣀⡀⠀⡸⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠉⠑⠤⠤⡑⠤⠤⠤⠖⠁⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⡀⠀⠀⠀⠀⢀⠤⠠⢀⠔⠚⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⠢⠖⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠲⢤⠞⠁⣀⠴⠒⠒⠒⠲⢀⡴⠚⠉⠀⠈⠉⠓⢄⠱⠤⠠⠤⣄⠀⠀⡀⠠⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠊⠀⠐⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠁⠉
⠀⠀⠀⢀⡴⠒⠒⠀⠀⢀⡤⣖⠋⠩⡍⠉⠉⠓⠲⣤⡀⢀⠔⠋⠁⠀⠀⠈⠙⠦⣄
⠀⠀⢠⠏⠀⠂⠀⠀⡰⠋⠀⠃⠘⠐⣇⠀⠀⠀⣍⠁⠛⣎⠀⠀⢀⠄⠚⢆⡀⠀⠘⣦
⠀⠀⢸⠀⠀⠀⠀⠰⠁⠀⠀⠐⠐⠉⠁⠀⠀⠀⠀⠓⠀⢸⡀⠀⠈⠢⣉⠔⠁⢀⠀⢸
⠀⠀⠸⡄⠀⠀⠀⢀⠀⠀⣀⠀⡀⠀⠸⡄⡄⠀⡀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⡼
⠀⠀⠀⠙⢦⣄⡀⠸⡄⠀⡆⢂⡑⠀⠀⠣⠂⠈⠁⠀⠀⡼⠀⢤⣀⣀⣘⣑⣠⡶⠚⠁
⠀⠀⠀⠀⠀⠀⣄⠀⡙⢦⡙⠃⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⡀⢰⠀⢈⡭⠁
⠀⠀⠀⠀⠀⠀⠘⡆⠃⡴⠈⣝⠒⠒⠒⠒⠂⡀⠀⠀⠀⠀⢱⠈⢠⡎
⠀⠀⠀⠀⠀⠀⢀⡇⢰⡇⠀⠈⢦⠀⡏⢠⠞⠀⠀⠀⠀⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⡸⠀⢸⠇⠀⠀⢸⠀⢰⠋⠀⠀⠀⠀⠀⠀⢰⠃⢸
⠀⠀⠀⠀⡤⠖⠒⠒⠶⢄⠀⠀⢸⠀⢸⢀⣄⣀⡀⢀⡤⠤⡼⠀⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡟⠀⢸⠀⠀⠀⠉⠳⠄⠀⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠃⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⢀⡠⠄⡀⠀⠀⢰⠀⢀⡀⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⡔⠁⠀⠀⢰⠀⢀⠜⠊⠁⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠎⠀⠀⠀⠀⡸⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢀⠎⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡄⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢰⠁⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⡄⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠒⠀⠈⠉⠉⠉⠉⠐⠒⠇⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡉
⠀⠀⠀⠀⣃⣀⡀⠀⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⢢⡀
⠀⠀⠀⠰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠈⠁⠒⠂⠤⢀⣀
⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠲⠀⠀⠀⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠊⠁⢀⡨⠃⠀⠀⠀⠀⠀⡌⠀⠀⠀⣀⠀⢡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⡠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡐⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠈⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠤⠀⠤⠔⠊⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠐⠒⠈
⣿⣿⡿⠿⣿⡿⢿⢿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢋⡉⠉⣉⡉⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠅⠀⠽⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⣀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠉⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢢⡀⠀⠀⠀⢀⠇⠸⡀⠀⠀⠀⢀⠔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⢄⠀⠀⡼⠀⠀⢧⠀⠀⡰⠋⠀⡇
⠀⠀⠀⠀⠀⠀⢻⡒⠤⣀⠀⠀⠸⠀⠀⠈⠳⣠⠃⠀⠀⠘⣤⠎⠀⠀⢠⠁⠀⠀⣀⠤⢒⡟
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠙⠢⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠔⠋⠁⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢀⠤⠒⠊⠉⠉⠉⠉⠑⠒⠤⡀⠀⠀⠀⠀⢀⠎
⠀⠘⠳⣒⠒⠒⠒⠂⠤⠵⠀⠀⣠⠞⡡⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠮⠔⠒⠒⠒⠒⣨⠟⠁
⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⡔⢡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⢘⣢⠀⠀⣸⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣔⡁
⣀⡠⠤⠒⠒⠉⠁⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠒⠒⠤⢄
⠈⠉⠑⠒⠤⢤⣀⡀⠀⠀⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⡤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠛⢄
⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠱⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠔⠥⠤⠤⠒⠒⠒⡲⠀⠀⠈⠢⣑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⢖⠒⠒⠒⠒⠤⠬⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⡀⠈⠑⠲⠭⠍⣉⣀⠠⠤⠖⠊⠁⢀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⡜⠀⣀⡤⠒⠉⡇⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⢸⠉⠒⢤⣀⠀⢣
⠀⠀⠀⠀⠀⠀⡼⠔⠊⠁⠀⠀⢠⠁⠀⢀⡔⠙⡄⠀⠀⢠⠋⠢⡀⠀⠀⡆⠀⠀⠈⠑⠢⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⠋⠀⠀⢱⠀⠀⡎⠀⠀⠙⢆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠜⠁⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠱⣤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠤⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢧⣠⡿⠁⣠⣽⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡁⣸⣿⣿⣵⠀⣀⡀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠛⠃⠰⠋⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣺⡟⢋⣠⠼⢿⣿⣾⣿⢗⠝⠋⠁⠀⠀⠀⢀⠴⠿⠿⢛⠁⠀⠠⠖⠟⠉⣧⠐⠎⠓⠀⠀⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠋⡄⡶⣷⣿⣿⣿⣿⢧⡀⠂⠄⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⢰⠁⠀⡘⢧⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣥⠟⢹⡿⢹⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠐⠃⠈⠆⠀⠀⡄⠀⠀⣧⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢼⣧⠌⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣡⠀⠀⢹⡀⠀⡀⠁⢰⠃⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠉⠀⠀⠀⠉⠁⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣧⠀⡀⠀⡞⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠁⢠⠃
⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⣰⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢼⠦⣄⣀⣠⢿⠀⣿
⠀⠠⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠜⠓⠀⠾⢊⡴⢂⣉⣿⡄⣿⡀
⢀⣈⣽⣿⣷⣷⣤⠄⡀⠀⣠⡀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠚⢙⠣⣃⠁⠚⣉⡐⢂⣔⣿⣿⣿⣷⠦⠄
⠀⢴⣿⣾⡿⠽⣿⡧⢹⣿⣿⣿⣿⡤⠀⡼⠙⠁⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣶⣿⣤⣴⣶⣮⣭⣥⣿⣿⣿⢿⣿⣿⢿⡟⠋
⠀⢸⣿⡟⠀⣀⡀⣸⣿⣿⠿⣯⠝⠂⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠻⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣭⢿⣄⠙⠆
⠀⣞⠏⠀⠉⠙⣿⠛⢉⡃⠈⠈⣀⠀⠀⡅⡀⢨⠀⠀⠀⠀⠀⠀⠀⢈⣉⣰⣾⡿⣽⣛⣉⡻⠦⠚⠛⠉⠉⠉⠉⠀⠹⣄
⠚⠁⠀⠀⠀⠀⠠⠀⠉⠀⠄⠠⢅⠀⠀⣧⡇⡈⠀⠀⠀⠐⠛⠙⠷⠿⠯⠶⠶⣿⣇⡱⠯⠻⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣉⡭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣴⣶⣴⣤⣶⣶⣶⣶⣶⣦⣾⣿⠀⣴⣶⣦⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠛⠛⠛⣿⡿⠟⠛⠛⠻⢿⣿⠀⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⡇⢸⣿⠀⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢉⣉⣉⡉⢻⡇⢸⣿⣿⡇⢸⣿⠀⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⢸⣿⠀⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣈⣉⣉⣁⣈⣁⣈⣉⣉⣁⣈⣉⣀⣉⣹⣿⡿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣡⣴⣾⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠆⢀⣠⣴⣾⣿⣿⡟⢉⣉⠙⠿⠿⠿⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⠿⠟⠷⠀⠉⠛⠿⣿⣿⣿⣧⡘⠛⣠⣶⣶⣶⡶⠞⠋⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⢸⣷⠀⠀⠀⢰⣤⣉⠛⠿⣿⣿⡿⠟⢋⣡⣴⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣶⣤⣡⣴⣾⣿⣿⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠖⡀⠀⠐⠂⠤⡀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠑⠄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠉⠁⠀⠀⠈⠁⠀⠓⠠⢤⠂⠀⠈⠁⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⡐
⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⡠⠋⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠑⢄⠔
⢀⠔⠈⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⡰⠟⠛⠛⠛⠀⠀⠀⠀⠙⠛⠛⠻⢦⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡀
⠃⠂⠉⠁⠢⡀⠀⠀⠌⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⡀⠀⣠⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⢡⠀⠁⠂⠀⠀⠊⢀
⠀⠀⠀⠀⠀⠱⡀⠈⠀⠀⠀⣤⣾⣿⢫⠃⣰⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⡏⡏⢉⣷⣦⡀⠀⠀⠃⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⢻⣏⠇⢠⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⡿⡜⠀⣾⣿⠉⠀⠀⠀⢠⠀⢀⠠⠐⠁
⠀⠀⠀⠀⢀⠠⠄⡇⠀⠀⠀⠀⠈⠻⣄⣾⣿⣿⣿⡿⠋⠀⠀⠈⠿⣿⣿⣹⠁⣼⡿⠃⠀⠀⠀⠀⠸⠉
⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⢂
⠀⡔⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠰⣶⣦⡐⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⣠⣶⡞⠀⠀⠀⠀⢀⠂⠀⠡
⠈⢀⠂⠈⠁⠐⠢⠀⢱⡀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣶⡶⠶⠶⠶⢶⣶⣾⣿⠿⠋⠀⠀⠀⠀⢀⠎⠀⠀⠀⠑⠂⠄⠐
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠉⠛⠡⠤⠀⠀⠠⠤⠘⠋⠁⠀⠀⠀⠀⠀⢠⠮⢀⡀⠀⠀⢀⠠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠊⠁⢀
⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢀⠤⠀⠀⠂⠁⠉⠐⠂⠀⠠⠤⠤⠄⠠⠀⠐⢅
⠀⠀⠀⠀⠀⠀⠀⠈⡄⢠⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠑⢄⠀⠀⠀⠢⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠜⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠘⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣐⣬⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠍⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢯⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⠀⠖⠡⠙⠛⠳⢽⣶⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠣⠀⢃⠘⠂⠀⠈⣿⠁⠀⠀⠘⣿⣠⠀⠁⢯⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡰⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠠⣸⣿⣷⡀⠀⠀⡼⠡⠇⠀⠀⠇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣏⢷⣠⠛⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠘⢠⡏⣿⣻⣷⠀⠀⠇⠀⠀⠁⢠⢀⡀⠀⠀⠀⠀⠛⠀⠦⠌⣉⠻⢼⣏⣴⣣⡴⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡿⠀⠹⡟⠃⠀⠈⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣩⡵⢈⣿⣶⣤⡙⣦⣤⣁⠀⠈⣿⠂⢀⠠⢒⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⠶⢾⡏⠠⠞⠈⢿⡈⢻⣸⣇⣙⣧⣴⣼⣿⡏⠶⢭⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⡀⠁⠀⠀⠘⣷⠀⠉⠉⠁⡰⢋⣴⣿⣿⣧⠘⡇⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠹⠆⠀⠀⣟⡤⠋⣸⠛⠟⠘⠷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⢠⡏⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢉⣉⠁⠀⠀⡁⢀⡀⠀⠀⠀⠉⠉⠉⠉⢙⠃⠀⠀⠠⠤⠄⠀⠀⠀⠉⠉⠁⠐⠒⠠⠀⠀⠀⠀⠹⡇⠀⢾⠆⣾⢰⠚⠈⠉⡉⠈⠠⠤⠸⠋
⠀⠀⠀⠠⣤⡀⠘⠛⠻⠶⡶⣡⢤⣴⣷⣶⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⠀⠤⠈⠙⠁⢀⠀⠠⢀⣀⡀⠐⠒⠠⠄⠈⣷⡀⠐⢀⡟⠀⡛⠂⠀⠀⠀⠠⠿⠛⠃
⠀⠀⠀⠀⢴⣟⣩⣤⣶⣆⢀⡤⠀⠀⠈⠉⠁⢀⠀⠀⠀⠀⠀⠀⠛⠀⢤⣶⣆⣥⣄⣀⢀⢀⠀⠀⠀⠁⠀⠀⠙⠃⢙⠈⠂⢸⠃⠀⠶⠶⠶⠒⠂
⠀⠀⠀⠀⢠⣶⣤⡀⠀⠈⠸⣇⠀⠀⢴⣶⣶⣯⣤⣿⢠⢣⣶⡤⠄⡄⠀⠀⠛⠋⠉⠉⠀⠀⠤⠶⠶⣧⣶⣤⣠⣀⢈⠀⢄⣉⠀⢀⠀⣀⡀⢀⣤
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠴⡦⡴⠴⠆⢦⡄⢀⠀⣤⢀⣀⡈⠀⠈⠀⠀⠃⢠⠟⠛⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠈⠁⠉⠉⠁⠀⠀⣦⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠔⣧⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠁⠶⠶⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⣠⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⣹⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⠆


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣻⣿⣿⣿⣿⣋⡁⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢞⠘⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠿⣿⡿⠿⠿⠟⠛⠉⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠷⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣽⡷⣾⣟⣻⣻⣿⣿⡽⣿⢶⣄⠀⣀⠔⠋⠀⠀⠐⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣿⡿⣶⠗⢿⣿⡏⠡⠎⢳⡀⠈⢦⠹⣿⡀⢀⣀⠀⠚⠁⠀⠈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣻⠅⠀⢿⣀⣼⣿⣿⠰⡖⡈⢿⡑⡈⣧⢻⣿⠉⢻⣷⠀⢘⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠤⢸⣹⣇⣾⣿⣿⣷⣆⣘⣿⣷⣷⠿⢺⠻⣦⣿⠿⡚⡟⣧⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀⣿⣖⣸⣆⣿⣿⡿⢿⣿⣏⣿⣭⣿⣴⡾⣿⣿⣿⠛⡄⣃⢡⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢷⣻⣏⣿⣧⣼⣿⣷⣾⣿⣿⢿⡟⣾⣿⣿⢿⡛⣿⡇⢡⠸⠈⡜⡗⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢺⠻⣿⡧⣈⠛⣿⢹⣿⣿⣿⣶⣿⣿⣿⠛⠀⣇⢻⣷⠈⡆⠆⢡⢻⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⡇⠉⢿⣿⣷⣿⡿⢿⣿⣾⡟⠉⠁⢸⣆⣀⣸⣨⣿⣿⣿⣼⡬⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢹⠀⠸⡄⠉⠀⣷⣀⣽⣷⣳⣶⣿⡿⠿⣻⢿⣿⣮⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣏⣦⣤⣷⣾⠿⢿⡟⠛⣿⣏⣽⣿⣶⣾⣿⠟⠁⢸⣿⠉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣽⣿⣷⣿⣷⠾⢿⠛⣉⣉⣥⡇⠀⠀⠀⠀⠀⢸⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣆⠀⠉⠉⠀⠀⠈⣻⣿⣿⣿⣷⣦⣤⣀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⣦⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣟⠛⠟⠀⠈⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠘⠛⠻⢯⣽⣷⡾⠁⠀⠀⠀⢀⣿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣾⣿⡇⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣀⠀⢀⡀⠀⣀⣀⣴⣿⣿⣿⠇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⡿⠀⠈⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠉⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠈⠛⠛⠛⠋⠁⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⢀⣤⡄⠒⠚⠛⠒⢠⣤⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢠⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⢘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣤⡄⢸⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⠀⣤⣄⣤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠘⠁⣸⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀⣾⣿⡇⢸⠀⠿⠀⠀⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣾⡏⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⡇⠈⣿⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠘⠁⠀⠀⠛⠋⠀⠀⠀⠀⣀⡀⠈⠛⠁⠀⠉⠀⠀⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠂⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⠗⠚⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⢀⠟⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠻⣄⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠙⢦⡄⠀⠀⠉⠒⠖⠀⠀⠀⢠⡴⠋⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⠀⠀⠀⠀⠈⢳⣦⣤⣤⣤⣤⢴⡟⠁⠀⠀⠀⠀⠀⠈⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣀⢀⣠⣤⠤⢼⡇⠀⠀⠀⠀⢰⣷⠦⠶⣤⣀⣀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⢉⡾⠉⣿⠀⠘⠃⠀⠀⠀⠀⢀⠇⠀⢰⡏⠻⣉⠑⢦⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠰⡏⠀⠀⠈⣷⠀⠘⢧⡀⢀⣤⠛⠀⢰⡎⠀⠀⠈⡷⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⢸⡄⠀⠀⢠⡄⠀⣠⠟⠛⢧⡀⢠⡞⠁⠀⠀⣤⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢳⡞⠁⠀⠀⠀⢳⣾⠃⠀⠀⣠⠉⠀⠀⠀⠀⠀⠉⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡀⠈⢣⡀⠀⠀⠀⢀⠃⠀⣀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠈⣇⠀⠘⢃⠀⠀⠀⠟⠀⢰⡇⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠃⢸⡄⠀⠀⠈⠳⣄⡸⠃⠀⢿⣀⡾⠋⠀⠀⠀⣿⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢀⡰⠞⠉⠀⠀⠀⠸⠁⠀⠀⠀⠀⠈⠙⢿⣿⠾⠉⠀⠀⠀⠀⢀⠉⠀⠀⠈⠉⢶⡄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⠶⠋⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⡜⠁⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⢿⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⣠⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⣠⠞⠁⠀⠀⠀⠀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⢀⣀⠀⣶⣽⣿⡅⠀⢠⣤⡀⣠⠾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⣿⡟⣿⠟⣍⠙⢦⣈⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡄⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠈⠛⣿⣇⠘⣋⠁⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡈⠉⠁⢈⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠈⠻⠶⠉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⠉⠉⠉⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣤⣤⣤⣤⣤⣴⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠇⢸⠀⣾⠀⣤⡘⠿⢤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠛⠀⠀⢰⠿⠶⠿⠶⠿⡁⠀⠈⢱⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⡀⠀⣀⣤⡀⣿⣄⣀⣴⣧⡀⣄⣤⣄⠀⣽⣤⠀⣤⡦⢄⣤⣤⣄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋
⣯⡀⣀⣀⣀⣀⣀⣠⠶⠖⠶⠶⠶⠖⠲⣶⠶⠖⢶⣄⢀⣀⣀⣀⣀⣀⣸⠛⠛⠛⠛⠿⡿⠛⠛⠛⠉⠛⠉⠀⠀⠀⠀⣠
⣿⠀⠉⠁⠈⠉⠈⠙⠷⠒⠺⠗⠒⠒⠒⠿⠒⠒⠛⠃⠈⠉⠀⠈⠉⠉⢹⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠛⠉⠉⠉⠙⠋⠉⠉⠙⠋⠉⠛⠉⠉⠋⠙⠋⠙⠋⠉⠙⠛⠉⠉⠙⠉⢻⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⠁⠀⠀⢀⣿⣆⠀⠀⠀⠀⠀⠀⢠⣾⡄⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣄⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⠀⠀⣀⣠⣶⡿⠛⠿⠿⠀⠀⠀⠀⠀⠀⠹⠿⠛⢿⣷⣤⣀⠀⠀⠈⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣧
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⠿⠿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡗⠀⠀⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢒⣶⣿⣶⡂⠀⠀⢤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠏⢻⠉⠉⠷⠈⡿⠋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠈⠐⡀⠀⠈⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣾⢿⠓⠀⠀⠀⠀⢠⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⢠⡀⠀⠀⠀⠀⣆⡀⣠⣷⣴⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣶⣽⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠑⠒⠓⠒⠉⠏⠉⠍⠉⢉⡙⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠒⠂⠂⣉⣁⣀⣤⡴⠒⠚⠀⠀⢠⢤⠖⠂⠁
⠀⠀⠀⠀⠀⢀⣀⣀⣢⣤⠤⠶⠶⠶⠾⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠈⠑⣶⣤⢤⠈⠁
⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠾⠿⠛⠛⠉⢀⡸⠀⠀⠀⠀⠀⣀⠔
⠀⠀⣀⠀⠤⠤⢄⡠⠤⠶⠞⣛⣩⣭⣤⠶⠶⡶⡶⠶⠶⢶⢦⣤⣤⣤⣤⣤⠤⢤⡶⢞⣉⣦⠀⣀⠠⠔⠈⠠
⠠⠠⠀⠒⠒⠒⠒⠚⠛⠉⠉⠉⠀⣀⣀⣀⡤⠤⠒⠒⠴⠒⠉⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠉⠀⣦⣤⣤⣶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣡⠤⠂⠀⠀⣀⡠⠤⠐⠀⠘⠇⠀⠀⠀⠀⠀⡠⢎⣤⡷⢖⣸⡟⢈⣩⡁
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠚⠛⠉⠉⠀⠠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈⣑⡫⠔⠋⠀⠉⠁⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣦⡙⣿⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡌⣷⣴⣷⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⢿⣿⡿⣾⡆⠀⠙⢷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠈⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣧⣀⣀⡀⠀⠀⠸⠿⠯⡃⠈⠉⠛⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⡿⠉⠀⢈⡁⠀⠀⠈⠛⠦⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡂⠀⠀⠀⢙⡋⠀⠀⠀⢰⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⠷⢶⣤⣾⣷⣤⡦⢄⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⢿⡿⢿⣿⠿⣿⢿⠟⠋⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡏⠀⠉⠀⣠⢡⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣇⢀⠀⠀⠀⠀⠋⠺⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣆⢠⠀⣤⠇⠀⠈⠀⠀⠀⠀⠀⠆⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠙⢿⣿⣿⣽⣴⡏⠀⠀⠀⠀⠀⢀⣴⣀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⣦⣠⣼⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⢿⣿⣿⣦⠀⠀⠀⠈⢹⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⢿⢿⣄⣀⡀⠠⠼⠿⠛⠛⠲⠔⠂⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡠⠷⠖⠒⠒⠒⠒⠒⠲⠼⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠸
⡇⠀⠀⠀⠀⠀⠀⢀⡴⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡇⠙⢄
⠹⢄⣀⣀⣀⡠⠔⠋⠀⡇⠀⠀⠀⠀⣼⣏⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣹⣦⠀⠀⠀⠀⢧⠀⠀⠙⠦⣄⣀⣀⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠆⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠉⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢢⠀⠀⠀⡔⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠈⡆⠀⢠⠃⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢣⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⡼⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡤⠤⠤⡑⠤⣀⠀⣠⠃⠀⠘⣄⠀⣀⡠⢊⡤⠤⢤⡀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠰⠃⠀⠀⠀⠈⢦⠀⠈⠀⠀⠀⠀⠀⠉⠀⡴⠁⠀⠀⠀⠈⢆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡇⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡼⠁